Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.12 | ||
Root | \(0.156434 + 0.987688i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.d.757.9 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.437016 | + | 1.34500i | 0.309017 | + | 0.951057i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61803 | + | 1.17557i | −0.809017 | + | 0.587785i | ||||
\(5\) | 4.29757i | 1.92193i | 0.276666 | + | 0.960966i | \(0.410770\pi\) | ||||
−0.276666 | + | 0.960966i | \(0.589230\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.28825 | − | 1.66251i | −0.809017 | − | 0.587785i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.78022 | + | 1.87811i | −1.82787 | + | 0.593910i | ||||
\(11\) | 1.60758i | 0.484703i | 0.970189 | + | 0.242351i | \(0.0779187\pi\) | ||||
−0.970189 | + | 0.242351i | \(0.922081\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.02967i | 1.67233i | 0.548478 | + | 0.836165i | \(0.315208\pi\) | ||||
−0.548478 | + | 0.836165i | \(0.684792\pi\) | |||||||
\(14\) | −0.437016 | − | 1.34500i | −0.116797 | − | 0.359466i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | − | 3.80423i | 0.309017 | − | 0.951057i | ||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.07768i | 0.706069i | 0.935610 | + | 0.353035i | \(0.114850\pi\) | ||||
−0.935610 | + | 0.353035i | \(0.885150\pi\) | |||||||
\(20\) | −5.05210 | − | 6.95362i | −1.12968 | − | 1.55488i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.16219 | + | 0.702537i | −0.460980 | + | 0.149781i | ||||
\(23\) | 5.95080 | 1.24083 | 0.620413 | − | 0.784275i | \(-0.286965\pi\) | ||||
0.620413 | + | 0.784275i | \(0.286965\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.4691 | −2.69382 | ||||||||
\(26\) | −8.10989 | + | 2.63506i | −1.59048 | + | 0.516778i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.61803 | − | 1.17557i | 0.305780 | − | 0.222162i | ||||
\(29\) | − | 3.53972i | − | 0.657310i | −0.944450 | − | 0.328655i | \(-0.893405\pi\) | ||
0.944450 | − | 0.328655i | \(-0.106595\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.08831 | −0.375071 | −0.187535 | − | 0.982258i | \(-0.560050\pi\) | ||||
−0.187535 | + | 0.982258i | \(0.560050\pi\) | |||||||
\(32\) | 5.65685 | 1.00000 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.38197 | + | 4.25325i | 0.237005 | + | 0.729427i | ||||
\(35\) | − | 4.29757i | − | 0.726422i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.48276i | 0.736961i | 0.929636 | + | 0.368480i | \(0.120122\pi\) | ||||
−0.929636 | + | 0.368480i | \(0.879878\pi\) | |||||||
\(38\) | −4.13948 | + | 1.34500i | −0.671512 | + | 0.218187i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.14475 | − | 9.83390i | 1.12968 | − | 1.55488i | ||||
\(41\) | −6.69568 | −1.04569 | −0.522845 | − | 0.852428i | \(-0.675129\pi\) | ||||
−0.522845 | + | 0.852428i | \(0.675129\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.2811i | − | 1.87284i | −0.350875 | − | 0.936422i | \(-0.614116\pi\) | ||
0.350875 | − | 0.936422i | \(-0.385884\pi\) | |||||||
\(44\) | −1.88982 | − | 2.60111i | −0.284901 | − | 0.392133i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.60059 | + | 8.00380i | 0.383437 | + | 1.18010i | ||||
\(47\) | 3.82734 | 0.558275 | 0.279138 | − | 0.960251i | \(-0.409951\pi\) | ||||
0.279138 | + | 0.960251i | \(0.409951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.88622 | − | 18.1159i | −0.832437 | − | 2.56198i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.08831 | − | 9.75621i | −0.982971 | − | 1.35294i | ||||
\(53\) | − | 8.63711i | − | 1.18640i | −0.805056 | − | 0.593199i | \(-0.797865\pi\) | ||
0.805056 | − | 0.593199i | \(-0.202135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.90868 | −0.931566 | ||||||||
\(56\) | 2.28825 | + | 1.66251i | 0.305780 | + | 0.222162i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.76091 | − | 1.54691i | 0.625139 | − | 0.203120i | ||||
\(59\) | − | 1.55265i | − | 0.202137i | −0.994879 | − | 0.101069i | \(-0.967774\pi\) | ||
0.994879 | − | 0.101069i | \(-0.0322262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.64886i | 0.467189i | 0.972334 | + | 0.233594i | \(0.0750487\pi\) | ||||
−0.972334 | + | 0.233594i | \(0.924951\pi\) | |||||||
\(62\) | −0.912623 | − | 2.80876i | −0.115903 | − | 0.356713i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.47214 | + | 7.60845i | 0.309017 | + | 0.951057i | ||||
\(65\) | −25.9129 | −3.21411 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.772361i | 0.0943590i | 0.998886 | + | 0.0471795i | \(0.0150233\pi\) | ||||
−0.998886 | + | 0.0471795i | \(0.984977\pi\) | |||||||
\(68\) | −5.11667 | + | 3.71748i | −0.620488 | + | 0.450811i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.78022 | − | 1.87811i | 0.690868 | − | 0.224477i | ||||
\(71\) | 7.36501 | 0.874066 | 0.437033 | − | 0.899446i | \(-0.356029\pi\) | ||||
0.437033 | + | 0.899446i | \(0.356029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.32739 | 0.155359 | 0.0776797 | − | 0.996978i | \(-0.475249\pi\) | ||||
0.0776797 | + | 0.996978i | \(0.475249\pi\) | |||||||
\(74\) | −6.02930 | + | 1.95904i | −0.700891 | + | 0.227733i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.61803 | − | 4.97980i | −0.415017 | − | 0.571222i | ||||
\(77\) | − | 1.60758i | − | 0.183200i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7401 | 1.43337 | 0.716685 | − | 0.697397i | \(-0.245659\pi\) | ||||
0.716685 | + | 0.697397i | \(0.245659\pi\) | |||||||
\(80\) | 16.3489 | + | 5.31209i | 1.82787 | + | 0.593910i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.92612 | − | 9.00567i | −0.323136 | − | 0.994510i | ||||
\(83\) | 7.08446i | 0.777620i | 0.921318 | + | 0.388810i | \(0.127114\pi\) | ||||
−0.921318 | + | 0.388810i | \(0.872886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.5901i | 1.47405i | ||||||||
\(86\) | 16.5180 | − | 5.36702i | 1.78118 | − | 0.578741i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.67261 | − | 3.67853i | 0.284901 | − | 0.392133i | ||||
\(89\) | 9.73307 | 1.03170 | 0.515852 | − | 0.856678i | \(-0.327475\pi\) | ||||
0.515852 | + | 0.856678i | \(0.327475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.02967i | − | 0.632081i | ||||||
\(92\) | −9.62859 | + | 6.99558i | −1.00385 | + | 0.729340i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.67261 | + | 5.14776i | 0.172517 | + | 0.530951i | ||||
\(95\) | −13.2266 | −1.35702 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1803 | −1.03366 | −0.516828 | − | 0.856089i | \(-0.672887\pi\) | ||||
−0.516828 | + | 0.856089i | \(0.672887\pi\) | |||||||
\(98\) | 0.437016 | + | 1.34500i | 0.0441453 | + | 0.135865i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 21.7935 | − | 15.8339i | 2.17935 | − | 1.58339i | ||||
\(101\) | 1.02749i | 0.102239i | 0.998693 | + | 0.0511194i | \(0.0162789\pi\) | ||||
−0.998693 | + | 0.0511194i | \(0.983721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.965118 | −0.0950959 | −0.0475479 | − | 0.998869i | \(-0.515141\pi\) | ||||
−0.0475479 | + | 0.998869i | \(0.515141\pi\) | |||||||
\(104\) | 10.0244 | − | 13.7974i | 0.982971 | − | 1.35294i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.6169 | − | 3.77455i | 1.12833 | − | 0.366617i | ||||
\(107\) | − | 16.0949i | − | 1.55595i | −0.628294 | − | 0.777976i | \(-0.716246\pi\) | ||
0.628294 | − | 0.777976i | \(-0.283754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.2686i | 1.94138i | 0.240327 | + | 0.970692i | \(0.422745\pi\) | ||||
−0.240327 | + | 0.970692i | \(0.577255\pi\) | |||||||
\(110\) | −3.01920 | − | 9.29215i | −0.287870 | − | 0.885972i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.23607 | + | 3.80423i | −0.116797 | + | 0.359466i | ||||
\(113\) | −0.951214 | −0.0894826 | −0.0447413 | − | 0.998999i | \(-0.514246\pi\) | ||||
−0.0447413 | + | 0.998999i | \(0.514246\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.5740i | 2.38478i | ||||||||
\(116\) | 4.16119 | + | 5.72739i | 0.386357 | + | 0.531775i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.08831 | − | 0.678531i | 0.192244 | − | 0.0624639i | ||||
\(119\) | −3.16228 | −0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.41570 | 0.765063 | ||||||||
\(122\) | −4.90770 | + | 1.59461i | −0.444323 | + | 0.144369i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.37895 | − | 2.45495i | 0.303439 | − | 0.220461i | ||||
\(125\) | − | 36.3966i | − | 3.25541i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6132 | −1.03050 | −0.515250 | − | 0.857040i | \(-0.672301\pi\) | ||||
−0.515250 | + | 0.857040i | \(0.672301\pi\) | |||||||
\(128\) | −9.15298 | + | 6.65003i | −0.809017 | + | 0.587785i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.3244 | − | 34.8528i | −0.993213 | − | 3.05680i | ||||
\(131\) | 10.0120i | 0.874752i | 0.899279 | + | 0.437376i | \(0.144092\pi\) | ||||
−0.899279 | + | 0.437376i | \(0.855908\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.07768i | − | 0.266869i | ||||||
\(134\) | −1.03882 | + | 0.337534i | −0.0897407 | + | 0.0291585i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.23607 | − | 5.25731i | −0.620488 | − | 0.450811i | ||||
\(137\) | −8.40383 | −0.717988 | −0.358994 | − | 0.933340i | \(-0.616880\pi\) | ||||
−0.358994 | + | 0.933340i | \(0.616880\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.61437i | − | 0.561024i | −0.959851 | − | 0.280512i | \(-0.909496\pi\) | ||
0.959851 | − | 0.280512i | \(-0.0905042\pi\) | |||||||
\(140\) | 5.05210 | + | 6.95362i | 0.426980 | + | 0.587688i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.21863 | + | 9.90592i | 0.270101 | + | 0.831286i | ||||
\(143\) | −9.69316 | −0.810583 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2122 | 1.26330 | ||||||||
\(146\) | 0.580091 | + | 1.78534i | 0.0480087 | + | 0.147755i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.26980 | − | 7.25325i | −0.433175 | − | 0.596214i | ||||
\(149\) | − | 16.9866i | − | 1.39160i | −0.718238 | − | 0.695798i | \(-0.755051\pi\) | ||
0.718238 | − | 0.695798i | \(-0.244949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5256 | −0.937937 | −0.468968 | − | 0.883215i | \(-0.655374\pi\) | ||||
−0.468968 | + | 0.883215i | \(0.655374\pi\) | |||||||
\(152\) | 5.11667 | − | 7.04250i | 0.415017 | − | 0.571222i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.16219 | − | 0.702537i | 0.174234 | − | 0.0566120i | ||||
\(155\) | − | 8.97464i | − | 0.720860i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.3889i | − | 0.829127i | −0.910020 | − | 0.414563i | \(-0.863934\pi\) | ||
0.910020 | − | 0.414563i | \(-0.136066\pi\) | |||||||
\(158\) | 5.56761 | + | 17.1354i | 0.442936 | + | 1.36322i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 24.3107i | 1.92193i | ||||||||
\(161\) | −5.95080 | −0.468988 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8743i | 0.930067i | 0.885293 | + | 0.465034i | \(0.153958\pi\) | ||||
−0.885293 | + | 0.465034i | \(0.846042\pi\) | |||||||
\(164\) | 10.8338 | − | 7.87124i | 0.845980 | − | 0.614641i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.52858 | + | 3.09602i | −0.739561 | + | 0.240298i | ||||
\(167\) | 15.0596 | 1.16535 | 0.582673 | − | 0.812706i | \(-0.302007\pi\) | ||||
0.582673 | + | 0.812706i | \(0.302007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.3570 | −1.79669 | ||||||||
\(170\) | −18.2787 | + | 5.93910i | −1.40191 | + | 0.455508i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.4373 | + | 19.8712i | 1.10083 | + | 1.51516i | ||||
\(173\) | 23.7854i | 1.80837i | 0.427142 | + | 0.904185i | \(0.359521\pi\) | ||||
−0.427142 | + | 0.904185i | \(0.640479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.4691 | 1.01817 | ||||||||
\(176\) | 6.11559 | + | 1.98707i | 0.460980 | + | 0.149781i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.25351 | + | 13.0910i | 0.318814 | + | 0.981209i | ||||
\(179\) | 22.1919i | 1.65870i | 0.558728 | + | 0.829351i | \(0.311290\pi\) | ||||
−0.558728 | + | 0.829351i | \(0.688710\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.60253i | 0.639421i | 0.947515 | + | 0.319711i | \(0.103586\pi\) | ||||
−0.947515 | + | 0.319711i | \(0.896414\pi\) | |||||||
\(182\) | 8.10989 | − | 2.63506i | 0.601145 | − | 0.195324i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.6169 | − | 9.89324i | −1.00385 | − | 0.729340i | ||||
\(185\) | −19.2650 | −1.41639 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.08361i | 0.371750i | ||||||||
\(188\) | −6.19277 | + | 4.49931i | −0.451654 | + | 0.328146i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.78022 | − | 17.7897i | −0.419341 | − | 1.29060i | ||||
\(191\) | −8.72989 | −0.631673 | −0.315836 | − | 0.948814i | \(-0.602285\pi\) | ||||
−0.315836 | + | 0.948814i | \(0.602285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8708 | −0.926459 | −0.463229 | − | 0.886238i | \(-0.653309\pi\) | ||||
−0.463229 | + | 0.886238i | \(0.653309\pi\) | |||||||
\(194\) | −4.44897 | − | 13.6925i | −0.319418 | − | 0.983066i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.61803 | + | 1.17557i | −0.115574 | + | 0.0839693i | ||||
\(197\) | 22.4345i | 1.59839i | 0.601072 | + | 0.799195i | \(0.294741\pi\) | ||||
−0.601072 | + | 0.799195i | \(0.705259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.9799 | −1.06189 | −0.530947 | − | 0.847405i | \(-0.678164\pi\) | ||||
−0.530947 | + | 0.847405i | \(0.678164\pi\) | |||||||
\(200\) | 30.8207 | + | 22.3925i | 2.17935 | + | 1.58339i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.38197 | + | 0.449028i | −0.0972348 | + | 0.0315935i | ||||
\(203\) | 3.53972i | 0.248440i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 28.7752i | − | 2.00974i | ||||||
\(206\) | −0.421772 | − | 1.29808i | −0.0293862 | − | 0.0904416i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.9382 | + | 7.45309i | 1.59048 | + | 0.516778i | ||||
\(209\) | −4.94761 | −0.342234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.50651i | 0.585612i | 0.956172 | + | 0.292806i | \(0.0945890\pi\) | ||||
−0.956172 | + | 0.292806i | \(0.905411\pi\) | |||||||
\(212\) | 10.1535 | + | 13.9751i | 0.697347 | + | 0.959816i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.6476 | − | 7.03373i | 1.47980 | − | 0.480816i | ||||
\(215\) | 52.7787 | 3.59948 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.08831 | 0.141763 | ||||||||
\(218\) | −27.2613 | + | 8.85772i | −1.84637 | + | 0.599921i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.1785 | − | 8.12164i | 0.753653 | − | 0.547561i | ||||
\(221\) | 19.0675i | 1.28262i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.3214 | 1.09296 | 0.546479 | − | 0.837473i | \(-0.315968\pi\) | ||||
0.546479 | + | 0.837473i | \(0.315968\pi\) | |||||||
\(224\) | −5.65685 | −0.377964 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.415696 | − | 1.27938i | −0.0276517 | − | 0.0851031i | ||||
\(227\) | − | 10.8279i | − | 0.718671i | −0.933208 | − | 0.359336i | \(-0.883003\pi\) | ||
0.933208 | − | 0.359336i | \(-0.116997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.9251i | − | 1.64710i | −0.567245 | − | 0.823549i | \(-0.691991\pi\) | ||
0.567245 | − | 0.823549i | \(-0.308009\pi\) | |||||||
\(230\) | −34.3969 | + | 11.1762i | −2.26807 | + | 0.736939i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.88481 | + | 8.09975i | −0.386357 | + | 0.531775i | ||||
\(233\) | −13.5950 | −0.890641 | −0.445321 | − | 0.895371i | \(-0.646910\pi\) | ||||
−0.445321 | + | 0.895371i | \(0.646910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.4483i | 1.07297i | ||||||||
\(236\) | 1.82525 | + | 2.51224i | 0.118813 | + | 0.163533i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.38197 | − | 4.25325i | −0.0895796 | − | 0.275698i | ||||
\(239\) | 3.82998 | 0.247741 | 0.123870 | − | 0.992298i | \(-0.460469\pi\) | ||||
0.123870 | + | 0.992298i | \(0.460469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.32509 | 0.343019 | 0.171509 | − | 0.985182i | \(-0.445136\pi\) | ||||
0.171509 | + | 0.985182i | \(0.445136\pi\) | |||||||
\(242\) | 3.67779 | + | 11.3191i | 0.236418 | + | 0.727618i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.28949 | − | 5.90398i | −0.274607 | − | 0.377963i | ||||
\(245\) | 4.29757i | 0.274562i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.5574 | −1.18078 | ||||||||
\(248\) | 4.77856 | + | 3.47182i | 0.303439 | + | 0.220461i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 48.9534 | − | 15.9059i | 3.09608 | − | 1.00598i | ||||
\(251\) | 19.2193i | 1.21311i | 0.795040 | + | 0.606556i | \(0.207450\pi\) | ||||
−0.795040 | + | 0.606556i | \(0.792550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.56636i | 0.601432i | ||||||||
\(254\) | −5.07513 | − | 15.6197i | −0.318442 | − | 0.980064i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(257\) | 0.655642 | 0.0408979 | 0.0204489 | − | 0.999791i | \(-0.493490\pi\) | ||||
0.0204489 | + | 0.999791i | \(0.493490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.48276i | − | 0.278545i | ||||||
\(260\) | 41.9280 | − | 30.4625i | 2.60027 | − | 1.88920i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.4661 | + | 4.37540i | −0.831939 | + | 0.270313i | ||||
\(263\) | 25.8211 | 1.59220 | 0.796098 | − | 0.605168i | \(-0.206894\pi\) | ||||
0.796098 | + | 0.605168i | \(0.206894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.1186 | 2.28018 | ||||||||
\(266\) | 4.13948 | − | 1.34500i | 0.253808 | − | 0.0824671i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.907965 | − | 1.24971i | −0.0554628 | − | 0.0763380i | ||||
\(269\) | − | 14.2078i | − | 0.866266i | −0.901330 | − | 0.433133i | \(-0.857408\pi\) | ||
0.901330 | − | 0.433133i | \(-0.142592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.52786 | 0.214302 | 0.107151 | − | 0.994243i | \(-0.465827\pi\) | ||||
0.107151 | + | 0.994243i | \(0.465827\pi\) | |||||||
\(272\) | 3.90879 | − | 12.0300i | 0.237005 | − | 0.729427i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.67261 | − | 11.3031i | −0.221870 | − | 0.682847i | ||||
\(275\) | − | 21.6526i | − | 1.30570i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9396i | 0.837548i | 0.908091 | + | 0.418774i | \(0.137540\pi\) | ||||
−0.908091 | + | 0.418774i | \(0.862460\pi\) | |||||||
\(278\) | 8.89631 | − | 2.89059i | 0.533565 | − | 0.173366i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.14475 | + | 9.83390i | −0.426980 | + | 0.587688i | ||||
\(281\) | 20.4105 | 1.21759 | 0.608793 | − | 0.793329i | \(-0.291654\pi\) | ||||
0.608793 | + | 0.793329i | \(0.291654\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.6867i | 1.76469i | 0.470600 | + | 0.882347i | \(0.344037\pi\) | ||||
−0.470600 | + | 0.882347i | \(0.655963\pi\) | |||||||
\(284\) | −11.9168 | + | 8.65809i | −0.707134 | + | 0.513763i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.23607 | − | 13.0373i | −0.250484 | − | 0.770910i | ||||
\(287\) | 6.69568 | 0.395233 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 6.64798 | + | 20.4604i | 0.390383 | + | 1.20147i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.14776 | + | 1.56044i | −0.125688 | + | 0.0913179i | ||||
\(293\) | 16.4504i | 0.961044i | 0.876983 | + | 0.480522i | \(0.159553\pi\) | ||||
−0.876983 | + | 0.480522i | \(0.840447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.67261 | 0.388494 | ||||||||
\(296\) | 7.45262 | − | 10.2577i | 0.433175 | − | 0.596214i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.8469 | − | 7.42341i | 1.32349 | − | 0.430027i | ||||
\(299\) | 35.8813i | 2.07507i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2811i | 0.707869i | ||||||||
\(302\) | −5.03685 | − | 15.5018i | −0.289838 | − | 0.892031i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.7082 | + | 3.80423i | 0.671512 | + | 0.218187i | ||||
\(305\) | −15.6812 | −0.897905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.8393i | − | 1.13229i | −0.824306 | − | 0.566145i | \(-0.808434\pi\) | ||
0.824306 | − | 0.566145i | \(-0.191566\pi\) | |||||||
\(308\) | 1.88982 | + | 2.60111i | 0.107683 | + | 0.148212i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.0709 | − | 3.92206i | 0.685579 | − | 0.222758i | ||||
\(311\) | 32.3919 | 1.83677 | 0.918387 | − | 0.395683i | \(-0.129492\pi\) | ||||
0.918387 | + | 0.395683i | \(0.129492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.02156 | −0.340359 | −0.170179 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170179 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(314\) | 13.9731 | − | 4.54013i | 0.788546 | − | 0.256214i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.6139 | + | 14.9768i | −1.15962 | + | 0.842514i | ||||
\(317\) | 5.23318i | 0.293925i | 0.989142 | + | 0.146962i | \(0.0469496\pi\) | ||||
−0.989142 | + | 0.146962i | \(0.953050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.69038 | 0.318600 | ||||||||
\(320\) | −32.6979 | + | 10.6242i | −1.82787 | + | 0.593910i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.60059 | − | 8.00380i | −0.144925 | − | 0.446034i | ||||
\(323\) | 9.73249i | 0.541530i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 81.2144i | − | 4.50496i | ||||||
\(326\) | −15.9709 | + | 5.18926i | −0.884547 | + | 0.287407i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.3214 | + | 11.1316i | 0.845980 | + | 0.614641i | ||||
\(329\) | −3.82734 | −0.211008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5740i | 0.910988i | 0.890239 | + | 0.455494i | \(0.150537\pi\) | ||||
−0.890239 | + | 0.455494i | \(0.849463\pi\) | |||||||
\(332\) | −8.32828 | − | 11.4629i | −0.457074 | − | 0.629108i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.58129 | + | 20.2551i | 0.360112 | + | 1.10831i | ||||
\(335\) | −3.31928 | −0.181352 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.70020 | 0.0926159 | 0.0463080 | − | 0.998927i | \(-0.485254\pi\) | ||||
0.0463080 | + | 0.998927i | \(0.485254\pi\) | |||||||
\(338\) | −10.2074 | − | 31.4150i | −0.555207 | − | 1.70875i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.9761 | − | 21.9893i | −0.866428 | − | 1.19254i | ||||
\(341\) | − | 3.35711i | − | 0.181798i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −20.4174 | + | 28.1021i | −1.10083 | + | 1.51516i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.9913 | + | 10.3946i | −1.71986 | + | 0.558817i | ||||
\(347\) | − | 24.0032i | − | 1.28856i | −0.764790 | − | 0.644279i | \(-0.777157\pi\) | ||
0.764790 | − | 0.644279i | \(-0.222843\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 21.3679i | − | 1.14380i | −0.820324 | − | 0.571898i | \(-0.806207\pi\) | ||
0.820324 | − | 0.571898i | \(-0.193793\pi\) | |||||||
\(350\) | 5.88622 | + | 18.1159i | 0.314632 | + | 0.968337i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.09383i | 0.484703i | ||||||||
\(353\) | 25.1560 | 1.33892 | 0.669460 | − | 0.742849i | \(-0.266526\pi\) | ||||
0.669460 | + | 0.742849i | \(0.266526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.6517i | 1.67990i | ||||||||
\(356\) | −15.7484 | + | 11.4419i | −0.834666 | + | 0.606420i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.8481 | + | 9.69822i | −1.57752 | + | 0.512567i | ||||
\(359\) | −18.1318 | −0.956957 | −0.478479 | − | 0.878099i | \(-0.658812\pi\) | ||||
−0.478479 | + | 0.878099i | \(0.658812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.52786 | 0.501467 | ||||||||
\(362\) | −11.5704 | + | 3.75944i | −0.608126 | + | 0.197592i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.08831 | + | 9.75621i | 0.371528 | + | 0.511365i | ||||
\(365\) | 5.70456i | 0.298590i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.6249 | −1.54641 | −0.773203 | − | 0.634158i | \(-0.781347\pi\) | ||||
−0.773203 | + | 0.634158i | \(0.781347\pi\) | |||||||
\(368\) | 7.35559 | − | 22.6382i | 0.383437 | − | 1.18010i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.41910 | − | 25.9113i | −0.437688 | − | 1.34707i | ||||
\(371\) | 8.63711i | 0.448416i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3696i | 1.52070i | 0.649514 | + | 0.760349i | \(0.274972\pi\) | ||||
−0.649514 | + | 0.760349i | \(0.725028\pi\) | |||||||
\(374\) | −6.83743 | + | 2.22162i | −0.353555 | + | 0.114877i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.75790 | − | 6.36298i | −0.451654 | − | 0.328146i | ||||
\(377\) | 21.3434 | 1.09924 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.1375i | − | 0.828930i | −0.910065 | − | 0.414465i | \(-0.863969\pi\) | ||
0.910065 | − | 0.414465i | \(-0.136031\pi\) | |||||||
\(380\) | 21.4010 | − | 15.5488i | 1.09785 | − | 0.797634i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.81510 | − | 11.7417i | −0.195198 | − | 0.600757i | ||||
\(383\) | 21.9227 | 1.12020 | 0.560099 | − | 0.828426i | \(-0.310763\pi\) | ||||
0.560099 | + | 0.828426i | \(0.310763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.90868 | 0.352099 | ||||||||
\(386\) | −5.62474 | − | 17.3112i | −0.286292 | − | 0.881115i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.4721 | − | 11.9677i | 0.836246 | − | 0.607568i | ||||
\(389\) | − | 27.7725i | − | 1.40812i | −0.710140 | − | 0.704061i | \(-0.751368\pi\) | ||
0.710140 | − | 0.704061i | \(-0.248632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.8181 | 0.951671 | ||||||||
\(392\) | −2.28825 | − | 1.66251i | −0.115574 | − | 0.0839693i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −30.1743 | + | 9.80423i | −1.52016 | + | 0.493930i | ||||
\(395\) | 54.7514i | 2.75484i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.6193i | 1.38617i | 0.720855 | + | 0.693086i | \(0.243749\pi\) | ||||
−0.720855 | + | 0.693086i | \(0.756251\pi\) | |||||||
\(398\) | −6.54644 | − | 20.1479i | −0.328143 | − | 1.00992i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.6487 | + | 51.2396i | −0.832437 | + | 2.56198i | ||||
\(401\) | 10.4439 | 0.521546 | 0.260773 | − | 0.965400i | \(-0.416023\pi\) | ||||
0.260773 | + | 0.965400i | \(0.416023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.5918i | − | 0.627242i | ||||||
\(404\) | −1.20788 | − | 1.66251i | −0.0600944 | − | 0.0827129i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.76091 | + | 1.54691i | −0.236280 | + | 0.0767721i | ||||
\(407\) | −7.20638 | −0.357207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1424 | 0.748745 | 0.374373 | − | 0.927278i | \(-0.377858\pi\) | ||||
0.374373 | + | 0.927278i | \(0.377858\pi\) | |||||||
\(410\) | 38.7025 | − | 12.5752i | 1.91138 | − | 0.621045i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.56159 | − | 1.13456i | 0.0769342 | − | 0.0558960i | ||||
\(413\) | 1.55265i | 0.0764007i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.4460 | −1.49453 | ||||||||
\(416\) | 34.1090i | 1.67233i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.16219 | − | 6.65453i | −0.105756 | − | 0.325484i | ||||
\(419\) | − | 19.9623i | − | 0.975222i | −0.873061 | − | 0.487611i | \(-0.837869\pi\) | ||
0.873061 | − | 0.487611i | \(-0.162131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.8339i | 0.625486i | 0.949838 | + | 0.312743i | \(0.101248\pi\) | ||||
−0.949838 | + | 0.312743i | \(0.898752\pi\) | |||||||
\(422\) | −11.4412 | + | 3.71748i | −0.556950 | + | 0.180964i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.3593 | + | 19.7638i | −0.697347 | + | 0.959816i | ||||
\(425\) | −42.5931 | −2.06607 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.64886i | − | 0.176581i | ||||||
\(428\) | 18.9207 | + | 26.0421i | 0.914566 | + | 1.25879i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.0652 | + | 70.9872i | 1.11230 | + | 3.42331i | ||||
\(431\) | −2.66364 | −0.128303 | −0.0641514 | − | 0.997940i | \(-0.520434\pi\) | ||||
−0.0641514 | + | 0.997940i | \(0.520434\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.2122 | −0.923280 | −0.461640 | − | 0.887067i | \(-0.652739\pi\) | ||||
−0.461640 | + | 0.887067i | \(0.652739\pi\) | |||||||
\(434\) | 0.912623 | + | 2.80876i | 0.0438073 | + | 0.134825i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.8272 | − | 32.7954i | −1.14112 | − | 1.57061i | ||||
\(437\) | 18.3147i | 0.876109i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.1209 | −1.67623 | −0.838114 | − | 0.545495i | \(-0.816342\pi\) | ||||
−0.838114 | + | 0.545495i | \(0.816342\pi\) | |||||||
\(440\) | 15.8088 | + | 11.4857i | 0.753653 | + | 0.547561i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.6457 | + | 8.33280i | −1.21984 | + | 0.396351i | ||||
\(443\) | 8.40943i | 0.399544i | 0.979842 | + | 0.199772i | \(0.0640202\pi\) | ||||
−0.979842 | + | 0.199772i | \(0.935980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.8286i | 1.98286i | ||||||||
\(446\) | 7.13269 | + | 21.9522i | 0.337743 | + | 1.03947i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.47214 | − | 7.60845i | −0.116797 | − | 0.359466i | ||||
\(449\) | −4.81067 | −0.227030 | −0.113515 | − | 0.993536i | \(-0.536211\pi\) | ||||
−0.113515 | + | 0.993536i | \(0.536211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 10.7638i | − | 0.506848i | ||||||
\(452\) | 1.53910 | − | 1.11822i | 0.0723930 | − | 0.0525966i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.5635 | − | 4.73195i | 0.683497 | − | 0.222082i | ||||
\(455\) | 25.9129 | 1.21482 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.8291 | −1.76957 | −0.884785 | − | 0.465999i | \(-0.845695\pi\) | ||||
−0.884785 | + | 0.465999i | \(0.845695\pi\) | |||||||
\(458\) | 33.5242 | − | 10.8927i | 1.56648 | − | 0.508981i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −30.0640 | − | 41.3795i | −1.40174 | − | 1.92933i | ||||
\(461\) | 10.5113i | 0.489558i | 0.969579 | + | 0.244779i | \(0.0787154\pi\) | ||||
−0.969579 | + | 0.244779i | \(0.921285\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.76163 | 0.221292 | 0.110646 | − | 0.993860i | \(-0.464708\pi\) | ||||
0.110646 | + | 0.993860i | \(0.464708\pi\) | |||||||
\(464\) | −13.4659 | − | 4.37534i | −0.625139 | − | 0.203120i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.94125 | − | 18.2853i | −0.275223 | − | 0.847050i | ||||
\(467\) | 19.7216i | 0.912609i | 0.889824 | + | 0.456305i | \(0.150827\pi\) | ||||
−0.889824 | + | 0.456305i | \(0.849173\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.772361i | − | 0.0356643i | ||||||
\(470\) | −22.1229 | + | 7.18816i | −1.02045 | + | 0.331565i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.58129 | + | 3.55284i | −0.118813 | + | 0.163533i | ||||
\(473\) | 19.7428 | 0.907773 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 41.4537i | − | 1.90203i | ||||||
\(476\) | 5.11667 | − | 3.71748i | 0.234522 | − | 0.170390i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.67376 | + | 5.15131i | 0.0765561 | + | 0.235615i | ||||
\(479\) | 2.49558 | 0.114026 | 0.0570131 | − | 0.998373i | \(-0.481842\pi\) | ||||
0.0570131 | + | 0.998373i | \(0.481842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.0296 | −1.23244 | ||||||||
\(482\) | 2.32715 | + | 7.16222i | 0.105999 | + | 0.326230i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.6169 | + | 9.89324i | −0.618949 | + | 0.449693i | ||||
\(485\) | − | 43.7507i | − | 1.98662i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0178 | −0.453951 | −0.226976 | − | 0.973900i | \(-0.572884\pi\) | ||||
−0.226976 | + | 0.973900i | \(0.572884\pi\) | |||||||
\(488\) | 6.06626 | − | 8.34949i | 0.274607 | − | 0.377963i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.78022 | + | 1.87811i | −0.261124 | + | 0.0848442i | ||||
\(491\) | − | 4.23469i | − | 0.191109i | −0.995424 | − | 0.0955544i | \(-0.969538\pi\) | ||
0.995424 | − | 0.0955544i | \(-0.0304624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 11.1936i | − | 0.504134i | ||||||
\(494\) | −8.10989 | − | 24.9597i | −0.364881 | − | 1.12299i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.58129 | + | 7.94438i | −0.115903 | + | 0.356713i | ||||
\(497\) | −7.36501 | −0.330366 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.1176i | 0.452925i | 0.974020 | + | 0.226463i | \(0.0727161\pi\) | ||||
−0.974020 | + | 0.226463i | \(0.927284\pi\) | |||||||
\(500\) | 42.7868 | + | 58.8910i | 1.91348 | + | 2.63369i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.8499 | + | 8.39915i | −1.15374 | + | 0.374873i | ||||
\(503\) | 21.6693 | 0.966186 | 0.483093 | − | 0.875569i | \(-0.339513\pi\) | ||||
0.483093 | + | 0.875569i | \(0.339513\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.41570 | −0.196496 | ||||||||
\(506\) | −12.8667 | + | 4.18065i | −0.571996 | + | 0.185853i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.7905 | − | 13.6521i | 0.833692 | − | 0.605713i | ||||
\(509\) | − | 13.8362i | − | 0.613280i | −0.951826 | − | 0.306640i | \(-0.900795\pi\) | ||
0.951826 | − | 0.306640i | \(-0.0992048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.32739 | −0.0587203 | ||||||||
\(512\) | 6.99226 | − | 21.5200i | 0.309017 | − | 0.951057i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.286526 | + | 0.881837i | 0.0126381 | + | 0.0388962i | ||||
\(515\) | − | 4.14766i | − | 0.182768i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.15275i | 0.270597i | ||||||||
\(518\) | 6.02930 | − | 1.95904i | 0.264912 | − | 0.0860751i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 59.2952 | + | 43.0805i | 2.60027 | + | 1.88920i | ||||
\(521\) | −19.5067 | −0.854603 | −0.427302 | − | 0.904109i | \(-0.640536\pi\) | ||||
−0.427302 | + | 0.904109i | \(0.640536\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.616566i | − | 0.0269606i | −0.999909 | − | 0.0134803i | \(-0.995709\pi\) | ||
0.999909 | − | 0.0134803i | \(-0.00429104\pi\) | |||||||
\(524\) | −11.7698 | − | 16.1997i | −0.514166 | − | 0.707689i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.2842 | + | 34.7293i | 0.492015 | + | 1.51427i | ||||
\(527\) | −6.60380 | −0.287666 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.4120 | 0.539651 | ||||||||
\(530\) | 16.2214 | + | 49.9244i | 0.704613 | + | 2.16858i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.61803 | + | 4.97980i | 0.156862 | + | 0.215902i | ||||
\(533\) | − | 40.3727i | − | 1.74874i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 69.1690 | 2.99044 | ||||||||
\(536\) | 1.28406 | − | 1.76735i | 0.0554628 | − | 0.0763380i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.1095 | − | 6.20905i | 0.823868 | − | 0.267691i | ||||
\(539\) | 1.60758i | 0.0692433i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 33.0638i | − | 1.42152i | −0.703432 | − | 0.710762i | \(-0.748350\pi\) | ||
0.703432 | − | 0.710762i | \(-0.251650\pi\) | |||||||
\(542\) | 1.54173 | + | 4.74497i | 0.0662231 | + | 0.203814i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.8885 | 0.766965 | ||||||||
\(545\) | −87.1059 | −3.73121 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 45.6463i | − | 1.95170i | −0.218450 | − | 0.975848i | \(-0.570100\pi\) | ||
0.218450 | − | 0.975848i | \(-0.429900\pi\) | |||||||
\(548\) | 13.5977 | − | 9.87930i | 0.580864 | − | 0.422023i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 29.1227 | − | 9.46255i | 1.24180 | − | 0.403485i | ||||
\(551\) | 10.8941 | 0.464106 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.7401 | −0.541763 | ||||||||
\(554\) | −18.7487 | + | 6.09182i | −0.796555 | + | 0.258816i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.77566 | + | 10.7023i | 0.329762 | + | 0.453878i | ||||
\(557\) | − | 0.0518694i | − | 0.00219778i | −0.999999 | − | 0.00109889i | \(-0.999650\pi\) | ||
0.999999 | − | 0.00109889i | \(-0.000349787\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 74.0508 | 3.13201 | ||||||||
\(560\) | −16.3489 | − | 5.31209i | −0.690868 | − | 0.224477i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.91970 | + | 27.4520i | 0.376255 | + | 1.15799i | ||||
\(563\) | 10.9105i | 0.459822i | 0.973212 | + | 0.229911i | \(0.0738436\pi\) | ||||
−0.973212 | + | 0.229911i | \(0.926156\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 4.08791i | − | 0.171980i | ||||||
\(566\) | −39.9286 | + | 12.9736i | −1.67832 | + | 0.545320i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.8529 | − | 12.2444i | −0.707134 | − | 0.513763i | ||||
\(569\) | −26.2746 | −1.10149 | −0.550745 | − | 0.834673i | \(-0.685656\pi\) | ||||
−0.550745 | + | 0.834673i | \(0.685656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.4590i | − | 1.02358i | −0.859111 | − | 0.511789i | \(-0.828983\pi\) | ||
0.859111 | − | 0.511789i | \(-0.171017\pi\) | |||||||
\(572\) | 15.6839 | − | 11.3950i | 0.655775 | − | 0.476449i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.92612 | + | 9.00567i | 0.122134 | + | 0.375889i | ||||
\(575\) | −80.1520 | −3.34257 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2538 | −0.426873 | −0.213436 | − | 0.976957i | \(-0.568466\pi\) | ||||
−0.213436 | + | 0.976957i | \(0.568466\pi\) | |||||||
\(578\) | −3.05911 | − | 9.41498i | −0.127242 | − | 0.391612i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24.6139 | + | 17.8830i | −1.02204 | + | 0.742552i | ||||
\(581\) | − | 7.08446i | − | 0.293913i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8848 | 0.575050 | ||||||||
\(584\) | −3.03740 | − | 2.20680i | −0.125688 | − | 0.0913179i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.1258 | + | 7.18910i | −0.914007 | + | 0.296979i | ||||
\(587\) | − | 25.3720i | − | 1.04722i | −0.851959 | − | 0.523608i | \(-0.824586\pi\) | ||
0.851959 | − | 0.523608i | \(-0.175414\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6.42714i | − | 0.264826i | ||||||
\(590\) | 2.91604 | + | 8.97464i | 0.120051 | + | 0.369480i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.0534 | + | 5.54099i | 0.700891 | + | 0.227733i | ||||
\(593\) | 7.14310 | 0.293332 | 0.146666 | − | 0.989186i | \(-0.453146\pi\) | ||||
0.146666 | + | 0.989186i | \(0.453146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 13.5901i | − | 0.557140i | ||||||
\(596\) | 19.9689 | + | 27.4849i | 0.817959 | + | 1.12582i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −48.2603 | + | 15.6807i | −1.97351 | + | 0.641232i | ||||
\(599\) | 3.00175 | 0.122648 | 0.0613242 | − | 0.998118i | \(-0.480468\pi\) | ||||
0.0613242 | + | 0.998118i | \(0.480468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.2516 | 0.866871 | 0.433435 | − | 0.901185i | \(-0.357301\pi\) | ||||
0.433435 | + | 0.901185i | \(0.357301\pi\) | |||||||
\(602\) | −16.5180 | + | 5.36702i | −0.673223 | + | 0.218743i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.6487 | − | 13.5491i | 0.758807 | − | 0.551305i | ||||
\(605\) | 36.1671i | 1.47040i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0614 | 0.976623 | 0.488312 | − | 0.872669i | \(-0.337613\pi\) | ||||
0.488312 | + | 0.872669i | \(0.337613\pi\) | |||||||
\(608\) | 17.4100i | 0.706069i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.85295 | − | 21.0912i | −0.277468 | − | 0.853958i | ||||
\(611\) | 23.0776i | 0.933620i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.9197i | 0.844939i | 0.906377 | + | 0.422469i | \(0.138837\pi\) | ||||
−0.906377 | + | 0.422469i | \(0.861163\pi\) | |||||||
\(614\) | 26.6838 | − | 8.67010i | 1.07687 | − | 0.349897i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.67261 | + | 3.67853i | −0.107683 | + | 0.148212i | ||||
\(617\) | 3.95122 | 0.159070 | 0.0795350 | − | 0.996832i | \(-0.474656\pi\) | ||||
0.0795350 | + | 0.996832i | \(0.474656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23.8651i | − | 0.959220i | −0.877482 | − | 0.479610i | \(-0.840778\pi\) | ||
0.877482 | − | 0.479610i | \(-0.159222\pi\) | |||||||
\(620\) | 10.5503 | + | 14.5213i | 0.423711 | + | 0.583188i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.1558 | + | 43.5670i | 0.567594 | + | 1.74688i | ||||
\(623\) | −9.73307 | −0.389947 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 89.0716 | 3.56286 | ||||||||
\(626\) | −2.63152 | − | 8.09898i | −0.105177 | − | 0.323700i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.2129 | + | 16.8096i | 0.487348 | + | 0.670778i | ||||
\(629\) | 14.1757i | 0.565223i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.3725 | 1.44797 | 0.723983 | − | 0.689818i | \(-0.242310\pi\) | ||||
0.723983 | + | 0.689818i | \(0.242310\pi\) | |||||||
\(632\) | −29.1524 | − | 21.1805i | −1.15962 | − | 0.842514i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.03861 | + | 2.28698i | −0.279539 | + | 0.0908277i | ||||
\(635\) | − | 49.9083i | − | 1.98055i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.02967i | 0.238904i | ||||||||
\(638\) | 2.48679 | + | 7.65354i | 0.0984528 | + | 0.303006i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28.5790 | − | 39.3356i | −1.12968 | − | 1.55488i | ||||
\(641\) | 0.876669 | 0.0346264 | 0.0173132 | − | 0.999850i | \(-0.494489\pi\) | ||||
0.0173132 | + | 0.999850i | \(0.494489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 15.2486i | − | 0.601347i | −0.953727 | − | 0.300674i | \(-0.902789\pi\) | ||
0.953727 | − | 0.300674i | \(-0.0972114\pi\) | |||||||
\(644\) | 9.62859 | − | 6.99558i | 0.379420 | − | 0.275664i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.0902 | + | 4.25325i | −0.515026 | + | 0.167342i | ||||
\(647\) | −9.53027 | −0.374673 | −0.187337 | − | 0.982296i | \(-0.559986\pi\) | ||||
−0.187337 | + | 0.982296i | \(0.559986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.49600 | 0.0979765 | ||||||||
\(650\) | 109.233 | − | 35.4920i | 4.28447 | − | 1.39211i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.9591 | − | 19.2130i | −0.546680 | − | 0.752440i | ||||
\(653\) | − | 9.29496i | − | 0.363740i | −0.983323 | − | 0.181870i | \(-0.941785\pi\) | ||
0.983323 | − | 0.181870i | \(-0.0582150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −43.0273 | −1.68121 | ||||||||
\(656\) | −8.27631 | + | 25.4719i | −0.323136 | + | 0.994510i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.67261 | − | 5.14776i | −0.0652051 | − | 0.200681i | ||||
\(659\) | − | 36.1879i | − | 1.40968i | −0.709366 | − | 0.704841i | \(-0.751018\pi\) | ||
0.709366 | − | 0.704841i | \(-0.248982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 19.8091i | − | 0.770483i | −0.922816 | − | 0.385242i | \(-0.874118\pi\) | ||
0.922816 | − | 0.385242i | \(-0.125882\pi\) | |||||||
\(662\) | −22.2919 | + | 7.24309i | −0.866401 | + | 0.281511i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.7780 | − | 16.2110i | 0.457074 | − | 0.629108i | ||||
\(665\) | 13.2266 | 0.512904 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 21.0642i | − | 0.815607i | ||||||
\(668\) | −24.3669 | + | 17.7036i | −0.942785 | + | 0.684974i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.45058 | − | 4.46442i | −0.0560407 | − | 0.172476i | ||||
\(671\) | −5.86582 | −0.226448 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.186375 | −0.00718421 | −0.00359211 | − | 0.999994i | \(-0.501143\pi\) | ||||
−0.00359211 | + | 0.999994i | \(0.501143\pi\) | |||||||
\(674\) | 0.743016 | + | 2.28677i | 0.0286199 | + | 0.0880830i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 37.7923 | − | 27.4577i | 1.45355 | − | 1.05607i | ||||
\(677\) | − | 3.31885i | − | 0.127554i | −0.997964 | − | 0.0637770i | \(-0.979685\pi\) | ||
0.997964 | − | 0.0637770i | \(-0.0203146\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.1803 | 0.390686 | ||||||||
\(680\) | 22.5937 | − | 31.0975i | 0.866428 | − | 1.19254i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.51531 | − | 1.46711i | 0.172900 | − | 0.0561786i | ||||
\(683\) | − | 17.9992i | − | 0.688720i | −0.938838 | − | 0.344360i | \(-0.888096\pi\) | ||
0.938838 | − | 0.344360i | \(-0.111904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.1161i | − | 1.37992i | ||||||
\(686\) | −0.437016 | − | 1.34500i | −0.0166853 | − | 0.0513522i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −46.7199 | − | 15.1802i | −1.78118 | − | 0.578741i | ||||
\(689\) | 52.0789 | 1.98405 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.67153i | − | 0.139671i | −0.997559 | − | 0.0698357i | \(-0.977752\pi\) | ||
0.997559 | − | 0.0698357i | \(-0.0222475\pi\) | |||||||
\(692\) | −27.9614 | − | 38.4856i | −1.06293 | − | 1.46300i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.2842 | − | 10.4898i | 1.22549 | − | 0.398187i | ||||
\(695\) | 28.4257 | 1.07825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.1736 | −0.802007 | ||||||||
\(698\) | 28.7397 | − | 9.33811i | 1.08782 | − | 0.353453i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −21.7935 | + | 15.8339i | −0.823717 | + | 0.598465i | ||||
\(701\) | − | 7.06843i | − | 0.266971i | −0.991051 | − | 0.133485i | \(-0.957383\pi\) | ||
0.991051 | − | 0.133485i | \(-0.0426169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.7965 | −0.520345 | ||||||||
\(704\) | −12.2312 | + | 3.97415i | −0.460980 | + | 0.149781i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.9936 | + | 33.8348i | 0.413749 | + | 1.27339i | ||||
\(707\) | − | 1.02749i | − | 0.0386426i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.4607i | 0.768417i | 0.923246 | + | 0.384209i | \(0.125526\pi\) | ||||
−0.923246 | + | 0.384209i | \(0.874474\pi\) | |||||||
\(710\) | −42.5714 | + | 13.8323i | −1.59768 | + | 0.519116i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −22.2717 | − | 16.1813i | −0.834666 | − | 0.606420i | ||||
\(713\) | −12.4271 | −0.465398 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 41.6571i | − | 1.55789i | ||||||
\(716\) | −26.0882 | − | 35.9073i | −0.974961 | − | 1.34192i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.92387 | − | 24.3872i | −0.295716 | − | 0.910120i | ||||
\(719\) | −40.5191 | −1.51111 | −0.755554 | − | 0.655087i | \(-0.772632\pi\) | ||||
−0.755554 | + | 0.655087i | \(0.772632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.965118 | 0.0359429 | ||||||||
\(722\) | 4.16383 | + | 12.8149i | 0.154962 | + | 0.476923i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.1129 | − | 13.9192i | −0.375842 | − | 0.517302i | ||||
\(725\) | 47.6769i | 1.77068i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.87078 | 0.254823 | 0.127412 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127412 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(728\) | −10.0244 | + | 13.7974i | −0.371528 | + | 0.511365i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.67261 | + | 2.49298i | −0.283976 | + | 0.0922694i | ||||
\(731\) | − | 38.8361i | − | 1.43641i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.5847i | 0.686442i | 0.939255 | + | 0.343221i | \(0.111518\pi\) | ||||
−0.939255 | + | 0.343221i | \(0.888482\pi\) | |||||||
\(734\) | −12.9465 | − | 39.8454i | −0.477866 | − | 1.47072i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33.6628 | 1.24083 | ||||||||
\(737\) | −1.24163 | −0.0457360 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.69519i | 0.172715i | 0.996264 | + | 0.0863576i | \(0.0275228\pi\) | ||||
−0.996264 | + | 0.0863576i | \(0.972477\pi\) | |||||||
\(740\) | 31.1714 | − | 22.6473i | 1.14588 | − | 0.832532i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.6169 | + | 3.77455i | −0.426469 | + | 0.138568i | ||||
\(743\) | −15.5867 | −0.571821 | −0.285911 | − | 0.958256i | \(-0.592296\pi\) | ||||
−0.285911 | + | 0.958256i | \(0.592296\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 73.0011 | 2.67455 | ||||||||
\(746\) | −39.5020 | + | 12.8350i | −1.44627 | + | 0.469922i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.97614 | − | 8.22545i | −0.218509 | − | 0.300752i | ||||
\(749\) | 16.0949i | 0.588095i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.7401 | −0.683835 | −0.341917 | − | 0.939730i | \(-0.611076\pi\) | ||||
−0.341917 | + | 0.939730i | \(0.611076\pi\) | |||||||
\(752\) | 4.73085 | − | 14.5601i | 0.172517 | − | 0.530951i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.32739 | + | 28.7068i | 0.339684 | + | 1.04544i | ||||
\(755\) | − | 49.5319i | − | 1.80265i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.9095i | 0.905352i | 0.891675 | + | 0.452676i | \(0.149531\pi\) | ||||
−0.891675 | + | 0.452676i | \(0.850469\pi\) | |||||||
\(758\) | 21.7049 | − | 7.05236i | 0.788359 | − | 0.256153i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 30.2656 | + | 21.9893i | 1.09785 | + | 0.797634i | ||||
\(761\) | 4.70991 | 0.170734 | 0.0853670 | − | 0.996350i | \(-0.472794\pi\) | ||||
0.0853670 | + | 0.996350i | \(0.472794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 20.2686i | − | 0.733774i | ||||||
\(764\) | 14.1253 | − | 10.2626i | 0.511034 | − | 0.371288i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.58057 | + | 29.4860i | 0.346160 | + | 1.06537i | ||||
\(767\) | 9.36195 | 0.338040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8989 | 0.501208 | 0.250604 | − | 0.968090i | \(-0.419371\pi\) | ||||
0.250604 | + | 0.968090i | \(0.419371\pi\) | |||||||
\(770\) | 3.01920 | + | 9.29215i | 0.108805 | + | 0.334866i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.8254 | − | 15.1305i | 0.749521 | − | 0.544559i | ||||
\(773\) | 14.8995i | 0.535899i | 0.963433 | + | 0.267949i | \(0.0863460\pi\) | ||||
−0.963433 | + | 0.267949i | \(0.913654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.1276 | 1.01037 | ||||||||
\(776\) | 23.2951 | + | 16.9249i | 0.836246 | + | 0.607568i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.3539 | − | 12.1370i | 1.33920 | − | 0.435134i | ||||
\(779\) | − | 20.6072i | − | 0.738329i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.8398i | 0.423662i | ||||||||
\(782\) | 8.22380 | + | 25.3102i | 0.294082 | + | 0.905092i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.23607 | − | 3.80423i | 0.0441453 | − | 0.135865i | ||||
\(785\) | 44.6472 | 1.59353 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.1839i | 0.363018i | 0.983389 | + | 0.181509i | \(0.0580981\pi\) | ||||
−0.983389 | + | 0.181509i | \(0.941902\pi\) | |||||||
\(788\) | −26.3733 | − | 36.2997i | −0.939510 | − | 1.29312i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −73.6404 | + | 23.9272i | −2.62001 | + | 0.851292i | ||||
\(791\) | 0.951214 | 0.0338213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.0014 | −0.781293 | ||||||||
\(794\) | −37.1478 | + | 12.0701i | −1.31833 | + | 0.428351i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.2379 | − | 17.6099i | 0.859091 | − | 0.624166i | ||||
\(797\) | 14.0210i | 0.496648i | 0.968677 | + | 0.248324i | \(0.0798798\pi\) | ||||
−0.968677 | + | 0.248324i | \(0.920120\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.1031 | 0.428177 | ||||||||
\(800\) | −76.1928 | −2.69382 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.56417 | + | 14.0471i | 0.161166 | + | 0.496019i | ||||
\(803\) | 2.13388i | 0.0753031i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 25.5740i | − | 0.901364i | ||||||
\(806\) | 16.9359 | − | 5.50282i | 0.596543 | − | 0.193828i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.70820 | − | 2.35114i | 0.0600944 | − | 0.0827129i | ||||
\(809\) | 28.0399 | 0.985831 | 0.492916 | − | 0.870077i | \(-0.335931\pi\) | ||||
0.492916 | + | 0.870077i | \(0.335931\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.2362i | − | 0.464785i | −0.972622 | − | 0.232393i | \(-0.925345\pi\) | ||
0.972622 | − | 0.232393i | \(-0.0746554\pi\) | |||||||
\(812\) | −4.16119 | − | 5.72739i | −0.146029 | − | 0.200992i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.14930 | − | 9.69256i | −0.110383 | − | 0.339724i | ||||
\(815\) | −51.0307 | −1.78753 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.7972 | 1.32236 | ||||||||
\(818\) | 6.61749 | + | 20.3665i | 0.231375 | + | 0.712099i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 33.8272 | + | 46.5592i | 1.18130 | + | 1.62592i | ||||
\(821\) | − | 13.8343i | − | 0.482821i | −0.970423 | − | 0.241411i | \(-0.922390\pi\) | ||
0.970423 | − | 0.241411i | \(-0.0776100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.4862 | 1.02782 | 0.513912 | − | 0.857843i | \(-0.328196\pi\) | ||||
0.513912 | + | 0.857843i | \(0.328196\pi\) | |||||||
\(824\) | 2.20843 | + | 1.60452i | 0.0769342 | + | 0.0558960i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.08831 | + | 0.678531i | −0.0726614 | + | 0.0236091i | ||||
\(827\) | 28.9797i | 1.00772i | 0.863784 | + | 0.503861i | \(0.168088\pi\) | ||||
−0.863784 | + | 0.503861i | \(0.831912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.5800i | 1.13155i | 0.824560 | + | 0.565774i | \(0.191423\pi\) | ||||
−0.824560 | + | 0.565774i | \(0.808577\pi\) | |||||||
\(830\) | −13.3054 | − | 40.9497i | −0.461836 | − | 1.42139i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −45.8765 | + | 14.9062i | −1.59048 | + | 0.516778i | ||||
\(833\) | 3.16228 | 0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.7197i | 2.23972i | ||||||||
\(836\) | 8.00541 | − | 5.81627i | 0.276873 | − | 0.201160i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.8492 | − | 8.72384i | 0.927491 | − | 0.301360i | ||||
\(839\) | 19.8215 | 0.684313 | 0.342157 | − | 0.939643i | \(-0.388843\pi\) | ||||
0.342157 | + | 0.939643i | \(0.388843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4704 | 0.567944 | ||||||||
\(842\) | −17.2616 | + | 5.60862i | −0.594872 | + | 0.193286i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | − | 13.7638i | −0.344214 | − | 0.473770i | ||||
\(845\) | − | 100.378i | − | 3.45311i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.41570 | −0.289167 | ||||||||
\(848\) | −32.8575 | − | 10.6760i | −1.12833 | − | 0.366617i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.6139 | − | 57.2876i | −0.638450 | − | 1.96495i | ||||
\(851\) | 26.6760i | 0.914441i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.4764i | − | 0.598381i | −0.954193 | − | 0.299190i | \(-0.903283\pi\) | ||
0.954193 | − | 0.299190i | \(-0.0967166\pi\) | |||||||
\(854\) | 4.90770 | − | 1.59461i | 0.167938 | − | 0.0545664i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.7579 | + | 36.8291i | −0.914566 | + | 1.25879i | ||||
\(857\) | 26.0767 | 0.890764 | 0.445382 | − | 0.895341i | \(-0.353068\pi\) | ||||
0.445382 | + | 0.895341i | \(0.353068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 40.6339i | − | 1.38641i | −0.720740 | − | 0.693205i | \(-0.756198\pi\) | ||
0.720740 | − | 0.693205i | \(-0.243802\pi\) | |||||||
\(860\) | −85.3978 | + | 62.0451i | −2.91204 | + | 2.11572i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.16405 | − | 3.58258i | −0.0396477 | − | 0.122023i | ||||
\(863\) | 41.4216 | 1.41001 | 0.705004 | − | 0.709204i | \(-0.250945\pi\) | ||||
0.705004 | + | 0.709204i | \(0.250945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −102.219 | −3.47556 | ||||||||
\(866\) | −8.39604 | − | 25.8404i | −0.285309 | − | 0.878091i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.37895 | + | 2.45495i | −0.114689 | + | 0.0833264i | ||||
\(869\) | 20.4806i | 0.694758i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.65709 | −0.157799 | ||||||||
\(872\) | 33.6968 | − | 46.3796i | 1.14112 | − | 1.57061i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.6332 | + | 8.00380i | −0.833229 | + | 0.270733i | ||||
\(875\) | 36.3966i | 1.23043i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 33.0093i | − | 1.11464i | −0.830296 | − | 0.557322i | \(-0.811829\pi\) | ||
0.830296 | − | 0.557322i | \(-0.188171\pi\) | |||||||
\(878\) | −15.3484 | − | 47.2375i | −0.517983 | − | 1.59419i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.53960 | + | 26.2822i | −0.287870 | + | 0.885972i | ||||
\(881\) | −18.0587 | −0.608414 | −0.304207 | − | 0.952606i | \(-0.598391\pi\) | ||||
−0.304207 | + | 0.952606i | \(0.598391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.6771i | 1.57081i | 0.618983 | + | 0.785404i | \(0.287545\pi\) | ||||
−0.618983 | + | 0.785404i | \(0.712455\pi\) | |||||||
\(884\) | −22.4152 | − | 30.8519i | −0.753904 | − | 1.03766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.3107 | + | 3.67506i | −0.379989 | + | 0.123466i | ||||
\(887\) | −29.2001 | −0.980444 | −0.490222 | − | 0.871598i | \(-0.663084\pi\) | ||||
−0.490222 | + | 0.871598i | \(0.663084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6132 | 0.389493 | ||||||||
\(890\) | −56.2593 | + | 18.2798i | −1.88582 | + | 0.612739i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.4085 | + | 19.1869i | −0.884222 | + | 0.642425i | ||||
\(893\) | 11.7793i | 0.394181i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −95.3714 | −3.18791 | ||||||||
\(896\) | 9.15298 | − | 6.65003i | 0.305780 | − | 0.222162i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.10234 | − | 6.47034i | −0.0701560 | − | 0.215918i | ||||
\(899\) | 7.39202i | 0.246538i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 27.3129i | − | 0.909926i | ||||||
\(902\) | 14.4773 | − | 4.70396i | 0.482042 | − | 0.156625i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.17661 | + | 1.58140i | 0.0723930 | + | 0.0525966i | ||||
\(905\) | −36.9700 | −1.22892 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 9.06592i | − | 0.301029i | −0.988608 | − | 0.150514i | \(-0.951907\pi\) | ||
0.988608 | − | 0.150514i | \(-0.0480930\pi\) | |||||||
\(908\) | 12.7289 | + | 17.5199i | 0.422424 | + | 0.581417i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.3244 | + | 34.8528i | 0.375399 | + | 1.15536i | ||||
\(911\) | −14.3571 | −0.475673 | −0.237837 | − | 0.971305i | \(-0.576438\pi\) | ||||
−0.237837 | + | 0.971305i | \(0.576438\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3888 | −0.376915 | ||||||||
\(914\) | −16.5319 | − | 50.8800i | −0.546827 | − | 1.68296i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.3012 | + | 40.3297i | 0.968140 | + | 1.33253i | ||||
\(917\) | − | 10.0120i | − | 0.330625i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.8788 | 1.64535 | 0.822675 | − | 0.568513i | \(-0.192481\pi\) | ||||
0.822675 | + | 0.568513i | \(0.192481\pi\) | |||||||
\(920\) | 42.5169 | − | 58.5195i | 1.40174 | − | 1.92933i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.1376 | + | 4.59359i | −0.465597 | + | 0.151282i | ||||
\(923\) | 44.4086i | 1.46173i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 60.3788i | − | 1.98524i | ||||||
\(926\) | 2.08091 | + | 6.40437i | 0.0683829 | + | 0.210461i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 20.0237i | − | 0.657310i | ||||||
\(929\) | −39.3069 | −1.28962 | −0.644809 | − | 0.764343i | \(-0.723063\pi\) | ||||
−0.644809 | + | 0.764343i | \(0.723063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.07768i | 0.100867i | ||||||||
\(932\) | 21.9973 | − | 15.9819i | 0.720544 | − | 0.523506i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.5256 | + | 8.61868i | −0.867943 | + | 0.282012i | ||||
\(935\) | −21.8472 | −0.714478 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.3504 | 1.22018 | 0.610092 | − | 0.792331i | \(-0.291133\pi\) | ||||
0.610092 | + | 0.792331i | \(0.291133\pi\) | |||||||
\(938\) | 1.03882 | − | 0.337534i | 0.0339188 | − | 0.0110209i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.3361 | − | 26.6139i | −0.630674 | − | 0.868049i | ||||
\(941\) | 38.7781i | 1.26413i | 0.774915 | + | 0.632065i | \(0.217792\pi\) | ||||
−0.774915 | + | 0.632065i | \(0.782208\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.8446 | −1.29752 | ||||||||
\(944\) | −5.90662 | − | 1.91918i | −0.192244 | − | 0.0624639i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.62790 | + | 26.5539i | 0.280517 | + | 0.863343i | ||||
\(947\) | 3.75328i | 0.121965i | 0.998139 | + | 0.0609826i | \(0.0194234\pi\) | ||||
−0.998139 | + | 0.0609826i | \(0.980577\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00373i | 0.259812i | ||||||||
\(950\) | 55.7551 | − | 18.1159i | 1.80893 | − | 0.587758i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.23607 | + | 5.25731i | 0.234522 | + | 0.170390i | ||||
\(953\) | 46.5443 | 1.50772 | 0.753859 | − | 0.657036i | \(-0.228190\pi\) | ||||
0.753859 | + | 0.657036i | \(0.228190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 37.5173i | − | 1.21403i | ||||||
\(956\) | −6.19704 | + | 4.50241i | −0.200426 | + | 0.145618i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.09061 | + | 3.35655i | 0.0352360 | + | 0.108445i | ||||
\(959\) | 8.40383 | 0.271374 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.6390 | −0.859322 | ||||||||
\(962\) | −11.8124 | − | 36.3547i | −0.380845 | − | 1.17212i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.61617 | + | 6.26001i | −0.277508 | + | 0.201621i | ||||
\(965\) | − | 55.3131i | − | 1.78059i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.6487 | −0.535388 | −0.267694 | − | 0.963504i | \(-0.586262\pi\) | ||||
−0.267694 | + | 0.963504i | \(0.586262\pi\) | |||||||
\(968\) | −19.2572 | − | 13.9912i | −0.618949 | − | 0.449693i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 58.8446 | − | 19.1198i | 1.88939 | − | 0.613899i | ||||
\(971\) | 5.74652i | 0.184415i | 0.995740 | + | 0.0922073i | \(0.0293922\pi\) | ||||
−0.995740 | + | 0.0922073i | \(0.970608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.61437i | 0.212047i | ||||||||
\(974\) | −4.37795 | − | 13.4739i | −0.140279 | − | 0.431733i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.8811 | + | 4.51024i | 0.444323 | + | 0.144369i | ||||
\(977\) | 27.6236 | 0.883758 | 0.441879 | − | 0.897075i | \(-0.354312\pi\) | ||||
0.441879 | + | 0.897075i | \(0.354312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.6467i | 0.500070i | ||||||||
\(980\) | −5.05210 | − | 6.95362i | −0.161383 | − | 0.222125i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.69565 | − | 1.85063i | 0.181755 | − | 0.0590559i | ||||
\(983\) | 2.19812 | 0.0701091 | 0.0350545 | − | 0.999385i | \(-0.488840\pi\) | ||||
0.0350545 | + | 0.999385i | \(0.488840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −96.4138 | −3.07200 | ||||||||
\(986\) | 15.0553 | − | 4.89177i | 0.479460 | − | 0.155786i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 30.0265 | − | 21.8156i | 0.955272 | − | 0.694045i | ||||
\(989\) | − | 73.0821i | − | 2.32388i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.62346 | 0.0833369 | 0.0416684 | − | 0.999131i | \(-0.486733\pi\) | ||||
0.0416684 | + | 0.999131i | \(0.486733\pi\) | |||||||
\(992\) | −11.8132 | −0.375071 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.21863 | − | 9.90592i | −0.102089 | − | 0.314197i | ||||
\(995\) | − | 64.3770i | − | 2.04089i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.1361i | 0.922749i | 0.887205 | + | 0.461375i | \(0.152644\pi\) | ||||
−0.887205 | + | 0.461375i | \(0.847356\pi\) | |||||||
\(998\) | −13.6081 | + | 4.42154i | −0.430757 | + | 0.139962i | ||||
\(999\) | 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 | 1512.2.c.d.757.12 | yes | 16 | |
3.2 | odd | 2 | inner | 1512.2.c.d.757.5 | ✓ | 16 | |
4.3 | odd | 2 | 6048.2.c.d.3025.16 | 16 | |||
8.3 | odd | 2 | 6048.2.c.d.3025.1 | 16 | |||
8.5 | even | 2 | inner | 1512.2.c.d.757.9 | yes | 16 | |
12.11 | even | 2 | 6048.2.c.d.3025.2 | 16 | |||
24.5 | odd | 2 | inner | 1512.2.c.d.757.8 | yes | 16 | |
24.11 | even | 2 | 6048.2.c.d.3025.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.d.757.5 | ✓ | 16 | 3.2 | odd | 2 | inner | |
1512.2.c.d.757.8 | yes | 16 | 24.5 | odd | 2 | inner | |
1512.2.c.d.757.9 | yes | 16 | 8.5 | even | 2 | inner | |
1512.2.c.d.757.12 | yes | 16 | 1.1 | even | 1 | trivial | |
6048.2.c.d.3025.1 | 16 | 8.3 | odd | 2 | |||
6048.2.c.d.3025.2 | 16 | 12.11 | even | 2 | |||
6048.2.c.d.3025.15 | 16 | 24.11 | even | 2 | |||
6048.2.c.d.3025.16 | 16 | 4.3 | odd | 2 |