Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1079,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1079");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.e (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: | \(14.0856109166\) |
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: | \( x^{16} - 8x^{14} + 49x^{12} - 104x^{10} + 160x^{8} - 104x^{6} + 49x^{4} - 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1079.4 | ||
Root | \(2.04058 + 1.17813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1079 |
Dual form | 1764.2.e.j.1079.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39033 | + | 0.258819i | −0.983111 | + | 0.183013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.86603 | − | 0.719687i | 0.933013 | − | 0.359843i | ||||
\(5\) | 0.732051i | 0.327383i | 0.986512 | + | 0.163692i | \(0.0523402\pi\) | ||||
−0.986512 | + | 0.163692i | \(0.947660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.40812 | + | 1.48356i | −0.851399 | + | 0.524519i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.189469 | − | 1.01779i | −0.0599153 | − | 0.321854i | ||||
\(11\) | −2.03558 | −0.613751 | −0.306876 | − | 0.951750i | \(-0.599284\pi\) | ||||
−0.306876 | + | 0.951750i | \(0.599284\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41421 | 0.392232 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.96410 | − | 2.68591i | 0.741025 | − | 0.671477i | ||||
\(17\) | − | 4.19615i | − | 1.01772i | −0.860850 | − | 0.508858i | \(-0.830068\pi\) | ||
0.860850 | − | 0.508858i | \(-0.169932\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.56131i | 1.27585i | 0.770097 | + | 0.637926i | \(0.220208\pi\) | ||||
−0.770097 | + | 0.637926i | \(0.779792\pi\) | |||||||
\(20\) | 0.526847 | + | 1.36603i | 0.117807 | + | 0.305453i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.83013 | − | 0.526847i | 0.603385 | − | 0.112324i | ||||
\(23\) | −2.03558 | −0.424448 | −0.212224 | − | 0.977221i | \(-0.568071\pi\) | ||||
−0.212224 | + | 0.977221i | \(0.568071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410 | 0.892820 | ||||||||
\(26\) | −1.96622 | + | 0.366025i | −0.385608 | + | 0.0717835i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.27792i | 0.980085i | 0.871699 | + | 0.490042i | \(0.163019\pi\) | ||||
−0.871699 | + | 0.490042i | \(0.836981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.63248i | − | 1.73004i | −0.501734 | − | 0.865022i | \(-0.667304\pi\) | ||
0.501734 | − | 0.865022i | \(-0.332696\pi\) | |||||||
\(32\) | −3.42591 | + | 4.50146i | −0.605621 | + | 0.795753i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.08604 | + | 5.83403i | 0.186255 | + | 1.00053i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.46410 | 0.569495 | 0.284747 | − | 0.958603i | \(-0.408090\pi\) | ||||
0.284747 | + | 0.958603i | \(0.408090\pi\) | |||||||
\(38\) | −1.43937 | − | 7.73205i | −0.233497 | − | 1.25430i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.08604 | − | 1.76287i | −0.171719 | − | 0.278734i | ||||
\(41\) | 8.73205i | 1.36372i | 0.731484 | + | 0.681859i | \(0.238828\pi\) | ||||
−0.731484 | + | 0.681859i | \(0.761172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.86488i | 1.19938i | 0.800231 | + | 0.599692i | \(0.204710\pi\) | ||||
−0.800231 | + | 0.599692i | \(0.795290\pi\) | |||||||
\(44\) | −3.79845 | + | 1.46498i | −0.572638 | + | 0.220854i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.83013 | − | 0.526847i | 0.417279 | − | 0.0776794i | ||||
\(47\) | 10.7436 | 1.56712 | 0.783560 | − | 0.621316i | \(-0.213402\pi\) | ||||
0.783560 | + | 0.621316i | \(0.213402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.20657 | + | 1.15539i | −0.877741 | + | 0.163397i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.63896 | − | 1.01779i | 0.365958 | − | 0.141142i | ||||
\(53\) | 9.14162i | 1.25570i | 0.778335 | + | 0.627849i | \(0.216064\pi\) | ||||
−0.778335 | + | 0.627849i | \(0.783936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.49015i | − | 0.200932i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.36603 | − | 7.33804i | −0.179368 | − | 0.963531i | ||||
\(59\) | −4.98614 | −0.649140 | −0.324570 | − | 0.945862i | \(-0.605220\pi\) | ||||
−0.324570 | + | 0.945862i | \(0.605220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.41902 | −1.20598 | −0.602991 | − | 0.797748i | \(-0.706025\pi\) | ||||
−0.602991 | + | 0.797748i | \(0.706025\pi\) | |||||||
\(62\) | 2.49307 | + | 13.3923i | 0.316620 | + | 1.70082i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.59808 | − | 7.14520i | 0.449760 | − | 0.893150i | ||||
\(65\) | 1.03528i | 0.128410i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.87875i | 0.351695i | 0.984417 | + | 0.175847i | \(0.0562666\pi\) | ||||
−0.984417 | + | 0.175847i | \(0.943733\pi\) | |||||||
\(68\) | −3.01992 | − | 7.83013i | −0.366219 | − | 0.949542i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.08704 | 1.07843 | 0.539217 | − | 0.842167i | \(-0.318720\pi\) | ||||
0.539217 | + | 0.842167i | \(0.318720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.69161 | 0.197989 | 0.0989943 | − | 0.995088i | \(-0.468437\pi\) | ||||
0.0989943 | + | 0.995088i | \(0.468437\pi\) | |||||||
\(74\) | −4.81624 | + | 0.896575i | −0.559876 | + | 0.104225i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00240 | + | 10.3776i | 0.459107 | + | 1.19039i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.98614i | 0.560984i | 0.959856 | + | 0.280492i | \(0.0904977\pi\) | ||||
−0.959856 | + | 0.280492i | \(0.909502\pi\) | |||||||
\(80\) | 1.96622 | + | 2.16987i | 0.219830 | + | 0.242599i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.26002 | − | 12.1404i | −0.249578 | − | 1.34068i | ||||
\(83\) | −13.6224 | −1.49525 | −0.747625 | − | 0.664121i | \(-0.768806\pi\) | ||||
−0.747625 | + | 0.664121i | \(0.768806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.07180 | 0.333183 | ||||||||
\(86\) | −2.03558 | − | 10.9348i | −0.219502 | − | 1.17913i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.90192 | − | 3.01992i | 0.522547 | − | 0.321924i | ||||
\(89\) | − | 8.73205i | − | 0.925596i | −0.886464 | − | 0.462798i | \(-0.846846\pi\) | ||
0.886464 | − | 0.462798i | \(-0.153154\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.79845 | + | 1.46498i | −0.396016 | + | 0.152735i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.9372 | + | 2.78066i | −1.54065 | + | 0.286803i | ||||
\(95\) | −4.07116 | −0.417693 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0759 | 1.53072 | 0.765362 | − | 0.643600i | \(-0.222560\pi\) | ||||
0.765362 | + | 0.643600i | \(0.222560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.33013 | − | 3.21276i | 0.833013 | − | 0.321276i | ||||
\(101\) | − | 5.26795i | − | 0.524181i | −0.965043 | − | 0.262090i | \(-0.915588\pi\) | ||
0.965043 | − | 0.262090i | \(-0.0844118\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6839i | 1.64392i | 0.569547 | + | 0.821959i | \(0.307119\pi\) | ||||
−0.569547 | + | 0.821959i | \(0.692881\pi\) | |||||||
\(104\) | −3.40559 | + | 2.09808i | −0.333946 | + | 0.205733i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.36603 | − | 12.7099i | −0.229809 | − | 1.23449i | ||||
\(107\) | 13.1582 | 1.27205 | 0.636026 | − | 0.771668i | \(-0.280577\pi\) | ||||
0.636026 | + | 0.771668i | \(0.280577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 0.385679 | + | 2.07180i | 0.0367731 | + | 0.197538i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.656339i | 0.0617432i | 0.999523 | + | 0.0308716i | \(0.00982829\pi\) | ||||
−0.999523 | + | 0.0308716i | \(0.990172\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.49015i | − | 0.138957i | ||||||
\(116\) | 3.79845 | + | 9.84873i | 0.352677 | + | 0.914431i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.93237 | − | 1.29051i | 0.638176 | − | 0.118801i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.85641 | −0.623310 | ||||||||
\(122\) | 13.0955 | − | 2.43782i | 1.18561 | − | 0.220710i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.93237 | − | 17.9744i | −0.622545 | − | 1.61415i | ||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.6085i | 1.65124i | 0.564227 | + | 0.825619i | \(0.309174\pi\) | ||||
−0.564227 | + | 0.825619i | \(0.690826\pi\) | |||||||
\(128\) | −3.15319 | + | 10.8654i | −0.278706 | + | 0.960377i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.267949 | − | 1.43937i | −0.0235007 | − | 0.126241i | ||||
\(131\) | 15.7298 | 1.37432 | 0.687158 | − | 0.726508i | \(-0.258858\pi\) | ||||
0.687158 | + | 0.726508i | \(0.258858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.745075 | − | 4.00240i | −0.0643646 | − | 0.345755i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.22526 | + | 10.1048i | 0.533812 | + | 0.866482i | ||||
\(137\) | 5.27792i | 0.450923i | 0.974252 | + | 0.225461i | \(0.0723890\pi\) | ||||
−0.974252 | + | 0.225461i | \(0.927611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.1226i | − | 0.943409i | −0.881757 | − | 0.471704i | \(-0.843639\pi\) | ||
0.881757 | − | 0.471704i | \(-0.156361\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.6340 | + | 2.35190i | −1.06022 | + | 0.197367i | ||||
\(143\) | −2.87875 | −0.240733 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.86370 | −0.320863 | ||||||||
\(146\) | −2.35190 | + | 0.437822i | −0.194645 | + | 0.0362344i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.46410 | − | 2.49307i | 0.531346 | − | 0.204929i | ||||
\(149\) | 4.24264i | 0.347571i | 0.984784 | + | 0.173785i | \(0.0555999\pi\) | ||||
−0.984784 | + | 0.173785i | \(0.944400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.86488i | 0.640035i | 0.947412 | + | 0.320018i | \(0.103689\pi\) | ||||
−0.947412 | + | 0.320018i | \(0.896311\pi\) | |||||||
\(152\) | −8.25056 | − | 13.3923i | −0.669209 | − | 1.08626i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.05146 | 0.566387 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.0759 | −1.20319 | −0.601593 | − | 0.798803i | \(-0.705467\pi\) | ||||
−0.601593 | + | 0.798803i | \(0.705467\pi\) | |||||||
\(158\) | −1.29051 | − | 6.93237i | −0.102667 | − | 0.551510i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.29530 | − | 2.50794i | −0.260516 | − | 0.198270i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.3660i | 1.90849i | 0.299021 | + | 0.954247i | \(0.403340\pi\) | ||||
−0.299021 | + | 0.954247i | \(0.596660\pi\) | |||||||
\(164\) | 6.28434 | + | 16.2942i | 0.490725 | + | 1.27237i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.9396 | − | 3.52573i | 1.47000 | − | 0.273650i | ||||
\(167\) | −10.7436 | −0.831367 | −0.415684 | − | 0.909509i | \(-0.636458\pi\) | ||||
−0.415684 | + | 0.909509i | \(0.636458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | −4.27081 | + | 0.795040i | −0.327556 | + | 0.0609767i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.66025 | + | 14.6761i | 0.431590 | + | 1.11904i | ||||
\(173\) | 9.66025i | 0.734456i | 0.930131 | + | 0.367228i | \(0.119693\pi\) | ||||
−0.930131 | + | 0.367228i | \(0.880307\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.03367 | + | 5.46739i | −0.454805 | + | 0.412120i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.26002 | + | 12.1404i | 0.169396 | + | 0.909963i | ||||
\(179\) | 17.2294 | 1.28778 | 0.643892 | − | 0.765117i | \(-0.277319\pi\) | ||||
0.643892 | + | 0.765117i | \(0.277319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.00052 | −0.371685 | −0.185843 | − | 0.982580i | \(-0.559501\pi\) | ||||
−0.185843 | + | 0.982580i | \(0.559501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.90192 | − | 3.01992i | 0.361375 | − | 0.222631i | ||||
\(185\) | 2.53590i | 0.186443i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.54161i | 0.624625i | ||||||||
\(188\) | 20.0479 | − | 7.73205i | 1.46214 | − | 0.563918i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.66025 | − | 1.05369i | 0.410638 | − | 0.0764430i | ||||
\(191\) | 13.1582 | 0.952095 | 0.476047 | − | 0.879420i | \(-0.342069\pi\) | ||||
0.476047 | + | 0.879420i | \(0.342069\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.85641 | −0.709480 | −0.354740 | − | 0.934965i | \(-0.615431\pi\) | ||||
−0.354740 | + | 0.934965i | \(0.615431\pi\) | |||||||
\(194\) | −20.9604 | + | 3.90192i | −1.50487 | + | 0.280142i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.3533i | 1.09388i | 0.837173 | + | 0.546938i | \(0.184207\pi\) | ||||
−0.837173 | + | 0.546938i | \(0.815793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.07116i | 0.288597i | 0.989534 | + | 0.144299i | \(0.0460926\pi\) | ||||
−0.989534 | + | 0.144299i | \(0.953907\pi\) | |||||||
\(200\) | −10.7501 | + | 6.62278i | −0.760146 | + | 0.468301i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.36345 | + | 7.32418i | 0.0959317 | + | 0.515327i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.39230 | −0.446458 | ||||||||
\(206\) | −4.31812 | − | 23.1962i | −0.300858 | − | 1.61615i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.19187 | − | 3.79845i | 0.290654 | − | 0.263375i | ||||
\(209\) | − | 11.3205i | − | 0.783056i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.4873i | 1.47924i | 0.673022 | + | 0.739622i | \(0.264996\pi\) | ||||
−0.673022 | + | 0.739622i | \(0.735004\pi\) | |||||||
\(212\) | 6.57910 | + | 17.0585i | 0.451855 | + | 1.17158i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.2942 | + | 3.40559i | −1.25057 | + | 0.232802i | ||||
\(215\) | −5.75749 | −0.392658 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.34197 | + | 1.55291i | −0.564989 | + | 0.105177i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.07244 | − | 2.78066i | −0.0723040 | − | 0.187472i | ||||
\(221\) | − | 5.93426i | − | 0.399181i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.1938i | − | 1.01745i | −0.860929 | − | 0.508726i | \(-0.830117\pi\) | ||
0.860929 | − | 0.508726i | \(-0.169883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.169873 | − | 0.912526i | −0.0112998 | − | 0.0607004i | ||||
\(227\) | 10.7436 | 0.713080 | 0.356540 | − | 0.934280i | \(-0.383956\pi\) | ||||
0.356540 | + | 0.934280i | \(0.383956\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.3543 | 1.67546 | 0.837730 | − | 0.546085i | \(-0.183882\pi\) | ||||
0.837730 | + | 0.546085i | \(0.183882\pi\) | |||||||
\(230\) | 0.385679 | + | 2.07180i | 0.0254309 | + | 0.136610i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.83013 | − | 12.7099i | −0.514073 | − | 0.834443i | ||||
\(233\) | 5.83272i | 0.382114i | 0.981579 | + | 0.191057i | \(0.0611916\pi\) | ||||
−0.981579 | + | 0.191057i | \(0.938808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.86488i | 0.513048i | ||||||||
\(236\) | −9.30426 | + | 3.58846i | −0.605656 | + | 0.233589i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.03558 | 0.131671 | 0.0658354 | − | 0.997830i | \(-0.479029\pi\) | ||||
0.0658354 | + | 0.997830i | \(0.479029\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0053 | 0.837747 | 0.418873 | − | 0.908045i | \(-0.362425\pi\) | ||||
0.418873 | + | 0.908045i | \(0.362425\pi\) | |||||||
\(242\) | 9.53266 | − | 1.77457i | 0.612782 | − | 0.114074i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −17.5761 | + | 6.77875i | −1.12520 | + | 0.433965i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.86488i | 0.500431i | ||||||||
\(248\) | 14.2904 | + | 23.1962i | 0.907441 | + | 1.47296i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.79315 | − | 9.63248i | −0.113409 | − | 0.609211i | ||||
\(251\) | 8.63624 | 0.545115 | 0.272557 | − | 0.962140i | \(-0.412131\pi\) | ||||
0.272557 | + | 0.962140i | \(0.412131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.14359 | 0.260505 | ||||||||
\(254\) | −4.81624 | − | 25.8719i | −0.302198 | − | 1.62335i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.57180 | − | 15.9226i | 0.0982373 | − | 0.995163i | ||||
\(257\) | 1.12436i | 0.0701354i | 0.999385 | + | 0.0350677i | \(0.0111647\pi\) | ||||
−0.999385 | + | 0.0350677i | \(0.988835\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.745075 | + | 1.93185i | 0.0462076 | + | 0.119808i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.8695 | + | 4.07116i | −1.35110 | + | 0.251517i | ||||
\(263\) | 2.03558 | 0.125519 | 0.0627597 | − | 0.998029i | \(-0.480010\pi\) | ||||
0.0627597 | + | 0.998029i | \(0.480010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.69213 | −0.411094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.07180 | + | 5.37182i | 0.126555 | + | 0.328136i | ||||
\(269\) | 3.66025i | 0.223170i | 0.993755 | + | 0.111585i | \(0.0355927\pi\) | ||||
−0.993755 | + | 0.111585i | \(0.964407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7036i | 0.832437i | 0.909265 | + | 0.416218i | \(0.136645\pi\) | ||||
−0.909265 | + | 0.416218i | \(0.863355\pi\) | |||||||
\(272\) | −11.2705 | − | 12.4378i | −0.683373 | − | 0.754154i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.36603 | − | 7.33804i | −0.0825246 | − | 0.443307i | ||||
\(275\) | −9.08704 | −0.547969 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.07180 | −0.424903 | −0.212452 | − | 0.977172i | \(-0.568145\pi\) | ||||
−0.212452 | + | 0.977172i | \(0.568145\pi\) | |||||||
\(278\) | 2.87875 | + | 15.4641i | 0.172656 | + | 0.927475i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.5612i | − | 1.40554i | −0.711417 | − | 0.702770i | \(-0.751946\pi\) | ||
0.711417 | − | 0.702770i | \(-0.248054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5.56131i | − | 0.330586i | −0.986245 | − | 0.165293i | \(-0.947143\pi\) | ||
0.986245 | − | 0.165293i | \(-0.0528569\pi\) | |||||||
\(284\) | 16.9567 | − | 6.53983i | 1.00619 | − | 0.388067i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00240 | − | 0.745075i | 0.236667 | − | 0.0440572i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.607695 | −0.0357468 | ||||||||
\(290\) | 5.37182 | − | 1.00000i | 0.315444 | − | 0.0587220i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.15660 | − | 1.21743i | 0.184726 | − | 0.0712449i | ||||
\(293\) | − | 31.1244i | − | 1.81830i | −0.416464 | − | 0.909152i | \(-0.636731\pi\) | ||
0.416464 | − | 0.909152i | \(-0.363269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.65011i | − | 0.212517i | ||||||
\(296\) | −8.34197 | + | 5.13922i | −0.484867 | + | 0.298711i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.09808 | − | 5.89866i | −0.0636098 | − | 0.341700i | ||||
\(299\) | −2.87875 | −0.166482 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.03558 | − | 10.9348i | −0.117135 | − | 0.629225i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.9372 | + | 16.4843i | 0.856706 | + | 0.945439i | ||||
\(305\) | − | 6.89520i | − | 0.394818i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.63248i | − | 0.549754i | −0.961479 | − | 0.274877i | \(-0.911363\pi\) | ||
0.961479 | − | 0.274877i | \(-0.0886372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.80385 | + | 1.82505i | −0.556821 | + | 0.103656i | ||||
\(311\) | −20.7159 | −1.17469 | −0.587346 | − | 0.809336i | \(-0.699827\pi\) | ||||
−0.587346 | + | 0.809336i | \(0.699827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.2533 | −1.71002 | −0.855008 | − | 0.518614i | \(-0.826448\pi\) | ||||
−0.855008 | + | 0.518614i | \(0.826448\pi\) | |||||||
\(314\) | 20.9604 | − | 3.90192i | 1.18286 | − | 0.220198i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.58846 | + | 9.30426i | 0.201866 | + | 0.523405i | ||||
\(317\) | 4.24264i | 0.238290i | 0.992877 | + | 0.119145i | \(0.0380154\pi\) | ||||
−0.992877 | + | 0.119145i | \(0.961985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.7436i | − | 0.601528i | ||||||
\(320\) | 5.23065 | + | 2.63397i | 0.292402 | + | 0.147244i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.3361 | 1.29846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.31319 | 0.350193 | ||||||||
\(326\) | −6.30639 | − | 33.8768i | −0.349279 | − | 1.87626i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.9546 | − | 21.0278i | −0.715296 | − | 1.16107i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 11.5150i | − | 0.632921i | −0.948606 | − | 0.316461i | \(-0.897506\pi\) | ||
0.948606 | − | 0.316461i | \(-0.102494\pi\) | |||||||
\(332\) | −25.4197 | + | 9.80385i | −1.39509 | + | 0.538056i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.9372 | − | 2.78066i | 0.817326 | − | 0.152151i | ||||
\(335\) | −2.10739 | −0.115139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.60770 | −0.0875767 | −0.0437884 | − | 0.999041i | \(-0.513943\pi\) | ||||
−0.0437884 | + | 0.999041i | \(0.513943\pi\) | |||||||
\(338\) | 15.2936 | − | 2.84701i | 0.831863 | − | 0.154857i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.73205 | − | 2.21073i | 0.310864 | − | 0.119894i | ||||
\(341\) | 19.6077i | 1.06182i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.6681 | − | 18.9396i | −0.629100 | − | 1.02115i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.50026 | − | 13.4309i | −0.134415 | − | 0.722051i | ||||
\(347\) | −20.2097 | −1.08491 | −0.542456 | − | 0.840084i | \(-0.682505\pi\) | ||||
−0.542456 | + | 0.840084i | \(0.682505\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.4896 | −0.615023 | −0.307511 | − | 0.951544i | \(-0.599496\pi\) | ||||
−0.307511 | + | 0.951544i | \(0.599496\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.97372 | − | 9.16309i | 0.371701 | − | 0.488394i | ||||
\(353\) | 28.1962i | 1.50073i | 0.661024 | + | 0.750365i | \(0.270122\pi\) | ||||
−0.661024 | + | 0.750365i | \(0.729878\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.65218i | 0.353061i | ||||||||
\(356\) | −6.28434 | − | 16.2942i | −0.333069 | − | 0.863592i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.9545 | + | 4.45929i | −1.26603 | + | 0.235681i | ||||
\(359\) | 9.08704 | 0.479596 | 0.239798 | − | 0.970823i | \(-0.422919\pi\) | ||||
0.239798 | + | 0.970823i | \(0.422919\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.9282 | −0.627800 | ||||||||
\(362\) | 6.95236 | − | 1.29423i | 0.365408 | − | 0.0680231i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.23835i | 0.0648181i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | −6.03367 | + | 5.46739i | −0.314527 | + | 0.285007i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.656339 | − | 3.52573i | −0.0341214 | − | 0.183294i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.9282 | 0.876509 | 0.438255 | − | 0.898851i | \(-0.355597\pi\) | ||||
0.438255 | + | 0.898851i | \(0.355597\pi\) | |||||||
\(374\) | −2.21073 | − | 11.8756i | −0.114314 | − | 0.614075i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −25.8719 | + | 15.9389i | −1.33424 | + | 0.821984i | ||||
\(377\) | 7.46410i | 0.384421i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.2448i | − | 1.39947i | −0.714403 | − | 0.699735i | \(-0.753302\pi\) | ||
0.714403 | − | 0.699735i | \(-0.246698\pi\) | |||||||
\(380\) | −7.59689 | + | 2.92996i | −0.389712 | + | 0.150304i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.2942 | + | 3.40559i | −0.936014 | + | 0.174245i | ||||
\(383\) | 21.4873 | 1.09795 | 0.548974 | − | 0.835839i | \(-0.315019\pi\) | ||||
0.548974 | + | 0.835839i | \(0.315019\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.7036 | − | 2.55103i | 0.697497 | − | 0.129844i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.1320 | − | 10.8499i | 1.42818 | − | 0.550821i | ||||
\(389\) | − | 32.6012i | − | 1.65295i | −0.562974 | − | 0.826474i | \(-0.690343\pi\) | ||
0.562974 | − | 0.826474i | \(-0.309657\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.54161i | 0.431968i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.97372 | − | 21.3461i | −0.200193 | − | 1.07540i | ||||
\(395\) | −3.65011 | −0.183657 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.3495 | 0.870746 | 0.435373 | − | 0.900250i | \(-0.356616\pi\) | ||||
0.435373 | + | 0.900250i | \(0.356616\pi\) | |||||||
\(398\) | −1.05369 | − | 5.66025i | −0.0528169 | − | 0.283723i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.2321 | − | 11.9902i | 0.661603 | − | 0.599508i | ||||
\(401\) | − | 38.2581i | − | 1.91052i | −0.295770 | − | 0.955259i | \(-0.595576\pi\) | ||
0.295770 | − | 0.955259i | \(-0.404424\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.6224i | − | 0.678579i | ||||||
\(404\) | −3.79127 | − | 9.83013i | −0.188623 | − | 0.489067i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.05146 | −0.349528 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.1769 | 0.503215 | 0.251608 | − | 0.967829i | \(-0.419041\pi\) | ||||
0.251608 | + | 0.967829i | \(0.419041\pi\) | |||||||
\(410\) | 8.88740 | − | 1.65445i | 0.438918 | − | 0.0817075i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.0072 | + | 31.1327i | 0.591553 | + | 1.53380i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9.97227i | − | 0.489520i | ||||||
\(416\) | −4.84497 | + | 6.36603i | −0.237544 | + | 0.312120i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.92996 | + | 15.7392i | 0.143309 | + | 0.769831i | ||||
\(419\) | 24.3660 | 1.19036 | 0.595179 | − | 0.803593i | \(-0.297081\pi\) | ||||
0.595179 | + | 0.803593i | \(0.297081\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.7128 | −1.44811 | −0.724057 | − | 0.689740i | \(-0.757725\pi\) | ||||
−0.724057 | + | 0.689740i | \(0.757725\pi\) | |||||||
\(422\) | −5.56131 | − | 29.8744i | −0.270720 | − | 1.45426i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.5622 | − | 22.0141i | −0.658638 | − | 1.06910i | ||||
\(425\) | − | 18.7321i | − | 0.908638i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.5536 | − | 9.46979i | 1.18684 | − | 0.457740i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00481 | − | 1.49015i | 0.386026 | − | 0.0718614i | ||||
\(431\) | 32.4232 | 1.56177 | 0.780884 | − | 0.624676i | \(-0.214769\pi\) | ||||
0.780884 | + | 0.624676i | \(0.214769\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.7985 | −0.711169 | −0.355585 | − | 0.934644i | \(-0.615718\pi\) | ||||
−0.355585 | + | 0.934644i | \(0.615718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.1962 | − | 4.31812i | 0.536198 | − | 0.206801i | ||||
\(437\) | − | 11.3205i | − | 0.541533i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 27.4073i | − | 1.30808i | −0.756461 | − | 0.654039i | \(-0.773073\pi\) | ||
0.756461 | − | 0.654039i | \(-0.226927\pi\) | |||||||
\(440\) | 2.21073 | + | 3.58846i | 0.105393 | + | 0.171073i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.53590 | + | 8.25056i | 0.0730552 | + | 0.392439i | ||||
\(443\) | −10.1779 | −0.483567 | −0.241784 | − | 0.970330i | \(-0.577732\pi\) | ||||
−0.241784 | + | 0.970330i | \(0.577732\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.39230 | 0.303024 | ||||||||
\(446\) | 3.93244 | + | 21.1244i | 0.186207 | + | 1.00027i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 32.3238i | − | 1.52546i | −0.646719 | − | 0.762728i | \(-0.723859\pi\) | ||
0.646719 | − | 0.762728i | \(-0.276141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 17.7748i | − | 0.836983i | ||||||
\(452\) | 0.472358 | + | 1.22474i | 0.0222179 | + | 0.0576072i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.9372 | + | 2.78066i | −0.701036 | + | 0.130503i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.9282 | −1.07254 | −0.536268 | − | 0.844048i | \(-0.680166\pi\) | ||||
−0.536268 | + | 0.844048i | \(0.680166\pi\) | |||||||
\(458\) | −35.2508 | + | 6.56218i | −1.64716 | + | 0.306630i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.07244 | − | 2.78066i | −0.0500028 | − | 0.129649i | ||||
\(461\) | − | 9.26795i | − | 0.431651i | −0.976432 | − | 0.215826i | \(-0.930756\pi\) | ||
0.976432 | − | 0.215826i | \(-0.0692443\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.09353i | − | 0.329664i | −0.986322 | − | 0.164832i | \(-0.947292\pi\) | ||
0.986322 | − | 0.164832i | \(-0.0527082\pi\) | |||||||
\(464\) | 14.1760 | + | 15.6443i | 0.658104 | + | 0.726268i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.50962 | − | 8.10940i | −0.0699317 | − | 0.375660i | ||||
\(467\) | −12.8510 | −0.594674 | −0.297337 | − | 0.954773i | \(-0.596099\pi\) | ||||
−0.297337 | + | 0.954773i | \(0.596099\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.03558 | − | 10.9348i | −0.0938944 | − | 0.504383i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0072 | − | 7.39725i | 0.552677 | − | 0.340486i | ||||
\(473\) | − | 16.0096i | − | 0.736123i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.8263i | 1.13911i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.83013 | + | 0.526847i | −0.129447 | + | 0.0240974i | ||||
\(479\) | 12.8510 | 0.587178 | 0.293589 | − | 0.955932i | \(-0.405150\pi\) | ||||
0.293589 | + | 0.955932i | \(0.405150\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.89898 | 0.223374 | ||||||||
\(482\) | −18.0817 | + | 3.36603i | −0.823597 | + | 0.153318i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.7942 | + | 4.93447i | −0.581556 | + | 0.224294i | ||||
\(485\) | 11.0363i | 0.501133i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13.6224i | − | 0.617289i | −0.951177 | − | 0.308644i | \(-0.900125\pi\) | ||
0.951177 | − | 0.308644i | \(-0.0998753\pi\) | |||||||
\(488\) | 22.6821 | − | 13.9737i | 1.02677 | − | 0.632561i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.1582 | −0.593822 | −0.296911 | − | 0.954905i | \(-0.595956\pi\) | ||||
−0.296911 | + | 0.954905i | \(0.595956\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.1469 | 0.997448 | ||||||||
\(494\) | −2.03558 | − | 10.9348i | −0.0915852 | − | 0.491979i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.8719 | − | 28.5516i | −1.16168 | − | 1.28201i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 29.3521i | − | 1.31398i | −0.753898 | − | 0.656991i | \(-0.771829\pi\) | ||
0.753898 | − | 0.656991i | \(-0.228171\pi\) | |||||||
\(500\) | 4.98614 | + | 12.9282i | 0.222987 | + | 0.578167i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0072 | + | 2.23522i | −0.535908 | + | 0.0997629i | ||||
\(503\) | 19.3799 | 0.864106 | 0.432053 | − | 0.901848i | \(-0.357789\pi\) | ||||
0.432053 | + | 0.901848i | \(0.357789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.85641 | 0.171608 | ||||||||
\(506\) | −5.76096 | + | 1.07244i | −0.256106 | + | 0.0476758i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.3923 | + | 34.7240i | 0.594187 | + | 1.54063i | ||||
\(509\) | 27.6603i | 1.22602i | 0.790075 | + | 0.613010i | \(0.210041\pi\) | ||||
−0.790075 | + | 0.613010i | \(0.789959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.93576 | + | 22.5445i | 0.0855493 | + | 0.996334i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.291005 | − | 1.56322i | −0.0128357 | − | 0.0689508i | ||||
\(515\) | −12.2135 | −0.538191 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.8695 | −0.961821 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.53590 | − | 2.49307i | −0.0673536 | − | 0.109328i | ||||
\(521\) | − | 9.66025i | − | 0.423223i | −0.977354 | − | 0.211612i | \(-0.932129\pi\) | ||
0.977354 | − | 0.211612i | \(-0.0678712\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.98030i | − | 0.130319i | −0.997875 | − | 0.0651597i | \(-0.979244\pi\) | ||
0.997875 | − | 0.0651597i | \(-0.0207557\pi\) | |||||||
\(524\) | 29.3521 | − | 11.3205i | 1.28225 | − | 0.494539i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.83013 | + | 0.526847i | −0.123399 | + | 0.0229716i | ||||
\(527\) | −40.4193 | −1.76069 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.8564 | −0.819844 | ||||||||
\(530\) | 9.30426 | − | 1.73205i | 0.404151 | − | 0.0752355i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.3490i | 0.534894i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.63248i | 0.416448i | ||||||||
\(536\) | −4.27081 | − | 6.93237i | −0.184471 | − | 0.299433i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.947343 | − | 5.08895i | −0.0408429 | − | 0.219400i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.8564 | 0.681720 | 0.340860 | − | 0.940114i | \(-0.389282\pi\) | ||||
0.340860 | + | 0.940114i | \(0.389282\pi\) | |||||||
\(542\) | −3.54676 | − | 19.0526i | −0.152347 | − | 0.818377i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.8888 | + | 14.3756i | 0.809851 | + | 0.616351i | ||||
\(545\) | 4.39230i | 0.188146i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.4734i | − | 1.13192i | −0.824432 | − | 0.565960i | \(-0.808505\pi\) | ||
0.824432 | − | 0.565960i | \(-0.191495\pi\) | |||||||
\(548\) | 3.79845 | + | 9.84873i | 0.162262 | + | 0.420717i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.6340 | − | 2.35190i | 0.538714 | − | 0.100285i | ||||
\(551\) | −29.3521 | −1.25044 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.83212 | − | 1.83032i | 0.417727 | − | 0.0777627i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00481 | − | 20.7551i | −0.339479 | − | 0.880212i | ||||
\(557\) | 18.9396i | 0.802496i | 0.915970 | + | 0.401248i | \(0.131423\pi\) | ||||
−0.915970 | + | 0.401248i | \(0.868577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.1226i | 0.470437i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.09808 | + | 32.7577i | 0.257232 | + | 1.38180i | ||||
\(563\) | −37.9884 | −1.60102 | −0.800510 | − | 0.599320i | \(-0.795438\pi\) | ||||
−0.800510 | + | 0.599320i | \(0.795438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.480473 | −0.0202137 | ||||||||
\(566\) | 1.43937 | + | 7.73205i | 0.0605014 | + | 0.325002i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.8827 | + | 13.4812i | −0.918177 | + | 0.565659i | ||||
\(569\) | − | 16.5916i | − | 0.695557i | −0.937577 | − | 0.347779i | \(-0.886936\pi\) | ||
0.937577 | − | 0.347779i | \(-0.113064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 0.771358i | − | 0.0322803i | −0.999870 | − | 0.0161402i | \(-0.994862\pi\) | ||
0.999870 | − | 0.0161402i | \(-0.00513780\pi\) | |||||||
\(572\) | −5.37182 | + | 2.07180i | −0.224607 | + | 0.0866262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.08704 | −0.378956 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.62587 | −0.317469 | −0.158735 | − | 0.987321i | \(-0.550741\pi\) | ||||
−0.158735 | + | 0.987321i | \(0.550741\pi\) | |||||||
\(578\) | 0.844896 | − | 0.157283i | 0.0351430 | − | 0.00654211i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.20977 | + | 2.78066i | −0.299369 | + | 0.115460i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.6085i | − | 0.770686i | ||||||
\(584\) | −4.07361 | + | 2.50962i | −0.168567 | + | 0.103849i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.05558 | + | 43.2731i | 0.332773 | + | 1.78759i | ||||
\(587\) | −16.5011 | −0.681074 | −0.340537 | − | 0.940231i | \(-0.610609\pi\) | ||||
−0.340537 | + | 0.940231i | \(0.610609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.5692 | 2.20728 | ||||||||
\(590\) | 0.944717 | + | 5.07484i | 0.0388934 | + | 0.208928i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.2679 | − | 9.30426i | 0.422010 | − | 0.382403i | ||||
\(593\) | − | 28.1962i | − | 1.15788i | −0.815371 | − | 0.578939i | \(-0.803467\pi\) | ||
0.815371 | − | 0.578939i | \(-0.196533\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.05337 | + | 7.91688i | 0.125071 | + | 0.324288i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.00240 | − | 0.745075i | 0.163670 | − | 0.0304684i | ||||
\(599\) | −31.3323 | −1.28020 | −0.640101 | − | 0.768290i | \(-0.721108\pi\) | ||||
−0.640101 | + | 0.768290i | \(0.721108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.4564 | 1.24234 | 0.621170 | − | 0.783676i | \(-0.286657\pi\) | ||||
0.621170 | + | 0.783676i | \(0.286657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.66025 | + | 14.6761i | 0.230312 | + | 0.597161i | ||||
\(605\) | − | 5.01924i | − | 0.204061i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.1029i | − | 0.572420i | −0.958167 | − | 0.286210i | \(-0.907604\pi\) | ||
0.958167 | − | 0.286210i | \(-0.0923955\pi\) | |||||||
\(608\) | −25.0340 | − | 19.0526i | −1.01526 | − | 0.772683i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.78461 | + | 9.58659i | 0.0722567 | + | 0.388150i | ||||
\(611\) | 15.1938 | 0.614675 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.3923 | 0.662079 | 0.331039 | − | 0.943617i | \(-0.392601\pi\) | ||||
0.331039 | + | 0.943617i | \(0.392601\pi\) | |||||||
\(614\) | 2.49307 | + | 13.3923i | 0.100612 | + | 0.540469i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10.3800i | − | 0.417882i | −0.977928 | − | 0.208941i | \(-0.932998\pi\) | ||
0.977928 | − | 0.208941i | \(-0.0670016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.3164i | 1.05775i | 0.848701 | + | 0.528873i | \(0.177385\pi\) | ||||
−0.848701 | + | 0.528873i | \(0.822615\pi\) | |||||||
\(620\) | 13.1582 | − | 5.07484i | 0.528446 | − | 0.203811i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.8019 | − | 5.36167i | 1.15485 | − | 0.214983i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 42.0620 | − | 7.83013i | 1.68114 | − | 0.312955i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.1320 | + | 10.8499i | −1.12259 | + | 0.432959i | ||||
\(629\) | − | 14.5359i | − | 0.579584i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.09353i | − | 0.282389i | −0.989982 | − | 0.141194i | \(-0.954906\pi\) | ||
0.989982 | − | 0.141194i | \(-0.0450943\pi\) | |||||||
\(632\) | −7.39725 | − | 12.0072i | −0.294247 | − | 0.477621i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.09808 | − | 5.89866i | −0.0436102 | − | 0.234266i | ||||
\(635\) | −13.6224 | −0.540588 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.78066 | + | 14.9372i | 0.110087 | + | 0.591368i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.95404 | − | 2.30830i | −0.314411 | − | 0.0912435i | ||||
\(641\) | − | 3.96524i | − | 0.156618i | −0.996929 | − | 0.0783088i | \(-0.975048\pi\) | ||
0.996929 | − | 0.0783088i | \(-0.0249520\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.58101i | − | 0.101785i | −0.998704 | − | 0.0508926i | \(-0.983793\pi\) | ||
0.998704 | − | 0.0508926i | \(-0.0162066\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −32.4449 | + | 6.03983i | −1.27653 | + | 0.237634i | ||||
\(647\) | 47.9607 | 1.88553 | 0.942764 | − | 0.333460i | \(-0.108216\pi\) | ||||
0.942764 | + | 0.333460i | \(0.108216\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1497 | 0.398410 | ||||||||
\(650\) | −8.77741 | + | 1.63397i | −0.344278 | + | 0.0640898i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.5359 | + | 45.4676i | 0.686759 | + | 1.78065i | ||||
\(653\) | 39.2190i | 1.53476i | 0.641193 | + | 0.767380i | \(0.278440\pi\) | ||||
−0.641193 | + | 0.767380i | \(0.721560\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.5150i | 0.449928i | ||||||||
\(656\) | 23.4535 | + | 25.8827i | 0.915705 | + | 1.01055i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.6170 | −1.85489 | −0.927447 | − | 0.373956i | \(-0.878001\pi\) | ||||
−0.927447 | + | 0.373956i | \(0.878001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.7338 | −1.19540 | −0.597702 | − | 0.801718i | \(-0.703920\pi\) | ||||
−0.597702 | + | 0.801718i | \(0.703920\pi\) | |||||||
\(662\) | 2.98030 | + | 16.0096i | 0.115833 | + | 0.622231i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32.8043 | − | 20.2097i | 1.27305 | − | 0.784287i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.7436i | − | 0.415995i | ||||||
\(668\) | −20.0479 | + | 7.73205i | −0.775676 | + | 0.299162i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.92996 | − | 0.545433i | 0.113194 | − | 0.0210719i | ||||
\(671\) | 19.1732 | 0.740173 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.0000 | −1.61898 | −0.809491 | − | 0.587133i | \(-0.800257\pi\) | ||||
−0.809491 | + | 0.587133i | \(0.800257\pi\) | |||||||
\(674\) | 2.23522 | − | 0.416102i | 0.0860976 | − | 0.0160277i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.5263 | + | 7.91656i | −0.789472 | + | 0.304483i | ||||
\(677\) | 24.8756i | 0.956049i | 0.878347 | + | 0.478024i | \(0.158647\pi\) | ||||
−0.878347 | + | 0.478024i | \(0.841353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.39725 | + | 4.55721i | −0.283672 | + | 0.174761i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.07484 | − | 27.2611i | −0.194326 | − | 1.04388i | ||||
\(683\) | 24.2808 | 0.929080 | 0.464540 | − | 0.885552i | \(-0.346220\pi\) | ||||
0.464540 | + | 0.885552i | \(0.346220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.86370 | −0.147625 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 21.1244 | + | 23.3123i | 0.805359 | + | 0.888774i | ||||
\(689\) | 12.9282i | 0.492525i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 37.4390i | − | 1.42425i | −0.702054 | − | 0.712124i | \(-0.747733\pi\) | ||
0.702054 | − | 0.712124i | \(-0.252267\pi\) | |||||||
\(692\) | 6.95236 | + | 18.0263i | 0.264289 | + | 0.685256i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0981 | − | 5.23065i | 1.06659 | − | 0.198553i | ||||
\(695\) | 8.14233 | 0.308856 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.6410 | 1.38788 | ||||||||
\(698\) | 15.9743 | − | 2.97372i | 0.604635 | − | 0.112557i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.2591i | 1.82272i | 0.411608 | + | 0.911361i | \(0.364967\pi\) | ||||
−0.411608 | + | 0.911361i | \(0.635033\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.2650i | 0.726591i | ||||||||
\(704\) | −7.32418 | + | 14.5446i | −0.276040 | + | 0.548172i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.29770 | − | 39.2019i | −0.274653 | − | 1.47538i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.928203 | −0.0348594 | −0.0174297 | − | 0.999848i | \(-0.505548\pi\) | ||||
−0.0174297 | + | 0.999848i | \(0.505548\pi\) | |||||||
\(710\) | −1.72171 | − | 9.24871i | −0.0646146 | − | 0.347098i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.9546 | + | 21.0278i | 0.485492 | + | 0.788051i | ||||
\(713\) | 19.6077i | 0.734314i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.10739i | − | 0.0788119i | ||||||
\(716\) | 32.1504 | − | 12.3998i | 1.20152 | − | 0.463401i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.6340 | + | 2.35190i | −0.471496 | + | 0.0877721i | ||||
\(719\) | −52.9468 | −1.97458 | −0.987291 | − | 0.158921i | \(-0.949198\pi\) | ||||
−0.987291 | + | 0.158921i | \(0.949198\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.5841 | − | 3.08725i | 0.617197 | − | 0.114895i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.33109 | + | 3.59881i | −0.346787 | + | 0.133749i | ||||
\(725\) | 23.5612i | 0.875039i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7233i | 0.397707i | 0.980029 | + | 0.198853i | \(0.0637218\pi\) | ||||
−0.980029 | + | 0.198853i | \(0.936278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.320508 | − | 1.72171i | −0.0118625 | − | 0.0637234i | ||||
\(731\) | 33.0023 | 1.22063 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1427 | 0.707050 | 0.353525 | − | 0.935425i | \(-0.384983\pi\) | ||||
0.353525 | + | 0.935425i | \(0.384983\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.97372 | − | 9.16309i | 0.257055 | − | 0.337756i | ||||
\(737\) | − | 5.85993i | − | 0.215853i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12.8510i | − | 0.472732i | −0.971664 | − | 0.236366i | \(-0.924043\pi\) | ||
0.971664 | − | 0.236366i | \(-0.0759565\pi\) | |||||||
\(740\) | 1.82505 | + | 4.73205i | 0.0670903 | + | 0.173954i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.3717 | −0.930797 | −0.465399 | − | 0.885101i | \(-0.654089\pi\) | ||||
−0.465399 | + | 0.885101i | \(0.654089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.10583 | −0.113789 | ||||||||
\(746\) | −23.5358 | + | 4.38134i | −0.861705 | + | 0.160412i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.14729 | + | 15.9389i | 0.224767 | + | 0.582783i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.0023i | 1.20427i | 0.798395 | + | 0.602135i | \(0.205683\pi\) | ||||
−0.798395 | + | 0.602135i | \(0.794317\pi\) | |||||||
\(752\) | 31.8452 | − | 28.8564i | 1.16128 | − | 1.05228i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.93185 | − | 10.3776i | −0.0703539 | − | 0.377928i | ||||
\(755\) | −5.75749 | −0.209537 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.6410 | 1.47712 | 0.738561 | − | 0.674186i | \(-0.235505\pi\) | ||||
0.738561 | + | 0.674186i | \(0.235505\pi\) | |||||||
\(758\) | 7.05146 | + | 37.8792i | 0.256121 | + | 1.37583i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.80385 | − | 6.03983i | 0.355623 | − | 0.219088i | ||||
\(761\) | − | 37.1244i | − | 1.34576i | −0.739753 | − | 0.672878i | \(-0.765058\pi\) | ||
0.739753 | − | 0.672878i | \(-0.234942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.5536 | − | 9.46979i | 0.888316 | − | 0.342605i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.8744 | + | 5.56131i | −1.07940 | + | 0.200938i | ||||
\(767\) | −7.05146 | −0.254614 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.72689 | −0.0983342 | −0.0491671 | − | 0.998791i | \(-0.515657\pi\) | ||||
−0.0491671 | + | 0.998791i | \(0.515657\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.3923 | + | 7.09353i | −0.661954 | + | 0.255302i | ||||
\(773\) | 11.5167i | 0.414225i | 0.978317 | + | 0.207113i | \(0.0664067\pi\) | ||||
−0.978317 | + | 0.207113i | \(0.933593\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 43.0004i | − | 1.54462i | ||||||
\(776\) | −36.3045 | + | 22.3660i | −1.30326 | + | 0.802894i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.43782 | + | 45.3264i | 0.302511 | + | 1.62503i | ||||
\(779\) | −48.5617 | −1.73990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.4974 | −0.661890 | ||||||||
\(782\) | −2.21073 | − | 11.8756i | −0.0790556 | − | 0.424672i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 11.0363i | − | 0.393903i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2967i | 1.04432i | 0.852849 | + | 0.522158i | \(0.174873\pi\) | ||||
−0.852849 | + | 0.522158i | \(0.825127\pi\) | |||||||
\(788\) | 11.0496 | + | 28.6496i | 0.393624 | + | 1.02060i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.07484 | − | 0.944717i | 0.180555 | − | 0.0336115i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.3205 | −0.473025 | ||||||||
\(794\) | −24.1215 | + | 4.49038i | −0.856040 | + | 0.159358i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.92996 | + | 7.59689i | 0.103850 | + | 0.269265i | ||||
\(797\) | 30.0526i | 1.06452i | 0.846582 | + | 0.532258i | \(0.178656\pi\) | ||||
−0.846582 | + | 0.532258i | \(0.821344\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 45.0819i | − | 1.59488i | ||||||
\(800\) | −15.2936 | + | 20.0950i | −0.540711 | + | 0.710465i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.90192 | + | 53.1913i | 0.349649 | + | 1.87825i | ||||
\(803\) | −3.44342 | −0.121516 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.52573 | + | 18.9396i | 0.124189 | + | 0.667118i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.81534 | + | 12.6858i | 0.274943 | + | 0.446287i | ||||
\(809\) | 24.7995i | 0.871904i | 0.899970 | + | 0.435952i | \(0.143588\pi\) | ||||
−0.899970 | + | 0.435952i | \(0.856412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.4390i | 1.31466i | 0.753602 | + | 0.657331i | \(0.228315\pi\) | ||||
−0.753602 | + | 0.657331i | \(0.771685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.80385 | − | 1.82505i | 0.343625 | − | 0.0639681i | ||||
\(815\) | −17.8372 | −0.624808 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.7391 | −1.53024 | ||||||||
\(818\) | −14.1492 | + | 2.63397i | −0.494716 | + | 0.0920948i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.9282 | + | 4.60046i | −0.416551 | + | 0.160655i | ||||
\(821\) | 5.55532i | 0.193882i | 0.995290 | + | 0.0969410i | \(0.0309058\pi\) | ||||
−0.995290 | + | 0.0969410i | \(0.969094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0161i | 0.976580i | 0.872681 | + | 0.488290i | \(0.162379\pi\) | ||||
−0.872681 | + | 0.488290i | \(0.837621\pi\) | |||||||
\(824\) | −24.7517 | − | 40.1769i | −0.862266 | − | 1.39963i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.2808 | −0.844327 | −0.422164 | − | 0.906520i | \(-0.638729\pi\) | ||||
−0.422164 | + | 0.906520i | \(0.638729\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.1619 | −1.77693 | −0.888463 | − | 0.458949i | \(-0.848226\pi\) | ||||
−0.888463 | + | 0.458949i | \(0.848226\pi\) | |||||||
\(830\) | 2.58101 | + | 13.8647i | 0.0895883 | + | 0.481252i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.08845 | − | 10.1048i | 0.176410 | − | 0.350322i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 7.86488i | − | 0.272176i | ||||||
\(836\) | −8.14722 | − | 21.1244i | −0.281778 | − | 0.730601i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.8768 | + | 6.30639i | −1.17025 | + | 0.217851i | ||||
\(839\) | −2.87875 | −0.0993854 | −0.0496927 | − | 0.998765i | \(-0.515824\pi\) | ||||
−0.0496927 | + | 0.998765i | \(0.515824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.14359 | 0.0394343 | ||||||||
\(842\) | 41.3106 | − | 7.69024i | 1.42366 | − | 0.265023i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.4641 | + | 40.0958i | 0.532296 | + | 1.38015i | ||||
\(845\) | − | 8.05256i | − | 0.277016i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.5536 | + | 27.0967i | 0.843172 | + | 0.930504i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.84821 | + | 26.0437i | 0.166292 | + | 0.893292i | ||||
\(851\) | −7.05146 | −0.241721 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.6307 | 0.535184 | 0.267592 | − | 0.963532i | \(-0.413772\pi\) | ||||
0.267592 | + | 0.963532i | \(0.413772\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.6865 | + | 19.5210i | −1.08302 | + | 0.667216i | ||||
\(857\) | − | 11.2679i | − | 0.384906i | −0.981306 | − | 0.192453i | \(-0.938356\pi\) | ||
0.981306 | − | 0.192453i | \(-0.0616443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 51.1427i | − | 1.74497i | −0.488645 | − | 0.872483i | \(-0.662509\pi\) | ||
0.488645 | − | 0.872483i | \(-0.337491\pi\) | |||||||
\(860\) | −10.7436 | + | 4.14359i | −0.366355 | + | 0.141295i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −45.0788 | + | 8.39173i | −1.53539 | + | 0.285824i | ||||
\(863\) | 31.3323 | 1.06656 | 0.533282 | − | 0.845938i | \(-0.320959\pi\) | ||||
0.533282 | + | 0.845938i | \(0.320959\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.07180 | −0.240448 | ||||||||
\(866\) | 20.5747 | − | 3.83013i | 0.699158 | − | 0.130153i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.1497i | − | 0.344305i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.07116i | 0.137946i | ||||||||
\(872\) | −14.4487 | + | 8.90138i | −0.489295 | + | 0.301439i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.92996 | + | 15.7392i | 0.0991075 | + | 0.532387i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.3205 | 0.787478 | 0.393739 | − | 0.919222i | \(-0.371181\pi\) | ||||
0.393739 | + | 0.919222i | \(0.371181\pi\) | |||||||
\(878\) | 7.09353 | + | 38.1051i | 0.239395 | + | 1.28599i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.00240 | − | 4.41695i | −0.134921 | − | 0.148895i | ||||
\(881\) | 42.4449i | 1.43000i | 0.699123 | + | 0.715002i | \(0.253574\pi\) | ||||
−0.699123 | + | 0.715002i | \(0.746426\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.40760i | 0.316591i | 0.987392 | + | 0.158295i | \(0.0505999\pi\) | ||||
−0.987392 | + | 0.158295i | \(0.949400\pi\) | |||||||
\(884\) | −4.27081 | − | 11.0735i | −0.143643 | − | 0.372441i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.1506 | − | 2.63424i | 0.475400 | − | 0.0884989i | ||||
\(887\) | 26.4734 | 0.888890 | 0.444445 | − | 0.895806i | \(-0.353401\pi\) | ||||
0.444445 | + | 0.895806i | \(0.353401\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.88740 | + | 1.65445i | −0.297906 | + | 0.0554573i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.9348 | − | 28.3520i | −0.366123 | − | 0.949295i | ||||
\(893\) | 59.7487i | 1.99941i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.6128i | 0.421599i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.36603 | + | 44.9407i | 0.279178 | + | 1.49969i | ||||
\(899\) | 50.8394 | 1.69559 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.3596 | 1.27794 | ||||||||
\(902\) | 4.60046 | + | 24.7128i | 0.153178 | + | 0.822847i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.973721 | − | 1.58054i | −0.0323855 | − | 0.0525680i | ||||
\(905\) | − | 3.66063i | − | 0.121684i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 17.8372i | − | 0.592273i | −0.955146 | − | 0.296137i | \(-0.904302\pi\) | ||
0.955146 | − | 0.296137i | \(-0.0956983\pi\) | |||||||
\(908\) | 20.0479 | − | 7.73205i | 0.665313 | − | 0.256597i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.4943 | 1.20911 | 0.604555 | − | 0.796563i | \(-0.293351\pi\) | ||||
0.604555 | + | 0.796563i | \(0.293351\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.7295 | 0.917711 | ||||||||
\(914\) | 31.8777 | − | 5.93426i | 1.05442 | − | 0.196288i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 47.3118 | − | 18.2472i | 1.56323 | − | 0.602903i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 29.3521i | − | 0.968238i | −0.875002 | − | 0.484119i | \(-0.839140\pi\) | ||
0.875002 | − | 0.484119i | \(-0.160860\pi\) | |||||||
\(920\) | 2.21073 | + | 3.58846i | 0.0728857 | + | 0.118308i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.39872 | + | 12.8855i | 0.0789977 | + | 0.424361i | ||||
\(923\) | 12.8510 | 0.422997 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4641 | 0.508457 | ||||||||
\(926\) | 1.83594 | + | 9.86233i | 0.0603327 | + | 0.324096i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.7583 | − | 18.0817i | −0.779905 | − | 0.593560i | ||||
\(929\) | − | 45.9090i | − | 1.50622i | −0.657892 | − | 0.753112i | \(-0.728552\pi\) | ||
0.657892 | − | 0.753112i | \(-0.271448\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.19773 | + | 10.8840i | 0.137501 | + | 0.356517i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.8671 | − | 3.32609i | 0.584631 | − | 0.108833i | ||||
\(935\) | −6.25289 | −0.204491 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.9513 | 1.79518 | 0.897590 | − | 0.440832i | \(-0.145317\pi\) | ||||
0.897590 | + | 0.440832i | \(0.145317\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.66025 | + | 14.6761i | 0.184617 | + | 0.478681i | ||||
\(941\) | − | 61.2295i | − | 1.99602i | −0.0630259 | − | 0.998012i | \(-0.520075\pi\) | ||
0.0630259 | − | 0.998012i | \(-0.479925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 17.7748i | − | 0.578827i | ||||||
\(944\) | −14.7794 | + | 13.3923i | −0.481029 | + | 0.435882i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.14359 | + | 22.2586i | 0.134720 | + | 0.723690i | ||||
\(947\) | 24.2808 | 0.789021 | 0.394511 | − | 0.918891i | \(-0.370914\pi\) | ||||
0.394511 | + | 0.918891i | \(0.370914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.39230 | 0.0776575 | ||||||||
\(950\) | −6.42551 | − | 34.5167i | −0.208471 | − | 1.11987i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.656339i | 0.0212609i | 0.999943 | + | 0.0106304i | \(0.00338384\pi\) | ||||
−0.999943 | + | 0.0106304i | \(0.996616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.63248i | 0.311700i | ||||||||
\(956\) | 3.79845 | − | 1.46498i | 0.122851 | − | 0.0473809i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.8671 | + | 3.32609i | −0.577261 | + | 0.107461i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −61.7846 | −1.99305 | ||||||||
\(962\) | −6.81119 | + | 1.26795i | −0.219602 | + | 0.0408803i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.2683 | − | 9.35976i | 0.781628 | − | 0.301458i | ||||
\(965\) | − | 7.21539i | − | 0.232272i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.3383i | − | 1.10424i | −0.833763 | − | 0.552122i | \(-0.813818\pi\) | ||
0.833763 | − | 0.552122i | \(-0.186182\pi\) | |||||||
\(968\) | 16.5110 | − | 10.1719i | 0.530685 | − | 0.326938i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.85641 | − | 15.3441i | −0.0917137 | − | 0.492669i | ||||
\(971\) | −23.5947 | −0.757188 | −0.378594 | − | 0.925563i | \(-0.623592\pi\) | ||||
−0.378594 | + | 0.925563i | \(0.623592\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.52573 | + | 18.9396i | 0.112972 | + | 0.606863i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9189 | + | 25.2986i | −0.893663 | + | 0.809789i | ||||
\(977\) | − | 26.3896i | − | 0.844278i | −0.906531 | − | 0.422139i | \(-0.861279\pi\) | ||
0.906531 | − | 0.422139i | \(-0.138721\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.7748i | 0.568085i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.2942 | − | 3.40559i | 0.583792 | − | 0.108677i | ||||
\(983\) | 12.0797 | 0.385281 | 0.192641 | − | 0.981269i | \(-0.438295\pi\) | ||||
0.192641 | + | 0.981269i | \(0.438295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2394 | −0.358116 | ||||||||
\(986\) | −30.7915 | + | 5.73205i | −0.980602 | + | 0.182546i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.66025 | + | 14.6761i | 0.180077 | + | 0.466908i | ||||
\(989\) | − | 16.0096i | − | 0.509076i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5947i | 0.749509i | 0.927124 | + | 0.374754i | \(0.122273\pi\) | ||||
−0.927124 | + | 0.374754i | \(0.877727\pi\) | |||||||
\(992\) | 43.3602 | + | 33.0000i | 1.37669 | + | 1.04775i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.98030 | −0.0944818 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.27792 | −0.167153 | −0.0835767 | − | 0.996501i | \(-0.526634\pi\) | ||||
−0.0835767 | + | 0.996501i | \(0.526634\pi\) | |||||||
\(998\) | 7.59689 | + | 40.8091i | 0.240476 | + | 1.29179i | ||||
\(999\) | 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 | 1764.2.e.j.1079.4 | yes | 16 | |
3.2 | odd | 2 | inner | 1764.2.e.j.1079.13 | yes | 16 | |
4.3 | odd | 2 | inner | 1764.2.e.j.1079.16 | yes | 16 | |
7.6 | odd | 2 | inner | 1764.2.e.j.1079.3 | yes | 16 | |
12.11 | even | 2 | inner | 1764.2.e.j.1079.1 | ✓ | 16 | |
21.20 | even | 2 | inner | 1764.2.e.j.1079.14 | yes | 16 | |
28.27 | even | 2 | inner | 1764.2.e.j.1079.15 | yes | 16 | |
84.83 | odd | 2 | inner | 1764.2.e.j.1079.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.e.j.1079.1 | ✓ | 16 | 12.11 | even | 2 | inner | |
1764.2.e.j.1079.2 | yes | 16 | 84.83 | odd | 2 | inner | |
1764.2.e.j.1079.3 | yes | 16 | 7.6 | odd | 2 | inner | |
1764.2.e.j.1079.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1764.2.e.j.1079.13 | yes | 16 | 3.2 | odd | 2 | inner | |
1764.2.e.j.1079.14 | yes | 16 | 21.20 | even | 2 | inner | |
1764.2.e.j.1079.15 | yes | 16 | 28.27 | even | 2 | inner | |
1764.2.e.j.1079.16 | yes | 16 | 4.3 | odd | 2 | inner |