Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
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, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
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.y (of order \(6\), degree \(2\), not 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 | 199.2 | ||
Root | \(0.500000 + 0.414256i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.199 |
Dual form | 1950.2.y.n.49.2 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | + | 0.500000i | −0.353553 | + | 0.204124i | ||||
\(7\) | 0.140141 | + | 0.242731i | 0.0529682 | + | 0.0917436i | 0.891294 | − | 0.453426i | \(-0.149798\pi\) |
−0.838326 | + | 0.545170i | \(0.816465\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.663862 | + | 0.383281i | 0.200162 | + | 0.115564i | 0.596731 | − | 0.802441i | \(-0.296466\pi\) |
−0.396569 | + | 0.918005i | \(0.629799\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −2.30441 | + | 2.77303i | −0.639129 | + | 0.769100i | ||||
\(14\) | 0.280281 | 0.0749083 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.92113 | − | 1.10917i | 0.465943 | − | 0.269012i | −0.248597 | − | 0.968607i | \(-0.579969\pi\) |
0.714540 | + | 0.699595i | \(0.246636\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.57097 | − | 2.63905i | 1.04865 | − | 0.605440i | 0.126381 | − | 0.991982i | \(-0.459664\pi\) |
0.922272 | + | 0.386541i | \(0.126330\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.280281i | − | 0.0611624i | ||||||
\(22\) | 0.663862 | − | 0.383281i | 0.141536 | − | 0.0817158i | ||||
\(23\) | 1.25727 | + | 0.725885i | 0.262159 | + | 0.151357i | 0.625319 | − | 0.780369i | \(-0.284969\pi\) |
−0.363160 | + | 0.931727i | \(0.618302\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.24931 | + | 3.38219i | 0.245009 | + | 0.663303i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.140141 | − | 0.242731i | 0.0264841 | − | 0.0458718i | ||||
\(29\) | 3.03030 | − | 5.24863i | 0.562712 | − | 0.974646i | −0.434546 | − | 0.900649i | \(-0.643091\pi\) |
0.997259 | − | 0.0739965i | \(-0.0235754\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.28110i | − | 0.589303i | −0.955605 | − | 0.294652i | \(-0.904796\pi\) | ||
0.955605 | − | 0.294652i | \(-0.0952036\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.383281 | − | 0.663862i | −0.0667207 | − | 0.115564i | ||||
\(34\) | − | 2.21833i | − | 0.380441i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 1.77303 | − | 3.07097i | 0.291484 | − | 0.504865i | −0.682677 | − | 0.730720i | \(-0.739184\pi\) |
0.974161 | + | 0.225855i | \(0.0725177\pi\) | |||||||
\(38\) | − | 5.27811i | − | 0.856222i | ||||||
\(39\) | 3.38219 | − | 1.24931i | 0.541584 | − | 0.200049i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92113 | + | 1.10917i | 0.300030 | + | 0.173223i | 0.642457 | − | 0.766322i | \(-0.277915\pi\) |
−0.342426 | + | 0.939545i | \(0.611249\pi\) | |||||||
\(42\) | −0.242731 | − | 0.140141i | −0.0374542 | − | 0.0216242i | ||||
\(43\) | −3.12533 | + | 1.80441i | −0.476609 | + | 0.275170i | −0.719002 | − | 0.695008i | \(-0.755401\pi\) |
0.242393 | + | 0.970178i | \(0.422068\pi\) | |||||||
\(44\) | − | 0.766562i | − | 0.115564i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25727 | − | 0.725885i | 0.185374 | − | 0.107026i | ||||
\(47\) | 1.06277 | 0.155021 | 0.0775104 | − | 0.996992i | \(-0.475303\pi\) | ||||
0.0775104 | + | 0.996992i | \(0.475303\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 3.46072 | − | 5.99414i | 0.494389 | − | 0.856306i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.21833 | −0.310629 | ||||||||
\(52\) | 3.55372 | + | 0.609166i | 0.492812 | + | 0.0844761i | ||||
\(53\) | − | 3.28110i | − | 0.450694i | −0.974279 | − | 0.225347i | \(-0.927648\pi\) | ||
0.974279 | − | 0.225347i | \(-0.0723515\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.140141 | − | 0.242731i | −0.0187271 | − | 0.0324362i | ||||
\(57\) | −5.27811 | −0.699102 | ||||||||
\(58\) | −3.03030 | − | 5.24863i | −0.397898 | − | 0.689179i | ||||
\(59\) | 4.32824 | − | 2.49891i | 0.563489 | − | 0.325331i | −0.191055 | − | 0.981579i | \(-0.561191\pi\) |
0.754545 | + | 0.656249i | \(0.227858\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.773028 | − | 1.33892i | −0.0989761 | − | 0.171432i | 0.812285 | − | 0.583261i | \(-0.198223\pi\) |
−0.911261 | + | 0.411829i | \(0.864890\pi\) | |||||||
\(62\) | −2.84152 | − | 1.64055i | −0.360873 | − | 0.208350i | ||||
\(63\) | −0.140141 | + | 0.242731i | −0.0176561 | + | 0.0305812i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.766562 | −0.0943573 | ||||||||
\(67\) | 3.71792 | − | 6.43963i | 0.454216 | − | 0.786726i | −0.544426 | − | 0.838809i | \(-0.683253\pi\) |
0.998643 | + | 0.0520827i | \(0.0165859\pi\) | |||||||
\(68\) | −1.92113 | − | 1.10917i | −0.232971 | − | 0.134506i | ||||
\(69\) | −0.725885 | − | 1.25727i | −0.0873863 | − | 0.151357i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.09811 | + | 1.21135i | −0.249000 | + | 0.143760i | −0.619306 | − | 0.785149i | \(-0.712586\pi\) |
0.370306 | + | 0.928910i | \(0.379253\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −14.2630 | −1.66936 | −0.834679 | − | 0.550737i | \(-0.814347\pi\) | ||||
−0.834679 | + | 0.550737i | \(0.814347\pi\) | |||||||
\(74\) | −1.77303 | − | 3.07097i | −0.206110 | − | 0.356994i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.57097 | − | 2.63905i | −0.524327 | − | 0.302720i | ||||
\(77\) | 0.214853i | 0.0244848i | ||||||||
\(78\) | 0.609166 | − | 3.55372i | 0.0689744 | − | 0.402379i | ||||
\(79\) | 14.4715 | 1.62817 | 0.814085 | − | 0.580746i | \(-0.197239\pi\) | ||||
0.814085 | + | 0.580746i | \(0.197239\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.92113 | − | 1.10917i | 0.212153 | − | 0.122487i | ||||
\(83\) | 4.42419 | 0.485617 | 0.242809 | − | 0.970074i | \(-0.421931\pi\) | ||||
0.242809 | + | 0.970074i | \(0.421931\pi\) | |||||||
\(84\) | −0.242731 | + | 0.140141i | −0.0264841 | + | 0.0152906i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.60882i | 0.389150i | ||||||||
\(87\) | −5.24863 | + | 3.03030i | −0.562712 | + | 0.324882i | ||||
\(88\) | −0.663862 | − | 0.383281i | −0.0707679 | − | 0.0408579i | ||||
\(89\) | 4.60275 | + | 2.65740i | 0.487890 | + | 0.281683i | 0.723699 | − | 0.690116i | \(-0.242441\pi\) |
−0.235809 | + | 0.971799i | \(0.575774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.996041 | − | 0.170738i | −0.104413 | − | 0.0178982i | ||||
\(92\) | − | 1.45177i | − | 0.151357i | ||||||
\(93\) | −1.64055 | + | 2.84152i | −0.170117 | + | 0.294652i | ||||
\(94\) | 0.531385 | − | 0.920385i | 0.0548081 | − | 0.0949305i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 0.633565 | + | 1.09737i | 0.0643288 | + | 0.111421i | 0.896396 | − | 0.443254i | \(-0.146176\pi\) |
−0.832067 | + | 0.554675i | \(0.812843\pi\) | |||||||
\(98\) | −3.46072 | − | 5.99414i | −0.349586 | − | 0.605500i | ||||
\(99\) | 0.766562i | 0.0770424i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.26374 | + | 3.92090i | −0.225250 | + | 0.390145i | −0.956394 | − | 0.292078i | \(-0.905653\pi\) |
0.731144 | + | 0.682223i | \(0.238987\pi\) | |||||||
\(102\) | −1.10917 | + | 1.92113i | −0.109824 | + | 0.190220i | ||||
\(103\) | − | 2.94271i | − | 0.289954i | −0.989435 | − | 0.144977i | \(-0.953689\pi\) | ||
0.989435 | − | 0.144977i | \(-0.0463108\pi\) | |||||||
\(104\) | 2.30441 | − | 2.77303i | 0.225966 | − | 0.271918i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.84152 | − | 1.64055i | −0.275992 | − | 0.159344i | ||||
\(107\) | −16.4967 | − | 9.52440i | −1.59480 | − | 0.920758i | −0.992467 | − | 0.122513i | \(-0.960905\pi\) |
−0.602333 | − | 0.798245i | \(-0.705762\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | − | 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 | ||||
\(112\) | −0.280281 | −0.0264841 | ||||||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | −2.63905 | + | 4.57097i | −0.247170 | + | 0.428111i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.06059 | −0.562712 | ||||||||
\(117\) | −3.55372 | − | 0.609166i | −0.328541 | − | 0.0563174i | ||||
\(118\) | − | 4.99783i | − | 0.460087i | ||||||
\(119\) | 0.538457 | + | 0.310878i | 0.0493603 | + | 0.0284982i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.20619 | − | 9.01739i | −0.473290 | − | 0.819763i | ||||
\(122\) | −1.54606 | −0.139973 | ||||||||
\(123\) | −1.10917 | − | 1.92113i | −0.100010 | − | 0.173223i | ||||
\(124\) | −2.84152 | + | 1.64055i | −0.255176 | + | 0.147326i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.140141 | + | 0.242731i | 0.0124847 | + | 0.0216242i | ||||
\(127\) | 2.74678 | + | 1.58585i | 0.243737 | + | 0.140722i | 0.616893 | − | 0.787047i | \(-0.288391\pi\) |
−0.373156 | + | 0.927769i | \(0.621724\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.60882 | 0.317739 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4345 | 1.34852 | 0.674259 | − | 0.738495i | \(-0.264463\pi\) | ||||
0.674259 | + | 0.738495i | \(0.264463\pi\) | |||||||
\(132\) | −0.383281 | + | 0.663862i | −0.0333603 | + | 0.0577818i | ||||
\(133\) | 1.28116 | + | 0.739677i | 0.111091 | + | 0.0641381i | ||||
\(134\) | −3.71792 | − | 6.43963i | −0.321180 | − | 0.556299i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.92113 | + | 1.10917i | −0.164736 | + | 0.0951102i | ||||
\(137\) | −0.834145 | − | 1.44478i | −0.0712658 | − | 0.123436i | 0.828191 | − | 0.560447i | \(-0.189371\pi\) |
−0.899456 | + | 0.437011i | \(0.856037\pi\) | |||||||
\(138\) | −1.45177 | −0.123583 | ||||||||
\(139\) | 1.05395 | + | 1.82549i | 0.0893949 | + | 0.154836i | 0.907256 | − | 0.420580i | \(-0.138173\pi\) |
−0.817861 | + | 0.575416i | \(0.804840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.920385 | − | 0.531385i | −0.0775104 | − | 0.0447507i | ||||
\(142\) | 2.42269i | 0.203308i | ||||||||
\(143\) | −2.59266 | + | 0.957671i | −0.216809 | + | 0.0800844i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.13150 | + | 12.3521i | −0.590207 | + | 1.02227i | ||||
\(147\) | −5.99414 | + | 3.46072i | −0.494389 | + | 0.285435i | ||||
\(148\) | −3.54606 | −0.291484 | ||||||||
\(149\) | 4.97167 | − | 2.87039i | 0.407295 | − | 0.235152i | −0.282332 | − | 0.959317i | \(-0.591108\pi\) |
0.689627 | + | 0.724165i | \(0.257775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.1710i | − | 1.31598i | −0.753029 | − | 0.657988i | \(-0.771408\pi\) | ||
0.753029 | − | 0.657988i | \(-0.228592\pi\) | |||||||
\(152\) | −4.57097 | + | 2.63905i | −0.370755 | + | 0.214055i | ||||
\(153\) | 1.92113 | + | 1.10917i | 0.155314 | + | 0.0896707i | ||||
\(154\) | 0.186068 | + | 0.107426i | 0.0149938 | + | 0.00865667i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.77303 | − | 2.30441i | −0.222020 | − | 0.184501i | ||||
\(157\) | − | 15.8401i | − | 1.26418i | −0.774896 | − | 0.632088i | \(-0.782198\pi\) | ||
0.774896 | − | 0.632088i | \(-0.217802\pi\) | |||||||
\(158\) | 7.23574 | − | 12.5327i | 0.575645 | − | 0.997046i | ||||
\(159\) | −1.64055 | + | 2.84152i | −0.130104 | + | 0.225347i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.406904i | 0.0320685i | ||||||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | 5.65740 | + | 9.79890i | 0.443121 | + | 0.767509i | 0.997919 | − | 0.0644763i | \(-0.0205377\pi\) |
−0.554798 | + | 0.831985i | \(0.687204\pi\) | |||||||
\(164\) | − | 2.21833i | − | 0.173223i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.21209 | − | 3.83146i | 0.171692 | − | 0.297379i | ||||
\(167\) | −0.725885 | + | 1.25727i | −0.0561707 | + | 0.0972904i | −0.892743 | − | 0.450565i | \(-0.851222\pi\) |
0.836573 | + | 0.547856i | \(0.184556\pi\) | |||||||
\(168\) | 0.280281i | 0.0216242i | ||||||||
\(169\) | −2.37937 | − | 12.7804i | −0.183028 | − | 0.983108i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.57097 | + | 2.63905i | 0.349551 | + | 0.201813i | ||||
\(172\) | 3.12533 | + | 1.80441i | 0.238304 | + | 0.137585i | ||||
\(173\) | 11.5530 | − | 6.67010i | 0.878355 | − | 0.507118i | 0.00823921 | − | 0.999966i | \(-0.497377\pi\) |
0.870116 | + | 0.492848i | \(0.164044\pi\) | |||||||
\(174\) | 6.06059i | 0.459452i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.663862 | + | 0.383281i | −0.0500405 | + | 0.0288909i | ||||
\(177\) | −4.99783 | −0.375660 | ||||||||
\(178\) | 4.60275 | − | 2.65740i | 0.344990 | − | 0.199180i | ||||
\(179\) | −12.6266 | + | 21.8699i | −0.943755 | + | 1.63463i | −0.185529 | + | 0.982639i | \(0.559400\pi\) |
−0.758226 | + | 0.651992i | \(0.773933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.314792 | −0.0233983 | −0.0116992 | − | 0.999932i | \(-0.503724\pi\) | ||||
−0.0116992 | + | 0.999932i | \(0.503724\pi\) | |||||||
\(182\) | −0.645884 | + | 0.777228i | −0.0478761 | + | 0.0576119i | ||||
\(183\) | 1.54606i | 0.114288i | ||||||||
\(184\) | −1.25727 | − | 0.725885i | −0.0926871 | − | 0.0535129i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.64055 | + | 2.84152i | 0.120291 | + | 0.208350i | ||||
\(187\) | 1.70049 | 0.124352 | ||||||||
\(188\) | −0.531385 | − | 0.920385i | −0.0387552 | − | 0.0671260i | ||||
\(189\) | 0.242731 | − | 0.140141i | 0.0176561 | − | 0.0101937i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2666 | + | 19.5143i | 0.815223 | + | 1.41201i | 0.909168 | + | 0.416430i | \(0.136719\pi\) |
−0.0939445 | + | 0.995577i | \(0.529948\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | −4.89181 | + | 8.47286i | −0.352120 | + | 0.609890i | −0.986621 | − | 0.163032i | \(-0.947872\pi\) |
0.634501 | + | 0.772922i | \(0.281206\pi\) | |||||||
\(194\) | 1.26713 | 0.0909746 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.92144 | −0.494389 | ||||||||
\(197\) | 6.22862 | − | 10.7883i | 0.443771 | − | 0.768634i | −0.554195 | − | 0.832387i | \(-0.686974\pi\) |
0.997966 | + | 0.0637530i | \(0.0203070\pi\) | |||||||
\(198\) | 0.663862 | + | 0.383281i | 0.0471786 | + | 0.0272386i | ||||
\(199\) | −7.53195 | − | 13.0457i | −0.533926 | − | 0.924787i | −0.999215 | − | 0.0396276i | \(-0.987383\pi\) |
0.465289 | − | 0.885159i | \(-0.345950\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.43963 | + | 3.71792i | −0.454216 | + | 0.262242i | ||||
\(202\) | 2.26374 | + | 3.92090i | 0.159276 | + | 0.275874i | ||||
\(203\) | 1.69867 | 0.119223 | ||||||||
\(204\) | 1.10917 | + | 1.92113i | 0.0776571 | + | 0.134506i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.54846 | − | 1.47135i | −0.177560 | − | 0.102514i | ||||
\(207\) | 1.45177i | 0.100905i | ||||||||
\(208\) | −1.24931 | − | 3.38219i | −0.0866238 | − | 0.234513i | ||||
\(209\) | 4.04600 | 0.279867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.53876 | + | 13.0575i | −0.518989 | + | 0.898916i | 0.480767 | + | 0.876848i | \(0.340358\pi\) |
−0.999756 | + | 0.0220676i | \(0.992975\pi\) | |||||||
\(212\) | −2.84152 | + | 1.64055i | −0.195156 | + | 0.112673i | ||||
\(213\) | 2.42269 | 0.166000 | ||||||||
\(214\) | −16.4967 | + | 9.52440i | −1.12769 | + | 0.651074i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0.796424 | − | 0.459815i | 0.0540648 | − | 0.0312143i | ||||
\(218\) | −7.83362 | − | 4.52274i | −0.530560 | − | 0.306319i | ||||
\(219\) | 12.3521 | + | 7.13150i | 0.834679 | + | 0.481902i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.35133 | + | 7.88333i | −0.0909004 | + | 0.530290i | ||||
\(222\) | 3.54606i | 0.237996i | ||||||||
\(223\) | −2.32817 | + | 4.03252i | −0.155906 | + | 0.270037i | −0.933389 | − | 0.358867i | \(-0.883163\pi\) |
0.777482 | + | 0.628905i | \(0.216496\pi\) | |||||||
\(224\) | −0.140141 | + | 0.242731i | −0.00936354 | + | 0.0162181i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.10218 | + | 5.37313i | 0.205899 | + | 0.356627i | 0.950419 | − | 0.310973i | \(-0.100655\pi\) |
−0.744520 | + | 0.667600i | \(0.767322\pi\) | |||||||
\(228\) | 2.63905 | + | 4.57097i | 0.174776 | + | 0.302720i | ||||
\(229\) | − | 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 | ||||
\(232\) | −3.03030 | + | 5.24863i | −0.198949 | + | 0.344589i | ||||
\(233\) | 0.970923i | 0.0636073i | 0.999494 | + | 0.0318036i | \(0.0101251\pi\) | ||||
−0.999494 | + | 0.0318036i | \(0.989875\pi\) | |||||||
\(234\) | −2.30441 | + | 2.77303i | −0.150644 | + | 0.181279i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.32824 | − | 2.49891i | −0.281745 | − | 0.162665i | ||||
\(237\) | −12.5327 | − | 7.23574i | −0.814085 | − | 0.470012i | ||||
\(238\) | 0.538457 | − | 0.310878i | 0.0349030 | − | 0.0201512i | ||||
\(239\) | 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 | −0.437624 | − | 0.899158i | \(-0.644180\pi\) |
0.559882 | + | 0.828572i | \(0.310847\pi\) | |||||||
\(242\) | −10.4124 | −0.669333 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −0.773028 | + | 1.33892i | −0.0494880 | + | 0.0857158i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.21833 | −0.141436 | ||||||||
\(247\) | −3.21524 | + | 18.7569i | −0.204581 | + | 1.19347i | ||||
\(248\) | 3.28110i | 0.208350i | ||||||||
\(249\) | −3.83146 | − | 2.21209i | −0.242809 | − | 0.140186i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.29487 | + | 9.17098i | 0.334209 | + | 0.578867i | 0.983333 | − | 0.181816i | \(-0.0581975\pi\) |
−0.649124 | + | 0.760683i | \(0.724864\pi\) | |||||||
\(252\) | 0.280281 | 0.0176561 | ||||||||
\(253\) | 0.556436 | + | 0.963775i | 0.0349828 | + | 0.0605920i | ||||
\(254\) | 2.74678 | − | 1.58585i | 0.172348 | − | 0.0995053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −5.93047 | − | 3.42396i | −0.369933 | − | 0.213581i | 0.303496 | − | 0.952833i | \(-0.401846\pi\) |
−0.673429 | + | 0.739252i | \(0.735179\pi\) | |||||||
\(258\) | 1.80441 | − | 3.12533i | 0.112338 | − | 0.194575i | ||||
\(259\) | 0.993893 | 0.0617575 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.06059 | 0.375141 | ||||||||
\(262\) | 7.71724 | − | 13.3667i | 0.476773 | − | 0.825795i | ||||
\(263\) | 22.7212 | + | 13.1181i | 1.40105 | + | 0.808898i | 0.994501 | − | 0.104730i | \(-0.0333979\pi\) |
0.406551 | + | 0.913628i | \(0.366731\pi\) | |||||||
\(264\) | 0.383281 | + | 0.663862i | 0.0235893 | + | 0.0408579i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.28116 | − | 0.739677i | 0.0785529 | − | 0.0453525i | ||||
\(267\) | −2.65740 | − | 4.60275i | −0.162630 | − | 0.281683i | ||||
\(268\) | −7.43584 | −0.454216 | ||||||||
\(269\) | 3.24938 | + | 5.62808i | 0.198118 | + | 0.343150i | 0.947918 | − | 0.318514i | \(-0.103184\pi\) |
−0.749800 | + | 0.661664i | \(0.769850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.35904 | + | 3.09404i | 0.325539 | + | 0.187950i | 0.653859 | − | 0.756617i | \(-0.273149\pi\) |
−0.328320 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(272\) | 2.21833i | 0.134506i | ||||||||
\(273\) | 0.777228 | + | 0.645884i | 0.0470400 | + | 0.0390906i | ||||
\(274\) | −1.66829 | −0.100785 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.725885 | + | 1.25727i | −0.0436931 | + | 0.0756787i | ||||
\(277\) | 25.1647 | − | 14.5289i | 1.51200 | − | 0.872955i | 0.512101 | − | 0.858925i | \(-0.328867\pi\) |
0.999902 | − | 0.0140299i | \(-0.00446601\pi\) | |||||||
\(278\) | 2.10790 | 0.126423 | ||||||||
\(279\) | 2.84152 | − | 1.64055i | 0.170117 | − | 0.0982172i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.1438i | − | 0.843746i | −0.906655 | − | 0.421873i | \(-0.861373\pi\) | ||
0.906655 | − | 0.421873i | \(-0.138627\pi\) | |||||||
\(282\) | −0.920385 | + | 0.531385i | −0.0548081 | + | 0.0316435i | ||||
\(283\) | −7.57409 | − | 4.37290i | −0.450233 | − | 0.259942i | 0.257696 | − | 0.966226i | \(-0.417037\pi\) |
−0.707928 | + | 0.706284i | \(0.750370\pi\) | |||||||
\(284\) | 2.09811 | + | 1.21135i | 0.124500 | + | 0.0718802i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.466963 | + | 2.72415i | −0.0276121 | + | 0.161082i | ||||
\(287\) | 0.621757i | 0.0367011i | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −6.03950 | + | 10.4607i | −0.355265 | + | 0.615337i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.26713i | − | 0.0742805i | ||||||
\(292\) | 7.13150 | + | 12.3521i | 0.417339 | + | 0.722853i | ||||
\(293\) | 15.7500 | + | 27.2798i | 0.920126 | + | 1.59371i | 0.799217 | + | 0.601042i | \(0.205248\pi\) |
0.120909 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(294\) | 6.92144i | 0.403667i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.77303 | + | 3.07097i | −0.103055 | + | 0.178497i | ||||
\(297\) | 0.383281 | − | 0.663862i | 0.0222402 | − | 0.0385212i | ||||
\(298\) | − | 5.74079i | − | 0.332555i | ||||||
\(299\) | −4.91017 | + | 1.81370i | −0.283962 | + | 0.104889i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.875972 | − | 0.505743i | −0.0504902 | − | 0.0291505i | ||||
\(302\) | −14.0045 | − | 8.08549i | −0.805867 | − | 0.465268i | ||||
\(303\) | 3.92090 | − | 2.26374i | 0.225250 | − | 0.130048i | ||||
\(304\) | 5.27811i | 0.302720i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.92113 | − | 1.10917i | 0.109824 | − | 0.0634068i | ||||
\(307\) | 7.03152 | 0.401310 | 0.200655 | − | 0.979662i | \(-0.435693\pi\) | ||||
0.200655 | + | 0.979662i | \(0.435693\pi\) | |||||||
\(308\) | 0.186068 | − | 0.107426i | 0.0106022 | − | 0.00612119i | ||||
\(309\) | −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 | \(0.419748\pi\) | |||||||
\(312\) | −3.38219 | + | 1.24931i | −0.191479 | + | 0.0707280i | ||||
\(313\) | − | 9.34134i | − | 0.528004i | −0.964522 | − | 0.264002i | \(-0.914958\pi\) | ||
0.964522 | − | 0.264002i | \(-0.0850425\pi\) | |||||||
\(314\) | −13.7179 | − | 7.92004i | −0.774147 | − | 0.446954i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.23574 | − | 12.5327i | −0.407042 | − | 0.705018i | ||||
\(317\) | 19.4697 | 1.09353 | 0.546763 | − | 0.837287i | \(-0.315860\pi\) | ||||
0.546763 | + | 0.837287i | \(0.315860\pi\) | |||||||
\(318\) | 1.64055 | + | 2.84152i | 0.0919975 | + | 0.159344i | ||||
\(319\) | 4.02340 | − | 2.32291i | 0.225267 | − | 0.130058i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.52440 | + | 16.4967i | 0.531600 | + | 0.920758i | ||||
\(322\) | 0.352389 | + | 0.203452i | 0.0196379 | + | 0.0113379i | ||||
\(323\) | 5.85429 | − | 10.1399i | 0.325742 | − | 0.564201i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.3148 | 0.626668 | ||||||||
\(327\) | −4.52274 | + | 7.83362i | −0.250108 | + | 0.433200i | ||||
\(328\) | −1.92113 | − | 1.10917i | −0.106077 | − | 0.0612434i | ||||
\(329\) | 0.148937 | + | 0.257967i | 0.00821117 | + | 0.0142222i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.4081 | − | 9.47320i | 0.901869 | − | 0.520694i | 0.0240626 | − | 0.999710i | \(-0.492340\pi\) |
0.877806 | + | 0.479016i | \(0.159007\pi\) | |||||||
\(332\) | −2.21209 | − | 3.83146i | −0.121404 | − | 0.210279i | ||||
\(333\) | 3.54606 | 0.194323 | ||||||||
\(334\) | 0.725885 | + | 1.25727i | 0.0397186 | + | 0.0687947i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.242731 | + | 0.140141i | 0.0132420 | + | 0.00764530i | ||||
\(337\) | − | 2.72966i | − | 0.148694i | −0.997232 | − | 0.0743469i | \(-0.976313\pi\) | ||
0.997232 | − | 0.0743469i | \(-0.0236872\pi\) | |||||||
\(338\) | −12.2578 | − | 4.32961i | −0.666738 | − | 0.235500i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.25758 | − | 2.17820i | 0.0681020 | − | 0.117956i | ||||
\(342\) | 4.57097 | − | 2.63905i | 0.247170 | − | 0.142704i | ||||
\(343\) | 3.90192 | 0.210684 | ||||||||
\(344\) | 3.12533 | − | 1.80441i | 0.168507 | − | 0.0972874i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 13.3402i | − | 0.717174i | ||||||
\(347\) | −10.9916 | + | 6.34600i | −0.590059 | + | 0.340671i | −0.765121 | − | 0.643887i | \(-0.777321\pi\) |
0.175062 | + | 0.984557i | \(0.443988\pi\) | |||||||
\(348\) | 5.24863 | + | 3.03030i | 0.281356 | + | 0.162441i | ||||
\(349\) | −1.04906 | − | 0.605676i | −0.0561549 | − | 0.0324211i | 0.471660 | − | 0.881781i | \(-0.343655\pi\) |
−0.527815 | + | 0.849360i | \(0.676988\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.77303 | + | 2.30441i | 0.148013 | + | 0.123000i | ||||
\(352\) | 0.766562i | 0.0408579i | ||||||||
\(353\) | −16.7901 | + | 29.0813i | −0.893647 | + | 1.54784i | −0.0581762 | + | 0.998306i | \(0.518529\pi\) |
−0.835471 | + | 0.549535i | \(0.814805\pi\) | |||||||
\(354\) | −2.49891 | + | 4.32824i | −0.132816 | + | 0.230044i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 5.31479i | − | 0.281683i | ||||||
\(357\) | −0.310878 | − | 0.538457i | −0.0164534 | − | 0.0284982i | ||||
\(358\) | 12.6266 | + | 21.8699i | 0.667335 | + | 1.15586i | ||||
\(359\) | 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 | ||||
\(362\) | −0.157396 | + | 0.272618i | −0.00827256 | + | 0.0143285i | ||||
\(363\) | 10.4124i | 0.546508i | ||||||||
\(364\) | 0.350157 | + | 0.947965i | 0.0183532 | + | 0.0496869i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.33892 | + | 0.773028i | 0.0699867 | + | 0.0404068i | ||||
\(367\) | 8.36421 | + | 4.82908i | 0.436608 | + | 0.252076i | 0.702158 | − | 0.712021i | \(-0.252220\pi\) |
−0.265550 | + | 0.964097i | \(0.585553\pi\) | |||||||
\(368\) | −1.25727 | + | 0.725885i | −0.0655397 | + | 0.0378394i | ||||
\(369\) | 2.21833i | 0.115482i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.796424 | − | 0.459815i | 0.0413483 | − | 0.0238724i | ||||
\(372\) | 3.28110 | 0.170117 | ||||||||
\(373\) | −10.6028 | + | 6.12153i | −0.548992 | + | 0.316961i | −0.748715 | − | 0.662892i | \(-0.769329\pi\) |
0.199723 | + | 0.979852i | \(0.435996\pi\) | |||||||
\(374\) | 0.850244 | − | 1.47267i | 0.0439651 | − | 0.0761498i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.06277 | −0.0548081 | ||||||||
\(377\) | 7.57154 | + | 20.4981i | 0.389954 | + | 1.05571i | ||||
\(378\) | − | 0.280281i | − | 0.0144161i | ||||||
\(379\) | −11.7669 | − | 6.79362i | −0.604425 | − | 0.348965i | 0.166355 | − | 0.986066i | \(-0.446800\pi\) |
−0.770780 | + | 0.637101i | \(0.780133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.58585 | − | 2.74678i | −0.0812458 | − | 0.140722i | ||||
\(382\) | 22.5332 | 1.15290 | ||||||||
\(383\) | 7.70686 | + | 13.3487i | 0.393802 | + | 0.682086i | 0.992948 | − | 0.118555i | \(-0.0378261\pi\) |
−0.599145 | + | 0.800640i | \(0.704493\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.89181 | + | 8.47286i | 0.248987 | + | 0.431257i | ||||
\(387\) | −3.12533 | − | 1.80441i | −0.158870 | − | 0.0917234i | ||||
\(388\) | 0.633565 | − | 1.09737i | 0.0321644 | − | 0.0557103i | ||||
\(389\) | −6.06059 | −0.307284 | −0.153642 | − | 0.988127i | \(-0.549100\pi\) | ||||
−0.153642 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22051 | 0.162868 | ||||||||
\(392\) | −3.46072 | + | 5.99414i | −0.174793 | + | 0.302750i | ||||
\(393\) | −13.3667 | − | 7.71724i | −0.674259 | − | 0.389283i | ||||
\(394\) | −6.22862 | − | 10.7883i | −0.313794 | − | 0.543506i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.663862 | − | 0.383281i | 0.0333603 | − | 0.0192606i | ||||
\(397\) | 8.49464 | + | 14.7131i | 0.426334 | + | 0.738432i | 0.996544 | − | 0.0830670i | \(-0.0264716\pi\) |
−0.570210 | + | 0.821499i | \(0.693138\pi\) | |||||||
\(398\) | −15.0639 | −0.755085 | ||||||||
\(399\) | −0.739677 | − | 1.28116i | −0.0370302 | − | 0.0641381i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.8156 | − | 9.70852i | −0.839733 | − | 0.484820i | 0.0174403 | − | 0.999848i | \(-0.494448\pi\) |
−0.857174 | + | 0.515028i | \(0.827782\pi\) | |||||||
\(402\) | 7.43584i | 0.370866i | ||||||||
\(403\) | 9.09858 | + | 7.56101i | 0.453233 | + | 0.376641i | ||||
\(404\) | 4.52747 | 0.225250 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.849335 | − | 1.47109i | 0.0421518 | − | 0.0730091i | ||||
\(407\) | 2.35409 | − | 1.35914i | 0.116688 | − | 0.0673699i | ||||
\(408\) | 2.21833 | 0.109824 | ||||||||
\(409\) | 0.803328 | − | 0.463802i | 0.0397220 | − | 0.0229335i | −0.480007 | − | 0.877264i | \(-0.659366\pi\) |
0.519730 | + | 0.854331i | \(0.326033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.66829i | 0.0822907i | ||||||||
\(412\) | −2.54846 | + | 1.47135i | −0.125554 | + | 0.0724885i | ||||
\(413\) | 1.21313 | + | 0.700398i | 0.0596940 | + | 0.0344643i | ||||
\(414\) | 1.25727 | + | 0.725885i | 0.0617914 | + | 0.0356753i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.55372 | − | 0.609166i | −0.174235 | − | 0.0298668i | ||||
\(417\) | − | 2.10790i | − | 0.103224i | ||||||
\(418\) | 2.02300 | − | 3.50393i | 0.0989481 | − | 0.171383i | ||||
\(419\) | −12.5907 | + | 21.8077i | −0.615096 | + | 1.06538i | 0.375271 | + | 0.926915i | \(0.377550\pi\) |
−0.990368 | + | 0.138463i | \(0.955784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 27.6912i | − | 1.34958i | −0.738008 | − | 0.674792i | \(-0.764233\pi\) | ||
0.738008 | − | 0.674792i | \(-0.235767\pi\) | |||||||
\(422\) | 7.53876 | + | 13.0575i | 0.366981 | + | 0.635630i | ||||
\(423\) | 0.531385 | + | 0.920385i | 0.0258368 | + | 0.0447507i | ||||
\(424\) | 3.28110i | 0.159344i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.21135 | − | 2.09811i | 0.0586899 | − | 0.101654i | ||||
\(427\) | 0.216665 | − | 0.375275i | 0.0104852 | − | 0.0181608i | ||||
\(428\) | 19.0488i | 0.920758i | ||||||||
\(429\) | 2.72415 | + | 0.466963i | 0.131523 | + | 0.0225452i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.0798174 | + | 0.0460826i | 0.00384467 | + | 0.00221972i | 0.501921 | − | 0.864913i | \(-0.332627\pi\) |
−0.498076 | + | 0.867133i | \(0.665960\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 3.48337 | − | 2.01113i | 0.167400 | − | 0.0966486i | −0.413959 | − | 0.910295i | \(-0.635854\pi\) |
0.581359 | + | 0.813647i | \(0.302521\pi\) | |||||||
\(434\) | − | 0.919631i | − | 0.0441437i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.83362 | + | 4.52274i | −0.375162 | + | 0.216600i | ||||
\(437\) | 7.66259 | 0.366552 | ||||||||
\(438\) | 12.3521 | − | 7.13150i | 0.590207 | − | 0.340756i | ||||
\(439\) | −12.9742 | + | 22.4719i | −0.619223 | + | 1.07253i | 0.370404 | + | 0.928871i | \(0.379219\pi\) |
−0.989628 | + | 0.143656i | \(0.954114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.92144 | 0.329592 | ||||||||
\(442\) | 6.15150 | + | 5.11195i | 0.292597 | + | 0.243151i | ||||
\(443\) | − | 15.0646i | − | 0.715740i | −0.933771 | − | 0.357870i | \(-0.883503\pi\) | ||
0.933771 | − | 0.357870i | \(-0.116497\pi\) | |||||||
\(444\) | 3.07097 | + | 1.77303i | 0.145742 | + | 0.0841442i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.32817 | + | 4.03252i | 0.110242 | + | 0.190945i | ||||
\(447\) | −5.74079 | −0.271530 | ||||||||
\(448\) | 0.140141 | + | 0.242731i | 0.00662102 | + | 0.0114679i | ||||
\(449\) | −29.8460 | + | 17.2316i | −1.40852 | + | 0.813208i | −0.995245 | − | 0.0973991i | \(-0.968948\pi\) |
−0.413273 | + | 0.910607i | \(0.635614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.850244 | + | 1.47267i | 0.0400364 | + | 0.0693451i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.08549 | + | 14.0045i | −0.379889 | + | 0.657988i | ||||
\(454\) | 6.20436 | 0.291185 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.27811 | 0.247170 | ||||||||
\(457\) | 20.8149 | − | 36.0525i | 0.973680 | − | 1.68646i | 0.289457 | − | 0.957191i | \(-0.406525\pi\) |
0.684223 | − | 0.729273i | \(-0.260141\pi\) | |||||||
\(458\) | −11.1379 | − | 6.43049i | −0.520442 | − | 0.300477i | ||||
\(459\) | −1.10917 | − | 1.92113i | −0.0517714 | − | 0.0896707i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.02737 | − | 3.47990i | 0.280722 | − | 0.162075i | −0.353028 | − | 0.935613i | \(-0.614848\pi\) |
0.633750 | + | 0.773538i | \(0.281515\pi\) | |||||||
\(462\) | −0.107426 | − | 0.186068i | −0.00499793 | − | 0.00865667i | ||||
\(463\) | −11.9289 | −0.554382 | −0.277191 | − | 0.960815i | \(-0.589403\pi\) | ||||
−0.277191 | + | 0.960815i | \(0.589403\pi\) | |||||||
\(464\) | 3.03030 | + | 5.24863i | 0.140678 | + | 0.243661i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.840844 | + | 0.485461i | 0.0389513 | + | 0.0224886i | ||||
\(467\) | 34.4406i | 1.59372i | 0.604164 | + | 0.796860i | \(0.293507\pi\) | ||||
−0.604164 | + | 0.796860i | \(0.706493\pi\) | |||||||
\(468\) | 1.24931 | + | 3.38219i | 0.0577492 | + | 0.156342i | ||||
\(469\) | 2.08413 | 0.0962361 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.92004 | + | 13.7179i | −0.364936 | + | 0.632088i | ||||
\(472\) | −4.32824 | + | 2.49891i | −0.199224 | + | 0.115022i | ||||
\(473\) | −2.76639 | −0.127199 | ||||||||
\(474\) | −12.5327 | + | 7.23574i | −0.575645 | + | 0.332349i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 0.621757i | − | 0.0284982i | ||||||
\(477\) | 2.84152 | − | 1.64055i | 0.130104 | − | 0.0751156i | ||||
\(478\) | 12.8158 | + | 7.39922i | 0.586182 | + | 0.338432i | ||||
\(479\) | 11.8896 | + | 6.86444i | 0.543248 | + | 0.313644i | 0.746394 | − | 0.665504i | \(-0.231783\pi\) |
−0.203146 | + | 0.979148i | \(0.565117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.43011 | + | 11.9934i | 0.201996 | + | 0.546854i | ||||
\(482\) | − | 2.19157i | − | 0.0998231i | ||||||
\(483\) | 0.203452 | − | 0.352389i | 0.00925738 | − | 0.0160343i | ||||
\(484\) | −5.20619 | + | 9.01739i | −0.236645 | + | 0.409881i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 4.76489 | + | 8.25303i | 0.215918 | + | 0.373981i | 0.953556 | − | 0.301215i | \(-0.0973923\pi\) |
−0.737638 | + | 0.675196i | \(0.764059\pi\) | |||||||
\(488\) | 0.773028 | + | 1.33892i | 0.0349933 | + | 0.0606102i | ||||
\(489\) | − | 11.3148i | − | 0.511673i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7409 | − | 28.9960i | 0.755505 | − | 1.30857i | −0.189618 | − | 0.981858i | \(-0.560725\pi\) |
0.945123 | − | 0.326715i | \(-0.105942\pi\) | |||||||
\(492\) | −1.10917 | + | 1.92113i | −0.0500051 | + | 0.0866113i | ||||
\(493\) | − | 13.4444i | − | 0.605506i | ||||||
\(494\) | 14.6363 | + | 12.1629i | 0.658520 | + | 0.547236i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.84152 | + | 1.64055i | 0.127588 | + | 0.0736629i | ||||
\(497\) | −0.588062 | − | 0.339518i | −0.0263782 | − | 0.0152294i | ||||
\(498\) | −3.83146 | + | 2.21209i | −0.171692 | + | 0.0991262i | ||||
\(499\) | − | 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 | ||||
\(502\) | 10.5897 | 0.472643 | ||||||||
\(503\) | 16.8861 | − | 9.74919i | 0.752914 | − | 0.434695i | −0.0738319 | − | 0.997271i | \(-0.523523\pi\) |
0.826746 | + | 0.562576i | \(0.190189\pi\) | |||||||
\(504\) | 0.140141 | − | 0.242731i | 0.00624236 | − | 0.0108121i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.11287 | 0.0494732 | ||||||||
\(507\) | −4.32961 | + | 12.2578i | −0.192285 | + | 0.544390i | ||||
\(508\) | − | 3.17171i | − | 0.140722i | ||||||
\(509\) | −29.5101 | − | 17.0377i | −1.30801 | − | 0.755181i | −0.326248 | − | 0.945284i | \(-0.605785\pi\) |
−0.981764 | + | 0.190103i | \(0.939118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.99883 | − | 3.46207i | −0.0884228 | − | 0.153153i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.63905 | − | 4.57097i | −0.116517 | − | 0.201813i | ||||
\(514\) | −5.93047 | + | 3.42396i | −0.261582 | + | 0.151024i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.80441 | − | 3.12533i | −0.0794348 | − | 0.137585i | ||||
\(517\) | 0.705532 | + | 0.407339i | 0.0310293 | + | 0.0179148i | ||||
\(518\) | 0.496946 | − | 0.860736i | 0.0218346 | − | 0.0378186i | ||||
\(519\) | −13.3402 | −0.585570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.10626 | −0.0484660 | −0.0242330 | − | 0.999706i | \(-0.507714\pi\) | ||||
−0.0242330 | + | 0.999706i | \(0.507714\pi\) | |||||||
\(522\) | 3.03030 | − | 5.24863i | 0.132633 | − | 0.229726i | ||||
\(523\) | 9.23044 | + | 5.32920i | 0.403619 | + | 0.233030i | 0.688044 | − | 0.725669i | \(-0.258469\pi\) |
−0.284425 | + | 0.958698i | \(0.591803\pi\) | |||||||
\(524\) | −7.71724 | − | 13.3667i | −0.337129 | − | 0.583925i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.7212 | − | 13.1181i | 0.990693 | − | 0.571977i | ||||
\(527\) | −3.63928 | − | 6.30343i | −0.158530 | − | 0.274582i | ||||
\(528\) | 0.766562 | 0.0333603 | ||||||||
\(529\) | −10.4462 | − | 18.0933i | −0.454182 | − | 0.786666i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.32824 | + | 2.49891i | 0.187830 | + | 0.108444i | ||||
\(532\) | − | 1.47935i | − | 0.0641381i | ||||||
\(533\) | −7.50283 | + | 2.77138i | −0.324983 | + | 0.120042i | ||||
\(534\) | −5.31479 | −0.229994 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.71792 | + | 6.43963i | −0.160590 | + | 0.278150i | ||||
\(537\) | 21.8699 | − | 12.6266i | 0.943755 | − | 0.544877i | ||||
\(538\) | 6.49875 | 0.280181 | ||||||||
\(539\) | 4.59488 | − | 2.65286i | 0.197916 | − | 0.114267i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 38.1486i | − | 1.64013i | −0.572267 | − | 0.820067i | \(-0.693936\pi\) | ||
0.572267 | − | 0.820067i | \(-0.306064\pi\) | |||||||
\(542\) | 5.35904 | − | 3.09404i | 0.230191 | − | 0.132901i | ||||
\(543\) | 0.272618 | + | 0.157396i | 0.0116992 | + | 0.00675452i | ||||
\(544\) | 1.92113 | + | 1.10917i | 0.0823678 | + | 0.0475551i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.947965 | − | 0.350157i | 0.0405692 | − | 0.0149853i | ||||
\(547\) | 26.9609i | 1.15277i | 0.817180 | + | 0.576383i | \(0.195536\pi\) | ||||
−0.817180 | + | 0.576383i | \(0.804464\pi\) | |||||||
\(548\) | −0.834145 | + | 1.44478i | −0.0356329 | + | 0.0617180i | ||||
\(549\) | 0.773028 | − | 1.33892i | 0.0329920 | − | 0.0571439i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 31.9885i | − | 1.36275i | ||||||
\(552\) | 0.725885 | + | 1.25727i | 0.0308957 | + | 0.0535129i | ||||
\(553\) | 2.02804 | + | 3.51267i | 0.0862411 | + | 0.149374i | ||||
\(554\) | − | 29.0577i | − | 1.23454i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.05395 | − | 1.82549i | 0.0446974 | − | 0.0774182i | ||||
\(557\) | −17.6236 | + | 30.5249i | −0.746735 | + | 1.29338i | 0.202645 | + | 0.979252i | \(0.435046\pi\) |
−0.949380 | + | 0.314130i | \(0.898287\pi\) | |||||||
\(558\) | − | 3.28110i | − | 0.138900i | ||||||
\(559\) | 2.19837 | − | 12.8247i | 0.0929812 | − | 0.542429i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.47267 | − | 0.850244i | −0.0621760 | − | 0.0358973i | ||||
\(562\) | −12.2489 | − | 7.07188i | −0.516687 | − | 0.298309i | ||||
\(563\) | 14.7368 | − | 8.50830i | 0.621082 | − | 0.358582i | −0.156208 | − | 0.987724i | \(-0.549927\pi\) |
0.777290 | + | 0.629142i | \(0.216594\pi\) | |||||||
\(564\) | 1.06277i | 0.0447507i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.57409 | + | 4.37290i | −0.318363 | + | 0.183807i | ||||
\(567\) | −0.280281 | −0.0117707 | ||||||||
\(568\) | 2.09811 | − | 1.21135i | 0.0880349 | − | 0.0508270i | ||||
\(569\) | −17.6968 | + | 30.6518i | −0.741889 | + | 1.28499i | 0.209746 | + | 0.977756i | \(0.432736\pi\) |
−0.951634 | + | 0.307233i | \(0.900597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5185 | −0.733125 | −0.366563 | − | 0.930393i | \(-0.619465\pi\) | ||||
−0.366563 | + | 0.930393i | \(0.619465\pi\) | |||||||
\(572\) | 2.12570 | + | 1.76647i | 0.0888799 | + | 0.0738600i | ||||
\(573\) | − | 22.5332i | − | 0.941339i | ||||||
\(574\) | 0.538457 | + | 0.310878i | 0.0224748 | + | 0.0129758i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 26.6215 | 1.10827 | 0.554133 | − | 0.832428i | \(-0.313050\pi\) | ||||
0.554133 | + | 0.832428i | \(0.313050\pi\) | |||||||
\(578\) | 6.03950 | + | 10.4607i | 0.251210 | + | 0.435109i | ||||
\(579\) | 8.47286 | − | 4.89181i | 0.352120 | − | 0.203297i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.620008 | + | 1.07389i | 0.0257223 | + | 0.0445523i | ||||
\(582\) | −1.09737 | − | 0.633565i | −0.0454873 | − | 0.0262621i | ||||
\(583\) | 1.25758 | − | 2.17820i | 0.0520838 | − | 0.0902118i | ||||
\(584\) | 14.2630 | 0.590207 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.5001 | 1.30126 | ||||||||
\(587\) | 8.32051 | − | 14.4115i | 0.343424 | − | 0.594828i | −0.641642 | − | 0.767004i | \(-0.721746\pi\) |
0.985066 | + | 0.172176i | \(0.0550798\pi\) | |||||||
\(588\) | 5.99414 | + | 3.46072i | 0.247194 | + | 0.142718i | ||||
\(589\) | −8.65900 | − | 14.9978i | −0.356788 | − | 0.617975i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.7883 | + | 6.22862i | −0.443771 | + | 0.256211i | ||||
\(592\) | 1.77303 | + | 3.07097i | 0.0728710 | + | 0.126216i | ||||
\(593\) | −24.7460 | −1.01620 | −0.508098 | − | 0.861300i | \(-0.669651\pi\) | ||||
−0.508098 | + | 0.861300i | \(0.669651\pi\) | |||||||
\(594\) | −0.383281 | − | 0.663862i | −0.0157262 | − | 0.0272386i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.97167 | − | 2.87039i | −0.203647 | − | 0.117576i | ||||
\(597\) | 15.0639i | 0.616524i | ||||||||
\(598\) | −0.884368 | + | 5.15918i | −0.0361645 | + | 0.210975i | ||||
\(599\) | 23.2517 | 0.950037 | 0.475019 | − | 0.879976i | \(-0.342441\pi\) | ||||
0.475019 | + | 0.879976i | \(0.342441\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.5985 | + | 28.7494i | −0.677067 | + | 1.17271i | 0.298793 | + | 0.954318i | \(0.403416\pi\) |
−0.975860 | + | 0.218396i | \(0.929917\pi\) | |||||||
\(602\) | −0.875972 | + | 0.505743i | −0.0357020 | + | 0.0206125i | ||||
\(603\) | 7.43584 | 0.302811 | ||||||||
\(604\) | −14.0045 | + | 8.08549i | −0.569834 | + | 0.328994i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 4.52747i | − | 0.183916i | ||||||
\(607\) | −34.1440 | + | 19.7130i | −1.38586 | + | 0.800128i | −0.992846 | − | 0.119404i | \(-0.961902\pi\) |
−0.393016 | + | 0.919532i | \(0.628568\pi\) | |||||||
\(608\) | 4.57097 | + | 2.63905i | 0.185377 | + | 0.107028i | ||||
\(609\) | −1.47109 | − | 0.849335i | −0.0596117 | − | 0.0344168i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.44906 | + | 2.94709i | −0.0990783 | + | 0.119226i | ||||
\(612\) | − | 2.21833i | − | 0.0896707i | ||||||
\(613\) | −5.21398 | + | 9.03087i | −0.210591 | + | 0.364753i | −0.951899 | − | 0.306410i | \(-0.900872\pi\) |
0.741309 | + | 0.671164i | \(0.234205\pi\) | |||||||
\(614\) | 3.51576 | − | 6.08947i | 0.141884 | − | 0.245751i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 0.214853i | − | 0.00865667i | ||||||
\(617\) | 10.1304 | + | 17.5464i | 0.407836 | + | 0.706393i | 0.994647 | − | 0.103331i | \(-0.0329502\pi\) |
−0.586811 | + | 0.809724i | \(0.699617\pi\) | |||||||
\(618\) | 1.47135 | + | 2.54846i | 0.0591866 | + | 0.102514i | ||||
\(619\) | 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 | ||||
\(622\) | 4.39922 | − | 7.61967i | 0.176393 | − | 0.305521i | ||||
\(623\) | 1.48964i | 0.0596810i | ||||||||
\(624\) | −0.609166 | + | 3.55372i | −0.0243861 | + | 0.142263i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.08984 | − | 4.67067i | −0.323335 | − | 0.186677i | ||||
\(627\) | −3.50393 | − | 2.02300i | −0.139934 | − | 0.0807907i | ||||
\(628\) | −13.7179 | + | 7.92004i | −0.547405 | + | 0.316044i | ||||
\(629\) | − | 7.86633i | − | 0.313651i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6461 | + | 18.2709i | −1.25981 | + | 0.727352i | −0.973038 | − | 0.230646i | \(-0.925916\pi\) |
−0.286773 | + | 0.957999i | \(0.592583\pi\) | |||||||
\(632\) | −14.4715 | −0.575645 | ||||||||
\(633\) | 13.0575 | − | 7.53876i | 0.518989 | − | 0.299639i | ||||
\(634\) | 9.73484 | − | 16.8612i | 0.386620 | − | 0.669645i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.28110 | 0.130104 | ||||||||
\(637\) | 8.64700 | + | 23.4097i | 0.342607 | + | 0.927524i | ||||
\(638\) | − | 4.64582i | − | 0.183930i | ||||||
\(639\) | −2.09811 | − | 1.21135i | −0.0830001 | − | 0.0479201i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9295 | − | 37.9830i | −0.866163 | − | 1.50024i | −0.865888 | − | 0.500238i | \(-0.833246\pi\) |
−0.000274574 | − | 1.00000i | \(-0.500087\pi\) | |||||||
\(642\) | 19.0488 | 0.751796 | ||||||||
\(643\) | −8.32615 | − | 14.4213i | −0.328351 | − | 0.568721i | 0.653834 | − | 0.756638i | \(-0.273160\pi\) |
−0.982185 | + | 0.187917i | \(0.939826\pi\) | |||||||
\(644\) | 0.352389 | − | 0.203452i | 0.0138861 | − | 0.00801713i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.85429 | − | 10.1399i | −0.230334 | − | 0.398950i | ||||
\(647\) | 8.13271 | + | 4.69543i | 0.319730 | + | 0.184596i | 0.651272 | − | 0.758844i | \(-0.274236\pi\) |
−0.331542 | + | 0.943440i | \(0.607569\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 3.83114 | 0.150386 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.919631 | −0.0360432 | ||||||||
\(652\) | 5.65740 | − | 9.79890i | 0.221561 | − | 0.383754i | ||||
\(653\) | 35.6061 | + | 20.5572i | 1.39337 | + | 0.804465i | 0.993687 | − | 0.112187i | \(-0.0357857\pi\) |
0.399686 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(654\) | 4.52274 | + | 7.83362i | 0.176853 | + | 0.306319i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.92113 | + | 1.10917i | −0.0750076 | + | 0.0433056i | ||||
\(657\) | −7.13150 | − | 12.3521i | −0.278226 | − | 0.481902i | ||||
\(658\) | 0.297874 | 0.0116123 | ||||||||
\(659\) | −1.72663 | − | 2.99061i | −0.0672600 | − | 0.116498i | 0.830434 | − | 0.557117i | \(-0.188092\pi\) |
−0.897694 | + | 0.440619i | \(0.854759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.3306 | + | 12.3152i | 0.829665 | + | 0.479007i | 0.853738 | − | 0.520703i | \(-0.174330\pi\) |
−0.0240732 | + | 0.999710i | \(0.507663\pi\) | |||||||
\(662\) | − | 18.9464i | − | 0.736373i | ||||||
\(663\) | 5.11195 | − | 6.15150i | 0.198532 | − | 0.238904i | ||||
\(664\) | −4.42419 | −0.171692 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.77303 | − | 3.07097i | 0.0687034 | − | 0.118998i | ||||
\(667\) | 7.61980 | − | 4.39929i | 0.295040 | − | 0.170341i | ||||
\(668\) | 1.45177 | 0.0561707 | ||||||||
\(669\) | 4.03252 | − | 2.32817i | 0.155906 | − | 0.0900124i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.18515i | − | 0.0457521i | ||||||
\(672\) | 0.242731 | − | 0.140141i | 0.00936354 | − | 0.00540604i | ||||
\(673\) | −14.7580 | − | 8.52052i | −0.568878 | − | 0.328442i | 0.187823 | − | 0.982203i | \(-0.439857\pi\) |
−0.756701 | + | 0.653761i | \(0.773190\pi\) | |||||||
\(674\) | −2.36395 | − | 1.36483i | −0.0910560 | − | 0.0525712i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.87847 | + | 8.45079i | −0.379941 | + | 0.325030i | ||||
\(677\) | − | 16.6324i | − | 0.639236i | −0.947546 | − | 0.319618i | \(-0.896445\pi\) | ||
0.947546 | − | 0.319618i | \(-0.103555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.177576 | + | 0.307571i | −0.00681475 | + | 0.0118035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.20436i | − | 0.237752i | ||||||
\(682\) | −1.25758 | − | 2.17820i | −0.0481554 | − | 0.0834075i | ||||
\(683\) | −24.4365 | − | 42.3252i | −0.935035 | − | 1.61953i | −0.774572 | − | 0.632486i | \(-0.782035\pi\) |
−0.160463 | − | 0.987042i | \(-0.551299\pi\) | |||||||
\(684\) | − | 5.27811i | − | 0.201813i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.95096 | − | 3.37916i | 0.0744880 | − | 0.129017i | ||||
\(687\) | −6.43049 | + | 11.1379i | −0.245339 | + | 0.424939i | ||||
\(688\) | − | 3.60882i | − | 0.137585i | ||||||
\(689\) | 9.09858 | + | 7.56101i | 0.346628 | + | 0.288051i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.0699 | + | 17.9382i | 1.18195 | + | 0.682401i | 0.956466 | − | 0.291845i | \(-0.0942690\pi\) |
0.225488 | + | 0.974246i | \(0.427602\pi\) | |||||||
\(692\) | −11.5530 | − | 6.67010i | −0.439177 | − | 0.253559i | ||||
\(693\) | −0.186068 | + | 0.107426i | −0.00706814 | + | 0.00408079i | ||||
\(694\) | 12.6920i | 0.481781i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.24863 | − | 3.03030i | 0.198949 | − | 0.114863i | ||||
\(697\) | 4.92099 | 0.186396 | ||||||||
\(698\) | −1.04906 | + | 0.605676i | −0.0397075 | + | 0.0229252i | ||||
\(699\) | 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 | \(0.699287\pi\) | |||||||
\(702\) | 3.38219 | − | 1.24931i | 0.127653 | − | 0.0471520i | ||||
\(703\) | − | 18.7165i | − | 0.705905i | ||||||
\(704\) | 0.663862 | + | 0.383281i | 0.0250202 | + | 0.0144454i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.7901 | + | 29.0813i | 0.631904 | + | 1.09449i | ||||
\(707\) | −1.26896 | −0.0477243 | ||||||||
\(708\) | 2.49891 | + | 4.32824i | 0.0939149 | + | 0.162665i | ||||
\(709\) | −9.78339 | + | 5.64844i | −0.367423 | + | 0.212132i | −0.672332 | − | 0.740250i | \(-0.734707\pi\) |
0.304909 | + | 0.952381i | \(0.401374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.23574 | + | 12.5327i | 0.271362 | + | 0.470012i | ||||
\(712\) | −4.60275 | − | 2.65740i | −0.172495 | − | 0.0995901i | ||||
\(713\) | 2.38170 | − | 4.12523i | 0.0891954 | − | 0.154491i | ||||
\(714\) | −0.621757 | −0.0232687 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25.2532 | 0.943755 | ||||||||
\(717\) | 7.39922 | − | 12.8158i | 0.276329 | − | 0.478616i | ||||
\(718\) | 19.0892 | + | 11.0211i | 0.712401 | + | 0.411305i | ||||
\(719\) | 6.01084 | + | 10.4111i | 0.224167 | + | 0.388268i | 0.956069 | − | 0.293141i | \(-0.0947007\pi\) |
−0.731902 | + | 0.681409i | \(0.761367\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.714286 | − | 0.412393i | 0.0266014 | − | 0.0153583i | ||||
\(722\) | −4.42920 | − | 7.67161i | −0.164838 | − | 0.285508i | ||||
\(723\) | −2.19157 | −0.0815052 | ||||||||
\(724\) | 0.157396 | + | 0.272618i | 0.00584958 | + | 0.0101318i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.01739 | + | 5.20619i | 0.334667 | + | 0.193220i | ||||
\(727\) | − | 4.18908i | − | 0.155364i | −0.996978 | − | 0.0776822i | \(-0.975248\pi\) | ||
0.996978 | − | 0.0776822i | \(-0.0247519\pi\) | |||||||
\(728\) | 0.996041 | + | 0.170738i | 0.0369157 | + | 0.00632796i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00278 | + | 6.93303i | −0.148048 | + | 0.256427i | ||||
\(732\) | 1.33892 | − | 0.773028i | 0.0494880 | − | 0.0285719i | ||||
\(733\) | −11.3923 | −0.420783 | −0.210391 | − | 0.977617i | \(-0.567474\pi\) | ||||
−0.210391 | + | 0.977617i | \(0.567474\pi\) | |||||||
\(734\) | 8.36421 | − | 4.82908i | 0.308729 | − | 0.178244i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.45177i | 0.0535129i | ||||||||
\(737\) | 4.93637 | − | 2.85002i | 0.181834 | − | 0.104982i | ||||
\(738\) | 1.92113 | + | 1.10917i | 0.0707178 | + | 0.0408290i | ||||
\(739\) | 17.6996 | + | 10.2189i | 0.651090 | + | 0.375907i | 0.788874 | − | 0.614555i | \(-0.210664\pi\) |
−0.137783 | + | 0.990462i | \(0.543998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.1629 | − | 14.6363i | 0.446817 | − | 0.537679i | ||||
\(742\) | − | 0.919631i | − | 0.0337607i | ||||||
\(743\) | −5.07638 | + | 8.79255i | −0.186234 | + | 0.322567i | −0.943992 | − | 0.329969i | \(-0.892962\pi\) |
0.757757 | + | 0.652536i | \(0.226295\pi\) | |||||||
\(744\) | 1.64055 | − | 2.84152i | 0.0601455 | − | 0.104175i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.2431i | 0.448250i | ||||||||
\(747\) | 2.21209 | + | 3.83146i | 0.0809362 | + | 0.140186i | ||||
\(748\) | −0.850244 | − | 1.47267i | −0.0310880 | − | 0.0538460i | ||||
\(749\) | − | 5.33902i | − | 0.195083i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.99084 | + | 15.5726i | −0.328080 | + | 0.568252i | −0.982131 | − | 0.188199i | \(-0.939735\pi\) |
0.654051 | + | 0.756451i | \(0.273068\pi\) | |||||||
\(752\) | −0.531385 | + | 0.920385i | −0.0193776 | + | 0.0335630i | ||||
\(753\) | − | 10.5897i | − | 0.385911i | ||||||
\(754\) | 21.5376 | + | 3.69191i | 0.784355 | + | 0.134451i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.242731 | − | 0.140141i | −0.00882803 | − | 0.00509686i | ||||
\(757\) | −38.9566 | − | 22.4916i | −1.41590 | − | 0.817470i | −0.419965 | − | 0.907540i | \(-0.637958\pi\) |
−0.995935 | + | 0.0900700i | \(0.971291\pi\) | |||||||
\(758\) | −11.7669 | + | 6.79362i | −0.427393 | + | 0.246755i | ||||
\(759\) | − | 1.11287i | − | 0.0403947i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.1697 | + | 22.6146i | −1.41990 | + | 0.819779i | −0.996289 | − | 0.0860657i | \(-0.972571\pi\) |
−0.423610 | + | 0.905845i | \(0.639237\pi\) | |||||||
\(762\) | −3.17171 | −0.114899 | ||||||||
\(763\) | 2.19562 | − | 1.26764i | 0.0794867 | − | 0.0458917i | ||||
\(764\) | 11.2666 | − | 19.5143i | 0.407612 | − | 0.706004i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.4137 | 0.556921 | ||||||||
\(767\) | −3.04450 | + | 17.7609i | −0.109931 | + | 0.641308i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −31.3010 | − | 18.0716i | −1.12874 | − | 0.651680i | −0.185125 | − | 0.982715i | \(-0.559269\pi\) |
−0.943619 | + | 0.331035i | \(0.892602\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.42396 | + | 5.93047i | 0.123311 | + | 0.213581i | ||||
\(772\) | 9.78362 | 0.352120 | ||||||||
\(773\) | −8.18850 | − | 14.1829i | −0.294520 | − | 0.510123i | 0.680353 | − | 0.732884i | \(-0.261826\pi\) |
−0.974873 | + | 0.222761i | \(0.928493\pi\) | |||||||
\(774\) | −3.12533 | + | 1.80441i | −0.112338 | + | 0.0648583i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.633565 | − | 1.09737i | −0.0227437 | − | 0.0393932i | ||||
\(777\) | −0.860736 | − | 0.496946i | −0.0308787 | − | 0.0178279i | ||||
\(778\) | −3.03030 | + | 5.24863i | −0.108641 | + | 0.188172i | ||||
\(779\) | 11.7086 | 0.419504 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.85714 | −0.0664538 | ||||||||
\(782\) | 1.61025 | − | 2.78904i | 0.0575825 | − | 0.0997359i | ||||
\(783\) | −5.24863 | − | 3.03030i | −0.187571 | − | 0.108294i | ||||
\(784\) | 3.46072 | + | 5.99414i | 0.123597 | + | 0.214077i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.3667 | + | 7.71724i | −0.476773 | + | 0.275265i | ||||
\(787\) | −22.5807 | − | 39.1108i | −0.804913 | − | 1.39415i | −0.916350 | − | 0.400379i | \(-0.868878\pi\) |
0.111436 | − | 0.993772i | \(-0.464455\pi\) | |||||||
\(788\) | −12.4572 | −0.443771 | ||||||||
\(789\) | −13.1181 | − | 22.7212i | −0.467017 | − | 0.808898i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 0.766562i | − | 0.0272386i | ||||||
\(793\) | 5.49425 | + | 0.941804i | 0.195106 | + | 0.0334444i | ||||
\(794\) | 16.9893 | 0.602927 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.53195 | + | 13.0457i | −0.266963 | + | 0.462393i | ||||
\(797\) | 23.3511 | − | 13.4818i | 0.827139 | − | 0.477549i | −0.0257329 | − | 0.999669i | \(-0.508192\pi\) |
0.852872 | + | 0.522120i | \(0.174859\pi\) | |||||||
\(798\) | −1.47935 | −0.0523686 | ||||||||
\(799\) | 2.04172 | − | 1.17879i | 0.0722308 | − | 0.0417025i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.31479i | 0.187789i | ||||||||
\(802\) | −16.8156 | + | 9.70852i | −0.593781 | + | 0.342820i | ||||
\(803\) | −9.46867 | − | 5.46674i | −0.334142 | − | 0.192917i | ||||
\(804\) | 6.43963 | + | 3.71792i | 0.227108 | + | 0.131121i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.0973 | − | 4.09910i | 0.390886 | − | 0.144385i | ||||
\(807\) | − | 6.49875i | − | 0.228767i | ||||||
\(808\) | 2.26374 | − | 3.92090i | 0.0796379 | − | 0.137937i | ||||
\(809\) | −5.02204 | + | 8.69843i | −0.176566 | + | 0.305821i | −0.940702 | − | 0.339234i | \(-0.889832\pi\) |
0.764136 | + | 0.645055i | \(0.223165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.8449i | 0.942652i | 0.881959 | + | 0.471326i | \(0.156224\pi\) | ||||
−0.881959 | + | 0.471326i | \(0.843776\pi\) | |||||||
\(812\) | −0.849335 | − | 1.47109i | −0.0298058 | − | 0.0516252i | ||||
\(813\) | −3.09404 | − | 5.35904i | −0.108513 | − | 0.187950i | ||||
\(814\) | − | 2.71827i | − | 0.0952754i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.10917 | − | 1.92113i | 0.0388286 | − | 0.0672531i | ||||
\(817\) | −9.52388 | + | 16.4958i | −0.333198 | + | 0.577117i | ||||
\(818\) | − | 0.927603i | − | 0.0324329i | ||||||
\(819\) | −0.350157 | − | 0.947965i | −0.0122355 | − | 0.0331246i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.4214 | − | 16.4091i | −0.991912 | − | 0.572681i | −0.0860669 | − | 0.996289i | \(-0.527430\pi\) |
−0.905845 | + | 0.423609i | \(0.860763\pi\) | |||||||
\(822\) | 1.44478 | + | 0.834145i | 0.0503925 | + | 0.0290941i | ||||
\(823\) | −7.68249 | + | 4.43549i | −0.267795 | + | 0.154611i | −0.627885 | − | 0.778306i | \(-0.716079\pi\) |
0.360090 | + | 0.932917i | \(0.382746\pi\) | |||||||
\(824\) | 2.94271i | 0.102514i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.21313 | − | 0.700398i | 0.0422100 | − | 0.0243700i | ||||
\(827\) | 0.892425 | 0.0310327 | 0.0155163 | − | 0.999880i | \(-0.495061\pi\) | ||||
0.0155163 | + | 0.999880i | \(0.495061\pi\) | |||||||
\(828\) | 1.25727 | − | 0.725885i | 0.0436931 | − | 0.0252262i | ||||
\(829\) | 5.74291 | − | 9.94701i | 0.199459 | − | 0.345474i | −0.748894 | − | 0.662690i | \(-0.769415\pi\) |
0.948353 | + | 0.317216i | \(0.102748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.0577 | −1.00800 | ||||||||
\(832\) | −2.30441 | + | 2.77303i | −0.0798911 | + | 0.0961374i | ||||
\(833\) | − | 15.3541i | − | 0.531986i | ||||||
\(834\) | −1.82549 | − | 1.05395i | −0.0632117 | − | 0.0364953i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.02300 | − | 3.50393i | −0.0699668 | − | 0.121186i | ||||
\(837\) | −3.28110 | −0.113411 | ||||||||
\(838\) | 12.5907 | + | 21.8077i | 0.434939 | + | 0.753336i | ||||
\(839\) | −24.1738 | + | 13.9568i | −0.834573 | + | 0.481841i | −0.855416 | − | 0.517942i | \(-0.826698\pi\) |
0.0208426 | + | 0.999783i | \(0.493365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.86540 | − | 6.69507i | −0.133290 | − | 0.230865i | ||||
\(842\) | −23.9812 | − | 13.8456i | −0.826448 | − | 0.477150i | ||||
\(843\) | −7.07188 | + | 12.2489i | −0.243568 | + | 0.421873i | ||||
\(844\) | 15.0775 | 0.518989 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.06277 | 0.0365388 | ||||||||
\(847\) | 1.45920 | − | 2.52740i | 0.0501386 | − | 0.0868426i | ||||
\(848\) | 2.84152 | + | 1.64055i | 0.0975781 | + | 0.0563367i | ||||
\(849\) | 4.37290 | + | 7.57409i | 0.150078 | + | 0.259942i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.45835 | − | 2.57403i | 0.152830 | − | 0.0882365i | ||||
\(852\) | −1.21135 | − | 2.09811i | −0.0415000 | − | 0.0718802i | ||||
\(853\) | 41.6937 | 1.42757 | 0.713783 | − | 0.700367i | \(-0.246980\pi\) | ||||
0.713783 | + | 0.700367i | \(0.246980\pi\) | |||||||
\(854\) | −0.216665 | − | 0.375275i | −0.00741413 | − | 0.0128417i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.4967 | + | 9.52440i | 0.563847 | + | 0.325537i | ||||
\(857\) | 4.57772i | 0.156372i | 0.996939 | + | 0.0781860i | \(0.0249128\pi\) | ||||
−0.996939 | + | 0.0781860i | \(0.975087\pi\) | |||||||
\(858\) | 1.76647 | − | 2.12570i | 0.0603065 | − | 0.0725701i | ||||
\(859\) | 32.0617 | 1.09393 | 0.546966 | − | 0.837155i | \(-0.315783\pi\) | ||||
0.546966 | + | 0.837155i | \(0.315783\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.310878 | − | 0.538457i | 0.0105947 | − | 0.0183506i | ||||
\(862\) | 0.0798174 | − | 0.0460826i | 0.00271859 | − | 0.00156958i | ||||
\(863\) | −30.7876 | −1.04802 | −0.524011 | − | 0.851711i | \(-0.675565\pi\) | ||||
−0.524011 | + | 0.851711i | \(0.675565\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 4.02225i | − | 0.136682i | ||||||
\(867\) | 10.4607 | − | 6.03950i | 0.355265 | − | 0.205112i | ||||
\(868\) | −0.796424 | − | 0.459815i | −0.0270324 | − | 0.0156072i | ||||
\(869\) | 9.60707 | + | 5.54664i | 0.325898 | + | 0.188157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.28965 | + | 25.1495i | 0.314768 | + | 0.852157i | ||||
\(872\) | 9.04549i | 0.306319i | ||||||||
\(873\) | −0.633565 | + | 1.09737i | −0.0214429 | + | 0.0371402i | ||||
\(874\) | 3.83130 | − | 6.63600i | 0.129596 | − | 0.224466i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 14.2630i | − | 0.481902i | ||||||
\(877\) | −20.3902 | − | 35.3169i | −0.688529 | − | 1.19257i | −0.972314 | − | 0.233679i | \(-0.924924\pi\) |
0.283785 | − | 0.958888i | \(-0.408410\pi\) | |||||||
\(878\) | 12.9742 | + | 22.4719i | 0.437857 | + | 0.758391i | ||||
\(879\) | − | 31.5001i | − | 1.06247i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.4928 | + | 37.2265i | −0.724109 | + | 1.25419i | 0.235230 | + | 0.971940i | \(0.424416\pi\) |
−0.959340 | + | 0.282254i | \(0.908918\pi\) | |||||||
\(882\) | 3.46072 | − | 5.99414i | 0.116529 | − | 0.201833i | ||||
\(883\) | − | 29.9139i | − | 1.00668i | −0.864088 | − | 0.503341i | \(-0.832104\pi\) | ||
0.864088 | − | 0.503341i | \(-0.167896\pi\) | |||||||
\(884\) | 7.50283 | − | 2.77138i | 0.252347 | − | 0.0932115i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.0463 | − | 7.53229i | −0.438299 | − | 0.253052i | ||||
\(887\) | −40.6116 | − | 23.4471i | −1.36360 | − | 0.787278i | −0.373503 | − | 0.927629i | \(-0.621843\pi\) |
−0.990102 | + | 0.140351i | \(0.955177\pi\) | |||||||
\(888\) | 3.07097 | − | 1.77303i | 0.103055 | − | 0.0594989i | ||||
\(889\) | 0.888970i | 0.0298151i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.663862 | + | 0.383281i | −0.0222402 | + | 0.0128404i | ||||
\(892\) | 4.65635 | 0.155906 | ||||||||
\(893\) | 4.85789 | − | 2.80470i | 0.162563 | − | 0.0938558i | ||||
\(894\) | −2.87039 | + | 4.97167i | −0.0960004 | + | 0.166277i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.280281 | 0.00936354 | ||||||||
\(897\) | 5.15918 | + | 0.884368i | 0.172260 | + | 0.0295282i | ||||
\(898\) | 34.4631i | 1.15005i | ||||||||
\(899\) | −17.2213 | − | 9.94271i | −0.574362 | − | 0.331608i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.63928 | − | 6.30343i | −0.121242 | − | 0.209998i | ||||
\(902\) | 1.70049 | 0.0566201 | ||||||||
\(903\) | 0.505743 | + | 0.875972i | 0.0168301 | + | 0.0291505i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.08549 | + | 14.0045i | 0.268622 | + | 0.465268i | ||||
\(907\) | −23.1269 | − | 13.3523i | −0.767915 | − | 0.443356i | 0.0642155 | − | 0.997936i | \(-0.479546\pi\) |
−0.832130 | + | 0.554580i | \(0.812879\pi\) | |||||||
\(908\) | 3.10218 | − | 5.37313i | 0.102949 | − | 0.178314i | ||||
\(909\) | −4.52747 | −0.150167 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.8401 | 0.955515 | 0.477758 | − | 0.878492i | \(-0.341450\pi\) | ||||
0.477758 | + | 0.878492i | \(0.341450\pi\) | |||||||
\(912\) | 2.63905 | − | 4.57097i | 0.0873878 | − | 0.151360i | ||||
\(913\) | 2.93705 | + | 1.69571i | 0.0972021 | + | 0.0561197i | ||||
\(914\) | −20.8149 | − | 36.0525i | −0.688496 | − | 1.19251i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.1379 | + | 6.43049i | −0.368008 | + | 0.212469i | ||||
\(917\) | 2.16300 | + | 3.74642i | 0.0714285 | + | 0.123718i | ||||
\(918\) | −2.21833 | −0.0732158 | ||||||||
\(919\) | 14.4493 | + | 25.0269i | 0.476637 | + | 0.825560i | 0.999642 | − | 0.0267702i | \(-0.00852225\pi\) |
−0.523005 | + | 0.852330i | \(0.675189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.08947 | − | 3.51576i | −0.200655 | − | 0.115848i | ||||
\(922\) | − | 6.95980i | − | 0.229209i | ||||||
\(923\) | 1.47582 | − | 8.60957i | 0.0485772 | − | 0.283387i | ||||
\(924\) | −0.214853 | −0.00706814 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.96444 | + | 10.3307i | −0.196004 | + | 0.339488i | ||||
\(927\) | 2.54846 | − | 1.47135i | 0.0837025 | − | 0.0483256i | ||||
\(928\) | 6.06059 | 0.198949 | ||||||||
\(929\) | 37.8896 | − | 21.8756i | 1.24312 | − | 0.717715i | 0.273391 | − | 0.961903i | \(-0.411855\pi\) |
0.969728 | + | 0.244188i | \(0.0785215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 36.5321i | − | 1.19729i | ||||||
\(932\) | 0.840844 | − | 0.485461i | 0.0275428 | − | 0.0159018i | ||||
\(933\) | −7.61967 | − | 4.39922i | −0.249457 | − | 0.144024i | ||||
\(934\) | 29.8264 | + | 17.2203i | 0.975950 | + | 0.563465i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.55372 | + | 0.609166i | 0.116157 | + | 0.0199112i | ||||
\(937\) | 6.71836i | 0.219479i | 0.993960 | + | 0.109740i | \(0.0350017\pi\) | ||||
−0.993960 | + | 0.109740i | \(0.964998\pi\) | |||||||
\(938\) | 1.04206 | − | 1.80491i | 0.0340246 | − | 0.0589323i | ||||
\(939\) | −4.67067 | + | 8.08984i | −0.152422 | + | 0.264002i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 33.9654i | − | 1.10724i | −0.832769 | − | 0.553621i | \(-0.813246\pi\) | ||
0.832769 | − | 0.553621i | \(-0.186754\pi\) | |||||||
\(942\) | 7.92004 | + | 13.7179i | 0.258049 | + | 0.446954i | ||||
\(943\) | 1.61025 | + | 2.78904i | 0.0524371 | + | 0.0908236i | ||||
\(944\) | 4.99783i | 0.162665i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.38319 | + | 2.39576i | −0.0449715 | + | 0.0778929i | ||||
\(947\) | −20.3751 | + | 35.2907i | −0.662101 | + | 1.14679i | 0.317962 | + | 0.948104i | \(0.397002\pi\) |
−0.980063 | + | 0.198689i | \(0.936332\pi\) | |||||||
\(948\) | 14.4715i | 0.470012i | ||||||||
\(949\) | 32.8678 | − | 39.5517i | 1.06694 | − | 1.28390i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.8612 | − | 9.73484i | −0.546763 | − | 0.315674i | ||||
\(952\) | −0.538457 | − | 0.310878i | −0.0174515 | − | 0.0100756i | ||||
\(953\) | 5.23614 | − | 3.02309i | 0.169615 | − | 0.0979274i | −0.412789 | − | 0.910827i | \(-0.635445\pi\) |
0.582404 | + | 0.812899i | \(0.302112\pi\) | |||||||
\(954\) | − | 3.28110i | − | 0.106230i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.8158 | − | 7.39922i | 0.414493 | − | 0.239308i | ||||
\(957\) | −4.64582 | −0.150178 | ||||||||
\(958\) | 11.8896 | − | 6.86444i | 0.384134 | − | 0.221780i | ||||
\(959\) | 0.233795 | − | 0.404945i | 0.00754964 | − | 0.0130764i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2344 | 0.652722 | ||||||||
\(962\) | 12.6017 | + | 2.16014i | 0.406295 | + | 0.0696456i | ||||
\(963\) | − | 19.0488i | − | 0.613839i | ||||||
\(964\) | −1.89795 | − | 1.09578i | −0.0611289 | − | 0.0352928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.203452 | − | 0.352389i | −0.00654596 | − | 0.0113379i | ||||
\(967\) | −39.8852 | −1.28262 | −0.641310 | − | 0.767282i | \(-0.721609\pi\) | ||||
−0.641310 | + | 0.767282i | \(0.721609\pi\) | |||||||
\(968\) | 5.20619 | + | 9.01739i | 0.167333 | + | 0.289830i | ||||
\(969\) | −10.1399 | + | 5.85429i | −0.325742 | + | 0.188067i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.5176 | + | 33.8055i | 0.626349 | + | 1.08487i | 0.988278 | + | 0.152663i | \(0.0487849\pi\) |
−0.361929 | + | 0.932206i | \(0.617882\pi\) | |||||||
\(972\) | −0.866025 | − | 0.500000i | −0.0277778 | − | 0.0160375i | ||||
\(973\) | −0.295402 | + | 0.511652i | −0.00947017 | + | 0.0164028i | ||||
\(974\) | 9.52978 | 0.305354 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.54606 | 0.0494880 | ||||||||
\(977\) | 21.0247 | − | 36.4159i | 0.672641 | − | 1.16505i | −0.304512 | − | 0.952509i | \(-0.598493\pi\) |
0.977153 | − | 0.212539i | \(-0.0681733\pi\) | |||||||
\(978\) | −9.79890 | − | 5.65740i | −0.313334 | − | 0.180904i | ||||
\(979\) | 2.03706 | + | 3.52829i | 0.0651047 | + | 0.112765i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.83362 | − | 4.52274i | 0.250108 | − | 0.144400i | ||||
\(982\) | −16.7409 | − | 28.9960i | −0.534223 | − | 0.925301i | ||||
\(983\) | −27.5124 | −0.877508 | −0.438754 | − | 0.898607i | \(-0.644580\pi\) | ||||
−0.438754 | + | 0.898607i | \(0.644580\pi\) | |||||||
\(984\) | 1.10917 | + | 1.92113i | 0.0353589 | + | 0.0612434i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.6432 | − | 6.72220i | −0.370795 | − | 0.214079i | ||||
\(987\) | − | 0.297874i | − | 0.00948144i | ||||||
\(988\) | 17.8516 | − | 6.59397i | 0.567934 | − | 0.209782i | ||||
\(989\) | −5.23918 | −0.166596 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.9614 | + | 48.4306i | −0.888224 | + | 1.53845i | −0.0462506 | + | 0.998930i | \(0.514727\pi\) |
−0.841973 | + | 0.539519i | \(0.818606\pi\) | |||||||
\(992\) | 2.84152 | − | 1.64055i | 0.0902182 | − | 0.0520875i | ||||
\(993\) | −18.9464 | −0.601246 | ||||||||
\(994\) | −0.588062 | + | 0.339518i | −0.0186522 | + | 0.0107688i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.42419i | 0.140186i | ||||||||
\(997\) | −25.6834 | + | 14.8283i | −0.813403 | + | 0.469618i | −0.848136 | − | 0.529778i | \(-0.822275\pi\) |
0.0347335 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(998\) | −13.0667 | − | 7.54409i | −0.413620 | − | 0.238804i | ||||
\(999\) | −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.y.n.199.2 | 12 | ||
5.2 | odd | 4 | 1950.2.bc.h.901.5 | yes | 12 | ||
5.3 | odd | 4 | 1950.2.bc.k.901.2 | yes | 12 | ||
5.4 | even | 2 | 1950.2.y.m.199.5 | 12 | |||
13.10 | even | 6 | 1950.2.y.m.49.5 | 12 | |||
65.23 | odd | 12 | 1950.2.bc.k.751.2 | yes | 12 | ||
65.49 | even | 6 | inner | 1950.2.y.n.49.2 | 12 | ||
65.62 | odd | 12 | 1950.2.bc.h.751.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.y.m.49.5 | 12 | 13.10 | even | 6 | |||
1950.2.y.m.199.5 | 12 | 5.4 | even | 2 | |||
1950.2.y.n.49.2 | 12 | 65.49 | even | 6 | inner | ||
1950.2.y.n.199.2 | 12 | 1.1 | even | 1 | trivial | ||
1950.2.bc.h.751.5 | ✓ | 12 | 65.62 | odd | 12 | ||
1950.2.bc.h.901.5 | yes | 12 | 5.2 | odd | 4 | ||
1950.2.bc.k.751.2 | yes | 12 | 65.23 | odd | 12 | ||
1950.2.bc.k.901.2 | yes | 12 | 5.3 | odd | 4 |