Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.a.1249.1 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803i | 1.14412i | 0.820211 | + | 0.572061i | \(0.193856\pi\) | ||||
−0.820211 | + | 0.572061i | \(0.806144\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −0.618034 | −0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | − 2.00000i | − 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0.618034i | 0.178411i | ||||||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 3.23607 | 0.864876 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | − 4.23607i | − 1.02740i | −0.857971 | − | 0.513699i | \(-0.828275\pi\) | ||||
0.857971 | − | 0.513699i | \(-0.171725\pi\) | |||||||
\(18\) | − 1.61803i | − 0.381374i | ||||||||
\(19\) | 6.70820 | 1.53897 | 0.769484 | − | 0.638666i | \(-0.220514\pi\) | ||||
0.769484 | + | 0.638666i | \(0.220514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | − 4.85410i | − 1.03490i | ||||||||
\(23\) | − 5.38197i | − 1.12222i | −0.827742 | − | 0.561109i | \(-0.810375\pi\) | ||||
0.827742 | − | 0.561109i | \(-0.189625\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.61803 | −0.317323 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 1.23607i | 0.233595i | ||||||||
\(29\) | 3.61803 | 0.671852 | 0.335926 | − | 0.941888i | \(-0.390951\pi\) | ||||
0.335926 | + | 0.941888i | \(0.390951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.70820 | 1.56404 | 0.782020 | − | 0.623254i | \(-0.214190\pi\) | ||||
0.782020 | + | 0.623254i | \(0.214190\pi\) | |||||||
\(32\) | − 3.38197i | − 0.597853i | ||||||||
\(33\) | 3.00000i | 0.522233i | ||||||||
\(34\) | 6.85410 | 1.17547 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | − 2.00000i | − 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 10.8541i | 1.76077i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.38197 | −1.46522 | −0.732608 | − | 0.680650i | \(-0.761697\pi\) | ||||
−0.732608 | + | 0.680650i | \(0.761697\pi\) | |||||||
\(42\) | − 3.23607i | − 0.499336i | ||||||||
\(43\) | 7.38197i | 1.12574i | 0.826546 | + | 0.562870i | \(0.190303\pi\) | ||||
−0.826546 | + | 0.562870i | \(0.809697\pi\) | |||||||
\(44\) | 1.85410 | 0.279516 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.70820 | 1.28395 | ||||||||
\(47\) | − 4.76393i | − 0.694891i | −0.937700 | − | 0.347445i | \(-0.887049\pi\) | ||||
0.937700 | − | 0.347445i | \(-0.112951\pi\) | |||||||
\(48\) | 4.85410i | 0.700629i | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.23607 | −0.593168 | ||||||||
\(52\) | − 0.618034i | − 0.0857059i | ||||||||
\(53\) | − 11.2361i | − 1.54339i | −0.635991 | − | 0.771696i | \(-0.719409\pi\) | ||||
0.635991 | − | 0.771696i | \(-0.280591\pi\) | |||||||
\(54\) | −1.61803 | −0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.47214 | 0.597614 | ||||||||
\(57\) | − 6.70820i | − 0.888523i | ||||||||
\(58\) | 5.85410i | 0.768681i | ||||||||
\(59\) | −3.94427 | −0.513500 | −0.256750 | − | 0.966478i | \(-0.582652\pi\) | ||||
−0.256750 | + | 0.966478i | \(0.582652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.70820 | 1.11497 | 0.557486 | − | 0.830187i | \(-0.311766\pi\) | ||||
0.557486 | + | 0.830187i | \(0.311766\pi\) | |||||||
\(62\) | 14.0902i | 1.78945i | ||||||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | −4.23607 | −0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.85410 | −0.597499 | ||||||||
\(67\) | − 13.1803i | − 1.61023i | −0.593115 | − | 0.805117i | \(-0.702102\pi\) | ||||
0.593115 | − | 0.805117i | \(-0.297898\pi\) | |||||||
\(68\) | 2.61803i | 0.317483i | ||||||||
\(69\) | −5.38197 | −0.647913 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0902 | 1.19748 | 0.598741 | − | 0.800942i | \(-0.295668\pi\) | ||||
0.598741 | + | 0.800942i | \(0.295668\pi\) | |||||||
\(72\) | − 2.23607i | − 0.263523i | ||||||||
\(73\) | − 15.7082i | − 1.83851i | −0.393667 | − | 0.919253i | \(-0.628794\pi\) | ||||
0.393667 | − | 0.919253i | \(-0.371206\pi\) | |||||||
\(74\) | 3.23607 | 0.376185 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.14590 | −0.475567 | ||||||||
\(77\) | 6.00000i | 0.683763i | ||||||||
\(78\) | 1.61803i | 0.183206i | ||||||||
\(79\) | 9.14590 | 1.02899 | 0.514497 | − | 0.857492i | \(-0.327979\pi\) | ||||
0.514497 | + | 0.857492i | \(0.327979\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 15.1803i | − 1.67639i | ||||||||
\(83\) | − 9.00000i | − 0.987878i | −0.869496 | − | 0.493939i | \(-0.835557\pi\) | ||||
0.869496 | − | 0.493939i | \(-0.164443\pi\) | |||||||
\(84\) | 1.23607 | 0.134866 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.9443 | −1.28798 | ||||||||
\(87\) | − 3.61803i | − 0.387894i | ||||||||
\(88\) | − 6.70820i | − 0.715097i | ||||||||
\(89\) | 11.1803 | 1.18511 | 0.592557 | − | 0.805529i | \(-0.298119\pi\) | ||||
0.592557 | + | 0.805529i | \(0.298119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 3.32624i | 0.346784i | ||||||||
\(93\) | − 8.70820i | − 0.902999i | ||||||||
\(94\) | 7.70820 | 0.795041 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.38197 | −0.345170 | ||||||||
\(97\) | 3.85410i | 0.391325i | 0.980671 | + | 0.195662i | \(0.0626857\pi\) | ||||
−0.980671 | + | 0.195662i | \(0.937314\pi\) | |||||||
\(98\) | 4.85410i | 0.490338i | ||||||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.38197 | −0.933541 | −0.466770 | − | 0.884379i | \(-0.654583\pi\) | ||||
−0.466770 | + | 0.884379i | \(0.654583\pi\) | |||||||
\(102\) | − 6.85410i | − 0.678657i | ||||||||
\(103\) | 14.4164i | 1.42049i | 0.703954 | + | 0.710245i | \(0.251416\pi\) | ||||
−0.703954 | + | 0.710245i | \(0.748584\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.1803 | 1.76583 | ||||||||
\(107\) | − 1.14590i | − 0.110778i | −0.998465 | − | 0.0553891i | \(-0.982360\pi\) | ||||
0.998465 | − | 0.0553891i | \(-0.0176399\pi\) | |||||||
\(108\) | − 0.618034i | − 0.0594703i | ||||||||
\(109\) | 4.14590 | 0.397105 | 0.198553 | − | 0.980090i | \(-0.436376\pi\) | ||||
0.198553 | + | 0.980090i | \(0.436376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 9.70820i | 0.917339i | ||||||||
\(113\) | 3.76393i | 0.354081i | 0.984204 | + | 0.177040i | \(0.0566523\pi\) | ||||
−0.984204 | + | 0.177040i | \(0.943348\pi\) | |||||||
\(114\) | 10.8541 | 1.01658 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.23607 | −0.207614 | ||||||||
\(117\) | − 1.00000i | − 0.0924500i | ||||||||
\(118\) | − 6.38197i | − 0.587508i | ||||||||
\(119\) | −8.47214 | −0.776639 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 14.0902i | 1.27566i | ||||||||
\(123\) | 9.38197i | 0.845943i | ||||||||
\(124\) | −5.38197 | −0.483315 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.23607 | −0.288292 | ||||||||
\(127\) | 13.6525i | 1.21146i | 0.795670 | + | 0.605731i | \(0.207119\pi\) | ||||
−0.795670 | + | 0.605731i | \(0.792881\pi\) | |||||||
\(128\) | − 13.6180i | − 1.20368i | ||||||||
\(129\) | 7.38197 | 0.649946 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.1803 | −1.23894 | −0.619471 | − | 0.785020i | \(-0.712653\pi\) | ||||
−0.619471 | + | 0.785020i | \(0.712653\pi\) | |||||||
\(132\) | − 1.85410i | − 0.161379i | ||||||||
\(133\) | − 13.4164i | − 1.16335i | ||||||||
\(134\) | 21.3262 | 1.84231 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.47214 | 0.812229 | ||||||||
\(137\) | 0.437694i | 0.0373947i | 0.999825 | + | 0.0186974i | \(0.00595190\pi\) | ||||
−0.999825 | + | 0.0186974i | \(0.994048\pi\) | |||||||
\(138\) | − 8.70820i | − 0.741292i | ||||||||
\(139\) | −13.4164 | −1.13796 | −0.568982 | − | 0.822350i | \(-0.692663\pi\) | ||||
−0.568982 | + | 0.822350i | \(0.692663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.76393 | −0.401195 | ||||||||
\(142\) | 16.3262i | 1.37007i | ||||||||
\(143\) | − 3.00000i | − 0.250873i | ||||||||
\(144\) | 4.85410 | 0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 25.4164 | 2.10348 | ||||||||
\(147\) | − 3.00000i | − 0.247436i | ||||||||
\(148\) | 1.23607i | 0.101604i | ||||||||
\(149\) | 13.0902 | 1.07239 | 0.536194 | − | 0.844095i | \(-0.319861\pi\) | ||||
0.536194 | + | 0.844095i | \(0.319861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.61803 | −0.538568 | −0.269284 | − | 0.963061i | \(-0.586787\pi\) | ||||
−0.269284 | + | 0.963061i | \(0.586787\pi\) | |||||||
\(152\) | 15.0000i | 1.21666i | ||||||||
\(153\) | 4.23607i | 0.342466i | ||||||||
\(154\) | −9.70820 | −0.782309 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.618034 | −0.0494823 | ||||||||
\(157\) | − 2.85410i | − 0.227782i | −0.993493 | − | 0.113891i | \(-0.963669\pi\) | ||||
0.993493 | − | 0.113891i | \(-0.0363315\pi\) | |||||||
\(158\) | 14.7984i | 1.17730i | ||||||||
\(159\) | −11.2361 | −0.891078 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7639 | −0.848317 | ||||||||
\(162\) | 1.61803i | 0.127125i | ||||||||
\(163\) | − 18.2705i | − 1.43106i | −0.698584 | − | 0.715528i | \(-0.746186\pi\) | ||||
0.698584 | − | 0.715528i | \(-0.253814\pi\) | |||||||
\(164\) | 5.79837 | 0.452777 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5623 | 1.13025 | ||||||||
\(167\) | 17.7984i | 1.37728i | 0.725104 | + | 0.688640i | \(0.241792\pi\) | ||||
−0.725104 | + | 0.688640i | \(0.758208\pi\) | |||||||
\(168\) | − 4.47214i | − 0.345033i | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.70820 | −0.512989 | ||||||||
\(172\) | − 4.56231i | − 0.347873i | ||||||||
\(173\) | − 0.909830i | − 0.0691731i | −0.999402 | − | 0.0345865i | \(-0.988989\pi\) | ||||
0.999402 | − | 0.0345865i | \(-0.0110114\pi\) | |||||||
\(174\) | 5.85410 | 0.443798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.5623 | 1.09768 | ||||||||
\(177\) | 3.94427i | 0.296470i | ||||||||
\(178\) | 18.0902i | 1.35592i | ||||||||
\(179\) | 15.6525 | 1.16992 | 0.584960 | − | 0.811062i | \(-0.301110\pi\) | ||||
0.584960 | + | 0.811062i | \(0.301110\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.4721 | −0.927047 | −0.463523 | − | 0.886085i | \(-0.653415\pi\) | ||||
−0.463523 | + | 0.886085i | \(0.653415\pi\) | |||||||
\(182\) | 3.23607i | 0.239873i | ||||||||
\(183\) | − 8.70820i | − 0.643729i | ||||||||
\(184\) | 12.0344 | 0.887191 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.0902 | 1.03314 | ||||||||
\(187\) | 12.7082i | 0.929316i | ||||||||
\(188\) | 2.94427i | 0.214733i | ||||||||
\(189\) | 2.00000 | 0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3262 | 1.25368 | 0.626841 | − | 0.779147i | \(-0.284347\pi\) | ||||
0.626841 | + | 0.779147i | \(0.284347\pi\) | |||||||
\(192\) | 4.23607i | 0.305712i | ||||||||
\(193\) | 11.0000i | 0.791797i | 0.918294 | + | 0.395899i | \(0.129567\pi\) | ||||
−0.918294 | + | 0.395899i | \(0.870433\pi\) | |||||||
\(194\) | −6.23607 | −0.447724 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.85410 | −0.132436 | ||||||||
\(197\) | − 0.0901699i | − 0.00642434i | −0.999995 | − | 0.00321217i | \(-0.998978\pi\) | ||||
0.999995 | − | 0.00321217i | \(-0.00102247\pi\) | |||||||
\(198\) | 4.85410i | 0.344966i | ||||||||
\(199\) | −11.7082 | −0.829973 | −0.414986 | − | 0.909828i | \(-0.636214\pi\) | ||||
−0.414986 | + | 0.909828i | \(0.636214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.1803 | −0.929669 | ||||||||
\(202\) | − 15.1803i | − 1.06808i | ||||||||
\(203\) | − 7.23607i | − 0.507872i | ||||||||
\(204\) | 2.61803 | 0.183299 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −23.3262 | −1.62522 | ||||||||
\(207\) | 5.38197i | 0.374072i | ||||||||
\(208\) | − 4.85410i | − 0.336571i | ||||||||
\(209\) | −20.1246 | −1.39205 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.00000 | −0.206529 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(212\) | 6.94427i | 0.476935i | ||||||||
\(213\) | − 10.0902i | − 0.691367i | ||||||||
\(214\) | 1.85410 | 0.126744 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | − 17.4164i | − 1.18230i | ||||||||
\(218\) | 6.70820i | 0.454337i | ||||||||
\(219\) | −15.7082 | −1.06146 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.23607 | 0.284949 | ||||||||
\(222\) | − 3.23607i | − 0.217191i | ||||||||
\(223\) | 10.1459i | 0.679420i | 0.940530 | + | 0.339710i | \(0.110329\pi\) | ||||
−0.940530 | + | 0.339710i | \(0.889671\pi\) | |||||||
\(224\) | −6.76393 | −0.451934 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.09017 | −0.405112 | ||||||||
\(227\) | 5.76393i | 0.382566i | 0.981535 | + | 0.191283i | \(0.0612648\pi\) | ||||
−0.981535 | + | 0.191283i | \(0.938735\pi\) | |||||||
\(228\) | 4.14590i | 0.274569i | ||||||||
\(229\) | 16.1803 | 1.06923 | 0.534613 | − | 0.845097i | \(-0.320457\pi\) | ||||
0.534613 | + | 0.845097i | \(0.320457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | 0.394771 | ||||||||
\(232\) | 8.09017i | 0.531146i | ||||||||
\(233\) | − 10.1803i | − 0.666936i | −0.942761 | − | 0.333468i | \(-0.891781\pi\) | ||||
0.942761 | − | 0.333468i | \(-0.108219\pi\) | |||||||
\(234\) | 1.61803 | 0.105774 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.43769 | 0.158680 | ||||||||
\(237\) | − 9.14590i | − 0.594090i | ||||||||
\(238\) | − 13.7082i | − 0.888571i | ||||||||
\(239\) | −21.3820 | −1.38308 | −0.691542 | − | 0.722336i | \(-0.743068\pi\) | ||||
−0.691542 | + | 0.722336i | \(0.743068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.32624 | 0.471924 | 0.235962 | − | 0.971762i | \(-0.424176\pi\) | ||||
0.235962 | + | 0.971762i | \(0.424176\pi\) | |||||||
\(242\) | − 3.23607i | − 0.208022i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −5.38197 | −0.344545 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.1803 | −0.967863 | ||||||||
\(247\) | 6.70820i | 0.426833i | ||||||||
\(248\) | 19.4721i | 1.23648i | ||||||||
\(249\) | −9.00000 | −0.570352 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9787 | −1.19793 | −0.598963 | − | 0.800777i | \(-0.704420\pi\) | ||||
−0.598963 | + | 0.800777i | \(0.704420\pi\) | |||||||
\(252\) | − 1.23607i | − 0.0778650i | ||||||||
\(253\) | 16.1459i | 1.01508i | ||||||||
\(254\) | −22.0902 | −1.38606 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 31.2148i | 1.94712i | 0.228422 | + | 0.973562i | \(0.426644\pi\) | ||||
−0.228422 | + | 0.973562i | \(0.573356\pi\) | |||||||
\(258\) | 11.9443i | 0.743618i | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.61803 | −0.223951 | ||||||||
\(262\) | − 22.9443i | − 1.41750i | ||||||||
\(263\) | 12.5066i | 0.771189i | 0.922668 | + | 0.385594i | \(0.126004\pi\) | ||||
−0.922668 | + | 0.385594i | \(0.873996\pi\) | |||||||
\(264\) | −6.70820 | −0.412861 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.7082 | 1.33102 | ||||||||
\(267\) | − 11.1803i | − 0.684226i | ||||||||
\(268\) | 8.14590i | 0.497590i | ||||||||
\(269\) | 20.5279 | 1.25161 | 0.625803 | − | 0.779981i | \(-0.284771\pi\) | ||||
0.625803 | + | 0.779981i | \(0.284771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.4164 | −0.693497 | −0.346749 | − | 0.937958i | \(-0.612714\pi\) | ||||
−0.346749 | + | 0.937958i | \(0.612714\pi\) | |||||||
\(272\) | 20.5623i | 1.24677i | ||||||||
\(273\) | − 2.00000i | − 0.121046i | ||||||||
\(274\) | −0.708204 | −0.0427842 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.32624 | 0.200216 | ||||||||
\(277\) | − 13.0557i | − 0.784443i | −0.919871 | − | 0.392221i | \(-0.871707\pi\) | ||||
0.919871 | − | 0.392221i | \(-0.128293\pi\) | |||||||
\(278\) | − 21.7082i | − 1.30197i | ||||||||
\(279\) | −8.70820 | −0.521347 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1803 | −0.845928 | −0.422964 | − | 0.906146i | \(-0.639010\pi\) | ||||
−0.422964 | + | 0.906146i | \(0.639010\pi\) | |||||||
\(282\) | − 7.70820i | − 0.459017i | ||||||||
\(283\) | − 2.29180i | − 0.136233i | −0.997677 | − | 0.0681166i | \(-0.978301\pi\) | ||||
0.997677 | − | 0.0681166i | \(-0.0216990\pi\) | |||||||
\(284\) | −6.23607 | −0.370043 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.85410 | 0.287029 | ||||||||
\(287\) | 18.7639i | 1.10760i | ||||||||
\(288\) | 3.38197i | 0.199284i | ||||||||
\(289\) | −0.944272 | −0.0555454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.85410 | 0.225931 | ||||||||
\(292\) | 9.70820i | 0.568130i | ||||||||
\(293\) | 6.32624i | 0.369583i | 0.982778 | + | 0.184791i | \(0.0591609\pi\) | ||||
−0.982778 | + | 0.184791i | \(0.940839\pi\) | |||||||
\(294\) | 4.85410 | 0.283097 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.47214 | 0.259938 | ||||||||
\(297\) | − 3.00000i | − 0.174078i | ||||||||
\(298\) | 21.1803i | 1.22694i | ||||||||
\(299\) | 5.38197 | 0.311247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.7639 | 0.850979 | ||||||||
\(302\) | − 10.7082i | − 0.616188i | ||||||||
\(303\) | 9.38197i | 0.538980i | ||||||||
\(304\) | −32.5623 | −1.86758 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.85410 | −0.391823 | ||||||||
\(307\) | 8.85410i | 0.505330i | 0.967554 | + | 0.252665i | \(0.0813071\pi\) | ||||
−0.967554 | + | 0.252665i | \(0.918693\pi\) | |||||||
\(308\) | − 3.70820i | − 0.211295i | ||||||||
\(309\) | 14.4164 | 0.820121 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5279 | −0.767095 | −0.383547 | − | 0.923521i | \(-0.625298\pi\) | ||||
−0.383547 | + | 0.923521i | \(0.625298\pi\) | |||||||
\(312\) | 2.23607i | 0.126592i | ||||||||
\(313\) | − 2.29180i | − 0.129540i | −0.997900 | − | 0.0647700i | \(-0.979369\pi\) | ||||
0.997900 | − | 0.0647700i | \(-0.0206314\pi\) | |||||||
\(314\) | 4.61803 | 0.260611 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.65248 | −0.317977 | ||||||||
\(317\) | 20.5623i | 1.15489i | 0.816428 | + | 0.577447i | \(0.195951\pi\) | ||||
−0.816428 | + | 0.577447i | \(0.804049\pi\) | |||||||
\(318\) | − 18.1803i | − 1.01950i | ||||||||
\(319\) | −10.8541 | −0.607713 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.14590 | −0.0639578 | ||||||||
\(322\) | − 17.4164i | − 0.970578i | ||||||||
\(323\) | − 28.4164i | − 1.58113i | ||||||||
\(324\) | −0.618034 | −0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.5623 | 1.63730 | ||||||||
\(327\) | − 4.14590i | − 0.229269i | ||||||||
\(328\) | − 20.9787i | − 1.15836i | ||||||||
\(329\) | −9.52786 | −0.525288 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.6869 | −1.68671 | −0.843353 | − | 0.537360i | \(-0.819422\pi\) | ||||
−0.843353 | + | 0.537360i | \(0.819422\pi\) | |||||||
\(332\) | 5.56231i | 0.305271i | ||||||||
\(333\) | 2.00000i | 0.109599i | ||||||||
\(334\) | −28.7984 | −1.57578 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.70820 | 0.529626 | ||||||||
\(337\) | − 33.1803i | − 1.80745i | −0.428115 | − | 0.903724i | \(-0.640822\pi\) | ||||
0.428115 | − | 0.903724i | \(-0.359178\pi\) | |||||||
\(338\) | 19.4164i | 1.05611i | ||||||||
\(339\) | 3.76393 | 0.204429 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.1246 | −1.41473 | ||||||||
\(342\) | − 10.8541i | − 0.586923i | ||||||||
\(343\) | − 20.0000i | − 1.07990i | ||||||||
\(344\) | −16.5066 | −0.889975 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.47214 | 0.0791425 | ||||||||
\(347\) | 12.2705i | 0.658715i | 0.944205 | + | 0.329358i | \(0.106832\pi\) | ||||
−0.944205 | + | 0.329358i | \(0.893168\pi\) | |||||||
\(348\) | 2.23607i | 0.119866i | ||||||||
\(349\) | −7.23607 | −0.387338 | −0.193669 | − | 0.981067i | \(-0.562039\pi\) | ||||
−0.193669 | + | 0.981067i | \(0.562039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 10.1459i | 0.540778i | ||||||||
\(353\) | 12.3820i | 0.659026i | 0.944151 | + | 0.329513i | \(0.106884\pi\) | ||||
−0.944151 | + | 0.329513i | \(0.893116\pi\) | |||||||
\(354\) | −6.38197 | −0.339198 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.90983 | −0.366220 | ||||||||
\(357\) | 8.47214i | 0.448393i | ||||||||
\(358\) | 25.3262i | 1.33853i | ||||||||
\(359\) | −23.9443 | −1.26373 | −0.631865 | − | 0.775078i | \(-0.717710\pi\) | ||||
−0.631865 | + | 0.775078i | \(0.717710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0000 | 1.36842 | ||||||||
\(362\) | − 20.1803i | − 1.06066i | ||||||||
\(363\) | 2.00000i | 0.104973i | ||||||||
\(364\) | −1.23607 | −0.0647876 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.0902 | 0.736505 | ||||||||
\(367\) | − 12.5279i | − 0.653949i | −0.945033 | − | 0.326975i | \(-0.893971\pi\) | ||||
0.945033 | − | 0.326975i | \(-0.106029\pi\) | |||||||
\(368\) | 26.1246i | 1.36184i | ||||||||
\(369\) | 9.38197 | 0.488406 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.4721 | −1.16670 | ||||||||
\(372\) | 5.38197i | 0.279042i | ||||||||
\(373\) | − 17.4164i | − 0.901787i | −0.892578 | − | 0.450894i | \(-0.851105\pi\) | ||||
0.892578 | − | 0.450894i | \(-0.148895\pi\) | |||||||
\(374\) | −20.5623 | −1.06325 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6525 | 0.549359 | ||||||||
\(377\) | 3.61803i | 0.186338i | ||||||||
\(378\) | 3.23607i | 0.166445i | ||||||||
\(379\) | 13.6180 | 0.699511 | 0.349756 | − | 0.936841i | \(-0.386265\pi\) | ||||
0.349756 | + | 0.936841i | \(0.386265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6525 | 0.699438 | ||||||||
\(382\) | 28.0344i | 1.43437i | ||||||||
\(383\) | − 5.05573i | − 0.258336i | −0.991623 | − | 0.129168i | \(-0.958769\pi\) | ||||
0.991623 | − | 0.129168i | \(-0.0412306\pi\) | |||||||
\(384\) | −13.6180 | −0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.7984 | −0.905913 | ||||||||
\(387\) | − 7.38197i | − 0.375246i | ||||||||
\(388\) | − 2.38197i | − 0.120926i | ||||||||
\(389\) | −0.652476 | −0.0330818 | −0.0165409 | − | 0.999863i | \(-0.505265\pi\) | ||||
−0.0165409 | + | 0.999863i | \(0.505265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.7984 | −1.15296 | ||||||||
\(392\) | 6.70820i | 0.338815i | ||||||||
\(393\) | 14.1803i | 0.715304i | ||||||||
\(394\) | 0.145898 | 0.00735024 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.85410 | −0.0931721 | ||||||||
\(397\) | − 2.52786i | − 0.126870i | −0.997986 | − | 0.0634349i | \(-0.979794\pi\) | ||||
0.997986 | − | 0.0634349i | \(-0.0202055\pi\) | |||||||
\(398\) | − 18.9443i | − 0.949591i | ||||||||
\(399\) | −13.4164 | −0.671660 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.2705 | 1.81126 | 0.905631 | − | 0.424066i | \(-0.139397\pi\) | ||||
0.905631 | + | 0.424066i | \(0.139397\pi\) | |||||||
\(402\) | − 21.3262i | − 1.06366i | ||||||||
\(403\) | 8.70820i | 0.433787i | ||||||||
\(404\) | 5.79837 | 0.288480 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.7082 | 0.581068 | ||||||||
\(407\) | 6.00000i | 0.297409i | ||||||||
\(408\) | − 9.47214i | − 0.468941i | ||||||||
\(409\) | 5.12461 | 0.253396 | 0.126698 | − | 0.991941i | \(-0.459562\pi\) | ||||
0.126698 | + | 0.991941i | \(0.459562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.437694 | 0.0215899 | ||||||||
\(412\) | − 8.90983i | − 0.438956i | ||||||||
\(413\) | 7.88854i | 0.388170i | ||||||||
\(414\) | −8.70820 | −0.427985 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.38197 | 0.165815 | ||||||||
\(417\) | 13.4164i | 0.657004i | ||||||||
\(418\) | − 32.5623i | − 1.59267i | ||||||||
\(419\) | −0.326238 | −0.0159378 | −0.00796888 | − | 0.999968i | \(-0.502537\pi\) | ||||
−0.00796888 | + | 0.999968i | \(0.502537\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.3607 | −1.47969 | −0.739844 | − | 0.672778i | \(-0.765101\pi\) | ||||
−0.739844 | + | 0.672778i | \(0.765101\pi\) | |||||||
\(422\) | − 4.85410i | − 0.236294i | ||||||||
\(423\) | 4.76393i | 0.231630i | ||||||||
\(424\) | 25.1246 | 1.22016 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.3262 | 0.791009 | ||||||||
\(427\) | − 17.4164i | − 0.842839i | ||||||||
\(428\) | 0.708204i | 0.0342323i | ||||||||
\(429\) | −3.00000 | −0.144841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.7639 | 1.43368 | 0.716839 | − | 0.697239i | \(-0.245588\pi\) | ||||
0.716839 | + | 0.697239i | \(0.245588\pi\) | |||||||
\(432\) | − 4.85410i | − 0.233543i | ||||||||
\(433\) | − 3.47214i | − 0.166860i | −0.996514 | − | 0.0834301i | \(-0.973412\pi\) | ||||
0.996514 | − | 0.0834301i | \(-0.0265875\pi\) | |||||||
\(434\) | 28.1803 | 1.35270 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.56231 | −0.122712 | ||||||||
\(437\) | − 36.1033i | − 1.72706i | ||||||||
\(438\) | − 25.4164i | − 1.21444i | ||||||||
\(439\) | 32.0344 | 1.52892 | 0.764460 | − | 0.644671i | \(-0.223006\pi\) | ||||
0.764460 | + | 0.644671i | \(0.223006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 6.85410i | 0.326016i | ||||||||
\(443\) | 19.4164i | 0.922501i | 0.887270 | + | 0.461251i | \(0.152599\pi\) | ||||
−0.887270 | + | 0.461251i | \(0.847401\pi\) | |||||||
\(444\) | 1.23607 | 0.0586612 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.4164 | −0.777339 | ||||||||
\(447\) | − 13.0902i | − 0.619144i | ||||||||
\(448\) | 8.47214i | 0.400271i | ||||||||
\(449\) | −16.5066 | −0.778994 | −0.389497 | − | 0.921028i | \(-0.627351\pi\) | ||||
−0.389497 | + | 0.921028i | \(0.627351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.1459 | 1.32534 | ||||||||
\(452\) | − 2.32624i | − 0.109417i | ||||||||
\(453\) | 6.61803i | 0.310942i | ||||||||
\(454\) | −9.32624 | −0.437702 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.0000 | 0.702439 | ||||||||
\(457\) | − 9.88854i | − 0.462567i | −0.972886 | − | 0.231283i | \(-0.925708\pi\) | ||||
0.972886 | − | 0.231283i | \(-0.0742924\pi\) | |||||||
\(458\) | 26.1803i | 1.22333i | ||||||||
\(459\) | 4.23607 | 0.197723 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.1803 | −0.893317 | −0.446659 | − | 0.894704i | \(-0.647386\pi\) | ||||
−0.446659 | + | 0.894704i | \(0.647386\pi\) | |||||||
\(462\) | 9.70820i | 0.451667i | ||||||||
\(463\) | 33.6869i | 1.56556i | 0.622296 | + | 0.782782i | \(0.286200\pi\) | ||||
−0.622296 | + | 0.782782i | \(0.713800\pi\) | |||||||
\(464\) | −17.5623 | −0.815310 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.4721 | 0.763057 | ||||||||
\(467\) | − 10.4164i | − 0.482014i | −0.970523 | − | 0.241007i | \(-0.922522\pi\) | ||||
0.970523 | − | 0.241007i | \(-0.0774777\pi\) | |||||||
\(468\) | 0.618034i | 0.0285686i | ||||||||
\(469\) | −26.3607 | −1.21722 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.85410 | −0.131510 | ||||||||
\(472\) | − 8.81966i | − 0.405958i | ||||||||
\(473\) | − 22.1459i | − 1.01827i | ||||||||
\(474\) | 14.7984 | 0.679712 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.23607 | 0.239995 | ||||||||
\(477\) | 11.2361i | 0.514464i | ||||||||
\(478\) | − 34.5967i | − 1.58242i | ||||||||
\(479\) | −4.79837 | −0.219243 | −0.109622 | − | 0.993973i | \(-0.534964\pi\) | ||||
−0.109622 | + | 0.993973i | \(0.534964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 11.8541i | 0.539940i | ||||||||
\(483\) | 10.7639i | 0.489776i | ||||||||
\(484\) | 1.23607 | 0.0561849 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.61803 | 0.0733955 | ||||||||
\(487\) | 16.6180i | 0.753035i | 0.926410 | + | 0.376518i | \(0.122879\pi\) | ||||
−0.926410 | + | 0.376518i | \(0.877121\pi\) | |||||||
\(488\) | 19.4721i | 0.881462i | ||||||||
\(489\) | −18.2705 | −0.826221 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.3262 | 1.00757 | 0.503785 | − | 0.863829i | \(-0.331941\pi\) | ||||
0.503785 | + | 0.863829i | \(0.331941\pi\) | |||||||
\(492\) | − 5.79837i | − 0.261411i | ||||||||
\(493\) | − 15.3262i | − 0.690259i | ||||||||
\(494\) | −10.8541 | −0.488349 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −42.2705 | −1.89800 | ||||||||
\(497\) | − 20.1803i | − 0.905212i | ||||||||
\(498\) | − 14.5623i | − 0.652553i | ||||||||
\(499\) | 15.0000 | 0.671492 | 0.335746 | − | 0.941953i | \(-0.391012\pi\) | ||||
0.335746 | + | 0.941953i | \(0.391012\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7984 | 0.795173 | ||||||||
\(502\) | − 30.7082i | − 1.37057i | ||||||||
\(503\) | 3.96556i | 0.176815i | 0.996084 | + | 0.0884077i | \(0.0281778\pi\) | ||||
−0.996084 | + | 0.0884077i | \(0.971822\pi\) | |||||||
\(504\) | −4.47214 | −0.199205 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −26.1246 | −1.16138 | ||||||||
\(507\) | − 12.0000i | − 0.532939i | ||||||||
\(508\) | − 8.43769i | − 0.374362i | ||||||||
\(509\) | −32.8885 | −1.45776 | −0.728880 | − | 0.684642i | \(-0.759959\pi\) | ||||
−0.728880 | + | 0.684642i | \(0.759959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.4164 | −1.38978 | ||||||||
\(512\) | − 5.29180i | − 0.233867i | ||||||||
\(513\) | 6.70820i | 0.296174i | ||||||||
\(514\) | −50.5066 | −2.22775 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.56231 | −0.200844 | ||||||||
\(517\) | 14.2918i | 0.628552i | ||||||||
\(518\) | − 6.47214i | − 0.284369i | ||||||||
\(519\) | −0.909830 | −0.0399371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.0902 | 1.75638 | 0.878191 | − | 0.478310i | \(-0.158750\pi\) | ||||
0.878191 | + | 0.478310i | \(0.158750\pi\) | |||||||
\(522\) | − 5.85410i | − 0.256227i | ||||||||
\(523\) | − 1.56231i | − 0.0683149i | −0.999416 | − | 0.0341574i | \(-0.989125\pi\) | ||||
0.999416 | − | 0.0341574i | \(-0.0108748\pi\) | |||||||
\(524\) | 8.76393 | 0.382854 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.2361 | −0.882334 | ||||||||
\(527\) | − 36.8885i | − 1.60689i | ||||||||
\(528\) | − 14.5623i | − 0.633743i | ||||||||
\(529\) | −5.96556 | −0.259372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.94427 | 0.171167 | ||||||||
\(532\) | 8.29180i | 0.359495i | ||||||||
\(533\) | − 9.38197i | − 0.406378i | ||||||||
\(534\) | 18.0902 | 0.782838 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 29.4721 | 1.27300 | ||||||||
\(537\) | − 15.6525i | − 0.675454i | ||||||||
\(538\) | 33.2148i | 1.43199i | ||||||||
\(539\) | −9.00000 | −0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.2918 | −1.13037 | −0.565186 | − | 0.824963i | \(-0.691196\pi\) | ||||
−0.565186 | + | 0.824963i | \(0.691196\pi\) | |||||||
\(542\) | − 18.4721i | − 0.793446i | ||||||||
\(543\) | 12.4721i | 0.535231i | ||||||||
\(544\) | −14.3262 | −0.614232 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.23607 | 0.138491 | ||||||||
\(547\) | 24.7082i | 1.05645i | 0.849106 | + | 0.528223i | \(0.177142\pi\) | ||||
−0.849106 | + | 0.528223i | \(0.822858\pi\) | |||||||
\(548\) | − 0.270510i | − 0.0115556i | ||||||||
\(549\) | −8.70820 | −0.371657 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.2705 | 1.03396 | ||||||||
\(552\) | − 12.0344i | − 0.512220i | ||||||||
\(553\) | − 18.2918i | − 0.777846i | ||||||||
\(554\) | 21.1246 | 0.897499 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.29180 | 0.351650 | ||||||||
\(557\) | − 37.6525i | − 1.59539i | −0.603063 | − | 0.797693i | \(-0.706053\pi\) | ||||
0.603063 | − | 0.797693i | \(-0.293947\pi\) | |||||||
\(558\) | − 14.0902i | − 0.596484i | ||||||||
\(559\) | −7.38197 | −0.312224 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.7082 | 0.536541 | ||||||||
\(562\) | − 22.9443i | − 0.967846i | ||||||||
\(563\) | − 9.00000i | − 0.379305i | −0.981851 | − | 0.189652i | \(-0.939264\pi\) | ||||
0.981851 | − | 0.189652i | \(-0.0607361\pi\) | |||||||
\(564\) | 2.94427 | 0.123976 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.70820 | 0.155867 | ||||||||
\(567\) | − 2.00000i | − 0.0839921i | ||||||||
\(568\) | 22.5623i | 0.946693i | ||||||||
\(569\) | 10.8541 | 0.455028 | 0.227514 | − | 0.973775i | \(-0.426940\pi\) | ||||
0.227514 | + | 0.973775i | \(0.426940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.1246 | −1.59547 | −0.797733 | − | 0.603011i | \(-0.793967\pi\) | ||||
−0.797733 | + | 0.603011i | \(0.793967\pi\) | |||||||
\(572\) | 1.85410i | 0.0775239i | ||||||||
\(573\) | − 17.3262i | − 0.723814i | ||||||||
\(574\) | −30.3607 | −1.26723 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | 3.72949i | 0.155261i | 0.996982 | + | 0.0776304i | \(0.0247354\pi\) | ||||
−0.996982 | + | 0.0776304i | \(0.975265\pi\) | |||||||
\(578\) | − 1.52786i | − 0.0635508i | ||||||||
\(579\) | 11.0000 | 0.457144 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | −0.746766 | ||||||||
\(582\) | 6.23607i | 0.258493i | ||||||||
\(583\) | 33.7082i | 1.39605i | ||||||||
\(584\) | 35.1246 | 1.45347 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.2361 | −0.422848 | ||||||||
\(587\) | 39.3050i | 1.62229i | 0.584846 | + | 0.811144i | \(0.301155\pi\) | ||||
−0.584846 | + | 0.811144i | \(0.698845\pi\) | |||||||
\(588\) | 1.85410i | 0.0764619i | ||||||||
\(589\) | 58.4164 | 2.40701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0901699 | −0.00370910 | ||||||||
\(592\) | 9.70820i | 0.399005i | ||||||||
\(593\) | − 17.6180i | − 0.723486i | −0.932278 | − | 0.361743i | \(-0.882182\pi\) | ||||
0.932278 | − | 0.361743i | \(-0.117818\pi\) | |||||||
\(594\) | 4.85410 | 0.199166 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.09017 | −0.331386 | ||||||||
\(597\) | 11.7082i | 0.479185i | ||||||||
\(598\) | 8.70820i | 0.356105i | ||||||||
\(599\) | −39.2705 | −1.60455 | −0.802275 | − | 0.596955i | \(-0.796377\pi\) | ||||
−0.802275 | + | 0.596955i | \(0.796377\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.7082 | −1.00787 | −0.503934 | − | 0.863742i | \(-0.668115\pi\) | ||||
−0.503934 | + | 0.863742i | \(0.668115\pi\) | |||||||
\(602\) | 23.8885i | 0.973624i | ||||||||
\(603\) | 13.1803i | 0.536745i | ||||||||
\(604\) | 4.09017 | 0.166427 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.1803 | −0.616659 | ||||||||
\(607\) | − 22.8541i | − 0.927619i | −0.885935 | − | 0.463810i | \(-0.846482\pi\) | ||||
0.885935 | − | 0.463810i | \(-0.153518\pi\) | |||||||
\(608\) | − 22.6869i | − 0.920076i | ||||||||
\(609\) | −7.23607 | −0.293220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.76393 | 0.192728 | ||||||||
\(612\) | − 2.61803i | − 0.105828i | ||||||||
\(613\) | 5.87539i | 0.237305i | 0.992936 | + | 0.118652i | \(0.0378574\pi\) | ||||
−0.992936 | + | 0.118652i | \(0.962143\pi\) | |||||||
\(614\) | −14.3262 | −0.578160 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.4164 | −0.540562 | ||||||||
\(617\) | 25.2361i | 1.01597i | 0.861367 | + | 0.507983i | \(0.169609\pi\) | ||||
−0.861367 | + | 0.507983i | \(0.830391\pi\) | |||||||
\(618\) | 23.3262i | 0.938319i | ||||||||
\(619\) | −34.2705 | −1.37745 | −0.688724 | − | 0.725024i | \(-0.741829\pi\) | ||||
−0.688724 | + | 0.725024i | \(0.741829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.38197 | 0.215971 | ||||||||
\(622\) | − 21.8885i | − 0.877651i | ||||||||
\(623\) | − 22.3607i | − 0.895862i | ||||||||
\(624\) | −4.85410 | −0.194320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.70820 | 0.148210 | ||||||||
\(627\) | 20.1246i | 0.803700i | ||||||||
\(628\) | 1.76393i | 0.0703886i | ||||||||
\(629\) | −8.47214 | −0.337806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7639 | −0.428505 | −0.214253 | − | 0.976778i | \(-0.568732\pi\) | ||||
−0.214253 | + | 0.976778i | \(0.568732\pi\) | |||||||
\(632\) | 20.4508i | 0.813491i | ||||||||
\(633\) | 3.00000i | 0.119239i | ||||||||
\(634\) | −33.2705 | −1.32134 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.94427 | 0.275358 | ||||||||
\(637\) | 3.00000i | 0.118864i | ||||||||
\(638\) | − 17.5623i | − 0.695298i | ||||||||
\(639\) | −10.0902 | −0.399161 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3262 | −0.921331 | −0.460666 | − | 0.887574i | \(-0.652389\pi\) | ||||
−0.460666 | + | 0.887574i | \(0.652389\pi\) | |||||||
\(642\) | − 1.85410i | − 0.0731756i | ||||||||
\(643\) | − 5.90983i | − 0.233061i | −0.993187 | − | 0.116530i | \(-0.962823\pi\) | ||||
0.993187 | − | 0.116530i | \(-0.0371773\pi\) | |||||||
\(644\) | 6.65248 | 0.262144 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 45.9787 | 1.80901 | ||||||||
\(647\) | − 19.0344i | − 0.748321i | −0.927364 | − | 0.374161i | \(-0.877931\pi\) | ||||
0.927364 | − | 0.374161i | \(-0.122069\pi\) | |||||||
\(648\) | 2.23607i | 0.0878410i | ||||||||
\(649\) | 11.8328 | 0.464479 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4164 | −0.682603 | ||||||||
\(652\) | 11.2918i | 0.442221i | ||||||||
\(653\) | − 29.6525i | − 1.16039i | −0.814477 | − | 0.580196i | \(-0.802976\pi\) | ||||
0.814477 | − | 0.580196i | \(-0.197024\pi\) | |||||||
\(654\) | 6.70820 | 0.262312 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 45.5410 | 1.77808 | ||||||||
\(657\) | 15.7082i | 0.612835i | ||||||||
\(658\) | − 15.4164i | − 0.600994i | ||||||||
\(659\) | 2.23607 | 0.0871048 | 0.0435524 | − | 0.999051i | \(-0.486132\pi\) | ||||
0.0435524 | + | 0.999051i | \(0.486132\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.88854 | 0.190142 | 0.0950712 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950712 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(662\) | − 49.6525i | − 1.92980i | ||||||||
\(663\) | − 4.23607i | − 0.164515i | ||||||||
\(664\) | 20.1246 | 0.780986 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.23607 | −0.125395 | ||||||||
\(667\) | − 19.4721i | − 0.753964i | ||||||||
\(668\) | − 11.0000i | − 0.425603i | ||||||||
\(669\) | 10.1459 | 0.392263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.1246 | −1.00853 | ||||||||
\(672\) | 6.76393i | 0.260924i | ||||||||
\(673\) | 46.7771i | 1.80312i | 0.432650 | + | 0.901562i | \(0.357579\pi\) | ||||
−0.432650 | + | 0.901562i | \(0.642421\pi\) | |||||||
\(674\) | 53.6869 | 2.06794 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.41641 | −0.285246 | ||||||||
\(677\) | − 44.8885i | − 1.72521i | −0.505881 | − | 0.862603i | \(-0.668832\pi\) | ||||
0.505881 | − | 0.862603i | \(-0.331168\pi\) | |||||||
\(678\) | 6.09017i | 0.233892i | ||||||||
\(679\) | 7.70820 | 0.295814 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.76393 | 0.220874 | ||||||||
\(682\) | − 42.2705i | − 1.61862i | ||||||||
\(683\) | 0.596748i | 0.0228339i | 0.999935 | + | 0.0114170i | \(0.00363421\pi\) | ||||
−0.999935 | + | 0.0114170i | \(0.996366\pi\) | |||||||
\(684\) | 4.14590 | 0.158522 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32.3607 | 1.23554 | ||||||||
\(687\) | − 16.1803i | − 0.617318i | ||||||||
\(688\) | − 35.8328i | − 1.36611i | ||||||||
\(689\) | 11.2361 | 0.428060 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0902 | 0.574057 | 0.287029 | − | 0.957922i | \(-0.407333\pi\) | ||||
0.287029 | + | 0.957922i | \(0.407333\pi\) | |||||||
\(692\) | 0.562306i | 0.0213757i | ||||||||
\(693\) | − 6.00000i | − 0.227921i | ||||||||
\(694\) | −19.8541 | −0.753651 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.09017 | 0.306657 | ||||||||
\(697\) | 39.7426i | 1.50536i | ||||||||
\(698\) | − 11.7082i | − 0.443162i | ||||||||
\(699\) | −10.1803 | −0.385056 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.6525 | −1.83758 | −0.918789 | − | 0.394748i | \(-0.870832\pi\) | ||||
−0.918789 | + | 0.394748i | \(0.870832\pi\) | |||||||
\(702\) | − 1.61803i | − 0.0610688i | ||||||||
\(703\) | − 13.4164i | − 0.506009i | ||||||||
\(704\) | 12.7082 | 0.478958 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.0344 | −0.754006 | ||||||||
\(707\) | 18.7639i | 0.705690i | ||||||||
\(708\) | − 2.43769i | − 0.0916142i | ||||||||
\(709\) | 5.20163 | 0.195351 | 0.0976756 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976756 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.14590 | −0.342998 | ||||||||
\(712\) | 25.0000i | 0.936915i | ||||||||
\(713\) | − 46.8673i | − 1.75519i | ||||||||
\(714\) | −13.7082 | −0.513017 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.67376 | −0.361525 | ||||||||
\(717\) | 21.3820i | 0.798524i | ||||||||
\(718\) | − 38.7426i | − 1.44586i | ||||||||
\(719\) | 35.1246 | 1.30993 | 0.654963 | − | 0.755661i | \(-0.272684\pi\) | ||||
0.654963 | + | 0.755661i | \(0.272684\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.8328 | 1.07379 | ||||||||
\(722\) | 42.0689i | 1.56564i | ||||||||
\(723\) | − 7.32624i | − 0.272466i | ||||||||
\(724\) | 7.70820 | 0.286473 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.23607 | −0.120102 | ||||||||
\(727\) | − 14.4377i | − 0.535464i | −0.963493 | − | 0.267732i | \(-0.913726\pi\) | ||||
0.963493 | − | 0.267732i | \(-0.0862743\pi\) | |||||||
\(728\) | 4.47214i | 0.165748i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.2705 | 1.15658 | ||||||||
\(732\) | 5.38197i | 0.198923i | ||||||||
\(733\) | 10.1459i | 0.374747i | 0.982289 | + | 0.187374i | \(0.0599975\pi\) | ||||
−0.982289 | + | 0.187374i | \(0.940002\pi\) | |||||||
\(734\) | 20.2705 | 0.748198 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.2016 | −0.670921 | ||||||||
\(737\) | 39.5410i | 1.45651i | ||||||||
\(738\) | 15.1803i | 0.558796i | ||||||||
\(739\) | 1.70820 | 0.0628373 | 0.0314186 | − | 0.999506i | \(-0.489997\pi\) | ||||
0.0314186 | + | 0.999506i | \(0.489997\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.70820 | 0.246432 | ||||||||
\(742\) | − 36.3607i | − 1.33484i | ||||||||
\(743\) | 16.5279i | 0.606349i | 0.952935 | + | 0.303174i | \(0.0980464\pi\) | ||||
−0.952935 | + | 0.303174i | \(0.901954\pi\) | |||||||
\(744\) | 19.4721 | 0.713883 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 28.1803 | 1.03176 | ||||||||
\(747\) | 9.00000i | 0.329293i | ||||||||
\(748\) | − 7.85410i | − 0.287174i | ||||||||
\(749\) | −2.29180 | −0.0837404 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2918 | 0.558006 | 0.279003 | − | 0.960290i | \(-0.409996\pi\) | ||||
0.279003 | + | 0.960290i | \(0.409996\pi\) | |||||||
\(752\) | 23.1246i | 0.843268i | ||||||||
\(753\) | 18.9787i | 0.691623i | ||||||||
\(754\) | −5.85410 | −0.213194 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.23607 | −0.0449554 | ||||||||
\(757\) | 32.2705i | 1.17289i | 0.809988 | + | 0.586446i | \(0.199473\pi\) | ||||
−0.809988 | + | 0.586446i | \(0.800527\pi\) | |||||||
\(758\) | 22.0344i | 0.800327i | ||||||||
\(759\) | 16.1459 | 0.586059 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.18034 | 0.115287 | 0.0576436 | − | 0.998337i | \(-0.481641\pi\) | ||||
0.0576436 | + | 0.998337i | \(0.481641\pi\) | |||||||
\(762\) | 22.0902i | 0.800242i | ||||||||
\(763\) | − 8.29180i | − 0.300183i | ||||||||
\(764\) | −10.7082 | −0.387409 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.18034 | 0.295568 | ||||||||
\(767\) | − 3.94427i | − 0.142419i | ||||||||
\(768\) | − 13.5623i | − 0.489388i | ||||||||
\(769\) | 36.3050 | 1.30919 | 0.654595 | − | 0.755980i | \(-0.272839\pi\) | ||||
0.654595 | + | 0.755980i | \(0.272839\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.2148 | 1.12417 | ||||||||
\(772\) | − 6.79837i | − 0.244679i | ||||||||
\(773\) | 41.7771i | 1.50262i | 0.659951 | + | 0.751309i | \(0.270577\pi\) | ||||
−0.659951 | + | 0.751309i | \(0.729423\pi\) | |||||||
\(774\) | 11.9443 | 0.429328 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.61803 | −0.309369 | ||||||||
\(777\) | 4.00000i | 0.143499i | ||||||||
\(778\) | − 1.05573i | − 0.0378497i | ||||||||
\(779\) | −62.9361 | −2.25492 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.2705 | −1.08316 | ||||||||
\(782\) | − 36.8885i | − 1.31913i | ||||||||
\(783\) | 3.61803i | 0.129298i | ||||||||
\(784\) | −14.5623 | −0.520082 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −22.9443 | −0.818395 | ||||||||
\(787\) | 17.1459i | 0.611185i | 0.952162 | + | 0.305593i | \(0.0988546\pi\) | ||||
−0.952162 | + | 0.305593i | \(0.901145\pi\) | |||||||
\(788\) | 0.0557281i | 0.00198523i | ||||||||
\(789\) | 12.5066 | 0.445246 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.52786 | 0.267660 | ||||||||
\(792\) | 6.70820i | 0.238366i | ||||||||
\(793\) | 8.70820i | 0.309237i | ||||||||
\(794\) | 4.09017 | 0.145155 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.23607 | 0.256476 | ||||||||
\(797\) | − 30.0132i | − 1.06312i | −0.847020 | − | 0.531560i | \(-0.821606\pi\) | ||||
0.847020 | − | 0.531560i | \(-0.178394\pi\) | |||||||
\(798\) | − 21.7082i | − 0.768462i | ||||||||
\(799\) | −20.1803 | −0.713929 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1803 | −0.395038 | ||||||||
\(802\) | 58.6869i | 2.07231i | ||||||||
\(803\) | 47.1246i | 1.66299i | ||||||||
\(804\) | 8.14590 | 0.287284 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.0902 | −0.496305 | ||||||||
\(807\) | − 20.5279i | − 0.722615i | ||||||||
\(808\) | − 20.9787i | − 0.738029i | ||||||||
\(809\) | 39.9230 | 1.40362 | 0.701809 | − | 0.712365i | \(-0.252376\pi\) | ||||
0.701809 | + | 0.712365i | \(0.252376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.7771 | −1.18607 | −0.593037 | − | 0.805175i | \(-0.702071\pi\) | ||||
−0.593037 | + | 0.805175i | \(0.702071\pi\) | |||||||
\(812\) | 4.47214i | 0.156941i | ||||||||
\(813\) | 11.4164i | 0.400391i | ||||||||
\(814\) | −9.70820 | −0.340272 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.5623 | 0.719825 | ||||||||
\(817\) | 49.5197i | 1.73248i | ||||||||
\(818\) | 8.29180i | 0.289916i | ||||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.94427 | 0.207457 | 0.103728 | − | 0.994606i | \(-0.466923\pi\) | ||||
0.103728 | + | 0.994606i | \(0.466923\pi\) | |||||||
\(822\) | 0.708204i | 0.0247014i | ||||||||
\(823\) | 28.5623i | 0.995619i | 0.867286 | + | 0.497810i | \(0.165862\pi\) | ||||
−0.867286 | + | 0.497810i | \(0.834138\pi\) | |||||||
\(824\) | −32.2361 | −1.12300 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.7639 | −0.444114 | ||||||||
\(827\) | 48.9787i | 1.70316i | 0.524227 | + | 0.851578i | \(0.324354\pi\) | ||||
−0.524227 | + | 0.851578i | \(0.675646\pi\) | |||||||
\(828\) | − 3.32624i | − 0.115595i | ||||||||
\(829\) | 50.1246 | 1.74090 | 0.870450 | − | 0.492257i | \(-0.163828\pi\) | ||||
0.870450 | + | 0.492257i | \(0.163828\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0557 | −0.452898 | ||||||||
\(832\) | − 4.23607i | − 0.146859i | ||||||||
\(833\) | − 12.7082i | − 0.440313i | ||||||||
\(834\) | −21.7082 | −0.751694 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.4377 | 0.430167 | ||||||||
\(837\) | 8.70820i | 0.301000i | ||||||||
\(838\) | − 0.527864i | − 0.0182348i | ||||||||
\(839\) | 3.21478 | 0.110987 | 0.0554933 | − | 0.998459i | \(-0.482327\pi\) | ||||
0.0554933 | + | 0.998459i | \(0.482327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9098 | −0.548615 | ||||||||
\(842\) | − 49.1246i | − 1.69295i | ||||||||
\(843\) | 14.1803i | 0.488397i | ||||||||
\(844\) | 1.85410 | 0.0638208 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.70820 | −0.265014 | ||||||||
\(847\) | 4.00000i | 0.137442i | ||||||||
\(848\) | 54.5410i | 1.87295i | ||||||||
\(849\) | −2.29180 | −0.0786542 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7639 | −0.368983 | ||||||||
\(852\) | 6.23607i | 0.213644i | ||||||||
\(853\) | 20.3951i | 0.698316i | 0.937064 | + | 0.349158i | \(0.113532\pi\) | ||||
−0.937064 | + | 0.349158i | \(0.886468\pi\) | |||||||
\(854\) | 28.1803 | 0.964311 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.56231 | 0.0875778 | ||||||||
\(857\) | 9.05573i | 0.309338i | 0.987966 | + | 0.154669i | \(0.0494311\pi\) | ||||
−0.987966 | + | 0.154669i | \(0.950569\pi\) | |||||||
\(858\) | − 4.85410i | − 0.165716i | ||||||||
\(859\) | −15.1246 | −0.516045 | −0.258023 | − | 0.966139i | \(-0.583071\pi\) | ||||
−0.258023 | + | 0.966139i | \(0.583071\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.7639 | 0.639473 | ||||||||
\(862\) | 48.1591i | 1.64030i | ||||||||
\(863\) | − 13.0689i | − 0.444870i | −0.974948 | − | 0.222435i | \(-0.928599\pi\) | ||||
0.974948 | − | 0.222435i | \(-0.0714005\pi\) | |||||||
\(864\) | 3.38197 | 0.115057 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.61803 | 0.190909 | ||||||||
\(867\) | 0.944272i | 0.0320692i | ||||||||
\(868\) | 10.7639i | 0.365352i | ||||||||
\(869\) | −27.4377 | −0.930760 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1803 | 0.446599 | ||||||||
\(872\) | 9.27051i | 0.313939i | ||||||||
\(873\) | − 3.85410i | − 0.130442i | ||||||||
\(874\) | 58.4164 | 1.97596 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.70820 | 0.328010 | ||||||||
\(877\) | 43.1246i | 1.45621i | 0.685463 | + | 0.728107i | \(0.259600\pi\) | ||||
−0.685463 | + | 0.728107i | \(0.740400\pi\) | |||||||
\(878\) | 51.8328i | 1.74927i | ||||||||
\(879\) | 6.32624 | 0.213379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0902 | 0.508401 | 0.254200 | − | 0.967152i | \(-0.418188\pi\) | ||||
0.254200 | + | 0.967152i | \(0.418188\pi\) | |||||||
\(882\) | − 4.85410i | − 0.163446i | ||||||||
\(883\) | − 29.2016i | − 0.982713i | −0.870959 | − | 0.491356i | \(-0.836501\pi\) | ||||
0.870959 | − | 0.491356i | \(-0.163499\pi\) | |||||||
\(884\) | −2.61803 | −0.0880540 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.4164 | −1.05545 | ||||||||
\(887\) | 42.9230i | 1.44121i | 0.693344 | + | 0.720606i | \(0.256136\pi\) | ||||
−0.693344 | + | 0.720606i | \(0.743864\pi\) | |||||||
\(888\) | − 4.47214i | − 0.150075i | ||||||||
\(889\) | 27.3050 | 0.915779 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | − 6.27051i | − 0.209952i | ||||||||
\(893\) | − 31.9574i | − 1.06941i | ||||||||
\(894\) | 21.1803 | 0.708377 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −27.2361 | −0.909893 | ||||||||
\(897\) | − 5.38197i | − 0.179699i | ||||||||
\(898\) | − 26.7082i | − 0.891264i | ||||||||
\(899\) | 31.5066 | 1.05080 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.5967 | −1.58568 | ||||||||
\(902\) | 45.5410i | 1.51635i | ||||||||
\(903\) | − 14.7639i | − 0.491313i | ||||||||
\(904\) | −8.41641 | −0.279926 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.7082 | −0.355756 | ||||||||
\(907\) | − 17.0000i | − 0.564476i | −0.959344 | − | 0.282238i | \(-0.908923\pi\) | ||||
0.959344 | − | 0.282238i | \(-0.0910767\pi\) | |||||||
\(908\) | − 3.56231i | − 0.118219i | ||||||||
\(909\) | 9.38197 | 0.311180 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8885 | 0.493279 | 0.246640 | − | 0.969107i | \(-0.420674\pi\) | ||||
0.246640 | + | 0.969107i | \(0.420674\pi\) | |||||||
\(912\) | 32.5623i | 1.07825i | ||||||||
\(913\) | 27.0000i | 0.893570i | ||||||||
\(914\) | 16.0000 | 0.529233 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 28.3607i | 0.936552i | ||||||||
\(918\) | 6.85410i | 0.226219i | ||||||||
\(919\) | 5.00000 | 0.164935 | 0.0824674 | − | 0.996594i | \(-0.473720\pi\) | ||||
0.0824674 | + | 0.996594i | \(0.473720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.85410 | 0.291753 | ||||||||
\(922\) | − 31.0344i | − 1.02206i | ||||||||
\(923\) | 10.0902i | 0.332122i | ||||||||
\(924\) | −3.70820 | −0.121991 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −54.5066 | −1.79120 | ||||||||
\(927\) | − 14.4164i | − 0.473497i | ||||||||
\(928\) | − 12.2361i | − 0.401669i | ||||||||
\(929\) | 29.5967 | 0.971038 | 0.485519 | − | 0.874226i | \(-0.338631\pi\) | ||||
0.485519 | + | 0.874226i | \(0.338631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.1246 | 0.659558 | ||||||||
\(932\) | 6.29180i | 0.206095i | ||||||||
\(933\) | 13.5279i | 0.442882i | ||||||||
\(934\) | 16.8541 | 0.551483 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.23607 | 0.0730882 | ||||||||
\(937\) | − 10.4164i | − 0.340289i | −0.985419 | − | 0.170145i | \(-0.945577\pi\) | ||||
0.985419 | − | 0.170145i | \(-0.0544235\pi\) | |||||||
\(938\) | − 42.6525i | − 1.39265i | ||||||||
\(939\) | −2.29180 | −0.0747899 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.9787 | 1.89005 | 0.945026 | − | 0.326995i | \(-0.106036\pi\) | ||||
0.945026 | + | 0.326995i | \(0.106036\pi\) | |||||||
\(942\) | − 4.61803i | − 0.150464i | ||||||||
\(943\) | 50.4934i | 1.64429i | ||||||||
\(944\) | 19.1459 | 0.623146 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.8328 | 1.16503 | ||||||||
\(947\) | − 23.8328i | − 0.774462i | −0.921983 | − | 0.387231i | \(-0.873432\pi\) | ||||
0.921983 | − | 0.387231i | \(-0.126568\pi\) | |||||||
\(948\) | 5.65248i | 0.183584i | ||||||||
\(949\) | 15.7082 | 0.509910 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.5623 | 0.666778 | ||||||||
\(952\) | − 18.9443i | − 0.613987i | ||||||||
\(953\) | 42.0557i | 1.36232i | 0.732135 | + | 0.681159i | \(0.238524\pi\) | ||||
−0.732135 | + | 0.681159i | \(0.761476\pi\) | |||||||
\(954\) | −18.1803 | −0.588610 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.2148 | 0.427397 | ||||||||
\(957\) | 10.8541i | 0.350863i | ||||||||
\(958\) | − 7.76393i | − 0.250841i | ||||||||
\(959\) | 0.875388 | 0.0282678 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.8328 | 1.44622 | ||||||||
\(962\) | 3.23607i | 0.104335i | ||||||||
\(963\) | 1.14590i | 0.0369260i | ||||||||
\(964\) | −4.52786 | −0.145833 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.4164 | −0.560364 | ||||||||
\(967\) | − 35.4164i | − 1.13891i | −0.822021 | − | 0.569457i | \(-0.807153\pi\) | ||||
0.822021 | − | 0.569457i | \(-0.192847\pi\) | |||||||
\(968\) | − 4.47214i | − 0.143740i | ||||||||
\(969\) | −28.4164 | −0.912867 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.8885 | 0.959169 | 0.479585 | − | 0.877496i | \(-0.340787\pi\) | ||||
0.479585 | + | 0.877496i | \(0.340787\pi\) | |||||||
\(972\) | 0.618034i | 0.0198234i | ||||||||
\(973\) | 26.8328i | 0.860221i | ||||||||
\(974\) | −26.8885 | −0.861565 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.2705 | −1.35305 | ||||||||
\(977\) | − 37.6525i | − 1.20461i | −0.798266 | − | 0.602305i | \(-0.794249\pi\) | ||||
0.798266 | − | 0.602305i | \(-0.205751\pi\) | |||||||
\(978\) | − 29.5623i | − 0.945298i | ||||||||
\(979\) | −33.5410 | −1.07198 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.14590 | −0.132368 | ||||||||
\(982\) | 36.1246i | 1.15278i | ||||||||
\(983\) | 24.6180i | 0.785193i | 0.919711 | + | 0.392597i | \(0.128423\pi\) | ||||
−0.919711 | + | 0.392597i | \(0.871577\pi\) | |||||||
\(984\) | −20.9787 | −0.668777 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.7984 | 0.789741 | ||||||||
\(987\) | 9.52786i | 0.303275i | ||||||||
\(988\) | − 4.14590i | − 0.131899i | ||||||||
\(989\) | 39.7295 | 1.26332 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | − 29.4508i | − 0.935065i | ||||||||
\(993\) | 30.6869i | 0.973820i | ||||||||
\(994\) | 32.6525 | 1.03567 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.56231 | 0.176248 | ||||||||
\(997\) | − 2.93112i | − 0.0928294i | −0.998922 | − | 0.0464147i | \(-0.985220\pi\) | ||||
0.998922 | − | 0.0464147i | \(-0.0147796\pi\) | |||||||
\(998\) | 24.2705i | 0.768270i | ||||||||
\(999\) | 2.00000 | 0.0632772 |
(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 | 1875.2.b.a.1249.4 | 4 | ||
5.2 | odd | 4 | 1875.2.a.b.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1875.2.a.c.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 1875.2.b.a.1249.1 | 4 | ||
15.2 | even | 4 | 5625.2.a.g.1.2 | 2 | |||
15.8 | even | 4 | 5625.2.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.b.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
1875.2.a.c.1.2 | yes | 2 | 5.3 | odd | 4 | ||
1875.2.b.a.1249.1 | 4 | 5.4 | even | 2 | inner | ||
1875.2.b.a.1249.4 | 4 | 1.1 | even | 1 | trivial | ||
5625.2.a.b.1.1 | 2 | 15.8 | even | 4 | |||
5625.2.a.g.1.2 | 2 | 15.2 | even | 4 |