Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(82,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.f (of order \(5\), degree \(4\), 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: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} + x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 82.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 891.82 |
Dual form | 891.2.f.b.163.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.118034 | − | 0.363271i | −0.0834626 | − | 0.256872i | 0.900613 | − | 0.434622i | \(-0.143118\pi\) |
−0.984076 | + | 0.177750i | \(0.943118\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.50000 | − | 1.08981i | 0.750000 | − | 0.544907i | ||||
\(5\) | −0.381966 | + | 1.17557i | −0.170820 | + | 0.525731i | −0.999418 | − | 0.0341136i | \(-0.989139\pi\) |
0.828598 | + | 0.559845i | \(0.189139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | −0.424304 | − | 0.905520i | \(-0.639481\pi\) |
0.730084 | + | 0.683358i | \(0.239481\pi\) | |||||||
\(8\) | −1.19098 | − | 0.865300i | −0.421076 | − | 0.305930i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.472136 | 0.149302 | ||||||||
\(11\) | 0.309017 | + | 3.30220i | 0.0931721 | + | 0.995650i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 6.15537i | −0.554700 | − | 1.70719i | −0.696734 | − | 0.717330i | \(-0.745364\pi\) |
0.142034 | − | 0.989862i | \(-0.454636\pi\) | |||||||
\(14\) | −0.309017 | − | 0.224514i | −0.0825883 | − | 0.0600039i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.972136 | − | 2.99193i | 0.243034 | − | 0.747982i | ||||
\(17\) | 1.50000 | − | 4.61653i | 0.363803 | − | 1.11967i | −0.586924 | − | 0.809642i | \(-0.699661\pi\) |
0.950727 | − | 0.310029i | \(-0.100339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.809017 | − | 0.587785i | −0.185601 | − | 0.134847i | 0.491105 | − | 0.871100i | \(-0.336593\pi\) |
−0.676706 | + | 0.736253i | \(0.736593\pi\) | |||||||
\(20\) | 0.708204 | + | 2.17963i | 0.158359 | + | 0.487380i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.16312 | − | 0.502029i | 0.247978 | − | 0.107033i | ||||
\(23\) | 4.61803 | 0.962927 | 0.481463 | − | 0.876466i | \(-0.340105\pi\) | ||||
0.481463 | + | 0.876466i | \(0.340105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.80902 | + | 2.04087i | 0.561803 | + | 0.408174i | ||||
\(26\) | −2.00000 | + | 1.45309i | −0.392232 | + | 0.284973i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.572949 | − | 1.76336i | 0.108277 | − | 0.333243i | ||||
\(29\) | 3.92705 | − | 2.85317i | 0.729235 | − | 0.529820i | −0.160086 | − | 0.987103i | \(-0.551177\pi\) |
0.889321 | + | 0.457283i | \(0.151177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.190983 | + | 0.587785i | 0.0343016 | + | 0.105569i | 0.966741 | − | 0.255756i | \(-0.0823244\pi\) |
−0.932440 | + | 0.361325i | \(0.882324\pi\) | |||||||
\(32\) | −4.14590 | −0.732898 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.85410 | −0.317976 | ||||||||
\(35\) | 0.381966 | + | 1.17557i | 0.0645640 | + | 0.198708i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.11803 | − | 2.99193i | 0.677001 | − | 0.491870i | −0.195361 | − | 0.980731i | \(-0.562588\pi\) |
0.872361 | + | 0.488862i | \(0.162588\pi\) | |||||||
\(38\) | −0.118034 | + | 0.363271i | −0.0191476 | + | 0.0589304i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.47214 | − | 1.06957i | 0.232765 | − | 0.169114i | ||||
\(41\) | 2.04508 | + | 1.48584i | 0.319389 | + | 0.232049i | 0.735915 | − | 0.677074i | \(-0.236752\pi\) |
−0.416526 | + | 0.909124i | \(0.636752\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.85410 | 0.282748 | 0.141374 | − | 0.989956i | \(-0.454848\pi\) | ||||
0.141374 | + | 0.989956i | \(0.454848\pi\) | |||||||
\(44\) | 4.06231 | + | 4.61653i | 0.612416 | + | 0.695967i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.545085 | − | 1.67760i | −0.0803684 | − | 0.247348i | ||||
\(47\) | −9.66312 | − | 7.02067i | −1.40951 | − | 1.02407i | −0.993393 | − | 0.114759i | \(-0.963391\pi\) |
−0.416117 | − | 0.909311i | \(-0.636609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.85410 | + | 5.70634i | −0.264872 | + | 0.815191i | ||||
\(50\) | 0.409830 | − | 1.26133i | 0.0579587 | − | 0.178379i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.70820 | − | 7.05342i | −1.34629 | − | 0.978134i | ||||
\(53\) | 1.26393 | + | 3.88998i | 0.173614 | + | 0.534330i | 0.999567 | − | 0.0294087i | \(-0.00936242\pi\) |
−0.825953 | + | 0.563739i | \(0.809362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | − | 0.898056i | −0.539360 | − | 0.121094i | ||||
\(56\) | −1.47214 | −0.196722 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.50000 | − | 1.08981i | −0.196960 | − | 0.143100i | ||||
\(59\) | −1.30902 | + | 0.951057i | −0.170419 | + | 0.123817i | −0.669726 | − | 0.742609i | \(-0.733588\pi\) |
0.499306 | + | 0.866426i | \(0.333588\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.35410 | − | 10.3229i | 0.429449 | − | 1.32171i | −0.469221 | − | 0.883081i | \(-0.655465\pi\) |
0.898669 | − | 0.438626i | \(-0.144535\pi\) | |||||||
\(62\) | 0.190983 | − | 0.138757i | 0.0242549 | − | 0.0176222i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.45492 | − | 4.47777i | −0.181864 | − | 0.559721i | ||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | 0.733017 | 0.366508 | − | 0.930415i | \(-0.380553\pi\) | ||||
0.366508 | + | 0.930415i | \(0.380553\pi\) | |||||||
\(68\) | −2.78115 | − | 8.55951i | −0.337264 | − | 1.03799i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.381966 | − | 0.277515i | 0.0456537 | − | 0.0331693i | ||||
\(71\) | −0.899187 | + | 2.76741i | −0.106714 | + | 0.328431i | −0.990129 | − | 0.140160i | \(-0.955238\pi\) |
0.883415 | + | 0.468591i | \(0.155238\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.118034 | − | 0.0857567i | 0.0138148 | − | 0.0100371i | −0.580856 | − | 0.814006i | \(-0.697282\pi\) |
0.594671 | + | 0.803969i | \(0.297282\pi\) | |||||||
\(74\) | −1.57295 | − | 1.14281i | −0.182852 | − | 0.132849i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.85410 | −0.212680 | ||||||||
\(77\) | 2.19098 | + | 2.48990i | 0.249686 | + | 0.283750i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26393 | + | 10.0453i | 0.367221 | + | 1.13019i | 0.948579 | + | 0.316542i | \(0.102522\pi\) |
−0.581357 | + | 0.813648i | \(0.697478\pi\) | |||||||
\(80\) | 3.14590 | + | 2.28563i | 0.351722 | + | 0.255541i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.298374 | − | 0.918300i | 0.0329499 | − | 0.101409i | ||||
\(83\) | −3.01722 | + | 9.28605i | −0.331183 | + | 1.01928i | 0.637389 | + | 0.770542i | \(0.280015\pi\) |
−0.968572 | + | 0.248734i | \(0.919985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.85410 | + | 3.52671i | 0.526501 | + | 0.382526i | ||||
\(86\) | −0.218847 | − | 0.673542i | −0.0235989 | − | 0.0726299i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.48936 | − | 4.20025i | 0.265366 | − | 0.447749i | ||||
\(89\) | −6.76393 | −0.716975 | −0.358488 | − | 0.933534i | \(-0.616707\pi\) | ||||
−0.358488 | + | 0.933534i | \(0.616707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.23607 | − | 3.80423i | −0.548889 | − | 0.398791i | ||||
\(92\) | 6.92705 | − | 5.03280i | 0.722195 | − | 0.524705i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.40983 | + | 4.33901i | −0.145413 | + | 0.447535i | ||||
\(95\) | 1.00000 | − | 0.726543i | 0.102598 | − | 0.0745417i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.85410 | + | 5.70634i | 0.188256 | + | 0.579391i | 0.999989 | − | 0.00463676i | \(-0.00147593\pi\) |
−0.811734 | + | 0.584028i | \(0.801476\pi\) | |||||||
\(98\) | 2.29180 | 0.231506 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.43769 | 0.643769 | ||||||||
\(101\) | −2.61803 | − | 8.05748i | −0.260504 | − | 0.801749i | −0.992695 | − | 0.120650i | \(-0.961502\pi\) |
0.732191 | − | 0.681099i | \(-0.238498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.28115 | − | 6.01661i | 0.815966 | − | 0.592834i | −0.0995880 | − | 0.995029i | \(-0.531752\pi\) |
0.915554 | + | 0.402195i | \(0.131752\pi\) | |||||||
\(104\) | −2.94427 | + | 9.06154i | −0.288710 | + | 0.888557i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.26393 | − | 0.918300i | 0.122764 | − | 0.0891932i | ||||
\(107\) | −11.3541 | − | 8.24924i | −1.09764 | − | 0.797484i | −0.116969 | − | 0.993136i | \(-0.537318\pi\) |
−0.980673 | + | 0.195652i | \(0.937318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.14590 | 0.684453 | 0.342226 | − | 0.939618i | \(-0.388819\pi\) | ||||
0.342226 | + | 0.939618i | \(0.388819\pi\) | |||||||
\(110\) | 0.145898 | + | 1.55909i | 0.0139108 | + | 0.148653i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.972136 | − | 2.99193i | −0.0918582 | − | 0.282711i | ||||
\(113\) | −13.9443 | − | 10.1311i | −1.31177 | − | 0.953054i | −0.999996 | − | 0.00289705i | \(-0.999078\pi\) |
−0.311771 | − | 0.950157i | \(-0.600922\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.76393 | + | 5.42882i | −0.164488 | + | 0.506240i | ||||
\(116\) | 2.78115 | − | 8.55951i | 0.258224 | − | 0.794730i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.500000 | + | 0.363271i | 0.0460287 | + | 0.0334418i | ||||
\(119\) | −1.50000 | − | 4.61653i | −0.137505 | − | 0.423196i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8090 | + | 2.04087i | −0.982638 | + | 0.185534i | ||||
\(122\) | −4.14590 | −0.375352 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.927051 | + | 0.673542i | 0.0832516 | + | 0.0604859i | ||||
\(125\) | −8.47214 | + | 6.15537i | −0.757771 | + | 0.550553i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.26393 | + | 10.0453i | −0.289627 | + | 0.891381i | 0.695346 | + | 0.718675i | \(0.255251\pi\) |
−0.984973 | + | 0.172706i | \(0.944749\pi\) | |||||||
\(128\) | −8.16312 | + | 5.93085i | −0.721525 | + | 0.524218i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.944272 | − | 2.90617i | −0.0828181 | − | 0.254888i | ||||
\(131\) | 21.2361 | 1.85540 | 0.927702 | − | 0.373322i | \(-0.121781\pi\) | ||||
0.927702 | + | 0.373322i | \(0.121781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | −0.708204 | − | 2.17963i | −0.0611795 | − | 0.188291i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.78115 | + | 4.20025i | −0.495730 | + | 0.360169i | ||||
\(137\) | −2.66312 | + | 8.19624i | −0.227526 | + | 0.700252i | 0.770500 | + | 0.637440i | \(0.220007\pi\) |
−0.998025 | + | 0.0628116i | \(0.979993\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.85410 | + | 5.70634i | −0.666176 | + | 0.484005i | −0.868743 | − | 0.495263i | \(-0.835072\pi\) |
0.202567 | + | 0.979268i | \(0.435072\pi\) | |||||||
\(140\) | 1.85410 | + | 1.34708i | 0.156700 | + | 0.113849i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.11146 | 0.0932713 | ||||||||
\(143\) | 19.7082 | − | 8.50651i | 1.64808 | − | 0.711350i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.85410 | + | 5.70634i | 0.153975 | + | 0.473886i | ||||
\(146\) | −0.0450850 | − | 0.0327561i | −0.00373126 | − | 0.00271092i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.91641 | − | 8.97578i | 0.239727 | − | 0.737805i | ||||
\(149\) | −4.69098 | + | 14.4374i | −0.384300 | + | 1.18275i | 0.552686 | + | 0.833389i | \(0.313603\pi\) |
−0.936987 | + | 0.349365i | \(0.886397\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.50000 | − | 2.54290i | −0.284826 | − | 0.206938i | 0.436194 | − | 0.899853i | \(-0.356326\pi\) |
−0.721020 | + | 0.692915i | \(0.756326\pi\) | |||||||
\(152\) | 0.454915 | + | 1.40008i | 0.0368985 | + | 0.113562i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.645898 | − | 1.08981i | 0.0520479 | − | 0.0878197i | ||||
\(155\) | −0.763932 | −0.0613605 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.78115 | − | 4.20025i | −0.461386 | − | 0.335217i | 0.332689 | − | 0.943037i | \(-0.392044\pi\) |
−0.794075 | + | 0.607820i | \(0.792044\pi\) | |||||||
\(158\) | 3.26393 | − | 2.37139i | 0.259664 | − | 0.188657i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.58359 | − | 4.87380i | 0.125194 | − | 0.385307i | ||||
\(161\) | 3.73607 | − | 2.71441i | 0.294443 | − | 0.213926i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.39919 | + | 19.6947i | 0.501223 | + | 1.54261i | 0.807029 | + | 0.590512i | \(0.201074\pi\) |
−0.305806 | + | 0.952094i | \(0.598926\pi\) | |||||||
\(164\) | 4.68692 | 0.365987 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.72949 | 0.289465 | ||||||||
\(167\) | −1.78115 | − | 5.48183i | −0.137830 | − | 0.424196i | 0.858190 | − | 0.513333i | \(-0.171589\pi\) |
−0.996019 | + | 0.0891363i | \(0.971589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.3713 | + | 16.9803i | −1.79779 | + | 1.30617i | ||||
\(170\) | 0.708204 | − | 2.17963i | 0.0543168 | − | 0.167170i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.78115 | − | 2.02063i | 0.212061 | − | 0.154071i | ||||
\(173\) | 18.6803 | + | 13.5721i | 1.42024 | + | 1.03186i | 0.991732 | + | 0.128327i | \(0.0409606\pi\) |
0.428508 | + | 0.903538i | \(0.359039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.47214 | 0.262469 | ||||||||
\(176\) | 10.1803 | + | 2.28563i | 0.767372 | + | 0.172286i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.798374 | + | 2.45714i | 0.0598407 | + | 0.184171i | ||||
\(179\) | 4.09017 | + | 2.97168i | 0.305714 | + | 0.222114i | 0.730055 | − | 0.683388i | \(-0.239494\pi\) |
−0.424341 | + | 0.905502i | \(0.639494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.06231 | + | 9.42481i | −0.227619 | + | 0.700540i | 0.770396 | + | 0.637566i | \(0.220059\pi\) |
−0.998015 | + | 0.0629745i | \(0.979941\pi\) | |||||||
\(182\) | −0.763932 | + | 2.35114i | −0.0566264 | + | 0.174278i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.50000 | − | 3.99598i | −0.405465 | − | 0.294588i | ||||
\(185\) | 1.94427 | + | 5.98385i | 0.142946 | + | 0.439942i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.7082 | + | 3.52671i | 1.14870 | + | 0.257899i | ||||
\(188\) | −22.1459 | −1.61516 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.381966 | − | 0.277515i | −0.0277107 | − | 0.0201330i | ||||
\(191\) | −4.80902 | + | 3.49396i | −0.347968 | + | 0.252814i | −0.748016 | − | 0.663680i | \(-0.768993\pi\) |
0.400048 | + | 0.916494i | \(0.368993\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.39919 | + | 10.4616i | −0.244679 | + | 0.753044i | 0.751010 | + | 0.660291i | \(0.229567\pi\) |
−0.995689 | + | 0.0927535i | \(0.970433\pi\) | |||||||
\(194\) | 1.85410 | − | 1.34708i | 0.133117 | − | 0.0967150i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.43769 | + | 10.5801i | 0.245550 | + | 0.755724i | ||||
\(197\) | 8.23607 | 0.586796 | 0.293398 | − | 0.955990i | \(-0.405214\pi\) | ||||
0.293398 | + | 0.955990i | \(0.405214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.14590 | −0.506559 | −0.253280 | − | 0.967393i | \(-0.581509\pi\) | ||||
−0.253280 | + | 0.967393i | \(0.581509\pi\) | |||||||
\(200\) | −1.57953 | − | 4.86128i | −0.111689 | − | 0.343745i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.61803 | + | 1.90211i | −0.184204 | + | 0.133832i | ||||
\(203\) | 1.50000 | − | 4.61653i | 0.105279 | − | 0.324017i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.52786 | + | 1.83660i | −0.176554 | + | 0.128274i | ||||
\(206\) | −3.16312 | − | 2.29814i | −0.220385 | − | 0.160119i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.3607 | −1.41176 | ||||||||
\(209\) | 1.69098 | − | 2.85317i | 0.116968 | − | 0.197358i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.32624 | + | 19.4702i | 0.435516 | + | 1.34038i | 0.892557 | + | 0.450935i | \(0.148909\pi\) |
−0.457041 | + | 0.889446i | \(0.651091\pi\) | |||||||
\(212\) | 6.13525 | + | 4.45752i | 0.421371 | + | 0.306144i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.65654 | + | 5.09831i | −0.113239 | + | 0.348513i | ||||
\(215\) | −0.708204 | + | 2.17963i | −0.0482991 | + | 0.148649i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.500000 | + | 0.363271i | 0.0339422 | + | 0.0246605i | ||||
\(218\) | −0.843459 | − | 2.59590i | −0.0571262 | − | 0.175816i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.97871 | + | 3.01217i | −0.470505 | + | 0.203081i | ||||
\(221\) | −31.4164 | −2.11330 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5451 | + | 9.11454i | 0.840081 | + | 0.610355i | 0.922393 | − | 0.386252i | \(-0.126230\pi\) |
−0.0823123 | + | 0.996607i | \(0.526230\pi\) | |||||||
\(224\) | −3.35410 | + | 2.43690i | −0.224105 | + | 0.162822i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.03444 | + | 6.26137i | −0.135329 | + | 0.416500i | ||||
\(227\) | 13.4443 | − | 9.76784i | 0.892328 | − | 0.648314i | −0.0441562 | − | 0.999025i | \(-0.514060\pi\) |
0.936484 | + | 0.350711i | \(0.114060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.14590 | + | 9.68208i | 0.207887 | + | 0.639810i | 0.999582 | + | 0.0288941i | \(0.00919856\pi\) |
−0.791696 | + | 0.610916i | \(0.790801\pi\) | |||||||
\(230\) | 2.18034 | 0.143767 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.14590 | −0.469151 | ||||||||
\(233\) | −3.43769 | − | 10.5801i | −0.225211 | − | 0.693128i | −0.998270 | − | 0.0587939i | \(-0.981275\pi\) |
0.773059 | − | 0.634334i | \(-0.218725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.9443 | − | 8.67802i | 0.779158 | − | 0.566092i | ||||
\(236\) | −0.927051 | + | 2.85317i | −0.0603459 | + | 0.185726i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.50000 | + | 1.08981i | −0.0972306 | + | 0.0706421i | ||||
\(239\) | −8.47214 | − | 6.15537i | −0.548017 | − | 0.398158i | 0.279037 | − | 0.960280i | \(-0.409985\pi\) |
−0.827054 | + | 0.562123i | \(0.809985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.8328 | −1.72845 | −0.864227 | − | 0.503102i | \(-0.832192\pi\) | ||||
−0.864227 | + | 0.503102i | \(0.832192\pi\) | |||||||
\(242\) | 2.01722 | + | 3.68571i | 0.129672 | + | 0.236927i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.21885 | − | 19.1396i | −0.398121 | − | 1.22529i | ||||
\(245\) | −6.00000 | − | 4.35926i | −0.383326 | − | 0.278503i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | + | 6.15537i | −0.127257 | + | 0.391657i | ||||
\(248\) | 0.281153 | − | 0.865300i | 0.0178532 | − | 0.0549466i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.23607 | + | 2.35114i | 0.204667 | + | 0.148699i | ||||
\(251\) | 6.35410 | + | 19.5559i | 0.401067 | + | 1.23436i | 0.924135 | + | 0.382067i | \(0.124788\pi\) |
−0.523067 | + | 0.852291i | \(0.675212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.42705 | + | 15.2497i | 0.0897179 | + | 0.958738i | ||||
\(254\) | 4.03444 | 0.253143 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.50000 | − | 3.26944i | −0.281250 | − | 0.204340i | ||||
\(257\) | 12.0623 | − | 8.76378i | 0.752426 | − | 0.546669i | −0.144152 | − | 0.989556i | \(-0.546045\pi\) |
0.896578 | + | 0.442886i | \(0.146045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.57295 | − | 4.84104i | 0.0977383 | − | 0.300808i | ||||
\(260\) | 12.0000 | − | 8.71851i | 0.744208 | − | 0.540699i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.50658 | − | 7.71445i | −0.154857 | − | 0.476601i | ||||
\(263\) | −12.7082 | −0.783621 | −0.391811 | − | 0.920046i | \(-0.628151\pi\) | ||||
−0.391811 | + | 0.920046i | \(0.628151\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.05573 | −0.310571 | ||||||||
\(266\) | 0.118034 | + | 0.363271i | 0.00723713 | + | 0.0222736i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.00000 | − | 6.53888i | 0.549762 | − | 0.399426i | ||||
\(269\) | −6.57295 | + | 20.2295i | −0.400760 | + | 1.23341i | 0.523625 | + | 0.851949i | \(0.324579\pi\) |
−0.924384 | + | 0.381463i | \(0.875421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.70820 | + | 6.32688i | −0.528986 | + | 0.384331i | −0.819978 | − | 0.572395i | \(-0.806015\pi\) |
0.290993 | + | 0.956725i | \(0.406015\pi\) | |||||||
\(272\) | −12.3541 | − | 8.97578i | −0.749077 | − | 0.544237i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.29180 | 0.198865 | ||||||||
\(275\) | −5.87132 | + | 9.90659i | −0.354054 | + | 0.597390i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.94427 | − | 18.2946i | −0.357157 | − | 1.09922i | −0.954748 | − | 0.297415i | \(-0.903876\pi\) |
0.597592 | − | 0.801801i | \(-0.296124\pi\) | |||||||
\(278\) | 3.00000 | + | 2.17963i | 0.179928 | + | 0.130725i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.562306 | − | 1.73060i | 0.0336042 | − | 0.103423i | ||||
\(281\) | −2.88197 | + | 8.86978i | −0.171924 | + | 0.529127i | −0.999480 | − | 0.0322566i | \(-0.989731\pi\) |
0.827556 | + | 0.561383i | \(0.189731\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7533 | + | 9.99235i | 0.817548 | + | 0.593984i | 0.916009 | − | 0.401157i | \(-0.131392\pi\) |
−0.0984610 | + | 0.995141i | \(0.531392\pi\) | |||||||
\(284\) | 1.66718 | + | 5.13107i | 0.0989292 | + | 0.304473i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.41641 | − | 6.15537i | −0.320279 | − | 0.363974i | ||||
\(287\) | 2.52786 | 0.149215 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.30902 | − | 3.85723i | −0.312295 | − | 0.226896i | ||||
\(290\) | 1.85410 | − | 1.34708i | 0.108877 | − | 0.0791035i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.0835921 | − | 0.257270i | 0.00489186 | − | 0.0150556i | ||||
\(293\) | 23.6074 | − | 17.1518i | 1.37916 | − | 1.00202i | 0.382200 | − | 0.924080i | \(-0.375166\pi\) |
0.996958 | − | 0.0779378i | \(-0.0248336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.618034 | − | 1.90211i | −0.0359833 | − | 0.110745i | ||||
\(296\) | −7.49342 | −0.435546 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.79837 | 0.335891 | ||||||||
\(299\) | −9.23607 | − | 28.4257i | −0.534136 | − | 1.64390i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.50000 | − | 1.08981i | 0.0864586 | − | 0.0628158i | ||||
\(302\) | −0.510643 | + | 1.57160i | −0.0293842 | + | 0.0904353i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.54508 | + | 1.84911i | −0.145971 | + | 0.106054i | ||||
\(305\) | 10.8541 | + | 7.88597i | 0.621504 | + | 0.451549i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.85410 | 0.448257 | 0.224129 | − | 0.974560i | \(-0.428046\pi\) | ||||
0.224129 | + | 0.974560i | \(0.428046\pi\) | |||||||
\(308\) | 6.00000 | + | 1.34708i | 0.341882 | + | 0.0767572i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.0901699 | + | 0.277515i | 0.00512131 | + | 0.0157618i | ||||
\(311\) | −12.2812 | − | 8.92278i | −0.696400 | − | 0.505964i | 0.182358 | − | 0.983232i | \(-0.441627\pi\) |
−0.878758 | + | 0.477268i | \(0.841627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.07295 | − | 3.30220i | 0.0606467 | − | 0.186651i | −0.916143 | − | 0.400851i | \(-0.868714\pi\) |
0.976790 | + | 0.214200i | \(0.0687144\pi\) | |||||||
\(314\) | −0.843459 | + | 2.59590i | −0.0475991 | + | 0.146495i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.8435 | + | 11.5109i | 0.891264 | + | 0.647541i | ||||
\(317\) | 6.47214 | + | 19.9192i | 0.363511 | + | 1.11877i | 0.950908 | + | 0.309474i | \(0.100153\pi\) |
−0.587397 | + | 0.809299i | \(0.699847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.6353 | + | 12.0862i | 0.595460 | + | 0.676698i | ||||
\(320\) | 5.81966 | 0.325329 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.42705 | − | 1.03681i | −0.0795264 | − | 0.0577793i | ||||
\(323\) | −3.92705 | + | 2.85317i | −0.218507 | + | 0.158755i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.94427 | − | 21.3723i | 0.385199 | − | 1.18552i | ||||
\(326\) | 6.39919 | − | 4.64928i | 0.354418 | − | 0.257500i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.14996 | − | 3.53922i | −0.0634961 | − | 0.195421i | ||||
\(329\) | −11.9443 | −0.658509 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4164 | 0.792397 | 0.396199 | − | 0.918165i | \(-0.370329\pi\) | ||||
0.396199 | + | 0.918165i | \(0.370329\pi\) | |||||||
\(332\) | 5.59424 | + | 17.2173i | 0.307024 | + | 0.944921i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.78115 | + | 1.29408i | −0.0974604 | + | 0.0708091i | ||||
\(335\) | −2.29180 | + | 7.05342i | −0.125214 | + | 0.385370i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.28115 | − | 6.74315i | 0.505577 | − | 0.367323i | −0.305566 | − | 0.952171i | \(-0.598846\pi\) |
0.811143 | + | 0.584848i | \(0.198846\pi\) | |||||||
\(338\) | 8.92705 | + | 6.48588i | 0.485568 | + | 0.352785i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.1246 | 0.603317 | ||||||||
\(341\) | −1.88197 | + | 0.812299i | −0.101914 | + | 0.0439885i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.01722 | + | 12.3637i | 0.216910 | + | 0.667579i | ||||
\(344\) | −2.20820 | − | 1.60435i | −0.119058 | − | 0.0865010i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.72542 | − | 8.38800i | 0.146520 | − | 0.450941i | ||||
\(347\) | −2.74671 | + | 8.45351i | −0.147451 | + | 0.453808i | −0.997318 | − | 0.0731894i | \(-0.976682\pi\) |
0.849867 | + | 0.526997i | \(0.176682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.35410 | + | 2.43690i | 0.179541 | + | 0.130444i | 0.673926 | − | 0.738799i | \(-0.264607\pi\) |
−0.494385 | + | 0.869243i | \(0.664607\pi\) | |||||||
\(350\) | −0.409830 | − | 1.26133i | −0.0219063 | − | 0.0674208i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.28115 | − | 13.6906i | −0.0682857 | − | 0.729710i | ||||
\(353\) | −16.4164 | −0.873757 | −0.436879 | − | 0.899520i | \(-0.643916\pi\) | ||||
−0.436879 | + | 0.899520i | \(0.643916\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.90983 | − | 2.11412i | −0.154438 | − | 0.112206i | ||||
\(356\) | −10.1459 | + | 7.37143i | −0.537732 | + | 0.390685i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.596748 | − | 1.83660i | 0.0315391 | − | 0.0970674i | ||||
\(359\) | 18.4894 | − | 13.4333i | 0.975831 | − | 0.708983i | 0.0190579 | − | 0.999818i | \(-0.493933\pi\) |
0.956773 | + | 0.290836i | \(0.0939333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.56231 | − | 17.1190i | −0.292753 | − | 0.901001i | ||||
\(362\) | 3.78522 | 0.198947 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0000 | −0.628971 | ||||||||
\(365\) | 0.0557281 | + | 0.171513i | 0.00291694 | + | 0.00897742i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2812 | − | 7.46969i | 0.536672 | − | 0.389915i | −0.286176 | − | 0.958177i | \(-0.592384\pi\) |
0.822847 | + | 0.568262i | \(0.192384\pi\) | |||||||
\(368\) | 4.48936 | − | 13.8168i | 0.234024 | − | 0.720252i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.94427 | − | 1.41260i | 0.101078 | − | 0.0734374i | ||||
\(371\) | 3.30902 | + | 2.40414i | 0.171796 | + | 0.124817i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.65248 | −0.292674 | −0.146337 | − | 0.989235i | \(-0.546748\pi\) | ||||
−0.146337 | + | 0.989235i | \(0.546748\pi\) | |||||||
\(374\) | −0.572949 | − | 6.12261i | −0.0296265 | − | 0.316593i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.43363 | + | 16.7230i | 0.280218 | + | 0.862422i | ||||
\(377\) | −25.4164 | − | 18.4661i | −1.30901 | − | 0.951053i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.88197 | − | 15.0251i | 0.250770 | − | 0.771790i | −0.743864 | − | 0.668331i | \(-0.767009\pi\) |
0.994634 | − | 0.103459i | \(-0.0329910\pi\) | |||||||
\(380\) | 0.708204 | − | 2.17963i | 0.0363301 | − | 0.111813i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.83688 | + | 1.33457i | 0.0939830 | + | 0.0682827i | ||||
\(383\) | 6.13525 | + | 18.8824i | 0.313497 | + | 0.964844i | 0.976369 | + | 0.216111i | \(0.0693374\pi\) |
−0.662872 | + | 0.748733i | \(0.730663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.76393 | + | 1.62460i | −0.191828 | + | 0.0827972i | ||||
\(386\) | 4.20163 | 0.213857 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.00000 | + | 6.53888i | 0.456906 | + | 0.331961i | ||||
\(389\) | 18.3262 | − | 13.3148i | 0.929177 | − | 0.675087i | −0.0166141 | − | 0.999862i | \(-0.505289\pi\) |
0.945791 | + | 0.324775i | \(0.105289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.92705 | − | 21.3193i | 0.350316 | − | 1.07816i | ||||
\(392\) | 7.14590 | − | 5.19180i | 0.360922 | − | 0.262225i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.972136 | − | 2.99193i | −0.0489755 | − | 0.150731i | ||||
\(395\) | −13.0557 | −0.656905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.12461 | −0.106631 | −0.0533156 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533156 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(398\) | 0.843459 | + | 2.59590i | 0.0422788 | + | 0.130121i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.83688 | − | 6.42037i | 0.441844 | − | 0.321018i | ||||
\(401\) | 4.50000 | − | 13.8496i | 0.224719 | − | 0.691615i | −0.773601 | − | 0.633673i | \(-0.781546\pi\) |
0.998320 | − | 0.0579414i | \(-0.0184537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.23607 | − | 2.35114i | 0.161200 | − | 0.117119i | ||||
\(404\) | −12.7082 | − | 9.23305i | −0.632257 | − | 0.459361i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.85410 | −0.0920175 | ||||||||
\(407\) | 11.1525 | + | 12.6740i | 0.552808 | + | 0.628227i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4271 | − | 32.0912i | −0.515584 | − | 1.58681i | −0.782216 | − | 0.623007i | \(-0.785911\pi\) |
0.266631 | − | 0.963799i | \(-0.414089\pi\) | |||||||
\(410\) | 0.965558 | + | 0.701519i | 0.0476855 | + | 0.0346456i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.86475 | − | 18.0498i | 0.288935 | − | 0.889251i | ||||
\(413\) | −0.500000 | + | 1.53884i | −0.0246034 | + | 0.0757215i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.76393 | − | 7.09391i | −0.479293 | − | 0.348226i | ||||
\(416\) | 8.29180 | + | 25.5195i | 0.406539 | + | 1.25120i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.23607 | − | 0.277515i | −0.0604581 | − | 0.0135737i | ||||
\(419\) | 8.09017 | 0.395231 | 0.197615 | − | 0.980280i | \(-0.436680\pi\) | ||||
0.197615 | + | 0.980280i | \(0.436680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.28115 | − | 6.01661i | −0.403599 | − | 0.293232i | 0.367407 | − | 0.930060i | \(-0.380246\pi\) |
−0.771005 | + | 0.636829i | \(0.780246\pi\) | |||||||
\(422\) | 6.32624 | − | 4.59628i | 0.307956 | − | 0.223743i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.86068 | − | 5.72658i | 0.0903626 | − | 0.278107i | ||||
\(425\) | 13.6353 | − | 9.90659i | 0.661407 | − | 0.480540i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.35410 | − | 10.3229i | −0.162316 | − | 0.499558i | ||||
\(428\) | −26.0213 | −1.25779 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.875388 | 0.0422150 | ||||||||
\(431\) | −10.5279 | − | 32.4014i | −0.507109 | − | 1.56072i | −0.797195 | − | 0.603722i | \(-0.793684\pi\) |
0.290086 | − | 0.957001i | \(-0.406316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.9271 | + | 8.66551i | −0.573177 | + | 0.416438i | −0.836258 | − | 0.548336i | \(-0.815261\pi\) |
0.263081 | + | 0.964774i | \(0.415261\pi\) | |||||||
\(434\) | 0.0729490 | − | 0.224514i | 0.00350166 | − | 0.0107770i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.7188 | − | 7.78770i | 0.513340 | − | 0.372963i | ||||
\(437\) | −3.73607 | − | 2.71441i | −0.178720 | − | 0.129848i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.708204 | −0.0338007 | −0.0169004 | − | 0.999857i | \(-0.505380\pi\) | ||||
−0.0169004 | + | 0.999857i | \(0.505380\pi\) | |||||||
\(440\) | 3.98684 | + | 4.53077i | 0.190065 | + | 0.215996i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.70820 | + | 11.4127i | 0.176381 | + | 0.542846i | ||||
\(443\) | 1.00000 | + | 0.726543i | 0.0475114 | + | 0.0345191i | 0.611288 | − | 0.791409i | \(-0.290652\pi\) |
−0.563776 | + | 0.825928i | \(0.690652\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.58359 | − | 7.95148i | 0.122474 | − | 0.376936i | ||||
\(446\) | 1.83030 | − | 5.63309i | 0.0866674 | − | 0.266735i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.80902 | − | 2.76741i | −0.179959 | − | 0.130748i | ||||
\(449\) | 2.30902 | + | 7.10642i | 0.108969 | + | 0.335373i | 0.990642 | − | 0.136489i | \(-0.0435820\pi\) |
−0.881672 | + | 0.471862i | \(0.843582\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.27458 | + | 7.21242i | −0.201282 | + | 0.339620i | ||||
\(452\) | −31.9574 | −1.50315 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.13525 | − | 3.73098i | −0.241009 | − | 0.175104i | ||||
\(455\) | 6.47214 | − | 4.70228i | 0.303418 | − | 0.220446i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.309017 | + | 0.951057i | −0.0144552 | + | 0.0444885i | −0.958024 | − | 0.286688i | \(-0.907446\pi\) |
0.943569 | + | 0.331177i | \(0.107446\pi\) | |||||||
\(458\) | 3.14590 | − | 2.28563i | 0.146998 | − | 0.106800i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.27051 | + | 10.0656i | 0.152488 | + | 0.469311i | ||||
\(461\) | −16.1459 | −0.751989 | −0.375995 | − | 0.926622i | \(-0.622699\pi\) | ||||
−0.375995 | + | 0.926622i | \(0.622699\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000 | 0.790057 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(464\) | −4.71885 | − | 14.5231i | −0.219067 | − | 0.674219i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.43769 | + | 2.49763i | −0.159248 | + | 0.115701i | ||||
\(467\) | −0.236068 | + | 0.726543i | −0.0109239 | + | 0.0336204i | −0.956370 | − | 0.292159i | \(-0.905627\pi\) |
0.945446 | + | 0.325779i | \(0.105627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.85410 | − | 3.52671i | 0.224142 | − | 0.162848i | ||||
\(470\) | −4.56231 | − | 3.31471i | −0.210443 | − | 0.152896i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.38197 | 0.109639 | ||||||||
\(473\) | 0.572949 | + | 6.12261i | 0.0263442 | + | 0.281518i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.07295 | − | 3.30220i | −0.0492303 | − | 0.151515i | ||||
\(476\) | −7.28115 | − | 5.29007i | −0.333731 | − | 0.242470i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.23607 | + | 3.80423i | −0.0565364 | + | 0.174001i | ||||
\(479\) | −3.63525 | + | 11.1882i | −0.166099 | + | 0.511200i | −0.999116 | − | 0.0420478i | \(-0.986612\pi\) |
0.833017 | + | 0.553248i | \(0.186612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.6525 | − | 19.3642i | −1.21525 | − | 0.882930i | ||||
\(482\) | 3.16718 | + | 9.74759i | 0.144261 | + | 0.443991i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.9894 | + | 14.8411i | −0.635880 | + | 0.674596i | ||||
\(485\) | −7.41641 | −0.336762 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5000 | + | 7.62870i | 0.475800 | + | 0.345689i | 0.799698 | − | 0.600403i | \(-0.204993\pi\) |
−0.323897 | + | 0.946092i | \(0.604993\pi\) | |||||||
\(488\) | −12.9271 | + | 9.39205i | −0.585180 | + | 0.425158i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.875388 | + | 2.69417i | −0.0395460 | + | 0.121710i | ||||
\(491\) | −5.92705 | + | 4.30625i | −0.267484 | + | 0.194339i | −0.713440 | − | 0.700716i | \(-0.752864\pi\) |
0.445956 | + | 0.895055i | \(0.352864\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.28115 | − | 22.4091i | −0.327927 | − | 1.00925i | ||||
\(494\) | 2.47214 | 0.111227 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.94427 | 0.0873004 | ||||||||
\(497\) | 0.899187 | + | 2.76741i | 0.0403340 | + | 0.124135i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.0795 | + | 22.5806i | −1.39131 | + | 1.01085i | −0.395591 | + | 0.918427i | \(0.629460\pi\) |
−0.995720 | + | 0.0924194i | \(0.970540\pi\) | |||||||
\(500\) | −6.00000 | + | 18.4661i | −0.268328 | + | 0.825829i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.35410 | − | 4.61653i | 0.283597 | − | 0.206046i | ||||
\(503\) | 7.70820 | + | 5.60034i | 0.343692 | + | 0.249707i | 0.746218 | − | 0.665702i | \(-0.231868\pi\) |
−0.402526 | + | 0.915409i | \(0.631868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.4721 | 0.466004 | ||||||||
\(506\) | 5.37132 | − | 2.31838i | 0.238784 | − | 0.103065i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.05166 | + | 18.6251i | 0.268499 | + | 0.826355i | ||||
\(509\) | 21.9894 | + | 15.9762i | 0.974661 | + | 0.708133i | 0.956509 | − | 0.291702i | \(-0.0942217\pi\) |
0.0181520 | + | 0.999835i | \(0.494222\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0450850 | − | 0.138757i | 0.00199444 | − | 0.00613826i | ||||
\(512\) | −6.89261 | + | 21.2133i | −0.304613 | + | 0.937503i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.60739 | − | 3.34747i | −0.203223 | − | 0.147650i | ||||
\(515\) | 3.90983 | + | 12.0332i | 0.172288 | + | 0.530247i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.1976 | − | 34.0790i | 0.888288 | − | 1.49879i | ||||
\(518\) | −1.94427 | −0.0854264 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.52786 | − | 6.92240i | −0.417824 | − | 0.303567i | ||||
\(521\) | 32.6525 | − | 23.7234i | 1.43053 | − | 1.03934i | 0.440613 | − | 0.897697i | \(-0.354761\pi\) |
0.989918 | − | 0.141645i | \(-0.0452390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(524\) | 31.8541 | − | 23.1434i | 1.39155 | − | 1.01102i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.50000 | + | 4.61653i | 0.0654031 | + | 0.201290i | ||||
\(527\) | 3.00000 | 0.130682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.67376 | −0.0727723 | ||||||||
\(530\) | 0.596748 | + | 1.83660i | 0.0259211 | + | 0.0797768i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.50000 | + | 1.08981i | −0.0650332 | + | 0.0472494i | ||||
\(533\) | 5.05573 | − | 15.5599i | 0.218988 | − | 0.673975i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0344 | − | 10.1966i | 0.606762 | − | 0.440838i | ||||
\(536\) | −7.14590 | − | 5.19180i | −0.308656 | − | 0.224252i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.12461 | 0.350277 | ||||||||
\(539\) | −19.4164 | − | 4.35926i | −0.836324 | − | 0.187766i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.68034 | − | 11.3269i | −0.158230 | − | 0.486982i | 0.840244 | − | 0.542209i | \(-0.182412\pi\) |
−0.998474 | + | 0.0552266i | \(0.982412\pi\) | |||||||
\(542\) | 3.32624 | + | 2.41665i | 0.142874 | + | 0.103804i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.21885 | + | 19.1396i | −0.266631 | + | 0.820605i | ||||
\(545\) | −2.72949 | + | 8.40051i | −0.116919 | + | 0.359838i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.1525 | + | 19.0009i | 1.11820 | + | 0.812419i | 0.983935 | − | 0.178526i | \(-0.0571330\pi\) |
0.134264 | + | 0.990946i | \(0.457133\pi\) | |||||||
\(548\) | 4.93769 | + | 15.1967i | 0.210928 | + | 0.649169i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.29180 | + | 0.963568i | 0.183003 | + | 0.0410867i | ||||
\(551\) | −4.85410 | −0.206792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.54508 | + | 6.20837i | 0.363374 | + | 0.264007i | ||||
\(554\) | −5.94427 | + | 4.31877i | −0.252548 | + | 0.183487i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.56231 | + | 17.1190i | −0.235894 | + | 0.726008i | ||||
\(557\) | 0.527864 | − | 0.383516i | 0.0223663 | − | 0.0162501i | −0.576546 | − | 0.817065i | \(-0.695600\pi\) |
0.598912 | + | 0.800815i | \(0.295600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.70820 | − | 11.4127i | −0.156840 | − | 0.482705i | ||||
\(560\) | 3.88854 | 0.164321 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.56231 | 0.150267 | ||||||||
\(563\) | −6.27458 | − | 19.3112i | −0.264442 | − | 0.813868i | −0.991821 | − | 0.127633i | \(-0.959262\pi\) |
0.727380 | − | 0.686235i | \(-0.240738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.2361 | − | 12.5227i | 0.725127 | − | 0.526835i | ||||
\(566\) | 2.00658 | − | 6.17561i | 0.0843428 | − | 0.259580i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.46556 | − | 2.51788i | 0.145412 | − | 0.105648i | ||||
\(569\) | −31.3885 | − | 22.8051i | −1.31588 | − | 0.956040i | −0.999974 | − | 0.00724836i | \(-0.997693\pi\) |
−0.315902 | − | 0.948792i | \(-0.602307\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.5279 | −0.775367 | −0.387683 | − | 0.921793i | \(-0.626725\pi\) | ||||
−0.387683 | + | 0.921793i | \(0.626725\pi\) | |||||||
\(572\) | 20.2918 | − | 34.2380i | 0.848443 | − | 1.43156i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.298374 | − | 0.918300i | −0.0124539 | − | 0.0383291i | ||||
\(575\) | 12.9721 | + | 9.42481i | 0.540975 | + | 0.393042i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9443 | − | 33.6830i | 0.455616 | − | 1.40224i | −0.414794 | − | 0.909915i | \(-0.636147\pi\) |
0.870410 | − | 0.492327i | \(-0.163853\pi\) | |||||||
\(578\) | −0.774575 | + | 2.38390i | −0.0322181 | + | 0.0991570i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.00000 | + | 6.53888i | 0.373705 | + | 0.271512i | ||||
\(581\) | 3.01722 | + | 9.28605i | 0.125175 | + | 0.385250i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.4549 | + | 5.37582i | −0.515830 | + | 0.222644i | ||||
\(584\) | −0.214782 | −0.00888773 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.01722 | − | 6.55139i | −0.372498 | − | 0.270636i | ||||
\(587\) | −10.8541 | + | 7.88597i | −0.447997 | + | 0.325489i | −0.788804 | − | 0.614644i | \(-0.789300\pi\) |
0.340808 | + | 0.940133i | \(0.389300\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.190983 | − | 0.587785i | 0.00786932 | − | 0.0242193i | ||||
\(590\) | −0.618034 | + | 0.449028i | −0.0254441 | + | 0.0184862i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.94834 | − | 15.2294i | −0.203375 | − | 0.625925i | ||||
\(593\) | −10.9443 | −0.449427 | −0.224714 | − | 0.974425i | \(-0.572145\pi\) | ||||
−0.224714 | + | 0.974425i | \(0.572145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | 0.245976 | ||||||||
\(596\) | 8.69756 | + | 26.7683i | 0.356266 | + | 1.09647i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.23607 | + | 6.71040i | −0.377691 | + | 0.274409i | ||||
\(599\) | −4.12868 | + | 12.7068i | −0.168693 | + | 0.519184i | −0.999289 | − | 0.0376909i | \(-0.988000\pi\) |
0.830596 | + | 0.556875i | \(0.188000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1353 | − | 10.2699i | 0.576589 | − | 0.418916i | −0.260904 | − | 0.965365i | \(-0.584021\pi\) |
0.837493 | + | 0.546448i | \(0.184021\pi\) | |||||||
\(602\) | −0.572949 | − | 0.416272i | −0.0233517 | − | 0.0169660i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.02129 | −0.326382 | ||||||||
\(605\) | 1.72949 | − | 13.4863i | 0.0703138 | − | 0.548296i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.10739 | − | 3.40820i | −0.0449476 | − | 0.138335i | 0.926064 | − | 0.377366i | \(-0.123170\pi\) |
−0.971012 | + | 0.239031i | \(0.923170\pi\) | |||||||
\(608\) | 3.35410 | + | 2.43690i | 0.136027 | + | 0.0988293i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.58359 | − | 4.87380i | 0.0641178 | − | 0.197334i | ||||
\(611\) | −23.8885 | + | 73.5214i | −0.966427 | + | 2.97436i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.0623 | − | 11.6699i | −0.648750 | − | 0.471345i | 0.214095 | − | 0.976813i | \(-0.431320\pi\) |
−0.862845 | + | 0.505468i | \(0.831320\pi\) | |||||||
\(614\) | −0.927051 | − | 2.85317i | −0.0374127 | − | 0.115145i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.454915 | − | 4.86128i | −0.0183290 | − | 0.195867i | ||||
\(617\) | −27.1591 | −1.09338 | −0.546691 | − | 0.837334i | \(-0.684113\pi\) | ||||
−0.546691 | + | 0.837334i | \(0.684113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.2984 | − | 16.2007i | −0.896247 | − | 0.651162i | 0.0412520 | − | 0.999149i | \(-0.486865\pi\) |
−0.937499 | + | 0.347987i | \(0.886865\pi\) | |||||||
\(620\) | −1.14590 | + | 0.832544i | −0.0460204 | + | 0.0334358i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.79180 | + | 5.51458i | −0.0718445 | + | 0.221115i | ||||
\(623\) | −5.47214 | + | 3.97574i | −0.219236 | + | 0.159285i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.36475 | + | 4.20025i | 0.0545898 | + | 0.168010i | ||||
\(626\) | −1.32624 | −0.0530071 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.2492 | −0.528702 | ||||||||
\(629\) | −7.63525 | − | 23.4989i | −0.304438 | − | 0.936962i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.80902 | − | 6.40013i | 0.350681 | − | 0.254785i | −0.398473 | − | 0.917180i | \(-0.630460\pi\) |
0.749155 | + | 0.662395i | \(0.230460\pi\) | |||||||
\(632\) | 4.80495 | − | 14.7881i | 0.191131 | − | 0.588240i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.47214 | − | 4.70228i | 0.257041 | − | 0.186751i | ||||
\(635\) | −10.5623 | − | 7.67396i | −0.419152 | − | 0.304532i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.8328 | 1.53861 | ||||||||
\(638\) | 3.13525 | − | 5.29007i | 0.124126 | − | 0.209436i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.85410 | − | 11.8617i | −0.152347 | − | 0.468875i | ||||
\(641\) | 16.5451 | + | 12.0207i | 0.653492 | + | 0.474789i | 0.864459 | − | 0.502704i | \(-0.167661\pi\) |
−0.210967 | + | 0.977493i | \(0.567661\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.11803 | + | 6.51864i | −0.0835271 | + | 0.257070i | −0.984094 | − | 0.177647i | \(-0.943152\pi\) |
0.900567 | + | 0.434717i | \(0.143152\pi\) | |||||||
\(644\) | 2.64590 | − | 8.14324i | 0.104263 | − | 0.320888i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.50000 | + | 1.08981i | 0.0590167 | + | 0.0428782i | ||||
\(647\) | −1.29180 | − | 3.97574i | −0.0507857 | − | 0.156302i | 0.922447 | − | 0.386123i | \(-0.126186\pi\) |
−0.973233 | + | 0.229821i | \(0.926186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.54508 | − | 4.02874i | −0.139157 | − | 0.158142i | ||||
\(650\) | −8.58359 | −0.336676 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 31.0623 | + | 22.5681i | 1.21649 | + | 0.883834i | ||||
\(653\) | 1.10081 | − | 0.799788i | 0.0430781 | − | 0.0312981i | −0.566038 | − | 0.824379i | \(-0.691524\pi\) |
0.609116 | + | 0.793081i | \(0.291524\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.11146 | + | 24.9645i | −0.316941 | + | 0.975444i | ||||
\(656\) | 6.43363 | − | 4.67430i | 0.251191 | − | 0.182501i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.40983 | + | 4.33901i | 0.0549609 | + | 0.169152i | ||||
\(659\) | 9.97871 | 0.388715 | 0.194358 | − | 0.980931i | \(-0.437738\pi\) | ||||
0.194358 | + | 0.980931i | \(0.437738\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.29180 | −0.166932 | −0.0834658 | − | 0.996511i | \(-0.526599\pi\) | ||||
−0.0834658 | + | 0.996511i | \(0.526599\pi\) | |||||||
\(662\) | −1.70163 | − | 5.23707i | −0.0661356 | − | 0.203544i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.6287 | − | 8.44873i | 0.451280 | − | 0.327874i | ||||
\(665\) | 0.381966 | − | 1.17557i | 0.0148120 | − | 0.0455867i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.1353 | − | 13.1760i | 0.702200 | − | 0.510178i | ||||
\(668\) | −8.64590 | − | 6.28161i | −0.334520 | − | 0.243043i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.83282 | 0.109441 | ||||||||
\(671\) | 35.1246 | + | 7.88597i | 1.35597 | + | 0.304434i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.13525 | − | 28.1154i | −0.352138 | − | 1.08377i | −0.957650 | − | 0.287934i | \(-0.907032\pi\) |
0.605512 | − | 0.795836i | \(-0.292968\pi\) | |||||||
\(674\) | −3.54508 | − | 2.57565i | −0.136552 | − | 0.0992105i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.5517 | + | 50.9408i | −0.636602 | + | 1.95926i | ||||
\(677\) | 1.87132 | − | 5.75934i | 0.0719208 | − | 0.221349i | −0.908635 | − | 0.417592i | \(-0.862874\pi\) |
0.980555 | + | 0.196243i | \(0.0628741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.85410 | + | 3.52671i | 0.186283 | + | 0.135343i | ||||
\(680\) | −2.72949 | − | 8.40051i | −0.104671 | − | 0.322145i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.517221 | + | 0.587785i | 0.0198054 | + | 0.0225075i | ||||
\(683\) | −5.52786 | −0.211518 | −0.105759 | − | 0.994392i | \(-0.533727\pi\) | ||||
−0.105759 | + | 0.994392i | \(0.533727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.61803 | − | 6.26137i | −0.329278 | − | 0.239235i | ||||
\(686\) | 4.01722 | − | 2.91868i | 0.153378 | − | 0.111436i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.80244 | − | 5.54734i | 0.0687173 | − | 0.211490i | ||||
\(689\) | 21.4164 | − | 15.5599i | 0.815900 | − | 0.592786i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.51064 | + | 13.8823i | 0.171593 | + | 0.528109i | 0.999461 | − | 0.0328134i | \(-0.0104467\pi\) |
−0.827869 | + | 0.560922i | \(0.810447\pi\) | |||||||
\(692\) | 42.8115 | 1.62745 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.39512 | 0.128877 | ||||||||
\(695\) | −3.70820 | − | 11.4127i | −0.140660 | − | 0.432908i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.92705 | − | 7.21242i | 0.376014 | − | 0.273190i | ||||
\(698\) | 0.489357 | − | 1.50609i | 0.0185224 | − | 0.0570062i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.20820 | − | 3.78398i | 0.196852 | − | 0.143021i | ||||
\(701\) | 38.6074 | + | 28.0499i | 1.45818 | + | 1.05943i | 0.983832 | + | 0.179094i | \(0.0573165\pi\) |
0.474349 | + | 0.880337i | \(0.342683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.09017 | −0.191979 | ||||||||
\(704\) | 14.3369 | − | 6.18812i | 0.540342 | − | 0.233224i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.93769 | + | 5.96361i | 0.0729261 | + | 0.224443i | ||||
\(707\) | −6.85410 | − | 4.97980i | −0.257775 | − | 0.187285i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.96149 | + | 24.5030i | −0.299000 | + | 0.920228i | 0.682848 | + | 0.730560i | \(0.260741\pi\) |
−0.981848 | + | 0.189668i | \(0.939259\pi\) | |||||||
\(710\) | −0.424538 | + | 1.30660i | −0.0159326 | + | 0.0490356i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.05573 | + | 5.85283i | 0.301901 | + | 0.219344i | ||||
\(713\) | 0.881966 | + | 2.71441i | 0.0330299 | + | 0.101656i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.47214 | + | 26.4176i | 0.0924526 | + | 0.987961i | ||||
\(716\) | 9.37384 | 0.350317 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.06231 | − | 5.13107i | −0.263563 | − | 0.191490i | ||||
\(719\) | 15.8541 | − | 11.5187i | 0.591258 | − | 0.429574i | −0.251507 | − | 0.967855i | \(-0.580926\pi\) |
0.842765 | + | 0.538281i | \(0.180926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.16312 | − | 9.73508i | 0.117801 | − | 0.362553i | ||||
\(722\) | −5.56231 | + | 4.04125i | −0.207008 | + | 0.150400i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.67783 | + | 17.4746i | 0.211015 | + | 0.649437i | ||||
\(725\) | 16.8541 | 0.625946 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.8328 | 0.698470 | 0.349235 | − | 0.937035i | \(-0.386441\pi\) | ||||
0.349235 | + | 0.937035i | \(0.386441\pi\) | |||||||
\(728\) | 2.94427 | + | 9.06154i | 0.109122 | + | 0.335843i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0557281 | − | 0.0404888i | 0.00206259 | − | 0.00149856i | ||||
\(731\) | 2.78115 | − | 8.55951i | 0.102865 | − | 0.316585i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.2148 | + | 28.4912i | −1.44843 | + | 1.05235i | −0.462236 | + | 0.886757i | \(0.652953\pi\) |
−0.986195 | + | 0.165590i | \(0.947047\pi\) | |||||||
\(734\) | −3.92705 | − | 2.85317i | −0.144950 | − | 0.105312i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.1459 | −0.705727 | ||||||||
\(737\) | 1.85410 | + | 19.8132i | 0.0682967 | + | 0.729828i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.1459 | + | 40.4589i | 0.483580 | + | 1.48831i | 0.834027 | + | 0.551723i | \(0.186029\pi\) |
−0.350448 | + | 0.936582i | \(0.613971\pi\) | |||||||
\(740\) | 9.43769 | + | 6.85689i | 0.346937 | + | 0.252064i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.482779 | − | 1.48584i | 0.0177234 | − | 0.0545469i | ||||
\(743\) | −13.0902 | + | 40.2874i | −0.480232 | + | 1.47800i | 0.358538 | + | 0.933515i | \(0.383275\pi\) |
−0.838770 | + | 0.544486i | \(0.816725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1803 | − | 11.0292i | −0.556165 | − | 0.404077i | ||||
\(746\) | 0.667184 | + | 2.05338i | 0.0244274 | + | 0.0751797i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27.4058 | − | 11.8290i | 1.00205 | − | 0.432509i | ||||
\(749\) | −14.0344 | −0.512807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.2812 | + | 18.3678i | 0.922522 | + | 0.670252i | 0.944151 | − | 0.329514i | \(-0.106885\pi\) |
−0.0216282 | + | 0.999766i | \(0.506885\pi\) | |||||||
\(752\) | −30.3992 | + | 22.0863i | −1.10854 | + | 0.805405i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.70820 | + | 11.4127i | −0.135045 | + | 0.415625i | ||||
\(755\) | 4.32624 | − | 3.14320i | 0.157448 | − | 0.114393i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.39919 | + | 10.4616i | 0.123546 | + | 0.380234i | 0.993633 | − | 0.112663i | \(-0.0359380\pi\) |
−0.870088 | + | 0.492897i | \(0.835938\pi\) | |||||||
\(758\) | −6.03444 | −0.219181 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.81966 | −0.0660060 | ||||||||
\(761\) | 2.15654 | + | 6.63715i | 0.0781746 | + | 0.240597i | 0.982505 | − | 0.186237i | \(-0.0596291\pi\) |
−0.904330 | + | 0.426833i | \(0.859629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.78115 | − | 4.20025i | 0.209292 | − | 0.152059i | ||||
\(764\) | −3.40576 | + | 10.4819i | −0.123216 | + | 0.379221i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.13525 | − | 4.45752i | 0.221676 | − | 0.161057i | ||||
\(767\) | 8.47214 | + | 6.15537i | 0.305911 | + | 0.222257i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.7984 | −0.569704 | −0.284852 | − | 0.958572i | \(-0.591944\pi\) | ||||
−0.284852 | + | 0.958572i | \(0.591944\pi\) | |||||||
\(770\) | 1.03444 | + | 1.17557i | 0.0372787 | + | 0.0423646i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.30244 | + | 19.3969i | 0.226830 | + | 0.698110i | ||||
\(773\) | −19.1353 | − | 13.9026i | −0.688247 | − | 0.500041i | 0.187836 | − | 0.982200i | \(-0.439853\pi\) |
−0.876083 | + | 0.482159i | \(0.839853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.663119 | + | 2.04087i | −0.0238199 | + | 0.0733102i | ||||
\(776\) | 2.72949 | − | 8.40051i | 0.0979830 | − | 0.301561i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.00000 | − | 5.08580i | −0.250962 | − | 0.182335i | ||||
\(779\) | −0.781153 | − | 2.40414i | −0.0279877 | − | 0.0861373i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.41641 | − | 2.11412i | −0.336946 | − | 0.0756490i | ||||
\(782\) | −8.56231 | −0.306187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.2705 | + | 11.0947i | 0.545375 | + | 0.396238i | ||||
\(785\) | 7.14590 | − | 5.19180i | 0.255048 | − | 0.185303i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1246 | − | 34.2380i | 0.396550 | − | 1.22045i | −0.531199 | − | 0.847247i | \(-0.678258\pi\) |
0.927748 | − | 0.373207i | \(-0.121742\pi\) | |||||||
\(788\) | 12.3541 | − | 8.97578i | 0.440097 | − | 0.319749i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.54102 | + | 4.74277i | 0.0548270 | + | 0.168740i | ||||
\(791\) | −17.2361 | −0.612844 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −70.2492 | −2.49462 | ||||||||
\(794\) | 0.250776 | + | 0.771810i | 0.00889972 | + | 0.0273905i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.7188 | + | 7.78770i | −0.379919 | + | 0.276028i | ||||
\(797\) | 7.50000 | − | 23.0826i | 0.265664 | − | 0.817629i | −0.725876 | − | 0.687825i | \(-0.758565\pi\) |
0.991540 | − | 0.129803i | \(-0.0414345\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.9058 | + | 34.0790i | −1.65941 | + | 1.20563i | ||||
\(800\) | −11.6459 | − | 8.46124i | −0.411745 | − | 0.299150i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.56231 | −0.196412 | ||||||||
\(803\) | 0.319660 | + | 0.363271i | 0.0112806 | + | 0.0128196i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.76393 | + | 5.42882i | 0.0621704 | + | 0.191341i | ||||
\(806\) | −1.23607 | − | 0.898056i | −0.0435386 | − | 0.0316327i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.85410 | + | 11.8617i | −0.135587 | + | 0.417293i | ||||
\(809\) | −5.59017 | + | 17.2048i | −0.196540 | + | 0.604888i | 0.803415 | + | 0.595419i | \(0.203014\pi\) |
−0.999955 | + | 0.00946853i | \(0.996986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.02786 | − | 5.10604i | −0.246782 | − | 0.179297i | 0.457518 | − | 0.889201i | \(-0.348739\pi\) |
−0.704299 | + | 0.709903i | \(0.748739\pi\) | |||||||
\(812\) | −2.78115 | − | 8.55951i | −0.0975993 | − | 0.300380i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.28773 | − | 5.54734i | 0.115235 | − | 0.194434i | ||||
\(815\) | −25.5967 | −0.896615 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.50000 | − | 1.08981i | −0.0524784 | − | 0.0381278i | ||||
\(818\) | −10.4271 | + | 7.57570i | −0.364573 | + | 0.264878i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.79024 | + | 5.50980i | −0.0625180 | + | 0.192411i | ||||
\(821\) | −30.9164 | + | 22.4621i | −1.07899 | + | 0.783932i | −0.977507 | − | 0.210905i | \(-0.932359\pi\) |
−0.101484 | + | 0.994837i | \(0.532359\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0689 | − | 40.2219i | −0.455553 | − | 1.40205i | −0.870485 | − | 0.492195i | \(-0.836195\pi\) |
0.414932 | − | 0.909852i | \(-0.363805\pi\) | |||||||
\(824\) | −15.0689 | −0.524949 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.618034 | 0.0215042 | ||||||||
\(827\) | −17.6246 | − | 54.2430i | −0.612868 | − | 1.88621i | −0.429147 | − | 0.903235i | \(-0.641186\pi\) |
−0.183721 | − | 0.982978i | \(-0.558814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.2254 | + | 25.5928i | −1.22343 | + | 0.888874i | −0.996380 | − | 0.0850096i | \(-0.972908\pi\) |
−0.227049 | + | 0.973883i | \(0.572908\pi\) | |||||||
\(830\) | −1.42454 | + | 4.38428i | −0.0494465 | + | 0.152181i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.6525 | + | 17.9111i | −0.854671 | + | 0.620955i | ||||
\(833\) | 23.5623 | + | 17.1190i | 0.816386 | + | 0.593139i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.12461 | 0.246557 | ||||||||
\(836\) | −0.572949 | − | 6.12261i | −0.0198159 | − | 0.211755i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.954915 | − | 2.93893i | −0.0329870 | − | 0.101524i | ||||
\(839\) | 13.9894 | + | 10.1639i | 0.482966 | + | 0.350896i | 0.802473 | − | 0.596689i | \(-0.203517\pi\) |
−0.319507 | + | 0.947584i | \(0.603517\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.68034 | + | 5.17155i | −0.0579428 | + | 0.178329i | ||||
\(842\) | −1.20820 | + | 3.71847i | −0.0416375 | + | 0.128147i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30.7082 | + | 22.3108i | 1.05702 | + | 0.767970i | ||||
\(845\) | −11.0344 | − | 33.9605i | −0.379596 | − | 1.16828i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.54508 | + | 8.00448i | −0.259252 | + | 0.275037i | ||||
\(848\) | 12.8673 | 0.441863 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.20820 | − | 3.78398i | −0.178640 | − | 0.129789i | ||||
\(851\) | 19.0172 | − | 13.8168i | 0.651902 | − | 0.473634i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.9508 | + | 33.7032i | −0.374950 | + | 1.15398i | 0.568562 | + | 0.822640i | \(0.307500\pi\) |
−0.943512 | + | 0.331337i | \(0.892500\pi\) | |||||||
\(854\) | −3.35410 | + | 2.43690i | −0.114775 | + | 0.0833889i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.38448 | + | 19.6494i | 0.218217 | + | 0.671603i | ||||
\(857\) | 25.3607 | 0.866304 | 0.433152 | − | 0.901321i | \(-0.357401\pi\) | ||||
0.433152 | + | 0.901321i | \(0.357401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.5623 | −1.11101 | −0.555506 | − | 0.831513i | \(-0.687475\pi\) | ||||
−0.555506 | + | 0.831513i | \(0.687475\pi\) | |||||||
\(860\) | 1.31308 | + | 4.04125i | 0.0447757 | + | 0.137806i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.5279 | + | 7.64894i | −0.358580 | + | 0.260524i | ||||
\(863\) | 4.46556 | − | 13.7436i | 0.152009 | − | 0.467837i | −0.845836 | − | 0.533443i | \(-0.820898\pi\) |
0.997846 | + | 0.0656059i | \(0.0208980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.0902 | + | 16.7760i | −0.785089 | + | 0.570401i | ||||
\(866\) | 4.55573 | + | 3.30993i | 0.154810 | + | 0.112476i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.14590 | 0.0388943 | ||||||||
\(869\) | −32.1631 | + | 13.8823i | −1.09106 | + | 0.470926i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | − | 36.9322i | −0.406604 | − | 1.25140i | ||||
\(872\) | −8.51064 | − | 6.18334i | −0.288207 | − | 0.209394i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.545085 | + | 1.67760i | −0.0184378 | + | 0.0567456i | ||||
\(875\) | −3.23607 | + | 9.95959i | −0.109399 | + | 0.336696i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.38197 | − | 6.81640i | −0.316806 | − | 0.230173i | 0.418005 | − | 0.908445i | \(-0.362729\pi\) |
−0.734812 | + | 0.678271i | \(0.762729\pi\) | |||||||
\(878\) | 0.0835921 | + | 0.257270i | 0.00282110 | + | 0.00868245i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.57546 | + | 11.0947i | −0.221659 | + | 0.374001i | ||||
\(881\) | 1.81966 | 0.0613059 | 0.0306530 | − | 0.999530i | \(-0.490241\pi\) | ||||
0.0306530 | + | 0.999530i | \(0.490241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.8435 | + | 20.9560i | 0.970660 | + | 0.705226i | 0.955602 | − | 0.294661i | \(-0.0952068\pi\) |
0.0150579 | + | 0.999887i | \(0.495207\pi\) | |||||||
\(884\) | −47.1246 | + | 34.2380i | −1.58497 | + | 1.15155i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.145898 | − | 0.449028i | 0.00490154 | − | 0.0150854i | ||||
\(887\) | 3.26393 | − | 2.37139i | 0.109592 | − | 0.0796233i | −0.531639 | − | 0.846971i | \(-0.678424\pi\) |
0.641232 | + | 0.767347i | \(0.278424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.26393 | + | 10.0453i | 0.109469 | + | 0.336910i | ||||
\(890\) | −3.19350 | −0.107046 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.7508 | 0.962647 | ||||||||
\(893\) | 3.69098 | + | 11.3597i | 0.123514 | + | 0.380137i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.05573 | + | 3.67320i | −0.168994 | + | 0.122782i | ||||
\(896\) | −3.11803 | + | 9.59632i | −0.104166 | + | 0.320591i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.30902 | − | 1.67760i | 0.0770529 | − | 0.0559822i | ||||
\(899\) | 2.42705 | + | 1.76336i | 0.0809467 | + | 0.0588112i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.8541 | 0.661436 | ||||||||
\(902\) | 3.12461 | + | 0.701519i | 0.104038 | + | 0.0233580i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.84095 | + | 24.1320i | 0.260786 | + | 0.802617i | ||||
\(905\) | −9.90983 | − | 7.19991i | −0.329414 | − | 0.239333i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.50658 | + | 13.8698i | −0.149638 | + | 0.460540i | −0.997578 | − | 0.0695527i | \(-0.977843\pi\) |
0.847940 | + | 0.530093i | \(0.177843\pi\) | |||||||
\(908\) | 9.52129 | − | 29.3035i | 0.315975 | − | 0.972471i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.47214 | − | 1.79611i | −0.0819505 | − | 0.0595405i | ||||
\(911\) | −5.92705 | − | 18.2416i | −0.196372 | − | 0.604371i | −0.999958 | − | 0.00918193i | \(-0.997077\pi\) |
0.803586 | − | 0.595189i | \(-0.202923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.5967 | − | 7.09391i | −1.04570 | − | 0.234774i | ||||
\(914\) | 0.381966 | 0.0126343 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.2705 | + | 11.0947i | 0.504552 | + | 0.366578i | ||||
\(917\) | 17.1803 | − | 12.4822i | 0.567345 | − | 0.412200i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.30244 | + | 25.5523i | −0.273872 | + | 0.842892i | 0.715643 | + | 0.698466i | \(0.246134\pi\) |
−0.989516 | + | 0.144426i | \(0.953866\pi\) | |||||||
\(920\) | 6.79837 | − | 4.93931i | 0.224136 | − | 0.162844i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.90576 | + | 5.86534i | 0.0627630 | + | 0.193165i | ||||
\(923\) | 18.8328 | 0.619890 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.6738 | 0.581110 | ||||||||
\(926\) | −2.00658 | − | 6.17561i | −0.0659402 | − | 0.202943i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.2812 | + | 11.8290i | −0.534455 | + | 0.388304i | ||||
\(929\) | −14.9164 | + | 45.9080i | −0.489391 | + | 1.50619i | 0.336127 | + | 0.941817i | \(0.390883\pi\) |
−0.825518 | + | 0.564375i | \(0.809117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.85410 | − | 3.52671i | 0.159087 | − | 0.115583i | ||||
\(932\) | −16.6869 | − | 12.1238i | −0.546598 | − | 0.397127i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.291796 | 0.00954786 | ||||||||
\(935\) | −10.1459 | + | 17.1190i | −0.331806 | + | 0.559852i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.11803 | − | 21.9071i | −0.232536 | − | 0.715672i | −0.997439 | − | 0.0715265i | \(-0.977213\pi\) |
0.764903 | − | 0.644146i | \(-0.222787\pi\) | |||||||
\(938\) | −1.85410 | − | 1.34708i | −0.0605386 | − | 0.0439838i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.45898 | − | 26.0341i | 0.275902 | − | 0.849138i | ||||
\(941\) | 8.39261 | − | 25.8298i | 0.273591 | − | 0.842027i | −0.715997 | − | 0.698103i | \(-0.754028\pi\) |
0.989589 | − | 0.143924i | \(-0.0459722\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.44427 | + | 6.86167i | 0.307548 | + | 0.223447i | ||||
\(944\) | 1.57295 | + | 4.84104i | 0.0511951 | + | 0.157562i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.15654 | − | 0.930812i | 0.0701152 | − | 0.0302633i | ||||
\(947\) | 36.7082 | 1.19286 | 0.596428 | − | 0.802666i | \(-0.296586\pi\) | ||||
0.596428 | + | 0.802666i | \(0.296586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.763932 | − | 0.555029i | −0.0247983 | − | 0.0180170i | ||||
\(950\) | −1.07295 | + | 0.779543i | −0.0348111 | + | 0.0252917i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.20820 | + | 6.79615i | −0.0715683 | + | 0.220265i | ||||
\(953\) | 7.68034 | − | 5.58009i | 0.248791 | − | 0.180757i | −0.456400 | − | 0.889775i | \(-0.650861\pi\) |
0.705191 | + | 0.709018i | \(0.250861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.27051 | − | 6.98791i | −0.0734720 | − | 0.226123i | ||||
\(956\) | −19.4164 | −0.627972 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.49342 | 0.145176 | ||||||||
\(959\) | 2.66312 | + | 8.19624i | 0.0859966 | + | 0.264670i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.7705 | − | 17.9968i | 0.799049 | − | 0.580543i | ||||
\(962\) | −3.88854 | + | 11.9677i | −0.125372 | + | 0.385854i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −40.2492 | + | 29.2428i | −1.29634 | + | 0.941846i | ||||
\(965\) | −11.0000 | − | 7.99197i | −0.354103 | − | 0.257271i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.4853 | 1.68781 | 0.843907 | − | 0.536490i | \(-0.180250\pi\) | ||||
0.843907 | + | 0.536490i | \(0.180250\pi\) | |||||||
\(968\) | 14.6393 | + | 6.92240i | 0.470526 | + | 0.222494i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.875388 | + | 2.69417i | 0.0281070 | + | 0.0865045i | ||||
\(971\) | −7.50000 | − | 5.44907i | −0.240686 | − | 0.174869i | 0.460903 | − | 0.887451i | \(-0.347526\pi\) |
−0.701589 | + | 0.712582i | \(0.747526\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.00000 | + | 9.23305i | −0.0961756 | + | 0.295998i | ||||
\(974\) | 1.53193 | − | 4.71479i | 0.0490862 | − | 0.151072i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.6246 | − | 20.0705i | −0.884242 | − | 0.642440i | ||||
\(977\) | 4.87132 | + | 14.9924i | 0.155847 | + | 0.479649i | 0.998246 | − | 0.0592062i | \(-0.0188570\pi\) |
−0.842398 | + | 0.538855i | \(0.818857\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.09017 | − | 22.3358i | −0.0668021 | − | 0.713857i | ||||
\(980\) | −13.7508 | −0.439252 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.26393 | + | 1.64484i | 0.0722450 | + | 0.0524890i | ||||
\(983\) | −7.48936 | + | 5.44134i | −0.238873 | + | 0.173552i | −0.700781 | − | 0.713376i | \(-0.747165\pi\) |
0.461908 | + | 0.886928i | \(0.347165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.14590 | + | 9.68208i | −0.100237 | + | 0.308497i | ||||
\(986\) | −7.28115 | + | 5.29007i | −0.231879 | + | 0.168470i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.70820 | + | 11.4127i | 0.117974 | + | 0.363086i | ||||
\(989\) | 8.56231 | 0.272265 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5967 | 0.654277 | 0.327139 | − | 0.944976i | \(-0.393916\pi\) | ||||
0.327139 | + | 0.944976i | \(0.393916\pi\) | |||||||
\(992\) | −0.791796 | − | 2.43690i | −0.0251396 | − | 0.0773716i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.899187 | − | 0.653298i | 0.0285205 | − | 0.0207213i | ||||
\(995\) | 2.72949 | − | 8.40051i | 0.0865307 | − | 0.266314i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.97214 | + | 4.33901i | −0.189139 | + | 0.137418i | −0.678325 | − | 0.734762i | \(-0.737294\pi\) |
0.489186 | + | 0.872180i | \(0.337294\pi\) | |||||||
\(998\) | 11.8713 | + | 8.62502i | 0.375780 | + | 0.273020i | ||||
\(999\) | 0 | 0 |
(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 | 891.2.f.b.82.1 | 4 | ||
3.2 | odd | 2 | 891.2.f.a.82.1 | 4 | |||
9.2 | odd | 6 | 297.2.n.a.280.1 | 8 | |||
9.4 | even | 3 | 99.2.m.a.16.1 | ✓ | 8 | ||
9.5 | odd | 6 | 297.2.n.a.181.1 | 8 | |||
9.7 | even | 3 | 99.2.m.a.49.1 | yes | 8 | ||
11.3 | even | 5 | 9801.2.a.n.1.2 | 2 | |||
11.8 | odd | 10 | 9801.2.a.bc.1.1 | 2 | |||
11.9 | even | 5 | inner | 891.2.f.b.163.1 | 4 | ||
33.8 | even | 10 | 9801.2.a.m.1.2 | 2 | |||
33.14 | odd | 10 | 9801.2.a.bb.1.1 | 2 | |||
33.20 | odd | 10 | 891.2.f.a.163.1 | 4 | |||
99.20 | odd | 30 | 297.2.n.a.64.1 | 8 | |||
99.25 | even | 15 | 1089.2.e.g.364.1 | 4 | |||
99.31 | even | 15 | 99.2.m.a.97.1 | yes | 8 | ||
99.52 | odd | 30 | 1089.2.e.d.364.2 | 4 | |||
99.58 | even | 15 | 1089.2.e.g.727.1 | 4 | |||
99.85 | odd | 30 | 1089.2.e.d.727.2 | 4 | |||
99.86 | odd | 30 | 297.2.n.a.262.1 | 8 | |||
99.97 | even | 15 | 99.2.m.a.31.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.a.16.1 | ✓ | 8 | 9.4 | even | 3 | ||
99.2.m.a.31.1 | yes | 8 | 99.97 | even | 15 | ||
99.2.m.a.49.1 | yes | 8 | 9.7 | even | 3 | ||
99.2.m.a.97.1 | yes | 8 | 99.31 | even | 15 | ||
297.2.n.a.64.1 | 8 | 99.20 | odd | 30 | |||
297.2.n.a.181.1 | 8 | 9.5 | odd | 6 | |||
297.2.n.a.262.1 | 8 | 99.86 | odd | 30 | |||
297.2.n.a.280.1 | 8 | 9.2 | odd | 6 | |||
891.2.f.a.82.1 | 4 | 3.2 | odd | 2 | |||
891.2.f.a.163.1 | 4 | 33.20 | odd | 10 | |||
891.2.f.b.82.1 | 4 | 1.1 | even | 1 | trivial | ||
891.2.f.b.163.1 | 4 | 11.9 | even | 5 | inner | ||
1089.2.e.d.364.2 | 4 | 99.52 | odd | 30 | |||
1089.2.e.d.727.2 | 4 | 99.85 | odd | 30 | |||
1089.2.e.g.364.1 | 4 | 99.25 | even | 15 | |||
1089.2.e.g.727.1 | 4 | 99.58 | even | 15 | |||
9801.2.a.m.1.2 | 2 | 33.8 | even | 10 | |||
9801.2.a.n.1.2 | 2 | 11.3 | even | 5 | |||
9801.2.a.bb.1.1 | 2 | 33.14 | odd | 10 | |||
9801.2.a.bc.1.1 | 2 | 11.8 | odd | 10 |