Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(2899,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3450.2899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.d (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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 138) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2899.2 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.2899 |
Dual form | 3450.2.d.x.2899.3 |
$q$-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 \(\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1151\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.47214i | 1.69031i | 0.534522 | + | 0.845154i | \(0.320491\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.23607 | −1.57873 | −0.789367 | − | 0.613922i | \(-0.789591\pi\) | ||||
−0.789367 | + | 0.613922i | \(0.789591\pi\) | |||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | 4.47214i | 1.24035i | 0.784465 | + | 0.620174i | \(0.212938\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | 4.47214 | 1.19523 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −5.70820 | −1.30955 | −0.654776 | − | 0.755823i | \(-0.727237\pi\) | ||||
−0.654776 | + | 0.755823i | \(0.727237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.47214 | −0.975900 | ||||||||
\(22\) | 5.23607i | 1.11633i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.47214 | 0.877058 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 4.47214i | − 0.845154i | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47214 | −0.444009 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 5.23607i | − 0.911482i | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 11.2361i | − 1.84720i | −0.383360 | − | 0.923599i | \(-0.625233\pi\) | ||||
0.383360 | − | 0.923599i | \(-0.374767\pi\) | |||||||
\(38\) | 5.70820i | 0.925993i | ||||||||
\(39\) | −4.47214 | −0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 4.47214i | 0.690066i | ||||||||
\(43\) | − 4.76393i | − 0.726493i | −0.931693 | − | 0.363246i | \(-0.881668\pi\) | ||||
0.931693 | − | 0.363246i | \(-0.118332\pi\) | |||||||
\(44\) | 5.23607 | 0.789367 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − 4.00000i | − 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −13.0000 | −1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | − 4.47214i | − 0.620174i | ||||||||
\(53\) | 5.23607i | 0.719229i | 0.933101 | + | 0.359615i | \(0.117092\pi\) | ||||
−0.933101 | + | 0.359615i | \(0.882908\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.47214 | −0.597614 | ||||||||
\(57\) | − 5.70820i | − 0.756070i | ||||||||
\(58\) | − 4.47214i | − 0.587220i | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.763932 | 0.0978115 | 0.0489057 | − | 0.998803i | \(-0.484427\pi\) | ||||
0.0489057 | + | 0.998803i | \(0.484427\pi\) | |||||||
\(62\) | 2.47214i | 0.313962i | ||||||||
\(63\) | − 4.47214i | − 0.563436i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.23607 | −0.644515 | ||||||||
\(67\) | − 9.70820i | − 1.18605i | −0.805186 | − | 0.593023i | \(-0.797934\pi\) | ||||
0.805186 | − | 0.593023i | \(-0.202066\pi\) | |||||||
\(68\) | − 4.00000i | − 0.485071i | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.94427 | 1.06149 | 0.530745 | − | 0.847532i | \(-0.321912\pi\) | ||||
0.530745 | + | 0.847532i | \(0.321912\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 4.47214i | − 0.523424i | −0.965146 | − | 0.261712i | \(-0.915713\pi\) | ||||
0.965146 | − | 0.261712i | \(-0.0842870\pi\) | |||||||
\(74\) | −11.2361 | −1.30617 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.70820 | 0.654776 | ||||||||
\(77\) | − 23.4164i | − 2.66855i | ||||||||
\(78\) | 4.47214i | 0.506370i | ||||||||
\(79\) | −4.47214 | −0.503155 | −0.251577 | − | 0.967837i | \(-0.580949\pi\) | ||||
−0.251577 | + | 0.967837i | \(0.580949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000i | 0.220863i | ||||||||
\(83\) | 13.2361i | 1.45285i | 0.687247 | + | 0.726424i | \(0.258819\pi\) | ||||
−0.687247 | + | 0.726424i | \(0.741181\pi\) | |||||||
\(84\) | 4.47214 | 0.487950 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.76393 | −0.513708 | ||||||||
\(87\) | 4.47214i | 0.479463i | ||||||||
\(88\) | − 5.23607i | − 0.558167i | ||||||||
\(89\) | 10.4721 | 1.11004 | 0.555022 | − | 0.831836i | \(-0.312710\pi\) | ||||
0.555022 | + | 0.831836i | \(0.312710\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.0000 | −2.09657 | ||||||||
\(92\) | − 1.00000i | − 0.104257i | ||||||||
\(93\) | − 2.47214i | − 0.256349i | ||||||||
\(94\) | −4.00000 | −0.412568 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − 0.472136i | − 0.0479381i | −0.999713 | − | 0.0239691i | \(-0.992370\pi\) | ||||
0.999713 | − | 0.0239691i | \(-0.00763032\pi\) | |||||||
\(98\) | 13.0000i | 1.31320i | ||||||||
\(99\) | 5.23607 | 0.526245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.47214 | 0.444994 | 0.222497 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222497 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(102\) | 4.00000i | 0.396059i | ||||||||
\(103\) | − 6.00000i | − 0.591198i | −0.955312 | − | 0.295599i | \(-0.904481\pi\) | ||||
0.955312 | − | 0.295599i | \(-0.0955191\pi\) | |||||||
\(104\) | −4.47214 | −0.438529 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.23607 | 0.508572 | ||||||||
\(107\) | 12.6525i | 1.22316i | 0.791182 | + | 0.611581i | \(0.209466\pi\) | ||||
−0.791182 | + | 0.611581i | \(0.790534\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −4.76393 | −0.456302 | −0.228151 | − | 0.973626i | \(-0.573268\pi\) | ||||
−0.228151 | + | 0.973626i | \(0.573268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.2361 | 1.06648 | ||||||||
\(112\) | 4.47214i | 0.422577i | ||||||||
\(113\) | − 5.52786i | − 0.520018i | −0.965606 | − | 0.260009i | \(-0.916275\pi\) | ||||
0.965606 | − | 0.260009i | \(-0.0837255\pi\) | |||||||
\(114\) | −5.70820 | −0.534622 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.47214 | −0.415227 | ||||||||
\(117\) | − 4.47214i | − 0.413449i | ||||||||
\(118\) | − 8.94427i | − 0.823387i | ||||||||
\(119\) | −17.8885 | −1.63984 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | − 0.763932i | − 0.0691632i | ||||||||
\(123\) | − 2.00000i | − 0.180334i | ||||||||
\(124\) | 2.47214 | 0.222004 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.47214 | −0.398410 | ||||||||
\(127\) | 4.00000i | 0.354943i | 0.984126 | + | 0.177471i | \(0.0567917\pi\) | ||||
−0.984126 | + | 0.177471i | \(0.943208\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 4.76393 | 0.419441 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.52786 | −0.832453 | −0.416227 | − | 0.909261i | \(-0.636648\pi\) | ||||
−0.416227 | + | 0.909261i | \(0.636648\pi\) | |||||||
\(132\) | 5.23607i | 0.455741i | ||||||||
\(133\) | − 25.5279i | − 2.21355i | ||||||||
\(134\) | −9.70820 | −0.838661 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | − 3.05573i | − 0.261068i | −0.991444 | − | 0.130534i | \(-0.958331\pi\) | ||||
0.991444 | − | 0.130534i | \(-0.0416692\pi\) | |||||||
\(138\) | 1.00000i | 0.0851257i | ||||||||
\(139\) | 16.9443 | 1.43719 | 0.718597 | − | 0.695427i | \(-0.244785\pi\) | ||||
0.718597 | + | 0.695427i | \(0.244785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | − 8.94427i | − 0.750587i | ||||||||
\(143\) | − 23.4164i | − 1.95818i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.47214 | −0.370117 | ||||||||
\(147\) | − 13.0000i | − 1.07222i | ||||||||
\(148\) | 11.2361i | 0.923599i | ||||||||
\(149\) | 11.7082 | 0.959173 | 0.479587 | − | 0.877494i | \(-0.340787\pi\) | ||||
0.479587 | + | 0.877494i | \(0.340787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4721 | −1.17773 | −0.588863 | − | 0.808233i | \(-0.700424\pi\) | ||||
−0.588863 | + | 0.808233i | \(0.700424\pi\) | |||||||
\(152\) | − 5.70820i | − 0.462996i | ||||||||
\(153\) | − 4.00000i | − 0.323381i | ||||||||
\(154\) | −23.4164 | −1.88695 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.47214 | 0.358057 | ||||||||
\(157\) | 6.65248i | 0.530925i | 0.964121 | + | 0.265463i | \(0.0855247\pi\) | ||||
−0.964121 | + | 0.265463i | \(0.914475\pi\) | |||||||
\(158\) | 4.47214i | 0.355784i | ||||||||
\(159\) | −5.23607 | −0.415247 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.47214 | −0.352454 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 2.47214i | − 0.193633i | −0.995302 | − | 0.0968163i | \(-0.969134\pi\) | ||||
0.995302 | − | 0.0968163i | \(-0.0308659\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.2361 | 1.02732 | ||||||||
\(167\) | − 16.9443i | − 1.31119i | −0.755114 | − | 0.655594i | \(-0.772418\pi\) | ||||
0.755114 | − | 0.655594i | \(-0.227582\pi\) | |||||||
\(168\) | − 4.47214i | − 0.345033i | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.70820 | 0.436517 | ||||||||
\(172\) | 4.76393i | 0.363246i | ||||||||
\(173\) | − 17.4164i | − 1.32414i | −0.749440 | − | 0.662072i | \(-0.769677\pi\) | ||||
0.749440 | − | 0.662072i | \(-0.230323\pi\) | |||||||
\(174\) | 4.47214 | 0.339032 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.23607 | −0.394683 | ||||||||
\(177\) | 8.94427i | 0.672293i | ||||||||
\(178\) | − 10.4721i | − 0.784920i | ||||||||
\(179\) | −19.4164 | −1.45125 | −0.725625 | − | 0.688090i | \(-0.758449\pi\) | ||||
−0.725625 | + | 0.688090i | \(0.758449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.2361 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(182\) | 20.0000i | 1.48250i | ||||||||
\(183\) | 0.763932i | 0.0564715i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.47214 | −0.181266 | ||||||||
\(187\) | − 20.9443i | − 1.53160i | ||||||||
\(188\) | 4.00000i | 0.291730i | ||||||||
\(189\) | 4.47214 | 0.325300 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.47214 | 0.468307 | 0.234154 | − | 0.972200i | \(-0.424768\pi\) | ||||
0.234154 | + | 0.972200i | \(0.424768\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | 23.8885i | 1.71954i | 0.510686 | + | 0.859768i | \(0.329392\pi\) | ||||
−0.510686 | + | 0.859768i | \(0.670608\pi\) | |||||||
\(194\) | −0.472136 | −0.0338974 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0000 | 0.928571 | ||||||||
\(197\) | − 2.94427i | − 0.209771i | −0.994484 | − | 0.104885i | \(-0.966552\pi\) | ||||
0.994484 | − | 0.104885i | \(-0.0334476\pi\) | |||||||
\(198\) | − 5.23607i | − 0.372111i | ||||||||
\(199\) | −17.4164 | −1.23462 | −0.617308 | − | 0.786721i | \(-0.711777\pi\) | ||||
−0.617308 | + | 0.786721i | \(0.711777\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.70820 | 0.684764 | ||||||||
\(202\) | − 4.47214i | − 0.314658i | ||||||||
\(203\) | 20.0000i | 1.40372i | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.00000 | −0.418040 | ||||||||
\(207\) | − 1.00000i | − 0.0695048i | ||||||||
\(208\) | 4.47214i | 0.310087i | ||||||||
\(209\) | 29.8885 | 2.06743 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4164 | −1.61205 | −0.806026 | − | 0.591880i | \(-0.798386\pi\) | ||||
−0.806026 | + | 0.591880i | \(0.798386\pi\) | |||||||
\(212\) | − 5.23607i | − 0.359615i | ||||||||
\(213\) | 8.94427i | 0.612851i | ||||||||
\(214\) | 12.6525 | 0.864905 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | − 11.0557i | − 0.750512i | ||||||||
\(218\) | 4.76393i | 0.322654i | ||||||||
\(219\) | 4.47214 | 0.302199 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.8885 | −1.20331 | ||||||||
\(222\) | − 11.2361i | − 0.754116i | ||||||||
\(223\) | 19.4164i | 1.30022i | 0.759841 | + | 0.650109i | \(0.225277\pi\) | ||||
−0.759841 | + | 0.650109i | \(0.774723\pi\) | |||||||
\(224\) | 4.47214 | 0.298807 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.52786 | −0.367708 | ||||||||
\(227\) | 9.23607i | 0.613019i | 0.951868 | + | 0.306510i | \(0.0991612\pi\) | ||||
−0.951868 | + | 0.306510i | \(0.900839\pi\) | |||||||
\(228\) | 5.70820i | 0.378035i | ||||||||
\(229\) | −17.7082 | −1.17019 | −0.585096 | − | 0.810964i | \(-0.698943\pi\) | ||||
−0.585096 | + | 0.810964i | \(0.698943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.4164 | 1.54069 | ||||||||
\(232\) | 4.47214i | 0.293610i | ||||||||
\(233\) | 19.8885i | 1.30294i | 0.758674 | + | 0.651471i | \(0.225848\pi\) | ||||
−0.758674 | + | 0.651471i | \(0.774152\pi\) | |||||||
\(234\) | −4.47214 | −0.292353 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.94427 | −0.582223 | ||||||||
\(237\) | − 4.47214i | − 0.290496i | ||||||||
\(238\) | 17.8885i | 1.15954i | ||||||||
\(239\) | 4.94427 | 0.319818 | 0.159909 | − | 0.987132i | \(-0.448880\pi\) | ||||
0.159909 | + | 0.987132i | \(0.448880\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4721 | −0.803401 | −0.401700 | − | 0.915771i | \(-0.631581\pi\) | ||||
−0.401700 | + | 0.915771i | \(0.631581\pi\) | |||||||
\(242\) | − 16.4164i | − 1.05529i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.763932 | −0.0489057 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | − 25.5279i | − 1.62430i | ||||||||
\(248\) | − 2.47214i | − 0.156981i | ||||||||
\(249\) | −13.2361 | −0.838802 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.7082 | −1.24397 | −0.621985 | − | 0.783029i | \(-0.713674\pi\) | ||||
−0.621985 | + | 0.783029i | \(0.713674\pi\) | |||||||
\(252\) | 4.47214i | 0.281718i | ||||||||
\(253\) | − 5.23607i | − 0.329189i | ||||||||
\(254\) | 4.00000 | 0.250982 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.8885i | 0.741587i | 0.928715 | + | 0.370793i | \(0.120914\pi\) | ||||
−0.928715 | + | 0.370793i | \(0.879086\pi\) | |||||||
\(258\) | − 4.76393i | − 0.296589i | ||||||||
\(259\) | 50.2492 | 3.12233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.47214 | −0.276818 | ||||||||
\(262\) | 9.52786i | 0.588633i | ||||||||
\(263\) | 24.9443i | 1.53813i | 0.639171 | + | 0.769065i | \(0.279278\pi\) | ||||
−0.639171 | + | 0.769065i | \(0.720722\pi\) | |||||||
\(264\) | 5.23607 | 0.322258 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −25.5279 | −1.56521 | ||||||||
\(267\) | 10.4721i | 0.640884i | ||||||||
\(268\) | 9.70820i | 0.593023i | ||||||||
\(269\) | 13.0557 | 0.796022 | 0.398011 | − | 0.917381i | \(-0.369701\pi\) | ||||
0.398011 | + | 0.917381i | \(0.369701\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.9443 | −1.02929 | −0.514646 | − | 0.857403i | \(-0.672076\pi\) | ||||
−0.514646 | + | 0.857403i | \(0.672076\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | − 20.0000i | − 1.21046i | ||||||||
\(274\) | −3.05573 | −0.184603 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 20.4721i | 1.23005i | 0.788507 | + | 0.615026i | \(0.210854\pi\) | ||||
−0.788507 | + | 0.615026i | \(0.789146\pi\) | |||||||
\(278\) | − 16.9443i | − 1.01625i | ||||||||
\(279\) | 2.47214 | 0.148003 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5279 | −0.807005 | −0.403502 | − | 0.914979i | \(-0.632207\pi\) | ||||
−0.403502 | + | 0.914979i | \(0.632207\pi\) | |||||||
\(282\) | − 4.00000i | − 0.238197i | ||||||||
\(283\) | − 3.81966i | − 0.227055i | −0.993535 | − | 0.113528i | \(-0.963785\pi\) | ||||
0.993535 | − | 0.113528i | \(-0.0362150\pi\) | |||||||
\(284\) | −8.94427 | −0.530745 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.4164 | −1.38464 | ||||||||
\(287\) | − 8.94427i | − 0.527964i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.472136 | 0.0276771 | ||||||||
\(292\) | 4.47214i | 0.261712i | ||||||||
\(293\) | 0.291796i | 0.0170469i | 0.999964 | + | 0.00852345i | \(0.00271313\pi\) | ||||
−0.999964 | + | 0.00852345i | \(0.997287\pi\) | |||||||
\(294\) | −13.0000 | −0.758175 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.2361 | 0.653083 | ||||||||
\(297\) | 5.23607i | 0.303827i | ||||||||
\(298\) | − 11.7082i | − 0.678238i | ||||||||
\(299\) | −4.47214 | −0.258630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.3050 | 1.22800 | ||||||||
\(302\) | 14.4721i | 0.832778i | ||||||||
\(303\) | 4.47214i | 0.256917i | ||||||||
\(304\) | −5.70820 | −0.327388 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | − 15.4164i | − 0.879861i | −0.898032 | − | 0.439930i | \(-0.855003\pi\) | ||||
0.898032 | − | 0.439930i | \(-0.144997\pi\) | |||||||
\(308\) | 23.4164i | 1.33427i | ||||||||
\(309\) | 6.00000 | 0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9443 | −1.18764 | −0.593820 | − | 0.804598i | \(-0.702381\pi\) | ||||
−0.593820 | + | 0.804598i | \(0.702381\pi\) | |||||||
\(312\) | − 4.47214i | − 0.253185i | ||||||||
\(313\) | 15.5279i | 0.877687i | 0.898564 | + | 0.438843i | \(0.144612\pi\) | ||||
−0.898564 | + | 0.438843i | \(0.855388\pi\) | |||||||
\(314\) | 6.65248 | 0.375421 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.47214 | 0.251577 | ||||||||
\(317\) | − 19.5279i | − 1.09679i | −0.836218 | − | 0.548397i | \(-0.815238\pi\) | ||||
0.836218 | − | 0.548397i | \(-0.184762\pi\) | |||||||
\(318\) | 5.23607i | 0.293624i | ||||||||
\(319\) | −23.4164 | −1.31107 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6525 | −0.706192 | ||||||||
\(322\) | 4.47214i | 0.249222i | ||||||||
\(323\) | − 22.8328i | − 1.27045i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.47214 | −0.136919 | ||||||||
\(327\) | − 4.76393i | − 0.263446i | ||||||||
\(328\) | − 2.00000i | − 0.110432i | ||||||||
\(329\) | 17.8885 | 0.986227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4721 | −0.575601 | −0.287800 | − | 0.957690i | \(-0.592924\pi\) | ||||
−0.287800 | + | 0.957690i | \(0.592924\pi\) | |||||||
\(332\) | − 13.2361i | − 0.726424i | ||||||||
\(333\) | 11.2361i | 0.615733i | ||||||||
\(334\) | −16.9443 | −0.927149 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.47214 | −0.243975 | ||||||||
\(337\) | 19.8885i | 1.08340i | 0.840573 | + | 0.541699i | \(0.182219\pi\) | ||||
−0.840573 | + | 0.541699i | \(0.817781\pi\) | |||||||
\(338\) | 7.00000i | 0.380750i | ||||||||
\(339\) | 5.52786 | 0.300232 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9443 | 0.700972 | ||||||||
\(342\) | − 5.70820i | − 0.308664i | ||||||||
\(343\) | − 26.8328i | − 1.44884i | ||||||||
\(344\) | 4.76393 | 0.256854 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.4164 | −0.936312 | ||||||||
\(347\) | − 30.4721i | − 1.63583i | −0.575339 | − | 0.817915i | \(-0.695130\pi\) | ||||
0.575339 | − | 0.817915i | \(-0.304870\pi\) | |||||||
\(348\) | − 4.47214i | − 0.239732i | ||||||||
\(349\) | −3.88854 | −0.208149 | −0.104074 | − | 0.994570i | \(-0.533188\pi\) | ||||
−0.104074 | + | 0.994570i | \(0.533188\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 5.23607i | 0.279083i | ||||||||
\(353\) | − 3.88854i | − 0.206966i | −0.994631 | − | 0.103483i | \(-0.967001\pi\) | ||||
0.994631 | − | 0.103483i | \(-0.0329988\pi\) | |||||||
\(354\) | 8.94427 | 0.475383 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.4721 | −0.555022 | ||||||||
\(357\) | − 17.8885i | − 0.946762i | ||||||||
\(358\) | 19.4164i | 1.02619i | ||||||||
\(359\) | −29.3050 | −1.54666 | −0.773328 | − | 0.634006i | \(-0.781409\pi\) | ||||
−0.773328 | + | 0.634006i | \(0.781409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5836 | 0.714926 | ||||||||
\(362\) | 11.2361i | 0.590555i | ||||||||
\(363\) | 16.4164i | 0.861638i | ||||||||
\(364\) | 20.0000 | 1.04828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.763932 | 0.0399314 | ||||||||
\(367\) | − 9.41641i | − 0.491532i | −0.969329 | − | 0.245766i | \(-0.920960\pi\) | ||||
0.969329 | − | 0.245766i | \(-0.0790396\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.4164 | −1.21572 | ||||||||
\(372\) | 2.47214i | 0.128174i | ||||||||
\(373\) | − 35.5967i | − 1.84313i | −0.388224 | − | 0.921565i | \(-0.626911\pi\) | ||||
0.388224 | − | 0.921565i | \(-0.373089\pi\) | |||||||
\(374\) | −20.9443 | −1.08300 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | 20.0000i | 1.03005i | ||||||||
\(378\) | − 4.47214i | − 0.230022i | ||||||||
\(379\) | −13.7082 | −0.704143 | −0.352072 | − | 0.935973i | \(-0.614523\pi\) | ||||
−0.352072 | + | 0.935973i | \(0.614523\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | − 6.47214i | − 0.331143i | ||||||||
\(383\) | 7.05573i | 0.360531i | 0.983618 | + | 0.180265i | \(0.0576957\pi\) | ||||
−0.983618 | + | 0.180265i | \(0.942304\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.8885 | 1.21589 | ||||||||
\(387\) | 4.76393i | 0.242164i | ||||||||
\(388\) | 0.472136i | 0.0239691i | ||||||||
\(389\) | −23.7082 | −1.20205 | −0.601027 | − | 0.799229i | \(-0.705242\pi\) | ||||
−0.601027 | + | 0.799229i | \(0.705242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | − 13.0000i | − 0.656599i | ||||||||
\(393\) | − 9.52786i | − 0.480617i | ||||||||
\(394\) | −2.94427 | −0.148330 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.23607 | −0.263122 | ||||||||
\(397\) | − 26.9443i | − 1.35229i | −0.736767 | − | 0.676147i | \(-0.763648\pi\) | ||||
0.736767 | − | 0.676147i | \(-0.236352\pi\) | |||||||
\(398\) | 17.4164i | 0.873006i | ||||||||
\(399\) | 25.5279 | 1.27799 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.94427 | 0.446656 | 0.223328 | − | 0.974743i | \(-0.428308\pi\) | ||||
0.223328 | + | 0.974743i | \(0.428308\pi\) | |||||||
\(402\) | − 9.70820i | − 0.484201i | ||||||||
\(403\) | − 11.0557i | − 0.550725i | ||||||||
\(404\) | −4.47214 | −0.222497 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.0000 | 0.992583 | ||||||||
\(407\) | 58.8328i | 2.91623i | ||||||||
\(408\) | − 4.00000i | − 0.198030i | ||||||||
\(409\) | 35.8885 | 1.77457 | 0.887287 | − | 0.461217i | \(-0.152587\pi\) | ||||
0.887287 | + | 0.461217i | \(0.152587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.05573 | 0.150728 | ||||||||
\(412\) | 6.00000i | 0.295599i | ||||||||
\(413\) | 40.0000i | 1.96827i | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.47214 | 0.219265 | ||||||||
\(417\) | 16.9443i | 0.829765i | ||||||||
\(418\) | − 29.8885i | − 1.46190i | ||||||||
\(419\) | −28.0689 | −1.37125 | −0.685627 | − | 0.727953i | \(-0.740472\pi\) | ||||
−0.685627 | + | 0.727953i | \(0.740472\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.763932 | −0.0372318 | −0.0186159 | − | 0.999827i | \(-0.505926\pi\) | ||||
−0.0186159 | + | 0.999827i | \(0.505926\pi\) | |||||||
\(422\) | 23.4164i | 1.13989i | ||||||||
\(423\) | 4.00000i | 0.194487i | ||||||||
\(424\) | −5.23607 | −0.254286 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.94427 | 0.433351 | ||||||||
\(427\) | 3.41641i | 0.165332i | ||||||||
\(428\) | − 12.6525i | − 0.611581i | ||||||||
\(429\) | 23.4164 | 1.13055 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.4164 | −1.12793 | −0.563964 | − | 0.825799i | \(-0.690724\pi\) | ||||
−0.563964 | + | 0.825799i | \(0.690724\pi\) | |||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | − 21.4164i | − 1.02921i | −0.857428 | − | 0.514603i | \(-0.827939\pi\) | ||||
0.857428 | − | 0.514603i | \(-0.172061\pi\) | |||||||
\(434\) | −11.0557 | −0.530692 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.76393 | 0.228151 | ||||||||
\(437\) | − 5.70820i | − 0.273060i | ||||||||
\(438\) | − 4.47214i | − 0.213687i | ||||||||
\(439\) | −19.0557 | −0.909480 | −0.454740 | − | 0.890624i | \(-0.650268\pi\) | ||||
−0.454740 | + | 0.890624i | \(0.650268\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | 0.619048 | ||||||||
\(442\) | 17.8885i | 0.850871i | ||||||||
\(443\) | − 15.0557i | − 0.715319i | −0.933852 | − | 0.357660i | \(-0.883575\pi\) | ||||
0.933852 | − | 0.357660i | \(-0.116425\pi\) | |||||||
\(444\) | −11.2361 | −0.533240 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.4164 | 0.919394 | ||||||||
\(447\) | 11.7082i | 0.553779i | ||||||||
\(448\) | − 4.47214i | − 0.211289i | ||||||||
\(449\) | −15.8885 | −0.749827 | −0.374913 | − | 0.927060i | \(-0.622328\pi\) | ||||
−0.374913 | + | 0.927060i | \(0.622328\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.4721 | 0.493114 | ||||||||
\(452\) | 5.52786i | 0.260009i | ||||||||
\(453\) | − 14.4721i | − 0.679960i | ||||||||
\(454\) | 9.23607 | 0.433470 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.70820 | 0.267311 | ||||||||
\(457\) | − 27.5279i | − 1.28770i | −0.765152 | − | 0.643850i | \(-0.777336\pi\) | ||||
0.765152 | − | 0.643850i | \(-0.222664\pi\) | |||||||
\(458\) | 17.7082i | 0.827450i | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0000 | 1.02464 | 0.512321 | − | 0.858794i | \(-0.328786\pi\) | ||||
0.512321 | + | 0.858794i | \(0.328786\pi\) | |||||||
\(462\) | − 23.4164i | − 1.08943i | ||||||||
\(463\) | 24.0000i | 1.11537i | 0.830051 | + | 0.557687i | \(0.188311\pi\) | ||||
−0.830051 | + | 0.557687i | \(0.811689\pi\) | |||||||
\(464\) | 4.47214 | 0.207614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.8885 | 0.921319 | ||||||||
\(467\) | 17.8197i | 0.824596i | 0.911049 | + | 0.412298i | \(0.135274\pi\) | ||||
−0.911049 | + | 0.412298i | \(0.864726\pi\) | |||||||
\(468\) | 4.47214i | 0.206725i | ||||||||
\(469\) | 43.4164 | 2.00478 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.65248 | −0.306530 | ||||||||
\(472\) | 8.94427i | 0.411693i | ||||||||
\(473\) | 24.9443i | 1.14694i | ||||||||
\(474\) | −4.47214 | −0.205412 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.8885 | 0.819920 | ||||||||
\(477\) | − 5.23607i | − 0.239743i | ||||||||
\(478\) | − 4.94427i | − 0.226146i | ||||||||
\(479\) | 28.9443 | 1.32250 | 0.661249 | − | 0.750167i | \(-0.270027\pi\) | ||||
0.661249 | + | 0.750167i | \(0.270027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.2492 | 2.29117 | ||||||||
\(482\) | 12.4721i | 0.568090i | ||||||||
\(483\) | − 4.47214i | − 0.203489i | ||||||||
\(484\) | −16.4164 | −0.746200 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − 9.88854i | − 0.448093i | −0.974578 | − | 0.224046i | \(-0.928073\pi\) | ||||
0.974578 | − | 0.224046i | \(-0.0719267\pi\) | |||||||
\(488\) | 0.763932i | 0.0345816i | ||||||||
\(489\) | 2.47214 | 0.111794 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3050 | 1.32251 | 0.661257 | − | 0.750159i | \(-0.270023\pi\) | ||||
0.661257 | + | 0.750159i | \(0.270023\pi\) | |||||||
\(492\) | 2.00000i | 0.0901670i | ||||||||
\(493\) | 17.8885i | 0.805659i | ||||||||
\(494\) | −25.5279 | −1.14855 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.47214 | −0.111002 | ||||||||
\(497\) | 40.0000i | 1.79425i | ||||||||
\(498\) | 13.2361i | 0.593122i | ||||||||
\(499\) | −0.583592 | −0.0261252 | −0.0130626 | − | 0.999915i | \(-0.504158\pi\) | ||||
−0.0130626 | + | 0.999915i | \(0.504158\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.9443 | 0.757014 | ||||||||
\(502\) | 19.7082i | 0.879620i | ||||||||
\(503\) | 10.4721i | 0.466929i | 0.972365 | + | 0.233465i | \(0.0750063\pi\) | ||||
−0.972365 | + | 0.233465i | \(0.924994\pi\) | |||||||
\(504\) | 4.47214 | 0.199205 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.23607 | −0.232772 | ||||||||
\(507\) | − 7.00000i | − 0.310881i | ||||||||
\(508\) | − 4.00000i | − 0.177471i | ||||||||
\(509\) | 33.4164 | 1.48116 | 0.740578 | − | 0.671970i | \(-0.234552\pi\) | ||||
0.740578 | + | 0.671970i | \(0.234552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | 0.884748 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 5.70820i | 0.252023i | ||||||||
\(514\) | 11.8885 | 0.524381 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.76393 | −0.209720 | ||||||||
\(517\) | 20.9443i | 0.921128i | ||||||||
\(518\) | − 50.2492i | − 2.20782i | ||||||||
\(519\) | 17.4164 | 0.764495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0000 | 0.700973 | 0.350486 | − | 0.936568i | \(-0.386016\pi\) | ||||
0.350486 | + | 0.936568i | \(0.386016\pi\) | |||||||
\(522\) | 4.47214i | 0.195740i | ||||||||
\(523\) | 25.7082i | 1.12414i | 0.827089 | + | 0.562071i | \(0.189995\pi\) | ||||
−0.827089 | + | 0.562071i | \(0.810005\pi\) | |||||||
\(524\) | 9.52786 | 0.416227 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.9443 | 1.08762 | ||||||||
\(527\) | − 9.88854i | − 0.430752i | ||||||||
\(528\) | − 5.23607i | − 0.227871i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.94427 | −0.388148 | ||||||||
\(532\) | 25.5279i | 1.10677i | ||||||||
\(533\) | − 8.94427i | − 0.387419i | ||||||||
\(534\) | 10.4721 | 0.453174 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.70820 | 0.419331 | ||||||||
\(537\) | − 19.4164i | − 0.837880i | ||||||||
\(538\) | − 13.0557i | − 0.562872i | ||||||||
\(539\) | 68.0689 | 2.93193 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.11146 | 0.348739 | 0.174369 | − | 0.984680i | \(-0.444211\pi\) | ||||
0.174369 | + | 0.984680i | \(0.444211\pi\) | |||||||
\(542\) | 16.9443i | 0.727819i | ||||||||
\(543\) | − 11.2361i | − 0.482186i | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −20.0000 | −0.855921 | ||||||||
\(547\) | − 41.3050i | − 1.76607i | −0.469305 | − | 0.883036i | \(-0.655496\pi\) | ||||
0.469305 | − | 0.883036i | \(-0.344504\pi\) | |||||||
\(548\) | 3.05573i | 0.130534i | ||||||||
\(549\) | −0.763932 | −0.0326038 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.5279 | −1.08752 | ||||||||
\(552\) | − 1.00000i | − 0.0425628i | ||||||||
\(553\) | − 20.0000i | − 0.850487i | ||||||||
\(554\) | 20.4721 | 0.869778 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.9443 | −0.718597 | ||||||||
\(557\) | 15.1246i | 0.640850i | 0.947274 | + | 0.320425i | \(0.103826\pi\) | ||||
−0.947274 | + | 0.320425i | \(0.896174\pi\) | |||||||
\(558\) | − 2.47214i | − 0.104654i | ||||||||
\(559\) | 21.3050 | 0.901103 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.9443 | 0.884268 | ||||||||
\(562\) | 13.5279i | 0.570639i | ||||||||
\(563\) | 24.6525i | 1.03898i | 0.854477 | + | 0.519489i | \(0.173878\pi\) | ||||
−0.854477 | + | 0.519489i | \(0.826122\pi\) | |||||||
\(564\) | −4.00000 | −0.168430 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.81966 | −0.160552 | ||||||||
\(567\) | 4.47214i | 0.187812i | ||||||||
\(568\) | 8.94427i | 0.375293i | ||||||||
\(569\) | −20.0000 | −0.838444 | −0.419222 | − | 0.907884i | \(-0.637697\pi\) | ||||
−0.419222 | + | 0.907884i | \(0.637697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.2918 | −0.598093 | −0.299047 | − | 0.954239i | \(-0.596669\pi\) | ||||
−0.299047 | + | 0.954239i | \(0.596669\pi\) | |||||||
\(572\) | 23.4164i | 0.979089i | ||||||||
\(573\) | 6.47214i | 0.270377i | ||||||||
\(574\) | −8.94427 | −0.373327 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 34.3607i | 1.43045i | 0.698892 | + | 0.715227i | \(0.253677\pi\) | ||||
−0.698892 | + | 0.715227i | \(0.746323\pi\) | |||||||
\(578\) | − 1.00000i | − 0.0415945i | ||||||||
\(579\) | −23.8885 | −0.992774 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −59.1935 | −2.45576 | ||||||||
\(582\) | − 0.472136i | − 0.0195707i | ||||||||
\(583\) | − 27.4164i | − 1.13547i | ||||||||
\(584\) | 4.47214 | 0.185058 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.291796 | 0.0120540 | ||||||||
\(587\) | − 6.47214i | − 0.267134i | −0.991040 | − | 0.133567i | \(-0.957357\pi\) | ||||
0.991040 | − | 0.133567i | \(-0.0426431\pi\) | |||||||
\(588\) | 13.0000i | 0.536111i | ||||||||
\(589\) | 14.1115 | 0.581452 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.94427 | 0.121111 | ||||||||
\(592\) | − 11.2361i | − 0.461800i | ||||||||
\(593\) | 33.7771i | 1.38706i | 0.720428 | + | 0.693529i | \(0.243945\pi\) | ||||
−0.720428 | + | 0.693529i | \(0.756055\pi\) | |||||||
\(594\) | 5.23607 | 0.214838 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.7082 | −0.479587 | ||||||||
\(597\) | − 17.4164i | − 0.712806i | ||||||||
\(598\) | 4.47214i | 0.182879i | ||||||||
\(599\) | −33.8885 | −1.38465 | −0.692324 | − | 0.721587i | \(-0.743413\pi\) | ||||
−0.692324 | + | 0.721587i | \(0.743413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.3607 | −0.422621 | −0.211310 | − | 0.977419i | \(-0.567773\pi\) | ||||
−0.211310 | + | 0.977419i | \(0.567773\pi\) | |||||||
\(602\) | − 21.3050i | − 0.868325i | ||||||||
\(603\) | 9.70820i | 0.395349i | ||||||||
\(604\) | 14.4721 | 0.588863 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.47214 | 0.181668 | ||||||||
\(607\) | 17.5279i | 0.711434i | 0.934594 | + | 0.355717i | \(0.115763\pi\) | ||||
−0.934594 | + | 0.355717i | \(0.884237\pi\) | |||||||
\(608\) | 5.70820i | 0.231498i | ||||||||
\(609\) | −20.0000 | −0.810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.8885 | 0.723693 | ||||||||
\(612\) | 4.00000i | 0.161690i | ||||||||
\(613\) | − 25.1246i | − 1.01477i | −0.861718 | − | 0.507387i | \(-0.830612\pi\) | ||||
0.861718 | − | 0.507387i | \(-0.169388\pi\) | |||||||
\(614\) | −15.4164 | −0.622156 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.4164 | 0.943474 | ||||||||
\(617\) | − 20.3607i | − 0.819690i | −0.912155 | − | 0.409845i | \(-0.865583\pi\) | ||||
0.912155 | − | 0.409845i | \(-0.134417\pi\) | |||||||
\(618\) | − 6.00000i | − 0.241355i | ||||||||
\(619\) | −18.2918 | −0.735209 | −0.367605 | − | 0.929982i | \(-0.619822\pi\) | ||||
−0.367605 | + | 0.929982i | \(0.619822\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 20.9443i | 0.839789i | ||||||||
\(623\) | 46.8328i | 1.87632i | ||||||||
\(624\) | −4.47214 | −0.179029 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.5279 | 0.620618 | ||||||||
\(627\) | 29.8885i | 1.19363i | ||||||||
\(628\) | − 6.65248i | − 0.265463i | ||||||||
\(629\) | 44.9443 | 1.79205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.00000 | −0.238856 | −0.119428 | − | 0.992843i | \(-0.538106\pi\) | ||||
−0.119428 | + | 0.992843i | \(0.538106\pi\) | |||||||
\(632\) | − 4.47214i | − 0.177892i | ||||||||
\(633\) | − 23.4164i | − 0.930719i | ||||||||
\(634\) | −19.5279 | −0.775551 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.23607 | 0.207624 | ||||||||
\(637\) | − 58.1378i | − 2.30350i | ||||||||
\(638\) | 23.4164i | 0.927064i | ||||||||
\(639\) | −8.94427 | −0.353830 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.00000 | 0.157991 | 0.0789953 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789953 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(642\) | 12.6525i | 0.499353i | ||||||||
\(643\) | − 32.5410i | − 1.28329i | −0.767001 | − | 0.641646i | \(-0.778252\pi\) | ||||
0.767001 | − | 0.641646i | \(-0.221748\pi\) | |||||||
\(644\) | 4.47214 | 0.176227 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.8328 | −0.898345 | ||||||||
\(647\) | − 12.9443i | − 0.508892i | −0.967087 | − | 0.254446i | \(-0.918107\pi\) | ||||
0.967087 | − | 0.254446i | \(-0.0818931\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −46.8328 | −1.83835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.0557 | 0.433308 | ||||||||
\(652\) | 2.47214i | 0.0968163i | ||||||||
\(653\) | 9.41641i | 0.368493i | 0.982880 | + | 0.184246i | \(0.0589844\pi\) | ||||
−0.982880 | + | 0.184246i | \(0.941016\pi\) | |||||||
\(654\) | −4.76393 | −0.186284 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | 4.47214i | 0.174475i | ||||||||
\(658\) | − 17.8885i | − 0.697368i | ||||||||
\(659\) | 32.6525 | 1.27196 | 0.635980 | − | 0.771706i | \(-0.280596\pi\) | ||||
0.635980 | + | 0.771706i | \(0.280596\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.81966 | 0.148568 | 0.0742838 | − | 0.997237i | \(-0.476333\pi\) | ||||
0.0742838 | + | 0.997237i | \(0.476333\pi\) | |||||||
\(662\) | 10.4721i | 0.407011i | ||||||||
\(663\) | − 17.8885i | − 0.694733i | ||||||||
\(664\) | −13.2361 | −0.513659 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.2361 | 0.435389 | ||||||||
\(667\) | 4.47214i | 0.173162i | ||||||||
\(668\) | 16.9443i | 0.655594i | ||||||||
\(669\) | −19.4164 | −0.750682 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 4.47214i | 0.172516i | ||||||||
\(673\) | 4.47214i | 0.172388i | 0.996278 | + | 0.0861941i | \(0.0274705\pi\) | ||||
−0.996278 | + | 0.0861941i | \(0.972529\pi\) | |||||||
\(674\) | 19.8885 | 0.766078 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.00000 | 0.269231 | ||||||||
\(677\) | − 19.1246i | − 0.735019i | −0.930020 | − | 0.367509i | \(-0.880211\pi\) | ||||
0.930020 | − | 0.367509i | \(-0.119789\pi\) | |||||||
\(678\) | − 5.52786i | − 0.212296i | ||||||||
\(679\) | 2.11146 | 0.0810303 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.23607 | −0.353927 | ||||||||
\(682\) | − 12.9443i | − 0.495662i | ||||||||
\(683\) | 14.4721i | 0.553761i | 0.960904 | + | 0.276880i | \(0.0893006\pi\) | ||||
−0.960904 | + | 0.276880i | \(0.910699\pi\) | |||||||
\(684\) | −5.70820 | −0.218259 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.8328 | −1.02448 | ||||||||
\(687\) | − 17.7082i | − 0.675610i | ||||||||
\(688\) | − 4.76393i | − 0.181623i | ||||||||
\(689\) | −23.4164 | −0.892094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.5836 | 0.630870 | 0.315435 | − | 0.948947i | \(-0.397850\pi\) | ||||
0.315435 | + | 0.948947i | \(0.397850\pi\) | |||||||
\(692\) | 17.4164i | 0.662072i | ||||||||
\(693\) | 23.4164i | 0.889516i | ||||||||
\(694\) | −30.4721 | −1.15671 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.47214 | −0.169516 | ||||||||
\(697\) | − 8.00000i | − 0.303022i | ||||||||
\(698\) | 3.88854i | 0.147184i | ||||||||
\(699\) | −19.8885 | −0.752254 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.12461 | −0.118015 | −0.0590075 | − | 0.998258i | \(-0.518794\pi\) | ||||
−0.0590075 | + | 0.998258i | \(0.518794\pi\) | |||||||
\(702\) | − 4.47214i | − 0.168790i | ||||||||
\(703\) | 64.1378i | 2.41900i | ||||||||
\(704\) | 5.23607 | 0.197342 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.88854 | −0.146347 | ||||||||
\(707\) | 20.0000i | 0.752177i | ||||||||
\(708\) | − 8.94427i | − 0.336146i | ||||||||
\(709\) | −35.0132 | −1.31495 | −0.657473 | − | 0.753478i | \(-0.728375\pi\) | ||||
−0.657473 | + | 0.753478i | \(0.728375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.47214 | 0.167718 | ||||||||
\(712\) | 10.4721i | 0.392460i | ||||||||
\(713\) | − 2.47214i | − 0.0925822i | ||||||||
\(714\) | −17.8885 | −0.669462 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.4164 | 0.725625 | ||||||||
\(717\) | 4.94427i | 0.184647i | ||||||||
\(718\) | 29.3050i | 1.09365i | ||||||||
\(719\) | 3.05573 | 0.113959 | 0.0569797 | − | 0.998375i | \(-0.481853\pi\) | ||||
0.0569797 | + | 0.998375i | \(0.481853\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.8328 | 0.999306 | ||||||||
\(722\) | − 13.5836i | − 0.505529i | ||||||||
\(723\) | − 12.4721i | − 0.463844i | ||||||||
\(724\) | 11.2361 | 0.417585 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.4164 | 0.609270 | ||||||||
\(727\) | 19.3050i | 0.715981i | 0.933725 | + | 0.357991i | \(0.116538\pi\) | ||||
−0.933725 | + | 0.357991i | \(0.883462\pi\) | |||||||
\(728\) | − 20.0000i | − 0.741249i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.0557 | 0.704802 | ||||||||
\(732\) | − 0.763932i | − 0.0282357i | ||||||||
\(733\) | − 21.7082i | − 0.801811i | −0.916119 | − | 0.400905i | \(-0.868696\pi\) | ||||
0.916119 | − | 0.400905i | \(-0.131304\pi\) | |||||||
\(734\) | −9.41641 | −0.347566 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 50.8328i | 1.87245i | ||||||||
\(738\) | − 2.00000i | − 0.0736210i | ||||||||
\(739\) | 32.9443 | 1.21187 | 0.605937 | − | 0.795512i | \(-0.292798\pi\) | ||||
0.605937 | + | 0.795512i | \(0.292798\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.5279 | 0.937790 | ||||||||
\(742\) | 23.4164i | 0.859643i | ||||||||
\(743\) | − 4.00000i | − 0.146746i | −0.997305 | − | 0.0733729i | \(-0.976624\pi\) | ||||
0.997305 | − | 0.0733729i | \(-0.0233763\pi\) | |||||||
\(744\) | 2.47214 | 0.0906329 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.5967 | −1.30329 | ||||||||
\(747\) | − 13.2361i | − 0.484282i | ||||||||
\(748\) | 20.9443i | 0.765798i | ||||||||
\(749\) | −56.5836 | −2.06752 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0000 | −0.656829 | −0.328415 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328415 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(752\) | − 4.00000i | − 0.145865i | ||||||||
\(753\) | − 19.7082i | − 0.718207i | ||||||||
\(754\) | 20.0000 | 0.728357 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.47214 | −0.162650 | ||||||||
\(757\) | 1.34752i | 0.0489766i | 0.999700 | + | 0.0244883i | \(0.00779565\pi\) | ||||
−0.999700 | + | 0.0244883i | \(0.992204\pi\) | |||||||
\(758\) | 13.7082i | 0.497904i | ||||||||
\(759\) | 5.23607 | 0.190057 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.05573 | −0.183270 | −0.0916350 | − | 0.995793i | \(-0.529209\pi\) | ||||
−0.0916350 | + | 0.995793i | \(0.529209\pi\) | |||||||
\(762\) | 4.00000i | 0.144905i | ||||||||
\(763\) | − 21.3050i | − 0.771291i | ||||||||
\(764\) | −6.47214 | −0.234154 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.05573 | 0.254934 | ||||||||
\(767\) | 40.0000i | 1.44432i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −12.4721 | −0.449757 | −0.224878 | − | 0.974387i | \(-0.572198\pi\) | ||||
−0.224878 | + | 0.974387i | \(0.572198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.8885 | −0.428155 | ||||||||
\(772\) | − 23.8885i | − 0.859768i | ||||||||
\(773\) | − 38.1803i | − 1.37325i | −0.727011 | − | 0.686626i | \(-0.759091\pi\) | ||||
0.727011 | − | 0.686626i | \(-0.240909\pi\) | |||||||
\(774\) | 4.76393 | 0.171236 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.472136 | 0.0169487 | ||||||||
\(777\) | 50.2492i | 1.80268i | ||||||||
\(778\) | 23.7082i | 0.849980i | ||||||||
\(779\) | 11.4164 | 0.409035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.8328 | −1.67581 | ||||||||
\(782\) | 4.00000i | 0.143040i | ||||||||
\(783\) | − 4.47214i | − 0.159821i | ||||||||
\(784\) | −13.0000 | −0.464286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.52786 | −0.339848 | ||||||||
\(787\) | − 35.2361i | − 1.25603i | −0.778201 | − | 0.628015i | \(-0.783868\pi\) | ||||
0.778201 | − | 0.628015i | \(-0.216132\pi\) | |||||||
\(788\) | 2.94427i | 0.104885i | ||||||||
\(789\) | −24.9443 | −0.888040 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.7214 | 0.878990 | ||||||||
\(792\) | 5.23607i | 0.186056i | ||||||||
\(793\) | 3.41641i | 0.121320i | ||||||||
\(794\) | −26.9443 | −0.956216 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.4164 | 0.617308 | ||||||||
\(797\) | − 41.5967i | − 1.47343i | −0.676202 | − | 0.736716i | \(-0.736375\pi\) | ||||
0.676202 | − | 0.736716i | \(-0.263625\pi\) | |||||||
\(798\) | − 25.5279i | − 0.903677i | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.4721 | −0.370015 | ||||||||
\(802\) | − 8.94427i | − 0.315833i | ||||||||
\(803\) | 23.4164i | 0.826347i | ||||||||
\(804\) | −9.70820 | −0.342382 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.0557 | −0.389421 | ||||||||
\(807\) | 13.0557i | 0.459583i | ||||||||
\(808\) | 4.47214i | 0.157329i | ||||||||
\(809\) | −42.9443 | −1.50984 | −0.754920 | − | 0.655817i | \(-0.772324\pi\) | ||||
−0.754920 | + | 0.655817i | \(0.772324\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.3050 | 1.45041 | 0.725207 | − | 0.688531i | \(-0.241744\pi\) | ||||
0.725207 | + | 0.688531i | \(0.241744\pi\) | |||||||
\(812\) | − 20.0000i | − 0.701862i | ||||||||
\(813\) | − 16.9443i | − 0.594262i | ||||||||
\(814\) | 58.8328 | 2.06209 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 27.1935i | 0.951380i | ||||||||
\(818\) | − 35.8885i | − 1.25481i | ||||||||
\(819\) | 20.0000 | 0.698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.5279 | 1.37953 | 0.689766 | − | 0.724032i | \(-0.257713\pi\) | ||||
0.689766 | + | 0.724032i | \(0.257713\pi\) | |||||||
\(822\) | − 3.05573i | − 0.106581i | ||||||||
\(823\) | − 52.3607i | − 1.82518i | −0.408877 | − | 0.912589i | \(-0.634080\pi\) | ||||
0.408877 | − | 0.912589i | \(-0.365920\pi\) | |||||||
\(824\) | 6.00000 | 0.209020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 40.0000 | 1.39178 | ||||||||
\(827\) | 21.5967i | 0.750993i | 0.926824 | + | 0.375496i | \(0.122528\pi\) | ||||
−0.926824 | + | 0.375496i | \(0.877472\pi\) | |||||||
\(828\) | 1.00000i | 0.0347524i | ||||||||
\(829\) | 6.00000 | 0.208389 | 0.104194 | − | 0.994557i | \(-0.466774\pi\) | ||||
0.104194 | + | 0.994557i | \(0.466774\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.4721 | −0.710171 | ||||||||
\(832\) | − 4.47214i | − 0.155043i | ||||||||
\(833\) | − 52.0000i | − 1.80169i | ||||||||
\(834\) | 16.9443 | 0.586732 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −29.8885 | −1.03372 | ||||||||
\(837\) | 2.47214i | 0.0854495i | ||||||||
\(838\) | 28.0689i | 0.969623i | ||||||||
\(839\) | 45.8885 | 1.58425 | 0.792124 | − | 0.610360i | \(-0.208975\pi\) | ||||
0.792124 | + | 0.610360i | \(0.208975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0.763932i | 0.0263268i | ||||||||
\(843\) | − 13.5279i | − 0.465924i | ||||||||
\(844\) | 23.4164 | 0.806026 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | 73.4164i | 2.52262i | ||||||||
\(848\) | 5.23607i | 0.179807i | ||||||||
\(849\) | 3.81966 | 0.131090 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.2361 | 0.385167 | ||||||||
\(852\) | − 8.94427i | − 0.306426i | ||||||||
\(853\) | − 26.0000i | − 0.890223i | −0.895475 | − | 0.445112i | \(-0.853164\pi\) | ||||
0.895475 | − | 0.445112i | \(-0.146836\pi\) | |||||||
\(854\) | 3.41641 | 0.116907 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.6525 | −0.432453 | ||||||||
\(857\) | 22.0000i | 0.751506i | 0.926720 | + | 0.375753i | \(0.122616\pi\) | ||||
−0.926720 | + | 0.375753i | \(0.877384\pi\) | |||||||
\(858\) | − 23.4164i | − 0.799423i | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.94427 | 0.304820 | ||||||||
\(862\) | 23.4164i | 0.797566i | ||||||||
\(863\) | 14.8328i | 0.504915i | 0.967608 | + | 0.252457i | \(0.0812388\pi\) | ||||
−0.967608 | + | 0.252457i | \(0.918761\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.4164 | −0.727759 | ||||||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | 11.0557i | 0.375256i | ||||||||
\(869\) | 23.4164 | 0.794347 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.4164 | 1.47111 | ||||||||
\(872\) | − 4.76393i | − 0.161327i | ||||||||
\(873\) | 0.472136i | 0.0159794i | ||||||||
\(874\) | −5.70820 | −0.193083 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.47214 | −0.151099 | ||||||||
\(877\) | 48.2492i | 1.62926i | 0.579981 | + | 0.814630i | \(0.303060\pi\) | ||||
−0.579981 | + | 0.814630i | \(0.696940\pi\) | |||||||
\(878\) | 19.0557i | 0.643100i | ||||||||
\(879\) | −0.291796 | −0.00984204 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.4164 | 1.32797 | 0.663986 | − | 0.747745i | \(-0.268863\pi\) | ||||
0.663986 | + | 0.747745i | \(0.268863\pi\) | |||||||
\(882\) | − 13.0000i | − 0.437733i | ||||||||
\(883\) | 13.5279i | 0.455249i | 0.973749 | + | 0.227624i | \(0.0730958\pi\) | ||||
−0.973749 | + | 0.227624i | \(0.926904\pi\) | |||||||
\(884\) | 17.8885 | 0.601657 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.0557 | −0.505807 | ||||||||
\(887\) | 16.9443i | 0.568933i | 0.958686 | + | 0.284466i | \(0.0918164\pi\) | ||||
−0.958686 | + | 0.284466i | \(0.908184\pi\) | |||||||
\(888\) | 11.2361i | 0.377058i | ||||||||
\(889\) | −17.8885 | −0.599963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.23607 | −0.175415 | ||||||||
\(892\) | − 19.4164i | − 0.650109i | ||||||||
\(893\) | 22.8328i | 0.764071i | ||||||||
\(894\) | 11.7082 | 0.391581 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.47214 | −0.149404 | ||||||||
\(897\) | − 4.47214i | − 0.149320i | ||||||||
\(898\) | 15.8885i | 0.530208i | ||||||||
\(899\) | −11.0557 | −0.368729 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.9443 | −0.697755 | ||||||||
\(902\) | − 10.4721i | − 0.348684i | ||||||||
\(903\) | 21.3050i | 0.708984i | ||||||||
\(904\) | 5.52786 | 0.183854 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.4721 | −0.480805 | ||||||||
\(907\) | − 4.18034i | − 0.138806i | −0.997589 | − | 0.0694030i | \(-0.977891\pi\) | ||||
0.997589 | − | 0.0694030i | \(-0.0221094\pi\) | |||||||
\(908\) | − 9.23607i | − 0.306510i | ||||||||
\(909\) | −4.47214 | −0.148331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.5836 | 0.549439 | 0.274719 | − | 0.961524i | \(-0.411415\pi\) | ||||
0.274719 | + | 0.961524i | \(0.411415\pi\) | |||||||
\(912\) | − 5.70820i | − 0.189018i | ||||||||
\(913\) | − 69.3050i | − 2.29366i | ||||||||
\(914\) | −27.5279 | −0.910541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.7082 | 0.585096 | ||||||||
\(917\) | − 42.6099i | − 1.40710i | ||||||||
\(918\) | − 4.00000i | − 0.132020i | ||||||||
\(919\) | 16.4721 | 0.543366 | 0.271683 | − | 0.962387i | \(-0.412420\pi\) | ||||
0.271683 | + | 0.962387i | \(0.412420\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.4164 | 0.507988 | ||||||||
\(922\) | − 22.0000i | − 0.724531i | ||||||||
\(923\) | 40.0000i | 1.31662i | ||||||||
\(924\) | −23.4164 | −0.770343 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24.0000 | 0.788689 | ||||||||
\(927\) | 6.00000i | 0.197066i | ||||||||
\(928\) | − 4.47214i | − 0.146805i | ||||||||
\(929\) | 24.8328 | 0.814738 | 0.407369 | − | 0.913264i | \(-0.366446\pi\) | ||||
0.407369 | + | 0.913264i | \(0.366446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 74.2067 | 2.43202 | ||||||||
\(932\) | − 19.8885i | − 0.651471i | ||||||||
\(933\) | − 20.9443i | − 0.685685i | ||||||||
\(934\) | 17.8197 | 0.583077 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.47214 | 0.146176 | ||||||||
\(937\) | 30.0000i | 0.980057i | 0.871706 | + | 0.490029i | \(0.163014\pi\) | ||||
−0.871706 | + | 0.490029i | \(0.836986\pi\) | |||||||
\(938\) | − 43.4164i | − 1.41760i | ||||||||
\(939\) | −15.5279 | −0.506733 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.1803 | 1.24464 | 0.622322 | − | 0.782762i | \(-0.286190\pi\) | ||||
0.622322 | + | 0.782762i | \(0.286190\pi\) | |||||||
\(942\) | 6.65248i | 0.216749i | ||||||||
\(943\) | − 2.00000i | − 0.0651290i | ||||||||
\(944\) | 8.94427 | 0.291111 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.9443 | 0.811008 | ||||||||
\(947\) | 47.1935i | 1.53358i | 0.641897 | + | 0.766791i | \(0.278148\pi\) | ||||
−0.641897 | + | 0.766791i | \(0.721852\pi\) | |||||||
\(948\) | 4.47214i | 0.145248i | ||||||||
\(949\) | 20.0000 | 0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.5279 | 0.633234 | ||||||||
\(952\) | − 17.8885i | − 0.579771i | ||||||||
\(953\) | − 47.7771i | − 1.54765i | −0.633398 | − | 0.773826i | \(-0.718341\pi\) | ||||
0.633398 | − | 0.773826i | \(-0.281659\pi\) | |||||||
\(954\) | −5.23607 | −0.169524 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.94427 | −0.159909 | ||||||||
\(957\) | − 23.4164i | − 0.756945i | ||||||||
\(958\) | − 28.9443i | − 0.935147i | ||||||||
\(959\) | 13.6656 | 0.441286 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | − 50.2492i | − 1.62010i | ||||||||
\(963\) | − 12.6525i | − 0.407720i | ||||||||
\(964\) | 12.4721 | 0.401700 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.47214 | −0.143889 | ||||||||
\(967\) | − 15.4164i | − 0.495758i | −0.968791 | − | 0.247879i | \(-0.920266\pi\) | ||||
0.968791 | − | 0.247879i | \(-0.0797336\pi\) | |||||||
\(968\) | 16.4164i | 0.527643i | ||||||||
\(969\) | 22.8328 | 0.733496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.1246 | −0.613738 | −0.306869 | − | 0.951752i | \(-0.599281\pi\) | ||||
−0.306869 | + | 0.951752i | \(0.599281\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | 75.7771i | 2.42930i | ||||||||
\(974\) | −9.88854 | −0.316849 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.763932 | 0.0244529 | ||||||||
\(977\) | − 1.16718i | − 0.0373415i | −0.999826 | − | 0.0186708i | \(-0.994057\pi\) | ||||
0.999826 | − | 0.0186708i | \(-0.00594343\pi\) | |||||||
\(978\) | − 2.47214i | − 0.0790502i | ||||||||
\(979\) | −54.8328 | −1.75246 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.76393 | 0.152101 | ||||||||
\(982\) | − 29.3050i | − 0.935159i | ||||||||
\(983\) | 0.583592i | 0.0186137i | 0.999957 | + | 0.00930685i | \(0.00296250\pi\) | ||||
−0.999957 | + | 0.00930685i | \(0.997037\pi\) | |||||||
\(984\) | 2.00000 | 0.0637577 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.8885 | 0.569687 | ||||||||
\(987\) | 17.8885i | 0.569399i | ||||||||
\(988\) | 25.5279i | 0.812150i | ||||||||
\(989\) | 4.76393 | 0.151484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4721 | −0.332658 | −0.166329 | − | 0.986070i | \(-0.553191\pi\) | ||||
−0.166329 | + | 0.986070i | \(0.553191\pi\) | |||||||
\(992\) | 2.47214i | 0.0784904i | ||||||||
\(993\) | − 10.4721i | − 0.332323i | ||||||||
\(994\) | 40.0000 | 1.26872 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.2361 | 0.419401 | ||||||||
\(997\) | − 5.05573i | − 0.160117i | −0.996790 | − | 0.0800583i | \(-0.974489\pi\) | ||||
0.996790 | − | 0.0800583i | \(-0.0255106\pi\) | |||||||
\(998\) | 0.583592i | 0.0184733i | ||||||||
\(999\) | −11.2361 | −0.355493 |
(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 | 3450.2.d.x.2899.2 | 4 | ||
5.2 | odd | 4 | 138.2.a.d.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 3450.2.a.be.1.2 | 2 | |||
5.4 | even | 2 | inner | 3450.2.d.x.2899.3 | 4 | ||
15.2 | even | 4 | 414.2.a.f.1.1 | 2 | |||
20.7 | even | 4 | 1104.2.a.j.1.2 | 2 | |||
35.27 | even | 4 | 6762.2.a.cb.1.1 | 2 | |||
40.27 | even | 4 | 4416.2.a.bl.1.1 | 2 | |||
40.37 | odd | 4 | 4416.2.a.bh.1.1 | 2 | |||
60.47 | odd | 4 | 3312.2.a.bc.1.1 | 2 | |||
115.22 | even | 4 | 3174.2.a.s.1.1 | 2 | |||
345.137 | odd | 4 | 9522.2.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.a.d.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
414.2.a.f.1.1 | 2 | 15.2 | even | 4 | |||
1104.2.a.j.1.2 | 2 | 20.7 | even | 4 | |||
3174.2.a.s.1.1 | 2 | 115.22 | even | 4 | |||
3312.2.a.bc.1.1 | 2 | 60.47 | odd | 4 | |||
3450.2.a.be.1.2 | 2 | 5.3 | odd | 4 | |||
3450.2.d.x.2899.2 | 4 | 1.1 | even | 1 | trivial | ||
3450.2.d.x.2899.3 | 4 | 5.4 | even | 2 | inner | ||
4416.2.a.bh.1.1 | 2 | 40.37 | odd | 4 | |||
4416.2.a.bl.1.1 | 2 | 40.27 | even | 4 | |||
6762.2.a.cb.1.1 | 2 | 35.27 | even | 4 | |||
9522.2.a.q.1.2 | 2 | 345.137 | odd | 4 |