Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 16x^{7} + 37x^{6} + 97x^{5} - 72x^{4} - 182x^{3} + 24x^{2} + 70x - 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.14979\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(5\) | −1.03642 | −0.463502 | −0.231751 | − | 0.972775i | \(-0.574445\pi\) | ||||
−0.231751 | + | 0.972775i | \(0.574445\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.58814 | 0.978225 | 0.489112 | − | 0.872221i | \(-0.337321\pi\) | ||||
0.489112 | + | 0.872221i | \(0.337321\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.03642 | 0.327745 | ||||||||
\(11\) | 0.328441 | 0.0990288 | 0.0495144 | − | 0.998773i | \(-0.484233\pi\) | ||||
0.0495144 | + | 0.998773i | \(0.484233\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.550837 | −0.152775 | −0.0763873 | − | 0.997078i | \(-0.524339\pi\) | ||||
−0.0763873 | + | 0.997078i | \(0.524339\pi\) | |||||||
\(14\) | −2.58814 | −0.691709 | ||||||||
\(15\) | 1.03642 | 0.267603 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.668814 | −0.153436 | −0.0767182 | − | 0.997053i | \(-0.524444\pi\) | ||||
−0.0767182 | + | 0.997053i | \(0.524444\pi\) | |||||||
\(20\) | −1.03642 | −0.231751 | ||||||||
\(21\) | −2.58814 | −0.564778 | ||||||||
\(22\) | −0.328441 | −0.0700239 | ||||||||
\(23\) | 2.85502 | 0.595313 | 0.297657 | − | 0.954673i | \(-0.403795\pi\) | ||||
0.297657 | + | 0.954673i | \(0.403795\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.92583 | −0.785166 | ||||||||
\(26\) | 0.550837 | 0.108028 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.58814 | 0.489112 | ||||||||
\(29\) | 4.26895 | 0.792724 | 0.396362 | − | 0.918094i | \(-0.370273\pi\) | ||||
0.396362 | + | 0.918094i | \(0.370273\pi\) | |||||||
\(30\) | −1.03642 | −0.189224 | ||||||||
\(31\) | −1.05963 | −0.190316 | −0.0951579 | − | 0.995462i | \(-0.530336\pi\) | ||||
−0.0951579 | + | 0.995462i | \(0.530336\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.328441 | −0.0571743 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −2.68240 | −0.453409 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.8012 | −1.77570 | −0.887851 | − | 0.460131i | \(-0.847802\pi\) | ||||
−0.887851 | + | 0.460131i | \(0.847802\pi\) | |||||||
\(38\) | 0.668814 | 0.108496 | ||||||||
\(39\) | 0.550837 | 0.0882045 | ||||||||
\(40\) | 1.03642 | 0.163873 | ||||||||
\(41\) | 0.525599 | 0.0820848 | 0.0410424 | − | 0.999157i | \(-0.486932\pi\) | ||||
0.0410424 | + | 0.999157i | \(0.486932\pi\) | |||||||
\(42\) | 2.58814 | 0.399359 | ||||||||
\(43\) | −5.46997 | −0.834162 | −0.417081 | − | 0.908869i | \(-0.636947\pi\) | ||||
−0.417081 | + | 0.908869i | \(0.636947\pi\) | |||||||
\(44\) | 0.328441 | 0.0495144 | ||||||||
\(45\) | −1.03642 | −0.154501 | ||||||||
\(46\) | −2.85502 | −0.420950 | ||||||||
\(47\) | −3.44760 | −0.502885 | −0.251442 | − | 0.967872i | \(-0.580905\pi\) | ||||
−0.251442 | + | 0.967872i | \(0.580905\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −0.301536 | −0.0430765 | ||||||||
\(50\) | 3.92583 | 0.555196 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −0.550837 | −0.0763873 | ||||||||
\(53\) | 7.70645 | 1.05856 | 0.529281 | − | 0.848446i | \(-0.322462\pi\) | ||||
0.529281 | + | 0.848446i | \(0.322462\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.340403 | −0.0459000 | ||||||||
\(56\) | −2.58814 | −0.345855 | ||||||||
\(57\) | 0.668814 | 0.0885866 | ||||||||
\(58\) | −4.26895 | −0.560540 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 1.03642 | 0.133801 | ||||||||
\(61\) | 4.66400 | 0.597164 | 0.298582 | − | 0.954384i | \(-0.403486\pi\) | ||||
0.298582 | + | 0.954384i | \(0.403486\pi\) | |||||||
\(62\) | 1.05963 | 0.134574 | ||||||||
\(63\) | 2.58814 | 0.326075 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.570899 | 0.0708113 | ||||||||
\(66\) | 0.328441 | 0.0404283 | ||||||||
\(67\) | −1.71988 | −0.210117 | −0.105058 | − | 0.994466i | \(-0.533503\pi\) | ||||
−0.105058 | + | 0.994466i | \(0.533503\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −2.85502 | −0.343704 | ||||||||
\(70\) | 2.68240 | 0.320608 | ||||||||
\(71\) | 1.62984 | 0.193427 | 0.0967134 | − | 0.995312i | \(-0.469167\pi\) | ||||
0.0967134 | + | 0.995312i | \(0.469167\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −15.3355 | −1.79488 | −0.897441 | − | 0.441134i | \(-0.854576\pi\) | ||||
−0.897441 | + | 0.441134i | \(0.854576\pi\) | |||||||
\(74\) | 10.8012 | 1.25561 | ||||||||
\(75\) | 3.92583 | 0.453316 | ||||||||
\(76\) | −0.668814 | −0.0767182 | ||||||||
\(77\) | 0.850052 | 0.0968724 | ||||||||
\(78\) | −0.550837 | −0.0623700 | ||||||||
\(79\) | −2.43182 | −0.273601 | −0.136800 | − | 0.990599i | \(-0.543682\pi\) | ||||
−0.136800 | + | 0.990599i | \(0.543682\pi\) | |||||||
\(80\) | −1.03642 | −0.115875 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.525599 | −0.0580427 | ||||||||
\(83\) | −10.0619 | −1.10444 | −0.552218 | − | 0.833700i | \(-0.686218\pi\) | ||||
−0.552218 | + | 0.833700i | \(0.686218\pi\) | |||||||
\(84\) | −2.58814 | −0.282389 | ||||||||
\(85\) | −1.03642 | −0.112416 | ||||||||
\(86\) | 5.46997 | 0.589842 | ||||||||
\(87\) | −4.26895 | −0.457679 | ||||||||
\(88\) | −0.328441 | −0.0350120 | ||||||||
\(89\) | 2.38147 | 0.252435 | 0.126218 | − | 0.992003i | \(-0.459716\pi\) | ||||
0.126218 | + | 0.992003i | \(0.459716\pi\) | |||||||
\(90\) | 1.03642 | 0.109248 | ||||||||
\(91\) | −1.42564 | −0.149448 | ||||||||
\(92\) | 2.85502 | 0.297657 | ||||||||
\(93\) | 1.05963 | 0.109879 | ||||||||
\(94\) | 3.44760 | 0.355593 | ||||||||
\(95\) | 0.693173 | 0.0711180 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −6.24513 | −0.634097 | −0.317048 | − | 0.948409i | \(-0.602692\pi\) | ||||
−0.317048 | + | 0.948409i | \(0.602692\pi\) | |||||||
\(98\) | 0.301536 | 0.0304597 | ||||||||
\(99\) | 0.328441 | 0.0330096 | ||||||||
\(100\) | −3.92583 | −0.392583 | ||||||||
\(101\) | 11.5557 | 1.14983 | 0.574916 | − | 0.818212i | \(-0.305035\pi\) | ||||
0.574916 | + | 0.818212i | \(0.305035\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 12.9285 | 1.27388 | 0.636940 | − | 0.770913i | \(-0.280200\pi\) | ||||
0.636940 | + | 0.770913i | \(0.280200\pi\) | |||||||
\(104\) | 0.550837 | 0.0540140 | ||||||||
\(105\) | 2.68240 | 0.261776 | ||||||||
\(106\) | −7.70645 | −0.748517 | ||||||||
\(107\) | 16.3152 | 1.57725 | 0.788626 | − | 0.614874i | \(-0.210793\pi\) | ||||
0.788626 | + | 0.614874i | \(0.210793\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −12.8397 | −1.22982 | −0.614910 | − | 0.788597i | \(-0.710808\pi\) | ||||
−0.614910 | + | 0.788597i | \(0.710808\pi\) | |||||||
\(110\) | 0.340403 | 0.0324562 | ||||||||
\(111\) | 10.8012 | 1.02520 | ||||||||
\(112\) | 2.58814 | 0.244556 | ||||||||
\(113\) | −7.28064 | −0.684905 | −0.342453 | − | 0.939535i | \(-0.611258\pi\) | ||||
−0.342453 | + | 0.939535i | \(0.611258\pi\) | |||||||
\(114\) | −0.668814 | −0.0626402 | ||||||||
\(115\) | −2.95900 | −0.275929 | ||||||||
\(116\) | 4.26895 | 0.396362 | ||||||||
\(117\) | −0.550837 | −0.0509249 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | 2.58814 | 0.237254 | ||||||||
\(120\) | −1.03642 | −0.0946119 | ||||||||
\(121\) | −10.8921 | −0.990193 | ||||||||
\(122\) | −4.66400 | −0.422258 | ||||||||
\(123\) | −0.525599 | −0.0473917 | ||||||||
\(124\) | −1.05963 | −0.0951579 | ||||||||
\(125\) | 9.25092 | 0.827427 | ||||||||
\(126\) | −2.58814 | −0.230570 | ||||||||
\(127\) | −5.99189 | −0.531695 | −0.265847 | − | 0.964015i | \(-0.585652\pi\) | ||||
−0.265847 | + | 0.964015i | \(0.585652\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.46997 | 0.481604 | ||||||||
\(130\) | −0.570899 | −0.0500711 | ||||||||
\(131\) | −19.2336 | −1.68045 | −0.840224 | − | 0.542240i | \(-0.817576\pi\) | ||||
−0.840224 | + | 0.542240i | \(0.817576\pi\) | |||||||
\(132\) | −0.328441 | −0.0285871 | ||||||||
\(133\) | −1.73098 | −0.150095 | ||||||||
\(134\) | 1.71988 | 0.148575 | ||||||||
\(135\) | 1.03642 | 0.0892009 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 11.8369 | 1.01129 | 0.505647 | − | 0.862741i | \(-0.331254\pi\) | ||||
0.505647 | + | 0.862741i | \(0.331254\pi\) | |||||||
\(138\) | 2.85502 | 0.243036 | ||||||||
\(139\) | 10.1241 | 0.858712 | 0.429356 | − | 0.903135i | \(-0.358741\pi\) | ||||
0.429356 | + | 0.903135i | \(0.358741\pi\) | |||||||
\(140\) | −2.68240 | −0.226704 | ||||||||
\(141\) | 3.44760 | 0.290341 | ||||||||
\(142\) | −1.62984 | −0.136773 | ||||||||
\(143\) | −0.180918 | −0.0151291 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.42443 | −0.367429 | ||||||||
\(146\) | 15.3355 | 1.26917 | ||||||||
\(147\) | 0.301536 | 0.0248702 | ||||||||
\(148\) | −10.8012 | −0.887851 | ||||||||
\(149\) | −2.04923 | −0.167880 | −0.0839399 | − | 0.996471i | \(-0.526750\pi\) | ||||
−0.0839399 | + | 0.996471i | \(0.526750\pi\) | |||||||
\(150\) | −3.92583 | −0.320543 | ||||||||
\(151\) | −16.3006 | −1.32652 | −0.663261 | − | 0.748388i | \(-0.730828\pi\) | ||||
−0.663261 | + | 0.748388i | \(0.730828\pi\) | |||||||
\(152\) | 0.668814 | 0.0542480 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −0.850052 | −0.0684991 | ||||||||
\(155\) | 1.09823 | 0.0882116 | ||||||||
\(156\) | 0.550837 | 0.0441022 | ||||||||
\(157\) | 3.98312 | 0.317888 | 0.158944 | − | 0.987288i | \(-0.449191\pi\) | ||||
0.158944 | + | 0.987288i | \(0.449191\pi\) | |||||||
\(158\) | 2.43182 | 0.193465 | ||||||||
\(159\) | −7.70645 | −0.611161 | ||||||||
\(160\) | 1.03642 | 0.0819363 | ||||||||
\(161\) | 7.38919 | 0.582350 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 21.0239 | 1.64672 | 0.823359 | − | 0.567521i | \(-0.192098\pi\) | ||||
0.823359 | + | 0.567521i | \(0.192098\pi\) | |||||||
\(164\) | 0.525599 | 0.0410424 | ||||||||
\(165\) | 0.340403 | 0.0265004 | ||||||||
\(166\) | 10.0619 | 0.780955 | ||||||||
\(167\) | −16.2720 | −1.25916 | −0.629581 | − | 0.776935i | \(-0.716773\pi\) | ||||
−0.629581 | + | 0.776935i | \(0.716773\pi\) | |||||||
\(168\) | 2.58814 | 0.199679 | ||||||||
\(169\) | −12.6966 | −0.976660 | ||||||||
\(170\) | 1.03642 | 0.0794899 | ||||||||
\(171\) | −0.668814 | −0.0511455 | ||||||||
\(172\) | −5.46997 | −0.417081 | ||||||||
\(173\) | −10.0347 | −0.762923 | −0.381462 | − | 0.924385i | \(-0.624579\pi\) | ||||
−0.381462 | + | 0.924385i | \(0.624579\pi\) | |||||||
\(174\) | 4.26895 | 0.323628 | ||||||||
\(175\) | −10.1606 | −0.768069 | ||||||||
\(176\) | 0.328441 | 0.0247572 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −2.38147 | −0.178499 | ||||||||
\(179\) | 10.2121 | 0.763286 | 0.381643 | − | 0.924310i | \(-0.375358\pi\) | ||||
0.381643 | + | 0.924310i | \(0.375358\pi\) | |||||||
\(180\) | −1.03642 | −0.0772503 | ||||||||
\(181\) | 9.52101 | 0.707691 | 0.353846 | − | 0.935304i | \(-0.384874\pi\) | ||||
0.353846 | + | 0.935304i | \(0.384874\pi\) | |||||||
\(182\) | 1.42564 | 0.105676 | ||||||||
\(183\) | −4.66400 | −0.344773 | ||||||||
\(184\) | −2.85502 | −0.210475 | ||||||||
\(185\) | 11.1946 | 0.823041 | ||||||||
\(186\) | −1.05963 | −0.0776961 | ||||||||
\(187\) | 0.328441 | 0.0240180 | ||||||||
\(188\) | −3.44760 | −0.251442 | ||||||||
\(189\) | −2.58814 | −0.188259 | ||||||||
\(190\) | −0.693173 | −0.0502881 | ||||||||
\(191\) | 8.89557 | 0.643661 | 0.321830 | − | 0.946797i | \(-0.395702\pi\) | ||||
0.321830 | + | 0.946797i | \(0.395702\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −15.2739 | −1.09944 | −0.549719 | − | 0.835350i | \(-0.685265\pi\) | ||||
−0.549719 | + | 0.835350i | \(0.685265\pi\) | |||||||
\(194\) | 6.24513 | 0.448374 | ||||||||
\(195\) | −0.570899 | −0.0408829 | ||||||||
\(196\) | −0.301536 | −0.0215383 | ||||||||
\(197\) | 11.2776 | 0.803496 | 0.401748 | − | 0.915750i | \(-0.368403\pi\) | ||||
0.401748 | + | 0.915750i | \(0.368403\pi\) | |||||||
\(198\) | −0.328441 | −0.0233413 | ||||||||
\(199\) | 1.48477 | 0.105253 | 0.0526264 | − | 0.998614i | \(-0.483241\pi\) | ||||
0.0526264 | + | 0.998614i | \(0.483241\pi\) | |||||||
\(200\) | 3.92583 | 0.277598 | ||||||||
\(201\) | 1.71988 | 0.121311 | ||||||||
\(202\) | −11.5557 | −0.813055 | ||||||||
\(203\) | 11.0486 | 0.775462 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −0.544742 | −0.0380464 | ||||||||
\(206\) | −12.9285 | −0.900769 | ||||||||
\(207\) | 2.85502 | 0.198438 | ||||||||
\(208\) | −0.550837 | −0.0381937 | ||||||||
\(209\) | −0.219666 | −0.0151946 | ||||||||
\(210\) | −2.68240 | −0.185103 | ||||||||
\(211\) | −5.42501 | −0.373473 | −0.186737 | − | 0.982410i | \(-0.559791\pi\) | ||||
−0.186737 | + | 0.982410i | \(0.559791\pi\) | |||||||
\(212\) | 7.70645 | 0.529281 | ||||||||
\(213\) | −1.62984 | −0.111675 | ||||||||
\(214\) | −16.3152 | −1.11528 | ||||||||
\(215\) | 5.66919 | 0.386635 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −2.74248 | −0.186172 | ||||||||
\(218\) | 12.8397 | 0.869615 | ||||||||
\(219\) | 15.3355 | 1.03628 | ||||||||
\(220\) | −0.340403 | −0.0229500 | ||||||||
\(221\) | −0.550837 | −0.0370533 | ||||||||
\(222\) | −10.8012 | −0.724927 | ||||||||
\(223\) | 21.1595 | 1.41695 | 0.708474 | − | 0.705737i | \(-0.249384\pi\) | ||||
0.708474 | + | 0.705737i | \(0.249384\pi\) | |||||||
\(224\) | −2.58814 | −0.172927 | ||||||||
\(225\) | −3.92583 | −0.261722 | ||||||||
\(226\) | 7.28064 | 0.484301 | ||||||||
\(227\) | 14.3490 | 0.952377 | 0.476189 | − | 0.879343i | \(-0.342018\pi\) | ||||
0.476189 | + | 0.879343i | \(0.342018\pi\) | |||||||
\(228\) | 0.668814 | 0.0442933 | ||||||||
\(229\) | 15.2853 | 1.01008 | 0.505042 | − | 0.863095i | \(-0.331477\pi\) | ||||
0.505042 | + | 0.863095i | \(0.331477\pi\) | |||||||
\(230\) | 2.95900 | 0.195111 | ||||||||
\(231\) | −0.850052 | −0.0559293 | ||||||||
\(232\) | −4.26895 | −0.280270 | ||||||||
\(233\) | −25.3127 | −1.65829 | −0.829145 | − | 0.559034i | \(-0.811172\pi\) | ||||
−0.829145 | + | 0.559034i | \(0.811172\pi\) | |||||||
\(234\) | 0.550837 | 0.0360093 | ||||||||
\(235\) | 3.57317 | 0.233088 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | 2.43182 | 0.157963 | ||||||||
\(238\) | −2.58814 | −0.167764 | ||||||||
\(239\) | 21.1023 | 1.36499 | 0.682496 | − | 0.730890i | \(-0.260895\pi\) | ||||
0.682496 | + | 0.730890i | \(0.260895\pi\) | |||||||
\(240\) | 1.03642 | 0.0669007 | ||||||||
\(241\) | 26.8020 | 1.72647 | 0.863234 | − | 0.504804i | \(-0.168435\pi\) | ||||
0.863234 | + | 0.504804i | \(0.168435\pi\) | |||||||
\(242\) | 10.8921 | 0.700172 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.66400 | 0.298582 | ||||||||
\(245\) | 0.312518 | 0.0199660 | ||||||||
\(246\) | 0.525599 | 0.0335110 | ||||||||
\(247\) | 0.368407 | 0.0234412 | ||||||||
\(248\) | 1.05963 | 0.0672868 | ||||||||
\(249\) | 10.0619 | 0.637647 | ||||||||
\(250\) | −9.25092 | −0.585079 | ||||||||
\(251\) | −17.0612 | −1.07689 | −0.538446 | − | 0.842660i | \(-0.680988\pi\) | ||||
−0.538446 | + | 0.842660i | \(0.680988\pi\) | |||||||
\(252\) | 2.58814 | 0.163037 | ||||||||
\(253\) | 0.937707 | 0.0589531 | ||||||||
\(254\) | 5.99189 | 0.375965 | ||||||||
\(255\) | 1.03642 | 0.0649032 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.4862 | −1.77692 | −0.888460 | − | 0.458953i | \(-0.848225\pi\) | ||||
−0.888460 | + | 0.458953i | \(0.848225\pi\) | |||||||
\(258\) | −5.46997 | −0.340545 | ||||||||
\(259\) | −27.9549 | −1.73704 | ||||||||
\(260\) | 0.570899 | 0.0354056 | ||||||||
\(261\) | 4.26895 | 0.264241 | ||||||||
\(262\) | 19.2336 | 1.18826 | ||||||||
\(263\) | −12.6911 | −0.782569 | −0.391284 | − | 0.920270i | \(-0.627969\pi\) | ||||
−0.391284 | + | 0.920270i | \(0.627969\pi\) | |||||||
\(264\) | 0.328441 | 0.0202142 | ||||||||
\(265\) | −7.98713 | −0.490645 | ||||||||
\(266\) | 1.73098 | 0.106133 | ||||||||
\(267\) | −2.38147 | −0.145744 | ||||||||
\(268\) | −1.71988 | −0.105058 | ||||||||
\(269\) | −23.1876 | −1.41377 | −0.706886 | − | 0.707327i | \(-0.749901\pi\) | ||||
−0.706886 | + | 0.707327i | \(0.749901\pi\) | |||||||
\(270\) | −1.03642 | −0.0630746 | ||||||||
\(271\) | −7.63277 | −0.463658 | −0.231829 | − | 0.972757i | \(-0.574471\pi\) | ||||
−0.231829 | + | 0.972757i | \(0.574471\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 1.42564 | 0.0862838 | ||||||||
\(274\) | −11.8369 | −0.715092 | ||||||||
\(275\) | −1.28941 | −0.0777541 | ||||||||
\(276\) | −2.85502 | −0.171852 | ||||||||
\(277\) | 16.4901 | 0.990796 | 0.495398 | − | 0.868666i | \(-0.335022\pi\) | ||||
0.495398 | + | 0.868666i | \(0.335022\pi\) | |||||||
\(278\) | −10.1241 | −0.607201 | ||||||||
\(279\) | −1.05963 | −0.0634386 | ||||||||
\(280\) | 2.68240 | 0.160304 | ||||||||
\(281\) | −16.5257 | −0.985838 | −0.492919 | − | 0.870075i | \(-0.664070\pi\) | ||||
−0.492919 | + | 0.870075i | \(0.664070\pi\) | |||||||
\(282\) | −3.44760 | −0.205302 | ||||||||
\(283\) | −22.5142 | −1.33833 | −0.669164 | − | 0.743115i | \(-0.733348\pi\) | ||||
−0.669164 | + | 0.743115i | \(0.733348\pi\) | |||||||
\(284\) | 1.62984 | 0.0967134 | ||||||||
\(285\) | −0.693173 | −0.0410600 | ||||||||
\(286\) | 0.180918 | 0.0106979 | ||||||||
\(287\) | 1.36032 | 0.0802973 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 4.42443 | 0.259811 | ||||||||
\(291\) | 6.24513 | 0.366096 | ||||||||
\(292\) | −15.3355 | −0.897441 | ||||||||
\(293\) | 25.7742 | 1.50575 | 0.752873 | − | 0.658166i | \(-0.228668\pi\) | ||||
0.752873 | + | 0.658166i | \(0.228668\pi\) | |||||||
\(294\) | −0.301536 | −0.0175859 | ||||||||
\(295\) | −1.03642 | −0.0603428 | ||||||||
\(296\) | 10.8012 | 0.627805 | ||||||||
\(297\) | −0.328441 | −0.0190581 | ||||||||
\(298\) | 2.04923 | 0.118709 | ||||||||
\(299\) | −1.57265 | −0.0909488 | ||||||||
\(300\) | 3.92583 | 0.226658 | ||||||||
\(301\) | −14.1570 | −0.815998 | ||||||||
\(302\) | 16.3006 | 0.937993 | ||||||||
\(303\) | −11.5557 | −0.663856 | ||||||||
\(304\) | −0.668814 | −0.0383591 | ||||||||
\(305\) | −4.83386 | −0.276786 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −21.8614 | −1.24770 | −0.623849 | − | 0.781545i | \(-0.714432\pi\) | ||||
−0.623849 | + | 0.781545i | \(0.714432\pi\) | |||||||
\(308\) | 0.850052 | 0.0484362 | ||||||||
\(309\) | −12.9285 | −0.735475 | ||||||||
\(310\) | −1.09823 | −0.0623750 | ||||||||
\(311\) | −14.8414 | −0.841576 | −0.420788 | − | 0.907159i | \(-0.638246\pi\) | ||||
−0.420788 | + | 0.907159i | \(0.638246\pi\) | |||||||
\(312\) | −0.550837 | −0.0311850 | ||||||||
\(313\) | 2.76592 | 0.156339 | 0.0781696 | − | 0.996940i | \(-0.475092\pi\) | ||||
0.0781696 | + | 0.996940i | \(0.475092\pi\) | |||||||
\(314\) | −3.98312 | −0.224781 | ||||||||
\(315\) | −2.68240 | −0.151136 | ||||||||
\(316\) | −2.43182 | −0.136800 | ||||||||
\(317\) | −4.05645 | −0.227833 | −0.113916 | − | 0.993490i | \(-0.536340\pi\) | ||||
−0.113916 | + | 0.993490i | \(0.536340\pi\) | |||||||
\(318\) | 7.70645 | 0.432156 | ||||||||
\(319\) | 1.40210 | 0.0785025 | ||||||||
\(320\) | −1.03642 | −0.0579377 | ||||||||
\(321\) | −16.3152 | −0.910626 | ||||||||
\(322\) | −7.38919 | −0.411784 | ||||||||
\(323\) | −0.668814 | −0.0372138 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.16249 | 0.119953 | ||||||||
\(326\) | −21.0239 | −1.16441 | ||||||||
\(327\) | 12.8397 | 0.710037 | ||||||||
\(328\) | −0.525599 | −0.0290213 | ||||||||
\(329\) | −8.92288 | −0.491934 | ||||||||
\(330\) | −0.340403 | −0.0187386 | ||||||||
\(331\) | 11.3405 | 0.623328 | 0.311664 | − | 0.950192i | \(-0.399114\pi\) | ||||
0.311664 | + | 0.950192i | \(0.399114\pi\) | |||||||
\(332\) | −10.0619 | −0.552218 | ||||||||
\(333\) | −10.8012 | −0.591901 | ||||||||
\(334\) | 16.2720 | 0.890362 | ||||||||
\(335\) | 1.78252 | 0.0973893 | ||||||||
\(336\) | −2.58814 | −0.141195 | ||||||||
\(337\) | −17.8392 | −0.971761 | −0.485880 | − | 0.874025i | \(-0.661501\pi\) | ||||
−0.485880 | + | 0.874025i | \(0.661501\pi\) | |||||||
\(338\) | 12.6966 | 0.690603 | ||||||||
\(339\) | 7.28064 | 0.395430 | ||||||||
\(340\) | −1.03642 | −0.0562078 | ||||||||
\(341\) | −0.348027 | −0.0188467 | ||||||||
\(342\) | 0.668814 | 0.0361653 | ||||||||
\(343\) | −18.8974 | −1.02036 | ||||||||
\(344\) | 5.46997 | 0.294921 | ||||||||
\(345\) | 2.95900 | 0.159307 | ||||||||
\(346\) | 10.0347 | 0.539468 | ||||||||
\(347\) | 6.47083 | 0.347372 | 0.173686 | − | 0.984801i | \(-0.444432\pi\) | ||||
0.173686 | + | 0.984801i | \(0.444432\pi\) | |||||||
\(348\) | −4.26895 | −0.228840 | ||||||||
\(349\) | 12.5865 | 0.673742 | 0.336871 | − | 0.941551i | \(-0.390631\pi\) | ||||
0.336871 | + | 0.941551i | \(0.390631\pi\) | |||||||
\(350\) | 10.1606 | 0.543107 | ||||||||
\(351\) | 0.550837 | 0.0294015 | ||||||||
\(352\) | −0.328441 | −0.0175060 | ||||||||
\(353\) | −14.9803 | −0.797324 | −0.398662 | − | 0.917098i | \(-0.630525\pi\) | ||||
−0.398662 | + | 0.917098i | \(0.630525\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | −1.68920 | −0.0896537 | ||||||||
\(356\) | 2.38147 | 0.126218 | ||||||||
\(357\) | −2.58814 | −0.136979 | ||||||||
\(358\) | −10.2121 | −0.539725 | ||||||||
\(359\) | −30.6875 | −1.61962 | −0.809812 | − | 0.586690i | \(-0.800431\pi\) | ||||
−0.809812 | + | 0.586690i | \(0.800431\pi\) | |||||||
\(360\) | 1.03642 | 0.0546242 | ||||||||
\(361\) | −18.5527 | −0.976457 | ||||||||
\(362\) | −9.52101 | −0.500413 | ||||||||
\(363\) | 10.8921 | 0.571688 | ||||||||
\(364\) | −1.42564 | −0.0747240 | ||||||||
\(365\) | 15.8940 | 0.831931 | ||||||||
\(366\) | 4.66400 | 0.243791 | ||||||||
\(367\) | −19.9254 | −1.04010 | −0.520050 | − | 0.854136i | \(-0.674087\pi\) | ||||
−0.520050 | + | 0.854136i | \(0.674087\pi\) | |||||||
\(368\) | 2.85502 | 0.148828 | ||||||||
\(369\) | 0.525599 | 0.0273616 | ||||||||
\(370\) | −11.1946 | −0.581978 | ||||||||
\(371\) | 19.9454 | 1.03551 | ||||||||
\(372\) | 1.05963 | 0.0549394 | ||||||||
\(373\) | −21.3022 | −1.10298 | −0.551492 | − | 0.834180i | \(-0.685941\pi\) | ||||
−0.551492 | + | 0.834180i | \(0.685941\pi\) | |||||||
\(374\) | −0.328441 | −0.0169833 | ||||||||
\(375\) | −9.25092 | −0.477715 | ||||||||
\(376\) | 3.44760 | 0.177797 | ||||||||
\(377\) | −2.35149 | −0.121108 | ||||||||
\(378\) | 2.58814 | 0.133120 | ||||||||
\(379\) | 8.95772 | 0.460127 | 0.230064 | − | 0.973176i | \(-0.426107\pi\) | ||||
0.230064 | + | 0.973176i | \(0.426107\pi\) | |||||||
\(380\) | 0.693173 | 0.0355590 | ||||||||
\(381\) | 5.99189 | 0.306974 | ||||||||
\(382\) | −8.89557 | −0.455137 | ||||||||
\(383\) | 2.75199 | 0.140620 | 0.0703101 | − | 0.997525i | \(-0.477601\pi\) | ||||
0.0703101 | + | 0.997525i | \(0.477601\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.881011 | −0.0449005 | ||||||||
\(386\) | 15.2739 | 0.777420 | ||||||||
\(387\) | −5.46997 | −0.278054 | ||||||||
\(388\) | −6.24513 | −0.317048 | ||||||||
\(389\) | −20.0517 | −1.01666 | −0.508330 | − | 0.861162i | \(-0.669737\pi\) | ||||
−0.508330 | + | 0.861162i | \(0.669737\pi\) | |||||||
\(390\) | 0.570899 | 0.0289086 | ||||||||
\(391\) | 2.85502 | 0.144385 | ||||||||
\(392\) | 0.301536 | 0.0152299 | ||||||||
\(393\) | 19.2336 | 0.970207 | ||||||||
\(394\) | −11.2776 | −0.568158 | ||||||||
\(395\) | 2.52038 | 0.126814 | ||||||||
\(396\) | 0.328441 | 0.0165048 | ||||||||
\(397\) | 8.78347 | 0.440830 | 0.220415 | − | 0.975406i | \(-0.429259\pi\) | ||||
0.220415 | + | 0.975406i | \(0.429259\pi\) | |||||||
\(398\) | −1.48477 | −0.0744249 | ||||||||
\(399\) | 1.73098 | 0.0866576 | ||||||||
\(400\) | −3.92583 | −0.196292 | ||||||||
\(401\) | 2.40824 | 0.120262 | 0.0601308 | − | 0.998191i | \(-0.480848\pi\) | ||||
0.0601308 | + | 0.998191i | \(0.480848\pi\) | |||||||
\(402\) | −1.71988 | −0.0857797 | ||||||||
\(403\) | 0.583685 | 0.0290754 | ||||||||
\(404\) | 11.5557 | 0.574916 | ||||||||
\(405\) | −1.03642 | −0.0515002 | ||||||||
\(406\) | −11.0486 | −0.548335 | ||||||||
\(407\) | −3.54755 | −0.175846 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 26.4894 | 1.30982 | 0.654909 | − | 0.755708i | \(-0.272707\pi\) | ||||
0.654909 | + | 0.755708i | \(0.272707\pi\) | |||||||
\(410\) | 0.544742 | 0.0269029 | ||||||||
\(411\) | −11.8369 | −0.583870 | ||||||||
\(412\) | 12.9285 | 0.636940 | ||||||||
\(413\) | 2.58814 | 0.127354 | ||||||||
\(414\) | −2.85502 | −0.140317 | ||||||||
\(415\) | 10.4284 | 0.511908 | ||||||||
\(416\) | 0.550837 | 0.0270070 | ||||||||
\(417\) | −10.1241 | −0.495778 | ||||||||
\(418\) | 0.219666 | 0.0107442 | ||||||||
\(419\) | −22.8269 | −1.11517 | −0.557583 | − | 0.830121i | \(-0.688271\pi\) | ||||
−0.557583 | + | 0.830121i | \(0.688271\pi\) | |||||||
\(420\) | 2.68240 | 0.130888 | ||||||||
\(421\) | −26.9101 | −1.31152 | −0.655759 | − | 0.754970i | \(-0.727651\pi\) | ||||
−0.655759 | + | 0.754970i | \(0.727651\pi\) | |||||||
\(422\) | 5.42501 | 0.264086 | ||||||||
\(423\) | −3.44760 | −0.167628 | ||||||||
\(424\) | −7.70645 | −0.374258 | ||||||||
\(425\) | −3.92583 | −0.190431 | ||||||||
\(426\) | 1.62984 | 0.0789662 | ||||||||
\(427\) | 12.0711 | 0.584160 | ||||||||
\(428\) | 16.3152 | 0.788626 | ||||||||
\(429\) | 0.180918 | 0.00873478 | ||||||||
\(430\) | −5.66919 | −0.273393 | ||||||||
\(431\) | −24.9651 | −1.20253 | −0.601263 | − | 0.799051i | \(-0.705336\pi\) | ||||
−0.601263 | + | 0.799051i | \(0.705336\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −4.17199 | −0.200493 | −0.100247 | − | 0.994963i | \(-0.531963\pi\) | ||||
−0.100247 | + | 0.994963i | \(0.531963\pi\) | |||||||
\(434\) | 2.74248 | 0.131643 | ||||||||
\(435\) | 4.42443 | 0.212135 | ||||||||
\(436\) | −12.8397 | −0.614910 | ||||||||
\(437\) | −1.90948 | −0.0913428 | ||||||||
\(438\) | −15.3355 | −0.732758 | ||||||||
\(439\) | −34.4803 | −1.64566 | −0.822828 | − | 0.568291i | \(-0.807605\pi\) | ||||
−0.822828 | + | 0.568291i | \(0.807605\pi\) | |||||||
\(440\) | 0.340403 | 0.0162281 | ||||||||
\(441\) | −0.301536 | −0.0143588 | ||||||||
\(442\) | 0.550837 | 0.0262006 | ||||||||
\(443\) | −23.0099 | −1.09323 | −0.546617 | − | 0.837382i | \(-0.684085\pi\) | ||||
−0.546617 | + | 0.837382i | \(0.684085\pi\) | |||||||
\(444\) | 10.8012 | 0.512601 | ||||||||
\(445\) | −2.46820 | −0.117004 | ||||||||
\(446\) | −21.1595 | −1.00193 | ||||||||
\(447\) | 2.04923 | 0.0969254 | ||||||||
\(448\) | 2.58814 | 0.122278 | ||||||||
\(449\) | −10.4492 | −0.493129 | −0.246564 | − | 0.969126i | \(-0.579302\pi\) | ||||
−0.246564 | + | 0.969126i | \(0.579302\pi\) | |||||||
\(450\) | 3.92583 | 0.185065 | ||||||||
\(451\) | 0.172628 | 0.00812875 | ||||||||
\(452\) | −7.28064 | −0.342453 | ||||||||
\(453\) | 16.3006 | 0.765868 | ||||||||
\(454\) | −14.3490 | −0.673432 | ||||||||
\(455\) | 1.47757 | 0.0692693 | ||||||||
\(456\) | −0.668814 | −0.0313201 | ||||||||
\(457\) | 36.1241 | 1.68981 | 0.844907 | − | 0.534914i | \(-0.179656\pi\) | ||||
0.844907 | + | 0.534914i | \(0.179656\pi\) | |||||||
\(458\) | −15.2853 | −0.714237 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −2.95900 | −0.137964 | ||||||||
\(461\) | 40.3554 | 1.87954 | 0.939768 | − | 0.341812i | \(-0.111041\pi\) | ||||
0.939768 | + | 0.341812i | \(0.111041\pi\) | |||||||
\(462\) | 0.850052 | 0.0395480 | ||||||||
\(463\) | 4.06042 | 0.188704 | 0.0943519 | − | 0.995539i | \(-0.469922\pi\) | ||||
0.0943519 | + | 0.995539i | \(0.469922\pi\) | |||||||
\(464\) | 4.26895 | 0.198181 | ||||||||
\(465\) | −1.09823 | −0.0509290 | ||||||||
\(466\) | 25.3127 | 1.17259 | ||||||||
\(467\) | −37.1361 | −1.71845 | −0.859226 | − | 0.511596i | \(-0.829054\pi\) | ||||
−0.859226 | + | 0.511596i | \(0.829054\pi\) | |||||||
\(468\) | −0.550837 | −0.0254624 | ||||||||
\(469\) | −4.45128 | −0.205541 | ||||||||
\(470\) | −3.57317 | −0.164818 | ||||||||
\(471\) | −3.98312 | −0.183533 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −1.79656 | −0.0826061 | ||||||||
\(474\) | −2.43182 | −0.111697 | ||||||||
\(475\) | 2.62565 | 0.120473 | ||||||||
\(476\) | 2.58814 | 0.118627 | ||||||||
\(477\) | 7.70645 | 0.352854 | ||||||||
\(478\) | −21.1023 | −0.965195 | ||||||||
\(479\) | −19.2776 | −0.880816 | −0.440408 | − | 0.897798i | \(-0.645166\pi\) | ||||
−0.440408 | + | 0.897798i | \(0.645166\pi\) | |||||||
\(480\) | −1.03642 | −0.0473059 | ||||||||
\(481\) | 5.94968 | 0.271282 | ||||||||
\(482\) | −26.8020 | −1.22080 | ||||||||
\(483\) | −7.38919 | −0.336220 | ||||||||
\(484\) | −10.8921 | −0.495097 | ||||||||
\(485\) | 6.47258 | 0.293905 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −9.52560 | −0.431646 | −0.215823 | − | 0.976432i | \(-0.569243\pi\) | ||||
−0.215823 | + | 0.976432i | \(0.569243\pi\) | |||||||
\(488\) | −4.66400 | −0.211129 | ||||||||
\(489\) | −21.0239 | −0.950733 | ||||||||
\(490\) | −0.312518 | −0.0141181 | ||||||||
\(491\) | 10.8049 | 0.487619 | 0.243810 | − | 0.969823i | \(-0.421603\pi\) | ||||
0.243810 | + | 0.969823i | \(0.421603\pi\) | |||||||
\(492\) | −0.525599 | −0.0236958 | ||||||||
\(493\) | 4.26895 | 0.192264 | ||||||||
\(494\) | −0.368407 | −0.0165754 | ||||||||
\(495\) | −0.340403 | −0.0153000 | ||||||||
\(496\) | −1.05963 | −0.0475789 | ||||||||
\(497\) | 4.21826 | 0.189215 | ||||||||
\(498\) | −10.0619 | −0.450884 | ||||||||
\(499\) | 25.4680 | 1.14010 | 0.570052 | − | 0.821609i | \(-0.306923\pi\) | ||||
0.570052 | + | 0.821609i | \(0.306923\pi\) | |||||||
\(500\) | 9.25092 | 0.413714 | ||||||||
\(501\) | 16.2720 | 0.726977 | ||||||||
\(502\) | 17.0612 | 0.761477 | ||||||||
\(503\) | 27.2165 | 1.21352 | 0.606761 | − | 0.794884i | \(-0.292468\pi\) | ||||
0.606761 | + | 0.794884i | \(0.292468\pi\) | |||||||
\(504\) | −2.58814 | −0.115285 | ||||||||
\(505\) | −11.9765 | −0.532949 | ||||||||
\(506\) | −0.937707 | −0.0416862 | ||||||||
\(507\) | 12.6966 | 0.563875 | ||||||||
\(508\) | −5.99189 | −0.265847 | ||||||||
\(509\) | 23.6190 | 1.04689 | 0.523446 | − | 0.852059i | \(-0.324646\pi\) | ||||
0.523446 | + | 0.852059i | \(0.324646\pi\) | |||||||
\(510\) | −1.03642 | −0.0458935 | ||||||||
\(511\) | −39.6904 | −1.75580 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.668814 | 0.0295289 | ||||||||
\(514\) | 28.4862 | 1.25647 | ||||||||
\(515\) | −13.3993 | −0.590445 | ||||||||
\(516\) | 5.46997 | 0.240802 | ||||||||
\(517\) | −1.13234 | −0.0498001 | ||||||||
\(518\) | 27.9549 | 1.22827 | ||||||||
\(519\) | 10.0347 | 0.440474 | ||||||||
\(520\) | −0.570899 | −0.0250356 | ||||||||
\(521\) | 27.6475 | 1.21126 | 0.605630 | − | 0.795746i | \(-0.292921\pi\) | ||||
0.605630 | + | 0.795746i | \(0.292921\pi\) | |||||||
\(522\) | −4.26895 | −0.186847 | ||||||||
\(523\) | −34.7234 | −1.51835 | −0.759175 | − | 0.650887i | \(-0.774397\pi\) | ||||
−0.759175 | + | 0.650887i | \(0.774397\pi\) | |||||||
\(524\) | −19.2336 | −0.840224 | ||||||||
\(525\) | 10.1606 | 0.443445 | ||||||||
\(526\) | 12.6911 | 0.553360 | ||||||||
\(527\) | −1.05963 | −0.0461583 | ||||||||
\(528\) | −0.328441 | −0.0142936 | ||||||||
\(529\) | −14.8489 | −0.645602 | ||||||||
\(530\) | 7.98713 | 0.346939 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | −1.73098 | −0.0750477 | ||||||||
\(533\) | −0.289519 | −0.0125405 | ||||||||
\(534\) | 2.38147 | 0.103056 | ||||||||
\(535\) | −16.9094 | −0.731058 | ||||||||
\(536\) | 1.71988 | 0.0742874 | ||||||||
\(537\) | −10.2121 | −0.440683 | ||||||||
\(538\) | 23.1876 | 0.999688 | ||||||||
\(539\) | −0.0990368 | −0.00426582 | ||||||||
\(540\) | 1.03642 | 0.0446005 | ||||||||
\(541\) | −26.7090 | −1.14831 | −0.574156 | − | 0.818746i | \(-0.694670\pi\) | ||||
−0.574156 | + | 0.818746i | \(0.694670\pi\) | |||||||
\(542\) | 7.63277 | 0.327856 | ||||||||
\(543\) | −9.52101 | −0.408586 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 13.3073 | 0.570024 | ||||||||
\(546\) | −1.42564 | −0.0610119 | ||||||||
\(547\) | −9.15536 | −0.391455 | −0.195728 | − | 0.980658i | \(-0.562707\pi\) | ||||
−0.195728 | + | 0.980658i | \(0.562707\pi\) | |||||||
\(548\) | 11.8369 | 0.505647 | ||||||||
\(549\) | 4.66400 | 0.199055 | ||||||||
\(550\) | 1.28941 | 0.0549804 | ||||||||
\(551\) | −2.85513 | −0.121633 | ||||||||
\(552\) | 2.85502 | 0.121518 | ||||||||
\(553\) | −6.29388 | −0.267643 | ||||||||
\(554\) | −16.4901 | −0.700599 | ||||||||
\(555\) | −11.1946 | −0.475183 | ||||||||
\(556\) | 10.1241 | 0.429356 | ||||||||
\(557\) | −38.3282 | −1.62402 | −0.812008 | − | 0.583646i | \(-0.801626\pi\) | ||||
−0.812008 | + | 0.583646i | \(0.801626\pi\) | |||||||
\(558\) | 1.05963 | 0.0448578 | ||||||||
\(559\) | 3.01306 | 0.127439 | ||||||||
\(560\) | −2.68240 | −0.113352 | ||||||||
\(561\) | −0.328441 | −0.0138668 | ||||||||
\(562\) | 16.5257 | 0.697093 | ||||||||
\(563\) | 10.5817 | 0.445966 | 0.222983 | − | 0.974822i | \(-0.428421\pi\) | ||||
0.222983 | + | 0.974822i | \(0.428421\pi\) | |||||||
\(564\) | 3.44760 | 0.145170 | ||||||||
\(565\) | 7.54581 | 0.317455 | ||||||||
\(566\) | 22.5142 | 0.946341 | ||||||||
\(567\) | 2.58814 | 0.108692 | ||||||||
\(568\) | −1.62984 | −0.0683867 | ||||||||
\(569\) | 5.49223 | 0.230246 | 0.115123 | − | 0.993351i | \(-0.463274\pi\) | ||||
0.115123 | + | 0.993351i | \(0.463274\pi\) | |||||||
\(570\) | 0.693173 | 0.0290338 | ||||||||
\(571\) | −31.3251 | −1.31091 | −0.655457 | − | 0.755232i | \(-0.727524\pi\) | ||||
−0.655457 | + | 0.755232i | \(0.727524\pi\) | |||||||
\(572\) | −0.180918 | −0.00756454 | ||||||||
\(573\) | −8.89557 | −0.371618 | ||||||||
\(574\) | −1.36032 | −0.0567788 | ||||||||
\(575\) | −11.2083 | −0.467420 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −46.1827 | −1.92261 | −0.961305 | − | 0.275485i | \(-0.911161\pi\) | ||||
−0.961305 | + | 0.275485i | \(0.911161\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 15.2739 | 0.634761 | ||||||||
\(580\) | −4.42443 | −0.183714 | ||||||||
\(581\) | −26.0416 | −1.08039 | ||||||||
\(582\) | −6.24513 | −0.258869 | ||||||||
\(583\) | 2.53112 | 0.104828 | ||||||||
\(584\) | 15.3355 | 0.634587 | ||||||||
\(585\) | 0.570899 | 0.0236038 | ||||||||
\(586\) | −25.7742 | −1.06472 | ||||||||
\(587\) | −40.6530 | −1.67793 | −0.838965 | − | 0.544185i | \(-0.816839\pi\) | ||||
−0.838965 | + | 0.544185i | \(0.816839\pi\) | |||||||
\(588\) | 0.301536 | 0.0124351 | ||||||||
\(589\) | 0.708698 | 0.0292014 | ||||||||
\(590\) | 1.03642 | 0.0426688 | ||||||||
\(591\) | −11.2776 | −0.463899 | ||||||||
\(592\) | −10.8012 | −0.443926 | ||||||||
\(593\) | 1.53525 | 0.0630452 | 0.0315226 | − | 0.999503i | \(-0.489964\pi\) | ||||
0.0315226 | + | 0.999503i | \(0.489964\pi\) | |||||||
\(594\) | 0.328441 | 0.0134761 | ||||||||
\(595\) | −2.68240 | −0.109968 | ||||||||
\(596\) | −2.04923 | −0.0839399 | ||||||||
\(597\) | −1.48477 | −0.0607677 | ||||||||
\(598\) | 1.57265 | 0.0643105 | ||||||||
\(599\) | −27.4789 | −1.12276 | −0.561378 | − | 0.827560i | \(-0.689729\pi\) | ||||
−0.561378 | + | 0.827560i | \(0.689729\pi\) | |||||||
\(600\) | −3.92583 | −0.160271 | ||||||||
\(601\) | −9.76324 | −0.398251 | −0.199125 | − | 0.979974i | \(-0.563810\pi\) | ||||
−0.199125 | + | 0.979974i | \(0.563810\pi\) | |||||||
\(602\) | 14.1570 | 0.576998 | ||||||||
\(603\) | −1.71988 | −0.0700388 | ||||||||
\(604\) | −16.3006 | −0.663261 | ||||||||
\(605\) | 11.2888 | 0.458956 | ||||||||
\(606\) | 11.5557 | 0.469417 | ||||||||
\(607\) | 20.6299 | 0.837341 | 0.418671 | − | 0.908138i | \(-0.362496\pi\) | ||||
0.418671 | + | 0.908138i | \(0.362496\pi\) | |||||||
\(608\) | 0.668814 | 0.0271240 | ||||||||
\(609\) | −11.0486 | −0.447713 | ||||||||
\(610\) | 4.83386 | 0.195717 | ||||||||
\(611\) | 1.89907 | 0.0768280 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 28.7830 | 1.16253 | 0.581267 | − | 0.813713i | \(-0.302557\pi\) | ||||
0.581267 | + | 0.813713i | \(0.302557\pi\) | |||||||
\(614\) | 21.8614 | 0.882256 | ||||||||
\(615\) | 0.544742 | 0.0219661 | ||||||||
\(616\) | −0.850052 | −0.0342496 | ||||||||
\(617\) | 31.0962 | 1.25189 | 0.625944 | − | 0.779868i | \(-0.284714\pi\) | ||||
0.625944 | + | 0.779868i | \(0.284714\pi\) | |||||||
\(618\) | 12.9285 | 0.520059 | ||||||||
\(619\) | −15.4426 | −0.620691 | −0.310346 | − | 0.950624i | \(-0.600445\pi\) | ||||
−0.310346 | + | 0.950624i | \(0.600445\pi\) | |||||||
\(620\) | 1.09823 | 0.0441058 | ||||||||
\(621\) | −2.85502 | −0.114568 | ||||||||
\(622\) | 14.8414 | 0.595084 | ||||||||
\(623\) | 6.16357 | 0.246938 | ||||||||
\(624\) | 0.550837 | 0.0220511 | ||||||||
\(625\) | 10.0413 | 0.401653 | ||||||||
\(626\) | −2.76592 | −0.110548 | ||||||||
\(627\) | 0.219666 | 0.00877262 | ||||||||
\(628\) | 3.98312 | 0.158944 | ||||||||
\(629\) | −10.8012 | −0.430671 | ||||||||
\(630\) | 2.68240 | 0.106869 | ||||||||
\(631\) | −31.2165 | −1.24271 | −0.621354 | − | 0.783530i | \(-0.713417\pi\) | ||||
−0.621354 | + | 0.783530i | \(0.713417\pi\) | |||||||
\(632\) | 2.43182 | 0.0967324 | ||||||||
\(633\) | 5.42501 | 0.215625 | ||||||||
\(634\) | 4.05645 | 0.161102 | ||||||||
\(635\) | 6.21012 | 0.246441 | ||||||||
\(636\) | −7.70645 | −0.305581 | ||||||||
\(637\) | 0.166097 | 0.00658100 | ||||||||
\(638\) | −1.40210 | −0.0555096 | ||||||||
\(639\) | 1.62984 | 0.0644756 | ||||||||
\(640\) | 1.03642 | 0.0409681 | ||||||||
\(641\) | −0.703361 | −0.0277811 | −0.0138906 | − | 0.999904i | \(-0.504422\pi\) | ||||
−0.0138906 | + | 0.999904i | \(0.504422\pi\) | |||||||
\(642\) | 16.3152 | 0.643910 | ||||||||
\(643\) | 38.4973 | 1.51819 | 0.759094 | − | 0.650982i | \(-0.225643\pi\) | ||||
0.759094 | + | 0.650982i | \(0.225643\pi\) | |||||||
\(644\) | 7.38919 | 0.291175 | ||||||||
\(645\) | −5.66919 | −0.223224 | ||||||||
\(646\) | 0.668814 | 0.0263141 | ||||||||
\(647\) | −47.1976 | −1.85553 | −0.927764 | − | 0.373167i | \(-0.878272\pi\) | ||||
−0.927764 | + | 0.373167i | \(0.878272\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.328441 | 0.0128924 | ||||||||
\(650\) | −2.16249 | −0.0848199 | ||||||||
\(651\) | 2.74248 | 0.107486 | ||||||||
\(652\) | 21.0239 | 0.823359 | ||||||||
\(653\) | −36.9305 | −1.44520 | −0.722601 | − | 0.691265i | \(-0.757054\pi\) | ||||
−0.722601 | + | 0.691265i | \(0.757054\pi\) | |||||||
\(654\) | −12.8397 | −0.502072 | ||||||||
\(655\) | 19.9341 | 0.778890 | ||||||||
\(656\) | 0.525599 | 0.0205212 | ||||||||
\(657\) | −15.3355 | −0.598294 | ||||||||
\(658\) | 8.92288 | 0.347850 | ||||||||
\(659\) | −1.37589 | −0.0535971 | −0.0267986 | − | 0.999641i | \(-0.508531\pi\) | ||||
−0.0267986 | + | 0.999641i | \(0.508531\pi\) | |||||||
\(660\) | 0.340403 | 0.0132502 | ||||||||
\(661\) | 13.3061 | 0.517547 | 0.258774 | − | 0.965938i | \(-0.416682\pi\) | ||||
0.258774 | + | 0.965938i | \(0.416682\pi\) | |||||||
\(662\) | −11.3405 | −0.440760 | ||||||||
\(663\) | 0.550837 | 0.0213927 | ||||||||
\(664\) | 10.0619 | 0.390477 | ||||||||
\(665\) | 1.79403 | 0.0695694 | ||||||||
\(666\) | 10.8012 | 0.418537 | ||||||||
\(667\) | 12.1879 | 0.471919 | ||||||||
\(668\) | −16.2720 | −0.629581 | ||||||||
\(669\) | −21.1595 | −0.818075 | ||||||||
\(670\) | −1.78252 | −0.0688647 | ||||||||
\(671\) | 1.53185 | 0.0591364 | ||||||||
\(672\) | 2.58814 | 0.0998396 | ||||||||
\(673\) | −37.6570 | −1.45157 | −0.725786 | − | 0.687921i | \(-0.758524\pi\) | ||||
−0.725786 | + | 0.687921i | \(0.758524\pi\) | |||||||
\(674\) | 17.8392 | 0.687138 | ||||||||
\(675\) | 3.92583 | 0.151105 | ||||||||
\(676\) | −12.6966 | −0.488330 | ||||||||
\(677\) | −25.4476 | −0.978029 | −0.489014 | − | 0.872276i | \(-0.662643\pi\) | ||||
−0.489014 | + | 0.872276i | \(0.662643\pi\) | |||||||
\(678\) | −7.28064 | −0.279611 | ||||||||
\(679\) | −16.1633 | −0.620289 | ||||||||
\(680\) | 1.03642 | 0.0397449 | ||||||||
\(681\) | −14.3490 | −0.549855 | ||||||||
\(682\) | 0.348027 | 0.0133267 | ||||||||
\(683\) | 51.0745 | 1.95431 | 0.977157 | − | 0.212520i | \(-0.0681672\pi\) | ||||
0.977157 | + | 0.212520i | \(0.0681672\pi\) | |||||||
\(684\) | −0.668814 | −0.0255727 | ||||||||
\(685\) | −12.2680 | −0.468736 | ||||||||
\(686\) | 18.8974 | 0.721506 | ||||||||
\(687\) | −15.2853 | −0.583172 | ||||||||
\(688\) | −5.46997 | −0.208541 | ||||||||
\(689\) | −4.24500 | −0.161722 | ||||||||
\(690\) | −2.95900 | −0.112647 | ||||||||
\(691\) | 27.7144 | 1.05430 | 0.527152 | − | 0.849771i | \(-0.323260\pi\) | ||||
0.527152 | + | 0.849771i | \(0.323260\pi\) | |||||||
\(692\) | −10.0347 | −0.381462 | ||||||||
\(693\) | 0.850052 | 0.0322908 | ||||||||
\(694\) | −6.47083 | −0.245629 | ||||||||
\(695\) | −10.4928 | −0.398014 | ||||||||
\(696\) | 4.26895 | 0.161814 | ||||||||
\(697\) | 0.525599 | 0.0199085 | ||||||||
\(698\) | −12.5865 | −0.476407 | ||||||||
\(699\) | 25.3127 | 0.957414 | ||||||||
\(700\) | −10.1606 | −0.384035 | ||||||||
\(701\) | 20.4898 | 0.773890 | 0.386945 | − | 0.922103i | \(-0.373530\pi\) | ||||
0.386945 | + | 0.922103i | \(0.373530\pi\) | |||||||
\(702\) | −0.550837 | −0.0207900 | ||||||||
\(703\) | 7.22398 | 0.272457 | ||||||||
\(704\) | 0.328441 | 0.0123786 | ||||||||
\(705\) | −3.57317 | −0.134573 | ||||||||
\(706\) | 14.9803 | 0.563793 | ||||||||
\(707\) | 29.9077 | 1.12479 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −37.3032 | −1.40095 | −0.700476 | − | 0.713676i | \(-0.747029\pi\) | ||||
−0.700476 | + | 0.713676i | \(0.747029\pi\) | |||||||
\(710\) | 1.68920 | 0.0633947 | ||||||||
\(711\) | −2.43182 | −0.0912002 | ||||||||
\(712\) | −2.38147 | −0.0892493 | ||||||||
\(713\) | −3.02528 | −0.113297 | ||||||||
\(714\) | 2.58814 | 0.0968587 | ||||||||
\(715\) | 0.187507 | 0.00701235 | ||||||||
\(716\) | 10.2121 | 0.381643 | ||||||||
\(717\) | −21.1023 | −0.788078 | ||||||||
\(718\) | 30.6875 | 1.14525 | ||||||||
\(719\) | 12.1722 | 0.453945 | 0.226972 | − | 0.973901i | \(-0.427117\pi\) | ||||
0.226972 | + | 0.973901i | \(0.427117\pi\) | |||||||
\(720\) | −1.03642 | −0.0386251 | ||||||||
\(721\) | 33.4607 | 1.24614 | ||||||||
\(722\) | 18.5527 | 0.690460 | ||||||||
\(723\) | −26.8020 | −0.996777 | ||||||||
\(724\) | 9.52101 | 0.353846 | ||||||||
\(725\) | −16.7592 | −0.622420 | ||||||||
\(726\) | −10.8921 | −0.404245 | ||||||||
\(727\) | −14.0671 | −0.521719 | −0.260859 | − | 0.965377i | \(-0.584006\pi\) | ||||
−0.260859 | + | 0.965377i | \(0.584006\pi\) | |||||||
\(728\) | 1.42564 | 0.0528378 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.8940 | −0.588264 | ||||||||
\(731\) | −5.46997 | −0.202314 | ||||||||
\(732\) | −4.66400 | −0.172386 | ||||||||
\(733\) | 41.5921 | 1.53624 | 0.768119 | − | 0.640307i | \(-0.221193\pi\) | ||||
0.768119 | + | 0.640307i | \(0.221193\pi\) | |||||||
\(734\) | 19.9254 | 0.735462 | ||||||||
\(735\) | −0.312518 | −0.0115274 | ||||||||
\(736\) | −2.85502 | −0.105237 | ||||||||
\(737\) | −0.564879 | −0.0208076 | ||||||||
\(738\) | −0.525599 | −0.0193476 | ||||||||
\(739\) | −4.13980 | −0.152285 | −0.0761425 | − | 0.997097i | \(-0.524260\pi\) | ||||
−0.0761425 | + | 0.997097i | \(0.524260\pi\) | |||||||
\(740\) | 11.1946 | 0.411520 | ||||||||
\(741\) | −0.368407 | −0.0135338 | ||||||||
\(742\) | −19.9454 | −0.732218 | ||||||||
\(743\) | 19.5951 | 0.718876 | 0.359438 | − | 0.933169i | \(-0.382968\pi\) | ||||
0.359438 | + | 0.933169i | \(0.382968\pi\) | |||||||
\(744\) | −1.05963 | −0.0388480 | ||||||||
\(745\) | 2.12387 | 0.0778125 | ||||||||
\(746\) | 21.3022 | 0.779927 | ||||||||
\(747\) | −10.0619 | −0.368146 | ||||||||
\(748\) | 0.328441 | 0.0120090 | ||||||||
\(749\) | 42.2260 | 1.54291 | ||||||||
\(750\) | 9.25092 | 0.337796 | ||||||||
\(751\) | 0.815625 | 0.0297626 | 0.0148813 | − | 0.999889i | \(-0.495263\pi\) | ||||
0.0148813 | + | 0.999889i | \(0.495263\pi\) | |||||||
\(752\) | −3.44760 | −0.125721 | ||||||||
\(753\) | 17.0612 | 0.621744 | ||||||||
\(754\) | 2.35149 | 0.0856364 | ||||||||
\(755\) | 16.8943 | 0.614845 | ||||||||
\(756\) | −2.58814 | −0.0941297 | ||||||||
\(757\) | 6.60362 | 0.240013 | 0.120006 | − | 0.992773i | \(-0.461708\pi\) | ||||
0.120006 | + | 0.992773i | \(0.461708\pi\) | |||||||
\(758\) | −8.95772 | −0.325359 | ||||||||
\(759\) | −0.937707 | −0.0340366 | ||||||||
\(760\) | −0.693173 | −0.0251440 | ||||||||
\(761\) | 30.5922 | 1.10897 | 0.554484 | − | 0.832194i | \(-0.312916\pi\) | ||||
0.554484 | + | 0.832194i | \(0.312916\pi\) | |||||||
\(762\) | −5.99189 | −0.217063 | ||||||||
\(763\) | −33.2309 | −1.20304 | ||||||||
\(764\) | 8.89557 | 0.321830 | ||||||||
\(765\) | −1.03642 | −0.0374719 | ||||||||
\(766\) | −2.75199 | −0.0994336 | ||||||||
\(767\) | −0.550837 | −0.0198896 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −4.82043 | −0.173829 | −0.0869146 | − | 0.996216i | \(-0.527701\pi\) | ||||
−0.0869146 | + | 0.996216i | \(0.527701\pi\) | |||||||
\(770\) | 0.881011 | 0.0317495 | ||||||||
\(771\) | 28.4862 | 1.02591 | ||||||||
\(772\) | −15.2739 | −0.549719 | ||||||||
\(773\) | −47.9006 | −1.72286 | −0.861432 | − | 0.507873i | \(-0.830432\pi\) | ||||
−0.861432 | + | 0.507873i | \(0.830432\pi\) | |||||||
\(774\) | 5.46997 | 0.196614 | ||||||||
\(775\) | 4.15994 | 0.149430 | ||||||||
\(776\) | 6.24513 | 0.224187 | ||||||||
\(777\) | 27.9549 | 1.00288 | ||||||||
\(778\) | 20.0517 | 0.718888 | ||||||||
\(779\) | −0.351528 | −0.0125948 | ||||||||
\(780\) | −0.570899 | −0.0204415 | ||||||||
\(781\) | 0.535308 | 0.0191548 | ||||||||
\(782\) | −2.85502 | −0.102095 | ||||||||
\(783\) | −4.26895 | −0.152560 | ||||||||
\(784\) | −0.301536 | −0.0107691 | ||||||||
\(785\) | −4.12819 | −0.147341 | ||||||||
\(786\) | −19.2336 | −0.686040 | ||||||||
\(787\) | −1.68498 | −0.0600631 | −0.0300316 | − | 0.999549i | \(-0.509561\pi\) | ||||
−0.0300316 | + | 0.999549i | \(0.509561\pi\) | |||||||
\(788\) | 11.2776 | 0.401748 | ||||||||
\(789\) | 12.6911 | 0.451816 | ||||||||
\(790\) | −2.52038 | −0.0896712 | ||||||||
\(791\) | −18.8433 | −0.669991 | ||||||||
\(792\) | −0.328441 | −0.0116707 | ||||||||
\(793\) | −2.56910 | −0.0912314 | ||||||||
\(794\) | −8.78347 | −0.311714 | ||||||||
\(795\) | 7.98713 | 0.283274 | ||||||||
\(796\) | 1.48477 | 0.0526264 | ||||||||
\(797\) | −21.3264 | −0.755419 | −0.377710 | − | 0.925924i | \(-0.623288\pi\) | ||||
−0.377710 | + | 0.925924i | \(0.623288\pi\) | |||||||
\(798\) | −1.73098 | −0.0612762 | ||||||||
\(799\) | −3.44760 | −0.121967 | ||||||||
\(800\) | 3.92583 | 0.138799 | ||||||||
\(801\) | 2.38147 | 0.0841451 | ||||||||
\(802\) | −2.40824 | −0.0850379 | ||||||||
\(803\) | −5.03681 | −0.177745 | ||||||||
\(804\) | 1.71988 | 0.0606554 | ||||||||
\(805\) | −7.65831 | −0.269920 | ||||||||
\(806\) | −0.583685 | −0.0205594 | ||||||||
\(807\) | 23.1876 | 0.816242 | ||||||||
\(808\) | −11.5557 | −0.406527 | ||||||||
\(809\) | 16.0214 | 0.563283 | 0.281642 | − | 0.959520i | \(-0.409121\pi\) | ||||
0.281642 | + | 0.959520i | \(0.409121\pi\) | |||||||
\(810\) | 1.03642 | 0.0364161 | ||||||||
\(811\) | −45.8477 | −1.60993 | −0.804965 | − | 0.593322i | \(-0.797816\pi\) | ||||
−0.804965 | + | 0.593322i | \(0.797816\pi\) | |||||||
\(812\) | 11.0486 | 0.387731 | ||||||||
\(813\) | 7.63277 | 0.267693 | ||||||||
\(814\) | 3.54755 | 0.124342 | ||||||||
\(815\) | −21.7896 | −0.763256 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 3.65839 | 0.127991 | ||||||||
\(818\) | −26.4894 | −0.926181 | ||||||||
\(819\) | −1.42564 | −0.0498160 | ||||||||
\(820\) | −0.544742 | −0.0190232 | ||||||||
\(821\) | 3.10196 | 0.108259 | 0.0541296 | − | 0.998534i | \(-0.482762\pi\) | ||||
0.0541296 | + | 0.998534i | \(0.482762\pi\) | |||||||
\(822\) | 11.8369 | 0.412859 | ||||||||
\(823\) | −8.80778 | −0.307020 | −0.153510 | − | 0.988147i | \(-0.549058\pi\) | ||||
−0.153510 | + | 0.988147i | \(0.549058\pi\) | |||||||
\(824\) | −12.9285 | −0.450385 | ||||||||
\(825\) | 1.28941 | 0.0448913 | ||||||||
\(826\) | −2.58814 | −0.0900529 | ||||||||
\(827\) | 8.61291 | 0.299500 | 0.149750 | − | 0.988724i | \(-0.452153\pi\) | ||||
0.149750 | + | 0.988724i | \(0.452153\pi\) | |||||||
\(828\) | 2.85502 | 0.0992189 | ||||||||
\(829\) | 46.1638 | 1.60334 | 0.801668 | − | 0.597770i | \(-0.203946\pi\) | ||||
0.801668 | + | 0.597770i | \(0.203946\pi\) | |||||||
\(830\) | −10.4284 | −0.361974 | ||||||||
\(831\) | −16.4901 | −0.572036 | ||||||||
\(832\) | −0.550837 | −0.0190968 | ||||||||
\(833\) | −0.301536 | −0.0104476 | ||||||||
\(834\) | 10.1241 | 0.350568 | ||||||||
\(835\) | 16.8646 | 0.583623 | ||||||||
\(836\) | −0.219666 | −0.00759731 | ||||||||
\(837\) | 1.05963 | 0.0366263 | ||||||||
\(838\) | 22.8269 | 0.788542 | ||||||||
\(839\) | −2.27098 | −0.0784029 | −0.0392014 | − | 0.999231i | \(-0.512481\pi\) | ||||
−0.0392014 | + | 0.999231i | \(0.512481\pi\) | |||||||
\(840\) | −2.68240 | −0.0925516 | ||||||||
\(841\) | −10.7761 | −0.371589 | ||||||||
\(842\) | 26.9101 | 0.927383 | ||||||||
\(843\) | 16.5257 | 0.569174 | ||||||||
\(844\) | −5.42501 | −0.186737 | ||||||||
\(845\) | 13.1590 | 0.452683 | ||||||||
\(846\) | 3.44760 | 0.118531 | ||||||||
\(847\) | −28.1903 | −0.968632 | ||||||||
\(848\) | 7.70645 | 0.264641 | ||||||||
\(849\) | 22.5142 | 0.772684 | ||||||||
\(850\) | 3.92583 | 0.134655 | ||||||||
\(851\) | −30.8376 | −1.05710 | ||||||||
\(852\) | −1.62984 | −0.0558375 | ||||||||
\(853\) | 47.2041 | 1.61624 | 0.808118 | − | 0.589020i | \(-0.200486\pi\) | ||||
0.808118 | + | 0.589020i | \(0.200486\pi\) | |||||||
\(854\) | −12.0711 | −0.413064 | ||||||||
\(855\) | 0.693173 | 0.0237060 | ||||||||
\(856\) | −16.3152 | −0.557642 | ||||||||
\(857\) | 37.8605 | 1.29329 | 0.646645 | − | 0.762791i | \(-0.276172\pi\) | ||||
0.646645 | + | 0.762791i | \(0.276172\pi\) | |||||||
\(858\) | −0.180918 | −0.00617642 | ||||||||
\(859\) | −5.19943 | −0.177402 | −0.0887012 | − | 0.996058i | \(-0.528272\pi\) | ||||
−0.0887012 | + | 0.996058i | \(0.528272\pi\) | |||||||
\(860\) | 5.66919 | 0.193318 | ||||||||
\(861\) | −1.36032 | −0.0463597 | ||||||||
\(862\) | 24.9651 | 0.850314 | ||||||||
\(863\) | 22.3597 | 0.761132 | 0.380566 | − | 0.924754i | \(-0.375729\pi\) | ||||
0.380566 | + | 0.924754i | \(0.375729\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 10.4002 | 0.353616 | ||||||||
\(866\) | 4.17199 | 0.141770 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −2.74248 | −0.0930858 | ||||||||
\(869\) | −0.798709 | −0.0270943 | ||||||||
\(870\) | −4.42443 | −0.150002 | ||||||||
\(871\) | 0.947372 | 0.0321005 | ||||||||
\(872\) | 12.8397 | 0.434807 | ||||||||
\(873\) | −6.24513 | −0.211366 | ||||||||
\(874\) | 1.90948 | 0.0645891 | ||||||||
\(875\) | 23.9427 | 0.809410 | ||||||||
\(876\) | 15.3355 | 0.518138 | ||||||||
\(877\) | 1.27995 | 0.0432210 | 0.0216105 | − | 0.999766i | \(-0.493121\pi\) | ||||
0.0216105 | + | 0.999766i | \(0.493121\pi\) | |||||||
\(878\) | 34.4803 | 1.16365 | ||||||||
\(879\) | −25.7742 | −0.869343 | ||||||||
\(880\) | −0.340403 | −0.0114750 | ||||||||
\(881\) | −49.0833 | −1.65366 | −0.826829 | − | 0.562453i | \(-0.809858\pi\) | ||||
−0.826829 | + | 0.562453i | \(0.809858\pi\) | |||||||
\(882\) | 0.301536 | 0.0101532 | ||||||||
\(883\) | 8.00208 | 0.269291 | 0.134646 | − | 0.990894i | \(-0.457010\pi\) | ||||
0.134646 | + | 0.990894i | \(0.457010\pi\) | |||||||
\(884\) | −0.550837 | −0.0185266 | ||||||||
\(885\) | 1.03642 | 0.0348389 | ||||||||
\(886\) | 23.0099 | 0.773034 | ||||||||
\(887\) | −5.45354 | −0.183112 | −0.0915560 | − | 0.995800i | \(-0.529184\pi\) | ||||
−0.0915560 | + | 0.995800i | \(0.529184\pi\) | |||||||
\(888\) | −10.8012 | −0.362464 | ||||||||
\(889\) | −15.5079 | −0.520117 | ||||||||
\(890\) | 2.46820 | 0.0827344 | ||||||||
\(891\) | 0.328441 | 0.0110032 | ||||||||
\(892\) | 21.1595 | 0.708474 | ||||||||
\(893\) | 2.30581 | 0.0771609 | ||||||||
\(894\) | −2.04923 | −0.0685366 | ||||||||
\(895\) | −10.5840 | −0.353784 | ||||||||
\(896\) | −2.58814 | −0.0864637 | ||||||||
\(897\) | 1.57265 | 0.0525093 | ||||||||
\(898\) | 10.4492 | 0.348695 | ||||||||
\(899\) | −4.52352 | −0.150868 | ||||||||
\(900\) | −3.92583 | −0.130861 | ||||||||
\(901\) | 7.70645 | 0.256739 | ||||||||
\(902\) | −0.172628 | −0.00574790 | ||||||||
\(903\) | 14.1570 | 0.471117 | ||||||||
\(904\) | 7.28064 | 0.242151 | ||||||||
\(905\) | −9.86777 | −0.328016 | ||||||||
\(906\) | −16.3006 | −0.541550 | ||||||||
\(907\) | −38.1407 | −1.26644 | −0.633220 | − | 0.773972i | \(-0.718267\pi\) | ||||
−0.633220 | + | 0.773972i | \(0.718267\pi\) | |||||||
\(908\) | 14.3490 | 0.476189 | ||||||||
\(909\) | 11.5557 | 0.383278 | ||||||||
\(910\) | −1.47757 | −0.0489808 | ||||||||
\(911\) | 53.8433 | 1.78391 | 0.891953 | − | 0.452128i | \(-0.149335\pi\) | ||||
0.891953 | + | 0.452128i | \(0.149335\pi\) | |||||||
\(912\) | 0.668814 | 0.0221467 | ||||||||
\(913\) | −3.30474 | −0.109371 | ||||||||
\(914\) | −36.1241 | −1.19488 | ||||||||
\(915\) | 4.83386 | 0.159803 | ||||||||
\(916\) | 15.2853 | 0.505042 | ||||||||
\(917\) | −49.7792 | −1.64386 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −28.3433 | −0.934958 | −0.467479 | − | 0.884004i | \(-0.654838\pi\) | ||||
−0.467479 | + | 0.884004i | \(0.654838\pi\) | |||||||
\(920\) | 2.95900 | 0.0975555 | ||||||||
\(921\) | 21.8614 | 0.720359 | ||||||||
\(922\) | −40.3554 | −1.32903 | ||||||||
\(923\) | −0.897778 | −0.0295507 | ||||||||
\(924\) | −0.850052 | −0.0279647 | ||||||||
\(925\) | 42.4036 | 1.39422 | ||||||||
\(926\) | −4.06042 | −0.133434 | ||||||||
\(927\) | 12.9285 | 0.424627 | ||||||||
\(928\) | −4.26895 | −0.140135 | ||||||||
\(929\) | 29.4579 | 0.966484 | 0.483242 | − | 0.875487i | \(-0.339459\pi\) | ||||
0.483242 | + | 0.875487i | \(0.339459\pi\) | |||||||
\(930\) | 1.09823 | 0.0360122 | ||||||||
\(931\) | 0.201671 | 0.00660951 | ||||||||
\(932\) | −25.3127 | −0.829145 | ||||||||
\(933\) | 14.8414 | 0.485884 | ||||||||
\(934\) | 37.1361 | 1.21513 | ||||||||
\(935\) | −0.340403 | −0.0111324 | ||||||||
\(936\) | 0.550837 | 0.0180047 | ||||||||
\(937\) | −32.6271 | −1.06588 | −0.532941 | − | 0.846153i | \(-0.678913\pi\) | ||||
−0.532941 | + | 0.846153i | \(0.678913\pi\) | |||||||
\(938\) | 4.45128 | 0.145340 | ||||||||
\(939\) | −2.76592 | −0.0902624 | ||||||||
\(940\) | 3.57317 | 0.116544 | ||||||||
\(941\) | 37.6241 | 1.22651 | 0.613255 | − | 0.789885i | \(-0.289860\pi\) | ||||
0.613255 | + | 0.789885i | \(0.289860\pi\) | |||||||
\(942\) | 3.98312 | 0.129777 | ||||||||
\(943\) | 1.50060 | 0.0488661 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 2.68240 | 0.0872585 | ||||||||
\(946\) | 1.79656 | 0.0584113 | ||||||||
\(947\) | −48.2651 | −1.56840 | −0.784202 | − | 0.620505i | \(-0.786928\pi\) | ||||
−0.784202 | + | 0.620505i | \(0.786928\pi\) | |||||||
\(948\) | 2.43182 | 0.0789817 | ||||||||
\(949\) | 8.44735 | 0.274212 | ||||||||
\(950\) | −2.62565 | −0.0851874 | ||||||||
\(951\) | 4.05645 | 0.131539 | ||||||||
\(952\) | −2.58814 | −0.0838821 | ||||||||
\(953\) | 9.60362 | 0.311092 | 0.155546 | − | 0.987829i | \(-0.450286\pi\) | ||||
0.155546 | + | 0.987829i | \(0.450286\pi\) | |||||||
\(954\) | −7.70645 | −0.249506 | ||||||||
\(955\) | −9.21955 | −0.298338 | ||||||||
\(956\) | 21.1023 | 0.682496 | ||||||||
\(957\) | −1.40210 | −0.0453234 | ||||||||
\(958\) | 19.2776 | 0.622831 | ||||||||
\(959\) | 30.6355 | 0.989272 | ||||||||
\(960\) | 1.03642 | 0.0334503 | ||||||||
\(961\) | −29.8772 | −0.963780 | ||||||||
\(962\) | −5.94968 | −0.191825 | ||||||||
\(963\) | 16.3152 | 0.525750 | ||||||||
\(964\) | 26.8020 | 0.863234 | ||||||||
\(965\) | 15.8302 | 0.509591 | ||||||||
\(966\) | 7.38919 | 0.237743 | ||||||||
\(967\) | −38.0539 | −1.22373 | −0.611866 | − | 0.790961i | \(-0.709581\pi\) | ||||
−0.611866 | + | 0.790961i | \(0.709581\pi\) | |||||||
\(968\) | 10.8921 | 0.350086 | ||||||||
\(969\) | 0.668814 | 0.0214854 | ||||||||
\(970\) | −6.47258 | −0.207822 | ||||||||
\(971\) | 20.7233 | 0.665043 | 0.332521 | − | 0.943096i | \(-0.392101\pi\) | ||||
0.332521 | + | 0.943096i | \(0.392101\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 26.2025 | 0.840013 | ||||||||
\(974\) | 9.52560 | 0.305220 | ||||||||
\(975\) | −2.16249 | −0.0692552 | ||||||||
\(976\) | 4.66400 | 0.149291 | ||||||||
\(977\) | −27.0974 | −0.866922 | −0.433461 | − | 0.901172i | \(-0.642708\pi\) | ||||
−0.433461 | + | 0.901172i | \(0.642708\pi\) | |||||||
\(978\) | 21.0239 | 0.672270 | ||||||||
\(979\) | 0.782173 | 0.0249984 | ||||||||
\(980\) | 0.312518 | 0.00998302 | ||||||||
\(981\) | −12.8397 | −0.409940 | ||||||||
\(982\) | −10.8049 | −0.344799 | ||||||||
\(983\) | −15.5362 | −0.495527 | −0.247764 | − | 0.968821i | \(-0.579696\pi\) | ||||
−0.247764 | + | 0.968821i | \(0.579696\pi\) | |||||||
\(984\) | 0.525599 | 0.0167555 | ||||||||
\(985\) | −11.6884 | −0.372422 | ||||||||
\(986\) | −4.26895 | −0.135951 | ||||||||
\(987\) | 8.92288 | 0.284018 | ||||||||
\(988\) | 0.368407 | 0.0117206 | ||||||||
\(989\) | −15.6169 | −0.496588 | ||||||||
\(990\) | 0.340403 | 0.0108187 | ||||||||
\(991\) | 25.2340 | 0.801586 | 0.400793 | − | 0.916169i | \(-0.368735\pi\) | ||||
0.400793 | + | 0.916169i | \(0.368735\pi\) | |||||||
\(992\) | 1.05963 | 0.0336434 | ||||||||
\(993\) | −11.3405 | −0.359879 | ||||||||
\(994\) | −4.21826 | −0.133795 | ||||||||
\(995\) | −1.53885 | −0.0487848 | ||||||||
\(996\) | 10.0619 | 0.318823 | ||||||||
\(997\) | −55.9970 | −1.77344 | −0.886721 | − | 0.462304i | \(-0.847023\pi\) | ||||
−0.886721 | + | 0.462304i | \(0.847023\pi\) | |||||||
\(998\) | −25.4680 | −0.806175 | ||||||||
\(999\) | 10.8012 | 0.341734 |
(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 | 6018.2.a.u.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.u.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |