Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,2,Mod(2204,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2205.2204");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.g (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: | \(17.6070136457\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2204.7 | ||
Character | \(\chi\) | \(=\) | 2205.2204 |
Dual form | 2205.2.g.b.2204.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times\).
\(n\) | \(442\) | \(1081\) | \(1226\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91314 | −1.35280 | −0.676399 | − | 0.736536i | \(-0.736460\pi\) | ||||
−0.676399 | + | 0.736536i | \(0.736460\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.66012 | 0.830062 | ||||||||
\(5\) | 0.630583 | − | 2.14531i | 0.282005 | − | 0.959413i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.650234 | 0.229892 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.20640 | + | 4.10429i | −0.381496 | + | 1.29789i | ||||
\(11\) | 3.22740i | 0.973099i | 0.873653 | + | 0.486549i | \(0.161745\pi\) | ||||
−0.873653 | + | 0.486549i | \(0.838255\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.86146 | −1.34833 | −0.674164 | − | 0.738582i | \(-0.735496\pi\) | ||||
−0.674164 | + | 0.738582i | \(0.735496\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.56424 | −1.14106 | ||||||||
\(17\) | 0.729142i | 0.176843i | 0.996083 | + | 0.0884215i | \(0.0281822\pi\) | ||||
−0.996083 | + | 0.0884215i | \(0.971818\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.87149i | 1.80584i | 0.429805 | + | 0.902922i | \(0.358582\pi\) | ||||
−0.429805 | + | 0.902922i | \(0.641418\pi\) | |||||||
\(20\) | 1.04685 | − | 3.56148i | 0.234082 | − | 0.796372i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 6.17449i | − | 1.31641i | ||||||
\(23\) | 4.86820 | 1.01509 | 0.507545 | − | 0.861625i | \(-0.330553\pi\) | ||||
0.507545 | + | 0.861625i | \(0.330553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.20473 | − | 2.70560i | −0.840946 | − | 0.541119i | ||||
\(26\) | 9.30068 | 1.82401 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.75958i | − | 1.44092i | −0.693498 | − | 0.720459i | \(-0.743931\pi\) | ||
0.693498 | − | 0.720459i | \(-0.256069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.42896i | − | 0.256648i | −0.991732 | − | 0.128324i | \(-0.959040\pi\) | ||
0.991732 | − | 0.128324i | \(-0.0409597\pi\) | |||||||
\(32\) | 7.43158 | 1.31373 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.39495i | − | 0.239233i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.16538i | − | 0.520385i | −0.965557 | − | 0.260193i | \(-0.916214\pi\) | ||
0.965557 | − | 0.260193i | \(-0.0837861\pi\) | |||||||
\(38\) | − | 15.0593i | − | 2.44294i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.410026 | − | 1.39495i | 0.0648309 | − | 0.220562i | ||||
\(41\) | 1.40264 | 0.219056 | 0.109528 | − | 0.993984i | \(-0.465066\pi\) | ||||
0.109528 | + | 0.993984i | \(0.465066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.42489i | − | 0.979787i | −0.871782 | − | 0.489893i | \(-0.837036\pi\) | ||
0.871782 | − | 0.489893i | \(-0.162964\pi\) | |||||||
\(44\) | 5.35789i | 0.807732i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.31357 | −1.37321 | ||||||||
\(47\) | − | 4.87049i | − | 0.710434i | −0.934784 | − | 0.355217i | \(-0.884407\pi\) | ||
0.934784 | − | 0.355217i | \(-0.115593\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8.04426 | + | 5.17620i | 1.13763 | + | 0.732025i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.07063 | −1.11919 | ||||||||
\(53\) | −1.52147 | −0.208990 | −0.104495 | − | 0.994525i | \(-0.533323\pi\) | ||||
−0.104495 | + | 0.994525i | \(0.533323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92379 | + | 2.03515i | 0.933603 | + | 0.274419i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.8452i | 1.94927i | ||||||||
\(59\) | 6.30162 | 0.820402 | 0.410201 | − | 0.911995i | \(-0.365459\pi\) | ||||
0.410201 | + | 0.911995i | \(0.365459\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.37224i | 0.303735i | 0.988401 | + | 0.151867i | \(0.0485286\pi\) | ||||
−0.988401 | + | 0.151867i | \(0.951471\pi\) | |||||||
\(62\) | 2.73380i | 0.347193i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.08921 | −0.636152 | ||||||||
\(65\) | −3.06556 | + | 10.4294i | −0.380235 | + | 1.29360i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 11.1259i | − | 1.35924i | −0.733562 | − | 0.679622i | \(-0.762144\pi\) | ||
0.733562 | − | 0.679622i | \(-0.237856\pi\) | |||||||
\(68\) | 1.21047i | 0.146791i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.1351i | − | 1.20282i | −0.798942 | − | 0.601408i | \(-0.794607\pi\) | ||
0.798942 | − | 0.601408i | \(-0.205393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.8239 | −1.61796 | −0.808982 | − | 0.587833i | \(-0.799981\pi\) | ||||
−0.808982 | + | 0.587833i | \(0.799981\pi\) | |||||||
\(74\) | 6.05583i | 0.703976i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.0676i | 1.49896i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.98037 | 0.447827 | 0.223913 | − | 0.974609i | \(-0.428117\pi\) | ||||
0.223913 | + | 0.974609i | \(0.428117\pi\) | |||||||
\(80\) | −2.87813 | + | 9.79171i | −0.321785 | + | 1.09475i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.68346 | −0.296339 | ||||||||
\(83\) | − | 4.19208i | − | 0.460141i | −0.973174 | − | 0.230070i | \(-0.926104\pi\) | ||
0.973174 | − | 0.230070i | \(-0.0738957\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.56424 | + | 0.459785i | 0.169665 | + | 0.0498706i | ||||
\(86\) | 12.2917i | 1.32545i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.09857i | 0.223708i | ||||||||
\(89\) | 11.2734 | 1.19498 | 0.597491 | − | 0.801875i | \(-0.296164\pi\) | ||||
0.597491 | + | 0.801875i | \(0.296164\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.08181 | 0.842587 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.31795i | 0.961073i | ||||||||
\(95\) | 16.8868 | + | 4.96363i | 1.73255 | + | 0.509258i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.21388 | 0.224785 | 0.112393 | − | 0.993664i | \(-0.464149\pi\) | ||||
0.112393 | + | 0.993664i | \(0.464149\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.98037 | − | 4.49162i | −0.698037 | − | 0.449162i | ||||
\(101\) | −11.7021 | −1.16440 | −0.582201 | − | 0.813045i | \(-0.697808\pi\) | ||||
−0.582201 | + | 0.813045i | \(0.697808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.585261 | −0.0576674 | −0.0288337 | − | 0.999584i | \(-0.509179\pi\) | ||||
−0.0288337 | + | 0.999584i | \(0.509179\pi\) | |||||||
\(104\) | −3.16109 | −0.309970 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.91079 | 0.282721 | ||||||||
\(107\) | −1.69215 | −0.163586 | −0.0817929 | − | 0.996649i | \(-0.526065\pi\) | ||||
−0.0817929 | + | 0.996649i | \(0.526065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4028 | −1.28375 | −0.641877 | − | 0.766808i | \(-0.721844\pi\) | ||||
−0.641877 | + | 0.766808i | \(0.721844\pi\) | |||||||
\(110\) | −13.2462 | − | 3.89353i | −1.26298 | − | 0.371233i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2129 | −1.33704 | −0.668520 | − | 0.743694i | \(-0.733072\pi\) | ||||
−0.668520 | + | 0.743694i | \(0.733072\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.06981 | − | 10.4438i | 0.286261 | − | 0.973891i | ||||
\(116\) | − | 12.8819i | − | 1.19605i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.0559 | −1.10984 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.583868 | 0.0530789 | ||||||||
\(122\) | − | 4.53844i | − | 0.410891i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 2.37224i | − | 0.213034i | ||||||
\(125\) | −8.45578 | + | 7.31436i | −0.756308 | + | 0.654216i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.08954i | 0.185417i | 0.995693 | + | 0.0927084i | \(0.0295524\pi\) | ||||
−0.995693 | + | 0.0927084i | \(0.970448\pi\) | |||||||
\(128\) | −5.12676 | −0.453146 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.86485 | − | 19.9529i | 0.514382 | − | 1.74998i | ||||
\(131\) | −11.2048 | −0.978969 | −0.489484 | − | 0.872012i | \(-0.662815\pi\) | ||||
−0.489484 | + | 0.872012i | \(0.662815\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 21.2855i | 1.83878i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.474113i | 0.0406548i | ||||||||
\(137\) | 7.03990 | 0.601459 | 0.300730 | − | 0.953709i | \(-0.402770\pi\) | ||||
0.300730 | + | 0.953709i | \(0.402770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.45903i | − | 0.547848i | −0.961751 | − | 0.273924i | \(-0.911678\pi\) | ||
0.961751 | − | 0.273924i | \(-0.0883216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.3899i | 1.62717i | ||||||||
\(143\) | − | 15.6899i | − | 1.31206i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.6467 | − | 4.89306i | −1.38243 | − | 0.406346i | ||||
\(146\) | 26.4471 | 2.18878 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5.25492i | − | 0.431952i | ||||||
\(149\) | − | 23.5515i | − | 1.92942i | −0.263320 | − | 0.964709i | \(-0.584818\pi\) | ||
0.263320 | − | 0.964709i | \(-0.415182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1088 | 1.47368 | 0.736838 | − | 0.676069i | \(-0.236318\pi\) | ||||
0.736838 | + | 0.676069i | \(0.236318\pi\) | |||||||
\(152\) | 5.11831i | 0.415150i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.06556 | − | 0.901075i | −0.246231 | − | 0.0723761i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.48454 | 0.198288 | 0.0991441 | − | 0.995073i | \(-0.468390\pi\) | ||||
0.0991441 | + | 0.995073i | \(0.468390\pi\) | |||||||
\(158\) | −7.61502 | −0.605819 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.68623 | − | 15.9431i | 0.370479 | − | 1.26041i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.93771i | 0.308425i | 0.988038 | + | 0.154212i | \(0.0492840\pi\) | ||||
−0.988038 | + | 0.154212i | \(0.950716\pi\) | |||||||
\(164\) | 2.32856 | 0.181830 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.02006i | 0.622478i | ||||||||
\(167\) | − | 5.31832i | − | 0.411544i | −0.978600 | − | 0.205772i | \(-0.934029\pi\) | ||
0.978600 | − | 0.205772i | \(-0.0659705\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6338 | 0.817986 | ||||||||
\(170\) | −2.99261 | − | 0.879635i | −0.229523 | − | 0.0674649i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 10.6661i | − | 0.813283i | ||||||
\(173\) | 7.45501i | 0.566794i | 0.959003 | + | 0.283397i | \(0.0914614\pi\) | ||||
−0.959003 | + | 0.283397i | \(0.908539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 14.7306i | − | 1.11036i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −21.5677 | −1.61657 | ||||||||
\(179\) | − | 13.3070i | − | 0.994611i | −0.867576 | − | 0.497305i | \(-0.834323\pi\) | ||
0.867576 | − | 0.497305i | \(-0.165677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.95814i | − | 0.740183i | −0.928995 | − | 0.370091i | \(-0.879326\pi\) | ||
0.928995 | − | 0.370091i | \(-0.120674\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.16547 | 0.233361 | ||||||||
\(185\) | −6.79073 | − | 1.99604i | −0.499264 | − | 0.146751i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.35324 | −0.172086 | ||||||||
\(188\) | − | 8.08561i | − | 0.589704i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −32.3069 | − | 9.49614i | −2.34379 | − | 0.688922i | ||||
\(191\) | − | 24.6113i | − | 1.78081i | −0.455171 | − | 0.890404i | \(-0.650422\pi\) | ||
0.455171 | − | 0.890404i | \(-0.349578\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.5143i | 0.900797i | 0.892828 | + | 0.450399i | \(0.148718\pi\) | ||||
−0.892828 | + | 0.450399i | \(0.851282\pi\) | |||||||
\(194\) | −4.23547 | −0.304089 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.6968 | 1.11835 | 0.559177 | − | 0.829049i | \(-0.311117\pi\) | ||||
0.559177 | + | 0.829049i | \(0.311117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7958i | 1.40328i | 0.712529 | + | 0.701642i | \(0.247550\pi\) | ||||
−0.712529 | + | 0.701642i | \(0.752450\pi\) | |||||||
\(200\) | −2.73406 | − | 1.75927i | −0.193327 | − | 0.124399i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.3878 | 1.57520 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.884484 | − | 3.00911i | 0.0617750 | − | 0.210165i | ||||
\(206\) | 1.11969 | 0.0780124 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.1889 | 1.53852 | ||||||||
\(209\) | −25.4045 | −1.75726 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5839 | 0.797466 | 0.398733 | − | 0.917067i | \(-0.369450\pi\) | ||||
0.398733 | + | 0.917067i | \(0.369450\pi\) | |||||||
\(212\) | −2.52582 | −0.173474 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.23732 | 0.221299 | ||||||||
\(215\) | −13.7834 | − | 4.05143i | −0.940020 | − | 0.276305i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 25.6415 | 1.73666 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.4943 | + | 3.37859i | 0.774948 | + | 0.227785i | ||||
\(221\) | − | 3.54470i | − | 0.238442i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.1321 | −1.61600 | −0.808002 | − | 0.589180i | \(-0.799451\pi\) | ||||
−0.808002 | + | 0.589180i | \(0.799451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27.1914 | 1.80874 | ||||||||
\(227\) | 10.1888i | 0.676255i | 0.941100 | + | 0.338128i | \(0.109794\pi\) | ||||
−0.941100 | + | 0.338128i | \(0.890206\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.2548i | − | 1.73497i | −0.497467 | − | 0.867483i | \(-0.665736\pi\) | ||
0.497467 | − | 0.867483i | \(-0.334264\pi\) | |||||||
\(230\) | −5.87298 | + | 19.9805i | −0.387253 | + | 1.31748i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 5.04554i | − | 0.331256i | ||||||
\(233\) | −18.3933 | −1.20499 | −0.602494 | − | 0.798124i | \(-0.705826\pi\) | ||||
−0.602494 | + | 0.798124i | \(0.705826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.4487 | − | 3.07125i | −0.681599 | − | 0.200346i | ||||
\(236\) | 10.4615 | 0.680984 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.961317i | − | 0.0621824i | −0.999517 | − | 0.0310912i | \(-0.990102\pi\) | ||
0.999517 | − | 0.0310912i | \(-0.00989824\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.51054i | − | 0.419381i | −0.977768 | − | 0.209690i | \(-0.932754\pi\) | ||
0.977768 | − | 0.209690i | \(-0.0672456\pi\) | |||||||
\(242\) | −1.11702 | −0.0718050 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.93821i | 0.252118i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 38.2670i | − | 2.43487i | ||||||
\(248\) | − | 0.929155i | − | 0.0590014i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.1771 | − | 13.9934i | 1.02313 | − | 0.885022i | ||||
\(251\) | −2.02506 | −0.127820 | −0.0639102 | − | 0.997956i | \(-0.520357\pi\) | ||||
−0.0639102 | + | 0.997956i | \(0.520357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.7116i | 0.987783i | ||||||||
\(254\) | − | 3.99759i | − | 0.250831i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.9867 | 1.24917 | ||||||||
\(257\) | − | 18.1902i | − | 1.13467i | −0.823486 | − | 0.567337i | \(-0.807974\pi\) | ||
0.823486 | − | 0.567337i | \(-0.192026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.08920 | + | 17.3140i | −0.315619 | + | 1.07377i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.4364 | 1.32435 | ||||||||
\(263\) | −19.5607 | −1.20616 | −0.603082 | − | 0.797679i | \(-0.706061\pi\) | ||||
−0.603082 | + | 0.797679i | \(0.706061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.959411 | + | 3.26402i | −0.0589362 | + | 0.200507i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 18.4704i | − | 1.12826i | ||||||
\(269\) | −4.61602 | −0.281444 | −0.140722 | − | 0.990049i | \(-0.544942\pi\) | ||||
−0.140722 | + | 0.990049i | \(0.544942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7809i | 0.654894i | 0.944870 | + | 0.327447i | \(0.106188\pi\) | ||||
−0.944870 | + | 0.327447i | \(0.893812\pi\) | |||||||
\(272\) | − | 3.32798i | − | 0.201788i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.4684 | −0.813653 | ||||||||
\(275\) | 8.73205 | − | 13.5704i | 0.526562 | − | 0.818323i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 20.5068i | − | 1.23213i | −0.787694 | − | 0.616067i | \(-0.788725\pi\) | ||
0.787694 | − | 0.616067i | \(-0.211275\pi\) | |||||||
\(278\) | 12.3571i | 0.741127i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.714666i | 0.0426334i | 0.999773 | + | 0.0213167i | \(0.00678583\pi\) | ||||
−0.999773 | + | 0.0213167i | \(0.993214\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.0219 | −1.66573 | −0.832866 | − | 0.553475i | \(-0.813301\pi\) | ||||
−0.832866 | + | 0.553475i | \(0.813301\pi\) | |||||||
\(284\) | − | 16.8255i | − | 0.998411i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 30.0171i | 1.77495i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4684 | 0.968727 | ||||||||
\(290\) | 31.8476 | + | 9.36113i | 1.87015 | + | 0.549704i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.9494 | −1.34301 | ||||||||
\(293\) | − | 9.79171i | − | 0.572038i | −0.958224 | − | 0.286019i | \(-0.907668\pi\) | ||
0.958224 | − | 0.286019i | \(-0.0923321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.97370 | − | 13.5190i | 0.231358 | − | 0.787104i | ||||
\(296\) | − | 2.05824i | − | 0.119633i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 45.0575i | 2.61011i | ||||||||
\(299\) | −23.6666 | −1.36867 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −34.6448 | −1.99359 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 35.9273i | − | 2.06057i | ||||||
\(305\) | 5.08920 | + | 1.49590i | 0.291407 | + | 0.0856548i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.4778 | −1.45410 | −0.727048 | − | 0.686586i | \(-0.759108\pi\) | ||||
−0.727048 | + | 0.686586i | \(0.759108\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.86485 | + | 1.72389i | 0.333101 | + | 0.0979102i | ||||
\(311\) | −10.1084 | −0.573198 | −0.286599 | − | 0.958051i | \(-0.592525\pi\) | ||||
−0.286599 | + | 0.958051i | \(0.592525\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.4751 | −1.32689 | −0.663445 | − | 0.748225i | \(-0.730906\pi\) | ||||
−0.663445 | + | 0.748225i | \(0.730906\pi\) | |||||||
\(314\) | −4.75329 | −0.268244 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.60790 | 0.371724 | ||||||||
\(317\) | 31.4312 | 1.76535 | 0.882677 | − | 0.469980i | \(-0.155739\pi\) | ||||
0.882677 | + | 0.469980i | \(0.155739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.0433 | 1.40215 | ||||||||
\(320\) | −3.20917 | + | 10.9180i | −0.179398 | + | 0.610332i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.73943 | −0.319351 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.4411 | + | 13.1532i | 1.13387 | + | 0.729606i | ||||
\(326\) | − | 7.53340i | − | 0.417236i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.912047 | 0.0503593 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.17843 | −0.0647722 | −0.0323861 | − | 0.999475i | \(-0.510311\pi\) | ||||
−0.0323861 | + | 0.999475i | \(0.510311\pi\) | |||||||
\(332\) | − | 6.95937i | − | 0.381945i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.1747i | 0.556736i | ||||||||
\(335\) | −23.8685 | − | 7.01580i | −1.30408 | − | 0.383314i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.92868i | 0.214009i | 0.994259 | + | 0.107004i | \(0.0341259\pi\) | ||||
−0.994259 | + | 0.107004i | \(0.965874\pi\) | |||||||
\(338\) | −20.3440 | −1.10657 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.59683 | + | 0.763299i | 0.140833 | + | 0.0413957i | ||||
\(341\) | 4.61182 | 0.249744 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 4.17768i | − | 0.225245i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 14.2625i | − | 0.766758i | ||||||
\(347\) | −4.83065 | −0.259323 | −0.129661 | − | 0.991558i | \(-0.541389\pi\) | ||||
−0.129661 | + | 0.991558i | \(0.541389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.0461i | − | 0.858927i | −0.903084 | − | 0.429463i | \(-0.858703\pi\) | ||
0.903084 | − | 0.429463i | \(-0.141297\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.9847i | 1.27839i | ||||||||
\(353\) | 5.88094i | 0.313011i | 0.987677 | + | 0.156505i | \(0.0500229\pi\) | ||||
−0.987677 | + | 0.156505i | \(0.949977\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.7430 | − | 6.39103i | −1.15400 | − | 0.339200i | ||||
\(356\) | 18.7153 | 0.991909 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.4582i | 1.34551i | ||||||||
\(359\) | 8.08631i | 0.426779i | 0.976967 | + | 0.213389i | \(0.0684503\pi\) | ||||
−0.976967 | + | 0.213389i | \(0.931550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −42.9604 | −2.26107 | ||||||||
\(362\) | 19.0514i | 1.00132i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.71711 | + | 29.6566i | −0.456275 | + | 1.55230i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.5697 | 0.969329 | 0.484665 | − | 0.874700i | \(-0.338942\pi\) | ||||
0.484665 | + | 0.874700i | \(0.338942\pi\) | |||||||
\(368\) | −22.2196 | −1.15828 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.9916 | + | 3.81870i | 0.675404 | + | 0.198525i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.64346i | − | 0.136873i | −0.997655 | − | 0.0684365i | \(-0.978199\pi\) | ||
0.997655 | − | 0.0684365i | \(-0.0218011\pi\) | |||||||
\(374\) | 4.50208 | 0.232797 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 3.16696i | − | 0.163323i | ||||||
\(377\) | 37.7229i | 1.94283i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.8582 | −1.22551 | −0.612756 | − | 0.790272i | \(-0.709939\pi\) | ||||
−0.612756 | + | 0.790272i | \(0.709939\pi\) | |||||||
\(380\) | 28.0342 | + | 8.24023i | 1.43812 | + | 0.422715i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 47.0849i | 2.40907i | ||||||||
\(383\) | − | 11.1150i | − | 0.567952i | −0.958831 | − | 0.283976i | \(-0.908346\pi\) | ||
0.958831 | − | 0.283976i | \(-0.0916536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 23.9416i | − | 1.21860i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.67531 | 0.186586 | ||||||||
\(389\) | 12.5813i | 0.637896i | 0.947772 | + | 0.318948i | \(0.103330\pi\) | ||||
−0.947772 | + | 0.318948i | \(0.896670\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.54961i | 0.179512i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −30.0303 | −1.51291 | ||||||||
\(395\) | 2.50995 | − | 8.53914i | 0.126289 | − | 0.429651i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6309 | 1.43694 | 0.718471 | − | 0.695557i | \(-0.244842\pi\) | ||||
0.718471 | + | 0.695557i | \(0.244842\pi\) | |||||||
\(398\) | − | 37.8722i | − | 1.89836i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.1914 | + | 12.3490i | 0.959569 | + | 0.617449i | ||||
\(401\) | 11.8928i | 0.593897i | 0.954894 | + | 0.296948i | \(0.0959689\pi\) | ||||
−0.954894 | + | 0.296948i | \(0.904031\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.94681i | 0.346045i | ||||||||
\(404\) | −19.4269 | −0.966525 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2160 | 0.506386 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.4170i | − | 0.712877i | −0.934319 | − | 0.356438i | \(-0.883991\pi\) | ||
0.934319 | − | 0.356438i | \(-0.116009\pi\) | |||||||
\(410\) | −1.69215 | + | 5.75686i | −0.0835691 | + | 0.284311i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.971605 | −0.0478675 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.99333 | − | 2.64346i | −0.441465 | − | 0.129762i | ||||
\(416\) | −36.1283 | −1.77134 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 48.6024 | 2.37722 | ||||||||
\(419\) | 34.9400 | 1.70693 | 0.853466 | − | 0.521149i | \(-0.174496\pi\) | ||||
0.853466 | + | 0.521149i | \(0.174496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.8515 | 1.16245 | 0.581226 | − | 0.813742i | \(-0.302573\pi\) | ||||
0.581226 | + | 0.813742i | \(0.302573\pi\) | |||||||
\(422\) | −22.1616 | −1.07881 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.989309 | −0.0480451 | ||||||||
\(425\) | 1.97276 | − | 3.06585i | 0.0956931 | − | 0.148715i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.80917 | −0.135786 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.3696 | + | 7.75097i | 1.27166 | + | 0.373785i | ||||
\(431\) | 8.15855i | 0.392984i | 0.980505 | + | 0.196492i | \(0.0629549\pi\) | ||||
−0.980505 | + | 0.196492i | \(0.937045\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.2667 | 1.21424 | 0.607121 | − | 0.794610i | \(-0.292324\pi\) | ||||
0.607121 | + | 0.794610i | \(0.292324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.2503 | −1.06560 | ||||||||
\(437\) | 38.3200i | 1.83309i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.794714i | 0.0379296i | 0.999820 | + | 0.0189648i | \(0.00603705\pi\) | ||||
−0.999820 | + | 0.0189648i | \(0.993963\pi\) | |||||||
\(440\) | 4.50208 | + | 1.32332i | 0.214628 | + | 0.0630868i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.78152i | 0.322564i | ||||||||
\(443\) | 22.6489 | 1.07608 | 0.538040 | − | 0.842919i | \(-0.319165\pi\) | ||||
0.538040 | + | 0.842919i | \(0.319165\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.10884 | − | 24.1851i | 0.336992 | − | 1.14648i | ||||
\(446\) | 46.1682 | 2.18613 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.15664i | 0.101778i | 0.998704 | + | 0.0508891i | \(0.0162055\pi\) | ||||
−0.998704 | + | 0.0508891i | \(0.983794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.52690i | 0.213163i | ||||||||
\(452\) | −23.5952 | −1.10983 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 19.4927i | − | 0.914836i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 5.47333i | − | 0.256032i | −0.991772 | − | 0.128016i | \(-0.959139\pi\) | ||
0.991772 | − | 0.128016i | \(-0.0408608\pi\) | |||||||
\(458\) | 50.2292i | 2.34706i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.09626 | − | 17.3380i | 0.237614 | − | 0.808389i | ||||
\(461\) | 10.1084 | 0.470797 | 0.235399 | − | 0.971899i | \(-0.424360\pi\) | ||||
0.235399 | + | 0.971899i | \(0.424360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0455i | 0.559800i | 0.960029 | + | 0.279900i | \(0.0903014\pi\) | ||||
−0.960029 | + | 0.279900i | \(0.909699\pi\) | |||||||
\(464\) | 35.4165i | 1.64417i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.1891 | 1.63010 | ||||||||
\(467\) | 19.9327i | 0.922376i | 0.887302 | + | 0.461188i | \(0.152577\pi\) | ||||
−0.887302 | + | 0.461188i | \(0.847423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19.9899 | + | 5.87574i | 0.922066 | + | 0.271028i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.09753 | 0.188604 | ||||||||
\(473\) | 20.7357 | 0.953429 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.2971 | − | 33.0975i | 0.977176 | − | 1.51862i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.83914i | 0.0841202i | ||||||||
\(479\) | 19.3858 | 0.885760 | 0.442880 | − | 0.896581i | \(-0.353957\pi\) | ||||
0.442880 | + | 0.896581i | \(0.353957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.3884i | 0.701650i | ||||||||
\(482\) | 12.4556i | 0.567337i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.969293 | 0.0440588 | ||||||||
\(485\) | 1.39603 | − | 4.74946i | 0.0633906 | − | 0.215662i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.84816i | − | 0.0837483i | −0.999123 | − | 0.0418742i | \(-0.986667\pi\) | ||
0.999123 | − | 0.0418742i | \(-0.0133329\pi\) | |||||||
\(488\) | 1.54251i | 0.0698262i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 25.4836i | − | 1.15006i | −0.818133 | − | 0.575030i | \(-0.804991\pi\) | ||
0.818133 | − | 0.575030i | \(-0.195009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.65783 | 0.254816 | ||||||||
\(494\) | 73.2102i | 3.29388i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.52209i | 0.292851i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.2284 | −1.17414 | −0.587072 | − | 0.809535i | \(-0.699719\pi\) | ||||
−0.587072 | + | 0.809535i | \(0.699719\pi\) | |||||||
\(500\) | −14.0376 | + | 12.1427i | −0.627782 | + | 0.543039i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.87422 | 0.172915 | ||||||||
\(503\) | − | 4.25713i | − | 0.189816i | −0.995486 | − | 0.0949081i | \(-0.969744\pi\) | ||
0.995486 | − | 0.0949081i | \(-0.0302557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.37914 | + | 25.1046i | −0.328367 | + | 1.11714i | ||||
\(506\) | − | 30.0587i | − | 1.33627i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.46889i | 0.153907i | ||||||||
\(509\) | −19.1192 | −0.847443 | −0.423722 | − | 0.905792i | \(-0.639277\pi\) | ||||
−0.423722 | + | 0.905792i | \(0.639277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −27.9839 | −1.23672 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34.8005i | 1.53498i | ||||||||
\(515\) | −0.369055 | + | 1.25557i | −0.0162625 | + | 0.0553269i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.7190 | 0.691322 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.99333 | + | 6.78152i | −0.0874132 | + | 0.297389i | ||||
\(521\) | 22.8135 | 0.999478 | 0.499739 | − | 0.866176i | \(-0.333429\pi\) | ||||
0.499739 | + | 0.866176i | \(0.333429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.12936 | −0.136838 | −0.0684188 | − | 0.997657i | \(-0.521795\pi\) | ||||
−0.0684188 | + | 0.997657i | \(0.521795\pi\) | |||||||
\(524\) | −18.6014 | −0.812604 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 37.4224 | 1.63169 | ||||||||
\(527\) | 1.04191 | 0.0453864 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.699384 | 0.0304080 | ||||||||
\(530\) | 1.83549 | − | 6.24455i | 0.0797287 | − | 0.271246i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.81890 | −0.295359 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.06704 | + | 3.63018i | −0.0461321 | + | 0.156946i | ||||
\(536\) | − | 7.23443i | − | 0.312480i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.83112 | 0.380737 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.4617 | −0.965703 | −0.482852 | − | 0.875702i | \(-0.660399\pi\) | ||||
−0.482852 | + | 0.875702i | \(0.660399\pi\) | |||||||
\(542\) | − | 20.6254i | − | 0.885939i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.41868i | 0.232324i | ||||||||
\(545\) | −8.45157 | + | 28.7532i | −0.362026 | + | 1.23165i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4567i | 0.447097i | 0.974693 | + | 0.223549i | \(0.0717642\pi\) | ||||
−0.974693 | + | 0.223549i | \(0.928236\pi\) | |||||||
\(548\) | 11.6871 | 0.499248 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.7057 | + | 25.9621i | −0.712332 | + | 1.10703i | ||||
\(551\) | 61.0794 | 2.60207 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 39.2324i | 1.66683i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 10.7228i | − | 0.454747i | ||||||
\(557\) | 31.2478 | 1.32401 | 0.662006 | − | 0.749499i | \(-0.269705\pi\) | ||||
0.662006 | + | 0.749499i | \(0.269705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.2344i | 1.32107i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 1.36726i | − | 0.0576744i | ||||||
\(563\) | − | 29.8708i | − | 1.25890i | −0.777040 | − | 0.629452i | \(-0.783280\pi\) | ||
0.777040 | − | 0.629452i | \(-0.216720\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.96243 | + | 30.4912i | −0.377052 | + | 1.28277i | ||||
\(566\) | 53.6100 | 2.25340 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.59019i | − | 0.276518i | ||||||
\(569\) | 28.8927i | 1.21125i | 0.795752 | + | 0.605623i | \(0.207076\pi\) | ||||
−0.795752 | + | 0.605623i | \(0.792924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.37687 | −0.308712 | −0.154356 | − | 0.988015i | \(-0.549330\pi\) | ||||
−0.154356 | + | 0.988015i | \(0.549330\pi\) | |||||||
\(572\) | − | 26.0472i | − | 1.08909i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.4695 | − | 13.1714i | −0.853636 | − | 0.549285i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0757 | 0.752502 | 0.376251 | − | 0.926518i | \(-0.377213\pi\) | ||||
0.376251 | + | 0.926518i | \(0.377213\pi\) | |||||||
\(578\) | −31.5063 | −1.31049 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27.6356 | − | 8.12308i | −1.14751 | − | 0.337292i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.91039i | − | 0.203367i | ||||||
\(584\) | −8.98876 | −0.371958 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.7330i | 0.773852i | ||||||||
\(587\) | − | 35.0876i | − | 1.44822i | −0.689684 | − | 0.724111i | \(-0.742250\pi\) | ||
0.689684 | − | 0.724111i | \(-0.257750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.2480 | 0.463466 | ||||||||
\(590\) | −7.60226 | + | 25.8637i | −0.312980 | + | 1.06479i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.4475i | 0.593790i | ||||||||
\(593\) | − | 7.05792i | − | 0.289834i | −0.989444 | − | 0.144917i | \(-0.953709\pi\) | ||
0.989444 | − | 0.144917i | \(-0.0462915\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 39.0984i | − | 1.60153i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 45.2776 | 1.85154 | ||||||||
\(599\) | − | 4.88666i | − | 0.199664i | −0.995004 | − | 0.0998318i | \(-0.968170\pi\) | ||
0.995004 | − | 0.0998318i | \(-0.0318305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1905i | 1.47624i | 0.674669 | + | 0.738121i | \(0.264286\pi\) | ||||
−0.674669 | + | 0.738121i | \(0.735714\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30.0629 | 1.22324 | ||||||||
\(605\) | 0.368177 | − | 1.25258i | 0.0149685 | − | 0.0509246i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.9254 | −0.686982 | −0.343491 | − | 0.939156i | \(-0.611609\pi\) | ||||
−0.343491 | + | 0.939156i | \(0.611609\pi\) | |||||||
\(608\) | 58.4976i | 2.37239i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.73638 | − | 2.86187i | −0.394214 | − | 0.115874i | ||||
\(611\) | 23.6777i | 0.957897i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.6055i | 0.751469i | 0.926727 | + | 0.375735i | \(0.122610\pi\) | ||||
−0.926727 | + | 0.375735i | \(0.877390\pi\) | |||||||
\(614\) | 48.7428 | 1.96710 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.6022 | −1.79562 | −0.897809 | − | 0.440384i | \(-0.854842\pi\) | ||||
−0.897809 | + | 0.440384i | \(0.854842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 11.3181i | − | 0.454912i | −0.973788 | − | 0.227456i | \(-0.926959\pi\) | ||
0.973788 | − | 0.227456i | \(-0.0730408\pi\) | |||||||
\(620\) | −5.08920 | − | 1.49590i | −0.204387 | − | 0.0600766i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.3389 | 0.775420 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.3595 | + | 22.7526i | 0.414380 | + | 0.910104i | ||||
\(626\) | 44.9112 | 1.79501 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.12465 | 0.164591 | ||||||||
\(629\) | 2.30801 | 0.0920265 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.29394 | −0.250558 | −0.125279 | − | 0.992122i | \(-0.539983\pi\) | ||||
−0.125279 | + | 0.992122i | \(0.539983\pi\) | |||||||
\(632\) | 2.58817 | 0.102952 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −60.1325 | −2.38817 | ||||||||
\(635\) | 4.48272 | + | 1.31763i | 0.177891 | + | 0.0522885i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −47.9114 | −1.89683 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.23285 | + | 10.9985i | −0.127789 | + | 0.434754i | ||||
\(641\) | − | 0.590103i | − | 0.0233077i | −0.999932 | − | 0.0116538i | \(-0.996290\pi\) | ||
0.999932 | − | 0.0116538i | \(-0.00370961\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.7107 | −1.13224 | −0.566119 | − | 0.824323i | \(-0.691556\pi\) | ||||
−0.566119 | + | 0.824323i | \(0.691556\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.9804 | 0.432017 | ||||||||
\(647\) | 11.9284i | 0.468954i | 0.972122 | + | 0.234477i | \(0.0753378\pi\) | ||||
−0.972122 | + | 0.234477i | \(0.924662\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3379i | 0.798332i | ||||||||
\(650\) | −39.1069 | − | 25.1639i | −1.53390 | − | 0.987009i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.53708i | 0.256012i | ||||||||
\(653\) | −15.9929 | −0.625852 | −0.312926 | − | 0.949777i | \(-0.601309\pi\) | ||||
−0.312926 | + | 0.949777i | \(0.601309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.06556 | + | 24.0378i | −0.276074 | + | 0.939235i | ||||
\(656\) | −6.40200 | −0.249956 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.6958i | 1.07887i | 0.842026 | + | 0.539437i | \(0.181363\pi\) | ||||
−0.842026 | + | 0.539437i | \(0.818637\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 41.7412i | − | 1.62355i | −0.583973 | − | 0.811773i | \(-0.698503\pi\) | ||
0.583973 | − | 0.811773i | \(-0.301497\pi\) | |||||||
\(662\) | 2.25450 | 0.0876237 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.72583i | − | 0.105783i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 37.7752i | − | 1.46266i | ||||||
\(668\) | − | 8.82907i | − | 0.341607i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 45.6639 | + | 13.4222i | 1.76415 | + | 0.518547i | ||||
\(671\) | −7.65618 | −0.295564 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.91950i | 0.305274i | 0.988282 | + | 0.152637i | \(0.0487766\pi\) | ||||
−0.988282 | + | 0.152637i | \(0.951223\pi\) | |||||||
\(674\) | − | 7.51613i | − | 0.289511i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.6535 | 0.678979 | ||||||||
\(677\) | − | 10.6672i | − | 0.409974i | −0.978765 | − | 0.204987i | \(-0.934285\pi\) | ||
0.978765 | − | 0.204987i | \(-0.0657152\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.01712 | + | 0.298967i | 0.0390048 | + | 0.0114649i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.82307 | −0.337853 | ||||||||
\(683\) | 2.20926 | 0.0845349 | 0.0422674 | − | 0.999106i | \(-0.486542\pi\) | ||||
0.0422674 | + | 0.999106i | \(0.486542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.43924 | − | 15.1028i | 0.169615 | − | 0.577048i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 29.3247i | 1.11799i | ||||||||
\(689\) | 7.39655 | 0.281786 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.26644i | 0.352512i | 0.984344 | + | 0.176256i | \(0.0563987\pi\) | ||||
−0.984344 | + | 0.176256i | \(0.943601\pi\) | |||||||
\(692\) | 12.3762i | 0.470474i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.24172 | 0.350811 | ||||||||
\(695\) | −13.8566 | − | 4.07295i | −0.525612 | − | 0.154496i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.02273i | 0.0387385i | ||||||||
\(698\) | 30.6985i | 1.16195i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.99882i | − | 0.264342i | −0.991227 | − | 0.132171i | \(-0.957805\pi\) | ||
0.991227 | − | 0.132171i | \(-0.0421948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.9163 | 0.939734 | ||||||||
\(704\) | − | 16.4249i | − | 0.619038i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 11.2511i | − | 0.423441i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.1611 | −1.17028 | −0.585139 | − | 0.810933i | \(-0.698960\pi\) | ||||
−0.585139 | + | 0.810933i | \(0.698960\pi\) | |||||||
\(710\) | 41.5974 | + | 12.2270i | 1.56112 | + | 0.458870i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.33037 | 0.274717 | ||||||||
\(713\) | − | 6.95644i | − | 0.260521i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.6597 | − | 9.89379i | −1.25880 | − | 0.370007i | ||||
\(716\) | − | 22.0912i | − | 0.825588i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 15.4703i | − | 0.577345i | ||||||
\(719\) | −9.06160 | −0.337941 | −0.168970 | − | 0.985621i | \(-0.554044\pi\) | ||||
−0.168970 | + | 0.985621i | \(0.554044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 82.1894 | 3.05877 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 16.5317i | − | 0.614397i | ||||||
\(725\) | −20.9943 | + | 32.6269i | −0.779708 | + | 1.21173i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.0567 | −0.632599 | −0.316300 | − | 0.948659i | \(-0.602441\pi\) | ||||
−0.316300 | + | 0.948659i | \(0.602441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.6771 | − | 56.7373i | 0.617247 | − | 2.09994i | ||||
\(731\) | 4.68466 | 0.173268 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.9660 | −0.589718 | −0.294859 | − | 0.955541i | \(-0.595273\pi\) | ||||
−0.294859 | + | 0.955541i | \(0.595273\pi\) | |||||||
\(734\) | −35.5265 | −1.31131 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.1784 | 1.33355 | ||||||||
\(737\) | 35.9078 | 1.32268 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.8515 | −0.509536 | −0.254768 | − | 0.967002i | \(-0.581999\pi\) | ||||
−0.254768 | + | 0.967002i | \(0.581999\pi\) | |||||||
\(740\) | −11.2734 | − | 3.31366i | −0.414420 | − | 0.121813i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.6801 | 1.01548 | 0.507741 | − | 0.861510i | \(-0.330481\pi\) | ||||
0.507741 | + | 0.861510i | \(0.330481\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −50.5254 | − | 14.8512i | −1.85111 | − | 0.544106i | ||||
\(746\) | 5.05732i | 0.185161i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.90666 | −0.142842 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.3332 | 1.21635 | 0.608173 | − | 0.793805i | \(-0.291903\pi\) | ||||
0.608173 | + | 0.793805i | \(0.291903\pi\) | |||||||
\(752\) | 22.2301i | 0.810647i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 72.1693i | − | 2.62825i | ||||||
\(755\) | 11.4191 | − | 38.8491i | 0.415585 | − | 1.41386i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.1442i | 0.368697i | 0.982861 | + | 0.184348i | \(0.0590175\pi\) | ||||
−0.982861 | + | 0.184348i | \(0.940983\pi\) | |||||||
\(758\) | 45.6442 | 1.65787 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.9804 | + | 3.22752i | 0.398300 | + | 0.117074i | ||||
\(761\) | 14.7011 | 0.532916 | 0.266458 | − | 0.963847i | \(-0.414147\pi\) | ||||
0.266458 | + | 0.963847i | \(0.414147\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 40.8577i | − | 1.47818i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.2647i | 0.768324i | ||||||||
\(767\) | −30.6351 | −1.10617 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4992i | 0.811340i | 0.914020 | + | 0.405670i | \(0.132962\pi\) | ||||
−0.914020 | + | 0.405670i | \(0.867038\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.7752i | 0.747717i | ||||||||
\(773\) | − | 21.2531i | − | 0.764421i | −0.924075 | − | 0.382211i | \(-0.875163\pi\) | ||
0.924075 | − | 0.382211i | \(-0.124837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.86618 | + | 6.00837i | −0.138877 | + | 0.215827i | ||||
\(776\) | 1.43954 | 0.0516764 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 24.0698i | − | 0.862945i | ||||||
\(779\) | 11.0409i | 0.395581i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.7101 | 1.17046 | ||||||||
\(782\) | − | 6.79092i | − | 0.242843i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.56671 | − | 5.33012i | 0.0559183 | − | 0.190240i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.7190 | −0.560323 | −0.280162 | − | 0.959953i | \(-0.590388\pi\) | ||||
−0.280162 | + | 0.959953i | \(0.590388\pi\) | |||||||
\(788\) | 26.0587 | 0.928302 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.80190 | + | 16.3366i | −0.170844 | + | 0.581230i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11.5326i | − | 0.409533i | ||||||
\(794\) | −54.7750 | −1.94389 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32.8634i | 1.16481i | ||||||||
\(797\) | − | 39.5812i | − | 1.40204i | −0.713143 | − | 0.701019i | \(-0.752729\pi\) | ||
0.713143 | − | 0.701019i | \(-0.247271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.55128 | 0.125635 | ||||||||
\(800\) | −31.2478 | − | 20.1068i | −1.10478 | − | 0.710884i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 22.7526i | − | 0.803422i | ||||||
\(803\) | − | 44.6153i | − | 1.57444i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 13.2903i | − | 0.468130i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.60909 | −0.267687 | ||||||||
\(809\) | − | 44.0002i | − | 1.54697i | −0.633817 | − | 0.773483i | \(-0.718513\pi\) | ||
0.633817 | − | 0.773483i | \(-0.281487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.9306i | 1.57773i | 0.614567 | + | 0.788864i | \(0.289331\pi\) | ||||
−0.614567 | + | 0.788864i | \(0.710669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −19.5446 | −0.685038 | ||||||||
\(815\) | 8.44761 | + | 2.48305i | 0.295907 | + | 0.0869775i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.5735 | 1.76934 | ||||||||
\(818\) | 27.5819i | 0.964378i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.46835 | − | 4.99549i | 0.0512771 | − | 0.174450i | ||||
\(821\) | 15.1296i | 0.528027i | 0.964519 | + | 0.264014i | \(0.0850464\pi\) | ||||
−0.964519 | + | 0.264014i | \(0.914954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 31.5796i | − | 1.10079i | −0.834903 | − | 0.550397i | \(-0.814476\pi\) | ||
0.834903 | − | 0.550397i | \(-0.185524\pi\) | |||||||
\(824\) | −0.380556 | −0.0132573 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.6368 | 1.69127 | 0.845633 | − | 0.533765i | \(-0.179223\pi\) | ||||
0.845633 | + | 0.533765i | \(0.179223\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.7538i | 1.62383i | 0.583778 | + | 0.811914i | \(0.301574\pi\) | ||||
−0.583778 | + | 0.811914i | \(0.698426\pi\) | |||||||
\(830\) | 17.2055 | + | 5.05732i | 0.597213 | + | 0.175542i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.7410 | 0.857741 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.4095 | − | 3.35364i | −0.394841 | − | 0.116058i | ||||
\(836\) | −42.1746 | −1.45864 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −66.8453 | −2.30913 | ||||||||
\(839\) | 29.1067 | 1.00488 | 0.502438 | − | 0.864613i | \(-0.332437\pi\) | ||||
0.502438 | + | 0.864613i | \(0.332437\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.2110 | −1.07624 | ||||||||
\(842\) | −45.6314 | −1.57256 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.2306 | 0.661946 | ||||||||
\(845\) | 6.70551 | − | 22.8129i | 0.230676 | − | 0.784786i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.94434 | 0.238469 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.77418 | + | 5.86541i | −0.129453 | + | 0.201182i | ||||
\(851\) | − | 15.4097i | − | 0.528238i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.4915 | 0.975531 | 0.487766 | − | 0.872975i | \(-0.337812\pi\) | ||||
0.487766 | + | 0.872975i | \(0.337812\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.10029 | −0.0376071 | ||||||||
\(857\) | − | 40.5552i | − | 1.38534i | −0.721255 | − | 0.692670i | \(-0.756434\pi\) | ||
0.721255 | − | 0.692670i | \(-0.243566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 37.7225i | − | 1.28707i | −0.765415 | − | 0.643537i | \(-0.777466\pi\) | ||
0.765415 | − | 0.643537i | \(-0.222534\pi\) | |||||||
\(860\) | −22.8821 | − | 6.72587i | −0.780274 | − | 0.229350i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 15.6085i | − | 0.531627i | ||||||
\(863\) | 25.6790 | 0.874124 | 0.437062 | − | 0.899431i | \(-0.356019\pi\) | ||||
0.437062 | + | 0.899431i | \(0.356019\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.9933 | + | 4.70100i | 0.543789 | + | 0.159839i | ||||
\(866\) | −48.3389 | −1.64262 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.8463i | 0.435779i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.0881i | 1.83271i | ||||||||
\(872\) | −8.71494 | −0.295125 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 73.3117i | − | 2.47981i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.0454i | 0.643117i | 0.946890 | + | 0.321559i | \(0.104207\pi\) | ||||
−0.946890 | + | 0.321559i | \(0.895793\pi\) | |||||||
\(878\) | − | 1.52040i | − | 0.0513111i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −31.6018 | − | 9.28889i | −1.06530 | − | 0.313128i | ||||
\(881\) | 30.7115 | 1.03470 | 0.517349 | − | 0.855774i | \(-0.326919\pi\) | ||||
0.517349 | + | 0.855774i | \(0.326919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.8466i | − | 1.23999i | −0.784607 | − | 0.619993i | \(-0.787135\pi\) | ||
0.784607 | − | 0.619993i | \(-0.212865\pi\) | |||||||
\(884\) | − | 5.88463i | − | 0.197922i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −43.3306 | −1.45572 | ||||||||
\(887\) | 33.8772i | 1.13748i | 0.822516 | + | 0.568742i | \(0.192570\pi\) | ||||
−0.822516 | + | 0.568742i | \(0.807430\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −13.6002 | + | 46.2695i | −0.455881 | + | 1.55096i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −40.0622 | −1.34138 | ||||||||
\(893\) | 38.3380 | 1.28293 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.5476 | − | 8.39116i | −0.954242 | − | 0.280486i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 4.12597i | − | 0.137685i | ||||||
\(899\) | −11.0881 | −0.369809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.10937i | − | 0.0369583i | ||||||
\(902\) | − | 8.66061i | − | 0.288367i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.24172 | −0.307375 | ||||||||
\(905\) | −21.3633 | − | 6.27944i | −0.710141 | − | 0.208736i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.06681i | − | 0.0354230i | −0.999843 | − | 0.0177115i | \(-0.994362\pi\) | ||
0.999843 | − | 0.0177115i | \(-0.00563803\pi\) | |||||||
\(908\) | 16.9147i | 0.561333i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.61157i | 0.318445i | 0.987243 | + | 0.159223i | \(0.0508988\pi\) | ||||
−0.987243 | + | 0.159223i | \(0.949101\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.5295 | 0.447763 | ||||||||
\(914\) | 10.4713i | 0.346359i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 43.5862i | − | 1.44013i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.83188 | −0.225363 | −0.112681 | − | 0.993631i | \(-0.535944\pi\) | ||||
−0.112681 | + | 0.993631i | \(0.535944\pi\) | |||||||
\(920\) | 1.99609 | − | 6.79092i | 0.0658092 | − | 0.223890i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.3389 | −0.636894 | ||||||||
\(923\) | 49.2714i | 1.62179i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.56424 | + | 13.3096i | −0.281590 | + | 0.437616i | ||||
\(926\) | − | 23.0447i | − | 0.757296i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 57.6659i | − | 1.89298i | ||||||
\(929\) | −53.8766 | −1.76764 | −0.883818 | − | 0.467832i | \(-0.845035\pi\) | ||||
−0.883818 | + | 0.467832i | \(0.845035\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −30.5352 | −1.00021 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 38.1342i | − | 1.24779i | ||||||
\(935\) | −1.48391 | + | 5.04843i | −0.0485291 | + | 0.165101i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.6036 | −0.705759 | −0.352880 | − | 0.935669i | \(-0.614797\pi\) | ||||
−0.352880 | + | 0.935669i | \(0.614797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.3462 | − | 5.09865i | −0.565769 | − | 0.166300i | ||||
\(941\) | −58.2013 | −1.89731 | −0.948654 | − | 0.316316i | \(-0.897554\pi\) | ||||
−0.948654 | + | 0.316316i | \(0.897554\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.82835 | 0.222362 | ||||||||
\(944\) | −28.7621 | −0.936127 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.6704 | −1.28980 | ||||||||
\(947\) | 20.4695 | 0.665168 | 0.332584 | − | 0.943074i | \(-0.392079\pi\) | ||||
0.332584 | + | 0.943074i | \(0.392079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 67.2043 | 2.18155 | ||||||||
\(950\) | −40.7444 | + | 63.3203i | −1.32192 | + | 2.05438i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.4745 | −0.339303 | −0.169651 | − | 0.985504i | \(-0.554264\pi\) | ||||
−0.169651 | + | 0.985504i | \(0.554264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52.7988 | − | 15.5194i | −1.70853 | − | 0.502197i | ||||
\(956\) | − | 1.59590i | − | 0.0516152i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.0879 | −1.19825 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.9581 | 0.934132 | ||||||||
\(962\) | − | 29.4402i | − | 0.949190i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 10.8083i | − | 0.348112i | ||||||
\(965\) | 26.8470 | + | 7.89129i | 0.864236 | + | 0.254030i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 43.1242i | − | 1.38678i | −0.720562 | − | 0.693391i | \(-0.756116\pi\) | ||
0.720562 | − | 0.693391i | \(-0.243884\pi\) | |||||||
\(968\) | 0.379651 | 0.0122024 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.67081 | + | 9.08640i | −0.0857547 | + | 0.291747i | ||||
\(971\) | −8.35144 | −0.268010 | −0.134005 | − | 0.990981i | \(-0.542784\pi\) | ||||
−0.134005 | + | 0.990981i | \(0.542784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.53581i | 0.113295i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 10.8275i | − | 0.346579i | ||||||
\(977\) | −26.8088 | −0.857690 | −0.428845 | − | 0.903378i | \(-0.641079\pi\) | ||||
−0.428845 | + | 0.903378i | \(0.641079\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.3840i | 1.16284i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 48.7538i | 1.55580i | ||||||||
\(983\) | 29.4574i | 0.939546i | 0.882787 | + | 0.469773i | \(0.155664\pi\) | ||||
−0.882787 | + | 0.469773i | \(0.844336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.89816 | − | 33.6746i | 0.315382 | − | 1.07296i | ||||
\(986\) | −10.8243 | −0.344714 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 63.5279i | − | 2.02109i | ||||||
\(989\) | − | 31.2777i | − | 0.994572i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.00667 | −0.159042 | −0.0795211 | − | 0.996833i | \(-0.525339\pi\) | ||||
−0.0795211 | + | 0.996833i | \(0.525339\pi\) | |||||||
\(992\) | − | 10.6194i | − | 0.337166i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.4681 | + | 12.4829i | 1.34633 | + | 0.395734i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.87919 | 0.281207 | 0.140603 | − | 0.990066i | \(-0.455096\pi\) | ||||
0.140603 | + | 0.990066i | \(0.455096\pi\) | |||||||
\(998\) | 50.1787 | 1.58838 | ||||||||
\(999\) | 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 | 2205.2.g.b.2204.7 | 24 | ||
3.2 | odd | 2 | inner | 2205.2.g.b.2204.17 | 24 | ||
5.4 | even | 2 | inner | 2205.2.g.b.2204.19 | 24 | ||
7.4 | even | 3 | 315.2.bb.b.89.9 | yes | 24 | ||
7.5 | odd | 6 | 315.2.bb.b.269.10 | yes | 24 | ||
7.6 | odd | 2 | inner | 2205.2.g.b.2204.8 | 24 | ||
15.14 | odd | 2 | inner | 2205.2.g.b.2204.5 | 24 | ||
21.5 | even | 6 | 315.2.bb.b.269.3 | yes | 24 | ||
21.11 | odd | 6 | 315.2.bb.b.89.4 | yes | 24 | ||
21.20 | even | 2 | inner | 2205.2.g.b.2204.18 | 24 | ||
35.4 | even | 6 | 315.2.bb.b.89.3 | ✓ | 24 | ||
35.12 | even | 12 | 1575.2.bk.i.1151.4 | 24 | |||
35.18 | odd | 12 | 1575.2.bk.i.26.3 | 24 | |||
35.19 | odd | 6 | 315.2.bb.b.269.4 | yes | 24 | ||
35.32 | odd | 12 | 1575.2.bk.i.26.9 | 24 | |||
35.33 | even | 12 | 1575.2.bk.i.1151.10 | 24 | |||
35.34 | odd | 2 | inner | 2205.2.g.b.2204.20 | 24 | ||
105.32 | even | 12 | 1575.2.bk.i.26.4 | 24 | |||
105.47 | odd | 12 | 1575.2.bk.i.1151.9 | 24 | |||
105.53 | even | 12 | 1575.2.bk.i.26.10 | 24 | |||
105.68 | odd | 12 | 1575.2.bk.i.1151.3 | 24 | |||
105.74 | odd | 6 | 315.2.bb.b.89.10 | yes | 24 | ||
105.89 | even | 6 | 315.2.bb.b.269.9 | yes | 24 | ||
105.104 | even | 2 | inner | 2205.2.g.b.2204.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bb.b.89.3 | ✓ | 24 | 35.4 | even | 6 | ||
315.2.bb.b.89.4 | yes | 24 | 21.11 | odd | 6 | ||
315.2.bb.b.89.9 | yes | 24 | 7.4 | even | 3 | ||
315.2.bb.b.89.10 | yes | 24 | 105.74 | odd | 6 | ||
315.2.bb.b.269.3 | yes | 24 | 21.5 | even | 6 | ||
315.2.bb.b.269.4 | yes | 24 | 35.19 | odd | 6 | ||
315.2.bb.b.269.9 | yes | 24 | 105.89 | even | 6 | ||
315.2.bb.b.269.10 | yes | 24 | 7.5 | odd | 6 | ||
1575.2.bk.i.26.3 | 24 | 35.18 | odd | 12 | |||
1575.2.bk.i.26.4 | 24 | 105.32 | even | 12 | |||
1575.2.bk.i.26.9 | 24 | 35.32 | odd | 12 | |||
1575.2.bk.i.26.10 | 24 | 105.53 | even | 12 | |||
1575.2.bk.i.1151.3 | 24 | 105.68 | odd | 12 | |||
1575.2.bk.i.1151.4 | 24 | 35.12 | even | 12 | |||
1575.2.bk.i.1151.9 | 24 | 105.47 | odd | 12 | |||
1575.2.bk.i.1151.10 | 24 | 35.33 | even | 12 | |||
2205.2.g.b.2204.5 | 24 | 15.14 | odd | 2 | inner | ||
2205.2.g.b.2204.6 | 24 | 105.104 | even | 2 | inner | ||
2205.2.g.b.2204.7 | 24 | 1.1 | even | 1 | trivial | ||
2205.2.g.b.2204.8 | 24 | 7.6 | odd | 2 | inner | ||
2205.2.g.b.2204.17 | 24 | 3.2 | odd | 2 | inner | ||
2205.2.g.b.2204.18 | 24 | 21.20 | even | 2 | inner | ||
2205.2.g.b.2204.19 | 24 | 5.4 | even | 2 | inner | ||
2205.2.g.b.2204.20 | 24 | 35.34 | odd | 2 | inner |