Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, 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("1134.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.73205 | 1.66902 | 0.834512 | − | 0.550990i | \(-0.185750\pi\) | ||||
0.834512 | + | 0.550990i | \(0.185750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.73205 | −1.18018 | ||||||||
\(11\) | −4.19615 | −1.26519 | −0.632594 | − | 0.774484i | \(-0.718010\pi\) | ||||
−0.632594 | + | 0.774484i | \(0.718010\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.464102 | 0.128719 | 0.0643593 | − | 0.997927i | \(-0.479500\pi\) | ||||
0.0643593 | + | 0.997927i | \(0.479500\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.00000 | 1.69775 | 0.848875 | − | 0.528594i | \(-0.177281\pi\) | ||||
0.848875 | + | 0.528594i | \(0.177281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.73205 | −0.626775 | −0.313388 | − | 0.949625i | \(-0.601464\pi\) | ||||
−0.313388 | + | 0.949625i | \(0.601464\pi\) | |||||||
\(20\) | 3.73205 | 0.834512 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.19615 | 0.894623 | ||||||||
\(23\) | 6.19615 | 1.29199 | 0.645994 | − | 0.763343i | \(-0.276443\pi\) | ||||
0.645994 | + | 0.763343i | \(0.276443\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.92820 | 1.78564 | ||||||||
\(26\) | −0.464102 | −0.0910178 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 8.46410 | 1.57174 | 0.785872 | − | 0.618389i | \(-0.212214\pi\) | ||||
0.785872 | + | 0.618389i | \(0.212214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.19615 | −0.394441 | −0.197220 | − | 0.980359i | \(-0.563191\pi\) | ||||
−0.197220 | + | 0.980359i | \(0.563191\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.00000 | −1.20049 | ||||||||
\(35\) | −3.73205 | −0.630832 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.66025 | −1.09494 | −0.547470 | − | 0.836826i | \(-0.684409\pi\) | ||||
−0.547470 | + | 0.836826i | \(0.684409\pi\) | |||||||
\(38\) | 2.73205 | 0.443197 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.73205 | −0.590089 | ||||||||
\(41\) | 9.46410 | 1.47804 | 0.739022 | − | 0.673681i | \(-0.235288\pi\) | ||||
0.739022 | + | 0.673681i | \(0.235288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.46410 | 0.833268 | 0.416634 | − | 0.909074i | \(-0.363210\pi\) | ||||
0.416634 | + | 0.909074i | \(0.363210\pi\) | |||||||
\(44\) | −4.19615 | −0.632594 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.19615 | −0.913573 | ||||||||
\(47\) | 1.26795 | 0.184949 | 0.0924747 | − | 0.995715i | \(-0.470522\pi\) | ||||
0.0924747 | + | 0.995715i | \(0.470522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.92820 | −1.26264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.464102 | 0.0643593 | ||||||||
\(53\) | −2.53590 | −0.348332 | −0.174166 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174166 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.6603 | −2.11163 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.46410 | −1.11139 | ||||||||
\(59\) | −6.19615 | −0.806670 | −0.403335 | − | 0.915052i | \(-0.632149\pi\) | ||||
−0.403335 | + | 0.915052i | \(0.632149\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.92820 | −1.27118 | −0.635588 | − | 0.772028i | \(-0.719242\pi\) | ||||
−0.635588 | + | 0.772028i | \(0.719242\pi\) | |||||||
\(62\) | 2.19615 | 0.278912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.73205 | 0.214834 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.26795 | −0.399244 | −0.199622 | − | 0.979873i | \(-0.563971\pi\) | ||||
−0.199622 | + | 0.979873i | \(0.563971\pi\) | |||||||
\(68\) | 7.00000 | 0.848875 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.73205 | 0.446065 | ||||||||
\(71\) | 13.4641 | 1.59789 | 0.798947 | − | 0.601401i | \(-0.205391\pi\) | ||||
0.798947 | + | 0.601401i | \(0.205391\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.7321 | 1.37313 | 0.686566 | − | 0.727067i | \(-0.259117\pi\) | ||||
0.686566 | + | 0.727067i | \(0.259117\pi\) | |||||||
\(74\) | 6.66025 | 0.774239 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.73205 | −0.313388 | ||||||||
\(77\) | 4.19615 | 0.478196 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1244 | 1.70162 | 0.850811 | − | 0.525471i | \(-0.176111\pi\) | ||||
0.850811 | + | 0.525471i | \(0.176111\pi\) | |||||||
\(80\) | 3.73205 | 0.417256 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.46410 | −1.04514 | ||||||||
\(83\) | −14.5885 | −1.60129 | −0.800646 | − | 0.599138i | \(-0.795510\pi\) | ||||
−0.800646 | + | 0.599138i | \(0.795510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.1244 | 2.83358 | ||||||||
\(86\) | −5.46410 | −0.589209 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.19615 | 0.447311 | ||||||||
\(89\) | −3.92820 | −0.416389 | −0.208194 | − | 0.978087i | \(-0.566759\pi\) | ||||
−0.208194 | + | 0.978087i | \(0.566759\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.464102 | −0.0486511 | ||||||||
\(92\) | 6.19615 | 0.645994 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.26795 | −0.130779 | ||||||||
\(95\) | −10.1962 | −1.04610 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.92820 | −0.297314 | −0.148657 | − | 0.988889i | \(-0.547495\pi\) | ||||
−0.148657 | + | 0.988889i | \(0.547495\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.92820 | 0.892820 | ||||||||
\(101\) | −4.92820 | −0.490375 | −0.245187 | − | 0.969476i | \(-0.578849\pi\) | ||||
−0.245187 | + | 0.969476i | \(0.578849\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3923 | 1.22105 | 0.610525 | − | 0.791997i | \(-0.290958\pi\) | ||||
0.610525 | + | 0.791997i | \(0.290958\pi\) | |||||||
\(104\) | −0.464102 | −0.0455089 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.53590 | 0.246308 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.19615 | −0.689266 | −0.344633 | − | 0.938737i | \(-0.611997\pi\) | ||||
−0.344633 | + | 0.938737i | \(0.611997\pi\) | |||||||
\(110\) | 15.6603 | 1.49315 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −2.26795 | −0.213351 | −0.106675 | − | 0.994294i | \(-0.534021\pi\) | ||||
−0.106675 | + | 0.994294i | \(0.534021\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.1244 | 2.15636 | ||||||||
\(116\) | 8.46410 | 0.785872 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.19615 | 0.570402 | ||||||||
\(119\) | −7.00000 | −0.641689 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.60770 | 0.600700 | ||||||||
\(122\) | 9.92820 | 0.898857 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.19615 | −0.197220 | ||||||||
\(125\) | 14.6603 | 1.31125 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.73205 | −0.151911 | ||||||||
\(131\) | 17.4641 | 1.52585 | 0.762923 | − | 0.646490i | \(-0.223764\pi\) | ||||
0.762923 | + | 0.646490i | \(0.223764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.73205 | 0.236899 | ||||||||
\(134\) | 3.26795 | 0.282308 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.00000 | −0.600245 | ||||||||
\(137\) | −11.7321 | −1.00234 | −0.501168 | − | 0.865350i | \(-0.667096\pi\) | ||||
−0.501168 | + | 0.865350i | \(0.667096\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.73205 | −0.571005 | −0.285503 | − | 0.958378i | \(-0.592161\pi\) | ||||
−0.285503 | + | 0.958378i | \(0.592161\pi\) | |||||||
\(140\) | −3.73205 | −0.315416 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.4641 | −1.12988 | ||||||||
\(143\) | −1.94744 | −0.162853 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 31.5885 | 2.62328 | ||||||||
\(146\) | −11.7321 | −0.970951 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.66025 | −0.547470 | ||||||||
\(149\) | 9.00000 | 0.737309 | 0.368654 | − | 0.929567i | \(-0.379819\pi\) | ||||
0.368654 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.1962 | −1.31802 | −0.659012 | − | 0.752132i | \(-0.729025\pi\) | ||||
−0.659012 | + | 0.752132i | \(0.729025\pi\) | |||||||
\(152\) | 2.73205 | 0.221599 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.19615 | −0.338136 | ||||||||
\(155\) | −8.19615 | −0.658331 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | −0.0798087 | −0.0399043 | − | 0.999204i | \(-0.512705\pi\) | ||||
−0.0399043 | + | 0.999204i | \(0.512705\pi\) | |||||||
\(158\) | −15.1244 | −1.20323 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.73205 | −0.295045 | ||||||||
\(161\) | −6.19615 | −0.488325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.53590 | −0.511931 | −0.255966 | − | 0.966686i | \(-0.582393\pi\) | ||||
−0.255966 | + | 0.966686i | \(0.582393\pi\) | |||||||
\(164\) | 9.46410 | 0.739022 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5885 | 1.13228 | ||||||||
\(167\) | −12.1962 | −0.943767 | −0.471883 | − | 0.881661i | \(-0.656426\pi\) | ||||
−0.471883 | + | 0.881661i | \(0.656426\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7846 | −0.983432 | ||||||||
\(170\) | −26.1244 | −2.00365 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.46410 | 0.416634 | ||||||||
\(173\) | 9.73205 | 0.739914 | 0.369957 | − | 0.929049i | \(-0.379372\pi\) | ||||
0.369957 | + | 0.929049i | \(0.379372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.92820 | −0.674909 | ||||||||
\(176\) | −4.19615 | −0.316297 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.92820 | 0.294431 | ||||||||
\(179\) | 8.19615 | 0.612609 | 0.306305 | − | 0.951934i | \(-0.400907\pi\) | ||||
0.306305 | + | 0.951934i | \(0.400907\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.39230 | 0.326477 | 0.163239 | − | 0.986587i | \(-0.447806\pi\) | ||||
0.163239 | + | 0.986587i | \(0.447806\pi\) | |||||||
\(182\) | 0.464102 | 0.0344015 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.19615 | −0.456786 | ||||||||
\(185\) | −24.8564 | −1.82748 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −29.3731 | −2.14797 | ||||||||
\(188\) | 1.26795 | 0.0924747 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.1962 | 0.739707 | ||||||||
\(191\) | 11.6603 | 0.843706 | 0.421853 | − | 0.906664i | \(-0.361380\pi\) | ||||
0.421853 | + | 0.906664i | \(0.361380\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.85641 | −0.637498 | −0.318749 | − | 0.947839i | \(-0.603263\pi\) | ||||
−0.318749 | + | 0.947839i | \(0.603263\pi\) | |||||||
\(194\) | 2.92820 | 0.210233 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −25.7846 | −1.83708 | −0.918539 | − | 0.395331i | \(-0.870630\pi\) | ||||
−0.918539 | + | 0.395331i | \(0.870630\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.12436 | 0.363256 | 0.181628 | − | 0.983367i | \(-0.441863\pi\) | ||||
0.181628 | + | 0.983367i | \(0.441863\pi\) | |||||||
\(200\) | −8.92820 | −0.631319 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.92820 | 0.346747 | ||||||||
\(203\) | −8.46410 | −0.594063 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 35.3205 | 2.46689 | ||||||||
\(206\) | −12.3923 | −0.863413 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.464102 | 0.0321797 | ||||||||
\(209\) | 11.4641 | 0.792988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.7321 | −1.42725 | −0.713627 | − | 0.700526i | \(-0.752949\pi\) | ||||
−0.713627 | + | 0.700526i | \(0.752949\pi\) | |||||||
\(212\) | −2.53590 | −0.174166 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.3923 | 1.39074 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.19615 | 0.149085 | ||||||||
\(218\) | 7.19615 | 0.487385 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −15.6603 | −1.05581 | ||||||||
\(221\) | 3.24871 | 0.218532 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.5359 | −1.24126 | −0.620628 | − | 0.784105i | \(-0.713122\pi\) | ||||
−0.620628 | + | 0.784105i | \(0.713122\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.26795 | 0.150862 | ||||||||
\(227\) | −5.07180 | −0.336627 | −0.168313 | − | 0.985734i | \(-0.553832\pi\) | ||||
−0.168313 | + | 0.985734i | \(0.553832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.46410 | 0.294996 | 0.147498 | − | 0.989062i | \(-0.452878\pi\) | ||||
0.147498 | + | 0.989062i | \(0.452878\pi\) | |||||||
\(230\) | −23.1244 | −1.52477 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.46410 | −0.555695 | ||||||||
\(233\) | −13.1962 | −0.864509 | −0.432254 | − | 0.901752i | \(-0.642282\pi\) | ||||
−0.432254 | + | 0.901752i | \(0.642282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.73205 | 0.308685 | ||||||||
\(236\) | −6.19615 | −0.403335 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.00000 | 0.453743 | ||||||||
\(239\) | 28.0526 | 1.81457 | 0.907285 | − | 0.420517i | \(-0.138151\pi\) | ||||
0.907285 | + | 0.420517i | \(0.138151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7321 | −1.14222 | −0.571111 | − | 0.820873i | \(-0.693487\pi\) | ||||
−0.571111 | + | 0.820873i | \(0.693487\pi\) | |||||||
\(242\) | −6.60770 | −0.424759 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.92820 | −0.635588 | ||||||||
\(245\) | 3.73205 | 0.238432 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.26795 | −0.0806777 | ||||||||
\(248\) | 2.19615 | 0.139456 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.6603 | −0.927196 | ||||||||
\(251\) | 16.0526 | 1.01323 | 0.506614 | − | 0.862173i | \(-0.330897\pi\) | ||||
0.506614 | + | 0.862173i | \(0.330897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.0000 | −1.63461 | ||||||||
\(254\) | −12.0000 | −0.752947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.464102 | −0.0289499 | −0.0144749 | − | 0.999895i | \(-0.504608\pi\) | ||||
−0.0144749 | + | 0.999895i | \(0.504608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.66025 | 0.413848 | ||||||||
\(260\) | 1.73205 | 0.107417 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.4641 | −1.07894 | ||||||||
\(263\) | −23.6603 | −1.45895 | −0.729477 | − | 0.684005i | \(-0.760236\pi\) | ||||
−0.729477 | + | 0.684005i | \(0.760236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.46410 | −0.581375 | ||||||||
\(266\) | −2.73205 | −0.167513 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.26795 | −0.199622 | ||||||||
\(269\) | −25.5885 | −1.56016 | −0.780078 | − | 0.625682i | \(-0.784821\pi\) | ||||
−0.780078 | + | 0.625682i | \(0.784821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.5167 | 1.55003 | 0.775013 | − | 0.631945i | \(-0.217743\pi\) | ||||
0.775013 | + | 0.631945i | \(0.217743\pi\) | |||||||
\(272\) | 7.00000 | 0.424437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.7321 | 0.708759 | ||||||||
\(275\) | −37.4641 | −2.25917 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.7846 | 1.36899 | 0.684497 | − | 0.729015i | \(-0.260022\pi\) | ||||
0.684497 | + | 0.729015i | \(0.260022\pi\) | |||||||
\(278\) | 6.73205 | 0.403762 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.73205 | 0.223033 | ||||||||
\(281\) | −2.80385 | −0.167264 | −0.0836318 | − | 0.996497i | \(-0.526652\pi\) | ||||
−0.0836318 | + | 0.996497i | \(0.526652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.3205 | −1.14848 | −0.574242 | − | 0.818685i | \(-0.694703\pi\) | ||||
−0.574242 | + | 0.818685i | \(0.694703\pi\) | |||||||
\(284\) | 13.4641 | 0.798947 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.94744 | 0.115155 | ||||||||
\(287\) | −9.46410 | −0.558648 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0000 | 1.88235 | ||||||||
\(290\) | −31.5885 | −1.85494 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.7321 | 0.686566 | ||||||||
\(293\) | 20.6603 | 1.20698 | 0.603492 | − | 0.797369i | \(-0.293775\pi\) | ||||
0.603492 | + | 0.797369i | \(0.293775\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.1244 | −1.34635 | ||||||||
\(296\) | 6.66025 | 0.387119 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.00000 | −0.521356 | ||||||||
\(299\) | 2.87564 | 0.166303 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.46410 | −0.314946 | ||||||||
\(302\) | 16.1962 | 0.931984 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.73205 | −0.156694 | ||||||||
\(305\) | −37.0526 | −2.12162 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.85641 | 0.334243 | 0.167121 | − | 0.985936i | \(-0.446553\pi\) | ||||
0.167121 | + | 0.985936i | \(0.446553\pi\) | |||||||
\(308\) | 4.19615 | 0.239098 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.19615 | 0.465510 | ||||||||
\(311\) | −0.196152 | −0.0111228 | −0.00556139 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00556139 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.58846 | −0.315878 | −0.157939 | − | 0.987449i | \(-0.550485\pi\) | ||||
−0.157939 | + | 0.987449i | \(0.550485\pi\) | |||||||
\(314\) | 1.00000 | 0.0564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.1244 | 0.850811 | ||||||||
\(317\) | −10.6077 | −0.595788 | −0.297894 | − | 0.954599i | \(-0.596284\pi\) | ||||
−0.297894 | + | 0.954599i | \(0.596284\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −35.5167 | −1.98855 | ||||||||
\(320\) | 3.73205 | 0.208628 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.19615 | 0.345298 | ||||||||
\(323\) | −19.1244 | −1.06411 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.14359 | 0.229845 | ||||||||
\(326\) | 6.53590 | 0.361990 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.46410 | −0.522568 | ||||||||
\(329\) | −1.26795 | −0.0699043 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.39230 | −0.461283 | −0.230641 | − | 0.973039i | \(-0.574082\pi\) | ||||
−0.230641 | + | 0.973039i | \(0.574082\pi\) | |||||||
\(332\) | −14.5885 | −0.800646 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1962 | 0.667344 | ||||||||
\(335\) | −12.1962 | −0.666347 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.39230 | 0.239264 | 0.119632 | − | 0.992818i | \(-0.461829\pi\) | ||||
0.119632 | + | 0.992818i | \(0.461829\pi\) | |||||||
\(338\) | 12.7846 | 0.695391 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 26.1244 | 1.41679 | ||||||||
\(341\) | 9.21539 | 0.499041 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.46410 | −0.294605 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.73205 | −0.523198 | ||||||||
\(347\) | 14.5359 | 0.780328 | 0.390164 | − | 0.920745i | \(-0.372418\pi\) | ||||
0.390164 | + | 0.920745i | \(0.372418\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.46410 | −0.292487 | −0.146243 | − | 0.989249i | \(-0.546718\pi\) | ||||
−0.146243 | + | 0.989249i | \(0.546718\pi\) | |||||||
\(350\) | 8.92820 | 0.477233 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.19615 | 0.223656 | ||||||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 50.2487 | 2.66692 | ||||||||
\(356\) | −3.92820 | −0.208194 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.19615 | −0.433180 | ||||||||
\(359\) | 2.92820 | 0.154545 | 0.0772723 | − | 0.997010i | \(-0.475379\pi\) | ||||
0.0772723 | + | 0.997010i | \(0.475379\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5359 | −0.607153 | ||||||||
\(362\) | −4.39230 | −0.230854 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.464102 | −0.0243255 | ||||||||
\(365\) | 43.7846 | 2.29179 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1244 | −0.685086 | −0.342543 | − | 0.939502i | \(-0.611288\pi\) | ||||
−0.342543 | + | 0.939502i | \(0.611288\pi\) | |||||||
\(368\) | 6.19615 | 0.322997 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 24.8564 | 1.29222 | ||||||||
\(371\) | 2.53590 | 0.131657 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.8564 | −1.75302 | −0.876509 | − | 0.481385i | \(-0.840134\pi\) | ||||
−0.876509 | + | 0.481385i | \(0.840134\pi\) | |||||||
\(374\) | 29.3731 | 1.51885 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.26795 | −0.0653895 | ||||||||
\(377\) | 3.92820 | 0.202313 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5167 | 0.899770 | 0.449885 | − | 0.893086i | \(-0.351465\pi\) | ||||
0.449885 | + | 0.893086i | \(0.351465\pi\) | |||||||
\(380\) | −10.1962 | −0.523052 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.6603 | −0.596590 | ||||||||
\(383\) | −35.7128 | −1.82484 | −0.912420 | − | 0.409256i | \(-0.865788\pi\) | ||||
−0.912420 | + | 0.409256i | \(0.865788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.6603 | 0.798120 | ||||||||
\(386\) | 8.85641 | 0.450779 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.92820 | −0.148657 | ||||||||
\(389\) | −6.53590 | −0.331383 | −0.165692 | − | 0.986178i | \(-0.552986\pi\) | ||||
−0.165692 | + | 0.986178i | \(0.552986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.3731 | 2.19347 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.7846 | 1.29901 | ||||||||
\(395\) | 56.4449 | 2.84005 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0000 | −1.05396 | −0.526980 | − | 0.849878i | \(-0.676676\pi\) | ||||
−0.526980 | + | 0.849878i | \(0.676676\pi\) | |||||||
\(398\) | −5.12436 | −0.256861 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.92820 | 0.446410 | ||||||||
\(401\) | −34.5167 | −1.72368 | −0.861840 | − | 0.507180i | \(-0.830688\pi\) | ||||
−0.861840 | + | 0.507180i | \(0.830688\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.01924 | −0.0507719 | ||||||||
\(404\) | −4.92820 | −0.245187 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.46410 | 0.420066 | ||||||||
\(407\) | 27.9474 | 1.38530 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.6603 | 1.71384 | 0.856920 | − | 0.515450i | \(-0.172375\pi\) | ||||
0.856920 | + | 0.515450i | \(0.172375\pi\) | |||||||
\(410\) | −35.3205 | −1.74436 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.3923 | 0.610525 | ||||||||
\(413\) | 6.19615 | 0.304893 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −54.4449 | −2.67259 | ||||||||
\(416\) | −0.464102 | −0.0227545 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.4641 | −0.560728 | ||||||||
\(419\) | −2.53590 | −0.123887 | −0.0619434 | − | 0.998080i | \(-0.519730\pi\) | ||||
−0.0619434 | + | 0.998080i | \(0.519730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.1244 | −1.17575 | −0.587875 | − | 0.808952i | \(-0.700035\pi\) | ||||
−0.587875 | + | 0.808952i | \(0.700035\pi\) | |||||||
\(422\) | 20.7321 | 1.00922 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.53590 | 0.123154 | ||||||||
\(425\) | 62.4974 | 3.03157 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.92820 | 0.480459 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.3923 | −0.983404 | ||||||||
\(431\) | −21.4641 | −1.03389 | −0.516945 | − | 0.856019i | \(-0.672931\pi\) | ||||
−0.516945 | + | 0.856019i | \(0.672931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2679 | 0.589560 | 0.294780 | − | 0.955565i | \(-0.404754\pi\) | ||||
0.294780 | + | 0.955565i | \(0.404754\pi\) | |||||||
\(434\) | −2.19615 | −0.105419 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.19615 | −0.344633 | ||||||||
\(437\) | −16.9282 | −0.809786 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.3205 | −0.540298 | −0.270149 | − | 0.962818i | \(-0.587073\pi\) | ||||
−0.270149 | + | 0.962818i | \(0.587073\pi\) | |||||||
\(440\) | 15.6603 | 0.746573 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.24871 | −0.154525 | ||||||||
\(443\) | −18.7321 | −0.889987 | −0.444993 | − | 0.895534i | \(-0.646794\pi\) | ||||
−0.444993 | + | 0.895534i | \(0.646794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6603 | −0.694963 | ||||||||
\(446\) | 18.5359 | 0.877700 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −11.8564 | −0.559538 | −0.279769 | − | 0.960067i | \(-0.590258\pi\) | ||||
−0.279769 | + | 0.960067i | \(0.590258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.7128 | −1.87000 | ||||||||
\(452\) | −2.26795 | −0.106675 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.07180 | 0.238031 | ||||||||
\(455\) | −1.73205 | −0.0811998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.8564 | 0.975622 | 0.487811 | − | 0.872949i | \(-0.337796\pi\) | ||||
0.487811 | + | 0.872949i | \(0.337796\pi\) | |||||||
\(458\) | −4.46410 | −0.208594 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 23.1244 | 1.07818 | ||||||||
\(461\) | 34.7846 | 1.62008 | 0.810040 | − | 0.586374i | \(-0.199445\pi\) | ||||
0.810040 | + | 0.586374i | \(0.199445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.5885 | −1.51451 | −0.757257 | − | 0.653117i | \(-0.773461\pi\) | ||||
−0.757257 | + | 0.653117i | \(0.773461\pi\) | |||||||
\(464\) | 8.46410 | 0.392936 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.1962 | 0.611300 | ||||||||
\(467\) | 14.5885 | 0.675073 | 0.337537 | − | 0.941312i | \(-0.390406\pi\) | ||||
0.337537 | + | 0.941312i | \(0.390406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.26795 | 0.150900 | ||||||||
\(470\) | −4.73205 | −0.218273 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.19615 | 0.285201 | ||||||||
\(473\) | −22.9282 | −1.05424 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.3923 | −1.11920 | ||||||||
\(476\) | −7.00000 | −0.320844 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.0526 | −1.28309 | ||||||||
\(479\) | 23.5167 | 1.07450 | 0.537252 | − | 0.843422i | \(-0.319462\pi\) | ||||
0.537252 | + | 0.843422i | \(0.319462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.09103 | −0.140939 | ||||||||
\(482\) | 17.7321 | 0.807673 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.60770 | 0.300350 | ||||||||
\(485\) | −10.9282 | −0.496224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.5885 | −1.29547 | −0.647733 | − | 0.761867i | \(-0.724283\pi\) | ||||
−0.647733 | + | 0.761867i | \(0.724283\pi\) | |||||||
\(488\) | 9.92820 | 0.449429 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.73205 | −0.168597 | ||||||||
\(491\) | 33.4641 | 1.51021 | 0.755107 | − | 0.655602i | \(-0.227585\pi\) | ||||
0.755107 | + | 0.655602i | \(0.227585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 59.2487 | 2.66843 | ||||||||
\(494\) | 1.26795 | 0.0570477 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.19615 | −0.0986102 | ||||||||
\(497\) | −13.4641 | −0.603947 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.1962 | 1.35177 | 0.675883 | − | 0.737009i | \(-0.263763\pi\) | ||||
0.675883 | + | 0.737009i | \(0.263763\pi\) | |||||||
\(500\) | 14.6603 | 0.655626 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.0526 | −0.716461 | ||||||||
\(503\) | 1.94744 | 0.0868321 | 0.0434161 | − | 0.999057i | \(-0.486176\pi\) | ||||
0.0434161 | + | 0.999057i | \(0.486176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.3923 | −0.818447 | ||||||||
\(506\) | 26.0000 | 1.15584 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | 4.14359 | 0.183662 | 0.0918308 | − | 0.995775i | \(-0.470728\pi\) | ||||
0.0918308 | + | 0.995775i | \(0.470728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7321 | −0.518995 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.464102 | 0.0204706 | ||||||||
\(515\) | 46.2487 | 2.03796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.32051 | −0.233996 | ||||||||
\(518\) | −6.66025 | −0.292635 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.73205 | −0.0759555 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.1769 | −1.27582 | −0.637909 | − | 0.770112i | \(-0.720200\pi\) | ||||
−0.637909 | + | 0.770112i | \(0.720200\pi\) | |||||||
\(524\) | 17.4641 | 0.762923 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.6603 | 1.03164 | ||||||||
\(527\) | −15.3731 | −0.669661 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.3923 | 0.669231 | ||||||||
\(530\) | 9.46410 | 0.411094 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.73205 | 0.118449 | ||||||||
\(533\) | 4.39230 | 0.190252 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.26795 | 0.141154 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.5885 | 1.10320 | ||||||||
\(539\) | −4.19615 | −0.180741 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.6603 | 0.888254 | 0.444127 | − | 0.895964i | \(-0.353514\pi\) | ||||
0.444127 | + | 0.895964i | \(0.353514\pi\) | |||||||
\(542\) | −25.5167 | −1.09603 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.00000 | −0.300123 | ||||||||
\(545\) | −26.8564 | −1.15040 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.2679 | −0.823838 | −0.411919 | − | 0.911220i | \(-0.635141\pi\) | ||||
−0.411919 | + | 0.911220i | \(0.635141\pi\) | |||||||
\(548\) | −11.7321 | −0.501168 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 37.4641 | 1.59747 | ||||||||
\(551\) | −23.1244 | −0.985131 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1244 | −0.643153 | ||||||||
\(554\) | −22.7846 | −0.968025 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.73205 | −0.285503 | ||||||||
\(557\) | 10.0718 | 0.426756 | 0.213378 | − | 0.976970i | \(-0.431553\pi\) | ||||
0.213378 | + | 0.976970i | \(0.431553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.53590 | 0.107257 | ||||||||
\(560\) | −3.73205 | −0.157708 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.80385 | 0.118273 | ||||||||
\(563\) | −35.7128 | −1.50512 | −0.752558 | − | 0.658526i | \(-0.771180\pi\) | ||||
−0.752558 | + | 0.658526i | \(0.771180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.46410 | −0.356087 | ||||||||
\(566\) | 19.3205 | 0.812102 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.4641 | −0.564941 | ||||||||
\(569\) | 12.8038 | 0.536765 | 0.268383 | − | 0.963312i | \(-0.413511\pi\) | ||||
0.268383 | + | 0.963312i | \(0.413511\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.2679 | −0.806339 | −0.403169 | − | 0.915125i | \(-0.632091\pi\) | ||||
−0.403169 | + | 0.915125i | \(0.632091\pi\) | |||||||
\(572\) | −1.94744 | −0.0814266 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.46410 | 0.395024 | ||||||||
\(575\) | 55.3205 | 2.30702 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.33975 | 0.305558 | 0.152779 | − | 0.988260i | \(-0.451178\pi\) | ||||
0.152779 | + | 0.988260i | \(0.451178\pi\) | |||||||
\(578\) | −32.0000 | −1.33102 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 31.5885 | 1.31164 | ||||||||
\(581\) | 14.5885 | 0.605231 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.6410 | 0.440706 | ||||||||
\(584\) | −11.7321 | −0.485476 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.6603 | −0.853467 | ||||||||
\(587\) | 11.2679 | 0.465078 | 0.232539 | − | 0.972587i | \(-0.425297\pi\) | ||||
0.232539 | + | 0.972587i | \(0.425297\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 23.1244 | 0.952015 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.66025 | −0.273735 | ||||||||
\(593\) | 40.1769 | 1.64987 | 0.824934 | − | 0.565229i | \(-0.191212\pi\) | ||||
0.824934 | + | 0.565229i | \(0.191212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.1244 | −1.07099 | ||||||||
\(596\) | 9.00000 | 0.368654 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.87564 | −0.117594 | ||||||||
\(599\) | 9.12436 | 0.372811 | 0.186406 | − | 0.982473i | \(-0.440316\pi\) | ||||
0.186406 | + | 0.982473i | \(0.440316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.80385 | 0.359116 | 0.179558 | − | 0.983747i | \(-0.442533\pi\) | ||||
0.179558 | + | 0.983747i | \(0.442533\pi\) | |||||||
\(602\) | 5.46410 | 0.222700 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.1962 | −0.659012 | ||||||||
\(605\) | 24.6603 | 1.00258 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.58846 | 0.267417 | 0.133709 | − | 0.991021i | \(-0.457311\pi\) | ||||
0.133709 | + | 0.991021i | \(0.457311\pi\) | |||||||
\(608\) | 2.73205 | 0.110799 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.0526 | 1.50021 | ||||||||
\(611\) | 0.588457 | 0.0238064 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.7846 | −0.597145 | −0.298572 | − | 0.954387i | \(-0.596510\pi\) | ||||
−0.298572 | + | 0.954387i | \(0.596510\pi\) | |||||||
\(614\) | −5.85641 | −0.236345 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.19615 | −0.169068 | ||||||||
\(617\) | −39.9808 | −1.60956 | −0.804782 | − | 0.593570i | \(-0.797718\pi\) | ||||
−0.804782 | + | 0.593570i | \(0.797718\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.7128 | 1.27465 | 0.637323 | − | 0.770597i | \(-0.280042\pi\) | ||||
0.637323 | + | 0.770597i | \(0.280042\pi\) | |||||||
\(620\) | −8.19615 | −0.329165 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.196152 | 0.00786500 | ||||||||
\(623\) | 3.92820 | 0.157380 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 5.58846 | 0.223360 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | −0.0399043 | ||||||||
\(629\) | −46.6218 | −1.85893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6603 | 0.543806 | 0.271903 | − | 0.962325i | \(-0.412347\pi\) | ||||
0.271903 | + | 0.962325i | \(0.412347\pi\) | |||||||
\(632\) | −15.1244 | −0.601615 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.6077 | 0.421285 | ||||||||
\(635\) | 44.7846 | 1.77722 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.464102 | 0.0183884 | ||||||||
\(638\) | 35.5167 | 1.40612 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.73205 | −0.147522 | ||||||||
\(641\) | −19.4449 | −0.768026 | −0.384013 | − | 0.923328i | \(-0.625458\pi\) | ||||
−0.384013 | + | 0.923328i | \(0.625458\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.5885 | −1.60065 | −0.800326 | − | 0.599565i | \(-0.795340\pi\) | ||||
−0.800326 | + | 0.599565i | \(0.795340\pi\) | |||||||
\(644\) | −6.19615 | −0.244163 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.1244 | 0.752438 | ||||||||
\(647\) | 16.3923 | 0.644448 | 0.322224 | − | 0.946663i | \(-0.395570\pi\) | ||||
0.322224 | + | 0.946663i | \(0.395570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.0000 | 1.02059 | ||||||||
\(650\) | −4.14359 | −0.162525 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.53590 | −0.255966 | ||||||||
\(653\) | 18.2487 | 0.714127 | 0.357064 | − | 0.934080i | \(-0.383778\pi\) | ||||
0.357064 | + | 0.934080i | \(0.383778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 65.1769 | 2.54667 | ||||||||
\(656\) | 9.46410 | 0.369511 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.26795 | 0.0494298 | ||||||||
\(659\) | −15.6077 | −0.607989 | −0.303995 | − | 0.952674i | \(-0.598321\pi\) | ||||
−0.303995 | + | 0.952674i | \(0.598321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.8564 | 0.577847 | 0.288924 | − | 0.957352i | \(-0.406703\pi\) | ||||
0.288924 | + | 0.957352i | \(0.406703\pi\) | |||||||
\(662\) | 8.39230 | 0.326176 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.5885 | 0.566142 | ||||||||
\(665\) | 10.1962 | 0.395390 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 52.4449 | 2.03067 | ||||||||
\(668\) | −12.1962 | −0.471883 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.1962 | 0.471178 | ||||||||
\(671\) | 41.6603 | 1.60828 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3205 | 0.629109 | 0.314555 | − | 0.949239i | \(-0.398145\pi\) | ||||
0.314555 | + | 0.949239i | \(0.398145\pi\) | |||||||
\(674\) | −4.39230 | −0.169185 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7846 | −0.491716 | ||||||||
\(677\) | 36.0000 | 1.38359 | 0.691796 | − | 0.722093i | \(-0.256820\pi\) | ||||
0.691796 | + | 0.722093i | \(0.256820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.92820 | 0.112374 | ||||||||
\(680\) | −26.1244 | −1.00182 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.21539 | −0.352876 | ||||||||
\(683\) | 25.8564 | 0.989368 | 0.494684 | − | 0.869073i | \(-0.335284\pi\) | ||||
0.494684 | + | 0.869073i | \(0.335284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −43.7846 | −1.67292 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.46410 | 0.208317 | ||||||||
\(689\) | −1.17691 | −0.0448369 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 9.73205 | 0.369957 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.5359 | −0.551775 | ||||||||
\(695\) | −25.1244 | −0.953021 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 66.2487 | 2.50935 | ||||||||
\(698\) | 5.46410 | 0.206819 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.92820 | −0.337454 | ||||||||
\(701\) | 6.60770 | 0.249569 | 0.124785 | − | 0.992184i | \(-0.460176\pi\) | ||||
0.124785 | + | 0.992184i | \(0.460176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.1962 | 0.686281 | ||||||||
\(704\) | −4.19615 | −0.158148 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | 4.92820 | 0.185344 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.1244 | −1.05623 | −0.528116 | − | 0.849172i | \(-0.677101\pi\) | ||||
−0.528116 | + | 0.849172i | \(0.677101\pi\) | |||||||
\(710\) | −50.2487 | −1.88580 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.92820 | 0.147216 | ||||||||
\(713\) | −13.6077 | −0.509612 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.26795 | −0.271806 | ||||||||
\(716\) | 8.19615 | 0.306305 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.92820 | −0.109280 | ||||||||
\(719\) | −2.53590 | −0.0945731 | −0.0472865 | − | 0.998881i | \(-0.515057\pi\) | ||||
−0.0472865 | + | 0.998881i | \(0.515057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3923 | −0.461514 | ||||||||
\(722\) | 11.5359 | 0.429322 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.39230 | 0.163239 | ||||||||
\(725\) | 75.5692 | 2.80657 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.6795 | 0.618608 | 0.309304 | − | 0.950963i | \(-0.399904\pi\) | ||||
0.309304 | + | 0.950963i | \(0.399904\pi\) | |||||||
\(728\) | 0.464102 | 0.0172008 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −43.7846 | −1.62054 | ||||||||
\(731\) | 38.2487 | 1.41468 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.6795 | 0.468328 | 0.234164 | − | 0.972197i | \(-0.424765\pi\) | ||||
0.234164 | + | 0.972197i | \(0.424765\pi\) | |||||||
\(734\) | 13.1244 | 0.484429 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.19615 | −0.228393 | ||||||||
\(737\) | 13.7128 | 0.505118 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.7321 | −0.615498 | −0.307749 | − | 0.951468i | \(-0.599576\pi\) | ||||
−0.307749 | + | 0.951468i | \(0.599576\pi\) | |||||||
\(740\) | −24.8564 | −0.913740 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.53590 | −0.0930958 | ||||||||
\(743\) | −19.6077 | −0.719337 | −0.359668 | − | 0.933080i | \(-0.617110\pi\) | ||||
−0.359668 | + | 0.933080i | \(0.617110\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.5885 | 1.23059 | ||||||||
\(746\) | 33.8564 | 1.23957 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.3731 | −1.07399 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.8564 | −1.81929 | −0.909643 | − | 0.415391i | \(-0.863645\pi\) | ||||
−0.909643 | + | 0.415391i | \(0.863645\pi\) | |||||||
\(752\) | 1.26795 | 0.0462373 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.92820 | −0.143057 | ||||||||
\(755\) | −60.4449 | −2.19981 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.7846 | −0.755429 | −0.377715 | − | 0.925922i | \(-0.623290\pi\) | ||||
−0.377715 | + | 0.925922i | \(0.623290\pi\) | |||||||
\(758\) | −17.5167 | −0.636234 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.1962 | 0.369853 | ||||||||
\(761\) | 37.0000 | 1.34125 | 0.670624 | − | 0.741797i | \(-0.266026\pi\) | ||||
0.670624 | + | 0.741797i | \(0.266026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.19615 | 0.260518 | ||||||||
\(764\) | 11.6603 | 0.421853 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35.7128 | 1.29036 | ||||||||
\(767\) | −2.87564 | −0.103833 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.5885 | −1.28335 | −0.641676 | − | 0.766976i | \(-0.721761\pi\) | ||||
−0.641676 | + | 0.766976i | \(0.721761\pi\) | |||||||
\(770\) | −15.6603 | −0.564356 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.85641 | −0.318749 | ||||||||
\(773\) | 20.1244 | 0.723823 | 0.361911 | − | 0.932213i | \(-0.382124\pi\) | ||||
0.361911 | + | 0.932213i | \(0.382124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.6077 | −0.704329 | ||||||||
\(776\) | 2.92820 | 0.105116 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.53590 | 0.234323 | ||||||||
\(779\) | −25.8564 | −0.926402 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −56.4974 | −2.02164 | ||||||||
\(782\) | −43.3731 | −1.55102 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −3.73205 | −0.133203 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.60770 | −0.271185 | −0.135593 | − | 0.990765i | \(-0.543294\pi\) | ||||
−0.135593 | + | 0.990765i | \(0.543294\pi\) | |||||||
\(788\) | −25.7846 | −0.918539 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −56.4449 | −2.00822 | ||||||||
\(791\) | 2.26795 | 0.0806390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.60770 | −0.163624 | ||||||||
\(794\) | 21.0000 | 0.745262 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.12436 | 0.181628 | ||||||||
\(797\) | 29.4449 | 1.04299 | 0.521495 | − | 0.853254i | \(-0.325374\pi\) | ||||
0.521495 | + | 0.853254i | \(0.325374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.87564 | 0.313998 | ||||||||
\(800\) | −8.92820 | −0.315660 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34.5167 | 1.21883 | ||||||||
\(803\) | −49.2295 | −1.73727 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.1244 | −0.815026 | ||||||||
\(806\) | 1.01924 | 0.0359011 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.92820 | 0.173374 | ||||||||
\(809\) | 7.87564 | 0.276893 | 0.138446 | − | 0.990370i | \(-0.455789\pi\) | ||||
0.138446 | + | 0.990370i | \(0.455789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.80385 | 0.274030 | 0.137015 | − | 0.990569i | \(-0.456249\pi\) | ||||
0.137015 | + | 0.990569i | \(0.456249\pi\) | |||||||
\(812\) | −8.46410 | −0.297032 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.9474 | −0.979557 | ||||||||
\(815\) | −24.3923 | −0.854425 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.9282 | −0.522272 | ||||||||
\(818\) | −34.6603 | −1.21187 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35.3205 | 1.23345 | ||||||||
\(821\) | 12.0718 | 0.421309 | 0.210654 | − | 0.977561i | \(-0.432441\pi\) | ||||
0.210654 | + | 0.977561i | \(0.432441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.7846 | −1.42166 | −0.710831 | − | 0.703363i | \(-0.751681\pi\) | ||||
−0.710831 | + | 0.703363i | \(0.751681\pi\) | |||||||
\(824\) | −12.3923 | −0.431706 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.19615 | −0.215592 | ||||||||
\(827\) | 11.3205 | 0.393653 | 0.196826 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196826 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | 54.4449 | 1.88981 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.464102 | 0.0160898 | ||||||||
\(833\) | 7.00000 | 0.242536 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.5167 | −1.57517 | ||||||||
\(836\) | 11.4641 | 0.396494 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.53590 | 0.0876012 | ||||||||
\(839\) | −5.46410 | −0.188642 | −0.0943209 | − | 0.995542i | \(-0.530068\pi\) | ||||
−0.0943209 | + | 0.995542i | \(0.530068\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.6410 | 1.47038 | ||||||||
\(842\) | 24.1244 | 0.831380 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.7321 | −0.713627 | ||||||||
\(845\) | −47.7128 | −1.64137 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.60770 | −0.227043 | ||||||||
\(848\) | −2.53590 | −0.0870831 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −62.4974 | −2.14364 | ||||||||
\(851\) | −41.2679 | −1.41465 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.71281 | 0.195603 | 0.0978015 | − | 0.995206i | \(-0.468819\pi\) | ||||
0.0978015 | + | 0.995206i | \(0.468819\pi\) | |||||||
\(854\) | −9.92820 | −0.339736 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.8564 | 0.370848 | 0.185424 | − | 0.982659i | \(-0.440634\pi\) | ||||
0.185424 | + | 0.982659i | \(0.440634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.60770 | 0.123093 | 0.0615465 | − | 0.998104i | \(-0.480397\pi\) | ||||
0.0615465 | + | 0.998104i | \(0.480397\pi\) | |||||||
\(860\) | 20.3923 | 0.695372 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.4641 | 0.731070 | ||||||||
\(863\) | 17.1244 | 0.582920 | 0.291460 | − | 0.956583i | \(-0.405859\pi\) | ||||
0.291460 | + | 0.956583i | \(0.405859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.3205 | 1.23493 | ||||||||
\(866\) | −12.2679 | −0.416882 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.19615 | 0.0745423 | ||||||||
\(869\) | −63.4641 | −2.15287 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.51666 | −0.0513901 | ||||||||
\(872\) | 7.19615 | 0.243692 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.9282 | 0.572605 | ||||||||
\(875\) | −14.6603 | −0.495607 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.51666 | 0.287587 | 0.143794 | − | 0.989608i | \(-0.454070\pi\) | ||||
0.143794 | + | 0.989608i | \(0.454070\pi\) | |||||||
\(878\) | 11.3205 | 0.382049 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.6603 | −0.527907 | ||||||||
\(881\) | −18.2487 | −0.614815 | −0.307407 | − | 0.951578i | \(-0.599461\pi\) | ||||
−0.307407 | + | 0.951578i | \(0.599461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.66025 | 0.257788 | 0.128894 | − | 0.991658i | \(-0.458857\pi\) | ||||
0.128894 | + | 0.991658i | \(0.458857\pi\) | |||||||
\(884\) | 3.24871 | 0.109266 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.7321 | 0.629316 | ||||||||
\(887\) | 2.44486 | 0.0820905 | 0.0410452 | − | 0.999157i | \(-0.486931\pi\) | ||||
0.0410452 | + | 0.999157i | \(0.486931\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 14.6603 | 0.491413 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.5359 | −0.620628 | ||||||||
\(893\) | −3.46410 | −0.115922 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.5885 | 1.02246 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.8564 | 0.395653 | ||||||||
\(899\) | −18.5885 | −0.619960 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.7513 | −0.591381 | ||||||||
\(902\) | 39.7128 | 1.32229 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.26795 | 0.0754309 | ||||||||
\(905\) | 16.3923 | 0.544899 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.0000 | −1.19536 | −0.597680 | − | 0.801735i | \(-0.703911\pi\) | ||||
−0.597680 | + | 0.801735i | \(0.703911\pi\) | |||||||
\(908\) | −5.07180 | −0.168313 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.73205 | 0.0574169 | ||||||||
\(911\) | −6.24871 | −0.207029 | −0.103515 | − | 0.994628i | \(-0.533009\pi\) | ||||
−0.103515 | + | 0.994628i | \(0.533009\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 61.2154 | 2.02593 | ||||||||
\(914\) | −20.8564 | −0.689869 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.46410 | 0.147498 | ||||||||
\(917\) | −17.4641 | −0.576715 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.9808 | −0.824039 | −0.412020 | − | 0.911175i | \(-0.635176\pi\) | ||||
−0.412020 | + | 0.911175i | \(0.635176\pi\) | |||||||
\(920\) | −23.1244 | −0.762387 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.7846 | −1.14557 | ||||||||
\(923\) | 6.24871 | 0.205679 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59.4641 | −1.95517 | ||||||||
\(926\) | 32.5885 | 1.07092 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.46410 | −0.277848 | ||||||||
\(929\) | 45.4974 | 1.49272 | 0.746361 | − | 0.665541i | \(-0.231799\pi\) | ||||
0.746361 | + | 0.665541i | \(0.231799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.73205 | −0.0895393 | ||||||||
\(932\) | −13.1962 | −0.432254 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.5885 | −0.477349 | ||||||||
\(935\) | −109.622 | −3.58502 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.8372 | 1.75878 | 0.879392 | − | 0.476099i | \(-0.157950\pi\) | ||||
0.879392 | + | 0.476099i | \(0.157950\pi\) | |||||||
\(938\) | −3.26795 | −0.106702 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.73205 | 0.154342 | ||||||||
\(941\) | −9.87564 | −0.321937 | −0.160968 | − | 0.986960i | \(-0.551462\pi\) | ||||
−0.160968 | + | 0.986960i | \(0.551462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.6410 | 1.90961 | ||||||||
\(944\) | −6.19615 | −0.201668 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9282 | 0.745460 | ||||||||
\(947\) | 2.24871 | 0.0730733 | 0.0365366 | − | 0.999332i | \(-0.488367\pi\) | ||||
0.0365366 | + | 0.999332i | \(0.488367\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.44486 | 0.176748 | ||||||||
\(950\) | 24.3923 | 0.791391 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.00000 | 0.226871 | ||||||||
\(953\) | −10.4115 | −0.337263 | −0.168631 | − | 0.985679i | \(-0.553935\pi\) | ||||
−0.168631 | + | 0.985679i | \(0.553935\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.5167 | 1.40817 | ||||||||
\(956\) | 28.0526 | 0.907285 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.5167 | −0.759789 | ||||||||
\(959\) | 11.7321 | 0.378848 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.1769 | −0.844417 | ||||||||
\(962\) | 3.09103 | 0.0996590 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.7321 | −0.571111 | ||||||||
\(965\) | −33.0526 | −1.06400 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.6603 | 0.439284 | 0.219642 | − | 0.975581i | \(-0.429511\pi\) | ||||
0.219642 | + | 0.975581i | \(0.429511\pi\) | |||||||
\(968\) | −6.60770 | −0.212379 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.9282 | 0.350883 | ||||||||
\(971\) | 33.1244 | 1.06301 | 0.531506 | − | 0.847055i | \(-0.321626\pi\) | ||||
0.531506 | + | 0.847055i | \(0.321626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.73205 | 0.215820 | ||||||||
\(974\) | 28.5885 | 0.916033 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.92820 | −0.317794 | ||||||||
\(977\) | 2.28719 | 0.0731736 | 0.0365868 | − | 0.999330i | \(-0.488351\pi\) | ||||
0.0365868 | + | 0.999330i | \(0.488351\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.4833 | 0.526810 | ||||||||
\(980\) | 3.73205 | 0.119216 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33.4641 | −1.06788 | ||||||||
\(983\) | −10.6410 | −0.339396 | −0.169698 | − | 0.985496i | \(-0.554279\pi\) | ||||
−0.169698 | + | 0.985496i | \(0.554279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −96.2295 | −3.06613 | ||||||||
\(986\) | −59.2487 | −1.88686 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.26795 | −0.0403388 | ||||||||
\(989\) | 33.8564 | 1.07657 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.3397 | −0.328453 | −0.164226 | − | 0.986423i | \(-0.552513\pi\) | ||||
−0.164226 | + | 0.986423i | \(0.552513\pi\) | |||||||
\(992\) | 2.19615 | 0.0697279 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.4641 | 0.427055 | ||||||||
\(995\) | 19.1244 | 0.606283 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.24871 | −0.229569 | −0.114784 | − | 0.993390i | \(-0.536618\pi\) | ||||
−0.114784 | + | 0.993390i | \(0.536618\pi\) | |||||||
\(998\) | −30.1962 | −0.955843 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1134.2.a.l.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 1134.2.a.m.1.1 | yes | 2 | ||
4.3 | odd | 2 | 9072.2.a.bp.1.2 | 2 | |||
7.6 | odd | 2 | 7938.2.a.bg.1.1 | 2 | |||
9.2 | odd | 6 | 1134.2.f.r.757.2 | 4 | |||
9.4 | even | 3 | 1134.2.f.s.379.1 | 4 | |||
9.5 | odd | 6 | 1134.2.f.r.379.2 | 4 | |||
9.7 | even | 3 | 1134.2.f.s.757.1 | 4 | |||
12.11 | even | 2 | 9072.2.a.y.1.1 | 2 | |||
21.20 | even | 2 | 7938.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.a.l.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1134.2.a.m.1.1 | yes | 2 | 3.2 | odd | 2 | ||
1134.2.f.r.379.2 | 4 | 9.5 | odd | 6 | |||
1134.2.f.r.757.2 | 4 | 9.2 | odd | 6 | |||
1134.2.f.s.379.1 | 4 | 9.4 | even | 3 | |||
1134.2.f.s.757.1 | 4 | 9.7 | even | 3 | |||
7938.2.a.bg.1.1 | 2 | 7.6 | odd | 2 | |||
7938.2.a.bt.1.2 | 2 | 21.20 | even | 2 | |||
9072.2.a.y.1.1 | 2 | 12.11 | even | 2 | |||
9072.2.a.bp.1.2 | 2 | 4.3 | odd | 2 |