Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(961,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.h (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.279290944.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 26x^{4} + 169x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(3.75054i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.961 |
Dual form | 1110.2.h.f.961.6 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 2.75054 | 1.03960 | 0.519802 | − | 0.854287i | \(-0.326006\pi\) | ||||
0.519802 | + | 0.854287i | \(0.326006\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 4.75054 | 1.43234 | 0.716170 | − | 0.697926i | \(-0.245893\pi\) | ||||
0.716170 | + | 0.697926i | \(0.245893\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 6.75054i | 1.87226i | 0.351652 | + | 0.936131i | \(0.385620\pi\) | ||||
−0.351652 | + | 0.936131i | \(0.614380\pi\) | |||||||
\(14\) | − | 2.75054i | − | 0.735111i | ||||||
\(15\) | − | 1.00000i | − | 0.258199i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.06651i | 1.71388i | 0.515415 | + | 0.856941i | \(0.327638\pi\) | ||||
−0.515415 | + | 0.856941i | \(0.672362\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | − | 6.75054i | − | 1.54868i | −0.632770 | − | 0.774339i | \(-0.718082\pi\) | ||
0.632770 | − | 0.774339i | \(-0.281918\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 2.75054 | 0.600216 | ||||||||
\(22\) | − | 4.75054i | − | 1.01282i | ||||||
\(23\) | 5.06651i | 1.05644i | 0.849107 | + | 0.528221i | \(0.177141\pi\) | ||||
−0.849107 | + | 0.528221i | \(0.822859\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 6.75054 | 1.32389 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.75054 | −0.519802 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 0.315979i | 0.0567515i | 0.999597 | + | 0.0283758i | \(0.00903350\pi\) | ||||
−0.999597 | + | 0.0283758i | \(0.990966\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 4.75054 | 0.826962 | ||||||||
\(34\) | 7.06651 | 1.21190 | ||||||||
\(35\) | − | 2.75054i | − | 0.464925i | ||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −4.90852 | − | 3.59255i | −0.806957 | − | 0.590611i | ||||
\(38\) | −6.75054 | −1.09508 | ||||||||
\(39\) | 6.75054i | 1.08095i | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | − | 2.75054i | − | 0.424417i | ||||||
\(43\) | − | 9.81705i | − | 1.49709i | −0.663086 | − | 0.748543i | \(-0.730754\pi\) | ||
0.663086 | − | 0.748543i | \(-0.269246\pi\) | |||||||
\(44\) | −4.75054 | −0.716170 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 5.06651 | 0.747017 | ||||||||
\(47\) | 3.50107 | 0.510684 | 0.255342 | − | 0.966851i | \(-0.417812\pi\) | ||||
0.255342 | + | 0.966851i | \(0.417812\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0.565444 | 0.0807777 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 7.06651i | 0.989510i | ||||||||
\(52\) | − | 6.75054i | − | 0.936131i | ||||||
\(53\) | 4.75054 | 0.652536 | 0.326268 | − | 0.945277i | \(-0.394209\pi\) | ||||
0.326268 | + | 0.945277i | \(0.394209\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | − | 4.75054i | − | 0.640562i | ||||||
\(56\) | 2.75054i | 0.367556i | ||||||||
\(57\) | − | 6.75054i | − | 0.894130i | ||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | − | 11.8170i | − | 1.53845i | −0.638979 | − | 0.769224i | \(-0.720643\pi\) | ||
0.638979 | − | 0.769224i | \(-0.279357\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 2.00000i | 0.256074i | 0.991769 | + | 0.128037i | \(0.0408676\pi\) | ||||
−0.991769 | + | 0.128037i | \(0.959132\pi\) | |||||||
\(62\) | 0.315979 | 0.0401294 | ||||||||
\(63\) | 2.75054 | 0.346535 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.75054 | 0.837301 | ||||||||
\(66\) | − | 4.75054i | − | 0.584750i | ||||||
\(67\) | 15.0021 | 1.83280 | 0.916402 | − | 0.400260i | \(-0.131080\pi\) | ||||
0.916402 | + | 0.400260i | \(0.131080\pi\) | |||||||
\(68\) | − | 7.06651i | − | 0.856941i | ||||||
\(69\) | 5.06651i | 0.609937i | ||||||||
\(70\) | −2.75054 | −0.328752 | ||||||||
\(71\) | −14.1330 | −1.67728 | −0.838641 | − | 0.544685i | \(-0.816649\pi\) | ||||
−0.838641 | + | 0.544685i | \(0.816649\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −6.43456 | −0.753108 | −0.376554 | − | 0.926395i | \(-0.622891\pi\) | ||||
−0.376554 | + | 0.926395i | \(0.622891\pi\) | |||||||
\(74\) | −3.59255 | + | 4.90852i | −0.417625 | + | 0.570604i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 6.75054i | 0.774339i | ||||||||
\(77\) | 13.0665 | 1.48907 | ||||||||
\(78\) | 6.75054 | 0.764348 | ||||||||
\(79\) | − | 8.31598i | − | 0.935621i | −0.883829 | − | 0.467810i | \(-0.845043\pi\) | ||
0.883829 | − | 0.467810i | \(-0.154957\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000i | 0.220863i | ||||||||
\(83\) | 4.43456 | 0.486756 | 0.243378 | − | 0.969932i | \(-0.421744\pi\) | ||||
0.243378 | + | 0.969932i | \(0.421744\pi\) | |||||||
\(84\) | −2.75054 | −0.300108 | ||||||||
\(85\) | 7.06651 | 0.766471 | ||||||||
\(86\) | −9.81705 | −1.05860 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | 4.75054i | 0.506409i | ||||||||
\(89\) | 6.25161i | 0.662669i | 0.943513 | + | 0.331334i | \(0.107499\pi\) | ||||
−0.943513 | + | 0.331334i | \(0.892501\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 18.5676i | 1.94641i | ||||||||
\(92\) | − | 5.06651i | − | 0.528221i | ||||||
\(93\) | 0.315979i | 0.0327655i | ||||||||
\(94\) | − | 3.50107i | − | 0.361108i | ||||||
\(95\) | −6.75054 | −0.692590 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | − | 11.5011i | − | 1.16776i | −0.811841 | − | 0.583878i | \(-0.801534\pi\) | ||
0.811841 | − | 0.583878i | \(-0.198466\pi\) | |||||||
\(98\) | − | 0.565444i | − | 0.0571185i | ||||||
\(99\) | 4.75054 | 0.477447 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.18509 | 0.714943 | 0.357472 | − | 0.933924i | \(-0.383639\pi\) | ||||
0.357472 | + | 0.933924i | \(0.383639\pi\) | |||||||
\(102\) | 7.06651 | 0.699689 | ||||||||
\(103\) | 0.631958i | 0.0622687i | 0.999515 | + | 0.0311344i | \(0.00991198\pi\) | ||||
−0.999515 | + | 0.0311344i | \(0.990088\pi\) | |||||||
\(104\) | −6.75054 | −0.661944 | ||||||||
\(105\) | − | 2.75054i | − | 0.268425i | ||||||
\(106\) | − | 4.75054i | − | 0.461413i | ||||||
\(107\) | −12.0687 | −1.16672 | −0.583360 | − | 0.812213i | \(-0.698262\pi\) | ||||
−0.583360 | + | 0.812213i | \(0.698262\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | − | 4.56758i | − | 0.437495i | −0.975781 | − | 0.218748i | \(-0.929803\pi\) | ||
0.975781 | − | 0.218748i | \(-0.0701971\pi\) | |||||||
\(110\) | −4.75054 | −0.452946 | ||||||||
\(111\) | −4.90852 | − | 3.59255i | −0.465897 | − | 0.340989i | ||||
\(112\) | 2.75054 | 0.259901 | ||||||||
\(113\) | − | 2.00000i | − | 0.188144i | −0.995565 | − | 0.0940721i | \(-0.970012\pi\) | ||
0.995565 | − | 0.0940721i | \(-0.0299884\pi\) | |||||||
\(114\) | −6.75054 | −0.632246 | ||||||||
\(115\) | 5.06651 | 0.472455 | ||||||||
\(116\) | − | 2.00000i | − | 0.185695i | ||||||
\(117\) | 6.75054i | 0.624087i | ||||||||
\(118\) | −11.8170 | −1.08785 | ||||||||
\(119\) | 19.4367i | 1.78176i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 11.5676 | 1.05160 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | − | 0.315979i | − | 0.0283758i | ||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | − | 2.75054i | − | 0.245037i | ||||||
\(127\) | −14.7505 | −1.30890 | −0.654449 | − | 0.756106i | \(-0.727099\pi\) | ||||
−0.654449 | + | 0.756106i | \(0.727099\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | − | 9.81705i | − | 0.864343i | ||||||
\(130\) | − | 6.75054i | − | 0.592061i | ||||||
\(131\) | 7.18509i | 0.627764i | 0.949462 | + | 0.313882i | \(0.101630\pi\) | ||||
−0.949462 | + | 0.313882i | \(0.898370\pi\) | |||||||
\(132\) | −4.75054 | −0.413481 | ||||||||
\(133\) | − | 18.5676i | − | 1.61001i | ||||||
\(134\) | − | 15.0021i | − | 1.29599i | ||||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | −7.06651 | −0.605949 | ||||||||
\(137\) | −1.68402 | −0.143876 | −0.0719378 | − | 0.997409i | \(-0.522918\pi\) | ||||
−0.0719378 | + | 0.997409i | \(0.522918\pi\) | |||||||
\(138\) | 5.06651 | 0.431290 | ||||||||
\(139\) | −23.0021 | −1.95102 | −0.975508 | − | 0.219964i | \(-0.929406\pi\) | ||||
−0.975508 | + | 0.219964i | \(0.929406\pi\) | |||||||
\(140\) | 2.75054i | 0.232463i | ||||||||
\(141\) | 3.50107 | 0.294843 | ||||||||
\(142\) | 14.1330i | 1.18602i | ||||||||
\(143\) | 32.0687i | 2.68172i | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 6.43456i | 0.532528i | ||||||||
\(147\) | 0.565444 | 0.0466370 | ||||||||
\(148\) | 4.90852 | + | 3.59255i | 0.403478 | + | 0.295305i | ||||
\(149\) | −7.81705 | −0.640398 | −0.320199 | − | 0.947350i | \(-0.603750\pi\) | ||||
−0.320199 | + | 0.947350i | \(0.603750\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 16.4346 | 1.33743 | 0.668713 | − | 0.743521i | \(-0.266846\pi\) | ||||
0.668713 | + | 0.743521i | \(0.266846\pi\) | |||||||
\(152\) | 6.75054 | 0.547541 | ||||||||
\(153\) | 7.06651i | 0.571294i | ||||||||
\(154\) | − | 13.0665i | − | 1.05293i | ||||||
\(155\) | 0.315979 | 0.0253801 | ||||||||
\(156\) | − | 6.75054i | − | 0.540475i | ||||||
\(157\) | −5.81705 | −0.464251 | −0.232126 | − | 0.972686i | \(-0.574568\pi\) | ||||
−0.232126 | + | 0.972686i | \(0.574568\pi\) | |||||||
\(158\) | −8.31598 | −0.661584 | ||||||||
\(159\) | 4.75054 | 0.376742 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 13.9356i | 1.09828i | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 18.2516i | − | 1.42958i | −0.699341 | − | 0.714788i | \(-0.746523\pi\) | ||
0.699341 | − | 0.714788i | \(-0.253477\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | − | 4.75054i | − | 0.369829i | ||||||
\(166\) | − | 4.43456i | − | 0.344188i | ||||||
\(167\) | − | 5.06651i | − | 0.392059i | −0.980598 | − | 0.196029i | \(-0.937195\pi\) | ||
0.980598 | − | 0.196029i | \(-0.0628048\pi\) | |||||||
\(168\) | 2.75054i | 0.212208i | ||||||||
\(169\) | −32.5697 | −2.50536 | ||||||||
\(170\) | − | 7.06651i | − | 0.541977i | ||||||
\(171\) | − | 6.75054i | − | 0.516226i | ||||||
\(172\) | 9.81705i | 0.748543i | ||||||||
\(173\) | 4.11858 | 0.313130 | 0.156565 | − | 0.987668i | \(-0.449958\pi\) | ||||
0.156565 | + | 0.987668i | \(0.449958\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | −2.75054 | −0.207921 | ||||||||
\(176\) | 4.75054 | 0.358085 | ||||||||
\(177\) | − | 11.8170i | − | 0.888224i | ||||||
\(178\) | 6.25161 | 0.468578 | ||||||||
\(179\) | 9.68402i | 0.723818i | 0.932213 | + | 0.361909i | \(0.117875\pi\) | ||||
−0.932213 | + | 0.361909i | \(0.882125\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 10.6320 | 0.790267 | 0.395134 | − | 0.918624i | \(-0.370698\pi\) | ||||
0.395134 | + | 0.918624i | \(0.370698\pi\) | |||||||
\(182\) | 18.5676 | 1.37632 | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | −5.06651 | −0.373508 | ||||||||
\(185\) | −3.59255 | + | 4.90852i | −0.264129 | + | 0.360882i | ||||
\(186\) | 0.315979 | 0.0231687 | ||||||||
\(187\) | 33.5697i | 2.45486i | ||||||||
\(188\) | −3.50107 | −0.255342 | ||||||||
\(189\) | 2.75054 | 0.200072 | ||||||||
\(190\) | 6.75054i | 0.489735i | ||||||||
\(191\) | − | 6.93349i | − | 0.501689i | −0.968027 | − | 0.250845i | \(-0.919292\pi\) | ||
0.968027 | − | 0.250845i | \(-0.0807084\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 0.498930i | 0.0359137i | 0.999839 | + | 0.0179569i | \(0.00571616\pi\) | ||||
−0.999839 | + | 0.0179569i | \(0.994284\pi\) | |||||||
\(194\) | −11.5011 | −0.825729 | ||||||||
\(195\) | 6.75054 | 0.483416 | ||||||||
\(196\) | −0.565444 | −0.0403889 | ||||||||
\(197\) | −16.7505 | −1.19343 | −0.596713 | − | 0.802455i | \(-0.703527\pi\) | ||||
−0.596713 | + | 0.802455i | \(0.703527\pi\) | |||||||
\(198\) | − | 4.75054i | − | 0.337606i | ||||||
\(199\) | − | 3.31812i | − | 0.235215i | −0.993060 | − | 0.117608i | \(-0.962477\pi\) | ||
0.993060 | − | 0.117608i | \(-0.0375225\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 15.0021 | 1.05817 | ||||||||
\(202\) | − | 7.18509i | − | 0.505541i | ||||||
\(203\) | 5.50107i | 0.386099i | ||||||||
\(204\) | − | 7.06651i | − | 0.494755i | ||||||
\(205\) | 2.00000i | 0.139686i | ||||||||
\(206\) | 0.631958 | 0.0440306 | ||||||||
\(207\) | 5.06651i | 0.352147i | ||||||||
\(208\) | 6.75054i | 0.468065i | ||||||||
\(209\) | − | 32.0687i | − | 2.21824i | ||||||
\(210\) | −2.75054 | −0.189805 | ||||||||
\(211\) | −13.5011 | −0.929452 | −0.464726 | − | 0.885455i | \(-0.653847\pi\) | ||||
−0.464726 | + | 0.885455i | \(0.653847\pi\) | |||||||
\(212\) | −4.75054 | −0.326268 | ||||||||
\(213\) | −14.1330 | −0.968379 | ||||||||
\(214\) | 12.0687i | 0.824996i | ||||||||
\(215\) | −9.81705 | −0.669517 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0.869112i | 0.0589992i | ||||||||
\(218\) | −4.56758 | −0.309356 | ||||||||
\(219\) | −6.43456 | −0.434807 | ||||||||
\(220\) | 4.75054i | 0.320281i | ||||||||
\(221\) | −47.7028 | −3.20883 | ||||||||
\(222\) | −3.59255 | + | 4.90852i | −0.241116 | + | 0.329439i | ||||
\(223\) | 25.3181 | 1.69543 | 0.847713 | − | 0.530455i | \(-0.177979\pi\) | ||||
0.847713 | + | 0.530455i | \(0.177979\pi\) | |||||||
\(224\) | − | 2.75054i | − | 0.183778i | ||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −2.00000 | −0.133038 | ||||||||
\(227\) | 4.63196i | 0.307434i | 0.988115 | + | 0.153717i | \(0.0491244\pi\) | ||||
−0.988115 | + | 0.153717i | \(0.950876\pi\) | |||||||
\(228\) | 6.75054i | 0.447065i | ||||||||
\(229\) | 20.1330 | 1.33043 | 0.665214 | − | 0.746653i | \(-0.268340\pi\) | ||||
0.665214 | + | 0.746653i | \(0.268340\pi\) | |||||||
\(230\) | − | 5.06651i | − | 0.334076i | ||||||
\(231\) | 13.0665 | 0.859714 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | −6.31598 | −0.413774 | −0.206887 | − | 0.978365i | \(-0.566333\pi\) | ||||
−0.206887 | + | 0.978365i | \(0.566333\pi\) | |||||||
\(234\) | 6.75054 | 0.441296 | ||||||||
\(235\) | − | 3.50107i | − | 0.228385i | ||||||
\(236\) | 11.8170i | 0.769224i | ||||||||
\(237\) | − | 8.31598i | − | 0.540181i | ||||||
\(238\) | 19.4367 | 1.25989 | ||||||||
\(239\) | − | 12.6320i | − | 0.817093i | −0.912737 | − | 0.408547i | \(-0.866036\pi\) | ||
0.912737 | − | 0.408547i | \(-0.133964\pi\) | |||||||
\(240\) | − | 1.00000i | − | 0.0645497i | ||||||
\(241\) | − | 16.6320i | − | 1.07136i | −0.844422 | − | 0.535679i | \(-0.820056\pi\) | ||
0.844422 | − | 0.535679i | \(-0.179944\pi\) | |||||||
\(242\) | − | 11.5676i | − | 0.743593i | ||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | − | 2.00000i | − | 0.128037i | ||||||
\(245\) | − | 0.565444i | − | 0.0361249i | ||||||
\(246\) | 2.00000i | 0.127515i | ||||||||
\(247\) | 45.5697 | 2.89953 | ||||||||
\(248\) | −0.315979 | −0.0200647 | ||||||||
\(249\) | 4.43456 | 0.281029 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 1.68402i | 0.106294i | 0.998587 | + | 0.0531472i | \(0.0169253\pi\) | ||||
−0.998587 | + | 0.0531472i | \(0.983075\pi\) | |||||||
\(252\) | −2.75054 | −0.173267 | ||||||||
\(253\) | 24.0687i | 1.51318i | ||||||||
\(254\) | 14.7505i | 0.925531i | ||||||||
\(255\) | 7.06651 | 0.442522 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.43242i | 0.214108i | 0.994253 | + | 0.107054i | \(0.0341418\pi\) | ||||
−0.994253 | + | 0.107054i | \(0.965858\pi\) | |||||||
\(258\) | −9.81705 | −0.611183 | ||||||||
\(259\) | −13.5011 | − | 9.88142i | −0.838916 | − | 0.614002i | ||||
\(260\) | −6.75054 | −0.418650 | ||||||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 7.18509 | 0.443896 | ||||||||
\(263\) | 6.86911 | 0.423568 | 0.211784 | − | 0.977317i | \(-0.432073\pi\) | ||||
0.211784 | + | 0.977317i | \(0.432073\pi\) | |||||||
\(264\) | 4.75054i | 0.292375i | ||||||||
\(265\) | − | 4.75054i | − | 0.291823i | ||||||
\(266\) | −18.5676 | −1.13845 | ||||||||
\(267\) | 6.25161i | 0.382592i | ||||||||
\(268\) | −15.0021 | −0.916402 | ||||||||
\(269\) | −9.24946 | −0.563950 | −0.281975 | − | 0.959422i | \(-0.590989\pi\) | ||||
−0.281975 | + | 0.959422i | \(0.590989\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 14.3702 | 0.872926 | 0.436463 | − | 0.899722i | \(-0.356231\pi\) | ||||
0.436463 | + | 0.899722i | \(0.356231\pi\) | |||||||
\(272\) | 7.06651i | 0.428470i | ||||||||
\(273\) | 18.5676i | 1.12376i | ||||||||
\(274\) | 1.68402i | 0.101735i | ||||||||
\(275\) | −4.75054 | −0.286468 | ||||||||
\(276\) | − | 5.06651i | − | 0.304968i | ||||||
\(277\) | 26.3846i | 1.58530i | 0.609678 | + | 0.792650i | \(0.291299\pi\) | ||||
−0.609678 | + | 0.792650i | \(0.708701\pi\) | |||||||
\(278\) | 23.0021i | 1.37958i | ||||||||
\(279\) | 0.315979i | 0.0189172i | ||||||||
\(280\) | 2.75054 | 0.164376 | ||||||||
\(281\) | 15.7527i | 0.939726i | 0.882739 | + | 0.469863i | \(0.155697\pi\) | ||||
−0.882739 | + | 0.469863i | \(0.844303\pi\) | |||||||
\(282\) | − | 3.50107i | − | 0.208486i | ||||||
\(283\) | 12.3846i | 0.736190i | 0.929788 | + | 0.368095i | \(0.119990\pi\) | ||||
−0.929788 | + | 0.368095i | \(0.880010\pi\) | |||||||
\(284\) | 14.1330 | 0.838641 | ||||||||
\(285\) | −6.75054 | −0.399867 | ||||||||
\(286\) | 32.0687 | 1.89626 | ||||||||
\(287\) | −5.50107 | −0.324718 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −32.9356 | −1.93739 | ||||||||
\(290\) | − | 2.00000i | − | 0.117444i | ||||||
\(291\) | − | 11.5011i | − | 0.674205i | ||||||
\(292\) | 6.43456 | 0.376554 | ||||||||
\(293\) | 0.750535 | 0.0438467 | 0.0219234 | − | 0.999760i | \(-0.493021\pi\) | ||||
0.0219234 | + | 0.999760i | \(0.493021\pi\) | |||||||
\(294\) | − | 0.565444i | − | 0.0329774i | ||||||
\(295\) | −11.8170 | −0.688015 | ||||||||
\(296\) | 3.59255 | − | 4.90852i | 0.208812 | − | 0.285302i | ||||
\(297\) | 4.75054 | 0.275654 | ||||||||
\(298\) | 7.81705i | 0.452830i | ||||||||
\(299\) | −34.2017 | −1.97793 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − | 27.0021i | − | 1.55638i | ||||||
\(302\) | − | 16.4346i | − | 0.945702i | ||||||
\(303\) | 7.18509 | 0.412773 | ||||||||
\(304\) | − | 6.75054i | − | 0.387170i | ||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 7.06651 | 0.403966 | ||||||||
\(307\) | 18.3702 | 1.04844 | 0.524221 | − | 0.851582i | \(-0.324357\pi\) | ||||
0.524221 | + | 0.851582i | \(0.324357\pi\) | |||||||
\(308\) | −13.0665 | −0.744534 | ||||||||
\(309\) | 0.631958i | 0.0359509i | ||||||||
\(310\) | − | 0.315979i | − | 0.0179464i | ||||||
\(311\) | 35.0021i | 1.98479i | 0.123097 | + | 0.992395i | \(0.460717\pi\) | ||||
−0.123097 | + | 0.992395i | \(0.539283\pi\) | |||||||
\(312\) | −6.75054 | −0.382174 | ||||||||
\(313\) | 1.36804i | 0.0773263i | 0.999252 | + | 0.0386631i | \(0.0123099\pi\) | ||||
−0.999252 | + | 0.0386631i | \(0.987690\pi\) | |||||||
\(314\) | 5.81705i | 0.328275i | ||||||||
\(315\) | − | 2.75054i | − | 0.154975i | ||||||
\(316\) | 8.31598i | 0.467810i | ||||||||
\(317\) | 10.0542 | 0.564700 | 0.282350 | − | 0.959311i | \(-0.408886\pi\) | ||||
0.282350 | + | 0.959311i | \(0.408886\pi\) | |||||||
\(318\) | − | 4.75054i | − | 0.266397i | ||||||
\(319\) | 9.50107i | 0.531958i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −12.0687 | −0.673607 | ||||||||
\(322\) | 13.9356 | 0.776602 | ||||||||
\(323\) | 47.7028 | 2.65425 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | − | 6.75054i | − | 0.374452i | ||||||
\(326\) | −18.2516 | −1.01086 | ||||||||
\(327\) | − | 4.56758i | − | 0.252588i | ||||||
\(328\) | − | 2.00000i | − | 0.110432i | ||||||
\(329\) | 9.62982 | 0.530909 | ||||||||
\(330\) | −4.75054 | −0.261508 | ||||||||
\(331\) | 26.3160i | 1.44646i | 0.690609 | + | 0.723229i | \(0.257343\pi\) | ||||
−0.690609 | + | 0.723229i | \(0.742657\pi\) | |||||||
\(332\) | −4.43456 | −0.243378 | ||||||||
\(333\) | −4.90852 | − | 3.59255i | −0.268986 | − | 0.196870i | ||||
\(334\) | −5.06651 | −0.277227 | ||||||||
\(335\) | − | 15.0021i | − | 0.819655i | ||||||
\(336\) | 2.75054 | 0.150054 | ||||||||
\(337\) | −26.7006 | −1.45448 | −0.727238 | − | 0.686386i | \(-0.759196\pi\) | ||||
−0.727238 | + | 0.686386i | \(0.759196\pi\) | |||||||
\(338\) | 32.5697i | 1.77156i | ||||||||
\(339\) | − | 2.00000i | − | 0.108625i | ||||||
\(340\) | −7.06651 | −0.383236 | ||||||||
\(341\) | 1.50107i | 0.0812875i | ||||||||
\(342\) | −6.75054 | −0.365027 | ||||||||
\(343\) | −17.6985 | −0.955628 | ||||||||
\(344\) | 9.81705 | 0.529300 | ||||||||
\(345\) | 5.06651 | 0.272772 | ||||||||
\(346\) | − | 4.11858i | − | 0.221416i | ||||||
\(347\) | − | 13.5011i | − | 0.724775i | −0.932027 | − | 0.362388i | \(-0.881962\pi\) | ||
0.932027 | − | 0.362388i | \(-0.118038\pi\) | |||||||
\(348\) | − | 2.00000i | − | 0.107211i | ||||||
\(349\) | −9.36804 | −0.501460 | −0.250730 | − | 0.968057i | \(-0.580671\pi\) | ||||
−0.250730 | + | 0.968057i | \(0.580671\pi\) | |||||||
\(350\) | 2.75054i | 0.147022i | ||||||||
\(351\) | 6.75054i | 0.360317i | ||||||||
\(352\) | − | 4.75054i | − | 0.253204i | ||||||
\(353\) | 13.6341i | 0.725670i | 0.931853 | + | 0.362835i | \(0.118191\pi\) | ||||
−0.931853 | + | 0.362835i | \(0.881809\pi\) | |||||||
\(354\) | −11.8170 | −0.628069 | ||||||||
\(355\) | 14.1330i | 0.750103i | ||||||||
\(356\) | − | 6.25161i | − | 0.331334i | ||||||
\(357\) | 19.4367i | 1.02870i | ||||||||
\(358\) | 9.68402 | 0.511816 | ||||||||
\(359\) | 8.86911 | 0.468094 | 0.234047 | − | 0.972225i | \(-0.424803\pi\) | ||||
0.234047 | + | 0.972225i | \(0.424803\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −26.5697 | −1.39841 | ||||||||
\(362\) | − | 10.6320i | − | 0.558803i | ||||||
\(363\) | 11.5676 | 0.607141 | ||||||||
\(364\) | − | 18.5676i | − | 0.973206i | ||||||
\(365\) | 6.43456i | 0.336800i | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 2.11858 | 0.110589 | 0.0552944 | − | 0.998470i | \(-0.482390\pi\) | ||||
0.0552944 | + | 0.998470i | \(0.482390\pi\) | |||||||
\(368\) | 5.06651i | 0.264110i | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 4.90852 | + | 3.59255i | 0.255182 | + | 0.186768i | ||||
\(371\) | 13.0665 | 0.678380 | ||||||||
\(372\) | − | 0.315979i | − | 0.0163828i | ||||||
\(373\) | 23.0810 | 1.19509 | 0.597544 | − | 0.801836i | \(-0.296143\pi\) | ||||
0.597544 | + | 0.801836i | \(0.296143\pi\) | |||||||
\(374\) | 33.5697 | 1.73585 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 3.50107i | 0.180554i | ||||||||
\(377\) | −13.5011 | −0.695341 | ||||||||
\(378\) | − | 2.75054i | − | 0.141472i | ||||||
\(379\) | −8.50321 | −0.436781 | −0.218390 | − | 0.975862i | \(-0.570081\pi\) | ||||
−0.218390 | + | 0.975862i | \(0.570081\pi\) | |||||||
\(380\) | 6.75054 | 0.346295 | ||||||||
\(381\) | −14.7505 | −0.755693 | ||||||||
\(382\) | −6.93349 | −0.354748 | ||||||||
\(383\) | 15.1995i | 0.776660i | 0.921520 | + | 0.388330i | \(0.126948\pi\) | ||||
−0.921520 | + | 0.388330i | \(0.873052\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − | 13.0665i | − | 0.665931i | ||||||
\(386\) | 0.498930 | 0.0253948 | ||||||||
\(387\) | − | 9.81705i | − | 0.499029i | ||||||
\(388\) | 11.5011i | 0.583878i | ||||||||
\(389\) | 32.1330i | 1.62921i | 0.580017 | + | 0.814605i | \(0.303046\pi\) | ||||
−0.580017 | + | 0.814605i | \(0.696954\pi\) | |||||||
\(390\) | − | 6.75054i | − | 0.341827i | ||||||
\(391\) | −35.8026 | −1.81062 | ||||||||
\(392\) | 0.565444i | 0.0285592i | ||||||||
\(393\) | 7.18509i | 0.362440i | ||||||||
\(394\) | 16.7505i | 0.843880i | ||||||||
\(395\) | −8.31598 | −0.418422 | ||||||||
\(396\) | −4.75054 | −0.238723 | ||||||||
\(397\) | −28.8192 | −1.44639 | −0.723197 | − | 0.690642i | \(-0.757328\pi\) | ||||
−0.723197 | + | 0.690642i | \(0.757328\pi\) | |||||||
\(398\) | −3.31812 | −0.166322 | ||||||||
\(399\) | − | 18.5676i | − | 0.929542i | ||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 10.6175i | 0.530213i | 0.964219 | + | 0.265106i | \(0.0854071\pi\) | ||||
−0.964219 | + | 0.265106i | \(0.914593\pi\) | |||||||
\(402\) | − | 15.0021i | − | 0.748239i | ||||||
\(403\) | −2.13303 | −0.106254 | ||||||||
\(404\) | −7.18509 | −0.357472 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 5.50107 | 0.273014 | ||||||||
\(407\) | −23.3181 | − | 17.0665i | −1.15584 | − | 0.845956i | ||||
\(408\) | −7.06651 | −0.349845 | ||||||||
\(409\) | − | 37.6384i | − | 1.86110i | −0.366167 | − | 0.930549i | \(-0.619330\pi\) | ||
0.366167 | − | 0.930549i | \(-0.380670\pi\) | |||||||
\(410\) | 2.00000 | 0.0987730 | ||||||||
\(411\) | −1.68402 | −0.0830666 | ||||||||
\(412\) | − | 0.631958i | − | 0.0311344i | ||||||
\(413\) | − | 32.5032i | − | 1.59938i | ||||||
\(414\) | 5.06651 | 0.249006 | ||||||||
\(415\) | − | 4.43456i | − | 0.217684i | ||||||
\(416\) | 6.75054 | 0.330972 | ||||||||
\(417\) | −23.0021 | −1.12642 | ||||||||
\(418\) | −32.0687 | −1.56853 | ||||||||
\(419\) | 22.0145 | 1.07548 | 0.537738 | − | 0.843112i | \(-0.319279\pi\) | ||||
0.537738 | + | 0.843112i | \(0.319279\pi\) | |||||||
\(420\) | 2.75054i | 0.134212i | ||||||||
\(421\) | − | 3.26392i | − | 0.159074i | −0.996832 | − | 0.0795368i | \(-0.974656\pi\) | ||
0.996832 | − | 0.0795368i | \(-0.0253441\pi\) | |||||||
\(422\) | 13.5011i | 0.657222i | ||||||||
\(423\) | 3.50107 | 0.170228 | ||||||||
\(424\) | 4.75054i | 0.230706i | ||||||||
\(425\) | − | 7.06651i | − | 0.342776i | ||||||
\(426\) | 14.1330i | 0.684747i | ||||||||
\(427\) | 5.50107i | 0.266215i | ||||||||
\(428\) | 12.0687 | 0.583360 | ||||||||
\(429\) | 32.0687i | 1.54829i | ||||||||
\(430\) | 9.81705i | 0.473420i | ||||||||
\(431\) | − | 26.5676i | − | 1.27972i | −0.768493 | − | 0.639858i | \(-0.778993\pi\) | ||
0.768493 | − | 0.639858i | \(-0.221007\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 8.56758 | 0.411732 | 0.205866 | − | 0.978580i | \(-0.433999\pi\) | ||||
0.205866 | + | 0.978580i | \(0.433999\pi\) | |||||||
\(434\) | 0.869112 | 0.0417187 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | 4.56758i | 0.218748i | ||||||||
\(437\) | 34.2017 | 1.63609 | ||||||||
\(438\) | 6.43456i | 0.307455i | ||||||||
\(439\) | − | 8.31598i | − | 0.396900i | −0.980111 | − | 0.198450i | \(-0.936409\pi\) | ||
0.980111 | − | 0.198450i | \(-0.0635907\pi\) | |||||||
\(440\) | 4.75054 | 0.226473 | ||||||||
\(441\) | 0.565444 | 0.0269259 | ||||||||
\(442\) | 47.7028i | 2.26899i | ||||||||
\(443\) | 35.2682 | 1.67564 | 0.837821 | − | 0.545944i | \(-0.183829\pi\) | ||||
0.837821 | + | 0.545944i | \(0.183829\pi\) | |||||||
\(444\) | 4.90852 | + | 3.59255i | 0.232948 | + | 0.170495i | ||||
\(445\) | 6.25161 | 0.296355 | ||||||||
\(446\) | − | 25.3181i | − | 1.19885i | ||||||
\(447\) | −7.81705 | −0.369734 | ||||||||
\(448\) | −2.75054 | −0.129951 | ||||||||
\(449\) | − | 30.3203i | − | 1.43090i | −0.698663 | − | 0.715451i | \(-0.746221\pi\) | ||
0.698663 | − | 0.715451i | \(-0.253779\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −9.50107 | −0.447388 | ||||||||
\(452\) | 2.00000i | 0.0940721i | ||||||||
\(453\) | 16.4346 | 0.772163 | ||||||||
\(454\) | 4.63196 | 0.217389 | ||||||||
\(455\) | 18.5676 | 0.870462 | ||||||||
\(456\) | 6.75054 | 0.316123 | ||||||||
\(457\) | − | 10.6320i | − | 0.497342i | −0.968588 | − | 0.248671i | \(-0.920006\pi\) | ||
0.968588 | − | 0.248671i | \(-0.0799938\pi\) | |||||||
\(458\) | − | 20.1330i | − | 0.940755i | ||||||
\(459\) | 7.06651i | 0.329837i | ||||||||
\(460\) | −5.06651 | −0.236227 | ||||||||
\(461\) | − | 30.5032i | − | 1.42068i | −0.703861 | − | 0.710338i | \(-0.748542\pi\) | ||
0.703861 | − | 0.710338i | \(-0.251458\pi\) | |||||||
\(462\) | − | 13.0665i | − | 0.607909i | ||||||
\(463\) | − | 39.5054i | − | 1.83597i | −0.396616 | − | 0.917985i | \(-0.629815\pi\) | ||
0.396616 | − | 0.917985i | \(-0.370185\pi\) | |||||||
\(464\) | 2.00000i | 0.0928477i | ||||||||
\(465\) | 0.315979 | 0.0146532 | ||||||||
\(466\) | 6.31598i | 0.292582i | ||||||||
\(467\) | − | 16.6320i | − | 0.769635i | −0.922993 | − | 0.384818i | \(-0.874264\pi\) | ||
0.922993 | − | 0.384818i | \(-0.125736\pi\) | |||||||
\(468\) | − | 6.75054i | − | 0.312044i | ||||||
\(469\) | 41.2639 | 1.90539 | ||||||||
\(470\) | −3.50107 | −0.161492 | ||||||||
\(471\) | −5.81705 | −0.268036 | ||||||||
\(472\) | 11.8170 | 0.543924 | ||||||||
\(473\) | − | 46.6362i | − | 2.14434i | ||||||
\(474\) | −8.31598 | −0.381966 | ||||||||
\(475\) | 6.75054i | 0.309736i | ||||||||
\(476\) | − | 19.4367i | − | 0.890880i | ||||||
\(477\) | 4.75054 | 0.217512 | ||||||||
\(478\) | −12.6320 | −0.577772 | ||||||||
\(479\) | 33.2038i | 1.51712i | 0.651602 | + | 0.758561i | \(0.274097\pi\) | ||||
−0.651602 | + | 0.758561i | \(0.725903\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 24.2516 | − | 33.1352i | 1.10578 | − | 1.51083i | ||||
\(482\) | −16.6320 | −0.757565 | ||||||||
\(483\) | 13.9356i | 0.634093i | ||||||||
\(484\) | −11.5676 | −0.525799 | ||||||||
\(485\) | −11.5011 | −0.522237 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 11.6341i | 0.527191i | 0.964633 | + | 0.263596i | \(0.0849085\pi\) | ||||
−0.964633 | + | 0.263596i | \(0.915092\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | − | 18.2516i | − | 0.825366i | ||||||
\(490\) | −0.565444 | −0.0255442 | ||||||||
\(491\) | −4.75054 | −0.214389 | −0.107194 | − | 0.994238i | \(-0.534187\pi\) | ||||
−0.107194 | + | 0.994238i | \(0.534187\pi\) | |||||||
\(492\) | 2.00000 | 0.0901670 | ||||||||
\(493\) | −14.1330 | −0.636520 | ||||||||
\(494\) | − | 45.5697i | − | 2.05028i | ||||||
\(495\) | − | 4.75054i | − | 0.213521i | ||||||
\(496\) | 0.315979i | 0.0141879i | ||||||||
\(497\) | −38.8734 | −1.74371 | ||||||||
\(498\) | − | 4.43456i | − | 0.198717i | ||||||
\(499\) | − | 9.12072i | − | 0.408299i | −0.978940 | − | 0.204150i | \(-0.934557\pi\) | ||
0.978940 | − | 0.204150i | \(-0.0654429\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | − | 5.06651i | − | 0.226355i | ||||||
\(502\) | 1.68402 | 0.0751615 | ||||||||
\(503\) | 9.26392i | 0.413058i | 0.978441 | + | 0.206529i | \(0.0662167\pi\) | ||||
−0.978441 | + | 0.206529i | \(0.933783\pi\) | |||||||
\(504\) | 2.75054i | 0.122519i | ||||||||
\(505\) | − | 7.18509i | − | 0.319732i | ||||||
\(506\) | 24.0687 | 1.06998 | ||||||||
\(507\) | −32.5697 | −1.44647 | ||||||||
\(508\) | 14.7505 | 0.654449 | ||||||||
\(509\) | 23.0166 | 1.02019 | 0.510096 | − | 0.860117i | \(-0.329610\pi\) | ||||
0.510096 | + | 0.860117i | \(0.329610\pi\) | |||||||
\(510\) | − | 7.06651i | − | 0.312911i | ||||||
\(511\) | −17.6985 | −0.782934 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 6.75054i | − | 0.298043i | ||||||
\(514\) | 3.43242 | 0.151397 | ||||||||
\(515\) | 0.631958 | 0.0278474 | ||||||||
\(516\) | 9.81705i | 0.432172i | ||||||||
\(517\) | 16.6320 | 0.731473 | ||||||||
\(518\) | −9.88142 | + | 13.5011i | −0.434165 | + | 0.593203i | ||||
\(519\) | 4.11858 | 0.180785 | ||||||||
\(520\) | 6.75054i | 0.296031i | ||||||||
\(521\) | 30.6320 | 1.34201 | 0.671005 | − | 0.741453i | \(-0.265863\pi\) | ||||
0.671005 | + | 0.741453i | \(0.265863\pi\) | |||||||
\(522\) | 2.00000 | 0.0875376 | ||||||||
\(523\) | 15.5553i | 0.680185i | 0.940392 | + | 0.340092i | \(0.110458\pi\) | ||||
−0.940392 | + | 0.340092i | \(0.889542\pi\) | |||||||
\(524\) | − | 7.18509i | − | 0.313882i | ||||||
\(525\) | −2.75054 | −0.120043 | ||||||||
\(526\) | − | 6.86911i | − | 0.299508i | ||||||
\(527\) | −2.23287 | −0.0972654 | ||||||||
\(528\) | 4.75054 | 0.206741 | ||||||||
\(529\) | −2.66957 | −0.116068 | ||||||||
\(530\) | −4.75054 | −0.206350 | ||||||||
\(531\) | − | 11.8170i | − | 0.512816i | ||||||
\(532\) | 18.5676i | 0.805007i | ||||||||
\(533\) | − | 13.5011i | − | 0.584796i | ||||||
\(534\) | 6.25161 | 0.270533 | ||||||||
\(535\) | 12.0687i | 0.521773i | ||||||||
\(536\) | 15.0021i | 0.647994i | ||||||||
\(537\) | 9.68402i | 0.417896i | ||||||||
\(538\) | 9.24946i | 0.398773i | ||||||||
\(539\) | 2.68616 | 0.115701 | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | − | 3.43242i | − | 0.147571i | −0.997274 | − | 0.0737855i | \(-0.976492\pi\) | ||
0.997274 | − | 0.0737855i | \(-0.0235080\pi\) | |||||||
\(542\) | − | 14.3702i | − | 0.617252i | ||||||
\(543\) | 10.6320 | 0.456261 | ||||||||
\(544\) | 7.06651 | 0.302974 | ||||||||
\(545\) | −4.56758 | −0.195654 | ||||||||
\(546\) | 18.5676 | 0.794619 | ||||||||
\(547\) | 17.3825i | 0.743222i | 0.928389 | + | 0.371611i | \(0.121194\pi\) | ||||
−0.928389 | + | 0.371611i | \(0.878806\pi\) | |||||||
\(548\) | 1.68402 | 0.0719378 | ||||||||
\(549\) | 2.00000i | 0.0853579i | ||||||||
\(550\) | 4.75054i | 0.202564i | ||||||||
\(551\) | 13.5011 | 0.575165 | ||||||||
\(552\) | −5.06651 | −0.215645 | ||||||||
\(553\) | − | 22.8734i | − | 0.972676i | ||||||
\(554\) | 26.3846 | 1.12098 | ||||||||
\(555\) | −3.59255 | + | 4.90852i | −0.152495 | + | 0.208355i | ||||
\(556\) | 23.0021 | 0.975508 | ||||||||
\(557\) | − | 17.0021i | − | 0.720404i | −0.932874 | − | 0.360202i | \(-0.882708\pi\) | ||
0.932874 | − | 0.360202i | \(-0.117292\pi\) | |||||||
\(558\) | 0.315979 | 0.0133765 | ||||||||
\(559\) | 66.2703 | 2.80294 | ||||||||
\(560\) | − | 2.75054i | − | 0.116231i | ||||||
\(561\) | 33.5697i | 1.41731i | ||||||||
\(562\) | 15.7527 | 0.664487 | ||||||||
\(563\) | − | 38.8734i | − | 1.63832i | −0.573566 | − | 0.819159i | \(-0.694441\pi\) | ||
0.573566 | − | 0.819159i | \(-0.305559\pi\) | |||||||
\(564\) | −3.50107 | −0.147422 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 12.3846 | 0.520565 | ||||||||
\(567\) | 2.75054 | 0.115512 | ||||||||
\(568\) | − | 14.1330i | − | 0.593009i | ||||||
\(569\) | 10.3804i | 0.435167i | 0.976042 | + | 0.217584i | \(0.0698174\pi\) | ||||
−0.976042 | + | 0.217584i | \(0.930183\pi\) | |||||||
\(570\) | 6.75054i | 0.282749i | ||||||||
\(571\) | −8.99786 | −0.376549 | −0.188274 | − | 0.982116i | \(-0.560289\pi\) | ||||
−0.188274 | + | 0.982116i | \(0.560289\pi\) | |||||||
\(572\) | − | 32.0687i | − | 1.34086i | ||||||
\(573\) | − | 6.93349i | − | 0.289651i | ||||||
\(574\) | 5.50107i | 0.229610i | ||||||||
\(575\) | − | 5.06651i | − | 0.211288i | ||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 26.8691i | 1.11858i | 0.828973 | + | 0.559288i | \(0.188925\pi\) | ||||
−0.828973 | + | 0.559288i | \(0.811075\pi\) | |||||||
\(578\) | 32.9356i | 1.36994i | ||||||||
\(579\) | 0.498930i | 0.0207348i | ||||||||
\(580\) | −2.00000 | −0.0830455 | ||||||||
\(581\) | 12.1974 | 0.506034 | ||||||||
\(582\) | −11.5011 | −0.476735 | ||||||||
\(583\) | 22.5676 | 0.934654 | ||||||||
\(584\) | − | 6.43456i | − | 0.266264i | ||||||
\(585\) | 6.75054 | 0.279100 | ||||||||
\(586\) | − | 0.750535i | − | 0.0310043i | ||||||
\(587\) | − | 7.87125i | − | 0.324881i | −0.986718 | − | 0.162441i | \(-0.948063\pi\) | ||
0.986718 | − | 0.162441i | \(-0.0519366\pi\) | |||||||
\(588\) | −0.565444 | −0.0233185 | ||||||||
\(589\) | 2.13303 | 0.0878899 | ||||||||
\(590\) | 11.8170i | 0.486500i | ||||||||
\(591\) | −16.7505 | −0.689025 | ||||||||
\(592\) | −4.90852 | − | 3.59255i | −0.201739 | − | 0.147653i | ||||
\(593\) | 33.0810 | 1.35847 | 0.679236 | − | 0.733920i | \(-0.262311\pi\) | ||||
0.679236 | + | 0.733920i | \(0.262311\pi\) | |||||||
\(594\) | − | 4.75054i | − | 0.194917i | ||||||
\(595\) | 19.4367 | 0.796827 | ||||||||
\(596\) | 7.81705 | 0.320199 | ||||||||
\(597\) | − | 3.31812i | − | 0.135802i | ||||||
\(598\) | 34.2017i | 1.39861i | ||||||||
\(599\) | −16.5032 | −0.674303 | −0.337151 | − | 0.941450i | \(-0.609463\pi\) | ||||
−0.337151 | + | 0.941450i | \(0.609463\pi\) | |||||||
\(600\) | − | 1.00000i | − | 0.0408248i | ||||||
\(601\) | −30.0687 | −1.22653 | −0.613263 | − | 0.789879i | \(-0.710143\pi\) | ||||
−0.613263 | + | 0.789879i | \(0.710143\pi\) | |||||||
\(602\) | −27.0021 | −1.10053 | ||||||||
\(603\) | 15.0021 | 0.610934 | ||||||||
\(604\) | −16.4346 | −0.668713 | ||||||||
\(605\) | − | 11.5676i | − | 0.470289i | ||||||
\(606\) | − | 7.18509i | − | 0.291874i | ||||||
\(607\) | − | 7.36804i | − | 0.299060i | −0.988757 | − | 0.149530i | \(-0.952224\pi\) | ||
0.988757 | − | 0.149530i | \(-0.0477760\pi\) | |||||||
\(608\) | −6.75054 | −0.273770 | ||||||||
\(609\) | 5.50107i | 0.222915i | ||||||||
\(610\) | − | 2.00000i | − | 0.0809776i | ||||||
\(611\) | 23.6341i | 0.956133i | ||||||||
\(612\) | − | 7.06651i | − | 0.285647i | ||||||
\(613\) | −9.18509 | −0.370982 | −0.185491 | − | 0.982646i | \(-0.559388\pi\) | ||||
−0.185491 | + | 0.982646i | \(0.559388\pi\) | |||||||
\(614\) | − | 18.3702i | − | 0.741360i | ||||||
\(615\) | 2.00000i | 0.0806478i | ||||||||
\(616\) | 13.0665i | 0.526465i | ||||||||
\(617\) | 7.18509 | 0.289261 | 0.144630 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144630 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(618\) | 0.631958 | 0.0254211 | ||||||||
\(619\) | −34.0043 | −1.36675 | −0.683374 | − | 0.730069i | \(-0.739488\pi\) | ||||
−0.683374 | + | 0.730069i | \(0.739488\pi\) | |||||||
\(620\) | −0.315979 | −0.0126900 | ||||||||
\(621\) | 5.06651i | 0.203312i | ||||||||
\(622\) | 35.0021 | 1.40346 | ||||||||
\(623\) | 17.1953i | 0.688914i | ||||||||
\(624\) | 6.75054i | 0.270238i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.36804 | 0.0546779 | ||||||||
\(627\) | − | 32.0687i | − | 1.28070i | ||||||
\(628\) | 5.81705 | 0.232126 | ||||||||
\(629\) | 25.3868 | − | 34.6862i | 1.01224 | − | 1.38303i | ||||
\(630\) | −2.75054 | −0.109584 | ||||||||
\(631\) | 5.81705i | 0.231573i | 0.993274 | + | 0.115787i | \(0.0369389\pi\) | ||||
−0.993274 | + | 0.115787i | \(0.963061\pi\) | |||||||
\(632\) | 8.31598 | 0.330792 | ||||||||
\(633\) | −13.5011 | −0.536619 | ||||||||
\(634\) | − | 10.0542i | − | 0.399303i | ||||||
\(635\) | 14.7505i | 0.585357i | ||||||||
\(636\) | −4.75054 | −0.188371 | ||||||||
\(637\) | 3.81705i | 0.151237i | ||||||||
\(638\) | 9.50107 | 0.376151 | ||||||||
\(639\) | −14.1330 | −0.559094 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −13.1309 | −0.518639 | −0.259319 | − | 0.965792i | \(-0.583498\pi\) | ||||
−0.259319 | + | 0.965792i | \(0.583498\pi\) | |||||||
\(642\) | 12.0687i | 0.476312i | ||||||||
\(643\) | 22.2516i | 0.877518i | 0.898605 | + | 0.438759i | \(0.144582\pi\) | ||||
−0.898605 | + | 0.438759i | \(0.855418\pi\) | |||||||
\(644\) | − | 13.9356i | − | 0.549141i | ||||||
\(645\) | −9.81705 | −0.386546 | ||||||||
\(646\) | − | 47.7028i | − | 1.87684i | ||||||
\(647\) | − | 24.0687i | − | 0.946236i | −0.880999 | − | 0.473118i | \(-0.843128\pi\) | ||
0.880999 | − | 0.473118i | \(-0.156872\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | − | 56.1373i | − | 2.20358i | ||||||
\(650\) | −6.75054 | −0.264778 | ||||||||
\(651\) | 0.869112i | 0.0340632i | ||||||||
\(652\) | 18.2516i | 0.714788i | ||||||||
\(653\) | − | 25.3680i | − | 0.992728i | −0.868114 | − | 0.496364i | \(-0.834668\pi\) | ||
0.868114 | − | 0.496364i | \(-0.165332\pi\) | |||||||
\(654\) | −4.56758 | −0.178607 | ||||||||
\(655\) | 7.18509 | 0.280745 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | −6.43456 | −0.251036 | ||||||||
\(658\) | − | 9.62982i | − | 0.375409i | ||||||
\(659\) | −18.4490 | −0.718671 | −0.359336 | − | 0.933208i | \(-0.616997\pi\) | ||||
−0.359336 | + | 0.933208i | \(0.616997\pi\) | |||||||
\(660\) | 4.75054i | 0.184914i | ||||||||
\(661\) | − | 18.9378i | − | 0.736594i | −0.929708 | − | 0.368297i | \(-0.879941\pi\) | ||
0.929708 | − | 0.368297i | \(-0.120059\pi\) | |||||||
\(662\) | 26.3160 | 1.02280 | ||||||||
\(663\) | −47.7028 | −1.85262 | ||||||||
\(664\) | 4.43456i | 0.172094i | ||||||||
\(665\) | −18.5676 | −0.720020 | ||||||||
\(666\) | −3.59255 | + | 4.90852i | −0.139208 | + | 0.190201i | ||||
\(667\) | −10.1330 | −0.392352 | ||||||||
\(668\) | 5.06651i | 0.196029i | ||||||||
\(669\) | 25.3181 | 0.978855 | ||||||||
\(670\) | −15.0021 | −0.579583 | ||||||||
\(671\) | 9.50107i | 0.366785i | ||||||||
\(672\) | − | 2.75054i | − | 0.106104i | ||||||
\(673\) | −35.5697 | −1.37111 | −0.685556 | − | 0.728020i | \(-0.740441\pi\) | ||||
−0.685556 | + | 0.728020i | \(0.740441\pi\) | |||||||
\(674\) | 26.7006i | 1.02847i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 32.5697 | 1.25268 | ||||||||
\(677\) | −40.8878 | −1.57145 | −0.785724 | − | 0.618578i | \(-0.787709\pi\) | ||||
−0.785724 | + | 0.618578i | \(0.787709\pi\) | |||||||
\(678\) | −2.00000 | −0.0768095 | ||||||||
\(679\) | − | 31.6341i | − | 1.21401i | ||||||
\(680\) | 7.06651i | 0.270988i | ||||||||
\(681\) | 4.63196i | 0.177497i | ||||||||
\(682\) | 1.50107 | 0.0574790 | ||||||||
\(683\) | − | 14.3702i | − | 0.549860i | −0.961464 | − | 0.274930i | \(-0.911345\pi\) | ||
0.961464 | − | 0.274930i | \(-0.0886546\pi\) | |||||||
\(684\) | 6.75054i | 0.258113i | ||||||||
\(685\) | 1.68402i | 0.0643431i | ||||||||
\(686\) | 17.6985i | 0.675731i | ||||||||
\(687\) | 20.1330 | 0.768123 | ||||||||
\(688\) | − | 9.81705i | − | 0.374272i | ||||||
\(689\) | 32.0687i | 1.22172i | ||||||||
\(690\) | − | 5.06651i | − | 0.192879i | ||||||
\(691\) | −17.7671 | −0.675893 | −0.337947 | − | 0.941165i | \(-0.609732\pi\) | ||||
−0.337947 | + | 0.941165i | \(0.609732\pi\) | |||||||
\(692\) | −4.11858 | −0.156565 | ||||||||
\(693\) | 13.0665 | 0.496356 | ||||||||
\(694\) | −13.5011 | −0.512494 | ||||||||
\(695\) | 23.0021i | 0.872521i | ||||||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | − | 14.1330i | − | 0.535327i | ||||||
\(698\) | 9.36804i | 0.354586i | ||||||||
\(699\) | −6.31598 | −0.238892 | ||||||||
\(700\) | 2.75054 | 0.103960 | ||||||||
\(701\) | 28.1330i | 1.06257i | 0.847193 | + | 0.531285i | \(0.178291\pi\) | ||||
−0.847193 | + | 0.531285i | \(0.821709\pi\) | |||||||
\(702\) | 6.75054 | 0.254783 | ||||||||
\(703\) | −24.2516 | + | 33.1352i | −0.914667 | + | 1.24972i | ||||
\(704\) | −4.75054 | −0.179043 | ||||||||
\(705\) | − | 3.50107i | − | 0.131858i | ||||||
\(706\) | 13.6341 | 0.513126 | ||||||||
\(707\) | 19.7628 | 0.743258 | ||||||||
\(708\) | 11.8170i | 0.444112i | ||||||||
\(709\) | − | 34.0687i | − | 1.27948i | −0.768593 | − | 0.639738i | \(-0.779043\pi\) | ||
0.768593 | − | 0.639738i | \(-0.220957\pi\) | |||||||
\(710\) | 14.1330 | 0.530403 | ||||||||
\(711\) | − | 8.31598i | − | 0.311874i | ||||||
\(712\) | −6.25161 | −0.234289 | ||||||||
\(713\) | −1.60091 | −0.0599547 | ||||||||
\(714\) | 19.4367 | 0.727400 | ||||||||
\(715\) | 32.0687 | 1.19930 | ||||||||
\(716\) | − | 9.68402i | − | 0.361909i | ||||||
\(717\) | − | 12.6320i | − | 0.471749i | ||||||
\(718\) | − | 8.86911i | − | 0.330992i | ||||||
\(719\) | −40.2661 | −1.50167 | −0.750835 | − | 0.660490i | \(-0.770349\pi\) | ||||
−0.750835 | + | 0.660490i | \(0.770349\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | 1.73822i | 0.0647348i | ||||||||
\(722\) | 26.5697i | 0.988823i | ||||||||
\(723\) | − | 16.6320i | − | 0.618549i | ||||||
\(724\) | −10.6320 | −0.395134 | ||||||||
\(725\) | − | 2.00000i | − | 0.0742781i | ||||||
\(726\) | − | 11.5676i | − | 0.429313i | ||||||
\(727\) | − | 13.1352i | − | 0.487156i | −0.969881 | − | 0.243578i | \(-0.921679\pi\) | ||
0.969881 | − | 0.243578i | \(-0.0783213\pi\) | |||||||
\(728\) | −18.5676 | −0.688160 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.43456 | 0.238154 | ||||||||
\(731\) | 69.3723 | 2.56583 | ||||||||
\(732\) | − | 2.00000i | − | 0.0739221i | ||||||
\(733\) | −7.05206 | −0.260474 | −0.130237 | − | 0.991483i | \(-0.541574\pi\) | ||||
−0.130237 | + | 0.991483i | \(0.541574\pi\) | |||||||
\(734\) | − | 2.11858i | − | 0.0781981i | ||||||
\(735\) | − | 0.565444i | − | 0.0208567i | ||||||
\(736\) | 5.06651 | 0.186754 | ||||||||
\(737\) | 71.2682 | 2.62520 | ||||||||
\(738\) | 2.00000i | 0.0736210i | ||||||||
\(739\) | 24.7404 | 0.910089 | 0.455045 | − | 0.890469i | \(-0.349623\pi\) | ||||
0.455045 | + | 0.890469i | \(0.349623\pi\) | |||||||
\(740\) | 3.59255 | − | 4.90852i | 0.132065 | − | 0.180441i | ||||
\(741\) | 45.5697 | 1.67405 | ||||||||
\(742\) | − | 13.0665i | − | 0.479687i | ||||||
\(743\) | 1.36804 | 0.0501886 | 0.0250943 | − | 0.999685i | \(-0.492011\pi\) | ||||
0.0250943 | + | 0.999685i | \(0.492011\pi\) | |||||||
\(744\) | −0.315979 | −0.0115844 | ||||||||
\(745\) | 7.81705i | 0.286395i | ||||||||
\(746\) | − | 23.0810i | − | 0.845054i | ||||||
\(747\) | 4.43456 | 0.162252 | ||||||||
\(748\) | − | 33.5697i | − | 1.22743i | ||||||
\(749\) | −33.1953 | −1.21293 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 16.0000 | 0.583848 | 0.291924 | − | 0.956441i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956441i | \(0.405705\pi\) | |||||||
\(752\) | 3.50107 | 0.127671 | ||||||||
\(753\) | 1.68402i | 0.0613691i | ||||||||
\(754\) | 13.5011i | 0.491680i | ||||||||
\(755\) | − | 16.4346i | − | 0.598115i | ||||||
\(756\) | −2.75054 | −0.100036 | ||||||||
\(757\) | 49.6239i | 1.80361i | 0.432141 | + | 0.901806i | \(0.357758\pi\) | ||||
−0.432141 | + | 0.901806i | \(0.642242\pi\) | |||||||
\(758\) | 8.50321i | 0.308851i | ||||||||
\(759\) | 24.0687i | 0.873637i | ||||||||
\(760\) | − | 6.75054i | − | 0.244868i | ||||||
\(761\) | −30.6320 | −1.11041 | −0.555204 | − | 0.831714i | \(-0.687360\pi\) | ||||
−0.555204 | + | 0.831714i | \(0.687360\pi\) | |||||||
\(762\) | 14.7505i | 0.534356i | ||||||||
\(763\) | − | 12.5633i | − | 0.454822i | ||||||
\(764\) | 6.93349i | 0.250845i | ||||||||
\(765\) | 7.06651 | 0.255490 | ||||||||
\(766\) | 15.1995 | 0.549182 | ||||||||
\(767\) | 79.7714 | 2.88038 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | − | 29.1352i | − | 1.05064i | −0.850904 | − | 0.525321i | \(-0.823945\pi\) | ||
0.850904 | − | 0.525321i | \(-0.176055\pi\) | |||||||
\(770\) | −13.0665 | −0.470884 | ||||||||
\(771\) | 3.43242i | 0.123615i | ||||||||
\(772\) | − | 0.498930i | − | 0.0179569i | ||||||
\(773\) | 46.2516 | 1.66355 | 0.831777 | − | 0.555109i | \(-0.187324\pi\) | ||||
0.831777 | + | 0.555109i | \(0.187324\pi\) | |||||||
\(774\) | −9.81705 | −0.352867 | ||||||||
\(775\) | − | 0.315979i | − | 0.0113503i | ||||||
\(776\) | 11.5011 | 0.412864 | ||||||||
\(777\) | −13.5011 | − | 9.88142i | −0.484348 | − | 0.354494i | ||||
\(778\) | 32.1330 | 1.15202 | ||||||||
\(779\) | 13.5011i | 0.483726i | ||||||||
\(780\) | −6.75054 | −0.241708 | ||||||||
\(781\) | −67.1395 | −2.40244 | ||||||||
\(782\) | 35.8026i | 1.28030i | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 0.565444 | 0.0201944 | ||||||||
\(785\) | 5.81705i | 0.207619i | ||||||||
\(786\) | 7.18509 | 0.256284 | ||||||||
\(787\) | 15.8713 | 0.565749 | 0.282875 | − | 0.959157i | \(-0.408712\pi\) | ||||
0.282875 | + | 0.959157i | \(0.408712\pi\) | |||||||
\(788\) | 16.7505 | 0.596713 | ||||||||
\(789\) | 6.86911 | 0.244547 | ||||||||
\(790\) | 8.31598i | 0.295869i | ||||||||
\(791\) | − | 5.50107i | − | 0.195596i | ||||||
\(792\) | 4.75054i | 0.168803i | ||||||||
\(793\) | −13.5011 | −0.479437 | ||||||||
\(794\) | 28.8192i | 1.02275i | ||||||||
\(795\) | − | 4.75054i | − | 0.168484i | ||||||
\(796\) | 3.31812i | 0.117608i | ||||||||
\(797\) | 46.1373i | 1.63427i | 0.576448 | + | 0.817134i | \(0.304438\pi\) | ||||
−0.576448 | + | 0.817134i | \(0.695562\pi\) | |||||||
\(798\) | −18.5676 | −0.657285 | ||||||||
\(799\) | 24.7404i | 0.875251i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 6.25161i | 0.220890i | ||||||||
\(802\) | 10.6175 | 0.374917 | ||||||||
\(803\) | −30.5676 | −1.07871 | ||||||||
\(804\) | −15.0021 | −0.529085 | ||||||||
\(805\) | 13.9356 | 0.491166 | ||||||||
\(806\) | 2.13303i | 0.0751327i | ||||||||
\(807\) | −9.24946 | −0.325597 | ||||||||
\(808\) | 7.18509i | 0.252771i | ||||||||
\(809\) | − | 2.74625i | − | 0.0965531i | −0.998834 | − | 0.0482766i | \(-0.984627\pi\) | ||
0.998834 | − | 0.0482766i | \(-0.0153729\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −16.5032 | −0.579506 | −0.289753 | − | 0.957101i | \(-0.593573\pi\) | ||||
−0.289753 | + | 0.957101i | \(0.593573\pi\) | |||||||
\(812\) | − | 5.50107i | − | 0.193050i | ||||||
\(813\) | 14.3702 | 0.503984 | ||||||||
\(814\) | −17.0665 | + | 23.3181i | −0.598181 | + | 0.817300i | ||||
\(815\) | −18.2516 | −0.639326 | ||||||||
\(816\) | 7.06651i | 0.247377i | ||||||||
\(817\) | −66.2703 | −2.31851 | ||||||||
\(818\) | −37.6384 | −1.31600 | ||||||||
\(819\) | 18.5676i | 0.648804i | ||||||||
\(820\) | − | 2.00000i | − | 0.0698430i | ||||||
\(821\) | −39.0166 | −1.36169 | −0.680844 | − | 0.732428i | \(-0.738387\pi\) | ||||
−0.680844 | + | 0.732428i | \(0.738387\pi\) | |||||||
\(822\) | 1.68402i | 0.0587370i | ||||||||
\(823\) | 3.14534 | 0.109640 | 0.0548198 | − | 0.998496i | \(-0.482542\pi\) | ||||
0.0548198 | + | 0.998496i | \(0.482542\pi\) | |||||||
\(824\) | −0.631958 | −0.0220153 | ||||||||
\(825\) | −4.75054 | −0.165392 | ||||||||
\(826\) | −32.5032 | −1.13093 | ||||||||
\(827\) | − | 14.1330i | − | 0.491454i | −0.969339 | − | 0.245727i | \(-0.920973\pi\) | ||
0.969339 | − | 0.245727i | \(-0.0790266\pi\) | |||||||
\(828\) | − | 5.06651i | − | 0.176074i | ||||||
\(829\) | 4.56758i | 0.158639i | 0.996849 | + | 0.0793194i | \(0.0252747\pi\) | ||||
−0.996849 | + | 0.0793194i | \(0.974725\pi\) | |||||||
\(830\) | −4.43456 | −0.153926 | ||||||||
\(831\) | 26.3846i | 0.915273i | ||||||||
\(832\) | − | 6.75054i | − | 0.234033i | ||||||
\(833\) | 3.99572i | 0.138443i | ||||||||
\(834\) | 23.0021i | 0.796499i | ||||||||
\(835\) | −5.06651 | −0.175334 | ||||||||
\(836\) | 32.0687i | 1.10912i | ||||||||
\(837\) | 0.315979i | 0.0109218i | ||||||||
\(838\) | − | 22.0145i | − | 0.760477i | ||||||
\(839\) | 42.3702 | 1.46278 | 0.731391 | − | 0.681959i | \(-0.238872\pi\) | ||||
0.731391 | + | 0.681959i | \(0.238872\pi\) | |||||||
\(840\) | 2.75054 | 0.0949025 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | −3.26392 | −0.112482 | ||||||||
\(843\) | 15.7527i | 0.542551i | ||||||||
\(844\) | 13.5011 | 0.464726 | ||||||||
\(845\) | 32.5697i | 1.12043i | ||||||||
\(846\) | − | 3.50107i | − | 0.120369i | ||||||
\(847\) | 31.8170 | 1.09325 | ||||||||
\(848\) | 4.75054 | 0.163134 | ||||||||
\(849\) | 12.3846i | 0.425040i | ||||||||
\(850\) | −7.06651 | −0.242379 | ||||||||
\(851\) | 18.2017 | − | 24.8691i | 0.623946 | − | 0.852502i | ||||
\(852\) | 14.1330 | 0.484190 | ||||||||
\(853\) | 20.6175i | 0.705930i | 0.935637 | + | 0.352965i | \(0.114827\pi\) | ||||
−0.935637 | + | 0.352965i | \(0.885173\pi\) | |||||||
\(854\) | 5.50107 | 0.188243 | ||||||||
\(855\) | −6.75054 | −0.230863 | ||||||||
\(856\) | − | 12.0687i | − | 0.412498i | ||||||
\(857\) | 3.30367i | 0.112851i | 0.998407 | + | 0.0564256i | \(0.0179704\pi\) | ||||
−0.998407 | + | 0.0564256i | \(0.982030\pi\) | |||||||
\(858\) | 32.0687 | 1.09481 | ||||||||
\(859\) | 41.3868i | 1.41210i | 0.708163 | + | 0.706049i | \(0.249524\pi\) | ||||
−0.708163 | + | 0.706049i | \(0.750476\pi\) | |||||||
\(860\) | 9.81705 | 0.334759 | ||||||||
\(861\) | −5.50107 | −0.187476 | ||||||||
\(862\) | −26.5676 | −0.904896 | ||||||||
\(863\) | −46.5032 | −1.58299 | −0.791494 | − | 0.611177i | \(-0.790696\pi\) | ||||
−0.791494 | + | 0.611177i | \(0.790696\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | − | 4.11858i | − | 0.140036i | ||||||
\(866\) | − | 8.56758i | − | 0.291138i | ||||||
\(867\) | −32.9356 | −1.11855 | ||||||||
\(868\) | − | 0.869112i | − | 0.0294996i | ||||||
\(869\) | − | 39.5054i | − | 1.34013i | ||||||
\(870\) | − | 2.00000i | − | 0.0678064i | ||||||
\(871\) | 101.272i | 3.43149i | ||||||||
\(872\) | 4.56758 | 0.154678 | ||||||||
\(873\) | − | 11.5011i | − | 0.389252i | ||||||
\(874\) | − | 34.2017i | − | 1.15689i | ||||||
\(875\) | 2.75054i | 0.0929851i | ||||||||
\(876\) | 6.43456 | 0.217403 | ||||||||
\(877\) | −14.4490 | −0.487908 | −0.243954 | − | 0.969787i | \(-0.578445\pi\) | ||||
−0.243954 | + | 0.969787i | \(0.578445\pi\) | |||||||
\(878\) | −8.31598 | −0.280651 | ||||||||
\(879\) | 0.750535 | 0.0253149 | ||||||||
\(880\) | − | 4.75054i | − | 0.160141i | ||||||
\(881\) | −22.7404 | −0.766142 | −0.383071 | − | 0.923719i | \(-0.625134\pi\) | ||||
−0.383071 | + | 0.923719i | \(0.625134\pi\) | |||||||
\(882\) | − | 0.565444i | − | 0.0190395i | ||||||
\(883\) | − | 47.8900i | − | 1.61163i | −0.592170 | − | 0.805813i | \(-0.701729\pi\) | ||
0.592170 | − | 0.805813i | \(-0.298271\pi\) | |||||||
\(884\) | 47.7028 | 1.60442 | ||||||||
\(885\) | −11.8170 | −0.397226 | ||||||||
\(886\) | − | 35.2682i | − | 1.18486i | ||||||
\(887\) | −40.3991 | −1.35647 | −0.678234 | − | 0.734846i | \(-0.737255\pi\) | ||||
−0.678234 | + | 0.734846i | \(0.737255\pi\) | |||||||
\(888\) | 3.59255 | − | 4.90852i | 0.120558 | − | 0.164719i | ||||
\(889\) | −40.5719 | −1.36074 | ||||||||
\(890\) | − | 6.25161i | − | 0.209554i | ||||||
\(891\) | 4.75054 | 0.159149 | ||||||||
\(892\) | −25.3181 | −0.847713 | ||||||||
\(893\) | − | 23.6341i | − | 0.790885i | ||||||
\(894\) | 7.81705i | 0.261441i | ||||||||
\(895\) | 9.68402 | 0.323701 | ||||||||
\(896\) | 2.75054i | 0.0918889i | ||||||||
\(897\) | −34.2017 | −1.14196 | ||||||||
\(898\) | −30.3203 | −1.01180 | ||||||||
\(899\) | −0.631958 | −0.0210770 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 33.5697i | 1.11837i | ||||||||
\(902\) | 9.50107i | 0.316351i | ||||||||
\(903\) | − | 27.0021i | − | 0.898575i | ||||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | − | 10.6320i | − | 0.353418i | ||||||
\(906\) | − | 16.4346i | − | 0.546002i | ||||||
\(907\) | 42.5177i | 1.41178i | 0.708324 | + | 0.705888i | \(0.249452\pi\) | ||||
−0.708324 | + | 0.705888i | \(0.750548\pi\) | |||||||
\(908\) | − | 4.63196i | − | 0.153717i | ||||||
\(909\) | 7.18509 | 0.238314 | ||||||||
\(910\) | − | 18.5676i | − | 0.615509i | ||||||
\(911\) | − | 24.0000i | − | 0.795155i | −0.917568 | − | 0.397578i | \(-0.869851\pi\) | ||
0.917568 | − | 0.397578i | \(-0.130149\pi\) | |||||||
\(912\) | − | 6.75054i | − | 0.223533i | ||||||
\(913\) | 21.0665 | 0.697200 | ||||||||
\(914\) | −10.6320 | −0.351674 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | −20.1330 | −0.665214 | ||||||||
\(917\) | 19.7628i | 0.652627i | ||||||||
\(918\) | 7.06651 | 0.233230 | ||||||||
\(919\) | 43.8213i | 1.44553i | 0.691093 | + | 0.722766i | \(0.257130\pi\) | ||||
−0.691093 | + | 0.722766i | \(0.742870\pi\) | |||||||
\(920\) | 5.06651i | 0.167038i | ||||||||
\(921\) | 18.3702 | 0.605318 | ||||||||
\(922\) | −30.5032 | −1.00457 | ||||||||
\(923\) | − | 95.4055i | − | 3.14031i | ||||||
\(924\) | −13.0665 | −0.429857 | ||||||||
\(925\) | 4.90852 | + | 3.59255i | 0.161391 | + | 0.118122i | ||||
\(926\) | −39.5054 | −1.29823 | ||||||||
\(927\) | 0.631958i | 0.0207562i | ||||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 7.86697 | 0.258107 | 0.129053 | − | 0.991638i | \(-0.458806\pi\) | ||||
0.129053 | + | 0.991638i | \(0.458806\pi\) | |||||||
\(930\) | − | 0.315979i | − | 0.0103614i | ||||||
\(931\) | − | 3.81705i | − | 0.125099i | ||||||
\(932\) | 6.31598 | 0.206887 | ||||||||
\(933\) | 35.0021i | 1.14592i | ||||||||
\(934\) | −16.6320 | −0.544214 | ||||||||
\(935\) | 33.5697 | 1.09785 | ||||||||
\(936\) | −6.75054 | −0.220648 | ||||||||
\(937\) | −53.0021 | −1.73150 | −0.865752 | − | 0.500473i | \(-0.833160\pi\) | ||||
−0.865752 | + | 0.500473i | \(0.833160\pi\) | |||||||
\(938\) | − | 41.2639i | − | 1.34731i | ||||||
\(939\) | 1.36804i | 0.0446443i | ||||||||
\(940\) | 3.50107i | 0.114192i | ||||||||
\(941\) | 44.5574 | 1.45253 | 0.726265 | − | 0.687415i | \(-0.241254\pi\) | ||||
0.726265 | + | 0.687415i | \(0.241254\pi\) | |||||||
\(942\) | 5.81705i | 0.189530i | ||||||||
\(943\) | − | 10.1330i | − | 0.329977i | ||||||
\(944\) | − | 11.8170i | − | 0.384612i | ||||||
\(945\) | − | 2.75054i | − | 0.0894749i | ||||||
\(946\) | −46.6362 | −1.51627 | ||||||||
\(947\) | 46.0043i | 1.49494i | 0.664297 | + | 0.747469i | \(0.268731\pi\) | ||||
−0.664297 | + | 0.747469i | \(0.731269\pi\) | |||||||
\(948\) | 8.31598i | 0.270090i | ||||||||
\(949\) | − | 43.4367i | − | 1.41001i | ||||||
\(950\) | 6.75054 | 0.219016 | ||||||||
\(951\) | 10.0542 | 0.326030 | ||||||||
\(952\) | −19.4367 | −0.629947 | ||||||||
\(953\) | 48.9522 | 1.58572 | 0.792859 | − | 0.609405i | \(-0.208592\pi\) | ||||
0.792859 | + | 0.609405i | \(0.208592\pi\) | |||||||
\(954\) | − | 4.75054i | − | 0.153804i | ||||||
\(955\) | −6.93349 | −0.224362 | ||||||||
\(956\) | 12.6320i | 0.408547i | ||||||||
\(957\) | 9.50107i | 0.307126i | ||||||||
\(958\) | 33.2038 | 1.07277 | ||||||||
\(959\) | −4.63196 | −0.149574 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 30.9002 | 0.996779 | ||||||||
\(962\) | −33.1352 | − | 24.2516i | −1.06832 | − | 0.781903i | ||||
\(963\) | −12.0687 | −0.388907 | ||||||||
\(964\) | 16.6320i | 0.535679i | ||||||||
\(965\) | 0.498930 | 0.0160611 | ||||||||
\(966\) | 13.9356 | 0.448371 | ||||||||
\(967\) | 23.2682i | 0.748255i | 0.927377 | + | 0.374127i | \(0.122058\pi\) | ||||
−0.927377 | + | 0.374127i | \(0.877942\pi\) | |||||||
\(968\) | 11.5676i | 0.371796i | ||||||||
\(969\) | 47.7028 | 1.53243 | ||||||||
\(970\) | 11.5011i | 0.369277i | ||||||||
\(971\) | −57.8170 | −1.85544 | −0.927719 | − | 0.373280i | \(-0.878233\pi\) | ||||
−0.927719 | + | 0.373280i | \(0.878233\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −63.2682 | −2.02829 | ||||||||
\(974\) | 11.6341 | 0.372781 | ||||||||
\(975\) | − | 6.75054i | − | 0.216190i | ||||||
\(976\) | 2.00000i | 0.0640184i | ||||||||
\(977\) | − | 27.4324i | − | 0.877641i | −0.898575 | − | 0.438820i | \(-0.855396\pi\) | ||
0.898575 | − | 0.438820i | \(-0.144604\pi\) | |||||||
\(978\) | −18.2516 | −0.583622 | ||||||||
\(979\) | 29.6985i | 0.949167i | ||||||||
\(980\) | 0.565444i | 0.0180624i | ||||||||
\(981\) | − | 4.56758i | − | 0.145832i | ||||||
\(982\) | 4.75054i | 0.151596i | ||||||||
\(983\) | 23.7671 | 0.758054 | 0.379027 | − | 0.925386i | \(-0.376259\pi\) | ||||
0.379027 | + | 0.925386i | \(0.376259\pi\) | |||||||
\(984\) | − | 2.00000i | − | 0.0637577i | ||||||
\(985\) | 16.7505i | 0.533716i | ||||||||
\(986\) | 14.1330i | 0.450087i | ||||||||
\(987\) | 9.62982 | 0.306520 | ||||||||
\(988\) | −45.5697 | −1.44977 | ||||||||
\(989\) | 49.7382 | 1.58158 | ||||||||
\(990\) | −4.75054 | −0.150982 | ||||||||
\(991\) | − | 27.5842i | − | 0.876240i | −0.898916 | − | 0.438120i | \(-0.855644\pi\) | ||
0.898916 | − | 0.438120i | \(-0.144356\pi\) | |||||||
\(992\) | 0.315979 | 0.0100324 | ||||||||
\(993\) | 26.3160i | 0.835112i | ||||||||
\(994\) | 38.8734i | 1.23299i | ||||||||
\(995\) | −3.31812 | −0.105191 | ||||||||
\(996\) | −4.43456 | −0.140514 | ||||||||
\(997\) | 43.6196i | 1.38145i | 0.723118 | + | 0.690724i | \(0.242708\pi\) | ||||
−0.723118 | + | 0.690724i | \(0.757292\pi\) | |||||||
\(998\) | −9.12072 | −0.288711 | ||||||||
\(999\) | −4.90852 | − | 3.59255i | −0.155299 | − | 0.113663i |
(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 | 1110.2.h.f.961.3 | ✓ | 6 | |
3.2 | odd | 2 | 3330.2.h.m.2071.6 | 6 | |||
37.36 | even | 2 | inner | 1110.2.h.f.961.6 | yes | 6 | |
111.110 | odd | 2 | 3330.2.h.m.2071.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.h.f.961.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1110.2.h.f.961.6 | yes | 6 | 37.36 | even | 2 | inner | |
3330.2.h.m.2071.3 | 6 | 111.110 | odd | 2 | |||
3330.2.h.m.2071.6 | 6 | 3.2 | odd | 2 |