Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(76,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.c (of order \(2\), degree \(1\), 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: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.3 | ||
Root | \(0.0566033 - 1.17421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 231.76 |
Dual form | 231.2.c.a.76.14 |
$q$-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 \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.08529i | − | 1.47452i | −0.675610 | − | 0.737260i | \(-0.736119\pi\) | ||
0.675610 | − | 0.737260i | \(-0.263881\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −2.34841 | −1.17421 | ||||||||
\(5\) | 0.833366i | 0.372692i | 0.982484 | + | 0.186346i | \(0.0596646\pi\) | ||||
−0.982484 | + | 0.186346i | \(0.940335\pi\) | |||||||
\(6\) | −2.08529 | −0.851314 | ||||||||
\(7\) | −2.19849 | − | 1.47195i | −0.830952 | − | 0.556344i | ||||
\(8\) | 0.726543i | 0.256872i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.73781 | 0.549542 | ||||||||
\(11\) | −1.23607 | − | 3.07768i | −0.372689 | − | 0.927957i | ||||
\(12\) | 2.34841i | 0.677929i | ||||||||
\(13\) | −4.54963 | −1.26184 | −0.630921 | − | 0.775847i | \(-0.717323\pi\) | ||||
−0.630921 | + | 0.775847i | \(0.717323\pi\) | |||||||
\(14\) | −3.06943 | + | 4.58448i | −0.820341 | + | 1.22525i | ||||
\(15\) | 0.833366 | 0.215174 | ||||||||
\(16\) | −3.18178 | −0.795445 | ||||||||
\(17\) | 6.38178 | 1.54781 | 0.773905 | − | 0.633302i | \(-0.218301\pi\) | ||||
0.773905 | + | 0.633302i | \(0.218301\pi\) | |||||||
\(18\) | 2.08529i | 0.491506i | ||||||||
\(19\) | 2.56484 | 0.588414 | 0.294207 | − | 0.955742i | \(-0.404945\pi\) | ||||
0.294207 | + | 0.955742i | \(0.404945\pi\) | |||||||
\(20\) | − | 1.95709i | − | 0.437618i | ||||||
\(21\) | −1.47195 | + | 2.19849i | −0.321206 | + | 0.479750i | ||||
\(22\) | −6.41785 | + | 2.57755i | −1.36829 | + | 0.549536i | ||||
\(23\) | 9.16896 | 1.91186 | 0.955931 | − | 0.293593i | \(-0.0948510\pi\) | ||||
0.955931 | + | 0.293593i | \(0.0948510\pi\) | |||||||
\(24\) | 0.726543 | 0.148305 | ||||||||
\(25\) | 4.30550 | 0.861100 | ||||||||
\(26\) | 9.48728i | 1.86061i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 5.16297 | + | 3.45675i | 0.975709 | + | 0.653264i | ||||
\(29\) | 0.152649i | 0.0283463i | 0.999900 | + | 0.0141731i | \(0.00451160\pi\) | ||||
−0.999900 | + | 0.0141731i | \(0.995488\pi\) | |||||||
\(30\) | − | 1.73781i | − | 0.317278i | ||||||
\(31\) | − | 8.36356i | − | 1.50214i | −0.660223 | − | 0.751070i | \(-0.729538\pi\) | ||
0.660223 | − | 0.751070i | \(-0.270462\pi\) | |||||||
\(32\) | 8.08800i | 1.42977i | ||||||||
\(33\) | −3.07768 | + | 1.23607i | −0.535756 | + | 0.215172i | ||||
\(34\) | − | 13.3078i | − | 2.28227i | ||||||
\(35\) | 1.22667 | − | 1.83215i | 0.207345 | − | 0.309689i | ||||
\(36\) | 2.34841 | 0.391402 | ||||||||
\(37\) | −5.30550 | −0.872219 | −0.436110 | − | 0.899894i | \(-0.643644\pi\) | ||||
−0.436110 | + | 0.899894i | \(0.643644\pi\) | |||||||
\(38\) | − | 5.34841i | − | 0.867627i | ||||||
\(39\) | 4.54963i | 0.728524i | ||||||||
\(40\) | −0.605476 | −0.0957341 | ||||||||
\(41\) | −3.21147 | −0.501547 | −0.250774 | − | 0.968046i | \(-0.580685\pi\) | ||||
−0.250774 | + | 0.968046i | \(0.580685\pi\) | |||||||
\(42\) | 4.58448 | + | 3.06943i | 0.707401 | + | 0.473624i | ||||
\(43\) | 5.66138i | 0.863353i | 0.902029 | + | 0.431676i | \(0.142078\pi\) | ||||
−0.902029 | + | 0.431676i | \(0.857922\pi\) | |||||||
\(44\) | 2.90280 | + | 7.22768i | 0.437613 | + | 1.08961i | ||||
\(45\) | − | 0.833366i | − | 0.124231i | ||||||
\(46\) | − | 19.1199i | − | 2.81908i | ||||||
\(47\) | − | 6.00233i | − | 0.875530i | −0.899089 | − | 0.437765i | \(-0.855770\pi\) | ||
0.899089 | − | 0.437765i | \(-0.144230\pi\) | |||||||
\(48\) | 3.18178i | 0.459250i | ||||||||
\(49\) | 2.66673 | + | 6.47214i | 0.380962 | + | 0.924591i | ||||
\(50\) | − | 8.97820i | − | 1.26971i | ||||||
\(51\) | − | 6.38178i | − | 0.893628i | ||||||
\(52\) | 10.6844 | 1.48166 | ||||||||
\(53\) | 4.69683 | 0.645159 | 0.322579 | − | 0.946542i | \(-0.395450\pi\) | ||||
0.322579 | + | 0.946542i | \(0.395450\pi\) | |||||||
\(54\) | 2.08529 | 0.283771 | ||||||||
\(55\) | 2.56484 | − | 1.03010i | 0.345842 | − | 0.138898i | ||||
\(56\) | 1.06943 | − | 1.59730i | 0.142909 | − | 0.213448i | ||||
\(57\) | − | 2.56484i | − | 0.339721i | ||||||
\(58\) | 0.318317 | 0.0417971 | ||||||||
\(59\) | − | 1.05806i | − | 0.137747i | −0.997625 | − | 0.0688737i | \(-0.978059\pi\) | ||
0.997625 | − | 0.0688737i | \(-0.0219405\pi\) | |||||||
\(60\) | −1.95709 | −0.252659 | ||||||||
\(61\) | −8.34114 | −1.06797 | −0.533987 | − | 0.845493i | \(-0.679307\pi\) | ||||
−0.533987 | + | 0.845493i | \(0.679307\pi\) | |||||||
\(62\) | −17.4404 | −2.21493 | ||||||||
\(63\) | 2.19849 | + | 1.47195i | 0.276984 | + | 0.185448i | ||||
\(64\) | 10.5022 | 1.31278 | ||||||||
\(65\) | − | 3.79151i | − | 0.470279i | ||||||
\(66\) | 2.57755 | + | 6.41785i | 0.317275 | + | 0.789982i | ||||
\(67\) | 4.33560 | 0.529678 | 0.264839 | − | 0.964293i | \(-0.414681\pi\) | ||||
0.264839 | + | 0.964293i | \(0.414681\pi\) | |||||||
\(68\) | −14.9871 | −1.81745 | ||||||||
\(69\) | − | 9.16896i | − | 1.10381i | ||||||
\(70\) | −3.82055 | − | 2.55796i | −0.456643 | − | 0.305735i | ||||
\(71\) | −4.80540 | −0.570297 | −0.285148 | − | 0.958483i | \(-0.592043\pi\) | ||||
−0.285148 | + | 0.958483i | \(0.592043\pi\) | |||||||
\(72\) | − | 0.726543i | − | 0.0856239i | ||||||
\(73\) | 10.6673 | 1.24851 | 0.624255 | − | 0.781221i | \(-0.285403\pi\) | ||||
0.624255 | + | 0.781221i | \(0.285403\pi\) | |||||||
\(74\) | 11.0635i | 1.28610i | ||||||||
\(75\) | − | 4.30550i | − | 0.497157i | ||||||
\(76\) | −6.02330 | −0.690919 | ||||||||
\(77\) | −1.81271 | + | 8.58569i | −0.206577 | + | 0.978430i | ||||
\(78\) | 9.48728 | 1.07422 | ||||||||
\(79\) | 5.70254i | 0.641586i | 0.947149 | + | 0.320793i | \(0.103949\pi\) | ||||
−0.947149 | + | 0.320793i | \(0.896051\pi\) | |||||||
\(80\) | − | 2.65159i | − | 0.296456i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.69683i | 0.739541i | ||||||||
\(83\) | 10.7533 | 1.18033 | 0.590165 | − | 0.807282i | \(-0.299062\pi\) | ||||
0.590165 | + | 0.807282i | \(0.299062\pi\) | |||||||
\(84\) | 3.45675 | − | 5.16297i | 0.377162 | − | 0.563326i | ||||
\(85\) | 5.31836i | 0.576857i | ||||||||
\(86\) | 11.8056 | 1.27303 | ||||||||
\(87\) | 0.152649 | 0.0163657 | ||||||||
\(88\) | 2.23607 | − | 0.898056i | 0.238366 | − | 0.0957331i | ||||
\(89\) | − | 8.13887i | − | 0.862718i | −0.902180 | − | 0.431359i | \(-0.858034\pi\) | ||
0.902180 | − | 0.431359i | \(-0.141966\pi\) | |||||||
\(90\) | −1.73781 | −0.183181 | ||||||||
\(91\) | 10.0023 | + | 6.69683i | 1.04853 | + | 0.702018i | ||||
\(92\) | −21.5325 | −2.24492 | ||||||||
\(93\) | −8.36356 | −0.867261 | ||||||||
\(94\) | −12.5166 | −1.29099 | ||||||||
\(95\) | 2.13745i | 0.219297i | ||||||||
\(96\) | 8.08800 | 0.825478 | ||||||||
\(97\) | 17.7572i | 1.80297i | 0.432808 | + | 0.901486i | \(0.357523\pi\) | ||||
−0.432808 | + | 0.901486i | \(0.642477\pi\) | |||||||
\(98\) | 13.4962 | − | 5.56090i | 1.36333 | − | 0.561735i | ||||
\(99\) | 1.23607 | + | 3.07768i | 0.124230 | + | 0.309319i | ||||
\(100\) | −10.1111 | −1.01111 | ||||||||
\(101\) | −2.10689 | −0.209643 | −0.104822 | − | 0.994491i | \(-0.533427\pi\) | ||||
−0.104822 | + | 0.994491i | \(0.533427\pi\) | |||||||
\(102\) | −13.3078 | −1.31767 | ||||||||
\(103\) | − | 10.6110i | − | 1.04553i | −0.852476 | − | 0.522767i | \(-0.824900\pi\) | ||
0.852476 | − | 0.522767i | \(-0.175100\pi\) | |||||||
\(104\) | − | 3.30550i | − | 0.324131i | ||||||
\(105\) | −1.83215 | − | 1.22667i | −0.178799 | − | 0.119711i | ||||
\(106\) | − | 9.79423i | − | 0.951299i | ||||||
\(107\) | 13.5700i | 1.31186i | 0.754821 | + | 0.655931i | \(0.227724\pi\) | ||||
−0.754821 | + | 0.655931i | \(0.772276\pi\) | |||||||
\(108\) | − | 2.34841i | − | 0.225976i | ||||||
\(109\) | − | 6.68708i | − | 0.640506i | −0.947332 | − | 0.320253i | \(-0.896232\pi\) | ||
0.947332 | − | 0.320253i | \(-0.103768\pi\) | |||||||
\(110\) | −2.14805 | − | 5.34841i | −0.204808 | − | 0.509951i | ||||
\(111\) | 5.30550i | 0.503576i | ||||||||
\(112\) | 6.99512 | + | 4.68342i | 0.660976 | + | 0.442541i | ||||
\(113\) | −1.33346 | −0.125442 | −0.0627208 | − | 0.998031i | \(-0.519978\pi\) | ||||
−0.0627208 | + | 0.998031i | \(0.519978\pi\) | |||||||
\(114\) | −5.34841 | −0.500925 | ||||||||
\(115\) | 7.64110i | 0.712536i | ||||||||
\(116\) | − | 0.358484i | − | 0.0332844i | ||||||
\(117\) | 4.54963 | 0.420614 | ||||||||
\(118\) | −2.20635 | −0.203111 | ||||||||
\(119\) | −14.0303 | − | 9.39366i | −1.28615 | − | 0.861115i | ||||
\(120\) | 0.605476i | 0.0552721i | ||||||||
\(121\) | −7.94427 | + | 7.60845i | −0.722207 | + | 0.691677i | ||||
\(122\) | 17.3937i | 1.57475i | ||||||||
\(123\) | 3.21147i | 0.289568i | ||||||||
\(124\) | 19.6411i | 1.76382i | ||||||||
\(125\) | 7.75489i | 0.693618i | ||||||||
\(126\) | 3.06943 | − | 4.58448i | 0.273447 | − | 0.408418i | ||||
\(127\) | 0.226413i | 0.0200909i | 0.999950 | + | 0.0100455i | \(0.00319762\pi\) | ||||
−0.999950 | + | 0.0100455i | \(0.996802\pi\) | |||||||
\(128\) | − | 5.72414i | − | 0.505948i | ||||||
\(129\) | 5.66138 | 0.498457 | ||||||||
\(130\) | −7.90637 | −0.693435 | ||||||||
\(131\) | −0.305299 | −0.0266741 | −0.0133370 | − | 0.999911i | \(-0.504245\pi\) | ||||
−0.0133370 | + | 0.999911i | \(0.504245\pi\) | |||||||
\(132\) | 7.22768 | − | 2.90280i | 0.629088 | − | 0.252656i | ||||
\(133\) | −5.63877 | − | 3.77531i | −0.488943 | − | 0.327361i | ||||
\(134\) | − | 9.04096i | − | 0.781020i | ||||||
\(135\) | −0.833366 | −0.0717247 | ||||||||
\(136\) | 4.63663i | 0.397588i | ||||||||
\(137\) | −11.7572 | −1.00449 | −0.502243 | − | 0.864726i | \(-0.667492\pi\) | ||||
−0.502243 | + | 0.864726i | \(0.667492\pi\) | |||||||
\(138\) | −19.1199 | −1.62759 | ||||||||
\(139\) | −9.83195 | −0.833935 | −0.416968 | − | 0.908921i | \(-0.636907\pi\) | ||||
−0.416968 | + | 0.908921i | \(0.636907\pi\) | |||||||
\(140\) | −2.88073 | + | 4.30264i | −0.243466 | + | 0.363640i | ||||
\(141\) | −6.00233 | −0.505487 | ||||||||
\(142\) | 10.0206i | 0.840913i | ||||||||
\(143\) | 5.62366 | + | 14.0023i | 0.470274 | + | 1.17093i | ||||
\(144\) | 3.18178 | 0.265148 | ||||||||
\(145\) | −0.127213 | −0.0105644 | ||||||||
\(146\) | − | 22.2443i | − | 1.84095i | ||||||
\(147\) | 6.47214 | − | 2.66673i | 0.533813 | − | 0.219948i | ||||
\(148\) | 12.4595 | 1.02417 | ||||||||
\(149\) | − | 14.3816i | − | 1.17819i | −0.808065 | − | 0.589093i | \(-0.799485\pi\) | ||
0.808065 | − | 0.589093i | \(-0.200515\pi\) | |||||||
\(150\) | −8.97820 | −0.733067 | ||||||||
\(151\) | − | 2.98506i | − | 0.242920i | −0.992596 | − | 0.121460i | \(-0.961242\pi\) | ||
0.992596 | − | 0.121460i | \(-0.0387577\pi\) | |||||||
\(152\) | 1.86346i | 0.151147i | ||||||||
\(153\) | −6.38178 | −0.515936 | ||||||||
\(154\) | 17.9036 | + | 3.78001i | 1.44271 | + | 0.304602i | ||||
\(155\) | 6.96990 | 0.559836 | ||||||||
\(156\) | − | 10.6844i | − | 0.855438i | ||||||
\(157\) | 17.3983i | 1.38854i | 0.719716 | + | 0.694268i | \(0.244272\pi\) | ||||
−0.719716 | + | 0.694268i | \(0.755728\pi\) | |||||||
\(158\) | 11.8914 | 0.946031 | ||||||||
\(159\) | − | 4.69683i | − | 0.372483i | ||||||
\(160\) | −6.74026 | −0.532865 | ||||||||
\(161\) | −20.1579 | − | 13.4962i | −1.58866 | − | 1.06365i | ||||
\(162\) | − | 2.08529i | − | 0.163835i | ||||||
\(163\) | 4.39152 | 0.343970 | 0.171985 | − | 0.985100i | \(-0.444982\pi\) | ||||
0.171985 | + | 0.985100i | \(0.444982\pi\) | |||||||
\(164\) | 7.54186 | 0.588920 | ||||||||
\(165\) | −1.03010 | − | 2.56484i | −0.0801929 | − | 0.199672i | ||||
\(166\) | − | 22.4238i | − | 1.74042i | ||||||
\(167\) | −2.86501 | −0.221701 | −0.110851 | − | 0.993837i | \(-0.535358\pi\) | ||||
−0.110851 | + | 0.993837i | \(0.535358\pi\) | |||||||
\(168\) | −1.59730 | − | 1.06943i | −0.123234 | − | 0.0825086i | ||||
\(169\) | 7.69916 | 0.592243 | ||||||||
\(170\) | 11.0903 | 0.850586 | ||||||||
\(171\) | −2.56484 | −0.196138 | ||||||||
\(172\) | − | 13.2953i | − | 1.01376i | ||||||
\(173\) | 20.4220 | 1.55266 | 0.776329 | − | 0.630328i | \(-0.217079\pi\) | ||||
0.776329 | + | 0.630328i | \(0.217079\pi\) | |||||||
\(174\) | − | 0.318317i | − | 0.0241316i | ||||||
\(175\) | −9.46561 | − | 6.33748i | −0.715533 | − | 0.479068i | ||||
\(176\) | 3.93290 | + | 9.79251i | 0.296453 | + | 0.738138i | ||||
\(177\) | −1.05806 | −0.0795285 | ||||||||
\(178\) | −16.9719 | −1.27209 | ||||||||
\(179\) | 4.58825 | 0.342942 | 0.171471 | − | 0.985189i | \(-0.445148\pi\) | ||||
0.171471 | + | 0.985189i | \(0.445148\pi\) | |||||||
\(180\) | 1.95709i | 0.145873i | ||||||||
\(181\) | 6.03029i | 0.448228i | 0.974563 | + | 0.224114i | \(0.0719488\pi\) | ||||
−0.974563 | + | 0.224114i | \(0.928051\pi\) | |||||||
\(182\) | 13.9648 | − | 20.8577i | 1.03514 | − | 1.54608i | ||||
\(183\) | 8.34114i | 0.616595i | ||||||||
\(184\) | 6.66164i | 0.491103i | ||||||||
\(185\) | − | 4.42142i | − | 0.325069i | ||||||
\(186\) | 17.4404i | 1.27879i | ||||||||
\(187\) | −7.88831 | − | 19.6411i | −0.576851 | − | 1.43630i | ||||
\(188\) | 14.0960i | 1.02805i | ||||||||
\(189\) | 1.47195 | − | 2.19849i | 0.107069 | − | 0.159917i | ||||
\(190\) | 4.45718 | 0.323358 | ||||||||
\(191\) | 23.7800 | 1.72066 | 0.860329 | − | 0.509739i | \(-0.170258\pi\) | ||||
0.860329 | + | 0.509739i | \(0.170258\pi\) | |||||||
\(192\) | − | 10.5022i | − | 0.757933i | ||||||
\(193\) | 4.63569i | 0.333684i | 0.985984 | + | 0.166842i | \(0.0533570\pi\) | ||||
−0.985984 | + | 0.166842i | \(0.946643\pi\) | |||||||
\(194\) | 37.0289 | 2.65852 | ||||||||
\(195\) | −3.79151 | −0.271516 | ||||||||
\(196\) | −6.26259 | − | 15.1993i | −0.447328 | − | 1.08566i | ||||
\(197\) | − | 6.62048i | − | 0.471690i | −0.971791 | − | 0.235845i | \(-0.924214\pi\) | ||
0.971791 | − | 0.235845i | \(-0.0757858\pi\) | |||||||
\(198\) | 6.41785 | − | 2.57755i | 0.456097 | − | 0.183179i | ||||
\(199\) | 10.9699i | 0.777636i | 0.921315 | + | 0.388818i | \(0.127116\pi\) | ||||
−0.921315 | + | 0.388818i | \(0.872884\pi\) | |||||||
\(200\) | 3.12813i | 0.221192i | ||||||||
\(201\) | − | 4.33560i | − | 0.305810i | ||||||
\(202\) | 4.39346i | 0.309123i | ||||||||
\(203\) | 0.224692 | − | 0.335598i | 0.0157703 | − | 0.0235544i | ||||
\(204\) | 14.9871i | 1.04930i | ||||||||
\(205\) | − | 2.67633i | − | 0.186923i | ||||||
\(206\) | −22.1270 | −1.54166 | ||||||||
\(207\) | −9.16896 | −0.637287 | ||||||||
\(208\) | 14.4759 | 1.00373 | ||||||||
\(209\) | −3.17031 | − | 7.89375i | −0.219295 | − | 0.546022i | ||||
\(210\) | −2.55796 | + | 3.82055i | −0.176516 | + | 0.263643i | ||||
\(211\) | − | 12.4960i | − | 0.860259i | −0.902767 | − | 0.430130i | \(-0.858468\pi\) | ||
0.902767 | − | 0.430130i | \(-0.141532\pi\) | |||||||
\(212\) | −11.0301 | −0.757550 | ||||||||
\(213\) | 4.80540i | 0.329261i | ||||||||
\(214\) | 28.2973 | 1.93437 | ||||||||
\(215\) | −4.71800 | −0.321765 | ||||||||
\(216\) | −0.726543 | −0.0494350 | ||||||||
\(217\) | −12.3107 | + | 18.3872i | −0.835707 | + | 1.24821i | ||||
\(218\) | −13.9445 | −0.944438 | ||||||||
\(219\) | − | 10.6673i | − | 0.720827i | ||||||
\(220\) | −6.02330 | + | 2.41909i | −0.406091 | + | 0.163095i | ||||
\(221\) | −29.0348 | −1.95309 | ||||||||
\(222\) | 11.0635 | 0.742532 | ||||||||
\(223\) | − | 9.44958i | − | 0.632791i | −0.948627 | − | 0.316395i | \(-0.897527\pi\) | ||
0.948627 | − | 0.316395i | \(-0.102473\pi\) | |||||||
\(224\) | 11.9051 | − | 17.7814i | 0.795445 | − | 1.18807i | ||||
\(225\) | −4.30550 | −0.287033 | ||||||||
\(226\) | 2.78065i | 0.184966i | ||||||||
\(227\) | 5.43497 | 0.360732 | 0.180366 | − | 0.983600i | \(-0.442272\pi\) | ||||
0.180366 | + | 0.983600i | \(0.442272\pi\) | |||||||
\(228\) | 6.02330i | 0.398903i | ||||||||
\(229\) | 18.9746i | 1.25387i | 0.779070 | + | 0.626937i | \(0.215692\pi\) | ||||
−0.779070 | + | 0.626937i | \(0.784308\pi\) | |||||||
\(230\) | 15.9339 | 1.05065 | ||||||||
\(231\) | 8.58569 | + | 1.81271i | 0.564897 | + | 0.119267i | ||||
\(232\) | −0.110906 | −0.00728135 | ||||||||
\(233\) | 12.5083i | 0.819445i | 0.912210 | + | 0.409722i | \(0.134374\pi\) | ||||
−0.912210 | + | 0.409722i | \(0.865626\pi\) | |||||||
\(234\) | − | 9.48728i | − | 0.620203i | ||||||
\(235\) | 5.00214 | 0.326303 | ||||||||
\(236\) | 2.48476i | 0.161744i | ||||||||
\(237\) | 5.70254 | 0.370420 | ||||||||
\(238\) | −19.5885 | + | 29.2572i | −1.26973 | + | 1.89646i | ||||
\(239\) | 6.99955i | 0.452763i | 0.974039 | + | 0.226382i | \(0.0726896\pi\) | ||||
−0.974039 | + | 0.226382i | \(0.927310\pi\) | |||||||
\(240\) | −2.65159 | −0.171159 | ||||||||
\(241\) | −4.24433 | −0.273402 | −0.136701 | − | 0.990612i | \(-0.543650\pi\) | ||||
−0.136701 | + | 0.990612i | \(0.543650\pi\) | |||||||
\(242\) | 15.8658 | + | 16.5661i | 1.01989 | + | 1.06491i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 19.5885 | 1.25402 | ||||||||
\(245\) | −5.39366 | + | 2.22236i | −0.344588 | + | 0.141982i | ||||
\(246\) | 6.69683 | 0.426974 | ||||||||
\(247\) | −11.6691 | −0.742485 | ||||||||
\(248\) | 6.07648 | 0.385857 | ||||||||
\(249\) | − | 10.7533i | − | 0.681464i | ||||||
\(250\) | 16.1711 | 1.02275 | ||||||||
\(251\) | 24.3403i | 1.53634i | 0.640244 | + | 0.768172i | \(0.278833\pi\) | ||||
−0.640244 | + | 0.768172i | \(0.721167\pi\) | |||||||
\(252\) | −5.16297 | − | 3.45675i | −0.325236 | − | 0.217755i | ||||
\(253\) | −11.3335 | − | 28.2192i | −0.712529 | − | 1.77412i | ||||
\(254\) | 0.472136 | 0.0296244 | ||||||||
\(255\) | 5.31836 | 0.333048 | ||||||||
\(256\) | 9.06799 | 0.566750 | ||||||||
\(257\) | − | 25.1111i | − | 1.56639i | −0.621778 | − | 0.783194i | \(-0.713589\pi\) | ||
0.621778 | − | 0.783194i | \(-0.286411\pi\) | |||||||
\(258\) | − | 11.8056i | − | 0.734984i | ||||||
\(259\) | 11.6641 | + | 7.80943i | 0.724772 | + | 0.485254i | ||||
\(260\) | 8.90403i | 0.552204i | ||||||||
\(261\) | − | 0.152649i | − | 0.00944876i | ||||||
\(262\) | 0.636635i | 0.0393314i | ||||||||
\(263\) | − | 11.1167i | − | 0.685483i | −0.939430 | − | 0.342742i | \(-0.888644\pi\) | ||
0.939430 | − | 0.342742i | \(-0.111356\pi\) | |||||||
\(264\) | −0.898056 | − | 2.23607i | −0.0552715 | − | 0.137620i | ||||
\(265\) | 3.91418i | 0.240446i | ||||||||
\(266\) | −7.87259 | + | 11.7584i | −0.482700 | + | 0.720956i | ||||
\(267\) | −8.13887 | −0.498091 | ||||||||
\(268\) | −10.1818 | −0.621951 | ||||||||
\(269\) | − | 12.8054i | − | 0.780759i | −0.920654 | − | 0.390380i | \(-0.872344\pi\) | ||
0.920654 | − | 0.390380i | \(-0.127656\pi\) | |||||||
\(270\) | 1.73781i | 0.105759i | ||||||||
\(271\) | 15.5828 | 0.946589 | 0.473295 | − | 0.880904i | \(-0.343065\pi\) | ||||
0.473295 | + | 0.880904i | \(0.343065\pi\) | |||||||
\(272\) | −20.3054 | −1.23120 | ||||||||
\(273\) | 6.69683 | − | 10.0023i | 0.405310 | − | 0.605369i | ||||
\(274\) | 24.5171i | 1.48113i | ||||||||
\(275\) | −5.32189 | − | 13.2510i | −0.320922 | − | 0.799064i | ||||
\(276\) | 21.5325i | 1.29611i | ||||||||
\(277\) | − | 4.98214i | − | 0.299348i | −0.988735 | − | 0.149674i | \(-0.952178\pi\) | ||
0.988735 | − | 0.149674i | \(-0.0478224\pi\) | |||||||
\(278\) | 20.5024i | 1.22965i | ||||||||
\(279\) | 8.36356i | 0.500713i | ||||||||
\(280\) | 1.33113 | + | 0.891229i | 0.0795504 | + | 0.0532611i | ||||
\(281\) | 25.2269i | 1.50491i | 0.658642 | + | 0.752457i | \(0.271131\pi\) | ||||
−0.658642 | + | 0.752457i | \(0.728869\pi\) | |||||||
\(282\) | 12.5166i | 0.745351i | ||||||||
\(283\) | 20.7634 | 1.23425 | 0.617127 | − | 0.786864i | \(-0.288296\pi\) | ||||
0.617127 | + | 0.786864i | \(0.288296\pi\) | |||||||
\(284\) | 11.2851 | 0.669646 | ||||||||
\(285\) | 2.13745 | 0.126611 | ||||||||
\(286\) | 29.1988 | − | 11.7269i | 1.72656 | − | 0.693428i | ||||
\(287\) | 7.06039 | + | 4.72712i | 0.416761 | + | 0.279033i | ||||
\(288\) | − | 8.08800i | − | 0.476590i | ||||||
\(289\) | 23.7271 | 1.39571 | ||||||||
\(290\) | 0.265275i | 0.0155775i | ||||||||
\(291\) | 17.7572 | 1.04095 | ||||||||
\(292\) | −25.0512 | −1.46601 | ||||||||
\(293\) | −4.37155 | −0.255388 | −0.127694 | − | 0.991814i | \(-0.540758\pi\) | ||||
−0.127694 | + | 0.991814i | \(0.540758\pi\) | |||||||
\(294\) | −5.56090 | − | 13.4962i | −0.324318 | − | 0.787117i | ||||
\(295\) | 0.881749 | 0.0513374 | ||||||||
\(296\) | − | 3.85467i | − | 0.224048i | ||||||
\(297\) | 3.07768 | − | 1.23607i | 0.178585 | − | 0.0717239i | ||||
\(298\) | −29.9897 | −1.73726 | ||||||||
\(299\) | −41.7154 | −2.41246 | ||||||||
\(300\) | 10.1111i | 0.583765i | ||||||||
\(301\) | 8.33327 | − | 12.4465i | 0.480322 | − | 0.717405i | ||||
\(302\) | −6.22469 | −0.358191 | ||||||||
\(303\) | 2.10689i | 0.121038i | ||||||||
\(304\) | −8.16074 | −0.468051 | ||||||||
\(305\) | − | 6.95122i | − | 0.398026i | ||||||
\(306\) | 13.3078i | 0.760758i | ||||||||
\(307\) | 4.47930 | 0.255647 | 0.127824 | − | 0.991797i | \(-0.459201\pi\) | ||||
0.127824 | + | 0.991797i | \(0.459201\pi\) | |||||||
\(308\) | 4.25699 | − | 20.1628i | 0.242565 | − | 1.14888i | ||||
\(309\) | −10.6110 | −0.603639 | ||||||||
\(310\) | − | 14.5342i | − | 0.825489i | ||||||
\(311\) | − | 22.8841i | − | 1.29764i | −0.760943 | − | 0.648819i | \(-0.775263\pi\) | ||
0.760943 | − | 0.648819i | \(-0.224737\pi\) | |||||||
\(312\) | −3.30550 | −0.187137 | ||||||||
\(313\) | 5.30317i | 0.299753i | 0.988705 | + | 0.149877i | \(0.0478876\pi\) | ||||
−0.988705 | + | 0.149877i | \(0.952112\pi\) | |||||||
\(314\) | 36.2804 | 2.04742 | ||||||||
\(315\) | −1.22667 | + | 1.83215i | −0.0691151 | + | 0.103230i | ||||
\(316\) | − | 13.3919i | − | 0.753355i | ||||||
\(317\) | −22.0951 | −1.24099 | −0.620493 | − | 0.784212i | \(-0.713068\pi\) | ||||
−0.620493 | + | 0.784212i | \(0.713068\pi\) | |||||||
\(318\) | −9.79423 | −0.549233 | ||||||||
\(319\) | 0.469806 | − | 0.188685i | 0.0263041 | − | 0.0105643i | ||||
\(320\) | 8.75220i | 0.489263i | ||||||||
\(321\) | 13.5700 | 0.757404 | ||||||||
\(322\) | −28.1435 | + | 42.0350i | −1.56838 | + | 2.34252i | ||||
\(323\) | 16.3682 | 0.910752 | ||||||||
\(324\) | −2.34841 | −0.130467 | ||||||||
\(325\) | −19.5885 | −1.08657 | ||||||||
\(326\) | − | 9.15757i | − | 0.507191i | ||||||
\(327\) | −6.68708 | −0.369796 | ||||||||
\(328\) | − | 2.33327i | − | 0.128833i | ||||||
\(329\) | −8.83512 | + | 13.1961i | −0.487096 | + | 0.727523i | ||||
\(330\) | −5.34841 | + | 2.14805i | −0.294421 | + | 0.118246i | ||||
\(331\) | −19.7316 | −1.08455 | −0.542273 | − | 0.840202i | \(-0.682436\pi\) | ||||
−0.542273 | + | 0.840202i | \(0.682436\pi\) | |||||||
\(332\) | −25.2533 | −1.38595 | ||||||||
\(333\) | 5.30550 | 0.290740 | ||||||||
\(334\) | 5.97437i | 0.326903i | ||||||||
\(335\) | 3.61314i | 0.197407i | ||||||||
\(336\) | 4.68342 | − | 6.99512i | 0.255501 | − | 0.381615i | ||||
\(337\) | − | 31.4052i | − | 1.71075i | −0.518009 | − | 0.855375i | \(-0.673327\pi\) | ||
0.518009 | − | 0.855375i | \(-0.326673\pi\) | |||||||
\(338\) | − | 16.0549i | − | 0.873274i | ||||||
\(339\) | 1.33346i | 0.0724238i | ||||||||
\(340\) | − | 12.4897i | − | 0.677349i | ||||||
\(341\) | −25.7404 | + | 10.3379i | −1.39392 | + | 0.559830i | ||||
\(342\) | 5.34841i | 0.289209i | ||||||||
\(343\) | 3.66387 | − | 18.1542i | 0.197830 | − | 0.980236i | ||||
\(344\) | −4.11324 | −0.221771 | ||||||||
\(345\) | 7.64110 | 0.411383 | ||||||||
\(346\) | − | 42.5858i | − | 2.28942i | ||||||
\(347\) | 7.14333i | 0.383474i | 0.981446 | + | 0.191737i | \(0.0614121\pi\) | ||||
−0.981446 | + | 0.191737i | \(0.938588\pi\) | |||||||
\(348\) | −0.358484 | −0.0192167 | ||||||||
\(349\) | −12.1326 | −0.649446 | −0.324723 | − | 0.945809i | \(-0.605271\pi\) | ||||
−0.324723 | + | 0.945809i | \(0.605271\pi\) | |||||||
\(350\) | −13.2155 | + | 19.7385i | −0.706396 | + | 1.05507i | ||||
\(351\) | − | 4.54963i | − | 0.242841i | ||||||
\(352\) | 24.8923 | − | 9.99732i | 1.32676 | − | 0.532859i | ||||
\(353\) | 14.7173i | 0.783320i | 0.920110 | + | 0.391660i | \(0.128099\pi\) | ||||
−0.920110 | + | 0.391660i | \(0.871901\pi\) | |||||||
\(354\) | 2.20635i | 0.117266i | ||||||||
\(355\) | − | 4.00466i | − | 0.212545i | ||||||
\(356\) | 19.1134i | 1.01301i | ||||||||
\(357\) | −9.39366 | + | 14.0303i | −0.497165 | + | 0.742562i | ||||
\(358\) | − | 9.56781i | − | 0.505675i | ||||||
\(359\) | 6.55732i | 0.346082i | 0.984915 | + | 0.173041i | \(0.0553593\pi\) | ||||
−0.984915 | + | 0.173041i | \(0.944641\pi\) | |||||||
\(360\) | 0.605476 | 0.0319114 | ||||||||
\(361\) | −12.4216 | −0.653769 | ||||||||
\(362\) | 12.5749 | 0.660921 | ||||||||
\(363\) | 7.60845 | + | 7.94427i | 0.399340 | + | 0.416966i | ||||
\(364\) | −23.4896 | − | 15.7269i | −1.23119 | − | 0.824315i | ||||
\(365\) | 8.88974i | 0.465310i | ||||||||
\(366\) | 17.3937 | 0.909181 | ||||||||
\(367\) | − | 32.6759i | − | 1.70567i | −0.522184 | − | 0.852833i | \(-0.674883\pi\) | ||
0.522184 | − | 0.852833i | \(-0.325117\pi\) | |||||||
\(368\) | −29.1736 | −1.52078 | ||||||||
\(369\) | 3.21147 | 0.167182 | ||||||||
\(370\) | −9.21993 | −0.479321 | ||||||||
\(371\) | −10.3259 | − | 6.91349i | −0.536096 | − | 0.358931i | ||||
\(372\) | 19.6411 | 1.01834 | ||||||||
\(373\) | 21.9040i | 1.13415i | 0.823668 | + | 0.567073i | \(0.191924\pi\) | ||||
−0.823668 | + | 0.567073i | \(0.808076\pi\) | |||||||
\(374\) | −40.9573 | + | 16.4494i | −2.11785 | + | 0.850577i | ||||
\(375\) | 7.75489 | 0.400461 | ||||||||
\(376\) | 4.36095 | 0.224899 | ||||||||
\(377\) | − | 0.694498i | − | 0.0357685i | ||||||
\(378\) | −4.58448 | − | 3.06943i | −0.235800 | − | 0.157875i | ||||
\(379\) | −14.0023 | −0.719251 | −0.359626 | − | 0.933097i | \(-0.617096\pi\) | ||||
−0.359626 | + | 0.933097i | \(0.617096\pi\) | |||||||
\(380\) | − | 5.01961i | − | 0.257500i | ||||||
\(381\) | 0.226413 | 0.0115995 | ||||||||
\(382\) | − | 49.5880i | − | 2.53714i | ||||||
\(383\) | 7.05573i | 0.360531i | 0.983618 | + | 0.180265i | \(0.0576957\pi\) | ||||
−0.983618 | + | 0.180265i | \(0.942304\pi\) | |||||||
\(384\) | −5.72414 | −0.292109 | ||||||||
\(385\) | −7.15502 | − | 1.51065i | −0.364654 | − | 0.0769898i | ||||
\(386\) | 9.66673 | 0.492024 | ||||||||
\(387\) | − | 5.66138i | − | 0.287784i | ||||||
\(388\) | − | 41.7013i | − | 2.11706i | ||||||
\(389\) | −2.44938 | −0.124189 | −0.0620944 | − | 0.998070i | \(-0.519778\pi\) | ||||
−0.0620944 | + | 0.998070i | \(0.519778\pi\) | |||||||
\(390\) | 7.90637i | 0.400355i | ||||||||
\(391\) | 58.5143 | 2.95920 | ||||||||
\(392\) | −4.70228 | + | 1.93749i | −0.237501 | + | 0.0978582i | ||||
\(393\) | 0.305299i | 0.0154003i | ||||||||
\(394\) | −13.8056 | −0.695516 | ||||||||
\(395\) | −4.75230 | −0.239114 | ||||||||
\(396\) | −2.90280 | − | 7.22768i | −0.145871 | − | 0.363204i | ||||
\(397\) | 4.75702i | 0.238748i | 0.992849 | + | 0.119374i | \(0.0380888\pi\) | ||||
−0.992849 | + | 0.119374i | \(0.961911\pi\) | |||||||
\(398\) | 22.8754 | 1.14664 | ||||||||
\(399\) | −3.77531 | + | 5.63877i | −0.189002 | + | 0.282292i | ||||
\(400\) | −13.6992 | −0.684958 | ||||||||
\(401\) | 18.3682 | 0.917265 | 0.458633 | − | 0.888626i | \(-0.348339\pi\) | ||||
0.458633 | + | 0.888626i | \(0.348339\pi\) | |||||||
\(402\) | −9.04096 | −0.450922 | ||||||||
\(403\) | 38.0511i | 1.89546i | ||||||||
\(404\) | 4.94784 | 0.246164 | ||||||||
\(405\) | 0.833366i | 0.0414103i | ||||||||
\(406\) | −0.699818 | − | 0.468547i | −0.0347314 | − | 0.0232536i | ||||
\(407\) | 6.55796 | + | 16.3287i | 0.325066 | + | 0.809381i | ||||
\(408\) | 4.63663 | 0.229548 | ||||||||
\(409\) | 34.7230 | 1.71694 | 0.858472 | − | 0.512861i | \(-0.171414\pi\) | ||||
0.858472 | + | 0.512861i | \(0.171414\pi\) | |||||||
\(410\) | −5.58091 | −0.275621 | ||||||||
\(411\) | 11.7572i | 0.579941i | ||||||||
\(412\) | 24.9190i | 1.22767i | ||||||||
\(413\) | −1.55741 | + | 2.32613i | −0.0766350 | + | 0.114461i | ||||
\(414\) | 19.1199i | 0.939692i | ||||||||
\(415\) | 8.96145i | 0.439900i | ||||||||
\(416\) | − | 36.7974i | − | 1.80414i | ||||||
\(417\) | 9.83195i | 0.481473i | ||||||||
\(418\) | −16.4607 | + | 6.61100i | −0.805120 | + | 0.323355i | ||||
\(419\) | − | 35.6737i | − | 1.74278i | −0.490595 | − | 0.871388i | \(-0.663221\pi\) | ||
0.490595 | − | 0.871388i | \(-0.336779\pi\) | |||||||
\(420\) | 4.30264 | + | 2.88073i | 0.209947 | + | 0.140565i | ||||
\(421\) | 1.24958 | 0.0609008 | 0.0304504 | − | 0.999536i | \(-0.490306\pi\) | ||||
0.0304504 | + | 0.999536i | \(0.490306\pi\) | |||||||
\(422\) | −26.0577 | −1.26847 | ||||||||
\(423\) | 6.00233i | 0.291843i | ||||||||
\(424\) | 3.41245i | 0.165723i | ||||||||
\(425\) | 27.4768 | 1.33282 | ||||||||
\(426\) | 10.0206 | 0.485502 | ||||||||
\(427\) | 18.3379 | + | 12.2777i | 0.887435 | + | 0.594161i | ||||
\(428\) | − | 31.8680i | − | 1.54040i | ||||||
\(429\) | 14.0023 | − | 5.62366i | 0.676039 | − | 0.271513i | ||||
\(430\) | 9.83838i | 0.474449i | ||||||||
\(431\) | 31.7177i | 1.52779i | 0.645343 | + | 0.763893i | \(0.276715\pi\) | ||||
−0.645343 | + | 0.763893i | \(0.723285\pi\) | |||||||
\(432\) | − | 3.18178i | − | 0.153083i | ||||||
\(433\) | − | 13.7273i | − | 0.659693i | −0.944035 | − | 0.329846i | \(-0.893003\pi\) | ||
0.944035 | − | 0.329846i | \(-0.106997\pi\) | |||||||
\(434\) | 38.3426 | + | 25.6714i | 1.84050 | + | 1.23227i | ||||
\(435\) | 0.127213i | 0.00609938i | ||||||||
\(436\) | 15.7040i | 0.752087i | ||||||||
\(437\) | 23.5169 | 1.12497 | ||||||||
\(438\) | −22.2443 | −1.06287 | ||||||||
\(439\) | −30.4630 | −1.45392 | −0.726959 | − | 0.686680i | \(-0.759067\pi\) | ||||
−0.726959 | + | 0.686680i | \(0.759067\pi\) | |||||||
\(440\) | 0.748409 | + | 1.86346i | 0.0356790 | + | 0.0888371i | ||||
\(441\) | −2.66673 | − | 6.47214i | −0.126987 | − | 0.308197i | ||||
\(442\) | 60.5457i | 2.87987i | ||||||||
\(443\) | −16.8613 | −0.801106 | −0.400553 | − | 0.916274i | \(-0.631182\pi\) | ||||
−0.400553 | + | 0.916274i | \(0.631182\pi\) | |||||||
\(444\) | − | 12.4595i | − | 0.591302i | ||||||
\(445\) | 6.78265 | 0.321529 | ||||||||
\(446\) | −19.7051 | −0.933062 | ||||||||
\(447\) | −14.3816 | −0.680226 | ||||||||
\(448\) | −23.0891 | − | 15.4588i | −1.09086 | − | 0.730357i | ||||
\(449\) | 30.0652 | 1.41887 | 0.709433 | − | 0.704773i | \(-0.248951\pi\) | ||||
0.709433 | + | 0.704773i | \(0.248951\pi\) | |||||||
\(450\) | 8.97820i | 0.423236i | ||||||||
\(451\) | 3.96959 | + | 9.88388i | 0.186921 | + | 0.465414i | ||||
\(452\) | 3.13152 | 0.147294 | ||||||||
\(453\) | −2.98506 | −0.140250 | ||||||||
\(454\) | − | 11.3335i | − | 0.531906i | ||||||
\(455\) | −5.58091 | + | 8.33560i | −0.261637 | + | 0.390779i | ||||
\(456\) | 1.86346 | 0.0872646 | ||||||||
\(457\) | 7.39433i | 0.345892i | 0.984931 | + | 0.172946i | \(0.0553286\pi\) | ||||
−0.984931 | + | 0.172946i | \(0.944671\pi\) | |||||||
\(458\) | 39.5674 | 1.84886 | ||||||||
\(459\) | 6.38178i | 0.297876i | ||||||||
\(460\) | − | 17.9445i | − | 0.836665i | ||||||
\(461\) | 17.1351 | 0.798062 | 0.399031 | − | 0.916938i | \(-0.369347\pi\) | ||||
0.399031 | + | 0.916938i | \(0.369347\pi\) | |||||||
\(462\) | 3.78001 | − | 17.9036i | 0.175862 | − | 0.832951i | ||||
\(463\) | 11.6131 | 0.539708 | 0.269854 | − | 0.962901i | \(-0.413025\pi\) | ||||
0.269854 | + | 0.962901i | \(0.413025\pi\) | |||||||
\(464\) | − | 0.485697i | − | 0.0225479i | ||||||
\(465\) | − | 6.96990i | − | 0.323222i | ||||||
\(466\) | 26.0833 | 1.20829 | ||||||||
\(467\) | 6.99786i | 0.323823i | 0.986805 | + | 0.161911i | \(0.0517658\pi\) | ||||
−0.986805 | + | 0.161911i | \(0.948234\pi\) | |||||||
\(468\) | −10.6844 | −0.493888 | ||||||||
\(469\) | −9.53178 | − | 6.38178i | −0.440137 | − | 0.294683i | ||||
\(470\) | − | 10.4309i | − | 0.481141i | ||||||
\(471\) | 17.3983 | 0.801672 | ||||||||
\(472\) | 0.768724 | 0.0353834 | ||||||||
\(473\) | 17.4239 | − | 6.99785i | 0.801154 | − | 0.321762i | ||||
\(474\) | − | 11.8914i | − | 0.546191i | ||||||
\(475\) | 11.0429 | 0.506683 | ||||||||
\(476\) | 32.9489 | + | 22.0602i | 1.51021 | + | 1.01113i | ||||
\(477\) | −4.69683 | −0.215053 | ||||||||
\(478\) | 14.5961 | 0.667608 | ||||||||
\(479\) | −5.70597 | −0.260712 | −0.130356 | − | 0.991467i | \(-0.541612\pi\) | ||||
−0.130356 | + | 0.991467i | \(0.541612\pi\) | |||||||
\(480\) | 6.74026i | 0.307650i | ||||||||
\(481\) | 24.1381 | 1.10060 | ||||||||
\(482\) | 8.85065i | 0.403136i | ||||||||
\(483\) | −13.4962 | + | 20.1579i | −0.614101 | + | 0.917216i | ||||
\(484\) | 18.6564 | − | 17.8678i | 0.848020 | − | 0.812173i | ||||
\(485\) | −14.7983 | −0.671954 | ||||||||
\(486\) | −2.08529 | −0.0945905 | ||||||||
\(487\) | −28.3981 | −1.28684 | −0.643421 | − | 0.765513i | \(-0.722485\pi\) | ||||
−0.643421 | + | 0.765513i | \(0.722485\pi\) | |||||||
\(488\) | − | 6.06019i | − | 0.274332i | ||||||
\(489\) | − | 4.39152i | − | 0.198591i | ||||||
\(490\) | 4.63426 | + | 11.2473i | 0.209354 | + | 0.508102i | ||||
\(491\) | 10.3585i | 0.467475i | 0.972300 | + | 0.233737i | \(0.0750956\pi\) | ||||
−0.972300 | + | 0.233737i | \(0.924904\pi\) | |||||||
\(492\) | − | 7.54186i | − | 0.340013i | ||||||
\(493\) | 0.974174i | 0.0438746i | ||||||||
\(494\) | 24.3333i | 1.09481i | ||||||||
\(495\) | −2.56484 | + | 1.03010i | −0.115281 | + | 0.0462994i | ||||
\(496\) | 26.6110i | 1.19487i | ||||||||
\(497\) | 10.5646 | + | 7.07331i | 0.473889 | + | 0.317281i | ||||
\(498\) | −22.4238 | −1.00483 | ||||||||
\(499\) | −3.88621 | −0.173971 | −0.0869854 | − | 0.996210i | \(-0.527723\pi\) | ||||
−0.0869854 | + | 0.996210i | \(0.527723\pi\) | |||||||
\(500\) | − | 18.2117i | − | 0.814451i | ||||||
\(501\) | 2.86501i | 0.127999i | ||||||||
\(502\) | 50.7564 | 2.26537 | ||||||||
\(503\) | 11.7922 | 0.525787 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(504\) | −1.06943 | + | 1.59730i | −0.0476364 | + | 0.0711493i | ||||
\(505\) | − | 1.75581i | − | 0.0781324i | ||||||
\(506\) | −58.8450 | + | 23.6335i | −2.61598 | + | 1.05064i | ||||
\(507\) | − | 7.69916i | − | 0.341932i | ||||||
\(508\) | − | 0.531712i | − | 0.0235909i | ||||||
\(509\) | 23.6895i | 1.05002i | 0.851097 | + | 0.525009i | \(0.175938\pi\) | ||||
−0.851097 | + | 0.525009i | \(0.824062\pi\) | |||||||
\(510\) | − | 11.0903i | − | 0.491086i | ||||||
\(511\) | −23.4519 | − | 15.7017i | −1.03745 | − | 0.694601i | ||||
\(512\) | − | 30.3576i | − | 1.34163i | ||||||
\(513\) | 2.56484i | 0.113240i | ||||||||
\(514\) | −52.3638 | −2.30967 | ||||||||
\(515\) | 8.84285 | 0.389662 | ||||||||
\(516\) | −13.2953 | −0.585292 | ||||||||
\(517\) | −18.4733 | + | 7.41929i | −0.812454 | + | 0.326300i | ||||
\(518\) | 16.2849 | − | 24.3230i | 0.715517 | − | 1.06869i | ||||
\(519\) | − | 20.4220i | − | 0.896428i | ||||||
\(520\) | 2.75469 | 0.120801 | ||||||||
\(521\) | 20.1109i | 0.881075i | 0.897734 | + | 0.440537i | \(0.145212\pi\) | ||||
−0.897734 | + | 0.440537i | \(0.854788\pi\) | |||||||
\(522\) | −0.318317 | −0.0139324 | ||||||||
\(523\) | −34.8202 | −1.52258 | −0.761290 | − | 0.648411i | \(-0.775434\pi\) | ||||
−0.761290 | + | 0.648411i | \(0.775434\pi\) | |||||||
\(524\) | 0.716968 | 0.0313209 | ||||||||
\(525\) | −6.33748 | + | 9.46561i | −0.276590 | + | 0.413113i | ||||
\(526\) | −23.1814 | −1.01076 | ||||||||
\(527\) | − | 53.3744i | − | 2.32503i | ||||||
\(528\) | 9.79251 | − | 3.93290i | 0.426164 | − | 0.171157i | ||||
\(529\) | 61.0699 | 2.65521 | ||||||||
\(530\) | 8.16217 | 0.354542 | ||||||||
\(531\) | 1.05806i | 0.0459158i | ||||||||
\(532\) | 13.2422 | + | 8.86599i | 0.574121 | + | 0.384389i | ||||
\(533\) | 14.6110 | 0.632873 | ||||||||
\(534\) | 16.9719i | 0.734444i | ||||||||
\(535\) | −11.3088 | −0.488921 | ||||||||
\(536\) | 3.15000i | 0.136059i | ||||||||
\(537\) | − | 4.58825i | − | 0.197998i | ||||||
\(538\) | −26.7029 | −1.15124 | ||||||||
\(539\) | 16.6229 | − | 16.2074i | 0.716000 | − | 0.698100i | ||||
\(540\) | 1.95709 | 0.0842196 | ||||||||
\(541\) | 38.9979i | 1.67665i | 0.545169 | + | 0.838326i | \(0.316465\pi\) | ||||
−0.545169 | + | 0.838326i | \(0.683535\pi\) | |||||||
\(542\) | − | 32.4946i | − | 1.39576i | ||||||
\(543\) | 6.03029 | 0.258785 | ||||||||
\(544\) | 51.6159i | 2.21301i | ||||||||
\(545\) | 5.57278 | 0.238712 | ||||||||
\(546\) | −20.8577 | − | 13.9648i | −0.892628 | − | 0.597638i | ||||
\(547\) | 19.6262i | 0.839155i | 0.907720 | + | 0.419577i | \(0.137822\pi\) | ||||
−0.907720 | + | 0.419577i | \(0.862178\pi\) | |||||||
\(548\) | 27.6108 | 1.17948 | ||||||||
\(549\) | 8.34114 | 0.355991 | ||||||||
\(550\) | −27.6321 | + | 11.0977i | −1.17823 | + | 0.473206i | ||||
\(551\) | 0.391520i | 0.0166793i | ||||||||
\(552\) | 6.66164 | 0.283538 | ||||||||
\(553\) | 8.39385 | − | 12.5370i | 0.356943 | − | 0.533127i | ||||
\(554\) | −10.3892 | −0.441394 | ||||||||
\(555\) | −4.42142 | −0.187679 | ||||||||
\(556\) | 23.0895 | 0.979213 | ||||||||
\(557\) | − | 26.6169i | − | 1.12779i | −0.825846 | − | 0.563896i | \(-0.809302\pi\) | ||
0.825846 | − | 0.563896i | \(-0.190698\pi\) | |||||||
\(558\) | 17.4404 | 0.738311 | ||||||||
\(559\) | − | 25.7572i | − | 1.08941i | ||||||
\(560\) | −3.90300 | + | 5.82949i | −0.164932 | + | 0.246341i | ||||
\(561\) | −19.6411 | + | 7.88831i | −0.829248 | + | 0.333045i | ||||
\(562\) | 52.6054 | 2.21902 | ||||||||
\(563\) | 13.8173 | 0.582328 | 0.291164 | − | 0.956673i | \(-0.405957\pi\) | ||||
0.291164 | + | 0.956673i | \(0.405957\pi\) | |||||||
\(564\) | 14.0960 | 0.593547 | ||||||||
\(565\) | − | 1.11126i | − | 0.0467511i | ||||||
\(566\) | − | 43.2975i | − | 1.81993i | ||||||
\(567\) | −2.19849 | − | 1.47195i | −0.0923280 | − | 0.0618161i | ||||
\(568\) | − | 3.49133i | − | 0.146493i | ||||||
\(569\) | − | 23.8065i | − | 0.998019i | −0.866597 | − | 0.499009i | \(-0.833697\pi\) | ||
0.866597 | − | 0.499009i | \(-0.166303\pi\) | |||||||
\(570\) | − | 4.45718i | − | 0.186691i | ||||||
\(571\) | − | 47.0206i | − | 1.96775i | −0.178852 | − | 0.983876i | \(-0.557238\pi\) | ||
0.178852 | − | 0.983876i | \(-0.442762\pi\) | |||||||
\(572\) | −13.2067 | − | 32.8833i | −0.552199 | − | 1.37492i | ||||
\(573\) | − | 23.7800i | − | 0.993422i | ||||||
\(574\) | 9.85739 | − | 14.7229i | 0.411440 | − | 0.614523i | ||||
\(575\) | 39.4770 | 1.64630 | ||||||||
\(576\) | −10.5022 | −0.437593 | ||||||||
\(577\) | − | 25.0301i | − | 1.04202i | −0.853552 | − | 0.521008i | \(-0.825556\pi\) | ||
0.853552 | − | 0.521008i | \(-0.174444\pi\) | |||||||
\(578\) | − | 49.4778i | − | 2.05801i | ||||||
\(579\) | 4.63569 | 0.192653 | ||||||||
\(580\) | 0.298748 | 0.0124048 | ||||||||
\(581\) | −23.6411 | − | 15.8284i | −0.980798 | − | 0.656671i | ||||
\(582\) | − | 37.0289i | − | 1.53490i | ||||||
\(583\) | −5.80560 | − | 14.4554i | −0.240443 | − | 0.598679i | ||||
\(584\) | 7.75023i | 0.320707i | ||||||||
\(585\) | 3.79151i | 0.156760i | ||||||||
\(586\) | 9.11592i | 0.376575i | ||||||||
\(587\) | 18.2754i | 0.754307i | 0.926151 | + | 0.377153i | \(0.123097\pi\) | ||||
−0.926151 | + | 0.377153i | \(0.876903\pi\) | |||||||
\(588\) | −15.1993 | + | 6.26259i | −0.626807 | + | 0.258265i | ||||
\(589\) | − | 21.4512i | − | 0.883880i | ||||||
\(590\) | − | 1.83870i | − | 0.0756980i | ||||||
\(591\) | −6.62048 | −0.272330 | ||||||||
\(592\) | 16.8809 | 0.693802 | ||||||||
\(593\) | 15.6189 | 0.641390 | 0.320695 | − | 0.947183i | \(-0.396084\pi\) | ||||
0.320695 | + | 0.947183i | \(0.396084\pi\) | |||||||
\(594\) | −2.57755 | − | 6.41785i | −0.105758 | − | 0.263327i | ||||
\(595\) | 7.82835 | − | 11.6924i | 0.320931 | − | 0.479340i | ||||
\(596\) | 33.7739i | 1.38343i | ||||||||
\(597\) | 10.9699 | 0.448968 | ||||||||
\(598\) | 86.9885i | 3.55723i | ||||||||
\(599\) | −20.9864 | −0.857480 | −0.428740 | − | 0.903428i | \(-0.641042\pi\) | ||||
−0.428740 | + | 0.903428i | \(0.641042\pi\) | |||||||
\(600\) | 3.12813 | 0.127705 | ||||||||
\(601\) | −23.0535 | −0.940370 | −0.470185 | − | 0.882568i | \(-0.655813\pi\) | ||||
−0.470185 | + | 0.882568i | \(0.655813\pi\) | |||||||
\(602\) | −25.9545 | − | 17.3772i | −1.05783 | − | 0.708243i | ||||
\(603\) | −4.33560 | −0.176559 | ||||||||
\(604\) | 7.01015i | 0.285239i | ||||||||
\(605\) | −6.34062 | − | 6.62048i | −0.257783 | − | 0.269161i | ||||
\(606\) | 4.39346 | 0.178472 | ||||||||
\(607\) | 6.14682 | 0.249492 | 0.124746 | − | 0.992189i | \(-0.460188\pi\) | ||||
0.124746 | + | 0.992189i | \(0.460188\pi\) | |||||||
\(608\) | 20.7444i | 0.841296i | ||||||||
\(609\) | −0.335598 | − | 0.224692i | −0.0135991 | − | 0.00910498i | ||||
\(610\) | −14.4953 | −0.586897 | ||||||||
\(611\) | 27.3084i | 1.10478i | ||||||||
\(612\) | 14.9871 | 0.605816 | ||||||||
\(613\) | 36.4382i | 1.47173i | 0.677131 | + | 0.735863i | \(0.263223\pi\) | ||||
−0.677131 | + | 0.735863i | \(0.736777\pi\) | |||||||
\(614\) | − | 9.34061i | − | 0.376956i | ||||||
\(615\) | −2.67633 | −0.107920 | ||||||||
\(616\) | −6.23787 | − | 1.31701i | −0.251331 | − | 0.0530638i | ||||
\(617\) | 13.9441 | 0.561367 | 0.280684 | − | 0.959800i | \(-0.409439\pi\) | ||||
0.280684 | + | 0.959800i | \(0.409439\pi\) | |||||||
\(618\) | 22.1270i | 0.890077i | ||||||||
\(619\) | − | 18.9140i | − | 0.760217i | −0.924942 | − | 0.380109i | \(-0.875887\pi\) | ||
0.924942 | − | 0.380109i | \(-0.124113\pi\) | |||||||
\(620\) | −16.3682 | −0.657363 | ||||||||
\(621\) | 9.16896i | 0.367938i | ||||||||
\(622\) | −47.7198 | −1.91339 | ||||||||
\(623\) | −11.9800 | + | 17.8932i | −0.479969 | + | 0.716877i | ||||
\(624\) | − | 14.4759i | − | 0.579501i | ||||||
\(625\) | 15.0649 | 0.602594 | ||||||||
\(626\) | 11.0586 | 0.441992 | ||||||||
\(627\) | −7.89375 | + | 3.17031i | −0.315246 | + | 0.126610i | ||||
\(628\) | − | 40.8584i | − | 1.63043i | ||||||
\(629\) | −33.8585 | −1.35003 | ||||||||
\(630\) | 3.82055 | + | 2.55796i | 0.152214 | + | 0.101912i | ||||
\(631\) | −45.4030 | −1.80746 | −0.903732 | − | 0.428099i | \(-0.859184\pi\) | ||||
−0.903732 | + | 0.428099i | \(0.859184\pi\) | |||||||
\(632\) | −4.14314 | −0.164805 | ||||||||
\(633\) | −12.4960 | −0.496671 | ||||||||
\(634\) | 46.0747i | 1.82986i | ||||||||
\(635\) | −0.188685 | −0.00748773 | ||||||||
\(636\) | 11.0301i | 0.437372i | ||||||||
\(637\) | −12.1326 | − | 29.4458i | −0.480713 | − | 1.16669i | ||||
\(638\) | −0.393462 | − | 0.979680i | −0.0155773 | − | 0.0387859i | ||||
\(639\) | 4.80540 | 0.190099 | ||||||||
\(640\) | 4.77030 | 0.188563 | ||||||||
\(641\) | 7.70129 | 0.304183 | 0.152091 | − | 0.988366i | \(-0.451399\pi\) | ||||
0.152091 | + | 0.988366i | \(0.451399\pi\) | |||||||
\(642\) | − | 28.2973i | − | 1.11681i | ||||||
\(643\) | − | 19.5852i | − | 0.772364i | −0.922423 | − | 0.386182i | \(-0.873794\pi\) | ||
0.922423 | − | 0.386182i | \(-0.126206\pi\) | |||||||
\(644\) | 47.3391 | + | 31.6948i | 1.86542 | + | 1.24895i | ||||
\(645\) | 4.71800i | 0.185771i | ||||||||
\(646\) | − | 34.1324i | − | 1.34292i | ||||||
\(647\) | 24.7896i | 0.974581i | 0.873240 | + | 0.487291i | \(0.162015\pi\) | ||||
−0.873240 | + | 0.487291i | \(0.837985\pi\) | |||||||
\(648\) | 0.726543i | 0.0285413i | ||||||||
\(649\) | −3.25637 | + | 1.30783i | −0.127824 | + | 0.0513369i | ||||
\(650\) | 40.8475i | 1.60217i | ||||||||
\(651\) | 18.3872 | + | 12.3107i | 0.720652 | + | 0.482496i | ||||
\(652\) | −10.3131 | −0.403892 | ||||||||
\(653\) | 10.2731 | 0.402017 | 0.201008 | − | 0.979590i | \(-0.435578\pi\) | ||||
0.201008 | + | 0.979590i | \(0.435578\pi\) | |||||||
\(654\) | 13.9445i | 0.545272i | ||||||||
\(655\) | − | 0.254425i | − | 0.00994122i | ||||||
\(656\) | 10.2182 | 0.398953 | ||||||||
\(657\) | −10.6673 | −0.416170 | ||||||||
\(658\) | 27.5176 | + | 18.4238i | 1.07275 | + | 0.718233i | ||||
\(659\) | − | 18.6488i | − | 0.726455i | −0.931701 | − | 0.363227i | \(-0.881675\pi\) | ||
0.931701 | − | 0.363227i | \(-0.118325\pi\) | |||||||
\(660\) | 2.41909 | + | 6.02330i | 0.0941631 | + | 0.234456i | ||||
\(661\) | 46.2521i | 1.79900i | 0.436922 | + | 0.899499i | \(0.356068\pi\) | ||||
−0.436922 | + | 0.899499i | \(0.643932\pi\) | |||||||
\(662\) | 41.1460i | 1.59918i | ||||||||
\(663\) | 29.0348i | 1.12762i | ||||||||
\(664\) | 7.81275i | 0.303193i | ||||||||
\(665\) | 3.14621 | − | 4.69916i | 0.122005 | − | 0.182226i | ||||
\(666\) | − | 11.0635i | − | 0.428701i | ||||||
\(667\) | 1.39964i | 0.0541941i | ||||||||
\(668\) | 6.72824 | 0.260323 | ||||||||
\(669\) | −9.44958 | −0.365342 | ||||||||
\(670\) | 7.53442 | 0.291080 | ||||||||
\(671\) | 10.3102 | + | 25.6714i | 0.398021 | + | 0.991033i | ||||
\(672\) | −17.7814 | − | 11.9051i | −0.685933 | − | 0.459250i | ||||
\(673\) | 24.9823i | 0.962996i | 0.876447 | + | 0.481498i | \(0.159907\pi\) | ||||
−0.876447 | + | 0.481498i | \(0.840093\pi\) | |||||||
\(674\) | −65.4888 | −2.52253 | ||||||||
\(675\) | 4.30550i | 0.165719i | ||||||||
\(676\) | −18.0808 | −0.695416 | ||||||||
\(677\) | −0.707252 | −0.0271819 | −0.0135909 | − | 0.999908i | \(-0.504326\pi\) | ||||
−0.0135909 | + | 0.999908i | \(0.504326\pi\) | |||||||
\(678\) | 2.78065 | 0.106790 | ||||||||
\(679\) | 26.1377 | − | 39.0391i | 1.00307 | − | 1.49818i | ||||
\(680\) | −3.86401 | −0.148178 | ||||||||
\(681\) | − | 5.43497i | − | 0.208269i | ||||||
\(682\) | 21.5575 | + | 53.6760i | 0.825480 | + | 2.05536i | ||||
\(683\) | −33.2295 | −1.27149 | −0.635747 | − | 0.771898i | \(-0.719308\pi\) | ||||
−0.635747 | + | 0.771898i | \(0.719308\pi\) | |||||||
\(684\) | 6.02330 | 0.230306 | ||||||||
\(685\) | − | 9.79806i | − | 0.374365i | ||||||
\(686\) | −37.8567 | − | 7.64021i | −1.44538 | − | 0.291705i | ||||
\(687\) | 18.9746 | 0.723925 | ||||||||
\(688\) | − | 18.0133i | − | 0.686750i | ||||||
\(689\) | −21.3688 | −0.814088 | ||||||||
\(690\) | − | 15.9339i | − | 0.606592i | ||||||
\(691\) | 2.11146i | 0.0803236i | 0.999193 | + | 0.0401618i | \(0.0127873\pi\) | ||||
−0.999193 | + | 0.0401618i | \(0.987213\pi\) | |||||||
\(692\) | −47.9594 | −1.82314 | ||||||||
\(693\) | 1.81271 | − | 8.58569i | 0.0688591 | − | 0.326143i | ||||
\(694\) | 14.8959 | 0.565440 | ||||||||
\(695\) | − | 8.19361i | − | 0.310801i | ||||||
\(696\) | 0.110906i | 0.00420389i | ||||||||
\(697\) | −20.4949 | −0.776299 | ||||||||
\(698\) | 25.3000i | 0.957620i | ||||||||
\(699\) | 12.5083 | 0.473107 | ||||||||
\(700\) | 22.2292 | + | 14.8830i | 0.840184 | + | 0.562525i | ||||
\(701\) | 3.16145i | 0.119406i | 0.998216 | + | 0.0597031i | \(0.0190154\pi\) | ||||
−0.998216 | + | 0.0597031i | \(0.980985\pi\) | |||||||
\(702\) | −9.48728 | −0.358074 | ||||||||
\(703\) | −13.6077 | −0.513226 | ||||||||
\(704\) | −12.9815 | − | 32.3225i | −0.489258 | − | 1.21820i | ||||
\(705\) | − | 5.00214i | − | 0.188391i | ||||||
\(706\) | 30.6897 | 1.15502 | ||||||||
\(707\) | 4.63198 | + | 3.10123i | 0.174203 | + | 0.116634i | ||||
\(708\) | 2.48476 | 0.0933829 | ||||||||
\(709\) | −37.2542 | −1.39911 | −0.699556 | − | 0.714578i | \(-0.746619\pi\) | ||||
−0.699556 | + | 0.714578i | \(0.746619\pi\) | |||||||
\(710\) | −8.35086 | −0.313402 | ||||||||
\(711\) | − | 5.70254i | − | 0.213862i | ||||||
\(712\) | 5.91323 | 0.221608 | ||||||||
\(713\) | − | 76.6852i | − | 2.87188i | ||||||
\(714\) | 29.2572 | + | 19.5885i | 1.09492 | + | 0.733079i | ||||
\(715\) | −11.6691 | + | 4.68656i | −0.436398 | + | 0.175267i | ||||
\(716\) | −10.7751 | −0.402685 | ||||||||
\(717\) | 6.99955 | 0.261403 | ||||||||
\(718\) | 13.6739 | 0.510305 | ||||||||
\(719\) | 21.3405i | 0.795865i | 0.917415 | + | 0.397932i | \(0.130272\pi\) | ||||
−0.917415 | + | 0.397932i | \(0.869728\pi\) | |||||||
\(720\) | 2.65159i | 0.0988188i | ||||||||
\(721\) | −15.6189 | + | 23.3282i | −0.581677 | + | 0.868788i | ||||
\(722\) | 25.9026i | 0.963995i | ||||||||
\(723\) | 4.24433i | 0.157848i | ||||||||
\(724\) | − | 14.1616i | − | 0.526312i | ||||||
\(725\) | 0.657232i | 0.0244090i | ||||||||
\(726\) | 16.5661 | − | 15.8658i | 0.614825 | − | 0.588835i | ||||
\(727\) | 13.7013i | 0.508153i | 0.967184 | + | 0.254076i | \(0.0817715\pi\) | ||||
−0.967184 | + | 0.254076i | \(0.918229\pi\) | |||||||
\(728\) | −4.86553 | + | 7.26712i | −0.180329 | + | 0.269337i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 18.5376 | 0.686109 | ||||||||
\(731\) | 36.1297i | 1.33631i | ||||||||
\(732\) | − | 19.5885i | − | 0.724010i | ||||||
\(733\) | 14.7641 | 0.545324 | 0.272662 | − | 0.962110i | \(-0.412096\pi\) | ||||
0.272662 | + | 0.962110i | \(0.412096\pi\) | |||||||
\(734\) | −68.1385 | −2.51504 | ||||||||
\(735\) | 2.22236 | + | 5.39366i | 0.0819731 | + | 0.198948i | ||||
\(736\) | 74.1586i | 2.73352i | ||||||||
\(737\) | −5.35909 | − | 13.3436i | −0.197405 | − | 0.491518i | ||||
\(738\) | − | 6.69683i | − | 0.246514i | ||||||
\(739\) | − | 32.3486i | − | 1.18996i | −0.803740 | − | 0.594981i | \(-0.797160\pi\) | ||
0.803740 | − | 0.594981i | \(-0.202840\pi\) | |||||||
\(740\) | 10.3833i | 0.381699i | ||||||||
\(741\) | 11.6691i | 0.428674i | ||||||||
\(742\) | −14.4166 | + | 21.5325i | −0.529250 | + | 0.790484i | ||||
\(743\) | − | 2.71032i | − | 0.0994318i | −0.998763 | − | 0.0497159i | \(-0.984168\pi\) | ||
0.998763 | − | 0.0497159i | \(-0.0158316\pi\) | |||||||
\(744\) | − | 6.07648i | − | 0.222775i | ||||||
\(745\) | 11.9851 | 0.439101 | ||||||||
\(746\) | 45.6760 | 1.67232 | ||||||||
\(747\) | −10.7533 | −0.393444 | ||||||||
\(748\) | 18.5250 | + | 46.1254i | 0.677342 | + | 1.68651i | ||||
\(749\) | 19.9744 | − | 29.8336i | 0.729848 | − | 1.09009i | ||||
\(750\) | − | 16.1711i | − | 0.590487i | ||||||
\(751\) | −9.39637 | −0.342879 | −0.171439 | − | 0.985195i | \(-0.554842\pi\) | ||||
−0.171439 | + | 0.985195i | \(0.554842\pi\) | |||||||
\(752\) | 19.0981i | 0.696436i | ||||||||
\(753\) | 24.3403 | 0.887008 | ||||||||
\(754\) | −1.44823 | −0.0527413 | ||||||||
\(755\) | 2.48764 | 0.0905346 | ||||||||
\(756\) | −3.45675 | + | 5.16297i | −0.125721 | + | 0.187775i | ||||
\(757\) | 11.9724 | 0.435145 | 0.217573 | − | 0.976044i | \(-0.430186\pi\) | ||||
0.217573 | + | 0.976044i | \(0.430186\pi\) | |||||||
\(758\) | 29.1988i | 1.06055i | ||||||||
\(759\) | −28.2192 | + | 11.3335i | −1.02429 | + | 0.411379i | ||||
\(760\) | −1.55295 | −0.0563313 | ||||||||
\(761\) | 15.5977 | 0.565415 | 0.282707 | − | 0.959206i | \(-0.408767\pi\) | ||||
0.282707 | + | 0.959206i | \(0.408767\pi\) | |||||||
\(762\) | − | 0.472136i | − | 0.0171037i | ||||||
\(763\) | −9.84304 | + | 14.7015i | −0.356342 | + | 0.532230i | ||||
\(764\) | −55.8452 | −2.02041 | ||||||||
\(765\) | − | 5.31836i | − | 0.192286i | ||||||
\(766\) | 14.7132 | 0.531610 | ||||||||
\(767\) | 4.81377i | 0.173815i | ||||||||
\(768\) | − | 9.06799i | − | 0.327213i | ||||||
\(769\) | 15.4093 | 0.555675 | 0.277837 | − | 0.960628i | \(-0.410382\pi\) | ||||
0.277837 | + | 0.960628i | \(0.410382\pi\) | |||||||
\(770\) | −3.15013 | + | 14.9203i | −0.113523 | + | 0.537689i | ||||
\(771\) | −25.1111 | −0.904354 | ||||||||
\(772\) | − | 10.8865i | − | 0.391814i | ||||||
\(773\) | 1.78230i | 0.0641048i | 0.999486 | + | 0.0320524i | \(0.0102043\pi\) | ||||
−0.999486 | + | 0.0320524i | \(0.989796\pi\) | |||||||
\(774\) | −11.8056 | −0.424343 | ||||||||
\(775\) | − | 36.0093i | − | 1.29349i | ||||||
\(776\) | −12.9014 | −0.463132 | ||||||||
\(777\) | 7.80943 | − | 11.6641i | 0.280162 | − | 0.418447i | ||||
\(778\) | 5.10766i | 0.183119i | ||||||||
\(779\) | −8.23689 | −0.295117 | ||||||||
\(780\) | 8.90403 | 0.318815 | ||||||||
\(781\) | 5.93981 | + | 14.7895i | 0.212543 | + | 0.529210i | ||||
\(782\) | − | 122.019i | − | 4.36339i | ||||||
\(783\) | −0.152649 | −0.00545524 | ||||||||
\(784\) | −8.48495 | − | 20.5929i | −0.303034 | − | 0.735461i | ||||
\(785\) | −14.4992 | −0.517497 | ||||||||
\(786\) | 0.636635 | 0.0227080 | ||||||||
\(787\) | −1.57687 | −0.0562093 | −0.0281046 | − | 0.999605i | \(-0.508947\pi\) | ||||
−0.0281046 | + | 0.999605i | \(0.508947\pi\) | |||||||
\(788\) | 15.5476i | 0.553862i | ||||||||
\(789\) | −11.1167 | −0.395764 | ||||||||
\(790\) | 9.90990i | 0.352579i | ||||||||
\(791\) | 2.93161 | + | 1.96279i | 0.104236 | + | 0.0697888i | ||||
\(792\) | −2.23607 | + | 0.898056i | −0.0794552 | + | 0.0319110i | ||||
\(793\) | 37.9491 | 1.34761 | ||||||||
\(794\) | 9.91975 | 0.352039 | ||||||||
\(795\) | 3.91418 | 0.138821 | ||||||||
\(796\) | − | 25.7619i | − | 0.913105i | ||||||
\(797\) | 16.8334i | 0.596268i | 0.954524 | + | 0.298134i | \(0.0963643\pi\) | ||||
−0.954524 | + | 0.298134i | \(0.903636\pi\) | |||||||
\(798\) | 11.7584 | + | 7.87259i | 0.416244 | + | 0.278687i | ||||
\(799\) | − | 38.3055i | − | 1.35515i | ||||||
\(800\) | 34.8229i | 1.23118i | ||||||||
\(801\) | 8.13887i | 0.287573i | ||||||||
\(802\) | − | 38.3030i | − | 1.35252i | ||||||
\(803\) | −13.1855 | − | 32.8305i | −0.465305 | − | 1.15856i | ||||
\(804\) | 10.1818i | 0.359084i | ||||||||
\(805\) | 11.2473 | − | 16.7989i | 0.396416 | − | 0.592083i | ||||
\(806\) | 79.3474 | 2.79489 | ||||||||
\(807\) | −12.8054 | −0.450772 | ||||||||
\(808\) | − | 1.53074i | − | 0.0538514i | ||||||
\(809\) | − | 22.2453i | − | 0.782104i | −0.920369 | − | 0.391052i | \(-0.872111\pi\) | ||
0.920369 | − | 0.391052i | \(-0.127889\pi\) | |||||||
\(810\) | 1.73781 | 0.0610602 | ||||||||
\(811\) | −44.2460 | −1.55369 | −0.776843 | − | 0.629695i | \(-0.783180\pi\) | ||||
−0.776843 | + | 0.629695i | \(0.783180\pi\) | |||||||
\(812\) | −0.527670 | + | 0.788124i | −0.0185176 | + | 0.0276577i | ||||
\(813\) | − | 15.5828i | − | 0.546513i | ||||||
\(814\) | 34.0499 | − | 13.6752i | 1.19345 | − | 0.479316i | ||||
\(815\) | 3.65974i | 0.128195i | ||||||||
\(816\) | 20.3054i | 0.710832i | ||||||||
\(817\) | 14.5205i | 0.508009i | ||||||||
\(818\) | − | 72.4074i | − | 2.53167i | ||||||
\(819\) | −10.0023 | − | 6.69683i | −0.349510 | − | 0.234006i | ||||
\(820\) | 6.28513i | 0.219486i | ||||||||
\(821\) | 1.97420i | 0.0689000i | 0.999406 | + | 0.0344500i | \(0.0109679\pi\) | ||||
−0.999406 | + | 0.0344500i | \(0.989032\pi\) | |||||||
\(822\) | 24.5171 | 0.855134 | ||||||||
\(823\) | −2.45171 | −0.0854614 | −0.0427307 | − | 0.999087i | \(-0.513606\pi\) | ||||
−0.0427307 | + | 0.999087i | \(0.513606\pi\) | |||||||
\(824\) | 7.70935 | 0.268568 | ||||||||
\(825\) | −13.2510 | + | 5.32189i | −0.461340 | + | 0.185285i | ||||
\(826\) | 4.85065 | + | 3.24764i | 0.168776 | + | 0.113000i | ||||
\(827\) | − | 25.4279i | − | 0.884215i | −0.896962 | − | 0.442108i | \(-0.854231\pi\) | ||
0.896962 | − | 0.442108i | \(-0.145769\pi\) | |||||||
\(828\) | 21.5325 | 0.748307 | ||||||||
\(829\) | 36.0606i | 1.25244i | 0.779648 | + | 0.626218i | \(0.215398\pi\) | ||||
−0.779648 | + | 0.626218i | \(0.784602\pi\) | |||||||
\(830\) | 18.6872 | 0.648642 | ||||||||
\(831\) | −4.98214 | −0.172829 | ||||||||
\(832\) | −47.7813 | −1.65652 | ||||||||
\(833\) | 17.0185 | + | 41.3037i | 0.589656 | + | 1.43109i | ||||
\(834\) | 20.5024 | 0.709941 | ||||||||
\(835\) | − | 2.38760i | − | 0.0826264i | ||||||
\(836\) | 7.44520 | + | 18.5378i | 0.257498 | + | 0.641143i | ||||
\(837\) | 8.36356 | 0.289087 | ||||||||
\(838\) | −74.3899 | −2.56976 | ||||||||
\(839\) | 20.1790i | 0.696657i | 0.937372 | + | 0.348329i | \(0.113251\pi\) | ||||
−0.937372 | + | 0.348329i | \(0.886749\pi\) | |||||||
\(840\) | 0.891229 | − | 1.33113i | 0.0307503 | − | 0.0459285i | ||||
\(841\) | 28.9767 | 0.999196 | ||||||||
\(842\) | − | 2.60573i | − | 0.0897994i | ||||||
\(843\) | 25.2269 | 0.868862 | ||||||||
\(844\) | 29.3458i | 1.01012i | ||||||||
\(845\) | 6.41621i | 0.220724i | ||||||||
\(846\) | 12.5166 | 0.430328 | ||||||||
\(847\) | 28.6647 | − | 5.03355i | 0.984930 | − | 0.172955i | ||||
\(848\) | −14.9443 | −0.513188 | ||||||||
\(849\) | − | 20.7634i | − | 0.712597i | ||||||
\(850\) | − | 57.2969i | − | 1.96527i | ||||||
\(851\) | −48.6460 | −1.66756 | ||||||||
\(852\) | − | 11.2851i | − | 0.386620i | ||||||
\(853\) | 31.3640 | 1.07388 | 0.536942 | − | 0.843619i | \(-0.319579\pi\) | ||||
0.536942 | + | 0.843619i | \(0.319579\pi\) | |||||||
\(854\) | 25.6026 | − | 38.2398i | 0.876102 | − | 1.30854i | ||||
\(855\) | − | 2.13745i | − | 0.0730991i | ||||||
\(856\) | −9.85919 | −0.336980 | ||||||||
\(857\) | −6.51959 | −0.222705 | −0.111353 | − | 0.993781i | \(-0.535518\pi\) | ||||
−0.111353 | + | 0.993781i | \(0.535518\pi\) | |||||||
\(858\) | −11.7269 | − | 29.1988i | −0.400351 | − | 0.996832i | ||||
\(859\) | 39.4585i | 1.34631i | 0.739503 | + | 0.673153i | \(0.235061\pi\) | ||||
−0.739503 | + | 0.673153i | \(0.764939\pi\) | |||||||
\(860\) | 11.0798 | 0.377819 | ||||||||
\(861\) | 4.72712 | − | 7.06039i | 0.161100 | − | 0.240617i | ||||
\(862\) | 66.1404 | 2.25275 | ||||||||
\(863\) | 23.0120 | 0.783338 | 0.391669 | − | 0.920106i | \(-0.371898\pi\) | ||||
0.391669 | + | 0.920106i | \(0.371898\pi\) | |||||||
\(864\) | −8.08800 | −0.275159 | ||||||||
\(865\) | 17.0190i | 0.578664i | ||||||||
\(866\) | −28.6254 | −0.972729 | ||||||||
\(867\) | − | 23.7271i | − | 0.805815i | ||||||
\(868\) | 28.9107 | − | 43.1808i | 0.981293 | − | 1.46565i | ||||
\(869\) | 17.5506 | − | 7.04873i | 0.595364 | − | 0.239112i | ||||
\(870\) | 0.265275 | 0.00899366 | ||||||||
\(871\) | −19.7254 | −0.668369 | ||||||||
\(872\) | 4.85845 | 0.164528 | ||||||||
\(873\) | − | 17.7572i | − | 0.600991i | ||||||
\(874\) | − | 49.0394i | − | 1.65878i | ||||||
\(875\) | 11.4148 | − | 17.0491i | 0.385891 | − | 0.576363i | ||||
\(876\) | 25.0512i | 0.846401i | ||||||||
\(877\) | − | 25.6849i | − | 0.867317i | −0.901077 | − | 0.433659i | \(-0.857222\pi\) | ||
0.901077 | − | 0.433659i | \(-0.142778\pi\) | |||||||
\(878\) | 63.5240i | 2.14383i | ||||||||
\(879\) | 4.37155i | 0.147449i | ||||||||
\(880\) | −8.16074 | + | 3.27754i | −0.275099 | + | 0.110486i | ||||
\(881\) | 5.88948i | 0.198422i | 0.995066 | + | 0.0992108i | \(0.0316318\pi\) | ||||
−0.995066 | + | 0.0992108i | \(0.968368\pi\) | |||||||
\(882\) | −13.4962 | + | 5.56090i | −0.454442 | + | 0.187245i | ||||
\(883\) | −38.5578 | −1.29757 | −0.648787 | − | 0.760970i | \(-0.724723\pi\) | ||||
−0.648787 | + | 0.760970i | \(0.724723\pi\) | |||||||
\(884\) | 68.1856 | 2.29333 | ||||||||
\(885\) | − | 0.881749i | − | 0.0296397i | ||||||
\(886\) | 35.1607i | 1.18125i | ||||||||
\(887\) | −52.9627 | −1.77831 | −0.889157 | − | 0.457602i | \(-0.848709\pi\) | ||||
−0.889157 | + | 0.457602i | \(0.848709\pi\) | |||||||
\(888\) | −3.85467 | −0.129354 | ||||||||
\(889\) | 0.333269 | − | 0.497767i | 0.0111775 | − | 0.0166946i | ||||
\(890\) | − | 14.1438i | − | 0.474100i | ||||||
\(891\) | −1.23607 | − | 3.07768i | −0.0414098 | − | 0.103106i | ||||
\(892\) | 22.1915i | 0.743027i | ||||||||
\(893\) | − | 15.3950i | − | 0.515174i | ||||||
\(894\) | 29.9897i | 1.00301i | ||||||||
\(895\) | 3.82369i | 0.127812i | ||||||||
\(896\) | −8.42565 | + | 12.5845i | −0.281481 | + | 0.420418i | ||||
\(897\) | 41.7154i | 1.39284i | ||||||||
\(898\) | − | 62.6946i | − | 2.09215i | ||||||
\(899\) | 1.27669 | 0.0425801 | ||||||||
\(900\) | 10.1111 | 0.337037 | ||||||||
\(901\) | 29.9741 | 0.998583 | ||||||||
\(902\) | 20.6107 | − | 8.27773i | 0.686262 | − | 0.275618i | ||||
\(903\) | −12.4465 | − | 8.33327i | −0.414194 | − | 0.277314i | ||||
\(904\) | − | 0.968817i | − | 0.0322224i | ||||||
\(905\) | −5.02544 | −0.167051 | ||||||||
\(906\) | 6.22469i | 0.206802i | ||||||||
\(907\) | 15.7828 | 0.524061 | 0.262030 | − | 0.965060i | \(-0.415608\pi\) | ||||
0.262030 | + | 0.965060i | \(0.415608\pi\) | |||||||
\(908\) | −12.7636 | −0.423574 | ||||||||
\(909\) | 2.10689 | 0.0698811 | ||||||||
\(910\) | 17.3821 | + | 11.6378i | 0.576211 | + | 0.385789i | ||||
\(911\) | −19.9066 | −0.659536 | −0.329768 | − | 0.944062i | \(-0.606971\pi\) | ||||
−0.329768 | + | 0.944062i | \(0.606971\pi\) | |||||||
\(912\) | 8.16074i | 0.270229i | ||||||||
\(913\) | −13.2918 | − | 33.0953i | −0.439896 | − | 1.09530i | ||||
\(914\) | 15.4193 | 0.510025 | ||||||||
\(915\) | −6.95122 | −0.229800 | ||||||||
\(916\) | − | 44.5601i | − | 1.47231i | ||||||
\(917\) | 0.671197 | + | 0.449384i | 0.0221649 | + | 0.0148400i | ||||
\(918\) | 13.3078 | 0.439224 | ||||||||
\(919\) | 49.7644i | 1.64158i | 0.571233 | + | 0.820788i | \(0.306465\pi\) | ||||
−0.571233 | + | 0.820788i | \(0.693535\pi\) | |||||||
\(920\) | −5.55158 | −0.183030 | ||||||||
\(921\) | − | 4.47930i | − | 0.147598i | ||||||
\(922\) | − | 35.7316i | − | 1.17676i | ||||||
\(923\) | 21.8628 | 0.719624 | ||||||||
\(924\) | −20.1628 | − | 4.25699i | −0.663306 | − | 0.140045i | ||||
\(925\) | −22.8428 | −0.751068 | ||||||||
\(926\) | − | 24.2167i | − | 0.795810i | ||||||
\(927\) | 10.6110i | 0.348511i | ||||||||
\(928\) | −1.23463 | −0.0405287 | ||||||||
\(929\) | 30.3929i | 0.997159i | 0.866844 | + | 0.498580i | \(0.166145\pi\) | ||||
−0.866844 | + | 0.498580i | \(0.833855\pi\) | |||||||
\(930\) | −14.5342 | −0.476596 | ||||||||
\(931\) | 6.83973 | + | 16.6000i | 0.224163 | + | 0.544042i | ||||
\(932\) | − | 29.3746i | − | 0.962198i | ||||||
\(933\) | −22.8841 | −0.749191 | ||||||||
\(934\) | 14.5925 | 0.477483 | ||||||||
\(935\) | 16.3682 | − | 6.57385i | 0.535298 | − | 0.214988i | ||||
\(936\) | 3.30550i | 0.108044i | ||||||||
\(937\) | −31.4972 | −1.02897 | −0.514485 | − | 0.857499i | \(-0.672017\pi\) | ||||
−0.514485 | + | 0.857499i | \(0.672017\pi\) | |||||||
\(938\) | −13.3078 | + | 19.8765i | −0.434516 | + | 0.648990i | ||||
\(939\) | 5.30317 | 0.173062 | ||||||||
\(940\) | −11.7471 | −0.383148 | ||||||||
\(941\) | 11.1507 | 0.363501 | 0.181751 | − | 0.983345i | \(-0.441824\pi\) | ||||
0.181751 | + | 0.983345i | \(0.441824\pi\) | |||||||
\(942\) | − | 36.2804i | − | 1.18208i | ||||||
\(943\) | −29.4458 | −0.958889 | ||||||||
\(944\) | 3.36651i | 0.109570i | ||||||||
\(945\) | 1.83215 | + | 1.22667i | 0.0595998 | + | 0.0399036i | ||||
\(946\) | −14.5925 | − | 36.3339i | −0.474444 | − | 1.18132i | ||||
\(947\) | 41.5978 | 1.35175 | 0.675873 | − | 0.737018i | \(-0.263767\pi\) | ||||
0.675873 | + | 0.737018i | \(0.263767\pi\) | |||||||
\(948\) | −13.3919 | −0.434950 | ||||||||
\(949\) | −48.5322 | −1.57542 | ||||||||
\(950\) | − | 23.0276i | − | 0.747114i | ||||||
\(951\) | 22.0951i | 0.716484i | ||||||||
\(952\) | 6.82489 | − | 10.1936i | 0.221196 | − | 0.330377i | ||||
\(953\) | 50.6311i | 1.64010i | 0.572290 | + | 0.820051i | \(0.306055\pi\) | ||||
−0.572290 | + | 0.820051i | \(0.693945\pi\) | |||||||
\(954\) | 9.79423i | 0.317100i | ||||||||
\(955\) | 19.8174i | 0.641276i | ||||||||
\(956\) | − | 16.4378i | − | 0.531638i | ||||||
\(957\) | −0.188685 | − | 0.469806i | −0.00609932 | − | 0.0151867i | ||||
\(958\) | 11.8986i | 0.384425i | ||||||||
\(959\) | 25.8481 | + | 17.3060i | 0.834680 | + | 0.558841i | ||||
\(960\) | 8.75220 | 0.282476 | ||||||||
\(961\) | −38.9491 | −1.25642 | ||||||||
\(962\) | − | 50.3348i | − | 1.62286i | ||||||
\(963\) | − | 13.5700i | − | 0.437288i | ||||||
\(964\) | 9.96745 | 0.321030 | ||||||||
\(965\) | −3.86322 | −0.124362 | ||||||||
\(966\) | 42.0350 | + | 28.1435i | 1.35245 | + | 0.905503i | ||||
\(967\) | 42.1819i | 1.35648i | 0.734841 | + | 0.678240i | \(0.237257\pi\) | ||||
−0.734841 | + | 0.678240i | \(0.762743\pi\) | |||||||
\(968\) | −5.52786 | − | 5.77185i | −0.177672 | − | 0.185514i | ||||
\(969\) | − | 16.3682i | − | 0.525823i | ||||||
\(970\) | 30.8586i | 0.990809i | ||||||||
\(971\) | 13.7805i | 0.442238i | 0.975247 | + | 0.221119i | \(0.0709709\pi\) | ||||
−0.975247 | + | 0.221119i | \(0.929029\pi\) | |||||||
\(972\) | 2.34841i | 0.0753254i | ||||||||
\(973\) | 21.6155 | + | 14.4721i | 0.692960 | + | 0.463955i | ||||
\(974\) | 59.2182i | 1.89747i | ||||||||
\(975\) | 19.5885i | 0.627332i | ||||||||
\(976\) | 26.5397 | 0.849514 | ||||||||
\(977\) | 32.4238 | 1.03733 | 0.518664 | − | 0.854978i | \(-0.326430\pi\) | ||||
0.518664 | + | 0.854978i | \(0.326430\pi\) | |||||||
\(978\) | −9.15757 | −0.292827 | ||||||||
\(979\) | −25.0489 | + | 10.0602i | −0.800565 | + | 0.321525i | ||||
\(980\) | 12.6665 | − | 5.21903i | 0.404618 | − | 0.166716i | ||||
\(981\) | 6.68708i | 0.213502i | ||||||||
\(982\) | 21.6005 | 0.689300 | ||||||||
\(983\) | − | 6.88408i | − | 0.219568i | −0.993955 | − | 0.109784i | \(-0.964984\pi\) | ||
0.993955 | − | 0.109784i | \(-0.0350159\pi\) | |||||||
\(984\) | −2.33327 | −0.0743819 | ||||||||
\(985\) | 5.51728 | 0.175795 | ||||||||
\(986\) | 2.03143 | 0.0646940 | ||||||||
\(987\) | 13.1961 | + | 8.83512i | 0.420036 | + | 0.281225i | ||||
\(988\) | 27.4038 | 0.871831 | ||||||||
\(989\) | 51.9090i | 1.65061i | ||||||||
\(990\) | 2.14805 | + | 5.34841i | 0.0682694 | + | 0.169984i | ||||
\(991\) | −9.45618 | −0.300385 | −0.150193 | − | 0.988657i | \(-0.547989\pi\) | ||||
−0.150193 | + | 0.988657i | \(0.547989\pi\) | |||||||
\(992\) | 67.6445 | 2.14771 | ||||||||
\(993\) | 19.7316i | 0.626163i | ||||||||
\(994\) | 14.7499 | − | 22.0303i | 0.467837 | − | 0.698758i | ||||
\(995\) | −9.14194 | −0.289819 | ||||||||
\(996\) | 25.2533i | 0.800180i | ||||||||
\(997\) | 10.2348 | 0.324138 | 0.162069 | − | 0.986779i | \(-0.448183\pi\) | ||||
0.162069 | + | 0.986779i | \(0.448183\pi\) | |||||||
\(998\) | 8.10386i | 0.256523i | ||||||||
\(999\) | − | 5.30550i | − | 0.167859i |
(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 | 231.2.c.a.76.3 | ✓ | 16 | |
3.2 | odd | 2 | 693.2.c.e.307.13 | 16 | |||
4.3 | odd | 2 | 3696.2.q.e.769.14 | 16 | |||
7.6 | odd | 2 | inner | 231.2.c.a.76.4 | yes | 16 | |
11.10 | odd | 2 | inner | 231.2.c.a.76.13 | yes | 16 | |
21.20 | even | 2 | 693.2.c.e.307.14 | 16 | |||
28.27 | even | 2 | 3696.2.q.e.769.3 | 16 | |||
33.32 | even | 2 | 693.2.c.e.307.3 | 16 | |||
44.43 | even | 2 | 3696.2.q.e.769.13 | 16 | |||
77.76 | even | 2 | inner | 231.2.c.a.76.14 | yes | 16 | |
231.230 | odd | 2 | 693.2.c.e.307.4 | 16 | |||
308.307 | odd | 2 | 3696.2.q.e.769.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.c.a.76.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
231.2.c.a.76.4 | yes | 16 | 7.6 | odd | 2 | inner | |
231.2.c.a.76.13 | yes | 16 | 11.10 | odd | 2 | inner | |
231.2.c.a.76.14 | yes | 16 | 77.76 | even | 2 | inner | |
693.2.c.e.307.3 | 16 | 33.32 | even | 2 | |||
693.2.c.e.307.4 | 16 | 231.230 | odd | 2 | |||
693.2.c.e.307.13 | 16 | 3.2 | odd | 2 | |||
693.2.c.e.307.14 | 16 | 21.20 | even | 2 | |||
3696.2.q.e.769.3 | 16 | 28.27 | even | 2 | |||
3696.2.q.e.769.4 | 16 | 308.307 | odd | 2 | |||
3696.2.q.e.769.13 | 16 | 44.43 | even | 2 | |||
3696.2.q.e.769.14 | 16 | 4.3 | odd | 2 |