Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1063,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.1063");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.e (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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} + 54x^{8} - 114x^{7} + 120x^{6} + 46x^{5} + 9x^{4} - 4x^{3} + 8x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 798) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1063.5 | ||
Root | \(1.25342 - 1.25342i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1063 |
Dual form | 2394.2.e.b.1063.8 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.50684i | 1.12109i | 0.828124 | + | 0.560546i | \(0.189409\pi\) | ||||
−0.828124 | + | 0.560546i | \(0.810591\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.53963 | − | 0.741811i | −0.959890 | − | 0.280378i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.50684 | 0.792731 | ||||||||
\(11\) | 4.07545 | 1.22880 | 0.614398 | − | 0.788997i | \(-0.289399\pi\) | ||||
0.614398 | + | 0.788997i | \(0.289399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.506836 | −0.140571 | −0.0702855 | − | 0.997527i | \(-0.522391\pi\) | ||||
−0.0702855 | + | 0.997527i | \(0.522391\pi\) | |||||||
\(14\) | −0.741811 | + | 2.53963i | −0.198257 | + | 0.678744i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.30760i | − | 0.559676i | −0.960047 | − | 0.279838i | \(-0.909719\pi\) | ||
0.960047 | − | 0.279838i | \(-0.0902807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.30085 | − | 0.709018i | −0.986682 | − | 0.162660i | ||||
\(20\) | − | 2.50684i | − | 0.560546i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.07545i | − | 0.868889i | ||||||
\(23\) | 6.34027 | 1.32204 | 0.661019 | − | 0.750369i | \(-0.270124\pi\) | ||||
0.661019 | + | 0.750369i | \(0.270124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.28423 | −0.256845 | ||||||||
\(26\) | 0.506836i | 0.0993987i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.53963 | + | 0.741811i | 0.479945 | + | 0.140189i | ||||
\(29\) | 8.66728i | 1.60947i | 0.593632 | + | 0.804737i | \(0.297694\pi\) | ||||
−0.593632 | + | 0.804737i | \(0.702306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.39640 | −0.250802 | −0.125401 | − | 0.992106i | \(-0.540022\pi\) | ||||
−0.125401 | + | 0.992106i | \(0.540022\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.30760 | −0.395751 | ||||||||
\(35\) | 1.85960 | − | 6.36643i | 0.314329 | − | 1.07612i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.68285i | − | 0.276660i | −0.990386 | − | 0.138330i | \(-0.955827\pi\) | ||
0.990386 | − | 0.138330i | \(-0.0441734\pi\) | |||||||
\(38\) | −0.709018 | + | 4.30085i | −0.115018 | + | 0.697690i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.50684 | −0.396366 | ||||||||
\(41\) | 0.402139 | 0.0628036 | 0.0314018 | − | 0.999507i | \(-0.490003\pi\) | ||||
0.0314018 | + | 0.999507i | \(0.490003\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.73509 | −1.02709 | −0.513546 | − | 0.858062i | \(-0.671668\pi\) | ||||
−0.513546 | + | 0.858062i | \(0.671668\pi\) | |||||||
\(44\) | −4.07545 | −0.614398 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 6.34027i | − | 0.934822i | ||||||
\(47\) | 5.33646i | 0.778403i | 0.921153 | + | 0.389202i | \(0.127249\pi\) | ||||
−0.921153 | + | 0.389202i | \(0.872751\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.89943 | + | 3.76785i | 0.842776 | + | 0.538264i | ||||
\(50\) | 1.28423i | 0.181617i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.506836 | 0.0702855 | ||||||||
\(53\) | 1.66122i | 0.228187i | 0.993470 | + | 0.114093i | \(0.0363963\pi\) | ||||
−0.993470 | + | 0.114093i | \(0.963604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2165i | 1.37759i | ||||||||
\(56\) | 0.741811 | − | 2.53963i | 0.0991286 | − | 0.339372i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.66728 | 1.13807 | ||||||||
\(59\) | −9.42907 | −1.22756 | −0.613780 | − | 0.789477i | \(-0.710352\pi\) | ||||
−0.613780 | + | 0.789477i | \(0.710352\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.31706i | 0.680779i | 0.940284 | + | 0.340390i | \(0.110559\pi\) | ||||
−0.940284 | + | 0.340390i | \(0.889441\pi\) | |||||||
\(62\) | 1.39640i | 0.177343i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 1.27056i | − | 0.157593i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.06939i | − | 0.374986i | −0.982266 | − | 0.187493i | \(-0.939964\pi\) | ||
0.982266 | − | 0.187493i | \(-0.0600362\pi\) | |||||||
\(68\) | 2.30760i | 0.279838i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.36643 | − | 1.85960i | −0.760934 | − | 0.222264i | ||||
\(71\) | 8.08532i | 0.959551i | 0.877391 | + | 0.479775i | \(0.159282\pi\) | ||||
−0.877391 | + | 0.479775i | \(0.840718\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5144i | 1.58174i | 0.611984 | + | 0.790870i | \(0.290372\pi\) | ||||
−0.611984 | + | 0.790870i | \(0.709628\pi\) | |||||||
\(74\) | −1.68285 | −0.195628 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.30085 | + | 0.709018i | 0.493341 | + | 0.0813299i | ||||
\(77\) | −10.3501 | − | 3.02321i | −1.17951 | − | 0.344527i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.37893i | − | 0.380159i | −0.981769 | − | 0.190079i | \(-0.939125\pi\) | ||
0.981769 | − | 0.190079i | \(-0.0608745\pi\) | |||||||
\(80\) | 2.50684i | 0.280273i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 0.402139i | − | 0.0444089i | ||||||
\(83\) | 10.5106i | 1.15368i | 0.816856 | + | 0.576842i | \(0.195715\pi\) | ||||
−0.816856 | + | 0.576842i | \(0.804285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.78478 | 0.627448 | ||||||||
\(86\) | 6.73509i | 0.726264i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.07545i | 0.434445i | ||||||||
\(89\) | −11.7389 | −1.24432 | −0.622162 | − | 0.782889i | \(-0.713745\pi\) | ||||
−0.622162 | + | 0.782889i | \(0.713745\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.28718 | + | 0.375977i | 0.134933 | + | 0.0394130i | ||||
\(92\) | −6.34027 | −0.661019 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.33646 | 0.550414 | ||||||||
\(95\) | 1.77739 | − | 10.7815i | 0.182356 | − | 1.10616i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.87048 | 0.494523 | 0.247261 | − | 0.968949i | \(-0.420469\pi\) | ||||
0.247261 | + | 0.968949i | \(0.420469\pi\) | |||||||
\(98\) | 3.76785 | − | 5.89943i | 0.380610 | − | 0.595933i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.28423 | 0.128423 | ||||||||
\(101\) | 10.8277i | 1.07740i | 0.842498 | + | 0.538700i | \(0.181084\pi\) | ||||
−0.842498 | + | 0.538700i | \(0.818916\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.51407 | 0.543317 | 0.271659 | − | 0.962394i | \(-0.412428\pi\) | ||||
0.271659 | + | 0.962394i | \(0.412428\pi\) | |||||||
\(104\) | − | 0.506836i | − | 0.0496994i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.66122 | 0.161352 | ||||||||
\(107\) | 1.64796i | 0.159315i | 0.996822 | + | 0.0796573i | \(0.0253826\pi\) | ||||
−0.996822 | + | 0.0796573i | \(0.974617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0910i | 1.73281i | 0.499345 | + | 0.866403i | \(0.333574\pi\) | ||||
−0.499345 | + | 0.866403i | \(0.666426\pi\) | |||||||
\(110\) | 10.2165 | 0.974104 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.53963 | − | 0.741811i | −0.239972 | − | 0.0700945i | ||||
\(113\) | 2.33655i | 0.219804i | 0.993942 | + | 0.109902i | \(0.0350538\pi\) | ||||
−0.993942 | + | 0.109902i | \(0.964946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.8940i | 1.48213i | ||||||||
\(116\) | − | 8.66728i | − | 0.804737i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.42907i | 0.868016i | ||||||||
\(119\) | −1.71180 | + | 5.86046i | −0.156921 | + | 0.537227i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.60931 | 0.509937 | ||||||||
\(122\) | 5.31706 | 0.481384 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.39640 | 0.125401 | ||||||||
\(125\) | 9.31483i | 0.833144i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.29418i | − | 0.114840i | −0.998350 | − | 0.0574200i | \(-0.981713\pi\) | ||
0.998350 | − | 0.0574200i | \(-0.0182874\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.27056 | −0.111435 | ||||||||
\(131\) | 4.38528i | 0.383144i | 0.981479 | + | 0.191572i | \(0.0613585\pi\) | ||||
−0.981479 | + | 0.191572i | \(0.938642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.3966 | + | 4.99106i | 0.901500 | + | 0.432780i | ||||
\(134\) | −3.06939 | −0.265155 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.30760 | 0.197875 | ||||||||
\(137\) | 17.3945 | 1.48611 | 0.743056 | − | 0.669229i | \(-0.233375\pi\) | ||||
0.743056 | + | 0.669229i | \(0.233375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.29012i | − | 0.363884i | −0.983309 | − | 0.181942i | \(-0.941762\pi\) | ||
0.983309 | − | 0.181942i | \(-0.0582382\pi\) | |||||||
\(140\) | −1.85960 | + | 6.36643i | −0.157165 | + | 0.538062i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.08532 | 0.678505 | ||||||||
\(143\) | −2.06559 | −0.172733 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.7275 | −1.80437 | ||||||||
\(146\) | 13.5144 | 1.11846 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.68285i | 0.138330i | ||||||||
\(149\) | 9.33082 | 0.764410 | 0.382205 | − | 0.924077i | \(-0.375165\pi\) | ||||
0.382205 | + | 0.924077i | \(0.375165\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.62713i | 0.620687i | 0.950624 | + | 0.310344i | \(0.100444\pi\) | ||||
−0.950624 | + | 0.310344i | \(0.899556\pi\) | |||||||
\(152\) | 0.709018 | − | 4.30085i | 0.0575089 | − | 0.348845i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.02321 | + | 10.3501i | −0.243618 | + | 0.834038i | ||||
\(155\) | − | 3.50056i | − | 0.281171i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.0191i | − | 1.03904i | −0.854458 | − | 0.519520i | \(-0.826111\pi\) | ||
0.854458 | − | 0.519520i | \(-0.173889\pi\) | |||||||
\(158\) | −3.37893 | −0.268813 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.50684 | 0.198183 | ||||||||
\(161\) | −16.1019 | − | 4.70328i | −1.26901 | − | 0.370671i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.37938 | −0.343020 | −0.171510 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171510 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(164\) | −0.402139 | −0.0314018 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.5106 | 0.815777 | ||||||||
\(167\) | 2.29406 | 0.177520 | 0.0887600 | − | 0.996053i | \(-0.471710\pi\) | ||||
0.0887600 | + | 0.996053i | \(0.471710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7431 | −0.980240 | ||||||||
\(170\) | − | 5.78478i | − | 0.443673i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.73509 | 0.513546 | ||||||||
\(173\) | −22.4568 | −1.70736 | −0.853681 | − | 0.520797i | \(-0.825635\pi\) | ||||
−0.853681 | + | 0.520797i | \(0.825635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.26146 | + | 0.952654i | 0.246543 | + | 0.0720139i | ||||
\(176\) | 4.07545 | 0.307199 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.7389i | 0.879870i | ||||||||
\(179\) | − | 12.0887i | − | 0.903555i | −0.892131 | − | 0.451777i | \(-0.850790\pi\) | ||
0.892131 | − | 0.451777i | \(-0.149210\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6113 | −1.08605 | −0.543025 | − | 0.839716i | \(-0.682721\pi\) | ||||
−0.543025 | + | 0.839716i | \(0.682721\pi\) | |||||||
\(182\) | 0.375977 | − | 1.28718i | 0.0278692 | − | 0.0954118i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.34027i | 0.467411i | ||||||||
\(185\) | 4.21864 | 0.310161 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.40453i | − | 0.687727i | ||||||
\(188\) | − | 5.33646i | − | 0.389202i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.7815 | − | 1.77739i | −0.782174 | − | 0.128946i | ||||
\(191\) | −0.142938 | −0.0103427 | −0.00517133 | − | 0.999987i | \(-0.501646\pi\) | ||||
−0.00517133 | + | 0.999987i | \(0.501646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.94006i | 0.427575i | 0.976880 | + | 0.213787i | \(0.0685800\pi\) | ||||
−0.976880 | + | 0.213787i | \(0.931420\pi\) | |||||||
\(194\) | − | 4.87048i | − | 0.349680i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.89943 | − | 3.76785i | −0.421388 | − | 0.269132i | ||||
\(197\) | −9.50252 | −0.677027 | −0.338513 | − | 0.940962i | \(-0.609924\pi\) | ||||
−0.338513 | + | 0.940962i | \(0.609924\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.3287i | 1.65373i | 0.562404 | + | 0.826863i | \(0.309877\pi\) | ||||
−0.562404 | + | 0.826863i | \(0.690123\pi\) | |||||||
\(200\) | − | 1.28423i | − | 0.0908086i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.8277 | 0.761836 | ||||||||
\(203\) | 6.42948 | − | 22.0117i | 0.451261 | − | 1.54492i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00810i | 0.0704086i | ||||||||
\(206\) | − | 5.51407i | − | 0.384183i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.506836 | −0.0351428 | ||||||||
\(209\) | −17.5279 | − | 2.88957i | −1.21243 | − | 0.199876i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 23.1860i | − | 1.59619i | −0.602532 | − | 0.798095i | \(-0.705841\pi\) | ||
0.602532 | − | 0.798095i | \(-0.294159\pi\) | |||||||
\(212\) | − | 1.66122i | − | 0.114093i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.64796 | 0.112652 | ||||||||
\(215\) | − | 16.8838i | − | 1.15146i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.54635 | + | 1.03587i | 0.240742 | + | 0.0703193i | ||||
\(218\) | 18.0910 | 1.22528 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 10.2165i | − | 0.688796i | ||||||
\(221\) | 1.16958i | 0.0786742i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.0366 | 1.54264 | 0.771322 | − | 0.636446i | \(-0.219596\pi\) | ||||
0.771322 | + | 0.636446i | \(0.219596\pi\) | |||||||
\(224\) | −0.741811 | + | 2.53963i | −0.0495643 | + | 0.169686i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.33655 | 0.155425 | ||||||||
\(227\) | 17.6866 | 1.17390 | 0.586951 | − | 0.809623i | \(-0.300328\pi\) | ||||
0.586951 | + | 0.809623i | \(0.300328\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.87815i | − | 0.256275i | −0.991756 | − | 0.128138i | \(-0.959100\pi\) | ||
0.991756 | − | 0.128138i | \(-0.0408999\pi\) | |||||||
\(230\) | 15.8940 | 1.04802 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.66728 | −0.569035 | ||||||||
\(233\) | 21.9618 | 1.43877 | 0.719384 | − | 0.694613i | \(-0.244424\pi\) | ||||
0.719384 | + | 0.694613i | \(0.244424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.3776 | −0.872661 | ||||||||
\(236\) | 9.42907 | 0.613780 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.86046 | + | 1.71180i | 0.379877 | + | 0.110960i | ||||
\(239\) | 5.77182 | 0.373348 | 0.186674 | − | 0.982422i | \(-0.440229\pi\) | ||||
0.186674 | + | 0.982422i | \(0.440229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8837 | −0.701079 | −0.350539 | − | 0.936548i | \(-0.614002\pi\) | ||||
−0.350539 | + | 0.936548i | \(0.614002\pi\) | |||||||
\(242\) | − | 5.60931i | − | 0.360580i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5.31706i | − | 0.340390i | ||||||
\(245\) | −9.44538 | + | 14.7889i | −0.603443 | + | 0.944829i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.17983 | + | 0.359356i | 0.138699 | + | 0.0228653i | ||||
\(248\) | − | 1.39640i | − | 0.0886717i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.31483 | 0.589122 | ||||||||
\(251\) | − | 23.2434i | − | 1.46711i | −0.679629 | − | 0.733556i | \(-0.737859\pi\) | ||
0.679629 | − | 0.733556i | \(-0.262141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.8395 | 1.62451 | ||||||||
\(254\) | −1.29418 | −0.0812042 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.4331 | −1.83599 | −0.917995 | − | 0.396593i | \(-0.870192\pi\) | ||||
−0.917995 | + | 0.396593i | \(0.870192\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.24836 | + | 4.27383i | −0.0775693 | + | 0.265563i | ||||
\(260\) | 1.27056i | 0.0787965i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.38528 | 0.270923 | ||||||||
\(263\) | 9.57036 | 0.590134 | 0.295067 | − | 0.955477i | \(-0.404658\pi\) | ||||
0.295067 | + | 0.955477i | \(0.404658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.16441 | −0.255818 | ||||||||
\(266\) | 4.99106 | − | 10.3966i | 0.306021 | − | 0.637457i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.06939i | 0.187493i | ||||||||
\(269\) | 20.3251 | 1.23924 | 0.619621 | − | 0.784901i | \(-0.287286\pi\) | ||||
0.619621 | + | 0.784901i | \(0.287286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.0034i | − | 1.64034i | −0.572120 | − | 0.820170i | \(-0.693879\pi\) | ||
0.572120 | − | 0.820170i | \(-0.306121\pi\) | |||||||
\(272\) | − | 2.30760i | − | 0.139919i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 17.3945i | − | 1.05084i | ||||||
\(275\) | −5.23381 | −0.315610 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.93416 | 0.116213 | 0.0581063 | − | 0.998310i | \(-0.481494\pi\) | ||||
0.0581063 | + | 0.998310i | \(0.481494\pi\) | |||||||
\(278\) | −4.29012 | −0.257305 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.36643 | + | 1.85960i | 0.380467 | + | 0.111132i | ||||
\(281\) | 26.0581i | 1.55450i | 0.629194 | + | 0.777248i | \(0.283385\pi\) | ||||
−0.629194 | + | 0.777248i | \(0.716615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.4608i | 1.21627i | 0.793835 | + | 0.608133i | \(0.208081\pi\) | ||||
−0.793835 | + | 0.608133i | \(0.791919\pi\) | |||||||
\(284\) | − | 8.08532i | − | 0.479775i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.06559i | 0.122141i | ||||||||
\(287\) | −1.02129 | − | 0.298311i | −0.0602846 | − | 0.0176088i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.6750 | 0.686763 | ||||||||
\(290\) | 21.7275i | 1.27588i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 13.5144i | − | 0.790870i | ||||||
\(293\) | 16.4410 | 0.960495 | 0.480248 | − | 0.877133i | \(-0.340547\pi\) | ||||
0.480248 | + | 0.877133i | \(0.340547\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 23.6371i | − | 1.37621i | ||||||
\(296\) | 1.68285 | 0.0978139 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 9.33082i | − | 0.540520i | ||||||
\(299\) | −3.21348 | −0.185840 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.1046 | + | 4.99616i | 0.985895 | + | 0.287974i | ||||
\(302\) | 7.62713 | 0.438892 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.30085 | − | 0.709018i | −0.246671 | − | 0.0406650i | ||||
\(305\) | −13.3290 | −0.763216 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.09858 | −0.462210 | −0.231105 | − | 0.972929i | \(-0.574234\pi\) | ||||
−0.231105 | + | 0.972929i | \(0.574234\pi\) | |||||||
\(308\) | 10.3501 | + | 3.02321i | 0.589754 | + | 0.172264i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.50056 | −0.198818 | ||||||||
\(311\) | 8.87438i | 0.503220i | 0.967829 | + | 0.251610i | \(0.0809600\pi\) | ||||
−0.967829 | + | 0.251610i | \(0.919040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9535i | 1.29741i | 0.761039 | + | 0.648706i | \(0.224689\pi\) | ||||
−0.761039 | + | 0.648706i | \(0.775311\pi\) | |||||||
\(314\) | −13.0191 | −0.734712 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.37893i | 0.190079i | ||||||||
\(317\) | − | 19.9885i | − | 1.12267i | −0.827589 | − | 0.561334i | \(-0.810288\pi\) | ||
0.827589 | − | 0.561334i | \(-0.189712\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.3231i | 1.97771i | ||||||||
\(320\) | − | 2.50684i | − | 0.140136i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.70328 | + | 16.1019i | −0.262104 | + | 0.897326i | ||||
\(323\) | −1.63613 | + | 9.92465i | −0.0910368 | + | 0.552222i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.650893 | 0.0361050 | ||||||||
\(326\) | 4.37938i | 0.242552i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.402139i | 0.0222044i | ||||||||
\(329\) | 3.95865 | − | 13.5526i | 0.218247 | − | 0.747181i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 19.4117i | − | 1.06697i | −0.845811 | − | 0.533483i | \(-0.820883\pi\) | ||
0.845811 | − | 0.533483i | \(-0.179117\pi\) | |||||||
\(332\) | − | 10.5106i | − | 0.576842i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2.29406i | − | 0.125526i | ||||||
\(335\) | 7.69446 | 0.420394 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.3229i | 1.43390i | 0.697124 | + | 0.716951i | \(0.254463\pi\) | ||||
−0.697124 | + | 0.716951i | \(0.745537\pi\) | |||||||
\(338\) | 12.7431i | 0.693134i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.78478 | −0.313724 | ||||||||
\(341\) | −5.69098 | −0.308184 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.1873 | − | 13.9452i | −0.658055 | − | 0.752970i | ||||
\(344\) | − | 6.73509i | − | 0.363132i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.4568i | 1.20729i | ||||||||
\(347\) | 6.55866 | 0.352087 | 0.176044 | − | 0.984382i | \(-0.443670\pi\) | ||||
0.176044 | + | 0.984382i | \(0.443670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 28.8644i | − | 1.54508i | −0.634968 | − | 0.772539i | \(-0.718987\pi\) | ||
0.634968 | − | 0.772539i | \(-0.281013\pi\) | |||||||
\(350\) | 0.952654 | − | 3.26146i | 0.0509215 | − | 0.174332i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.07545i | − | 0.217222i | ||||||
\(353\) | 34.6309i | 1.84321i | 0.388124 | + | 0.921607i | \(0.373123\pi\) | ||||
−0.388124 | + | 0.921607i | \(0.626877\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.2686 | −1.07574 | ||||||||
\(356\) | 11.7389 | 0.622162 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0887 | −0.638910 | ||||||||
\(359\) | −11.1407 | −0.587983 | −0.293992 | − | 0.955808i | \(-0.594984\pi\) | ||||
−0.293992 | + | 0.955808i | \(0.594984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.9946 | + | 6.09875i | 0.947084 | + | 0.320987i | ||||
\(362\) | 14.6113i | 0.767953i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.28718 | − | 0.375977i | −0.0674663 | − | 0.0197065i | ||||
\(365\) | −33.8784 | −1.77327 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0195i | 0.575213i | 0.957749 | + | 0.287607i | \(0.0928595\pi\) | ||||
−0.957749 | + | 0.287607i | \(0.907140\pi\) | |||||||
\(368\) | 6.34027 | 0.330509 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 4.21864i | − | 0.219317i | ||||||
\(371\) | 1.23231 | − | 4.21889i | 0.0639785 | − | 0.219034i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 27.0191i | − | 1.39900i | −0.714634 | − | 0.699499i | \(-0.753407\pi\) | ||
0.714634 | − | 0.699499i | \(-0.246593\pi\) | |||||||
\(374\) | −9.40453 | −0.486296 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.33646 | −0.275207 | ||||||||
\(377\) | − | 4.39289i | − | 0.226245i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.9769i | − | 1.28298i | −0.767133 | − | 0.641488i | \(-0.778318\pi\) | ||
0.767133 | − | 0.641488i | \(-0.221682\pi\) | |||||||
\(380\) | −1.77739 | + | 10.7815i | −0.0911782 | + | 0.553080i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.142938i | 0.00731337i | ||||||||
\(383\) | 12.4870 | 0.638057 | 0.319029 | − | 0.947745i | \(-0.396643\pi\) | ||||
0.319029 | + | 0.947745i | \(0.396643\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.57870 | − | 25.9461i | 0.386246 | − | 1.32234i | ||||
\(386\) | 5.94006 | 0.302341 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.87048 | −0.247261 | ||||||||
\(389\) | −31.4241 | −1.59327 | −0.796634 | − | 0.604462i | \(-0.793388\pi\) | ||||
−0.796634 | + | 0.604462i | \(0.793388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14.6308i | − | 0.739913i | ||||||
\(392\) | −3.76785 | + | 5.89943i | −0.190305 | + | 0.297966i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.50252i | 0.478730i | ||||||||
\(395\) | 8.47041 | 0.426193 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 37.1197i | − | 1.86299i | −0.363759 | − | 0.931493i | \(-0.618507\pi\) | ||
0.363759 | − | 0.931493i | \(-0.381493\pi\) | |||||||
\(398\) | 23.3287 | 1.16936 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.28423 | −0.0642114 | ||||||||
\(401\) | 38.8566i | 1.94041i | 0.242289 | + | 0.970204i | \(0.422102\pi\) | ||||
−0.242289 | + | 0.970204i | \(0.577898\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.707748 | 0.0352554 | ||||||||
\(404\) | − | 10.8277i | − | 0.538700i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.0117 | − | 6.42948i | −1.09242 | − | 0.319090i | ||||
\(407\) | − | 6.85839i | − | 0.339958i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.77207 | 0.483198 | 0.241599 | − | 0.970376i | \(-0.422328\pi\) | ||||
0.241599 | + | 0.970376i | \(0.422328\pi\) | |||||||
\(410\) | 1.00810 | 0.0497864 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.51407 | −0.271659 | ||||||||
\(413\) | 23.9463 | + | 6.99459i | 1.17832 | + | 0.344181i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.3482 | −1.29338 | ||||||||
\(416\) | 0.506836i | 0.0248497i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.88957 | + | 17.5279i | −0.141333 | + | 0.857318i | ||||
\(419\) | − | 30.2647i | − | 1.47853i | −0.673416 | − | 0.739264i | \(-0.735174\pi\) | ||
0.673416 | − | 0.739264i | \(-0.264826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 21.7967i | − | 1.06231i | −0.847276 | − | 0.531153i | \(-0.821759\pi\) | ||
0.847276 | − | 0.531153i | \(-0.178241\pi\) | |||||||
\(422\) | −23.1860 | −1.12868 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.66122 | −0.0806761 | ||||||||
\(425\) | 2.96349i | 0.143750i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.94425 | − | 13.5034i | 0.190876 | − | 0.653473i | ||||
\(428\) | − | 1.64796i | − | 0.0796573i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.8838 | −0.814208 | ||||||||
\(431\) | 31.4075i | 1.51285i | 0.654082 | + | 0.756423i | \(0.273055\pi\) | ||||
−0.654082 | + | 0.756423i | \(0.726945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5121 | −0.649348 | −0.324674 | − | 0.945826i | \(-0.605255\pi\) | ||||
−0.324674 | + | 0.945826i | \(0.605255\pi\) | |||||||
\(434\) | 1.03587 | − | 3.54635i | 0.0497232 | − | 0.170230i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 18.0910i | − | 0.866403i | ||||||
\(437\) | −27.2685 | − | 4.49536i | −1.30443 | − | 0.215042i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.4310 | 1.26148 | 0.630742 | − | 0.775993i | \(-0.282751\pi\) | ||||
0.630742 | + | 0.775993i | \(0.282751\pi\) | |||||||
\(440\) | −10.2165 | −0.487052 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.16958 | 0.0556311 | ||||||||
\(443\) | 27.7520 | 1.31854 | 0.659269 | − | 0.751907i | \(-0.270866\pi\) | ||||
0.659269 | + | 0.751907i | \(0.270866\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 29.4276i | − | 1.39500i | ||||||
\(446\) | − | 23.0366i | − | 1.09081i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.53963 | + | 0.741811i | 0.119986 | + | 0.0350473i | ||||
\(449\) | 15.1061i | 0.712900i | 0.934314 | + | 0.356450i | \(0.116013\pi\) | ||||
−0.934314 | + | 0.356450i | \(0.883987\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.63890 | 0.0771728 | ||||||||
\(452\) | − | 2.33655i | − | 0.109902i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 17.6866i | − | 0.830073i | ||||||
\(455\) | −0.942512 | + | 3.22674i | −0.0441856 | + | 0.151272i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.9766 | −0.981245 | −0.490623 | − | 0.871372i | \(-0.663231\pi\) | ||||
−0.490623 | + | 0.871372i | \(0.663231\pi\) | |||||||
\(458\) | −3.87815 | −0.181214 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 15.8940i | − | 0.741063i | ||||||
\(461\) | 7.85663i | 0.365920i | 0.983120 | + | 0.182960i | \(0.0585678\pi\) | ||||
−0.983120 | + | 0.182960i | \(0.941432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6622 | 0.588463 | 0.294231 | − | 0.955734i | \(-0.404936\pi\) | ||||
0.294231 | + | 0.955734i | \(0.404936\pi\) | |||||||
\(464\) | 8.66728i | 0.402368i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 21.9618i | − | 1.01736i | ||||||
\(467\) | − | 8.29420i | − | 0.383810i | −0.981414 | − | 0.191905i | \(-0.938534\pi\) | ||
0.981414 | − | 0.191905i | \(-0.0614665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.27691 | + | 7.79512i | −0.105138 | + | 0.359945i | ||||
\(470\) | 13.3776i | 0.617065i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 9.42907i | − | 0.434008i | ||||||
\(473\) | −27.4485 | −1.26209 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.52327 | + | 0.910540i | 0.253425 | + | 0.0417784i | ||||
\(476\) | 1.71180 | − | 5.86046i | 0.0784605 | − | 0.268614i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 5.77182i | − | 0.263997i | ||||||
\(479\) | 3.93055i | 0.179591i | 0.995960 | + | 0.0897957i | \(0.0286214\pi\) | ||||
−0.995960 | + | 0.0897957i | \(0.971379\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.852932i | 0.0388903i | ||||||||
\(482\) | 10.8837i | 0.495738i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.60931 | −0.254969 | ||||||||
\(485\) | 12.2095i | 0.554405i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0464i | 0.863077i | 0.902095 | + | 0.431538i | \(0.142029\pi\) | ||||
−0.902095 | + | 0.431538i | \(0.857971\pi\) | |||||||
\(488\) | −5.31706 | −0.240692 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 14.7889 | + | 9.44538i | 0.668095 | + | 0.426699i | ||||
\(491\) | −19.5088 | −0.880419 | −0.440209 | − | 0.897895i | \(-0.645096\pi\) | ||||
−0.440209 | + | 0.897895i | \(0.645096\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0006 | 0.900784 | ||||||||
\(494\) | 0.359356 | − | 2.17983i | 0.0161682 | − | 0.0980750i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.39640 | −0.0627004 | ||||||||
\(497\) | 5.99778 | − | 20.5337i | 0.269037 | − | 0.921063i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9906 | −0.671074 | −0.335537 | − | 0.942027i | \(-0.608918\pi\) | ||||
−0.335537 | + | 0.942027i | \(0.608918\pi\) | |||||||
\(500\) | − | 9.31483i | − | 0.416572i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.2434 | −1.03740 | ||||||||
\(503\) | − | 3.32055i | − | 0.148056i | −0.997256 | − | 0.0740279i | \(-0.976415\pi\) | ||
0.997256 | − | 0.0740279i | \(-0.0235854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.1433 | −1.20786 | ||||||||
\(506\) | − | 25.8395i | − | 1.14870i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.29418i | 0.0574200i | ||||||||
\(509\) | 7.68285 | 0.340537 | 0.170268 | − | 0.985398i | \(-0.445537\pi\) | ||||
0.170268 | + | 0.985398i | \(0.445537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0251 | − | 34.3215i | 0.443485 | − | 1.51830i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.4331i | 1.29824i | ||||||||
\(515\) | 13.8229i | 0.609108i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.7485i | 0.956498i | ||||||||
\(518\) | 4.27383 | + | 1.24836i | 0.187781 | + | 0.0548498i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.27056 | 0.0557175 | ||||||||
\(521\) | −37.1281 | −1.62661 | −0.813306 | − | 0.581836i | \(-0.802335\pi\) | ||||
−0.813306 | + | 0.581836i | \(0.802335\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7335 | −1.08152 | −0.540761 | − | 0.841177i | \(-0.681863\pi\) | ||||
−0.540761 | + | 0.841177i | \(0.681863\pi\) | |||||||
\(524\) | − | 4.38528i | − | 0.191572i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 9.57036i | − | 0.417288i | ||||||
\(527\) | 3.22235i | 0.140368i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.1990 | 0.747784 | ||||||||
\(530\) | 4.16441i | 0.180891i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.3966 | − | 4.99106i | −0.450750 | − | 0.216390i | ||||
\(533\) | −0.203819 | −0.00882837 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.13117 | −0.178606 | ||||||||
\(536\) | 3.06939 | 0.132578 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 20.3251i | − | 0.876276i | ||||||
\(539\) | 24.0429 | + | 15.3557i | 1.03560 | + | 0.661416i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.9110 | −1.41496 | −0.707478 | − | 0.706735i | \(-0.750167\pi\) | ||||
−0.707478 | + | 0.706735i | \(0.750167\pi\) | |||||||
\(542\) | −27.0034 | −1.15990 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.30760 | −0.0989377 | ||||||||
\(545\) | −45.3512 | −1.94263 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.6086i | 1.77905i | 0.456883 | + | 0.889527i | \(0.348966\pi\) | ||||
−0.456883 | + | 0.889527i | \(0.651034\pi\) | |||||||
\(548\) | −17.3945 | −0.743056 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.23381i | 0.223170i | ||||||||
\(551\) | 6.14526 | − | 37.2767i | 0.261797 | − | 1.58804i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.50652 | + | 8.58122i | −0.106588 | + | 0.364910i | ||||
\(554\) | − | 1.93416i | − | 0.0821748i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.29012i | 0.181942i | ||||||||
\(557\) | 8.31329 | 0.352245 | 0.176123 | − | 0.984368i | \(-0.443644\pi\) | ||||
0.176123 | + | 0.984368i | \(0.443644\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.41359 | 0.144379 | ||||||||
\(560\) | 1.85960 | − | 6.36643i | 0.0785824 | − | 0.269031i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.0581 | 1.09920 | ||||||||
\(563\) | −8.97656 | −0.378317 | −0.189159 | − | 0.981947i | \(-0.560576\pi\) | ||||
−0.189159 | + | 0.981947i | \(0.560576\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.85736 | −0.246421 | ||||||||
\(566\) | 20.4608 | 0.860030 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.08532 | −0.339252 | ||||||||
\(569\) | − | 33.0391i | − | 1.38507i | −0.721383 | − | 0.692536i | \(-0.756493\pi\) | ||
0.721383 | − | 0.692536i | \(-0.243507\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.4576 | −0.897973 | −0.448987 | − | 0.893538i | \(-0.648215\pi\) | ||||
−0.448987 | + | 0.893538i | \(0.648215\pi\) | |||||||
\(572\) | 2.06559 | 0.0863665 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.298311 | + | 1.02129i | −0.0124513 | + | 0.0426276i | ||||
\(575\) | −8.14235 | −0.339559 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22.0341i | − | 0.917293i | −0.888619 | − | 0.458646i | \(-0.848334\pi\) | ||
0.888619 | − | 0.458646i | \(-0.151666\pi\) | |||||||
\(578\) | − | 11.6750i | − | 0.485615i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.7275 | 0.902184 | ||||||||
\(581\) | 7.79684 | − | 26.6929i | 0.323468 | − | 1.10741i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.77023i | 0.280394i | ||||||||
\(584\) | −13.5144 | −0.559229 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 16.4410i | − | 0.679173i | ||||||
\(587\) | 47.5397i | 1.96217i | 0.193573 | + | 0.981086i | \(0.437992\pi\) | ||||
−0.193573 | + | 0.981086i | \(0.562008\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00572 | + | 0.990075i | 0.247461 | + | 0.0407953i | ||||
\(590\) | −23.6371 | −0.973126 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.68285i | − | 0.0691649i | ||||||
\(593\) | − | 36.0330i | − | 1.47970i | −0.672774 | − | 0.739848i | \(-0.734897\pi\) | ||
0.672774 | − | 0.739848i | \(-0.265103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.6912 | − | 4.29121i | −0.602281 | − | 0.175923i | ||||
\(596\) | −9.33082 | −0.382205 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.21348i | 0.131409i | ||||||||
\(599\) | − | 19.8527i | − | 0.811161i | −0.914059 | − | 0.405580i | \(-0.867069\pi\) | ||
0.914059 | − | 0.405580i | \(-0.132931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.8582 | −1.34032 | −0.670158 | − | 0.742219i | \(-0.733774\pi\) | ||||
−0.670158 | + | 0.742219i | \(0.733774\pi\) | |||||||
\(602\) | 4.99616 | − | 17.1046i | 0.203628 | − | 0.697133i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 7.62713i | − | 0.310344i | ||||||
\(605\) | 14.0616i | 0.571686i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.9412 | 0.687621 | 0.343810 | − | 0.939039i | \(-0.388282\pi\) | ||||
0.343810 | + | 0.939039i | \(0.388282\pi\) | |||||||
\(608\) | −0.709018 | + | 4.30085i | −0.0287545 | + | 0.174422i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.3290i | 0.539675i | ||||||||
\(611\) | − | 2.70471i | − | 0.109421i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.2574 | 0.616242 | 0.308121 | − | 0.951347i | \(-0.400300\pi\) | ||||
0.308121 | + | 0.951347i | \(0.400300\pi\) | |||||||
\(614\) | 8.09858i | 0.326832i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.02321 | − | 10.3501i | 0.121809 | − | 0.417019i | ||||
\(617\) | 46.9250 | 1.88913 | 0.944564 | − | 0.328328i | \(-0.106485\pi\) | ||||
0.944564 | + | 0.328328i | \(0.106485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.50433i | − | 0.341818i | −0.985287 | − | 0.170909i | \(-0.945330\pi\) | ||
0.985287 | − | 0.170909i | \(-0.0546704\pi\) | |||||||
\(620\) | 3.50056i | 0.140586i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.87438 | 0.355830 | ||||||||
\(623\) | 29.8125 | + | 8.70806i | 1.19441 | + | 0.348881i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.7719 | −1.19088 | ||||||||
\(626\) | 22.9535 | 0.917408 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.0191i | 0.519520i | ||||||||
\(629\) | −3.88336 | −0.154840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.6369 | 1.73716 | 0.868579 | − | 0.495552i | \(-0.165034\pi\) | ||||
0.868579 | + | 0.495552i | \(0.165034\pi\) | |||||||
\(632\) | 3.37893 | 0.134406 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.9885 | −0.793846 | ||||||||
\(635\) | 3.24430 | 0.128746 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.99005 | − | 1.90968i | −0.118470 | − | 0.0756644i | ||||
\(638\) | 35.3231 | 1.39845 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.50684 | −0.0990914 | ||||||||
\(641\) | − | 16.0386i | − | 0.633488i | −0.948511 | − | 0.316744i | \(-0.897410\pi\) | ||
0.948511 | − | 0.316744i | \(-0.102590\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.3835i | 1.43482i | 0.696649 | + | 0.717412i | \(0.254673\pi\) | ||||
−0.696649 | + | 0.717412i | \(0.745327\pi\) | |||||||
\(644\) | 16.1019 | + | 4.70328i | 0.634505 | + | 0.185335i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.92465 | + | 1.63613i | 0.390480 | + | 0.0643727i | ||||
\(647\) | − | 31.7012i | − | 1.24630i | −0.782101 | − | 0.623151i | \(-0.785852\pi\) | ||
0.782101 | − | 0.623151i | \(-0.214148\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.4277 | −1.50842 | ||||||||
\(650\) | − | 0.650893i | − | 0.0255301i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.37938 | 0.171510 | ||||||||
\(653\) | −4.26096 | −0.166744 | −0.0833721 | − | 0.996518i | \(-0.526569\pi\) | ||||
−0.0833721 | + | 0.996518i | \(0.526569\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.9932 | −0.429539 | ||||||||
\(656\) | 0.402139 | 0.0157009 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.5526 | − | 3.95865i | −0.528337 | − | 0.154324i | ||||
\(659\) | 0.0621626i | 0.00242151i | 0.999999 | + | 0.00121076i | \(0.000385395\pi\) | ||||
−0.999999 | + | 0.00121076i | \(0.999615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2637 | 0.632585 | 0.316293 | − | 0.948662i | \(-0.397562\pi\) | ||||
0.316293 | + | 0.948662i | \(0.397562\pi\) | |||||||
\(662\) | −19.4117 | −0.754458 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.5106 | −0.407889 | ||||||||
\(665\) | −12.5118 | + | 26.0626i | −0.485185 | + | 1.01066i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.9529i | 2.12779i | ||||||||
\(668\) | −2.29406 | −0.0887600 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 7.69446i | − | 0.297263i | ||||||
\(671\) | 21.6694i | 0.836538i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.20897i | 0.200791i | 0.994948 | + | 0.100395i | \(0.0320108\pi\) | ||||
−0.994948 | + | 0.100395i | \(0.967989\pi\) | |||||||
\(674\) | 26.3229 | 1.01392 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.7431 | 0.490120 | ||||||||
\(677\) | −40.7978 | −1.56799 | −0.783993 | − | 0.620770i | \(-0.786820\pi\) | ||||
−0.783993 | + | 0.620770i | \(0.786820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.3692 | − | 3.61298i | −0.474687 | − | 0.138653i | ||||
\(680\) | 5.78478i | 0.221836i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.69098i | 0.217919i | ||||||||
\(683\) | 9.91494i | 0.379385i | 0.981844 | + | 0.189692i | \(0.0607491\pi\) | ||||
−0.981844 | + | 0.189692i | \(0.939251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.6052i | 1.66607i | ||||||||
\(686\) | −13.9452 | + | 12.1873i | −0.532430 | + | 0.465315i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.73509 | −0.256773 | ||||||||
\(689\) | − | 0.841968i | − | 0.0320764i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.4742i | − | 0.702790i | −0.936227 | − | 0.351395i | \(-0.885707\pi\) | ||
0.936227 | − | 0.351395i | \(-0.114293\pi\) | |||||||
\(692\) | 22.4568 | 0.853681 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 6.55866i | − | 0.248963i | ||||||
\(695\) | 10.7546 | 0.407947 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.927978i | − | 0.0351497i | ||||||
\(698\) | −28.8644 | −1.09253 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.26146 | − | 0.952654i | −0.123272 | − | 0.0360069i | ||||
\(701\) | 3.23079 | 0.122025 | 0.0610126 | − | 0.998137i | \(-0.480567\pi\) | ||||
0.0610126 | + | 0.998137i | \(0.480567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.19317 | + | 7.23770i | −0.0450014 | + | 0.272975i | ||||
\(704\) | −4.07545 | −0.153599 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34.6309 | 1.30335 | ||||||||
\(707\) | 8.03213 | − | 27.4984i | 0.302079 | − | 1.03418i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.7361 | 0.928984 | 0.464492 | − | 0.885577i | \(-0.346237\pi\) | ||||
0.464492 | + | 0.885577i | \(0.346237\pi\) | |||||||
\(710\) | 20.2686i | 0.760666i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 11.7389i | − | 0.439935i | ||||||
\(713\) | −8.85358 | −0.331569 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.17809i | − | 0.193649i | ||||||
\(716\) | 12.0887i | 0.451777i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.1407i | 0.415767i | ||||||||
\(719\) | 13.1215i | 0.489349i | 0.969605 | + | 0.244675i | \(0.0786811\pi\) | ||||
−0.969605 | + | 0.244675i | \(0.921319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0037 | − | 4.09039i | −0.521524 | − | 0.152334i | ||||
\(722\) | 6.09875 | − | 17.9946i | 0.226972 | − | 0.669689i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.6113 | 0.543025 | ||||||||
\(725\) | − | 11.1308i | − | 0.413386i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.24285i | − | 0.194446i | −0.995263 | − | 0.0972232i | \(-0.969004\pi\) | ||
0.995263 | − | 0.0972232i | \(-0.0309961\pi\) | |||||||
\(728\) | −0.375977 | + | 1.28718i | −0.0139346 | + | 0.0477059i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 33.8784i | 1.25389i | ||||||||
\(731\) | 15.5419i | 0.574839i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 28.0831i | − | 1.03727i | −0.854995 | − | 0.518636i | \(-0.826440\pi\) | ||
0.854995 | − | 0.518636i | \(-0.173560\pi\) | |||||||
\(734\) | 11.0195 | 0.406737 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.34027i | − | 0.233706i | ||||||
\(737\) | − | 12.5092i | − | 0.460781i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.2496 | 1.37025 | 0.685125 | − | 0.728425i | \(-0.259747\pi\) | ||||
0.685125 | + | 0.728425i | \(0.259747\pi\) | |||||||
\(740\) | −4.21864 | −0.155080 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.21889 | − | 1.23231i | −0.154880 | − | 0.0452396i | ||||
\(743\) | − | 22.4717i | − | 0.824408i | −0.911092 | − | 0.412204i | \(-0.864759\pi\) | ||
0.911092 | − | 0.412204i | \(-0.135241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.3908i | 0.856974i | ||||||||
\(746\) | −27.0191 | −0.989241 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.40453i | 0.343864i | ||||||||
\(749\) | 1.22248 | − | 4.18521i | 0.0446683 | − | 0.152924i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.1905i | 1.57604i | 0.615647 | + | 0.788022i | \(0.288895\pi\) | ||||
−0.615647 | + | 0.788022i | \(0.711105\pi\) | |||||||
\(752\) | 5.33646i | 0.194601i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.39289 | −0.159980 | ||||||||
\(755\) | −19.1200 | −0.695847 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.50229 | 0.309021 | 0.154511 | − | 0.987991i | \(-0.450620\pi\) | ||||
0.154511 | + | 0.987991i | \(0.450620\pi\) | |||||||
\(758\) | −24.9769 | −0.907200 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.7815 | + | 1.77739i | 0.391087 | + | 0.0644728i | ||||
\(761\) | − | 4.95250i | − | 0.179528i | −0.995963 | − | 0.0897639i | \(-0.971389\pi\) | ||
0.995963 | − | 0.0897639i | \(-0.0286113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.4201 | − | 45.9445i | 0.485841 | − | 1.66330i | ||||
\(764\) | 0.142938 | 0.00517133 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 12.4870i | − | 0.451174i | ||||||
\(767\) | 4.77899 | 0.172559 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.92509i | − | 0.213664i | −0.994277 | − | 0.106832i | \(-0.965929\pi\) | ||
0.994277 | − | 0.106832i | \(-0.0340708\pi\) | |||||||
\(770\) | −25.9461 | − | 7.57870i | −0.935032 | − | 0.273118i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 5.94006i | − | 0.213787i | ||||||
\(773\) | 17.3774 | 0.625023 | 0.312512 | − | 0.949914i | \(-0.398830\pi\) | ||||
0.312512 | + | 0.949914i | \(0.398830\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.79330 | 0.0644172 | ||||||||
\(776\) | 4.87048i | 0.174840i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.4241i | 1.12661i | ||||||||
\(779\) | −1.72954 | − | 0.285124i | −0.0619672 | − | 0.0102156i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.9513i | 1.17909i | ||||||||
\(782\) | −14.6308 | −0.523197 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.89943 | + | 3.76785i | 0.210694 | + | 0.134566i | ||||
\(785\) | 32.6368 | 1.16486 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.7715 | 0.419609 | 0.209805 | − | 0.977743i | \(-0.432717\pi\) | ||||
0.209805 | + | 0.977743i | \(0.432717\pi\) | |||||||
\(788\) | 9.50252 | 0.338513 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 8.47041i | − | 0.301364i | ||||||
\(791\) | 1.73328 | − | 5.93398i | 0.0616284 | − | 0.210988i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.69488i | − | 0.0956979i | ||||||
\(794\) | −37.1197 | −1.31733 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 23.3287i | − | 0.826863i | ||||||
\(797\) | 1.38112 | 0.0489218 | 0.0244609 | − | 0.999701i | \(-0.492213\pi\) | ||||
0.0244609 | + | 0.999701i | \(0.492213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.3144 | 0.435654 | ||||||||
\(800\) | 1.28423i | 0.0454043i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38.8566 | 1.37208 | ||||||||
\(803\) | 55.0772i | 1.94363i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.7904 | − | 40.3649i | 0.415555 | − | 1.42268i | ||||
\(806\) | − | 0.707748i | − | 0.0249294i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.8277 | −0.380918 | ||||||||
\(809\) | 0.562056 | 0.0197608 | 0.00988042 | − | 0.999951i | \(-0.496855\pi\) | ||||
0.00988042 | + | 0.999951i | \(0.496855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0061 | 0.948311 | 0.474156 | − | 0.880441i | \(-0.342753\pi\) | ||||
0.474156 | + | 0.880441i | \(0.342753\pi\) | |||||||
\(812\) | −6.42948 | + | 22.0117i | −0.225631 | + | 0.772459i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.85839 | −0.240387 | ||||||||
\(815\) | − | 10.9784i | − | 0.384556i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.9666 | + | 4.77530i | 1.01341 | + | 0.167067i | ||||
\(818\) | − | 9.77207i | − | 0.341672i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 1.00810i | − | 0.0352043i | ||||||
\(821\) | −5.06969 | −0.176933 | −0.0884667 | − | 0.996079i | \(-0.528197\pi\) | ||||
−0.0884667 | + | 0.996079i | \(0.528197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.8564 | −1.49388 | −0.746941 | − | 0.664890i | \(-0.768478\pi\) | ||||
−0.746941 | + | 0.664890i | \(0.768478\pi\) | |||||||
\(824\) | 5.51407i | 0.192092i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.99459 | − | 23.9463i | 0.243373 | − | 0.833200i | ||||
\(827\) | − | 35.3843i | − | 1.23043i | −0.788358 | − | 0.615217i | \(-0.789069\pi\) | ||
0.788358 | − | 0.615217i | \(-0.210931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.4298 | 0.987407 | 0.493703 | − | 0.869630i | \(-0.335643\pi\) | ||||
0.493703 | + | 0.869630i | \(0.335643\pi\) | |||||||
\(830\) | 26.3482i | 0.914561i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.506836 | 0.0175714 | ||||||||
\(833\) | 8.69470 | − | 13.6136i | 0.301253 | − | 0.471682i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.75084i | 0.199016i | ||||||||
\(836\) | 17.5279 | + | 2.88957i | 0.606215 | + | 0.0999378i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.2647 | −1.04548 | ||||||||
\(839\) | 15.7323 | 0.543139 | 0.271569 | − | 0.962419i | \(-0.412457\pi\) | ||||
0.271569 | + | 0.962419i | \(0.412457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −46.1218 | −1.59041 | ||||||||
\(842\) | −21.7967 | −0.751164 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.1860i | 0.798095i | ||||||||
\(845\) | − | 31.9449i | − | 1.09894i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.2456 | − | 4.16105i | −0.489483 | − | 0.142975i | ||||
\(848\) | 1.66122i | 0.0570466i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.96349 | 0.101647 | ||||||||
\(851\) | − | 10.6698i | − | 0.365755i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.5022i | 0.975896i | 0.872873 | + | 0.487948i | \(0.162254\pi\) | ||||
−0.872873 | + | 0.487948i | \(0.837746\pi\) | |||||||
\(854\) | −13.5034 | − | 3.94425i | −0.462075 | − | 0.134969i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.64796 | −0.0563262 | ||||||||
\(857\) | 51.1600 | 1.74759 | 0.873796 | − | 0.486293i | \(-0.161651\pi\) | ||||
0.873796 | + | 0.486293i | \(0.161651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44.1527i | − | 1.50647i | −0.657752 | − | 0.753235i | \(-0.728492\pi\) | ||
0.657752 | − | 0.753235i | \(-0.271508\pi\) | |||||||
\(860\) | 16.8838i | 0.575732i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.4075 | 1.06974 | ||||||||
\(863\) | − | 17.8212i | − | 0.606640i | −0.952889 | − | 0.303320i | \(-0.901905\pi\) | ||
0.952889 | − | 0.303320i | \(-0.0980952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 56.2956i | − | 1.91411i | ||||||
\(866\) | 13.5121i | 0.459159i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.54635 | − | 1.03587i | −0.120371 | − | 0.0351596i | ||||
\(869\) | − | 13.7706i | − | 0.467137i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.55568i | 0.0527122i | ||||||||
\(872\) | −18.0910 | −0.612640 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.49536 | + | 27.2685i | −0.152058 | + | 0.922372i | ||||
\(875\) | 6.90984 | − | 23.6562i | 0.233595 | − | 0.799726i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.47255i | 0.218563i | 0.994011 | + | 0.109281i | \(0.0348549\pi\) | ||||
−0.994011 | + | 0.109281i | \(0.965145\pi\) | |||||||
\(878\) | − | 26.4310i | − | 0.892004i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.2165i | 0.344398i | ||||||||
\(881\) | 4.78225i | 0.161118i | 0.996750 | + | 0.0805590i | \(0.0256706\pi\) | ||||
−0.996750 | + | 0.0805590i | \(0.974329\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.8380 | 0.600297 | 0.300148 | − | 0.953892i | \(-0.402964\pi\) | ||||
0.300148 | + | 0.953892i | \(0.402964\pi\) | |||||||
\(884\) | − | 1.16958i | − | 0.0393371i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 27.7520i | − | 0.932348i | ||||||
\(887\) | 57.0906 | 1.91692 | 0.958458 | − | 0.285234i | \(-0.0920712\pi\) | ||||
0.958458 | + | 0.285234i | \(0.0920712\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.960038 | + | 3.28674i | −0.0321986 | + | 0.110234i | ||||
\(890\) | −29.4276 | −0.986414 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.0366 | −0.771322 | ||||||||
\(893\) | 3.78365 | − | 22.9513i | 0.126615 | − | 0.768037i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.3045 | 1.01297 | ||||||||
\(896\) | 0.741811 | − | 2.53963i | 0.0247822 | − | 0.0848431i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.1061 | 0.504097 | ||||||||
\(899\) | − | 12.1030i | − | 0.403659i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.83344 | 0.127711 | ||||||||
\(902\) | − | 1.63890i | − | 0.0545694i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.33655 | −0.0777126 | ||||||||
\(905\) | − | 36.6282i | − | 1.21756i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 32.8683i | − | 1.09137i | −0.837989 | − | 0.545687i | \(-0.816269\pi\) | ||
0.837989 | − | 0.545687i | \(-0.183731\pi\) | |||||||
\(908\) | −17.6866 | −0.586951 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.22674 | + | 0.942512i | 0.106965 | + | 0.0312440i | ||||
\(911\) | 35.4594i | 1.17482i | 0.809289 | + | 0.587411i | \(0.199853\pi\) | ||||
−0.809289 | + | 0.587411i | \(0.800147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.8353i | 1.41764i | ||||||||
\(914\) | 20.9766i | 0.693845i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.87815i | 0.128138i | ||||||||
\(917\) | 3.25305 | − | 11.1370i | 0.107425 | − | 0.367776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.4663 | −0.576161 | −0.288080 | − | 0.957606i | \(-0.593017\pi\) | ||||
−0.288080 | + | 0.957606i | \(0.593017\pi\) | |||||||
\(920\) | −15.8940 | −0.524010 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.85663 | 0.258744 | ||||||||
\(923\) | − | 4.09793i | − | 0.134885i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.16117i | 0.0710588i | ||||||||
\(926\) | − | 12.6622i | − | 0.416106i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.66728 | 0.284517 | ||||||||
\(929\) | 20.8426i | 0.683825i | 0.939732 | + | 0.341912i | \(0.111075\pi\) | ||||
−0.939732 | + | 0.341912i | \(0.888925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.7011 | − | 20.3877i | −0.743998 | − | 0.668181i | ||||
\(932\) | −21.9618 | −0.719384 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.29420 | −0.271394 | ||||||||
\(935\) | 23.5756 | 0.771005 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.44662i | − | 0.275939i | −0.990436 | − | 0.137969i | \(-0.955942\pi\) | ||
0.990436 | − | 0.137969i | \(-0.0440576\pi\) | |||||||
\(938\) | 7.79512 | + | 2.27691i | 0.254520 | + | 0.0743437i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.3776 | 0.436331 | ||||||||
\(941\) | 36.0231 | 1.17432 | 0.587160 | − | 0.809471i | \(-0.300246\pi\) | ||||
0.587160 | + | 0.809471i | \(0.300246\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.54967 | 0.0830288 | ||||||||
\(944\) | −9.42907 | −0.306890 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.4485i | 0.892429i | ||||||||
\(947\) | −34.9342 | −1.13521 | −0.567605 | − | 0.823301i | \(-0.692130\pi\) | ||||
−0.567605 | + | 0.823301i | \(0.692130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6.84958i | − | 0.222347i | ||||||
\(950\) | 0.910540 | − | 5.52327i | 0.0295418 | − | 0.179198i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.86046 | − | 1.71180i | −0.189938 | − | 0.0554799i | ||||
\(953\) | − | 44.7390i | − | 1.44924i | −0.689149 | − | 0.724620i | \(-0.742015\pi\) | ||
0.689149 | − | 0.724620i | \(-0.257985\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.358323i | − | 0.0115951i | ||||||
\(956\) | −5.77182 | −0.186674 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.93055 | 0.126990 | ||||||||
\(959\) | −44.1756 | − | 12.9034i | −1.42650 | − | 0.416674i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0501 | −0.937099 | ||||||||
\(962\) | 0.852932 | 0.0274996 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.8837 | 0.350539 | ||||||||
\(965\) | −14.8908 | −0.479351 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.5592 | −0.950559 | −0.475280 | − | 0.879835i | \(-0.657653\pi\) | ||||
−0.475280 | + | 0.879835i | \(0.657653\pi\) | |||||||
\(968\) | 5.60931i | 0.180290i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.2095 | 0.392024 | ||||||||
\(971\) | −33.7683 | −1.08368 | −0.541838 | − | 0.840483i | \(-0.682272\pi\) | ||||
−0.541838 | + | 0.840483i | \(0.682272\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.18246 | + | 10.8953i | −0.102025 | + | 0.349288i | ||||
\(974\) | 19.0464 | 0.610287 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.31706i | 0.170195i | ||||||||
\(977\) | 51.1745i | 1.63722i | 0.574351 | + | 0.818609i | \(0.305255\pi\) | ||||
−0.574351 | + | 0.818609i | \(0.694745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47.8414 | −1.52902 | ||||||||
\(980\) | 9.44538 | − | 14.7889i | 0.301722 | − | 0.472414i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.5088i | 0.622550i | ||||||||
\(983\) | 57.3236 | 1.82834 | 0.914170 | − | 0.405331i | \(-0.132844\pi\) | ||||
0.914170 | + | 0.405331i | \(0.132844\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 23.8213i | − | 0.759009i | ||||||
\(986\) | − | 20.0006i | − | 0.636950i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.17983 | − | 0.359356i | −0.0693495 | − | 0.0114326i | ||||
\(989\) | −42.7023 | −1.35785 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 52.1178i | − | 1.65558i | −0.561041 | − | 0.827788i | \(-0.689599\pi\) | ||
0.561041 | − | 0.827788i | \(-0.310401\pi\) | |||||||
\(992\) | 1.39640i | 0.0443359i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.5337 | − | 5.99778i | −0.651290 | − | 0.190238i | ||||
\(995\) | −58.4811 | −1.85398 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.2597i | 0.483281i | 0.970366 | + | 0.241640i | \(0.0776854\pi\) | ||||
−0.970366 | + | 0.241640i | \(0.922315\pi\) | |||||||
\(998\) | 14.9906i | 0.474521i | ||||||||
\(999\) | 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 | 2394.2.e.b.1063.5 | 12 | ||
3.2 | odd | 2 | 798.2.e.b.265.8 | yes | 12 | ||
7.6 | odd | 2 | 2394.2.e.a.1063.2 | 12 | |||
19.18 | odd | 2 | 2394.2.e.a.1063.11 | 12 | |||
21.20 | even | 2 | 798.2.e.a.265.11 | yes | 12 | ||
57.56 | even | 2 | 798.2.e.a.265.2 | ✓ | 12 | ||
133.132 | even | 2 | inner | 2394.2.e.b.1063.8 | 12 | ||
399.398 | odd | 2 | 798.2.e.b.265.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.e.a.265.2 | ✓ | 12 | 57.56 | even | 2 | ||
798.2.e.a.265.11 | yes | 12 | 21.20 | even | 2 | ||
798.2.e.b.265.5 | yes | 12 | 399.398 | odd | 2 | ||
798.2.e.b.265.8 | yes | 12 | 3.2 | odd | 2 | ||
2394.2.e.a.1063.2 | 12 | 7.6 | odd | 2 | |||
2394.2.e.a.1063.11 | 12 | 19.18 | odd | 2 | |||
2394.2.e.b.1063.5 | 12 | 1.1 | even | 1 | trivial | ||
2394.2.e.b.1063.8 | 12 | 133.132 | even | 2 | inner |