Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(1,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.23607 | −0.467190 | −0.233595 | − | 0.972334i | \(-0.575049\pi\) | ||||
−0.233595 | + | 0.972334i | \(0.575049\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.38197 | 0.416678 | 0.208339 | − | 0.978057i | \(-0.433194\pi\) | ||||
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.85410 | 0.791585 | 0.395793 | − | 0.918340i | \(-0.370470\pi\) | ||||
0.395793 | + | 0.918340i | \(0.370470\pi\) | |||||||
\(14\) | 1.23607 | 0.330353 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.85410 | −1.17729 | −0.588646 | − | 0.808391i | \(-0.700339\pi\) | ||||
−0.588646 | + | 0.808391i | \(0.700339\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.23607 | −0.269732 | ||||||||
\(22\) | −1.38197 | −0.294636 | ||||||||
\(23\) | 3.09017 | 0.644345 | 0.322172 | − | 0.946681i | \(-0.395587\pi\) | ||||
0.322172 | + | 0.946681i | \(0.395587\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.85410 | −0.559735 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.23607 | −0.233595 | ||||||||
\(29\) | 9.32624 | 1.73184 | 0.865919 | − | 0.500183i | \(-0.166734\pi\) | ||||
0.865919 | + | 0.500183i | \(0.166734\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.14590 | 0.385415 | 0.192707 | − | 0.981256i | \(-0.438273\pi\) | ||||
0.192707 | + | 0.981256i | \(0.438273\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.38197 | 0.240569 | ||||||||
\(34\) | 4.85410 | 0.832472 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.85410 | 1.29121 | 0.645603 | − | 0.763673i | \(-0.276606\pi\) | ||||
0.645603 | + | 0.763673i | \(0.276606\pi\) | |||||||
\(38\) | −6.00000 | −0.973329 | ||||||||
\(39\) | 2.85410 | 0.457022 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.23607 | −0.505389 | −0.252694 | − | 0.967546i | \(-0.581317\pi\) | ||||
−0.252694 | + | 0.967546i | \(0.581317\pi\) | |||||||
\(42\) | 1.23607 | 0.190729 | ||||||||
\(43\) | 0.145898 | 0.0222492 | 0.0111246 | − | 0.999938i | \(-0.496459\pi\) | ||||
0.0111246 | + | 0.999938i | \(0.496459\pi\) | |||||||
\(44\) | 1.38197 | 0.208339 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.09017 | −0.455621 | ||||||||
\(47\) | −10.8541 | −1.58323 | −0.791617 | − | 0.611018i | \(-0.790760\pi\) | ||||
−0.791617 | + | 0.611018i | \(0.790760\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.85410 | −0.679710 | ||||||||
\(52\) | 2.85410 | 0.395793 | ||||||||
\(53\) | −3.23607 | −0.444508 | −0.222254 | − | 0.974989i | \(-0.571341\pi\) | ||||
−0.222254 | + | 0.974989i | \(0.571341\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.23607 | 0.165177 | ||||||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | −9.32624 | −1.22460 | ||||||||
\(59\) | 6.38197 | 0.830861 | 0.415431 | − | 0.909625i | \(-0.363631\pi\) | ||||
0.415431 | + | 0.909625i | \(0.363631\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4164 | 1.71780 | 0.858898 | − | 0.512148i | \(-0.171150\pi\) | ||||
0.858898 | + | 0.512148i | \(0.171150\pi\) | |||||||
\(62\) | −2.14590 | −0.272529 | ||||||||
\(63\) | −1.23607 | −0.155730 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.38197 | −0.170108 | ||||||||
\(67\) | 2.38197 | 0.291003 | 0.145502 | − | 0.989358i | \(-0.453520\pi\) | ||||
0.145502 | + | 0.989358i | \(0.453520\pi\) | |||||||
\(68\) | −4.85410 | −0.588646 | ||||||||
\(69\) | 3.09017 | 0.372013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.94427 | −1.06149 | −0.530745 | − | 0.847532i | \(-0.678088\pi\) | ||||
−0.530745 | + | 0.847532i | \(0.678088\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 12.0000 | 1.40449 | 0.702247 | − | 0.711934i | \(-0.252180\pi\) | ||||
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(74\) | −7.85410 | −0.913021 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | −1.70820 | −0.194668 | ||||||||
\(78\) | −2.85410 | −0.323163 | ||||||||
\(79\) | −1.14590 | −0.128924 | −0.0644618 | − | 0.997920i | \(-0.520533\pi\) | ||||
−0.0644618 | + | 0.997920i | \(0.520533\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.23607 | 0.357364 | ||||||||
\(83\) | 8.18034 | 0.897909 | 0.448954 | − | 0.893555i | \(-0.351797\pi\) | ||||
0.448954 | + | 0.893555i | \(0.351797\pi\) | |||||||
\(84\) | −1.23607 | −0.134866 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.145898 | −0.0157326 | ||||||||
\(87\) | 9.32624 | 0.999878 | ||||||||
\(88\) | −1.38197 | −0.147318 | ||||||||
\(89\) | −9.23607 | −0.979021 | −0.489511 | − | 0.871997i | \(-0.662825\pi\) | ||||
−0.489511 | + | 0.871997i | \(0.662825\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.52786 | −0.369821 | ||||||||
\(92\) | 3.09017 | 0.322172 | ||||||||
\(93\) | 2.14590 | 0.222519 | ||||||||
\(94\) | 10.8541 | 1.11952 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 18.1803 | 1.84593 | 0.922967 | − | 0.384879i | \(-0.125757\pi\) | ||||
0.922967 | + | 0.384879i | \(0.125757\pi\) | |||||||
\(98\) | 5.47214 | 0.552769 | ||||||||
\(99\) | 1.38197 | 0.138893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.32624 | −0.231469 | −0.115735 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115735 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(102\) | 4.85410 | 0.480628 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | −2.85410 | −0.279868 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.23607 | 0.314315 | ||||||||
\(107\) | −8.18034 | −0.790823 | −0.395412 | − | 0.918504i | \(-0.629398\pi\) | ||||
−0.395412 | + | 0.918504i | \(0.629398\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −13.4164 | −1.28506 | −0.642529 | − | 0.766261i | \(-0.722115\pi\) | ||||
−0.642529 | + | 0.766261i | \(0.722115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.85410 | 0.745478 | ||||||||
\(112\) | −1.23607 | −0.116797 | ||||||||
\(113\) | 12.3262 | 1.15955 | 0.579777 | − | 0.814775i | \(-0.303139\pi\) | ||||
0.579777 | + | 0.814775i | \(0.303139\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.32624 | 0.865919 | ||||||||
\(117\) | 2.85410 | 0.263862 | ||||||||
\(118\) | −6.38197 | −0.587508 | ||||||||
\(119\) | 6.00000 | 0.550019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.09017 | −0.826379 | ||||||||
\(122\) | −13.4164 | −1.21466 | ||||||||
\(123\) | −3.23607 | −0.291786 | ||||||||
\(124\) | 2.14590 | 0.192707 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.23607 | 0.110118 | ||||||||
\(127\) | −13.4164 | −1.19051 | −0.595257 | − | 0.803535i | \(-0.702950\pi\) | ||||
−0.595257 | + | 0.803535i | \(0.702950\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.145898 | 0.0128456 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.8885 | 1.56293 | 0.781465 | − | 0.623949i | \(-0.214473\pi\) | ||||
0.781465 | + | 0.623949i | \(0.214473\pi\) | |||||||
\(132\) | 1.38197 | 0.120285 | ||||||||
\(133\) | −7.41641 | −0.643084 | ||||||||
\(134\) | −2.38197 | −0.205771 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.85410 | 0.416236 | ||||||||
\(137\) | 4.61803 | 0.394545 | 0.197273 | − | 0.980349i | \(-0.436792\pi\) | ||||
0.197273 | + | 0.980349i | \(0.436792\pi\) | |||||||
\(138\) | −3.09017 | −0.263053 | ||||||||
\(139\) | −21.2361 | −1.80122 | −0.900610 | − | 0.434628i | \(-0.856880\pi\) | ||||
−0.900610 | + | 0.434628i | \(0.856880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.8541 | −0.914080 | ||||||||
\(142\) | 8.94427 | 0.750587 | ||||||||
\(143\) | 3.94427 | 0.329837 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.0000 | −0.993127 | ||||||||
\(147\) | −5.47214 | −0.451334 | ||||||||
\(148\) | 7.85410 | 0.645603 | ||||||||
\(149\) | −20.4721 | −1.67714 | −0.838571 | − | 0.544792i | \(-0.816609\pi\) | ||||
−0.838571 | + | 0.544792i | \(0.816609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8541 | −1.45295 | −0.726473 | − | 0.687195i | \(-0.758842\pi\) | ||||
−0.726473 | + | 0.687195i | \(0.758842\pi\) | |||||||
\(152\) | −6.00000 | −0.486664 | ||||||||
\(153\) | −4.85410 | −0.392431 | ||||||||
\(154\) | 1.70820 | 0.137651 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.85410 | 0.228511 | ||||||||
\(157\) | −0.437694 | −0.0349318 | −0.0174659 | − | 0.999847i | \(-0.505560\pi\) | ||||
−0.0174659 | + | 0.999847i | \(0.505560\pi\) | |||||||
\(158\) | 1.14590 | 0.0911628 | ||||||||
\(159\) | −3.23607 | −0.256637 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.81966 | −0.301031 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 20.2705 | 1.58771 | 0.793854 | − | 0.608108i | \(-0.208071\pi\) | ||||
0.793854 | + | 0.608108i | \(0.208071\pi\) | |||||||
\(164\) | −3.23607 | −0.252694 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.18034 | −0.634918 | ||||||||
\(167\) | −23.0902 | −1.78677 | −0.893385 | − | 0.449291i | \(-0.851677\pi\) | ||||
−0.893385 | + | 0.449291i | \(0.851677\pi\) | |||||||
\(168\) | 1.23607 | 0.0953647 | ||||||||
\(169\) | −4.85410 | −0.373392 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | 0.458831 | ||||||||
\(172\) | 0.145898 | 0.0111246 | ||||||||
\(173\) | −9.23607 | −0.702205 | −0.351103 | − | 0.936337i | \(-0.614193\pi\) | ||||
−0.351103 | + | 0.936337i | \(0.614193\pi\) | |||||||
\(174\) | −9.32624 | −0.707020 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.38197 | 0.104170 | ||||||||
\(177\) | 6.38197 | 0.479698 | ||||||||
\(178\) | 9.23607 | 0.692273 | ||||||||
\(179\) | 7.41641 | 0.554328 | 0.277164 | − | 0.960823i | \(-0.410605\pi\) | ||||
0.277164 | + | 0.960823i | \(0.410605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.41641 | 0.551257 | 0.275629 | − | 0.961264i | \(-0.411114\pi\) | ||||
0.275629 | + | 0.961264i | \(0.411114\pi\) | |||||||
\(182\) | 3.52786 | 0.261503 | ||||||||
\(183\) | 13.4164 | 0.991769 | ||||||||
\(184\) | −3.09017 | −0.227810 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.14590 | −0.157345 | ||||||||
\(187\) | −6.70820 | −0.490552 | ||||||||
\(188\) | −10.8541 | −0.791617 | ||||||||
\(189\) | −1.23607 | −0.0899107 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −17.1246 | −1.23266 | −0.616328 | − | 0.787489i | \(-0.711381\pi\) | ||||
−0.616328 | + | 0.787489i | \(0.711381\pi\) | |||||||
\(194\) | −18.1803 | −1.30527 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.47214 | −0.390867 | ||||||||
\(197\) | −1.52786 | −0.108856 | −0.0544279 | − | 0.998518i | \(-0.517334\pi\) | ||||
−0.0544279 | + | 0.998518i | \(0.517334\pi\) | |||||||
\(198\) | −1.38197 | −0.0982120 | ||||||||
\(199\) | −15.6180 | −1.10713 | −0.553567 | − | 0.832805i | \(-0.686734\pi\) | ||||
−0.553567 | + | 0.832805i | \(0.686734\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.38197 | 0.168011 | ||||||||
\(202\) | 2.32624 | 0.163674 | ||||||||
\(203\) | −11.5279 | −0.809097 | ||||||||
\(204\) | −4.85410 | −0.339855 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | 3.09017 | 0.214782 | ||||||||
\(208\) | 2.85410 | 0.197896 | ||||||||
\(209\) | 8.29180 | 0.573556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.41641 | 0.235195 | 0.117598 | − | 0.993061i | \(-0.462481\pi\) | ||||
0.117598 | + | 0.993061i | \(0.462481\pi\) | |||||||
\(212\) | −3.23607 | −0.222254 | ||||||||
\(213\) | −8.94427 | −0.612851 | ||||||||
\(214\) | 8.18034 | 0.559197 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −2.65248 | −0.180062 | ||||||||
\(218\) | 13.4164 | 0.908674 | ||||||||
\(219\) | 12.0000 | 0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8541 | −0.931928 | ||||||||
\(222\) | −7.85410 | −0.527133 | ||||||||
\(223\) | −21.7082 | −1.45369 | −0.726844 | − | 0.686802i | \(-0.759014\pi\) | ||||
−0.726844 | + | 0.686802i | \(0.759014\pi\) | |||||||
\(224\) | 1.23607 | 0.0825883 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.3262 | −0.819929 | ||||||||
\(227\) | −16.4721 | −1.09329 | −0.546647 | − | 0.837363i | \(-0.684096\pi\) | ||||
−0.546647 | + | 0.837363i | \(0.684096\pi\) | |||||||
\(228\) | 6.00000 | 0.397360 | ||||||||
\(229\) | −1.70820 | −0.112881 | −0.0564406 | − | 0.998406i | \(-0.517975\pi\) | ||||
−0.0564406 | + | 0.998406i | \(0.517975\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.70820 | −0.112392 | ||||||||
\(232\) | −9.32624 | −0.612298 | ||||||||
\(233\) | 7.32624 | 0.479958 | 0.239979 | − | 0.970778i | \(-0.422859\pi\) | ||||
0.239979 | + | 0.970778i | \(0.422859\pi\) | |||||||
\(234\) | −2.85410 | −0.186578 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.38197 | 0.415431 | ||||||||
\(237\) | −1.14590 | −0.0744341 | ||||||||
\(238\) | −6.00000 | −0.388922 | ||||||||
\(239\) | −26.6525 | −1.72401 | −0.862003 | − | 0.506904i | \(-0.830790\pi\) | ||||
−0.862003 | + | 0.506904i | \(0.830790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0901699 | 0.00580836 | 0.00290418 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290418 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(242\) | 9.09017 | 0.584338 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 13.4164 | 0.858898 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.23607 | 0.206324 | ||||||||
\(247\) | 17.1246 | 1.08961 | ||||||||
\(248\) | −2.14590 | −0.136265 | ||||||||
\(249\) | 8.18034 | 0.518408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.90983 | 0.499264 | 0.249632 | − | 0.968341i | \(-0.419690\pi\) | ||||
0.249632 | + | 0.968341i | \(0.419690\pi\) | |||||||
\(252\) | −1.23607 | −0.0778650 | ||||||||
\(253\) | 4.27051 | 0.268485 | ||||||||
\(254\) | 13.4164 | 0.841820 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.5066 | 1.46630 | 0.733150 | − | 0.680067i | \(-0.238049\pi\) | ||||
0.733150 | + | 0.680067i | \(0.238049\pi\) | |||||||
\(258\) | −0.145898 | −0.00908321 | ||||||||
\(259\) | −9.70820 | −0.603238 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.32624 | 0.577280 | ||||||||
\(262\) | −17.8885 | −1.10516 | ||||||||
\(263\) | −15.9787 | −0.985290 | −0.492645 | − | 0.870230i | \(-0.663970\pi\) | ||||
−0.492645 | + | 0.870230i | \(0.663970\pi\) | |||||||
\(264\) | −1.38197 | −0.0850541 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.41641 | 0.454729 | ||||||||
\(267\) | −9.23607 | −0.565238 | ||||||||
\(268\) | 2.38197 | 0.145502 | ||||||||
\(269\) | 22.6180 | 1.37905 | 0.689523 | − | 0.724264i | \(-0.257820\pi\) | ||||
0.689523 | + | 0.724264i | \(0.257820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.56231 | −0.520123 | −0.260062 | − | 0.965592i | \(-0.583743\pi\) | ||||
−0.260062 | + | 0.965592i | \(0.583743\pi\) | |||||||
\(272\) | −4.85410 | −0.294323 | ||||||||
\(273\) | −3.52786 | −0.213516 | ||||||||
\(274\) | −4.61803 | −0.278986 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.09017 | 0.186006 | ||||||||
\(277\) | 14.3607 | 0.862850 | 0.431425 | − | 0.902149i | \(-0.358011\pi\) | ||||
0.431425 | + | 0.902149i | \(0.358011\pi\) | |||||||
\(278\) | 21.2361 | 1.27365 | ||||||||
\(279\) | 2.14590 | 0.128472 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4721 | 1.34058 | 0.670288 | − | 0.742101i | \(-0.266171\pi\) | ||||
0.670288 | + | 0.742101i | \(0.266171\pi\) | |||||||
\(282\) | 10.8541 | 0.646352 | ||||||||
\(283\) | −21.0902 | −1.25368 | −0.626840 | − | 0.779148i | \(-0.715652\pi\) | ||||
−0.626840 | + | 0.779148i | \(0.715652\pi\) | |||||||
\(284\) | −8.94427 | −0.530745 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.94427 | −0.233230 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 6.56231 | 0.386018 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.1803 | 1.06575 | ||||||||
\(292\) | 12.0000 | 0.702247 | ||||||||
\(293\) | −15.5967 | −0.911172 | −0.455586 | − | 0.890192i | \(-0.650570\pi\) | ||||
−0.455586 | + | 0.890192i | \(0.650570\pi\) | |||||||
\(294\) | 5.47214 | 0.319141 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.85410 | −0.456510 | ||||||||
\(297\) | 1.38197 | 0.0801898 | ||||||||
\(298\) | 20.4721 | 1.18592 | ||||||||
\(299\) | 8.81966 | 0.510054 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.180340 | −0.0103946 | ||||||||
\(302\) | 17.8541 | 1.02739 | ||||||||
\(303\) | −2.32624 | −0.133639 | ||||||||
\(304\) | 6.00000 | 0.344124 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.85410 | 0.277491 | ||||||||
\(307\) | −33.0902 | −1.88856 | −0.944278 | − | 0.329149i | \(-0.893238\pi\) | ||||
−0.944278 | + | 0.329149i | \(0.893238\pi\) | |||||||
\(308\) | −1.70820 | −0.0973340 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.47214 | −0.253592 | −0.126796 | − | 0.991929i | \(-0.540469\pi\) | ||||
−0.126796 | + | 0.991929i | \(0.540469\pi\) | |||||||
\(312\) | −2.85410 | −0.161582 | ||||||||
\(313\) | 30.9443 | 1.74907 | 0.874537 | − | 0.484959i | \(-0.161166\pi\) | ||||
0.874537 | + | 0.484959i | \(0.161166\pi\) | |||||||
\(314\) | 0.437694 | 0.0247005 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.14590 | −0.0644618 | ||||||||
\(317\) | 9.70820 | 0.545267 | 0.272634 | − | 0.962118i | \(-0.412105\pi\) | ||||
0.272634 | + | 0.962118i | \(0.412105\pi\) | |||||||
\(318\) | 3.23607 | 0.181470 | ||||||||
\(319\) | 12.8885 | 0.721620 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.18034 | −0.456582 | ||||||||
\(322\) | 3.81966 | 0.212861 | ||||||||
\(323\) | −29.1246 | −1.62054 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.2705 | −1.12268 | ||||||||
\(327\) | −13.4164 | −0.741929 | ||||||||
\(328\) | 3.23607 | 0.178682 | ||||||||
\(329\) | 13.4164 | 0.739671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.4164 | −1.17715 | −0.588576 | − | 0.808442i | \(-0.700311\pi\) | ||||
−0.588576 | + | 0.808442i | \(0.700311\pi\) | |||||||
\(332\) | 8.18034 | 0.448954 | ||||||||
\(333\) | 7.85410 | 0.430402 | ||||||||
\(334\) | 23.0902 | 1.26344 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.23607 | −0.0674330 | ||||||||
\(337\) | −12.9443 | −0.705119 | −0.352560 | − | 0.935789i | \(-0.614689\pi\) | ||||
−0.352560 | + | 0.935789i | \(0.614689\pi\) | |||||||
\(338\) | 4.85410 | 0.264028 | ||||||||
\(339\) | 12.3262 | 0.669469 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.96556 | 0.160594 | ||||||||
\(342\) | −6.00000 | −0.324443 | ||||||||
\(343\) | 15.4164 | 0.832408 | ||||||||
\(344\) | −0.145898 | −0.00786629 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.23607 | 0.496534 | ||||||||
\(347\) | 24.3607 | 1.30775 | 0.653875 | − | 0.756603i | \(-0.273142\pi\) | ||||
0.653875 | + | 0.756603i | \(0.273142\pi\) | |||||||
\(348\) | 9.32624 | 0.499939 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.85410 | 0.152341 | ||||||||
\(352\) | −1.38197 | −0.0736590 | ||||||||
\(353\) | 1.20163 | 0.0639561 | 0.0319781 | − | 0.999489i | \(-0.489819\pi\) | ||||
0.0319781 | + | 0.999489i | \(0.489819\pi\) | |||||||
\(354\) | −6.38197 | −0.339198 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.23607 | −0.489511 | ||||||||
\(357\) | 6.00000 | 0.317554 | ||||||||
\(358\) | −7.41641 | −0.391969 | ||||||||
\(359\) | 23.8885 | 1.26079 | 0.630395 | − | 0.776275i | \(-0.282893\pi\) | ||||
0.630395 | + | 0.776275i | \(0.282893\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −7.41641 | −0.389798 | ||||||||
\(363\) | −9.09017 | −0.477110 | ||||||||
\(364\) | −3.52786 | −0.184910 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.4164 | −0.701287 | ||||||||
\(367\) | 10.2918 | 0.537227 | 0.268614 | − | 0.963248i | \(-0.413434\pi\) | ||||
0.268614 | + | 0.963248i | \(0.413434\pi\) | |||||||
\(368\) | 3.09017 | 0.161086 | ||||||||
\(369\) | −3.23607 | −0.168463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 2.14590 | 0.111260 | ||||||||
\(373\) | −32.7426 | −1.69535 | −0.847675 | − | 0.530516i | \(-0.821998\pi\) | ||||
−0.847675 | + | 0.530516i | \(0.821998\pi\) | |||||||
\(374\) | 6.70820 | 0.346873 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.8541 | 0.559758 | ||||||||
\(377\) | 26.6180 | 1.37090 | ||||||||
\(378\) | 1.23607 | 0.0635765 | ||||||||
\(379\) | −1.23607 | −0.0634925 | −0.0317463 | − | 0.999496i | \(-0.510107\pi\) | ||||
−0.0317463 | + | 0.999496i | \(0.510107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.4164 | −0.687343 | ||||||||
\(382\) | −6.00000 | −0.306987 | ||||||||
\(383\) | 17.8885 | 0.914062 | 0.457031 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457031 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.1246 | 0.871620 | ||||||||
\(387\) | 0.145898 | 0.00741641 | ||||||||
\(388\) | 18.1803 | 0.922967 | ||||||||
\(389\) | 18.2705 | 0.926352 | 0.463176 | − | 0.886266i | \(-0.346710\pi\) | ||||
0.463176 | + | 0.886266i | \(0.346710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.0000 | −0.758583 | ||||||||
\(392\) | 5.47214 | 0.276385 | ||||||||
\(393\) | 17.8885 | 0.902358 | ||||||||
\(394\) | 1.52786 | 0.0769727 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.38197 | 0.0694464 | ||||||||
\(397\) | 32.4721 | 1.62973 | 0.814865 | − | 0.579651i | \(-0.196811\pi\) | ||||
0.814865 | + | 0.579651i | \(0.196811\pi\) | |||||||
\(398\) | 15.6180 | 0.782861 | ||||||||
\(399\) | −7.41641 | −0.371285 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4721 | −0.522954 | −0.261477 | − | 0.965210i | \(-0.584209\pi\) | ||||
−0.261477 | + | 0.965210i | \(0.584209\pi\) | |||||||
\(402\) | −2.38197 | −0.118802 | ||||||||
\(403\) | 6.12461 | 0.305089 | ||||||||
\(404\) | −2.32624 | −0.115735 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.5279 | 0.572118 | ||||||||
\(407\) | 10.8541 | 0.538018 | ||||||||
\(408\) | 4.85410 | 0.240314 | ||||||||
\(409\) | 13.5623 | 0.670613 | 0.335306 | − | 0.942109i | \(-0.391160\pi\) | ||||
0.335306 | + | 0.942109i | \(0.391160\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.61803 | 0.227791 | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | −7.88854 | −0.388170 | ||||||||
\(414\) | −3.09017 | −0.151874 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.85410 | −0.139934 | ||||||||
\(417\) | −21.2361 | −1.03993 | ||||||||
\(418\) | −8.29180 | −0.405565 | ||||||||
\(419\) | −8.94427 | −0.436956 | −0.218478 | − | 0.975842i | \(-0.570109\pi\) | ||||
−0.218478 | + | 0.975842i | \(0.570109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4721 | 0.705329 | 0.352664 | − | 0.935750i | \(-0.385276\pi\) | ||||
0.352664 | + | 0.935750i | \(0.385276\pi\) | |||||||
\(422\) | −3.41641 | −0.166308 | ||||||||
\(423\) | −10.8541 | −0.527744 | ||||||||
\(424\) | 3.23607 | 0.157157 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.94427 | 0.433351 | ||||||||
\(427\) | −16.5836 | −0.802536 | ||||||||
\(428\) | −8.18034 | −0.395412 | ||||||||
\(429\) | 3.94427 | 0.190431 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.7082 | −1.04565 | −0.522824 | − | 0.852441i | \(-0.675121\pi\) | ||||
−0.522824 | + | 0.852441i | \(0.675121\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −0.180340 | −0.00866658 | −0.00433329 | − | 0.999991i | \(-0.501379\pi\) | ||||
−0.00433329 | + | 0.999991i | \(0.501379\pi\) | |||||||
\(434\) | 2.65248 | 0.127323 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.4164 | −0.642529 | ||||||||
\(437\) | 18.5410 | 0.886937 | ||||||||
\(438\) | −12.0000 | −0.573382 | ||||||||
\(439\) | 28.3262 | 1.35194 | 0.675969 | − | 0.736930i | \(-0.263725\pi\) | ||||
0.675969 | + | 0.736930i | \(0.263725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.47214 | −0.260578 | ||||||||
\(442\) | 13.8541 | 0.658972 | ||||||||
\(443\) | 32.6525 | 1.55137 | 0.775683 | − | 0.631123i | \(-0.217406\pi\) | ||||
0.775683 | + | 0.631123i | \(0.217406\pi\) | |||||||
\(444\) | 7.85410 | 0.372739 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.7082 | 1.02791 | ||||||||
\(447\) | −20.4721 | −0.968299 | ||||||||
\(448\) | −1.23607 | −0.0583987 | ||||||||
\(449\) | 2.94427 | 0.138949 | 0.0694744 | − | 0.997584i | \(-0.477868\pi\) | ||||
0.0694744 | + | 0.997584i | \(0.477868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.47214 | −0.210585 | ||||||||
\(452\) | 12.3262 | 0.579777 | ||||||||
\(453\) | −17.8541 | −0.838859 | ||||||||
\(454\) | 16.4721 | 0.773076 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.00000 | −0.280976 | ||||||||
\(457\) | −22.9443 | −1.07329 | −0.536644 | − | 0.843809i | \(-0.680308\pi\) | ||||
−0.536644 | + | 0.843809i | \(0.680308\pi\) | |||||||
\(458\) | 1.70820 | 0.0798191 | ||||||||
\(459\) | −4.85410 | −0.226570 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.9787 | −0.744203 | −0.372101 | − | 0.928192i | \(-0.621363\pi\) | ||||
−0.372101 | + | 0.928192i | \(0.621363\pi\) | |||||||
\(462\) | 1.70820 | 0.0794728 | ||||||||
\(463\) | −2.29180 | −0.106509 | −0.0532544 | − | 0.998581i | \(-0.516959\pi\) | ||||
−0.0532544 | + | 0.998581i | \(0.516959\pi\) | |||||||
\(464\) | 9.32624 | 0.432960 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.32624 | −0.339381 | ||||||||
\(467\) | 2.29180 | 0.106052 | 0.0530258 | − | 0.998593i | \(-0.483113\pi\) | ||||
0.0530258 | + | 0.998593i | \(0.483113\pi\) | |||||||
\(468\) | 2.85410 | 0.131931 | ||||||||
\(469\) | −2.94427 | −0.135954 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.437694 | −0.0201679 | ||||||||
\(472\) | −6.38197 | −0.293754 | ||||||||
\(473\) | 0.201626 | 0.00927078 | ||||||||
\(474\) | 1.14590 | 0.0526328 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | −3.23607 | −0.148169 | ||||||||
\(478\) | 26.6525 | 1.21906 | ||||||||
\(479\) | 6.65248 | 0.303959 | 0.151980 | − | 0.988384i | \(-0.451435\pi\) | ||||
0.151980 | + | 0.988384i | \(0.451435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.4164 | 1.02210 | ||||||||
\(482\) | −0.0901699 | −0.00410713 | ||||||||
\(483\) | −3.81966 | −0.173801 | ||||||||
\(484\) | −9.09017 | −0.413190 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −17.5967 | −0.797385 | −0.398692 | − | 0.917085i | \(-0.630536\pi\) | ||||
−0.398692 | + | 0.917085i | \(0.630536\pi\) | |||||||
\(488\) | −13.4164 | −0.607332 | ||||||||
\(489\) | 20.2705 | 0.916664 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.61803 | 0.118150 | 0.0590751 | − | 0.998254i | \(-0.481185\pi\) | ||||
0.0590751 | + | 0.998254i | \(0.481185\pi\) | |||||||
\(492\) | −3.23607 | −0.145893 | ||||||||
\(493\) | −45.2705 | −2.03888 | ||||||||
\(494\) | −17.1246 | −0.770473 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.14590 | 0.0963537 | ||||||||
\(497\) | 11.0557 | 0.495917 | ||||||||
\(498\) | −8.18034 | −0.366570 | ||||||||
\(499\) | 13.2361 | 0.592528 | 0.296264 | − | 0.955106i | \(-0.404259\pi\) | ||||
0.296264 | + | 0.955106i | \(0.404259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.0902 | −1.03159 | ||||||||
\(502\) | −7.90983 | −0.353033 | ||||||||
\(503\) | −10.4721 | −0.466929 | −0.233465 | − | 0.972365i | \(-0.575006\pi\) | ||||
−0.233465 | + | 0.972365i | \(0.575006\pi\) | |||||||
\(504\) | 1.23607 | 0.0550588 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.27051 | −0.189847 | ||||||||
\(507\) | −4.85410 | −0.215578 | ||||||||
\(508\) | −13.4164 | −0.595257 | ||||||||
\(509\) | 2.94427 | 0.130503 | 0.0652513 | − | 0.997869i | \(-0.479215\pi\) | ||||
0.0652513 | + | 0.997869i | \(0.479215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.8328 | −0.656165 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.00000 | 0.264906 | ||||||||
\(514\) | −23.5066 | −1.03683 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.145898 | 0.00642280 | ||||||||
\(517\) | −15.0000 | −0.659699 | ||||||||
\(518\) | 9.70820 | 0.426554 | ||||||||
\(519\) | −9.23607 | −0.405418 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.18034 | −0.358387 | −0.179194 | − | 0.983814i | \(-0.557349\pi\) | ||||
−0.179194 | + | 0.983814i | \(0.557349\pi\) | |||||||
\(522\) | −9.32624 | −0.408198 | ||||||||
\(523\) | 11.9098 | 0.520781 | 0.260390 | − | 0.965503i | \(-0.416149\pi\) | ||||
0.260390 | + | 0.965503i | \(0.416149\pi\) | |||||||
\(524\) | 17.8885 | 0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.9787 | 0.696705 | ||||||||
\(527\) | −10.4164 | −0.453746 | ||||||||
\(528\) | 1.38197 | 0.0601424 | ||||||||
\(529\) | −13.4508 | −0.584820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.38197 | 0.276954 | ||||||||
\(532\) | −7.41641 | −0.321542 | ||||||||
\(533\) | −9.23607 | −0.400059 | ||||||||
\(534\) | 9.23607 | 0.399684 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.38197 | −0.102885 | ||||||||
\(537\) | 7.41641 | 0.320042 | ||||||||
\(538\) | −22.6180 | −0.975133 | ||||||||
\(539\) | −7.56231 | −0.325732 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7082 | 0.503375 | 0.251688 | − | 0.967809i | \(-0.419014\pi\) | ||||
0.251688 | + | 0.967809i | \(0.419014\pi\) | |||||||
\(542\) | 8.56231 | 0.367783 | ||||||||
\(543\) | 7.41641 | 0.318269 | ||||||||
\(544\) | 4.85410 | 0.208118 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.52786 | 0.150979 | ||||||||
\(547\) | −5.43769 | −0.232499 | −0.116250 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116250 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(548\) | 4.61803 | 0.197273 | ||||||||
\(549\) | 13.4164 | 0.572598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 55.9574 | 2.38387 | ||||||||
\(552\) | −3.09017 | −0.131526 | ||||||||
\(553\) | 1.41641 | 0.0602318 | ||||||||
\(554\) | −14.3607 | −0.610127 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.2361 | −0.900610 | ||||||||
\(557\) | 10.3607 | 0.438996 | 0.219498 | − | 0.975613i | \(-0.429558\pi\) | ||||
0.219498 | + | 0.975613i | \(0.429558\pi\) | |||||||
\(558\) | −2.14590 | −0.0908431 | ||||||||
\(559\) | 0.416408 | 0.0176122 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.70820 | −0.283221 | ||||||||
\(562\) | −22.4721 | −0.947930 | ||||||||
\(563\) | −12.6525 | −0.533238 | −0.266619 | − | 0.963802i | \(-0.585907\pi\) | ||||
−0.266619 | + | 0.963802i | \(0.585907\pi\) | |||||||
\(564\) | −10.8541 | −0.457040 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.0902 | 0.886486 | ||||||||
\(567\) | −1.23607 | −0.0519100 | ||||||||
\(568\) | 8.94427 | 0.375293 | ||||||||
\(569\) | −13.0557 | −0.547325 | −0.273662 | − | 0.961826i | \(-0.588235\pi\) | ||||
−0.273662 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.3607 | 0.517278 | 0.258639 | − | 0.965974i | \(-0.416726\pi\) | ||||
0.258639 | + | 0.965974i | \(0.416726\pi\) | |||||||
\(572\) | 3.94427 | 0.164918 | ||||||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | −4.00000 | −0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 4.11146 | 0.171162 | 0.0855811 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855811 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(578\) | −6.56231 | −0.272956 | ||||||||
\(579\) | −17.1246 | −0.711675 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.1115 | −0.419494 | ||||||||
\(582\) | −18.1803 | −0.753599 | ||||||||
\(583\) | −4.47214 | −0.185217 | ||||||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.5967 | 0.644296 | ||||||||
\(587\) | 18.6525 | 0.769870 | 0.384935 | − | 0.922944i | \(-0.374224\pi\) | ||||
0.384935 | + | 0.922944i | \(0.374224\pi\) | |||||||
\(588\) | −5.47214 | −0.225667 | ||||||||
\(589\) | 12.8754 | 0.530521 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.52786 | −0.0628479 | ||||||||
\(592\) | 7.85410 | 0.322802 | ||||||||
\(593\) | 34.7984 | 1.42900 | 0.714499 | − | 0.699636i | \(-0.246655\pi\) | ||||
0.714499 | + | 0.699636i | \(0.246655\pi\) | |||||||
\(594\) | −1.38197 | −0.0567028 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.4721 | −0.838571 | ||||||||
\(597\) | −15.6180 | −0.639204 | ||||||||
\(598\) | −8.81966 | −0.360663 | ||||||||
\(599\) | −31.8885 | −1.30293 | −0.651465 | − | 0.758678i | \(-0.725845\pi\) | ||||
−0.651465 | + | 0.758678i | \(0.725845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.6869 | 1.65965 | 0.829827 | − | 0.558021i | \(-0.188439\pi\) | ||||
0.829827 | + | 0.558021i | \(0.188439\pi\) | |||||||
\(602\) | 0.180340 | 0.00735011 | ||||||||
\(603\) | 2.38197 | 0.0970012 | ||||||||
\(604\) | −17.8541 | −0.726473 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.32624 | 0.0944970 | ||||||||
\(607\) | −47.4164 | −1.92457 | −0.962286 | − | 0.272039i | \(-0.912302\pi\) | ||||
−0.962286 | + | 0.272039i | \(0.912302\pi\) | |||||||
\(608\) | −6.00000 | −0.243332 | ||||||||
\(609\) | −11.5279 | −0.467133 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.9787 | −1.25326 | ||||||||
\(612\) | −4.85410 | −0.196215 | ||||||||
\(613\) | 37.7771 | 1.52580 | 0.762901 | − | 0.646515i | \(-0.223774\pi\) | ||||
0.762901 | + | 0.646515i | \(0.223774\pi\) | |||||||
\(614\) | 33.0902 | 1.33541 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.70820 | 0.0688255 | ||||||||
\(617\) | −31.3050 | −1.26029 | −0.630145 | − | 0.776478i | \(-0.717005\pi\) | ||||
−0.630145 | + | 0.776478i | \(0.717005\pi\) | |||||||
\(618\) | 4.00000 | 0.160904 | ||||||||
\(619\) | −47.7082 | −1.91755 | −0.958777 | − | 0.284159i | \(-0.908286\pi\) | ||||
−0.958777 | + | 0.284159i | \(0.908286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.09017 | 0.124004 | ||||||||
\(622\) | 4.47214 | 0.179316 | ||||||||
\(623\) | 11.4164 | 0.457389 | ||||||||
\(624\) | 2.85410 | 0.114256 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.9443 | −1.23678 | ||||||||
\(627\) | 8.29180 | 0.331142 | ||||||||
\(628\) | −0.437694 | −0.0174659 | ||||||||
\(629\) | −38.1246 | −1.52013 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.0344 | −0.598512 | −0.299256 | − | 0.954173i | \(-0.596738\pi\) | ||||
−0.299256 | + | 0.954173i | \(0.596738\pi\) | |||||||
\(632\) | 1.14590 | 0.0455814 | ||||||||
\(633\) | 3.41641 | 0.135790 | ||||||||
\(634\) | −9.70820 | −0.385562 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.23607 | −0.128318 | ||||||||
\(637\) | −15.6180 | −0.618809 | ||||||||
\(638\) | −12.8885 | −0.510262 | ||||||||
\(639\) | −8.94427 | −0.353830 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.6525 | −1.21070 | −0.605350 | − | 0.795959i | \(-0.706967\pi\) | ||||
−0.605350 | + | 0.795959i | \(0.706967\pi\) | |||||||
\(642\) | 8.18034 | 0.322852 | ||||||||
\(643\) | −31.5623 | −1.24470 | −0.622348 | − | 0.782741i | \(-0.713821\pi\) | ||||
−0.622348 | + | 0.782741i | \(0.713821\pi\) | |||||||
\(644\) | −3.81966 | −0.150516 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29.1246 | 1.14589 | ||||||||
\(647\) | 12.6180 | 0.496066 | 0.248033 | − | 0.968752i | \(-0.420216\pi\) | ||||
0.248033 | + | 0.968752i | \(0.420216\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 8.81966 | 0.346202 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.65248 | −0.103959 | ||||||||
\(652\) | 20.2705 | 0.793854 | ||||||||
\(653\) | −9.88854 | −0.386969 | −0.193484 | − | 0.981103i | \(-0.561979\pi\) | ||||
−0.193484 | + | 0.981103i | \(0.561979\pi\) | |||||||
\(654\) | 13.4164 | 0.524623 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.23607 | −0.126347 | ||||||||
\(657\) | 12.0000 | 0.468165 | ||||||||
\(658\) | −13.4164 | −0.523026 | ||||||||
\(659\) | 2.02129 | 0.0787381 | 0.0393691 | − | 0.999225i | \(-0.487465\pi\) | ||||
0.0393691 | + | 0.999225i | \(0.487465\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.70820 | 0.222023 | 0.111012 | − | 0.993819i | \(-0.464591\pi\) | ||||
0.111012 | + | 0.993819i | \(0.464591\pi\) | |||||||
\(662\) | 21.4164 | 0.832372 | ||||||||
\(663\) | −13.8541 | −0.538049 | ||||||||
\(664\) | −8.18034 | −0.317459 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.85410 | −0.304340 | ||||||||
\(667\) | 28.8197 | 1.11590 | ||||||||
\(668\) | −23.0902 | −0.893385 | ||||||||
\(669\) | −21.7082 | −0.839288 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.5410 | 0.715768 | ||||||||
\(672\) | 1.23607 | 0.0476824 | ||||||||
\(673\) | 47.3050 | 1.82347 | 0.911736 | − | 0.410777i | \(-0.134742\pi\) | ||||
0.911736 | + | 0.410777i | \(0.134742\pi\) | |||||||
\(674\) | 12.9443 | 0.498595 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.85410 | −0.186696 | ||||||||
\(677\) | 31.2361 | 1.20050 | 0.600250 | − | 0.799813i | \(-0.295068\pi\) | ||||
0.600250 | + | 0.799813i | \(0.295068\pi\) | |||||||
\(678\) | −12.3262 | −0.473386 | ||||||||
\(679\) | −22.4721 | −0.862401 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.4721 | −0.631214 | ||||||||
\(682\) | −2.96556 | −0.113557 | ||||||||
\(683\) | 10.7639 | 0.411870 | 0.205935 | − | 0.978566i | \(-0.433976\pi\) | ||||
0.205935 | + | 0.978566i | \(0.433976\pi\) | |||||||
\(684\) | 6.00000 | 0.229416 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.4164 | −0.588601 | ||||||||
\(687\) | −1.70820 | −0.0651720 | ||||||||
\(688\) | 0.145898 | 0.00556231 | ||||||||
\(689\) | −9.23607 | −0.351866 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.7639 | 1.01815 | 0.509074 | − | 0.860723i | \(-0.329988\pi\) | ||||
0.509074 | + | 0.860723i | \(0.329988\pi\) | |||||||
\(692\) | −9.23607 | −0.351103 | ||||||||
\(693\) | −1.70820 | −0.0648893 | ||||||||
\(694\) | −24.3607 | −0.924719 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.32624 | −0.353510 | ||||||||
\(697\) | 15.7082 | 0.594991 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.32624 | 0.277104 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.2148 | 0.461346 | 0.230673 | − | 0.973031i | \(-0.425907\pi\) | ||||
0.230673 | + | 0.973031i | \(0.425907\pi\) | |||||||
\(702\) | −2.85410 | −0.107721 | ||||||||
\(703\) | 47.1246 | 1.77734 | ||||||||
\(704\) | 1.38197 | 0.0520848 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.20163 | −0.0452238 | ||||||||
\(707\) | 2.87539 | 0.108140 | ||||||||
\(708\) | 6.38197 | 0.239849 | ||||||||
\(709\) | −6.87539 | −0.258211 | −0.129105 | − | 0.991631i | \(-0.541211\pi\) | ||||
−0.129105 | + | 0.991631i | \(0.541211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.14590 | −0.0429745 | ||||||||
\(712\) | 9.23607 | 0.346136 | ||||||||
\(713\) | 6.63119 | 0.248340 | ||||||||
\(714\) | −6.00000 | −0.224544 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.41641 | 0.277164 | ||||||||
\(717\) | −26.6525 | −0.995355 | ||||||||
\(718\) | −23.8885 | −0.891513 | ||||||||
\(719\) | −7.23607 | −0.269860 | −0.134930 | − | 0.990855i | \(-0.543081\pi\) | ||||
−0.134930 | + | 0.990855i | \(0.543081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.94427 | 0.184134 | ||||||||
\(722\) | −17.0000 | −0.632674 | ||||||||
\(723\) | 0.0901699 | 0.00335346 | ||||||||
\(724\) | 7.41641 | 0.275629 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.09017 | 0.337368 | ||||||||
\(727\) | −7.34752 | −0.272505 | −0.136252 | − | 0.990674i | \(-0.543506\pi\) | ||||
−0.136252 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(728\) | 3.52786 | 0.130751 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.708204 | −0.0261939 | ||||||||
\(732\) | 13.4164 | 0.495885 | ||||||||
\(733\) | −34.6869 | −1.28119 | −0.640595 | − | 0.767879i | \(-0.721312\pi\) | ||||
−0.640595 | + | 0.767879i | \(0.721312\pi\) | |||||||
\(734\) | −10.2918 | −0.379877 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.09017 | −0.113905 | ||||||||
\(737\) | 3.29180 | 0.121255 | ||||||||
\(738\) | 3.23607 | 0.119121 | ||||||||
\(739\) | 8.65248 | 0.318286 | 0.159143 | − | 0.987256i | \(-0.449127\pi\) | ||||
0.159143 | + | 0.987256i | \(0.449127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.1246 | 0.629088 | ||||||||
\(742\) | −4.00000 | −0.146845 | ||||||||
\(743\) | 19.6180 | 0.719716 | 0.359858 | − | 0.933007i | \(-0.382825\pi\) | ||||
0.359858 | + | 0.933007i | \(0.382825\pi\) | |||||||
\(744\) | −2.14590 | −0.0786724 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32.7426 | 1.19879 | ||||||||
\(747\) | 8.18034 | 0.299303 | ||||||||
\(748\) | −6.70820 | −0.245276 | ||||||||
\(749\) | 10.1115 | 0.369465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.4164 | −1.58429 | −0.792144 | − | 0.610335i | \(-0.791035\pi\) | ||||
−0.792144 | + | 0.610335i | \(0.791035\pi\) | |||||||
\(752\) | −10.8541 | −0.395808 | ||||||||
\(753\) | 7.90983 | 0.288250 | ||||||||
\(754\) | −26.6180 | −0.969372 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.23607 | −0.0449554 | ||||||||
\(757\) | −4.83282 | −0.175652 | −0.0878258 | − | 0.996136i | \(-0.527992\pi\) | ||||
−0.0878258 | + | 0.996136i | \(0.527992\pi\) | |||||||
\(758\) | 1.23607 | 0.0448960 | ||||||||
\(759\) | 4.27051 | 0.155010 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.6525 | −1.18365 | −0.591826 | − | 0.806066i | \(-0.701593\pi\) | ||||
−0.591826 | + | 0.806066i | \(0.701593\pi\) | |||||||
\(762\) | 13.4164 | 0.486025 | ||||||||
\(763\) | 16.5836 | 0.600366 | ||||||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.8885 | −0.646339 | ||||||||
\(767\) | 18.2148 | 0.657698 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −22.9230 | −0.826624 | −0.413312 | − | 0.910589i | \(-0.635628\pi\) | ||||
−0.413312 | + | 0.910589i | \(0.635628\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.5066 | 0.846569 | ||||||||
\(772\) | −17.1246 | −0.616328 | ||||||||
\(773\) | 6.47214 | 0.232787 | 0.116393 | − | 0.993203i | \(-0.462867\pi\) | ||||
0.116393 | + | 0.993203i | \(0.462867\pi\) | |||||||
\(774\) | −0.145898 | −0.00524420 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.1803 | −0.652636 | ||||||||
\(777\) | −9.70820 | −0.348280 | ||||||||
\(778\) | −18.2705 | −0.655030 | ||||||||
\(779\) | −19.4164 | −0.695665 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3607 | −0.442300 | ||||||||
\(782\) | 15.0000 | 0.536399 | ||||||||
\(783\) | 9.32624 | 0.333293 | ||||||||
\(784\) | −5.47214 | −0.195433 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.8885 | −0.638063 | ||||||||
\(787\) | 38.5623 | 1.37460 | 0.687299 | − | 0.726375i | \(-0.258796\pi\) | ||||
0.687299 | + | 0.726375i | \(0.258796\pi\) | |||||||
\(788\) | −1.52786 | −0.0544279 | ||||||||
\(789\) | −15.9787 | −0.568857 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.2361 | −0.541732 | ||||||||
\(792\) | −1.38197 | −0.0491060 | ||||||||
\(793\) | 38.2918 | 1.35978 | ||||||||
\(794\) | −32.4721 | −1.15239 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.6180 | −0.553567 | ||||||||
\(797\) | −34.4721 | −1.22107 | −0.610533 | − | 0.791991i | \(-0.709045\pi\) | ||||
−0.610533 | + | 0.791991i | \(0.709045\pi\) | |||||||
\(798\) | 7.41641 | 0.262538 | ||||||||
\(799\) | 52.6869 | 1.86393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.23607 | −0.326340 | ||||||||
\(802\) | 10.4721 | 0.369784 | ||||||||
\(803\) | 16.5836 | 0.585222 | ||||||||
\(804\) | 2.38197 | 0.0840055 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.12461 | −0.215730 | ||||||||
\(807\) | 22.6180 | 0.796193 | ||||||||
\(808\) | 2.32624 | 0.0818368 | ||||||||
\(809\) | −29.5279 | −1.03814 | −0.519072 | − | 0.854730i | \(-0.673722\pi\) | ||||
−0.519072 | + | 0.854730i | \(0.673722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.0000 | −1.19390 | −0.596951 | − | 0.802278i | \(-0.703621\pi\) | ||||
−0.596951 | + | 0.802278i | \(0.703621\pi\) | |||||||
\(812\) | −11.5279 | −0.404549 | ||||||||
\(813\) | −8.56231 | −0.300293 | ||||||||
\(814\) | −10.8541 | −0.380436 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.85410 | −0.169928 | ||||||||
\(817\) | 0.875388 | 0.0306260 | ||||||||
\(818\) | −13.5623 | −0.474195 | ||||||||
\(819\) | −3.52786 | −0.123274 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.2148 | 1.26390 | 0.631952 | − | 0.775007i | \(-0.282254\pi\) | ||||
0.631952 | + | 0.775007i | \(0.282254\pi\) | |||||||
\(822\) | −4.61803 | −0.161072 | ||||||||
\(823\) | −15.1246 | −0.527211 | −0.263605 | − | 0.964631i | \(-0.584912\pi\) | ||||
−0.263605 | + | 0.964631i | \(0.584912\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.88854 | 0.274478 | ||||||||
\(827\) | −18.0000 | −0.625921 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(828\) | 3.09017 | 0.107391 | ||||||||
\(829\) | 34.1803 | 1.18713 | 0.593566 | − | 0.804785i | \(-0.297720\pi\) | ||||
0.593566 | + | 0.804785i | \(0.297720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.3607 | 0.498166 | ||||||||
\(832\) | 2.85410 | 0.0989482 | ||||||||
\(833\) | 26.5623 | 0.920329 | ||||||||
\(834\) | 21.2361 | 0.735345 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.29180 | 0.286778 | ||||||||
\(837\) | 2.14590 | 0.0741731 | ||||||||
\(838\) | 8.94427 | 0.308975 | ||||||||
\(839\) | −11.1246 | −0.384064 | −0.192032 | − | 0.981389i | \(-0.561508\pi\) | ||||
−0.192032 | + | 0.981389i | \(0.561508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.9787 | 1.99927 | ||||||||
\(842\) | −14.4721 | −0.498743 | ||||||||
\(843\) | 22.4721 | 0.773981 | ||||||||
\(844\) | 3.41641 | 0.117598 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.8541 | 0.373172 | ||||||||
\(847\) | 11.2361 | 0.386076 | ||||||||
\(848\) | −3.23607 | −0.111127 | ||||||||
\(849\) | −21.0902 | −0.723813 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.2705 | 0.831982 | ||||||||
\(852\) | −8.94427 | −0.306426 | ||||||||
\(853\) | −29.0902 | −0.996028 | −0.498014 | − | 0.867169i | \(-0.665937\pi\) | ||||
−0.498014 | + | 0.867169i | \(0.665937\pi\) | |||||||
\(854\) | 16.5836 | 0.567479 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.18034 | 0.279598 | ||||||||
\(857\) | 12.3262 | 0.421056 | 0.210528 | − | 0.977588i | \(-0.432482\pi\) | ||||
0.210528 | + | 0.977588i | \(0.432482\pi\) | |||||||
\(858\) | −3.94427 | −0.134655 | ||||||||
\(859\) | −15.7082 | −0.535957 | −0.267979 | − | 0.963425i | \(-0.586356\pi\) | ||||
−0.267979 | + | 0.963425i | \(0.586356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | 21.7082 | 0.739384 | ||||||||
\(863\) | −8.56231 | −0.291464 | −0.145732 | − | 0.989324i | \(-0.546554\pi\) | ||||
−0.145732 | + | 0.989324i | \(0.546554\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.180340 | 0.00612820 | ||||||||
\(867\) | 6.56231 | 0.222868 | ||||||||
\(868\) | −2.65248 | −0.0900309 | ||||||||
\(869\) | −1.58359 | −0.0537197 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.79837 | 0.230354 | ||||||||
\(872\) | 13.4164 | 0.454337 | ||||||||
\(873\) | 18.1803 | 0.615311 | ||||||||
\(874\) | −18.5410 | −0.627159 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | 26.3951 | 0.891300 | 0.445650 | − | 0.895207i | \(-0.352973\pi\) | ||||
0.445650 | + | 0.895207i | \(0.352973\pi\) | |||||||
\(878\) | −28.3262 | −0.955964 | ||||||||
\(879\) | −15.5967 | −0.526065 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.05573 | −0.170332 | −0.0851659 | − | 0.996367i | \(-0.527142\pi\) | ||||
−0.0851659 | + | 0.996367i | \(0.527142\pi\) | |||||||
\(882\) | 5.47214 | 0.184256 | ||||||||
\(883\) | 46.9787 | 1.58096 | 0.790480 | − | 0.612488i | \(-0.209831\pi\) | ||||
0.790480 | + | 0.612488i | \(0.209831\pi\) | |||||||
\(884\) | −13.8541 | −0.465964 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.6525 | −1.09698 | ||||||||
\(887\) | 54.4721 | 1.82900 | 0.914498 | − | 0.404591i | \(-0.132586\pi\) | ||||
0.914498 | + | 0.404591i | \(0.132586\pi\) | |||||||
\(888\) | −7.85410 | −0.263566 | ||||||||
\(889\) | 16.5836 | 0.556196 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.38197 | 0.0462976 | ||||||||
\(892\) | −21.7082 | −0.726844 | ||||||||
\(893\) | −65.1246 | −2.17931 | ||||||||
\(894\) | 20.4721 | 0.684691 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.23607 | 0.0412941 | ||||||||
\(897\) | 8.81966 | 0.294480 | ||||||||
\(898\) | −2.94427 | −0.0982516 | ||||||||
\(899\) | 20.0132 | 0.667476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7082 | 0.523316 | ||||||||
\(902\) | 4.47214 | 0.148906 | ||||||||
\(903\) | −0.180340 | −0.00600134 | ||||||||
\(904\) | −12.3262 | −0.409965 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.8541 | 0.593163 | ||||||||
\(907\) | 23.1459 | 0.768547 | 0.384273 | − | 0.923219i | \(-0.374452\pi\) | ||||
0.384273 | + | 0.923219i | \(0.374452\pi\) | |||||||
\(908\) | −16.4721 | −0.546647 | ||||||||
\(909\) | −2.32624 | −0.0771564 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5279 | 1.24335 | 0.621677 | − | 0.783274i | \(-0.286452\pi\) | ||||
0.621677 | + | 0.783274i | \(0.286452\pi\) | |||||||
\(912\) | 6.00000 | 0.198680 | ||||||||
\(913\) | 11.3050 | 0.374139 | ||||||||
\(914\) | 22.9443 | 0.758929 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.70820 | −0.0564406 | ||||||||
\(917\) | −22.1115 | −0.730185 | ||||||||
\(918\) | 4.85410 | 0.160209 | ||||||||
\(919\) | 21.8885 | 0.722036 | 0.361018 | − | 0.932559i | \(-0.382429\pi\) | ||||
0.361018 | + | 0.932559i | \(0.382429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.0902 | −1.09036 | ||||||||
\(922\) | 15.9787 | 0.526231 | ||||||||
\(923\) | −25.5279 | −0.840260 | ||||||||
\(924\) | −1.70820 | −0.0561958 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.29180 | 0.0753131 | ||||||||
\(927\) | −4.00000 | −0.131377 | ||||||||
\(928\) | −9.32624 | −0.306149 | ||||||||
\(929\) | −24.5410 | −0.805165 | −0.402582 | − | 0.915384i | \(-0.631887\pi\) | ||||
−0.402582 | + | 0.915384i | \(0.631887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.8328 | −1.07605 | ||||||||
\(932\) | 7.32624 | 0.239979 | ||||||||
\(933\) | −4.47214 | −0.146411 | ||||||||
\(934\) | −2.29180 | −0.0749899 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.85410 | −0.0932892 | ||||||||
\(937\) | −27.4164 | −0.895655 | −0.447828 | − | 0.894120i | \(-0.647802\pi\) | ||||
−0.447828 | + | 0.894120i | \(0.647802\pi\) | |||||||
\(938\) | 2.94427 | 0.0961339 | ||||||||
\(939\) | 30.9443 | 1.00983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.4508 | −0.731877 | −0.365938 | − | 0.930639i | \(-0.619252\pi\) | ||||
−0.365938 | + | 0.930639i | \(0.619252\pi\) | |||||||
\(942\) | 0.437694 | 0.0142608 | ||||||||
\(943\) | −10.0000 | −0.325645 | ||||||||
\(944\) | 6.38197 | 0.207715 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.201626 | −0.00655543 | ||||||||
\(947\) | −55.3050 | −1.79717 | −0.898585 | − | 0.438800i | \(-0.855404\pi\) | ||||
−0.898585 | + | 0.438800i | \(0.855404\pi\) | |||||||
\(948\) | −1.14590 | −0.0372170 | ||||||||
\(949\) | 34.2492 | 1.11178 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.70820 | 0.314810 | ||||||||
\(952\) | −6.00000 | −0.194461 | ||||||||
\(953\) | −1.63932 | −0.0531028 | −0.0265514 | − | 0.999647i | \(-0.508453\pi\) | ||||
−0.0265514 | + | 0.999647i | \(0.508453\pi\) | |||||||
\(954\) | 3.23607 | 0.104772 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.6525 | −0.862003 | ||||||||
\(957\) | 12.8885 | 0.416627 | ||||||||
\(958\) | −6.65248 | −0.214932 | ||||||||
\(959\) | −5.70820 | −0.184328 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3951 | −0.851456 | ||||||||
\(962\) | −22.4164 | −0.722734 | ||||||||
\(963\) | −8.18034 | −0.263608 | ||||||||
\(964\) | 0.0901699 | 0.00290418 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.81966 | 0.122896 | ||||||||
\(967\) | 39.0132 | 1.25458 | 0.627289 | − | 0.778786i | \(-0.284164\pi\) | ||||
0.627289 | + | 0.778786i | \(0.284164\pi\) | |||||||
\(968\) | 9.09017 | 0.292169 | ||||||||
\(969\) | −29.1246 | −0.935617 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.0902 | 1.67165 | 0.835827 | − | 0.548994i | \(-0.184989\pi\) | ||||
0.835827 | + | 0.548994i | \(0.184989\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 26.2492 | 0.841511 | ||||||||
\(974\) | 17.5967 | 0.563836 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.4164 | 0.429449 | ||||||||
\(977\) | −54.2837 | −1.73669 | −0.868344 | − | 0.495962i | \(-0.834815\pi\) | ||||
−0.868344 | + | 0.495962i | \(0.834815\pi\) | |||||||
\(978\) | −20.2705 | −0.648179 | ||||||||
\(979\) | −12.7639 | −0.407937 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.4164 | −0.428353 | ||||||||
\(982\) | −2.61803 | −0.0835448 | ||||||||
\(983\) | −24.9787 | −0.796697 | −0.398349 | − | 0.917234i | \(-0.630417\pi\) | ||||
−0.398349 | + | 0.917234i | \(0.630417\pi\) | |||||||
\(984\) | 3.23607 | 0.103162 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 45.2705 | 1.44171 | ||||||||
\(987\) | 13.4164 | 0.427049 | ||||||||
\(988\) | 17.1246 | 0.544806 | ||||||||
\(989\) | 0.450850 | 0.0143362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.68692 | −0.275949 | −0.137975 | − | 0.990436i | \(-0.544059\pi\) | ||||
−0.137975 | + | 0.990436i | \(0.544059\pi\) | |||||||
\(992\) | −2.14590 | −0.0681323 | ||||||||
\(993\) | −21.4164 | −0.679629 | ||||||||
\(994\) | −11.0557 | −0.350666 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.18034 | 0.259204 | ||||||||
\(997\) | −38.2705 | −1.21204 | −0.606020 | − | 0.795450i | \(-0.707235\pi\) | ||||
−0.606020 | + | 0.795450i | \(0.707235\pi\) | |||||||
\(998\) | −13.2361 | −0.418980 | ||||||||
\(999\) | 7.85410 | 0.248493 |
(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 | 750.2.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 2250.2.a.n.1.1 | 2 | |||
4.3 | odd | 2 | 6000.2.a.d.1.2 | 2 | |||
5.2 | odd | 4 | 750.2.c.b.499.1 | 4 | |||
5.3 | odd | 4 | 750.2.c.b.499.4 | 4 | |||
5.4 | even | 2 | 750.2.a.f.1.2 | yes | 2 | ||
15.2 | even | 4 | 2250.2.c.b.1999.3 | 4 | |||
15.8 | even | 4 | 2250.2.c.b.1999.2 | 4 | |||
15.14 | odd | 2 | 2250.2.a.c.1.2 | 2 | |||
20.3 | even | 4 | 6000.2.f.a.1249.1 | 4 | |||
20.7 | even | 4 | 6000.2.f.a.1249.4 | 4 | |||
20.19 | odd | 2 | 6000.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
750.2.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
750.2.a.f.1.2 | yes | 2 | 5.4 | even | 2 | ||
750.2.c.b.499.1 | 4 | 5.2 | odd | 4 | |||
750.2.c.b.499.4 | 4 | 5.3 | odd | 4 | |||
2250.2.a.c.1.2 | 2 | 15.14 | odd | 2 | |||
2250.2.a.n.1.1 | 2 | 3.2 | odd | 2 | |||
2250.2.c.b.1999.2 | 4 | 15.8 | even | 4 | |||
2250.2.c.b.1999.3 | 4 | 15.2 | even | 4 | |||
6000.2.a.d.1.2 | 2 | 4.3 | odd | 2 | |||
6000.2.a.y.1.1 | 2 | 20.19 | odd | 2 | |||
6000.2.f.a.1249.1 | 4 | 20.3 | even | 4 | |||
6000.2.f.a.1249.4 | 4 | 20.7 | even | 4 |