Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(49,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.z (of order \(6\), 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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.8 | ||
Root | \(0.517063 - 1.65307i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.69 |
Dual form | 260.2.z.a.49.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.86320 | + | 1.65307i | 1.65307 | + | 0.954401i | 0.975799 | + | 0.218669i | \(0.0701715\pi\) |
0.677273 | + | 0.735732i | \(0.263162\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.877236 | − | 2.05681i | −0.392312 | − | 0.919832i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.517063 | + | 0.895580i | 0.195432 | + | 0.338497i | 0.947042 | − | 0.321110i | \(-0.104056\pi\) |
−0.751610 | + | 0.659607i | \(0.770723\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.96529 | + | 6.86809i | 1.32176 | + | 2.28936i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.96091 | − | 1.70948i | −0.892749 | − | 0.515429i | −0.0179086 | − | 0.999840i | \(-0.505701\pi\) |
−0.874841 | + | 0.484411i | \(0.839034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.57672 | − | 0.455025i | 0.992005 | − | 0.126201i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.888345 | − | 7.33919i | 0.229370 | − | 1.89497i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.07508 | − | 1.19805i | 0.503280 | − | 0.290569i | −0.226787 | − | 0.973944i | \(-0.572822\pi\) |
0.730067 | + | 0.683375i | \(0.239489\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.37246 | + | 3.10179i | −1.23253 | + | 0.711600i | −0.967556 | − | 0.252656i | \(-0.918696\pi\) |
−0.264972 | + | 0.964256i | \(0.585363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.41897i | 0.746080i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.28304 | − | 3.62751i | −1.31010 | − | 0.756389i | −0.327991 | − | 0.944681i | \(-0.606371\pi\) |
−0.982113 | + | 0.188292i | \(0.939705\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.46091 | + | 3.60861i | −0.692183 | + | 0.721722i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.3012i | 3.13717i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.902796 | − | 1.56369i | 0.167645 | − | 0.290370i | −0.769946 | − | 0.638109i | \(-0.779717\pi\) |
0.937591 | + | 0.347739i | \(0.113050\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.80053i | − | 1.04181i | −0.853616 | − | 0.520903i | \(-0.825595\pi\) | ||
0.853616 | − | 0.520903i | \(-0.174405\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.65180 | − | 9.78921i | −0.983852 | − | 1.70408i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.38845 | − | 1.84913i | 0.234691 | − | 0.312561i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.713520 | + | 1.23585i | −0.117302 | + | 0.203173i | −0.918698 | − | 0.394962i | \(-0.870758\pi\) |
0.801396 | + | 0.598135i | \(0.204091\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.9931 | + | 4.60975i | 1.76030 | + | 0.738151i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.60158 | − | 2.07937i | −0.562472 | − | 0.324744i | 0.191665 | − | 0.981460i | \(-0.438611\pi\) |
−0.754137 | + | 0.656717i | \(0.771945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86864 | − | 1.07886i | 0.284965 | − | 0.164525i | −0.350704 | − | 0.936486i | \(-0.614058\pi\) |
0.635669 | + | 0.771962i | \(0.280724\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.6478 | − | 14.1808i | 1.58729 | − | 2.11394i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50894 | 0.511832 | 0.255916 | − | 0.966699i | \(-0.417623\pi\) | ||||
0.255916 | + | 0.966699i | \(0.417623\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.96529 | − | 5.13604i | 0.423613 | − | 0.733719i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.92183 | 1.10928 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.55382i | 0.625515i | 0.949833 | + | 0.312757i | \(0.101253\pi\) | ||||
−0.949833 | + | 0.312757i | \(0.898747\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.918661 | + | 7.58965i | −0.123872 | + | 1.02339i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −20.5099 | −2.71661 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.06250 | + | 2.92283i | −0.659081 | + | 0.380520i | −0.791927 | − | 0.610616i | \(-0.790922\pi\) |
0.132846 | + | 0.991137i | \(0.457588\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.90280 | − | 3.29574i | −0.243628 | − | 0.421976i | 0.718117 | − | 0.695922i | \(-0.245004\pi\) |
−0.961745 | + | 0.273946i | \(0.911671\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.10061 | + | 7.10247i | −0.516629 | + | 0.894827i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.07353 | − | 6.95747i | −0.505259 | − | 0.862968i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.80822 | + | 6.59603i | −0.465248 | + | 0.805833i | −0.999213 | − | 0.0396734i | \(-0.987368\pi\) |
0.533965 | + | 0.845507i | \(0.320702\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.9931 | − | 20.7726i | −1.44380 | − | 2.50073i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.49745 | − | 5.48336i | 1.12714 | − | 0.650755i | 0.183926 | − | 0.982940i | \(-0.441119\pi\) |
0.943214 | + | 0.332185i | \(0.107786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.15345 | 0.837248 | 0.418624 | − | 0.908160i | \(-0.362513\pi\) | ||||
0.418624 | + | 0.908160i | \(0.362513\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −15.8746 | + | 4.61105i | −1.83304 | + | 0.532438i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.53565i | − | 0.402924i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8524 | −1.44601 | −0.723005 | − | 0.690843i | \(-0.757240\pi\) | ||||
−0.723005 | + | 0.690843i | \(0.757240\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −15.0512 | + | 26.0694i | −1.67236 | + | 2.89660i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.706694 | −0.0775698 | −0.0387849 | − | 0.999248i | \(-0.512349\pi\) | ||||
−0.0387849 | + | 0.999248i | \(0.512349\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.28448 | − | 3.21707i | −0.464718 | − | 0.348940i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.16978 | − | 2.98477i | 0.554258 | − | 0.320001i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.06250 | + | 2.92283i | 0.536623 | + | 0.309820i | 0.743709 | − | 0.668503i | \(-0.233065\pi\) |
−0.207086 | + | 0.978323i | \(0.566398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.25690 | + | 2.96796i | 0.236588 | + | 0.311127i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.58870 | − | 16.6081i | 0.994302 | − | 1.72218i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.0927 | + | 8.32912i | 1.13809 | + | 0.854550i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.99794 | + | 13.8528i | 0.812068 | + | 1.40654i | 0.911414 | + | 0.411490i | \(0.134992\pi\) |
−0.0993461 | + | 0.995053i | \(0.531675\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 27.1144i | − | 2.72510i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.99562 | − | 5.18857i | 0.298076 | − | 0.516282i | −0.677620 | − | 0.735412i | \(-0.736989\pi\) |
0.975696 | + | 0.219130i | \(0.0703219\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.7096i | 1.15378i | 0.816822 | + | 0.576890i | \(0.195734\pi\) | ||||
−0.816822 | + | 0.576890i | \(0.804266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.03216 | − | 2.99924i | 0.686269 | − | 0.292696i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.7452 | − | 6.78110i | −1.13545 | − | 0.655554i | −0.190152 | − | 0.981755i | \(-0.560898\pi\) |
−0.945300 | + | 0.326201i | \(0.894231\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.39533i | 0.133648i | 0.997765 | + | 0.0668240i | \(0.0212866\pi\) | ||||
−0.997765 | + | 0.0668240i | \(0.978713\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.08591 | + | 2.35900i | −0.387817 | + | 0.223906i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.65133 | − | 2.10810i | 0.343488 | − | 0.198313i | −0.318325 | − | 0.947982i | \(-0.603120\pi\) |
0.661813 | + | 0.749669i | \(0.269787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.94939 | + | 16.1052i | −0.181782 | + | 1.50182i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.3079 | + | 22.7609i | 1.60012 | + | 2.10425i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.14589 | + | 1.23893i | 0.196714 | + | 0.113573i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.344677 | + | 0.596999i | 0.0313343 | + | 0.0542726i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.87471 | − | 11.9073i | −0.619871 | − | 1.07365i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4583 | + | 3.95283i | 0.935415 | + | 0.353552i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.16978 | + | 2.98477i | 0.458744 | + | 0.264856i | 0.711516 | − | 0.702670i | \(-0.248009\pi\) |
−0.252772 | + | 0.967526i | \(0.581342\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.13374 | 0.628091 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.0556 | 1.66489 | 0.832447 | − | 0.554105i | \(-0.186940\pi\) | ||||
0.832447 | + | 0.554105i | \(0.186940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.55581 | − | 3.20765i | −0.481750 | − | 0.278138i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 33.5285 | − | 14.3000i | 2.88567 | − | 1.23075i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.231497 | + | 0.400964i | 0.0197781 | + | 0.0342567i | 0.875745 | − | 0.482774i | \(-0.160371\pi\) |
−0.855967 | + | 0.517031i | \(0.827037\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.65970 | + | 8.07084i | 0.395231 | + | 0.684559i | 0.993131 | − | 0.117011i | \(-0.0373314\pi\) |
−0.597900 | + | 0.801571i | \(0.703998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0468 | + | 5.80053i | 0.846095 | + | 0.488493i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.3682 | − | 4.76707i | −0.950659 | − | 0.398642i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00817 | − | 0.485154i | −0.332861 | − | 0.0402899i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.9805 | − | 9.80368i | 1.40053 | − | 0.808594i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.44524 | + | 5.45321i | −0.773784 | + | 0.446744i | −0.834223 | − | 0.551427i | \(-0.814083\pi\) |
0.0604387 | + | 0.998172i | \(0.480750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.85943i | 0.395455i | 0.980257 | + | 0.197727i | \(0.0633561\pi\) | ||||
−0.980257 | + | 0.197727i | \(0.936644\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.4566 | + | 9.50121i | 1.33044 | + | 0.768127i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.9306 | + | 5.08844i | −0.958287 | + | 0.408713i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.80782i | − | 0.702940i | −0.936199 | − | 0.351470i | \(-0.885682\pi\) | ||
0.936199 | − | 0.351470i | \(-0.114318\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.52779 | + | 13.0385i | −0.596992 | + | 1.03402i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.50261i | − | 0.591289i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.30996 | + | 16.1253i | 0.729212 | + | 1.26303i | 0.957217 | + | 0.289372i | \(0.0934466\pi\) |
−0.228004 | + | 0.973660i | \(0.573220\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.1766 | + | 20.2121i | −1.18149 | + | 1.57351i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.18849 | − | 12.4508i | 0.556262 | − | 0.963474i | −0.441542 | − | 0.897240i | \(-0.645568\pi\) |
0.997804 | − | 0.0662334i | \(-0.0210982\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5859 | − | 3.25499i | 0.968147 | − | 0.250384i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −42.6068 | − | 24.5990i | −3.25822 | − | 1.88113i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9947 | + | 10.9666i | −1.44414 | + | 0.833773i | −0.998122 | − | 0.0612532i | \(-0.980490\pi\) |
−0.446014 | + | 0.895026i | \(0.647157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.02131 | − | 1.23365i | −0.379575 | − | 0.0932548i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.3266 | −1.45268 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.06250 | + | 8.76850i | −0.378389 | + | 0.655388i | −0.990828 | − | 0.135129i | \(-0.956855\pi\) |
0.612439 | + | 0.790518i | \(0.290188\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.272578 | 0.0202606 | 0.0101303 | − | 0.999949i | \(-0.496775\pi\) | ||||
0.0101303 | + | 0.999949i | \(0.496775\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.5818i | − | 0.930076i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.16784 | + | 0.383439i | 0.232904 | + | 0.0281910i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.19217 | −0.599071 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.5990 | + | 8.42876i | −1.06192 | + | 0.613102i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.39587 | + | 12.8100i | 0.535147 | + | 0.926901i | 0.999156 | + | 0.0410710i | \(0.0130770\pi\) |
−0.464010 | + | 0.885830i | \(0.653590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50212 | − | 6.06585i | 0.252088 | − | 0.436629i | −0.712013 | − | 0.702167i | \(-0.752216\pi\) |
0.964101 | + | 0.265538i | \(0.0855494\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.162148 | − | 26.6545i | −0.0116117 | − | 1.90877i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.81643 | + | 8.34230i | −0.343157 | + | 0.594365i | −0.985017 | − | 0.172457i | \(-0.944829\pi\) |
0.641861 | + | 0.766821i | \(0.278163\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.96091 | + | 3.39640i | 0.139006 | + | 0.240765i | 0.927120 | − | 0.374763i | \(-0.122276\pi\) |
−0.788115 | + | 0.615528i | \(0.788943\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.8074 | + | 12.5905i | −1.53818 | + | 0.888067i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.86721 | 0.131052 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.11744 | + | 9.23186i | −0.0780451 | + | 0.644781i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 57.5366i | − | 3.99907i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.2099 | 1.46712 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.29429 | − | 12.6341i | 0.502160 | − | 0.869766i | −0.497837 | − | 0.867271i | \(-0.665872\pi\) |
0.999997 | − | 0.00249580i | \(-0.000794440\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.2575 | 2.48433 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.85825 | − | 2.89702i | −0.263131 | − | 0.197575i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.19484 | − | 2.99924i | 0.352649 | − | 0.203602i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.4818 | + | 11.8252i | 1.38403 | + | 0.799070i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.87684 | − | 5.22929i | 0.462586 | − | 0.351760i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.50165 | + | 2.60093i | −0.100558 | + | 0.174171i | −0.911915 | − | 0.410380i | \(-0.865396\pi\) |
0.811357 | + | 0.584551i | \(0.198729\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −38.5078 | − | 9.46067i | −2.56719 | − | 0.630711i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.84058 | + | 10.1162i | 0.387653 | + | 0.671435i | 0.992133 | − | 0.125185i | \(-0.0399526\pi\) |
−0.604480 | + | 0.796620i | \(0.706619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.5293i | 1.22445i | 0.790684 | + | 0.612224i | \(0.209725\pi\) | ||||
−0.790684 | + | 0.612224i | \(0.790275\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.84468 | − | 10.1233i | 0.384552 | − | 0.666063i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.1750i | 0.732097i | 0.930596 | + | 0.366048i | \(0.119290\pi\) | ||||
−0.930596 | + | 0.366048i | \(0.880710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.07817 | − | 7.21722i | −0.200798 | − | 0.470800i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −36.7991 | − | 21.2460i | −2.39036 | − | 1.38007i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.16507i | − | 0.140047i | −0.997545 | − | 0.0700235i | \(-0.977693\pi\) | ||
0.997545 | − | 0.0700235i | \(-0.0223074\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7318 | − | 9.66011i | 1.07779 | − | 0.622262i | 0.147491 | − | 0.989063i | \(-0.452880\pi\) |
0.930299 | + | 0.366801i | \(0.119547\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −43.8375 | + | 25.3096i | −2.81218 | + | 1.62361i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.1651 | − | 1.59352i | −0.841087 | − | 0.101806i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.8044 | + | 13.5389i | −1.13287 | + | 0.861457i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.02341 | − | 1.16822i | −0.128228 | − | 0.0740327i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.87684 | − | 6.71488i | −0.244704 | − | 0.423840i | 0.717344 | − | 0.696719i | \(-0.245357\pi\) |
−0.962048 | + | 0.272879i | \(0.912024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4024 | + | 21.4815i | 0.779730 | + | 1.35053i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.94931 | − | 16.2937i | −0.435183 | − | 1.02035i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4216 | + | 8.90366i | 0.961973 | + | 0.555395i | 0.896780 | − | 0.442477i | \(-0.145900\pi\) |
0.0651933 | + | 0.997873i | \(0.479234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.47574 | −0.0916980 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.3194 | 0.886348 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.3815 | − | 8.30316i | −0.886801 | − | 0.511995i | −0.0139065 | − | 0.999903i | \(-0.504427\pi\) |
−0.872895 | + | 0.487908i | \(0.837760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.36633 | − | 3.99477i | 0.575369 | − | 0.245397i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.66330 | + | 16.7373i | 0.591385 | + | 1.02431i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.96967 | − | 5.14362i | −0.181064 | − | 0.313612i | 0.761179 | − | 0.648542i | \(-0.224621\pi\) |
−0.942243 | + | 0.334930i | \(0.891287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.37246 | − | 4.83384i | −0.508591 | − | 0.293635i | 0.223663 | − | 0.974666i | \(-0.428198\pi\) |
−0.732254 | + | 0.681031i | \(0.761532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.55572 | + | 12.2287i | 0.0941562 | + | 0.740115i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.4163 | − | 4.76841i | 0.989942 | − | 0.287546i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.9423 | − | 10.3590i | 1.07805 | − | 0.622411i | 0.147679 | − | 0.989035i | \(-0.452820\pi\) |
0.930369 | + | 0.366624i | \(0.119487\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 39.8386 | − | 23.0008i | 2.38507 | − | 1.37702i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.7700i | − | 1.65662i | −0.560272 | − | 0.828309i | \(-0.689303\pi\) | ||
0.560272 | − | 0.828309i | \(-0.310697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.1502 | − | 12.7885i | −1.31670 | − | 0.760194i | −0.333500 | − | 0.942750i | \(-0.608230\pi\) |
−0.983196 | + | 0.182556i | \(0.941563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.9921 | + | 42.1850i | 1.06576 | + | 2.49882i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.30067i | − | 0.253861i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.62937 | + | 9.75035i | −0.331139 | + | 0.573550i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 52.8847i | 3.10016i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.1987 | − | 24.5929i | −0.829497 | − | 1.43673i | −0.898434 | − | 0.439109i | \(-0.855294\pi\) |
0.0689370 | − | 0.997621i | \(-0.478039\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.4527 | + | 7.84856i | 0.608580 | + | 0.456961i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.8667 | − | 48.2665i | 1.61699 | − | 2.80071i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.1233 | − | 10.1157i | −1.39509 | − | 0.585005i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.93241 | + | 1.11568i | 0.111382 | + | 0.0643067i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.1542 | − | 9.90396i | 0.985481 | − | 0.568968i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.10950 | + | 6.80483i | −0.292569 | + | 0.389643i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5519 | −0.659302 | −0.329651 | − | 0.944103i | \(-0.606931\pi\) | ||||
−0.329651 | + | 0.944103i | \(0.606931\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.3568 | + | 33.5269i | −1.10117 | + | 1.90728i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.03807 | −0.0588634 | −0.0294317 | − | 0.999567i | \(-0.509370\pi\) | ||||
−0.0294317 | + | 0.999567i | \(0.509370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 29.6339i | − | 1.67501i | −0.546432 | − | 0.837504i | \(-0.684014\pi\) | ||
0.546432 | − | 0.837504i | \(-0.315986\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.2056 | + | 2.20363i | 1.02577 | + | 0.124161i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.4445 | −1.14828 | −0.574138 | − | 0.818759i | \(-0.694663\pi\) | ||||
−0.574138 | + | 0.818759i | \(0.694663\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.34620 | + | 3.08663i | −0.299330 | + | 0.172818i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.4193 | − | 38.8313i | −1.25132 | − | 2.16735i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.43219 | + | 12.8729i | −0.413538 | + | 0.716269i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.7367 | + | 14.4818i | −0.595567 | + | 0.803306i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.30657 | + | 3.99510i | −0.127554 | + | 0.220930i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.81435 | + | 3.14254i | 0.100028 | + | 0.173254i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.39587 | − | 2.53796i | 0.241619 | − | 0.139499i | −0.374302 | − | 0.927307i | \(-0.622118\pi\) |
0.615921 | + | 0.787808i | \(0.288784\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.3173 | −0.620182 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.9075 | + | 2.04650i | 0.923754 | + | 0.111812i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.4909i | − | 0.571473i | −0.958308 | − | 0.285737i | \(-0.907762\pi\) | ||
0.958308 | − | 0.285737i | \(-0.0922382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.9393 | 0.757081 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.91593 | + | 17.1749i | −0.536977 | + | 0.930072i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.3719 | 0.722012 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −32.2045 | + | 42.8899i | −1.73383 | + | 2.30912i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.6247 | − | 15.9491i | 1.48297 | − | 0.856193i | 0.483158 | − | 0.875533i | \(-0.339490\pi\) |
0.999813 | + | 0.0193399i | \(0.00615647\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.4661 | − | 16.4349i | −1.52376 | − | 0.879741i | −0.999605 | − | 0.0281153i | \(-0.991049\pi\) |
−0.524151 | − | 0.851625i | \(-0.675617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.41745 | + | 58.3049i | 0.395914 | + | 3.11209i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.6825 | + | 23.6988i | −0.728245 | + | 1.26136i | 0.229379 | + | 0.973337i | \(0.426330\pi\) |
−0.957624 | + | 0.288021i | \(0.907003\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.6097 | − | 14.7242i | −1.04078 | − | 0.781481i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.09609 | + | 7.09463i | 0.216788 | + | 0.375488i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.625579i | 0.0330168i | 0.999864 | + | 0.0165084i | \(0.00525502\pi\) | ||||
−0.999864 | + | 0.0165084i | \(0.994745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.74225 | − | 16.8741i | 0.512750 | − | 0.888109i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.27911i | 0.119622i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.27526 | − | 14.7133i | −0.328462 | − | 0.770127i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.44490 | − | 1.98891i | −0.179822 | − | 0.103820i | 0.407387 | − | 0.913256i | \(-0.366440\pi\) |
−0.587209 | + | 0.809435i | \(0.699773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 32.9813i | − | 1.71694i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.07831 | + | 2.35461i | −0.211735 | + | 0.122245i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.4645 | − | 14.1246i | 1.26672 | − | 0.731343i | 0.292357 | − | 0.956309i | \(-0.405560\pi\) |
0.974367 | + | 0.224966i | \(0.0722271\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.4098 | + | 28.6060i | 1.20888 | + | 1.47721i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.51754 | − | 6.00368i | 0.129660 | − | 0.309205i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.1642 | − | 8.17771i | −0.727567 | − | 0.420061i | 0.0899646 | − | 0.995945i | \(-0.471325\pi\) |
−0.817531 | + | 0.575884i | \(0.804658\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.86809 | + | 17.0920i | 0.505557 | + | 0.875651i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.4332 | + | 18.0708i | 0.533111 | + | 0.923376i | 0.999252 | + | 0.0386654i | \(0.0123106\pi\) |
−0.466141 | + | 0.884710i | \(0.654356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.27215 | + | 3.10160i | −0.370623 | + | 0.158072i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.8194 | + | 8.55600i | 0.753314 | + | 0.434926i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.54177 | −0.179575 | −0.0897874 | − | 0.995961i | \(-0.528619\pi\) | ||||
−0.0897874 | + | 0.995961i | \(0.528619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.3837 | −0.879133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 54.5600 | + | 31.5002i | 2.75219 | + | 1.58898i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.2746 | + | 26.4349i | 0.567286 | + | 1.33009i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.8394 | − | 23.9705i | −0.694578 | − | 1.20305i | −0.970323 | − | 0.241814i | \(-0.922258\pi\) |
0.275744 | − | 0.961231i | \(-0.411076\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.6049 | − | 18.3683i | −0.530911 | − | 0.919565i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6799 | + | 6.16604i | 0.533328 | + | 0.307917i | 0.742371 | − | 0.669989i | \(-0.233701\pi\) |
−0.209043 | + | 0.977907i | \(0.567035\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.63939 | − | 20.7469i | −0.131477 | − | 1.03348i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 66.8233 | + | 8.08837i | 3.32047 | + | 0.401914i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.22534 | − | 2.43950i | 0.209442 | − | 0.120922i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.2917 | − | 18.0663i | 1.54728 | − | 0.893321i | 0.548929 | − | 0.835869i | \(-0.315036\pi\) |
0.998348 | − | 0.0574521i | \(-0.0182976\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.53072i | 0.0755049i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.23526 | − | 3.02258i | −0.257610 | − | 0.148731i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.619938 | + | 1.45353i | 0.0304315 | + | 0.0713512i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.8113i | 1.50883i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.26566 | − | 10.8524i | 0.306097 | − | 0.530176i | −0.671408 | − | 0.741088i | \(-0.734310\pi\) |
0.977505 | + | 0.210912i | \(0.0676434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 7.74907i | − | 0.377667i | −0.982009 | − | 0.188833i | \(-0.939529\pi\) | ||
0.982009 | − | 0.188833i | \(-0.0604706\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.9140 | + | 24.0997i | 0.676521 | + | 1.17177i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.85838 | + | 11.6345i | −0.138652 | + | 0.564356i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.96773 | − | 3.40821i | 0.0952252 | − | 0.164935i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.6693 | − | 32.4416i | −1.19104 | − | 1.56629i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.9375 | − | 10.9336i | −0.912188 | − | 0.526652i | −0.0310532 | − | 0.999518i | \(-0.509886\pi\) |
−0.881134 | + | 0.472866i | \(0.843219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.219232 | + | 0.126574i | −0.0105356 | + | 0.00608275i | −0.505259 | − | 0.862968i | \(-0.668603\pi\) |
0.494723 | + | 0.869051i | \(0.335270\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.6742 | − | 8.01489i | −0.511790 | − | 0.384285i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 45.0072 | 2.15299 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.98432 | − | 12.0972i | 0.333344 | − | 0.577368i | −0.649822 | − | 0.760087i | \(-0.725156\pi\) |
0.983165 | + | 0.182719i | \(0.0584897\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 47.0330 | 2.23967 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.5957i | 1.35862i | 0.733851 | + | 0.679310i | \(0.237721\pi\) | ||||
−0.733851 | + | 0.679310i | \(0.762279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.57070 | − | 12.9766i | 0.0744585 | − | 0.615149i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.0582 | −1.70549 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7293 | − | 9.08129i | 0.742309 | − | 0.428572i | −0.0805990 | − | 0.996747i | \(-0.525683\pi\) |
0.822908 | + | 0.568174i | \(0.192350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.10932 | + | 12.3137i | 0.334765 | + | 0.579829i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.03298 | + | 13.9135i | −0.377422 | + | 0.653715i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.12470 | − | 7.24562i | 0.193369 | − | 0.339680i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.53992 | + | 7.86337i | −0.212368 | + | 0.367833i | −0.952455 | − | 0.304678i | \(-0.901451\pi\) |
0.740087 | + | 0.672511i | \(0.234784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.5296 | + | 33.8263i | 0.911564 | + | 1.57888i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.7734 | + | 18.9217i | −1.52641 | + | 0.881273i | −0.526900 | + | 0.849927i | \(0.676646\pi\) |
−0.999509 | + | 0.0313456i | \(0.990021\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5694 | 0.723570 | 0.361785 | − | 0.932262i | \(-0.382167\pi\) | ||||
0.361785 | + | 0.932262i | \(0.382167\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −42.5712 | − | 5.15288i | −1.97419 | − | 0.238959i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.19255i | 0.194008i | 0.995284 | + | 0.0970040i | \(0.0309260\pi\) | ||||
−0.995284 | + | 0.0970040i | \(0.969074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.87636 | −0.363697 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.5599 | − | 25.2186i | 0.670887 | − | 1.16201i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.37719 | −0.339204 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.40048 | − | 30.1222i | 0.339557 | − | 1.38210i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.2760 | + | 18.0572i | −1.43203 | + | 0.826783i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.7058 | − | 6.18102i | −0.489162 | − | 0.282418i | 0.235064 | − | 0.971980i | \(-0.424470\pi\) |
−0.724227 | + | 0.689562i | \(0.757803\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.98972 | + | 4.74497i | −0.0907234 | + | 0.216352i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.4024 | − | 21.4815i | 0.564327 | − | 0.977443i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.4766 | − | 28.6024i | 0.975200 | − | 1.29877i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.695283 | + | 1.20427i | 0.0315063 | + | 0.0545705i | 0.881349 | − | 0.472467i | \(-0.156636\pi\) |
−0.849842 | + | 0.527037i | \(0.823303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 61.5601i | 2.78384i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.90025 | + | 5.02338i | −0.130886 | + | 0.226702i | −0.924019 | − | 0.382348i | \(-0.875116\pi\) |
0.793132 | + | 0.609050i | \(0.208449\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.32637i | − | 0.194850i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −55.7692 | + | 23.7857i | −2.50664 | + | 1.06909i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.82157 | + | 5.67049i | 0.440558 | + | 0.254356i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 27.8242i | − | 1.24558i | −0.782388 | − | 0.622792i | \(-0.785998\pi\) | ||
0.782388 | − | 0.622792i | \(-0.214002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.1642 | − | 23.7662i | 1.83908 | − | 1.06179i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.71140 | − | 5.02953i | 0.388422 | − | 0.224256i | −0.293054 | − | 0.956096i | \(-0.594672\pi\) |
0.681476 | + | 0.731840i | \(0.261338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2998 | − | 1.60982i | −0.591832 | − | 0.0716360i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 41.4168 | + | 11.4857i | 1.83938 | + | 0.510097i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.00505 | + | 1.15762i | 0.0888724 | + | 0.0513105i | 0.543778 | − | 0.839229i | \(-0.316994\pi\) |
−0.454905 | + | 0.890540i | \(0.650327\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.69878 | + | 6.40648i | 0.163625 | + | 0.283406i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −50.5630 | − | 87.5777i | −2.23241 | − | 3.86665i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.0844 | − | 10.2721i | 1.06128 | − | 0.452642i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3897 | − | 5.99849i | −0.456938 | − | 0.263813i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −72.5141 | −3.18301 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.78299 | −0.121925 | −0.0609626 | − | 0.998140i | \(-0.519417\pi\) | ||||
−0.0609626 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.6078 | − | 13.6300i | −1.03230 | − | 0.595997i | −0.114655 | − | 0.993405i | \(-0.536576\pi\) |
−0.917642 | + | 0.397408i | \(0.869910\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.3377 | − | 11.8328i | −0.538463 | − | 0.516424i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.94931 | − | 12.0366i | −0.302717 | − | 0.524321i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.8177 | + | 25.6650i | 0.644248 | + | 1.11587i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −40.1485 | − | 23.1798i | −1.74230 | − | 1.00592i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.8280 | − | 5.79854i | −0.598958 | − | 0.251162i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.64410 | + | 30.1063i | −0.157548 | + | 1.30161i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.9899 | + | 16.7373i | −1.25101 | + | 0.722269i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.5599 | + | 10.1382i | −0.756361 | + | 0.436685i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5466i | 0.969353i | 0.874693 | + | 0.484677i | \(0.161063\pi\) | ||||
−0.874693 | + | 0.484677i | \(0.838937\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.780447 | + | 0.450591i | 0.0334922 | + | 0.0193367i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.86992 | − | 1.22403i | 0.122934 | − | 0.0524317i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.51141i | 0.0646233i | 0.999478 | + | 0.0323117i | \(0.0102869\pi\) | ||||
−0.999478 | + | 0.0323117i | \(0.989713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.0903 | − | 26.1371i | 0.644038 | − | 1.11551i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.2011i | 0.477185i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.64551 | − | 11.5104i | −0.282596 | − | 0.489470i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.43631 | + | 6.33452i | 0.358101 | + | 0.268886i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.5294 | + | 30.3618i | −0.742745 | + | 1.28647i | 0.208496 | + | 0.978023i | \(0.433143\pi\) |
−0.951241 | + | 0.308449i | \(0.900190\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.19271 | − | 4.70907i | 0.261924 | − | 0.199172i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.4559 | − | 13.5422i | −0.990307 | − | 0.571754i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4393 | + | 10.6460i | −0.777125 | + | 0.448674i | −0.835411 | − | 0.549626i | \(-0.814770\pi\) |
0.0582852 | + | 0.998300i | \(0.481437\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.53903 | − | 5.66079i | −0.317169 | − | 0.238151i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −31.1297 | −1.30732 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.488701 | − | 0.846455i | 0.0204874 | − | 0.0354853i | −0.855600 | − | 0.517638i | \(-0.826812\pi\) |
0.876087 | + | 0.482152i | \(0.160145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.5468 | −1.02725 | −0.513625 | − | 0.858015i | \(-0.671698\pi\) | ||||
−0.513625 | + | 0.858015i | \(0.671698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.9036i | 2.04298i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.8353 | − | 10.1185i | 1.45273 | − | 0.421971i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.8270 | −0.991932 | −0.495966 | − | 0.868342i | \(-0.665186\pi\) | ||||
−0.495966 | + | 0.868342i | \(0.665186\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.0546 | − | 11.5785i | 0.833439 | − | 0.481186i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.365406 | − | 0.632901i | −0.0151596 | − | 0.0262572i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.78468 | − | 13.4835i | 0.322409 | − | 0.558428i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.6318 | − | 55.5657i | 1.30781 | − | 2.29736i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.63094 | + | 13.2172i | −0.314963 | + | 0.545532i | −0.979430 | − | 0.201786i | \(-0.935325\pi\) |
0.664467 | + | 0.747318i | \(0.268659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.9921 | + | 31.1632i | 0.741350 | + | 1.28406i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.5809 | + | 15.9238i | −1.13452 | + | 0.655018i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.9654 | −1.47692 | −0.738461 | − | 0.674296i | \(-0.764447\pi\) | ||||
−0.738461 | + | 0.674296i | \(0.764447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.665790 | − | 5.50052i | 0.0272947 | − | 0.225500i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.9661i | 0.530668i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.60243 | 0.269768 | 0.134884 | − | 0.990861i | \(-0.456934\pi\) | ||||
0.134884 | + | 0.990861i | \(0.456934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9409 | + | 25.8783i | −0.609451 | + | 1.05560i | 0.381881 | + | 0.924212i | \(0.375277\pi\) |
−0.991331 | + | 0.131388i | \(0.958057\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −60.4028 | −2.45979 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.925548 | − | 1.23264i | 0.0376289 | − | 0.0501141i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2089 | − | 12.2450i | 0.860843 | − | 0.497008i | −0.00345162 | − | 0.999994i | \(-0.501099\pi\) |
0.864294 | + | 0.502986i | \(0.167765\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.34620 | + | 3.08663i | 0.216639 | + | 0.125077i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.5505 | − | 1.59666i | 0.507740 | − | 0.0645938i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.3530 | − | 28.3242i | 0.660490 | − | 1.14400i | −0.319997 | − | 0.947419i | \(-0.603682\pi\) |
0.980487 | − | 0.196584i | \(-0.0629848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.4604 | + | 24.5855i | −0.744394 | + | 0.991383i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.18390 | − | 12.4429i | −0.289213 | − | 0.500932i | 0.684409 | − | 0.729098i | \(-0.260060\pi\) |
−0.973622 | + | 0.228167i | \(0.926727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 11.1681i | − | 0.448883i | −0.974488 | − | 0.224442i | \(-0.927944\pi\) | ||
0.974488 | − | 0.224442i | \(-0.0720558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 59.1329 | − | 102.421i | 2.37292 | − | 4.11002i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.04516i | 0.242194i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.04414 | − | 24.9782i | −0.0417655 | − | 0.999127i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 60.7282 | + | 35.0614i | 2.42525 | + | 1.40022i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.41932i | 0.136337i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.0259 | − | 20.7996i | 1.43417 | − | 0.828018i | 0.436734 | − | 0.899591i | \(-0.356135\pi\) |
0.997435 | + | 0.0715729i | \(0.0228019\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 41.7701 | − | 24.1160i | 1.66021 | − | 0.958524i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.60399 | − | 13.2516i | 0.0636524 | − | 0.525873i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.26901 | − | 19.7195i | 0.327630 | − | 0.781313i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 75.3203 | + | 43.4862i | 2.97963 | + | 1.72029i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.68565 | + | 4.65169i | 0.106077 | + | 0.183731i | 0.914178 | − | 0.405314i | \(-0.132838\pi\) |
−0.808101 | + | 0.589044i | \(0.799504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.77839 | + | 15.2046i | 0.346186 | + | 0.599612i | 0.985568 | − | 0.169277i | \(-0.0541433\pi\) |
−0.639383 | + | 0.768889i | \(0.720810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.25798 | − | 14.6727i | −0.246408 | − | 0.577738i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.6893 | − | 18.8732i | −1.28515 | − | 0.741982i | −0.307365 | − | 0.951592i | \(-0.599447\pi\) |
−0.977785 | + | 0.209610i | \(0.932781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.9862 | 0.784525 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.8319 | 0.777272 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.0118 | − | 6.35766i | −0.430925 | − | 0.248794i | 0.268816 | − | 0.963192i | \(-0.413368\pi\) |
−0.699741 | + | 0.714397i | \(0.746701\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.7162 | − | 39.1936i | −0.653157 | − | 1.53142i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.3655 | + | 49.1305i | 1.10664 | + | 1.91676i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.0625 | + | 19.1608i | 0.430934 | + | 0.746399i | 0.996954 | − | 0.0779923i | \(-0.0248510\pi\) |
−0.566020 | + | 0.824391i | \(0.691518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.612035 | + | 0.353359i | 0.0238054 | + | 0.0137441i | 0.511855 | − | 0.859072i | \(-0.328958\pi\) |
−0.488050 | + | 0.872816i | \(0.662292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.3342 | − | 3.60463i | 1.10041 | − | 0.139992i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.72376 | + | 14.2411i | −0.0668445 | + | 0.552246i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.3446 | + | 6.54981i | −0.439265 | + | 0.253610i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.59903 | + | 4.96466i | −0.332458 | + | 0.191945i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.0112i | 0.502292i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3244 | + | 13.4663i | 0.899090 | + | 0.519090i | 0.876905 | − | 0.480664i | \(-0.159604\pi\) |
0.0221849 | + | 0.999754i | \(0.492938\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −58.8247 | − | 56.4171i | −2.26416 | − | 2.17150i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.5208i | 0.827111i | 0.910479 | + | 0.413556i | \(0.135713\pi\) | ||||
−0.910479 | + | 0.413556i | \(0.864287\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.27088 | + | 14.3256i | −0.317407 | + | 0.549766i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.6196i | 1.47991i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.2786 | + | 17.8031i | 0.393300 | + | 0.681215i | 0.992883 | − | 0.119098i | \(-0.0380001\pi\) |
−0.599583 | + | 0.800313i | \(0.704667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.621628 | − | 0.827884i | 0.0237512 | − | 0.0316318i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.6302 | + | 53.0531i | −1.16862 | + | 2.02410i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.07210 | + | 16.2877i | 0.0789407 | + | 0.620514i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.2344 | + | 9.95031i | 0.655629 | + | 0.378528i | 0.790610 | − | 0.612321i | \(-0.209764\pi\) |
−0.134980 | + | 0.990848i | \(0.543097\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.2831 | − | 14.0199i | 0.922440 | − | 0.532571i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.5125 | − | 16.6641i | 0.474626 | − | 0.632106i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.96475 | −0.377442 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.4730 | + | 31.9962i | −0.698714 | + | 1.21021i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.37131 | 0.0895631 | 0.0447816 | − | 0.998997i | \(-0.485741\pi\) | ||||
0.0447816 | + | 0.998997i | \(0.485741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.85276i | − | 0.333888i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.11715 | − | 25.7528i | 0.117399 | − | 0.969907i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.19571 | 0.233014 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.916777 | + | 0.529301i | −0.0344303 | + | 0.0198783i | −0.517116 | − | 0.855915i | \(-0.672995\pi\) |
0.482686 | + | 0.875793i | \(0.339661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −50.9636 | − | 88.2715i | −1.91128 | − | 3.31044i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.0415 | + | 36.4450i | −0.788011 | + | 1.36487i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.167682 | + | 27.5641i | 0.00627095 | + | 1.03084i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.57902 | − | 6.19905i | 0.133661 | − | 0.231508i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.60426 | − | 9.70687i | −0.209004 | − | 0.362005i | 0.742397 | − | 0.669960i | \(-0.233689\pi\) |
−0.951401 | + | 0.307955i | \(0.900355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4869 | + | 6.05460i | −0.390551 | + | 0.225485i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 63.8754 | 2.37555 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.51824 | + | 8.66963i | 0.0935252 | + | 0.321982i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.9060i | 1.44294i | 0.692443 | + | 0.721472i | \(0.256534\pi\) | ||||
−0.692443 | + | 0.721472i | \(0.743466\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −77.0471 | −2.85360 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.58505 | − | 4.47745i | 0.0956117 | − | 0.165604i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.7392 | 0.913765 | 0.456882 | − | 0.889527i | \(-0.348966\pi\) | ||||
0.456882 | + | 0.889527i | \(0.348966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35.0602 | − | 26.3254i | −1.29321 | − | 0.971028i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.5516 | − | 13.0202i | 0.830700 | − | 0.479605i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.302370 | + | 0.174574i | 0.0111229 | + | 0.00642179i | 0.505551 | − | 0.862797i | \(-0.331289\pi\) |
−0.494428 | + | 0.869218i | \(0.664623\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −73.3584 | + | 9.33253i | −2.69489 | + | 0.342839i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.85776 | − | 6.68184i | 0.141528 | − | 0.245133i | −0.786544 | − | 0.617534i | \(-0.788132\pi\) |
0.928072 | + | 0.372401i | \(0.121465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.5019 | + | 14.6433i | 0.714495 | + | 0.536489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.80225 | − | 4.85364i | −0.102529 | − | 0.177585i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 14.0250i | − | 0.512463i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.71161 | − | 2.96460i | 0.0624575 | − | 0.108180i | −0.833106 | − | 0.553114i | \(-0.813440\pi\) |
0.895563 | + | 0.444934i | \(0.146773\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 25.6348i | − | 0.934183i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.99491 | − | 4.26286i | 0.363752 | − | 0.155142i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.76835 | − | 5.63976i | −0.355037 | − | 0.204981i | 0.311865 | − | 0.950127i | \(-0.399046\pi\) |
−0.666901 | + | 0.745146i | \(0.732380\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 82.0079i | 2.97670i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.1329 | + | 19.1293i | −1.20107 | + | 0.693435i | −0.960792 | − | 0.277270i | \(-0.910570\pi\) |
−0.240273 | + | 0.970705i | \(0.577237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.24963 | + | 0.721472i | −0.0452395 | + | 0.0261190i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.10586 | − | 42.1828i | 0.184603 | − | 1.52512i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.7772 | + | 12.7577i | −0.605789 | + | 0.460655i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.7503 | + | 19.4857i | 1.21707 | + | 0.702674i | 0.964289 | − | 0.264851i | \(-0.0853228\pi\) |
0.252777 | + | 0.967525i | \(0.418656\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.4368 | + | 50.9860i | 1.06014 | + | 1.83622i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.4410 | + | 25.0126i | 0.519407 | + | 0.899640i | 0.999746 | + | 0.0225567i | \(0.00718064\pi\) |
−0.480338 | + | 0.877083i | \(0.659486\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.9319 | + | 20.0752i | 0.751895 | + | 0.721121i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.22534 | − | 2.43950i | −0.151583 | − | 0.0875167i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.7991 | 0.924350 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.4949 | −1.34167 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.4900 | + | 14.7167i | 0.910939 | + | 0.525931i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.1160 | + | 7.72653i | −0.646587 | + | 0.275772i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.52068 | + | 2.63389i | 0.0542062 | + | 0.0938879i | 0.891855 | − | 0.452321i | \(-0.149404\pi\) |
−0.837649 | + | 0.546209i | \(0.816070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.4514 | − | 47.5473i | −0.977297 | − | 1.69273i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.77594 | + | 2.18004i | 0.134257 | + | 0.0775132i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.30542 | − | 10.9221i | −0.294934 | − | 0.387856i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.4213 | + | 4.04536i | 1.18533 | + | 0.143474i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.6254 | − | 21.1457i | 1.29734 | − | 0.749018i | 0.317394 | − | 0.948294i | \(-0.397192\pi\) |
0.979944 | + | 0.199275i | \(0.0638589\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.28133 | − | 4.20388i | 0.257595 | − | 0.148723i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 46.3595i | 1.63803i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.1807 | − | 12.2287i | −0.747452 | − | 0.431542i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.4314 | + | 6.58156i | −0.543887 | + | 0.231970i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 19.6363i | − | 0.691230i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.6250 | − | 30.5274i | 0.619662 | − | 1.07329i | −0.369886 | − | 0.929077i | \(-0.620603\pi\) |
0.989547 | − | 0.144208i | \(-0.0460635\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.1607i | − | 1.05908i | −0.848284 | − | 0.529542i | \(-0.822364\pi\) | ||
0.848284 | − | 0.529542i | \(-0.177636\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.9814 | − | 27.6806i | −0.560492 | − | 0.970800i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.9997 | − | 33.2945i | 0.875700 | − | 1.16626i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.69281 | + | 11.5923i | −0.234152 | + | 0.405563i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.4350 | + | 27.2694i | −0.399570 | + | 0.952872i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.92434 | + | 2.26572i | 0.136960 | + | 0.0790741i | 0.566915 | − | 0.823777i | \(-0.308137\pi\) |
−0.429954 | + | 0.902851i | \(0.641470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.2729 | + | 9.97249i | −0.602094 | + | 0.347619i | −0.769865 | − | 0.638207i | \(-0.779676\pi\) |
0.167771 | + | 0.985826i | \(0.446343\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 54.8858 | + | 13.4845i | 1.91088 | + | 0.469469i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.3377 | 0.429025 | 0.214512 | − | 0.976721i | \(-0.431184\pi\) | ||||
0.214512 | + | 0.976721i | \(0.431184\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.7968 | − | 32.5570i | 0.652840 | − | 1.13075i | −0.329591 | − | 0.944124i | \(-0.606911\pi\) |
0.982431 | − | 0.186628i | \(-0.0597559\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 68.4966 | 2.37612 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 14.2102i | − | 0.492355i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.9150 | − | 3.86303i | −1.10446 | − | 0.133686i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 94.5557 | 3.26832 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.7606 | + | 11.9861i | −0.716736 | + | 0.413808i | −0.813550 | − | 0.581495i | \(-0.802468\pi\) |
0.0968144 | + | 0.995302i | \(0.469135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8699 | + | 22.2914i | 0.443790 | + | 0.768667i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 45.9058 | − | 79.5111i | 1.58108 | − | 2.73851i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.7357 | − | 23.0314i | −0.610127 | − | 0.792304i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.356440 | + | 0.617372i | −0.0122474 | + | 0.0212132i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −42.2804 | − | 73.2319i | −1.45106 | − | 2.51331i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.96614 | − | 5.17660i | 0.307355 | − | 0.177452i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.8952 | −1.33175 | −0.665873 | − | 0.746065i | \(-0.731941\pi\) | ||||
−0.665873 | + | 0.746065i | \(0.731941\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.2193 | + | 109.213i | −0.452090 | + | 3.73501i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.4570i | 1.51862i | 0.650727 | + | 0.759312i | \(0.274464\pi\) | ||||
−0.650727 | + | 0.759312i | \(0.725536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.8129 | −1.59724 | −0.798618 | − | 0.601838i | \(-0.794435\pi\) | ||||
−0.798618 | + | 0.601838i | \(0.794435\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.10932 | − | 12.3137i | 0.242285 | − | 0.419650i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.9384 | −0.985073 | −0.492537 | − | 0.870292i | \(-0.663930\pi\) | ||||
−0.492537 | + | 0.870292i | \(0.663930\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.2189 | + | 29.4481i | 1.33348 | + | 1.00126i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32.2361 | + | 18.6115i | −1.09479 | + | 0.632079i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.0549 | + | 21.9710i | 1.29092 | + | 0.745315i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.6196 | + | 25.3250i | −0.359831 | + | 0.858105i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −63.4283 | + | 109.861i | −2.14672 | + | 3.71824i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.86750 | + | 11.4101i | 0.0631331 | + | 0.385731i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.912276 | − | 1.58011i | −0.0308054 | − | 0.0533565i | 0.850212 | − | 0.526441i | \(-0.176474\pi\) |
−0.881017 | + | 0.473084i | \(0.843141\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 93.8858i | − | 3.16669i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.47740 | + | 9.48714i | −0.184538 | + | 0.319630i | −0.943421 | − | 0.331598i | \(-0.892412\pi\) |
0.758882 | + | 0.651228i | \(0.225746\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.8747i | − | 0.534227i | −0.963665 | − | 0.267113i | \(-0.913930\pi\) | ||
0.963665 | − | 0.267113i | \(-0.0860698\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.9540 | + | 39.7511i | 0.569902 | + | 1.33622i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.15751 | + | 2.97769i | 0.173172 | + | 0.0999811i | 0.584081 | − | 0.811695i | \(-0.301455\pi\) |
−0.410908 | + | 0.911677i | \(0.634788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.17327i | 0.207045i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 89.1306 | − | 51.4596i | 2.98599 | − | 1.72396i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.8517 | + | 10.8840i | −0.630847 | + | 0.364220i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.4761 | + | 2.72054i | 0.751294 | + | 0.0909375i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −52.3480 | − | 68.8408i | −1.74785 | − | 2.29853i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.07023 | − | 5.23670i | −0.302509 | − | 0.174654i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.45569 | + | 9.44953i | 0.181755 | + | 0.314809i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.68860 | + | 6.38884i | 0.122749 | + | 0.212607i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.239115 | − | 0.560641i | −0.00794847 | − | 0.0186363i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.0723 | + | 19.0943i | 1.09815 | + | 0.634015i | 0.935734 | − | 0.352707i | \(-0.114739\pi\) |
0.162413 | + | 0.986723i | \(0.448072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 47.5141 | 1.57594 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.7516 | 1.11824 | 0.559121 | − | 0.829086i | \(-0.311139\pi\) | ||||
0.559121 | + | 0.829086i | \(0.311139\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.09246 | + | 1.20808i | 0.0692504 | + | 0.0399817i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25.8784 | + | 11.0372i | −0.855514 | + | 0.364880i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.85294 | + | 17.0658i | 0.325373 | + | 0.563562i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.5062 | − | 18.1973i | −0.346568 | − | 0.600273i | 0.639070 | − | 0.769149i | \(-0.279320\pi\) |
−0.985637 | + | 0.168876i | \(0.945986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.0755 | − | 19.0961i | −1.08987 | − | 0.629239i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.4747 | − | 23.9340i | 1.03600 | − | 0.787798i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.99028 | − | 6.85199i | −0.0654400 | − | 0.225292i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −80.4225 | + | 46.4319i | −2.64142 | + | 1.52502i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.3099 | + | 19.2315i | −1.09286 | + | 0.630965i | −0.934337 | − | 0.356390i | \(-0.884008\pi\) |
−0.158526 | + | 0.987355i | \(0.550674\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.7909i | 1.20577i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.97220 | − | 1.71600i | −0.0973054 | − | 0.0561793i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.18647 | + | 16.8497i | 0.235023 | + | 0.551045i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 45.7434i | − | 1.49437i | −0.664615 | − | 0.747186i | \(-0.731404\pi\) | ||
0.664615 | − | 0.747186i | \(-0.268596\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.9870 | − | 84.8479i | 1.59863 | − | 2.76891i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 58.6037i | 1.91043i | 0.295917 | + | 0.955214i | \(0.404375\pi\) | ||||
−0.295917 | + | 0.955214i | \(0.595625\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.0859 | + | 26.1296i | 0.491265 | + | 0.850896i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30.1431 | + | 22.6334i | 0.980556 | + | 0.736265i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.3516 | − | 35.2500i | 0.661338 | − | 1.14547i | −0.318926 | − | 0.947780i | \(-0.603322\pi\) |
0.980264 | − | 0.197692i | \(-0.0633446\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.5859 | − | 3.25499i | 0.830554 | − | 0.105662i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −58.5367 | − | 33.7962i | −1.89818 | − | 1.09592i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.60814 | + | 1.50581i | −0.0844859 | + | 0.0487779i | −0.541648 | − | 0.840606i | \(-0.682199\pi\) |
0.457162 | + | 0.889384i | \(0.348866\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.8598 | − | 26.4493i | 0.642649 | − | 0.855879i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.4097 | −0.659752 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.239397 | + | 0.414647i | −0.00773052 | + | 0.0133897i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.64620 | −0.0853612 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 107.556i | − | 3.46595i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.5485 | − | 1.88201i | −0.500523 | − | 0.0605839i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.8156 | 1.21607 | 0.608033 | − | 0.793912i | \(-0.291959\pi\) | ||||
0.608033 | + | 0.793912i | \(0.291959\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −42.5597 | + | 24.5719i | −1.36722 | + | 0.789362i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.8681 | − | 22.2882i | −0.412957 | − | 0.715262i | 0.582255 | − | 0.813006i | \(-0.302171\pi\) |
−0.995212 | + | 0.0977445i | \(0.968837\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.81872 | + | 8.34626i | −0.154481 | + | 0.267569i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −54.6809 | + | 23.7158i | −1.75119 | + | 0.759513i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0613 | − | 20.8908i | 0.385875 | − | 0.668355i | −0.606015 | − | 0.795453i | \(-0.707233\pi\) |
0.991890 | + | 0.127098i | \(0.0405663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.99308 | − | 17.3085i | −0.319380 | − | 0.553183i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.58322 | + | 5.53288i | −0.305969 | + | 0.176651i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.5964 | −0.720715 | −0.360357 | − | 0.932814i | \(-0.617345\pi\) | ||||
−0.360357 | + | 0.932814i | \(0.617345\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.3837 | + | 2.58831i | 0.681340 | + | 0.0824703i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.9970i | 0.381868i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.6543 | −0.497779 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.57562 | + | 13.1214i | −0.240648 | + | 0.416814i | −0.960899 | − | 0.276899i | \(-0.910693\pi\) |
0.720251 | + | 0.693713i | \(0.244026\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.7817 | 0.532552 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.26556 | − | 7.01267i | 0.166930 | − | 0.222317i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.3633 | + | 26.7679i | −1.46834 | + | 0.847747i | −0.999371 | − | 0.0354673i | \(-0.988708\pi\) |
−0.468970 | + | 0.883214i | \(0.655375\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.1459 | − | 11.6312i | −0.637388 | − | 0.367996i |
(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 | 260.2.z.a.69.8 | yes | 16 | |
3.2 | odd | 2 | 2340.2.cr.a.1369.6 | 16 | |||
4.3 | odd | 2 | 1040.2.df.d.849.1 | 16 | |||
5.2 | odd | 4 | 1300.2.y.e.901.8 | 16 | |||
5.3 | odd | 4 | 1300.2.y.e.901.1 | 16 | |||
5.4 | even | 2 | inner | 260.2.z.a.69.1 | yes | 16 | |
13.4 | even | 6 | 3380.2.d.d.1689.2 | 16 | |||
13.6 | odd | 12 | 3380.2.c.e.2029.1 | 16 | |||
13.7 | odd | 12 | 3380.2.c.e.2029.2 | 16 | |||
13.9 | even | 3 | 3380.2.d.d.1689.1 | 16 | |||
13.10 | even | 6 | inner | 260.2.z.a.49.1 | ✓ | 16 | |
15.14 | odd | 2 | 2340.2.cr.a.1369.3 | 16 | |||
20.19 | odd | 2 | 1040.2.df.d.849.8 | 16 | |||
39.23 | odd | 6 | 2340.2.cr.a.829.3 | 16 | |||
52.23 | odd | 6 | 1040.2.df.d.49.8 | 16 | |||
65.4 | even | 6 | 3380.2.d.d.1689.15 | 16 | |||
65.9 | even | 6 | 3380.2.d.d.1689.16 | 16 | |||
65.19 | odd | 12 | 3380.2.c.e.2029.15 | 16 | |||
65.23 | odd | 12 | 1300.2.y.e.101.1 | 16 | |||
65.49 | even | 6 | inner | 260.2.z.a.49.8 | yes | 16 | |
65.59 | odd | 12 | 3380.2.c.e.2029.16 | 16 | |||
65.62 | odd | 12 | 1300.2.y.e.101.8 | 16 | |||
195.179 | odd | 6 | 2340.2.cr.a.829.6 | 16 | |||
260.179 | odd | 6 | 1040.2.df.d.49.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.z.a.49.1 | ✓ | 16 | 13.10 | even | 6 | inner | |
260.2.z.a.49.8 | yes | 16 | 65.49 | even | 6 | inner | |
260.2.z.a.69.1 | yes | 16 | 5.4 | even | 2 | inner | |
260.2.z.a.69.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1040.2.df.d.49.1 | 16 | 260.179 | odd | 6 | |||
1040.2.df.d.49.8 | 16 | 52.23 | odd | 6 | |||
1040.2.df.d.849.1 | 16 | 4.3 | odd | 2 | |||
1040.2.df.d.849.8 | 16 | 20.19 | odd | 2 | |||
1300.2.y.e.101.1 | 16 | 65.23 | odd | 12 | |||
1300.2.y.e.101.8 | 16 | 65.62 | odd | 12 | |||
1300.2.y.e.901.1 | 16 | 5.3 | odd | 4 | |||
1300.2.y.e.901.8 | 16 | 5.2 | odd | 4 | |||
2340.2.cr.a.829.3 | 16 | 39.23 | odd | 6 | |||
2340.2.cr.a.829.6 | 16 | 195.179 | odd | 6 | |||
2340.2.cr.a.1369.3 | 16 | 15.14 | odd | 2 | |||
2340.2.cr.a.1369.6 | 16 | 3.2 | odd | 2 | |||
3380.2.c.e.2029.1 | 16 | 13.6 | odd | 12 | |||
3380.2.c.e.2029.2 | 16 | 13.7 | odd | 12 | |||
3380.2.c.e.2029.15 | 16 | 65.19 | odd | 12 | |||
3380.2.c.e.2029.16 | 16 | 65.59 | odd | 12 | |||
3380.2.d.d.1689.1 | 16 | 13.9 | even | 3 | |||
3380.2.d.d.1689.2 | 16 | 13.4 | even | 6 | |||
3380.2.d.d.1689.15 | 16 | 65.4 | even | 6 | |||
3380.2.d.d.1689.16 | 16 | 65.9 | even | 6 |