Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 30 x^{10} - 53 x^{9} + 798 x^{8} - 1096 x^{7} + 4060 x^{6} - 915 x^{5} + 10392 x^{4} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.6 | ||
Root | \(2.33000 - 4.03568i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.841 |
Dual form | 4020.2.q.j.3781.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37984 | − | 4.12200i | 0.899495 | − | 1.55797i | 0.0713530 | − | 0.997451i | \(-0.477268\pi\) |
0.828142 | − | 0.560519i | \(-0.189398\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.09011 | − | 3.62018i | 0.630193 | − | 1.09153i | −0.357319 | − | 0.933982i | \(-0.616309\pi\) |
0.987512 | − | 0.157544i | \(-0.0503576\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.68241 | − | 2.91403i | −0.408045 | − | 0.706755i | 0.586625 | − | 0.809858i | \(-0.300456\pi\) |
−0.994671 | + | 0.103103i | \(0.967123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.14970 | + | 3.72339i | 0.493175 | + | 0.854205i | 0.999969 | − | 0.00786249i | \(-0.00250273\pi\) |
−0.506794 | + | 0.862067i | \(0.669169\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.37984 | − | 4.12200i | 0.519323 | − | 0.899495i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.737700 | − | 1.27773i | −0.153821 | − | 0.266426i | 0.778808 | − | 0.627262i | \(-0.215825\pi\) |
−0.932629 | + | 0.360836i | \(0.882491\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.87246 | − | 4.97524i | 0.533402 | − | 0.923880i | −0.465837 | − | 0.884871i | \(-0.654247\pi\) |
0.999239 | − | 0.0390090i | \(-0.0124201\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.32025 | − | 2.28674i | 0.237124 | − | 0.410711i | −0.722764 | − | 0.691095i | \(-0.757129\pi\) |
0.959888 | + | 0.280384i | \(0.0904619\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.09011 | − | 3.62018i | 0.363842 | − | 0.630193i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.37984 | + | 4.12200i | −0.402266 | + | 0.696745i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.02524 | + | 8.70397i | 0.826144 | + | 1.43092i | 0.901042 | + | 0.433732i | \(0.142804\pi\) |
−0.0748976 | + | 0.997191i | \(0.523863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0825512 | + | 0.142983i | −0.0128923 | + | 0.0223302i | −0.872400 | − | 0.488793i | \(-0.837437\pi\) |
0.859507 | + | 0.511124i | \(0.170771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.29940 | −1.11315 | −0.556574 | − | 0.830798i | \(-0.687885\pi\) | ||||
−0.556574 | + | 0.830798i | \(0.687885\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.73280 | − | 4.73335i | 0.398620 | − | 0.690430i | −0.594936 | − | 0.803773i | \(-0.702823\pi\) |
0.993556 | + | 0.113343i | \(0.0361559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.82727 | − | 13.5572i | −1.11818 | − | 1.93675i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.68241 | − | 2.91403i | −0.235585 | − | 0.408045i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.64050 | 0.225340 | 0.112670 | − | 0.993632i | \(-0.464060\pi\) | ||||
0.112670 | + | 0.993632i | \(0.464060\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.09011 | + | 3.62018i | −0.281831 | + | 0.488145i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.14970 | + | 3.72339i | 0.284735 | + | 0.493175i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.85112 | −1.15232 | −0.576159 | − | 0.817338i | \(-0.695449\pi\) | ||||
−0.576159 | + | 0.817338i | \(0.695449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.86271 | + | 6.69041i | 0.494569 | + | 0.856619i | 0.999980 | − | 0.00625940i | \(-0.00199244\pi\) |
−0.505411 | + | 0.862879i | \(0.668659\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.37984 | − | 4.12200i | 0.299832 | − | 0.519323i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.500000 | − | 0.866025i | −0.0620174 | − | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.11483 | + | 7.56954i | 0.380537 | + | 0.924766i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.737700 | − | 1.27773i | −0.0888086 | − | 0.153821i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.87027 | − | 11.8997i | 0.815351 | − | 1.41223i | −0.0937239 | − | 0.995598i | \(-0.529877\pi\) |
0.909075 | − | 0.416632i | \(-0.136790\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.88057 | − | 11.9175i | −0.805310 | − | 1.39484i | −0.916082 | − | 0.400992i | \(-0.868666\pi\) |
0.110772 | − | 0.993846i | \(-0.464668\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.94827 | − | 17.2309i | −1.13371 | − | 1.96364i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.08037 | + | 3.60330i | −0.234059 | + | 0.405403i | −0.958999 | − | 0.283410i | \(-0.908534\pi\) |
0.724940 | + | 0.688813i | \(0.241868\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.24720 | + | 12.5525i | 0.795483 | + | 1.37782i | 0.922532 | + | 0.385921i | \(0.126116\pi\) |
−0.127049 | + | 0.991896i | \(0.540551\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.68241 | + | 2.91403i | 0.182483 | + | 0.316070i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.87246 | − | 4.97524i | 0.307960 | − | 0.533402i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.17586 | −0.972639 | −0.486319 | − | 0.873781i | \(-0.661661\pi\) | ||||
−0.486319 | + | 0.873781i | \(0.661661\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.75968 | 0.498950 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.32025 | − | 2.28674i | 0.136904 | − | 0.237124i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.14970 | − | 3.72339i | −0.220555 | − | 0.382012i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.67804 | − | 13.2988i | −0.779587 | − | 1.35028i | −0.932180 | − | 0.361995i | \(-0.882096\pi\) |
0.152593 | − | 0.988289i | \(-0.451238\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.09011 | − | 3.62018i | 0.210064 | − | 0.363842i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.495102 | − | 0.857541i | 0.0492644 | − | 0.0853285i | −0.840342 | − | 0.542057i | \(-0.817646\pi\) |
0.889606 | + | 0.456729i | \(0.150979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.62783 | + | 14.9438i | −0.850126 | + | 1.47246i | 0.0309685 | + | 0.999520i | \(0.490141\pi\) |
−0.881094 | + | 0.472941i | \(0.843192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.37984 | + | 4.12200i | −0.232248 | + | 0.402266i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0259 | 1.16259 | 0.581295 | − | 0.813693i | \(-0.302546\pi\) | ||||
0.581295 | + | 0.813693i | \(0.302546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3958 | −1.66622 | −0.833108 | − | 0.553110i | \(-0.813441\pi\) | ||||
−0.833108 | + | 0.553110i | \(0.813441\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.02524 | + | 8.70397i | 0.476975 | + | 0.826144i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.32025 | − | 4.01879i | 0.218271 | − | 0.378056i | −0.736009 | − | 0.676972i | \(-0.763292\pi\) |
0.954279 | + | 0.298916i | \(0.0966251\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.737700 | + | 1.27773i | 0.0687908 | + | 0.119149i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.0155 | −1.46814 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.23715 | − | 5.60691i | −0.294287 | − | 0.509719i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0825512 | + | 0.142983i | −0.00744339 | + | 0.0128923i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.04294 | + | 12.1987i | −0.624960 | + | 1.08246i | 0.363589 | + | 0.931559i | \(0.381551\pi\) |
−0.988549 | + | 0.150902i | \(0.951782\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.29940 | −0.642677 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.52373 | 0.482610 | 0.241305 | − | 0.970449i | \(-0.422425\pi\) | ||||
0.241305 | + | 0.970449i | \(0.422425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.4638 | 1.77443 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.8550 | 1.52545 | 0.762727 | − | 0.646720i | \(-0.223860\pi\) | ||||
0.762727 | + | 0.646720i | \(0.223860\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2254 | −1.12177 | −0.560883 | − | 0.827895i | \(-0.689538\pi\) | ||||
−0.560883 | + | 0.827895i | \(0.689538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.73280 | − | 4.73335i | 0.230143 | − | 0.398620i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.18023 | 0.349568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.87246 | + | 4.97524i | −0.238545 | + | 0.413172i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.82727 | − | 13.5572i | −0.645582 | − | 1.11818i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.55580 | 0.700919 | 0.350459 | − | 0.936578i | \(-0.386025\pi\) | ||||
0.350459 | + | 0.936578i | \(0.386025\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3253 | − | 17.8839i | −0.840258 | − | 1.45537i | −0.889677 | − | 0.456591i | \(-0.849070\pi\) |
0.0494190 | − | 0.998778i | \(-0.484263\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.68241 | − | 2.91403i | −0.136015 | − | 0.235585i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.32025 | + | 2.28674i | −0.106045 | + | 0.183675i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.92713 | − | 10.2661i | −0.473036 | − | 0.819323i | 0.526487 | − | 0.850183i | \(-0.323509\pi\) |
−0.999524 | + | 0.0308600i | \(0.990175\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.64050 | 0.130100 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.02242 | −0.553445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.41720 | + | 11.1149i | −0.502634 | + | 0.870587i | 0.497362 | + | 0.867543i | \(0.334302\pi\) |
−0.999995 | + | 0.00304373i | \(0.999031\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.09011 | + | 3.62018i | −0.162715 | + | 0.281831i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.50686 | + | 2.60995i | −0.116604 | + | 0.201964i | −0.918420 | − | 0.395607i | \(-0.870534\pi\) |
0.801816 | + | 0.597571i | \(0.203867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.14970 | + | 3.72339i | 0.164392 | + | 0.284735i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.85464 | − | 15.3367i | −0.673206 | − | 1.16603i | −0.976990 | − | 0.213286i | \(-0.931583\pi\) |
0.303784 | − | 0.952741i | \(-0.401750\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.37984 | − | 4.12200i | 0.179899 | − | 0.311594i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.85112 | −0.665291 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.57826 | 0.342195 | 0.171097 | − | 0.985254i | \(-0.445269\pi\) | ||||
0.171097 | + | 0.985254i | \(0.445269\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.07453 | + | 5.32524i | −0.228528 | + | 0.395822i | −0.957372 | − | 0.288858i | \(-0.906725\pi\) |
0.728844 | + | 0.684680i | \(0.240058\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.86271 | + | 6.69041i | 0.285540 | + | 0.494569i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.02524 | − | 8.70397i | −0.369463 | − | 0.639929i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.0657 | −1.02859 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.37984 | − | 4.12200i | 0.173108 | − | 0.299832i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.02453 | − | 1.77454i | −0.0741325 | − | 0.128401i | 0.826576 | − | 0.562825i | \(-0.190285\pi\) |
−0.900709 | + | 0.434424i | \(0.856952\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.4218 | 1.68594 | 0.842970 | − | 0.537961i | \(-0.180805\pi\) | ||||
0.842970 | + | 0.537961i | \(0.180805\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.500000 | − | 0.866025i | −0.0358057 | − | 0.0620174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.38680 | − | 16.2584i | 0.668782 | − | 1.15836i | −0.309463 | − | 0.950912i | \(-0.600149\pi\) |
0.978245 | − | 0.207453i | \(-0.0665174\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.28243 | + | 10.8815i | 0.445350 | + | 0.771369i | 0.998077 | − | 0.0619939i | \(-0.0197459\pi\) |
−0.552727 | + | 0.833363i | \(0.686413\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.11483 | + | 7.56954i | 0.219703 | + | 0.533914i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.6720 | − | 23.6806i | −0.959585 | − | 1.66205i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0825512 | − | 0.142983i | 0.00576563 | − | 0.00998636i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.737700 | − | 1.27773i | −0.0512737 | − | 0.0888086i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.9725 | 1.24318 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.05487 | − | 7.02324i | −0.279149 | − | 0.483500i | 0.692025 | − | 0.721874i | \(-0.256719\pi\) |
−0.971173 | + | 0.238374i | \(0.923386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.87027 | − | 11.8997i | 0.470743 | − | 0.815351i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.29940 | 0.497815 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.28397 | − | 10.8842i | −0.426584 | − | 0.738864i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.88057 | − | 11.9175i | −0.464946 | − | 0.805310i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.68241 | − | 2.91403i | 0.113171 | − | 0.196019i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.57513 | 0.105478 | 0.0527391 | − | 0.998608i | \(-0.483205\pi\) | ||||
0.0527391 | + | 0.998608i | \(0.483205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2481 | − | 22.9463i | 0.879305 | − | 1.52300i | 0.0271993 | − | 0.999630i | \(-0.491341\pi\) |
0.852105 | − | 0.523370i | \(-0.175326\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1723 | + | 21.0830i | 0.804368 | + | 1.39321i | 0.916717 | + | 0.399538i | \(0.130829\pi\) |
−0.112349 | + | 0.993669i | \(0.535837\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.94827 | − | 17.2309i | −0.654548 | − | 1.13371i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.45772 | + | 5.98895i | −0.226523 | + | 0.392349i | −0.956775 | − | 0.290828i | \(-0.906069\pi\) |
0.730252 | + | 0.683178i | \(0.239402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.73280 | + | 4.73335i | −0.178268 | + | 0.308770i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.08037 | + | 3.60330i | −0.135134 | + | 0.234059i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.25531 | + | 7.37041i | −0.275253 | + | 0.476752i | −0.970199 | − | 0.242310i | \(-0.922095\pi\) |
0.694946 | + | 0.719062i | \(0.255428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8854 | 0.894436 | 0.447218 | − | 0.894425i | \(-0.352415\pi\) | ||||
0.447218 | + | 0.894425i | \(0.352415\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.82727 | + | 13.5572i | 0.500066 | + | 0.866139i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.14970 | + | 3.72339i | −0.136782 | + | 0.236914i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.24720 | + | 12.5525i | 0.459272 | + | 0.795483i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00722 | + | 1.74456i | 0.0635752 | + | 0.110115i | 0.896061 | − | 0.443931i | \(-0.146416\pi\) |
−0.832486 | + | 0.554046i | \(0.813083\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.16750 | −0.387748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.68241 | + | 2.91403i | 0.105357 | + | 0.182483i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.98982 | − | 13.8388i | 0.498391 | − | 0.863239i | −0.501607 | − | 0.865095i | \(-0.667258\pi\) |
0.999998 | + | 0.00185682i | \(0.000591045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 47.8370 | 2.97245 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.87246 | − | 4.97524i | 0.177801 | − | 0.307960i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.5143 | 1.38829 | 0.694144 | − | 0.719836i | \(-0.255783\pi\) | ||||
0.694144 | + | 0.719836i | \(0.255783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.64050 | −0.100775 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.17586 | −0.561553 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.8898 | −1.39562 | −0.697808 | − | 0.716285i | \(-0.745841\pi\) | ||||
−0.697808 | + | 0.716285i | \(0.745841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4504 | 0.999293 | 0.499646 | − | 0.866229i | \(-0.333463\pi\) | ||||
0.499646 | + | 0.866229i | \(0.333463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.75968 | 0.288069 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.09011 | − | 3.62018i | 0.126039 | − | 0.218305i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2683 | −0.857298 | −0.428649 | − | 0.903471i | \(-0.641010\pi\) | ||||
−0.428649 | + | 0.903471i | \(0.641010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.32025 | − | 2.28674i | 0.0790413 | − | 0.136904i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.96740 | − | 10.3358i | −0.355985 | − | 0.616584i | 0.631301 | − | 0.775538i | \(-0.282521\pi\) |
−0.987286 | + | 0.158954i | \(0.949188\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.1591 | 1.43611 | 0.718055 | − | 0.695986i | \(-0.245032\pi\) | ||||
0.718055 | + | 0.695986i | \(0.245032\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.14970 | − | 3.72339i | −0.127337 | − | 0.220555i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.392917 | + | 0.680553i | 0.0231932 | + | 0.0401718i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.83897 | − | 4.91724i | 0.166998 | − | 0.289249i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.67804 | − | 13.2988i | −0.450095 | − | 0.779587i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.6256 | −1.49706 | −0.748530 | − | 0.663100i | \(-0.769240\pi\) | ||||
−0.748530 | + | 0.663100i | \(0.769240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.85112 | 0.515332 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.09011 | − | 3.62018i | 0.121281 | − | 0.210064i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.737700 | − | 1.27773i | 0.0426623 | − | 0.0738932i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.3714 | + | 30.0882i | −1.00127 | + | 1.73425i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.495102 | − | 0.857541i | 0.0284428 | − | 0.0492644i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.86271 | − | 6.69041i | −0.221178 | − | 0.383092i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.79669 | − | 6.57606i | −0.216689 | − | 0.375316i | 0.737105 | − | 0.675778i | \(-0.236192\pi\) |
−0.953794 | + | 0.300463i | \(0.902859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.62783 | + | 14.9438i | −0.490820 | + | 0.850126i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.1269 | −1.70834 | −0.854169 | − | 0.519995i | \(-0.825934\pi\) | ||||
−0.854169 | + | 0.519995i | \(0.825934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.75311 | 0.551279 | 0.275639 | − | 0.961261i | \(-0.411110\pi\) | ||||
0.275639 | + | 0.961261i | \(0.411110\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.37984 | + | 4.12200i | −0.134089 | + | 0.232248i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.81690 | + | 15.2713i | 0.495206 | + | 0.857722i | 0.999985 | − | 0.00552649i | \(-0.00175914\pi\) |
−0.504778 | + | 0.863249i | \(0.668426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0075 | − | 20.7977i | −0.672293 | − | 1.16445i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0259 | 0.671221 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.23337 | − | 12.5286i | 0.402476 | − | 0.697108i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.3958 | −0.961990 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.0073 | − | 22.5292i | −0.717113 | − | 1.24208i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.03476 | − | 5.25636i | 0.166805 | − | 0.288915i | −0.770490 | − | 0.637453i | \(-0.779988\pi\) |
0.937295 | + | 0.348537i | \(0.113322\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.02524 | + | 8.70397i | 0.275381 | + | 0.476975i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.11483 | − | 7.56954i | −0.170181 | − | 0.413568i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.20173 | + | 12.4738i | 0.392303 | + | 0.679489i | 0.992753 | − | 0.120174i | \(-0.0383451\pi\) |
−0.600450 | + | 0.799662i | \(0.705012\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.32025 | − | 4.01879i | 0.126019 | − | 0.218271i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.51895 | − | 9.55910i | −0.298868 | − | 0.517654i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −41.1928 | −2.22420 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.737700 | + | 1.27773i | 0.0397164 | + | 0.0687908i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.30032 | + | 14.3766i | −0.445584 | + | 0.771775i | −0.998093 | − | 0.0617326i | \(-0.980337\pi\) |
0.552508 | + | 0.833507i | \(0.313671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.7268 | 1.27007 | 0.635034 | − | 0.772484i | \(-0.280986\pi\) | ||||
0.635034 | + | 0.772484i | \(0.280986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.500000 | + | 0.866025i | 0.0266880 | + | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.7981 | + | 30.8272i | 0.947296 | + | 1.64077i | 0.751087 | + | 0.660203i | \(0.229530\pi\) |
0.196210 | + | 0.980562i | \(0.437137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.87027 | + | 11.8997i | −0.364636 | + | 0.631568i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.0155 | −0.847630 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.8601 | −0.837063 | −0.418532 | − | 0.908202i | \(-0.637455\pi\) | ||||
−0.418532 | + | 0.908202i | \(0.637455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.257564 | − | 0.446113i | 0.0135560 | − | 0.0234797i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.23715 | − | 5.60691i | −0.169906 | − | 0.294287i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.88057 | + | 11.9175i | 0.360145 | + | 0.623790i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.83216 | − | 6.63750i | 0.200037 | − | 0.346475i | −0.748503 | − | 0.663131i | \(-0.769227\pi\) |
0.948540 | + | 0.316657i | \(0.102560\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0825512 | + | 0.142983i | −0.00429745 | + | 0.00744339i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.90413 | − | 6.76215i | 0.202692 | − | 0.351073i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.53394 | + | 2.65685i | −0.0794242 | + | 0.137567i | −0.903002 | − | 0.429637i | \(-0.858641\pi\) |
0.823577 | + | 0.567204i | \(0.191975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.74492 | 0.295878 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.73354 | − | 13.3949i | −0.397245 | − | 0.688049i | 0.596140 | − | 0.802881i | \(-0.296701\pi\) |
−0.993385 | + | 0.114832i | \(0.963367\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.04294 | + | 12.1987i | −0.360821 | + | 0.624960i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.0084 | + | 19.0671i | 0.562502 | + | 0.974282i | 0.997277 | + | 0.0737432i | \(0.0234945\pi\) |
−0.434775 | + | 0.900539i | \(0.643172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.94827 | + | 17.2309i | 0.507011 | + | 0.878168i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.29940 | −0.371050 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.582458 | − | 1.00885i | −0.0295318 | − | 0.0511506i | 0.850882 | − | 0.525357i | \(-0.176068\pi\) |
−0.880414 | + | 0.474207i | \(0.842735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.48223 | + | 4.29935i | −0.125532 | + | 0.217427i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.52373 | 0.278635 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.08037 | − | 3.60330i | 0.104675 | − | 0.181302i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.7246 | 1.49183 | 0.745916 | − | 0.666040i | \(-0.232012\pi\) | ||||
0.745916 | + | 0.666040i | \(0.232012\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.4638 | 1.02447 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.7299 | 1.23495 | 0.617476 | − | 0.786590i | \(-0.288155\pi\) | ||||
0.617476 | + | 0.786590i | \(0.288155\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.64050 | 0.131533 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.0133 | 2.08252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.02136 | − | 13.8934i | 0.396631 | − | 0.686985i | −0.596677 | − | 0.802481i | \(-0.703513\pi\) |
0.993308 | + | 0.115497i | \(0.0368460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.8550 | 0.880721 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.0642 | + | 36.4843i | −1.03650 | + | 1.79528i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.24720 | − | 12.5525i | −0.355751 | − | 0.616179i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.2254 | −0.647652 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.83738 | − | 13.5747i | −0.382881 | − | 0.663169i | 0.608592 | − | 0.793483i | \(-0.291735\pi\) |
−0.991473 | + | 0.130314i | \(0.958401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.19572 | + | 8.99925i | 0.253224 | + | 0.438596i | 0.964412 | − | 0.264406i | \(-0.0851758\pi\) |
−0.711188 | + | 0.703002i | \(0.751842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.73280 | − | 4.73335i | 0.132873 | − | 0.230143i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.68241 | − | 2.91403i | −0.0816090 | − | 0.141351i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.7705 | 1.77945 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.18023 | 0.201823 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.8276 | + | 23.9500i | −0.666050 | + | 1.15363i | 0.312949 | + | 0.949770i | \(0.398683\pi\) |
−0.978999 | + | 0.203863i | \(0.934650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.7804 | + | 32.5286i | −0.902528 | + | 1.56322i | −0.0783256 | + | 0.996928i | \(0.524957\pi\) |
−0.824202 | + | 0.566296i | \(0.808376\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.87246 | + | 4.97524i | −0.137724 | + | 0.238545i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.17167 | − | 5.49349i | 0.151721 | − | 0.262789i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0704578 | − | 0.122037i | −0.00336277 | − | 0.00582449i | 0.864339 | − | 0.502909i | \(-0.167737\pi\) |
−0.867702 | + | 0.497085i | \(0.834404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.82727 | − | 13.5572i | −0.372727 | − | 0.645582i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.6504 | − | 18.4471i | 0.506016 | − | 0.876446i | −0.493959 | − | 0.869485i | \(-0.664451\pi\) |
0.999976 | − | 0.00696104i | \(-0.00221579\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.17586 | 0.434977 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.55580 | 0.404676 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.1422 | + | 22.7629i | −0.620217 | + | 1.07425i | 0.369228 | + | 0.929339i | \(0.379622\pi\) |
−0.989445 | + | 0.144908i | \(0.953711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.345083 | + | 0.597701i | 0.0162493 | + | 0.0281447i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.3253 | − | 17.8839i | −0.485123 | − | 0.840258i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.75968 | −0.223137 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.9722 | + | 27.6646i | −0.747146 | + | 1.29409i | 0.202039 | + | 0.979377i | \(0.435243\pi\) |
−0.949185 | + | 0.314718i | \(0.898090\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.68241 | − | 2.91403i | −0.0785283 | − | 0.136015i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.9942 | −0.791497 | −0.395749 | − | 0.918359i | \(-0.629515\pi\) | ||||
−0.395749 | + | 0.918359i | \(0.629515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.34997 | + | 10.9985i | 0.295108 | + | 0.511143i | 0.975010 | − | 0.222161i | \(-0.0713109\pi\) |
−0.679902 | + | 0.733303i | \(0.737978\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.32025 | + | 2.28674i | −0.0612252 | + | 0.106045i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.1079 | − | 19.2395i | −0.514013 | − | 0.890297i | −0.999868 | − | 0.0162576i | \(-0.994825\pi\) |
0.485854 | − | 0.874040i | \(-0.338509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.6144 | + | 5.17496i | 1.78305 | + | 0.238957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.92713 | − | 10.2661i | −0.273108 | − | 0.473036i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.2566 | + | 26.4252i | −0.701499 | + | 1.21503i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.14970 | + | 3.72339i | 0.0986351 | + | 0.170841i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.64050 | 0.0751134 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.32237 | − | 4.02246i | −0.106112 | − | 0.183791i | 0.808080 | − | 0.589072i | \(-0.200507\pi\) |
−0.914192 | + | 0.405282i | \(0.867173\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.02524 | + | 8.70397i | −0.229131 | + | 0.396867i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.02242 | −0.319531 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.67804 | + | 13.2988i | 0.348642 | + | 0.603866i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.12363 | − | 5.41028i | −0.141545 | − | 0.245163i | 0.786534 | − | 0.617547i | \(-0.211874\pi\) |
−0.928079 | + | 0.372384i | \(0.878540\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.41720 | + | 11.1149i | −0.290196 | + | 0.502634i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.5224 | −1.42258 | −0.711292 | − | 0.702897i | \(-0.751890\pi\) | ||||
−0.711292 | + | 0.702897i | \(0.751890\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.3307 | −0.870609 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.09011 | + | 3.62018i | −0.0939436 | + | 0.162715i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.7003 | − | 56.6386i | −1.46681 | − | 2.54059i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.3739 | + | 23.1643i | 0.598700 | + | 1.03698i | 0.993013 | + | 0.118002i | \(0.0376490\pi\) |
−0.394314 | + | 0.918976i | \(0.629018\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.50686 | + | 2.60995i | −0.0673213 | + | 0.116604i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.2605 | + | 28.1640i | −0.725021 | + | 1.25577i | 0.233945 | + | 0.972250i | \(0.424837\pi\) |
−0.958965 | + | 0.283523i | \(0.908497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.495102 | + | 0.857541i | −0.0220317 | + | 0.0381601i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5835 | 0.735053 | 0.367526 | − | 0.930013i | \(-0.380205\pi\) | ||||
0.367526 | + | 0.930013i | \(0.380205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −65.4986 | −2.89749 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.14970 | + | 3.72339i | 0.0949117 | + | 0.164392i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.62783 | − | 14.9438i | 0.380188 | − | 0.658505i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.4237 | − | 19.7865i | −0.502415 | − | 0.870208i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.85464 | − | 15.3367i | −0.388676 | − | 0.673206i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.5696 | −0.944980 | −0.472490 | − | 0.881336i | \(-0.656645\pi\) | ||||
−0.472490 | + | 0.881336i | \(0.656645\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.42836 | + | 16.3304i | 0.412273 | + | 0.714078i | 0.995138 | − | 0.0984910i | \(-0.0314016\pi\) |
−0.582865 | + | 0.812569i | \(0.698068\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.37984 | − | 4.12200i | 0.103865 | − | 0.179899i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.88483 | −0.387029 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.4116 | − | 18.0334i | 0.452678 | − | 0.784062i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.85112 | −0.384106 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.165102 | −0.00715138 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0259 | −0.519926 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.57826 | 0.197566 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −65.4395 | −2.81868 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0366 | 1.46335 | 0.731675 | − | 0.681654i | \(-0.238739\pi\) | ||||
0.731675 | + | 0.681654i | \(0.238739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.07453 | + | 5.32524i | −0.131941 | + | 0.228528i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.3958 | 0.745155 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.82050 | + | 6.61731i | −0.163353 | + | 0.282936i | −0.936069 | − | 0.351816i | \(-0.885564\pi\) |
0.772716 | + | 0.634752i | \(0.218898\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.86271 | + | 6.69041i | 0.164856 | + | 0.285540i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.6997 | 1.05224 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.90187 | + | 17.1505i | 0.421070 | + | 0.729315i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.02524 | − | 8.70397i | −0.213310 | − | 0.369463i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.3554 | + | 38.7206i | −0.947227 | + | 1.64064i | −0.195996 | + | 0.980605i | \(0.562794\pi\) |
−0.751230 | + | 0.660040i | \(0.770539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.64970 | − | 6.32147i | −0.154366 | − | 0.267370i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.0657 | −0.593856 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.5230 | 0.696359 | 0.348180 | − | 0.937428i | \(-0.386800\pi\) | ||||
0.348180 | + | 0.937428i | \(0.386800\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.32025 | + | 4.01879i | −0.0976137 | + | 0.169072i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.37984 | − | 4.12200i | 0.0999438 | − | 0.173108i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.995243 | − | 1.72381i | 0.0417228 | − | 0.0722659i | −0.844410 | − | 0.535698i | \(-0.820049\pi\) |
0.886133 | + | 0.463432i | \(0.153382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.49896 | − | 12.9886i | 0.313822 | − | 0.543555i | −0.665365 | − | 0.746519i | \(-0.731724\pi\) |
0.979186 | + | 0.202963i | \(0.0650573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.02453 | − | 1.77454i | −0.0428004 | − | 0.0741325i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.737700 | − | 1.27773i | −0.0307642 | − | 0.0532852i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.99157 | + | 17.3059i | −0.415954 | + | 0.720454i | −0.995528 | − | 0.0944658i | \(-0.969886\pi\) |
0.579574 | + | 0.814920i | \(0.303219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.4218 | 0.973378 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 68.9886 | 2.86213 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.42883 | − | 5.93892i | 0.142008 | − | 0.245965i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | − | 0.866025i | −0.0206725 | − | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.973887 | − | 1.68682i | −0.0401966 | − | 0.0696226i | 0.845227 | − | 0.534407i | \(-0.179465\pi\) |
−0.885424 | + | 0.464785i | \(0.846132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3526 | 0.467775 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.38680 | − | 16.2584i | 0.386122 | − | 0.668782i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.11496 | + | 7.12732i | 0.168981 | + | 0.292684i | 0.938062 | − | 0.346468i | \(-0.112619\pi\) |
−0.769081 | + | 0.639152i | \(0.779286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0155 | 0.656571 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.28243 | + | 10.8815i | 0.257123 | + | 0.445350i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.01255 | − | 12.1461i | 0.286525 | − | 0.496276i | −0.686453 | − | 0.727174i | \(-0.740833\pi\) |
0.972978 | + | 0.230899i | \(0.0741666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0927989 | + | 0.160732i | 0.00378534 | + | 0.00655641i | 0.867912 | − | 0.496718i | \(-0.165462\pi\) |
−0.864127 | + | 0.503275i | \(0.832128\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.11483 | + | 7.56954i | 0.126846 | + | 0.308255i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.23715 | + | 5.60691i | 0.131609 | + | 0.227953i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.63638 | + | 6.29840i | −0.147596 | + | 0.255644i | −0.930339 | − | 0.366702i | \(-0.880487\pi\) |
0.782742 | + | 0.622346i | \(0.213820\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.6720 | − | 23.6806i | −0.554017 | − | 0.959585i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.46560 | 0.221115 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.58148 | + | 11.3995i | 0.265824 | + | 0.460420i | 0.967779 | − | 0.251801i | \(-0.0810228\pi\) |
−0.701955 | + | 0.712221i | \(0.747689\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0825512 | − | 0.142983i | 0.00332879 | − | 0.00576563i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.7706 | 0.554382 | 0.277191 | − | 0.960815i | \(-0.410596\pi\) | ||||
0.277191 | + | 0.960815i | \(0.410596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5226 | + | 19.9578i | 0.463134 | + | 0.802172i | 0.999115 | − | 0.0420584i | \(-0.0133915\pi\) |
−0.535981 | + | 0.844230i | \(0.680058\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.737700 | − | 1.27773i | −0.0296029 | − | 0.0512737i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.8371 | + | 37.8229i | −0.874883 | + | 1.51534i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.9725 | 0.717752 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9091 | − | 29.2873i | 0.674208 | − | 1.16776i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9125 | − | 24.0972i | −0.553849 | − | 0.959294i | −0.997992 | − | 0.0633384i | \(-0.979825\pi\) |
0.444143 | − | 0.895956i | \(-0.353508\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.05487 | − | 7.02324i | −0.161167 | − | 0.279149i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.04294 | − | 12.1987i | 0.279490 | − | 0.484092i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.82727 | − | 13.5572i | 0.310128 | − | 0.537157i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.87027 | − | 11.8997i | 0.271784 | − | 0.470743i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.347927 | + | 0.602628i | −0.0137423 | + | 0.0238024i | −0.872815 | − | 0.488052i | \(-0.837708\pi\) |
0.859072 | + | 0.511854i | \(0.171041\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.154256 | −0.00608325 | −0.00304163 | − | 0.999995i | \(-0.500968\pi\) | ||||
−0.00304163 | + | 0.999995i | \(0.500968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.29940 | 0.287414 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.2371 | − | 35.0517i | −0.795602 | − | 1.37802i | −0.922456 | − | 0.386102i | \(-0.873821\pi\) |
0.126854 | − | 0.991921i | \(-0.459512\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.4998 | + | 32.0427i | −0.726182 | + | 1.25778i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.28397 | − | 10.8842i | −0.246288 | − | 0.426584i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.68089 | + | 16.7678i | 0.378842 | + | 0.656174i | 0.990894 | − | 0.134644i | \(-0.0429889\pi\) |
−0.612052 | + | 0.790818i | \(0.709656\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.52373 | −0.215830 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.88057 | − | 11.9175i | −0.268437 | − | 0.464946i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.54663 | + | 9.60704i | −0.216066 | + | 0.374237i | −0.953602 | − | 0.301071i | \(-0.902656\pi\) |
0.737536 | + | 0.675308i | \(0.235989\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0676 | −0.430480 | −0.215240 | − | 0.976561i | \(-0.569053\pi\) | ||||
−0.215240 | + | 0.976561i | \(0.569053\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.68241 | − | 2.91403i | 0.0653395 | − | 0.113171i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.4638 | −0.793551 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.47605 | −0.328194 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.57513 | 0.0608979 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.2940 | 1.24670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.29659 | 0.358357 | 0.179179 | − | 0.983817i | \(-0.442656\pi\) | ||||
0.179179 | + | 0.983817i | \(0.442656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.4619 | + | 25.0487i | −0.555815 | + | 0.962699i | 0.442025 | + | 0.897003i | \(0.354260\pi\) |
−0.997840 | + | 0.0656964i | \(0.979073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −73.0900 | −2.80494 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.2481 | − | 22.9463i | 0.507667 | − | 0.879305i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.6605 | − | 23.6606i | −0.522704 | − | 0.905349i | −0.999651 | − | 0.0264173i | \(-0.991590\pi\) |
0.476947 | − | 0.878932i | \(-0.341743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.8550 | −0.682204 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.1723 | + | 21.0830i | 0.464402 | + | 0.804368i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.820251 | + | 1.42072i | 0.0312491 | + | 0.0541250i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.33577 | − | 7.50978i | 0.164941 | − | 0.285686i | −0.771694 | − | 0.635995i | \(-0.780590\pi\) |
0.936634 | + | 0.350309i | \(0.113923\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.94827 | − | 17.2309i | −0.377903 | − | 0.654548i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.2254 | 0.501669 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.555541 | 0.0210426 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.45772 | + | 5.98895i | −0.130783 | + | 0.226523i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.91040 | + | 3.30891i | −0.0721548 | + | 0.124976i | −0.899845 | − | 0.436209i | \(-0.856321\pi\) |
0.827691 | + | 0.561185i | \(0.189654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.6055 | + | 37.4219i | −0.814868 | + | 1.41139i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.73280 | + | 4.73335i | −0.102923 | + | 0.178268i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.35652 | − | 4.08162i | −0.0886262 | − | 0.153505i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3083 | + | 17.8545i | 0.387136 | + | 0.670539i | 0.992063 | − | 0.125742i | \(-0.0401310\pi\) |
−0.604927 | + | 0.796281i | \(0.706798\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.08037 | + | 3.60330i | −0.0780198 | + | 0.135134i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.89579 | −0.145899 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.18023 | −0.156332 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.25531 | + | 7.37041i | −0.158917 | + | 0.275253i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.49936 | − | 7.79312i | −0.167798 | − | 0.290634i | 0.769847 | − | 0.638228i | \(-0.220332\pi\) |
−0.937645 | + | 0.347593i | \(0.886999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.0657 | + | 71.1279i | 1.52937 | + | 2.64894i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.8854 | 0.516403 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.87246 | − | 4.97524i | 0.106680 | − | 0.184776i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.74353 | − | 11.6801i | −0.250104 | − | 0.433193i | 0.713450 | − | 0.700706i | \(-0.247131\pi\) |
−0.963554 | + | 0.267513i | \(0.913798\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.2806 | + | 21.2706i | 0.454215 | + | 0.786723i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.5363 | − | 37.3019i | 0.795461 | − | 1.37778i | −0.127085 | − | 0.991892i | \(-0.540562\pi\) |
0.922546 | − | 0.385887i | \(-0.126104\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.82727 | + | 13.5572i | 0.288713 | + | 0.500066i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.9134 | + | 4.54495i | 1.24922 | + | 0.167415i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.41568 | + | 5.91613i | 0.125648 | + | 0.217628i | 0.921986 | − | 0.387223i | \(-0.126566\pi\) |
−0.796338 | + | 0.604852i | \(0.793232\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.14970 | + | 3.72339i | −0.0789713 | + | 0.136782i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.1047 | + | 34.8223i | 0.737570 | + | 1.27751i | 0.953587 | + | 0.301118i | \(0.0973599\pi\) |
−0.216017 | + | 0.976390i | \(0.569307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.55580 | −0.313460 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.24720 | + | 12.5525i | 0.265161 | + | 0.459272i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.6198 | − | 49.5709i | 1.04574 | − | 1.81128i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.0195 | −1.27788 | −0.638941 | − | 0.769256i | \(-0.720627\pi\) | ||||
−0.638941 | + | 0.769256i | \(0.720627\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.00722 | + | 1.74456i | 0.0367052 | + | 0.0635752i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.3253 | + | 17.8839i | 0.375775 | + | 0.650861i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.47460 | − | 11.2143i | 0.235323 | − | 0.407592i | −0.724043 | − | 0.689755i | \(-0.757718\pi\) |
0.959367 | + | 0.282163i | \(0.0910518\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.16750 | −0.223866 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0939 | −0.873403 | −0.436701 | − | 0.899607i | \(-0.643853\pi\) | ||||
−0.436701 | + | 0.899607i | \(0.643853\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.3992 | + | 71.7055i | −1.49875 | + | 2.59592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.68241 | + | 2.91403i | 0.0608278 | + | 0.105357i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.42556 | − | 7.66529i | −0.159798 | − | 0.276778i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5293 | − | 26.8975i | 0.560000 | − | 0.969948i | −0.437496 | − | 0.899220i | \(-0.644135\pi\) |
0.997496 | − | 0.0707275i | \(-0.0225321\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.98982 | − | 13.8388i | 0.287746 | − | 0.498391i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.3293 | + | 47.3358i | −0.982968 | + | 1.70255i | −0.332327 | + | 0.943164i | \(0.607834\pi\) |
−0.650641 | + | 0.759386i | \(0.725500\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.32025 | − | 2.28674i | 0.0474248 | − | 0.0821422i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 47.8370 | 1.71614 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.709842 | −0.0254327 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.7193 | − | 49.7433i | −1.02766 | − | 1.77996i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.87246 | − | 4.97524i | 0.102653 | − | 0.177801i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.92713 | + | 10.2661i | 0.211548 | + | 0.366412i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.62025 | + | 6.27046i | 0.129048 | + | 0.223518i | 0.923308 | − | 0.384060i | \(-0.125475\pi\) |
−0.794260 | + | 0.607578i | \(0.792141\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.5143 | 0.801529 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0436 | − | 19.1282i | −0.392667 | − | 0.680119i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.86271 | + | 6.69041i | −0.137169 | + | 0.237583i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.64050 | −0.0581826 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.8520 | − | 23.9924i | 0.490663 | − | 0.849853i | −0.509279 | − | 0.860601i | \(-0.670088\pi\) |
0.999942 | + | 0.0107482i | \(0.00342132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.3908 | −0.650620 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.17586 | −0.324213 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −57.5247 | −2.03000 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.02242 | 0.247508 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.8898 | −0.805759 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.0156 | 1.44203 | 0.721016 | − | 0.692918i | \(-0.243675\pi\) | ||||
0.721016 | + | 0.692918i | \(0.243675\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.72130 | − | 16.8378i | 0.341361 | − | 0.591255i | −0.643325 | − | 0.765593i | \(-0.722445\pi\) |
0.984686 | + | 0.174339i | \(0.0557788\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.4504 | 0.576942 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.41720 | − | 11.1149i | 0.224785 | − | 0.389338i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.6915 | − | 27.1785i | −0.548978 | − | 0.950857i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.75968 | 0.166317 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.17982 | + | 8.97171i | 0.180777 | + | 0.313115i | 0.942145 | − | 0.335205i | \(-0.108805\pi\) |
−0.761368 | + | 0.648320i | \(0.775472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.398838 | + | 0.690808i | 0.0139026 | + | 0.0240801i | 0.872893 | − | 0.487912i | \(-0.162241\pi\) |
−0.858990 | + | 0.511992i | \(0.828908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.09011 | − | 3.62018i | 0.0727684 | − | 0.126039i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.77393 | + | 3.07254i | 0.0616856 | + | 0.106843i | 0.895219 | − | 0.445626i | \(-0.147019\pi\) |
−0.833533 | + | 0.552469i | \(0.813686\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.5893 | 0.402511 | 0.201256 | − | 0.979539i | \(-0.435498\pi\) | ||||
0.201256 | + | 0.979539i | \(0.435498\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2683 | −0.494961 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.3374 | + | 45.6177i | −0.912537 | + | 1.58056i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50686 | − | 2.60995i | 0.0521469 | − | 0.0903210i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.32025 | − | 2.28674i | 0.0456345 | − | 0.0790413i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.3569 | − | 23.1349i | 0.461133 | − | 0.798705i | −0.537885 | − | 0.843018i | \(-0.680777\pi\) |
0.999018 | + | 0.0443129i | \(0.0141098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00204 | − | 3.46763i | −0.0690359 | − | 0.119574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.96740 | − | 10.3358i | −0.205528 | − | 0.355985i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.8156 | −1.05884 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.1591 | 0.829139 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.41423 | − | 12.8418i | 0.254157 | − | 0.440212i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.26560 | − | 12.5844i | −0.248769 | − | 0.430881i | 0.714415 | − | 0.699722i | \(-0.246693\pi\) |
−0.963185 | + | 0.268841i | \(0.913359\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.14970 | − | 3.72339i | −0.0735183 | − | 0.127337i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.3070 | −0.522878 | −0.261439 | − | 0.965220i | \(-0.584197\pi\) | ||||
−0.261439 | + | 0.965220i | \(0.584197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0840 | + | 20.9302i | −0.412302 | + | 0.714128i | −0.995141 | − | 0.0984599i | \(-0.968608\pi\) |
0.582839 | + | 0.812587i | \(0.301942\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.392917 | + | 0.680553i | 0.0133906 | + | 0.0231932i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.49398 | −0.152977 | −0.0764884 | − | 0.997070i | \(-0.524371\pi\) | ||||
−0.0764884 | + | 0.997070i | \(0.524371\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.85464 | + | 15.3367i | 0.301067 | + | 0.521463i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.83897 | − | 4.91724i | 0.0964165 | − | 0.166998i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.69640 | + | 15.0626i | 0.295005 | + | 0.510964i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.99800 | + | 6.48229i | −0.169351 | + | 0.219644i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.67804 | − | 13.2988i | −0.259862 | − | 0.450095i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.37984 | + | 4.12200i | −0.0804532 | + | 0.139349i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.1460 | + | 36.6259i | 0.714049 | + | 1.23677i | 0.963325 | + | 0.268337i | \(0.0864741\pi\) |
−0.249276 | + | 0.968433i | \(0.580193\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.6256 | −0.864329 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.2266 | − | 24.6413i | −0.479308 | − | 0.830185i | 0.520411 | − | 0.853916i | \(-0.325779\pi\) |
−0.999718 | + | 0.0237308i | \(0.992446\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.07395 | − | 10.5204i | 0.204405 | − | 0.354040i | −0.745538 | − | 0.666463i | \(-0.767807\pi\) |
0.949943 | + | 0.312423i | \(0.101141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.85112 | 0.297527 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.3334 | + | 31.7543i | 0.615574 | + | 1.06621i | 0.990283 | + | 0.139064i | \(0.0444092\pi\) |
−0.374709 | + | 0.927142i | \(0.622257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.5221 | + | 58.0620i | 1.12430 | + | 1.94734i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.09011 | − | 3.62018i | 0.0700214 | − | 0.121281i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.4988 | 0.786358 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.57826 | −0.153034 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.737700 | − | 1.27773i | 0.0246311 | − | 0.0426623i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.58473 | − | 13.1371i | −0.252965 | − | 0.438148i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.76000 | − | 4.78046i | −0.0919490 | − | 0.159260i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.3714 | + | 30.0882i | −0.578084 | + | 1.00127i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.07453 | − | 5.32524i | 0.102201 | − | 0.177017i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.0942 | + | 40.0003i | −0.766830 | + | 1.32819i | 0.172444 | + | 0.985019i | \(0.444834\pi\) |
−0.939274 | + | 0.343169i | \(0.888500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.495102 | − | 0.857541i | 0.0164215 | − | 0.0284428i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.0532440 | 0.00176405 | 0.000882026 | − | 1.00000i | \(-0.499719\pi\) | ||||
0.000882026 | 1.00000i | \(0.499719\pi\) | ||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 60.5899 | 2.00523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.86271 | − | 6.69041i | −0.127697 | − | 0.221178i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1456 | − | 22.7688i | 0.434105 | − | 0.751892i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.1909 | + | 38.4358i | 0.732011 | + | 1.26788i | 0.956023 | + | 0.293293i | \(0.0947512\pi\) |
−0.224012 | + | 0.974586i | \(0.571915\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.79669 | − | 6.57606i | −0.125105 | − | 0.216689i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.7405 | 0.452276 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.02524 | + | 8.70397i | 0.165229 | + | 0.286185i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.62783 | + | 14.9438i | −0.283375 | + | 0.490820i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.01781 | 0.295865 | 0.147932 | − | 0.988997i | \(-0.452738\pi\) | ||||
0.147932 | + | 0.988997i | \(0.452738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.6526 | − | 58.2880i | 1.10292 | − | 1.91031i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.1269 | −0.986310 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.0657 | 0.459999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.5780 | 1.19495 | 0.597476 | − | 0.801887i | \(-0.296170\pi\) | ||||
0.597476 | + | 0.801887i | \(0.296170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.75311 | 0.318281 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.383115 | −0.0124892 | −0.00624460 | − | 0.999981i | \(-0.501988\pi\) | ||||
−0.00624460 | + | 0.999981i | \(0.501988\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.243592 | 0.00793245 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.37984 | + | 4.12200i | −0.0774162 | + | 0.134089i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.5386 | 1.67478 | 0.837389 | − | 0.546607i | \(-0.184081\pi\) | ||||
0.837389 | + | 0.546607i | \(0.184081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.88057 | − | 11.9175i | 0.223353 | − | 0.386858i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.81690 | + | 15.2713i | 0.285907 | + | 0.495206i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.9346 | 1.22882 | 0.614411 | − | 0.788986i | \(-0.289394\pi\) | ||||
0.614411 | + | 0.788986i | \(0.289394\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.02453 | + | 1.77454i | 0.0331531 | + | 0.0574228i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0075 | − | 20.7977i | −0.388148 | − | 0.672293i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.4920 | − | 73.5983i | 1.37214 | − | 2.37661i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0139 | + | 20.8086i | 0.387544 | + | 0.671247i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0259 | 0.387530 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.4218 | −0.753975 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0439 | + | 41.6452i | −0.773199 | + | 1.33922i | 0.162603 | + | 0.986692i | \(0.448011\pi\) |
−0.935801 | + | 0.352528i | \(0.885322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.23337 | − | 12.5286i | 0.232369 | − | 0.402476i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.670821 | + | 1.16190i | −0.0215277 | + | 0.0372870i | −0.876589 | − | 0.481241i | \(-0.840186\pi\) |
0.855061 | + | 0.518528i | \(0.173520\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.4744 | + | 54.5152i | −1.00902 | + | 1.74768i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | + | 0.866025i | 0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.2826 | − | 38.5946i | −0.712883 | − | 1.23475i | −0.963770 | − | 0.266734i | \(-0.914056\pi\) |
0.250887 | − | 0.968016i | \(-0.419278\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.1786 | + | 33.2183i | −0.612950 | + | 1.06166i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.3958 | −0.555405 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.0240 | −1.27657 | −0.638284 | − | 0.769801i | \(-0.720356\pi\) | ||||
−0.638284 | + | 0.769801i | \(0.720356\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.38680 | + | 16.2584i | −0.299088 | + | 0.518036i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.0073 | − | 22.5292i | −0.414025 | − | 0.717113i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.38477 | + | 9.32669i | 0.171226 | + | 0.296571i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.09980 | −0.257299 | −0.128649 | − | 0.991690i | \(-0.541064\pi\) | ||||
−0.128649 | + | 0.991690i | \(0.541064\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.03476 | − | 5.25636i | 0.0963051 | − | 0.166805i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.28243 | − | 10.8815i | −0.199167 | − | 0.344967i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.3062 | 1.18150 | 0.590750 | − | 0.806855i | \(-0.298832\pi\) | ||||
0.590750 | + | 0.806855i | \(0.298832\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.02524 | + | 8.70397i | 0.158992 | + | 0.275381i |
(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 | 4020.2.q.j.841.6 | ✓ | 12 | |
67.29 | even | 3 | inner | 4020.2.q.j.3781.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.j.841.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
4020.2.q.j.3781.6 | yes | 12 | 67.29 | even | 3 | inner |