Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23607 | 1.58114 | 0.790569 | − | 0.612372i | \(-0.209785\pi\) | ||||
0.790569 | + | 0.612372i | \(0.209785\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.00000 | 1.50000 | ||||||||
\(5\) | −0.618034 | −0.276393 | −0.138197 | − | 0.990405i | \(-0.544131\pi\) | ||||
−0.138197 | + | 0.990405i | \(0.544131\pi\) | |||||||
\(6\) | −2.23607 | −0.912871 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.38197 | −0.437016 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.00000 | −0.866025 | ||||||||
\(13\) | 3.23607 | 0.897524 | 0.448762 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448762 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(14\) | 2.23607 | 0.597614 | ||||||||
\(15\) | 0.618034 | 0.159576 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.85410 | 1.17729 | 0.588646 | − | 0.808391i | \(-0.299661\pi\) | ||||
0.588646 | + | 0.808391i | \(0.299661\pi\) | |||||||
\(18\) | 2.23607 | 0.527046 | ||||||||
\(19\) | 2.85410 | 0.654776 | 0.327388 | − | 0.944890i | \(-0.393832\pi\) | ||||
0.327388 | + | 0.944890i | \(0.393832\pi\) | |||||||
\(20\) | −1.85410 | −0.414590 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.38197 | 0.913703 | 0.456852 | − | 0.889543i | \(-0.348977\pi\) | ||||
0.456852 | + | 0.889543i | \(0.348977\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | −4.61803 | −0.923607 | ||||||||
\(26\) | 7.23607 | 1.41911 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.00000 | 0.566947 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 1.38197 | 0.252311 | ||||||||
\(31\) | −3.09017 | −0.555011 | −0.277505 | − | 0.960724i | \(-0.589508\pi\) | ||||
−0.277505 | + | 0.960724i | \(0.589508\pi\) | |||||||
\(32\) | −6.70820 | −1.18585 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.8541 | 1.86146 | ||||||||
\(35\) | −0.618034 | −0.104467 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 4.61803 | 0.759200 | 0.379600 | − | 0.925151i | \(-0.376062\pi\) | ||||
0.379600 | + | 0.925151i | \(0.376062\pi\) | |||||||
\(38\) | 6.38197 | 1.03529 | ||||||||
\(39\) | −3.23607 | −0.518186 | ||||||||
\(40\) | −1.38197 | −0.218508 | ||||||||
\(41\) | 7.38197 | 1.15287 | 0.576435 | − | 0.817143i | \(-0.304444\pi\) | ||||
0.576435 | + | 0.817143i | \(0.304444\pi\) | |||||||
\(42\) | −2.23607 | −0.345033 | ||||||||
\(43\) | 9.70820 | 1.48049 | 0.740244 | − | 0.672339i | \(-0.234710\pi\) | ||||
0.740244 | + | 0.672339i | \(0.234710\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.618034 | −0.0921311 | ||||||||
\(46\) | 9.79837 | 1.44469 | ||||||||
\(47\) | 4.47214 | 0.652328 | 0.326164 | − | 0.945313i | \(-0.394244\pi\) | ||||
0.326164 | + | 0.945313i | \(0.394244\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −10.3262 | −1.46035 | ||||||||
\(51\) | −4.85410 | −0.679710 | ||||||||
\(52\) | 9.70820 | 1.34629 | ||||||||
\(53\) | 6.76393 | 0.929098 | 0.464549 | − | 0.885548i | \(-0.346217\pi\) | ||||
0.464549 | + | 0.885548i | \(0.346217\pi\) | |||||||
\(54\) | −2.23607 | −0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | −2.85410 | −0.378035 | ||||||||
\(58\) | −13.4164 | −1.76166 | ||||||||
\(59\) | 3.23607 | 0.421300 | 0.210650 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210650 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(60\) | 1.85410 | 0.239364 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | −6.90983 | −0.877549 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 14.5623 | 1.76594 | ||||||||
\(69\) | −4.38197 | −0.527527 | ||||||||
\(70\) | −1.38197 | −0.165177 | ||||||||
\(71\) | −4.94427 | −0.586777 | −0.293389 | − | 0.955993i | \(-0.594783\pi\) | ||||
−0.293389 | + | 0.955993i | \(0.594783\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | 13.7082 | 1.60442 | 0.802212 | − | 0.597039i | \(-0.203656\pi\) | ||||
0.802212 | + | 0.597039i | \(0.203656\pi\) | |||||||
\(74\) | 10.3262 | 1.20040 | ||||||||
\(75\) | 4.61803 | 0.533245 | ||||||||
\(76\) | 8.56231 | 0.982164 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.23607 | −0.819323 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0.618034 | 0.0690983 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.5066 | 1.82285 | ||||||||
\(83\) | 16.4721 | 1.80805 | 0.904026 | − | 0.427478i | \(-0.140598\pi\) | ||||
0.904026 | + | 0.427478i | \(0.140598\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | 21.7082 | 2.34086 | ||||||||
\(87\) | 6.00000 | 0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.61803 | 0.595510 | 0.297755 | − | 0.954642i | \(-0.403762\pi\) | ||||
0.297755 | + | 0.954642i | \(0.403762\pi\) | |||||||
\(90\) | −1.38197 | −0.145672 | ||||||||
\(91\) | 3.23607 | 0.339232 | ||||||||
\(92\) | 13.1459 | 1.37055 | ||||||||
\(93\) | 3.09017 | 0.320436 | ||||||||
\(94\) | 10.0000 | 1.03142 | ||||||||
\(95\) | −1.76393 | −0.180976 | ||||||||
\(96\) | 6.70820 | 0.684653 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 2.23607 | 0.225877 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.8541 | −1.38541 | ||||||||
\(101\) | −6.79837 | −0.676463 | −0.338232 | − | 0.941063i | \(-0.609829\pi\) | ||||
−0.338232 | + | 0.941063i | \(0.609829\pi\) | |||||||
\(102\) | −10.8541 | −1.07472 | ||||||||
\(103\) | 1.32624 | 0.130678 | 0.0653391 | − | 0.997863i | \(-0.479187\pi\) | ||||
0.0653391 | + | 0.997863i | \(0.479187\pi\) | |||||||
\(104\) | 7.23607 | 0.709555 | ||||||||
\(105\) | 0.618034 | 0.0603139 | ||||||||
\(106\) | 15.1246 | 1.46903 | ||||||||
\(107\) | 15.7984 | 1.52729 | 0.763643 | − | 0.645638i | \(-0.223409\pi\) | ||||
0.763643 | + | 0.645638i | \(0.223409\pi\) | |||||||
\(108\) | −3.00000 | −0.288675 | ||||||||
\(109\) | −17.5623 | −1.68216 | −0.841082 | − | 0.540908i | \(-0.818081\pi\) | ||||
−0.841082 | + | 0.540908i | \(0.818081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.61803 | −0.438324 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −5.23607 | −0.492568 | −0.246284 | − | 0.969198i | \(-0.579210\pi\) | ||||
−0.246284 | + | 0.969198i | \(0.579210\pi\) | |||||||
\(114\) | −6.38197 | −0.597726 | ||||||||
\(115\) | −2.70820 | −0.252541 | ||||||||
\(116\) | −18.0000 | −1.67126 | ||||||||
\(117\) | 3.23607 | 0.299175 | ||||||||
\(118\) | 7.23607 | 0.666134 | ||||||||
\(119\) | 4.85410 | 0.444975 | ||||||||
\(120\) | 1.38197 | 0.126156 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.38197 | −0.665609 | ||||||||
\(124\) | −9.27051 | −0.832516 | ||||||||
\(125\) | 5.94427 | 0.531672 | ||||||||
\(126\) | 2.23607 | 0.199205 | ||||||||
\(127\) | 0.291796 | 0.0258927 | 0.0129464 | − | 0.999916i | \(-0.495879\pi\) | ||||
0.0129464 | + | 0.999916i | \(0.495879\pi\) | |||||||
\(128\) | −15.6525 | −1.38350 | ||||||||
\(129\) | −9.70820 | −0.854760 | ||||||||
\(130\) | −4.47214 | −0.392232 | ||||||||
\(131\) | −16.6525 | −1.45493 | −0.727467 | − | 0.686143i | \(-0.759302\pi\) | ||||
−0.727467 | + | 0.686143i | \(0.759302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.85410 | 0.247482 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.618034 | 0.0531919 | ||||||||
\(136\) | 10.8541 | 0.930732 | ||||||||
\(137\) | 8.18034 | 0.698894 | 0.349447 | − | 0.936956i | \(-0.386370\pi\) | ||||
0.349447 | + | 0.936956i | \(0.386370\pi\) | |||||||
\(138\) | −9.79837 | −0.834093 | ||||||||
\(139\) | 13.1459 | 1.11502 | 0.557510 | − | 0.830170i | \(-0.311757\pi\) | ||||
0.557510 | + | 0.830170i | \(0.311757\pi\) | |||||||
\(140\) | −1.85410 | −0.156700 | ||||||||
\(141\) | −4.47214 | −0.376622 | ||||||||
\(142\) | −11.0557 | −0.927776 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 3.70820 | 0.307950 | ||||||||
\(146\) | 30.6525 | 2.53682 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 13.8541 | 1.13880 | ||||||||
\(149\) | −4.94427 | −0.405051 | −0.202525 | − | 0.979277i | \(-0.564915\pi\) | ||||
−0.202525 | + | 0.979277i | \(0.564915\pi\) | |||||||
\(150\) | 10.3262 | 0.843134 | ||||||||
\(151\) | −15.5279 | −1.26364 | −0.631820 | − | 0.775115i | \(-0.717692\pi\) | ||||
−0.631820 | + | 0.775115i | \(0.717692\pi\) | |||||||
\(152\) | 6.38197 | 0.517646 | ||||||||
\(153\) | 4.85410 | 0.392431 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.90983 | 0.153401 | ||||||||
\(156\) | −9.70820 | −0.777278 | ||||||||
\(157\) | −23.1246 | −1.84554 | −0.922772 | − | 0.385345i | \(-0.874082\pi\) | ||||
−0.922772 | + | 0.385345i | \(0.874082\pi\) | |||||||
\(158\) | −22.3607 | −1.77892 | ||||||||
\(159\) | −6.76393 | −0.536415 | ||||||||
\(160\) | 4.14590 | 0.327762 | ||||||||
\(161\) | 4.38197 | 0.345347 | ||||||||
\(162\) | 2.23607 | 0.175682 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 22.1459 | 1.72930 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 36.8328 | 2.85878 | ||||||||
\(167\) | −21.2361 | −1.64330 | −0.821648 | − | 0.569995i | \(-0.806945\pi\) | ||||
−0.821648 | + | 0.569995i | \(0.806945\pi\) | |||||||
\(168\) | −2.23607 | −0.172516 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | −6.70820 | −0.514496 | ||||||||
\(171\) | 2.85410 | 0.218259 | ||||||||
\(172\) | 29.1246 | 2.22073 | ||||||||
\(173\) | −13.6180 | −1.03536 | −0.517680 | − | 0.855574i | \(-0.673204\pi\) | ||||
−0.517680 | + | 0.855574i | \(0.673204\pi\) | |||||||
\(174\) | 13.4164 | 1.01710 | ||||||||
\(175\) | −4.61803 | −0.349091 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.23607 | −0.243238 | ||||||||
\(178\) | 12.5623 | 0.941585 | ||||||||
\(179\) | −14.7984 | −1.10608 | −0.553041 | − | 0.833154i | \(-0.686533\pi\) | ||||
−0.553041 | + | 0.833154i | \(0.686533\pi\) | |||||||
\(180\) | −1.85410 | −0.138197 | ||||||||
\(181\) | −19.8885 | −1.47830 | −0.739152 | − | 0.673539i | \(-0.764773\pi\) | ||||
−0.739152 | + | 0.673539i | \(0.764773\pi\) | |||||||
\(182\) | 7.23607 | 0.536373 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.79837 | 0.722346 | ||||||||
\(185\) | −2.85410 | −0.209838 | ||||||||
\(186\) | 6.90983 | 0.506653 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 13.4164 | 0.978492 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −3.94427 | −0.286148 | ||||||||
\(191\) | 4.90983 | 0.355263 | 0.177631 | − | 0.984097i | \(-0.443157\pi\) | ||||
0.177631 | + | 0.984097i | \(0.443157\pi\) | |||||||
\(192\) | 13.0000 | 0.938194 | ||||||||
\(193\) | −21.8541 | −1.57309 | −0.786546 | − | 0.617531i | \(-0.788133\pi\) | ||||
−0.786546 | + | 0.617531i | \(0.788133\pi\) | |||||||
\(194\) | −13.4164 | −0.963242 | ||||||||
\(195\) | 2.00000 | 0.143223 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | 22.4721 | 1.60107 | 0.800537 | − | 0.599284i | \(-0.204548\pi\) | ||||
0.800537 | + | 0.599284i | \(0.204548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1459 | 0.931888 | 0.465944 | − | 0.884814i | \(-0.345715\pi\) | ||||
0.465944 | + | 0.884814i | \(0.345715\pi\) | |||||||
\(200\) | −10.3262 | −0.730175 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.2016 | −1.06958 | ||||||||
\(203\) | −6.00000 | −0.421117 | ||||||||
\(204\) | −14.5623 | −1.01957 | ||||||||
\(205\) | −4.56231 | −0.318645 | ||||||||
\(206\) | 2.96556 | 0.206620 | ||||||||
\(207\) | 4.38197 | 0.304568 | ||||||||
\(208\) | −3.23607 | −0.224381 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.38197 | 0.0953647 | ||||||||
\(211\) | −18.3607 | −1.26400 | −0.632001 | − | 0.774968i | \(-0.717766\pi\) | ||||
−0.632001 | + | 0.774968i | \(0.717766\pi\) | |||||||
\(212\) | 20.2918 | 1.39365 | ||||||||
\(213\) | 4.94427 | 0.338776 | ||||||||
\(214\) | 35.3262 | 2.41485 | ||||||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | −3.09017 | −0.209774 | ||||||||
\(218\) | −39.2705 | −2.65973 | ||||||||
\(219\) | −13.7082 | −0.926315 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.7082 | 1.05665 | ||||||||
\(222\) | −10.3262 | −0.693052 | ||||||||
\(223\) | 19.6180 | 1.31372 | 0.656860 | − | 0.754012i | \(-0.271884\pi\) | ||||
0.656860 | + | 0.754012i | \(0.271884\pi\) | |||||||
\(224\) | −6.70820 | −0.448211 | ||||||||
\(225\) | −4.61803 | −0.307869 | ||||||||
\(226\) | −11.7082 | −0.778818 | ||||||||
\(227\) | 12.4721 | 0.827805 | 0.413902 | − | 0.910321i | \(-0.364165\pi\) | ||||
0.413902 | + | 0.910321i | \(0.364165\pi\) | |||||||
\(228\) | −8.56231 | −0.567053 | ||||||||
\(229\) | 16.1803 | 1.06923 | 0.534613 | − | 0.845097i | \(-0.320457\pi\) | ||||
0.534613 | + | 0.845097i | \(0.320457\pi\) | |||||||
\(230\) | −6.05573 | −0.399303 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.4164 | −0.880830 | ||||||||
\(233\) | −15.7082 | −1.02908 | −0.514539 | − | 0.857467i | \(-0.672037\pi\) | ||||
−0.514539 | + | 0.857467i | \(0.672037\pi\) | |||||||
\(234\) | 7.23607 | 0.473037 | ||||||||
\(235\) | −2.76393 | −0.180299 | ||||||||
\(236\) | 9.70820 | 0.631950 | ||||||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | 10.8541 | 0.703567 | ||||||||
\(239\) | −19.0344 | −1.23124 | −0.615618 | − | 0.788045i | \(-0.711093\pi\) | ||||
−0.615618 | + | 0.788045i | \(0.711093\pi\) | |||||||
\(240\) | −0.618034 | −0.0398939 | ||||||||
\(241\) | 12.0000 | 0.772988 | 0.386494 | − | 0.922292i | \(-0.373686\pi\) | ||||
0.386494 | + | 0.922292i | \(0.373686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.618034 | −0.0394847 | ||||||||
\(246\) | −16.5066 | −1.05242 | ||||||||
\(247\) | 9.23607 | 0.587677 | ||||||||
\(248\) | −6.90983 | −0.438775 | ||||||||
\(249\) | −16.4721 | −1.04388 | ||||||||
\(250\) | 13.2918 | 0.840647 | ||||||||
\(251\) | 27.7082 | 1.74893 | 0.874463 | − | 0.485092i | \(-0.161214\pi\) | ||||
0.874463 | + | 0.485092i | \(0.161214\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.652476 | 0.0409400 | ||||||||
\(255\) | 3.00000 | 0.187867 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | 24.4508 | 1.52520 | 0.762601 | − | 0.646869i | \(-0.223922\pi\) | ||||
0.762601 | + | 0.646869i | \(0.223922\pi\) | |||||||
\(258\) | −21.7082 | −1.35149 | ||||||||
\(259\) | 4.61803 | 0.286951 | ||||||||
\(260\) | −6.00000 | −0.372104 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | −37.2361 | −2.30045 | ||||||||
\(263\) | 10.8541 | 0.669293 | 0.334646 | − | 0.942344i | \(-0.391383\pi\) | ||||
0.334646 | + | 0.942344i | \(0.391383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.18034 | −0.256796 | ||||||||
\(266\) | 6.38197 | 0.391303 | ||||||||
\(267\) | −5.61803 | −0.343818 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4164 | −0.818013 | −0.409006 | − | 0.912532i | \(-0.634125\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634125\pi\) | |||||||
\(270\) | 1.38197 | 0.0841038 | ||||||||
\(271\) | −22.5066 | −1.36718 | −0.683589 | − | 0.729868i | \(-0.739582\pi\) | ||||
−0.683589 | + | 0.729868i | \(0.739582\pi\) | |||||||
\(272\) | −4.85410 | −0.294323 | ||||||||
\(273\) | −3.23607 | −0.195856 | ||||||||
\(274\) | 18.2918 | 1.10505 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.1459 | −0.791290 | ||||||||
\(277\) | −0.0901699 | −0.00541779 | −0.00270889 | − | 0.999996i | \(-0.500862\pi\) | ||||
−0.00270889 | + | 0.999996i | \(0.500862\pi\) | |||||||
\(278\) | 29.3951 | 1.76300 | ||||||||
\(279\) | −3.09017 | −0.185004 | ||||||||
\(280\) | −1.38197 | −0.0825883 | ||||||||
\(281\) | −26.9443 | −1.60736 | −0.803680 | − | 0.595061i | \(-0.797128\pi\) | ||||
−0.803680 | + | 0.595061i | \(0.797128\pi\) | |||||||
\(282\) | −10.0000 | −0.595491 | ||||||||
\(283\) | −17.2705 | −1.02663 | −0.513313 | − | 0.858202i | \(-0.671582\pi\) | ||||
−0.513313 | + | 0.858202i | \(0.671582\pi\) | |||||||
\(284\) | −14.8328 | −0.880166 | ||||||||
\(285\) | 1.76393 | 0.104486 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.38197 | 0.435744 | ||||||||
\(288\) | −6.70820 | −0.395285 | ||||||||
\(289\) | 6.56231 | 0.386018 | ||||||||
\(290\) | 8.29180 | 0.486911 | ||||||||
\(291\) | 6.00000 | 0.351726 | ||||||||
\(292\) | 41.1246 | 2.40664 | ||||||||
\(293\) | −18.2148 | −1.06412 | −0.532059 | − | 0.846707i | \(-0.678582\pi\) | ||||
−0.532059 | + | 0.846707i | \(0.678582\pi\) | |||||||
\(294\) | −2.23607 | −0.130410 | ||||||||
\(295\) | −2.00000 | −0.116445 | ||||||||
\(296\) | 10.3262 | 0.600200 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.0557 | −0.640441 | ||||||||
\(299\) | 14.1803 | 0.820070 | ||||||||
\(300\) | 13.8541 | 0.799867 | ||||||||
\(301\) | 9.70820 | 0.559572 | ||||||||
\(302\) | −34.7214 | −1.99799 | ||||||||
\(303\) | 6.79837 | 0.390556 | ||||||||
\(304\) | −2.85410 | −0.163694 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.8541 | 0.620488 | ||||||||
\(307\) | −17.5623 | −1.00233 | −0.501167 | − | 0.865351i | \(-0.667096\pi\) | ||||
−0.501167 | + | 0.865351i | \(0.667096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.32624 | −0.0754470 | ||||||||
\(310\) | 4.27051 | 0.242549 | ||||||||
\(311\) | 20.6525 | 1.17109 | 0.585547 | − | 0.810638i | \(-0.300880\pi\) | ||||
0.585547 | + | 0.810638i | \(0.300880\pi\) | |||||||
\(312\) | −7.23607 | −0.409662 | ||||||||
\(313\) | −7.81966 | −0.441993 | −0.220997 | − | 0.975275i | \(-0.570931\pi\) | ||||
−0.220997 | + | 0.975275i | \(0.570931\pi\) | |||||||
\(314\) | −51.7082 | −2.91806 | ||||||||
\(315\) | −0.618034 | −0.0348223 | ||||||||
\(316\) | −30.0000 | −1.68763 | ||||||||
\(317\) | 6.76393 | 0.379900 | 0.189950 | − | 0.981794i | \(-0.439167\pi\) | ||||
0.189950 | + | 0.981794i | \(0.439167\pi\) | |||||||
\(318\) | −15.1246 | −0.848146 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.03444 | 0.449139 | ||||||||
\(321\) | −15.7984 | −0.881779 | ||||||||
\(322\) | 9.79837 | 0.546042 | ||||||||
\(323\) | 13.8541 | 0.770863 | ||||||||
\(324\) | 3.00000 | 0.166667 | ||||||||
\(325\) | −14.9443 | −0.828959 | ||||||||
\(326\) | −22.3607 | −1.23844 | ||||||||
\(327\) | 17.5623 | 0.971198 | ||||||||
\(328\) | 16.5066 | 0.911423 | ||||||||
\(329\) | 4.47214 | 0.246557 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.4164 | 0.957292 | 0.478646 | − | 0.878008i | \(-0.341128\pi\) | ||||
0.478646 | + | 0.878008i | \(0.341128\pi\) | |||||||
\(332\) | 49.4164 | 2.71208 | ||||||||
\(333\) | 4.61803 | 0.253067 | ||||||||
\(334\) | −47.4853 | −2.59828 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 27.0902 | 1.47570 | 0.737848 | − | 0.674967i | \(-0.235842\pi\) | ||||
0.737848 | + | 0.674967i | \(0.235842\pi\) | |||||||
\(338\) | −5.65248 | −0.307454 | ||||||||
\(339\) | 5.23607 | 0.284384 | ||||||||
\(340\) | −9.00000 | −0.488094 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.38197 | 0.345097 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 21.7082 | 1.17043 | ||||||||
\(345\) | 2.70820 | 0.145805 | ||||||||
\(346\) | −30.4508 | −1.63705 | ||||||||
\(347\) | −14.5066 | −0.778754 | −0.389377 | − | 0.921078i | \(-0.627310\pi\) | ||||
−0.389377 | + | 0.921078i | \(0.627310\pi\) | |||||||
\(348\) | 18.0000 | 0.964901 | ||||||||
\(349\) | −21.7082 | −1.16201 | −0.581007 | − | 0.813899i | \(-0.697341\pi\) | ||||
−0.581007 | + | 0.813899i | \(0.697341\pi\) | |||||||
\(350\) | −10.3262 | −0.551961 | ||||||||
\(351\) | −3.23607 | −0.172729 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | −7.23607 | −0.384593 | ||||||||
\(355\) | 3.05573 | 0.162181 | ||||||||
\(356\) | 16.8541 | 0.893266 | ||||||||
\(357\) | −4.85410 | −0.256906 | ||||||||
\(358\) | −33.0902 | −1.74887 | ||||||||
\(359\) | 6.43769 | 0.339768 | 0.169884 | − | 0.985464i | \(-0.445661\pi\) | ||||
0.169884 | + | 0.985464i | \(0.445661\pi\) | |||||||
\(360\) | −1.38197 | −0.0728360 | ||||||||
\(361\) | −10.8541 | −0.571269 | ||||||||
\(362\) | −44.4721 | −2.33740 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.70820 | 0.508848 | ||||||||
\(365\) | −8.47214 | −0.443452 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.72949 | 0.142478 | 0.0712391 | − | 0.997459i | \(-0.477305\pi\) | ||||
0.0712391 | + | 0.997459i | \(0.477305\pi\) | |||||||
\(368\) | −4.38197 | −0.228426 | ||||||||
\(369\) | 7.38197 | 0.384290 | ||||||||
\(370\) | −6.38197 | −0.331783 | ||||||||
\(371\) | 6.76393 | 0.351166 | ||||||||
\(372\) | 9.27051 | 0.480654 | ||||||||
\(373\) | 16.3262 | 0.845341 | 0.422670 | − | 0.906284i | \(-0.361093\pi\) | ||||
0.422670 | + | 0.906284i | \(0.361093\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.94427 | −0.306961 | ||||||||
\(376\) | 10.0000 | 0.515711 | ||||||||
\(377\) | −19.4164 | −0.999996 | ||||||||
\(378\) | −2.23607 | −0.115011 | ||||||||
\(379\) | 21.5279 | 1.10581 | 0.552906 | − | 0.833244i | \(-0.313519\pi\) | ||||
0.552906 | + | 0.833244i | \(0.313519\pi\) | |||||||
\(380\) | −5.29180 | −0.271463 | ||||||||
\(381\) | −0.291796 | −0.0149492 | ||||||||
\(382\) | 10.9787 | 0.561720 | ||||||||
\(383\) | −20.8328 | −1.06451 | −0.532254 | − | 0.846585i | \(-0.678655\pi\) | ||||
−0.532254 | + | 0.846585i | \(0.678655\pi\) | |||||||
\(384\) | 15.6525 | 0.798762 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −48.8673 | −2.48728 | ||||||||
\(387\) | 9.70820 | 0.493496 | ||||||||
\(388\) | −18.0000 | −0.913812 | ||||||||
\(389\) | 15.2361 | 0.772499 | 0.386250 | − | 0.922394i | \(-0.373770\pi\) | ||||
0.386250 | + | 0.922394i | \(0.373770\pi\) | |||||||
\(390\) | 4.47214 | 0.226455 | ||||||||
\(391\) | 21.2705 | 1.07570 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | 16.6525 | 0.840006 | ||||||||
\(394\) | 50.2492 | 2.53152 | ||||||||
\(395\) | 6.18034 | 0.310967 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.5410 | 1.53281 | 0.766405 | − | 0.642358i | \(-0.222044\pi\) | ||||
0.766405 | + | 0.642358i | \(0.222044\pi\) | |||||||
\(398\) | 29.3951 | 1.47344 | ||||||||
\(399\) | −2.85410 | −0.142884 | ||||||||
\(400\) | 4.61803 | 0.230902 | ||||||||
\(401\) | 7.41641 | 0.370358 | 0.185179 | − | 0.982705i | \(-0.440714\pi\) | ||||
0.185179 | + | 0.982705i | \(0.440714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0000 | −0.498135 | ||||||||
\(404\) | −20.3951 | −1.01470 | ||||||||
\(405\) | −0.618034 | −0.0307104 | ||||||||
\(406\) | −13.4164 | −0.665845 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −10.8541 | −0.537358 | ||||||||
\(409\) | −22.1803 | −1.09675 | −0.548374 | − | 0.836233i | \(-0.684753\pi\) | ||||
−0.548374 | + | 0.836233i | \(0.684753\pi\) | |||||||
\(410\) | −10.2016 | −0.503822 | ||||||||
\(411\) | −8.18034 | −0.403506 | ||||||||
\(412\) | 3.97871 | 0.196017 | ||||||||
\(413\) | 3.23607 | 0.159236 | ||||||||
\(414\) | 9.79837 | 0.481564 | ||||||||
\(415\) | −10.1803 | −0.499733 | ||||||||
\(416\) | −21.7082 | −1.06433 | ||||||||
\(417\) | −13.1459 | −0.643757 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.23607 | −0.158092 | −0.0790461 | − | 0.996871i | \(-0.525187\pi\) | ||||
−0.0790461 | + | 0.996871i | \(0.525187\pi\) | |||||||
\(420\) | 1.85410 | 0.0904709 | ||||||||
\(421\) | 9.79837 | 0.477544 | 0.238772 | − | 0.971076i | \(-0.423255\pi\) | ||||
0.238772 | + | 0.971076i | \(0.423255\pi\) | |||||||
\(422\) | −41.0557 | −1.99856 | ||||||||
\(423\) | 4.47214 | 0.217443 | ||||||||
\(424\) | 15.1246 | 0.734516 | ||||||||
\(425\) | −22.4164 | −1.08736 | ||||||||
\(426\) | 11.0557 | 0.535652 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 47.3951 | 2.29093 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.4164 | −0.646997 | ||||||||
\(431\) | 15.0902 | 0.726868 | 0.363434 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363434 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −31.2361 | −1.50111 | −0.750555 | − | 0.660808i | \(-0.770214\pi\) | ||||
−0.750555 | + | 0.660808i | \(0.770214\pi\) | |||||||
\(434\) | −6.90983 | −0.331682 | ||||||||
\(435\) | −3.70820 | −0.177795 | ||||||||
\(436\) | −52.6869 | −2.52325 | ||||||||
\(437\) | 12.5066 | 0.598271 | ||||||||
\(438\) | −30.6525 | −1.46463 | ||||||||
\(439\) | 1.85410 | 0.0884915 | 0.0442457 | − | 0.999021i | \(-0.485912\pi\) | ||||
0.0442457 | + | 0.999021i | \(0.485912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 35.1246 | 1.67071 | ||||||||
\(443\) | 20.3820 | 0.968376 | 0.484188 | − | 0.874964i | \(-0.339115\pi\) | ||||
0.484188 | + | 0.874964i | \(0.339115\pi\) | |||||||
\(444\) | −13.8541 | −0.657487 | ||||||||
\(445\) | −3.47214 | −0.164595 | ||||||||
\(446\) | 43.8673 | 2.07717 | ||||||||
\(447\) | 4.94427 | 0.233856 | ||||||||
\(448\) | −13.0000 | −0.614192 | ||||||||
\(449\) | −41.8885 | −1.97684 | −0.988421 | − | 0.151734i | \(-0.951514\pi\) | ||||
−0.988421 | + | 0.151734i | \(0.951514\pi\) | |||||||
\(450\) | −10.3262 | −0.486784 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −15.7082 | −0.738852 | ||||||||
\(453\) | 15.5279 | 0.729563 | ||||||||
\(454\) | 27.8885 | 1.30887 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | −6.38197 | −0.298863 | ||||||||
\(457\) | 21.4164 | 1.00182 | 0.500909 | − | 0.865500i | \(-0.332999\pi\) | ||||
0.500909 | + | 0.865500i | \(0.332999\pi\) | |||||||
\(458\) | 36.1803 | 1.69060 | ||||||||
\(459\) | −4.85410 | −0.226570 | ||||||||
\(460\) | −8.12461 | −0.378812 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.4164 | −1.08825 | −0.544126 | − | 0.839003i | \(-0.683139\pi\) | ||||
−0.544126 | + | 0.839003i | \(0.683139\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | −1.90983 | −0.0885662 | ||||||||
\(466\) | −35.1246 | −1.62712 | ||||||||
\(467\) | 26.1803 | 1.21148 | 0.605741 | − | 0.795662i | \(-0.292877\pi\) | ||||
0.605741 | + | 0.795662i | \(0.292877\pi\) | |||||||
\(468\) | 9.70820 | 0.448762 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.18034 | −0.285078 | ||||||||
\(471\) | 23.1246 | 1.06553 | ||||||||
\(472\) | 7.23607 | 0.333067 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 22.3607 | 1.02706 | ||||||||
\(475\) | −13.1803 | −0.604755 | ||||||||
\(476\) | 14.5623 | 0.667462 | ||||||||
\(477\) | 6.76393 | 0.309699 | ||||||||
\(478\) | −42.5623 | −1.94675 | ||||||||
\(479\) | −0.944272 | −0.0431449 | −0.0215724 | − | 0.999767i | \(-0.506867\pi\) | ||||
−0.0215724 | + | 0.999767i | \(0.506867\pi\) | |||||||
\(480\) | −4.14590 | −0.189233 | ||||||||
\(481\) | 14.9443 | 0.681400 | ||||||||
\(482\) | 26.8328 | 1.22220 | ||||||||
\(483\) | −4.38197 | −0.199386 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.70820 | 0.168381 | ||||||||
\(486\) | −2.23607 | −0.101430 | ||||||||
\(487\) | 27.7082 | 1.25558 | 0.627789 | − | 0.778383i | \(-0.283960\pi\) | ||||
0.627789 | + | 0.778383i | \(0.283960\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.0000 | 0.452216 | ||||||||
\(490\) | −1.38197 | −0.0624309 | ||||||||
\(491\) | 1.50658 | 0.0679909 | 0.0339955 | − | 0.999422i | \(-0.489177\pi\) | ||||
0.0339955 | + | 0.999422i | \(0.489177\pi\) | |||||||
\(492\) | −22.1459 | −0.998414 | ||||||||
\(493\) | −29.1246 | −1.31171 | ||||||||
\(494\) | 20.6525 | 0.929199 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.09017 | 0.138753 | ||||||||
\(497\) | −4.94427 | −0.221781 | ||||||||
\(498\) | −36.8328 | −1.65052 | ||||||||
\(499\) | 21.1246 | 0.945668 | 0.472834 | − | 0.881152i | \(-0.343231\pi\) | ||||
0.472834 | + | 0.881152i | \(0.343231\pi\) | |||||||
\(500\) | 17.8328 | 0.797508 | ||||||||
\(501\) | 21.2361 | 0.948758 | ||||||||
\(502\) | 61.9574 | 2.76530 | ||||||||
\(503\) | −14.4721 | −0.645281 | −0.322640 | − | 0.946522i | \(-0.604570\pi\) | ||||
−0.322640 | + | 0.946522i | \(0.604570\pi\) | |||||||
\(504\) | 2.23607 | 0.0996024 | ||||||||
\(505\) | 4.20163 | 0.186970 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.52786 | 0.112266 | ||||||||
\(508\) | 0.875388 | 0.0388391 | ||||||||
\(509\) | −27.0902 | −1.20075 | −0.600375 | − | 0.799718i | \(-0.704982\pi\) | ||||
−0.600375 | + | 0.799718i | \(0.704982\pi\) | |||||||
\(510\) | 6.70820 | 0.297044 | ||||||||
\(511\) | 13.7082 | 0.606415 | ||||||||
\(512\) | 11.1803 | 0.494106 | ||||||||
\(513\) | −2.85410 | −0.126012 | ||||||||
\(514\) | 54.6738 | 2.41156 | ||||||||
\(515\) | −0.819660 | −0.0361185 | ||||||||
\(516\) | −29.1246 | −1.28214 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 10.3262 | 0.453709 | ||||||||
\(519\) | 13.6180 | 0.597765 | ||||||||
\(520\) | −4.47214 | −0.196116 | ||||||||
\(521\) | −12.3262 | −0.540022 | −0.270011 | − | 0.962857i | \(-0.587027\pi\) | ||||
−0.270011 | + | 0.962857i | \(0.587027\pi\) | |||||||
\(522\) | −13.4164 | −0.587220 | ||||||||
\(523\) | 13.1459 | 0.574830 | 0.287415 | − | 0.957806i | \(-0.407204\pi\) | ||||
0.287415 | + | 0.957806i | \(0.407204\pi\) | |||||||
\(524\) | −49.9574 | −2.18240 | ||||||||
\(525\) | 4.61803 | 0.201548 | ||||||||
\(526\) | 24.2705 | 1.05824 | ||||||||
\(527\) | −15.0000 | −0.653410 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.79837 | −0.165147 | ||||||||
\(530\) | −9.34752 | −0.406031 | ||||||||
\(531\) | 3.23607 | 0.140433 | ||||||||
\(532\) | 8.56231 | 0.371223 | ||||||||
\(533\) | 23.8885 | 1.03473 | ||||||||
\(534\) | −12.5623 | −0.543624 | ||||||||
\(535\) | −9.76393 | −0.422132 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.7984 | 0.638597 | ||||||||
\(538\) | −30.0000 | −1.29339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.85410 | 0.0797878 | ||||||||
\(541\) | −16.3262 | −0.701920 | −0.350960 | − | 0.936390i | \(-0.614145\pi\) | ||||
−0.350960 | + | 0.936390i | \(0.614145\pi\) | |||||||
\(542\) | −50.3262 | −2.16170 | ||||||||
\(543\) | 19.8885 | 0.853499 | ||||||||
\(544\) | −32.5623 | −1.39610 | ||||||||
\(545\) | 10.8541 | 0.464939 | ||||||||
\(546\) | −7.23607 | −0.309675 | ||||||||
\(547\) | −36.4721 | −1.55944 | −0.779718 | − | 0.626131i | \(-0.784638\pi\) | ||||
−0.779718 | + | 0.626131i | \(0.784638\pi\) | |||||||
\(548\) | 24.5410 | 1.04834 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.1246 | −0.729533 | ||||||||
\(552\) | −9.79837 | −0.417046 | ||||||||
\(553\) | −10.0000 | −0.425243 | ||||||||
\(554\) | −0.201626 | −0.00856627 | ||||||||
\(555\) | 2.85410 | 0.121150 | ||||||||
\(556\) | 39.4377 | 1.67253 | ||||||||
\(557\) | 22.3607 | 0.947452 | 0.473726 | − | 0.880672i | \(-0.342909\pi\) | ||||
0.473726 | + | 0.880672i | \(0.342909\pi\) | |||||||
\(558\) | −6.90983 | −0.292516 | ||||||||
\(559\) | 31.4164 | 1.32877 | ||||||||
\(560\) | 0.618034 | 0.0261167 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −60.2492 | −2.54146 | ||||||||
\(563\) | −9.52786 | −0.401552 | −0.200776 | − | 0.979637i | \(-0.564346\pi\) | ||||
−0.200776 | + | 0.979637i | \(0.564346\pi\) | |||||||
\(564\) | −13.4164 | −0.564933 | ||||||||
\(565\) | 3.23607 | 0.136142 | ||||||||
\(566\) | −38.6180 | −1.62324 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −11.0557 | −0.463888 | ||||||||
\(569\) | 11.5967 | 0.486161 | 0.243080 | − | 0.970006i | \(-0.421842\pi\) | ||||
0.243080 | + | 0.970006i | \(0.421842\pi\) | |||||||
\(570\) | 3.94427 | 0.165207 | ||||||||
\(571\) | 15.3475 | 0.642274 | 0.321137 | − | 0.947033i | \(-0.395935\pi\) | ||||
0.321137 | + | 0.947033i | \(0.395935\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.90983 | −0.205111 | ||||||||
\(574\) | 16.5066 | 0.688971 | ||||||||
\(575\) | −20.2361 | −0.843902 | ||||||||
\(576\) | −13.0000 | −0.541667 | ||||||||
\(577\) | −35.7082 | −1.48655 | −0.743276 | − | 0.668985i | \(-0.766729\pi\) | ||||
−0.743276 | + | 0.668985i | \(0.766729\pi\) | |||||||
\(578\) | 14.6738 | 0.610348 | ||||||||
\(579\) | 21.8541 | 0.908225 | ||||||||
\(580\) | 11.1246 | 0.461924 | ||||||||
\(581\) | 16.4721 | 0.683379 | ||||||||
\(582\) | 13.4164 | 0.556128 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 30.6525 | 1.26841 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | −40.7295 | −1.68252 | ||||||||
\(587\) | −1.41641 | −0.0584614 | −0.0292307 | − | 0.999573i | \(-0.509306\pi\) | ||||
−0.0292307 | + | 0.999573i | \(0.509306\pi\) | |||||||
\(588\) | −3.00000 | −0.123718 | ||||||||
\(589\) | −8.81966 | −0.363408 | ||||||||
\(590\) | −4.47214 | −0.184115 | ||||||||
\(591\) | −22.4721 | −0.924380 | ||||||||
\(592\) | −4.61803 | −0.189800 | ||||||||
\(593\) | 22.5066 | 0.924234 | 0.462117 | − | 0.886819i | \(-0.347090\pi\) | ||||
0.462117 | + | 0.886819i | \(0.347090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.00000 | −0.122988 | ||||||||
\(596\) | −14.8328 | −0.607576 | ||||||||
\(597\) | −13.1459 | −0.538026 | ||||||||
\(598\) | 31.7082 | 1.29664 | ||||||||
\(599\) | −23.6180 | −0.965007 | −0.482503 | − | 0.875894i | \(-0.660272\pi\) | ||||
−0.482503 | + | 0.875894i | \(0.660272\pi\) | |||||||
\(600\) | 10.3262 | 0.421567 | ||||||||
\(601\) | 3.52786 | 0.143905 | 0.0719523 | − | 0.997408i | \(-0.477077\pi\) | ||||
0.0719523 | + | 0.997408i | \(0.477077\pi\) | |||||||
\(602\) | 21.7082 | 0.884760 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −46.5836 | −1.89546 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.2016 | 0.617524 | ||||||||
\(607\) | −11.9787 | −0.486201 | −0.243100 | − | 0.970001i | \(-0.578164\pi\) | ||||
−0.243100 | + | 0.970001i | \(0.578164\pi\) | |||||||
\(608\) | −19.1459 | −0.776469 | ||||||||
\(609\) | 6.00000 | 0.243132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.4721 | 0.585480 | ||||||||
\(612\) | 14.5623 | 0.588646 | ||||||||
\(613\) | −21.9787 | −0.887712 | −0.443856 | − | 0.896098i | \(-0.646390\pi\) | ||||
−0.443856 | + | 0.896098i | \(0.646390\pi\) | |||||||
\(614\) | −39.2705 | −1.58483 | ||||||||
\(615\) | 4.56231 | 0.183970 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.0689 | −0.566392 | −0.283196 | − | 0.959062i | \(-0.591395\pi\) | ||||
−0.283196 | + | 0.959062i | \(0.591395\pi\) | |||||||
\(618\) | −2.96556 | −0.119292 | ||||||||
\(619\) | −36.6869 | −1.47457 | −0.737286 | − | 0.675581i | \(-0.763893\pi\) | ||||
−0.737286 | + | 0.675581i | \(0.763893\pi\) | |||||||
\(620\) | 5.72949 | 0.230102 | ||||||||
\(621\) | −4.38197 | −0.175842 | ||||||||
\(622\) | 46.1803 | 1.85166 | ||||||||
\(623\) | 5.61803 | 0.225082 | ||||||||
\(624\) | 3.23607 | 0.129546 | ||||||||
\(625\) | 19.4164 | 0.776656 | ||||||||
\(626\) | −17.4853 | −0.698853 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −69.3738 | −2.76832 | ||||||||
\(629\) | 22.4164 | 0.893801 | ||||||||
\(630\) | −1.38197 | −0.0550588 | ||||||||
\(631\) | −45.3050 | −1.80356 | −0.901781 | − | 0.432194i | \(-0.857740\pi\) | ||||
−0.901781 | + | 0.432194i | \(0.857740\pi\) | |||||||
\(632\) | −22.3607 | −0.889460 | ||||||||
\(633\) | 18.3607 | 0.729772 | ||||||||
\(634\) | 15.1246 | 0.600675 | ||||||||
\(635\) | −0.180340 | −0.00715657 | ||||||||
\(636\) | −20.2918 | −0.804622 | ||||||||
\(637\) | 3.23607 | 0.128218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.94427 | −0.195592 | ||||||||
\(640\) | 9.67376 | 0.382389 | ||||||||
\(641\) | 12.7639 | 0.504145 | 0.252073 | − | 0.967708i | \(-0.418888\pi\) | ||||
0.252073 | + | 0.967708i | \(0.418888\pi\) | |||||||
\(642\) | −35.3262 | −1.39422 | ||||||||
\(643\) | 10.2705 | 0.405029 | 0.202515 | − | 0.979279i | \(-0.435089\pi\) | ||||
0.202515 | + | 0.979279i | \(0.435089\pi\) | |||||||
\(644\) | 13.1459 | 0.518021 | ||||||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 30.9787 | 1.21884 | ||||||||
\(647\) | 36.4721 | 1.43387 | 0.716934 | − | 0.697141i | \(-0.245545\pi\) | ||||
0.716934 | + | 0.697141i | \(0.245545\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −33.4164 | −1.31070 | ||||||||
\(651\) | 3.09017 | 0.121113 | ||||||||
\(652\) | −30.0000 | −1.17489 | ||||||||
\(653\) | 16.3607 | 0.640243 | 0.320121 | − | 0.947377i | \(-0.396276\pi\) | ||||
0.320121 | + | 0.947377i | \(0.396276\pi\) | |||||||
\(654\) | 39.2705 | 1.53560 | ||||||||
\(655\) | 10.2918 | 0.402134 | ||||||||
\(656\) | −7.38197 | −0.288217 | ||||||||
\(657\) | 13.7082 | 0.534808 | ||||||||
\(658\) | 10.0000 | 0.389841 | ||||||||
\(659\) | −25.8541 | −1.00713 | −0.503566 | − | 0.863957i | \(-0.667979\pi\) | ||||
−0.503566 | + | 0.863957i | \(0.667979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.5410 | −1.26570 | −0.632849 | − | 0.774275i | \(-0.718115\pi\) | ||||
−0.632849 | + | 0.774275i | \(0.718115\pi\) | |||||||
\(662\) | 38.9443 | 1.51361 | ||||||||
\(663\) | −15.7082 | −0.610056 | ||||||||
\(664\) | 36.8328 | 1.42939 | ||||||||
\(665\) | −1.76393 | −0.0684023 | ||||||||
\(666\) | 10.3262 | 0.400134 | ||||||||
\(667\) | −26.2918 | −1.01802 | ||||||||
\(668\) | −63.7082 | −2.46494 | ||||||||
\(669\) | −19.6180 | −0.758477 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.70820 | 0.258775 | ||||||||
\(673\) | −44.8328 | −1.72818 | −0.864089 | − | 0.503339i | \(-0.832105\pi\) | ||||
−0.864089 | + | 0.503339i | \(0.832105\pi\) | |||||||
\(674\) | 60.5755 | 2.33328 | ||||||||
\(675\) | 4.61803 | 0.177748 | ||||||||
\(676\) | −7.58359 | −0.291677 | ||||||||
\(677\) | 34.3607 | 1.32059 | 0.660294 | − | 0.751007i | \(-0.270432\pi\) | ||||
0.660294 | + | 0.751007i | \(0.270432\pi\) | |||||||
\(678\) | 11.7082 | 0.449651 | ||||||||
\(679\) | −6.00000 | −0.230259 | ||||||||
\(680\) | −6.70820 | −0.257248 | ||||||||
\(681\) | −12.4721 | −0.477933 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.7984 | 1.02541 | 0.512706 | − | 0.858564i | \(-0.328643\pi\) | ||||
0.512706 | + | 0.858564i | \(0.328643\pi\) | |||||||
\(684\) | 8.56231 | 0.327388 | ||||||||
\(685\) | −5.05573 | −0.193169 | ||||||||
\(686\) | 2.23607 | 0.0853735 | ||||||||
\(687\) | −16.1803 | −0.617318 | ||||||||
\(688\) | −9.70820 | −0.370122 | ||||||||
\(689\) | 21.8885 | 0.833887 | ||||||||
\(690\) | 6.05573 | 0.230538 | ||||||||
\(691\) | 48.7426 | 1.85426 | 0.927129 | − | 0.374743i | \(-0.122269\pi\) | ||||
0.927129 | + | 0.374743i | \(0.122269\pi\) | |||||||
\(692\) | −40.8541 | −1.55304 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.4377 | −1.23132 | ||||||||
\(695\) | −8.12461 | −0.308184 | ||||||||
\(696\) | 13.4164 | 0.508548 | ||||||||
\(697\) | 35.8328 | 1.35726 | ||||||||
\(698\) | −48.5410 | −1.83730 | ||||||||
\(699\) | 15.7082 | 0.594139 | ||||||||
\(700\) | −13.8541 | −0.523636 | ||||||||
\(701\) | 39.5967 | 1.49555 | 0.747774 | − | 0.663953i | \(-0.231123\pi\) | ||||
0.747774 | + | 0.663953i | \(0.231123\pi\) | |||||||
\(702\) | −7.23607 | −0.273108 | ||||||||
\(703\) | 13.1803 | 0.497106 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.76393 | 0.104096 | ||||||||
\(706\) | −40.2492 | −1.51480 | ||||||||
\(707\) | −6.79837 | −0.255679 | ||||||||
\(708\) | −9.70820 | −0.364857 | ||||||||
\(709\) | −8.03444 | −0.301740 | −0.150870 | − | 0.988554i | \(-0.548207\pi\) | ||||
−0.150870 | + | 0.988554i | \(0.548207\pi\) | |||||||
\(710\) | 6.83282 | 0.256431 | ||||||||
\(711\) | −10.0000 | −0.375029 | ||||||||
\(712\) | 12.5623 | 0.470792 | ||||||||
\(713\) | −13.5410 | −0.507115 | ||||||||
\(714\) | −10.8541 | −0.406205 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −44.3951 | −1.65912 | ||||||||
\(717\) | 19.0344 | 0.710854 | ||||||||
\(718\) | 14.3951 | 0.537221 | ||||||||
\(719\) | 39.0132 | 1.45495 | 0.727473 | − | 0.686137i | \(-0.240695\pi\) | ||||
0.727473 | + | 0.686137i | \(0.240695\pi\) | |||||||
\(720\) | 0.618034 | 0.0230328 | ||||||||
\(721\) | 1.32624 | 0.0493917 | ||||||||
\(722\) | −24.2705 | −0.903255 | ||||||||
\(723\) | −12.0000 | −0.446285 | ||||||||
\(724\) | −59.6656 | −2.21746 | ||||||||
\(725\) | 27.7082 | 1.02906 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.8541 | −0.699260 | −0.349630 | − | 0.936888i | \(-0.613693\pi\) | ||||
−0.349630 | + | 0.936888i | \(0.613693\pi\) | |||||||
\(728\) | 7.23607 | 0.268187 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −18.9443 | −0.701159 | ||||||||
\(731\) | 47.1246 | 1.74297 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0689 | −0.667389 | −0.333695 | − | 0.942681i | \(-0.608295\pi\) | ||||
−0.333695 | + | 0.942681i | \(0.608295\pi\) | |||||||
\(734\) | 6.10333 | 0.225278 | ||||||||
\(735\) | 0.618034 | 0.0227965 | ||||||||
\(736\) | −29.3951 | −1.08352 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 16.5066 | 0.607616 | ||||||||
\(739\) | 41.1246 | 1.51279 | 0.756397 | − | 0.654113i | \(-0.226958\pi\) | ||||
0.756397 | + | 0.654113i | \(0.226958\pi\) | |||||||
\(740\) | −8.56231 | −0.314757 | ||||||||
\(741\) | −9.23607 | −0.339295 | ||||||||
\(742\) | 15.1246 | 0.555242 | ||||||||
\(743\) | −16.3262 | −0.598952 | −0.299476 | − | 0.954104i | \(-0.596812\pi\) | ||||
−0.299476 | + | 0.954104i | \(0.596812\pi\) | |||||||
\(744\) | 6.90983 | 0.253327 | ||||||||
\(745\) | 3.05573 | 0.111953 | ||||||||
\(746\) | 36.5066 | 1.33660 | ||||||||
\(747\) | 16.4721 | 0.602684 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.7984 | 0.577260 | ||||||||
\(750\) | −13.2918 | −0.485348 | ||||||||
\(751\) | 24.0000 | 0.875772 | 0.437886 | − | 0.899030i | \(-0.355727\pi\) | ||||
0.437886 | + | 0.899030i | \(0.355727\pi\) | |||||||
\(752\) | −4.47214 | −0.163082 | ||||||||
\(753\) | −27.7082 | −1.00974 | ||||||||
\(754\) | −43.4164 | −1.58113 | ||||||||
\(755\) | 9.59675 | 0.349261 | ||||||||
\(756\) | −3.00000 | −0.109109 | ||||||||
\(757\) | 10.5623 | 0.383894 | 0.191947 | − | 0.981405i | \(-0.438520\pi\) | ||||
0.191947 | + | 0.981405i | \(0.438520\pi\) | |||||||
\(758\) | 48.1378 | 1.74844 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.94427 | −0.143074 | ||||||||
\(761\) | 1.41641 | 0.0513447 | 0.0256724 | − | 0.999670i | \(-0.491827\pi\) | ||||
0.0256724 | + | 0.999670i | \(0.491827\pi\) | |||||||
\(762\) | −0.652476 | −0.0236367 | ||||||||
\(763\) | −17.5623 | −0.635798 | ||||||||
\(764\) | 14.7295 | 0.532894 | ||||||||
\(765\) | −3.00000 | −0.108465 | ||||||||
\(766\) | −46.5836 | −1.68313 | ||||||||
\(767\) | 10.4721 | 0.378127 | ||||||||
\(768\) | 9.00000 | 0.324760 | ||||||||
\(769\) | 1.05573 | 0.0380705 | 0.0190353 | − | 0.999819i | \(-0.493941\pi\) | ||||
0.0190353 | + | 0.999819i | \(0.493941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.4508 | −0.880576 | ||||||||
\(772\) | −65.5623 | −2.35964 | ||||||||
\(773\) | 8.47214 | 0.304722 | 0.152361 | − | 0.988325i | \(-0.451312\pi\) | ||||
0.152361 | + | 0.988325i | \(0.451312\pi\) | |||||||
\(774\) | 21.7082 | 0.780285 | ||||||||
\(775\) | 14.2705 | 0.512612 | ||||||||
\(776\) | −13.4164 | −0.481621 | ||||||||
\(777\) | −4.61803 | −0.165671 | ||||||||
\(778\) | 34.0689 | 1.22143 | ||||||||
\(779\) | 21.0689 | 0.754871 | ||||||||
\(780\) | 6.00000 | 0.214834 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 47.5623 | 1.70082 | ||||||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 14.2918 | 0.510096 | ||||||||
\(786\) | 37.2361 | 1.32817 | ||||||||
\(787\) | −25.8541 | −0.921599 | −0.460800 | − | 0.887504i | \(-0.652437\pi\) | ||||
−0.460800 | + | 0.887504i | \(0.652437\pi\) | |||||||
\(788\) | 67.4164 | 2.40161 | ||||||||
\(789\) | −10.8541 | −0.386416 | ||||||||
\(790\) | 13.8197 | 0.491681 | ||||||||
\(791\) | −5.23607 | −0.186173 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 68.2918 | 2.42359 | ||||||||
\(795\) | 4.18034 | 0.148261 | ||||||||
\(796\) | 39.4377 | 1.39783 | ||||||||
\(797\) | 41.5623 | 1.47221 | 0.736106 | − | 0.676866i | \(-0.236662\pi\) | ||||
0.736106 | + | 0.676866i | \(0.236662\pi\) | |||||||
\(798\) | −6.38197 | −0.225919 | ||||||||
\(799\) | 21.7082 | 0.767981 | ||||||||
\(800\) | 30.9787 | 1.09526 | ||||||||
\(801\) | 5.61803 | 0.198503 | ||||||||
\(802\) | 16.5836 | 0.585587 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.70820 | −0.0954516 | ||||||||
\(806\) | −22.3607 | −0.787621 | ||||||||
\(807\) | 13.4164 | 0.472280 | ||||||||
\(808\) | −15.2016 | −0.534791 | ||||||||
\(809\) | 7.23607 | 0.254407 | 0.127203 | − | 0.991877i | \(-0.459400\pi\) | ||||
0.127203 | + | 0.991877i | \(0.459400\pi\) | |||||||
\(810\) | −1.38197 | −0.0485573 | ||||||||
\(811\) | 8.58359 | 0.301411 | 0.150705 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150705 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(812\) | −18.0000 | −0.631676 | ||||||||
\(813\) | 22.5066 | 0.789340 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.18034 | 0.216488 | ||||||||
\(816\) | 4.85410 | 0.169928 | ||||||||
\(817\) | 27.7082 | 0.969387 | ||||||||
\(818\) | −49.5967 | −1.73411 | ||||||||
\(819\) | 3.23607 | 0.113077 | ||||||||
\(820\) | −13.6869 | −0.477968 | ||||||||
\(821\) | −10.9443 | −0.381958 | −0.190979 | − | 0.981594i | \(-0.561166\pi\) | ||||
−0.190979 | + | 0.981594i | \(0.561166\pi\) | |||||||
\(822\) | −18.2918 | −0.638000 | ||||||||
\(823\) | 4.83282 | 0.168461 | 0.0842307 | − | 0.996446i | \(-0.473157\pi\) | ||||
0.0842307 | + | 0.996446i | \(0.473157\pi\) | |||||||
\(824\) | 2.96556 | 0.103310 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.23607 | 0.251775 | ||||||||
\(827\) | 29.8673 | 1.03859 | 0.519293 | − | 0.854596i | \(-0.326195\pi\) | ||||
0.519293 | + | 0.854596i | \(0.326195\pi\) | |||||||
\(828\) | 13.1459 | 0.456852 | ||||||||
\(829\) | −30.2492 | −1.05060 | −0.525299 | − | 0.850917i | \(-0.676047\pi\) | ||||
−0.525299 | + | 0.850917i | \(0.676047\pi\) | |||||||
\(830\) | −22.7639 | −0.790148 | ||||||||
\(831\) | 0.0901699 | 0.00312796 | ||||||||
\(832\) | −42.0689 | −1.45848 | ||||||||
\(833\) | 4.85410 | 0.168185 | ||||||||
\(834\) | −29.3951 | −1.01787 | ||||||||
\(835\) | 13.1246 | 0.454196 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.09017 | 0.106812 | ||||||||
\(838\) | −7.23607 | −0.249966 | ||||||||
\(839\) | −40.2492 | −1.38956 | −0.694779 | − | 0.719224i | \(-0.744498\pi\) | ||||
−0.694779 | + | 0.719224i | \(0.744498\pi\) | |||||||
\(840\) | 1.38197 | 0.0476824 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 21.9098 | 0.755063 | ||||||||
\(843\) | 26.9443 | 0.928010 | ||||||||
\(844\) | −55.0820 | −1.89600 | ||||||||
\(845\) | 1.56231 | 0.0537450 | ||||||||
\(846\) | 10.0000 | 0.343807 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.76393 | −0.232274 | ||||||||
\(849\) | 17.2705 | 0.592722 | ||||||||
\(850\) | −50.1246 | −1.71926 | ||||||||
\(851\) | 20.2361 | 0.693683 | ||||||||
\(852\) | 14.8328 | 0.508164 | ||||||||
\(853\) | −41.7082 | −1.42806 | −0.714031 | − | 0.700114i | \(-0.753132\pi\) | ||||
−0.714031 | + | 0.700114i | \(0.753132\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.76393 | −0.0603252 | ||||||||
\(856\) | 35.3262 | 1.20743 | ||||||||
\(857\) | −34.3607 | −1.17374 | −0.586869 | − | 0.809682i | \(-0.699640\pi\) | ||||
−0.586869 | + | 0.809682i | \(0.699640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0000 | 0.409435 | 0.204717 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(860\) | −18.0000 | −0.613795 | ||||||||
\(861\) | −7.38197 | −0.251577 | ||||||||
\(862\) | 33.7426 | 1.14928 | ||||||||
\(863\) | −12.3262 | −0.419590 | −0.209795 | − | 0.977745i | \(-0.567280\pi\) | ||||
−0.209795 | + | 0.977745i | \(0.567280\pi\) | |||||||
\(864\) | 6.70820 | 0.228218 | ||||||||
\(865\) | 8.41641 | 0.286166 | ||||||||
\(866\) | −69.8460 | −2.37346 | ||||||||
\(867\) | −6.56231 | −0.222868 | ||||||||
\(868\) | −9.27051 | −0.314662 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −8.29180 | −0.281118 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −39.2705 | −1.32987 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | 27.9656 | 0.945949 | ||||||||
\(875\) | 5.94427 | 0.200953 | ||||||||
\(876\) | −41.1246 | −1.38947 | ||||||||
\(877\) | 12.4721 | 0.421154 | 0.210577 | − | 0.977577i | \(-0.432466\pi\) | ||||
0.210577 | + | 0.977577i | \(0.432466\pi\) | |||||||
\(878\) | 4.14590 | 0.139917 | ||||||||
\(879\) | 18.2148 | 0.614369 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.3262 | 0.381591 | 0.190795 | − | 0.981630i | \(-0.438893\pi\) | ||||
0.190795 | + | 0.981630i | \(0.438893\pi\) | |||||||
\(882\) | 2.23607 | 0.0752923 | ||||||||
\(883\) | 19.5967 | 0.659483 | 0.329742 | − | 0.944071i | \(-0.393038\pi\) | ||||
0.329742 | + | 0.944071i | \(0.393038\pi\) | |||||||
\(884\) | 47.1246 | 1.58497 | ||||||||
\(885\) | 2.00000 | 0.0672293 | ||||||||
\(886\) | 45.5755 | 1.53114 | ||||||||
\(887\) | 27.5967 | 0.926608 | 0.463304 | − | 0.886199i | \(-0.346664\pi\) | ||||
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(888\) | −10.3262 | −0.346526 | ||||||||
\(889\) | 0.291796 | 0.00978653 | ||||||||
\(890\) | −7.76393 | −0.260248 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 58.8541 | 1.97058 | ||||||||
\(893\) | 12.7639 | 0.427129 | ||||||||
\(894\) | 11.0557 | 0.369759 | ||||||||
\(895\) | 9.14590 | 0.305714 | ||||||||
\(896\) | −15.6525 | −0.522913 | ||||||||
\(897\) | −14.1803 | −0.473468 | ||||||||
\(898\) | −93.6656 | −3.12566 | ||||||||
\(899\) | 18.5410 | 0.618378 | ||||||||
\(900\) | −13.8541 | −0.461803 | ||||||||
\(901\) | 32.8328 | 1.09382 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.70820 | −0.323069 | ||||||||
\(904\) | −11.7082 | −0.389409 | ||||||||
\(905\) | 12.2918 | 0.408593 | ||||||||
\(906\) | 34.7214 | 1.15354 | ||||||||
\(907\) | 16.2918 | 0.540960 | 0.270480 | − | 0.962726i | \(-0.412818\pi\) | ||||
0.270480 | + | 0.962726i | \(0.412818\pi\) | |||||||
\(908\) | 37.4164 | 1.24171 | ||||||||
\(909\) | −6.79837 | −0.225488 | ||||||||
\(910\) | −4.47214 | −0.148250 | ||||||||
\(911\) | −0.944272 | −0.0312851 | −0.0156426 | − | 0.999878i | \(-0.504979\pi\) | ||||
−0.0156426 | + | 0.999878i | \(0.504979\pi\) | |||||||
\(912\) | 2.85410 | 0.0945088 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 47.8885 | 1.58401 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 48.5410 | 1.60384 | ||||||||
\(917\) | −16.6525 | −0.549913 | ||||||||
\(918\) | −10.8541 | −0.358239 | ||||||||
\(919\) | −30.4721 | −1.00518 | −0.502592 | − | 0.864524i | \(-0.667620\pi\) | ||||
−0.502592 | + | 0.864524i | \(0.667620\pi\) | |||||||
\(920\) | −6.05573 | −0.199651 | ||||||||
\(921\) | 17.5623 | 0.578698 | ||||||||
\(922\) | −13.4164 | −0.441846 | ||||||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.3262 | −0.701202 | ||||||||
\(926\) | −52.3607 | −1.72068 | ||||||||
\(927\) | 1.32624 | 0.0435594 | ||||||||
\(928\) | 40.2492 | 1.32125 | ||||||||
\(929\) | 23.7295 | 0.778539 | 0.389270 | − | 0.921124i | \(-0.372727\pi\) | ||||
0.389270 | + | 0.921124i | \(0.372727\pi\) | |||||||
\(930\) | −4.27051 | −0.140036 | ||||||||
\(931\) | 2.85410 | 0.0935394 | ||||||||
\(932\) | −47.1246 | −1.54362 | ||||||||
\(933\) | −20.6525 | −0.676132 | ||||||||
\(934\) | 58.5410 | 1.91552 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.23607 | 0.236518 | ||||||||
\(937\) | 34.0689 | 1.11298 | 0.556491 | − | 0.830854i | \(-0.312147\pi\) | ||||
0.556491 | + | 0.830854i | \(0.312147\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.81966 | 0.255185 | ||||||||
\(940\) | −8.29180 | −0.270449 | ||||||||
\(941\) | −0.493422 | −0.0160851 | −0.00804255 | − | 0.999968i | \(-0.502560\pi\) | ||||
−0.00804255 | + | 0.999968i | \(0.502560\pi\) | |||||||
\(942\) | 51.7082 | 1.68474 | ||||||||
\(943\) | 32.3475 | 1.05338 | ||||||||
\(944\) | −3.23607 | −0.105325 | ||||||||
\(945\) | 0.618034 | 0.0201046 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.8541 | 0.450198 | 0.225099 | − | 0.974336i | \(-0.427729\pi\) | ||||
0.225099 | + | 0.974336i | \(0.427729\pi\) | |||||||
\(948\) | 30.0000 | 0.974355 | ||||||||
\(949\) | 44.3607 | 1.44001 | ||||||||
\(950\) | −29.4721 | −0.956202 | ||||||||
\(951\) | −6.76393 | −0.219336 | ||||||||
\(952\) | 10.8541 | 0.351783 | ||||||||
\(953\) | 11.8885 | 0.385108 | 0.192554 | − | 0.981286i | \(-0.438323\pi\) | ||||
0.192554 | + | 0.981286i | \(0.438323\pi\) | |||||||
\(954\) | 15.1246 | 0.489677 | ||||||||
\(955\) | −3.03444 | −0.0981922 | ||||||||
\(956\) | −57.1033 | −1.84685 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.11146 | −0.0682181 | ||||||||
\(959\) | 8.18034 | 0.264157 | ||||||||
\(960\) | −8.03444 | −0.259310 | ||||||||
\(961\) | −21.4508 | −0.691963 | ||||||||
\(962\) | 33.4164 | 1.07739 | ||||||||
\(963\) | 15.7984 | 0.509095 | ||||||||
\(964\) | 36.0000 | 1.15948 | ||||||||
\(965\) | 13.5066 | 0.434792 | ||||||||
\(966\) | −9.79837 | −0.315258 | ||||||||
\(967\) | −3.63932 | −0.117033 | −0.0585163 | − | 0.998286i | \(-0.518637\pi\) | ||||
−0.0585163 | + | 0.998286i | \(0.518637\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.8541 | −0.445058 | ||||||||
\(970\) | 8.29180 | 0.266234 | ||||||||
\(971\) | 54.5410 | 1.75030 | 0.875152 | − | 0.483848i | \(-0.160761\pi\) | ||||
0.875152 | + | 0.483848i | \(0.160761\pi\) | |||||||
\(972\) | −3.00000 | −0.0962250 | ||||||||
\(973\) | 13.1459 | 0.421438 | ||||||||
\(974\) | 61.9574 | 1.98524 | ||||||||
\(975\) | 14.9443 | 0.478600 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.6393 | −0.436361 | −0.218180 | − | 0.975908i | \(-0.570012\pi\) | ||||
−0.218180 | + | 0.975908i | \(0.570012\pi\) | |||||||
\(978\) | 22.3607 | 0.715016 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.85410 | −0.0592271 | ||||||||
\(981\) | −17.5623 | −0.560721 | ||||||||
\(982\) | 3.36881 | 0.107503 | ||||||||
\(983\) | −10.9443 | −0.349068 | −0.174534 | − | 0.984651i | \(-0.555842\pi\) | ||||
−0.174534 | + | 0.984651i | \(0.555842\pi\) | |||||||
\(984\) | −16.5066 | −0.526210 | ||||||||
\(985\) | −13.8885 | −0.442526 | ||||||||
\(986\) | −65.1246 | −2.07399 | ||||||||
\(987\) | −4.47214 | −0.142350 | ||||||||
\(988\) | 27.7082 | 0.881515 | ||||||||
\(989\) | 42.5410 | 1.35273 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.2361 | −1.05578 | −0.527889 | − | 0.849313i | \(-0.677016\pi\) | ||||
−0.527889 | + | 0.849313i | \(0.677016\pi\) | |||||||
\(992\) | 20.7295 | 0.658162 | ||||||||
\(993\) | −17.4164 | −0.552693 | ||||||||
\(994\) | −11.0557 | −0.350666 | ||||||||
\(995\) | −8.12461 | −0.257568 | ||||||||
\(996\) | −49.4164 | −1.56582 | ||||||||
\(997\) | −44.4296 | −1.40710 | −0.703549 | − | 0.710647i | \(-0.748403\pi\) | ||||
−0.703549 | + | 0.710647i | \(0.748403\pi\) | |||||||
\(998\) | 47.2361 | 1.49523 | ||||||||
\(999\) | −4.61803 | −0.146108 |
(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 | 2541.2.a.w.1.2 | 2 | ||
3.2 | odd | 2 | 7623.2.a.bk.1.1 | 2 | |||
11.3 | even | 5 | 231.2.j.e.64.1 | ✓ | 4 | ||
11.4 | even | 5 | 231.2.j.e.148.1 | yes | 4 | ||
11.10 | odd | 2 | 2541.2.a.v.1.1 | 2 | |||
33.14 | odd | 10 | 693.2.m.a.64.1 | 4 | |||
33.26 | odd | 10 | 693.2.m.a.379.1 | 4 | |||
33.32 | even | 2 | 7623.2.a.bj.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.e.64.1 | ✓ | 4 | 11.3 | even | 5 | ||
231.2.j.e.148.1 | yes | 4 | 11.4 | even | 5 | ||
693.2.m.a.64.1 | 4 | 33.14 | odd | 10 | |||
693.2.m.a.379.1 | 4 | 33.26 | odd | 10 | |||
2541.2.a.v.1.1 | 2 | 11.10 | odd | 2 | |||
2541.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7623.2.a.bj.1.2 | 2 | 33.32 | even | 2 | |||
7623.2.a.bk.1.1 | 2 | 3.2 | odd | 2 |