Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.a (trivial) |
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: | yes |
Analytic conductor: | \(9.44630255912\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.381966 | −0.270091 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) | ||||
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | −0.381966 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | 0.145898 | 0.0595626 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.47214 | 0.520479 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 0.145898 | 0.0461370 | ||||||||
\(11\) | 4.85410 | 1.46357 | 0.731783 | − | 0.681537i | \(-0.238688\pi\) | ||||
0.731783 | + | 0.681537i | \(0.238688\pi\) | |||||||
\(12\) | 0.708204 | 0.204441 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.381966 | 0.102085 | ||||||||
\(15\) | 0.145898 | 0.0376707 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | 7.47214 | 1.81226 | 0.906130 | − | 0.423000i | \(-0.139023\pi\) | ||||
0.906130 | + | 0.423000i | \(0.139023\pi\) | |||||||
\(18\) | 1.09017 | 0.256956 | ||||||||
\(19\) | −4.85410 | −1.11361 | −0.556804 | − | 0.830644i | \(-0.687972\pi\) | ||||
−0.556804 | + | 0.830644i | \(0.687972\pi\) | |||||||
\(20\) | 0.708204 | 0.158359 | ||||||||
\(21\) | 0.381966 | 0.0833518 | ||||||||
\(22\) | −1.85410 | −0.395296 | ||||||||
\(23\) | 4.47214 | 0.932505 | 0.466252 | − | 0.884652i | \(-0.345604\pi\) | ||||
0.466252 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(24\) | −0.562306 | −0.114780 | ||||||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 1.85410 | 0.350392 | ||||||||
\(29\) | −4.09017 | −0.759525 | −0.379763 | − | 0.925084i | \(-0.623994\pi\) | ||||
−0.379763 | + | 0.925084i | \(0.623994\pi\) | |||||||
\(30\) | −0.0557281 | −0.0101745 | ||||||||
\(31\) | −8.70820 | −1.56404 | −0.782020 | − | 0.623254i | \(-0.785810\pi\) | ||||
−0.782020 | + | 0.623254i | \(0.785810\pi\) | |||||||
\(32\) | −4.14590 | −0.732898 | ||||||||
\(33\) | −1.85410 | −0.322758 | ||||||||
\(34\) | −2.85410 | −0.489474 | ||||||||
\(35\) | 0.381966 | 0.0645640 | ||||||||
\(36\) | 5.29180 | 0.881966 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 1.85410 | 0.300775 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.562306 | −0.0889084 | ||||||||
\(41\) | −5.23607 | −0.817736 | −0.408868 | − | 0.912593i | \(-0.634076\pi\) | ||||
−0.408868 | + | 0.912593i | \(0.634076\pi\) | |||||||
\(42\) | −0.145898 | −0.0225126 | ||||||||
\(43\) | −7.56231 | −1.15324 | −0.576620 | − | 0.817012i | \(-0.695629\pi\) | ||||
−0.576620 | + | 0.817012i | \(0.695629\pi\) | |||||||
\(44\) | −9.00000 | −1.35680 | ||||||||
\(45\) | 1.09017 | 0.162513 | ||||||||
\(46\) | −1.70820 | −0.251861 | ||||||||
\(47\) | −2.23607 | −0.326164 | −0.163082 | − | 0.986613i | \(-0.552144\pi\) | ||||
−0.163082 | + | 0.986613i | \(0.552144\pi\) | |||||||
\(48\) | −1.20163 | −0.173440 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.85410 | 0.262210 | ||||||||
\(51\) | −2.85410 | −0.399654 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.23607 | 1.13131 | 0.565655 | − | 0.824642i | \(-0.308623\pi\) | ||||
0.565655 | + | 0.824642i | \(0.308623\pi\) | |||||||
\(54\) | −0.854102 | −0.116229 | ||||||||
\(55\) | −1.85410 | −0.250007 | ||||||||
\(56\) | −1.47214 | −0.196722 | ||||||||
\(57\) | 1.85410 | 0.245582 | ||||||||
\(58\) | 1.56231 | 0.205141 | ||||||||
\(59\) | −2.23607 | −0.291111 | −0.145556 | − | 0.989350i | \(-0.546497\pi\) | ||||
−0.145556 | + | 0.989350i | \(0.546497\pi\) | |||||||
\(60\) | −0.270510 | −0.0349227 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 3.32624 | 0.422433 | ||||||||
\(63\) | 2.85410 | 0.359583 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.708204 | 0.0871739 | ||||||||
\(67\) | −0.708204 | −0.0865209 | −0.0432604 | − | 0.999064i | \(-0.513775\pi\) | ||||
−0.0432604 | + | 0.999064i | \(0.513775\pi\) | |||||||
\(68\) | −13.8541 | −1.68006 | ||||||||
\(69\) | −1.70820 | −0.205644 | ||||||||
\(70\) | −0.145898 | −0.0174382 | ||||||||
\(71\) | −8.18034 | −0.970828 | −0.485414 | − | 0.874284i | \(-0.661331\pi\) | ||||
−0.485414 | + | 0.874284i | \(0.661331\pi\) | |||||||
\(72\) | −4.20163 | −0.495166 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 1.52786 | 0.177611 | ||||||||
\(75\) | 1.85410 | 0.214093 | ||||||||
\(76\) | 9.00000 | 1.03237 | ||||||||
\(77\) | −4.85410 | −0.553176 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | −1.20163 | −0.134346 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | 6.70820 | 0.736321 | 0.368161 | − | 0.929762i | \(-0.379988\pi\) | ||||
0.368161 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(84\) | −0.708204 | −0.0772714 | ||||||||
\(85\) | −2.85410 | −0.309571 | ||||||||
\(86\) | 2.88854 | 0.311480 | ||||||||
\(87\) | 1.56231 | 0.167497 | ||||||||
\(88\) | 7.14590 | 0.761755 | ||||||||
\(89\) | −16.0902 | −1.70555 | −0.852777 | − | 0.522275i | \(-0.825084\pi\) | ||||
−0.852777 | + | 0.522275i | \(0.825084\pi\) | |||||||
\(90\) | −0.416408 | −0.0438932 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.29180 | −0.864479 | ||||||||
\(93\) | 3.32624 | 0.344915 | ||||||||
\(94\) | 0.854102 | 0.0880939 | ||||||||
\(95\) | 1.85410 | 0.190227 | ||||||||
\(96\) | 1.58359 | 0.161625 | ||||||||
\(97\) | −12.1459 | −1.23323 | −0.616615 | − | 0.787265i | \(-0.711496\pi\) | ||||
−0.616615 | + | 0.787265i | \(0.711496\pi\) | |||||||
\(98\) | −0.381966 | −0.0385844 | ||||||||
\(99\) | −13.8541 | −1.39239 | ||||||||
\(100\) | 9.00000 | 0.900000 | ||||||||
\(101\) | 8.56231 | 0.851981 | 0.425991 | − | 0.904728i | \(-0.359926\pi\) | ||||
0.425991 | + | 0.904728i | \(0.359926\pi\) | |||||||
\(102\) | 1.09017 | 0.107943 | ||||||||
\(103\) | 4.70820 | 0.463913 | 0.231957 | − | 0.972726i | \(-0.425487\pi\) | ||||
0.231957 | + | 0.972726i | \(0.425487\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.145898 | −0.0142382 | ||||||||
\(106\) | −3.14590 | −0.305557 | ||||||||
\(107\) | −5.61803 | −0.543116 | −0.271558 | − | 0.962422i | \(-0.587539\pi\) | ||||
−0.271558 | + | 0.962422i | \(0.587539\pi\) | |||||||
\(108\) | −4.14590 | −0.398939 | ||||||||
\(109\) | −10.7082 | −1.02566 | −0.512830 | − | 0.858490i | \(-0.671403\pi\) | ||||
−0.512830 | + | 0.858490i | \(0.671403\pi\) | |||||||
\(110\) | 0.708204 | 0.0675246 | ||||||||
\(111\) | 1.52786 | 0.145018 | ||||||||
\(112\) | −3.14590 | −0.297259 | ||||||||
\(113\) | −7.47214 | −0.702919 | −0.351460 | − | 0.936203i | \(-0.614315\pi\) | ||||
−0.351460 | + | 0.936203i | \(0.614315\pi\) | |||||||
\(114\) | −0.708204 | −0.0663294 | ||||||||
\(115\) | −1.70820 | −0.159291 | ||||||||
\(116\) | 7.58359 | 0.704119 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.854102 | 0.0786265 | ||||||||
\(119\) | −7.47214 | −0.684970 | ||||||||
\(120\) | 0.214782 | 0.0196068 | ||||||||
\(121\) | 12.5623 | 1.14203 | ||||||||
\(122\) | 2.29180 | 0.207489 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 16.1459 | 1.44994 | ||||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | −1.09017 | −0.0971201 | ||||||||
\(127\) | −14.1459 | −1.25525 | −0.627623 | − | 0.778518i | \(-0.715972\pi\) | ||||
−0.627623 | + | 0.778518i | \(0.715972\pi\) | |||||||
\(128\) | 10.0902 | 0.891853 | ||||||||
\(129\) | 2.88854 | 0.254322 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.326238 | 0.0285035 | 0.0142518 | − | 0.999898i | \(-0.495463\pi\) | ||||
0.0142518 | + | 0.999898i | \(0.495463\pi\) | |||||||
\(132\) | 3.43769 | 0.299213 | ||||||||
\(133\) | 4.85410 | 0.420904 | ||||||||
\(134\) | 0.270510 | 0.0233685 | ||||||||
\(135\) | −0.854102 | −0.0735094 | ||||||||
\(136\) | 11.0000 | 0.943242 | ||||||||
\(137\) | 0.381966 | 0.0326336 | 0.0163168 | − | 0.999867i | \(-0.494806\pi\) | ||||
0.0163168 | + | 0.999867i | \(0.494806\pi\) | |||||||
\(138\) | 0.652476 | 0.0555424 | ||||||||
\(139\) | −15.5623 | −1.31998 | −0.659989 | − | 0.751275i | \(-0.729439\pi\) | ||||
−0.659989 | + | 0.751275i | \(0.729439\pi\) | |||||||
\(140\) | −0.708204 | −0.0598542 | ||||||||
\(141\) | 0.854102 | 0.0719284 | ||||||||
\(142\) | 3.12461 | 0.262212 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −8.97871 | −0.748226 | ||||||||
\(145\) | 1.56231 | 0.129742 | ||||||||
\(146\) | −0.763932 | −0.0632235 | ||||||||
\(147\) | −0.381966 | −0.0315040 | ||||||||
\(148\) | 7.41641 | 0.609625 | ||||||||
\(149\) | 4.85410 | 0.397664 | 0.198832 | − | 0.980034i | \(-0.436285\pi\) | ||||
0.198832 | + | 0.980034i | \(0.436285\pi\) | |||||||
\(150\) | −0.708204 | −0.0578246 | ||||||||
\(151\) | 14.7082 | 1.19694 | 0.598468 | − | 0.801146i | \(-0.295776\pi\) | ||||
0.598468 | + | 0.801146i | \(0.295776\pi\) | |||||||
\(152\) | −7.14590 | −0.579609 | ||||||||
\(153\) | −21.3262 | −1.72412 | ||||||||
\(154\) | 1.85410 | 0.149408 | ||||||||
\(155\) | 3.32624 | 0.267170 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.14590 | 0.650113 | 0.325057 | − | 0.945695i | \(-0.394617\pi\) | ||||
0.325057 | + | 0.945695i | \(0.394617\pi\) | |||||||
\(158\) | −1.52786 | −0.121550 | ||||||||
\(159\) | −3.14590 | −0.249486 | ||||||||
\(160\) | 1.58359 | 0.125194 | ||||||||
\(161\) | −4.47214 | −0.352454 | ||||||||
\(162\) | −2.94427 | −0.231324 | ||||||||
\(163\) | −9.70820 | −0.760405 | −0.380203 | − | 0.924903i | \(-0.624146\pi\) | ||||
−0.380203 | + | 0.924903i | \(0.624146\pi\) | |||||||
\(164\) | 9.70820 | 0.758083 | ||||||||
\(165\) | 0.708204 | 0.0551336 | ||||||||
\(166\) | −2.56231 | −0.198874 | ||||||||
\(167\) | −9.76393 | −0.755556 | −0.377778 | − | 0.925896i | \(-0.623312\pi\) | ||||
−0.377778 | + | 0.925896i | \(0.623312\pi\) | |||||||
\(168\) | 0.562306 | 0.0433828 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.09017 | 0.0836122 | ||||||||
\(171\) | 13.8541 | 1.05945 | ||||||||
\(172\) | 14.0213 | 1.06911 | ||||||||
\(173\) | −9.00000 | −0.684257 | −0.342129 | − | 0.939653i | \(-0.611148\pi\) | ||||
−0.342129 | + | 0.939653i | \(0.611148\pi\) | |||||||
\(174\) | −0.596748 | −0.0452393 | ||||||||
\(175\) | 4.85410 | 0.366936 | ||||||||
\(176\) | 15.2705 | 1.15106 | ||||||||
\(177\) | 0.854102 | 0.0641982 | ||||||||
\(178\) | 6.14590 | 0.460655 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | −2.02129 | −0.150658 | ||||||||
\(181\) | −3.70820 | −0.275629 | −0.137814 | − | 0.990458i | \(-0.544008\pi\) | ||||
−0.137814 | + | 0.990458i | \(0.544008\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.29180 | 0.169414 | ||||||||
\(184\) | 6.58359 | 0.485349 | ||||||||
\(185\) | 1.52786 | 0.112331 | ||||||||
\(186\) | −1.27051 | −0.0931583 | ||||||||
\(187\) | 36.2705 | 2.65236 | ||||||||
\(188\) | 4.14590 | 0.302371 | ||||||||
\(189\) | −2.23607 | −0.162650 | ||||||||
\(190\) | −0.708204 | −0.0513785 | ||||||||
\(191\) | 23.6180 | 1.70894 | 0.854470 | − | 0.519500i | \(-0.173882\pi\) | ||||
0.854470 | + | 0.519500i | \(0.173882\pi\) | |||||||
\(192\) | 1.79837 | 0.129786 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 4.63932 | 0.333084 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.85410 | −0.132436 | ||||||||
\(197\) | −7.79837 | −0.555611 | −0.277806 | − | 0.960637i | \(-0.589607\pi\) | ||||
−0.277806 | + | 0.960637i | \(0.589607\pi\) | |||||||
\(198\) | 5.29180 | 0.376072 | ||||||||
\(199\) | 2.41641 | 0.171295 | 0.0856473 | − | 0.996326i | \(-0.472704\pi\) | ||||
0.0856473 | + | 0.996326i | \(0.472704\pi\) | |||||||
\(200\) | −7.14590 | −0.505291 | ||||||||
\(201\) | 0.270510 | 0.0190803 | ||||||||
\(202\) | −3.27051 | −0.230112 | ||||||||
\(203\) | 4.09017 | 0.287074 | ||||||||
\(204\) | 5.29180 | 0.370500 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | −1.79837 | −0.125299 | ||||||||
\(207\) | −12.7639 | −0.887155 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.5623 | −1.62984 | ||||||||
\(210\) | 0.0557281 | 0.00384560 | ||||||||
\(211\) | −8.70820 | −0.599497 | −0.299749 | − | 0.954018i | \(-0.596903\pi\) | ||||
−0.299749 | + | 0.954018i | \(0.596903\pi\) | |||||||
\(212\) | −15.2705 | −1.04878 | ||||||||
\(213\) | 3.12461 | 0.214095 | ||||||||
\(214\) | 2.14590 | 0.146691 | ||||||||
\(215\) | 2.88854 | 0.196997 | ||||||||
\(216\) | 3.29180 | 0.223978 | ||||||||
\(217\) | 8.70820 | 0.591151 | ||||||||
\(218\) | 4.09017 | 0.277021 | ||||||||
\(219\) | −0.763932 | −0.0516217 | ||||||||
\(220\) | 3.43769 | 0.231769 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.583592 | −0.0391681 | ||||||||
\(223\) | 13.2705 | 0.888659 | 0.444330 | − | 0.895863i | \(-0.353442\pi\) | ||||
0.444330 | + | 0.895863i | \(0.353442\pi\) | |||||||
\(224\) | 4.14590 | 0.277009 | ||||||||
\(225\) | 13.8541 | 0.923607 | ||||||||
\(226\) | 2.85410 | 0.189852 | ||||||||
\(227\) | 7.47214 | 0.495943 | 0.247972 | − | 0.968767i | \(-0.420236\pi\) | ||||
0.247972 | + | 0.968767i | \(0.420236\pi\) | |||||||
\(228\) | −3.43769 | −0.227667 | ||||||||
\(229\) | −27.1246 | −1.79244 | −0.896222 | − | 0.443605i | \(-0.853699\pi\) | ||||
−0.896222 | + | 0.443605i | \(0.853699\pi\) | |||||||
\(230\) | 0.652476 | 0.0430230 | ||||||||
\(231\) | 1.85410 | 0.121991 | ||||||||
\(232\) | −6.02129 | −0.395317 | ||||||||
\(233\) | 0.381966 | 0.0250234 | 0.0125117 | − | 0.999922i | \(-0.496017\pi\) | ||||
0.0125117 | + | 0.999922i | \(0.496017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.854102 | 0.0557155 | ||||||||
\(236\) | 4.14590 | 0.269875 | ||||||||
\(237\) | −1.52786 | −0.0992454 | ||||||||
\(238\) | 2.85410 | 0.185004 | ||||||||
\(239\) | 11.2918 | 0.730406 | 0.365203 | − | 0.930928i | \(-0.381000\pi\) | ||||
0.365203 | + | 0.930928i | \(0.381000\pi\) | |||||||
\(240\) | 0.458980 | 0.0296271 | ||||||||
\(241\) | −4.43769 | −0.285857 | −0.142929 | − | 0.989733i | \(-0.545652\pi\) | ||||
−0.142929 | + | 0.989733i | \(0.545652\pi\) | |||||||
\(242\) | −4.79837 | −0.308451 | ||||||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | 11.1246 | 0.712180 | ||||||||
\(245\) | −0.381966 | −0.0244029 | ||||||||
\(246\) | −0.763932 | −0.0487065 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −12.8197 | −0.814049 | ||||||||
\(249\) | −2.56231 | −0.162380 | ||||||||
\(250\) | −1.43769 | −0.0909278 | ||||||||
\(251\) | 5.23607 | 0.330498 | 0.165249 | − | 0.986252i | \(-0.447157\pi\) | ||||
0.165249 | + | 0.986252i | \(0.447157\pi\) | |||||||
\(252\) | −5.29180 | −0.333352 | ||||||||
\(253\) | 21.7082 | 1.36478 | ||||||||
\(254\) | 5.40325 | 0.339030 | ||||||||
\(255\) | 1.09017 | 0.0682691 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | −25.7426 | −1.60578 | −0.802891 | − | 0.596126i | \(-0.796706\pi\) | ||||
−0.802891 | + | 0.596126i | \(0.796706\pi\) | |||||||
\(258\) | −1.10333 | −0.0686900 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.6738 | 0.722588 | ||||||||
\(262\) | −0.124612 | −0.00769854 | ||||||||
\(263\) | 9.00000 | 0.554964 | 0.277482 | − | 0.960731i | \(-0.410500\pi\) | ||||
0.277482 | + | 0.960731i | \(0.410500\pi\) | |||||||
\(264\) | −2.72949 | −0.167989 | ||||||||
\(265\) | −3.14590 | −0.193251 | ||||||||
\(266\) | −1.85410 | −0.113682 | ||||||||
\(267\) | 6.14590 | 0.376123 | ||||||||
\(268\) | 1.31308 | 0.0802093 | ||||||||
\(269\) | 13.7426 | 0.837904 | 0.418952 | − | 0.908008i | \(-0.362398\pi\) | ||||
0.418952 | + | 0.908008i | \(0.362398\pi\) | |||||||
\(270\) | 0.326238 | 0.0198542 | ||||||||
\(271\) | −18.4164 | −1.11872 | −0.559359 | − | 0.828926i | \(-0.688952\pi\) | ||||
−0.559359 | + | 0.828926i | \(0.688952\pi\) | |||||||
\(272\) | 23.5066 | 1.42530 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.145898 | −0.00881402 | ||||||||
\(275\) | −23.5623 | −1.42086 | ||||||||
\(276\) | 3.16718 | 0.190642 | ||||||||
\(277\) | −5.00000 | −0.300421 | −0.150210 | − | 0.988654i | \(-0.547995\pi\) | ||||
−0.150210 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(278\) | 5.94427 | 0.356514 | ||||||||
\(279\) | 24.8541 | 1.48798 | ||||||||
\(280\) | 0.562306 | 0.0336042 | ||||||||
\(281\) | 2.18034 | 0.130068 | 0.0650341 | − | 0.997883i | \(-0.479284\pi\) | ||||
0.0650341 | + | 0.997883i | \(0.479284\pi\) | |||||||
\(282\) | −0.326238 | −0.0194272 | ||||||||
\(283\) | −13.4164 | −0.797523 | −0.398761 | − | 0.917055i | \(-0.630560\pi\) | ||||
−0.398761 | + | 0.917055i | \(0.630560\pi\) | |||||||
\(284\) | 15.1672 | 0.900007 | ||||||||
\(285\) | −0.708204 | −0.0419504 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.23607 | 0.309075 | ||||||||
\(288\) | 11.8328 | 0.697255 | ||||||||
\(289\) | 38.8328 | 2.28428 | ||||||||
\(290\) | −0.596748 | −0.0350422 | ||||||||
\(291\) | 4.63932 | 0.271962 | ||||||||
\(292\) | −3.70820 | −0.217006 | ||||||||
\(293\) | 11.2361 | 0.656418 | 0.328209 | − | 0.944605i | \(-0.393555\pi\) | ||||
0.328209 | + | 0.944605i | \(0.393555\pi\) | |||||||
\(294\) | 0.145898 | 0.00850895 | ||||||||
\(295\) | 0.854102 | 0.0497277 | ||||||||
\(296\) | −5.88854 | −0.342265 | ||||||||
\(297\) | 10.8541 | 0.629819 | ||||||||
\(298\) | −1.85410 | −0.107405 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.43769 | −0.198475 | ||||||||
\(301\) | 7.56231 | 0.435884 | ||||||||
\(302\) | −5.61803 | −0.323282 | ||||||||
\(303\) | −3.27051 | −0.187886 | ||||||||
\(304\) | −15.2705 | −0.875824 | ||||||||
\(305\) | 2.29180 | 0.131228 | ||||||||
\(306\) | 8.14590 | 0.465670 | ||||||||
\(307\) | −1.85410 | −0.105819 | −0.0529096 | − | 0.998599i | \(-0.516850\pi\) | ||||
−0.0529096 | + | 0.998599i | \(0.516850\pi\) | |||||||
\(308\) | 9.00000 | 0.512823 | ||||||||
\(309\) | −1.79837 | −0.102306 | ||||||||
\(310\) | −1.27051 | −0.0721601 | ||||||||
\(311\) | −12.3262 | −0.698957 | −0.349478 | − | 0.936944i | \(-0.613641\pi\) | ||||
−0.349478 | + | 0.936944i | \(0.613641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.1246 | −0.854894 | −0.427447 | − | 0.904041i | \(-0.640587\pi\) | ||||
−0.427447 | + | 0.904041i | \(0.640587\pi\) | |||||||
\(314\) | −3.11146 | −0.175590 | ||||||||
\(315\) | −1.09017 | −0.0614241 | ||||||||
\(316\) | −7.41641 | −0.417206 | ||||||||
\(317\) | −21.7639 | −1.22238 | −0.611192 | − | 0.791482i | \(-0.709310\pi\) | ||||
−0.611192 | + | 0.791482i | \(0.709310\pi\) | |||||||
\(318\) | 1.20163 | 0.0673838 | ||||||||
\(319\) | −19.8541 | −1.11162 | ||||||||
\(320\) | 1.79837 | 0.100532 | ||||||||
\(321\) | 2.14590 | 0.119772 | ||||||||
\(322\) | 1.70820 | 0.0951945 | ||||||||
\(323\) | −36.2705 | −2.01815 | ||||||||
\(324\) | −14.2918 | −0.793989 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.70820 | 0.205378 | ||||||||
\(327\) | 4.09017 | 0.226187 | ||||||||
\(328\) | −7.70820 | −0.425614 | ||||||||
\(329\) | 2.23607 | 0.123278 | ||||||||
\(330\) | −0.270510 | −0.0148911 | ||||||||
\(331\) | 16.8541 | 0.926385 | 0.463193 | − | 0.886258i | \(-0.346704\pi\) | ||||
0.463193 | + | 0.886258i | \(0.346704\pi\) | |||||||
\(332\) | −12.4377 | −0.682607 | ||||||||
\(333\) | 11.4164 | 0.625615 | ||||||||
\(334\) | 3.72949 | 0.204069 | ||||||||
\(335\) | 0.270510 | 0.0147795 | ||||||||
\(336\) | 1.20163 | 0.0655541 | ||||||||
\(337\) | 8.56231 | 0.466419 | 0.233209 | − | 0.972427i | \(-0.425077\pi\) | ||||
0.233209 | + | 0.972427i | \(0.425077\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.85410 | 0.155014 | ||||||||
\(340\) | 5.29180 | 0.286988 | ||||||||
\(341\) | −42.2705 | −2.28908 | ||||||||
\(342\) | −5.29180 | −0.286148 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −11.1327 | −0.600237 | ||||||||
\(345\) | 0.652476 | 0.0351281 | ||||||||
\(346\) | 3.43769 | 0.184812 | ||||||||
\(347\) | 35.2361 | 1.89157 | 0.945786 | − | 0.324792i | \(-0.105294\pi\) | ||||
0.945786 | + | 0.324792i | \(0.105294\pi\) | |||||||
\(348\) | −2.89667 | −0.155278 | ||||||||
\(349\) | −7.29180 | −0.390321 | −0.195160 | − | 0.980771i | \(-0.562523\pi\) | ||||
−0.195160 | + | 0.980771i | \(0.562523\pi\) | |||||||
\(350\) | −1.85410 | −0.0991059 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.1246 | −1.07265 | ||||||||
\(353\) | −28.8541 | −1.53575 | −0.767874 | − | 0.640600i | \(-0.778686\pi\) | ||||
−0.767874 | + | 0.640600i | \(0.778686\pi\) | |||||||
\(354\) | −0.326238 | −0.0173393 | ||||||||
\(355\) | 3.12461 | 0.165837 | ||||||||
\(356\) | 29.8328 | 1.58114 | ||||||||
\(357\) | 2.85410 | 0.151055 | ||||||||
\(358\) | 3.43769 | 0.181688 | ||||||||
\(359\) | 10.9098 | 0.575799 | 0.287899 | − | 0.957661i | \(-0.407043\pi\) | ||||
0.287899 | + | 0.957661i | \(0.407043\pi\) | |||||||
\(360\) | 1.60488 | 0.0845845 | ||||||||
\(361\) | 4.56231 | 0.240121 | ||||||||
\(362\) | 1.41641 | 0.0744447 | ||||||||
\(363\) | −4.79837 | −0.251849 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.763932 | −0.0399860 | ||||||||
\(366\) | −0.875388 | −0.0457573 | ||||||||
\(367\) | 25.4164 | 1.32673 | 0.663363 | − | 0.748298i | \(-0.269129\pi\) | ||||
0.663363 | + | 0.748298i | \(0.269129\pi\) | |||||||
\(368\) | 14.0689 | 0.733391 | ||||||||
\(369\) | 14.9443 | 0.777968 | ||||||||
\(370\) | −0.583592 | −0.0303395 | ||||||||
\(371\) | −8.23607 | −0.427595 | ||||||||
\(372\) | −6.16718 | −0.319754 | ||||||||
\(373\) | −0.437694 | −0.0226629 | −0.0113315 | − | 0.999936i | \(-0.503607\pi\) | ||||
−0.0113315 | + | 0.999936i | \(0.503607\pi\) | |||||||
\(374\) | −13.8541 | −0.716379 | ||||||||
\(375\) | −1.43769 | −0.0742422 | ||||||||
\(376\) | −3.29180 | −0.169761 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.854102 | 0.0439303 | ||||||||
\(379\) | 12.8541 | 0.660271 | 0.330135 | − | 0.943934i | \(-0.392906\pi\) | ||||
0.330135 | + | 0.943934i | \(0.392906\pi\) | |||||||
\(380\) | −3.43769 | −0.176350 | ||||||||
\(381\) | 5.40325 | 0.276817 | ||||||||
\(382\) | −9.02129 | −0.461569 | ||||||||
\(383\) | −24.9787 | −1.27635 | −0.638176 | − | 0.769890i | \(-0.720311\pi\) | ||||
−0.638176 | + | 0.769890i | \(0.720311\pi\) | |||||||
\(384\) | −3.85410 | −0.196679 | ||||||||
\(385\) | 1.85410 | 0.0944938 | ||||||||
\(386\) | −2.29180 | −0.116649 | ||||||||
\(387\) | 21.5836 | 1.09716 | ||||||||
\(388\) | 22.5197 | 1.14327 | ||||||||
\(389\) | 23.8885 | 1.21120 | 0.605599 | − | 0.795770i | \(-0.292934\pi\) | ||||
0.605599 | + | 0.795770i | \(0.292934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.4164 | 1.68994 | ||||||||
\(392\) | 1.47214 | 0.0743541 | ||||||||
\(393\) | −0.124612 | −0.00628583 | ||||||||
\(394\) | 2.97871 | 0.150065 | ||||||||
\(395\) | −1.52786 | −0.0768752 | ||||||||
\(396\) | 25.6869 | 1.29082 | ||||||||
\(397\) | 25.4164 | 1.27561 | 0.637806 | − | 0.770197i | \(-0.279842\pi\) | ||||
0.637806 | + | 0.770197i | \(0.279842\pi\) | |||||||
\(398\) | −0.922986 | −0.0462651 | ||||||||
\(399\) | −1.85410 | −0.0928212 | ||||||||
\(400\) | −15.2705 | −0.763525 | ||||||||
\(401\) | 20.4508 | 1.02127 | 0.510633 | − | 0.859799i | \(-0.329411\pi\) | ||||
0.510633 | + | 0.859799i | \(0.329411\pi\) | |||||||
\(402\) | −0.103326 | −0.00515341 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −15.8754 | −0.789830 | ||||||||
\(405\) | −2.94427 | −0.146302 | ||||||||
\(406\) | −1.56231 | −0.0775359 | ||||||||
\(407\) | −19.4164 | −0.962436 | ||||||||
\(408\) | −4.20163 | −0.208011 | ||||||||
\(409\) | −34.5623 | −1.70900 | −0.854498 | − | 0.519455i | \(-0.826135\pi\) | ||||
−0.854498 | + | 0.519455i | \(0.826135\pi\) | |||||||
\(410\) | −0.763932 | −0.0377279 | ||||||||
\(411\) | −0.145898 | −0.00719662 | ||||||||
\(412\) | −8.72949 | −0.430071 | ||||||||
\(413\) | 2.23607 | 0.110030 | ||||||||
\(414\) | 4.87539 | 0.239612 | ||||||||
\(415\) | −2.56231 | −0.125779 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.94427 | 0.291092 | ||||||||
\(418\) | 9.00000 | 0.440204 | ||||||||
\(419\) | 5.94427 | 0.290397 | 0.145198 | − | 0.989403i | \(-0.453618\pi\) | ||||
0.145198 | + | 0.989403i | \(0.453618\pi\) | |||||||
\(420\) | 0.270510 | 0.0131995 | ||||||||
\(421\) | 25.4164 | 1.23872 | 0.619360 | − | 0.785107i | \(-0.287392\pi\) | ||||
0.619360 | + | 0.785107i | \(0.287392\pi\) | |||||||
\(422\) | 3.32624 | 0.161919 | ||||||||
\(423\) | 6.38197 | 0.310302 | ||||||||
\(424\) | 12.1246 | 0.588823 | ||||||||
\(425\) | −36.2705 | −1.75938 | ||||||||
\(426\) | −1.19350 | −0.0578250 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | 10.4164 | 0.503496 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.10333 | −0.0532071 | ||||||||
\(431\) | 16.7984 | 0.809149 | 0.404575 | − | 0.914505i | \(-0.367420\pi\) | ||||
0.404575 | + | 0.914505i | \(0.367420\pi\) | |||||||
\(432\) | 7.03444 | 0.338445 | ||||||||
\(433\) | 1.00000 | 0.0480569 | 0.0240285 | − | 0.999711i | \(-0.492351\pi\) | ||||
0.0240285 | + | 0.999711i | \(0.492351\pi\) | |||||||
\(434\) | −3.32624 | −0.159665 | ||||||||
\(435\) | −0.596748 | −0.0286119 | ||||||||
\(436\) | 19.8541 | 0.950839 | ||||||||
\(437\) | −21.7082 | −1.03844 | ||||||||
\(438\) | 0.291796 | 0.0139426 | ||||||||
\(439\) | 8.14590 | 0.388783 | 0.194391 | − | 0.980924i | \(-0.437727\pi\) | ||||
0.194391 | + | 0.980924i | \(0.437727\pi\) | |||||||
\(440\) | −2.72949 | −0.130123 | ||||||||
\(441\) | −2.85410 | −0.135910 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.763932 | −0.0362955 | −0.0181478 | − | 0.999835i | \(-0.505777\pi\) | ||||
−0.0181478 | + | 0.999835i | \(0.505777\pi\) | |||||||
\(444\) | −2.83282 | −0.134439 | ||||||||
\(445\) | 6.14590 | 0.291344 | ||||||||
\(446\) | −5.06888 | −0.240019 | ||||||||
\(447\) | −1.85410 | −0.0876960 | ||||||||
\(448\) | 4.70820 | 0.222442 | ||||||||
\(449\) | −28.4721 | −1.34368 | −0.671842 | − | 0.740695i | \(-0.734496\pi\) | ||||
−0.671842 | + | 0.740695i | \(0.734496\pi\) | |||||||
\(450\) | −5.29180 | −0.249458 | ||||||||
\(451\) | −25.4164 | −1.19681 | ||||||||
\(452\) | 13.8541 | 0.651642 | ||||||||
\(453\) | −5.61803 | −0.263958 | ||||||||
\(454\) | −2.85410 | −0.133950 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.72949 | 0.127820 | ||||||||
\(457\) | 11.4164 | 0.534037 | 0.267019 | − | 0.963691i | \(-0.413962\pi\) | ||||
0.267019 | + | 0.963691i | \(0.413962\pi\) | |||||||
\(458\) | 10.3607 | 0.484123 | ||||||||
\(459\) | 16.7082 | 0.779872 | ||||||||
\(460\) | 3.16718 | 0.147671 | ||||||||
\(461\) | −39.2148 | −1.82641 | −0.913207 | − | 0.407495i | \(-0.866402\pi\) | ||||
−0.913207 | + | 0.407495i | \(0.866402\pi\) | |||||||
\(462\) | −0.708204 | −0.0329486 | ||||||||
\(463\) | 6.70820 | 0.311757 | 0.155878 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155878 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(464\) | −12.8673 | −0.597347 | ||||||||
\(465\) | −1.27051 | −0.0589185 | ||||||||
\(466\) | −0.145898 | −0.00675860 | ||||||||
\(467\) | 33.6525 | 1.55725 | 0.778625 | − | 0.627489i | \(-0.215917\pi\) | ||||
0.778625 | + | 0.627489i | \(0.215917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.708204 | 0.0327018 | ||||||||
\(470\) | −0.326238 | −0.0150482 | ||||||||
\(471\) | −3.11146 | −0.143368 | ||||||||
\(472\) | −3.29180 | −0.151517 | ||||||||
\(473\) | −36.7082 | −1.68785 | ||||||||
\(474\) | 0.583592 | 0.0268053 | ||||||||
\(475\) | 23.5623 | 1.08111 | ||||||||
\(476\) | 13.8541 | 0.635002 | ||||||||
\(477\) | −23.5066 | −1.07629 | ||||||||
\(478\) | −4.31308 | −0.197276 | ||||||||
\(479\) | 21.9787 | 1.00423 | 0.502117 | − | 0.864800i | \(-0.332555\pi\) | ||||
0.502117 | + | 0.864800i | \(0.332555\pi\) | |||||||
\(480\) | −0.604878 | −0.0276088 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.69505 | 0.0772073 | ||||||||
\(483\) | 1.70820 | 0.0777260 | ||||||||
\(484\) | −23.2918 | −1.05872 | ||||||||
\(485\) | 4.63932 | 0.210661 | ||||||||
\(486\) | 3.68692 | 0.167242 | ||||||||
\(487\) | 16.9787 | 0.769379 | 0.384689 | − | 0.923046i | \(-0.374309\pi\) | ||||
0.384689 | + | 0.923046i | \(0.374309\pi\) | |||||||
\(488\) | −8.83282 | −0.399843 | ||||||||
\(489\) | 3.70820 | 0.167691 | ||||||||
\(490\) | 0.145898 | 0.00659100 | ||||||||
\(491\) | 14.6180 | 0.659703 | 0.329851 | − | 0.944033i | \(-0.393001\pi\) | ||||
0.329851 | + | 0.944033i | \(0.393001\pi\) | |||||||
\(492\) | −3.70820 | −0.167179 | ||||||||
\(493\) | −30.5623 | −1.37646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.29180 | 0.237849 | ||||||||
\(496\) | −27.3951 | −1.23008 | ||||||||
\(497\) | 8.18034 | 0.366938 | ||||||||
\(498\) | 0.978714 | 0.0438572 | ||||||||
\(499\) | −8.14590 | −0.364660 | −0.182330 | − | 0.983237i | \(-0.558364\pi\) | ||||
−0.182330 | + | 0.983237i | \(0.558364\pi\) | |||||||
\(500\) | −6.97871 | −0.312098 | ||||||||
\(501\) | 3.72949 | 0.166621 | ||||||||
\(502\) | −2.00000 | −0.0892644 | ||||||||
\(503\) | 24.3820 | 1.08714 | 0.543569 | − | 0.839364i | \(-0.317073\pi\) | ||||
0.543569 | + | 0.839364i | \(0.317073\pi\) | |||||||
\(504\) | 4.20163 | 0.187155 | ||||||||
\(505\) | −3.27051 | −0.145536 | ||||||||
\(506\) | −8.29180 | −0.368615 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.2279 | 1.16368 | ||||||||
\(509\) | −30.5967 | −1.35618 | −0.678089 | − | 0.734980i | \(-0.737191\pi\) | ||||
−0.678089 | + | 0.734980i | \(0.737191\pi\) | |||||||
\(510\) | −0.416408 | −0.0184389 | ||||||||
\(511\) | −2.00000 | −0.0884748 | ||||||||
\(512\) | −22.3050 | −0.985749 | ||||||||
\(513\) | −10.8541 | −0.479220 | ||||||||
\(514\) | 9.83282 | 0.433707 | ||||||||
\(515\) | −1.79837 | −0.0792458 | ||||||||
\(516\) | −5.35565 | −0.235770 | ||||||||
\(517\) | −10.8541 | −0.477363 | ||||||||
\(518\) | −1.52786 | −0.0671305 | ||||||||
\(519\) | 3.43769 | 0.150898 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.6525 | −0.554315 | −0.277158 | − | 0.960824i | \(-0.589392\pi\) | ||||
−0.277158 | + | 0.960824i | \(0.589392\pi\) | |||||||
\(522\) | −4.45898 | −0.195164 | ||||||||
\(523\) | −39.1246 | −1.71080 | −0.855400 | − | 0.517968i | \(-0.826689\pi\) | ||||
−0.855400 | + | 0.517968i | \(0.826689\pi\) | |||||||
\(524\) | −0.604878 | −0.0264242 | ||||||||
\(525\) | −1.85410 | −0.0809196 | ||||||||
\(526\) | −3.43769 | −0.149891 | ||||||||
\(527\) | −65.0689 | −2.83445 | ||||||||
\(528\) | −5.83282 | −0.253841 | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | 1.20163 | 0.0521953 | ||||||||
\(531\) | 6.38197 | 0.276954 | ||||||||
\(532\) | −9.00000 | −0.390199 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.34752 | −0.101587 | ||||||||
\(535\) | 2.14590 | 0.0927753 | ||||||||
\(536\) | −1.04257 | −0.0450323 | ||||||||
\(537\) | 3.43769 | 0.148347 | ||||||||
\(538\) | −5.24922 | −0.226310 | ||||||||
\(539\) | 4.85410 | 0.209081 | ||||||||
\(540\) | 1.58359 | 0.0681470 | ||||||||
\(541\) | −1.72949 | −0.0743566 | −0.0371783 | − | 0.999309i | \(-0.511837\pi\) | ||||
−0.0371783 | + | 0.999309i | \(0.511837\pi\) | |||||||
\(542\) | 7.03444 | 0.302155 | ||||||||
\(543\) | 1.41641 | 0.0607839 | ||||||||
\(544\) | −30.9787 | −1.32820 | ||||||||
\(545\) | 4.09017 | 0.175204 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.00000 | −0.128271 | −0.0641354 | − | 0.997941i | \(-0.520429\pi\) | ||||
−0.0641354 | + | 0.997941i | \(0.520429\pi\) | |||||||
\(548\) | −0.708204 | −0.0302530 | ||||||||
\(549\) | 17.1246 | 0.730861 | ||||||||
\(550\) | 9.00000 | 0.383761 | ||||||||
\(551\) | 19.8541 | 0.845813 | ||||||||
\(552\) | −2.51471 | −0.107033 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 1.90983 | 0.0811409 | ||||||||
\(555\) | −0.583592 | −0.0247721 | ||||||||
\(556\) | 28.8541 | 1.22369 | ||||||||
\(557\) | −18.9787 | −0.804154 | −0.402077 | − | 0.915606i | \(-0.631712\pi\) | ||||
−0.402077 | + | 0.915606i | \(0.631712\pi\) | |||||||
\(558\) | −9.49342 | −0.401889 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.20163 | 0.0507780 | ||||||||
\(561\) | −13.8541 | −0.584921 | ||||||||
\(562\) | −0.832816 | −0.0351302 | ||||||||
\(563\) | −38.9443 | −1.64131 | −0.820653 | − | 0.571427i | \(-0.806390\pi\) | ||||
−0.820653 | + | 0.571427i | \(0.806390\pi\) | |||||||
\(564\) | −1.58359 | −0.0666813 | ||||||||
\(565\) | 2.85410 | 0.120073 | ||||||||
\(566\) | 5.12461 | 0.215404 | ||||||||
\(567\) | −7.70820 | −0.323714 | ||||||||
\(568\) | −12.0426 | −0.505295 | ||||||||
\(569\) | −2.94427 | −0.123430 | −0.0617151 | − | 0.998094i | \(-0.519657\pi\) | ||||
−0.0617151 | + | 0.998094i | \(0.519657\pi\) | |||||||
\(570\) | 0.270510 | 0.0113304 | ||||||||
\(571\) | −35.6869 | −1.49345 | −0.746726 | − | 0.665132i | \(-0.768375\pi\) | ||||
−0.746726 | + | 0.665132i | \(0.768375\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.02129 | −0.376870 | ||||||||
\(574\) | −2.00000 | −0.0834784 | ||||||||
\(575\) | −21.7082 | −0.905295 | ||||||||
\(576\) | 13.4377 | 0.559904 | ||||||||
\(577\) | −9.83282 | −0.409345 | −0.204673 | − | 0.978830i | \(-0.565613\pi\) | ||||
−0.204673 | + | 0.978830i | \(0.565613\pi\) | |||||||
\(578\) | −14.8328 | −0.616964 | ||||||||
\(579\) | −2.29180 | −0.0952438 | ||||||||
\(580\) | −2.89667 | −0.120278 | ||||||||
\(581\) | −6.70820 | −0.278303 | ||||||||
\(582\) | −1.77206 | −0.0734544 | ||||||||
\(583\) | 39.9787 | 1.65575 | ||||||||
\(584\) | 2.94427 | 0.121835 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.29180 | −0.177292 | ||||||||
\(587\) | 31.0902 | 1.28323 | 0.641614 | − | 0.767027i | \(-0.278265\pi\) | ||||
0.641614 | + | 0.767027i | \(0.278265\pi\) | |||||||
\(588\) | 0.708204 | 0.0292058 | ||||||||
\(589\) | 42.2705 | 1.74173 | ||||||||
\(590\) | −0.326238 | −0.0134310 | ||||||||
\(591\) | 2.97871 | 0.122528 | ||||||||
\(592\) | −12.5836 | −0.517182 | ||||||||
\(593\) | −19.2016 | −0.788516 | −0.394258 | − | 0.919000i | \(-0.628998\pi\) | ||||
−0.394258 | + | 0.919000i | \(0.628998\pi\) | |||||||
\(594\) | −4.14590 | −0.170108 | ||||||||
\(595\) | 2.85410 | 0.117007 | ||||||||
\(596\) | −9.00000 | −0.368654 | ||||||||
\(597\) | −0.922986 | −0.0377753 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.50658 | −0.347569 | −0.173785 | − | 0.984784i | \(-0.555600\pi\) | ||||
−0.173785 | + | 0.984784i | \(0.555600\pi\) | |||||||
\(600\) | 2.72949 | 0.111431 | ||||||||
\(601\) | −33.3951 | −1.36222 | −0.681108 | − | 0.732183i | \(-0.738501\pi\) | ||||
−0.681108 | + | 0.732183i | \(0.738501\pi\) | |||||||
\(602\) | −2.88854 | −0.117728 | ||||||||
\(603\) | 2.02129 | 0.0823131 | ||||||||
\(604\) | −27.2705 | −1.10962 | ||||||||
\(605\) | −4.79837 | −0.195082 | ||||||||
\(606\) | 1.24922 | 0.0507462 | ||||||||
\(607\) | −23.0000 | −0.933541 | −0.466771 | − | 0.884378i | \(-0.654583\pi\) | ||||
−0.466771 | + | 0.884378i | \(0.654583\pi\) | |||||||
\(608\) | 20.1246 | 0.816161 | ||||||||
\(609\) | −1.56231 | −0.0633078 | ||||||||
\(610\) | −0.875388 | −0.0354434 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 39.5410 | 1.59835 | ||||||||
\(613\) | −14.4377 | −0.583133 | −0.291566 | − | 0.956551i | \(-0.594176\pi\) | ||||
−0.291566 | + | 0.956551i | \(0.594176\pi\) | |||||||
\(614\) | 0.708204 | 0.0285808 | ||||||||
\(615\) | −0.763932 | −0.0308047 | ||||||||
\(616\) | −7.14590 | −0.287916 | ||||||||
\(617\) | −17.9443 | −0.722409 | −0.361205 | − | 0.932487i | \(-0.617634\pi\) | ||||
−0.361205 | + | 0.932487i | \(0.617634\pi\) | |||||||
\(618\) | 0.686918 | 0.0276319 | ||||||||
\(619\) | 17.4164 | 0.700025 | 0.350012 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350012 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(620\) | −6.16718 | −0.247680 | ||||||||
\(621\) | 10.0000 | 0.401286 | ||||||||
\(622\) | 4.70820 | 0.188782 | ||||||||
\(623\) | 16.0902 | 0.644639 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 5.77709 | 0.230899 | ||||||||
\(627\) | 9.00000 | 0.359425 | ||||||||
\(628\) | −15.1033 | −0.602688 | ||||||||
\(629\) | −29.8885 | −1.19173 | ||||||||
\(630\) | 0.416408 | 0.0165901 | ||||||||
\(631\) | 39.3951 | 1.56830 | 0.784148 | − | 0.620574i | \(-0.213101\pi\) | ||||
0.784148 | + | 0.620574i | \(0.213101\pi\) | |||||||
\(632\) | 5.88854 | 0.234234 | ||||||||
\(633\) | 3.32624 | 0.132206 | ||||||||
\(634\) | 8.31308 | 0.330155 | ||||||||
\(635\) | 5.40325 | 0.214422 | ||||||||
\(636\) | 5.83282 | 0.231286 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.58359 | 0.300237 | ||||||||
\(639\) | 23.3475 | 0.923614 | ||||||||
\(640\) | −3.85410 | −0.152347 | ||||||||
\(641\) | −9.49342 | −0.374968 | −0.187484 | − | 0.982268i | \(-0.560033\pi\) | ||||
−0.187484 | + | 0.982268i | \(0.560033\pi\) | |||||||
\(642\) | −0.819660 | −0.0323494 | ||||||||
\(643\) | 7.00000 | 0.276053 | 0.138027 | − | 0.990429i | \(-0.455924\pi\) | ||||
0.138027 | + | 0.990429i | \(0.455924\pi\) | |||||||
\(644\) | 8.29180 | 0.326743 | ||||||||
\(645\) | −1.10333 | −0.0434434 | ||||||||
\(646\) | 13.8541 | 0.545082 | ||||||||
\(647\) | 29.2361 | 1.14939 | 0.574694 | − | 0.818368i | \(-0.305121\pi\) | ||||
0.574694 | + | 0.818368i | \(0.305121\pi\) | |||||||
\(648\) | 11.3475 | 0.445773 | ||||||||
\(649\) | −10.8541 | −0.426061 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.32624 | −0.130366 | ||||||||
\(652\) | 18.0000 | 0.704934 | ||||||||
\(653\) | −2.61803 | −0.102452 | −0.0512258 | − | 0.998687i | \(-0.516313\pi\) | ||||
−0.0512258 | + | 0.998687i | \(0.516313\pi\) | |||||||
\(654\) | −1.56231 | −0.0610910 | ||||||||
\(655\) | −0.124612 | −0.00486899 | ||||||||
\(656\) | −16.4721 | −0.643129 | ||||||||
\(657\) | −5.70820 | −0.222698 | ||||||||
\(658\) | −0.854102 | −0.0332964 | ||||||||
\(659\) | 11.8885 | 0.463112 | 0.231556 | − | 0.972822i | \(-0.425618\pi\) | ||||
0.231556 | + | 0.972822i | \(0.425618\pi\) | |||||||
\(660\) | −1.31308 | −0.0511117 | ||||||||
\(661\) | −18.5410 | −0.721162 | −0.360581 | − | 0.932728i | \(-0.617422\pi\) | ||||
−0.360581 | + | 0.932728i | \(0.617422\pi\) | |||||||
\(662\) | −6.43769 | −0.250208 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.87539 | 0.383239 | ||||||||
\(665\) | −1.85410 | −0.0718990 | ||||||||
\(666\) | −4.36068 | −0.168973 | ||||||||
\(667\) | −18.2918 | −0.708261 | ||||||||
\(668\) | 18.1033 | 0.700439 | ||||||||
\(669\) | −5.06888 | −0.195974 | ||||||||
\(670\) | −0.103326 | −0.00399181 | ||||||||
\(671\) | −29.1246 | −1.12434 | ||||||||
\(672\) | −1.58359 | −0.0610884 | ||||||||
\(673\) | 41.2492 | 1.59004 | 0.795020 | − | 0.606583i | \(-0.207460\pi\) | ||||
0.795020 | + | 0.606583i | \(0.207460\pi\) | |||||||
\(674\) | −3.27051 | −0.125975 | ||||||||
\(675\) | −10.8541 | −0.417775 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.25735 | 0.0483240 | 0.0241620 | − | 0.999708i | \(-0.492308\pi\) | ||||
0.0241620 | + | 0.999708i | \(0.492308\pi\) | |||||||
\(678\) | −1.09017 | −0.0418677 | ||||||||
\(679\) | 12.1459 | 0.466117 | ||||||||
\(680\) | −4.20163 | −0.161125 | ||||||||
\(681\) | −2.85410 | −0.109369 | ||||||||
\(682\) | 16.1459 | 0.618258 | ||||||||
\(683\) | 7.47214 | 0.285913 | 0.142957 | − | 0.989729i | \(-0.454339\pi\) | ||||
0.142957 | + | 0.989729i | \(0.454339\pi\) | |||||||
\(684\) | −25.6869 | −0.982164 | ||||||||
\(685\) | −0.145898 | −0.00557448 | ||||||||
\(686\) | 0.381966 | 0.0145835 | ||||||||
\(687\) | 10.3607 | 0.395285 | ||||||||
\(688\) | −23.7902 | −0.906995 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.249224 | −0.00948778 | ||||||||
\(691\) | −0.854102 | −0.0324916 | −0.0162458 | − | 0.999868i | \(-0.505171\pi\) | ||||
−0.0162458 | + | 0.999868i | \(0.505171\pi\) | |||||||
\(692\) | 16.6869 | 0.634341 | ||||||||
\(693\) | 13.8541 | 0.526274 | ||||||||
\(694\) | −13.4590 | −0.510896 | ||||||||
\(695\) | 5.94427 | 0.225479 | ||||||||
\(696\) | 2.29993 | 0.0871785 | ||||||||
\(697\) | −39.1246 | −1.48195 | ||||||||
\(698\) | 2.78522 | 0.105422 | ||||||||
\(699\) | −0.145898 | −0.00551837 | ||||||||
\(700\) | −9.00000 | −0.340168 | ||||||||
\(701\) | 6.76393 | 0.255470 | 0.127735 | − | 0.991808i | \(-0.459229\pi\) | ||||
0.127735 | + | 0.991808i | \(0.459229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.4164 | 0.732304 | ||||||||
\(704\) | −22.8541 | −0.861346 | ||||||||
\(705\) | −0.326238 | −0.0122868 | ||||||||
\(706\) | 11.0213 | 0.414792 | ||||||||
\(707\) | −8.56231 | −0.322019 | ||||||||
\(708\) | −1.58359 | −0.0595150 | ||||||||
\(709\) | −3.43769 | −0.129105 | −0.0645527 | − | 0.997914i | \(-0.520562\pi\) | ||||
−0.0645527 | + | 0.997914i | \(0.520562\pi\) | |||||||
\(710\) | −1.19350 | −0.0447911 | ||||||||
\(711\) | −11.4164 | −0.428149 | ||||||||
\(712\) | −23.6869 | −0.887705 | ||||||||
\(713\) | −38.9443 | −1.45847 | ||||||||
\(714\) | −1.09017 | −0.0407986 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.6869 | 0.623619 | ||||||||
\(717\) | −4.31308 | −0.161075 | ||||||||
\(718\) | −4.16718 | −0.155518 | ||||||||
\(719\) | −32.1246 | −1.19805 | −0.599023 | − | 0.800732i | \(-0.704444\pi\) | ||||
−0.599023 | + | 0.800732i | \(0.704444\pi\) | |||||||
\(720\) | 3.42956 | 0.127812 | ||||||||
\(721\) | −4.70820 | −0.175343 | ||||||||
\(722\) | −1.74265 | −0.0648546 | ||||||||
\(723\) | 1.69505 | 0.0630395 | ||||||||
\(724\) | 6.87539 | 0.255522 | ||||||||
\(725\) | 19.8541 | 0.737363 | ||||||||
\(726\) | 1.83282 | 0.0680222 | ||||||||
\(727\) | −17.2918 | −0.641317 | −0.320659 | − | 0.947195i | \(-0.603904\pi\) | ||||
−0.320659 | + | 0.947195i | \(0.603904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 0.291796 | 0.0107999 | ||||||||
\(731\) | −56.5066 | −2.08997 | ||||||||
\(732\) | −4.24922 | −0.157056 | ||||||||
\(733\) | −1.27051 | −0.0469274 | −0.0234637 | − | 0.999725i | \(-0.507469\pi\) | ||||
−0.0234637 | + | 0.999725i | \(0.507469\pi\) | |||||||
\(734\) | −9.70820 | −0.358336 | ||||||||
\(735\) | 0.145898 | 0.00538153 | ||||||||
\(736\) | −18.5410 | −0.683431 | ||||||||
\(737\) | −3.43769 | −0.126629 | ||||||||
\(738\) | −5.70820 | −0.210122 | ||||||||
\(739\) | 47.1246 | 1.73351 | 0.866753 | − | 0.498737i | \(-0.166203\pi\) | ||||
0.866753 | + | 0.498737i | \(0.166203\pi\) | |||||||
\(740\) | −2.83282 | −0.104136 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.14590 | 0.115490 | ||||||||
\(743\) | −23.6738 | −0.868506 | −0.434253 | − | 0.900791i | \(-0.642988\pi\) | ||||
−0.434253 | + | 0.900791i | \(0.642988\pi\) | |||||||
\(744\) | 4.89667 | 0.179521 | ||||||||
\(745\) | −1.85410 | −0.0679290 | ||||||||
\(746\) | 0.167184 | 0.00612105 | ||||||||
\(747\) | −19.1459 | −0.700512 | ||||||||
\(748\) | −67.2492 | −2.45888 | ||||||||
\(749\) | 5.61803 | 0.205278 | ||||||||
\(750\) | 0.549150 | 0.0200521 | ||||||||
\(751\) | 9.29180 | 0.339062 | 0.169531 | − | 0.985525i | \(-0.445775\pi\) | ||||
0.169531 | + | 0.985525i | \(0.445775\pi\) | |||||||
\(752\) | −7.03444 | −0.256520 | ||||||||
\(753\) | −2.00000 | −0.0728841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.61803 | −0.204461 | ||||||||
\(756\) | 4.14590 | 0.150785 | ||||||||
\(757\) | 28.0000 | 1.01768 | 0.508839 | − | 0.860862i | \(-0.330075\pi\) | ||||
0.508839 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(758\) | −4.90983 | −0.178333 | ||||||||
\(759\) | −8.29180 | −0.300973 | ||||||||
\(760\) | 2.72949 | 0.0990090 | ||||||||
\(761\) | 22.1459 | 0.802788 | 0.401394 | − | 0.915905i | \(-0.368526\pi\) | ||||
0.401394 | + | 0.915905i | \(0.368526\pi\) | |||||||
\(762\) | −2.06386 | −0.0747657 | ||||||||
\(763\) | 10.7082 | 0.387663 | ||||||||
\(764\) | −43.7902 | −1.58428 | ||||||||
\(765\) | 8.14590 | 0.294516 | ||||||||
\(766\) | 9.54102 | 0.344731 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.12461 | −0.0766653 | ||||||||
\(769\) | −8.41641 | −0.303503 | −0.151752 | − | 0.988419i | \(-0.548491\pi\) | ||||
−0.151752 | + | 0.988419i | \(0.548491\pi\) | |||||||
\(770\) | −0.708204 | −0.0255219 | ||||||||
\(771\) | 9.83282 | 0.354120 | ||||||||
\(772\) | −11.1246 | −0.400384 | ||||||||
\(773\) | 19.3607 | 0.696355 | 0.348178 | − | 0.937429i | \(-0.386801\pi\) | ||||
0.348178 | + | 0.937429i | \(0.386801\pi\) | |||||||
\(774\) | −8.24420 | −0.296332 | ||||||||
\(775\) | 42.2705 | 1.51840 | ||||||||
\(776\) | −17.8804 | −0.641869 | ||||||||
\(777\) | −1.52786 | −0.0548118 | ||||||||
\(778\) | −9.12461 | −0.327133 | ||||||||
\(779\) | 25.4164 | 0.910637 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.7082 | −1.42087 | ||||||||
\(782\) | −12.7639 | −0.456437 | ||||||||
\(783\) | −9.14590 | −0.326848 | ||||||||
\(784\) | 3.14590 | 0.112354 | ||||||||
\(785\) | −3.11146 | −0.111053 | ||||||||
\(786\) | 0.0475975 | 0.00169775 | ||||||||
\(787\) | −29.4164 | −1.04858 | −0.524291 | − | 0.851539i | \(-0.675670\pi\) | ||||
−0.524291 | + | 0.851539i | \(0.675670\pi\) | |||||||
\(788\) | 14.4590 | 0.515080 | ||||||||
\(789\) | −3.43769 | −0.122385 | ||||||||
\(790\) | 0.583592 | 0.0207633 | ||||||||
\(791\) | 7.47214 | 0.265679 | ||||||||
\(792\) | −20.3951 | −0.724709 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9.70820 | −0.344531 | ||||||||
\(795\) | 1.20163 | 0.0426173 | ||||||||
\(796\) | −4.48027 | −0.158799 | ||||||||
\(797\) | 14.1803 | 0.502293 | 0.251147 | − | 0.967949i | \(-0.419192\pi\) | ||||
0.251147 | + | 0.967949i | \(0.419192\pi\) | |||||||
\(798\) | 0.708204 | 0.0250701 | ||||||||
\(799\) | −16.7082 | −0.591094 | ||||||||
\(800\) | 20.1246 | 0.711512 | ||||||||
\(801\) | 45.9230 | 1.62261 | ||||||||
\(802\) | −7.81153 | −0.275835 | ||||||||
\(803\) | 9.70820 | 0.342595 | ||||||||
\(804\) | −0.501553 | −0.0176884 | ||||||||
\(805\) | 1.70820 | 0.0602063 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.24922 | −0.184781 | ||||||||
\(808\) | 12.6049 | 0.443438 | ||||||||
\(809\) | 22.4164 | 0.788119 | 0.394059 | − | 0.919085i | \(-0.371070\pi\) | ||||
0.394059 | + | 0.919085i | \(0.371070\pi\) | |||||||
\(810\) | 1.12461 | 0.0395148 | ||||||||
\(811\) | −5.72949 | −0.201190 | −0.100595 | − | 0.994927i | \(-0.532075\pi\) | ||||
−0.100595 | + | 0.994927i | \(0.532075\pi\) | |||||||
\(812\) | −7.58359 | −0.266132 | ||||||||
\(813\) | 7.03444 | 0.246709 | ||||||||
\(814\) | 7.41641 | 0.259945 | ||||||||
\(815\) | 3.70820 | 0.129893 | ||||||||
\(816\) | −8.97871 | −0.314318 | ||||||||
\(817\) | 36.7082 | 1.28426 | ||||||||
\(818\) | 13.2016 | 0.461584 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.70820 | −0.129496 | ||||||||
\(821\) | −37.3607 | −1.30390 | −0.651948 | − | 0.758263i | \(-0.726048\pi\) | ||||
−0.651948 | + | 0.758263i | \(0.726048\pi\) | |||||||
\(822\) | 0.0557281 | 0.00194374 | ||||||||
\(823\) | −11.5836 | −0.403779 | −0.201889 | − | 0.979408i | \(-0.564708\pi\) | ||||
−0.201889 | + | 0.979408i | \(0.564708\pi\) | |||||||
\(824\) | 6.93112 | 0.241457 | ||||||||
\(825\) | 9.00000 | 0.313340 | ||||||||
\(826\) | −0.854102 | −0.0297180 | ||||||||
\(827\) | 30.9787 | 1.07724 | 0.538618 | − | 0.842550i | \(-0.318947\pi\) | ||||
0.538618 | + | 0.842550i | \(0.318947\pi\) | |||||||
\(828\) | 23.6656 | 0.822438 | ||||||||
\(829\) | −12.5623 | −0.436307 | −0.218153 | − | 0.975914i | \(-0.570003\pi\) | ||||
−0.218153 | + | 0.975914i | \(0.570003\pi\) | |||||||
\(830\) | 0.978714 | 0.0339717 | ||||||||
\(831\) | 1.90983 | 0.0662513 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.47214 | 0.258894 | ||||||||
\(834\) | −2.27051 | −0.0786213 | ||||||||
\(835\) | 3.72949 | 0.129064 | ||||||||
\(836\) | 43.6869 | 1.51094 | ||||||||
\(837\) | −19.4721 | −0.673055 | ||||||||
\(838\) | −2.27051 | −0.0784335 | ||||||||
\(839\) | 28.7426 | 0.992306 | 0.496153 | − | 0.868235i | \(-0.334745\pi\) | ||||
0.496153 | + | 0.868235i | \(0.334745\pi\) | |||||||
\(840\) | −0.214782 | −0.00741067 | ||||||||
\(841\) | −12.2705 | −0.423121 | ||||||||
\(842\) | −9.70820 | −0.334567 | ||||||||
\(843\) | −0.832816 | −0.0286837 | ||||||||
\(844\) | 16.1459 | 0.555765 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.43769 | −0.0838096 | ||||||||
\(847\) | −12.5623 | −0.431646 | ||||||||
\(848\) | 25.9098 | 0.889747 | ||||||||
\(849\) | 5.12461 | 0.175876 | ||||||||
\(850\) | 13.8541 | 0.475192 | ||||||||
\(851\) | −17.8885 | −0.613211 | ||||||||
\(852\) | −5.79335 | −0.198477 | ||||||||
\(853\) | 26.1246 | 0.894490 | 0.447245 | − | 0.894412i | \(-0.352405\pi\) | ||||
0.447245 | + | 0.894412i | \(0.352405\pi\) | |||||||
\(854\) | −2.29180 | −0.0784236 | ||||||||
\(855\) | −5.29180 | −0.180976 | ||||||||
\(856\) | −8.27051 | −0.282680 | ||||||||
\(857\) | 29.4508 | 1.00602 | 0.503011 | − | 0.864280i | \(-0.332226\pi\) | ||||
0.503011 | + | 0.864280i | \(0.332226\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.2492 | 1.23681 | 0.618404 | − | 0.785861i | \(-0.287780\pi\) | ||||
0.618404 | + | 0.785861i | \(0.287780\pi\) | |||||||
\(860\) | −5.35565 | −0.182626 | ||||||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | −6.41641 | −0.218544 | ||||||||
\(863\) | 23.8885 | 0.813175 | 0.406588 | − | 0.913612i | \(-0.366719\pi\) | ||||
0.406588 | + | 0.913612i | \(0.366719\pi\) | |||||||
\(864\) | −9.27051 | −0.315389 | ||||||||
\(865\) | 3.43769 | 0.116885 | ||||||||
\(866\) | −0.381966 | −0.0129797 | ||||||||
\(867\) | −14.8328 | −0.503749 | ||||||||
\(868\) | −16.1459 | −0.548027 | ||||||||
\(869\) | 19.4164 | 0.658657 | ||||||||
\(870\) | 0.227937 | 0.00772780 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.7639 | −0.533834 | ||||||||
\(873\) | 34.6656 | 1.17325 | ||||||||
\(874\) | 8.29180 | 0.280474 | ||||||||
\(875\) | −3.76393 | −0.127244 | ||||||||
\(876\) | 1.41641 | 0.0478560 | ||||||||
\(877\) | 12.7082 | 0.429126 | 0.214563 | − | 0.976710i | \(-0.431167\pi\) | ||||
0.214563 | + | 0.976710i | \(0.431167\pi\) | |||||||
\(878\) | −3.11146 | −0.105007 | ||||||||
\(879\) | −4.29180 | −0.144759 | ||||||||
\(880\) | −5.83282 | −0.196624 | ||||||||
\(881\) | 12.5967 | 0.424395 | 0.212198 | − | 0.977227i | \(-0.431938\pi\) | ||||
0.212198 | + | 0.977227i | \(0.431938\pi\) | |||||||
\(882\) | 1.09017 | 0.0367079 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.326238 | −0.0109664 | ||||||||
\(886\) | 0.291796 | 0.00980308 | ||||||||
\(887\) | 23.3475 | 0.783933 | 0.391967 | − | 0.919979i | \(-0.371795\pi\) | ||||
0.391967 | + | 0.919979i | \(0.371795\pi\) | |||||||
\(888\) | 2.24922 | 0.0754790 | ||||||||
\(889\) | 14.1459 | 0.474438 | ||||||||
\(890\) | −2.34752 | −0.0786892 | ||||||||
\(891\) | 37.4164 | 1.25350 | ||||||||
\(892\) | −24.6049 | −0.823832 | ||||||||
\(893\) | 10.8541 | 0.363219 | ||||||||
\(894\) | 0.708204 | 0.0236859 | ||||||||
\(895\) | 3.43769 | 0.114909 | ||||||||
\(896\) | −10.0902 | −0.337089 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.8754 | 0.362916 | ||||||||
\(899\) | 35.6180 | 1.18793 | ||||||||
\(900\) | −25.6869 | −0.856231 | ||||||||
\(901\) | 61.5410 | 2.05023 | ||||||||
\(902\) | 9.70820 | 0.323248 | ||||||||
\(903\) | −2.88854 | −0.0961247 | ||||||||
\(904\) | −11.0000 | −0.365855 | ||||||||
\(905\) | 1.41641 | 0.0470830 | ||||||||
\(906\) | 2.14590 | 0.0712927 | ||||||||
\(907\) | −24.0000 | −0.796907 | −0.398453 | − | 0.917189i | \(-0.630453\pi\) | ||||
−0.398453 | + | 0.917189i | \(0.630453\pi\) | |||||||
\(908\) | −13.8541 | −0.459765 | ||||||||
\(909\) | −24.4377 | −0.810547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.6869 | 1.24862 | 0.624312 | − | 0.781175i | \(-0.285380\pi\) | ||||
0.624312 | + | 0.781175i | \(0.285380\pi\) | |||||||
\(912\) | 5.83282 | 0.193144 | ||||||||
\(913\) | 32.5623 | 1.07766 | ||||||||
\(914\) | −4.36068 | −0.144238 | ||||||||
\(915\) | −0.875388 | −0.0289394 | ||||||||
\(916\) | 50.2918 | 1.66169 | ||||||||
\(917\) | −0.326238 | −0.0107733 | ||||||||
\(918\) | −6.38197 | −0.210636 | ||||||||
\(919\) | −30.0000 | −0.989609 | −0.494804 | − | 0.869004i | \(-0.664760\pi\) | ||||
−0.494804 | + | 0.869004i | \(0.664760\pi\) | |||||||
\(920\) | −2.51471 | −0.0829075 | ||||||||
\(921\) | 0.708204 | 0.0233361 | ||||||||
\(922\) | 14.9787 | 0.493298 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.43769 | −0.113092 | ||||||||
\(925\) | 19.4164 | 0.638408 | ||||||||
\(926\) | −2.56231 | −0.0842026 | ||||||||
\(927\) | −13.4377 | −0.441352 | ||||||||
\(928\) | 16.9574 | 0.556655 | ||||||||
\(929\) | 47.0689 | 1.54428 | 0.772140 | − | 0.635452i | \(-0.219186\pi\) | ||||
0.772140 | + | 0.635452i | \(0.219186\pi\) | |||||||
\(930\) | 0.485292 | 0.0159133 | ||||||||
\(931\) | −4.85410 | −0.159087 | ||||||||
\(932\) | −0.708204 | −0.0231980 | ||||||||
\(933\) | 4.70820 | 0.154140 | ||||||||
\(934\) | −12.8541 | −0.420599 | ||||||||
\(935\) | −13.8541 | −0.453078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.1246 | −1.83351 | −0.916756 | − | 0.399449i | \(-0.869202\pi\) | ||||
−0.916756 | + | 0.399449i | \(0.869202\pi\) | |||||||
\(938\) | −0.270510 | −0.00883246 | ||||||||
\(939\) | 5.77709 | 0.188528 | ||||||||
\(940\) | −1.58359 | −0.0516511 | ||||||||
\(941\) | −51.6525 | −1.68382 | −0.841911 | − | 0.539616i | \(-0.818569\pi\) | ||||
−0.841911 | + | 0.539616i | \(0.818569\pi\) | |||||||
\(942\) | 1.18847 | 0.0387225 | ||||||||
\(943\) | −23.4164 | −0.762543 | ||||||||
\(944\) | −7.03444 | −0.228952 | ||||||||
\(945\) | 0.854102 | 0.0277839 | ||||||||
\(946\) | 14.0213 | 0.455871 | ||||||||
\(947\) | −45.8673 | −1.49049 | −0.745243 | − | 0.666793i | \(-0.767666\pi\) | ||||
−0.745243 | + | 0.666793i | \(0.767666\pi\) | |||||||
\(948\) | 2.83282 | 0.0920056 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −9.00000 | −0.291999 | ||||||||
\(951\) | 8.31308 | 0.269570 | ||||||||
\(952\) | −11.0000 | −0.356512 | ||||||||
\(953\) | −44.7771 | −1.45047 | −0.725236 | − | 0.688500i | \(-0.758269\pi\) | ||||
−0.725236 | + | 0.688500i | \(0.758269\pi\) | |||||||
\(954\) | 8.97871 | 0.290697 | ||||||||
\(955\) | −9.02129 | −0.291922 | ||||||||
\(956\) | −20.9361 | −0.677123 | ||||||||
\(957\) | 7.58359 | 0.245143 | ||||||||
\(958\) | −8.39512 | −0.271234 | ||||||||
\(959\) | −0.381966 | −0.0123343 | ||||||||
\(960\) | −0.686918 | −0.0221702 | ||||||||
\(961\) | 44.8328 | 1.44622 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.0344 | 0.516703 | ||||||||
\(964\) | 8.22794 | 0.265004 | ||||||||
\(965\) | −2.29180 | −0.0737755 | ||||||||
\(966\) | −0.652476 | −0.0209931 | ||||||||
\(967\) | 39.0000 | 1.25416 | 0.627078 | − | 0.778957i | \(-0.284251\pi\) | ||||
0.627078 | + | 0.778957i | \(0.284251\pi\) | |||||||
\(968\) | 18.4934 | 0.594401 | ||||||||
\(969\) | 13.8541 | 0.445058 | ||||||||
\(970\) | −1.77206 | −0.0568975 | ||||||||
\(971\) | 58.4164 | 1.87467 | 0.937336 | − | 0.348427i | \(-0.113284\pi\) | ||||
0.937336 | + | 0.348427i | \(0.113284\pi\) | |||||||
\(972\) | 17.8967 | 0.574036 | ||||||||
\(973\) | 15.5623 | 0.498905 | ||||||||
\(974\) | −6.48529 | −0.207802 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.8754 | −0.604186 | ||||||||
\(977\) | 31.4721 | 1.00688 | 0.503441 | − | 0.864029i | \(-0.332067\pi\) | ||||
0.503441 | + | 0.864029i | \(0.332067\pi\) | |||||||
\(978\) | −1.41641 | −0.0452917 | ||||||||
\(979\) | −78.1033 | −2.49619 | ||||||||
\(980\) | 0.708204 | 0.0226227 | ||||||||
\(981\) | 30.5623 | 0.975779 | ||||||||
\(982\) | −5.58359 | −0.178180 | ||||||||
\(983\) | −20.6180 | −0.657613 | −0.328807 | − | 0.944397i | \(-0.606646\pi\) | ||||
−0.328807 | + | 0.944397i | \(0.606646\pi\) | |||||||
\(984\) | 2.94427 | 0.0938600 | ||||||||
\(985\) | 2.97871 | 0.0949097 | ||||||||
\(986\) | 11.6738 | 0.371768 | ||||||||
\(987\) | −0.854102 | −0.0271864 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.8197 | −1.07540 | ||||||||
\(990\) | −2.02129 | −0.0642407 | ||||||||
\(991\) | −22.8541 | −0.725984 | −0.362992 | − | 0.931792i | \(-0.618245\pi\) | ||||
−0.362992 | + | 0.931792i | \(0.618245\pi\) | |||||||
\(992\) | 36.1033 | 1.14628 | ||||||||
\(993\) | −6.43769 | −0.204294 | ||||||||
\(994\) | −3.12461 | −0.0991067 | ||||||||
\(995\) | −0.922986 | −0.0292606 | ||||||||
\(996\) | 4.75078 | 0.150534 | ||||||||
\(997\) | 49.0000 | 1.55185 | 0.775923 | − | 0.630828i | \(-0.217285\pi\) | ||||
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(998\) | 3.11146 | 0.0984914 | ||||||||
\(999\) | −8.94427 | −0.282984 |
(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 | 1183.2.a.c.1.2 | 2 | ||
7.6 | odd | 2 | 8281.2.a.n.1.2 | 2 | |||
13.4 | even | 6 | 91.2.f.a.29.2 | yes | 4 | ||
13.5 | odd | 4 | 1183.2.c.c.337.3 | 4 | |||
13.8 | odd | 4 | 1183.2.c.c.337.2 | 4 | |||
13.10 | even | 6 | 91.2.f.a.22.2 | ✓ | 4 | ||
13.12 | even | 2 | 1183.2.a.g.1.1 | 2 | |||
39.17 | odd | 6 | 819.2.o.c.757.1 | 4 | |||
39.23 | odd | 6 | 819.2.o.c.568.1 | 4 | |||
52.23 | odd | 6 | 1456.2.s.h.113.2 | 4 | |||
52.43 | odd | 6 | 1456.2.s.h.1121.2 | 4 | |||
91.4 | even | 6 | 637.2.h.g.471.1 | 4 | |||
91.10 | odd | 6 | 637.2.g.c.373.2 | 4 | |||
91.17 | odd | 6 | 637.2.h.f.471.1 | 4 | |||
91.23 | even | 6 | 637.2.h.g.165.1 | 4 | |||
91.30 | even | 6 | 637.2.g.b.263.2 | 4 | |||
91.62 | odd | 6 | 637.2.f.c.295.2 | 4 | |||
91.69 | odd | 6 | 637.2.f.c.393.2 | 4 | |||
91.75 | odd | 6 | 637.2.h.f.165.1 | 4 | |||
91.82 | odd | 6 | 637.2.g.c.263.2 | 4 | |||
91.88 | even | 6 | 637.2.g.b.373.2 | 4 | |||
91.90 | odd | 2 | 8281.2.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.a.22.2 | ✓ | 4 | 13.10 | even | 6 | ||
91.2.f.a.29.2 | yes | 4 | 13.4 | even | 6 | ||
637.2.f.c.295.2 | 4 | 91.62 | odd | 6 | |||
637.2.f.c.393.2 | 4 | 91.69 | odd | 6 | |||
637.2.g.b.263.2 | 4 | 91.30 | even | 6 | |||
637.2.g.b.373.2 | 4 | 91.88 | even | 6 | |||
637.2.g.c.263.2 | 4 | 91.82 | odd | 6 | |||
637.2.g.c.373.2 | 4 | 91.10 | odd | 6 | |||
637.2.h.f.165.1 | 4 | 91.75 | odd | 6 | |||
637.2.h.f.471.1 | 4 | 91.17 | odd | 6 | |||
637.2.h.g.165.1 | 4 | 91.23 | even | 6 | |||
637.2.h.g.471.1 | 4 | 91.4 | even | 6 | |||
819.2.o.c.568.1 | 4 | 39.23 | odd | 6 | |||
819.2.o.c.757.1 | 4 | 39.17 | odd | 6 | |||
1183.2.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1183.2.a.g.1.1 | 2 | 13.12 | even | 2 | |||
1183.2.c.c.337.2 | 4 | 13.8 | odd | 4 | |||
1183.2.c.c.337.3 | 4 | 13.5 | odd | 4 | |||
1456.2.s.h.113.2 | 4 | 52.23 | odd | 6 | |||
1456.2.s.h.1121.2 | 4 | 52.43 | odd | 6 | |||
8281.2.a.n.1.2 | 2 | 7.6 | odd | 2 | |||
8281.2.a.bb.1.1 | 2 | 91.90 | odd | 2 |