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 | 961.6 | ||
Root | \(-3.75054i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.961 |
Dual form | 1110.2.h.f.961.3 |
$q$-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 | \(-0.614380\pi\) | ||
0.351652 | − | 0.936131i | \(-0.385620\pi\) | |||||||
\(14\) | 2.75054i | 0.735111i | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 7.06651i | − | 1.71388i | −0.515415 | − | 0.856941i | \(-0.672362\pi\) | ||
0.515415 | − | 0.856941i | \(-0.327638\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 6.75054i | 1.54868i | 0.632770 | + | 0.774339i | \(0.281918\pi\) | ||||
−0.632770 | + | 0.774339i | \(0.718082\pi\) | |||||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 2.75054 | 0.600216 | ||||||||
\(22\) | 4.75054i | 1.01282i | ||||||||
\(23\) | − | 5.06651i | − | 1.05644i | −0.849107 | − | 0.528221i | \(-0.822859\pi\) | ||
0.849107 | − | 0.528221i | \(-0.177141\pi\) | |||||||
\(24\) | − | 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 | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − | 0.315979i | − | 0.0567515i | −0.999597 | − | 0.0283758i | \(-0.990966\pi\) | ||
0.999597 | − | 0.0283758i | \(-0.00903350\pi\) | |||||||
\(32\) | 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 | \(0.269246\pi\) | ||||
−0.663086 | + | 0.748543i | \(0.730754\pi\) | |||||||
\(44\) | −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 | \(0.279357\pi\) | ||||
−0.638979 | + | 0.769224i | \(0.720643\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | − | 2.00000i | − | 0.256074i | −0.991769 | − | 0.128037i | \(-0.959132\pi\) | ||
0.991769 | − | 0.128037i | \(-0.0408676\pi\) | |||||||
\(62\) | 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 | \(0.154957\pi\) | ||||
−0.883829 | + | 0.467810i | \(0.845043\pi\) | |||||||
\(80\) | 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 | \(-0.892501\pi\) | ||
0.943513 | − | 0.331334i | \(-0.107499\pi\) | |||||||
\(90\) | −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 | \(0.198466\pi\) | ||||
−0.811841 | + | 0.583878i | \(0.801534\pi\) | |||||||
\(98\) | 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 | \(-0.990088\pi\) | ||
0.999515 | − | 0.0311344i | \(-0.00991198\pi\) | |||||||
\(104\) | −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 | \(0.0701971\pi\) | ||||
−0.975781 | + | 0.218748i | \(0.929803\pi\) | |||||||
\(110\) | −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 | \(0.0299884\pi\) | ||||
−0.995565 | + | 0.0940721i | \(0.970012\pi\) | |||||||
\(114\) | −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 | \(-0.898370\pi\) | ||
0.949462 | − | 0.313882i | \(-0.101630\pi\) | |||||||
\(132\) | −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 | \(0.253477\pi\) | ||||
−0.699341 | + | 0.714788i | \(0.746523\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 4.75054i | 0.369829i | ||||||||
\(166\) | 4.43456i | 0.344188i | ||||||||
\(167\) | 5.06651i | 0.392059i | 0.980598 | + | 0.196029i | \(0.0628048\pi\) | ||||
−0.980598 | + | 0.196029i | \(0.937195\pi\) | |||||||
\(168\) | − | 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 | \(-0.882125\pi\) | ||
0.932213 | − | 0.361909i | \(-0.117875\pi\) | |||||||
\(180\) | − | 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 | \(0.0807084\pi\) | ||||
−0.968027 | + | 0.250845i | \(0.919292\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − | 0.498930i | − | 0.0359137i | −0.999839 | − | 0.0179569i | \(-0.994284\pi\) | ||
0.999839 | − | 0.0179569i | \(-0.00571616\pi\) | |||||||
\(194\) | −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 | \(0.0375225\pi\) | ||||
−0.993060 | + | 0.117608i | \(0.962477\pi\) | |||||||
\(200\) | 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 | \(-0.950876\pi\) | ||
0.988115 | − | 0.153717i | \(-0.0491244\pi\) | |||||||
\(228\) | − | 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 | \(0.133964\pi\) | ||||
−0.912737 | + | 0.408547i | \(0.866036\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 16.6320i | 1.07136i | 0.844422 | + | 0.535679i | \(0.179944\pi\) | ||||
−0.844422 | + | 0.535679i | \(0.820056\pi\) | |||||||
\(242\) | 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 | \(-0.983075\pi\) | ||
0.998587 | − | 0.0531472i | \(-0.0169253\pi\) | |||||||
\(252\) | −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 | \(-0.965858\pi\) | ||
0.994253 | − | 0.107054i | \(-0.0341418\pi\) | |||||||
\(258\) | −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 | \(-0.708701\pi\) | ||
0.609678 | − | 0.792650i | \(-0.291299\pi\) | |||||||
\(278\) | − | 23.0021i | − | 1.37958i | ||||||
\(279\) | − | 0.315979i | − | 0.0189172i | ||||||
\(280\) | 2.75054 | 0.164376 | ||||||||
\(281\) | − | 15.7527i | − | 0.939726i | −0.882739 | − | 0.469863i | \(-0.844303\pi\) | ||
0.882739 | − | 0.469863i | \(-0.155697\pi\) | |||||||
\(282\) | 3.50107i | 0.208486i | ||||||||
\(283\) | − | 12.3846i | − | 0.736190i | −0.929788 | − | 0.368095i | \(-0.880010\pi\) | ||
0.929788 | − | 0.368095i | \(-0.119990\pi\) | |||||||
\(284\) | 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 | \(-0.539283\pi\) | ||
0.123097 | − | 0.992395i | \(-0.460717\pi\) | |||||||
\(312\) | −6.75054 | −0.382174 | ||||||||
\(313\) | − | 1.36804i | − | 0.0773263i | −0.999252 | − | 0.0386631i | \(-0.987690\pi\) | ||
0.999252 | − | 0.0386631i | \(-0.0123099\pi\) | |||||||
\(314\) | − | 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 | \(-0.742657\pi\) | ||
0.690609 | − | 0.723229i | \(-0.257343\pi\) | |||||||
\(332\) | −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 | \(0.118038\pi\) | ||||
−0.932027 | + | 0.362388i | \(0.881962\pi\) | |||||||
\(348\) | 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 | \(-0.881809\pi\) | ||
0.931853 | − | 0.362835i | \(-0.118191\pi\) | |||||||
\(354\) | −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 | \(-0.873052\pi\) | ||
0.921520 | − | 0.388330i | \(-0.126948\pi\) | |||||||
\(384\) | − | 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 | \(-0.696954\pi\) | ||
0.580017 | − | 0.814605i | \(-0.303046\pi\) | |||||||
\(390\) | 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 | \(-0.914593\pi\) | ||
0.964219 | − | 0.265106i | \(-0.0854071\pi\) | |||||||
\(402\) | 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 | \(0.380670\pi\) | ||||
−0.366167 | + | 0.930549i | \(0.619330\pi\) | |||||||
\(410\) | 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 | \(0.0253441\pi\) | ||||
−0.996832 | + | 0.0795368i | \(0.974656\pi\) | |||||||
\(422\) | − | 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 | \(0.221007\pi\) | ||||
−0.768493 | + | 0.639858i | \(0.778993\pi\) | |||||||
\(432\) | 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 | \(0.0635907\pi\) | ||||
−0.980111 | + | 0.198450i | \(0.936409\pi\) | |||||||
\(440\) | 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 | \(0.253779\pi\) | ||||
−0.698663 | + | 0.715451i | \(0.746221\pi\) | |||||||
\(450\) | − | 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 | \(0.0799938\pi\) | ||||
−0.968588 | + | 0.248671i | \(0.920006\pi\) | |||||||
\(458\) | 20.1330i | 0.940755i | ||||||||
\(459\) | − | 7.06651i | − | 0.329837i | ||||||
\(460\) | −5.06651 | −0.236227 | ||||||||
\(461\) | 30.5032i | 1.42068i | 0.703861 | + | 0.710338i | \(0.251458\pi\) | ||||
−0.703861 | + | 0.710338i | \(0.748542\pi\) | |||||||
\(462\) | 13.0665i | 0.607909i | ||||||||
\(463\) | 39.5054i | 1.83597i | 0.396616 | + | 0.917985i | \(0.370185\pi\) | ||||
−0.396616 | + | 0.917985i | \(0.629815\pi\) | |||||||
\(464\) | − | 2.00000i | − | 0.0928477i | ||||||
\(465\) | 0.315979 | 0.0146532 | ||||||||
\(466\) | − | 6.31598i | − | 0.292582i | ||||||
\(467\) | 16.6320i | 0.769635i | 0.922993 | + | 0.384818i | \(0.125736\pi\) | ||||
−0.922993 | + | 0.384818i | \(0.874264\pi\) | |||||||
\(468\) | 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 | \(-0.725903\pi\) | ||
0.651602 | − | 0.758561i | \(-0.274097\pi\) | |||||||
\(480\) | −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 | \(-0.915092\pi\) | ||
0.964633 | − | 0.263596i | \(-0.0849085\pi\) | |||||||
\(488\) | −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 | \(0.0654429\pi\) | ||||
−0.978940 | + | 0.204150i | \(0.934557\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 5.06651i | 0.226355i | ||||||||
\(502\) | 1.68402 | 0.0751615 | ||||||||
\(503\) | − | 9.26392i | − | 0.413058i | −0.978441 | − | 0.206529i | \(-0.933783\pi\) | ||
0.978441 | − | 0.206529i | \(-0.0662167\pi\) | |||||||
\(504\) | − | 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 | \(-0.889542\pi\) | ||
0.940392 | − | 0.340092i | \(-0.110458\pi\) | |||||||
\(524\) | 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 | \(0.0235080\pi\) | ||||
−0.997274 | + | 0.0737855i | \(0.976492\pi\) | |||||||
\(542\) | 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 | \(-0.878806\pi\) | ||
0.928389 | − | 0.371611i | \(-0.121194\pi\) | |||||||
\(548\) | 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 | \(0.117292\pi\) | ||||
−0.932874 | + | 0.360202i | \(0.882708\pi\) | |||||||
\(558\) | 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 | \(0.305559\pi\) | ||||
−0.573566 | + | 0.819159i | \(0.694441\pi\) | |||||||
\(564\) | −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 | \(-0.930183\pi\) | ||
0.976042 | − | 0.217584i | \(-0.0698174\pi\) | |||||||
\(570\) | − | 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 | \(-0.811075\pi\) | ||
0.828973 | − | 0.559288i | \(-0.188925\pi\) | |||||||
\(578\) | − | 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 | \(0.0519366\pi\) | ||||
−0.986718 | + | 0.162441i | \(0.948063\pi\) | |||||||
\(588\) | −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 | \(0.0477760\pi\) | ||||
−0.988757 | + | 0.149530i | \(0.952224\pi\) | |||||||
\(608\) | −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 | \(-0.963061\pi\) | ||
0.993274 | − | 0.115787i | \(-0.0369389\pi\) | |||||||
\(632\) | 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 | \(-0.855418\pi\) | ||
0.898605 | − | 0.438759i | \(-0.144582\pi\) | |||||||
\(644\) | 13.9356i | 0.549141i | ||||||||
\(645\) | −9.81705 | −0.386546 | ||||||||
\(646\) | 47.7028i | 1.87684i | ||||||||
\(647\) | 24.0687i | 0.946236i | 0.880999 | + | 0.473118i | \(0.156872\pi\) | ||||
−0.880999 | + | 0.473118i | \(0.843128\pi\) | |||||||
\(648\) | − | 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 | \(0.165332\pi\) | ||||
−0.868114 | + | 0.496364i | \(0.834668\pi\) | |||||||
\(654\) | −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 | \(0.120059\pi\) | ||||
−0.929708 | + | 0.368297i | \(0.879941\pi\) | |||||||
\(662\) | 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 | \(0.0886546\pi\) | ||||
−0.961464 | + | 0.274930i | \(0.911345\pi\) | |||||||
\(684\) | − | 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 | \(-0.821709\pi\) | ||
0.847193 | − | 0.531285i | \(-0.178291\pi\) | |||||||
\(702\) | 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 | \(0.220957\pi\) | ||||
−0.768593 | + | 0.639738i | \(0.779043\pi\) | |||||||
\(710\) | 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 | \(0.0783213\pi\) | ||||
−0.969881 | + | 0.243578i | \(0.921679\pi\) | |||||||
\(728\) | −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 | \(-0.642242\pi\) | ||
0.432141 | − | 0.901806i | \(-0.357758\pi\) | |||||||
\(758\) | − | 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 | \(0.176055\pi\) | ||||
−0.850904 | + | 0.525321i | \(0.823945\pi\) | |||||||
\(770\) | −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 | \(-0.695562\pi\) | ||
0.576448 | − | 0.817134i | \(-0.304438\pi\) | |||||||
\(798\) | −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 | \(0.0153729\pi\) | ||||
−0.998834 | + | 0.0482766i | \(0.984627\pi\) | |||||||
\(810\) | −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 | \(0.0790266\pi\) | ||||
−0.969339 | + | 0.245727i | \(0.920973\pi\) | |||||||
\(828\) | 5.06651i | 0.176074i | ||||||||
\(829\) | − | 4.56758i | − | 0.158639i | −0.996849 | − | 0.0793194i | \(-0.974725\pi\) | ||
0.996849 | − | 0.0793194i | \(-0.0252747\pi\) | |||||||
\(830\) | −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 | \(-0.885173\pi\) | ||
0.935637 | − | 0.352965i | \(-0.114827\pi\) | |||||||
\(854\) | 5.50107 | 0.188243 | ||||||||
\(855\) | −6.75054 | −0.230863 | ||||||||
\(856\) | 12.0687i | 0.412498i | ||||||||
\(857\) | − | 3.30367i | − | 0.112851i | −0.998407 | − | 0.0564256i | \(-0.982030\pi\) | ||
0.998407 | − | 0.0564256i | \(-0.0179704\pi\) | |||||||
\(858\) | 32.0687 | 1.09481 | ||||||||
\(859\) | − | 41.3868i | − | 1.41210i | −0.708163 | − | 0.706049i | \(-0.750476\pi\) | ||
0.708163 | − | 0.706049i | \(-0.249524\pi\) | |||||||
\(860\) | 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 | \(0.298271\pi\) | ||||
−0.592170 | + | 0.805813i | \(0.701729\pi\) | |||||||
\(884\) | 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 | \(-0.750548\pi\) | ||
0.708324 | − | 0.705888i | \(-0.249452\pi\) | |||||||
\(908\) | 4.63196i | 0.153717i | ||||||||
\(909\) | 7.18509 | 0.238314 | ||||||||
\(910\) | 18.5676i | 0.615509i | ||||||||
\(911\) | 24.0000i | 0.795155i | 0.917568 | + | 0.397578i | \(0.130149\pi\) | ||||
−0.917568 | + | 0.397578i | \(0.869851\pi\) | |||||||
\(912\) | 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 | \(-0.742870\pi\) | ||
0.691093 | − | 0.722766i | \(-0.257130\pi\) | |||||||
\(920\) | − | 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 | \(-0.731269\pi\) | ||
0.664297 | − | 0.747469i | \(-0.268731\pi\) | |||||||
\(948\) | − | 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 | \(-0.877942\pi\) | ||
0.927377 | − | 0.374127i | \(-0.122058\pi\) | |||||||
\(968\) | − | 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 | \(0.144604\pi\) | ||||
−0.898575 | + | 0.438820i | \(0.855396\pi\) | |||||||
\(978\) | −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 | \(0.144356\pi\) | ||||
−0.898916 | + | 0.438120i | \(0.855644\pi\) | |||||||
\(992\) | 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 | \(-0.757292\pi\) | ||
0.723118 | − | 0.690724i | \(-0.242708\pi\) | |||||||
\(998\) | −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.961.6 | yes | 6 | |
3.2 | odd | 2 | 3330.2.h.m.2071.3 | 6 | |||
37.36 | even | 2 | inner | 1110.2.h.f.961.3 | ✓ | 6 | |
111.110 | odd | 2 | 3330.2.h.m.2071.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.h.f.961.3 | ✓ | 6 | 37.36 | even | 2 | inner | |
1110.2.h.f.961.6 | yes | 6 | 1.1 | even | 1 | trivial | |
3330.2.h.m.2071.3 | 6 | 3.2 | odd | 2 | |||
3330.2.h.m.2071.6 | 6 | 111.110 | odd | 2 |