Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1261,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.1261");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.t (of order \(3\), degree \(2\), 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: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1261.1 | ||
Root | \(0.356769 - 0.617942i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.1261 |
Dual form | 3420.2.t.v.3241.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.20440 | −0.833185 | −0.416593 | − | 0.909093i | \(-0.636776\pi\) | ||||
−0.416593 | + | 0.909093i | \(0.636776\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.20440 | 0.363141 | 0.181570 | − | 0.983378i | \(-0.441882\pi\) | ||||
0.181570 | + | 0.983378i | \(0.441882\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.07031 | − | 1.85383i | −0.259588 | − | 0.449619i | 0.706544 | − | 0.707669i | \(-0.250253\pi\) |
−0.966131 | + | 0.258050i | \(0.916920\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.30660 | − | 0.673184i | 0.988002 | − | 0.154439i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.63409 | + | 8.02649i | −0.966276 | + | 1.67364i | −0.260127 | + | 0.965574i | \(0.583765\pi\) |
−0.706148 | + | 0.708064i | \(0.749569\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.16599 | − | 7.21570i | 0.773605 | − | 1.33992i | −0.161971 | − | 0.986796i | \(-0.551785\pi\) |
0.935575 | − | 0.353127i | \(-0.114882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.26819 | 1.48501 | 0.742505 | − | 0.669840i | \(-0.233637\pi\) | ||||
0.742505 | + | 0.669840i | \(0.233637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.10220 | + | 1.90907i | 0.186306 | + | 0.322691i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.20440 | −0.362401 | −0.181201 | − | 0.983446i | \(-0.557998\pi\) | ||||
−0.181201 | + | 0.983446i | \(0.557998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.30660 | − | 5.72720i | −0.516405 | − | 0.894439i | −0.999819 | − | 0.0190471i | \(-0.993937\pi\) |
0.483414 | − | 0.875392i | \(-0.339397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.17251 | − | 2.03084i | −0.178806 | − | 0.309701i | 0.762666 | − | 0.646793i | \(-0.223890\pi\) |
−0.941472 | + | 0.337092i | \(0.890557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.16599 | + | 7.21570i | −0.607672 | + | 1.05252i | 0.383951 | + | 0.923353i | \(0.374563\pi\) |
−0.991623 | + | 0.129165i | \(0.958770\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.14061 | −0.305802 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.134095 | − | 0.232259i | 0.0184193 | − | 0.0319032i | −0.856669 | − | 0.515867i | \(-0.827470\pi\) |
0.875088 | + | 0.483964i | \(0.160803\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.602201 | − | 1.04304i | −0.0812007 | − | 0.140644i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.16599 | − | 7.21570i | −0.542366 | − | 0.939405i | −0.998768 | − | 0.0496310i | \(-0.984195\pi\) |
0.456402 | − | 0.889774i | \(-0.349138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70440 | − | 2.95211i | 0.218226 | − | 0.377979i | −0.736040 | − | 0.676939i | \(-0.763306\pi\) |
0.954266 | + | 0.298960i | \(0.0966396\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.06379 | − | 1.84253i | 0.129962 | − | 0.225101i | −0.793699 | − | 0.608310i | \(-0.791848\pi\) |
0.923662 | + | 0.383209i | \(0.125181\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.23630 | − | 9.06953i | −0.621434 | − | 1.07636i | −0.989219 | − | 0.146444i | \(-0.953217\pi\) |
0.367785 | − | 0.929911i | \(-0.380116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.42969 | + | 4.20835i | 0.284374 | + | 0.492550i | 0.972457 | − | 0.233082i | \(-0.0748809\pi\) |
−0.688083 | + | 0.725632i | \(0.741548\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.65498 | −0.302564 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.20440 | − | 14.2104i | −0.923067 | − | 1.59880i | −0.794640 | − | 0.607080i | \(-0.792341\pi\) |
−0.128427 | − | 0.991719i | \(-0.540993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.73181 | 0.629148 | 0.314574 | − | 0.949233i | \(-0.398138\pi\) | ||||
0.314574 | + | 0.949233i | \(0.398138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.07031 | + | 1.85383i | −0.116091 | + | 0.201076i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.40880 | + | 9.36832i | −0.573332 | + | 0.993040i | 0.422889 | + | 0.906182i | \(0.361016\pi\) |
−0.996221 | + | 0.0868585i | \(0.972317\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10220 | + | 1.90907i | −0.115542 | + | 0.200125i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.73630 | − | 3.39304i | −0.280738 | − | 0.348118i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.87039 | − | 13.6319i | −0.799117 | − | 1.38411i | −0.920192 | − | 0.391468i | \(-0.871967\pi\) |
0.121075 | − | 0.992643i | \(-0.461366\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.27471 | + | 9.13606i | −0.524853 | + | 0.909072i | 0.474728 | + | 0.880133i | \(0.342546\pi\) |
−0.999581 | + | 0.0289397i | \(0.990787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.731811 | −0.0721075 | −0.0360537 | − | 0.999350i | \(-0.511479\pi\) | ||||
−0.0360537 | + | 0.999350i | \(0.511479\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.3958 | 1.29502 | 0.647509 | − | 0.762058i | \(-0.275811\pi\) | ||||
0.647509 | + | 0.762058i | \(0.275811\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.96811 | − | 5.14091i | −0.284293 | − | 0.492410i | 0.688144 | − | 0.725574i | \(-0.258426\pi\) |
−0.972437 | + | 0.233164i | \(0.925092\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.6132 | −1.46877 | −0.734383 | − | 0.678735i | \(-0.762529\pi\) | ||||
−0.734383 | + | 0.678735i | \(0.762529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.26819 | 0.864263 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.35939 | + | 4.08658i | 0.216285 | + | 0.374616i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.54942 | −0.868129 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.67699 | − | 13.2969i | 0.681223 | − | 1.17991i | −0.293385 | − | 0.955994i | \(-0.594782\pi\) |
0.974608 | − | 0.223918i | \(-0.0718849\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.89780 | − | 6.75119i | −0.340552 | − | 0.589854i | 0.643983 | − | 0.765040i | \(-0.277281\pi\) |
−0.984535 | + | 0.175186i | \(0.943947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.49348 | + | 1.48397i | −0.823189 | + | 0.128676i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.23630 | − | 14.2657i | 0.703674 | − | 1.21880i | −0.263494 | − | 0.964661i | \(-0.584875\pi\) |
0.967168 | − | 0.254138i | \(-0.0817919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.76819 | − | 16.9190i | 0.828527 | − | 1.43505i | −0.0706667 | − | 0.997500i | \(-0.522513\pi\) |
0.899194 | − | 0.437551i | \(-0.144154\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.602201 | − | 1.04304i | 0.0503586 | − | 0.0872236i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.33198 | −0.691933 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.83850 | − | 4.91642i | −0.232539 | − | 0.402769i | 0.726016 | − | 0.687678i | \(-0.241370\pi\) |
−0.958555 | + | 0.284909i | \(0.908037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2264 | −1.15773 | −0.578864 | − | 0.815424i | \(-0.696504\pi\) | ||||
−0.578864 | + | 0.815424i | \(0.696504\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.13409 | − | 7.16046i | −0.332058 | − | 0.575142i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.327492 | + | 0.567233i | 0.0261367 | + | 0.0452701i | 0.878798 | − | 0.477194i | \(-0.158346\pi\) |
−0.852661 | + | 0.522464i | \(0.825013\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.2154 | − | 17.6936i | 0.805087 | − | 1.39445i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6770 | −0.992939 | −0.496469 | − | 0.868054i | \(-0.665370\pi\) | ||||
−0.496469 | + | 0.868054i | \(0.665370\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.89780 | + | 6.75119i | −0.301621 | + | 0.522422i | −0.976503 | − | 0.215503i | \(-0.930861\pi\) |
0.674882 | + | 0.737925i | \(0.264194\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.37039 | − | 9.30179i | −0.408303 | − | 0.707202i | 0.586397 | − | 0.810024i | \(-0.300546\pi\) |
−0.994700 | + | 0.102822i | \(0.967213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.10220 | − | 1.90907i | 0.0833185 | − | 0.144312i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.54942 | 0.115809 | 0.0579044 | − | 0.998322i | \(-0.481558\pi\) | ||||
0.0579044 | + | 0.998322i | \(0.481558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.11320 | − | 7.12428i | 0.305732 | − | 0.529544i | −0.671692 | − | 0.740831i | \(-0.734432\pi\) |
0.977424 | + | 0.211287i | \(0.0677655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.10220 | + | 1.90907i | 0.0810354 | + | 0.140357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.28908 | − | 2.23275i | −0.0942668 | − | 0.163275i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2812 | −1.17807 | −0.589034 | − | 0.808108i | \(-0.700492\pi\) | ||||
−0.589034 | + | 0.808108i | \(0.700492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.60669 | − | 14.9072i | −0.619523 | − | 1.07304i | −0.989573 | − | 0.144033i | \(-0.953993\pi\) |
0.370050 | − | 0.929012i | \(-0.379341\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.2044 | 0.727034 | 0.363517 | − | 0.931588i | \(-0.381576\pi\) | ||||
0.363517 | + | 0.931588i | \(0.381576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.03189 | + | 8.71550i | −0.356701 | + | 0.617825i | −0.987408 | − | 0.158197i | \(-0.949432\pi\) |
0.630706 | + | 0.776022i | \(0.282765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.18351 | + | 15.9063i | −0.644556 | + | 1.11640i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.30660 | + | 5.72720i | −0.230943 | + | 0.400005i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.18688 | − | 0.810784i | 0.358784 | − | 0.0560831i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.12758 | + | 10.6133i | 0.421840 | + | 0.730648i | 0.996119 | − | 0.0880113i | \(-0.0280512\pi\) |
−0.574280 | + | 0.818659i | \(0.694718\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.17251 | + | 2.03084i | −0.0799644 | + | 0.138502i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.2264 | −1.23729 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.14061 | −0.143993 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0748 | + | 17.4501i | 0.674658 | + | 1.16854i | 0.976569 | + | 0.215206i | \(0.0690422\pi\) |
−0.301911 | + | 0.953336i | \(0.597624\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.25515 | 0.547914 | 0.273957 | − | 0.961742i | \(-0.411667\pi\) | ||||
0.273957 | + | 0.961742i | \(0.411667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.6860 | −1.76346 | −0.881729 | − | 0.471756i | \(-0.843620\pi\) | ||||
−0.881729 | + | 0.471756i | \(0.843620\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00448 | + | 12.1321i | 0.458879 | + | 0.794802i | 0.998902 | − | 0.0468485i | \(-0.0149178\pi\) |
−0.540023 | + | 0.841650i | \(0.681584\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.33198 | 0.543518 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.2682 | 0.793563 | 0.396782 | − | 0.917913i | \(-0.370127\pi\) | ||||
0.396782 | + | 0.917913i | \(0.370127\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.93621 | + | 8.54977i | −0.317969 | + | 0.550739i | −0.980064 | − | 0.198681i | \(-0.936334\pi\) |
0.662095 | + | 0.749420i | \(0.269668\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.07031 | + | 1.85383i | 0.0683794 | + | 0.118437i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.57031 | − | 4.06622i | 0.0999162 | − | 0.258727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.4198 | − | 24.9758i | 0.910170 | − | 1.57646i | 0.0963474 | − | 0.995348i | \(-0.469284\pi\) |
0.813823 | − | 0.581113i | \(-0.197383\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.58131 | + | 9.66711i | −0.350894 | + | 0.607766i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.39780 | + | 4.15311i | −0.149571 | + | 0.259064i | −0.931069 | − | 0.364844i | \(-0.881122\pi\) |
0.781498 | + | 0.623907i | \(0.214456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.85939 | 0.301948 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.2044 | + | 17.6745i | 0.629230 | + | 1.08986i | 0.987706 | + | 0.156320i | \(0.0499631\pi\) |
−0.358476 | + | 0.933539i | \(0.616704\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.268189 | −0.0164747 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.563788 | + | 0.976509i | 0.0343747 | + | 0.0595388i | 0.882701 | − | 0.469935i | \(-0.155723\pi\) |
−0.848326 | + | 0.529474i | \(0.822389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.83850 | − | 17.0408i | −0.597646 | − | 1.03515i | −0.993168 | − | 0.116697i | \(-0.962769\pi\) |
0.395522 | − | 0.918457i | \(-0.370564\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.602201 | + | 1.04304i | −0.0363141 | + | 0.0628978i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.35398 | 0.441858 | 0.220929 | − | 0.975290i | \(-0.429091\pi\) | ||||
0.220929 | + | 0.975290i | \(0.429091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.73630 | − | 11.6676i | 0.401854 | − | 0.696031i | −0.592096 | − | 0.805867i | \(-0.701699\pi\) |
0.993950 | + | 0.109836i | \(0.0350327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.6595 | − | 18.4627i | −0.633640 | − | 1.09750i | −0.986802 | − | 0.161934i | \(-0.948227\pi\) |
0.353162 | − | 0.935562i | \(-0.385106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.28908 | + | 12.6251i | 0.430261 | + | 0.745233i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.20889 | − | 10.7541i | 0.365229 | − | 0.632594i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.08580 | −0.472377 | −0.236189 | − | 0.971707i | \(-0.575898\pi\) | ||||
−0.236189 | + | 0.971707i | \(0.575898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.16599 | + | 7.21570i | −0.242553 | + | 0.420115i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.63409 | + | 8.02649i | 0.267997 | + | 0.464184i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.58468 | + | 4.47679i | 0.148978 | + | 0.258038i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.40880 | −0.195187 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.2922 | − | 24.7549i | −0.815701 | − | 1.41284i | −0.908824 | − | 0.417180i | \(-0.863018\pi\) |
0.0931229 | − | 0.995655i | \(-0.470315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.7408 | 0.609054 | 0.304527 | − | 0.952504i | \(-0.401502\pi\) | ||||
0.304527 | + | 0.952504i | \(0.401502\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.71092 | + | 9.89160i | −0.322800 | + | 0.559107i | −0.981065 | − | 0.193680i | \(-0.937958\pi\) |
0.658264 | + | 0.752787i | \(0.271291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.62309 | − | 2.81128i | 0.0911619 | − | 0.157897i | −0.816838 | − | 0.576867i | \(-0.804275\pi\) |
0.908000 | + | 0.418970i | \(0.137609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.01752 | − | 8.69060i | 0.280927 | − | 0.486580i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.85735 | − | 7.26318i | −0.325912 | − | 0.404134i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.18351 | − | 15.9063i | 0.506303 | − | 0.876943i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.1208 | 1.93042 | 0.965208 | − | 0.261483i | \(-0.0842116\pi\) | ||||
0.965208 | + | 0.261483i | \(0.0842116\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.12758 | −0.116242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.93621 | − | 13.7459i | −0.432313 | − | 0.748788i | 0.564759 | − | 0.825256i | \(-0.308969\pi\) |
−0.997072 | + | 0.0764677i | \(0.975636\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.95822 | 0.539268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1496 | 1.08798 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.3221 | − | 28.2707i | −0.876216 | − | 1.51765i | −0.855462 | − | 0.517866i | \(-0.826727\pi\) |
−0.0207537 | − | 0.999785i | \(-0.506607\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.7538 | −1.16446 | −0.582228 | − | 0.813026i | \(-0.697819\pi\) | ||||
−0.582228 | + | 0.813026i | \(0.697819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.67699 | −0.461830 | −0.230915 | − | 0.972974i | \(-0.574172\pi\) | ||||
−0.230915 | + | 0.972974i | \(0.574172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.23630 | + | 9.06953i | −0.277914 | + | 0.481361i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.81109 | + | 10.0651i | 0.306697 | + | 0.531216i | 0.977638 | − | 0.210296i | \(-0.0674427\pi\) |
−0.670940 | + | 0.741511i | \(0.734109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0936 | − | 5.79827i | 0.952297 | − | 0.305172i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.42969 | − | 4.20835i | 0.127176 | − | 0.220275i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.3046 | + | 26.5083i | −0.798892 | + | 1.38372i | 0.121446 | + | 0.992598i | \(0.461247\pi\) |
−0.920338 | + | 0.391123i | \(0.872087\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.295598 | + | 0.511992i | −0.0153467 | + | 0.0265813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.70980 | 0.243864 | 0.121932 | − | 0.992538i | \(-0.461091\pi\) | ||||
0.121932 | + | 0.992538i | \(0.461091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.16599 | − | 7.21570i | −0.214559 | − | 0.371628i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0638 | 0.516942 | 0.258471 | − | 0.966019i | \(-0.416781\pi\) | ||||
0.258471 | + | 0.966019i | \(0.416781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.7219 | + | 23.7671i | 0.701158 | + | 1.21444i | 0.968060 | + | 0.250717i | \(0.0806664\pi\) |
−0.266903 | + | 0.963723i | \(0.586000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.32749 | + | 2.29928i | 0.0676553 | + | 0.117182i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.257185 | − | 0.445458i | 0.0130398 | − | 0.0225856i | −0.859432 | − | 0.511250i | \(-0.829183\pi\) |
0.872472 | + | 0.488665i | \(0.162516\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.8396 | 1.00333 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.20440 | + | 14.2104i | −0.412808 | + | 0.715005i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.55278 | − | 2.68950i | −0.0779320 | − | 0.134982i | 0.824426 | − | 0.565970i | \(-0.191498\pi\) |
−0.902358 | + | 0.430988i | \(0.858165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.51752 | − | 11.2887i | −0.325470 | − | 0.563730i | 0.656138 | − | 0.754641i | \(-0.272189\pi\) |
−0.981607 | + | 0.190911i | \(0.938856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.13409 | − | 7.16046i | 0.205934 | − | 0.356688i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.65498 | −0.131603 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7747 | + | 23.8585i | −0.681115 | + | 1.17973i | 0.293525 | + | 0.955951i | \(0.405172\pi\) |
−0.974641 | + | 0.223775i | \(0.928162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.18351 | + | 15.9063i | 0.451891 | + | 0.782698i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.86591 | − | 4.96389i | −0.140682 | − | 0.243668i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5494 | −0.808492 | −0.404246 | − | 0.914650i | \(-0.632466\pi\) | ||||
−0.404246 | + | 0.914650i | \(0.632466\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.93418 | + | 13.7424i | 0.386688 | + | 0.669764i | 0.992002 | − | 0.126223i | \(-0.0402856\pi\) |
−0.605314 | + | 0.795987i | \(0.706952\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.14061 | 0.103835 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.75719 | + | 6.50764i | −0.181823 | + | 0.314927i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4472 | − | 19.8272i | 0.551393 | − | 0.955041i | −0.446781 | − | 0.894643i | \(-0.647430\pi\) |
0.998174 | − | 0.0603975i | \(-0.0192368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.6660 | − | 18.4740i | 0.512575 | − | 0.887805i | −0.487319 | − | 0.873224i | \(-0.662025\pi\) |
0.999894 | − | 0.0145814i | \(-0.00464157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.5539 | + | 37.6865i | −0.696208 | + | 1.80279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.08783 | + | 8.81238i | 0.242829 | + | 0.420592i | 0.961519 | − | 0.274739i | \(-0.0885913\pi\) |
−0.718690 | + | 0.695331i | \(0.755258\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.30660 | + | 5.72720i | −0.157101 | + | 0.272108i | −0.933822 | − | 0.357737i | \(-0.883548\pi\) |
0.776721 | + | 0.629845i | \(0.216882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.8176 | 0.512804 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.9870 | −0.518507 | −0.259253 | − | 0.965809i | \(-0.583476\pi\) | ||||
−0.259253 | + | 0.965809i | \(0.583476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.98248 | − | 6.89785i | −0.187528 | − | 0.324807i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.20440 | 0.103344 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.5494 | 0.587037 | 0.293518 | − | 0.955953i | \(-0.405174\pi\) | ||||
0.293518 | + | 0.955953i | \(0.405174\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.6386 | − | 20.1586i | −0.542063 | − | 0.938880i | −0.998785 | − | 0.0492710i | \(-0.984310\pi\) |
0.456723 | − | 0.889609i | \(-0.349023\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.3958 | −1.08729 | −0.543647 | − | 0.839314i | \(-0.682957\pi\) | ||||
−0.543647 | + | 0.839314i | \(0.682957\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6352 | 0.584688 | 0.292344 | − | 0.956313i | \(-0.405565\pi\) | ||||
0.292344 | + | 0.956313i | \(0.405565\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.34502 | + | 4.06169i | −0.108283 | + | 0.187551i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.41217 | − | 2.44595i | −0.0649316 | − | 0.112465i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.57031 | + | 4.06622i | −0.0720506 | + | 0.186571i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.01752 | − | 3.49445i | 0.0921830 | − | 0.159666i | −0.816246 | − | 0.577704i | \(-0.803949\pi\) |
0.908429 | + | 0.418038i | \(0.137282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.10220 | + | 1.90907i | −0.0502560 | + | 0.0870460i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.87039 | + | 13.6319i | −0.357376 | + | 0.618993i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.54942 | 0.296782 | 0.148391 | − | 0.988929i | \(-0.452591\pi\) | ||||
0.148391 | + | 0.988929i | \(0.452591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.04290 | + | 1.80635i | 0.0470653 | + | 0.0815195i | 0.888598 | − | 0.458686i | \(-0.151680\pi\) |
−0.841533 | + | 0.540206i | \(0.818346\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.8355 | −0.803273 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.5429 | + | 19.9929i | 0.517770 | + | 0.896803i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0539 | + | 20.8780i | 0.539607 | + | 0.934626i | 0.998925 | + | 0.0463546i | \(0.0147604\pi\) |
−0.459318 | + | 0.888272i | \(0.651906\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.13858 | + | 7.16823i | −0.184530 | + | 0.319616i | −0.943418 | − | 0.331606i | \(-0.892410\pi\) |
0.758888 | + | 0.651221i | \(0.225743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5494 | 0.469443 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.86591 | + | 4.96389i | −0.127029 | + | 0.220021i | −0.922524 | − | 0.385939i | \(-0.873877\pi\) |
0.795495 | + | 0.605960i | \(0.207211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.35602 | − | 9.27690i | −0.236936 | − | 0.410386i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.365905 | + | 0.633767i | 0.0161237 | + | 0.0279271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.01752 | + | 8.69060i | −0.220670 | + | 0.382212i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8086 | −0.648778 | −0.324389 | − | 0.945924i | \(-0.605159\pi\) | ||||
−0.324389 | + | 0.945924i | \(0.605159\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.79356 | + | 13.4988i | −0.340789 | + | 0.590263i | −0.984579 | − | 0.174938i | \(-0.944027\pi\) |
0.643791 | + | 0.765202i | \(0.277361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.84950 | − | 15.3278i | −0.385490 | − | 0.667689i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31.4497 | − | 54.4724i | −1.36738 | − | 2.36837i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.61320 | −0.286450 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.69788 | − | 11.6011i | −0.289575 | − | 0.501558i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.57816 | −0.111049 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0539 | + | 24.3421i | −0.604224 | + | 1.04655i | 0.387949 | + | 0.921681i | \(0.373184\pi\) |
−0.992174 | + | 0.124867i | \(0.960150\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.96811 | + | 5.14091i | −0.127140 | + | 0.220212i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.6835 | − | 37.5569i | 0.927120 | − | 1.60582i | 0.139004 | − | 0.990292i | \(-0.455610\pi\) |
0.788116 | − | 0.615527i | \(-0.211057\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.0838 | − | 33.8796i | 0.557387 | − | 1.44332i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0858 | + | 31.3255i | 0.769086 | + | 1.33210i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.65814 | − | 14.9963i | 0.366857 | − | 0.635415i | −0.622215 | − | 0.782846i | \(-0.713767\pi\) |
0.989072 | + | 0.147431i | \(0.0471005\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.34502 | −0.0991836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.35398 | −0.352078 | −0.176039 | − | 0.984383i | \(-0.556329\pi\) | ||||
−0.176039 | + | 0.984383i | \(0.556329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.80660 | + | 13.5214i | 0.328426 | + | 0.568851i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.6640 | 0.447056 | 0.223528 | − | 0.974697i | \(-0.428243\pi\) | ||||
0.223528 | + | 0.974697i | \(0.428243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.56512 | −0.107347 | −0.0536735 | − | 0.998559i | \(-0.517093\pi\) | ||||
−0.0536735 | + | 0.998559i | \(0.517093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.63409 | − | 8.02649i | −0.193255 | − | 0.334728i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.4218 | 0.850172 | 0.425086 | − | 0.905153i | \(-0.360244\pi\) | ||||
0.425086 | + | 0.905153i | \(0.360244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.6352 | −0.524197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.161504 | − | 0.279733i | 0.00668880 | − | 0.0115853i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.40432 | − | 7.62850i | −0.181786 | − | 0.314862i | 0.760703 | − | 0.649100i | \(-0.224854\pi\) |
−0.942489 | + | 0.334238i | \(0.891521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.6078 | − | 5.56601i | 1.46719 | − | 0.229343i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.4726 | − | 28.5314i | 0.676448 | − | 1.17164i | −0.299595 | − | 0.954066i | \(-0.596852\pi\) |
0.976043 | − | 0.217576i | \(-0.0698151\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.35939 | − | 4.08658i | 0.0967254 | − | 0.167533i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.56379 | + | 16.5650i | −0.390766 | + | 0.676826i | −0.992551 | − | 0.121832i | \(-0.961123\pi\) |
0.601785 | + | 0.798658i | \(0.294456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3100 | 0.787670 | 0.393835 | − | 0.919181i | \(-0.371148\pi\) | ||||
0.393835 | + | 0.919181i | \(0.371148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.77471 | + | 8.27004i | 0.194120 | + | 0.336225i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.8773 | 1.49680 | 0.748402 | − | 0.663245i | \(-0.230821\pi\) | ||||
0.748402 | + | 0.663245i | \(0.230821\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.16599 | + | 7.21570i | 0.168538 | + | 0.291916i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.2603 | + | 24.6996i | 0.575970 | + | 0.997609i | 0.995936 | + | 0.0900688i | \(0.0287087\pi\) |
−0.419966 | + | 0.907540i | \(0.637958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.64713 | + | 9.78112i | −0.227345 | + | 0.393773i | −0.957020 | − | 0.290021i | \(-0.906338\pi\) |
0.729675 | + | 0.683794i | \(0.239671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.2044 | 1.09344 | 0.546719 | − | 0.837316i | \(-0.315877\pi\) | ||||
0.546719 | + | 0.837316i | \(0.315877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.9232 | − | 20.6515i | 0.477692 | − | 0.827387i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.35939 | + | 4.08658i | 0.0940749 | + | 0.162942i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.19136 | + | 7.25965i | −0.166856 | + | 0.289002i | −0.937313 | − | 0.348490i | \(-0.886695\pi\) |
0.770457 | + | 0.637492i | \(0.220028\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.3540 | −0.609304 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.07031 | + | 1.85383i | −0.0424071 | + | 0.0734513i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.55594 | + | 16.5514i | 0.377437 | + | 0.653740i | 0.990689 | − | 0.136148i | \(-0.0434722\pi\) |
−0.613252 | + | 0.789888i | \(0.710139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.1112 | + | 41.7618i | 0.950852 | + | 1.64692i | 0.743588 | + | 0.668638i | \(0.233123\pi\) |
0.207264 | + | 0.978285i | \(0.433544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.0817 | 1.18263 | 0.591317 | − | 0.806439i | \(-0.298608\pi\) | ||||
0.591317 | + | 0.806439i | \(0.298608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.01752 | − | 8.69060i | −0.196955 | − | 0.341136i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.9124 | −1.64016 | −0.820079 | − | 0.572250i | \(-0.806071\pi\) | ||||
−0.820079 | + | 0.572250i | \(0.806071\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.89780 | + | 6.75119i | −0.152300 | + | 0.263791i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.0936 | + | 34.8032i | −0.782737 | + | 1.35574i | 0.147604 | + | 0.989047i | \(0.452844\pi\) |
−0.930341 | + | 0.366694i | \(0.880489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.757185 | − | 1.31148i | 0.0294511 | − | 0.0510108i | −0.850924 | − | 0.525289i | \(-0.823957\pi\) |
0.880375 | + | 0.474278i | \(0.157291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.03189 | + | 7.47961i | 0.233907 | + | 0.290047i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.6112 | + | 66.8765i | 1.49503 | + | 2.58947i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.05278 | − | 3.55553i | 0.0792468 | − | 0.137260i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.76686 | −0.299390 | −0.149695 | − | 0.988732i | \(-0.547829\pi\) | ||||
−0.149695 | + | 0.988732i | \(0.547829\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.19136 | −0.237953 | −0.118977 | − | 0.992897i | \(-0.537961\pi\) | ||||
−0.118977 | + | 0.992897i | \(0.537961\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.3495 | + | 30.0502i | 0.665813 | + | 1.15322i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.92317 | −0.111852 | −0.0559261 | − | 0.998435i | \(-0.517811\pi\) | ||||
−0.0559261 | + | 0.998435i | \(0.517811\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.4726 | −0.629385 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.134095 | − | 0.232259i | −0.00510860 | − | 0.00884835i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.35805 | −0.0897046 | −0.0448523 | − | 0.998994i | \(-0.514282\pi\) | ||||
−0.0448523 | + | 0.998994i | \(0.514282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.5364 | −0.741057 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.07816 | + | 12.2597i | −0.268104 | + | 0.464370i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.2792 | + | 21.2682i | 0.463779 | + | 0.803288i | 0.999145 | − | 0.0413314i | \(-0.0131599\pi\) |
−0.535367 | + | 0.844620i | \(0.679827\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.49348 | + | 1.48397i | −0.358053 | + | 0.0559689i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.6276 | − | 20.1396i | 0.437300 | − | 0.757426i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.63858 | + | 6.30220i | −0.136650 | + | 0.236684i | −0.926226 | − | 0.376968i | \(-0.876967\pi\) |
0.789577 | + | 0.613652i | \(0.210300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38.3156 | + | 66.3645i | −1.43493 | + | 2.48537i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.20440 | −0.0450421 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.4452 | + | 28.4839i | 0.613302 | + | 1.06227i | 0.990680 | + | 0.136211i | \(0.0434924\pi\) |
−0.377378 | + | 0.926059i | \(0.623174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.61320 | 0.0600789 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.16599 | + | 7.21570i | 0.154721 | + | 0.267985i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9551 | − | 24.1709i | −0.517565 | − | 0.896449i | −0.999792 | − | 0.0204023i | \(-0.993505\pi\) |
0.482227 | − | 0.876046i | \(-0.339828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.50989 | + | 4.34725i | −0.0928315 | + | 0.160789i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.89710 | −0.180878 | −0.0904392 | − | 0.995902i | \(-0.528827\pi\) | ||||
−0.0904392 | + | 0.995902i | \(0.528827\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.28123 | − | 2.21915i | 0.0471946 | − | 0.0817435i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5936 | + | 20.0808i | 0.426479 | + | 0.738684i | 0.996557 | − | 0.0829069i | \(-0.0264204\pi\) |
−0.570078 | + | 0.821591i | \(0.693087\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.9901 | + | 34.6239i | 0.733366 | + | 1.27023i | 0.955436 | + | 0.295197i | \(0.0953852\pi\) |
−0.222070 | + | 0.975031i | \(0.571281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.83850 | + | 4.91642i | −0.103994 | + | 0.180124i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.5296 | −1.07899 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.2936 | − | 17.8290i | 0.375617 | − | 0.650589i | −0.614802 | − | 0.788682i | \(-0.710764\pi\) |
0.990419 | + | 0.138093i | \(0.0440973\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.11320 | + | 12.3204i | 0.258876 | + | 0.448386i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.3176 | + | 29.9950i | 0.629419 | + | 1.09019i | 0.987668 | + | 0.156560i | \(0.0500404\pi\) |
−0.358249 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.3890 | −0.884102 | −0.442051 | − | 0.896990i | \(-0.645749\pi\) | ||||
−0.442051 | + | 0.896990i | \(0.645749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.54290 | + | 11.3326i | 0.236869 | + | 0.410269i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.33198 | −0.300850 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.27471 | + | 5.67196i | −0.118089 | + | 0.204536i | −0.919010 | − | 0.394233i | \(-0.871010\pi\) |
0.800921 | + | 0.598770i | \(0.204343\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7363 | + | 32.4522i | −0.673898 | + | 1.16723i | 0.302892 | + | 0.953025i | \(0.402048\pi\) |
−0.976790 | + | 0.214200i | \(0.931286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.13409 | + | 7.16046i | −0.148501 | + | 0.257211i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.0957 | − | 22.4388i | −0.648345 | − | 0.803955i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.30660 | − | 10.9234i | −0.225668 | − | 0.390868i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.327492 | − | 0.567233i | 0.0116887 | − | 0.0202454i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.8306 | −0.457363 | −0.228682 | − | 0.973501i | \(-0.573441\pi\) | ||||
−0.228682 | + | 0.973501i | \(0.573441\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.4178 | 1.22376 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.70440 | − | 2.95211i | −0.0605251 | − | 0.104833i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.3032 | 1.00255 | 0.501276 | − | 0.865287i | \(-0.332864\pi\) | ||||
0.501276 | + | 0.865287i | \(0.332864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.8355 | 0.630976 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.92633 | + | 5.06855i | 0.103268 | + | 0.178865i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.4308 | −0.720091 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 55.4946 | 1.95109 | 0.975543 | − | 0.219808i | \(-0.0705432\pi\) | ||||
0.975543 | + | 0.219808i | \(0.0705432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8540 | − | 20.5317i | 0.416250 | − | 0.720966i | −0.579309 | − | 0.815108i | \(-0.696678\pi\) |
0.995559 | + | 0.0941424i | \(0.0300109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.33850 | + | 10.9786i | 0.222028 | + | 0.384563i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.41665 | − | 7.95672i | −0.224490 | − | 0.278370i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.3625 | − | 19.6805i | 0.396555 | − | 0.686854i | −0.596743 | − | 0.802432i | \(-0.703539\pi\) |
0.993298 | + | 0.115578i | \(0.0368722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.94722 | − | 17.2291i | 0.345899 | − | 0.599114i | −0.639618 | − | 0.768693i | \(-0.720907\pi\) |
0.985517 | + | 0.169579i | \(0.0542408\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.37109 | 0.151814 | 0.0759071 | − | 0.997115i | \(-0.475815\pi\) | ||||
0.0759071 | + | 0.997115i | \(0.475815\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.29111 | + | 3.96833i | 0.0793824 | + | 0.137494i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.79560 | 0.269778 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.22396 | + | 2.11996i | 0.0422558 | + | 0.0731891i | 0.886380 | − | 0.462959i | \(-0.153212\pi\) |
−0.844124 | + | 0.536148i | \(0.819879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.2109 | − | 35.0063i | −0.696928 | − | 1.20712i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.0507 | 0.723312 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.2154 | − | 17.6936i | 0.350180 | − | 0.606529i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.96607 | + | 15.5297i | 0.306992 | + | 0.531727i | 0.977703 | − | 0.209993i | \(-0.0673440\pi\) |
−0.670711 | + | 0.741719i | \(0.734011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.0474 | − | 50.3115i | −0.992240 | − | 1.71861i | −0.603801 | − | 0.797135i | \(-0.706348\pi\) |
−0.388438 | − | 0.921475i | \(-0.626985\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0409 | + | 17.3913i | −0.342590 | + | 0.593383i | −0.984913 | − | 0.173051i | \(-0.944637\pi\) |
0.642323 | + | 0.766434i | \(0.277971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.6262 | 0.974449 | 0.487224 | − | 0.873277i | \(-0.338009\pi\) | ||||
0.487224 | + | 0.873277i | \(0.338009\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.37039 | + | 9.30179i | −0.182599 | + | 0.316270i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.88139 | − | 17.1151i | −0.335203 | − | 0.580589i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.06379 | − | 1.84253i | −0.0360451 | − | 0.0624319i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.20440 | −0.0745224 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.5200 | − | 44.2019i | −0.861748 | − | 1.49259i | −0.870240 | − | 0.492628i | \(-0.836036\pi\) |
0.00849182 | − | 0.999964i | \(-0.497297\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.2992 | 0.481751 | 0.240876 | − | 0.970556i | \(-0.422565\pi\) | ||||
0.240876 | + | 0.970556i | \(0.422565\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.6999 | + | 25.4610i | −0.494692 | + | 0.856831i | −0.999981 | − | 0.00611882i | \(-0.998052\pi\) |
0.505290 | + | 0.862950i | \(0.331386\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.46811 | − | 11.2031i | 0.217178 | − | 0.376163i | −0.736766 | − | 0.676147i | \(-0.763648\pi\) |
0.953944 | + | 0.299985i | \(0.0969815\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.9232 | + | 29.3118i | −0.567585 | + | 0.983086i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0838 | + | 33.8796i | −0.437831 | + | 1.13374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.774708 | − | 1.34183i | −0.0258956 | − | 0.0448526i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.4452 | − | 59.6608i | 1.14881 | − | 1.98980i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.574090 | −0.0191257 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.22641 | −0.273455 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.00000 | + | 8.66025i | 0.166022 | + | 0.287559i | 0.937018 | − | 0.349281i | \(-0.113574\pi\) |
−0.770996 | + | 0.636841i | \(0.780241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.10964 | 0.103027 | 0.0515134 | − | 0.998672i | \(-0.483596\pi\) | ||||
0.0515134 | + | 0.998672i | \(0.483596\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.90340 | 0.228469 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.59231 | + | 14.8823i | 0.283743 | + | 0.491458i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.4987 | 0.775150 | 0.387575 | − | 0.921838i | \(-0.373313\pi\) | ||||
0.387575 | + | 0.921838i | \(0.373313\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.4726 | −0.344710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.10220 | − | 1.90907i | 0.0362401 | − | 0.0627698i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.3221 | − | 38.6630i | −0.732364 | − | 1.26849i | −0.955870 | − | 0.293789i | \(-0.905084\pi\) |
0.223506 | − | 0.974703i | \(-0.428250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.21877 | + | 1.44103i | −0.302133 | + | 0.0472277i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.28908 | + | 2.23275i | −0.0421574 | + | 0.0730188i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.7363 | − | 20.3279i | 0.383408 | − | 0.664082i | −0.608139 | − | 0.793831i | \(-0.708084\pi\) |
0.991547 | + | 0.129748i | \(0.0414170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.0858 | − | 34.7896i | 0.654778 | − | 1.13411i | −0.327171 | − | 0.944965i | \(-0.606095\pi\) |
0.981949 | − | 0.189144i | \(-0.0605713\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.2924 | 1.99596 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.68148 | + | 16.7688i | 0.314606 | + | 0.544913i | 0.979354 | − | 0.202155i | \(-0.0647944\pi\) |
−0.664748 | + | 0.747068i | \(0.731461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.85939 | 0.157742 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.41981 | + | 4.19123i | 0.0783852 | + | 0.135767i | 0.902553 | − | 0.430578i | \(-0.141690\pi\) |
−0.824168 | + | 0.566345i | \(0.808357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.14061 | + | 14.1000i | 0.263424 | + | 0.456264i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.1561 | + | 31.4473i | −0.586291 | + | 1.01549i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.3630 | 1.20526 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.60669 | + | 14.9072i | −0.277059 | + | 0.479880i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5364 | − | 23.4457i | −0.435301 | − | 0.753963i | 0.562020 | − | 0.827124i | \(-0.310025\pi\) |
−0.997320 | + | 0.0731612i | \(0.976691\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.61769 | + | 2.80192i | 0.0519141 | + | 0.0899179i | 0.890815 | − | 0.454367i | \(-0.150134\pi\) |
−0.838901 | + | 0.544285i | \(0.816801\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.5330 | + | 37.2963i | −0.690317 | + | 1.19566i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.93214 | 0.0618147 | 0.0309074 | − | 0.999522i | \(-0.490160\pi\) | ||||
0.0309074 | + | 0.999522i | \(0.490160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.51437 | + | 11.2832i | −0.208200 | + | 0.360613i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.18555 | − | 12.4457i | −0.229183 | − | 0.396957i | 0.728383 | − | 0.685170i | \(-0.240272\pi\) |
−0.957566 | + | 0.288213i | \(0.906939\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.10220 | − | 8.83727i | −0.162570 | − | 0.281579i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.7340 | 0.691102 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7956 | − | 30.8229i | −0.565296 | − | 0.979121i | −0.997022 | − | 0.0771164i | \(-0.975429\pi\) |
0.431726 | − | 0.902005i | \(-0.357905\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0638 | 0.319044 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.7902 | + | 41.2058i | −0.753443 | + | 1.30500i | 0.192702 | + | 0.981257i | \(0.438275\pi\) |
−0.946145 | + | 0.323744i | \(0.895058\pi\) | |||||||
\(998\) | 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 | 3420.2.t.v.1261.1 | 6 | ||
3.2 | odd | 2 | 380.2.i.b.121.3 | ✓ | 6 | ||
12.11 | even | 2 | 1520.2.q.i.881.1 | 6 | |||
15.2 | even | 4 | 1900.2.s.c.349.6 | 12 | |||
15.8 | even | 4 | 1900.2.s.c.349.1 | 12 | |||
15.14 | odd | 2 | 1900.2.i.c.501.1 | 6 | |||
19.11 | even | 3 | inner | 3420.2.t.v.3241.1 | 6 | ||
57.11 | odd | 6 | 380.2.i.b.201.3 | yes | 6 | ||
57.26 | odd | 6 | 7220.2.a.n.1.1 | 3 | |||
57.50 | even | 6 | 7220.2.a.o.1.3 | 3 | |||
228.11 | even | 6 | 1520.2.q.i.961.1 | 6 | |||
285.68 | even | 12 | 1900.2.s.c.49.6 | 12 | |||
285.182 | even | 12 | 1900.2.s.c.49.1 | 12 | |||
285.239 | odd | 6 | 1900.2.i.c.201.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.b.121.3 | ✓ | 6 | 3.2 | odd | 2 | ||
380.2.i.b.201.3 | yes | 6 | 57.11 | odd | 6 | ||
1520.2.q.i.881.1 | 6 | 12.11 | even | 2 | |||
1520.2.q.i.961.1 | 6 | 228.11 | even | 6 | |||
1900.2.i.c.201.1 | 6 | 285.239 | odd | 6 | |||
1900.2.i.c.501.1 | 6 | 15.14 | odd | 2 | |||
1900.2.s.c.49.1 | 12 | 285.182 | even | 12 | |||
1900.2.s.c.49.6 | 12 | 285.68 | even | 12 | |||
1900.2.s.c.349.1 | 12 | 15.8 | even | 4 | |||
1900.2.s.c.349.6 | 12 | 15.2 | even | 4 | |||
3420.2.t.v.1261.1 | 6 | 1.1 | even | 1 | trivial | ||
3420.2.t.v.3241.1 | 6 | 19.11 | even | 3 | inner | ||
7220.2.a.n.1.1 | 3 | 57.26 | odd | 6 | |||
7220.2.a.o.1.3 | 3 | 57.50 | even | 6 |