Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,2,Mod(5,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("168.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.ba (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: | \(1.34148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 101.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.101 |
Dual form | 168.2.ba.b.5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.500000 | − | 0.866025i | ||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | −3.62132 | + | 2.09077i | −1.61950 | + | 0.935021i | −0.632456 | + | 0.774597i | \(0.717953\pi\) |
−0.987048 | + | 0.160424i | \(0.948714\pi\) | |||||||
\(6\) | − | 2.44949i | − | 1.00000i | ||||||
\(7\) | 1.62132 | + | 2.09077i | 0.612801 | + | 0.790237i | ||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 5.12132 | + | 2.95680i | 1.61950 | + | 0.935021i | ||||
\(11\) | 0.0857864 | − | 0.148586i | 0.0258656 | − | 0.0448005i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) |
0.878668 | + | 0.477432i | \(0.158432\pi\) | |||||||
\(12\) | −3.00000 | + | 1.73205i | −0.866025 | + | 0.500000i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 1.41421 | − | 3.46410i | 0.377964 | − | 0.925820i | ||||
\(15\) | −7.24264 | −1.87004 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 2.12132 | − | 3.67423i | 0.500000 | − | 0.866025i | ||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | − | 8.36308i | − | 1.87004i | ||||||
\(21\) | 0.621320 | + | 4.54026i | 0.135583 | + | 0.990766i | ||||
\(22\) | −0.242641 | −0.0517312 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.866025 | + | 0.500000i | ||||
\(25\) | 6.24264 | − | 10.8126i | 1.24853 | − | 2.16251i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −5.24264 | + | 0.717439i | −0.990766 | + | 0.135583i | ||||
\(29\) | 10.4142 | 1.93387 | 0.966935 | − | 0.255021i | \(-0.0820825\pi\) | ||||
0.966935 | + | 0.255021i | \(0.0820825\pi\) | |||||||
\(30\) | 5.12132 | + | 8.87039i | 0.935021 | + | 1.61950i | ||||
\(31\) | −5.37868 | − | 3.10538i | −0.966039 | − | 0.557743i | −0.0680129 | − | 0.997684i | \(-0.521666\pi\) |
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | −2.82843 | + | 4.89898i | −0.500000 | + | 0.866025i | ||||
\(33\) | 0.257359 | − | 0.148586i | 0.0448005 | − | 0.0258656i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.2426 | − | 4.18154i | −1.73132 | − | 0.706809i | ||||
\(36\) | −6.00000 | −1.00000 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.2426 | + | 5.91359i | −1.61950 | + | 0.935021i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 5.12132 | − | 3.97141i | 0.790237 | − | 0.612801i | ||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0.171573 | + | 0.297173i | 0.0258656 | + | 0.0448005i | ||||
\(45\) | −10.8640 | − | 6.27231i | −1.61950 | − | 0.935021i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | − | 6.92820i | − | 1.00000i | ||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | −17.6569 | −2.49706 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.03553 | − | 8.72180i | 0.691684 | − | 1.19803i | −0.279602 | − | 0.960116i | \(-0.590203\pi\) |
0.971286 | − | 0.237915i | \(-0.0764641\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.866025 | − | 0.500000i | ||||
\(55\) | 0.717439i | 0.0967394i | ||||||||
\(56\) | 4.58579 | + | 5.91359i | 0.612801 | + | 0.790237i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.36396 | − | 12.7548i | −0.966935 | − | 1.67478i | ||||
\(59\) | 3.98528 | + | 2.30090i | 0.518839 | + | 0.299552i | 0.736460 | − | 0.676481i | \(-0.236496\pi\) |
−0.217620 | + | 0.976034i | \(0.569829\pi\) | |||||||
\(60\) | 7.24264 | − | 12.5446i | 0.935021 | − | 1.61950i | ||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 8.78335i | 1.11549i | ||||||||
\(63\) | −3.00000 | + | 7.34847i | −0.377964 | + | 0.925820i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.363961 | − | 0.210133i | −0.0448005 | − | 0.0258656i | ||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.12132 | + | 15.5014i | 0.253546 | + | 1.85277i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 4.24264 | + | 7.34847i | 0.500000 | + | 0.866025i | ||||
\(73\) | 8.48528 | + | 4.89898i | 0.993127 | + | 0.573382i | 0.906208 | − | 0.422833i | \(-0.138964\pi\) |
0.0869195 | + | 0.996215i | \(0.472298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18.7279 | − | 10.8126i | 2.16251 | − | 1.24853i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.449747 | − | 0.0615465i | 0.0512535 | − | 0.00701388i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.86396 | − | 6.69258i | −0.434730 | − | 0.752974i | 0.562544 | − | 0.826767i | \(-0.309823\pi\) |
−0.997274 | + | 0.0737937i | \(0.976489\pi\) | |||||||
\(80\) | 14.4853 | + | 8.36308i | 1.61950 | + | 0.935021i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.76127i | 0.412854i | 0.978462 | + | 0.206427i | \(0.0661835\pi\) | ||||
−0.978462 | + | 0.206427i | \(0.933816\pi\) | |||||||
\(84\) | −8.48528 | − | 3.46410i | −0.925820 | − | 0.377964i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.6213 | + | 9.01897i | 1.67478 | + | 0.966935i | ||||
\(88\) | 0.242641 | − | 0.420266i | 0.0258656 | − | 0.0448005i | ||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 17.7408i | 1.87004i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.37868 | − | 9.31615i | −0.557743 | − | 0.966039i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | + | 4.89898i | −0.866025 | + | 0.500000i | ||||
\(97\) | − | 11.5300i | − | 1.17070i | −0.810782 | − | 0.585348i | \(-0.800958\pi\) | ||
0.810782 | − | 0.585348i | \(-0.199042\pi\) | |||||||
\(98\) | 9.53553 | − | 2.65962i | 0.963234 | − | 0.268662i | ||||
\(99\) | 0.514719 | 0.0517312 | ||||||||
\(100\) | 12.4853 | + | 21.6251i | 1.24853 | + | 2.16251i | ||||
\(101\) | 3.00000 | + | 1.73205i | 0.298511 | + | 0.172345i | 0.641774 | − | 0.766894i | \(-0.278199\pi\) |
−0.343263 | + | 0.939239i | \(0.611532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7279 | − | 7.34847i | 1.25412 | − | 0.724066i | 0.282194 | − | 0.959357i | \(-0.408938\pi\) |
0.971925 | + | 0.235291i | \(0.0756043\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.7426 | − | 15.1427i | −1.14596 | − | 1.47778i | ||||
\(106\) | −14.2426 | −1.38337 | ||||||||
\(107\) | −10.3284 | − | 17.8894i | −0.998487 | − | 1.72943i | −0.546869 | − | 0.837218i | \(-0.684180\pi\) |
−0.451618 | − | 0.892211i | \(-0.649153\pi\) | |||||||
\(108\) | −9.00000 | − | 5.19615i | −0.866025 | − | 0.500000i | ||||
\(109\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(110\) | 0.878680 | − | 0.507306i | 0.0837788 | − | 0.0483697i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000 | − | 9.79796i | 0.377964 | − | 0.925820i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.4142 | + | 18.0379i | −0.966935 | + | 1.67478i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.50794i | − | 0.599104i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −20.4853 | −1.87004 | ||||||||
\(121\) | 5.48528 | + | 9.50079i | 0.498662 | + | 0.863708i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.7574 | − | 6.21076i | 0.966039 | − | 0.557743i | ||||
\(125\) | 31.3000i | 2.79956i | ||||||||
\(126\) | 11.1213 | − | 1.52192i | 0.990766 | − | 0.135583i | ||||
\(127\) | 6.75736 | 0.599619 | 0.299809 | − | 0.953999i | \(-0.403077\pi\) | ||||
0.299809 | + | 0.953999i | \(0.403077\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.4706 | + | 10.6640i | −1.61378 | + | 0.931717i | −0.625297 | + | 0.780387i | \(0.715022\pi\) |
−0.988483 | + | 0.151330i | \(0.951644\pi\) | |||||||
\(132\) | 0.594346i | 0.0517312i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.8640 | − | 18.8169i | −0.935021 | − | 1.61950i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 17.4853 | − | 13.5592i | 1.47778 | − | 1.14596i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | − | 10.3923i | 0.500000 | − | 0.866025i | ||||
\(145\) | −37.7132 | + | 21.7737i | −3.13191 | + | 1.80821i | ||||
\(146\) | − | 13.8564i | − | 1.14676i | ||||||
\(147\) | −8.48528 | + | 8.66025i | −0.699854 | + | 0.714286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.41421 | − | 2.44949i | −0.115857 | − | 0.200670i | 0.802265 | − | 0.596968i | \(-0.203628\pi\) |
−0.918122 | + | 0.396298i | \(0.870295\pi\) | |||||||
\(150\) | −26.4853 | − | 15.2913i | −2.16251 | − | 1.24853i | ||||
\(151\) | −11.1066 | + | 19.2372i | −0.903842 | + | 1.56550i | −0.0813788 | + | 0.996683i | \(0.525932\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.393398 | − | 0.507306i | −0.0317009 | − | 0.0408799i | ||||
\(155\) | 25.9706 | 2.08601 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(158\) | −5.46447 | + | 9.46473i | −0.434730 | + | 0.752974i | ||||
\(159\) | 15.1066 | − | 8.72180i | 1.19803 | − | 0.691684i | ||||
\(160\) | − | 23.6544i | − | 1.87004i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.7279 | 1.00000 | ||||||||
\(163\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.621320 | + | 1.07616i | −0.0483697 | + | 0.0837788i | ||||
\(166\) | 4.60660 | − | 2.65962i | 0.357542 | − | 0.206427i | ||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 1.75736 | + | 12.8418i | 0.135583 | + | 0.990766i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.0000 | − | 8.66025i | 1.14043 | − | 0.658427i | 0.193892 | − | 0.981023i | \(-0.437889\pi\) |
0.946537 | + | 0.322596i | \(0.104555\pi\) | |||||||
\(174\) | − | 25.5095i | − | 1.93387i | ||||||
\(175\) | 32.7279 | − | 4.47871i | 2.47400 | − | 0.338559i | ||||
\(176\) | −0.686292 | −0.0517312 | ||||||||
\(177\) | 3.98528 | + | 6.90271i | 0.299552 | + | 0.518839i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.65685 | + | 9.79796i | −0.422813 | + | 0.732334i | −0.996213 | − | 0.0869415i | \(-0.972291\pi\) |
0.573400 | + | 0.819275i | \(0.305624\pi\) | |||||||
\(180\) | 21.7279 | − | 12.5446i | 1.61950 | − | 0.935021i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.60660 | + | 13.1750i | −0.557743 | + | 0.966039i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.8640 | + | 8.42463i | −0.790237 | + | 0.612801i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | 10.7426 | − | 18.6068i | 0.773272 | − | 1.33935i | −0.162488 | − | 0.986710i | \(-0.551952\pi\) |
0.935760 | − | 0.352636i | \(-0.114715\pi\) | |||||||
\(194\) | −14.1213 | + | 8.15295i | −1.01385 | + | 0.585348i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.0000 | − | 9.79796i | −0.714286 | − | 0.699854i | ||||
\(197\) | −14.1421 | −1.00759 | −0.503793 | − | 0.863825i | \(-0.668062\pi\) | ||||
−0.503793 | + | 0.863825i | \(0.668062\pi\) | |||||||
\(198\) | −0.363961 | − | 0.630399i | −0.0258656 | − | 0.0448005i | ||||
\(199\) | −21.2132 | − | 12.2474i | −1.50376 | − | 0.868199i | −0.999990 | − | 0.00436292i | \(-0.998611\pi\) |
−0.503774 | − | 0.863836i | \(-0.668055\pi\) | |||||||
\(200\) | 17.6569 | − | 30.5826i | 1.24853 | − | 2.16251i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 4.89898i | − | 0.344691i | ||||||
\(203\) | 16.8848 | + | 21.7737i | 1.18508 | + | 1.52822i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −18.0000 | − | 10.3923i | −1.25412 | − | 0.724066i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −10.2426 | + | 25.0892i | −0.706809 | + | 1.73132i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 10.0711 | + | 17.4436i | 0.691684 | + | 1.19803i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.6066 | + | 25.2994i | −0.998487 | + | 1.72943i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 1.00000i | ||||||||
\(217\) | −2.22792 | − | 16.2804i | −0.151241 | − | 1.10519i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.48528 | + | 14.6969i | 0.573382 | + | 0.993127i | ||||
\(220\) | −1.24264 | − | 0.717439i | −0.0837788 | − | 0.0483697i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.8651i | 1.99992i | 0.00910984 | + | 0.999959i | \(0.497100\pi\) | ||||
−0.00910984 | + | 0.999959i | \(0.502900\pi\) | |||||||
\(224\) | −14.8284 | + | 2.02922i | −0.990766 | + | 0.135583i | ||||
\(225\) | 37.4558 | 2.49706 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.7132 | − | 14.8455i | −1.70665 | − | 0.985332i | −0.938647 | − | 0.344881i | \(-0.887919\pi\) |
−0.767999 | − | 0.640451i | \(-0.778747\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.727922 | + | 0.297173i | 0.0478938 | + | 0.0195525i | ||||
\(232\) | 29.4558 | 1.93387 | ||||||||
\(233\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.97056 | + | 4.60181i | −0.518839 | + | 0.299552i | ||||
\(237\) | − | 13.3852i | − | 0.869459i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 14.4853 | + | 25.0892i | 0.935021 | + | 1.61950i | ||||
\(241\) | −20.2279 | − | 11.6786i | −1.30300 | − | 0.752285i | −0.322078 | − | 0.946713i | \(-0.604381\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 7.75736 | − | 13.4361i | 0.498662 | − | 0.863708i | ||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.86396 | − | 28.1946i | −0.502410 | − | 1.80129i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −15.2132 | − | 8.78335i | −0.966039 | − | 0.557743i | ||||
\(249\) | −3.25736 | + | 5.64191i | −0.206427 | + | 0.357542i | ||||
\(250\) | 38.3345 | − | 22.1324i | 2.42449 | − | 1.39978i | ||||
\(251\) | − | 20.4874i | − | 1.29316i | −0.762848 | − | 0.646578i | \(-0.776200\pi\) | ||
0.762848 | − | 0.646578i | \(-0.223800\pi\) | |||||||
\(252\) | −9.72792 | − | 12.5446i | −0.612801 | − | 0.790237i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.77817 | − | 8.27604i | −0.299809 | − | 0.519285i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.6213 | + | 27.0569i | 0.966935 | + | 1.67478i | ||||
\(262\) | 26.1213 | + | 15.0812i | 1.61378 | + | 0.931717i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0.727922 | − | 0.420266i | 0.0448005 | − | 0.0258656i | ||||
\(265\) | 42.1126i | 2.58696i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.8345 | + | 10.8741i | 1.14836 | + | 0.663007i | 0.948487 | − | 0.316815i | \(-0.102613\pi\) |
0.199874 | + | 0.979822i | \(0.435947\pi\) | |||||||
\(270\) | −15.3640 | + | 26.6112i | −0.935021 | + | 1.61950i | ||||
\(271\) | −5.89340 | + | 3.40256i | −0.357998 | + | 0.206691i | −0.668202 | − | 0.743980i | \(-0.732936\pi\) |
0.310204 | + | 0.950670i | \(0.399603\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.07107 | − | 1.85514i | −0.0645878 | − | 0.111869i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 18.6323i | − | 1.11549i | ||||||
\(280\) | −28.9706 | − | 11.8272i | −1.73132 | − | 0.706809i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.9706 | −1.00000 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 53.3345 | + | 30.7927i | 3.13191 | + | 1.80821i | ||||
\(291\) | 9.98528 | − | 17.2950i | 0.585348 | − | 1.01385i | ||||
\(292\) | −16.9706 | + | 9.79796i | −0.993127 | + | 0.573382i | ||||
\(293\) | − | 3.34101i | − | 0.195184i | −0.995227 | − | 0.0975919i | \(-0.968886\pi\) | ||
0.995227 | − | 0.0975919i | \(-0.0311140\pi\) | |||||||
\(294\) | 16.6066 | + | 4.26858i | 0.968517 | + | 0.248949i | ||||
\(295\) | −19.2426 | −1.12035 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.772078 | + | 0.445759i | 0.0448005 | + | 0.0258656i | ||||
\(298\) | −2.00000 | + | 3.46410i | −0.115857 | + | 0.200670i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 43.2503i | 2.49706i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 31.4142 | 1.80768 | ||||||||
\(303\) | 3.00000 | + | 5.19615i | 0.172345 | + | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | −0.343146 | + | 0.840532i | −0.0195525 | + | 0.0478938i | ||||
\(309\) | 25.4558 | 1.44813 | ||||||||
\(310\) | −18.3640 | − | 31.8073i | −1.04300 | − | 1.80653i | ||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2574 | − | 12.2729i | 1.20154 | − | 0.693708i | 0.240640 | − | 0.970614i | \(-0.422643\pi\) |
0.960897 | + | 0.276907i | \(0.0893093\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.50000 | − | 32.8835i | −0.253546 | − | 1.85277i | ||||
\(316\) | 15.4558 | 0.869459 | ||||||||
\(317\) | −15.2782 | − | 26.4626i | −0.858108 | − | 1.48629i | −0.873732 | − | 0.486408i | \(-0.838307\pi\) |
0.0156238 | − | 0.999878i | \(-0.495027\pi\) | |||||||
\(318\) | −21.3640 | − | 12.3345i | −1.19803 | − | 0.691684i | ||||
\(319\) | 0.893398 | − | 1.54741i | 0.0500207 | − | 0.0866384i | ||||
\(320\) | −28.9706 | + | 16.7262i | −1.61950 | + | 0.935021i | ||||
\(321\) | − | 35.7787i | − | 1.99697i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.500000 | − | 0.866025i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.75736 | 0.0967394 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −6.51472 | − | 3.76127i | −0.357542 | − | 0.206427i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.4853 | − | 11.2328i | 0.790237 | − | 0.612801i | ||||
\(337\) | 36.4558 | 1.98588 | 0.992938 | − | 0.118633i | \(-0.0378512\pi\) | ||||
0.992938 | + | 0.118633i | \(0.0378512\pi\) | |||||||
\(338\) | 9.19239 | + | 15.9217i | 0.500000 | + | 0.866025i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.922836 | + | 0.532799i | −0.0499743 | + | 0.0288527i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.2132 | − | 12.2474i | −1.14043 | − | 0.658427i | ||||
\(347\) | 14.1421 | − | 24.4949i | 0.759190 | − | 1.31495i | −0.184075 | − | 0.982912i | \(-0.558929\pi\) |
0.943264 | − | 0.332043i | \(-0.107738\pi\) | |||||||
\(348\) | −31.2426 | + | 18.0379i | −1.67478 | + | 0.966935i | ||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −28.6274 | − | 36.9164i | −1.53020 | − | 1.97327i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.485281 | + | 0.840532i | 0.0258656 | + | 0.0448005i | ||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 5.63604 | − | 9.76191i | 0.299552 | − | 0.518839i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.0000 | 0.845626 | ||||||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | −30.7279 | − | 17.7408i | −1.61950 | − | 0.935021i | ||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.0016i | 0.997324i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.9706 | −2.14450 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.3787 | − | 15.2297i | −1.37696 | − | 0.794986i | −0.385164 | − | 0.922848i | \(-0.625855\pi\) |
−0.991792 | + | 0.127862i | \(0.959188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.3995 | − | 3.61269i | 1.37059 | − | 0.187561i | ||||
\(372\) | 21.5147 | 1.11549 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.1066 | + | 46.9500i | −1.39978 | + | 2.42449i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 18.0000 | + | 7.34847i | 0.925820 | + | 0.377964i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.1360 | + | 5.85204i | 0.519285 | + | 0.299809i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | − | 19.5959i | − | 1.00000i | ||||||
\(385\) | −1.50000 | + | 1.16320i | −0.0764471 | + | 0.0592821i | ||||
\(386\) | −30.3848 | −1.54654 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.9706 | + | 11.5300i | 1.01385 | + | 0.585348i | ||||
\(389\) | −15.5563 | + | 26.9444i | −0.788738 | + | 1.36613i | 0.138002 | + | 0.990432i | \(0.455932\pi\) |
−0.926740 | + | 0.375703i | \(0.877401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.92893 | + | 19.1757i | −0.248949 | + | 0.968517i | ||||
\(393\) | −36.9411 | −1.86343 | ||||||||
\(394\) | 10.0000 | + | 17.3205i | 0.503793 | + | 0.872595i | ||||
\(395\) | 27.9853 | + | 16.1573i | 1.40809 | + | 0.812962i | ||||
\(396\) | −0.514719 | + | 0.891519i | −0.0258656 | + | 0.0448005i | ||||
\(397\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(398\) | 34.6410i | 1.73640i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −49.9411 | −2.49706 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.00000 | + | 3.46410i | −0.298511 | + | 0.172345i | ||||
\(405\) | − | 37.6339i | − | 1.87004i | ||||||
\(406\) | 14.7279 | − | 36.0759i | 0.730934 | − | 1.79042i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.47056 | + | 5.46783i | 0.468289 | + | 0.270367i | 0.715523 | − | 0.698589i | \(-0.246188\pi\) |
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 29.3939i | 1.44813i | ||||||||
\(413\) | 1.65076 | + | 12.0628i | 0.0812285 | + | 0.593572i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.86396 | − | 13.6208i | −0.386027 | − | 0.668618i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.3923i | 0.507697i | 0.967244 | + | 0.253849i | \(0.0816965\pi\) | ||||
−0.967244 | + | 0.253849i | \(0.918303\pi\) | |||||||
\(420\) | 37.9706 | − | 5.19615i | 1.85277 | − | 0.253546i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.2426 | − | 24.6690i | 0.691684 | − | 1.19803i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 41.3137 | 1.99697 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 18.0000 | − | 10.3923i | 0.866025 | − | 0.500000i | ||||
\(433\) | − | 39.1918i | − | 1.88344i | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||
0.336399 | − | 0.941720i | \(-0.390791\pi\) | |||||||
\(434\) | −18.3640 | + | 14.2406i | −0.881498 | + | 0.683572i | ||||
\(435\) | −75.4264 | −3.61642 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.0000 | − | 20.7846i | 0.573382 | − | 0.993127i | ||||
\(439\) | 36.1066 | − | 20.8462i | 1.72327 | − | 0.994933i | 0.811366 | − | 0.584539i | \(-0.198725\pi\) |
0.911908 | − | 0.410394i | \(-0.134609\pi\) | |||||||
\(440\) | 2.02922i | 0.0967394i | ||||||||
\(441\) | −20.2279 | + | 5.64191i | −0.963234 | + | 0.268662i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.5711 | + | 35.6301i | 0.977361 | + | 1.69284i | 0.671913 | + | 0.740630i | \(0.265473\pi\) |
0.305448 | + | 0.952209i | \(0.401194\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 36.5772 | − | 21.1178i | 1.73198 | − | 0.999959i | ||||
\(447\) | − | 4.89898i | − | 0.231714i | ||||||
\(448\) | 12.9706 | + | 16.7262i | 0.612801 | + | 0.790237i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | −26.4853 | − | 45.8739i | −1.24853 | − | 2.16251i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.3198 | + | 19.2372i | −1.56550 | + | 0.903842i | ||||
\(454\) | 41.9895i | 1.97066i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9853 | + | 31.1514i | 0.841316 | + | 1.45720i | 0.888783 | + | 0.458329i | \(0.151552\pi\) |
−0.0474665 | + | 0.998873i | \(0.515115\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 38.1051i | − | 1.77473i | −0.461065 | − | 0.887366i | \(-0.652533\pi\) | ||
0.461065 | − | 0.887366i | \(-0.347467\pi\) | |||||||
\(462\) | −0.150758 | − | 1.10165i | −0.00701388 | − | 0.0512535i | ||||
\(463\) | −26.0000 | −1.20832 | −0.604161 | − | 0.796862i | \(-0.706492\pi\) | ||||
−0.604161 | + | 0.796862i | \(0.706492\pi\) | |||||||
\(464\) | −20.8284 | − | 36.0759i | −0.966935 | − | 1.67478i | ||||
\(465\) | 38.9558 | + | 22.4912i | 1.80653 | + | 1.04300i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.0000 | − | 8.66025i | 0.694117 | − | 0.400749i | −0.111035 | − | 0.993816i | \(-0.535417\pi\) |
0.805153 | + | 0.593068i | \(0.202083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.2721 | + | 6.50794i | 0.518839 | + | 0.299552i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −16.3934 | + | 9.46473i | −0.752974 | + | 0.434730i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.2132 | 1.38337 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 20.4853 | − | 35.4815i | 0.935021 | − | 1.61950i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 33.0321i | 1.50457i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.9411 | −0.997324 | ||||||||
\(485\) | 24.1066 | + | 41.7539i | 1.09462 | + | 1.89595i | ||||
\(486\) | 19.0919 | + | 11.0227i | 0.866025 | + | 0.500000i | ||||
\(487\) | 18.5919 | − | 32.2021i | 0.842479 | − | 1.45922i | −0.0453143 | − | 0.998973i | \(-0.514429\pi\) |
0.887793 | − | 0.460243i | \(-0.152238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −28.9706 | + | 29.5680i | −1.30876 | + | 1.33574i | ||||
\(491\) | −21.6863 | −0.978689 | −0.489344 | − | 0.872091i | \(-0.662764\pi\) | ||||
−0.489344 | + | 0.872091i | \(0.662764\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.86396 | + | 1.07616i | −0.0837788 | + | 0.0483697i | ||||
\(496\) | 24.8431i | 1.11549i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.21320 | 0.412854 | ||||||||
\(499\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(500\) | −54.2132 | − | 31.3000i | −2.42449 | − | 1.39978i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.0919 | + | 14.4868i | −1.11991 | + | 0.646578i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | −8.48528 | + | 20.7846i | −0.377964 | + | 0.925820i | ||||
\(505\) | −14.4853 | −0.644587 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.5000 | − | 11.2583i | −0.866025 | − | 0.500000i | ||||
\(508\) | −6.75736 | + | 11.7041i | −0.299809 | + | 0.519285i | ||||
\(509\) | 17.3787 | − | 10.0336i | 0.770296 | − | 0.444731i | −0.0626839 | − | 0.998033i | \(-0.519966\pi\) |
0.832980 | + | 0.553303i | \(0.186633\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.51472 | + | 25.6836i | 0.155482 | + | 1.13618i | ||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −30.7279 | + | 53.2223i | −1.35403 | + | 2.34526i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.0000 | 1.31685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 22.0919 | − | 38.2643i | 0.966935 | − | 1.67478i | ||||
\(523\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(524\) | − | 42.6559i | − | 1.86343i | ||||||
\(525\) | 52.9706 | + | 21.6251i | 2.31182 | + | 0.943799i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.02944 | − | 0.594346i | −0.0448005 | − | 0.0258656i | ||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 51.5772 | − | 29.7781i | 2.24037 | − | 1.29348i | ||||
\(531\) | 13.8054i | 0.599104i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 74.8051 | + | 43.1887i | 3.23411 | + | 1.86721i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.9706 | + | 9.79796i | −0.732334 | + | 0.422813i | ||||
\(538\) | − | 30.7566i | − | 1.32601i | ||||||
\(539\) | 0.857864 | + | 0.840532i | 0.0369508 | + | 0.0362043i | ||||
\(540\) | 43.4558 | 1.87004 | ||||||||
\(541\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(542\) | 8.33452 | + | 4.81194i | 0.357998 | + | 0.206691i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.51472 | + | 2.62357i | −0.0645878 | + | 0.111869i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.72792 | − | 18.9295i | 0.328625 | − | 0.804963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.9645 | + | 27.6513i | −0.676436 | + | 1.17162i | 0.299611 | + | 0.954062i | \(0.403143\pi\) |
−0.976047 | + | 0.217560i | \(0.930190\pi\) | |||||||
\(558\) | −22.8198 | + | 13.1750i | −0.966039 | + | 0.557743i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 6.00000 | + | 43.8446i | 0.253546 | + | 1.85277i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.71320 | − | 2.72117i | −0.198638 | − | 0.114684i | 0.397382 | − | 0.917653i | \(-0.369919\pi\) |
−0.596020 | + | 0.802970i | \(0.703252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.5919 | + | 3.22848i | −0.990766 | + | 0.135583i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.500000 | + | 0.866025i | ||||
\(577\) | −41.2279 | − | 23.8030i | −1.71634 | − | 0.990930i | −0.925361 | − | 0.379088i | \(-0.876238\pi\) |
−0.790980 | − | 0.611842i | \(-0.790429\pi\) | |||||||
\(578\) | 12.0208 | − | 20.8207i | 0.500000 | − | 0.866025i | ||||
\(579\) | 32.2279 | − | 18.6068i | 1.33935 | − | 0.773272i | ||||
\(580\) | − | 87.0949i | − | 3.61642i | ||||||
\(581\) | −7.86396 | + | 6.09823i | −0.326252 | + | 0.252997i | ||||
\(582\) | −28.2426 | −1.17070 | ||||||||
\(583\) | −0.863961 | − | 1.49642i | −0.0357816 | − | 0.0619756i | ||||
\(584\) | 24.0000 | + | 13.8564i | 0.993127 | + | 0.573382i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.09188 | + | 2.36245i | −0.169034 | + | 0.0975919i | ||||
\(587\) | − | 30.5316i | − | 1.26017i | −0.776525 | − | 0.630087i | \(-0.783019\pi\) | ||
0.776525 | − | 0.630087i | \(-0.216981\pi\) | |||||||
\(588\) | −6.51472 | − | 23.3572i | −0.268662 | − | 0.963234i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 13.6066 | + | 23.5673i | 0.560175 | + | 0.970251i | ||||
\(591\) | −21.2132 | − | 12.2474i | −0.872595 | − | 0.503793i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | − | 1.26080i | − | 0.0517312i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.65685 | 0.231714 | ||||||||
\(597\) | −21.2132 | − | 36.7423i | −0.868199 | − | 1.50376i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 52.9706 | − | 30.5826i | 2.16251 | − | 1.24853i | ||||
\(601\) | 22.7628i | 0.928516i | 0.885700 | + | 0.464258i | \(0.153679\pi\) | ||||
−0.885700 | + | 0.464258i | \(0.846321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.2132 | − | 38.4744i | −0.903842 | − | 1.56550i | ||||
\(605\) | −39.7279 | − | 22.9369i | −1.61517 | − | 0.932519i | ||||
\(606\) | 4.24264 | − | 7.34847i | 0.172345 | − | 0.298511i | ||||
\(607\) | −35.5919 | + | 20.5490i | −1.44463 | + | 0.834058i | −0.998154 | − | 0.0607380i | \(-0.980655\pi\) |
−0.446476 | + | 0.894795i | \(0.647321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.47056 | + | 47.2832i | 0.262200 | + | 1.91601i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.27208 | − | 0.174080i | 0.0512535 | − | 0.00701388i | ||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | −18.0000 | − | 31.1769i | −0.724066 | − | 1.25412i | ||||
\(619\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(620\) | −25.9706 | + | 44.9823i | −1.04300 | + | 1.80653i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −34.2279 | − | 59.2845i | −1.36912 | − | 2.37138i | ||||
\(626\) | −30.0624 | − | 17.3566i | −1.20154 | − | 0.693708i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −37.0919 | + | 28.7635i | −1.47778 | + | 1.14596i | ||||
\(631\) | 20.7574 | 0.826337 | 0.413169 | − | 0.910654i | \(-0.364422\pi\) | ||||
0.413169 | + | 0.910654i | \(0.364422\pi\) | |||||||
\(632\) | −10.9289 | − | 18.9295i | −0.434730 | − | 0.752974i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.6066 | + | 37.4237i | −0.858108 | + | 1.48629i | ||||
\(635\) | −24.4706 | + | 14.1281i | −0.971085 | + | 0.560656i | ||||
\(636\) | 34.8872i | 1.38337i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.52691 | −0.100041 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.9706 | + | 23.6544i | 1.61950 | + | 0.935021i | ||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | −43.8198 | + | 25.2994i | −1.72943 | + | 0.998487i | ||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | −12.7279 | + | 22.0454i | −0.500000 | + | 0.866025i | ||||
\(649\) | 0.683766 | − | 0.394773i | 0.0268402 | − | 0.0154962i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.7574 | − | 26.3500i | 0.421614 | − | 1.03274i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.52082 | + | 7.83028i | 0.176913 | + | 0.306423i | 0.940822 | − | 0.338902i | \(-0.110055\pi\) |
−0.763909 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.5919 | − | 77.2354i | 1.74235 | − | 3.01784i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.3939i | 1.14676i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.2548 | 1.76288 | 0.881439 | − | 0.472298i | \(-0.156575\pi\) | ||||
0.881439 | + | 0.472298i | \(0.156575\pi\) | |||||||
\(660\) | −1.24264 | − | 2.15232i | −0.0483697 | − | 0.0837788i | ||||
\(661\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.6385i | 0.412854i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.8640 | + | 44.7977i | −0.999959 | + | 1.73198i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −24.0000 | − | 9.79796i | −0.925820 | − | 0.377964i | ||||
\(673\) | −50.9411 | −1.96364 | −0.981818 | − | 0.189824i | \(-0.939208\pi\) | ||||
−0.981818 | + | 0.189824i | \(0.939208\pi\) | |||||||
\(674\) | −25.7782 | − | 44.6491i | −0.992938 | − | 1.71982i | ||||
\(675\) | 56.1838 | + | 32.4377i | 2.16251 | + | 1.24853i | ||||
\(676\) | 13.0000 | − | 22.5167i | 0.500000 | − | 0.866025i | ||||
\(677\) | −24.6213 | + | 14.2151i | −0.946274 | + | 0.546332i | −0.891922 | − | 0.452190i | \(-0.850643\pi\) |
−0.0543526 | + | 0.998522i | \(0.517310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.1066 | − | 18.6938i | 0.925126 | − | 0.717404i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.7132 | − | 44.5366i | −0.985332 | − | 1.70665i | ||||
\(682\) | 1.30509 | + | 0.753492i | 0.0499743 | + | 0.0288527i | ||||
\(683\) | 21.0858 | − | 36.5217i | 0.806825 | − | 1.39746i | −0.108227 | − | 0.994126i | \(-0.534517\pi\) |
0.915052 | − | 0.403336i | \(-0.132149\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 21.0208 | + | 15.6245i | 0.802578 | + | 0.596547i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(692\) | 34.6410i | 1.31685i | ||||||||
\(693\) | 0.834524 | + | 1.07616i | 0.0317009 | + | 0.0408799i | ||||
\(694\) | −40.0000 | −1.51838 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 44.1838 | + | 25.5095i | 1.67478 | + | 0.966935i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.9706 | + | 61.1651i | −0.943799 | + | 2.31182i | ||||
\(701\) | −51.3848 | −1.94078 | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.686292 | − | 1.18869i | 0.0258656 | − | 0.0448005i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.24264 | + | 9.08052i | 0.0467343 | + | 0.341508i | ||||
\(708\) | −15.9411 | −0.599104 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.5919 | − | 20.0777i | 0.434730 | − | 0.752974i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.3137 | − | 19.5959i | −0.422813 | − | 0.732334i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 50.1785i | 1.87004i | ||||||||
\(721\) | 36.0000 | + | 14.6969i | 1.34071 | + | 0.547343i | ||||
\(722\) | −26.8701 | −1.00000 | ||||||||
\(723\) | −20.2279 | − | 35.0358i | −0.752285 | − | 1.30300i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 65.0122 | − | 112.604i | 2.41449 | − | 4.18202i | ||||
\(726\) | 23.2721 | − | 13.4361i | 0.863708 | − | 0.498662i | ||||
\(727\) | − | 28.6764i | − | 1.06355i | −0.846886 | − | 0.531775i | \(-0.821525\pi\) | ||
0.846886 | − | 0.531775i | \(-0.178475\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 28.9706 | + | 50.1785i | 1.07225 | + | 1.85719i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(734\) | 43.0762i | 1.58997i | ||||||||
\(735\) | 12.6213 | − | 49.1023i | 0.465544 | − | 1.81117i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.0919 | − | 29.7781i | −0.847730 | − | 1.09319i | ||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | −15.2132 | − | 26.3500i | −0.557743 | − | 0.966039i | ||||
\(745\) | 10.2426 | + | 5.91359i | 0.375261 | + | 0.216657i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.77208 | + | 5.64191i | −0.357542 | + | 0.206427i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.6569 | − | 50.5988i | 0.754785 | − | 1.84884i | ||||
\(750\) | 76.6690 | 2.79956 | ||||||||
\(751\) | 25.8345 | + | 44.7467i | 0.942715 | + | 1.63283i | 0.760263 | + | 0.649616i | \(0.225070\pi\) |
0.182453 | + | 0.983215i | \(0.441596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.7426 | − | 30.7312i | 0.646578 | − | 1.11991i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 92.8854i | − | 3.38045i | ||||||
\(756\) | −3.72792 | − | 27.2416i | −0.135583 | − | 0.990766i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | − | 16.5521i | − | 0.599619i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −24.0000 | + | 13.8564i | −0.866025 | + | 0.500000i | ||||
\(769\) | 47.0116i | 1.69528i | 0.530572 | + | 0.847640i | \(0.321977\pi\) | ||||
−0.530572 | + | 0.847640i | \(0.678023\pi\) | |||||||
\(770\) | 2.48528 | + | 1.01461i | 0.0895633 | + | 0.0365641i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.4853 | + | 37.2136i | 0.773272 | + | 1.33935i | ||||
\(773\) | 45.0000 | + | 25.9808i | 1.61854 | + | 0.934463i | 0.987299 | + | 0.158874i | \(0.0507865\pi\) |
0.631239 | + | 0.775589i | \(0.282547\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −67.1543 | + | 38.7716i | −2.41225 | + | 1.39272i | ||||
\(776\) | − | 32.6118i | − | 1.17070i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.0000 | 1.57748 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 54.1138i | 1.93387i | ||||||||
\(784\) | 26.9706 | − | 7.52255i | 0.963234 | − | 0.268662i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 26.1213 | + | 45.2435i | 0.931717 | + | 1.61378i | ||||
\(787\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(788\) | 14.1421 | − | 24.4949i | 0.503793 | − | 0.872595i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 45.6998i | − | 1.62592i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.45584 | 0.0517312 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.4706 | + | 63.1689i | −1.29348 | + | 2.24037i | ||||
\(796\) | 42.4264 | − | 24.4949i | 1.50376 | − | 0.868199i | ||||
\(797\) | 55.2006i | 1.95530i | 0.210230 | + | 0.977652i | \(0.432579\pi\) | ||||
−0.210230 | + | 0.977652i | \(0.567421\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 35.3137 | + | 61.1651i | 1.24853 | + | 2.16251i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.45584 | − | 0.840532i | 0.0513756 | − | 0.0296617i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.8345 | + | 32.6224i | 0.663007 | + | 1.14836i | ||||
\(808\) | 8.48528 | + | 4.89898i | 0.298511 | + | 0.172345i | ||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | −46.0919 | + | 26.6112i | −1.61950 | + | 0.935021i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | −54.5980 | + | 7.47156i | −1.91601 | + | 0.262200i | ||||
\(813\) | −11.7868 | −0.413381 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 15.4654i | − | 0.540734i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5208 | + | 44.2033i | 0.890683 | + | 1.54271i | 0.839059 | + | 0.544041i | \(0.183106\pi\) |
0.0516239 | + | 0.998667i | \(0.483560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0000 | + | 39.8372i | −0.801730 | + | 1.38864i | 0.116747 | + | 0.993162i | \(0.462753\pi\) |
−0.918477 | + | 0.395475i | \(0.870580\pi\) | |||||||
\(824\) | 36.0000 | − | 20.7846i | 1.25412 | − | 0.724066i | ||||
\(825\) | − | 3.71029i | − | 0.129176i | ||||||
\(826\) | 13.6066 | − | 10.5515i | 0.473434 | − | 0.367132i | ||||
\(827\) | −19.2843 | −0.670580 | −0.335290 | − | 0.942115i | \(-0.608834\pi\) | ||||
−0.335290 | + | 0.942115i | \(0.608834\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(830\) | −11.1213 | + | 19.2627i | −0.386027 | + | 0.668618i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.1360 | − | 27.9484i | 0.557743 | − | 0.966039i | ||||
\(838\) | 12.7279 | − | 7.34847i | 0.439679 | − | 0.253849i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | −33.2132 | − | 42.8300i | −1.14596 | − | 1.47778i | ||||
\(841\) | 79.4558 | 2.73986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.0772 | − | 27.1800i | 1.61950 | − | 0.935021i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9706 | + | 26.8723i | −0.376953 | + | 0.923342i | ||||
\(848\) | −40.2843 | −1.38337 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29.2132 | − | 50.5988i | −0.998487 | − | 1.72943i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | −25.4558 | − | 14.6969i | −0.866025 | − | 0.500000i | ||||
\(865\) | −36.2132 | + | 62.7231i | −1.23129 | + | 2.13265i | ||||
\(866\) | −48.0000 | + | 27.7128i | −1.63111 | + | 0.941720i | ||||
\(867\) | 29.4449i | 1.00000i | ||||||||
\(868\) | 30.4264 | + | 12.4215i | 1.03274 | + | 0.421614i | ||||
\(869\) | −1.32590 | −0.0449781 | ||||||||
\(870\) | 53.3345 | + | 92.3781i | 1.80821 | + | 3.13191i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.9558 | − | 17.2950i | 1.01385 | − | 0.585348i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −65.4411 | + | 50.7473i | −2.21231 | + | 1.71557i | ||||
\(876\) | −33.9411 | −1.14676 | ||||||||
\(877\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | −51.0624 | − | 29.4809i | −1.72327 | − | 0.994933i | ||||
\(879\) | 2.89340 | − | 5.01151i | 0.0975919 | − | 0.169034i | ||||
\(880\) | 2.48528 | − | 1.43488i | 0.0837788 | − | 0.0483697i | ||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 21.2132 | + | 20.7846i | 0.714286 | + | 0.699854i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.8640 | − | 16.6646i | −0.970251 | − | 0.560175i | ||||
\(886\) | 29.0919 | − | 50.3886i | 0.977361 | − | 1.69284i | ||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9558 | + | 14.1281i | 0.367447 | + | 0.473841i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.772078 | + | 1.33728i | 0.0258656 | + | 0.0448005i | ||||
\(892\) | −51.7279 | − | 29.8651i | −1.73198 | − | 0.999959i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −6.00000 | + | 3.46410i | −0.200670 | + | 0.115857i | ||||
\(895\) | − | 47.3087i | − | 1.58136i | ||||||
\(896\) | 11.3137 | − | 27.7128i | 0.377964 | − | 0.925820i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −56.0147 | − | 32.3401i | −1.86820 | − | 1.07860i | ||||
\(900\) | −37.4558 | + | 64.8754i | −1.24853 | + | 2.16251i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 47.1213 | + | 27.2055i | 1.56550 | + | 0.903842i | ||||
\(907\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(908\) | 51.4264 | − | 29.6910i | 1.70665 | − | 0.985332i | ||||
\(909\) | 10.3923i | 0.344691i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.558875 | + | 0.322666i | 0.0184960 | + | 0.0106787i | ||||
\(914\) | 25.4350 | − | 44.0548i | 0.841316 | − | 1.45720i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −52.2426 | − | 21.3280i | −1.72520 | − | 0.704312i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0000 | − | 43.3013i | −0.824674 | − | 1.42838i | −0.902168 | − | 0.431384i | \(-0.858025\pi\) |
0.0774944 | − | 0.996993i | \(-0.475308\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −46.6690 | + | 26.9444i | −1.53696 | + | 0.887366i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.24264 | + | 0.963625i | −0.0408799 | + | 0.0317009i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.3848 | + | 31.8434i | 0.604161 | + | 1.04644i | ||||
\(927\) | 38.1838 | + | 22.0454i | 1.25412 | + | 0.724066i | ||||
\(928\) | −29.4558 | + | 51.0190i | −0.966935 | + | 1.67478i | ||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | − | 63.6146i | − | 2.08601i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.2132 | − | 12.2474i | −0.694117 | − | 0.400749i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 60.0274i | − | 1.96101i | −0.196492 | − | 0.980505i | \(-0.562955\pi\) | ||
0.196492 | − | 0.980505i | \(-0.437045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.5147 | 1.38742 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5624 | − | 11.2944i | −0.637718 | − | 0.368186i | 0.146017 | − | 0.989282i | \(-0.453354\pi\) |
−0.783735 | + | 0.621096i | \(0.786688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 18.4072i | − | 0.599104i | ||||||
\(945\) | 21.7279 | − | 53.2223i | 0.706809 | − | 1.73132i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.2843 | + | 48.9898i | 0.919115 | + | 1.59195i | 0.800762 | + | 0.598983i | \(0.204428\pi\) |
0.118354 | + | 0.992972i | \(0.462238\pi\) | |||||||
\(948\) | 23.1838 | + | 13.3852i | 0.752974 | + | 0.434730i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 52.9251i | − | 1.71622i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | −21.3640 | − | 37.0035i | −0.691684 | − | 1.19803i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.68019 | − | 1.54741i | 0.0866384 | − | 0.0500207i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −57.9411 | −1.87004 | ||||||||
\(961\) | 3.78680 | + | 6.55892i | 0.122155 | + | 0.211578i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.9853 | − | 53.6681i | 0.998487 | − | 1.72943i | ||||
\(964\) | 40.4558 | − | 23.3572i | 1.30300 | − | 0.752285i | ||||
\(965\) | 89.8416i | 2.89210i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.2426 | −1.13333 | −0.566663 | − | 0.823949i | \(-0.691766\pi\) | ||||
−0.566663 | + | 0.823949i | \(0.691766\pi\) | |||||||
\(968\) | 15.5147 | + | 26.8723i | 0.498662 | + | 0.863708i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.0919 | − | 59.0489i | 1.09462 | − | 1.89595i | ||||
\(971\) | −48.1690 | + | 27.8104i | −1.54582 | + | 0.892479i | −0.547364 | + | 0.836894i | \(0.684369\pi\) |
−0.998454 | + | 0.0555842i | \(0.982298\pi\) | |||||||
\(972\) | − | 31.1769i | − | 1.00000i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −52.5858 | −1.68496 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 56.6985 | + | 14.5738i | 1.81117 | + | 0.465544i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.3345 | + | 26.5602i | 0.489344 | + | 0.847569i | ||||
\(983\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 51.2132 | − | 29.5680i | 1.63179 | − | 0.942113i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 2.63604 | + | 1.52192i | 0.0837788 | + | 0.0483697i | ||||
\(991\) | −25.1066 | + | 43.4859i | −0.797537 | + | 1.38138i | 0.123678 | + | 0.992322i | \(0.460531\pi\) |
−0.921215 | + | 0.389053i | \(0.872802\pi\) | |||||||
\(992\) | 30.4264 | − | 17.5667i | 0.966039 | − | 0.557743i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 102.426 | 3.24714 | ||||||||
\(996\) | −6.51472 | − | 11.2838i | −0.206427 | − | 0.357542i | ||||
\(997\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 168.2.ba.b.101.1 | yes | 4 | |
3.2 | odd | 2 | 168.2.ba.a.101.2 | yes | 4 | ||
4.3 | odd | 2 | 672.2.bi.a.17.1 | 4 | |||
7.5 | odd | 6 | inner | 168.2.ba.b.5.1 | yes | 4 | |
8.3 | odd | 2 | 672.2.bi.b.17.2 | 4 | |||
8.5 | even | 2 | 168.2.ba.a.101.2 | yes | 4 | ||
12.11 | even | 2 | 672.2.bi.b.17.2 | 4 | |||
21.5 | even | 6 | 168.2.ba.a.5.2 | ✓ | 4 | ||
24.5 | odd | 2 | CM | 168.2.ba.b.101.1 | yes | 4 | |
24.11 | even | 2 | 672.2.bi.a.17.1 | 4 | |||
28.19 | even | 6 | 672.2.bi.a.593.1 | 4 | |||
56.5 | odd | 6 | 168.2.ba.a.5.2 | ✓ | 4 | ||
56.19 | even | 6 | 672.2.bi.b.593.2 | 4 | |||
84.47 | odd | 6 | 672.2.bi.b.593.2 | 4 | |||
168.5 | even | 6 | inner | 168.2.ba.b.5.1 | yes | 4 | |
168.131 | odd | 6 | 672.2.bi.a.593.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.ba.a.5.2 | ✓ | 4 | 21.5 | even | 6 | ||
168.2.ba.a.5.2 | ✓ | 4 | 56.5 | odd | 6 | ||
168.2.ba.a.101.2 | yes | 4 | 3.2 | odd | 2 | ||
168.2.ba.a.101.2 | yes | 4 | 8.5 | even | 2 | ||
168.2.ba.b.5.1 | yes | 4 | 7.5 | odd | 6 | inner | |
168.2.ba.b.5.1 | yes | 4 | 168.5 | even | 6 | inner | |
168.2.ba.b.101.1 | yes | 4 | 1.1 | even | 1 | trivial | |
168.2.ba.b.101.1 | yes | 4 | 24.5 | odd | 2 | CM | |
672.2.bi.a.17.1 | 4 | 4.3 | odd | 2 | |||
672.2.bi.a.17.1 | 4 | 24.11 | even | 2 | |||
672.2.bi.a.593.1 | 4 | 28.19 | even | 6 | |||
672.2.bi.a.593.1 | 4 | 168.131 | odd | 6 | |||
672.2.bi.b.17.2 | 4 | 8.3 | odd | 2 | |||
672.2.bi.b.17.2 | 4 | 12.11 | even | 2 | |||
672.2.bi.b.593.2 | 4 | 56.19 | even | 6 | |||
672.2.bi.b.593.2 | 4 | 84.47 | odd | 6 |