Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(4409,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.4409");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4409.13 | ||
Character | \(\chi\) | \(=\) | 4410.4409 |
Dual form | 4410.2.d.d.4409.14 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.526370 | − | 2.17323i | 0.235400 | − | 0.971899i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.526370 | − | 2.17323i | 0.166453 | − | 0.687236i | ||||
\(11\) | 4.41847i | 1.33222i | 0.745853 | + | 0.666110i | \(0.232042\pi\) | ||||
−0.745853 | + | 0.666110i | \(0.767958\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.94214 | −1.37070 | −0.685351 | − | 0.728212i | \(-0.740351\pi\) | ||||
−0.685351 | + | 0.728212i | \(0.740351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.22951i | − | 1.26834i | −0.773192 | − | 0.634172i | \(-0.781341\pi\) | ||
0.773192 | − | 0.634172i | \(-0.218659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.97179i | 1.14061i | 0.821434 | + | 0.570304i | \(0.193174\pi\) | ||||
−0.821434 | + | 0.570304i | \(0.806826\pi\) | |||||||
\(20\) | 0.526370 | − | 2.17323i | 0.117700 | − | 0.485949i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.41847i | 0.942022i | ||||||||
\(23\) | −7.71767 | −1.60925 | −0.804623 | − | 0.593786i | \(-0.797632\pi\) | ||||
−0.804623 | + | 0.593786i | \(0.797632\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.44587 | − | 2.28785i | −0.889174 | − | 0.457570i | ||||
\(26\) | −4.94214 | −0.969233 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.2237i | 1.89850i | 0.314527 | + | 0.949248i | \(0.398154\pi\) | ||||
−0.314527 | + | 0.949248i | \(0.601846\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.43420i | 1.15562i | 0.816173 | + | 0.577808i | \(0.196092\pi\) | ||||
−0.816173 | + | 0.577808i | \(0.803908\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.22951i | − | 0.896854i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.25293i | 1.52117i | 0.649237 | + | 0.760586i | \(0.275088\pi\) | ||||
−0.649237 | + | 0.760586i | \(0.724912\pi\) | |||||||
\(38\) | 4.97179i | 0.806531i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.526370 | − | 2.17323i | 0.0832264 | − | 0.343618i | ||||
\(41\) | −6.79316 | −1.06091 | −0.530457 | − | 0.847712i | \(-0.677980\pi\) | ||||
−0.530457 | + | 0.847712i | \(0.677980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.08223i | 0.317538i | 0.987316 | + | 0.158769i | \(0.0507524\pi\) | ||||
−0.987316 | + | 0.158769i | \(0.949248\pi\) | |||||||
\(44\) | 4.41847i | 0.666110i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.71767 | −1.13791 | ||||||||
\(47\) | 7.83497i | 1.14285i | 0.820655 | + | 0.571424i | \(0.193609\pi\) | ||||
−0.820655 | + | 0.571424i | \(0.806391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.44587 | − | 2.28785i | −0.628741 | − | 0.323551i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.94214 | −0.685351 | ||||||||
\(53\) | 5.67297 | 0.779242 | 0.389621 | − | 0.920975i | \(-0.372606\pi\) | ||||
0.389621 | + | 0.920975i | \(0.372606\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.60237 | + | 2.32575i | 1.29478 | + | 0.313604i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.2237i | 1.34244i | ||||||||
\(59\) | 12.1340 | 1.57971 | 0.789855 | − | 0.613294i | \(-0.210156\pi\) | ||||
0.789855 | + | 0.613294i | \(0.210156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.76571i | − | 0.866260i | −0.901331 | − | 0.433130i | \(-0.857409\pi\) | ||
0.901331 | − | 0.433130i | \(-0.142591\pi\) | |||||||
\(62\) | 6.43420i | 0.817144i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.60139 | + | 10.7404i | −0.322663 | + | 1.33218i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.40838i | − | 0.294231i | −0.989119 | − | 0.147115i | \(-0.953001\pi\) | ||
0.989119 | − | 0.147115i | \(-0.0469989\pi\) | |||||||
\(68\) | − | 5.22951i | − | 0.634172i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.4298i | − | 1.23779i | −0.785474 | − | 0.618895i | \(-0.787581\pi\) | ||
0.785474 | − | 0.618895i | \(-0.212419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.202603 | −0.0237129 | −0.0118564 | − | 0.999930i | \(-0.503774\pi\) | ||||
−0.0118564 | + | 0.999930i | \(0.503774\pi\) | |||||||
\(74\) | 9.25293i | 1.07563i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.97179i | 0.570304i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.736672 | −0.0828821 | −0.0414411 | − | 0.999141i | \(-0.513195\pi\) | ||||
−0.0414411 | + | 0.999141i | \(0.513195\pi\) | |||||||
\(80\) | 0.526370 | − | 2.17323i | 0.0588500 | − | 0.242975i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.79316 | −0.750179 | ||||||||
\(83\) | − | 3.96971i | − | 0.435732i | −0.975979 | − | 0.217866i | \(-0.930090\pi\) | ||
0.975979 | − | 0.217866i | \(-0.0699096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.3649 | − | 2.75266i | −1.23270 | − | 0.298568i | ||||
\(86\) | 2.08223i | 0.224533i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.41847i | 0.471011i | ||||||||
\(89\) | 6.61837 | 0.701546 | 0.350773 | − | 0.936461i | \(-0.385919\pi\) | ||||
0.350773 | + | 0.936461i | \(0.385919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.71767 | −0.804623 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.83497i | 0.808115i | ||||||||
\(95\) | 10.8049 | + | 2.61700i | 1.10855 | + | 0.268499i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.5487 | −1.47719 | −0.738597 | − | 0.674147i | \(-0.764511\pi\) | ||||
−0.738597 | + | 0.674147i | \(0.764511\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.44587 | − | 2.28785i | −0.444587 | − | 0.228785i | ||||
\(101\) | 5.16164 | 0.513602 | 0.256801 | − | 0.966464i | \(-0.417332\pi\) | ||||
0.256801 | + | 0.966464i | \(0.417332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.62070 | 0.455292 | 0.227646 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227646 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(104\) | −4.94214 | −0.484617 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.67297 | 0.551008 | ||||||||
\(107\) | 10.1677 | 0.982944 | 0.491472 | − | 0.870893i | \(-0.336459\pi\) | ||||
0.491472 | + | 0.870893i | \(0.336459\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.18677 | −0.879933 | −0.439966 | − | 0.898014i | \(-0.645010\pi\) | ||||
−0.439966 | + | 0.898014i | \(0.645010\pi\) | |||||||
\(110\) | 9.60237 | + | 2.32575i | 0.915550 | + | 0.221752i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.19926 | −0.677249 | −0.338625 | − | 0.940922i | \(-0.609962\pi\) | ||||
−0.338625 | + | 0.940922i | \(0.609962\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.06235 | + | 16.7723i | −0.378816 | + | 1.56402i | ||||
\(116\) | 10.2237i | 0.949248i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.1340 | 1.11702 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.52291 | −0.774810 | ||||||||
\(122\) | − | 6.76571i | − | 0.612538i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.43420i | 0.577808i | ||||||||
\(125\) | −7.31220 | + | 8.45765i | −0.654023 | + | 0.756475i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.64476i | 0.412155i | 0.978536 | + | 0.206078i | \(0.0660700\pi\) | ||||
−0.978536 | + | 0.206078i | \(0.933930\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.60139 | + | 10.7404i | −0.228157 | + | 0.941996i | ||||
\(131\) | 6.16011 | 0.538211 | 0.269106 | − | 0.963111i | \(-0.413272\pi\) | ||||
0.269106 | + | 0.963111i | \(0.413272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.40838i | − | 0.208053i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.22951i | − | 0.448427i | ||||||
\(137\) | −11.6165 | −0.992462 | −0.496231 | − | 0.868190i | \(-0.665283\pi\) | ||||
−0.496231 | + | 0.868190i | \(0.665283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.1955i | − | 1.28886i | −0.764663 | − | 0.644431i | \(-0.777094\pi\) | ||
0.764663 | − | 0.644431i | \(-0.222906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 10.4298i | − | 0.875249i | ||||||
\(143\) | − | 21.8367i | − | 1.82608i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.2185 | + | 5.38146i | 1.84515 | + | 0.446906i | ||||
\(146\) | −0.202603 | −0.0167675 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.25293i | 0.760586i | ||||||||
\(149\) | 4.18853i | 0.343138i | 0.985172 | + | 0.171569i | \(0.0548837\pi\) | ||||
−0.985172 | + | 0.171569i | \(0.945116\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.3287 | −1.32881 | −0.664407 | − | 0.747371i | \(-0.731316\pi\) | ||||
−0.664407 | + | 0.747371i | \(0.731316\pi\) | |||||||
\(152\) | 4.97179i | 0.403266i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.9830 | + | 3.38677i | 1.12314 | + | 0.272032i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.1873 | −0.892845 | −0.446423 | − | 0.894822i | \(-0.647302\pi\) | ||||
−0.446423 | + | 0.894822i | \(0.647302\pi\) | |||||||
\(158\) | −0.736672 | −0.0586065 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.526370 | − | 2.17323i | 0.0416132 | − | 0.171809i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.35228i | 0.732527i | 0.930511 | + | 0.366263i | \(0.119363\pi\) | ||||
−0.930511 | + | 0.366263i | \(0.880637\pi\) | |||||||
\(164\) | −6.79316 | −0.530457 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 3.96971i | − | 0.308109i | ||||||
\(167\) | − | 2.72339i | − | 0.210742i | −0.994433 | − | 0.105371i | \(-0.966397\pi\) | ||
0.994433 | − | 0.105371i | \(-0.0336030\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4247 | 0.878826 | ||||||||
\(170\) | −11.3649 | − | 2.75266i | −0.871651 | − | 0.211119i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.08223i | 0.158769i | ||||||||
\(173\) | 3.90918i | 0.297210i | 0.988897 | + | 0.148605i | \(0.0474782\pi\) | ||||
−0.988897 | + | 0.148605i | \(0.952522\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.41847i | 0.333055i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.61837 | 0.496068 | ||||||||
\(179\) | 24.3957i | 1.82342i | 0.410832 | + | 0.911711i | \(0.365238\pi\) | ||||
−0.410832 | + | 0.911711i | \(0.634762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.0352i | − | 1.63786i | −0.573893 | − | 0.818930i | \(-0.694568\pi\) | ||
0.573893 | − | 0.818930i | \(-0.305432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.71767 | −0.568954 | ||||||||
\(185\) | 20.1088 | + | 4.87046i | 1.47842 | + | 0.358084i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.1065 | 1.68971 | ||||||||
\(188\) | 7.83497i | 0.571424i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.8049 | + | 2.61700i | 0.783866 | + | 0.189857i | ||||
\(191\) | 26.8532i | 1.94303i | 0.236983 | + | 0.971514i | \(0.423842\pi\) | ||||
−0.236983 | + | 0.971514i | \(0.576158\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.9798i | − | 1.00629i | −0.864202 | − | 0.503145i | \(-0.832176\pi\) | ||
0.864202 | − | 0.503145i | \(-0.167824\pi\) | |||||||
\(194\) | −14.5487 | −1.04453 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.2214 | 0.799493 | 0.399746 | − | 0.916626i | \(-0.369098\pi\) | ||||
0.399746 | + | 0.916626i | \(0.369098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.80074i | 0.127651i | 0.997961 | + | 0.0638254i | \(0.0203301\pi\) | ||||
−0.997961 | + | 0.0638254i | \(0.979670\pi\) | |||||||
\(200\) | −4.44587 | − | 2.28785i | −0.314370 | − | 0.161775i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.16164 | 0.363171 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.57572 | + | 14.7631i | −0.249739 | + | 1.03110i | ||||
\(206\) | 4.62070 | 0.321940 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.94214 | −0.342676 | ||||||||
\(209\) | −21.9677 | −1.51954 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.70144 | 0.117132 | 0.0585659 | − | 0.998284i | \(-0.481347\pi\) | ||||
0.0585659 | + | 0.998284i | \(0.481347\pi\) | |||||||
\(212\) | 5.67297 | 0.389621 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.1677 | 0.695046 | ||||||||
\(215\) | 4.52517 | + | 1.09603i | 0.308614 | + | 0.0747483i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.18677 | −0.622207 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.60237 | + | 2.32575i | 0.647391 | + | 0.156802i | ||||
\(221\) | 25.8450i | 1.73852i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.22392 | 0.215890 | 0.107945 | − | 0.994157i | \(-0.465573\pi\) | ||||
0.107945 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.19926 | −0.478888 | ||||||||
\(227\) | 2.34174i | 0.155427i | 0.996976 | + | 0.0777135i | \(0.0247620\pi\) | ||||
−0.996976 | + | 0.0777135i | \(0.975238\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.6386i | − | 0.769102i | −0.923104 | − | 0.384551i | \(-0.874356\pi\) | ||
0.923104 | − | 0.384551i | \(-0.125644\pi\) | |||||||
\(230\) | −4.06235 | + | 16.7723i | −0.267863 | + | 1.10593i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.2237i | 0.671220i | ||||||||
\(233\) | 0.0869816 | 0.00569836 | 0.00284918 | − | 0.999996i | \(-0.499093\pi\) | ||||
0.00284918 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.0272 | + | 4.12409i | 1.11073 | + | 0.269026i | ||||
\(236\) | 12.1340 | 0.789855 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.6099i | − | 0.880351i | −0.897912 | − | 0.440175i | \(-0.854916\pi\) | ||
0.897912 | − | 0.440175i | \(-0.145084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.13807i | − | 0.330972i | −0.986212 | − | 0.165486i | \(-0.947081\pi\) | ||
0.986212 | − | 0.165486i | \(-0.0529193\pi\) | |||||||
\(242\) | −8.52291 | −0.547874 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.76571i | − | 0.433130i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 24.5713i | − | 1.56343i | ||||||
\(248\) | 6.43420i | 0.408572i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.31220 | + | 8.45765i | −0.462464 | + | 0.534909i | ||||
\(251\) | −11.2861 | −0.712372 | −0.356186 | − | 0.934415i | \(-0.615923\pi\) | ||||
−0.356186 | + | 0.934415i | \(0.615923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 34.1003i | − | 2.14387i | ||||||
\(254\) | 4.64476i | 0.291438i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.2550i | 0.702066i | 0.936363 | + | 0.351033i | \(0.114169\pi\) | ||||
−0.936363 | + | 0.351033i | \(0.885831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.60139 | + | 10.7404i | −0.161332 | + | 0.666092i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.16011 | 0.380573 | ||||||||
\(263\) | 26.0470 | 1.60613 | 0.803064 | − | 0.595893i | \(-0.203202\pi\) | ||||
0.803064 | + | 0.595893i | \(0.203202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.98608 | − | 12.3287i | 0.183434 | − | 0.757345i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2.40838i | − | 0.147115i | ||||||
\(269\) | 8.34906 | 0.509051 | 0.254526 | − | 0.967066i | \(-0.418081\pi\) | ||||
0.254526 | + | 0.967066i | \(0.418081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5200i | 1.24650i | 0.782022 | + | 0.623251i | \(0.214189\pi\) | ||||
−0.782022 | + | 0.623251i | \(0.785811\pi\) | |||||||
\(272\) | − | 5.22951i | − | 0.317086i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.6165 | −0.701777 | ||||||||
\(275\) | 10.1088 | − | 19.6440i | 0.609583 | − | 1.18458i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.2070i | 1.57463i | 0.616552 | + | 0.787314i | \(0.288529\pi\) | ||||
−0.616552 | + | 0.787314i | \(0.711471\pi\) | |||||||
\(278\) | − | 15.1955i | − | 0.911363i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 15.9485i | − | 0.951408i | −0.879605 | − | 0.475704i | \(-0.842193\pi\) | ||
0.879605 | − | 0.475704i | \(-0.157807\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.03048 | −0.0612558 | −0.0306279 | − | 0.999531i | \(-0.509751\pi\) | ||||
−0.0306279 | + | 0.999531i | \(0.509751\pi\) | |||||||
\(284\) | − | 10.4298i | − | 0.618895i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 21.8367i | − | 1.29123i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3478 | −0.608694 | ||||||||
\(290\) | 22.2185 | + | 5.38146i | 1.30472 | + | 0.316010i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.202603 | −0.0118564 | ||||||||
\(293\) | 11.5472i | 0.674593i | 0.941398 | + | 0.337297i | \(0.109513\pi\) | ||||
−0.941398 | + | 0.337297i | \(0.890487\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.38697 | − | 26.3700i | 0.371864 | − | 1.53532i | ||||
\(296\) | 9.25293i | 0.537815i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.18853i | 0.242635i | ||||||||
\(299\) | 38.1418 | 2.20580 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.3287 | −0.939614 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.97179i | 0.285152i | ||||||||
\(305\) | −14.7034 | − | 3.56127i | −0.841917 | − | 0.203917i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.8139 | −1.92986 | −0.964931 | − | 0.262502i | \(-0.915452\pi\) | ||||
−0.964931 | + | 0.262502i | \(0.915452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.9830 | + | 3.38677i | 0.794181 | + | 0.192356i | ||||
\(311\) | −28.2780 | −1.60350 | −0.801749 | − | 0.597661i | \(-0.796097\pi\) | ||||
−0.801749 | + | 0.597661i | \(0.796097\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0532 | −0.794333 | −0.397166 | − | 0.917747i | \(-0.630006\pi\) | ||||
−0.397166 | + | 0.917747i | \(0.630006\pi\) | |||||||
\(314\) | −11.1873 | −0.631337 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.736672 | −0.0414411 | ||||||||
\(317\) | 3.56582 | 0.200276 | 0.100138 | − | 0.994974i | \(-0.468072\pi\) | ||||
0.100138 | + | 0.994974i | \(0.468072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.1732 | −2.52922 | ||||||||
\(320\) | 0.526370 | − | 2.17323i | 0.0294250 | − | 0.121487i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.0000 | 1.44668 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.9721 | + | 11.3069i | 1.21879 | + | 0.627192i | ||||
\(326\) | 9.35228i | 0.517975i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.79316 | −0.375089 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.7995 | −0.593595 | −0.296798 | − | 0.954940i | \(-0.595919\pi\) | ||||
−0.296798 | + | 0.954940i | \(0.595919\pi\) | |||||||
\(332\) | − | 3.96971i | − | 0.217866i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2.72339i | − | 0.149017i | ||||||
\(335\) | −5.23397 | − | 1.26770i | −0.285963 | − | 0.0692619i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.75187i | 0.204377i | 0.994765 | + | 0.102189i | \(0.0325845\pi\) | ||||
−0.994765 | + | 0.102189i | \(0.967415\pi\) | |||||||
\(338\) | 11.4247 | 0.621424 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.3649 | − | 2.75266i | −0.616350 | − | 0.149284i | ||||
\(341\) | −28.4293 | −1.53954 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.08223i | 0.112266i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.90918i | 0.210159i | ||||||||
\(347\) | 31.8993 | 1.71245 | 0.856223 | − | 0.516606i | \(-0.172805\pi\) | ||||
0.856223 | + | 0.516606i | \(0.172805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.4147i | 1.68159i | 0.541354 | + | 0.840795i | \(0.317912\pi\) | ||||
−0.541354 | + | 0.840795i | \(0.682088\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.41847i | 0.235505i | ||||||||
\(353\) | 32.8117i | 1.74639i | 0.487371 | + | 0.873195i | \(0.337956\pi\) | ||||
−0.487371 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.6664 | − | 5.48994i | −1.20301 | − | 0.291376i | ||||
\(356\) | 6.61837 | 0.350773 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.3957i | 1.28935i | ||||||||
\(359\) | − | 1.53908i | − | 0.0812295i | −0.999175 | − | 0.0406148i | \(-0.987068\pi\) | ||
0.999175 | − | 0.0406148i | \(-0.0129316\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.71871 | −0.300985 | ||||||||
\(362\) | − | 22.0352i | − | 1.15814i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.106644 | + | 0.440303i | −0.00558201 | + | 0.0230465i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.8442 | −0.983661 | −0.491831 | − | 0.870691i | \(-0.663672\pi\) | ||||
−0.491831 | + | 0.870691i | \(0.663672\pi\) | |||||||
\(368\) | −7.71767 | −0.402311 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.1088 | + | 4.87046i | 1.04540 | + | 0.253203i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.72346i | 0.348128i | 0.984734 | + | 0.174064i | \(0.0556899\pi\) | ||||
−0.984734 | + | 0.174064i | \(0.944310\pi\) | |||||||
\(374\) | 23.1065 | 1.19481 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.83497i | 0.404058i | ||||||||
\(377\) | − | 50.5270i | − | 2.60228i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.1124 | −1.08447 | −0.542235 | − | 0.840227i | \(-0.682422\pi\) | ||||
−0.542235 | + | 0.840227i | \(0.682422\pi\) | |||||||
\(380\) | 10.8049 | + | 2.61700i | 0.554277 | + | 0.134249i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26.8532i | 1.37393i | ||||||||
\(383\) | 1.15349i | 0.0589407i | 0.999566 | + | 0.0294704i | \(0.00938207\pi\) | ||||
−0.999566 | + | 0.0294704i | \(0.990618\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 13.9798i | − | 0.711554i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.5487 | −0.738597 | ||||||||
\(389\) | − | 11.5150i | − | 0.583833i | −0.956444 | − | 0.291916i | \(-0.905707\pi\) | ||
0.956444 | − | 0.291916i | \(-0.0942929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.3597i | 2.04108i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.2214 | 0.565327 | ||||||||
\(395\) | −0.387762 | + | 1.60096i | −0.0195104 | + | 0.0805530i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.89542 | 0.295883 | 0.147941 | − | 0.988996i | \(-0.452735\pi\) | ||||
0.147941 | + | 0.988996i | \(0.452735\pi\) | |||||||
\(398\) | 1.80074i | 0.0902628i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.44587 | − | 2.28785i | −0.222293 | − | 0.114392i | ||||
\(401\) | 19.1472i | 0.956166i | 0.878315 | + | 0.478083i | \(0.158668\pi\) | ||||
−0.878315 | + | 0.478083i | \(0.841332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 31.7987i | − | 1.58401i | ||||||
\(404\) | 5.16164 | 0.256801 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.8838 | −2.02654 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0702i | 0.942962i | 0.881876 | + | 0.471481i | \(0.156280\pi\) | ||||
−0.881876 | + | 0.471481i | \(0.843720\pi\) | |||||||
\(410\) | −3.57572 | + | 14.7631i | −0.176592 | + | 0.729098i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.62070 | 0.227646 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.62709 | − | 2.08954i | −0.423487 | − | 0.102571i | ||||
\(416\) | −4.94214 | −0.242308 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.9677 | −1.07448 | ||||||||
\(419\) | 2.48991 | 0.121640 | 0.0608199 | − | 0.998149i | \(-0.480628\pi\) | ||||
0.0608199 | + | 0.998149i | \(0.480628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.61083 | 0.370929 | 0.185465 | − | 0.982651i | \(-0.440621\pi\) | ||||
0.185465 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(422\) | 1.70144 | 0.0828248 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.67297 | 0.275504 | ||||||||
\(425\) | −11.9643 | + | 23.2497i | −0.580355 | + | 1.12778i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.1677 | 0.491472 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.52517 | + | 1.09603i | 0.218223 | + | 0.0528550i | ||||
\(431\) | 9.28436i | 0.447212i | 0.974680 | + | 0.223606i | \(0.0717828\pi\) | ||||
−0.974680 | + | 0.223606i | \(0.928217\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.5306 | −1.22692 | −0.613460 | − | 0.789726i | \(-0.710223\pi\) | ||||
−0.613460 | + | 0.789726i | \(0.710223\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.18677 | −0.439966 | ||||||||
\(437\) | − | 38.3706i | − | 1.83552i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.10460i | 0.434539i | 0.976112 | + | 0.217269i | \(0.0697150\pi\) | ||||
−0.976112 | + | 0.217269i | \(0.930285\pi\) | |||||||
\(440\) | 9.60237 | + | 2.32575i | 0.457775 | + | 0.110876i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25.8450i | 1.22932i | ||||||||
\(443\) | −21.6070 | −1.02658 | −0.513289 | − | 0.858216i | \(-0.671573\pi\) | ||||
−0.513289 | + | 0.858216i | \(0.671573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.48371 | − | 14.3833i | 0.165144 | − | 0.681832i | ||||
\(446\) | 3.22392 | 0.152657 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13.3403i | − | 0.629566i | −0.949164 | − | 0.314783i | \(-0.898068\pi\) | ||
0.949164 | − | 0.314783i | \(-0.101932\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 30.0154i | − | 1.41337i | ||||||
\(452\) | −7.19926 | −0.338625 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.34174i | 0.109904i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 31.7813i | − | 1.48667i | −0.668921 | − | 0.743334i | \(-0.733243\pi\) | ||
0.668921 | − | 0.743334i | \(-0.266757\pi\) | |||||||
\(458\) | − | 11.6386i | − | 0.543837i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.06235 | + | 16.7723i | −0.189408 | + | 0.782012i | ||||
\(461\) | −4.61323 | −0.214860 | −0.107430 | − | 0.994213i | \(-0.534262\pi\) | ||||
−0.107430 | + | 0.994213i | \(0.534262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.0850i | − | 0.654587i | −0.944923 | − | 0.327293i | \(-0.893863\pi\) | ||
0.944923 | − | 0.327293i | \(-0.106137\pi\) | |||||||
\(464\) | 10.2237i | 0.474624i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0869816 | 0.00402935 | ||||||||
\(467\) | − | 39.9154i | − | 1.84707i | −0.383520 | − | 0.923533i | \(-0.625288\pi\) | ||
0.383520 | − | 0.923533i | \(-0.374712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.0272 | + | 4.12409i | 0.785406 | + | 0.190230i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.1340 | 0.558512 | ||||||||
\(473\) | −9.20029 | −0.423030 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3747 | − | 22.1039i | 0.521907 | − | 1.01420i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 13.6099i | − | 0.622502i | ||||||
\(479\) | 22.3228 | 1.01995 | 0.509977 | − | 0.860188i | \(-0.329654\pi\) | ||||
0.509977 | + | 0.860188i | \(0.329654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 45.7293i | − | 2.08507i | ||||||
\(482\) | − | 5.13807i | − | 0.234033i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.52291 | −0.387405 | ||||||||
\(485\) | −7.65798 | + | 31.6176i | −0.347731 | + | 1.43568i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 41.2767i | − | 1.87043i | −0.354085 | − | 0.935213i | \(-0.615208\pi\) | ||
0.354085 | − | 0.935213i | \(-0.384792\pi\) | |||||||
\(488\) | − | 6.76571i | − | 0.306269i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.6041i | 0.659075i | 0.944143 | + | 0.329537i | \(0.106893\pi\) | ||||
−0.944143 | + | 0.329537i | \(0.893107\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.4651 | 2.40795 | ||||||||
\(494\) | − | 24.5713i | − | 1.10551i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.43420i | 0.288904i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.6787 | 0.612342 | 0.306171 | − | 0.951976i | \(-0.400952\pi\) | ||||
0.306171 | + | 0.951976i | \(0.400952\pi\) | |||||||
\(500\) | −7.31220 | + | 8.45765i | −0.327011 | + | 0.378237i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.2861 | −0.503723 | ||||||||
\(503\) | 7.92976i | 0.353570i | 0.984249 | + | 0.176785i | \(0.0565698\pi\) | ||||
−0.984249 | + | 0.176785i | \(0.943430\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.71693 | − | 11.2174i | 0.120902 | − | 0.499169i | ||||
\(506\) | − | 34.1003i | − | 1.51594i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.64476i | 0.206078i | ||||||||
\(509\) | −3.47370 | −0.153969 | −0.0769845 | − | 0.997032i | \(-0.524529\pi\) | ||||
−0.0769845 | + | 0.997032i | \(0.524529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.2550i | 0.496435i | ||||||||
\(515\) | 2.43220 | − | 10.0419i | 0.107176 | − | 0.442497i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.6186 | −1.52252 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.60139 | + | 10.7404i | −0.114079 | + | 0.470998i | ||||
\(521\) | −18.7795 | −0.822746 | −0.411373 | − | 0.911467i | \(-0.634951\pi\) | ||||
−0.411373 | + | 0.911467i | \(0.634951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0104 | −0.525176 | −0.262588 | − | 0.964908i | \(-0.584576\pi\) | ||||
−0.262588 | + | 0.964908i | \(0.584576\pi\) | |||||||
\(524\) | 6.16011 | 0.269106 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.0470 | 1.13570 | ||||||||
\(527\) | 33.6477 | 1.46572 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.5624 | 1.58967 | ||||||||
\(530\) | 2.98608 | − | 12.3287i | 0.129707 | − | 0.535523i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.5727 | 1.45420 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.35195 | − | 22.0967i | 0.231385 | − | 0.955322i | ||||
\(536\) | − | 2.40838i | − | 0.104026i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.34906 | 0.359954 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.18448 | −0.179905 | −0.0899523 | − | 0.995946i | \(-0.528671\pi\) | ||||
−0.0899523 | + | 0.995946i | \(0.528671\pi\) | |||||||
\(542\) | 20.5200i | 0.881410i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 5.22951i | − | 0.224214i | ||||||
\(545\) | −4.83564 | + | 19.9650i | −0.207136 | + | 0.855206i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.8675i | − | 0.934986i | −0.883997 | − | 0.467493i | \(-0.845157\pi\) | ||
0.883997 | − | 0.467493i | \(-0.154843\pi\) | |||||||
\(548\) | −11.6165 | −0.496231 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.1088 | − | 19.6440i | 0.431041 | − | 0.837621i | ||||
\(551\) | −50.8302 | −2.16544 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.2070i | 1.11343i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 15.1955i | − | 0.644431i | ||||||
\(557\) | 21.3530 | 0.904755 | 0.452377 | − | 0.891827i | \(-0.350576\pi\) | ||||
0.452377 | + | 0.891827i | \(0.350576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10.2907i | − | 0.435250i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 15.9485i | − | 0.672747i | ||||||
\(563\) | 15.5975i | 0.657356i | 0.944442 | + | 0.328678i | \(0.106603\pi\) | ||||
−0.944442 | + | 0.328678i | \(0.893397\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.78947 | + | 15.6457i | −0.159424 | + | 0.658218i | ||||
\(566\) | −1.03048 | −0.0433144 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 10.4298i | − | 0.437625i | ||||||
\(569\) | − | 19.9293i | − | 0.835481i | −0.908566 | − | 0.417741i | \(-0.862822\pi\) | ||
0.908566 | − | 0.417741i | \(-0.137178\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.2857 | −1.51851 | −0.759255 | − | 0.650793i | \(-0.774436\pi\) | ||||
−0.759255 | + | 0.650793i | \(0.774436\pi\) | |||||||
\(572\) | − | 21.8367i | − | 0.913039i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.3117 | + | 17.6569i | 1.43090 | + | 0.736342i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.4529 | −1.14288 | −0.571439 | − | 0.820645i | \(-0.693615\pi\) | ||||
−0.571439 | + | 0.820645i | \(0.693615\pi\) | |||||||
\(578\) | −10.3478 | −0.430412 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 22.2185 | + | 5.38146i | 0.922573 | + | 0.223453i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.0659i | 1.03812i | ||||||||
\(584\) | −0.202603 | −0.00838377 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.5472i | 0.477010i | ||||||||
\(587\) | − | 21.0716i | − | 0.869719i | −0.900498 | − | 0.434859i | \(-0.856798\pi\) | ||
0.900498 | − | 0.434859i | \(-0.143202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.9895 | −1.31810 | ||||||||
\(590\) | 6.38697 | − | 26.3700i | 0.262947 | − | 1.08563i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.25293i | 0.380293i | ||||||||
\(593\) | − | 5.31080i | − | 0.218088i | −0.994037 | − | 0.109044i | \(-0.965221\pi\) | ||
0.994037 | − | 0.109044i | \(-0.0347790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.18853i | 0.171569i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 38.1418 | 1.55973 | ||||||||
\(599\) | − | 6.56822i | − | 0.268370i | −0.990956 | − | 0.134185i | \(-0.957158\pi\) | ||
0.990956 | − | 0.134185i | \(-0.0428417\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.0755i | − | 0.900479i | −0.892908 | − | 0.450239i | \(-0.851339\pi\) | ||
0.892908 | − | 0.450239i | \(-0.148661\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.3287 | −0.664407 | ||||||||
\(605\) | −4.48621 | + | 18.5223i | −0.182390 | + | 0.753037i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.461776 | −0.0187429 | −0.00937145 | − | 0.999956i | \(-0.502983\pi\) | ||||
−0.00937145 | + | 0.999956i | \(0.502983\pi\) | |||||||
\(608\) | 4.97179i | 0.201633i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.7034 | − | 3.56127i | −0.595325 | − | 0.144191i | ||||
\(611\) | − | 38.7215i | − | 1.56650i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.1411i | 1.37895i | 0.724312 | + | 0.689473i | \(0.242158\pi\) | ||||
−0.724312 | + | 0.689473i | \(0.757842\pi\) | |||||||
\(614\) | −33.8139 | −1.36462 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.1936 | 1.09477 | 0.547387 | − | 0.836880i | \(-0.315623\pi\) | ||||
0.547387 | + | 0.836880i | \(0.315623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.75549i | 0.0705591i | 0.999377 | + | 0.0352795i | \(0.0112322\pi\) | ||||
−0.999377 | + | 0.0352795i | \(0.988768\pi\) | |||||||
\(620\) | 13.9830 | + | 3.38677i | 0.561571 | + | 0.136016i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.2780 | −1.13384 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5315 | + | 20.3429i | 0.581260 | + | 0.813718i | ||||
\(626\) | −14.0532 | −0.561678 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.1873 | −0.446423 | ||||||||
\(629\) | 48.3883 | 1.92937 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6710 | 1.22099 | 0.610496 | − | 0.792019i | \(-0.290970\pi\) | ||||
0.610496 | + | 0.792019i | \(0.290970\pi\) | |||||||
\(632\) | −0.736672 | −0.0293033 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.56582 | 0.141617 | ||||||||
\(635\) | 10.0941 | + | 2.44486i | 0.400573 | + | 0.0970213i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −45.1732 | −1.78843 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.526370 | − | 2.17323i | 0.0208066 | − | 0.0859045i | ||||
\(641\) | 14.2174i | 0.561553i | 0.959773 | + | 0.280777i | \(0.0905920\pi\) | ||||
−0.959773 | + | 0.280777i | \(0.909408\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.4526 | 1.59529 | 0.797647 | − | 0.603124i | \(-0.206078\pi\) | ||||
0.797647 | + | 0.603124i | \(0.206078\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.0000 | 1.02296 | ||||||||
\(647\) | − | 12.9418i | − | 0.508793i | −0.967100 | − | 0.254397i | \(-0.918123\pi\) | ||
0.967100 | − | 0.254397i | \(-0.0818768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 53.6137i | 2.10452i | ||||||||
\(650\) | 21.9721 | + | 11.3069i | 0.861817 | + | 0.443492i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.35228i | 0.366263i | ||||||||
\(653\) | 20.3866 | 0.797791 | 0.398895 | − | 0.916996i | \(-0.369394\pi\) | ||||
0.398895 | + | 0.916996i | \(0.369394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.24250 | − | 13.3873i | 0.126695 | − | 0.523087i | ||||
\(656\) | −6.79316 | −0.265228 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.4950i | 0.408829i | 0.978884 | + | 0.204414i | \(0.0655290\pi\) | ||||
−0.978884 | + | 0.204414i | \(0.934471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.03266i | − | 0.117957i | −0.998259 | − | 0.0589783i | \(-0.981216\pi\) | ||
0.998259 | − | 0.0589783i | \(-0.0187843\pi\) | |||||||
\(662\) | −10.7995 | −0.419735 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.96971i | − | 0.154055i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 78.9033i | − | 3.05515i | ||||||
\(668\) | − | 2.72339i | − | 0.105371i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.23397 | − | 1.26770i | −0.202206 | − | 0.0489756i | ||||
\(671\) | 29.8941 | 1.15405 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.2777i | − | 0.434724i | −0.976091 | − | 0.217362i | \(-0.930255\pi\) | ||
0.976091 | − | 0.217362i | \(-0.0697452\pi\) | |||||||
\(674\) | 3.75187i | 0.144517i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.4247 | 0.439413 | ||||||||
\(677\) | 39.9757i | 1.53639i | 0.640216 | + | 0.768195i | \(0.278845\pi\) | ||||
−0.640216 | + | 0.768195i | \(0.721155\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.3649 | − | 2.75266i | −0.435826 | − | 0.105560i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.4293 | −1.08862 | ||||||||
\(683\) | −6.07806 | −0.232571 | −0.116285 | − | 0.993216i | \(-0.537099\pi\) | ||||
−0.116285 | + | 0.993216i | \(0.537099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.11456 | + | 25.2453i | −0.233626 | + | 0.964573i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.08223i | 0.0793844i | ||||||||
\(689\) | −28.0366 | −1.06811 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 28.5091i | − | 1.08454i | −0.840205 | − | 0.542269i | \(-0.817565\pi\) | ||
0.840205 | − | 0.542269i | \(-0.182435\pi\) | |||||||
\(692\) | 3.90918i | 0.148605i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.8993 | 1.21088 | ||||||||
\(695\) | −33.0232 | − | 7.99843i | −1.25264 | − | 0.303398i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.5249i | 1.34560i | ||||||||
\(698\) | 31.4147i | 1.18906i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 17.1007i | − | 0.645885i | −0.946419 | − | 0.322943i | \(-0.895328\pi\) | ||
0.946419 | − | 0.322943i | \(-0.104672\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.0036 | −1.73506 | ||||||||
\(704\) | 4.41847i | 0.166528i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.8117i | 1.23488i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.8197 | 1.11990 | 0.559950 | − | 0.828526i | \(-0.310820\pi\) | ||||
0.559950 | + | 0.828526i | \(0.310820\pi\) | |||||||
\(710\) | −22.6664 | − | 5.48994i | −0.850654 | − | 0.206034i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.61837 | 0.248034 | ||||||||
\(713\) | − | 49.6570i | − | 1.85967i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −47.4562 | − | 11.4942i | −1.77476 | − | 0.429858i | ||||
\(716\) | 24.3957i | 0.911711i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 1.53908i | − | 0.0574379i | ||||||
\(719\) | 13.6376 | 0.508597 | 0.254298 | − | 0.967126i | \(-0.418155\pi\) | ||||
0.254298 | + | 0.967126i | \(0.418155\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.71871 | −0.212828 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 22.0352i | − | 0.818930i | ||||||
\(725\) | 23.3903 | − | 45.4533i | 0.868694 | − | 1.68809i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.3907 | −0.682075 | −0.341037 | − | 0.940050i | \(-0.610778\pi\) | ||||
−0.341037 | + | 0.940050i | \(0.610778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.106644 | + | 0.440303i | −0.00394708 | + | 0.0162964i | ||||
\(731\) | 10.8891 | 0.402747 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.2037 | 1.59577 | 0.797883 | − | 0.602813i | \(-0.205953\pi\) | ||||
0.797883 | + | 0.602813i | \(0.205953\pi\) | |||||||
\(734\) | −18.8442 | −0.695553 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.71767 | −0.284477 | ||||||||
\(737\) | 10.6414 | 0.391980 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.1476 | 1.36650 | 0.683249 | − | 0.730186i | \(-0.260566\pi\) | ||||
0.683249 | + | 0.730186i | \(0.260566\pi\) | |||||||
\(740\) | 20.1088 | + | 4.87046i | 0.739212 | + | 0.179042i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.11107 | −0.334253 | −0.167126 | − | 0.985935i | \(-0.553449\pi\) | ||||
−0.167126 | + | 0.985935i | \(0.553449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.10265 | + | 2.20472i | 0.333495 | + | 0.0807747i | ||||
\(746\) | 6.72346i | 0.246163i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 23.1065 | 0.844856 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.1898 | 0.882698 | 0.441349 | − | 0.897336i | \(-0.354500\pi\) | ||||
0.441349 | + | 0.897336i | \(0.354500\pi\) | |||||||
\(752\) | 7.83497i | 0.285712i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 50.5270i | − | 1.84009i | ||||||
\(755\) | −8.59496 | + | 35.4861i | −0.312803 | + | 1.29147i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.1258i | 1.67647i | 0.545310 | + | 0.838235i | \(0.316412\pi\) | ||||
−0.545310 | + | 0.838235i | \(0.683588\pi\) | |||||||
\(758\) | −21.1124 | −0.766836 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.8049 | + | 2.61700i | 0.391933 | + | 0.0949287i | ||||
\(761\) | 32.8441 | 1.19060 | 0.595299 | − | 0.803504i | \(-0.297034\pi\) | ||||
0.595299 | + | 0.803504i | \(0.297034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 26.8532i | 0.971514i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.15349i | 0.0416774i | ||||||||
\(767\) | −59.9678 | −2.16531 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.7778i | 1.50655i | 0.657708 | + | 0.753273i | \(0.271526\pi\) | ||||
−0.657708 | + | 0.753273i | \(0.728474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 13.9798i | − | 0.503145i | ||||||
\(773\) | 19.8712i | 0.714717i | 0.933967 | + | 0.357359i | \(0.116323\pi\) | ||||
−0.933967 | + | 0.357359i | \(0.883677\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.7205 | − | 28.6056i | 0.528775 | − | 1.02754i | ||||
\(776\) | −14.5487 | −0.522267 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 11.5150i | − | 0.412832i | ||||||
\(779\) | − | 33.7742i | − | 1.21009i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.0838 | 1.64901 | ||||||||
\(782\) | 40.3597i | 1.44326i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.88867 | + | 24.3126i | −0.210176 | + | 0.867755i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.5693 | −1.41049 | −0.705246 | − | 0.708963i | \(-0.749163\pi\) | ||||
−0.705246 | + | 0.708963i | \(0.749163\pi\) | |||||||
\(788\) | 11.2214 | 0.399746 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.387762 | + | 1.60096i | −0.0137960 | + | 0.0569596i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.4371i | 1.18739i | ||||||||
\(794\) | 5.89542 | 0.209221 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.80074i | 0.0638254i | ||||||||
\(797\) | − | 37.8029i | − | 1.33905i | −0.742790 | − | 0.669524i | \(-0.766498\pi\) | ||
0.742790 | − | 0.669524i | \(-0.233502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.9731 | 1.44952 | ||||||||
\(800\) | −4.44587 | − | 2.28785i | −0.157185 | − | 0.0808876i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.1472i | 0.676112i | ||||||||
\(803\) | − | 0.895196i | − | 0.0315908i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 31.7987i | − | 1.12006i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.16164 | 0.181586 | ||||||||
\(809\) | − | 12.9081i | − | 0.453826i | −0.973915 | − | 0.226913i | \(-0.927137\pi\) | ||
0.973915 | − | 0.226913i | \(-0.0728633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.57478i | − | 0.125527i | −0.998028 | − | 0.0627637i | \(-0.980009\pi\) | ||
0.998028 | − | 0.0627637i | \(-0.0199914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −40.8838 | −1.43298 | ||||||||
\(815\) | 20.3247 | + | 4.92276i | 0.711942 | + | 0.172437i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.3524 | −0.362186 | ||||||||
\(818\) | 19.0702i | 0.666775i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.57572 | + | 14.7631i | −0.124869 | + | 0.515550i | ||||
\(821\) | − | 41.2899i | − | 1.44103i | −0.693440 | − | 0.720514i | \(-0.743906\pi\) | ||
0.693440 | − | 0.720514i | \(-0.256094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 12.5211i | − | 0.436459i | −0.975897 | − | 0.218229i | \(-0.929972\pi\) | ||
0.975897 | − | 0.218229i | \(-0.0700281\pi\) | |||||||
\(824\) | 4.62070 | 0.160970 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.4665 | −0.989877 | −0.494938 | − | 0.868928i | \(-0.664809\pi\) | ||||
−0.494938 | + | 0.868928i | \(0.664809\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 42.3188i | − | 1.46979i | −0.678179 | − | 0.734897i | \(-0.737231\pi\) | ||
0.678179 | − | 0.734897i | \(-0.262769\pi\) | |||||||
\(830\) | −8.62709 | − | 2.08954i | −0.299451 | − | 0.0725288i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.94214 | −0.171338 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.91855 | − | 1.43351i | −0.204820 | − | 0.0496086i | ||||
\(836\) | −21.9677 | −0.759770 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.48991 | 0.0860124 | ||||||||
\(839\) | 48.5307 | 1.67547 | 0.837733 | − | 0.546080i | \(-0.183880\pi\) | ||||
0.837733 | + | 0.546080i | \(0.183880\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −75.5244 | −2.60429 | ||||||||
\(842\) | 7.61083 | 0.262287 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.70144 | 0.0585659 | ||||||||
\(845\) | 6.01364 | − | 24.8286i | 0.206876 | − | 0.854130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.67297 | 0.194811 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.9643 | + | 23.2497i | −0.410373 | + | 0.797459i | ||||
\(851\) | − | 71.4110i | − | 2.44794i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.69534 | 0.263483 | 0.131742 | − | 0.991284i | \(-0.457943\pi\) | ||||
0.131742 | + | 0.991284i | \(0.457943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1677 | 0.347523 | ||||||||
\(857\) | 6.59617i | 0.225321i | 0.993634 | + | 0.112660i | \(0.0359372\pi\) | ||||
−0.993634 | + | 0.112660i | \(0.964063\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.46161i | − | 0.186348i | −0.995650 | − | 0.0931738i | \(-0.970299\pi\) | ||
0.995650 | − | 0.0931738i | \(-0.0297012\pi\) | |||||||
\(860\) | 4.52517 | + | 1.09603i | 0.154307 | + | 0.0373741i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.28436i | 0.316226i | ||||||||
\(863\) | 46.8283 | 1.59405 | 0.797027 | − | 0.603943i | \(-0.206405\pi\) | ||||
0.797027 | + | 0.603943i | \(0.206405\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.49555 | + | 2.05768i | 0.288858 | + | 0.0699631i | ||||
\(866\) | −25.5306 | −0.867564 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 3.25497i | − | 0.110417i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9026i | 0.403303i | ||||||||
\(872\) | −9.18677 | −0.311103 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 38.3706i | − | 1.29791i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9375i | 0.639474i | 0.947506 | + | 0.319737i | \(0.103595\pi\) | ||||
−0.947506 | + | 0.319737i | \(0.896405\pi\) | |||||||
\(878\) | 9.10460i | 0.307265i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.60237 | + | 2.32575i | 0.323696 | + | 0.0784011i | ||||
\(881\) | −2.20766 | −0.0743778 | −0.0371889 | − | 0.999308i | \(-0.511840\pi\) | ||||
−0.0371889 | + | 0.999308i | \(0.511840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.4582i | − | 0.351948i | −0.984395 | − | 0.175974i | \(-0.943693\pi\) | ||
0.984395 | − | 0.175974i | \(-0.0563074\pi\) | |||||||
\(884\) | 25.8450i | 0.869261i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.6070 | −0.725900 | ||||||||
\(887\) | 12.6894i | 0.426068i | 0.977045 | + | 0.213034i | \(0.0683345\pi\) | ||||
−0.977045 | + | 0.213034i | \(0.931666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.48371 | − | 14.3833i | 0.116774 | − | 0.482128i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.22392 | 0.107945 | ||||||||
\(893\) | −38.9538 | −1.30354 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53.0176 | + | 12.8412i | 1.77218 | + | 0.429233i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 13.3403i | − | 0.445170i | ||||||
\(899\) | −65.7814 | −2.19393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 29.6669i | − | 0.988347i | ||||||
\(902\) | − | 30.0154i | − | 0.999403i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.19926 | −0.239444 | ||||||||
\(905\) | −47.8875 | − | 11.5986i | −1.59183 | − | 0.385552i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 29.8458i | − | 0.991013i | −0.868604 | − | 0.495506i | \(-0.834982\pi\) | ||
0.868604 | − | 0.495506i | \(-0.165018\pi\) | |||||||
\(908\) | 2.34174i | 0.0777135i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 43.2244i | − | 1.43209i | −0.698055 | − | 0.716044i | \(-0.745951\pi\) | ||
0.698055 | − | 0.716044i | \(-0.254049\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.5401 | 0.580491 | ||||||||
\(914\) | − | 31.7813i | − | 1.05123i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 11.6386i | − | 0.384551i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.99346 | 0.296667 | 0.148333 | − | 0.988937i | \(-0.452609\pi\) | ||||
0.148333 | + | 0.988937i | \(0.452609\pi\) | |||||||
\(920\) | −4.06235 | + | 16.7723i | −0.133932 | + | 0.552966i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.61323 | −0.151929 | ||||||||
\(923\) | 51.5455i | 1.69664i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.1693 | − | 41.1373i | 0.696042 | − | 1.35259i | ||||
\(926\) | − | 14.0850i | − | 0.462863i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.2237i | 0.335610i | ||||||||
\(929\) | 1.64006 | 0.0538088 | 0.0269044 | − | 0.999638i | \(-0.491435\pi\) | ||||
0.0269044 | + | 0.999638i | \(0.491435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.0869816 | 0.00284918 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 39.9154i | − | 1.30607i | ||||||
\(935\) | 12.1626 | − | 50.2157i | 0.397758 | − | 1.64223i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.6237 | −0.935095 | −0.467547 | − | 0.883968i | \(-0.654862\pi\) | ||||
−0.467547 | + | 0.883968i | \(0.654862\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17.0272 | + | 4.12409i | 0.555366 | + | 0.134513i | ||||
\(941\) | −47.0222 | −1.53288 | −0.766440 | − | 0.642316i | \(-0.777974\pi\) | ||||
−0.766440 | + | 0.642316i | \(0.777974\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.4274 | 1.70727 | ||||||||
\(944\) | 12.1340 | 0.394928 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.20029 | −0.299127 | ||||||||
\(947\) | 12.0543 | 0.391714 | 0.195857 | − | 0.980632i | \(-0.437251\pi\) | ||||
0.195857 | + | 0.980632i | \(0.437251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00129 | 0.0325033 | ||||||||
\(950\) | 11.3747 | − | 22.1039i | 0.369044 | − | 0.717146i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.3751 | 1.08113 | 0.540563 | − | 0.841304i | \(-0.318211\pi\) | ||||
0.540563 | + | 0.841304i | \(0.318211\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 58.3582 | + | 14.1347i | 1.88843 | + | 0.457388i | ||||
\(956\) | − | 13.6099i | − | 0.440175i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.3228 | 0.721217 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.3989 | −0.335449 | ||||||||
\(962\) | − | 45.7293i | − | 1.47437i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 5.13807i | − | 0.165486i | ||||||
\(965\) | −30.3814 | − | 7.35856i | −0.978011 | − | 0.236880i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.1284i | 1.93360i | 0.255535 | + | 0.966800i | \(0.417749\pi\) | ||||
−0.255535 | + | 0.966800i | \(0.582251\pi\) | |||||||
\(968\) | −8.52291 | −0.273937 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.65798 | + | 31.6176i | −0.245883 | + | 1.01518i | ||||
\(971\) | −18.8075 | −0.603562 | −0.301781 | − | 0.953377i | \(-0.597581\pi\) | ||||
−0.301781 | + | 0.953377i | \(0.597581\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 41.2767i | − | 1.32259i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 6.76571i | − | 0.216565i | ||||||
\(977\) | −44.7033 | −1.43019 | −0.715093 | − | 0.699029i | \(-0.753616\pi\) | ||||
−0.715093 | + | 0.699029i | \(0.753616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.2431i | 0.934614i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.6041i | 0.466036i | ||||||||
\(983\) | − | 28.9964i | − | 0.924842i | −0.886660 | − | 0.462421i | \(-0.846981\pi\) | ||
0.886660 | − | 0.462421i | \(-0.153019\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.90662 | − | 24.3867i | 0.188201 | − | 0.777026i | ||||
\(986\) | 53.4651 | 1.70267 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 24.5713i | − | 0.781717i | ||||||
\(989\) | − | 16.0700i | − | 0.510996i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.2764 | 1.85121 | 0.925605 | − | 0.378491i | \(-0.123557\pi\) | ||||
0.925605 | + | 0.378491i | \(0.123557\pi\) | |||||||
\(992\) | 6.43420i | 0.204286i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.91342 | + | 0.947854i | 0.124064 | + | 0.0300490i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.40483 | 0.0761618 | 0.0380809 | − | 0.999275i | \(-0.487876\pi\) | ||||
0.0380809 | + | 0.999275i | \(0.487876\pi\) | |||||||
\(998\) | 13.6787 | 0.432992 | ||||||||
\(999\) | 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 | 4410.2.d.d.4409.13 | yes | 24 | |
3.2 | odd | 2 | 4410.2.d.c.4409.12 | yes | 24 | ||
5.4 | even | 2 | 4410.2.d.c.4409.14 | yes | 24 | ||
7.6 | odd | 2 | inner | 4410.2.d.d.4409.12 | yes | 24 | |
15.14 | odd | 2 | inner | 4410.2.d.d.4409.11 | yes | 24 | |
21.20 | even | 2 | 4410.2.d.c.4409.13 | yes | 24 | ||
35.34 | odd | 2 | 4410.2.d.c.4409.11 | ✓ | 24 | ||
105.104 | even | 2 | inner | 4410.2.d.d.4409.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.d.c.4409.11 | ✓ | 24 | 35.34 | odd | 2 | ||
4410.2.d.c.4409.12 | yes | 24 | 3.2 | odd | 2 | ||
4410.2.d.c.4409.13 | yes | 24 | 21.20 | even | 2 | ||
4410.2.d.c.4409.14 | yes | 24 | 5.4 | even | 2 | ||
4410.2.d.d.4409.11 | yes | 24 | 15.14 | odd | 2 | inner | |
4410.2.d.d.4409.12 | yes | 24 | 7.6 | odd | 2 | inner | |
4410.2.d.d.4409.13 | yes | 24 | 1.1 | even | 1 | trivial | |
4410.2.d.d.4409.14 | yes | 24 | 105.104 | even | 2 | inner |