Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.bc (of order \(6\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 751.2 | ||
Root | \(0.500000 + 0.414256i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.751 |
Dual form | 1950.2.bc.k.901.2 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | 0.242731 | + | 0.140141i | 0.0917436 | + | 0.0529682i | 0.545170 | − | 0.838326i | \(-0.316465\pi\) |
−0.453426 | + | 0.891294i | \(0.649798\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.663862 | − | 0.383281i | 0.200162 | − | 0.115564i | −0.396569 | − | 0.918005i | \(-0.629799\pi\) |
0.596731 | + | 0.802441i | \(0.296466\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.77303 | + | 2.30441i | −0.769100 | + | 0.639129i | ||||
\(14\) | −0.280281 | −0.0749083 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.10917 | + | 1.92113i | −0.269012 | + | 0.465943i | −0.968607 | − | 0.248597i | \(-0.920031\pi\) |
0.699595 | + | 0.714540i | \(0.253364\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −4.57097 | − | 2.63905i | −1.04865 | − | 0.605440i | −0.126381 | − | 0.991982i | \(-0.540336\pi\) |
−0.922272 | + | 0.386541i | \(0.873670\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.280281i | 0.0611624i | ||||||||
\(22\) | −0.383281 | + | 0.663862i | −0.0817158 | + | 0.141536i | ||||
\(23\) | −0.725885 | − | 1.25727i | −0.151357 | − | 0.262159i | 0.780369 | − | 0.625319i | \(-0.215031\pi\) |
−0.931727 | + | 0.363160i | \(0.881698\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.24931 | − | 3.38219i | 0.245009 | − | 0.663303i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.242731 | − | 0.140141i | 0.0458718 | − | 0.0264841i | ||||
\(29\) | −3.03030 | − | 5.24863i | −0.562712 | − | 0.974646i | −0.997259 | − | 0.0739965i | \(-0.976425\pi\) |
0.434546 | − | 0.900649i | \(-0.356909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.28110i | 0.589303i | 0.955605 | + | 0.294652i | \(0.0952036\pi\) | ||||
−0.955605 | + | 0.294652i | \(0.904796\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0.663862 | + | 0.383281i | 0.115564 | + | 0.0667207i | ||||
\(34\) | − | 2.21833i | − | 0.380441i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −3.07097 | + | 1.77303i | −0.504865 | + | 0.291484i | −0.730720 | − | 0.682677i | \(-0.760816\pi\) |
0.225855 | + | 0.974161i | \(0.427482\pi\) | |||||||
\(38\) | 5.27811 | 0.856222 | ||||||||
\(39\) | −3.38219 | − | 1.24931i | −0.541584 | − | 0.200049i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92113 | − | 1.10917i | 0.300030 | − | 0.173223i | −0.342426 | − | 0.939545i | \(-0.611249\pi\) |
0.642457 | + | 0.766322i | \(0.277915\pi\) | |||||||
\(42\) | −0.140141 | − | 0.242731i | −0.0216242 | − | 0.0374542i | ||||
\(43\) | −1.80441 | + | 3.12533i | −0.275170 | + | 0.476609i | −0.970178 | − | 0.242393i | \(-0.922068\pi\) |
0.695008 | + | 0.719002i | \(0.255401\pi\) | |||||||
\(44\) | − | 0.766562i | − | 0.115564i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25727 | + | 0.725885i | 0.185374 | + | 0.107026i | ||||
\(47\) | 1.06277i | 0.155021i | 0.996992 | + | 0.0775104i | \(0.0246971\pi\) | ||||
−0.996992 | + | 0.0775104i | \(0.975303\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −3.46072 | − | 5.99414i | −0.494389 | − | 0.856306i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.21833 | −0.310629 | ||||||||
\(52\) | 0.609166 | + | 3.55372i | 0.0844761 | + | 0.492812i | ||||
\(53\) | 3.28110 | 0.450694 | 0.225347 | − | 0.974279i | \(-0.427648\pi\) | ||||
0.225347 | + | 0.974279i | \(0.427648\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.140141 | + | 0.242731i | −0.0187271 | + | 0.0324362i | ||||
\(57\) | − | 5.27811i | − | 0.699102i | ||||||
\(58\) | 5.24863 | + | 3.03030i | 0.689179 | + | 0.397898i | ||||
\(59\) | −4.32824 | − | 2.49891i | −0.563489 | − | 0.325331i | 0.191055 | − | 0.981579i | \(-0.438809\pi\) |
−0.754545 | + | 0.656249i | \(0.772142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.773028 | + | 1.33892i | −0.0989761 | + | 0.171432i | −0.911261 | − | 0.411829i | \(-0.864890\pi\) |
0.812285 | + | 0.583261i | \(0.198223\pi\) | |||||||
\(62\) | −1.64055 | − | 2.84152i | −0.208350 | − | 0.360873i | ||||
\(63\) | −0.242731 | + | 0.140141i | −0.0305812 | + | 0.0176561i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.766562 | −0.0943573 | ||||||||
\(67\) | −6.43963 | + | 3.71792i | −0.786726 | + | 0.454216i | −0.838809 | − | 0.544426i | \(-0.816747\pi\) |
0.0520827 | + | 0.998643i | \(0.483414\pi\) | |||||||
\(68\) | 1.10917 | + | 1.92113i | 0.134506 | + | 0.232971i | ||||
\(69\) | 0.725885 | − | 1.25727i | 0.0873863 | − | 0.151357i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.09811 | − | 1.21135i | −0.249000 | − | 0.143760i | 0.370306 | − | 0.928910i | \(-0.379253\pi\) |
−0.619306 | + | 0.785149i | \(0.712586\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 14.2630i | 1.66936i | 0.550737 | + | 0.834679i | \(0.314347\pi\) | ||||
−0.550737 | + | 0.834679i | \(0.685653\pi\) | |||||||
\(74\) | 1.77303 | − | 3.07097i | 0.206110 | − | 0.356994i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.57097 | + | 2.63905i | −0.524327 | + | 0.302720i | ||||
\(77\) | 0.214853 | 0.0244848 | ||||||||
\(78\) | 3.55372 | − | 0.609166i | 0.402379 | − | 0.0689744i | ||||
\(79\) | −14.4715 | −1.62817 | −0.814085 | − | 0.580746i | \(-0.802761\pi\) | ||||
−0.814085 | + | 0.580746i | \(0.802761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.10917 | + | 1.92113i | −0.122487 | + | 0.212153i | ||||
\(83\) | − | 4.42419i | − | 0.485617i | −0.970074 | − | 0.242809i | \(-0.921931\pi\) | ||
0.970074 | − | 0.242809i | \(-0.0780687\pi\) | |||||||
\(84\) | 0.242731 | + | 0.140141i | 0.0264841 | + | 0.0152906i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 3.60882i | − | 0.389150i | ||||||
\(87\) | 3.03030 | − | 5.24863i | 0.324882 | − | 0.562712i | ||||
\(88\) | 0.383281 | + | 0.663862i | 0.0408579 | + | 0.0707679i | ||||
\(89\) | −4.60275 | + | 2.65740i | −0.487890 | + | 0.281683i | −0.723699 | − | 0.690116i | \(-0.757559\pi\) |
0.235809 | + | 0.971799i | \(0.424226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.996041 | + | 0.170738i | −0.104413 | + | 0.0178982i | ||||
\(92\) | −1.45177 | −0.151357 | ||||||||
\(93\) | −2.84152 | + | 1.64055i | −0.294652 | + | 0.170117i | ||||
\(94\) | −0.531385 | − | 0.920385i | −0.0548081 | − | 0.0949305i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 1.09737 | + | 0.633565i | 0.111421 | + | 0.0643288i | 0.554675 | − | 0.832067i | \(-0.312843\pi\) |
−0.443254 | + | 0.896396i | \(0.646176\pi\) | |||||||
\(98\) | 5.99414 | + | 3.46072i | 0.605500 | + | 0.349586i | ||||
\(99\) | 0.766562i | 0.0770424i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.26374 | − | 3.92090i | −0.225250 | − | 0.390145i | 0.731144 | − | 0.682223i | \(-0.238987\pi\) |
−0.956394 | + | 0.292078i | \(0.905653\pi\) | |||||||
\(102\) | 1.92113 | − | 1.10917i | 0.190220 | − | 0.109824i | ||||
\(103\) | 2.94271 | 0.289954 | 0.144977 | − | 0.989435i | \(-0.453689\pi\) | ||||
0.144977 | + | 0.989435i | \(0.453689\pi\) | |||||||
\(104\) | −2.30441 | − | 2.77303i | −0.225966 | − | 0.271918i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.84152 | + | 1.64055i | −0.275992 | + | 0.159344i | ||||
\(107\) | −9.52440 | − | 16.4967i | −0.920758 | − | 1.59480i | −0.798245 | − | 0.602333i | \(-0.794238\pi\) |
−0.122513 | − | 0.992467i | \(-0.539095\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | − | 9.04549i | − | 0.866401i | −0.901298 | − | 0.433200i | \(-0.857384\pi\) | ||
0.901298 | − | 0.433200i | \(-0.142616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.07097 | − | 1.77303i | −0.291484 | − | 0.168288i | ||||
\(112\) | − | 0.280281i | − | 0.0264841i | ||||||
\(113\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(114\) | 2.63905 | + | 4.57097i | 0.247170 | + | 0.428111i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.06059 | −0.562712 | ||||||||
\(117\) | −0.609166 | − | 3.55372i | −0.0563174 | − | 0.328541i | ||||
\(118\) | 4.99783 | 0.460087 | ||||||||
\(119\) | −0.538457 | + | 0.310878i | −0.0493603 | + | 0.0284982i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.20619 | + | 9.01739i | −0.473290 | + | 0.819763i | ||||
\(122\) | − | 1.54606i | − | 0.139973i | ||||||
\(123\) | 1.92113 | + | 1.10917i | 0.173223 | + | 0.100010i | ||||
\(124\) | 2.84152 | + | 1.64055i | 0.255176 | + | 0.147326i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.140141 | − | 0.242731i | 0.0124847 | − | 0.0216242i | ||||
\(127\) | 1.58585 | + | 2.74678i | 0.140722 | + | 0.243737i | 0.927769 | − | 0.373156i | \(-0.121724\pi\) |
−0.787047 | + | 0.616893i | \(0.788391\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −3.60882 | −0.317739 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4345 | 1.34852 | 0.674259 | − | 0.738495i | \(-0.264463\pi\) | ||||
0.674259 | + | 0.738495i | \(0.264463\pi\) | |||||||
\(132\) | 0.663862 | − | 0.383281i | 0.0577818 | − | 0.0333603i | ||||
\(133\) | −0.739677 | − | 1.28116i | −0.0641381 | − | 0.111091i | ||||
\(134\) | 3.71792 | − | 6.43963i | 0.321180 | − | 0.556299i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.92113 | − | 1.10917i | −0.164736 | − | 0.0951102i | ||||
\(137\) | −1.44478 | − | 0.834145i | −0.123436 | − | 0.0712658i | 0.437011 | − | 0.899456i | \(-0.356037\pi\) |
−0.560447 | + | 0.828191i | \(0.689371\pi\) | |||||||
\(138\) | 1.45177i | 0.123583i | ||||||||
\(139\) | −1.05395 | + | 1.82549i | −0.0893949 | + | 0.154836i | −0.907256 | − | 0.420580i | \(-0.861827\pi\) |
0.817861 | + | 0.575416i | \(0.195160\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.920385 | + | 0.531385i | −0.0775104 | + | 0.0447507i | ||||
\(142\) | 2.42269 | 0.203308 | ||||||||
\(143\) | −0.957671 | + | 2.59266i | −0.0800844 | + | 0.216809i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.13150 | − | 12.3521i | −0.590207 | − | 1.02227i | ||||
\(147\) | 3.46072 | − | 5.99414i | 0.285435 | − | 0.494389i | ||||
\(148\) | 3.54606i | 0.291484i | ||||||||
\(149\) | −4.97167 | − | 2.87039i | −0.407295 | − | 0.235152i | 0.282332 | − | 0.959317i | \(-0.408892\pi\) |
−0.689627 | + | 0.724165i | \(0.742225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.1710i | 1.31598i | 0.753029 | + | 0.657988i | \(0.228592\pi\) | ||||
−0.753029 | + | 0.657988i | \(0.771408\pi\) | |||||||
\(152\) | 2.63905 | − | 4.57097i | 0.214055 | − | 0.370755i | ||||
\(153\) | −1.10917 | − | 1.92113i | −0.0896707 | − | 0.155314i | ||||
\(154\) | −0.186068 | + | 0.107426i | −0.0149938 | + | 0.00865667i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.77303 | + | 2.30441i | −0.222020 | + | 0.184501i | ||||
\(157\) | −15.8401 | −1.26418 | −0.632088 | − | 0.774896i | \(-0.717802\pi\) | ||||
−0.632088 | + | 0.774896i | \(0.717802\pi\) | |||||||
\(158\) | 12.5327 | − | 7.23574i | 0.997046 | − | 0.575645i | ||||
\(159\) | 1.64055 | + | 2.84152i | 0.130104 | + | 0.225347i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.406904i | − | 0.0320685i | ||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | −9.79890 | − | 5.65740i | −0.767509 | − | 0.443121i | 0.0644763 | − | 0.997919i | \(-0.479462\pi\) |
−0.831985 | + | 0.554798i | \(0.812796\pi\) | |||||||
\(164\) | − | 2.21833i | − | 0.173223i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.21209 | + | 3.83146i | 0.171692 | + | 0.297379i | ||||
\(167\) | 1.25727 | − | 0.725885i | 0.0972904 | − | 0.0561707i | −0.450565 | − | 0.892743i | \(-0.648778\pi\) |
0.547856 | + | 0.836573i | \(0.315444\pi\) | |||||||
\(168\) | −0.280281 | −0.0216242 | ||||||||
\(169\) | 2.37937 | − | 12.7804i | 0.183028 | − | 0.983108i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.57097 | − | 2.63905i | 0.349551 | − | 0.201813i | ||||
\(172\) | 1.80441 | + | 3.12533i | 0.137585 | + | 0.238304i | ||||
\(173\) | 6.67010 | − | 11.5530i | 0.507118 | − | 0.878355i | −0.492848 | − | 0.870116i | \(-0.664044\pi\) |
0.999966 | − | 0.00823921i | \(-0.00262265\pi\) | |||||||
\(174\) | 6.06059i | 0.459452i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.663862 | − | 0.383281i | −0.0500405 | − | 0.0288909i | ||||
\(177\) | − | 4.99783i | − | 0.375660i | ||||||
\(178\) | 2.65740 | − | 4.60275i | 0.199180 | − | 0.344990i | ||||
\(179\) | 12.6266 | + | 21.8699i | 0.943755 | + | 1.63463i | 0.758226 | + | 0.651992i | \(0.226067\pi\) |
0.185529 | + | 0.982639i | \(0.440600\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.314792 | −0.0233983 | −0.0116992 | − | 0.999932i | \(-0.503724\pi\) | ||||
−0.0116992 | + | 0.999932i | \(0.503724\pi\) | |||||||
\(182\) | 0.777228 | − | 0.645884i | 0.0576119 | − | 0.0478761i | ||||
\(183\) | −1.54606 | −0.114288 | ||||||||
\(184\) | 1.25727 | − | 0.725885i | 0.0926871 | − | 0.0535129i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.64055 | − | 2.84152i | 0.120291 | − | 0.208350i | ||||
\(187\) | 1.70049i | 0.124352i | ||||||||
\(188\) | 0.920385 | + | 0.531385i | 0.0671260 | + | 0.0387552i | ||||
\(189\) | −0.242731 | − | 0.140141i | −0.0176561 | − | 0.0101937i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2666 | − | 19.5143i | 0.815223 | − | 1.41201i | −0.0939445 | − | 0.995577i | \(-0.529948\pi\) |
0.909168 | − | 0.416430i | \(-0.136719\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −8.47286 | + | 4.89181i | −0.609890 | + | 0.352120i | −0.772922 | − | 0.634501i | \(-0.781206\pi\) |
0.163032 | + | 0.986621i | \(0.447872\pi\) | |||||||
\(194\) | −1.26713 | −0.0909746 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.92144 | −0.494389 | ||||||||
\(197\) | −10.7883 | + | 6.22862i | −0.768634 | + | 0.443771i | −0.832387 | − | 0.554195i | \(-0.813026\pi\) |
0.0637530 | + | 0.997966i | \(0.479693\pi\) | |||||||
\(198\) | −0.383281 | − | 0.663862i | −0.0272386 | − | 0.0471786i | ||||
\(199\) | 7.53195 | − | 13.0457i | 0.533926 | − | 0.924787i | −0.465289 | − | 0.885159i | \(-0.654050\pi\) |
0.999215 | − | 0.0396276i | \(-0.0126171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.43963 | − | 3.71792i | −0.454216 | − | 0.262242i | ||||
\(202\) | 3.92090 | + | 2.26374i | 0.275874 | + | 0.159276i | ||||
\(203\) | − | 1.69867i | − | 0.119223i | ||||||
\(204\) | −1.10917 | + | 1.92113i | −0.0776571 | + | 0.134506i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.54846 | + | 1.47135i | −0.177560 | + | 0.102514i | ||||
\(207\) | 1.45177 | 0.100905 | ||||||||
\(208\) | 3.38219 | + | 1.24931i | 0.234513 | + | 0.0866238i | ||||
\(209\) | −4.04600 | −0.279867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.53876 | − | 13.0575i | −0.518989 | − | 0.898916i | −0.999756 | − | 0.0220676i | \(-0.992975\pi\) |
0.480767 | − | 0.876848i | \(-0.340358\pi\) | |||||||
\(212\) | 1.64055 | − | 2.84152i | 0.112673 | − | 0.195156i | ||||
\(213\) | − | 2.42269i | − | 0.166000i | ||||||
\(214\) | 16.4967 | + | 9.52440i | 1.12769 | + | 0.651074i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −0.459815 | + | 0.796424i | −0.0312143 | + | 0.0540648i | ||||
\(218\) | 4.52274 | + | 7.83362i | 0.306319 | + | 0.530560i | ||||
\(219\) | −12.3521 | + | 7.13150i | −0.834679 | + | 0.481902i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.35133 | − | 7.88333i | −0.0909004 | − | 0.530290i | ||||
\(222\) | 3.54606 | 0.237996 | ||||||||
\(223\) | −4.03252 | + | 2.32817i | −0.270037 | + | 0.155906i | −0.628905 | − | 0.777482i | \(-0.716496\pi\) |
0.358867 | + | 0.933389i | \(0.383163\pi\) | |||||||
\(224\) | 0.140141 | + | 0.242731i | 0.00936354 | + | 0.0162181i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.37313 | + | 3.10218i | 0.356627 | + | 0.205899i | 0.667600 | − | 0.744520i | \(-0.267322\pi\) |
−0.310973 | + | 0.950419i | \(0.600655\pi\) | |||||||
\(228\) | −4.57097 | − | 2.63905i | −0.302720 | − | 0.174776i | ||||
\(229\) | − | 12.8610i | − | 0.849878i | −0.905222 | − | 0.424939i | \(-0.860296\pi\) | ||
0.905222 | − | 0.424939i | \(-0.139704\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.107426 | + | 0.186068i | 0.00706814 | + | 0.0122424i | ||||
\(232\) | 5.24863 | − | 3.03030i | 0.344589 | − | 0.198949i | ||||
\(233\) | −0.970923 | −0.0636073 | −0.0318036 | − | 0.999494i | \(-0.510125\pi\) | ||||
−0.0318036 | + | 0.999494i | \(0.510125\pi\) | |||||||
\(234\) | 2.30441 | + | 2.77303i | 0.150644 | + | 0.181279i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.32824 | + | 2.49891i | −0.281745 | + | 0.162665i | ||||
\(237\) | −7.23574 | − | 12.5327i | −0.470012 | − | 0.814085i | ||||
\(238\) | 0.310878 | − | 0.538457i | 0.0201512 | − | 0.0349030i | ||||
\(239\) | 14.7984i | 0.957231i | 0.878025 | + | 0.478616i | \(0.158861\pi\) | ||||
−0.878025 | + | 0.478616i | \(0.841139\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.89795 | + | 1.09578i | 0.122258 | + | 0.0705856i | 0.559882 | − | 0.828572i | \(-0.310847\pi\) |
−0.437624 | + | 0.899158i | \(0.644180\pi\) | |||||||
\(242\) | − | 10.4124i | − | 0.669333i | ||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0.773028 | + | 1.33892i | 0.0494880 | + | 0.0857158i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.21833 | −0.141436 | ||||||||
\(247\) | 18.7569 | − | 3.21524i | 1.19347 | − | 0.204581i | ||||
\(248\) | −3.28110 | −0.208350 | ||||||||
\(249\) | 3.83146 | − | 2.21209i | 0.242809 | − | 0.140186i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.29487 | − | 9.17098i | 0.334209 | − | 0.578867i | −0.649124 | − | 0.760683i | \(-0.724864\pi\) |
0.983333 | + | 0.181816i | \(0.0581975\pi\) | |||||||
\(252\) | 0.280281i | 0.0176561i | ||||||||
\(253\) | −0.963775 | − | 0.556436i | −0.0605920 | − | 0.0349828i | ||||
\(254\) | −2.74678 | − | 1.58585i | −0.172348 | − | 0.0995053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.42396 | − | 5.93047i | −0.213581 | − | 0.369933i | 0.739252 | − | 0.673429i | \(-0.235179\pi\) |
−0.952833 | + | 0.303496i | \(0.901846\pi\) | |||||||
\(258\) | 3.12533 | − | 1.80441i | 0.194575 | − | 0.112338i | ||||
\(259\) | −0.993893 | −0.0617575 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.06059 | 0.375141 | ||||||||
\(262\) | −13.3667 | + | 7.71724i | −0.825795 | + | 0.476773i | ||||
\(263\) | −13.1181 | − | 22.7212i | −0.808898 | − | 1.40105i | −0.913628 | − | 0.406551i | \(-0.866731\pi\) |
0.104730 | − | 0.994501i | \(-0.466602\pi\) | |||||||
\(264\) | −0.383281 | + | 0.663862i | −0.0235893 | + | 0.0408579i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.28116 | + | 0.739677i | 0.0785529 | + | 0.0453525i | ||||
\(267\) | −4.60275 | − | 2.65740i | −0.281683 | − | 0.162630i | ||||
\(268\) | 7.43584i | 0.454216i | ||||||||
\(269\) | −3.24938 | + | 5.62808i | −0.198118 | + | 0.343150i | −0.947918 | − | 0.318514i | \(-0.896816\pi\) |
0.749800 | + | 0.661664i | \(0.230150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.35904 | − | 3.09404i | 0.325539 | − | 0.187950i | −0.328320 | − | 0.944567i | \(-0.606482\pi\) |
0.653859 | + | 0.756617i | \(0.273149\pi\) | |||||||
\(272\) | 2.21833 | 0.134506 | ||||||||
\(273\) | −0.645884 | − | 0.777228i | −0.0390906 | − | 0.0470400i | ||||
\(274\) | 1.66829 | 0.100785 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.725885 | − | 1.25727i | −0.0436931 | − | 0.0756787i | ||||
\(277\) | −14.5289 | + | 25.1647i | −0.872955 | + | 1.51200i | −0.0140299 | + | 0.999902i | \(0.504466\pi\) |
−0.858925 | + | 0.512101i | \(0.828867\pi\) | |||||||
\(278\) | − | 2.10790i | − | 0.126423i | ||||||
\(279\) | −2.84152 | − | 1.64055i | −0.170117 | − | 0.0982172i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1438i | 0.843746i | 0.906655 | + | 0.421873i | \(0.138627\pi\) | ||||
−0.906655 | + | 0.421873i | \(0.861373\pi\) | |||||||
\(282\) | 0.531385 | − | 0.920385i | 0.0316435 | − | 0.0548081i | ||||
\(283\) | 4.37290 | + | 7.57409i | 0.259942 | + | 0.450233i | 0.966226 | − | 0.257696i | \(-0.0829632\pi\) |
−0.706284 | + | 0.707928i | \(0.749630\pi\) | |||||||
\(284\) | −2.09811 | + | 1.21135i | −0.124500 | + | 0.0718802i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.466963 | − | 2.72415i | −0.0276121 | − | 0.161082i | ||||
\(287\) | 0.621757 | 0.0367011 | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | 6.03950 | + | 10.4607i | 0.355265 | + | 0.615337i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.26713i | 0.0742805i | ||||||||
\(292\) | 12.3521 | + | 7.13150i | 0.722853 | + | 0.417339i | ||||
\(293\) | −27.2798 | − | 15.7500i | −1.59371 | − | 0.920126i | −0.992664 | − | 0.120909i | \(-0.961419\pi\) |
−0.601042 | − | 0.799217i | \(-0.705248\pi\) | |||||||
\(294\) | 6.92144i | 0.403667i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.77303 | − | 3.07097i | −0.103055 | − | 0.178497i | ||||
\(297\) | −0.663862 | + | 0.383281i | −0.0385212 | + | 0.0222402i | ||||
\(298\) | 5.74079 | 0.332555 | ||||||||
\(299\) | 4.91017 | + | 1.81370i | 0.283962 | + | 0.104889i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.875972 | + | 0.505743i | −0.0504902 | + | 0.0291505i | ||||
\(302\) | −8.08549 | − | 14.0045i | −0.465268 | − | 0.805867i | ||||
\(303\) | 2.26374 | − | 3.92090i | 0.130048 | − | 0.225250i | ||||
\(304\) | 5.27811i | 0.302720i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.92113 | + | 1.10917i | 0.109824 | + | 0.0634068i | ||||
\(307\) | 7.03152i | 0.401310i | 0.979662 | + | 0.200655i | \(0.0643070\pi\) | ||||
−0.979662 | + | 0.200655i | \(0.935693\pi\) | |||||||
\(308\) | 0.107426 | − | 0.186068i | 0.00612119 | − | 0.0106022i | ||||
\(309\) | 1.47135 | + | 2.54846i | 0.0837025 | + | 0.144977i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.79844 | 0.498914 | 0.249457 | − | 0.968386i | \(-0.419748\pi\) | ||||
0.249457 | + | 0.968386i | \(0.419748\pi\) | |||||||
\(312\) | 1.24931 | − | 3.38219i | 0.0707280 | − | 0.191479i | ||||
\(313\) | 9.34134 | 0.528004 | 0.264002 | − | 0.964522i | \(-0.414958\pi\) | ||||
0.264002 | + | 0.964522i | \(0.414958\pi\) | |||||||
\(314\) | 13.7179 | − | 7.92004i | 0.774147 | − | 0.446954i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.23574 | + | 12.5327i | −0.407042 | + | 0.705018i | ||||
\(317\) | 19.4697i | 1.09353i | 0.837287 | + | 0.546763i | \(0.184140\pi\) | ||||
−0.837287 | + | 0.546763i | \(0.815860\pi\) | |||||||
\(318\) | −2.84152 | − | 1.64055i | −0.159344 | − | 0.0919975i | ||||
\(319\) | −4.02340 | − | 2.32291i | −0.225267 | − | 0.130058i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.52440 | − | 16.4967i | 0.531600 | − | 0.920758i | ||||
\(322\) | 0.203452 | + | 0.352389i | 0.0113379 | + | 0.0196379i | ||||
\(323\) | 10.1399 | − | 5.85429i | 0.564201 | − | 0.325742i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.3148 | 0.626668 | ||||||||
\(327\) | 7.83362 | − | 4.52274i | 0.433200 | − | 0.250108i | ||||
\(328\) | 1.10917 | + | 1.92113i | 0.0612434 | + | 0.106077i | ||||
\(329\) | −0.148937 | + | 0.257967i | −0.00821117 | + | 0.0142222i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.4081 | + | 9.47320i | 0.901869 | + | 0.520694i | 0.877806 | − | 0.479016i | \(-0.159007\pi\) |
0.0240626 | + | 0.999710i | \(0.492340\pi\) | |||||||
\(332\) | −3.83146 | − | 2.21209i | −0.210279 | − | 0.121404i | ||||
\(333\) | − | 3.54606i | − | 0.194323i | ||||||
\(334\) | −0.725885 | + | 1.25727i | −0.0397186 | + | 0.0687947i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.242731 | − | 0.140141i | 0.0132420 | − | 0.00764530i | ||||
\(337\) | −2.72966 | −0.148694 | −0.0743469 | − | 0.997232i | \(-0.523687\pi\) | ||||
−0.0743469 | + | 0.997232i | \(0.523687\pi\) | |||||||
\(338\) | 4.32961 | + | 12.2578i | 0.235500 | + | 0.666738i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.25758 | + | 2.17820i | 0.0681020 | + | 0.117956i | ||||
\(342\) | −2.63905 | + | 4.57097i | −0.142704 | + | 0.247170i | ||||
\(343\) | − | 3.90192i | − | 0.210684i | ||||||
\(344\) | −3.12533 | − | 1.80441i | −0.168507 | − | 0.0972874i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.3402i | 0.717174i | ||||||||
\(347\) | 6.34600 | − | 10.9916i | 0.340671 | − | 0.590059i | −0.643887 | − | 0.765121i | \(-0.722679\pi\) |
0.984557 | + | 0.175062i | \(0.0560125\pi\) | |||||||
\(348\) | −3.03030 | − | 5.24863i | −0.162441 | − | 0.281356i | ||||
\(349\) | 1.04906 | − | 0.605676i | 0.0561549 | − | 0.0324211i | −0.471660 | − | 0.881781i | \(-0.656345\pi\) |
0.527815 | + | 0.849360i | \(0.323012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.77303 | − | 2.30441i | 0.148013 | − | 0.123000i | ||||
\(352\) | 0.766562 | 0.0408579 | ||||||||
\(353\) | −29.0813 | + | 16.7901i | −1.54784 | + | 0.893647i | −0.549535 | + | 0.835471i | \(0.685195\pi\) |
−0.998306 | + | 0.0581762i | \(0.981471\pi\) | |||||||
\(354\) | 2.49891 | + | 4.32824i | 0.132816 | + | 0.230044i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.31479i | 0.281683i | ||||||||
\(357\) | −0.538457 | − | 0.310878i | −0.0284982 | − | 0.0164534i | ||||
\(358\) | −21.8699 | − | 12.6266i | −1.15586 | − | 0.667335i | ||||
\(359\) | 22.0423i | 1.16335i | 0.813423 | + | 0.581673i | \(0.197602\pi\) | ||||
−0.813423 | + | 0.581673i | \(0.802398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.42920 | + | 7.67161i | 0.233116 | + | 0.403769i | ||||
\(362\) | 0.272618 | − | 0.157396i | 0.0143285 | − | 0.00827256i | ||||
\(363\) | −10.4124 | −0.546508 | ||||||||
\(364\) | −0.350157 | + | 0.947965i | −0.0183532 | + | 0.0496869i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.33892 | − | 0.773028i | 0.0699867 | − | 0.0404068i | ||||
\(367\) | 4.82908 | + | 8.36421i | 0.252076 | + | 0.436608i | 0.964097 | − | 0.265550i | \(-0.0855534\pi\) |
−0.712021 | + | 0.702158i | \(0.752220\pi\) | |||||||
\(368\) | −0.725885 | + | 1.25727i | −0.0378394 | + | 0.0655397i | ||||
\(369\) | 2.21833i | 0.115482i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.796424 | + | 0.459815i | 0.0413483 | + | 0.0238724i | ||||
\(372\) | 3.28110i | 0.170117i | ||||||||
\(373\) | −6.12153 | + | 10.6028i | −0.316961 | + | 0.548992i | −0.979852 | − | 0.199723i | \(-0.935996\pi\) |
0.662892 | + | 0.748715i | \(0.269329\pi\) | |||||||
\(374\) | −0.850244 | − | 1.47267i | −0.0439651 | − | 0.0761498i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.06277 | −0.0548081 | ||||||||
\(377\) | 20.4981 | + | 7.57154i | 1.05571 | + | 0.389954i | ||||
\(378\) | 0.280281 | 0.0144161 | ||||||||
\(379\) | 11.7669 | − | 6.79362i | 0.604425 | − | 0.348965i | −0.166355 | − | 0.986066i | \(-0.553200\pi\) |
0.770780 | + | 0.637101i | \(0.219867\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.58585 | + | 2.74678i | −0.0812458 | + | 0.140722i | ||||
\(382\) | 22.5332i | 1.15290i | ||||||||
\(383\) | −13.3487 | − | 7.70686i | −0.682086 | − | 0.393802i | 0.118555 | − | 0.992948i | \(-0.462174\pi\) |
−0.800640 | + | 0.599145i | \(0.795507\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.89181 | − | 8.47286i | 0.248987 | − | 0.431257i | ||||
\(387\) | −1.80441 | − | 3.12533i | −0.0917234 | − | 0.158870i | ||||
\(388\) | 1.09737 | − | 0.633565i | 0.0557103 | − | 0.0321644i | ||||
\(389\) | 6.06059 | 0.307284 | 0.153642 | − | 0.988127i | \(-0.450900\pi\) | ||||
0.153642 | + | 0.988127i | \(0.450900\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22051 | 0.162868 | ||||||||
\(392\) | 5.99414 | − | 3.46072i | 0.302750 | − | 0.174793i | ||||
\(393\) | 7.71724 | + | 13.3667i | 0.389283 | + | 0.674259i | ||||
\(394\) | 6.22862 | − | 10.7883i | 0.313794 | − | 0.543506i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.663862 | + | 0.383281i | 0.0333603 | + | 0.0192606i | ||||
\(397\) | 14.7131 | + | 8.49464i | 0.738432 | + | 0.426334i | 0.821499 | − | 0.570210i | \(-0.193138\pi\) |
−0.0830670 | + | 0.996544i | \(0.526472\pi\) | |||||||
\(398\) | 15.0639i | 0.755085i | ||||||||
\(399\) | 0.739677 | − | 1.28116i | 0.0370302 | − | 0.0641381i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.8156 | + | 9.70852i | −0.839733 | + | 0.484820i | −0.857174 | − | 0.515028i | \(-0.827782\pi\) |
0.0174403 | + | 0.999848i | \(0.494448\pi\) | |||||||
\(402\) | 7.43584 | 0.370866 | ||||||||
\(403\) | −7.56101 | − | 9.09858i | −0.376641 | − | 0.453233i | ||||
\(404\) | −4.52747 | −0.225250 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.849335 | + | 1.47109i | 0.0421518 | + | 0.0730091i | ||||
\(407\) | −1.35914 | + | 2.35409i | −0.0673699 | + | 0.116688i | ||||
\(408\) | − | 2.21833i | − | 0.109824i | ||||||
\(409\) | −0.803328 | − | 0.463802i | −0.0397220 | − | 0.0229335i | 0.480007 | − | 0.877264i | \(-0.340634\pi\) |
−0.519730 | + | 0.854331i | \(0.673967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.66829i | − | 0.0822907i | ||||||
\(412\) | 1.47135 | − | 2.54846i | 0.0724885 | − | 0.125554i | ||||
\(413\) | −0.700398 | − | 1.21313i | −0.0344643 | − | 0.0596940i | ||||
\(414\) | −1.25727 | + | 0.725885i | −0.0617914 | + | 0.0356753i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.55372 | + | 0.609166i | −0.174235 | + | 0.0298668i | ||||
\(417\) | −2.10790 | −0.103224 | ||||||||
\(418\) | 3.50393 | − | 2.02300i | 0.171383 | − | 0.0989481i | ||||
\(419\) | 12.5907 | + | 21.8077i | 0.615096 | + | 1.06538i | 0.990368 | + | 0.138463i | \(0.0442163\pi\) |
−0.375271 | + | 0.926915i | \(0.622450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.6912i | 1.34958i | 0.738008 | + | 0.674792i | \(0.235767\pi\) | ||||
−0.738008 | + | 0.674792i | \(0.764233\pi\) | |||||||
\(422\) | 13.0575 | + | 7.53876i | 0.635630 | + | 0.366981i | ||||
\(423\) | −0.920385 | − | 0.531385i | −0.0447507 | − | 0.0258368i | ||||
\(424\) | 3.28110i | 0.159344i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.21135 | + | 2.09811i | 0.0586899 | + | 0.101654i | ||||
\(427\) | −0.375275 | + | 0.216665i | −0.0181608 | + | 0.0104852i | ||||
\(428\) | −19.0488 | −0.920758 | ||||||||
\(429\) | −2.72415 | + | 0.466963i | −0.131523 | + | 0.0225452i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.0798174 | − | 0.0460826i | 0.00384467 | − | 0.00221972i | −0.498076 | − | 0.867133i | \(-0.665960\pi\) |
0.501921 | + | 0.864913i | \(0.332627\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 2.01113 | − | 3.48337i | 0.0966486 | − | 0.167400i | −0.813647 | − | 0.581359i | \(-0.802521\pi\) |
0.910295 | + | 0.413959i | \(0.135854\pi\) | |||||||
\(434\) | − | 0.919631i | − | 0.0441437i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.83362 | − | 4.52274i | −0.375162 | − | 0.216600i | ||||
\(437\) | 7.66259i | 0.366552i | ||||||||
\(438\) | 7.13150 | − | 12.3521i | 0.340756 | − | 0.590207i | ||||
\(439\) | 12.9742 | + | 22.4719i | 0.619223 | + | 1.07253i | 0.989628 | + | 0.143656i | \(0.0458858\pi\) |
−0.370404 | + | 0.928871i | \(0.620781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.92144 | 0.329592 | ||||||||
\(442\) | 5.11195 | + | 6.15150i | 0.243151 | + | 0.292597i | ||||
\(443\) | 15.0646 | 0.715740 | 0.357870 | − | 0.933771i | \(-0.383503\pi\) | ||||
0.357870 | + | 0.933771i | \(0.383503\pi\) | |||||||
\(444\) | −3.07097 | + | 1.77303i | −0.145742 | + | 0.0841442i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.32817 | − | 4.03252i | 0.110242 | − | 0.190945i | ||||
\(447\) | − | 5.74079i | − | 0.271530i | ||||||
\(448\) | −0.242731 | − | 0.140141i | −0.0114679 | − | 0.00662102i | ||||
\(449\) | 29.8460 | + | 17.2316i | 1.40852 | + | 0.813208i | 0.995245 | − | 0.0973991i | \(-0.0310523\pi\) |
0.413273 | + | 0.910607i | \(0.364386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.850244 | − | 1.47267i | 0.0400364 | − | 0.0693451i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.0045 | + | 8.08549i | −0.657988 | + | 0.379889i | ||||
\(454\) | −6.20436 | −0.291185 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.27811 | 0.247170 | ||||||||
\(457\) | −36.0525 | + | 20.8149i | −1.68646 | + | 0.973680i | −0.729273 | + | 0.684223i | \(0.760141\pi\) |
−0.957191 | + | 0.289457i | \(0.906525\pi\) | |||||||
\(458\) | 6.43049 | + | 11.1379i | 0.300477 | + | 0.520442i | ||||
\(459\) | 1.10917 | − | 1.92113i | 0.0517714 | − | 0.0896707i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.02737 | + | 3.47990i | 0.280722 | + | 0.162075i | 0.633750 | − | 0.773538i | \(-0.281515\pi\) |
−0.353028 | + | 0.935613i | \(0.614848\pi\) | |||||||
\(462\) | −0.186068 | − | 0.107426i | −0.00865667 | − | 0.00499793i | ||||
\(463\) | 11.9289i | 0.554382i | 0.960815 | + | 0.277191i | \(0.0894035\pi\) | ||||
−0.960815 | + | 0.277191i | \(0.910597\pi\) | |||||||
\(464\) | −3.03030 | + | 5.24863i | −0.140678 | + | 0.243661i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.840844 | − | 0.485461i | 0.0389513 | − | 0.0224886i | ||||
\(467\) | 34.4406 | 1.59372 | 0.796860 | − | 0.604164i | \(-0.206493\pi\) | ||||
0.796860 | + | 0.604164i | \(0.206493\pi\) | |||||||
\(468\) | −3.38219 | − | 1.24931i | −0.156342 | − | 0.0577492i | ||||
\(469\) | −2.08413 | −0.0962361 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.92004 | − | 13.7179i | −0.364936 | − | 0.632088i | ||||
\(472\) | 2.49891 | − | 4.32824i | 0.115022 | − | 0.199224i | ||||
\(473\) | 2.76639i | 0.127199i | ||||||||
\(474\) | 12.5327 | + | 7.23574i | 0.575645 | + | 0.332349i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.621757i | 0.0284982i | ||||||||
\(477\) | −1.64055 | + | 2.84152i | −0.0751156 | + | 0.130104i | ||||
\(478\) | −7.39922 | − | 12.8158i | −0.338432 | − | 0.586182i | ||||
\(479\) | −11.8896 | + | 6.86444i | −0.543248 | + | 0.313644i | −0.746394 | − | 0.665504i | \(-0.768217\pi\) |
0.203146 | + | 0.979148i | \(0.434883\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.43011 | − | 11.9934i | 0.201996 | − | 0.546854i | ||||
\(482\) | −2.19157 | −0.0998231 | ||||||||
\(483\) | 0.352389 | − | 0.203452i | 0.0160343 | − | 0.00925738i | ||||
\(484\) | 5.20619 | + | 9.01739i | 0.236645 | + | 0.409881i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 8.25303 | + | 4.76489i | 0.373981 | + | 0.215918i | 0.675196 | − | 0.737638i | \(-0.264059\pi\) |
−0.301215 | + | 0.953556i | \(0.597392\pi\) | |||||||
\(488\) | −1.33892 | − | 0.773028i | −0.0606102 | − | 0.0349933i | ||||
\(489\) | − | 11.3148i | − | 0.511673i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7409 | + | 28.9960i | 0.755505 | + | 1.30857i | 0.945123 | + | 0.326715i | \(0.105942\pi\) |
−0.189618 | + | 0.981858i | \(0.560725\pi\) | |||||||
\(492\) | 1.92113 | − | 1.10917i | 0.0866113 | − | 0.0500051i | ||||
\(493\) | 13.4444 | 0.605506 | ||||||||
\(494\) | −14.6363 | + | 12.1629i | −0.658520 | + | 0.547236i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.84152 | − | 1.64055i | 0.127588 | − | 0.0736629i | ||||
\(497\) | −0.339518 | − | 0.588062i | −0.0152294 | − | 0.0263782i | ||||
\(498\) | −2.21209 | + | 3.83146i | −0.0991262 | + | 0.171692i | ||||
\(499\) | − | 15.0882i | − | 0.675439i | −0.941247 | − | 0.337720i | \(-0.890344\pi\) | ||
0.941247 | − | 0.337720i | \(-0.109656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.25727 | + | 0.725885i | 0.0561707 | + | 0.0324301i | ||||
\(502\) | 10.5897i | 0.472643i | ||||||||
\(503\) | 9.74919 | − | 16.8861i | 0.434695 | − | 0.752914i | −0.562576 | − | 0.826746i | \(-0.690189\pi\) |
0.997271 | + | 0.0738319i | \(0.0235228\pi\) | |||||||
\(504\) | −0.140141 | − | 0.242731i | −0.00624236 | − | 0.0108121i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.11287 | 0.0494732 | ||||||||
\(507\) | 12.2578 | − | 4.32961i | 0.544390 | − | 0.192285i | ||||
\(508\) | 3.17171 | 0.140722 | ||||||||
\(509\) | 29.5101 | − | 17.0377i | 1.30801 | − | 0.755181i | 0.326248 | − | 0.945284i | \(-0.394215\pi\) |
0.981764 | + | 0.190103i | \(0.0608821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.99883 | + | 3.46207i | −0.0884228 | + | 0.153153i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 4.57097 | + | 2.63905i | 0.201813 | + | 0.116517i | ||||
\(514\) | 5.93047 | + | 3.42396i | 0.261582 | + | 0.151024i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.80441 | + | 3.12533i | −0.0794348 | + | 0.137585i | ||||
\(517\) | 0.407339 | + | 0.705532i | 0.0179148 | + | 0.0310293i | ||||
\(518\) | 0.860736 | − | 0.496946i | 0.0378186 | − | 0.0218346i | ||||
\(519\) | 13.3402 | 0.585570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.10626 | −0.0484660 | −0.0242330 | − | 0.999706i | \(-0.507714\pi\) | ||||
−0.0242330 | + | 0.999706i | \(0.507714\pi\) | |||||||
\(522\) | −5.24863 | + | 3.03030i | −0.229726 | + | 0.132633i | ||||
\(523\) | −5.32920 | − | 9.23044i | −0.233030 | − | 0.403619i | 0.725669 | − | 0.688044i | \(-0.241531\pi\) |
−0.958698 | + | 0.284425i | \(0.908197\pi\) | |||||||
\(524\) | 7.71724 | − | 13.3667i | 0.337129 | − | 0.583925i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.7212 | + | 13.1181i | 0.990693 | + | 0.571977i | ||||
\(527\) | −6.30343 | − | 3.63928i | −0.274582 | − | 0.158530i | ||||
\(528\) | − | 0.766562i | − | 0.0333603i | ||||||
\(529\) | 10.4462 | − | 18.0933i | 0.454182 | − | 0.786666i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.32824 | − | 2.49891i | 0.187830 | − | 0.108444i | ||||
\(532\) | −1.47935 | −0.0641381 | ||||||||
\(533\) | −2.77138 | + | 7.50283i | −0.120042 | + | 0.324983i | ||||
\(534\) | 5.31479 | 0.229994 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.71792 | − | 6.43963i | −0.160590 | − | 0.278150i | ||||
\(537\) | −12.6266 | + | 21.8699i | −0.544877 | + | 0.943755i | ||||
\(538\) | − | 6.49875i | − | 0.280181i | ||||||
\(539\) | −4.59488 | − | 2.65286i | −0.197916 | − | 0.114267i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.1486i | 1.64013i | 0.572267 | + | 0.820067i | \(0.306064\pi\) | ||||
−0.572267 | + | 0.820067i | \(0.693936\pi\) | |||||||
\(542\) | −3.09404 | + | 5.35904i | −0.132901 | + | 0.230191i | ||||
\(543\) | −0.157396 | − | 0.272618i | −0.00675452 | − | 0.0116992i | ||||
\(544\) | −1.92113 | + | 1.10917i | −0.0823678 | + | 0.0475551i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.947965 | + | 0.350157i | 0.0405692 | + | 0.0149853i | ||||
\(547\) | 26.9609 | 1.15277 | 0.576383 | − | 0.817180i | \(-0.304464\pi\) | ||||
0.576383 | + | 0.817180i | \(0.304464\pi\) | |||||||
\(548\) | −1.44478 | + | 0.834145i | −0.0617180 | + | 0.0356329i | ||||
\(549\) | −0.773028 | − | 1.33892i | −0.0329920 | − | 0.0571439i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.9885i | 1.36275i | ||||||||
\(552\) | 1.25727 | + | 0.725885i | 0.0535129 | + | 0.0308957i | ||||
\(553\) | −3.51267 | − | 2.02804i | −0.149374 | − | 0.0862411i | ||||
\(554\) | − | 29.0577i | − | 1.23454i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.05395 | + | 1.82549i | 0.0446974 | + | 0.0774182i | ||||
\(557\) | 30.5249 | − | 17.6236i | 1.29338 | − | 0.746735i | 0.314130 | − | 0.949380i | \(-0.398287\pi\) |
0.979252 | + | 0.202645i | \(0.0649539\pi\) | |||||||
\(558\) | 3.28110 | 0.138900 | ||||||||
\(559\) | −2.19837 | − | 12.8247i | −0.0929812 | − | 0.542429i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.47267 | + | 0.850244i | −0.0621760 | + | 0.0358973i | ||||
\(562\) | −7.07188 | − | 12.2489i | −0.298309 | − | 0.516687i | ||||
\(563\) | 8.50830 | − | 14.7368i | 0.358582 | − | 0.621082i | −0.629142 | − | 0.777290i | \(-0.716594\pi\) |
0.987724 | + | 0.156208i | \(0.0499270\pi\) | |||||||
\(564\) | 1.06277i | 0.0447507i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.57409 | − | 4.37290i | −0.318363 | − | 0.183807i | ||||
\(567\) | − | 0.280281i | − | 0.0117707i | ||||||
\(568\) | 1.21135 | − | 2.09811i | 0.0508270 | − | 0.0880349i | ||||
\(569\) | 17.6968 | + | 30.6518i | 0.741889 | + | 1.28499i | 0.951634 | + | 0.307233i | \(0.0994030\pi\) |
−0.209746 | + | 0.977756i | \(0.567264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5185 | −0.733125 | −0.366563 | − | 0.930393i | \(-0.619465\pi\) | ||||
−0.366563 | + | 0.930393i | \(0.619465\pi\) | |||||||
\(572\) | 1.76647 | + | 2.12570i | 0.0738600 | + | 0.0888799i | ||||
\(573\) | 22.5332 | 0.941339 | ||||||||
\(574\) | −0.538457 | + | 0.310878i | −0.0224748 | + | 0.0129758i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 26.6215i | 1.10827i | 0.832428 | + | 0.554133i | \(0.186950\pi\) | ||||
−0.832428 | + | 0.554133i | \(0.813050\pi\) | |||||||
\(578\) | −10.4607 | − | 6.03950i | −0.435109 | − | 0.251210i | ||||
\(579\) | −8.47286 | − | 4.89181i | −0.352120 | − | 0.203297i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.620008 | − | 1.07389i | 0.0257223 | − | 0.0445523i | ||||
\(582\) | −0.633565 | − | 1.09737i | −0.0262621 | − | 0.0454873i | ||||
\(583\) | 2.17820 | − | 1.25758i | 0.0902118 | − | 0.0520838i | ||||
\(584\) | −14.2630 | −0.590207 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.5001 | 1.30126 | ||||||||
\(587\) | −14.4115 | + | 8.32051i | −0.594828 | + | 0.343424i | −0.767004 | − | 0.641642i | \(-0.778254\pi\) |
0.172176 | + | 0.985066i | \(0.444920\pi\) | |||||||
\(588\) | −3.46072 | − | 5.99414i | −0.142718 | − | 0.247194i | ||||
\(589\) | 8.65900 | − | 14.9978i | 0.356788 | − | 0.617975i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.7883 | − | 6.22862i | −0.443771 | − | 0.256211i | ||||
\(592\) | 3.07097 | + | 1.77303i | 0.126216 | + | 0.0728710i | ||||
\(593\) | 24.7460i | 1.01620i | 0.861300 | + | 0.508098i | \(0.169651\pi\) | ||||
−0.861300 | + | 0.508098i | \(0.830349\pi\) | |||||||
\(594\) | 0.383281 | − | 0.663862i | 0.0157262 | − | 0.0272386i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.97167 | + | 2.87039i | −0.203647 | + | 0.117576i | ||||
\(597\) | 15.0639 | 0.616524 | ||||||||
\(598\) | −5.15918 | + | 0.884368i | −0.210975 | + | 0.0361645i | ||||
\(599\) | −23.2517 | −0.950037 | −0.475019 | − | 0.879976i | \(-0.657559\pi\) | ||||
−0.475019 | + | 0.879976i | \(0.657559\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.5985 | − | 28.7494i | −0.677067 | − | 1.17271i | −0.975860 | − | 0.218396i | \(-0.929917\pi\) |
0.298793 | − | 0.954318i | \(-0.403416\pi\) | |||||||
\(602\) | 0.505743 | − | 0.875972i | 0.0206125 | − | 0.0357020i | ||||
\(603\) | − | 7.43584i | − | 0.302811i | ||||||
\(604\) | 14.0045 | + | 8.08549i | 0.569834 | + | 0.328994i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.52747i | 0.183916i | ||||||||
\(607\) | 19.7130 | − | 34.1440i | 0.800128 | − | 1.38586i | −0.119404 | − | 0.992846i | \(-0.538098\pi\) |
0.919532 | − | 0.393016i | \(-0.128568\pi\) | |||||||
\(608\) | −2.63905 | − | 4.57097i | −0.107028 | − | 0.185377i | ||||
\(609\) | 1.47109 | − | 0.849335i | 0.0596117 | − | 0.0344168i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.44906 | − | 2.94709i | −0.0990783 | − | 0.119226i | ||||
\(612\) | −2.21833 | −0.0896707 | ||||||||
\(613\) | −9.03087 | + | 5.21398i | −0.364753 | + | 0.210591i | −0.671164 | − | 0.741309i | \(-0.734205\pi\) |
0.306410 | + | 0.951899i | \(0.400872\pi\) | |||||||
\(614\) | −3.51576 | − | 6.08947i | −0.141884 | − | 0.245751i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.214853i | 0.00865667i | ||||||||
\(617\) | 17.5464 | + | 10.1304i | 0.706393 | + | 0.407836i | 0.809724 | − | 0.586811i | \(-0.199617\pi\) |
−0.103331 | + | 0.994647i | \(0.532950\pi\) | |||||||
\(618\) | −2.54846 | − | 1.47135i | −0.102514 | − | 0.0591866i | ||||
\(619\) | 27.8009i | 1.11741i | 0.829365 | + | 0.558707i | \(0.188702\pi\) | ||||
−0.829365 | + | 0.558707i | \(0.811298\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.725885 | + | 1.25727i | 0.0291288 | + | 0.0504525i | ||||
\(622\) | −7.61967 | + | 4.39922i | −0.305521 | + | 0.176393i | ||||
\(623\) | −1.48964 | −0.0596810 | ||||||||
\(624\) | 0.609166 | + | 3.55372i | 0.0243861 | + | 0.142263i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.08984 | + | 4.67067i | −0.323335 | + | 0.186677i | ||||
\(627\) | −2.02300 | − | 3.50393i | −0.0807907 | − | 0.139934i | ||||
\(628\) | −7.92004 | + | 13.7179i | −0.316044 | + | 0.547405i | ||||
\(629\) | − | 7.86633i | − | 0.313651i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6461 | − | 18.2709i | −1.25981 | − | 0.727352i | −0.286773 | − | 0.957999i | \(-0.592583\pi\) |
−0.973038 | + | 0.230646i | \(0.925916\pi\) | |||||||
\(632\) | − | 14.4715i | − | 0.575645i | ||||||
\(633\) | 7.53876 | − | 13.0575i | 0.299639 | − | 0.518989i | ||||
\(634\) | −9.73484 | − | 16.8612i | −0.386620 | − | 0.669645i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.28110 | 0.130104 | ||||||||
\(637\) | 23.4097 | + | 8.64700i | 0.927524 | + | 0.342607i | ||||
\(638\) | 4.64582 | 0.183930 | ||||||||
\(639\) | 2.09811 | − | 1.21135i | 0.0830001 | − | 0.0479201i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9295 | + | 37.9830i | −0.866163 | + | 1.50024i | −0.000274574 | 1.00000i | \(0.500087\pi\) | |
−0.865888 | + | 0.500238i | \(0.833246\pi\) | |||||||
\(642\) | 19.0488i | 0.751796i | ||||||||
\(643\) | 14.4213 | + | 8.32615i | 0.568721 | + | 0.328351i | 0.756638 | − | 0.653834i | \(-0.226840\pi\) |
−0.187917 | + | 0.982185i | \(0.560174\pi\) | |||||||
\(644\) | −0.352389 | − | 0.203452i | −0.0138861 | − | 0.00801713i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.85429 | + | 10.1399i | −0.230334 | + | 0.398950i | ||||
\(647\) | 4.69543 | + | 8.13271i | 0.184596 | + | 0.319730i | 0.943440 | − | 0.331542i | \(-0.107569\pi\) |
−0.758844 | + | 0.651272i | \(0.774236\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −3.83114 | −0.150386 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.919631 | −0.0360432 | ||||||||
\(652\) | −9.79890 | + | 5.65740i | −0.383754 | + | 0.221561i | ||||
\(653\) | −20.5572 | − | 35.6061i | −0.804465 | − | 1.39337i | −0.916652 | − | 0.399686i | \(-0.869119\pi\) |
0.112187 | − | 0.993687i | \(-0.464214\pi\) | |||||||
\(654\) | −4.52274 | + | 7.83362i | −0.176853 | + | 0.306319i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.92113 | − | 1.10917i | −0.0750076 | − | 0.0433056i | ||||
\(657\) | −12.3521 | − | 7.13150i | −0.481902 | − | 0.278226i | ||||
\(658\) | − | 0.297874i | − | 0.0116123i | ||||||
\(659\) | 1.72663 | − | 2.99061i | 0.0672600 | − | 0.116498i | −0.830434 | − | 0.557117i | \(-0.811908\pi\) |
0.897694 | + | 0.440619i | \(0.145241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.3306 | − | 12.3152i | 0.829665 | − | 0.479007i | −0.0240732 | − | 0.999710i | \(-0.507663\pi\) |
0.853738 | + | 0.520703i | \(0.174330\pi\) | |||||||
\(662\) | −18.9464 | −0.736373 | ||||||||
\(663\) | 6.15150 | − | 5.11195i | 0.238904 | − | 0.198532i | ||||
\(664\) | 4.42419 | 0.171692 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.77303 | + | 3.07097i | 0.0687034 | + | 0.118998i | ||||
\(667\) | −4.39929 | + | 7.61980i | −0.170341 | + | 0.295040i | ||||
\(668\) | − | 1.45177i | − | 0.0561707i | ||||||
\(669\) | −4.03252 | − | 2.32817i | −0.155906 | − | 0.0900124i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.18515i | 0.0457521i | ||||||||
\(672\) | −0.140141 | + | 0.242731i | −0.00540604 | + | 0.00936354i | ||||
\(673\) | 8.52052 | + | 14.7580i | 0.328442 | + | 0.568878i | 0.982203 | − | 0.187823i | \(-0.0601431\pi\) |
−0.653761 | + | 0.756701i | \(0.726810\pi\) | |||||||
\(674\) | 2.36395 | − | 1.36483i | 0.0910560 | − | 0.0525712i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.87847 | − | 8.45079i | −0.379941 | − | 0.325030i | ||||
\(677\) | −16.6324 | −0.639236 | −0.319618 | − | 0.947546i | \(-0.603555\pi\) | ||||
−0.319618 | + | 0.947546i | \(0.603555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.177576 | + | 0.307571i | 0.00681475 | + | 0.0118035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.20436i | 0.237752i | ||||||||
\(682\) | −2.17820 | − | 1.25758i | −0.0834075 | − | 0.0481554i | ||||
\(683\) | 42.3252 | + | 24.4365i | 1.61953 | + | 0.935035i | 0.987042 | + | 0.160463i | \(0.0512987\pi\) |
0.632486 | + | 0.774572i | \(0.282035\pi\) | |||||||
\(684\) | − | 5.27811i | − | 0.201813i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.95096 | + | 3.37916i | 0.0744880 | + | 0.129017i | ||||
\(687\) | 11.1379 | − | 6.43049i | 0.424939 | − | 0.245339i | ||||
\(688\) | 3.60882 | 0.137585 | ||||||||
\(689\) | −9.09858 | + | 7.56101i | −0.346628 | + | 0.288051i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.0699 | − | 17.9382i | 1.18195 | − | 0.682401i | 0.225488 | − | 0.974246i | \(-0.427602\pi\) |
0.956466 | + | 0.291845i | \(0.0942690\pi\) | |||||||
\(692\) | −6.67010 | − | 11.5530i | −0.253559 | − | 0.439177i | ||||
\(693\) | −0.107426 | + | 0.186068i | −0.00408079 | + | 0.00706814i | ||||
\(694\) | 12.6920i | 0.481781i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.24863 | + | 3.03030i | 0.198949 | + | 0.114863i | ||||
\(697\) | 4.92099i | 0.186396i | ||||||||
\(698\) | −0.605676 | + | 1.04906i | −0.0229252 | + | 0.0397075i | ||||
\(699\) | −0.485461 | − | 0.840844i | −0.0183618 | − | 0.0318036i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.0288 | −1.17194 | −0.585971 | − | 0.810332i | \(-0.699287\pi\) | ||||
−0.585971 | + | 0.810332i | \(0.699287\pi\) | |||||||
\(702\) | −1.24931 | + | 3.38219i | −0.0471520 | + | 0.127653i | ||||
\(703\) | 18.7165 | 0.705905 | ||||||||
\(704\) | −0.663862 | + | 0.383281i | −0.0250202 | + | 0.0144454i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.7901 | − | 29.0813i | 0.631904 | − | 1.09449i | ||||
\(707\) | − | 1.26896i | − | 0.0477243i | ||||||
\(708\) | −4.32824 | − | 2.49891i | −0.162665 | − | 0.0939149i | ||||
\(709\) | 9.78339 | + | 5.64844i | 0.367423 | + | 0.212132i | 0.672332 | − | 0.740250i | \(-0.265293\pi\) |
−0.304909 | + | 0.952381i | \(0.598626\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.23574 | − | 12.5327i | 0.271362 | − | 0.470012i | ||||
\(712\) | −2.65740 | − | 4.60275i | −0.0995901 | − | 0.172495i | ||||
\(713\) | 4.12523 | − | 2.38170i | 0.154491 | − | 0.0891954i | ||||
\(714\) | 0.621757 | 0.0232687 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25.2532 | 0.943755 | ||||||||
\(717\) | −12.8158 | + | 7.39922i | −0.478616 | + | 0.276329i | ||||
\(718\) | −11.0211 | − | 19.0892i | −0.411305 | − | 0.712401i | ||||
\(719\) | −6.01084 | + | 10.4111i | −0.224167 | + | 0.388268i | −0.956069 | − | 0.293141i | \(-0.905299\pi\) |
0.731902 | + | 0.681409i | \(0.238633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.714286 | + | 0.412393i | 0.0266014 | + | 0.0153583i | ||||
\(722\) | −7.67161 | − | 4.42920i | −0.285508 | − | 0.164838i | ||||
\(723\) | 2.19157i | 0.0815052i | ||||||||
\(724\) | −0.157396 | + | 0.272618i | −0.00584958 | + | 0.0101318i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.01739 | − | 5.20619i | 0.334667 | − | 0.193220i | ||||
\(727\) | −4.18908 | −0.155364 | −0.0776822 | − | 0.996978i | \(-0.524752\pi\) | ||||
−0.0776822 | + | 0.996978i | \(0.524752\pi\) | |||||||
\(728\) | −0.170738 | − | 0.996041i | −0.00632796 | − | 0.0369157i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00278 | − | 6.93303i | −0.148048 | − | 0.256427i | ||||
\(732\) | −0.773028 | + | 1.33892i | −0.0285719 | + | 0.0494880i | ||||
\(733\) | 11.3923i | 0.420783i | 0.977617 | + | 0.210391i | \(0.0674738\pi\) | ||||
−0.977617 | + | 0.210391i | \(0.932526\pi\) | |||||||
\(734\) | −8.36421 | − | 4.82908i | −0.308729 | − | 0.178244i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.45177i | − | 0.0535129i | ||||||
\(737\) | −2.85002 | + | 4.93637i | −0.104982 | + | 0.181834i | ||||
\(738\) | −1.10917 | − | 1.92113i | −0.0408290 | − | 0.0707178i | ||||
\(739\) | −17.6996 | + | 10.2189i | −0.651090 | + | 0.375907i | −0.788874 | − | 0.614555i | \(-0.789336\pi\) |
0.137783 | + | 0.990462i | \(0.456002\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.1629 | + | 14.6363i | 0.446817 | + | 0.537679i | ||||
\(742\) | −0.919631 | −0.0337607 | ||||||||
\(743\) | −8.79255 | + | 5.07638i | −0.322567 | + | 0.186234i | −0.652536 | − | 0.757757i | \(-0.726295\pi\) |
0.329969 | + | 0.943992i | \(0.392962\pi\) | |||||||
\(744\) | −1.64055 | − | 2.84152i | −0.0601455 | − | 0.104175i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 12.2431i | − | 0.448250i | ||||||
\(747\) | 3.83146 | + | 2.21209i | 0.140186 | + | 0.0809362i | ||||
\(748\) | 1.47267 | + | 0.850244i | 0.0538460 | + | 0.0310880i | ||||
\(749\) | − | 5.33902i | − | 0.195083i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.99084 | − | 15.5726i | −0.328080 | − | 0.568252i | 0.654051 | − | 0.756451i | \(-0.273068\pi\) |
−0.982131 | + | 0.188199i | \(0.939735\pi\) | |||||||
\(752\) | 0.920385 | − | 0.531385i | 0.0335630 | − | 0.0193776i | ||||
\(753\) | 10.5897 | 0.385911 | ||||||||
\(754\) | −21.5376 | + | 3.69191i | −0.784355 | + | 0.134451i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.242731 | + | 0.140141i | −0.00882803 | + | 0.00509686i | ||||
\(757\) | −22.4916 | − | 38.9566i | −0.817470 | − | 1.41590i | −0.907540 | − | 0.419965i | \(-0.862042\pi\) |
0.0900700 | − | 0.995935i | \(-0.471291\pi\) | |||||||
\(758\) | −6.79362 | + | 11.7669i | −0.246755 | + | 0.427393i | ||||
\(759\) | − | 1.11287i | − | 0.0403947i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.1697 | − | 22.6146i | −1.41990 | − | 0.819779i | −0.423610 | − | 0.905845i | \(-0.639237\pi\) |
−0.996289 | + | 0.0860657i | \(0.972571\pi\) | |||||||
\(762\) | − | 3.17171i | − | 0.114899i | ||||||
\(763\) | 1.26764 | − | 2.19562i | 0.0458917 | − | 0.0794867i | ||||
\(764\) | −11.2666 | − | 19.5143i | −0.407612 | − | 0.706004i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.4137 | 0.556921 | ||||||||
\(767\) | 17.7609 | − | 3.04450i | 0.641308 | − | 0.109931i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 31.3010 | − | 18.0716i | 1.12874 | − | 0.651680i | 0.185125 | − | 0.982715i | \(-0.440731\pi\) |
0.943619 | + | 0.331035i | \(0.107398\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.42396 | − | 5.93047i | 0.123311 | − | 0.213581i | ||||
\(772\) | 9.78362i | 0.352120i | ||||||||
\(773\) | 14.1829 | + | 8.18850i | 0.510123 | + | 0.294520i | 0.732884 | − | 0.680353i | \(-0.238174\pi\) |
−0.222761 | + | 0.974873i | \(0.571507\pi\) | |||||||
\(774\) | 3.12533 | + | 1.80441i | 0.112338 | + | 0.0648583i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.633565 | + | 1.09737i | −0.0227437 | + | 0.0393932i | ||||
\(777\) | −0.496946 | − | 0.860736i | −0.0178279 | − | 0.0308787i | ||||
\(778\) | −5.24863 | + | 3.03030i | −0.188172 | + | 0.108641i | ||||
\(779\) | −11.7086 | −0.419504 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.85714 | −0.0664538 | ||||||||
\(782\) | −2.78904 | + | 1.61025i | −0.0997359 | + | 0.0575825i | ||||
\(783\) | 3.03030 | + | 5.24863i | 0.108294 | + | 0.187571i | ||||
\(784\) | −3.46072 | + | 5.99414i | −0.123597 | + | 0.214077i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.3667 | − | 7.71724i | −0.476773 | − | 0.275265i | ||||
\(787\) | −39.1108 | − | 22.5807i | −1.39415 | − | 0.804913i | −0.400379 | − | 0.916350i | \(-0.631122\pi\) |
−0.993772 | + | 0.111436i | \(0.964455\pi\) | |||||||
\(788\) | 12.4572i | 0.443771i | ||||||||
\(789\) | 13.1181 | − | 22.7212i | 0.467017 | − | 0.808898i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.766562 | −0.0272386 | ||||||||
\(793\) | −0.941804 | − | 5.49425i | −0.0334444 | − | 0.195106i | ||||
\(794\) | −16.9893 | −0.602927 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.53195 | − | 13.0457i | −0.266963 | − | 0.462393i | ||||
\(797\) | −13.4818 | + | 23.3511i | −0.477549 | + | 0.827139i | −0.999669 | − | 0.0257329i | \(-0.991808\pi\) |
0.522120 | + | 0.852872i | \(0.325141\pi\) | |||||||
\(798\) | 1.47935i | 0.0523686i | ||||||||
\(799\) | −2.04172 | − | 1.17879i | −0.0722308 | − | 0.0417025i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5.31479i | − | 0.187789i | ||||||
\(802\) | 9.70852 | − | 16.8156i | 0.342820 | − | 0.593781i | ||||
\(803\) | 5.46674 | + | 9.46867i | 0.192917 | + | 0.334142i | ||||
\(804\) | −6.43963 | + | 3.71792i | −0.227108 | + | 0.131121i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.0973 | + | 4.09910i | 0.390886 | + | 0.144385i | ||||
\(807\) | −6.49875 | −0.228767 | ||||||||
\(808\) | 3.92090 | − | 2.26374i | 0.137937 | − | 0.0796379i | ||||
\(809\) | 5.02204 | + | 8.69843i | 0.176566 | + | 0.305821i | 0.940702 | − | 0.339234i | \(-0.110168\pi\) |
−0.764136 | + | 0.645055i | \(0.776835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 26.8449i | − | 0.942652i | −0.881959 | − | 0.471326i | \(-0.843776\pi\) | ||
0.881959 | − | 0.471326i | \(-0.156224\pi\) | |||||||
\(812\) | −1.47109 | − | 0.849335i | −0.0516252 | − | 0.0298058i | ||||
\(813\) | 5.35904 | + | 3.09404i | 0.187950 | + | 0.108513i | ||||
\(814\) | − | 2.71827i | − | 0.0952754i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.10917 | + | 1.92113i | 0.0388286 | + | 0.0672531i | ||||
\(817\) | 16.4958 | − | 9.52388i | 0.577117 | − | 0.333198i | ||||
\(818\) | 0.927603 | 0.0324329 | ||||||||
\(819\) | 0.350157 | − | 0.947965i | 0.0122355 | − | 0.0331246i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.4214 | + | 16.4091i | −0.991912 | + | 0.572681i | −0.905845 | − | 0.423609i | \(-0.860763\pi\) |
−0.0860669 | + | 0.996289i | \(0.527430\pi\) | |||||||
\(822\) | 0.834145 | + | 1.44478i | 0.0290941 | + | 0.0503925i | ||||
\(823\) | −4.43549 | + | 7.68249i | −0.154611 | + | 0.267795i | −0.932917 | − | 0.360090i | \(-0.882746\pi\) |
0.778306 | + | 0.627885i | \(0.216079\pi\) | |||||||
\(824\) | 2.94271i | 0.102514i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.21313 | + | 0.700398i | 0.0422100 | + | 0.0243700i | ||||
\(827\) | 0.892425i | 0.0310327i | 0.999880 | + | 0.0155163i | \(0.00493920\pi\) | ||||
−0.999880 | + | 0.0155163i | \(0.995061\pi\) | |||||||
\(828\) | 0.725885 | − | 1.25727i | 0.0252262 | − | 0.0436931i | ||||
\(829\) | −5.74291 | − | 9.94701i | −0.199459 | − | 0.345474i | 0.748894 | − | 0.662690i | \(-0.230585\pi\) |
−0.948353 | + | 0.317216i | \(0.897252\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.0577 | −1.00800 | ||||||||
\(832\) | 2.77303 | − | 2.30441i | 0.0961374 | − | 0.0798911i | ||||
\(833\) | 15.3541 | 0.531986 | ||||||||
\(834\) | 1.82549 | − | 1.05395i | 0.0632117 | − | 0.0364953i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.02300 | + | 3.50393i | −0.0699668 | + | 0.121186i | ||||
\(837\) | − | 3.28110i | − | 0.113411i | ||||||
\(838\) | −21.8077 | − | 12.5907i | −0.753336 | − | 0.434939i | ||||
\(839\) | 24.1738 | + | 13.9568i | 0.834573 | + | 0.481841i | 0.855416 | − | 0.517942i | \(-0.173302\pi\) |
−0.0208426 | + | 0.999783i | \(0.506635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.86540 | + | 6.69507i | −0.133290 | + | 0.230865i | ||||
\(842\) | −13.8456 | − | 23.9812i | −0.477150 | − | 0.826448i | ||||
\(843\) | −12.2489 | + | 7.07188i | −0.421873 | + | 0.243568i | ||||
\(844\) | −15.0775 | −0.518989 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.06277 | 0.0365388 | ||||||||
\(847\) | −2.52740 | + | 1.45920i | −0.0868426 | + | 0.0501386i | ||||
\(848\) | −1.64055 | − | 2.84152i | −0.0563367 | − | 0.0975781i | ||||
\(849\) | −4.37290 | + | 7.57409i | −0.150078 | + | 0.259942i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.45835 | + | 2.57403i | 0.152830 | + | 0.0882365i | ||||
\(852\) | −2.09811 | − | 1.21135i | −0.0718802 | − | 0.0415000i | ||||
\(853\) | − | 41.6937i | − | 1.42757i | −0.700367 | − | 0.713783i | \(-0.746980\pi\) | ||
0.700367 | − | 0.713783i | \(-0.253020\pi\) | |||||||
\(854\) | 0.216665 | − | 0.375275i | 0.00741413 | − | 0.0128417i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.4967 | − | 9.52440i | 0.563847 | − | 0.325537i | ||||
\(857\) | 4.57772 | 0.156372 | 0.0781860 | − | 0.996939i | \(-0.475087\pi\) | ||||
0.0781860 | + | 0.996939i | \(0.475087\pi\) | |||||||
\(858\) | 2.12570 | − | 1.76647i | 0.0725701 | − | 0.0603065i | ||||
\(859\) | −32.0617 | −1.09393 | −0.546966 | − | 0.837155i | \(-0.684217\pi\) | ||||
−0.546966 | + | 0.837155i | \(0.684217\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.310878 | + | 0.538457i | 0.0105947 | + | 0.0183506i | ||||
\(862\) | −0.0460826 | + | 0.0798174i | −0.00156958 | + | 0.00271859i | ||||
\(863\) | 30.7876i | 1.04802i | 0.851711 | + | 0.524011i | \(0.175565\pi\) | ||||
−0.851711 | + | 0.524011i | \(0.824435\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.02225i | 0.136682i | ||||||||
\(867\) | −6.03950 | + | 10.4607i | −0.205112 | + | 0.355265i | ||||
\(868\) | 0.459815 | + | 0.796424i | 0.0156072 | + | 0.0270324i | ||||
\(869\) | −9.60707 | + | 5.54664i | −0.325898 | + | 0.188157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.28965 | − | 25.1495i | 0.314768 | − | 0.852157i | ||||
\(872\) | 9.04549 | 0.306319 | ||||||||
\(873\) | −1.09737 | + | 0.633565i | −0.0371402 | + | 0.0214429i | ||||
\(874\) | −3.83130 | − | 6.63600i | −0.129596 | − | 0.224466i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.2630i | 0.481902i | ||||||||
\(877\) | −35.3169 | − | 20.3902i | −1.19257 | − | 0.688529i | −0.233679 | − | 0.972314i | \(-0.575076\pi\) |
−0.958888 | + | 0.283785i | \(0.908410\pi\) | |||||||
\(878\) | −22.4719 | − | 12.9742i | −0.758391 | − | 0.437857i | ||||
\(879\) | − | 31.5001i | − | 1.06247i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.4928 | − | 37.2265i | −0.724109 | − | 1.25419i | −0.959340 | − | 0.282254i | \(-0.908918\pi\) |
0.235230 | − | 0.971940i | \(-0.424416\pi\) | |||||||
\(882\) | −5.99414 | + | 3.46072i | −0.201833 | + | 0.116529i | ||||
\(883\) | 29.9139 | 1.00668 | 0.503341 | − | 0.864088i | \(-0.332104\pi\) | ||||
0.503341 | + | 0.864088i | \(0.332104\pi\) | |||||||
\(884\) | −7.50283 | − | 2.77138i | −0.252347 | − | 0.0932115i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.0463 | + | 7.53229i | −0.438299 | + | 0.253052i | ||||
\(887\) | −23.4471 | − | 40.6116i | −0.787278 | − | 1.36360i | −0.927629 | − | 0.373503i | \(-0.878157\pi\) |
0.140351 | − | 0.990102i | \(-0.455177\pi\) | |||||||
\(888\) | 1.77303 | − | 3.07097i | 0.0594989 | − | 0.103055i | ||||
\(889\) | 0.888970i | 0.0298151i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.663862 | − | 0.383281i | −0.0222402 | − | 0.0128404i | ||||
\(892\) | 4.65635i | 0.155906i | ||||||||
\(893\) | 2.80470 | − | 4.85789i | 0.0938558 | − | 0.162563i | ||||
\(894\) | 2.87039 | + | 4.97167i | 0.0960004 | + | 0.166277i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.280281 | 0.00936354 | ||||||||
\(897\) | 0.884368 | + | 5.15918i | 0.0295282 | + | 0.172260i | ||||
\(898\) | −34.4631 | −1.15005 | ||||||||
\(899\) | 17.2213 | − | 9.94271i | 0.574362 | − | 0.331608i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.63928 | + | 6.30343i | −0.121242 | + | 0.209998i | ||||
\(902\) | 1.70049i | 0.0566201i | ||||||||
\(903\) | −0.875972 | − | 0.505743i | −0.0291505 | − | 0.0168301i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.08549 | − | 14.0045i | 0.268622 | − | 0.465268i | ||||
\(907\) | −13.3523 | − | 23.1269i | −0.443356 | − | 0.767915i | 0.554580 | − | 0.832130i | \(-0.312879\pi\) |
−0.997936 | + | 0.0642155i | \(0.979546\pi\) | |||||||
\(908\) | 5.37313 | − | 3.10218i | 0.178314 | − | 0.102949i | ||||
\(909\) | 4.52747 | 0.150167 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.8401 | 0.955515 | 0.477758 | − | 0.878492i | \(-0.341450\pi\) | ||||
0.477758 | + | 0.878492i | \(0.341450\pi\) | |||||||
\(912\) | −4.57097 | + | 2.63905i | −0.151360 | + | 0.0873878i | ||||
\(913\) | −1.69571 | − | 2.93705i | −0.0561197 | − | 0.0972021i | ||||
\(914\) | 20.8149 | − | 36.0525i | 0.688496 | − | 1.19251i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.1379 | − | 6.43049i | −0.368008 | − | 0.212469i | ||||
\(917\) | 3.74642 | + | 2.16300i | 0.123718 | + | 0.0714285i | ||||
\(918\) | 2.21833i | 0.0732158i | ||||||||
\(919\) | −14.4493 | + | 25.0269i | −0.476637 | + | 0.825560i | −0.999642 | − | 0.0267702i | \(-0.991478\pi\) |
0.523005 | + | 0.852330i | \(0.324811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.08947 | + | 3.51576i | −0.200655 | + | 0.115848i | ||||
\(922\) | −6.95980 | −0.229209 | ||||||||
\(923\) | 8.60957 | − | 1.47582i | 0.283387 | − | 0.0485772i | ||||
\(924\) | 0.214853 | 0.00706814 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.96444 | − | 10.3307i | −0.196004 | − | 0.339488i | ||||
\(927\) | −1.47135 | + | 2.54846i | −0.0483256 | + | 0.0837025i | ||||
\(928\) | − | 6.06059i | − | 0.198949i | ||||||
\(929\) | −37.8896 | − | 21.8756i | −1.24312 | − | 0.717715i | −0.273391 | − | 0.961903i | \(-0.588145\pi\) |
−0.969728 | + | 0.244188i | \(0.921479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.5321i | 1.19729i | ||||||||
\(932\) | −0.485461 | + | 0.840844i | −0.0159018 | + | 0.0275428i | ||||
\(933\) | 4.39922 | + | 7.61967i | 0.144024 | + | 0.249457i | ||||
\(934\) | −29.8264 | + | 17.2203i | −0.975950 | + | 0.563465i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.55372 | − | 0.609166i | 0.116157 | − | 0.0199112i | ||||
\(937\) | 6.71836 | 0.219479 | 0.109740 | − | 0.993960i | \(-0.464998\pi\) | ||||
0.109740 | + | 0.993960i | \(0.464998\pi\) | |||||||
\(938\) | 1.80491 | − | 1.04206i | 0.0589323 | − | 0.0340246i | ||||
\(939\) | 4.67067 | + | 8.08984i | 0.152422 | + | 0.264002i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.9654i | 1.10724i | 0.832769 | + | 0.553621i | \(0.186754\pi\) | ||||
−0.832769 | + | 0.553621i | \(0.813246\pi\) | |||||||
\(942\) | 13.7179 | + | 7.92004i | 0.446954 | + | 0.258049i | ||||
\(943\) | −2.78904 | − | 1.61025i | −0.0908236 | − | 0.0524371i | ||||
\(944\) | 4.99783i | 0.162665i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.38319 | − | 2.39576i | −0.0449715 | − | 0.0778929i | ||||
\(947\) | 35.2907 | − | 20.3751i | 1.14679 | − | 0.662101i | 0.198689 | − | 0.980063i | \(-0.436332\pi\) |
0.948104 | + | 0.317962i | \(0.102998\pi\) | |||||||
\(948\) | −14.4715 | −0.470012 | ||||||||
\(949\) | −32.8678 | − | 39.5517i | −1.06694 | − | 1.28390i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.8612 | + | 9.73484i | −0.546763 | + | 0.315674i | ||||
\(952\) | −0.310878 | − | 0.538457i | −0.0100756 | − | 0.0174515i | ||||
\(953\) | 3.02309 | − | 5.23614i | 0.0979274 | − | 0.169615i | −0.812899 | − | 0.582404i | \(-0.802112\pi\) |
0.910827 | + | 0.412789i | \(0.135445\pi\) | |||||||
\(954\) | − | 3.28110i | − | 0.106230i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.8158 | + | 7.39922i | 0.414493 | + | 0.239308i | ||||
\(957\) | − | 4.64582i | − | 0.150178i | ||||||
\(958\) | 6.86444 | − | 11.8896i | 0.221780 | − | 0.384134i | ||||
\(959\) | −0.233795 | − | 0.404945i | −0.00754964 | − | 0.0130764i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2344 | 0.652722 | ||||||||
\(962\) | 2.16014 | + | 12.6017i | 0.0696456 | + | 0.406295i | ||||
\(963\) | 19.0488 | 0.613839 | ||||||||
\(964\) | 1.89795 | − | 1.09578i | 0.0611289 | − | 0.0352928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.203452 | + | 0.352389i | −0.00654596 | + | 0.0113379i | ||||
\(967\) | − | 39.8852i | − | 1.28262i | −0.767282 | − | 0.641310i | \(-0.778391\pi\) | ||
0.767282 | − | 0.641310i | \(-0.221609\pi\) | |||||||
\(968\) | −9.01739 | − | 5.20619i | −0.289830 | − | 0.167333i | ||||
\(969\) | 10.1399 | + | 5.85429i | 0.325742 | + | 0.188067i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.5176 | − | 33.8055i | 0.626349 | − | 1.08487i | −0.361929 | − | 0.932206i | \(-0.617882\pi\) |
0.988278 | − | 0.152663i | \(-0.0487849\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −0.511652 | + | 0.295402i | −0.0164028 | + | 0.00947017i | ||||
\(974\) | −9.52978 | −0.305354 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.54606 | 0.0494880 | ||||||||
\(977\) | −36.4159 | + | 21.0247i | −1.16505 | + | 0.672641i | −0.952509 | − | 0.304512i | \(-0.901507\pi\) |
−0.212539 | + | 0.977153i | \(0.568173\pi\) | |||||||
\(978\) | 5.65740 | + | 9.79890i | 0.180904 | + | 0.313334i | ||||
\(979\) | −2.03706 | + | 3.52829i | −0.0651047 | + | 0.112765i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.83362 | + | 4.52274i | 0.250108 | + | 0.144400i | ||||
\(982\) | −28.9960 | − | 16.7409i | −0.925301 | − | 0.534223i | ||||
\(983\) | 27.5124i | 0.877508i | 0.898607 | + | 0.438754i | \(0.144580\pi\) | ||||
−0.898607 | + | 0.438754i | \(0.855420\pi\) | |||||||
\(984\) | −1.10917 | + | 1.92113i | −0.0353589 | + | 0.0612434i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.6432 | + | 6.72220i | −0.370795 | + | 0.214079i | ||||
\(987\) | −0.297874 | −0.00948144 | ||||||||
\(988\) | 6.59397 | − | 17.8516i | 0.209782 | − | 0.567934i | ||||
\(989\) | 5.23918 | 0.166596 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.9614 | − | 48.4306i | −0.888224 | − | 1.53845i | −0.841973 | − | 0.539519i | \(-0.818606\pi\) |
−0.0462506 | − | 0.998930i | \(-0.514727\pi\) | |||||||
\(992\) | −1.64055 | + | 2.84152i | −0.0520875 | + | 0.0902182i | ||||
\(993\) | 18.9464i | 0.601246i | ||||||||
\(994\) | 0.588062 | + | 0.339518i | 0.0186522 | + | 0.0107688i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 4.42419i | − | 0.140186i | ||||||
\(997\) | 14.8283 | − | 25.6834i | 0.469618 | − | 0.813403i | −0.529778 | − | 0.848136i | \(-0.677725\pi\) |
0.999397 | + | 0.0347335i | \(0.0110582\pi\) | |||||||
\(998\) | 7.54409 | + | 13.0667i | 0.238804 | + | 0.413620i | ||||
\(999\) | 3.07097 | − | 1.77303i | 0.0971613 | − | 0.0560961i |
(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 | 1950.2.bc.k.751.2 | yes | 12 | |
5.2 | odd | 4 | 1950.2.y.m.49.5 | 12 | |||
5.3 | odd | 4 | 1950.2.y.n.49.2 | 12 | |||
5.4 | even | 2 | 1950.2.bc.h.751.5 | ✓ | 12 | ||
13.4 | even | 6 | inner | 1950.2.bc.k.901.2 | yes | 12 | |
65.4 | even | 6 | 1950.2.bc.h.901.5 | yes | 12 | ||
65.17 | odd | 12 | 1950.2.y.n.199.2 | 12 | |||
65.43 | odd | 12 | 1950.2.y.m.199.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.m.49.5 | 12 | 5.2 | odd | 4 | |||
1950.2.y.m.199.5 | 12 | 65.43 | odd | 12 | |||
1950.2.y.n.49.2 | 12 | 5.3 | odd | 4 | |||
1950.2.y.n.199.2 | 12 | 65.17 | odd | 12 | |||
1950.2.bc.h.751.5 | ✓ | 12 | 5.4 | even | 2 | ||
1950.2.bc.h.901.5 | yes | 12 | 65.4 | even | 6 | ||
1950.2.bc.k.751.2 | yes | 12 | 1.1 | even | 1 | trivial | |
1950.2.bc.k.901.2 | yes | 12 | 13.4 | even | 6 | inner |