Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(149,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.3 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.149 |
Dual form | 1850.2.b.l.149.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 2.73205i | − 1.57735i | −0.614810 | − | 0.788675i | \(-0.710767\pi\) | ||||
0.614810 | − | 0.788675i | \(-0.289233\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.73205 | 1.11536 | ||||||||
\(7\) | 1.26795i | 0.479240i | 0.970867 | + | 0.239620i | \(0.0770228\pi\) | ||||
−0.970867 | + | 0.239620i | \(0.922977\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −4.46410 | −1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.46410 | 0.441443 | 0.220722 | − | 0.975337i | \(-0.429159\pi\) | ||||
0.220722 | + | 0.975337i | \(0.429159\pi\) | |||||||
\(12\) | 2.73205i | 0.788675i | ||||||||
\(13\) | 1.46410i | 0.406069i | 0.979172 | + | 0.203034i | \(0.0650803\pi\) | ||||
−0.979172 | + | 0.203034i | \(0.934920\pi\) | |||||||
\(14\) | −1.26795 | −0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.46410i | 0.355097i | 0.984112 | + | 0.177548i | \(0.0568166\pi\) | ||||
−0.984112 | + | 0.177548i | \(0.943183\pi\) | |||||||
\(18\) | − 4.46410i | − 1.05220i | ||||||||
\(19\) | 4.19615 | 0.962663 | 0.481332 | − | 0.876539i | \(-0.340153\pi\) | ||||
0.481332 | + | 0.876539i | \(0.340153\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.46410 | 0.755929 | ||||||||
\(22\) | 1.46410i | 0.312148i | ||||||||
\(23\) | − 8.00000i | − 1.66812i | −0.551677 | − | 0.834058i | \(-0.686012\pi\) | ||||
0.551677 | − | 0.834058i | \(-0.313988\pi\) | |||||||
\(24\) | −2.73205 | −0.557678 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.46410 | −0.287134 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | − 1.26795i | − 0.239620i | ||||||||
\(29\) | 8.92820 | 1.65793 | 0.828963 | − | 0.559304i | \(-0.188931\pi\) | ||||
0.828963 | + | 0.559304i | \(0.188931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.73205 | −0.490691 | −0.245345 | − | 0.969436i | \(-0.578901\pi\) | ||||
−0.245345 | + | 0.969436i | \(0.578901\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 4.00000i | − 0.696311i | ||||||||
\(34\) | −1.46410 | −0.251091 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.46410 | 0.744017 | ||||||||
\(37\) | − 1.00000i | − 0.164399i | ||||||||
\(38\) | 4.19615i | 0.680706i | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 3.46410i | 0.534522i | ||||||||
\(43\) | − 6.92820i | − 1.05654i | −0.849076 | − | 0.528271i | \(-0.822841\pi\) | ||||
0.849076 | − | 0.528271i | \(-0.177159\pi\) | |||||||
\(44\) | −1.46410 | −0.220722 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 1.26795i | 0.184949i | 0.995715 | + | 0.0924747i | \(0.0294777\pi\) | ||||
−0.995715 | + | 0.0924747i | \(0.970522\pi\) | |||||||
\(48\) | − 2.73205i | − 0.394338i | ||||||||
\(49\) | 5.39230 | 0.770329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | − 1.46410i | − 0.203034i | ||||||||
\(53\) | − 6.00000i | − 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.26795 | 0.169437 | ||||||||
\(57\) | − 11.4641i | − 1.51846i | ||||||||
\(58\) | 8.92820i | 1.17233i | ||||||||
\(59\) | −0.196152 | −0.0255369 | −0.0127684 | − | 0.999918i | \(-0.504064\pi\) | ||||
−0.0127684 | + | 0.999918i | \(0.504064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820 | 1.14314 | 0.571570 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571570 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(62\) | − 2.73205i | − 0.346971i | ||||||||
\(63\) | − 5.66025i | − 0.713125i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | − 13.6603i | − 1.66887i | −0.551110 | − | 0.834433i | \(-0.685795\pi\) | ||||
0.551110 | − | 0.834433i | \(-0.314205\pi\) | |||||||
\(68\) | − 1.46410i | − 0.177548i | ||||||||
\(69\) | −21.8564 | −2.63120 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.9282 | −1.29694 | −0.648470 | − | 0.761241i | \(-0.724591\pi\) | ||||
−0.648470 | + | 0.761241i | \(0.724591\pi\) | |||||||
\(72\) | 4.46410i | 0.526099i | ||||||||
\(73\) | 12.9282i | 1.51313i | 0.653917 | + | 0.756566i | \(0.273124\pi\) | ||||
−0.653917 | + | 0.756566i | \(0.726876\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.19615 | −0.481332 | ||||||||
\(77\) | 1.85641i | 0.211557i | ||||||||
\(78\) | 4.00000i | 0.452911i | ||||||||
\(79\) | −5.26795 | −0.592691 | −0.296345 | − | 0.955081i | \(-0.595768\pi\) | ||||
−0.296345 | + | 0.955081i | \(0.595768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | − 2.00000i | − 0.220863i | ||||||||
\(83\) | − 5.26795i | − 0.578233i | −0.957294 | − | 0.289116i | \(-0.906639\pi\) | ||||
0.957294 | − | 0.289116i | \(-0.0933614\pi\) | |||||||
\(84\) | −3.46410 | −0.377964 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.92820 | 0.747087 | ||||||||
\(87\) | − 24.3923i | − 2.61513i | ||||||||
\(88\) | − 1.46410i | − 0.156074i | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.85641 | −0.194604 | ||||||||
\(92\) | 8.00000i | 0.834058i | ||||||||
\(93\) | 7.46410i | 0.773991i | ||||||||
\(94\) | −1.26795 | −0.130779 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.73205 | 0.278839 | ||||||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | 5.39230i | 0.544705i | ||||||||
\(99\) | −6.53590 | −0.656883 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.53590 | −0.252331 | −0.126166 | − | 0.992009i | \(-0.540267\pi\) | ||||
−0.126166 | + | 0.992009i | \(0.540267\pi\) | |||||||
\(102\) | 4.00000i | 0.396059i | ||||||||
\(103\) | − 13.4641i | − 1.32666i | −0.748328 | − | 0.663329i | \(-0.769143\pi\) | ||||
0.748328 | − | 0.663329i | \(-0.230857\pi\) | |||||||
\(104\) | 1.46410 | 0.143567 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | − 6.73205i | − 0.650812i | −0.945574 | − | 0.325406i | \(-0.894499\pi\) | ||||
0.945574 | − | 0.325406i | \(-0.105501\pi\) | |||||||
\(108\) | − 4.00000i | − 0.384900i | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.73205 | −0.259315 | ||||||||
\(112\) | 1.26795i | 0.119810i | ||||||||
\(113\) | − 17.4641i | − 1.64288i | −0.570292 | − | 0.821442i | \(-0.693170\pi\) | ||||
0.570292 | − | 0.821442i | \(-0.306830\pi\) | |||||||
\(114\) | 11.4641 | 1.07371 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.92820 | −0.828963 | ||||||||
\(117\) | − 6.53590i | − 0.604244i | ||||||||
\(118\) | − 0.196152i | − 0.0180573i | ||||||||
\(119\) | −1.85641 | −0.170177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 8.92820i | 0.808322i | ||||||||
\(123\) | 5.46410i | 0.492681i | ||||||||
\(124\) | 2.73205 | 0.245345 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.66025 | 0.504256 | ||||||||
\(127\) | 13.6603i | 1.21215i | 0.795407 | + | 0.606076i | \(0.207257\pi\) | ||||
−0.795407 | + | 0.606076i | \(0.792743\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −18.9282 | −1.66654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5885 | 1.09986 | 0.549929 | − | 0.835211i | \(-0.314655\pi\) | ||||
0.549929 | + | 0.835211i | \(0.314655\pi\) | |||||||
\(132\) | 4.00000i | 0.348155i | ||||||||
\(133\) | 5.32051i | 0.461347i | ||||||||
\(134\) | 13.6603 | 1.18007 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.46410 | 0.125546 | ||||||||
\(137\) | − 2.00000i | − 0.170872i | −0.996344 | − | 0.0854358i | \(-0.972772\pi\) | ||||
0.996344 | − | 0.0854358i | \(-0.0272282\pi\) | |||||||
\(138\) | − 21.8564i | − 1.86054i | ||||||||
\(139\) | 6.92820 | 0.587643 | 0.293821 | − | 0.955860i | \(-0.405073\pi\) | ||||
0.293821 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.46410 | 0.291730 | ||||||||
\(142\) | − 10.9282i | − 0.917074i | ||||||||
\(143\) | 2.14359i | 0.179256i | ||||||||
\(144\) | −4.46410 | −0.372008 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.9282 | −1.06995 | ||||||||
\(147\) | − 14.7321i | − 1.21508i | ||||||||
\(148\) | 1.00000i | 0.0821995i | ||||||||
\(149\) | 16.3923 | 1.34291 | 0.671455 | − | 0.741045i | \(-0.265670\pi\) | ||||
0.671455 | + | 0.741045i | \(0.265670\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.39230 | 0.682956 | 0.341478 | − | 0.939890i | \(-0.389073\pi\) | ||||
0.341478 | + | 0.939890i | \(0.389073\pi\) | |||||||
\(152\) | − 4.19615i | − 0.340353i | ||||||||
\(153\) | − 6.53590i | − 0.528396i | ||||||||
\(154\) | −1.85641 | −0.149593 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | − 16.9282i | − 1.35102i | −0.737352 | − | 0.675509i | \(-0.763924\pi\) | ||||
0.737352 | − | 0.675509i | \(-0.236076\pi\) | |||||||
\(158\) | − 5.26795i | − 0.419096i | ||||||||
\(159\) | −16.3923 | −1.29999 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.1436 | 0.799427 | ||||||||
\(162\) | − 2.46410i | − 0.193598i | ||||||||
\(163\) | 23.3205i | 1.82660i | 0.407284 | + | 0.913302i | \(0.366476\pi\) | ||||
−0.407284 | + | 0.913302i | \(0.633524\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.26795 | 0.408872 | ||||||||
\(167\) | − 5.46410i | − 0.422825i | −0.977397 | − | 0.211412i | \(-0.932194\pi\) | ||||
0.977397 | − | 0.211412i | \(-0.0678063\pi\) | |||||||
\(168\) | − 3.46410i | − 0.267261i | ||||||||
\(169\) | 10.8564 | 0.835108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.7321 | −1.43248 | ||||||||
\(172\) | 6.92820i | 0.528271i | ||||||||
\(173\) | 10.0000i | 0.760286i | 0.924928 | + | 0.380143i | \(0.124125\pi\) | ||||
−0.924928 | + | 0.380143i | \(0.875875\pi\) | |||||||
\(174\) | 24.3923 | 1.84918 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.46410 | 0.110361 | ||||||||
\(177\) | 0.535898i | 0.0402806i | ||||||||
\(178\) | 2.00000i | 0.149906i | ||||||||
\(179\) | 17.6603 | 1.31999 | 0.659995 | − | 0.751270i | \(-0.270559\pi\) | ||||
0.659995 | + | 0.751270i | \(0.270559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.46410 | −0.108826 | −0.0544129 | − | 0.998519i | \(-0.517329\pi\) | ||||
−0.0544129 | + | 0.998519i | \(0.517329\pi\) | |||||||
\(182\) | − 1.85641i | − 0.137606i | ||||||||
\(183\) | − 24.3923i | − 1.80313i | ||||||||
\(184\) | −8.00000 | −0.589768 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.46410 | −0.547294 | ||||||||
\(187\) | 2.14359i | 0.156755i | ||||||||
\(188\) | − 1.26795i | − 0.0924747i | ||||||||
\(189\) | −5.07180 | −0.368919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.26795 | −0.381175 | −0.190588 | − | 0.981670i | \(-0.561039\pi\) | ||||
−0.190588 | + | 0.981670i | \(0.561039\pi\) | |||||||
\(192\) | 2.73205i | 0.197169i | ||||||||
\(193\) | − 11.8564i | − 0.853443i | −0.904383 | − | 0.426721i | \(-0.859668\pi\) | ||||
0.904383 | − | 0.426721i | \(-0.140332\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.39230 | −0.385165 | ||||||||
\(197\) | − 18.7846i | − 1.33835i | −0.743106 | − | 0.669174i | \(-0.766648\pi\) | ||||
0.743106 | − | 0.669174i | \(-0.233352\pi\) | |||||||
\(198\) | − 6.53590i | − 0.464486i | ||||||||
\(199\) | −26.0526 | −1.84682 | −0.923408 | − | 0.383819i | \(-0.874609\pi\) | ||||
−0.923408 | + | 0.383819i | \(0.874609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.3205 | −2.63239 | ||||||||
\(202\) | − 2.53590i | − 0.178425i | ||||||||
\(203\) | 11.3205i | 0.794544i | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.4641 | 0.938088 | ||||||||
\(207\) | 35.7128i | 2.48221i | ||||||||
\(208\) | 1.46410i | 0.101517i | ||||||||
\(209\) | 6.14359 | 0.424961 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.85641 | 0.678543 | 0.339272 | − | 0.940688i | \(-0.389819\pi\) | ||||
0.339272 | + | 0.940688i | \(0.389819\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 29.8564i | 2.04573i | ||||||||
\(214\) | 6.73205 | 0.460194 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | − 3.46410i | − 0.235159i | ||||||||
\(218\) | − 2.00000i | − 0.135457i | ||||||||
\(219\) | 35.3205 | 2.38674 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.14359 | −0.144194 | ||||||||
\(222\) | − 2.73205i | − 0.183363i | ||||||||
\(223\) | − 22.0526i | − 1.47675i | −0.674391 | − | 0.738374i | \(-0.735594\pi\) | ||||
0.674391 | − | 0.738374i | \(-0.264406\pi\) | |||||||
\(224\) | −1.26795 | −0.0847184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.4641 | 1.16169 | ||||||||
\(227\) | − 3.60770i | − 0.239451i | −0.992807 | − | 0.119726i | \(-0.961799\pi\) | ||||
0.992807 | − | 0.119726i | \(-0.0382015\pi\) | |||||||
\(228\) | 11.4641i | 0.759229i | ||||||||
\(229\) | −15.8564 | −1.04782 | −0.523910 | − | 0.851773i | \(-0.675527\pi\) | ||||
−0.523910 | + | 0.851773i | \(0.675527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.07180 | 0.333700 | ||||||||
\(232\) | − 8.92820i | − 0.586165i | ||||||||
\(233\) | 15.0718i | 0.987386i | 0.869636 | + | 0.493693i | \(0.164353\pi\) | ||||
−0.869636 | + | 0.493693i | \(0.835647\pi\) | |||||||
\(234\) | 6.53590 | 0.427265 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.196152 | 0.0127684 | ||||||||
\(237\) | 14.3923i | 0.934881i | ||||||||
\(238\) | − 1.85641i | − 0.120333i | ||||||||
\(239\) | 17.2679 | 1.11697 | 0.558485 | − | 0.829514i | \(-0.311383\pi\) | ||||
0.558485 | + | 0.829514i | \(0.311383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.92820 | −0.575116 | −0.287558 | − | 0.957763i | \(-0.592843\pi\) | ||||
−0.287558 | + | 0.957763i | \(0.592843\pi\) | |||||||
\(242\) | − 8.85641i | − 0.569311i | ||||||||
\(243\) | 18.7321i | 1.20166i | ||||||||
\(244\) | −8.92820 | −0.571570 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.46410 | −0.348378 | ||||||||
\(247\) | 6.14359i | 0.390907i | ||||||||
\(248\) | 2.73205i | 0.173485i | ||||||||
\(249\) | −14.3923 | −0.912075 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.7321 | 1.43483 | 0.717417 | − | 0.696644i | \(-0.245324\pi\) | ||||
0.717417 | + | 0.696644i | \(0.245324\pi\) | |||||||
\(252\) | 5.66025i | 0.356562i | ||||||||
\(253\) | − 11.7128i | − 0.736378i | ||||||||
\(254\) | −13.6603 | −0.857121 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.4641i | 1.58841i | 0.607652 | + | 0.794204i | \(0.292112\pi\) | ||||
−0.607652 | + | 0.794204i | \(0.707888\pi\) | |||||||
\(258\) | − 18.9282i | − 1.17842i | ||||||||
\(259\) | 1.26795 | 0.0787865 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −39.8564 | −2.46705 | ||||||||
\(262\) | 12.5885i | 0.777717i | ||||||||
\(263\) | 30.0526i | 1.85312i | 0.376147 | + | 0.926560i | \(0.377249\pi\) | ||||
−0.376147 | + | 0.926560i | \(0.622751\pi\) | |||||||
\(264\) | −4.00000 | −0.246183 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.32051 | −0.326221 | ||||||||
\(267\) | − 5.46410i | − 0.334398i | ||||||||
\(268\) | 13.6603i | 0.834433i | ||||||||
\(269\) | 0.392305 | 0.0239192 | 0.0119596 | − | 0.999928i | \(-0.496193\pi\) | ||||
0.0119596 | + | 0.999928i | \(0.496193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.7846 | 1.01959 | 0.509796 | − | 0.860295i | \(-0.329721\pi\) | ||||
0.509796 | + | 0.860295i | \(0.329721\pi\) | |||||||
\(272\) | 1.46410i | 0.0887742i | ||||||||
\(273\) | 5.07180i | 0.306959i | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 21.8564 | 1.31560 | ||||||||
\(277\) | 26.2487i | 1.57713i | 0.614950 | + | 0.788566i | \(0.289176\pi\) | ||||
−0.614950 | + | 0.788566i | \(0.710824\pi\) | |||||||
\(278\) | 6.92820i | 0.415526i | ||||||||
\(279\) | 12.1962 | 0.730165 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.92820 | 0.293992 | 0.146996 | − | 0.989137i | \(-0.453040\pi\) | ||||
0.146996 | + | 0.989137i | \(0.453040\pi\) | |||||||
\(282\) | 3.46410i | 0.206284i | ||||||||
\(283\) | − 4.39230i | − 0.261095i | −0.991442 | − | 0.130548i | \(-0.958326\pi\) | ||||
0.991442 | − | 0.130548i | \(-0.0416736\pi\) | |||||||
\(284\) | 10.9282 | 0.648470 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.14359 | −0.126753 | ||||||||
\(287\) | − 2.53590i | − 0.149689i | ||||||||
\(288\) | − 4.46410i | − 0.263050i | ||||||||
\(289\) | 14.8564 | 0.873906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.46410 | 0.320311 | ||||||||
\(292\) | − 12.9282i | − 0.756566i | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 14.7321 | 0.859191 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 5.85641i | 0.339823i | ||||||||
\(298\) | 16.3923i | 0.949581i | ||||||||
\(299\) | 11.7128 | 0.677369 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.78461 | 0.506336 | ||||||||
\(302\) | 8.39230i | 0.482923i | ||||||||
\(303\) | 6.92820i | 0.398015i | ||||||||
\(304\) | 4.19615 | 0.240666 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.53590 | 0.373632 | ||||||||
\(307\) | 12.5885i | 0.718461i | 0.933249 | + | 0.359231i | \(0.116961\pi\) | ||||
−0.933249 | + | 0.359231i | \(0.883039\pi\) | |||||||
\(308\) | − 1.85641i | − 0.105779i | ||||||||
\(309\) | −36.7846 | −2.09260 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.1244 | 1.53808 | 0.769041 | − | 0.639200i | \(-0.220734\pi\) | ||||
0.769041 | + | 0.639200i | \(0.220734\pi\) | |||||||
\(312\) | − 4.00000i | − 0.226455i | ||||||||
\(313\) | 3.85641i | 0.217977i | 0.994043 | + | 0.108988i | \(0.0347612\pi\) | ||||
−0.994043 | + | 0.108988i | \(0.965239\pi\) | |||||||
\(314\) | 16.9282 | 0.955314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.26795 | 0.296345 | ||||||||
\(317\) | 31.8564i | 1.78923i | 0.446834 | + | 0.894617i | \(0.352552\pi\) | ||||
−0.446834 | + | 0.894617i | \(0.647448\pi\) | |||||||
\(318\) | − 16.3923i | − 0.919235i | ||||||||
\(319\) | 13.0718 | 0.731880 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.3923 | −1.02656 | ||||||||
\(322\) | 10.1436i | 0.565280i | ||||||||
\(323\) | 6.14359i | 0.341839i | ||||||||
\(324\) | 2.46410 | 0.136895 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.3205 | −1.29160 | ||||||||
\(327\) | 5.46410i | 0.302166i | ||||||||
\(328\) | 2.00000i | 0.110432i | ||||||||
\(329\) | −1.60770 | −0.0886351 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.87564 | −0.487850 | −0.243925 | − | 0.969794i | \(-0.578435\pi\) | ||||
−0.243925 | + | 0.969794i | \(0.578435\pi\) | |||||||
\(332\) | 5.26795i | 0.289116i | ||||||||
\(333\) | 4.46410i | 0.244631i | ||||||||
\(334\) | 5.46410 | 0.298982 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.46410 | 0.188982 | ||||||||
\(337\) | − 26.0000i | − 1.41631i | −0.706057 | − | 0.708155i | \(-0.749528\pi\) | ||||
0.706057 | − | 0.708155i | \(-0.250472\pi\) | |||||||
\(338\) | 10.8564i | 0.590511i | ||||||||
\(339\) | −47.7128 | −2.59140 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | − 18.7321i | − 1.01291i | ||||||||
\(343\) | 15.7128i | 0.848412i | ||||||||
\(344\) | −6.92820 | −0.373544 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.0000 | −0.537603 | ||||||||
\(347\) | − 17.0718i | − 0.916462i | −0.888833 | − | 0.458231i | \(-0.848483\pi\) | ||||
0.888833 | − | 0.458231i | \(-0.151517\pi\) | |||||||
\(348\) | 24.3923i | 1.30756i | ||||||||
\(349\) | −19.3205 | −1.03420 | −0.517102 | − | 0.855924i | \(-0.672989\pi\) | ||||
−0.517102 | + | 0.855924i | \(0.672989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.85641 | −0.312592 | ||||||||
\(352\) | 1.46410i | 0.0780369i | ||||||||
\(353\) | 15.8564i | 0.843951i | 0.906607 | + | 0.421976i | \(0.138663\pi\) | ||||
−0.906607 | + | 0.421976i | \(0.861337\pi\) | |||||||
\(354\) | −0.535898 | −0.0284827 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | 5.07180i | 0.268428i | ||||||||
\(358\) | 17.6603i | 0.933373i | ||||||||
\(359\) | −8.39230 | −0.442929 | −0.221464 | − | 0.975168i | \(-0.571084\pi\) | ||||
−0.221464 | + | 0.975168i | \(0.571084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.39230 | −0.0732792 | ||||||||
\(362\) | − 1.46410i | − 0.0769515i | ||||||||
\(363\) | 24.1962i | 1.26997i | ||||||||
\(364\) | 1.85641 | 0.0973021 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 24.3923 | 1.27501 | ||||||||
\(367\) | 21.6603i | 1.13066i | 0.824866 | + | 0.565328i | \(0.191250\pi\) | ||||
−0.824866 | + | 0.565328i | \(0.808750\pi\) | |||||||
\(368\) | − 8.00000i | − 0.417029i | ||||||||
\(369\) | 8.92820 | 0.464784 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.60770 | 0.394972 | ||||||||
\(372\) | − 7.46410i | − 0.386996i | ||||||||
\(373\) | 30.7846i | 1.59397i | 0.604001 | + | 0.796983i | \(0.293572\pi\) | ||||
−0.604001 | + | 0.796983i | \(0.706428\pi\) | |||||||
\(374\) | −2.14359 | −0.110843 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.26795 | 0.0653895 | ||||||||
\(377\) | 13.0718i | 0.673232i | ||||||||
\(378\) | − 5.07180i | − 0.260865i | ||||||||
\(379\) | −11.6077 | −0.596247 | −0.298124 | − | 0.954527i | \(-0.596361\pi\) | ||||
−0.298124 | + | 0.954527i | \(0.596361\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 37.3205 | 1.91199 | ||||||||
\(382\) | − 5.26795i | − 0.269532i | ||||||||
\(383\) | − 8.00000i | − 0.408781i | −0.978889 | − | 0.204390i | \(-0.934479\pi\) | ||||
0.978889 | − | 0.204390i | \(-0.0655212\pi\) | |||||||
\(384\) | −2.73205 | −0.139419 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.8564 | 0.603475 | ||||||||
\(387\) | 30.9282i | 1.57217i | ||||||||
\(388\) | − 2.00000i | − 0.101535i | ||||||||
\(389\) | −15.8564 | −0.803952 | −0.401976 | − | 0.915650i | \(-0.631676\pi\) | ||||
−0.401976 | + | 0.915650i | \(0.631676\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.7128 | 0.592342 | ||||||||
\(392\) | − 5.39230i | − 0.272353i | ||||||||
\(393\) | − 34.3923i | − 1.73486i | ||||||||
\(394\) | 18.7846 | 0.946355 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.53590 | 0.328441 | ||||||||
\(397\) | 22.0000i | 1.10415i | 0.833795 | + | 0.552074i | \(0.186163\pi\) | ||||
−0.833795 | + | 0.552074i | \(0.813837\pi\) | |||||||
\(398\) | − 26.0526i | − 1.30590i | ||||||||
\(399\) | 14.5359 | 0.727705 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.0718 | −0.952400 | −0.476200 | − | 0.879337i | \(-0.657986\pi\) | ||||
−0.476200 | + | 0.879337i | \(0.657986\pi\) | |||||||
\(402\) | − 37.3205i | − 1.86138i | ||||||||
\(403\) | − 4.00000i | − 0.199254i | ||||||||
\(404\) | 2.53590 | 0.126166 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.3205 | −0.561827 | ||||||||
\(407\) | − 1.46410i | − 0.0725728i | ||||||||
\(408\) | − 4.00000i | − 0.198030i | ||||||||
\(409\) | −16.9282 | −0.837046 | −0.418523 | − | 0.908206i | \(-0.637452\pi\) | ||||
−0.418523 | + | 0.908206i | \(0.637452\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.46410 | −0.269524 | ||||||||
\(412\) | 13.4641i | 0.663329i | ||||||||
\(413\) | − 0.248711i | − 0.0122383i | ||||||||
\(414\) | −35.7128 | −1.75519 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.46410 | −0.0717835 | ||||||||
\(417\) | − 18.9282i | − 0.926918i | ||||||||
\(418\) | 6.14359i | 0.300493i | ||||||||
\(419\) | 34.2487 | 1.67316 | 0.836580 | − | 0.547846i | \(-0.184552\pi\) | ||||
0.836580 | + | 0.547846i | \(0.184552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.8564 | −1.35764 | −0.678819 | − | 0.734306i | \(-0.737508\pi\) | ||||
−0.678819 | + | 0.734306i | \(0.737508\pi\) | |||||||
\(422\) | 9.85641i | 0.479802i | ||||||||
\(423\) | − 5.66025i | − 0.275211i | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −29.8564 | −1.44655 | ||||||||
\(427\) | 11.3205i | 0.547838i | ||||||||
\(428\) | 6.73205i | 0.325406i | ||||||||
\(429\) | 5.85641 | 0.282750 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.19615 | 0.394795 | 0.197397 | − | 0.980324i | \(-0.436751\pi\) | ||||
0.197397 | + | 0.980324i | \(0.436751\pi\) | |||||||
\(432\) | 4.00000i | 0.192450i | ||||||||
\(433\) | − 34.0000i | − 1.63394i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) | ||||
0.576683 | − | 0.816968i | \(-0.304347\pi\) | |||||||
\(434\) | 3.46410 | 0.166282 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | − 33.5692i | − 1.60583i | ||||||||
\(438\) | 35.3205i | 1.68768i | ||||||||
\(439\) | 31.5167 | 1.50421 | 0.752104 | − | 0.659044i | \(-0.229039\pi\) | ||||
0.752104 | + | 0.659044i | \(0.229039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.0718 | −1.14628 | ||||||||
\(442\) | − 2.14359i | − 0.101960i | ||||||||
\(443\) | − 39.1244i | − 1.85885i | −0.369006 | − | 0.929427i | \(-0.620302\pi\) | ||||
0.369006 | − | 0.929427i | \(-0.379698\pi\) | |||||||
\(444\) | 2.73205 | 0.129657 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 22.0526 | 1.04422 | ||||||||
\(447\) | − 44.7846i | − 2.11824i | ||||||||
\(448\) | − 1.26795i | − 0.0599050i | ||||||||
\(449\) | −33.7128 | −1.59101 | −0.795503 | − | 0.605950i | \(-0.792793\pi\) | ||||
−0.795503 | + | 0.605950i | \(0.792793\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.92820 | −0.137884 | ||||||||
\(452\) | 17.4641i | 0.821442i | ||||||||
\(453\) | − 22.9282i | − 1.07726i | ||||||||
\(454\) | 3.60770 | 0.169318 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.4641 | −0.536856 | ||||||||
\(457\) | 4.14359i | 0.193829i | 0.995293 | + | 0.0969146i | \(0.0308974\pi\) | ||||
−0.995293 | + | 0.0969146i | \(0.969103\pi\) | |||||||
\(458\) | − 15.8564i | − 0.740921i | ||||||||
\(459\) | −5.85641 | −0.273354 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.7846 | −1.24748 | −0.623742 | − | 0.781630i | \(-0.714388\pi\) | ||||
−0.623742 | + | 0.781630i | \(0.714388\pi\) | |||||||
\(462\) | 5.07180i | 0.235961i | ||||||||
\(463\) | 5.07180i | 0.235706i | 0.993031 | + | 0.117853i | \(0.0376012\pi\) | ||||
−0.993031 | + | 0.117853i | \(0.962399\pi\) | |||||||
\(464\) | 8.92820 | 0.414481 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.0718 | −0.698188 | ||||||||
\(467\) | − 37.1769i | − 1.72034i | −0.510005 | − | 0.860171i | \(-0.670357\pi\) | ||||
0.510005 | − | 0.860171i | \(-0.329643\pi\) | |||||||
\(468\) | 6.53590i | 0.302122i | ||||||||
\(469\) | 17.3205 | 0.799787 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −46.2487 | −2.13103 | ||||||||
\(472\) | 0.196152i | 0.00902865i | ||||||||
\(473\) | − 10.1436i | − 0.466403i | ||||||||
\(474\) | −14.3923 | −0.661060 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.85641 | 0.0850883 | ||||||||
\(477\) | 26.7846i | 1.22638i | ||||||||
\(478\) | 17.2679i | 0.789818i | ||||||||
\(479\) | 34.0526 | 1.55590 | 0.777951 | − | 0.628325i | \(-0.216259\pi\) | ||||
0.777951 | + | 0.628325i | \(0.216259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.46410 | 0.0667573 | ||||||||
\(482\) | − 8.92820i | − 0.406669i | ||||||||
\(483\) | − 27.7128i | − 1.26098i | ||||||||
\(484\) | 8.85641 | 0.402564 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.7321 | −0.849703 | ||||||||
\(487\) | 16.3923i | 0.742806i | 0.928472 | + | 0.371403i | \(0.121123\pi\) | ||||
−0.928472 | + | 0.371403i | \(0.878877\pi\) | |||||||
\(488\) | − 8.92820i | − 0.404161i | ||||||||
\(489\) | 63.7128 | 2.88119 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.07180 | −0.0483695 | −0.0241848 | − | 0.999708i | \(-0.507699\pi\) | ||||
−0.0241848 | + | 0.999708i | \(0.507699\pi\) | |||||||
\(492\) | − 5.46410i | − 0.246341i | ||||||||
\(493\) | 13.0718i | 0.588724i | ||||||||
\(494\) | −6.14359 | −0.276413 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.73205 | −0.122673 | ||||||||
\(497\) | − 13.8564i | − 0.621545i | ||||||||
\(498\) | − 14.3923i | − 0.644935i | ||||||||
\(499\) | −40.5885 | −1.81699 | −0.908494 | − | 0.417897i | \(-0.862767\pi\) | ||||
−0.908494 | + | 0.417897i | \(0.862767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.9282 | −0.666943 | ||||||||
\(502\) | 22.7321i | 1.01458i | ||||||||
\(503\) | − 5.07180i | − 0.226140i | −0.993587 | − | 0.113070i | \(-0.963932\pi\) | ||||
0.993587 | − | 0.113070i | \(-0.0360685\pi\) | |||||||
\(504\) | −5.66025 | −0.252128 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.7128 | 0.520698 | ||||||||
\(507\) | − 29.6603i | − 1.31726i | ||||||||
\(508\) | − 13.6603i | − 0.606076i | ||||||||
\(509\) | 2.00000 | 0.0886484 | 0.0443242 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443242 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3923 | −0.725153 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 16.7846i | 0.741059i | ||||||||
\(514\) | −25.4641 | −1.12317 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 18.9282 | 0.833268 | ||||||||
\(517\) | 1.85641i | 0.0816447i | ||||||||
\(518\) | 1.26795i | 0.0557105i | ||||||||
\(519\) | 27.3205 | 1.19924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.4641 | 1.46609 | 0.733044 | − | 0.680181i | \(-0.238099\pi\) | ||||
0.733044 | + | 0.680181i | \(0.238099\pi\) | |||||||
\(522\) | − 39.8564i | − 1.74447i | ||||||||
\(523\) | − 4.78461i | − 0.209216i | −0.994514 | − | 0.104608i | \(-0.966641\pi\) | ||||
0.994514 | − | 0.104608i | \(-0.0333589\pi\) | |||||||
\(524\) | −12.5885 | −0.549929 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.0526 | −1.31035 | ||||||||
\(527\) | − 4.00000i | − 0.174243i | ||||||||
\(528\) | − 4.00000i | − 0.174078i | ||||||||
\(529\) | −41.0000 | −1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.875644 | 0.0379997 | ||||||||
\(532\) | − 5.32051i | − 0.230673i | ||||||||
\(533\) | − 2.92820i | − 0.126835i | ||||||||
\(534\) | 5.46410 | 0.236455 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.6603 | −0.590033 | ||||||||
\(537\) | − 48.2487i | − 2.08209i | ||||||||
\(538\) | 0.392305i | 0.0169135i | ||||||||
\(539\) | 7.89488 | 0.340057 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 16.7846i | 0.720961i | ||||||||
\(543\) | 4.00000i | 0.171656i | ||||||||
\(544\) | −1.46410 | −0.0627728 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.07180 | −0.217053 | ||||||||
\(547\) | 4.00000i | 0.171028i | 0.996337 | + | 0.0855138i | \(0.0272532\pi\) | ||||
−0.996337 | + | 0.0855138i | \(0.972747\pi\) | |||||||
\(548\) | 2.00000i | 0.0854358i | ||||||||
\(549\) | −39.8564 | −1.70103 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.4641 | 1.59602 | ||||||||
\(552\) | 21.8564i | 0.930270i | ||||||||
\(553\) | − 6.67949i | − 0.284041i | ||||||||
\(554\) | −26.2487 | −1.11520 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.92820 | −0.293821 | ||||||||
\(557\) | 32.1051i | 1.36034i | 0.733056 | + | 0.680169i | \(0.238094\pi\) | ||||
−0.733056 | + | 0.680169i | \(0.761906\pi\) | |||||||
\(558\) | 12.1962i | 0.516304i | ||||||||
\(559\) | 10.1436 | 0.429028 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.85641 | 0.247258 | ||||||||
\(562\) | 4.92820i | 0.207884i | ||||||||
\(563\) | 17.0718i | 0.719490i | 0.933051 | + | 0.359745i | \(0.117136\pi\) | ||||
−0.933051 | + | 0.359745i | \(0.882864\pi\) | |||||||
\(564\) | −3.46410 | −0.145865 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.39230 | 0.184622 | ||||||||
\(567\) | − 3.12436i | − 0.131211i | ||||||||
\(568\) | 10.9282i | 0.458537i | ||||||||
\(569\) | 22.0000 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | − 2.14359i | − 0.0896281i | ||||||||
\(573\) | 14.3923i | 0.601247i | ||||||||
\(574\) | 2.53590 | 0.105846 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.46410 | 0.186004 | ||||||||
\(577\) | 3.60770i | 0.150190i | 0.997176 | + | 0.0750952i | \(0.0239261\pi\) | ||||
−0.997176 | + | 0.0750952i | \(0.976074\pi\) | |||||||
\(578\) | 14.8564i | 0.617945i | ||||||||
\(579\) | −32.3923 | −1.34618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.67949 | 0.277112 | ||||||||
\(582\) | 5.46410i | 0.226494i | ||||||||
\(583\) | − 8.78461i | − 0.363821i | ||||||||
\(584\) | 12.9282 | 0.534973 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | − 3.21539i | − 0.132713i | −0.997796 | − | 0.0663567i | \(-0.978862\pi\) | ||||
0.997796 | − | 0.0663567i | \(-0.0211375\pi\) | |||||||
\(588\) | 14.7321i | 0.607540i | ||||||||
\(589\) | −11.4641 | −0.472370 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −51.3205 | −2.11104 | ||||||||
\(592\) | − 1.00000i | − 0.0410997i | ||||||||
\(593\) | 6.78461i | 0.278611i | 0.990249 | + | 0.139305i | \(0.0444869\pi\) | ||||
−0.990249 | + | 0.139305i | \(0.955513\pi\) | |||||||
\(594\) | −5.85641 | −0.240291 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.3923 | −0.671455 | ||||||||
\(597\) | 71.1769i | 2.91308i | ||||||||
\(598\) | 11.7128i | 0.478973i | ||||||||
\(599\) | −2.53590 | −0.103614 | −0.0518070 | − | 0.998657i | \(-0.516498\pi\) | ||||
−0.0518070 | + | 0.998657i | \(0.516498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 48.3923 | 1.97396 | 0.986982 | − | 0.160833i | \(-0.0514180\pi\) | ||||
0.986982 | + | 0.160833i | \(0.0514180\pi\) | |||||||
\(602\) | 8.78461i | 0.358034i | ||||||||
\(603\) | 60.9808i | 2.48333i | ||||||||
\(604\) | −8.39230 | −0.341478 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.92820 | −0.281439 | ||||||||
\(607\) | 40.7846i | 1.65540i | 0.561174 | + | 0.827698i | \(0.310350\pi\) | ||||
−0.561174 | + | 0.827698i | \(0.689650\pi\) | |||||||
\(608\) | 4.19615i | 0.170176i | ||||||||
\(609\) | 30.9282 | 1.25327 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.85641 | −0.0751022 | ||||||||
\(612\) | 6.53590i | 0.264198i | ||||||||
\(613\) | 3.07180i | 0.124069i | 0.998074 | + | 0.0620344i | \(0.0197588\pi\) | ||||
−0.998074 | + | 0.0620344i | \(0.980241\pi\) | |||||||
\(614\) | −12.5885 | −0.508029 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.85641 | 0.0747967 | ||||||||
\(617\) | − 12.9282i | − 0.520470i | −0.965545 | − | 0.260235i | \(-0.916200\pi\) | ||||
0.965545 | − | 0.260235i | \(-0.0838000\pi\) | |||||||
\(618\) | − 36.7846i | − 1.47969i | ||||||||
\(619\) | −9.85641 | −0.396162 | −0.198081 | − | 0.980186i | \(-0.563471\pi\) | ||||
−0.198081 | + | 0.980186i | \(0.563471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.0000 | 1.28412 | ||||||||
\(622\) | 27.1244i | 1.08759i | ||||||||
\(623\) | 2.53590i | 0.101599i | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.85641 | −0.154133 | ||||||||
\(627\) | − 16.7846i | − 0.670313i | ||||||||
\(628\) | 16.9282i | 0.675509i | ||||||||
\(629\) | 1.46410 | 0.0583776 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.9808 | −0.835231 | −0.417615 | − | 0.908624i | \(-0.637134\pi\) | ||||
−0.417615 | + | 0.908624i | \(0.637134\pi\) | |||||||
\(632\) | 5.26795i | 0.209548i | ||||||||
\(633\) | − 26.9282i | − 1.07030i | ||||||||
\(634\) | −31.8564 | −1.26518 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.3923 | 0.649997 | ||||||||
\(637\) | 7.89488i | 0.312807i | ||||||||
\(638\) | 13.0718i | 0.517517i | ||||||||
\(639\) | 48.7846 | 1.92989 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.4641 | −0.531800 | −0.265900 | − | 0.964001i | \(-0.585669\pi\) | ||||
−0.265900 | + | 0.964001i | \(0.585669\pi\) | |||||||
\(642\) | − 18.3923i | − 0.725886i | ||||||||
\(643\) | 41.4641i | 1.63518i | 0.575798 | + | 0.817592i | \(0.304692\pi\) | ||||
−0.575798 | + | 0.817592i | \(0.695308\pi\) | |||||||
\(644\) | −10.1436 | −0.399714 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.14359 | −0.241716 | ||||||||
\(647\) | − 19.7128i | − 0.774991i | −0.921872 | − | 0.387495i | \(-0.873340\pi\) | ||||
0.921872 | − | 0.387495i | \(-0.126660\pi\) | |||||||
\(648\) | 2.46410i | 0.0967991i | ||||||||
\(649\) | −0.287187 | −0.0112731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.46410 | −0.370927 | ||||||||
\(652\) | − 23.3205i | − 0.913302i | ||||||||
\(653\) | − 18.0000i | − 0.704394i | −0.935926 | − | 0.352197i | \(-0.885435\pi\) | ||||
0.935926 | − | 0.352197i | \(-0.114565\pi\) | |||||||
\(654\) | −5.46410 | −0.213663 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | − 57.7128i | − 2.25159i | ||||||||
\(658\) | − 1.60770i | − 0.0626745i | ||||||||
\(659\) | −6.92820 | −0.269884 | −0.134942 | − | 0.990853i | \(-0.543085\pi\) | ||||
−0.134942 | + | 0.990853i | \(0.543085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.9282 | −1.74750 | −0.873752 | − | 0.486371i | \(-0.838320\pi\) | ||||
−0.873752 | + | 0.486371i | \(0.838320\pi\) | |||||||
\(662\) | − 8.87564i | − 0.344962i | ||||||||
\(663\) | 5.85641i | 0.227444i | ||||||||
\(664\) | −5.26795 | −0.204436 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.46410 | −0.172980 | ||||||||
\(667\) | − 71.4256i | − 2.76561i | ||||||||
\(668\) | 5.46410i | 0.211412i | ||||||||
\(669\) | −60.2487 | −2.32935 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.0718 | 0.504631 | ||||||||
\(672\) | 3.46410i | 0.133631i | ||||||||
\(673\) | − 19.0718i | − 0.735164i | −0.929991 | − | 0.367582i | \(-0.880186\pi\) | ||||
0.929991 | − | 0.367582i | \(-0.119814\pi\) | |||||||
\(674\) | 26.0000 | 1.00148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8564 | −0.417554 | ||||||||
\(677\) | 31.8564i | 1.22434i | 0.790726 | + | 0.612171i | \(0.209703\pi\) | ||||
−0.790726 | + | 0.612171i | \(0.790297\pi\) | |||||||
\(678\) | − 47.7128i | − 1.83240i | ||||||||
\(679\) | −2.53590 | −0.0973188 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.85641 | −0.377698 | ||||||||
\(682\) | − 4.00000i | − 0.153168i | ||||||||
\(683\) | 36.7846i | 1.40752i | 0.710436 | + | 0.703762i | \(0.248498\pi\) | ||||
−0.710436 | + | 0.703762i | \(0.751502\pi\) | |||||||
\(684\) | 18.7321 | 0.716238 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.7128 | −0.599918 | ||||||||
\(687\) | 43.3205i | 1.65278i | ||||||||
\(688\) | − 6.92820i | − 0.264135i | ||||||||
\(689\) | 8.78461 | 0.334667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3923 | 0.775760 | 0.387880 | − | 0.921710i | \(-0.373208\pi\) | ||||
0.387880 | + | 0.921710i | \(0.373208\pi\) | |||||||
\(692\) | − 10.0000i | − 0.380143i | ||||||||
\(693\) | − 8.28719i | − 0.314804i | ||||||||
\(694\) | 17.0718 | 0.648037 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −24.3923 | −0.924588 | ||||||||
\(697\) | − 2.92820i | − 0.110914i | ||||||||
\(698\) | − 19.3205i | − 0.731292i | ||||||||
\(699\) | 41.1769 | 1.55745 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.8564 | 0.598888 | 0.299444 | − | 0.954114i | \(-0.403199\pi\) | ||||
0.299444 | + | 0.954114i | \(0.403199\pi\) | |||||||
\(702\) | − 5.85641i | − 0.221036i | ||||||||
\(703\) | − 4.19615i | − 0.158261i | ||||||||
\(704\) | −1.46410 | −0.0551804 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.8564 | −0.596764 | ||||||||
\(707\) | − 3.21539i | − 0.120927i | ||||||||
\(708\) | − 0.535898i | − 0.0201403i | ||||||||
\(709\) | −16.1436 | −0.606285 | −0.303143 | − | 0.952945i | \(-0.598036\pi\) | ||||
−0.303143 | + | 0.952945i | \(0.598036\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.5167 | 0.881944 | ||||||||
\(712\) | − 2.00000i | − 0.0749532i | ||||||||
\(713\) | 21.8564i | 0.818529i | ||||||||
\(714\) | −5.07180 | −0.189807 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.6603 | −0.659995 | ||||||||
\(717\) | − 47.1769i | − 1.76185i | ||||||||
\(718\) | − 8.39230i | − 0.313198i | ||||||||
\(719\) | −8.39230 | −0.312980 | −0.156490 | − | 0.987680i | \(-0.550018\pi\) | ||||
−0.156490 | + | 0.987680i | \(0.550018\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.0718 | 0.635787 | ||||||||
\(722\) | − 1.39230i | − 0.0518162i | ||||||||
\(723\) | 24.3923i | 0.907160i | ||||||||
\(724\) | 1.46410 | 0.0544129 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −24.1962 | −0.898003 | ||||||||
\(727\) | 32.7846i | 1.21591i | 0.793970 | + | 0.607957i | \(0.208011\pi\) | ||||
−0.793970 | + | 0.607957i | \(0.791989\pi\) | |||||||
\(728\) | 1.85641i | 0.0688030i | ||||||||
\(729\) | 43.7846 | 1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1436 | 0.375174 | ||||||||
\(732\) | 24.3923i | 0.901566i | ||||||||
\(733\) | 0.143594i | 0.00530375i | 0.999996 | + | 0.00265187i | \(0.000844119\pi\) | ||||
−0.999996 | + | 0.00265187i | \(0.999156\pi\) | |||||||
\(734\) | −21.6603 | −0.799495 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | − 20.0000i | − 0.736709i | ||||||||
\(738\) | 8.92820i | 0.328652i | ||||||||
\(739\) | 6.92820 | 0.254858 | 0.127429 | − | 0.991848i | \(-0.459327\pi\) | ||||
0.127429 | + | 0.991848i | \(0.459327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.7846 | 0.616598 | ||||||||
\(742\) | 7.60770i | 0.279287i | ||||||||
\(743\) | − 7.12436i | − 0.261367i | −0.991424 | − | 0.130684i | \(-0.958283\pi\) | ||||
0.991424 | − | 0.130684i | \(-0.0417172\pi\) | |||||||
\(744\) | 7.46410 | 0.273647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.7846 | −1.12710 | ||||||||
\(747\) | 23.5167i | 0.860430i | ||||||||
\(748\) | − 2.14359i | − 0.0783775i | ||||||||
\(749\) | 8.53590 | 0.311895 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.392305 | 0.0143154 | 0.00715770 | − | 0.999974i | \(-0.497722\pi\) | ||||
0.00715770 | + | 0.999974i | \(0.497722\pi\) | |||||||
\(752\) | 1.26795i | 0.0462373i | ||||||||
\(753\) | − 62.1051i | − 2.26324i | ||||||||
\(754\) | −13.0718 | −0.476047 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.07180 | 0.184459 | ||||||||
\(757\) | 53.7128i | 1.95223i | 0.217265 | + | 0.976113i | \(0.430286\pi\) | ||||
−0.217265 | + | 0.976113i | \(0.569714\pi\) | |||||||
\(758\) | − 11.6077i | − 0.421610i | ||||||||
\(759\) | −32.0000 | −1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | 37.3205i | 1.35198i | ||||||||
\(763\) | − 2.53590i | − 0.0918057i | ||||||||
\(764\) | 5.26795 | 0.190588 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.00000 | 0.289052 | ||||||||
\(767\) | − 0.287187i | − 0.0103697i | ||||||||
\(768\) | − 2.73205i | − 0.0985844i | ||||||||
\(769\) | −20.9282 | −0.754690 | −0.377345 | − | 0.926073i | \(-0.623163\pi\) | ||||
−0.377345 | + | 0.926073i | \(0.623163\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 69.5692 | 2.50547 | ||||||||
\(772\) | 11.8564i | 0.426721i | ||||||||
\(773\) | − 38.7846i | − 1.39499i | −0.716592 | − | 0.697493i | \(-0.754299\pi\) | ||||
0.716592 | − | 0.697493i | \(-0.245701\pi\) | |||||||
\(774\) | −30.9282 | −1.11169 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | − 3.46410i | − 0.124274i | ||||||||
\(778\) | − 15.8564i | − 0.568480i | ||||||||
\(779\) | −8.39230 | −0.300686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | −0.572525 | ||||||||
\(782\) | 11.7128i | 0.418849i | ||||||||
\(783\) | 35.7128i | 1.27627i | ||||||||
\(784\) | 5.39230 | 0.192582 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34.3923 | 1.22673 | ||||||||
\(787\) | − 11.8038i | − 0.420762i | −0.977620 | − | 0.210381i | \(-0.932530\pi\) | ||||
0.977620 | − | 0.210381i | \(-0.0674704\pi\) | |||||||
\(788\) | 18.7846i | 0.669174i | ||||||||
\(789\) | 82.1051 | 2.92302 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.1436 | 0.787336 | ||||||||
\(792\) | 6.53590i | 0.232243i | ||||||||
\(793\) | 13.0718i | 0.464193i | ||||||||
\(794\) | −22.0000 | −0.780751 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.0526 | 0.923408 | ||||||||
\(797\) | − 17.4641i | − 0.618610i | −0.950963 | − | 0.309305i | \(-0.899904\pi\) | ||||
0.950963 | − | 0.309305i | \(-0.100096\pi\) | |||||||
\(798\) | 14.5359i | 0.514565i | ||||||||
\(799\) | −1.85641 | −0.0656749 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.92820 | −0.315463 | ||||||||
\(802\) | − 19.0718i | − 0.673449i | ||||||||
\(803\) | 18.9282i | 0.667962i | ||||||||
\(804\) | 37.3205 | 1.31619 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | − 1.07180i | − 0.0377290i | ||||||||
\(808\) | 2.53590i | 0.0892126i | ||||||||
\(809\) | 39.5692 | 1.39118 | 0.695590 | − | 0.718439i | \(-0.255143\pi\) | ||||
0.695590 | + | 0.718439i | \(0.255143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1436 | −0.496649 | −0.248324 | − | 0.968677i | \(-0.579880\pi\) | ||||
−0.248324 | + | 0.968677i | \(0.579880\pi\) | |||||||
\(812\) | − 11.3205i | − 0.397272i | ||||||||
\(813\) | − 45.8564i | − 1.60825i | ||||||||
\(814\) | 1.46410 | 0.0513167 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | − 29.0718i | − 1.01709i | ||||||||
\(818\) | − 16.9282i | − 0.591881i | ||||||||
\(819\) | 8.28719 | 0.289578 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | − 5.46410i | − 0.190582i | ||||||||
\(823\) | − 10.4449i | − 0.364085i | −0.983291 | − | 0.182043i | \(-0.941729\pi\) | ||||
0.983291 | − | 0.182043i | \(-0.0582709\pi\) | |||||||
\(824\) | −13.4641 | −0.469044 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.248711 | 0.00865377 | ||||||||
\(827\) | − 4.39230i | − 0.152735i | −0.997080 | − | 0.0763677i | \(-0.975668\pi\) | ||||
0.997080 | − | 0.0763677i | \(-0.0243323\pi\) | |||||||
\(828\) | − 35.7128i | − 1.24111i | ||||||||
\(829\) | −31.5692 | −1.09644 | −0.548222 | − | 0.836333i | \(-0.684695\pi\) | ||||
−0.548222 | + | 0.836333i | \(0.684695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 71.7128 | 2.48769 | ||||||||
\(832\) | − 1.46410i | − 0.0507586i | ||||||||
\(833\) | 7.89488i | 0.273541i | ||||||||
\(834\) | 18.9282 | 0.655430 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.14359 | −0.212481 | ||||||||
\(837\) | − 10.9282i | − 0.377734i | ||||||||
\(838\) | 34.2487i | 1.18310i | ||||||||
\(839\) | −32.7846 | −1.13185 | −0.565925 | − | 0.824457i | \(-0.691481\pi\) | ||||
−0.565925 | + | 0.824457i | \(0.691481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.7128 | 1.74872 | ||||||||
\(842\) | − 27.8564i | − 0.959995i | ||||||||
\(843\) | − 13.4641i | − 0.463728i | ||||||||
\(844\) | −9.85641 | −0.339272 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.66025 | 0.194604 | ||||||||
\(847\) | − 11.2295i | − 0.385849i | ||||||||
\(848\) | − 6.00000i | − 0.206041i | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | − 29.8564i | − 1.02286i | ||||||||
\(853\) | − 30.0000i | − 1.02718i | −0.858036 | − | 0.513590i | \(-0.828315\pi\) | ||||
0.858036 | − | 0.513590i | \(-0.171685\pi\) | |||||||
\(854\) | −11.3205 | −0.387380 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.73205 | −0.230097 | ||||||||
\(857\) | 4.14359i | 0.141542i | 0.997493 | + | 0.0707712i | \(0.0225460\pi\) | ||||
−0.997493 | + | 0.0707712i | \(0.977454\pi\) | |||||||
\(858\) | 5.85641i | 0.199934i | ||||||||
\(859\) | 14.4449 | 0.492852 | 0.246426 | − | 0.969162i | \(-0.420744\pi\) | ||||
0.246426 | + | 0.969162i | \(0.420744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.92820 | −0.236113 | ||||||||
\(862\) | 8.19615i | 0.279162i | ||||||||
\(863\) | 38.4449i | 1.30868i | 0.756201 | + | 0.654339i | \(0.227053\pi\) | ||||
−0.756201 | + | 0.654339i | \(0.772947\pi\) | |||||||
\(864\) | −4.00000 | −0.136083 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.0000 | 1.15537 | ||||||||
\(867\) | − 40.5885i | − 1.37846i | ||||||||
\(868\) | 3.46410i | 0.117579i | ||||||||
\(869\) | −7.71281 | −0.261639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.677674 | ||||||||
\(872\) | 2.00000i | 0.0677285i | ||||||||
\(873\) | − 8.92820i | − 0.302174i | ||||||||
\(874\) | 33.5692 | 1.13550 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −35.3205 | −1.19337 | ||||||||
\(877\) | 50.7846i | 1.71487i | 0.514589 | + | 0.857437i | \(0.327945\pi\) | ||||
−0.514589 | + | 0.857437i | \(0.672055\pi\) | |||||||
\(878\) | 31.5167i | 1.06364i | ||||||||
\(879\) | 16.3923 | 0.552899 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.3205 | 1.59427 | 0.797134 | − | 0.603802i | \(-0.206348\pi\) | ||||
0.797134 | + | 0.603802i | \(0.206348\pi\) | |||||||
\(882\) | − 24.0718i | − 0.810540i | ||||||||
\(883\) | − 34.2487i | − 1.15256i | −0.817252 | − | 0.576280i | \(-0.804504\pi\) | ||||
0.817252 | − | 0.576280i | \(-0.195496\pi\) | |||||||
\(884\) | 2.14359 | 0.0720969 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.1244 | 1.31441 | ||||||||
\(887\) | − 20.1962i | − 0.678120i | −0.940765 | − | 0.339060i | \(-0.889891\pi\) | ||||
0.940765 | − | 0.339060i | \(-0.110109\pi\) | |||||||
\(888\) | 2.73205i | 0.0916816i | ||||||||
\(889\) | −17.3205 | −0.580911 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.60770 | −0.120862 | ||||||||
\(892\) | 22.0526i | 0.738374i | ||||||||
\(893\) | 5.32051i | 0.178044i | ||||||||
\(894\) | 44.7846 | 1.49782 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.26795 | 0.0423592 | ||||||||
\(897\) | − 32.0000i | − 1.06845i | ||||||||
\(898\) | − 33.7128i | − 1.12501i | ||||||||
\(899\) | −24.3923 | −0.813529 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.78461 | 0.292658 | ||||||||
\(902\) | − 2.92820i | − 0.0974985i | ||||||||
\(903\) | − 24.0000i | − 0.798670i | ||||||||
\(904\) | −17.4641 | −0.580847 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 22.9282 | 0.761739 | ||||||||
\(907\) | − 5.75129i | − 0.190968i | −0.995431 | − | 0.0954842i | \(-0.969560\pi\) | ||||
0.995431 | − | 0.0954842i | \(-0.0304399\pi\) | |||||||
\(908\) | 3.60770i | 0.119726i | ||||||||
\(909\) | 11.3205 | 0.375478 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.9090 | −0.924665 | −0.462333 | − | 0.886707i | \(-0.652987\pi\) | ||||
−0.462333 | + | 0.886707i | \(0.652987\pi\) | |||||||
\(912\) | − 11.4641i | − 0.379614i | ||||||||
\(913\) | − 7.71281i | − 0.255257i | ||||||||
\(914\) | −4.14359 | −0.137058 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.8564 | 0.523910 | ||||||||
\(917\) | 15.9615i | 0.527096i | ||||||||
\(918\) | − 5.85641i | − 0.193290i | ||||||||
\(919\) | 13.2679 | 0.437669 | 0.218835 | − | 0.975762i | \(-0.429774\pi\) | ||||
0.218835 | + | 0.975762i | \(0.429774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.3923 | 1.13326 | ||||||||
\(922\) | − 26.7846i | − 0.882104i | ||||||||
\(923\) | − 16.0000i | − 0.526646i | ||||||||
\(924\) | −5.07180 | −0.166850 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.07180 | −0.166670 | ||||||||
\(927\) | 60.1051i | 1.97411i | ||||||||
\(928\) | 8.92820i | 0.293083i | ||||||||
\(929\) | 15.8564 | 0.520232 | 0.260116 | − | 0.965577i | \(-0.416239\pi\) | ||||
0.260116 | + | 0.965577i | \(0.416239\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.6269 | 0.741568 | ||||||||
\(932\) | − 15.0718i | − 0.493693i | ||||||||
\(933\) | − 74.1051i | − 2.42609i | ||||||||
\(934\) | 37.1769 | 1.21647 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.53590 | −0.213633 | ||||||||
\(937\) | − 3.85641i | − 0.125983i | −0.998014 | − | 0.0629917i | \(-0.979936\pi\) | ||||
0.998014 | − | 0.0629917i | \(-0.0200642\pi\) | |||||||
\(938\) | 17.3205i | 0.565535i | ||||||||
\(939\) | 10.5359 | 0.343826 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.3923 | 0.925563 | 0.462781 | − | 0.886472i | \(-0.346852\pi\) | ||||
0.462781 | + | 0.886472i | \(0.346852\pi\) | |||||||
\(942\) | − 46.2487i | − 1.50686i | ||||||||
\(943\) | 16.0000i | 0.521032i | ||||||||
\(944\) | −0.196152 | −0.00638422 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.1436 | 0.329797 | ||||||||
\(947\) | 45.1769i | 1.46805i | 0.679121 | + | 0.734026i | \(0.262361\pi\) | ||||
−0.679121 | + | 0.734026i | \(0.737639\pi\) | |||||||
\(948\) | − 14.3923i | − 0.467440i | ||||||||
\(949\) | −18.9282 | −0.614435 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 87.0333 | 2.82225 | ||||||||
\(952\) | 1.85641i | 0.0601665i | ||||||||
\(953\) | − 11.8564i | − 0.384067i | −0.981388 | − | 0.192033i | \(-0.938492\pi\) | ||||
0.981388 | − | 0.192033i | \(-0.0615082\pi\) | |||||||
\(954\) | −26.7846 | −0.867184 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17.2679 | −0.558485 | ||||||||
\(957\) | − 35.7128i | − 1.15443i | ||||||||
\(958\) | 34.0526i | 1.10019i | ||||||||
\(959\) | 2.53590 | 0.0818884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5359 | −0.759223 | ||||||||
\(962\) | 1.46410i | 0.0472045i | ||||||||
\(963\) | 30.0526i | 0.968430i | ||||||||
\(964\) | 8.92820 | 0.287558 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 27.7128 | 0.891645 | ||||||||
\(967\) | 23.6077i | 0.759172i | 0.925156 | + | 0.379586i | \(0.123934\pi\) | ||||
−0.925156 | + | 0.379586i | \(0.876066\pi\) | |||||||
\(968\) | 8.85641i | 0.284656i | ||||||||
\(969\) | 16.7846 | 0.539199 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.9282 | 0.479069 | 0.239534 | − | 0.970888i | \(-0.423005\pi\) | ||||
0.239534 | + | 0.970888i | \(0.423005\pi\) | |||||||
\(972\) | − 18.7321i | − 0.600831i | ||||||||
\(973\) | 8.78461i | 0.281622i | ||||||||
\(974\) | −16.3923 | −0.525243 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.92820 | 0.285785 | ||||||||
\(977\) | 34.0000i | 1.08776i | 0.839164 | + | 0.543878i | \(0.183045\pi\) | ||||
−0.839164 | + | 0.543878i | \(0.816955\pi\) | |||||||
\(978\) | 63.7128i | 2.03731i | ||||||||
\(979\) | 2.92820 | 0.0935858 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.92820 | 0.285056 | ||||||||
\(982\) | − 1.07180i | − 0.0342024i | ||||||||
\(983\) | − 38.4449i | − 1.22620i | −0.790005 | − | 0.613100i | \(-0.789922\pi\) | ||||
0.790005 | − | 0.613100i | \(-0.210078\pi\) | |||||||
\(984\) | 5.46410 | 0.174189 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.0718 | −0.416291 | ||||||||
\(987\) | 4.39230i | 0.139809i | ||||||||
\(988\) | − 6.14359i | − 0.195454i | ||||||||
\(989\) | −55.4256 | −1.76243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.94744 | 0.188927 | 0.0944633 | − | 0.995528i | \(-0.469886\pi\) | ||||
0.0944633 | + | 0.995528i | \(0.469886\pi\) | |||||||
\(992\) | − 2.73205i | − 0.0867427i | ||||||||
\(993\) | 24.2487i | 0.769510i | ||||||||
\(994\) | 13.8564 | 0.439499 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.3923 | 0.456038 | ||||||||
\(997\) | 4.14359i | 0.131229i | 0.997845 | + | 0.0656145i | \(0.0209007\pi\) | ||||
−0.997845 | + | 0.0656145i | \(0.979099\pi\) | |||||||
\(998\) | − 40.5885i | − 1.28481i | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 1850.2.b.l.149.3 | 4 | ||
5.2 | odd | 4 | 370.2.a.e.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1850.2.a.x.1.2 | 2 | |||
5.4 | even | 2 | inner | 1850.2.b.l.149.2 | 4 | ||
15.2 | even | 4 | 3330.2.a.bd.1.2 | 2 | |||
20.7 | even | 4 | 2960.2.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.a.e.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
1850.2.a.x.1.2 | 2 | 5.3 | odd | 4 | |||
1850.2.b.l.149.2 | 4 | 5.4 | even | 2 | inner | ||
1850.2.b.l.149.3 | 4 | 1.1 | even | 1 | trivial | ||
2960.2.a.q.1.2 | 2 | 20.7 | even | 4 | |||
3330.2.a.bd.1.2 | 2 | 15.2 | even | 4 |