Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(1,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.a (trivial) |
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: | yes |
Analytic conductor: | \(3.91266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.41421 | 1.97120 | 0.985599 | − | 0.169102i | \(-0.0540867\pi\) | ||||
0.985599 | + | 0.169102i | \(0.0540867\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.41421 | −1.39385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.65685 | 2.88562 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −0.828427 | −0.249780 | −0.124890 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124890 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(12\) | 3.41421 | 0.985599 | ||||||||
\(13\) | −4.82843 | −1.33916 | −0.669582 | − | 0.742738i | \(-0.733527\pi\) | ||||
−0.669582 | + | 0.742738i | \(0.733527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.58579 | 0.627145 | 0.313573 | − | 0.949564i | \(-0.398474\pi\) | ||||
0.313573 | + | 0.949564i | \(0.398474\pi\) | |||||||
\(18\) | −8.65685 | −2.04044 | ||||||||
\(19\) | 0.585786 | 0.134389 | 0.0671943 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671943 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.828427 | 0.176621 | ||||||||
\(23\) | −1.17157 | −0.244290 | −0.122145 | − | 0.992512i | \(-0.538977\pi\) | ||||
−0.122145 | + | 0.992512i | \(0.538977\pi\) | |||||||
\(24\) | −3.41421 | −0.696923 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.82843 | 0.946932 | ||||||||
\(27\) | 19.3137 | 3.71692 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.82843 | −0.896616 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(30\) | −3.41421 | −0.623347 | ||||||||
\(31\) | −2.82843 | −0.508001 | −0.254000 | − | 0.967204i | \(-0.581746\pi\) | ||||
−0.254000 | + | 0.967204i | \(0.581746\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.82843 | −0.492366 | ||||||||
\(34\) | −2.58579 | −0.443459 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.65685 | 1.44281 | ||||||||
\(37\) | −7.65685 | −1.25878 | −0.629390 | − | 0.777090i | \(-0.716695\pi\) | ||||
−0.629390 | + | 0.777090i | \(0.716695\pi\) | |||||||
\(38\) | −0.585786 | −0.0950271 | ||||||||
\(39\) | −16.4853 | −2.63976 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −3.07107 | −0.479620 | −0.239810 | − | 0.970820i | \(-0.577085\pi\) | ||||
−0.239810 | + | 0.970820i | \(0.577085\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.82843 | −1.34632 | −0.673161 | − | 0.739496i | \(-0.735064\pi\) | ||||
−0.673161 | + | 0.739496i | \(0.735064\pi\) | |||||||
\(44\) | −0.828427 | −0.124890 | ||||||||
\(45\) | 8.65685 | 1.29049 | ||||||||
\(46\) | 1.17157 | 0.172739 | ||||||||
\(47\) | 5.17157 | 0.754351 | 0.377176 | − | 0.926142i | \(-0.376895\pi\) | ||||
0.377176 | + | 0.926142i | \(0.376895\pi\) | |||||||
\(48\) | 3.41421 | 0.492799 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 8.82843 | 1.23623 | ||||||||
\(52\) | −4.82843 | −0.669582 | ||||||||
\(53\) | 6.48528 | 0.890822 | 0.445411 | − | 0.895326i | \(-0.353058\pi\) | ||||
0.445411 | + | 0.895326i | \(0.353058\pi\) | |||||||
\(54\) | −19.3137 | −2.62826 | ||||||||
\(55\) | −0.828427 | −0.111705 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 4.82843 | 0.634004 | ||||||||
\(59\) | 8.58579 | 1.11777 | 0.558887 | − | 0.829244i | \(-0.311229\pi\) | ||||
0.558887 | + | 0.829244i | \(0.311229\pi\) | |||||||
\(60\) | 3.41421 | 0.440773 | ||||||||
\(61\) | 9.31371 | 1.19250 | 0.596249 | − | 0.802799i | \(-0.296657\pi\) | ||||
0.596249 | + | 0.802799i | \(0.296657\pi\) | |||||||
\(62\) | 2.82843 | 0.359211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.82843 | −0.598893 | ||||||||
\(66\) | 2.82843 | 0.348155 | ||||||||
\(67\) | 1.65685 | 0.202417 | 0.101208 | − | 0.994865i | \(-0.467729\pi\) | ||||
0.101208 | + | 0.994865i | \(0.467729\pi\) | |||||||
\(68\) | 2.58579 | 0.313573 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48528 | −0.532305 | −0.266152 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266152 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(72\) | −8.65685 | −1.02022 | ||||||||
\(73\) | −9.41421 | −1.10185 | −0.550925 | − | 0.834555i | \(-0.685725\pi\) | ||||
−0.550925 | + | 0.834555i | \(0.685725\pi\) | |||||||
\(74\) | 7.65685 | 0.890091 | ||||||||
\(75\) | 3.41421 | 0.394239 | ||||||||
\(76\) | 0.585786 | 0.0671943 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.4853 | 1.86659 | ||||||||
\(79\) | −6.82843 | −0.768258 | −0.384129 | − | 0.923279i | \(-0.625498\pi\) | ||||
−0.384129 | + | 0.923279i | \(0.625498\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 39.9706 | 4.44117 | ||||||||
\(82\) | 3.07107 | 0.339143 | ||||||||
\(83\) | −2.24264 | −0.246162 | −0.123081 | − | 0.992397i | \(-0.539277\pi\) | ||||
−0.123081 | + | 0.992397i | \(0.539277\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58579 | 0.280468 | ||||||||
\(86\) | 8.82843 | 0.951994 | ||||||||
\(87\) | −16.4853 | −1.76741 | ||||||||
\(88\) | 0.828427 | 0.0883106 | ||||||||
\(89\) | 12.7279 | 1.34916 | 0.674579 | − | 0.738203i | \(-0.264325\pi\) | ||||
0.674579 | + | 0.738203i | \(0.264325\pi\) | |||||||
\(90\) | −8.65685 | −0.912513 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.17157 | −0.122145 | ||||||||
\(93\) | −9.65685 | −1.00137 | ||||||||
\(94\) | −5.17157 | −0.533407 | ||||||||
\(95\) | 0.585786 | 0.0601004 | ||||||||
\(96\) | −3.41421 | −0.348462 | ||||||||
\(97\) | −7.75736 | −0.787641 | −0.393820 | − | 0.919187i | \(-0.628847\pi\) | ||||
−0.393820 | + | 0.919187i | \(0.628847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.17157 | −0.720770 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.3137 | 1.32476 | 0.662382 | − | 0.749166i | \(-0.269546\pi\) | ||||
0.662382 | + | 0.749166i | \(0.269546\pi\) | |||||||
\(102\) | −8.82843 | −0.874145 | ||||||||
\(103\) | −14.8284 | −1.46109 | −0.730544 | − | 0.682865i | \(-0.760734\pi\) | ||||
−0.730544 | + | 0.682865i | \(0.760734\pi\) | |||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.48528 | −0.629906 | ||||||||
\(107\) | 9.65685 | 0.933563 | 0.466782 | − | 0.884373i | \(-0.345413\pi\) | ||||
0.466782 | + | 0.884373i | \(0.345413\pi\) | |||||||
\(108\) | 19.3137 | 1.85846 | ||||||||
\(109\) | 2.48528 | 0.238047 | 0.119023 | − | 0.992891i | \(-0.462024\pi\) | ||||
0.119023 | + | 0.992891i | \(0.462024\pi\) | |||||||
\(110\) | 0.828427 | 0.0789874 | ||||||||
\(111\) | −26.1421 | −2.48130 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.3137 | −1.44059 | −0.720296 | − | 0.693667i | \(-0.755994\pi\) | ||||
−0.720296 | + | 0.693667i | \(0.755994\pi\) | |||||||
\(114\) | −2.00000 | −0.187317 | ||||||||
\(115\) | −1.17157 | −0.109250 | ||||||||
\(116\) | −4.82843 | −0.448308 | ||||||||
\(117\) | −41.7990 | −3.86432 | ||||||||
\(118\) | −8.58579 | −0.790386 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.41421 | −0.311674 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | −9.31371 | −0.843224 | ||||||||
\(123\) | −10.4853 | −0.945426 | ||||||||
\(124\) | −2.82843 | −0.254000 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82843 | 0.250982 | 0.125491 | − | 0.992095i | \(-0.459949\pi\) | ||||
0.125491 | + | 0.992095i | \(0.459949\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −30.1421 | −2.65387 | ||||||||
\(130\) | 4.82843 | 0.423481 | ||||||||
\(131\) | −6.24264 | −0.545422 | −0.272711 | − | 0.962096i | \(-0.587920\pi\) | ||||
−0.272711 | + | 0.962096i | \(0.587920\pi\) | |||||||
\(132\) | −2.82843 | −0.246183 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.65685 | −0.143130 | ||||||||
\(135\) | 19.3137 | 1.66226 | ||||||||
\(136\) | −2.58579 | −0.221729 | ||||||||
\(137\) | −16.0000 | −1.36697 | −0.683486 | − | 0.729964i | \(-0.739537\pi\) | ||||
−0.683486 | + | 0.729964i | \(0.739537\pi\) | |||||||
\(138\) | 4.00000 | 0.340503 | ||||||||
\(139\) | 19.8995 | 1.68785 | 0.843927 | − | 0.536459i | \(-0.180238\pi\) | ||||
0.843927 | + | 0.536459i | \(0.180238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.6569 | 1.48698 | ||||||||
\(142\) | 4.48528 | 0.376396 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 8.65685 | 0.721405 | ||||||||
\(145\) | −4.82843 | −0.400979 | ||||||||
\(146\) | 9.41421 | 0.779126 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.65685 | −0.629390 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | −3.41421 | −0.278769 | ||||||||
\(151\) | −11.3137 | −0.920697 | −0.460348 | − | 0.887738i | \(-0.652275\pi\) | ||||
−0.460348 | + | 0.887738i | \(0.652275\pi\) | |||||||
\(152\) | −0.585786 | −0.0475136 | ||||||||
\(153\) | 22.3848 | 1.80970 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.82843 | −0.227185 | ||||||||
\(156\) | −16.4853 | −1.31988 | ||||||||
\(157\) | 6.48528 | 0.517582 | 0.258791 | − | 0.965933i | \(-0.416676\pi\) | ||||
0.258791 | + | 0.965933i | \(0.416676\pi\) | |||||||
\(158\) | 6.82843 | 0.543240 | ||||||||
\(159\) | 22.1421 | 1.75599 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −39.9706 | −3.14038 | ||||||||
\(163\) | −20.1421 | −1.57765 | −0.788827 | − | 0.614615i | \(-0.789311\pi\) | ||||
−0.788827 | + | 0.614615i | \(0.789311\pi\) | |||||||
\(164\) | −3.07107 | −0.239810 | ||||||||
\(165\) | −2.82843 | −0.220193 | ||||||||
\(166\) | 2.24264 | 0.174063 | ||||||||
\(167\) | 15.7990 | 1.22256 | 0.611281 | − | 0.791413i | \(-0.290654\pi\) | ||||
0.611281 | + | 0.791413i | \(0.290654\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | −2.58579 | −0.198321 | ||||||||
\(171\) | 5.07107 | 0.387794 | ||||||||
\(172\) | −8.82843 | −0.673161 | ||||||||
\(173\) | −8.82843 | −0.671213 | −0.335606 | − | 0.942002i | \(-0.608941\pi\) | ||||
−0.335606 | + | 0.942002i | \(0.608941\pi\) | |||||||
\(174\) | 16.4853 | 1.24975 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.828427 | −0.0624450 | ||||||||
\(177\) | 29.3137 | 2.20335 | ||||||||
\(178\) | −12.7279 | −0.953998 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 8.65685 | 0.645244 | ||||||||
\(181\) | −2.48528 | −0.184730 | −0.0923648 | − | 0.995725i | \(-0.529443\pi\) | ||||
−0.0923648 | + | 0.995725i | \(0.529443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.7990 | 2.35065 | ||||||||
\(184\) | 1.17157 | 0.0863695 | ||||||||
\(185\) | −7.65685 | −0.562943 | ||||||||
\(186\) | 9.65685 | 0.708075 | ||||||||
\(187\) | −2.14214 | −0.156648 | ||||||||
\(188\) | 5.17157 | 0.377176 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.585786 | −0.0424974 | ||||||||
\(191\) | 10.1421 | 0.733859 | 0.366930 | − | 0.930249i | \(-0.380409\pi\) | ||||
0.366930 | + | 0.930249i | \(0.380409\pi\) | |||||||
\(192\) | 3.41421 | 0.246400 | ||||||||
\(193\) | 5.65685 | 0.407189 | 0.203595 | − | 0.979055i | \(-0.434738\pi\) | ||||
0.203595 | + | 0.979055i | \(0.434738\pi\) | |||||||
\(194\) | 7.75736 | 0.556946 | ||||||||
\(195\) | −16.4853 | −1.18054 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.7990 | −1.83810 | −0.919051 | − | 0.394139i | \(-0.871043\pi\) | ||||
−0.919051 | + | 0.394139i | \(0.871043\pi\) | |||||||
\(198\) | 7.17157 | 0.509661 | ||||||||
\(199\) | 16.4853 | 1.16861 | 0.584305 | − | 0.811534i | \(-0.301367\pi\) | ||||
0.584305 | + | 0.811534i | \(0.301367\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 5.65685 | 0.399004 | ||||||||
\(202\) | −13.3137 | −0.936749 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.82843 | 0.618114 | ||||||||
\(205\) | −3.07107 | −0.214493 | ||||||||
\(206\) | 14.8284 | 1.03315 | ||||||||
\(207\) | −10.1421 | −0.704927 | ||||||||
\(208\) | −4.82843 | −0.334791 | ||||||||
\(209\) | −0.485281 | −0.0335676 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6274 | 1.28236 | 0.641182 | − | 0.767389i | \(-0.278444\pi\) | ||||
0.641182 | + | 0.767389i | \(0.278444\pi\) | |||||||
\(212\) | 6.48528 | 0.445411 | ||||||||
\(213\) | −15.3137 | −1.04928 | ||||||||
\(214\) | −9.65685 | −0.660129 | ||||||||
\(215\) | −8.82843 | −0.602094 | ||||||||
\(216\) | −19.3137 | −1.31413 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.48528 | −0.168324 | ||||||||
\(219\) | −32.1421 | −2.17196 | ||||||||
\(220\) | −0.828427 | −0.0558525 | ||||||||
\(221\) | −12.4853 | −0.839851 | ||||||||
\(222\) | 26.1421 | 1.75455 | ||||||||
\(223\) | −7.31371 | −0.489762 | −0.244881 | − | 0.969553i | \(-0.578749\pi\) | ||||
−0.244881 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.65685 | 0.577124 | ||||||||
\(226\) | 15.3137 | 1.01865 | ||||||||
\(227\) | 18.2426 | 1.21081 | 0.605403 | − | 0.795919i | \(-0.293012\pi\) | ||||
0.605403 | + | 0.795919i | \(0.293012\pi\) | |||||||
\(228\) | 2.00000 | 0.132453 | ||||||||
\(229\) | −16.1421 | −1.06670 | −0.533351 | − | 0.845894i | \(-0.679068\pi\) | ||||
−0.533351 | + | 0.845894i | \(0.679068\pi\) | |||||||
\(230\) | 1.17157 | 0.0772512 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.82843 | 0.317002 | ||||||||
\(233\) | 23.3137 | 1.52733 | 0.763666 | − | 0.645612i | \(-0.223397\pi\) | ||||
0.763666 | + | 0.645612i | \(0.223397\pi\) | |||||||
\(234\) | 41.7990 | 2.73249 | ||||||||
\(235\) | 5.17157 | 0.337356 | ||||||||
\(236\) | 8.58579 | 0.558887 | ||||||||
\(237\) | −23.3137 | −1.51439 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.65685 | 0.107173 | 0.0535865 | − | 0.998563i | \(-0.482935\pi\) | ||||
0.0535865 | + | 0.998563i | \(0.482935\pi\) | |||||||
\(240\) | 3.41421 | 0.220387 | ||||||||
\(241\) | −13.4142 | −0.864085 | −0.432043 | − | 0.901853i | \(-0.642207\pi\) | ||||
−0.432043 | + | 0.901853i | \(0.642207\pi\) | |||||||
\(242\) | 10.3137 | 0.662990 | ||||||||
\(243\) | 78.5269 | 5.03750 | ||||||||
\(244\) | 9.31371 | 0.596249 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4853 | 0.668517 | ||||||||
\(247\) | −2.82843 | −0.179969 | ||||||||
\(248\) | 2.82843 | 0.179605 | ||||||||
\(249\) | −7.65685 | −0.485233 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 0.585786 | 0.0369745 | 0.0184873 | − | 0.999829i | \(-0.494115\pi\) | ||||
0.0184873 | + | 0.999829i | \(0.494115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.970563 | 0.0610188 | ||||||||
\(254\) | −2.82843 | −0.177471 | ||||||||
\(255\) | 8.82843 | 0.552858 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.89949 | −0.617514 | −0.308757 | − | 0.951141i | \(-0.599913\pi\) | ||||
−0.308757 | + | 0.951141i | \(0.599913\pi\) | |||||||
\(258\) | 30.1421 | 1.87657 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.82843 | −0.299446 | ||||||||
\(261\) | −41.7990 | −2.58729 | ||||||||
\(262\) | 6.24264 | 0.385672 | ||||||||
\(263\) | 28.0000 | 1.72655 | 0.863277 | − | 0.504730i | \(-0.168408\pi\) | ||||
0.863277 | + | 0.504730i | \(0.168408\pi\) | |||||||
\(264\) | 2.82843 | 0.174078 | ||||||||
\(265\) | 6.48528 | 0.398388 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 43.4558 | 2.65945 | ||||||||
\(268\) | 1.65685 | 0.101208 | ||||||||
\(269\) | 18.4853 | 1.12707 | 0.563534 | − | 0.826093i | \(-0.309441\pi\) | ||||
0.563534 | + | 0.826093i | \(0.309441\pi\) | |||||||
\(270\) | −19.3137 | −1.17539 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 2.58579 | 0.156786 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.0000 | 0.966595 | ||||||||
\(275\) | −0.828427 | −0.0499560 | ||||||||
\(276\) | −4.00000 | −0.240772 | ||||||||
\(277\) | −8.14214 | −0.489214 | −0.244607 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244607 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(278\) | −19.8995 | −1.19349 | ||||||||
\(279\) | −24.4853 | −1.46590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.00000 | 0.477240 | 0.238620 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238620 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(282\) | −17.6569 | −1.05145 | ||||||||
\(283\) | −2.24264 | −0.133311 | −0.0666556 | − | 0.997776i | \(-0.521233\pi\) | ||||
−0.0666556 | + | 0.997776i | \(0.521233\pi\) | |||||||
\(284\) | −4.48528 | −0.266152 | ||||||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −8.65685 | −0.510110 | ||||||||
\(289\) | −10.3137 | −0.606689 | ||||||||
\(290\) | 4.82843 | 0.283535 | ||||||||
\(291\) | −26.4853 | −1.55259 | ||||||||
\(292\) | −9.41421 | −0.550925 | ||||||||
\(293\) | −8.34315 | −0.487412 | −0.243706 | − | 0.969849i | \(-0.578363\pi\) | ||||
−0.243706 | + | 0.969849i | \(0.578363\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.58579 | 0.499884 | ||||||||
\(296\) | 7.65685 | 0.445046 | ||||||||
\(297\) | −16.0000 | −0.928414 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 5.65685 | 0.327144 | ||||||||
\(300\) | 3.41421 | 0.197120 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.3137 | 0.651031 | ||||||||
\(303\) | 45.4558 | 2.61137 | ||||||||
\(304\) | 0.585786 | 0.0335972 | ||||||||
\(305\) | 9.31371 | 0.533301 | ||||||||
\(306\) | −22.3848 | −1.27965 | ||||||||
\(307\) | 14.9289 | 0.852039 | 0.426020 | − | 0.904714i | \(-0.359915\pi\) | ||||
0.426020 | + | 0.904714i | \(0.359915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −50.6274 | −2.88009 | ||||||||
\(310\) | 2.82843 | 0.160644 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 16.4853 | 0.933295 | ||||||||
\(313\) | 14.3848 | 0.813076 | 0.406538 | − | 0.913634i | \(-0.366736\pi\) | ||||
0.406538 | + | 0.913634i | \(0.366736\pi\) | |||||||
\(314\) | −6.48528 | −0.365986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.82843 | −0.384129 | ||||||||
\(317\) | 10.4853 | 0.588912 | 0.294456 | − | 0.955665i | \(-0.404862\pi\) | ||||
0.294456 | + | 0.955665i | \(0.404862\pi\) | |||||||
\(318\) | −22.1421 | −1.24167 | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 32.9706 | 1.84024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51472 | 0.0842812 | ||||||||
\(324\) | 39.9706 | 2.22059 | ||||||||
\(325\) | −4.82843 | −0.267833 | ||||||||
\(326\) | 20.1421 | 1.11557 | ||||||||
\(327\) | 8.48528 | 0.469237 | ||||||||
\(328\) | 3.07107 | 0.169571 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.82843 | 0.155700 | ||||||||
\(331\) | 33.7990 | 1.85776 | 0.928880 | − | 0.370380i | \(-0.120773\pi\) | ||||
0.928880 | + | 0.370380i | \(0.120773\pi\) | |||||||
\(332\) | −2.24264 | −0.123081 | ||||||||
\(333\) | −66.2843 | −3.63236 | ||||||||
\(334\) | −15.7990 | −0.864482 | ||||||||
\(335\) | 1.65685 | 0.0905236 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | −10.3137 | −0.560992 | ||||||||
\(339\) | −52.2843 | −2.83969 | ||||||||
\(340\) | 2.58579 | 0.140234 | ||||||||
\(341\) | 2.34315 | 0.126888 | ||||||||
\(342\) | −5.07107 | −0.274212 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.82843 | 0.475997 | ||||||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | 8.82843 | 0.474619 | ||||||||
\(347\) | −3.17157 | −0.170259 | −0.0851295 | − | 0.996370i | \(-0.527130\pi\) | ||||
−0.0851295 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(348\) | −16.4853 | −0.883704 | ||||||||
\(349\) | 2.48528 | 0.133034 | 0.0665170 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665170 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −93.2548 | −4.97757 | ||||||||
\(352\) | 0.828427 | 0.0441553 | ||||||||
\(353\) | −2.38478 | −0.126929 | −0.0634644 | − | 0.997984i | \(-0.520215\pi\) | ||||
−0.0634644 | + | 0.997984i | \(0.520215\pi\) | |||||||
\(354\) | −29.3137 | −1.55801 | ||||||||
\(355\) | −4.48528 | −0.238054 | ||||||||
\(356\) | 12.7279 | 0.674579 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.00000 | −0.211407 | ||||||||
\(359\) | 28.2843 | 1.49279 | 0.746393 | − | 0.665505i | \(-0.231784\pi\) | ||||
0.746393 | + | 0.665505i | \(0.231784\pi\) | |||||||
\(360\) | −8.65685 | −0.456256 | ||||||||
\(361\) | −18.6569 | −0.981940 | ||||||||
\(362\) | 2.48528 | 0.130623 | ||||||||
\(363\) | −35.2132 | −1.84821 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.41421 | −0.492762 | ||||||||
\(366\) | −31.7990 | −1.66216 | ||||||||
\(367\) | 24.9706 | 1.30345 | 0.651726 | − | 0.758454i | \(-0.274045\pi\) | ||||
0.651726 | + | 0.758454i | \(0.274045\pi\) | |||||||
\(368\) | −1.17157 | −0.0610725 | ||||||||
\(369\) | −26.5858 | −1.38400 | ||||||||
\(370\) | 7.65685 | 0.398061 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.65685 | −0.500685 | ||||||||
\(373\) | −30.4853 | −1.57847 | −0.789234 | − | 0.614093i | \(-0.789522\pi\) | ||||
−0.789234 | + | 0.614093i | \(0.789522\pi\) | |||||||
\(374\) | 2.14214 | 0.110767 | ||||||||
\(375\) | 3.41421 | 0.176309 | ||||||||
\(376\) | −5.17157 | −0.266704 | ||||||||
\(377\) | 23.3137 | 1.20072 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.4853 | 1.77139 | 0.885695 | − | 0.464268i | \(-0.153682\pi\) | ||||
0.885695 | + | 0.464268i | \(0.153682\pi\) | |||||||
\(380\) | 0.585786 | 0.0300502 | ||||||||
\(381\) | 9.65685 | 0.494736 | ||||||||
\(382\) | −10.1421 | −0.518917 | ||||||||
\(383\) | −32.4853 | −1.65992 | −0.829960 | − | 0.557823i | \(-0.811637\pi\) | ||||
−0.829960 | + | 0.557823i | \(0.811637\pi\) | |||||||
\(384\) | −3.41421 | −0.174231 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.65685 | −0.287926 | ||||||||
\(387\) | −76.4264 | −3.88497 | ||||||||
\(388\) | −7.75736 | −0.393820 | ||||||||
\(389\) | 28.1421 | 1.42686 | 0.713431 | − | 0.700725i | \(-0.247140\pi\) | ||||
0.713431 | + | 0.700725i | \(0.247140\pi\) | |||||||
\(390\) | 16.4853 | 0.834765 | ||||||||
\(391\) | −3.02944 | −0.153205 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.3137 | −1.07513 | ||||||||
\(394\) | 25.7990 | 1.29973 | ||||||||
\(395\) | −6.82843 | −0.343575 | ||||||||
\(396\) | −7.17157 | −0.360385 | ||||||||
\(397\) | 33.7990 | 1.69632 | 0.848161 | − | 0.529738i | \(-0.177710\pi\) | ||||
0.848161 | + | 0.529738i | \(0.177710\pi\) | |||||||
\(398\) | −16.4853 | −0.826332 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | −5.65685 | −0.282138 | ||||||||
\(403\) | 13.6569 | 0.680296 | ||||||||
\(404\) | 13.3137 | 0.662382 | ||||||||
\(405\) | 39.9706 | 1.98615 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.34315 | 0.314418 | ||||||||
\(408\) | −8.82843 | −0.437072 | ||||||||
\(409\) | −10.5858 | −0.523433 | −0.261717 | − | 0.965145i | \(-0.584289\pi\) | ||||
−0.261717 | + | 0.965145i | \(0.584289\pi\) | |||||||
\(410\) | 3.07107 | 0.151669 | ||||||||
\(411\) | −54.6274 | −2.69457 | ||||||||
\(412\) | −14.8284 | −0.730544 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.1421 | 0.498459 | ||||||||
\(415\) | −2.24264 | −0.110087 | ||||||||
\(416\) | 4.82843 | 0.236733 | ||||||||
\(417\) | 67.9411 | 3.32709 | ||||||||
\(418\) | 0.485281 | 0.0237359 | ||||||||
\(419\) | −20.8701 | −1.01957 | −0.509785 | − | 0.860302i | \(-0.670275\pi\) | ||||
−0.509785 | + | 0.860302i | \(0.670275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.3137 | 0.843819 | 0.421909 | − | 0.906638i | \(-0.361360\pi\) | ||||
0.421909 | + | 0.906638i | \(0.361360\pi\) | |||||||
\(422\) | −18.6274 | −0.906768 | ||||||||
\(423\) | 44.7696 | 2.17677 | ||||||||
\(424\) | −6.48528 | −0.314953 | ||||||||
\(425\) | 2.58579 | 0.125429 | ||||||||
\(426\) | 15.3137 | 0.741952 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.65685 | 0.466782 | ||||||||
\(429\) | 13.6569 | 0.659359 | ||||||||
\(430\) | 8.82843 | 0.425745 | ||||||||
\(431\) | −22.3431 | −1.07623 | −0.538116 | − | 0.842871i | \(-0.680864\pi\) | ||||
−0.538116 | + | 0.842871i | \(0.680864\pi\) | |||||||
\(432\) | 19.3137 | 0.929231 | ||||||||
\(433\) | 10.5858 | 0.508720 | 0.254360 | − | 0.967110i | \(-0.418135\pi\) | ||||
0.254360 | + | 0.967110i | \(0.418135\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.4853 | −0.790409 | ||||||||
\(436\) | 2.48528 | 0.119023 | ||||||||
\(437\) | −0.686292 | −0.0328298 | ||||||||
\(438\) | 32.1421 | 1.53581 | ||||||||
\(439\) | −24.9706 | −1.19178 | −0.595890 | − | 0.803066i | \(-0.703201\pi\) | ||||
−0.595890 | + | 0.803066i | \(0.703201\pi\) | |||||||
\(440\) | 0.828427 | 0.0394937 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.4853 | 0.593864 | ||||||||
\(443\) | 3.02944 | 0.143933 | 0.0719665 | − | 0.997407i | \(-0.477073\pi\) | ||||
0.0719665 | + | 0.997407i | \(0.477073\pi\) | |||||||
\(444\) | −26.1421 | −1.24065 | ||||||||
\(445\) | 12.7279 | 0.603361 | ||||||||
\(446\) | 7.31371 | 0.346314 | ||||||||
\(447\) | −20.4853 | −0.968921 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.6274 | −0.784696 | −0.392348 | − | 0.919817i | \(-0.628337\pi\) | ||||
−0.392348 | + | 0.919817i | \(0.628337\pi\) | |||||||
\(450\) | −8.65685 | −0.408088 | ||||||||
\(451\) | 2.54416 | 0.119800 | ||||||||
\(452\) | −15.3137 | −0.720296 | ||||||||
\(453\) | −38.6274 | −1.81487 | ||||||||
\(454\) | −18.2426 | −0.856170 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 21.6569 | 1.01306 | 0.506532 | − | 0.862221i | \(-0.330927\pi\) | ||||
0.506532 | + | 0.862221i | \(0.330927\pi\) | |||||||
\(458\) | 16.1421 | 0.754272 | ||||||||
\(459\) | 49.9411 | 2.33105 | ||||||||
\(460\) | −1.17157 | −0.0546249 | ||||||||
\(461\) | −12.8284 | −0.597479 | −0.298740 | − | 0.954335i | \(-0.596566\pi\) | ||||
−0.298740 | + | 0.954335i | \(0.596566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9706 | −0.788689 | −0.394344 | − | 0.918963i | \(-0.629028\pi\) | ||||
−0.394344 | + | 0.918963i | \(0.629028\pi\) | |||||||
\(464\) | −4.82843 | −0.224154 | ||||||||
\(465\) | −9.65685 | −0.447826 | ||||||||
\(466\) | −23.3137 | −1.07999 | ||||||||
\(467\) | −15.8995 | −0.735741 | −0.367870 | − | 0.929877i | \(-0.619913\pi\) | ||||
−0.367870 | + | 0.929877i | \(0.619913\pi\) | |||||||
\(468\) | −41.7990 | −1.93216 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.17157 | −0.238547 | ||||||||
\(471\) | 22.1421 | 1.02026 | ||||||||
\(472\) | −8.58579 | −0.395193 | ||||||||
\(473\) | 7.31371 | 0.336285 | ||||||||
\(474\) | 23.3137 | 1.07083 | ||||||||
\(475\) | 0.585786 | 0.0268777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 56.1421 | 2.57057 | ||||||||
\(478\) | −1.65685 | −0.0757827 | ||||||||
\(479\) | −17.1716 | −0.784589 | −0.392295 | − | 0.919840i | \(-0.628319\pi\) | ||||
−0.392295 | + | 0.919840i | \(0.628319\pi\) | |||||||
\(480\) | −3.41421 | −0.155837 | ||||||||
\(481\) | 36.9706 | 1.68571 | ||||||||
\(482\) | 13.4142 | 0.611001 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.3137 | −0.468805 | ||||||||
\(485\) | −7.75736 | −0.352244 | ||||||||
\(486\) | −78.5269 | −3.56205 | ||||||||
\(487\) | 31.7990 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(488\) | −9.31371 | −0.421612 | ||||||||
\(489\) | −68.7696 | −3.10987 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.2843 | 1.45697 | 0.728484 | − | 0.685062i | \(-0.240225\pi\) | ||||
0.728484 | + | 0.685062i | \(0.240225\pi\) | |||||||
\(492\) | −10.4853 | −0.472713 | ||||||||
\(493\) | −12.4853 | −0.562309 | ||||||||
\(494\) | 2.82843 | 0.127257 | ||||||||
\(495\) | −7.17157 | −0.322338 | ||||||||
\(496\) | −2.82843 | −0.127000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.65685 | 0.343112 | ||||||||
\(499\) | 30.3431 | 1.35835 | 0.679173 | − | 0.733978i | \(-0.262339\pi\) | ||||
0.679173 | + | 0.733978i | \(0.262339\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 53.9411 | 2.40991 | ||||||||
\(502\) | −0.585786 | −0.0261449 | ||||||||
\(503\) | 17.6569 | 0.787280 | 0.393640 | − | 0.919265i | \(-0.371216\pi\) | ||||
0.393640 | + | 0.919265i | \(0.371216\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3137 | 0.592452 | ||||||||
\(506\) | −0.970563 | −0.0431468 | ||||||||
\(507\) | 35.2132 | 1.56387 | ||||||||
\(508\) | 2.82843 | 0.125491 | ||||||||
\(509\) | 5.79899 | 0.257036 | 0.128518 | − | 0.991707i | \(-0.458978\pi\) | ||||
0.128518 | + | 0.991707i | \(0.458978\pi\) | |||||||
\(510\) | −8.82843 | −0.390929 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 11.3137 | 0.499512 | ||||||||
\(514\) | 9.89949 | 0.436648 | ||||||||
\(515\) | −14.8284 | −0.653419 | ||||||||
\(516\) | −30.1421 | −1.32693 | ||||||||
\(517\) | −4.28427 | −0.188422 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.1421 | −1.32309 | ||||||||
\(520\) | 4.82843 | 0.211741 | ||||||||
\(521\) | 19.0711 | 0.835519 | 0.417759 | − | 0.908558i | \(-0.362816\pi\) | ||||
0.417759 | + | 0.908558i | \(0.362816\pi\) | |||||||
\(522\) | 41.7990 | 1.82949 | ||||||||
\(523\) | 23.8995 | 1.04505 | 0.522526 | − | 0.852623i | \(-0.324990\pi\) | ||||
0.522526 | + | 0.852623i | \(0.324990\pi\) | |||||||
\(524\) | −6.24264 | −0.272711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.0000 | −1.22086 | ||||||||
\(527\) | −7.31371 | −0.318590 | ||||||||
\(528\) | −2.82843 | −0.123091 | ||||||||
\(529\) | −21.6274 | −0.940322 | ||||||||
\(530\) | −6.48528 | −0.281703 | ||||||||
\(531\) | 74.3259 | 3.22547 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.8284 | 0.642290 | ||||||||
\(534\) | −43.4558 | −1.88052 | ||||||||
\(535\) | 9.65685 | 0.417502 | ||||||||
\(536\) | −1.65685 | −0.0715652 | ||||||||
\(537\) | 13.6569 | 0.589337 | ||||||||
\(538\) | −18.4853 | −0.796957 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.3137 | 0.831130 | ||||||||
\(541\) | −14.9706 | −0.643635 | −0.321817 | − | 0.946802i | \(-0.604294\pi\) | ||||
−0.321817 | + | 0.946802i | \(0.604294\pi\) | |||||||
\(542\) | −12.0000 | −0.515444 | ||||||||
\(543\) | −8.48528 | −0.364138 | ||||||||
\(544\) | −2.58579 | −0.110865 | ||||||||
\(545\) | 2.48528 | 0.106458 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4853 | −0.448318 | −0.224159 | − | 0.974553i | \(-0.571964\pi\) | ||||
−0.224159 | + | 0.974553i | \(0.571964\pi\) | |||||||
\(548\) | −16.0000 | −0.683486 | ||||||||
\(549\) | 80.6274 | 3.44109 | ||||||||
\(550\) | 0.828427 | 0.0353243 | ||||||||
\(551\) | −2.82843 | −0.120495 | ||||||||
\(552\) | 4.00000 | 0.170251 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.14214 | 0.345926 | ||||||||
\(555\) | −26.1421 | −1.10967 | ||||||||
\(556\) | 19.8995 | 0.843927 | ||||||||
\(557\) | 15.1716 | 0.642840 | 0.321420 | − | 0.946937i | \(-0.395840\pi\) | ||||
0.321420 | + | 0.946937i | \(0.395840\pi\) | |||||||
\(558\) | 24.4853 | 1.03654 | ||||||||
\(559\) | 42.6274 | 1.80295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.31371 | −0.308785 | ||||||||
\(562\) | −8.00000 | −0.337460 | ||||||||
\(563\) | −36.5858 | −1.54191 | −0.770954 | − | 0.636891i | \(-0.780220\pi\) | ||||
−0.770954 | + | 0.636891i | \(0.780220\pi\) | |||||||
\(564\) | 17.6569 | 0.743488 | ||||||||
\(565\) | −15.3137 | −0.644253 | ||||||||
\(566\) | 2.24264 | 0.0942652 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.48528 | 0.188198 | ||||||||
\(569\) | −29.3137 | −1.22889 | −0.614447 | − | 0.788958i | \(-0.710621\pi\) | ||||
−0.614447 | + | 0.788958i | \(0.710621\pi\) | |||||||
\(570\) | −2.00000 | −0.0837708 | ||||||||
\(571\) | −2.20101 | −0.0921094 | −0.0460547 | − | 0.998939i | \(-0.514665\pi\) | ||||
−0.0460547 | + | 0.998939i | \(0.514665\pi\) | |||||||
\(572\) | 4.00000 | 0.167248 | ||||||||
\(573\) | 34.6274 | 1.44658 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.17157 | −0.0488580 | ||||||||
\(576\) | 8.65685 | 0.360702 | ||||||||
\(577\) | 6.10051 | 0.253967 | 0.126984 | − | 0.991905i | \(-0.459470\pi\) | ||||
0.126984 | + | 0.991905i | \(0.459470\pi\) | |||||||
\(578\) | 10.3137 | 0.428994 | ||||||||
\(579\) | 19.3137 | 0.802650 | ||||||||
\(580\) | −4.82843 | −0.200490 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 26.4853 | 1.09785 | ||||||||
\(583\) | −5.37258 | −0.222510 | ||||||||
\(584\) | 9.41421 | 0.389563 | ||||||||
\(585\) | −41.7990 | −1.72818 | ||||||||
\(586\) | 8.34315 | 0.344652 | ||||||||
\(587\) | 17.0711 | 0.704598 | 0.352299 | − | 0.935887i | \(-0.385400\pi\) | ||||
0.352299 | + | 0.935887i | \(0.385400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.65685 | −0.0682695 | ||||||||
\(590\) | −8.58579 | −0.353471 | ||||||||
\(591\) | −88.0833 | −3.62326 | ||||||||
\(592\) | −7.65685 | −0.314695 | ||||||||
\(593\) | 3.27208 | 0.134368 | 0.0671841 | − | 0.997741i | \(-0.478599\pi\) | ||||
0.0671841 | + | 0.997741i | \(0.478599\pi\) | |||||||
\(594\) | 16.0000 | 0.656488 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 56.2843 | 2.30356 | ||||||||
\(598\) | −5.65685 | −0.231326 | ||||||||
\(599\) | −10.8284 | −0.442438 | −0.221219 | − | 0.975224i | \(-0.571003\pi\) | ||||
−0.221219 | + | 0.975224i | \(0.571003\pi\) | |||||||
\(600\) | −3.41421 | −0.139385 | ||||||||
\(601\) | 6.58579 | 0.268640 | 0.134320 | − | 0.990938i | \(-0.457115\pi\) | ||||
0.134320 | + | 0.990938i | \(0.457115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3431 | 0.584098 | ||||||||
\(604\) | −11.3137 | −0.460348 | ||||||||
\(605\) | −10.3137 | −0.419312 | ||||||||
\(606\) | −45.4558 | −1.84652 | ||||||||
\(607\) | 16.2843 | 0.660958 | 0.330479 | − | 0.943813i | \(-0.392790\pi\) | ||||
0.330479 | + | 0.943813i | \(0.392790\pi\) | |||||||
\(608\) | −0.585786 | −0.0237568 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.31371 | −0.377101 | ||||||||
\(611\) | −24.9706 | −1.01020 | ||||||||
\(612\) | 22.3848 | 0.904851 | ||||||||
\(613\) | −12.3431 | −0.498535 | −0.249267 | − | 0.968435i | \(-0.580190\pi\) | ||||
−0.249267 | + | 0.968435i | \(0.580190\pi\) | |||||||
\(614\) | −14.9289 | −0.602483 | ||||||||
\(615\) | −10.4853 | −0.422807 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.3137 | −1.34116 | −0.670580 | − | 0.741837i | \(-0.733955\pi\) | ||||
−0.670580 | + | 0.741837i | \(0.733955\pi\) | |||||||
\(618\) | 50.6274 | 2.03653 | ||||||||
\(619\) | 29.0711 | 1.16846 | 0.584232 | − | 0.811586i | \(-0.301396\pi\) | ||||
0.584232 | + | 0.811586i | \(0.301396\pi\) | |||||||
\(620\) | −2.82843 | −0.113592 | ||||||||
\(621\) | −22.6274 | −0.908007 | ||||||||
\(622\) | −4.00000 | −0.160385 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −16.4853 | −0.659939 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −14.3848 | −0.574931 | ||||||||
\(627\) | −1.65685 | −0.0661684 | ||||||||
\(628\) | 6.48528 | 0.258791 | ||||||||
\(629\) | −19.7990 | −0.789437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4853 | −0.497031 | −0.248516 | − | 0.968628i | \(-0.579943\pi\) | ||||
−0.248516 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(632\) | 6.82843 | 0.271620 | ||||||||
\(633\) | 63.5980 | 2.52779 | ||||||||
\(634\) | −10.4853 | −0.416424 | ||||||||
\(635\) | 2.82843 | 0.112243 | ||||||||
\(636\) | 22.1421 | 0.877993 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | −38.8284 | −1.53603 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −24.6274 | −0.972724 | −0.486362 | − | 0.873757i | \(-0.661676\pi\) | ||||
−0.486362 | + | 0.873757i | \(0.661676\pi\) | |||||||
\(642\) | −32.9706 | −1.30124 | ||||||||
\(643\) | 4.78680 | 0.188773 | 0.0943864 | − | 0.995536i | \(-0.469911\pi\) | ||||
0.0943864 | + | 0.995536i | \(0.469911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.1421 | −1.18685 | ||||||||
\(646\) | −1.51472 | −0.0595958 | ||||||||
\(647\) | −23.1127 | −0.908654 | −0.454327 | − | 0.890835i | \(-0.650120\pi\) | ||||
−0.454327 | + | 0.890835i | \(0.650120\pi\) | |||||||
\(648\) | −39.9706 | −1.57019 | ||||||||
\(649\) | −7.11270 | −0.279198 | ||||||||
\(650\) | 4.82843 | 0.189386 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.1421 | −0.788827 | ||||||||
\(653\) | 4.34315 | 0.169960 | 0.0849802 | − | 0.996383i | \(-0.472917\pi\) | ||||
0.0849802 | + | 0.996383i | \(0.472917\pi\) | |||||||
\(654\) | −8.48528 | −0.331801 | ||||||||
\(655\) | −6.24264 | −0.243920 | ||||||||
\(656\) | −3.07107 | −0.119905 | ||||||||
\(657\) | −81.4975 | −3.17952 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.1716 | −1.05845 | −0.529227 | − | 0.848480i | \(-0.677518\pi\) | ||||
−0.529227 | + | 0.848480i | \(0.677518\pi\) | |||||||
\(660\) | −2.82843 | −0.110096 | ||||||||
\(661\) | −38.2843 | −1.48909 | −0.744543 | − | 0.667575i | \(-0.767332\pi\) | ||||
−0.744543 | + | 0.667575i | \(0.767332\pi\) | |||||||
\(662\) | −33.7990 | −1.31364 | ||||||||
\(663\) | −42.6274 | −1.65551 | ||||||||
\(664\) | 2.24264 | 0.0870313 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 66.2843 | 2.56846 | ||||||||
\(667\) | 5.65685 | 0.219034 | ||||||||
\(668\) | 15.7990 | 0.611281 | ||||||||
\(669\) | −24.9706 | −0.965418 | ||||||||
\(670\) | −1.65685 | −0.0640099 | ||||||||
\(671\) | −7.71573 | −0.297862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.0000 | −1.85026 | −0.925132 | − | 0.379646i | \(-0.876046\pi\) | ||||
−0.925132 | + | 0.379646i | \(0.876046\pi\) | |||||||
\(674\) | −6.00000 | −0.231111 | ||||||||
\(675\) | 19.3137 | 0.743385 | ||||||||
\(676\) | 10.3137 | 0.396681 | ||||||||
\(677\) | 39.4558 | 1.51641 | 0.758206 | − | 0.652015i | \(-0.226076\pi\) | ||||
0.758206 | + | 0.652015i | \(0.226076\pi\) | |||||||
\(678\) | 52.2843 | 2.00797 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.58579 | −0.0991604 | ||||||||
\(681\) | 62.2843 | 2.38674 | ||||||||
\(682\) | −2.34315 | −0.0897237 | ||||||||
\(683\) | 33.6569 | 1.28784 | 0.643922 | − | 0.765091i | \(-0.277306\pi\) | ||||
0.643922 | + | 0.765091i | \(0.277306\pi\) | |||||||
\(684\) | 5.07107 | 0.193897 | ||||||||
\(685\) | −16.0000 | −0.611329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −55.1127 | −2.10268 | ||||||||
\(688\) | −8.82843 | −0.336581 | ||||||||
\(689\) | −31.3137 | −1.19296 | ||||||||
\(690\) | 4.00000 | 0.152277 | ||||||||
\(691\) | 1.75736 | 0.0668531 | 0.0334265 | − | 0.999441i | \(-0.489358\pi\) | ||||
0.0334265 | + | 0.999441i | \(0.489358\pi\) | |||||||
\(692\) | −8.82843 | −0.335606 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.17157 | 0.120391 | ||||||||
\(695\) | 19.8995 | 0.754831 | ||||||||
\(696\) | 16.4853 | 0.624873 | ||||||||
\(697\) | −7.94113 | −0.300792 | ||||||||
\(698\) | −2.48528 | −0.0940693 | ||||||||
\(699\) | 79.5980 | 3.01067 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.48528 | 0.0938678 | 0.0469339 | − | 0.998898i | \(-0.485055\pi\) | ||||
0.0469339 | + | 0.998898i | \(0.485055\pi\) | |||||||
\(702\) | 93.2548 | 3.51968 | ||||||||
\(703\) | −4.48528 | −0.169166 | ||||||||
\(704\) | −0.828427 | −0.0312225 | ||||||||
\(705\) | 17.6569 | 0.664996 | ||||||||
\(706\) | 2.38478 | 0.0897522 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 29.3137 | 1.10168 | ||||||||
\(709\) | 45.1127 | 1.69424 | 0.847121 | − | 0.531399i | \(-0.178334\pi\) | ||||
0.847121 | + | 0.531399i | \(0.178334\pi\) | |||||||
\(710\) | 4.48528 | 0.168330 | ||||||||
\(711\) | −59.1127 | −2.21690 | ||||||||
\(712\) | −12.7279 | −0.476999 | ||||||||
\(713\) | 3.31371 | 0.124099 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | 5.65685 | 0.211259 | ||||||||
\(718\) | −28.2843 | −1.05556 | ||||||||
\(719\) | 41.4558 | 1.54604 | 0.773021 | − | 0.634380i | \(-0.218745\pi\) | ||||
0.773021 | + | 0.634380i | \(0.218745\pi\) | |||||||
\(720\) | 8.65685 | 0.322622 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.6569 | 0.694336 | ||||||||
\(723\) | −45.7990 | −1.70328 | ||||||||
\(724\) | −2.48528 | −0.0923648 | ||||||||
\(725\) | −4.82843 | −0.179323 | ||||||||
\(726\) | 35.2132 | 1.30688 | ||||||||
\(727\) | −3.51472 | −0.130354 | −0.0651768 | − | 0.997874i | \(-0.520761\pi\) | ||||
−0.0651768 | + | 0.997874i | \(0.520761\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 148.196 | 5.48874 | ||||||||
\(730\) | 9.41421 | 0.348436 | ||||||||
\(731\) | −22.8284 | −0.844340 | ||||||||
\(732\) | 31.7990 | 1.17532 | ||||||||
\(733\) | 34.0000 | 1.25582 | 0.627909 | − | 0.778287i | \(-0.283911\pi\) | ||||
0.627909 | + | 0.778287i | \(0.283911\pi\) | |||||||
\(734\) | −24.9706 | −0.921680 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.17157 | 0.0431847 | ||||||||
\(737\) | −1.37258 | −0.0505597 | ||||||||
\(738\) | 26.5858 | 0.978636 | ||||||||
\(739\) | 3.17157 | 0.116668 | 0.0583341 | − | 0.998297i | \(-0.481421\pi\) | ||||
0.0583341 | + | 0.998297i | \(0.481421\pi\) | |||||||
\(740\) | −7.65685 | −0.281472 | ||||||||
\(741\) | −9.65685 | −0.354753 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 51.7990 | 1.90032 | 0.950160 | − | 0.311762i | \(-0.100919\pi\) | ||||
0.950160 | + | 0.311762i | \(0.100919\pi\) | |||||||
\(744\) | 9.65685 | 0.354037 | ||||||||
\(745\) | −6.00000 | −0.219823 | ||||||||
\(746\) | 30.4853 | 1.11615 | ||||||||
\(747\) | −19.4142 | −0.710329 | ||||||||
\(748\) | −2.14214 | −0.0783242 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.41421 | −0.124669 | ||||||||
\(751\) | −39.3137 | −1.43458 | −0.717289 | − | 0.696776i | \(-0.754617\pi\) | ||||
−0.717289 | + | 0.696776i | \(0.754617\pi\) | |||||||
\(752\) | 5.17157 | 0.188588 | ||||||||
\(753\) | 2.00000 | 0.0728841 | ||||||||
\(754\) | −23.3137 | −0.849035 | ||||||||
\(755\) | −11.3137 | −0.411748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.65685 | 0.132911 | 0.0664553 | − | 0.997789i | \(-0.478831\pi\) | ||||
0.0664553 | + | 0.997789i | \(0.478831\pi\) | |||||||
\(758\) | −34.4853 | −1.25256 | ||||||||
\(759\) | 3.31371 | 0.120280 | ||||||||
\(760\) | −0.585786 | −0.0212487 | ||||||||
\(761\) | 22.3848 | 0.811448 | 0.405724 | − | 0.913996i | \(-0.367020\pi\) | ||||
0.405724 | + | 0.913996i | \(0.367020\pi\) | |||||||
\(762\) | −9.65685 | −0.349831 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.1421 | 0.366930 | ||||||||
\(765\) | 22.3848 | 0.809323 | ||||||||
\(766\) | 32.4853 | 1.17374 | ||||||||
\(767\) | −41.4558 | −1.49688 | ||||||||
\(768\) | 3.41421 | 0.123200 | ||||||||
\(769\) | 19.5563 | 0.705220 | 0.352610 | − | 0.935770i | \(-0.385294\pi\) | ||||
0.352610 | + | 0.935770i | \(0.385294\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.7990 | −1.21724 | ||||||||
\(772\) | 5.65685 | 0.203595 | ||||||||
\(773\) | −2.00000 | −0.0719350 | −0.0359675 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359675 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(774\) | 76.4264 | 2.74709 | ||||||||
\(775\) | −2.82843 | −0.101600 | ||||||||
\(776\) | 7.75736 | 0.278473 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.1421 | −1.00894 | ||||||||
\(779\) | −1.79899 | −0.0644555 | ||||||||
\(780\) | −16.4853 | −0.590268 | ||||||||
\(781\) | 3.71573 | 0.132959 | ||||||||
\(782\) | 3.02944 | 0.108332 | ||||||||
\(783\) | −93.2548 | −3.33266 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.48528 | 0.231470 | ||||||||
\(786\) | 21.3137 | 0.760235 | ||||||||
\(787\) | −1.27208 | −0.0453447 | −0.0226723 | − | 0.999743i | \(-0.507217\pi\) | ||||
−0.0226723 | + | 0.999743i | \(0.507217\pi\) | |||||||
\(788\) | −25.7990 | −0.919051 | ||||||||
\(789\) | 95.5980 | 3.40338 | ||||||||
\(790\) | 6.82843 | 0.242945 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.17157 | 0.254831 | ||||||||
\(793\) | −44.9706 | −1.59695 | ||||||||
\(794\) | −33.7990 | −1.19948 | ||||||||
\(795\) | 22.1421 | 0.785301 | ||||||||
\(796\) | 16.4853 | 0.584305 | ||||||||
\(797\) | −41.7990 | −1.48060 | −0.740298 | − | 0.672279i | \(-0.765316\pi\) | ||||
−0.740298 | + | 0.672279i | \(0.765316\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.3726 | 0.473088 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 110.184 | 3.89315 | ||||||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | 7.79899 | 0.275220 | ||||||||
\(804\) | 5.65685 | 0.199502 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.6569 | −0.481042 | ||||||||
\(807\) | 63.1127 | 2.22167 | ||||||||
\(808\) | −13.3137 | −0.468375 | ||||||||
\(809\) | 3.02944 | 0.106509 | 0.0532547 | − | 0.998581i | \(-0.483040\pi\) | ||||
0.0532547 | + | 0.998581i | \(0.483040\pi\) | |||||||
\(810\) | −39.9706 | −1.40442 | ||||||||
\(811\) | 32.5858 | 1.14424 | 0.572121 | − | 0.820169i | \(-0.306121\pi\) | ||||
0.572121 | + | 0.820169i | \(0.306121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.9706 | 1.43690 | ||||||||
\(814\) | −6.34315 | −0.222327 | ||||||||
\(815\) | −20.1421 | −0.705548 | ||||||||
\(816\) | 8.82843 | 0.309057 | ||||||||
\(817\) | −5.17157 | −0.180930 | ||||||||
\(818\) | 10.5858 | 0.370123 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.07107 | −0.107246 | ||||||||
\(821\) | 17.3137 | 0.604253 | 0.302126 | − | 0.953268i | \(-0.402304\pi\) | ||||
0.302126 | + | 0.953268i | \(0.402304\pi\) | |||||||
\(822\) | 54.6274 | 1.90535 | ||||||||
\(823\) | 20.2843 | 0.707065 | 0.353533 | − | 0.935422i | \(-0.384980\pi\) | ||||
0.353533 | + | 0.935422i | \(0.384980\pi\) | |||||||
\(824\) | 14.8284 | 0.516573 | ||||||||
\(825\) | −2.82843 | −0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.37258 | −0.186823 | −0.0934115 | − | 0.995628i | \(-0.529777\pi\) | ||||
−0.0934115 | + | 0.995628i | \(0.529777\pi\) | |||||||
\(828\) | −10.1421 | −0.352464 | ||||||||
\(829\) | −5.02944 | −0.174680 | −0.0873398 | − | 0.996179i | \(-0.527837\pi\) | ||||
−0.0873398 | + | 0.996179i | \(0.527837\pi\) | |||||||
\(830\) | 2.24264 | 0.0778432 | ||||||||
\(831\) | −27.7990 | −0.964336 | ||||||||
\(832\) | −4.82843 | −0.167396 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −67.9411 | −2.35261 | ||||||||
\(835\) | 15.7990 | 0.546747 | ||||||||
\(836\) | −0.485281 | −0.0167838 | ||||||||
\(837\) | −54.6274 | −1.88820 | ||||||||
\(838\) | 20.8701 | 0.720944 | ||||||||
\(839\) | −42.1421 | −1.45491 | −0.727454 | − | 0.686156i | \(-0.759297\pi\) | ||||
−0.727454 | + | 0.686156i | \(0.759297\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | −17.3137 | −0.596670 | ||||||||
\(843\) | 27.3137 | 0.940734 | ||||||||
\(844\) | 18.6274 | 0.641182 | ||||||||
\(845\) | 10.3137 | 0.354802 | ||||||||
\(846\) | −44.7696 | −1.53921 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.48528 | 0.222705 | ||||||||
\(849\) | −7.65685 | −0.262783 | ||||||||
\(850\) | −2.58579 | −0.0886917 | ||||||||
\(851\) | 8.97056 | 0.307507 | ||||||||
\(852\) | −15.3137 | −0.524639 | ||||||||
\(853\) | −43.1716 | −1.47817 | −0.739083 | − | 0.673614i | \(-0.764741\pi\) | ||||
−0.739083 | + | 0.673614i | \(0.764741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.07107 | 0.173427 | ||||||||
\(856\) | −9.65685 | −0.330064 | ||||||||
\(857\) | −4.92893 | −0.168369 | −0.0841846 | − | 0.996450i | \(-0.526829\pi\) | ||||
−0.0841846 | + | 0.996450i | \(0.526829\pi\) | |||||||
\(858\) | −13.6569 | −0.466237 | ||||||||
\(859\) | −7.21320 | −0.246111 | −0.123056 | − | 0.992400i | \(-0.539269\pi\) | ||||
−0.123056 | + | 0.992400i | \(0.539269\pi\) | |||||||
\(860\) | −8.82843 | −0.301047 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.3431 | 0.761011 | ||||||||
\(863\) | −4.97056 | −0.169200 | −0.0846000 | − | 0.996415i | \(-0.526961\pi\) | ||||
−0.0846000 | + | 0.996415i | \(0.526961\pi\) | |||||||
\(864\) | −19.3137 | −0.657066 | ||||||||
\(865\) | −8.82843 | −0.300176 | ||||||||
\(866\) | −10.5858 | −0.359720 | ||||||||
\(867\) | −35.2132 | −1.19590 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.65685 | 0.191896 | ||||||||
\(870\) | 16.4853 | 0.558903 | ||||||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | −2.48528 | −0.0841622 | ||||||||
\(873\) | −67.1543 | −2.27283 | ||||||||
\(874\) | 0.686292 | 0.0232142 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.1421 | −1.08598 | ||||||||
\(877\) | −30.2843 | −1.02263 | −0.511314 | − | 0.859394i | \(-0.670841\pi\) | ||||
−0.511314 | + | 0.859394i | \(0.670841\pi\) | |||||||
\(878\) | 24.9706 | 0.842716 | ||||||||
\(879\) | −28.4853 | −0.960785 | ||||||||
\(880\) | −0.828427 | −0.0279263 | ||||||||
\(881\) | −2.38478 | −0.0803452 | −0.0401726 | − | 0.999193i | \(-0.512791\pi\) | ||||
−0.0401726 | + | 0.999193i | \(0.512791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.6569 | −1.40186 | −0.700932 | − | 0.713228i | \(-0.747233\pi\) | ||||
−0.700932 | + | 0.713228i | \(0.747233\pi\) | |||||||
\(884\) | −12.4853 | −0.419925 | ||||||||
\(885\) | 29.3137 | 0.985370 | ||||||||
\(886\) | −3.02944 | −0.101776 | ||||||||
\(887\) | −55.1127 | −1.85050 | −0.925252 | − | 0.379354i | \(-0.876146\pi\) | ||||
−0.925252 | + | 0.379354i | \(0.876146\pi\) | |||||||
\(888\) | 26.1421 | 0.877273 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.7279 | −0.426641 | ||||||||
\(891\) | −33.1127 | −1.10932 | ||||||||
\(892\) | −7.31371 | −0.244881 | ||||||||
\(893\) | 3.02944 | 0.101376 | ||||||||
\(894\) | 20.4853 | 0.685130 | ||||||||
\(895\) | 4.00000 | 0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.3137 | 0.644866 | ||||||||
\(898\) | 16.6274 | 0.554864 | ||||||||
\(899\) | 13.6569 | 0.455482 | ||||||||
\(900\) | 8.65685 | 0.288562 | ||||||||
\(901\) | 16.7696 | 0.558675 | ||||||||
\(902\) | −2.54416 | −0.0847111 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.3137 | 0.509326 | ||||||||
\(905\) | −2.48528 | −0.0826135 | ||||||||
\(906\) | 38.6274 | 1.28331 | ||||||||
\(907\) | 0.284271 | 0.00943907 | 0.00471954 | − | 0.999989i | \(-0.498498\pi\) | ||||
0.00471954 | + | 0.999989i | \(0.498498\pi\) | |||||||
\(908\) | 18.2426 | 0.605403 | ||||||||
\(909\) | 115.255 | 3.82276 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.2843 | 1.20215 | 0.601076 | − | 0.799192i | \(-0.294739\pi\) | ||||
0.601076 | + | 0.799192i | \(0.294739\pi\) | |||||||
\(912\) | 2.00000 | 0.0662266 | ||||||||
\(913\) | 1.85786 | 0.0614863 | ||||||||
\(914\) | −21.6569 | −0.716345 | ||||||||
\(915\) | 31.7990 | 1.05124 | ||||||||
\(916\) | −16.1421 | −0.533351 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −49.9411 | −1.64830 | ||||||||
\(919\) | 15.5147 | 0.511783 | 0.255892 | − | 0.966705i | \(-0.417631\pi\) | ||||
0.255892 | + | 0.966705i | \(0.417631\pi\) | |||||||
\(920\) | 1.17157 | 0.0386256 | ||||||||
\(921\) | 50.9706 | 1.67954 | ||||||||
\(922\) | 12.8284 | 0.422482 | ||||||||
\(923\) | 21.6569 | 0.712844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.65685 | −0.251756 | ||||||||
\(926\) | 16.9706 | 0.557687 | ||||||||
\(927\) | −128.368 | −4.21614 | ||||||||
\(928\) | 4.82843 | 0.158501 | ||||||||
\(929\) | −17.2132 | −0.564747 | −0.282373 | − | 0.959305i | \(-0.591122\pi\) | ||||
−0.282373 | + | 0.959305i | \(0.591122\pi\) | |||||||
\(930\) | 9.65685 | 0.316661 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 23.3137 | 0.763666 | ||||||||
\(933\) | 13.6569 | 0.447105 | ||||||||
\(934\) | 15.8995 | 0.520247 | ||||||||
\(935\) | −2.14214 | −0.0700553 | ||||||||
\(936\) | 41.7990 | 1.36624 | ||||||||
\(937\) | 20.2426 | 0.661298 | 0.330649 | − | 0.943754i | \(-0.392732\pi\) | ||||
0.330649 | + | 0.943754i | \(0.392732\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.1127 | 1.60273 | ||||||||
\(940\) | 5.17157 | 0.168678 | ||||||||
\(941\) | −50.0000 | −1.62995 | −0.814977 | − | 0.579494i | \(-0.803250\pi\) | ||||
−0.814977 | + | 0.579494i | \(0.803250\pi\) | |||||||
\(942\) | −22.1421 | −0.721430 | ||||||||
\(943\) | 3.59798 | 0.117166 | ||||||||
\(944\) | 8.58579 | 0.279444 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.31371 | −0.237789 | ||||||||
\(947\) | −4.82843 | −0.156903 | −0.0784514 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784514 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(948\) | −23.3137 | −0.757194 | ||||||||
\(949\) | 45.4558 | 1.47556 | ||||||||
\(950\) | −0.585786 | −0.0190054 | ||||||||
\(951\) | 35.7990 | 1.16086 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.343146 | 0.0111156 | 0.00555779 | − | 0.999985i | \(-0.498231\pi\) | ||||
0.00555779 | + | 0.999985i | \(0.498231\pi\) | |||||||
\(954\) | −56.1421 | −1.81767 | ||||||||
\(955\) | 10.1421 | 0.328192 | ||||||||
\(956\) | 1.65685 | 0.0535865 | ||||||||
\(957\) | 13.6569 | 0.441463 | ||||||||
\(958\) | 17.1716 | 0.554788 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.41421 | 0.110193 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | −36.9706 | −1.19198 | ||||||||
\(963\) | 83.5980 | 2.69391 | ||||||||
\(964\) | −13.4142 | −0.432043 | ||||||||
\(965\) | 5.65685 | 0.182101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.4558 | −1.20450 | −0.602249 | − | 0.798308i | \(-0.705729\pi\) | ||||
−0.602249 | + | 0.798308i | \(0.705729\pi\) | |||||||
\(968\) | 10.3137 | 0.331495 | ||||||||
\(969\) | 5.17157 | 0.166135 | ||||||||
\(970\) | 7.75736 | 0.249074 | ||||||||
\(971\) | −33.3553 | −1.07042 | −0.535212 | − | 0.844718i | \(-0.679768\pi\) | ||||
−0.535212 | + | 0.844718i | \(0.679768\pi\) | |||||||
\(972\) | 78.5269 | 2.51875 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.7990 | −1.01891 | ||||||||
\(975\) | −16.4853 | −0.527952 | ||||||||
\(976\) | 9.31371 | 0.298125 | ||||||||
\(977\) | −12.6863 | −0.405870 | −0.202935 | − | 0.979192i | \(-0.565048\pi\) | ||||
−0.202935 | + | 0.979192i | \(0.565048\pi\) | |||||||
\(978\) | 68.7696 | 2.19901 | ||||||||
\(979\) | −10.5442 | −0.336993 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.5147 | 0.686912 | ||||||||
\(982\) | −32.2843 | −1.03023 | ||||||||
\(983\) | −12.2010 | −0.389152 | −0.194576 | − | 0.980887i | \(-0.562333\pi\) | ||||
−0.194576 | + | 0.980887i | \(0.562333\pi\) | |||||||
\(984\) | 10.4853 | 0.334259 | ||||||||
\(985\) | −25.7990 | −0.822024 | ||||||||
\(986\) | 12.4853 | 0.397612 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.82843 | −0.0899843 | ||||||||
\(989\) | 10.3431 | 0.328893 | ||||||||
\(990\) | 7.17157 | 0.227928 | ||||||||
\(991\) | 44.7696 | 1.42215 | 0.711076 | − | 0.703115i | \(-0.248208\pi\) | ||||
0.711076 | + | 0.703115i | \(0.248208\pi\) | |||||||
\(992\) | 2.82843 | 0.0898027 | ||||||||
\(993\) | 115.397 | 3.66201 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.4853 | 0.522619 | ||||||||
\(996\) | −7.65685 | −0.242617 | ||||||||
\(997\) | −18.2843 | −0.579069 | −0.289534 | − | 0.957168i | \(-0.593500\pi\) | ||||
−0.289534 | + | 0.957168i | \(0.593500\pi\) | |||||||
\(998\) | −30.3431 | −0.960495 | ||||||||
\(999\) | −147.882 | −4.67879 |
(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 | 490.2.a.m.1.2 | yes | 2 | |
3.2 | odd | 2 | 4410.2.a.bt.1.2 | 2 | |||
4.3 | odd | 2 | 3920.2.a.bm.1.1 | 2 | |||
5.2 | odd | 4 | 2450.2.c.t.99.1 | 4 | |||
5.3 | odd | 4 | 2450.2.c.t.99.4 | 4 | |||
5.4 | even | 2 | 2450.2.a.bn.1.1 | 2 | |||
7.2 | even | 3 | 490.2.e.i.361.1 | 4 | |||
7.3 | odd | 6 | 490.2.e.j.471.2 | 4 | |||
7.4 | even | 3 | 490.2.e.i.471.1 | 4 | |||
7.5 | odd | 6 | 490.2.e.j.361.2 | 4 | |||
7.6 | odd | 2 | 490.2.a.l.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 4410.2.a.by.1.2 | 2 | |||
28.27 | even | 2 | 3920.2.a.ca.1.2 | 2 | |||
35.13 | even | 4 | 2450.2.c.w.99.3 | 4 | |||
35.27 | even | 4 | 2450.2.c.w.99.2 | 4 | |||
35.34 | odd | 2 | 2450.2.a.bs.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
490.2.a.l.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
490.2.a.m.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
490.2.e.i.361.1 | 4 | 7.2 | even | 3 | |||
490.2.e.i.471.1 | 4 | 7.4 | even | 3 | |||
490.2.e.j.361.2 | 4 | 7.5 | odd | 6 | |||
490.2.e.j.471.2 | 4 | 7.3 | odd | 6 | |||
2450.2.a.bn.1.1 | 2 | 5.4 | even | 2 | |||
2450.2.a.bs.1.2 | 2 | 35.34 | odd | 2 | |||
2450.2.c.t.99.1 | 4 | 5.2 | odd | 4 | |||
2450.2.c.t.99.4 | 4 | 5.3 | odd | 4 | |||
2450.2.c.w.99.2 | 4 | 35.27 | even | 4 | |||
2450.2.c.w.99.3 | 4 | 35.13 | even | 4 | |||
3920.2.a.bm.1.1 | 2 | 4.3 | odd | 2 | |||
3920.2.a.ca.1.2 | 2 | 28.27 | even | 2 | |||
4410.2.a.bt.1.2 | 2 | 3.2 | odd | 2 | |||
4410.2.a.by.1.2 | 2 | 21.20 | even | 2 |