Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,2,Mod(11,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.k (of order \(4\), degree \(2\), 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: | \(0.383281929702\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.163368480538624.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 35.4 | ||
Root | \(1.35164 - 0.416001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.35 |
Dual form | 48.2.k.a.11.4 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.416001 | − | 1.35164i | 0.294157 | − | 0.955757i | ||||
\(3\) | −1.43726 | − | 0.966579i | −0.829804 | − | 0.558055i | ||||
\(4\) | −1.65389 | − | 1.12457i | −0.826943 | − | 0.562285i | ||||
\(5\) | 1.57184 | + | 1.57184i | 0.702949 | + | 0.702949i | 0.965042 | − | 0.262094i | \(-0.0844130\pi\) |
−0.262094 | + | 0.965042i | \(0.584413\pi\) | |||||||
\(6\) | −1.90437 | + | 1.54057i | −0.777458 | + | 0.628935i | ||||
\(7\) | 2.24914 | 0.850095 | 0.425048 | − | 0.905171i | \(-0.360257\pi\) | ||||
0.425048 | + | 0.905171i | \(0.360257\pi\) | |||||||
\(8\) | −2.20804 | + | 1.76765i | −0.780659 | + | 0.624957i | ||||
\(9\) | 1.13145 | + | 2.77846i | 0.377150 | + | 0.926152i | ||||
\(10\) | 2.77846 | − | 1.47068i | 0.878625 | − | 0.465071i | ||||
\(11\) | −1.13145 | + | 1.13145i | −0.341145 | + | 0.341145i | −0.856798 | − | 0.515653i | \(-0.827549\pi\) |
0.515653 | + | 0.856798i | \(0.327549\pi\) | |||||||
\(12\) | 1.29008 | + | 3.21492i | 0.372415 | + | 0.928066i | ||||
\(13\) | −3.24914 | − | 3.24914i | −0.901149 | − | 0.901149i | 0.0943862 | − | 0.995536i | \(-0.469911\pi\) |
−0.995536 | + | 0.0943862i | \(0.969911\pi\) | |||||||
\(14\) | 0.935644 | − | 3.04004i | 0.250061 | − | 0.812485i | ||||
\(15\) | −0.739839 | − | 3.77846i | −0.191026 | − | 0.975593i | ||||
\(16\) | 1.47068 | + | 3.71982i | 0.367671 | + | 0.929956i | ||||
\(17\) | 1.66400i | 0.403580i | 0.979429 | + | 0.201790i | \(0.0646758\pi\) | ||||
−0.979429 | + | 0.201790i | \(0.935324\pi\) | |||||||
\(18\) | 4.22617 | − | 0.373476i | 0.996118 | − | 0.0880293i | ||||
\(19\) | −3.77846 | + | 3.77846i | −0.866838 | + | 0.866838i | −0.992121 | − | 0.125283i | \(-0.960016\pi\) |
0.125283 | + | 0.992121i | \(0.460016\pi\) | |||||||
\(20\) | −0.832001 | − | 4.36729i | −0.186041 | − | 0.976556i | ||||
\(21\) | −3.23261 | − | 2.17397i | −0.705412 | − | 0.474400i | ||||
\(22\) | 1.05863 | + | 2.00000i | 0.225701 | + | 0.426401i | ||||
\(23\) | − | 2.26290i | − | 0.471847i | −0.971772 | − | 0.235923i | \(-0.924189\pi\) | ||
0.971772 | − | 0.235923i | \(-0.0758114\pi\) | |||||||
\(24\) | 4.88210 | − | 0.406327i | 0.996554 | − | 0.0829412i | ||||
\(25\) | − | 0.0586332i | − | 0.0117266i | ||||||
\(26\) | −5.74333 | + | 3.04004i | −1.12636 | + | 0.596201i | ||||
\(27\) | 1.05941 | − | 5.08701i | 0.203884 | − | 0.978995i | ||||
\(28\) | −3.71982 | − | 2.52932i | −0.702981 | − | 0.477996i | ||||
\(29\) | 3.23584 | − | 3.23584i | 0.600881 | − | 0.600881i | −0.339665 | − | 0.940546i | \(-0.610314\pi\) |
0.940546 | + | 0.339665i | \(0.110314\pi\) | |||||||
\(30\) | −5.41491 | − | 0.571841i | −0.988622 | − | 0.104403i | ||||
\(31\) | 1.30777i | 0.234883i | 0.993080 | + | 0.117442i | \(0.0374693\pi\) | ||||
−0.993080 | + | 0.117442i | \(0.962531\pi\) | |||||||
\(32\) | 5.63969 | − | 0.440392i | 0.996965 | − | 0.0778511i | ||||
\(33\) | 2.71982 | − | 0.532554i | 0.473461 | − | 0.0927058i | ||||
\(34\) | 2.24914 | + | 0.692226i | 0.385724 | + | 0.118716i | ||||
\(35\) | 3.53529 | + | 3.53529i | 0.597573 | + | 0.597573i | ||||
\(36\) | 1.25328 | − | 5.86765i | 0.208880 | − | 0.977941i | ||||
\(37\) | 2.30777 | − | 2.30777i | 0.379396 | − | 0.379396i | −0.491488 | − | 0.870884i | \(-0.663547\pi\) |
0.870884 | + | 0.491488i | \(0.163547\pi\) | |||||||
\(38\) | 3.53529 | + | 6.67897i | 0.573500 | + | 1.08347i | ||||
\(39\) | 1.52932 | + | 7.81042i | 0.244887 | + | 1.25067i | ||||
\(40\) | −6.24914 | − | 0.692226i | −0.988076 | − | 0.109451i | ||||
\(41\) | −10.2143 | −1.59520 | −0.797600 | − | 0.603187i | \(-0.793897\pi\) | ||||
−0.797600 | + | 0.603187i | \(0.793897\pi\) | |||||||
\(42\) | −4.28321 | + | 3.46496i | −0.660913 | + | 0.534655i | ||||
\(43\) | 3.77846 | + | 3.77846i | 0.576209 | + | 0.576209i | 0.933857 | − | 0.357647i | \(-0.116421\pi\) |
−0.357647 | + | 0.933857i | \(0.616421\pi\) | |||||||
\(44\) | 3.14368 | − | 0.598895i | 0.473928 | − | 0.0902867i | ||||
\(45\) | −2.58884 | + | 6.14575i | −0.385921 | + | 0.916154i | ||||
\(46\) | −3.05863 | − | 0.941367i | −0.450971 | − | 0.138797i | ||||
\(47\) | 3.74258 | 0.545911 | 0.272955 | − | 0.962027i | \(-0.411999\pi\) | ||||
0.272955 | + | 0.962027i | \(0.411999\pi\) | |||||||
\(48\) | 1.48175 | − | 6.76790i | 0.213872 | − | 0.976862i | ||||
\(49\) | −1.94137 | −0.277338 | ||||||||
\(50\) | −0.0792512 | − | 0.0243914i | −0.0112078 | − | 0.00344947i | ||||
\(51\) | 1.60839 | − | 2.39161i | 0.225220 | − | 0.334892i | ||||
\(52\) | 1.71982 | + | 9.02760i | 0.238497 | + | 1.25190i | ||||
\(53\) | −0.972946 | − | 0.972946i | −0.133644 | − | 0.133644i | 0.637120 | − | 0.770765i | \(-0.280126\pi\) |
−0.770765 | + | 0.637120i | \(0.780126\pi\) | |||||||
\(54\) | −6.43511 | − | 3.54815i | −0.875708 | − | 0.482841i | ||||
\(55\) | −3.55691 | −0.479614 | ||||||||
\(56\) | −4.96619 | + | 3.97568i | −0.663635 | + | 0.531273i | ||||
\(57\) | 9.08281 | − | 1.77846i | 1.20305 | − | 0.235562i | ||||
\(58\) | −3.02760 | − | 5.71982i | −0.397543 | − | 0.751050i | ||||
\(59\) | −3.88352 | + | 3.88352i | −0.505591 | + | 0.505591i | −0.913170 | − | 0.407579i | \(-0.866373\pi\) |
0.407579 | + | 0.913170i | \(0.366373\pi\) | |||||||
\(60\) | −3.02553 | + | 7.08114i | −0.390594 | + | 0.914171i | ||||
\(61\) | 4.19051 | + | 4.19051i | 0.536539 | + | 0.536539i | 0.922511 | − | 0.385971i | \(-0.126134\pi\) |
−0.385971 | + | 0.922511i | \(0.626134\pi\) | |||||||
\(62\) | 1.76765 | + | 0.544035i | 0.224491 | + | 0.0690925i | ||||
\(63\) | 2.54479 | + | 6.24914i | 0.320613 | + | 0.787318i | ||||
\(64\) | 1.75086 | − | 7.80605i | 0.218857 | − | 0.975757i | ||||
\(65\) | − | 10.2143i | − | 1.26692i | ||||||
\(66\) | 0.411625 | − | 3.89778i | 0.0506675 | − | 0.479783i | ||||
\(67\) | 8.02760 | − | 8.02760i | 0.980727 | − | 0.980727i | −0.0190906 | − | 0.999818i | \(-0.506077\pi\) |
0.999818 | + | 0.0190906i | \(0.00607710\pi\) | |||||||
\(68\) | 1.87129 | − | 2.75207i | 0.226927 | − | 0.333738i | ||||
\(69\) | −2.18727 | + | 3.25238i | −0.263316 | + | 0.391540i | ||||
\(70\) | 6.24914 | − | 3.30777i | 0.746915 | − | 0.395355i | ||||
\(71\) | − | 11.0950i | − | 1.31674i | −0.752695 | − | 0.658370i | \(-0.771246\pi\) | ||
0.752695 | − | 0.658370i | \(-0.228754\pi\) | |||||||
\(72\) | −7.40961 | − | 4.13494i | −0.873231 | − | 0.487307i | ||||
\(73\) | − | 6.38101i | − | 0.746841i | −0.927662 | − | 0.373421i | \(-0.878185\pi\) | ||
0.927662 | − | 0.373421i | \(-0.121815\pi\) | |||||||
\(74\) | −2.15925 | − | 4.07933i | −0.251008 | − | 0.474212i | ||||
\(75\) | −0.0566736 | + | 0.0842713i | −0.00654410 | + | 0.00973081i | ||||
\(76\) | 10.4983 | − | 2.00000i | 1.20424 | − | 0.229416i | ||||
\(77\) | −2.54479 | + | 2.54479i | −0.290005 | + | 0.290005i | ||||
\(78\) | 11.1931 | + | 1.18205i | 1.26737 | + | 0.133841i | ||||
\(79\) | 2.69223i | 0.302899i | 0.988465 | + | 0.151450i | \(0.0483941\pi\) | ||||
−0.988465 | + | 0.151450i | \(0.951606\pi\) | |||||||
\(80\) | −3.53529 | + | 8.15865i | −0.395258 | + | 0.912165i | ||||
\(81\) | −6.43965 | + | 6.28736i | −0.715516 | + | 0.698596i | ||||
\(82\) | −4.24914 | + | 13.8061i | −0.469239 | + | 1.52462i | ||||
\(83\) | −2.61113 | − | 2.61113i | −0.286608 | − | 0.286608i | 0.549129 | − | 0.835738i | \(-0.314960\pi\) |
−0.835738 | + | 0.549129i | \(0.814960\pi\) | |||||||
\(84\) | 2.90158 | + | 7.23080i | 0.316588 | + | 0.788945i | ||||
\(85\) | −2.61555 | + | 2.61555i | −0.283696 | + | 0.283696i | ||||
\(86\) | 6.67897 | − | 3.53529i | 0.720212 | − | 0.381220i | ||||
\(87\) | −7.77846 | + | 1.52306i | −0.833938 | + | 0.163289i | ||||
\(88\) | 0.498281 | − | 4.49828i | 0.0531169 | − | 0.479518i | ||||
\(89\) | 7.35247 | 0.779360 | 0.389680 | − | 0.920950i | \(-0.372586\pi\) | ||||
0.389680 | + | 0.920950i | \(0.372586\pi\) | |||||||
\(90\) | 7.22991 | + | 6.05582i | 0.762100 | + | 0.638340i | ||||
\(91\) | −7.30777 | − | 7.30777i | −0.766063 | − | 0.766063i | ||||
\(92\) | −2.54479 | + | 3.74258i | −0.265312 | + | 0.390191i | ||||
\(93\) | 1.26407 | − | 1.87961i | 0.131078 | − | 0.194907i | ||||
\(94\) | 1.55691 | − | 5.05863i | 0.160583 | − | 0.521758i | ||||
\(95\) | −11.8783 | −1.21868 | ||||||||
\(96\) | −8.53138 | − | 4.81824i | −0.870731 | − | 0.491760i | ||||
\(97\) | −5.67418 | −0.576126 | −0.288063 | − | 0.957611i | \(-0.593011\pi\) | ||||
−0.288063 | + | 0.957611i | \(0.593011\pi\) | |||||||
\(98\) | −0.807610 | + | 2.62404i | −0.0815809 | + | 0.265068i | ||||
\(99\) | −4.42386 | − | 1.86351i | −0.444614 | − | 0.187289i | ||||
\(100\) | −0.0659371 | + | 0.0969726i | −0.00659371 | + | 0.00969726i | ||||
\(101\) | 10.3064 | + | 10.3064i | 1.02553 | + | 1.02553i | 0.999666 | + | 0.0258621i | \(0.00823308\pi\) |
0.0258621 | + | 0.999666i | \(0.491767\pi\) | |||||||
\(102\) | −2.56351 | − | 3.16888i | −0.253826 | − | 0.313766i | ||||
\(103\) | −8.13187 | −0.801257 | −0.400629 | − | 0.916241i | \(-0.631208\pi\) | ||||
−0.400629 | + | 0.916241i | \(0.631208\pi\) | |||||||
\(104\) | 12.9176 | + | 1.43090i | 1.26667 | + | 0.140311i | ||||
\(105\) | −1.66400 | − | 8.49828i | −0.162390 | − | 0.829347i | ||||
\(106\) | −1.71982 | + | 0.910331i | −0.167044 | + | 0.0884192i | ||||
\(107\) | 2.40384 | − | 2.40384i | 0.232388 | − | 0.232388i | −0.581301 | − | 0.813689i | \(-0.697456\pi\) |
0.813689 | + | 0.581301i | \(0.197456\pi\) | |||||||
\(108\) | −7.47284 | + | 7.22195i | −0.719075 | + | 0.694933i | ||||
\(109\) | 8.92332 | + | 8.92332i | 0.854699 | + | 0.854699i | 0.990708 | − | 0.136009i | \(-0.0434275\pi\) |
−0.136009 | + | 0.990708i | \(0.543427\pi\) | |||||||
\(110\) | −1.47968 | + | 4.80768i | −0.141082 | + | 0.458395i | ||||
\(111\) | −5.54752 | + | 1.08623i | −0.526548 | + | 0.103100i | ||||
\(112\) | 3.30777 | + | 8.36641i | 0.312555 | + | 0.790551i | ||||
\(113\) | 15.9027i | 1.49600i | 0.663697 | + | 0.748002i | \(0.268986\pi\) | ||||
−0.663697 | + | 0.748002i | \(0.731014\pi\) | |||||||
\(114\) | 1.37461 | − | 13.0166i | 0.128744 | − | 1.21911i | ||||
\(115\) | 3.55691 | − | 3.55691i | 0.331684 | − | 0.331684i | ||||
\(116\) | −8.99065 | + | 1.71279i | −0.834761 | + | 0.159028i | ||||
\(117\) | 5.35136 | − | 12.7038i | 0.494734 | − | 1.17447i | ||||
\(118\) | 3.63359 | + | 6.86469i | 0.334499 | + | 0.631946i | ||||
\(119\) | 3.74258i | 0.343081i | ||||||||
\(120\) | 8.31257 | + | 7.03520i | 0.758830 | + | 0.642223i | ||||
\(121\) | 8.43965i | 0.767241i | ||||||||
\(122\) | 7.40733 | − | 3.92082i | 0.670628 | − | 0.354975i | ||||
\(123\) | 14.6806 | + | 9.87290i | 1.32370 | + | 0.890209i | ||||
\(124\) | 1.47068 | − | 2.16291i | 0.132071 | − | 0.194235i | ||||
\(125\) | 7.95137 | − | 7.95137i | 0.711192 | − | 0.711192i | ||||
\(126\) | 9.50525 | − | 0.840001i | 0.846795 | − | 0.0748332i | ||||
\(127\) | − | 7.42504i | − | 0.658866i | −0.944179 | − | 0.329433i | \(-0.893142\pi\) | ||
0.944179 | − | 0.329433i | \(-0.106858\pi\) | |||||||
\(128\) | −9.82265 | − | 5.61386i | −0.868208 | − | 0.496200i | ||||
\(129\) | −1.77846 | − | 9.08281i | −0.156584 | − | 0.799697i | ||||
\(130\) | −13.8061 | − | 4.24914i | −1.21087 | − | 0.372674i | ||||
\(131\) | 3.88352 | + | 3.88352i | 0.339305 | + | 0.339305i | 0.856106 | − | 0.516801i | \(-0.172877\pi\) |
−0.516801 | + | 0.856106i | \(0.672877\pi\) | |||||||
\(132\) | −5.09718 | − | 2.17785i | −0.443652 | − | 0.189557i | ||||
\(133\) | −8.49828 | + | 8.49828i | −0.736894 | + | 0.736894i | ||||
\(134\) | −7.51097 | − | 14.1899i | −0.648849 | − | 1.22582i | ||||
\(135\) | 9.66119 | − | 6.33074i | 0.831503 | − | 0.544864i | ||||
\(136\) | −2.94137 | − | 3.67418i | −0.252220 | − | 0.315058i | ||||
\(137\) | −2.72911 | −0.233164 | −0.116582 | − | 0.993181i | \(-0.537194\pi\) | ||||
−0.116582 | + | 0.993181i | \(0.537194\pi\) | |||||||
\(138\) | 3.48615 | + | 4.30940i | 0.296761 | + | 0.366841i | ||||
\(139\) | −0.0275977 | − | 0.0275977i | −0.00234080 | − | 0.00234080i | 0.705935 | − | 0.708276i | \(-0.250527\pi\) |
−0.708276 | + | 0.705935i | \(0.750527\pi\) | |||||||
\(140\) | −1.87129 | − | 9.82265i | −0.158153 | − | 0.830166i | ||||
\(141\) | −5.37907 | − | 3.61750i | −0.452999 | − | 0.304648i | ||||
\(142\) | −14.9966 | − | 4.61555i | −1.25848 | − | 0.387328i | ||||
\(143\) | 7.35247 | 0.614845 | ||||||||
\(144\) | −8.67137 | + | 8.29502i | −0.722614 | + | 0.691252i | ||||
\(145\) | 10.1725 | 0.844777 | ||||||||
\(146\) | −8.62486 | − | 2.65451i | −0.713799 | − | 0.219689i | ||||
\(147\) | 2.79025 | + | 1.87649i | 0.230136 | + | 0.154770i | ||||
\(148\) | −6.41205 | + | 1.22154i | −0.527067 | + | 0.100410i | ||||
\(149\) | −12.5693 | − | 12.5693i | −1.02972 | − | 1.02972i | −0.999545 | − | 0.0301744i | \(-0.990394\pi\) |
−0.0301744 | − | 0.999545i | \(-0.509606\pi\) | |||||||
\(150\) | 0.0903285 | + | 0.111659i | 0.00737529 | + | 0.00911696i | ||||
\(151\) | 16.8647 | 1.37243 | 0.686214 | − | 0.727399i | \(-0.259271\pi\) | ||||
0.686214 | + | 0.727399i | \(0.259271\pi\) | |||||||
\(152\) | 1.66400 | − | 15.0219i | 0.134968 | − | 1.21844i | ||||
\(153\) | −4.62336 | + | 1.88273i | −0.373777 | + | 0.152210i | ||||
\(154\) | 2.38101 | + | 4.49828i | 0.191868 | + | 0.362482i | ||||
\(155\) | −2.05561 | + | 2.05561i | −0.165111 | + | 0.165111i | ||||
\(156\) | 6.25405 | − | 14.6374i | 0.500725 | − | 1.17193i | ||||
\(157\) | −5.36641 | − | 5.36641i | −0.428286 | − | 0.428286i | 0.459758 | − | 0.888044i | \(-0.347936\pi\) |
−0.888044 | + | 0.459758i | \(0.847936\pi\) | |||||||
\(158\) | 3.63893 | + | 1.11997i | 0.289498 | + | 0.0890999i | ||||
\(159\) | 0.457950 | + | 2.33881i | 0.0363178 | + | 0.185480i | ||||
\(160\) | 9.55691 | + | 8.17246i | 0.755540 | + | 0.646090i | ||||
\(161\) | − | 5.08957i | − | 0.401115i | ||||||
\(162\) | 5.81938 | + | 11.3197i | 0.457214 | + | 0.889357i | ||||
\(163\) | −8.77502 | + | 8.77502i | −0.687313 | + | 0.687313i | −0.961637 | − | 0.274325i | \(-0.911546\pi\) |
0.274325 | + | 0.961637i | \(0.411546\pi\) | |||||||
\(164\) | 16.8932 | + | 11.4867i | 1.31914 | + | 0.896957i | ||||
\(165\) | 5.11222 | + | 3.43804i | 0.397986 | + | 0.267651i | ||||
\(166\) | −4.61555 | + | 2.44309i | −0.358236 | + | 0.189620i | ||||
\(167\) | 16.9678i | 1.31301i | 0.754321 | + | 0.656505i | \(0.227966\pi\) | ||||
−0.754321 | + | 0.656505i | \(0.772034\pi\) | |||||||
\(168\) | 10.9805 | − | 0.913888i | 0.847166 | − | 0.0705080i | ||||
\(169\) | 8.11383i | 0.624141i | ||||||||
\(170\) | 2.44722 | + | 4.62336i | 0.187693 | + | 0.354596i | ||||
\(171\) | −14.7734 | − | 6.22315i | −1.12975 | − | 0.475896i | ||||
\(172\) | −2.00000 | − | 10.4983i | −0.152499 | − | 0.800486i | ||||
\(173\) | −16.3119 | + | 16.3119i | −1.24017 | + | 1.24017i | −0.280241 | + | 0.959930i | \(0.590414\pi\) |
−0.959930 | + | 0.280241i | \(0.909586\pi\) | |||||||
\(174\) | −1.17721 | + | 11.1473i | −0.0892441 | + | 0.845075i | ||||
\(175\) | − | 0.131874i | − | 0.00996875i | ||||||
\(176\) | −5.87279 | − | 2.54479i | −0.442678 | − | 0.191821i | ||||
\(177\) | 9.33537 | − | 1.82791i | 0.701689 | − | 0.137394i | ||||
\(178\) | 3.05863 | − | 9.93793i | 0.229254 | − | 0.744879i | ||||
\(179\) | 1.33873 | + | 1.33873i | 0.100062 | + | 0.100062i | 0.755365 | − | 0.655304i | \(-0.227459\pi\) |
−0.655304 | + | 0.755365i | \(0.727459\pi\) | |||||||
\(180\) | 11.1930 | − | 7.25305i | 0.834275 | − | 0.540610i | ||||
\(181\) | 10.2457 | − | 10.2457i | 0.761557 | − | 0.761557i | −0.215047 | − | 0.976604i | \(-0.568990\pi\) |
0.976604 | + | 0.215047i | \(0.0689904\pi\) | |||||||
\(182\) | −12.9176 | + | 6.83747i | −0.957513 | + | 0.506827i | ||||
\(183\) | −1.97240 | − | 10.0733i | −0.145804 | − | 0.744641i | ||||
\(184\) | 4.00000 | + | 4.99656i | 0.294884 | + | 0.368351i | ||||
\(185\) | 7.25491 | 0.533391 | ||||||||
\(186\) | −2.01472 | − | 2.49049i | −0.147726 | − | 0.182612i | ||||
\(187\) | −1.88273 | − | 1.88273i | −0.137679 | − | 0.137679i | ||||
\(188\) | −6.18980 | − | 4.20879i | −0.451437 | − | 0.306958i | ||||
\(189\) | 2.38276 | − | 11.4414i | 0.173320 | − | 0.832239i | ||||
\(190\) | −4.94137 | + | 16.0552i | −0.358484 | + | 1.16477i | ||||
\(191\) | 24.5398 | 1.77563 | 0.887817 | − | 0.460197i | \(-0.152221\pi\) | ||||
0.887817 | + | 0.460197i | \(0.152221\pi\) | |||||||
\(192\) | −10.0616 | + | 9.52701i | −0.726135 | + | 0.687553i | ||||
\(193\) | 8.38101 | 0.603279 | 0.301639 | − | 0.953422i | \(-0.402466\pi\) | ||||
0.301639 | + | 0.953422i | \(0.402466\pi\) | |||||||
\(194\) | −2.36046 | + | 7.66948i | −0.169471 | + | 0.550636i | ||||
\(195\) | −9.87290 | + | 14.6806i | −0.707013 | + | 1.05130i | ||||
\(196\) | 3.21080 | + | 2.18320i | 0.229343 | + | 0.155943i | ||||
\(197\) | −1.28995 | − | 1.28995i | −0.0919052 | − | 0.0919052i | 0.659659 | − | 0.751565i | \(-0.270701\pi\) |
−0.751565 | + | 0.659659i | \(0.770701\pi\) | |||||||
\(198\) | −4.35913 | + | 5.20426i | −0.309790 | + | 0.369851i | ||||
\(199\) | −13.0992 | −0.928579 | −0.464290 | − | 0.885683i | \(-0.653690\pi\) | ||||
−0.464290 | + | 0.885683i | \(0.653690\pi\) | |||||||
\(200\) | 0.103643 | + | 0.129464i | 0.00732864 | + | 0.00915450i | ||||
\(201\) | −19.2971 | + | 3.77846i | −1.36111 | + | 0.266512i | ||||
\(202\) | 18.2181 | − | 9.64315i | 1.28182 | − | 0.678489i | ||||
\(203\) | 7.27787 | − | 7.27787i | 0.510806 | − | 0.510806i | ||||
\(204\) | −5.34963 | + | 2.14670i | −0.374549 | + | 0.150299i | ||||
\(205\) | −16.0552 | − | 16.0552i | −1.12134 | − | 1.12134i | ||||
\(206\) | −3.38287 | + | 10.9914i | −0.235695 | + | 0.765807i | ||||
\(207\) | 6.28736 | − | 2.56035i | 0.437002 | − | 0.177957i | ||||
\(208\) | 7.30777 | − | 16.8647i | 0.506703 | − | 1.16936i | ||||
\(209\) | − | 8.55026i | − | 0.591434i | ||||||
\(210\) | −12.1789 | − | 1.28615i | −0.840423 | − | 0.0887528i | ||||
\(211\) | −8.47068 | + | 8.47068i | −0.583146 | + | 0.583146i | −0.935766 | − | 0.352621i | \(-0.885291\pi\) |
0.352621 | + | 0.935766i | \(0.385291\pi\) | |||||||
\(212\) | 0.514997 | + | 2.70329i | 0.0353701 | + | 0.185663i | ||||
\(213\) | −10.7242 | + | 15.9465i | −0.734813 | + | 1.09264i | ||||
\(214\) | −2.24914 | − | 4.24914i | −0.153748 | − | 0.290465i | ||||
\(215\) | 11.8783i | 0.810091i | ||||||||
\(216\) | 6.65281 | + | 13.1050i | 0.452666 | + | 0.891680i | ||||
\(217\) | 2.94137i | 0.199673i | ||||||||
\(218\) | 15.7733 | − | 8.34905i | 1.06830 | − | 0.565469i | ||||
\(219\) | −6.16776 | + | 9.17120i | −0.416778 | + | 0.619732i | ||||
\(220\) | 5.88273 | + | 4.00000i | 0.396614 | + | 0.269680i | ||||
\(221\) | 5.40658 | − | 5.40658i | 0.363686 | − | 0.363686i | ||||
\(222\) | −0.839576 | + | 7.95015i | −0.0563486 | + | 0.533579i | ||||
\(223\) | − | 21.5715i | − | 1.44454i | −0.691613 | − | 0.722268i | \(-0.743100\pi\) | ||
0.691613 | − | 0.722268i | \(-0.256900\pi\) | |||||||
\(224\) | 12.6844 | − | 0.990504i | 0.847515 | − | 0.0661808i | ||||
\(225\) | 0.162910 | − | 0.0663404i | 0.0108606 | − | 0.00442269i | ||||
\(226\) | 21.4948 | + | 6.61555i | 1.42982 | + | 0.440060i | ||||
\(227\) | −16.7523 | − | 16.7523i | −1.11189 | − | 1.11189i | −0.992895 | − | 0.118994i | \(-0.962033\pi\) |
−0.118994 | − | 0.992895i | \(-0.537967\pi\) | |||||||
\(228\) | −17.0219 | − | 7.27290i | −1.12731 | − | 0.481659i | ||||
\(229\) | 3.36641 | − | 3.36641i | 0.222458 | − | 0.222458i | −0.587074 | − | 0.809533i | \(-0.699720\pi\) |
0.809533 | + | 0.587074i | \(0.199720\pi\) | |||||||
\(230\) | −3.32801 | − | 6.28736i | −0.219442 | − | 0.414576i | ||||
\(231\) | 6.11727 | − | 1.19779i | 0.402487 | − | 0.0788087i | ||||
\(232\) | −1.42504 | + | 12.8647i | −0.0935585 | + | 0.844608i | ||||
\(233\) | 0.501329 | 0.0328431 | 0.0164216 | − | 0.999865i | \(-0.494773\pi\) | ||||
0.0164216 | + | 0.999865i | \(0.494773\pi\) | |||||||
\(234\) | −14.9449 | − | 12.5179i | −0.976979 | − | 0.818324i | ||||
\(235\) | 5.88273 | + | 5.88273i | 0.383747 | + | 0.383747i | ||||
\(236\) | 10.7902 | − | 2.05561i | 0.702382 | − | 0.133809i | ||||
\(237\) | 2.60225 | − | 3.86944i | 0.169034 | − | 0.251347i | ||||
\(238\) | 5.05863 | + | 1.55691i | 0.327902 | + | 0.100920i | ||||
\(239\) | −30.4585 | −1.97019 | −0.985097 | − | 0.171999i | \(-0.944978\pi\) | ||||
−0.985097 | + | 0.171999i | \(0.944978\pi\) | |||||||
\(240\) | 12.9671 | − | 8.30899i | 0.837024 | − | 0.536343i | ||||
\(241\) | −15.4948 | −0.998111 | −0.499055 | − | 0.866570i | \(-0.666320\pi\) | ||||
−0.499055 | + | 0.866570i | \(0.666320\pi\) | |||||||
\(242\) | 11.4074 | + | 3.51090i | 0.733296 | + | 0.225689i | ||||
\(243\) | 15.3327 | − | 2.81216i | 0.983593 | − | 0.180400i | ||||
\(244\) | −2.21811 | − | 11.6431i | −0.142000 | − | 0.745376i | ||||
\(245\) | −3.05152 | − | 3.05152i | −0.194954 | − | 0.194954i | ||||
\(246\) | 19.4518 | − | 15.7358i | 1.24020 | − | 1.00328i | ||||
\(247\) | 24.5535 | 1.56230 | ||||||||
\(248\) | −2.31168 | − | 2.88761i | −0.146792 | − | 0.183364i | ||||
\(249\) | 1.22901 | + | 6.27674i | 0.0778856 | + | 0.397772i | ||||
\(250\) | −7.43965 | − | 14.0552i | −0.470525 | − | 0.888929i | ||||
\(251\) | 12.2265 | − | 12.2265i | 0.771730 | − | 0.771730i | −0.206679 | − | 0.978409i | \(-0.566266\pi\) |
0.978409 | + | 0.206679i | \(0.0662656\pi\) | |||||||
\(252\) | 2.81881 | − | 13.1972i | 0.177568 | − | 0.831343i | ||||
\(253\) | 2.56035 | + | 2.56035i | 0.160968 | + | 0.160968i | ||||
\(254\) | −10.0360 | − | 3.08882i | −0.629716 | − | 0.193810i | ||||
\(255\) | 6.28736 | − | 1.23109i | 0.393730 | − | 0.0770941i | ||||
\(256\) | −11.6742 | + | 10.9414i | −0.729636 | + | 0.683835i | ||||
\(257\) | 7.48515i | 0.466911i | 0.972367 | + | 0.233455i | \(0.0750033\pi\) | ||||
−0.972367 | + | 0.233455i | \(0.924997\pi\) | |||||||
\(258\) | −13.0166 | − | 1.37461i | −0.810377 | − | 0.0855798i | ||||
\(259\) | 5.19051 | − | 5.19051i | 0.322522 | − | 0.322522i | ||||
\(260\) | −11.4867 | + | 16.8932i | −0.712372 | + | 1.04767i | ||||
\(261\) | 12.6518 | + | 5.32946i | 0.783129 | + | 0.329885i | ||||
\(262\) | 6.86469 | − | 3.63359i | 0.424102 | − | 0.224484i | ||||
\(263\) | − | 10.2659i | − | 0.633023i | −0.948589 | − | 0.316511i | \(-0.897488\pi\) | ||
0.948589 | − | 0.316511i | \(-0.102512\pi\) | |||||||
\(264\) | −5.06411 | + | 5.98358i | −0.311674 | + | 0.368264i | ||||
\(265\) | − | 3.05863i | − | 0.187890i | ||||||
\(266\) | 7.95137 | + | 15.0219i | 0.487530 | + | 0.921055i | ||||
\(267\) | −10.5674 | − | 7.10675i | −0.646716 | − | 0.434926i | ||||
\(268\) | −22.3043 | + | 4.24914i | −1.36245 | + | 0.259558i | ||||
\(269\) | 2.76963 | − | 2.76963i | 0.168867 | − | 0.168867i | −0.617614 | − | 0.786481i | \(-0.711901\pi\) |
0.786481 | + | 0.617614i | \(0.211901\pi\) | |||||||
\(270\) | −4.53785 | − | 15.6921i | −0.276165 | − | 0.954990i | ||||
\(271\) | 28.6854i | 1.74251i | 0.490830 | + | 0.871255i | \(0.336694\pi\) | ||||
−0.490830 | + | 0.871255i | \(0.663306\pi\) | |||||||
\(272\) | −6.18980 | + | 2.44722i | −0.375312 | + | 0.148385i | ||||
\(273\) | 3.43965 | + | 17.5667i | 0.208177 | + | 1.06319i | ||||
\(274\) | −1.13531 | + | 3.68879i | −0.0685867 | + | 0.222848i | ||||
\(275\) | 0.0663404 | + | 0.0663404i | 0.00400048 | + | 0.00400048i | ||||
\(276\) | 7.27502 | − | 2.91933i | 0.437905 | − | 0.175723i | ||||
\(277\) | −0.806055 | + | 0.806055i | −0.0484311 | + | 0.0484311i | −0.730908 | − | 0.682476i | \(-0.760903\pi\) |
0.682476 | + | 0.730908i | \(0.260903\pi\) | |||||||
\(278\) | −0.0487829 | + | 0.0258216i | −0.00292580 | + | 0.00154868i | ||||
\(279\) | −3.63359 | + | 1.47968i | −0.217538 | + | 0.0885861i | ||||
\(280\) | −14.0552 | − | 1.55691i | −0.839959 | − | 0.0930434i | ||||
\(281\) | 22.3228 | 1.33167 | 0.665833 | − | 0.746101i | \(-0.268076\pi\) | ||||
0.665833 | + | 0.746101i | \(0.268076\pi\) | |||||||
\(282\) | −7.12727 | + | 5.76570i | −0.424422 | + | 0.343343i | ||||
\(283\) | 8.08279 | + | 8.08279i | 0.480472 | + | 0.480472i | 0.905282 | − | 0.424810i | \(-0.139659\pi\) |
−0.424810 | + | 0.905282i | \(0.639659\pi\) | |||||||
\(284\) | −12.4772 | + | 18.3500i | −0.740383 | + | 1.08887i | ||||
\(285\) | 17.0722 | + | 11.4813i | 1.01127 | + | 0.680093i | ||||
\(286\) | 3.05863 | − | 9.93793i | 0.180861 | − | 0.587642i | ||||
\(287\) | −22.9733 | −1.35607 | ||||||||
\(288\) | 7.60463 | + | 15.1713i | 0.448107 | + | 0.893980i | ||||
\(289\) | 14.2311 | 0.837123 | ||||||||
\(290\) | 4.23175 | − | 13.7496i | 0.248497 | − | 0.807402i | ||||
\(291\) | 8.15529 | + | 5.48455i | 0.478071 | + | 0.321510i | ||||
\(292\) | −7.17590 | + | 10.5535i | −0.419938 | + | 0.617595i | ||||
\(293\) | −6.37953 | − | 6.37953i | −0.372696 | − | 0.372696i | 0.495762 | − | 0.868458i | \(-0.334889\pi\) |
−0.868458 | + | 0.495762i | \(0.834889\pi\) | |||||||
\(294\) | 3.69709 | − | 2.99081i | 0.215619 | − | 0.174428i | ||||
\(295\) | −12.2086 | −0.710809 | ||||||||
\(296\) | −1.01633 | + | 9.17498i | −0.0590727 | + | 0.533285i | ||||
\(297\) | 4.55702 | + | 6.95436i | 0.264425 | + | 0.403533i | ||||
\(298\) | −22.2181 | + | 11.7604i | −1.28706 | + | 0.681262i | ||||
\(299\) | −7.35247 | + | 7.35247i | −0.425204 | + | 0.425204i | ||||
\(300\) | 0.188501 | − | 0.0756417i | 0.0108831 | − | 0.00436717i | ||||
\(301\) | 8.49828 | + | 8.49828i | 0.489833 | + | 0.489833i | ||||
\(302\) | 7.01572 | − | 22.7951i | 0.403709 | − | 1.31171i | ||||
\(303\) | −4.85106 | − | 24.7750i | −0.278686 | − | 1.42329i | ||||
\(304\) | −19.6121 | − | 8.49828i | −1.12483 | − | 0.487410i | ||||
\(305\) | 13.1736i | 0.754319i | ||||||||
\(306\) | 0.621466 | + | 7.03236i | 0.0355268 | + | 0.402013i | ||||
\(307\) | −6.58795 | + | 6.58795i | −0.375994 | + | 0.375994i | −0.869655 | − | 0.493661i | \(-0.835659\pi\) |
0.493661 | + | 0.869655i | \(0.335659\pi\) | |||||||
\(308\) | 7.07058 | − | 1.34700i | 0.402884 | − | 0.0767523i | ||||
\(309\) | 11.6876 | + | 7.86010i | 0.664887 | + | 0.447146i | ||||
\(310\) | 1.92332 | + | 3.63359i | 0.109237 | + | 0.206374i | ||||
\(311\) | − | 9.52861i | − | 0.540318i | −0.962816 | − | 0.270159i | \(-0.912924\pi\) | ||
0.962816 | − | 0.270159i | \(-0.0870763\pi\) | |||||||
\(312\) | −17.1828 | − | 14.5424i | −0.972787 | − | 0.823302i | ||||
\(313\) | − | 25.1690i | − | 1.42264i | −0.702870 | − | 0.711319i | \(-0.748098\pi\) | ||
0.702870 | − | 0.711319i | \(-0.251902\pi\) | |||||||
\(314\) | −9.48590 | + | 5.02105i | −0.535321 | + | 0.283354i | ||||
\(315\) | −5.82265 | + | 13.8227i | −0.328069 | + | 0.778818i | ||||
\(316\) | 3.02760 | − | 4.45264i | 0.170316 | − | 0.250480i | ||||
\(317\) | −15.5287 | + | 15.5287i | −0.872178 | + | 0.872178i | −0.992709 | − | 0.120532i | \(-0.961540\pi\) |
0.120532 | + | 0.992709i | \(0.461540\pi\) | |||||||
\(318\) | 3.35175 | + | 0.353961i | 0.187957 | + | 0.0198491i | ||||
\(319\) | 7.32238i | 0.409975i | ||||||||
\(320\) | 15.0219 | − | 9.51780i | 0.839752 | − | 0.532061i | ||||
\(321\) | −5.77846 | + | 1.13145i | −0.322522 | + | 0.0631513i | ||||
\(322\) | −6.87930 | − | 2.11727i | −0.383368 | − | 0.117991i | ||||
\(323\) | −6.28736 | − | 6.28736i | −0.349838 | − | 0.349838i | ||||
\(324\) | 17.7210 | − | 3.15675i | 0.984502 | − | 0.175375i | ||||
\(325\) | −0.190507 | + | 0.190507i | −0.0105674 | + | 0.0105674i | ||||
\(326\) | 8.21029 | + | 15.5111i | 0.454726 | + | 0.859082i | ||||
\(327\) | −4.20006 | − | 21.4503i | −0.232264 | − | 1.18620i | ||||
\(328\) | 22.5535 | − | 18.0552i | 1.24531 | − | 0.996931i | ||||
\(329\) | 8.41758 | 0.464076 | ||||||||
\(330\) | 6.77370 | − | 5.47968i | 0.372880 | − | 0.301646i | ||||
\(331\) | 2.58795 | + | 2.58795i | 0.142247 | + | 0.142247i | 0.774644 | − | 0.632397i | \(-0.217929\pi\) |
−0.632397 | + | 0.774644i | \(0.717929\pi\) | |||||||
\(332\) | 1.38211 | + | 7.25491i | 0.0758533 | + | 0.398165i | ||||
\(333\) | 9.02318 | + | 3.80092i | 0.494467 | + | 0.208289i | ||||
\(334\) | 22.9345 | + | 7.05863i | 1.25492 | + | 0.386231i | ||||
\(335\) | 25.2362 | 1.37880 | ||||||||
\(336\) | 3.33266 | − | 15.2220i | 0.181811 | − | 0.830426i | ||||
\(337\) | −23.1690 | −1.26210 | −0.631049 | − | 0.775743i | \(-0.717375\pi\) | ||||
−0.631049 | + | 0.775743i | \(0.717375\pi\) | |||||||
\(338\) | 10.9670 | + | 3.37536i | 0.596527 | + | 0.183595i | ||||
\(339\) | 15.3713 | − | 22.8564i | 0.834852 | − | 1.24139i | ||||
\(340\) | 7.26719 | − | 1.38445i | 0.394119 | − | 0.0750825i | ||||
\(341\) | −1.47968 | − | 1.47968i | −0.0801291 | − | 0.0801291i | ||||
\(342\) | −14.5572 | + | 17.3796i | −0.787165 | + | 0.939779i | ||||
\(343\) | −20.1104 | −1.08586 | ||||||||
\(344\) | −15.0219 | − | 1.66400i | −0.809929 | − | 0.0897170i | ||||
\(345\) | −8.55026 | + | 1.67418i | −0.460331 | + | 0.0901349i | ||||
\(346\) | 15.2621 | + | 28.8337i | 0.820497 | + | 1.55011i | ||||
\(347\) | 6.72235 | − | 6.72235i | 0.360875 | − | 0.360875i | −0.503260 | − | 0.864135i | \(-0.667866\pi\) |
0.864135 | + | 0.503260i | \(0.167866\pi\) | |||||||
\(348\) | 14.5775 | + | 6.22846i | 0.781435 | + | 0.333880i | ||||
\(349\) | −2.75086 | − | 2.75086i | −0.147250 | − | 0.147250i | 0.629638 | − | 0.776888i | \(-0.283203\pi\) |
−0.776888 | + | 0.629638i | \(0.783203\pi\) | |||||||
\(350\) | −0.178247 | − | 0.0548598i | −0.00952771 | − | 0.00293238i | ||||
\(351\) | −19.9706 | + | 13.0862i | −1.06595 | + | 0.698491i | ||||
\(352\) | −5.88273 | + | 6.87930i | −0.313551 | + | 0.366668i | ||||
\(353\) | − | 23.1928i | − | 1.23443i | −0.786796 | − | 0.617213i | \(-0.788262\pi\) | ||
0.786796 | − | 0.617213i | \(-0.211738\pi\) | |||||||
\(354\) | 1.41284 | − | 13.3785i | 0.0750915 | − | 0.711060i | ||||
\(355\) | 17.4396 | − | 17.4396i | 0.925600 | − | 0.925600i | ||||
\(356\) | −12.1602 | − | 8.26837i | −0.644487 | − | 0.438223i | ||||
\(357\) | 3.61750 | − | 5.37907i | 0.191458 | − | 0.284690i | ||||
\(358\) | 2.36641 | − | 1.25258i | 0.125068 | − | 0.0662008i | ||||
\(359\) | 27.3664i | 1.44434i | 0.691713 | + | 0.722172i | \(0.256856\pi\) | ||||
−0.691713 | + | 0.722172i | \(0.743144\pi\) | |||||||
\(360\) | −5.14726 | − | 18.1462i | −0.271284 | − | 0.956388i | ||||
\(361\) | − | 9.55348i | − | 0.502815i | ||||||
\(362\) | −9.58633 | − | 18.1108i | −0.503846 | − | 0.951881i | ||||
\(363\) | 8.15759 | − | 12.1300i | 0.428162 | − | 0.636659i | ||||
\(364\) | 3.86813 | + | 20.3043i | 0.202745 | + | 1.06424i | ||||
\(365\) | 10.0299 | − | 10.0299i | 0.524991 | − | 0.524991i | ||||
\(366\) | −14.4361 | − | 1.52452i | −0.754585 | − | 0.0796879i | ||||
\(367\) | 26.0406i | 1.35931i | 0.733533 | + | 0.679654i | \(0.237870\pi\) | ||||
−0.733533 | + | 0.679654i | \(0.762130\pi\) | |||||||
\(368\) | 8.41758 | − | 3.32801i | 0.438797 | − | 0.173484i | ||||
\(369\) | −11.5569 | − | 28.3799i | −0.601629 | − | 1.47740i | ||||
\(370\) | 3.01805 | − | 9.80605i | 0.156901 | − | 0.509793i | ||||
\(371\) | −2.18829 | − | 2.18829i | −0.113611 | − | 0.113611i | ||||
\(372\) | −4.20438 | + | 1.68714i | −0.217987 | + | 0.0874740i | ||||
\(373\) | −13.1319 | + | 13.1319i | −0.679943 | + | 0.679943i | −0.959987 | − | 0.280044i | \(-0.909651\pi\) |
0.280044 | + | 0.959987i | \(0.409651\pi\) | |||||||
\(374\) | −3.32801 | + | 1.76157i | −0.172087 | + | 0.0910885i | ||||
\(375\) | −19.1138 | + | 3.74258i | −0.987034 | + | 0.193266i | ||||
\(376\) | −8.26375 | + | 6.61555i | −0.426170 | + | 0.341171i | ||||
\(377\) | −21.0274 | −1.08297 | ||||||||
\(378\) | −14.4735 | − | 7.98028i | −0.744435 | − | 0.410461i | ||||
\(379\) | −17.4526 | − | 17.4526i | −0.896482 | − | 0.896482i | 0.0986413 | − | 0.995123i | \(-0.468550\pi\) |
−0.995123 | + | 0.0986413i | \(0.968550\pi\) | |||||||
\(380\) | 19.6453 | + | 13.3579i | 1.00778 | + | 0.685248i | ||||
\(381\) | −7.17689 | + | 10.6717i | −0.367683 | + | 0.546729i | ||||
\(382\) | 10.2086 | − | 33.1690i | 0.522315 | − | 1.69707i | ||||
\(383\) | 26.4965 | 1.35391 | 0.676953 | − | 0.736027i | \(-0.263300\pi\) | ||||
0.676953 | + | 0.736027i | \(0.263300\pi\) | |||||||
\(384\) | 8.69149 | + | 17.5630i | 0.443536 | + | 0.896257i | ||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | 3.48651 | − | 11.3282i | 0.177459 | − | 0.576588i | ||||
\(387\) | −6.22315 | + | 14.7734i | −0.316341 | + | 0.750975i | ||||
\(388\) | 9.38445 | + | 6.38101i | 0.476423 | + | 0.323947i | ||||
\(389\) | 2.35506 | + | 2.35506i | 0.119406 | + | 0.119406i | 0.764285 | − | 0.644879i | \(-0.223092\pi\) |
−0.644879 | + | 0.764285i | \(0.723092\pi\) | |||||||
\(390\) | 15.7358 | + | 19.4518i | 0.796813 | + | 0.984979i | ||||
\(391\) | 3.76547 | 0.190428 | ||||||||
\(392\) | 4.28661 | − | 3.43165i | 0.216507 | − | 0.173324i | ||||
\(393\) | −1.82791 | − | 9.33537i | −0.0922058 | − | 0.470907i | ||||
\(394\) | −2.28018 | + | 1.20693i | −0.114874 | + | 0.0608045i | ||||
\(395\) | −4.23175 | + | 4.23175i | −0.212923 | + | 0.212923i | ||||
\(396\) | 5.22092 | + | 8.05697i | 0.262361 | + | 0.404878i | ||||
\(397\) | 4.68879 | + | 4.68879i | 0.235324 | + | 0.235324i | 0.814910 | − | 0.579587i | \(-0.196786\pi\) |
−0.579587 | + | 0.814910i | \(0.696786\pi\) | |||||||
\(398\) | −5.44928 | + | 17.7055i | −0.273148 | + | 0.887496i | ||||
\(399\) | 20.4285 | − | 4.00000i | 1.02271 | − | 0.200250i | ||||
\(400\) | 0.218105 | − | 0.0862308i | 0.0109053 | − | 0.00431154i | ||||
\(401\) | − | 5.18714i | − | 0.259033i | −0.991577 | − | 0.129517i | \(-0.958657\pi\) | ||
0.991577 | − | 0.129517i | \(-0.0413426\pi\) | |||||||
\(402\) | −2.92047 | + | 27.6546i | −0.145660 | + | 1.37929i | ||||
\(403\) | 4.24914 | − | 4.24914i | 0.211665 | − | 0.211665i | ||||
\(404\) | −5.45536 | − | 28.6360i | −0.271414 | − | 1.42469i | ||||
\(405\) | −20.0048 | − | 0.239367i | −0.994048 | − | 0.0118943i | ||||
\(406\) | −6.80949 | − | 12.8647i | −0.337949 | − | 0.638464i | ||||
\(407\) | 5.22225i | 0.258858i | ||||||||
\(408\) | 0.676130 | + | 8.12383i | 0.0334734 | + | 0.402189i | ||||
\(409\) | − | 14.8793i | − | 0.735734i | −0.929878 | − | 0.367867i | \(-0.880088\pi\) | ||
0.929878 | − | 0.367867i | \(-0.119912\pi\) | |||||||
\(410\) | −28.3799 | + | 15.0219i | −1.40158 | + | 0.741881i | ||||
\(411\) | 3.92245 | + | 2.63790i | 0.193480 | + | 0.130118i | ||||
\(412\) | 13.4492 | + | 9.14486i | 0.662595 | + | 0.450535i | ||||
\(413\) | −8.73458 | + | 8.73458i | −0.429801 | + | 0.429801i | ||||
\(414\) | −0.845139 | − | 9.56339i | −0.0415363 | − | 0.470015i | ||||
\(415\) | − | 8.20855i | − | 0.402942i | ||||||
\(416\) | −19.7550 | − | 16.8932i | −0.968570 | − | 0.828259i | ||||
\(417\) | 0.0129898 | + | 0.0663404i | 0.000636111 | + | 0.00324870i | ||||
\(418\) | −11.5569 | − | 3.55691i | −0.565267 | − | 0.173974i | ||||
\(419\) | 25.3026 | + | 25.3026i | 1.23611 | + | 1.23611i | 0.961578 | + | 0.274533i | \(0.0885232\pi\) |
0.274533 | + | 0.961578i | \(0.411477\pi\) | |||||||
\(420\) | −6.80484 | + | 15.9265i | −0.332042 | + | 0.777133i | ||||
\(421\) | 7.13187 | − | 7.13187i | 0.347586 | − | 0.347586i | −0.511623 | − | 0.859210i | \(-0.670956\pi\) |
0.859210 | + | 0.511623i | \(0.170956\pi\) | |||||||
\(422\) | 7.92554 | + | 14.9732i | 0.385809 | + | 0.728882i | ||||
\(423\) | 4.23453 | + | 10.3986i | 0.205890 | + | 0.505597i | ||||
\(424\) | 3.86813 | + | 0.428478i | 0.187853 | + | 0.0208087i | ||||
\(425\) | 0.0975657 | 0.00473263 | ||||||||
\(426\) | 17.0927 | + | 21.1291i | 0.828144 | + | 1.02371i | ||||
\(427\) | 9.42504 | + | 9.42504i | 0.456110 | + | 0.456110i | ||||
\(428\) | −6.67897 | + | 1.27239i | −0.322840 | + | 0.0615035i | ||||
\(429\) | −10.5674 | − | 7.10675i | −0.510200 | − | 0.343117i | ||||
\(430\) | 16.0552 | + | 4.94137i | 0.774250 | + | 0.238294i | ||||
\(431\) | −15.4882 | −0.746038 | −0.373019 | − | 0.927824i | \(-0.621677\pi\) | ||||
−0.373019 | + | 0.927824i | \(0.621677\pi\) | |||||||
\(432\) | 20.4808 | − | 3.54056i | 0.985384 | − | 0.170345i | ||||
\(433\) | 25.5500 | 1.22786 | 0.613928 | − | 0.789362i | \(-0.289588\pi\) | ||||
0.613928 | + | 0.789362i | \(0.289588\pi\) | |||||||
\(434\) | 3.97568 | + | 1.22361i | 0.190839 | + | 0.0587352i | ||||
\(435\) | −14.6205 | − | 9.83249i | −0.700999 | − | 0.471432i | ||||
\(436\) | −4.72326 | − | 24.7931i | −0.226203 | − | 1.18737i | ||||
\(437\) | 8.55026 | + | 8.55026i | 0.409014 | + | 0.409014i | ||||
\(438\) | 9.83041 | + | 12.1518i | 0.469715 | + | 0.580637i | ||||
\(439\) | 2.63703 | 0.125859 | 0.0629293 | − | 0.998018i | \(-0.479956\pi\) | ||||
0.0629293 | + | 0.998018i | \(0.479956\pi\) | |||||||
\(440\) | 7.85380 | − | 6.28736i | 0.374415 | − | 0.299738i | ||||
\(441\) | −2.19656 | − | 5.39400i | −0.104598 | − | 0.256857i | ||||
\(442\) | −5.05863 | − | 9.55691i | −0.240615 | − | 0.454576i | ||||
\(443\) | −14.8580 | + | 14.8580i | −0.705927 | + | 0.705927i | −0.965676 | − | 0.259749i | \(-0.916360\pi\) |
0.259749 | + | 0.965676i | \(0.416360\pi\) | |||||||
\(444\) | 10.3965 | + | 4.44208i | 0.493397 | + | 0.210812i | ||||
\(445\) | 11.5569 | + | 11.5569i | 0.547850 | + | 0.547850i | ||||
\(446\) | −29.1570 | − | 8.97377i | −1.38063 | − | 0.424920i | ||||
\(447\) | 5.91617 | + | 30.2147i | 0.279825 | + | 1.42910i | ||||
\(448\) | 3.93793 | − | 17.5569i | 0.186050 | − | 0.829486i | ||||
\(449\) | 31.7079i | 1.49639i | 0.663480 | + | 0.748194i | \(0.269079\pi\) | ||||
−0.663480 | + | 0.748194i | \(0.730921\pi\) | |||||||
\(450\) | −0.0218981 | − | 0.247794i | −0.00103229 | − | 0.0116811i | ||||
\(451\) | 11.5569 | − | 11.5569i | 0.544194 | − | 0.544194i | ||||
\(452\) | 17.8837 | − | 26.3013i | 0.841180 | − | 1.23711i | ||||
\(453\) | −24.2390 | − | 16.3011i | −1.13885 | − | 0.765891i | ||||
\(454\) | −29.6121 | + | 15.6742i | −1.38977 | + | 0.735626i | ||||
\(455\) | − | 22.9733i | − | 1.07701i | ||||||
\(456\) | −16.9115 | + | 19.9821i | −0.791954 | + | 0.935747i | ||||
\(457\) | 23.8759i | 1.11687i | 0.829550 | + | 0.558433i | \(0.188597\pi\) | ||||
−0.829550 | + | 0.558433i | \(0.811403\pi\) | |||||||
\(458\) | −3.14976 | − | 5.95061i | −0.147179 | − | 0.278054i | ||||
\(459\) | 8.46480 | + | 1.76286i | 0.395103 | + | 0.0822833i | ||||
\(460\) | −9.88273 | + | 1.88273i | −0.460785 | + | 0.0877829i | ||||
\(461\) | −0.921303 | + | 0.921303i | −0.0429094 | + | 0.0429094i | −0.728236 | − | 0.685327i | \(-0.759659\pi\) |
0.685327 | + | 0.728236i | \(0.259659\pi\) | |||||||
\(462\) | 0.925802 | − | 8.76665i | 0.0430722 | − | 0.407862i | ||||
\(463\) | − | 26.1510i | − | 1.21534i | −0.794190 | − | 0.607670i | \(-0.792105\pi\) | ||
0.794190 | − | 0.607670i | \(-0.207895\pi\) | |||||||
\(464\) | 16.7957 | + | 7.27787i | 0.779719 | + | 0.337866i | ||||
\(465\) | 4.94137 | − | 0.967542i | 0.229150 | − | 0.0448687i | ||||
\(466\) | 0.208553 | − | 0.677618i | 0.00966104 | − | 0.0313901i | ||||
\(467\) | 16.2510 | + | 16.2510i | 0.752005 | + | 0.752005i | 0.974853 | − | 0.222848i | \(-0.0715355\pi\) |
−0.222848 | + | 0.974853i | \(0.571535\pi\) | |||||||
\(468\) | −23.1369 | + | 14.9927i | −1.06950 | + | 0.693039i | ||||
\(469\) | 18.0552 | − | 18.0552i | 0.833711 | − | 0.833711i | ||||
\(470\) | 10.3986 | − | 5.50414i | 0.479651 | − | 0.253887i | ||||
\(471\) | 2.52588 | + | 12.9000i | 0.116386 | + | 0.594400i | ||||
\(472\) | 1.71027 | − | 15.4396i | 0.0787217 | − | 0.710667i | ||||
\(473\) | −8.55026 | −0.393141 | ||||||||
\(474\) | −4.14757 | − | 5.12701i | −0.190504 | − | 0.235491i | ||||
\(475\) | 0.221543 | + | 0.221543i | 0.0101651 | + | 0.0101651i | ||||
\(476\) | 4.20879 | − | 6.18980i | 0.192910 | − | 0.283709i | ||||
\(477\) | 1.60245 | − | 3.80413i | 0.0733712 | − | 0.174179i | ||||
\(478\) | −12.6707 | + | 41.1690i | −0.579546 | + | 1.88303i | ||||
\(479\) | −11.7456 | −0.536669 | −0.268335 | − | 0.963326i | \(-0.586473\pi\) | ||||
−0.268335 | + | 0.963326i | \(0.586473\pi\) | |||||||
\(480\) | −5.83646 | − | 20.9835i | −0.266397 | − | 0.957761i | ||||
\(481\) | −14.9966 | −0.683784 | ||||||||
\(482\) | −6.44587 | + | 20.9435i | −0.293601 | + | 0.953951i | ||||
\(483\) | −4.91948 | + | 7.31506i | −0.223844 | + | 0.332847i | ||||
\(484\) | 9.49098 | − | 13.9582i | 0.431408 | − | 0.634465i | ||||
\(485\) | −8.91891 | − | 8.91891i | −0.404987 | − | 0.404987i | ||||
\(486\) | 2.57737 | − | 21.8942i | 0.116912 | − | 0.993142i | ||||
\(487\) | −0.783513 | −0.0355044 | −0.0177522 | − | 0.999842i | \(-0.505651\pi\) | ||||
−0.0177522 | + | 0.999842i | \(0.505651\pi\) | |||||||
\(488\) | −16.6601 | − | 1.84547i | −0.754169 | − | 0.0835403i | ||||
\(489\) | 21.0938 | − | 4.13026i | 0.953893 | − | 0.186777i | ||||
\(490\) | −5.39400 | + | 2.85514i | −0.243676 | + | 0.128982i | ||||
\(491\) | 10.0382 | − | 10.0382i | 0.453018 | − | 0.453018i | −0.443337 | − | 0.896355i | \(-0.646206\pi\) |
0.896355 | + | 0.443337i | \(0.146206\pi\) | |||||||
\(492\) | −13.1773 | − | 32.8380i | −0.594076 | − | 1.48045i | ||||
\(493\) | 5.38445 | + | 5.38445i | 0.242504 | + | 0.242504i | ||||
\(494\) | 10.2143 | − | 33.1876i | 0.459561 | − | 1.49318i | ||||
\(495\) | −4.02447 | − | 9.88273i | −0.180886 | − | 0.444196i | ||||
\(496\) | −4.86469 | + | 1.92332i | −0.218431 | + | 0.0863597i | ||||
\(497\) | − | 24.9543i | − | 1.11935i | ||||||
\(498\) | 8.99519 | + | 0.949937i | 0.403084 | + | 0.0425677i | ||||
\(499\) | −29.9655 | + | 29.9655i | −1.34144 | + | 1.34144i | −0.446815 | + | 0.894627i | \(0.647442\pi\) |
−0.894627 | + | 0.446815i | \(0.852558\pi\) | |||||||
\(500\) | −22.0925 | + | 4.20879i | −0.988008 | + | 0.188223i | ||||
\(501\) | 16.4008 | − | 24.3872i | 0.732732 | − | 1.08954i | ||||
\(502\) | −11.4396 | − | 21.6121i | −0.510576 | − | 0.964596i | ||||
\(503\) | − | 21.7131i | − | 0.968138i | −0.875030 | − | 0.484069i | \(-0.839158\pi\) | ||
0.875030 | − | 0.484069i | \(-0.160842\pi\) | |||||||
\(504\) | −16.6652 | − | 9.30006i | −0.742329 | − | 0.414257i | ||||
\(505\) | 32.4001i | 1.44179i | ||||||||
\(506\) | 4.52579 | − | 2.39558i | 0.201196 | − | 0.106496i | ||||
\(507\) | 7.84266 | − | 11.6617i | 0.348305 | − | 0.517914i | ||||
\(508\) | −8.34998 | + | 12.2802i | −0.370470 | + | 0.544845i | ||||
\(509\) | 16.1276 | − | 16.1276i | 0.714842 | − | 0.714842i | −0.252702 | − | 0.967544i | \(-0.581319\pi\) |
0.967544 | + | 0.252702i | \(0.0813192\pi\) | |||||||
\(510\) | 0.951545 | − | 9.01042i | 0.0421351 | − | 0.398988i | ||||
\(511\) | − | 14.3518i | − | 0.634886i | ||||||
\(512\) | 9.93237 | + | 20.3310i | 0.438953 | + | 0.898510i | ||||
\(513\) | 15.2181 | + | 23.2240i | 0.671896 | + | 1.02536i | ||||
\(514\) | 10.1173 | + | 3.11383i | 0.446253 | + | 0.137345i | ||||
\(515\) | −12.7820 | − | 12.7820i | −0.563243 | − | 0.563243i | ||||
\(516\) | −7.27290 | + | 17.0219i | −0.320171 | + | 0.749349i | ||||
\(517\) | −4.23453 | + | 4.23453i | −0.186235 | + | 0.186235i | ||||
\(518\) | −4.85647 | − | 9.17498i | −0.213381 | − | 0.403125i | ||||
\(519\) | 39.2112 | − | 7.67774i | 1.72118 | − | 0.337015i | ||||
\(520\) | 18.0552 | + | 22.5535i | 0.791773 | + | 0.989035i | ||||
\(521\) | 5.68847 | 0.249216 | 0.124608 | − | 0.992206i | \(-0.460233\pi\) | ||||
0.124608 | + | 0.992206i | \(0.460233\pi\) | |||||||
\(522\) | 12.4667 | − | 14.8837i | 0.545653 | − | 0.651443i | ||||
\(523\) | 13.6612 | + | 13.6612i | 0.597362 | + | 0.597362i | 0.939610 | − | 0.342248i | \(-0.111188\pi\) |
−0.342248 | + | 0.939610i | \(0.611188\pi\) | |||||||
\(524\) | −2.05561 | − | 10.7902i | −0.0897998 | − | 0.471372i | ||||
\(525\) | −0.127467 | + | 0.189538i | −0.00556311 | + | 0.00827211i | ||||
\(526\) | −13.8759 | − | 4.27062i | −0.605016 | − | 0.186208i | ||||
\(527\) | −2.17614 | −0.0947941 | ||||||||
\(528\) | 5.98101 | + | 9.33405i | 0.260290 | + | 0.406212i | ||||
\(529\) | 17.8793 | 0.777361 | ||||||||
\(530\) | −4.13419 | − | 1.27239i | −0.179578 | − | 0.0552692i | ||||
\(531\) | −15.1842 | − | 6.39619i | −0.658938 | − | 0.277571i | ||||
\(532\) | 23.6121 | − | 4.49828i | 1.02371 | − | 0.195025i | ||||
\(533\) | 33.1876 | + | 33.1876i | 1.43751 | + | 1.43751i | ||||
\(534\) | −14.0019 | + | 11.3270i | −0.605920 | + | 0.490167i | ||||
\(535\) | 7.55691 | 0.326714 | ||||||||
\(536\) | −3.53529 | + | 31.9152i | −0.152701 | + | 1.37853i | ||||
\(537\) | −0.630120 | − | 3.21811i | −0.0271917 | − | 0.138871i | ||||
\(538\) | −2.59139 | − | 4.89572i | −0.111723 | − | 0.211070i | ||||
\(539\) | 2.19656 | − | 2.19656i | 0.0946124 | − | 0.0946124i | ||||
\(540\) | −23.0979 | − | 0.394357i | −0.993975 | − | 0.0169704i | ||||
\(541\) | −24.5715 | − | 24.5715i | −1.05641 | − | 1.05641i | −0.998311 | − | 0.0581016i | \(-0.981495\pi\) |
−0.0581016 | − | 0.998311i | \(-0.518505\pi\) | |||||||
\(542\) | 38.7724 | + | 11.9331i | 1.66542 | + | 0.512572i | ||||
\(543\) | −24.6291 | + | 4.82248i | −1.05693 | + | 0.206953i | ||||
\(544\) | 0.732814 | + | 9.38445i | 0.0314191 | + | 0.402355i | ||||
\(545\) | 28.0521i | 1.20162i | ||||||||
\(546\) | 25.1749 | + | 2.65859i | 1.07739 | + | 0.113777i | ||||
\(547\) | 3.56990 | − | 3.56990i | 0.152638 | − | 0.152638i | −0.626657 | − | 0.779295i | \(-0.715577\pi\) |
0.779295 | + | 0.626657i | \(0.215577\pi\) | |||||||
\(548\) | 4.51364 | + | 3.06908i | 0.192813 | + | 0.131104i | ||||
\(549\) | −6.90180 | + | 16.3845i | −0.294562 | + | 0.699273i | ||||
\(550\) | 0.117266 | − | 0.0620710i | 0.00500025 | − | 0.00264672i | ||||
\(551\) | 24.4530i | 1.04173i | ||||||||
\(552\) | −0.919477 | − | 11.0477i | −0.0391356 | − | 0.470221i | ||||
\(553\) | 6.05520i | 0.257493i | ||||||||
\(554\) | 0.754180 | + | 1.42482i | 0.0320421 | + | 0.0605348i | ||||
\(555\) | −10.4272 | − | 7.01244i | −0.442610 | − | 0.297662i | ||||
\(556\) | 0.0146079 | + | 0.0766789i | 0.000619513 | + | 0.00325191i | ||||
\(557\) | 18.1602 | − | 18.1602i | 0.769473 | − | 0.769473i | −0.208540 | − | 0.978014i | \(-0.566871\pi\) |
0.978014 | + | 0.208540i | \(0.0668713\pi\) | |||||||
\(558\) | 0.488423 | + | 5.52687i | 0.0206766 | + | 0.233971i | ||||
\(559\) | − | 24.5535i | − | 1.03850i | ||||||
\(560\) | −7.95137 | + | 18.3500i | −0.336007 | + | 0.775427i | ||||
\(561\) | 0.886172 | + | 4.52579i | 0.0374142 | + | 0.191079i | ||||
\(562\) | 9.28629 | − | 30.1725i | 0.391719 | − | 1.27275i | ||||
\(563\) | −6.91748 | − | 6.91748i | −0.291537 | − | 0.291537i | 0.546150 | − | 0.837687i | \(-0.316093\pi\) |
−0.837687 | + | 0.546150i | \(0.816093\pi\) | |||||||
\(564\) | 4.82824 | + | 12.0321i | 0.203305 | + | 0.506641i | ||||
\(565\) | −24.9966 | + | 24.9966i | −1.05161 | + | 1.05161i | ||||
\(566\) | 14.2875 | − | 7.56262i | 0.600549 | − | 0.317880i | ||||
\(567\) | −14.4837 | + | 14.1412i | −0.608257 | + | 0.593873i | ||||
\(568\) | 19.6121 | + | 24.4983i | 0.822906 | + | 1.02793i | ||||
\(569\) | −36.2961 | −1.52161 | −0.760807 | − | 0.648979i | \(-0.775196\pi\) | ||||
−0.760807 | + | 0.648979i | \(0.775196\pi\) | |||||||
\(570\) | 22.6207 | − | 18.2993i | 0.947475 | − | 0.766474i | ||||
\(571\) | −33.5224 | − | 33.5224i | −1.40287 | − | 1.40287i | −0.790814 | − | 0.612056i | \(-0.790343\pi\) |
−0.612056 | − | 0.790814i | \(-0.709657\pi\) | |||||||
\(572\) | −12.1602 | − | 8.26837i | −0.508442 | − | 0.345718i | ||||
\(573\) | −35.2701 | − | 23.7196i | −1.47343 | − | 0.990901i | ||||
\(574\) | −9.55691 | + | 31.0518i | −0.398898 | + | 1.29608i | ||||
\(575\) | −0.132681 | −0.00553317 | ||||||||
\(576\) | 23.6698 | − | 3.96746i | 0.986242 | − | 0.165311i | ||||
\(577\) | −18.9345 | −0.788253 | −0.394127 | − | 0.919056i | \(-0.628953\pi\) | ||||
−0.394127 | + | 0.919056i | \(0.628953\pi\) | |||||||
\(578\) | 5.92015 | − | 19.2354i | 0.246246 | − | 0.800086i | ||||
\(579\) | −12.0457 | − | 8.10092i | −0.500603 | − | 0.336663i | ||||
\(580\) | −16.8241 | − | 11.4396i | −0.698583 | − | 0.475006i | ||||
\(581\) | −5.87279 | − | 5.87279i | −0.243644 | − | 0.243644i | ||||
\(582\) | 10.8058 | − | 8.74148i | 0.447913 | − | 0.362346i | ||||
\(583\) | 2.20168 | 0.0911842 | ||||||||
\(584\) | 11.2794 | + | 14.0895i | 0.466744 | + | 0.583028i | ||||
\(585\) | 28.3799 | − | 11.5569i | 1.17336 | − | 0.477820i | ||||
\(586\) | −11.2767 | + | 5.96896i | −0.465838 | + | 0.246576i | ||||
\(587\) | −29.6211 | + | 29.6211i | −1.22259 | + | 1.22259i | −0.255885 | + | 0.966707i | \(0.582367\pi\) |
−0.966707 | + | 0.255885i | \(0.917633\pi\) | |||||||
\(588\) | −2.50453 | − | 6.24133i | −0.103285 | − | 0.257388i | ||||
\(589\) | −4.94137 | − | 4.94137i | −0.203605 | − | 0.203605i | ||||
\(590\) | −5.07877 | + | 16.5016i | −0.209090 | + | 0.679361i | ||||
\(591\) | 0.607159 | + | 3.10084i | 0.0249752 | + | 0.127551i | ||||
\(592\) | 11.9785 | + | 5.19051i | 0.492314 | + | 0.213329i | ||||
\(593\) | − | 21.6263i | − | 0.888086i | −0.896005 | − | 0.444043i | \(-0.853544\pi\) | ||
0.896005 | − | 0.444043i | \(-0.146456\pi\) | |||||||
\(594\) | 11.2955 | − | 3.26645i | 0.463462 | − | 0.134024i | ||||
\(595\) | −5.88273 | + | 5.88273i | −0.241169 | + | 0.241169i | ||||
\(596\) | 6.65315 | + | 34.9233i | 0.272524 | + | 1.43052i | ||||
\(597\) | 18.8270 | + | 12.6614i | 0.770539 | + | 0.518198i | ||||
\(598\) | 6.87930 | + | 12.9966i | 0.281315 | + | 0.531469i | ||||
\(599\) | − | 29.8079i | − | 1.21792i | −0.793201 | − | 0.608959i | \(-0.791587\pi\) | ||
0.793201 | − | 0.608959i | \(-0.208413\pi\) | |||||||
\(600\) | −0.0238243 | − | 0.286253i | −0.000972621 | − | 0.0116862i | ||||
\(601\) | 32.8432i | 1.33970i | 0.742495 | + | 0.669851i | \(0.233642\pi\) | ||||
−0.742495 | + | 0.669851i | \(0.766358\pi\) | |||||||
\(602\) | 15.0219 | − | 7.95137i | 0.612249 | − | 0.324073i | ||||
\(603\) | 31.3872 | + | 13.2215i | 1.27818 | + | 0.538422i | ||||
\(604\) | −27.8923 | − | 18.9655i | −1.13492 | − | 0.771696i | ||||
\(605\) | −13.2658 | + | 13.2658i | −0.539331 | + | 0.539331i | ||||
\(606\) | −35.5051 | − | 3.74951i | −1.44229 | − | 0.152313i | ||||
\(607\) | − | 6.95597i | − | 0.282334i | −0.989986 | − | 0.141167i | \(-0.954915\pi\) | ||
0.989986 | − | 0.141167i | \(-0.0450855\pi\) | |||||||
\(608\) | −19.6453 | + | 22.9733i | −0.796722 | + | 0.931691i | ||||
\(609\) | −17.4948 | + | 3.42557i | −0.708927 | + | 0.138811i | ||||
\(610\) | 17.8061 | + | 5.48024i | 0.720946 | + | 0.221888i | ||||
\(611\) | −12.1602 | − | 12.1602i | −0.491947 | − | 0.491947i | ||||
\(612\) | 9.76378 | + | 2.08547i | 0.394677 | + | 0.0842999i | ||||
\(613\) | −13.5389 | + | 13.5389i | −0.546830 | + | 0.546830i | −0.925522 | − | 0.378693i | \(-0.876374\pi\) |
0.378693 | + | 0.925522i | \(0.376374\pi\) | |||||||
\(614\) | 6.16398 | + | 11.6452i | 0.248758 | + | 0.469960i | ||||
\(615\) | 7.55691 | + | 38.5942i | 0.304724 | + | 1.55627i | ||||
\(616\) | 1.12070 | − | 10.1173i | 0.0451545 | − | 0.407636i | ||||
\(617\) | 8.91891 | 0.359062 | 0.179531 | − | 0.983752i | \(-0.442542\pi\) | ||||
0.179531 | + | 0.983752i | \(0.442542\pi\) | |||||||
\(618\) | 15.4861 | − | 12.5277i | 0.622944 | − | 0.503939i | ||||
\(619\) | −1.64658 | − | 1.64658i | −0.0661818 | − | 0.0661818i | 0.673241 | − | 0.739423i | \(-0.264902\pi\) |
−0.739423 | + | 0.673241i | \(0.764902\pi\) | |||||||
\(620\) | 5.71143 | − | 1.08807i | 0.229377 | − | 0.0436979i | ||||
\(621\) | −11.5114 | − | 2.39734i | −0.461936 | − | 0.0962018i | ||||
\(622\) | −12.8793 | − | 3.96391i | −0.516413 | − | 0.158938i | ||||
\(623\) | 16.5367 | 0.662531 | ||||||||
\(624\) | −26.8043 | + | 17.1754i | −1.07303 | + | 0.687568i | ||||
\(625\) | 24.7034 | 0.988136 | ||||||||
\(626\) | −34.0196 | − | 10.4703i | −1.35970 | − | 0.418479i | ||||
\(627\) | −8.26451 | + | 12.2890i | −0.330053 | + | 0.490774i | ||||
\(628\) | 2.84053 | + | 14.9103i | 0.113349 | + | 0.594987i | ||||
\(629\) | 3.84014 | + | 3.84014i | 0.153116 | + | 0.153116i | ||||
\(630\) | 16.2611 | + | 13.6204i | 0.647857 | + | 0.542649i | ||||
\(631\) | 19.2457 | 0.766159 | 0.383080 | − | 0.923715i | \(-0.374863\pi\) | ||||
0.383080 | + | 0.923715i | \(0.374863\pi\) | |||||||
\(632\) | −4.75890 | − | 5.94454i | −0.189299 | − | 0.236461i | ||||
\(633\) | 20.3622 | − | 3.98701i | 0.809324 | − | 0.158469i | ||||
\(634\) | 14.5293 | + | 27.4492i | 0.577033 | + | 1.09015i | ||||
\(635\) | 11.6710 | − | 11.6710i | 0.463149 | − | 0.463149i | ||||
\(636\) | 1.87276 | − | 4.38312i | 0.0742597 | − | 0.173802i | ||||
\(637\) | 6.30777 | + | 6.30777i | 0.249923 | + | 0.249923i | ||||
\(638\) | 9.89726 | + | 3.04612i | 0.391836 | + | 0.120597i | ||||
\(639\) | 30.8271 | − | 12.5535i | 1.21950 | − | 0.496608i | ||||
\(640\) | −6.61555 | − | 24.2637i | −0.261502 | − | 0.959109i | ||||
\(641\) | − | 16.6343i | − | 0.657016i | −0.944501 | − | 0.328508i | \(-0.893454\pi\) | ||
0.944501 | − | 0.328508i | \(-0.106546\pi\) | |||||||
\(642\) | −0.874526 | + | 8.28110i | −0.0345148 | + | 0.326829i | ||||
\(643\) | −4.77502 | + | 4.77502i | −0.188308 | + | 0.188308i | −0.794964 | − | 0.606656i | \(-0.792511\pi\) |
0.606656 | + | 0.794964i | \(0.292511\pi\) | |||||||
\(644\) | −5.72358 | + | 8.41758i | −0.225541 | + | 0.331699i | ||||
\(645\) | 11.4813 | − | 17.0722i | 0.452075 | − | 0.672217i | ||||
\(646\) | −11.1138 | + | 5.88273i | −0.437268 | + | 0.231453i | ||||
\(647\) | − | 48.2095i | − | 1.89531i | −0.319293 | − | 0.947656i | \(-0.603445\pi\) | ||
0.319293 | − | 0.947656i | \(-0.396555\pi\) | |||||||
\(648\) | 3.10516 | − | 25.2657i | 0.121982 | − | 0.992532i | ||||
\(649\) | − | 8.78801i | − | 0.344960i | ||||||
\(650\) | 0.178247 | + | 0.336749i | 0.00699143 | + | 0.0132084i | ||||
\(651\) | 2.84306 | − | 4.22752i | 0.111428 | − | 0.165689i | ||||
\(652\) | 24.3810 | − | 4.64476i | 0.954834 | − | 0.181903i | ||||
\(653\) | 24.2281 | − | 24.2281i | 0.948121 | − | 0.948121i | −0.0505983 | − | 0.998719i | \(-0.516113\pi\) |
0.998719 | + | 0.0505983i | \(0.0161128\pi\) | |||||||
\(654\) | −30.7404 | − | 3.24633i | −1.20204 | − | 0.126942i | ||||
\(655\) | 12.2086i | 0.477028i | ||||||||
\(656\) | −15.0219 | − | 37.9953i | −0.586509 | − | 1.48347i | ||||
\(657\) | 17.7294 | − | 7.21979i | 0.691689 | − | 0.281671i | ||||
\(658\) | 3.50172 | − | 11.3776i | 0.136511 | − | 0.443544i | ||||
\(659\) | −9.47442 | − | 9.47442i | −0.369071 | − | 0.369071i | 0.498067 | − | 0.867138i | \(-0.334043\pi\) |
−0.867138 | + | 0.498067i | \(0.834043\pi\) | |||||||
\(660\) | −4.58872 | − | 11.4352i | −0.178616 | − | 0.445114i | ||||
\(661\) | 23.0406 | − | 23.0406i | 0.896175 | − | 0.896175i | −0.0989204 | − | 0.995095i | \(-0.531539\pi\) |
0.995095 | + | 0.0989204i | \(0.0315389\pi\) | |||||||
\(662\) | 4.57458 | − | 2.42140i | 0.177796 | − | 0.0941104i | ||||
\(663\) | −12.9966 | + | 2.54479i | −0.504745 | + | 0.0988313i | ||||
\(664\) | 10.3810 | + | 1.14992i | 0.402862 | + | 0.0446255i | ||||
\(665\) | −26.7159 | −1.03600 | ||||||||
\(666\) | 8.89115 | − | 10.6149i | 0.344525 | − | 0.411321i | ||||
\(667\) | −7.32238 | − | 7.32238i | −0.283524 | − | 0.283524i | ||||
\(668\) | 19.0815 | − | 28.0629i | 0.738286 | − | 1.08579i | ||||
\(669\) | −20.8506 | + | 31.0039i | −0.806130 | + | 1.19868i | ||||
\(670\) | 10.4983 | − | 34.1104i | 0.405584 | − | 1.31780i | ||||
\(671\) | −9.48269 | −0.366075 | ||||||||
\(672\) | −19.1883 | − | 10.8369i | −0.740204 | − | 0.418043i | ||||
\(673\) | 29.7846 | 1.14811 | 0.574055 | − | 0.818816i | \(-0.305369\pi\) | ||||
0.574055 | + | 0.818816i | \(0.305369\pi\) | |||||||
\(674\) | −9.63833 | + | 31.3163i | −0.371255 | + | 1.20626i | ||||
\(675\) | −0.298267 | − | 0.0621166i | −0.0114803 | − | 0.00239087i | ||||
\(676\) | 9.12457 | − | 13.4194i | 0.350945 | − | 0.516129i | ||||
\(677\) | −5.59631 | − | 5.59631i | −0.215084 | − | 0.215084i | 0.591339 | − | 0.806423i | \(-0.298599\pi\) |
−0.806423 | + | 0.591339i | \(0.798599\pi\) | |||||||
\(678\) | −24.4993 | − | 30.2848i | −0.940889 | − | 1.16308i | ||||
\(679\) | −12.7620 | −0.489762 | ||||||||
\(680\) | 1.15187 | − | 10.3986i | 0.0441721 | − | 0.398768i | ||||
\(681\) | 7.88503 | + | 40.2699i | 0.302155 | + | 1.54314i | ||||
\(682\) | −2.61555 | + | 1.38445i | −0.100154 | + | 0.0530134i | ||||
\(683\) | −19.5790 | + | 19.5790i | −0.749168 | + | 0.749168i | −0.974323 | − | 0.225155i | \(-0.927711\pi\) |
0.225155 | + | 0.974323i | \(0.427711\pi\) | |||||||
\(684\) | 17.4352 | + | 26.9061i | 0.666651 | + | 1.02878i | ||||
\(685\) | −4.28973 | − | 4.28973i | −0.163902 | − | 0.163902i | ||||
\(686\) | −8.36594 | + | 27.1821i | −0.319413 | + | 1.03782i | ||||
\(687\) | −8.09231 | + | 1.58451i | −0.308741 | + | 0.0604529i | ||||
\(688\) | −8.49828 | + | 19.6121i | −0.323994 | + | 0.747705i | ||||
\(689\) | 6.32248i | 0.240867i | ||||||||
\(690\) | −1.29402 | + | 12.2534i | −0.0492624 | + | 0.466478i | ||||
\(691\) | 3.98701 | − | 3.98701i | 0.151673 | − | 0.151673i | −0.627192 | − | 0.778865i | \(-0.715796\pi\) |
0.778865 | + | 0.627192i | \(0.215796\pi\) | |||||||
\(692\) | 45.3219 | − | 8.63416i | 1.72288 | − | 0.328221i | ||||
\(693\) | −9.94988 | − | 4.19129i | −0.377965 | − | 0.159214i | ||||
\(694\) | −6.28973 | − | 11.8827i | −0.238755 | − | 0.451062i | ||||
\(695\) | − | 0.0867582i | − | 0.00329093i | ||||||
\(696\) | 14.4829 | − | 17.1125i | 0.548973 | − | 0.648649i | ||||
\(697\) | − | 16.9966i | − | 0.643791i | ||||||
\(698\) | −4.86254 | + | 2.57383i | −0.184050 | + | 0.0974207i | ||||
\(699\) | −0.720541 | − | 0.484574i | −0.0272534 | − | 0.0183283i | ||||
\(700\) | −0.148302 | + | 0.218105i | −0.00560528 | + | 0.00824360i | ||||
\(701\) | −15.2117 | + | 15.2117i | −0.574537 | + | 0.574537i | −0.933393 | − | 0.358856i | \(-0.883167\pi\) |
0.358856 | + | 0.933393i | \(0.383167\pi\) | |||||||
\(702\) | 9.38016 | + | 32.4370i | 0.354031 | + | 1.22426i | ||||
\(703\) | 17.4396i | 0.657749i | ||||||||
\(704\) | 6.85114 | + | 10.8132i | 0.258212 | + | 0.407536i | ||||
\(705\) | −2.76891 | − | 14.1412i | −0.104283 | − | 0.532587i | ||||
\(706\) | −31.3484 | − | 9.64820i | −1.17981 | − | 0.363115i | ||||
\(707\) | 23.1806 | + | 23.1806i | 0.871796 | + | 0.871796i | ||||
\(708\) | −17.4953 | − | 7.47513i | −0.657512 | − | 0.280932i | ||||
\(709\) | 20.3009 | − | 20.3009i | 0.762416 | − | 0.762416i | −0.214342 | − | 0.976759i | \(-0.568761\pi\) |
0.976759 | + | 0.214342i | \(0.0687608\pi\) | |||||||
\(710\) | −16.3173 | − | 30.8271i | −0.612377 | − | 1.15692i | ||||
\(711\) | −7.48024 | + | 3.04612i | −0.280531 | + | 0.114238i | ||||
\(712\) | −16.2345 | + | 12.9966i | −0.608415 | + | 0.487067i | ||||
\(713\) | 2.95936 | 0.110829 | ||||||||
\(714\) | −5.76570 | − | 7.12727i | −0.215776 | − | 0.266731i | ||||
\(715\) | 11.5569 | + | 11.5569i | 0.432204 | + | 0.432204i | ||||
\(716\) | −0.708614 | − | 3.71961i | −0.0264822 | − | 0.139009i | ||||
\(717\) | 43.7768 | + | 29.4405i | 1.63488 | + | 1.09948i | ||||
\(718\) | 36.9897 | + | 11.3845i | 1.38044 | + | 0.424864i | ||||
\(719\) | 3.52314 | 0.131391 | 0.0656954 | − | 0.997840i | \(-0.479073\pi\) | ||||
0.0656954 | + | 0.997840i | \(0.479073\pi\) | |||||||
\(720\) | −26.6685 | − | 0.591559i | −0.993875 | − | 0.0220461i | ||||
\(721\) | −18.2897 | −0.681145 | ||||||||
\(722\) | −12.9129 | − | 3.97425i | −0.480569 | − | 0.147906i | ||||
\(723\) | 22.2702 | + | 14.9770i | 0.828236 | + | 0.557000i | ||||
\(724\) | −28.4672 | + | 5.42322i | −1.05798 | + | 0.201552i | ||||
\(725\) | −0.189728 | − | 0.189728i | −0.00704631 | − | 0.00704631i | ||||
\(726\) | −13.0019 | − | 16.0722i | −0.482545 | − | 0.596497i | ||||
\(727\) | 20.3664 | 0.755348 | 0.377674 | − | 0.925939i | \(-0.376724\pi\) | ||||
0.377674 | + | 0.925939i | \(0.376724\pi\) | |||||||
\(728\) | 29.0534 | + | 3.21829i | 1.07679 | + | 0.119278i | ||||
\(729\) | −24.7553 | − | 10.7785i | −0.916863 | − | 0.399202i | ||||
\(730\) | −9.38445 | − | 17.7294i | −0.347334 | − | 0.656194i | ||||
\(731\) | −6.28736 | + | 6.28736i | −0.232547 | + | 0.232547i | ||||
\(732\) | −8.06602 | + | 18.8782i | −0.298129 | + | 0.697760i | ||||
\(733\) | 2.48024 | + | 2.48024i | 0.0916096 | + | 0.0916096i | 0.751426 | − | 0.659817i | \(-0.229366\pi\) |
−0.659817 | + | 0.751426i | \(0.729366\pi\) | |||||||
\(734\) | 35.1976 | + | 10.8329i | 1.29917 | + | 0.399850i | ||||
\(735\) | 1.43630 | + | 7.33537i | 0.0529787 | + | 0.270569i | ||||
\(736\) | −0.996562 | − | 12.7620i | −0.0367338 | − | 0.470415i | ||||
\(737\) | 18.1656i | 0.669140i | ||||||||
\(738\) | −43.1672 | + | 3.81479i | −1.58901 | + | 0.140424i | ||||
\(739\) | 15.7931 | − | 15.7931i | 0.580957 | − | 0.580957i | −0.354209 | − | 0.935166i | \(-0.615250\pi\) |
0.935166 | + | 0.354209i | \(0.115250\pi\) | |||||||
\(740\) | −11.9988 | − | 8.15865i | −0.441084 | − | 0.299918i | ||||
\(741\) | −35.2898 | − | 23.7329i | −1.29640 | − | 0.871849i | ||||
\(742\) | −3.86813 | + | 2.04746i | −0.142003 | + | 0.0751647i | ||||
\(743\) | 38.5942i | 1.41588i | 0.706271 | + | 0.707941i | \(0.250376\pi\) | ||||
−0.706271 | + | 0.707941i | \(0.749624\pi\) | |||||||
\(744\) | 0.531384 | + | 6.38468i | 0.0194815 | + | 0.234074i | ||||
\(745\) | − | 39.5139i | − | 1.44768i | ||||||
\(746\) | 12.2868 | + | 23.2125i | 0.449850 | + | 0.849870i | ||||
\(747\) | 4.30055 | − | 10.2093i | 0.157349 | − | 0.373537i | ||||
\(748\) | 0.996562 | + | 5.23109i | 0.0364379 | + | 0.191268i | ||||
\(749\) | 5.40658 | − | 5.40658i | 0.197552 | − | 0.197552i | ||||
\(750\) | −2.89273 | + | 27.3920i | −0.105628 | + | 1.00022i | ||||
\(751\) | 17.6527i | 0.644156i | 0.946713 | + | 0.322078i | \(0.104381\pi\) | ||||
−0.946713 | + | 0.322078i | \(0.895619\pi\) | |||||||
\(752\) | 5.50414 | + | 13.9217i | 0.200716 | + | 0.507673i | ||||
\(753\) | −29.3906 | + | 5.75481i | −1.07105 | + | 0.209717i | ||||
\(754\) | −8.74742 | + | 28.4216i | −0.318562 | + | 1.03505i | ||||
\(755\) | 26.5086 | + | 26.5086i | 0.964747 | + | 0.964747i | ||||
\(756\) | −16.8075 | + | 16.2432i | −0.611282 | + | 0.590759i | ||||
\(757\) | −32.7440 | + | 32.7440i | −1.19010 | + | 1.19010i | −0.213062 | + | 0.977039i | \(0.568343\pi\) |
−0.977039 | + | 0.213062i | \(0.931657\pi\) | |||||||
\(758\) | −30.8501 | + | 16.3295i | −1.12053 | + | 0.593113i | ||||
\(759\) | −1.20512 | − | 6.15468i | −0.0437429 | − | 0.223401i | ||||
\(760\) | 26.2277 | − | 20.9966i | 0.951377 | − | 0.761625i | ||||
\(761\) | −6.69113 | −0.242553 | −0.121277 | − | 0.992619i | \(-0.538699\pi\) | ||||
−0.121277 | + | 0.992619i | \(0.538699\pi\) | |||||||
\(762\) | 11.4388 | + | 14.1401i | 0.414384 | + | 0.512240i | ||||
\(763\) | 20.0698 | + | 20.0698i | 0.726576 | + | 0.726576i | ||||
\(764\) | −40.5860 | − | 27.5967i | −1.46835 | − | 0.998413i | ||||
\(765\) | −10.2265 | − | 4.30783i | −0.369741 | − | 0.155750i | ||||
\(766\) | 11.0225 | − | 35.8138i | 0.398261 | − | 1.29400i | ||||
\(767\) | 25.2362 | 0.911227 | ||||||||
\(768\) | 27.3546 | − | 4.44160i | 0.987073 | − | 0.160272i | ||||
\(769\) | −5.03265 | −0.181482 | −0.0907411 | − | 0.995875i | \(-0.528924\pi\) | ||||
−0.0907411 | + | 0.995875i | \(0.528924\pi\) | |||||||
\(770\) | −3.32801 | + | 10.8132i | −0.119933 | + | 0.389679i | ||||
\(771\) | 7.23499 | − | 10.7581i | 0.260562 | − | 0.387445i | ||||
\(772\) | −13.8613 | − | 9.42504i | −0.498877 | − | 0.339215i | ||||
\(773\) | −10.6859 | − | 10.6859i | −0.384344 | − | 0.384344i | 0.488320 | − | 0.872665i | \(-0.337610\pi\) |
−0.872665 | + | 0.488320i | \(0.837610\pi\) | |||||||
\(774\) | 17.3796 | + | 14.5572i | 0.624696 | + | 0.523249i | ||||
\(775\) | 0.0766789 | 0.00275439 | ||||||||
\(776\) | 12.5288 | − | 10.0299i | 0.449758 | − | 0.360054i | ||||
\(777\) | −12.4772 | + | 2.44309i | −0.447616 | + | 0.0876452i | ||||
\(778\) | 4.16291 | − | 2.20350i | 0.149248 | − | 0.0789992i | ||||
\(779\) | 38.5942 | − | 38.5942i | 1.38278 | − | 1.38278i | ||||
\(780\) | 32.8380 | − | 13.1773i | 1.17579 | − | 0.471821i | ||||
\(781\) | 12.5535 | + | 12.5535i | 0.449199 | + | 0.449199i | ||||
\(782\) | 1.56644 | − | 5.08957i | 0.0560157 | − | 0.182003i | ||||
\(783\) | −13.0327 | − | 19.8888i | −0.465750 | − | 0.710769i | ||||
\(784\) | −2.85514 | − | 7.22154i | −0.101969 | − | 0.257912i | ||||
\(785\) | − | 16.8703i | − | 0.602126i | ||||||
\(786\) | −13.3785 | − | 1.41284i | −0.477196 | − | 0.0503942i | ||||
\(787\) | 16.0974 | − | 16.0974i | 0.573810 | − | 0.573810i | −0.359381 | − | 0.933191i | \(-0.617012\pi\) |
0.933191 | + | 0.359381i | \(0.117012\pi\) | |||||||
\(788\) | 0.682792 | + | 3.58407i | 0.0243235 | + | 0.127677i | ||||
\(789\) | −9.92281 | + | 14.7548i | −0.353262 | + | 0.525285i | ||||
\(790\) | 3.95941 | + | 7.48024i | 0.140870 | + | 0.266135i | ||||
\(791\) | 35.7675i | 1.27175i | ||||||||
\(792\) | 13.0621 | − | 3.70512i | 0.464140 | − | 0.131656i | ||||
\(793\) | − | 27.2311i | − | 0.967005i | ||||||
\(794\) | 8.28812 | − | 4.38704i | 0.294134 | − | 0.155690i | ||||
\(795\) | −2.95641 | + | 4.39606i | −0.104853 | + | 0.155912i | ||||
\(796\) | 21.6646 | + | 14.7310i | 0.767882 | + | 0.522126i | ||||
\(797\) | −2.63695 | + | 2.63695i | −0.0934055 | + | 0.0934055i | −0.752266 | − | 0.658860i | \(-0.771039\pi\) |
0.658860 | + | 0.752266i | \(0.271039\pi\) | |||||||
\(798\) | 3.09170 | − | 29.2761i | 0.109445 | − | 1.03636i | ||||
\(799\) | 6.22766i | 0.220319i | ||||||||
\(800\) | −0.0258216 | − | 0.330673i | −0.000912931 | − | 0.0116910i | ||||
\(801\) | 8.31894 | + | 20.4285i | 0.293935 | + | 0.721806i | ||||
\(802\) | −7.01117 | − | 2.15785i | −0.247573 | − | 0.0761965i | ||||
\(803\) | 7.21979 | + | 7.21979i | 0.254781 | + | 0.254781i | ||||
\(804\) | 36.1643 | + | 15.4518i | 1.27542 | + | 0.544942i | ||||
\(805\) | 8.00000 | − | 8.00000i | 0.281963 | − | 0.281963i | ||||
\(806\) | −3.97568 | − | 7.51097i | −0.140037 | − | 0.264563i | ||||
\(807\) | −6.65775 | + | 1.30362i | −0.234364 | + | 0.0458896i | ||||
\(808\) | −40.9751 | − | 4.53887i | −1.44150 | − | 0.159677i | ||||
\(809\) | 6.62090 | 0.232778 | 0.116389 | − | 0.993204i | \(-0.462868\pi\) | ||||
0.116389 | + | 0.993204i | \(0.462868\pi\) | |||||||
\(810\) | −8.64556 | + | 26.9399i | −0.303774 | + | 0.946570i | ||||
\(811\) | 4.01299 | + | 4.01299i | 0.140915 | + | 0.140915i | 0.774045 | − | 0.633130i | \(-0.218230\pi\) |
−0.633130 | + | 0.774045i | \(0.718230\pi\) | |||||||
\(812\) | −20.2212 | + | 3.85230i | −0.709626 | + | 0.135189i | ||||
\(813\) | 27.7267 | − | 41.2284i | 0.972417 | − | 1.44594i | ||||
\(814\) | 7.05863 | + | 2.17246i | 0.247405 | + | 0.0761447i | ||||
\(815\) | −27.5859 | −0.966291 | ||||||||
\(816\) | 11.2618 | + | 2.46563i | 0.394242 | + | 0.0863143i | ||||
\(817\) | −28.5535 | −0.998960 | ||||||||
\(818\) | −20.1115 | − | 6.18980i | −0.703183 | − | 0.216421i | ||||
\(819\) | 12.0360 | − | 28.5727i | 0.420571 | − | 0.998411i | ||||
\(820\) | 8.49828 | + | 44.6087i | 0.296773 | + | 1.55780i | ||||
\(821\) | 7.91085 | + | 7.91085i | 0.276090 | + | 0.276090i | 0.831546 | − | 0.555456i | \(-0.187456\pi\) |
−0.555456 | + | 0.831546i | \(0.687456\pi\) | |||||||
\(822\) | 5.19725 | − | 4.20439i | 0.181275 | − | 0.146645i | ||||
\(823\) | −44.9751 | −1.56773 | −0.783866 | − | 0.620930i | \(-0.786755\pi\) | ||||
−0.783866 | + | 0.620930i | \(0.786755\pi\) | |||||||
\(824\) | 17.9555 | − | 14.3743i | 0.625509 | − | 0.500751i | ||||
\(825\) | −0.0312253 | − | 0.159472i | −0.00108713 | − | 0.00555210i | ||||
\(826\) | 8.17246 | + | 15.4396i | 0.284356 | + | 0.537214i | ||||
\(827\) | −9.75631 | + | 9.75631i | −0.339260 | + | 0.339260i | −0.856089 | − | 0.516829i | \(-0.827112\pi\) |
0.516829 | + | 0.856089i | \(0.327112\pi\) | |||||||
\(828\) | −13.2779 | − | 2.83605i | −0.461438 | − | 0.0985595i | ||||
\(829\) | 18.6336 | + | 18.6336i | 0.647171 | + | 0.647171i | 0.952308 | − | 0.305137i | \(-0.0987023\pi\) |
−0.305137 | + | 0.952308i | \(0.598702\pi\) | |||||||
\(830\) | −11.0950 | − | 3.41476i | −0.385115 | − | 0.118528i | ||||
\(831\) | 1.93763 | − | 0.379397i | 0.0672156 | − | 0.0131611i | ||||
\(832\) | −31.0518 | + | 19.6742i | −1.07653 | + | 0.682079i | ||||
\(833\) | − | 3.23044i | − | 0.111928i | ||||||
\(834\) | 0.0950724 | + | 0.0100401i | 0.00329209 | + | 0.000347661i | ||||
\(835\) | −26.6707 | + | 26.6707i | −0.922979 | + | 0.922979i | ||||
\(836\) | −9.61537 | + | 14.1412i | −0.332554 | + | 0.489082i | ||||
\(837\) | 6.65266 | + | 1.38547i | 0.229949 | + | 0.0478888i | ||||
\(838\) | 44.7259 | − | 23.6742i | 1.54503 | − | 0.817811i | ||||
\(839\) | − | 37.8109i | − | 1.30538i | −0.757626 | − | 0.652689i | \(-0.773641\pi\) | ||
0.757626 | − | 0.652689i | \(-0.226359\pi\) | |||||||
\(840\) | 18.6961 | + | 15.8232i | 0.645078 | + | 0.545951i | ||||
\(841\) | 8.05863i | 0.277884i | ||||||||
\(842\) | −6.67290 | − | 12.6066i | −0.229963 | − | 0.434453i | ||||
\(843\) | −32.0837 | − | 21.5767i | −1.10502 | − | 0.743142i | ||||
\(844\) | 23.5354 | − | 4.48367i | 0.810123 | − | 0.154334i | ||||
\(845\) | −12.7536 | + | 12.7536i | −0.438739 | + | 0.438739i | ||||
\(846\) | 15.8168 | − | 1.39776i | 0.543792 | − | 0.0480561i | ||||
\(847\) | 18.9820i | 0.652228i | ||||||||
\(848\) | 2.18829 | − | 5.05008i | 0.0751463 | − | 0.173421i | ||||
\(849\) | −3.80444 | − | 19.4298i | −0.130568 | − | 0.666828i | ||||
\(850\) | 0.0405874 | − | 0.131874i | 0.00139214 | − | 0.00452325i | ||||
\(851\) | −5.22225 | − | 5.22225i | −0.179017 | − | 0.179017i | ||||
\(852\) | 35.6696 | − | 14.3135i | 1.22202 | − | 0.490374i | ||||
\(853\) | 24.0992 | − | 24.0992i | 0.825142 | − | 0.825142i | −0.161699 | − | 0.986840i | \(-0.551697\pi\) |
0.986840 | + | 0.161699i | \(0.0516972\pi\) | |||||||
\(854\) | 16.6601 | − | 8.81848i | 0.570098 | − | 0.301762i | ||||
\(855\) | −13.4396 | − | 33.0033i | −0.459626 | − | 1.12869i | ||||
\(856\) | −1.05863 | + | 9.55691i | −0.0361833 | + | 0.326649i | ||||
\(857\) | 0.794026 | 0.0271234 | 0.0135617 | − | 0.999908i | \(-0.495683\pi\) | ||||
0.0135617 | + | 0.999908i | \(0.495683\pi\) | |||||||
\(858\) | −14.0019 | + | 11.3270i | −0.478016 | + | 0.386698i | ||||
\(859\) | 2.65775 | + | 2.65775i | 0.0906814 | + | 0.0906814i | 0.750992 | − | 0.660311i | \(-0.229576\pi\) |
−0.660311 | + | 0.750992i | \(0.729576\pi\) | |||||||
\(860\) | 13.3579 | − | 19.6453i | 0.455502 | − | 0.669899i | ||||
\(861\) | 33.0187 | + | 22.2055i | 1.12527 | + | 0.756762i | ||||
\(862\) | −6.44309 | + | 20.9345i | −0.219452 | + | 0.713032i | ||||
\(863\) | −21.4069 | −0.728699 | −0.364349 | − | 0.931262i | \(-0.618709\pi\) | ||||
−0.364349 | + | 0.931262i | \(0.618709\pi\) | |||||||
\(864\) | 3.73446 | − | 29.1557i | 0.127049 | − | 0.991896i | ||||
\(865\) | −51.2794 | −1.74355 | ||||||||
\(866\) | 10.6288 | − | 34.5346i | 0.361182 | − | 1.17353i | ||||
\(867\) | −20.4538 | − | 13.7555i | −0.694648 | − | 0.467161i | ||||
\(868\) | 3.30777 | − | 4.86469i | 0.112273 | − | 0.165118i | ||||
\(869\) | −3.04612 | − | 3.04612i | −0.103332 | − | 0.103332i | ||||
\(870\) | −19.3722 | + | 15.6714i | −0.656778 | + | 0.531310i | ||||
\(871\) | −52.1656 | −1.76756 | ||||||||
\(872\) | −35.4763 | − | 3.92976i | −1.20138 | − | 0.133078i | ||||
\(873\) | −6.42004 | − | 15.7655i | −0.217286 | − | 0.533580i | ||||
\(874\) | 15.1138 | − | 8.00000i | 0.511233 | − | 0.270604i | ||||
\(875\) | 17.8837 | − | 17.8837i | 0.604581 | − | 0.604581i | ||||
\(876\) | 20.5144 | − | 8.23204i | 0.693118 | − | 0.278135i | ||||
\(877\) | −20.0923 | − | 20.0923i | −0.678470 | − | 0.678470i | 0.281184 | − | 0.959654i | \(-0.409273\pi\) |
−0.959654 | + | 0.281184i | \(0.909273\pi\) | |||||||
\(878\) | 1.09701 | − | 3.56433i | 0.0370222 | − | 0.120290i | ||||
\(879\) | 3.00274 | + | 15.3354i | 0.101280 | + | 0.517249i | ||||
\(880\) | −5.23109 | − | 13.2311i | −0.176340 | − | 0.446020i | ||||
\(881\) | − | 10.8132i | − | 0.364305i | −0.983270 | − | 0.182152i | \(-0.941694\pi\) | ||
0.983270 | − | 0.182152i | \(-0.0583064\pi\) | |||||||
\(882\) | −8.20455 | + | 0.725055i | −0.276261 | + | 0.0244139i | ||||
\(883\) | 12.5665 | − | 12.5665i | 0.422895 | − | 0.422895i | −0.463304 | − | 0.886199i | \(-0.653336\pi\) |
0.886199 | + | 0.463304i | \(0.153336\pi\) | |||||||
\(884\) | −15.0219 | + | 2.86179i | −0.505243 | + | 0.0962525i | ||||
\(885\) | 17.5469 | + | 11.8005i | 0.589833 | + | 0.396671i | ||||
\(886\) | 13.9018 | + | 26.2637i | 0.467041 | + | 0.882348i | ||||
\(887\) | 12.0977i | 0.406201i | 0.979158 | + | 0.203101i | \(0.0651018\pi\) | ||||
−0.979158 | + | 0.203101i | \(0.934898\pi\) | |||||||
\(888\) | 10.3291 | − | 12.2045i | 0.346621 | − | 0.409556i | ||||
\(889\) | − | 16.7000i | − | 0.560099i | ||||||
\(890\) | 20.4285 | − | 10.8132i | 0.684766 | − | 0.362458i | ||||
\(891\) | 0.172302 | − | 14.4000i | 0.00577235 | − | 0.482417i | ||||
\(892\) | −24.2587 | + | 35.6769i | −0.812241 | + | 1.19455i | ||||
\(893\) | −14.1412 | + | 14.1412i | −0.473216 | + | 0.473216i | ||||
\(894\) | 43.3006 | + | 4.57276i | 1.44819 | + | 0.152936i | ||||
\(895\) | 4.20855i | 0.140676i | ||||||||
\(896\) | −22.0925 | − | 12.6264i | −0.738060 | − | 0.421817i | ||||
\(897\) | 17.6742 | − | 3.46069i | 0.590124 | − | 0.115549i | ||||
\(898\) | 42.8578 | + | 13.1905i | 1.43018 | + | 0.440173i | ||||
\(899\) | 4.23175 | + | 4.23175i | 0.141137 | + | 0.141137i | ||||
\(900\) | −0.344039 | − | 0.0734839i | −0.0114680 | − | 0.00244946i | ||||
\(901\) | 1.61899 | − | 1.61899i | 0.0539362 | − | 0.0539362i | ||||
\(902\) | −10.8132 | − | 20.4285i | −0.360039 | − | 0.680196i | ||||
\(903\) | −4.00000 | − | 20.4285i | −0.133112 | − | 0.679819i | ||||
\(904\) | −28.1104 | − | 35.1138i | −0.934938 | − | 1.16787i | ||||
\(905\) | 32.2092 | 1.07067 | ||||||||
\(906\) | −32.1167 | + | 25.9812i | −1.06701 | + | 0.863169i | ||||
\(907\) | −14.3388 | − | 14.3388i | −0.476112 | − | 0.476112i | 0.427774 | − | 0.903886i | \(-0.359298\pi\) |
−0.903886 | + | 0.427774i | \(0.859298\pi\) | |||||||
\(908\) | 8.86727 | + | 46.5455i | 0.294271 | + | 1.54467i | ||||
\(909\) | −16.9748 | + | 40.2972i | −0.563018 | + | 1.33657i | ||||
\(910\) | −31.0518 | − | 9.55691i | −1.02936 | − | 0.316809i | ||||
\(911\) | 28.0629 | 0.929765 | 0.464882 | − | 0.885372i | \(-0.346097\pi\) | ||||
0.464882 | + | 0.885372i | \(0.346097\pi\) | |||||||
\(912\) | 19.9735 | + | 31.1709i | 0.661388 | + | 1.03217i | ||||
\(913\) | 5.90871 | 0.195550 | ||||||||
\(914\) | 32.2717 | + | 9.93237i | 1.06745 | + | 0.328534i | ||||
\(915\) | 12.7334 | − | 18.9340i | 0.420952 | − | 0.625937i | ||||
\(916\) | −9.35342 | + | 1.78189i | −0.309046 | + | 0.0588755i | ||||
\(917\) | 8.73458 | + | 8.73458i | 0.288441 | + | 0.288441i | ||||
\(918\) | 5.90412 | − | 10.7080i | 0.194865 | − | 0.353418i | ||||
\(919\) | 25.4734 | 0.840289 | 0.420144 | − | 0.907457i | \(-0.361979\pi\) | ||||
0.420144 | + | 0.907457i | \(0.361979\pi\) | |||||||
\(920\) | −1.56644 | + | 14.1412i | −0.0516439 | + | 0.466220i | ||||
\(921\) | 15.8364 | − | 3.10084i | 0.521827 | − | 0.102176i | ||||
\(922\) | 0.862012 | + | 1.62854i | 0.0283888 | + | 0.0536330i | ||||
\(923\) | −36.0494 | + | 36.0494i | −1.18658 | + | 1.18658i | ||||
\(924\) | −11.4643 | − | 4.89829i | −0.377147 | − | 0.161142i | ||||
\(925\) | −0.135312 | − | 0.135312i | −0.00444903 | − | 0.00444903i | ||||
\(926\) | −35.3468 | − | 10.8788i | −1.16157 | − | 0.357500i | ||||
\(927\) | −9.20080 | − | 22.5941i | −0.302194 | − | 0.742086i | ||||
\(928\) | 16.8241 | − | 19.6742i | 0.552278 | − | 0.645837i | ||||
\(929\) | 43.3502i | 1.42227i | 0.703054 | + | 0.711137i | \(0.251819\pi\) | ||||
−0.703054 | + | 0.711137i | \(0.748181\pi\) | |||||||
\(930\) | 0.747838 | − | 7.08147i | 0.0245226 | − | 0.232211i | ||||
\(931\) | 7.33537 | − | 7.33537i | 0.240407 | − | 0.240407i | ||||
\(932\) | −0.829141 | − | 0.563779i | −0.0271594 | − | 0.0184672i | ||||
\(933\) | −9.21016 | + | 13.6951i | −0.301527 | + | 0.448358i | ||||
\(934\) | 28.7259 | − | 15.2051i | 0.939941 | − | 0.497527i | ||||
\(935\) | − | 5.91872i | − | 0.193563i | ||||||
\(936\) | 10.6399 | + | 37.5099i | 0.347775 | + | 1.22605i | ||||
\(937\) | 15.5500i | 0.507998i | 0.967205 | + | 0.253999i | \(0.0817459\pi\) | ||||
−0.967205 | + | 0.253999i | \(0.918254\pi\) | |||||||
\(938\) | −16.8932 | − | 31.9152i | −0.551584 | − | 1.04207i | ||||
\(939\) | −24.3279 | + | 36.1745i | −0.793910 | + | 1.18051i | ||||
\(940\) | −3.11383 | − | 16.3449i | −0.101562 | − | 0.533113i | ||||
\(941\) | −1.85373 | + | 1.85373i | −0.0604299 | + | 0.0604299i | −0.736676 | − | 0.676246i | \(-0.763606\pi\) |
0.676246 | + | 0.736676i | \(0.263606\pi\) | |||||||
\(942\) | 18.4870 | + | 1.95232i | 0.602338 | + | 0.0636099i | ||||
\(943\) | 23.1138i | 0.752690i | ||||||||
\(944\) | −20.1574 | − | 8.73458i | −0.656069 | − | 0.284287i | ||||
\(945\) | 21.7294 | − | 14.2387i | 0.706857 | − | 0.463186i | ||||
\(946\) | −3.55691 | + | 11.5569i | −0.115645 | + | 0.375748i | ||||
\(947\) | −31.2499 | − | 31.2499i | −1.01549 | − | 1.01549i | −0.999878 | − | 0.0156087i | \(-0.995031\pi\) |
−0.0156087 | − | 0.999878i | \(-0.504969\pi\) | |||||||
\(948\) | −8.65528 | + | 3.47320i | −0.281110 | + | 0.112804i | ||||
\(949\) | −20.7328 | + | 20.7328i | −0.673016 | + | 0.673016i | ||||
\(950\) | 0.391609 | − | 0.207285i | 0.0127055 | − | 0.00672522i | ||||
\(951\) | 37.3285 | − | 7.30909i | 1.21046 | − | 0.237014i | ||||
\(952\) | −6.61555 | − | 8.26375i | −0.214411 | − | 0.267830i | ||||
\(953\) | 48.9411 | 1.58536 | 0.792679 | − | 0.609639i | \(-0.208686\pi\) | ||||
0.792679 | + | 0.609639i | \(0.208686\pi\) | |||||||
\(954\) | −4.47521 | − | 3.74846i | −0.144890 | − | 0.121361i | ||||
\(955\) | 38.5726 | + | 38.5726i | 1.24818 | + | 1.24818i | ||||
\(956\) | 50.3749 | + | 34.2527i | 1.62924 | + | 1.10781i | ||||
\(957\) | 7.07766 | − | 10.5242i | 0.228788 | − | 0.340199i | ||||
\(958\) | −4.88617 | + | 15.8759i | −0.157865 | + | 0.512926i | ||||
\(959\) | −6.13815 | −0.198211 | ||||||||
\(960\) | −30.7902 | − | 0.840321i | −0.993749 | − | 0.0271212i | ||||
\(961\) | 29.2897 | 0.944830 | ||||||||
\(962\) | −6.23858 | + | 20.2700i | −0.201140 | + | 0.653532i | ||||
\(963\) | 9.39880 | + | 3.95915i | 0.302872 | + | 0.127582i | ||||
\(964\) | 25.6267 | + | 17.4250i | 0.825381 | + | 0.561223i | ||||
\(965\) | 13.1736 | + | 13.1736i | 0.424074 | + | 0.424074i | ||||
\(966\) | 7.84085 | + | 9.69245i | 0.252275 | + | 0.311850i | ||||
\(967\) | 18.5129 | 0.595334 | 0.297667 | − | 0.954670i | \(-0.403791\pi\) | ||||
0.297667 | + | 0.954670i | \(0.403791\pi\) | |||||||
\(968\) | −14.9183 | − | 18.6351i | −0.479492 | − | 0.598953i | ||||
\(969\) | 2.95936 | + | 15.1138i | 0.0950683 | + | 0.485526i | ||||
\(970\) | −15.7655 | + | 8.34492i | −0.506199 | + | 0.267939i | ||||
\(971\) | 0.0663404 | − | 0.0663404i | 0.00212897 | − | 0.00212897i | −0.706041 | − | 0.708170i | \(-0.749521\pi\) |
0.708170 | + | 0.706041i | \(0.249521\pi\) | |||||||
\(972\) | −28.5210 | − | 12.5917i | −0.914812 | − | 0.403879i | ||||
\(973\) | −0.0620710 | − | 0.0620710i | −0.00198991 | − | 0.00198991i | ||||
\(974\) | −0.325942 | + | 1.05903i | −0.0104439 | + | 0.0339336i | ||||
\(975\) | 0.457950 | − | 0.0896687i | 0.0146661 | − | 0.00287170i | ||||
\(976\) | −9.42504 | + | 21.7509i | −0.301688 | + | 0.696228i | ||||
\(977\) | 3.42557i | 0.109594i | 0.998498 | + | 0.0547969i | \(0.0174511\pi\) | ||||
−0.998498 | + | 0.0547969i | \(0.982549\pi\) | |||||||
\(978\) | 3.19238 | − | 30.2295i | 0.102081 | − | 0.966632i | ||||
\(979\) | −8.31894 | + | 8.31894i | −0.265875 | + | 0.265875i | ||||
\(980\) | 1.61522 | + | 8.47852i | 0.0515963 | + | 0.270836i | ||||
\(981\) | −14.6968 | + | 34.8893i | −0.469232 | + | 1.11393i | ||||
\(982\) | −9.39218 | − | 17.7440i | −0.299717 | − | 0.566233i | ||||
\(983\) | 30.5911i | 0.975706i | 0.872926 | + | 0.487853i | \(0.162220\pi\) | ||||
−0.872926 | + | 0.487853i | \(0.837780\pi\) | |||||||
\(984\) | −49.8671 | + | 4.15034i | −1.58970 | + | 0.132308i | ||||
\(985\) | − | 4.05520i | − | 0.129209i | ||||||
\(986\) | 9.51780 | − | 5.03793i | 0.303109 | − | 0.160440i | ||||
\(987\) | −12.0983 | − | 8.13626i | −0.385092 | − | 0.258980i | ||||
\(988\) | −40.6087 | − | 27.6121i | −1.29193 | − | 0.878458i | ||||
\(989\) | 8.55026 | − | 8.55026i | 0.271882 | − | 0.271882i | ||||
\(990\) | −15.0321 | + | 1.32842i | −0.477752 | + | 0.0422201i | ||||
\(991\) | − | 24.2975i | − | 0.771834i | −0.922533 | − | 0.385917i | \(-0.873885\pi\) | ||
0.922533 | − | 0.385917i | \(-0.126115\pi\) | |||||||
\(992\) | 0.575933 | + | 7.37543i | 0.0182859 | + | 0.234170i | ||||
\(993\) | −1.21811 | − | 6.22102i | −0.0386554 | − | 0.197418i | ||||
\(994\) | −33.7294 | − | 10.3810i | −1.06983 | − | 0.329266i | ||||
\(995\) | −20.5899 | − | 20.5899i | −0.652743 | − | 0.652743i | ||||
\(996\) | 5.02598 | − | 11.7631i | 0.159254 | − | 0.372729i | ||||
\(997\) | 10.3078 | − | 10.3078i | 0.326450 | − | 0.326450i | −0.524785 | − | 0.851235i | \(-0.675854\pi\) |
0.851235 | + | 0.524785i | \(0.175854\pi\) | |||||||
\(998\) | 28.0371 | + | 52.9684i | 0.887498 | + | 1.67669i | ||||
\(999\) | −9.29478 | − | 14.1845i | −0.294074 | − | 0.448779i |
(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 | 48.2.k.a.35.4 | yes | 12 | |
3.2 | odd | 2 | inner | 48.2.k.a.35.3 | yes | 12 | |
4.3 | odd | 2 | 192.2.k.a.47.5 | 12 | |||
8.3 | odd | 2 | 384.2.k.a.95.2 | 12 | |||
8.5 | even | 2 | 384.2.k.b.95.5 | 12 | |||
12.11 | even | 2 | 192.2.k.a.47.2 | 12 | |||
16.3 | odd | 4 | 384.2.k.b.287.2 | 12 | |||
16.5 | even | 4 | 192.2.k.a.143.2 | 12 | |||
16.11 | odd | 4 | inner | 48.2.k.a.11.3 | ✓ | 12 | |
16.13 | even | 4 | 384.2.k.a.287.5 | 12 | |||
24.5 | odd | 2 | 384.2.k.b.95.2 | 12 | |||
24.11 | even | 2 | 384.2.k.a.95.5 | 12 | |||
48.5 | odd | 4 | 192.2.k.a.143.5 | 12 | |||
48.11 | even | 4 | inner | 48.2.k.a.11.4 | yes | 12 | |
48.29 | odd | 4 | 384.2.k.a.287.2 | 12 | |||
48.35 | even | 4 | 384.2.k.b.287.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.3 | ✓ | 12 | 16.11 | odd | 4 | inner | |
48.2.k.a.11.4 | yes | 12 | 48.11 | even | 4 | inner | |
48.2.k.a.35.3 | yes | 12 | 3.2 | odd | 2 | inner | |
48.2.k.a.35.4 | yes | 12 | 1.1 | even | 1 | trivial | |
192.2.k.a.47.2 | 12 | 12.11 | even | 2 | |||
192.2.k.a.47.5 | 12 | 4.3 | odd | 2 | |||
192.2.k.a.143.2 | 12 | 16.5 | even | 4 | |||
192.2.k.a.143.5 | 12 | 48.5 | odd | 4 | |||
384.2.k.a.95.2 | 12 | 8.3 | odd | 2 | |||
384.2.k.a.95.5 | 12 | 24.11 | even | 2 | |||
384.2.k.a.287.2 | 12 | 48.29 | odd | 4 | |||
384.2.k.a.287.5 | 12 | 16.13 | even | 4 | |||
384.2.k.b.95.2 | 12 | 24.5 | odd | 2 | |||
384.2.k.b.95.5 | 12 | 8.5 | even | 2 | |||
384.2.k.b.287.2 | 12 | 16.3 | odd | 4 | |||
384.2.k.b.287.5 | 12 | 48.35 | even | 4 |