Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [861,2,Mod(247,861)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(861, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("861.247");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 861 = 3 \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 861.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.87511961403\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.7873200.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 12x^{4} + 36x^{2} + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 247.1 | ||
Root | \(0.616380i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 861.247 |
Dual form | 861.2.i.c.739.1 |
$q$-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 \(\left(\mathbb{Z}/861\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(493\) | \(575\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | −1.27624 | + | 2.21051i | −0.570751 | + | 0.988569i | 0.425738 | + | 0.904846i | \(0.360014\pi\) |
−0.996489 | + | 0.0837229i | \(0.973319\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.58628 | − | 0.557835i | −0.977520 | − | 0.210842i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.08628 | − | 5.34559i | −0.930547 | − | 1.61175i | −0.782388 | − | 0.622791i | \(-0.785999\pi\) |
−0.148159 | − | 0.988964i | \(-0.547335\pi\) | |||||||
\(12\) | −1.00000 | + | 1.73205i | −0.288675 | + | 0.500000i | ||||
\(13\) | −2.06760 | −0.573449 | −0.286725 | − | 0.958013i | \(-0.592567\pi\) | ||||
−0.286725 | + | 0.958013i | \(0.592567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.55247 | −0.659046 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.223763 | − | 0.387568i | 0.0513347 | − | 0.0889143i | −0.839216 | − | 0.543798i | \(-0.816986\pi\) |
0.890551 | + | 0.454884i | \(0.150319\pi\) | |||||||
\(20\) | −5.10495 | −1.14150 | ||||||||
\(21\) | −0.810038 | − | 2.51870i | −0.176765 | − | 0.549625i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.276237 | − | 0.478457i | 0.0575995 | − | 0.0997652i | −0.835788 | − | 0.549052i | \(-0.814989\pi\) |
0.893387 | + | 0.449287i | \(0.148322\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.757563 | − | 1.31214i | −0.151513 | − | 0.262428i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.62008 | − | 5.03740i | −0.306166 | − | 0.951978i | ||||
\(29\) | −5.10495 | −0.947965 | −0.473983 | − | 0.880534i | \(-0.657184\pi\) | ||||
−0.473983 | + | 0.880534i | \(0.657184\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.86251 | + | 6.69007i | 0.693728 | + | 1.20157i | 0.970608 | + | 0.240667i | \(0.0773662\pi\) |
−0.276880 | + | 0.960905i | \(0.589300\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.08628 | − | 5.34559i | 0.537252 | − | 0.930547i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.53380 | − | 5.00505i | 0.766352 | − | 0.846008i | ||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.03380 | − | 1.79060i | −0.165541 | − | 0.286725i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6201 | −1.61955 | −0.809773 | − | 0.586743i | \(-0.800410\pi\) | ||||
−0.809773 | + | 0.586743i | \(0.800410\pi\) | |||||||
\(44\) | 6.17255 | − | 10.6912i | 0.930547 | − | 1.61175i | ||||
\(45\) | −1.27624 | − | 2.21051i | −0.190250 | − | 0.329523i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.15388 | − | 7.19473i | 0.605905 | − | 1.04946i | −0.386003 | − | 0.922498i | \(-0.626144\pi\) |
0.991908 | − | 0.126961i | \(-0.0405222\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | 6.37764 | + | 2.88543i | 0.911091 | + | 0.412205i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | −2.06760 | − | 3.58119i | −0.286725 | − | 0.496622i | ||||
\(53\) | 2.06760 | + | 3.58119i | 0.284007 | + | 0.491914i | 0.972368 | − | 0.233454i | \(-0.0750028\pi\) |
−0.688361 | + | 0.725368i | \(0.741669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.7553 | 2.12444 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.447525 | 0.0592762 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.06760 | − | 7.04529i | −0.529557 | − | 0.917219i | −0.999406 | − | 0.0344721i | \(-0.989025\pi\) |
0.469849 | − | 0.882747i | \(-0.344308\pi\) | |||||||
\(60\) | −2.55247 | − | 4.42102i | −0.329523 | − | 0.570751i | ||||
\(61\) | −3.87764 | + | 6.71627i | −0.496481 | + | 0.859930i | −0.999992 | − | 0.00405884i | \(-0.998708\pi\) |
0.503511 | + | 0.863989i | \(0.332041\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.77624 | − | 1.96086i | 0.223785 | − | 0.247045i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.63875 | − | 4.57045i | 0.327297 | − | 0.566894i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0338006 | + | 0.0585444i | 0.00412940 | + | 0.00715234i | 0.868083 | − | 0.496420i | \(-0.165352\pi\) |
−0.863953 | + | 0.503572i | \(0.832019\pi\) | |||||||
\(68\) | −2.00000 | + | 3.46410i | −0.242536 | + | 0.420084i | ||||
\(69\) | 0.552475 | 0.0665101 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.13520 | 0.253402 | 0.126701 | − | 0.991941i | \(-0.459561\pi\) | ||||
0.126701 | + | 0.991941i | \(0.459561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.31004 | + | 9.19726i | 0.621493 | + | 1.07646i | 0.989208 | + | 0.146519i | \(0.0468069\pi\) |
−0.367715 | + | 0.929939i | \(0.619860\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.757563 | − | 1.31214i | 0.0874759 | − | 0.151513i | ||||
\(76\) | 0.895051 | 0.102669 | ||||||||
\(77\) | 5.00000 | + | 15.5468i | 0.569803 | + | 1.77172i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.39631 | + | 14.5428i | −0.944659 | + | 1.63620i | −0.188227 | + | 0.982126i | \(0.560274\pi\) |
−0.756432 | + | 0.654072i | \(0.773059\pi\) | |||||||
\(80\) | −5.10495 | − | 8.84203i | −0.570751 | − | 0.988569i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.9278 | −1.52878 | −0.764389 | − | 0.644755i | \(-0.776959\pi\) | ||||
−0.764389 | + | 0.644755i | \(0.776959\pi\) | |||||||
\(84\) | 3.55247 | − | 3.92172i | 0.387607 | − | 0.427895i | ||||
\(85\) | −5.10495 | −0.553709 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.55247 | − | 4.42102i | −0.273654 | − | 0.473983i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.15388 | + | 10.6588i | −0.652310 | + | 1.12983i | 0.330251 | + | 0.943893i | \(0.392866\pi\) |
−0.982561 | + | 0.185940i | \(0.940467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.34739 | + | 1.15338i | 0.560558 | + | 0.120907i | ||||
\(92\) | 1.10495 | 0.115199 | ||||||||
\(93\) | −3.86251 | + | 6.69007i | −0.400524 | + | 0.693728i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.571149 | + | 0.989258i | 0.0585986 | + | 0.101496i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2099 | 1.64587 | 0.822933 | − | 0.568139i | \(-0.192336\pi\) | ||||
0.822933 | + | 0.568139i | \(0.192336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.17255 | 0.620365 | ||||||||
\(100\) | 1.51513 | − | 2.62428i | 0.151513 | − | 0.262428i | ||||
\(101\) | 6.10495 | + | 10.5741i | 0.607465 | + | 1.05216i | 0.991657 | + | 0.128907i | \(0.0411469\pi\) |
−0.384192 | + | 0.923253i | \(0.625520\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.05247 | − | 7.01909i | 0.399302 | − | 0.691612i | −0.594338 | − | 0.804216i | \(-0.702586\pi\) |
0.993640 | + | 0.112604i | \(0.0359191\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.60140 | + | 1.42386i | 0.644231 | + | 0.138955i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.27624 | + | 2.21051i | −0.123379 | + | 0.213698i | −0.921098 | − | 0.389331i | \(-0.872706\pi\) |
0.797719 | + | 0.603029i | \(0.206040\pi\) | |||||||
\(108\) | −1.00000 | − | 1.73205i | −0.0962250 | − | 0.166667i | ||||
\(109\) | −2.29136 | − | 3.96876i | −0.219473 | − | 0.380138i | 0.735174 | − | 0.677878i | \(-0.237100\pi\) |
−0.954647 | + | 0.297740i | \(0.903767\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | 7.10495 | − | 7.84345i | 0.671355 | − | 0.741136i | ||||
\(113\) | −15.0328 | −1.41416 | −0.707082 | − | 0.707131i | \(-0.749989\pi\) | ||||
−0.707082 | + | 0.707131i | \(0.749989\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.705089 | + | 1.22125i | 0.0657499 | + | 0.113882i | ||||
\(116\) | −5.10495 | − | 8.84203i | −0.473983 | − | 0.820962i | ||||
\(117\) | 1.03380 | − | 1.79060i | 0.0955749 | − | 0.165541i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.62008 | − | 5.03740i | −0.148512 | − | 0.461777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.5502 | + | 23.4696i | −1.23184 | + | 2.13360i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.500000 | − | 0.866025i | −0.0450835 | − | 0.0780869i | ||||
\(124\) | −7.72503 | + | 13.3801i | −0.693728 | + | 1.20157i | ||||
\(125\) | −8.89505 | −0.795598 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.24015 | −0.198781 | −0.0993907 | − | 0.995048i | \(-0.531689\pi\) | ||||
−0.0993907 | + | 0.995048i | \(0.531689\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.31004 | − | 9.19726i | −0.467523 | − | 0.809773i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.27624 | − | 14.3349i | 0.723098 | − | 1.25244i | −0.236654 | − | 0.971594i | \(-0.576051\pi\) |
0.959752 | − | 0.280849i | \(-0.0906159\pi\) | |||||||
\(132\) | 12.3451 | 1.07450 | ||||||||
\(133\) | −0.794911 | + | 0.877536i | −0.0689276 | + | 0.0760920i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.27624 | − | 2.21051i | 0.109841 | − | 0.190250i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0676012 | + | 0.117089i | 0.00577556 | + | 0.0100036i | 0.868899 | − | 0.494990i | \(-0.164828\pi\) |
−0.863123 | + | 0.504993i | \(0.831495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.37535 | −0.710388 | −0.355194 | − | 0.934793i | \(-0.615585\pi\) | ||||
−0.355194 | + | 0.934793i | \(0.615585\pi\) | |||||||
\(140\) | 13.2028 | + | 2.84772i | 1.11584 | + | 0.240676i | ||||
\(141\) | 8.30775 | 0.699639 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.38119 | + | 11.0525i | 0.533622 | + | 0.924260i | ||||
\(144\) | −2.00000 | − | 3.46410i | −0.166667 | − | 0.288675i | ||||
\(145\) | 6.51513 | − | 11.2845i | 0.541052 | − | 0.937129i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.689962 | + | 6.96591i | 0.0569071 | + | 0.574539i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 1.08628 | − | 1.88148i | 0.0889911 | − | 0.154137i | −0.818094 | − | 0.575085i | \(-0.804969\pi\) |
0.907085 | + | 0.420948i | \(0.138302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.05019 | + | 13.9433i | 0.655115 | + | 1.13469i | 0.981865 | + | 0.189582i | \(0.0607132\pi\) |
−0.326750 | + | 0.945111i | \(0.605953\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.7179 | −1.58378 | ||||||||
\(156\) | 2.06760 | − | 3.58119i | 0.165541 | − | 0.286725i | ||||
\(157\) | 5.00000 | + | 8.66025i | 0.399043 | + | 0.691164i | 0.993608 | − | 0.112884i | \(-0.0360089\pi\) |
−0.594565 | + | 0.804048i | \(0.702676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.06760 | + | 3.58119i | −0.163971 | + | 0.284007i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.981326 | + | 1.08333i | −0.0773393 | + | 0.0853781i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.29491 | + | 5.70695i | −0.258077 | + | 0.447003i | −0.965727 | − | 0.259561i | \(-0.916422\pi\) |
0.707649 | + | 0.706564i | \(0.249756\pi\) | |||||||
\(164\) | −1.00000 | − | 1.73205i | −0.0780869 | − | 0.135250i | ||||
\(165\) | 7.87764 | + | 13.6445i | 0.613273 | + | 1.06222i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.86480 | −0.299067 | −0.149534 | − | 0.988757i | \(-0.547777\pi\) | ||||
−0.149534 | + | 0.988757i | \(0.547777\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.72503 | −0.671156 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.223763 | + | 0.387568i | 0.0171116 | + | 0.0296381i | ||||
\(172\) | −10.6201 | − | 18.3945i | −0.809773 | − | 1.40257i | ||||
\(173\) | 2.93240 | − | 5.07906i | 0.222946 | − | 0.386154i | −0.732755 | − | 0.680492i | \(-0.761766\pi\) |
0.955701 | + | 0.294338i | \(0.0950993\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.22731 | + | 3.81615i | 0.0927759 | + | 0.288474i | ||||
\(176\) | 24.6902 | 1.86109 | ||||||||
\(177\) | 4.06760 | − | 7.04529i | 0.305740 | − | 0.529557i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.72503 | + | 8.18398i | 0.353165 | + | 0.611700i | 0.986802 | − | 0.161931i | \(-0.0517721\pi\) |
−0.633637 | + | 0.773630i | \(0.718439\pi\) | |||||||
\(180\) | 2.55247 | − | 4.42102i | 0.190250 | − | 0.329523i | ||||
\(181\) | 7.89758 | 0.587022 | 0.293511 | − | 0.955956i | \(-0.405176\pi\) | ||||
0.293511 | + | 0.955956i | \(0.405176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.75528 | −0.573287 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.27624 | + | 2.21051i | 0.0938308 | + | 0.162520i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.17255 | − | 10.6912i | 0.451382 | − | 0.781816i | ||||
\(188\) | 16.6155 | 1.21181 | ||||||||
\(189\) | 2.58628 | + | 0.557835i | 0.188124 | + | 0.0405766i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.60140 | + | 4.50576i | −0.188231 | + | 0.326025i | −0.944660 | − | 0.328050i | \(-0.893609\pi\) |
0.756430 | + | 0.654075i | \(0.226942\pi\) | |||||||
\(192\) | −4.00000 | − | 6.92820i | −0.288675 | − | 0.500000i | ||||
\(193\) | −6.65388 | − | 11.5249i | −0.478957 | − | 0.829577i | 0.520752 | − | 0.853708i | \(-0.325652\pi\) |
−0.999709 | + | 0.0241308i | \(0.992318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.27750 | 0.377930 | ||||||||
\(196\) | 1.37992 | + | 13.9318i | 0.0985660 | + | 0.995131i | ||||
\(197\) | 19.5106 | 1.39007 | 0.695035 | − | 0.718976i | \(-0.255389\pi\) | ||||
0.695035 | + | 0.718976i | \(0.255389\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.06760 | − | 1.84914i | −0.0756802 | − | 0.131082i | 0.825702 | − | 0.564107i | \(-0.190779\pi\) |
−0.901382 | + | 0.433025i | \(0.857446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0338006 | + | 0.0585444i | −0.00238411 | + | 0.00412940i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.2028 | + | 2.84772i | 0.926655 | + | 0.199871i | ||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 1.27624 | − | 2.21051i | 0.0891363 | − | 0.154389i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.276237 | + | 0.478457i | 0.0191998 | + | 0.0332551i | ||||
\(208\) | 4.13520 | − | 7.16238i | 0.286725 | − | 0.496622i | ||||
\(209\) | −2.76237 | −0.191077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.6902 | 1.14900 | 0.574500 | − | 0.818504i | \(-0.305196\pi\) | ||||
0.574500 | + | 0.818504i | \(0.305196\pi\) | |||||||
\(212\) | −4.13520 | + | 7.16238i | −0.284007 | + | 0.491914i | ||||
\(213\) | 1.06760 | + | 1.84914i | 0.0731508 | + | 0.126701i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.5537 | − | 23.4758i | 0.924357 | − | 1.60103i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.25756 | − | 19.4570i | −0.424791 | − | 1.32083i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.31004 | + | 9.19726i | −0.358819 | + | 0.621493i | ||||
\(220\) | 15.7553 | + | 27.2889i | 1.06222 | + | 1.83982i | ||||
\(221\) | −2.06760 | − | 3.58119i | −0.139082 | − | 0.240897i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.9652 | 1.06911 | 0.534554 | − | 0.845135i | \(-0.320480\pi\) | ||||
0.534554 | + | 0.845135i | \(0.320480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.51513 | 0.101008 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.06760 | + | 7.04529i | 0.269976 | + | 0.467612i | 0.968855 | − | 0.247627i | \(-0.0796508\pi\) |
−0.698879 | + | 0.715240i | \(0.746318\pi\) | |||||||
\(228\) | 0.447525 | + | 0.775137i | 0.0296381 | + | 0.0513347i | ||||
\(229\) | 0.0885602 | − | 0.153391i | 0.00585222 | − | 0.0101363i | −0.863084 | − | 0.505060i | \(-0.831471\pi\) |
0.868937 | + | 0.494923i | \(0.164804\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.9639 | + | 12.1035i | −0.721373 | + | 0.796353i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.08628 | − | 14.0058i | 0.529750 | − | 0.917553i | −0.469648 | − | 0.882854i | \(-0.655619\pi\) |
0.999398 | − | 0.0346995i | \(-0.0110474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.6027 | + | 18.3644i | 0.691642 | + | 1.19796i | ||||
\(236\) | 8.13520 | − | 14.0906i | 0.529557 | − | 0.917219i | ||||
\(237\) | −16.7926 | −1.09080 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.4501 | 1.64623 | 0.823113 | − | 0.567877i | \(-0.192235\pi\) | ||||
0.823113 | + | 0.567877i | \(0.192235\pi\) | |||||||
\(240\) | 5.10495 | − | 8.84203i | 0.329523 | − | 0.570751i | ||||
\(241\) | 6.81004 | + | 11.7953i | 0.438673 | + | 0.759804i | 0.997587 | − | 0.0694213i | \(-0.0221153\pi\) |
−0.558914 | + | 0.829225i | \(0.688782\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −15.5106 | −0.992962 | ||||||||
\(245\) | −14.5177 | + | 10.4153i | −0.927499 | + | 0.665411i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.462652 | + | 0.801337i | −0.0294378 | + | 0.0509878i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.96391 | − | 12.0619i | −0.441320 | − | 0.764389i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.58273 | 0.0999009 | 0.0499504 | − | 0.998752i | \(-0.484094\pi\) | ||||
0.0499504 | + | 0.998752i | \(0.484094\pi\) | |||||||
\(252\) | 5.17255 | + | 1.11567i | 0.325840 | + | 0.0702807i | ||||
\(253\) | −3.41018 | −0.214396 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.55247 | − | 4.42102i | −0.159842 | − | 0.276855i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −4.22148 | + | 7.31181i | −0.263329 | + | 0.456098i | −0.967124 | − | 0.254304i | \(-0.918154\pi\) |
0.703796 | + | 0.710402i | \(0.251487\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.77624 | + | 1.96086i | −0.110370 | + | 0.121842i | ||||
\(260\) | 10.5550 | 0.654593 | ||||||||
\(261\) | 2.55247 | − | 4.42102i | 0.157994 | − | 0.273654i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.70635 | − | 6.41959i | −0.228543 | − | 0.395849i | 0.728833 | − | 0.684691i | \(-0.240063\pi\) |
−0.957377 | + | 0.288842i | \(0.906730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5550 | −0.648388 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.3078 | −0.753222 | ||||||||
\(268\) | −0.0676012 | + | 0.117089i | −0.00412940 | + | 0.00715234i | ||||
\(269\) | 10.6877 | + | 18.5116i | 0.651639 | + | 1.12867i | 0.982725 | + | 0.185072i | \(0.0592517\pi\) |
−0.331086 | + | 0.943601i | \(0.607415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.20280 | + | 5.54742i | −0.194556 | + | 0.336982i | −0.946755 | − | 0.321955i | \(-0.895660\pi\) |
0.752199 | + | 0.658937i | \(0.228993\pi\) | |||||||
\(272\) | −8.00000 | −0.485071 | ||||||||
\(273\) | 1.67484 | + | 5.20766i | 0.101366 | + | 0.315182i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.67610 | + | 8.09924i | −0.281979 | + | 0.488402i | ||||
\(276\) | 0.552475 | + | 0.956914i | 0.0332551 | + | 0.0575995i | ||||
\(277\) | −6.31004 | − | 10.9293i | −0.379133 | − | 0.656678i | 0.611803 | − | 0.791010i | \(-0.290445\pi\) |
−0.990936 | + | 0.134332i | \(0.957111\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.72503 | −0.462485 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.4430 | −1.21952 | −0.609762 | − | 0.792584i | \(-0.708735\pi\) | ||||
−0.609762 | + | 0.792584i | \(0.708735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.672550 | − | 1.16489i | −0.0399790 | − | 0.0692456i | 0.845344 | − | 0.534223i | \(-0.179396\pi\) |
−0.885323 | + | 0.464977i | \(0.846062\pi\) | |||||||
\(284\) | 2.13520 | + | 3.69828i | 0.126701 | + | 0.219452i | ||||
\(285\) | −0.571149 | + | 0.989258i | −0.0338319 | + | 0.0585986i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.58628 | + | 0.557835i | 0.152663 | + | 0.0329280i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.10495 | + | 14.0382i | 0.475121 | + | 0.822933i | ||||
\(292\) | −10.6201 | + | 18.3945i | −0.621493 | + | 1.07646i | ||||
\(293\) | −24.3824 | −1.42444 | −0.712219 | − | 0.701957i | \(-0.752310\pi\) | ||||
−0.712219 | + | 0.701957i | \(0.752310\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7649 | 1.20898 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.08628 | + | 5.34559i | 0.179084 | + | 0.310182i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.571149 | + | 0.989258i | −0.0330304 | + | 0.0572103i | ||||
\(300\) | 3.03025 | 0.174952 | ||||||||
\(301\) | 27.4664 | + | 5.92426i | 1.58314 | + | 0.341468i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.10495 | + | 10.5741i | −0.350720 | + | 0.607465i | ||||
\(304\) | 0.895051 | + | 1.55027i | 0.0513347 | + | 0.0889143i | ||||
\(305\) | −9.89758 | − | 17.1431i | −0.566734 | − | 0.981611i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.2099 | −1.09637 | −0.548183 | − | 0.836358i | \(-0.684680\pi\) | ||||
−0.548183 | + | 0.836358i | \(0.684680\pi\) | |||||||
\(308\) | −21.9278 | + | 24.2070i | −1.24945 | + | 1.37932i | ||||
\(309\) | 8.10495 | 0.461074 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4990 | + | 26.8450i | 0.878866 | + | 1.52224i | 0.852586 | + | 0.522587i | \(0.175033\pi\) |
0.0262802 | + | 0.999655i | \(0.491634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.16900 | − | 14.1491i | 0.461739 | − | 0.799756i | −0.537308 | − | 0.843386i | \(-0.680559\pi\) |
0.999048 | + | 0.0436298i | \(0.0138922\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.06760 | + | 6.42891i | 0.116496 | + | 0.362228i | ||||
\(316\) | −33.5853 | −1.88932 | ||||||||
\(317\) | 11.7740 | − | 20.3931i | 0.661291 | − | 1.14539i | −0.318986 | − | 0.947760i | \(-0.603342\pi\) |
0.980277 | − | 0.197630i | \(-0.0633245\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.7553 | + | 27.2889i | 0.882126 | + | 1.52789i | ||||
\(320\) | 10.2099 | − | 17.6841i | 0.570751 | − | 0.988569i | ||||
\(321\) | −2.55247 | −0.142465 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.895051 | 0.0498020 | ||||||||
\(324\) | 1.00000 | − | 1.73205i | 0.0555556 | − | 0.0962250i | ||||
\(325\) | 1.56634 | + | 2.71298i | 0.0868848 | + | 0.150489i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.29136 | − | 3.96876i | 0.126713 | − | 0.219473i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.7565 | + | 16.2904i | −0.813554 | + | 0.898117i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4639 | − | 21.5881i | 0.685079 | − | 1.18659i | −0.288333 | − | 0.957530i | \(-0.593101\pi\) |
0.973412 | − | 0.229061i | \(-0.0735655\pi\) | |||||||
\(332\) | −13.9278 | − | 24.1237i | −0.764389 | − | 1.32396i | ||||
\(333\) | 0.500000 | + | 0.866025i | 0.0273998 | + | 0.0474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.172550 | −0.00942744 | ||||||||
\(336\) | 10.3451 | + | 2.23134i | 0.564372 | + | 0.121730i | ||||
\(337\) | −27.0000 | −1.47078 | −0.735392 | − | 0.677642i | \(-0.763002\pi\) | ||||
−0.735392 | + | 0.677642i | \(0.763002\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.51639 | − | 13.0188i | −0.408234 | − | 0.707082i | ||||
\(340\) | −5.10495 | − | 8.84203i | −0.276855 | − | 0.479526i | ||||
\(341\) | 23.8416 | − | 41.2948i | 1.29109 | − | 2.23624i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.8847 | − | 11.0202i | −0.803700 | − | 0.595035i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.705089 | + | 1.22125i | −0.0379607 | + | 0.0657499i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.6877 | − | 21.9757i | −0.681110 | − | 1.17972i | −0.974642 | − | 0.223768i | \(-0.928164\pi\) |
0.293532 | − | 0.955949i | \(-0.405169\pi\) | |||||||
\(348\) | 5.10495 | − | 8.84203i | 0.273654 | − | 0.473983i | ||||
\(349\) | 29.9652 | 1.60400 | 0.802000 | − | 0.597325i | \(-0.203770\pi\) | ||||
0.802000 | + | 0.597325i | \(0.203770\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.06760 | 0.110360 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.55247 | + | 13.0813i | 0.401978 | + | 0.696246i | 0.993965 | − | 0.109702i | \(-0.0349896\pi\) |
−0.591987 | + | 0.805948i | \(0.701656\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.72503 | + | 4.71988i | −0.144629 | + | 0.250505i | ||||
\(356\) | −24.6155 | −1.30462 | ||||||||
\(357\) | 3.55247 | − | 3.92172i | 0.188017 | − | 0.207560i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.2086 | + | 22.8780i | −0.697125 | + | 1.20746i | 0.272334 | + | 0.962203i | \(0.412204\pi\) |
−0.969459 | + | 0.245253i | \(0.921129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.39986 | + | 16.2810i | 0.494730 | + | 0.856897i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.1004 | −1.42240 | ||||||||
\(364\) | 3.34967 | + | 10.4153i | 0.175570 | + | 0.545911i | ||||
\(365\) | −27.1075 | −1.41887 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.79491 | + | 6.57298i | 0.198093 | + | 0.343107i | 0.947910 | − | 0.318538i | \(-0.103192\pi\) |
−0.749817 | + | 0.661645i | \(0.769859\pi\) | |||||||
\(368\) | 1.10495 | + | 1.91383i | 0.0575995 | + | 0.0997652i | ||||
\(369\) | 0.500000 | − | 0.866025i | 0.0260290 | − | 0.0450835i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.34967 | − | 10.4153i | −0.173906 | − | 0.540737i | ||||
\(372\) | −15.4501 | −0.801048 | ||||||||
\(373\) | −8.60495 | + | 14.9042i | −0.445547 | + | 0.771711i | −0.998090 | − | 0.0617738i | \(-0.980324\pi\) |
0.552543 | + | 0.833485i | \(0.313658\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.44753 | − | 7.70334i | −0.229669 | − | 0.397799i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.5550 | 0.543610 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.3708 | 1.30321 | 0.651605 | − | 0.758559i | \(-0.274096\pi\) | ||||
0.651605 | + | 0.758559i | \(0.274096\pi\) | |||||||
\(380\) | −1.14230 | + | 1.97852i | −0.0585986 | + | 0.101496i | ||||
\(381\) | −1.12008 | − | 1.94003i | −0.0573832 | − | 0.0993907i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.41727 | − | 9.38299i | 0.276810 | − | 0.479448i | −0.693780 | − | 0.720187i | \(-0.744056\pi\) |
0.970590 | + | 0.240738i | \(0.0773895\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −40.7475 | − | 8.78885i | −2.07668 | − | 0.447921i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.31004 | − | 9.19726i | 0.269924 | − | 0.467523i | ||||
\(388\) | 16.2099 | + | 28.0764i | 0.822933 | + | 1.42536i | ||||
\(389\) | −7.13646 | − | 12.3607i | −0.361833 | − | 0.626713i | 0.626429 | − | 0.779478i | \(-0.284516\pi\) |
−0.988263 | + | 0.152765i | \(0.951182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.10495 | 0.0558797 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.5525 | 0.834962 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.4314 | − | 37.1202i | −1.07833 | − | 1.86772i | ||||
\(396\) | 6.17255 | + | 10.6912i | 0.310182 | + | 0.537252i | ||||
\(397\) | 8.93138 | − | 15.4696i | 0.448253 | − | 0.776397i | −0.550020 | − | 0.835152i | \(-0.685380\pi\) |
0.998272 | + | 0.0587550i | \(0.0187131\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.15742 | − | 0.249646i | −0.0579437 | − | 0.0124979i | ||||
\(400\) | 6.06051 | 0.303025 | ||||||||
\(401\) | −7.86023 | + | 13.6143i | −0.392521 | + | 0.679866i | −0.992781 | − | 0.119938i | \(-0.961730\pi\) |
0.600260 | + | 0.799805i | \(0.295064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.98614 | − | 13.8324i | −0.397818 | − | 0.689041i | ||||
\(404\) | −12.2099 | + | 21.1482i | −0.607465 | + | 1.05216i | ||||
\(405\) | 2.55247 | 0.126833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.17255 | −0.305962 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5502 | − | 20.0055i | −0.571120 | − | 0.989209i | −0.996451 | − | 0.0841713i | \(-0.973176\pi\) |
0.425331 | − | 0.905038i | \(-0.360158\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0676012 | + | 0.117089i | −0.00333452 | + | 0.00577556i | ||||
\(412\) | 16.2099 | 0.798604 | ||||||||
\(413\) | 6.58982 | + | 20.4901i | 0.324264 | + | 1.00825i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.7752 | − | 30.7876i | 0.872551 | − | 1.51130i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.18768 | − | 7.25327i | −0.205071 | − | 0.355194i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.3451 | 1.09163 | 0.545815 | − | 0.837906i | \(-0.316220\pi\) | ||||
0.545815 | + | 0.837906i | \(0.316220\pi\) | |||||||
\(420\) | 4.13520 | + | 12.8578i | 0.201777 | + | 0.627398i | ||||
\(421\) | −34.8325 | −1.69763 | −0.848816 | − | 0.528688i | \(-0.822684\pi\) | ||||
−0.848816 | + | 0.528688i | \(0.822684\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.15388 | + | 7.19473i | 0.201968 | + | 0.349820i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.51513 | − | 2.62428i | 0.0734944 | − | 0.127296i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.7752 | − | 15.2070i | 0.666629 | − | 0.735920i | ||||
\(428\) | −5.10495 | −0.246757 | ||||||||
\(429\) | −6.38119 | + | 11.0525i | −0.308087 | + | 0.533622i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.24598 | − | 14.2825i | −0.397195 | − | 0.687962i | 0.596184 | − | 0.802848i | \(-0.296683\pi\) |
−0.993379 | + | 0.114886i | \(0.963350\pi\) | |||||||
\(432\) | 2.00000 | − | 3.46410i | 0.0962250 | − | 0.166667i | ||||
\(433\) | −19.9349 | −0.958011 | −0.479006 | − | 0.877812i | \(-0.659003\pi\) | ||||
−0.479006 | + | 0.877812i | \(0.659003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.0303 | 0.624753 | ||||||||
\(436\) | 4.58273 | − | 7.93752i | 0.219473 | − | 0.380138i | ||||
\(437\) | −0.123623 | − | 0.214122i | −0.00591370 | − | 0.0102428i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9452 | − | 22.4218i | 0.617843 | − | 1.07013i | −0.372036 | − | 0.928218i | \(-0.621340\pi\) |
0.989879 | − | 0.141917i | \(-0.0453265\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.68768 | + | 4.08048i | −0.270842 | + | 0.194309i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.7926 | + | 27.3536i | −0.750330 | + | 1.29961i | 0.197332 | + | 0.980337i | \(0.436772\pi\) |
−0.947663 | + | 0.319274i | \(0.896561\pi\) | |||||||
\(444\) | 1.00000 | + | 1.73205i | 0.0474579 | + | 0.0821995i | ||||
\(445\) | −15.7076 | − | 27.2064i | −0.744612 | − | 1.28971i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.17255 | 0.102758 | ||||||||
\(448\) | 20.6902 | + | 4.46268i | 0.977520 | + | 0.210842i | ||||
\(449\) | −10.0630 | −0.474904 | −0.237452 | − | 0.971399i | \(-0.576312\pi\) | ||||
−0.237452 | + | 0.971399i | \(0.576312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.08628 | + | 5.34559i | 0.145327 | + | 0.251714i | ||||
\(452\) | −15.0328 | − | 26.0375i | −0.707082 | − | 1.22470i | ||||
\(453\) | −8.05019 | + | 13.9433i | −0.378231 | + | 0.655115i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.37409 | + | 10.3485i | −0.439464 | + | 0.485143i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.56886 | − | 14.8417i | 0.400835 | − | 0.694266i | −0.592992 | − | 0.805208i | \(-0.702054\pi\) |
0.993827 | + | 0.110942i | \(0.0353869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | −1.41018 | + | 2.44250i | −0.0657499 | + | 0.113882i | ||||
\(461\) | 6.89758 | 0.321252 | 0.160626 | − | 0.987015i | \(-0.448649\pi\) | ||||
0.160626 | + | 0.987015i | \(0.448649\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1726 | −1.16987 | −0.584934 | − | 0.811081i | \(-0.698880\pi\) | ||||
−0.584934 | + | 0.811081i | \(0.698880\pi\) | |||||||
\(464\) | 10.2099 | − | 17.6841i | 0.473983 | − | 0.820962i | ||||
\(465\) | −9.85897 | − | 17.0762i | −0.457199 | − | 0.791891i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.79136 | + | 8.29889i | −0.221718 | + | 0.384027i | −0.955330 | − | 0.295542i | \(-0.904500\pi\) |
0.733612 | + | 0.679569i | \(0.237833\pi\) | |||||||
\(468\) | 4.13520 | 0.191150 | ||||||||
\(469\) | −0.0547596 | − | 0.170267i | −0.00252856 | − | 0.00786220i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.00000 | + | 8.66025i | −0.230388 | + | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.7765 | + | 56.7705i | 1.50706 | + | 2.61031i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.678058 | −0.0311114 | ||||||||
\(476\) | 7.10495 | − | 7.84345i | 0.325655 | − | 0.359504i | ||||
\(477\) | −4.13520 | −0.189338 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.98133 | + | 10.3600i | 0.273294 | + | 0.473359i | 0.969703 | − | 0.244286i | \(-0.0785536\pi\) |
−0.696409 | + | 0.717645i | \(0.745220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.03380 | + | 1.79060i | −0.0471373 | + | 0.0816441i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.42885 | − | 0.308190i | −0.0650150 | − | 0.0140231i | ||||
\(484\) | −54.2008 | −2.46367 | ||||||||
\(485\) | −20.6877 | + | 35.8321i | −0.939379 | + | 1.62705i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.87535 | + | 17.1046i | 0.447495 | + | 0.775084i | 0.998222 | − | 0.0596012i | \(-0.0189829\pi\) |
−0.550727 | + | 0.834685i | \(0.685650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.58982 | −0.298002 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.75985 | 0.214809 | 0.107404 | − | 0.994215i | \(-0.465746\pi\) | ||||
0.107404 | + | 0.994215i | \(0.465746\pi\) | |||||||
\(492\) | 1.00000 | − | 1.73205i | 0.0450835 | − | 0.0780869i | ||||
\(493\) | −5.10495 | − | 8.84203i | −0.229915 | − | 0.398225i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.87764 | + | 13.6445i | −0.354074 | + | 0.613273i | ||||
\(496\) | −30.9001 | −1.38746 | ||||||||
\(497\) | −5.52222 | − | 1.19109i | −0.247705 | − | 0.0534278i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.73889 | − | 4.74390i | 0.122610 | − | 0.212366i | −0.798186 | − | 0.602410i | \(-0.794207\pi\) |
0.920796 | + | 0.390045i | \(0.127540\pi\) | |||||||
\(500\) | −8.89505 | − | 15.4067i | −0.397799 | − | 0.689008i | ||||
\(501\) | −1.93240 | − | 3.34701i | −0.0863332 | − | 0.149534i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.00709 | 0.134080 | 0.0670399 | − | 0.997750i | \(-0.478645\pi\) | ||||
0.0670399 | + | 0.997750i | \(0.478645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.1655 | −1.38684 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.36251 | − | 7.55609i | −0.193746 | − | 0.335578i | ||||
\(508\) | −2.24015 | − | 3.88006i | −0.0993907 | − | 0.172150i | ||||
\(509\) | −15.8602 | + | 27.4707i | −0.702992 | + | 1.21762i | 0.264419 | + | 0.964408i | \(0.414820\pi\) |
−0.967411 | + | 0.253210i | \(0.918514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.60266 | − | 26.7488i | −0.380559 | − | 1.18330i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.223763 | + | 0.387568i | −0.00987936 | + | 0.0171116i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.3438 | + | 17.9161i | 0.455804 | + | 0.789476i | ||||
\(516\) | 10.6201 | − | 18.3945i | 0.467523 | − | 0.809773i | ||||
\(517\) | −51.2800 | −2.25529 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.86480 | 0.257436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0560 | + | 20.8816i | 0.528184 | + | 0.914841i | 0.999460 | + | 0.0328557i | \(0.0104602\pi\) |
−0.471276 | + | 0.881986i | \(0.656206\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5875 | − | 30.4625i | 0.769049 | − | 1.33203i | −0.169030 | − | 0.985611i | \(-0.554063\pi\) |
0.938079 | − | 0.346422i | \(-0.112603\pi\) | |||||||
\(524\) | 33.1049 | 1.44620 | ||||||||
\(525\) | −2.69122 | + | 2.97095i | −0.117455 | + | 0.129663i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.72503 | + | 13.3801i | −0.336507 | + | 0.582848i | ||||
\(528\) | 12.3451 | + | 21.3823i | 0.537252 | + | 0.930547i | ||||
\(529\) | 11.3474 | + | 19.6542i | 0.493365 | + | 0.854533i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.13520 | 0.353038 | ||||||||
\(532\) | −2.31485 | − | 0.499291i | −0.100361 | − | 0.0216470i | ||||
\(533\) | 2.06760 | 0.0895578 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.25756 | − | 5.64227i | −0.140837 | − | 0.243936i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.72503 | + | 8.18398i | −0.203900 | + | 0.353165i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.25883 | − | 42.9975i | −0.183441 | − | 1.85203i | ||||
\(540\) | 5.10495 | 0.219682 | ||||||||
\(541\) | −8.31004 | + | 14.3934i | −0.357276 | + | 0.618821i | −0.987505 | − | 0.157589i | \(-0.949628\pi\) |
0.630228 | + | 0.776410i | \(0.282961\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.94879 | + | 6.83950i | 0.169459 | + | 0.293511i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.6973 | 0.501057 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6760 | 0.798529 | 0.399264 | − | 0.916836i | \(-0.369266\pi\) | ||||
0.399264 | + | 0.916836i | \(0.369266\pi\) | |||||||
\(548\) | −0.135202 | + | 0.234178i | −0.00577556 | + | 0.0100036i | ||||
\(549\) | −3.87764 | − | 6.71627i | −0.165494 | − | 0.286643i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.14230 | + | 1.97852i | −0.0486635 | + | 0.0842876i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.8277 | − | 32.9280i | 1.26840 | − | 1.40024i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.27624 | + | 2.21051i | −0.0541733 | + | 0.0938308i | ||||
\(556\) | −8.37535 | − | 14.5065i | −0.355194 | − | 0.615214i | ||||
\(557\) | 14.8416 | + | 25.7063i | 0.628857 | + | 1.08921i | 0.987781 | + | 0.155845i | \(0.0498102\pi\) |
−0.358925 | + | 0.933367i | \(0.616856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.9581 | 0.928728 | ||||||||
\(560\) | 8.27040 | + | 25.7156i | 0.349488 | + | 1.08668i | ||||
\(561\) | 12.3451 | 0.521211 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.638750 | + | 1.10635i | 0.0269201 | + | 0.0466270i | 0.879172 | − | 0.476505i | \(-0.158097\pi\) |
−0.852251 | + | 0.523132i | \(0.824763\pi\) | |||||||
\(564\) | 8.30775 | + | 14.3895i | 0.349820 | + | 0.605905i | ||||
\(565\) | 19.1854 | − | 33.2301i | 0.807136 | − | 1.39800i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.810038 | + | 2.51870i | 0.0340184 | + | 0.105775i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.47904 | + | 9.48998i | −0.229693 | + | 0.397841i | −0.957717 | − | 0.287711i | \(-0.907106\pi\) |
0.728024 | + | 0.685552i | \(0.240439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.6867 | − | 28.9021i | −0.698315 | − | 1.20952i | −0.969050 | − | 0.246863i | \(-0.920600\pi\) |
0.270736 | − | 0.962654i | \(-0.412733\pi\) | |||||||
\(572\) | −12.7624 | + | 22.1051i | −0.533622 | + | 0.924260i | ||||
\(573\) | −5.20280 | −0.217350 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.837069 | −0.0349082 | ||||||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | −13.2939 | − | 23.0257i | −0.553432 | − | 0.958572i | −0.998024 | − | 0.0628388i | \(-0.979985\pi\) |
0.444592 | − | 0.895733i | \(-0.353349\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.65388 | − | 11.5249i | 0.276526 | − | 0.478957i | ||||
\(580\) | 26.0605 | 1.08210 | ||||||||
\(581\) | 36.0212 | + | 7.76944i | 1.49441 | + | 0.322331i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.7624 | − | 22.1051i | 0.528563 | − | 0.915499i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.63875 | + | 4.57045i | 0.109099 | + | 0.188965i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.2472 | −1.33099 | −0.665493 | − | 0.746404i | \(-0.731779\pi\) | ||||
−0.665493 | + | 0.746404i | \(0.731779\pi\) | |||||||
\(588\) | −11.3754 | + | 8.16096i | −0.469112 | + | 0.336552i | ||||
\(589\) | 3.45714 | 0.142449 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.75528 | + | 16.8966i | 0.401279 | + | 0.695035i | ||||
\(592\) | 2.00000 | + | 3.46410i | 0.0821995 | + | 0.142374i | ||||
\(593\) | −14.3940 | + | 24.9312i | −0.591092 | + | 1.02380i | 0.402994 | + | 0.915203i | \(0.367970\pi\) |
−0.994086 | + | 0.108598i | \(0.965364\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.2028 | + | 2.84772i | 0.541262 | + | 0.116745i | ||||
\(596\) | 4.34510 | 0.177982 | ||||||||
\(597\) | 1.06760 | − | 1.84914i | 0.0436940 | − | 0.0756802i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.03609 | − | 1.79455i | −0.0423333 | − | 0.0733234i | 0.844082 | − | 0.536213i | \(-0.180146\pi\) |
−0.886416 | + | 0.462890i | \(0.846812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.38245 | −0.301136 | −0.150568 | − | 0.988600i | \(-0.548110\pi\) | ||||
−0.150568 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0676012 | −0.00275294 | ||||||||
\(604\) | −16.1004 | + | 27.8867i | −0.655115 | + | 1.13469i | ||||
\(605\) | −34.5865 | − | 59.9056i | −1.40614 | − | 2.43551i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.39758 | − | 12.8130i | 0.300258 | − | 0.520063i | −0.675936 | − | 0.736960i | \(-0.736260\pi\) |
0.976194 | + | 0.216898i | \(0.0695938\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.13520 | + | 12.8578i | 0.167567 | + | 0.521025i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.58856 | + | 14.8758i | −0.347456 | + | 0.601811i | ||||
\(612\) | −2.00000 | − | 3.46410i | −0.0808452 | − | 0.140028i | ||||
\(613\) | −16.0328 | − | 27.7696i | −0.647558 | − | 1.12160i | −0.983704 | − | 0.179793i | \(-0.942457\pi\) |
0.336147 | − | 0.941810i | \(-0.390876\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.55247 | 0.102926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.6155 | 1.71564 | 0.857818 | − | 0.513954i | \(-0.171820\pi\) | ||||
0.857818 | + | 0.513954i | \(0.171820\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.61779 | + | 14.9265i | 0.346378 | + | 0.599945i | 0.985603 | − | 0.169075i | \(-0.0540780\pi\) |
−0.639225 | + | 0.769020i | \(0.720745\pi\) | |||||||
\(620\) | −19.7179 | − | 34.1525i | −0.791891 | − | 1.37160i | ||||
\(621\) | −0.276237 | + | 0.478457i | −0.0110850 | + | 0.0191998i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.8615 | − | 24.1338i | 0.875862 | − | 0.966901i | ||||
\(624\) | 8.27040 | 0.331081 | ||||||||
\(625\) | 15.1400 | − | 26.2233i | 0.605600 | − | 1.04893i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.38119 | − | 2.39229i | −0.0551593 | − | 0.0955387i | ||||
\(628\) | −10.0000 | + | 17.3205i | −0.399043 | + | 0.691164i | ||||
\(629\) | 2.00000 | 0.0797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.1352 | −0.881188 | −0.440594 | − | 0.897706i | \(-0.645232\pi\) | ||||
−0.440594 | + | 0.897706i | \(0.645232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.34510 | + | 14.4541i | 0.331688 | + | 0.574500i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.85897 | − | 4.95187i | 0.113455 | − | 0.196509i | ||||
\(636\) | −8.27040 | −0.327943 | ||||||||
\(637\) | −13.1864 | − | 5.96592i | −0.522465 | − | 0.236378i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.06760 | + | 1.84914i | −0.0422337 | + | 0.0731508i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.39860 | + | 12.8147i | 0.292227 | + | 0.506152i | 0.974336 | − | 0.225098i | \(-0.0722704\pi\) |
−0.682109 | + | 0.731251i | \(0.738937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.2986 | 1.78640 | 0.893201 | − | 0.449657i | \(-0.148454\pi\) | ||||
0.893201 | + | 0.449657i | \(0.148454\pi\) | |||||||
\(644\) | −2.85770 | − | 0.616380i | −0.112609 | − | 0.0242888i | ||||
\(645\) | 27.1075 | 1.06736 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.8602 | + | 18.8105i | 0.426960 | + | 0.739516i | 0.996601 | − | 0.0823775i | \(-0.0262513\pi\) |
−0.569642 | + | 0.821893i | \(0.692918\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.1075 | + | 43.4874i | −0.985555 | + | 1.70703i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.7215 | − | 15.1477i | 0.537787 | − | 0.593686i | ||||
\(652\) | −13.1796 | −0.516155 | ||||||||
\(653\) | 24.4616 | − | 42.3688i | 0.957258 | − | 1.65802i | 0.228142 | − | 0.973628i | \(-0.426735\pi\) |
0.729115 | − | 0.684391i | \(-0.239932\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.1249 | + | 36.5894i | 0.825418 | + | 1.42967i | ||||
\(656\) | 2.00000 | − | 3.46410i | 0.0780869 | − | 0.135250i | ||||
\(657\) | −10.6201 | −0.414329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.4198 | −1.41871 | −0.709357 | − | 0.704849i | \(-0.751015\pi\) | ||||
−0.709357 | + | 0.704849i | \(0.751015\pi\) | |||||||
\(660\) | −15.7553 | + | 27.2889i | −0.613273 | + | 1.06222i | ||||
\(661\) | 0.934684 | + | 1.61892i | 0.0363550 | + | 0.0629687i | 0.883630 | − | 0.468185i | \(-0.155092\pi\) |
−0.847275 | + | 0.531154i | \(0.821759\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.06760 | − | 3.58119i | 0.0802990 | − | 0.139082i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.925304 | − | 2.87710i | −0.0358818 | − | 0.111569i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.41018 | + | 2.44250i | −0.0546023 | + | 0.0945739i | ||||
\(668\) | −3.86480 | − | 6.69403i | −0.149534 | − | 0.259000i | ||||
\(669\) | 7.98259 | + | 13.8262i | 0.308625 | + | 0.534554i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.8698 | 1.84799 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.8325 | −1.72817 | −0.864083 | − | 0.503349i | \(-0.832101\pi\) | ||||
−0.864083 | + | 0.503349i | \(0.832101\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.757563 | + | 1.31214i | 0.0291586 | + | 0.0505042i | ||||
\(676\) | −8.72503 | − | 15.1122i | −0.335578 | − | 0.581238i | ||||
\(677\) | 1.06886 | − | 1.85133i | 0.0410798 | − | 0.0711522i | −0.844754 | − | 0.535154i | \(-0.820254\pi\) |
0.885834 | + | 0.464002i | \(0.153587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.9233 | − | 9.04246i | −1.60887 | − | 0.347018i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.06760 | + | 7.04529i | −0.155871 | + | 0.269976i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.2215 | − | 26.3644i | −0.582434 | − | 1.00880i | −0.995190 | − | 0.0979632i | \(-0.968767\pi\) |
0.412756 | − | 0.910841i | \(-0.364566\pi\) | |||||||
\(684\) | −0.447525 | + | 0.775137i | −0.0171116 | + | 0.0296381i | ||||
\(685\) | −0.345101 | −0.0131856 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.177120 | 0.00675756 | ||||||||
\(688\) | 21.2402 | − | 36.7890i | 0.809773 | − | 1.40257i | ||||
\(689\) | −4.27497 | − | 7.40447i | −0.162864 | − | 0.282088i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.10850 | + | 15.7764i | −0.346504 | + | 0.600162i | −0.985626 | − | 0.168943i | \(-0.945964\pi\) |
0.639122 | + | 0.769105i | \(0.279298\pi\) | |||||||
\(692\) | 11.7296 | 0.445892 | ||||||||
\(693\) | −15.9639 | − | 3.44327i | −0.606419 | − | 0.130799i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.6889 | − | 18.5138i | 0.405455 | − | 0.702268i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.00000 | − | 1.73205i | −0.0378777 | − | 0.0656061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.1726 | 0.611702 | ||||||||
\(700\) | −5.38245 | + | 5.94191i | −0.203437 | + | 0.224583i | ||||
\(701\) | −23.2427 | −0.877864 | −0.438932 | − | 0.898520i | \(-0.644643\pi\) | ||||
−0.438932 | + | 0.898520i | \(0.644643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.223763 | − | 0.387568i | −0.00843937 | − | 0.0146174i | ||||
\(704\) | 24.6902 | + | 42.7647i | 0.930547 | + | 1.61175i | ||||
\(705\) | −10.6027 | + | 18.3644i | −0.399319 | + | 0.691642i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.89048 | − | 30.7530i | −0.371970 | − | 1.15659i | ||||
\(708\) | 16.2704 | 0.611479 | ||||||||
\(709\) | 17.3451 | − | 30.0426i | 0.651409 | − | 1.12827i | −0.331372 | − | 0.943500i | \(-0.607512\pi\) |
0.982781 | − | 0.184773i | \(-0.0591551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.39631 | − | 14.5428i | −0.314886 | − | 0.545399i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.26788 | 0.159833 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32.5756 | −1.21826 | ||||||||
\(716\) | −9.45005 | + | 16.3680i | −0.353165 | + | 0.611700i | ||||
\(717\) | 12.7250 | + | 22.0404i | 0.475225 | + | 0.823113i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.1493 | + | 29.7035i | −0.639561 | + | 1.10775i | 0.345968 | + | 0.938246i | \(0.387551\pi\) |
−0.985529 | + | 0.169506i | \(0.945783\pi\) | |||||||
\(720\) | 10.2099 | 0.380500 | ||||||||
\(721\) | −14.3963 | + | 15.8927i | −0.536147 | + | 0.591875i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.81004 | + | 11.7953i | −0.253268 | + | 0.438673i | ||||
\(724\) | 7.89758 | + | 13.6790i | 0.293511 | + | 0.508376i | ||||
\(725\) | 3.86732 | + | 6.69840i | 0.143629 | + | 0.248772i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.6226 | 0.468146 | 0.234073 | − | 0.972219i | \(-0.424794\pi\) | ||||
0.234073 | + | 0.972219i | \(0.424794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.6201 | − | 18.3945i | −0.392798 | − | 0.680346i | ||||
\(732\) | −7.75528 | − | 13.4325i | −0.286643 | − | 0.496481i | ||||
\(733\) | −17.3229 | + | 30.0041i | −0.639835 | + | 1.10823i | 0.345633 | + | 0.938370i | \(0.387664\pi\) |
−0.985469 | + | 0.169857i | \(0.945669\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.2788 | − | 7.36499i | −0.600451 | − | 0.271662i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.208636 | − | 0.361368i | 0.00768521 | − | 0.0133112i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.4150 | + | 31.8957i | 0.677406 | + | 1.17330i | 0.975759 | + | 0.218846i | \(0.0702294\pi\) |
−0.298353 | + | 0.954456i | \(0.596437\pi\) | |||||||
\(740\) | −2.55247 | + | 4.42102i | −0.0938308 | + | 0.162520i | ||||
\(741\) | −0.925304 | −0.0339919 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.3451 | 1.03988 | 0.519940 | − | 0.854203i | \(-0.325954\pi\) | ||||
0.519940 | + | 0.854203i | \(0.325954\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.77269 | + | 4.80244i | 0.101584 | + | 0.175948i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.96391 | − | 12.0619i | 0.254796 | − | 0.441320i | ||||
\(748\) | 24.6902 | 0.902763 | ||||||||
\(749\) | 4.53380 | − | 5.00505i | 0.165661 | − | 0.182881i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.27852 | − | 2.21447i | 0.0466539 | − | 0.0808070i | −0.841755 | − | 0.539859i | \(-0.818478\pi\) |
0.888409 | + | 0.459052i | \(0.151811\pi\) | |||||||
\(752\) | 16.6155 | + | 28.7789i | 0.605905 | + | 1.04946i | ||||
\(753\) | 0.791364 | + | 1.37068i | 0.0288389 | + | 0.0499504i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41.0958 | −1.49563 | ||||||||
\(756\) | 1.62008 | + | 5.03740i | 0.0589216 | + | 0.183208i | ||||
\(757\) | 44.9258 | 1.63286 | 0.816428 | − | 0.577448i | \(-0.195951\pi\) | ||||
0.816428 | + | 0.577448i | \(0.195951\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.70509 | − | 2.95330i | −0.0618908 | − | 0.107198i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.48487 | − | 9.50008i | 0.198827 | − | 0.344378i | −0.749322 | − | 0.662206i | \(-0.769620\pi\) |
0.948148 | + | 0.317829i | \(0.102954\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.71218 | + | 11.5425i | 0.134390 | + | 0.417867i | ||||
\(764\) | −10.4056 | −0.376462 | ||||||||
\(765\) | 2.55247 | − | 4.42102i | 0.0922849 | − | 0.159842i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.41018 | + | 14.5669i | 0.303674 | + | 0.525979i | ||||
\(768\) | 8.00000 | − | 13.8564i | 0.288675 | − | 0.500000i | ||||
\(769\) | 29.1751 | 1.05208 | 0.526040 | − | 0.850460i | \(-0.323676\pi\) | ||||
0.526040 | + | 0.850460i | \(0.323676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.44296 | −0.304066 | ||||||||
\(772\) | 13.3078 | − | 23.0497i | 0.478957 | − | 0.829577i | ||||
\(773\) | 21.5292 | + | 37.2897i | 0.774353 | + | 1.34122i | 0.935158 | + | 0.354232i | \(0.115258\pi\) |
−0.160805 | + | 0.986986i | \(0.551409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.85220 | − | 10.1363i | 0.210217 | − | 0.364107i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.58628 | − | 0.557835i | −0.0927821 | − | 0.0200122i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.223763 | + | 0.387568i | −0.00801713 | + | 0.0138861i | ||||
\(780\) | 5.27750 | + | 9.14090i | 0.188965 | + | 0.327297i | ||||
\(781\) | −6.58982 | − | 11.4139i | −0.235802 | − | 0.408422i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.10495 | 0.182436 | ||||||||
\(784\) | −22.7507 | + | 16.3219i | −0.812525 | + | 0.582926i | ||||
\(785\) | −25.5247 | −0.911017 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.4629 | + | 21.5864i | 0.444254 | + | 0.769471i | 0.998000 | − | 0.0632151i | \(-0.0201354\pi\) |
−0.553746 | + | 0.832686i | \(0.686802\pi\) | |||||||
\(788\) | 19.5106 | + | 33.7933i | 0.695035 | + | 1.20384i | ||||
\(789\) | 3.70635 | − | 6.41959i | 0.131950 | − | 0.228543i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.8789 | + | 8.38582i | 1.38237 | + | 0.298165i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.01741 | − | 13.8866i | 0.284707 | − | 0.493126i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.27750 | − | 9.14090i | −0.187174 | − | 0.324194i | ||||
\(796\) | 2.13520 | − | 3.69828i | 0.0756802 | − | 0.131082i | ||||
\(797\) | −0.137727 | −0.00487855 | −0.00243928 | − | 0.999997i | \(-0.500776\pi\) | ||||
−0.00243928 | + | 0.999997i | \(0.500776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.6155 | 0.587814 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.15388 | − | 10.6588i | −0.217437 | − | 0.376611i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.7765 | − | 56.7705i | 1.15666 | − | 2.00339i | ||||
\(804\) | −0.135202 | −0.00476822 | ||||||||
\(805\) | −1.14230 | − | 3.55181i | −0.0402607 | − | 0.125185i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.6877 | + | 18.5116i | −0.376224 | + | 0.651639i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.741174 | − | 1.28375i | −0.0260583 | − | 0.0451343i | 0.852702 | − | 0.522397i | \(-0.174962\pi\) |
−0.878760 | + | 0.477263i | \(0.841629\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.1004 | 0.916508 | 0.458254 | − | 0.888821i | \(-0.348475\pi\) | ||||
0.458254 | + | 0.888821i | \(0.348475\pi\) | |||||||
\(812\) | 8.27040 | + | 25.7156i | 0.290234 | + | 0.902442i | ||||
\(813\) | −6.40561 | −0.224654 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.41018 | − | 14.5669i | −0.294596 | − | 0.510255i | ||||
\(816\) | −4.00000 | − | 6.92820i | −0.140028 | − | 0.242536i | ||||
\(817\) | −2.37638 | + | 4.11601i | −0.0831389 | + | 0.144001i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.67255 | + | 4.05428i | −0.128329 | + | 0.141668i | ||||
\(820\) | 5.10495 | 0.178273 | ||||||||
\(821\) | 3.34510 | − | 5.79388i | 0.116745 | − | 0.202208i | −0.801731 | − | 0.597685i | \(-0.796087\pi\) |
0.918476 | + | 0.395477i | \(0.129421\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.52222 | − | 9.56477i | −0.192493 | − | 0.333407i | 0.753583 | − | 0.657353i | \(-0.228324\pi\) |
−0.946076 | + | 0.323946i | \(0.894990\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.35220 | −0.325602 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.6902 | 0.858562 | 0.429281 | − | 0.903171i | \(-0.358767\pi\) | ||||
0.429281 | + | 0.903171i | \(0.358767\pi\) | |||||||
\(828\) | −0.552475 | + | 0.956914i | −0.0191998 | + | 0.0332551i | ||||
\(829\) | 11.3300 | + | 19.6241i | 0.393506 | + | 0.681573i | 0.992909 | − | 0.118875i | \(-0.0379286\pi\) |
−0.599403 | + | 0.800447i | \(0.704595\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.31004 | − | 10.9293i | 0.218893 | − | 0.379133i | ||||
\(832\) | 16.5408 | 0.573449 | ||||||||
\(833\) | 1.37992 | + | 13.9318i | 0.0478115 | + | 0.482709i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.93240 | − | 8.54317i | 0.170693 | − | 0.295648i | ||||
\(836\) | −2.76237 | − | 4.78457i | −0.0955387 | − | 0.165478i | ||||
\(837\) | −3.86251 | − | 6.69007i | −0.133508 | − | 0.231243i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.1776 | −1.45613 | −0.728066 | − | 0.685507i | \(-0.759581\pi\) | ||||
−0.728066 | + | 0.685507i | \(0.759581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.93949 | −0.101362 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.2215 | − | 17.7041i | −0.352046 | − | 0.609762i | ||||
\(844\) | 16.6902 | + | 28.9083i | 0.574500 | + | 0.995064i | ||||
\(845\) | 11.1352 | − | 19.2867i | 0.383063 | − | 0.663484i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.1367 | − | 53.1401i | 1.65400 | − | 1.82592i | ||||
\(848\) | −16.5408 | −0.568014 | ||||||||
\(849\) | 0.672550 | − | 1.16489i | 0.0230819 | − | 0.0399790i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.276237 | − | 0.478457i | −0.00946929 | − | 0.0164013i | ||||
\(852\) | −2.13520 | + | 3.69828i | −0.0731508 | + | 0.126701i | ||||
\(853\) | −28.9652 | −0.991749 | −0.495874 | − | 0.868394i | \(-0.665152\pi\) | ||||
−0.495874 | + | 0.868394i | \(0.665152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.14230 | −0.0390657 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.3405 | − | 47.3552i | −0.933935 | − | 1.61762i | −0.776523 | − | 0.630089i | \(-0.783018\pi\) |
−0.157412 | − | 0.987533i | \(-0.550315\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.2949 | + | 26.4916i | −0.521856 | + | 0.903880i | 0.477821 | + | 0.878457i | \(0.341427\pi\) |
−0.999677 | + | 0.0254233i | \(0.991907\pi\) | |||||||
\(860\) | 54.2149 | 1.84871 | ||||||||
\(861\) | 0.810038 | + | 2.51870i | 0.0276060 | + | 0.0858370i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.3509 | + | 21.3924i | −0.420431 | + | 0.728207i | −0.995982 | − | 0.0895587i | \(-0.971454\pi\) |
0.575551 | + | 0.817766i | \(0.304788\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.48487 | + | 12.9642i | 0.254493 | + | 0.440795i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 27.4430 | − | 30.2954i | 0.931475 | − | 1.02829i | ||||
\(869\) | 103.653 | 3.51620 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0698862 | − | 0.121046i | −0.00236800 | − | 0.00410150i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.10495 | + | 14.0382i | −0.274311 | + | 0.475121i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.0050 | + | 4.96197i | 0.777713 | + | 0.167745i | ||||
\(876\) | −21.2402 | −0.717638 | ||||||||
\(877\) | 3.11779 | − | 5.40017i | 0.105280 | − | 0.182351i | −0.808572 | − | 0.588397i | \(-0.799759\pi\) |
0.913853 | + | 0.406046i | \(0.133093\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.1912 | − | 21.1158i | −0.411200 | − | 0.712219i | ||||
\(880\) | −31.5106 | + | 54.5779i | −1.06222 | + | 1.83982i | ||||
\(881\) | −42.2755 | −1.42430 | −0.712148 | − | 0.702029i | \(-0.752278\pi\) | ||||
−0.712148 | + | 0.702029i | \(0.752278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.9723 | 0.470204 | 0.235102 | − | 0.971971i | \(-0.424458\pi\) | ||||
0.235102 | + | 0.971971i | \(0.424458\pi\) | |||||||
\(884\) | 4.13520 | − | 7.16238i | 0.139082 | − | 0.240897i | ||||
\(885\) | 10.3824 | + | 17.9829i | 0.349002 | + | 0.604490i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0328 | − | 26.0375i | 0.504751 | − | 0.874255i | −0.495234 | − | 0.868760i | \(-0.664918\pi\) |
0.999985 | − | 0.00549503i | \(-0.00174913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.79365 | + | 1.24964i | 0.194313 | + | 0.0419114i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.08628 | + | 5.34559i | −0.103394 | + | 0.179084i | ||||
\(892\) | 15.9652 | + | 27.6525i | 0.534554 | + | 0.925874i | ||||
\(893\) | −1.85897 | − | 3.21982i | −0.0622079 | − | 0.107747i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.1210 | −0.806277 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.14230 | −0.0381402 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.7179 | − | 34.1525i | −0.657630 | − | 1.13905i | ||||
\(900\) | 1.51513 | + | 2.62428i | 0.0505042 | + | 0.0874759i | ||||
\(901\) | −4.13520 | + | 7.16238i | −0.137764 | + | 0.238614i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.60266 | + | 26.7488i | 0.286279 | + | 0.890143i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0792 | + | 17.4577i | −0.335043 | + | 0.580312i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.0048 | − | 25.9891i | −0.498227 | − | 0.862954i | 0.501771 | − | 0.865000i | \(-0.332682\pi\) |
−0.999998 | + | 0.00204662i | \(0.999349\pi\) | |||||||
\(908\) | −8.13520 | + | 14.0906i | −0.269976 | + | 0.467612i | ||||
\(909\) | −12.2099 | −0.404977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4056 | 0.477279 | 0.238640 | − | 0.971108i | \(-0.423299\pi\) | ||||
0.238640 | + | 0.971108i | \(0.423299\pi\) | |||||||
\(912\) | −0.895051 | + | 1.55027i | −0.0296381 | + | 0.0513347i | ||||
\(913\) | 42.9851 | + | 74.4524i | 1.42260 | + | 2.46401i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.89758 | − | 17.1431i | 0.327204 | − | 0.566734i | ||||
\(916\) | 0.354241 | 0.0117044 | ||||||||
\(917\) | −29.4011 | + | 32.4571i | −0.970911 | + | 1.07183i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.18894 | + | 3.79135i | −0.0722065 | + | 0.125065i | −0.899868 | − | 0.436162i | \(-0.856337\pi\) |
0.827662 | + | 0.561227i | \(0.189671\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.60495 | − | 16.6363i | −0.316494 | − | 0.548183i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.41475 | −0.145313 | ||||||||
\(924\) | −31.9278 | − | 6.88654i | −1.05035 | − | 0.226550i | ||||
\(925\) | −1.51513 | −0.0498171 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.05247 | + | 7.01909i | 0.133101 | + | 0.230537i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.79720 | + | 4.84489i | −0.0917730 | + | 0.158956i | −0.908257 | − | 0.418412i | \(-0.862587\pi\) |
0.816484 | + | 0.577368i | \(0.195920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.54538 | − | 1.82612i | 0.0834215 | − | 0.0598486i | ||||
\(932\) | 32.3451 | 1.05950 | ||||||||
\(933\) | −15.4990 | + | 26.8450i | −0.507414 | + | 0.878866i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.7553 | + | 27.2889i | 0.515253 | + | 0.892444i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0328 | −1.11180 | −0.555901 | − | 0.831248i | \(-0.687627\pi\) | ||||
−0.555901 | + | 0.831248i | \(0.687627\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.3380 | 0.533171 | ||||||||
\(940\) | −21.2053 | + | 36.7287i | −0.691642 | + | 1.19796i | ||||
\(941\) | 1.09785 | + | 1.90154i | 0.0357890 | + | 0.0619884i | 0.883365 | − | 0.468685i | \(-0.155272\pi\) |
−0.847576 | + | 0.530674i | \(0.821939\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.276237 | + | 0.478457i | −0.00899552 | + | 0.0155807i | ||||
\(944\) | 32.5408 | 1.05911 | ||||||||
\(945\) | −4.53380 | + | 5.00505i | −0.147485 | + | 0.162814i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.07343 | + | 7.05539i | −0.132369 | + | 0.229269i | −0.924589 | − | 0.380966i | \(-0.875592\pi\) |
0.792220 | + | 0.610235i | \(0.208925\pi\) | |||||||
\(948\) | −16.7926 | − | 29.0857i | −0.545399 | − | 0.944659i | ||||
\(949\) | −10.9790 | − | 19.0163i | −0.356395 | − | 0.617294i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.5479 | 0.763593 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.5156 | −0.696959 | −0.348479 | − | 0.937316i | \(-0.613302\pi\) | ||||
−0.348479 | + | 0.937316i | \(0.613302\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.64001 | − | 11.5008i | −0.214866 | − | 0.372158i | ||||
\(956\) | 25.4501 | + | 44.0808i | 0.823113 | + | 1.42567i | ||||
\(957\) | −15.7553 | + | 27.2889i | −0.509296 | + | 0.882126i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.109519 | − | 0.340534i | −0.00353656 | − | 0.0109964i | ||||
\(960\) | 20.4198 | 0.659046 | ||||||||
\(961\) | −14.3380 | + | 24.8342i | −0.462516 | + | 0.801102i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.27624 | − | 2.21051i | −0.0411262 | − | 0.0712326i | ||||
\(964\) | −13.6201 | + | 23.5907i | −0.438673 | + | 0.759804i | ||||
\(965\) | 33.9677 | 1.09346 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.8371 | 1.66697 | 0.833484 | − | 0.552544i | \(-0.186343\pi\) | ||||
0.833484 | + | 0.552544i | \(0.186343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.447525 | + | 0.775137i | 0.0143766 | + | 0.0249010i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.93240 | + | 5.07906i | −0.0941052 | + | 0.162995i | −0.909235 | − | 0.416284i | \(-0.863332\pi\) |
0.815130 | + | 0.579279i | \(0.196666\pi\) | |||||||
\(972\) | 2.00000 | 0.0641500 | ||||||||
\(973\) | 21.6610 | + | 4.67207i | 0.694419 | + | 0.149780i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.56634 | + | 2.71298i | −0.0501630 | + | 0.0868848i | ||||
\(976\) | −15.5106 | − | 26.8651i | −0.496481 | − | 0.859930i | ||||
\(977\) | −30.6902 | − | 53.1570i | −0.981867 | − | 1.70064i | −0.655109 | − | 0.755535i | \(-0.727377\pi\) |
−0.326758 | − | 0.945108i | \(-0.605956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75.9702 | 2.42802 | ||||||||
\(980\) | −32.5575 | − | 14.7300i | −1.04001 | − | 0.470532i | ||||
\(981\) | 4.58273 | 0.146315 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.34841 | − | 4.06756i | −0.0749026 | − | 0.129735i | 0.826141 | − | 0.563463i | \(-0.190531\pi\) |
−0.901044 | + | 0.433728i | \(0.857198\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.9001 | + | 43.1282i | −0.793383 | + | 1.37418i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.4861 | − | 4.63436i | −0.683911 | − | 0.147513i | ||||
\(988\) | −1.85061 | −0.0588757 | ||||||||
\(989\) | −2.93366 | + | 5.08125i | −0.0932850 | + | 0.161574i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.82643 | − | 6.62757i | −0.121550 | − | 0.210532i | 0.798829 | − | 0.601558i | \(-0.205453\pi\) |
−0.920379 | + | 0.391027i | \(0.872120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.9278 | 0.791061 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.45005 | 0.172778 | ||||||||
\(996\) | 13.9278 | − | 24.1237i | 0.441320 | − | 0.764389i | ||||
\(997\) | −16.0164 | − | 27.7412i | −0.507244 | − | 0.878573i | −0.999965 | − | 0.00838510i | \(-0.997331\pi\) |
0.492721 | − | 0.870188i | \(-0.336002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.500000 | + | 0.866025i | −0.0158193 | + | 0.0273998i |
(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 | 861.2.i.c.247.1 | ✓ | 6 | |
7.2 | even | 3 | 6027.2.a.p.1.3 | 3 | |||
7.4 | even | 3 | inner | 861.2.i.c.739.1 | yes | 6 | |
7.5 | odd | 6 | 6027.2.a.q.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.c.247.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
861.2.i.c.739.1 | yes | 6 | 7.4 | even | 3 | inner | |
6027.2.a.p.1.3 | 3 | 7.2 | even | 3 | |||
6027.2.a.q.1.1 | 3 | 7.5 | odd | 6 |