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 | 1349.6 | ||
Root | \(-5.87958 - 3.39457i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1349 |
Dual form | 1620.3.t.e.269.6 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | 2.77776 | − | 4.15741i | 0.555552 | − | 0.831482i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.02120 | + | 4.63104i | −1.14589 | + | 0.661578i | −0.947881 | − | 0.318623i | \(-0.896779\pi\) |
−0.198005 | + | 0.980201i | \(0.563446\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.2457 | − | 7.64741i | 1.20415 | − | 0.695219i | 0.242678 | − | 0.970107i | \(-0.421974\pi\) |
0.961476 | + | 0.274888i | \(0.0886408\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.59808 | − | 1.50000i | −0.199852 | − | 0.115385i | 0.396734 | − | 0.917933i | \(-0.370143\pi\) |
−0.596586 | + | 0.802549i | \(0.703477\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00858 | −0.235799 | −0.117899 | − | 0.993026i | \(-0.537616\pi\) | ||||
−0.117899 | + | 0.993026i | \(0.537616\pi\) | |||||||
\(18\) | 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 | 0.0800840 | + | 0.996788i | \(0.474481\pi\) |
−0.903286 | + | 0.429039i | \(0.858852\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.56808 | − | 23.0966i | −0.382723 | − | 0.923863i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39.7371 | − | 22.9422i | 1.37024 | − | 0.791111i | 0.379286 | − | 0.925280i | \(-0.376170\pi\) |
0.990959 | + | 0.134168i | \(0.0428363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.3931 | + | 24.9296i | −0.464295 | + | 0.804182i | −0.999169 | − | 0.0407496i | \(-0.987025\pi\) |
0.534875 | + | 0.844931i | \(0.320359\pi\) | |||||||
\(32\) | 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 | 0.182892 | − | 0.983133i | \(-0.441454\pi\) |
−0.759972 | + | 0.649956i | \(0.774787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.4039 | − | 18.1310i | 0.730323 | − | 0.421652i | −0.0882173 | − | 0.996101i | \(-0.528117\pi\) |
0.818540 | + | 0.574449i | \(0.194784\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0214 | + | 17.3576i | 0.213222 | + | 0.369312i | 0.952721 | − | 0.303846i | \(-0.0982708\pi\) |
−0.739499 | + | 0.673158i | \(0.764938\pi\) | |||||||
\(48\) | 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 | \(-0.683973\pi\) | ||||
−0.546322 | + | 0.837575i | \(0.683973\pi\) | |||||||
\(54\) | 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 | −0.279732 | − | 0.960078i | \(-0.590246\pi\) |
−0.971318 | + | 0.237784i | \(0.923579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.8931 | + | 32.7239i | 0.309723 | + | 0.536457i | 0.978302 | − | 0.207185i | \(-0.0664302\pi\) |
−0.668578 | + | 0.743642i | \(0.733097\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.4529 | + | 6.63462i | −0.206968 | + | 0.102071i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 50.4983 | + | 29.1552i | 0.753706 | + | 0.435153i | 0.827032 | − | 0.562156i | \(-0.190028\pi\) |
−0.0733252 | + | 0.997308i | \(0.523361\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 125.628i | 1.76940i | 0.466158 | + | 0.884701i | \(0.345638\pi\) | ||||
−0.466158 | + | 0.884701i | \(0.654362\pi\) | |||||||
\(72\) | 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 | 0.715811 | − | 0.698294i | \(-0.246057\pi\) |
−0.962646 | + | 0.270763i | \(0.912724\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 32.9637 | + | 57.0947i | 0.397153 | + | 0.687888i | 0.993373 | − | 0.114932i | \(-0.0366650\pi\) |
−0.596221 | + | 0.802821i | \(0.703332\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.1349 | + | 16.6653i | −0.130998 | + | 0.196062i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 85.2307i | − | 0.957648i | −0.877911 | − | 0.478824i | \(-0.841063\pi\) | ||
0.877911 | − | 0.478824i | \(-0.158937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.7863 | 0.305344 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −77.1836 | + | 115.519i | −0.812459 | + | 1.21599i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −140.195 | + | 80.9415i | −1.44531 | + | 0.834448i | −0.998197 | − | 0.0600306i | \(-0.980880\pi\) |
−0.447110 | + | 0.894479i | \(0.647547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −63.3974 | + | 36.6025i | −0.627697 | + | 0.362401i | −0.779860 | − | 0.625955i | \(-0.784710\pi\) |
0.152163 | + | 0.988355i | \(0.451376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −133.637 | − | 77.1552i | −1.29744 | − | 0.749080i | −0.317482 | − | 0.948264i | \(-0.602837\pi\) |
−0.979962 | + | 0.199184i | \(0.936171\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −149.679 | −1.39887 | −0.699435 | − | 0.714696i | \(-0.746565\pi\) | ||||
−0.699435 | + | 0.714696i | \(0.746565\pi\) | |||||||
\(108\) | 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 | \(-0.969857\pi\) |
0.579646 | + | 0.814868i | \(0.303191\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83.7450 | + | 169.809i | 0.728218 | + | 1.47660i | ||||
\(116\) | 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 | 0.848981 | − | 0.528424i | \(-0.177217\pi\) |
−0.0331379 | + | 0.999451i | \(0.510550\pi\) | |||||||
\(132\) | 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 | \(-0.0753580\pi\) |
−0.689170 | + | 0.724600i | \(0.742025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −31.4657 | + | 54.5001i | −0.226372 | + | 0.392087i | −0.956730 | − | 0.290977i | \(-0.906020\pi\) |
0.730358 | + | 0.683064i | \(0.239353\pi\) | |||||||
\(140\) | 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 | 0.996373 | + | 0.0850984i | \(0.0271204\pi\) |
0.571884 | + | 0.820335i | \(0.306213\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −38.0725 | − | 65.9435i | −0.252136 | − | 0.436712i | 0.711978 | − | 0.702202i | \(-0.247800\pi\) |
−0.964114 | + | 0.265490i | \(0.914466\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 63.6620 | + | 129.087i | 0.410722 | + | 0.832817i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 98.4999 | + | 56.8690i | 0.627388 | + | 0.362223i | 0.779740 | − | 0.626104i | \(-0.215351\pi\) |
−0.152352 | + | 0.988326i | \(0.548685\pi\) | |||||||
\(158\) | 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 | 0.367677 | + | 0.929953i | \(0.380153\pi\) |
−0.989202 | + | 0.146559i | \(0.953180\pi\) | |||||||
\(168\) | 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 | \(-0.218525\pi\) |
−0.935656 | + | 0.352913i | \(0.885191\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 183.709 | + | 140.952i | 1.04976 | + | 0.805441i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 70.9865i | 0.396573i | 0.980144 | + | 0.198286i | \(0.0635376\pi\) | ||||
−0.980144 | + | 0.198286i | \(0.936462\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | 142.642 | + | 95.3062i | 0.771040 | + | 0.515169i | ||||
\(186\) | 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 | −0.160478 | − | 0.987039i | \(-0.551304\pi\) |
0.774562 | + | 0.632498i | \(0.217970\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −171.574 | − | 99.0585i | −0.888986 | − | 0.513257i | −0.0153756 | − | 0.999882i | \(-0.504894\pi\) |
−0.873611 | + | 0.486625i | \(0.838228\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −143.452 | −0.728183 | −0.364091 | − | 0.931363i | \(-0.618620\pi\) | ||||
−0.364091 | + | 0.931363i | \(0.618620\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | −122.514 | + | 60.4205i | −0.597629 | + | 0.294734i | ||||
\(206\) | 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 | −0.998811 | − | 0.0487540i | \(-0.984475\pi\) |
0.541628 | + | 0.840619i | \(0.317808\pi\) | |||||||
\(212\) | 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 | \(-0.600290\pi\) |
0.668453 | + | 0.743755i | \(0.266957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 36.9722 | + | 64.0378i | 0.162873 | + | 0.282105i | 0.935898 | − | 0.352271i | \(-0.114590\pi\) |
−0.773025 | + | 0.634376i | \(0.781257\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 137.573 | − | 238.283i | 0.600753 | − | 1.04054i | −0.391954 | − | 0.919985i | \(-0.628201\pi\) |
0.992707 | − | 0.120550i | \(-0.0384660\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −310.955 | −1.33457 | −0.667286 | − | 0.744801i | \(-0.732544\pi\) | ||||
−0.667286 | + | 0.744801i | \(0.732544\pi\) | |||||||
\(234\) | 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 | 0.416567 | − | 0.909105i | \(-0.363233\pi\) |
−0.579024 | + | 0.815310i | \(0.696566\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 80.5000 | + | 139.430i | 0.334025 | + | 0.578548i | 0.983297 | − | 0.182008i | \(-0.0582597\pi\) |
−0.649272 | + | 0.760556i | \(0.724926\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −81.3543 | − | 164.961i | −0.332058 | − | 0.673311i | ||||
\(246\) | 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 | \(0.0444899\pi\) | ||||
−0.990248 | + | 0.139315i | \(0.955510\pi\) | |||||||
\(252\) | 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 | \(-0.756155\pi\) |
0.960741 | + | 0.277446i | \(0.0894879\pi\) | |||||||
\(258\) | 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 | 0.916591 | + | 0.399825i | \(0.130929\pi\) |
−0.112037 | + | 0.993704i | \(0.535738\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −160.861 | + | 240.756i | −0.607021 | + | 0.908514i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 330.998i | 1.23048i | 0.788341 | + | 0.615239i | \(0.210940\pi\) | ||||
−0.788341 | + | 0.615239i | \(0.789060\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −303.365 | − | 232.759i | −1.10314 | − | 0.846397i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8833 | + | 8.59286i | −0.0537302 | + | 0.0310212i | −0.526624 | − | 0.850098i | \(-0.676543\pi\) |
0.472894 | + | 0.881119i | \(0.343209\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −255.409 | + | 147.461i | −0.908930 | + | 0.524771i | −0.880087 | − | 0.474813i | \(-0.842516\pi\) |
−0.0288429 | + | 0.999584i | \(0.509182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −400.809 | − | 231.407i | −1.41629 | − | 0.817693i | −0.420316 | − | 0.907378i | \(-0.638081\pi\) |
−0.995970 | + | 0.0896849i | \(0.971414\pi\) | |||||||
\(284\) | 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 | \(-0.723748\pi\) |
0.983964 | + | 0.178367i | \(0.0570813\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −382.201 | + | 188.491i | −1.29560 | + | 0.638953i | ||||
\(296\) | 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 | 0.141515 | − | 0.989936i | \(-0.454803\pi\) |
−0.786552 | + | 0.617523i | \(0.788136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 235.290 | − | 135.845i | 0.751725 | − | 0.434009i | −0.0745916 | − | 0.997214i | \(-0.523765\pi\) |
0.826317 | + | 0.563205i | \(0.190432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −139.443 | − | 241.523i | −0.439885 | − | 0.761902i | 0.557796 | − | 0.829978i | \(-0.311647\pi\) |
−0.997680 | + | 0.0680759i | \(0.978314\pi\) | |||||||
\(318\) | 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 | 0.943102 | + | 0.332503i | \(0.107893\pi\) |
−0.183595 | + | 0.983002i | \(0.558773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 261.482 | − | 128.956i | 0.780545 | − | 0.384943i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −62.5037 | − | 36.0865i | −0.185471 | − | 0.107082i | 0.404390 | − | 0.914587i | \(-0.367484\pi\) |
−0.589861 | + | 0.807505i | \(0.700817\pi\) | |||||||
\(338\) | 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 | \(-0.944273\pi\) |
0.643200 | + | 0.765698i | \(0.277606\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −192.534 | − | 333.479i | −0.551674 | − | 0.955528i | −0.998154 | − | 0.0607342i | \(-0.980656\pi\) |
0.446480 | − | 0.894794i | \(-0.352678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −273.302 | − | 473.374i | −0.774228 | − | 1.34100i | −0.935228 | − | 0.354047i | \(-0.884805\pi\) |
0.161000 | − | 0.986954i | \(-0.448528\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 522.285 | + | 348.963i | 1.47123 | + | 0.982996i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 110.450i | 0.307660i | 0.988097 | + | 0.153830i | \(0.0491609\pi\) | ||||
−0.988097 | + | 0.153830i | \(0.950839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 411.076 | 1.13872 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 131.746 | + | 88.0261i | 0.360949 | + | 0.241167i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 452.215 | − | 261.087i | 1.23219 | − | 0.711407i | 0.264707 | − | 0.964329i | \(-0.414725\pi\) |
0.967487 | + | 0.252921i | \(0.0813914\pi\) | |||||||
\(368\) | 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 | \(-0.129195\pi\) |
0.117450 | + | 0.993079i | \(0.462528\pi\) | |||||||
\(374\) | 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 | −0.141043 | − | 0.990004i | \(-0.545045\pi\) |
0.927889 | − | 0.372855i | \(-0.121621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 313.291 | + | 635.257i | 0.813743 | + | 1.65002i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 580.081 | − | 334.910i | 1.49121 | − | 0.860951i | 0.491262 | − | 0.871012i | \(-0.336536\pi\) |
0.999949 | + | 0.0100609i | \(0.00320253\pi\) | |||||||
\(390\) | 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 | 0.243889 | − | 0.969803i | \(-0.421577\pi\) |
−0.717930 | + | 0.696115i | \(0.754910\pi\) | |||||||
\(402\) | 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 | −0.956567 | − | 0.291513i | \(-0.905841\pi\) |
0.730741 | + | 0.682654i | \(0.239175\pi\) | |||||||
\(410\) | 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 | 0.354651 | − | 0.934999i | \(-0.384600\pi\) |
−0.632408 | + | 0.774636i | \(0.717933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 63.5343 | + | 110.045i | 0.150913 | + | 0.261389i | 0.931563 | − | 0.363579i | \(-0.118445\pi\) |
−0.780650 | + | 0.624968i | \(0.785112\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.3544 | + | 92.5844i | 0.0902456 | + | 0.217846i | ||||
\(426\) | 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 | \(0.0117297\pi\) | ||||
−0.999321 | + | 0.0368417i | \(0.988270\pi\) | |||||||
\(432\) | 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 | −0.851242 | − | 0.524774i | \(-0.824150\pi\) |
−0.0288467 | − | 0.999584i | \(-0.509183\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −183.538 | − | 317.897i | −0.414306 | − | 0.717600i | 0.581049 | − | 0.813869i | \(-0.302642\pi\) |
−0.995355 | + | 0.0962688i | \(0.969309\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −354.339 | − | 236.751i | −0.796267 | − | 0.532024i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 526.562i | − | 1.17274i | −0.810042 | − | 0.586372i | \(-0.800556\pi\) | ||
0.810042 | − | 0.586372i | \(-0.199444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −417.863 | −0.926525 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 77.1836 | − | 115.519i | 0.169634 | − | 0.253888i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −397.177 | + | 229.310i | −0.869097 | + | 0.501773i | −0.867048 | − | 0.498225i | \(-0.833986\pi\) |
−0.00204894 | + | 0.999998i | \(0.500652\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 304.753 | − | 175.949i | 0.661069 | − | 0.381668i | −0.131615 | − | 0.991301i | \(-0.542016\pi\) |
0.792684 | + | 0.609633i | \(0.208683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −383.352 | − | 221.328i | −0.827974 | − | 0.478031i | 0.0251847 | − | 0.999683i | \(-0.491983\pi\) |
−0.853158 | + | 0.521652i | \(0.825316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 646.819 | 1.38505 | 0.692526 | − | 0.721393i | \(-0.256498\pi\) | ||||
0.692526 | + | 0.721393i | \(0.256498\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | 265.861 | + | 641.768i | 0.559708 | + | 1.35109i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 169.261 | − | 97.7231i | 0.353364 | − | 0.204015i | −0.312802 | − | 0.949818i | \(-0.601268\pi\) |
0.666166 | + | 0.745804i | \(0.267934\pi\) | |||||||
\(480\) | 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 | 0.909465 | − | 0.415780i | \(-0.136492\pi\) |
0.0946561 | + | 0.995510i | \(0.469825\pi\) | |||||||
\(492\) | 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 | −0.850910 | − | 0.525312i | \(-0.823949\pi\) |
0.880388 | + | 0.474253i | \(0.157282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 465.500 | 0.925447 | 0.462724 | − | 0.886503i | \(-0.346872\pi\) | ||||
0.462724 | + | 0.886503i | \(0.346872\pi\) | |||||||
\(504\) | 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 | 0.185764 | − | 0.982594i | \(-0.440524\pi\) |
−0.758070 | + | 0.652173i | \(0.773857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −146.756 | − | 254.188i | −0.287193 | − | 0.497433i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −691.977 | + | 341.264i | −1.34364 | + | 0.662648i | ||||
\(516\) | 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 | \(-0.863380\pi\) | ||
0.909297 | − | 0.416147i | \(-0.136620\pi\) | |||||||
\(522\) | 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 | ||||||||
\(535\) | −415.773 | + | 622.277i | −0.777145 | + | 1.16313i | ||||
\(536\) | 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 | ||||||||
\(545\) | 368.658 | − | 551.761i | 0.676436 | − | 1.01241i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 526.753 | − | 304.121i | 0.962985 | − | 0.555980i | 0.0658946 | − | 0.997827i | \(-0.479010\pi\) |
0.897090 | + | 0.441847i | \(0.145677\pi\) | |||||||
\(548\) | 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 | \(-0.475020\pi\) | ||||
0.0783949 | + | 0.996922i | \(0.475020\pi\) | |||||||
\(558\) | 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 | \(-0.862838\pi\) |
0.816027 | + | 0.578013i | \(0.196172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 207.857 | + | 421.469i | 0.367888 | + | 0.745963i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −563.801 | + | 325.511i | −0.990863 | + | 0.572075i | −0.905532 | − | 0.424278i | \(-0.860528\pi\) |
−0.0853310 | + | 0.996353i | \(0.527195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 57.8244 | − | 100.155i | 0.101269 | − | 0.175403i | −0.810939 | − | 0.585131i | \(-0.801043\pi\) |
0.912208 | + | 0.409728i | \(0.134376\pi\) | |||||||
\(572\) | 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 | 0.994371 | + | 0.105952i | \(0.0337889\pi\) |
−0.405429 | + | 0.914127i | \(0.632878\pi\) | |||||||
\(588\) | 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 | \(-0.716921\pi\) | ||||
−0.629941 | + | 0.776643i | \(0.716921\pi\) | |||||||
\(594\) | 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 | 0.793054 | − | 0.609151i | \(-0.208490\pi\) |
−0.131013 | + | 0.991381i | \(0.541823\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 81.6756 | + | 141.466i | 0.135899 | + | 0.235385i | 0.925941 | − | 0.377669i | \(-0.123274\pi\) |
−0.790041 | + | 0.613054i | \(0.789941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −249.752 | − | 506.420i | −0.412813 | − | 0.837057i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −124.558 | − | 71.9135i | −0.205202 | − | 0.118474i | 0.393877 | − | 0.919163i | \(-0.371133\pi\) |
−0.599080 | + | 0.800689i | \(0.704467\pi\) | |||||||
\(608\) | 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 | −0.471291 | − | 0.881978i | \(-0.656212\pi\) |
0.999461 | − | 0.0328386i | \(-0.0104547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −257.176 | − | 445.441i | −0.415469 | − | 0.719614i | 0.580008 | − | 0.814611i | \(-0.303049\pi\) |
−0.995478 | + | 0.0949965i | \(0.969716\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 394.707 | + | 683.653i | 0.633559 | + | 1.09736i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −441.904 | + | 441.980i | −0.707046 | + | 0.707168i | ||||
\(626\) | 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 | ||||||||
\(635\) | 620.459 | + | 414.558i | 0.977100 | + | 0.652847i | ||||
\(636\) | 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 | −0.595633 | − | 0.803257i | \(-0.703099\pi\) |
0.397825 | + | 0.917461i | \(0.369765\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 768.852 | + | 443.897i | 1.19573 | + | 0.690353i | 0.959600 | − | 0.281369i | \(-0.0907886\pi\) |
0.236127 | + | 0.971722i | \(0.424122\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 250.322 | 0.386896 | 0.193448 | − | 0.981111i | \(-0.438033\pi\) | ||||
0.193448 | + | 0.981111i | \(0.438033\pi\) | |||||||
\(648\) | 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 | −0.221131 | − | 0.975244i | \(-0.570975\pi\) |
0.955152 | − | 0.296117i | \(-0.0956920\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 553.405 | − | 272.924i | 0.844894 | − | 0.416678i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −720.930 | + | 416.229i | −1.09398 | + | 0.631607i | −0.934632 | − | 0.355616i | \(-0.884271\pi\) |
−0.159343 | + | 0.987223i | \(0.550938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −643.260 | + | 1114.16i | −0.973161 | + | 1.68556i | −0.287287 | + | 0.957845i | \(0.592753\pi\) |
−0.685874 | + | 0.727720i | \(0.740580\pi\) | |||||||
\(662\) | 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 | \(-0.389886\pi\) |
0.984259 | + | 0.176731i | \(0.0565522\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −450.827 | − | 780.856i | −0.665919 | − | 1.15341i | −0.979035 | − | 0.203691i | \(-0.934706\pi\) |
0.313116 | − | 0.949715i | \(-0.398627\pi\) | |||||||
\(678\) | 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 | \(-0.448923\pi\) | ||||
0.159775 | + | 0.987153i | \(0.448923\pi\) | |||||||
\(684\) | 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 | 0.988694 | − | 0.149946i | \(-0.0479100\pi\) |
−0.624204 | + | 0.781261i | \(0.714577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 139.175 | + | 282.204i | 0.200252 | + | 0.406049i | ||||
\(696\) | 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 | \(0.0868807\pi\) | ||||
−0.962982 | + | 0.269567i | \(0.913119\pi\) | |||||||
\(702\) | 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 | −0.878150 | − | 0.478385i | \(-0.841223\pi\) |
0.0247821 | − | 0.999693i | \(-0.492111\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −545.029 | − | 944.018i | −0.764416 | − | 1.32401i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −127.456 | + | 190.760i | −0.178260 | + | 0.266798i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 462.113i | − | 0.642717i | −0.946958 | − | 0.321358i | \(-0.895861\pi\) | ||
0.946958 | − | 0.321358i | \(-0.104139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1429.24 | 1.98230 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −910.094 | − | 698.278i | −1.25530 | − | 0.963142i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −462.352 | + | 266.939i | −0.635972 | + | 0.367179i | −0.783061 | − | 0.621944i | \(-0.786343\pi\) |
0.147089 | + | 0.989123i | \(0.453010\pi\) | |||||||
\(728\) | 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 | \(-0.451737\pi\) |
−0.780569 | + | 0.625069i | \(0.785071\pi\) | |||||||
\(734\) | 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 | 0.374873 | + | 0.927076i | \(0.377686\pi\) |
−0.990308 | + | 0.138889i | \(0.955647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1209.95 | − | 596.716i | 1.62410 | − | 0.800961i | ||||
\(746\) | 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 | 0.427601 | + | 0.903967i | \(0.359359\pi\) |
−0.996659 | + | 0.0816701i | \(0.973975\pi\) | |||||||
\(752\) | 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 | 0.997396 | − | 0.0721147i | \(-0.0229748\pi\) |
0.436245 | + | 0.899828i | \(0.356308\pi\) | |||||||
\(762\) | 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 | −0.175092 | − | 0.984552i | \(-0.556022\pi\) |
0.940193 | − | 0.340642i | \(-0.110644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 112.317 | 0.145300 | 0.0726499 | − | 0.997358i | \(-0.476854\pi\) | ||||
0.0726499 | + | 0.997358i | \(0.476854\pi\) | |||||||
\(774\) | 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 | ||||||||
\(785\) | 510.037 | − | 251.536i | 0.649728 | − | 0.320428i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −423.438 | − | 244.472i | −0.538041 | − | 0.310638i | 0.206244 | − | 0.978501i | \(-0.433876\pi\) |
−0.744284 | + | 0.667863i | \(0.767209\pi\) | |||||||
\(788\) | 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 | 0.159349 | + | 0.987222i | \(0.449061\pi\) |
−0.934634 | + | 0.355611i | \(0.884273\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | −1458.13 | − | 974.245i | −1.81134 | − | 1.21024i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1251.84i | 1.54739i | 0.633558 | + | 0.773695i | \(0.281594\pi\) | ||||
−0.633558 | + | 0.773695i | \(0.718406\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | 375.743 | + | 251.052i | 0.461034 | + | 0.308039i | ||||
\(816\) | 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 | 0.119948 | − | 0.992780i | \(-0.461727\pi\) |
0.919747 | + | 0.392512i | \(0.128394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 780.229 | + | 450.466i | 0.948031 | + | 0.547346i | 0.892469 | − | 0.451109i | \(-0.148972\pi\) |
0.0555622 | + | 0.998455i | \(0.482305\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1571.67 | −1.90045 | −0.950223 | − | 0.311572i | \(-0.899145\pi\) | ||||
−0.950223 | + | 0.311572i | \(0.899145\pi\) | |||||||
\(828\) | 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 | ||||||||
\(835\) | 459.092 | + | 930.896i | 0.549811 | + | 1.11485i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −590.496 | + | 340.923i | −0.703809 | + | 0.406344i | −0.808764 | − | 0.588133i | \(-0.799863\pi\) |
0.104956 | + | 0.994477i | \(0.466530\pi\) | |||||||
\(840\) | 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 | −0.607800 | + | 0.794091i | \(0.707948\pi\) |
−0.991602 | + | 0.129325i | \(0.958719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 787.158 | + | 1363.40i | 0.918504 | + | 1.59089i | 0.801689 | + | 0.597741i | \(0.203935\pi\) |
0.116814 | + | 0.993154i | \(0.462732\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −387.191 | + | 670.634i | −0.450746 | + | 0.780715i | −0.998433 | − | 0.0559685i | \(-0.982175\pi\) |
0.547686 | + | 0.836684i | \(0.315509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 505.662 | 0.585935 | 0.292968 | − | 0.956122i | \(-0.405357\pi\) | ||||
0.292968 | + | 0.956122i | \(0.405357\pi\) | |||||||
\(864\) | 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 | ||||||||
\(875\) | 1096.29 | − | 372.221i | 1.25291 | − | 0.425395i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 799.928 | + | 461.838i | 0.912118 | + | 0.526612i | 0.881112 | − | 0.472908i | \(-0.156796\pi\) |
0.0310061 | + | 0.999519i | \(0.490129\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 599.650i | 0.680646i | 0.940309 | + | 0.340323i | \(0.110536\pi\) | ||||
−0.940309 | + | 0.340323i | \(0.889464\pi\) | |||||||
\(882\) | 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 | \(-0.968525\pi\) |
0.583052 | + | 0.812435i | \(0.301858\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | 295.120 | + | 197.184i | 0.329743 | + | 0.220317i | ||||
\(896\) | 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 | ||||||||
\(905\) | −263.697 | + | 394.668i | −0.291377 | + | 0.436097i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 925.543 | − | 534.363i | 1.02044 | − | 0.589154i | 0.106212 | − | 0.994344i | \(-0.466128\pi\) |
0.914233 | + | 0.405190i | \(0.132794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 917.491 | − | 529.714i | 1.00713 | − | 0.581464i | 0.0967764 | − | 0.995306i | \(-0.469147\pi\) |
0.910349 | + | 0.413842i | \(0.135813\pi\) | |||||||
\(912\) | 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 | ||||||||
\(925\) | 792.454 | − | 328.285i | 0.856707 | − | 0.354903i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −875.024 | + | 505.195i | −0.941899 | + | 0.543806i | −0.890555 | − | 0.454875i | \(-0.849684\pi\) |
−0.0513440 | + | 0.998681i | \(0.516350\pi\) | |||||||
\(930\) | 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 | −0.332347 | − | 0.943157i | \(-0.607841\pi\) |
−0.982972 | + | 0.183757i | \(0.941174\pi\) | |||||||
\(942\) | 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 | −1.00000 | 0.000636505i | \(-0.999797\pi\) | |
0.499449 | − | 0.866343i | \(-0.333536\pi\) | |||||||
\(948\) | 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 | \(-0.426669\pi\) | ||||
0.228343 | + | 0.973581i | \(0.426669\pi\) | |||||||
\(954\) | 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 | ||||||||
\(965\) | −888.419 | + | 438.144i | −0.920642 | + | 0.454035i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1099.46 | − | 634.776i | −1.13698 | − | 0.656439i | −0.191303 | − | 0.981531i | \(-0.561271\pi\) |
−0.945682 | + | 0.325093i | \(0.894605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 763.925i | − | 0.786740i | −0.919380 | − | 0.393370i | \(-0.871309\pi\) | ||
0.919380 | − | 0.393370i | \(-0.128691\pi\) | |||||||
\(972\) | 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 | \(-0.855051\pi\) |
0.829922 | + | 0.557879i | \(0.188385\pi\) | |||||||
\(978\) | 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 | \(-0.144222\pi\) |
−0.828647 | + | 0.559771i | \(0.810889\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −398.475 | + | 596.388i | −0.404544 | + | 0.605470i | ||||
\(986\) | 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 | ||||||||
\(995\) | −913.502 | + | 1367.22i | −0.918092 | + | 1.37409i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 720.117 | − | 415.760i | 0.722284 | − | 0.417011i | −0.0933090 | − | 0.995637i | \(-0.529744\pi\) |
0.815593 | + | 0.578627i | \(0.196411\pi\) | |||||||
\(998\) | 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.1349.6 | 16 | ||
3.2 | odd | 2 | inner | 1620.3.t.e.1349.3 | 16 | ||
5.4 | even | 2 | inner | 1620.3.t.e.1349.4 | 16 | ||
9.2 | odd | 6 | inner | 1620.3.t.e.269.4 | 16 | ||
9.4 | even | 3 | 540.3.b.c.269.1 | ✓ | 8 | ||
9.5 | odd | 6 | 540.3.b.c.269.8 | yes | 8 | ||
9.7 | even | 3 | inner | 1620.3.t.e.269.5 | 16 | ||
15.14 | odd | 2 | inner | 1620.3.t.e.1349.5 | 16 | ||
36.23 | even | 6 | 2160.3.c.n.1889.8 | 8 | |||
36.31 | odd | 6 | 2160.3.c.n.1889.1 | 8 | |||
45.4 | even | 6 | 540.3.b.c.269.7 | yes | 8 | ||
45.13 | odd | 12 | 2700.3.g.o.701.2 | 4 | |||
45.14 | odd | 6 | 540.3.b.c.269.2 | yes | 8 | ||
45.22 | odd | 12 | 2700.3.g.p.701.4 | 4 | |||
45.23 | even | 12 | 2700.3.g.o.701.1 | 4 | |||
45.29 | odd | 6 | inner | 1620.3.t.e.269.6 | 16 | ||
45.32 | even | 12 | 2700.3.g.p.701.3 | 4 | |||
45.34 | even | 6 | inner | 1620.3.t.e.269.3 | 16 | ||
180.59 | even | 6 | 2160.3.c.n.1889.2 | 8 | |||
180.139 | odd | 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 | 9.4 | even | 3 | ||
540.3.b.c.269.2 | yes | 8 | 45.14 | odd | 6 | ||
540.3.b.c.269.7 | yes | 8 | 45.4 | even | 6 | ||
540.3.b.c.269.8 | yes | 8 | 9.5 | odd | 6 | ||
1620.3.t.e.269.3 | 16 | 45.34 | even | 6 | inner | ||
1620.3.t.e.269.4 | 16 | 9.2 | odd | 6 | inner | ||
1620.3.t.e.269.5 | 16 | 9.7 | even | 3 | inner | ||
1620.3.t.e.269.6 | 16 | 45.29 | odd | 6 | inner | ||
1620.3.t.e.1349.3 | 16 | 3.2 | odd | 2 | inner | ||
1620.3.t.e.1349.4 | 16 | 5.4 | even | 2 | inner | ||
1620.3.t.e.1349.5 | 16 | 15.14 | odd | 2 | inner | ||
1620.3.t.e.1349.6 | 16 | 1.1 | even | 1 | trivial | ||
2160.3.c.n.1889.1 | 8 | 36.31 | odd | 6 | |||
2160.3.c.n.1889.2 | 8 | 180.59 | even | 6 | |||
2160.3.c.n.1889.7 | 8 | 180.139 | odd | 6 | |||
2160.3.c.n.1889.8 | 8 | 36.23 | even | 6 | |||
2700.3.g.o.701.1 | 4 | 45.23 | even | 12 | |||
2700.3.g.o.701.2 | 4 | 45.13 | odd | 12 | |||
2700.3.g.p.701.3 | 4 | 45.32 | even | 12 | |||
2700.3.g.p.701.4 | 4 | 45.22 | odd | 12 |