Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.3 | ||
Root | \(-1.93600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.j.1084.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.93600i | − | 1.36896i | −0.729031 | − | 0.684481i | \(-0.760029\pi\) | ||
0.729031 | − | 0.684481i | \(-0.239971\pi\) | |||||||
\(3\) | 2.41423i | 1.39386i | 0.717141 | + | 0.696928i | \(0.245450\pi\) | ||||
−0.717141 | + | 0.696928i | \(0.754550\pi\) | |||||||
\(4\) | −1.74811 | −0.874056 | ||||||||
\(5\) | −0.825597 | + | 2.07807i | −0.369218 | + | 0.929343i | ||||
\(6\) | 4.67396 | 1.90814 | ||||||||
\(7\) | 1.46100i | 0.552207i | 0.961128 | + | 0.276103i | \(0.0890432\pi\) | ||||
−0.961128 | + | 0.276103i | \(0.910957\pi\) | |||||||
\(8\) | − | 0.487655i | − | 0.172412i | ||||||
\(9\) | −2.82851 | −0.942835 | ||||||||
\(10\) | 4.02316 | + | 1.59836i | 1.27223 | + | 0.505446i | ||||
\(11\) | −2.89488 | −0.872839 | −0.436419 | − | 0.899743i | \(-0.643754\pi\) | ||||
−0.436419 | + | 0.899743i | \(0.643754\pi\) | |||||||
\(12\) | − | 4.22035i | − | 1.21831i | ||||||
\(13\) | − | 6.12528i | − | 1.69885i | −0.527713 | − | 0.849423i | \(-0.676950\pi\) | ||
0.527713 | − | 0.849423i | \(-0.323050\pi\) | |||||||
\(14\) | 2.82851 | 0.755950 | ||||||||
\(15\) | −5.01695 | − | 1.99318i | −1.29537 | − | 0.514637i | ||||
\(16\) | −4.44033 | −1.11008 | ||||||||
\(17\) | − | 6.29889i | − | 1.52771i | −0.645391 | − | 0.763853i | \(-0.723305\pi\) | ||
0.645391 | − | 0.763853i | \(-0.276695\pi\) | |||||||
\(18\) | 5.47600i | 1.29071i | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.44324 | − | 3.63271i | 0.322718 | − | 0.812298i | ||||
\(21\) | −3.52719 | −0.769697 | ||||||||
\(22\) | 5.60450i | 1.19488i | ||||||||
\(23\) | − | 0.508852i | − | 0.106103i | −0.998592 | − | 0.0530515i | \(-0.983105\pi\) | ||
0.998592 | − | 0.0530515i | \(-0.0168947\pi\) | |||||||
\(24\) | 1.17731 | 0.240318 | ||||||||
\(25\) | −3.63678 | − | 3.43130i | −0.727356 | − | 0.686261i | ||||
\(26\) | −11.8586 | −2.32565 | ||||||||
\(27\) | 0.414027i | 0.0796795i | ||||||||
\(28\) | − | 2.55400i | − | 0.482660i | ||||||
\(29\) | 1.72159 | 0.319691 | 0.159845 | − | 0.987142i | \(-0.448900\pi\) | ||||
0.159845 | + | 0.987142i | \(0.448900\pi\) | |||||||
\(30\) | −3.85881 | + | 9.71283i | −0.704519 | + | 1.77331i | ||||
\(31\) | 8.44484 | 1.51674 | 0.758369 | − | 0.651826i | \(-0.225997\pi\) | ||||
0.758369 | + | 0.651826i | \(0.225997\pi\) | |||||||
\(32\) | 7.62118i | 1.34725i | ||||||||
\(33\) | − | 6.98890i | − | 1.21661i | ||||||
\(34\) | −12.1947 | −2.09137 | ||||||||
\(35\) | −3.03607 | − | 1.20620i | −0.513189 | − | 0.203885i | ||||
\(36\) | 4.94455 | 0.824091 | ||||||||
\(37\) | 3.13569i | 0.515504i | 0.966211 | + | 0.257752i | \(0.0829817\pi\) | ||||
−0.966211 | + | 0.257752i | \(0.917018\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.7878 | 2.36795 | ||||||||
\(40\) | 1.01338 | + | 0.402607i | 0.160230 | + | 0.0636577i | ||||
\(41\) | −7.44400 | −1.16256 | −0.581279 | − | 0.813704i | \(-0.697447\pi\) | ||||
−0.581279 | + | 0.813704i | \(0.697447\pi\) | |||||||
\(42\) | 6.82866i | 1.05369i | ||||||||
\(43\) | − | 6.90372i | − | 1.05281i | −0.850235 | − | 0.526404i | \(-0.823540\pi\) | ||
0.850235 | − | 0.526404i | \(-0.176460\pi\) | |||||||
\(44\) | 5.06057 | 0.762910 | ||||||||
\(45\) | 2.33521 | − | 5.87784i | 0.348112 | − | 0.876217i | ||||
\(46\) | −0.985139 | −0.145251 | ||||||||
\(47\) | − | 0.316851i | − | 0.0462175i | −0.999733 | − | 0.0231087i | \(-0.992644\pi\) | ||
0.999733 | − | 0.0231087i | \(-0.00735640\pi\) | |||||||
\(48\) | − | 10.7200i | − | 1.54729i | ||||||
\(49\) | 4.86547 | 0.695068 | ||||||||
\(50\) | −6.64302 | + | 7.04082i | −0.939465 | + | 0.995722i | ||||
\(51\) | 15.2070 | 2.12940 | ||||||||
\(52\) | 10.7077i | 1.48489i | ||||||||
\(53\) | − | 4.34236i | − | 0.596468i | −0.954493 | − | 0.298234i | \(-0.903602\pi\) | ||
0.954493 | − | 0.298234i | \(-0.0963977\pi\) | |||||||
\(54\) | 0.801557 | 0.109078 | ||||||||
\(55\) | 2.39000 | − | 6.01577i | 0.322268 | − | 0.811166i | ||||
\(56\) | 0.712465 | 0.0952071 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 3.33300i | − | 0.437644i | ||||||
\(59\) | 2.25084 | 0.293035 | 0.146517 | − | 0.989208i | \(-0.453194\pi\) | ||||
0.146517 | + | 0.989208i | \(0.453194\pi\) | |||||||
\(60\) | 8.77019 | + | 3.48431i | 1.13223 | + | 0.449822i | ||||
\(61\) | −6.29374 | −0.805831 | −0.402916 | − | 0.915237i | \(-0.632003\pi\) | ||||
−0.402916 | + | 0.915237i | \(0.632003\pi\) | |||||||
\(62\) | − | 16.3492i | − | 2.07636i | ||||||
\(63\) | − | 4.13245i | − | 0.520640i | ||||||
\(64\) | 5.87399 | 0.734249 | ||||||||
\(65\) | 12.7288 | + | 5.05701i | 1.57881 | + | 0.627245i | ||||
\(66\) | −13.5305 | −1.66549 | ||||||||
\(67\) | − | 10.0324i | − | 1.22565i | −0.790217 | − | 0.612827i | \(-0.790032\pi\) | ||
0.790217 | − | 0.612827i | \(-0.209968\pi\) | |||||||
\(68\) | 11.0112i | 1.33530i | ||||||||
\(69\) | 1.22849 | 0.147892 | ||||||||
\(70\) | −2.33521 | + | 5.87784i | −0.279111 | + | 0.702537i | ||||
\(71\) | 6.63567 | 0.787509 | 0.393754 | − | 0.919216i | \(-0.371176\pi\) | ||||
0.393754 | + | 0.919216i | \(0.371176\pi\) | |||||||
\(72\) | 1.37933i | 0.162556i | ||||||||
\(73\) | − | 12.9644i | − | 1.51737i | −0.651458 | − | 0.758685i | \(-0.725842\pi\) | ||
0.651458 | − | 0.758685i | \(-0.274158\pi\) | |||||||
\(74\) | 6.07070 | 0.705705 | ||||||||
\(75\) | 8.28396 | − | 8.78002i | 0.956549 | − | 1.01383i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.22942i | − | 0.481987i | ||||||
\(78\) | − | 28.6293i | − | 3.24163i | ||||||
\(79\) | 14.6730 | 1.65084 | 0.825420 | − | 0.564519i | \(-0.190938\pi\) | ||||
0.825420 | + | 0.564519i | \(0.190938\pi\) | |||||||
\(80\) | 3.66592 | − | 9.22733i | 0.409863 | − | 1.03165i | ||||
\(81\) | −9.48507 | −1.05390 | ||||||||
\(82\) | 14.4116i | 1.59150i | ||||||||
\(83\) | 4.94202i | 0.542458i | 0.962515 | + | 0.271229i | \(0.0874300\pi\) | ||||
−0.962515 | + | 0.271229i | \(0.912570\pi\) | |||||||
\(84\) | 6.16593 | 0.672758 | ||||||||
\(85\) | 13.0896 | + | 5.20035i | 1.41976 | + | 0.564057i | ||||
\(86\) | −13.3656 | −1.44125 | ||||||||
\(87\) | 4.15631i | 0.445603i | ||||||||
\(88\) | 1.41170i | 0.150488i | ||||||||
\(89\) | −5.35408 | −0.567532 | −0.283766 | − | 0.958894i | \(-0.591584\pi\) | ||||
−0.283766 | + | 0.958894i | \(0.591584\pi\) | |||||||
\(90\) | −11.3795 | − | 4.52097i | −1.19951 | − | 0.476552i | ||||
\(91\) | 8.94904 | 0.938114 | ||||||||
\(92\) | 0.889530i | 0.0927400i | ||||||||
\(93\) | 20.3878i | 2.11411i | ||||||||
\(94\) | −0.613425 | −0.0632700 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −18.3993 | −1.87787 | ||||||||
\(97\) | 15.9482i | 1.61929i | 0.586918 | + | 0.809646i | \(0.300341\pi\) | ||||
−0.586918 | + | 0.809646i | \(0.699659\pi\) | |||||||
\(98\) | − | 9.41958i | − | 0.951521i | ||||||
\(99\) | 8.18818 | 0.822943 | ||||||||
\(100\) | 6.35750 | + | 5.99830i | 0.635750 | + | 0.599830i | ||||
\(101\) | −6.24001 | −0.620904 | −0.310452 | − | 0.950589i | \(-0.600480\pi\) | ||||
−0.310452 | + | 0.950589i | \(0.600480\pi\) | |||||||
\(102\) | − | 29.4408i | − | 2.91507i | ||||||
\(103\) | − | 7.93296i | − | 0.781658i | −0.920463 | − | 0.390829i | \(-0.872188\pi\) | ||
0.920463 | − | 0.390829i | \(-0.127812\pi\) | |||||||
\(104\) | −2.98702 | −0.292902 | ||||||||
\(105\) | 2.91204 | − | 7.32977i | 0.284186 | − | 0.715312i | ||||
\(106\) | −8.40682 | −0.816543 | ||||||||
\(107\) | − | 17.3832i | − | 1.68050i | −0.542200 | − | 0.840250i | \(-0.682408\pi\) | ||
0.542200 | − | 0.840250i | \(-0.317592\pi\) | |||||||
\(108\) | − | 0.723765i | − | 0.0696443i | ||||||
\(109\) | 8.66544 | 0.829999 | 0.414999 | − | 0.909822i | \(-0.363782\pi\) | ||||
0.414999 | + | 0.909822i | \(0.363782\pi\) | |||||||
\(110\) | −11.6466 | − | 4.62706i | −1.11046 | − | 0.441173i | ||||
\(111\) | −7.57027 | −0.718538 | ||||||||
\(112\) | − | 6.48733i | − | 0.612995i | ||||||
\(113\) | 9.86985i | 0.928477i | 0.885710 | + | 0.464239i | \(0.153672\pi\) | ||||
−0.885710 | + | 0.464239i | \(0.846328\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.05743 | + | 0.420107i | 0.0986060 | + | 0.0391752i | ||||
\(116\) | −3.00953 | −0.279428 | ||||||||
\(117\) | 17.3254i | 1.60173i | ||||||||
\(118\) | − | 4.35764i | − | 0.401153i | ||||||
\(119\) | 9.20269 | 0.843609 | ||||||||
\(120\) | −0.971985 | + | 2.44654i | −0.0887297 | + | 0.223337i | ||||
\(121\) | −2.61968 | −0.238153 | ||||||||
\(122\) | 12.1847i | 1.10315i | ||||||||
\(123\) | − | 17.9715i | − | 1.62044i | ||||||
\(124\) | −14.7625 | −1.32571 | ||||||||
\(125\) | 10.1330 | − | 4.72462i | 0.906324 | − | 0.422583i | ||||
\(126\) | −8.00044 | −0.712736 | ||||||||
\(127\) | − | 11.9797i | − | 1.06303i | −0.847049 | − | 0.531515i | \(-0.821623\pi\) | ||
0.847049 | − | 0.531515i | \(-0.178377\pi\) | |||||||
\(128\) | 3.87030i | 0.342089i | ||||||||
\(129\) | 16.6672 | 1.46746 | ||||||||
\(130\) | 9.79039 | − | 24.6430i | 0.858674 | − | 2.16133i | ||||
\(131\) | −8.04755 | −0.703118 | −0.351559 | − | 0.936166i | \(-0.614348\pi\) | ||||
−0.351559 | + | 0.936166i | \(0.614348\pi\) | |||||||
\(132\) | 12.2174i | 1.06339i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −19.4228 | −1.67787 | ||||||||
\(135\) | −0.860378 | − | 0.341819i | −0.0740495 | − | 0.0294191i | ||||
\(136\) | −3.07169 | −0.263395 | ||||||||
\(137\) | − | 3.13952i | − | 0.268227i | −0.990966 | − | 0.134113i | \(-0.957181\pi\) | ||
0.990966 | − | 0.134113i | \(-0.0428187\pi\) | |||||||
\(138\) | − | 2.37835i | − | 0.202459i | ||||||
\(139\) | −18.7439 | −1.58983 | −0.794917 | − | 0.606719i | \(-0.792485\pi\) | ||||
−0.794917 | + | 0.606719i | \(0.792485\pi\) | |||||||
\(140\) | 5.30739 | + | 2.10857i | 0.448556 | + | 0.178207i | ||||
\(141\) | 0.764951 | 0.0644205 | ||||||||
\(142\) | − | 12.8467i | − | 1.07807i | ||||||
\(143\) | 17.7319i | 1.48282i | ||||||||
\(144\) | 12.5595 | 1.04662 | ||||||||
\(145\) | −1.42134 | + | 3.57758i | −0.118036 | + | 0.297102i | ||||
\(146\) | −25.0992 | −2.07722 | ||||||||
\(147\) | 11.7464i | 0.968824i | ||||||||
\(148\) | − | 5.48153i | − | 0.450579i | ||||||
\(149\) | 8.91189 | 0.730090 | 0.365045 | − | 0.930990i | \(-0.381054\pi\) | ||||
0.365045 | + | 0.930990i | \(0.381054\pi\) | |||||||
\(150\) | −16.9982 | − | 16.0378i | −1.38789 | − | 1.30948i | ||||
\(151\) | 1.41610 | 0.115241 | 0.0576204 | − | 0.998339i | \(-0.481649\pi\) | ||||
0.0576204 | + | 0.998339i | \(0.481649\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.8164i | 1.44037i | ||||||||
\(154\) | −8.18818 | −0.659822 | ||||||||
\(155\) | −6.97203 | + | 17.5490i | −0.560007 | + | 1.40957i | ||||
\(156\) | −25.8508 | −2.06972 | ||||||||
\(157\) | − | 4.37921i | − | 0.349499i | −0.984613 | − | 0.174750i | \(-0.944088\pi\) | ||
0.984613 | − | 0.174750i | \(-0.0559116\pi\) | |||||||
\(158\) | − | 28.4070i | − | 2.25994i | ||||||
\(159\) | 10.4834 | 0.831391 | ||||||||
\(160\) | −15.8374 | − | 6.29203i | −1.25205 | − | 0.497428i | ||||
\(161\) | 0.743434 | 0.0585908 | ||||||||
\(162\) | 18.3631i | 1.44274i | ||||||||
\(163\) | 3.09759i | 0.242622i | 0.992615 | + | 0.121311i | \(0.0387098\pi\) | ||||
−0.992615 | + | 0.121311i | \(0.961290\pi\) | |||||||
\(164\) | 13.0130 | 1.01614 | ||||||||
\(165\) | 14.5234 | + | 5.77002i | 1.13065 | + | 0.449195i | ||||
\(166\) | 9.56778 | 0.742604 | ||||||||
\(167\) | − | 3.25702i | − | 0.252036i | −0.992028 | − | 0.126018i | \(-0.959780\pi\) | ||
0.992028 | − | 0.126018i | \(-0.0402197\pi\) | |||||||
\(168\) | 1.72005i | 0.132705i | ||||||||
\(169\) | −24.5190 | −1.88608 | ||||||||
\(170\) | 10.0679 | − | 25.3414i | 0.772172 | − | 1.94360i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.0685i | 0.920213i | ||||||||
\(173\) | − | 10.5204i | − | 0.799848i | −0.916548 | − | 0.399924i | \(-0.869036\pi\) | ||
0.916548 | − | 0.399924i | \(-0.130964\pi\) | |||||||
\(174\) | 8.04663 | 0.610013 | ||||||||
\(175\) | 5.01314 | − | 5.31334i | 0.378958 | − | 0.401651i | ||||
\(176\) | 12.8542 | 0.968922 | ||||||||
\(177\) | 5.43405i | 0.408448i | ||||||||
\(178\) | 10.3655i | 0.776929i | ||||||||
\(179\) | −14.3853 | −1.07521 | −0.537605 | − | 0.843197i | \(-0.680671\pi\) | ||||
−0.537605 | + | 0.843197i | \(0.680671\pi\) | |||||||
\(180\) | −4.08220 | + | 10.2751i | −0.304270 | + | 0.765863i | ||||
\(181\) | −8.13512 | −0.604679 | −0.302339 | − | 0.953200i | \(-0.597768\pi\) | ||||
−0.302339 | + | 0.953200i | \(0.597768\pi\) | |||||||
\(182\) | − | 17.3254i | − | 1.28424i | ||||||
\(183\) | − | 15.1945i | − | 1.12321i | ||||||
\(184\) | −0.248144 | −0.0182934 | ||||||||
\(185\) | −6.51618 | − | 2.58881i | −0.479079 | − | 0.190333i | ||||
\(186\) | 39.4708 | 2.89414 | ||||||||
\(187\) | 18.2345i | 1.33344i | ||||||||
\(188\) | 0.553891i | 0.0403967i | ||||||||
\(189\) | −0.604894 | −0.0439995 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.19452 | −0.448220 | −0.224110 | − | 0.974564i | \(-0.571947\pi\) | ||||
−0.224110 | + | 0.974564i | \(0.571947\pi\) | |||||||
\(192\) | 14.1812i | 1.02344i | ||||||||
\(193\) | − | 12.5560i | − | 0.903798i | −0.892069 | − | 0.451899i | \(-0.850747\pi\) | ||
0.892069 | − | 0.451899i | \(-0.149253\pi\) | |||||||
\(194\) | 30.8758 | 2.21675 | ||||||||
\(195\) | −12.2088 | + | 30.7302i | −0.874289 | + | 2.20063i | ||||
\(196\) | −8.50540 | −0.607528 | ||||||||
\(197\) | 3.43662i | 0.244849i | 0.992478 | + | 0.122425i | \(0.0390670\pi\) | ||||
−0.992478 | + | 0.122425i | \(0.960933\pi\) | |||||||
\(198\) | − | 15.8523i | − | 1.12658i | ||||||
\(199\) | 0.866118 | 0.0613975 | 0.0306987 | − | 0.999529i | \(-0.490227\pi\) | ||||
0.0306987 | + | 0.999529i | \(0.490227\pi\) | |||||||
\(200\) | −1.67329 | + | 1.77349i | −0.118320 | + | 0.125405i | ||||
\(201\) | 24.2205 | 1.70839 | ||||||||
\(202\) | 12.0807i | 0.849994i | ||||||||
\(203\) | 2.51524i | 0.176535i | ||||||||
\(204\) | −26.5835 | −1.86122 | ||||||||
\(205\) | 6.14575 | − | 15.4692i | 0.429238 | − | 1.08041i | ||||
\(206\) | −15.3582 | −1.07006 | ||||||||
\(207\) | 1.43929i | 0.100038i | ||||||||
\(208\) | 27.1982i | 1.88586i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −14.1905 | − | 5.63773i | −0.979235 | − | 0.389040i | ||||
\(211\) | 7.97947 | 0.549329 | 0.274665 | − | 0.961540i | \(-0.411433\pi\) | ||||
0.274665 | + | 0.961540i | \(0.411433\pi\) | |||||||
\(212\) | 7.59093i | 0.521347i | ||||||||
\(213\) | 16.0200i | 1.09767i | ||||||||
\(214\) | −33.6540 | −2.30054 | ||||||||
\(215\) | 14.3464 | + | 5.69969i | 0.978419 | + | 0.388716i | ||||
\(216\) | 0.201902 | 0.0137377 | ||||||||
\(217\) | 12.3379i | 0.837553i | ||||||||
\(218\) | − | 16.7763i | − | 1.13624i | ||||||
\(219\) | 31.2991 | 2.11500 | ||||||||
\(220\) | −4.17799 | + | 10.5162i | −0.281680 | + | 0.709005i | ||||
\(221\) | −38.5824 | −2.59534 | ||||||||
\(222\) | 14.6561i | 0.983651i | ||||||||
\(223\) | − | 15.2911i | − | 1.02397i | −0.858995 | − | 0.511985i | \(-0.828911\pi\) | ||
0.858995 | − | 0.511985i | \(-0.171089\pi\) | |||||||
\(224\) | −11.1346 | −0.743959 | ||||||||
\(225\) | 10.2866 | + | 9.70546i | 0.685777 | + | 0.647031i | ||||
\(226\) | 19.1081 | 1.27105 | ||||||||
\(227\) | − | 7.39075i | − | 0.490541i | −0.969455 | − | 0.245271i | \(-0.921123\pi\) | ||
0.969455 | − | 0.245271i | \(-0.0788769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00545 | 0.0664417 | 0.0332209 | − | 0.999448i | \(-0.489424\pi\) | ||||
0.0332209 | + | 0.999448i | \(0.489424\pi\) | |||||||
\(230\) | 0.813328 | − | 2.04719i | 0.0536293 | − | 0.134988i | ||||
\(231\) | 10.2108 | 0.671821 | ||||||||
\(232\) | − | 0.839541i | − | 0.0551185i | ||||||
\(233\) | − | 17.0150i | − | 1.11469i | −0.830281 | − | 0.557344i | \(-0.811820\pi\) | ||
0.830281 | − | 0.557344i | \(-0.188180\pi\) | |||||||
\(234\) | 33.5420 | 2.19271 | ||||||||
\(235\) | 0.658440 | + | 0.261591i | 0.0429519 | + | 0.0170643i | ||||
\(236\) | −3.93473 | −0.256129 | ||||||||
\(237\) | 35.4240i | 2.30103i | ||||||||
\(238\) | − | 17.8164i | − | 1.15487i | ||||||
\(239\) | −8.40908 | −0.543938 | −0.271969 | − | 0.962306i | \(-0.587675\pi\) | ||||
−0.271969 | + | 0.962306i | \(0.587675\pi\) | |||||||
\(240\) | 22.2769 | + | 8.85038i | 1.43797 | + | 0.571289i | ||||
\(241\) | 13.0814 | 0.842648 | 0.421324 | − | 0.906910i | \(-0.361566\pi\) | ||||
0.421324 | + | 0.906910i | \(0.361566\pi\) | |||||||
\(242\) | 5.07171i | 0.326022i | ||||||||
\(243\) | − | 21.6571i | − | 1.38930i | ||||||
\(244\) | 11.0022 | 0.704342 | ||||||||
\(245\) | −4.01692 | + | 10.1108i | −0.256632 | + | 0.645956i | ||||
\(246\) | −34.7930 | −2.21832 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 4.11817i | − | 0.261504i | ||||||
\(249\) | −11.9312 | −0.756108 | ||||||||
\(250\) | −9.14688 | − | 19.6176i | −0.578500 | − | 1.24072i | ||||
\(251\) | 13.6747 | 0.863137 | 0.431568 | − | 0.902080i | \(-0.357960\pi\) | ||||
0.431568 | + | 0.902080i | \(0.357960\pi\) | |||||||
\(252\) | 7.22399i | 0.455069i | ||||||||
\(253\) | 1.47306i | 0.0926107i | ||||||||
\(254\) | −23.1928 | −1.45525 | ||||||||
\(255\) | −12.5548 | + | 31.6012i | −0.786214 | + | 1.97894i | ||||
\(256\) | 19.2409 | 1.20256 | ||||||||
\(257\) | 2.94446i | 0.183670i | 0.995774 | + | 0.0918352i | \(0.0292733\pi\) | ||||
−0.995774 | + | 0.0918352i | \(0.970727\pi\) | |||||||
\(258\) | − | 32.2677i | − | 2.00890i | ||||||
\(259\) | −4.58124 | −0.284665 | ||||||||
\(260\) | −22.2513 | − | 8.84022i | −1.37997 | − | 0.548247i | ||||
\(261\) | −4.86952 | −0.301416 | ||||||||
\(262\) | 15.5801i | 0.962541i | ||||||||
\(263\) | 13.1907i | 0.813370i | 0.913568 | + | 0.406685i | \(0.133315\pi\) | ||||
−0.913568 | + | 0.406685i | \(0.866685\pi\) | |||||||
\(264\) | −3.40817 | −0.209759 | ||||||||
\(265\) | 9.02374 | + | 3.58504i | 0.554324 | + | 0.220227i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.9260i | − | 0.791058i | ||||||
\(268\) | 17.5378i | 1.07129i | ||||||||
\(269\) | −30.9906 | −1.88953 | −0.944765 | − | 0.327749i | \(-0.893710\pi\) | ||||
−0.944765 | + | 0.327749i | \(0.893710\pi\) | |||||||
\(270\) | −0.661764 | + | 1.66570i | −0.0402737 | + | 0.101371i | ||||
\(271\) | −7.50772 | −0.456062 | −0.228031 | − | 0.973654i | \(-0.573229\pi\) | ||||
−0.228031 | + | 0.973654i | \(0.573229\pi\) | |||||||
\(272\) | 27.9691i | 1.69588i | ||||||||
\(273\) | 21.6050i | 1.30760i | ||||||||
\(274\) | −6.07812 | −0.367192 | ||||||||
\(275\) | 10.5280 | + | 9.93320i | 0.634864 | + | 0.598995i | ||||
\(276\) | −2.14753 | −0.129266 | ||||||||
\(277\) | 9.58988i | 0.576200i | 0.957600 | + | 0.288100i | \(0.0930236\pi\) | ||||
−0.957600 | + | 0.288100i | \(0.906976\pi\) | |||||||
\(278\) | 36.2882i | 2.17642i | ||||||||
\(279\) | −23.8863 | −1.43003 | ||||||||
\(280\) | −0.588209 | + | 1.48055i | −0.0351522 | + | 0.0884800i | ||||
\(281\) | −16.4874 | −0.983555 | −0.491778 | − | 0.870721i | \(-0.663653\pi\) | ||||
−0.491778 | + | 0.870721i | \(0.663653\pi\) | |||||||
\(282\) | − | 1.48095i | − | 0.0881892i | ||||||
\(283\) | 29.3679i | 1.74574i | 0.487951 | + | 0.872871i | \(0.337744\pi\) | ||||
−0.487951 | + | 0.872871i | \(0.662256\pi\) | |||||||
\(284\) | −11.5999 | −0.688327 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 34.3291 | 2.02992 | ||||||||
\(287\) | − | 10.8757i | − | 0.641972i | ||||||
\(288\) | − | 21.5566i | − | 1.27023i | ||||||
\(289\) | −22.6760 | −1.33388 | ||||||||
\(290\) | 6.92622 | + | 2.75172i | 0.406722 | + | 0.161586i | ||||
\(291\) | −38.5026 | −2.25706 | ||||||||
\(292\) | 22.6633i | 1.32627i | ||||||||
\(293\) | − | 0.995738i | − | 0.0581717i | −0.999577 | − | 0.0290858i | \(-0.990740\pi\) | ||
0.999577 | − | 0.0290858i | \(-0.00925961\pi\) | |||||||
\(294\) | 22.7410 | 1.32628 | ||||||||
\(295\) | −1.85829 | + | 4.67742i | −0.108194 | + | 0.272330i | ||||
\(296\) | 1.52913 | 0.0888790 | ||||||||
\(297\) | − | 1.19856i | − | 0.0695473i | ||||||
\(298\) | − | 17.2535i | − | 0.999466i | ||||||
\(299\) | −3.11686 | −0.180253 | ||||||||
\(300\) | −14.4813 | + | 15.3485i | −0.836077 | + | 0.886144i | ||||
\(301\) | 10.0864 | 0.581368 | ||||||||
\(302\) | − | 2.74158i | − | 0.157760i | ||||||
\(303\) | − | 15.0648i | − | 0.865451i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.19610 | − | 13.0789i | 0.297528 | − | 0.748893i | ||||
\(306\) | 34.4927 | 1.97182 | ||||||||
\(307\) | − | 9.86517i | − | 0.563035i | −0.959556 | − | 0.281518i | \(-0.909162\pi\) | ||
0.959556 | − | 0.281518i | \(-0.0908378\pi\) | |||||||
\(308\) | 7.39351i | 0.421284i | ||||||||
\(309\) | 19.1520 | 1.08952 | ||||||||
\(310\) | 33.9749 | + | 13.4979i | 1.92965 | + | 0.766629i | ||||
\(311\) | 0.418188 | 0.0237133 | 0.0118566 | − | 0.999930i | \(-0.496226\pi\) | ||||
0.0118566 | + | 0.999930i | \(0.496226\pi\) | |||||||
\(312\) | − | 7.21136i | − | 0.408263i | ||||||
\(313\) | 6.86188i | 0.387856i | 0.981016 | + | 0.193928i | \(0.0621228\pi\) | ||||
−0.981016 | + | 0.193928i | \(0.937877\pi\) | |||||||
\(314\) | −8.47817 | −0.478451 | ||||||||
\(315\) | 8.58754 | + | 3.41174i | 0.483853 | + | 0.192230i | ||||
\(316\) | −25.6500 | −1.44293 | ||||||||
\(317\) | 11.9255i | 0.669804i | 0.942253 | + | 0.334902i | \(0.108703\pi\) | ||||
−0.942253 | + | 0.334902i | \(0.891297\pi\) | |||||||
\(318\) | − | 20.2960i | − | 1.13814i | ||||||
\(319\) | −4.98378 | −0.279038 | ||||||||
\(320\) | −4.84955 | + | 12.2066i | −0.271098 | + | 0.682369i | ||||
\(321\) | 41.9671 | 2.34237 | ||||||||
\(322\) | − | 1.43929i | − | 0.0802085i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 16.5810 | 0.921165 | ||||||||
\(325\) | −21.0177 | + | 22.2763i | −1.16585 | + | 1.23567i | ||||
\(326\) | 5.99694 | 0.332140 | ||||||||
\(327\) | 20.9204i | 1.15690i | ||||||||
\(328\) | 3.63010i | 0.200439i | ||||||||
\(329\) | 0.462920 | 0.0255216 | ||||||||
\(330\) | 11.1708 | − | 28.1175i | 0.614931 | − | 1.54782i | ||||
\(331\) | 7.96898 | 0.438015 | 0.219007 | − | 0.975723i | \(-0.429718\pi\) | ||||
0.219007 | + | 0.975723i | \(0.429718\pi\) | |||||||
\(332\) | − | 8.63922i | − | 0.474139i | ||||||
\(333\) | − | 8.86930i | − | 0.486035i | ||||||
\(334\) | −6.30561 | −0.345028 | ||||||||
\(335\) | 20.8481 | + | 8.28273i | 1.13905 | + | 0.452534i | ||||
\(336\) | 15.6619 | 0.854427 | ||||||||
\(337\) | − | 4.04620i | − | 0.220410i | −0.993909 | − | 0.110205i | \(-0.964849\pi\) | ||
0.993909 | − | 0.110205i | \(-0.0351508\pi\) | |||||||
\(338\) | 47.4689i | 2.58197i | ||||||||
\(339\) | −23.8281 | −1.29416 | ||||||||
\(340\) | −22.8820 | − | 9.09079i | −1.24095 | − | 0.493017i | ||||
\(341\) | −24.4468 | −1.32387 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3355i | 0.936028i | ||||||||
\(344\) | −3.36664 | −0.181517 | ||||||||
\(345\) | −1.01423 | + | 2.55288i | −0.0546045 | + | 0.137443i | ||||
\(346\) | −20.3675 | −1.09496 | ||||||||
\(347\) | 3.26228i | 0.175129i | 0.996159 | + | 0.0875643i | \(0.0279083\pi\) | ||||
−0.996159 | + | 0.0875643i | \(0.972092\pi\) | |||||||
\(348\) | − | 7.26569i | − | 0.389482i | ||||||
\(349\) | 6.32235 | 0.338428 | 0.169214 | − | 0.985579i | \(-0.445877\pi\) | ||||
0.169214 | + | 0.985579i | \(0.445877\pi\) | |||||||
\(350\) | −10.2866 | − | 9.70546i | −0.549844 | − | 0.518779i | ||||
\(351\) | 2.53603 | 0.135363 | ||||||||
\(352\) | − | 22.0624i | − | 1.17593i | ||||||
\(353\) | − | 6.35500i | − | 0.338242i | −0.985595 | − | 0.169121i | \(-0.945907\pi\) | ||
0.985595 | − | 0.169121i | \(-0.0540929\pi\) | |||||||
\(354\) | 10.5203 | 0.559150 | ||||||||
\(355\) | −5.47839 | + | 13.7894i | −0.290763 | + | 0.731866i | ||||
\(356\) | 9.35954 | 0.496055 | ||||||||
\(357\) | 22.2174i | 1.17587i | ||||||||
\(358\) | 27.8500i | 1.47192i | ||||||||
\(359\) | 2.70761 | 0.142902 | 0.0714512 | − | 0.997444i | \(-0.477237\pi\) | ||||
0.0714512 | + | 0.997444i | \(0.477237\pi\) | |||||||
\(360\) | −2.86636 | − | 1.13878i | −0.151070 | − | 0.0600187i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 15.7496i | 0.827782i | ||||||||
\(363\) | − | 6.32451i | − | 0.331951i | ||||||
\(364\) | −15.6439 | −0.819965 | ||||||||
\(365\) | 26.9410 | + | 10.7034i | 1.41016 | + | 0.560241i | ||||
\(366\) | −29.4167 | −1.53764 | ||||||||
\(367\) | − | 23.2443i | − | 1.21334i | −0.794953 | − | 0.606671i | \(-0.792505\pi\) | ||
0.794953 | − | 0.606671i | \(-0.207495\pi\) | |||||||
\(368\) | 2.25947i | 0.117783i | ||||||||
\(369\) | 21.0554 | 1.09610 | ||||||||
\(370\) | −5.01195 | + | 12.6154i | −0.260559 | + | 0.655841i | ||||
\(371\) | 6.34419 | 0.329374 | ||||||||
\(372\) | − | 35.6401i | − | 1.84785i | ||||||
\(373\) | − | 6.24784i | − | 0.323501i | −0.986832 | − | 0.161750i | \(-0.948286\pi\) | ||
0.986832 | − | 0.161750i | \(-0.0517140\pi\) | |||||||
\(374\) | 35.3021 | 1.82543 | ||||||||
\(375\) | 11.4063 | + | 24.4634i | 0.589020 | + | 1.26329i | ||||
\(376\) | −0.154514 | −0.00796845 | ||||||||
\(377\) | − | 10.5452i | − | 0.543105i | ||||||
\(378\) | 1.17108i | 0.0602337i | ||||||||
\(379\) | 13.0469 | 0.670176 | 0.335088 | − | 0.942187i | \(-0.391234\pi\) | ||||
0.335088 | + | 0.942187i | \(0.391234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.9219 | 1.48171 | ||||||||
\(382\) | 11.9926i | 0.613596i | ||||||||
\(383\) | − | 1.83744i | − | 0.0938889i | −0.998898 | − | 0.0469445i | \(-0.985052\pi\) | ||
0.998898 | − | 0.0469445i | \(-0.0149484\pi\) | |||||||
\(384\) | −9.34379 | −0.476823 | ||||||||
\(385\) | 8.78905 | + | 3.49180i | 0.447931 | + | 0.177959i | ||||
\(386\) | −24.3084 | −1.23726 | ||||||||
\(387\) | 19.5272i | 0.992624i | ||||||||
\(388\) | − | 27.8792i | − | 1.41535i | ||||||
\(389\) | −18.6941 | −0.947828 | −0.473914 | − | 0.880571i | \(-0.657159\pi\) | ||||
−0.473914 | + | 0.880571i | \(0.657159\pi\) | |||||||
\(390\) | 59.4938 | + | 23.6363i | 3.01258 | + | 1.19687i | ||||
\(391\) | −3.20520 | −0.162094 | ||||||||
\(392\) | − | 2.37267i | − | 0.119838i | ||||||
\(393\) | − | 19.4286i | − | 0.980045i | ||||||
\(394\) | 6.65332 | 0.335189 | ||||||||
\(395\) | −12.1140 | + | 30.4916i | −0.609521 | + | 1.53420i | ||||
\(396\) | −14.3139 | −0.719298 | ||||||||
\(397\) | − | 24.9631i | − | 1.25286i | −0.779477 | − | 0.626431i | \(-0.784515\pi\) | ||
0.779477 | − | 0.626431i | \(-0.215485\pi\) | |||||||
\(398\) | − | 1.67681i | − | 0.0840508i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.1485 | + | 15.2361i | 0.807424 | + | 0.761806i | ||||
\(401\) | 25.4399 | 1.27041 | 0.635203 | − | 0.772345i | \(-0.280916\pi\) | ||||
0.635203 | + | 0.772345i | \(0.280916\pi\) | |||||||
\(402\) | − | 46.8911i | − | 2.33871i | ||||||
\(403\) | − | 51.7270i | − | 2.57670i | ||||||
\(404\) | 10.9082 | 0.542705 | ||||||||
\(405\) | 7.83085 | − | 19.7107i | 0.389118 | − | 0.979431i | ||||
\(406\) | 4.86952 | 0.241670 | ||||||||
\(407\) | − | 9.07743i | − | 0.449951i | ||||||
\(408\) | − | 7.41575i | − | 0.367135i | ||||||
\(409\) | 26.8692 | 1.32859 | 0.664297 | − | 0.747468i | \(-0.268731\pi\) | ||||
0.664297 | + | 0.747468i | \(0.268731\pi\) | |||||||
\(410\) | −29.9484 | − | 11.8982i | −1.47905 | − | 0.587610i | ||||
\(411\) | 7.57951 | 0.373870 | ||||||||
\(412\) | 13.8677i | 0.683213i | ||||||||
\(413\) | 3.28849i | 0.161816i | ||||||||
\(414\) | 2.78647 | 0.136948 | ||||||||
\(415\) | −10.2699 | − | 4.08012i | −0.504129 | − | 0.200285i | ||||
\(416\) | 46.6818 | 2.28877 | ||||||||
\(417\) | − | 45.2520i | − | 2.21600i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.0428 | −1.02801 | −0.514004 | − | 0.857788i | \(-0.671838\pi\) | ||||
−0.514004 | + | 0.857788i | \(0.671838\pi\) | |||||||
\(420\) | −5.09058 | + | 12.8133i | −0.248395 | + | 0.625223i | ||||
\(421\) | 2.52939 | 0.123275 | 0.0616376 | − | 0.998099i | \(-0.480368\pi\) | ||||
0.0616376 | + | 0.998099i | \(0.480368\pi\) | |||||||
\(422\) | − | 15.4483i | − | 0.752011i | ||||||
\(423\) | 0.896215i | 0.0435755i | ||||||||
\(424\) | −2.11757 | −0.102838 | ||||||||
\(425\) | −21.6134 | + | 22.9077i | −1.04840 | + | 1.11119i | ||||
\(426\) | 31.0148 | 1.50267 | ||||||||
\(427\) | − | 9.19517i | − | 0.444985i | ||||||
\(428\) | 30.3878i | 1.46885i | ||||||||
\(429\) | −42.8089 | −2.06684 | ||||||||
\(430\) | 11.0346 | − | 27.7748i | 0.532137 | − | 1.33942i | ||||
\(431\) | −30.2212 | −1.45570 | −0.727852 | − | 0.685734i | \(-0.759481\pi\) | ||||
−0.727852 | + | 0.685734i | \(0.759481\pi\) | |||||||
\(432\) | − | 1.83841i | − | 0.0884507i | ||||||
\(433\) | − | 13.0760i | − | 0.628392i | −0.949358 | − | 0.314196i | \(-0.898265\pi\) | ||
0.949358 | − | 0.314196i | \(-0.101735\pi\) | |||||||
\(434\) | 23.8863 | 1.14658 | ||||||||
\(435\) | −8.63711 | − | 3.43144i | −0.414118 | − | 0.164525i | ||||
\(436\) | −15.1482 | −0.725466 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 60.5952i | − | 2.89535i | ||||||
\(439\) | 38.3642 | 1.83102 | 0.915512 | − | 0.402290i | \(-0.131786\pi\) | ||||
0.915512 | + | 0.402290i | \(0.131786\pi\) | |||||||
\(440\) | −2.93362 | − | 1.16550i | −0.139855 | − | 0.0555629i | ||||
\(441\) | −13.7620 | −0.655334 | ||||||||
\(442\) | 74.6958i | 3.55292i | ||||||||
\(443\) | − | 11.5357i | − | 0.548079i | −0.961718 | − | 0.274039i | \(-0.911640\pi\) | ||
0.961718 | − | 0.274039i | \(-0.0883599\pi\) | |||||||
\(444\) | 13.2337 | 0.628043 | ||||||||
\(445\) | 4.42032 | − | 11.1262i | 0.209543 | − | 0.527431i | ||||
\(446\) | −29.6037 | −1.40177 | ||||||||
\(447\) | 21.5153i | 1.01764i | ||||||||
\(448\) | 8.58191i | 0.405457i | ||||||||
\(449\) | −20.1918 | −0.952909 | −0.476455 | − | 0.879199i | \(-0.658078\pi\) | ||||
−0.476455 | + | 0.879199i | \(0.658078\pi\) | |||||||
\(450\) | 18.7898 | − | 19.9150i | 0.885760 | − | 0.938802i | ||||
\(451\) | 21.5495 | 1.01473 | ||||||||
\(452\) | − | 17.2536i | − | 0.811541i | ||||||
\(453\) | 3.41880i | 0.160629i | ||||||||
\(454\) | −14.3085 | −0.671533 | ||||||||
\(455\) | −7.38830 | + | 18.5968i | −0.346369 | + | 0.871830i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.6887i | − | 0.827442i | −0.910404 | − | 0.413721i | \(-0.864229\pi\) | ||
0.910404 | − | 0.413721i | \(-0.135771\pi\) | |||||||
\(458\) | − | 1.94655i | − | 0.0909562i | ||||||
\(459\) | 2.60791 | 0.121727 | ||||||||
\(460\) | −1.84851 | − | 0.734394i | −0.0861872 | − | 0.0342413i | ||||
\(461\) | 24.9640 | 1.16269 | 0.581345 | − | 0.813657i | \(-0.302527\pi\) | ||||
0.581345 | + | 0.813657i | \(0.302527\pi\) | |||||||
\(462\) | − | 19.7681i | − | 0.919697i | ||||||
\(463\) | − | 17.4046i | − | 0.808860i | −0.914569 | − | 0.404430i | \(-0.867470\pi\) | ||
0.914569 | − | 0.404430i | \(-0.132530\pi\) | |||||||
\(464\) | −7.64441 | −0.354883 | ||||||||
\(465\) | −42.3673 | − | 16.8321i | −1.96474 | − | 0.780570i | ||||
\(466\) | −32.9411 | −1.52597 | ||||||||
\(467\) | 14.6807i | 0.679342i | 0.940544 | + | 0.339671i | \(0.110316\pi\) | ||||
−0.940544 | + | 0.339671i | \(0.889684\pi\) | |||||||
\(468\) | − | 30.2867i | − | 1.40000i | ||||||
\(469\) | 14.6574 | 0.676814 | ||||||||
\(470\) | 0.506442 | − | 1.27474i | 0.0233604 | − | 0.0587995i | ||||
\(471\) | 10.5724 | 0.487151 | ||||||||
\(472\) | − | 1.09763i | − | 0.0505227i | ||||||
\(473\) | 19.9854i | 0.918931i | ||||||||
\(474\) | 68.5810 | 3.15003 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.0873 | −0.737362 | ||||||||
\(477\) | 12.2824i | 0.562372i | ||||||||
\(478\) | 16.2800i | 0.744631i | ||||||||
\(479\) | −2.88202 | −0.131683 | −0.0658415 | − | 0.997830i | \(-0.520973\pi\) | ||||
−0.0658415 | + | 0.997830i | \(0.520973\pi\) | |||||||
\(480\) | 15.1904 | − | 38.2351i | 0.693344 | − | 1.74518i | ||||
\(481\) | 19.2069 | 0.875761 | ||||||||
\(482\) | − | 25.3257i | − | 1.15355i | ||||||
\(483\) | 1.79482i | 0.0816671i | ||||||||
\(484\) | 4.57950 | 0.208159 | ||||||||
\(485\) | −33.1415 | − | 13.1668i | −1.50488 | − | 0.597873i | ||||
\(486\) | −41.9282 | −1.90190 | ||||||||
\(487\) | − | 22.9093i | − | 1.03812i | −0.854737 | − | 0.519061i | \(-0.826282\pi\) | ||
0.854737 | − | 0.519061i | \(-0.173718\pi\) | |||||||
\(488\) | 3.06918i | 0.138935i | ||||||||
\(489\) | −7.47828 | −0.338180 | ||||||||
\(490\) | 19.5746 | + | 7.77678i | 0.884289 | + | 0.351319i | ||||
\(491\) | −21.2033 | −0.956889 | −0.478445 | − | 0.878118i | \(-0.658799\pi\) | ||||
−0.478445 | + | 0.878118i | \(0.658799\pi\) | |||||||
\(492\) | 31.4163i | 1.41635i | ||||||||
\(493\) | − | 10.8441i | − | 0.488393i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.76014 | + | 17.0156i | −0.303846 | + | 0.764796i | ||||
\(496\) | −37.4978 | −1.68370 | ||||||||
\(497\) | 9.69472i | 0.434868i | ||||||||
\(498\) | 23.0988i | 1.03508i | ||||||||
\(499\) | 36.5201 | 1.63487 | 0.817433 | − | 0.576024i | \(-0.195396\pi\) | ||||
0.817433 | + | 0.576024i | \(0.195396\pi\) | |||||||
\(500\) | −17.7137 | + | 8.25916i | −0.792179 | + | 0.369361i | ||||
\(501\) | 7.86320 | 0.351302 | ||||||||
\(502\) | − | 26.4742i | − | 1.18160i | ||||||
\(503\) | 32.6315i | 1.45497i | 0.686125 | + | 0.727483i | \(0.259310\pi\) | ||||
−0.686125 | + | 0.727483i | \(0.740690\pi\) | |||||||
\(504\) | −2.01521 | −0.0897646 | ||||||||
\(505\) | 5.15173 | − | 12.9672i | 0.229249 | − | 0.577033i | ||||
\(506\) | 2.85186 | 0.126781 | ||||||||
\(507\) | − | 59.1945i | − | 2.62892i | ||||||
\(508\) | 20.9419i | 0.929148i | ||||||||
\(509\) | −43.2651 | −1.91769 | −0.958846 | − | 0.283927i | \(-0.908363\pi\) | ||||
−0.958846 | + | 0.283927i | \(0.908363\pi\) | |||||||
\(510\) | 61.1801 | + | 24.3062i | 2.70910 | + | 1.07630i | ||||
\(511\) | 18.9410 | 0.837902 | ||||||||
\(512\) | − | 29.5099i | − | 1.30416i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.70049 | 0.251438 | ||||||||
\(515\) | 16.4853 | + | 6.54943i | 0.726428 | + | 0.288602i | ||||
\(516\) | −29.1361 | −1.28265 | ||||||||
\(517\) | 0.917245i | 0.0403404i | ||||||||
\(518\) | 8.86930i | 0.389695i | ||||||||
\(519\) | 25.3986 | 1.11487 | ||||||||
\(520\) | 2.46608 | − | 6.20725i | 0.108145 | − | 0.272206i | ||||
\(521\) | 38.7647 | 1.69831 | 0.849156 | − | 0.528142i | \(-0.177111\pi\) | ||||
0.849156 | + | 0.528142i | \(0.177111\pi\) | |||||||
\(522\) | 9.42741i | 0.412627i | ||||||||
\(523\) | 27.6586i | 1.20943i | 0.796443 | + | 0.604714i | \(0.206712\pi\) | ||||
−0.796443 | + | 0.604714i | \(0.793288\pi\) | |||||||
\(524\) | 14.0680 | 0.614564 | ||||||||
\(525\) | 12.8276 | + | 12.1029i | 0.559843 | + | 0.528213i | ||||
\(526\) | 25.5372 | 1.11347 | ||||||||
\(527\) | − | 53.1931i | − | 2.31713i | ||||||
\(528\) | 31.0330i | 1.35054i | ||||||||
\(529\) | 22.7411 | 0.988742 | ||||||||
\(530\) | 6.94065 | − | 17.4700i | 0.301482 | − | 0.758848i | ||||
\(531\) | −6.36652 | −0.276284 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.5966i | 1.97501i | ||||||||
\(534\) | −25.0248 | −1.08293 | ||||||||
\(535\) | 36.1236 | + | 14.3515i | 1.56176 | + | 0.620471i | ||||
\(536\) | −4.89235 | −0.211318 | ||||||||
\(537\) | − | 34.7295i | − | 1.49869i | ||||||
\(538\) | 59.9979i | 2.58669i | ||||||||
\(539\) | −14.0850 | −0.606682 | ||||||||
\(540\) | 1.50404 | + | 0.597539i | 0.0647235 | + | 0.0257140i | ||||
\(541\) | −4.19755 | −0.180467 | −0.0902335 | − | 0.995921i | \(-0.528761\pi\) | ||||
−0.0902335 | + | 0.995921i | \(0.528761\pi\) | |||||||
\(542\) | 14.5350i | 0.624331i | ||||||||
\(543\) | − | 19.6400i | − | 0.842835i | ||||||
\(544\) | 48.0050 | 2.05820 | ||||||||
\(545\) | −7.15417 | + | 18.0074i | −0.306451 | + | 0.771353i | ||||
\(546\) | 41.8274 | 1.79005 | ||||||||
\(547\) | 14.4970i | 0.619848i | 0.950761 | + | 0.309924i | \(0.100304\pi\) | ||||
−0.950761 | + | 0.309924i | \(0.899696\pi\) | |||||||
\(548\) | 5.48823i | 0.234445i | ||||||||
\(549\) | 17.8019 | 0.759766 | ||||||||
\(550\) | 19.2307 | − | 20.3823i | 0.820001 | − | 0.869105i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 0.599077i | − | 0.0254984i | ||||||
\(553\) | 21.4373i | 0.911605i | ||||||||
\(554\) | 18.5661 | 0.788796 | ||||||||
\(555\) | 6.24999 | − | 15.7316i | 0.265297 | − | 0.667768i | ||||
\(556\) | 32.7664 | 1.38960 | ||||||||
\(557\) | − | 28.9192i | − | 1.22535i | −0.790337 | − | 0.612673i | \(-0.790094\pi\) | ||
0.790337 | − | 0.612673i | \(-0.209906\pi\) | |||||||
\(558\) | 46.2439i | 1.95766i | ||||||||
\(559\) | −42.2872 | −1.78856 | ||||||||
\(560\) | 13.4811 | + | 5.35592i | 0.569682 | + | 0.226329i | ||||
\(561\) | −44.0223 | −1.85862 | ||||||||
\(562\) | 31.9197i | 1.34645i | ||||||||
\(563\) | − | 24.5426i | − | 1.03435i | −0.855880 | − | 0.517174i | \(-0.826984\pi\) | ||
0.855880 | − | 0.517174i | \(-0.173016\pi\) | |||||||
\(564\) | −1.33722 | −0.0563072 | ||||||||
\(565\) | −20.5103 | − | 8.14852i | −0.862874 | − | 0.342811i | ||||
\(566\) | 56.8564 | 2.38985 | ||||||||
\(567\) | − | 13.8577i | − | 0.581969i | ||||||
\(568\) | − | 3.23592i | − | 0.135776i | ||||||
\(569\) | −0.454757 | −0.0190644 | −0.00953221 | − | 0.999955i | \(-0.503034\pi\) | ||||
−0.00953221 | + | 0.999955i | \(0.503034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0492 | −1.00643 | −0.503213 | − | 0.864162i | \(-0.667849\pi\) | ||||
−0.503213 | + | 0.864162i | \(0.667849\pi\) | |||||||
\(572\) | − | 30.9974i | − | 1.29607i | ||||||
\(573\) | − | 14.9550i | − | 0.624754i | ||||||
\(574\) | −21.0554 | −0.878835 | ||||||||
\(575\) | −1.74603 | + | 1.85058i | −0.0728143 | + | 0.0771746i | ||||
\(576\) | −16.6146 | −0.692275 | ||||||||
\(577\) | 31.5181i | 1.31211i | 0.754711 | + | 0.656057i | \(0.227777\pi\) | ||||
−0.754711 | + | 0.656057i | \(0.772223\pi\) | |||||||
\(578\) | 43.9009i | 1.82604i | ||||||||
\(579\) | 30.3130 | 1.25976 | ||||||||
\(580\) | 2.48466 | − | 6.25402i | 0.103170 | − | 0.259684i | ||||
\(581\) | −7.22031 | −0.299549 | ||||||||
\(582\) | 74.5412i | 3.08983i | ||||||||
\(583\) | 12.5706i | 0.520621i | ||||||||
\(584\) | −6.32216 | −0.261613 | ||||||||
\(585\) | −36.0034 | − | 14.3038i | −1.48856 | − | 0.591389i | ||||
\(586\) | −1.92775 | −0.0796348 | ||||||||
\(587\) | − | 0.243299i | − | 0.0100420i | −0.999987 | − | 0.00502101i | \(-0.998402\pi\) | ||
0.999987 | − | 0.00502101i | \(-0.00159824\pi\) | |||||||
\(588\) | − | 20.5340i | − | 0.846807i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 9.05550 | + | 3.59766i | 0.372809 | + | 0.148113i | ||||
\(591\) | −8.29680 | −0.341285 | ||||||||
\(592\) | − | 13.9235i | − | 0.572251i | ||||||
\(593\) | 38.5061i | 1.58126i | 0.612296 | + | 0.790628i | \(0.290246\pi\) | ||||
−0.612296 | + | 0.790628i | \(0.709754\pi\) | |||||||
\(594\) | −2.32041 | −0.0952076 | ||||||||
\(595\) | −7.59772 | + | 19.1239i | −0.311476 | + | 0.784002i | ||||
\(596\) | −15.5790 | −0.638140 | ||||||||
\(597\) | 2.09101i | 0.0855792i | ||||||||
\(598\) | 6.03425i | 0.246759i | ||||||||
\(599\) | −14.3109 | −0.584728 | −0.292364 | − | 0.956307i | \(-0.594442\pi\) | ||||
−0.292364 | + | 0.956307i | \(0.594442\pi\) | |||||||
\(600\) | −4.28162 | − | 4.03971i | −0.174796 | − | 0.164921i | ||||
\(601\) | 36.8537 | 1.50329 | 0.751647 | − | 0.659566i | \(-0.229260\pi\) | ||||
0.751647 | + | 0.659566i | \(0.229260\pi\) | |||||||
\(602\) | − | 19.5272i | − | 0.795870i | ||||||
\(603\) | 28.3767i | 1.15559i | ||||||||
\(604\) | −2.47551 | −0.100727 | ||||||||
\(605\) | 2.16280 | − | 5.44389i | 0.0879304 | − | 0.221326i | ||||
\(606\) | −29.1656 | −1.18477 | ||||||||
\(607\) | 45.1585i | 1.83293i | 0.400119 | + | 0.916463i | \(0.368969\pi\) | ||||
−0.400119 | + | 0.916463i | \(0.631031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.07237 | −0.246065 | ||||||||
\(610\) | −25.3207 | − | 10.0597i | −1.02521 | − | 0.407304i | ||||
\(611\) | −1.94080 | −0.0785164 | ||||||||
\(612\) | − | 31.1452i | − | 1.25897i | ||||||
\(613\) | − | 12.8540i | − | 0.519167i | −0.965721 | − | 0.259583i | \(-0.916415\pi\) | ||
0.965721 | − | 0.259583i | \(-0.0835852\pi\) | |||||||
\(614\) | −19.0990 | −0.770774 | ||||||||
\(615\) | 37.3462 | + | 14.8372i | 1.50594 | + | 0.598295i | ||||
\(616\) | −2.06250 | −0.0831004 | ||||||||
\(617\) | 42.2758i | 1.70196i | 0.525199 | + | 0.850979i | \(0.323991\pi\) | ||||
−0.525199 | + | 0.850979i | \(0.676009\pi\) | |||||||
\(618\) | − | 37.0783i | − | 1.49151i | ||||||
\(619\) | −25.2048 | −1.01307 | −0.506533 | − | 0.862221i | \(-0.669073\pi\) | ||||
−0.506533 | + | 0.862221i | \(0.669073\pi\) | |||||||
\(620\) | 12.1879 | − | 30.6776i | 0.489478 | − | 1.23204i | ||||
\(621\) | 0.210678 | 0.00845423 | ||||||||
\(622\) | − | 0.809614i | − | 0.0324626i | ||||||
\(623\) | − | 7.82233i | − | 0.313395i | ||||||
\(624\) | −65.6628 | −2.62861 | ||||||||
\(625\) | 1.45231 | + | 24.9578i | 0.0580926 | + | 0.998311i | ||||
\(626\) | 13.2846 | 0.530960 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.65535i | 0.305482i | ||||||||
\(629\) | 19.7513 | 0.787538 | ||||||||
\(630\) | 6.60514 | − | 16.6255i | 0.263155 | − | 0.662376i | ||||
\(631\) | 1.49432 | 0.0594880 | 0.0297440 | − | 0.999558i | \(-0.490531\pi\) | ||||
0.0297440 | + | 0.999558i | \(0.490531\pi\) | |||||||
\(632\) | − | 7.15536i | − | 0.284625i | ||||||
\(633\) | 19.2643i | 0.765686i | ||||||||
\(634\) | 23.0878 | 0.916936 | ||||||||
\(635\) | 24.8948 | + | 9.89044i | 0.987919 | + | 0.392490i | ||||
\(636\) | −18.3262 | −0.726683 | ||||||||
\(637\) | − | 29.8024i | − | 1.18081i | ||||||
\(638\) | 9.64863i | 0.381993i | ||||||||
\(639\) | −18.7690 | −0.742491 | ||||||||
\(640\) | −8.04277 | − | 3.19531i | −0.317918 | − | 0.126306i | ||||
\(641\) | −6.57587 | −0.259731 | −0.129866 | − | 0.991532i | \(-0.541455\pi\) | ||||
−0.129866 | + | 0.991532i | \(0.541455\pi\) | |||||||
\(642\) | − | 81.2485i | − | 3.20662i | ||||||
\(643\) | − | 4.60673i | − | 0.181672i | −0.995866 | − | 0.0908359i | \(-0.971046\pi\) | ||
0.995866 | − | 0.0908359i | \(-0.0289539\pi\) | |||||||
\(644\) | −1.29961 | −0.0512116 | ||||||||
\(645\) | −13.7604 | + | 34.6356i | −0.541814 | + | 1.36378i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.53706i | 0.139056i | 0.997580 | + | 0.0695281i | \(0.0221494\pi\) | ||||
−0.997580 | + | 0.0695281i | \(0.977851\pi\) | |||||||
\(648\) | 4.62544i | 0.181705i | ||||||||
\(649\) | −6.51592 | −0.255772 | ||||||||
\(650\) | 43.1270 | + | 40.6903i | 1.69158 | + | 1.59601i | ||||
\(651\) | −29.7866 | −1.16743 | ||||||||
\(652\) | − | 5.41493i | − | 0.212065i | ||||||
\(653\) | − | 48.6489i | − | 1.90378i | −0.306444 | − | 0.951889i | \(-0.599139\pi\) | ||
0.306444 | − | 0.951889i | \(-0.400861\pi\) | |||||||
\(654\) | 40.5019 | 1.58375 | ||||||||
\(655\) | 6.64403 | − | 16.7234i | 0.259604 | − | 0.653437i | ||||
\(656\) | 33.0538 | 1.29053 | ||||||||
\(657\) | 36.6699i | 1.43063i | ||||||||
\(658\) | − | 0.896215i | − | 0.0349381i | ||||||
\(659\) | 21.2450 | 0.827588 | 0.413794 | − | 0.910371i | \(-0.364203\pi\) | ||||
0.413794 | + | 0.910371i | \(0.364203\pi\) | |||||||
\(660\) | −25.3886 | − | 10.0866i | −0.988251 | − | 0.392622i | ||||
\(661\) | 14.7872 | 0.575154 | 0.287577 | − | 0.957757i | \(-0.407150\pi\) | ||||
0.287577 | + | 0.957757i | \(0.407150\pi\) | |||||||
\(662\) | − | 15.4280i | − | 0.599625i | ||||||
\(663\) | − | 93.1469i | − | 3.61753i | ||||||
\(664\) | 2.41000 | 0.0935262 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −17.1710 | −0.665363 | ||||||||
\(667\) | − | 0.876033i | − | 0.0339201i | ||||||
\(668\) | 5.69364i | 0.220294i | ||||||||
\(669\) | 36.9163 | 1.42727 | ||||||||
\(670\) | 16.0354 | − | 40.3620i | 0.619501 | − | 1.55932i | ||||
\(671\) | 18.2196 | 0.703361 | ||||||||
\(672\) | − | 26.8814i | − | 1.03697i | ||||||
\(673\) | − | 6.36313i | − | 0.245280i | −0.992451 | − | 0.122640i | \(-0.960864\pi\) | ||
0.992451 | − | 0.122640i | \(-0.0391361\pi\) | |||||||
\(674\) | −7.83345 | −0.301733 | ||||||||
\(675\) | 1.42065 | − | 1.50572i | 0.0546809 | − | 0.0579553i | ||||
\(676\) | 42.8620 | 1.64854 | ||||||||
\(677\) | 45.6873i | 1.75591i | 0.478746 | + | 0.877953i | \(0.341091\pi\) | ||||
−0.478746 | + | 0.877953i | \(0.658909\pi\) | |||||||
\(678\) | 46.1313i | 1.77166i | ||||||||
\(679\) | −23.3003 | −0.894184 | ||||||||
\(680\) | 2.53598 | − | 6.38319i | 0.0972502 | − | 0.244784i | ||||
\(681\) | 17.8430 | 0.683744 | ||||||||
\(682\) | 47.3291i | 1.81232i | ||||||||
\(683\) | 15.8141i | 0.605109i | 0.953132 | + | 0.302554i | \(0.0978394\pi\) | ||||
−0.953132 | + | 0.302554i | \(0.902161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.52415 | + | 2.59198i | 0.249275 | + | 0.0990343i | ||||
\(686\) | 33.5616 | 1.28139 | ||||||||
\(687\) | 2.42738i | 0.0926102i | ||||||||
\(688\) | 30.6548i | 1.16870i | ||||||||
\(689\) | −26.5981 | −1.01331 | ||||||||
\(690\) | 4.94239 | + | 1.96356i | 0.188154 | + | 0.0747515i | ||||
\(691\) | −35.2478 | −1.34089 | −0.670444 | − | 0.741960i | \(-0.733896\pi\) | ||||
−0.670444 | + | 0.741960i | \(0.733896\pi\) | |||||||
\(692\) | 18.3908i | 0.699113i | ||||||||
\(693\) | 11.9629i | 0.454435i | ||||||||
\(694\) | 6.31580 | 0.239744 | ||||||||
\(695\) | 15.4749 | − | 38.9511i | 0.586996 | − | 1.47750i | ||||
\(696\) | 2.02684 | 0.0768273 | ||||||||
\(697\) | 46.8890i | 1.77605i | ||||||||
\(698\) | − | 12.2401i | − | 0.463295i | ||||||
\(699\) | 41.0781 | 1.55372 | ||||||||
\(700\) | −8.76353 | + | 9.28832i | −0.331230 | + | 0.351065i | ||||
\(701\) | −51.0439 | −1.92790 | −0.963951 | − | 0.266079i | \(-0.914272\pi\) | ||||
−0.963951 | + | 0.266079i | \(0.914272\pi\) | |||||||
\(702\) | − | 4.90976i | − | 0.185307i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −17.0045 | −0.640880 | ||||||||
\(705\) | −0.631542 | + | 1.58963i | −0.0237852 | + | 0.0598688i | ||||
\(706\) | −12.3033 | −0.463041 | ||||||||
\(707\) | − | 9.11667i | − | 0.342867i | ||||||
\(708\) | − | 9.49934i | − | 0.357007i | ||||||
\(709\) | −1.76418 | −0.0662552 | −0.0331276 | − | 0.999451i | \(-0.510547\pi\) | ||||
−0.0331276 | + | 0.999451i | \(0.510547\pi\) | |||||||
\(710\) | 26.6963 | + | 10.6062i | 1.00190 | + | 0.398043i | ||||
\(711\) | −41.5026 | −1.55647 | ||||||||
\(712\) | 2.61095i | 0.0978493i | ||||||||
\(713\) | − | 4.29717i | − | 0.160930i | ||||||
\(714\) | 43.0130 | 1.60972 | ||||||||
\(715\) | −36.8482 | − | 14.6394i | −1.37805 | − | 0.547484i | ||||
\(716\) | 25.1472 | 0.939793 | ||||||||
\(717\) | − | 20.3015i | − | 0.758172i | ||||||
\(718\) | − | 5.24195i | − | 0.195628i | ||||||
\(719\) | 51.5725 | 1.92333 | 0.961665 | − | 0.274227i | \(-0.0884220\pi\) | ||||
0.961665 | + | 0.274227i | \(0.0884220\pi\) | |||||||
\(720\) | −10.3691 | + | 26.0995i | −0.386433 | + | 0.972673i | ||||
\(721\) | 11.5901 | 0.431637 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.5815i | 1.17453i | ||||||||
\(724\) | 14.2211 | 0.528523 | ||||||||
\(725\) | −6.26103 | − | 5.90729i | −0.232529 | − | 0.219391i | ||||
\(726\) | −12.2443 | −0.454428 | ||||||||
\(727\) | 39.7695i | 1.47497i | 0.675364 | + | 0.737484i | \(0.263986\pi\) | ||||
−0.675364 | + | 0.737484i | \(0.736014\pi\) | |||||||
\(728\) | − | 4.36404i | − | 0.161742i | ||||||
\(729\) | 23.8299 | 0.882589 | ||||||||
\(730\) | 20.7218 | − | 52.1579i | 0.766948 | − | 1.93045i | ||||
\(731\) | −43.4858 | −1.60838 | ||||||||
\(732\) | 26.5618i | 0.981751i | ||||||||
\(733\) | 32.2476i | 1.19109i | 0.803321 | + | 0.595547i | \(0.203065\pi\) | ||||
−0.803321 | + | 0.595547i | \(0.796935\pi\) | |||||||
\(734\) | −45.0010 | −1.66102 | ||||||||
\(735\) | −24.4098 | − | 9.69777i | −0.900370 | − | 0.357708i | ||||
\(736\) | 3.87805 | 0.142947 | ||||||||
\(737\) | 29.0426i | 1.06980i | ||||||||
\(738\) | − | 40.7633i | − | 1.50052i | ||||||
\(739\) | 33.2127 | 1.22175 | 0.610875 | − | 0.791727i | \(-0.290818\pi\) | ||||
0.610875 | + | 0.791727i | \(0.290818\pi\) | |||||||
\(740\) | 11.3910 | + | 4.52554i | 0.418742 | + | 0.166362i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 12.2824i | − | 0.450900i | ||||||
\(743\) | 21.0511i | 0.772290i | 0.922438 | + | 0.386145i | \(0.126194\pi\) | ||||
−0.922438 | + | 0.386145i | \(0.873806\pi\) | |||||||
\(744\) | 9.94220 | 0.364499 | ||||||||
\(745\) | −7.35763 | + | 18.5196i | −0.269563 | + | 0.678504i | ||||
\(746\) | −12.0958 | −0.442860 | ||||||||
\(747\) | − | 13.9785i | − | 0.511448i | ||||||
\(748\) | − | 31.8760i | − | 1.16550i | ||||||
\(749\) | 25.3969 | 0.927983 | ||||||||
\(750\) | 47.3613 | − | 22.0827i | 1.72939 | − | 0.806345i | ||||
\(751\) | −9.54033 | −0.348132 | −0.174066 | − | 0.984734i | \(-0.555691\pi\) | ||||
−0.174066 | + | 0.984734i | \(0.555691\pi\) | |||||||
\(752\) | 1.40692i | 0.0513052i | ||||||||
\(753\) | 33.0138i | 1.20309i | ||||||||
\(754\) | −20.4155 | −0.743490 | ||||||||
\(755\) | −1.16913 | + | 2.94277i | −0.0425490 | + | 0.107098i | ||||
\(756\) | 1.05742 | 0.0384581 | ||||||||
\(757\) | 36.0653i | 1.31082i | 0.755275 | + | 0.655408i | \(0.227503\pi\) | ||||
−0.755275 | + | 0.655408i | \(0.772497\pi\) | |||||||
\(758\) | − | 25.2589i | − | 0.917445i | ||||||
\(759\) | −3.55632 | −0.129086 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.0993 | −0.474848 | −0.237424 | − | 0.971406i | \(-0.576303\pi\) | ||||
−0.237424 | + | 0.971406i | \(0.576303\pi\) | |||||||
\(762\) | − | 55.9928i | − | 2.02841i | ||||||
\(763\) | 12.6602i | 0.458331i | ||||||||
\(764\) | 10.8287 | 0.391769 | ||||||||
\(765\) | −37.0239 | − | 14.7092i | −1.33860 | − | 0.531813i | ||||
\(766\) | −3.55730 | −0.128530 | ||||||||
\(767\) | − | 13.7870i | − | 0.497821i | ||||||
\(768\) | 46.4519i | 1.67619i | ||||||||
\(769\) | 43.3213 | 1.56221 | 0.781103 | − | 0.624402i | \(-0.214657\pi\) | ||||
0.781103 | + | 0.624402i | \(0.214657\pi\) | |||||||
\(770\) | 6.76014 | − | 17.0156i | 0.243618 | − | 0.613201i | ||||
\(771\) | −7.10861 | −0.256010 | ||||||||
\(772\) | 21.9492i | 0.789970i | ||||||||
\(773\) | 2.58122i | 0.0928401i | 0.998922 | + | 0.0464200i | \(0.0147813\pi\) | ||||
−0.998922 | + | 0.0464200i | \(0.985219\pi\) | |||||||
\(774\) | 37.8048 | 1.35886 | ||||||||
\(775\) | −30.7120 | − | 28.9768i | −1.10321 | − | 1.04088i | ||||
\(776\) | 7.77721 | 0.279186 | ||||||||
\(777\) | − | 11.0602i | − | 0.396781i | ||||||
\(778\) | 36.1918i | 1.29754i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 21.3423 | − | 53.7198i | 0.764178 | − | 1.92348i | ||||
\(781\) | −19.2094 | −0.687368 | ||||||||
\(782\) | 6.20529i | 0.221901i | ||||||||
\(783\) | 0.712783i | 0.0254728i | ||||||||
\(784\) | −21.6043 | −0.771582 | ||||||||
\(785\) | 9.10032 | + | 3.61546i | 0.324804 | + | 0.129041i | ||||
\(786\) | −37.6139 | −1.34164 | ||||||||
\(787\) | − | 32.3874i | − | 1.15449i | −0.816572 | − | 0.577243i | \(-0.804128\pi\) | ||
0.816572 | − | 0.577243i | \(-0.195872\pi\) | |||||||
\(788\) | − | 6.00761i | − | 0.214012i | ||||||
\(789\) | −31.8453 | −1.13372 | ||||||||
\(790\) | 59.0318 | + | 23.4527i | 2.10026 | + | 0.834410i | ||||
\(791\) | −14.4199 | −0.512711 | ||||||||
\(792\) | − | 3.99301i | − | 0.141885i | ||||||
\(793\) | 38.5509i | 1.36898i | ||||||||
\(794\) | −48.3286 | −1.71512 | ||||||||
\(795\) | −8.65510 | + | 21.7854i | −0.306965 | + | 0.772647i | ||||
\(796\) | −1.51407 | −0.0536648 | ||||||||
\(797\) | − | 0.660265i | − | 0.0233878i | −0.999932 | − | 0.0116939i | \(-0.996278\pi\) | ||
0.999932 | − | 0.0116939i | \(-0.00372236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.99581 | −0.0706067 | ||||||||
\(800\) | 26.1506 | − | 27.7166i | 0.924563 | − | 0.979928i | ||||
\(801\) | 15.1441 | 0.535089 | ||||||||
\(802\) | − | 49.2517i | − | 1.73914i | ||||||
\(803\) | 37.5304i | 1.32442i | ||||||||
\(804\) | −42.3402 | −1.49322 | ||||||||
\(805\) | −0.613777 | + | 1.54491i | −0.0216328 | + | 0.0544509i | ||||
\(806\) | −100.144 | −3.52741 | ||||||||
\(807\) | − | 74.8184i | − | 2.63373i | ||||||
\(808\) | 3.04297i | 0.107051i | ||||||||
\(809\) | 39.0366 | 1.37246 | 0.686228 | − | 0.727387i | \(-0.259265\pi\) | ||||
0.686228 | + | 0.727387i | \(0.259265\pi\) | |||||||
\(810\) | −38.1600 | − | 15.1606i | −1.34080 | − | 0.532688i | ||||
\(811\) | −29.9982 | −1.05338 | −0.526690 | − | 0.850057i | \(-0.676567\pi\) | ||||
−0.526690 | + | 0.850057i | \(0.676567\pi\) | |||||||
\(812\) | − | 4.39693i | − | 0.154302i | ||||||
\(813\) | − | 18.1254i | − | 0.635684i | ||||||
\(814\) | −17.5739 | −0.615966 | ||||||||
\(815\) | −6.43701 | − | 2.55736i | −0.225479 | − | 0.0895803i | ||||
\(816\) | −67.5239 | −2.36381 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 52.0188i | − | 1.81880i | ||||||
\(819\) | −25.3124 | −0.884487 | ||||||||
\(820\) | −10.7435 | + | 27.0419i | −0.375178 | + | 0.944343i | ||||
\(821\) | −36.5733 | −1.27642 | −0.638208 | − | 0.769864i | \(-0.720324\pi\) | ||||
−0.638208 | + | 0.769864i | \(0.720324\pi\) | |||||||
\(822\) | − | 14.6740i | − | 0.511814i | ||||||
\(823\) | − | 1.19784i | − | 0.0417542i | −0.999782 | − | 0.0208771i | \(-0.993354\pi\) | ||
0.999782 | − | 0.0208771i | \(-0.00664588\pi\) | |||||||
\(824\) | −3.86855 | −0.134767 | ||||||||
\(825\) | −23.9810 | + | 25.4171i | −0.834913 | + | 0.884909i | ||||
\(826\) | 6.36652 | 0.221520 | ||||||||
\(827\) | 0.0989534i | 0.00344095i | 0.999999 | + | 0.00172047i | \(0.000547644\pi\) | ||||
−0.999999 | + | 0.00172047i | \(0.999452\pi\) | |||||||
\(828\) | − | 2.51604i | − | 0.0874385i | ||||||
\(829\) | −3.38031 | −0.117403 | −0.0587015 | − | 0.998276i | \(-0.518696\pi\) | ||||
−0.0587015 | + | 0.998276i | \(0.518696\pi\) | |||||||
\(830\) | −7.89913 | + | 19.8826i | −0.274183 | + | 0.690133i | ||||
\(831\) | −23.1522 | −0.803140 | ||||||||
\(832\) | − | 35.9798i | − | 1.24738i | ||||||
\(833\) | − | 30.6471i | − | 1.06186i | ||||||
\(834\) | −87.6080 | −3.03362 | ||||||||
\(835\) | 6.76833 | + | 2.68899i | 0.234228 | + | 0.0930563i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.49639i | 0.120853i | ||||||||
\(838\) | 40.7389i | 1.40730i | ||||||||
\(839\) | 11.7241 | 0.404759 | 0.202380 | − | 0.979307i | \(-0.435133\pi\) | ||||
0.202380 | + | 0.979307i | \(0.435133\pi\) | |||||||
\(840\) | −3.57440 | − | 1.42007i | −0.123328 | − | 0.0489971i | ||||
\(841\) | −26.0361 | −0.897798 | ||||||||
\(842\) | − | 4.89692i | − | 0.168759i | ||||||
\(843\) | − | 39.8043i | − | 1.37093i | ||||||
\(844\) | −13.9490 | −0.480145 | ||||||||
\(845\) | 20.2428 | − | 50.9523i | 0.696374 | − | 1.75281i | ||||
\(846\) | 1.73508 | 0.0596532 | ||||||||
\(847\) | − | 3.82736i | − | 0.131510i | ||||||
\(848\) | 19.2815i | 0.662129i | ||||||||
\(849\) | −70.9009 | −2.43331 | ||||||||
\(850\) | 44.3493 | + | 41.8436i | 1.52117 | + | 1.43523i | ||||
\(851\) | 1.59560 | 0.0546964 | ||||||||
\(852\) | − | 28.0048i | − | 0.959429i | ||||||
\(853\) | 11.8398i | 0.405389i | 0.979242 | + | 0.202694i | \(0.0649698\pi\) | ||||
−0.979242 | + | 0.202694i | \(0.935030\pi\) | |||||||
\(854\) | −17.8019 | −0.609168 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.47701 | −0.289738 | ||||||||
\(857\) | − | 52.7265i | − | 1.80110i | −0.434749 | − | 0.900552i | \(-0.643163\pi\) | ||
0.434749 | − | 0.900552i | \(-0.356837\pi\) | |||||||
\(858\) | 82.8783i | 2.82942i | ||||||||
\(859\) | 5.72563 | 0.195356 | 0.0976779 | − | 0.995218i | \(-0.468858\pi\) | ||||
0.0976779 | + | 0.995218i | \(0.468858\pi\) | |||||||
\(860\) | −25.0792 | − | 9.96371i | −0.855194 | − | 0.339760i | ||||
\(861\) | 26.2564 | 0.894817 | ||||||||
\(862\) | 58.5084i | 1.99280i | ||||||||
\(863\) | 10.4374i | 0.355293i | 0.984094 | + | 0.177646i | \(0.0568483\pi\) | ||||
−0.984094 | + | 0.177646i | \(0.943152\pi\) | |||||||
\(864\) | −3.15537 | −0.107348 | ||||||||
\(865\) | 21.8621 | + | 8.68558i | 0.743333 | + | 0.295319i | ||||
\(866\) | −25.3152 | −0.860244 | ||||||||
\(867\) | − | 54.7451i | − | 1.85924i | ||||||
\(868\) | − | 21.5681i | − | 0.732068i | ||||||
\(869\) | −42.4765 | −1.44092 | ||||||||
\(870\) | −6.64327 | + | 16.7215i | −0.225228 | + | 0.566911i | ||||
\(871\) | −61.4513 | −2.08220 | ||||||||
\(872\) | − | 4.22575i | − | 0.143102i | ||||||
\(873\) | − | 45.1095i | − | 1.52673i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.90268 | + | 14.8044i | 0.233353 | + | 0.500478i | ||||
\(876\) | −54.7143 | −1.84863 | ||||||||
\(877\) | 16.9211i | 0.571386i | 0.958321 | + | 0.285693i | \(0.0922238\pi\) | ||||
−0.958321 | + | 0.285693i | \(0.907776\pi\) | |||||||
\(878\) | − | 74.2733i | − | 2.50660i | ||||||
\(879\) | 2.40394 | 0.0810829 | ||||||||
\(880\) | −10.6124 | + | 26.7120i | −0.357744 | + | 0.900461i | ||||
\(881\) | −28.2082 | −0.950360 | −0.475180 | − | 0.879889i | \(-0.657617\pi\) | ||||
−0.475180 | + | 0.879889i | \(0.657617\pi\) | |||||||
\(882\) | 26.6433i | 0.897128i | ||||||||
\(883\) | − | 2.89071i | − | 0.0972800i | −0.998816 | − | 0.0486400i | \(-0.984511\pi\) | ||
0.998816 | − | 0.0486400i | \(-0.0154887\pi\) | |||||||
\(884\) | 67.4465 | 2.26847 | ||||||||
\(885\) | −11.2924 | − | 4.48634i | −0.379589 | − | 0.150807i | ||||
\(886\) | −22.3332 | −0.750299 | ||||||||
\(887\) | − | 32.9315i | − | 1.10573i | −0.833270 | − | 0.552866i | \(-0.813534\pi\) | ||
0.833270 | − | 0.552866i | \(-0.186466\pi\) | |||||||
\(888\) | 3.69168i | 0.123885i | ||||||||
\(889\) | 17.5024 | 0.587013 | ||||||||
\(890\) | −21.5403 | − | 8.55775i | −0.722034 | − | 0.286857i | ||||
\(891\) | 27.4581 | 0.919882 | ||||||||
\(892\) | 26.7306i | 0.895007i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 41.6538 | 1.39311 | ||||||||
\(895\) | 11.8765 | − | 29.8937i | 0.396987 | − | 0.999238i | ||||
\(896\) | −5.65451 | −0.188904 | ||||||||
\(897\) | − | 7.52481i | − | 0.251246i | ||||||
\(898\) | 39.0914i | 1.30450i | ||||||||
\(899\) | 14.5385 | 0.484887 | ||||||||
\(900\) | −17.9822 | − | 16.9662i | −0.599407 | − | 0.565541i | ||||
\(901\) | −27.3520 | −0.911228 | ||||||||
\(902\) | − | 41.7199i | − | 1.38912i | ||||||
\(903\) | 24.3508i | 0.810343i | ||||||||
\(904\) | 4.81308 | 0.160081 | ||||||||
\(905\) | 6.71633 | − | 16.9054i | 0.223258 | − | 0.561954i | ||||
\(906\) | 6.61881 | 0.219895 | ||||||||
\(907\) | 22.8800i | 0.759717i | 0.925045 | + | 0.379859i | \(0.124027\pi\) | ||||
−0.925045 | + | 0.379859i | \(0.875973\pi\) | |||||||
\(908\) | 12.9199i | 0.428761i | ||||||||
\(909\) | 17.6499 | 0.585410 | ||||||||
\(910\) | 36.0034 | + | 14.3038i | 1.19350 | + | 0.474166i | ||||
\(911\) | 11.6167 | 0.384880 | 0.192440 | − | 0.981309i | \(-0.438360\pi\) | ||||
0.192440 | + | 0.981309i | \(0.438360\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 14.3066i | − | 0.473478i | ||||||
\(914\) | −34.2454 | −1.13274 | ||||||||
\(915\) | 31.5754 | + | 12.5446i | 1.04385 | + | 0.414711i | ||||
\(916\) | −1.75763 | −0.0580738 | ||||||||
\(917\) | − | 11.7575i | − | 0.388266i | ||||||
\(918\) | − | 5.04892i | − | 0.166639i | ||||||
\(919\) | 12.4353 | 0.410203 | 0.205101 | − | 0.978741i | \(-0.434248\pi\) | ||||
0.205101 | + | 0.978741i | \(0.434248\pi\) | |||||||
\(920\) | 0.204867 | − | 0.515662i | 0.00675427 | − | 0.0170009i | ||||
\(921\) | 23.8168 | 0.784790 | ||||||||
\(922\) | − | 48.3305i | − | 1.59168i | ||||||
\(923\) | − | 40.6453i | − | 1.33786i | ||||||
\(924\) | −17.8496 | −0.587209 | ||||||||
\(925\) | 10.7595 | − | 11.4038i | 0.353770 | − | 0.374954i | ||||
\(926\) | −33.6954 | −1.10730 | ||||||||
\(927\) | 22.4384i | 0.736974i | ||||||||
\(928\) | 13.1205i | 0.430703i | ||||||||
\(929\) | 15.7247 | 0.515910 | 0.257955 | − | 0.966157i | \(-0.416951\pi\) | ||||
0.257955 | + | 0.966157i | \(0.416951\pi\) | |||||||
\(930\) | −32.5870 | + | 82.0233i | −1.06857 | + | 2.68965i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.7441i | 0.974301i | ||||||||
\(933\) | 1.00960i | 0.0330529i | ||||||||
\(934\) | 28.4219 | 0.929993 | ||||||||
\(935\) | −37.8927 | − | 15.0544i | −1.23922 | − | 0.492331i | ||||
\(936\) | 8.44881 | 0.276158 | ||||||||
\(937\) | − | 16.4857i | − | 0.538563i | −0.963061 | − | 0.269282i | \(-0.913214\pi\) | ||
0.963061 | − | 0.269282i | \(-0.0867862\pi\) | |||||||
\(938\) | − | 28.3767i | − | 0.926533i | ||||||
\(939\) | −16.5661 | −0.540616 | ||||||||
\(940\) | −1.15103 | − | 0.457291i | −0.0375424 | − | 0.0149152i | ||||
\(941\) | −13.7308 | −0.447611 | −0.223806 | − | 0.974634i | \(-0.571848\pi\) | ||||
−0.223806 | + | 0.974634i | \(0.571848\pi\) | |||||||
\(942\) | − | 20.4683i | − | 0.666892i | ||||||
\(943\) | 3.78789i | 0.123351i | ||||||||
\(944\) | −9.99448 | −0.325293 | ||||||||
\(945\) | 0.499399 | − | 1.25701i | 0.0162454 | − | 0.0408907i | ||||
\(946\) | 38.6919 | 1.25798 | ||||||||
\(947\) | − | 45.7355i | − | 1.48620i | −0.669179 | − | 0.743101i | \(-0.733354\pi\) | ||
0.669179 | − | 0.743101i | \(-0.266646\pi\) | |||||||
\(948\) | − | 61.9251i | − | 2.01123i | ||||||
\(949\) | −79.4106 | −2.57778 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.7909 | −0.933610 | ||||||||
\(952\) | − | 4.48774i | − | 0.145448i | ||||||
\(953\) | 32.7211i | 1.05994i | 0.848016 | + | 0.529971i | \(0.177797\pi\) | ||||
−0.848016 | + | 0.529971i | \(0.822203\pi\) | |||||||
\(954\) | 23.7787 | 0.769865 | ||||||||
\(955\) | 5.11418 | − | 12.8727i | 0.165491 | − | 0.416550i | ||||
\(956\) | 14.7000 | 0.475433 | ||||||||
\(957\) | − | 12.0320i | − | 0.388939i | ||||||
\(958\) | 5.57961i | 0.180269i | ||||||||
\(959\) | 4.58684 | 0.148117 | ||||||||
\(960\) | −29.4695 | − | 11.7079i | −0.951124 | − | 0.377872i | ||||
\(961\) | 40.3153 | 1.30049 | ||||||||
\(962\) | − | 37.1847i | − | 1.19888i | ||||||
\(963\) | 49.1685i | 1.58443i | ||||||||
\(964\) | −22.8678 | −0.736522 | ||||||||
\(965\) | 26.0922 | + | 10.3662i | 0.839938 | + | 0.333699i | ||||
\(966\) | 3.47478 | 0.111799 | ||||||||
\(967\) | − | 11.4909i | − | 0.369523i | −0.982783 | − | 0.184761i | \(-0.940849\pi\) | ||
0.982783 | − | 0.184761i | \(-0.0591512\pi\) | |||||||
\(968\) | 1.27750i | 0.0410604i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.4909 | + | 64.1621i | −0.818465 | + | 2.06012i | ||||
\(971\) | −54.4334 | −1.74685 | −0.873425 | − | 0.486959i | \(-0.838106\pi\) | ||||
−0.873425 | + | 0.486959i | \(0.838106\pi\) | |||||||
\(972\) | 37.8590i | 1.21433i | ||||||||
\(973\) | − | 27.3848i | − | 0.877917i | ||||||
\(974\) | −44.3526 | −1.42115 | ||||||||
\(975\) | −53.7800 | − | 50.7415i | −1.72234 | − | 1.62503i | ||||
\(976\) | 27.9463 | 0.894539 | ||||||||
\(977\) | − | 23.6834i | − | 0.757698i | −0.925459 | − | 0.378849i | \(-0.876320\pi\) | ||
0.925459 | − | 0.378849i | \(-0.123680\pi\) | |||||||
\(978\) | 14.4780i | 0.462955i | ||||||||
\(979\) | 15.4994 | 0.495364 | ||||||||
\(980\) | 7.02203 | − | 17.6748i | 0.224311 | − | 0.564602i | ||||
\(981\) | −24.5103 | −0.782552 | ||||||||
\(982\) | 41.0496i | 1.30994i | ||||||||
\(983\) | 4.93140i | 0.157287i | 0.996903 | + | 0.0786436i | \(0.0250589\pi\) | ||||
−0.996903 | + | 0.0786436i | \(0.974941\pi\) | |||||||
\(984\) | −8.76391 | −0.279383 | ||||||||
\(985\) | −7.14156 | − | 2.83727i | −0.227549 | − | 0.0904029i | ||||
\(986\) | −20.9942 | −0.668592 | ||||||||
\(987\) | 1.11760i | 0.0355735i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.51297 | −0.111706 | ||||||||
\(990\) | 32.9423 | + | 13.0877i | 1.04698 | + | 0.415953i | ||||
\(991\) | −12.3542 | −0.392445 | −0.196223 | − | 0.980559i | \(-0.562867\pi\) | ||||
−0.196223 | + | 0.980559i | \(0.562867\pi\) | |||||||
\(992\) | 64.3596i | 2.04342i | ||||||||
\(993\) | 19.2389i | 0.610530i | ||||||||
\(994\) | 18.7690 | 0.595317 | ||||||||
\(995\) | −0.715064 | + | 1.79986i | −0.0226691 | + | 0.0570593i | ||||
\(996\) | 20.8571 | 0.660881 | ||||||||
\(997\) | 33.3639i | 1.05664i | 0.849044 | + | 0.528322i | \(0.177179\pi\) | ||||
−0.849044 | + | 0.528322i | \(0.822821\pi\) | |||||||
\(998\) | − | 70.7032i | − | 2.23807i | ||||||
\(999\) | −1.29826 | −0.0410750 |
(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 | 1805.2.b.j.1084.3 | yes | 16 | |
5.2 | odd | 4 | 9025.2.a.ck.1.14 | 16 | |||
5.3 | odd | 4 | 9025.2.a.ck.1.3 | 16 | |||
5.4 | even | 2 | inner | 1805.2.b.j.1084.14 | yes | 16 | |
19.18 | odd | 2 | 1805.2.b.i.1084.14 | yes | 16 | ||
95.18 | even | 4 | 9025.2.a.cl.1.14 | 16 | |||
95.37 | even | 4 | 9025.2.a.cl.1.3 | 16 | |||
95.94 | odd | 2 | 1805.2.b.i.1084.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.b.i.1084.3 | ✓ | 16 | 95.94 | odd | 2 | ||
1805.2.b.i.1084.14 | yes | 16 | 19.18 | odd | 2 | ||
1805.2.b.j.1084.3 | yes | 16 | 1.1 | even | 1 | trivial | |
1805.2.b.j.1084.14 | yes | 16 | 5.4 | even | 2 | inner | |
9025.2.a.ck.1.3 | 16 | 5.3 | odd | 4 | |||
9025.2.a.ck.1.14 | 16 | 5.2 | odd | 4 | |||
9025.2.a.cl.1.3 | 16 | 95.37 | even | 4 | |||
9025.2.a.cl.1.14 | 16 | 95.18 | even | 4 |