Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1305,2,Mod(784,1305)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1305.784");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1305 = 3^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1305.c (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: | \(10.4204774638\) |
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: |
\( x^{12} + 20x^{10} + 148x^{8} + 502x^{6} + 792x^{4} + 496x^{2} + 45 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 784.8 | ||
Root | \(1.27263i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1305.784 |
Dual form | 1305.2.c.l.784.5 |
$q$-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 \(\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times\).
\(n\) | \(146\) | \(262\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.27263i | 0.899884i | 0.893058 | + | 0.449942i | \(0.148555\pi\) | ||||
−0.893058 | + | 0.449942i | \(0.851445\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.380419 | 0.190209 | ||||||||
\(5\) | −1.10723 | − | 1.94269i | −0.495169 | − | 0.868796i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.255813i | 0.0966884i | 0.998831 | + | 0.0483442i | \(0.0153944\pi\) | ||||
−0.998831 | + | 0.0483442i | \(0.984606\pi\) | |||||||
\(8\) | 3.02939i | 1.07105i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.47232 | − | 1.40909i | 0.781816 | − | 0.445595i | ||||
\(11\) | −4.63446 | −1.39734 | −0.698672 | − | 0.715442i | \(-0.746225\pi\) | ||||
−0.698672 | + | 0.715442i | \(0.746225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.02700i | − | 1.39424i | −0.716955 | − | 0.697120i | \(-0.754465\pi\) | ||
0.716955 | − | 0.697120i | \(-0.245535\pi\) | |||||||
\(14\) | −0.325555 | −0.0870083 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.09444 | −0.773611 | ||||||||
\(17\) | − | 0.336444i | − | 0.0815995i | −0.999167 | − | 0.0407998i | \(-0.987009\pi\) | ||
0.999167 | − | 0.0407998i | \(-0.0129906\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.91437 | 0.668602 | 0.334301 | − | 0.942466i | \(-0.391500\pi\) | ||||
0.334301 | + | 0.942466i | \(0.391500\pi\) | |||||||
\(20\) | −0.421212 | − | 0.739035i | −0.0941859 | − | 0.165253i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 5.89795i | − | 1.25745i | ||||||
\(23\) | − | 8.65656i | − | 1.80502i | −0.430671 | − | 0.902509i | \(-0.641723\pi\) | ||
0.430671 | − | 0.902509i | \(-0.358277\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.54807 | + | 4.30201i | −0.509614 | + | 0.860403i | ||||
\(26\) | 6.39750 | 1.25465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0973162i | 0.0183910i | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.26943 | −0.587207 | −0.293603 | − | 0.955927i | \(-0.594854\pi\) | ||||
−0.293603 | + | 0.955927i | \(0.594854\pi\) | |||||||
\(32\) | 2.12070i | 0.374890i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.428167 | 0.0734301 | ||||||||
\(35\) | 0.496966 | − | 0.283245i | 0.0840025 | − | 0.0478771i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.86954i | − | 0.636148i | −0.948066 | − | 0.318074i | \(-0.896964\pi\) | ||
0.948066 | − | 0.318074i | \(-0.103036\pi\) | |||||||
\(38\) | 3.70891i | 0.601664i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.88515 | − | 3.35424i | 0.930524 | − | 0.530351i | ||||
\(41\) | −5.71649 | −0.892765 | −0.446383 | − | 0.894842i | \(-0.647288\pi\) | ||||
−0.446383 | + | 0.894842i | \(0.647288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.98619i | − | 1.06538i | −0.846309 | − | 0.532692i | \(-0.821180\pi\) | ||
0.846309 | − | 0.532692i | \(-0.178820\pi\) | |||||||
\(44\) | −1.76304 | −0.265788 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.0166 | 1.62431 | ||||||||
\(47\) | − | 0.336444i | − | 0.0490753i | −0.999699 | − | 0.0245377i | \(-0.992189\pi\) | ||
0.999699 | − | 0.0245377i | \(-0.00781137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.93456 | 0.990651 | ||||||||
\(50\) | −5.47486 | − | 3.24275i | −0.774263 | − | 0.458594i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.91237i | − | 0.265197i | ||||||
\(53\) | − | 6.01484i | − | 0.826202i | −0.910685 | − | 0.413101i | \(-0.864446\pi\) | ||
0.910685 | − | 0.413101i | \(-0.135554\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.13143 | + | 9.00332i | 0.691922 | + | 1.21401i | ||||
\(56\) | −0.774958 | −0.103558 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.27263i | 0.167104i | ||||||||
\(59\) | −13.2799 | −1.72890 | −0.864451 | − | 0.502718i | \(-0.832334\pi\) | ||||
−0.864451 | + | 0.502718i | \(0.832334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.77792 | −0.995861 | −0.497930 | − | 0.867217i | \(-0.665906\pi\) | ||||
−0.497930 | + | 0.867217i | \(0.665906\pi\) | |||||||
\(62\) | − | 4.16077i | − | 0.528418i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.88775 | −1.11097 | ||||||||
\(65\) | −9.76589 | + | 5.56606i | −1.21131 | + | 0.690385i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 11.2605i | − | 1.37569i | −0.725856 | − | 0.687847i | \(-0.758556\pi\) | ||
0.725856 | − | 0.687847i | \(-0.241444\pi\) | |||||||
\(68\) | − | 0.127989i | − | 0.0155210i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.360465 | + | 0.632452i | 0.0430839 | + | 0.0755925i | ||||
\(71\) | 13.9668 | 1.65756 | 0.828778 | − | 0.559578i | \(-0.189037\pi\) | ||||
0.828778 | + | 0.559578i | \(0.189037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.46426i | − | 0.990667i | −0.868703 | − | 0.495333i | \(-0.835046\pi\) | ||
0.868703 | − | 0.495333i | \(-0.164954\pi\) | |||||||
\(74\) | 4.92448 | 0.572459 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.10868 | 0.127174 | ||||||||
\(77\) | − | 1.18556i | − | 0.135107i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.3102 | 1.72253 | 0.861267 | − | 0.508153i | \(-0.169672\pi\) | ||||
0.861267 | + | 0.508153i | \(0.169672\pi\) | |||||||
\(80\) | 3.42627 | + | 6.01154i | 0.383069 | + | 0.672111i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 7.27496i | − | 0.803385i | ||||||
\(83\) | − | 7.60521i | − | 0.834781i | −0.908727 | − | 0.417390i | \(-0.862945\pi\) | ||
0.908727 | − | 0.417390i | \(-0.137055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.653605 | + | 0.372521i | −0.0708934 | + | 0.0404056i | ||||
\(86\) | 8.89082 | 0.958722 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 14.0396i | − | 1.49662i | ||||||
\(89\) | −13.0383 | −1.38206 | −0.691029 | − | 0.722827i | \(-0.742843\pi\) | ||||
−0.691029 | + | 0.722827i | \(0.742843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.28597 | 0.134807 | ||||||||
\(92\) | − | 3.29312i | − | 0.343331i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.428167 | 0.0441621 | ||||||||
\(95\) | −3.22689 | − | 5.66171i | −0.331071 | − | 0.580879i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.5445i | 1.17216i | 0.810253 | + | 0.586081i | \(0.199330\pi\) | ||||
−0.810253 | + | 0.586081i | \(0.800670\pi\) | |||||||
\(98\) | 8.82511i | 0.891471i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.969334 | + | 1.63657i | −0.0969334 | + | 0.163657i | ||||
\(101\) | 8.19832 | 0.815763 | 0.407882 | − | 0.913035i | \(-0.366268\pi\) | ||||
0.407882 | + | 0.913035i | \(0.366268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.73014i | 0.170476i | 0.996361 | + | 0.0852380i | \(0.0271651\pi\) | ||||
−0.996361 | + | 0.0852380i | \(0.972835\pi\) | |||||||
\(104\) | 15.2287 | 1.49330 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.65465 | 0.743486 | ||||||||
\(107\) | 5.38921i | 0.520995i | 0.965475 | + | 0.260497i | \(0.0838865\pi\) | ||||
−0.965475 | + | 0.260497i | \(0.916113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.2391 | −1.36386 | −0.681929 | − | 0.731418i | \(-0.738859\pi\) | ||||
−0.681929 | + | 0.731418i | \(0.738859\pi\) | |||||||
\(110\) | −11.4579 | + | 6.53040i | −1.09247 | + | 0.622649i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 0.791600i | − | 0.0747992i | ||||||
\(113\) | 9.89466i | 0.930811i | 0.885098 | + | 0.465406i | \(0.154091\pi\) | ||||
−0.885098 | + | 0.465406i | \(0.845909\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.8170 | + | 9.58483i | −1.56819 | + | 0.893790i | ||||
\(116\) | 0.380419 | 0.0353210 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 16.9004i | − | 1.55581i | ||||||
\(119\) | 0.0860668 | 0.00788973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4783 | 0.952569 | ||||||||
\(122\) | − | 9.89840i | − | 0.896159i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.24375 | −0.111692 | ||||||||
\(125\) | 11.1788 | + | 0.186778i | 0.999860 | + | 0.0167059i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2226i | 1.08458i | 0.840191 | + | 0.542291i | \(0.182443\pi\) | ||||
−0.840191 | + | 0.542291i | \(0.817557\pi\) | |||||||
\(128\) | − | 7.06940i | − | 0.624852i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.08352 | − | 12.4283i | −0.621266 | − | 1.09004i | ||||
\(131\) | 12.0464 | 1.05250 | 0.526250 | − | 0.850330i | \(-0.323598\pi\) | ||||
0.526250 | + | 0.850330i | \(0.323598\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.745535i | 0.0646461i | ||||||||
\(134\) | 14.3305 | 1.23796 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.01922 | 0.0873972 | ||||||||
\(137\) | − | 5.47512i | − | 0.467771i | −0.972264 | − | 0.233886i | \(-0.924856\pi\) | ||
0.972264 | − | 0.233886i | \(-0.0751441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.71403 | −0.230201 | −0.115100 | − | 0.993354i | \(-0.536719\pi\) | ||||
−0.115100 | + | 0.993354i | \(0.536719\pi\) | |||||||
\(140\) | 0.189055 | − | 0.107752i | 0.0159781 | − | 0.00910668i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.7745i | 1.49161i | ||||||||
\(143\) | 23.2975i | 1.94823i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.10723 | − | 1.94269i | −0.0919507 | − | 0.161331i | ||||
\(146\) | 10.7719 | 0.891485 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.47204i | − | 0.121001i | ||||||
\(149\) | −3.70395 | −0.303439 | −0.151720 | − | 0.988424i | \(-0.548481\pi\) | ||||
−0.151720 | + | 0.988424i | \(0.548481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3481 | 1.24901 | 0.624505 | − | 0.781021i | \(-0.285301\pi\) | ||||
0.624505 | + | 0.781021i | \(0.285301\pi\) | |||||||
\(152\) | 8.82875i | 0.716107i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.50877 | 0.121580 | ||||||||
\(155\) | 3.62002 | + | 6.35148i | 0.290767 | + | 0.510163i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8231i | 1.74168i | 0.491571 | + | 0.870838i | \(0.336423\pi\) | ||||
−0.491571 | + | 0.870838i | \(0.663577\pi\) | |||||||
\(158\) | 19.4842i | 1.55008i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.11985 | − | 2.34811i | 0.325703 | − | 0.185634i | ||||
\(161\) | 2.21447 | 0.174524 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.08019i | 0.241259i | 0.992698 | + | 0.120630i | \(0.0384914\pi\) | ||||
−0.992698 | + | 0.120630i | \(0.961509\pi\) | |||||||
\(164\) | −2.17466 | −0.169812 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.67861 | 0.751206 | ||||||||
\(167\) | 8.55017i | 0.661632i | 0.943695 | + | 0.330816i | \(0.107324\pi\) | ||||
−0.943695 | + | 0.330816i | \(0.892676\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2707 | −0.943903 | ||||||||
\(170\) | −0.474081 | − | 0.831796i | −0.0363603 | − | 0.0637958i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 2.65768i | − | 0.202646i | ||||||
\(173\) | − | 5.76340i | − | 0.438183i | −0.975704 | − | 0.219092i | \(-0.929691\pi\) | ||
0.975704 | − | 0.219092i | \(-0.0703093\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.10051 | − | 0.651831i | −0.0831910 | − | 0.0492738i | ||||
\(176\) | 14.3411 | 1.08100 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 16.5929i | − | 1.24369i | ||||||
\(179\) | 14.1430 | 1.05710 | 0.528548 | − | 0.848903i | \(-0.322736\pi\) | ||||
0.528548 | + | 0.848903i | \(0.322736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0322 | −1.11734 | −0.558668 | − | 0.829391i | \(-0.688688\pi\) | ||||
−0.558668 | + | 0.829391i | \(0.688688\pi\) | |||||||
\(182\) | 1.63657i | 0.121310i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 26.2241 | 1.93326 | ||||||||
\(185\) | −7.51731 | + | 4.28448i | −0.552683 | + | 0.315001i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.55924i | 0.114023i | ||||||||
\(188\) | − | 0.127989i | − | 0.00933459i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.20525 | − | 4.10662i | 0.522724 | − | 0.297926i | ||||
\(191\) | 12.2634 | 0.887346 | 0.443673 | − | 0.896189i | \(-0.353675\pi\) | ||||
0.443673 | + | 0.896189i | \(0.353675\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.34203i | − | 0.600472i | −0.953865 | − | 0.300236i | \(-0.902935\pi\) | ||
0.953865 | − | 0.300236i | \(-0.0970655\pi\) | |||||||
\(194\) | −14.6918 | −1.05481 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.63804 | 0.188431 | ||||||||
\(197\) | 6.69263i | 0.476830i | 0.971163 | + | 0.238415i | \(0.0766279\pi\) | ||||
−0.971163 | + | 0.238415i | \(0.923372\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5583 | −0.890235 | −0.445117 | − | 0.895472i | \(-0.646838\pi\) | ||||
−0.445117 | + | 0.895472i | \(0.646838\pi\) | |||||||
\(200\) | −13.0325 | − | 7.71910i | −0.921535 | − | 0.545822i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.4334i | 0.734092i | ||||||||
\(203\) | 0.255813i | 0.0179546i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.32948 | + | 11.1054i | 0.442070 | + | 0.775631i | ||||
\(206\) | −2.20183 | −0.153409 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.5558i | 1.07860i | ||||||||
\(209\) | −13.5065 | −0.934267 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6479 | −0.939563 | −0.469782 | − | 0.882783i | \(-0.655667\pi\) | ||||
−0.469782 | + | 0.882783i | \(0.655667\pi\) | |||||||
\(212\) | − | 2.28816i | − | 0.157151i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.85846 | −0.468835 | ||||||||
\(215\) | −13.5720 | + | 7.73534i | −0.925602 | + | 0.527546i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.836364i | − | 0.0567761i | ||||||
\(218\) | − | 18.1211i | − | 1.22731i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.95209 | + | 3.42503i | 0.131610 | + | 0.230916i | ||||
\(221\) | −1.69130 | −0.113769 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.4721i | − | 0.902158i | −0.892484 | − | 0.451079i | \(-0.851039\pi\) | ||
0.892484 | − | 0.451079i | \(-0.148961\pi\) | |||||||
\(224\) | −0.542503 | −0.0362475 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.5922 | −0.837622 | ||||||||
\(227\) | − | 1.54298i | − | 0.102411i | −0.998688 | − | 0.0512057i | \(-0.983694\pi\) | ||
0.998688 | − | 0.0512057i | \(-0.0163064\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.89526 | −0.521734 | −0.260867 | − | 0.965375i | \(-0.584008\pi\) | ||||
−0.260867 | + | 0.965375i | \(0.584008\pi\) | |||||||
\(230\) | −12.1979 | − | 21.4018i | −0.804307 | − | 1.41119i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.02939i | 0.198889i | ||||||||
\(233\) | − | 28.4782i | − | 1.86567i | −0.360301 | − | 0.932836i | \(-0.617326\pi\) | ||
0.360301 | − | 0.932836i | \(-0.382674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.653605 | + | 0.372521i | −0.0426365 | + | 0.0243006i | ||||
\(236\) | −5.05194 | −0.328853 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.109531i | 0.00709984i | ||||||||
\(239\) | 8.88508 | 0.574728 | 0.287364 | − | 0.957821i | \(-0.407221\pi\) | ||||
0.287364 | + | 0.957821i | \(0.407221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.8901 | −1.92539 | −0.962695 | − | 0.270589i | \(-0.912782\pi\) | ||||
−0.962695 | + | 0.270589i | \(0.912782\pi\) | |||||||
\(242\) | 13.3349i | 0.857202i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.95887 | −0.189422 | ||||||||
\(245\) | −7.67817 | − | 13.4717i | −0.490540 | − | 0.860674i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 14.6505i | − | 0.932192i | ||||||
\(248\) | − | 9.90437i | − | 0.628928i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.237699 | + | 14.2264i | −0.0150334 | + | 0.899758i | ||||
\(251\) | 15.9551 | 1.00708 | 0.503539 | − | 0.863973i | \(-0.332031\pi\) | ||||
0.503539 | + | 0.863973i | \(0.332031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.1185i | 2.52223i | ||||||||
\(254\) | −15.5548 | −0.975998 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.77878 | −0.548674 | ||||||||
\(257\) | − | 17.1593i | − | 1.07037i | −0.844735 | − | 0.535185i | \(-0.820242\pi\) | ||
0.844735 | − | 0.535185i | \(-0.179758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.989880 | 0.0615081 | ||||||||
\(260\) | −3.71513 | + | 2.11743i | −0.230403 | + | 0.131318i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.3306i | 0.947128i | ||||||||
\(263\) | − | 1.72781i | − | 0.106542i | −0.998580 | − | 0.0532708i | \(-0.983035\pi\) | ||
0.998580 | − | 0.0532708i | \(-0.0169647\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.6850 | + | 6.65983i | −0.717801 | + | 0.409110i | ||||
\(266\) | −0.948789 | −0.0581740 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4.28372i | − | 0.261670i | ||||||
\(269\) | −4.97931 | −0.303594 | −0.151797 | − | 0.988412i | \(-0.548506\pi\) | ||||
−0.151797 | + | 0.988412i | \(0.548506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0881 | 0.795047 | 0.397524 | − | 0.917592i | \(-0.369870\pi\) | ||||
0.397524 | + | 0.917592i | \(0.369870\pi\) | |||||||
\(272\) | 1.04111i | 0.0631263i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.96779 | 0.420939 | ||||||||
\(275\) | 11.8089 | − | 19.9375i | 0.712106 | − | 1.20228i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.8147i | 1.25063i | 0.780371 | + | 0.625316i | \(0.215030\pi\) | ||||
−0.780371 | + | 0.625316i | \(0.784970\pi\) | |||||||
\(278\) | − | 3.45394i | − | 0.207154i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.858059 | + | 1.50550i | 0.0512788 | + | 0.0899709i | ||||
\(281\) | −3.93338 | −0.234646 | −0.117323 | − | 0.993094i | \(-0.537431\pi\) | ||||
−0.117323 | + | 0.993094i | \(0.537431\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.47745i | 0.325600i | 0.986659 | + | 0.162800i | \(0.0520526\pi\) | ||||
−0.986659 | + | 0.162800i | \(0.947947\pi\) | |||||||
\(284\) | 5.31324 | 0.315282 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.6490 | −1.75318 | ||||||||
\(287\) | − | 1.46235i | − | 0.0863201i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8868 | 0.993342 | ||||||||
\(290\) | 2.47232 | − | 1.40909i | 0.145180 | − | 0.0827449i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 3.21996i | − | 0.188434i | ||||||
\(293\) | 11.9974i | 0.700893i | 0.936583 | + | 0.350446i | \(0.113970\pi\) | ||||
−0.936583 | + | 0.350446i | \(0.886030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.7040 | + | 25.7988i | 0.856099 | + | 1.50206i | ||||
\(296\) | 11.7223 | 0.681347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 4.71375i | − | 0.273060i | ||||||
\(299\) | −43.5166 | −2.51663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.78716 | 0.103010 | ||||||||
\(302\) | 19.5324i | 1.12396i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.01836 | −0.517238 | ||||||||
\(305\) | 8.61197 | + | 15.1101i | 0.493120 | + | 0.865200i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.4807i | − | 1.51133i | −0.654957 | − | 0.755666i | \(-0.727313\pi\) | ||
0.654957 | − | 0.755666i | \(-0.272687\pi\) | |||||||
\(308\) | − | 0.451009i | − | 0.0256986i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.08307 | + | 4.60694i | −0.459088 | + | 0.261656i | ||||
\(311\) | 1.71530 | 0.0972660 | 0.0486330 | − | 0.998817i | \(-0.484514\pi\) | ||||
0.0486330 | + | 0.998817i | \(0.484514\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.3782i | 1.88665i | 0.331871 | + | 0.943325i | \(0.392320\pi\) | ||||
−0.331871 | + | 0.943325i | \(0.607680\pi\) | |||||||
\(314\) | −27.7727 | −1.56731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.82429 | 0.327642 | ||||||||
\(317\) | − | 17.9712i | − | 1.00936i | −0.863305 | − | 0.504682i | \(-0.831610\pi\) | ||
0.863305 | − | 0.504682i | \(-0.168390\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.63446 | −0.259480 | ||||||||
\(320\) | 9.84080 | + | 17.2661i | 0.550118 | + | 0.965205i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.81819i | 0.157052i | ||||||||
\(323\) | − | 0.980521i | − | 0.0545577i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.6262 | + | 12.8092i | 1.19961 | + | 0.710524i | ||||
\(326\) | −3.91994 | −0.217105 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 17.3175i | − | 0.956196i | ||||||
\(329\) | 0.0860668 | 0.00474501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.49393 | 0.356939 | 0.178469 | − | 0.983945i | \(-0.442885\pi\) | ||||
0.178469 | + | 0.983945i | \(0.442885\pi\) | |||||||
\(332\) | − | 2.89317i | − | 0.158783i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.8812 | −0.595392 | ||||||||
\(335\) | −21.8757 | + | 12.4680i | −1.19520 | + | 0.681202i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.36156i | 0.346536i | 0.984875 | + | 0.173268i | \(0.0554327\pi\) | ||||
−0.984875 | + | 0.173268i | \(0.944567\pi\) | |||||||
\(338\) | − | 15.6161i | − | 0.849403i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.248643 | + | 0.141714i | −0.0134846 | + | 0.00768552i | ||||
\(341\) | 15.1521 | 0.820530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.56465i | 0.192473i | ||||||||
\(344\) | 21.1639 | 1.14108 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.33466 | 0.394314 | ||||||||
\(347\) | 21.6036i | 1.15974i | 0.814708 | + | 0.579871i | \(0.196897\pi\) | ||||
−0.814708 | + | 0.579871i | \(0.803103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.12603 | 0.220861 | 0.110431 | − | 0.993884i | \(-0.464777\pi\) | ||||
0.110431 | + | 0.993884i | \(0.464777\pi\) | |||||||
\(350\) | 0.829538 | − | 1.40054i | 0.0443407 | − | 0.0748622i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 9.82830i | − | 0.523850i | ||||||
\(353\) | − | 7.07724i | − | 0.376684i | −0.982104 | − | 0.188342i | \(-0.939689\pi\) | ||
0.982104 | − | 0.188342i | \(-0.0603113\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.4645 | − | 27.1331i | −0.820771 | − | 1.44008i | ||||
\(356\) | −4.96002 | −0.262881 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.9988i | 0.951264i | ||||||||
\(359\) | −14.4359 | −0.761900 | −0.380950 | − | 0.924596i | \(-0.624403\pi\) | ||||
−0.380950 | + | 0.924596i | \(0.624403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5064 | −0.552971 | ||||||||
\(362\) | − | 19.1304i | − | 1.00547i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.489209 | 0.0256415 | ||||||||
\(365\) | −16.4434 | + | 9.37190i | −0.860688 | + | 0.490548i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.4145i | 0.804630i | 0.915501 | + | 0.402315i | \(0.131794\pi\) | ||||
−0.915501 | + | 0.402315i | \(0.868206\pi\) | |||||||
\(368\) | 26.7873i | 1.39638i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.45255 | − | 9.56673i | −0.283464 | − | 0.497351i | ||||
\(371\) | 1.53868 | 0.0798841 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 29.8574i | − | 1.54596i | −0.634432 | − | 0.772979i | \(-0.718766\pi\) | ||
0.634432 | − | 0.772979i | \(-0.281234\pi\) | |||||||
\(374\) | −1.98433 | −0.102607 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.01922 | 0.0525621 | ||||||||
\(377\) | − | 5.02700i | − | 0.258904i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.3451 | −1.91829 | −0.959144 | − | 0.282920i | \(-0.908697\pi\) | ||||
−0.959144 | + | 0.282920i | \(0.908697\pi\) | |||||||
\(380\) | −1.22757 | − | 2.15382i | −0.0629729 | − | 0.110489i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.6067i | 0.798508i | ||||||||
\(383\) | 25.8159i | 1.31913i | 0.751647 | + | 0.659566i | \(0.229260\pi\) | ||||
−0.751647 | + | 0.659566i | \(0.770740\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.30317 | + | 1.31269i | −0.117380 | + | 0.0669008i | ||||
\(386\) | 10.6163 | 0.540355 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.39173i | 0.222956i | ||||||||
\(389\) | 20.6935 | 1.04920 | 0.524600 | − | 0.851349i | \(-0.324215\pi\) | ||||
0.524600 | + | 0.851349i | \(0.324215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.91245 | −0.147289 | ||||||||
\(392\) | 21.0075i | 1.06104i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.51723 | −0.429092 | ||||||||
\(395\) | −16.9520 | − | 29.7430i | −0.852946 | − | 1.49653i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.38045i | 0.119471i | 0.998214 | + | 0.0597357i | \(0.0190258\pi\) | ||||
−0.998214 | + | 0.0597357i | \(0.980974\pi\) | |||||||
\(398\) | − | 15.9820i | − | 0.801108i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.88487 | − | 13.3123i | 0.394243 | − | 0.665617i | ||||
\(401\) | 32.0936 | 1.60268 | 0.801339 | − | 0.598211i | \(-0.204121\pi\) | ||||
0.801339 | + | 0.598211i | \(0.204121\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.4354i | 0.818707i | ||||||||
\(404\) | 3.11879 | 0.155166 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.325555 | −0.0161570 | ||||||||
\(407\) | 17.9332i | 0.888918i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.5011 | 1.55763 | 0.778815 | − | 0.627253i | \(-0.215821\pi\) | ||||
0.778815 | + | 0.627253i | \(0.215821\pi\) | |||||||
\(410\) | −14.1330 | + | 8.05507i | −0.697978 | + | 0.397812i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.658179i | 0.0324261i | ||||||||
\(413\) | − | 3.39719i | − | 0.167165i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.7746 | + | 8.42074i | −0.725255 | + | 0.413358i | ||||
\(416\) | 10.6608 | 0.522686 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 17.1888i | − | 0.840732i | ||||||
\(419\) | −3.15481 | −0.154123 | −0.0770613 | − | 0.997026i | \(-0.524554\pi\) | ||||
−0.0770613 | + | 0.997026i | \(0.524554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.9631 | −0.583048 | −0.291524 | − | 0.956564i | \(-0.594162\pi\) | ||||
−0.291524 | + | 0.956564i | \(0.594162\pi\) | |||||||
\(422\) | − | 17.3687i | − | 0.845497i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.2213 | 0.884904 | ||||||||
\(425\) | 1.44739 | + | 0.857282i | 0.0702085 | + | 0.0415843i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.98970i | − | 0.0962882i | ||||||
\(428\) | 2.05016i | 0.0990981i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.84420 | − | 17.2721i | −0.474730 | − | 0.832934i | ||||
\(431\) | 31.2658 | 1.50602 | 0.753011 | − | 0.658008i | \(-0.228601\pi\) | ||||
0.753011 | + | 0.658008i | \(0.228601\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.6459i | 1.47275i | 0.676575 | + | 0.736373i | \(0.263463\pi\) | ||||
−0.676575 | + | 0.736373i | \(0.736537\pi\) | |||||||
\(434\) | 1.06438 | 0.0510919 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.41682 | −0.259419 | ||||||||
\(437\) | − | 25.2284i | − | 1.20684i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.717425 | −0.0342408 | −0.0171204 | − | 0.999853i | \(-0.505450\pi\) | ||||
−0.0171204 | + | 0.999853i | \(0.505450\pi\) | |||||||
\(440\) | −27.2745 | + | 15.5451i | −1.30026 | + | 0.741083i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.15240i | − | 0.102379i | ||||||
\(443\) | 27.0649i | 1.28589i | 0.765911 | + | 0.642947i | \(0.222288\pi\) | ||||
−0.765911 | + | 0.642947i | \(0.777712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.4365 | + | 25.3294i | 0.684353 | + | 1.20073i | ||||
\(446\) | 17.1450 | 0.811838 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.27361i | − | 0.107418i | ||||||
\(449\) | −30.3663 | −1.43307 | −0.716536 | − | 0.697550i | \(-0.754273\pi\) | ||||
−0.716536 | + | 0.697550i | \(0.754273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.4929 | 1.24750 | ||||||||
\(452\) | 3.76411i | 0.177049i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.96364 | 0.0921584 | ||||||||
\(455\) | −1.42387 | − | 2.49825i | −0.0667522 | − | 0.117120i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.43167i | − | 0.113749i | −0.998381 | − | 0.0568743i | \(-0.981887\pi\) | ||
0.998381 | − | 0.0568743i | \(-0.0181134\pi\) | |||||||
\(458\) | − | 10.0477i | − | 0.469500i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.39750 | + | 3.64625i | −0.298285 | + | 0.170007i | ||||
\(461\) | −8.28439 | −0.385842 | −0.192921 | − | 0.981214i | \(-0.561796\pi\) | ||||
−0.192921 | + | 0.981214i | \(0.561796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.05654i | 0.327945i | 0.986465 | + | 0.163973i | \(0.0524309\pi\) | ||||
−0.986465 | + | 0.163973i | \(0.947569\pi\) | |||||||
\(464\) | −3.09444 | −0.143656 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.2422 | 1.67889 | ||||||||
\(467\) | − | 6.07165i | − | 0.280963i | −0.990083 | − | 0.140481i | \(-0.955135\pi\) | ||
0.990083 | − | 0.140481i | \(-0.0448650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.88060 | 0.133014 | ||||||||
\(470\) | −0.474081 | − | 0.831796i | −0.0218677 | − | 0.0383679i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 40.2301i | − | 1.85174i | ||||||
\(473\) | 32.3773i | 1.48871i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.42603 | + | 12.5377i | −0.340729 | + | 0.575267i | ||||
\(476\) | 0.0327414 | 0.00150070 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.3074i | 0.517188i | ||||||||
\(479\) | −29.7675 | −1.36011 | −0.680055 | − | 0.733161i | \(-0.738044\pi\) | ||||
−0.680055 | + | 0.733161i | \(0.738044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.4522 | −0.886943 | ||||||||
\(482\) | − | 38.0390i | − | 1.73263i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.98613 | 0.181188 | ||||||||
\(485\) | 22.4273 | − | 12.7824i | 1.01837 | − | 0.580419i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 41.9050i | − | 1.89890i | −0.313923 | − | 0.949448i | \(-0.601643\pi\) | ||
0.313923 | − | 0.949448i | \(-0.398357\pi\) | |||||||
\(488\) | − | 23.5623i | − | 1.06662i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.1444 | − | 9.77145i | 0.774507 | − | 0.441429i | ||||
\(491\) | 7.22435 | 0.326030 | 0.163015 | − | 0.986624i | \(-0.447878\pi\) | ||||
0.163015 | + | 0.986624i | \(0.447878\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.336444i | − | 0.0151527i | ||||||
\(494\) | 18.6447 | 0.838864 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.1171 | 0.454270 | ||||||||
\(497\) | 3.57290i | 0.160266i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5607 | 0.696593 | 0.348296 | − | 0.937384i | \(-0.386760\pi\) | ||||
0.348296 | + | 0.937384i | \(0.386760\pi\) | |||||||
\(500\) | 4.25262 | + | 0.0710538i | 0.190183 | + | 0.00317762i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.3049i | 0.906253i | ||||||||
\(503\) | − | 38.5096i | − | 1.71706i | −0.512765 | − | 0.858529i | \(-0.671379\pi\) | ||
0.512765 | − | 0.858529i | \(-0.328621\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.07745 | − | 15.9268i | −0.403941 | − | 0.708732i | ||||
\(506\) | −51.0560 | −2.26971 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.64971i | 0.206298i | ||||||||
\(509\) | 31.6646 | 1.40351 | 0.701754 | − | 0.712419i | \(-0.252400\pi\) | ||||
0.701754 | + | 0.712419i | \(0.252400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.16527 | 0.0957860 | ||||||||
\(512\) | − | 25.3109i | − | 1.11860i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.8375 | 0.963209 | ||||||||
\(515\) | 3.36113 | − | 1.91567i | 0.148109 | − | 0.0844145i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.55924i | 0.0685751i | ||||||||
\(518\) | 1.25975i | 0.0553502i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16.8617 | − | 29.5847i | −0.739437 | − | 1.29737i | ||||
\(521\) | −20.2023 | −0.885079 | −0.442539 | − | 0.896749i | \(-0.645922\pi\) | ||||
−0.442539 | + | 0.896749i | \(0.645922\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 12.1052i | − | 0.529325i | −0.964341 | − | 0.264663i | \(-0.914739\pi\) | ||
0.964341 | − | 0.264663i | \(-0.0852606\pi\) | |||||||
\(524\) | 4.58268 | 0.200195 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.19886 | 0.0958751 | ||||||||
\(527\) | 1.09998i | 0.0479158i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −51.9361 | −2.25809 | ||||||||
\(530\) | −8.47548 | − | 14.8706i | −0.368151 | − | 0.645938i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.283615i | 0.0122963i | ||||||||
\(533\) | 28.7368i | 1.24473i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4696 | − | 5.96711i | 0.452638 | − | 0.257981i | ||||
\(536\) | 34.1125 | 1.47344 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 6.33681i | − | 0.273199i | ||||||
\(539\) | −32.1380 | −1.38428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.4279 | −0.620304 | −0.310152 | − | 0.950687i | \(-0.600380\pi\) | ||||
−0.310152 | + | 0.950687i | \(0.600380\pi\) | |||||||
\(542\) | 16.6563i | 0.715450i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.713495 | 0.0305909 | ||||||||
\(545\) | 15.7660 | + | 27.6621i | 0.675341 | + | 1.18492i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 41.9178i | − | 1.79228i | −0.443774 | − | 0.896139i | \(-0.646361\pi\) | ||
0.443774 | − | 0.896139i | \(-0.353639\pi\) | |||||||
\(548\) | − | 2.08284i | − | 0.0889744i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.3731 | + | 15.0284i | 1.08191 | + | 0.640813i | ||||
\(551\) | 2.91437 | 0.124156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.91656i | 0.166549i | ||||||||
\(554\) | −26.4893 | −1.12542 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.03247 | −0.0437863 | ||||||||
\(557\) | 3.60324i | 0.152674i | 0.997082 | + | 0.0763372i | \(0.0243225\pi\) | ||||
−0.997082 | + | 0.0763372i | \(0.975677\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.1196 | −1.48540 | ||||||||
\(560\) | −1.53783 | + | 0.876486i | −0.0649853 | + | 0.0370383i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 5.00573i | − | 0.211154i | ||||||
\(563\) | − | 15.5829i | − | 0.656741i | −0.944549 | − | 0.328370i | \(-0.893501\pi\) | ||
0.944549 | − | 0.328370i | \(-0.106499\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2222 | − | 10.9557i | 0.808685 | − | 0.460909i | ||||
\(566\) | −6.97075 | −0.293003 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.3109i | 1.77532i | ||||||||
\(569\) | 36.9718 | 1.54994 | 0.774970 | − | 0.631998i | \(-0.217765\pi\) | ||||
0.774970 | + | 0.631998i | \(0.217765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.9692 | 1.25417 | 0.627086 | − | 0.778950i | \(-0.284248\pi\) | ||||
0.627086 | + | 0.778950i | \(0.284248\pi\) | |||||||
\(572\) | 8.86279i | 0.370572i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.86103 | 0.0776780 | ||||||||
\(575\) | 37.2407 | + | 22.0575i | 1.55304 | + | 0.919863i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 7.12327i | − | 0.296546i | −0.988946 | − | 0.148273i | \(-0.952629\pi\) | ||
0.988946 | − | 0.148273i | \(-0.0473714\pi\) | |||||||
\(578\) | 21.4906i | 0.893892i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.421212 | − | 0.739035i | −0.0174899 | − | 0.0306867i | ||||
\(581\) | 1.94552 | 0.0807136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.8756i | 1.15449i | ||||||||
\(584\) | 25.6415 | 1.06105 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.2682 | −0.630722 | ||||||||
\(587\) | − | 7.87237i | − | 0.324928i | −0.986715 | − | 0.162464i | \(-0.948056\pi\) | ||
0.986715 | − | 0.162464i | \(-0.0519441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.52833 | −0.392608 | ||||||||
\(590\) | −32.8322 | + | 18.7127i | −1.35168 | + | 0.770390i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.9741i | 0.492131i | ||||||||
\(593\) | 17.9188i | 0.735836i | 0.929858 | + | 0.367918i | \(0.119929\pi\) | ||||
−0.929858 | + | 0.367918i | \(0.880071\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0952959 | − | 0.167201i | −0.00390675 | − | 0.00685457i | ||||
\(596\) | −1.40905 | −0.0577170 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 55.3804i | − | 2.26467i | ||||||
\(599\) | 20.1934 | 0.825078 | 0.412539 | − | 0.910940i | \(-0.364642\pi\) | ||||
0.412539 | + | 0.910940i | \(0.364642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2527 | 0.948496 | 0.474248 | − | 0.880391i | \(-0.342720\pi\) | ||||
0.474248 | + | 0.880391i | \(0.342720\pi\) | |||||||
\(602\) | 2.27439i | 0.0926973i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.83870 | 0.237573 | ||||||||
\(605\) | −11.6019 | − | 20.3560i | −0.471683 | − | 0.827589i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.6177i | − | 0.715082i | −0.933897 | − | 0.357541i | \(-0.883615\pi\) | ||
0.933897 | − | 0.357541i | \(-0.116385\pi\) | |||||||
\(608\) | 6.18050i | 0.250652i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.2295 | + | 10.9598i | −0.778580 | + | 0.443750i | ||||
\(611\) | −1.69130 | −0.0684228 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13.4161i | − | 0.541873i | −0.962597 | − | 0.270937i | \(-0.912667\pi\) | ||
0.962597 | − | 0.270937i | \(-0.0873334\pi\) | |||||||
\(614\) | 33.7001 | 1.36002 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.59151 | 0.144706 | ||||||||
\(617\) | 7.99166i | 0.321732i | 0.986976 | + | 0.160866i | \(0.0514287\pi\) | ||||
−0.986976 | + | 0.160866i | \(0.948571\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0770 | 0.605996 | 0.302998 | − | 0.952991i | \(-0.402012\pi\) | ||||
0.302998 | + | 0.952991i | \(0.402012\pi\) | |||||||
\(620\) | 1.37712 | + | 2.41622i | 0.0553066 | + | 0.0970378i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.18294i | 0.0875281i | ||||||||
\(623\) | − | 3.33538i | − | 0.133629i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0147 | − | 21.9237i | −0.480586 | − | 0.876947i | ||||
\(626\) | −42.4781 | −1.69776 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.30193i | 0.331283i | ||||||||
\(629\) | −1.30188 | −0.0519094 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.5154 | 0.418611 | 0.209306 | − | 0.977850i | \(-0.432880\pi\) | ||||
0.209306 | + | 0.977850i | \(0.432880\pi\) | |||||||
\(632\) | 46.3805i | 1.84492i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.8707 | 0.908311 | ||||||||
\(635\) | 23.7447 | − | 13.5333i | 0.942281 | − | 0.537052i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 34.8600i | − | 1.38121i | ||||||
\(638\) | − | 5.89795i | − | 0.233502i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.7336 | + | 7.82747i | −0.542870 | + | 0.309408i | ||||
\(641\) | 27.2479 | 1.07623 | 0.538113 | − | 0.842873i | \(-0.319137\pi\) | ||||
0.538113 | + | 0.842873i | \(0.319137\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.3023i | − | 1.43162i | −0.698293 | − | 0.715812i | \(-0.746057\pi\) | ||
0.698293 | − | 0.715812i | \(-0.253943\pi\) | |||||||
\(644\) | 0.842424 | 0.0331962 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.24784 | 0.0490955 | ||||||||
\(647\) | 8.77892i | 0.345135i | 0.984998 | + | 0.172567i | \(0.0552063\pi\) | ||||
−0.984998 | + | 0.172567i | \(0.944794\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.5454 | 2.41587 | ||||||||
\(650\) | −16.3013 | + | 27.5221i | −0.639389 | + | 1.07951i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.17176i | 0.0458898i | ||||||||
\(653\) | − | 44.1466i | − | 1.72759i | −0.503845 | − | 0.863794i | \(-0.668082\pi\) | ||
0.503845 | − | 0.863794i | \(-0.331918\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.3382 | − | 23.4024i | −0.521166 | − | 0.914408i | ||||
\(656\) | 17.6894 | 0.690653 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.109531i | 0.00426996i | ||||||||
\(659\) | 22.7653 | 0.886810 | 0.443405 | − | 0.896321i | \(-0.353770\pi\) | ||||
0.443405 | + | 0.896321i | \(0.353770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.3474 | 1.14148 | 0.570740 | − | 0.821131i | \(-0.306656\pi\) | ||||
0.570740 | + | 0.821131i | \(0.306656\pi\) | |||||||
\(662\) | 8.26435i | 0.321203i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.0391 | 0.894092 | ||||||||
\(665\) | 1.44834 | − | 0.825481i | 0.0561643 | − | 0.0320108i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.65656i | − | 0.335183i | ||||||
\(668\) | 3.25264i | 0.125849i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −15.8672 | − | 27.8397i | −0.613002 | − | 1.07554i | ||||
\(671\) | 36.0465 | 1.39156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.2267i | 1.62772i | 0.581060 | + | 0.813860i | \(0.302638\pi\) | ||||
−0.581060 | + | 0.813860i | \(0.697362\pi\) | |||||||
\(674\) | −8.09590 | −0.311842 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.66802 | −0.179539 | ||||||||
\(677\) | − | 19.9803i | − | 0.767907i | −0.923353 | − | 0.383953i | \(-0.874562\pi\) | ||
0.923353 | − | 0.383953i | \(-0.125438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.95323 | −0.113334 | ||||||||
\(680\) | −1.12851 | − | 1.98002i | −0.0432764 | − | 0.0759304i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.2829i | 0.738381i | ||||||||
\(683\) | − | 23.0491i | − | 0.881950i | −0.897519 | − | 0.440975i | \(-0.854633\pi\) | ||
0.897519 | − | 0.440975i | \(-0.145367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.6364 | + | 6.06223i | −0.406398 | + | 0.231626i | ||||
\(686\) | −4.53647 | −0.173203 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 21.6184i | 0.824193i | ||||||||
\(689\) | −30.2366 | −1.15192 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.01208 | 0.152627 | 0.0763134 | − | 0.997084i | \(-0.475685\pi\) | ||||
0.0763134 | + | 0.997084i | \(0.475685\pi\) | |||||||
\(692\) | − | 2.19250i | − | 0.0833465i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.4933 | −1.04363 | ||||||||
\(695\) | 3.00506 | + | 5.27250i | 0.113988 | + | 0.199997i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.92328i | 0.0728493i | ||||||||
\(698\) | 5.25090i | 0.198750i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.418656 | − | 0.247969i | −0.0158237 | − | 0.00937234i | ||||
\(701\) | −4.49887 | −0.169920 | −0.0849599 | − | 0.996384i | \(-0.527076\pi\) | ||||
−0.0849599 | + | 0.996384i | \(0.527076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11.2773i | − | 0.425330i | ||||||
\(704\) | 41.1900 | 1.55240 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00670 | 0.338971 | ||||||||
\(707\) | 2.09724i | 0.0788748i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.7777 | −1.38121 | −0.690607 | − | 0.723230i | \(-0.742657\pi\) | ||||
−0.690607 | + | 0.723230i | \(0.742657\pi\) | |||||||
\(710\) | 34.5304 | − | 19.6806i | 1.29590 | − | 0.738598i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 39.4981i | − | 1.48025i | ||||||
\(713\) | 28.3020i | 1.05992i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45.2597 | − | 25.7957i | 1.69262 | − | 0.964705i | ||||
\(716\) | 5.38026 | 0.201070 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 18.3716i | − | 0.685621i | ||||||
\(719\) | −25.4279 | −0.948300 | −0.474150 | − | 0.880444i | \(-0.657245\pi\) | ||||
−0.474150 | + | 0.880444i | \(0.657245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.442594 | −0.0164831 | ||||||||
\(722\) | − | 13.3708i | − | 0.497609i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.71854 | −0.212528 | ||||||||
\(725\) | −2.54807 | + | 4.30201i | −0.0946330 | + | 0.159773i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6265i | 0.431205i | 0.976481 | + | 0.215602i | \(0.0691715\pi\) | ||||
−0.976481 | + | 0.215602i | \(0.930829\pi\) | |||||||
\(728\) | 3.89571i | 0.144385i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.9269 | − | 20.9263i | −0.441436 | − | 0.774519i | ||||
\(731\) | −2.35046 | −0.0869349 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 25.6926i | − | 0.948978i | −0.880261 | − | 0.474489i | \(-0.842633\pi\) | ||
0.880261 | − | 0.474489i | \(-0.157367\pi\) | |||||||
\(734\) | −19.6169 | −0.724073 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.3580 | 0.676683 | ||||||||
\(737\) | 52.1866i | 1.92232i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.3612 | 1.22721 | 0.613606 | − | 0.789612i | \(-0.289718\pi\) | ||||
0.613606 | + | 0.789612i | \(0.289718\pi\) | |||||||
\(740\) | −2.85972 | + | 1.62990i | −0.105126 | + | 0.0599162i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.95816i | 0.0718864i | ||||||||
\(743\) | − | 25.6430i | − | 0.940750i | −0.882467 | − | 0.470375i | \(-0.844119\pi\) | ||
0.882467 | − | 0.470375i | \(-0.155881\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.10113 | + | 7.19562i | 0.150254 | + | 0.263627i | ||||
\(746\) | 37.9973 | 1.39118 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.593162i | 0.0216882i | ||||||||
\(749\) | −1.37863 | −0.0503741 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.6411 | 1.70196 | 0.850979 | − | 0.525200i | \(-0.176009\pi\) | ||||
0.850979 | + | 0.525200i | \(0.176009\pi\) | |||||||
\(752\) | 1.04111i | 0.0379652i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.39750 | 0.232983 | ||||||||
\(755\) | −16.9939 | − | 29.8165i | −0.618472 | − | 1.08514i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.69262i | 0.0978650i | 0.998802 | + | 0.0489325i | \(0.0155819\pi\) | ||||
−0.998802 | + | 0.0489325i | \(0.984418\pi\) | |||||||
\(758\) | − | 47.5264i | − | 1.72624i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.1515 | − | 9.77549i | 0.622151 | − | 0.354594i | ||||
\(761\) | 0.471501 | 0.0170919 | 0.00854595 | − | 0.999963i | \(-0.497280\pi\) | ||||
0.00854595 | + | 0.999963i | \(0.497280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.64255i | − | 0.131869i | ||||||
\(764\) | 4.66521 | 0.168781 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.8540 | −1.18706 | ||||||||
\(767\) | 66.7583i | 2.41050i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.04380 | −0.326128 | −0.163064 | − | 0.986616i | \(-0.552138\pi\) | ||||
−0.163064 | + | 0.986616i | \(0.552138\pi\) | |||||||
\(770\) | −1.67056 | − | 2.93108i | −0.0602029 | − | 0.105629i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 3.17346i | − | 0.114215i | ||||||
\(773\) | 9.91726i | 0.356699i | 0.983967 | + | 0.178350i | \(0.0570758\pi\) | ||||
−0.983967 | + | 0.178350i | \(0.942924\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.33074 | − | 14.0651i | 0.299249 | − | 0.505234i | ||||
\(776\) | −34.9726 | −1.25544 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.3351i | 0.944159i | ||||||||
\(779\) | −16.6600 | −0.596905 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −64.7287 | −2.31617 | ||||||||
\(782\) | − | 3.70646i | − | 0.132543i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21.4586 | −0.766379 | ||||||||
\(785\) | 42.3955 | − | 24.1633i | 1.51316 | − | 0.862425i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.53609i | 0.304279i | 0.988359 | + | 0.152139i | \(0.0486162\pi\) | ||||
−0.988359 | + | 0.152139i | \(0.951384\pi\) | |||||||
\(788\) | 2.54600i | 0.0906976i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 37.8517 | − | 21.5735i | 1.34670 | − | 0.767552i | ||||
\(791\) | −2.53119 | −0.0899986 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.0996i | 1.38847i | ||||||||
\(794\) | −3.02943 | −0.107510 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.77741 | −0.169331 | ||||||||
\(797\) | − | 12.5563i | − | 0.444768i | −0.974959 | − | 0.222384i | \(-0.928616\pi\) | ||
0.974959 | − | 0.222384i | \(-0.0713838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.113194 | −0.00400453 | ||||||||
\(800\) | −9.12327 | − | 5.40369i | −0.322556 | − | 0.191049i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.8432i | 1.44222i | ||||||||
\(803\) | 39.2273i | 1.38430i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.45193 | − | 4.30201i | −0.0864191 | − | 0.151626i | ||||
\(806\) | −20.9162 | −0.736741 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.8359i | 0.873723i | ||||||||
\(809\) | 16.4082 | 0.576883 | 0.288441 | − | 0.957498i | \(-0.406863\pi\) | ||||
0.288441 | + | 0.957498i | \(0.406863\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.4688 | 1.03479 | 0.517394 | − | 0.855747i | \(-0.326902\pi\) | ||||
0.517394 | + | 0.855747i | \(0.326902\pi\) | |||||||
\(812\) | 0.0973162i | 0.00341513i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.8223 | −0.799923 | ||||||||
\(815\) | 5.98385 | − | 3.41049i | 0.209605 | − | 0.119464i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 20.3603i | − | 0.712318i | ||||||
\(818\) | 40.0892i | 1.40169i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.40785 | + | 4.22468i | 0.0840859 | + | 0.147532i | ||||
\(821\) | 28.5209 | 0.995385 | 0.497693 | − | 0.867353i | \(-0.334181\pi\) | ||||
0.497693 | + | 0.867353i | \(0.334181\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 16.7546i | − | 0.584028i | −0.956414 | − | 0.292014i | \(-0.905675\pi\) | ||
0.956414 | − | 0.292014i | \(-0.0943253\pi\) | |||||||
\(824\) | −5.24127 | −0.182588 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.32336 | 0.150429 | ||||||||
\(827\) | 3.38369i | 0.117662i | 0.998268 | + | 0.0588312i | \(0.0187374\pi\) | ||||
−0.998268 | + | 0.0588312i | \(0.981263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.4434 | 0.501639 | 0.250819 | − | 0.968034i | \(-0.419300\pi\) | ||||
0.250819 | + | 0.968034i | \(0.419300\pi\) | |||||||
\(830\) | −10.7165 | − | 18.8025i | −0.371974 | − | 0.652645i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 44.6787i | 1.54896i | ||||||||
\(833\) | − | 2.33309i | − | 0.0808367i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.6103 | − | 9.46702i | 0.574823 | − | 0.327620i | ||||
\(836\) | −5.13814 | −0.177706 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 4.01490i | − | 0.138692i | ||||||
\(839\) | 27.6642 | 0.955075 | 0.477538 | − | 0.878611i | \(-0.341529\pi\) | ||||
0.477538 | + | 0.878611i | \(0.341529\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | − | 15.2246i | − | 0.524675i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.19193 | −0.178714 | ||||||||
\(845\) | 13.5866 | + | 23.8382i | 0.467392 | + | 0.820060i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.68048i | 0.0921024i | ||||||||
\(848\) | 18.6126i | 0.639159i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.09100 | + | 1.84198i | −0.0374210 | + | 0.0631795i | ||||
\(851\) | −33.4969 | −1.14826 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 4.26068i | − | 0.145883i | −0.997336 | − | 0.0729415i | \(-0.976761\pi\) | ||
0.997336 | − | 0.0729415i | \(-0.0232386\pi\) | |||||||
\(854\) | 2.53214 | 0.0866481 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.3260 | −0.558011 | ||||||||
\(857\) | − | 28.7104i | − | 0.980729i | −0.871518 | − | 0.490364i | \(-0.836864\pi\) | ||
0.871518 | − | 0.490364i | \(-0.163136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.3734 | 1.34340 | 0.671701 | − | 0.740822i | \(-0.265564\pi\) | ||||
0.671701 | + | 0.740822i | \(0.265564\pi\) | |||||||
\(860\) | −5.16304 | + | 2.94267i | −0.176058 | + | 0.100344i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.7898i | 1.35525i | ||||||||
\(863\) | 22.1235i | 0.753094i | 0.926398 | + | 0.376547i | \(0.122889\pi\) | ||||
−0.926398 | + | 0.376547i | \(0.877111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.1965 | + | 6.38142i | −0.380692 | + | 0.216975i | ||||
\(866\) | −39.0008 | −1.32530 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 0.318168i | − | 0.0107993i | ||||||
\(869\) | −70.9546 | −2.40697 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −56.6068 | −1.91805 | ||||||||
\(872\) | − | 43.1357i | − | 1.46076i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.1064 | 1.08602 | ||||||||
\(875\) | −0.0477803 | + | 2.85968i | −0.00161527 | + | 0.0966749i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 32.3439i | − | 1.09217i | −0.837728 | − | 0.546087i | \(-0.816117\pi\) | ||
0.837728 | − | 0.546087i | \(-0.183883\pi\) | |||||||
\(878\) | − | 0.913015i | − | 0.0308128i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.8789 | − | 27.8603i | −0.535278 | − | 0.939169i | ||||
\(881\) | −54.6109 | −1.83989 | −0.919944 | − | 0.392051i | \(-0.871766\pi\) | ||||
−0.919944 | + | 0.392051i | \(0.871766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 47.5511i | − | 1.60022i | −0.599852 | − | 0.800111i | \(-0.704774\pi\) | ||
0.599852 | − | 0.800111i | \(-0.295226\pi\) | |||||||
\(884\) | −0.643403 | −0.0216400 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.4436 | −1.15715 | ||||||||
\(887\) | − | 10.4630i | − | 0.351312i | −0.984452 | − | 0.175656i | \(-0.943795\pi\) | ||
0.984452 | − | 0.175656i | \(-0.0562047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.12671 | −0.104866 | ||||||||
\(890\) | −32.2349 | + | 18.3722i | −1.08052 | + | 0.615838i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 5.12504i | − | 0.171599i | ||||||
\(893\) | − | 0.980521i | − | 0.0328119i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.6596 | − | 27.4754i | −0.523442 | − | 0.918402i | ||||
\(896\) | 1.80845 | 0.0604160 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 38.6449i | − | 1.28960i | ||||||
\(899\) | −3.26943 | −0.109042 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.02365 | −0.0674177 | ||||||||
\(902\) | 33.7156i | 1.12261i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29.9747 | −0.996945 | ||||||||
\(905\) | 16.6442 | + | 29.2029i | 0.553271 | + | 0.970738i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.7211i | 0.355989i | 0.984032 | + | 0.177994i | \(0.0569609\pi\) | ||||
−0.984032 | + | 0.177994i | \(0.943039\pi\) | |||||||
\(908\) | − | 0.586980i | − | 0.0194796i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.17934 | − | 1.81206i | 0.105394 | − | 0.0600692i | ||||
\(911\) | −3.57634 | −0.118489 | −0.0592447 | − | 0.998243i | \(-0.518869\pi\) | ||||
−0.0592447 | + | 0.998243i | \(0.518869\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.2461i | 1.16648i | ||||||||
\(914\) | 3.09461 | 0.102361 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.00351 | −0.0992386 | ||||||||
\(917\) | 3.08163i | 0.101765i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.2776 | 0.734870 | 0.367435 | − | 0.930049i | \(-0.380236\pi\) | ||||
0.367435 | + | 0.930049i | \(0.380236\pi\) | |||||||
\(920\) | −29.0362 | − | 50.9452i | −0.957294 | − | 1.67961i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 10.5429i | − | 0.347213i | ||||||
\(923\) | − | 70.2112i | − | 2.31103i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.6468 | + | 9.85986i | 0.547344 | + | 0.324190i | ||||
\(926\) | −8.98035 | −0.295113 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.12070i | 0.0696153i | ||||||||
\(929\) | 21.1779 | 0.694826 | 0.347413 | − | 0.937712i | \(-0.387060\pi\) | ||||
0.347413 | + | 0.937712i | \(0.387060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.2099 | 0.662352 | ||||||||
\(932\) | − | 10.8337i | − | 0.354868i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.72695 | 0.252834 | ||||||||
\(935\) | 3.02911 | − | 1.72644i | 0.0990624 | − | 0.0564605i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 34.4462i | − | 1.12531i | −0.826693 | − | 0.562654i | \(-0.809780\pi\) | ||
0.826693 | − | 0.562654i | \(-0.190220\pi\) | |||||||
\(938\) | 3.66593i | 0.119697i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.248643 | + | 0.141714i | −0.00810986 | + | 0.00462220i | ||||
\(941\) | 0.296167 | 0.00965477 | 0.00482738 | − | 0.999988i | \(-0.498463\pi\) | ||||
0.00482738 | + | 0.999988i | \(0.498463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.4851i | 1.61146i | ||||||||
\(944\) | 41.0940 | 1.33750 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.2042 | −1.33966 | ||||||||
\(947\) | − | 46.9467i | − | 1.52556i | −0.646656 | − | 0.762782i | \(-0.723833\pi\) | ||
0.646656 | − | 0.762782i | \(-0.276167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.5498 | −1.38123 | ||||||||
\(950\) | −15.9558 | − | 9.45057i | −0.517674 | − | 0.306617i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.260730i | 0.00845029i | ||||||||
\(953\) | − | 1.91375i | − | 0.0619926i | −0.999519 | − | 0.0309963i | \(-0.990132\pi\) | ||
0.999519 | − | 0.0309963i | \(-0.00986801\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.5784 | − | 23.8239i | −0.439386 | − | 0.770923i | ||||
\(956\) | 3.38005 | 0.109319 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 37.8829i | − | 1.22394i | ||||||
\(959\) | 1.40061 | 0.0452280 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.3108 | −0.655188 | ||||||||
\(962\) | − | 24.7554i | − | 0.798145i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.3707 | −0.366227 | ||||||||
\(965\) | −16.2060 | + | 9.23656i | −0.521688 | + | 0.297335i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.01326i | 0.129058i | 0.997916 | + | 0.0645288i | \(0.0205544\pi\) | ||||
−0.997916 | + | 0.0645288i | \(0.979446\pi\) | |||||||
\(968\) | 31.7427i | 1.02025i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.2672 | + | 28.5416i | 0.522309 | + | 0.916414i | ||||
\(971\) | −4.54751 | −0.145937 | −0.0729683 | − | 0.997334i | \(-0.523247\pi\) | ||||
−0.0729683 | + | 0.997334i | \(0.523247\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 0.694284i | − | 0.0222577i | ||||||
\(974\) | 53.3295 | 1.70879 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.0683 | 0.770409 | ||||||||
\(977\) | 44.2333i | 1.41515i | 0.706639 | + | 0.707574i | \(0.250211\pi\) | ||||
−0.706639 | + | 0.707574i | \(0.749789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60.4256 | 1.93121 | ||||||||
\(980\) | −2.92092 | − | 5.12488i | −0.0933053 | − | 0.163708i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.19391i | 0.293389i | ||||||||
\(983\) | − | 34.2083i | − | 1.09107i | −0.838087 | − | 0.545537i | \(-0.816326\pi\) | ||
0.838087 | − | 0.545537i | \(-0.183674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0017 | − | 7.41030i | 0.414269 | − | 0.236112i | ||||
\(986\) | 0.428167 | 0.0136356 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 5.57334i | − | 0.177312i | ||||||
\(989\) | −60.4764 | −1.92304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.76770 | −0.0561528 | −0.0280764 | − | 0.999606i | \(-0.508938\pi\) | ||||
−0.0280764 | + | 0.999606i | \(0.508938\pi\) | |||||||
\(992\) | − | 6.93347i | − | 0.220138i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.54697 | −0.144221 | ||||||||
\(995\) | 13.9050 | + | 24.3969i | 0.440817 | + | 0.773433i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.7398i | 0.751848i | 0.926650 | + | 0.375924i | \(0.122675\pi\) | ||||
−0.926650 | + | 0.375924i | \(0.877325\pi\) | |||||||
\(998\) | 19.8030i | 0.626853i | ||||||||
\(999\) | 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 | 1305.2.c.l.784.8 | yes | 12 | |
3.2 | odd | 2 | 1305.2.c.k.784.5 | ✓ | 12 | ||
5.2 | odd | 4 | 6525.2.a.cf.1.5 | 12 | |||
5.3 | odd | 4 | 6525.2.a.cf.1.8 | 12 | |||
5.4 | even | 2 | inner | 1305.2.c.l.784.5 | yes | 12 | |
15.2 | even | 4 | 6525.2.a.ce.1.8 | 12 | |||
15.8 | even | 4 | 6525.2.a.ce.1.5 | 12 | |||
15.14 | odd | 2 | 1305.2.c.k.784.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1305.2.c.k.784.5 | ✓ | 12 | 3.2 | odd | 2 | ||
1305.2.c.k.784.8 | yes | 12 | 15.14 | odd | 2 | ||
1305.2.c.l.784.5 | yes | 12 | 5.4 | even | 2 | inner | |
1305.2.c.l.784.8 | yes | 12 | 1.1 | even | 1 | trivial | |
6525.2.a.ce.1.5 | 12 | 15.8 | even | 4 | |||
6525.2.a.ce.1.8 | 12 | 15.2 | even | 4 | |||
6525.2.a.cf.1.5 | 12 | 5.2 | odd | 4 | |||
6525.2.a.cf.1.8 | 12 | 5.3 | odd | 4 |