Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1049,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.f (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: | \(16.7685844245\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.3 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1049 |
Dual form | 2100.2.f.h.1049.4 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.61803 | − | 0.618034i | 0.934172 | − | 0.356822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.381966 | + | 2.61803i | 0.144370 | + | 0.989524i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | − | 2.00000i | 0.745356 | − | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23607i | 1.57873i | 0.613922 | + | 0.789367i | \(0.289591\pi\) | ||||
−0.613922 | + | 0.789367i | \(0.710409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23607 | 0.897524 | 0.448762 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448762 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214i | 1.08465i | 0.840168 | + | 0.542326i | \(0.182456\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.76393i | − | 0.634089i | −0.948411 | − | 0.317045i | \(-0.897309\pi\) | ||
0.948411 | − | 0.317045i | \(-0.102691\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.23607 | + | 4.00000i | 0.487950 | + | 0.872872i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.70820 | −1.19024 | −0.595121 | − | 0.803636i | \(-0.702896\pi\) | ||||
−0.595121 | + | 0.803636i | \(0.702896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.38197 | − | 4.61803i | 0.458410 | − | 0.888741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000i | 0.742781i | 0.928477 | + | 0.371391i | \(0.121119\pi\) | ||||
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.23607i | 0.222004i | 0.993820 | + | 0.111002i | \(0.0354061\pi\) | ||||
−0.993820 | + | 0.111002i | \(0.964594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.23607 | + | 8.47214i | 0.563327 | + | 1.47481i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.47214i | 0.735215i | 0.929981 | + | 0.367607i | \(0.119823\pi\) | ||||
−0.929981 | + | 0.367607i | \(0.880177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.23607 | − | 2.00000i | 0.838442 | − | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4721 | −1.94782 | −0.973910 | − | 0.226934i | \(-0.927130\pi\) | ||||
−0.973910 | + | 0.226934i | \(0.927130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.76393i | − | 0.421496i | −0.977540 | − | 0.210748i | \(-0.932410\pi\) | ||
0.977540 | − | 0.210748i | \(-0.0675899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.23607i | − | 0.180299i | −0.995928 | − | 0.0901495i | \(-0.971266\pi\) | ||
0.995928 | − | 0.0901495i | \(-0.0287345\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.70820 | + | 2.00000i | −0.958315 | + | 0.285714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.76393 | + | 7.23607i | 0.387028 | + | 1.01325i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.76393 | 0.654376 | 0.327188 | − | 0.944959i | \(-0.393899\pi\) | ||||
0.327188 | + | 0.944959i | \(0.393899\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.70820 | − | 4.47214i | −0.226257 | − | 0.592349i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9443i | 1.65734i | 0.559734 | + | 0.828672i | \(0.310903\pi\) | ||||
−0.559734 | + | 0.828672i | \(0.689097\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.09017 | + | 5.09017i | 0.767289 | + | 0.641301i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.70820i | 0.453029i | 0.974008 | + | 0.226515i | \(0.0727331\pi\) | ||||
−0.974008 | + | 0.226515i | \(0.927267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.23607 | + | 3.52786i | −1.11189 | + | 0.424705i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.1803i | − | 1.20818i | −0.796915 | − | 0.604092i | \(-0.793536\pi\) | ||
0.796915 | − | 0.604092i | \(-0.206464\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2361 | 1.31508 | 0.657541 | − | 0.753419i | \(-0.271597\pi\) | ||||
0.657541 | + | 0.753419i | \(0.271597\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.7082 | + | 2.00000i | −1.56219 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.52786 | −0.171898 | −0.0859491 | − | 0.996300i | \(-0.527392\pi\) | ||||
−0.0859491 | + | 0.996300i | \(0.527392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.76393i | − | 0.303381i | −0.988428 | − | 0.151690i | \(-0.951528\pi\) | ||
0.988428 | − | 0.151690i | \(-0.0484717\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.47214 | + | 6.47214i | 0.265041 | + | 0.693886i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.52786 | 0.373953 | 0.186976 | − | 0.982364i | \(-0.440131\pi\) | ||||
0.186976 | + | 0.982364i | \(0.440131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23607 | + | 8.47214i | 0.129575 | + | 0.888121i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.763932 | + | 2.00000i | 0.0792161 | + | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.18034 | 0.830588 | 0.415294 | − | 0.909687i | \(-0.363679\pi\) | ||||
0.415294 | + | 0.909687i | \(0.363679\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.4721 | + | 11.7082i | 1.05249 | + | 1.17672i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9443 | 1.08900 | 0.544498 | − | 0.838762i | \(-0.316720\pi\) | ||||
0.544498 | + | 0.838762i | \(0.316720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2361 | 1.50125 | 0.750627 | − | 0.660726i | \(-0.229751\pi\) | ||||
0.750627 | + | 0.660726i | \(0.229751\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7082 | 1.32522 | 0.662611 | − | 0.748964i | \(-0.269448\pi\) | ||||
0.662611 | + | 0.748964i | \(0.269448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9443 | −1.43140 | −0.715701 | − | 0.698407i | \(-0.753893\pi\) | ||||
−0.715701 | + | 0.698407i | \(0.753893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.76393 | + | 7.23607i | 0.262341 | + | 0.686817i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.7639 | 1.20073 | 0.600365 | − | 0.799726i | \(-0.295022\pi\) | ||||
0.600365 | + | 0.799726i | \(0.295022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.23607 | − | 6.47214i | 0.668975 | − | 0.598349i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.7082 | + | 1.70820i | −1.07329 | + | 0.156591i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.4164 | −1.49240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −20.1803 | + | 7.70820i | −1.81960 | + | 0.695025i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.1246i | − | 1.69703i | −0.529167 | − | 0.848517i | \(-0.677496\pi\) | ||
0.529167 | − | 0.848517i | \(-0.322504\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.70820 | − | 4.47214i | −0.150399 | − | 0.393750i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4164 | −0.997456 | −0.498728 | − | 0.866758i | \(-0.666199\pi\) | ||||
−0.498728 | + | 0.866758i | \(0.666199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.23607 | − | 1.05573i | 0.627447 | − | 0.0915432i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.23607 | −0.276476 | −0.138238 | − | 0.990399i | \(-0.544144\pi\) | ||||
−0.138238 | + | 0.990399i | \(0.544144\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.7639i | − | 0.912985i | −0.889727 | − | 0.456492i | \(-0.849106\pi\) | ||
0.889727 | − | 0.456492i | \(-0.150894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.763932 | − | 2.00000i | −0.0643347 | − | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.9443i | 1.41695i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.61803 | + | 7.38197i | −0.793282 | + | 0.608854i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.4164i | − | 0.935269i | −0.883922 | − | 0.467634i | \(-0.845106\pi\) | ||
0.883922 | − | 0.467634i | \(-0.154894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.94427 | + | 10.0000i | 0.723102 | + | 0.808452i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.1803 | 1.92980 | 0.964901 | − | 0.262615i | \(-0.0845850\pi\) | ||||
0.964901 | + | 0.262615i | \(0.0845850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.70820 | − | 2.94427i | 0.611300 | − | 0.233496i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18034 | − | 14.9443i | −0.171835 | − | 1.17777i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.6525i | − | 0.991018i | −0.868603 | − | 0.495509i | \(-0.834981\pi\) | ||
0.868603 | − | 0.495509i | \(-0.165019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.2361i | 1.02424i | 0.858915 | + | 0.512119i | \(0.171139\pi\) | ||||
−0.858915 | + | 0.512119i | \(0.828861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.52786 | − | 6.18034i | −0.422726 | − | 0.472622i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000i | 0.152057i | 0.997106 | + | 0.0760286i | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.4721 | − | 5.52786i | 1.08779 | − | 0.415500i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.2361i | − | 1.28828i | −0.764906 | − | 0.644142i | \(-0.777215\pi\) | ||
0.764906 | − | 0.644142i | \(-0.222785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.47214i | − | 0.183752i | −0.995770 | − | 0.0918762i | \(-0.970714\pi\) | ||
0.995770 | − | 0.0918762i | \(-0.0292864\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | + | 20.9443i | 0.591377 | + | 1.54825i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.4164 | −1.71238 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.0000 | + | 4.47214i | 0.945611 | + | 0.325300i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.76393i | 0.199991i | 0.994988 | + | 0.0999956i | \(0.0318829\pi\) | ||||
−0.994988 | + | 0.0999956i | \(0.968117\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.00000i | − | 0.431889i | −0.976406 | − | 0.215945i | \(-0.930717\pi\) | ||
0.976406 | − | 0.215945i | \(-0.0692831\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.7639 | 1.47937 | 0.739684 | − | 0.672954i | \(-0.234975\pi\) | ||||
0.739684 | + | 0.672954i | \(0.234975\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 13.2361i | − | 0.938280i | −0.883124 | − | 0.469140i | \(-0.844564\pi\) | ||
0.883124 | − | 0.469140i | \(-0.155436\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.29180 | + | 6.00000i | 0.161651 | + | 0.423207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.4721 | + | 1.52786i | −0.735000 | + | 0.107235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.7639 | + | 11.4164i | −0.887155 | + | 0.793495i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.4721 | 1.00106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.29180 | − | 16.4721i | −0.431107 | − | 1.12865i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.23607 | + | 0.472136i | −0.219679 | + | 0.0320507i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.1803 | − | 6.94427i | 1.22851 | − | 0.469250i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.4721i | 0.973501i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.70820 | −0.114390 | −0.0571949 | − | 0.998363i | \(-0.518216\pi\) | ||||
−0.0571949 | + | 0.998363i | \(0.518216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 18.7639i | − | 1.24541i | −0.782458 | − | 0.622703i | \(-0.786035\pi\) | ||
0.782458 | − | 0.622703i | \(-0.213965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.8885i | 1.44644i | 0.690620 | + | 0.723218i | \(0.257338\pi\) | ||||
−0.690620 | + | 0.723218i | \(0.742662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.9443 | + | 11.7082i | −1.37803 | + | 0.770343i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.1803 | −1.58411 | −0.792053 | − | 0.610452i | \(-0.790988\pi\) | ||||
−0.792053 | + | 0.610452i | \(0.790988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.47214 | + | 0.944272i | −0.160582 | + | 0.0613371i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.1803i | 1.43473i | 0.696699 | + | 0.717363i | \(0.254651\pi\) | ||||
−0.696699 | + | 0.717363i | \(0.745349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 28.3607i | − | 1.82687i | −0.406982 | − | 0.913436i | \(-0.633419\pi\) | ||
0.406982 | − | 0.913436i | \(-0.366581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.90983 | − | 15.0902i | −0.250816 | − | 0.968035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.94427i | − | 0.569110i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.70820 | − | 4.47214i | −0.108253 | − | 0.283410i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.3607 | 1.53763 | 0.768816 | − | 0.639470i | \(-0.220846\pi\) | ||||
0.768816 | + | 0.639470i | \(0.220846\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 29.8885i | − | 1.87908i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.52786i | 0.469575i | 0.972047 | + | 0.234788i | \(0.0754395\pi\) | ||||
−0.972047 | + | 0.234788i | \(0.924561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.7082 | + | 1.70820i | −0.727512 | + | 0.106143i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | + | 8.94427i | 0.495188 | + | 0.553637i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.180340 | 0.0111202 | 0.00556012 | − | 0.999985i | \(-0.498230\pi\) | ||||
0.00556012 | + | 0.999985i | \(0.498230\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.70820 | − | 2.18034i | 0.349336 | − | 0.133435i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.4721 | −1.73598 | −0.867988 | − | 0.496584i | \(-0.834587\pi\) | ||||
−0.867988 | + | 0.496584i | \(0.834587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1246i | 1.16174i | 0.813997 | + | 0.580869i | \(0.197287\pi\) | ||||
−0.813997 | + | 0.580869i | \(0.802713\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.23607 | + | 12.9443i | 0.437947 | + | 0.783423i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.4164i | 1.52712i | 0.645735 | + | 0.763562i | \(0.276551\pi\) | ||||
−0.645735 | + | 0.763562i | \(0.723449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.47214 | + | 2.76393i | 0.148003 | + | 0.165472i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4164i | 0.919666i | 0.888005 | + | 0.459833i | \(0.152091\pi\) | ||||
−0.888005 | + | 0.459833i | \(0.847909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.6525 | −1.34655 | −0.673275 | − | 0.739392i | \(-0.735113\pi\) | ||||
−0.673275 | + | 0.739392i | \(0.735113\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.76393 | − | 32.6525i | −0.281206 | − | 1.92741i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.2361 | − | 5.05573i | 0.775912 | − | 0.296372i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.0000i | − | 0.817889i | −0.912559 | − | 0.408944i | \(-0.865897\pi\) | ||
0.912559 | − | 0.408944i | \(-0.134103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.1803 | + | 12.4721i | 1.40309 | + | 0.723707i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.4721 | −1.06827 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.23607 | − | 1.05573i | 0.417080 | − | 0.0608512i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.7082 | − | 6.76393i | 1.01731 | − | 0.388578i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.18034 | −0.238585 | −0.119292 | − | 0.992859i | \(-0.538063\pi\) | ||||
−0.119292 | + | 0.992859i | \(0.538063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.6525 | − | 9.41641i | 1.40243 | − | 0.535681i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3607 | 0.700910 | 0.350455 | − | 0.936580i | \(-0.386027\pi\) | ||||
0.350455 | + | 0.936580i | \(0.386027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7082 | −1.00093 | −0.500463 | − | 0.865758i | \(-0.666837\pi\) | ||||
−0.500463 | + | 0.865758i | \(0.666837\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.1803 | −0.908778 | −0.454389 | − | 0.890803i | \(-0.650142\pi\) | ||||
−0.454389 | + | 0.890803i | \(0.650142\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.9443 | −1.17265 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.1803 | − | 8.47214i | 1.23799 | − | 0.472869i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.3607 | 0.687767 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.1803 | + | 9.23607i | −1.33718 | + | 0.510756i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.23607 | − | 0.472136i | 0.178410 | − | 0.0260297i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.05573 | −0.167958 | −0.0839790 | − | 0.996468i | \(-0.526763\pi\) | ||||
−0.0839790 | + | 0.996468i | \(0.526763\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.94427 | + | 10.0000i | 0.490143 | + | 0.547997i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.00000i | − | 0.108947i | −0.998515 | − | 0.0544735i | \(-0.982652\pi\) | ||
0.998515 | − | 0.0544735i | \(-0.0173480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.6525 | − | 7.88854i | 1.12169 | − | 0.428447i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.47214 | −0.350486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.79837 | − | 16.7984i | −0.421073 | − | 0.907027i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.34752 | −0.0723389 | −0.0361694 | − | 0.999346i | \(-0.511516\pi\) | ||||
−0.0361694 | + | 0.999346i | \(0.511516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.94427i | 0.478776i | 0.970924 | + | 0.239388i | \(0.0769468\pi\) | ||||
−0.970924 | + | 0.239388i | \(0.923053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.70820 | − | 14.9443i | 0.411433 | − | 0.797666i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.41641i | − | 0.0753878i | −0.999289 | − | 0.0376939i | \(-0.987999\pi\) | ||
0.999289 | − | 0.0376939i | \(-0.0120012\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.8885 | + | 10.0000i | −0.946762 | + | 0.529256i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0689i | 1.27031i | 0.772386 | + | 0.635154i | \(0.219063\pi\) | ||||
−0.772386 | + | 0.635154i | \(0.780937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.3607 | 0.597931 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.5623 | + | 10.1459i | −1.39416 | + | 0.532522i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.65248 | 0.347256 | 0.173628 | − | 0.984811i | \(-0.444451\pi\) | ||||
0.173628 | + | 0.984811i | \(0.444451\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.8885 | + | 24.9443i | −1.45182 | + | 1.29855i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.81966 | + | 12.4721i | 0.0944720 | + | 0.647521i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4721i | 0.852895i | 0.904512 | + | 0.426447i | \(0.140235\pi\) | ||||
−0.904512 | + | 0.426447i | \(0.859765\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.9443i | 0.666664i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.4721 | −0.537917 | −0.268959 | − | 0.963152i | \(-0.586680\pi\) | ||||
−0.268959 | + | 0.963152i | \(0.586680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.8197 | − | 30.9443i | −0.605540 | − | 1.58532i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 10.7639i | − | 0.550011i | −0.961443 | − | 0.275006i | \(-0.911320\pi\) | ||
0.961443 | − | 0.275006i | \(-0.0886797\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.52786 | − | 6.18034i | −0.280997 | − | 0.314164i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.47214i | 0.328150i | 0.986448 | + | 0.164075i | \(0.0524640\pi\) | ||||
−0.986448 | + | 0.164075i | \(0.947536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.5279i | − | 1.29100i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.4721 | + | 7.05573i | −0.931796 | + | 0.355914i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.70820 | −0.487241 | −0.243620 | − | 0.969871i | \(-0.578335\pi\) | ||||
−0.243620 | + | 0.969871i | \(0.578335\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.0557 | − | 6.18034i | 0.553479 | − | 0.309404i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.0557i | − | 0.552097i | −0.961144 | − | 0.276048i | \(-0.910975\pi\) | ||
0.961144 | − | 0.276048i | \(-0.0890250\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000i | 0.199254i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.4164 | −1.16071 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.0000i | − | 0.593362i | −0.954977 | − | 0.296681i | \(-0.904120\pi\) | ||
0.954977 | − | 0.296681i | \(-0.0958798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.23607 | + | 2.00000i | −0.258276 | + | 0.0986527i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.41641 | + | 23.4164i | 0.168110 | + | 1.15225i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.65248 | − | 17.4164i | −0.325773 | − | 0.852885i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0000 | 1.36789 | 0.683945 | − | 0.729534i | \(-0.260263\pi\) | ||||
0.683945 | + | 0.729534i | \(0.260263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.5279 | 1.14668 | 0.573339 | − | 0.819318i | \(-0.305648\pi\) | ||||
0.573339 | + | 0.819318i | \(0.305648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.47214 | − | 2.76393i | −0.120199 | − | 0.134387i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.8885 | + | 4.94427i | −1.63998 | + | 0.239270i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.4721 | + | 27.4164i | 0.505599 | + | 1.32368i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.23607i | − | 0.252213i | −0.992017 | − | 0.126106i | \(-0.959752\pi\) | ||
0.992017 | − | 0.126106i | \(-0.0402480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.34752 | 0.0647579 | 0.0323789 | − | 0.999476i | \(-0.489692\pi\) | ||||
0.0323789 | + | 0.999476i | \(0.489692\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.7771i | 0.754720i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 18.1803i | − | 0.867700i | −0.900985 | − | 0.433850i | \(-0.857155\pi\) | ||
0.900985 | − | 0.433850i | \(-0.142845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | + | 17.8885i | −0.523810 | + | 0.851835i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.0689 | 1.61866 | 0.809331 | − | 0.587353i | \(-0.199830\pi\) | ||||
0.809331 | + | 0.587353i | \(0.199830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.05573 | − | 18.4721i | −0.333724 | − | 0.873702i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.88854i | − | 0.277898i | −0.990300 | − | 0.138949i | \(-0.955628\pi\) | ||
0.990300 | − | 0.138949i | \(-0.0443723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 65.3050i | − | 3.07509i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.4721 | + | 5.52786i | −0.679960 | + | 0.259722i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.9443i | 1.26040i | 0.776433 | + | 0.630200i | \(0.217027\pi\) | ||||
−0.776433 | + | 0.630200i | \(0.782973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.6525 | + | 10.6525i | 0.963975 | + | 0.497215i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.5279 | −0.723205 | −0.361602 | − | 0.932332i | \(-0.617770\pi\) | ||||
−0.361602 | + | 0.932332i | \(0.617770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.2361i | − | 1.17282i | −0.810015 | − | 0.586410i | \(-0.800541\pi\) | ||
0.810015 | − | 0.586410i | \(-0.199459\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 30.5410i | − | 1.41327i | −0.707578 | − | 0.706635i | \(-0.750212\pi\) | ||
0.707578 | − | 0.706635i | \(-0.249788\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.70820 | + | 1.41641i | −0.448283 | + | 0.0654036i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39.1246 | − | 14.9443i | 1.80277 | − | 0.688596i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.4721 | 0.665430 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6525 | − | 9.52786i | 0.487743 | − | 0.436251i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.94427 | 0.225910 | 0.112955 | − | 0.993600i | \(-0.463968\pi\) | ||||
0.112955 | + | 0.993600i | \(0.463968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.4721i | 0.659873i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.7639 | − | 22.8328i | −0.580779 | − | 1.03893i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.23607i | − | 0.0560116i | −0.999608 | − | 0.0280058i | \(-0.991084\pi\) | ||
0.999608 | − | 0.0280058i | \(-0.00891569\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.81966 | − | 20.4721i | −0.353617 | − | 0.925782i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.875388i | − | 0.0395057i | −0.999805 | − | 0.0197529i | \(-0.993712\pi\) | ||
0.999805 | − | 0.0197529i | \(-0.00628794\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.8885 | −0.805659 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.6525 | − | 3.88854i | 1.19553 | − | 0.174425i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.3607 | −1.26960 | −0.634799 | − | 0.772677i | \(-0.718917\pi\) | ||||
−0.634799 | + | 0.772677i | \(0.718917\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.18034 | + | 21.4164i | 0.365471 | + | 0.956815i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.6525i | − | 0.564146i | −0.959393 | − | 0.282073i | \(-0.908978\pi\) | ||
0.959393 | − | 0.282073i | \(-0.0910220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.09017 | + | 1.56231i | −0.181651 | + | 0.0693844i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.05573 | 0.224091 | 0.112046 | − | 0.993703i | \(-0.464260\pi\) | ||||
0.112046 | + | 0.993703i | \(0.464260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.29180 | + | 29.4164i | 0.189858 | + | 1.30131i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.7639 | − | 6.58359i | −0.563541 | − | 0.290673i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.47214 | 0.284644 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.23607 | + | 3.23607i | 0.0542574 | + | 0.142048i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.8885 | 1.22182 | 0.610910 | − | 0.791700i | \(-0.290804\pi\) | ||||
0.610910 | + | 0.791700i | \(0.290804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.7082 | −0.949233 | −0.474617 | − | 0.880193i | \(-0.657413\pi\) | ||||
−0.474617 | + | 0.880193i | \(0.657413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.52786 | −0.240798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.58359 | 0.416678 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0000 | − | 17.8885i | 0.867926 | − | 0.776297i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.3607 | −1.74822 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.6525 | − | 27.8885i | −0.459688 | − | 1.20348i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.4721 | − | 35.1246i | −0.451067 | − | 1.51292i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.11146 | −0.348739 | −0.174369 | − | 0.984680i | \(-0.555789\pi\) | ||||
−0.174369 | + | 0.984680i | \(0.555789\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.52786 | − | 4.00000i | −0.0655669 | − | 0.171656i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.29180i | − | 0.183504i | −0.995782 | − | 0.0917520i | \(-0.970753\pi\) | ||
0.995782 | − | 0.0917520i | \(-0.0292467\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.8885 | + | 28.9443i | 1.10490 | + | 1.23531i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.0557 | 0.470990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.583592 | − | 4.00000i | −0.0248169 | − | 0.170097i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.18034 | −0.346612 | −0.173306 | − | 0.984868i | \(-0.555445\pi\) | ||||
−0.173306 | + | 0.984868i | \(0.555445\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.94427i | − | 0.378302i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.8885 | + | 14.4721i | −1.59966 | + | 0.611014i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 40.0689i | − | 1.68870i | −0.535790 | − | 0.844351i | \(-0.679986\pi\) | ||
0.535790 | − | 0.844351i | \(-0.320014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.7984 | − | 0.798374i | 0.999438 | − | 0.0335286i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 13.8885i | − | 0.582238i | −0.956687 | − | 0.291119i | \(-0.905972\pi\) | ||
0.956687 | − | 0.291119i | \(-0.0940276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.8328 | −1.95989 | −0.979946 | − | 0.199262i | \(-0.936145\pi\) | ||||
−0.979946 | + | 0.199262i | \(0.936145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.70820 | + | 4.47214i | 0.0713612 | + | 0.186826i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0689 | 1.08526 | 0.542631 | − | 0.839971i | \(-0.317428\pi\) | ||||
0.542631 | + | 0.839971i | \(0.317428\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.70820 | − | 9.70820i | −0.154108 | − | 0.403459i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.23607 | − | 1.05573i | 0.300203 | − | 0.0437990i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.9443i | 1.03309i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.7082i | 0.813445i | 0.913552 | + | 0.406722i | \(0.133328\pi\) | ||||
−0.913552 | + | 0.406722i | \(0.866672\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.41641 | 0.140771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.5967 | − | 12.8328i | 1.38199 | − | 0.527872i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.4721i | − | 1.16921i | −0.811318 | − | 0.584605i | \(-0.801249\pi\) | ||
0.811318 | − | 0.584605i | \(-0.198751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.18034 | − | 21.4164i | −0.334799 | − | 0.876515i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 0.652476i | − | 0.0266594i | −0.999911 | − | 0.0133297i | \(-0.995757\pi\) | ||
0.999911 | − | 0.0133297i | \(-0.00424311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.3050i | − | 0.705884i | −0.935645 | − | 0.352942i | \(-0.885181\pi\) | ||
0.935645 | − | 0.352942i | \(-0.114819\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.41641 | + | 8.29180i | 0.302019 | + | 0.337668i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.0689 | −0.733393 | −0.366697 | − | 0.930341i | \(-0.619511\pi\) | ||||
−0.366697 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.0000 | + | 8.94427i | −0.648353 | + | 0.362440i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.00000i | − | 0.161823i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.3607i | − | 0.903139i | −0.892236 | − | 0.451570i | \(-0.850864\pi\) | ||
0.892236 | − | 0.451570i | \(-0.149136\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.5410 | 1.63212 | 0.816060 | − | 0.577967i | \(-0.196154\pi\) | ||||
0.816060 | + | 0.577967i | \(0.196154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.70820i | − | 0.309819i | −0.987929 | − | 0.154909i | \(-0.950491\pi\) | ||
0.987929 | − | 0.154909i | \(-0.0495086\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.5967 | + | 26.3607i | −0.545619 | + | 1.05782i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.34752 | + | 9.23607i | 0.0539874 | + | 0.370035i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.4164 | − | 8.94427i | 0.935161 | − | 0.357200i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.94427 | −0.356066 | −0.178033 | − | 0.984025i | \(-0.556973\pi\) | ||||
−0.178033 | + | 0.984025i | \(0.556973\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.9443 | + | 4.94427i | −0.514489 | + | 0.196517i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.7082 | + | 6.47214i | −0.860110 | + | 0.256435i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.3607 | − | 22.7639i | −0.805456 | − | 0.900527i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 39.4164i | − | 1.55685i | −0.627735 | − | 0.778427i | \(-0.716018\pi\) | ||
0.627735 | − | 0.778427i | \(-0.283982\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.7082 | −1.48707 | −0.743533 | − | 0.668699i | \(-0.766851\pi\) | ||||
−0.743533 | + | 0.668699i | \(0.766851\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.1246i | 1.22363i | 0.790999 | + | 0.611817i | \(0.209561\pi\) | ||||
−0.790999 | + | 0.611817i | \(0.790439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 46.8328i | 1.83835i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.94427 | + | 2.76393i | −0.193781 | + | 0.108327i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.5967 | 1.07994 | 0.539972 | − | 0.841683i | \(-0.318435\pi\) | ||||
0.539972 | + | 0.841683i | \(0.318435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.1246 | − | 22.4721i | 0.980204 | − | 0.876722i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 41.2361i | − | 1.60633i | −0.595757 | − | 0.803165i | \(-0.703148\pi\) | ||
0.595757 | − | 0.803165i | \(-0.296852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 30.8328i | − | 1.19926i | −0.800278 | − | 0.599629i | \(-0.795315\pi\) | ||
0.800278 | − | 0.599629i | \(-0.204685\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.94427 | + | 23.4164i | 0.347367 | + | 0.909418i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 22.8328i | − | 0.884090i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.76393 | + | 1.05573i | −0.106860 | + | 0.0408168i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −67.7771 | −2.61651 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.94427i | − | 0.113493i | −0.998389 | − | 0.0567467i | \(-0.981927\pi\) | ||
0.998389 | − | 0.0567467i | \(-0.0180727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000i | 0.230599i | 0.993331 | + | 0.115299i | \(0.0367827\pi\) | ||||
−0.993331 | + | 0.115299i | \(0.963217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.12461 | + | 21.4164i | 0.119912 | + | 0.821886i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.5967 | − | 30.3607i | −0.444388 | − | 1.16342i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.7082 | −1.28981 | −0.644904 | − | 0.764263i | \(-0.723103\pi\) | ||||
−0.644904 | + | 0.764263i | \(0.723103\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.5279 | + | 35.4164i | 0.516120 | + | 1.35122i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.4164 | 0.587318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.1803i | − | 0.539446i | −0.962938 | − | 0.269723i | \(-0.913068\pi\) | ||
0.962938 | − | 0.269723i | \(-0.0869321\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.6525 | + | 31.8885i | −1.01244 | + | 1.21135i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 55.7771i | − | 2.11271i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −39.1246 | + | 14.9443i | −1.47983 | + | 0.565244i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.9443i | 0.791054i | 0.918454 | + | 0.395527i | \(0.129438\pi\) | ||||
−0.918454 | + | 0.395527i | \(0.870562\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3607 | 0.466192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.18034 | + | 28.6525i | 0.157218 | + | 1.07759i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.05573 | 0.189872 | 0.0949359 | − | 0.995483i | \(-0.469735\pi\) | ||||
0.0949359 | + | 0.995483i | \(0.469735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.41641 | + | 3.05573i | −0.128125 | + | 0.114599i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.05573i | − | 0.264239i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.7082 | + | 35.8885i | 0.511942 | + | 1.34028i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.8885 | 1.56218 | 0.781090 | − | 0.624419i | \(-0.214664\pi\) | ||||
0.781090 | + | 0.624419i | \(0.214664\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.81966 | + | 39.8885i | 0.216735 | + | 1.48553i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.5279 | − | 45.8885i | −0.651868 | − | 1.70661i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.70820 | 0.360057 | 0.180029 | − | 0.983661i | \(-0.442381\pi\) | ||||
0.180029 | + | 0.983661i | \(0.442381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6525 | − | 22.0000i | −0.579721 | − | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.3607 | 0.457176 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.3475 | 0.640745 | 0.320373 | − | 0.947292i | \(-0.396192\pi\) | ||||
0.320373 | + | 0.947292i | \(0.396192\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.4164 | −0.715213 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.36068 | 0.160410 | 0.0802051 | − | 0.996778i | \(-0.474442\pi\) | ||||
0.0802051 | + | 0.996778i | \(0.474442\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.52786 | − | 14.4721i | −0.203071 | − | 0.531647i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.65248 | −0.244056 | −0.122028 | − | 0.992527i | \(-0.538940\pi\) | ||||
−0.122028 | + | 0.992527i | \(0.538940\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.52786 | − | 6.18034i | −0.202254 | − | 0.226127i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.23607 | + | 35.8885i | 0.191322 | + | 1.31134i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.0000 | −1.60558 | −0.802791 | − | 0.596260i | \(-0.796653\pi\) | ||||
−0.802791 | + | 0.596260i | \(0.796653\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.4164 | − | 15.0557i | 1.43641 | − | 0.548661i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.3050i | 0.992415i | 0.868204 | + | 0.496208i | \(0.165275\pi\) | ||||
−0.868204 | + | 0.496208i | \(0.834725\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.4721 | − | 48.3607i | −0.670496 | − | 1.75538i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3050 | −1.13480 | −0.567402 | − | 0.823441i | \(-0.692051\pi\) | ||||
−0.567402 | + | 0.823441i | \(0.692051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.70820 | − | 39.1246i | −0.206651 | − | 1.41641i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.9443 | 1.04512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.58359i | 0.165289i | 0.996579 | + | 0.0826443i | \(0.0263365\pi\) | ||||
−0.996579 | + | 0.0826443i | \(0.973663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.65248 | + | 12.1803i | 0.167555 | + | 0.438664i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.0000i | 0.647415i | 0.946157 | + | 0.323708i | \(0.104929\pi\) | ||||
−0.946157 | + | 0.323708i | \(0.895071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.8885 | + | 10.0000i | −0.641748 | + | 0.358748i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.4721i | 1.23509i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53.3050 | 1.90740 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.4721 | + | 9.52786i | 0.660140 | + | 0.340498i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.7082 | 1.05898 | 0.529492 | − | 0.848315i | \(-0.322383\pi\) | ||||
0.529492 | + | 0.848315i | \(0.322383\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.291796 | − | 0.111456i | 0.0103882 | − | 0.00396795i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.87539 | + | 33.4164i | 0.173349 | + | 1.18815i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.8885i | 1.48751i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 24.8328i | − | 0.879623i | −0.898090 | − | 0.439812i | \(-0.855045\pi\) | ||
0.898090 | − | 0.439812i | \(-0.144955\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.52786 | 0.195562 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.88854 | − | 7.05573i | 0.278728 | − | 0.249302i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58.8328i | 2.07616i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −46.0689 | + | 17.5967i | −1.62170 | + | 0.619435i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.3607i | 1.13774i | 0.822427 | + | 0.568870i | \(0.192619\pi\) | ||||
−0.822427 | + | 0.568870i | \(0.807381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.7082i | 0.411131i | 0.978643 | + | 0.205565i | \(0.0659033\pi\) | ||||
−0.978643 | + | 0.205565i | \(0.934097\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.8197 | + | 30.9443i | 0.414534 | + | 1.08526i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.63932 | −0.267266 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.7082 | + | 16.4721i | 0.688660 | + | 0.575583i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.83282i | − | 0.238467i | −0.992866 | − | 0.119233i | \(-0.961956\pi\) | ||
0.992866 | − | 0.119233i | \(-0.0380437\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.5967i | 1.31054i | 0.755395 | + | 0.655270i | \(0.227445\pi\) | ||||
−0.755395 | + | 0.655270i | \(0.772555\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.2918 | −0.914255 | −0.457128 | − | 0.889401i | \(-0.651122\pi\) | ||||
−0.457128 | + | 0.889401i | \(0.651122\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24.3607i | − | 0.846081i | −0.906111 | − | 0.423041i | \(-0.860963\pi\) | ||
0.906111 | − | 0.423041i | \(-0.139037\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.7082 | + | 41.1246i | 0.544912 | + | 1.42660i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.94427 | − | 30.0000i | −0.309901 | − | 1.03944i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.70820 | + | 2.94427i | 0.197304 | + | 0.101769i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.94427 | −0.170695 | −0.0853476 | − | 0.996351i | \(-0.527200\pi\) | ||||
−0.0853476 | + | 0.996351i | \(0.527200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | 0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.52786 | + | 24.9443i | 0.328157 | + | 0.859126i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.27051 | − | 42.9787i | −0.215457 | − | 1.47677i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −36.6525 | + | 14.0000i | −1.25791 | + | 0.480479i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 25.5279i | − | 0.875084i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.1246 | 0.723293 | 0.361646 | − | 0.932315i | \(-0.382215\pi\) | ||||
0.361646 | + | 0.932315i | \(0.382215\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.5279i | − | 0.667059i | −0.942740 | − | 0.333530i | \(-0.891760\pi\) | ||
0.942740 | − | 0.333530i | \(-0.108240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44.6525i | − | 1.52352i | −0.647858 | − | 0.761761i | \(-0.724335\pi\) | ||
0.647858 | − | 0.761761i | \(-0.275665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.8885 | − | 49.8885i | −0.950439 | − | 1.70020i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.3475 | 0.726678 | 0.363339 | − | 0.931657i | \(-0.381637\pi\) | ||||
0.363339 | + | 0.931657i | \(0.381637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.85410 | + | 1.85410i | −0.164854 | + | 0.0629686i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.00000i | − | 0.271381i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000i | 0.406604i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.2918 | − | 16.3607i | 0.619083 | − | 0.553725i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.5279i | 0.794480i | 0.917715 | + | 0.397240i | \(0.130032\pi\) | ||||
−0.917715 | + | 0.397240i | \(0.869968\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.65248 | − | 22.6525i | −0.291841 | − | 0.764049i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.8328 | 1.24093 | 0.620465 | − | 0.784234i | \(-0.286944\pi\) | ||||
0.620465 | + | 0.784234i | \(0.286944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.5967i | 0.457567i | 0.973477 | + | 0.228783i | \(0.0734748\pi\) | ||||
−0.973477 | + | 0.228783i | \(0.926525\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 6.18034i | − | 0.207516i | −0.994603 | − | 0.103758i | \(-0.966913\pi\) | ||
0.994603 | − | 0.103758i | \(-0.0330867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.0689 | − | 7.30495i | 1.67926 | − | 0.245000i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.8328 | + | 5.23607i | 1.56896 | + | 0.175415i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.41641 | −0.114326 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.8885 | + | 11.4164i | −0.997949 | + | 0.381183i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.94427 | −0.164901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.3050i | 0.709771i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.0557 | − | 6.18034i | 0.367912 | − | 0.205669i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.7639i | 0.755864i | 0.925833 | + | 0.377932i | \(0.123365\pi\) | ||||
−0.925833 | + | 0.377932i | \(0.876635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.4721 | − | 21.8885i | 0.811690 | − | 0.725997i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.0689i | − | 0.399860i | −0.979810 | − | 0.199930i | \(-0.935929\pi\) | ||
0.979810 | − | 0.199930i | \(-0.0640715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4721 | 0.478958 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.36068 | − | 29.8885i | −0.144002 | − | 0.987007i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.5279 | 0.842087 | 0.421043 | − | 0.907041i | \(-0.361664\pi\) | ||||
0.421043 | + | 0.907041i | \(0.361664\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.76393 | + | 2.58359i | −0.222879 | + | 0.0851323i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 32.9443i | − | 1.08437i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.0689 | − | 30.4721i | 1.11897 | − | 1.00084i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.8885 | −0.521286 | −0.260643 | − | 0.965435i | \(-0.583935\pi\) | ||||
−0.260643 | + | 0.965435i | \(0.583935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.52786 | + | 18.5410i | 0.181168 | + | 0.607657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.0000 | − | 7.63932i | 0.654771 | − | 0.250100i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.2361 | 0.628415 | 0.314207 | − | 0.949354i | \(-0.398261\pi\) | ||||
0.314207 | + | 0.949354i | \(0.398261\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.6525 | + | 10.9443i | −0.935038 | + | 0.357153i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.2492 | 1.18169 | 0.590845 | − | 0.806785i | \(-0.298794\pi\) | ||||
0.590845 | + | 0.806785i | \(0.298794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 71.1935 | 2.31838 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.7639 | 0.674737 | 0.337369 | − | 0.941373i | \(-0.390463\pi\) | ||||
0.337369 | + | 0.941373i | \(0.390463\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.3607 | 1.18032 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.1803 | + | 10.0000i | −0.848956 | + | 0.324272i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.70820 | 0.314480 | 0.157240 | − | 0.987560i | \(-0.449740\pi\) | ||||
0.157240 | + | 0.987560i | \(0.449740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −33.8885 | + | 12.9443i | −1.09546 | + | 0.418429i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.23607 | − | 8.47214i | −0.0399147 | − | 0.273580i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.4721 | 0.950714 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.6525 | − | 27.4164i | 0.987762 | − | 0.883481i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 21.8197i | − | 0.701673i | −0.936437 | − | 0.350836i | \(-0.885897\pi\) | ||
0.936437 | − | 0.350836i | \(-0.114103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.0000 | − | 7.63932i | 0.642493 | − | 0.245410i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.4164 | −0.879834 | −0.439917 | − | 0.898038i | \(-0.644992\pi\) | ||||
−0.439917 | + | 0.898038i | \(0.644992\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.1803 | − | 4.11146i | 0.903420 | − | 0.131807i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.9574 | −1.40632 | −0.703161 | − | 0.711030i | \(-0.748229\pi\) | ||||
−0.703161 | + | 0.711030i | \(0.748229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.4721i | 0.590372i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.4164 | + | 29.8885i | −1.06690 | + | 0.954268i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.5410i | 0.846527i | 0.906007 | + | 0.423264i | \(0.139116\pi\) | ||||
−0.906007 | + | 0.423264i | \(0.860884\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.94427 | − | 2.76393i | 0.157378 | − | 0.0879769i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.7771i | 0.501682i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.7771 | −1.00943 | −0.504716 | − | 0.863285i | \(-0.668403\pi\) | ||||
−0.504716 | + | 0.863285i | \(0.668403\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.94427 | + | 1.88854i | −0.156902 | + | 0.0599311i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.0689 | 1.33233 | 0.666167 | − | 0.745802i | \(-0.267934\pi\) | ||||
0.666167 | + | 0.745802i | \(0.267934\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.6525 | + | 10.6525i | 0.653415 | + | 0.337029i |
(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 | 2100.2.f.h.1049.3 | 4 | ||
3.2 | odd | 2 | 2100.2.f.g.1049.4 | 4 | |||
5.2 | odd | 4 | 420.2.d.d.41.1 | yes | 4 | ||
5.3 | odd | 4 | 2100.2.d.g.1301.4 | 4 | |||
5.4 | even | 2 | 2100.2.f.b.1049.2 | 4 | |||
7.6 | odd | 2 | 2100.2.f.a.1049.2 | 4 | |||
15.2 | even | 4 | 420.2.d.c.41.3 | ✓ | 4 | ||
15.8 | even | 4 | 2100.2.d.h.1301.2 | 4 | |||
15.14 | odd | 2 | 2100.2.f.a.1049.1 | 4 | |||
20.7 | even | 4 | 1680.2.f.f.881.4 | 4 | |||
21.20 | even | 2 | 2100.2.f.b.1049.1 | 4 | |||
35.13 | even | 4 | 2100.2.d.h.1301.1 | 4 | |||
35.27 | even | 4 | 420.2.d.c.41.4 | yes | 4 | ||
35.34 | odd | 2 | 2100.2.f.g.1049.3 | 4 | |||
60.47 | odd | 4 | 1680.2.f.j.881.2 | 4 | |||
105.62 | odd | 4 | 420.2.d.d.41.2 | yes | 4 | ||
105.83 | odd | 4 | 2100.2.d.g.1301.3 | 4 | |||
105.104 | even | 2 | inner | 2100.2.f.h.1049.4 | 4 | ||
140.27 | odd | 4 | 1680.2.f.j.881.1 | 4 | |||
420.167 | even | 4 | 1680.2.f.f.881.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.d.c.41.3 | ✓ | 4 | 15.2 | even | 4 | ||
420.2.d.c.41.4 | yes | 4 | 35.27 | even | 4 | ||
420.2.d.d.41.1 | yes | 4 | 5.2 | odd | 4 | ||
420.2.d.d.41.2 | yes | 4 | 105.62 | odd | 4 | ||
1680.2.f.f.881.3 | 4 | 420.167 | even | 4 | |||
1680.2.f.f.881.4 | 4 | 20.7 | even | 4 | |||
1680.2.f.j.881.1 | 4 | 140.27 | odd | 4 | |||
1680.2.f.j.881.2 | 4 | 60.47 | odd | 4 | |||
2100.2.d.g.1301.3 | 4 | 105.83 | odd | 4 | |||
2100.2.d.g.1301.4 | 4 | 5.3 | odd | 4 | |||
2100.2.d.h.1301.1 | 4 | 35.13 | even | 4 | |||
2100.2.d.h.1301.2 | 4 | 15.8 | even | 4 | |||
2100.2.f.a.1049.1 | 4 | 15.14 | odd | 2 | |||
2100.2.f.a.1049.2 | 4 | 7.6 | odd | 2 | |||
2100.2.f.b.1049.1 | 4 | 21.20 | even | 2 | |||
2100.2.f.b.1049.2 | 4 | 5.4 | even | 2 | |||
2100.2.f.g.1049.3 | 4 | 35.34 | odd | 2 | |||
2100.2.f.g.1049.4 | 4 | 3.2 | odd | 2 | |||
2100.2.f.h.1049.3 | 4 | 1.1 | even | 1 | trivial | ||
2100.2.f.h.1049.4 | 4 | 105.104 | even | 2 | inner |