Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,5,Mod(19,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.72131867102\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 4x^{2} + 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 12) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-0.651388 - 1.12824i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 36.19 |
Dual form | 36.5.d.b.19.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.30278 | − | 2.25647i | −0.825694 | − | 0.564118i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.81665 | + | 14.9053i | 0.363541 | + | 0.931578i | ||||
\(5\) | 22.8444 | 0.913776 | 0.456888 | − | 0.889524i | \(-0.348964\pi\) | ||||
0.456888 | + | 0.889524i | \(0.348964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 56.8882i | − | 1.16098i | −0.814266 | − | 0.580492i | \(-0.802860\pi\) | ||
0.814266 | − | 0.580492i | \(-0.197140\pi\) | |||||||
\(8\) | 14.4222 | − | 62.3538i | 0.225347 | − | 0.974279i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −75.4500 | − | 51.5478i | −0.754500 | − | 0.515478i | ||||
\(11\) | − | 134.561i | − | 1.11207i | −0.831157 | − | 0.556037i | \(-0.812321\pi\) | ||
0.831157 | − | 0.556037i | \(-0.187679\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 247.066 | 1.46193 | 0.730966 | − | 0.682414i | \(-0.239070\pi\) | ||||
0.730966 | + | 0.682414i | \(0.239070\pi\) | |||||||
\(14\) | −128.367 | + | 187.889i | −0.654932 | + | 0.958617i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −188.333 | + | 173.397i | −0.735676 | + | 0.677334i | ||||
\(17\) | 92.3112 | 0.319416 | 0.159708 | − | 0.987164i | \(-0.448945\pi\) | ||||
0.159708 | + | 0.987164i | \(0.448945\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 29.5600i | − | 0.0818836i | −0.999162 | − | 0.0409418i | \(-0.986964\pi\) | ||
0.999162 | − | 0.0409418i | \(-0.0130358\pi\) | |||||||
\(20\) | 132.878 | + | 340.502i | 0.332195 | + | 0.851254i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −303.633 | + | 444.425i | −0.627342 | + | 0.918233i | ||||
\(23\) | 571.038i | 1.07947i | 0.841836 | + | 0.539733i | \(0.181475\pi\) | ||||
−0.841836 | + | 0.539733i | \(0.818525\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −103.133 | −0.165013 | ||||||||
\(26\) | −816.005 | − | 557.499i | −1.20711 | − | 0.824703i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 847.933 | − | 330.899i | 1.08155 | − | 0.422065i | ||||
\(29\) | −20.0891 | −0.0238872 | −0.0119436 | − | 0.999929i | \(-0.503802\pi\) | ||||
−0.0119436 | + | 0.999929i | \(0.503802\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 474.736i | − | 0.494002i | −0.969015 | − | 0.247001i | \(-0.920555\pi\) | ||
0.969015 | − | 0.247001i | \(-0.0794452\pi\) | |||||||
\(32\) | 1013.29 | − | 147.724i | 0.989540 | − | 0.144262i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −304.883 | − | 208.298i | −0.263740 | − | 0.180188i | ||||
\(35\) | − | 1299.58i | − | 1.06088i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −755.867 | −0.552131 | −0.276065 | − | 0.961139i | \(-0.589031\pi\) | ||||
−0.276065 | + | 0.961139i | \(0.589031\pi\) | |||||||
\(38\) | −66.7013 | + | 97.6300i | −0.0461920 | + | 0.0676108i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 329.467 | − | 1424.44i | 0.205917 | − | 0.890273i | ||||
\(41\) | −541.822 | −0.322321 | −0.161161 | − | 0.986928i | \(-0.551524\pi\) | ||||
−0.161161 | + | 0.986928i | \(0.551524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3097.06i | 1.67499i | 0.546444 | + | 0.837496i | \(0.315981\pi\) | ||||
−0.546444 | + | 0.837496i | \(0.684019\pi\) | |||||||
\(44\) | 2005.67 | − | 782.695i | 1.03598 | − | 0.404284i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1288.53 | − | 1886.01i | 0.608947 | − | 0.891309i | ||||
\(47\) | 1050.16i | 0.475401i | 0.971338 | + | 0.237701i | \(0.0763937\pi\) | ||||
−0.971338 | + | 0.237701i | \(0.923606\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −835.266 | −0.347882 | ||||||||
\(50\) | 340.625 | + | 232.717i | 0.136250 | + | 0.0930867i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1437.10 | + | 3682.59i | 0.531472 | + | 1.36190i | ||||
\(53\) | −1768.35 | −0.629532 | −0.314766 | − | 0.949169i | \(-0.601926\pi\) | ||||
−0.314766 | + | 0.949169i | \(0.601926\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3073.97i | − | 1.01619i | ||||||
\(56\) | −3547.20 | − | 820.453i | −1.13112 | − | 0.261624i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 66.3499 | + | 45.3306i | 0.0197235 | + | 0.0134752i | ||||
\(59\) | 2582.98i | 0.742024i | 0.928628 | + | 0.371012i | \(0.120989\pi\) | ||||
−0.928628 | + | 0.371012i | \(0.879011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2403.33 | −0.645883 | −0.322941 | − | 0.946419i | \(-0.604672\pi\) | ||||
−0.322941 | + | 0.946419i | \(0.604672\pi\) | |||||||
\(62\) | −1071.23 | + | 1567.95i | −0.278676 | + | 0.407895i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3680.00 | − | 1798.56i | −0.898438 | − | 0.439101i | ||||
\(65\) | 5644.09 | 1.33588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 379.816i | − | 0.0846104i | −0.999105 | − | 0.0423052i | \(-0.986530\pi\) | ||
0.999105 | − | 0.0423052i | \(-0.0134702\pi\) | |||||||
\(68\) | 536.942 | + | 1375.92i | 0.116121 | + | 0.297561i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2932.46 | + | 4292.21i | −0.598462 | + | 0.875962i | ||||
\(71\) | − | 702.517i | − | 0.139361i | −0.997569 | − | 0.0696803i | \(-0.977802\pi\) | ||
0.997569 | − | 0.0696803i | \(-0.0221979\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9824.92 | 1.84367 | 0.921836 | − | 0.387581i | \(-0.126689\pi\) | ||||
0.921836 | + | 0.387581i | \(0.126689\pi\) | |||||||
\(74\) | 2496.46 | + | 1705.59i | 0.455891 | + | 0.311467i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 440.599 | − | 171.940i | 0.0762810 | − | 0.0297680i | ||||
\(77\) | −7654.93 | −1.29110 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3756.40i | 0.601890i | 0.953641 | + | 0.300945i | \(0.0973021\pi\) | ||||
−0.953641 | + | 0.300945i | \(0.902698\pi\) | |||||||
\(80\) | −4302.36 | + | 3961.16i | −0.672243 | + | 0.618931i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1789.52 | + | 1222.61i | 0.266139 | + | 0.181827i | ||||
\(83\) | − | 10433.6i | − | 1.51452i | −0.653111 | − | 0.757262i | \(-0.726537\pi\) | ||
0.653111 | − | 0.757262i | \(-0.273463\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2108.79 | 0.291875 | ||||||||
\(86\) | 6988.43 | − | 10228.9i | 0.944893 | − | 1.38303i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8390.39 | − | 1940.67i | −1.08347 | − | 0.250603i | ||||
\(89\) | 11923.5 | 1.50530 | 0.752651 | − | 0.658419i | \(-0.228775\pi\) | ||||
0.752651 | + | 0.658419i | \(0.228775\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14055.2i | − | 1.69728i | ||||||
\(92\) | −8511.46 | + | 3321.53i | −1.00561 | + | 0.392430i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2369.66 | − | 3468.45i | 0.268183 | − | 0.392536i | ||||
\(95\) | − | 675.280i | − | 0.0748233i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2199.06 | −0.233718 | −0.116859 | − | 0.993148i | \(-0.537283\pi\) | ||||
−0.116859 | + | 0.993148i | \(0.537283\pi\) | |||||||
\(98\) | 2758.70 | + | 1884.76i | 0.287244 | + | 0.196247i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −599.889 | − | 1537.22i | −0.0599889 | − | 0.153722i | ||||
\(101\) | 874.835 | 0.0857597 | 0.0428799 | − | 0.999080i | \(-0.486347\pi\) | ||||
0.0428799 | + | 0.999080i | \(0.486347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3036.94i | 0.286260i | 0.989704 | + | 0.143130i | \(0.0457168\pi\) | ||||
−0.989704 | + | 0.143130i | \(0.954283\pi\) | |||||||
\(104\) | 3563.24 | − | 15405.5i | 0.329442 | − | 1.42433i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5840.48 | + | 3990.25i | 0.519801 | + | 0.355131i | ||||
\(107\) | 19057.6i | 1.66457i | 0.554350 | + | 0.832284i | \(0.312967\pi\) | ||||
−0.554350 | + | 0.832284i | \(0.687033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13132.7 | −1.10535 | −0.552675 | − | 0.833397i | \(-0.686393\pi\) | ||||
−0.552675 | + | 0.833397i | \(0.686393\pi\) | |||||||
\(110\) | −6936.32 | + | 10152.6i | −0.573250 | + | 0.839060i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9864.26 | + | 10713.9i | 0.786373 | + | 0.854108i | ||||
\(113\) | −14541.5 | −1.13882 | −0.569408 | − | 0.822055i | \(-0.692827\pi\) | ||||
−0.569408 | + | 0.822055i | \(0.692827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13045.0i | 0.986391i | ||||||||
\(116\) | −116.852 | − | 299.434i | −0.00868397 | − | 0.0222528i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5828.44 | − | 8531.02i | 0.418589 | − | 0.612685i | ||||
\(119\) | − | 5251.42i | − | 0.370836i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3465.66 | −0.236709 | ||||||||
\(122\) | 7937.66 | + | 5423.05i | 0.533301 | + | 0.364354i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7076.06 | − | 2761.38i | 0.460202 | − | 0.179590i | ||||
\(125\) | −16633.8 | −1.06456 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 25959.7i | 1.60951i | 0.593609 | + | 0.804753i | \(0.297702\pi\) | ||||
−0.593609 | + | 0.804753i | \(0.702298\pi\) | |||||||
\(128\) | 8095.81 | + | 14244.1i | 0.494129 | + | 0.869388i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18641.2 | − | 12735.7i | −1.10303 | − | 0.753594i | ||||
\(131\) | 16440.3i | 0.958003i | 0.877814 | + | 0.479002i | \(0.159001\pi\) | ||||
−0.877814 | + | 0.479002i | \(0.840999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1681.61 | −0.0950655 | ||||||||
\(134\) | −857.045 | + | 1254.45i | −0.0477303 | + | 0.0698623i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1331.33 | − | 5755.96i | 0.0719794 | − | 0.311200i | ||||
\(137\) | 31618.7 | 1.68462 | 0.842312 | − | 0.538990i | \(-0.181194\pi\) | ||||
0.842312 | + | 0.538990i | \(0.181194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12895.9i | − | 0.667453i | −0.942670 | − | 0.333726i | \(-0.891694\pi\) | ||
0.942670 | − | 0.333726i | \(-0.108306\pi\) | |||||||
\(140\) | 19370.5 | − | 7559.19i | 0.988292 | − | 0.385673i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1585.21 | + | 2320.25i | −0.0786159 | + | 0.115069i | ||||
\(143\) | − | 33245.5i | − | 1.62578i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −458.924 | −0.0218276 | ||||||||
\(146\) | −32449.5 | − | 22169.7i | −1.52231 | − | 1.04005i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4396.62 | − | 11266.4i | −0.200722 | − | 0.514353i | ||||
\(149\) | −31474.8 | −1.41772 | −0.708859 | − | 0.705350i | \(-0.750790\pi\) | ||||
−0.708859 | + | 0.705350i | \(0.750790\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 39479.3i | − | 1.73147i | −0.500502 | − | 0.865735i | \(-0.666851\pi\) | ||
0.500502 | − | 0.865735i | \(-0.333149\pi\) | |||||||
\(152\) | −1843.18 | − | 426.320i | −0.0797774 | − | 0.0184522i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 25282.5 | + | 17273.1i | 1.06605 | + | 0.728333i | ||||
\(155\) | − | 10845.1i | − | 0.451408i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2619.07 | 0.106255 | 0.0531273 | − | 0.998588i | \(-0.483081\pi\) | ||||
0.0531273 | + | 0.998588i | \(0.483081\pi\) | |||||||
\(158\) | 8476.21 | − | 12406.5i | 0.339537 | − | 0.496977i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 23148.0 | − | 3374.67i | 0.904218 | − | 0.131823i | ||||
\(161\) | 32485.3 | 1.25324 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7123.14i | 0.268100i | 0.990975 | + | 0.134050i | \(0.0427982\pi\) | ||||
−0.990975 | + | 0.134050i | \(0.957202\pi\) | |||||||
\(164\) | −3151.59 | − | 8075.99i | −0.117177 | − | 0.300267i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −23543.0 | + | 34459.7i | −0.854371 | + | 1.25053i | ||||
\(167\) | 48670.8i | 1.74516i | 0.488472 | + | 0.872580i | \(0.337555\pi\) | ||||
−0.488472 | + | 0.872580i | \(0.662445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32480.8 | 1.13724 | ||||||||
\(170\) | −6964.87 | − | 4758.44i | −0.240999 | − | 0.164652i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −46162.4 | + | 18014.5i | −1.56039 | + | 0.608928i | ||||
\(173\) | 27575.9 | 0.921377 | 0.460689 | − | 0.887562i | \(-0.347603\pi\) | ||||
0.460689 | + | 0.887562i | \(0.347603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5867.05i | 0.191577i | ||||||||
\(176\) | 23332.5 | + | 25342.3i | 0.753245 | + | 0.818126i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −39380.7 | − | 26905.1i | −1.24292 | − | 0.849169i | ||||
\(179\) | − | 42280.0i | − | 1.31956i | −0.751459 | − | 0.659780i | \(-0.770649\pi\) | ||
0.751459 | − | 0.659780i | \(-0.229351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1006.79 | −0.0307313 | −0.0153657 | − | 0.999882i | \(-0.504891\pi\) | ||||
−0.0153657 | + | 0.999882i | \(0.504891\pi\) | |||||||
\(182\) | −31715.1 | + | 46421.1i | −0.957466 | + | 1.40143i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 35606.4 | + | 8235.62i | 1.05170 | + | 0.243254i | ||||
\(185\) | −17267.3 | −0.504524 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 12421.5i | − | 0.355214i | ||||||
\(188\) | −15652.9 | + | 6108.43i | −0.442874 | + | 0.172828i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1523.75 | + | 2230.30i | −0.0422092 | + | 0.0617811i | ||||
\(191\) | − | 6906.62i | − | 0.189321i | −0.995510 | − | 0.0946605i | \(-0.969823\pi\) | ||
0.995510 | − | 0.0946605i | \(-0.0301766\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 28207.8 | 0.757278 | 0.378639 | − | 0.925545i | \(-0.376392\pi\) | ||||
0.378639 | + | 0.925545i | \(0.376392\pi\) | |||||||
\(194\) | 7262.99 | + | 4962.11i | 0.192980 | + | 0.131845i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4858.45 | − | 12449.8i | −0.126469 | − | 0.324080i | ||||
\(197\) | −38453.6 | −0.990843 | −0.495422 | − | 0.868653i | \(-0.664986\pi\) | ||||
−0.495422 | + | 0.868653i | \(0.664986\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5490.10i | 0.138635i | 0.997595 | + | 0.0693176i | \(0.0220822\pi\) | ||||
−0.997595 | + | 0.0693176i | \(0.977918\pi\) | |||||||
\(200\) | −1487.40 | + | 6430.73i | −0.0371851 | + | 0.160768i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2889.38 | − | 1974.04i | −0.0708113 | − | 0.0483787i | ||||
\(203\) | 1142.83i | 0.0277326i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12377.6 | −0.294529 | ||||||||
\(206\) | 6852.77 | − | 10030.3i | 0.161485 | − | 0.236363i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −46530.8 | + | 42840.7i | −1.07551 | + | 0.990215i | ||||
\(209\) | −3977.62 | −0.0910606 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 46471.5i | 1.04381i | 0.853004 | + | 0.521905i | \(0.174778\pi\) | ||||
−0.853004 | + | 0.521905i | \(0.825222\pi\) | |||||||
\(212\) | −10285.9 | − | 26357.8i | −0.228861 | − | 0.586458i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 43003.0 | − | 62943.1i | 0.939013 | − | 1.37442i | ||||
\(215\) | 70750.5i | 1.53057i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27006.9 | −0.573529 | ||||||||
\(218\) | 43374.2 | + | 29633.5i | 0.912681 | + | 0.623548i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 45818.2 | − | 17880.2i | 0.946658 | − | 0.369426i | ||||
\(221\) | 22807.0 | 0.466964 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 48307.2i | − | 0.971409i | −0.874123 | − | 0.485704i | \(-0.838563\pi\) | ||
0.874123 | − | 0.485704i | \(-0.161437\pi\) | |||||||
\(224\) | −8403.75 | − | 57644.1i | −0.167486 | − | 1.14884i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 48027.4 | + | 32812.6i | 0.940313 | + | 0.642427i | ||||
\(227\) | − | 19108.6i | − | 0.370832i | −0.982660 | − | 0.185416i | \(-0.940637\pi\) | ||
0.982660 | − | 0.185416i | \(-0.0593633\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −73378.5 | −1.39926 | −0.699629 | − | 0.714506i | \(-0.746651\pi\) | ||||
−0.699629 | + | 0.714506i | \(0.746651\pi\) | |||||||
\(230\) | 29435.7 | − | 43084.8i | 0.556441 | − | 0.814457i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −289.730 | + | 1252.63i | −0.00538291 | + | 0.0232728i | ||||
\(233\) | 34041.9 | 0.627049 | 0.313524 | − | 0.949580i | \(-0.398490\pi\) | ||||
0.313524 | + | 0.949580i | \(0.398490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23990.3i | 0.434411i | ||||||||
\(236\) | −38500.0 | + | 15024.3i | −0.691253 | + | 0.269756i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11849.7 | + | 17344.2i | −0.209196 | + | 0.306197i | ||||
\(239\) | − | 35114.3i | − | 0.614735i | −0.951591 | − | 0.307368i | \(-0.900552\pi\) | ||
0.951591 | − | 0.307368i | \(-0.0994482\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19621.0 | −0.337821 | −0.168910 | − | 0.985631i | \(-0.554025\pi\) | ||||
−0.168910 | + | 0.985631i | \(0.554025\pi\) | |||||||
\(242\) | 11446.3 | + | 7820.17i | 0.195449 | + | 0.133532i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13979.3 | − | 35822.2i | −0.234805 | − | 0.601690i | ||||
\(245\) | −19081.2 | −0.317887 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7303.28i | − | 0.119708i | ||||||
\(248\) | −29601.6 | − | 6846.74i | −0.481296 | − | 0.111322i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 54937.6 | + | 37533.7i | 0.879002 | + | 0.600539i | ||||
\(251\) | 560.729i | 0.00890032i | 0.999990 | + | 0.00445016i | \(0.00141654\pi\) | ||||
−0.999990 | + | 0.00445016i | \(0.998583\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 76839.4 | 1.20045 | ||||||||
\(254\) | 58577.5 | − | 85739.2i | 0.907952 | − | 1.32896i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5402.70 | − | 65312.9i | 0.0824386 | − | 0.996596i | ||||
\(257\) | −80511.1 | −1.21896 | −0.609480 | − | 0.792801i | \(-0.708622\pi\) | ||||
−0.609480 | + | 0.792801i | \(0.708622\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 42999.9i | 0.641015i | ||||||||
\(260\) | 32829.7 | + | 84126.5i | 0.485647 | + | 1.24448i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 37097.1 | − | 54298.6i | 0.540427 | − | 0.791017i | ||||
\(263\) | − | 34821.7i | − | 0.503430i | −0.967801 | − | 0.251715i | \(-0.919005\pi\) | ||
0.967801 | − | 0.251715i | \(-0.0809945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −40397.0 | −0.575251 | ||||||||
\(266\) | 5553.99 | + | 3794.52i | 0.0784950 | + | 0.0536282i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5661.26 | − | 2209.26i | 0.0788212 | − | 0.0307593i | ||||
\(269\) | 28469.5 | 0.393438 | 0.196719 | − | 0.980460i | \(-0.436971\pi\) | ||||
0.196719 | + | 0.980460i | \(0.436971\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 37653.7i | 0.512706i | 0.966583 | + | 0.256353i | \(0.0825210\pi\) | ||||
−0.966583 | + | 0.256353i | \(0.917479\pi\) | |||||||
\(272\) | −17385.2 | + | 16006.5i | −0.234987 | + | 0.216351i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −104429. | − | 71346.8i | −1.39098 | − | 0.950327i | ||||
\(275\) | 13877.7i | 0.183506i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25920.1 | 0.337814 | 0.168907 | − | 0.985632i | \(-0.445976\pi\) | ||||
0.168907 | + | 0.985632i | \(0.445976\pi\) | |||||||
\(278\) | −29099.2 | + | 42592.1i | −0.376522 | + | 0.551112i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −81033.6 | − | 18742.8i | −1.03359 | − | 0.239066i | ||||
\(281\) | −49815.6 | −0.630889 | −0.315444 | − | 0.948944i | \(-0.602154\pi\) | ||||
−0.315444 | + | 0.948944i | \(0.602154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 73403.9i | − | 0.916530i | −0.888816 | − | 0.458265i | \(-0.848471\pi\) | ||
0.888816 | − | 0.458265i | \(-0.151529\pi\) | |||||||
\(284\) | 10471.2 | − | 4086.30i | 0.129825 | − | 0.0506633i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −75017.6 | + | 109802.i | −0.917131 | + | 1.34239i | ||||
\(287\) | 30823.3i | 0.374209i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −74999.6 | −0.897974 | ||||||||
\(290\) | 1515.72 | + | 1035.55i | 0.0180229 | + | 0.0123133i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 57148.2 | + | 146443.i | 0.670250 | + | 1.71752i | ||||
\(293\) | 130683. | 1.52224 | 0.761120 | − | 0.648611i | \(-0.224650\pi\) | ||||
0.761120 | + | 0.648611i | \(0.224650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 59006.8i | 0.678044i | ||||||||
\(296\) | −10901.3 | + | 47131.2i | −0.124421 | + | 0.537929i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 103954. | + | 71022.0i | 1.17060 | + | 0.799761i | ||||
\(299\) | 141084.i | 1.57811i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 176186. | 1.94464 | ||||||||
\(302\) | −89083.9 | + | 130391.i | −0.976754 | + | 1.42966i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5125.62 | + | 5567.12i | 0.0554625 | + | 0.0602398i | ||||
\(305\) | −54902.6 | −0.590192 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 139512.i | − | 1.48025i | −0.672469 | − | 0.740126i | \(-0.734766\pi\) | ||
0.672469 | − | 0.740126i | \(-0.265234\pi\) | |||||||
\(308\) | −44526.1 | − | 114099.i | −0.469368 | − | 1.20276i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24471.6 | + | 35818.8i | −0.254647 | + | 0.372725i | ||||
\(311\) | − | 132034.i | − | 1.36510i | −0.730837 | − | 0.682552i | \(-0.760870\pi\) | ||
0.730837 | − | 0.682552i | \(-0.239130\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 39526.3 | 0.403458 | 0.201729 | − | 0.979441i | \(-0.435344\pi\) | ||||
0.201729 | + | 0.979441i | \(0.435344\pi\) | |||||||
\(314\) | −8650.20 | − | 5909.86i | −0.0877338 | − | 0.0599402i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −55990.0 | + | 21849.7i | −0.560708 | + | 0.218812i | ||||
\(317\) | 91959.1 | 0.915116 | 0.457558 | − | 0.889180i | \(-0.348724\pi\) | ||||
0.457558 | + | 0.889180i | \(0.348724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2703.21i | 0.0265643i | ||||||||
\(320\) | −84067.4 | − | 41087.0i | −0.820971 | − | 0.401241i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −107292. | − | 73302.2i | −1.03479 | − | 0.706977i | ||||
\(323\) | − | 2728.72i | − | 0.0261549i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25480.7 | −0.241237 | ||||||||
\(326\) | 16073.2 | − | 23526.1i | 0.151240 | − | 0.221368i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7814.26 | + | 33784.7i | −0.0726341 | + | 0.314031i | ||||
\(329\) | 59741.8 | 0.551933 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3244.08i | − | 0.0296098i | −0.999890 | − | 0.0148049i | \(-0.995287\pi\) | ||
0.999890 | − | 0.0148049i | \(-0.00471272\pi\) | |||||||
\(332\) | 155515. | − | 60688.4i | 1.41090 | − | 0.550591i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 109824. | − | 160749.i | 0.984477 | − | 1.44097i | ||||
\(335\) | − | 8676.68i | − | 0.0773150i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5591.21 | 0.0492318 | 0.0246159 | − | 0.999697i | \(-0.492164\pi\) | ||||
0.0246159 | + | 0.999697i | \(0.492164\pi\) | |||||||
\(338\) | −107277. | − | 73292.1i | −0.939016 | − | 0.641540i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12266.1 | + | 31432.1i | 0.106108 | + | 0.271904i | ||||
\(341\) | −63881.0 | −0.549367 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 89071.8i | − | 0.757098i | ||||||
\(344\) | 193113. | + | 44666.4i | 1.63191 | + | 0.377454i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −91077.0 | − | 62224.3i | −0.760775 | − | 0.519766i | ||||
\(347\) | − | 170630.i | − | 1.41708i | −0.705668 | − | 0.708542i | \(-0.749353\pi\) | ||
0.705668 | − | 0.708542i | \(-0.250647\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −96101.4 | −0.789003 | −0.394502 | − | 0.918895i | \(-0.629083\pi\) | ||||
−0.394502 | + | 0.918895i | \(0.629083\pi\) | |||||||
\(350\) | 13238.8 | − | 19377.5i | 0.108072 | − | 0.158184i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19877.9 | − | 136349.i | −0.160430 | − | 1.10044i | ||||
\(353\) | −205914. | −1.65248 | −0.826242 | − | 0.563316i | \(-0.809526\pi\) | ||||
−0.826242 | + | 0.563316i | \(0.809526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 16048.6i | − | 0.127344i | ||||||
\(356\) | 69354.9 | + | 177723.i | 0.547239 | + | 1.40231i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −95403.8 | + | 139641.i | −0.744388 | + | 1.08955i | ||||
\(359\) | − | 78435.2i | − | 0.608586i | −0.952578 | − | 0.304293i | \(-0.901580\pi\) | ||
0.952578 | − | 0.304293i | \(-0.0984202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129447. | 0.993295 | ||||||||
\(362\) | 3325.20 | + | 2271.79i | 0.0253747 | + | 0.0173361i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 209496. | − | 81754.0i | 1.58115 | − | 0.617030i | ||||
\(365\) | 224445. | 1.68470 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 221785.i | 1.64664i | 0.567574 | + | 0.823322i | \(0.307882\pi\) | ||||
−0.567574 | + | 0.823322i | \(0.692118\pi\) | |||||||
\(368\) | −99016.5 | − | 107545.i | −0.731159 | − | 0.794138i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 57030.1 | + | 38963.3i | 0.416582 | + | 0.284611i | ||||
\(371\) | 100599.i | 0.730876i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25883.8 | −0.186042 | −0.0930208 | − | 0.995664i | \(-0.529652\pi\) | ||||
−0.0930208 | + | 0.995664i | \(0.529652\pi\) | |||||||
\(374\) | −28028.7 | + | 41025.4i | −0.200383 | + | 0.293298i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 65481.6 | + | 15145.6i | 0.463173 | + | 0.107130i | ||||
\(377\) | −4963.35 | −0.0349214 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 147801.i | 1.02896i | 0.857503 | + | 0.514479i | \(0.172015\pi\) | ||||
−0.857503 | + | 0.514479i | \(0.827985\pi\) | |||||||
\(380\) | 10065.2 | − | 3927.87i | 0.0697038 | − | 0.0272013i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15584.6 | + | 22811.0i | −0.106800 | + | 0.156321i | ||||
\(383\) | 226231.i | 1.54225i | 0.636683 | + | 0.771126i | \(0.280306\pi\) | ||||
−0.636683 | + | 0.771126i | \(0.719694\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −174872. | −1.17978 | ||||||||
\(386\) | −93164.2 | − | 63650.2i | −0.625280 | − | 0.427194i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12791.2 | − | 32777.5i | −0.0849662 | − | 0.217727i | ||||
\(389\) | −256419. | −1.69453 | −0.847267 | − | 0.531167i | \(-0.821754\pi\) | ||||
−0.847267 | + | 0.531167i | \(0.821754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52713.2i | 0.344799i | ||||||||
\(392\) | −12046.4 | + | 52082.0i | −0.0783943 | + | 0.338934i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 127004. | + | 86769.6i | 0.818133 | + | 0.558953i | ||||
\(395\) | 85812.7i | 0.549993i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −56667.7 | −0.359546 | −0.179773 | − | 0.983708i | \(-0.557536\pi\) | ||||
−0.179773 | + | 0.983708i | \(0.557536\pi\) | |||||||
\(398\) | 12388.3 | − | 18132.6i | 0.0782067 | − | 0.114470i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19423.3 | − | 17883.0i | 0.121396 | − | 0.111769i | ||||
\(401\) | −10912.0 | −0.0678605 | −0.0339302 | − | 0.999424i | \(-0.510802\pi\) | ||||
−0.0339302 | + | 0.999424i | \(0.510802\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 117291.i | − | 0.722198i | ||||||
\(404\) | 5088.61 | + | 13039.6i | 0.0311772 | + | 0.0798919i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2578.77 | − | 3774.52i | 0.0156445 | − | 0.0228987i | ||||
\(407\) | 101710.i | 0.614010i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −289576. | −1.73108 | −0.865538 | − | 0.500844i | \(-0.833023\pi\) | ||||
−0.865538 | + | 0.500844i | \(0.833023\pi\) | |||||||
\(410\) | 40880.4 | + | 27929.7i | 0.243191 | + | 0.166149i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −45266.3 | + | 17664.8i | −0.266674 | + | 0.104067i | ||||
\(413\) | 146941. | 0.861477 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 238348.i | − | 1.38394i | ||||||
\(416\) | 250350. | − | 36497.7i | 1.44664 | − | 0.210901i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13137.2 | + | 8975.39i | 0.0751882 | + | 0.0513690i | ||||
\(419\) | 69837.9i | 0.397798i | 0.980020 | + | 0.198899i | \(0.0637366\pi\) | ||||
−0.980020 | + | 0.198899i | \(0.936263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16207.0 | 0.0914405 | 0.0457203 | − | 0.998954i | \(-0.485442\pi\) | ||||
0.0457203 | + | 0.998954i | \(0.485442\pi\) | |||||||
\(422\) | 104862. | − | 153485.i | 0.588832 | − | 0.861867i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25503.6 | + | 110264.i | −0.141863 | + | 0.613339i | ||||
\(425\) | −9520.32 | −0.0527077 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 136721.i | 0.749859i | ||||||||
\(428\) | −284059. | + | 110852.i | −1.55067 | + | 0.605138i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 159647. | − | 233673.i | 0.863421 | − | 1.26378i | ||||
\(431\) | − | 105264.i | − | 0.566662i | −0.959022 | − | 0.283331i | \(-0.908560\pi\) | ||
0.959022 | − | 0.283331i | \(-0.0914395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 131799. | 0.702970 | 0.351485 | − | 0.936193i | \(-0.385677\pi\) | ||||
0.351485 | + | 0.936193i | \(0.385677\pi\) | |||||||
\(434\) | 89197.7 | + | 60940.3i | 0.473559 | + | 0.323538i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −76388.1 | − | 195746.i | −0.401840 | − | 1.02972i | ||||
\(437\) | 16879.9 | 0.0883906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 149053.i | 0.773414i | 0.922203 | + | 0.386707i | \(0.126388\pi\) | ||||
−0.922203 | + | 0.386707i | \(0.873612\pi\) | |||||||
\(440\) | −191674. | − | 44333.4i | −0.990049 | − | 0.228995i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −75326.4 | − | 51463.4i | −0.385569 | − | 0.263423i | ||||
\(443\) | − | 248933.i | − | 1.26845i | −0.773147 | − | 0.634227i | \(-0.781318\pi\) | ||
0.773147 | − | 0.634227i | \(-0.218682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 272385. | 1.37551 | ||||||||
\(446\) | −109004. | + | 159548.i | −0.547990 | + | 0.802086i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −102317. | + | 209349.i | −0.509789 | + | 1.04307i | ||||
\(449\) | −243749. | −1.20906 | −0.604532 | − | 0.796581i | \(-0.706640\pi\) | ||||
−0.604532 | + | 0.796581i | \(0.706640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 72908.1i | 0.358445i | ||||||||
\(452\) | −84583.1 | − | 216745.i | −0.414006 | − | 1.06090i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −43118.1 | + | 63111.5i | −0.209193 | + | 0.306194i | ||||
\(455\) | − | 321082.i | − | 1.55093i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 343278. | 1.64367 | 0.821833 | − | 0.569729i | \(-0.192952\pi\) | ||||
0.821833 | + | 0.569729i | \(0.192952\pi\) | |||||||
\(458\) | 242353. | + | 165577.i | 1.15536 | + | 0.789347i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −194439. | + | 75878.4i | −0.918900 | + | 0.358593i | ||||
\(461\) | 155524. | 0.731804 | 0.365902 | − | 0.930653i | \(-0.380761\pi\) | ||||
0.365902 | + | 0.930653i | \(0.380761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 321457.i | − | 1.49955i | −0.661694 | − | 0.749774i | \(-0.730162\pi\) | ||
0.661694 | − | 0.749774i | \(-0.269838\pi\) | |||||||
\(464\) | 3783.45 | − | 3483.40i | 0.0175732 | − | 0.0161796i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −112433. | − | 76814.6i | −0.517750 | − | 0.353730i | ||||
\(467\) | − | 81219.7i | − | 0.372415i | −0.982510 | − | 0.186208i | \(-0.940380\pi\) | ||
0.982510 | − | 0.186208i | \(-0.0596197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21607.1 | −0.0982313 | ||||||||
\(470\) | 54133.5 | − | 79234.7i | 0.245059 | − | 0.358690i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 161059. | + | 37252.3i | 0.722938 | + | 0.167213i | ||||
\(473\) | 416743. | 1.86271 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3048.61i | 0.0135118i | ||||||||
\(476\) | 78273.7 | − | 30545.7i | 0.345463 | − | 0.134814i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −79234.5 | + | 115975.i | −0.346784 | + | 0.507583i | ||||
\(479\) | 346051.i | 1.50824i | 0.656738 | + | 0.754119i | \(0.271936\pi\) | ||||
−0.656738 | + | 0.754119i | \(0.728064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −186749. | −0.807178 | ||||||||
\(482\) | 64803.6 | + | 44274.2i | 0.278936 | + | 0.190571i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20158.5 | − | 51656.5i | −0.0860534 | − | 0.220513i | ||||
\(485\) | −50236.2 | −0.213566 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 94439.7i | − | 0.398196i | −0.979980 | − | 0.199098i | \(-0.936199\pi\) | ||
0.979980 | − | 0.199098i | \(-0.0638012\pi\) | |||||||
\(488\) | −34661.3 | + | 149857.i | −0.145548 | + | 0.629270i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 63020.8 | + | 43056.1i | 0.262477 | + | 0.179326i | ||||
\(491\) | − | 175728.i | − | 0.728915i | −0.931220 | − | 0.364458i | \(-0.881254\pi\) | ||
0.931220 | − | 0.364458i | \(-0.118746\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1854.45 | −0.00762995 | ||||||||
\(494\) | −16479.7 | + | 24121.1i | −0.0675296 | + | 0.0988424i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 82318.0 | + | 89408.5i | 0.334604 | + | 0.363426i | ||||
\(497\) | −39964.9 | −0.161795 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37294.6i | 0.149777i | 0.997192 | + | 0.0748885i | \(0.0238601\pi\) | ||||
−0.997192 | + | 0.0748885i | \(0.976140\pi\) | |||||||
\(500\) | −96752.9 | − | 247930.i | −0.387011 | − | 0.991722i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1265.27 | − | 1851.96i | 0.00502084 | − | 0.00734894i | ||||
\(503\) | 250727.i | 0.990979i | 0.868614 | + | 0.495489i | \(0.165011\pi\) | ||||
−0.868614 | + | 0.495489i | \(0.834989\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19985.1 | 0.0783652 | ||||||||
\(506\) | −253783. | − | 173386.i | −0.991202 | − | 0.677194i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −386936. | + | 150999.i | −1.49938 | + | 0.585121i | ||||
\(509\) | −151144. | −0.583383 | −0.291692 | − | 0.956512i | \(-0.594218\pi\) | ||||
−0.291692 | + | 0.956512i | \(0.594218\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 558922.i | − | 2.14047i | ||||||
\(512\) | −165221. | + | 203523.i | −0.630267 | + | 0.776378i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 265910. | + | 181671.i | 1.00649 | + | 0.687638i | ||||
\(515\) | 69377.0i | 0.261578i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 141311. | 0.528682 | ||||||||
\(518\) | 97028.2 | − | 142019.i | 0.361608 | − | 0.529282i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 81400.2 | − | 351930.i | 0.301036 | − | 1.30152i | ||||
\(521\) | 179715. | 0.662079 | 0.331039 | − | 0.943617i | \(-0.392601\pi\) | ||||
0.331039 | + | 0.943617i | \(0.392601\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 305226.i | 1.11588i | 0.829881 | + | 0.557941i | \(0.188408\pi\) | ||||
−0.829881 | + | 0.557941i | \(0.811592\pi\) | |||||||
\(524\) | −245047. | + | 95627.5i | −0.892455 | + | 0.348273i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −78574.3 | + | 115008.i | −0.283994 | + | 0.415679i | ||||
\(527\) | − | 43823.5i | − | 0.157792i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −46243.2 | −0.165248 | ||||||||
\(530\) | 133422. | + | 91154.8i | 0.474982 | + | 0.324510i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9781.36 | − | 25064.9i | −0.0345602 | − | 0.0885609i | ||||
\(533\) | −133866. | −0.471211 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 435360.i | 1.52104i | ||||||||
\(536\) | −23683.0 | − | 5477.79i | −0.0824341 | − | 0.0190667i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −94028.5 | − | 64240.8i | −0.324859 | − | 0.221945i | ||||
\(539\) | 112394.i | 0.386871i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −282083. | −0.963789 | −0.481895 | − | 0.876229i | \(-0.660051\pi\) | ||||
−0.481895 | + | 0.876229i | \(0.660051\pi\) | |||||||
\(542\) | 84964.5 | − | 124362.i | 0.289227 | − | 0.423338i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 93537.9 | − | 13636.6i | 0.316075 | − | 0.0460795i | ||||
\(545\) | −300008. | −1.01004 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 296270.i | − | 0.990176i | −0.868843 | − | 0.495088i | \(-0.835136\pi\) | ||
0.868843 | − | 0.495088i | \(-0.164864\pi\) | |||||||
\(548\) | 183915. | + | 471285.i | 0.612430 | + | 1.56936i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 31314.6 | − | 45834.8i | 0.103519 | − | 0.151520i | ||||
\(551\) | 593.834i | 0.00195597i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 213695. | 0.698785 | ||||||||
\(554\) | −85608.4 | − | 58488.1i | −0.278931 | − | 0.190567i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 192216. | − | 75010.7i | 0.621785 | − | 0.242646i | ||||
\(557\) | 116573. | 0.375739 | 0.187869 | − | 0.982194i | \(-0.439842\pi\) | ||||
0.187869 | + | 0.982194i | \(0.439842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 765179.i | 2.44872i | ||||||||
\(560\) | 225343. | + | 244753.i | 0.718569 | + | 0.780463i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 164530. | + | 112408.i | 0.520921 | + | 0.355896i | ||||
\(563\) | 117383.i | 0.370329i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) | ||||
−0.982708 | + | 0.185164i | \(0.940718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −332193. | −1.04062 | ||||||||
\(566\) | −165634. | + | 242437.i | −0.517031 | + | 0.756773i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43804.6 | − | 10131.8i | −0.135776 | − | 0.0314045i | ||||
\(569\) | 222193. | 0.686288 | 0.343144 | − | 0.939283i | \(-0.388508\pi\) | ||||
0.343144 | + | 0.939283i | \(0.388508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 117091.i | − | 0.359131i | −0.983746 | − | 0.179565i | \(-0.942531\pi\) | ||
0.983746 | − | 0.179565i | \(-0.0574691\pi\) | |||||||
\(572\) | 495533. | − | 193378.i | 1.51454 | − | 0.591036i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 69551.9 | − | 101802.i | 0.211098 | − | 0.308982i | ||||
\(575\) | − | 58892.8i | − | 0.178126i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −335932. | −1.00902 | −0.504510 | − | 0.863406i | \(-0.668327\pi\) | ||||
−0.504510 | + | 0.863406i | \(0.668327\pi\) | |||||||
\(578\) | 247707. | + | 169235.i | 0.741451 | + | 0.506563i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2669.40 | − | 6840.38i | −0.00793521 | − | 0.0203341i | ||||
\(581\) | −593546. | −1.75834 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 237952.i | 0.700086i | ||||||||
\(584\) | 141697. | − | 612622.i | 0.415466 | − | 1.79625i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −431616. | − | 294882.i | −1.25690 | − | 0.858723i | ||||
\(587\) | − | 396842.i | − | 1.15170i | −0.817554 | − | 0.575852i | \(-0.804670\pi\) | ||
0.817554 | − | 0.575852i | \(-0.195330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14033.2 | −0.0404507 | ||||||||
\(590\) | 133147. | − | 194886.i | 0.382497 | − | 0.559857i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 142355. | − | 131065.i | 0.406189 | − | 0.373977i | ||||
\(593\) | −13679.6 | −0.0389012 | −0.0194506 | − | 0.999811i | \(-0.506192\pi\) | ||||
−0.0194506 | + | 0.999811i | \(0.506192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 119965.i | − | 0.338862i | ||||||
\(596\) | −183078. | − | 469139.i | −0.515399 | − | 1.32072i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 318353. | − | 465970.i | 0.890239 | − | 1.30303i | ||||
\(599\) | 124021.i | 0.345654i | 0.984952 | + | 0.172827i | \(0.0552902\pi\) | ||||
−0.984952 | + | 0.172827i | \(0.944710\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 484678. | 1.34185 | 0.670926 | − | 0.741525i | \(-0.265897\pi\) | ||||
0.670926 | + | 0.741525i | \(0.265897\pi\) | |||||||
\(602\) | −581903. | − | 397559.i | −1.60567 | − | 1.09701i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 588448. | − | 229637.i | 1.61300 | − | 0.629460i | ||||
\(605\) | −79170.9 | −0.216299 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 298924.i | − | 0.811303i | −0.914028 | − | 0.405651i | \(-0.867045\pi\) | ||
0.914028 | − | 0.405651i | \(-0.132955\pi\) | |||||||
\(608\) | −4366.72 | − | 29952.8i | −0.0118127 | − | 0.0810271i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 181331. | + | 123886.i | 0.487318 | + | 0.332938i | ||||
\(611\) | 259460.i | 0.695004i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −155694. | −0.414334 | −0.207167 | − | 0.978306i | \(-0.566424\pi\) | ||||
−0.207167 | + | 0.978306i | \(0.566424\pi\) | |||||||
\(614\) | −314806. | + | 460777.i | −0.835037 | + | 1.22223i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −110401. | + | 477314.i | −0.290945 | + | 1.25789i | ||||
\(617\) | 625050. | 1.64189 | 0.820946 | − | 0.571007i | \(-0.193447\pi\) | ||||
0.820946 | + | 0.571007i | \(0.193447\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 368822.i | − | 0.962576i | −0.876563 | − | 0.481288i | \(-0.840169\pi\) | ||
0.876563 | − | 0.481288i | \(-0.159831\pi\) | |||||||
\(620\) | 161649. | − | 63082.0i | 0.420522 | − | 0.164105i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −297932. | + | 436079.i | −0.770080 | + | 1.12716i | ||||
\(623\) | − | 678307.i | − | 1.74763i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −315531. | −0.807758 | ||||||||
\(626\) | −130547. | − | 89190.1i | −0.333133 | − | 0.227598i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15234.2 | + | 39037.9i | 0.0386279 | + | 0.0989845i | ||||
\(629\) | −69775.0 | −0.176359 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 457172.i | − | 1.14821i | −0.818782 | − | 0.574105i | \(-0.805350\pi\) | ||
0.818782 | − | 0.574105i | \(-0.194650\pi\) | |||||||
\(632\) | 234226. | + | 54175.5i | 0.586409 | + | 0.135634i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −303720. | − | 207503.i | −0.755606 | − | 0.516234i | ||||
\(635\) | 593035.i | 1.47073i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −206366. | −0.508580 | ||||||||
\(638\) | 6099.73 | − | 8928.11i | 0.0149854 | − | 0.0219340i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 184944. | + | 325397.i | 0.451524 | + | 0.794427i | ||||
\(641\) | 728866. | 1.77391 | 0.886955 | − | 0.461855i | \(-0.152816\pi\) | ||||
0.886955 | + | 0.461855i | \(0.152816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 201261.i | 0.486786i | 0.969928 | + | 0.243393i | \(0.0782604\pi\) | ||||
−0.969928 | + | 0.243393i | \(0.921740\pi\) | |||||||
\(644\) | 188956. | + | 484202.i | 0.455605 | + | 1.16749i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6157.28 | + | 9012.34i | −0.0147545 | + | 0.0215960i | ||||
\(647\) | − | 284857.i | − | 0.680484i | −0.940338 | − | 0.340242i | \(-0.889491\pi\) | ||
0.940338 | − | 0.340242i | \(-0.110509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 347569. | 0.825186 | ||||||||
\(650\) | 84157.0 | + | 57496.5i | 0.199188 | + | 0.136086i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −106172. | + | 41432.8i | −0.249756 | + | 0.0974652i | ||||
\(653\) | −639617. | −1.50001 | −0.750005 | − | 0.661433i | \(-0.769949\pi\) | ||||
−0.750005 | + | 0.661433i | \(0.769949\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 375569.i | 0.875401i | ||||||||
\(656\) | 102043. | − | 93950.5i | 0.237124 | − | 0.218319i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −197314. | − | 134806.i | −0.455728 | − | 0.311356i | ||||
\(659\) | 372398.i | 0.857505i | 0.903422 | + | 0.428753i | \(0.141047\pi\) | ||||
−0.903422 | + | 0.428753i | \(0.858953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −137125. | −0.313843 | −0.156922 | − | 0.987611i | \(-0.550157\pi\) | ||||
−0.156922 | + | 0.987611i | \(0.550157\pi\) | |||||||
\(662\) | −7320.19 | + | 10714.5i | −0.0167035 | + | 0.0244487i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −650572. | − | 150475.i | −1.47557 | − | 0.341293i | ||||
\(665\) | −38415.5 | −0.0868686 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11471.7i | − | 0.0257854i | ||||||
\(668\) | −725450. | + | 283101.i | −1.62575 | + | 0.634437i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19578.7 | + | 28657.1i | −0.0436148 | + | 0.0638385i | ||||
\(671\) | 323394.i | 0.718269i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 840931. | 1.85665 | 0.928325 | − | 0.371770i | \(-0.121249\pi\) | ||||
0.928325 | + | 0.371770i | \(0.121249\pi\) | |||||||
\(674\) | −18466.5 | − | 12616.4i | −0.0406504 | − | 0.0277726i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 188930. | + | 484135.i | 0.413435 | + | 1.05943i | ||||
\(677\) | −207006. | −0.451653 | −0.225827 | − | 0.974168i | \(-0.572508\pi\) | ||||
−0.225827 | + | 0.974168i | \(0.572508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 125100.i | 0.271343i | ||||||||
\(680\) | 30413.5 | − | 131491.i | 0.0657731 | − | 0.284367i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 210985. | + | 144146.i | 0.453609 | + | 0.309908i | ||||
\(683\) | − | 241334.i | − | 0.517341i | −0.965966 | − | 0.258670i | \(-0.916716\pi\) | ||
0.965966 | − | 0.258670i | \(-0.0832844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 722311. | 1.53937 | ||||||||
\(686\) | −200988. | + | 294184.i | −0.427093 | + | 0.625131i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −537022. | − | 583279.i | −1.13453 | − | 1.23225i | ||||
\(689\) | −436901. | −0.920333 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 628208.i | 1.31567i | 0.753161 | + | 0.657836i | \(0.228528\pi\) | ||||
−0.753161 | + | 0.657836i | \(0.771472\pi\) | |||||||
\(692\) | 160399. | + | 411026.i | 0.334958 | + | 0.858335i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −385022. | + | 563552.i | −0.799404 | + | 1.17008i | ||||
\(695\) | − | 294598.i | − | 0.609903i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50016.2 | −0.102954 | ||||||||
\(698\) | 317401. | + | 216850.i | 0.651475 | + | 0.445091i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −87449.8 | + | 34126.6i | −0.178469 | + | 0.0696461i | ||||
\(701\) | 470333. | 0.957127 | 0.478563 | − | 0.878053i | \(-0.341158\pi\) | ||||
0.478563 | + | 0.878053i | \(0.341158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22343.4i | 0.0452105i | ||||||||
\(704\) | −242016. | + | 495184.i | −0.488313 | + | 0.999129i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 680089. | + | 464640.i | 1.36445 | + | 0.932196i | ||||
\(707\) | − | 49767.8i | − | 0.0995656i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −666498. | −1.32589 | −0.662944 | − | 0.748669i | \(-0.730693\pi\) | ||||
−0.662944 | + | 0.748669i | \(0.730693\pi\) | |||||||
\(710\) | −36213.2 | + | 53004.9i | −0.0718373 | + | 0.105147i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 171963. | − | 743476.i | 0.339215 | − | 1.46658i | ||||
\(713\) | 271092. | 0.533259 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 759474.i | − | 1.48560i | ||||||
\(716\) | 630195. | − | 245928.i | 1.22927 | − | 0.479714i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −176987. | + | 259054.i | −0.343315 | + | 0.502506i | ||||
\(719\) | − | 551482.i | − | 1.06678i | −0.845870 | − | 0.533388i | \(-0.820918\pi\) | ||
0.845870 | − | 0.533388i | \(-0.179082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 172766. | 0.332344 | ||||||||
\(722\) | −427535. | − | 292094.i | −0.820158 | − | 0.560336i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5856.14 | − | 15006.4i | −0.0111721 | − | 0.0286286i | ||||
\(725\) | 2071.85 | 0.00394169 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 735388.i | − | 1.39139i | −0.718339 | − | 0.695694i | \(-0.755097\pi\) | ||
0.718339 | − | 0.695694i | \(-0.244903\pi\) | |||||||
\(728\) | −876393. | − | 202706.i | −1.65362 | − | 0.382477i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −741290. | − | 506453.i | −1.39105 | − | 0.950372i | ||||
\(731\) | 285893.i | 0.535019i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 372734. | 0.693731 | 0.346866 | − | 0.937915i | \(-0.387246\pi\) | ||||
0.346866 | + | 0.937915i | \(0.387246\pi\) | |||||||
\(734\) | 500452. | − | 732506.i | 0.928902 | − | 1.35962i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 84356.0 | + | 578626.i | 0.155726 | + | 1.06817i | ||||
\(737\) | −51108.4 | −0.0940931 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 962125.i | − | 1.76174i | −0.473356 | − | 0.880871i | \(-0.656957\pi\) | ||
0.473356 | − | 0.880871i | \(-0.343043\pi\) | |||||||
\(740\) | −100438. | − | 257374.i | −0.183415 | − | 0.470004i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 226998. | − | 332254.i | 0.412301 | − | 0.603480i | ||||
\(743\) | 557423.i | 1.00973i | 0.863197 | + | 0.504867i | \(0.168459\pi\) | ||||
−0.863197 | + | 0.504867i | \(0.831541\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −719022. | −1.29548 | ||||||||
\(746\) | 85488.3 | + | 58406.1i | 0.153613 | + | 0.104949i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 185145. | − | 72251.5i | 0.330910 | − | 0.129135i | ||||
\(749\) | 1.08415e6 | 1.93254 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 619927.i | 1.09916i | 0.835441 | + | 0.549580i | \(0.185212\pi\) | ||||
−0.835441 | + | 0.549580i | \(0.814788\pi\) | |||||||
\(752\) | −182095. | − | 197780.i | −0.322005 | − | 0.349741i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16392.8 | + | 11199.7i | 0.0288344 | + | 0.0196998i | ||||
\(755\) | − | 901881.i | − | 1.58218i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −66502.8 | −0.116051 | −0.0580254 | − | 0.998315i | \(-0.518480\pi\) | ||||
−0.0580254 | + | 0.998315i | \(0.518480\pi\) | |||||||
\(758\) | 333508. | − | 488152.i | 0.580454 | − | 0.849604i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −42106.3 | − | 9739.03i | −0.0728987 | − | 0.0168612i | ||||
\(761\) | −417057. | −0.720156 | −0.360078 | − | 0.932922i | \(-0.617250\pi\) | ||||
−0.360078 | + | 0.932922i | \(0.617250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 747093.i | 1.28329i | ||||||||
\(764\) | 102945. | − | 40173.4i | 0.176367 | − | 0.0688260i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 510485. | − | 747192.i | 0.870013 | − | 1.27343i | ||||
\(767\) | 638169.i | 1.08479i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −284602. | −0.481266 | −0.240633 | − | 0.970616i | \(-0.577355\pi\) | ||||
−0.240633 | + | 0.970616i | \(0.577355\pi\) | |||||||
\(770\) | 577564. | + | 394595.i | 0.974134 | + | 0.665534i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 164075. | + | 420445.i | 0.275301 | + | 0.705463i | ||||
\(773\) | −690220. | −1.15512 | −0.577562 | − | 0.816347i | \(-0.695996\pi\) | ||||
−0.577562 | + | 0.816347i | \(0.695996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48960.9i | 0.0815167i | ||||||||
\(776\) | −31715.3 | + | 137120.i | −0.0526677 | + | 0.227707i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 846893. | + | 578602.i | 1.39917 | + | 0.955918i | ||||
\(779\) | 16016.2i | 0.0263928i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −94531.3 | −0.154979 | ||||||||
\(782\) | 118946. | − | 174100.i | 0.194507 | − | 0.284698i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 157308. | − | 144833.i | 0.255929 | − | 0.235632i | ||||
\(785\) | 59831.1 | 0.0970929 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 855688.i | 1.38155i | 0.723071 | + | 0.690774i | \(0.242730\pi\) | ||||
−0.723071 | + | 0.690774i | \(0.757270\pi\) | |||||||
\(788\) | −223672. | − | 573161.i | −0.360212 | − | 0.923048i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 193634. | − | 283420.i | 0.310261 | − | 0.454126i | ||||
\(791\) | 827242.i | 1.32215i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −593782. | −0.944236 | ||||||||
\(794\) | 187161. | + | 127869.i | 0.296875 | + | 0.202827i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −81831.3 | + | 31934.0i | −0.129150 | + | 0.0503996i | ||||
\(797\) | −579975. | −0.913046 | −0.456523 | − | 0.889712i | \(-0.650905\pi\) | ||||
−0.456523 | + | 0.889712i | \(0.650905\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 96941.7i | 0.151851i | ||||||||
\(800\) | −104503. | + | 15235.2i | −0.163287 | + | 0.0238050i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 36040.0 | + | 24622.7i | 0.0560320 | + | 0.0382814i | ||||
\(803\) | − | 1.32205e6i | − | 2.05030i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 742108. | 1.14518 | ||||||||
\(806\) | −264665. | + | 387387.i | −0.407405 | + | 0.596314i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12617.1 | − | 54549.3i | 0.0193257 | − | 0.0835539i | ||||
\(809\) | 60860.6 | 0.0929907 | 0.0464953 | − | 0.998919i | \(-0.485195\pi\) | ||||
0.0464953 | + | 0.998919i | \(0.485195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 103330.i | 0.157103i | 0.996910 | + | 0.0785515i | \(0.0250295\pi\) | ||||
−0.996910 | + | 0.0785515i | \(0.974970\pi\) | |||||||
\(812\) | −17034.2 | + | 6647.47i | −0.0258351 | + | 0.0100819i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 229506. | − | 335926.i | 0.346375 | − | 0.506985i | ||||
\(815\) | 162724.i | 0.244983i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 91549.0 | 0.137154 | ||||||||
\(818\) | 956404. | + | 653421.i | 1.42934 | + | 0.976531i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −71996.2 | − | 184491.i | −0.107073 | − | 0.274377i | ||||
\(821\) | −533333. | −0.791247 | −0.395623 | − | 0.918413i | \(-0.629471\pi\) | ||||
−0.395623 | + | 0.918413i | \(0.629471\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 728807.i | − | 1.07600i | −0.842945 | − | 0.538000i | \(-0.819180\pi\) | ||
0.842945 | − | 0.538000i | \(-0.180820\pi\) | |||||||
\(824\) | 189365. | + | 43799.3i | 0.278897 | + | 0.0645079i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −485314. | − | 331569.i | −0.711317 | − | 0.485975i | ||||
\(827\) | 768434.i | 1.12356i | 0.827287 | + | 0.561779i | \(0.189883\pi\) | ||||
−0.827287 | + | 0.561779i | \(0.810117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −401672. | −0.584471 | −0.292235 | − | 0.956346i | \(-0.594399\pi\) | ||||
−0.292235 | + | 0.956346i | \(0.594399\pi\) | |||||||
\(830\) | −537827. | + | 787211.i | −0.780704 | + | 1.14271i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −909205. | − | 444364.i | −1.31345 | − | 0.641936i | ||||
\(833\) | −77104.4 | −0.111119 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.11185e6i | 1.59469i | ||||||||
\(836\) | −23136.4 | − | 59287.4i | −0.0331043 | − | 0.0848301i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 157587. | − | 230659.i | 0.224405 | − | 0.328460i | ||||
\(839\) | − | 429703.i | − | 0.610443i | −0.952281 | − | 0.305221i | \(-0.901270\pi\) | ||
0.952281 | − | 0.305221i | \(-0.0987305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −706877. | −0.999429 | ||||||||
\(842\) | −53528.1 | − | 36570.7i | −0.0755019 | − | 0.0515833i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −692669. | + | 270308.i | −0.972391 | + | 0.379468i | ||||
\(845\) | 742006. | 1.03919 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 197155.i | 0.274815i | ||||||||
\(848\) | 333040. | − | 306628.i | 0.463132 | − | 0.426403i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 31443.5 | + | 21482.4i | 0.0435204 | + | 0.0297334i | ||||
\(851\) | − | 431629.i | − | 0.596007i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −732176. | −1.00628 | −0.503138 | − | 0.864206i | \(-0.667821\pi\) | ||||
−0.503138 | + | 0.864206i | \(0.667821\pi\) | |||||||
\(854\) | 308507. | − | 451559.i | 0.423009 | − | 0.619154i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.18832e6 | + | 274853.i | 1.62175 | + | 0.375105i | ||||
\(857\) | −430159. | −0.585689 | −0.292844 | − | 0.956160i | \(-0.594602\pi\) | ||||
−0.292844 | + | 0.956160i | \(0.594602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 489975.i | − | 0.664030i | −0.943274 | − | 0.332015i | \(-0.892272\pi\) | ||
0.943274 | − | 0.332015i | \(-0.107728\pi\) | |||||||
\(860\) | −1.05455e6 | + | 411531.i | −1.42584 | + | 0.556424i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −237525. | + | 347662.i | −0.319665 | + | 0.467890i | ||||
\(863\) | 999093.i | 1.34148i | 0.741692 | + | 0.670740i | \(0.234023\pi\) | ||||
−0.741692 | + | 0.670740i | \(0.765977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 629955. | 0.841933 | ||||||||
\(866\) | −435303. | − | 297401.i | −0.580438 | − | 0.396559i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −157090. | − | 402544.i | −0.208501 | − | 0.534287i | ||||
\(869\) | 505464. | 0.669347 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 93839.8i | − | 0.123695i | ||||||
\(872\) | −189402. | + | 818872.i | −0.249087 | + | 1.07692i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −55750.4 | − | 38089.0i | −0.0729836 | − | 0.0498628i | ||||
\(875\) | 946265.i | 1.23594i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 634599. | 0.825087 | 0.412544 | − | 0.910938i | \(-0.364640\pi\) | ||||
0.412544 | + | 0.910938i | \(0.364640\pi\) | |||||||
\(878\) | 336334. | − | 492289.i | 0.436297 | − | 0.638603i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 533018. | + | 578930.i | 0.688298 | + | 0.747585i | ||||
\(881\) | −312649. | −0.402815 | −0.201407 | − | 0.979508i | \(-0.564552\pi\) | ||||
−0.201407 | + | 0.979508i | \(0.564552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 209047.i | − | 0.268116i | −0.990973 | − | 0.134058i | \(-0.957199\pi\) | ||
0.990973 | − | 0.134058i | \(-0.0428008\pi\) | |||||||
\(884\) | 132660. | + | 339944.i | 0.169761 | + | 0.435014i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −561710. | + | 822169.i | −0.715558 | + | 1.04735i | ||||
\(887\) | − | 178008.i | − | 0.226252i | −0.993581 | − | 0.113126i | \(-0.963914\pi\) | ||
0.993581 | − | 0.113126i | \(-0.0360864\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.47680e6 | 1.86861 | ||||||||
\(890\) | −899628. | − | 614631.i | −1.13575 | − | 0.775951i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 720031. | − | 280986.i | 0.904943 | − | 0.353147i | ||||
\(893\) | 31042.8 | 0.0389276 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 965863.i | − | 1.20578i | ||||||
\(896\) | 810319. | − | 460556.i | 1.00935 | − | 0.573676i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 805047. | + | 550012.i | 0.998317 | + | 0.682055i | ||||
\(899\) | 9537.04i | 0.0118003i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −163239. | −0.201082 | ||||||||
\(902\) | 164515. | − | 240799.i | 0.202205 | − | 0.295966i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −209721. | + | 906720.i | −0.256629 | + | 1.10952i | ||||
\(905\) | −22999.5 | −0.0280815 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 62871.2i | − | 0.0764253i | −0.999270 | − | 0.0382126i | \(-0.987834\pi\) | ||
0.999270 | − | 0.0382126i | \(-0.0121664\pi\) | |||||||
\(908\) | 284819. | − | 111148.i | 0.345459 | − | 0.134813i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −724513. | + | 1.06046e6i | −0.874910 | + | 1.28060i | ||||
\(911\) | − | 1.45791e6i | − | 1.75669i | −0.478027 | − | 0.878345i | \(-0.658648\pi\) | ||
0.478027 | − | 0.878345i | \(-0.341352\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.40395e6 | −1.68426 | ||||||||
\(914\) | −1.13377e6 | − | 774598.i | −1.35716 | − | 0.927222i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −426817. | − | 1.09372e6i | −0.508687 | − | 1.30352i | ||||
\(917\) | 935258. | 1.11223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 315989.i | − | 0.374146i | −0.982346 | − | 0.187073i | \(-0.940100\pi\) | ||
0.982346 | − | 0.187073i | \(-0.0599001\pi\) | |||||||
\(920\) | 813407. | + | 188138.i | 0.961020 | + | 0.222280i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −513660. | − | 350935.i | −0.604246 | − | 0.412824i | ||||
\(923\) | − | 173568.i | − | 0.203736i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 77954.8 | 0.0911086 | ||||||||
\(926\) | −725358. | + | 1.06170e6i | −0.845923 | + | 1.23817i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20356.1 | + | 2967.65i | −0.0236373 | + | 0.00344601i | ||||
\(929\) | −122547. | −0.141994 | −0.0709971 | − | 0.997477i | \(-0.522618\pi\) | ||||
−0.0709971 | + | 0.997477i | \(0.522618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24690.4i | 0.0284859i | ||||||||
\(932\) | 198010. | + | 507403.i | 0.227958 | + | 0.584145i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −183270. | + | 268250.i | −0.210086 | + | 0.307501i | ||||
\(935\) | − | 283761.i | − | 0.324586i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 495399. | 0.564256 | 0.282128 | − | 0.959377i | \(-0.408960\pi\) | ||||
0.282128 | + | 0.959377i | \(0.408960\pi\) | |||||||
\(938\) | 71363.3 | + | 48755.7i | 0.0811090 | + | 0.0554141i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −357582. | + | 139543.i | −0.404687 | + | 0.157926i | ||||
\(941\) | 1.14226e6 | 1.28999 | 0.644994 | − | 0.764188i | \(-0.276860\pi\) | ||||
0.644994 | + | 0.764188i | \(0.276860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 309401.i | − | 0.347935i | ||||||
\(944\) | −447883. | − | 486461.i | −0.502598 | − | 0.545889i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.37641e6 | − | 940370.i | −1.53803 | − | 1.05079i | ||||
\(947\) | 527337.i | 0.588015i | 0.955803 | + | 0.294007i | \(0.0949890\pi\) | ||||
−0.955803 | + | 0.294007i | \(0.905011\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.42741e6 | 2.69532 | ||||||||
\(950\) | 6879.10 | − | 10068.9i | 0.00762227 | − | 0.0111566i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −327446. | − | 75737.0i | −0.361298 | − | 0.0835669i | ||||
\(953\) | 259379. | 0.285594 | 0.142797 | − | 0.989752i | \(-0.454390\pi\) | ||||
0.142797 | + | 0.989752i | \(0.454390\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 157778.i | − | 0.172997i | ||||||
\(956\) | 523387. | − | 204248.i | 0.572674 | − | 0.223481i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 780856. | − | 1.14293e6i | 0.850824 | − | 1.24534i | ||||
\(959\) | − | 1.79873e6i | − | 1.95582i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 698146. | 0.755962 | ||||||||
\(962\) | 616791. | + | 421395.i | 0.666482 | + | 0.455344i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −114128. | − | 292455.i | −0.122812 | − | 0.314706i | ||||
\(965\) | 644391. | 0.691982 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.03870e6i | 1.11081i | 0.831581 | + | 0.555403i | \(0.187436\pi\) | ||||
−0.831581 | + | 0.555403i | \(0.812564\pi\) | |||||||
\(968\) | −49982.4 | + | 216097.i | −0.0533417 | + | 0.230621i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 165919. | + | 113357.i | 0.176341 | + | 0.120477i | ||||
\(971\) | − | 1.15698e6i | − | 1.22713i | −0.789646 | − | 0.613563i | \(-0.789736\pi\) | ||
0.789646 | − | 0.613563i | \(-0.210264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −733622. | −0.774902 | ||||||||
\(974\) | −213101. | + | 311913.i | −0.224630 | + | 0.328788i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 452626. | − | 416731.i | 0.475160 | − | 0.437478i | ||||
\(977\) | −1.09732e6 | −1.14960 | −0.574799 | − | 0.818295i | \(-0.694920\pi\) | ||||
−0.574799 | + | 0.818295i | \(0.694920\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.60444e6i | − | 1.67401i | ||||||
\(980\) | −110988. | − | 284409.i | −0.115565 | − | 0.296136i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −396525. | + | 580389.i | −0.411195 | + | 0.601861i | ||||
\(983\) | 1.71299e6i | 1.77276i | 0.462963 | + | 0.886378i | \(0.346786\pi\) | ||||
−0.462963 | + | 0.886378i | \(0.653214\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −878451. | −0.905409 | ||||||||
\(986\) | 6124.84 | + | 4184.52i | 0.00630000 | + | 0.00430419i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 108857. | − | 42480.6i | 0.111518 | − | 0.0435188i | ||||
\(989\) | −1.76854e6 | −1.80810 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.03974e6i | 1.05872i | 0.848399 | + | 0.529358i | \(0.177567\pi\) | ||||
−0.848399 | + | 0.529358i | \(0.822433\pi\) | |||||||
\(992\) | −70130.0 | − | 481045.i | −0.0712657 | − | 0.488835i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 131995. | + | 90179.7i | 0.133593 | + | 0.0912717i | ||||
\(995\) | 125418.i | 0.126682i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.11868e6 | −1.12542 | −0.562709 | − | 0.826655i | \(-0.690241\pi\) | ||||
−0.562709 | + | 0.826655i | \(0.690241\pi\) | |||||||
\(998\) | 84154.4 | − | 123176.i | 0.0844920 | − | 0.123670i | ||||
\(999\) | 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 | 36.5.d.b.19.1 | 4 | ||
3.2 | odd | 2 | 12.5.d.a.7.4 | yes | 4 | ||
4.3 | odd | 2 | inner | 36.5.d.b.19.2 | 4 | ||
8.3 | odd | 2 | 576.5.g.m.127.2 | 4 | |||
8.5 | even | 2 | 576.5.g.m.127.1 | 4 | |||
12.11 | even | 2 | 12.5.d.a.7.3 | ✓ | 4 | ||
15.2 | even | 4 | 300.5.f.a.199.4 | 8 | |||
15.8 | even | 4 | 300.5.f.a.199.5 | 8 | |||
15.14 | odd | 2 | 300.5.c.a.151.1 | 4 | |||
24.5 | odd | 2 | 192.5.g.d.127.4 | 4 | |||
24.11 | even | 2 | 192.5.g.d.127.2 | 4 | |||
48.5 | odd | 4 | 768.5.b.g.127.2 | 8 | |||
48.11 | even | 4 | 768.5.b.g.127.6 | 8 | |||
48.29 | odd | 4 | 768.5.b.g.127.7 | 8 | |||
48.35 | even | 4 | 768.5.b.g.127.3 | 8 | |||
60.23 | odd | 4 | 300.5.f.a.199.3 | 8 | |||
60.47 | odd | 4 | 300.5.f.a.199.6 | 8 | |||
60.59 | even | 2 | 300.5.c.a.151.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.5.d.a.7.3 | ✓ | 4 | 12.11 | even | 2 | ||
12.5.d.a.7.4 | yes | 4 | 3.2 | odd | 2 | ||
36.5.d.b.19.1 | 4 | 1.1 | even | 1 | trivial | ||
36.5.d.b.19.2 | 4 | 4.3 | odd | 2 | inner | ||
192.5.g.d.127.2 | 4 | 24.11 | even | 2 | |||
192.5.g.d.127.4 | 4 | 24.5 | odd | 2 | |||
300.5.c.a.151.1 | 4 | 15.14 | odd | 2 | |||
300.5.c.a.151.2 | 4 | 60.59 | even | 2 | |||
300.5.f.a.199.3 | 8 | 60.23 | odd | 4 | |||
300.5.f.a.199.4 | 8 | 15.2 | even | 4 | |||
300.5.f.a.199.5 | 8 | 15.8 | even | 4 | |||
300.5.f.a.199.6 | 8 | 60.47 | odd | 4 | |||
576.5.g.m.127.1 | 4 | 8.5 | even | 2 | |||
576.5.g.m.127.2 | 4 | 8.3 | odd | 2 | |||
768.5.b.g.127.2 | 8 | 48.5 | odd | 4 | |||
768.5.b.g.127.3 | 8 | 48.35 | even | 4 | |||
768.5.b.g.127.6 | 8 | 48.11 | even | 4 | |||
768.5.b.g.127.7 | 8 | 48.29 | odd | 4 |