Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(31,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.s (of order \(6\), degree \(2\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.7 | ||
Character | \(\chi\) | \(=\) | 1216.31 |
Dual form | 1216.2.s.i.863.7 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.132709 | + | 0.0766197i | −0.0766197 | + | 0.0442364i | −0.537820 | − | 0.843059i | \(-0.680752\pi\) |
0.461201 | + | 0.887296i | \(0.347419\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.14027 | − | 0.658336i | 0.509945 | − | 0.294417i | −0.222866 | − | 0.974849i | \(-0.571541\pi\) |
0.732811 | + | 0.680432i | \(0.238208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.40635i | − | 0.531549i | −0.964035 | − | 0.265774i | \(-0.914372\pi\) | ||
0.964035 | − | 0.265774i | \(-0.0856277\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.48826 | + | 2.57774i | −0.496086 | + | 0.859247i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.27622 | −0.987818 | −0.493909 | − | 0.869514i | \(-0.664432\pi\) | ||||
−0.493909 | + | 0.869514i | \(0.664432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.31710 | + | 4.01334i | −0.642649 | + | 1.11310i | 0.342190 | + | 0.939631i | \(0.388831\pi\) |
−0.984839 | + | 0.173470i | \(0.944502\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.100883 | + | 0.174735i | −0.0260479 | + | 0.0451163i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.24968 | − | 3.89655i | −0.545627 | − | 0.945053i | −0.998567 | − | 0.0535125i | \(-0.982958\pi\) |
0.452940 | − | 0.891541i | \(-0.350375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.56396 | − | 3.52507i | −0.588213 | − | 0.808706i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.107754 | + | 0.186635i | 0.0235138 | + | 0.0407271i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.100883 | − | 0.0582449i | −0.0210356 | − | 0.0121449i | 0.489445 | − | 0.872034i | \(-0.337199\pi\) |
−0.510481 | + | 0.859889i | \(0.670533\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.63319 | + | 2.82876i | −0.326637 | + | 0.565753i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.915838i | − | 0.176253i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.34070 | + | 5.78625i | −0.620352 | + | 1.07448i | 0.369069 | + | 0.929402i | \(0.379677\pi\) |
−0.989420 | + | 0.145078i | \(0.953657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43586 | −0.437494 | −0.218747 | − | 0.975782i | \(-0.570197\pi\) | ||||
−0.218747 | + | 0.975782i | \(0.570197\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.434785 | − | 0.251023i | 0.0756863 | − | 0.0436975i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.925849 | − | 1.60362i | −0.156497 | − | 0.271061i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.87096 | −1.45838 | −0.729189 | − | 0.684313i | \(-0.760102\pi\) | ||||
−0.729189 | + | 0.684313i | \(0.760102\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.710143i | − | 0.113714i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.96478 | − | 3.44377i | 0.931542 | − | 0.537826i | 0.0442428 | − | 0.999021i | \(-0.485912\pi\) |
0.887299 | + | 0.461195i | \(0.152579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.01334 | − | 6.95131i | −0.612029 | − | 1.06006i | −0.990898 | − | 0.134615i | \(-0.957020\pi\) |
0.378869 | − | 0.925450i | \(-0.376313\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.91910i | 0.584225i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.69223 | + | 4.44111i | 1.12203 | + | 0.647802i | 0.941918 | − | 0.335844i | \(-0.109022\pi\) |
0.180109 | + | 0.983647i | \(0.442355\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.02219 | 0.717456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.597106 | + | 0.344739i | 0.0836116 | + | 0.0482732i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.47034 | + | 4.27876i | −0.339328 | + | 0.587733i | −0.984306 | − | 0.176468i | \(-0.943533\pi\) |
0.644979 | + | 0.764201i | \(0.276866\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.73578 | + | 2.15685i | −0.503733 | + | 0.290830i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.610351 | + | 0.271360i | 0.0808430 | + | 0.0359424i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.19309 | + | 5.30763i | −1.19684 | + | 0.690995i | −0.959849 | − | 0.280517i | \(-0.909494\pi\) |
−0.236990 | + | 0.971512i | \(0.576161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.55511 | + | 5.51665i | 1.22341 | + | 0.706334i | 0.965643 | − | 0.259873i | \(-0.0836808\pi\) |
0.257764 | + | 0.966208i | \(0.417014\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.62520 | + | 2.09301i | 0.456732 | + | 0.263694i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.10173i | 0.756827i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.900991 | − | 0.520188i | −0.110074 | − | 0.0635510i | 0.443952 | − | 0.896050i | \(-0.353576\pi\) |
−0.554026 | + | 0.832499i | \(0.686909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0178508 | 0.00214899 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.84910 | + | 4.93478i | 0.338126 | + | 0.585651i | 0.984080 | − | 0.177725i | \(-0.0568737\pi\) |
−0.645954 | + | 0.763376i | \(0.723540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.104749 | + | 0.181430i | 0.0122599 | + | 0.0212348i | 0.872090 | − | 0.489345i | \(-0.162764\pi\) |
−0.859830 | + | 0.510580i | \(0.829431\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 0.500537i | − | 0.0577971i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.60750i | 0.525074i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.20635 | − | 14.2138i | −0.923286 | − | 1.59918i | −0.794295 | − | 0.607533i | \(-0.792159\pi\) |
−0.128991 | − | 0.991646i | \(-0.541174\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.39461 | − | 7.61168i | −0.488289 | − | 0.845742i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.9470 | −1.86018 | −0.930090 | − | 0.367331i | \(-0.880272\pi\) | ||||
−0.930090 | + | 0.367331i | \(0.880272\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.13049 | − | 2.96209i | −0.556479 | − | 0.321283i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.02385i | − | 0.109769i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.18052 | − | 2.99098i | −0.549134 | − | 0.317043i | 0.199638 | − | 0.979870i | \(-0.436023\pi\) |
−0.748773 | + | 0.662827i | \(0.769357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.64415 | + | 3.25865i | 0.591667 | + | 0.341599i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.323262 | − | 0.186635i | 0.0335207 | − | 0.0193532i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.24429 | − | 2.33159i | −0.538053 | − | 0.239216i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.71904 | + | 3.30189i | −0.580680 | + | 0.335256i | −0.761404 | − | 0.648278i | \(-0.775489\pi\) |
0.180723 | + | 0.983534i | \(0.442156\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.87587 | − | 8.44525i | 0.490043 | − | 0.848779i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.14027 | − | 0.658336i | −0.113461 | − | 0.0655069i | 0.442195 | − | 0.896919i | \(-0.354200\pi\) |
−0.555657 | + | 0.831412i | \(0.687533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820 | 0.682656 | 0.341328 | − | 0.939944i | \(-0.389123\pi\) | ||||
0.341328 | + | 0.939944i | \(0.389123\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.245737 | + | 0.141877i | 0.0239815 | + | 0.0138457i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.5230i | − | 1.30732i | −0.756788 | − | 0.653660i | \(-0.773233\pi\) | ||
0.756788 | − | 0.653660i | \(-0.226767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0365602 | + | 0.0633241i | 0.00350183 | + | 0.00606535i | 0.867771 | − | 0.496964i | \(-0.165552\pi\) |
−0.864269 | + | 0.503030i | \(0.832219\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.17726 | − | 0.679691i | 0.111740 | − | 0.0645134i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.905579i | − | 0.0851897i | −0.999092 | − | 0.0425948i | \(-0.986438\pi\) | ||
0.999092 | − | 0.0425948i | \(-0.0135625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.153379 | −0.0143026 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.89690 | − | 11.9458i | −0.637619 | − | 1.10439i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.47991 | + | 3.16382i | −0.502342 | + | 0.290027i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.266374 | −0.0242158 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.527721 | + | 0.914039i | −0.0475830 | + | 0.0824161i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8841i | 0.973504i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.93840 | + | 17.2138i | −0.881890 | + | 1.52748i | −0.0326529 | + | 0.999467i | \(0.510396\pi\) |
−0.849237 | + | 0.528012i | \(0.822938\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.06522 | + | 0.615002i | 0.0937870 | + | 0.0541479i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.99102 | + | 8.64470i | 0.436068 | + | 0.755291i | 0.997382 | − | 0.0723114i | \(-0.0230375\pi\) |
−0.561315 | + | 0.827603i | \(0.689704\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.95747 | + | 3.60581i | −0.429867 | + | 0.312664i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.602929 | − | 1.04430i | −0.0518919 | − | 0.0898794i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.61649 | + | 2.79984i | −0.138106 | + | 0.239207i | −0.926780 | − | 0.375605i | \(-0.877435\pi\) |
0.788674 | + | 0.614812i | \(0.210768\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.258114 | + | 0.447067i | −0.0218930 | + | 0.0379197i | −0.876764 | − | 0.480920i | \(-0.840303\pi\) |
0.854871 | + | 0.518840i | \(0.173636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.36111 | −0.114626 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.59134 | − | 13.1486i | 0.634820 | − | 1.09954i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.79720i | 0.730568i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.666491 | + | 0.384799i | −0.0549713 | + | 0.0317377i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.53431 | − | 2.61789i | 0.371465 | − | 0.214466i | −0.302633 | − | 0.953107i | \(-0.597866\pi\) |
0.674098 | + | 0.738642i | \(0.264532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.89996 | 0.480132 | 0.240066 | − | 0.970757i | \(-0.422831\pi\) | ||||
0.240066 | + | 0.970757i | \(0.422831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.3924 | 1.08271 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.77755 | + | 1.60362i | −0.223098 | + | 0.128806i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.77213 | − | 5.06459i | 0.700093 | − | 0.404199i | −0.107289 | − | 0.994228i | \(-0.534217\pi\) |
0.807382 | + | 0.590029i | \(0.200884\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 0.757108i | − | 0.0600426i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0819125 | + | 0.141877i | −0.00645561 | + | 0.0111814i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.33790 | 0.339770 | 0.169885 | − | 0.985464i | \(-0.445660\pi\) | ||||
0.169885 | + | 0.985464i | \(0.445660\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.330515 | − | 0.572469i | 0.0257306 | − | 0.0445667i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.34705 | − | 4.06522i | 0.181620 | − | 0.314576i | −0.760812 | − | 0.648972i | \(-0.775199\pi\) |
0.942432 | + | 0.334396i | \(0.108532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.23794 | − | 7.34032i | −0.325995 | − | 0.564640i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9025 | − | 1.36300i | 0.986682 | − | 0.104232i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.67077 | + | 8.09001i | 0.355112 | + | 0.615072i | 0.987137 | − | 0.159876i | \(-0.0511095\pi\) |
−0.632025 | + | 0.774948i | \(0.717776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.97822 | + | 2.29683i | 0.300725 | + | 0.173624i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.813339 | − | 1.40874i | 0.0611343 | − | 0.105888i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.3623i | 1.07349i | 0.843744 | + | 0.536746i | \(0.180347\pi\) | ||||
−0.843744 | + | 0.536746i | \(0.819653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.43167 | − | 5.94382i | 0.255074 | − | 0.441801i | −0.709842 | − | 0.704361i | \(-0.751234\pi\) |
0.964916 | + | 0.262560i | \(0.0845669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.69074 | −0.124983 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.1153 | + | 5.84008i | −0.743692 | + | 0.429371i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.37044 | + | 12.7660i | 0.538980 | + | 0.933541i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.28799 | −0.0936872 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.7670i | − | 0.851432i | −0.904857 | − | 0.425716i | \(-0.860022\pi\) | ||
0.904857 | − | 0.425716i | \(-0.139978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.1805 | − | 6.45508i | 0.804792 | − | 0.464647i | −0.0403523 | − | 0.999186i | \(-0.512848\pi\) |
0.845144 | + | 0.534539i | \(0.179515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.467513 | − | 0.809756i | −0.0334793 | − | 0.0579879i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.0600i | − | 1.35797i | −0.734153 | − | 0.678984i | \(-0.762421\pi\) | ||
0.734153 | − | 0.678984i | \(-0.237579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.47429 | − | 3.73794i | −0.458951 | − | 0.264975i | 0.252652 | − | 0.967557i | \(-0.418697\pi\) |
−0.711603 | + | 0.702582i | \(0.752030\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.159427 | 0.0112451 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.13748 | + | 4.69818i | 0.571139 | + | 0.329747i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.53431 | − | 7.85366i | 0.316690 | − | 0.548523i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.300280 | − | 0.173367i | 0.0208709 | − | 0.0120498i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.40010 | + | 11.5489i | 0.581047 | + | 0.798855i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.5429 | − | 7.24164i | 0.863488 | − | 0.498535i | −0.00169088 | − | 0.999999i | \(-0.500538\pi\) |
0.865179 | + | 0.501464i | \(0.167205\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.756204 | − | 0.436594i | −0.0518142 | − | 0.0299150i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.15260 | − | 5.28425i | −0.624202 | − | 0.360383i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.42567i | 0.232549i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0278022 | − | 0.0160516i | −0.00187870 | − | 0.00108467i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.8509 | 1.40259 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1563 | + | 19.3233i | 0.747083 | + | 1.29399i | 0.949215 | + | 0.314627i | \(0.101880\pi\) |
−0.202132 | + | 0.979358i | \(0.564787\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.86121 | − | 8.41986i | −0.324081 | − | 0.561324i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.40040i | 0.358437i | 0.983809 | + | 0.179219i | \(0.0573570\pi\) | ||||
−0.983809 | + | 0.179219i | \(0.942643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.5441i | − | 1.42368i | −0.702344 | − | 0.711838i | \(-0.747863\pi\) | ||
0.702344 | − | 0.711838i | \(-0.252137\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.353026 | − | 0.611458i | −0.0232274 | − | 0.0402310i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.91744 | − | 15.4455i | −0.584201 | − | 1.01187i | −0.994975 | − | 0.100128i | \(-0.968075\pi\) |
0.410774 | − | 0.911737i | \(-0.365259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.6950 | 0.762896 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.17812 | + | 1.25754i | 0.141484 | + | 0.0816857i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.2985i | 1.50705i | 0.657417 | + | 0.753527i | \(0.271649\pi\) | ||||
−0.657417 | + | 0.753527i | \(0.728351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3142 | − | 7.10963i | −0.793230 | − | 0.457972i | 0.0478682 | − | 0.998854i | \(-0.484757\pi\) |
−0.841099 | + | 0.540882i | \(0.818091\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.54583 | + | 2.04718i | 0.227465 | + | 0.131327i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.72666 | − | 3.30629i | 0.365863 | − | 0.211231i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.0883 | − | 2.12209i | 1.27819 | − | 0.135025i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.24903 | − | 1.29848i | 0.142527 | − | 0.0822877i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.52605 | + | 9.57139i | −0.348801 | + | 0.604141i | −0.986037 | − | 0.166528i | \(-0.946744\pi\) |
0.637236 | + | 0.770669i | \(0.280078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.330515 | + | 0.190823i | 0.0207793 | + | 0.0119969i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.907817 | 0.0568497 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.18382 | + | 4.14758i | 0.448114 | + | 0.258719i | 0.707033 | − | 0.707180i | \(-0.250033\pi\) |
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.4756i | 0.775199i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.94364 | − | 17.2229i | −0.615496 | − | 1.06607i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.0845 | + | 10.4411i | −1.11514 | + | 0.643826i | −0.940156 | − | 0.340745i | \(-0.889321\pi\) |
−0.174984 | + | 0.984571i | \(0.555987\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.50526i | 0.399615i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.916671 | 0.0560994 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.6259 | + | 21.8687i | 0.769814 | + | 1.33336i | 0.937663 | + | 0.347545i | \(0.112984\pi\) |
−0.167849 | + | 0.985813i | \(0.553682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0602105 | − | 0.0347625i | 0.00365753 | − | 0.00211167i | −0.498170 | − | 0.867079i | \(-0.665994\pi\) |
0.501828 | + | 0.864968i | \(0.332661\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.998708 | −0.0604445 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.35068 | − | 9.26765i | 0.322658 | − | 0.558861i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 30.6016i | − | 1.83867i | −0.393476 | − | 0.919335i | \(-0.628727\pi\) | ||
0.393476 | − | 0.919335i | \(-0.371273\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.62520 | − | 6.27902i | 0.217035 | − | 0.375915i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8343 | + | 9.14196i | 0.944598 | + | 0.545364i | 0.891399 | − | 0.453220i | \(-0.149725\pi\) |
0.0531992 | + | 0.998584i | \(0.483058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.55189 | − | 6.15205i | −0.211138 | − | 0.365702i | 0.740933 | − | 0.671579i | \(-0.234384\pi\) |
−0.952071 | + | 0.305877i | \(0.901050\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.874612 | − | 0.0923926i | 0.0518075 | − | 0.00547286i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.84313 | − | 8.38854i | −0.285881 | − | 0.495160i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.62209 | + | 2.80955i | −0.0954172 | + | 0.165267i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.505980 | − | 0.876383i | 0.0296611 | − | 0.0513745i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.04737 | 0.294871 | 0.147435 | − | 0.989072i | \(-0.452898\pi\) | ||||
0.147435 | + | 0.989072i | \(0.452898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.98841 | + | 12.1043i | −0.406881 | + | 0.704739i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.00049i | 0.174106i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.467513 | − | 0.269919i | 0.0270370 | − | 0.0156098i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.77595 | + | 5.64415i | −0.563476 | + | 0.325323i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.201766 | 0.0115912 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.5272 | 0.831827 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.2869 | − | 13.4447i | 1.32905 | − | 0.767330i | 0.343900 | − | 0.939006i | \(-0.388252\pi\) |
0.985153 | + | 0.171676i | \(0.0549184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.919437 | + | 0.530837i | −0.0523049 | + | 0.0301983i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.98606i | − | 0.226029i | −0.993593 | − | 0.113014i | \(-0.963949\pi\) | ||
0.993593 | − | 0.113014i | \(-0.0360506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.77747 | − | 10.0069i | 0.326562 | − | 0.565622i | −0.655265 | − | 0.755399i | \(-0.727443\pi\) |
0.981827 | + | 0.189777i | \(0.0607765\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.51161 | 0.310544 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.75089 | + | 8.22878i | −0.266836 | + | 0.462174i | −0.968043 | − | 0.250784i | \(-0.919312\pi\) |
0.701207 | + | 0.712958i | \(0.252645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.9449 | − | 18.9571i | 0.612794 | − | 1.06139i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.03613 | + | 1.79463i | 0.0578312 | + | 0.100166i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.96755 | + | 17.9209i | −0.443326 | + | 0.997144i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.56853 | − | 13.1091i | −0.419826 | − | 0.727161i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.00970375 | − | 0.00560246i | −0.000536618 | − | 0.000309817i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.24574 | − | 10.8179i | 0.344339 | − | 0.596412i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 15.5237i | − | 0.853257i | −0.904427 | − | 0.426629i | \(-0.859701\pi\) | ||
0.904427 | − | 0.426629i | \(-0.140299\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.2023 | − | 22.8670i | 0.723481 | − | 1.25311i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.36983 | −0.0748420 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.28096 | + | 5.35837i | −0.505566 | + | 0.291889i | −0.731009 | − | 0.682368i | \(-0.760950\pi\) |
0.225443 | + | 0.974256i | \(0.427617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0693852 | + | 0.120179i | 0.00376849 | + | 0.00652721i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.98043 | 0.432164 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9074i | − | 0.912912i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0203548 | − | 0.0117518i | 0.00109587 | − | 0.000632698i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.6781 | + | 23.6912i | 0.734281 | + | 1.27181i | 0.955038 | + | 0.296483i | \(0.0958137\pi\) |
−0.220758 | + | 0.975329i | \(0.570853\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.17256i | 0.169823i | 0.996388 | + | 0.0849115i | \(0.0270608\pi\) | ||||
−0.996388 | + | 0.0849115i | \(0.972939\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.67557 | + | 2.12209i | 0.196187 | + | 0.113269i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.8670 | −1.64288 | −0.821442 | − | 0.570292i | \(-0.806830\pi\) | ||||
−0.821442 | + | 0.570292i | \(0.806830\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.49749 | + | 3.75133i | 0.344851 | + | 0.199100i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.484823 | − | 0.839738i | 0.0256595 | − | 0.0444436i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.49046 | − | 4.32462i | 0.395331 | − | 0.228245i | −0.289136 | − | 0.957288i | \(-0.593368\pi\) |
0.684468 | + | 0.729043i | \(0.260035\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.85223 | + | 18.0763i | −0.308012 | + | 0.951383i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0353503 | − | 0.0204095i | 0.00185541 | − | 0.00107122i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.238884 | + | 0.137920i | 0.0125037 | + | 0.00721904i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.5039 | − | 11.8379i | −1.07029 | − | 0.617934i | −0.142032 | − | 0.989862i | \(-0.545363\pi\) |
−0.928262 | + | 0.371928i | \(0.878697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.5009i | 1.06723i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.01742 | + | 3.47416i | 0.312409 | + | 0.180369i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.6176 | −1.06754 | −0.533769 | − | 0.845630i | \(-0.679225\pi\) | ||||
−0.533769 | + | 0.845630i | \(0.679225\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.833937 | − | 1.44442i | −0.0430643 | − | 0.0745896i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.4815 | − | 26.8147i | −0.797336 | − | 1.38103i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.6788i | 1.37040i | 0.728357 | + | 0.685198i | \(0.240284\pi\) | ||||
−0.728357 | + | 0.685198i | \(0.759716\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3.04591i | − | 0.156047i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.09527 | − | 8.82527i | −0.260356 | − | 0.450950i | 0.705980 | − | 0.708231i | \(-0.250507\pi\) |
−0.966337 | + | 0.257281i | \(0.917173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.03328 | + | 5.25380i | 0.154591 | + | 0.267759i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.8916 | 1.21448 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.8239 | + | 17.7962i | 1.56284 | + | 0.902304i | 0.996968 | + | 0.0778073i | \(0.0247919\pi\) |
0.565867 | + | 0.824496i | \(0.308541\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.524129i | 0.0265063i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.32471 | − | 0.764821i | −0.0668228 | − | 0.0385801i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.7149 | − | 10.8051i | −0.941650 | − | 0.543662i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.16833 | − | 3.56129i | 0.309580 | − | 0.178736i | −0.337159 | − | 0.941448i | \(-0.609466\pi\) |
0.646738 | + | 0.762712i | \(0.276133\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.381625 | − | 0.858365i | 0.0191052 | − | 0.0429720i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.84947 | + | 2.79984i | −0.242171 | + | 0.139817i | −0.616174 | − | 0.787610i | \(-0.711318\pi\) |
0.374003 | + | 0.927427i | \(0.377985\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.64415 | − | 9.77595i | 0.281155 | − | 0.486975i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.0221 | − | 5.78625i | −0.498001 | − | 0.287521i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.0632 | 1.44061 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.1134 | − | 11.0351i | −0.945095 | − | 0.545651i | −0.0535414 | − | 0.998566i | \(-0.517051\pi\) |
−0.891554 | + | 0.452915i | \(0.850384\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.495420i | − | 0.0244373i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.46437 | + | 12.9287i | 0.367298 | + | 0.636178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.3242 | + | 11.1569i | −0.948590 | + | 0.547668i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 0.0791066i | − | 0.00387387i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.2900 | −1.52862 | −0.764308 | − | 0.644852i | \(-0.776919\pi\) | ||||
−0.764308 | + | 0.644852i | \(0.776919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.59530 | + | 13.1555i | 0.370172 | + | 0.641157i | 0.989592 | − | 0.143903i | \(-0.0459653\pi\) |
−0.619419 | + | 0.785060i | \(0.712632\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.8960 | + | 13.2190i | −1.11324 | + | 0.642732i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.6966 | 0.712889 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.75832 | − | 13.4378i | 0.375451 | − | 0.650301i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.32659i | 0.112329i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2414 | + | 22.9348i | −0.637816 | + | 1.10473i | 0.348095 | + | 0.937459i | \(0.386829\pi\) |
−0.985911 | + | 0.167270i | \(0.946505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.39956 | + | 5.42684i | 0.451714 | + | 0.260797i | 0.708554 | − | 0.705657i | \(-0.249348\pi\) |
−0.256840 | + | 0.966454i | \(0.582681\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.674039 | − | 1.16747i | −0.0323177 | − | 0.0559759i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0533429 | + | 0.504957i | 0.00255174 | + | 0.0241554i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5459 | + | 32.1224i | 0.885148 | + | 1.53312i | 0.845544 | + | 0.533905i | \(0.179276\pi\) |
0.0396035 | + | 0.999215i | \(0.487391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.47432 | + | 12.9459i | −0.355920 | + | 0.616471i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.80227 | + | 15.2460i | −0.418208 | + | 0.724358i | −0.995759 | − | 0.0919965i | \(-0.970675\pi\) |
0.577551 | + | 0.816355i | \(0.304008\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.87627 | −0.373371 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.401163 | + | 0.694835i | −0.0189744 | + | 0.0328646i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.5796i | − | 1.39595i | −0.716124 | − | 0.697973i | \(-0.754085\pi\) | ||
0.716124 | − | 0.697973i | \(-0.245915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.5419 | + | 11.2825i | −0.920193 | + | 0.531274i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.782980 | + | 0.452054i | −0.0367876 | + | 0.0212393i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.58115 | 0.402290 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.3590 | 1.04591 | 0.522955 | − | 0.852360i | \(-0.324829\pi\) | ||||
0.522955 | + | 0.852360i | \(0.324829\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.56861 | + | 2.06034i | −0.166569 | + | 0.0961685i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.3417 | + | 15.2084i | −1.22686 | + | 0.708325i | −0.966371 | − | 0.257153i | \(-0.917216\pi\) |
−0.260485 | + | 0.965478i | \(0.583882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.6274i | − | 1.33043i | −0.746652 | − | 0.665214i | \(-0.768340\pi\) | ||
0.746652 | − | 0.665214i | \(-0.231660\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.245737 | − | 0.425630i | 0.0113958 | − | 0.0197381i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.27622 | −0.151605 | −0.0758027 | − | 0.997123i | \(-0.524152\pi\) | ||||
−0.0758027 | + | 0.997123i | \(0.524152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.731564 | + | 1.26711i | −0.0337805 | + | 0.0585095i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.776096 | + | 1.34424i | −0.0357606 | + | 0.0619392i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.1486 | + | 22.7740i | 0.604573 | + | 1.04715i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.1590 | − | 1.49574i | 0.649660 | − | 0.0686291i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.35302 | − | 12.7358i | −0.336672 | − | 0.583132i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.9345 | + | 15.5506i | 1.23067 | + | 0.710526i | 0.967169 | − | 0.254133i | \(-0.0817902\pi\) |
0.263499 | + | 0.964660i | \(0.415124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.5549 | − | 35.6022i | 0.937225 | − | 1.62332i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.0251044i | − | 0.00114229i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.34751 | + | 7.53010i | −0.197410 | + | 0.341924i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.8846 | −0.674488 | −0.337244 | − | 0.941417i | \(-0.609495\pi\) | ||||
−0.337244 | + | 0.941417i | \(0.609495\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.575679 | + | 0.332368i | −0.0260331 | + | 0.0150302i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8367 | − | 27.4299i | −0.714698 | − | 1.23789i | −0.963076 | − | 0.269231i | \(-0.913231\pi\) |
0.248377 | − | 0.968663i | \(-0.420103\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.0619 | 1.35392 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 12.8398i | − | 0.577108i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.94002 | − | 4.00682i | 0.311302 | − | 0.179730i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.1702 | − | 19.3473i | −0.500047 | − | 0.866106i | −1.00000 | 5.37306e-5i | \(-0.999983\pi\) | |
0.499953 | − | 0.866052i | \(-0.333350\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.719322i | 0.0321370i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.3683 | − | 10.6049i | −0.819001 | − | 0.472851i | 0.0310706 | − | 0.999517i | \(-0.490108\pi\) |
−0.850072 | + | 0.526667i | \(0.823442\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.73363 | −0.0771453 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.12483 | + | 0.649419i | 0.0499553 | + | 0.0288417i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.93051 | + | 3.34373i | −0.0855681 | + | 0.148208i | −0.905633 | − | 0.424062i | \(-0.860604\pi\) |
0.820065 | + | 0.572270i | \(0.193937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.255153 | − | 0.147313i | 0.0112873 | − | 0.00651673i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.22839 | + | 2.34817i | −0.142537 | + | 0.103674i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.90003 | − | 4.56109i | 0.348117 | − | 0.200985i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.2014 | − | 14.5501i | −1.10836 | − | 0.639911i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.23971 | − | 0.715746i | −0.0544171 | − | 0.0314178i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.0368i | 1.62261i | 0.584620 | + | 0.811307i | \(0.301243\pi\) | ||||
−0.584620 | + | 0.811307i | \(0.698757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.3903 | − | 11.7723i | −0.891604 | − | 0.514768i | −0.0171370 | − | 0.999853i | \(-0.505455\pi\) |
−0.874467 | + | 0.485085i | \(0.838788\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.703929 | −0.0307220 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.47991 | + | 9.49147i | 0.238708 | + | 0.413455i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4932 | − | 19.9068i | −0.499705 | − | 0.865514i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 31.5965i | − | 1.37117i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.9182i | 1.38253i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.90269 | − | 15.4199i | −0.384897 | − | 0.666661i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.10044 | − | 1.90602i | −0.0474874 | − | 0.0822506i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.4538 | −0.708716 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.1064 | − | 10.4537i | −0.778456 | − | 0.449442i | 0.0574271 | − | 0.998350i | \(-0.481710\pi\) |
−0.835883 | + | 0.548908i | \(0.815044\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.05173i | 0.0451342i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0833770 | + | 0.0481378i | 0.00357148 | + | 0.00206200i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4537 | − | 6.03547i | −0.446970 | − | 0.258058i | 0.259580 | − | 0.965722i | \(-0.416416\pi\) |
−0.706550 | + | 0.707664i | \(0.749749\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.4410 | + | 16.4204i | −1.21383 | + | 0.700806i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.9624 | − | 3.05954i | 1.23384 | − | 0.130341i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.9895 | + | 11.5410i | −0.850042 | + | 0.490772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.894930 | − | 1.55006i | 0.0379877 | − | 0.0657966i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.52452 | − | 4.92164i | −0.361196 | − | 0.208536i | 0.308409 | − | 0.951254i | \(-0.400203\pi\) |
−0.669605 | + | 0.742717i | \(0.733537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.1973 | 1.57328 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.95625 | − | 1.12944i | −0.0825930 | − | 0.0476851i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.94787i | 0.334963i | 0.985875 | + | 0.167481i | \(0.0535634\pi\) | ||||
−0.985875 | + | 0.167481i | \(0.946437\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.596175 | − | 1.03261i | −0.0250813 | − | 0.0434420i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.7047 | + | 6.18034i | −0.449553 | + | 0.259550i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.6989i | 1.11927i | 0.828738 | + | 0.559637i | \(0.189060\pi\) | ||||
−0.828738 | + | 0.559637i | \(0.810940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.44613 | 0.311611 | 0.155805 | − | 0.987788i | \(-0.450203\pi\) | ||||
0.155805 | + | 0.987788i | \(0.450203\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.901586 | + | 1.56159i | 0.0376643 | + | 0.0652365i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.329522 | − | 0.190250i | 0.0137420 | − | 0.00793395i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.2403 | 1.67523 | 0.837613 | − | 0.546264i | \(-0.183951\pi\) | ||||
0.837613 | + | 0.546264i | \(0.183951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.989173 | + | 1.71330i | −0.0411086 | + | 0.0712022i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.8334i | 0.988777i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.09339 | − | 14.0182i | 0.335194 | − | 0.580573i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.7287 | − | 9.08096i | −0.650301 | − | 0.375451i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.4442 | − | 35.4103i | −0.843821 | − | 1.46154i | −0.886641 | − | 0.462458i | \(-0.846968\pi\) |
0.0428204 | − | 0.999083i | \(-0.486366\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.24545 | + | 8.58659i | 0.257339 | + | 0.353804i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.46037 | + | 2.52944i | 0.0600716 | + | 0.104047i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.479363 | + | 0.830281i | −0.0196851 | + | 0.0340956i | −0.875700 | − | 0.482855i | \(-0.839600\pi\) |
0.856015 | + | 0.516951i | \(0.172933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.16572 | + | 7.21524i | −0.170778 | + | 0.295796i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.14560 | 0.0468862 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.5798 | + | 25.2529i | −0.595713 | + | 1.03180i | 0.397733 | + | 0.917501i | \(0.369797\pi\) |
−0.993446 | + | 0.114304i | \(0.963536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.5037i | − | 1.44823i | −0.689682 | − | 0.724113i | \(-0.742250\pi\) | ||
0.689682 | − | 0.724113i | \(-0.257750\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.68182 | − | 1.54835i | 0.109212 | − | 0.0630536i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.303739 | + | 0.175364i | −0.0123487 | + | 0.00712955i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.41509 | 0.219792 | 0.109896 | − | 0.993943i | \(-0.464948\pi\) | ||||
0.109896 | + | 0.993943i | \(0.464948\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.43989 | −0.0583474 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.6474 | + | 20.5810i | −1.44214 | + | 0.832619i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.93813 | + | 2.27368i | −0.159060 | + | 0.0918332i | −0.577417 | − | 0.816449i | \(-0.695939\pi\) |
0.418357 | + | 0.908283i | \(0.362606\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.38967i | 0.0560369i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.233626 | − | 0.404652i | 0.00940542 | − | 0.0162907i | −0.861284 | − | 0.508123i | \(-0.830339\pi\) |
0.870690 | + | 0.491833i | \(0.163673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.20501 | 0.169014 | 0.0845069 | − | 0.996423i | \(-0.473068\pi\) | ||||
0.0845069 | + | 0.996423i | \(0.473068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0533429 | + | 0.0923926i | −0.00214058 | + | 0.00370759i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.20635 | + | 7.28561i | −0.168524 | + | 0.291892i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00054 | − | 1.73298i | −0.0400214 | − | 0.0693192i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.99965 | − | 0.889034i | −0.0798581 | − | 0.0355046i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.9568 | + | 34.5662i | 0.795730 | + | 1.37824i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5333 | − | 13.0096i | −0.897037 | − | 0.517905i | −0.0207994 | − | 0.999784i | \(-0.506621\pi\) |
−0.876238 | + | 0.481879i | \(0.839954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.10970 | + | 1.92207i | −0.0441068 | + | 0.0763952i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.1712i | 1.03857i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.6369 | + | 20.1558i | −0.461072 | + | 0.798600i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.9608 | −0.670958 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.9714 | + | 16.1493i | −1.10480 | + | 0.637858i | −0.937478 | − | 0.348044i | \(-0.886846\pi\) |
−0.167324 | + | 0.985902i | \(0.553513\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.85776 | + | 3.21773i | 0.0732628 | + | 0.126895i | 0.900330 | − | 0.435209i | \(-0.143325\pi\) |
−0.827067 | + | 0.562104i | \(0.809992\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.61951 | 0.0637682 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 37.7366i | − | 1.48358i | −0.670634 | − | 0.741789i | \(-0.733978\pi\) | ||
0.670634 | − | 0.741789i | \(-0.266022\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.1186 | − | 17.3890i | 1.18226 | − | 0.682577i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.262474 | − | 0.454618i | −0.0102872 | − | 0.0178179i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.76815i | 0.264858i | 0.991192 | + | 0.132429i | \(0.0422777\pi\) | ||||
−0.991192 | + | 0.132429i | \(0.957722\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.3822 | + | 6.57154i | 0.444741 | + | 0.256771i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.623572 | −0.0243279 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.3912 | − | 21.5878i | −1.45655 | − | 0.840942i | −0.457715 | − | 0.889099i | \(-0.651332\pi\) |
−0.998840 | + | 0.0481567i | \(0.984665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.7222 | + | 25.4995i | −0.572626 | + | 0.991817i | 0.423669 | + | 0.905817i | \(0.360742\pi\) |
−0.996295 | + | 0.0859999i | \(0.972592\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.76711 | + | 1.59759i | −0.107466 | + | 0.0620454i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.27902 | + | 7.37529i | −0.127155 | + | 0.286001i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.674039 | − | 0.389157i | 0.0260989 | − | 0.0150682i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.96110 | − | 1.70959i | −0.114483 | − | 0.0660966i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.3047 | − | 18.0738i | −1.20850 | − | 0.697730i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.1793i | 1.66444i | 0.554447 | + | 0.832219i | \(0.312930\pi\) | ||||
−0.554447 | + | 0.832219i | \(0.687070\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.59069 | + | 1.49574i | 0.0997157 | + | 0.0575709i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.2822 | 0.548910 | 0.274455 | − | 0.961600i | \(-0.411503\pi\) | ||||
0.274455 | + | 0.961600i | \(0.411503\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.64360 | + | 8.04295i | 0.178205 | + | 0.308660i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.413778 | − | 0.716684i | −0.0158560 | − | 0.0274634i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.48052i | 0.209706i | 0.994488 | + | 0.104853i | \(0.0334373\pi\) | ||||
−0.994488 | + | 0.104853i | \(0.966563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.25677i | 0.162643i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.65071 | + | 2.85911i | 0.0629783 | + | 0.109082i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.4481 | − | 19.8287i | −0.436137 | − | 0.755412i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.8769 | − | 6.85716i | −0.451168 | − | 0.260482i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.679704i | 0.0257826i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.8376 | − | 15.4947i | −1.01655 | − | 0.586904i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.36685 | + | 1.36650i | 0.0895227 | + | 0.0516859i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.12070 | + | 5.26584i | −0.344484 | + | 0.198888i | −0.662253 | − | 0.749280i | \(-0.730400\pi\) |
0.317769 | + | 0.948168i | \(0.397066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.7448 | + | 31.2708i | 0.857836 | + | 1.17940i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.55203 | + | 0.896065i | −0.0584529 | + | 0.0337478i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.925849 | + | 1.60362i | −0.0348201 | + | 0.0603102i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.8847 | + | 16.6766i | 1.08479 | + | 0.626303i | 0.932184 | − | 0.361985i | \(-0.117901\pi\) |
0.152604 | + | 0.988287i | \(0.451234\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.8527 | 1.83212 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.245737 | + | 0.141877i | 0.00920294 | + | 0.00531332i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 19.9906i | − | 0.747607i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.78512 | − | 3.09192i | −0.0666666 | − | 0.115470i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.7303 | + | 21.7836i | −1.40710 | + | 0.812391i | −0.995108 | − | 0.0987944i | \(-0.968501\pi\) |
−0.411995 | + | 0.911186i | \(0.635168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 9.74345i | − | 0.362865i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.17895 | 0.0810361 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.9120 | − | 18.9001i | −0.405260 | − | 0.701931i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.6536 | + | 15.3885i | −0.988528 | + | 0.570727i | −0.904834 | − | 0.425765i | \(-0.860005\pi\) |
−0.0836937 | + | 0.996492i | \(0.526672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.7402 | 0.953341 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0574 | + | 31.2764i | −0.667879 | + | 1.15680i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.99593i | 0.258400i | 0.991619 | + | 0.129200i | \(0.0412410\pi\) | ||||
−0.991619 | + | 0.129200i | \(0.958759\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.506654 | + | 0.877550i | −0.0186882 | + | 0.0323689i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.95185 | + | 1.70425i | 0.108733 | + | 0.0627768i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1634 | + | 24.5318i | 0.521011 | + | 0.902417i | 0.999701 | + | 0.0244334i | \(0.00777816\pi\) |
−0.478691 | + | 0.877984i | \(0.658889\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.50330 | + | 1.82078i | −0.0919612 | + | 0.0668880i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.78665 | + | 11.7548i | 0.248978 | + | 0.431242i | 0.963243 | − | 0.268633i | \(-0.0865720\pi\) |
−0.714265 | + | 0.699876i | \(0.753239\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.44690 | − | 5.97020i | 0.126285 | − | 0.218731i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.2216 | − | 43.6851i | 0.922810 | − | 1.59835i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.0181 | −0.694904 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.22439 | + | 3.85276i | −0.0811693 | + | 0.140589i | −0.903752 | − | 0.428056i | \(-0.859199\pi\) |
0.822583 | + | 0.568645i | \(0.192532\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.69362i | − | 0.0617188i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.72756 | − | 3.88416i | 0.244841 | − | 0.141359i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.0331 | + | 10.9888i | −0.691770 | + | 0.399394i | −0.804275 | − | 0.594258i | \(-0.797446\pi\) |
0.112505 | + | 0.993651i | \(0.464113\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.0584833 | −0.00212281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.7566 | 1.25992 | 0.629962 | − | 0.776626i | \(-0.283070\pi\) | ||||
0.629962 | + | 0.776626i | \(0.283070\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0890556 | − | 0.0514163i | 0.00322403 | − | 0.00186139i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.2710 | − | 8.81670i | 0.552123 | − | 0.318769i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 49.1933i | − | 1.77627i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.7808 | + | 34.2613i | −0.713313 | + | 1.23549i | 0.250294 | + | 0.968170i | \(0.419473\pi\) |
−0.963607 | + | 0.267324i | \(0.913861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.27115 | −0.0457792 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.95429 | − | 3.38492i | 0.0702908 | − | 0.121747i | −0.828738 | − | 0.559637i | \(-0.810941\pi\) |
0.899029 | + | 0.437890i | \(0.144274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.97822 | − | 6.89048i | 0.142902 | − | 0.247513i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.955881 | − | 1.65563i | −0.0342920 | − | 0.0593955i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.4330 | − | 12.1966i | −0.982888 | − | 0.436988i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.33428 | − | 16.1674i | −0.334007 | − | 0.578517i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.29927 | + | 3.05954i | 0.189381 | + | 0.109339i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.66841 | − | 11.5500i | 0.238006 | − | 0.412238i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 50.8902i | − | 1.81404i | −0.421089 | − | 0.907019i | \(-0.638352\pi\) | ||
0.421089 | − | 0.907019i | \(-0.361648\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.59999 | − | 2.77126i | 0.0569612 | − | 0.0986596i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.27356 | −0.0452825 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.2804 | + | 25.5653i | −1.57244 | + | 0.907850i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.498432 | − | 0.863309i | −0.0176775 | − | 0.0306184i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.1212 | −1.59828 | −0.799138 | − | 0.601148i | \(-0.794710\pi\) | ||||
−0.799138 | + | 0.601148i | \(0.794710\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 39.9642i | − | 1.41383i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.4199 | − | 8.90269i | 0.544836 | − | 0.314561i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.343180 | − | 0.594404i | −0.0121105 | − | 0.0209761i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.215704i | 0.00760256i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.35115 | − | 1.93478i | −0.117966 | − | 0.0681077i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.1281 | −0.883456 | −0.441728 | − | 0.897149i | \(-0.645634\pi\) | ||||
−0.441728 | + | 0.897149i | \(0.645634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.6921 | − | 14.8333i | −0.902170 | − | 0.520868i | −0.0242664 | − | 0.999706i | \(-0.507725\pi\) |
−0.877904 | + | 0.478837i | \(0.841058\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.00532699 | + | 0.00922662i | −0.000186826 | + | 0.000323592i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.94638 | − | 2.85579i | 0.173264 | − | 0.100034i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.2138 | + | 31.9702i | −0.497278 | + | 1.11849i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.7999 | + | 9.69943i | −0.587036 | + | 0.338925i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.5238 | + | 21.0870i | 1.27469 | + | 0.735943i | 0.975867 | − | 0.218366i | \(-0.0700726\pi\) |
0.298823 | + | 0.954308i | \(0.403406\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.52058 | + | 0.877908i | 0.0530041 | + | 0.0306019i | 0.526268 | − | 0.850319i | \(-0.323591\pi\) |
−0.473264 | + | 0.880921i | \(0.656924\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.63987i | 0.0570930i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.8493 | + | 10.3053i | 0.620680 | + | 0.358350i | 0.777134 | − | 0.629335i | \(-0.216673\pi\) |
−0.156453 | + | 0.987685i | \(0.550006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.0322 | −0.765211 | −0.382606 | − | 0.923912i | \(-0.624973\pi\) | ||||
−0.382606 | + | 0.923912i | \(0.624973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.34468 | + | 4.06111i | 0.0813362 | + | 0.140878i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.2983 | − | 19.5692i | −0.391463 | − | 0.678034i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 6.18060i | − | 0.213888i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.23086i | 0.0771097i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.5701 | − | 32.1643i | −0.641109 | − | 1.11043i | −0.985185 | − | 0.171492i | \(-0.945141\pi\) |
0.344076 | − | 0.938942i | \(-0.388192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.82049 | − | 13.5455i | −0.269672 | − | 0.467086i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.80182 | −0.0964998 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.66480 | − | 5.57997i | −0.332479 | − | 0.191957i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.374615i | 0.0128719i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.942737 | + | 0.544290i | 0.0323547 | + | 0.0186800i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.894930 | + | 0.516688i | 0.0306778 | + | 0.0177118i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.1348 | − | 14.5116i | 0.860601 | − | 0.496868i | −0.00361260 | − | 0.999993i | \(-0.501150\pi\) |
0.864213 | + | 0.503125i | \(0.167817\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.8151 | − | 10.0484i | 0.472466 | − | 0.343648i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.7972 | − | 12.5846i | 0.744578 | − | 0.429882i | −0.0791537 | − | 0.996862i | \(-0.525222\pi\) |
0.823731 | + | 0.566980i | \(0.191888\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.2793 | + | 28.1966i | −0.555443 | + | 0.962056i | 0.442426 | + | 0.896805i | \(0.354118\pi\) |
−0.997869 | + | 0.0652505i | \(0.979215\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.28546 | + | 0.742158i | 0.0438082 | + | 0.0252927i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.6750 | 0.669746 | 0.334873 | − | 0.942263i | \(-0.391307\pi\) | ||||
0.334873 | + | 0.942263i | \(0.391307\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.6519 | + | 6.14987i | 0.362175 | + | 0.209102i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 0.497137i | − | 0.0168837i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.8858 | + | 46.5676i | 0.912038 | + | 1.57970i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.17538 | − | 2.41066i | 0.141477 | − | 0.0816820i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 19.6563i | − | 0.665264i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.3068 | 0.517465 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9490 | − | 24.1603i | −0.471023 | − | 0.815836i | 0.528428 | − | 0.848978i | \(-0.322782\pi\) |
−0.999451 | + | 0.0331425i | \(0.989448\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.669833 | + | 0.386728i | −0.0225929 | + | 0.0130440i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.70445 | −0.326951 | −0.163476 | − | 0.986547i | \(-0.552271\pi\) | ||||
−0.163476 | + | 0.986547i | \(0.552271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.4195 | + | 18.0470i | −0.350643 | + | 0.607331i | −0.986362 | − | 0.164589i | \(-0.947370\pi\) |
0.635719 | + | 0.771920i | \(0.280704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 2.14180i | − | 0.0719959i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0498 | + | 20.8709i | −0.404594 | + | 0.700777i | −0.994274 | − | 0.106860i | \(-0.965920\pi\) |
0.589680 | + | 0.807637i | \(0.299254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.2086 | + | 13.9768i | 0.811930 | + | 0.468768i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.3977 | + | 24.9375i | 0.482341 | + | 0.835439i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.06734 | − | 38.5025i | −0.136108 | − | 1.28844i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.45525 | + | 16.3770i | 0.316054 | + | 0.547422i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0413622 | + | 0.0716414i | −0.00138104 | + | 0.00239204i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.13748 | − | 14.0945i | 0.271400 | − | 0.470079i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.2299 | 0.740585 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.864906 | − | 1.49806i | 0.0287823 | − | 0.0498524i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.03676i | − | 0.300392i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.7097 | − | 24.6585i | 1.41815 | − | 0.818771i | 0.422017 | − | 0.906588i | \(-0.361322\pi\) |
0.996137 | + | 0.0878168i | \(0.0279890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.39404 | − | 1.95955i | 0.112573 | − | 0.0649941i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.7040 | −0.619691 | −0.309845 | − | 0.950787i | \(-0.600277\pi\) | ||||
−0.309845 | + | 0.950787i | \(0.600277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.5223 | 1.83752 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.92790 | + | 1.11307i | −0.0637344 | + | 0.0367971i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.1574 | − | 7.01910i | 0.401474 | − | 0.231791i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.8088i | 0.983302i | 0.870792 | + | 0.491651i | \(0.163606\pi\) | ||||
−0.870792 | + | 0.491651i | \(0.836394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.06026 | + | 3.56847i | −0.0678878 | + | 0.117585i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.4066 | −0.869185 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.4879 | − | 25.0939i | 0.476361 | − | 0.825081i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.3110 | + | 17.8591i | −0.338656 | + | 0.586570i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.73298 | − | 3.00161i | −0.0568572 | − | 0.0984796i | 0.836196 | − | 0.548431i | \(-0.184775\pi\) |
−0.893053 | + | 0.449951i | \(0.851441\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.8767 | − | 17.7036i | −0.422016 | − | 0.580211i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.305411 | + | 0.528987i | 0.00999870 | + | 0.0173183i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.8086 | + | 9.70445i | 0.549700 | + | 0.317370i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.7679 | − | 23.8467i | 0.449779 | − | 0.779039i | −0.548593 | − | 0.836090i | \(-0.684836\pi\) |
0.998371 | + | 0.0570504i | \(0.0181696\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.77067i | 0.0577837i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.09119 | − | 1.88999i | 0.0355717 | − | 0.0616120i | −0.847691 | − | 0.530490i | \(-0.822008\pi\) |
0.883263 | + | 0.468878i | \(0.155341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.802327 | −0.0261274 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.46865 | + | 0.847928i | −0.0477753 | + | 0.0275831i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.6884 | + | 30.6371i | 0.574794 | + | 0.995573i | 0.996064 | + | 0.0886376i | \(0.0282513\pi\) |
−0.421270 | + | 0.906935i | \(0.638415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.970853 | −0.0315152 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.45605i | − | 0.0472155i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.5449 | − | 15.3257i | 0.859872 | − | 0.496448i | −0.00409718 | − | 0.999992i | \(-0.501304\pi\) |
0.863970 | + | 0.503544i | \(0.167971\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.74665 | − | 13.4176i | −0.250676 | − | 0.434183i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.35437i | 0.108431i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.93755 | + | 2.27334i | 0.127150 | + | 0.0734101i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0666 | −0.808599 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.8588 | + | 20.1258i | 1.12331 | + | 0.648543i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.49922 | − | 14.7211i | 0.273600 | − | 0.473888i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.4331 | + | 15.2611i | −0.850030 | + | 0.490765i | −0.860661 | − | 0.509178i | \(-0.829949\pi\) |
0.0106307 | + | 0.999943i | \(0.496616\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.315725 | − | 2.98874i | −0.0101426 | − | 0.0960121i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.06048 | + | 2.92167i | −0.162398 | + | 0.0937608i | −0.578997 | − | 0.815330i | \(-0.696556\pi\) |
0.416598 | + | 0.909091i | \(0.363222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.628731 | + | 0.362998i | 0.0201562 | + | 0.0116372i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00883 | + | 1.15980i | 0.0643340 | + | 0.0371432i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.6943i | 0.726054i | 0.931779 | + | 0.363027i | \(0.118257\pi\) | ||||
−0.931779 | + | 0.363027i | \(0.881743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.9725 | + | 9.79910i | 0.542445 | + | 0.313181i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.217644 | −0.00694884 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.5144 | + | 45.9243i | 0.845679 | + | 1.46476i | 0.885031 | + | 0.465533i | \(0.154137\pi\) |
−0.0393519 | + | 0.999225i | \(0.512529\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.5479 | − | 21.7336i | −0.399808 | − | 0.692489i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.91419i | 0.0609292i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.935026i | 0.0297321i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.6987 | − | 21.9948i | −0.403387 | − | 0.698687i | 0.590745 | − | 0.806858i | \(-0.298834\pi\) |
−0.994132 | + | 0.108171i | \(0.965500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.18942 | + | 2.06013i | 0.0377450 | + | 0.0653763i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.84327 | −0.312053 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.3070 | − | 18.6525i | −1.02317 | − | 0.590729i | −0.108151 | − | 0.994134i | \(-0.534493\pi\) |
−0.915021 | + | 0.403405i | \(0.867826\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.12437i | 0.257044i |
(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 | 1216.2.s.i.31.7 | ✓ | 32 | |
4.3 | odd | 2 | inner | 1216.2.s.i.31.9 | yes | 32 | |
8.3 | odd | 2 | inner | 1216.2.s.i.31.8 | yes | 32 | |
8.5 | even | 2 | inner | 1216.2.s.i.31.10 | yes | 32 | |
19.8 | odd | 6 | inner | 1216.2.s.i.863.8 | yes | 32 | |
76.27 | even | 6 | inner | 1216.2.s.i.863.10 | yes | 32 | |
152.27 | even | 6 | inner | 1216.2.s.i.863.7 | yes | 32 | |
152.141 | odd | 6 | inner | 1216.2.s.i.863.9 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.s.i.31.7 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1216.2.s.i.31.8 | yes | 32 | 8.3 | odd | 2 | inner | |
1216.2.s.i.31.9 | yes | 32 | 4.3 | odd | 2 | inner | |
1216.2.s.i.31.10 | yes | 32 | 8.5 | even | 2 | inner | |
1216.2.s.i.863.7 | yes | 32 | 152.27 | even | 6 | inner | |
1216.2.s.i.863.8 | yes | 32 | 19.8 | odd | 6 | inner | |
1216.2.s.i.863.9 | yes | 32 | 152.141 | odd | 6 | inner | |
1216.2.s.i.863.10 | yes | 32 | 76.27 | even | 6 | inner |