Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(249,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (of order \(6\), degree \(2\), not 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: | \(11.1790562830\) |
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: | \( x^{16} - 15x^{14} + 170x^{12} - 789x^{10} + 2754x^{8} - 960x^{6} + 269x^{4} - 18x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 849.5 | ||
Root | \(-0.462601 + 0.267083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.849 |
Dual form | 1400.2.bh.j.249.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.403424 | − | 0.232917i | 0.232917 | − | 0.134475i | −0.379000 | − | 0.925397i | \(-0.623732\pi\) |
0.611917 | + | 0.790922i | \(0.290399\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.02469 | − | 1.70312i | 0.765261 | − | 0.643720i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.39150 | + | 2.41015i | −0.463833 | + | 0.803382i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.688377 | − | 1.19230i | −0.207554 | − | 0.359493i | 0.743390 | − | 0.668858i | \(-0.233217\pi\) |
−0.950943 | + | 0.309365i | \(0.899883\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.12091i | 1.42029i | 0.704058 | + | 0.710143i | \(0.251370\pi\) | ||||
−0.704058 | + | 0.710143i | \(0.748630\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.292641 | + | 0.168956i | −0.0709758 | + | 0.0409779i | −0.535068 | − | 0.844809i | \(-0.679714\pi\) |
0.464092 | + | 0.885787i | \(0.346381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.99649 | − | 5.19008i | 0.687443 | − | 1.19069i | −0.285219 | − | 0.958462i | \(-0.592066\pi\) |
0.972662 | − | 0.232224i | \(-0.0746002\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.420123 | − | 1.15867i | 0.0916785 | − | 0.252842i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.67065 | + | 3.27395i | 1.18241 | + | 0.682666i | 0.956571 | − | 0.291498i | \(-0.0941537\pi\) |
0.225841 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.69392i | 0.518445i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.99299 | 1.48426 | 0.742130 | − | 0.670256i | \(-0.233816\pi\) | ||||
0.742130 | + | 0.670256i | \(0.233816\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.62442 | + | 6.27767i | 0.650964 | + | 1.12750i | 0.982889 | + | 0.184198i | \(0.0589686\pi\) |
−0.331925 | + | 0.943306i | \(0.607698\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.555416 | − | 0.320670i | −0.0966856 | − | 0.0558214i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.24169 | − | 3.02629i | −0.861728 | − | 0.497519i | 0.00286250 | − | 0.999996i | \(-0.499089\pi\) |
−0.864591 | + | 0.502477i | \(0.832422\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.19275 | + | 2.06590i | 0.190993 | + | 0.330809i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.68457 | 1.04395 | 0.521977 | − | 0.852960i | \(-0.325195\pi\) | ||||
0.521977 | + | 0.852960i | \(0.325195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.02949i | 0.766990i | 0.923543 | + | 0.383495i | \(0.125280\pi\) | ||||
−0.923543 | + | 0.383495i | \(0.874720\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.75590 | − | 3.32317i | −0.839584 | − | 0.484734i | 0.0175390 | − | 0.999846i | \(-0.494417\pi\) |
−0.857123 | + | 0.515112i | \(0.827750\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.19875 | − | 6.89659i | 0.171250 | − | 0.985228i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0787056 | + | 0.136322i | −0.0110210 | + | 0.0190889i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.21934 | + | 2.43604i | −0.579571 | + | 0.334616i | −0.760963 | − | 0.648795i | \(-0.775273\pi\) |
0.181392 | + | 0.983411i | \(0.441940\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.79174i | − | 0.369775i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.301249 | + | 0.521778i | 0.0392192 | + | 0.0679297i | 0.884969 | − | 0.465650i | \(-0.154180\pi\) |
−0.845749 | + | 0.533580i | \(0.820846\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.54103 | − | 11.3294i | 0.837494 | − | 1.45058i | −0.0544903 | − | 0.998514i | \(-0.517353\pi\) |
0.891984 | − | 0.452067i | \(-0.149313\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.28742 | + | 7.24970i | 0.162199 | + | 0.913376i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4834 | − | 6.05258i | 1.28075 | − | 0.739440i | 0.303763 | − | 0.952748i | \(-0.401757\pi\) |
0.976985 | + | 0.213307i | \(0.0684236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.05024 | 0.367205 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.39251 | −0.165260 | −0.0826301 | − | 0.996580i | \(-0.526332\pi\) | ||||
−0.0826301 | + | 0.996580i | \(0.526332\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.45941 | − | 0.842589i | 0.170811 | − | 0.0986176i | −0.412157 | − | 0.911113i | \(-0.635225\pi\) |
0.582968 | + | 0.812495i | \(0.301891\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.42439 | − | 1.24166i | −0.390246 | − | 0.141500i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.80812 | − | 6.59585i | 0.428447 | − | 0.742091i | −0.568289 | − | 0.822829i | \(-0.692394\pi\) |
0.996735 | + | 0.0807379i | \(0.0257277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.54704 | − | 6.14365i | −0.394115 | − | 0.682628i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.49532i | 0.822719i | 0.911473 | + | 0.411359i | \(0.134946\pi\) | ||||
−0.911473 | + | 0.411359i | \(0.865054\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.22457 | − | 1.86170i | 0.345710 | − | 0.199596i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.19525 | + | 10.7305i | −0.656695 | + | 1.13743i | 0.324771 | + | 0.945793i | \(0.394713\pi\) |
−0.981466 | + | 0.191636i | \(0.938621\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.72154 | + | 10.3683i | 0.914265 | + | 1.08689i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.92436 | + | 1.68838i | 0.303242 | + | 0.175077i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.691577i | 0.0702190i | 0.999383 | + | 0.0351095i | \(0.0111780\pi\) | ||||
−0.999383 | + | 0.0351095i | \(0.988822\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.83151 | 0.385081 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00687 | − | 3.47600i | −0.199691 | − | 0.345875i | 0.748737 | − | 0.662867i | \(-0.230660\pi\) |
−0.948428 | + | 0.316992i | \(0.897327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.88615 | + | 3.39837i | 0.579979 | + | 0.334851i | 0.761125 | − | 0.648605i | \(-0.224647\pi\) |
−0.181146 | + | 0.983456i | \(0.557981\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.47233 | + | 4.89150i | 0.819051 | + | 0.472879i | 0.850089 | − | 0.526639i | \(-0.176548\pi\) |
−0.0310384 | + | 0.999518i | \(0.509881\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.29087 | + | 3.96791i | 0.219426 | + | 0.380057i | 0.954633 | − | 0.297786i | \(-0.0962482\pi\) |
−0.735207 | + | 0.677843i | \(0.762915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.81950 | −0.267615 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.6688i | 1.66214i | 0.556166 | + | 0.831071i | \(0.312272\pi\) | ||||
−0.556166 | + | 0.831071i | \(0.687728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.3421 | − | 7.12574i | −1.14103 | − | 0.658775i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.304754 | + | 0.840487i | −0.0279368 | + | 0.0770473i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.55227 | − | 7.88477i | 0.413843 | − | 0.716797i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.69672 | − | 1.55695i | 0.243155 | − | 0.140385i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.8513i | 1.31784i | 0.752212 | + | 0.658921i | \(0.228987\pi\) | ||||
−0.752212 | + | 0.658921i | \(0.771013\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.17145 | + | 2.02902i | 0.103141 | + | 0.178645i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.527297 | − | 0.913306i | 0.0460702 | − | 0.0797959i | −0.842071 | − | 0.539367i | \(-0.818664\pi\) |
0.888141 | + | 0.459571i | \(0.151997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.77236 | − | 15.6117i | −0.240394 | − | 1.35371i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0734 | + | 8.12528i | −1.20237 | + | 0.694190i | −0.961082 | − | 0.276263i | \(-0.910904\pi\) |
−0.241290 | + | 0.970453i | \(0.577570\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.32591 | 0.366918 | 0.183459 | − | 0.983027i | \(-0.441270\pi\) | ||||
0.183459 | + | 0.983027i | \(0.441270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.09609 | −0.260738 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.10568 | − | 3.52512i | 0.510583 | − | 0.294785i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.12273 | − | 3.06146i | −0.0926011 | − | 0.252505i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.83908 | − | 6.64949i | 0.314510 | − | 0.544747i | −0.664823 | − | 0.747001i | \(-0.731493\pi\) |
0.979333 | + | 0.202253i | \(0.0648265\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.46934 | − | 2.54497i | −0.119573 | − | 0.207107i | 0.800025 | − | 0.599966i | \(-0.204819\pi\) |
−0.919599 | + | 0.392859i | \(0.871486\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.940410i | − | 0.0760276i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2314 | − | 7.63916i | 1.05598 | − | 0.609671i | 0.131664 | − | 0.991294i | \(-0.457968\pi\) |
0.924318 | + | 0.381623i | \(0.124635\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.13479 | + | 1.96551i | −0.0899947 | + | 0.155875i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.0573 | − | 3.02907i | 1.34430 | − | 0.238724i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.35397 | − | 3.09112i | −0.419355 | − | 0.242115i | 0.275446 | − | 0.961316i | \(-0.411174\pi\) |
−0.694801 | + | 0.719202i | \(0.744508\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.1162i | − | 1.40188i | −0.713222 | − | 0.700938i | \(-0.752765\pi\) | ||
0.713222 | − | 0.700938i | \(-0.247235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.2237 | −1.01721 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.33924 | + | 14.4440i | 0.637718 | + | 1.10456i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.8145 | − | 10.2852i | −1.35441 | − | 0.781969i | −0.365546 | − | 0.930793i | \(-0.619118\pi\) |
−0.988864 | + | 0.148825i | \(0.952451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.243062 | + | 0.140332i | 0.0182697 | + | 0.0105480i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.62559 | − | 8.01175i | −0.345733 | − | 0.598826i | 0.639754 | − | 0.768580i | \(-0.279036\pi\) |
−0.985487 | + | 0.169753i | \(0.945703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2763 | −1.06115 | −0.530575 | − | 0.847638i | \(-0.678024\pi\) | ||||
−0.530575 | + | 0.847638i | \(0.678024\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.09408i | − | 0.450487i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.402894 | + | 0.232611i | 0.0294626 | + | 0.0170102i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.58807 | + | 5.45435i | 0.333733 | + | 0.396746i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.7418 | + | 20.3374i | −0.849608 | + | 1.47156i | 0.0319498 | + | 0.999489i | \(0.489828\pi\) |
−0.881558 | + | 0.472075i | \(0.843505\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1046 | + | 6.98862i | −0.871311 | + | 0.503052i | −0.867784 | − | 0.496942i | \(-0.834456\pi\) |
−0.00352746 | + | 0.999994i | \(0.501123\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.69017i | 0.619149i | 0.950875 | + | 0.309575i | \(0.100187\pi\) | ||||
−0.950875 | + | 0.309575i | \(0.899813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.28433 | − | 7.42067i | −0.303708 | − | 0.526037i | 0.673265 | − | 0.739401i | \(-0.264891\pi\) |
−0.976973 | + | 0.213364i | \(0.931558\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.81950 | − | 4.88352i | 0.198872 | − | 0.344457i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.1833 | − | 13.6130i | 1.13585 | − | 0.955448i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.7814 | + | 9.11140i | −1.09688 | + | 0.633286i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.25087 | −0.570725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.1457 | −1.59342 | −0.796709 | − | 0.604363i | \(-0.793428\pi\) | ||||
−0.796709 | + | 0.604363i | \(0.793428\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.561771 | + | 0.324339i | −0.0384919 | + | 0.0222233i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0300 | + | 6.53753i | 1.22395 | + | 0.443796i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.392507 | − | 0.679842i | 0.0265231 | − | 0.0459394i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.865210 | − | 1.49859i | −0.0582003 | − | 0.100806i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.69158i | − | 0.180241i | −0.995931 | − | 0.0901207i | \(-0.971275\pi\) | ||
0.995931 | − | 0.0901207i | \(-0.0287253\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.54628 | + | 5.51155i | −0.633609 | + | 0.365814i | −0.782148 | − | 0.623092i | \(-0.785876\pi\) |
0.148540 | + | 0.988906i | \(0.452543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.48876 | + | 2.57861i | −0.0983801 | + | 0.170399i | −0.911014 | − | 0.412375i | \(-0.864699\pi\) |
0.812634 | + | 0.582774i | \(0.198033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.67069 | + | 0.296684i | −0.109923 | + | 0.0195204i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.06152 | + | 0.612871i | 0.0695428 | + | 0.0401505i | 0.534368 | − | 0.845252i | \(-0.320550\pi\) |
−0.464825 | + | 0.885402i | \(0.653883\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3.54790i | − | 0.230461i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.2381 | 1.11504 | 0.557519 | − | 0.830164i | \(-0.311753\pi\) | ||||
0.557519 | + | 0.830164i | \(0.311753\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.07200 | − | 3.58881i | −0.133469 | − | 0.231176i | 0.791542 | − | 0.611114i | \(-0.209278\pi\) |
−0.925012 | + | 0.379939i | \(0.875945\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.86093 | − | 5.69321i | −0.632579 | − | 0.365220i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.5779 | + | 15.3448i | 1.69111 | + | 0.976365i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.74579 | + | 3.02380i | 0.110635 | + | 0.191625i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.6481 | −1.17706 | −0.588528 | − | 0.808477i | \(-0.700292\pi\) | ||||
−0.588528 | + | 0.808477i | \(0.700292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.01486i | − | 0.566759i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.19333 | − | 4.73042i | −0.511086 | − | 0.295075i | 0.222194 | − | 0.975002i | \(-0.428678\pi\) |
−0.733280 | + | 0.679927i | \(0.762011\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.7669 | + | 2.79993i | −0.979710 | + | 0.173979i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.1222 | + | 19.2643i | −0.688449 | + | 1.19243i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.37097 | + | 1.36888i | −0.146200 | + | 0.0844087i | −0.571316 | − | 0.820730i | \(-0.693567\pi\) |
0.425116 | + | 0.905139i | \(0.360233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.77192i | 0.353235i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.14003 | − | 15.8310i | −0.557277 | − | 0.965232i | −0.997722 | − | 0.0674530i | \(-0.978513\pi\) |
0.440445 | − | 0.897779i | \(-0.354821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.7087 | − | 27.2082i | 0.954233 | − | 1.65278i | 0.218120 | − | 0.975922i | \(-0.430007\pi\) |
0.736113 | − | 0.676859i | \(-0.236659\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.93343 | + | 2.15141i | 0.359107 | + | 0.130210i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.81483 | − | 5.08924i | 0.529632 | − | 0.305783i | −0.211235 | − | 0.977435i | \(-0.567748\pi\) |
0.740866 | + | 0.671652i | \(0.234415\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.1735 | −1.20776 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.4261 | −1.57645 | −0.788224 | − | 0.615389i | \(-0.788999\pi\) | ||||
−0.788224 | + | 0.615389i | \(0.788999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.78990 | − | 4.49750i | 0.463062 | − | 0.267349i | −0.250269 | − | 0.968176i | \(-0.580519\pi\) |
0.713331 | + | 0.700828i | \(0.247186\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.5342 | − | 11.3846i | 0.798898 | − | 0.672014i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.44291 | + | 14.6235i | −0.496642 | + | 0.860209i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.161080 | + | 0.278999i | 0.00944268 | + | 0.0163552i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 34.1092i | − | 1.99268i | −0.0854640 | − | 0.996341i | \(-0.527237\pi\) | ||
0.0854640 | − | 0.996341i | \(-0.472763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.21197 | − | 1.85443i | 0.186377 | − | 0.107605i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.7656 | + | 29.0389i | −0.969580 | + | 1.67936i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.56583 | + | 10.1832i | 0.493726 | + | 0.586948i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.61924 | − | 0.934868i | −0.0930229 | − | 0.0537068i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5815i | 0.946354i | 0.880967 | + | 0.473177i | \(0.156893\pi\) | ||||
−0.880967 | + | 0.473177i | \(0.843107\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.16615 | 0.180116 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0080 | + | 25.9947i | 0.851028 | + | 1.47402i | 0.880282 | + | 0.474451i | \(0.157354\pi\) |
−0.0292538 | + | 0.999572i | \(0.509313\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.31601 | − | 4.80125i | −0.470048 | − | 0.271383i | 0.246212 | − | 0.969216i | \(-0.420814\pi\) |
−0.716260 | + | 0.697833i | \(0.754148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.4430 | − | 12.3801i | −1.20436 | − | 0.695337i | −0.242837 | − | 0.970067i | \(-0.578078\pi\) |
−0.961521 | + | 0.274730i | \(0.911411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.50219 | − | 9.53008i | −0.308064 | − | 0.533582i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.55726 | 0.254361 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.02511i | 0.112680i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.84839 | + | 1.06717i | 0.102216 | + | 0.0590145i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.3137 | + | 3.07460i | −0.954534 | + | 0.169508i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.98261 | − | 17.2904i | 0.548694 | − | 0.950366i | −0.449670 | − | 0.893195i | \(-0.648458\pi\) |
0.998364 | − | 0.0571715i | \(-0.0182082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.5876 | − | 8.42216i | 0.799396 | − | 0.461531i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.9421i | 1.30421i | 0.758128 | + | 0.652106i | \(0.226114\pi\) | ||||
−0.758128 | + | 0.652106i | \(0.773886\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.11537 | + | 7.12803i | 0.223516 | + | 0.387141i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.98993 | − | 8.64282i | 0.270220 | − | 0.468035i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.31864 | − | 16.0051i | −0.503159 | − | 0.864194i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.73590 | − | 1.57957i | 0.146871 | − | 0.0847958i | −0.424764 | − | 0.905304i | \(-0.639643\pi\) |
0.571634 | + | 0.820508i | \(0.306310\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.6022 | 1.85221 | 0.926107 | − | 0.377261i | \(-0.123134\pi\) | ||||
0.926107 | + | 0.377261i | \(0.123134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.7953 | −0.736340 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.35078 | − | 5.39867i | 0.497692 | − | 0.287342i | −0.230068 | − | 0.973175i | \(-0.573895\pi\) |
0.727760 | + | 0.685832i | \(0.240562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0728186 | + | 0.410055i | 0.00385397 | + | 0.0217024i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.81062 | + | 3.13608i | −0.0955606 | + | 0.165516i | −0.909842 | − | 0.414954i | \(-0.863798\pi\) |
0.814282 | + | 0.580470i | \(0.197131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.45796 | − | 14.6496i | −0.445156 | − | 0.771032i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 4.24121i | − | 0.222606i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.42679 | + | 4.86521i | −0.439875 | + | 0.253962i | −0.703545 | − | 0.710651i | \(-0.748400\pi\) |
0.263670 | + | 0.964613i | \(0.415067\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.30157 | + | 16.1108i | −0.484220 | + | 0.838694i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.39400 | + | 12.1183i | −0.228125 | + | 0.629150i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.68250 | − | 2.70344i | −0.242451 | − | 0.139979i | 0.373852 | − | 0.927488i | \(-0.378037\pi\) |
−0.616303 | + | 0.787509i | \(0.711370\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.9314i | 2.10807i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.67144 | 0.496789 | 0.248394 | − | 0.968659i | \(-0.420097\pi\) | ||||
0.248394 | + | 0.968659i | \(0.420097\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.45913 | + | 5.99139i | 0.177217 | + | 0.306948i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.1001 | − | 16.2236i | −1.43585 | − | 0.828986i | −0.438288 | − | 0.898835i | \(-0.644415\pi\) |
−0.997558 | + | 0.0698489i | \(0.977748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.1218 | − | 6.99853i | −0.616186 | − | 0.355755i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.67216 | + | 4.62831i | 0.135484 | + | 0.234665i | 0.925782 | − | 0.378057i | \(-0.123408\pi\) |
−0.790298 | + | 0.612722i | \(0.790075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.21262 | −0.111897 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.491266i | − | 0.0247811i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.64112 | − | 5.56630i | −0.483874 | − | 0.279365i | 0.238156 | − | 0.971227i | \(-0.423457\pi\) |
−0.722029 | + | 0.691862i | \(0.756791\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.75467 | − | 5.65241i | −0.238031 | − | 0.282975i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0980 | + | 31.3466i | −0.903770 | + | 1.56538i | −0.0812106 | + | 0.996697i | \(0.525879\pi\) |
−0.822560 | + | 0.568679i | \(0.807455\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.1474 | + | 18.5603i | −1.60138 | + | 0.924555i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.33292i | 0.413047i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.2830 | − | 29.9350i | −0.854589 | − | 1.48019i | −0.877026 | − | 0.480444i | \(-0.840476\pi\) |
0.0224363 | − | 0.999748i | \(-0.492858\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.78503 | + | 6.55587i | −0.186702 | + | 0.323377i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.49859 | + | 0.543376i | 0.0737406 | + | 0.0267378i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.74518 | − | 1.00758i | 0.0854616 | − | 0.0493413i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.60984 | 0.127499 | 0.0637494 | − | 0.997966i | \(-0.479694\pi\) | ||||
0.0637494 | + | 0.997966i | \(0.479694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.9541 | −1.36240 | −0.681201 | − | 0.732097i | \(-0.738542\pi\) | ||||
−0.681201 | + | 0.732097i | \(0.738542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.0186 | − | 9.24837i | 0.778853 | − | 0.449671i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.05178 | − | 34.0787i | −0.292866 | − | 1.64919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.64212 | − | 2.84424i | 0.0792824 | − | 0.137321i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.0933 | − | 33.0706i | −0.919692 | − | 1.59295i | −0.799882 | − | 0.600157i | \(-0.795105\pi\) |
−0.119810 | − | 0.992797i | \(-0.538229\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.7257i | 0.659617i | 0.944048 | + | 0.329809i | \(0.106984\pi\) | ||||
−0.944048 | + | 0.329809i | \(0.893016\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.9841 | − | 19.6208i | 1.62568 | − | 0.938588i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.49329 | − | 14.7108i | 0.405363 | − | 0.702109i | −0.589001 | − | 0.808132i | \(-0.700479\pi\) |
0.994364 | + | 0.106023i | \(0.0338119\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.9537 | + | 12.4858i | 0.712083 | + | 0.594561i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.20222 | + | 1.27145i | 0.104631 | + | 0.0604086i | 0.551402 | − | 0.834240i | \(-0.314093\pi\) |
−0.446772 | + | 0.894648i | \(0.647426\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 3.57675i | − | 0.169175i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.5205 | −1.62912 | −0.814561 | − | 0.580078i | \(-0.803022\pi\) | ||||
−0.814561 | + | 0.580078i | \(0.803022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.60150 | − | 7.97004i | −0.216676 | − | 0.375294i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.18553 | − | 0.684469i | −0.0557013 | − | 0.0321591i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.6401 | + | 9.60719i | 0.778393 | + | 0.449405i | 0.835860 | − | 0.548942i | \(-0.184969\pi\) |
−0.0574676 | + | 0.998347i | \(0.518303\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.455154 | − | 0.788350i | −0.0212448 | − | 0.0367970i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.48457 | 0.255442 | 0.127721 | − | 0.991810i | \(-0.459234\pi\) | ||||
0.127721 | + | 0.991810i | \(0.459234\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.55056i | 0.118534i | 0.998242 | + | 0.0592672i | \(0.0188764\pi\) | ||||
−0.998242 | + | 0.0592672i | \(0.981124\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.7908 | − | 10.8488i | −0.869532 | − | 0.502025i | −0.00233950 | − | 0.999997i | \(-0.500745\pi\) |
−0.867193 | + | 0.497973i | \(0.834078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.9173 | − | 30.1091i | 0.504115 | − | 1.39031i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.55858 | − | 6.16365i | 0.163971 | − | 0.284006i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.99668 | − | 3.46219i | 0.275728 | − | 0.159191i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 13.5590i | − | 0.620823i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.0337 | + | 32.9674i | 0.869673 | + | 1.50632i | 0.862331 | + | 0.506344i | \(0.169004\pi\) |
0.00734135 | + | 0.999973i | \(0.497663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.4974 | − | 26.8422i | 0.706619 | − | 1.22390i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.17579 | − | 5.19493i | 0.281008 | − | 0.236377i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.462071 | − | 0.266777i | 0.0209384 | − | 0.0120888i | −0.489494 | − | 0.872007i | \(-0.662819\pi\) |
0.510433 | + | 0.859918i | \(0.329485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.87990 | −0.130233 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.7255 | 1.02559 | 0.512793 | − | 0.858512i | \(-0.328611\pi\) | ||||
0.512793 | + | 0.858512i | \(0.328611\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.33907 | + | 1.35046i | −0.105347 | + | 0.0608219i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.81940 | + | 2.37161i | −0.126467 | + | 0.106381i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.03285 | − | 12.1813i | 0.314834 | − | 0.545308i | −0.664568 | − | 0.747227i | \(-0.731385\pi\) |
0.979402 | + | 0.201919i | \(0.0647179\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.21958 | − | 7.30853i | −0.188517 | − | 0.326521i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.2757i | 0.681108i | 0.940225 | + | 0.340554i | \(0.110615\pi\) | ||||
−0.940225 | + | 0.340554i | \(0.889385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.33477 | + | 3.08003i | −0.236926 | + | 0.136789i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.7371 | − | 18.5973i | 0.475916 | − | 0.824310i | −0.523704 | − | 0.851900i | \(-0.675450\pi\) |
0.999619 | + | 0.0275905i | \(0.00878344\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.51982 | − | 4.19153i | 0.0672327 | − | 0.185422i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.9817 | + | 8.07231i | 0.617305 | + | 0.356401i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.15037i | 0.402433i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.58239 | −0.420620 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.1514 | + | 33.1712i | 0.839039 | + | 1.45326i | 0.890699 | + | 0.454594i | \(0.150216\pi\) |
−0.0516595 | + | 0.998665i | \(0.516451\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.8504 | − | 18.3889i | −1.39272 | − | 0.804089i | −0.399106 | − | 0.916905i | \(-0.630680\pi\) |
−0.993616 | + | 0.112816i | \(0.964013\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.12130 | − | 1.22474i | −0.0924054 | − | 0.0533503i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.93752 | + | 17.2123i | 0.432066 | + | 0.748360i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.67675 | −0.0727647 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.2311i | 1.48271i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.73215 | − | 2.15476i | −0.161054 | − | 0.0929846i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.04803 | + | 3.31818i | −0.389726 | + | 0.142924i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.31686 | + | 14.4052i | −0.357570 | + | 0.619329i | −0.987554 | − | 0.157279i | \(-0.949728\pi\) |
0.629985 | + | 0.776608i | \(0.283061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.75941 | + | 3.32520i | −0.247160 | + | 0.142698i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.0493i | 0.942761i | 0.881930 | + | 0.471380i | \(0.156244\pi\) | ||||
−0.881930 | + | 0.471380i | \(0.843756\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.2037 | + | 31.5297i | 0.776914 | + | 1.34566i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.9509 | − | 41.4843i | 1.02034 | − | 1.76729i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.52328 | − | 19.8403i | −0.149825 | − | 0.843693i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.2923 | + | 16.3346i | −1.19878 | + | 0.692118i | −0.960284 | − | 0.279025i | \(-0.909989\pi\) |
−0.238500 | + | 0.971143i | \(0.576656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.7556 | −1.08934 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.216717 | 0.00914978 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.6647 | − | 17.7043i | 1.29236 | − | 0.746147i | 0.313292 | − | 0.949657i | \(-0.398568\pi\) |
0.979073 | + | 0.203510i | \(0.0652349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.6450 | − | 6.39796i | −0.741022 | − | 0.268689i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.49112 | + | 11.2429i | −0.272122 | + | 0.471329i | −0.969405 | − | 0.245467i | \(-0.921059\pi\) |
0.697283 | + | 0.716796i | \(0.254392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50250 | − | 4.33445i | −0.104726 | − | 0.181391i | 0.808900 | − | 0.587946i | \(-0.200063\pi\) |
−0.913626 | + | 0.406555i | \(0.866730\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.9395i | 0.457004i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.8172 | − | 22.4111i | 1.61598 | − | 0.932986i | 0.628034 | − | 0.778186i | \(-0.283860\pi\) |
0.987946 | − | 0.154800i | \(-0.0494733\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.25554 | + | 5.63876i | −0.135296 | + | 0.234339i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7654 | + | 15.1757i | 0.529600 | + | 0.629595i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.80900 | + | 3.35383i | 0.240584 | + | 0.138901i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 23.1092i | − | 0.953819i | −0.878952 | − | 0.476910i | \(-0.841757\pi\) | ||
0.878952 | − | 0.476910i | \(-0.158243\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 43.4422 | 1.79000 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.02409 | + | 3.50583i | 0.0832599 | + | 0.144210i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.3551 | + | 20.4123i | 1.45186 | + | 0.838231i | 0.998587 | − | 0.0531407i | \(-0.0169232\pi\) |
0.453272 | + | 0.891372i | \(0.350257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.45680 | − | 1.99579i | −0.141477 | − | 0.0816821i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.4893 | + | 33.7565i | 0.796313 | + | 1.37925i | 0.922002 | + | 0.387185i | \(0.126552\pi\) |
−0.125689 | + | 0.992070i | \(0.540114\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.31217 | 0.339060 | 0.169530 | − | 0.985525i | \(-0.445775\pi\) | ||||
0.169530 | + | 0.985525i | \(0.445775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.6886i | 1.37191i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.03976 | − | 0.600305i | −0.0422025 | − | 0.0243656i | 0.478750 | − | 0.877951i | \(-0.341090\pi\) |
−0.520953 | + | 0.853585i | \(0.674423\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.35804 | − | 9.26121i | 0.136075 | − | 0.375283i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.0176 | − | 29.4754i | 0.688460 | − | 1.19245i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0342 | − | 9.25733i | 0.647614 | − | 0.373900i | −0.139927 | − | 0.990162i | \(-0.544687\pi\) |
0.787542 | + | 0.616262i | \(0.211354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.81137i | − | 0.113181i | −0.998397 | − | 0.0565907i | \(-0.981977\pi\) | ||
0.998397 | − | 0.0565907i | \(-0.0180230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.4829 | − | 38.9416i | −0.903665 | − | 1.56519i | −0.822699 | − | 0.568478i | \(-0.807533\pi\) |
−0.0809667 | − | 0.996717i | \(-0.525801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.81976 | + | 15.2763i | −0.353925 | + | 0.613016i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.73186 | + | 32.2772i | 0.229642 | + | 1.29316i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.32860 | + | 1.92177i | −0.132932 | + | 0.0767481i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.04524 | 0.0815491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.37270 | −0.373121 | −0.186561 | − | 0.982443i | \(-0.559734\pi\) | ||||
−0.186561 | + | 0.982443i | \(0.559734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.33755 | + | 5.39104i | −0.371134 | + | 0.214274i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.3168 | + | 6.13870i | 1.39930 | + | 0.243224i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.93767 | − | 3.35615i | 0.0766531 | − | 0.132767i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.4118 | + | 38.8184i | 0.885213 | + | 1.53323i | 0.845470 | + | 0.534024i | \(0.179321\pi\) |
0.0397433 | + | 0.999210i | \(0.487346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.1709i | 0.716589i | 0.933609 | + | 0.358294i | \(0.116642\pi\) | ||||
−0.933609 | + | 0.358294i | \(0.883358\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.4151 | + | 10.0546i | −0.684658 | + | 0.395288i | −0.801608 | − | 0.597850i | \(-0.796022\pi\) |
0.116949 | + | 0.993138i | \(0.462688\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.414745 | − | 0.718360i | 0.0162802 | − | 0.0281981i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.79643 | − | 1.56209i | 0.344759 | − | 0.0612231i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.50074 | + | 3.75320i | 0.254394 | + | 0.146874i | 0.621774 | − | 0.783196i | \(-0.286412\pi\) |
−0.367381 | + | 0.930071i | \(0.619745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.68985i | 0.182968i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.5476 | 1.61847 | 0.809233 | − | 0.587488i | \(-0.199883\pi\) | ||||
0.809233 | + | 0.587488i | \(0.199883\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.631987 | + | 1.09463i | 0.0245814 | + | 0.0425763i | 0.878054 | − | 0.478561i | \(-0.158841\pi\) |
−0.853473 | + | 0.521137i | \(0.825508\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.698093 | − | 0.403044i | −0.0271117 | − | 0.0156529i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.3254 | + | 26.1687i | 1.75501 | + | 1.01325i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.626914 | − | 1.08585i | −0.0242379 | − | 0.0419813i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.0108 | −0.695299 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0432i | 0.926798i | 0.886150 | + | 0.463399i | \(0.153370\pi\) | ||||
−0.886150 | + | 0.463399i | \(0.846630\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.4734 | − | 11.2430i | −0.748424 | − | 0.432103i | 0.0766999 | − | 0.997054i | \(-0.475562\pi\) |
−0.825124 | + | 0.564951i | \(0.808895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.17784 | + | 1.40023i | 0.0452013 | + | 0.0537359i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.56747 | + | 4.44698i | −0.0983855 | + | 0.170409i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.9393 | − | 7.47052i | 0.495110 | − | 0.285852i | −0.231582 | − | 0.972815i | \(-0.574390\pi\) |
0.726692 | + | 0.686964i | \(0.241057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.38703i | 0.0529186i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.4747 | − | 21.6069i | −0.475250 | − | 0.823157i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.7159 | − | 32.4168i | 0.711985 | − | 1.23319i | −0.252127 | − | 0.967694i | \(-0.581130\pi\) |
0.964111 | − | 0.265499i | \(-0.0855367\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.75762 | − | 6.52552i | 0.294688 | − | 0.247884i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.95618 | + | 1.12940i | −0.0740954 | + | 0.0427790i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.570993 | 0.0215969 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.8376 | −1.69349 | −0.846747 | − | 0.531996i | \(-0.821442\pi\) | ||||
−0.846747 | + | 0.531996i | \(0.821442\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.4134 | + | 18.1365i | −1.18478 | + | 0.684032i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.98334 | − | 3.61988i | −0.375462 | − | 0.136140i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.64589 | − | 16.7072i | 0.362259 | − | 0.627451i | −0.626073 | − | 0.779764i | \(-0.715339\pi\) |
0.988332 | + | 0.152313i | \(0.0486723\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.5980 | + | 18.3562i | 0.397455 | + | 0.688413i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 47.4647i | 1.77757i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.95426 | − | 4.01504i | 0.259712 | − | 0.149945i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.20008 | − | 3.81065i | 0.0820491 | − | 0.142113i | −0.822081 | − | 0.569371i | \(-0.807187\pi\) |
0.904130 | + | 0.427258i | \(0.140520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.7055 | − | 3.14418i | 0.659386 | − | 0.117095i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.67179 | − | 0.965209i | −0.0621746 | − | 0.0358965i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 43.4378i | − | 1.61102i | −0.592583 | − | 0.805509i | \(-0.701892\pi\) | ||
0.592583 | − | 0.805509i | \(-0.298108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.9780 | 0.591779 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.849763 | − | 1.47183i | −0.0314296 | − | 0.0544377i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.90992 | − | 5.14414i | −0.329095 | − | 0.190003i | 0.326344 | − | 0.945251i | \(-0.394183\pi\) |
−0.655439 | + | 0.755248i | \(0.727517\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.4330 | − | 8.33292i | −0.531648 | − | 0.306947i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.7268 | + | 25.5075i | 0.541733 | + | 0.938309i | 0.998805 | + | 0.0488793i | \(0.0155650\pi\) |
−0.457072 | + | 0.889430i | \(0.651102\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.2962 | 0.525186 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.9240i | − | 0.657569i | −0.944405 | − | 0.328785i | \(-0.893361\pi\) | ||
0.944405 | − | 0.328785i | \(-0.106639\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.0648 | − | 10.4297i | −0.660958 | − | 0.381604i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.4847 | − | 4.52563i | 0.931189 | − | 0.165363i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.6091 | − | 20.1075i | 0.423621 | − | 0.733732i | −0.572670 | − | 0.819786i | \(-0.694092\pi\) |
0.996291 | + | 0.0860536i | \(0.0274256\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.52308 | + | 4.34345i | −0.274156 | + | 0.158284i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 40.8014i | − | 1.48295i | −0.670978 | − | 0.741477i | \(-0.734126\pi\) | ||
0.670978 | − | 0.741477i | \(-0.265874\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.09971 | − | 3.63681i | −0.0762148 | − | 0.132008i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.21467 | − | 3.83592i | 0.0802816 | − | 0.139052i | −0.823089 | − | 0.567912i | \(-0.807751\pi\) |
0.903371 | + | 0.428860i | \(0.141085\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3962 | + | 4.13216i | 0.412568 | + | 0.149594i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.67198 | + | 1.54267i | −0.0964795 | + | 0.0557025i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.66676 | 0.132227 | 0.0661133 | − | 0.997812i | \(-0.478940\pi\) | ||||
0.0661133 | + | 0.997812i | \(0.478940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.40718 | −0.158721 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.03664 | + | 3.48526i | −0.217123 | + | 0.125356i | −0.604617 | − | 0.796516i | \(-0.706674\pi\) |
0.387495 | + | 0.921872i | \(0.373341\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.70862 | + | 4.80195i | −0.204795 | + | 0.172269i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0303 | − | 34.6934i | 0.717659 | − | 1.24302i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.958570 | + | 1.66029i | 0.0343003 | + | 0.0594099i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.5325i | 0.769507i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.8229 | + | 13.1768i | −0.813550 | + | 0.469703i | −0.848187 | − | 0.529697i | \(-0.822306\pi\) |
0.0346371 | + | 0.999400i | \(0.488972\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.637671 | + | 1.10448i | −0.0227017 | + | 0.0393204i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.0921 | + | 35.7739i | 1.06995 | + | 1.27197i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 58.0169 | + | 33.4961i | 2.06024 | + | 1.18948i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.31451i | − | 0.117406i | −0.998275 | − | 0.0587030i | \(-0.981304\pi\) | ||
0.998275 | − | 0.0587030i | \(-0.0186965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.24588 | 0.0794535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.2414 | − | 29.8629i | −0.609193 | − | 1.05515i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.00924 | − | 1.16004i | −0.0709047 | − | 0.0409369i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.37462 | − | 4.25774i | −0.259599 | − | 0.149879i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4935 | − | 28.5677i | −0.579882 | − | 1.00439i | −0.995492 | − | 0.0948426i | \(-0.969765\pi\) |
0.415610 | − | 0.909543i | \(-0.363568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.1575 | 1.05897 | 0.529486 | − | 0.848319i | \(-0.322385\pi\) | ||||
0.529486 | + | 0.848319i | \(0.322385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 14.6353i | − | 0.513281i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.1035 | + | 15.0708i | 0.913244 | + | 0.527262i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −37.1251 | + | 6.59275i | −1.29725 | + | 0.230369i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.92451 | − | 5.06541i | 0.102066 | − | 0.176784i | −0.810470 | − | 0.585781i | \(-0.800788\pi\) |
0.912536 | + | 0.408997i | \(0.134121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.27063 | − | 1.88830i | 0.114007 | − | 0.0658220i | −0.441912 | − | 0.897058i | \(-0.645700\pi\) |
0.555919 | + | 0.831236i | \(0.312366\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 19.7854i | − | 0.688005i | −0.938969 | − | 0.344002i | \(-0.888217\pi\) | ||
0.938969 | − | 0.344002i | \(-0.111783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.1945 | − | 36.7100i | −0.736117 | − | 1.27499i | −0.954232 | − | 0.299069i | \(-0.903324\pi\) |
0.218115 | − | 0.975923i | \(-0.430009\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.37074 | − | 4.10625i | 0.0822402 | − | 0.142444i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.814419 | + | 2.22076i | 0.0282179 | + | 0.0769448i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.9115 | + | 9.76388i | −0.584548 | + | 0.337489i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.0442 | 1.14081 | 0.570406 | − | 0.821363i | \(-0.306786\pi\) | ||||
0.570406 | + | 0.821363i | \(0.306786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.8879 | 1.20303 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.6609 | + | 6.15508i | −0.367182 | + | 0.211992i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.21177 | − | 23.7173i | −0.144718 | − | 0.814936i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.09509 | − | 3.62880i | 0.0719033 | − | 0.124540i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.8159 | − | 34.3221i | −0.679279 | − | 1.17655i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 39.3487i | − | 1.34727i | −0.739062 | − | 0.673637i | \(-0.764731\pi\) | ||
0.739062 | − | 0.673637i | \(-0.235269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.0488 | − | 19.0807i | 1.12893 | − | 0.651786i | 0.185261 | − | 0.982689i | \(-0.440687\pi\) |
0.943665 | + | 0.330904i | \(0.107353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.786198 | − | 1.36173i | 0.0268247 | − | 0.0464618i | −0.852301 | − | 0.523051i | \(-0.824794\pi\) |
0.879126 | + | 0.476589i | \(0.158127\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.80834 | − | 7.74518i | 0.0957081 | − | 0.263955i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.9205 | − | 16.1199i | −0.950425 | − | 0.548728i | −0.0572118 | − | 0.998362i | \(-0.518221\pi\) |
−0.893213 | + | 0.449634i | \(0.851554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.86599i | 0.267143i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4857 | −0.355703 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.9947 | + | 53.6844i | 1.05022 | + | 1.81903i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.66680 | − | 0.962329i | −0.0564127 | − | 0.0325699i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7319 | + | 11.3922i | 0.666299 | + | 0.384688i | 0.794673 | − | 0.607038i | \(-0.207642\pi\) |
−0.128374 | + | 0.991726i | \(0.540976\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.94462 | − | 13.7605i | −0.267966 | − | 0.464130i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.2816 | −0.346396 | −0.173198 | − | 0.984887i | \(-0.555410\pi\) | ||||
−0.173198 | + | 0.984887i | \(0.555410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.8161i | 1.23896i | 0.785013 | + | 0.619480i | \(0.212656\pi\) | ||||
−0.785013 | + | 0.619480i | \(0.787344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.7579 | − | 10.8299i | −0.629830 | − | 0.363632i | 0.150857 | − | 0.988556i | \(-0.451797\pi\) |
−0.780686 | + | 0.624923i | \(0.785130\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.2936 | + | 30.0694i | 0.848321 | + | 1.00849i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.88340 | + | 8.45830i | −0.163600 | + | 0.283364i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.4950 | + | 19.9157i | −1.15433 | + | 0.666454i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.6200i | 0.521536i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.9699 | + | 50.1774i | 0.966201 | + | 1.67351i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.823168 | − | 1.42577i | 0.0274237 | − | 0.0474992i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.82750 | + | 2.11301i | 0.193927 | + | 0.0703165i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.4881 | − | 8.94204i | 0.514273 | − | 0.296916i | −0.220315 | − | 0.975429i | \(-0.570709\pi\) |
0.734588 | + | 0.678513i | \(0.237375\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.1702 | 0.370493 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5178 | −0.447865 | −0.223932 | − | 0.974605i | \(-0.571889\pi\) | ||||
−0.223932 | + | 0.974605i | \(0.571889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.93671 | − | 5.15961i | 0.295762 | − | 0.170758i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.487857 | − | 2.74721i | −0.0161104 | − | 0.0907210i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.520988 | − | 0.902377i | 0.0171858 | − | 0.0297667i | −0.857305 | − | 0.514809i | \(-0.827863\pi\) |
0.874490 | + | 0.485043i | \(0.161196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.86211 | + | 6.68937i | 0.127261 | + | 0.220422i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 7.13090i | − | 0.234717i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.3811 | + | 9.45765i | −0.538027 | + | 0.310630i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.16632 | + | 5.48422i | −0.103883 | + | 0.179931i | −0.913281 | − | 0.407329i | \(-0.866460\pi\) |
0.809398 | + | 0.587260i | \(0.199794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.2018 | − | 26.8872i | −1.05537 | − | 0.881193i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.1092 | + | 6.99126i | 0.396438 | + | 0.228884i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.2670i | 0.694761i | 0.937724 | + | 0.347381i | \(0.112929\pi\) | ||||
−0.937724 | + | 0.347381i | \(0.887071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.47317 | −0.145976 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.05639 | − | 13.9541i | −0.262631 | − | 0.454890i | 0.704309 | − | 0.709893i | \(-0.251257\pi\) |
−0.966940 | + | 0.255003i | \(0.917923\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.9058 | + | 21.8849i | 1.23438 | + | 0.712672i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.0148 | + | 8.09142i | 0.455418 | + | 0.262936i | 0.710116 | − | 0.704085i | \(-0.248643\pi\) |
−0.254698 | + | 0.967021i | \(0.581976\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.31482 | + | 7.47349i | 0.140065 | + | 0.242600i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.5342 | −0.374021 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.4950i | 0.404753i | 0.979308 | + | 0.202377i | \(0.0648665\pi\) | ||||
−0.979308 | + | 0.202377i | \(0.935134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.43944 | − | 2.56311i | −0.143507 | − | 0.0828536i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.6559 | + | 40.4199i | −0.473265 | + | 1.30523i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.7728 | + | 18.6590i | −0.347509 | + | 0.601904i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.5785 | + | 13.6130i | −0.759806 | + | 0.438674i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.6562i | 0.921521i | 0.887524 | + | 0.460761i | \(0.152423\pi\) | ||||
−0.887524 | + | 0.460761i | \(0.847577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.471682 | + | 0.816977i | 0.0151526 | + | 0.0262451i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.93705 | + | 13.7474i | −0.254712 | + | 0.441174i | −0.964817 | − | 0.262921i | \(-0.915314\pi\) |
0.710105 | + | 0.704096i | \(0.248647\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.75862 | − | 7.36754i | 0.280789 | − | 0.236193i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.9357 | + | 12.6646i | −0.701785 | + | 0.405176i | −0.808012 | − | 0.589166i | \(-0.799456\pi\) |
0.106227 | + | 0.994342i | \(0.466123\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0587 | 0.545197 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.7510 | −0.407108 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.60540 | − | 4.96833i | 0.274470 | − | 0.158465i | −0.356447 | − | 0.934315i | \(-0.616012\pi\) |
0.630917 | + | 0.775850i | \(0.282679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.26863 | + | 5.27302i | −0.199533 | + | 0.167842i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.4663 | + | 28.5205i | −0.523598 | + | 0.906898i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.1869 | − | 26.3045i | −0.482428 | − | 0.835590i | 0.517368 | − | 0.855763i | \(-0.326912\pi\) |
−0.999797 | + | 0.0201729i | \(0.993578\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.30049i | − | 0.295142i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.585811 | + | 0.338218i | −0.0185528 | + | 0.0107115i | −0.509248 | − | 0.860620i | \(-0.670076\pi\) |
0.490695 | + | 0.871331i | \(0.336743\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.15258 | − | 14.1207i | 0.257936 | − | 0.446759i |
(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 | 1400.2.bh.j.849.5 | 16 | ||
5.2 | odd | 4 | 1400.2.q.l.401.3 | ✓ | 8 | ||
5.3 | odd | 4 | 1400.2.q.m.401.2 | yes | 8 | ||
5.4 | even | 2 | inner | 1400.2.bh.j.849.4 | 16 | ||
7.4 | even | 3 | inner | 1400.2.bh.j.249.4 | 16 | ||
35.2 | odd | 12 | 9800.2.a.ct.1.2 | 4 | |||
35.4 | even | 6 | inner | 1400.2.bh.j.249.5 | 16 | ||
35.12 | even | 12 | 9800.2.a.ck.1.3 | 4 | |||
35.18 | odd | 12 | 1400.2.q.m.1201.2 | yes | 8 | ||
35.23 | odd | 12 | 9800.2.a.cj.1.3 | 4 | |||
35.32 | odd | 12 | 1400.2.q.l.1201.3 | yes | 8 | ||
35.33 | even | 12 | 9800.2.a.cu.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.l.401.3 | ✓ | 8 | 5.2 | odd | 4 | ||
1400.2.q.l.1201.3 | yes | 8 | 35.32 | odd | 12 | ||
1400.2.q.m.401.2 | yes | 8 | 5.3 | odd | 4 | ||
1400.2.q.m.1201.2 | yes | 8 | 35.18 | odd | 12 | ||
1400.2.bh.j.249.4 | 16 | 7.4 | even | 3 | inner | ||
1400.2.bh.j.249.5 | 16 | 35.4 | even | 6 | inner | ||
1400.2.bh.j.849.4 | 16 | 5.4 | even | 2 | inner | ||
1400.2.bh.j.849.5 | 16 | 1.1 | even | 1 | trivial | ||
9800.2.a.cj.1.3 | 4 | 35.23 | odd | 12 | |||
9800.2.a.ck.1.3 | 4 | 35.12 | even | 12 | |||
9800.2.a.ct.1.2 | 4 | 35.2 | odd | 12 | |||
9800.2.a.cu.1.2 | 4 | 35.33 | even | 12 |