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: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.4 | ||
Root | \(2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.149 |
Dual form | 1850.2.b.i.149.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.30278i | 1.90686i | 0.301617 | + | 0.953429i | \(0.402474\pi\) | ||||
−0.301617 | + | 0.953429i | \(0.597526\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.30278 | −1.34835 | ||||||||
\(7\) | 2.60555i | 0.984806i | 0.870367 | + | 0.492403i | \(0.163881\pi\) | ||||
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −7.90833 | −2.63611 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.30278 | −0.694313 | −0.347156 | − | 0.937807i | \(-0.612853\pi\) | ||||
−0.347156 | + | 0.937807i | \(0.612853\pi\) | |||||||
\(12\) | − 3.30278i | − 0.953429i | ||||||||
\(13\) | 1.30278i | 0.361325i | 0.983545 | + | 0.180662i | \(0.0578242\pi\) | ||||
−0.983545 | + | 0.180662i | \(0.942176\pi\) | |||||||
\(14\) | −2.60555 | −0.696363 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.00000i | 1.45521i | 0.685994 | + | 0.727607i | \(0.259367\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(18\) | − 7.90833i | − 1.86401i | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.60555 | −1.87789 | ||||||||
\(22\) | − 2.30278i | − 0.490953i | ||||||||
\(23\) | 3.90833i | 0.814942i | 0.913218 | + | 0.407471i | \(0.133589\pi\) | ||||
−0.913218 | + | 0.407471i | \(0.866411\pi\) | |||||||
\(24\) | 3.30278 | 0.674176 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.30278 | −0.255495 | ||||||||
\(27\) | − 16.2111i | − 3.11983i | ||||||||
\(28\) | − 2.60555i | − 0.492403i | ||||||||
\(29\) | 3.90833 | 0.725758 | 0.362879 | − | 0.931836i | \(-0.381794\pi\) | ||||
0.362879 | + | 0.931836i | \(0.381794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.302776 | −0.0543801 | −0.0271901 | − | 0.999630i | \(-0.508656\pi\) | ||||
−0.0271901 | + | 0.999630i | \(0.508656\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 7.60555i | − 1.32396i | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.90833 | 1.31805 | ||||||||
\(37\) | − 1.00000i | − 0.164399i | ||||||||
\(38\) | − 2.00000i | − 0.324443i | ||||||||
\(39\) | −4.30278 | −0.688996 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.90833 | 1.54742 | 0.773710 | − | 0.633540i | \(-0.218399\pi\) | ||||
0.773710 | + | 0.633540i | \(0.218399\pi\) | |||||||
\(42\) | − 8.60555i | − 1.32787i | ||||||||
\(43\) | 0.605551i | 0.0923457i | 0.998933 | + | 0.0461729i | \(0.0147025\pi\) | ||||
−0.998933 | + | 0.0461729i | \(0.985297\pi\) | |||||||
\(44\) | 2.30278 | 0.347156 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.90833 | −0.576251 | ||||||||
\(47\) | − 4.60555i | − 0.671789i | −0.941900 | − | 0.335894i | \(-0.890961\pi\) | ||||
0.941900 | − | 0.335894i | \(-0.109039\pi\) | |||||||
\(48\) | 3.30278i | 0.476715i | ||||||||
\(49\) | 0.211103 | 0.0301575 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.8167 | −2.77489 | ||||||||
\(52\) | − 1.30278i | − 0.180662i | ||||||||
\(53\) | − 6.00000i | − 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 16.2111 | 2.20605 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.60555 | 0.348181 | ||||||||
\(57\) | − 6.60555i | − 0.874927i | ||||||||
\(58\) | 3.90833i | 0.513188i | ||||||||
\(59\) | −10.6056 | −1.38073 | −0.690363 | − | 0.723464i | \(-0.742549\pi\) | ||||
−0.690363 | + | 0.723464i | \(0.742549\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.51388 | 0.962054 | 0.481027 | − | 0.876706i | \(-0.340264\pi\) | ||||
0.481027 | + | 0.876706i | \(0.340264\pi\) | |||||||
\(62\) | − 0.302776i | − 0.0384525i | ||||||||
\(63\) | − 20.6056i | − 2.59606i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.60555 | 0.936179 | ||||||||
\(67\) | 3.51388i | 0.429289i | 0.976692 | + | 0.214644i | \(0.0688592\pi\) | ||||
−0.976692 | + | 0.214644i | \(0.931141\pi\) | |||||||
\(68\) | − 6.00000i | − 0.727607i | ||||||||
\(69\) | −12.9083 | −1.55398 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 7.90833i | 0.932005i | ||||||||
\(73\) | − 12.3028i | − 1.43993i | −0.694010 | − | 0.719965i | \(-0.744158\pi\) | ||||
0.694010 | − | 0.719965i | \(-0.255842\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | − 6.00000i | − 0.683763i | ||||||||
\(78\) | − 4.30278i | − 0.487193i | ||||||||
\(79\) | −9.11943 | −1.02602 | −0.513008 | − | 0.858384i | \(-0.671469\pi\) | ||||
−0.513008 | + | 0.858384i | \(0.671469\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.8167 | 3.31296 | ||||||||
\(82\) | 9.90833i | 1.09419i | ||||||||
\(83\) | 2.78890i | 0.306121i | 0.988217 | + | 0.153061i | \(0.0489130\pi\) | ||||
−0.988217 | + | 0.153061i | \(0.951087\pi\) | |||||||
\(84\) | 8.60555 | 0.938943 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.605551 | −0.0652983 | ||||||||
\(87\) | 12.9083i | 1.38392i | ||||||||
\(88\) | 2.30278i | 0.245477i | ||||||||
\(89\) | 9.21110 | 0.976375 | 0.488187 | − | 0.872739i | \(-0.337658\pi\) | ||||
0.488187 | + | 0.872739i | \(0.337658\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.39445 | −0.355835 | ||||||||
\(92\) | − 3.90833i | − 0.407471i | ||||||||
\(93\) | − 1.00000i | − 0.103695i | ||||||||
\(94\) | 4.60555 | 0.475026 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.30278 | −0.337088 | ||||||||
\(97\) | 16.4222i | 1.66742i | 0.552201 | + | 0.833711i | \(0.313788\pi\) | ||||
−0.552201 | + | 0.833711i | \(0.686212\pi\) | |||||||
\(98\) | 0.211103i | 0.0213246i | ||||||||
\(99\) | 18.2111 | 1.83028 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4222 | −1.23606 | −0.618028 | − | 0.786156i | \(-0.712068\pi\) | ||||
−0.618028 | + | 0.786156i | \(0.712068\pi\) | |||||||
\(102\) | − 19.8167i | − 1.96214i | ||||||||
\(103\) | − 0.302776i | − 0.0298334i | −0.999889 | − | 0.0149167i | \(-0.995252\pi\) | ||||
0.999889 | − | 0.0149167i | \(-0.00474830\pi\) | |||||||
\(104\) | 1.30278 | 0.127748 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | − 0.697224i | − 0.0674032i | −0.999432 | − | 0.0337016i | \(-0.989270\pi\) | ||||
0.999432 | − | 0.0337016i | \(-0.0107296\pi\) | |||||||
\(108\) | 16.2111i | 1.55991i | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.30278 | 0.313486 | ||||||||
\(112\) | 2.60555i | 0.246201i | ||||||||
\(113\) | − 3.21110i | − 0.302075i | −0.988528 | − | 0.151038i | \(-0.951739\pi\) | ||||
0.988528 | − | 0.151038i | \(-0.0482614\pi\) | |||||||
\(114\) | 6.60555 | 0.618667 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.90833 | −0.362879 | ||||||||
\(117\) | − 10.3028i | − 0.952492i | ||||||||
\(118\) | − 10.6056i | − 0.976320i | ||||||||
\(119\) | −15.6333 | −1.43310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.69722 | −0.517929 | ||||||||
\(122\) | 7.51388i | 0.680275i | ||||||||
\(123\) | 32.7250i | 2.95071i | ||||||||
\(124\) | 0.302776 | 0.0271901 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 20.6056 | 1.83569 | ||||||||
\(127\) | 19.2111i | 1.70471i | 0.522964 | + | 0.852355i | \(0.324826\pi\) | ||||
−0.522964 | + | 0.852355i | \(0.675174\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −2.00000 | −0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.6056 | 0.926611 | 0.463306 | − | 0.886199i | \(-0.346663\pi\) | ||||
0.463306 | + | 0.886199i | \(0.346663\pi\) | |||||||
\(132\) | 7.60555i | 0.661978i | ||||||||
\(133\) | − 5.21110i | − 0.451860i | ||||||||
\(134\) | −3.51388 | −0.303553 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | − 0.908327i | − 0.0776036i | −0.999247 | − | 0.0388018i | \(-0.987646\pi\) | ||||
0.999247 | − | 0.0388018i | \(-0.0123541\pi\) | |||||||
\(138\) | − 12.9083i | − 1.09883i | ||||||||
\(139\) | 1.90833 | 0.161862 | 0.0809311 | − | 0.996720i | \(-0.474211\pi\) | ||||
0.0809311 | + | 0.996720i | \(0.474211\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.2111 | 1.28101 | ||||||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | − 3.00000i | − 0.250873i | ||||||||
\(144\) | −7.90833 | −0.659027 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.3028 | 1.01818 | ||||||||
\(147\) | 0.697224i | 0.0575061i | ||||||||
\(148\) | 1.00000i | 0.0821995i | ||||||||
\(149\) | −19.8167 | −1.62344 | −0.811722 | − | 0.584044i | \(-0.801469\pi\) | ||||
−0.811722 | + | 0.584044i | \(0.801469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.6056 | −1.67686 | −0.838428 | − | 0.545012i | \(-0.816525\pi\) | ||||
−0.838428 | + | 0.545012i | \(0.816525\pi\) | |||||||
\(152\) | 2.00000i | 0.162221i | ||||||||
\(153\) | − 47.4500i | − 3.83610i | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.30278 | 0.344498 | ||||||||
\(157\) | 7.21110i | 0.575509i | 0.957704 | + | 0.287754i | \(0.0929087\pi\) | ||||
−0.957704 | + | 0.287754i | \(0.907091\pi\) | |||||||
\(158\) | − 9.11943i | − 0.725503i | ||||||||
\(159\) | 19.8167 | 1.57156 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.1833 | −0.802560 | ||||||||
\(162\) | 29.8167i | 2.34262i | ||||||||
\(163\) | 8.42221i | 0.659678i | 0.944037 | + | 0.329839i | \(0.106994\pi\) | ||||
−0.944037 | + | 0.329839i | \(0.893006\pi\) | |||||||
\(164\) | −9.90833 | −0.773710 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.78890 | −0.216460 | ||||||||
\(167\) | 5.51388i | 0.426677i | 0.976978 | + | 0.213338i | \(0.0684337\pi\) | ||||
−0.976978 | + | 0.213338i | \(0.931566\pi\) | |||||||
\(168\) | 8.60555i | 0.663933i | ||||||||
\(169\) | 11.3028 | 0.869444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.8167 | 1.20953 | ||||||||
\(172\) | − 0.605551i | − 0.0461729i | ||||||||
\(173\) | − 8.78890i | − 0.668207i | −0.942536 | − | 0.334104i | \(-0.891566\pi\) | ||||
0.942536 | − | 0.334104i | \(-0.108434\pi\) | |||||||
\(174\) | −12.9083 | −0.978578 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.30278 | −0.173578 | ||||||||
\(177\) | − 35.0278i | − 2.63285i | ||||||||
\(178\) | 9.21110i | 0.690401i | ||||||||
\(179\) | 13.8167 | 1.03271 | 0.516353 | − | 0.856376i | \(-0.327289\pi\) | ||||
0.516353 | + | 0.856376i | \(0.327289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | − 3.39445i | − 0.251613i | ||||||||
\(183\) | 24.8167i | 1.83450i | ||||||||
\(184\) | 3.90833 | 0.288126 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | − 13.8167i | − 1.01037i | ||||||||
\(188\) | 4.60555i | 0.335894i | ||||||||
\(189\) | 42.2389 | 3.07242 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.51388 | −0.398970 | −0.199485 | − | 0.979901i | \(-0.563927\pi\) | ||||
−0.199485 | + | 0.979901i | \(0.563927\pi\) | |||||||
\(192\) | − 3.30278i | − 0.238357i | ||||||||
\(193\) | − 4.00000i | − 0.287926i | −0.989583 | − | 0.143963i | \(-0.954015\pi\) | ||||
0.989583 | − | 0.143963i | \(-0.0459847\pi\) | |||||||
\(194\) | −16.4222 | −1.17905 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.211103 | −0.0150788 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 18.2111i | 1.29421i | ||||||||
\(199\) | −26.4222 | −1.87302 | −0.936510 | − | 0.350640i | \(-0.885964\pi\) | ||||
−0.936510 | + | 0.350640i | \(0.885964\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.6056 | −0.818592 | ||||||||
\(202\) | − 12.4222i | − 0.874023i | ||||||||
\(203\) | 10.1833i | 0.714731i | ||||||||
\(204\) | 19.8167 | 1.38744 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.302776 | 0.0210954 | ||||||||
\(207\) | − 30.9083i | − 2.14828i | ||||||||
\(208\) | 1.30278i | 0.0903312i | ||||||||
\(209\) | 4.60555 | 0.318573 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3028 | 0.709272 | 0.354636 | − | 0.935004i | \(-0.384605\pi\) | ||||
0.354636 | + | 0.935004i | \(0.384605\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 19.8167i | 1.35781i | ||||||||
\(214\) | 0.697224 | 0.0476613 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −16.2111 | −1.10303 | ||||||||
\(217\) | − 0.788897i | − 0.0535538i | ||||||||
\(218\) | − 2.00000i | − 0.135457i | ||||||||
\(219\) | 40.6333 | 2.74574 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.81665 | −0.525805 | ||||||||
\(222\) | 3.30278i | 0.221668i | ||||||||
\(223\) | − 5.81665i | − 0.389512i | −0.980852 | − | 0.194756i | \(-0.937609\pi\) | ||||
0.980852 | − | 0.194756i | \(-0.0623915\pi\) | |||||||
\(224\) | −2.60555 | −0.174091 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.21110 | 0.213599 | ||||||||
\(227\) | − 13.8167i | − 0.917044i | −0.888683 | − | 0.458522i | \(-0.848379\pi\) | ||||
0.888683 | − | 0.458522i | \(-0.151621\pi\) | |||||||
\(228\) | 6.60555i | 0.437463i | ||||||||
\(229\) | −24.6056 | −1.62598 | −0.812990 | − | 0.582277i | \(-0.802162\pi\) | ||||
−0.812990 | + | 0.582277i | \(0.802162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.8167 | 1.30384 | ||||||||
\(232\) | − 3.90833i | − 0.256594i | ||||||||
\(233\) | 8.51388i | 0.557763i | 0.960326 | + | 0.278881i | \(0.0899636\pi\) | ||||
−0.960326 | + | 0.278881i | \(0.910036\pi\) | |||||||
\(234\) | 10.3028 | 0.673514 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.6056 | 0.690363 | ||||||||
\(237\) | − 30.1194i | − 1.95647i | ||||||||
\(238\) | − 15.6333i | − 1.01336i | ||||||||
\(239\) | 17.5139 | 1.13288 | 0.566439 | − | 0.824103i | \(-0.308321\pi\) | ||||
0.566439 | + | 0.824103i | \(0.308321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | − 5.69722i | − 0.366231i | ||||||||
\(243\) | 49.8444i | 3.19752i | ||||||||
\(244\) | −7.51388 | −0.481027 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −32.7250 | −2.08647 | ||||||||
\(247\) | − 2.60555i | − 0.165787i | ||||||||
\(248\) | 0.302776i | 0.0192263i | ||||||||
\(249\) | −9.21110 | −0.583730 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.2111 | −1.33883 | −0.669416 | − | 0.742887i | \(-0.733456\pi\) | ||||
−0.669416 | + | 0.742887i | \(0.733456\pi\) | |||||||
\(252\) | 20.6056i | 1.29803i | ||||||||
\(253\) | − 9.00000i | − 0.565825i | ||||||||
\(254\) | −19.2111 | −1.20541 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 3.21110i | − 0.200303i | −0.994972 | − | 0.100152i | \(-0.968067\pi\) | ||||
0.994972 | − | 0.100152i | \(-0.0319328\pi\) | |||||||
\(258\) | − 2.00000i | − 0.124515i | ||||||||
\(259\) | 2.60555 | 0.161901 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.9083 | −1.91318 | ||||||||
\(262\) | 10.6056i | 0.655213i | ||||||||
\(263\) | 13.8167i | 0.851971i | 0.904730 | + | 0.425986i | \(0.140073\pi\) | ||||
−0.904730 | + | 0.425986i | \(0.859927\pi\) | |||||||
\(264\) | −7.60555 | −0.468089 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.21110 | 0.319513 | ||||||||
\(267\) | 30.4222i | 1.86181i | ||||||||
\(268\) | − 3.51388i | − 0.214644i | ||||||||
\(269\) | 21.2111 | 1.29326 | 0.646632 | − | 0.762802i | \(-0.276177\pi\) | ||||
0.646632 | + | 0.762802i | \(0.276177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.4222 | −1.36205 | −0.681026 | − | 0.732259i | \(-0.738466\pi\) | ||||
−0.681026 | + | 0.732259i | \(0.738466\pi\) | |||||||
\(272\) | 6.00000i | 0.363803i | ||||||||
\(273\) | − 11.2111i | − 0.678527i | ||||||||
\(274\) | 0.908327 | 0.0548740 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.9083 | 0.776990 | ||||||||
\(277\) | − 0.119429i | − 0.00717582i | −0.999994 | − | 0.00358791i | \(-0.998858\pi\) | ||||
0.999994 | − | 0.00358791i | \(-0.00114207\pi\) | |||||||
\(278\) | 1.90833i | 0.114454i | ||||||||
\(279\) | 2.39445 | 0.143352 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 15.2111i | 0.905808i | ||||||||
\(283\) | 24.6056i | 1.46265i | 0.682030 | + | 0.731324i | \(0.261097\pi\) | ||||
−0.682030 | + | 0.731324i | \(0.738903\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | 25.8167i | 1.52391i | ||||||||
\(288\) | − 7.90833i | − 0.466003i | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −54.2389 | −3.17954 | ||||||||
\(292\) | 12.3028i | 0.719965i | ||||||||
\(293\) | 11.0278i | 0.644248i | 0.946697 | + | 0.322124i | \(0.104397\pi\) | ||||
−0.946697 | + | 0.322124i | \(0.895603\pi\) | |||||||
\(294\) | −0.697224 | −0.0406630 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 37.3305i | 2.16614i | ||||||||
\(298\) | − 19.8167i | − 1.14795i | ||||||||
\(299\) | −5.09167 | −0.294459 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.57779 | −0.0909426 | ||||||||
\(302\) | − 20.6056i | − 1.18572i | ||||||||
\(303\) | − 41.0278i | − 2.35698i | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 47.4500 | 2.71253 | ||||||||
\(307\) | − 17.9083i | − 1.02208i | −0.859556 | − | 0.511041i | \(-0.829260\pi\) | ||||
0.859556 | − | 0.511041i | \(-0.170740\pi\) | |||||||
\(308\) | 6.00000i | 0.341882i | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.9083 | 0.902078 | 0.451039 | − | 0.892504i | \(-0.351053\pi\) | ||||
0.451039 | + | 0.892504i | \(0.351053\pi\) | |||||||
\(312\) | 4.30278i | 0.243597i | ||||||||
\(313\) | − 9.02776i | − 0.510279i | −0.966904 | − | 0.255139i | \(-0.917879\pi\) | ||||
0.966904 | − | 0.255139i | \(-0.0821214\pi\) | |||||||
\(314\) | −7.21110 | −0.406946 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.11943 | 0.513008 | ||||||||
\(317\) | − 9.21110i | − 0.517347i | −0.965965 | − | 0.258674i | \(-0.916715\pi\) | ||||
0.965965 | − | 0.258674i | \(-0.0832854\pi\) | |||||||
\(318\) | 19.8167i | 1.11126i | ||||||||
\(319\) | −9.00000 | −0.503903 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.30278 | 0.128528 | ||||||||
\(322\) | − 10.1833i | − 0.567496i | ||||||||
\(323\) | − 12.0000i | − 0.667698i | ||||||||
\(324\) | −29.8167 | −1.65648 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.42221 | −0.466463 | ||||||||
\(327\) | − 6.60555i | − 0.365288i | ||||||||
\(328\) | − 9.90833i | − 0.547096i | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2111 | −0.726148 | −0.363074 | − | 0.931760i | \(-0.618273\pi\) | ||||
−0.363074 | + | 0.931760i | \(0.618273\pi\) | |||||||
\(332\) | − 2.78890i | − 0.153061i | ||||||||
\(333\) | 7.90833i | 0.433374i | ||||||||
\(334\) | −5.51388 | −0.301706 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.60555 | −0.469471 | ||||||||
\(337\) | − 6.11943i | − 0.333347i | −0.986012 | − | 0.166673i | \(-0.946697\pi\) | ||||
0.986012 | − | 0.166673i | \(-0.0533025\pi\) | |||||||
\(338\) | 11.3028i | 0.614790i | ||||||||
\(339\) | 10.6056 | 0.576014 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.697224 | 0.0377568 | ||||||||
\(342\) | 15.8167i | 0.855267i | ||||||||
\(343\) | 18.7889i | 1.01451i | ||||||||
\(344\) | 0.605551 | 0.0326491 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.78890 | 0.472494 | ||||||||
\(347\) | − 10.1833i | − 0.546671i | −0.961919 | − | 0.273335i | \(-0.911873\pi\) | ||||
0.961919 | − | 0.273335i | \(-0.0881269\pi\) | |||||||
\(348\) | − 12.9083i | − 0.691959i | ||||||||
\(349\) | −28.2389 | −1.51159 | −0.755796 | − | 0.654807i | \(-0.772750\pi\) | ||||
−0.755796 | + | 0.654807i | \(0.772750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.1194 | 1.12727 | ||||||||
\(352\) | − 2.30278i | − 0.122738i | ||||||||
\(353\) | 10.1833i | 0.542005i | 0.962579 | + | 0.271002i | \(0.0873551\pi\) | ||||
−0.962579 | + | 0.271002i | \(0.912645\pi\) | |||||||
\(354\) | 35.0278 | 1.86170 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.21110 | −0.488187 | ||||||||
\(357\) | − 51.6333i | − 2.73272i | ||||||||
\(358\) | 13.8167i | 0.730233i | ||||||||
\(359\) | −3.21110 | −0.169476 | −0.0847378 | − | 0.996403i | \(-0.527005\pi\) | ||||
−0.0847378 | + | 0.996403i | \(0.527005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 20.0000i | 1.05118i | ||||||||
\(363\) | − 18.8167i | − 0.987618i | ||||||||
\(364\) | 3.39445 | 0.177917 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −24.8167 | −1.29719 | ||||||||
\(367\) | − 3.81665i | − 0.199228i | −0.995026 | − | 0.0996139i | \(-0.968239\pi\) | ||||
0.995026 | − | 0.0996139i | \(-0.0317607\pi\) | |||||||
\(368\) | 3.90833i | 0.203736i | ||||||||
\(369\) | −78.3583 | −4.07917 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.6333 | 0.811641 | ||||||||
\(372\) | 1.00000i | 0.0518476i | ||||||||
\(373\) | − 17.8167i | − 0.922511i | −0.887267 | − | 0.461256i | \(-0.847399\pi\) | ||||
0.887267 | − | 0.461256i | \(-0.152601\pi\) | |||||||
\(374\) | 13.8167 | 0.714442 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.60555 | −0.237513 | ||||||||
\(377\) | 5.09167i | 0.262235i | ||||||||
\(378\) | 42.2389i | 2.17253i | ||||||||
\(379\) | −24.3305 | −1.24978 | −0.624888 | − | 0.780715i | \(-0.714855\pi\) | ||||
−0.624888 | + | 0.780715i | \(0.714855\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −63.4500 | −3.25064 | ||||||||
\(382\) | − 5.51388i | − 0.282115i | ||||||||
\(383\) | − 36.8444i | − 1.88266i | −0.337486 | − | 0.941331i | \(-0.609576\pi\) | ||||
0.337486 | − | 0.941331i | \(-0.390424\pi\) | |||||||
\(384\) | 3.30278 | 0.168544 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.00000 | 0.203595 | ||||||||
\(387\) | − 4.78890i | − 0.243433i | ||||||||
\(388\) | − 16.4222i | − 0.833711i | ||||||||
\(389\) | 37.1194 | 1.88203 | 0.941015 | − | 0.338365i | \(-0.109874\pi\) | ||||
0.941015 | + | 0.338365i | \(0.109874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.4500 | −1.18592 | ||||||||
\(392\) | − 0.211103i | − 0.0106623i | ||||||||
\(393\) | 35.0278i | 1.76692i | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.2111 | −0.915142 | ||||||||
\(397\) | − 6.18335i | − 0.310333i | −0.987888 | − | 0.155167i | \(-0.950409\pi\) | ||||
0.987888 | − | 0.155167i | \(-0.0495914\pi\) | |||||||
\(398\) | − 26.4222i | − 1.32443i | ||||||||
\(399\) | 17.2111 | 0.861633 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.81665 | −0.390345 | −0.195173 | − | 0.980769i | \(-0.562527\pi\) | ||||
−0.195173 | + | 0.980769i | \(0.562527\pi\) | |||||||
\(402\) | − 11.6056i | − 0.578832i | ||||||||
\(403\) | − 0.394449i | − 0.0196489i | ||||||||
\(404\) | 12.4222 | 0.618028 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.1833 | −0.505391 | ||||||||
\(407\) | 2.30278i | 0.114144i | ||||||||
\(408\) | 19.8167i | 0.981071i | ||||||||
\(409\) | −31.0278 | −1.53422 | −0.767112 | − | 0.641513i | \(-0.778307\pi\) | ||||
−0.767112 | + | 0.641513i | \(0.778307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00000 | 0.147979 | ||||||||
\(412\) | 0.302776i | 0.0149167i | ||||||||
\(413\) | − 27.6333i | − 1.35975i | ||||||||
\(414\) | 30.9083 | 1.51906 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.30278 | −0.0638738 | ||||||||
\(417\) | 6.30278i | 0.308648i | ||||||||
\(418\) | 4.60555i | 0.225265i | ||||||||
\(419\) | −36.1472 | −1.76591 | −0.882953 | − | 0.469462i | \(-0.844448\pi\) | ||||
−0.882953 | + | 0.469462i | \(0.844448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.72498 | −0.181544 | −0.0907722 | − | 0.995872i | \(-0.528934\pi\) | ||||
−0.0907722 | + | 0.995872i | \(0.528934\pi\) | |||||||
\(422\) | 10.3028i | 0.501531i | ||||||||
\(423\) | 36.4222i | 1.77091i | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −19.8167 | −0.960120 | ||||||||
\(427\) | 19.5778i | 0.947436i | ||||||||
\(428\) | 0.697224i | 0.0337016i | ||||||||
\(429\) | 9.90833 | 0.478379 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.21110 | 0.443683 | 0.221842 | − | 0.975083i | \(-0.428793\pi\) | ||||
0.221842 | + | 0.975083i | \(0.428793\pi\) | |||||||
\(432\) | − 16.2111i | − 0.779957i | ||||||||
\(433\) | 34.9361i | 1.67892i | 0.543421 | + | 0.839461i | \(0.317129\pi\) | ||||
−0.543421 | + | 0.839461i | \(0.682871\pi\) | |||||||
\(434\) | 0.788897 | 0.0378683 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | − 7.81665i | − 0.373921i | ||||||||
\(438\) | 40.6333i | 1.94153i | ||||||||
\(439\) | −30.3305 | −1.44760 | −0.723799 | − | 0.690011i | \(-0.757606\pi\) | ||||
−0.723799 | + | 0.690011i | \(0.757606\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.66947 | −0.0794985 | ||||||||
\(442\) | − 7.81665i | − 0.371800i | ||||||||
\(443\) | 32.7250i | 1.55481i | 0.629000 | + | 0.777405i | \(0.283465\pi\) | ||||
−0.629000 | + | 0.777405i | \(0.716535\pi\) | |||||||
\(444\) | −3.30278 | −0.156743 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.81665 | 0.275427 | ||||||||
\(447\) | − 65.4500i | − 3.09568i | ||||||||
\(448\) | − 2.60555i | − 0.123101i | ||||||||
\(449\) | 15.2111 | 0.717856 | 0.358928 | − | 0.933365i | \(-0.383142\pi\) | ||||
0.358928 | + | 0.933365i | \(0.383142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.8167 | −1.07439 | ||||||||
\(452\) | 3.21110i | 0.151038i | ||||||||
\(453\) | − 68.0555i | − 3.19753i | ||||||||
\(454\) | 13.8167 | 0.648448 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.60555 | −0.309333 | ||||||||
\(457\) | 2.60555i | 0.121883i | 0.998141 | + | 0.0609413i | \(0.0194102\pi\) | ||||
−0.998141 | + | 0.0609413i | \(0.980590\pi\) | |||||||
\(458\) | − 24.6056i | − 1.14974i | ||||||||
\(459\) | 97.2666 | 4.54002 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.4222 | 0.578560 | 0.289280 | − | 0.957245i | \(-0.406584\pi\) | ||||
0.289280 | + | 0.957245i | \(0.406584\pi\) | |||||||
\(462\) | 19.8167i | 0.921954i | ||||||||
\(463\) | 26.6972i | 1.24073i | 0.784315 | + | 0.620363i | \(0.213015\pi\) | ||||
−0.784315 | + | 0.620363i | \(0.786985\pi\) | |||||||
\(464\) | 3.90833 | 0.181440 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.51388 | −0.394398 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 10.3028i | 0.476246i | ||||||||
\(469\) | −9.15559 | −0.422766 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.8167 | −1.09741 | ||||||||
\(472\) | 10.6056i | 0.488160i | ||||||||
\(473\) | − 1.39445i | − 0.0641168i | ||||||||
\(474\) | 30.1194 | 1.38343 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 15.6333 | 0.716551 | ||||||||
\(477\) | 47.4500i | 2.17258i | ||||||||
\(478\) | 17.5139i | 0.801066i | ||||||||
\(479\) | 13.1194 | 0.599442 | 0.299721 | − | 0.954027i | \(-0.403106\pi\) | ||||
0.299721 | + | 0.954027i | \(0.403106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.30278 | 0.0594015 | ||||||||
\(482\) | 8.00000i | 0.364390i | ||||||||
\(483\) | − 33.6333i | − 1.53037i | ||||||||
\(484\) | 5.69722 | 0.258965 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −49.8444 | −2.26099 | ||||||||
\(487\) | 37.2111i | 1.68620i | 0.537760 | + | 0.843098i | \(0.319271\pi\) | ||||
−0.537760 | + | 0.843098i | \(0.680729\pi\) | |||||||
\(488\) | − 7.51388i | − 0.340137i | ||||||||
\(489\) | −27.8167 | −1.25791 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.7250 | 0.799917 | 0.399959 | − | 0.916533i | \(-0.369025\pi\) | ||||
0.399959 | + | 0.916533i | \(0.369025\pi\) | |||||||
\(492\) | − 32.7250i | − 1.47536i | ||||||||
\(493\) | 23.4500i | 1.05613i | ||||||||
\(494\) | 2.60555 | 0.117229 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.302776 | −0.0135950 | ||||||||
\(497\) | 15.6333i | 0.701250i | ||||||||
\(498\) | − 9.21110i | − 0.412759i | ||||||||
\(499\) | 42.2389 | 1.89087 | 0.945436 | − | 0.325809i | \(-0.105637\pi\) | ||||
0.945436 | + | 0.325809i | \(0.105637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.2111 | −0.813612 | ||||||||
\(502\) | − 21.2111i | − 0.946698i | ||||||||
\(503\) | − 6.48612i | − 0.289202i | −0.989490 | − | 0.144601i | \(-0.953810\pi\) | ||||
0.989490 | − | 0.144601i | \(-0.0461898\pi\) | |||||||
\(504\) | −20.6056 | −0.917844 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | 0.400099 | ||||||||
\(507\) | 37.3305i | 1.65791i | ||||||||
\(508\) | − 19.2111i | − 0.852355i | ||||||||
\(509\) | 4.18335 | 0.185424 | 0.0927118 | − | 0.995693i | \(-0.470446\pi\) | ||||
0.0927118 | + | 0.995693i | \(0.470446\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.0555 | 1.41805 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 32.4222i | 1.43148i | ||||||||
\(514\) | 3.21110 | 0.141636 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.00000 | 0.0880451 | ||||||||
\(517\) | 10.6056i | 0.466432i | ||||||||
\(518\) | 2.60555i | 0.114481i | ||||||||
\(519\) | 29.0278 | 1.27418 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.6333 | 1.47350 | 0.736751 | − | 0.676164i | \(-0.236359\pi\) | ||||
0.736751 | + | 0.676164i | \(0.236359\pi\) | |||||||
\(522\) | − 30.9083i | − 1.35282i | ||||||||
\(523\) | − 18.2389i | − 0.797530i | −0.917053 | − | 0.398765i | \(-0.869439\pi\) | ||||
0.917053 | − | 0.398765i | \(-0.130561\pi\) | |||||||
\(524\) | −10.6056 | −0.463306 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.8167 | −0.602435 | ||||||||
\(527\) | − 1.81665i | − 0.0791347i | ||||||||
\(528\) | − 7.60555i | − 0.330989i | ||||||||
\(529\) | 7.72498 | 0.335869 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 83.8722 | 3.63974 | ||||||||
\(532\) | 5.21110i | 0.225930i | ||||||||
\(533\) | 12.9083i | 0.559122i | ||||||||
\(534\) | −30.4222 | −1.31650 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.51388 | 0.151776 | ||||||||
\(537\) | 45.6333i | 1.96922i | ||||||||
\(538\) | 21.2111i | 0.914476i | ||||||||
\(539\) | −0.486122 | −0.0209387 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.9361 | 1.11508 | 0.557540 | − | 0.830150i | \(-0.311745\pi\) | ||||
0.557540 | + | 0.830150i | \(0.311745\pi\) | |||||||
\(542\) | − 22.4222i | − 0.963116i | ||||||||
\(543\) | 66.0555i | 2.83471i | ||||||||
\(544\) | −6.00000 | −0.257248 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.2111 | 0.479791 | ||||||||
\(547\) | 20.6056i | 0.881030i | 0.897745 | + | 0.440515i | \(0.145204\pi\) | ||||
−0.897745 | + | 0.440515i | \(0.854796\pi\) | |||||||
\(548\) | 0.908327i | 0.0388018i | ||||||||
\(549\) | −59.4222 | −2.53608 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.81665 | −0.333001 | ||||||||
\(552\) | 12.9083i | 0.549415i | ||||||||
\(553\) | − 23.7611i | − 1.01043i | ||||||||
\(554\) | 0.119429 | 0.00507407 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.90833 | −0.0809311 | ||||||||
\(557\) | − 11.5139i | − 0.487859i | −0.969793 | − | 0.243929i | \(-0.921564\pi\) | ||||
0.969793 | − | 0.243929i | \(-0.0784365\pi\) | |||||||
\(558\) | 2.39445i | 0.101365i | ||||||||
\(559\) | −0.788897 | −0.0333668 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 45.6333 | 1.92664 | ||||||||
\(562\) | − 12.0000i | − 0.506189i | ||||||||
\(563\) | − 28.0555i | − 1.18240i | −0.806525 | − | 0.591199i | \(-0.798655\pi\) | ||||
0.806525 | − | 0.591199i | \(-0.201345\pi\) | |||||||
\(564\) | −15.2111 | −0.640503 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.6056 | −1.03425 | ||||||||
\(567\) | 77.6888i | 3.26262i | ||||||||
\(568\) | − 6.00000i | − 0.251754i | ||||||||
\(569\) | −18.4222 | −0.772299 | −0.386150 | − | 0.922436i | \(-0.626195\pi\) | ||||
−0.386150 | + | 0.922436i | \(0.626195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.6972 | −0.698757 | −0.349379 | − | 0.936982i | \(-0.613607\pi\) | ||||
−0.349379 | + | 0.936982i | \(0.613607\pi\) | |||||||
\(572\) | 3.00000i | 0.125436i | ||||||||
\(573\) | − 18.2111i | − 0.760780i | ||||||||
\(574\) | −25.8167 | −1.07757 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.90833 | 0.329514 | ||||||||
\(577\) | − 22.2389i | − 0.925816i | −0.886406 | − | 0.462908i | \(-0.846806\pi\) | ||||
0.886406 | − | 0.462908i | \(-0.153194\pi\) | |||||||
\(578\) | − 19.0000i | − 0.790296i | ||||||||
\(579\) | 13.2111 | 0.549035 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.26662 | −0.301470 | ||||||||
\(582\) | − 54.2389i | − 2.24827i | ||||||||
\(583\) | 13.8167i | 0.572227i | ||||||||
\(584\) | −12.3028 | −0.509092 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.0278 | −0.455552 | ||||||||
\(587\) | 45.6333i | 1.88349i | 0.336330 | + | 0.941744i | \(0.390814\pi\) | ||||
−0.336330 | + | 0.941744i | \(0.609186\pi\) | |||||||
\(588\) | − 0.697224i | − 0.0287530i | ||||||||
\(589\) | 0.605551 | 0.0249513 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8167 | −0.815148 | ||||||||
\(592\) | − 1.00000i | − 0.0410997i | ||||||||
\(593\) | 18.4861i | 0.759134i | 0.925164 | + | 0.379567i | \(0.123927\pi\) | ||||
−0.925164 | + | 0.379567i | \(0.876073\pi\) | |||||||
\(594\) | −37.3305 | −1.53169 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.8167 | 0.811722 | ||||||||
\(597\) | − 87.2666i | − 3.57158i | ||||||||
\(598\) | − 5.09167i | − 0.208214i | ||||||||
\(599\) | 20.7889 | 0.849411 | 0.424706 | − | 0.905331i | \(-0.360378\pi\) | ||||
0.424706 | + | 0.905331i | \(0.360378\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3028 | −0.991331 | −0.495665 | − | 0.868514i | \(-0.665076\pi\) | ||||
−0.495665 | + | 0.868514i | \(0.665076\pi\) | |||||||
\(602\) | − 1.57779i | − 0.0643061i | ||||||||
\(603\) | − 27.7889i | − 1.13165i | ||||||||
\(604\) | 20.6056 | 0.838428 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 41.0278 | 1.66664 | ||||||||
\(607\) | 13.4861i | 0.547385i | 0.961817 | + | 0.273692i | \(0.0882450\pi\) | ||||
−0.961817 | + | 0.273692i | \(0.911755\pi\) | |||||||
\(608\) | − 2.00000i | − 0.0811107i | ||||||||
\(609\) | −33.6333 | −1.36289 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | 47.4500i | 1.91805i | ||||||||
\(613\) | − 29.8167i | − 1.20428i | −0.798389 | − | 0.602142i | \(-0.794314\pi\) | ||||
0.798389 | − | 0.602142i | \(-0.205686\pi\) | |||||||
\(614\) | 17.9083 | 0.722721 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | −0.241747 | ||||||||
\(617\) | 42.5694i | 1.71378i | 0.515500 | + | 0.856890i | \(0.327606\pi\) | ||||
−0.515500 | + | 0.856890i | \(0.672394\pi\) | |||||||
\(618\) | 1.00000i | 0.0402259i | ||||||||
\(619\) | 6.30278 | 0.253330 | 0.126665 | − | 0.991946i | \(-0.459573\pi\) | ||||
0.126665 | + | 0.991946i | \(0.459573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 63.3583 | 2.54248 | ||||||||
\(622\) | 15.9083i | 0.637866i | ||||||||
\(623\) | 24.0000i | 0.961540i | ||||||||
\(624\) | −4.30278 | −0.172249 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.02776 | 0.360822 | ||||||||
\(627\) | 15.2111i | 0.607473i | ||||||||
\(628\) | − 7.21110i | − 0.287754i | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.6972 | 0.585087 | 0.292544 | − | 0.956252i | \(-0.405498\pi\) | ||||
0.292544 | + | 0.956252i | \(0.405498\pi\) | |||||||
\(632\) | 9.11943i | 0.362751i | ||||||||
\(633\) | 34.0278i | 1.35248i | ||||||||
\(634\) | 9.21110 | 0.365820 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −19.8167 | −0.785781 | ||||||||
\(637\) | 0.275019i | 0.0108967i | ||||||||
\(638\) | − 9.00000i | − 0.356313i | ||||||||
\(639\) | −47.4500 | −1.87709 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.5139 | −0.810249 | −0.405125 | − | 0.914261i | \(-0.632772\pi\) | ||||
−0.405125 | + | 0.914261i | \(0.632772\pi\) | |||||||
\(642\) | 2.30278i | 0.0908833i | ||||||||
\(643\) | − 8.18335i | − 0.322720i | −0.986896 | − | 0.161360i | \(-0.948412\pi\) | ||||
0.986896 | − | 0.161360i | \(-0.0515880\pi\) | |||||||
\(644\) | 10.1833 | 0.401280 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | − 20.9361i | − 0.823082i | −0.911391 | − | 0.411541i | \(-0.864991\pi\) | ||||
0.911391 | − | 0.411541i | \(-0.135009\pi\) | |||||||
\(648\) | − 29.8167i | − 1.17131i | ||||||||
\(649\) | 24.4222 | 0.958655 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.60555 | 0.102120 | ||||||||
\(652\) | − 8.42221i | − 0.329839i | ||||||||
\(653\) | − 3.90833i | − 0.152945i | −0.997072 | − | 0.0764723i | \(-0.975634\pi\) | ||||
0.997072 | − | 0.0764723i | \(-0.0243657\pi\) | |||||||
\(654\) | 6.60555 | 0.258297 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.90833 | 0.386855 | ||||||||
\(657\) | 97.2944i | 3.79581i | ||||||||
\(658\) | 12.0000i | 0.467809i | ||||||||
\(659\) | 16.8806 | 0.657574 | 0.328787 | − | 0.944404i | \(-0.393360\pi\) | ||||
0.328787 | + | 0.944404i | \(0.393360\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.5139 | −1.18685 | −0.593426 | − | 0.804888i | \(-0.702225\pi\) | ||||
−0.593426 | + | 0.804888i | \(0.702225\pi\) | |||||||
\(662\) | − 13.2111i | − 0.513464i | ||||||||
\(663\) | − 25.8167i | − 1.00264i | ||||||||
\(664\) | 2.78890 | 0.108230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.90833 | −0.306441 | ||||||||
\(667\) | 15.2750i | 0.591451i | ||||||||
\(668\) | − 5.51388i | − 0.213338i | ||||||||
\(669\) | 19.2111 | 0.742744 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.3028 | −0.667966 | ||||||||
\(672\) | − 8.60555i | − 0.331966i | ||||||||
\(673\) | 20.6972i | 0.797819i | 0.916990 | + | 0.398910i | \(0.130611\pi\) | ||||
−0.916990 | + | 0.398910i | \(0.869389\pi\) | |||||||
\(674\) | 6.11943 | 0.235712 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.3028 | −0.434722 | ||||||||
\(677\) | − 14.2389i | − 0.547244i | −0.961837 | − | 0.273622i | \(-0.911778\pi\) | ||||
0.961837 | − | 0.273622i | \(-0.0882217\pi\) | |||||||
\(678\) | 10.6056i | 0.407304i | ||||||||
\(679\) | −42.7889 | −1.64209 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.6333 | 1.74867 | ||||||||
\(682\) | 0.697224i | 0.0266981i | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | −15.8167 | −0.604765 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.7889 | −0.717363 | ||||||||
\(687\) | − 81.2666i | − 3.10051i | ||||||||
\(688\) | 0.605551i | 0.0230864i | ||||||||
\(689\) | 7.81665 | 0.297791 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 8.78890i | 0.334104i | ||||||||
\(693\) | 47.4500i | 1.80247i | ||||||||
\(694\) | 10.1833 | 0.386555 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.9083 | 0.489289 | ||||||||
\(697\) | 59.4500i | 2.25183i | ||||||||
\(698\) | − 28.2389i | − 1.06886i | ||||||||
\(699\) | −28.1194 | −1.06357 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.1194 | 1.51529 | 0.757645 | − | 0.652667i | \(-0.226350\pi\) | ||||
0.757645 | + | 0.652667i | \(0.226350\pi\) | |||||||
\(702\) | 21.1194i | 0.797101i | ||||||||
\(703\) | 2.00000i | 0.0754314i | ||||||||
\(704\) | 2.30278 | 0.0867891 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.1833 | −0.383255 | ||||||||
\(707\) | − 32.3667i | − 1.21727i | ||||||||
\(708\) | 35.0278i | 1.31642i | ||||||||
\(709\) | 41.3305 | 1.55220 | 0.776100 | − | 0.630609i | \(-0.217195\pi\) | ||||
0.776100 | + | 0.630609i | \(0.217195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 72.1194 | 2.70469 | ||||||||
\(712\) | − 9.21110i | − 0.345201i | ||||||||
\(713\) | − 1.18335i | − 0.0443167i | ||||||||
\(714\) | 51.6333 | 1.93233 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.8167 | −0.516353 | ||||||||
\(717\) | 57.8444i | 2.16024i | ||||||||
\(718\) | − 3.21110i | − 0.119837i | ||||||||
\(719\) | 51.6333 | 1.92560 | 0.962799 | − | 0.270220i | \(-0.0870963\pi\) | ||||
0.962799 | + | 0.270220i | \(0.0870963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.788897 | 0.0293801 | ||||||||
\(722\) | − 15.0000i | − 0.558242i | ||||||||
\(723\) | 26.4222i | 0.982652i | ||||||||
\(724\) | −20.0000 | −0.743294 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 18.8167 | 0.698352 | ||||||||
\(727\) | − 19.0917i | − 0.708071i | −0.935232 | − | 0.354035i | \(-0.884809\pi\) | ||||
0.935232 | − | 0.354035i | \(-0.115191\pi\) | |||||||
\(728\) | 3.39445i | 0.125807i | ||||||||
\(729\) | −75.1749 | −2.78426 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.63331 | −0.134383 | ||||||||
\(732\) | − 24.8167i | − 0.917250i | ||||||||
\(733\) | − 13.6333i | − 0.503558i | −0.967785 | − | 0.251779i | \(-0.918984\pi\) | ||||
0.967785 | − | 0.251779i | \(-0.0810156\pi\) | |||||||
\(734\) | 3.81665 | 0.140875 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.90833 | −0.144063 | ||||||||
\(737\) | − 8.09167i | − 0.298061i | ||||||||
\(738\) | − 78.3583i | − 2.88441i | ||||||||
\(739\) | 2.66947 | 0.0981980 | 0.0490990 | − | 0.998794i | \(-0.484365\pi\) | ||||
0.0490990 | + | 0.998794i | \(0.484365\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.60555 | 0.316133 | ||||||||
\(742\) | 15.6333i | 0.573917i | ||||||||
\(743\) | − 29.4500i | − 1.08041i | −0.841532 | − | 0.540207i | \(-0.818346\pi\) | ||||
0.841532 | − | 0.540207i | \(-0.181654\pi\) | |||||||
\(744\) | −1.00000 | −0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.8167 | 0.652314 | ||||||||
\(747\) | − 22.0555i | − 0.806969i | ||||||||
\(748\) | 13.8167i | 0.505187i | ||||||||
\(749\) | 1.81665 | 0.0663791 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | 0.510867 | 0.255434 | − | 0.966827i | \(-0.417782\pi\) | ||||
0.255434 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(752\) | − 4.60555i | − 0.167947i | ||||||||
\(753\) | − 70.0555i | − 2.55296i | ||||||||
\(754\) | −5.09167 | −0.185428 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −42.2389 | −1.53621 | ||||||||
\(757\) | − 5.69722i | − 0.207069i | −0.994626 | − | 0.103535i | \(-0.966985\pi\) | ||||
0.994626 | − | 0.103535i | \(-0.0330152\pi\) | |||||||
\(758\) | − 24.3305i | − 0.883725i | ||||||||
\(759\) | 29.7250 | 1.07895 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.8806 | 0.611920 | 0.305960 | − | 0.952044i | \(-0.401023\pi\) | ||||
0.305960 | + | 0.952044i | \(0.401023\pi\) | |||||||
\(762\) | − 63.4500i | − 2.29855i | ||||||||
\(763\) | − 5.21110i | − 0.188655i | ||||||||
\(764\) | 5.51388 | 0.199485 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.8444 | 1.33124 | ||||||||
\(767\) | − 13.8167i | − 0.498890i | ||||||||
\(768\) | 3.30278i | 0.119179i | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6056 | 0.381950 | ||||||||
\(772\) | 4.00000i | 0.143963i | ||||||||
\(773\) | 22.0555i | 0.793282i | 0.917974 | + | 0.396641i | \(0.129824\pi\) | ||||
−0.917974 | + | 0.396641i | \(0.870176\pi\) | |||||||
\(774\) | 4.78890 | 0.172133 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.4222 | 0.589523 | ||||||||
\(777\) | 8.60555i | 0.308722i | ||||||||
\(778\) | 37.1194i | 1.33080i | ||||||||
\(779\) | −19.8167 | −0.710005 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8167 | −0.494399 | ||||||||
\(782\) | − 23.4500i | − 0.838569i | ||||||||
\(783\) | − 63.3583i | − 2.26424i | ||||||||
\(784\) | 0.211103 | 0.00753938 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −35.0278 | −1.24940 | ||||||||
\(787\) | − 10.7889i | − 0.384583i | −0.981338 | − | 0.192291i | \(-0.938408\pi\) | ||||
0.981338 | − | 0.192291i | \(-0.0615919\pi\) | |||||||
\(788\) | − 6.00000i | − 0.213741i | ||||||||
\(789\) | −45.6333 | −1.62459 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.36669 | 0.297485 | ||||||||
\(792\) | − 18.2111i | − 0.647103i | ||||||||
\(793\) | 9.78890i | 0.347614i | ||||||||
\(794\) | 6.18335 | 0.219439 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.4222 | 0.936510 | ||||||||
\(797\) | − 22.3305i | − 0.790988i | −0.918469 | − | 0.395494i | \(-0.870573\pi\) | ||||
0.918469 | − | 0.395494i | \(-0.129427\pi\) | |||||||
\(798\) | 17.2111i | 0.609266i | ||||||||
\(799\) | 27.6333 | 0.977596 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −72.8444 | −2.57383 | ||||||||
\(802\) | − 7.81665i | − 0.276016i | ||||||||
\(803\) | 28.3305i | 0.999763i | ||||||||
\(804\) | 11.6056 | 0.409296 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.394449 | 0.0138939 | ||||||||
\(807\) | 70.0555i | 2.46607i | ||||||||
\(808\) | 12.4222i | 0.437012i | ||||||||
\(809\) | 35.4500 | 1.24635 | 0.623177 | − | 0.782081i | \(-0.285842\pi\) | ||||
0.623177 | + | 0.782081i | \(0.285842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.14719 | −0.250972 | −0.125486 | − | 0.992095i | \(-0.540049\pi\) | ||||
−0.125486 | + | 0.992095i | \(0.540049\pi\) | |||||||
\(812\) | − 10.1833i | − 0.357365i | ||||||||
\(813\) | − 74.0555i | − 2.59724i | ||||||||
\(814\) | −2.30278 | −0.0807122 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −19.8167 | −0.693722 | ||||||||
\(817\) | − 1.21110i | − 0.0423711i | ||||||||
\(818\) | − 31.0278i | − 1.08486i | ||||||||
\(819\) | 26.8444 | 0.938020 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.21110 | −0.112068 | −0.0560341 | − | 0.998429i | \(-0.517846\pi\) | ||||
−0.0560341 | + | 0.998429i | \(0.517846\pi\) | |||||||
\(822\) | 3.00000i | 0.104637i | ||||||||
\(823\) | 44.8444i | 1.56318i | 0.623794 | + | 0.781589i | \(0.285590\pi\) | ||||
−0.623794 | + | 0.781589i | \(0.714410\pi\) | |||||||
\(824\) | −0.302776 | −0.0105477 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.6333 | 0.961486 | ||||||||
\(827\) | − 34.6056i | − 1.20335i | −0.798740 | − | 0.601676i | \(-0.794500\pi\) | ||||
0.798740 | − | 0.601676i | \(-0.205500\pi\) | |||||||
\(828\) | 30.9083i | 1.07414i | ||||||||
\(829\) | 27.7250 | 0.962928 | 0.481464 | − | 0.876466i | \(-0.340105\pi\) | ||||
0.481464 | + | 0.876466i | \(0.340105\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.394449 | 0.0136833 | ||||||||
\(832\) | − 1.30278i | − 0.0451656i | ||||||||
\(833\) | 1.26662i | 0.0438856i | ||||||||
\(834\) | −6.30278 | −0.218247 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.60555 | −0.159286 | ||||||||
\(837\) | 4.90833i | 0.169657i | ||||||||
\(838\) | − 36.1472i | − 1.24868i | ||||||||
\(839\) | 12.9722 | 0.447852 | 0.223926 | − | 0.974606i | \(-0.428113\pi\) | ||||
0.223926 | + | 0.974606i | \(0.428113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.7250 | −0.473275 | ||||||||
\(842\) | − 3.72498i | − 0.128371i | ||||||||
\(843\) | − 39.6333i | − 1.36504i | ||||||||
\(844\) | −10.3028 | −0.354636 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −36.4222 | −1.25222 | ||||||||
\(847\) | − 14.8444i | − 0.510060i | ||||||||
\(848\) | − 6.00000i | − 0.206041i | ||||||||
\(849\) | −81.2666 | −2.78906 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.90833 | 0.133976 | ||||||||
\(852\) | − 19.8167i | − 0.678907i | ||||||||
\(853\) | 42.5416i | 1.45660i | 0.685260 | + | 0.728299i | \(0.259689\pi\) | ||||
−0.685260 | + | 0.728299i | \(0.740311\pi\) | |||||||
\(854\) | −19.5778 | −0.669938 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.697224 | −0.0238306 | ||||||||
\(857\) | − 42.8444i | − 1.46354i | −0.681553 | − | 0.731769i | \(-0.738695\pi\) | ||||
0.681553 | − | 0.731769i | \(-0.261305\pi\) | |||||||
\(858\) | 9.90833i | 0.338265i | ||||||||
\(859\) | −48.0555 | −1.63963 | −0.819816 | − | 0.572626i | \(-0.805925\pi\) | ||||
−0.819816 | + | 0.572626i | \(0.805925\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −85.2666 | −2.90588 | ||||||||
\(862\) | 9.21110i | 0.313731i | ||||||||
\(863\) | 12.0000i | 0.408485i | 0.978920 | + | 0.204242i | \(0.0654731\pi\) | ||||
−0.978920 | + | 0.204242i | \(0.934527\pi\) | |||||||
\(864\) | 16.2111 | 0.551513 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −34.9361 | −1.18718 | ||||||||
\(867\) | − 62.7527i | − 2.13119i | ||||||||
\(868\) | 0.788897i | 0.0267769i | ||||||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.57779 | −0.155113 | ||||||||
\(872\) | 2.00000i | 0.0677285i | ||||||||
\(873\) | − 129.872i | − 4.39551i | ||||||||
\(874\) | 7.81665 | 0.264402 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −40.6333 | −1.37287 | ||||||||
\(877\) | 7.21110i | 0.243502i | 0.992561 | + | 0.121751i | \(0.0388509\pi\) | ||||
−0.992561 | + | 0.121751i | \(0.961149\pi\) | |||||||
\(878\) | − 30.3305i | − 1.02361i | ||||||||
\(879\) | −36.4222 | −1.22849 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.5416 | −0.961592 | −0.480796 | − | 0.876832i | \(-0.659652\pi\) | ||||
−0.480796 | + | 0.876832i | \(0.659652\pi\) | |||||||
\(882\) | − 1.66947i | − 0.0562139i | ||||||||
\(883\) | 26.4222i | 0.889178i | 0.895735 | + | 0.444589i | \(0.146650\pi\) | ||||
−0.895735 | + | 0.444589i | \(0.853350\pi\) | |||||||
\(884\) | 7.81665 | 0.262903 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.7250 | −1.09942 | ||||||||
\(887\) | 0.422205i | 0.0141763i | 0.999975 | + | 0.00708813i | \(0.00225624\pi\) | ||||
−0.999975 | + | 0.00708813i | \(0.997744\pi\) | |||||||
\(888\) | − 3.30278i | − 0.110834i | ||||||||
\(889\) | −50.0555 | −1.67881 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −68.6611 | −2.30023 | ||||||||
\(892\) | 5.81665i | 0.194756i | ||||||||
\(893\) | 9.21110i | 0.308238i | ||||||||
\(894\) | 65.4500 | 2.18897 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.60555 | 0.0870454 | ||||||||
\(897\) | − 16.8167i | − 0.561492i | ||||||||
\(898\) | 15.2111i | 0.507601i | ||||||||
\(899\) | −1.18335 | −0.0394668 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | − 22.8167i | − 0.759711i | ||||||||
\(903\) | − 5.21110i | − 0.173415i | ||||||||
\(904\) | −3.21110 | −0.106800 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 68.0555 | 2.26099 | ||||||||
\(907\) | − 26.0000i | − 0.863316i | −0.902037 | − | 0.431658i | \(-0.857929\pi\) | ||||
0.902037 | − | 0.431658i | \(-0.142071\pi\) | |||||||
\(908\) | 13.8167i | 0.458522i | ||||||||
\(909\) | 98.2389 | 3.25838 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.5778 | −0.582378 | −0.291189 | − | 0.956665i | \(-0.594051\pi\) | ||||
−0.291189 | + | 0.956665i | \(0.594051\pi\) | |||||||
\(912\) | − 6.60555i | − 0.218732i | ||||||||
\(913\) | − 6.42221i | − 0.212544i | ||||||||
\(914\) | −2.60555 | −0.0861840 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.6056 | 0.812990 | ||||||||
\(917\) | 27.6333i | 0.912532i | ||||||||
\(918\) | 97.2666i | 3.21028i | ||||||||
\(919\) | 9.57779 | 0.315942 | 0.157971 | − | 0.987444i | \(-0.449505\pi\) | ||||
0.157971 | + | 0.987444i | \(0.449505\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 59.1472 | 1.94897 | ||||||||
\(922\) | 12.4222i | 0.409104i | ||||||||
\(923\) | 7.81665i | 0.257288i | ||||||||
\(924\) | −19.8167 | −0.651920 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26.6972 | −0.877325 | ||||||||
\(927\) | 2.39445i | 0.0786440i | ||||||||
\(928\) | 3.90833i | 0.128297i | ||||||||
\(929\) | 18.4861 | 0.606510 | 0.303255 | − | 0.952909i | \(-0.401927\pi\) | ||||
0.303255 | + | 0.952909i | \(0.401927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.422205 | −0.0138372 | ||||||||
\(932\) | − 8.51388i | − 0.278881i | ||||||||
\(933\) | 52.5416i | 1.72014i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.3028 | −0.336757 | ||||||||
\(937\) | 18.0917i | 0.591029i | 0.955338 | + | 0.295515i | \(0.0954911\pi\) | ||||
−0.955338 | + | 0.295515i | \(0.904509\pi\) | |||||||
\(938\) | − 9.15559i | − 0.298941i | ||||||||
\(939\) | 29.8167 | 0.973030 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.8167 | 0.450410 | 0.225205 | − | 0.974311i | \(-0.427695\pi\) | ||||
0.225205 | + | 0.974311i | \(0.427695\pi\) | |||||||
\(942\) | − 23.8167i | − 0.775989i | ||||||||
\(943\) | 38.7250i | 1.26106i | ||||||||
\(944\) | −10.6056 | −0.345181 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.39445 | 0.0453374 | ||||||||
\(947\) | 3.63331i | 0.118067i | 0.998256 | + | 0.0590333i | \(0.0188018\pi\) | ||||
−0.998256 | + | 0.0590333i | \(0.981198\pi\) | |||||||
\(948\) | 30.1194i | 0.978234i | ||||||||
\(949\) | 16.0278 | 0.520283 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.4222 | 0.986508 | ||||||||
\(952\) | 15.6333i | 0.506678i | ||||||||
\(953\) | 49.7527i | 1.61165i | 0.592154 | + | 0.805825i | \(0.298278\pi\) | ||||
−0.592154 | + | 0.805825i | \(0.701722\pi\) | |||||||
\(954\) | −47.4500 | −1.53625 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17.5139 | −0.566439 | ||||||||
\(957\) | − 29.7250i | − 0.960872i | ||||||||
\(958\) | 13.1194i | 0.423870i | ||||||||
\(959\) | 2.36669 | 0.0764245 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9083 | −0.997043 | ||||||||
\(962\) | 1.30278i | 0.0420032i | ||||||||
\(963\) | 5.51388i | 0.177682i | ||||||||
\(964\) | −8.00000 | −0.257663 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 33.6333 | 1.08213 | ||||||||
\(967\) | 6.72498i | 0.216261i | 0.994137 | + | 0.108130i | \(0.0344864\pi\) | ||||
−0.994137 | + | 0.108130i | \(0.965514\pi\) | |||||||
\(968\) | 5.69722i | 0.183116i | ||||||||
\(969\) | 39.6333 | 1.27321 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.5416 | −0.723395 | −0.361698 | − | 0.932295i | \(-0.617803\pi\) | ||||
−0.361698 | + | 0.932295i | \(0.617803\pi\) | |||||||
\(972\) | − 49.8444i | − 1.59876i | ||||||||
\(973\) | 4.97224i | 0.159403i | ||||||||
\(974\) | −37.2111 | −1.19232 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.51388 | 0.240513 | ||||||||
\(977\) | − 18.0000i | − 0.575871i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) | ||||
0.957650 | − | 0.287936i | \(-0.0929689\pi\) | |||||||
\(978\) | − 27.8167i | − 0.889479i | ||||||||
\(979\) | −21.2111 | −0.677910 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.8167 | 0.504987 | ||||||||
\(982\) | 17.7250i | 0.565627i | ||||||||
\(983\) | − 12.0000i | − 0.382741i | −0.981518 | − | 0.191370i | \(-0.938707\pi\) | ||||
0.981518 | − | 0.191370i | \(-0.0612931\pi\) | |||||||
\(984\) | 32.7250 | 1.04323 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −23.4500 | −0.746799 | ||||||||
\(987\) | 39.6333i | 1.26154i | ||||||||
\(988\) | 2.60555i | 0.0828936i | ||||||||
\(989\) | −2.36669 | −0.0752564 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.6972 | 1.61045 | 0.805225 | − | 0.592969i | \(-0.202044\pi\) | ||||
0.805225 | + | 0.592969i | \(0.202044\pi\) | |||||||
\(992\) | − 0.302776i | − 0.00961314i | ||||||||
\(993\) | − 43.6333i | − 1.38466i | ||||||||
\(994\) | −15.6333 | −0.495858 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.21110 | 0.291865 | ||||||||
\(997\) | 52.4222i | 1.66023i | 0.557594 | + | 0.830114i | \(0.311725\pi\) | ||||
−0.557594 | + | 0.830114i | \(0.688275\pi\) | |||||||
\(998\) | 42.2389i | 1.33705i | ||||||||
\(999\) | −16.2111 | −0.512897 |
(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.i.149.4 | 4 | ||
5.2 | odd | 4 | 74.2.a.a.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 1850.2.a.u.1.1 | 2 | |||
5.4 | even | 2 | inner | 1850.2.b.i.149.1 | 4 | ||
15.2 | even | 4 | 666.2.a.j.1.2 | 2 | |||
20.7 | even | 4 | 592.2.a.f.1.1 | 2 | |||
35.27 | even | 4 | 3626.2.a.a.1.1 | 2 | |||
40.27 | even | 4 | 2368.2.a.ba.1.2 | 2 | |||
40.37 | odd | 4 | 2368.2.a.s.1.1 | 2 | |||
55.32 | even | 4 | 8954.2.a.p.1.2 | 2 | |||
60.47 | odd | 4 | 5328.2.a.bf.1.2 | 2 | |||
185.147 | odd | 4 | 2738.2.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.a.a.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
592.2.a.f.1.1 | 2 | 20.7 | even | 4 | |||
666.2.a.j.1.2 | 2 | 15.2 | even | 4 | |||
1850.2.a.u.1.1 | 2 | 5.3 | odd | 4 | |||
1850.2.b.i.149.1 | 4 | 5.4 | even | 2 | inner | ||
1850.2.b.i.149.4 | 4 | 1.1 | even | 1 | trivial | ||
2368.2.a.s.1.1 | 2 | 40.37 | odd | 4 | |||
2368.2.a.ba.1.2 | 2 | 40.27 | even | 4 | |||
2738.2.a.l.1.2 | 2 | 185.147 | odd | 4 | |||
3626.2.a.a.1.1 | 2 | 35.27 | even | 4 | |||
5328.2.a.bf.1.2 | 2 | 60.47 | odd | 4 | |||
8954.2.a.p.1.2 | 2 | 55.32 | even | 4 |