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 | 5.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.5 |
Dual form | 168.2.ba.b.101.2 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||
\(5\) | 0.621320 | + | 0.358719i | 0.277863 | + | 0.160424i | 0.632456 | − | 0.774597i | \(-0.282047\pi\) |
−0.354593 | + | 0.935021i | \(0.615380\pi\) | |||||||
\(6\) | − | 2.44949i | − | 1.00000i | ||||||
\(7\) | −2.62132 | + | 0.358719i | −0.990766 | + | 0.135583i | ||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0.878680 | − | 0.507306i | 0.277863 | − | 0.160424i | ||||
\(11\) | 2.91421 | + | 5.04757i | 0.878668 | + | 1.52190i | 0.852803 | + | 0.522233i | \(0.174901\pi\) |
0.0258656 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(12\) | −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 | ||||
\(15\) | 1.24264 | 0.320848 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | −2.12132 | − | 3.67423i | −0.500000 | − | 0.866025i | ||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | − | 1.43488i | − | 0.320848i | ||||||
\(21\) | −3.62132 | + | 2.80821i | −0.790237 | + | 0.612801i | ||||
\(22\) | 8.24264 | 1.75734 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.866025 | + | 0.500000i | ||||
\(25\) | −2.24264 | − | 3.88437i | −0.448528 | − | 0.776874i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 3.24264 | + | 4.18154i | 0.612801 | + | 0.790237i | ||||
\(29\) | 7.58579 | 1.40865 | 0.704323 | − | 0.709880i | \(-0.251251\pi\) | ||||
0.704323 | + | 0.709880i | \(0.251251\pi\) | |||||||
\(30\) | 0.878680 | − | 1.52192i | 0.160424 | − | 0.277863i | ||||
\(31\) | −9.62132 | + | 5.55487i | −1.72804 | + | 0.997684i | −0.830014 | + | 0.557743i | \(0.811667\pi\) |
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.500000 | + | 0.866025i | ||||
\(33\) | 8.74264 | + | 5.04757i | 1.52190 | + | 0.878668i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.75736 | − | 0.717439i | −0.297048 | − | 0.121269i | ||||
\(36\) | −6.00000 | −1.00000 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.75736 | − | 1.01461i | −0.277863 | − | 0.160424i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0.878680 | + | 6.42090i | 0.135583 | + | 0.990766i | ||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 5.82843 | − | 10.0951i | 0.878668 | − | 1.52190i | ||||
\(45\) | 1.86396 | − | 1.07616i | 0.277863 | − | 0.160424i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 6.92820i | 1.00000i | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | −6.34315 | −0.897056 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.03553 | − | 3.52565i | −0.279602 | − | 0.484285i | 0.691684 | − | 0.722200i | \(-0.256869\pi\) |
−0.971286 | + | 0.237915i | \(0.923536\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.866025 | − | 0.500000i | ||||
\(55\) | 4.18154i | 0.563839i | ||||||||
\(56\) | 7.41421 | − | 1.01461i | 0.990766 | − | 0.135583i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.36396 | − | 9.29065i | 0.704323 | − | 1.21992i | ||||
\(59\) | −12.9853 | + | 7.49706i | −1.69054 | + | 0.976034i | −0.736460 | + | 0.676481i | \(0.763504\pi\) |
−0.954080 | + | 0.299552i | \(0.903163\pi\) | |||||||
\(60\) | −1.24264 | − | 2.15232i | −0.160424 | − | 0.277863i | ||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 15.7116i | 1.99537i | ||||||||
\(63\) | −3.00000 | + | 7.34847i | −0.377964 | + | 0.925820i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.3640 | − | 7.13834i | 1.52190 | − | 0.878668i | ||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.12132 | + | 1.64501i | −0.253546 | + | 0.196616i | ||||
\(71\) | 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 | \(-0.861036\pi\) |
−0.0869195 | + | 0.996215i | \(0.527702\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.72792 | − | 3.88437i | −0.776874 | − | 0.448528i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.44975 | − | 12.1859i | −1.07690 | − | 1.38871i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.86396 | − | 15.3528i | 0.997274 | − | 1.72733i | 0.434730 | − | 0.900561i | \(-0.356844\pi\) |
0.562544 | − | 0.826767i | \(-0.309823\pi\) | |||||||
\(80\) | −2.48528 | + | 1.43488i | −0.277863 | + | 0.160424i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.5592i | − | 1.48832i | −0.668002 | − | 0.744160i | \(-0.732850\pi\) | ||
0.668002 | − | 0.744160i | \(-0.267150\pi\) | |||||||
\(84\) | 8.48528 | + | 3.46410i | 0.925820 | + | 0.377964i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.3787 | − | 6.56948i | 1.21992 | − | 0.704323i | ||||
\(88\) | −8.24264 | − | 14.2767i | −0.878668 | − | 1.52190i | ||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | − | 3.04384i | − | 0.320848i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.62132 | + | 16.6646i | −0.997684 | + | 1.72804i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | + | 4.89898i | 0.866025 | + | 0.500000i | ||||
\(97\) | − | 8.06591i | − | 0.818969i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) | ||
0.912317 | − | 0.409484i | \(-0.134291\pi\) | |||||||
\(98\) | 2.46447 | − | 9.58783i | 0.248949 | − | 0.968517i | ||||
\(99\) | 17.4853 | 1.75734 | ||||||||
\(100\) | −4.48528 | + | 7.76874i | −0.448528 | + | 0.776874i | ||||
\(101\) | 3.00000 | − | 1.73205i | 0.298511 | − | 0.172345i | −0.343263 | − | 0.939239i | \(-0.611532\pi\) |
0.641774 | + | 0.766894i | \(0.278199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7279 | − | 7.34847i | −1.25412 | − | 0.724066i | −0.282194 | − | 0.959357i | \(-0.591062\pi\) |
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.25736 | + | 0.445759i | −0.317886 | + | 0.0435017i | ||||
\(106\) | −5.75736 | −0.559204 | ||||||||
\(107\) | −4.67157 | + | 8.09140i | −0.451618 | + | 0.782225i | −0.998487 | − | 0.0549930i | \(-0.982486\pi\) |
0.546869 | + | 0.837218i | \(0.315820\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.866025 | + | 0.500000i | ||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 5.12132 | + | 2.95680i | 0.488299 | + | 0.281919i | ||||
\(111\) | 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 | ||||||||
\(116\) | −7.58579 | − | 13.1390i | −0.704323 | − | 1.21992i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 21.2049i | 1.95207i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.51472 | −0.320848 | ||||||||
\(121\) | −11.4853 | + | 19.8931i | −1.04412 | + | 1.80846i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 19.2426 | + | 11.1097i | 1.72804 | + | 0.997684i | ||||
\(125\) | − | 6.80511i | − | 0.608668i | ||||||
\(126\) | 6.87868 | + | 8.87039i | 0.612801 | + | 0.790237i | ||||
\(127\) | 15.2426 | 1.35257 | 0.676283 | − | 0.736642i | \(-0.263590\pi\) | ||||
0.676283 | + | 0.736642i | \(0.263590\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4706 | + | 8.93193i | 1.35167 | + | 0.780387i | 0.988483 | − | 0.151330i | \(-0.0483556\pi\) |
0.363186 | + | 0.931717i | \(0.381689\pi\) | |||||||
\(132\) | − | 20.1903i | − | 1.75734i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.86396 | − | 3.22848i | 0.160424 | − | 0.277863i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0.514719 | + | 3.76127i | 0.0435017 | + | 0.317886i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | + | 10.3923i | 0.500000 | + | 0.866025i | ||||
\(145\) | 4.71320 | + | 2.72117i | 0.391410 | + | 0.225981i | ||||
\(146\) | 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 | \(-0.796372\pi\) |
0.918122 | + | 0.396298i | \(0.129705\pi\) | |||||||
\(150\) | −9.51472 | + | 5.49333i | −0.776874 | + | 0.448528i | ||||
\(151\) | 10.1066 | + | 17.5051i | 0.822464 | + | 1.42455i | 0.903842 | + | 0.427865i | \(0.140734\pi\) |
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −21.6066 | + | 2.95680i | −1.74111 | + | 0.238265i | ||||
\(155\) | −7.97056 | −0.640211 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(158\) | −12.5355 | − | 21.7122i | −0.997274 | − | 1.72733i | ||||
\(159\) | −6.10660 | − | 3.52565i | −0.484285 | − | 0.279602i | ||||
\(160\) | 4.05845i | 0.320848i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.7279 | −1.00000 | ||||||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.62132 | + | 6.27231i | 0.281919 | + | 0.488299i | ||||
\(166\) | −16.6066 | − | 9.58783i | −1.28892 | − | 0.744160i | ||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 10.2426 | − | 7.94282i | 0.790237 | − | 0.612801i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.0000 | + | 8.66025i | 1.14043 | + | 0.658427i | 0.946537 | − | 0.322596i | \(-0.104555\pi\) |
0.193892 | + | 0.981023i | \(0.437889\pi\) | |||||||
\(174\) | − | 18.5813i | − | 1.40865i | ||||||
\(175\) | 7.27208 | + | 9.37769i | 0.549717 | + | 0.708887i | ||||
\(176\) | −23.3137 | −1.75734 | ||||||||
\(177\) | −12.9853 | + | 22.4912i | −0.976034 | + | 1.69054i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.65685 | + | 9.79796i | 0.422813 | + | 0.732334i | 0.996213 | − | 0.0869415i | \(-0.0277093\pi\) |
−0.573400 | + | 0.819275i | \(0.694376\pi\) | |||||||
\(180\) | −3.72792 | − | 2.15232i | −0.277863 | − | 0.160424i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.6066 | + | 23.5673i | 0.997684 | + | 1.72804i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.86396 | + | 13.6208i | 0.135583 | + | 0.990766i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.866025 | − | 0.500000i | ||||
\(193\) | 2.25736 | + | 3.90986i | 0.162488 | + | 0.281438i | 0.935760 | − | 0.352636i | \(-0.114715\pi\) |
−0.773272 | + | 0.634074i | \(0.781381\pi\) | |||||||
\(194\) | −9.87868 | − | 5.70346i | −0.709248 | − | 0.409484i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.0000 | − | 9.79796i | −0.714286 | − | 0.699854i | ||||
\(197\) | 14.1421 | 1.00759 | 0.503793 | − | 0.863825i | \(-0.331938\pi\) | ||||
0.503793 | + | 0.863825i | \(0.331938\pi\) | |||||||
\(198\) | 12.3640 | − | 21.4150i | 0.878668 | − | 1.52190i | ||||
\(199\) | 21.2132 | − | 12.2474i | 1.50376 | − | 0.868199i | 0.503774 | − | 0.863836i | \(-0.331945\pi\) |
0.999990 | − | 0.00436292i | \(-0.00138876\pi\) | |||||||
\(200\) | 6.34315 | + | 10.9867i | 0.448528 | + | 0.776874i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 4.89898i | − | 0.344691i | ||||||
\(203\) | −19.8848 | + | 2.72117i | −1.39564 | + | 0.190989i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −18.0000 | + | 10.3923i | −1.25412 | + | 0.724066i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.75736 | + | 4.30463i | −0.121269 | + | 0.297048i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | −4.07107 | + | 7.05130i | −0.279602 | + | 0.484285i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.60660 | + | 11.4430i | 0.451618 | + | 0.782225i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 1.00000i | ||||||||
\(217\) | 23.2279 | − | 18.0125i | 1.57681 | − | 1.22277i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.48528 | + | 14.6969i | −0.573382 | + | 0.993127i | ||||
\(220\) | 7.24264 | − | 4.18154i | 0.488299 | − | 0.281919i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.1682i | − | 1.01574i | −0.861435 | − | 0.507869i | \(-0.830434\pi\) | ||
0.861435 | − | 0.507869i | \(-0.169566\pi\) | |||||||
\(224\) | −9.17157 | − | 11.8272i | −0.612801 | − | 0.790237i | ||||
\(225\) | −13.4558 | −0.897056 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.7132 | − | 9.64937i | 1.10929 | − | 0.640451i | 0.170648 | − | 0.985332i | \(-0.445414\pi\) |
0.938647 | + | 0.344881i | \(0.112081\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.7279 | − | 10.0951i | −1.62698 | − | 0.664211i | ||||
\(232\) | −21.4558 | −1.40865 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 25.9706 | + | 14.9941i | 1.69054 | + | 0.976034i | ||||
\(237\) | − | 30.7057i | − | 1.99455i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −2.48528 | + | 4.30463i | −0.160424 | + | 0.277863i | ||||
\(241\) | 5.22792 | − | 3.01834i | 0.336760 | − | 0.194429i | −0.322078 | − | 0.946713i | \(-0.604381\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | 16.2426 | + | 28.1331i | 1.04412 | + | 1.80846i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.86396 | + | 1.25024i | 0.310747 | + | 0.0798748i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 27.2132 | − | 15.7116i | 1.72804 | − | 0.997684i | ||||
\(249\) | −11.7426 | − | 20.3389i | −0.744160 | − | 1.28892i | ||||
\(250\) | −8.33452 | − | 4.81194i | −0.527122 | − | 0.304334i | ||||
\(251\) | 10.6895i | 0.674714i | 0.941377 | + | 0.337357i | \(0.109533\pi\) | ||||
−0.941377 | + | 0.337357i | \(0.890467\pi\) | |||||||
\(252\) | 15.7279 | − | 2.15232i | 0.990766 | − | 0.135583i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.7782 | − | 18.6683i | 0.676283 | − | 1.17136i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.3787 | − | 19.7085i | 0.704323 | − | 1.21992i | ||||
\(262\) | 21.8787 | − | 12.6317i | 1.35167 | − | 0.780387i | ||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | −24.7279 | − | 14.2767i | −1.52190 | − | 0.878668i | ||||
\(265\) | − | 2.92074i | − | 0.179420i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.8345 | + | 16.0703i | −1.69710 | + | 0.979822i | −0.748614 | + | 0.663007i | \(0.769280\pi\) |
−0.948487 | + | 0.316815i | \(0.897387\pi\) | |||||||
\(270\) | −2.63604 | − | 4.56575i | −0.160424 | − | 0.277863i | ||||
\(271\) | −27.1066 | − | 15.6500i | −1.64661 | − | 0.950670i | −0.978406 | − | 0.206691i | \(-0.933731\pi\) |
−0.668202 | − | 0.743980i | \(-0.732936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.0711 | − | 22.6398i | 0.788215 | − | 1.36523i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.3292i | 1.99537i | ||||||||
\(280\) | 4.97056 | + | 2.02922i | 0.297048 | + | 0.121269i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(284\) | 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 | ||||
\(290\) | 6.66548 | − | 3.84831i | 0.391410 | − | 0.225981i | ||||
\(291\) | −6.98528 | − | 12.0989i | −0.409484 | − | 0.709248i | ||||
\(292\) | 16.9706 | + | 9.79796i | 0.993127 | + | 0.573382i | ||||
\(293\) | 27.8359i | 1.62619i | 0.582130 | + | 0.813095i | \(0.302219\pi\) | ||||
−0.582130 | + | 0.813095i | \(0.697781\pi\) | |||||||
\(294\) | −4.60660 | − | 16.5160i | −0.268662 | − | 0.963234i | ||||
\(295\) | −10.7574 | −0.626318 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.2279 | − | 15.1427i | 1.52190 | − | 0.878668i | ||||
\(298\) | −2.00000 | − | 3.46410i | −0.115857 | − | 0.200670i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 15.5375i | 0.897056i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 28.5858 | 1.64493 | ||||||||
\(303\) | 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 | \(0.5\pi\) | |||||||||
\(308\) | −11.6569 | + | 28.5533i | −0.664211 | + | 1.62698i | ||||
\(309\) | −25.4558 | −1.44813 | ||||||||
\(310\) | −5.63604 | + | 9.76191i | −0.320106 | + | 0.554439i | ||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.7426 | + | 17.1719i | 1.68115 | + | 0.970614i | 0.960897 | + | 0.276907i | \(0.0893093\pi\) |
0.720257 | + | 0.693708i | \(0.244024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.50000 | + | 3.48960i | −0.253546 | + | 0.196616i | ||||
\(316\) | −35.4558 | −1.99455 | ||||||||
\(317\) | 0.278175 | − | 0.481813i | 0.0156238 | − | 0.0270613i | −0.858108 | − | 0.513470i | \(-0.828360\pi\) |
0.873732 | + | 0.486408i | \(0.161693\pi\) | |||||||
\(318\) | −8.63604 | + | 4.98602i | −0.484285 | + | 0.279602i | ||||
\(319\) | 22.1066 | + | 38.2898i | 1.23773 | + | 2.14381i | ||||
\(320\) | 4.97056 | + | 2.86976i | 0.277863 | + | 0.160424i | ||||
\(321\) | 16.1828i | 0.903236i | ||||||||
\(322\) | 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 | ||||||||
\(330\) | 10.2426 | 0.563839 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | −23.4853 | + | 13.5592i | −1.28892 | + | 0.744160i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.48528 | − | 18.1610i | −0.135583 | − | 0.990766i | ||||
\(337\) | −14.4558 | −0.787460 | −0.393730 | − | 0.919226i | \(-0.628816\pi\) | ||||
−0.393730 | + | 0.919226i | \(0.628816\pi\) | |||||||
\(338\) | −9.19239 | + | 15.9217i | −0.500000 | + | 0.866025i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −56.0772 | − | 32.3762i | −3.03675 | − | 1.75327i | ||||
\(342\) | 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 | −0.943264 | − | 0.332043i | \(-0.892262\pi\) |
0.184075 | − | 0.982912i | \(-0.441071\pi\) | |||||||
\(348\) | −22.7574 | − | 13.1390i | −1.21992 | − | 0.704323i | ||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 16.6274 | − | 2.27541i | 0.888773 | − | 0.121626i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.4853 | + | 28.5533i | −0.878668 | + | 1.52190i | ||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 18.3640 | + | 31.8073i | 0.976034 | + | 1.69054i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.0000 | 0.845626 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | −5.27208 | + | 3.04384i | −0.277863 | + | 0.160424i | ||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 39.7862i | 2.08823i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.02944 | −0.367938 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.6213 | + | 17.6792i | −1.59842 | + | 0.922848i | −0.606628 | + | 0.794986i | \(0.707478\pi\) |
−0.991792 | + | 0.127862i | \(0.959188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.60051 | + | 8.51167i | 0.342681 | + | 0.441904i | ||||
\(372\) | 38.4853 | 1.99537 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.89340 | − | 10.2077i | −0.304334 | − | 0.527122i | ||||
\(376\) | 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 | ||||||||
\(381\) | 22.8640 | − | 13.2005i | 1.17136 | − | 0.676283i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | − | 19.5959i | − | 1.00000i | ||||||
\(385\) | −1.50000 | − | 10.9612i | −0.0764471 | − | 0.558632i | ||||
\(386\) | 6.38478 | 0.324977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.9706 | + | 8.06591i | −0.709248 | + | 0.409484i | ||||
\(389\) | 15.5563 | + | 26.9444i | 0.788738 | + | 1.36613i | 0.926740 | + | 0.375703i | \(0.122599\pi\) |
−0.138002 | + | 0.990432i | \(0.544068\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −19.0711 | + | 5.31925i | −0.963234 | + | 0.268662i | ||||
\(393\) | 30.9411 | 1.56077 | ||||||||
\(394\) | 10.0000 | − | 17.3205i | 0.503793 | − | 0.872595i | ||||
\(395\) | 11.0147 | − | 6.35935i | 0.554211 | − | 0.319974i | ||||
\(396\) | −17.4853 | − | 30.2854i | −0.878668 | − | 1.52190i | ||||
\(397\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(398\) | − | 34.6410i | − | 1.73640i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.9411 | 0.897056 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.00000 | − | 3.46410i | −0.298511 | − | 0.172345i | ||||
\(405\) | − | 6.45695i | − | 0.320848i | ||||||
\(406\) | −10.7279 | + | 26.2779i | −0.532418 | + | 1.30415i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.4706 | + | 14.1281i | −1.20999 | + | 0.698589i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 29.3939i | 1.44813i | ||||||||
\(413\) | 31.3492 | − | 24.3103i | 1.54260 | − | 1.19623i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.86396 | − | 8.42463i | 0.238762 | − | 0.413549i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 10.3923i | − | 0.507697i | −0.967244 | − | 0.253849i | \(-0.918303\pi\) | ||
0.967244 | − | 0.253849i | \(-0.0816965\pi\) | |||||||
\(420\) | 4.02944 | + | 5.19615i | 0.196616 | + | 0.253546i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.75736 | + | 9.97204i | 0.279602 | + | 0.484285i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.6863 | 0.903236 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.866025 | + | 0.500000i | ||||
\(433\) | − | 39.1918i | − | 1.88344i | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||
0.336399 | − | 0.941720i | \(-0.390791\pi\) | |||||||
\(434\) | −5.63604 | − | 41.1850i | −0.270539 | − | 1.97694i | ||||
\(435\) | 9.42641 | 0.451962 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.0000 | + | 20.7846i | 0.573382 | + | 0.993127i | ||||
\(439\) | 14.8934 | + | 8.59871i | 0.710823 | + | 0.410394i | 0.811366 | − | 0.584539i | \(-0.198725\pi\) |
−0.100543 | + | 0.994933i | \(0.532058\pi\) | |||||||
\(440\) | − | 11.8272i | − | 0.563839i | ||||||
\(441\) | 5.22792 | − | 20.3389i | 0.248949 | − | 0.968517i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.42893 | − | 11.1352i | 0.305448 | − | 0.529051i | −0.671913 | − | 0.740630i | \(-0.734527\pi\) |
0.977361 | + | 0.211579i | \(0.0678605\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.5772 | − | 10.7255i | −0.879654 | − | 0.507869i | ||||
\(447\) | − | 4.89898i | − | 0.231714i | ||||||
\(448\) | −20.9706 | + | 2.86976i | −0.990766 | + | 0.135583i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | −9.51472 | + | 16.4800i | −0.448528 | + | 0.776874i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 30.3198 | + | 17.5051i | 1.42455 | + | 0.822464i | ||||
\(454\) | − | 27.2925i | − | 1.28090i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.01472 | − | 1.75754i | 0.0474665 | − | 0.0822145i | −0.841316 | − | 0.540544i | \(-0.818219\pi\) |
0.888783 | + | 0.458329i | \(0.151552\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.1051i | 1.77473i | 0.461065 | + | 0.887366i | \(0.347467\pi\) | ||||
−0.461065 | + | 0.887366i | \(0.652533\pi\) | |||||||
\(462\) | −29.8492 | + | 23.1471i | −1.38871 | + | 1.07690i | ||||
\(463\) | −26.0000 | −1.20832 | −0.604161 | − | 0.796862i | \(-0.706492\pi\) | ||||
−0.604161 | + | 0.796862i | \(0.706492\pi\) | |||||||
\(464\) | −15.1716 | + | 26.2779i | −0.704323 | + | 1.21992i | ||||
\(465\) | −11.9558 | + | 6.90271i | −0.554439 | + | 0.320106i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.0000 | + | 8.66025i | 0.694117 | + | 0.400749i | 0.805153 | − | 0.593068i | \(-0.202083\pi\) |
−0.111035 | + | 0.993816i | \(0.535417\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36.7279 | − | 21.2049i | 1.69054 | − | 0.976034i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −37.6066 | − | 21.7122i | −1.72733 | − | 0.997274i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.2132 | −0.559204 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 3.51472 | + | 6.08767i | 0.160424 | + | 0.277863i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 8.53716i | − | 0.388857i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 45.9411 | 2.08823 | ||||||||
\(485\) | 2.89340 | − | 5.01151i | 0.131382 | − | 0.227561i | ||||
\(486\) | −19.0919 | + | 11.0227i | −0.866025 | + | 0.500000i | ||||
\(487\) | −19.5919 | − | 33.9341i | −0.887793 | − | 1.53770i | −0.842479 | − | 0.538730i | \(-0.818904\pi\) |
−0.0453143 | − | 0.998973i | \(-0.514429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.97056 | − | 5.07306i | 0.224547 | − | 0.229177i | ||||
\(491\) | −44.3137 | −1.99985 | −0.999925 | − | 0.0122607i | \(-0.996097\pi\) | ||||
−0.999925 | + | 0.0122607i | \(0.996097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.8640 | + | 6.27231i | 0.488299 | + | 0.281919i | ||||
\(496\) | − | 44.4390i | − | 1.99537i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −33.2132 | −1.48832 | ||||||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −11.7868 | + | 6.80511i | −0.527122 | + | 0.304334i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.0919 | + | 7.55860i | 0.584319 | + | 0.337357i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 8.48528 | − | 20.7846i | 0.377964 | − | 0.925820i | ||||
\(505\) | 2.48528 | 0.110594 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.5000 | + | 11.2583i | −0.866025 | + | 0.500000i | ||||
\(508\) | −15.2426 | − | 26.4010i | −0.676283 | − | 1.17136i | ||||
\(509\) | 21.6213 | + | 12.4831i | 0.958348 | + | 0.553303i | 0.895664 | − | 0.444731i | \(-0.146701\pi\) |
0.0626839 | + | 0.998033i | \(0.480034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4853 | − | 15.8856i | 0.906215 | − | 0.702739i | ||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.27208 | − | 9.13151i | −0.232316 | − | 0.402382i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.0000 | 1.31685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | −16.0919 | − | 27.8720i | −0.704323 | − | 1.21992i | ||||
\(523\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(524\) | − | 35.7277i | − | 1.56077i | ||||||
\(525\) | 19.0294 | + | 7.76874i | 0.830513 | + | 0.339055i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −34.9706 | + | 20.1903i | −1.52190 | + | 0.878668i | ||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | −3.57716 | − | 2.06528i | −0.155382 | − | 0.0897099i | ||||
\(531\) | 44.9823i | 1.95207i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.80509 | + | 3.35157i | −0.250976 | + | 0.144901i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.9706 | + | 9.79796i | 0.732334 | + | 0.422813i | ||||
\(538\) | 45.4536i | 1.95964i | ||||||||
\(539\) | 29.1421 | + | 28.5533i | 1.25524 | + | 1.22988i | ||||
\(540\) | −7.45584 | −0.320848 | ||||||||
\(541\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | −38.3345 | + | 22.1324i | −1.64661 | + | 0.950670i | ||||
\(543\) | 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 | ||||||||
\(550\) | −18.4853 | − | 32.0174i | −0.788215 | − | 1.36523i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.7279 | + | 43.4244i | −0.753868 | + | 1.84659i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.0355 | − | 39.8987i | −0.976047 | − | 1.69056i | −0.676436 | − | 0.736501i | \(-0.736477\pi\) |
−0.299611 | − | 0.954062i | \(-0.596857\pi\) | |||||||
\(558\) | 40.8198 | + | 23.5673i | 1.72804 | + | 0.997684i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 6.00000 | − | 4.65279i | 0.253546 | − | 0.196616i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.7132 | − | 21.7737i | 1.58942 | − | 0.917653i | 0.596020 | − | 0.802970i | \(-0.296748\pi\) |
0.993402 | − | 0.114684i | \(-0.0365854\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.5919 | + | 18.8169i | 0.612801 | + | 0.790237i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.500000 | − | 0.866025i | ||||
\(577\) | −15.7721 | + | 9.10601i | −0.656600 | + | 0.379088i | −0.790980 | − | 0.611842i | \(-0.790429\pi\) |
0.134380 | + | 0.990930i | \(0.457096\pi\) | |||||||
\(578\) | −12.0208 | − | 20.8207i | −0.500000 | − | 0.866025i | ||||
\(579\) | 6.77208 | + | 3.90986i | 0.281438 | + | 0.162488i | ||||
\(580\) | − | 10.8847i | − | 0.451962i | ||||||
\(581\) | 4.86396 | + | 35.5431i | 0.201791 | + | 1.47458i | ||||
\(582\) | −19.7574 | −0.818969 | ||||||||
\(583\) | 11.8640 | − | 20.5490i | 0.491355 | − | 0.851052i | ||||
\(584\) | 24.0000 | − | 13.8564i | 0.993127 | − | 0.573382i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.0919 | + | 19.6830i | 1.40832 | + | 0.813095i | ||||
\(587\) | − | 47.8521i | − | 1.97507i | −0.157409 | − | 0.987534i | \(-0.550314\pi\) | ||
0.157409 | − | 0.987534i | \(-0.449686\pi\) | |||||||
\(588\) | −23.4853 | − | 6.03668i | −0.968517 | − | 0.248949i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −7.60660 | + | 13.1750i | −0.313159 | + | 0.542407i | ||||
\(591\) | 21.2132 | − | 12.2474i | 0.872595 | − | 0.503793i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | − | 42.8300i | − | 1.75734i | ||||||
\(595\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 19.0294 | + | 10.9867i | 0.776874 | + | 0.448528i | ||||
\(601\) | 26.2269i | 1.06982i | 0.844909 | + | 0.534910i | \(0.179654\pi\) | ||||
−0.844909 | + | 0.534910i | \(0.820346\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.2132 | − | 35.0103i | 0.822464 | − | 1.42455i | ||||
\(605\) | −14.2721 | + | 8.23999i | −0.580242 | + | 0.335003i | ||||
\(606\) | −4.24264 | − | 7.34847i | −0.172345 | − | 0.298511i | ||||
\(607\) | 2.59188 | + | 1.49642i | 0.105201 | + | 0.0607380i | 0.551678 | − | 0.834058i | \(-0.313988\pi\) |
−0.446476 | + | 0.894795i | \(0.647321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −27.4706 | + | 21.3025i | −1.11316 | + | 0.863220i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 26.7279 | + | 34.4669i | 1.07690 | + | 1.38871i | ||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | −18.0000 | + | 31.1769i | −0.724066 | + | 1.25412i | ||||
\(619\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(620\) | 7.97056 | + | 13.8054i | 0.320106 | + | 0.554439i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.77208 | + | 15.1937i | −0.350883 | + | 0.607747i | ||||
\(626\) | 42.0624 | − | 24.2848i | 1.68115 | − | 0.970614i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.09188 | + | 7.97887i | 0.0435017 | + | 0.317886i | ||||
\(631\) | 29.2426 | 1.16413 | 0.582066 | − | 0.813142i | \(-0.302245\pi\) | ||||
0.582066 | + | 0.813142i | \(0.302245\pi\) | |||||||
\(632\) | −25.0711 | + | 43.4244i | −0.997274 | + | 1.72733i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.393398 | − | 0.681386i | −0.0156238 | − | 0.0270613i | ||||
\(635\) | 9.47056 | + | 5.46783i | 0.375828 | + | 0.216984i | ||||
\(636\) | 14.1026i | 0.559204i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 62.5269 | 2.47546 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.02944 | − | 4.05845i | 0.277863 | − | 0.160424i | ||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 19.8198 | + | 11.4430i | 0.782225 | + | 0.451618i | ||||
\(643\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 12.7279 | + | 22.0454i | 0.500000 | + | 0.866025i | ||||
\(649\) | −75.6838 | − | 43.6960i | −2.97085 | − | 1.71522i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.2426 | − | 47.1347i | 0.754179 | − | 1.84735i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.5208 | + | 33.8110i | −0.763909 | + | 1.32313i | 0.176913 | + | 0.984226i | \(0.443389\pi\) |
−0.940822 | + | 0.338902i | \(0.889945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.40812 | + | 11.0992i | 0.250386 | + | 0.433681i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.3939i | 1.14676i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.2548 | −1.76288 | −0.881439 | − | 0.472298i | \(-0.843425\pi\) | ||||
−0.881439 | + | 0.472298i | \(0.843425\pi\) | |||||||
\(660\) | 7.24264 | − | 12.5446i | 0.281919 | − | 0.488299i | ||||
\(661\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 38.3513i | 1.48832i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.1360 | − | 22.7523i | −0.507869 | − | 0.879654i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −24.0000 | − | 9.79796i | −0.925820 | − | 0.377964i | ||||
\(673\) | 16.9411 | 0.653032 | 0.326516 | − | 0.945192i | \(-0.394125\pi\) | ||||
0.326516 | + | 0.945192i | \(0.394125\pi\) | |||||||
\(674\) | −10.2218 | + | 17.7047i | −0.393730 | + | 0.681960i | ||||
\(675\) | −20.1838 | + | 11.6531i | −0.776874 | + | 0.448528i | ||||
\(676\) | 13.0000 | + | 22.5167i | 0.500000 | + | 0.866025i | ||||
\(677\) | −20.3787 | − | 11.7656i | −0.783216 | − | 0.452190i | 0.0543526 | − | 0.998522i | \(-0.482690\pi\) |
−0.837569 | + | 0.546332i | \(0.816024\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.89340 | + | 21.1433i | 0.111038 | + | 0.811407i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.7132 | − | 28.9481i | 0.640451 | − | 1.10929i | ||||
\(682\) | −79.3051 | + | 45.7868i | −3.03675 | + | 1.75327i | ||||
\(683\) | 23.9142 | + | 41.4206i | 0.915052 | + | 1.58492i | 0.806825 | + | 0.590790i | \(0.201184\pi\) |
0.108227 | + | 0.994126i | \(0.465483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.02082 | + | 26.0168i | −0.115335 | + | 0.993327i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(692\) | − | 34.6410i | − | 1.31685i | ||||||
\(693\) | −45.8345 | + | 6.27231i | −1.74111 | + | 0.238265i | ||||
\(694\) | −40.0000 | −1.51838 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −32.1838 | + | 18.5813i | −1.21992 | + | 0.704323i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.97056 | − | 21.9733i | 0.339055 | − | 0.830513i | ||||
\(701\) | −14.6152 | −0.552009 | −0.276005 | − | 0.961156i | \(-0.589011\pi\) | ||||
−0.276005 | + | 0.961156i | \(0.589011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 23.3137 | + | 40.3805i | 0.878668 | + | 1.52190i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.24264 | + | 5.61642i | −0.272388 | + | 0.211227i | ||||
\(708\) | 51.9411 | 1.95207 | ||||||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.5919 | − | 46.0585i | −0.997274 | − | 1.72733i | ||||
\(712\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 8.60927i | 0.320848i | ||||||||
\(721\) | 36.0000 | + | 14.6969i | 1.34071 | + | 0.547343i | ||||
\(722\) | 26.8701 | 1.00000 | ||||||||
\(723\) | 5.22792 | − | 9.05503i | 0.194429 | − | 0.336760i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.0122 | − | 29.4660i | −0.631817 | − | 1.09434i | ||||
\(726\) | 48.7279 | + | 28.1331i | 1.80846 | + | 1.04412i | ||||
\(727\) | − | 25.2123i | − | 0.935074i | −0.883974 | − | 0.467537i | \(-0.845142\pi\) | ||
0.883974 | − | 0.467537i | \(-0.154858\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −4.97056 | + | 8.60927i | −0.183969 | + | 0.318643i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(734\) | 50.0044i | 1.84570i | ||||||||
\(735\) | 8.37868 | − | 2.33696i | 0.309052 | − | 0.0861999i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.0919 | − | 2.06528i | 0.554040 | − | 0.0758187i | ||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 27.2132 | − | 47.1347i | 0.997684 | − | 1.72804i | ||||
\(745\) | 1.75736 | − | 1.01461i | 0.0643847 | − | 0.0371725i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.2279 | − | 20.3389i | −1.28892 | − | 0.744160i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.34315 | − | 22.8859i | 0.341391 | − | 0.836234i | ||||
\(750\) | −16.6690 | −0.608668 | ||||||||
\(751\) | −20.8345 | + | 36.0865i | −0.760263 | + | 1.31681i | 0.182453 | + | 0.983215i | \(0.441596\pi\) |
−0.942715 | + | 0.333599i | \(0.891737\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.25736 | + | 16.0342i | 0.337357 | + | 0.584319i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.5017i | 0.527772i | ||||||||
\(756\) | 21.7279 | − | 16.8493i | 0.790237 | − | 0.612801i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | − | 37.3367i | − | 1.35257i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −24.0000 | − | 13.8564i | −0.866025 | − | 0.500000i | ||||
\(769\) | 1.97824i | 0.0713370i | 0.999364 | + | 0.0356685i | \(0.0113561\pi\) | ||||
−0.999364 | + | 0.0356685i | \(0.988644\pi\) | |||||||
\(770\) | −14.4853 | − | 5.91359i | −0.522013 | − | 0.213111i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.51472 | − | 7.81972i | 0.162488 | − | 0.281438i | ||||
\(773\) | 45.0000 | − | 25.9808i | 1.61854 | − | 0.934463i | 0.631239 | − | 0.775589i | \(-0.282547\pi\) |
0.987299 | − | 0.158874i | \(-0.0507865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.1543 | + | 24.9152i | 1.55015 | + | 0.894979i | ||||
\(776\) | 22.8138i | 0.818969i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.0000 | 1.57748 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 39.4169i | − | 1.40865i | ||||||
\(784\) | −6.97056 | + | 27.1185i | −0.248949 | + | 0.968517i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 21.8787 | − | 37.8950i | 0.780387 | − | 1.35167i | ||||
\(787\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(788\) | −14.1421 | − | 24.4949i | −0.503793 | − | 0.872595i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 17.9870i | − | 0.639947i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −49.4558 | −1.75734 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.52944 | − | 4.38111i | −0.0897099 | − | 0.155382i | ||||
\(796\) | −42.4264 | − | 24.4949i | −1.50376 | − | 0.868199i | ||||
\(797\) | 37.8801i | 1.34178i | 0.741557 | + | 0.670890i | \(0.234088\pi\) | ||||
−0.741557 | + | 0.670890i | \(0.765912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 12.6863 | − | 21.9733i | 0.448528 | − | 0.776874i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −49.4558 | − | 28.5533i | −1.74526 | − | 1.00763i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.8345 | + | 48.2108i | −0.979822 | + | 1.69710i | ||||
\(808\) | −8.48528 | + | 4.89898i | −0.298511 | + | 0.172345i | ||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | −7.90812 | − | 4.56575i | −0.277863 | − | 0.160424i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 24.5980 | + | 31.7203i | 0.863220 | + | 1.11316i | ||||
\(813\) | −54.2132 | −1.90134 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 39.9603i | 1.39718i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.47918 | − | 2.56202i | 0.0516239 | − | 0.0894152i | −0.839059 | − | 0.544041i | \(-0.816894\pi\) |
0.890683 | + | 0.454626i | \(0.150227\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0000 | − | 39.8372i | −0.801730 | − | 1.38864i | −0.918477 | − | 0.395475i | \(-0.870580\pi\) |
0.116747 | − | 0.993162i | \(-0.462753\pi\) | |||||||
\(824\) | 36.0000 | + | 20.7846i | 1.25412 | + | 0.724066i | ||||
\(825\) | − | 45.2795i | − | 1.57643i | ||||||
\(826\) | −7.60660 | − | 55.5848i | −0.264668 | − | 1.93404i | ||||
\(827\) | 37.2843 | 1.29650 | 0.648251 | − | 0.761427i | \(-0.275501\pi\) | ||||
0.648251 | + | 0.761427i | \(0.275501\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(830\) | −6.87868 | − | 11.9142i | −0.238762 | − | 0.413549i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.8640 | + | 49.9938i | 0.997684 | + | 1.72804i | ||||
\(838\) | −12.7279 | − | 7.34847i | −0.439679 | − | 0.253849i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 9.21320 | − | 1.26080i | 0.317886 | − | 0.0435017i | ||||
\(841\) | 28.5442 | 0.984281 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.07716 | − | 4.66335i | −0.277863 | − | 0.160424i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.9706 | − | 56.2662i | 0.789278 | − | 1.93333i | ||||
\(848\) | 16.2843 | 0.559204 | ||||||||
\(849\) | 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 | ||||||||
\(856\) | 13.2132 | − | 22.8859i | 0.451618 | − | 0.782225i | ||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.866025 | − | 0.500000i | ||||
\(865\) | 6.21320 | + | 10.7616i | 0.211255 | + | 0.365905i | ||||
\(866\) | −48.0000 | − | 27.7128i | −1.63111 | − | 0.941720i | ||||
\(867\) | − | 29.4449i | − | 1.00000i | ||||||
\(868\) | −54.4264 | − | 22.2195i | −1.84735 | − | 0.754179i | ||||
\(869\) | 103.326 | 3.50509 | ||||||||
\(870\) | 6.66548 | − | 11.5449i | 0.225981 | − | 0.391410i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.9558 | − | 12.0989i | −0.709248 | − | 0.409484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.44113 | + | 17.8384i | 0.0825251 | + | 0.603047i | ||||
\(876\) | 33.9411 | 1.14676 | ||||||||
\(877\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(878\) | 21.0624 | − | 12.1604i | 0.710823 | − | 0.410394i | ||||
\(879\) | 24.1066 | + | 41.7539i | 0.813095 | + | 1.40832i | ||||
\(880\) | −14.4853 | − | 8.36308i | −0.488299 | − | 0.281919i | ||||
\(881\) | 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 | ||||||||
\(885\) | −16.1360 | + | 9.31615i | −0.542407 | + | 0.313159i | ||||
\(886\) | −9.09188 | − | 15.7476i | −0.305448 | − | 0.529051i | ||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39.9558 | + | 5.46783i | −1.34008 | + | 0.183385i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.2279 | − | 45.4281i | 0.878668 | − | 1.52190i | ||||
\(892\) | −26.2721 | + | 15.1682i | −0.879654 | + | 0.507869i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −6.00000 | − | 3.46410i | −0.200670 | − | 0.115857i | ||||
\(895\) | 8.11689i | 0.271318i | ||||||||
\(896\) | −11.3137 | + | 27.7128i | −0.377964 | + | 0.925820i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −72.9853 | + | 42.1381i | −2.43420 | + | 1.40538i | ||||
\(900\) | 13.4558 | + | 23.3062i | 0.448528 | + | 0.776874i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 42.8787 | − | 24.7560i | 1.42455 | − | 0.822464i | ||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | −33.4264 | − | 19.2987i | −1.10929 | − | 0.640451i | ||||
\(909\) | − | 10.3923i | − | 0.344691i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68.4411 | − | 39.5145i | 2.26507 | − | 1.30774i | ||||
\(914\) | −1.43503 | − | 2.48554i | −0.0474665 | − | 0.0822145i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43.7574 | − | 17.8639i | −1.44500 | − | 0.589917i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0000 | + | 43.3013i | −0.824674 | + | 1.42838i | 0.0774944 | + | 0.996993i | \(0.475308\pi\) |
−0.902168 | + | 0.431384i | \(0.858025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 46.6690 | + | 26.9444i | 1.53696 | + | 0.887366i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 7.24264 | + | 52.9251i | 0.238265 | + | 1.74111i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.3848 | + | 31.8434i | −0.604161 | + | 1.04644i | ||||
\(927\) | −38.1838 | + | 22.0454i | −1.25412 | + | 0.724066i | ||||
\(928\) | 21.4558 | + | 37.1626i | 0.704323 | + | 1.21992i | ||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 19.5238i | 0.640211i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.2132 | − | 12.2474i | 0.694117 | − | 0.400749i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.4315i | 1.32084i | 0.750896 | + | 0.660420i | \(0.229622\pi\) | ||||
−0.750896 | + | 0.660420i | \(0.770378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.4853 | 1.94123 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.5624 | − | 30.3469i | 1.71349 | − | 0.989282i | 0.783735 | − | 0.621096i | \(-0.213312\pi\) |
0.929752 | − | 0.368186i | \(-0.120021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 59.9764i | − | 1.95207i | ||||||
\(945\) | −3.72792 | + | 9.13151i | −0.121269 | + | 0.297048i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.2843 | + | 48.9898i | −0.919115 | + | 1.59195i | −0.118354 | + | 0.992972i | \(0.537762\pi\) |
−0.800762 | + | 0.598983i | \(0.795572\pi\) | |||||||
\(948\) | −53.1838 | + | 30.7057i | −1.72733 | + | 0.997274i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 0.963625i | − | 0.0312477i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | −8.63604 | + | 14.9581i | −0.279602 | + | 0.484285i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 66.3198 | + | 38.2898i | 2.14381 | + | 1.23773i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.94113 | 0.320848 | ||||||||
\(961\) | 46.2132 | − | 80.0436i | 1.49075 | − | 2.58205i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.0147 | + | 24.2742i | 0.451618 | + | 0.782225i | ||||
\(964\) | −10.4558 | − | 6.03668i | −0.336760 | − | 0.194429i | ||||
\(965\) | 3.23903i | 0.104268i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.7574 | −0.860459 | −0.430229 | − | 0.902720i | \(-0.641567\pi\) | ||||
−0.430229 | + | 0.902720i | \(0.641567\pi\) | |||||||
\(968\) | 32.4853 | − | 56.2662i | 1.04412 | − | 1.80846i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.09188 | − | 7.08735i | −0.131382 | − | 0.227561i | ||||
\(971\) | 45.1690 | + | 26.0784i | 1.44954 | + | 0.836894i | 0.998454 | − | 0.0555842i | \(-0.0177021\pi\) |
0.451090 | + | 0.892479i | \(0.351035\pi\) | |||||||
\(972\) | 31.1769i | 1.00000i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −55.4142 | −1.77559 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.69848 | − | 9.67487i | −0.0861999 | − | 0.309052i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.3345 | + | 54.2730i | −0.999925 | + | 1.73192i | ||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.78680 | + | 5.07306i | 0.279971 | + | 0.161641i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 15.3640 | − | 8.87039i | 0.488299 | − | 0.281919i | ||||
\(991\) | −3.89340 | − | 6.74356i | −0.123678 | − | 0.214216i | 0.797537 | − | 0.603269i | \(-0.206136\pi\) |
−0.921215 | + | 0.389053i | \(0.872802\pi\) | |||||||
\(992\) | −54.4264 | − | 31.4231i | −1.72804 | − | 0.997684i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.5736 | 0.557120 | ||||||||
\(996\) | −23.4853 | + | 40.6777i | −0.744160 | + | 1.28892i | ||||
\(997\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(998\) | 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.5.2 | yes | 4 | |
3.2 | odd | 2 | 168.2.ba.a.5.1 | ✓ | 4 | ||
4.3 | odd | 2 | 672.2.bi.a.593.2 | 4 | |||
7.3 | odd | 6 | inner | 168.2.ba.b.101.2 | yes | 4 | |
8.3 | odd | 2 | 672.2.bi.b.593.1 | 4 | |||
8.5 | even | 2 | 168.2.ba.a.5.1 | ✓ | 4 | ||
12.11 | even | 2 | 672.2.bi.b.593.1 | 4 | |||
21.17 | even | 6 | 168.2.ba.a.101.1 | yes | 4 | ||
24.5 | odd | 2 | CM | 168.2.ba.b.5.2 | yes | 4 | |
24.11 | even | 2 | 672.2.bi.a.593.2 | 4 | |||
28.3 | even | 6 | 672.2.bi.a.17.2 | 4 | |||
56.3 | even | 6 | 672.2.bi.b.17.1 | 4 | |||
56.45 | odd | 6 | 168.2.ba.a.101.1 | yes | 4 | ||
84.59 | odd | 6 | 672.2.bi.b.17.1 | 4 | |||
168.59 | odd | 6 | 672.2.bi.a.17.2 | 4 | |||
168.101 | even | 6 | inner | 168.2.ba.b.101.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.ba.a.5.1 | ✓ | 4 | 3.2 | odd | 2 | ||
168.2.ba.a.5.1 | ✓ | 4 | 8.5 | even | 2 | ||
168.2.ba.a.101.1 | yes | 4 | 21.17 | even | 6 | ||
168.2.ba.a.101.1 | yes | 4 | 56.45 | odd | 6 | ||
168.2.ba.b.5.2 | yes | 4 | 1.1 | even | 1 | trivial | |
168.2.ba.b.5.2 | yes | 4 | 24.5 | odd | 2 | CM | |
168.2.ba.b.101.2 | yes | 4 | 7.3 | odd | 6 | inner | |
168.2.ba.b.101.2 | yes | 4 | 168.101 | even | 6 | inner | |
672.2.bi.a.17.2 | 4 | 28.3 | even | 6 | |||
672.2.bi.a.17.2 | 4 | 168.59 | odd | 6 | |||
672.2.bi.a.593.2 | 4 | 4.3 | odd | 2 | |||
672.2.bi.a.593.2 | 4 | 24.11 | even | 2 | |||
672.2.bi.b.17.1 | 4 | 56.3 | even | 6 | |||
672.2.bi.b.17.1 | 4 | 84.59 | odd | 6 | |||
672.2.bi.b.593.1 | 4 | 8.3 | odd | 2 | |||
672.2.bi.b.593.1 | 4 | 12.11 | even | 2 |