Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(881,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.f (of order \(2\), degree \(1\), not 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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.2 | ||
Root | \(0.348228 - 1.69668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.881 |
Dual form | 1680.2.f.k.881.1 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.69668 | + | 0.348228i | −0.979581 | + | 0.201049i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63166 | + | 0.272689i | 0.994674 | + | 0.103067i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.75748 | − | 1.18166i | 0.919158 | − | 0.393888i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.13162i | 0.944219i | 0.881540 | + | 0.472109i | \(0.156507\pi\) | ||||
−0.881540 | + | 0.472109i | \(0.843493\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.34145i | − | 1.20410i | −0.798458 | − | 0.602051i | \(-0.794350\pi\) | ||
0.798458 | − | 0.602051i | \(-0.205650\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.69668 | − | 0.348228i | 0.438082 | − | 0.0899120i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.791039 | 0.191855 | 0.0959276 | − | 0.995388i | \(-0.469418\pi\) | ||||
0.0959276 | + | 0.995388i | \(0.469418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.768290i | − | 0.176258i | −0.996109 | − | 0.0881289i | \(-0.971911\pi\) | ||
0.996109 | − | 0.0881289i | \(-0.0280887\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.56006 | + | 0.453750i | −0.995086 | + | 0.0990165i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.32787i | 1.31945i | 0.751506 | + | 0.659726i | \(0.229328\pi\) | ||||
−0.751506 | + | 0.659726i | \(0.770672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.26708 | + | 2.96514i | −0.821199 | + | 0.570642i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.96574i | − | 1.10781i | −0.832580 | − | 0.553905i | \(-0.813137\pi\) | ||
0.832580 | − | 0.553905i | \(-0.186863\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.49220i | − | 0.986428i | −0.869908 | − | 0.493214i | \(-0.835822\pi\) | ||
0.869908 | − | 0.493214i | \(-0.164178\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.09052 | − | 5.31337i | −0.189834 | − | 0.924939i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.63166 | − | 0.272689i | −0.444832 | − | 0.0460928i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.83534 | 0.301728 | 0.150864 | − | 0.988555i | \(-0.451794\pi\) | ||||
0.150864 | + | 0.988555i | \(0.451794\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.51181 | + | 7.36607i | 0.242084 | + | 1.17952i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.60516 | 0.250684 | 0.125342 | − | 0.992114i | \(-0.459997\pi\) | ||||
0.125342 | + | 0.992114i | \(0.459997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.18441 | −0.943113 | −0.471557 | − | 0.881836i | \(-0.656308\pi\) | ||||
−0.471557 | + | 0.881836i | \(0.656308\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.75748 | + | 1.18166i | −0.411060 | + | 0.176152i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.24695 | 0.473617 | 0.236808 | − | 0.971556i | \(-0.423899\pi\) | ||||
0.236808 | + | 0.971556i | \(0.423899\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.85128 | + | 1.43525i | 0.978755 | + | 0.205035i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.34214 | + | 0.275462i | −0.187938 | + | 0.0385724i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.0560i | − | 1.38130i | −0.723189 | − | 0.690651i | \(-0.757324\pi\) | ||
0.723189 | − | 0.690651i | \(-0.242676\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.13162i | − | 0.422267i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.267540 | + | 1.30354i | 0.0354365 | + | 0.172659i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.30114 | 1.21091 | 0.605453 | − | 0.795881i | \(-0.292992\pi\) | ||||
0.605453 | + | 0.795881i | \(0.292992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1365i | 1.68195i | 0.541071 | + | 0.840977i | \(0.318019\pi\) | ||||
−0.541071 | + | 0.840977i | \(0.681981\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.57897 | − | 2.35781i | 0.954860 | − | 0.297056i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.34145i | 0.538491i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.64216 | 0.322792 | 0.161396 | − | 0.986890i | \(-0.448400\pi\) | ||||
0.161396 | + | 0.986890i | \(0.448400\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.20354 | − | 10.7364i | −0.265275 | − | 1.29251i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.227035i | − | 0.0269441i | −0.999909 | − | 0.0134721i | \(-0.995712\pi\) | ||
0.999909 | − | 0.0134721i | \(-0.00428842\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.7756i | 1.84639i | 0.384327 | + | 0.923197i | \(0.374434\pi\) | ||||
−0.384327 | + | 0.923197i | \(0.625566\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.69668 | + | 0.348228i | −0.195916 | + | 0.0402099i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.853957 | + | 8.24136i | −0.0973174 | + | 0.939190i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6345 | 1.53400 | 0.767002 | − | 0.641645i | \(-0.221748\pi\) | ||||
0.767002 | + | 0.641645i | \(0.221748\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.20734 | − | 6.51682i | 0.689704 | − | 0.724091i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.74892 | 0.301733 | 0.150866 | − | 0.988554i | \(-0.451794\pi\) | ||||
0.150866 | + | 0.988554i | \(0.451794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.791039 | −0.0858002 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.07744 | + | 10.1220i | 0.222725 | + | 1.08519i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.6351 | 1.76331 | 0.881657 | − | 0.471892i | \(-0.156429\pi\) | ||||
0.881657 | + | 0.471892i | \(0.156429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18386 | − | 11.4252i | 0.124103 | − | 1.19769i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.91254 | + | 9.31853i | 0.198321 | + | 0.966287i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.768290i | 0.0788248i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.11396i | − | 0.620779i | −0.950609 | − | 0.310389i | \(-0.899541\pi\) | ||
0.950609 | − | 0.310389i | \(-0.100459\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.70052 | + | 8.63536i | 0.371917 | + | 0.867886i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.20483 | 0.119885 | 0.0599425 | − | 0.998202i | \(-0.480908\pi\) | ||||
0.0599425 | + | 0.998202i | \(0.480908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.42563i | − | 0.140471i | −0.997530 | − | 0.0702355i | \(-0.977625\pi\) | ||
0.997530 | − | 0.0702355i | \(-0.0223751\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.56006 | − | 0.453750i | 0.445016 | − | 0.0442815i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.2184i | − | 1.08453i | −0.840208 | − | 0.542264i | \(-0.817567\pi\) | ||
0.840208 | − | 0.542264i | \(-0.182433\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.1783 | 1.54960 | 0.774798 | − | 0.632209i | \(-0.217851\pi\) | ||||
0.774798 | + | 0.632209i | \(0.217851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.11399 | + | 0.639115i | −0.295567 | + | 0.0606621i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.91036i | − | 0.461928i | −0.972962 | − | 0.230964i | \(-0.925812\pi\) | ||
0.972962 | − | 0.230964i | \(-0.0741879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.32787i | − | 0.590077i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.13014 | − | 11.9714i | −0.474282 | − | 1.10676i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.08175 | + | 0.215707i | 0.190833 | + | 0.0197739i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.19296 | 0.108451 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.72345 | + | 0.558962i | −0.245565 | + | 0.0503999i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.25616 | 0.555144 | 0.277572 | − | 0.960705i | \(-0.410470\pi\) | ||||
0.277572 | + | 0.960705i | \(0.410470\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4930 | − | 2.15358i | 0.923856 | − | 0.189612i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.05057 | 0.790752 | 0.395376 | − | 0.918519i | \(-0.370614\pi\) | ||||
0.395376 | + | 0.918519i | \(0.370614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.209504 | − | 2.02188i | 0.0181663 | − | 0.175319i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.26708 | − | 2.96514i | 0.367251 | − | 0.255199i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.29111i | − | 0.452050i | −0.974122 | − | 0.226025i | \(-0.927427\pi\) | ||
0.974122 | − | 0.226025i | \(-0.0725731\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.3215i | 1.55401i | 0.629494 | + | 0.777006i | \(0.283262\pi\) | ||||
−0.629494 | + | 0.777006i | \(0.716738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.50905 | + | 1.13068i | −0.463946 | + | 0.0952203i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.5958 | 1.13694 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.96574i | 0.495428i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.1243 | − | 0.0493581i | −0.999992 | − | 0.00407099i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.3480i | 1.91274i | 0.292160 | + | 0.956370i | \(0.405626\pi\) | ||||
−0.292160 | + | 0.956370i | \(0.594374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.14170 | 0.743941 | 0.371971 | − | 0.928245i | \(-0.378682\pi\) | ||||
0.371971 | + | 0.928245i | \(0.378682\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.18127 | − | 0.934743i | 0.176345 | − | 0.0755695i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.49220i | 0.441144i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.2610i | − | 1.21796i | −0.793185 | − | 0.608981i | \(-0.791579\pi\) | ||
0.793185 | − | 0.608981i | \(-0.208421\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.50179 | + | 17.0619i | 0.277710 | + | 1.35310i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.72554 | + | 16.6528i | −0.135991 | + | 1.31242i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.02683 | −0.393732 | −0.196866 | − | 0.980430i | \(-0.563076\pi\) | ||||
−0.196866 | + | 0.980430i | \(0.563076\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.09052 | + | 5.31337i | 0.0848966 | + | 0.413645i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.9872 | −1.70142 | −0.850710 | − | 0.525635i | \(-0.823828\pi\) | ||||
−0.850710 | + | 0.525635i | \(0.823828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.84820 | −0.449862 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.907861 | − | 2.11854i | −0.0694258 | − | 0.162009i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.9508 | 1.44081 | 0.720403 | − | 0.693556i | \(-0.243957\pi\) | ||||
0.720403 | + | 0.693556i | \(0.243957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.63166 | + | 0.272689i | 0.198935 | + | 0.0206133i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.7811 | + | 3.23892i | −1.18618 | + | 0.243452i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.39906i | − | 0.104571i | −0.998632 | − | 0.0522853i | \(-0.983349\pi\) | ||
0.998632 | − | 0.0522853i | \(-0.0166505\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3999i | 0.996006i | 0.867175 | + | 0.498003i | \(0.165933\pi\) | ||||
−0.867175 | + | 0.498003i | \(0.834067\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.57449 | − | 22.2885i | −0.338156 | − | 1.64761i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.83534 | −0.134937 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.47723i | 0.181153i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.0381 | + | 6.63966i | −0.875640 | + | 0.482964i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 22.3132i | − | 1.61452i | −0.590193 | − | 0.807262i | \(-0.700948\pi\) | ||
0.590193 | − | 0.807262i | \(-0.299052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.2441 | −0.737385 | −0.368692 | − | 0.929551i | \(-0.620194\pi\) | ||||
−0.368692 | + | 0.929551i | \(0.620194\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.51181 | − | 7.36607i | −0.108263 | − | 0.527495i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.79870i | 0.128152i | 0.997945 | + | 0.0640761i | \(0.0204100\pi\) | ||||
−0.997945 | + | 0.0640761i | \(0.979590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.1953i | − | 1.00628i | −0.864204 | − | 0.503141i | \(-0.832178\pi\) | ||
0.864204 | − | 0.503141i | \(-0.167822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.48292 | + | 0.920074i | −0.316201 | + | 0.0648970i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.62679 | − | 15.6998i | 0.114178 | − | 1.10191i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.60516 | −0.112109 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.47742 | + | 17.4489i | 0.519716 | + | 1.21278i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.40599 | 0.166426 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.9123 | −1.50851 | −0.754254 | − | 0.656583i | \(-0.772001\pi\) | ||||
−0.754254 | + | 0.656583i | \(0.772001\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0790599 | + | 0.385207i | 0.00541710 | + | 0.0263940i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.18441 | 0.421773 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.49766 | − | 14.4536i | 0.101668 | − | 0.981175i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.49350 | − | 26.7662i | −0.371216 | − | 1.80869i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.43426i | − | 0.231013i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.77721i | 0.319905i | 0.987125 | + | 0.159953i | \(0.0511342\pi\) | ||||
−0.987125 | + | 0.159953i | \(0.948866\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.75748 | − | 1.18166i | 0.183832 | − | 0.0787776i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.9326 | −1.32297 | −0.661487 | − | 0.749957i | \(-0.730074\pi\) | ||||
−0.661487 | + | 0.749957i | \(0.730074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.04167i | 0.399245i | 0.979873 | + | 0.199622i | \(0.0639715\pi\) | ||||
−0.979873 | + | 0.199622i | \(0.936028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.42097 | − | 14.2804i | −0.0934932 | − | 0.939579i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.52570i | − | 0.427513i | −0.976887 | − | 0.213756i | \(-0.931430\pi\) | ||
0.976887 | − | 0.213756i | \(-0.0685699\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.24695 | −0.211808 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.1335 | + | 4.74792i | −1.50268 | + | 0.308410i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.42646i | 0.221639i | 0.993841 | + | 0.110820i | \(0.0353476\pi\) | ||||
−0.993841 | + | 0.110820i | \(0.964652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.6681i | 0.751607i | 0.926699 | + | 0.375804i | \(0.122633\pi\) | ||||
−0.926699 | + | 0.375804i | \(0.877367\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.26255 | + | 13.2186i | −0.530043 | + | 0.847971i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.85128 | − | 1.43525i | −0.437712 | − | 0.0916947i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.33549 | −0.212232 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.66404 | + | 0.957248i | −0.295572 | + | 0.0606631i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5770 | 1.36193 | 0.680966 | − | 0.732315i | \(-0.261560\pi\) | ||||
0.680966 | + | 0.732315i | \(0.261560\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.8165 | −1.24585 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.34214 | − | 0.275462i | 0.0840483 | − | 0.0172501i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.2123 | −1.07367 | −0.536837 | − | 0.843686i | \(-0.680381\pi\) | ||||
−0.536837 | + | 0.843686i | \(0.680381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.82999 | + | 0.500476i | 0.300121 | + | 0.0310981i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.04951 | − | 16.4504i | −0.436354 | − | 1.01825i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.1528i | 1.48933i | 0.667440 | + | 0.744663i | \(0.267390\pi\) | ||||
−0.667440 | + | 0.744663i | \(0.732610\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0560i | 0.617737i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.2244 | + | 5.79279i | −1.72731 | + | 0.354513i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8931 | 0.969021 | 0.484511 | − | 0.874785i | \(-0.338998\pi\) | ||||
0.484511 | + | 0.874785i | \(0.338998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.5408i | − | 1.67299i | −0.547977 | − | 0.836494i | \(-0.684602\pi\) | ||
0.547977 | − | 0.836494i | \(-0.315398\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.96994 | + | 19.7973i | 0.119226 | + | 1.19818i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.13162i | 0.188844i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.5866 | 1.77769 | 0.888843 | − | 0.458212i | \(-0.151510\pi\) | ||||
0.888843 | + | 0.458212i | \(0.151510\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.48994 | − | 15.1446i | −0.388542 | − | 0.906684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.58240i | 0.571638i | 0.958284 | + | 0.285819i | \(0.0922656\pi\) | ||||
−0.958284 | + | 0.285819i | \(0.907734\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.41762i | 0.322044i | 0.986951 | + | 0.161022i | \(0.0514790\pi\) | ||||
−0.986951 | + | 0.161022i | \(0.948521\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.267540 | − | 1.30354i | −0.0158477 | − | 0.0772153i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.22424 | + | 0.437709i | 0.249349 | + | 0.0258372i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3743 | −0.963192 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.12905 | + | 10.3735i | 0.124807 | + | 0.608103i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.92094 | 0.229064 | 0.114532 | − | 0.993420i | \(-0.463463\pi\) | ||||
0.114532 | + | 0.993420i | \(0.463463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.30114 | −0.541534 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.28569 | − | 13.3629i | −0.538810 | − | 0.775392i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.4721 | 1.58875 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.2753 | − | 1.68642i | −0.938091 | − | 0.0972035i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.04421 | + | 0.419555i | −0.117437 | + | 0.0241028i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13.1365i | − | 0.752193i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.1163i | − | 1.14810i | −0.818820 | − | 0.574050i | \(-0.805372\pi\) | ||
0.818820 | − | 0.574050i | \(-0.194628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.496442 | + | 2.41884i | 0.0282416 | + | 0.137603i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.92125 | −0.449173 | −0.224586 | − | 0.974454i | \(-0.572103\pi\) | ||||
−0.224586 | + | 0.974454i | \(0.572103\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.13951i | − | 0.403549i | −0.979432 | − | 0.201774i | \(-0.935329\pi\) | ||
0.979432 | − | 0.201774i | \(-0.0646708\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.57897 | + | 2.35781i | −0.427026 | + | 0.132847i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.9008i | − | 0.612249i | −0.951991 | − | 0.306125i | \(-0.900968\pi\) | ||
0.951991 | − | 0.306125i | \(-0.0990324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.6824 | 1.04602 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.90657 | + | 19.0341i | 0.218043 | + | 1.06238i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.607747i | − | 0.0338160i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.34145i | − | 0.240820i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.4494 | + | 5.63372i | −1.51796 | + | 0.311545i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.54488 | + | 0.885407i | 0.471094 | + | 0.0488141i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.5105 | −1.34722 | −0.673608 | − | 0.739088i | \(-0.735257\pi\) | ||||
−0.673608 | + | 0.739088i | \(0.735257\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.06090 | − | 2.16875i | 0.277336 | − | 0.118847i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.64216 | −0.144357 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.4917 | −1.33415 | −0.667074 | − | 0.744991i | \(-0.732454\pi\) | ||||
−0.667074 | + | 0.744991i | \(0.732454\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.70992 | + | 8.33133i | 0.0928703 | + | 0.452496i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.1995 | 0.931404 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6389 | + | 5.64535i | 0.952410 | + | 0.304821i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.20354 | + | 10.7364i | 0.118634 | + | 0.578028i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9427i | 0.748482i | 0.927332 | + | 0.374241i | \(0.122097\pi\) | ||||
−0.927332 | + | 0.374241i | \(0.877903\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.2380i | − | 1.19037i | −0.803588 | − | 0.595185i | \(-0.797079\pi\) | ||
0.803588 | − | 0.595185i | \(-0.202921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.8730 | + | 18.5253i | 0.687111 | + | 0.988808i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.30187 | −0.388639 | −0.194320 | − | 0.980938i | \(-0.562250\pi\) | ||||
−0.194320 | + | 0.980938i | \(0.562250\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.227035i | 0.0120498i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.60718 | + | 0.358934i | −0.190912 | + | 0.0189968i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 22.4577i | − | 1.18527i | −0.805471 | − | 0.592635i | \(-0.798088\pi\) | ||
0.805471 | − | 0.592635i | \(-0.201912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4097 | 0.968933 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.02408 | + | 0.415423i | −0.106237 | + | 0.0218041i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 15.7756i | − | 0.825733i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.5325i | 1.80258i | 0.433216 | + | 0.901290i | \(0.357379\pi\) | ||||
−0.433216 | + | 0.901290i | \(0.642621\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.42619 | − | 1.89676i | 0.230418 | − | 0.0987415i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.74216 | − | 26.4641i | 0.142366 | − | 1.37395i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.87066 | 0.407527 | 0.203764 | − | 0.979020i | \(-0.434683\pi\) | ||||
0.203764 | + | 0.979020i | \(0.434683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.69668 | − | 0.348228i | 0.0876164 | − | 0.0179824i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.9000 | −1.33392 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.3198 | −1.71152 | −0.855761 | − | 0.517371i | \(-0.826911\pi\) | ||||
−0.855761 | + | 0.517371i | \(0.826911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.6147 | + | 2.17857i | −0.543809 | + | 0.111611i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.9800 | 0.714345 | 0.357172 | − | 0.934038i | \(-0.383741\pi\) | ||||
0.357172 | + | 0.934038i | \(0.383741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.853957 | − | 8.24136i | 0.0435217 | − | 0.420019i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.0534 | + | 7.30790i | −0.866871 | + | 0.371481i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 17.5098i | − | 0.887783i | −0.896081 | − | 0.443892i | \(-0.853598\pi\) | ||
0.896081 | − | 0.443892i | \(-0.146402\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.00559i | 0.253144i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.3560 | + | 3.15166i | −0.774606 | + | 0.158980i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.6345 | −0.686027 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3263i | 0.919769i | 0.887979 | + | 0.459884i | \(0.152109\pi\) | ||||
−0.887979 | + | 0.459884i | \(0.847891\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.348612 | + | 3.50344i | 0.0174524 | + | 0.175392i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 0.472174i | − | 0.0235793i | −0.999930 | − | 0.0117896i | \(-0.996247\pi\) | ||
0.999930 | − | 0.0117896i | \(-0.00375284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.8441 | −1.18776 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.20734 | + | 6.51682i | −0.308445 | + | 0.323823i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.74758i | 0.284897i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.30432i | − | 0.361176i | −0.983559 | − | 0.180588i | \(-0.942200\pi\) | ||
0.983559 | − | 0.180588i | \(-0.0578000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.84251 | + | 8.97734i | 0.0908843 | + | 0.442819i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.4775 | + | 2.53632i | 1.20446 | + | 0.124804i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.74892 | −0.134939 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.38006 | − | 31.0858i | −0.312433 | − | 1.52228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.396150 | −0.0193532 | −0.00967659 | − | 0.999953i | \(-0.503080\pi\) | ||||
−0.00967659 | + | 0.999953i | \(0.503080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0098 | −1.21891 | −0.609453 | − | 0.792823i | \(-0.708611\pi\) | ||||
−0.609453 | + | 0.792823i | \(0.708611\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.95339 | − | 3.83681i | 0.435329 | − | 0.186552i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.791039 | 0.0383710 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.58217 | + | 34.5708i | −0.173353 | + | 1.67300i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.0677 | + | 4.73442i | −1.11372 | + | 0.228580i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.2731i | 1.21736i | 0.793415 | + | 0.608681i | \(0.208301\pi\) | ||||
−0.793415 | + | 0.608681i | \(0.791699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.3865i | − | 0.643316i | −0.946856 | − | 0.321658i | \(-0.895760\pi\) | ||
0.946856 | − | 0.321658i | \(-0.104240\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.07744 | − | 10.1220i | −0.0996055 | − | 0.485312i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.86163 | 0.232563 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3616i | 0.828622i | 0.910135 | + | 0.414311i | \(0.135977\pi\) | ||||
−0.910135 | + | 0.414311i | \(0.864023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5882 | − | 4.13826i | 0.980391 | − | 0.197060i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.2288i | 1.43621i | 0.695933 | + | 0.718107i | \(0.254991\pi\) | ||||
−0.695933 | + | 0.718107i | \(0.745009\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.6351 | −0.788578 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.13040 | − | 39.6141i | −0.384555 | − | 1.87368i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 37.1531i | − | 1.75336i | −0.481071 | − | 0.876681i | \(-0.659752\pi\) | ||
0.481071 | − | 0.876681i | \(-0.340248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.02675i | 0.236701i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.5106 | + | 3.18339i | −0.728751 | + | 0.149569i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.18386 | + | 11.4252i | −0.0555004 | + | 0.535623i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.31615 | 0.342235 | 0.171118 | − | 0.985251i | \(-0.445262\pi\) | ||||
0.171118 | + | 0.985251i | \(0.445262\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.37542 | + | 2.34554i | −0.157551 | + | 0.109481i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.8550 | 0.971313 | 0.485656 | − | 0.874150i | \(-0.338581\pi\) | ||||
0.485656 | + | 0.874150i | \(0.338581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.79424 | −0.222807 | −0.111404 | − | 0.993775i | \(-0.535535\pi\) | ||||
−0.111404 | + | 0.993775i | \(0.535535\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.91254 | − | 9.31853i | −0.0886917 | − | 0.432136i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.3144 | −0.477292 | −0.238646 | − | 0.971107i | \(-0.576704\pi\) | ||||
−0.238646 | + | 0.971107i | \(0.576704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.95328 | + | 0.720488i | 0.321073 | + | 0.0332691i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.31431 | + | 25.8931i | 0.244870 | + | 1.19309i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 19.3672i | − | 0.890505i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.768290i | − | 0.0352515i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.8828 | − | 27.7292i | −0.544078 | − | 1.26963i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.1291 | 1.23956 | 0.619780 | − | 0.784775i | \(-0.287222\pi\) | ||||
0.619780 | + | 0.784775i | \(0.287222\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7.96803i | − | 0.363311i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.87127 | − | 28.8554i | −0.130647 | − | 1.31297i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.11396i | 0.277621i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5407 | 0.477646 | 0.238823 | − | 0.971063i | \(-0.423238\pi\) | ||||
0.238823 | + | 0.971063i | \(0.423238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.52895 | − | 1.75048i | 0.385692 | − | 0.0791595i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.2238i | − | 1.18346i | −0.806134 | − | 0.591732i | \(-0.798444\pi\) | ||
0.806134 | − | 0.591732i | \(-0.201556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.71914i | − | 0.212539i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.70052 | − | 8.63536i | −0.166326 | − | 0.388131i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0619099 | − | 0.597480i | 0.00277704 | − | 0.0268006i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.7873 | −0.751505 | −0.375752 | − | 0.926720i | \(-0.622616\pi\) | ||||
−0.375752 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 37.3053 | − | 7.65655i | 1.66668 | − | 0.342069i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.4191 | 0.821267 | 0.410634 | − | 0.911800i | \(-0.365308\pi\) | ||||
0.410634 | + | 0.911800i | \(0.365308\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.20483 | −0.0536142 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.92255 | − | 2.03650i | 0.440676 | − | 0.0904444i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.5649 | 1.39909 | 0.699544 | − | 0.714589i | \(-0.253386\pi\) | ||||
0.699544 | + | 0.714589i | \(0.253386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.30183 | + | 41.5160i | −0.190302 | + | 1.83656i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.27809 | + | 3.27835i | 0.100580 | + | 0.144743i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.42563i | 0.0628205i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1682i | 0.447198i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.1536 | + | 6.59921i | −1.41139 | + | 0.289673i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.0356 | −0.833963 | −0.416981 | − | 0.908915i | \(-0.636912\pi\) | ||||
−0.416981 | + | 0.908915i | \(0.636912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 32.7943i | − | 1.43400i | −0.697075 | − | 0.716998i | \(-0.745516\pi\) | ||
0.697075 | − | 0.716998i | \(-0.254484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.56006 | + | 0.453750i | −0.199017 | + | 0.0198033i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.34455i | − | 0.189251i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0419 | −0.740952 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.6477 | − | 10.9908i | 1.11301 | − | 0.476962i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.96873i | − | 0.301849i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.2184i | 0.485015i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.487191 | + | 2.37376i | 0.0210239 | + | 0.102435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.49465 | + | 21.4556i | −0.193598 | + | 0.924158i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.0191 | −1.84954 | −0.924769 | − | 0.380530i | \(-0.875742\pi\) | ||||
−0.924769 | + | 0.380530i | \(0.875742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.66621 | − | 22.7354i | −0.200246 | − | 0.975669i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.1783 | −0.693001 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.93124 | −0.0825739 | −0.0412869 | − | 0.999147i | \(-0.513146\pi\) | ||||
−0.0412869 | + | 0.999147i | \(0.513146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.5229 | + | 36.2235i | 0.662502 | + | 1.54598i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.58342 | −0.195260 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.8814 | + | 3.71798i | 1.52583 | + | 0.158105i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.11399 | − | 0.639115i | 0.132181 | − | 0.0271289i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.2956i | 1.74975i | 0.484347 | + | 0.874876i | \(0.339057\pi\) | ||||
−0.484347 | + | 0.874876i | \(0.660943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.8493i | 1.13560i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.862641 | − | 4.20308i | −0.0364207 | − | 0.177454i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.7986 | −1.67731 | −0.838656 | − | 0.544662i | \(-0.816658\pi\) | ||||
−0.838656 | + | 0.544662i | \(0.816658\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.91036i | 0.206580i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.1127 | − | 15.4574i | 0.760661 | − | 0.649150i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.6458i | 0.907439i | 0.891145 | + | 0.453720i | \(0.149903\pi\) | ||||
−0.891145 | + | 0.453720i | \(0.850097\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.2486 | 0.805531 | 0.402765 | − | 0.915303i | \(-0.368049\pi\) | ||||
0.402765 | + | 0.915303i | \(0.368049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.77006 | + | 37.8584i | 0.324599 | + | 1.58156i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.32787i | 0.263890i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.0237908i | − | 0.000990422i | −1.00000 | 0.000495211i | \(-0.999842\pi\) | |||
1.00000 | 0.000495211i | \(-0.000157631\pi\) | ||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.3810 | − | 3.56727i | 0.722328 | − | 0.148251i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.23421 | + | 0.749598i | 0.300126 | + | 0.0310986i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.4916 | 1.30425 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.13014 | + | 11.9714i | 0.212105 | + | 0.494958i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.4193 | 1.17299 | 0.586495 | − | 0.809953i | \(-0.300508\pi\) | ||||
0.586495 | + | 0.809953i | \(0.300508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.21960 | −0.173866 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.626358 | − | 3.05183i | −0.0257649 | − | 0.125536i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.6292 | −1.66844 | −0.834221 | − | 0.551430i | \(-0.814082\pi\) | ||||
−0.834221 | + | 0.551430i | \(0.814082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.08175 | − | 0.215707i | −0.0853433 | − | 0.00884314i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.94321 | + | 24.0850i | 0.202312 | + | 0.985734i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.26519i | − | 0.215130i | −0.994198 | − | 0.107565i | \(-0.965695\pi\) | ||
0.994198 | − | 0.107565i | \(-0.0343054\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 40.1818i | − | 1.63905i | −0.573042 | − | 0.819526i | \(-0.694237\pi\) | ||
0.573042 | − | 0.819526i | \(-0.305763\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.28570 | − | 3.12215i | 0.296697 | − | 0.127144i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.19296 | −0.0485009 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 39.9601i | − | 1.62193i | −0.585095 | − | 0.810965i | \(-0.698943\pi\) | ||
0.585095 | − | 0.810965i | \(-0.301057\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.70696 | + | 27.2041i | 0.109692 | + | 1.10237i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14.0965i | − | 0.570283i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.7062 | 1.07865 | 0.539327 | − | 0.842096i | \(-0.318679\pi\) | ||||
0.539327 | + | 0.842096i | \(0.318679\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.72345 | − | 0.558962i | 0.109820 | − | 0.0225395i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.8390i | 1.04024i | 0.854093 | + | 0.520120i | \(0.174113\pi\) | ||||
−0.854093 | + | 0.520120i | \(0.825887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23.7203i | − | 0.953398i | −0.879066 | − | 0.476699i | \(-0.841833\pi\) | ||
0.879066 | − | 0.476699i | \(-0.158167\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.7630 | − | 27.0015i | −0.752934 | − | 1.08353i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 43.7778 | + | 4.53619i | 1.75392 | + | 0.181739i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.08221 | + | 0.837832i | −0.163028 | + | 0.0334598i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.45182 | 0.0578880 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.2580 | −0.607411 | −0.303706 | − | 0.952766i | \(-0.598224\pi\) | ||||
−0.303706 | + | 0.952766i | \(0.598224\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.1783 | − | 7.63048i | 1.47771 | − | 0.303284i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.25616 | −0.248268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.23106 | − | 29.7445i | 0.246884 | − | 1.17852i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.268279 | − | 0.626044i | −0.0106130 | − | 0.0247659i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.3042i | 0.801967i | 0.916085 | + | 0.400984i | \(0.131332\pi\) | ||||
−0.916085 | + | 0.400984i | \(0.868668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.2942i | 1.39187i | 0.718105 | + | 0.695934i | \(0.245010\pi\) | ||||
−0.718105 | + | 0.695934i | \(0.754990\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4930 | + | 2.15358i | −0.413161 | + | 0.0847972i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.1983 | −1.42310 | −0.711551 | − | 0.702635i | \(-0.752007\pi\) | ||||
−0.711551 | + | 0.702635i | \(0.752007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.1276i | 1.14336i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.49209 | + | 25.0447i | 0.0976727 | + | 0.981581i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 29.0293i | − | 1.13601i | −0.823027 | − | 0.568003i | \(-0.807716\pi\) | ||
0.823027 | − | 0.568003i | \(-0.192284\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.05057 | −0.353635 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.6415 | + | 43.5008i | 0.727273 | + | 1.69713i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.26171i | − | 0.0491491i | −0.999698 | − | 0.0245745i | \(-0.992177\pi\) | ||
0.999698 | − | 0.0245745i | \(-0.00782310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.5711i | − | 0.411170i | −0.978639 | − | 0.205585i | \(-0.934090\pi\) | ||
0.978639 | − | 0.205585i | \(-0.0659097\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.19590 | + | 5.82685i | 0.0464450 | + | 0.226296i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.209504 | + | 2.02188i | −0.00812421 | + | 0.0784051i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.7504 | 1.46170 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.66356 | − | 8.10541i | −0.0643168 | − | 0.313373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.1385 | −1.58813 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.2901 | −0.705030 | −0.352515 | − | 0.935806i | \(-0.614673\pi\) | ||||
−0.352515 | + | 0.935806i | \(0.614673\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.26708 | + | 2.96514i | −0.164240 | + | 0.114128i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.52037 | 0.327464 | 0.163732 | − | 0.986505i | \(-0.447647\pi\) | ||||
0.163732 | + | 0.986505i | \(0.447647\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.66721 | − | 16.0899i | 0.0639816 | − | 0.617473i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.8193 | − | 6.94108i | 1.29596 | − | 0.265983i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.6010i | 0.558692i | 0.960190 | + | 0.279346i | \(0.0901177\pi\) | ||||
−0.960190 | + | 0.279346i | \(0.909882\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.29111i | 0.202163i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.10387 | − | 10.2508i | −0.0802678 | − | 0.391092i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.6577 | −1.66323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.8458i | 1.28756i | 0.765212 | + | 0.643778i | \(0.222634\pi\) | ||||
−0.765212 | + | 0.643778i | \(0.777366\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.38376 | + | 23.7344i | 0.280486 | + | 0.901597i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 18.3215i | − | 0.694975i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.26975 | 0.0480951 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.27243 | + | 11.0721i | 0.0859512 | + | 0.418784i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.51324i | 0.0571545i | 0.999592 | + | 0.0285772i | \(0.00909765\pi\) | ||||
−0.999592 | + | 0.0285772i | \(0.990902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.41007i | − | 0.0531818i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.50905 | − | 1.13068i | 0.207483 | − | 0.0425838i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.17070 | + | 0.328543i | 0.119246 | + | 0.0123561i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.87428 | 0.107946 | 0.0539729 | − | 0.998542i | \(-0.482812\pi\) | ||||
0.0539729 | + | 0.998542i | \(0.482812\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.5968 | − | 16.1114i | 1.40999 | − | 0.604226i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34.7539 | 1.30154 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.5958 | −0.508453 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.19319 | − | 5.81361i | −0.0445604 | − | 0.217113i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.5502 | 0.915566 | 0.457783 | − | 0.889064i | \(-0.348644\pi\) | ||||
0.457783 | + | 0.889064i | \(0.348644\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.388752 | − | 3.75176i | 0.0144779 | − | 0.139723i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.06315 | − | 19.7970i | −0.151110 | − | 0.736260i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.96574i | − | 0.221562i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 43.1067i | − | 1.59874i | −0.600839 | − | 0.799370i | \(-0.705167\pi\) | ||
0.600839 | − | 0.799370i | \(-0.294833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.41588 | − | 25.3050i | 0.348736 | − | 0.937221i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.89211 | −0.180941 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.8194i | 0.547367i | 0.961820 | + | 0.273684i | \(0.0882421\pi\) | ||||
−0.961820 | + | 0.273684i | \(0.911758\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.1243 | + | 0.0493581i | 0.447210 | + | 0.00182060i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.27425i | 0.304786i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3445 | 0.527672 | 0.263836 | − | 0.964568i | \(-0.415012\pi\) | ||||
0.263836 | + | 0.964568i | \(0.415012\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.65928 | − | 1.16151i | 0.207899 | − | 0.0426691i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.81720i | 0.140040i | 0.997546 | + | 0.0700198i | \(0.0223062\pi\) | ||||
−0.997546 | + | 0.0700198i | \(0.977694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 23.3480i | − | 0.855403i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.58007 | − | 3.24830i | 0.277340 | − | 0.118849i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.05914 | − | 29.5231i | 0.111779 | − | 1.07875i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.2840 | −0.849644 | −0.424822 | − | 0.905277i | \(-0.639663\pi\) | ||||
−0.424822 | + | 0.905277i | \(0.639663\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.6094 | + | 7.51372i | −1.33412 | + | 0.273815i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.14170 | −0.332701 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.1461 | 1.56817 | 0.784086 | − | 0.620652i | \(-0.213132\pi\) | ||||
0.784086 | + | 0.620652i | \(0.213132\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.6223 | − | 6.90064i | 1.22041 | − | 0.250477i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.4395 | −0.704682 | −0.352341 | − | 0.935872i | \(-0.614614\pi\) | ||||
−0.352341 | + | 0.935872i | \(0.614614\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.5757 | + | 4.41163i | 1.54134 | + | 0.159712i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.18127 | + | 0.934743i | −0.0788640 | + | 0.0337957i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 40.3805i | − | 1.45805i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 29.2444i | − | 1.05458i | −0.849686 | − | 0.527290i | \(-0.823208\pi\) | ||
0.849686 | − | 0.527290i | \(-0.176792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.2038 | − | 5.99380i | 1.05175 | − | 0.215861i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.6142 | −0.633539 | −0.316770 | − | 0.948503i | \(-0.602598\pi\) | ||||
−0.316770 | + | 0.948503i | \(0.602598\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.49220i | − | 0.197286i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.36924 | + | 0.832785i | −0.300245 | + | 0.0298760i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.23323i | − | 0.0441850i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.710988 | 0.0254411 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.6893 | + | 25.4563i | 0.632163 | + | 0.909733i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.2610i | 0.544689i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 14.8565i | − | 0.529578i | −0.964306 | − | 0.264789i | \(-0.914698\pi\) | ||
0.964306 | − | 0.264789i | \(-0.0853023\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.41068 | − | 40.9797i | −0.299428 | − | 1.45892i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.33900 | − | 12.9224i | 0.0476093 | − | 0.459468i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.0314 | 2.02524 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.50179 | − | 17.0619i | −0.124196 | − | 0.605123i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.6741 | −0.838579 | −0.419290 | − | 0.907853i | \(-0.637721\pi\) | ||||
−0.419290 | + | 0.907853i | \(0.637721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.56847 | 0.0908658 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.8708 | − | 19.6571i | 1.62076 | − | 0.694548i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −49.4032 | −1.74340 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.72554 | − | 16.6528i | 0.0608172 | − | 0.586934i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.9656 | + | 5.53443i | −0.949235 | + | 0.194821i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.1376i | 1.34085i | 0.741979 | + | 0.670423i | \(0.233887\pi\) | ||||
−0.741979 | + | 0.670423i | \(0.766113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4174i | 1.13833i | 0.822224 | + | 0.569164i | \(0.192733\pi\) | ||||
−0.822224 | + | 0.569164i | \(0.807267\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.59048 | + | 46.7281i | 0.336353 | + | 1.63883i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.02683 | 0.176082 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.75142i | 0.166231i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.2363 | − | 32.9037i | −0.357686 | − | 1.14975i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2789i | 1.05674i | 0.849014 | + | 0.528370i | \(0.177197\pi\) | ||||
−0.849014 | + | 0.528370i | \(0.822803\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.2258 | 0.705027 | 0.352513 | − | 0.935807i | \(-0.385327\pi\) | ||||
0.352513 | + | 0.935807i | \(0.385327\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.09052 | − | 5.31337i | −0.0379669 | − | 0.184988i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 35.8039i | − | 1.24502i | −0.782611 | − | 0.622512i | \(-0.786112\pi\) | ||
0.782611 | − | 0.622512i | \(-0.213888\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.3995i | 1.78518i | 0.450871 | + | 0.892589i | \(0.351113\pi\) | ||||
−0.450871 | + | 0.892589i | \(0.648887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.1991 | + | 10.3029i | −1.74139 | + | 0.357403i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.41963 | + | 1.13534i | 0.187779 | + | 0.0393371i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.9872 | 0.760898 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.2851 | + | 23.4356i | 0.562897 | + | 0.810054i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.5046 | −1.36385 | −0.681925 | − | 0.731422i | \(-0.738857\pi\) | ||||
−0.681925 | + | 0.731422i | \(0.738857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.59010 | −0.227245 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.33686 | − | 16.2583i | −0.114927 | − | 0.559966i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.84820 | 0.201184 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.13948 | + | 0.325308i | 0.107874 | + | 0.0111777i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.88656 | − | 9.19199i | −0.0647467 | − | 0.315468i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.6138i | 0.398115i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 50.6339i | − | 1.73367i | −0.498594 | − | 0.866836i | \(-0.666150\pi\) | ||
0.498594 | − | 0.866836i | \(-0.333850\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.907861 | + | 2.11854i | 0.0310482 | + | 0.0724525i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.4930 | −1.34905 | −0.674527 | − | 0.738250i | \(-0.735652\pi\) | ||||
−0.674527 | + | 0.738250i | \(0.735652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 16.7650i | − | 0.572014i | −0.958228 | − | 0.286007i | \(-0.907672\pi\) | ||
0.958228 | − | 0.286007i | \(-0.0923280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.31963 | + | 0.728343i | −0.249452 | + | 0.0248219i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.8252i | 0.981220i | 0.871379 | + | 0.490610i | \(0.163226\pi\) | ||||
−0.871379 | + | 0.490610i | \(0.836774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.9508 | −0.644348 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.7819 | − | 5.70197i | 0.943524 | − | 0.193649i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.6981i | 1.44843i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 11.4708i | − | 0.388674i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.22465 | − | 16.8591i | −0.244517 | − | 0.570594i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.63166 | − | 0.272689i | −0.0889664 | − | 0.00921856i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8225 | −0.905733 | −0.452866 | − | 0.891578i | \(-0.649599\pi\) | ||||
−0.452866 | + | 0.891578i | \(0.649599\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.65260 | + | 1.36538i | −0.224387 | + | 0.0460531i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.0356 | −0.405491 | −0.202745 | − | 0.979232i | \(-0.564986\pi\) | ||||
−0.202745 | + | 0.979232i | \(0.564986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.41892 | −0.182361 | −0.0911807 | − | 0.995834i | \(-0.529064\pi\) | ||||
−0.0911807 | + | 0.995834i | \(0.529064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.7811 | − | 3.23892i | 0.530476 | − | 0.108875i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.8010 | −0.899889 | −0.449945 | − | 0.893056i | \(-0.648556\pi\) | ||||
−0.449945 | + | 0.893056i | \(0.648556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.4641 | + | 1.70598i | 0.552188 | + | 0.0572168i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.4082 | + | 19.4390i | 0.683700 | + | 0.651231i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.49460i | − | 0.0834786i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.39906i | 0.0467654i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −46.6115 | + | 9.56655i | −1.55631 | + | 0.319418i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.7651 | −1.09278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.95471i | − | 0.265010i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.2012 | − | 2.80618i | 0.938479 | − | 0.0933838i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 13.3999i | − | 0.445427i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.7667 | 1.68568 | 0.842840 | − | 0.538165i | \(-0.180882\pi\) | ||||
0.842840 | + | 0.538165i | \(0.180882\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.32228 | − | 1.42370i | 0.110193 | − | 0.0472213i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 9.33951i | − | 0.309432i | −0.987959 | − | 0.154716i | \(-0.950554\pi\) | ||
0.987959 | − | 0.154716i | \(-0.0494462\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.60856i | 0.284902i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.57449 | + | 22.2885i | 0.151228 | + | 0.736834i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.8180 | + | 2.46799i | 0.786541 | + | 0.0815002i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.07625 | 0.200437 | 0.100219 | − | 0.994965i | \(-0.468046\pi\) | ||||
0.100219 | + | 0.994965i | \(0.468046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.00506 | + | 34.1311i | 0.230825 | + | 1.12466i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.985662 | −0.0324435 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.83534 | 0.0603455 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.68461 | − | 3.93113i | −0.0553299 | − | 0.129115i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.6804 | 0.612883 | 0.306442 | − | 0.951889i | \(-0.400862\pi\) | ||||
0.306442 | + | 0.951889i | \(0.400862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.10269 | − | 5.26377i | 0.0361391 | − | 0.172513i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.4399 | − | 2.75840i | 0.440001 | − | 0.0903059i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.47723i | − | 0.0810142i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.6614i | 1.98172i | 0.134889 | + | 0.990861i | \(0.456932\pi\) | ||||
−0.134889 | + | 0.990861i | \(0.543068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.48617 | + | 12.1135i | 0.0811332 | + | 0.395309i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.6348 | −1.22686 | −0.613429 | − | 0.789750i | \(-0.710210\pi\) | ||||
−0.613429 | + | 0.789750i | \(0.710210\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1573i | 0.330766i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.0381 | − | 6.63966i | 0.391598 | − | 0.215988i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.53338i | 0.309793i | 0.987931 | + | 0.154897i | \(0.0495044\pi\) | ||||
−0.987931 | + | 0.154897i | \(0.950496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 68.4890 | 2.22325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.79596 | + | 18.4952i | 0.123092 | + | 0.599748i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.837324i | 0.0271236i | 0.999908 | + | 0.0135618i | \(0.00431699\pi\) | ||||
−0.999908 | + | 0.0135618i | \(0.995683\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.3132i | 0.722037i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −31.6982 | + | 6.50574i | −1.02466 | + | 0.210301i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.44282 | − | 13.9244i | 0.0465912 | − | 0.449642i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.835734 | 0.0269592 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.2564 | − | 30.9346i | −0.427183 | − | 0.996852i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.2441 | 0.329769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.8394 | 0.573677 | 0.286838 | − | 0.957979i | \(-0.407396\pi\) | ||||
0.286838 | + | 0.957979i | \(0.407396\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.211634 | + | 1.03116i | 0.00679867 | + | 0.0331255i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.5383 | −0.562830 | −0.281415 | − | 0.959586i | \(-0.590804\pi\) | ||||
−0.281415 | + | 0.959586i | \(0.590804\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.99607 | + | 48.2160i | −0.160167 | + | 1.54574i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.51181 | + | 7.36607i | 0.0484168 | + | 0.235903i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 0.391252i | − | 0.0125173i | −0.999980 | − | 0.00625863i | \(-0.998008\pi\) | ||
0.999980 | − | 0.00625863i | \(-0.00199220\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 52.0947i | 1.66495i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 44.6112 | − | 19.1173i | 1.42432 | − | 0.610368i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.5956 | 0.943952 | 0.471976 | − | 0.881611i | \(-0.343541\pi\) | ||||
0.471976 | + | 0.881611i | \(0.343541\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.79870i | − | 0.0573114i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.8063 | + | 1.47331i | −0.471289 | + | 0.0468959i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 39.1341i | − | 1.24439i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.06251 | −0.287880 | −0.143940 | − | 0.989586i | \(-0.545977\pi\) | ||||
−0.143940 | + | 0.989586i | \(0.545977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.5865 | − | 8.53522i | 1.31971 | − | 0.270857i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.1953i | 0.450023i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0383191i | 0.00121358i | 1.00000 | 0.000606789i | \(0.000193147\pi\) | |||||
−1.00000 | 0.000606789i | \(0.999807\pi\) | ||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.83153 | + | 5.44204i | −0.247779 | + | 0.172178i |
(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 | 1680.2.f.k.881.2 | 16 | ||
3.2 | odd | 2 | 1680.2.f.l.881.16 | 16 | |||
4.3 | odd | 2 | 840.2.f.a.41.15 | ✓ | 16 | ||
7.6 | odd | 2 | 1680.2.f.l.881.15 | 16 | |||
12.11 | even | 2 | 840.2.f.b.41.1 | yes | 16 | ||
21.20 | even | 2 | inner | 1680.2.f.k.881.1 | 16 | ||
28.27 | even | 2 | 840.2.f.b.41.2 | yes | 16 | ||
84.83 | odd | 2 | 840.2.f.a.41.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.f.a.41.15 | ✓ | 16 | 4.3 | odd | 2 | ||
840.2.f.a.41.16 | yes | 16 | 84.83 | odd | 2 | ||
840.2.f.b.41.1 | yes | 16 | 12.11 | even | 2 | ||
840.2.f.b.41.2 | yes | 16 | 28.27 | even | 2 | ||
1680.2.f.k.881.1 | 16 | 21.20 | even | 2 | inner | ||
1680.2.f.k.881.2 | 16 | 1.1 | even | 1 | trivial | ||
1680.2.f.l.881.15 | 16 | 7.6 | odd | 2 | |||
1680.2.f.l.881.16 | 16 | 3.2 | odd | 2 |