Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(100,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.n (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.5 | ||
Root | \(-1.02197 + 1.77010i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.100 |
Dual form | 819.2.n.d.172.5 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.777343 | + | 1.34640i | 0.549665 | + | 0.952047i | 0.998297 | + | 0.0583310i | \(0.0185779\pi\) |
−0.448632 | + | 0.893716i | \(0.648089\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.208526 | + | 0.361177i | −0.104263 | + | 0.180588i | ||||
\(5\) | −0.595756 | + | 1.03188i | −0.266430 | + | 0.461470i | −0.967937 | − | 0.251192i | \(-0.919177\pi\) |
0.701507 | + | 0.712662i | \(0.252511\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.337371 | − | 2.62415i | 0.127514 | − | 0.991837i | ||||
\(8\) | 2.46099 | 0.870091 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.85243 | −0.585789 | ||||||||
\(11\) | −2.11614 | −0.638040 | −0.319020 | − | 0.947748i | \(-0.603354\pi\) | ||||
−0.319020 | + | 0.947748i | \(0.603354\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.86133 | + | 2.19381i | 0.793590 | + | 0.608453i | ||||
\(14\) | 3.79541 | − | 1.58563i | 1.01437 | − | 0.423778i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.33009 | + | 4.03583i | 0.582521 | + | 1.00896i | ||||
\(17\) | −0.453151 | + | 0.784881i | −0.109905 | + | 0.190362i | −0.915732 | − | 0.401790i | \(-0.868388\pi\) |
0.805826 | + | 0.592152i | \(0.201721\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.69028 | 1.53486 | 0.767428 | − | 0.641135i | \(-0.221536\pi\) | ||||
0.767428 | + | 0.641135i | \(0.221536\pi\) | |||||||
\(20\) | −0.248461 | − | 0.430346i | −0.0555575 | − | 0.0962284i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.64497 | − | 2.84917i | −0.350708 | − | 0.607444i | ||||
\(23\) | 1.79866 | + | 3.11538i | 0.375048 | + | 0.649601i | 0.990334 | − | 0.138702i | \(-0.0442930\pi\) |
−0.615287 | + | 0.788303i | \(0.710960\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.79015 | + | 3.10063i | 0.358030 | + | 0.620126i | ||||
\(26\) | −0.729501 | + | 5.55783i | −0.143067 | + | 1.08998i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.877433 | + | 0.669054i | 0.165819 | + | 0.126439i | ||||
\(29\) | 4.25772 | − | 7.37459i | 0.790639 | − | 1.36943i | −0.134932 | − | 0.990855i | \(-0.543082\pi\) |
0.925572 | − | 0.378573i | \(-0.123585\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.64390 | + | 4.57937i | 0.474859 | + | 0.822479i | 0.999585 | − | 0.0287913i | \(-0.00916583\pi\) |
−0.524727 | + | 0.851271i | \(0.675832\pi\) | |||||||
\(32\) | −1.16156 | + | 2.01189i | −0.205337 | + | 0.355655i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.40902 | −0.241644 | ||||||||
\(35\) | 2.50682 | + | 1.91148i | 0.423730 | + | 0.323099i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.49579 | − | 4.32284i | −0.410306 | − | 0.710670i | 0.584617 | − | 0.811309i | \(-0.301245\pi\) |
−0.994923 | + | 0.100639i | \(0.967911\pi\) | |||||||
\(38\) | 5.20065 | + | 9.00778i | 0.843656 | + | 1.46126i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.46615 | + | 2.53944i | −0.231818 | + | 0.401521i | ||||
\(41\) | 0.768181 | − | 1.33053i | 0.119970 | − | 0.207794i | −0.799786 | − | 0.600286i | \(-0.795054\pi\) |
0.919755 | + | 0.392492i | \(0.128387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.71636 | − | 4.70488i | −0.414242 | − | 0.717488i | 0.581107 | − | 0.813827i | \(-0.302620\pi\) |
−0.995349 | + | 0.0963397i | \(0.969286\pi\) | |||||||
\(44\) | 0.441269 | − | 0.764301i | 0.0665238 | − | 0.115223i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.79636 | + | 4.84344i | −0.412301 | + | 0.714126i | ||||
\(47\) | −1.59337 | + | 2.75979i | −0.232416 | + | 0.402557i | −0.958519 | − | 0.285030i | \(-0.907997\pi\) |
0.726102 | + | 0.687587i | \(0.241330\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77236 | − | 1.77063i | −0.967480 | − | 0.252947i | ||||
\(50\) | −2.78312 | + | 4.82051i | −0.393593 | + | 0.681723i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.38901 | + | 0.575982i | −0.192621 | + | 0.0798743i | ||||
\(53\) | −1.41239 | − | 2.44632i | −0.194006 | − | 0.336029i | 0.752568 | − | 0.658514i | \(-0.228815\pi\) |
−0.946574 | + | 0.322486i | \(0.895482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.26070 | − | 2.18360i | 0.169993 | − | 0.294436i | ||||
\(56\) | 0.830268 | − | 6.45801i | 0.110949 | − | 0.862988i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13.2389 | 1.73835 | ||||||||
\(59\) | −5.12298 | + | 8.87327i | −0.666956 | + | 1.15520i | 0.311795 | + | 0.950149i | \(0.399070\pi\) |
−0.978751 | + | 0.205052i | \(0.934264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.26845 | −1.05867 | −0.529333 | − | 0.848414i | \(-0.677558\pi\) | ||||
−0.529333 | + | 0.848414i | \(0.677558\pi\) | |||||||
\(62\) | −4.11044 | + | 7.11949i | −0.522026 | + | 0.904176i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.70861 | 0.713576 | ||||||||
\(65\) | −3.96840 | + | 1.64557i | −0.492219 | + | 0.204108i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.74363 | −0.457358 | −0.228679 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228679 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(68\) | −0.188987 | − | 0.327336i | −0.0229181 | − | 0.0396953i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.624956 | + | 4.86105i | −0.0746965 | + | 0.581007i | ||||
\(71\) | −1.26510 | − | 2.19122i | −0.150140 | − | 0.260050i | 0.781139 | − | 0.624357i | \(-0.214639\pi\) |
−0.931279 | + | 0.364307i | \(0.881306\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86522 | + | 4.96271i | 0.335349 | + | 0.580841i | 0.983552 | − | 0.180627i | \(-0.0578125\pi\) |
−0.648203 | + | 0.761468i | \(0.724479\pi\) | |||||||
\(74\) | 3.88018 | − | 6.72066i | 0.451061 | − | 0.781261i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.39510 | + | 2.41638i | −0.160028 | + | 0.277177i | ||||
\(77\) | −0.713925 | + | 5.55307i | −0.0813593 | + | 0.632831i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.03620 | + | 5.25885i | −0.341599 | + | 0.591667i | −0.984730 | − | 0.174089i | \(-0.944302\pi\) |
0.643131 | + | 0.765756i | \(0.277635\pi\) | |||||||
\(80\) | −5.55265 | −0.620805 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.38856 | 0.263773 | ||||||||
\(83\) | 11.6309 | 1.27665 | 0.638327 | − | 0.769766i | \(-0.279627\pi\) | ||||
0.638327 | + | 0.769766i | \(0.279627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.539935 | − | 0.935195i | −0.0585642 | − | 0.101436i | ||||
\(86\) | 4.22310 | − | 7.31462i | 0.455388 | − | 0.788755i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.20780 | −0.555153 | ||||||||
\(89\) | −8.87557 | − | 15.3729i | −0.940808 | − | 1.62953i | −0.763934 | − | 0.645295i | \(-0.776735\pi\) |
−0.176875 | − | 0.984233i | \(-0.556599\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.72222 | − | 6.76844i | 0.704680 | − | 0.709525i | ||||
\(92\) | −1.50027 | −0.156414 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.95437 | −0.511004 | ||||||||
\(95\) | −3.98577 | + | 6.90356i | −0.408932 | + | 0.708291i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.10217 | − | 5.37312i | −0.314978 | − | 0.545557i | 0.664455 | − | 0.747328i | \(-0.268664\pi\) |
−0.979433 | + | 0.201771i | \(0.935330\pi\) | |||||||
\(98\) | −2.88048 | − | 10.4947i | −0.290972 | − | 1.06012i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.49317 | −0.149317 | ||||||||
\(101\) | 7.22266 | 0.718682 | 0.359341 | − | 0.933206i | \(-0.383001\pi\) | ||||
0.359341 | + | 0.933206i | \(0.383001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.96322 | + | 8.59656i | −0.489041 | + | 0.847044i | −0.999921 | − | 0.0126084i | \(-0.995987\pi\) |
0.510879 | + | 0.859652i | \(0.329320\pi\) | |||||||
\(104\) | 7.04170 | + | 5.39894i | 0.690496 | + | 0.529409i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.19582 | − | 3.80327i | 0.213277 | − | 0.369406i | ||||
\(107\) | −1.10003 | − | 1.90531i | −0.106344 | − | 0.184193i | 0.807942 | − | 0.589261i | \(-0.200581\pi\) |
−0.914287 | + | 0.405068i | \(0.867248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.87291 | − | 11.9042i | −0.658305 | − | 1.14022i | −0.981054 | − | 0.193734i | \(-0.937940\pi\) |
0.322749 | − | 0.946485i | \(-0.395393\pi\) | |||||||
\(110\) | 3.91999 | 0.373757 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.3767 | − | 4.75293i | 1.07500 | − | 0.449110i | ||||
\(113\) | −8.04736 | − | 13.9384i | −0.757032 | − | 1.31122i | −0.944358 | − | 0.328920i | \(-0.893315\pi\) |
0.187326 | − | 0.982298i | \(-0.440018\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.28626 | −0.399696 | ||||||||
\(116\) | 1.77569 | + | 3.07558i | 0.164869 | + | 0.285561i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.9293 | −1.46641 | ||||||||
\(119\) | 1.90677 | + | 1.45394i | 0.174793 | + | 0.133282i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.52196 | −0.592905 | ||||||||
\(122\) | −6.42743 | − | 11.1326i | −0.581912 | − | 1.00790i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.20528 | −0.198040 | ||||||||
\(125\) | −10.2235 | −0.914420 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.83921 | − | 13.5779i | 0.695617 | − | 1.20484i | −0.274355 | − | 0.961628i | \(-0.588464\pi\) |
0.969972 | − | 0.243216i | \(-0.0782023\pi\) | |||||||
\(128\) | 6.76067 | + | 11.7098i | 0.597565 | + | 1.03501i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.30041 | − | 4.06387i | −0.464876 | − | 0.356425i | ||||
\(131\) | −4.76884 | + | 8.25988i | −0.416656 | + | 0.721669i | −0.995601 | − | 0.0936976i | \(-0.970131\pi\) |
0.578945 | + | 0.815367i | \(0.303465\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.25711 | − | 17.5563i | 0.195716 | − | 1.52233i | ||||
\(134\) | −2.91009 | − | 5.04042i | −0.251393 | − | 0.435426i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.11520 | + | 1.93158i | −0.0956277 | + | 0.165632i | ||||
\(137\) | −1.38231 | + | 2.39422i | −0.118098 | + | 0.204552i | −0.919014 | − | 0.394225i | \(-0.871013\pi\) |
0.800916 | + | 0.598777i | \(0.204346\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3983 | + | 19.7425i | 0.966795 | + | 1.67454i | 0.704714 | + | 0.709492i | \(0.251075\pi\) |
0.262081 | + | 0.965046i | \(0.415591\pi\) | |||||||
\(140\) | −1.21312 | + | 0.506812i | −0.102527 | + | 0.0428335i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.96684 | − | 3.40666i | 0.165053 | − | 0.285881i | ||||
\(143\) | −6.05497 | − | 4.64240i | −0.506342 | − | 0.388217i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.07312 | + | 8.78691i | 0.421300 | + | 0.729713i | ||||
\(146\) | −4.45452 | + | 7.71546i | −0.368659 | + | 0.638536i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.08175 | 0.171119 | ||||||||
\(149\) | 14.4116 | 1.18065 | 0.590323 | − | 0.807167i | \(-0.299000\pi\) | ||||
0.590323 | + | 0.807167i | \(0.299000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.62901 | − | 13.2138i | −0.620840 | − | 1.07533i | −0.989330 | − | 0.145695i | \(-0.953458\pi\) |
0.368489 | − | 0.929632i | \(-0.379875\pi\) | |||||||
\(152\) | 16.4647 | 1.33546 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.03161 | + | 3.35542i | −0.647206 | + | 0.270387i | ||||
\(155\) | −6.30048 | −0.506067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.70745 | + | 9.88559i | 0.455504 | + | 0.788956i | 0.998717 | − | 0.0506387i | \(-0.0161257\pi\) |
−0.543213 | + | 0.839595i | \(0.682792\pi\) | |||||||
\(158\) | −9.44068 | −0.751060 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.38402 | − | 2.39719i | −0.109416 | − | 0.189514i | ||||
\(161\) | 8.78205 | − | 3.66893i | 0.692122 | − | 0.289152i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.4077 | −1.12850 | −0.564249 | − | 0.825605i | \(-0.690834\pi\) | ||||
−0.564249 | + | 0.825605i | \(0.690834\pi\) | |||||||
\(164\) | 0.320371 | + | 0.554899i | 0.0250168 | + | 0.0433303i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.04118 | + | 15.6598i | 0.701731 | + | 1.21543i | ||||
\(167\) | 3.88595 | − | 6.73066i | 0.300704 | − | 0.520834i | −0.675592 | − | 0.737276i | \(-0.736112\pi\) |
0.976296 | + | 0.216442i | \(0.0694452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.37442 | + | 12.5544i | 0.259571 | + | 0.965724i | ||||
\(170\) | 0.839430 | − | 1.45394i | 0.0643813 | − | 0.111512i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.26573 | 0.172760 | ||||||||
\(173\) | −6.09461 | −0.463365 | −0.231682 | − | 0.972791i | \(-0.574423\pi\) | ||||
−0.231682 | + | 0.972791i | \(0.574423\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.74048 | − | 3.65156i | 0.660718 | − | 0.276032i | ||||
\(176\) | −4.93078 | − | 8.54037i | −0.371672 | − | 0.643754i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.7987 | − | 23.9001i | 1.03426 | − | 1.79139i | ||||
\(179\) | −18.5298 | −1.38498 | −0.692490 | − | 0.721428i | \(-0.743486\pi\) | ||||
−0.692490 | + | 0.721428i | \(0.743486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.60520 | −0.416631 | −0.208316 | − | 0.978062i | \(-0.566798\pi\) | ||||
−0.208316 | + | 0.978062i | \(0.566798\pi\) | |||||||
\(182\) | 14.3385 | + | 3.78938i | 1.06284 | + | 0.280887i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.42650 | + | 7.66692i | 0.326326 | + | 0.565212i | ||||
\(185\) | 5.94753 | 0.437271 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.958931 | − | 1.66092i | 0.0701240 | − | 0.121458i | ||||
\(188\) | −0.664516 | − | 1.15097i | −0.0484648 | − | 0.0839435i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.3933 | −0.899102 | ||||||||
\(191\) | −0.503703 | −0.0364466 | −0.0182233 | − | 0.999834i | \(-0.505801\pi\) | ||||
−0.0182233 | + | 0.999834i | \(0.505801\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.71244 | −0.267227 | −0.133614 | − | 0.991033i | \(-0.542658\pi\) | ||||
−0.133614 | + | 0.991033i | \(0.542658\pi\) | |||||||
\(194\) | 4.82290 | − | 8.35351i | 0.346264 | − | 0.599747i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.05172 | − | 2.07680i | 0.146552 | − | 0.148343i | ||||
\(197\) | −3.72225 | + | 6.44713i | −0.265200 | + | 0.459339i | −0.967616 | − | 0.252427i | \(-0.918771\pi\) |
0.702416 | + | 0.711766i | \(0.252105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.75278 | + | 6.50001i | −0.266028 | + | 0.460773i | −0.967832 | − | 0.251596i | \(-0.919045\pi\) |
0.701805 | + | 0.712369i | \(0.252378\pi\) | |||||||
\(200\) | 4.40554 | + | 7.63062i | 0.311519 | + | 0.539566i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.61449 | + | 9.72458i | 0.395034 | + | 0.684219i | ||||
\(203\) | −17.9156 | − | 13.6609i | −1.25743 | − | 0.958807i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.915297 | + | 1.58534i | 0.0639271 | + | 0.110725i | ||||
\(206\) | −15.4325 | −1.07523 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.18668 | + | 16.6596i | −0.151619 | + | 1.15513i | ||||
\(209\) | −14.1576 | −0.979299 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.89531 | + | 3.28278i | −0.130479 | + | 0.225996i | −0.923861 | − | 0.382728i | \(-0.874985\pi\) |
0.793383 | + | 0.608723i | \(0.208318\pi\) | |||||||
\(212\) | 1.17807 | 0.0809105 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.71020 | − | 2.96216i | 0.116907 | − | 0.202489i | ||||
\(215\) | 6.47316 | 0.441466 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.9089 | − | 5.39305i | 0.876317 | − | 0.366104i | ||||
\(218\) | 10.6852 | − | 18.5073i | 0.723695 | − | 1.25348i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.525777 | + | 0.910673i | 0.0354479 | + | 0.0613975i | ||||
\(221\) | −3.01849 | + | 1.25168i | −0.203046 | + | 0.0841970i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.43440 | + | 4.21650i | −0.163019 | + | 0.282358i | −0.935950 | − | 0.352133i | \(-0.885457\pi\) |
0.772931 | + | 0.634490i | \(0.218790\pi\) | |||||||
\(224\) | 4.88762 | + | 3.72687i | 0.326568 | + | 0.249012i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.5111 | − | 21.6699i | 0.832228 | − | 1.44146i | ||||
\(227\) | 12.0884 | − | 20.9376i | 0.802332 | − | 1.38968i | −0.115745 | − | 0.993279i | \(-0.536925\pi\) |
0.918077 | − | 0.396402i | \(-0.129741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.8561 | − | 18.8034i | 0.717394 | − | 1.24256i | −0.244635 | − | 0.969615i | \(-0.578668\pi\) |
0.962029 | − | 0.272947i | \(-0.0879985\pi\) | |||||||
\(230\) | −3.33190 | − | 5.77101i | −0.219699 | − | 0.380529i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.4782 | − | 18.1488i | 0.687928 | − | 1.19153i | ||||
\(233\) | 1.89842 | − | 3.28816i | 0.124370 | − | 0.215414i | −0.797117 | − | 0.603825i | \(-0.793642\pi\) |
0.921486 | + | 0.388411i | \(0.126976\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.89851 | − | 3.28832i | −0.123845 | − | 0.214507i | ||||
\(236\) | −2.13655 | − | 3.70061i | −0.139077 | − | 0.240889i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.475362 | + | 3.69748i | −0.0308131 | + | 0.239672i | ||||
\(239\) | −21.9100 | −1.41724 | −0.708619 | − | 0.705592i | \(-0.750681\pi\) | ||||
−0.708619 | + | 0.705592i | \(0.750681\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3744 | − | 17.9690i | 0.668273 | − | 1.15748i | −0.310114 | − | 0.950699i | \(-0.600367\pi\) |
0.978387 | − | 0.206783i | \(-0.0662994\pi\) | |||||||
\(242\) | −5.06980 | − | 8.78115i | −0.325899 | − | 0.564474i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.72418 | − | 2.98637i | 0.110380 | − | 0.191183i | ||||
\(245\) | 5.86175 | − | 5.93340i | 0.374493 | − | 0.379071i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.1431 | + | 14.6772i | 1.21805 | + | 0.933887i | ||||
\(248\) | 6.50661 | + | 11.2698i | 0.413170 | + | 0.715632i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.94719 | − | 13.7649i | −0.502624 | − | 0.870571i | ||||
\(251\) | 6.62891 | + | 11.4816i | 0.418413 | + | 0.724713i | 0.995780 | − | 0.0917718i | \(-0.0292530\pi\) |
−0.577367 | + | 0.816485i | \(0.695920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.80622 | − | 6.59257i | −0.239295 | − | 0.414472i | ||||
\(254\) | 24.3750 | 1.52943 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.80213 | + | 8.31753i | −0.300133 | + | 0.519845i | ||||
\(257\) | −6.58555 | − | 11.4065i | −0.410795 | − | 0.711518i | 0.584182 | − | 0.811623i | \(-0.301416\pi\) |
−0.994977 | + | 0.100105i | \(0.968082\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.1858 | + | 5.09094i | −0.757189 | + | 0.316336i | ||||
\(260\) | 0.233169 | − | 1.77644i | 0.0144605 | − | 0.110170i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.8281 | −0.916084 | ||||||||
\(263\) | 19.1406 | 1.18026 | 0.590129 | − | 0.807309i | \(-0.299077\pi\) | ||||
0.590129 | + | 0.807309i | \(0.299077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.36575 | 0.206756 | ||||||||
\(266\) | 25.3924 | − | 10.6083i | 1.55691 | − | 0.650438i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.780643 | − | 1.35211i | 0.0476854 | − | 0.0825935i | ||||
\(269\) | −14.2411 | + | 24.6663i | −0.868296 | + | 1.50393i | −0.00455867 | + | 0.999990i | \(0.501451\pi\) |
−0.863737 | + | 0.503943i | \(0.831882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.97371 | − | 15.5429i | −0.545114 | − | 0.944165i | −0.998600 | − | 0.0529014i | \(-0.983153\pi\) |
0.453486 | − | 0.891263i | \(-0.350180\pi\) | |||||||
\(272\) | −4.22353 | −0.256089 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29811 | −0.259658 | ||||||||
\(275\) | −3.78821 | − | 6.56137i | −0.228437 | − | 0.395665i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.71943 | + | 11.6384i | −0.403732 | + | 0.699284i | −0.994173 | − | 0.107797i | \(-0.965620\pi\) |
0.590441 | + | 0.807081i | \(0.298954\pi\) | |||||||
\(278\) | −17.7209 | + | 30.6934i | −1.06283 | + | 1.84087i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.16925 | + | 4.70413i | 0.368683 | + | 0.281126i | ||||
\(281\) | 29.9530 | 1.78685 | 0.893424 | − | 0.449214i | \(-0.148296\pi\) | ||||
0.893424 | + | 0.449214i | \(0.148296\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.89122 | −0.587972 | −0.293986 | − | 0.955810i | \(-0.594982\pi\) | ||||
−0.293986 | + | 0.955810i | \(0.594982\pi\) | |||||||
\(284\) | 1.05523 | 0.0626161 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.54373 | − | 11.7611i | 0.0912824 | − | 0.695451i | ||||
\(287\) | −3.23235 | − | 2.46471i | −0.190800 | − | 0.145487i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.08931 | + | 14.0111i | 0.475842 | + | 0.824182i | ||||
\(290\) | −7.88712 | + | 13.6609i | −0.463148 | + | 0.802195i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.38989 | −0.139858 | ||||||||
\(293\) | 3.95529 | + | 6.85076i | 0.231071 | + | 0.400226i | 0.958123 | − | 0.286356i | \(-0.0924438\pi\) |
−0.727053 | + | 0.686581i | \(0.759111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.10409 | − | 10.5726i | −0.355394 | − | 0.615561i | ||||
\(296\) | −6.14212 | − | 10.6385i | −0.357003 | − | 0.618348i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.2028 | + | 19.4038i | 0.648959 | + | 1.12403i | ||||
\(299\) | −1.68797 | + | 12.8601i | −0.0976175 | + | 0.743716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.2628 | + | 5.54086i | −0.764452 | + | 0.319370i | ||||
\(302\) | 11.8607 | − | 20.5434i | 0.682508 | − | 1.18214i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.5889 | + | 27.0008i | 0.894086 | + | 1.54860i | ||||
\(305\) | 4.92598 | − | 8.53204i | 0.282061 | − | 0.488543i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.27238 | 0.0726187 | 0.0363094 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363094 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(308\) | −1.85677 | − | 1.41581i | −0.105799 | − | 0.0806733i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.89763 | − | 8.48295i | −0.278167 | − | 0.481799i | ||||
\(311\) | 12.3817 | + | 21.4458i | 0.702103 | + | 1.21608i | 0.967727 | + | 0.252002i | \(0.0810888\pi\) |
−0.265624 | + | 0.964077i | \(0.585578\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.18826 | + | 2.05812i | −0.0671642 | + | 0.116332i | −0.897652 | − | 0.440705i | \(-0.854728\pi\) |
0.830488 | + | 0.557037i | \(0.188062\pi\) | |||||||
\(314\) | −8.87330 | + | 15.3690i | −0.500749 | + | 0.867323i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.26625 | − | 2.19321i | −0.0712322 | − | 0.123378i | ||||
\(317\) | −9.88979 | + | 17.1296i | −0.555466 | + | 0.962096i | 0.442401 | + | 0.896817i | \(0.354127\pi\) |
−0.997867 | + | 0.0652782i | \(0.979207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00993 | + | 15.6057i | −0.504459 | + | 0.873749i | ||||
\(320\) | −3.40093 | + | 5.89059i | −0.190118 | + | 0.329294i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.7665 | + | 8.97212i | 0.655722 | + | 0.499997i | ||||
\(323\) | −3.03171 | + | 5.25108i | −0.168689 | + | 0.292178i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.67997 | + | 12.7992i | −0.0931882 | + | 0.709970i | ||||
\(326\) | −11.1997 | − | 19.3985i | −0.620295 | − | 1.07438i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.89049 | − | 3.27442i | 0.104385 | − | 0.180799i | ||||
\(329\) | 6.70456 | + | 5.11231i | 0.369634 | + | 0.281851i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.92773 | 0.215888 | 0.107944 | − | 0.994157i | \(-0.465573\pi\) | ||||
0.107944 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(332\) | −2.42533 | + | 4.20080i | −0.133107 | + | 0.230549i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0829 | 0.661145 | ||||||||
\(335\) | 2.23029 | − | 3.86298i | 0.121854 | − | 0.211057i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.14099 | −0.388995 | −0.194497 | − | 0.980903i | \(-0.562308\pi\) | ||||
−0.194497 | + | 0.980903i | \(0.562308\pi\) | |||||||
\(338\) | −14.2802 | + | 14.3024i | −0.776738 | + | 0.777948i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.450361 | 0.0244243 | ||||||||
\(341\) | −5.59486 | − | 9.69059i | −0.302979 | − | 0.524775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.93120 | + | 17.1744i | −0.374250 | + | 0.927328i | ||||
\(344\) | −6.68494 | − | 11.5787i | −0.360428 | − | 0.624280i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.73761 | − | 8.20578i | −0.254695 | − | 0.441145i | ||||
\(347\) | 5.03498 | − | 8.72085i | 0.270292 | − | 0.468160i | −0.698644 | − | 0.715469i | \(-0.746213\pi\) |
0.968937 | + | 0.247309i | \(0.0795464\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.14418 | − | 5.44588i | 0.168304 | − | 0.291512i | −0.769520 | − | 0.638623i | \(-0.779504\pi\) |
0.937824 | + | 0.347112i | \(0.112838\pi\) | |||||||
\(350\) | 11.7108 | + | 8.92964i | 0.625969 | + | 0.477310i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.45803 | − | 4.25743i | 0.131013 | − | 0.226922i | ||||
\(353\) | −34.1672 | −1.81854 | −0.909269 | − | 0.416210i | \(-0.863358\pi\) | ||||
−0.909269 | + | 0.416210i | \(0.863358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.01477 | 0.160007 | ||||||||
\(356\) | 7.40313 | 0.392365 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.4040 | − | 24.9484i | −0.761274 | − | 1.31857i | ||||
\(359\) | 9.34327 | − | 16.1830i | 0.493119 | − | 0.854107i | −0.506850 | − | 0.862034i | \(-0.669190\pi\) |
0.999969 | + | 0.00792750i | \(0.00252343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.7599 | 1.35578 | ||||||||
\(362\) | −4.35716 | − | 7.54683i | −0.229007 | − | 0.396653i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.04285 | + | 3.83930i | 0.0546602 | + | 0.201234i | ||||
\(365\) | −6.82788 | −0.357388 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.0611 | −1.62137 | −0.810687 | − | 0.585479i | \(-0.800906\pi\) | ||||
−0.810687 | + | 0.585479i | \(0.800906\pi\) | |||||||
\(368\) | −8.38209 | + | 14.5182i | −0.436946 | + | 0.756813i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.62327 | + | 8.00775i | 0.240353 | + | 0.416303i | ||||
\(371\) | −6.89603 | + | 2.88100i | −0.358024 | + | 0.149574i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.93704 | −0.152074 | −0.0760371 | − | 0.997105i | \(-0.524227\pi\) | ||||
−0.0760371 | + | 0.997105i | \(0.524227\pi\) | |||||||
\(374\) | 2.98168 | 0.154179 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.92126 | + | 6.79182i | −0.202223 | + | 0.350261i | ||||
\(377\) | 28.3612 | − | 11.7605i | 1.46068 | − | 0.605698i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.04254 | + | 8.73394i | −0.259018 | + | 0.448632i | −0.965979 | − | 0.258620i | \(-0.916732\pi\) |
0.706961 | + | 0.707252i | \(0.250066\pi\) | |||||||
\(380\) | −1.66227 | − | 2.87914i | −0.0852727 | − | 0.147697i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.391550 | − | 0.678184i | −0.0200334 | − | 0.0346989i | ||||
\(383\) | −3.68931 | −0.188515 | −0.0942576 | − | 0.995548i | \(-0.530048\pi\) | ||||
−0.0942576 | + | 0.995548i | \(0.530048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.30477 | − | 4.04496i | −0.270356 | − | 0.206150i | ||||
\(386\) | −2.88584 | − | 4.99842i | −0.146885 | − | 0.254413i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.58753 | 0.131362 | ||||||||
\(389\) | 11.3333 | + | 19.6299i | 0.574623 | + | 0.995277i | 0.996082 | + | 0.0884295i | \(0.0281848\pi\) |
−0.421459 | + | 0.906847i | \(0.638482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.26027 | −0.164879 | ||||||||
\(392\) | −16.6667 | − | 4.35750i | −0.841796 | − | 0.220087i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.5739 | −0.583084 | ||||||||
\(395\) | −3.61767 | − | 6.26598i | −0.182025 | − | 0.315276i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.1360 | −1.46229 | −0.731146 | − | 0.682221i | \(-0.761014\pi\) | ||||
−0.731146 | + | 0.682221i | \(0.761014\pi\) | |||||||
\(398\) | −11.6688 | −0.584904 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.34241 | + | 14.4495i | −0.417120 | + | 0.722474i | ||||
\(401\) | 4.06026 | + | 7.03258i | 0.202760 | + | 0.351190i | 0.949417 | − | 0.314019i | \(-0.101676\pi\) |
−0.746657 | + | 0.665209i | \(0.768342\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.48118 | + | 18.9033i | −0.123596 | + | 0.941641i | ||||
\(404\) | −1.50611 | + | 2.60866i | −0.0749318 | + | 0.129786i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.46641 | − | 34.7408i | 0.221664 | − | 1.72416i | ||||
\(407\) | 5.28144 | + | 9.14773i | 0.261791 | + | 0.453436i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.16131 | − | 7.20759i | 0.205763 | − | 0.356393i | −0.744612 | − | 0.667497i | \(-0.767366\pi\) |
0.950376 | + | 0.311105i | \(0.100699\pi\) | |||||||
\(410\) | −1.42300 | + | 2.46471i | −0.0702769 | + | 0.121723i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.06992 | − | 3.58520i | −0.101978 | − | 0.176630i | ||||
\(413\) | 21.5565 | + | 16.4371i | 1.06072 | + | 0.808816i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.92915 | + | 12.0016i | −0.340139 | + | 0.589138i | ||||
\(416\) | −7.73731 | + | 3.20843i | −0.379353 | + | 0.157306i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.0053 | − | 19.0617i | −0.538286 | − | 0.932339i | ||||
\(419\) | −6.50832 | + | 11.2727i | −0.317952 | + | 0.550710i | −0.980061 | − | 0.198699i | \(-0.936329\pi\) |
0.662108 | + | 0.749408i | \(0.269662\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.89681 | −0.433604 | −0.216802 | − | 0.976216i | \(-0.569563\pi\) | ||||
−0.216802 | + | 0.976216i | \(0.569563\pi\) | |||||||
\(422\) | −5.89323 | −0.286878 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.47587 | − | 6.02038i | −0.168803 | − | 0.292376i | ||||
\(425\) | −3.24484 | −0.157398 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.78954 | + | 21.6977i | −0.134995 | + | 1.05002i | ||||
\(428\) | 0.917539 | 0.0443509 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.03187 | + | 8.71545i | 0.242658 | + | 0.420296i | ||||
\(431\) | 8.95743 | 0.431464 | 0.215732 | − | 0.976453i | \(-0.430786\pi\) | ||||
0.215732 | + | 0.976453i | \(0.430786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.0864547 | + | 0.149744i | 0.00415475 | + | 0.00719624i | 0.868095 | − | 0.496398i | \(-0.165344\pi\) |
−0.863941 | + | 0.503594i | \(0.832011\pi\) | |||||||
\(434\) | 17.2959 | + | 13.1883i | 0.830229 | + | 0.633060i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.73271 | 0.274547 | ||||||||
\(437\) | 12.0336 | + | 20.8428i | 0.575644 | + | 0.997045i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.77080 | − | 8.26327i | −0.227698 | − | 0.394384i | 0.729428 | − | 0.684058i | \(-0.239787\pi\) |
−0.957125 | + | 0.289674i | \(0.906453\pi\) | |||||||
\(440\) | 3.10257 | − | 5.37382i | 0.147909 | − | 0.256187i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.03166 | − | 3.09111i | −0.191767 | − | 0.147029i | ||||
\(443\) | −6.93676 | + | 12.0148i | −0.329576 | + | 0.570842i | −0.982428 | − | 0.186644i | \(-0.940239\pi\) |
0.652852 | + | 0.757485i | \(0.273572\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.1507 | 1.00264 | ||||||||
\(446\) | −7.56945 | −0.358424 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.92592 | − | 14.9803i | 0.0909912 | − | 0.707751i | ||||
\(449\) | −10.6456 | − | 18.4388i | −0.502398 | − | 0.870180i | −0.999996 | − | 0.00277167i | \(-0.999118\pi\) |
0.497598 | − | 0.867408i | \(-0.334216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.62558 | + | 2.81558i | −0.0765455 | + | 0.132581i | ||||
\(452\) | 6.71232 | 0.315721 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 37.5872 | 1.76406 | ||||||||
\(455\) | 2.97941 | + | 10.9689i | 0.139677 | + | 0.514228i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.84282 | − | 8.38801i | −0.226538 | − | 0.392375i | 0.730242 | − | 0.683189i | \(-0.239407\pi\) |
−0.956780 | + | 0.290814i | \(0.906074\pi\) | |||||||
\(458\) | 33.7558 | 1.57730 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.893795 | − | 1.54810i | 0.0416734 | − | 0.0721804i | ||||
\(461\) | −0.687178 | − | 1.19023i | −0.0320051 | − | 0.0554344i | 0.849579 | − | 0.527461i | \(-0.176856\pi\) |
−0.881584 | + | 0.472027i | \(0.843523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.7710 | 1.47653 | 0.738263 | − | 0.674513i | \(-0.235646\pi\) | ||||
0.738263 | + | 0.674513i | \(0.235646\pi\) | |||||||
\(464\) | 39.6834 | 1.84226 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.90290 | 0.273446 | ||||||||
\(467\) | −14.5605 | + | 25.2195i | −0.673778 | + | 1.16702i | 0.303046 | + | 0.952976i | \(0.401996\pi\) |
−0.976824 | + | 0.214042i | \(0.931337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.26299 | + | 9.82387i | −0.0583197 | + | 0.453624i | ||||
\(470\) | 2.95160 | − | 5.11231i | 0.136147 | − | 0.235813i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.6076 | + | 21.8370i | −0.580312 | + | 1.00513i | ||||
\(473\) | 5.74820 | + | 9.95618i | 0.264303 | + | 0.457786i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.9766 | + | 20.7441i | 0.549525 | + | 0.951804i | ||||
\(476\) | −0.922738 | + | 0.385498i | −0.0422936 | + | 0.0176693i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.0316 | − | 29.4995i | −0.779005 | − | 1.34928i | ||||
\(479\) | −9.72184 | −0.444202 | −0.222101 | − | 0.975024i | \(-0.571292\pi\) | ||||
−0.222101 | + | 0.975024i | \(0.571292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.34219 | − | 17.8444i | 0.106795 | − | 0.813633i | ||||
\(482\) | 32.2578 | 1.46930 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.36000 | − | 2.35558i | 0.0618180 | − | 0.107072i | ||||
\(485\) | 7.39254 | 0.335678 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.55666 | − | 14.8206i | 0.387739 | − | 0.671584i | −0.604406 | − | 0.796676i | \(-0.706589\pi\) |
0.992145 | + | 0.125093i | \(0.0399228\pi\) | |||||||
\(488\) | −20.3486 | −0.921137 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.5453 | + | 3.27996i | 0.566739 | + | 0.148174i | ||||
\(491\) | −12.8607 | + | 22.2753i | −0.580394 | + | 1.00527i | 0.415038 | + | 0.909804i | \(0.363768\pi\) |
−0.995432 | + | 0.0954681i | \(0.969565\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.85879 | + | 6.68361i | 0.173791 | + | 0.301015i | ||||
\(494\) | −4.88057 | + | 37.1835i | −0.219587 | + | 1.67296i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.3210 | + | 21.3407i | −0.553231 | + | 0.958224i | ||||
\(497\) | −6.17691 | + | 2.58057i | −0.277072 | + | 0.115754i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.70198 | + | 4.67996i | −0.120957 | + | 0.209504i | −0.920145 | − | 0.391577i | \(-0.871930\pi\) |
0.799188 | + | 0.601081i | \(0.205263\pi\) | |||||||
\(500\) | 2.13187 | − | 3.69250i | 0.0953400 | − | 0.165134i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.3059 | + | 17.8503i | −0.459974 | + | 0.796699i | ||||
\(503\) | −6.30847 | − | 10.9266i | −0.281281 | − | 0.487193i | 0.690420 | − | 0.723409i | \(-0.257426\pi\) |
−0.971700 | + | 0.236216i | \(0.924093\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.30294 | + | 7.45292i | −0.191478 | + | 0.331650i | ||||
\(506\) | 5.91749 | − | 10.2494i | 0.263064 | − | 0.455641i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.26935 | + | 5.66268i | 0.145054 | + | 0.251241i | ||||
\(509\) | −0.979379 | − | 1.69633i | −0.0434102 | − | 0.0751887i | 0.843504 | − | 0.537123i | \(-0.180489\pi\) |
−0.886914 | + | 0.461934i | \(0.847156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.9895 | − | 5.84450i | 0.618861 | − | 0.258546i | ||||
\(512\) | 12.1111 | 0.535240 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.2385 | − | 17.7335i | 0.451599 | − | 0.782193i | ||||
\(515\) | −5.91374 | − | 10.2429i | −0.260590 | − | 0.451356i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.37178 | − | 5.84010i | 0.148291 | − | 0.256847i | ||||
\(518\) | −16.3270 | − | 12.4495i | −0.717367 | − | 0.547001i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.76618 | + | 4.04974i | −0.428276 | + | 0.177593i | ||||
\(521\) | −19.5477 | − | 33.8576i | −0.856401 | − | 1.48333i | −0.875339 | − | 0.483509i | \(-0.839362\pi\) |
0.0189387 | − | 0.999821i | \(-0.493971\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.35634 | + | 7.54540i | 0.190489 | + | 0.329937i | 0.945413 | − | 0.325876i | \(-0.105659\pi\) |
−0.754923 | + | 0.655813i | \(0.772326\pi\) | |||||||
\(524\) | −1.98885 | − | 3.44479i | −0.0868834 | − | 0.150486i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.8788 | + | 25.7708i | 0.648746 | + | 1.12366i | ||||
\(527\) | −4.79235 | −0.208758 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.02961 | − | 8.71154i | 0.218679 | − | 0.378763i | ||||
\(530\) | 2.61634 | + | 4.53164i | 0.113647 | + | 0.196842i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.87028 | + | 4.47616i | 0.254509 | + | 0.194066i | ||||
\(533\) | 5.11694 | − | 2.12184i | 0.221639 | − | 0.0919072i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.62140 | 0.113333 | ||||||||
\(536\) | −9.21304 | −0.397943 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −44.2809 | −1.90909 | ||||||||
\(539\) | 14.3313 | + | 3.74690i | 0.617291 | + | 0.161390i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7497 | − | 18.6190i | 0.462165 | − | 0.800493i | −0.536904 | − | 0.843644i | \(-0.680406\pi\) |
0.999069 | + | 0.0431505i | \(0.0137395\pi\) | |||||||
\(542\) | 13.9513 | − | 24.1644i | 0.599260 | − | 1.03795i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.05273 | − | 1.82338i | −0.0451353 | − | 0.0781767i | ||||
\(545\) | 16.3783 | 0.701569 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.2968 | −1.29540 | −0.647699 | − | 0.761896i | \(-0.724269\pi\) | ||||
−0.647699 | + | 0.761896i | \(0.724269\pi\) | |||||||
\(548\) | −0.576493 | − | 0.998514i | −0.0246265 | − | 0.0426544i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.88947 | − | 10.2009i | 0.251128 | − | 0.434967i | ||||
\(551\) | 28.4854 | − | 49.3381i | 1.21352 | − | 2.10187i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7757 | + | 9.74164i | 0.543278 | + | 0.414257i | ||||
\(554\) | −20.8932 | −0.887668 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.50738 | −0.403203 | ||||||||
\(557\) | 17.6840 | 0.749296 | 0.374648 | − | 0.927167i | \(-0.377764\pi\) | ||||
0.374648 | + | 0.927167i | \(0.377764\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.54918 | − | 19.4214i | 0.107819 | − | 0.821437i | ||||
\(560\) | −1.87330 | + | 14.5710i | −0.0791616 | + | 0.615737i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.2838 | + | 40.3287i | 0.982167 | + | 1.70116i | ||||
\(563\) | −20.8695 | + | 36.1471i | −0.879545 | + | 1.52342i | −0.0277042 | + | 0.999616i | \(0.508820\pi\) |
−0.851841 | + | 0.523801i | \(0.824514\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.1770 | 0.806784 | ||||||||
\(566\) | −7.68887 | − | 13.3175i | −0.323187 | − | 0.559777i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.11340 | − | 5.39257i | −0.130636 | − | 0.226267i | ||||
\(569\) | 2.73388 | + | 4.73521i | 0.114610 | + | 0.198510i | 0.917624 | − | 0.397450i | \(-0.130105\pi\) |
−0.803014 | + | 0.595960i | \(0.796771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.67621 | − | 8.09944i | −0.195693 | − | 0.338951i | 0.751434 | − | 0.659808i | \(-0.229362\pi\) |
−0.947128 | + | 0.320857i | \(0.896029\pi\) | |||||||
\(572\) | 2.93934 | − | 1.21886i | 0.122900 | − | 0.0509630i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.805833 | − | 6.26795i | 0.0336348 | − | 0.261619i | ||||
\(575\) | −6.43976 | + | 11.1540i | −0.268557 | + | 0.465154i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.68462 | + | 2.91786i | 0.0701318 | + | 0.121472i | 0.898959 | − | 0.438033i | \(-0.144325\pi\) |
−0.828827 | + | 0.559505i | \(0.810991\pi\) | |||||||
\(578\) | −12.5763 | + | 21.7829i | −0.523107 | + | 0.906048i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.23151 | −0.175704 | ||||||||
\(581\) | 3.92392 | − | 30.5212i | 0.162792 | − | 1.26623i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.98881 | + | 5.17676i | 0.123784 | + | 0.214400i | ||||
\(584\) | 7.05128 | + | 12.2132i | 0.291784 | + | 0.505385i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.14924 | + | 10.6508i | −0.254023 | + | 0.439980i | ||||
\(587\) | −6.57639 | + | 11.3906i | −0.271437 | + | 0.470142i | −0.969230 | − | 0.246157i | \(-0.920832\pi\) |
0.697793 | + | 0.716299i | \(0.254165\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.6884 | + | 30.6373i | 0.728840 | + | 1.26239i | ||||
\(590\) | 9.48995 | − | 16.4371i | 0.390695 | − | 0.676704i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.6308 | − | 20.1452i | 0.478024 | − | 0.827961i | ||||
\(593\) | 19.2958 | − | 33.4213i | 0.792384 | − | 1.37245i | −0.132102 | − | 0.991236i | \(-0.542173\pi\) |
0.924487 | − | 0.381214i | \(-0.124494\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.63625 | + | 1.10136i | −0.108076 | + | 0.0451515i | ||||
\(596\) | −3.00519 | + | 5.20515i | −0.123097 | + | 0.213211i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.6269 | + | 7.72400i | −0.761710 | + | 0.315858i | ||||
\(599\) | 9.20762 | + | 15.9481i | 0.376213 | + | 0.651620i | 0.990508 | − | 0.137457i | \(-0.0438927\pi\) |
−0.614295 | + | 0.789077i | \(0.710559\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7018 | − | 35.8566i | 0.844445 | − | 1.46262i | −0.0416571 | − | 0.999132i | \(-0.513264\pi\) |
0.886102 | − | 0.463490i | \(-0.153403\pi\) | |||||||
\(602\) | −17.7699 | − | 13.5498i | −0.724248 | − | 0.552248i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.36338 | 0.258922 | ||||||||
\(605\) | 3.88549 | − | 6.72987i | 0.157968 | − | 0.273608i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.3051 | 0.499449 | 0.249724 | − | 0.968317i | \(-0.419660\pi\) | ||||
0.249724 | + | 0.968317i | \(0.419660\pi\) | |||||||
\(608\) | −7.77119 | + | 13.4601i | −0.315163 | + | 0.545879i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.3167 | 0.620155 | ||||||||
\(611\) | −10.6136 | + | 4.40114i | −0.429380 | + | 0.178051i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.2224 | 1.05911 | 0.529556 | − | 0.848275i | \(-0.322358\pi\) | ||||
0.529556 | + | 0.848275i | \(0.322358\pi\) | |||||||
\(614\) | 0.989078 | + | 1.71313i | 0.0399160 | + | 0.0691365i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.75696 | + | 13.6661i | −0.0707900 | + | 0.550621i | ||||
\(617\) | −9.41259 | − | 16.3031i | −0.378936 | − | 0.656337i | 0.611971 | − | 0.790880i | \(-0.290377\pi\) |
−0.990908 | + | 0.134543i | \(0.957043\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.90415 | + | 13.6904i | 0.317695 | + | 0.550263i | 0.980007 | − | 0.198965i | \(-0.0637580\pi\) |
−0.662312 | + | 0.749228i | \(0.730425\pi\) | |||||||
\(620\) | 1.31381 | − | 2.27559i | 0.0527639 | − | 0.0913898i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.2497 | + | 33.3415i | −0.771843 | + | 1.33687i | ||||
\(623\) | −43.3353 | + | 18.1045i | −1.73619 | + | 0.725340i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.86003 | + | 4.95371i | −0.114401 | + | 0.198149i | ||||
\(626\) | −3.69473 | −0.147671 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.76060 | −0.189969 | ||||||||
\(629\) | 4.52389 | 0.180379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.33817 | + | 14.4421i | 0.331937 | + | 0.574933i | 0.982892 | − | 0.184184i | \(-0.0589644\pi\) |
−0.650954 | + | 0.759117i | \(0.725631\pi\) | |||||||
\(632\) | −7.47206 | + | 12.9420i | −0.297222 | + | 0.514804i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30.7511 | −1.22128 | ||||||||
\(635\) | 9.34050 | + | 16.1782i | 0.370667 | + | 0.642013i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.4935 | − | 19.9236i | −0.613877 | − | 0.789402i | ||||
\(638\) | −28.0152 | −1.10913 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.1108 | −0.636837 | ||||||||
\(641\) | 24.6232 | − | 42.6487i | 0.972559 | − | 1.68452i | 0.284792 | − | 0.958589i | \(-0.408075\pi\) |
0.687767 | − | 0.725932i | \(-0.258591\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.4355 | − | 37.1275i | −0.845335 | − | 1.46416i | −0.885330 | − | 0.464964i | \(-0.846067\pi\) |
0.0399940 | − | 0.999200i | \(-0.487266\pi\) | |||||||
\(644\) | −0.506149 | + | 3.93694i | −0.0199450 | + | 0.155137i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.42672 | −0.370889 | ||||||||
\(647\) | −4.25859 | −0.167422 | −0.0837112 | − | 0.996490i | \(-0.526677\pi\) | ||||
−0.0837112 | + | 0.996490i | \(0.526677\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.8409 | − | 18.7771i | 0.425544 | − | 0.737064i | ||||
\(650\) | −18.5387 | + | 7.68744i | −0.727148 | + | 0.301526i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.00437 | − | 5.20373i | 0.117660 | − | 0.203794i | ||||
\(653\) | −1.04776 | − | 1.81477i | −0.0410020 | − | 0.0710176i | 0.844796 | − | 0.535088i | \(-0.179722\pi\) |
−0.885798 | + | 0.464071i | \(0.846388\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.68213 | − | 9.84174i | −0.222019 | − | 0.384549i | ||||
\(656\) | 7.15971 | 0.279540 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.67146 | + | 13.0010i | −0.0651604 | + | 0.506833i | ||||
\(659\) | 12.7259 | + | 22.0419i | 0.495732 | + | 0.858632i | 0.999988 | − | 0.00492170i | \(-0.00156663\pi\) |
−0.504256 | + | 0.863554i | \(0.668233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.8108 | 1.08171 | 0.540857 | − | 0.841115i | \(-0.318100\pi\) | ||||
0.540857 | + | 0.841115i | \(0.318100\pi\) | |||||||
\(662\) | 3.05319 | + | 5.28829i | 0.118666 | + | 0.205535i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.6234 | 1.11080 | ||||||||
\(665\) | 16.7713 | + | 12.7883i | 0.650364 | + | 0.495911i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.6329 | 1.18611 | ||||||||
\(668\) | 1.62064 | + | 2.80703i | 0.0627044 | + | 0.108607i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.93481 | 0.267915 | ||||||||
\(671\) | 17.4972 | 0.675472 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.76033 | + | 13.4413i | −0.299139 | + | 0.518124i | −0.975939 | − | 0.218043i | \(-0.930033\pi\) |
0.676800 | + | 0.736167i | \(0.263366\pi\) | |||||||
\(674\) | −5.55100 | − | 9.61462i | −0.213817 | − | 0.370341i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.23802 | − | 1.39915i | −0.201462 | − | 0.0538136i | ||||
\(677\) | 17.2813 | − | 29.9321i | 0.664175 | − | 1.15038i | −0.315334 | − | 0.948981i | \(-0.602116\pi\) |
0.979508 | − | 0.201403i | \(-0.0645502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.1465 | + | 6.32783i | −0.581268 | + | 0.242840i | ||||
\(680\) | −1.32877 | − | 2.30150i | −0.0509562 | − | 0.0882587i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.69826 | − | 15.0658i | 0.333074 | − | 0.576900i | ||||
\(683\) | 23.5032 | − | 40.7087i | 0.899325 | − | 1.55768i | 0.0709661 | − | 0.997479i | \(-0.477392\pi\) |
0.828359 | − | 0.560198i | \(-0.189275\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.64703 | − | 2.85275i | −0.0629299 | − | 0.108998i | ||||
\(686\) | −28.5114 | + | 4.01821i | −1.08857 | + | 0.153416i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.6587 | − | 21.9255i | 0.482609 | − | 0.835904i | ||||
\(689\) | 1.32546 | − | 10.0982i | 0.0504960 | − | 0.384713i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.50301 | − | 16.4597i | −0.361512 | − | 0.626156i | 0.626698 | − | 0.779262i | \(-0.284406\pi\) |
−0.988210 | + | 0.153106i | \(0.951073\pi\) | |||||||
\(692\) | 1.27088 | − | 2.20123i | 0.0483117 | − | 0.0836784i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.6556 | 0.594280 | ||||||||
\(695\) | −27.1625 | −1.03033 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.696205 | + | 1.20586i | 0.0263706 | + | 0.0456753i | ||||
\(698\) | 9.77644 | 0.370044 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.503753 | + | 3.91830i | −0.0190401 | + | 0.148098i | ||||
\(701\) | 45.4648 | 1.71718 | 0.858591 | − | 0.512662i | \(-0.171341\pi\) | ||||
0.858591 | + | 0.512662i | \(0.171341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.6976 | − | 28.9210i | −0.629760 | − | 1.09078i | ||||
\(704\) | −12.0802 | −0.455290 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.5597 | − | 46.0027i | −0.999586 | − | 1.73133i | ||||
\(707\) | 2.43672 | − | 18.9534i | 0.0916423 | − | 0.712815i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.78779 | −0.367588 | −0.183794 | − | 0.982965i | \(-0.558838\pi\) | ||||
−0.183794 | + | 0.982965i | \(0.558838\pi\) | |||||||
\(710\) | 2.34351 | + | 4.05908i | 0.0879504 | + | 0.152334i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21.8427 | − | 37.8326i | −0.818589 | − | 1.41784i | ||||
\(713\) | −9.51099 | + | 16.4735i | −0.356189 | + | 0.616938i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.39768 | − | 3.48226i | 0.314055 | − | 0.130229i | ||||
\(716\) | 3.86393 | − | 6.69252i | 0.144402 | − | 0.250111i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.0517 | 1.08420 | ||||||||
\(719\) | 27.8403 | 1.03827 | 0.519133 | − | 0.854693i | \(-0.326255\pi\) | ||||
0.519133 | + | 0.854693i | \(0.326255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.8842 | + | 15.9245i | 0.777770 | + | 0.593059i | ||||
\(722\) | 20.0243 | + | 34.6830i | 0.745226 | + | 1.29077i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.16883 | − | 2.02447i | 0.0434391 | − | 0.0752388i | ||||
\(725\) | 30.4879 | 1.13229 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.5650 | −0.540186 | −0.270093 | − | 0.962834i | \(-0.587055\pi\) | ||||
−0.270093 | + | 0.962834i | \(0.587055\pi\) | |||||||
\(728\) | 16.5433 | − | 16.6571i | 0.613136 | − | 0.617352i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.30761 | − | 9.19305i | −0.196444 | − | 0.340250i | ||||
\(731\) | 4.92370 | 0.182109 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.83030 | + | 15.2945i | −0.326155 | + | 0.564916i | −0.981745 | − | 0.190200i | \(-0.939086\pi\) |
0.655591 | + | 0.755116i | \(0.272420\pi\) | |||||||
\(734\) | −24.1451 | − | 41.8206i | −0.891213 | − | 1.54363i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.35705 | −0.308045 | ||||||||
\(737\) | 7.92205 | 0.291812 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.96559 | 0.329804 | 0.164902 | − | 0.986310i | \(-0.447269\pi\) | ||||
0.164902 | + | 0.986310i | \(0.447269\pi\) | |||||||
\(740\) | −1.24021 | + | 2.14811i | −0.0455911 | + | 0.0789661i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.23955 | − | 7.04528i | −0.339195 | − | 0.258640i | ||||
\(743\) | −13.1839 | + | 22.8352i | −0.483671 | + | 0.837743i | −0.999824 | − | 0.0187532i | \(-0.994030\pi\) |
0.516153 | + | 0.856497i | \(0.327364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.58580 | + | 14.8710i | −0.314560 | + | 0.544833i | ||||
\(746\) | −2.28309 | − | 3.95442i | −0.0835898 | − | 0.144782i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.399923 | + | 0.692688i | 0.0146226 | + | 0.0253272i | ||||
\(749\) | −5.37095 | + | 2.24385i | −0.196250 | + | 0.0819887i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.1438 | + | 17.5696i | 0.370152 | + | 0.641123i | 0.989589 | − | 0.143924i | \(-0.0459721\pi\) |
−0.619436 | + | 0.785047i | \(0.712639\pi\) | |||||||
\(752\) | −14.8507 | −0.541550 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.8807 | + | 29.0435i | 1.37953 | + | 1.05770i | ||||
\(755\) | 18.1801 | 0.661642 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.4992 | + | 21.6493i | −0.454292 | + | 0.786857i | −0.998647 | − | 0.0519981i | \(-0.983441\pi\) |
0.544355 | + | 0.838855i | \(0.316774\pi\) | |||||||
\(758\) | −15.6791 | −0.569492 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.80895 | + | 16.9896i | −0.355808 | + | 0.616277i | ||||
\(761\) | −20.1422 | −0.730154 | −0.365077 | − | 0.930977i | \(-0.618957\pi\) | ||||
−0.365077 | + | 0.930977i | \(0.618957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.5572 | + | 14.0194i | −1.21485 | + | 0.507537i | ||||
\(764\) | 0.105035 | − | 0.181926i | 0.00380003 | − | 0.00658184i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.86786 | − | 4.96729i | −0.103620 | − | 0.179475i | ||||
\(767\) | −34.1248 | + | 14.1505i | −1.23217 | + | 0.510945i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.33610 | + | 7.51034i | −0.156364 | + | 0.270830i | −0.933555 | − | 0.358435i | \(-0.883311\pi\) |
0.777191 | + | 0.629265i | \(0.216644\pi\) | |||||||
\(770\) | 1.32249 | − | 10.2867i | 0.0476594 | − | 0.370706i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.774139 | − | 1.34085i | 0.0278619 | − | 0.0482582i | ||||
\(773\) | 1.17283 | − | 2.03141i | 0.0421839 | − | 0.0730647i | −0.844163 | − | 0.536087i | \(-0.819902\pi\) |
0.886346 | + | 0.463023i | \(0.153235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.46596 | + | 16.3955i | −0.340027 | + | 0.588945i | ||||
\(776\) | −7.63441 | − | 13.2232i | −0.274059 | − | 0.474685i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.6198 | + | 30.5184i | −0.631701 | + | 1.09414i | ||||
\(779\) | 5.13935 | − | 8.90161i | 0.184136 | − | 0.318933i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.67713 | + | 4.63693i | 0.0957953 | + | 0.165922i | ||||
\(782\) | −2.53435 | − | 4.38962i | −0.0906281 | − | 0.156973i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.63423 | − | 31.4578i | −0.308365 | − | 1.12349i | ||||
\(785\) | −13.6010 | −0.485440 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.0583 | − | 29.5459i | 0.608063 | − | 1.05320i | −0.383496 | − | 0.923543i | \(-0.625280\pi\) |
0.991559 | − | 0.129654i | \(-0.0413866\pi\) | |||||||
\(788\) | −1.55237 | − | 2.68878i | −0.0553009 | − | 0.0957840i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.62434 | − | 9.74164i | 0.200105 | − | 0.346592i | ||||
\(791\) | −39.2915 | + | 16.4151i | −1.39705 | + | 0.583653i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.6588 | − | 18.1394i | −0.840148 | − | 0.644149i | ||||
\(794\) | −22.6486 | − | 39.2286i | −0.803770 | − | 1.39217i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.56510 | − | 2.71084i | −0.0554736 | − | 0.0960830i | ||||
\(797\) | −17.0422 | − | 29.5180i | −0.603666 | − | 1.04558i | −0.992261 | − | 0.124172i | \(-0.960373\pi\) |
0.388594 | − | 0.921409i | \(-0.372961\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.44407 | − | 2.50121i | −0.0510876 | − | 0.0884863i | ||||
\(800\) | −8.31749 | −0.294068 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.31243 | + | 10.9335i | −0.222900 | + | 0.386074i | ||||
\(803\) | −6.06320 | − | 10.5018i | −0.213966 | − | 0.370600i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.44606 | + | 11.2478i | −0.0509670 | + | 0.396433i | ||||
\(806\) | −27.3801 | + | 11.3537i | −0.964423 | + | 0.399917i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.7749 | 0.625319 | ||||||||
\(809\) | 26.5205 | 0.932413 | 0.466206 | − | 0.884676i | \(-0.345620\pi\) | ||||
0.466206 | + | 0.884676i | \(0.345620\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.5463 | 1.84515 | 0.922575 | − | 0.385818i | \(-0.126081\pi\) | ||||
0.922575 | + | 0.385818i | \(0.126081\pi\) | |||||||
\(812\) | 8.66987 | − | 3.62207i | 0.304253 | − | 0.127110i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.21099 | + | 14.2219i | −0.287795 | + | 0.498476i | ||||
\(815\) | 8.58347 | − | 14.8670i | 0.300666 | − | 0.520768i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.1732 | − | 31.4770i | −0.635801 | − | 1.10124i | ||||
\(818\) | 12.9391 | 0.452403 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.763451 | −0.0266609 | ||||||||
\(821\) | −15.3773 | − | 26.6343i | −0.536671 | − | 0.929542i | −0.999080 | − | 0.0428753i | \(-0.986348\pi\) |
0.462409 | − | 0.886667i | \(-0.346985\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.8519 | − | 25.7243i | 0.517705 | − | 0.896691i | −0.482084 | − | 0.876125i | \(-0.660120\pi\) |
0.999789 | − | 0.0205659i | \(-0.00654678\pi\) | |||||||
\(824\) | −12.2144 | + | 21.1560i | −0.425510 | + | 0.737006i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.37408 | + | 41.8008i | −0.186988 | + | 1.45444i | ||||
\(827\) | −14.8351 | −0.515866 | −0.257933 | − | 0.966163i | \(-0.583041\pi\) | ||||
−0.257933 | + | 0.966163i | \(0.583041\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.5849 | 0.506554 | 0.253277 | − | 0.967394i | \(-0.418492\pi\) | ||||
0.253277 | + | 0.967394i | \(0.418492\pi\) | |||||||
\(830\) | −21.5453 | −0.747849 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.3342 | + | 12.5236i | 0.566287 | + | 0.434177i | ||||
\(833\) | 4.45864 | − | 4.51314i | 0.154483 | − | 0.156371i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.63015 | + | 8.01966i | 0.160233 | + | 0.277532i | ||||
\(836\) | 2.95221 | − | 5.11339i | 0.102104 | − | 0.176850i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.2368 | −0.699069 | ||||||||
\(839\) | 18.4043 | + | 31.8772i | 0.635386 | + | 1.10052i | 0.986433 | + | 0.164164i | \(0.0524925\pi\) |
−0.351047 | + | 0.936358i | \(0.614174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.7564 | − | 37.6832i | −0.750221 | − | 1.29942i | ||||
\(842\) | −6.91588 | − | 11.9787i | −0.238337 | − | 0.412812i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.790442 | − | 1.36909i | −0.0272082 | − | 0.0471259i | ||||
\(845\) | −14.9650 | − | 3.99737i | −0.514811 | − | 0.137514i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.20032 | + | 17.1146i | −0.0756040 | + | 0.588065i | ||||
\(848\) | 6.58196 | − | 11.4003i | 0.226025 | − | 0.391488i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.52235 | − | 4.36884i | −0.0865160 | − | 0.149850i | ||||
\(851\) | 8.97819 | − | 15.5507i | 0.307768 | − | 0.533070i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.10728 | −0.140630 | −0.0703152 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703152 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(854\) | −31.3822 | + | 13.1107i | −1.07388 | + | 0.448640i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.70717 | − | 4.68895i | −0.0925291 | − | 0.160265i | ||||
\(857\) | −19.1656 | − | 33.1958i | −0.654684 | − | 1.13395i | −0.981973 | − | 0.189022i | \(-0.939468\pi\) |
0.327288 | − | 0.944925i | \(-0.393865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.7185 | − | 34.1534i | 0.672785 | − | 1.16530i | −0.304326 | − | 0.952568i | \(-0.598431\pi\) |
0.977111 | − | 0.212730i | \(-0.0682356\pi\) | |||||||
\(860\) | −1.34982 | + | 2.33796i | −0.0460284 | + | 0.0797236i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.96300 | + | 12.0603i | 0.237161 | + | 0.410775i | ||||
\(863\) | −19.3220 | + | 33.4667i | −0.657728 | + | 1.13922i | 0.323474 | + | 0.946237i | \(0.395149\pi\) |
−0.981202 | + | 0.192982i | \(0.938184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.63090 | − | 6.28891i | 0.123454 | − | 0.213829i | ||||
\(866\) | −0.134410 | + | 0.232805i | −0.00456744 | + | 0.00791104i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.744000 | + | 5.78701i | −0.0252530 | + | 0.196424i | ||||
\(869\) | 6.42502 | − | 11.1285i | 0.217954 | − | 0.377507i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.7118 | − | 8.21281i | −0.362955 | − | 0.278280i | ||||
\(872\) | −16.9142 | − | 29.2962i | −0.572786 | − | 0.992094i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.7084 | + | 32.4040i | −0.632822 | + | 1.09608i | ||||
\(875\) | −3.44913 | + | 26.8281i | −0.116602 | + | 0.906955i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −58.0741 | −1.96102 | −0.980512 | − | 0.196458i | \(-0.937056\pi\) | ||||
−0.980512 | + | 0.196458i | \(0.937056\pi\) | |||||||
\(878\) | 7.41710 | − | 12.8468i | 0.250315 | − | 0.433558i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.7502 | 0.396098 | ||||||||
\(881\) | 10.8118 | − | 18.7266i | 0.364259 | − | 0.630916i | −0.624398 | − | 0.781107i | \(-0.714655\pi\) |
0.988657 | + | 0.150191i | \(0.0479888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.7329 | −0.765022 | −0.382511 | − | 0.923951i | \(-0.624941\pi\) | ||||
−0.382511 | + | 0.923951i | \(0.624941\pi\) | |||||||
\(884\) | 0.177356 | − | 1.35122i | 0.00596513 | − | 0.0454464i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.5690 | −0.724624 | ||||||||
\(887\) | −8.16585 | − | 14.1437i | −0.274182 | − | 0.474898i | 0.695746 | − | 0.718288i | \(-0.255074\pi\) |
−0.969929 | + | 0.243390i | \(0.921741\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.9858 | − | 25.1521i | −1.10631 | − | 0.843574i | ||||
\(890\) | 16.4413 | + | 28.4772i | 0.551115 | + | 0.954559i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.01527 | − | 1.75850i | −0.0339937 | − | 0.0588788i | ||||
\(893\) | −10.6601 | + | 18.4638i | −0.356726 | + | 0.617867i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0392 | − | 19.1205i | 0.369000 | − | 0.639127i | ||||
\(896\) | 33.0093 | − | 13.7905i | 1.10276 | − | 0.460708i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.5506 | − | 28.6665i | 0.552301 | − | 0.956614i | ||||
\(899\) | 45.0280 | 1.50177 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.56010 | 0.0852893 | ||||||||
\(902\) | −5.05453 | −0.168297 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.8045 | − | 34.3023i | −0.658687 | − | 1.14088i | ||||
\(905\) | 3.33933 | − | 5.78389i | 0.111003 | − | 0.192263i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.4096 | 0.478463 | 0.239232 | − | 0.970963i | \(-0.423105\pi\) | ||||
0.239232 | + | 0.970963i | \(0.423105\pi\) | |||||||
\(908\) | 5.04146 | + | 8.73207i | 0.167307 | + | 0.289784i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.4524 | + | 12.5380i | −0.412794 | + | 0.415632i | ||||
\(911\) | 1.32236 | 0.0438118 | 0.0219059 | − | 0.999760i | \(-0.493027\pi\) | ||||
0.0219059 | + | 0.999760i | \(0.493027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.6125 | −0.814556 | ||||||||
\(914\) | 7.52907 | − | 13.0407i | 0.249039 | − | 0.431349i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.52757 | + | 7.84197i | 0.149595 | + | 0.259106i | ||||
\(917\) | 20.0663 | + | 15.3008i | 0.662648 | + | 0.505278i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.4458 | −0.905354 | −0.452677 | − | 0.891675i | \(-0.649531\pi\) | ||||
−0.452677 | + | 0.891675i | \(0.649531\pi\) | |||||||
\(920\) | −10.5484 | −0.347772 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.06835 | − | 1.85043i | 0.0351841 | − | 0.0609407i | ||||
\(923\) | 1.18724 | − | 9.04520i | 0.0390785 | − | 0.297726i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.93569 | − | 15.4771i | 0.293804 | − | 0.508883i | ||||
\(926\) | 24.6970 | + | 42.7765i | 0.811594 | + | 1.40572i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.89123 | + | 17.1321i | 0.324696 | + | 0.562389i | ||||
\(929\) | 28.6389 | 0.939611 | 0.469805 | − | 0.882770i | \(-0.344324\pi\) | ||||
0.469805 | + | 0.882770i | \(0.344324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.3090 | − | 11.8460i | −1.48494 | − | 0.388237i | ||||
\(932\) | 0.791738 | + | 1.37133i | 0.0259343 | + | 0.0449194i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −45.2739 | −1.48141 | ||||||||
\(935\) | 1.14258 | + | 1.97900i | 0.0373663 | + | 0.0647203i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.9990 | 0.914688 | 0.457344 | − | 0.889290i | \(-0.348801\pi\) | ||||
0.457344 | + | 0.889290i | \(0.348801\pi\) | |||||||
\(938\) | −14.2086 | + | 5.93602i | −0.463928 | + | 0.193818i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.58356 | 0.0516499 | ||||||||
\(941\) | 14.4502 | + | 25.0284i | 0.471062 | + | 0.815903i | 0.999452 | − | 0.0330983i | \(-0.0105375\pi\) |
−0.528390 | + | 0.849002i | \(0.677204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.52680 | 0.179977 | ||||||||
\(944\) | −47.7480 | −1.55406 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.93666 | + | 15.4787i | −0.290556 | + | 0.503257i | ||||
\(947\) | 15.0617 | + | 26.0877i | 0.489441 | + | 0.847736i | 0.999926 | − | 0.0121504i | \(-0.00386769\pi\) |
−0.510486 | + | 0.859886i | \(0.670534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.68888 | + | 20.4857i | −0.0872847 | + | 0.664993i | ||||
\(950\) | −18.6199 | + | 32.2506i | −0.604109 | + | 1.04635i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.69254 | + | 3.57812i | 0.152086 | + | 0.115968i | ||||
\(953\) | 2.46511 | + | 4.26969i | 0.0798527 | + | 0.138309i | 0.903186 | − | 0.429249i | \(-0.141222\pi\) |
−0.823334 | + | 0.567558i | \(0.807888\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.300084 | − | 0.519760i | 0.00971048 | − | 0.0168190i | ||||
\(956\) | 4.56879 | − | 7.91337i | 0.147765 | − | 0.255937i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.55721 | − | 13.0895i | −0.244162 | − | 0.422902i | ||||
\(959\) | 5.81646 | + | 4.43513i | 0.187823 | + | 0.143218i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.51957 | − | 2.63197i | 0.0490184 | − | 0.0849024i | ||||
\(962\) | 25.8463 | − | 10.7177i | 0.833318 | − | 0.345552i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.32665 | + | 7.49398i | 0.139352 | + | 0.241365i | ||||
\(965\) | 2.21171 | − | 3.83079i | 0.0711974 | − | 0.123317i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.1431 | 0.937180 | 0.468590 | − | 0.883416i | \(-0.344762\pi\) | ||||
0.468590 | + | 0.883416i | \(0.344762\pi\) | |||||||
\(968\) | −16.0505 | −0.515882 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.74654 | + | 9.95331i | 0.184510 | + | 0.319581i | ||||
\(971\) | −14.5769 | −0.467794 | −0.233897 | − | 0.972261i | \(-0.575148\pi\) | ||||
−0.233897 | + | 0.972261i | \(0.575148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55.6528 | − | 23.2504i | 1.78415 | − | 0.745375i | ||||
\(974\) | 26.6058 | 0.852506 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.2662 | − | 33.3700i | −0.616696 | − | 1.06815i | ||||
\(977\) | −52.5218 | −1.68032 | −0.840161 | − | 0.542337i | \(-0.817540\pi\) | ||||
−0.840161 | + | 0.542337i | \(0.817540\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.7819 | + | 32.5313i | 0.600273 | + | 1.03970i | ||||
\(980\) | 0.920681 | + | 3.35439i | 0.0294101 | + | 0.107152i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −39.9886 | −1.27609 | ||||||||
\(983\) | −3.01884 | − | 5.22879i | −0.0962862 | − | 0.166773i | 0.813858 | − | 0.581063i | \(-0.197363\pi\) |
−0.910145 | + | 0.414291i | \(0.864030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.43511 | − | 7.68183i | −0.141314 | − | 0.244764i | ||||
\(986\) | −5.99920 | + | 10.3909i | −0.191054 | + | 0.330914i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.29289 | + | 3.85348i | −0.295646 | + | 0.122596i | ||||
\(989\) | 9.77166 | − | 16.9250i | 0.310721 | − | 0.538184i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3484 | 0.995813 | 0.497907 | − | 0.867231i | \(-0.334102\pi\) | ||||
0.497907 | + | 0.867231i | \(0.334102\pi\) | |||||||
\(992\) | −12.2842 | −0.390025 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.27605 | − | 6.31060i | −0.262500 | − | 0.200160i | ||||
\(995\) | −4.47148 | − | 7.74483i | −0.141755 | − | 0.245528i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.74017 | + | 4.74611i | −0.0867819 | + | 0.150311i | −0.906149 | − | 0.422958i | \(-0.860992\pi\) |
0.819367 | + | 0.573269i | \(0.194325\pi\) | |||||||
\(998\) | −8.40146 | −0.265944 | ||||||||
\(999\) | 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 | 819.2.n.d.100.5 | 12 | ||
3.2 | odd | 2 | 91.2.g.b.9.2 | ✓ | 12 | ||
7.4 | even | 3 | 819.2.s.d.802.2 | 12 | |||
13.3 | even | 3 | 819.2.s.d.289.2 | 12 | |||
21.2 | odd | 6 | 637.2.f.k.295.2 | 12 | |||
21.5 | even | 6 | 637.2.f.j.295.2 | 12 | |||
21.11 | odd | 6 | 91.2.h.b.74.5 | yes | 12 | ||
21.17 | even | 6 | 637.2.h.l.165.5 | 12 | |||
21.20 | even | 2 | 637.2.g.l.373.2 | 12 | |||
39.17 | odd | 6 | 1183.2.e.g.170.5 | 12 | |||
39.29 | odd | 6 | 91.2.h.b.16.5 | yes | 12 | ||
39.35 | odd | 6 | 1183.2.e.h.170.2 | 12 | |||
91.81 | even | 3 | inner | 819.2.n.d.172.5 | 12 | ||
273.68 | even | 6 | 637.2.f.j.393.2 | 12 | |||
273.74 | odd | 6 | 1183.2.e.h.508.2 | 12 | |||
273.95 | odd | 6 | 1183.2.e.g.508.5 | 12 | |||
273.107 | odd | 6 | 637.2.f.k.393.2 | 12 | |||
273.146 | even | 6 | 637.2.h.l.471.5 | 12 | |||
273.152 | even | 6 | 8281.2.a.ca.1.5 | 6 | |||
273.173 | even | 6 | 8281.2.a.cf.1.2 | 6 | |||
273.185 | even | 6 | 637.2.g.l.263.2 | 12 | |||
273.191 | odd | 6 | 8281.2.a.bz.1.5 | 6 | |||
273.212 | odd | 6 | 8281.2.a.ce.1.2 | 6 | |||
273.263 | odd | 6 | 91.2.g.b.81.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.2 | ✓ | 12 | 3.2 | odd | 2 | ||
91.2.g.b.81.2 | yes | 12 | 273.263 | odd | 6 | ||
91.2.h.b.16.5 | yes | 12 | 39.29 | odd | 6 | ||
91.2.h.b.74.5 | yes | 12 | 21.11 | odd | 6 | ||
637.2.f.j.295.2 | 12 | 21.5 | even | 6 | |||
637.2.f.j.393.2 | 12 | 273.68 | even | 6 | |||
637.2.f.k.295.2 | 12 | 21.2 | odd | 6 | |||
637.2.f.k.393.2 | 12 | 273.107 | odd | 6 | |||
637.2.g.l.263.2 | 12 | 273.185 | even | 6 | |||
637.2.g.l.373.2 | 12 | 21.20 | even | 2 | |||
637.2.h.l.165.5 | 12 | 21.17 | even | 6 | |||
637.2.h.l.471.5 | 12 | 273.146 | even | 6 | |||
819.2.n.d.100.5 | 12 | 1.1 | even | 1 | trivial | ||
819.2.n.d.172.5 | 12 | 91.81 | even | 3 | inner | ||
819.2.s.d.289.2 | 12 | 13.3 | even | 3 | |||
819.2.s.d.802.2 | 12 | 7.4 | even | 3 | |||
1183.2.e.g.170.5 | 12 | 39.17 | odd | 6 | |||
1183.2.e.g.508.5 | 12 | 273.95 | odd | 6 | |||
1183.2.e.h.170.2 | 12 | 39.35 | odd | 6 | |||
1183.2.e.h.508.2 | 12 | 273.74 | odd | 6 | |||
8281.2.a.bz.1.5 | 6 | 273.191 | odd | 6 | |||
8281.2.a.ca.1.5 | 6 | 273.152 | even | 6 | |||
8281.2.a.ce.1.2 | 6 | 273.212 | odd | 6 | |||
8281.2.a.cf.1.2 | 6 | 273.173 | even | 6 |