Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(307,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.t (of order \(4\), 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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 6x^{10} - 24x^{9} + 18x^{8} + 40x^{7} - 82x^{6} + 12x^{5} + 228x^{4} - 284x^{3} + 124x^{2} - 16x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.2 | ||
Root | \(0.563963 + 1.36153i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.343 |
Dual form | 390.2.t.a.307.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.04698 | + | 1.97581i | 0.468223 | + | 0.883610i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | 2.54214 | 0.960838 | 0.480419 | − | 0.877039i | \(-0.340485\pi\) | ||||
0.480419 | + | 0.877039i | \(0.340485\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −1.97581 | + | 1.04698i | −0.624807 | + | 0.331084i | ||||
\(11\) | −1.89487 | − | 1.89487i | −0.571323 | − | 0.571323i | 0.361175 | − | 0.932498i | \(-0.382376\pi\) |
−0.932498 | + | 0.361175i | \(0.882376\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 1.52886 | + | 3.26536i | 0.424029 | + | 0.905649i | ||||
\(14\) | 2.54214i | 0.679415i | ||||||||
\(15\) | 0.656785 | − | 2.13744i | 0.169581 | − | 0.551884i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.27822 | − | 1.27822i | −0.310013 | − | 0.310013i | 0.534902 | − | 0.844914i | \(-0.320349\pi\) |
−0.844914 | + | 0.534902i | \(0.820349\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.13392 | + | 6.13392i | 1.40722 | + | 1.40722i | 0.773850 | + | 0.633369i | \(0.218328\pi\) |
0.633369 | + | 0.773850i | \(0.281672\pi\) | |||||||
\(20\) | −1.04698 | − | 1.97581i | −0.234112 | − | 0.441805i | ||||
\(21\) | −1.79756 | − | 1.79756i | −0.392261 | − | 0.392261i | ||||
\(22\) | 1.89487 | − | 1.89487i | 0.403987 | − | 0.403987i | ||||
\(23\) | −0.312184 | + | 0.312184i | −0.0650949 | + | 0.0650949i | −0.738905 | − | 0.673810i | \(-0.764657\pi\) |
0.673810 | + | 0.738905i | \(0.264657\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | −2.80767 | + | 4.13727i | −0.561534 | + | 0.827454i | ||||
\(26\) | −3.26536 | + | 1.52886i | −0.640390 | + | 0.299834i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −2.54214 | −0.480419 | ||||||||
\(29\) | 10.6134i | 1.97086i | 0.170069 | + | 0.985432i | \(0.445601\pi\) | ||||
−0.170069 | + | 0.985432i | \(0.554399\pi\) | |||||||
\(30\) | 2.13744 | + | 0.656785i | 0.390241 | + | 0.119912i | ||||
\(31\) | 1.00000 | − | 1.00000i | 0.179605 | − | 0.179605i | −0.611578 | − | 0.791184i | \(-0.709465\pi\) |
0.791184 | + | 0.611578i | \(0.209465\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.67974i | 0.466484i | ||||||||
\(34\) | 1.27822 | − | 1.27822i | 0.219212 | − | 0.219212i | ||||
\(35\) | 2.66157 | + | 5.02279i | 0.449887 | + | 0.849007i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −3.18391 | −0.523431 | −0.261716 | − | 0.965145i | \(-0.584288\pi\) | ||||
−0.261716 | + | 0.965145i | \(0.584288\pi\) | |||||||
\(38\) | −6.13392 | + | 6.13392i | −0.995054 | + | 0.995054i | ||||
\(39\) | 1.22789 | − | 3.39003i | 0.196620 | − | 0.542839i | ||||
\(40\) | 1.97581 | − | 1.04698i | 0.312403 | − | 0.165542i | ||||
\(41\) | 4.77370 | − | 4.77370i | 0.745527 | − | 0.745527i | −0.228109 | − | 0.973636i | \(-0.573254\pi\) |
0.973636 | + | 0.228109i | \(0.0732541\pi\) | |||||||
\(42\) | 1.79756 | − | 1.79756i | 0.277370 | − | 0.277370i | ||||
\(43\) | 5.88519 | − | 5.88519i | 0.897483 | − | 0.897483i | −0.0977303 | − | 0.995213i | \(-0.531158\pi\) |
0.995213 | + | 0.0977303i | \(0.0311583\pi\) | |||||||
\(44\) | 1.89487 | + | 1.89487i | 0.285662 | + | 0.285662i | ||||
\(45\) | −1.97581 | + | 1.04698i | −0.294537 | + | 0.156074i | ||||
\(46\) | −0.312184 | − | 0.312184i | −0.0460291 | − | 0.0460291i | ||||
\(47\) | −5.18357 | −0.756101 | −0.378051 | − | 0.925785i | \(-0.623406\pi\) | ||||
−0.378051 | + | 0.925785i | \(0.623406\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | −0.537526 | −0.0767894 | ||||||||
\(50\) | −4.13727 | − | 2.80767i | −0.585098 | − | 0.397065i | ||||
\(51\) | 1.80767i | 0.253124i | ||||||||
\(52\) | −1.52886 | − | 3.26536i | −0.212015 | − | 0.452824i | ||||
\(53\) | −6.13727 | − | 6.13727i | −0.843019 | − | 0.843019i | 0.146232 | − | 0.989250i | \(-0.453285\pi\) |
−0.989250 | + | 0.146232i | \(0.953285\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 1.76001 | − | 5.72778i | 0.237320 | − | 0.772334i | ||||
\(56\) | − | 2.54214i | − | 0.339708i | ||||||
\(57\) | − | 8.67468i | − | 1.14899i | ||||||
\(58\) | −10.6134 | −1.39361 | ||||||||
\(59\) | 7.78281 | − | 7.78281i | 1.01324 | − | 1.01324i | 0.0133238 | − | 0.999911i | \(-0.495759\pi\) |
0.999911 | − | 0.0133238i | \(-0.00424123\pi\) | |||||||
\(60\) | −0.656785 | + | 2.13744i | −0.0847905 | + | 0.275942i | ||||
\(61\) | 6.41410 | 0.821241 | 0.410621 | − | 0.911806i | \(-0.365312\pi\) | ||||
0.410621 | + | 0.911806i | \(0.365312\pi\) | |||||||
\(62\) | 1.00000 | + | 1.00000i | 0.127000 | + | 0.127000i | ||||
\(63\) | 2.54214i | 0.320279i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.85106 | + | 6.43950i | −0.601700 | + | 0.798722i | ||||
\(66\) | −2.67974 | −0.329854 | ||||||||
\(67\) | − | 11.3845i | − | 1.39084i | −0.718603 | − | 0.695420i | \(-0.755218\pi\) | ||
0.718603 | − | 0.695420i | \(-0.244782\pi\) | |||||||
\(68\) | 1.27822 | + | 1.27822i | 0.155006 | + | 0.155006i | ||||
\(69\) | 0.441495 | 0.0531498 | ||||||||
\(70\) | −5.02279 | + | 2.66157i | −0.600338 | + | 0.318118i | ||||
\(71\) | −7.30734 | + | 7.30734i | −0.867222 | + | 0.867222i | −0.992164 | − | 0.124942i | \(-0.960126\pi\) |
0.124942 | + | 0.992164i | \(0.460126\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | − | 14.5716i | − | 1.70547i | −0.522340 | − | 0.852737i | \(-0.674941\pi\) | ||
0.522340 | − | 0.852737i | \(-0.325059\pi\) | |||||||
\(74\) | − | 3.18391i | − | 0.370122i | ||||||
\(75\) | 4.91081 | − | 0.940168i | 0.567052 | − | 0.108561i | ||||
\(76\) | −6.13392 | − | 6.13392i | −0.703609 | − | 0.703609i | ||||
\(77\) | −4.81701 | − | 4.81701i | −0.548950 | − | 0.548950i | ||||
\(78\) | 3.39003 | + | 1.22789i | 0.383845 | + | 0.139032i | ||||
\(79\) | 3.04259i | 0.342318i | 0.985243 | + | 0.171159i | \(0.0547512\pi\) | ||||
−0.985243 | + | 0.171159i | \(0.945249\pi\) | |||||||
\(80\) | 1.04698 | + | 1.97581i | 0.117056 | + | 0.220903i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.77370 | + | 4.77370i | 0.527167 | + | 0.527167i | ||||
\(83\) | −3.42655 | −0.376112 | −0.188056 | − | 0.982158i | \(-0.560219\pi\) | ||||
−0.188056 | + | 0.982158i | \(0.560219\pi\) | |||||||
\(84\) | 1.79756 | + | 1.79756i | 0.196130 | + | 0.196130i | ||||
\(85\) | 1.18725 | − | 3.86378i | 0.128775 | − | 0.419086i | ||||
\(86\) | 5.88519 | + | 5.88519i | 0.634616 | + | 0.634616i | ||||
\(87\) | 7.50483 | − | 7.50483i | 0.804602 | − | 0.804602i | ||||
\(88\) | −1.89487 | + | 1.89487i | −0.201993 | + | 0.201993i | ||||
\(89\) | −2.37506 | + | 2.37506i | −0.251756 | + | 0.251756i | −0.821690 | − | 0.569935i | \(-0.806969\pi\) |
0.569935 | + | 0.821690i | \(0.306969\pi\) | |||||||
\(90\) | −1.04698 | − | 1.97581i | −0.110361 | − | 0.208269i | ||||
\(91\) | 3.88657 | + | 8.30101i | 0.407423 | + | 0.870182i | ||||
\(92\) | 0.312184 | − | 0.312184i | 0.0325475 | − | 0.0325475i | ||||
\(93\) | −1.41421 | −0.146647 | ||||||||
\(94\) | − | 5.18357i | − | 0.534644i | ||||||
\(95\) | −5.69740 | + | 18.5416i | −0.584540 | + | 1.90233i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 7.40145i | 0.751503i | 0.926720 | + | 0.375751i | \(0.122615\pi\) | ||||
−0.926720 | + | 0.375751i | \(0.877385\pi\) | |||||||
\(98\) | − | 0.537526i | − | 0.0542983i | ||||||
\(99\) | 1.89487 | − | 1.89487i | 0.190441 | − | 0.190441i | ||||
\(100\) | 2.80767 | − | 4.13727i | 0.280767 | − | 0.413727i | ||||
\(101\) | − | 1.83957i | − | 0.183044i | −0.995803 | − | 0.0915218i | \(-0.970827\pi\) | ||
0.995803 | − | 0.0915218i | \(-0.0291731\pi\) | |||||||
\(102\) | −1.80767 | −0.178986 | ||||||||
\(103\) | 1.21254 | − | 1.21254i | 0.119475 | − | 0.119475i | −0.644841 | − | 0.764317i | \(-0.723077\pi\) |
0.764317 | + | 0.644841i | \(0.223077\pi\) | |||||||
\(104\) | 3.26536 | − | 1.52886i | 0.320195 | − | 0.149917i | ||||
\(105\) | 1.66964 | − | 5.43366i | 0.162940 | − | 0.530271i | ||||
\(106\) | 6.13727 | − | 6.13727i | 0.596104 | − | 0.596104i | ||||
\(107\) | 14.2793 | − | 14.2793i | 1.38043 | − | 1.38043i | 0.536578 | − | 0.843851i | \(-0.319717\pi\) |
0.843851 | − | 0.536578i | \(-0.180283\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | −4.17757 | − | 4.17757i | −0.400139 | − | 0.400139i | 0.478143 | − | 0.878282i | \(-0.341310\pi\) |
−0.878282 | + | 0.478143i | \(0.841310\pi\) | |||||||
\(110\) | 5.72778 | + | 1.76001i | 0.546123 | + | 0.167811i | ||||
\(111\) | 2.25136 | + | 2.25136i | 0.213690 | + | 0.213690i | ||||
\(112\) | 2.54214 | 0.240210 | ||||||||
\(113\) | −6.49114 | − | 6.49114i | −0.610635 | − | 0.610635i | 0.332476 | − | 0.943112i | \(-0.392116\pi\) |
−0.943112 | + | 0.332476i | \(0.892116\pi\) | |||||||
\(114\) | 8.67468 | 0.812458 | ||||||||
\(115\) | −0.943668 | − | 0.289967i | −0.0879975 | − | 0.0270396i | ||||
\(116\) | − | 10.6134i | − | 0.985432i | ||||||
\(117\) | −3.26536 | + | 1.52886i | −0.301883 | + | 0.141343i | ||||
\(118\) | 7.78281 | + | 7.78281i | 0.716465 | + | 0.716465i | ||||
\(119\) | −3.24940 | − | 3.24940i | −0.297872 | − | 0.297872i | ||||
\(120\) | −2.13744 | − | 0.656785i | −0.195120 | − | 0.0599560i | ||||
\(121\) | − | 3.81897i | − | 0.347179i | ||||||
\(122\) | 6.41410i | 0.580705i | ||||||||
\(123\) | −6.75103 | −0.608720 | ||||||||
\(124\) | −1.00000 | + | 1.00000i | −0.0898027 | + | 0.0898027i | ||||
\(125\) | −11.1140 | − | 1.21580i | −0.994070 | − | 0.108744i | ||||
\(126\) | −2.54214 | −0.226472 | ||||||||
\(127\) | 7.48269 | + | 7.48269i | 0.663981 | + | 0.663981i | 0.956316 | − | 0.292335i | \(-0.0944322\pi\) |
−0.292335 | + | 0.956316i | \(0.594432\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −8.32291 | −0.732791 | ||||||||
\(130\) | −6.43950 | − | 4.85106i | −0.564782 | − | 0.425466i | ||||
\(131\) | 8.80803 | 0.769561 | 0.384781 | − | 0.923008i | \(-0.374277\pi\) | ||||
0.384781 | + | 0.923008i | \(0.374277\pi\) | |||||||
\(132\) | − | 2.67974i | − | 0.233242i | ||||||
\(133\) | 15.5933 | + | 15.5933i | 1.35211 | + | 1.35211i | ||||
\(134\) | 11.3845 | 0.983473 | ||||||||
\(135\) | 2.13744 | + | 0.656785i | 0.183961 | + | 0.0565270i | ||||
\(136\) | −1.27822 | + | 1.27822i | −0.109606 | + | 0.109606i | ||||
\(137\) | −1.55709 | −0.133031 | −0.0665155 | − | 0.997785i | \(-0.521188\pi\) | ||||
−0.0665155 | + | 0.997785i | \(0.521188\pi\) | |||||||
\(138\) | 0.441495i | 0.0375826i | ||||||||
\(139\) | 0.0179185i | 0.00151983i | 1.00000 | 0.000759913i | \(0.000241888\pi\) | |||||
−1.00000 | 0.000759913i | \(0.999758\pi\) | ||||||||
\(140\) | −2.66157 | − | 5.02279i | −0.224943 | − | 0.424503i | ||||
\(141\) | 3.66534 | + | 3.66534i | 0.308677 | + | 0.308677i | ||||
\(142\) | −7.30734 | − | 7.30734i | −0.613219 | − | 0.613219i | ||||
\(143\) | 3.29044 | − | 9.08440i | 0.275161 | − | 0.759676i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −20.9701 | + | 11.1120i | −1.74148 | + | 0.922804i | ||||
\(146\) | 14.5716 | 1.20595 | ||||||||
\(147\) | 0.380088 | + | 0.380088i | 0.0313491 | + | 0.0313491i | ||||
\(148\) | 3.18391 | 0.261716 | ||||||||
\(149\) | 10.2158 | + | 10.2158i | 0.836912 | + | 0.836912i | 0.988451 | − | 0.151539i | \(-0.0484229\pi\) |
−0.151539 | + | 0.988451i | \(0.548423\pi\) | |||||||
\(150\) | 0.940168 | + | 4.91081i | 0.0767644 | + | 0.400966i | ||||
\(151\) | −3.29704 | − | 3.29704i | −0.268310 | − | 0.268310i | 0.560109 | − | 0.828419i | \(-0.310759\pi\) |
−0.828419 | + | 0.560109i | \(0.810759\pi\) | |||||||
\(152\) | 6.13392 | − | 6.13392i | 0.497527 | − | 0.497527i | ||||
\(153\) | 1.27822 | − | 1.27822i | 0.103338 | − | 0.103338i | ||||
\(154\) | 4.81701 | − | 4.81701i | 0.388166 | − | 0.388166i | ||||
\(155\) | 3.02279 | + | 0.928834i | 0.242796 | + | 0.0746057i | ||||
\(156\) | −1.22789 | + | 3.39003i | −0.0983102 | + | 0.271419i | ||||
\(157\) | −12.2613 | + | 12.2613i | −0.978560 | + | 0.978560i | −0.999775 | − | 0.0212147i | \(-0.993247\pi\) |
0.0212147 | + | 0.999775i | \(0.493247\pi\) | |||||||
\(158\) | −3.04259 | −0.242056 | ||||||||
\(159\) | 8.67941i | 0.688322i | ||||||||
\(160\) | −1.97581 | + | 1.04698i | −0.156202 | + | 0.0827709i | ||||
\(161\) | −0.793616 | + | 0.793616i | −0.0625457 | + | 0.0625457i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 13.8216i | − | 1.08259i | −0.840832 | − | 0.541296i | \(-0.817934\pi\) | ||
0.840832 | − | 0.541296i | \(-0.182066\pi\) | |||||||
\(164\) | −4.77370 | + | 4.77370i | −0.372764 | + | 0.372764i | ||||
\(165\) | −5.29467 | + | 2.80564i | −0.412190 | + | 0.218418i | ||||
\(166\) | − | 3.42655i | − | 0.265952i | ||||||
\(167\) | −17.5562 | −1.35854 | −0.679268 | − | 0.733890i | \(-0.737703\pi\) | ||||
−0.679268 | + | 0.733890i | \(0.737703\pi\) | |||||||
\(168\) | −1.79756 | + | 1.79756i | −0.138685 | + | 0.138685i | ||||
\(169\) | −8.32518 | + | 9.98455i | −0.640399 | + | 0.768043i | ||||
\(170\) | 3.86378 | + | 1.18725i | 0.296338 | + | 0.0910579i | ||||
\(171\) | −6.13392 | + | 6.13392i | −0.469073 | + | 0.469073i | ||||
\(172\) | −5.88519 | + | 5.88519i | −0.448741 | + | 0.448741i | ||||
\(173\) | −1.23037 | + | 1.23037i | −0.0935431 | + | 0.0935431i | −0.752330 | − | 0.658787i | \(-0.771070\pi\) |
0.658787 | + | 0.752330i | \(0.271070\pi\) | |||||||
\(174\) | 7.50483 | + | 7.50483i | 0.568940 | + | 0.568940i | ||||
\(175\) | −7.13749 | + | 10.5175i | −0.539544 | + | 0.795049i | ||||
\(176\) | −1.89487 | − | 1.89487i | −0.142831 | − | 0.142831i | ||||
\(177\) | −11.0065 | −0.827303 | ||||||||
\(178\) | −2.37506 | − | 2.37506i | −0.178018 | − | 0.178018i | ||||
\(179\) | −0.271184 | −0.0202692 | −0.0101346 | − | 0.999949i | \(-0.503226\pi\) | ||||
−0.0101346 | + | 0.999949i | \(0.503226\pi\) | |||||||
\(180\) | 1.97581 | − | 1.04698i | 0.147268 | − | 0.0780372i | ||||
\(181\) | − | 23.7110i | − | 1.76242i | −0.472723 | − | 0.881211i | \(-0.656729\pi\) | ||
0.472723 | − | 0.881211i | \(-0.343271\pi\) | |||||||
\(182\) | −8.30101 | + | 3.88657i | −0.615312 | + | 0.288092i | ||||
\(183\) | −4.53545 | − | 4.53545i | −0.335270 | − | 0.335270i | ||||
\(184\) | 0.312184 | + | 0.312184i | 0.0230145 | + | 0.0230145i | ||||
\(185\) | −3.33348 | − | 6.29080i | −0.245083 | − | 0.462509i | ||||
\(186\) | − | 1.41421i | − | 0.103695i | ||||||
\(187\) | 4.84409i | 0.354235i | ||||||||
\(188\) | 5.18357 | 0.378051 | ||||||||
\(189\) | 1.79756 | − | 1.79756i | 0.130754 | − | 0.130754i | ||||
\(190\) | −18.5416 | − | 5.69740i | −1.34515 | − | 0.413333i | ||||
\(191\) | 8.88620 | 0.642983 | 0.321492 | − | 0.946912i | \(-0.395816\pi\) | ||||
0.321492 | + | 0.946912i | \(0.395816\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 18.6866i | 1.34509i | 0.740057 | + | 0.672544i | \(0.234799\pi\) | ||||
−0.740057 | + | 0.672544i | \(0.765201\pi\) | |||||||
\(194\) | −7.40145 | −0.531393 | ||||||||
\(195\) | 7.98363 | − | 1.12320i | 0.571720 | − | 0.0804339i | ||||
\(196\) | 0.537526 | 0.0383947 | ||||||||
\(197\) | − | 5.31391i | − | 0.378600i | −0.981919 | − | 0.189300i | \(-0.939378\pi\) | ||
0.981919 | − | 0.189300i | \(-0.0606219\pi\) | |||||||
\(198\) | 1.89487 | + | 1.89487i | 0.134662 | + | 0.134662i | ||||
\(199\) | −14.0316 | −0.994671 | −0.497335 | − | 0.867558i | \(-0.665688\pi\) | ||||
−0.497335 | + | 0.867558i | \(0.665688\pi\) | |||||||
\(200\) | 4.13727 | + | 2.80767i | 0.292549 | + | 0.198532i | ||||
\(201\) | −8.05007 | + | 8.05007i | −0.567808 | + | 0.567808i | ||||
\(202\) | 1.83957 | 0.129431 | ||||||||
\(203\) | 26.9808i | 1.89368i | ||||||||
\(204\) | − | 1.80767i | − | 0.126562i | ||||||
\(205\) | 14.4299 | + | 4.43398i | 1.00783 | + | 0.309682i | ||||
\(206\) | 1.21254 | + | 1.21254i | 0.0844818 | + | 0.0844818i | ||||
\(207\) | −0.312184 | − | 0.312184i | −0.0216983 | − | 0.0216983i | ||||
\(208\) | 1.52886 | + | 3.26536i | 0.106007 | + | 0.226412i | ||||
\(209\) | − | 23.2459i | − | 1.60795i | ||||||
\(210\) | 5.43366 | + | 1.66964i | 0.374958 | + | 0.115216i | ||||
\(211\) | −12.1389 | −0.835676 | −0.417838 | − | 0.908522i | \(-0.637212\pi\) | ||||
−0.417838 | + | 0.908522i | \(0.637212\pi\) | |||||||
\(212\) | 6.13727 | + | 6.13727i | 0.421509 | + | 0.421509i | ||||
\(213\) | 10.3341 | 0.708084 | ||||||||
\(214\) | 14.2793 | + | 14.2793i | 0.976110 | + | 0.976110i | ||||
\(215\) | 17.7897 | + | 5.46636i | 1.21325 | + | 0.372803i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | 2.54214 | − | 2.54214i | 0.172572 | − | 0.172572i | ||||
\(218\) | 4.17757 | − | 4.17757i | 0.282941 | − | 0.282941i | ||||
\(219\) | −10.3037 | + | 10.3037i | −0.696257 | + | 0.696257i | ||||
\(220\) | −1.76001 | + | 5.72778i | −0.118660 | + | 0.386167i | ||||
\(221\) | 2.21963 | − | 6.12805i | 0.149308 | − | 0.412217i | ||||
\(222\) | −2.25136 | + | 2.25136i | −0.151102 | + | 0.151102i | ||||
\(223\) | 14.0062 | 0.937922 | 0.468961 | − | 0.883219i | \(-0.344628\pi\) | ||||
0.468961 | + | 0.883219i | \(0.344628\pi\) | |||||||
\(224\) | 2.54214i | 0.169854i | ||||||||
\(225\) | −4.13727 | − | 2.80767i | −0.275818 | − | 0.187178i | ||||
\(226\) | 6.49114 | − | 6.49114i | 0.431784 | − | 0.431784i | ||||
\(227\) | − | 7.16607i | − | 0.475628i | −0.971311 | − | 0.237814i | \(-0.923569\pi\) | ||
0.971311 | − | 0.237814i | \(-0.0764309\pi\) | |||||||
\(228\) | 8.67468i | 0.574495i | ||||||||
\(229\) | −1.54327 | + | 1.54327i | −0.101982 | + | 0.101982i | −0.756257 | − | 0.654275i | \(-0.772974\pi\) |
0.654275 | + | 0.756257i | \(0.272974\pi\) | |||||||
\(230\) | 0.289967 | − | 0.943668i | 0.0191199 | − | 0.0622236i | ||||
\(231\) | 6.81228i | 0.448215i | ||||||||
\(232\) | 10.6134 | 0.696806 | ||||||||
\(233\) | 4.01556 | − | 4.01556i | 0.263068 | − | 0.263068i | −0.563231 | − | 0.826299i | \(-0.690442\pi\) |
0.826299 | + | 0.563231i | \(0.190442\pi\) | |||||||
\(234\) | −1.52886 | − | 3.26536i | −0.0999446 | − | 0.213463i | ||||
\(235\) | −5.42709 | − | 10.2418i | −0.354024 | − | 0.668099i | ||||
\(236\) | −7.78281 | + | 7.78281i | −0.506618 | + | 0.506618i | ||||
\(237\) | 2.15144 | − | 2.15144i | 0.139751 | − | 0.139751i | ||||
\(238\) | 3.24940 | − | 3.24940i | 0.210628 | − | 0.210628i | ||||
\(239\) | 0.248851 | + | 0.248851i | 0.0160969 | + | 0.0160969i | 0.715109 | − | 0.699013i | \(-0.246377\pi\) |
−0.699013 | + | 0.715109i | \(0.746377\pi\) | |||||||
\(240\) | 0.656785 | − | 2.13744i | 0.0423953 | − | 0.137971i | ||||
\(241\) | 16.0560 | + | 16.0560i | 1.03426 | + | 1.03426i | 0.999392 | + | 0.0348663i | \(0.0111005\pi\) |
0.0348663 | + | 0.999392i | \(0.488899\pi\) | |||||||
\(242\) | 3.81897 | 0.245493 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −6.41410 | −0.410621 | ||||||||
\(245\) | −0.562778 | − | 1.06205i | −0.0359546 | − | 0.0678519i | ||||
\(246\) | − | 6.75103i | − | 0.430430i | ||||||
\(247\) | −10.6516 | + | 29.4074i | −0.677744 | + | 1.87115i | ||||
\(248\) | −1.00000 | − | 1.00000i | −0.0635001 | − | 0.0635001i | ||||
\(249\) | 2.42293 | + | 2.42293i | 0.153547 | + | 0.153547i | ||||
\(250\) | 1.21580 | − | 11.1140i | 0.0768938 | − | 0.702913i | ||||
\(251\) | 20.4132i | 1.28847i | 0.764827 | + | 0.644236i | \(0.222825\pi\) | ||||
−0.764827 | + | 0.644236i | \(0.777175\pi\) | |||||||
\(252\) | − | 2.54214i | − | 0.160140i | ||||||
\(253\) | 1.18309 | 0.0743805 | ||||||||
\(254\) | −7.48269 | + | 7.48269i | −0.469506 | + | 0.469506i | ||||
\(255\) | −3.57162 | + | 1.89259i | −0.223663 | + | 0.118519i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.5444 | − | 12.5444i | −0.782500 | − | 0.782500i | 0.197752 | − | 0.980252i | \(-0.436636\pi\) |
−0.980252 | + | 0.197752i | \(0.936636\pi\) | |||||||
\(258\) | − | 8.32291i | − | 0.518162i | ||||||
\(259\) | −8.09394 | −0.502933 | ||||||||
\(260\) | 4.85106 | − | 6.43950i | 0.300850 | − | 0.399361i | ||||
\(261\) | −10.6134 | −0.656955 | ||||||||
\(262\) | 8.80803i | 0.544162i | ||||||||
\(263\) | −3.40213 | − | 3.40213i | −0.209785 | − | 0.209785i | 0.594391 | − | 0.804176i | \(-0.297393\pi\) |
−0.804176 | + | 0.594391i | \(0.797393\pi\) | |||||||
\(264\) | 2.67974 | 0.164927 | ||||||||
\(265\) | 5.70050 | − | 18.5517i | 0.350179 | − | 1.13962i | ||||
\(266\) | −15.5933 | + | 15.5933i | −0.956086 | + | 0.956086i | ||||
\(267\) | 3.35884 | 0.205558 | ||||||||
\(268\) | 11.3845i | 0.695420i | ||||||||
\(269\) | − | 11.6328i | − | 0.709262i | −0.935006 | − | 0.354631i | \(-0.884606\pi\) | ||
0.935006 | − | 0.354631i | \(-0.115394\pi\) | |||||||
\(270\) | −0.656785 | + | 2.13744i | −0.0399706 | + | 0.130080i | ||||
\(271\) | −15.4392 | − | 15.4392i | −0.937863 | − | 0.937863i | 0.0603160 | − | 0.998179i | \(-0.480789\pi\) |
−0.998179 | + | 0.0603160i | \(0.980789\pi\) | |||||||
\(272\) | −1.27822 | − | 1.27822i | −0.0775032 | − | 0.0775032i | ||||
\(273\) | 3.12148 | − | 8.61792i | 0.188920 | − | 0.521580i | ||||
\(274\) | − | 1.55709i | − | 0.0940671i | ||||||
\(275\) | 13.1597 | − | 2.51941i | 0.793561 | − | 0.151926i | ||||
\(276\) | −0.441495 | −0.0265749 | ||||||||
\(277\) | 11.5065 | + | 11.5065i | 0.691357 | + | 0.691357i | 0.962531 | − | 0.271173i | \(-0.0874116\pi\) |
−0.271173 | + | 0.962531i | \(0.587412\pi\) | |||||||
\(278\) | −0.0179185 | −0.00107468 | ||||||||
\(279\) | 1.00000 | + | 1.00000i | 0.0598684 | + | 0.0598684i | ||||
\(280\) | 5.02279 | − | 2.66157i | 0.300169 | − | 0.159059i | ||||
\(281\) | 15.8122 | + | 15.8122i | 0.943276 | + | 0.943276i | 0.998475 | − | 0.0551994i | \(-0.0175795\pi\) |
−0.0551994 | + | 0.998475i | \(0.517579\pi\) | |||||||
\(282\) | −3.66534 | + | 3.66534i | −0.218268 | + | 0.218268i | ||||
\(283\) | 7.26001 | − | 7.26001i | 0.431563 | − | 0.431563i | −0.457597 | − | 0.889160i | \(-0.651290\pi\) |
0.889160 | + | 0.457597i | \(0.151290\pi\) | |||||||
\(284\) | 7.30734 | − | 7.30734i | 0.433611 | − | 0.433611i | ||||
\(285\) | 17.1395 | − | 9.08221i | 1.01526 | − | 0.537983i | ||||
\(286\) | 9.08440 | + | 3.29044i | 0.537172 | + | 0.194568i | ||||
\(287\) | 12.1354 | − | 12.1354i | 0.716331 | − | 0.716331i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | − | 13.7323i | − | 0.807784i | ||||||
\(290\) | −11.1120 | − | 20.9701i | −0.652521 | − | 1.23141i | ||||
\(291\) | 5.23361 | − | 5.23361i | 0.306800 | − | 0.306800i | ||||
\(292\) | 14.5716i | 0.852737i | ||||||||
\(293\) | 9.22562i | 0.538966i | 0.963005 | + | 0.269483i | \(0.0868529\pi\) | ||||
−0.963005 | + | 0.269483i | \(0.913147\pi\) | |||||||
\(294\) | −0.380088 | + | 0.380088i | −0.0221672 | + | 0.0221672i | ||||
\(295\) | 23.5258 | + | 7.22893i | 1.36973 | + | 0.420885i | ||||
\(296\) | 3.18391i | 0.185061i | ||||||||
\(297\) | −2.67974 | −0.155495 | ||||||||
\(298\) | −10.2158 | + | 10.2158i | −0.591786 | + | 0.591786i | ||||
\(299\) | −1.49668 | − | 0.542109i | −0.0865553 | − | 0.0313510i | ||||
\(300\) | −4.91081 | + | 0.940168i | −0.283526 | + | 0.0542806i | ||||
\(301\) | 14.9610 | − | 14.9610i | 0.862336 | − | 0.862336i | ||||
\(302\) | 3.29704 | − | 3.29704i | 0.189724 | − | 0.189724i | ||||
\(303\) | −1.30077 | + | 1.30077i | −0.0747273 | + | 0.0747273i | ||||
\(304\) | 6.13392 | + | 6.13392i | 0.351805 | + | 0.351805i | ||||
\(305\) | 6.71543 | + | 12.6731i | 0.384524 | + | 0.725657i | ||||
\(306\) | 1.27822 | + | 1.27822i | 0.0730707 | + | 0.0730707i | ||||
\(307\) | −20.3901 | −1.16373 | −0.581863 | − | 0.813287i | \(-0.697676\pi\) | ||||
−0.581863 | + | 0.813287i | \(0.697676\pi\) | |||||||
\(308\) | 4.81701 | + | 4.81701i | 0.274475 | + | 0.274475i | ||||
\(309\) | −1.71479 | −0.0975512 | ||||||||
\(310\) | −0.928834 | + | 3.02279i | −0.0527542 | + | 0.171683i | ||||
\(311\) | − | 19.1186i | − | 1.08412i | −0.840340 | − | 0.542059i | \(-0.817645\pi\) | ||
0.840340 | − | 0.542059i | \(-0.182355\pi\) | |||||||
\(312\) | −3.39003 | − | 1.22789i | −0.191922 | − | 0.0695158i | ||||
\(313\) | 1.87309 | + | 1.87309i | 0.105873 | + | 0.105873i | 0.758059 | − | 0.652186i | \(-0.226148\pi\) |
−0.652186 | + | 0.758059i | \(0.726148\pi\) | |||||||
\(314\) | −12.2613 | − | 12.2613i | −0.691947 | − | 0.691947i | ||||
\(315\) | −5.02279 | + | 2.66157i | −0.283002 | + | 0.149962i | ||||
\(316\) | − | 3.04259i | − | 0.171159i | ||||||
\(317\) | 10.7007i | 0.601014i | 0.953780 | + | 0.300507i | \(0.0971558\pi\) | ||||
−0.953780 | + | 0.300507i | \(0.902844\pi\) | |||||||
\(318\) | −8.67941 | −0.486717 | ||||||||
\(319\) | 20.1110 | − | 20.1110i | 1.12600 | − | 1.12600i | ||||
\(320\) | −1.04698 | − | 1.97581i | −0.0585279 | − | 0.110451i | ||||
\(321\) | −20.1939 | −1.12712 | ||||||||
\(322\) | −0.793616 | − | 0.793616i | −0.0442265 | − | 0.0442265i | ||||
\(323\) | − | 15.6810i | − | 0.872512i | ||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −17.8022 | − | 2.84276i | −0.987489 | − | 0.157688i | ||||
\(326\) | 13.8216 | 0.765508 | ||||||||
\(327\) | 5.90798i | 0.326712i | ||||||||
\(328\) | −4.77370 | − | 4.77370i | −0.263584 | − | 0.263584i | ||||
\(329\) | −13.1774 | −0.726491 | ||||||||
\(330\) | −2.80564 | − | 5.29467i | −0.154445 | − | 0.291462i | ||||
\(331\) | 5.98236 | − | 5.98236i | 0.328820 | − | 0.328820i | −0.523317 | − | 0.852138i | \(-0.675306\pi\) |
0.852138 | + | 0.523317i | \(0.175306\pi\) | |||||||
\(332\) | 3.42655 | 0.188056 | ||||||||
\(333\) | − | 3.18391i | − | 0.174477i | ||||||
\(334\) | − | 17.5562i | − | 0.960630i | ||||||
\(335\) | 22.4937 | − | 11.9194i | 1.22896 | − | 0.651224i | ||||
\(336\) | −1.79756 | − | 1.79756i | −0.0980652 | − | 0.0980652i | ||||
\(337\) | 14.5767 | + | 14.5767i | 0.794042 | + | 0.794042i | 0.982149 | − | 0.188107i | \(-0.0602351\pi\) |
−0.188107 | + | 0.982149i | \(0.560235\pi\) | |||||||
\(338\) | −9.98455 | − | 8.32518i | −0.543088 | − | 0.452830i | ||||
\(339\) | 9.17986i | 0.498582i | ||||||||
\(340\) | −1.18725 | + | 3.86378i | −0.0643877 | + | 0.209543i | ||||
\(341\) | −3.78973 | −0.205225 | ||||||||
\(342\) | −6.13392 | − | 6.13392i | −0.331685 | − | 0.331685i | ||||
\(343\) | −19.1614 | −1.03462 | ||||||||
\(344\) | −5.88519 | − | 5.88519i | −0.317308 | − | 0.317308i | ||||
\(345\) | 0.462236 | + | 0.872312i | 0.0248860 | + | 0.0469637i | ||||
\(346\) | −1.23037 | − | 1.23037i | −0.0661450 | − | 0.0661450i | ||||
\(347\) | 13.7628 | − | 13.7628i | 0.738826 | − | 0.738826i | −0.233525 | − | 0.972351i | \(-0.575026\pi\) |
0.972351 | + | 0.233525i | \(0.0750259\pi\) | |||||||
\(348\) | −7.50483 | + | 7.50483i | −0.402301 | + | 0.402301i | ||||
\(349\) | −13.0900 | + | 13.0900i | −0.700689 | + | 0.700689i | −0.964559 | − | 0.263869i | \(-0.915001\pi\) |
0.263869 | + | 0.964559i | \(0.415001\pi\) | |||||||
\(350\) | −10.5175 | − | 7.13749i | −0.562185 | − | 0.381515i | ||||
\(351\) | 3.39003 | + | 1.22789i | 0.180946 | + | 0.0655401i | ||||
\(352\) | 1.89487 | − | 1.89487i | 0.100997 | − | 0.100997i | ||||
\(353\) | −31.4265 | −1.67267 | −0.836333 | − | 0.548222i | \(-0.815305\pi\) | ||||
−0.836333 | + | 0.548222i | \(0.815305\pi\) | |||||||
\(354\) | − | 11.0065i | − | 0.584992i | ||||||
\(355\) | −22.0886 | − | 6.78731i | −1.17234 | − | 0.360233i | ||||
\(356\) | 2.37506 | − | 2.37506i | 0.125878 | − | 0.125878i | ||||
\(357\) | 4.59535i | 0.243212i | ||||||||
\(358\) | − | 0.271184i | − | 0.0143325i | ||||||
\(359\) | 19.6376 | − | 19.6376i | 1.03643 | − | 1.03643i | 0.0371233 | − | 0.999311i | \(-0.488181\pi\) |
0.999311 | − | 0.0371233i | \(-0.0118194\pi\) | |||||||
\(360\) | 1.04698 | + | 1.97581i | 0.0551806 | + | 0.104134i | ||||
\(361\) | 56.2501i | 2.96053i | ||||||||
\(362\) | 23.7110 | 1.24622 | ||||||||
\(363\) | −2.70042 | + | 2.70042i | −0.141735 | + | 0.141735i | ||||
\(364\) | −3.88657 | − | 8.30101i | −0.203712 | − | 0.435091i | ||||
\(365\) | 28.7907 | − | 15.2561i | 1.50697 | − | 0.798543i | ||||
\(366\) | 4.53545 | − | 4.53545i | 0.237072 | − | 0.237072i | ||||
\(367\) | 6.26943 | − | 6.26943i | 0.327261 | − | 0.327261i | −0.524283 | − | 0.851544i | \(-0.675667\pi\) |
0.851544 | + | 0.524283i | \(0.175667\pi\) | |||||||
\(368\) | −0.312184 | + | 0.312184i | −0.0162737 | + | 0.0162737i | ||||
\(369\) | 4.77370 | + | 4.77370i | 0.248509 | + | 0.248509i | ||||
\(370\) | 6.29080 | − | 3.33348i | 0.327043 | − | 0.173300i | ||||
\(371\) | −15.6018 | − | 15.6018i | −0.810005 | − | 0.810005i | ||||
\(372\) | 1.41421 | 0.0733236 | ||||||||
\(373\) | 12.7183 | + | 12.7183i | 0.658530 | + | 0.658530i | 0.955032 | − | 0.296502i | \(-0.0958202\pi\) |
−0.296502 | + | 0.955032i | \(0.595820\pi\) | |||||||
\(374\) | −4.84409 | −0.250482 | ||||||||
\(375\) | 6.99911 | + | 8.71851i | 0.361433 | + | 0.450222i | ||||
\(376\) | 5.18357i | 0.267322i | ||||||||
\(377\) | −34.6567 | + | 16.2264i | −1.78491 | + | 0.835704i | ||||
\(378\) | 1.79756 | + | 1.79756i | 0.0924567 | + | 0.0924567i | ||||
\(379\) | −8.37591 | − | 8.37591i | −0.430242 | − | 0.430242i | 0.458469 | − | 0.888711i | \(-0.348398\pi\) |
−0.888711 | + | 0.458469i | \(0.848398\pi\) | |||||||
\(380\) | 5.69740 | − | 18.5416i | 0.292270 | − | 0.951163i | ||||
\(381\) | − | 10.5821i | − | 0.542138i | ||||||
\(382\) | 8.88620i | 0.454658i | ||||||||
\(383\) | 1.62824 | 0.0831991 | 0.0415995 | − | 0.999134i | \(-0.486755\pi\) | ||||
0.0415995 | + | 0.999134i | \(0.486755\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 4.47420 | − | 14.5608i | 0.228027 | − | 0.742088i | ||||
\(386\) | −18.6866 | −0.951121 | ||||||||
\(387\) | 5.88519 | + | 5.88519i | 0.299161 | + | 0.299161i | ||||
\(388\) | − | 7.40145i | − | 0.375751i | ||||||
\(389\) | 5.38166 | 0.272861 | 0.136430 | − | 0.990650i | \(-0.456437\pi\) | ||||
0.136430 | + | 0.990650i | \(0.456437\pi\) | |||||||
\(390\) | 1.12320 | + | 7.98363i | 0.0568753 | + | 0.404267i | ||||
\(391\) | 0.798078 | 0.0403605 | ||||||||
\(392\) | 0.537526i | 0.0271492i | ||||||||
\(393\) | −6.22822 | − | 6.22822i | −0.314172 | − | 0.314172i | ||||
\(394\) | 5.31391 | 0.267711 | ||||||||
\(395\) | −6.01159 | + | 3.18553i | −0.302476 | + | 0.160281i | ||||
\(396\) | −1.89487 | + | 1.89487i | −0.0952206 | + | 0.0952206i | ||||
\(397\) | 11.3423 | 0.569254 | 0.284627 | − | 0.958638i | \(-0.408130\pi\) | ||||
0.284627 | + | 0.958638i | \(0.408130\pi\) | |||||||
\(398\) | − | 14.0316i | − | 0.703338i | ||||||
\(399\) | − | 22.0522i | − | 1.10399i | ||||||
\(400\) | −2.80767 | + | 4.13727i | −0.140384 | + | 0.206863i | ||||
\(401\) | −15.9787 | − | 15.9787i | −0.797936 | − | 0.797936i | 0.184833 | − | 0.982770i | \(-0.440825\pi\) |
−0.982770 | + | 0.184833i | \(0.940825\pi\) | |||||||
\(402\) | −8.05007 | − | 8.05007i | −0.401501 | − | 0.401501i | ||||
\(403\) | 4.79422 | + | 1.73650i | 0.238817 | + | 0.0865014i | ||||
\(404\) | 1.83957i | 0.0915218i | ||||||||
\(405\) | −1.04698 | − | 1.97581i | −0.0520248 | − | 0.0981789i | ||||
\(406\) | −26.9808 | −1.33904 | ||||||||
\(407\) | 6.03307 | + | 6.03307i | 0.299048 | + | 0.299048i | ||||
\(408\) | 1.80767 | 0.0894930 | ||||||||
\(409\) | −9.21508 | − | 9.21508i | −0.455657 | − | 0.455657i | 0.441570 | − | 0.897227i | \(-0.354422\pi\) |
−0.897227 | + | 0.441570i | \(0.854422\pi\) | |||||||
\(410\) | −4.43398 | + | 14.4299i | −0.218978 | + | 0.712642i | ||||
\(411\) | 1.10103 | + | 1.10103i | 0.0543097 | + | 0.0543097i | ||||
\(412\) | −1.21254 | + | 1.21254i | −0.0597377 | + | 0.0597377i | ||||
\(413\) | 19.7850 | − | 19.7850i | 0.973555 | − | 0.973555i | ||||
\(414\) | 0.312184 | − | 0.312184i | 0.0153430 | − | 0.0153430i | ||||
\(415\) | −3.58752 | − | 6.77022i | −0.176105 | − | 0.332337i | ||||
\(416\) | −3.26536 | + | 1.52886i | −0.160098 | + | 0.0749585i | ||||
\(417\) | 0.0126703 | − | 0.0126703i | 0.000620466 | − | 0.000620466i | ||||
\(418\) | 23.2459 | 1.13700 | ||||||||
\(419\) | 22.6047i | 1.10431i | 0.833740 | + | 0.552157i | \(0.186195\pi\) | ||||
−0.833740 | + | 0.552157i | \(0.813805\pi\) | |||||||
\(420\) | −1.66964 | + | 5.43366i | −0.0814700 | + | 0.265136i | ||||
\(421\) | 0.328119 | − | 0.328119i | 0.0159916 | − | 0.0159916i | −0.699066 | − | 0.715057i | \(-0.746401\pi\) |
0.715057 | + | 0.699066i | \(0.246401\pi\) | |||||||
\(422\) | − | 12.1389i | − | 0.590912i | ||||||
\(423\) | − | 5.18357i | − | 0.252034i | ||||||
\(424\) | −6.13727 | + | 6.13727i | −0.298052 | + | 0.298052i | ||||
\(425\) | 8.87713 | − | 1.69951i | 0.430604 | − | 0.0824385i | ||||
\(426\) | 10.3341i | 0.500691i | ||||||||
\(427\) | 16.3055 | 0.789080 | ||||||||
\(428\) | −14.2793 | + | 14.2793i | −0.690214 | + | 0.690214i | ||||
\(429\) | −8.75034 | + | 4.09695i | −0.422470 | + | 0.197803i | ||||
\(430\) | −5.46636 | + | 17.7897i | −0.263611 | + | 0.857895i | ||||
\(431\) | −1.62855 | + | 1.62855i | −0.0784446 | + | 0.0784446i | −0.745240 | − | 0.666796i | \(-0.767665\pi\) |
0.666796 | + | 0.745240i | \(0.267665\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 24.3982 | − | 24.3982i | 1.17250 | − | 1.17250i | 0.190891 | − | 0.981611i | \(-0.438862\pi\) |
0.981611 | − | 0.190891i | \(-0.0611376\pi\) | |||||||
\(434\) | 2.54214 | + | 2.54214i | 0.122027 | + | 0.122027i | ||||
\(435\) | 22.6855 | + | 6.97074i | 1.08769 | + | 0.334221i | ||||
\(436\) | 4.17757 | + | 4.17757i | 0.200069 | + | 0.200069i | ||||
\(437\) | −3.82983 | −0.183206 | ||||||||
\(438\) | −10.3037 | − | 10.3037i | −0.492328 | − | 0.492328i | ||||
\(439\) | −26.5637 | −1.26782 | −0.633909 | − | 0.773407i | \(-0.718551\pi\) | ||||
−0.633909 | + | 0.773407i | \(0.718551\pi\) | |||||||
\(440\) | −5.72778 | − | 1.76001i | −0.273061 | − | 0.0839054i | ||||
\(441\) | − | 0.537526i | − | 0.0255965i | ||||||
\(442\) | 6.12805 | + | 2.21963i | 0.291482 | + | 0.105577i | ||||
\(443\) | 17.7803 | + | 17.7803i | 0.844765 | + | 0.844765i | 0.989474 | − | 0.144709i | \(-0.0462246\pi\) |
−0.144709 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(444\) | −2.25136 | − | 2.25136i | −0.106845 | − | 0.106845i | ||||
\(445\) | −7.17930 | − | 2.20603i | −0.340332 | − | 0.104576i | ||||
\(446\) | 14.0062i | 0.663211i | ||||||||
\(447\) | − | 14.4473i | − | 0.683336i | ||||||
\(448\) | −2.54214 | −0.120105 | ||||||||
\(449\) | 0.365829 | − | 0.365829i | 0.0172646 | − | 0.0172646i | −0.698422 | − | 0.715686i | \(-0.746114\pi\) |
0.715686 | + | 0.698422i | \(0.246114\pi\) | |||||||
\(450\) | 2.80767 | − | 4.13727i | 0.132355 | − | 0.195033i | ||||
\(451\) | −18.0910 | −0.851874 | ||||||||
\(452\) | 6.49114 | + | 6.49114i | 0.305318 | + | 0.305318i | ||||
\(453\) | 4.66272i | 0.219074i | ||||||||
\(454\) | 7.16607 | 0.336320 | ||||||||
\(455\) | −12.3321 | + | 16.3701i | −0.578137 | + | 0.767443i | ||||
\(456\) | −8.67468 | −0.406229 | ||||||||
\(457\) | − | 13.6966i | − | 0.640700i | −0.947299 | − | 0.320350i | \(-0.896199\pi\) | ||
0.947299 | − | 0.320350i | \(-0.103801\pi\) | |||||||
\(458\) | −1.54327 | − | 1.54327i | −0.0721123 | − | 0.0721123i | ||||
\(459\) | −1.80767 | −0.0843748 | ||||||||
\(460\) | 0.943668 | + | 0.289967i | 0.0439987 | + | 0.0135198i | ||||
\(461\) | 6.04660 | − | 6.04660i | 0.281618 | − | 0.281618i | −0.552136 | − | 0.833754i | \(-0.686187\pi\) |
0.833754 | + | 0.552136i | \(0.186187\pi\) | |||||||
\(462\) | −6.81228 | −0.316936 | ||||||||
\(463\) | − | 10.1801i | − | 0.473108i | −0.971618 | − | 0.236554i | \(-0.923982\pi\) | ||
0.971618 | − | 0.236554i | \(-0.0760181\pi\) | |||||||
\(464\) | 10.6134i | 0.492716i | ||||||||
\(465\) | −1.48065 | − | 2.79422i | −0.0686636 | − | 0.129579i | ||||
\(466\) | 4.01556 | + | 4.01556i | 0.186017 | + | 0.186017i | ||||
\(467\) | 18.6160 | + | 18.6160i | 0.861447 | + | 0.861447i | 0.991506 | − | 0.130059i | \(-0.0415168\pi\) |
−0.130059 | + | 0.991506i | \(0.541517\pi\) | |||||||
\(468\) | 3.26536 | − | 1.52886i | 0.150941 | − | 0.0706715i | ||||
\(469\) | − | 28.9410i | − | 1.33637i | ||||||
\(470\) | 10.2418 | − | 5.42709i | 0.472417 | − | 0.250333i | ||||
\(471\) | 17.3401 | 0.798991 | ||||||||
\(472\) | −7.78281 | − | 7.78281i | −0.358233 | − | 0.358233i | ||||
\(473\) | −22.3033 | −1.02551 | ||||||||
\(474\) | 2.15144 | + | 2.15144i | 0.0988188 | + | 0.0988188i | ||||
\(475\) | −42.5997 | + | 8.15565i | −1.95461 | + | 0.374207i | ||||
\(476\) | 3.24940 | + | 3.24940i | 0.148936 | + | 0.148936i | ||||
\(477\) | 6.13727 | − | 6.13727i | 0.281006 | − | 0.281006i | ||||
\(478\) | −0.248851 | + | 0.248851i | −0.0113822 | + | 0.0113822i | ||||
\(479\) | −19.0736 | + | 19.0736i | −0.871495 | + | 0.871495i | −0.992635 | − | 0.121140i | \(-0.961345\pi\) |
0.121140 | + | 0.992635i | \(0.461345\pi\) | |||||||
\(480\) | 2.13744 | + | 0.656785i | 0.0975602 | + | 0.0299780i | ||||
\(481\) | −4.86774 | − | 10.3966i | −0.221950 | − | 0.474045i | ||||
\(482\) | −16.0560 | + | 16.0560i | −0.731331 | + | 0.731331i | ||||
\(483\) | 1.12234 | 0.0510684 | ||||||||
\(484\) | 3.81897i | 0.173590i | ||||||||
\(485\) | −14.6239 | + | 7.74916i | −0.664036 | + | 0.351871i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | 0.609311i | 0.0276105i | 0.999905 | + | 0.0138053i | \(0.00439449\pi\) | ||||
−0.999905 | + | 0.0138053i | \(0.995606\pi\) | |||||||
\(488\) | − | 6.41410i | − | 0.290353i | ||||||
\(489\) | −9.77335 | + | 9.77335i | −0.441966 | + | 0.441966i | ||||
\(490\) | 1.06205 | − | 0.562778i | 0.0479785 | − | 0.0254237i | ||||
\(491\) | − | 5.96894i | − | 0.269374i | −0.990888 | − | 0.134687i | \(-0.956997\pi\) | ||
0.990888 | − | 0.134687i | \(-0.0430030\pi\) | |||||||
\(492\) | 6.75103 | 0.304360 | ||||||||
\(493\) | 13.5663 | − | 13.5663i | 0.610993 | − | 0.610993i | ||||
\(494\) | −29.4074 | − | 10.6516i | −1.32310 | − | 0.479237i | ||||
\(495\) | 5.72778 | + | 1.76001i | 0.257445 | + | 0.0791068i | ||||
\(496\) | 1.00000 | − | 1.00000i | 0.0449013 | − | 0.0449013i | ||||
\(497\) | −18.5763 | + | 18.5763i | −0.833260 | + | 0.833260i | ||||
\(498\) | −2.42293 | + | 2.42293i | −0.108574 | + | 0.108574i | ||||
\(499\) | −30.0733 | − | 30.0733i | −1.34627 | − | 1.34627i | −0.889679 | − | 0.456587i | \(-0.849072\pi\) |
−0.456587 | − | 0.889679i | \(-0.650928\pi\) | |||||||
\(500\) | 11.1140 | + | 1.21580i | 0.497035 | + | 0.0543721i | ||||
\(501\) | 12.4141 | + | 12.4141i | 0.554620 | + | 0.554620i | ||||
\(502\) | −20.4132 | −0.911088 | ||||||||
\(503\) | 7.94020 | + | 7.94020i | 0.354036 | + | 0.354036i | 0.861609 | − | 0.507573i | \(-0.169457\pi\) |
−0.507573 | + | 0.861609i | \(0.669457\pi\) | |||||||
\(504\) | 2.54214 | 0.113236 | ||||||||
\(505\) | 3.63464 | − | 1.92599i | 0.161739 | − | 0.0857053i | ||||
\(506\) | 1.18309i | 0.0525950i | ||||||||
\(507\) | 12.9469 | − | 1.17335i | 0.574994 | − | 0.0521104i | ||||
\(508\) | −7.48269 | − | 7.48269i | −0.331991 | − | 0.331991i | ||||
\(509\) | 22.1730 | + | 22.1730i | 0.982803 | + | 0.982803i | 0.999855 | − | 0.0170515i | \(-0.00542792\pi\) |
−0.0170515 | + | 0.999855i | \(0.505428\pi\) | |||||||
\(510\) | −1.89259 | − | 3.57162i | −0.0838054 | − | 0.158154i | ||||
\(511\) | − | 37.0430i | − | 1.63869i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 8.67468 | 0.382996 | ||||||||
\(514\) | 12.5444 | − | 12.5444i | 0.553311 | − | 0.553311i | ||||
\(515\) | 3.66526 | + | 1.12625i | 0.161511 | + | 0.0496285i | ||||
\(516\) | 8.32291 | 0.366396 | ||||||||
\(517\) | 9.82217 | + | 9.82217i | 0.431978 | + | 0.431978i | ||||
\(518\) | − | 8.09394i | − | 0.355627i | ||||||
\(519\) | 1.74000 | 0.0763776 | ||||||||
\(520\) | 6.43950 | + | 4.85106i | 0.282391 | + | 0.212733i | ||||
\(521\) | 10.9719 | 0.480686 | 0.240343 | − | 0.970688i | \(-0.422740\pi\) | ||||
0.240343 | + | 0.970688i | \(0.422740\pi\) | |||||||
\(522\) | − | 10.6134i | − | 0.464537i | ||||||
\(523\) | −13.4112 | − | 13.4112i | −0.586431 | − | 0.586431i | 0.350232 | − | 0.936663i | \(-0.386103\pi\) |
−0.936663 | + | 0.350232i | \(0.886103\pi\) | |||||||
\(524\) | −8.80803 | −0.384781 | ||||||||
\(525\) | 12.4840 | − | 2.39004i | 0.544845 | − | 0.104310i | ||||
\(526\) | 3.40213 | − | 3.40213i | 0.148340 | − | 0.148340i | ||||
\(527\) | −2.55643 | −0.111360 | ||||||||
\(528\) | 2.67974i | 0.116621i | ||||||||
\(529\) | 22.8051i | 0.991525i | ||||||||
\(530\) | 18.5517 | + | 5.70050i | 0.805834 | + | 0.247614i | ||||
\(531\) | 7.78281 | + | 7.78281i | 0.337745 | + | 0.337745i | ||||
\(532\) | −15.5933 | − | 15.5933i | −0.676055 | − | 0.676055i | ||||
\(533\) | 22.8862 | + | 8.28955i | 0.991311 | + | 0.359060i | ||||
\(534\) | 3.35884i | 0.145351i | ||||||||
\(535\) | 43.1632 | + | 13.2631i | 1.86611 | + | 0.573412i | ||||
\(536\) | −11.3845 | −0.491736 | ||||||||
\(537\) | 0.191756 | + | 0.191756i | 0.00827488 | + | 0.00827488i | ||||
\(538\) | 11.6328 | 0.501524 | ||||||||
\(539\) | 1.01854 | + | 1.01854i | 0.0438716 | + | 0.0438716i | ||||
\(540\) | −2.13744 | − | 0.656785i | −0.0919806 | − | 0.0282635i | ||||
\(541\) | 25.6187 | + | 25.6187i | 1.10143 | + | 1.10143i | 0.994238 | + | 0.107194i | \(0.0341867\pi\) |
0.107194 | + | 0.994238i | \(0.465813\pi\) | |||||||
\(542\) | 15.4392 | − | 15.4392i | 0.663170 | − | 0.663170i | ||||
\(543\) | −16.7662 | + | 16.7662i | −0.719506 | + | 0.719506i | ||||
\(544\) | 1.27822 | − | 1.27822i | 0.0548031 | − | 0.0548031i | ||||
\(545\) | 3.88027 | − | 12.6279i | 0.166212 | − | 0.540921i | ||||
\(546\) | 8.61792 | + | 3.12148i | 0.368813 | + | 0.133587i | ||||
\(547\) | −2.33129 | + | 2.33129i | −0.0996787 | + | 0.0996787i | −0.755188 | − | 0.655509i | \(-0.772454\pi\) |
0.655509 | + | 0.755188i | \(0.272454\pi\) | |||||||
\(548\) | 1.55709 | 0.0665155 | ||||||||
\(549\) | 6.41410i | 0.273747i | ||||||||
\(550\) | 2.51941 | + | 13.1597i | 0.107428 | + | 0.561132i | ||||
\(551\) | −65.1020 | + | 65.1020i | −2.77344 | + | 2.77344i | ||||
\(552\) | − | 0.441495i | − | 0.0187913i | ||||||
\(553\) | 7.73469i | 0.328913i | ||||||||
\(554\) | −11.5065 | + | 11.5065i | −0.488864 | + | 0.488864i | ||||
\(555\) | −2.09114 | + | 6.80540i | −0.0887640 | + | 0.288873i | ||||
\(556\) | − | 0.0179185i | − | 0.000759913i | ||||||
\(557\) | 18.8191 | 0.797390 | 0.398695 | − | 0.917084i | \(-0.369463\pi\) | ||||
0.398695 | + | 0.917084i | \(0.369463\pi\) | |||||||
\(558\) | −1.00000 | + | 1.00000i | −0.0423334 | + | 0.0423334i | ||||
\(559\) | 28.2149 | + | 10.2197i | 1.19336 | + | 0.432245i | ||||
\(560\) | 2.66157 | + | 5.02279i | 0.112472 | + | 0.212252i | ||||
\(561\) | 3.42529 | − | 3.42529i | 0.144616 | − | 0.144616i | ||||
\(562\) | −15.8122 | + | 15.8122i | −0.666997 | + | 0.666997i | ||||
\(563\) | 24.6636 | − | 24.6636i | 1.03945 | − | 1.03945i | 0.0402560 | − | 0.999189i | \(-0.487183\pi\) |
0.999189 | − | 0.0402560i | \(-0.0128173\pi\) | |||||||
\(564\) | −3.66534 | − | 3.66534i | −0.154339 | − | 0.154339i | ||||
\(565\) | 6.02919 | − | 19.6214i | 0.253650 | − | 0.825477i | ||||
\(566\) | 7.26001 | + | 7.26001i | 0.305161 | + | 0.305161i | ||||
\(567\) | −2.54214 | −0.106760 | ||||||||
\(568\) | 7.30734 | + | 7.30734i | 0.306609 | + | 0.306609i | ||||
\(569\) | 21.7286 | 0.910912 | 0.455456 | − | 0.890258i | \(-0.349476\pi\) | ||||
0.455456 | + | 0.890258i | \(0.349476\pi\) | |||||||
\(570\) | 9.08221 | + | 17.1395i | 0.380412 | + | 0.717896i | ||||
\(571\) | 38.0193i | 1.59106i | 0.605916 | + | 0.795529i | \(0.292807\pi\) | ||||
−0.605916 | + | 0.795529i | \(0.707193\pi\) | |||||||
\(572\) | −3.29044 | + | 9.08440i | −0.137580 | + | 0.379838i | ||||
\(573\) | −6.28350 | − | 6.28350i | −0.262497 | − | 0.262497i | ||||
\(574\) | 12.1354 | + | 12.1354i | 0.506523 | + | 0.506523i | ||||
\(575\) | −0.415080 | − | 2.16810i | −0.0173100 | − | 0.0904160i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 3.70152i | − | 0.154096i | −0.997027 | − | 0.0770481i | \(-0.975450\pi\) | ||
0.997027 | − | 0.0770481i | \(-0.0245495\pi\) | |||||||
\(578\) | 13.7323 | 0.571190 | ||||||||
\(579\) | 13.2134 | − | 13.2134i | 0.549130 | − | 0.549130i | ||||
\(580\) | 20.9701 | − | 11.1120i | 0.870738 | − | 0.461402i | ||||
\(581\) | −8.71076 | −0.361383 | ||||||||
\(582\) | 5.23361 | + | 5.23361i | 0.216940 | + | 0.216940i | ||||
\(583\) | 23.2586i | 0.963272i | ||||||||
\(584\) | −14.5716 | −0.602976 | ||||||||
\(585\) | −6.43950 | − | 4.85106i | −0.266241 | − | 0.200567i | ||||
\(586\) | −9.22562 | −0.381107 | ||||||||
\(587\) | − | 16.4699i | − | 0.679784i | −0.940464 | − | 0.339892i | \(-0.889609\pi\) | ||
0.940464 | − | 0.339892i | \(-0.110391\pi\) | |||||||
\(588\) | −0.380088 | − | 0.380088i | −0.0156746 | − | 0.0156746i | ||||
\(589\) | 12.2678 | 0.505488 | ||||||||
\(590\) | −7.22893 | + | 23.5258i | −0.297610 | + | 0.968542i | ||||
\(591\) | −3.75750 | + | 3.75750i | −0.154563 | + | 0.154563i | ||||
\(592\) | −3.18391 | −0.130858 | ||||||||
\(593\) | 45.4038i | 1.86451i | 0.361800 | + | 0.932256i | \(0.382162\pi\) | ||||
−0.361800 | + | 0.932256i | \(0.617838\pi\) | |||||||
\(594\) | − | 2.67974i | − | 0.109951i | ||||||
\(595\) | 3.01816 | − | 9.82227i | 0.123732 | − | 0.402674i | ||||
\(596\) | −10.2158 | − | 10.2158i | −0.418456 | − | 0.418456i | ||||
\(597\) | 9.92181 | + | 9.92181i | 0.406073 | + | 0.406073i | ||||
\(598\) | 0.542109 | − | 1.49668i | 0.0221685 | − | 0.0612038i | ||||
\(599\) | 27.0486i | 1.10517i | 0.833455 | + | 0.552587i | \(0.186359\pi\) | ||||
−0.833455 | + | 0.552587i | \(0.813641\pi\) | |||||||
\(600\) | −0.940168 | − | 4.91081i | −0.0383822 | − | 0.200483i | ||||
\(601\) | 20.2837 | 0.827391 | 0.413696 | − | 0.910415i | \(-0.364238\pi\) | ||||
0.413696 | + | 0.910415i | \(0.364238\pi\) | |||||||
\(602\) | 14.9610 | + | 14.9610i | 0.609763 | + | 0.609763i | ||||
\(603\) | 11.3845 | 0.463614 | ||||||||
\(604\) | 3.29704 | + | 3.29704i | 0.134155 | + | 0.134155i | ||||
\(605\) | 7.54557 | − | 3.99838i | 0.306771 | − | 0.162557i | ||||
\(606\) | −1.30077 | − | 1.30077i | −0.0528401 | − | 0.0528401i | ||||
\(607\) | 2.23846 | − | 2.23846i | 0.0908562 | − | 0.0908562i | −0.660218 | − | 0.751074i | \(-0.729536\pi\) |
0.751074 | + | 0.660218i | \(0.229536\pi\) | |||||||
\(608\) | −6.13392 | + | 6.13392i | −0.248763 | + | 0.248763i | ||||
\(609\) | 19.0783 | − | 19.0783i | 0.773093 | − | 0.773093i | ||||
\(610\) | −12.6731 | + | 6.71543i | −0.513117 | + | 0.271900i | ||||
\(611\) | −7.92495 | − | 16.9262i | −0.320609 | − | 0.684762i | ||||
\(612\) | −1.27822 | + | 1.27822i | −0.0516688 | + | 0.0516688i | ||||
\(613\) | −22.1399 | −0.894224 | −0.447112 | − | 0.894478i | \(-0.647547\pi\) | ||||
−0.447112 | + | 0.894478i | \(0.647547\pi\) | |||||||
\(614\) | − | 20.3901i | − | 0.822878i | ||||||
\(615\) | −7.06819 | − | 13.3388i | −0.285017 | − | 0.537871i | ||||
\(616\) | −4.81701 | + | 4.81701i | −0.194083 | + | 0.194083i | ||||
\(617\) | − | 24.8208i | − | 0.999249i | −0.866242 | − | 0.499625i | \(-0.833471\pi\) | ||
0.866242 | − | 0.499625i | \(-0.166529\pi\) | |||||||
\(618\) | − | 1.71479i | − | 0.0689791i | ||||||
\(619\) | −2.19943 | + | 2.19943i | −0.0884025 | + | 0.0884025i | −0.749925 | − | 0.661523i | \(-0.769911\pi\) |
0.661523 | + | 0.749925i | \(0.269911\pi\) | |||||||
\(620\) | −3.02279 | − | 0.928834i | −0.121398 | − | 0.0373029i | ||||
\(621\) | 0.441495i | 0.0177166i | ||||||||
\(622\) | 19.1186 | 0.766587 | ||||||||
\(623\) | −6.03773 | + | 6.03773i | −0.241896 | + | 0.241896i | ||||
\(624\) | 1.22789 | − | 3.39003i | 0.0491551 | − | 0.135710i | ||||
\(625\) | −9.23397 | − | 23.2322i | −0.369359 | − | 0.929287i | ||||
\(626\) | −1.87309 | + | 1.87309i | −0.0748638 | + | 0.0748638i | ||||
\(627\) | −16.4373 | + | 16.4373i | −0.656445 | + | 0.656445i | ||||
\(628\) | 12.2613 | − | 12.2613i | 0.489280 | − | 0.489280i | ||||
\(629\) | 4.06972 | + | 4.06972i | 0.162270 | + | 0.162270i | ||||
\(630\) | −2.66157 | − | 5.02279i | −0.106039 | − | 0.200113i | ||||
\(631\) | −23.0251 | − | 23.0251i | −0.916616 | − | 0.916616i | 0.0801660 | − | 0.996782i | \(-0.474455\pi\) |
−0.996782 | + | 0.0801660i | \(0.974455\pi\) | |||||||
\(632\) | 3.04259 | 0.121028 | ||||||||
\(633\) | 8.58349 | + | 8.58349i | 0.341163 | + | 0.341163i | ||||
\(634\) | −10.7007 | −0.424981 | ||||||||
\(635\) | −6.95017 | + | 22.6186i | −0.275809 | + | 0.897592i | ||||
\(636\) | − | 8.67941i | − | 0.344161i | ||||||
\(637\) | −0.821801 | − | 1.75522i | −0.0325609 | − | 0.0695442i | ||||
\(638\) | 20.1110 | + | 20.1110i | 0.796203 | + | 0.796203i | ||||
\(639\) | −7.30734 | − | 7.30734i | −0.289074 | − | 0.289074i | ||||
\(640\) | 1.97581 | − | 1.04698i | 0.0781008 | − | 0.0413855i | ||||
\(641\) | 23.0969i | 0.912275i | 0.889909 | + | 0.456137i | \(0.150767\pi\) | ||||
−0.889909 | + | 0.456137i | \(0.849233\pi\) | |||||||
\(642\) | − | 20.1939i | − | 0.796991i | ||||||
\(643\) | −41.5694 | −1.63934 | −0.819669 | − | 0.572838i | \(-0.805842\pi\) | ||||
−0.819669 | + | 0.572838i | \(0.805842\pi\) | |||||||
\(644\) | 0.793616 | − | 0.793616i | 0.0312729 | − | 0.0312729i | ||||
\(645\) | −8.71391 | − | 16.4445i | −0.343110 | − | 0.647502i | ||||
\(646\) | 15.6810 | 0.616959 | ||||||||
\(647\) | −30.3385 | − | 30.3385i | −1.19273 | − | 1.19273i | −0.976298 | − | 0.216432i | \(-0.930558\pi\) |
−0.216432 | − | 0.976298i | \(-0.569442\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −29.4947 | −1.15777 | ||||||||
\(650\) | 2.84276 | − | 17.8022i | 0.111502 | − | 0.698260i | ||||
\(651\) | −3.59513 | −0.140904 | ||||||||
\(652\) | 13.8216i | 0.541296i | ||||||||
\(653\) | 16.6272 | + | 16.6272i | 0.650673 | + | 0.650673i | 0.953155 | − | 0.302482i | \(-0.0978153\pi\) |
−0.302482 | + | 0.953155i | \(0.597815\pi\) | |||||||
\(654\) | −5.90798 | −0.231020 | ||||||||
\(655\) | 9.22182 | + | 17.4030i | 0.360326 | + | 0.679992i | ||||
\(656\) | 4.77370 | − | 4.77370i | 0.186382 | − | 0.186382i | ||||
\(657\) | 14.5716 | 0.568491 | ||||||||
\(658\) | − | 13.1774i | − | 0.513707i | ||||||
\(659\) | 22.8052i | 0.888365i | 0.895936 | + | 0.444182i | \(0.146506\pi\) | ||||
−0.895936 | + | 0.444182i | \(0.853494\pi\) | |||||||
\(660\) | 5.29467 | − | 2.80564i | 0.206095 | − | 0.109209i | ||||
\(661\) | −3.97661 | − | 3.97661i | −0.154672 | − | 0.154672i | 0.625529 | − | 0.780201i | \(-0.284883\pi\) |
−0.780201 | + | 0.625529i | \(0.784883\pi\) | |||||||
\(662\) | 5.98236 | + | 5.98236i | 0.232511 | + | 0.232511i | ||||
\(663\) | −5.90270 | + | 2.76367i | −0.229242 | + | 0.107332i | ||||
\(664\) | 3.42655i | 0.132976i | ||||||||
\(665\) | −14.4836 | + | 47.1353i | −0.561649 | + | 1.82783i | ||||
\(666\) | 3.18391 | 0.123374 | ||||||||
\(667\) | −3.31335 | − | 3.31335i | −0.128293 | − | 0.128293i | ||||
\(668\) | 17.5562 | 0.679268 | ||||||||
\(669\) | −9.90386 | − | 9.90386i | −0.382905 | − | 0.382905i | ||||
\(670\) | 11.9194 | + | 22.4937i | 0.460485 | + | 0.869007i | ||||
\(671\) | −12.1539 | − | 12.1539i | −0.469194 | − | 0.469194i | ||||
\(672\) | 1.79756 | − | 1.79756i | 0.0693425 | − | 0.0693425i | ||||
\(673\) | −9.80835 | + | 9.80835i | −0.378084 | + | 0.378084i | −0.870411 | − | 0.492327i | \(-0.836147\pi\) |
0.492327 | + | 0.870411i | \(0.336147\pi\) | |||||||
\(674\) | −14.5767 | + | 14.5767i | −0.561472 | + | 0.561472i | ||||
\(675\) | 0.940168 | + | 4.91081i | 0.0361871 | + | 0.189017i | ||||
\(676\) | 8.32518 | − | 9.98455i | 0.320199 | − | 0.384021i | ||||
\(677\) | −13.0375 | + | 13.0375i | −0.501071 | + | 0.501071i | −0.911771 | − | 0.410700i | \(-0.865285\pi\) |
0.410700 | + | 0.911771i | \(0.365285\pi\) | |||||||
\(678\) | −9.17986 | −0.352550 | ||||||||
\(679\) | 18.8155i | 0.722073i | ||||||||
\(680\) | −3.86378 | − | 1.18725i | −0.148169 | − | 0.0455290i | ||||
\(681\) | −5.06717 | + | 5.06717i | −0.194174 | + | 0.194174i | ||||
\(682\) | − | 3.78973i | − | 0.145116i | ||||||
\(683\) | − | 4.09726i | − | 0.156777i | −0.996923 | − | 0.0783887i | \(-0.975022\pi\) | ||
0.996923 | − | 0.0783887i | \(-0.0249775\pi\) | |||||||
\(684\) | 6.13392 | − | 6.13392i | 0.234536 | − | 0.234536i | ||||
\(685\) | −1.63024 | − | 3.07651i | −0.0622882 | − | 0.117548i | ||||
\(686\) | − | 19.1614i | − | 0.731587i | ||||||
\(687\) | 2.18251 | 0.0832681 | ||||||||
\(688\) | 5.88519 | − | 5.88519i | 0.224371 | − | 0.224371i | ||||
\(689\) | 10.6574 | − | 29.4234i | 0.406014 | − | 1.12094i | ||||
\(690\) | −0.872312 | + | 0.462236i | −0.0332083 | + | 0.0175970i | ||||
\(691\) | 9.86360 | − | 9.86360i | 0.375229 | − | 0.375229i | −0.494149 | − | 0.869377i | \(-0.664520\pi\) |
0.869377 | + | 0.494149i | \(0.164520\pi\) | |||||||
\(692\) | 1.23037 | − | 1.23037i | 0.0467715 | − | 0.0467715i | ||||
\(693\) | 4.81701 | − | 4.81701i | 0.182983 | − | 0.182983i | ||||
\(694\) | 13.7628 | + | 13.7628i | 0.522429 | + | 0.522429i | ||||
\(695\) | −0.0354035 | + | 0.0187603i | −0.00134293 | + | 0.000711617i | ||||
\(696\) | −7.50483 | − | 7.50483i | −0.284470 | − | 0.284470i | ||||
\(697\) | −12.2036 | −0.462246 | ||||||||
\(698\) | −13.0900 | − | 13.0900i | −0.495462 | − | 0.495462i | ||||
\(699\) | −5.67886 | −0.214794 | ||||||||
\(700\) | 7.13749 | − | 10.5175i | 0.269772 | − | 0.397525i | ||||
\(701\) | − | 20.4861i | − | 0.773749i | −0.922132 | − | 0.386875i | \(-0.873555\pi\) | ||
0.922132 | − | 0.386875i | \(-0.126445\pi\) | |||||||
\(702\) | −1.22789 | + | 3.39003i | −0.0463439 | + | 0.127948i | ||||
\(703\) | −19.5298 | − | 19.5298i | −0.736582 | − | 0.736582i | ||||
\(704\) | 1.89487 | + | 1.89487i | 0.0714154 | + | 0.0714154i | ||||
\(705\) | −3.40449 | + | 11.0796i | −0.128220 | + | 0.417280i | ||||
\(706\) | − | 31.4265i | − | 1.18275i | ||||||
\(707\) | − | 4.67643i | − | 0.175875i | ||||||
\(708\) | 11.0065 | 0.413651 | ||||||||
\(709\) | 12.6265 | − | 12.6265i | 0.474198 | − | 0.474198i | −0.429072 | − | 0.903270i | \(-0.641159\pi\) |
0.903270 | + | 0.429072i | \(0.141159\pi\) | |||||||
\(710\) | 6.78731 | − | 22.0886i | 0.254723 | − | 0.828969i | ||||
\(711\) | −3.04259 | −0.114106 | ||||||||
\(712\) | 2.37506 | + | 2.37506i | 0.0890090 | + | 0.0890090i | ||||
\(713\) | 0.624369i | 0.0233828i | ||||||||
\(714\) | −4.59535 | −0.171977 | ||||||||
\(715\) | 21.3941 | − | 3.00988i | 0.800094 | − | 0.112563i | ||||
\(716\) | 0.271184 | 0.0101346 | ||||||||
\(717\) | − | 0.351929i | − | 0.0131430i | ||||||
\(718\) | 19.6376 | + | 19.6376i | 0.732870 | + | 0.732870i | ||||
\(719\) | −26.6297 | −0.993121 | −0.496560 | − | 0.868002i | \(-0.665404\pi\) | ||||
−0.496560 | + | 0.868002i | \(0.665404\pi\) | |||||||
\(720\) | −1.97581 | + | 1.04698i | −0.0736342 | + | 0.0390186i | ||||
\(721\) | 3.08245 | − | 3.08245i | 0.114796 | − | 0.114796i | ||||
\(722\) | −56.2501 | −2.09341 | ||||||||
\(723\) | − | 22.7066i | − | 0.844468i | ||||||
\(724\) | 23.7110i | 0.881211i | ||||||||
\(725\) | −43.9106 | − | 29.7990i | −1.63080 | − | 1.10671i | ||||
\(726\) | −2.70042 | − | 2.70042i | −0.100222 | − | 0.100222i | ||||
\(727\) | −16.2441 | − | 16.2441i | −0.602459 | − | 0.602459i | 0.338506 | − | 0.940964i | \(-0.390079\pi\) |
−0.940964 | + | 0.338506i | \(0.890079\pi\) | |||||||
\(728\) | 8.30101 | − | 3.88657i | 0.307656 | − | 0.144046i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 15.2561 | + | 28.7907i | 0.564655 | + | 1.06559i | ||||
\(731\) | −15.0451 | −0.556462 | ||||||||
\(732\) | 4.53545 | + | 4.53545i | 0.167635 | + | 0.167635i | ||||
\(733\) | −11.8939 | −0.439312 | −0.219656 | − | 0.975577i | \(-0.570493\pi\) | ||||
−0.219656 | + | 0.975577i | \(0.570493\pi\) | |||||||
\(734\) | 6.26943 | + | 6.26943i | 0.231409 | + | 0.231409i | ||||
\(735\) | −0.353039 | + | 1.14893i | −0.0130220 | + | 0.0423788i | ||||
\(736\) | −0.312184 | − | 0.312184i | −0.0115073 | − | 0.0115073i | ||||
\(737\) | −21.5721 | + | 21.5721i | −0.794620 | + | 0.794620i | ||||
\(738\) | −4.77370 | + | 4.77370i | −0.175722 | + | 0.175722i | ||||
\(739\) | −13.3121 | + | 13.3121i | −0.489693 | + | 0.489693i | −0.908209 | − | 0.418517i | \(-0.862550\pi\) |
0.418517 | + | 0.908209i | \(0.362550\pi\) | |||||||
\(740\) | 3.33348 | + | 6.29080i | 0.122541 | + | 0.231255i | ||||
\(741\) | 28.3260 | − | 13.2624i | 1.04058 | − | 0.487205i | ||||
\(742\) | 15.6018 | − | 15.6018i | 0.572760 | − | 0.572760i | ||||
\(743\) | −45.7126 | −1.67703 | −0.838515 | − | 0.544878i | \(-0.816576\pi\) | ||||
−0.838515 | + | 0.544878i | \(0.816576\pi\) | |||||||
\(744\) | 1.41421i | 0.0518476i | ||||||||
\(745\) | −9.48880 | + | 30.8803i | −0.347643 | + | 1.13137i | ||||
\(746\) | −12.7183 | + | 12.7183i | −0.465651 | + | 0.465651i | ||||
\(747\) | − | 3.42655i | − | 0.125371i | ||||||
\(748\) | − | 4.84409i | − | 0.177118i | ||||||
\(749\) | 36.2999 | − | 36.2999i | 1.32637 | − | 1.32637i | ||||
\(750\) | −8.71851 | + | 6.99911i | −0.318355 | + | 0.255571i | ||||
\(751\) | 26.7596i | 0.976471i | 0.872712 | + | 0.488236i | \(0.162359\pi\) | ||||
−0.872712 | + | 0.488236i | \(0.837641\pi\) | |||||||
\(752\) | −5.18357 | −0.189025 | ||||||||
\(753\) | 14.4343 | − | 14.4343i | 0.526017 | − | 0.526017i | ||||
\(754\) | −16.2264 | − | 34.6567i | −0.590932 | − | 1.26212i | ||||
\(755\) | 3.06240 | − | 9.96627i | 0.111452 | − | 0.362710i | ||||
\(756\) | −1.79756 | + | 1.79756i | −0.0653768 | + | 0.0653768i | ||||
\(757\) | −8.63345 | + | 8.63345i | −0.313788 | + | 0.313788i | −0.846375 | − | 0.532587i | \(-0.821220\pi\) |
0.532587 | + | 0.846375i | \(0.321220\pi\) | |||||||
\(758\) | 8.37591 | − | 8.37591i | 0.304227 | − | 0.304227i | ||||
\(759\) | −0.836574 | − | 0.836574i | −0.0303657 | − | 0.0303657i | ||||
\(760\) | 18.5416 | + | 5.69740i | 0.672574 | + | 0.206666i | ||||
\(761\) | 4.99238 | + | 4.99238i | 0.180973 | + | 0.180973i | 0.791780 | − | 0.610806i | \(-0.209155\pi\) |
−0.610806 | + | 0.791780i | \(0.709155\pi\) | |||||||
\(762\) | 10.5821 | 0.383350 | ||||||||
\(763\) | −10.6200 | − | 10.6200i | −0.384469 | − | 0.384469i | ||||
\(764\) | −8.88620 | −0.321492 | ||||||||
\(765\) | 3.86378 | + | 1.18725i | 0.139695 | + | 0.0429251i | ||||
\(766\) | 1.62824i | 0.0588306i | ||||||||
\(767\) | 37.3125 | + | 13.5149i | 1.34728 | + | 0.487994i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | −34.2212 | − | 34.2212i | −1.23405 | − | 1.23405i | −0.962395 | − | 0.271653i | \(-0.912430\pi\) |
−0.271653 | − | 0.962395i | \(-0.587570\pi\) | |||||||
\(770\) | 14.5608 | + | 4.47420i | 0.524736 | + | 0.161239i | ||||
\(771\) | 17.7405i | 0.638908i | ||||||||
\(772\) | − | 18.6866i | − | 0.672544i | ||||||
\(773\) | 16.3484 | 0.588010 | 0.294005 | − | 0.955804i | \(-0.405012\pi\) | ||||
0.294005 | + | 0.955804i | \(0.405012\pi\) | |||||||
\(774\) | −5.88519 | + | 5.88519i | −0.211539 | + | 0.211539i | ||||
\(775\) | 1.32960 | + | 6.94494i | 0.0477606 | + | 0.249470i | ||||
\(776\) | 7.40145 | 0.265696 | ||||||||
\(777\) | 5.72328 | + | 5.72328i | 0.205321 | + | 0.205321i | ||||
\(778\) | 5.38166i | 0.192942i | ||||||||
\(779\) | 58.5631 | 2.09824 | ||||||||
\(780\) | −7.98363 | + | 1.12320i | −0.285860 | + | 0.0402169i | ||||
\(781\) | 27.6929 | 0.990928 | ||||||||
\(782\) | 0.798078i | 0.0285392i | ||||||||
\(783\) | 7.50483 | + | 7.50483i | 0.268201 | + | 0.268201i | ||||
\(784\) | −0.537526 | −0.0191974 | ||||||||
\(785\) | −37.0634 | − | 11.3887i | −1.32285 | − | 0.406481i | ||||
\(786\) | 6.22822 | − | 6.22822i | 0.222153 | − | 0.222153i | ||||
\(787\) | −21.5385 | −0.767766 | −0.383883 | − | 0.923382i | \(-0.625413\pi\) | ||||
−0.383883 | + | 0.923382i | \(0.625413\pi\) | |||||||
\(788\) | 5.31391i | 0.189300i | ||||||||
\(789\) | 4.81134i | 0.171288i | ||||||||
\(790\) | −3.18553 | − | 6.01159i | −0.113336 | − | 0.213883i | ||||
\(791\) | −16.5014 | − | 16.5014i | −0.586722 | − | 0.586722i | ||||
\(792\) | −1.89487 | − | 1.89487i | −0.0673311 | − | 0.0673311i | ||||
\(793\) | 9.80625 | + | 20.9444i | 0.348230 | + | 0.743756i | ||||
\(794\) | 11.3423i | 0.402523i | ||||||||
\(795\) | −17.1489 | + | 9.08716i | −0.608208 | + | 0.322288i | ||||
\(796\) | 14.0316 | 0.497335 | ||||||||
\(797\) | 28.9089 | + | 28.9089i | 1.02401 | + | 1.02401i | 0.999705 | + | 0.0243011i | \(0.00773604\pi\) |
0.0243011 | + | 0.999705i | \(0.492264\pi\) | |||||||
\(798\) | 22.0522 | 0.780641 | ||||||||
\(799\) | 6.62572 | + | 6.62572i | 0.234401 | + | 0.234401i | ||||
\(800\) | −4.13727 | − | 2.80767i | −0.146275 | − | 0.0992661i | ||||
\(801\) | −2.37506 | − | 2.37506i | −0.0839185 | − | 0.0839185i | ||||
\(802\) | 15.9787 | − | 15.9787i | 0.564226 | − | 0.564226i | ||||
\(803\) | −27.6112 | + | 27.6112i | −0.974377 | + | 0.974377i | ||||
\(804\) | 8.05007 | − | 8.05007i | 0.283904 | − | 0.283904i | ||||
\(805\) | −2.39894 | − | 0.737137i | −0.0845514 | − | 0.0259807i | ||||
\(806\) | −1.73650 | + | 4.79422i | −0.0611657 | + | 0.168869i | ||||
\(807\) | −8.22561 | + | 8.22561i | −0.289555 | + | 0.289555i | ||||
\(808\) | −1.83957 | −0.0647157 | ||||||||
\(809\) | − | 2.34413i | − | 0.0824152i | −0.999151 | − | 0.0412076i | \(-0.986880\pi\) | ||
0.999151 | − | 0.0412076i | \(-0.0131205\pi\) | |||||||
\(810\) | 1.97581 | − | 1.04698i | 0.0694230 | − | 0.0367871i | ||||
\(811\) | 14.4497 | − | 14.4497i | 0.507397 | − | 0.507397i | −0.406329 | − | 0.913727i | \(-0.633191\pi\) |
0.913727 | + | 0.406329i | \(0.133191\pi\) | |||||||
\(812\) | − | 26.9808i | − | 0.946841i | ||||||
\(813\) | 21.8343i | 0.765762i | ||||||||
\(814\) | −6.03307 | + | 6.03307i | −0.211459 | + | 0.211459i | ||||
\(815\) | 27.3089 | − | 14.4709i | 0.956589 | − | 0.506894i | ||||
\(816\) | 1.80767i | 0.0632811i | ||||||||
\(817\) | 72.1986 | 2.52591 | ||||||||
\(818\) | 9.21508 | − | 9.21508i | 0.322198 | − | 0.322198i | ||||
\(819\) | −8.30101 | + | 3.88657i | −0.290061 | + | 0.135808i | ||||
\(820\) | −14.4299 | − | 4.43398i | −0.503914 | − | 0.154841i | ||||
\(821\) | 25.0645 | − | 25.0645i | 0.874757 | − | 0.874757i | −0.118230 | − | 0.992986i | \(-0.537722\pi\) |
0.992986 | + | 0.118230i | \(0.0377219\pi\) | |||||||
\(822\) | −1.10103 | + | 1.10103i | −0.0384027 | + | 0.0384027i | ||||
\(823\) | 14.0958 | − | 14.0958i | 0.491350 | − | 0.491350i | −0.417381 | − | 0.908731i | \(-0.637052\pi\) |
0.908731 | + | 0.417381i | \(0.137052\pi\) | |||||||
\(824\) | −1.21254 | − | 1.21254i | −0.0422409 | − | 0.0422409i | ||||
\(825\) | −11.0868 | − | 7.52384i | −0.385994 | − | 0.261946i | ||||
\(826\) | 19.7850 | + | 19.7850i | 0.688408 | + | 0.688408i | ||||
\(827\) | −15.8830 | −0.552308 | −0.276154 | − | 0.961113i | \(-0.589060\pi\) | ||||
−0.276154 | + | 0.961113i | \(0.589060\pi\) | |||||||
\(828\) | 0.312184 | + | 0.312184i | 0.0108492 | + | 0.0108492i | ||||
\(829\) | 32.4225 | 1.12608 | 0.563040 | − | 0.826429i | \(-0.309632\pi\) | ||||
0.563040 | + | 0.826429i | \(0.309632\pi\) | |||||||
\(830\) | 6.77022 | − | 3.58752i | 0.234998 | − | 0.124525i | ||||
\(831\) | − | 16.2726i | − | 0.564491i | ||||||
\(832\) | −1.52886 | − | 3.26536i | −0.0530036 | − | 0.113206i | ||||
\(833\) | 0.687074 | + | 0.687074i | 0.0238057 | + | 0.0238057i | ||||
\(834\) | 0.0126703 | + | 0.0126703i | 0.000438736 | + | 0.000438736i | ||||
\(835\) | −18.3809 | − | 34.6877i | −0.636098 | − | 1.20042i | ||||
\(836\) | 23.2459i | 0.803977i | ||||||||
\(837\) | − | 1.41421i | − | 0.0488824i | ||||||
\(838\) | −22.6047 | −0.780868 | ||||||||
\(839\) | −11.9605 | + | 11.9605i | −0.412922 | + | 0.412922i | −0.882755 | − | 0.469833i | \(-0.844314\pi\) |
0.469833 | + | 0.882755i | \(0.344314\pi\) | |||||||
\(840\) | −5.43366 | − | 1.66964i | −0.187479 | − | 0.0576080i | ||||
\(841\) | −83.6449 | −2.88431 | ||||||||
\(842\) | 0.328119 | + | 0.328119i | 0.0113077 | + | 0.0113077i | ||||
\(843\) | − | 22.3618i | − | 0.770182i | ||||||
\(844\) | 12.1389 | 0.417838 | ||||||||
\(845\) | −28.4439 | − | 5.99539i | −0.978500 | − | 0.206248i | ||||
\(846\) | 5.18357 | 0.178215 | ||||||||
\(847\) | − | 9.70836i | − | 0.333583i | ||||||
\(848\) | −6.13727 | − | 6.13727i | −0.210755 | − | 0.210755i | ||||
\(849\) | −10.2672 | −0.352369 | ||||||||
\(850\) | 1.69951 | + | 8.87713i | 0.0582928 | + | 0.304483i | ||||
\(851\) | 0.993966 | − | 0.993966i | 0.0340727 | − | 0.0340727i | ||||
\(852\) | −10.3341 | −0.354042 | ||||||||
\(853\) | 27.1504i | 0.929611i | 0.885413 | + | 0.464806i | \(0.153876\pi\) | ||||
−0.885413 | + | 0.464806i | \(0.846124\pi\) | |||||||
\(854\) | 16.3055i | 0.557964i | ||||||||
\(855\) | −18.5416 | − | 5.69740i | −0.634108 | − | 0.194847i | ||||
\(856\) | −14.2793 | − | 14.2793i | −0.488055 | − | 0.488055i | ||||
\(857\) | 5.31779 | + | 5.31779i | 0.181652 | + | 0.181652i | 0.792075 | − | 0.610423i | \(-0.209001\pi\) |
−0.610423 | + | 0.792075i | \(0.709001\pi\) | |||||||
\(858\) | −4.09695 | − | 8.75034i | −0.139868 | − | 0.298732i | ||||
\(859\) | − | 9.67551i | − | 0.330124i | −0.986283 | − | 0.165062i | \(-0.947218\pi\) | ||
0.986283 | − | 0.165062i | \(-0.0527824\pi\) | |||||||
\(860\) | −17.7897 | − | 5.46636i | −0.606623 | − | 0.186401i | ||||
\(861\) | −17.1621 | −0.584882 | ||||||||
\(862\) | −1.62855 | − | 1.62855i | −0.0554687 | − | 0.0554687i | ||||
\(863\) | 11.6460 | 0.396435 | 0.198217 | − | 0.980158i | \(-0.436485\pi\) | ||||
0.198217 | + | 0.980158i | \(0.436485\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | −3.71914 | − | 1.14281i | −0.126455 | − | 0.0388566i | ||||
\(866\) | 24.3982 | + | 24.3982i | 0.829084 | + | 0.829084i | ||||
\(867\) | −9.71022 | + | 9.71022i | −0.329776 | + | 0.329776i | ||||
\(868\) | −2.54214 | + | 2.54214i | −0.0862858 | + | 0.0862858i | ||||
\(869\) | 5.76530 | − | 5.76530i | 0.195574 | − | 0.195574i | ||||
\(870\) | −6.97074 | + | 22.6855i | −0.236330 | + | 0.769111i | ||||
\(871\) | 37.1746 | − | 17.4053i | 1.25961 | − | 0.589757i | ||||
\(872\) | −4.17757 | + | 4.17757i | −0.141470 | + | 0.141470i | ||||
\(873\) | −7.40145 | −0.250501 | ||||||||
\(874\) | − | 3.82983i | − | 0.129546i | ||||||
\(875\) | −28.2534 | − | 3.09073i | −0.955140 | − | 0.104486i | ||||
\(876\) | 10.3037 | − | 10.3037i | 0.348129 | − | 0.348129i | ||||
\(877\) | − | 47.1519i | − | 1.59221i | −0.605160 | − | 0.796104i | \(-0.706891\pi\) | ||
0.605160 | − | 0.796104i | \(-0.293109\pi\) | |||||||
\(878\) | − | 26.5637i | − | 0.896483i | ||||||
\(879\) | 6.52350 | − | 6.52350i | 0.220032 | − | 0.220032i | ||||
\(880\) | 1.76001 | − | 5.72778i | 0.0593301 | − | 0.193084i | ||||
\(881\) | − | 31.6068i | − | 1.06486i | −0.846474 | − | 0.532430i | \(-0.821279\pi\) | ||
0.846474 | − | 0.532430i | \(-0.178721\pi\) | |||||||
\(882\) | 0.537526 | 0.0180994 | ||||||||
\(883\) | −3.02122 | + | 3.02122i | −0.101672 | + | 0.101672i | −0.756113 | − | 0.654441i | \(-0.772904\pi\) |
0.654441 | + | 0.756113i | \(0.272904\pi\) | |||||||
\(884\) | −2.21963 | + | 6.12805i | −0.0746541 | + | 0.206109i | ||||
\(885\) | −11.5236 | − | 21.7469i | −0.387362 | − | 0.731013i | ||||
\(886\) | −17.7803 | + | 17.7803i | −0.597339 | + | 0.597339i | ||||
\(887\) | 20.4002 | − | 20.4002i | 0.684972 | − | 0.684972i | −0.276144 | − | 0.961116i | \(-0.589057\pi\) |
0.961116 | + | 0.276144i | \(0.0890566\pi\) | |||||||
\(888\) | 2.25136 | − | 2.25136i | 0.0755508 | − | 0.0755508i | ||||
\(889\) | 19.0220 | + | 19.0220i | 0.637979 | + | 0.637979i | ||||
\(890\) | 2.20603 | − | 7.17930i | 0.0739464 | − | 0.240651i | ||||
\(891\) | 1.89487 | + | 1.89487i | 0.0634804 | + | 0.0634804i | ||||
\(892\) | −14.0062 | −0.468961 | ||||||||
\(893\) | −31.7956 | − | 31.7956i | −1.06400 | − | 1.06400i | ||||
\(894\) | 14.4473 | 0.483192 | ||||||||
\(895\) | −0.283924 | − | 0.535809i | −0.00949053 | − | 0.0179101i | ||||
\(896\) | − | 2.54214i | − | 0.0849269i | ||||||
\(897\) | 0.674984 | + | 1.44164i | 0.0225371 | + | 0.0481350i | ||||
\(898\) | 0.365829 | + | 0.365829i | 0.0122079 | + | 0.0122079i | ||||
\(899\) | 10.6134 | + | 10.6134i | 0.353978 | + | 0.353978i | ||||
\(900\) | 4.13727 | + | 2.80767i | 0.137909 | + | 0.0935890i | ||||
\(901\) | 15.6895i | 0.522693i | ||||||||
\(902\) | − | 18.0910i | − | 0.602366i | ||||||
\(903\) | −21.1580 | −0.704094 | ||||||||
\(904\) | −6.49114 | + | 6.49114i | −0.215892 | + | 0.215892i | ||||
\(905\) | 46.8484 | − | 24.8249i | 1.55729 | − | 0.825207i | ||||
\(906\) | −4.66272 | −0.154909 | ||||||||
\(907\) | 23.6195 | + | 23.6195i | 0.784274 | + | 0.784274i | 0.980549 | − | 0.196275i | \(-0.0628845\pi\) |
−0.196275 | + | 0.980549i | \(0.562884\pi\) | |||||||
\(908\) | 7.16607i | 0.237814i | ||||||||
\(909\) | 1.83957 | 0.0610145 | ||||||||
\(910\) | −16.3701 | − | 12.3321i | −0.542664 | − | 0.408804i | ||||
\(911\) | 27.6160 | 0.914959 | 0.457479 | − | 0.889220i | \(-0.348752\pi\) | ||||
0.457479 | + | 0.889220i | \(0.348752\pi\) | |||||||
\(912\) | − | 8.67468i | − | 0.287247i | ||||||
\(913\) | 6.49285 | + | 6.49285i | 0.214882 | + | 0.214882i | ||||
\(914\) | 13.6966 | 0.453043 | ||||||||
\(915\) | 4.21268 | − | 13.7097i | 0.139267 | − | 0.453230i | ||||
\(916\) | 1.54327 | − | 1.54327i | 0.0509911 | − | 0.0509911i | ||||
\(917\) | 22.3912 | 0.739424 | ||||||||
\(918\) | − | 1.80767i | − | 0.0596620i | ||||||
\(919\) | 43.2829i | 1.42777i | 0.700262 | + | 0.713886i | \(0.253066\pi\) | ||||
−0.700262 | + | 0.713886i | \(0.746934\pi\) | |||||||
\(920\) | −0.289967 | + | 0.943668i | −0.00955994 | + | 0.0311118i | ||||
\(921\) | 14.4180 | + | 14.4180i | 0.475089 | + | 0.475089i | ||||
\(922\) | 6.04660 | + | 6.04660i | 0.199134 | + | 0.199134i | ||||
\(923\) | −35.0330 | − | 12.6892i | −1.15313 | − | 0.417671i | ||||
\(924\) | − | 6.81228i | − | 0.224108i | ||||||
\(925\) | 8.93936 | − | 13.1727i | 0.293924 | − | 0.433115i | ||||
\(926\) | 10.1801 | 0.334538 | ||||||||
\(927\) | 1.21254 | + | 1.21254i | 0.0398251 | + | 0.0398251i | ||||
\(928\) | −10.6134 | −0.348403 | ||||||||
\(929\) | −25.4271 | − | 25.4271i | −0.834234 | − | 0.834234i | 0.153858 | − | 0.988093i | \(-0.450830\pi\) |
−0.988093 | + | 0.153858i | \(0.950830\pi\) | |||||||
\(930\) | 2.79422 | − | 1.48065i | 0.0916261 | − | 0.0485525i | ||||
\(931\) | −3.29714 | − | 3.29714i | −0.108060 | − | 0.108060i | ||||
\(932\) | −4.01556 | + | 4.01556i | −0.131534 | + | 0.131534i | ||||
\(933\) | −13.5189 | + | 13.5189i | −0.442589 | + | 0.442589i | ||||
\(934\) | −18.6160 | + | 18.6160i | −0.609135 | + | 0.609135i | ||||
\(935\) | −9.57102 | + | 5.07166i | −0.313006 | + | 0.165861i | ||||
\(936\) | 1.52886 | + | 3.26536i | 0.0499723 | + | 0.106732i | ||||
\(937\) | −27.4781 | + | 27.4781i | −0.897670 | + | 0.897670i | −0.995230 | − | 0.0975600i | \(-0.968896\pi\) |
0.0975600 | + | 0.995230i | \(0.468896\pi\) | |||||||
\(938\) | 28.9410 | 0.944959 | ||||||||
\(939\) | − | 2.64895i | − | 0.0864452i | ||||||
\(940\) | 5.42709 | + | 10.2418i | 0.177012 | + | 0.334049i | ||||
\(941\) | 25.6263 | − | 25.6263i | 0.835394 | − | 0.835394i | −0.152854 | − | 0.988249i | \(-0.548847\pi\) |
0.988249 | + | 0.152854i | \(0.0488465\pi\) | |||||||
\(942\) | 17.3401i | 0.564972i | ||||||||
\(943\) | 2.98055i | 0.0970600i | ||||||||
\(944\) | 7.78281 | − | 7.78281i | 0.253309 | − | 0.253309i | ||||
\(945\) | 5.43366 | + | 1.66964i | 0.176757 | + | 0.0543133i | ||||
\(946\) | − | 22.3033i | − | 0.725142i | ||||||
\(947\) | −25.4751 | −0.827828 | −0.413914 | − | 0.910316i | \(-0.635839\pi\) | ||||
−0.413914 | + | 0.910316i | \(0.635839\pi\) | |||||||
\(948\) | −2.15144 | + | 2.15144i | −0.0698754 | + | 0.0698754i | ||||
\(949\) | 47.5815 | − | 22.2779i | 1.54456 | − | 0.723171i | ||||
\(950\) | −8.15565 | − | 42.5997i | −0.264604 | − | 1.38212i | ||||
\(951\) | 7.56657 | − | 7.56657i | 0.245363 | − | 0.245363i | ||||
\(952\) | −3.24940 | + | 3.24940i | −0.105314 | + | 0.105314i | ||||
\(953\) | −3.21451 | + | 3.21451i | −0.104128 | + | 0.104128i | −0.757252 | − | 0.653123i | \(-0.773458\pi\) |
0.653123 | + | 0.757252i | \(0.273458\pi\) | |||||||
\(954\) | 6.13727 | + | 6.13727i | 0.198701 | + | 0.198701i | ||||
\(955\) | 9.30367 | + | 17.5575i | 0.301060 | + | 0.568147i | ||||
\(956\) | −0.248851 | − | 0.248851i | −0.00804843 | − | 0.00804843i | ||||
\(957\) | −28.4413 | −0.919376 | ||||||||
\(958\) | −19.0736 | − | 19.0736i | −0.616240 | − | 0.616240i | ||||
\(959\) | −3.95833 | −0.127821 | ||||||||
\(960\) | −0.656785 | + | 2.13744i | −0.0211976 | + | 0.0689855i | ||||
\(961\) | 29.0000i | 0.935484i | ||||||||
\(962\) | 10.3966 | − | 4.86774i | 0.335200 | − | 0.156942i | ||||
\(963\) | 14.2793 | + | 14.2793i | 0.460143 | + | 0.460143i | ||||
\(964\) | −16.0560 | − | 16.0560i | −0.517129 | − | 0.517129i | ||||
\(965\) | −36.9212 | + | 19.5644i | −1.18853 | + | 0.629802i | ||||
\(966\) | 1.12234i | 0.0361108i | ||||||||
\(967\) | − | 45.0288i | − | 1.44803i | −0.689785 | − | 0.724014i | \(-0.742295\pi\) | ||
0.689785 | − | 0.724014i | \(-0.257705\pi\) | |||||||
\(968\) | −3.81897 | −0.122746 | ||||||||
\(969\) | −11.0881 | + | 11.0881i | −0.356202 | + | 0.356202i | ||||
\(970\) | −7.74916 | − | 14.6239i | −0.248810 | − | 0.469544i | ||||
\(971\) | −4.63059 | −0.148603 | −0.0743013 | − | 0.997236i | \(-0.523673\pi\) | ||||
−0.0743013 | + | 0.997236i | \(0.523673\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 0.0455513i | 0.00146031i | ||||||||
\(974\) | −0.609311 | −0.0195236 | ||||||||
\(975\) | 10.5779 | + | 14.5982i | 0.338765 | + | 0.467517i | ||||
\(976\) | 6.41410 | 0.205310 | ||||||||
\(977\) | 51.1169i | 1.63538i | 0.575662 | + | 0.817688i | \(0.304744\pi\) | ||||
−0.575662 | + | 0.817688i | \(0.695256\pi\) | |||||||
\(978\) | −9.77335 | − | 9.77335i | −0.312517 | − | 0.312517i | ||||
\(979\) | 9.00083 | 0.287668 | ||||||||
\(980\) | 0.562778 | + | 1.06205i | 0.0179773 | + | 0.0339260i | ||||
\(981\) | 4.17757 | − | 4.17757i | 0.133380 | − | 0.133380i | ||||
\(982\) | 5.96894 | 0.190476 | ||||||||
\(983\) | 29.8942i | 0.953478i | 0.879045 | + | 0.476739i | \(0.158181\pi\) | ||||
−0.879045 | + | 0.476739i | \(0.841819\pi\) | |||||||
\(984\) | 6.75103i | 0.215215i | ||||||||
\(985\) | 10.4993 | − | 5.56355i | 0.334535 | − | 0.177269i | ||||
\(986\) | 13.5663 | + | 13.5663i | 0.432038 | + | 0.432038i | ||||
\(987\) | 9.31780 | + | 9.31780i | 0.296589 | + | 0.296589i | ||||
\(988\) | 10.6516 | − | 29.4074i | 0.338872 | − | 0.935574i | ||||
\(989\) | 3.67453i | 0.116843i | ||||||||
\(990\) | −1.76001 | + | 5.72778i | −0.0559369 | + | 0.182041i | ||||
\(991\) | 11.5138 | 0.365749 | 0.182874 | − | 0.983136i | \(-0.441460\pi\) | ||||
0.182874 | + | 0.983136i | \(0.441460\pi\) | |||||||
\(992\) | 1.00000 | + | 1.00000i | 0.0317500 | + | 0.0317500i | ||||
\(993\) | −8.46034 | −0.268481 | ||||||||
\(994\) | −18.5763 | − | 18.5763i | −0.589204 | − | 0.589204i | ||||
\(995\) | −14.6907 | − | 27.7237i | −0.465728 | − | 0.878901i | ||||
\(996\) | −2.42293 | − | 2.42293i | −0.0767736 | − | 0.0767736i | ||||
\(997\) | −21.2452 | + | 21.2452i | −0.672841 | + | 0.672841i | −0.958370 | − | 0.285529i | \(-0.907831\pi\) |
0.285529 | + | 0.958370i | \(0.407831\pi\) | |||||||
\(998\) | 30.0733 | − | 30.0733i | 0.951954 | − | 0.951954i | ||||
\(999\) | −2.25136 | + | 2.25136i | −0.0712299 | + | 0.0712299i |
(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 | 390.2.t.a.343.2 | yes | 12 | |
3.2 | odd | 2 | 1170.2.w.f.343.2 | 12 | |||
5.2 | odd | 4 | 390.2.j.a.187.1 | yes | 12 | ||
5.3 | odd | 4 | 1950.2.j.c.1357.4 | 12 | |||
5.4 | even | 2 | 1950.2.t.b.343.4 | 12 | |||
13.8 | odd | 4 | 390.2.j.a.73.1 | ✓ | 12 | ||
15.2 | even | 4 | 1170.2.m.f.577.5 | 12 | |||
39.8 | even | 4 | 1170.2.m.f.73.5 | 12 | |||
65.8 | even | 4 | 1950.2.t.b.307.4 | 12 | |||
65.34 | odd | 4 | 1950.2.j.c.1243.6 | 12 | |||
65.47 | even | 4 | inner | 390.2.t.a.307.2 | yes | 12 | |
195.47 | odd | 4 | 1170.2.w.f.307.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.j.a.73.1 | ✓ | 12 | 13.8 | odd | 4 | ||
390.2.j.a.187.1 | yes | 12 | 5.2 | odd | 4 | ||
390.2.t.a.307.2 | yes | 12 | 65.47 | even | 4 | inner | |
390.2.t.a.343.2 | yes | 12 | 1.1 | even | 1 | trivial | |
1170.2.m.f.73.5 | 12 | 39.8 | even | 4 | |||
1170.2.m.f.577.5 | 12 | 15.2 | even | 4 | |||
1170.2.w.f.307.2 | 12 | 195.47 | odd | 4 | |||
1170.2.w.f.343.2 | 12 | 3.2 | odd | 2 | |||
1950.2.j.c.1243.6 | 12 | 65.34 | odd | 4 | |||
1950.2.j.c.1357.4 | 12 | 5.3 | odd | 4 | |||
1950.2.t.b.307.4 | 12 | 65.8 | even | 4 | |||
1950.2.t.b.343.4 | 12 | 5.4 | even | 2 |