Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(337,1183)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.c (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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.3 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.337 |
Dual form | 1183.2.c.c.337.2 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.381966i | 0.270091i | 0.990839 | + | 0.135045i | \(0.0431180\pi\) | ||||
−0.990839 | + | 0.135045i | \(0.956882\pi\) | |||||||
\(3\) | −0.381966 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(4\) | 1.85410 | 0.927051 | ||||||||
\(5\) | 0.381966i | 0.170820i | 0.996346 | + | 0.0854102i | \(0.0272201\pi\) | ||||
−0.996346 | + | 0.0854102i | \(0.972780\pi\) | |||||||
\(6\) | − 0.145898i | − 0.0595626i | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 1.47214i | 0.520479i | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | −0.145898 | −0.0461370 | ||||||||
\(11\) | 4.85410i | 1.46357i | 0.681537 | + | 0.731783i | \(0.261312\pi\) | ||||
−0.681537 | + | 0.731783i | \(0.738688\pi\) | |||||||
\(12\) | −0.708204 | −0.204441 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.381966 | 0.102085 | ||||||||
\(15\) | − 0.145898i | − 0.0376707i | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −7.47214 | −1.81226 | −0.906130 | − | 0.423000i | \(-0.860977\pi\) | ||||
−0.906130 | + | 0.423000i | \(0.860977\pi\) | |||||||
\(18\) | − 1.09017i | − 0.256956i | ||||||||
\(19\) | 4.85410i | 1.11361i | 0.830644 | + | 0.556804i | \(0.187972\pi\) | ||||
−0.830644 | + | 0.556804i | \(0.812028\pi\) | |||||||
\(20\) | 0.708204i | 0.158359i | ||||||||
\(21\) | 0.381966i | 0.0833518i | ||||||||
\(22\) | −1.85410 | −0.395296 | ||||||||
\(23\) | −4.47214 | −0.932505 | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | − 0.562306i | − 0.114780i | ||||||||
\(25\) | 4.85410 | 0.970820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | − 1.85410i | − 0.350392i | ||||||||
\(29\) | −4.09017 | −0.759525 | −0.379763 | − | 0.925084i | \(-0.623994\pi\) | ||||
−0.379763 | + | 0.925084i | \(0.623994\pi\) | |||||||
\(30\) | 0.0557281 | 0.0101745 | ||||||||
\(31\) | 8.70820i | 1.56404i | 0.623254 | + | 0.782020i | \(0.285810\pi\) | ||||
−0.623254 | + | 0.782020i | \(0.714190\pi\) | |||||||
\(32\) | 4.14590i | 0.732898i | ||||||||
\(33\) | − 1.85410i | − 0.322758i | ||||||||
\(34\) | − 2.85410i | − 0.489474i | ||||||||
\(35\) | 0.381966 | 0.0645640 | ||||||||
\(36\) | −5.29180 | −0.881966 | ||||||||
\(37\) | − 4.00000i | − 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | −1.85410 | −0.300775 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.562306 | −0.0889084 | ||||||||
\(41\) | 5.23607i | 0.817736i | 0.912593 | + | 0.408868i | \(0.134076\pi\) | ||||
−0.912593 | + | 0.408868i | \(0.865924\pi\) | |||||||
\(42\) | −0.145898 | −0.0225126 | ||||||||
\(43\) | 7.56231 | 1.15324 | 0.576620 | − | 0.817012i | \(-0.304371\pi\) | ||||
0.576620 | + | 0.817012i | \(0.304371\pi\) | |||||||
\(44\) | 9.00000i | 1.35680i | ||||||||
\(45\) | − 1.09017i | − 0.162513i | ||||||||
\(46\) | − 1.70820i | − 0.251861i | ||||||||
\(47\) | − 2.23607i | − 0.326164i | −0.986613 | − | 0.163082i | \(-0.947856\pi\) | ||||
0.986613 | − | 0.163082i | \(-0.0521435\pi\) | |||||||
\(48\) | −1.20163 | −0.173440 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.85410i | 0.262210i | ||||||||
\(51\) | 2.85410 | 0.399654 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.23607 | 1.13131 | 0.565655 | − | 0.824642i | \(-0.308623\pi\) | ||||
0.565655 | + | 0.824642i | \(0.308623\pi\) | |||||||
\(54\) | 0.854102i | 0.116229i | ||||||||
\(55\) | −1.85410 | −0.250007 | ||||||||
\(56\) | 1.47214 | 0.196722 | ||||||||
\(57\) | − 1.85410i | − 0.245582i | ||||||||
\(58\) | − 1.56231i | − 0.205141i | ||||||||
\(59\) | − 2.23607i | − 0.291111i | −0.989350 | − | 0.145556i | \(-0.953503\pi\) | ||||
0.989350 | − | 0.145556i | \(-0.0464970\pi\) | |||||||
\(60\) | − 0.270510i | − 0.0349227i | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | −3.32624 | −0.422433 | ||||||||
\(63\) | 2.85410i | 0.359583i | ||||||||
\(64\) | 4.70820 | 0.588525 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.708204 | 0.0871739 | ||||||||
\(67\) | 0.708204i | 0.0865209i | 0.999064 | + | 0.0432604i | \(0.0137745\pi\) | ||||
−0.999064 | + | 0.0432604i | \(0.986225\pi\) | |||||||
\(68\) | −13.8541 | −1.68006 | ||||||||
\(69\) | 1.70820 | 0.205644 | ||||||||
\(70\) | 0.145898i | 0.0174382i | ||||||||
\(71\) | 8.18034i | 0.970828i | 0.874284 | + | 0.485414i | \(0.161331\pi\) | ||||
−0.874284 | + | 0.485414i | \(0.838669\pi\) | |||||||
\(72\) | − 4.20163i | − 0.495166i | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | 1.52786 | 0.177611 | ||||||||
\(75\) | −1.85410 | −0.214093 | ||||||||
\(76\) | 9.00000i | 1.03237i | ||||||||
\(77\) | 4.85410 | 0.553176 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 1.20163i | 0.134346i | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | − 6.70820i | − 0.736321i | −0.929762 | − | 0.368161i | \(-0.879988\pi\) | ||||
0.929762 | − | 0.368161i | \(-0.120012\pi\) | |||||||
\(84\) | 0.708204i | 0.0772714i | ||||||||
\(85\) | − 2.85410i | − 0.309571i | ||||||||
\(86\) | 2.88854i | 0.311480i | ||||||||
\(87\) | 1.56231 | 0.167497 | ||||||||
\(88\) | −7.14590 | −0.761755 | ||||||||
\(89\) | − 16.0902i | − 1.70555i | −0.522275 | − | 0.852777i | \(-0.674916\pi\) | ||||
0.522275 | − | 0.852777i | \(-0.325084\pi\) | |||||||
\(90\) | 0.416408 | 0.0438932 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.29180 | −0.864479 | ||||||||
\(93\) | − 3.32624i | − 0.344915i | ||||||||
\(94\) | 0.854102 | 0.0880939 | ||||||||
\(95\) | −1.85410 | −0.190227 | ||||||||
\(96\) | − 1.58359i | − 0.161625i | ||||||||
\(97\) | 12.1459i | 1.23323i | 0.787265 | + | 0.616615i | \(0.211496\pi\) | ||||
−0.787265 | + | 0.616615i | \(0.788504\pi\) | |||||||
\(98\) | − 0.381966i | − 0.0385844i | ||||||||
\(99\) | − 13.8541i | − 1.39239i | ||||||||
\(100\) | 9.00000 | 0.900000 | ||||||||
\(101\) | −8.56231 | −0.851981 | −0.425991 | − | 0.904728i | \(-0.640074\pi\) | ||||
−0.425991 | + | 0.904728i | \(0.640074\pi\) | |||||||
\(102\) | 1.09017i | 0.107943i | ||||||||
\(103\) | −4.70820 | −0.463913 | −0.231957 | − | 0.972726i | \(-0.574513\pi\) | ||||
−0.231957 | + | 0.972726i | \(0.574513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.145898 | −0.0142382 | ||||||||
\(106\) | 3.14590i | 0.305557i | ||||||||
\(107\) | −5.61803 | −0.543116 | −0.271558 | − | 0.962422i | \(-0.587539\pi\) | ||||
−0.271558 | + | 0.962422i | \(0.587539\pi\) | |||||||
\(108\) | 4.14590 | 0.398939 | ||||||||
\(109\) | 10.7082i | 1.02566i | 0.858490 | + | 0.512830i | \(0.171403\pi\) | ||||
−0.858490 | + | 0.512830i | \(0.828597\pi\) | |||||||
\(110\) | − 0.708204i | − 0.0675246i | ||||||||
\(111\) | 1.52786i | 0.145018i | ||||||||
\(112\) | − 3.14590i | − 0.297259i | ||||||||
\(113\) | −7.47214 | −0.702919 | −0.351460 | − | 0.936203i | \(-0.614315\pi\) | ||||
−0.351460 | + | 0.936203i | \(0.614315\pi\) | |||||||
\(114\) | 0.708204 | 0.0663294 | ||||||||
\(115\) | − 1.70820i | − 0.159291i | ||||||||
\(116\) | −7.58359 | −0.704119 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.854102 | 0.0786265 | ||||||||
\(119\) | 7.47214i | 0.684970i | ||||||||
\(120\) | 0.214782 | 0.0196068 | ||||||||
\(121\) | −12.5623 | −1.14203 | ||||||||
\(122\) | − 2.29180i | − 0.207489i | ||||||||
\(123\) | − 2.00000i | − 0.180334i | ||||||||
\(124\) | 16.1459i | 1.44994i | ||||||||
\(125\) | 3.76393i | 0.336656i | ||||||||
\(126\) | −1.09017 | −0.0971201 | ||||||||
\(127\) | 14.1459 | 1.25525 | 0.627623 | − | 0.778518i | \(-0.284028\pi\) | ||||
0.627623 | + | 0.778518i | \(0.284028\pi\) | |||||||
\(128\) | 10.0902i | 0.891853i | ||||||||
\(129\) | −2.88854 | −0.254322 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.326238 | 0.0285035 | 0.0142518 | − | 0.999898i | \(-0.495463\pi\) | ||||
0.0142518 | + | 0.999898i | \(0.495463\pi\) | |||||||
\(132\) | − 3.43769i | − 0.299213i | ||||||||
\(133\) | 4.85410 | 0.420904 | ||||||||
\(134\) | −0.270510 | −0.0233685 | ||||||||
\(135\) | 0.854102i | 0.0735094i | ||||||||
\(136\) | − 11.0000i | − 0.943242i | ||||||||
\(137\) | 0.381966i | 0.0326336i | 0.999867 | + | 0.0163168i | \(0.00519402\pi\) | ||||
−0.999867 | + | 0.0163168i | \(0.994806\pi\) | |||||||
\(138\) | 0.652476i | 0.0555424i | ||||||||
\(139\) | −15.5623 | −1.31998 | −0.659989 | − | 0.751275i | \(-0.729439\pi\) | ||||
−0.659989 | + | 0.751275i | \(0.729439\pi\) | |||||||
\(140\) | 0.708204 | 0.0598542 | ||||||||
\(141\) | 0.854102i | 0.0719284i | ||||||||
\(142\) | −3.12461 | −0.262212 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −8.97871 | −0.748226 | ||||||||
\(145\) | − 1.56231i | − 0.129742i | ||||||||
\(146\) | −0.763932 | −0.0632235 | ||||||||
\(147\) | 0.381966 | 0.0315040 | ||||||||
\(148\) | − 7.41641i | − 0.609625i | ||||||||
\(149\) | − 4.85410i | − 0.397664i | −0.980034 | − | 0.198832i | \(-0.936285\pi\) | ||||
0.980034 | − | 0.198832i | \(-0.0637147\pi\) | |||||||
\(150\) | − 0.708204i | − 0.0578246i | ||||||||
\(151\) | 14.7082i | 1.19694i | 0.801146 | + | 0.598468i | \(0.204224\pi\) | ||||
−0.801146 | + | 0.598468i | \(0.795776\pi\) | |||||||
\(152\) | −7.14590 | −0.579609 | ||||||||
\(153\) | 21.3262 | 1.72412 | ||||||||
\(154\) | 1.85410i | 0.149408i | ||||||||
\(155\) | −3.32624 | −0.267170 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.14590 | 0.650113 | 0.325057 | − | 0.945695i | \(-0.394617\pi\) | ||||
0.325057 | + | 0.945695i | \(0.394617\pi\) | |||||||
\(158\) | 1.52786i | 0.121550i | ||||||||
\(159\) | −3.14590 | −0.249486 | ||||||||
\(160\) | −1.58359 | −0.125194 | ||||||||
\(161\) | 4.47214i | 0.352454i | ||||||||
\(162\) | 2.94427i | 0.231324i | ||||||||
\(163\) | − 9.70820i | − 0.760405i | −0.924903 | − | 0.380203i | \(-0.875854\pi\) | ||||
0.924903 | − | 0.380203i | \(-0.124146\pi\) | |||||||
\(164\) | 9.70820i | 0.758083i | ||||||||
\(165\) | 0.708204 | 0.0551336 | ||||||||
\(166\) | 2.56231 | 0.198874 | ||||||||
\(167\) | − 9.76393i | − 0.755556i | −0.925896 | − | 0.377778i | \(-0.876688\pi\) | ||||
0.925896 | − | 0.377778i | \(-0.123312\pi\) | |||||||
\(168\) | −0.562306 | −0.0433828 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.09017 | 0.0836122 | ||||||||
\(171\) | − 13.8541i | − 1.05945i | ||||||||
\(172\) | 14.0213 | 1.06911 | ||||||||
\(173\) | 9.00000 | 0.684257 | 0.342129 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342129 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(174\) | 0.596748i | 0.0452393i | ||||||||
\(175\) | − 4.85410i | − 0.366936i | ||||||||
\(176\) | 15.2705i | 1.15106i | ||||||||
\(177\) | 0.854102i | 0.0641982i | ||||||||
\(178\) | 6.14590 | 0.460655 | ||||||||
\(179\) | 9.00000 | 0.672692 | 0.336346 | − | 0.941739i | \(-0.390809\pi\) | ||||
0.336346 | + | 0.941739i | \(0.390809\pi\) | |||||||
\(180\) | − 2.02129i | − 0.150658i | ||||||||
\(181\) | 3.70820 | 0.275629 | 0.137814 | − | 0.990458i | \(-0.455992\pi\) | ||||
0.137814 | + | 0.990458i | \(0.455992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.29180 | 0.169414 | ||||||||
\(184\) | − 6.58359i | − 0.485349i | ||||||||
\(185\) | 1.52786 | 0.112331 | ||||||||
\(186\) | 1.27051 | 0.0931583 | ||||||||
\(187\) | − 36.2705i | − 2.65236i | ||||||||
\(188\) | − 4.14590i | − 0.302371i | ||||||||
\(189\) | − 2.23607i | − 0.162650i | ||||||||
\(190\) | − 0.708204i | − 0.0513785i | ||||||||
\(191\) | 23.6180 | 1.70894 | 0.854470 | − | 0.519500i | \(-0.173882\pi\) | ||||
0.854470 | + | 0.519500i | \(0.173882\pi\) | |||||||
\(192\) | −1.79837 | −0.129786 | ||||||||
\(193\) | 6.00000i | 0.431889i | 0.976406 | + | 0.215945i | \(0.0692831\pi\) | ||||
−0.976406 | + | 0.215945i | \(0.930717\pi\) | |||||||
\(194\) | −4.63932 | −0.333084 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.85410 | −0.132436 | ||||||||
\(197\) | 7.79837i | 0.555611i | 0.960637 | + | 0.277806i | \(0.0896071\pi\) | ||||
−0.960637 | + | 0.277806i | \(0.910393\pi\) | |||||||
\(198\) | 5.29180 | 0.376072 | ||||||||
\(199\) | −2.41641 | −0.171295 | −0.0856473 | − | 0.996326i | \(-0.527296\pi\) | ||||
−0.0856473 | + | 0.996326i | \(0.527296\pi\) | |||||||
\(200\) | 7.14590i | 0.505291i | ||||||||
\(201\) | − 0.270510i | − 0.0190803i | ||||||||
\(202\) | − 3.27051i | − 0.230112i | ||||||||
\(203\) | 4.09017i | 0.287074i | ||||||||
\(204\) | 5.29180 | 0.370500 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | − 1.79837i | − 0.125299i | ||||||||
\(207\) | 12.7639 | 0.887155 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.5623 | −1.62984 | ||||||||
\(210\) | − 0.0557281i | − 0.00384560i | ||||||||
\(211\) | −8.70820 | −0.599497 | −0.299749 | − | 0.954018i | \(-0.596903\pi\) | ||||
−0.299749 | + | 0.954018i | \(0.596903\pi\) | |||||||
\(212\) | 15.2705 | 1.04878 | ||||||||
\(213\) | − 3.12461i | − 0.214095i | ||||||||
\(214\) | − 2.14590i | − 0.146691i | ||||||||
\(215\) | 2.88854i | 0.196997i | ||||||||
\(216\) | 3.29180i | 0.223978i | ||||||||
\(217\) | 8.70820 | 0.591151 | ||||||||
\(218\) | −4.09017 | −0.277021 | ||||||||
\(219\) | − 0.763932i | − 0.0516217i | ||||||||
\(220\) | −3.43769 | −0.231769 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.583592 | −0.0391681 | ||||||||
\(223\) | − 13.2705i | − 0.888659i | −0.895863 | − | 0.444330i | \(-0.853442\pi\) | ||||
0.895863 | − | 0.444330i | \(-0.146558\pi\) | |||||||
\(224\) | 4.14590 | 0.277009 | ||||||||
\(225\) | −13.8541 | −0.923607 | ||||||||
\(226\) | − 2.85410i | − 0.189852i | ||||||||
\(227\) | − 7.47214i | − 0.495943i | −0.968767 | − | 0.247972i | \(-0.920236\pi\) | ||||
0.968767 | − | 0.247972i | \(-0.0797639\pi\) | |||||||
\(228\) | − 3.43769i | − 0.227667i | ||||||||
\(229\) | − 27.1246i | − 1.79244i | −0.443605 | − | 0.896222i | \(-0.646301\pi\) | ||||
0.443605 | − | 0.896222i | \(-0.353699\pi\) | |||||||
\(230\) | 0.652476 | 0.0430230 | ||||||||
\(231\) | −1.85410 | −0.121991 | ||||||||
\(232\) | − 6.02129i | − 0.395317i | ||||||||
\(233\) | −0.381966 | −0.0250234 | −0.0125117 | − | 0.999922i | \(-0.503983\pi\) | ||||
−0.0125117 | + | 0.999922i | \(0.503983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.854102 | 0.0557155 | ||||||||
\(236\) | − 4.14590i | − 0.269875i | ||||||||
\(237\) | −1.52786 | −0.0992454 | ||||||||
\(238\) | −2.85410 | −0.185004 | ||||||||
\(239\) | − 11.2918i | − 0.730406i | −0.930928 | − | 0.365203i | \(-0.881000\pi\) | ||||
0.930928 | − | 0.365203i | \(-0.119000\pi\) | |||||||
\(240\) | − 0.458980i | − 0.0296271i | ||||||||
\(241\) | − 4.43769i | − 0.285857i | −0.989733 | − | 0.142929i | \(-0.954348\pi\) | ||||
0.989733 | − | 0.142929i | \(-0.0456519\pi\) | |||||||
\(242\) | − 4.79837i | − 0.308451i | ||||||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | −11.1246 | −0.712180 | ||||||||
\(245\) | − 0.381966i | − 0.0244029i | ||||||||
\(246\) | 0.763932 | 0.0487065 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −12.8197 | −0.814049 | ||||||||
\(249\) | 2.56231i | 0.162380i | ||||||||
\(250\) | −1.43769 | −0.0909278 | ||||||||
\(251\) | −5.23607 | −0.330498 | −0.165249 | − | 0.986252i | \(-0.552843\pi\) | ||||
−0.165249 | + | 0.986252i | \(0.552843\pi\) | |||||||
\(252\) | 5.29180i | 0.333352i | ||||||||
\(253\) | − 21.7082i | − 1.36478i | ||||||||
\(254\) | 5.40325i | 0.339030i | ||||||||
\(255\) | 1.09017i | 0.0682691i | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | 25.7426 | 1.60578 | 0.802891 | − | 0.596126i | \(-0.203294\pi\) | ||||
0.802891 | + | 0.596126i | \(0.203294\pi\) | |||||||
\(258\) | − 1.10333i | − 0.0686900i | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.6738 | 0.722588 | ||||||||
\(262\) | 0.124612i | 0.00769854i | ||||||||
\(263\) | 9.00000 | 0.554964 | 0.277482 | − | 0.960731i | \(-0.410500\pi\) | ||||
0.277482 | + | 0.960731i | \(0.410500\pi\) | |||||||
\(264\) | 2.72949 | 0.167989 | ||||||||
\(265\) | 3.14590i | 0.193251i | ||||||||
\(266\) | 1.85410i | 0.113682i | ||||||||
\(267\) | 6.14590i | 0.376123i | ||||||||
\(268\) | 1.31308i | 0.0802093i | ||||||||
\(269\) | 13.7426 | 0.837904 | 0.418952 | − | 0.908008i | \(-0.362398\pi\) | ||||
0.418952 | + | 0.908008i | \(0.362398\pi\) | |||||||
\(270\) | −0.326238 | −0.0198542 | ||||||||
\(271\) | − 18.4164i | − 1.11872i | −0.828926 | − | 0.559359i | \(-0.811048\pi\) | ||||
0.828926 | − | 0.559359i | \(-0.188952\pi\) | |||||||
\(272\) | −23.5066 | −1.42530 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.145898 | −0.00881402 | ||||||||
\(275\) | 23.5623i | 1.42086i | ||||||||
\(276\) | 3.16718 | 0.190642 | ||||||||
\(277\) | 5.00000 | 0.300421 | 0.150210 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | − 5.94427i | − 0.356514i | ||||||||
\(279\) | − 24.8541i | − 1.48798i | ||||||||
\(280\) | 0.562306i | 0.0336042i | ||||||||
\(281\) | 2.18034i | 0.130068i | 0.997883 | + | 0.0650341i | \(0.0207156\pi\) | ||||
−0.997883 | + | 0.0650341i | \(0.979284\pi\) | |||||||
\(282\) | −0.326238 | −0.0194272 | ||||||||
\(283\) | 13.4164 | 0.797523 | 0.398761 | − | 0.917055i | \(-0.369440\pi\) | ||||
0.398761 | + | 0.917055i | \(0.369440\pi\) | |||||||
\(284\) | 15.1672i | 0.900007i | ||||||||
\(285\) | 0.708204 | 0.0419504 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.23607 | 0.309075 | ||||||||
\(288\) | − 11.8328i | − 0.697255i | ||||||||
\(289\) | 38.8328 | 2.28428 | ||||||||
\(290\) | 0.596748 | 0.0350422 | ||||||||
\(291\) | − 4.63932i | − 0.271962i | ||||||||
\(292\) | 3.70820i | 0.217006i | ||||||||
\(293\) | 11.2361i | 0.656418i | 0.944605 | + | 0.328209i | \(0.106445\pi\) | ||||
−0.944605 | + | 0.328209i | \(0.893555\pi\) | |||||||
\(294\) | 0.145898i | 0.00850895i | ||||||||
\(295\) | 0.854102 | 0.0497277 | ||||||||
\(296\) | 5.88854 | 0.342265 | ||||||||
\(297\) | 10.8541i | 0.629819i | ||||||||
\(298\) | 1.85410 | 0.107405 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.43769 | −0.198475 | ||||||||
\(301\) | − 7.56231i | − 0.435884i | ||||||||
\(302\) | −5.61803 | −0.323282 | ||||||||
\(303\) | 3.27051 | 0.187886 | ||||||||
\(304\) | 15.2705i | 0.875824i | ||||||||
\(305\) | − 2.29180i | − 0.131228i | ||||||||
\(306\) | 8.14590i | 0.465670i | ||||||||
\(307\) | − 1.85410i | − 0.105819i | −0.998599 | − | 0.0529096i | \(-0.983150\pi\) | ||||
0.998599 | − | 0.0529096i | \(-0.0168495\pi\) | |||||||
\(308\) | 9.00000 | 0.512823 | ||||||||
\(309\) | 1.79837 | 0.102306 | ||||||||
\(310\) | − 1.27051i | − 0.0721601i | ||||||||
\(311\) | 12.3262 | 0.698957 | 0.349478 | − | 0.936944i | \(-0.386359\pi\) | ||||
0.349478 | + | 0.936944i | \(0.386359\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.1246 | −0.854894 | −0.427447 | − | 0.904041i | \(-0.640587\pi\) | ||||
−0.427447 | + | 0.904041i | \(0.640587\pi\) | |||||||
\(314\) | 3.11146i | 0.175590i | ||||||||
\(315\) | −1.09017 | −0.0614241 | ||||||||
\(316\) | 7.41641 | 0.417206 | ||||||||
\(317\) | 21.7639i | 1.22238i | 0.791482 | + | 0.611192i | \(0.209310\pi\) | ||||
−0.791482 | + | 0.611192i | \(0.790690\pi\) | |||||||
\(318\) | − 1.20163i | − 0.0673838i | ||||||||
\(319\) | − 19.8541i | − 1.11162i | ||||||||
\(320\) | 1.79837i | 0.100532i | ||||||||
\(321\) | 2.14590 | 0.119772 | ||||||||
\(322\) | −1.70820 | −0.0951945 | ||||||||
\(323\) | − 36.2705i | − 2.01815i | ||||||||
\(324\) | 14.2918 | 0.793989 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.70820 | 0.205378 | ||||||||
\(327\) | − 4.09017i | − 0.226187i | ||||||||
\(328\) | −7.70820 | −0.425614 | ||||||||
\(329\) | −2.23607 | −0.123278 | ||||||||
\(330\) | 0.270510i | 0.0148911i | ||||||||
\(331\) | − 16.8541i | − 0.926385i | −0.886258 | − | 0.463193i | \(-0.846704\pi\) | ||||
0.886258 | − | 0.463193i | \(-0.153296\pi\) | |||||||
\(332\) | − 12.4377i | − 0.682607i | ||||||||
\(333\) | 11.4164i | 0.625615i | ||||||||
\(334\) | 3.72949 | 0.204069 | ||||||||
\(335\) | −0.270510 | −0.0147795 | ||||||||
\(336\) | 1.20163i | 0.0655541i | ||||||||
\(337\) | −8.56231 | −0.466419 | −0.233209 | − | 0.972427i | \(-0.574923\pi\) | ||||
−0.233209 | + | 0.972427i | \(0.574923\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.85410 | 0.155014 | ||||||||
\(340\) | − 5.29180i | − 0.286988i | ||||||||
\(341\) | −42.2705 | −2.28908 | ||||||||
\(342\) | 5.29180 | 0.286148 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 11.1327i | 0.600237i | ||||||||
\(345\) | 0.652476i | 0.0351281i | ||||||||
\(346\) | 3.43769i | 0.184812i | ||||||||
\(347\) | 35.2361 | 1.89157 | 0.945786 | − | 0.324792i | \(-0.105294\pi\) | ||||
0.945786 | + | 0.324792i | \(0.105294\pi\) | |||||||
\(348\) | 2.89667 | 0.155278 | ||||||||
\(349\) | − 7.29180i | − 0.390321i | −0.980771 | − | 0.195160i | \(-0.937477\pi\) | ||||
0.980771 | − | 0.195160i | \(-0.0625228\pi\) | |||||||
\(350\) | 1.85410 | 0.0991059 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.1246 | −1.07265 | ||||||||
\(353\) | 28.8541i | 1.53575i | 0.640600 | + | 0.767874i | \(0.278686\pi\) | ||||
−0.640600 | + | 0.767874i | \(0.721314\pi\) | |||||||
\(354\) | −0.326238 | −0.0173393 | ||||||||
\(355\) | −3.12461 | −0.165837 | ||||||||
\(356\) | − 29.8328i | − 1.58114i | ||||||||
\(357\) | − 2.85410i | − 0.151055i | ||||||||
\(358\) | 3.43769i | 0.181688i | ||||||||
\(359\) | 10.9098i | 0.575799i | 0.957661 | + | 0.287899i | \(0.0929569\pi\) | ||||
−0.957661 | + | 0.287899i | \(0.907043\pi\) | |||||||
\(360\) | 1.60488 | 0.0845845 | ||||||||
\(361\) | −4.56231 | −0.240121 | ||||||||
\(362\) | 1.41641i | 0.0744447i | ||||||||
\(363\) | 4.79837 | 0.251849 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.763932 | −0.0399860 | ||||||||
\(366\) | 0.875388i | 0.0457573i | ||||||||
\(367\) | 25.4164 | 1.32673 | 0.663363 | − | 0.748298i | \(-0.269129\pi\) | ||||
0.663363 | + | 0.748298i | \(0.269129\pi\) | |||||||
\(368\) | −14.0689 | −0.733391 | ||||||||
\(369\) | − 14.9443i | − 0.777968i | ||||||||
\(370\) | 0.583592i | 0.0303395i | ||||||||
\(371\) | − 8.23607i | − 0.427595i | ||||||||
\(372\) | − 6.16718i | − 0.319754i | ||||||||
\(373\) | −0.437694 | −0.0226629 | −0.0113315 | − | 0.999936i | \(-0.503607\pi\) | ||||
−0.0113315 | + | 0.999936i | \(0.503607\pi\) | |||||||
\(374\) | 13.8541 | 0.716379 | ||||||||
\(375\) | − 1.43769i | − 0.0742422i | ||||||||
\(376\) | 3.29180 | 0.169761 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.854102 | 0.0439303 | ||||||||
\(379\) | − 12.8541i | − 0.660271i | −0.943934 | − | 0.330135i | \(-0.892906\pi\) | ||||
0.943934 | − | 0.330135i | \(-0.107094\pi\) | |||||||
\(380\) | −3.43769 | −0.176350 | ||||||||
\(381\) | −5.40325 | −0.276817 | ||||||||
\(382\) | 9.02129i | 0.461569i | ||||||||
\(383\) | 24.9787i | 1.27635i | 0.769890 | + | 0.638176i | \(0.220311\pi\) | ||||
−0.769890 | + | 0.638176i | \(0.779689\pi\) | |||||||
\(384\) | − 3.85410i | − 0.196679i | ||||||||
\(385\) | 1.85410i | 0.0944938i | ||||||||
\(386\) | −2.29180 | −0.116649 | ||||||||
\(387\) | −21.5836 | −1.09716 | ||||||||
\(388\) | 22.5197i | 1.14327i | ||||||||
\(389\) | −23.8885 | −1.21120 | −0.605599 | − | 0.795770i | \(-0.707066\pi\) | ||||
−0.605599 | + | 0.795770i | \(0.707066\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.4164 | 1.68994 | ||||||||
\(392\) | − 1.47214i | − 0.0743541i | ||||||||
\(393\) | −0.124612 | −0.00628583 | ||||||||
\(394\) | −2.97871 | −0.150065 | ||||||||
\(395\) | 1.52786i | 0.0768752i | ||||||||
\(396\) | − 25.6869i | − 1.29082i | ||||||||
\(397\) | 25.4164i | 1.27561i | 0.770197 | + | 0.637806i | \(0.220158\pi\) | ||||
−0.770197 | + | 0.637806i | \(0.779842\pi\) | |||||||
\(398\) | − 0.922986i | − 0.0462651i | ||||||||
\(399\) | −1.85410 | −0.0928212 | ||||||||
\(400\) | 15.2705 | 0.763525 | ||||||||
\(401\) | 20.4508i | 1.02127i | 0.859799 | + | 0.510633i | \(0.170589\pi\) | ||||
−0.859799 | + | 0.510633i | \(0.829411\pi\) | |||||||
\(402\) | 0.103326 | 0.00515341 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −15.8754 | −0.789830 | ||||||||
\(405\) | 2.94427i | 0.146302i | ||||||||
\(406\) | −1.56231 | −0.0775359 | ||||||||
\(407\) | 19.4164 | 0.962436 | ||||||||
\(408\) | 4.20163i | 0.208011i | ||||||||
\(409\) | 34.5623i | 1.70900i | 0.519455 | + | 0.854498i | \(0.326135\pi\) | ||||
−0.519455 | + | 0.854498i | \(0.673865\pi\) | |||||||
\(410\) | − 0.763932i | − 0.0377279i | ||||||||
\(411\) | − 0.145898i | − 0.00719662i | ||||||||
\(412\) | −8.72949 | −0.430071 | ||||||||
\(413\) | −2.23607 | −0.110030 | ||||||||
\(414\) | 4.87539i | 0.239612i | ||||||||
\(415\) | 2.56231 | 0.125779 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.94427 | 0.291092 | ||||||||
\(418\) | − 9.00000i | − 0.440204i | ||||||||
\(419\) | 5.94427 | 0.290397 | 0.145198 | − | 0.989403i | \(-0.453618\pi\) | ||||
0.145198 | + | 0.989403i | \(0.453618\pi\) | |||||||
\(420\) | −0.270510 | −0.0131995 | ||||||||
\(421\) | − 25.4164i | − 1.23872i | −0.785107 | − | 0.619360i | \(-0.787392\pi\) | ||||
0.785107 | − | 0.619360i | \(-0.212608\pi\) | |||||||
\(422\) | − 3.32624i | − 0.161919i | ||||||||
\(423\) | 6.38197i | 0.310302i | ||||||||
\(424\) | 12.1246i | 0.588823i | ||||||||
\(425\) | −36.2705 | −1.75938 | ||||||||
\(426\) | 1.19350 | 0.0578250 | ||||||||
\(427\) | 6.00000i | 0.290360i | ||||||||
\(428\) | −10.4164 | −0.503496 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.10333 | −0.0532071 | ||||||||
\(431\) | − 16.7984i | − 0.809149i | −0.914505 | − | 0.404575i | \(-0.867420\pi\) | ||||
0.914505 | − | 0.404575i | \(-0.132580\pi\) | |||||||
\(432\) | 7.03444 | 0.338445 | ||||||||
\(433\) | −1.00000 | −0.0480569 | −0.0240285 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240285 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(434\) | 3.32624i | 0.159665i | ||||||||
\(435\) | 0.596748i | 0.0286119i | ||||||||
\(436\) | 19.8541i | 0.950839i | ||||||||
\(437\) | − 21.7082i | − 1.03844i | ||||||||
\(438\) | 0.291796 | 0.0139426 | ||||||||
\(439\) | −8.14590 | −0.388783 | −0.194391 | − | 0.980924i | \(-0.562273\pi\) | ||||
−0.194391 | + | 0.980924i | \(0.562273\pi\) | |||||||
\(440\) | − 2.72949i | − 0.130123i | ||||||||
\(441\) | 2.85410 | 0.135910 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.763932 | −0.0362955 | −0.0181478 | − | 0.999835i | \(-0.505777\pi\) | ||||
−0.0181478 | + | 0.999835i | \(0.505777\pi\) | |||||||
\(444\) | 2.83282i | 0.134439i | ||||||||
\(445\) | 6.14590 | 0.291344 | ||||||||
\(446\) | 5.06888 | 0.240019 | ||||||||
\(447\) | 1.85410i | 0.0876960i | ||||||||
\(448\) | − 4.70820i | − 0.222442i | ||||||||
\(449\) | − 28.4721i | − 1.34368i | −0.740695 | − | 0.671842i | \(-0.765504\pi\) | ||||
0.740695 | − | 0.671842i | \(-0.234496\pi\) | |||||||
\(450\) | − 5.29180i | − 0.249458i | ||||||||
\(451\) | −25.4164 | −1.19681 | ||||||||
\(452\) | −13.8541 | −0.651642 | ||||||||
\(453\) | − 5.61803i | − 0.263958i | ||||||||
\(454\) | 2.85410 | 0.133950 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.72949 | 0.127820 | ||||||||
\(457\) | − 11.4164i | − 0.534037i | −0.963691 | − | 0.267019i | \(-0.913962\pi\) | ||||
0.963691 | − | 0.267019i | \(-0.0860385\pi\) | |||||||
\(458\) | 10.3607 | 0.484123 | ||||||||
\(459\) | −16.7082 | −0.779872 | ||||||||
\(460\) | − 3.16718i | − 0.147671i | ||||||||
\(461\) | 39.2148i | 1.82641i | 0.407495 | + | 0.913207i | \(0.366402\pi\) | ||||
−0.407495 | + | 0.913207i | \(0.633598\pi\) | |||||||
\(462\) | − 0.708204i | − 0.0329486i | ||||||||
\(463\) | 6.70820i | 0.311757i | 0.987776 | + | 0.155878i | \(0.0498208\pi\) | ||||
−0.987776 | + | 0.155878i | \(0.950179\pi\) | |||||||
\(464\) | −12.8673 | −0.597347 | ||||||||
\(465\) | 1.27051 | 0.0589185 | ||||||||
\(466\) | − 0.145898i | − 0.00675860i | ||||||||
\(467\) | −33.6525 | −1.55725 | −0.778625 | − | 0.627489i | \(-0.784083\pi\) | ||||
−0.778625 | + | 0.627489i | \(0.784083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.708204 | 0.0327018 | ||||||||
\(470\) | 0.326238i | 0.0150482i | ||||||||
\(471\) | −3.11146 | −0.143368 | ||||||||
\(472\) | 3.29180 | 0.151517 | ||||||||
\(473\) | 36.7082i | 1.68785i | ||||||||
\(474\) | − 0.583592i | − 0.0268053i | ||||||||
\(475\) | 23.5623i | 1.08111i | ||||||||
\(476\) | 13.8541i | 0.635002i | ||||||||
\(477\) | −23.5066 | −1.07629 | ||||||||
\(478\) | 4.31308 | 0.197276 | ||||||||
\(479\) | 21.9787i | 1.00423i | 0.864800 | + | 0.502117i | \(0.167445\pi\) | ||||
−0.864800 | + | 0.502117i | \(0.832555\pi\) | |||||||
\(480\) | 0.604878 | 0.0276088 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.69505 | 0.0772073 | ||||||||
\(483\) | − 1.70820i | − 0.0777260i | ||||||||
\(484\) | −23.2918 | −1.05872 | ||||||||
\(485\) | −4.63932 | −0.210661 | ||||||||
\(486\) | − 3.68692i | − 0.167242i | ||||||||
\(487\) | − 16.9787i | − 0.769379i | −0.923046 | − | 0.384689i | \(-0.874309\pi\) | ||||
0.923046 | − | 0.384689i | \(-0.125691\pi\) | |||||||
\(488\) | − 8.83282i | − 0.399843i | ||||||||
\(489\) | 3.70820i | 0.167691i | ||||||||
\(490\) | 0.145898 | 0.00659100 | ||||||||
\(491\) | −14.6180 | −0.659703 | −0.329851 | − | 0.944033i | \(-0.606999\pi\) | ||||
−0.329851 | + | 0.944033i | \(0.606999\pi\) | |||||||
\(492\) | − 3.70820i | − 0.167179i | ||||||||
\(493\) | 30.5623 | 1.37646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.29180 | 0.237849 | ||||||||
\(496\) | 27.3951i | 1.23008i | ||||||||
\(497\) | 8.18034 | 0.366938 | ||||||||
\(498\) | −0.978714 | −0.0438572 | ||||||||
\(499\) | 8.14590i | 0.364660i | 0.983237 | + | 0.182330i | \(0.0583640\pi\) | ||||
−0.983237 | + | 0.182330i | \(0.941636\pi\) | |||||||
\(500\) | 6.97871i | 0.312098i | ||||||||
\(501\) | 3.72949i | 0.166621i | ||||||||
\(502\) | − 2.00000i | − 0.0892644i | ||||||||
\(503\) | 24.3820 | 1.08714 | 0.543569 | − | 0.839364i | \(-0.317073\pi\) | ||||
0.543569 | + | 0.839364i | \(0.317073\pi\) | |||||||
\(504\) | −4.20163 | −0.187155 | ||||||||
\(505\) | − 3.27051i | − 0.145536i | ||||||||
\(506\) | 8.29180 | 0.368615 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.2279 | 1.16368 | ||||||||
\(509\) | 30.5967i | 1.35618i | 0.734980 | + | 0.678089i | \(0.237191\pi\) | ||||
−0.734980 | + | 0.678089i | \(0.762809\pi\) | |||||||
\(510\) | −0.416408 | −0.0184389 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 22.3050i | 0.985749i | ||||||||
\(513\) | 10.8541i | 0.479220i | ||||||||
\(514\) | 9.83282i | 0.433707i | ||||||||
\(515\) | − 1.79837i | − 0.0792458i | ||||||||
\(516\) | −5.35565 | −0.235770 | ||||||||
\(517\) | 10.8541 | 0.477363 | ||||||||
\(518\) | − 1.52786i | − 0.0671305i | ||||||||
\(519\) | −3.43769 | −0.150898 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.6525 | −0.554315 | −0.277158 | − | 0.960824i | \(-0.589392\pi\) | ||||
−0.277158 | + | 0.960824i | \(0.589392\pi\) | |||||||
\(522\) | 4.45898i | 0.195164i | ||||||||
\(523\) | −39.1246 | −1.71080 | −0.855400 | − | 0.517968i | \(-0.826689\pi\) | ||||
−0.855400 | + | 0.517968i | \(0.826689\pi\) | |||||||
\(524\) | 0.604878 | 0.0264242 | ||||||||
\(525\) | 1.85410i | 0.0809196i | ||||||||
\(526\) | 3.43769i | 0.149891i | ||||||||
\(527\) | − 65.0689i | − 2.83445i | ||||||||
\(528\) | − 5.83282i | − 0.253841i | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | −1.20163 | −0.0521953 | ||||||||
\(531\) | 6.38197i | 0.276954i | ||||||||
\(532\) | 9.00000 | 0.390199 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.34752 | −0.101587 | ||||||||
\(535\) | − 2.14590i | − 0.0927753i | ||||||||
\(536\) | −1.04257 | −0.0450323 | ||||||||
\(537\) | −3.43769 | −0.148347 | ||||||||
\(538\) | 5.24922i | 0.226310i | ||||||||
\(539\) | − 4.85410i | − 0.209081i | ||||||||
\(540\) | 1.58359i | 0.0681470i | ||||||||
\(541\) | − 1.72949i | − 0.0743566i | −0.999309 | − | 0.0371783i | \(-0.988163\pi\) | ||||
0.999309 | − | 0.0371783i | \(-0.0118369\pi\) | |||||||
\(542\) | 7.03444 | 0.302155 | ||||||||
\(543\) | −1.41641 | −0.0607839 | ||||||||
\(544\) | − 30.9787i | − 1.32820i | ||||||||
\(545\) | −4.09017 | −0.175204 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.00000 | −0.128271 | −0.0641354 | − | 0.997941i | \(-0.520429\pi\) | ||||
−0.0641354 | + | 0.997941i | \(0.520429\pi\) | |||||||
\(548\) | 0.708204i | 0.0302530i | ||||||||
\(549\) | 17.1246 | 0.730861 | ||||||||
\(550\) | −9.00000 | −0.383761 | ||||||||
\(551\) | − 19.8541i | − 0.845813i | ||||||||
\(552\) | 2.51471i | 0.107033i | ||||||||
\(553\) | − 4.00000i | − 0.170097i | ||||||||
\(554\) | 1.90983i | 0.0811409i | ||||||||
\(555\) | −0.583592 | −0.0247721 | ||||||||
\(556\) | −28.8541 | −1.22369 | ||||||||
\(557\) | − 18.9787i | − 0.804154i | −0.915606 | − | 0.402077i | \(-0.868288\pi\) | ||||
0.915606 | − | 0.402077i | \(-0.131712\pi\) | |||||||
\(558\) | 9.49342 | 0.401889 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.20163 | 0.0507780 | ||||||||
\(561\) | 13.8541i | 0.584921i | ||||||||
\(562\) | −0.832816 | −0.0351302 | ||||||||
\(563\) | 38.9443 | 1.64131 | 0.820653 | − | 0.571427i | \(-0.193610\pi\) | ||||
0.820653 | + | 0.571427i | \(0.193610\pi\) | |||||||
\(564\) | 1.58359i | 0.0666813i | ||||||||
\(565\) | − 2.85410i | − 0.120073i | ||||||||
\(566\) | 5.12461i | 0.215404i | ||||||||
\(567\) | − 7.70820i | − 0.323714i | ||||||||
\(568\) | −12.0426 | −0.505295 | ||||||||
\(569\) | 2.94427 | 0.123430 | 0.0617151 | − | 0.998094i | \(-0.480343\pi\) | ||||
0.0617151 | + | 0.998094i | \(0.480343\pi\) | |||||||
\(570\) | 0.270510i | 0.0113304i | ||||||||
\(571\) | 35.6869 | 1.49345 | 0.746726 | − | 0.665132i | \(-0.231625\pi\) | ||||
0.746726 | + | 0.665132i | \(0.231625\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.02129 | −0.376870 | ||||||||
\(574\) | 2.00000i | 0.0834784i | ||||||||
\(575\) | −21.7082 | −0.905295 | ||||||||
\(576\) | −13.4377 | −0.559904 | ||||||||
\(577\) | 9.83282i | 0.409345i | 0.978830 | + | 0.204673i | \(0.0656130\pi\) | ||||
−0.978830 | + | 0.204673i | \(0.934387\pi\) | |||||||
\(578\) | 14.8328i | 0.616964i | ||||||||
\(579\) | − 2.29180i | − 0.0952438i | ||||||||
\(580\) | − 2.89667i | − 0.120278i | ||||||||
\(581\) | −6.70820 | −0.278303 | ||||||||
\(582\) | 1.77206 | 0.0734544 | ||||||||
\(583\) | 39.9787i | 1.65575i | ||||||||
\(584\) | −2.94427 | −0.121835 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.29180 | −0.177292 | ||||||||
\(587\) | − 31.0902i | − 1.28323i | −0.767027 | − | 0.641614i | \(-0.778265\pi\) | ||||
0.767027 | − | 0.641614i | \(-0.221735\pi\) | |||||||
\(588\) | 0.708204 | 0.0292058 | ||||||||
\(589\) | −42.2705 | −1.74173 | ||||||||
\(590\) | 0.326238i | 0.0134310i | ||||||||
\(591\) | − 2.97871i | − 0.122528i | ||||||||
\(592\) | − 12.5836i | − 0.517182i | ||||||||
\(593\) | − 19.2016i | − 0.788516i | −0.919000 | − | 0.394258i | \(-0.871002\pi\) | ||||
0.919000 | − | 0.394258i | \(-0.128998\pi\) | |||||||
\(594\) | −4.14590 | −0.170108 | ||||||||
\(595\) | −2.85410 | −0.117007 | ||||||||
\(596\) | − 9.00000i | − 0.368654i | ||||||||
\(597\) | 0.922986 | 0.0377753 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.50658 | −0.347569 | −0.173785 | − | 0.984784i | \(-0.555600\pi\) | ||||
−0.173785 | + | 0.984784i | \(0.555600\pi\) | |||||||
\(600\) | − 2.72949i | − 0.111431i | ||||||||
\(601\) | −33.3951 | −1.36222 | −0.681108 | − | 0.732183i | \(-0.738501\pi\) | ||||
−0.681108 | + | 0.732183i | \(0.738501\pi\) | |||||||
\(602\) | 2.88854 | 0.117728 | ||||||||
\(603\) | − 2.02129i | − 0.0823131i | ||||||||
\(604\) | 27.2705i | 1.10962i | ||||||||
\(605\) | − 4.79837i | − 0.195082i | ||||||||
\(606\) | 1.24922i | 0.0507462i | ||||||||
\(607\) | −23.0000 | −0.933541 | −0.466771 | − | 0.884378i | \(-0.654583\pi\) | ||||
−0.466771 | + | 0.884378i | \(0.654583\pi\) | |||||||
\(608\) | −20.1246 | −0.816161 | ||||||||
\(609\) | − 1.56231i | − 0.0633078i | ||||||||
\(610\) | 0.875388 | 0.0354434 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 39.5410 | 1.59835 | ||||||||
\(613\) | 14.4377i | 0.583133i | 0.956551 | + | 0.291566i | \(0.0941765\pi\) | ||||
−0.956551 | + | 0.291566i | \(0.905824\pi\) | |||||||
\(614\) | 0.708204 | 0.0285808 | ||||||||
\(615\) | 0.763932 | 0.0308047 | ||||||||
\(616\) | 7.14590i | 0.287916i | ||||||||
\(617\) | 17.9443i | 0.722409i | 0.932487 | + | 0.361205i | \(0.117634\pi\) | ||||
−0.932487 | + | 0.361205i | \(0.882366\pi\) | |||||||
\(618\) | 0.686918i | 0.0276319i | ||||||||
\(619\) | 17.4164i | 0.700025i | 0.936745 | + | 0.350012i | \(0.113823\pi\) | ||||
−0.936745 | + | 0.350012i | \(0.886177\pi\) | |||||||
\(620\) | −6.16718 | −0.247680 | ||||||||
\(621\) | −10.0000 | −0.401286 | ||||||||
\(622\) | 4.70820i | 0.188782i | ||||||||
\(623\) | −16.0902 | −0.644639 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | − 5.77709i | − 0.230899i | ||||||||
\(627\) | 9.00000 | 0.359425 | ||||||||
\(628\) | 15.1033 | 0.602688 | ||||||||
\(629\) | 29.8885i | 1.19173i | ||||||||
\(630\) | − 0.416408i | − 0.0165901i | ||||||||
\(631\) | 39.3951i | 1.56830i | 0.620574 | + | 0.784148i | \(0.286899\pi\) | ||||
−0.620574 | + | 0.784148i | \(0.713101\pi\) | |||||||
\(632\) | 5.88854i | 0.234234i | ||||||||
\(633\) | 3.32624 | 0.132206 | ||||||||
\(634\) | −8.31308 | −0.330155 | ||||||||
\(635\) | 5.40325i | 0.214422i | ||||||||
\(636\) | −5.83282 | −0.231286 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.58359 | 0.300237 | ||||||||
\(639\) | − 23.3475i | − 0.923614i | ||||||||
\(640\) | −3.85410 | −0.152347 | ||||||||
\(641\) | 9.49342 | 0.374968 | 0.187484 | − | 0.982268i | \(-0.439967\pi\) | ||||
0.187484 | + | 0.982268i | \(0.439967\pi\) | |||||||
\(642\) | 0.819660i | 0.0323494i | ||||||||
\(643\) | − 7.00000i | − 0.276053i | −0.990429 | − | 0.138027i | \(-0.955924\pi\) | ||||
0.990429 | − | 0.138027i | \(-0.0440759\pi\) | |||||||
\(644\) | 8.29180i | 0.326743i | ||||||||
\(645\) | − 1.10333i | − 0.0434434i | ||||||||
\(646\) | 13.8541 | 0.545082 | ||||||||
\(647\) | −29.2361 | −1.14939 | −0.574694 | − | 0.818368i | \(-0.694879\pi\) | ||||
−0.574694 | + | 0.818368i | \(0.694879\pi\) | |||||||
\(648\) | 11.3475i | 0.445773i | ||||||||
\(649\) | 10.8541 | 0.426061 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.32624 | −0.130366 | ||||||||
\(652\) | − 18.0000i | − 0.704934i | ||||||||
\(653\) | −2.61803 | −0.102452 | −0.0512258 | − | 0.998687i | \(-0.516313\pi\) | ||||
−0.0512258 | + | 0.998687i | \(0.516313\pi\) | |||||||
\(654\) | 1.56231 | 0.0610910 | ||||||||
\(655\) | 0.124612i | 0.00486899i | ||||||||
\(656\) | 16.4721i | 0.643129i | ||||||||
\(657\) | − 5.70820i | − 0.222698i | ||||||||
\(658\) | − 0.854102i | − 0.0332964i | ||||||||
\(659\) | 11.8885 | 0.463112 | 0.231556 | − | 0.972822i | \(-0.425618\pi\) | ||||
0.231556 | + | 0.972822i | \(0.425618\pi\) | |||||||
\(660\) | 1.31308 | 0.0511117 | ||||||||
\(661\) | − 18.5410i | − 0.721162i | −0.932728 | − | 0.360581i | \(-0.882578\pi\) | ||||
0.932728 | − | 0.360581i | \(-0.117422\pi\) | |||||||
\(662\) | 6.43769 | 0.250208 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.87539 | 0.383239 | ||||||||
\(665\) | 1.85410i | 0.0718990i | ||||||||
\(666\) | −4.36068 | −0.168973 | ||||||||
\(667\) | 18.2918 | 0.708261 | ||||||||
\(668\) | − 18.1033i | − 0.700439i | ||||||||
\(669\) | 5.06888i | 0.195974i | ||||||||
\(670\) | − 0.103326i | − 0.00399181i | ||||||||
\(671\) | − 29.1246i | − 1.12434i | ||||||||
\(672\) | −1.58359 | −0.0610884 | ||||||||
\(673\) | −41.2492 | −1.59004 | −0.795020 | − | 0.606583i | \(-0.792540\pi\) | ||||
−0.795020 | + | 0.606583i | \(0.792540\pi\) | |||||||
\(674\) | − 3.27051i | − 0.125975i | ||||||||
\(675\) | 10.8541 | 0.417775 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.25735 | 0.0483240 | 0.0241620 | − | 0.999708i | \(-0.492308\pi\) | ||||
0.0241620 | + | 0.999708i | \(0.492308\pi\) | |||||||
\(678\) | 1.09017i | 0.0418677i | ||||||||
\(679\) | 12.1459 | 0.466117 | ||||||||
\(680\) | 4.20163 | 0.161125 | ||||||||
\(681\) | 2.85410i | 0.109369i | ||||||||
\(682\) | − 16.1459i | − 0.618258i | ||||||||
\(683\) | 7.47214i | 0.285913i | 0.989729 | + | 0.142957i | \(0.0456610\pi\) | ||||
−0.989729 | + | 0.142957i | \(0.954339\pi\) | |||||||
\(684\) | − 25.6869i | − 0.982164i | ||||||||
\(685\) | −0.145898 | −0.00557448 | ||||||||
\(686\) | −0.381966 | −0.0145835 | ||||||||
\(687\) | 10.3607i | 0.395285i | ||||||||
\(688\) | 23.7902 | 0.906995 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.249224 | −0.00948778 | ||||||||
\(691\) | 0.854102i | 0.0324916i | 0.999868 | + | 0.0162458i | \(0.00517142\pi\) | ||||
−0.999868 | + | 0.0162458i | \(0.994829\pi\) | |||||||
\(692\) | 16.6869 | 0.634341 | ||||||||
\(693\) | −13.8541 | −0.526274 | ||||||||
\(694\) | 13.4590i | 0.510896i | ||||||||
\(695\) | − 5.94427i | − 0.225479i | ||||||||
\(696\) | 2.29993i | 0.0871785i | ||||||||
\(697\) | − 39.1246i | − 1.48195i | ||||||||
\(698\) | 2.78522 | 0.105422 | ||||||||
\(699\) | 0.145898 | 0.00551837 | ||||||||
\(700\) | − 9.00000i | − 0.340168i | ||||||||
\(701\) | −6.76393 | −0.255470 | −0.127735 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127735 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.4164 | 0.732304 | ||||||||
\(704\) | 22.8541i | 0.861346i | ||||||||
\(705\) | −0.326238 | −0.0122868 | ||||||||
\(706\) | −11.0213 | −0.414792 | ||||||||
\(707\) | 8.56231i | 0.322019i | ||||||||
\(708\) | 1.58359i | 0.0595150i | ||||||||
\(709\) | − 3.43769i | − 0.129105i | −0.997914 | − | 0.0645527i | \(-0.979438\pi\) | ||||
0.997914 | − | 0.0645527i | \(-0.0205620\pi\) | |||||||
\(710\) | − 1.19350i | − 0.0447911i | ||||||||
\(711\) | −11.4164 | −0.428149 | ||||||||
\(712\) | 23.6869 | 0.887705 | ||||||||
\(713\) | − 38.9443i | − 1.45847i | ||||||||
\(714\) | 1.09017 | 0.0407986 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.6869 | 0.623619 | ||||||||
\(717\) | 4.31308i | 0.161075i | ||||||||
\(718\) | −4.16718 | −0.155518 | ||||||||
\(719\) | 32.1246 | 1.19805 | 0.599023 | − | 0.800732i | \(-0.295556\pi\) | ||||
0.599023 | + | 0.800732i | \(0.295556\pi\) | |||||||
\(720\) | − 3.42956i | − 0.127812i | ||||||||
\(721\) | 4.70820i | 0.175343i | ||||||||
\(722\) | − 1.74265i | − 0.0648546i | ||||||||
\(723\) | 1.69505i | 0.0630395i | ||||||||
\(724\) | 6.87539 | 0.255522 | ||||||||
\(725\) | −19.8541 | −0.737363 | ||||||||
\(726\) | 1.83282i | 0.0680222i | ||||||||
\(727\) | 17.2918 | 0.641317 | 0.320659 | − | 0.947195i | \(-0.396096\pi\) | ||||
0.320659 | + | 0.947195i | \(0.396096\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | − 0.291796i | − 0.0107999i | ||||||||
\(731\) | −56.5066 | −2.08997 | ||||||||
\(732\) | 4.24922 | 0.157056 | ||||||||
\(733\) | 1.27051i | 0.0469274i | 0.999725 | + | 0.0234637i | \(0.00746941\pi\) | ||||
−0.999725 | + | 0.0234637i | \(0.992531\pi\) | |||||||
\(734\) | 9.70820i | 0.358336i | ||||||||
\(735\) | 0.145898i | 0.00538153i | ||||||||
\(736\) | − 18.5410i | − 0.683431i | ||||||||
\(737\) | −3.43769 | −0.126629 | ||||||||
\(738\) | 5.70820 | 0.210122 | ||||||||
\(739\) | 47.1246i | 1.73351i | 0.498737 | + | 0.866753i | \(0.333797\pi\) | ||||
−0.498737 | + | 0.866753i | \(0.666203\pi\) | |||||||
\(740\) | 2.83282 | 0.104136 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.14590 | 0.115490 | ||||||||
\(743\) | 23.6738i | 0.868506i | 0.900791 | + | 0.434253i | \(0.142988\pi\) | ||||
−0.900791 | + | 0.434253i | \(0.857012\pi\) | |||||||
\(744\) | 4.89667 | 0.179521 | ||||||||
\(745\) | 1.85410 | 0.0679290 | ||||||||
\(746\) | − 0.167184i | − 0.00612105i | ||||||||
\(747\) | 19.1459i | 0.700512i | ||||||||
\(748\) | − 67.2492i | − 2.45888i | ||||||||
\(749\) | 5.61803i | 0.205278i | ||||||||
\(750\) | 0.549150 | 0.0200521 | ||||||||
\(751\) | −9.29180 | −0.339062 | −0.169531 | − | 0.985525i | \(-0.554225\pi\) | ||||
−0.169531 | + | 0.985525i | \(0.554225\pi\) | |||||||
\(752\) | − 7.03444i | − 0.256520i | ||||||||
\(753\) | 2.00000 | 0.0728841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.61803 | −0.204461 | ||||||||
\(756\) | − 4.14590i | − 0.150785i | ||||||||
\(757\) | 28.0000 | 1.01768 | 0.508839 | − | 0.860862i | \(-0.330075\pi\) | ||||
0.508839 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(758\) | 4.90983 | 0.178333 | ||||||||
\(759\) | 8.29180i | 0.300973i | ||||||||
\(760\) | − 2.72949i | − 0.0990090i | ||||||||
\(761\) | 22.1459i | 0.802788i | 0.915905 | + | 0.401394i | \(0.131474\pi\) | ||||
−0.915905 | + | 0.401394i | \(0.868526\pi\) | |||||||
\(762\) | − 2.06386i | − 0.0747657i | ||||||||
\(763\) | 10.7082 | 0.387663 | ||||||||
\(764\) | 43.7902 | 1.58428 | ||||||||
\(765\) | 8.14590i | 0.294516i | ||||||||
\(766\) | −9.54102 | −0.344731 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.12461 | −0.0766653 | ||||||||
\(769\) | 8.41641i | 0.303503i | 0.988419 | + | 0.151752i | \(0.0484914\pi\) | ||||
−0.988419 | + | 0.151752i | \(0.951509\pi\) | |||||||
\(770\) | −0.708204 | −0.0255219 | ||||||||
\(771\) | −9.83282 | −0.354120 | ||||||||
\(772\) | 11.1246i | 0.400384i | ||||||||
\(773\) | − 19.3607i | − 0.696355i | −0.937429 | − | 0.348178i | \(-0.886801\pi\) | ||||
0.937429 | − | 0.348178i | \(-0.113199\pi\) | |||||||
\(774\) | − 8.24420i | − 0.296332i | ||||||||
\(775\) | 42.2705i | 1.51840i | ||||||||
\(776\) | −17.8804 | −0.641869 | ||||||||
\(777\) | 1.52786 | 0.0548118 | ||||||||
\(778\) | − 9.12461i | − 0.327133i | ||||||||
\(779\) | −25.4164 | −0.910637 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.7082 | −1.42087 | ||||||||
\(782\) | 12.7639i | 0.456437i | ||||||||
\(783\) | −9.14590 | −0.326848 | ||||||||
\(784\) | −3.14590 | −0.112354 | ||||||||
\(785\) | 3.11146i | 0.111053i | ||||||||
\(786\) | − 0.0475975i | − 0.00169775i | ||||||||
\(787\) | − 29.4164i | − 1.04858i | −0.851539 | − | 0.524291i | \(-0.824330\pi\) | ||||
0.851539 | − | 0.524291i | \(-0.175670\pi\) | |||||||
\(788\) | 14.4590i | 0.515080i | ||||||||
\(789\) | −3.43769 | −0.122385 | ||||||||
\(790\) | −0.583592 | −0.0207633 | ||||||||
\(791\) | 7.47214i | 0.265679i | ||||||||
\(792\) | 20.3951 | 0.724709 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9.70820 | −0.344531 | ||||||||
\(795\) | − 1.20163i | − 0.0426173i | ||||||||
\(796\) | −4.48027 | −0.158799 | ||||||||
\(797\) | −14.1803 | −0.502293 | −0.251147 | − | 0.967949i | \(-0.580808\pi\) | ||||
−0.251147 | + | 0.967949i | \(0.580808\pi\) | |||||||
\(798\) | − 0.708204i | − 0.0250701i | ||||||||
\(799\) | 16.7082i | 0.591094i | ||||||||
\(800\) | 20.1246i | 0.711512i | ||||||||
\(801\) | 45.9230i | 1.62261i | ||||||||
\(802\) | −7.81153 | −0.275835 | ||||||||
\(803\) | −9.70820 | −0.342595 | ||||||||
\(804\) | − 0.501553i | − 0.0176884i | ||||||||
\(805\) | −1.70820 | −0.0602063 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.24922 | −0.184781 | ||||||||
\(808\) | − 12.6049i | − 0.443438i | ||||||||
\(809\) | 22.4164 | 0.788119 | 0.394059 | − | 0.919085i | \(-0.371070\pi\) | ||||
0.394059 | + | 0.919085i | \(0.371070\pi\) | |||||||
\(810\) | −1.12461 | −0.0395148 | ||||||||
\(811\) | 5.72949i | 0.201190i | 0.994927 | + | 0.100595i | \(0.0320746\pi\) | ||||
−0.994927 | + | 0.100595i | \(0.967925\pi\) | |||||||
\(812\) | 7.58359i | 0.266132i | ||||||||
\(813\) | 7.03444i | 0.246709i | ||||||||
\(814\) | 7.41641i | 0.259945i | ||||||||
\(815\) | 3.70820 | 0.129893 | ||||||||
\(816\) | 8.97871 | 0.314318 | ||||||||
\(817\) | 36.7082i | 1.28426i | ||||||||
\(818\) | −13.2016 | −0.461584 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.70820 | −0.129496 | ||||||||
\(821\) | 37.3607i | 1.30390i | 0.758263 | + | 0.651948i | \(0.226048\pi\) | ||||
−0.758263 | + | 0.651948i | \(0.773952\pi\) | |||||||
\(822\) | 0.0557281 | 0.00194374 | ||||||||
\(823\) | 11.5836 | 0.403779 | 0.201889 | − | 0.979408i | \(-0.435292\pi\) | ||||
0.201889 | + | 0.979408i | \(0.435292\pi\) | |||||||
\(824\) | − 6.93112i | − 0.241457i | ||||||||
\(825\) | − 9.00000i | − 0.313340i | ||||||||
\(826\) | − 0.854102i | − 0.0297180i | ||||||||
\(827\) | 30.9787i | 1.07724i | 0.842550 | + | 0.538618i | \(0.181053\pi\) | ||||
−0.842550 | + | 0.538618i | \(0.818947\pi\) | |||||||
\(828\) | 23.6656 | 0.822438 | ||||||||
\(829\) | 12.5623 | 0.436307 | 0.218153 | − | 0.975914i | \(-0.429997\pi\) | ||||
0.218153 | + | 0.975914i | \(0.429997\pi\) | |||||||
\(830\) | 0.978714i | 0.0339717i | ||||||||
\(831\) | −1.90983 | −0.0662513 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.47214 | 0.258894 | ||||||||
\(834\) | 2.27051i | 0.0786213i | ||||||||
\(835\) | 3.72949 | 0.129064 | ||||||||
\(836\) | −43.6869 | −1.51094 | ||||||||
\(837\) | 19.4721i | 0.673055i | ||||||||
\(838\) | 2.27051i | 0.0784335i | ||||||||
\(839\) | 28.7426i | 0.992306i | 0.868235 | + | 0.496153i | \(0.165255\pi\) | ||||
−0.868235 | + | 0.496153i | \(0.834745\pi\) | |||||||
\(840\) | − 0.214782i | − 0.00741067i | ||||||||
\(841\) | −12.2705 | −0.423121 | ||||||||
\(842\) | 9.70820 | 0.334567 | ||||||||
\(843\) | − 0.832816i | − 0.0286837i | ||||||||
\(844\) | −16.1459 | −0.555765 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.43769 | −0.0838096 | ||||||||
\(847\) | 12.5623i | 0.431646i | ||||||||
\(848\) | 25.9098 | 0.889747 | ||||||||
\(849\) | −5.12461 | −0.175876 | ||||||||
\(850\) | − 13.8541i | − 0.475192i | ||||||||
\(851\) | 17.8885i | 0.613211i | ||||||||
\(852\) | − 5.79335i | − 0.198477i | ||||||||
\(853\) | 26.1246i | 0.894490i | 0.894412 | + | 0.447245i | \(0.147595\pi\) | ||||
−0.894412 | + | 0.447245i | \(0.852405\pi\) | |||||||
\(854\) | −2.29180 | −0.0784236 | ||||||||
\(855\) | 5.29180 | 0.180976 | ||||||||
\(856\) | − 8.27051i | − 0.282680i | ||||||||
\(857\) | −29.4508 | −1.00602 | −0.503011 | − | 0.864280i | \(-0.667774\pi\) | ||||
−0.503011 | + | 0.864280i | \(0.667774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.2492 | 1.23681 | 0.618404 | − | 0.785861i | \(-0.287780\pi\) | ||||
0.618404 | + | 0.785861i | \(0.287780\pi\) | |||||||
\(860\) | 5.35565i | 0.182626i | ||||||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | 6.41641 | 0.218544 | ||||||||
\(863\) | − 23.8885i | − 0.813175i | −0.913612 | − | 0.406588i | \(-0.866719\pi\) | ||||
0.913612 | − | 0.406588i | \(-0.133281\pi\) | |||||||
\(864\) | 9.27051i | 0.315389i | ||||||||
\(865\) | 3.43769i | 0.116885i | ||||||||
\(866\) | − 0.381966i | − 0.0129797i | ||||||||
\(867\) | −14.8328 | −0.503749 | ||||||||
\(868\) | 16.1459 | 0.548027 | ||||||||
\(869\) | 19.4164i | 0.658657i | ||||||||
\(870\) | −0.227937 | −0.00772780 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.7639 | −0.533834 | ||||||||
\(873\) | − 34.6656i | − 1.17325i | ||||||||
\(874\) | 8.29180 | 0.280474 | ||||||||
\(875\) | 3.76393 | 0.127244 | ||||||||
\(876\) | − 1.41641i | − 0.0478560i | ||||||||
\(877\) | − 12.7082i | − 0.429126i | −0.976710 | − | 0.214563i | \(-0.931167\pi\) | ||||
0.976710 | − | 0.214563i | \(-0.0688327\pi\) | |||||||
\(878\) | − 3.11146i | − 0.105007i | ||||||||
\(879\) | − 4.29180i | − 0.144759i | ||||||||
\(880\) | −5.83282 | −0.196624 | ||||||||
\(881\) | −12.5967 | −0.424395 | −0.212198 | − | 0.977227i | \(-0.568062\pi\) | ||||
−0.212198 | + | 0.977227i | \(0.568062\pi\) | |||||||
\(882\) | 1.09017i | 0.0367079i | ||||||||
\(883\) | −29.0000 | −0.975928 | −0.487964 | − | 0.872864i | \(-0.662260\pi\) | ||||
−0.487964 | + | 0.872864i | \(0.662260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.326238 | −0.0109664 | ||||||||
\(886\) | − 0.291796i | − 0.00980308i | ||||||||
\(887\) | 23.3475 | 0.783933 | 0.391967 | − | 0.919979i | \(-0.371795\pi\) | ||||
0.391967 | + | 0.919979i | \(0.371795\pi\) | |||||||
\(888\) | −2.24922 | −0.0754790 | ||||||||
\(889\) | − 14.1459i | − 0.474438i | ||||||||
\(890\) | 2.34752i | 0.0786892i | ||||||||
\(891\) | 37.4164i | 1.25350i | ||||||||
\(892\) | − 24.6049i | − 0.823832i | ||||||||
\(893\) | 10.8541 | 0.363219 | ||||||||
\(894\) | −0.708204 | −0.0236859 | ||||||||
\(895\) | 3.43769i | 0.114909i | ||||||||
\(896\) | 10.0902 | 0.337089 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.8754 | 0.362916 | ||||||||
\(899\) | − 35.6180i | − 1.18793i | ||||||||
\(900\) | −25.6869 | −0.856231 | ||||||||
\(901\) | −61.5410 | −2.05023 | ||||||||
\(902\) | − 9.70820i | − 0.323248i | ||||||||
\(903\) | 2.88854i | 0.0961247i | ||||||||
\(904\) | − 11.0000i | − 0.365855i | ||||||||
\(905\) | 1.41641i | 0.0470830i | ||||||||
\(906\) | 2.14590 | 0.0712927 | ||||||||
\(907\) | 24.0000 | 0.796907 | 0.398453 | − | 0.917189i | \(-0.369547\pi\) | ||||
0.398453 | + | 0.917189i | \(0.369547\pi\) | |||||||
\(908\) | − 13.8541i | − 0.459765i | ||||||||
\(909\) | 24.4377 | 0.810547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.6869 | 1.24862 | 0.624312 | − | 0.781175i | \(-0.285380\pi\) | ||||
0.624312 | + | 0.781175i | \(0.285380\pi\) | |||||||
\(912\) | − 5.83282i | − 0.193144i | ||||||||
\(913\) | 32.5623 | 1.07766 | ||||||||
\(914\) | 4.36068 | 0.144238 | ||||||||
\(915\) | 0.875388i | 0.0289394i | ||||||||
\(916\) | − 50.2918i | − 1.66169i | ||||||||
\(917\) | − 0.326238i | − 0.0107733i | ||||||||
\(918\) | − 6.38197i | − 0.210636i | ||||||||
\(919\) | −30.0000 | −0.989609 | −0.494804 | − | 0.869004i | \(-0.664760\pi\) | ||||
−0.494804 | + | 0.869004i | \(0.664760\pi\) | |||||||
\(920\) | 2.51471 | 0.0829075 | ||||||||
\(921\) | 0.708204i | 0.0233361i | ||||||||
\(922\) | −14.9787 | −0.493298 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.43769 | −0.113092 | ||||||||
\(925\) | − 19.4164i | − 0.638408i | ||||||||
\(926\) | −2.56231 | −0.0842026 | ||||||||
\(927\) | 13.4377 | 0.441352 | ||||||||
\(928\) | − 16.9574i | − 0.556655i | ||||||||
\(929\) | − 47.0689i | − 1.54428i | −0.635452 | − | 0.772140i | \(-0.719186\pi\) | ||||
0.635452 | − | 0.772140i | \(-0.280814\pi\) | |||||||
\(930\) | 0.485292i | 0.0159133i | ||||||||
\(931\) | − 4.85410i | − 0.159087i | ||||||||
\(932\) | −0.708204 | −0.0231980 | ||||||||
\(933\) | −4.70820 | −0.154140 | ||||||||
\(934\) | − 12.8541i | − 0.420599i | ||||||||
\(935\) | 13.8541 | 0.453078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.1246 | −1.83351 | −0.916756 | − | 0.399449i | \(-0.869202\pi\) | ||||
−0.916756 | + | 0.399449i | \(0.869202\pi\) | |||||||
\(938\) | 0.270510i | 0.00883246i | ||||||||
\(939\) | 5.77709 | 0.188528 | ||||||||
\(940\) | 1.58359 | 0.0516511 | ||||||||
\(941\) | 51.6525i | 1.68382i | 0.539616 | + | 0.841911i | \(0.318569\pi\) | ||||
−0.539616 | + | 0.841911i | \(0.681431\pi\) | |||||||
\(942\) | − 1.18847i | − 0.0387225i | ||||||||
\(943\) | − 23.4164i | − 0.762543i | ||||||||
\(944\) | − 7.03444i | − 0.228952i | ||||||||
\(945\) | 0.854102 | 0.0277839 | ||||||||
\(946\) | −14.0213 | −0.455871 | ||||||||
\(947\) | − 45.8673i | − 1.49049i | −0.666793 | − | 0.745243i | \(-0.732334\pi\) | ||||
0.666793 | − | 0.745243i | \(-0.267666\pi\) | |||||||
\(948\) | −2.83282 | −0.0920056 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −9.00000 | −0.291999 | ||||||||
\(951\) | − 8.31308i | − 0.269570i | ||||||||
\(952\) | −11.0000 | −0.356512 | ||||||||
\(953\) | 44.7771 | 1.45047 | 0.725236 | − | 0.688500i | \(-0.241731\pi\) | ||||
0.725236 | + | 0.688500i | \(0.241731\pi\) | |||||||
\(954\) | − 8.97871i | − 0.290697i | ||||||||
\(955\) | 9.02129i | 0.291922i | ||||||||
\(956\) | − 20.9361i | − 0.677123i | ||||||||
\(957\) | 7.58359i | 0.245143i | ||||||||
\(958\) | −8.39512 | −0.271234 | ||||||||
\(959\) | 0.381966 | 0.0123343 | ||||||||
\(960\) | − 0.686918i | − 0.0221702i | ||||||||
\(961\) | −44.8328 | −1.44622 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.0344 | 0.516703 | ||||||||
\(964\) | − 8.22794i | − 0.265004i | ||||||||
\(965\) | −2.29180 | −0.0737755 | ||||||||
\(966\) | 0.652476 | 0.0209931 | ||||||||
\(967\) | − 39.0000i | − 1.25416i | −0.778957 | − | 0.627078i | \(-0.784251\pi\) | ||||
0.778957 | − | 0.627078i | \(-0.215749\pi\) | |||||||
\(968\) | − 18.4934i | − 0.594401i | ||||||||
\(969\) | 13.8541i | 0.445058i | ||||||||
\(970\) | − 1.77206i | − 0.0568975i | ||||||||
\(971\) | 58.4164 | 1.87467 | 0.937336 | − | 0.348427i | \(-0.113284\pi\) | ||||
0.937336 | + | 0.348427i | \(0.113284\pi\) | |||||||
\(972\) | −17.8967 | −0.574036 | ||||||||
\(973\) | 15.5623i | 0.498905i | ||||||||
\(974\) | 6.48529 | 0.207802 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.8754 | −0.604186 | ||||||||
\(977\) | − 31.4721i | − 1.00688i | −0.864029 | − | 0.503441i | \(-0.832067\pi\) | ||||
0.864029 | − | 0.503441i | \(-0.167933\pi\) | |||||||
\(978\) | −1.41641 | −0.0452917 | ||||||||
\(979\) | 78.1033 | 2.49619 | ||||||||
\(980\) | − 0.708204i | − 0.0226227i | ||||||||
\(981\) | − 30.5623i | − 0.975779i | ||||||||
\(982\) | − 5.58359i | − 0.178180i | ||||||||
\(983\) | − 20.6180i | − 0.657613i | −0.944397 | − | 0.328807i | \(-0.893354\pi\) | ||||
0.944397 | − | 0.328807i | \(-0.106646\pi\) | |||||||
\(984\) | 2.94427 | 0.0938600 | ||||||||
\(985\) | −2.97871 | −0.0949097 | ||||||||
\(986\) | 11.6738i | 0.371768i | ||||||||
\(987\) | 0.854102 | 0.0271864 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.8197 | −1.07540 | ||||||||
\(990\) | 2.02129i | 0.0642407i | ||||||||
\(991\) | −22.8541 | −0.725984 | −0.362992 | − | 0.931792i | \(-0.618245\pi\) | ||||
−0.362992 | + | 0.931792i | \(0.618245\pi\) | |||||||
\(992\) | −36.1033 | −1.14628 | ||||||||
\(993\) | 6.43769i | 0.204294i | ||||||||
\(994\) | 3.12461i | 0.0991067i | ||||||||
\(995\) | − 0.922986i | − 0.0292606i | ||||||||
\(996\) | 4.75078i | 0.150534i | ||||||||
\(997\) | 49.0000 | 1.55185 | 0.775923 | − | 0.630828i | \(-0.217285\pi\) | ||||
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(998\) | −3.11146 | −0.0984914 | ||||||||
\(999\) | − 8.94427i | − 0.282984i |
(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.c.c.337.3 | 4 | ||
13.2 | odd | 12 | 91.2.f.a.22.2 | ✓ | 4 | ||
13.5 | odd | 4 | 1183.2.a.g.1.1 | 2 | |||
13.6 | odd | 12 | 91.2.f.a.29.2 | yes | 4 | ||
13.8 | odd | 4 | 1183.2.a.c.1.2 | 2 | |||
13.12 | even | 2 | inner | 1183.2.c.c.337.2 | 4 | ||
39.2 | even | 12 | 819.2.o.c.568.1 | 4 | |||
39.32 | even | 12 | 819.2.o.c.757.1 | 4 | |||
52.15 | even | 12 | 1456.2.s.h.113.2 | 4 | |||
52.19 | even | 12 | 1456.2.s.h.1121.2 | 4 | |||
91.2 | odd | 12 | 637.2.h.g.165.1 | 4 | |||
91.6 | even | 12 | 637.2.f.c.393.2 | 4 | |||
91.19 | even | 12 | 637.2.g.c.263.2 | 4 | |||
91.32 | odd | 12 | 637.2.h.g.471.1 | 4 | |||
91.34 | even | 4 | 8281.2.a.n.1.2 | 2 | |||
91.41 | even | 12 | 637.2.f.c.295.2 | 4 | |||
91.45 | even | 12 | 637.2.h.f.471.1 | 4 | |||
91.54 | even | 12 | 637.2.h.f.165.1 | 4 | |||
91.58 | odd | 12 | 637.2.g.b.263.2 | 4 | |||
91.67 | odd | 12 | 637.2.g.b.373.2 | 4 | |||
91.80 | even | 12 | 637.2.g.c.373.2 | 4 | |||
91.83 | even | 4 | 8281.2.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.a.22.2 | ✓ | 4 | 13.2 | odd | 12 | ||
91.2.f.a.29.2 | yes | 4 | 13.6 | odd | 12 | ||
637.2.f.c.295.2 | 4 | 91.41 | even | 12 | |||
637.2.f.c.393.2 | 4 | 91.6 | even | 12 | |||
637.2.g.b.263.2 | 4 | 91.58 | odd | 12 | |||
637.2.g.b.373.2 | 4 | 91.67 | odd | 12 | |||
637.2.g.c.263.2 | 4 | 91.19 | even | 12 | |||
637.2.g.c.373.2 | 4 | 91.80 | even | 12 | |||
637.2.h.f.165.1 | 4 | 91.54 | even | 12 | |||
637.2.h.f.471.1 | 4 | 91.45 | even | 12 | |||
637.2.h.g.165.1 | 4 | 91.2 | odd | 12 | |||
637.2.h.g.471.1 | 4 | 91.32 | odd | 12 | |||
819.2.o.c.568.1 | 4 | 39.2 | even | 12 | |||
819.2.o.c.757.1 | 4 | 39.32 | even | 12 | |||
1183.2.a.c.1.2 | 2 | 13.8 | odd | 4 | |||
1183.2.a.g.1.1 | 2 | 13.5 | odd | 4 | |||
1183.2.c.c.337.2 | 4 | 13.12 | even | 2 | inner | ||
1183.2.c.c.337.3 | 4 | 1.1 | even | 1 | trivial | ||
1456.2.s.h.113.2 | 4 | 52.15 | even | 12 | |||
1456.2.s.h.1121.2 | 4 | 52.19 | even | 12 | |||
8281.2.a.n.1.2 | 2 | 91.34 | even | 4 | |||
8281.2.a.bb.1.1 | 2 | 91.83 | even | 4 |