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 | 1079.8 | ||
Root | \(-0.670418 - 0.387066i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1079 |
Dual form | 1764.2.e.j.1079.5 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.03295 | + | 0.965926i | −0.730406 | + | 0.683013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.133975 | − | 1.99551i | 0.0669873 | − | 0.997754i | ||||
\(5\) | 2.73205i | 1.22181i | 0.791704 | + | 0.610905i | \(0.209194\pi\) | ||||
−0.791704 | + | 0.610905i | \(0.790806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.78912 | + | 2.19067i | 0.632551 | + | 0.774519i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.63896 | − | 2.82207i | −0.834512 | − | 0.892418i | ||||
\(11\) | 5.64415 | 1.70177 | 0.850887 | − | 0.525348i | \(-0.176065\pi\) | ||||
0.850887 | + | 0.525348i | \(0.176065\pi\) | |||||||
\(12\) | 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 | ||||||||
\(16\) | −3.96410 | − | 0.534695i | −0.991025 | − | 0.133674i | ||||
\(17\) | − | 6.19615i | − | 1.50279i | −0.659854 | − | 0.751394i | \(-0.729382\pi\) | ||
0.659854 | − | 0.751394i | \(-0.270618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.13180i | − | 0.947901i | −0.880552 | − | 0.473950i | \(-0.842828\pi\) | ||
0.880552 | − | 0.473950i | \(-0.157172\pi\) | |||||||
\(20\) | 5.45183 | + | 0.366025i | 1.21907 | + | 0.0818458i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.83013 | + | 5.45183i | −1.24299 | + | 1.16233i | ||||
\(23\) | 5.64415 | 1.17689 | 0.588443 | − | 0.808539i | \(-0.299741\pi\) | ||||
0.588443 | + | 0.808539i | \(0.299741\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.46410 | −0.492820 | ||||||||
\(26\) | −1.46081 | + | 1.36603i | −0.286489 | + | 0.267900i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.378937i | − | 0.0703669i | −0.999381 | − | 0.0351835i | \(-0.988798\pi\) | ||
0.999381 | − | 0.0351835i | \(-0.0112016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.15649i | − | 1.28534i | −0.766141 | − | 0.642672i | \(-0.777826\pi\) | ||
0.766141 | − | 0.642672i | \(-0.222174\pi\) | |||||||
\(32\) | 4.61120 | − | 3.27671i | 0.815152 | − | 0.579247i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.98502 | + | 6.40032i | 1.02642 | + | 1.09765i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.46410 | −0.569495 | −0.284747 | − | 0.958603i | \(-0.591910\pi\) | ||||
−0.284747 | + | 0.958603i | \(0.591910\pi\) | |||||||
\(38\) | 3.99102 | + | 4.26795i | 0.647428 | + | 0.692353i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.98502 | + | 4.88798i | −0.946315 | + | 0.772857i | ||||
\(41\) | − | 5.26795i | − | 0.822715i | −0.911474 | − | 0.411358i | \(-0.865055\pi\) | ||
0.911474 | − | 0.411358i | \(-0.134945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.84325i | − | 0.891088i | −0.895260 | − | 0.445544i | \(-0.853010\pi\) | ||
0.895260 | − | 0.445544i | \(-0.146990\pi\) | |||||||
\(44\) | 0.756172 | − | 11.2629i | 0.113997 | − | 1.69795i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.83013 | + | 5.45183i | −0.859605 | + | 0.803828i | ||||
\(47\) | −2.13878 | −0.311973 | −0.155986 | − | 0.987759i | \(-0.549856\pi\) | ||||
−0.155986 | + | 0.987759i | \(0.549856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.54530 | − | 2.38014i | 0.359959 | − | 0.336603i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.189469 | − | 2.82207i | 0.0262746 | − | 0.391351i | ||||
\(53\) | 0.656339i | 0.0901551i | 0.998983 | + | 0.0450775i | \(0.0143535\pi\) | ||||
−0.998983 | + | 0.0450775i | \(0.985647\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.4201i | 2.07925i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.366025 | + | 0.391424i | 0.0480615 | + | 0.0513964i | ||||
\(59\) | −13.8253 | −1.79990 | −0.899949 | − | 0.435995i | \(-0.856397\pi\) | ||||
−0.899949 | + | 0.435995i | \(0.856397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.0759 | 1.93027 | 0.965134 | − | 0.261756i | \(-0.0843016\pi\) | ||||
0.965134 | + | 0.261756i | \(0.0843016\pi\) | |||||||
\(62\) | 6.91264 | + | 7.39230i | 0.877906 | + | 0.938824i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.59808 | + | 7.83876i | −0.199760 | + | 0.979845i | ||||
\(65\) | 3.86370i | 0.479233i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.98203i | 0.975160i | 0.873078 | + | 0.487580i | \(0.162120\pi\) | ||||
−0.873078 | + | 0.487580i | \(0.837880\pi\) | |||||||
\(68\) | −12.3645 | − | 0.830127i | −1.49941 | − | 0.100668i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9078 | 1.65055 | 0.825273 | − | 0.564733i | \(-0.191021\pi\) | ||||
0.825273 | + | 0.564733i | \(0.191021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0053 | −1.52216 | −0.761079 | − | 0.648659i | \(-0.775330\pi\) | ||||
−0.761079 | + | 0.648659i | \(0.775330\pi\) | |||||||
\(74\) | 3.57825 | − | 3.34607i | 0.415963 | − | 0.388972i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.24504 | − | 0.553557i | −0.945771 | − | 0.0634973i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.8253i | − | 1.55547i | −0.628595 | − | 0.777733i | \(-0.716370\pi\) | ||
0.628595 | − | 0.777733i | \(-0.283630\pi\) | |||||||
\(80\) | 1.46081 | − | 10.8301i | 0.163324 | − | 1.21085i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.08845 | + | 5.44153i | 0.561925 | + | 0.600917i | ||||
\(83\) | 10.1208 | 1.11090 | 0.555452 | − | 0.831549i | \(-0.312545\pi\) | ||||
0.555452 | + | 0.831549i | \(0.312545\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.9282 | 1.83612 | ||||||||
\(86\) | 5.64415 | + | 6.03579i | 0.608624 | + | 0.650856i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.0981 | + | 12.3645i | 1.07646 | + | 1.31806i | ||||
\(89\) | 5.26795i | 0.558401i | 0.960233 | + | 0.279201i | \(0.0900695\pi\) | ||||
−0.960233 | + | 0.279201i | \(0.909931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.756172 | − | 11.2629i | 0.0788364 | − | 1.17424i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.20925 | − | 2.06590i | 0.227867 | − | 0.213081i | ||||
\(95\) | 11.2883 | 1.15815 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.41902 | −0.956357 | −0.478178 | − | 0.878263i | \(-0.658703\pi\) | ||||
−0.478178 | + | 0.878263i | \(0.658703\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.330127 | + | 4.91713i | −0.0330127 | + | 0.491713i | ||||
\(101\) | 8.73205i | 0.868872i | 0.900703 | + | 0.434436i | \(0.143052\pi\) | ||||
−0.900703 | + | 0.434436i | \(0.856948\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.3954i | − | 1.22136i | −0.791879 | − | 0.610678i | \(-0.790897\pi\) | ||
0.791879 | − | 0.610678i | \(-0.209103\pi\) | |||||||
\(104\) | 2.53020 | + | 3.09808i | 0.248107 | + | 0.303791i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.633975 | − | 0.677966i | −0.0615771 | − | 0.0658498i | ||||
\(107\) | 2.61946 | 0.253233 | 0.126616 | − | 0.991952i | \(-0.459588\pi\) | ||||
0.126616 | + | 0.991952i | \(0.459588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | −14.8947 | − | 15.9282i | −1.42015 | − | 1.51869i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.14162i | 0.859971i | 0.902836 | + | 0.429986i | \(0.141481\pi\) | ||||
−0.902836 | + | 0.429986i | \(0.858519\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.4201i | 1.43793i | ||||||||
\(116\) | −0.756172 | − | 0.0507680i | −0.0702088 | − | 0.00471369i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.2808 | − | 13.3542i | 1.31466 | − | 1.22935i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8564 | 1.89604 | ||||||||
\(122\) | −15.5726 | + | 14.5622i | −1.40988 | + | 1.31840i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.2808 | − | 0.958788i | −1.28246 | − | 0.0861017i | ||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.70447i | − | 0.328719i | −0.986401 | − | 0.164359i | \(-0.947444\pi\) | ||
0.986401 | − | 0.164359i | \(-0.0525557\pi\) | |||||||
\(128\) | −5.92093 | − | 9.64068i | −0.523341 | − | 0.852123i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.73205 | − | 3.99102i | −0.327323 | − | 0.350035i | ||||
\(131\) | 11.6865 | 1.02105 | 0.510527 | − | 0.859862i | \(-0.329450\pi\) | ||||
0.510527 | + | 0.859862i | \(0.329450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.71005 | − | 8.24504i | −0.666047 | − | 0.712263i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.5737 | − | 11.0857i | 1.16394 | − | 0.950589i | ||||
\(137\) | − | 0.378937i | − | 0.0323748i | −0.999869 | − | 0.0161874i | \(-0.994847\pi\) | ||
0.999869 | − | 0.0161874i | \(-0.00515284\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.26361i | 0.700910i | 0.936580 | + | 0.350455i | \(0.113973\pi\) | ||||
−0.936580 | + | 0.350455i | \(0.886027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.3660 | + | 13.4339i | −1.20557 | + | 1.12734i | ||||
\(143\) | 7.98203 | 0.667491 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.03528 | 0.0859750 | ||||||||
\(146\) | 13.4339 | − | 12.5622i | 1.11179 | − | 1.03965i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.464102 | + | 6.91264i | −0.0381489 | + | 0.568216i | ||||
\(149\) | − | 4.24264i | − | 0.347571i | −0.984784 | − | 0.173785i | \(-0.944400\pi\) | ||
0.984784 | − | 0.173785i | \(-0.0555999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.84325i | − | 0.475517i | −0.971324 | − | 0.237759i | \(-0.923587\pi\) | ||
0.971324 | − | 0.237759i | \(-0.0764127\pi\) | |||||||
\(152\) | 9.05142 | − | 7.39230i | 0.734167 | − | 0.599595i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.5519 | 1.57045 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.41902 | 0.751720 | 0.375860 | − | 0.926677i | \(-0.377347\pi\) | ||||
0.375860 | + | 0.926677i | \(0.377347\pi\) | |||||||
\(158\) | 13.3542 | + | 14.2808i | 1.06240 | + | 1.13612i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.95215 | + | 12.5980i | 0.707730 | + | 0.995961i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2596i | 0.960245i | 0.877201 | + | 0.480123i | \(0.159408\pi\) | ||||
−0.877201 | + | 0.480123i | \(0.840592\pi\) | |||||||
\(164\) | −10.5122 | − | 0.705771i | −0.820867 | − | 0.0551115i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.4543 | + | 9.77595i | −0.811411 | + | 0.758761i | ||||
\(167\) | 2.13878 | 0.165504 | 0.0827518 | − | 0.996570i | \(-0.473629\pi\) | ||||
0.0827518 | + | 0.996570i | \(0.473629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | −17.4860 | + | 16.3514i | −1.34112 | + | 1.25409i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.6603 | − | 0.782847i | −0.889086 | − | 0.0596915i | ||||
\(173\) | 7.66025i | 0.582398i | 0.956662 | + | 0.291199i | \(0.0940542\pi\) | ||||
−0.956662 | + | 0.291199i | \(0.905946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22.3740 | − | 3.01790i | −1.68650 | − | 0.227482i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.08845 | − | 5.44153i | −0.381395 | − | 0.407860i | ||||
\(179\) | −8.66884 | −0.647939 | −0.323970 | − | 0.946067i | \(-0.605018\pi\) | ||||
−0.323970 | + | 0.946067i | \(0.605018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7985 | −1.09996 | −0.549981 | − | 0.835177i | \(-0.685365\pi\) | ||||
−0.549981 | + | 0.835177i | \(0.685365\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.0981 | + | 12.3645i | 0.744440 | + | 0.911521i | ||||
\(185\) | − | 9.46410i | − | 0.695815i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 34.9720i | − | 2.55741i | ||||||
\(188\) | −0.286542 | + | 4.26795i | −0.0208982 | + | 0.311272i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.6603 | + | 10.9037i | −0.845924 | + | 0.791034i | ||||
\(191\) | 2.61946 | 0.189537 | 0.0947687 | − | 0.995499i | \(-0.469789\pi\) | ||||
0.0947687 | + | 0.995499i | \(0.469789\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8564 | 1.28533 | 0.642666 | − | 0.766146i | \(-0.277828\pi\) | ||||
0.642666 | + | 0.766146i | \(0.277828\pi\) | |||||||
\(194\) | 9.72939 | − | 9.09808i | 0.698529 | − | 0.653204i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.8386i | 1.69843i | 0.528050 | + | 0.849213i | \(0.322923\pi\) | ||||
−0.528050 | + | 0.849213i | \(0.677077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2883i | 0.800206i | 0.916470 | + | 0.400103i | \(0.131026\pi\) | ||||
−0.916470 | + | 0.400103i | \(0.868974\pi\) | |||||||
\(200\) | −4.40858 | − | 5.39804i | −0.311734 | − | 0.381699i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.43451 | − | 9.01978i | −0.593450 | − | 0.634629i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.3923 | 1.00520 | ||||||||
\(206\) | 11.9730 | + | 12.8038i | 0.834202 | + | 0.892086i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.60609 | − | 0.756172i | −0.388712 | − | 0.0524311i | ||||
\(209\) | − | 23.3205i | − | 1.61311i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.27756i | 0.294479i | 0.989101 | + | 0.147240i | \(0.0470388\pi\) | ||||
−0.989101 | + | 0.147240i | \(0.952961\pi\) | |||||||
\(212\) | 1.30973 | + | 0.0879327i | 0.0899526 | + | 0.00603924i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.70577 | + | 2.53020i | −0.184963 | + | 0.172961i | ||||
\(215\) | 15.9641 | 1.08874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.19770 | + | 5.79555i | −0.419762 | + | 0.392525i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 30.7709 | + | 2.06590i | 2.07458 | + | 0.139283i | ||||
\(221\) | − | 8.76268i | − | 0.589442i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.02469i | − | 0.202548i | −0.994859 | − | 0.101274i | \(-0.967708\pi\) | ||
0.994859 | − | 0.101274i | \(-0.0322919\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.83013 | − | 9.44284i | −0.587371 | − | 0.628129i | ||||
\(227\) | −2.13878 | −0.141956 | −0.0709779 | − | 0.997478i | \(-0.522612\pi\) | ||||
−0.0709779 | + | 0.997478i | \(0.522612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.75839 | 0.380525 | 0.190263 | − | 0.981733i | \(-0.439066\pi\) | ||||
0.190263 | + | 0.981733i | \(0.439066\pi\) | |||||||
\(230\) | −14.8947 | − | 15.9282i | −0.982126 | − | 1.05027i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.830127 | − | 0.677966i | 0.0545005 | − | 0.0445106i | ||||
\(233\) | 28.4601i | 1.86449i | 0.361833 | + | 0.932243i | \(0.382151\pi\) | ||||
−0.361833 | + | 0.932243i | \(0.617849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5.84325i | − | 0.381172i | ||||||
\(236\) | −1.85224 | + | 27.5885i | −0.120570 | + | 1.79586i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.64415 | −0.365090 | −0.182545 | − | 0.983198i | \(-0.558433\pi\) | ||||
−0.182545 | + | 0.983198i | \(0.558433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.69161 | −0.108966 | −0.0544832 | − | 0.998515i | \(-0.517351\pi\) | ||||
−0.0544832 | + | 0.998515i | \(0.517351\pi\) | |||||||
\(242\) | −21.5436 | + | 20.1457i | −1.38488 | + | 1.29502i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.01978 | − | 30.0840i | 0.129303 | − | 1.92593i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.84325i | − | 0.371797i | ||||||
\(248\) | 15.6775 | − | 12.8038i | 0.995523 | − | 0.813045i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.69213 | − | 7.15649i | −0.423247 | − | 0.452616i | ||||
\(251\) | −23.9461 | −1.51146 | −0.755732 | − | 0.654881i | \(-0.772719\pi\) | ||||
−0.755732 | + | 0.654881i | \(0.772719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.8564 | 2.00280 | ||||||||
\(254\) | 3.57825 | + | 3.82654i | 0.224519 | + | 0.240098i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.4282 | + | 4.23917i | 0.964263 | + | 0.264948i | ||||
\(257\) | 23.1244i | 1.44246i | 0.692697 | + | 0.721229i | \(0.256422\pi\) | ||||
−0.692697 | + | 0.721229i | \(0.743578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.71005 | + | 0.517638i | 0.478157 | + | 0.0321026i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.0716 | + | 11.2883i | −0.745785 | + | 0.697393i | ||||
\(263\) | −5.64415 | −0.348033 | −0.174017 | − | 0.984743i | \(-0.555675\pi\) | ||||
−0.174017 | + | 0.984743i | \(0.555675\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.79315 | −0.110152 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.9282 | + | 1.06939i | 0.972970 | + | 0.0653234i | ||||
\(269\) | 13.6603i | 0.832880i | 0.909163 | + | 0.416440i | \(0.136722\pi\) | ||||
−0.909163 | + | 0.416440i | \(0.863278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4448i | 1.12044i | 0.828343 | + | 0.560221i | \(0.189284\pi\) | ||||
−0.828343 | + | 0.560221i | \(0.810716\pi\) | |||||||
\(272\) | −3.31305 | + | 24.5622i | −0.200883 | + | 1.48930i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.366025 | + | 0.391424i | 0.0221124 | + | 0.0236468i | ||||
\(275\) | −13.9078 | −0.838669 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9282 | −1.25745 | −0.628727 | − | 0.777626i | \(-0.716424\pi\) | ||||
−0.628727 | + | 0.777626i | \(0.716424\pi\) | |||||||
\(278\) | −7.98203 | − | 8.53590i | −0.478730 | − | 0.511949i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.933740i | − | 0.0557023i | −0.999612 | − | 0.0278511i | \(-0.991134\pi\) | ||
0.999612 | − | 0.0278511i | \(-0.00886644\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.13180i | 0.245610i | 0.992431 | + | 0.122805i | \(0.0391890\pi\) | ||||
−0.992431 | + | 0.122805i | \(0.960811\pi\) | |||||||
\(284\) | 1.86329 | − | 27.7530i | 0.110566 | − | 1.64684i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.24504 | + | 7.71005i | −0.487540 | + | 0.455905i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21.3923 | −1.25837 | ||||||||
\(290\) | −1.06939 | + | 1.00000i | −0.0627967 | + | 0.0587220i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.74238 | + | 25.9522i | −0.101965 | + | 1.51874i | ||||
\(293\) | 6.87564i | 0.401679i | 0.979624 | + | 0.200840i | \(0.0643670\pi\) | ||||
−0.979624 | + | 0.200840i | \(0.935633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 37.7714i | − | 2.19913i | ||||||
\(296\) | −6.19770 | − | 7.58871i | −0.360234 | − | 0.441085i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.09808 | + | 4.38244i | 0.237395 | + | 0.253868i | ||||
\(299\) | 7.98203 | 0.461613 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.64415 | + | 6.03579i | 0.324784 | + | 0.347321i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.20925 | + | 16.3789i | −0.126709 | + | 0.939394i | ||||
\(305\) | 41.1881i | 2.35842i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.15649i | − | 0.408443i | −0.978925 | − | 0.204221i | \(-0.934534\pi\) | ||
0.978925 | − | 0.204221i | \(-0.0654662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.1962 | + | 18.8857i | −1.14706 | + | 1.07263i | ||||
\(311\) | −25.5118 | −1.44664 | −0.723320 | − | 0.690513i | \(-0.757385\pi\) | ||||
−0.723320 | + | 0.690513i | \(0.757385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.859411 | −0.0485768 | −0.0242884 | − | 0.999705i | \(-0.507732\pi\) | ||||
−0.0242884 | + | 0.999705i | \(0.507732\pi\) | |||||||
\(314\) | −9.72939 | + | 9.09808i | −0.549061 | + | 0.513434i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.5885 | − | 1.85224i | −1.55197 | − | 0.104196i | ||||
\(317\) | − | 4.24264i | − | 0.238290i | −0.992877 | − | 0.119145i | \(-0.961985\pi\) | ||
0.992877 | − | 0.119145i | \(-0.0380154\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.13878i | − | 0.119749i | ||||||
\(320\) | −21.4159 | − | 4.36603i | −1.19718 | − | 0.244068i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.6013 | −1.42449 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.48477 | −0.193300 | ||||||||
\(326\) | −11.8419 | − | 12.6636i | −0.655860 | − | 0.701369i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.5403 | − | 9.42501i | 0.637209 | − | 0.520409i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 31.9281i | − | 1.75493i | −0.479642 | − | 0.877464i | \(-0.659234\pi\) | ||
0.479642 | − | 0.877464i | \(-0.340766\pi\) | |||||||
\(332\) | 1.35593 | − | 20.1962i | 0.0744164 | − | 1.10841i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.20925 | + | 2.06590i | −0.120885 | + | 0.113041i | ||||
\(335\) | −21.8073 | −1.19146 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.3923 | −1.21979 | −0.609893 | − | 0.792484i | \(-0.708788\pi\) | ||||
−0.609893 | + | 0.792484i | \(0.708788\pi\) | |||||||
\(338\) | 11.3625 | − | 10.6252i | 0.618036 | − | 0.577934i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.26795 | − | 33.7804i | 0.122997 | − | 1.83200i | ||||
\(341\) | − | 40.3923i | − | 2.18737i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.8006 | − | 10.4543i | 0.690164 | − | 0.563658i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.39924 | − | 7.91267i | −0.397785 | − | 0.425388i | ||||
\(347\) | −22.1714 | −1.19022 | −0.595110 | − | 0.803644i | \(-0.702892\pi\) | ||||
−0.595110 | + | 0.803644i | \(0.702892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.8033 | 1.22063 | 0.610316 | − | 0.792158i | \(-0.291043\pi\) | ||||
0.610316 | + | 0.792158i | \(0.291043\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.0263 | − | 18.4943i | 1.38721 | − | 0.985748i | ||||
\(353\) | − | 17.8038i | − | 0.947603i | −0.880632 | − | 0.473802i | \(-0.842881\pi\) | ||
0.880632 | − | 0.473802i | \(-0.157119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.9967i | 2.01665i | ||||||||
\(356\) | 10.5122 | + | 0.705771i | 0.557147 | + | 0.0374058i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.95448 | − | 8.37345i | 0.473259 | − | 0.442551i | ||||
\(359\) | 13.9078 | 0.734023 | 0.367012 | − | 0.930216i | \(-0.380381\pi\) | ||||
0.367012 | + | 0.930216i | \(0.380381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.92820 | 0.101484 | ||||||||
\(362\) | 15.2861 | − | 14.2942i | 0.803419 | − | 0.751288i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 35.5312i | − | 1.85979i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | −22.3740 | − | 3.01790i | −1.16632 | − | 0.157319i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.14162 | + | 9.77595i | 0.475250 | + | 0.508227i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.07180 | 0.159052 | 0.0795258 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795258 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(374\) | 33.7804 | + | 36.1244i | 1.74674 | + | 1.86795i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.82654 | − | 4.68536i | −0.197339 | − | 0.241629i | ||||
\(377\) | − | 0.535898i | − | 0.0276002i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.2416i | − | 1.03974i | −0.854245 | − | 0.519871i | \(-0.825980\pi\) | ||
0.854245 | − | 0.519871i | \(-0.174020\pi\) | |||||||
\(380\) | 1.51234 | − | 22.5259i | 0.0775817 | − | 1.15555i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.70577 | + | 2.53020i | −0.138439 | + | 0.129456i | ||||
\(383\) | −4.27756 | −0.218573 | −0.109286 | − | 0.994010i | \(-0.534857\pi\) | ||||
−0.109286 | + | 0.994010i | \(0.534857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.4448 | + | 17.2480i | −0.938815 | + | 0.877898i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.26191 | + | 18.7957i | −0.0640638 | + | 0.954209i | ||||
\(389\) | − | 21.2875i | − | 1.07932i | −0.841883 | − | 0.539660i | \(-0.818553\pi\) | ||
0.841883 | − | 0.539660i | \(-0.181447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 34.9720i | − | 1.76861i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.0263 | − | 24.6241i | −1.16005 | − | 1.24054i | ||||
\(395\) | 37.7714 | 1.90048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2485 | 1.11662 | 0.558310 | − | 0.829633i | \(-0.311450\pi\) | ||||
0.558310 | + | 0.829633i | \(0.311450\pi\) | |||||||
\(398\) | −10.9037 | − | 11.6603i | −0.546551 | − | 0.584476i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.76795 | + | 1.31754i | 0.488397 | + | 0.0658771i | ||||
\(401\) | − | 15.6307i | − | 0.780559i | −0.920696 | − | 0.390279i | \(-0.872378\pi\) | ||
0.920696 | − | 0.390279i | \(-0.127622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10.1208i | − | 0.504153i | ||||||
\(404\) | 17.4249 | + | 1.16987i | 0.866920 | + | 0.0582034i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.5519 | −0.969152 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.52004 | −0.223502 | −0.111751 | − | 0.993736i | \(-0.535646\pi\) | ||||
−0.111751 | + | 0.993736i | \(0.535646\pi\) | |||||||
\(410\) | −14.8665 | + | 13.9019i | −0.734206 | + | 0.686566i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24.7351 | − | 1.66067i | −1.21861 | − | 0.0818153i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.6506i | 1.35731i | ||||||||
\(416\) | 6.52122 | − | 4.63397i | 0.319729 | − | 0.227199i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 22.5259 | + | 24.0889i | 1.10178 | + | 1.17823i | ||||
\(419\) | −12.2596 | −0.598920 | −0.299460 | − | 0.954109i | \(-0.596807\pi\) | ||||
−0.299460 | + | 0.954109i | \(0.596807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.7128 | 1.25317 | 0.626583 | − | 0.779355i | \(-0.284453\pi\) | ||||
0.626583 | + | 0.779355i | \(0.284453\pi\) | |||||||
\(422\) | −4.13180 | − | 4.41851i | −0.201133 | − | 0.215090i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.43782 | + | 1.17427i | −0.0698268 | + | 0.0570276i | ||||
\(425\) | 15.2679i | 0.740604i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.350941 | − | 5.22715i | 0.0169634 | − | 0.252664i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.4901 | + | 15.4201i | −0.795223 | + | 0.743623i | ||||
\(431\) | −11.6935 | −0.563257 | −0.281629 | − | 0.959523i | \(-0.590875\pi\) | ||||
−0.281629 | + | 0.959523i | \(0.590875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00052 | −0.240309 | −0.120155 | − | 0.992755i | \(-0.538339\pi\) | ||||
−0.120155 | + | 0.992755i | \(0.538339\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.803848 | − | 11.9730i | 0.0384973 | − | 0.573405i | ||||
\(437\) | − | 23.3205i | − | 1.11557i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 36.8896i | − | 1.76064i | −0.474377 | − | 0.880322i | \(-0.657327\pi\) | ||
0.474377 | − | 0.880322i | \(-0.342673\pi\) | |||||||
\(440\) | −33.7804 | + | 27.5885i | −1.61042 | + | 1.31523i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.46410 | + | 9.05142i | 0.402596 | + | 0.430532i | ||||
\(443\) | 28.2207 | 1.34081 | 0.670404 | − | 0.741996i | \(-0.266121\pi\) | ||||
0.670404 | + | 0.741996i | \(0.266121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3923 | −0.682261 | ||||||||
\(446\) | 2.92163 | + | 3.12436i | 0.138343 | + | 0.147943i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.86800i | − | 0.324121i | −0.986781 | − | 0.162060i | \(-0.948186\pi\) | ||
0.986781 | − | 0.162060i | \(-0.0518139\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 29.7331i | − | 1.40008i | ||||||
\(452\) | 18.2422 | + | 1.22474i | 0.858040 | + | 0.0576072i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.20925 | − | 2.06590i | 0.103685 | − | 0.0969576i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.07180 | −0.424361 | −0.212180 | − | 0.977231i | \(-0.568056\pi\) | ||||
−0.212180 | + | 0.977231i | \(0.568056\pi\) | |||||||
\(458\) | −5.94813 | + | 5.56218i | −0.277938 | + | 0.259904i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 30.7709 | + | 2.06590i | 1.43470 | + | 0.0963232i | ||||
\(461\) | 12.7321i | 0.592991i | 0.955034 | + | 0.296495i | \(0.0958179\pi\) | ||||
−0.955034 | + | 0.296495i | \(0.904182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.6326i | 1.65599i | 0.560738 | + | 0.827994i | \(0.310518\pi\) | ||||
−0.560738 | + | 0.827994i | \(0.689482\pi\) | |||||||
\(464\) | −0.202616 | + | 1.50215i | −0.00940620 | + | 0.0697354i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.4904 | − | 29.3979i | −1.27347 | − | 1.36183i | ||||
\(467\) | −19.6685 | −0.910151 | −0.455076 | − | 0.890453i | \(-0.650388\pi\) | ||||
−0.455076 | + | 0.890453i | \(0.650388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.64415 | + | 6.03579i | 0.260345 | + | 0.278410i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −24.7351 | − | 30.2866i | −1.13853 | − | 1.39406i | ||||
\(473\) | − | 32.9802i | − | 1.51643i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1812i | 0.467145i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.83013 | − | 5.45183i | 0.266664 | − | 0.249361i | ||||
\(479\) | 19.6685 | 0.898678 | 0.449339 | − | 0.893361i | \(-0.351659\pi\) | ||||
0.449339 | + | 0.893361i | \(0.351659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.89898 | −0.223374 | ||||||||
\(482\) | 1.74735 | − | 1.63397i | 0.0795898 | − | 0.0744255i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.79423 | − | 41.6191i | 0.127010 | − | 1.89178i | ||||
\(485\) | − | 25.7332i | − | 1.16849i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.1208i | − | 0.458618i | −0.973354 | − | 0.229309i | \(-0.926353\pi\) | ||
0.973354 | − | 0.229309i | \(-0.0736466\pi\) | |||||||
\(488\) | 26.9726 | + | 33.0263i | 1.22099 | + | 1.49503i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.61946 | −0.118214 | −0.0591072 | − | 0.998252i | \(-0.518825\pi\) | ||||
−0.0591072 | + | 0.998252i | \(0.518825\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.34795 | −0.105747 | ||||||||
\(494\) | 5.64415 | + | 6.03579i | 0.253942 | + | 0.271563i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.82654 | + | 28.3691i | −0.171817 | + | 1.27381i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.56569i | 0.0700901i | 0.999386 | + | 0.0350451i | \(0.0111575\pi\) | ||||
−0.999386 | + | 0.0350451i | \(0.988843\pi\) | |||||||
\(500\) | 13.8253 | + | 0.928203i | 0.618285 | + | 0.0415105i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.7351 | − | 23.1301i | 1.10398 | − | 1.03235i | ||||
\(503\) | −26.0849 | −1.16307 | −0.581533 | − | 0.813522i | \(-0.697547\pi\) | ||||
−0.581533 | + | 0.813522i | \(0.697547\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.8564 | −1.06160 | ||||||||
\(506\) | −32.9061 | + | 30.7709i | −1.46285 | + | 1.36793i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.39230 | − | 0.496305i | −0.327980 | − | 0.0220200i | ||||
\(509\) | − | 10.3397i | − | 0.458301i | −0.973391 | − | 0.229151i | \(-0.926405\pi\) | ||
0.973391 | − | 0.229151i | \(-0.0735948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.0313 | + | 10.5236i | −0.885267 | + | 0.465084i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.3364 | − | 23.8863i | −0.985217 | − | 1.05358i | ||||
\(515\) | 33.8649 | 1.49227 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0716 | −0.530908 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.46410 | + | 6.91264i | −0.371175 | + | 0.303139i | ||||
\(521\) | − | 7.66025i | − | 0.335602i | −0.985821 | − | 0.167801i | \(-0.946333\pi\) | ||
0.985821 | − | 0.167801i | \(-0.0536666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.8402i | 1.34855i | 0.738481 | + | 0.674274i | \(0.235543\pi\) | ||||
−0.738481 | + | 0.674274i | \(0.764457\pi\) | |||||||
\(524\) | 1.56569 | − | 23.3205i | 0.0683977 | − | 1.01876i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.83013 | − | 5.45183i | 0.254206 | − | 0.237711i | ||||
\(527\) | −44.3427 | −1.93160 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.85641 | 0.385061 | ||||||||
\(530\) | 1.85224 | − | 1.73205i | 0.0804560 | − | 0.0752355i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7.45001i | − | 0.322696i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.15649i | 0.309402i | ||||||||
\(536\) | −17.4860 | + | 14.2808i | −0.755280 | + | 0.616838i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.1948 | − | 14.1104i | −0.568868 | − | 0.608341i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.8564 | −0.509747 | −0.254873 | − | 0.966974i | \(-0.582034\pi\) | ||||
−0.254873 | + | 0.966974i | \(0.582034\pi\) | |||||||
\(542\) | −17.8163 | − | 19.0526i | −0.765276 | − | 0.818377i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −20.3030 | − | 28.5717i | −0.870485 | − | 1.22500i | ||||
\(545\) | 16.3923i | 0.702169i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.54773i | 0.408231i | 0.978947 | + | 0.204116i | \(0.0654319\pi\) | ||||
−0.978947 | + | 0.204116i | \(0.934568\pi\) | |||||||
\(548\) | −0.756172 | − | 0.0507680i | −0.0323021 | − | 0.00216870i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.3660 | − | 13.4339i | 0.612569 | − | 0.572822i | ||||
\(551\) | −1.56569 | −0.0667008 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.6178 | − | 20.2151i | 0.918452 | − | 0.858857i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4901 | + | 1.10711i | 0.699336 | + | 0.0469521i | ||||
\(557\) | 10.4543i | 0.442963i | 0.975165 | + | 0.221481i | \(0.0710892\pi\) | ||||
−0.975165 | + | 0.221481i | \(0.928911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.26361i | − | 0.349513i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.901924 | + | 0.964508i | 0.0380454 | + | 0.0406853i | ||||
\(563\) | 22.3804 | 0.943221 | 0.471611 | − | 0.881807i | \(-0.343673\pi\) | ||||
0.471611 | + | 0.881807i | \(0.343673\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.9754 | −1.05072 | ||||||||
\(566\) | −3.99102 | − | 4.26795i | −0.167755 | − | 0.179395i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.8827 | + | 30.4673i | 1.04405 | + | 1.27838i | ||||
\(569\) | 11.6926i | 0.490181i | 0.969500 | + | 0.245091i | \(0.0788177\pi\) | ||||
−0.969500 | + | 0.245091i | \(0.921182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 29.7893i | − | 1.24665i | −0.781965 | − | 0.623323i | \(-0.785782\pi\) | ||
0.781965 | − | 0.623323i | \(-0.214218\pi\) | |||||||
\(572\) | 1.06939 | − | 15.9282i | 0.0447134 | − | 0.665992i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.9078 | −0.579993 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.7680 | 0.906214 | 0.453107 | − | 0.891456i | \(-0.350316\pi\) | ||||
0.453107 | + | 0.891456i | \(0.350316\pi\) | |||||||
\(578\) | 22.0972 | − | 20.6634i | 0.919122 | − | 0.859483i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.138701 | − | 2.06590i | 0.00575923 | − | 0.0857819i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.70447i | 0.153424i | ||||||||
\(584\) | −23.2681 | − | 28.4904i | −0.962842 | − | 1.17894i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.64136 | − | 7.10220i | −0.274352 | − | 0.293389i | ||||
\(587\) | 18.1028 | 0.747184 | 0.373592 | − | 0.927593i | \(-0.378126\pi\) | ||||
0.373592 | + | 0.927593i | \(0.378126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.5692 | −1.21838 | ||||||||
\(590\) | 36.4843 | + | 39.0160i | 1.50204 | + | 1.60626i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.7321 | + | 1.85224i | 0.564384 | + | 0.0761265i | ||||
\(593\) | 17.8038i | 0.731116i | 0.930788 | + | 0.365558i | \(0.119122\pi\) | ||||
−0.930788 | + | 0.365558i | \(0.880878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.46622 | − | 0.568406i | −0.346790 | − | 0.0232828i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.24504 | + | 7.71005i | −0.337165 | + | 0.315287i | ||||
\(599\) | −30.4350 | −1.24354 | −0.621770 | − | 0.783200i | \(-0.713586\pi\) | ||||
−0.621770 | + | 0.783200i | \(0.713586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.2543 | 1.64201 | 0.821004 | − | 0.570923i | \(-0.193414\pi\) | ||||
0.821004 | + | 0.570923i | \(0.193414\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.6603 | − | 0.782847i | −0.474449 | − | 0.0318536i | ||||
\(605\) | 56.9808i | 2.31660i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.1038i | 1.58717i | 0.608456 | + | 0.793587i | \(0.291789\pi\) | ||||
−0.608456 | + | 0.793587i | \(0.708211\pi\) | |||||||
\(608\) | −13.5387 | − | 19.0526i | −0.549068 | − | 0.772683i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −39.7846 | − | 42.5452i | −1.61083 | − | 1.72261i | ||||
\(611\) | −3.02469 | −0.122366 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.39230 | −0.177404 | −0.0887018 | − | 0.996058i | \(-0.528272\pi\) | ||||
−0.0887018 | + | 0.996058i | \(0.528272\pi\) | |||||||
\(614\) | 6.91264 | + | 7.39230i | 0.278971 | + | 0.298329i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.8749i | 1.40401i | 0.712172 | + | 0.702005i | \(0.247711\pi\) | ||||
−0.712172 | + | 0.702005i | \(0.752289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.23892i | − | 0.210570i | −0.994442 | − | 0.105285i | \(-0.966425\pi\) | ||
0.994442 | − | 0.105285i | \(-0.0335755\pi\) | |||||||
\(620\) | 2.61946 | − | 39.0160i | 0.105200 | − | 1.56692i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.3524 | − | 24.6425i | 1.05664 | − | 0.988074i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 0.887729 | − | 0.830127i | 0.0354808 | − | 0.0331785i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.26191 | − | 18.7957i | 0.0503557 | − | 0.750031i | ||||
\(629\) | 21.4641i | 0.855830i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.6326i | 1.41851i | 0.704951 | + | 0.709256i | \(0.250969\pi\) | ||||
−0.704951 | + | 0.709256i | \(0.749031\pi\) | |||||||
\(632\) | 30.2866 | − | 24.7351i | 1.20474 | − | 0.983911i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.09808 | + | 4.38244i | 0.162755 | + | 0.174049i | ||||
\(635\) | 10.1208 | 0.401632 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.06590 | + | 2.20925i | 0.0817898 | + | 0.0874652i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 26.3388 | − | 16.1763i | 1.04113 | − | 0.639423i | ||||
\(641\) | 18.6622i | 0.737112i | 0.929606 | + | 0.368556i | \(0.120148\pi\) | ||||
−0.929606 | + | 0.368556i | \(0.879852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 26.7084i | − | 1.05328i | −0.850090 | − | 0.526638i | \(-0.823452\pi\) | ||
0.850090 | − | 0.526638i | \(-0.176548\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.4449 | − | 24.7289i | 1.04046 | − | 0.972947i | ||||
\(647\) | 5.27017 | 0.207192 | 0.103596 | − | 0.994619i | \(-0.466965\pi\) | ||||
0.103596 | + | 0.994619i | \(0.466965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −78.0319 | −3.06302 | ||||||||
\(650\) | 3.59959 | − | 3.36603i | 0.141188 | − | 0.132026i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.4641 | + | 1.64247i | 0.958088 | + | 0.0643242i | ||||
\(653\) | − | 34.3201i | − | 1.34305i | −0.740983 | − | 0.671524i | \(-0.765640\pi\) | ||
0.740983 | − | 0.671524i | \(-0.234360\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.9281i | 1.24753i | ||||||||
\(656\) | −2.81674 | + | 20.8827i | −0.109975 | + | 0.815332i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.7182 | 0.573340 | 0.286670 | − | 0.958029i | \(-0.407452\pi\) | ||||
0.286670 | + | 0.958029i | \(0.407452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.8348 | −1.00486 | −0.502428 | − | 0.864619i | \(-0.667560\pi\) | ||||
−0.502428 | + | 0.864619i | \(0.667560\pi\) | |||||||
\(662\) | 30.8402 | + | 32.9802i | 1.19864 | + | 1.28181i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.1074 | + | 22.1714i | 0.702702 | + | 0.860416i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.13878i | − | 0.0828138i | ||||||
\(668\) | 0.286542 | − | 4.26795i | 0.0110866 | − | 0.165132i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 22.5259 | − | 21.0642i | 0.870251 | − | 0.813783i | ||||
\(671\) | 85.0905 | 3.28488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.0000 | −1.61898 | −0.809491 | − | 0.587133i | \(-0.800257\pi\) | ||||
−0.809491 | + | 0.587133i | \(0.800257\pi\) | |||||||
\(674\) | 23.1301 | − | 21.6293i | 0.890940 | − | 0.833130i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.47372 | + | 21.9506i | −0.0566816 | + | 0.844253i | ||||
\(677\) | − | 49.1244i | − | 1.88800i | −0.329942 | − | 0.944001i | \(-0.607029\pi\) | ||
0.329942 | − | 0.944001i | \(-0.392971\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 30.2866 | + | 37.0841i | 1.16144 | + | 1.42211i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 39.0160 | + | 41.7233i | 1.49400 | + | 1.59767i | ||||
\(683\) | 10.8831 | 0.416429 | 0.208214 | − | 0.978083i | \(-0.433235\pi\) | ||||
0.208214 | + | 0.978083i | \(0.433235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.03528 | 0.0395559 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.12436 | + | 23.1632i | −0.119115 | + | 0.883090i | ||||
\(689\) | 0.928203i | 0.0353617i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5025i | 0.513660i | 0.966457 | + | 0.256830i | \(0.0826781\pi\) | ||||
−0.966457 | + | 0.256830i | \(0.917322\pi\) | |||||||
\(692\) | 15.2861 | + | 1.02628i | 0.581090 | + | 0.0390133i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.9019 | − | 21.4159i | 0.869345 | − | 0.812936i | ||||
\(695\) | −22.5766 | −0.856379 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.6410 | −1.23637 | ||||||||
\(698\) | −23.5547 | + | 22.0263i | −0.891557 | + | 0.833707i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.9663i | − | 0.527499i | −0.964591 | − | 0.263749i | \(-0.915041\pi\) | ||
0.964591 | − | 0.263749i | \(-0.0849592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.3130i | 0.539824i | ||||||||
\(704\) | −9.01978 | + | 44.2431i | −0.339946 | + | 1.66748i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.1972 | + | 18.3905i | 0.647225 | + | 0.692136i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.9282 | 0.485529 | 0.242764 | − | 0.970085i | \(-0.421946\pi\) | ||||
0.242764 | + | 0.970085i | \(0.421946\pi\) | |||||||
\(710\) | −36.7020 | − | 39.2487i | −1.37740 | − | 1.47298i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.5403 | + | 9.42501i | −0.432493 | + | 0.353217i | ||||
\(713\) | − | 40.3923i | − | 1.51270i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.8073i | 0.815547i | ||||||||
\(716\) | −1.16140 | + | 17.2987i | −0.0434037 | + | 0.646484i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.3660 | + | 13.4339i | −0.536135 | + | 0.501347i | ||||
\(719\) | −19.0955 | −0.712140 | −0.356070 | − | 0.934459i | \(-0.615884\pi\) | ||||
−0.356070 | + | 0.934459i | \(0.615884\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.99174 | + | 1.86250i | −0.0741249 | + | 0.0693151i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.98262 | + | 29.5305i | −0.0736835 | + | 1.09749i | ||||
\(725\) | 0.933740i | 0.0346782i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.2850i | 1.82788i | 0.405850 | + | 0.913939i | \(0.366975\pi\) | ||||
−0.405850 | + | 0.913939i | \(0.633025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 34.3205 | + | 36.7020i | 1.27026 | + | 1.35840i | ||||
\(731\) | −36.2057 | −1.33912 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.9406 | 1.06895 | 0.534473 | − | 0.845186i | \(-0.320510\pi\) | ||||
0.534473 | + | 0.845186i | \(0.320510\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.0263 | − | 18.4943i | 0.959341 | − | 0.681708i | ||||
\(737\) | 45.0518i | 1.65950i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.6685i | 0.723519i | 0.932272 | + | 0.361759i | \(0.117824\pi\) | ||||
−0.932272 | + | 0.361759i | \(0.882176\pi\) | |||||||
\(740\) | −18.8857 | − | 1.26795i | −0.694252 | − | 0.0466107i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.2454 | 1.14628 | 0.573142 | − | 0.819456i | \(-0.305724\pi\) | ||||
0.573142 | + | 0.819456i | \(0.305724\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.5911 | 0.424665 | ||||||||
\(746\) | −3.17301 | + | 2.96713i | −0.116172 | + | 0.108634i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −69.7869 | − | 4.68536i | −2.55166 | − | 0.171314i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.2057i | 1.32116i | 0.750754 | + | 0.660582i | \(0.229690\pi\) | ||||
−0.750754 | + | 0.660582i | \(0.770310\pi\) | |||||||
\(752\) | 8.47834 | + | 1.14359i | 0.309173 | + | 0.0417026i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.517638 | + | 0.553557i | 0.0188513 | + | 0.0201593i | ||||
\(755\) | 15.9641 | 0.580992 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.6410 | −1.04098 | −0.520488 | − | 0.853869i | \(-0.674250\pi\) | ||||
−0.520488 | + | 0.853869i | \(0.674250\pi\) | |||||||
\(758\) | 19.5519 | + | 20.9086i | 0.710157 | + | 0.759434i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.1962 | + | 24.7289i | 0.732591 | + | 0.897013i | ||||
\(761\) | 12.8756i | 0.466742i | 0.972388 | + | 0.233371i | \(0.0749756\pi\) | ||||
−0.972388 | + | 0.233371i | \(0.925024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.350941 | − | 5.22715i | 0.0126966 | − | 0.189112i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.41851 | − | 4.13180i | 0.159647 | − | 0.149288i | ||||
\(767\) | −19.5519 | −0.705978 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.8690 | 0.608313 | 0.304156 | − | 0.952622i | \(-0.401625\pi\) | ||||
0.304156 | + | 0.952622i | \(0.401625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.39230 | − | 35.6326i | 0.0861009 | − | 1.28245i | ||||
\(773\) | 33.5167i | 1.20551i | 0.797926 | + | 0.602755i | \(0.205930\pi\) | ||||
−0.797926 | + | 0.602755i | \(0.794070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.6343i | 0.633444i | ||||||||
\(776\) | −16.8518 | − | 20.6340i | −0.604944 | − | 0.740717i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.5622 | + | 21.9890i | 0.737190 | + | 0.788343i | ||||
\(779\) | −21.7661 | −0.779852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 78.4974 | 2.80886 | ||||||||
\(782\) | 33.7804 | + | 36.1244i | 1.20798 | + | 1.29180i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.7332i | 0.918459i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.0791i | − | 1.28608i | −0.765832 | − | 0.643041i | \(-0.777673\pi\) | ||
0.765832 | − | 0.643041i | \(-0.222327\pi\) | |||||||
\(788\) | 47.5700 | + | 3.19376i | 1.69461 | + | 0.113773i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −39.0160 | + | 36.4843i | −1.38813 | + | 1.29805i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3205 | 0.757113 | ||||||||
\(794\) | −22.9816 | + | 21.4904i | −0.815586 | + | 0.762665i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.5259 | + | 1.51234i | 0.798409 | + | 0.0536036i | ||||
\(797\) | 8.05256i | 0.285236i | 0.989778 | + | 0.142618i | \(0.0455521\pi\) | ||||
−0.989778 | + | 0.142618i | \(0.954448\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2522i | 0.468829i | ||||||||
\(800\) | −11.3625 | + | 8.07416i | −0.401724 | + | 0.285465i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.0981 | + | 16.1457i | 0.533132 | + | 0.570125i | ||||
\(803\) | −73.4040 | −2.59037 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.77595 | + | 10.4543i | 0.344343 | + | 0.368237i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.1290 | + | 15.6227i | −0.672958 | + | 0.549605i | ||||
\(809\) | − | 34.5975i | − | 1.21638i | −0.793791 | − | 0.608191i | \(-0.791895\pi\) | ||
0.793791 | − | 0.608191i | \(-0.208105\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.5025i | − | 0.474138i | −0.971493 | − | 0.237069i | \(-0.923813\pi\) | ||
0.971493 | − | 0.237069i | \(-0.0761867\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.1962 | − | 18.8857i | 0.707875 | − | 0.661943i | ||||
\(815\) | −33.4938 | −1.17324 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.1432 | −0.844662 | ||||||||
\(818\) | 4.66898 | − | 4.36603i | 0.163247 | − | 0.152654i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.92820 | − | 28.7200i | 0.0673358 | − | 1.00294i | ||||
\(821\) | 14.0406i | 0.490020i | 0.969521 | + | 0.245010i | \(0.0787913\pi\) | ||||
−0.969521 | + | 0.245010i | \(0.921209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.0310i | 1.74397i | 0.489533 | + | 0.871985i | \(0.337167\pi\) | ||||
−0.489533 | + | 0.871985i | \(0.662833\pi\) | |||||||
\(824\) | 27.1543 | − | 22.1769i | 0.945963 | − | 0.772569i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.8831 | −0.378441 | −0.189221 | − | 0.981935i | \(-0.560596\pi\) | ||||
−0.189221 | + | 0.981935i | \(0.560596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.0197 | 1.28575 | 0.642874 | − | 0.765972i | \(-0.277742\pi\) | ||||
0.642874 | + | 0.765972i | \(0.277742\pi\) | |||||||
\(830\) | −26.7084 | − | 28.5617i | −0.927062 | − | 0.991390i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.26002 | + | 11.0857i | −0.0783521 | + | 0.384327i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.84325i | 0.202214i | ||||||||
\(836\) | −46.5363 | − | 3.12436i | −1.60949 | − | 0.108058i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.6636 | − | 11.8419i | 0.437455 | − | 0.409070i | ||||
\(839\) | 7.98203 | 0.275570 | 0.137785 | − | 0.990462i | \(-0.456002\pi\) | ||||
0.137785 | + | 0.990462i | \(0.456002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8564 | 0.995048 | ||||||||
\(842\) | −26.5601 | + | 24.8367i | −0.915320 | + | 0.855928i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.53590 | + | 0.573084i | 0.293818 | + | 0.0197264i | ||||
\(845\) | − | 30.0526i | − | 1.03384i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.350941 | − | 2.60179i | 0.0120514 | − | 0.0893460i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.7477 | − | 15.7710i | −0.505842 | − | 0.540942i | ||||
\(851\) | −19.5519 | −0.670231 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.2581 | −1.30993 | −0.654966 | − | 0.755658i | \(-0.727317\pi\) | ||||
−0.654966 | + | 0.755658i | \(0.727317\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.68653 | + | 5.73837i | 0.160182 | + | 0.196133i | ||||
\(857\) | 14.7321i | 0.503237i | 0.967826 | + | 0.251619i | \(0.0809629\pi\) | ||||
−0.967826 | + | 0.251619i | \(0.919037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.94227i | − | 0.168628i | −0.996439 | − | 0.0843140i | \(-0.973130\pi\) | ||
0.996439 | − | 0.0843140i | \(-0.0268699\pi\) | |||||||
\(860\) | 2.13878 | − | 31.8564i | 0.0729317 | − | 1.08629i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0788 | − | 11.2951i | 0.411407 | − | 0.384712i | ||||
\(863\) | 30.4350 | 1.03602 | 0.518009 | − | 0.855375i | \(-0.326673\pi\) | ||||
0.518009 | + | 0.855375i | \(0.326673\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.9282 | −0.711580 | ||||||||
\(866\) | 5.16529 | − | 4.83013i | 0.175524 | − | 0.164134i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 78.0319i | − | 2.64705i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.2883i | 0.382489i | ||||||||
\(872\) | 10.7347 | + | 13.1440i | 0.363524 | + | 0.445113i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.5259 | + | 24.0889i | 0.761949 | + | 0.814820i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3205 | −0.382266 | −0.191133 | − | 0.981564i | \(-0.561216\pi\) | ||||
−0.191133 | + | 0.981564i | \(0.561216\pi\) | |||||||
\(878\) | 35.6326 | + | 38.1051i | 1.20254 | + | 1.28599i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.24504 | − | 61.1268i | 0.277940 | − | 2.06059i | ||||
\(881\) | 16.4449i | 0.554042i | 0.960864 | + | 0.277021i | \(0.0893471\pi\) | ||||
−0.960864 | + | 0.277021i | \(0.910653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.7354i | 1.80834i | 0.427171 | + | 0.904171i | \(0.359510\pi\) | ||||
−0.427171 | + | 0.904171i | \(0.640490\pi\) | |||||||
\(884\) | −17.4860 | − | 1.17398i | −0.588118 | − | 0.0394851i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.1506 | + | 27.2591i | −0.979335 | + | 0.915789i | ||||
\(887\) | 9.54773 | 0.320581 | 0.160291 | − | 0.987070i | \(-0.448757\pi\) | ||||
0.160291 | + | 0.987070i | \(0.448757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.8665 | − | 13.9019i | 0.498328 | − | 0.465993i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.03579 | − | 0.405232i | −0.202093 | − | 0.0135682i | ||||
\(893\) | 8.83701i | 0.295719i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 23.6837i | − | 0.791659i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.63397 | + | 7.09430i | 0.221379 | + | 0.236740i | ||||
\(899\) | −2.71186 | −0.0904457 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.06678 | 0.135484 | ||||||||
\(902\) | 28.7200 | + | 30.7128i | 0.956270 | + | 1.02262i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.0263 | + | 16.3555i | −0.666064 | + | 0.543975i | ||||
\(905\) | − | 40.4302i | − | 1.34394i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.4938i | 1.11214i | 0.831134 | + | 0.556072i | \(0.187692\pi\) | ||||
−0.831134 | + | 0.556072i | \(0.812308\pi\) | |||||||
\(908\) | −0.286542 | + | 4.26795i | −0.00950923 | + | 0.141637i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.9818 | −0.761422 | −0.380711 | − | 0.924694i | \(-0.624321\pi\) | ||||
−0.380711 | + | 0.924694i | \(0.624321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.1233 | 1.89051 | ||||||||
\(914\) | 9.37072 | − | 8.76268i | 0.309956 | − | 0.289844i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.771478 | − | 11.4909i | 0.0254904 | − | 0.379670i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.56569i | 0.0516475i | 0.999667 | + | 0.0258238i | \(0.00822087\pi\) | ||||
−0.999667 | + | 0.0258238i | \(0.991779\pi\) | |||||||
\(920\) | −33.7804 | + | 27.5885i | −1.11371 | + | 0.909565i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.2982 | − | 13.1516i | −0.405020 | − | 0.433124i | ||||
\(923\) | 19.6685 | 0.647398 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.53590 | 0.280659 | ||||||||
\(926\) | −34.4184 | − | 36.8067i | −1.13106 | − | 1.20954i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.24167 | − | 1.74735i | −0.0407598 | − | 0.0573597i | ||||
\(929\) | − | 19.9090i | − | 0.653192i | −0.945164 | − | 0.326596i | \(-0.894098\pi\) | ||
0.945164 | − | 0.326596i | \(-0.105902\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 56.7924 | + | 3.81294i | 1.86030 | + | 0.124897i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.3166 | − | 18.9983i | 0.664780 | − | 0.621645i | ||||
\(935\) | 95.5453 | 3.12466 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.7594 | 0.514838 | 0.257419 | − | 0.966300i | \(-0.417128\pi\) | ||||
0.257419 | + | 0.966300i | \(0.417128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −11.6603 | − | 0.782847i | −0.380316 | − | 0.0255337i | ||||
\(941\) | − | 39.2295i | − | 1.27884i | −0.768856 | − | 0.639422i | \(-0.779174\pi\) | ||
0.768856 | − | 0.639422i | \(-0.220826\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 29.7331i | − | 0.968242i | ||||||
\(944\) | 54.8048 | + | 7.39230i | 1.78375 | + | 0.240599i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.8564 | + | 34.0669i | 1.03574 | + | 1.10761i | ||||
\(947\) | 10.8831 | 0.353652 | 0.176826 | − | 0.984242i | \(-0.443417\pi\) | ||||
0.176826 | + | 0.984242i | \(0.443417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3923 | −0.597039 | ||||||||
\(950\) | −9.83427 | − | 10.5167i | −0.319066 | − | 0.341206i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.14162i | 0.296126i | 0.988978 | + | 0.148063i | \(0.0473039\pi\) | ||||
−0.988978 | + | 0.148063i | \(0.952696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.15649i | 0.231579i | ||||||||
\(956\) | −0.756172 | + | 11.2629i | −0.0244564 | + | 0.364270i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.3166 | + | 18.9983i | −0.656400 | + | 0.613809i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2154 | −0.652109 | ||||||||
\(962\) | 5.06040 | − | 4.73205i | 0.163154 | − | 0.152567i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.226633 | + | 3.37563i | −0.00729937 | + | 0.108722i | ||||
\(965\) | 48.7846i | 1.57043i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.3910i | 0.494940i | 0.968895 | + | 0.247470i | \(0.0795992\pi\) | ||||
−0.968895 | + | 0.247470i | \(0.920401\pi\) | |||||||
\(968\) | 37.3147 | + | 45.6895i | 1.19934 | + | 1.46852i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.8564 | + | 26.5812i | 0.798091 | + | 0.853470i | ||||
\(971\) | −17.5298 | −0.562557 | −0.281278 | − | 0.959626i | \(-0.590758\pi\) | ||||
−0.281278 | + | 0.959626i | \(0.590758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.77595 | + | 10.4543i | 0.313242 | + | 0.334977i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −59.7623 | − | 8.06099i | −1.91294 | − | 0.258026i | ||||
\(977\) | 1.89469i | 0.0606164i | 0.999541 | + | 0.0303082i | \(0.00964888\pi\) | ||||
−0.999541 | + | 0.0303082i | \(0.990351\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.7331i | 0.950274i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.70577 | − | 2.53020i | 0.0863446 | − | 0.0807420i | ||||
\(983\) | 49.4579 | 1.57746 | 0.788731 | − | 0.614739i | \(-0.210739\pi\) | ||||
0.788731 | + | 0.614739i | \(0.210739\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −65.1282 | −2.07516 | ||||||||
\(986\) | 2.42532 | − | 2.26795i | 0.0772379 | − | 0.0722262i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.6603 | − | 0.782847i | −0.370962 | − | 0.0249057i | ||||
\(989\) | − | 32.9802i | − | 1.04871i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 17.5298i | − | 0.556851i | −0.960458 | − | 0.278426i | \(-0.910187\pi\) | ||
0.960458 | − | 0.278426i | \(-0.0898125\pi\) | |||||||
\(992\) | −23.4498 | − | 33.0000i | −0.744531 | − | 1.04775i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.8402 | −0.977700 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.378937 | −0.0120011 | −0.00600053 | − | 0.999982i | \(-0.501910\pi\) | ||||
−0.00600053 | + | 0.999982i | \(0.501910\pi\) | |||||||
\(998\) | −1.51234 | − | 1.61729i | −0.0478724 | − | 0.0511943i | ||||
\(999\) | 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.1079.8 | yes | 16 | |
3.2 | odd | 2 | inner | 1764.2.e.j.1079.9 | yes | 16 | |
4.3 | odd | 2 | inner | 1764.2.e.j.1079.12 | yes | 16 | |
7.6 | odd | 2 | inner | 1764.2.e.j.1079.7 | yes | 16 | |
12.11 | even | 2 | inner | 1764.2.e.j.1079.5 | ✓ | 16 | |
21.20 | even | 2 | inner | 1764.2.e.j.1079.10 | yes | 16 | |
28.27 | even | 2 | inner | 1764.2.e.j.1079.11 | yes | 16 | |
84.83 | odd | 2 | inner | 1764.2.e.j.1079.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.e.j.1079.5 | ✓ | 16 | 12.11 | even | 2 | inner | |
1764.2.e.j.1079.6 | yes | 16 | 84.83 | odd | 2 | inner | |
1764.2.e.j.1079.7 | yes | 16 | 7.6 | odd | 2 | inner | |
1764.2.e.j.1079.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1764.2.e.j.1079.9 | yes | 16 | 3.2 | odd | 2 | inner | |
1764.2.e.j.1079.10 | yes | 16 | 21.20 | even | 2 | inner | |
1764.2.e.j.1079.11 | yes | 16 | 28.27 | even | 2 | inner | |
1764.2.e.j.1079.12 | yes | 16 | 4.3 | odd | 2 | inner |