Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), degree \(2\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 223.2 | ||
Root | \(-1.96679 + 0.362960i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.223 |
Dual form | 384.3.l.b.31.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.69930 | + | 1.69930i | −0.339861 | + | 0.339861i | −0.856315 | − | 0.516454i | \(-0.827252\pi\) |
0.516454 | + | 0.856315i | \(0.327252\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.74280 | 0.820400 | 0.410200 | − | 0.911996i | \(-0.365459\pi\) | ||||
0.410200 | + | 0.911996i | \(0.365459\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.59560 | − | 5.59560i | −0.508691 | − | 0.508691i | 0.405434 | − | 0.914125i | \(-0.367121\pi\) |
−0.914125 | + | 0.405434i | \(0.867121\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.5782 | + | 13.5782i | 1.04447 | + | 1.04447i | 0.998964 | + | 0.0455110i | \(0.0144916\pi\) |
0.0455110 | + | 0.998964i | \(0.485508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 4.16243i | − | 0.277495i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.7023 | 1.15896 | 0.579481 | − | 0.814986i | \(-0.303255\pi\) | ||||
0.579481 | + | 0.814986i | \(0.303255\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.6943 | + | 21.6943i | −1.14181 | + | 1.14181i | −0.153687 | + | 0.988120i | \(0.549115\pi\) |
−0.988120 | + | 0.153687i | \(0.950885\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.03347 | + | 7.03347i | −0.334927 | + | 0.334927i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.9257 | −1.08373 | −0.541863 | − | 0.840467i | \(-0.682281\pi\) | ||||
−0.541863 | + | 0.840467i | \(0.682281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.2247i | 0.768989i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50581 | − | 1.50581i | −0.0519245 | − | 0.0519245i | 0.680668 | − | 0.732592i | \(-0.261690\pi\) |
−0.732592 | + | 0.680668i | \(0.761690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.20037i | 0.0709796i | 0.999370 | + | 0.0354898i | \(0.0112991\pi\) | ||||
−0.999370 | + | 0.0354898i | \(0.988701\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.7064 | 0.415344 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.75877 | + | 9.75877i | −0.278822 | + | 0.278822i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.6956 | + | 27.6956i | −0.748530 | + | 0.748530i | −0.974203 | − | 0.225673i | \(-0.927542\pi\) |
0.225673 | + | 0.974203i | \(0.427542\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −33.2596 | −0.852810 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 51.3127i | 1.25153i | 0.780012 | + | 0.625764i | \(0.215213\pi\) | ||||
−0.780012 | + | 0.625764i | \(0.784787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21.4400 | + | 21.4400i | 0.498606 | + | 0.498606i | 0.911004 | − | 0.412398i | \(-0.135309\pi\) |
−0.412398 | + | 0.911004i | \(0.635309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.09791 | + | 5.09791i | 0.113287 | + | 0.113287i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 76.5216i | 1.62812i | 0.580781 | + | 0.814060i | \(0.302747\pi\) | ||||
−0.580781 | + | 0.814060i | \(0.697253\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.0202 | −0.326944 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −24.1303 | + | 24.1303i | −0.473144 | + | 0.473144i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 56.5145 | − | 56.5145i | 1.06631 | − | 1.06631i | 0.0686712 | − | 0.997639i | \(-0.478124\pi\) |
0.997639 | − | 0.0686712i | \(-0.0218759\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.0173 | 0.345768 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 53.1400i | − | 0.932281i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −48.0041 | − | 48.0041i | −0.813628 | − | 0.813628i | 0.171547 | − | 0.985176i | \(-0.445123\pi\) |
−0.985176 | + | 0.171547i | \(0.945123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 51.5587 | + | 51.5587i | 0.845224 | + | 0.845224i | 0.989533 | − | 0.144308i | \(-0.0460957\pi\) |
−0.144308 | + | 0.989533i | \(0.546096\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 17.2284i | − | 0.273467i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −46.1469 | −0.709952 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 63.4445 | − | 63.4445i | 0.946934 | − | 0.946934i | −0.0517277 | − | 0.998661i | \(-0.516473\pi\) |
0.998661 | + | 0.0517277i | \(0.0164728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 30.5276 | − | 30.5276i | 0.442429 | − | 0.442429i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −43.4856 | −0.612473 | −0.306237 | − | 0.951955i | \(-0.599070\pi\) | ||||
−0.306237 | + | 0.951955i | \(0.599070\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 73.9992i | 1.01369i | 0.862038 | + | 0.506844i | \(0.169188\pi\) | ||||
−0.862038 | + | 0.506844i | \(0.830812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −23.5454 | − | 23.5454i | −0.313939 | − | 0.313939i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −32.1344 | − | 32.1344i | −0.417330 | − | 0.417330i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.12659i | 0.0522354i | 0.999659 | + | 0.0261177i | \(0.00831446\pi\) | ||||
−0.999659 | + | 0.0261177i | \(0.991686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 38.4428 | − | 38.4428i | 0.463166 | − | 0.463166i | −0.436526 | − | 0.899692i | \(-0.643791\pi\) |
0.899692 | + | 0.436526i | \(0.143791\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −33.4803 | + | 33.4803i | −0.393886 | + | 0.393886i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.68846 | 0.0423961 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 52.9839i | − | 0.595325i | −0.954671 | − | 0.297662i | \(-0.903793\pi\) | ||
0.954671 | − | 0.297662i | \(-0.0962070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 77.9767 | + | 77.9767i | 0.856887 | + | 0.856887i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.69489 | − | 2.69489i | −0.0289773 | − | 0.0289773i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 73.7305i | − | 0.776111i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 23.1008 | 0.238153 | 0.119077 | − | 0.992885i | \(-0.462007\pi\) | ||||
0.119077 | + | 0.992885i | \(0.462007\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.7868 | + | 16.7868i | −0.169564 | + | 0.169564i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.1216 | + | 16.1216i | −0.159619 | + | 0.159619i | −0.782398 | − | 0.622779i | \(-0.786004\pi\) |
0.622779 | + | 0.782398i | \(0.286004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 98.8380 | 0.959592 | 0.479796 | − | 0.877380i | \(-0.340711\pi\) | ||||
0.479796 | + | 0.877380i | \(0.340711\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 23.9040i | − | 0.227657i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.6655 | + | 15.6655i | 0.146406 | + | 0.146406i | 0.776511 | − | 0.630104i | \(-0.216988\pi\) |
−0.630104 | + | 0.776511i | \(0.716988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −84.6938 | − | 84.6938i | −0.777008 | − | 0.777008i | 0.202313 | − | 0.979321i | \(-0.435154\pi\) |
−0.979321 | + | 0.202313i | \(0.935154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 67.8401i | − | 0.611172i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 63.8537 | 0.565077 | 0.282538 | − | 0.959256i | \(-0.408824\pi\) | ||||
0.282538 | + | 0.959256i | \(0.408824\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 42.3563 | − | 42.3563i | 0.368316 | − | 0.368316i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 40.7345 | − | 40.7345i | 0.348158 | − | 0.348158i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 113.147 | 0.950812 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 58.3785i | − | 0.482467i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −62.8449 | − | 62.8449i | −0.510934 | − | 0.510934i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −75.1513 | − | 75.1513i | −0.601210 | − | 0.601210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 36.8901i | − | 0.290473i | −0.989397 | − | 0.145237i | \(-0.953606\pi\) | ||
0.989397 | − | 0.145237i | \(-0.0463944\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −52.5172 | −0.407110 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −40.4136 | + | 40.4136i | −0.308500 | + | 0.308500i | −0.844328 | − | 0.535827i | \(-0.820000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −124.586 | + | 124.586i | −0.936738 | + | 0.936738i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.4873 | −0.0924984 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 253.499i | − | 1.85036i | −0.379531 | − | 0.925179i | \(-0.623915\pi\) | ||
0.379531 | − | 0.925179i | \(-0.376085\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 67.8065 | + | 67.8065i | 0.487816 | + | 0.487816i | 0.907617 | − | 0.419800i | \(-0.137900\pi\) |
−0.419800 | + | 0.907617i | \(0.637900\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −93.7194 | − | 93.7194i | −0.664677 | − | 0.664677i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 151.956i | − | 1.06263i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.11766 | 0.0352942 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.6207 | − | 19.6207i | 0.133474 | − | 0.133474i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 43.9337 | − | 43.9337i | 0.294857 | − | 0.294857i | −0.544138 | − | 0.838996i | \(-0.683143\pi\) |
0.838996 | + | 0.544138i | \(0.183143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 223.084 | 1.47738 | 0.738688 | − | 0.674047i | \(-0.235446\pi\) | ||||
0.738688 | + | 0.674047i | \(0.235446\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 59.1070i | − | 0.386320i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.73909 | − | 3.73909i | −0.0241232 | − | 0.0241232i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 78.8526 | + | 78.8526i | 0.502246 | + | 0.502246i | 0.912135 | − | 0.409889i | \(-0.134433\pi\) |
−0.409889 | + | 0.912135i | \(0.634433\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 138.432i | 0.870639i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −143.143 | −0.889089 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 52.2425 | − | 52.2425i | 0.320506 | − | 0.320506i | −0.528455 | − | 0.848961i | \(-0.677228\pi\) |
0.848961 | + | 0.528455i | \(0.177228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −23.2913 | + | 23.2913i | −0.141159 | + | 0.141159i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −96.5201 | −0.577965 | −0.288982 | − | 0.957334i | \(-0.593317\pi\) | ||||
−0.288982 | + | 0.957334i | \(0.593317\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 199.734i | 1.18186i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 65.0830 | + | 65.0830i | 0.380602 | + | 0.380602i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 46.3076 | + | 46.3076i | 0.267674 | + | 0.267674i | 0.828162 | − | 0.560488i | \(-0.189386\pi\) |
−0.560488 | + | 0.828162i | \(0.689386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 110.404i | 0.630879i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 117.585 | 0.664325 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −93.5440 | + | 93.5440i | −0.522592 | + | 0.522592i | −0.918353 | − | 0.395761i | \(-0.870481\pi\) |
0.395761 | + | 0.918353i | \(0.370481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 115.810 | − | 115.810i | 0.639836 | − | 0.639836i | −0.310679 | − | 0.950515i | \(-0.600556\pi\) |
0.950515 | + | 0.310679i | \(0.100556\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −126.292 | −0.690123 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 94.1266i | − | 0.508792i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −110.246 | − | 110.246i | −0.589553 | − | 0.589553i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.1004 | + | 21.1004i | 0.111642 | + | 0.111642i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 35.2964i | − | 0.184798i | −0.995722 | − | 0.0923991i | \(-0.970546\pi\) | ||
0.995722 | − | 0.0923991i | \(-0.0294535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −364.339 | −1.88777 | −0.943884 | − | 0.330277i | \(-0.892858\pi\) | ||||
−0.943884 | + | 0.330277i | \(0.892858\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 56.5182 | − | 56.5182i | 0.289837 | − | 0.289837i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −130.582 | + | 130.582i | −0.662851 | + | 0.662851i | −0.956051 | − | 0.293200i | \(-0.905280\pi\) |
0.293200 | + | 0.956051i | \(0.405280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7493 | 0.0640670 | 0.0320335 | − | 0.999487i | \(-0.489802\pi\) | ||||
0.0320335 | + | 0.999487i | \(0.489802\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 155.407i | 0.773168i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.64756 | − | 8.64756i | −0.0425988 | − | 0.0425988i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −87.1958 | − | 87.1958i | −0.425346 | − | 0.425346i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 74.7771i | 0.361242i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 242.786 | 1.16165 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.59499 | − | 8.59499i | 0.0407345 | − | 0.0407345i | −0.686446 | − | 0.727181i | \(-0.740830\pi\) |
0.727181 | + | 0.686446i | \(0.240830\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 53.2588 | − | 53.2588i | 0.250041 | − | 0.250041i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −72.8663 | −0.338913 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.6363i | 0.0582317i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −90.6302 | − | 90.6302i | −0.413837 | − | 0.413837i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 267.522 | + | 267.522i | 1.21051 | + | 1.21051i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 50.5909i | 0.226865i | 0.993546 | + | 0.113433i | \(0.0361846\pi\) | ||||
−0.993546 | + | 0.113433i | \(0.963815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 57.6742 | 0.256330 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 31.7175 | − | 31.7175i | 0.139725 | − | 0.139725i | −0.633785 | − | 0.773509i | \(-0.718499\pi\) |
0.773509 | + | 0.633785i | \(0.218499\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 169.826 | − | 169.826i | 0.741599 | − | 0.741599i | −0.231287 | − | 0.972886i | \(-0.574294\pi\) |
0.972886 | + | 0.231287i | \(0.0742936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 78.7129 | 0.340749 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 363.082i | 1.55829i | 0.626844 | + | 0.779145i | \(0.284346\pi\) | ||||
−0.626844 | + | 0.779145i | \(0.715654\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −130.033 | − | 130.033i | −0.553334 | − | 0.553334i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.05402 | − | 5.05402i | −0.0213250 | − | 0.0213250i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.6282i | 0.115599i | 0.998328 | + | 0.0577996i | \(0.0184084\pi\) | ||||
−0.998328 | + | 0.0577996i | \(0.981592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 368.121 | 1.52747 | 0.763737 | − | 0.645527i | \(-0.223362\pi\) | ||||
0.763737 | + | 0.645527i | \(0.223362\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.2233 | − | 27.2233i | 0.111115 | − | 0.111115i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −589.139 | −2.38518 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 94.1651i | 0.378173i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 329.839 | + | 329.839i | 1.31410 | + | 1.31410i | 0.918365 | + | 0.395734i | \(0.129510\pi\) |
0.395734 | + | 0.918365i | \(0.370490\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 139.474 | + | 139.474i | 0.551281 | + | 0.551281i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 82.0096i | − | 0.321606i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.6762 | 0.0921252 | 0.0460626 | − | 0.998939i | \(-0.485333\pi\) | ||||
0.0460626 | + | 0.998939i | \(0.485333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −159.050 | + | 159.050i | −0.614094 | + | 0.614094i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.51743 | + | 4.51743i | −0.0173082 | + | 0.0173082i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −243.854 | −0.927202 | −0.463601 | − | 0.886044i | \(-0.653443\pi\) | ||||
−0.463601 | + | 0.886044i | \(0.653443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 192.071i | 0.724794i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 64.8918 | + | 64.8918i | 0.243040 | + | 0.243040i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −234.293 | − | 234.293i | −0.870976 | − | 0.870976i | 0.121603 | − | 0.992579i | \(-0.461197\pi\) |
−0.992579 | + | 0.121603i | \(0.961197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.9533i | 0.114219i | 0.998368 | + | 0.0571094i | \(0.0181884\pi\) | ||||
−0.998368 | + | 0.0571094i | \(0.981812\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −191.003 | −0.699646 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 107.574 | − | 107.574i | 0.391178 | − | 0.391178i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 41.4479 | − | 41.4479i | 0.149631 | − | 0.149631i | −0.628322 | − | 0.777953i | \(-0.716258\pi\) |
0.777953 | + | 0.628322i | \(0.216258\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.60110 | 0.0236599 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 93.3971i | − | 0.332374i | −0.986094 | − | 0.166187i | \(-0.946854\pi\) | ||
0.986094 | − | 0.166187i | \(-0.0531455\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 40.0982 | + | 40.0982i | 0.141690 | + | 0.141690i | 0.774394 | − | 0.632704i | \(-0.218055\pi\) |
−0.632704 | + | 0.774394i | \(0.718055\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 90.3011 | + | 90.3011i | 0.316846 | + | 0.316846i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 294.678i | 1.02675i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 99.1824 | 0.343192 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.2926 | + | 28.2926i | −0.0972256 | + | 0.0972256i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −141.326 | + | 141.326i | −0.482340 | + | 0.482340i | −0.905878 | − | 0.423538i | \(-0.860788\pi\) |
0.423538 | + | 0.905878i | \(0.360788\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 163.147 | 0.553041 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 41.1191i | − | 0.138448i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −338.445 | − | 338.445i | −1.13192 | − | 1.13192i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 123.126 | + | 123.126i | 0.409056 | + | 0.409056i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 39.4896i | − | 0.130329i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −175.228 | −0.574517 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −285.548 | + | 285.548i | −0.930125 | + | 0.930125i | −0.997713 | − | 0.0675885i | \(-0.978470\pi\) |
0.0675885 | + | 0.997713i | \(0.478470\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −121.051 | + | 121.051i | −0.391752 | + | 0.391752i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 365.454 | 1.17509 | 0.587547 | − | 0.809190i | \(-0.300094\pi\) | ||||
0.587547 | + | 0.809190i | \(0.300094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 461.508i | − | 1.47447i | −0.675638 | − | 0.737234i | \(-0.736132\pi\) | ||
0.675638 | − | 0.737234i | \(-0.263868\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29.2763 | + | 29.2763i | 0.0929406 | + | 0.0929406i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 319.216 | + | 319.216i | 1.00699 | + | 1.00699i | 0.999975 | + | 0.00701388i | \(0.00223261\pi\) |
0.00701388 | + | 0.999975i | \(0.497767\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.8518i | 0.0528270i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −38.3724 | −0.119540 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −427.429 | + | 427.429i | −1.32331 | + | 1.32331i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −261.037 | + | 261.037i | −0.803190 | + | 0.803190i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 207.457 | 0.634424 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 439.448i | 1.33571i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −85.7864 | − | 85.7864i | −0.259173 | − | 0.259173i | 0.565544 | − | 0.824718i | \(-0.308666\pi\) |
−0.824718 | + | 0.565544i | \(0.808666\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 83.0869 | + | 83.0869i | 0.249510 | + | 0.249510i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 215.623i | 0.643651i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 258.256 | 0.766339 | 0.383170 | − | 0.923678i | \(-0.374832\pi\) | ||||
0.383170 | + | 0.923678i | \(0.374832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −78.2045 | + | 78.2045i | −0.230692 | + | 0.230692i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.3124 | − | 12.3124i | 0.0361067 | − | 0.0361067i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −373.398 | −1.08862 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 103.751i | 0.300729i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.7237 | + | 27.7237i | 0.0798953 | + | 0.0798953i | 0.745925 | − | 0.666030i | \(-0.232008\pi\) |
−0.666030 | + | 0.745925i | \(0.732008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −321.089 | − | 321.089i | −0.920027 | − | 0.920027i | 0.0770037 | − | 0.997031i | \(-0.475465\pi\) |
−0.997031 | + | 0.0770037i | \(0.975465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 99.7788i | 0.284270i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −241.363 | −0.683748 | −0.341874 | − | 0.939746i | \(-0.611062\pi\) | ||||
−0.341874 | + | 0.939746i | \(0.611062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 73.8953 | − | 73.8953i | 0.208156 | − | 0.208156i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −138.576 | + | 138.576i | −0.388167 | + | 0.388167i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 363.821 | 1.01343 | 0.506714 | − | 0.862114i | \(-0.330860\pi\) | ||||
0.506714 | + | 0.862114i | \(0.330860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 580.287i | − | 1.60744i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 71.4988 | + | 71.4988i | 0.196966 | + | 0.196966i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −125.747 | − | 125.747i | −0.344513 | − | 0.344513i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 411.402i | − | 1.12099i | −0.828159 | − | 0.560493i | \(-0.810612\pi\) | ||
0.828159 | − | 0.560493i | \(-0.189388\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 153.938 | 0.417176 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 324.551 | − | 324.551i | 0.874801 | − | 0.874801i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 225.677 | − | 225.677i | 0.605033 | − | 0.605033i | −0.336611 | − | 0.941644i | \(-0.609281\pi\) |
0.941644 | + | 0.336611i | \(0.109281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 184.082 | 0.490886 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 40.8923i | − | 0.108468i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −157.180 | − | 157.180i | −0.414724 | − | 0.414724i | 0.468656 | − | 0.883381i | \(-0.344738\pi\) |
−0.883381 | + | 0.468656i | \(0.844738\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 45.1810 | + | 45.1810i | 0.118585 | + | 0.118585i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 703.356i | − | 1.83644i | −0.396072 | − | 0.918219i | \(-0.629627\pi\) | ||
0.396072 | − | 0.918219i | \(-0.370373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 109.212 | 0.283668 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 64.3201 | − | 64.3201i | 0.166202 | − | 0.166202i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.7401 | + | 10.7401i | −0.0276095 | + | 0.0276095i | −0.720777 | − | 0.693167i | \(-0.756215\pi\) |
0.693167 | + | 0.720777i | \(0.256215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −491.095 | −1.25600 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 98.9926i | − | 0.251890i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.01234 | − | 7.01234i | −0.0177528 | − | 0.0177528i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −365.020 | − | 365.020i | −0.919446 | − | 0.919446i | 0.0775433 | − | 0.996989i | \(-0.475292\pi\) |
−0.996989 | + | 0.0775433i | \(0.975292\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 305.173i | − | 0.764844i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 341.735 | 0.852207 | 0.426104 | − | 0.904674i | \(-0.359886\pi\) | ||||
0.426104 | + | 0.904674i | \(0.359886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.8770 | + | 29.8770i | −0.0741364 | + | 0.0741364i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.2937 | − | 15.2937i | 0.0377623 | − | 0.0377623i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 309.947 | 0.761541 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 368.259i | − | 0.900389i | −0.892931 | − | 0.450194i | \(-0.851355\pi\) | ||
0.892931 | − | 0.450194i | \(-0.148645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 310.472 | + | 310.472i | 0.755405 | + | 0.755405i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −275.678 | − | 275.678i | −0.667501 | − | 0.667501i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 130.652i | 0.314824i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −166.091 | −0.398300 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 407.140 | − | 407.140i | 0.971694 | − | 0.971694i | −0.0279165 | − | 0.999610i | \(-0.508887\pi\) |
0.999610 | + | 0.0279165i | \(0.00888725\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −57.5576 | + | 57.5576i | −0.136716 | + | 0.136716i | −0.772153 | − | 0.635437i | \(-0.780820\pi\) |
0.635437 | + | 0.772153i | \(0.280820\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 229.565 | 0.542706 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 378.772i | 0.891229i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 296.091 | + | 296.091i | 0.693422 | + | 0.693422i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 186.107 | + | 186.107i | 0.433817 | + | 0.433817i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 796.565i | 1.84818i | 0.382177 | + | 0.924089i | \(0.375174\pi\) | ||||
−0.382177 | + | 0.924089i | \(0.624826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −335.804 | −0.775529 | −0.387764 | − | 0.921758i | \(-0.626753\pi\) | ||||
−0.387764 | + | 0.921758i | \(0.626753\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.26782 | + | 6.26782i | −0.0144088 | + | 0.0144088i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 540.746 | − | 540.746i | 1.23741 | − | 1.23741i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 285.630 | 0.650638 | 0.325319 | − | 0.945604i | \(-0.394528\pi\) | ||||
0.325319 | + | 0.945604i | \(0.394528\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 48.0607i | 0.108981i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 111.596 | + | 111.596i | 0.251909 | + | 0.251909i | 0.821753 | − | 0.569844i | \(-0.192996\pi\) |
−0.569844 | + | 0.821753i | \(0.692996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 90.0358 | + | 90.0358i | 0.202328 | + | 0.202328i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 107.615i | 0.240750i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −99.6741 | −0.221991 | −0.110996 | − | 0.993821i | \(-0.535404\pi\) | ||||
−0.110996 | + | 0.993821i | \(0.535404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 287.125 | − | 287.125i | 0.636641 | − | 0.636641i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −273.221 | + | 273.221i | −0.603137 | + | 0.603137i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −265.012 | −0.582445 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.1643i | 0.0703813i | 0.999381 | + | 0.0351907i | \(0.0112039\pi\) | ||||
−0.999381 | + | 0.0351907i | \(0.988796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 72.3910 | + | 72.3910i | 0.157715 | + | 0.157715i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −165.361 | − | 165.361i | −0.358701 | − | 0.358701i | 0.504633 | − | 0.863334i | \(-0.331628\pi\) |
−0.863334 | + | 0.504633i | \(0.831628\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 923.215i | − | 1.99398i | −0.0774991 | − | 0.996992i | \(-0.524693\pi\) | ||
0.0774991 | − | 0.996992i | \(-0.475307\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.15887 | 0.0196965 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 507.842 | − | 507.842i | 1.08746 | − | 1.08746i | 0.0916660 | − | 0.995790i | \(-0.470781\pi\) |
0.995790 | − | 0.0916660i | \(-0.0292192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 364.349 | − | 364.349i | 0.776864 | − | 0.776864i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −193.149 | −0.410082 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 239.940i | − | 0.507272i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −417.068 | − | 417.068i | −0.878037 | − | 0.878037i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −169.543 | − | 169.543i | −0.355437 | − | 0.355437i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 52.3866i | 0.109367i | 0.998504 | + | 0.0546833i | \(0.0174149\pi\) | ||||
−0.998504 | + | 0.0546833i | \(0.982585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −752.112 | −1.56364 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 175.314 | − | 175.314i | 0.362969 | − | 0.362969i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −39.2554 | + | 39.2554i | −0.0809389 | + | 0.0809389i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 715.733 | 1.46968 | 0.734839 | − | 0.678241i | \(-0.237258\pi\) | ||||
0.734839 | + | 0.678241i | \(0.237258\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 127.968i | 0.261692i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3258 | − | 22.3258i | −0.0454701 | − | 0.0454701i | 0.684006 | − | 0.729476i | \(-0.260236\pi\) |
−0.729476 | + | 0.684006i | \(0.760236\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.6680 | − | 29.6680i | −0.0601784 | − | 0.0601784i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 57.0518i | − | 0.115256i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −249.729 | −0.502473 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 84.0984 | − | 84.0984i | 0.168534 | − | 0.168534i | −0.617801 | − | 0.786335i | \(-0.711976\pi\) |
0.786335 | + | 0.617801i | \(0.211976\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 118.213 | − | 118.213i | 0.235953 | − | 0.235953i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −327.870 | −0.651829 | −0.325914 | − | 0.945399i | \(-0.605672\pi\) | ||||
−0.325914 | + | 0.945399i | \(0.605672\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 54.7909i | − | 0.108497i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −244.623 | − | 244.623i | −0.482490 | − | 0.482490i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.6224 | − | 34.6224i | −0.0680205 | − | 0.0680205i | 0.672278 | − | 0.740299i | \(-0.265316\pi\) |
−0.740299 | + | 0.672278i | \(0.765316\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 424.963i | 0.831630i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −159.420 | −0.310760 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −167.956 | + | 167.956i | −0.326128 | + | 0.326128i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 428.184 | − | 428.184i | 0.828210 | − | 0.828210i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −113.430 | −0.218555 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 235.719i | − | 0.452436i | −0.974077 | − | 0.226218i | \(-0.927364\pi\) | ||
0.974077 | − | 0.226218i | \(-0.0726362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −185.851 | − | 185.851i | −0.355356 | − | 0.355356i | 0.506742 | − | 0.862098i | \(-0.330850\pi\) |
−0.862098 | + | 0.506742i | \(0.830850\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −135.216 | − | 135.216i | −0.257555 | − | 0.257555i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.3524i | 0.0822626i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 92.2900 | 0.174461 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −144.012 | + | 144.012i | −0.271209 | + | 0.271209i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −696.732 | + | 696.732i | −1.30719 | + | 1.30719i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −53.2408 | −0.0995155 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 229.135i | − | 0.426695i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 89.6428 | + | 89.6428i | 0.166313 | + | 0.166313i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 315.952 | + | 315.952i | 0.584015 | + | 0.584015i | 0.936004 | − | 0.351989i | \(-0.114494\pi\) |
−0.351989 | + | 0.936004i | \(0.614494\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 283.676i | 0.522424i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 287.841 | 0.528149 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −550.957 | + | 550.957i | −1.00723 | + | 1.00723i | −0.00725954 | + | 0.999974i | \(0.502311\pi\) |
−0.999974 | + | 0.00725954i | \(0.997689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 154.676 | − | 154.676i | 0.281741 | − | 0.281741i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.3350 | 0.118575 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.6982i | 0.0428539i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 115.281 | + | 115.281i | 0.207714 | + | 0.207714i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.35545 | − | 2.35545i | −0.00422882 | − | 0.00422882i | 0.704989 | − | 0.709218i | \(-0.250952\pi\) |
−0.709218 | + | 0.704989i | \(0.750952\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 582.233i | 1.04156i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 270.048 | 0.481368 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 269.210 | − | 269.210i | 0.478170 | − | 0.478170i | −0.426376 | − | 0.904546i | \(-0.640210\pi\) |
0.904546 | + | 0.426376i | \(0.140210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −108.507 | + | 108.507i | −0.192047 | + | 0.192047i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −51.6852 | −0.0911556 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 342.558i | 0.602035i | 0.953619 | + | 0.301018i | \(0.0973263\pi\) | ||||
−0.953619 | + | 0.301018i | \(0.902674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 153.948 | + | 153.948i | 0.269610 | + | 0.269610i | 0.828943 | − | 0.559333i | \(-0.188943\pi\) |
−0.559333 | + | 0.828943i | \(0.688943\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.2291 | + | 43.2291i | 0.0754435 | + | 0.0754435i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 479.190i | − | 0.833373i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 563.693 | 0.976938 | 0.488469 | − | 0.872581i | \(-0.337556\pi\) | ||||
0.488469 | + | 0.872581i | \(0.337556\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 446.223 | − | 446.223i | 0.770678 | − | 0.770678i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 220.769 | − | 220.769i | 0.379981 | − | 0.379981i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −632.465 | −1.08484 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 138.441i | 0.236651i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 176.603 | + | 176.603i | 0.300857 | + | 0.300857i | 0.841349 | − | 0.540492i | \(-0.181762\pi\) |
−0.540492 | + | 0.841349i | \(0.681762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −47.7355 | − | 47.7355i | −0.0810450 | − | 0.0810450i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 319.858i | − | 0.541215i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −996.597 | −1.68060 | −0.840301 | − | 0.542120i | \(-0.817622\pi\) | ||||
−0.840301 | + | 0.542120i | \(0.817622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −192.271 | + | 192.271i | −0.323144 | + | 0.323144i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.6147 | + | 15.6147i | −0.0261553 | + | 0.0261553i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 854.031 | 1.42576 | 0.712880 | − | 0.701286i | \(-0.247390\pi\) | ||||
0.712880 | + | 0.701286i | \(0.247390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 345.733i | 0.575263i | 0.957741 | + | 0.287631i | \(0.0928678\pi\) | ||||
−0.957741 | + | 0.287631i | \(0.907132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −190.334 | − | 190.334i | −0.315645 | − | 0.315645i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 99.2029 | + | 99.2029i | 0.163972 | + | 0.163972i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 526.354i | 0.867141i | 0.901120 | + | 0.433570i | \(0.142746\pi\) | ||||
−0.901120 | + | 0.433570i | \(0.857254\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.1821 | 0.0347818 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1039.02 | + | 1039.02i | −1.70053 | + | 1.70053i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −410.567 | + | 410.567i | −0.669767 | + | 0.669767i | −0.957662 | − | 0.287895i | \(-0.907045\pi\) |
0.287895 | + | 0.957662i | \(0.407045\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 213.585 | 0.347293 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 514.755i | − | 0.834287i | −0.908841 | − | 0.417144i | \(-0.863031\pi\) | ||
0.908841 | − | 0.417144i | \(-0.136969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 314.214 | + | 314.214i | 0.507615 | + | 0.507615i | 0.913794 | − | 0.406179i | \(-0.133139\pi\) |
−0.406179 | + | 0.913794i | \(0.633139\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −91.5828 | − | 91.5828i | −0.147476 | − | 0.147476i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 304.276i | − | 0.488404i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −225.209 | −0.360334 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −297.350 | + | 297.350i | −0.474243 | + | 0.474243i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −545.669 | + | 545.669i | −0.867518 | + | 0.867518i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 230.081 | 0.364629 | 0.182315 | − | 0.983240i | \(-0.441641\pi\) | ||||
0.182315 | + | 0.983240i | \(0.441641\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.0533i | 0.0332596i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 62.6875 | + | 62.6875i | 0.0987205 | + | 0.0987205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −217.526 | − | 217.526i | −0.341484 | − | 0.341484i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 130.457i | 0.204158i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 746.825 | 1.16509 | 0.582547 | − | 0.812797i | \(-0.302056\pi\) | ||||
0.582547 | + | 0.812797i | \(0.302056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 548.092 | − | 548.092i | 0.852398 | − | 0.852398i | −0.138030 | − | 0.990428i | \(-0.544077\pi\) |
0.990428 | + | 0.138030i | \(0.0440772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 89.2426 | − | 89.2426i | 0.138361 | − | 0.138361i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1055.00 | −1.63060 | −0.815302 | − | 0.579036i | \(-0.803429\pi\) | ||||
−0.815302 | + | 0.579036i | \(0.803429\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 537.223i | 0.827771i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.4762 | − | 15.4762i | −0.0237730 | − | 0.0237730i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 854.888 | + | 854.888i | 1.30917 | + | 1.30917i | 0.922015 | + | 0.387155i | \(0.126542\pi\) |
0.387155 | + | 0.922015i | \(0.373458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 137.350i | − | 0.209694i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 221.998 | 0.337896 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −768.766 | + | 768.766i | −1.16656 | + | 1.16656i | −0.183556 | + | 0.983009i | \(0.558761\pi\) |
−0.983009 | + | 0.183556i | \(0.941239\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −312.323 | + | 312.323i | −0.472500 | + | 0.472500i | −0.902723 | − | 0.430223i | \(-0.858435\pi\) |
0.430223 | + | 0.902723i | \(0.358435\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −655.292 | −0.988374 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 423.420i | − | 0.636721i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.5333 | + | 37.5333i | 0.0562719 | + | 0.0562719i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −61.9610 | − | 61.9610i | −0.0926173 | − | 0.0926173i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 577.004i | − | 0.859916i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 740.565 | 1.10039 | 0.550197 | − | 0.835035i | \(-0.314553\pi\) | ||||
0.550197 | + | 0.835035i | \(0.314553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −70.6362 | + | 70.6362i | −0.104646 | + | 0.104646i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 547.118 | − | 547.118i | 0.808151 | − | 0.808151i | −0.176203 | − | 0.984354i | \(-0.556381\pi\) |
0.984354 | + | 0.176203i | \(0.0563814\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 132.664 | 0.195381 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 77.6918i | 0.114085i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −407.623 | − | 407.623i | −0.596813 | − | 0.596813i | 0.342650 | − | 0.939463i | \(-0.388676\pi\) |
−0.939463 | + | 0.342650i | \(0.888676\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 430.772 | + | 430.772i | 0.628864 | + | 0.628864i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 415.987i | 0.605513i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1534.73 | 2.22747 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6037 | − | 17.6037i | 0.0254757 | − | 0.0254757i | −0.694254 | − | 0.719730i | \(-0.744266\pi\) |
0.719730 | + | 0.694254i | \(0.244266\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −96.4033 | + | 96.4033i | −0.139110 | + | 0.139110i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −230.448 | −0.331579 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1010.98i | 1.45047i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −444.682 | − | 444.682i | −0.636169 | − | 0.636169i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −164.273 | − | 164.273i | −0.234341 | − | 0.234341i | 0.580161 | − | 0.814502i | \(-0.302990\pi\) |
−0.814502 | + | 0.580161i | \(0.802990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1201.68i | − | 1.70935i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 318.516 | 0.451795 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −92.5829 | + | 92.5829i | −0.130952 | + | 0.130952i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −422.796 | + | 422.796i | −0.596327 | + | 0.596327i | −0.939333 | − | 0.343006i | \(-0.888555\pi\) |
0.343006 | + | 0.939333i | \(0.388555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.3798 | 0.0174118 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 54.8457i | − | 0.0769224i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 258.220 | + | 258.220i | 0.361146 | + | 0.361146i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.8375 | − | 33.8375i | −0.0471932 | − | 0.0471932i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1029.00i | 1.43115i | 0.698534 | + | 0.715577i | \(0.253836\pi\) | ||||
−0.698534 | + | 0.715577i | \(0.746164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 567.607 | 0.787250 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −450.855 | + | 450.855i | −0.623589 | + | 0.623589i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.9488 | − | 28.9488i | 0.0399293 | − | 0.0399293i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 475.001 | 0.653372 | 0.326686 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326686 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 422.419 | + | 422.419i | 0.577865 | + | 0.577865i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 344.939 | + | 344.939i | 0.470586 | + | 0.470586i | 0.902104 | − | 0.431519i | \(-0.142022\pi\) |
−0.431519 | + | 0.902104i | \(0.642022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 66.6831i | 0.0907253i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −710.021 | −0.963393 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 363.340 | − | 363.340i | 0.491665 | − | 0.491665i | −0.417166 | − | 0.908831i | \(-0.636976\pi\) |
0.908831 | + | 0.417166i | \(0.136976\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 721.544 | − | 721.544i | 0.973744 | − | 0.973744i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −271.667 | −0.365636 | −0.182818 | − | 0.983147i | \(-0.558522\pi\) | ||||
−0.182818 | + | 0.983147i | \(0.558522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 149.314i | 0.200421i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −115.328 | − | 115.328i | −0.154389 | − | 0.154389i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 89.9637 | + | 89.9637i | 0.120112 | + | 0.120112i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1105.27i | 1.47173i | 0.677128 | + | 0.735866i | \(0.263224\pi\) | ||||
−0.677128 | + | 0.735866i | \(0.736776\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −807.937 | −1.07296 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −379.087 | + | 379.087i | −0.502102 | + | 0.502102i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −554.565 | + | 554.565i | −0.732583 | + | 0.732583i | −0.971131 | − | 0.238548i | \(-0.923329\pi\) |
0.238548 | + | 0.971131i | \(0.423329\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −341.641 | −0.450119 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 188.496i | 0.247695i | 0.992301 | + | 0.123847i | \(0.0395234\pi\) | ||||
−0.992301 | + | 0.123847i | \(0.960477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −486.380 | − | 486.380i | −0.637457 | − | 0.637457i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 100.441 | + | 100.441i | 0.131295 | + | 0.131295i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1303.62i | − | 1.69963i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −593.354 | −0.771592 | −0.385796 | − | 0.922584i | \(-0.626073\pi\) | ||||
−0.385796 | + | 0.922584i | \(0.626073\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.9973 | + | 28.9973i | −0.0376100 | + | 0.0376100i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −514.720 | + | 514.720i | −0.665873 | + | 0.665873i | −0.956758 | − | 0.290885i | \(-0.906050\pi\) |
0.290885 | + | 0.956758i | \(0.406050\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.3015 | −0.0545826 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 389.592i | − | 0.501406i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1113.19 | − | 1113.19i | −1.42900 | − | 1.42900i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 243.328 | + | 243.328i | 0.311560 | + | 0.311560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 11.0654i | − | 0.0141320i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −267.989 | −0.341387 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 96.1835 | − | 96.1835i | 0.122215 | − | 0.122215i | −0.643354 | − | 0.765569i | \(-0.722458\pi\) |
0.765569 | + | 0.643354i | \(0.222458\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 298.659 | − | 298.659i | 0.378529 | − | 0.378529i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 366.699 | 0.463589 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1400.15i | 1.76563i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −235.237 | − | 235.237i | −0.295896 | − | 0.295896i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 664.410 | + | 664.410i | 0.833639 | + | 0.833639i | 0.988013 | − | 0.154374i | \(-0.0493359\pi\) |
−0.154374 | + | 0.988013i | \(0.549336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1507.66i | 1.88693i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −158.952 | −0.198442 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 414.070 | − | 414.070i | 0.515654 | − | 0.515654i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 243.244 | − | 243.244i | 0.302166 | − | 0.302166i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 573.897 | 0.711149 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1371.63i | − | 1.69547i | −0.530422 | − | 0.847734i | \(-0.677966\pi\) | ||
0.530422 | − | 0.847734i | \(-0.322034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 809.783 | + | 809.783i | 0.998500 | + | 0.998500i | 0.999999 | − | 0.00149916i | \(-0.000477196\pi\) |
−0.00149916 | + | 0.999999i | \(0.500477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.9099 | − | 37.9099i | −0.0466296 | − | 0.0466296i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 177.552i | 0.217855i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −930.255 | −1.13862 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 233.930 | − | 233.930i | 0.285629 | − | 0.285629i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1144.74 | − | 1144.74i | 1.39432 | − | 1.39432i | 0.578980 | − | 0.815342i | \(-0.303451\pi\) |
0.815342 | − | 0.578980i | \(-0.196549\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −439.361 | −0.533853 | −0.266926 | − | 0.963717i | \(-0.586008\pi\) | ||||
−0.266926 | + | 0.963717i | \(0.586008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 263.501i | 0.319395i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 911.996 | + | 911.996i | 1.10278 | + | 1.10278i | 0.994074 | + | 0.108701i | \(0.0346693\pi\) |
0.108701 | + | 0.994074i | \(0.465331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −470.575 | − | 470.575i | −0.567642 | − | 0.567642i | 0.363825 | − | 0.931467i | \(-0.381471\pi\) |
−0.931467 | + | 0.363825i | \(0.881471\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 101.526i | 0.122173i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −315.636 | −0.378915 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 164.017 | − | 164.017i | 0.196428 | − | 0.196428i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.08467 | + | 8.08467i | −0.00965910 | + | 0.00965910i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1432.91 | −1.70787 | −0.853937 | − | 0.520376i | \(-0.825792\pi\) | ||||
−0.853937 | + | 0.520376i | \(0.825792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 836.465i | − | 0.994608i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 114.388 | + | 114.388i | 0.135691 | + | 0.135691i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −339.408 | − | 339.408i | −0.401666 | − | 0.401666i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 335.256i | − | 0.395816i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −98.2201 | −0.115689 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 690.332 | − | 690.332i | 0.811201 | − | 0.811201i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −211.443 | + | 211.443i | −0.247881 | + | 0.247881i | −0.820101 | − | 0.572219i | \(-0.806083\pi\) |
0.572219 | + | 0.820101i | \(0.306083\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −221.192 | −0.258704 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 710.925i | 0.829551i | 0.909924 | + | 0.414775i | \(0.136140\pi\) | ||||
−0.909924 | + | 0.414775i | \(0.863860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 348.557 | + | 348.557i | 0.405771 | + | 0.405771i | 0.880261 | − | 0.474490i | \(-0.157368\pi\) |
−0.474490 | + | 0.880261i | \(0.657368\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −360.906 | − | 360.906i | −0.419171 | − | 0.419171i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1493.19i | 1.73023i | 0.501571 | + | 0.865116i | \(0.332755\pi\) | ||||
−0.501571 | + | 0.865116i | \(0.667245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −157.382 | −0.181944 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −121.473 | + | 121.473i | −0.140107 | + | 0.140107i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.0908 | − | 23.0908i | 0.0265717 | − | 0.0265717i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1722.92 | 1.97810 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 69.3025i | − | 0.0793843i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −431.579 | − | 431.579i | −0.493233 | − | 0.493233i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 332.929 | + | 332.929i | 0.379623 | + | 0.379623i | 0.870966 | − | 0.491343i | \(-0.163494\pi\) |
−0.491343 | + | 0.870966i | \(0.663494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 346.176i | − | 0.393829i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −637.491 | −0.723599 | −0.361799 | − | 0.932256i | \(-0.617838\pi\) | ||||
−0.361799 | + | 0.932256i | \(0.617838\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 134.646 | − | 134.646i | 0.152487 | − | 0.152487i | −0.626741 | − | 0.779228i | \(-0.715612\pi\) |
0.779228 | + | 0.626741i | \(0.215612\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −199.814 | + | 199.814i | −0.225778 | + | 0.225778i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.90891 | −0.00440688 | −0.00220344 | − | 0.999998i | \(-0.500701\pi\) | ||||
−0.00220344 | + | 0.999998i | \(0.500701\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 211.853i | − | 0.238304i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.3604 | + | 50.3604i | 0.0565212 | + | 0.0565212i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1660.08 | − | 1660.08i | −1.85900 | − | 1.85900i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 317.919i | − | 0.355217i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 829.018 | 0.924212 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.31333 | − | 3.31333i | 0.00368558 | − | 0.00368558i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1113.47 | − | 1113.47i | 1.23581 | − | 1.23581i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −301.596 | −0.333993 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 393.594i | 0.434910i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 697.707 | + | 697.707i | 0.769247 | + | 0.769247i | 0.977974 | − | 0.208727i | \(-0.0669319\pi\) |
−0.208727 | + | 0.977974i | \(0.566932\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.3647 | + | 48.3647i | 0.0532065 | + | 0.0532065i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 796.856i | − | 0.874705i | −0.899290 | − | 0.437353i | \(-0.855916\pi\) | ||
0.899290 | − | 0.437353i | \(-0.144084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −430.221 | −0.471216 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 214.609 | − | 214.609i | 0.234546 | − | 0.234546i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −232.087 | + | 232.087i | −0.253094 | + | 0.253094i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −420.532 | −0.457597 | −0.228798 | − | 0.973474i | \(-0.573480\pi\) | ||||
−0.228798 | + | 0.973474i | \(0.573480\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 699.448i | − | 0.759444i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −590.455 | − | 590.455i | −0.639713 | − | 0.639713i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −532.441 | − | 532.441i | −0.575612 | − | 0.575612i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 296.514i | − | 0.319864i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1178.38 | 1.26843 | 0.634217 | − | 0.773155i | \(-0.281323\pi\) | ||||
0.634217 | + | 0.773155i | \(0.281323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 347.548 | − | 347.548i | 0.373306 | − | 0.373306i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −447.588 | + | 447.588i | −0.479730 | + | 0.479730i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 374.684 | 0.400732 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 405.962i | 0.433257i | 0.976254 | + | 0.216629i | \(0.0695061\pi\) | ||||
−0.976254 | + | 0.216629i | \(0.930494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 565.230 | + | 565.230i | 0.601949 | + | 0.601949i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −429.859 | − | 429.859i | −0.456810 | − | 0.456810i | 0.440797 | − | 0.897607i | \(-0.354696\pi\) |
−0.897607 | + | 0.440797i | \(0.854696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1279.00i | − | 1.35631i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −71.7120 | −0.0758857 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 661.681 | − | 661.681i | 0.698713 | − | 0.698713i | −0.265420 | − | 0.964133i | \(-0.585511\pi\) |
0.964133 | + | 0.265420i | \(0.0855107\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1004.77 | + | 1004.77i | −1.05877 | + | 1.05877i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −781.915 | −0.822203 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.1854i | 0.0327234i | 0.999866 | + | 0.0163617i | \(0.00520833\pi\) | ||||
−0.999866 | + | 0.0163617i | \(0.994792\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 59.9794 | + | 59.9794i | 0.0628056 | + | 0.0628056i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.6392 | − | 20.6392i | −0.0215665 | − | 0.0215665i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1455.79i | − | 1.51803i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 956.158 | 0.994962 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.9964 | − | 46.9964i | 0.0488021 | − | 0.0488021i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 619.123 | − | 619.123i | 0.641578 | − | 0.641578i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1312.55 | 1.35734 | 0.678672 | − | 0.734442i | \(-0.262556\pi\) | ||||
0.678672 | + | 0.734442i | \(0.262556\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1046.98i | − | 1.08048i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 318.758 | + | 318.758i | 0.328278 | + | 0.328278i | 0.851931 | − | 0.523653i | \(-0.175431\pi\) |
−0.523653 | + | 0.851931i | \(0.675431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 389.399 | + | 389.399i | 0.400205 | + | 0.400205i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 639.407i | − | 0.655802i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −531.045 | −0.543546 | −0.271773 | − | 0.962361i | \(-0.587610\pi\) | ||||
−0.271773 | + | 0.962361i | \(0.587610\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −296.477 | + | 296.477i | −0.302836 | + | 0.302836i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −254.082 | + | 254.082i | −0.259003 | + | 0.259003i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1796.17 | 1.82723 | 0.913614 | − | 0.406582i | \(-0.133279\pi\) | ||||
0.913614 | + | 0.406582i | \(0.133279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 443.796i | − | 0.450554i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −538.212 | − | 538.212i | −0.545301 | − | 0.545301i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −534.408 | − | 534.408i | −0.540352 | − | 0.540352i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 506.064i | 0.510660i | 0.966854 | + | 0.255330i | \(0.0821841\pi\) | ||||
−0.966854 | + | 0.255330i | \(0.917816\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 210.133 | 0.211614 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.6650 | + | 21.6650i | −0.0217739 | + | 0.0217739i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 249.068 | − | 249.068i | 0.249817 | − | 0.249817i | −0.571078 | − | 0.820896i | \(-0.693475\pi\) |
0.820896 | + | 0.571078i | \(0.193475\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −203.520 | −0.203724 |
(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 | 384.3.l.b.223.2 | 16 | ||
3.2 | odd | 2 | 1152.3.m.c.991.6 | 16 | |||
4.3 | odd | 2 | 384.3.l.a.223.6 | 16 | |||
8.3 | odd | 2 | 48.3.l.a.19.8 | ✓ | 16 | ||
8.5 | even | 2 | 192.3.l.a.175.7 | 16 | |||
12.11 | even | 2 | 1152.3.m.f.991.6 | 16 | |||
16.3 | odd | 4 | 192.3.l.a.79.7 | 16 | |||
16.5 | even | 4 | 384.3.l.a.31.6 | 16 | |||
16.11 | odd | 4 | inner | 384.3.l.b.31.2 | 16 | ||
16.13 | even | 4 | 48.3.l.a.43.8 | yes | 16 | ||
24.5 | odd | 2 | 576.3.m.c.559.3 | 16 | |||
24.11 | even | 2 | 144.3.m.c.19.1 | 16 | |||
48.5 | odd | 4 | 1152.3.m.f.415.6 | 16 | |||
48.11 | even | 4 | 1152.3.m.c.415.6 | 16 | |||
48.29 | odd | 4 | 144.3.m.c.91.1 | 16 | |||
48.35 | even | 4 | 576.3.m.c.271.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.8 | ✓ | 16 | 8.3 | odd | 2 | ||
48.3.l.a.43.8 | yes | 16 | 16.13 | even | 4 | ||
144.3.m.c.19.1 | 16 | 24.11 | even | 2 | |||
144.3.m.c.91.1 | 16 | 48.29 | odd | 4 | |||
192.3.l.a.79.7 | 16 | 16.3 | odd | 4 | |||
192.3.l.a.175.7 | 16 | 8.5 | even | 2 | |||
384.3.l.a.31.6 | 16 | 16.5 | even | 4 | |||
384.3.l.a.223.6 | 16 | 4.3 | odd | 2 | |||
384.3.l.b.31.2 | 16 | 16.11 | odd | 4 | inner | ||
384.3.l.b.223.2 | 16 | 1.1 | even | 1 | trivial | ||
576.3.m.c.271.3 | 16 | 48.35 | even | 4 | |||
576.3.m.c.559.3 | 16 | 24.5 | odd | 2 | |||
1152.3.m.c.415.6 | 16 | 48.11 | even | 4 | |||
1152.3.m.c.991.6 | 16 | 3.2 | odd | 2 | |||
1152.3.m.f.415.6 | 16 | 48.5 | odd | 4 | |||
1152.3.m.f.991.6 | 16 | 12.11 | even | 2 |