Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(269,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.t (of order \(6\), 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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 81 x^{14} + 4781 x^{12} - 127980 x^{10} + 2502300 x^{8} - 12798000 x^{6} + 47810000 x^{4} + \cdots + 100000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{8}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.4 | ||
Root | \(1.27560 - 0.736469i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.269 |
Dual form | 1620.3.t.e.1349.4 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | −2.21154 | − | 4.48432i | −0.442308 | − | 0.896863i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.02120 | + | 4.63104i | 1.14589 | + | 0.661578i | 0.947881 | − | 0.318623i | \(-0.103221\pi\) |
0.198005 | + | 0.980201i | \(0.436554\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.2457 | + | 7.64741i | 1.20415 | + | 0.695219i | 0.961476 | − | 0.274888i | \(-0.0886408\pi\) |
0.242678 | + | 0.970107i | \(0.421974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59808 | − | 1.50000i | 0.199852 | − | 0.115385i | −0.396734 | − | 0.917933i | \(-0.629857\pi\) |
0.596586 | + | 0.802549i | \(0.296523\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00858 | 0.235799 | 0.117899 | − | 0.993026i | \(-0.462384\pi\) | ||||
0.117899 | + | 0.993026i | \(0.462384\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −27.7863 | −1.46243 | −0.731217 | − | 0.682144i | \(-0.761048\pi\) | ||||
−0.731217 | + | 0.682144i | \(0.761048\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.9336 | + | 32.7940i | 0.823202 | + | 1.42583i | 0.903286 | + | 0.429039i | \(0.141148\pi\) |
−0.0800840 | + | 0.996788i | \(0.525519\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15.2182 | + | 19.8345i | −0.608727 | + | 0.793380i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39.7371 | + | 22.9422i | 1.37024 | + | 0.791111i | 0.990959 | − | 0.134168i | \(-0.0428363\pi\) |
0.379286 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.3931 | − | 24.9296i | −0.464295 | − | 0.804182i | 0.534875 | − | 0.844931i | \(-0.320359\pi\) |
−0.999169 | + | 0.0407496i | \(0.987025\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.02785 | − | 46.2113i | 0.0865101 | − | 1.32032i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.3104i | 0.927309i | 0.886016 | + | 0.463655i | \(0.153462\pi\) | ||||
−0.886016 | + | 0.463655i | \(0.846538\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −23.6603 | + | 13.6603i | −0.577080 | + | 0.333177i | −0.759972 | − | 0.649956i | \(-0.774787\pi\) |
0.182892 | + | 0.983133i | \(0.441454\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −31.4039 | − | 18.1310i | −0.730323 | − | 0.421652i | 0.0882173 | − | 0.996101i | \(-0.471883\pi\) |
−0.818540 | + | 0.574449i | \(0.805216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0214 | + | 17.3576i | −0.213222 | + | 0.369312i | −0.952721 | − | 0.303846i | \(-0.901729\pi\) |
0.739499 | + | 0.673158i | \(0.235062\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.3931 | + | 31.8578i | 0.375370 | + | 0.650160i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 57.9102 | 1.09264 | 0.546322 | − | 0.837575i | \(-0.316027\pi\) | ||||
0.546322 | + | 0.837575i | \(0.316027\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | − | 76.3104i | 0.0909091 | − | 1.38746i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −73.8120 | + | 42.6154i | −1.25105 | + | 0.722294i | −0.971318 | − | 0.237784i | \(-0.923579\pi\) |
−0.279732 | + | 0.960078i | \(0.590246\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.8931 | − | 32.7239i | 0.309723 | − | 0.536457i | −0.668578 | − | 0.743642i | \(-0.733097\pi\) |
0.978302 | + | 0.207185i | \(0.0664302\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.4722 | − | 8.33328i | −0.191880 | − | 0.128204i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −50.4983 | + | 29.1552i | −0.753706 | + | 0.435153i | −0.827032 | − | 0.562156i | \(-0.809972\pi\) |
0.0733252 | + | 0.997308i | \(0.476639\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 125.628i | − | 1.76940i | −0.466158 | − | 0.884701i | \(-0.654362\pi\) | ||
0.466158 | − | 0.884701i | \(-0.345638\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 31.6896i | 0.434104i | 0.976160 | + | 0.217052i | \(0.0696441\pi\) | ||||
−0.976160 | + | 0.217052i | \(0.930356\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 70.8309 | + | 122.683i | 0.919882 | + | 1.59328i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19.5000 | + | 33.7750i | −0.246835 | + | 0.427532i | −0.962646 | − | 0.270763i | \(-0.912724\pi\) |
0.715811 | + | 0.698294i | \(0.246057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −32.9637 | + | 57.0947i | −0.397153 | + | 0.687888i | −0.993373 | − | 0.114932i | \(-0.963335\pi\) |
0.596221 | + | 0.802821i | \(0.296668\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.86513 | − | 17.9757i | −0.104296 | − | 0.211479i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 85.2307i | 0.957648i | 0.877911 | + | 0.478824i | \(0.158937\pi\) | ||||
−0.877911 | + | 0.478824i | \(0.841063\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.7863 | 0.305344 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 61.4504 | + | 124.602i | 0.646847 | + | 1.31160i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 140.195 | + | 80.9415i | 1.44531 | + | 0.834448i | 0.998197 | − | 0.0600306i | \(-0.0191198\pi\) |
0.447110 | + | 0.894479i | \(0.352453\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −63.3974 | − | 36.6025i | −0.627697 | − | 0.362401i | 0.152163 | − | 0.988355i | \(-0.451376\pi\) |
−0.779860 | + | 0.625955i | \(0.784710\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 133.637 | − | 77.1552i | 1.29744 | − | 0.749080i | 0.317482 | − | 0.948264i | \(-0.397163\pi\) |
0.979962 | + | 0.199184i | \(0.0638293\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 149.679 | 1.39887 | 0.699435 | − | 0.714696i | \(-0.253435\pi\) | ||||
0.699435 | + | 0.714696i | \(0.253435\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 132.718 | 1.21759 | 0.608796 | − | 0.793327i | \(-0.291653\pi\) | ||||
0.608796 | + | 0.793327i | \(0.291653\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 46.9937 | + | 81.3954i | 0.415873 | + | 0.720314i | 0.995520 | − | 0.0945544i | \(-0.0301426\pi\) |
−0.579646 | + | 0.814868i | \(0.696809\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 105.186 | − | 157.430i | 0.914663 | − | 1.36895i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 32.1536 | + | 18.5639i | 0.270198 | + | 0.155999i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56.4657 | + | 97.8014i | 0.466658 | + | 0.808276i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 122.600 | + | 24.3784i | 0.980798 | + | 0.195027i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 149.242i | 1.17513i | 0.809176 | + | 0.587566i | \(0.199914\pi\) | ||||
−0.809176 | + | 0.587566i | \(0.800086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 106.875 | − | 61.7046i | 0.815843 | − | 0.471027i | −0.0331379 | − | 0.999451i | \(-0.510550\pi\) |
0.848981 | + | 0.528424i | \(0.177217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −222.879 | − | 128.679i | −1.67578 | − | 0.967514i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −38.7623 | + | 67.1383i | −0.282937 | + | 0.490061i | −0.972107 | − | 0.234539i | \(-0.924642\pi\) |
0.689170 | + | 0.724600i | \(0.257975\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −31.4657 | − | 54.5001i | −0.226372 | − | 0.392087i | 0.730358 | − | 0.683064i | \(-0.239353\pi\) |
−0.956730 | + | 0.290977i | \(0.906020\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 45.8844 | 0.320870 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0000 | − | 228.931i | 0.103448 | − | 1.57884i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 233.670 | − | 134.910i | 1.56826 | − | 0.905433i | 0.571884 | − | 0.820335i | \(-0.306213\pi\) |
0.996373 | − | 0.0850984i | \(-0.0271204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −38.0725 | + | 65.9435i | −0.252136 | + | 0.436712i | −0.964114 | − | 0.265490i | \(-0.914466\pi\) |
0.711978 | + | 0.702202i | \(0.247800\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −79.9614 | + | 119.676i | −0.515880 | + | 0.772105i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −98.4999 | + | 56.8690i | −0.627388 | + | 0.362223i | −0.779740 | − | 0.626104i | \(-0.784649\pi\) |
0.152352 | + | 0.988326i | \(0.451315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 350.730i | 2.17845i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 90.3791i | 0.554473i | 0.960802 | + | 0.277237i | \(0.0894186\pi\) | ||||
−0.960802 | + | 0.277237i | \(0.910581\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 103.795 | + | 179.778i | 0.621525 | + | 1.07651i | 0.989202 | + | 0.146559i | \(0.0468198\pi\) |
−0.367677 | + | 0.929953i | \(0.619847\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −80.0000 | + | 138.564i | −0.473373 | + | 0.819906i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 28.0600 | − | 48.6014i | 0.162197 | − | 0.280933i | −0.773459 | − | 0.633846i | \(-0.781475\pi\) |
0.935656 | + | 0.352913i | \(0.114809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −213.923 | + | 88.6204i | −1.22241 | + | 0.506402i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 70.9865i | − | 0.396573i | −0.980144 | − | 0.198286i | \(-0.936462\pi\) | ||
0.980144 | − | 0.198286i | \(-0.0635376\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −94.9313 | −0.524482 | −0.262241 | − | 0.965002i | \(-0.584462\pi\) | ||||
−0.262241 | + | 0.965002i | \(0.584462\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 153.859 | − | 75.8789i | 0.831669 | − | 0.410156i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 53.0964 | + | 30.6552i | 0.283938 | + | 0.163932i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 117.290 | + | 67.7174i | 0.614084 | + | 0.354541i | 0.774562 | − | 0.632498i | \(-0.217970\pi\) |
−0.160478 | + | 0.987039i | \(0.551304\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 171.574 | − | 99.0585i | 0.888986 | − | 0.513257i | 0.0153756 | − | 0.999882i | \(-0.495106\pi\) |
0.873611 | + | 0.486625i | \(0.161772\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 143.452 | 0.728183 | 0.364091 | − | 0.931363i | \(-0.381380\pi\) | ||||
0.364091 | + | 0.931363i | \(0.381380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −328.863 | −1.65258 | −0.826288 | − | 0.563248i | \(-0.809552\pi\) | ||||
−0.826288 | + | 0.563248i | \(0.809552\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 212.493 | + | 368.048i | 1.04676 | + | 1.81305i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 113.583 | + | 75.8900i | 0.554062 | + | 0.370195i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −368.048 | − | 212.493i | −1.76100 | − | 1.01671i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −96.4657 | − | 167.083i | −0.457183 | − | 0.791865i | 0.541628 | − | 0.840619i | \(-0.317808\pi\) |
−0.998811 | + | 0.0487540i | \(0.984475\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.8544 | + | 180.922i | −0.0551366 | + | 0.841500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 266.621i | − | 1.22867i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4146 | − | 6.01287i | 0.0471248 | − | 0.0272075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −79.9608 | − | 46.1654i | −0.358569 | − | 0.207020i | 0.309884 | − | 0.950774i | \(-0.399710\pi\) |
−0.668453 | + | 0.743755i | \(0.733043\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −36.9722 | + | 64.0378i | −0.162873 | + | 0.282105i | −0.935898 | − | 0.352271i | \(-0.885410\pi\) |
0.773025 | + | 0.634376i | \(0.218743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 137.573 | + | 238.283i | 0.600753 | + | 1.04054i | 0.992707 | + | 0.120550i | \(0.0384660\pi\) |
−0.391954 | + | 0.919985i | \(0.628201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 310.955 | 1.33457 | 0.667286 | − | 0.744801i | \(-0.267456\pi\) | ||||
0.667286 | + | 0.744801i | \(0.267456\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 100.000 | + | 6.55218i | 0.425532 | + | 0.0278816i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −38.8272 | + | 22.4169i | −0.162457 | + | 0.0937946i | −0.579024 | − | 0.815310i | \(-0.696566\pi\) |
0.416567 | + | 0.909105i | \(0.363233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 80.5000 | − | 139.430i | 0.334025 | − | 0.578548i | −0.649272 | − | 0.760556i | \(-0.724926\pi\) |
0.983297 | + | 0.182008i | \(0.0582597\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 102.183 | − | 152.935i | 0.417075 | − | 0.624227i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −72.1908 | + | 41.6794i | −0.292271 | + | 0.168742i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 69.9359i | − | 0.278629i | −0.990248 | − | 0.139315i | \(-0.955510\pi\) | ||
0.990248 | − | 0.139315i | \(-0.0444899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 579.173i | 2.28922i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −61.7046 | − | 106.875i | −0.240096 | − | 0.415858i | 0.720646 | − | 0.693303i | \(-0.243845\pi\) |
−0.960741 | + | 0.277446i | \(0.910512\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −158.893 | + | 275.211i | −0.613487 | + | 1.06259i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −211.598 | + | 366.498i | −0.804554 | + | 1.39353i | 0.112037 | + | 0.993704i | \(0.464262\pi\) |
−0.916591 | + | 0.399825i | \(0.869071\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −128.071 | − | 259.688i | −0.483286 | − | 0.979953i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 330.998i | − | 1.23048i | −0.788341 | − | 0.615239i | \(-0.789060\pi\) | ||
0.788341 | − | 0.615239i | \(-0.210940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 142.931 | 0.527422 | 0.263711 | − | 0.964602i | \(-0.415054\pi\) | ||||
0.263711 | + | 0.964602i | \(0.415054\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −353.258 | + | 146.342i | −1.28457 | + | 0.532153i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8833 | + | 8.59286i | 0.0537302 | + | 0.0310212i | 0.526624 | − | 0.850098i | \(-0.323457\pi\) |
−0.472894 | + | 0.881119i | \(0.656791\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −255.409 | − | 147.461i | −0.908930 | − | 0.524771i | −0.0288429 | − | 0.999584i | \(-0.509182\pi\) |
−0.880087 | + | 0.474813i | \(0.842516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 400.809 | − | 231.407i | 1.41629 | − | 0.817693i | 0.420316 | − | 0.907378i | \(-0.361919\pi\) |
0.995970 | + | 0.0896849i | \(0.0285860\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −253.045 | −0.881691 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −272.931 | −0.944399 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −98.8910 | − | 171.284i | −0.337512 | − | 0.584588i | 0.646452 | − | 0.762955i | \(-0.276252\pi\) |
−0.983964 | + | 0.178367i | \(0.942919\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 354.339 | + | 236.751i | 1.20115 | + | 0.802544i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 98.3821 | + | 56.8009i | 0.329037 | + | 0.189970i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −167.931 | − | 290.866i | −0.557911 | − | 0.966331i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −188.527 | − | 12.3526i | −0.618122 | − | 0.0405005i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 304.221i | − | 0.990949i | −0.868622 | − | 0.495475i | \(-0.834994\pi\) | ||
0.868622 | − | 0.495475i | \(-0.165006\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −200.607 | + | 115.820i | −0.645038 | + | 0.372413i | −0.786552 | − | 0.617523i | \(-0.788136\pi\) |
0.141515 | + | 0.989936i | \(0.454803\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −235.290 | − | 135.845i | −0.751725 | − | 0.434009i | 0.0745916 | − | 0.997214i | \(-0.476235\pi\) |
−0.826317 | + | 0.563205i | \(0.809568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 139.443 | − | 241.523i | 0.439885 | − | 0.761902i | −0.557796 | − | 0.829978i | \(-0.688353\pi\) |
0.997680 | + | 0.0680759i | \(0.0216860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 350.897 | + | 607.771i | 1.09999 | + | 1.90524i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −111.383 | −0.344840 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.78626 | + | 74.3588i | −0.0301116 | + | 0.228796i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −160.768 | + | 92.8195i | −0.488657 | + | 0.282126i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 251.397 | − | 435.432i | 0.759507 | − | 1.31551i | −0.183595 | − | 0.983002i | \(-0.558773\pi\) |
0.943102 | − | 0.332503i | \(-0.107893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 242.420 | + | 161.972i | 0.723643 | + | 0.483500i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 62.5037 | − | 36.0865i | 0.185471 | − | 0.107082i | −0.404390 | − | 0.914587i | \(-0.632516\pi\) |
0.589861 | + | 0.807505i | \(0.299183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 440.281i | − | 1.29115i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 113.125i | − | 0.329810i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 118.505 | + | 205.258i | 0.341514 | + | 0.591520i | 0.984714 | − | 0.174178i | \(-0.0557269\pi\) |
−0.643200 | + | 0.765698i | \(0.722394\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −192.534 | + | 333.479i | −0.551674 | + | 0.955528i | 0.446480 | + | 0.894794i | \(0.352678\pi\) |
−0.998154 | + | 0.0607342i | \(0.980656\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 273.302 | − | 473.374i | 0.774228 | − | 1.34100i | −0.161000 | − | 0.986954i | \(-0.551472\pi\) |
0.935228 | − | 0.354047i | \(-0.115195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −563.354 | + | 277.830i | −1.58691 | + | 0.782621i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 110.450i | − | 0.307660i | −0.988097 | − | 0.153830i | \(-0.950839\pi\) | ||
0.988097 | − | 0.153830i | \(-0.0491609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 411.076 | 1.13872 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 142.106 | − | 70.0827i | 0.389332 | − | 0.192007i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −452.215 | − | 261.087i | −1.23219 | − | 0.711407i | −0.264707 | − | 0.964329i | \(-0.585275\pi\) |
−0.967487 | + | 0.252921i | \(0.918609\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 464.509 | + | 268.185i | 1.25205 | + | 0.722869i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −386.505 | + | 223.149i | −1.03621 | + | 0.598254i | −0.918757 | − | 0.394824i | \(-0.870805\pi\) |
−0.117450 | + | 0.993079i | \(0.537472\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 137.653 | 0.365128 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 488.657 | 1.28933 | 0.644666 | − | 0.764465i | \(-0.276997\pi\) | ||||
0.644666 | + | 0.764465i | \(0.276997\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −301.362 | − | 521.975i | −0.786847 | − | 1.36286i | −0.927889 | − | 0.372855i | \(-0.878379\pi\) |
0.141043 | − | 0.990004i | \(-0.454955\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 393.503 | − | 588.946i | 1.02209 | − | 1.52973i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 580.081 | + | 334.910i | 1.49121 | + | 0.860951i | 0.999949 | − | 0.0100609i | \(-0.00320253\pi\) |
0.491262 | + | 0.871012i | \(0.336536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 75.8970 | + | 131.457i | 0.194110 | + | 0.336208i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 194.583 | + | 12.7494i | 0.492615 | + | 0.0322770i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 696.842i | − | 1.75527i | −0.479329 | − | 0.877635i | \(-0.659120\pi\) | ||
0.479329 | − | 0.877635i | \(-0.340880\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −190.091 | + | 109.749i | −0.474041 | + | 0.273688i | −0.717930 | − | 0.696115i | \(-0.754910\pi\) |
0.243889 | + | 0.969803i | \(0.421577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −74.7889 | − | 43.1794i | −0.185580 | − | 0.107145i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −262.386 | + | 454.466i | −0.644683 | + | 1.11662i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −92.3626 | − | 159.977i | −0.225825 | − | 0.391141i | 0.730741 | − | 0.682654i | \(-0.239175\pi\) |
−0.956567 | + | 0.291513i | \(0.905841\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −789.414 | −1.91141 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 328.931 | + | 21.5522i | 0.792606 | + | 0.0519330i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −116.380 | + | 67.1921i | −0.277757 | + | 0.160363i | −0.632408 | − | 0.774636i | \(-0.717933\pi\) |
0.354651 | + | 0.934999i | \(0.384600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 63.5343 | − | 110.045i | 0.150913 | − | 0.261389i | −0.780650 | − | 0.624968i | \(-0.785112\pi\) |
0.931563 | + | 0.363579i | \(0.118445\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −61.0033 | + | 79.5081i | −0.143537 | + | 0.187078i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 303.091 | − | 174.990i | 0.709816 | − | 0.409812i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 31.7575i | − | 0.0736833i | −0.999321 | − | 0.0368417i | \(-0.988270\pi\) | ||
0.999321 | − | 0.0368417i | \(-0.0117297\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 708.056i | 1.63523i | 0.575763 | + | 0.817617i | \(0.304705\pi\) | ||||
−0.575763 | + | 0.817617i | \(0.695295\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −526.095 | − | 911.224i | −1.20388 | − | 2.08518i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −386.359 | + | 669.193i | −0.880088 | + | 1.52436i | −0.0288467 | + | 0.999584i | \(0.509183\pi\) |
−0.851242 | + | 0.524774i | \(0.824150\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 183.538 | − | 317.897i | 0.414306 | − | 0.717600i | −0.581049 | − | 0.813869i | \(-0.697358\pi\) |
0.995355 | + | 0.0962688i | \(0.0306908\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 382.201 | − | 188.491i | 0.858880 | − | 0.423576i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 526.562i | 1.17274i | 0.810042 | + | 0.586372i | \(0.199444\pi\) | ||||
−0.810042 | + | 0.586372i | \(0.800556\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −417.863 | −0.926525 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −61.4504 | − | 124.602i | −0.135056 | − | 0.273851i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 397.177 | + | 229.310i | 0.869097 | + | 0.501773i | 0.867048 | − | 0.498225i | \(-0.166014\pi\) |
0.00204894 | + | 0.999998i | \(0.499348\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 304.753 | + | 175.949i | 0.661069 | + | 0.381668i | 0.792684 | − | 0.609633i | \(-0.208683\pi\) |
−0.131615 | + | 0.991301i | \(0.542016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 383.352 | − | 221.328i | 0.827974 | − | 0.478031i | −0.0251847 | − | 0.999683i | \(-0.508017\pi\) |
0.853158 | + | 0.521652i | \(0.174684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −646.819 | −1.38505 | −0.692526 | − | 0.721393i | \(-0.743502\pi\) | ||||
−0.692526 | + | 0.721393i | \(0.743502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −540.076 | −1.15155 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −277.311 | − | 480.317i | −0.586281 | − | 1.01547i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 422.856 | − | 551.126i | 0.890224 | − | 1.16027i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 169.261 | + | 97.7231i | 0.353364 | + | 0.204015i | 0.666166 | − | 0.745804i | \(-0.267934\pi\) |
−0.312802 | + | 0.949818i | \(0.601268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.4657 | + | 89.1411i | 0.106997 | + | 0.185325i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 52.9209 | − | 807.683i | 0.109115 | − | 1.66533i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 179.069i | 0.367698i | 0.982955 | + | 0.183849i | \(0.0588557\pi\) | ||||
−0.982955 | + | 0.183849i | \(0.941144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 493.023 | − | 284.647i | 1.00412 | − | 0.579730i | 0.0946561 | − | 0.995510i | \(-0.469825\pi\) |
0.909465 | + | 0.415780i | \(0.136492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 159.289 | + | 91.9657i | 0.323102 | + | 0.186543i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 581.787 | − | 1007.68i | 1.17060 | − | 2.02753i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7099 | + | 25.4783i | 0.0294788 | + | 0.0510587i | 0.880388 | − | 0.474253i | \(-0.157282\pi\) |
−0.850910 | + | 0.525312i | \(0.823949\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −465.500 | −0.925447 | −0.462724 | − | 0.886503i | \(-0.653128\pi\) | ||||
−0.462724 | + | 0.886503i | \(0.653128\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.9313 | + | 365.242i | −0.0473887 | + | 0.723251i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −291.304 | + | 168.184i | −0.572306 | + | 0.330421i | −0.758070 | − | 0.652173i | \(-0.773857\pi\) |
0.185764 | + | 0.982594i | \(0.440524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −146.756 | + | 254.188i | −0.287193 | + | 0.497433i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −641.531 | − | 428.638i | −1.24569 | − | 0.832306i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −265.482 | + | 153.276i | −0.513505 | + | 0.296472i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 433.625i | 0.832294i | 0.909297 | + | 0.416147i | \(0.136620\pi\) | ||||
−0.909297 | + | 0.416147i | \(0.863380\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 185.331i | − | 0.354361i | −0.984178 | − | 0.177180i | \(-0.943302\pi\) | ||
0.984178 | − | 0.177180i | \(-0.0566976\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −57.6960 | − | 99.9324i | −0.109480 | − | 0.189625i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −452.466 | + | 783.694i | −0.855323 | + | 1.48146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.9808 | + | 70.9809i | −0.0768871 | + | 0.133172i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −331.021 | − | 671.208i | −0.618731 | − | 1.25459i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 562.639i | 1.04386i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 124.351 | 0.229854 | 0.114927 | − | 0.993374i | \(-0.463337\pi\) | ||||
0.114927 | + | 0.993374i | \(0.463337\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −293.510 | − | 595.148i | −0.538551 | − | 1.09201i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −526.753 | − | 304.121i | −0.962985 | − | 0.555980i | −0.0658946 | − | 0.997827i | \(-0.520990\pi\) |
−0.897090 | + | 0.441847i | \(0.854323\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1104.15 | − | 637.479i | −2.00389 | − | 1.15695i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −312.827 | + | 180.611i | −0.565691 | + | 0.326602i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −87.3319 | −0.156790 | −0.0783949 | − | 0.996922i | \(-0.524980\pi\) | ||||
−0.0783949 | + | 0.996922i | \(0.524980\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −108.786 | −0.194609 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 52.1115 | + | 90.2598i | 0.0925604 | + | 0.160319i | 0.908588 | − | 0.417694i | \(-0.137162\pi\) |
−0.816027 | + | 0.578013i | \(0.803828\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 261.074 | − | 390.744i | 0.462079 | − | 0.691582i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −563.801 | − | 325.511i | −0.990863 | − | 0.572075i | −0.0853310 | − | 0.996353i | \(-0.527195\pi\) |
−0.905532 | + | 0.424278i | \(0.860528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 57.8244 | + | 100.155i | 0.101269 | + | 0.175403i | 0.912208 | − | 0.409728i | \(-0.134376\pi\) |
−0.810939 | + | 0.585131i | \(0.801043\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −938.588 | − | 123.526i | −1.63233 | − | 0.214829i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 121.399i | − | 0.210398i | −0.994451 | − | 0.105199i | \(-0.966452\pi\) | ||
0.994451 | − | 0.105199i | \(-0.0335479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −528.816 | + | 305.312i | −0.910183 | + | 0.525495i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 767.061 | + | 442.863i | 1.31571 | + | 0.759627i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −345.709 | + | 598.786i | −0.588942 | + | 1.02008i | 0.405429 | + | 0.914127i | \(0.367122\pi\) |
−0.994371 | + | 0.105952i | \(0.966211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 399.931 | + | 692.701i | 0.679001 | + | 1.17606i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 747.110 | 1.25988 | 0.629941 | − | 0.776643i | \(-0.283079\pi\) | ||||
0.629941 | + | 0.776643i | \(0.283079\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.1374 | − | 185.242i | 0.0203990 | − | 0.311331i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 396.563 | − | 228.956i | 0.662041 | − | 0.382230i | −0.131013 | − | 0.991381i | \(-0.541823\pi\) |
0.793054 | + | 0.609151i | \(0.208490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 81.6756 | − | 141.466i | 0.135899 | − | 0.235385i | −0.790041 | − | 0.613054i | \(-0.789941\pi\) |
0.925941 | + | 0.377669i | \(0.123274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 313.696 | − | 469.502i | 0.518506 | − | 0.776036i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 124.558 | − | 71.9135i | 0.205202 | − | 0.118474i | −0.393877 | − | 0.919163i | \(-0.628867\pi\) |
0.599080 | + | 0.800689i | \(0.295533\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 60.1287i | 0.0984102i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 970.104i | − | 1.58255i | −0.611459 | − | 0.791276i | \(-0.709417\pi\) | ||
0.611459 | − | 0.791276i | \(-0.290583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −325.881 | − | 564.442i | −0.528169 | − | 0.914816i | −0.999461 | − | 0.0328386i | \(-0.989545\pi\) |
0.471291 | − | 0.881978i | \(-0.343788\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −257.176 | + | 445.441i | −0.415469 | + | 0.719614i | −0.995478 | − | 0.0949965i | \(-0.969716\pi\) |
0.580008 | + | 0.814611i | \(0.303049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −394.707 | + | 683.653i | −0.633559 | + | 1.09736i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −161.814 | − | 603.690i | −0.258902 | − | 0.965904i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 137.536i | 0.218658i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −552.794 | −0.876060 | −0.438030 | − | 0.898960i | \(-0.644324\pi\) | ||||
−0.438030 | + | 0.898960i | \(0.644324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 669.247 | − | 330.054i | 1.05393 | − | 0.519770i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 95.5735 | + | 55.1794i | 0.150037 | + | 0.0866239i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −126.795 | − | 73.2050i | −0.197808 | − | 0.114204i | 0.397825 | − | 0.917461i | \(-0.369765\pi\) |
−0.595633 | + | 0.803257i | \(0.703099\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −768.852 | + | 443.897i | −1.19573 | + | 0.690353i | −0.959600 | − | 0.281369i | \(-0.909211\pi\) |
−0.236127 | + | 0.971722i | \(0.575878\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −250.322 | −0.386896 | −0.193448 | − | 0.981111i | \(-0.561967\pi\) | ||||
−0.193448 | + | 0.981111i | \(0.561967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1303.59 | −2.00861 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −479.316 | − | 830.199i | −0.734021 | − | 1.27136i | −0.955152 | − | 0.296117i | \(-0.904308\pi\) |
0.221131 | − | 0.975244i | \(-0.429025\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −513.062 | − | 342.801i | −0.783301 | − | 0.523360i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −720.930 | − | 416.229i | −1.09398 | − | 0.631607i | −0.159343 | − | 0.987223i | \(-0.550938\pi\) |
−0.934632 | + | 0.355616i | \(0.884271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −643.260 | − | 1114.16i | −0.973161 | − | 1.68556i | −0.685874 | − | 0.727720i | \(-0.740580\pi\) |
−0.287287 | − | 0.957845i | \(-0.592753\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −84.1327 | + | 1284.04i | −0.126515 | + | 1.93089i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1737.52i | 2.60498i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 500.505 | − | 288.967i | 0.745910 | − | 0.430651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −890.605 | − | 514.191i | −1.32334 | − | 0.764028i | −0.339076 | − | 0.940759i | \(-0.610114\pi\) |
−0.984259 | + | 0.176731i | \(0.943448\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 450.827 | − | 780.856i | 0.665919 | − | 1.15341i | −0.313116 | − | 0.949715i | \(-0.601373\pi\) |
0.979035 | − | 0.203691i | \(-0.0652938\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 749.687 | + | 1298.50i | 1.10410 | + | 1.91237i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −218.253 | −0.319551 | −0.159775 | − | 0.987153i | \(-0.551077\pi\) | ||||
−0.159775 | + | 0.987153i | \(0.551077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 386.794 | + | 25.3434i | 0.564663 | + | 0.0369977i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 150.455 | − | 86.8653i | 0.218367 | − | 0.126074i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 251.863 | − | 436.239i | 0.364490 | − | 0.631315i | −0.624204 | − | 0.781261i | \(-0.714577\pi\) |
0.988694 | + | 0.149946i | \(0.0479100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −174.808 | + | 261.631i | −0.251523 | + | 0.376448i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −94.8441 | + | 54.7583i | −0.136075 | + | 0.0785628i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 377.933i | − | 0.539135i | −0.962982 | − | 0.269567i | \(-0.913119\pi\) | ||
0.962982 | − | 0.269567i | \(-0.0868807\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 953.359i | − | 1.35613i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −339.015 | − | 587.192i | −0.479513 | − | 0.830540i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −605.038 | + | 1047.96i | −0.853368 | + | 1.47808i | 0.0247821 | + | 0.999693i | \(0.492111\pi\) |
−0.878150 | + | 0.478385i | \(0.841223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 545.029 | − | 944.018i | 0.764416 | − | 1.32401i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −101.475 | − | 205.760i | −0.141923 | − | 0.287777i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 462.113i | 0.642717i | 0.946958 | + | 0.321358i | \(0.104139\pi\) | ||||
−0.946958 | + | 0.321358i | \(0.895861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1429.24 | 1.98230 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1059.77 | + | 439.026i | −1.46176 | + | 0.605553i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 462.352 | + | 266.939i | 0.635972 | + | 0.367179i | 0.783061 | − | 0.621944i | \(-0.213657\pi\) |
−0.147089 | + | 0.989123i | \(0.546990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −125.885 | − | 72.6797i | −0.172209 | − | 0.0994250i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 461.444 | − | 266.415i | 0.629528 | − | 0.363458i | −0.151041 | − | 0.988527i | \(-0.548263\pi\) |
0.780569 | + | 0.625069i | \(0.214929\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −891.847 | −1.21010 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.8626 | 0.0539413 | 0.0269706 | − | 0.999636i | \(-0.491414\pi\) | ||||
0.0269706 | + | 0.999636i | \(0.491414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 457.268 | + | 792.012i | 0.615435 | + | 1.06597i | 0.990308 | + | 0.138889i | \(0.0443531\pi\) |
−0.374873 | + | 0.927076i | \(0.622314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1121.75 | − | 749.493i | −1.50570 | − | 1.00603i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1200.61 | + | 693.170i | 1.60295 | + | 0.925461i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −427.363 | − | 740.214i | −0.569058 | − | 0.985638i | −0.996659 | − | 0.0816701i | \(-0.973975\pi\) |
0.427601 | − | 0.903967i | \(-0.359359\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 379.911 | + | 24.8924i | 0.503193 | + | 0.0329701i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 152.532i | 0.201495i | 0.994912 | + | 0.100748i | \(0.0321235\pi\) | ||||
−0.994912 | + | 0.100748i | \(0.967877\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1091.00 | − | 629.890i | 1.43364 | − | 0.827713i | 0.436245 | − | 0.899828i | \(-0.356308\pi\) |
0.997396 | + | 0.0721147i | \(0.0229748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1064.55 | + | 614.621i | 1.39522 | + | 0.805532i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −127.846 | + | 221.436i | −0.166683 | + | 0.288704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 588.363 | + | 1019.07i | 0.765101 | + | 1.32519i | 0.940193 | + | 0.340642i | \(0.110644\pi\) |
−0.175092 | + | 0.984552i | \(0.556022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −112.317 | −0.145300 | −0.0726499 | − | 0.997358i | \(-0.523146\pi\) | ||||
−0.0726499 | + | 0.997358i | \(0.523146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 713.504 | + | 93.9033i | 0.920650 | + | 0.121166i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 657.431 | − | 379.568i | 0.843942 | − | 0.487250i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 960.725 | − | 1664.02i | 1.23012 | − | 2.13063i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 472.855 | + | 315.937i | 0.602363 | + | 0.402467i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 423.438 | − | 244.472i | 0.538041 | − | 0.310638i | −0.206244 | − | 0.978501i | \(-0.566124\pi\) |
0.744284 | + | 0.667863i | \(0.232791\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 870.519i | 1.10053i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 113.359i | − | 0.142949i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 617.902 | + | 1070.24i | 0.775285 | + | 1.34283i | 0.934634 | + | 0.355611i | \(0.115727\pi\) |
−0.159349 | + | 0.987222i | \(0.550939\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.1717 | + | 69.5795i | −0.0502775 | + | 0.0870832i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −242.343 | + | 419.750i | −0.301797 | + | 0.522728i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1572.78 | − | 775.654i | 1.95377 | − | 0.963545i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1251.84i | − | 1.54739i | −0.633558 | − | 0.773695i | \(-0.718406\pi\) | ||
0.633558 | − | 0.773695i | \(-0.281594\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 340.580 | 0.419951 | 0.209975 | − | 0.977707i | \(-0.432662\pi\) | ||||
0.209975 | + | 0.977707i | \(0.432662\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 405.289 | − | 199.877i | 0.497287 | − | 0.245248i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 872.597 | + | 503.794i | 1.06805 | + | 0.616639i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 853.590 | + | 492.820i | 1.03970 | + | 0.600268i | 0.919747 | − | 0.392512i | \(-0.128394\pi\) |
0.119948 | + | 0.992780i | \(0.461727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −780.229 | + | 450.466i | −0.948031 | + | 0.547346i | −0.892469 | − | 0.451109i | \(-0.851028\pi\) |
−0.0555622 | + | 0.998455i | \(0.517695\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1571.67 | 1.90045 | 0.950223 | − | 0.311572i | \(-0.100855\pi\) | ||||
0.950223 | + | 0.311572i | \(0.100855\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 486.519 | 0.586875 | 0.293437 | − | 0.955978i | \(-0.405201\pi\) | ||||
0.293437 | + | 0.955978i | \(0.405201\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 73.7303 | + | 127.705i | 0.0885117 | + | 0.153307i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 576.633 | − | 863.033i | 0.690579 | − | 1.03357i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −590.496 | − | 340.923i | −0.703809 | − | 0.406344i | 0.104956 | − | 0.994477i | \(-0.466530\pi\) |
−0.808764 | + | 0.588133i | \(0.799863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 632.191 | + | 1094.99i | 0.751713 | + | 1.30201i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 798.288 | + | 52.3053i | 0.944720 | + | 0.0618998i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1045.98i | 1.23492i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1125.18 | + | 649.622i | −1.32218 | + | 0.763363i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1364.29 | + | 787.673i | 1.59940 | + | 0.923415i | 0.991602 | + | 0.129325i | \(0.0412809\pi\) |
0.607800 | + | 0.794091i | \(0.292052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −787.158 | + | 1363.40i | −0.918504 | + | 1.59089i | −0.116814 | + | 0.993154i | \(0.537268\pi\) |
−0.801689 | + | 0.597741i | \(0.796065\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −387.191 | − | 670.634i | −0.450746 | − | 0.780715i | 0.547686 | − | 0.836684i | \(-0.315509\pi\) |
−0.998433 | + | 0.0559685i | \(0.982175\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −505.662 | −0.585935 | −0.292968 | − | 0.956122i | \(-0.594643\pi\) | ||||
−0.292968 | + | 0.956122i | \(0.594643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −280.000 | − | 18.3461i | −0.323699 | − | 0.0212094i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −516.582 | + | 298.249i | −0.594456 | + | 0.343209i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −87.4657 | + | 151.495i | −0.100420 | + | 0.173932i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 870.500 | + | 763.309i | 0.994857 | + | 0.872353i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −799.928 | + | 461.838i | −0.912118 | + | 0.526612i | −0.881112 | − | 0.472908i | \(-0.843204\pi\) |
−0.0310061 | + | 0.999519i | \(0.509871\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 599.650i | − | 0.680646i | −0.940309 | − | 0.340323i | \(-0.889464\pi\) | ||
0.940309 | − | 0.340323i | \(-0.110536\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1628.09i | − | 1.84382i | −0.387406 | − | 0.921909i | \(-0.626629\pi\) | ||
0.387406 | − | 0.921909i | \(-0.373371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 365.500 | + | 633.064i | 0.412063 | + | 0.713714i | 0.995115 | − | 0.0987210i | \(-0.0314751\pi\) |
−0.583052 | + | 0.812435i | \(0.698142\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −691.145 | + | 1197.10i | −0.777441 | + | 1.34657i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 278.458 | − | 482.304i | 0.311824 | − | 0.540094i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −318.326 | + | 156.989i | −0.355671 | + | 0.175407i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1320.84i | − | 1.46923i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 232.137 | 0.257644 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 209.944 | + | 425.702i | 0.231983 | + | 0.470389i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −925.543 | − | 534.363i | −1.02044 | − | 0.589154i | −0.106212 | − | 0.994344i | \(-0.533872\pi\) |
−0.914233 | + | 0.405190i | \(0.867206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 917.491 | + | 529.714i | 1.00713 | + | 0.581464i | 0.910349 | − | 0.413842i | \(-0.135813\pi\) |
0.0967764 | + | 0.995306i | \(0.469147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −873.253 | + | 504.173i | −0.956466 | + | 0.552216i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1143.03 | 1.24648 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −874.802 | −0.951906 | −0.475953 | − | 0.879471i | \(-0.657897\pi\) | ||||
−0.475953 | + | 0.879471i | \(0.657897\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −188.441 | − | 326.390i | −0.204162 | − | 0.353619i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −680.530 | − | 522.142i | −0.735708 | − | 0.564478i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −875.024 | − | 505.195i | −0.941899 | − | 0.543806i | −0.0513440 | − | 0.998681i | \(-0.516350\pi\) |
−0.890555 | + | 0.454875i | \(0.849684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −511.076 | − | 885.210i | −0.548954 | − | 0.950817i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.0429 | − | 305.896i | 0.0214362 | − | 0.327162i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 611.705i | 0.652833i | 0.945226 | + | 0.326417i | \(0.105841\pi\) | ||||
−0.945226 | + | 0.326417i | \(0.894159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1237.72 | + | 714.595i | −1.31532 | + | 0.759400i | −0.982972 | − | 0.183757i | \(-0.941174\pi\) |
−0.332347 | + | 0.943157i | \(0.607841\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −895.951 | − | 517.277i | −0.950107 | − | 0.548544i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 474.022 | − | 821.030i | 0.500551 | − | 0.866980i | −0.499449 | − | 0.866343i | \(-0.666464\pi\) |
1.00000 | 0.000636505i | \(-0.000202606\pi\) | ||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.5343 | + | 82.3319i | 0.0500889 | + | 0.0867565i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −435.221 | −0.456686 | −0.228343 | − | 0.973581i | \(-0.573331\pi\) | ||||
−0.228343 | + | 0.973581i | \(0.573331\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.2748 | − | 675.725i | 0.0463610 | − | 0.707566i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −621.841 | + | 359.020i | −0.648427 | + | 0.374369i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.1756 | − | 114.619i | 0.0688611 | − | 0.119271i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −823.653 | − | 550.322i | −0.853527 | − | 0.570282i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1099.46 | − | 634.776i | 1.13698 | − | 0.656439i | 0.191303 | − | 0.981531i | \(-0.438729\pi\) |
0.945682 | + | 0.325093i | \(0.105395\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 763.925i | 0.786740i | 0.919380 | + | 0.393370i | \(0.128691\pi\) | ||||
−0.919380 | + | 0.393370i | \(0.871309\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 582.875i | − | 0.599050i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 66.6082 | + | 115.369i | 0.0681762 | + | 0.118085i | 0.898099 | − | 0.439794i | \(-0.144949\pi\) |
−0.829922 | + | 0.557879i | \(0.811615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −651.794 | + | 1128.94i | −0.665775 | + | 1.15316i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −69.2551 | + | 119.953i | −0.0704527 | + | 0.122028i | −0.899100 | − | 0.437744i | \(-0.855778\pi\) |
0.828647 | + | 0.559771i | \(0.189111\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −317.250 | − | 643.284i | −0.322081 | − | 0.653080i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1373.15i | − | 1.38842i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1011.72 | −1.02091 | −0.510453 | − | 0.859906i | \(-0.670522\pi\) | ||||
−0.510453 | + | 0.859906i | \(0.670522\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 727.293 | + | 1474.72i | 0.730948 | + | 1.48213i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −720.117 | − | 415.760i | −0.722284 | − | 0.417011i | 0.0933090 | − | 0.995637i | \(-0.470256\pi\) |
−0.815593 | + | 0.578627i | \(0.803589\pi\) | |||||||
\(998\) | 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 | 1620.3.t.e.269.4 | 16 | ||
3.2 | odd | 2 | inner | 1620.3.t.e.269.5 | 16 | ||
5.4 | even | 2 | inner | 1620.3.t.e.269.6 | 16 | ||
9.2 | odd | 6 | 540.3.b.c.269.1 | ✓ | 8 | ||
9.4 | even | 3 | inner | 1620.3.t.e.1349.3 | 16 | ||
9.5 | odd | 6 | inner | 1620.3.t.e.1349.6 | 16 | ||
9.7 | even | 3 | 540.3.b.c.269.8 | yes | 8 | ||
15.14 | odd | 2 | inner | 1620.3.t.e.269.3 | 16 | ||
36.7 | odd | 6 | 2160.3.c.n.1889.8 | 8 | |||
36.11 | even | 6 | 2160.3.c.n.1889.1 | 8 | |||
45.2 | even | 12 | 2700.3.g.p.701.4 | 4 | |||
45.4 | even | 6 | inner | 1620.3.t.e.1349.5 | 16 | ||
45.7 | odd | 12 | 2700.3.g.p.701.3 | 4 | |||
45.14 | odd | 6 | inner | 1620.3.t.e.1349.4 | 16 | ||
45.29 | odd | 6 | 540.3.b.c.269.7 | yes | 8 | ||
45.34 | even | 6 | 540.3.b.c.269.2 | yes | 8 | ||
45.38 | even | 12 | 2700.3.g.o.701.2 | 4 | |||
45.43 | odd | 12 | 2700.3.g.o.701.1 | 4 | |||
180.79 | odd | 6 | 2160.3.c.n.1889.2 | 8 | |||
180.119 | even | 6 | 2160.3.c.n.1889.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.3.b.c.269.1 | ✓ | 8 | 9.2 | odd | 6 | ||
540.3.b.c.269.2 | yes | 8 | 45.34 | even | 6 | ||
540.3.b.c.269.7 | yes | 8 | 45.29 | odd | 6 | ||
540.3.b.c.269.8 | yes | 8 | 9.7 | even | 3 | ||
1620.3.t.e.269.3 | 16 | 15.14 | odd | 2 | inner | ||
1620.3.t.e.269.4 | 16 | 1.1 | even | 1 | trivial | ||
1620.3.t.e.269.5 | 16 | 3.2 | odd | 2 | inner | ||
1620.3.t.e.269.6 | 16 | 5.4 | even | 2 | inner | ||
1620.3.t.e.1349.3 | 16 | 9.4 | even | 3 | inner | ||
1620.3.t.e.1349.4 | 16 | 45.14 | odd | 6 | inner | ||
1620.3.t.e.1349.5 | 16 | 45.4 | even | 6 | inner | ||
1620.3.t.e.1349.6 | 16 | 9.5 | odd | 6 | inner | ||
2160.3.c.n.1889.1 | 8 | 36.11 | even | 6 | |||
2160.3.c.n.1889.2 | 8 | 180.79 | odd | 6 | |||
2160.3.c.n.1889.7 | 8 | 180.119 | even | 6 | |||
2160.3.c.n.1889.8 | 8 | 36.7 | odd | 6 | |||
2700.3.g.o.701.1 | 4 | 45.43 | odd | 12 | |||
2700.3.g.o.701.2 | 4 | 45.38 | even | 12 | |||
2700.3.g.p.701.3 | 4 | 45.7 | odd | 12 | |||
2700.3.g.p.701.4 | 4 | 45.2 | even | 12 |