Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(163,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.163");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 8x^{12} + 4x^{10} + 160x^{8} + 64x^{6} - 2048x^{4} + 4096x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.12 | ||
Root | \(0.941181 + 1.76470i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.163 |
Dual form | 216.3.b.a.163.11 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.941181 | + | 1.76470i | 0.470590 | + | 0.882352i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.22836 | + | 3.32181i | −0.557089 | + | 0.830453i | ||||
\(5\) | 8.60639i | 1.72128i | 0.509216 | + | 0.860639i | \(0.329935\pi\) | ||||
−0.509216 | + | 0.860639i | \(0.670065\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.81948i | − | 0.688497i | −0.938879 | − | 0.344249i | \(-0.888134\pi\) | ||
0.938879 | − | 0.344249i | \(-0.111866\pi\) | |||||||
\(8\) | −7.95930 | − | 0.805966i | −0.994912 | − | 0.100746i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −15.1877 | + | 8.10017i | −1.51877 | + | 0.810017i | ||||
\(11\) | −9.93139 | −0.902854 | −0.451427 | − | 0.892308i | \(-0.649085\pi\) | ||||
−0.451427 | + | 0.892308i | \(0.649085\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.78729i | 0.445176i | 0.974913 | + | 0.222588i | \(0.0714504\pi\) | ||||
−0.974913 | + | 0.222588i | \(0.928550\pi\) | |||||||
\(14\) | 8.50495 | − | 4.53600i | 0.607497 | − | 0.324000i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.06885 | − | 14.8044i | −0.379303 | − | 0.925273i | ||||
\(17\) | 30.8667 | 1.81569 | 0.907843 | − | 0.419309i | \(-0.137728\pi\) | ||||
0.907843 | + | 0.419309i | \(0.137728\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.5944 | −0.978653 | −0.489327 | − | 0.872101i | \(-0.662757\pi\) | ||||
−0.489327 | + | 0.872101i | \(0.662757\pi\) | |||||||
\(20\) | −28.5888 | − | 19.1781i | −1.42944 | − | 0.958905i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.34723 | − | 17.5260i | −0.424874 | − | 0.796635i | ||||
\(23\) | 15.6966i | 0.682459i | 0.939980 | + | 0.341230i | \(0.110843\pi\) | ||||
−0.939980 | + | 0.341230i | \(0.889157\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −49.0699 | −1.96280 | ||||||||
\(26\) | −10.2128 | + | 5.44688i | −0.392802 | + | 0.209495i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.0094 | + | 10.7395i | 0.571764 | + | 0.383554i | ||||
\(29\) | 25.9792i | 0.895836i | 0.894075 | + | 0.447918i | \(0.147834\pi\) | ||||
−0.894075 | + | 0.447918i | \(0.852166\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 12.7847i | − | 0.412409i | −0.978509 | − | 0.206204i | \(-0.933889\pi\) | ||
0.978509 | − | 0.206204i | \(-0.0661112\pi\) | |||||||
\(32\) | 20.4134 | − | 24.6433i | 0.637920 | − | 0.770103i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 29.0511 | + | 54.4705i | 0.854445 | + | 1.60207i | ||||
\(35\) | 41.4783 | 1.18509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 63.2921i | 1.71060i | 0.518136 | + | 0.855298i | \(0.326626\pi\) | ||||
−0.518136 | + | 0.855298i | \(0.673374\pi\) | |||||||
\(38\) | −17.5007 | − | 32.8136i | −0.460545 | − | 0.863516i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.93646 | − | 68.5008i | 0.173411 | − | 1.71252i | ||||
\(41\) | −14.4473 | −0.352373 | −0.176187 | − | 0.984357i | \(-0.556376\pi\) | ||||
−0.176187 | + | 0.984357i | \(0.556376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 62.4861 | 1.45317 | 0.726583 | − | 0.687079i | \(-0.241107\pi\) | ||||
0.726583 | + | 0.687079i | \(0.241107\pi\) | |||||||
\(44\) | 22.1307 | − | 32.9902i | 0.502970 | − | 0.749777i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −27.6998 | + | 14.7733i | −0.602169 | + | 0.321159i | ||||
\(47\) | 26.7557i | 0.569269i | 0.958636 | + | 0.284635i | \(0.0918723\pi\) | ||||
−0.958636 | + | 0.284635i | \(0.908128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.7726 | 0.525972 | ||||||||
\(50\) | −46.1837 | − | 86.5939i | −0.923673 | − | 1.73188i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.2243 | − | 12.8961i | −0.369697 | − | 0.248003i | ||||
\(53\) | − | 14.2150i | − | 0.268207i | −0.990967 | − | 0.134104i | \(-0.957184\pi\) | ||
0.990967 | − | 0.134104i | \(-0.0428155\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 85.4734i | − | 1.55406i | ||||||
\(56\) | −3.88434 | + | 38.3597i | −0.0693631 | + | 0.684994i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −45.8456 | + | 24.4512i | −0.790442 | + | 0.421572i | ||||
\(59\) | 76.7922 | 1.30156 | 0.650782 | − | 0.759265i | \(-0.274441\pi\) | ||||
0.650782 | + | 0.759265i | \(0.274441\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 44.5930i | − | 0.731032i | −0.930805 | − | 0.365516i | \(-0.880893\pi\) | ||
0.930805 | − | 0.365516i | \(-0.119107\pi\) | |||||||
\(62\) | 22.5612 | − | 12.0327i | 0.363890 | − | 0.194076i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 62.7008 | + | 12.8298i | 0.979701 | + | 0.200466i | ||||
\(65\) | −49.8076 | −0.766271 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 88.6047 | 1.32246 | 0.661229 | − | 0.750184i | \(-0.270035\pi\) | ||||
0.661229 | + | 0.750184i | \(0.270035\pi\) | |||||||
\(68\) | −68.7820 | + | 102.533i | −1.01150 | + | 1.50784i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 39.0386 | + | 73.1969i | 0.557694 | + | 1.04567i | ||||
\(71\) | 114.263i | 1.60933i | 0.593728 | + | 0.804666i | \(0.297655\pi\) | ||||
−0.593728 | + | 0.804666i | \(0.702345\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28.3077 | 0.387777 | 0.193889 | − | 0.981024i | \(-0.437890\pi\) | ||||
0.193889 | + | 0.981024i | \(0.437890\pi\) | |||||||
\(74\) | −111.692 | + | 59.5693i | −1.50935 | + | 0.804990i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 41.4350 | − | 61.7671i | 0.545197 | − | 0.812725i | ||||
\(77\) | 47.8641i | 0.621612i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 115.116i | − | 1.45716i | −0.684960 | − | 0.728581i | \(-0.740180\pi\) | ||
0.684960 | − | 0.728581i | \(-0.259820\pi\) | |||||||
\(80\) | 127.412 | − | 52.2309i | 1.59265 | − | 0.652886i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.5975 | − | 25.4952i | −0.165823 | − | 0.310917i | ||||
\(83\) | −46.2135 | −0.556790 | −0.278395 | − | 0.960467i | \(-0.589802\pi\) | ||||
−0.278395 | + | 0.960467i | \(0.589802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 265.651i | 3.12530i | ||||||||
\(86\) | 58.8107 | + | 110.269i | 0.683846 | + | 1.28220i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 79.0469 | + | 8.00436i | 0.898260 | + | 0.0909587i | ||||
\(89\) | 33.8625 | 0.380478 | 0.190239 | − | 0.981738i | \(-0.439074\pi\) | ||||
0.190239 | + | 0.981738i | \(0.439074\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.8917 | 0.306502 | ||||||||
\(92\) | −52.1410 | − | 34.9775i | −0.566750 | − | 0.380191i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −47.2158 | + | 25.1819i | −0.502296 | + | 0.267893i | ||||
\(95\) | − | 160.031i | − | 1.68453i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −93.6047 | −0.964997 | −0.482499 | − | 0.875897i | \(-0.660271\pi\) | ||||
−0.482499 | + | 0.875897i | \(0.660271\pi\) | |||||||
\(98\) | 24.2567 | + | 45.4810i | 0.247517 | + | 0.464092i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 109.345 | − | 163.001i | 1.09345 | − | 1.63001i | ||||
\(101\) | − | 28.2006i | − | 0.279214i | −0.990207 | − | 0.139607i | \(-0.955416\pi\) | ||
0.990207 | − | 0.139607i | \(-0.0445839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 55.9057i | 0.542774i | 0.962470 | + | 0.271387i | \(0.0874823\pi\) | ||||
−0.962470 | + | 0.271387i | \(0.912518\pi\) | |||||||
\(104\) | 4.66436 | − | 46.0627i | 0.0448496 | − | 0.442911i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 25.0852 | − | 13.3789i | 0.236653 | − | 0.126216i | ||||
\(107\) | −169.036 | −1.57977 | −0.789886 | − | 0.613253i | \(-0.789860\pi\) | ||||
−0.789886 | + | 0.613253i | \(0.789860\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 84.7359i | − | 0.777393i | −0.921366 | − | 0.388697i | \(-0.872925\pi\) | ||
0.921366 | − | 0.388697i | \(-0.127075\pi\) | |||||||
\(110\) | 150.835 | − | 80.4459i | 1.37123 | − | 0.731327i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −71.3493 | + | 29.2487i | −0.637047 | + | 0.261149i | ||||
\(113\) | 75.2321 | 0.665771 | 0.332885 | − | 0.942967i | \(-0.391978\pi\) | ||||
0.332885 | + | 0.942967i | \(0.391978\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −135.091 | −1.17470 | ||||||||
\(116\) | −86.2981 | − | 57.8910i | −0.743949 | − | 0.499061i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 72.2754 | + | 135.516i | 0.612503 | + | 1.14844i | ||||
\(119\) | − | 148.761i | − | 1.25009i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −22.3675 | −0.184855 | ||||||||
\(122\) | 78.6933 | − | 41.9700i | 0.645027 | − | 0.344017i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 42.4682 | + | 28.4888i | 0.342486 | + | 0.229748i | ||||
\(125\) | − | 207.155i | − | 1.65724i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 58.4530i | − | 0.460260i | −0.973160 | − | 0.230130i | \(-0.926085\pi\) | ||
0.973160 | − | 0.230130i | \(-0.0739151\pi\) | |||||||
\(128\) | 36.3720 | + | 122.724i | 0.284156 | + | 0.958778i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −46.8780 | − | 87.8957i | −0.360600 | − | 0.676121i | ||||
\(131\) | −115.102 | −0.878639 | −0.439320 | − | 0.898331i | \(-0.644780\pi\) | ||||
−0.439320 | + | 0.898331i | \(0.644780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 89.6154i | 0.673800i | ||||||||
\(134\) | 83.3931 | + | 156.361i | 0.622336 | + | 1.16687i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −245.677 | − | 24.8775i | −1.80645 | − | 0.182923i | ||||
\(137\) | −50.2245 | −0.366602 | −0.183301 | − | 0.983057i | \(-0.558678\pi\) | ||||
−0.183301 | + | 0.983057i | \(0.558678\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 58.1186 | 0.418120 | 0.209060 | − | 0.977903i | \(-0.432960\pi\) | ||||
0.209060 | + | 0.977903i | \(0.432960\pi\) | |||||||
\(140\) | −92.4285 | + | 137.783i | −0.660203 | + | 0.984165i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −201.639 | + | 107.542i | −1.42000 | + | 0.757336i | ||||
\(143\) | − | 57.4758i | − | 0.401929i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −223.587 | −1.54198 | ||||||||
\(146\) | 26.6427 | + | 49.9547i | 0.182484 | + | 0.342156i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −210.244 | − | 141.037i | −1.42057 | − | 0.952955i | ||||
\(149\) | 125.603i | 0.842974i | 0.906834 | + | 0.421487i | \(0.138492\pi\) | ||||
−0.906834 | + | 0.421487i | \(0.861508\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 162.225i | − | 1.07433i | −0.843476 | − | 0.537167i | \(-0.819494\pi\) | ||
0.843476 | − | 0.537167i | \(-0.180506\pi\) | |||||||
\(152\) | 147.998 | + | 14.9865i | 0.973674 | + | 0.0985951i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −84.4660 | + | 45.0488i | −0.548480 | + | 0.292525i | ||||
\(155\) | 110.030 | 0.709870 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 157.397i | − | 1.00253i | −0.865293 | − | 0.501266i | \(-0.832868\pi\) | ||
0.865293 | − | 0.501266i | \(-0.167132\pi\) | |||||||
\(158\) | 203.145 | − | 108.345i | 1.28573 | − | 0.685726i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 212.090 | + | 175.686i | 1.32556 | + | 1.09804i | ||||
\(161\) | 75.6492 | 0.469871 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 166.269 | 1.02006 | 0.510029 | − | 0.860157i | \(-0.329635\pi\) | ||||
0.510029 | + | 0.860157i | \(0.329635\pi\) | |||||||
\(164\) | 32.1937 | − | 47.9912i | 0.196303 | − | 0.292629i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −43.4953 | − | 81.5532i | −0.262020 | − | 0.491284i | ||||
\(167\) | − | 158.709i | − | 0.950355i | −0.879890 | − | 0.475177i | \(-0.842384\pi\) | ||
0.879890 | − | 0.475177i | \(-0.157616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 135.507 | 0.801818 | ||||||||
\(170\) | −468.795 | + | 250.025i | −2.75761 | + | 1.47074i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −139.241 | + | 207.567i | −0.809543 | + | 1.20678i | ||||
\(173\) | − | 45.2251i | − | 0.261417i | −0.991421 | − | 0.130708i | \(-0.958275\pi\) | ||
0.991421 | − | 0.130708i | \(-0.0417251\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 236.491i | 1.35138i | ||||||||
\(176\) | 60.2721 | + | 147.028i | 0.342455 | + | 0.835386i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 31.8708 | + | 59.7574i | 0.179049 | + | 0.335715i | ||||
\(179\) | −34.1175 | −0.190601 | −0.0953003 | − | 0.995449i | \(-0.530381\pi\) | ||||
−0.0953003 | + | 0.995449i | \(0.530381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.4438i | 0.118474i | 0.998244 | + | 0.0592370i | \(0.0188668\pi\) | ||||
−0.998244 | + | 0.0592370i | \(0.981133\pi\) | |||||||
\(182\) | 26.2511 | + | 49.2206i | 0.144237 | + | 0.270443i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.6509 | − | 124.934i | 0.0687548 | − | 0.678987i | ||||
\(185\) | −544.716 | −2.94441 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −306.549 | −1.63930 | ||||||||
\(188\) | −88.8772 | − | 59.6212i | −0.472751 | − | 0.317134i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 282.407 | − | 150.618i | 1.48635 | − | 0.792725i | ||||
\(191\) | 172.809i | 0.904759i | 0.891826 | + | 0.452380i | \(0.149425\pi\) | ||||
−0.891826 | + | 0.452380i | \(0.850575\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 140.210 | 0.726475 | 0.363238 | − | 0.931697i | \(-0.381671\pi\) | ||||
0.363238 | + | 0.931697i | \(0.381671\pi\) | |||||||
\(194\) | −88.0990 | − | 165.185i | −0.454118 | − | 0.851467i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −57.4306 | + | 85.6118i | −0.293013 | + | 0.436795i | ||||
\(197\) | − | 329.507i | − | 1.67262i | −0.548253 | − | 0.836312i | \(-0.684707\pi\) | ||
0.548253 | − | 0.836312i | \(-0.315293\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 249.916i | 1.25586i | 0.778270 | + | 0.627930i | \(0.216098\pi\) | ||||
−0.778270 | + | 0.627930i | \(0.783902\pi\) | |||||||
\(200\) | 390.562 | + | 39.5487i | 1.95281 | + | 0.197743i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 49.7657 | − | 26.5419i | 0.246365 | − | 0.131395i | ||||
\(203\) | 125.206 | 0.616780 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 124.339i | − | 0.606532i | ||||||
\(206\) | −98.6570 | + | 52.6174i | −0.478917 | + | 0.255424i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 85.6771 | − | 35.1222i | 0.411909 | − | 0.168857i | ||||
\(209\) | 184.668 | 0.883581 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −84.9300 | −0.402512 | −0.201256 | − | 0.979539i | \(-0.564502\pi\) | ||||
−0.201256 | + | 0.979539i | \(0.564502\pi\) | |||||||
\(212\) | 47.2195 | + | 31.6761i | 0.222733 | + | 0.149415i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −159.093 | − | 298.298i | −0.743426 | − | 1.39392i | ||||
\(215\) | 537.780i | 2.50130i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −61.6154 | −0.283942 | ||||||||
\(218\) | 149.534 | − | 79.7518i | 0.685934 | − | 0.365834i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 283.926 | + | 190.465i | 1.29057 | + | 0.865751i | ||||
\(221\) | 178.634i | 0.808300i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.94316i | − | 0.00871371i | −0.999991 | − | 0.00435686i | \(-0.998613\pi\) | ||
0.999991 | − | 0.00435686i | \(-0.00138683\pi\) | |||||||
\(224\) | −118.768 | − | 98.3821i | −0.530214 | − | 0.439206i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 70.8070 | + | 132.762i | 0.313305 | + | 0.587444i | ||||
\(227\) | 203.658 | 0.897171 | 0.448586 | − | 0.893740i | \(-0.351928\pi\) | ||||
0.448586 | + | 0.893740i | \(0.351928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.9963i | − | 0.0873202i | −0.999046 | − | 0.0436601i | \(-0.986098\pi\) | ||
0.999046 | − | 0.0436601i | \(-0.0139019\pi\) | |||||||
\(230\) | −127.145 | − | 238.395i | −0.552803 | − | 1.03650i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.9384 | − | 206.776i | 0.0902516 | − | 0.891278i | ||||
\(233\) | −91.1197 | −0.391072 | −0.195536 | − | 0.980697i | \(-0.562645\pi\) | ||||
−0.195536 | + | 0.980697i | \(0.562645\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −230.270 | −0.979870 | ||||||||
\(236\) | −171.121 | + | 255.089i | −0.725087 | + | 1.08089i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 262.520 | − | 140.011i | 1.10302 | − | 0.588283i | ||||
\(239\) | − | 36.8504i | − | 0.154186i | −0.997024 | − | 0.0770929i | \(-0.975436\pi\) | ||
0.997024 | − | 0.0770929i | \(-0.0245638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 308.182 | 1.27876 | 0.639381 | − | 0.768890i | \(-0.279191\pi\) | ||||
0.639381 | + | 0.768890i | \(0.279191\pi\) | |||||||
\(242\) | −21.0519 | − | 39.4720i | −0.0869911 | − | 0.163107i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 148.129 | + | 99.3690i | 0.607087 | + | 0.407250i | ||||
\(245\) | 221.809i | 0.905344i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 107.611i | − | 0.435673i | ||||||
\(248\) | −10.3040 | + | 101.757i | −0.0415484 | + | 0.410310i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 365.567 | − | 194.970i | 1.46227 | − | 0.779881i | ||||
\(251\) | −228.334 | −0.909696 | −0.454848 | − | 0.890569i | \(-0.650306\pi\) | ||||
−0.454848 | + | 0.890569i | \(0.650306\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 155.889i | − | 0.616161i | ||||||
\(254\) | 103.152 | − | 55.0149i | 0.406111 | − | 0.216594i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −182.338 | + | 179.691i | −0.712259 | + | 0.701917i | ||||
\(257\) | 292.265 | 1.13722 | 0.568609 | − | 0.822608i | \(-0.307482\pi\) | ||||
0.568609 | + | 0.822608i | \(0.307482\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 305.035 | 1.17774 | ||||||||
\(260\) | 110.989 | − | 165.451i | 0.426881 | − | 0.636352i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −108.332 | − | 203.120i | −0.413479 | − | 0.775269i | ||||
\(263\) | − | 488.233i | − | 1.85640i | −0.372083 | − | 0.928199i | \(-0.621356\pi\) | ||
0.372083 | − | 0.928199i | \(-0.378644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 122.340 | 0.461659 | ||||||||
\(266\) | −158.145 | + | 84.3443i | −0.594528 | + | 0.317084i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −197.443 | + | 294.328i | −0.736728 | + | 1.09824i | ||||
\(269\) | 38.8093i | 0.144273i | 0.997395 | + | 0.0721363i | \(0.0229816\pi\) | ||||
−0.997395 | + | 0.0721363i | \(0.977018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 327.987i | 1.21028i | 0.796118 | + | 0.605142i | \(0.206884\pi\) | ||||
−0.796118 | + | 0.605142i | \(0.793116\pi\) | |||||||
\(272\) | −187.325 | − | 456.961i | −0.688695 | − | 1.68001i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −47.2703 | − | 88.6313i | −0.172519 | − | 0.323472i | ||||
\(275\) | 487.332 | 1.77212 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 418.966i | − | 1.51251i | −0.654275 | − | 0.756257i | \(-0.727026\pi\) | ||
0.654275 | − | 0.756257i | \(-0.272974\pi\) | |||||||
\(278\) | 54.7001 | + | 102.562i | 0.196763 | + | 0.368929i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −330.138 | − | 33.4301i | −1.17906 | − | 0.119393i | ||||
\(281\) | 201.185 | 0.715960 | 0.357980 | − | 0.933729i | \(-0.383466\pi\) | ||||
0.357980 | + | 0.933729i | \(0.383466\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 242.161 | 0.855692 | 0.427846 | − | 0.903852i | \(-0.359273\pi\) | ||||
0.427846 | + | 0.903852i | \(0.359273\pi\) | |||||||
\(284\) | −379.558 | − | 254.618i | −1.33647 | − | 0.896541i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 101.428 | − | 54.0951i | 0.354642 | − | 0.189144i | ||||
\(287\) | 69.6285i | 0.242608i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 663.752 | 2.29672 | ||||||||
\(290\) | −210.436 | − | 394.565i | −0.725642 | − | 1.36057i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −63.0797 | + | 94.0329i | −0.216026 | + | 0.322030i | ||||
\(293\) | 268.900i | 0.917749i | 0.888501 | + | 0.458874i | \(0.151747\pi\) | ||||
−0.888501 | + | 0.458874i | \(0.848253\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 660.904i | 2.24035i | ||||||||
\(296\) | 51.0112 | − | 503.760i | 0.172335 | − | 1.70189i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −221.652 | + | 118.215i | −0.743800 | + | 0.396696i | ||||
\(299\) | −90.8405 | −0.303814 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 301.151i | − | 1.00050i | ||||||
\(302\) | 286.278 | − | 152.683i | 0.947941 | − | 0.505572i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 112.847 | + | 275.278i | 0.371206 | + | 0.905521i | ||||
\(305\) | 383.784 | 1.25831 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −88.1714 | −0.287203 | −0.143602 | − | 0.989636i | \(-0.545868\pi\) | ||||
−0.143602 | + | 0.989636i | \(0.545868\pi\) | |||||||
\(308\) | −158.996 | − | 106.658i | −0.516219 | − | 0.346293i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 103.558 | + | 194.170i | 0.334058 | + | 0.626355i | ||||
\(311\) | − | 175.687i | − | 0.564909i | −0.959281 | − | 0.282455i | \(-0.908851\pi\) | ||
0.959281 | − | 0.282455i | \(-0.0911486\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −298.025 | −0.952157 | −0.476078 | − | 0.879403i | \(-0.657942\pi\) | ||||
−0.476078 | + | 0.879403i | \(0.657942\pi\) | |||||||
\(314\) | 277.760 | − | 148.140i | 0.884586 | − | 0.471782i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 382.393 | + | 256.519i | 1.21010 | + | 0.811769i | ||||
\(317\) | 157.658i | 0.497343i | 0.968588 | + | 0.248671i | \(0.0799939\pi\) | ||||
−0.968588 | + | 0.248671i | \(0.920006\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 258.010i | − | 0.808809i | ||||||
\(320\) | −110.419 | + | 539.628i | −0.345058 | + | 1.68634i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 71.1996 | + | 133.498i | 0.221117 | + | 0.414592i | ||||
\(323\) | −573.948 | −1.77693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 283.982i | − | 0.873790i | ||||||
\(326\) | 156.490 | + | 293.416i | 0.480029 | + | 0.900049i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 114.990 | + | 11.6440i | 0.350580 | + | 0.0355001i | ||||
\(329\) | 128.948 | 0.391940 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 171.458 | 0.518000 | 0.259000 | − | 0.965877i | \(-0.416607\pi\) | ||||
0.259000 | + | 0.965877i | \(0.416607\pi\) | |||||||
\(332\) | 102.980 | − | 153.513i | 0.310182 | − | 0.462387i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 280.075 | − | 149.374i | 0.838547 | − | 0.447228i | ||||
\(335\) | 762.567i | 2.27632i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −358.818 | −1.06474 | −0.532371 | − | 0.846511i | \(-0.678699\pi\) | ||||
−0.532371 | + | 0.846511i | \(0.678699\pi\) | |||||||
\(338\) | 127.537 | + | 239.130i | 0.377328 | + | 0.707486i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −882.441 | − | 591.964i | −2.59541 | − | 1.74107i | ||||
\(341\) | 126.970i | 0.372345i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 360.365i | − | 1.05063i | ||||||
\(344\) | −497.346 | − | 50.3617i | −1.44577 | − | 0.146400i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 79.8088 | − | 42.5650i | 0.230661 | − | 0.123020i | ||||
\(347\) | −167.974 | −0.484075 | −0.242037 | − | 0.970267i | \(-0.577816\pi\) | ||||
−0.242037 | + | 0.970267i | \(0.577816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 496.148i | 1.42163i | 0.703380 | + | 0.710814i | \(0.251673\pi\) | ||||
−0.703380 | + | 0.710814i | \(0.748327\pi\) | |||||||
\(350\) | −417.337 | + | 222.581i | −1.19239 | + | 0.635946i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −202.734 | + | 244.742i | −0.575948 | + | 0.695290i | ||||
\(353\) | 132.906 | 0.376505 | 0.188253 | − | 0.982121i | \(-0.439718\pi\) | ||||
0.188253 | + | 0.982121i | \(0.439718\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −983.388 | −2.77011 | ||||||||
\(356\) | −75.4578 | + | 112.485i | −0.211960 | + | 0.315969i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −32.1107 | − | 60.2073i | −0.0896948 | − | 0.168177i | ||||
\(359\) | 565.184i | 1.57433i | 0.616743 | + | 0.787164i | \(0.288452\pi\) | ||||
−0.616743 | + | 0.787164i | \(0.711548\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2479 | −0.0422381 | ||||||||
\(362\) | −37.8420 | + | 20.1825i | −0.104536 | + | 0.0557528i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −62.1527 | + | 92.6509i | −0.170749 | + | 0.254536i | ||||
\(365\) | 243.627i | 0.667472i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 615.679i | 1.67760i | 0.544441 | + | 0.838799i | \(0.316742\pi\) | ||||
−0.544441 | + | 0.838799i | \(0.683258\pi\) | |||||||
\(368\) | 232.377 | − | 95.2600i | 0.631461 | − | 0.258859i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −512.676 | − | 961.262i | −1.38561 | − | 2.59801i | ||||
\(371\) | −68.5088 | −0.184660 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 455.597i | − | 1.22144i | −0.791847 | − | 0.610720i | \(-0.790880\pi\) | ||
0.791847 | − | 0.610720i | \(-0.209120\pi\) | |||||||
\(374\) | −288.518 | − | 540.968i | −0.771439 | − | 1.44644i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.5641 | − | 212.956i | 0.0573514 | − | 0.566373i | ||||
\(377\) | −150.349 | −0.398804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −337.902 | −0.891562 | −0.445781 | − | 0.895142i | \(-0.647074\pi\) | ||||
−0.445781 | + | 0.895142i | \(0.647074\pi\) | |||||||
\(380\) | 531.592 | + | 356.606i | 1.39893 | + | 0.938436i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −304.957 | + | 162.644i | −0.798316 | + | 0.425771i | ||||
\(383\) | − | 218.893i | − | 0.571522i | −0.958301 | − | 0.285761i | \(-0.907754\pi\) | ||
0.958301 | − | 0.285761i | \(-0.0922464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −411.937 | −1.06997 | ||||||||
\(386\) | 131.963 | + | 247.429i | 0.341872 | + | 0.641007i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 208.585 | − | 310.937i | 0.537590 | − | 0.801384i | ||||
\(389\) | − | 142.868i | − | 0.367270i | −0.982994 | − | 0.183635i | \(-0.941214\pi\) | ||
0.982994 | − | 0.183635i | \(-0.0587865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 484.501i | 1.23913i | ||||||||
\(392\) | −205.132 | − | 20.7719i | −0.523296 | − | 0.0529894i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 581.482 | − | 310.126i | 1.47584 | − | 0.787121i | ||||
\(395\) | 990.731 | 2.50818 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 709.501i | 1.78716i | 0.448907 | + | 0.893579i | \(0.351814\pi\) | ||||
−0.448907 | + | 0.893579i | \(0.648186\pi\) | |||||||
\(398\) | −441.028 | + | 235.216i | −1.10811 | + | 0.590996i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 297.798 | + | 726.449i | 0.744495 | + | 1.81612i | ||||
\(401\) | −157.900 | −0.393766 | −0.196883 | − | 0.980427i | \(-0.563082\pi\) | ||||
−0.196883 | + | 0.980427i | \(0.563082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 73.9885 | 0.183594 | ||||||||
\(404\) | 93.6771 | + | 62.8410i | 0.231874 | + | 0.155547i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 117.842 | + | 220.952i | 0.290251 | + | 0.544217i | ||||
\(407\) | − | 628.578i | − | 1.54442i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 121.735 | 0.297641 | 0.148820 | − | 0.988864i | \(-0.452452\pi\) | ||||
0.148820 | + | 0.988864i | \(0.452452\pi\) | |||||||
\(410\) | 219.422 | − | 117.026i | 0.535175 | − | 0.285428i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −185.708 | − | 124.578i | −0.450748 | − | 0.302373i | ||||
\(413\) | − | 370.099i | − | 0.896123i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 397.732i | − | 0.958390i | ||||||
\(416\) | 142.618 | + | 118.138i | 0.342831 | + | 0.283986i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 173.806 | + | 325.885i | 0.415805 | + | 0.779629i | ||||
\(419\) | 24.2370 | 0.0578449 | 0.0289224 | − | 0.999582i | \(-0.490792\pi\) | ||||
0.0289224 | + | 0.999582i | \(0.490792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 280.461i | − | 0.666177i | −0.942895 | − | 0.333089i | \(-0.891909\pi\) | ||
0.942895 | − | 0.333089i | \(-0.108091\pi\) | |||||||
\(422\) | −79.9345 | − | 149.876i | −0.189418 | − | 0.355157i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.4568 | + | 113.141i | −0.0270208 | + | 0.266843i | ||||
\(425\) | −1514.63 | −3.56382 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −214.915 | −0.503313 | ||||||||
\(428\) | 376.672 | − | 561.504i | 0.880074 | − | 1.31193i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −949.022 | + | 506.148i | −2.20703 | + | 1.17709i | ||||
\(431\) | − | 537.398i | − | 1.24686i | −0.781878 | − | 0.623432i | \(-0.785738\pi\) | ||
0.781878 | − | 0.623432i | \(-0.214262\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −103.584 | −0.239224 | −0.119612 | − | 0.992821i | \(-0.538165\pi\) | ||||
−0.119612 | + | 0.992821i | \(0.538165\pi\) | |||||||
\(434\) | −57.9913 | − | 108.733i | −0.133620 | − | 0.250537i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 281.476 | + | 188.822i | 0.645588 | + | 0.433078i | ||||
\(437\) | − | 291.868i | − | 0.667891i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 557.858i | − | 1.27075i | −0.772205 | − | 0.635373i | \(-0.780846\pi\) | ||
0.772205 | − | 0.635373i | \(-0.219154\pi\) | |||||||
\(440\) | −68.8886 | + | 680.308i | −0.156565 | + | 1.54615i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −315.237 | + | 168.127i | −0.713205 | + | 0.380378i | ||||
\(443\) | 4.79025 | 0.0108132 | 0.00540660 | − | 0.999985i | \(-0.498279\pi\) | ||||
0.00540660 | + | 0.999985i | \(0.498279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 291.434i | 0.654908i | ||||||||
\(446\) | 3.42910 | − | 1.82886i | 0.00768856 | − | 0.00410059i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 61.8332 | − | 302.185i | 0.138020 | − | 0.674521i | ||||
\(449\) | 838.004 | 1.86638 | 0.933190 | − | 0.359384i | \(-0.117013\pi\) | ||||
0.933190 | + | 0.359384i | \(0.117013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 143.482 | 0.318141 | ||||||||
\(452\) | −167.644 | + | 249.907i | −0.370894 | + | 0.552891i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 191.679 | + | 359.396i | 0.422200 | + | 0.791620i | ||||
\(455\) | 240.047i | 0.527575i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 537.817 | 1.17684 | 0.588422 | − | 0.808554i | \(-0.299750\pi\) | ||||
0.588422 | + | 0.808554i | \(0.299750\pi\) | |||||||
\(458\) | 35.2876 | − | 18.8202i | 0.0770471 | − | 0.0410920i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 301.030 | − | 448.746i | 0.654414 | − | 0.975534i | ||||
\(461\) | − | 161.391i | − | 0.350088i | −0.984561 | − | 0.175044i | \(-0.943993\pi\) | ||
0.984561 | − | 0.175044i | \(-0.0560068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 485.576i | − | 1.04876i | −0.851484 | − | 0.524381i | \(-0.824297\pi\) | ||
0.851484 | − | 0.524381i | \(-0.175703\pi\) | |||||||
\(464\) | 384.606 | − | 157.664i | 0.828892 | − | 0.339793i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −85.7601 | − | 160.799i | −0.184035 | − | 0.345063i | ||||
\(467\) | 239.041 | 0.511864 | 0.255932 | − | 0.966695i | \(-0.417618\pi\) | ||||
0.255932 | + | 0.966695i | \(0.417618\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 427.029i | − | 0.910509i | ||||||
\(470\) | −216.725 | − | 406.357i | −0.461118 | − | 0.864590i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −611.212 | − | 61.8919i | −1.29494 | − | 0.131127i | ||||
\(473\) | −620.574 | −1.31200 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 912.426 | 1.92090 | ||||||||
\(476\) | 494.157 | + | 331.493i | 1.03814 | + | 0.696415i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 65.0300 | − | 34.6829i | 0.136046 | − | 0.0725583i | ||||
\(479\) | 416.528i | 0.869579i | 0.900532 | + | 0.434789i | \(0.143177\pi\) | ||||
−0.900532 | + | 0.434789i | \(0.856823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −366.289 | −0.761516 | ||||||||
\(482\) | 290.055 | + | 543.849i | 0.601773 | + | 1.12832i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 49.8428 | − | 74.3006i | 0.102981 | − | 0.153514i | ||||
\(485\) | − | 805.599i | − | 1.66103i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 404.821i | 0.831254i | 0.909535 | + | 0.415627i | \(0.136438\pi\) | ||||
−0.909535 | + | 0.415627i | \(0.863562\pi\) | |||||||
\(488\) | −35.9404 | + | 354.929i | −0.0736484 | + | 0.727313i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −391.427 | + | 208.763i | −0.798832 | + | 0.426046i | ||||
\(491\) | −508.547 | −1.03574 | −0.517869 | − | 0.855460i | \(-0.673275\pi\) | ||||
−0.517869 | + | 0.855460i | \(0.673275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 801.893i | 1.62656i | ||||||||
\(494\) | 189.902 | − | 101.282i | 0.384417 | − | 0.205023i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −189.269 | + | 77.5882i | −0.381590 | + | 0.156428i | ||||
\(497\) | 550.686 | 1.10802 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 745.549 | 1.49409 | 0.747043 | − | 0.664776i | \(-0.231473\pi\) | ||||
0.747043 | + | 0.664776i | \(0.231473\pi\) | |||||||
\(500\) | 688.130 | + | 461.615i | 1.37626 | + | 0.923231i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −214.903 | − | 402.941i | −0.428094 | − | 0.802672i | ||||
\(503\) | − | 290.768i | − | 0.578068i | −0.957319 | − | 0.289034i | \(-0.906666\pi\) | ||
0.957319 | − | 0.289034i | \(-0.0933341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 242.705 | 0.480605 | ||||||||
\(506\) | 275.097 | − | 146.719i | 0.543670 | − | 0.289959i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 194.170 | + | 130.254i | 0.382224 | + | 0.256406i | ||||
\(509\) | − | 215.775i | − | 0.423920i | −0.977278 | − | 0.211960i | \(-0.932015\pi\) | ||
0.977278 | − | 0.211960i | \(-0.0679846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 136.428i | − | 0.266983i | ||||||
\(512\) | −488.714 | − | 152.651i | −0.954520 | − | 0.298147i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 275.074 | + | 515.761i | 0.535164 | + | 1.00343i | ||||
\(515\) | −481.146 | −0.934264 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 265.721i | − | 0.513967i | ||||||
\(518\) | 287.093 | + | 538.296i | 0.554233 | + | 1.03918i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 396.434 | + | 40.1433i | 0.762373 | + | 0.0771986i | ||||
\(521\) | −747.187 | −1.43414 | −0.717070 | − | 0.697001i | \(-0.754517\pi\) | ||||
−0.717070 | + | 0.697001i | \(0.754517\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 289.683 | 0.553886 | 0.276943 | − | 0.960886i | \(-0.410679\pi\) | ||||
0.276943 | + | 0.960886i | \(0.410679\pi\) | |||||||
\(524\) | 256.488 | − | 382.346i | 0.489481 | − | 0.729668i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 861.586 | − | 459.515i | 1.63800 | − | 0.873604i | ||||
\(527\) | − | 394.620i | − | 0.748805i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 282.618 | 0.534250 | ||||||||
\(530\) | 115.144 | + | 215.893i | 0.217252 | + | 0.407346i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −297.685 | − | 199.695i | −0.559559 | − | 0.375367i | ||||
\(533\) | − | 83.6107i | − | 0.156868i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1454.79i | − | 2.71923i | ||||||
\(536\) | −705.231 | − | 71.4124i | −1.31573 | − | 0.133232i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −68.4869 | + | 36.5266i | −0.127299 | + | 0.0678933i | ||||
\(539\) | −255.958 | −0.474876 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 348.783i | 0.644700i | 0.946621 | + | 0.322350i | \(0.104473\pi\) | ||||
−0.946621 | + | 0.322350i | \(0.895527\pi\) | |||||||
\(542\) | −578.800 | + | 308.695i | −1.06790 | + | 0.569548i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 630.095 | − | 760.657i | 1.15826 | − | 1.39827i | ||||
\(545\) | 729.270 | 1.33811 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −730.849 | −1.33610 | −0.668052 | − | 0.744115i | \(-0.732872\pi\) | ||||
−0.668052 | + | 0.744115i | \(0.732872\pi\) | |||||||
\(548\) | 111.918 | − | 166.836i | 0.204230 | − | 0.304446i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 458.668 | + | 859.997i | 0.833942 | + | 1.56363i | ||||
\(551\) | − | 483.069i | − | 0.876712i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −554.798 | −1.00325 | ||||||||
\(554\) | 739.351 | − | 394.323i | 1.33457 | − | 0.711774i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −129.509 | + | 193.059i | −0.232930 | + | 0.347228i | ||||
\(557\) | 462.185i | 0.829776i | 0.909872 | + | 0.414888i | \(0.136179\pi\) | ||||
−0.909872 | + | 0.414888i | \(0.863821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 361.625i | 0.646914i | ||||||||
\(560\) | −251.726 | − | 614.060i | −0.449510 | − | 1.09654i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 189.351 | + | 355.032i | 0.336924 | + | 0.631729i | ||||
\(563\) | −161.225 | −0.286367 | −0.143184 | − | 0.989696i | \(-0.545734\pi\) | ||||
−0.143184 | + | 0.989696i | \(0.545734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 647.476i | 1.14598i | ||||||||
\(566\) | 227.917 | + | 427.342i | 0.402680 | + | 0.755021i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 92.0917 | − | 909.449i | 0.162133 | − | 1.60114i | ||||
\(569\) | −63.2844 | −0.111220 | −0.0556102 | − | 0.998453i | \(-0.517710\pi\) | ||||
−0.0556102 | + | 0.998453i | \(0.517710\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 268.584 | 0.470375 | 0.235188 | − | 0.971950i | \(-0.424430\pi\) | ||||
0.235188 | + | 0.971950i | \(0.424430\pi\) | |||||||
\(572\) | 190.924 | + | 128.077i | 0.333783 | + | 0.223910i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −122.874 | + | 65.5330i | −0.214066 | + | 0.114169i | ||||
\(575\) | − | 770.229i | − | 1.33953i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −989.322 | −1.71460 | −0.857298 | − | 0.514821i | \(-0.827858\pi\) | ||||
−0.857298 | + | 0.514821i | \(0.827858\pi\) | |||||||
\(578\) | 624.710 | + | 1171.33i | 1.08081 | + | 2.02651i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 498.233 | − | 742.715i | 0.859022 | − | 1.28054i | ||||
\(581\) | 222.725i | 0.383348i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 141.175i | 0.242152i | ||||||||
\(584\) | −225.310 | − | 22.8151i | −0.385804 | − | 0.0390669i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −474.529 | + | 253.084i | −0.809777 | + | 0.431884i | ||||
\(587\) | −856.358 | −1.45887 | −0.729436 | − | 0.684049i | \(-0.760217\pi\) | ||||
−0.729436 | + | 0.684049i | \(0.760217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 237.723i | 0.403605i | ||||||||
\(590\) | −1166.30 | + | 622.030i | −1.97678 | + | 1.05429i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 936.998 | − | 384.110i | 1.58277 | − | 0.648834i | ||||
\(593\) | 108.067 | 0.182238 | 0.0911189 | − | 0.995840i | \(-0.470956\pi\) | ||||
0.0911189 | + | 0.995840i | \(0.470956\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1280.30 | 2.15176 | ||||||||
\(596\) | −417.230 | − | 279.889i | −0.700050 | − | 0.469612i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −85.4973 | − | 160.306i | −0.142972 | − | 0.268071i | ||||
\(599\) | 556.750i | 0.929466i | 0.885451 | + | 0.464733i | \(0.153850\pi\) | ||||
−0.885451 | + | 0.464733i | \(0.846150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 260.078 | 0.432742 | 0.216371 | − | 0.976311i | \(-0.430578\pi\) | ||||
0.216371 | + | 0.976311i | \(0.430578\pi\) | |||||||
\(602\) | 531.441 | − | 283.437i | 0.882793 | − | 0.470826i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 538.879 | + | 361.494i | 0.892184 | + | 0.598500i | ||||
\(605\) | − | 192.503i | − | 0.318187i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.91926i | − | 0.0146940i | −0.999973 | − | 0.00734701i | \(-0.997661\pi\) | ||
0.999973 | − | 0.00734701i | \(-0.00233865\pi\) | |||||||
\(608\) | −379.576 | + | 458.228i | −0.624302 | + | 0.753664i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 361.210 | + | 677.265i | 0.592148 | + | 1.11027i | ||||
\(611\) | −154.843 | −0.253425 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 738.776i | 1.20518i | 0.798051 | + | 0.602590i | \(0.205865\pi\) | ||||
−0.798051 | + | 0.602590i | \(0.794135\pi\) | |||||||
\(614\) | −82.9852 | − | 155.596i | −0.135155 | − | 0.253414i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 38.5769 | − | 380.965i | 0.0626248 | − | 0.618449i | ||||
\(617\) | 357.548 | 0.579495 | 0.289747 | − | 0.957103i | \(-0.406429\pi\) | ||||
0.289747 | + | 0.957103i | \(0.406429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −408.256 | −0.659541 | −0.329770 | − | 0.944061i | \(-0.606971\pi\) | ||||
−0.329770 | + | 0.944061i | \(0.606971\pi\) | |||||||
\(620\) | −245.186 | + | 365.498i | −0.395461 | + | 0.589513i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 310.035 | − | 165.353i | 0.498449 | − | 0.265841i | ||||
\(623\) | − | 163.200i | − | 0.261958i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 556.109 | 0.889774 | ||||||||
\(626\) | −280.495 | − | 525.926i | −0.448076 | − | 0.840137i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 522.845 | + | 350.738i | 0.832555 | + | 0.558500i | ||||
\(629\) | 1953.62i | 3.10591i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 230.148i | − | 0.364735i | −0.983230 | − | 0.182367i | \(-0.941624\pi\) | ||
0.983230 | − | 0.182367i | \(-0.0583760\pi\) | |||||||
\(632\) | −92.7794 | + | 916.241i | −0.146803 | + | 1.44975i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −278.219 | + | 148.384i | −0.438831 | + | 0.234045i | ||||
\(635\) | 503.069 | 0.792235 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 149.154i | 0.234150i | ||||||||
\(638\) | 455.311 | − | 242.834i | 0.713654 | − | 0.380618i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1056.21 | + | 313.031i | −1.65032 | + | 0.489111i | ||||
\(641\) | 736.093 | 1.14835 | 0.574176 | − | 0.818732i | \(-0.305323\pi\) | ||||
0.574176 | + | 0.818732i | \(0.305323\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.9654 | 0.0341609 | 0.0170804 | − | 0.999854i | \(-0.494563\pi\) | ||||
0.0170804 | + | 0.999854i | \(0.494563\pi\) | |||||||
\(644\) | −168.574 | + | 251.292i | −0.261760 | + | 0.390206i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −540.188 | − | 1012.85i | −0.836205 | − | 1.56788i | ||||
\(647\) | 493.227i | 0.762329i | 0.924507 | + | 0.381164i | \(0.124477\pi\) | ||||
−0.924507 | + | 0.381164i | \(0.875523\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −762.654 | −1.17512 | ||||||||
\(650\) | 501.143 | − | 267.278i | 0.770990 | − | 0.411197i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −370.508 | + | 552.315i | −0.568263 | + | 0.847109i | ||||
\(653\) | − | 1024.37i | − | 1.56871i | −0.620310 | − | 0.784356i | \(-0.712993\pi\) | ||
0.620310 | − | 0.784356i | \(-0.287007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 990.610i | − | 1.51238i | ||||||
\(656\) | 87.6785 | + | 213.883i | 0.133656 | + | 0.326041i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 121.364 | + | 227.556i | 0.184443 | + | 0.345829i | ||||
\(659\) | 759.973 | 1.15322 | 0.576611 | − | 0.817019i | \(-0.304375\pi\) | ||||
0.576611 | + | 0.817019i | \(0.304375\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 215.108i | 0.325427i | 0.986673 | + | 0.162714i | \(0.0520247\pi\) | ||||
−0.986673 | + | 0.162714i | \(0.947975\pi\) | |||||||
\(662\) | 161.373 | + | 302.573i | 0.243766 | + | 0.457058i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 367.827 | + | 37.2465i | 0.553957 | + | 0.0560942i | ||||
\(665\) | −771.265 | −1.15980 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −407.785 | −0.611371 | ||||||||
\(668\) | 527.202 | + | 353.661i | 0.789224 | + | 0.529432i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1345.70 | + | 717.713i | −2.00851 | + | 1.07121i | ||||
\(671\) | 442.870i | 0.660015i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 475.353 | 0.706320 | 0.353160 | − | 0.935563i | \(-0.385107\pi\) | ||||
0.353160 | + | 0.935563i | \(0.385107\pi\) | |||||||
\(674\) | −337.713 | − | 633.207i | −0.501057 | − | 0.939477i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −301.959 | + | 450.130i | −0.446685 | + | 0.665872i | ||||
\(677\) | 47.6348i | 0.0703615i | 0.999381 | + | 0.0351808i | \(0.0112007\pi\) | ||||
−0.999381 | + | 0.0351808i | \(0.988799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 451.126i | 0.664398i | ||||||||
\(680\) | 214.105 | − | 2114.39i | 0.314861 | − | 3.10940i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −224.064 | + | 119.501i | −0.328539 | + | 0.175222i | ||||
\(683\) | −857.260 | −1.25514 | −0.627570 | − | 0.778561i | \(-0.715950\pi\) | ||||
−0.627570 | + | 0.778561i | \(0.715950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 432.251i | − | 0.631024i | ||||||
\(686\) | 635.938 | − | 339.169i | 0.927023 | − | 0.494415i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −379.219 | − | 925.067i | −0.551190 | − | 1.34457i | ||||
\(689\) | 82.2662 | 0.119399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −437.965 | −0.633813 | −0.316906 | − | 0.948457i | \(-0.602644\pi\) | ||||
−0.316906 | + | 0.948457i | \(0.602644\pi\) | |||||||
\(692\) | 150.229 | + | 100.778i | 0.217094 | + | 0.145632i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −158.094 | − | 296.424i | −0.227801 | − | 0.427124i | ||||
\(695\) | 500.191i | 0.719700i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −445.940 | −0.639799 | ||||||||
\(698\) | −875.554 | + | 466.965i | −1.25438 | + | 0.669004i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −785.580 | − | 526.987i | −1.12226 | − | 0.752839i | ||||
\(701\) | 4.79962i | 0.00684682i | 0.999994 | + | 0.00342341i | \(0.00108971\pi\) | ||||
−0.999994 | + | 0.00342341i | \(0.998910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1176.88i | − | 1.67408i | ||||||
\(704\) | −622.706 | − | 127.418i | −0.884526 | − | 0.180992i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 125.089 | + | 234.540i | 0.177180 | + | 0.332210i | ||||
\(707\) | −135.912 | −0.192238 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 117.092i | − | 0.165151i | −0.996585 | − | 0.0825753i | \(-0.973685\pi\) | ||
0.996585 | − | 0.0825753i | \(-0.0263145\pi\) | |||||||
\(710\) | −925.546 | − | 1735.39i | −1.30359 | − | 2.44421i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −269.522 | − | 27.2921i | −0.378542 | − | 0.0383315i | ||||
\(713\) | 200.675 | 0.281452 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 494.659 | 0.691831 | ||||||||
\(716\) | 76.0260 | − | 113.332i | 0.106182 | − | 0.158285i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −997.382 | + | 531.940i | −1.38911 | + | 0.740864i | ||||
\(719\) | − | 430.448i | − | 0.598676i | −0.954147 | − | 0.299338i | \(-0.903234\pi\) | ||
0.954147 | − | 0.299338i | \(-0.0967658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 269.436 | 0.373698 | ||||||||
\(722\) | −14.3511 | − | 26.9081i | −0.0198768 | − | 0.0372688i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −71.2323 | − | 47.7845i | −0.0983871 | − | 0.0660007i | ||||
\(725\) | − | 1274.80i | − | 1.75834i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1080.06i | − | 1.48564i | −0.669493 | − | 0.742818i | \(-0.733489\pi\) | ||
0.669493 | − | 0.742818i | \(-0.266511\pi\) | |||||||
\(728\) | −221.998 | − | 22.4798i | −0.304943 | − | 0.0308788i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −429.930 | + | 229.297i | −0.588945 | + | 0.314106i | ||||
\(731\) | 1928.74 | 2.63849 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 756.874i | 1.03257i | 0.856417 | + | 0.516285i | \(0.172685\pi\) | ||||
−0.856417 | + | 0.516285i | \(0.827315\pi\) | |||||||
\(734\) | −1086.49 | + | 579.465i | −1.48023 | + | 0.789462i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 386.815 | + | 320.420i | 0.525564 | + | 0.435354i | ||||
\(737\) | −879.968 | −1.19399 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 269.971 | 0.365319 | 0.182659 | − | 0.983176i | \(-0.441529\pi\) | ||||
0.182659 | + | 0.983176i | \(0.441529\pi\) | |||||||
\(740\) | 1213.82 | − | 1809.44i | 1.64030 | − | 2.44519i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −64.4792 | − | 120.898i | −0.0868992 | − | 0.162935i | ||||
\(743\) | 412.457i | 0.555123i | 0.960708 | + | 0.277562i | \(0.0895263\pi\) | ||||
−0.960708 | + | 0.277562i | \(0.910474\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1080.99 | −1.45099 | ||||||||
\(746\) | 803.994 | − | 428.799i | 1.07774 | − | 0.574798i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 683.101 | − | 1018.30i | 0.913236 | − | 1.36136i | ||||
\(749\) | 814.664i | 1.08767i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 982.058i | 1.30767i | 0.756639 | + | 0.653833i | \(0.226840\pi\) | ||||
−0.756639 | + | 0.653833i | \(0.773160\pi\) | |||||||
\(752\) | 396.100 | − | 162.376i | 0.526729 | − | 0.215925i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −141.506 | − | 265.322i | −0.187674 | − | 0.351886i | ||||
\(755\) | 1396.17 | 1.84923 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 96.0126i | 0.126833i | 0.997987 | + | 0.0634165i | \(0.0201997\pi\) | ||||
−0.997987 | + | 0.0634165i | \(0.979800\pi\) | |||||||
\(758\) | −318.027 | − | 596.297i | −0.419561 | − | 0.786671i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −128.979 | + | 1273.73i | −0.169710 | + | 1.67596i | ||||
\(761\) | −483.966 | −0.635960 | −0.317980 | − | 0.948097i | \(-0.603005\pi\) | ||||
−0.317980 | + | 0.948097i | \(0.603005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −408.383 | −0.535233 | ||||||||
\(764\) | −574.039 | − | 385.080i | −0.751359 | − | 0.504032i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 386.281 | − | 206.018i | 0.504284 | − | 0.268953i | ||||
\(767\) | 444.419i | 0.579425i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 395.882 | 0.514801 | 0.257400 | − | 0.966305i | \(-0.417134\pi\) | ||||
0.257400 | + | 0.966305i | \(0.417134\pi\) | |||||||
\(770\) | −387.707 | − | 726.947i | −0.503516 | − | 0.944087i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −312.437 | + | 465.750i | −0.404712 | + | 0.603303i | ||||
\(773\) | − | 51.0498i | − | 0.0660411i | −0.999455 | − | 0.0330206i | \(-0.989487\pi\) | ||
0.999455 | − | 0.0330206i | \(-0.0105127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 627.343i | 0.809474i | ||||||||
\(776\) | 745.028 | + | 75.4422i | 0.960087 | + | 0.0972194i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 252.120 | − | 134.465i | 0.324062 | − | 0.172834i | ||||
\(779\) | 268.639 | 0.344851 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1134.79i | − | 1.45299i | ||||||
\(782\) | −855.000 | + | 456.003i | −1.09335 | + | 0.583124i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −156.410 | − | 381.547i | −0.199503 | − | 0.486667i | ||||
\(785\) | 1354.62 | 1.72564 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −973.748 | −1.23729 | −0.618646 | − | 0.785670i | \(-0.712318\pi\) | ||||
−0.618646 | + | 0.785670i | \(0.712318\pi\) | |||||||
\(788\) | 1094.56 | + | 734.260i | 1.38904 | + | 0.931801i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 932.457 | + | 1748.35i | 1.18033 | + | 2.21310i | ||||
\(791\) | − | 362.579i | − | 0.458381i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 258.072 | 0.325438 | ||||||||
\(794\) | −1252.06 | + | 667.769i | −1.57690 | + | 0.841019i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −830.174 | − | 556.903i | −1.04293 | − | 0.699627i | ||||
\(797\) | 849.870i | 1.06634i | 0.846009 | + | 0.533168i | \(0.178999\pi\) | ||||
−0.846009 | + | 0.533168i | \(0.821001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 825.858i | 1.03361i | ||||||||
\(800\) | −1001.69 | + | 1209.24i | −1.25211 | + | 1.51156i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −148.613 | − | 278.647i | −0.185303 | − | 0.347441i | ||||
\(803\) | −281.135 | −0.350106 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 651.067i | 0.808778i | ||||||||
\(806\) | 69.6366 | + | 130.568i | 0.0863977 | + | 0.161995i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22.7287 | + | 224.457i | −0.0281296 | + | 0.277793i | ||||
\(809\) | −396.410 | −0.490000 | −0.245000 | − | 0.969523i | \(-0.578788\pi\) | ||||
−0.245000 | + | 0.969523i | \(0.578788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1531.93 | −1.88894 | −0.944470 | − | 0.328598i | \(-0.893424\pi\) | ||||
−0.944470 | + | 0.328598i | \(0.893424\pi\) | |||||||
\(812\) | −279.005 | + | 415.912i | −0.343602 | + | 0.512207i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1109.25 | − | 591.606i | 1.36272 | − | 0.726788i | ||||
\(815\) | 1430.98i | 1.75580i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1161.89 | −1.42214 | ||||||||
\(818\) | 114.575 | + | 214.826i | 0.140067 | + | 0.262624i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 413.031 | + | 277.072i | 0.503696 | + | 0.337893i | ||||
\(821\) | − | 790.420i | − | 0.962752i | −0.876514 | − | 0.481376i | \(-0.840137\pi\) | ||
0.876514 | − | 0.481376i | \(-0.159863\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1061.92i | 1.29031i | 0.764054 | + | 0.645153i | \(0.223206\pi\) | ||||
−0.764054 | + | 0.645153i | \(0.776794\pi\) | |||||||
\(824\) | 45.0581 | − | 444.970i | 0.0546821 | − | 0.540012i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 653.114 | − | 348.330i | 0.790695 | − | 0.421707i | ||||
\(827\) | 575.872 | 0.696339 | 0.348170 | − | 0.937432i | \(-0.386803\pi\) | ||||
0.348170 | + | 0.937432i | \(0.386803\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 849.875i | − | 1.02518i | −0.858633 | − | 0.512590i | \(-0.828686\pi\) | ||
0.858633 | − | 0.512590i | \(-0.171314\pi\) | |||||||
\(830\) | 701.879 | − | 374.337i | 0.845637 | − | 0.451009i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −74.2500 | + | 362.868i | −0.0892428 | + | 0.436139i | ||||
\(833\) | 795.515 | 0.955000 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1365.91 | 1.63582 | ||||||||
\(836\) | −411.507 | + | 613.433i | −0.492233 | + | 0.733772i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.8114 | + | 42.7711i | 0.0272212 | + | 0.0510395i | ||||
\(839\) | 1187.72i | 1.41564i | 0.706394 | + | 0.707819i | \(0.250321\pi\) | ||||
−0.706394 | + | 0.707819i | \(0.749679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 166.079 | 0.197478 | ||||||||
\(842\) | 494.930 | − | 263.964i | 0.587803 | − | 0.313497i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 189.254 | − | 282.121i | 0.224235 | − | 0.334267i | ||||
\(845\) | 1166.23i | 1.38015i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 107.800i | 0.127272i | ||||||||
\(848\) | −210.444 | + | 86.2686i | −0.248165 | + | 0.101732i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1425.54 | − | 2672.86i | −1.67710 | − | 3.14455i | ||||
\(851\) | −993.467 | −1.16741 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 941.579i | 1.10384i | 0.833896 | + | 0.551922i | \(0.186105\pi\) | ||||
−0.833896 | + | 0.551922i | \(0.813895\pi\) | |||||||
\(854\) | −202.274 | − | 379.261i | −0.236854 | − | 0.444099i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1345.41 | + | 136.237i | 1.57173 | + | 0.159155i | ||||
\(857\) | −1094.02 | −1.27657 | −0.638284 | − | 0.769801i | \(-0.720355\pi\) | ||||
−0.638284 | + | 0.769801i | \(0.720355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 811.069 | 0.944201 | 0.472101 | − | 0.881545i | \(-0.343496\pi\) | ||||
0.472101 | + | 0.881545i | \(0.343496\pi\) | |||||||
\(860\) | −1786.40 | − | 1198.37i | −2.07721 | − | 1.39345i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 948.348 | − | 505.789i | 1.10017 | − | 0.586762i | ||||
\(863\) | − | 64.9665i | − | 0.0752799i | −0.999291 | − | 0.0376399i | \(-0.988016\pi\) | ||
0.999291 | − | 0.0376399i | \(-0.0119840\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 389.224 | 0.449970 | ||||||||
\(866\) | −97.4912 | − | 182.795i | −0.112576 | − | 0.211079i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 137.301 | − | 204.675i | 0.158181 | − | 0.235800i | ||||
\(869\) | 1143.26i | 1.31560i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 512.781i | 0.588727i | ||||||||
\(872\) | −68.2942 | + | 674.438i | −0.0783191 | + | 0.773438i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 515.061 | − | 274.701i | 0.589314 | − | 0.314303i | ||||
\(875\) | −998.379 | −1.14100 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 180.847i | − | 0.206211i | −0.994670 | − | 0.103106i | \(-0.967122\pi\) | ||
0.994670 | − | 0.103106i | \(-0.0328779\pi\) | |||||||
\(878\) | 984.454 | − | 525.045i | 1.12125 | − | 0.598001i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1265.38 | + | 518.725i | −1.43793 | + | 0.589460i | ||||
\(881\) | 896.400 | 1.01748 | 0.508740 | − | 0.860920i | \(-0.330112\pi\) | ||||
0.508740 | + | 0.860920i | \(0.330112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 490.293 | 0.555258 | 0.277629 | − | 0.960688i | \(-0.410451\pi\) | ||||
0.277629 | + | 0.960688i | \(0.410451\pi\) | |||||||
\(884\) | −593.389 | − | 398.061i | −0.671255 | − | 0.450295i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.50849 | + | 8.45336i | 0.00508859 | + | 0.00954104i | ||||
\(887\) | 450.485i | 0.507875i | 0.967221 | + | 0.253938i | \(0.0817258\pi\) | ||||
−0.967221 | + | 0.253938i | \(0.918274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −281.713 | −0.316888 | ||||||||
\(890\) | −514.295 | + | 274.292i | −0.577860 | + | 0.308194i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.45480 | + | 4.33005i | 0.00723632 | + | 0.00485432i | ||||
\(893\) | − | 497.506i | − | 0.557117i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 293.629i | − | 0.328077i | ||||||
\(896\) | 591.464 | − | 175.294i | 0.660116 | − | 0.195640i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 788.714 | + | 1478.83i | 0.878300 | + | 1.64680i | ||||
\(899\) | 332.136 | 0.369450 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 438.769i | − | 0.486981i | ||||||
\(902\) | 135.042 | + | 253.203i | 0.149714 | + | 0.280713i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −598.794 | − | 60.6345i | −0.662383 | − | 0.0670735i | ||||
\(905\) | −184.554 | −0.203927 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 113.210 | 0.124818 | 0.0624091 | − | 0.998051i | \(-0.480122\pi\) | ||||
0.0624091 | + | 0.998051i | \(0.480122\pi\) | |||||||
\(908\) | −453.822 | + | 676.513i | −0.499804 | + | 0.745058i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −423.611 | + | 225.927i | −0.465507 | + | 0.248272i | ||||
\(911\) | − | 1580.60i | − | 1.73502i | −0.497423 | − | 0.867508i | \(-0.665720\pi\) | ||
0.497423 | − | 0.867508i | \(-0.334280\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 458.965 | 0.502700 | ||||||||
\(914\) | 506.183 | + | 949.088i | 0.553811 | + | 1.03839i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 66.4240 | + | 44.5589i | 0.0725153 | + | 0.0486451i | ||||
\(917\) | 554.730i | 0.604941i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 846.401i | − | 0.921002i | −0.887659 | − | 0.460501i | \(-0.847670\pi\) | ||
0.887659 | − | 0.460501i | \(-0.152330\pi\) | |||||||
\(920\) | 1075.23 | + | 108.878i | 1.16872 | + | 0.118346i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 284.807 | − | 151.898i | 0.308901 | − | 0.164748i | ||||
\(923\) | −661.270 | −0.716435 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3105.74i | − | 3.35755i | ||||||
\(926\) | 856.898 | − | 457.015i | 0.925376 | − | 0.493537i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 640.214 | + | 530.325i | 0.689886 | + | 0.571471i | ||||
\(929\) | 579.755 | 0.624063 | 0.312032 | − | 0.950072i | \(-0.398991\pi\) | ||||
0.312032 | + | 0.950072i | \(0.398991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −479.227 | −0.514744 | ||||||||
\(932\) | 203.047 | − | 302.682i | 0.217862 | − | 0.324767i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 224.980 | + | 421.836i | 0.240878 | + | 0.451644i | ||||
\(935\) | − | 2638.28i | − | 2.82169i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1810.65 | 1.93239 | 0.966196 | − | 0.257808i | \(-0.0830002\pi\) | ||||
0.966196 | + | 0.257808i | \(0.0830002\pi\) | |||||||
\(938\) | 753.579 | − | 401.911i | 0.803389 | − | 0.428477i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 513.123 | − | 764.912i | 0.545875 | − | 0.813736i | ||||
\(941\) | − | 1154.89i | − | 1.22730i | −0.789579 | − | 0.613649i | \(-0.789701\pi\) | ||
0.789579 | − | 0.613649i | \(-0.210299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 226.773i | − | 0.240480i | ||||||
\(944\) | −466.040 | − | 1136.86i | −0.493687 | − | 1.20430i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −584.072 | − | 1095.13i | −0.617413 | − | 1.15764i | ||||
\(947\) | 1.41679 | 0.00149608 | 0.000748039 | − | 1.00000i | \(-0.499762\pi\) | ||||
0.000748039 | 1.00000i | \(0.499762\pi\) | ||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 163.825i | 0.172629i | ||||||||
\(950\) | 858.758 | + | 1610.16i | 0.903956 | + | 1.69491i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −119.897 | + | 1184.04i | −0.125942 | + | 1.24373i | ||||
\(953\) | −662.875 | −0.695566 | −0.347783 | − | 0.937575i | \(-0.613065\pi\) | ||||
−0.347783 | + | 0.937575i | \(0.613065\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1487.26 | −1.55734 | ||||||||
\(956\) | 122.410 | + | 82.1158i | 0.128044 | + | 0.0858952i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −735.049 | + | 392.028i | −0.767274 | + | 0.409215i | ||||
\(959\) | 242.056i | 0.252404i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 797.552 | 0.829919 | ||||||||
\(962\) | −344.744 | − | 646.392i | −0.358362 | − | 0.671925i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −686.739 | + | 1023.72i | −0.712385 | + | 1.06195i | ||||
\(965\) | 1206.70i | 1.25047i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 843.335i | 0.872114i | 0.899919 | + | 0.436057i | \(0.143625\pi\) | ||||
−0.899919 | + | 0.436057i | \(0.856375\pi\) | |||||||
\(968\) | 178.030 | + | 18.0274i | 0.183915 | + | 0.0186234i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1421.64 | − | 758.214i | 1.46561 | − | 0.781664i | ||||
\(971\) | −289.643 | −0.298293 | −0.149147 | − | 0.988815i | \(-0.547653\pi\) | ||||
−0.149147 | + | 0.988815i | \(0.547653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 280.101i | − | 0.287874i | ||||||
\(974\) | −714.388 | + | 381.009i | −0.733458 | + | 0.391180i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −660.170 | + | 270.628i | −0.676404 | + | 0.277283i | ||||
\(977\) | 1403.92 | 1.43697 | 0.718484 | − | 0.695544i | \(-0.244836\pi\) | ||||
0.718484 | + | 0.695544i | \(0.244836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −336.302 | −0.343516 | ||||||||
\(980\) | −736.808 | − | 494.270i | −0.751845 | − | 0.504357i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −478.635 | − | 897.435i | −0.487408 | − | 0.913885i | ||||
\(983\) | 531.529i | 0.540722i | 0.962759 | + | 0.270361i | \(0.0871430\pi\) | ||||
−0.962759 | + | 0.270361i | \(0.912857\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2835.87 | 2.87905 | ||||||||
\(986\) | −1415.10 | + | 754.726i | −1.43520 | + | 0.765442i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 357.464 | + | 239.796i | 0.361806 | + | 0.242709i | ||||
\(989\) | 980.817i | 0.991726i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1549.03i | 1.56310i | 0.623846 | + | 0.781548i | \(0.285569\pi\) | ||||
−0.623846 | + | 0.781548i | \(0.714431\pi\) | |||||||
\(992\) | −315.056 | − | 260.979i | −0.317597 | − | 0.263084i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 518.295 | + | 971.797i | 0.521423 | + | 0.977663i | ||||
\(995\) | −2150.88 | −2.16168 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 411.253i | − | 0.412491i | −0.978500 | − | 0.206245i | \(-0.933876\pi\) | ||
0.978500 | − | 0.206245i | \(-0.0661245\pi\) | |||||||
\(998\) | 701.696 | + | 1315.67i | 0.703102 | + | 1.31831i | ||||
\(999\) | 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 | 216.3.b.a.163.12 | yes | 16 | |
3.2 | odd | 2 | inner | 216.3.b.a.163.5 | ✓ | 16 | |
4.3 | odd | 2 | 864.3.b.a.271.16 | 16 | |||
8.3 | odd | 2 | inner | 216.3.b.a.163.11 | yes | 16 | |
8.5 | even | 2 | 864.3.b.a.271.1 | 16 | |||
12.11 | even | 2 | 864.3.b.a.271.2 | 16 | |||
24.5 | odd | 2 | 864.3.b.a.271.15 | 16 | |||
24.11 | even | 2 | inner | 216.3.b.a.163.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.3.b.a.163.5 | ✓ | 16 | 3.2 | odd | 2 | inner | |
216.3.b.a.163.6 | yes | 16 | 24.11 | even | 2 | inner | |
216.3.b.a.163.11 | yes | 16 | 8.3 | odd | 2 | inner | |
216.3.b.a.163.12 | yes | 16 | 1.1 | even | 1 | trivial | |
864.3.b.a.271.1 | 16 | 8.5 | even | 2 | |||
864.3.b.a.271.2 | 16 | 12.11 | even | 2 | |||
864.3.b.a.271.15 | 16 | 24.5 | odd | 2 | |||
864.3.b.a.271.16 | 16 | 4.3 | odd | 2 |