Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(353,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1216.353");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1185.7 | ||
Character | \(\chi\) | \(=\) | 1216.1185 |
Dual form | 1216.2.t.d.353.7 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.495361 | − | 0.285997i | 0.285997 | − | 0.165120i | −0.350138 | − | 0.936698i | \(-0.613865\pi\) |
0.636135 | + | 0.771578i | \(0.280532\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.31453 | − | 1.91364i | 1.48230 | − | 0.855807i | 0.482503 | − | 0.875894i | \(-0.339728\pi\) |
0.999798 | + | 0.0200876i | \(0.00639450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.37943 | −0.899341 | −0.449671 | − | 0.893194i | \(-0.648459\pi\) | ||||
−0.449671 | + | 0.893194i | \(0.648459\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.33641 | + | 2.31473i | −0.445471 | + | 0.771578i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.62170i | − | 0.790473i | −0.918579 | − | 0.395237i | \(-0.870663\pi\) | ||
0.918579 | − | 0.395237i | \(-0.129337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.36594 | + | 0.788626i | 0.378844 | + | 0.218725i | 0.677315 | − | 0.735693i | \(-0.263143\pi\) |
−0.298471 | + | 0.954419i | \(0.596477\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.09459 | − | 1.89589i | 0.282622 | − | 0.489516i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.53509 | + | 2.65885i | 0.372314 | + | 0.644866i | 0.989921 | − | 0.141620i | \(-0.0452312\pi\) |
−0.617607 | + | 0.786487i | \(0.711898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0442721 | − | 4.35867i | 0.0101567 | − | 0.999948i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.17868 | + | 0.680510i | −0.257209 | + | 0.148499i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.47737 | − | 7.75503i | 0.933596 | − | 1.61704i | 0.156477 | − | 0.987682i | \(-0.449986\pi\) |
0.777119 | − | 0.629354i | \(-0.216680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.82405 | − | 8.35551i | 0.964811 | − | 1.67110i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.24482i | 0.624465i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.05237 | + | 4.64904i | 1.49529 | + | 0.863305i | 0.999985 | − | 0.00541604i | \(-0.00172399\pi\) |
0.495302 | + | 0.868721i | \(0.335057\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.38612 | 0.787771 | 0.393885 | − | 0.919160i | \(-0.371131\pi\) | ||||
0.393885 | + | 0.919160i | \(0.371131\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.749798 | − | 1.29869i | −0.130523 | − | 0.226073i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.88669 | + | 4.55338i | −1.33309 | + | 0.769662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.00890i | − | 1.15226i | −0.817359 | − | 0.576128i | \(-0.804563\pi\) | ||
0.817359 | − | 0.576128i | \(-0.195437\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.902177 | 0.144464 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.22065 | − | 10.7745i | −0.971502 | − | 1.68269i | −0.691027 | − | 0.722829i | \(-0.742841\pi\) |
−0.280475 | − | 0.959861i | \(-0.590492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35778 | − | 1.36127i | 0.359559 | − | 0.207591i | −0.309329 | − | 0.950955i | \(-0.600104\pi\) |
0.668887 | + | 0.743364i | \(0.266771\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.2297i | 1.52495i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.15544 | + | 2.00129i | −0.168539 | + | 0.291918i | −0.937906 | − | 0.346889i | \(-0.887238\pi\) |
0.769368 | + | 0.638806i | \(0.220571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.33830 | −0.191185 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.52085 | + | 0.878061i | 0.212961 | + | 0.122953i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.38780 | + | 0.801249i | 0.190630 | + | 0.110060i | 0.592277 | − | 0.805734i | \(-0.298229\pi\) |
−0.401648 | + | 0.915794i | \(0.631562\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.01700 | − | 8.68970i | −0.676492 | − | 1.17172i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.22464 | − | 2.17178i | −0.162207 | − | 0.287659i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4393 | + | 6.02711i | −1.35908 | + | 0.784663i | −0.989499 | − | 0.144537i | \(-0.953831\pi\) |
−0.369577 | + | 0.929200i | \(0.620497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.477247 | + | 0.275539i | 0.0611052 | + | 0.0352791i | 0.530241 | − | 0.847847i | \(-0.322101\pi\) |
−0.469136 | + | 0.883126i | \(0.655435\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.17990 | − | 5.50775i | 0.400630 | − | 0.693912i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.03659 | 0.748747 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.64072 | − | 4.41137i | −0.933463 | − | 0.538935i | −0.0455578 | − | 0.998962i | \(-0.514507\pi\) |
−0.887905 | + | 0.460027i | \(0.847840\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 5.12205i | − | 0.616622i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.63270 | + | 6.29203i | 0.431123 | + | 0.746726i | 0.996970 | − | 0.0777836i | \(-0.0247843\pi\) |
−0.565848 | + | 0.824510i | \(0.691451\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.80857 | − | 3.13253i | −0.211677 | − | 0.366635i | 0.740563 | − | 0.671987i | \(-0.234559\pi\) |
−0.952239 | + | 0.305352i | \(0.901226\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 5.51865i | − | 0.637239i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.23817i | 0.710905i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.99460 | + | 3.45475i | 0.224410 | + | 0.388690i | 0.956142 | − | 0.292903i | \(-0.0946212\pi\) |
−0.731732 | + | 0.681592i | \(0.761288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.08123 | − | 5.33684i | −0.342359 | − | 0.592983i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.25278i | 0.905861i | 0.891546 | + | 0.452930i | \(0.149621\pi\) | ||||
−0.891546 | + | 0.452930i | \(0.850379\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.1762 | + | 5.87522i | 1.10376 | + | 0.637257i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.31844 | 0.570196 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.83103 | + | 8.36758i | −0.512088 | + | 0.886962i | 0.487814 | + | 0.872948i | \(0.337794\pi\) |
−0.999902 | + | 0.0140145i | \(0.995539\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.25016 | − | 1.87648i | −0.340710 | − | 0.196709i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.17271 | − | 1.25442i | 0.225300 | − | 0.130077i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.19420 | − | 14.5317i | −0.840707 | − | 1.49092i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.67320 | + | 11.5583i | 0.677561 | + | 1.17357i | 0.975713 | + | 0.219051i | \(0.0702963\pi\) |
−0.298153 | + | 0.954518i | \(0.596370\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.06854 | + | 3.50367i | 0.609911 | + | 0.352133i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.57668 | − | 0.910298i | −0.156886 | − | 0.0905780i | 0.419502 | − | 0.907754i | \(-0.362205\pi\) |
−0.576388 | + | 0.817176i | \(0.695538\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.94561 | −0.979970 | −0.489985 | − | 0.871731i | \(-0.662998\pi\) | ||||
−0.489985 | + | 0.871731i | \(0.662998\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.60450 | + | 4.51113i | −0.254174 | + | 0.440242i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2581i | 1.28171i | 0.767662 | + | 0.640855i | \(0.221420\pi\) | ||||
−0.767662 | + | 0.640855i | \(0.778580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.54713 | − | 3.77999i | 0.627102 | − | 0.362057i | −0.152527 | − | 0.988299i | \(-0.548741\pi\) |
0.779629 | + | 0.626242i | \(0.215408\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00452 | − | 3.47193i | −0.190261 | − | 0.329541i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.07753 | 0.665798 | 0.332899 | − | 0.942963i | \(-0.391973\pi\) | ||||
0.332899 | + | 0.942963i | \(0.391973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 34.2723i | − | 3.19591i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.65092 | + | 2.10786i | −0.337527 | + | 0.194871i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.65264 | − | 6.32656i | −0.334837 | − | 0.579955i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.12668 | 0.375152 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.16293 | − | 3.55817i | −0.555692 | − | 0.320829i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 17.7896i | − | 1.59115i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.91907 | − | 5.05597i | 0.259025 | − | 0.448645i | −0.706956 | − | 0.707258i | \(-0.749932\pi\) |
0.965981 | + | 0.258613i | \(0.0832654\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.778635 | − | 1.34864i | 0.0685550 | − | 0.118741i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2631 | − | 7.08012i | 1.07143 | − | 0.618593i | 0.142861 | − | 0.989743i | \(-0.454370\pi\) |
0.928573 | + | 0.371150i | \(0.121036\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.105343 | + | 10.3712i | −0.00913436 | + | 0.899295i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.20942 | + | 10.7550i | 0.534422 | + | 0.925646i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.616142 | − | 1.06719i | 0.0526405 | − | 0.0911761i | −0.838504 | − | 0.544895i | \(-0.816570\pi\) |
0.891145 | + | 0.453719i | \(0.149903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.20766 | + | 3.00664i | 0.441708 | + | 0.255020i | 0.704322 | − | 0.709881i | \(-0.251251\pi\) |
−0.262614 | + | 0.964901i | \(0.584585\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.32181i | 0.111317i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.06754 | − | 3.58109i | 0.172897 | − | 0.299466i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 35.5864 | 2.95529 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.662940 | + | 0.382749i | −0.0546784 | + | 0.0315686i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.499112 | − | 0.288162i | 0.0408888 | − | 0.0236072i | −0.479416 | − | 0.877588i | \(-0.659152\pi\) |
0.520305 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2393 | 1.07740 | 0.538700 | − | 0.842498i | \(-0.318916\pi\) | ||||
0.538700 | + | 0.842498i | \(0.318916\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.20604 | −0.663419 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5379 | − | 8.39347i | 1.16771 | − | 0.674180i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3009 | + | 8.83396i | −1.22114 | + | 0.705027i | −0.965162 | − | 0.261655i | \(-0.915732\pi\) |
−0.255981 | + | 0.966682i | \(0.582399\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.916618 | 0.0726925 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6536 | + | 18.4526i | −0.839621 | + | 1.45427i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7739i | 1.47049i | 0.677803 | + | 0.735244i | \(0.262932\pi\) | ||||
−0.677803 | + | 0.735244i | \(0.737068\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.97045 | − | 2.86969i | −0.386949 | − | 0.223405i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.37890 | + | 4.12037i | −0.184085 | + | 0.318844i | −0.943268 | − | 0.332033i | \(-0.892265\pi\) |
0.759183 | + | 0.650877i | \(0.225599\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.25614 | − | 9.10390i | −0.404318 | − | 0.700300i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.0300 | + | 5.92746i | 0.767013 | + | 0.453284i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4488 | − | 8.34203i | 1.09852 | − | 0.634233i | 0.162690 | − | 0.986677i | \(-0.447983\pi\) |
0.935833 | + | 0.352445i | \(0.114649\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.4785 | + | 19.8814i | −0.867694 | + | 1.50289i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.44747 | + | 5.97119i | −0.259128 | + | 0.448822i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2627i | 1.29027i | 0.764067 | + | 0.645136i | \(0.223199\pi\) | ||||
−0.764067 | + | 0.645136i | \(0.776801\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.358255 | − | 0.206838i | −0.0266289 | − | 0.0153742i | 0.486626 | − | 0.873610i | \(-0.338227\pi\) |
−0.513255 | + | 0.858236i | \(0.671561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.315213 | 0.0233012 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.4125 | − | 23.2312i | −0.986109 | − | 1.70799i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.97072 | − | 4.02455i | 0.509749 | − | 0.294304i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 7.72082i | − | 0.561607i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.8774 | −1.80006 | −0.900031 | − | 0.435825i | \(-0.856457\pi\) | ||||
−0.900031 | + | 0.435825i | \(0.856457\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.75804 | − | 8.24117i | −0.342491 | − | 0.593212i | 0.642403 | − | 0.766367i | \(-0.277937\pi\) |
−0.984895 | + | 0.173154i | \(0.944604\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.99029 | − | 1.72644i | 0.214139 | − | 0.123633i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.85154i | 0.416905i | 0.978033 | + | 0.208452i | \(0.0668426\pi\) | ||||
−0.978033 | + | 0.208452i | \(0.933157\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.39537 | + | 14.5412i | −0.595132 | + | 1.03080i | 0.398397 | + | 0.917213i | \(0.369567\pi\) |
−0.993528 | + | 0.113585i | \(0.963767\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.04655 | −0.355956 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.1601 | − | 11.0621i | −1.34477 | − | 0.776405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −41.2370 | − | 23.8082i | −2.88012 | − | 1.66284i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.9672 | + | 20.7278i | 0.831779 | + | 1.44068i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.4271 | − | 0.116068i | −0.790432 | − | 0.00802862i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.15685 | + | 1.82261i | −0.217327 | + | 0.125474i | −0.604712 | − | 0.796444i | \(-0.706712\pi\) |
0.387385 | + | 0.921918i | \(0.373378\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.59900 | + | 2.07788i | 0.246599 | + | 0.142374i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.20995 | − | 9.02391i | 0.355316 | − | 0.615425i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.4365 | −0.708475 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.79179 | − | 1.03449i | −0.121078 | − | 0.0699042i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.84244i | 0.325738i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.66306 | + | 15.0049i | 0.580121 | + | 1.00480i | 0.995464 | + | 0.0951349i | \(0.0303283\pi\) |
−0.415343 | + | 0.909665i | \(0.636338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.8938 | + | 22.3328i | 0.859590 | + | 1.48885i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0900i | 1.00156i | 0.865575 | + | 0.500779i | \(0.166953\pi\) | ||||
−0.865575 | + | 0.500779i | \(0.833047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.04237i | 0.597536i | 0.954326 | + | 0.298768i | \(0.0965757\pi\) | ||||
−0.954326 | + | 0.298768i | \(0.903424\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.78409 | + | 3.09014i | 0.117385 | + | 0.203316i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.64804 | − | 9.78269i | −0.370015 | − | 0.640885i | 0.619552 | − | 0.784955i | \(-0.287314\pi\) |
−0.989567 | + | 0.144070i | \(0.953981\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.84442i | 0.576946i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.97609 | + | 1.14090i | 0.128361 | + | 0.0741093i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.47049 | 0.418541 | 0.209271 | − | 0.977858i | \(-0.432891\pi\) | ||||
0.209271 | + | 0.977858i | \(0.432891\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1454 | + | 17.5724i | −0.653524 | + | 1.13194i | 0.328737 | + | 0.944421i | \(0.393377\pi\) |
−0.982262 | + | 0.187516i | \(0.939956\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.4829 | − | 6.62967i | −0.736630 | − | 0.425293i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.43582 | + | 2.56102i | −0.283394 | + | 0.163618i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.49784 | − | 5.91877i | 0.222562 | − | 0.376602i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.36027 | + | 4.08810i | 0.149576 | + | 0.259073i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.81627 | + | 5.66742i | 0.619597 | + | 0.357725i | 0.776712 | − | 0.629856i | \(-0.216886\pi\) |
−0.157115 | + | 0.987580i | \(0.550219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.3314 | − | 11.7383i | −1.27822 | − | 0.737982i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.72118 | 0.420896 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.33679 | + | 4.04744i | −0.145765 | + | 0.252472i | −0.929658 | − | 0.368424i | \(-0.879898\pi\) |
0.783893 | + | 0.620896i | \(0.213231\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.6772i | 1.03627i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.5226 | + | 12.4261i | −1.33221 | + | 0.769154i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.51632 | + | 9.55454i | 0.340151 | + | 0.589158i | 0.984460 | − | 0.175606i | \(-0.0561886\pi\) |
−0.644310 | + | 0.764765i | \(0.722855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.13322 | 0.376761 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.52663i | 0.338224i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.9884 | − | 7.49889i | 0.791920 | − | 0.457215i | −0.0487182 | − | 0.998813i | \(-0.515514\pi\) |
0.840638 | + | 0.541597i | \(0.182180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.33304 | − | 14.4332i | −0.506196 | − | 0.876757i | −0.999974 | − | 0.00716938i | \(-0.997718\pi\) |
0.493778 | − | 0.869588i | \(-0.335615\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.14667 | −0.129922 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.9057 | − | 12.6472i | −1.32096 | − | 0.762657i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.6486i | 0.940235i | 0.882604 | + | 0.470118i | \(0.155789\pi\) | ||||
−0.882604 | + | 0.470118i | \(0.844211\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.86167 | + | 10.1527i | −0.350929 | + | 0.607826i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.50045 | − | 6.06295i | 0.208819 | − | 0.361685i | −0.742524 | − | 0.669820i | \(-0.766371\pi\) |
0.951343 | + | 0.308134i | \(0.0997047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.72756 | − | 0.997408i | 0.102693 | − | 0.0592897i | −0.447774 | − | 0.894147i | \(-0.647783\pi\) |
0.550467 | + | 0.834857i | \(0.314450\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.21509 | − | 4.85490i | −0.486620 | − | 0.287579i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.8016 | + | 25.6371i | 0.873712 | + | 1.51331i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.78700 | − | 6.55928i | 0.222765 | − | 0.385840i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.61128 | + | 3.81703i | 0.387560 | + | 0.223758i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 17.9363i | − | 1.04785i | −0.851765 | − | 0.523924i | \(-0.824468\pi\) | ||
0.851765 | − | 0.523924i | \(-0.175532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.0675 | + | 39.9540i | −1.34304 | + | 2.32621i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.50695 | 0.493623 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.2316 | − | 7.06194i | 0.707373 | − | 0.408402i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.61019 | + | 3.23904i | −0.323366 | + | 0.186695i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.04137 | −0.0598250 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.10913 | 0.120768 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.5431 | − | 14.7473i | 1.45782 | − | 0.841673i | 0.458916 | − | 0.888480i | \(-0.348238\pi\) |
0.998904 | + | 0.0468072i | \(0.0149046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.92666 | + | 2.84441i | −0.280268 | + | 0.161813i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.2270 | −1.03356 | −0.516779 | − | 0.856119i | \(-0.672869\pi\) | ||||
−0.516779 | + | 0.856119i | \(0.672869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.9213 | + | 25.8444i | −0.843401 | + | 1.46081i | 0.0436015 | + | 0.999049i | \(0.486117\pi\) |
−0.887003 | + | 0.461764i | \(0.847217\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 24.3408i | − | 1.37145i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.53123 | + | 3.19346i | 0.310665 | + | 0.179363i | 0.647224 | − | 0.762300i | \(-0.275930\pi\) |
−0.336559 | + | 0.941662i | \(0.609263\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1884 | − | 21.1109i | 0.682419 | − | 1.18198i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.79177 | + | 6.56754i | 0.211636 | + | 0.366565i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.6570 | − | 6.57324i | 0.648615 | − | 0.365745i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.1787 | − | 7.60875i | 0.731025 | − | 0.422057i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.16213 | − | 3.74492i | 0.119566 | − | 0.207094i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.74930 | − | 4.76193i | 0.151574 | − | 0.262533i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.22210i | 0.341997i | 0.985271 | + | 0.170999i | \(0.0546994\pi\) | ||||
−0.985271 | + | 0.170999i | \(0.945301\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.2237 | + | 9.36678i | 0.889055 | + | 0.513296i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.7672 | −1.84490 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.7925 | + | 25.6213i | 0.805797 | + | 1.39568i | 0.915752 | + | 0.401745i | \(0.131596\pi\) |
−0.109954 | + | 0.993937i | \(0.535070\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.50593 | − | 2.02415i | 0.190416 | − | 0.109937i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.4991i | − | 0.622712i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8404 | 1.07128 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.80177 | − | 16.9772i | −0.527710 | − | 0.914020i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.78717 | + | 3.34122i | −0.310671 | + | 0.179366i | −0.647227 | − | 0.762297i | \(-0.724071\pi\) |
0.336555 | + | 0.941664i | \(0.390738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1074i | 0.915736i | 0.889020 | + | 0.457868i | \(0.151387\pi\) | ||||
−0.889020 | + | 0.457868i | \(0.848613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.55895 | + | 4.43222i | −0.136586 | + | 0.236575i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.857173 | 0.0456227 | 0.0228114 | − | 0.999740i | \(-0.492738\pi\) | ||||
0.0228114 | + | 0.999740i | \(0.492738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.0814 | + | 13.9034i | 1.27811 | + | 0.737915i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.61875 | − | 2.08929i | −0.191525 | − | 0.110577i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.9279 | − | 31.0520i | −0.946198 | − | 1.63886i | −0.753335 | − | 0.657637i | \(-0.771556\pi\) |
−0.192863 | − | 0.981226i | \(-0.561777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9961 | − | 0.385936i | −0.999794 | − | 0.0203124i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.04419 | − | 1.18022i | 0.107292 | − | 0.0619452i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.9891 | − | 6.92190i | −0.627537 | − | 0.362309i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.60358 | − | 6.24158i | 0.188105 | − | 0.325808i | −0.756513 | − | 0.653978i | \(-0.773099\pi\) |
0.944618 | + | 0.328171i | \(0.106432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 33.2534 | 1.73110 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.30219 | − | 1.90652i | −0.171441 | − | 0.0989815i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.23956i | 0.0641818i | 0.999485 | + | 0.0320909i | \(0.0102166\pi\) | ||||
−0.999485 | + | 0.0320909i | \(0.989783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.08778 | − | 8.81229i | −0.262732 | − | 0.455064i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.33270 | + | 12.7006i | 0.377653 | + | 0.654115i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.69864i | 0.395453i | 0.980257 | + | 0.197726i | \(0.0633558\pi\) | ||||
−0.980257 | + | 0.197726i | \(0.936644\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3.33937i | − | 0.171081i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.13360 | − | 10.6237i | −0.313413 | − | 0.542846i | 0.665686 | − | 0.746232i | \(-0.268139\pi\) |
−0.979099 | + | 0.203385i | \(0.934806\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.9376 | + | 20.6766i | 0.608397 | + | 1.05378i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.27685i | 0.369903i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.7105 | − | 13.6893i | −1.20217 | − | 0.694074i | −0.241135 | − | 0.970492i | \(-0.577520\pi\) |
−0.961038 | + | 0.276417i | \(0.910853\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.4926 | 1.39036 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.04978 | − | 7.01443i | 0.204284 | − | 0.353831i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.2223 | + | 7.63390i | 0.665286 | + | 0.384103i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.94101 | + | 1.69799i | −0.147605 | + | 0.0852197i | −0.571984 | − | 0.820265i | \(-0.693826\pi\) |
0.424379 | + | 0.905485i | \(0.360493\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.91394 | + | 5.16760i | 0.145879 | + | 0.258704i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.4586 | − | 21.5789i | −0.622151 | − | 1.07760i | −0.989084 | − | 0.147350i | \(-0.952926\pi\) |
0.366934 | − | 0.930247i | \(-0.380408\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.99118 | + | 3.45901i | 0.298442 | + | 0.172306i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.4256 | − | 11.7927i | −1.01496 | − | 0.585986i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.3753 | −0.910827 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.57567 | − | 9.65734i | 0.275699 | − | 0.477525i | −0.694612 | − | 0.719384i | \(-0.744424\pi\) |
0.970311 | + | 0.241860i | \(0.0777574\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.704858i | − | 0.0347681i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.8395 | − | 14.3411i | 1.22227 | − | 0.705680i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.7929 | + | 27.3541i | 0.775242 | + | 1.34276i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.43956 | 0.168436 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.54457i | − | 0.270870i | −0.990786 | − | 0.135435i | \(-0.956757\pi\) | ||
0.990786 | − | 0.135435i | \(-0.0432432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.9281 | − | 11.5055i | 0.971235 | − | 0.560743i | 0.0716223 | − | 0.997432i | \(-0.477182\pi\) |
0.899612 | + | 0.436689i | \(0.143849\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.08830 | − | 5.34908i | −0.150158 | − | 0.260081i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.6214 | 1.43685 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.13558 | − | 0.655626i | −0.0549544 | − | 0.0317280i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 2.36524i | − | 0.114195i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.84478 | − | 6.65935i | 0.185196 | − | 0.320770i | −0.758446 | − | 0.651736i | \(-0.774041\pi\) |
0.943643 | + | 0.330966i | \(0.107375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.8560 | + | 23.9994i | −0.665879 | + | 1.15334i | 0.313167 | + | 0.949698i | \(0.398610\pi\) |
−0.979046 | + | 0.203639i | \(0.934723\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.6281 | − | 10.1776i | 0.845203 | − | 0.487978i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −33.6034 | − | 19.8587i | −1.60747 | − | 0.949971i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.4148 | − | 30.1634i | −0.831165 | − | 1.43962i | −0.897115 | − | 0.441797i | \(-0.854341\pi\) |
0.0659505 | − | 0.997823i | \(-0.478992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.78852 | − | 3.09780i | 0.0851675 | − | 0.147514i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.78938 | − | 3.91985i | −0.322573 | − | 0.186238i | 0.329966 | − | 0.943993i | \(-0.392963\pi\) |
−0.652539 | + | 0.757755i | \(0.726296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.9794i | 1.75299i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.164827 | − | 0.285488i | 0.00779604 | − | 0.0135031i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.7057 | −1.07155 | −0.535775 | − | 0.844361i | \(-0.679980\pi\) | ||||
−0.535775 | + | 0.844361i | \(0.679980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.2475 | + | 16.3087i | −1.33012 | + | 0.767946i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.55823 | − | 3.78640i | 0.308133 | − | 0.177900i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.3637 | −0.673379 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.5207 | −1.61481 | −0.807405 | − | 0.589998i | \(-0.799129\pi\) | ||||
−0.807405 | + | 0.589998i | \(0.799129\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.62749 | + | 4.98108i | −0.402697 | + | 0.232497i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.7449 | + | 6.78091i | −0.547014 | + | 0.315819i | −0.747917 | − | 0.663793i | \(-0.768946\pi\) |
0.200903 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0544 | −0.746112 | −0.373056 | − | 0.927809i | \(-0.621690\pi\) | ||||
−0.373056 | + | 0.927809i | \(0.621690\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.80101 | − | 8.31559i | 0.222641 | − | 0.385626i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 36.4819i | − | 1.68818i | −0.536201 | − | 0.844091i | \(-0.680141\pi\) | ||
0.536201 | − | 0.844091i | \(-0.319859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.1806 | + | 10.4966i | 0.839502 | + | 0.484686i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.05297 | + | 8.75200i | −0.232828 | + | 0.403271i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.56884 | − | 6.18141i | −0.164095 | − | 0.284221i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.2054 | − | 21.3964i | −1.66122 | − | 0.981734i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.70936 | + | 2.14160i | −0.169840 | + | 0.0980570i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.04549 | + | 10.4711i | −0.276225 | + | 0.478437i | −0.970444 | − | 0.241328i | \(-0.922417\pi\) |
0.694218 | + | 0.719765i | \(0.255750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.52740 | − | 9.57373i | 0.252028 | − | 0.436525i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.1876i | 0.554554i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.2370 | + | 25.5402i | 2.00870 | + | 1.15972i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.9780 | 1.53969 | 0.769845 | − | 0.638231i | \(-0.220334\pi\) | ||||
0.769845 | + | 0.638231i | \(0.220334\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.36928 | + | 9.29987i | 0.242807 | + | 0.420555i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.85946 | + | 5.11501i | −0.399822 | + | 0.230837i | −0.686407 | − | 0.727218i | \(-0.740813\pi\) |
0.286585 | + | 0.958055i | \(0.407480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.5467i | 1.28568i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 26.8191 | 1.20543 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.64377 | − | 14.9715i | −0.387726 | − | 0.671562i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.9924 | + | 14.4294i | −1.11881 | + | 0.645947i | −0.941098 | − | 0.338135i | \(-0.890204\pi\) |
−0.177716 | + | 0.984082i | \(0.556871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.72143i | 0.121584i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.5515 | − | 23.4718i | 0.604229 | − | 1.04656i | −0.387943 | − | 0.921683i | \(-0.626814\pi\) |
0.992173 | − | 0.124873i | \(-0.0398523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.96794 | −0.310069 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.20737 | − | 3.00648i | −0.231267 | − | 0.133522i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.2327 | + | 11.6814i | 0.896798 | + | 0.517767i | 0.876160 | − | 0.482020i | \(-0.160097\pi\) |
0.0206383 | + | 0.999787i | \(0.493430\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.30336 | + | 7.45364i | 0.190370 | + | 0.329730i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.1431 | + | 0.143655i | 0.624433 | + | 0.00634252i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.9650 | + | 19.0323i | −1.45261 | + | 0.838665i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.24678 | + | 3.02923i | 0.230753 | + | 0.133225i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.77158 | − | 8.26463i | 0.209449 | − | 0.362777i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.49127 | 0.109144 | 0.0545722 | − | 0.998510i | \(-0.482621\pi\) | ||||
0.0545722 | + | 0.998510i | \(0.482621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.6860 | + | 14.2525i | 1.07944 | + | 0.623217i | 0.930746 | − | 0.365666i | \(-0.119159\pi\) |
0.148697 | + | 0.988883i | \(0.452492\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.1313i | 0.573095i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.73309 | + | 11.6621i | 0.293298 | + | 0.508007i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.5937 | − | 49.5257i | −1.24320 | − | 2.15329i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 32.2188i | − | 1.39818i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 19.6230i | − | 0.849968i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.3713 | + | 43.9443i | 1.09690 | + | 1.89988i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.93707 | + | 8.55125i | 0.213050 | + | 0.369014i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.50862i | 0.151127i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.26285 | + | 3.03851i | 0.226267 | + | 0.130636i | 0.608849 | − | 0.793286i | \(-0.291632\pi\) |
−0.382581 | + | 0.923922i | \(0.624965\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.236620 | −0.0101544 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.4671 | − | 25.0577i | 0.619702 | − | 1.07336i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7508 | + | 9.67108i | 0.716212 | + | 0.413505i | 0.813357 | − | 0.581765i | \(-0.197638\pi\) |
−0.0971447 | + | 0.995270i | \(0.530971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.27560 | + | 0.736466i | −0.0544412 | + | 0.0314316i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.6201 | − | 34.8918i | 0.878447 | − | 1.48644i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.74602 | − | 8.22034i | −0.201821 | − | 0.349564i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.2881 | − | 7.67188i | −0.564047 | − | 0.325653i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.3179 | + | 11.1532i | 0.818525 | + | 0.472576i | 0.849908 | − | 0.526932i | \(-0.176658\pi\) |
−0.0313823 | + | 0.999507i | \(0.509991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.29412 | 0.181622 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.30201 | − | 3.98720i | 0.0971911 | − | 0.168340i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.2448i | 1.06394i | 0.846763 | + | 0.531970i | \(0.178548\pi\) | ||||
−0.846763 | + | 0.531970i | \(0.821452\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.4586 | − | 13.5439i | 0.986913 | − | 0.569794i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.33158 | + | 12.6987i | 0.307897 | + | 0.533294i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.1784 | −0.720155 | −0.360078 | − | 0.932922i | \(-0.617250\pi\) | ||||
−0.360078 | + | 0.932922i | \(0.617250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.64144i | 0.361633i | 0.983517 | + | 0.180816i | \(0.0578740\pi\) | ||||
−0.983517 | + | 0.180816i | \(0.942126\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.3233 | + | 7.11484i | −0.514812 | + | 0.297227i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −43.1981 | − | 74.8214i | −1.80149 | − | 3.12027i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.5806 | 1.02331 | 0.511653 | − | 0.859192i | \(-0.329034\pi\) | ||||
0.511653 | + | 0.859192i | \(0.329034\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.71389 | − | 2.72157i | −0.195903 | − | 0.113104i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 19.6369i | − | 0.814678i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.10064 | − | 3.63841i | 0.0869995 | − | 0.150688i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.06737 | + | 13.9731i | −0.333545 | + | 0.577716i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.7781 | + | 19.5018i | −1.39417 | + | 0.804926i | −0.993774 | − | 0.111415i | \(-0.964462\pi\) |
−0.400399 | + | 0.916341i | \(0.631128\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.194183 | − | 19.1177i | 0.00800117 | − | 0.787730i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.67352 | + | 2.89862i | 0.0688394 | + | 0.119233i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.40127 | + | 5.89117i | −0.139673 | + | 0.241921i | −0.927373 | − | 0.374138i | \(-0.877939\pi\) |
0.787700 | + | 0.616059i | \(0.211272\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.2135 | − | 13.9797i | −0.992659 | − | 0.573112i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.60418i | 0.393073i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.1953 | + | 31.5152i | −0.743439 | + | 1.28767i | 0.207481 | + | 0.978239i | \(0.433473\pi\) |
−0.950921 | + | 0.309435i | \(0.899860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.372849 | −0.0152088 | −0.00760441 | − | 0.999971i | \(-0.502421\pi\) | ||||
−0.00760441 | + | 0.999971i | \(0.502421\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.4223 | − | 11.7908i | 0.831661 | − | 0.480159i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.6780 | − | 7.89698i | 0.556089 | − | 0.321058i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.5367 | 1.28003 | 0.640017 | − | 0.768361i | \(-0.278927\pi\) | ||||
0.640017 | + | 0.768361i | \(0.278927\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.6549 | −0.512801 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.15653 | + | 1.82242i | −0.127700 | + | 0.0737274i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.9009 | + | 9.75775i | −0.682621 | + | 0.394112i | −0.800842 | − | 0.598876i | \(-0.795614\pi\) |
0.118221 | + | 0.992987i | \(0.462281\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.2362 | −1.09827 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.5156 | − | 32.0700i | 0.745410 | − | 1.29109i | −0.204592 | − | 0.978847i | \(-0.565587\pi\) |
0.950003 | − | 0.312241i | \(-0.101080\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.86666i | 0.356381i | 0.983996 | + | 0.178190i | \(0.0570243\pi\) | ||||
−0.983996 | + | 0.178190i | \(0.942976\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.1637 | + | 14.5282i | 1.00978 | + | 0.582998i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.4951 | − | 19.9101i | 0.460542 | − | 0.797682i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.92273 | − | 17.1867i | −0.396909 | − | 0.687467i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.69375 | + | 3.21063i | −0.227387 | + | 0.128220i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.6356 | − | 10.7593i | 0.743051 | − | 0.429001i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.13344 | + | 3.69522i | −0.0849307 | + | 0.147104i | −0.905362 | − | 0.424641i | \(-0.860400\pi\) |
0.820431 | + | 0.571746i | \(0.193734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.04252 | + | 1.80570i | −0.0414364 | + | 0.0717700i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 22.3442i | − | 0.886702i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.82803 | − | 1.05542i | −0.0724294 | − | 0.0418171i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.4192 | −0.768210 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.7085 | − | 20.2797i | −0.462458 | − | 0.801000i | 0.536625 | − | 0.843821i | \(-0.319699\pi\) |
−0.999083 | + | 0.0428208i | \(0.986366\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.6718 | − | 10.7802i | 0.736344 | − | 0.425128i | −0.0843944 | − | 0.996432i | \(-0.526896\pi\) |
0.820739 | + | 0.571304i | \(0.193562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 5.96012i | − | 0.234679i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.5504 | 1.08312 | 0.541559 | − | 0.840663i | \(-0.317834\pi\) | ||||
0.541559 | + | 0.840663i | \(0.317834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.8013 | + | 27.3686i | 0.620255 | + | 1.07431i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.16982 | + | 2.98480i | −0.202621 | + | 0.116984i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.9425i | 0.467348i | 0.972315 | + | 0.233674i | \(0.0750748\pi\) | ||||
−0.972315 | + | 0.233674i | \(0.924925\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.0976 | − | 46.9345i | 1.05879 | − | 1.83388i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.66796 | 0.377183 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.7336 | − | 17.7441i | −1.19721 | − | 0.691211i | −0.237279 | − | 0.971442i | \(-0.576256\pi\) |
−0.959933 | + | 0.280231i | \(0.909589\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5565 | − | 8.98158i | −0.605080 | − | 0.349343i | 0.165958 | − | 0.986133i | \(-0.446928\pi\) |
−0.771037 | + | 0.636790i | \(0.780262\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.38492 | + | 2.39876i | 0.0537859 | + | 0.0931599i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.4976 | + | 34.5771i | 0.756083 | + | 1.34084i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 72.1069 | − | 41.6309i | 2.79199 | − | 1.61196i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.58268 | + | 4.95521i | 0.331826 | + | 0.191580i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.722381 | − | 1.25120i | 0.0278872 | − | 0.0483020i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4280 | −1.09582 | −0.547909 | − | 0.836538i | \(-0.684576\pi\) | ||||
−0.547909 | + | 0.836538i | \(0.684576\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.1121 | + | 15.6532i | 1.04354 | + | 0.602491i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.7219i | 1.64194i | 0.570974 | + | 0.820968i | \(0.306566\pi\) | ||||
−0.570974 | + | 0.820968i | \(0.693434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8784 | − | 27.5023i | −0.609358 | − | 1.05544i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.31569 | + | 7.47499i | 0.165377 | + | 0.286442i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.28834i | 0.202353i | 0.994869 | + | 0.101176i | \(0.0322606\pi\) | ||||
−0.994869 | + | 0.101176i | \(0.967739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4.71630i | − | 0.180201i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.58609 | + | 4.47923i | 0.0986654 | + | 0.170893i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.26377 | + | 2.18892i | 0.0481458 | + | 0.0833911i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.46172i | − | 0.0936482i | −0.998903 | − | 0.0468241i | \(-0.985090\pi\) | ||
0.998903 | − | 0.0468241i | \(-0.0149100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.4397 | − | 8.33676i | −0.548518 | − | 0.316687i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.0146 | 0.872992 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0985 | − | 33.0796i | 0.723407 | − | 1.25298i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.59563 | − | 3.23064i | −0.211646 | − | 0.122194i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.3878 | − | 18.1217i | 1.18550 | − | 0.684449i | 0.228220 | − | 0.973610i | \(-0.426710\pi\) |
0.957280 | + | 0.289161i | \(0.0933763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.5495 | − | 0.310299i | −1.15220 | − | 0.0117031i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.52947 | + | 4.38118i | 0.0952655 | + | 0.165005i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.75161 | + | 2.16599i | 0.141094 | + | 0.0814605i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.9138 | + | 6.87845i | 0.447433 | + | 0.258325i | 0.706745 | − | 0.707468i | \(-0.250163\pi\) |
−0.259313 | + | 0.965793i | \(0.583496\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.6624 | −0.399872 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.6383 | − | 34.0145i | 0.735460 | − | 1.27385i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 15.8261i | − | 0.591864i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.20523 | − | 1.85054i | 0.119701 | − | 0.0691097i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.5301 | − | 37.2913i | −0.802938 | − | 1.39073i | −0.917674 | − | 0.397334i | \(-0.869935\pi\) |
0.114736 | − | 0.993396i | \(-0.463398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.6649 | 0.881328 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6062i | 0.431640i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 77.6901 | − | 44.8544i | 2.88534 | − | 1.66585i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.5087 | + | 18.2017i | 0.389747 | + | 0.675062i | 0.992415 | − | 0.122930i | \(-0.0392290\pi\) |
−0.602668 | + | 0.797992i | \(0.705896\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.9031 | 0.403819 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.23881 | + | 4.17933i | 0.267737 | + | 0.154578i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.1556i | − | 1.44624i | −0.690720 | − | 0.723122i | \(-0.742706\pi\) | ||
0.690720 | − | 0.723122i | \(-0.257294\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.46489 | + | 2.53726i | −0.0540332 | + | 0.0935883i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.5653 | + | 20.0317i | −0.426014 | + | 0.737877i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.9285 | + | 8.04160i | −0.512367 | + | 0.295815i | −0.733806 | − | 0.679359i | \(-0.762258\pi\) |
0.221439 | + | 0.975174i | \(0.428925\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0399413 | − | 3.93230i | 0.00146728 | − | 0.144457i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.2042 | − | 29.7985i | −0.631161 | − | 1.09320i | −0.987315 | − | 0.158775i | \(-0.949245\pi\) |
0.356154 | − | 0.934427i | \(-0.384088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.10288 | − | 1.91024i | 0.0404063 | − | 0.0699858i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.1030 | − | 11.0291i | −0.698942 | − | 0.403534i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 31.5468i | − | 1.15269i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.1770 | − | 28.0194i | 0.590307 | − | 1.02244i | −0.403884 | − | 0.914810i | \(-0.632340\pi\) |
0.994191 | − | 0.107631i | \(-0.0343266\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.48346 | 0.236270 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.8820 | − | 25.3353i | 1.59703 | − | 0.922046i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.1757 | + | 18.5767i | −1.16945 | + | 0.675180i | −0.953550 | − | 0.301236i | \(-0.902601\pi\) |
−0.215896 | + | 0.976416i | \(0.569267\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.4285 | −0.487423 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.8152 | 1.58830 | 0.794150 | − | 0.607721i | \(-0.207916\pi\) | ||||
0.794150 | + | 0.607721i | \(0.207916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.5785 | + | 8.99423i | −0.563978 | + | 0.325613i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.1991 | + | 15.7034i | −0.983387 | + | 0.567759i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.0125 | −0.686503 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.81793 | + | 10.0770i | −0.209800 | + | 0.363384i | −0.951651 | − | 0.307180i | \(-0.900615\pi\) |
0.741851 | + | 0.670564i | \(0.233948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.67325i | 0.0962749i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.2046 | − | 11.6652i | −0.726711 | − | 0.419567i | 0.0905070 | − | 0.995896i | \(-0.471151\pi\) |
−0.817218 | + | 0.576329i | \(0.804485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.1589 | − | 36.6483i | 0.760050 | − | 1.31645i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.76963 | + | 8.26123i | 0.171109 | + | 0.296370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.2378 | + | 26.6368i | −1.69247 | + | 0.954361i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.4958 | − | 9.52387i | 0.590267 | − | 0.340791i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.0853 | + | 26.1285i | −0.539104 | + | 0.933755i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.8101 | + | 58.5608i | −1.20673 | + | 2.09012i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 47.9991i | − | 1.71098i | −0.517815 | − | 0.855492i | \(-0.673255\pi\) | ||
0.517815 | − | 0.855492i | \(-0.326745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.46514 | + | 3.15530i | 0.194564 | + | 0.112332i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.8405 | −0.598779 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.434594 | + | 0.752739i | 0.0154329 | + | 0.0267305i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.03815 | − | 1.75408i | 0.107752 | − | 0.0622108i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.8257i | 0.560576i | 0.959916 | + | 0.280288i | \(0.0904299\pi\) | ||||
−0.959916 | + | 0.280288i | \(0.909570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.09483 | −0.250997 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.9125 | − | 22.3651i | −0.456240 | − | 0.790231i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.21256 | + | 4.74152i | −0.289815 | + | 0.167325i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 81.5487i | 2.87421i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.28931 | − | 7.42931i | 0.150991 | − | 0.261524i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.5885 | −0.548063 | −0.274031 | − | 0.961721i | \(-0.588357\pi\) | ||||
−0.274031 | + | 0.961721i | \(0.588357\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.1683 | + | 17.4177i | 1.05935 | + | 0.611618i | 0.925253 | − | 0.379350i | \(-0.123852\pi\) |
0.134100 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.25572 | − | 4.76644i | −0.289541 | − | 0.167166i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.9266 | + | 62.2267i | 1.25845 | + | 2.17971i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.82893 | − | 10.3371i | −0.203929 | − | 0.361648i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.68711 | − | 5.01551i | 0.303552 | − | 0.175256i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.5478 | + | 20.5235i | 1.24063 | + | 0.716276i | 0.969222 | − | 0.246190i | \(-0.0791786\pi\) |
0.271404 | + | 0.962465i | \(0.412512\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.83395 | − | 6.64060i | 0.133643 | − | 0.231477i | −0.791435 | − | 0.611253i | \(-0.790666\pi\) |
0.925078 | + | 0.379776i | \(0.123999\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.4683 | −0.503720 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.6903 | + | 6.17207i | 0.371740 | + | 0.214624i | 0.674218 | − | 0.738532i | \(-0.264481\pi\) |
−0.302478 | + | 0.953156i | \(0.597814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.6662i | 0.960887i | 0.877026 | + | 0.480444i | \(0.159524\pi\) | ||||
−0.877026 | + | 0.480444i | \(0.840476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.47546 | + | 7.75172i | 0.155252 | + | 0.268904i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.05441 | − | 3.55834i | −0.0711810 | − | 0.123289i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.2095i | 0.630164i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.2322i | 0.491936i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.03223 | + | 12.1802i | 0.242779 | + | 0.420506i | 0.961505 | − | 0.274788i | \(-0.0886076\pi\) |
−0.718726 | + | 0.695294i | \(0.755274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7271 | + | 49.7568i | 0.990590 | + | 1.71575i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 4.00446i | − | 0.137921i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.8432 | − | 20.1167i | −1.19864 | − | 0.692037i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.81915 | −0.337390 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.570510 | − | 0.988153i | 0.0195799 | − | 0.0339133i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.3542 | − | 31.3814i | −1.86324 | − | 1.07574i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.50368 | − | 4.33225i | 0.256921 | − | 0.148333i | −0.366008 | − | 0.930612i | \(-0.619276\pi\) |
0.622929 | + | 0.782278i | \(0.285942\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 44.5877 | + | 0.452889i | 1.52487 | + | 0.0154885i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.95703 | − | 12.0499i | −0.237648 | − | 0.411618i | 0.722391 | − | 0.691485i | \(-0.243043\pi\) |
−0.960039 | + | 0.279867i | \(0.909710\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5401 | − | 7.24001i | −0.427861 | − | 0.247026i | 0.270574 | − | 0.962699i | \(-0.412787\pi\) |
−0.698435 | + | 0.715673i | \(0.746120\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.6643 | + | 8.46642i | 0.499757 | + | 0.288535i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.5065 | 0.902291 | 0.451145 | − | 0.892450i | \(-0.351016\pi\) | ||||
0.451145 | + | 0.892450i | \(0.351016\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.9273 | − | 55.2997i | 1.08556 | − | 1.88025i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 4.33228i | − | 0.147132i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.05732 | − | 5.22925i | 0.307249 | − | 0.177390i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.95785 | − | 12.0513i | −0.235758 | − | 0.408344i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.6726 | −1.20733 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 42.3292i | 1.43099i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.4900 | − | 8.94317i | 0.523061 | − | 0.301989i | −0.215125 | − | 0.976586i | \(-0.569016\pi\) |
0.738186 | + | 0.674597i | \(0.235683\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.12971 | − | 8.88491i | −0.173021 | − | 0.299681i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.0705 | −0.541427 | −0.270714 | − | 0.962660i | \(-0.587260\pi\) | ||||
−0.270714 | + | 0.962660i | \(0.587260\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.4924 | − | 8.36718i | −0.487708 | − | 0.281578i | 0.235915 | − | 0.971774i | \(-0.424191\pi\) |
−0.723623 | + | 0.690196i | \(0.757525\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.3889i | 0.887052i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.8735 | + | 41.3502i | −0.801595 | + | 1.38840i | 0.116971 | + | 0.993135i | \(0.462681\pi\) |
−0.918566 | + | 0.395268i | \(0.870652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.94572 | + | 12.0303i | −0.232952 | + | 0.403485i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.9916 | + | 8.07807i | −0.468737 | + | 0.270625i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.67180 | + | 5.12480i | 0.290191 | + | 0.171495i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.0346 | + | 57.2176i | 1.10422 | + | 1.91257i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.03938 | − | 6.99641i | 0.134871 | − | 0.233603i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.3187 | + | 20.3913i | 1.17794 | + | 0.680086i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.91995i | 0.163907i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.85271 | + | 3.20899i | −0.0616543 | + | 0.106788i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.58326 | −0.0526293 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.5036 | − | 12.4151i | 0.714016 | − | 0.412237i | −0.0985303 | − | 0.995134i | \(-0.531414\pi\) |
0.812546 | + | 0.582897i | \(0.198081\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.21419 | − | 2.43306i | 0.139776 | − | 0.0806997i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.9835 | 0.430161 | 0.215081 | − | 0.976596i | \(-0.430999\pi\) | ||||
0.215081 | + | 0.976596i | \(0.430999\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.6363 | 0.716058 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.04478 | − | 0.603204i | 0.0345394 | − | 0.0199413i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.1793 | + | 16.8467i | −0.963585 | + | 0.556326i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.4768 | −1.63209 | −0.816045 | − | 0.577988i | \(-0.803838\pi\) | ||||
−0.816045 | + | 0.577988i | \(0.803838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.43535 | − | 14.6105i | 0.277954 | − | 0.481431i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.4594i | 0.377190i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.5629 | − | 33.8113i | −1.92554 | − | 1.11171i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.2914 | − | 23.0214i | 0.436548 | − | 0.756123i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.58486 | − | 16.6015i | −0.314469 | − | 0.544676i | 0.664856 | − | 0.746972i | \(-0.268493\pi\) |
−0.979324 | + | 0.202296i | \(0.935160\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0592493 | + | 5.83321i | −0.00194182 | + | 0.191176i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.02894 | + | 5.21286i | −0.295594 | + | 0.170661i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.4031 | − | 26.6789i | 0.503735 | − | 0.872494i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.9199 | + | 37.9663i | −0.716091 | + | 1.24031i | 0.246447 | + | 0.969156i | \(0.420737\pi\) |
−0.962537 | + | 0.271149i | \(0.912596\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.0698i | 0.557050i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.4920 | − | 14.7178i | −0.831017 | − | 0.479788i | 0.0231840 | − | 0.999731i | \(-0.492620\pi\) |
−0.854201 | + | 0.519944i | \(0.825953\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −111.409 | −3.62796 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.7749 | − | 25.5909i | −0.480627 | − | 0.832471i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.17630 | + | 0.679140i | −0.0382248 | + | 0.0220691i | −0.518991 | − | 0.854780i | \(-0.673692\pi\) |
0.480766 | + | 0.876849i | \(0.340359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 5.70513i | − | 0.185196i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.65327 | 0.118466 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.0604 | + | 33.0136i | 0.617428 | + | 1.06942i | 0.989953 | + | 0.141395i | \(0.0451587\pi\) |
−0.372525 | + | 0.928022i | \(0.621508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −82.4567 | + | 47.6064i | −2.66824 | + | 1.54051i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 13.9434i | − | 0.450725i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.46607 | + | 2.53930i | −0.0473418 | + | 0.0819984i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.7619 | −0.379417 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.6890 | − | 17.7183i | −0.988938 | − | 0.570964i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31.5413 | − | 18.2104i | −1.01535 | − | 0.586213i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.12156 | + | 15.7990i | 0.293330 | + | 0.508062i | 0.974595 | − | 0.223975i | \(-0.0719033\pi\) |
−0.681265 | + | 0.732037i | \(0.738570\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.89451 | − | 6.59000i | 0.125110 | − | 0.211701i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.6284 | − | 19.4153i | 1.07919 | − | 0.623068i | 0.148509 | − | 0.988911i | \(-0.452553\pi\) |
0.930677 | + | 0.365843i | \(0.119219\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.3913 | − | 7.15411i | −0.397246 | − | 0.229350i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.35215 | − | 7.53815i | 0.139380 | − | 0.241414i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.02782 | −0.128861 | −0.0644306 | − | 0.997922i | \(-0.520523\pi\) | ||||
−0.0644306 | + | 0.997922i | \(0.520523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.9373 | + | 12.6655i | 0.701120 | + | 0.404792i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.2065i | 0.645143i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.2147 | + | 36.7449i | 0.676643 | + | 1.17198i | 0.975986 | + | 0.217835i | \(0.0698995\pi\) |
−0.299342 | + | 0.954146i | \(0.596767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1977 | + | 19.3951i | 0.356790 | + | 0.617978i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 3.14516i | − | 0.100112i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 24.3796i | − | 0.775225i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4383 | + | 50.9886i | 0.935138 | + | 1.61971i | 0.774387 | + | 0.632712i | \(0.218058\pi\) |
0.160751 | + | 0.986995i | \(0.448608\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.77950 | + | 3.08218i | 0.0564707 | + | 0.0978101i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 64.2629i | 2.03727i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.1664 | − | 24.3448i | −1.33542 | − | 0.771007i | −0.349298 | − | 0.937012i | \(-0.613580\pi\) |
−0.986125 | + | 0.166005i | \(0.946913\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.7426 | 0.719544 |
(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 | 1216.2.t.d.1185.7 | yes | 24 | |
4.3 | odd | 2 | inner | 1216.2.t.d.1185.5 | yes | 24 | |
8.3 | odd | 2 | 1216.2.t.e.1185.7 | yes | 24 | ||
8.5 | even | 2 | 1216.2.t.e.1185.5 | yes | 24 | ||
19.11 | even | 3 | 1216.2.t.e.353.5 | yes | 24 | ||
76.11 | odd | 6 | 1216.2.t.e.353.7 | yes | 24 | ||
152.11 | odd | 6 | inner | 1216.2.t.d.353.5 | ✓ | 24 | |
152.125 | even | 6 | inner | 1216.2.t.d.353.7 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.t.d.353.5 | ✓ | 24 | 152.11 | odd | 6 | inner | |
1216.2.t.d.353.7 | yes | 24 | 152.125 | even | 6 | inner | |
1216.2.t.d.1185.5 | yes | 24 | 4.3 | odd | 2 | inner | |
1216.2.t.d.1185.7 | yes | 24 | 1.1 | even | 1 | trivial | |
1216.2.t.e.353.5 | yes | 24 | 19.11 | even | 3 | ||
1216.2.t.e.353.7 | yes | 24 | 76.11 | odd | 6 | ||
1216.2.t.e.1185.5 | yes | 24 | 8.5 | even | 2 | ||
1216.2.t.e.1185.7 | yes | 24 | 8.3 | odd | 2 |