Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.41421 | −1.39385 | −0.696923 | − | 0.717146i | \(-0.745448\pi\) | ||||
−0.696923 | + | 0.717146i | \(0.745448\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.41421 | 0.985599 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.41421 | −0.696923 | ||||||||
\(13\) | −2.76733 | −0.767518 | −0.383759 | − | 0.923433i | \(-0.625371\pi\) | ||||
−0.383759 | + | 0.923433i | \(0.625371\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.44949 | −1.07916 | −0.539580 | − | 0.841934i | \(-0.681417\pi\) | ||||
−0.539580 | + | 0.841934i | \(0.681417\pi\) | |||||||
\(18\) | −2.82843 | −0.666667 | ||||||||
\(19\) | 2.62106 | 0.601313 | 0.300657 | − | 0.953732i | \(-0.402794\pi\) | ||||
0.300657 | + | 0.953732i | \(0.402794\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.41421 | −0.526825 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.54587 | 0.322335 | 0.161168 | − | 0.986927i | \(-0.448474\pi\) | ||||
0.161168 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(24\) | 2.41421 | 0.492799 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.76733 | 0.542717 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 9.32780 | 1.73213 | 0.866065 | − | 0.499932i | \(-0.166641\pi\) | ||||
0.866065 | + | 0.499932i | \(0.166641\pi\) | |||||||
\(30\) | 2.41421 | 0.440773 | ||||||||
\(31\) | −10.1769 | −1.82782 | −0.913912 | − | 0.405912i | \(-0.866954\pi\) | ||||
−0.913912 | + | 0.405912i | \(0.866954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.44949 | 0.763081 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.82843 | 0.471405 | ||||||||
\(37\) | −4.39960 | −0.723290 | −0.361645 | − | 0.932316i | \(-0.617785\pi\) | ||||
−0.361645 | + | 0.932316i | \(0.617785\pi\) | |||||||
\(38\) | −2.62106 | −0.425193 | ||||||||
\(39\) | 6.68092 | 1.06980 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.80776 | −0.750846 | −0.375423 | − | 0.926854i | \(-0.622503\pi\) | ||||
−0.375423 | + | 0.926854i | \(0.622503\pi\) | |||||||
\(42\) | 2.41421 | 0.372521 | ||||||||
\(43\) | 11.1416 | 1.69908 | 0.849541 | − | 0.527523i | \(-0.176879\pi\) | ||||
0.849541 | + | 0.527523i | \(0.176879\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | −1.54587 | −0.227926 | ||||||||
\(47\) | −12.3424 | −1.80033 | −0.900163 | − | 0.435553i | \(-0.856553\pi\) | ||||
−0.900163 | + | 0.435553i | \(0.856553\pi\) | |||||||
\(48\) | −2.41421 | −0.348462 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 10.7420 | 1.50418 | ||||||||
\(52\) | −2.76733 | −0.383759 | ||||||||
\(53\) | 9.77729 | 1.34301 | 0.671507 | − | 0.740998i | \(-0.265647\pi\) | ||||
0.671507 | + | 0.740998i | \(0.265647\pi\) | |||||||
\(54\) | −0.414214 | −0.0563673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −6.32780 | −0.838138 | ||||||||
\(58\) | −9.32780 | −1.22480 | ||||||||
\(59\) | 0.510590 | 0.0664731 | 0.0332366 | − | 0.999448i | \(-0.489419\pi\) | ||||
0.0332366 | + | 0.999448i | \(0.489419\pi\) | |||||||
\(60\) | −2.41421 | −0.311674 | ||||||||
\(61\) | 2.63567 | 0.337464 | 0.168732 | − | 0.985662i | \(-0.446033\pi\) | ||||
0.168732 | + | 0.985662i | \(0.446033\pi\) | |||||||
\(62\) | 10.1769 | 1.29247 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.76733 | −0.343245 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.68556 | 0.328094 | 0.164047 | − | 0.986453i | \(-0.447545\pi\) | ||||
0.164047 | + | 0.986453i | \(0.447545\pi\) | |||||||
\(68\) | −4.44949 | −0.539580 | ||||||||
\(69\) | −3.73205 | −0.449286 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 14.8484 | 1.76218 | 0.881088 | − | 0.472952i | \(-0.156812\pi\) | ||||
0.881088 | + | 0.472952i | \(0.156812\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | −3.41421 | −0.399603 | −0.199802 | − | 0.979836i | \(-0.564030\pi\) | ||||
−0.199802 | + | 0.979836i | \(0.564030\pi\) | |||||||
\(74\) | 4.39960 | 0.511443 | ||||||||
\(75\) | −2.41421 | −0.278769 | ||||||||
\(76\) | 2.62106 | 0.300657 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.68092 | −0.756465 | ||||||||
\(79\) | −2.04524 | −0.230108 | −0.115054 | − | 0.993359i | \(-0.536704\pi\) | ||||
−0.115054 | + | 0.993359i | \(0.536704\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 4.80776 | 0.530929 | ||||||||
\(83\) | −4.27452 | −0.469189 | −0.234595 | − | 0.972093i | \(-0.575376\pi\) | ||||
−0.234595 | + | 0.972093i | \(0.575376\pi\) | |||||||
\(84\) | −2.41421 | −0.263412 | ||||||||
\(85\) | −4.44949 | −0.482615 | ||||||||
\(86\) | −11.1416 | −1.20143 | ||||||||
\(87\) | −22.5193 | −2.41432 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9700 | 1.26882 | 0.634411 | − | 0.772996i | \(-0.281243\pi\) | ||||
0.634411 | + | 0.772996i | \(0.281243\pi\) | |||||||
\(90\) | −2.82843 | −0.298142 | ||||||||
\(91\) | −2.76733 | −0.290095 | ||||||||
\(92\) | 1.54587 | 0.161168 | ||||||||
\(93\) | 24.5692 | 2.54771 | ||||||||
\(94\) | 12.3424 | 1.27302 | ||||||||
\(95\) | 2.62106 | 0.268915 | ||||||||
\(96\) | 2.41421 | 0.246400 | ||||||||
\(97\) | −2.35827 | −0.239446 | −0.119723 | − | 0.992807i | \(-0.538201\pi\) | ||||
−0.119723 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.464102 | 0.0461798 | 0.0230899 | − | 0.999733i | \(-0.492650\pi\) | ||||
0.0230899 | + | 0.999733i | \(0.492650\pi\) | |||||||
\(102\) | −10.7420 | −1.06362 | ||||||||
\(103\) | −12.4495 | −1.22668 | −0.613342 | − | 0.789817i | \(-0.710175\pi\) | ||||
−0.613342 | + | 0.789817i | \(0.710175\pi\) | |||||||
\(104\) | 2.76733 | 0.271359 | ||||||||
\(105\) | −2.41421 | −0.235603 | ||||||||
\(106\) | −9.77729 | −0.949655 | ||||||||
\(107\) | −18.4901 | −1.78750 | −0.893752 | − | 0.448561i | \(-0.851937\pi\) | ||||
−0.893752 | + | 0.448561i | \(0.851937\pi\) | |||||||
\(108\) | 0.414214 | 0.0398577 | ||||||||
\(109\) | −1.01461 | −0.0971822 | −0.0485911 | − | 0.998819i | \(-0.515473\pi\) | ||||
−0.0485911 | + | 0.998819i | \(0.515473\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.6216 | 1.00816 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −11.3324 | −1.06607 | −0.533034 | − | 0.846094i | \(-0.678948\pi\) | ||||
−0.533034 | + | 0.846094i | \(0.678948\pi\) | |||||||
\(114\) | 6.32780 | 0.592653 | ||||||||
\(115\) | 1.54587 | 0.144153 | ||||||||
\(116\) | 9.32780 | 0.866065 | ||||||||
\(117\) | −7.82718 | −0.723623 | ||||||||
\(118\) | −0.510590 | −0.0470036 | ||||||||
\(119\) | −4.44949 | −0.407884 | ||||||||
\(120\) | 2.41421 | 0.220387 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.63567 | −0.238623 | ||||||||
\(123\) | 11.6070 | 1.04656 | ||||||||
\(124\) | −10.1769 | −0.913912 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.82843 | −0.251976 | ||||||||
\(127\) | 18.1616 | 1.61158 | 0.805789 | − | 0.592203i | \(-0.201742\pi\) | ||||
0.805789 | + | 0.592203i | \(0.201742\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −26.8983 | −2.36826 | ||||||||
\(130\) | 2.76733 | 0.242711 | ||||||||
\(131\) | −1.25674 | −0.109802 | −0.0549008 | − | 0.998492i | \(-0.517484\pi\) | ||||
−0.0549008 | + | 0.998492i | \(0.517484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.62106 | 0.227275 | ||||||||
\(134\) | −2.68556 | −0.231997 | ||||||||
\(135\) | 0.414214 | 0.0356498 | ||||||||
\(136\) | 4.44949 | 0.381541 | ||||||||
\(137\) | −19.2526 | −1.64486 | −0.822431 | − | 0.568865i | \(-0.807383\pi\) | ||||
−0.822431 | + | 0.568865i | \(0.807383\pi\) | |||||||
\(138\) | 3.73205 | 0.317693 | ||||||||
\(139\) | −3.20612 | −0.271940 | −0.135970 | − | 0.990713i | \(-0.543415\pi\) | ||||
−0.135970 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 29.7972 | 2.50938 | ||||||||
\(142\) | −14.8484 | −1.24605 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.82843 | 0.235702 | ||||||||
\(145\) | 9.32780 | 0.774632 | ||||||||
\(146\) | 3.41421 | 0.282562 | ||||||||
\(147\) | −2.41421 | −0.199121 | ||||||||
\(148\) | −4.39960 | −0.361645 | ||||||||
\(149\) | 2.56993 | 0.210537 | 0.105268 | − | 0.994444i | \(-0.466430\pi\) | ||||
0.105268 | + | 0.994444i | \(0.466430\pi\) | |||||||
\(150\) | 2.41421 | 0.197120 | ||||||||
\(151\) | 10.0969 | 0.821673 | 0.410837 | − | 0.911709i | \(-0.365237\pi\) | ||||
0.410837 | + | 0.911709i | \(0.365237\pi\) | |||||||
\(152\) | −2.62106 | −0.212596 | ||||||||
\(153\) | −12.5851 | −1.01744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.1769 | −0.817428 | ||||||||
\(156\) | 6.68092 | 0.534902 | ||||||||
\(157\) | 7.83324 | 0.625160 | 0.312580 | − | 0.949891i | \(-0.398807\pi\) | ||||
0.312580 | + | 0.949891i | \(0.398807\pi\) | |||||||
\(158\) | 2.04524 | 0.162711 | ||||||||
\(159\) | −23.6045 | −1.87196 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.54587 | 0.121831 | ||||||||
\(162\) | 9.48528 | 0.745234 | ||||||||
\(163\) | −14.7062 | −1.15188 | −0.575940 | − | 0.817492i | \(-0.695364\pi\) | ||||
−0.575940 | + | 0.817492i | \(0.695364\pi\) | |||||||
\(164\) | −4.80776 | −0.375423 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.27452 | 0.331767 | ||||||||
\(167\) | 4.87351 | 0.377123 | 0.188562 | − | 0.982061i | \(-0.439617\pi\) | ||||
0.188562 | + | 0.982061i | \(0.439617\pi\) | |||||||
\(168\) | 2.41421 | 0.186261 | ||||||||
\(169\) | −5.34190 | −0.410915 | ||||||||
\(170\) | 4.44949 | 0.341260 | ||||||||
\(171\) | 7.41348 | 0.566923 | ||||||||
\(172\) | 11.1416 | 0.849541 | ||||||||
\(173\) | −6.38551 | −0.485481 | −0.242740 | − | 0.970091i | \(-0.578046\pi\) | ||||
−0.242740 | + | 0.970091i | \(0.578046\pi\) | |||||||
\(174\) | 22.5193 | 1.70718 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.23267 | −0.0926534 | ||||||||
\(178\) | −11.9700 | −0.897193 | ||||||||
\(179\) | −6.51523 | −0.486971 | −0.243486 | − | 0.969904i | \(-0.578291\pi\) | ||||
−0.243486 | + | 0.969904i | \(0.578291\pi\) | |||||||
\(180\) | 2.82843 | 0.210819 | ||||||||
\(181\) | −6.06591 | −0.450875 | −0.225438 | − | 0.974258i | \(-0.572381\pi\) | ||||
−0.225438 | + | 0.974258i | \(0.572381\pi\) | |||||||
\(182\) | 2.76733 | 0.205128 | ||||||||
\(183\) | −6.36308 | −0.470372 | ||||||||
\(184\) | −1.54587 | −0.113963 | ||||||||
\(185\) | −4.39960 | −0.323465 | ||||||||
\(186\) | −24.5692 | −1.80150 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.3424 | −0.900163 | ||||||||
\(189\) | 0.414214 | 0.0301296 | ||||||||
\(190\) | −2.62106 | −0.190152 | ||||||||
\(191\) | −7.72208 | −0.558750 | −0.279375 | − | 0.960182i | \(-0.590127\pi\) | ||||
−0.279375 | + | 0.960182i | \(0.590127\pi\) | |||||||
\(192\) | −2.41421 | −0.174231 | ||||||||
\(193\) | 3.22678 | 0.232269 | 0.116135 | − | 0.993233i | \(-0.462950\pi\) | ||||
0.116135 | + | 0.993233i | \(0.462950\pi\) | |||||||
\(194\) | 2.35827 | 0.169314 | ||||||||
\(195\) | 6.68092 | 0.478430 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 13.2066 | 0.940934 | 0.470467 | − | 0.882418i | \(-0.344086\pi\) | ||||
0.470467 | + | 0.882418i | \(0.344086\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.99270 | 0.424811 | 0.212406 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212406 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −6.48352 | −0.457312 | ||||||||
\(202\) | −0.464102 | −0.0326541 | ||||||||
\(203\) | 9.32780 | 0.654684 | ||||||||
\(204\) | 10.7420 | 0.752092 | ||||||||
\(205\) | −4.80776 | −0.335789 | ||||||||
\(206\) | 12.4495 | 0.867397 | ||||||||
\(207\) | 4.37237 | 0.303901 | ||||||||
\(208\) | −2.76733 | −0.191880 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.41421 | 0.166597 | ||||||||
\(211\) | 13.9343 | 0.959274 | 0.479637 | − | 0.877467i | \(-0.340768\pi\) | ||||
0.479637 | + | 0.877467i | \(0.340768\pi\) | |||||||
\(212\) | 9.77729 | 0.671507 | ||||||||
\(213\) | −35.8471 | −2.45620 | ||||||||
\(214\) | 18.4901 | 1.26396 | ||||||||
\(215\) | 11.1416 | 0.759852 | ||||||||
\(216\) | −0.414214 | −0.0281837 | ||||||||
\(217\) | −10.1769 | −0.690853 | ||||||||
\(218\) | 1.01461 | 0.0687182 | ||||||||
\(219\) | 8.24264 | 0.556986 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.3132 | 0.828275 | ||||||||
\(222\) | −10.6216 | −0.712874 | ||||||||
\(223\) | −5.69161 | −0.381139 | −0.190569 | − | 0.981674i | \(-0.561033\pi\) | ||||
−0.190569 | + | 0.981674i | \(0.561033\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 11.3324 | 0.753823 | ||||||||
\(227\) | 15.3326 | 1.01766 | 0.508831 | − | 0.860867i | \(-0.330078\pi\) | ||||
0.508831 | + | 0.860867i | \(0.330078\pi\) | |||||||
\(228\) | −6.32780 | −0.419069 | ||||||||
\(229\) | 14.3734 | 0.949821 | 0.474911 | − | 0.880034i | \(-0.342480\pi\) | ||||
0.474911 | + | 0.880034i | \(0.342480\pi\) | |||||||
\(230\) | −1.54587 | −0.101931 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.32780 | −0.612400 | ||||||||
\(233\) | −20.7201 | −1.35742 | −0.678710 | − | 0.734407i | \(-0.737461\pi\) | ||||
−0.678710 | + | 0.734407i | \(0.737461\pi\) | |||||||
\(234\) | 7.82718 | 0.511679 | ||||||||
\(235\) | −12.3424 | −0.805130 | ||||||||
\(236\) | 0.510590 | 0.0332366 | ||||||||
\(237\) | 4.93766 | 0.320735 | ||||||||
\(238\) | 4.44949 | 0.288418 | ||||||||
\(239\) | 22.0876 | 1.42873 | 0.714364 | − | 0.699774i | \(-0.246716\pi\) | ||||
0.714364 | + | 0.699774i | \(0.246716\pi\) | |||||||
\(240\) | −2.41421 | −0.155837 | ||||||||
\(241\) | −0.236073 | −0.0152068 | −0.00760339 | − | 0.999971i | \(-0.502420\pi\) | ||||
−0.00760339 | + | 0.999971i | \(0.502420\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6569 | 1.38929 | ||||||||
\(244\) | 2.63567 | 0.168732 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −11.6070 | −0.740033 | ||||||||
\(247\) | −7.25334 | −0.461519 | ||||||||
\(248\) | 10.1769 | 0.646234 | ||||||||
\(249\) | 10.3196 | 0.653978 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 14.5851 | 0.920601 | 0.460300 | − | 0.887763i | \(-0.347742\pi\) | ||||
0.460300 | + | 0.887763i | \(0.347742\pi\) | |||||||
\(252\) | 2.82843 | 0.178174 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −18.1616 | −1.13956 | ||||||||
\(255\) | 10.7420 | 0.672691 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.57973 | 0.597567 | 0.298784 | − | 0.954321i | \(-0.403419\pi\) | ||||
0.298784 | + | 0.954321i | \(0.403419\pi\) | |||||||
\(258\) | 26.8983 | 1.67461 | ||||||||
\(259\) | −4.39960 | −0.273378 | ||||||||
\(260\) | −2.76733 | −0.171622 | ||||||||
\(261\) | 26.3830 | 1.63307 | ||||||||
\(262\) | 1.25674 | 0.0776415 | ||||||||
\(263\) | −3.02066 | −0.186262 | −0.0931311 | − | 0.995654i | \(-0.529688\pi\) | ||||
−0.0931311 | + | 0.995654i | \(0.529688\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.77729 | 0.600614 | ||||||||
\(266\) | −2.62106 | −0.160708 | ||||||||
\(267\) | −28.8983 | −1.76854 | ||||||||
\(268\) | 2.68556 | 0.164047 | ||||||||
\(269\) | −28.6510 | −1.74688 | −0.873440 | − | 0.486932i | \(-0.838116\pi\) | ||||
−0.873440 | + | 0.486932i | \(0.838116\pi\) | |||||||
\(270\) | −0.414214 | −0.0252082 | ||||||||
\(271\) | 0.406899 | 0.0247173 | 0.0123587 | − | 0.999924i | \(-0.496066\pi\) | ||||
0.0123587 | + | 0.999924i | \(0.496066\pi\) | |||||||
\(272\) | −4.44949 | −0.269790 | ||||||||
\(273\) | 6.68092 | 0.404348 | ||||||||
\(274\) | 19.2526 | 1.16309 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.73205 | −0.224643 | ||||||||
\(277\) | 17.9993 | 1.08147 | 0.540736 | − | 0.841193i | \(-0.318146\pi\) | ||||
0.540736 | + | 0.841193i | \(0.318146\pi\) | |||||||
\(278\) | 3.20612 | 0.192290 | ||||||||
\(279\) | −28.7846 | −1.72329 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 13.9833 | 0.834171 | 0.417085 | − | 0.908867i | \(-0.363052\pi\) | ||||
0.417085 | + | 0.908867i | \(0.363052\pi\) | |||||||
\(282\) | −29.7972 | −1.77440 | ||||||||
\(283\) | 16.1309 | 0.958884 | 0.479442 | − | 0.877574i | \(-0.340839\pi\) | ||||
0.479442 | + | 0.877574i | \(0.340839\pi\) | |||||||
\(284\) | 14.8484 | 0.881088 | ||||||||
\(285\) | −6.32780 | −0.374827 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.80776 | −0.283793 | ||||||||
\(288\) | −2.82843 | −0.166667 | ||||||||
\(289\) | 2.79796 | 0.164586 | ||||||||
\(290\) | −9.32780 | −0.547748 | ||||||||
\(291\) | 5.69337 | 0.333752 | ||||||||
\(292\) | −3.41421 | −0.199802 | ||||||||
\(293\) | −16.1317 | −0.942421 | −0.471211 | − | 0.882021i | \(-0.656183\pi\) | ||||
−0.471211 | + | 0.882021i | \(0.656183\pi\) | |||||||
\(294\) | 2.41421 | 0.140800 | ||||||||
\(295\) | 0.510590 | 0.0297277 | ||||||||
\(296\) | 4.39960 | 0.255722 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.56993 | −0.148872 | ||||||||
\(299\) | −4.27792 | −0.247398 | ||||||||
\(300\) | −2.41421 | −0.139385 | ||||||||
\(301\) | 11.1416 | 0.642192 | ||||||||
\(302\) | −10.0969 | −0.581011 | ||||||||
\(303\) | −1.12044 | −0.0643676 | ||||||||
\(304\) | 2.62106 | 0.150328 | ||||||||
\(305\) | 2.63567 | 0.150918 | ||||||||
\(306\) | 12.5851 | 0.719440 | ||||||||
\(307\) | 27.0119 | 1.54165 | 0.770825 | − | 0.637047i | \(-0.219844\pi\) | ||||
0.770825 | + | 0.637047i | \(0.219844\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.0557 | 1.70981 | ||||||||
\(310\) | 10.1769 | 0.578009 | ||||||||
\(311\) | 24.9182 | 1.41298 | 0.706490 | − | 0.707723i | \(-0.250277\pi\) | ||||
0.706490 | + | 0.707723i | \(0.250277\pi\) | |||||||
\(312\) | −6.68092 | −0.378233 | ||||||||
\(313\) | 12.4044 | 0.701139 | 0.350569 | − | 0.936537i | \(-0.385988\pi\) | ||||
0.350569 | + | 0.936537i | \(0.385988\pi\) | |||||||
\(314\) | −7.83324 | −0.442055 | ||||||||
\(315\) | 2.82843 | 0.159364 | ||||||||
\(316\) | −2.04524 | −0.115054 | ||||||||
\(317\) | −30.0333 | −1.68684 | −0.843419 | − | 0.537256i | \(-0.819461\pi\) | ||||
−0.843419 | + | 0.537256i | \(0.819461\pi\) | |||||||
\(318\) | 23.6045 | 1.32367 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 44.6390 | 2.49151 | ||||||||
\(322\) | −1.54587 | −0.0861477 | ||||||||
\(323\) | −11.6624 | −0.648913 | ||||||||
\(324\) | −9.48528 | −0.526960 | ||||||||
\(325\) | −2.76733 | −0.153504 | ||||||||
\(326\) | 14.7062 | 0.814503 | ||||||||
\(327\) | 2.44949 | 0.135457 | ||||||||
\(328\) | 4.80776 | 0.265464 | ||||||||
\(329\) | −12.3424 | −0.680459 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.67752 | 0.531925 | 0.265962 | − | 0.963983i | \(-0.414310\pi\) | ||||
0.265962 | + | 0.963983i | \(0.414310\pi\) | |||||||
\(332\) | −4.27452 | −0.234595 | ||||||||
\(333\) | −12.4440 | −0.681924 | ||||||||
\(334\) | −4.87351 | −0.266666 | ||||||||
\(335\) | 2.68556 | 0.146728 | ||||||||
\(336\) | −2.41421 | −0.131706 | ||||||||
\(337\) | 17.9968 | 0.980346 | 0.490173 | − | 0.871625i | \(-0.336934\pi\) | ||||
0.490173 | + | 0.871625i | \(0.336934\pi\) | |||||||
\(338\) | 5.34190 | 0.290561 | ||||||||
\(339\) | 27.3590 | 1.48593 | ||||||||
\(340\) | −4.44949 | −0.241307 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.41348 | −0.400875 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −11.1416 | −0.600716 | ||||||||
\(345\) | −3.73205 | −0.200927 | ||||||||
\(346\) | 6.38551 | 0.343287 | ||||||||
\(347\) | 16.1806 | 0.868623 | 0.434311 | − | 0.900763i | \(-0.356992\pi\) | ||||
0.434311 | + | 0.900763i | \(0.356992\pi\) | |||||||
\(348\) | −22.5193 | −1.20716 | ||||||||
\(349\) | −9.94031 | −0.532092 | −0.266046 | − | 0.963960i | \(-0.585717\pi\) | ||||
−0.266046 | + | 0.963960i | \(0.585717\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −1.14626 | −0.0611831 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.9547 | −1.32821 | −0.664103 | − | 0.747642i | \(-0.731186\pi\) | ||||
−0.664103 | + | 0.747642i | \(0.731186\pi\) | |||||||
\(354\) | 1.23267 | 0.0655158 | ||||||||
\(355\) | 14.8484 | 0.788069 | ||||||||
\(356\) | 11.9700 | 0.634411 | ||||||||
\(357\) | 10.7420 | 0.568528 | ||||||||
\(358\) | 6.51523 | 0.344341 | ||||||||
\(359\) | −28.3933 | −1.49854 | −0.749271 | − | 0.662263i | \(-0.769596\pi\) | ||||
−0.749271 | + | 0.662263i | \(0.769596\pi\) | |||||||
\(360\) | −2.82843 | −0.149071 | ||||||||
\(361\) | −12.1300 | −0.638423 | ||||||||
\(362\) | 6.06591 | 0.318817 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.76733 | −0.145047 | ||||||||
\(365\) | −3.41421 | −0.178708 | ||||||||
\(366\) | 6.36308 | 0.332604 | ||||||||
\(367\) | 19.7164 | 1.02919 | 0.514593 | − | 0.857435i | \(-0.327943\pi\) | ||||
0.514593 | + | 0.857435i | \(0.327943\pi\) | |||||||
\(368\) | 1.54587 | 0.0805838 | ||||||||
\(369\) | −13.5984 | −0.707905 | ||||||||
\(370\) | 4.39960 | 0.228724 | ||||||||
\(371\) | 9.77729 | 0.507612 | ||||||||
\(372\) | 24.5692 | 1.27385 | ||||||||
\(373\) | −32.7705 | −1.69679 | −0.848396 | − | 0.529361i | \(-0.822432\pi\) | ||||
−0.848396 | + | 0.529361i | \(0.822432\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.41421 | −0.124669 | ||||||||
\(376\) | 12.3424 | 0.636512 | ||||||||
\(377\) | −25.8131 | −1.32944 | ||||||||
\(378\) | −0.414214 | −0.0213048 | ||||||||
\(379\) | −12.8332 | −0.659199 | −0.329600 | − | 0.944121i | \(-0.606914\pi\) | ||||
−0.329600 | + | 0.944121i | \(0.606914\pi\) | |||||||
\(380\) | 2.62106 | 0.134458 | ||||||||
\(381\) | −43.8459 | −2.24629 | ||||||||
\(382\) | 7.72208 | 0.395096 | ||||||||
\(383\) | 13.1557 | 0.672226 | 0.336113 | − | 0.941822i | \(-0.390888\pi\) | ||||
0.336113 | + | 0.941822i | \(0.390888\pi\) | |||||||
\(384\) | 2.41421 | 0.123200 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.22678 | −0.164239 | ||||||||
\(387\) | 31.5133 | 1.60191 | ||||||||
\(388\) | −2.35827 | −0.119723 | ||||||||
\(389\) | −20.8831 | −1.05882 | −0.529408 | − | 0.848367i | \(-0.677586\pi\) | ||||
−0.529408 | + | 0.848367i | \(0.677586\pi\) | |||||||
\(390\) | −6.68092 | −0.338301 | ||||||||
\(391\) | −6.87832 | −0.347851 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 3.03403 | 0.153047 | ||||||||
\(394\) | −13.2066 | −0.665341 | ||||||||
\(395\) | −2.04524 | −0.102907 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.01314 | −0.402168 | −0.201084 | − | 0.979574i | \(-0.564446\pi\) | ||||
−0.201084 | + | 0.979574i | \(0.564446\pi\) | |||||||
\(398\) | −5.99270 | −0.300387 | ||||||||
\(399\) | −6.32780 | −0.316786 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 4.25120 | 0.212295 | 0.106147 | − | 0.994350i | \(-0.466148\pi\) | ||||
0.106147 | + | 0.994350i | \(0.466148\pi\) | |||||||
\(402\) | 6.48352 | 0.323369 | ||||||||
\(403\) | 28.1628 | 1.40289 | ||||||||
\(404\) | 0.464102 | 0.0230899 | ||||||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | −9.32780 | −0.462931 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −10.7420 | −0.531809 | ||||||||
\(409\) | −5.90606 | −0.292036 | −0.146018 | − | 0.989282i | \(-0.546646\pi\) | ||||
−0.146018 | + | 0.989282i | \(0.546646\pi\) | |||||||
\(410\) | 4.80776 | 0.237438 | ||||||||
\(411\) | 46.4799 | 2.29268 | ||||||||
\(412\) | −12.4495 | −0.613342 | ||||||||
\(413\) | 0.510590 | 0.0251245 | ||||||||
\(414\) | −4.37237 | −0.214890 | ||||||||
\(415\) | −4.27452 | −0.209828 | ||||||||
\(416\) | 2.76733 | 0.135679 | ||||||||
\(417\) | 7.74026 | 0.379042 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0428 | 1.46768 | 0.733842 | − | 0.679320i | \(-0.237725\pi\) | ||||
0.733842 | + | 0.679320i | \(0.237725\pi\) | |||||||
\(420\) | −2.41421 | −0.117802 | ||||||||
\(421\) | −10.2288 | −0.498520 | −0.249260 | − | 0.968437i | \(-0.580187\pi\) | ||||
−0.249260 | + | 0.968437i | \(0.580187\pi\) | |||||||
\(422\) | −13.9343 | −0.678309 | ||||||||
\(423\) | −34.9096 | −1.69736 | ||||||||
\(424\) | −9.77729 | −0.474827 | ||||||||
\(425\) | −4.44949 | −0.215832 | ||||||||
\(426\) | 35.8471 | 1.73680 | ||||||||
\(427\) | 2.63567 | 0.127549 | ||||||||
\(428\) | −18.4901 | −0.893752 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.1416 | −0.537297 | ||||||||
\(431\) | 1.14626 | 0.0552136 | 0.0276068 | − | 0.999619i | \(-0.491211\pi\) | ||||
0.0276068 | + | 0.999619i | \(0.491211\pi\) | |||||||
\(432\) | 0.414214 | 0.0199289 | ||||||||
\(433\) | −9.29931 | −0.446896 | −0.223448 | − | 0.974716i | \(-0.571731\pi\) | ||||
−0.223448 | + | 0.974716i | \(0.571731\pi\) | |||||||
\(434\) | 10.1769 | 0.488507 | ||||||||
\(435\) | −22.5193 | −1.07972 | ||||||||
\(436\) | −1.01461 | −0.0485911 | ||||||||
\(437\) | 4.05181 | 0.193824 | ||||||||
\(438\) | −8.24264 | −0.393849 | ||||||||
\(439\) | −9.16604 | −0.437471 | −0.218736 | − | 0.975784i | \(-0.570193\pi\) | ||||
−0.218736 | + | 0.975784i | \(0.570193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.82843 | 0.134687 | ||||||||
\(442\) | −12.3132 | −0.585679 | ||||||||
\(443\) | −33.0771 | −1.57154 | −0.785771 | − | 0.618517i | \(-0.787734\pi\) | ||||
−0.785771 | + | 0.618517i | \(0.787734\pi\) | |||||||
\(444\) | 10.6216 | 0.504078 | ||||||||
\(445\) | 11.9700 | 0.567435 | ||||||||
\(446\) | 5.69161 | 0.269506 | ||||||||
\(447\) | −6.20436 | −0.293456 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −19.3933 | −0.915228 | −0.457614 | − | 0.889151i | \(-0.651296\pi\) | ||||
−0.457614 | + | 0.889151i | \(0.651296\pi\) | |||||||
\(450\) | −2.82843 | −0.133333 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −11.3324 | −0.533034 | ||||||||
\(453\) | −24.3761 | −1.14529 | ||||||||
\(454\) | −15.3326 | −0.719595 | ||||||||
\(455\) | −2.76733 | −0.129734 | ||||||||
\(456\) | 6.32780 | 0.296327 | ||||||||
\(457\) | 32.5206 | 1.52125 | 0.760624 | − | 0.649193i | \(-0.224893\pi\) | ||||
0.760624 | + | 0.649193i | \(0.224893\pi\) | |||||||
\(458\) | −14.3734 | −0.671625 | ||||||||
\(459\) | −1.84304 | −0.0860257 | ||||||||
\(460\) | 1.54587 | 0.0720764 | ||||||||
\(461\) | −42.2301 | −1.96685 | −0.983427 | − | 0.181306i | \(-0.941968\pi\) | ||||
−0.983427 | + | 0.181306i | \(0.941968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0593 | −1.02518 | −0.512592 | − | 0.858632i | \(-0.671315\pi\) | ||||
−0.512592 | + | 0.858632i | \(0.671315\pi\) | |||||||
\(464\) | 9.32780 | 0.433032 | ||||||||
\(465\) | 24.5692 | 1.13937 | ||||||||
\(466\) | 20.7201 | 0.959841 | ||||||||
\(467\) | −21.3716 | −0.988962 | −0.494481 | − | 0.869189i | \(-0.664642\pi\) | ||||
−0.494481 | + | 0.869189i | \(0.664642\pi\) | |||||||
\(468\) | −7.82718 | −0.361812 | ||||||||
\(469\) | 2.68556 | 0.124008 | ||||||||
\(470\) | 12.3424 | 0.569313 | ||||||||
\(471\) | −18.9111 | −0.871378 | ||||||||
\(472\) | −0.510590 | −0.0235018 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4.93766 | −0.226794 | ||||||||
\(475\) | 2.62106 | 0.120263 | ||||||||
\(476\) | −4.44949 | −0.203942 | ||||||||
\(477\) | 27.6544 | 1.26621 | ||||||||
\(478\) | −22.0876 | −1.01026 | ||||||||
\(479\) | 9.84888 | 0.450007 | 0.225003 | − | 0.974358i | \(-0.427761\pi\) | ||||
0.225003 | + | 0.974358i | \(0.427761\pi\) | |||||||
\(480\) | 2.41421 | 0.110193 | ||||||||
\(481\) | 12.1751 | 0.555138 | ||||||||
\(482\) | 0.236073 | 0.0107528 | ||||||||
\(483\) | −3.73205 | −0.169814 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.35827 | −0.107084 | ||||||||
\(486\) | −21.6569 | −0.982375 | ||||||||
\(487\) | −35.0712 | −1.58923 | −0.794615 | − | 0.607114i | \(-0.792327\pi\) | ||||
−0.794615 | + | 0.607114i | \(0.792327\pi\) | |||||||
\(488\) | −2.63567 | −0.119311 | ||||||||
\(489\) | 35.5040 | 1.60555 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −1.40389 | −0.0633569 | −0.0316784 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316784 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(492\) | 11.6070 | 0.523282 | ||||||||
\(493\) | −41.5040 | −1.86924 | ||||||||
\(494\) | 7.25334 | 0.326343 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.1769 | −0.456956 | ||||||||
\(497\) | 14.8484 | 0.666040 | ||||||||
\(498\) | −10.3196 | −0.462432 | ||||||||
\(499\) | −5.73573 | −0.256767 | −0.128383 | − | 0.991725i | \(-0.540979\pi\) | ||||
−0.128383 | + | 0.991725i | \(0.540979\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −11.7657 | −0.525652 | ||||||||
\(502\) | −14.5851 | −0.650963 | ||||||||
\(503\) | −10.7493 | −0.479288 | −0.239644 | − | 0.970861i | \(-0.577031\pi\) | ||||
−0.239644 | + | 0.970861i | \(0.577031\pi\) | |||||||
\(504\) | −2.82843 | −0.125988 | ||||||||
\(505\) | 0.464102 | 0.0206523 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.8965 | 0.572753 | ||||||||
\(508\) | 18.1616 | 0.805789 | ||||||||
\(509\) | 5.44632 | 0.241404 | 0.120702 | − | 0.992689i | \(-0.461485\pi\) | ||||
0.120702 | + | 0.992689i | \(0.461485\pi\) | |||||||
\(510\) | −10.7420 | −0.475665 | ||||||||
\(511\) | −3.41421 | −0.151036 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.08568 | 0.0479339 | ||||||||
\(514\) | −9.57973 | −0.422544 | ||||||||
\(515\) | −12.4495 | −0.548590 | ||||||||
\(516\) | −26.8983 | −1.18413 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.39960 | 0.193307 | ||||||||
\(519\) | 15.4160 | 0.676686 | ||||||||
\(520\) | 2.76733 | 0.121355 | ||||||||
\(521\) | −28.3689 | −1.24286 | −0.621432 | − | 0.783468i | \(-0.713449\pi\) | ||||
−0.621432 | + | 0.783468i | \(0.713449\pi\) | |||||||
\(522\) | −26.3830 | −1.15475 | ||||||||
\(523\) | −28.2428 | −1.23497 | −0.617486 | − | 0.786582i | \(-0.711849\pi\) | ||||
−0.617486 | + | 0.786582i | \(0.711849\pi\) | |||||||
\(524\) | −1.25674 | −0.0549008 | ||||||||
\(525\) | −2.41421 | −0.105365 | ||||||||
\(526\) | 3.02066 | 0.131707 | ||||||||
\(527\) | 45.2820 | 1.97251 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6103 | −0.896100 | ||||||||
\(530\) | −9.77729 | −0.424699 | ||||||||
\(531\) | 1.44417 | 0.0626715 | ||||||||
\(532\) | 2.62106 | 0.113637 | ||||||||
\(533\) | 13.3047 | 0.576288 | ||||||||
\(534\) | 28.8983 | 1.25055 | ||||||||
\(535\) | −18.4901 | −0.799396 | ||||||||
\(536\) | −2.68556 | −0.115999 | ||||||||
\(537\) | 15.7292 | 0.678764 | ||||||||
\(538\) | 28.6510 | 1.23523 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.414214 | 0.0178249 | ||||||||
\(541\) | 3.15698 | 0.135729 | 0.0678646 | − | 0.997695i | \(-0.478381\pi\) | ||||
0.0678646 | + | 0.997695i | \(0.478381\pi\) | |||||||
\(542\) | −0.406899 | −0.0174778 | ||||||||
\(543\) | 14.6444 | 0.628451 | ||||||||
\(544\) | 4.44949 | 0.190770 | ||||||||
\(545\) | −1.01461 | −0.0434612 | ||||||||
\(546\) | −6.68092 | −0.285917 | ||||||||
\(547\) | −18.8345 | −0.805305 | −0.402652 | − | 0.915353i | \(-0.631912\pi\) | ||||
−0.402652 | + | 0.915353i | \(0.631912\pi\) | |||||||
\(548\) | −19.2526 | −0.822431 | ||||||||
\(549\) | 7.45481 | 0.318164 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.4488 | 1.04155 | ||||||||
\(552\) | 3.73205 | 0.158847 | ||||||||
\(553\) | −2.04524 | −0.0869726 | ||||||||
\(554\) | −17.9993 | −0.764716 | ||||||||
\(555\) | 10.6216 | 0.450861 | ||||||||
\(556\) | −3.20612 | −0.135970 | ||||||||
\(557\) | −30.1283 | −1.27658 | −0.638288 | − | 0.769798i | \(-0.720357\pi\) | ||||
−0.638288 | + | 0.769798i | \(0.720357\pi\) | |||||||
\(558\) | 28.7846 | 1.21855 | ||||||||
\(559\) | −30.8325 | −1.30408 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.9833 | −0.589848 | ||||||||
\(563\) | −29.7041 | −1.25188 | −0.625939 | − | 0.779872i | \(-0.715284\pi\) | ||||
−0.625939 | + | 0.779872i | \(0.715284\pi\) | |||||||
\(564\) | 29.7972 | 1.25469 | ||||||||
\(565\) | −11.3324 | −0.476760 | ||||||||
\(566\) | −16.1309 | −0.678033 | ||||||||
\(567\) | −9.48528 | −0.398344 | ||||||||
\(568\) | −14.8484 | −0.623023 | ||||||||
\(569\) | −12.2387 | −0.513074 | −0.256537 | − | 0.966534i | \(-0.582582\pi\) | ||||
−0.256537 | + | 0.966534i | \(0.582582\pi\) | |||||||
\(570\) | 6.32780 | 0.265043 | ||||||||
\(571\) | −43.9882 | −1.84085 | −0.920425 | − | 0.390919i | \(-0.872157\pi\) | ||||
−0.920425 | + | 0.390919i | \(0.872157\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.6428 | 0.778812 | ||||||||
\(574\) | 4.80776 | 0.200672 | ||||||||
\(575\) | 1.54587 | 0.0644671 | ||||||||
\(576\) | 2.82843 | 0.117851 | ||||||||
\(577\) | −29.8582 | −1.24301 | −0.621506 | − | 0.783410i | \(-0.713479\pi\) | ||||
−0.621506 | + | 0.783410i | \(0.713479\pi\) | |||||||
\(578\) | −2.79796 | −0.116380 | ||||||||
\(579\) | −7.79015 | −0.323747 | ||||||||
\(580\) | 9.32780 | 0.387316 | ||||||||
\(581\) | −4.27452 | −0.177337 | ||||||||
\(582\) | −5.69337 | −0.235998 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.41421 | 0.141281 | ||||||||
\(585\) | −7.82718 | −0.323614 | ||||||||
\(586\) | 16.1317 | 0.666392 | ||||||||
\(587\) | −46.1626 | −1.90533 | −0.952667 | − | 0.304016i | \(-0.901672\pi\) | ||||
−0.952667 | + | 0.304016i | \(0.901672\pi\) | |||||||
\(588\) | −2.41421 | −0.0995605 | ||||||||
\(589\) | −26.6743 | −1.09909 | ||||||||
\(590\) | −0.510590 | −0.0210207 | ||||||||
\(591\) | −31.8836 | −1.31152 | ||||||||
\(592\) | −4.39960 | −0.180823 | ||||||||
\(593\) | 32.3523 | 1.32855 | 0.664276 | − | 0.747488i | \(-0.268740\pi\) | ||||
0.664276 | + | 0.747488i | \(0.268740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.44949 | −0.182411 | ||||||||
\(596\) | 2.56993 | 0.105268 | ||||||||
\(597\) | −14.4677 | −0.592122 | ||||||||
\(598\) | 4.27792 | 0.174937 | ||||||||
\(599\) | −27.7430 | −1.13355 | −0.566775 | − | 0.823873i | \(-0.691809\pi\) | ||||
−0.566775 | + | 0.823873i | \(0.691809\pi\) | |||||||
\(600\) | 2.41421 | 0.0985599 | ||||||||
\(601\) | −34.5468 | −1.40919 | −0.704596 | − | 0.709608i | \(-0.748872\pi\) | ||||
−0.704596 | + | 0.709608i | \(0.748872\pi\) | |||||||
\(602\) | −11.1416 | −0.454099 | ||||||||
\(603\) | 7.59592 | 0.309330 | ||||||||
\(604\) | 10.0969 | 0.410837 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.12044 | 0.0455148 | ||||||||
\(607\) | 42.8562 | 1.73948 | 0.869740 | − | 0.493511i | \(-0.164287\pi\) | ||||
0.869740 | + | 0.493511i | \(0.164287\pi\) | |||||||
\(608\) | −2.62106 | −0.106298 | ||||||||
\(609\) | −22.5193 | −0.912529 | ||||||||
\(610\) | −2.63567 | −0.106715 | ||||||||
\(611\) | 34.1555 | 1.38178 | ||||||||
\(612\) | −12.5851 | −0.508721 | ||||||||
\(613\) | 22.5795 | 0.911978 | 0.455989 | − | 0.889985i | \(-0.349286\pi\) | ||||
0.455989 | + | 0.889985i | \(0.349286\pi\) | |||||||
\(614\) | −27.0119 | −1.09011 | ||||||||
\(615\) | 11.6070 | 0.468038 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.0880 | −1.37233 | −0.686166 | − | 0.727445i | \(-0.740707\pi\) | ||||
−0.686166 | + | 0.727445i | \(0.740707\pi\) | |||||||
\(618\) | −30.0557 | −1.20902 | ||||||||
\(619\) | −2.64208 | −0.106194 | −0.0530971 | − | 0.998589i | \(-0.516909\pi\) | ||||
−0.0530971 | + | 0.998589i | \(0.516909\pi\) | |||||||
\(620\) | −10.1769 | −0.408714 | ||||||||
\(621\) | 0.640319 | 0.0256951 | ||||||||
\(622\) | −24.9182 | −0.999128 | ||||||||
\(623\) | 11.9700 | 0.479570 | ||||||||
\(624\) | 6.68092 | 0.267451 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.4044 | −0.495780 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.83324 | 0.312580 | ||||||||
\(629\) | 19.5760 | 0.780546 | ||||||||
\(630\) | −2.82843 | −0.112687 | ||||||||
\(631\) | 16.2313 | 0.646156 | 0.323078 | − | 0.946372i | \(-0.395282\pi\) | ||||
0.323078 | + | 0.946372i | \(0.395282\pi\) | |||||||
\(632\) | 2.04524 | 0.0813554 | ||||||||
\(633\) | −33.6403 | −1.33708 | ||||||||
\(634\) | 30.0333 | 1.19277 | ||||||||
\(635\) | 18.1616 | 0.720719 | ||||||||
\(636\) | −23.6045 | −0.935978 | ||||||||
\(637\) | −2.76733 | −0.109645 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 41.9975 | 1.66140 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −11.5324 | −0.455502 | −0.227751 | − | 0.973719i | \(-0.573137\pi\) | ||||
−0.227751 | + | 0.973719i | \(0.573137\pi\) | |||||||
\(642\) | −44.6390 | −1.76176 | ||||||||
\(643\) | −13.3722 | −0.527346 | −0.263673 | − | 0.964612i | \(-0.584934\pi\) | ||||
−0.263673 | + | 0.964612i | \(0.584934\pi\) | |||||||
\(644\) | 1.54587 | 0.0609157 | ||||||||
\(645\) | −26.8983 | −1.05912 | ||||||||
\(646\) | 11.6624 | 0.458851 | ||||||||
\(647\) | −49.1639 | −1.93283 | −0.966416 | − | 0.256984i | \(-0.917271\pi\) | ||||
−0.966416 | + | 0.256984i | \(0.917271\pi\) | |||||||
\(648\) | 9.48528 | 0.372617 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.76733 | 0.108543 | ||||||||
\(651\) | 24.5692 | 0.962943 | ||||||||
\(652\) | −14.7062 | −0.575940 | ||||||||
\(653\) | 27.7393 | 1.08552 | 0.542762 | − | 0.839887i | \(-0.317379\pi\) | ||||
0.542762 | + | 0.839887i | \(0.317379\pi\) | |||||||
\(654\) | −2.44949 | −0.0957826 | ||||||||
\(655\) | −1.25674 | −0.0491048 | ||||||||
\(656\) | −4.80776 | −0.187712 | ||||||||
\(657\) | −9.65685 | −0.376750 | ||||||||
\(658\) | 12.3424 | 0.481158 | ||||||||
\(659\) | 35.7841 | 1.39395 | 0.696975 | − | 0.717095i | \(-0.254529\pi\) | ||||
0.696975 | + | 0.717095i | \(0.254529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.25763 | 0.243394 | 0.121697 | − | 0.992567i | \(-0.461166\pi\) | ||||
0.121697 | + | 0.992567i | \(0.461166\pi\) | |||||||
\(662\) | −9.67752 | −0.376127 | ||||||||
\(663\) | −29.7267 | −1.15449 | ||||||||
\(664\) | 4.27452 | 0.165883 | ||||||||
\(665\) | 2.62106 | 0.101640 | ||||||||
\(666\) | 12.4440 | 0.482193 | ||||||||
\(667\) | 14.4195 | 0.558327 | ||||||||
\(668\) | 4.87351 | 0.188562 | ||||||||
\(669\) | 13.7408 | 0.531249 | ||||||||
\(670\) | −2.68556 | −0.103752 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.41421 | 0.0931303 | ||||||||
\(673\) | 34.4710 | 1.32876 | 0.664379 | − | 0.747396i | \(-0.268696\pi\) | ||||
0.664379 | + | 0.747396i | \(0.268696\pi\) | |||||||
\(674\) | −17.9968 | −0.693209 | ||||||||
\(675\) | 0.414214 | 0.0159431 | ||||||||
\(676\) | −5.34190 | −0.205458 | ||||||||
\(677\) | −39.4297 | −1.51541 | −0.757704 | − | 0.652598i | \(-0.773679\pi\) | ||||
−0.757704 | + | 0.652598i | \(0.773679\pi\) | |||||||
\(678\) | −27.3590 | −1.05071 | ||||||||
\(679\) | −2.35827 | −0.0905022 | ||||||||
\(680\) | 4.44949 | 0.170630 | ||||||||
\(681\) | −37.0162 | −1.41846 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.54298 | −0.288624 | −0.144312 | − | 0.989532i | \(-0.546097\pi\) | ||||
−0.144312 | + | 0.989532i | \(0.546097\pi\) | |||||||
\(684\) | 7.41348 | 0.283462 | ||||||||
\(685\) | −19.2526 | −0.735604 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −34.7005 | −1.32391 | ||||||||
\(688\) | 11.1416 | 0.424770 | ||||||||
\(689\) | −27.0570 | −1.03079 | ||||||||
\(690\) | 3.73205 | 0.142077 | ||||||||
\(691\) | −10.7272 | −0.408082 | −0.204041 | − | 0.978962i | \(-0.565408\pi\) | ||||
−0.204041 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(692\) | −6.38551 | −0.242740 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.1806 | −0.614209 | ||||||||
\(695\) | −3.20612 | −0.121615 | ||||||||
\(696\) | 22.5193 | 0.853592 | ||||||||
\(697\) | 21.3921 | 0.810283 | ||||||||
\(698\) | 9.94031 | 0.376246 | ||||||||
\(699\) | 50.0228 | 1.89203 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −32.4865 | −1.22700 | −0.613500 | − | 0.789695i | \(-0.710239\pi\) | ||||
−0.613500 | + | 0.789695i | \(0.710239\pi\) | |||||||
\(702\) | 1.14626 | 0.0432630 | ||||||||
\(703\) | −11.5316 | −0.434924 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.7972 | 1.12223 | ||||||||
\(706\) | 24.9547 | 0.939183 | ||||||||
\(707\) | 0.464102 | 0.0174543 | ||||||||
\(708\) | −1.23267 | −0.0463267 | ||||||||
\(709\) | −4.45805 | −0.167426 | −0.0837128 | − | 0.996490i | \(-0.526678\pi\) | ||||
−0.0837128 | + | 0.996490i | \(0.526678\pi\) | |||||||
\(710\) | −14.8484 | −0.557249 | ||||||||
\(711\) | −5.78482 | −0.216948 | ||||||||
\(712\) | −11.9700 | −0.448596 | ||||||||
\(713\) | −15.7321 | −0.589172 | ||||||||
\(714\) | −10.7420 | −0.402010 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.51523 | −0.243486 | ||||||||
\(717\) | −53.3242 | −1.99143 | ||||||||
\(718\) | 28.3933 | 1.05963 | ||||||||
\(719\) | 45.1213 | 1.68274 | 0.841370 | − | 0.540460i | \(-0.181750\pi\) | ||||
0.841370 | + | 0.540460i | \(0.181750\pi\) | |||||||
\(720\) | 2.82843 | 0.105409 | ||||||||
\(721\) | −12.4495 | −0.463643 | ||||||||
\(722\) | 12.1300 | 0.451433 | ||||||||
\(723\) | 0.569930 | 0.0211959 | ||||||||
\(724\) | −6.06591 | −0.225438 | ||||||||
\(725\) | 9.32780 | 0.346426 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.01388 | 0.334306 | 0.167153 | − | 0.985931i | \(-0.446543\pi\) | ||||
0.167153 | + | 0.985931i | \(0.446543\pi\) | |||||||
\(728\) | 2.76733 | 0.102564 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 3.41421 | 0.126366 | ||||||||
\(731\) | −49.5745 | −1.83358 | ||||||||
\(732\) | −6.36308 | −0.235186 | ||||||||
\(733\) | −46.3945 | −1.71362 | −0.856811 | − | 0.515631i | \(-0.827557\pi\) | ||||
−0.856811 | + | 0.515631i | \(0.827557\pi\) | |||||||
\(734\) | −19.7164 | −0.727744 | ||||||||
\(735\) | −2.41421 | −0.0890496 | ||||||||
\(736\) | −1.54587 | −0.0569814 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 13.5984 | 0.500564 | ||||||||
\(739\) | 26.8879 | 0.989089 | 0.494544 | − | 0.869152i | \(-0.335335\pi\) | ||||
0.494544 | + | 0.869152i | \(0.335335\pi\) | |||||||
\(740\) | −4.39960 | −0.161733 | ||||||||
\(741\) | 17.5111 | 0.643287 | ||||||||
\(742\) | −9.77729 | −0.358936 | ||||||||
\(743\) | 5.89670 | 0.216329 | 0.108165 | − | 0.994133i | \(-0.465503\pi\) | ||||
0.108165 | + | 0.994133i | \(0.465503\pi\) | |||||||
\(744\) | −24.5692 | −0.900751 | ||||||||
\(745\) | 2.56993 | 0.0941550 | ||||||||
\(746\) | 32.7705 | 1.19981 | ||||||||
\(747\) | −12.0902 | −0.442356 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.4901 | −0.675613 | ||||||||
\(750\) | 2.41421 | 0.0881546 | ||||||||
\(751\) | 32.7728 | 1.19590 | 0.597948 | − | 0.801535i | \(-0.295983\pi\) | ||||
0.597948 | + | 0.801535i | \(0.295983\pi\) | |||||||
\(752\) | −12.3424 | −0.450082 | ||||||||
\(753\) | −35.2114 | −1.28318 | ||||||||
\(754\) | 25.8131 | 0.940057 | ||||||||
\(755\) | 10.0969 | 0.367464 | ||||||||
\(756\) | 0.414214 | 0.0150648 | ||||||||
\(757\) | 42.6821 | 1.55131 | 0.775654 | − | 0.631158i | \(-0.217420\pi\) | ||||
0.775654 | + | 0.631158i | \(0.217420\pi\) | |||||||
\(758\) | 12.8332 | 0.466124 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.62106 | −0.0950759 | ||||||||
\(761\) | 13.3835 | 0.485153 | 0.242576 | − | 0.970132i | \(-0.422008\pi\) | ||||
0.242576 | + | 0.970132i | \(0.422008\pi\) | |||||||
\(762\) | 43.8459 | 1.58837 | ||||||||
\(763\) | −1.01461 | −0.0367314 | ||||||||
\(764\) | −7.72208 | −0.279375 | ||||||||
\(765\) | −12.5851 | −0.455014 | ||||||||
\(766\) | −13.1557 | −0.475335 | ||||||||
\(767\) | −1.41297 | −0.0510194 | ||||||||
\(768\) | −2.41421 | −0.0871154 | ||||||||
\(769\) | −24.1256 | −0.869990 | −0.434995 | − | 0.900433i | \(-0.643250\pi\) | ||||
−0.434995 | + | 0.900433i | \(0.643250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.1275 | −0.832917 | ||||||||
\(772\) | 3.22678 | 0.116135 | ||||||||
\(773\) | 18.1243 | 0.651886 | 0.325943 | − | 0.945389i | \(-0.394318\pi\) | ||||
0.325943 | + | 0.945389i | \(0.394318\pi\) | |||||||
\(774\) | −31.5133 | −1.13272 | ||||||||
\(775\) | −10.1769 | −0.365565 | ||||||||
\(776\) | 2.35827 | 0.0846571 | ||||||||
\(777\) | 10.6216 | 0.381047 | ||||||||
\(778\) | 20.8831 | 0.748696 | ||||||||
\(779\) | −12.6014 | −0.451494 | ||||||||
\(780\) | 6.68092 | 0.239215 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.87832 | 0.245968 | ||||||||
\(783\) | 3.86370 | 0.138077 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 7.83324 | 0.279580 | ||||||||
\(786\) | −3.03403 | −0.108220 | ||||||||
\(787\) | 13.1477 | 0.468665 | 0.234332 | − | 0.972157i | \(-0.424710\pi\) | ||||
0.234332 | + | 0.972157i | \(0.424710\pi\) | |||||||
\(788\) | 13.2066 | 0.470467 | ||||||||
\(789\) | 7.29253 | 0.259621 | ||||||||
\(790\) | 2.04524 | 0.0727665 | ||||||||
\(791\) | −11.3324 | −0.402936 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.29377 | −0.259009 | ||||||||
\(794\) | 8.01314 | 0.284376 | ||||||||
\(795\) | −23.6045 | −0.837165 | ||||||||
\(796\) | 5.99270 | 0.212406 | ||||||||
\(797\) | 28.3545 | 1.00437 | 0.502185 | − | 0.864760i | \(-0.332530\pi\) | ||||
0.502185 | + | 0.864760i | \(0.332530\pi\) | |||||||
\(798\) | 6.32780 | 0.224002 | ||||||||
\(799\) | 54.9175 | 1.94284 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 33.8564 | 1.19626 | ||||||||
\(802\) | −4.25120 | −0.150115 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.48352 | −0.228656 | ||||||||
\(805\) | 1.54587 | 0.0544846 | ||||||||
\(806\) | −28.1628 | −0.991992 | ||||||||
\(807\) | 69.1695 | 2.43488 | ||||||||
\(808\) | −0.464102 | −0.0163270 | ||||||||
\(809\) | −20.7073 | −0.728028 | −0.364014 | − | 0.931393i | \(-0.618594\pi\) | ||||
−0.364014 | + | 0.931393i | \(0.618594\pi\) | |||||||
\(810\) | 9.48528 | 0.333279 | ||||||||
\(811\) | 28.2526 | 0.992082 | 0.496041 | − | 0.868299i | \(-0.334787\pi\) | ||||
0.496041 | + | 0.868299i | \(0.334787\pi\) | |||||||
\(812\) | 9.32780 | 0.327342 | ||||||||
\(813\) | −0.982340 | −0.0344522 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.7062 | −0.515137 | ||||||||
\(816\) | 10.7420 | 0.376046 | ||||||||
\(817\) | 29.2029 | 1.02168 | ||||||||
\(818\) | 5.90606 | 0.206501 | ||||||||
\(819\) | −7.82718 | −0.273504 | ||||||||
\(820\) | −4.80776 | −0.167894 | ||||||||
\(821\) | −22.7165 | −0.792813 | −0.396406 | − | 0.918075i | \(-0.629743\pi\) | ||||
−0.396406 | + | 0.918075i | \(0.629743\pi\) | |||||||
\(822\) | −46.4799 | −1.62117 | ||||||||
\(823\) | −7.38572 | −0.257450 | −0.128725 | − | 0.991680i | \(-0.541088\pi\) | ||||
−0.128725 | + | 0.991680i | \(0.541088\pi\) | |||||||
\(824\) | 12.4495 | 0.433699 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.510590 | −0.0177657 | ||||||||
\(827\) | −26.2870 | −0.914088 | −0.457044 | − | 0.889444i | \(-0.651092\pi\) | ||||
−0.457044 | + | 0.889444i | \(0.651092\pi\) | |||||||
\(828\) | 4.37237 | 0.151950 | ||||||||
\(829\) | −32.9916 | −1.14585 | −0.572923 | − | 0.819609i | \(-0.694191\pi\) | ||||
−0.572923 | + | 0.819609i | \(0.694191\pi\) | |||||||
\(830\) | 4.27452 | 0.148371 | ||||||||
\(831\) | −43.4541 | −1.50741 | ||||||||
\(832\) | −2.76733 | −0.0959398 | ||||||||
\(833\) | −4.44949 | −0.154166 | ||||||||
\(834\) | −7.74026 | −0.268023 | ||||||||
\(835\) | 4.87351 | 0.168655 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.21541 | −0.145706 | ||||||||
\(838\) | −30.0428 | −1.03781 | ||||||||
\(839\) | −16.8466 | −0.581609 | −0.290805 | − | 0.956782i | \(-0.593923\pi\) | ||||
−0.290805 | + | 0.956782i | \(0.593923\pi\) | |||||||
\(840\) | 2.41421 | 0.0832983 | ||||||||
\(841\) | 58.0079 | 2.00027 | ||||||||
\(842\) | 10.2288 | 0.352507 | ||||||||
\(843\) | −33.7586 | −1.16271 | ||||||||
\(844\) | 13.9343 | 0.479637 | ||||||||
\(845\) | −5.34190 | −0.183767 | ||||||||
\(846\) | 34.9096 | 1.20022 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.77729 | 0.335754 | ||||||||
\(849\) | −38.9435 | −1.33654 | ||||||||
\(850\) | 4.44949 | 0.152616 | ||||||||
\(851\) | −6.80119 | −0.233142 | ||||||||
\(852\) | −35.8471 | −1.22810 | ||||||||
\(853\) | 48.8392 | 1.67222 | 0.836112 | − | 0.548559i | \(-0.184823\pi\) | ||||
0.836112 | + | 0.548559i | \(0.184823\pi\) | |||||||
\(854\) | −2.63567 | −0.0901909 | ||||||||
\(855\) | 7.41348 | 0.253536 | ||||||||
\(856\) | 18.4901 | 0.631978 | ||||||||
\(857\) | 16.4322 | 0.561312 | 0.280656 | − | 0.959808i | \(-0.409448\pi\) | ||||
0.280656 | + | 0.959808i | \(0.409448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2477 | 0.349646 | 0.174823 | − | 0.984600i | \(-0.444065\pi\) | ||||
0.174823 | + | 0.984600i | \(0.444065\pi\) | |||||||
\(860\) | 11.1416 | 0.379926 | ||||||||
\(861\) | 11.6070 | 0.395564 | ||||||||
\(862\) | −1.14626 | −0.0390419 | ||||||||
\(863\) | 43.4437 | 1.47884 | 0.739421 | − | 0.673243i | \(-0.235099\pi\) | ||||
0.739421 | + | 0.673243i | \(0.235099\pi\) | |||||||
\(864\) | −0.414214 | −0.0140918 | ||||||||
\(865\) | −6.38551 | −0.217114 | ||||||||
\(866\) | 9.29931 | 0.316003 | ||||||||
\(867\) | −6.75487 | −0.229407 | ||||||||
\(868\) | −10.1769 | −0.345426 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 22.5193 | 0.763476 | ||||||||
\(871\) | −7.43183 | −0.251818 | ||||||||
\(872\) | 1.01461 | 0.0343591 | ||||||||
\(873\) | −6.67020 | −0.225752 | ||||||||
\(874\) | −4.05181 | −0.137055 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 8.24264 | 0.278493 | ||||||||
\(877\) | −18.6670 | −0.630339 | −0.315170 | − | 0.949035i | \(-0.602061\pi\) | ||||
−0.315170 | + | 0.949035i | \(0.602061\pi\) | |||||||
\(878\) | 9.16604 | 0.309339 | ||||||||
\(879\) | 38.9453 | 1.31359 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.7108 | −1.80956 | −0.904782 | − | 0.425875i | \(-0.859966\pi\) | ||||
−0.904782 | + | 0.425875i | \(0.859966\pi\) | |||||||
\(882\) | −2.82843 | −0.0952381 | ||||||||
\(883\) | −30.0729 | −1.01203 | −0.506016 | − | 0.862524i | \(-0.668882\pi\) | ||||
−0.506016 | + | 0.862524i | \(0.668882\pi\) | |||||||
\(884\) | 12.3132 | 0.414137 | ||||||||
\(885\) | −1.23267 | −0.0414359 | ||||||||
\(886\) | 33.0771 | 1.11125 | ||||||||
\(887\) | −31.8197 | −1.06840 | −0.534200 | − | 0.845358i | \(-0.679387\pi\) | ||||
−0.534200 | + | 0.845358i | \(0.679387\pi\) | |||||||
\(888\) | −10.6216 | −0.356437 | ||||||||
\(889\) | 18.1616 | 0.609119 | ||||||||
\(890\) | −11.9700 | −0.401237 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.69161 | −0.190569 | ||||||||
\(893\) | −32.3502 | −1.08256 | ||||||||
\(894\) | 6.20436 | 0.207505 | ||||||||
\(895\) | −6.51523 | −0.217780 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 10.3278 | 0.344835 | ||||||||
\(898\) | 19.3933 | 0.647164 | ||||||||
\(899\) | −94.9281 | −3.16603 | ||||||||
\(900\) | 2.82843 | 0.0942809 | ||||||||
\(901\) | −43.5040 | −1.44933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.8983 | −0.895118 | ||||||||
\(904\) | 11.3324 | 0.376912 | ||||||||
\(905\) | −6.06591 | −0.201638 | ||||||||
\(906\) | 24.3761 | 0.809840 | ||||||||
\(907\) | −31.8443 | −1.05737 | −0.528686 | − | 0.848817i | \(-0.677315\pi\) | ||||
−0.528686 | + | 0.848817i | \(0.677315\pi\) | |||||||
\(908\) | 15.3326 | 0.508831 | ||||||||
\(909\) | 1.31268 | 0.0435388 | ||||||||
\(910\) | 2.76733 | 0.0917360 | ||||||||
\(911\) | 0.187429 | 0.00620980 | 0.00310490 | − | 0.999995i | \(-0.499012\pi\) | ||||
0.00310490 | + | 0.999995i | \(0.499012\pi\) | |||||||
\(912\) | −6.32780 | −0.209535 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −32.5206 | −1.07568 | ||||||||
\(915\) | −6.36308 | −0.210357 | ||||||||
\(916\) | 14.3734 | 0.474911 | ||||||||
\(917\) | −1.25674 | −0.0415011 | ||||||||
\(918\) | 1.84304 | 0.0608294 | ||||||||
\(919\) | −39.6436 | −1.30772 | −0.653861 | − | 0.756615i | \(-0.726852\pi\) | ||||
−0.653861 | + | 0.756615i | \(0.726852\pi\) | |||||||
\(920\) | −1.54587 | −0.0509657 | ||||||||
\(921\) | −65.2125 | −2.14882 | ||||||||
\(922\) | 42.2301 | 1.39078 | ||||||||
\(923\) | −41.0903 | −1.35250 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.39960 | −0.144658 | ||||||||
\(926\) | 22.0593 | 0.724915 | ||||||||
\(927\) | −35.2125 | −1.15653 | ||||||||
\(928\) | −9.32780 | −0.306200 | ||||||||
\(929\) | −18.4828 | −0.606401 | −0.303200 | − | 0.952927i | \(-0.598055\pi\) | ||||
−0.303200 | + | 0.952927i | \(0.598055\pi\) | |||||||
\(930\) | −24.5692 | −0.805656 | ||||||||
\(931\) | 2.62106 | 0.0859019 | ||||||||
\(932\) | −20.7201 | −0.678710 | ||||||||
\(933\) | −60.1578 | −1.96948 | ||||||||
\(934\) | 21.3716 | 0.699301 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.82718 | 0.255839 | ||||||||
\(937\) | −1.93426 | −0.0631894 | −0.0315947 | − | 0.999501i | \(-0.510059\pi\) | ||||
−0.0315947 | + | 0.999501i | \(0.510059\pi\) | |||||||
\(938\) | −2.68556 | −0.0876867 | ||||||||
\(939\) | −29.9469 | −0.977280 | ||||||||
\(940\) | −12.3424 | −0.402565 | ||||||||
\(941\) | −17.7819 | −0.579672 | −0.289836 | − | 0.957076i | \(-0.593601\pi\) | ||||
−0.289836 | + | 0.957076i | \(0.593601\pi\) | |||||||
\(942\) | 18.9111 | 0.616157 | ||||||||
\(943\) | −7.43216 | −0.242024 | ||||||||
\(944\) | 0.510590 | 0.0166183 | ||||||||
\(945\) | 0.414214 | 0.0134744 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.6440 | 0.443371 | 0.221686 | − | 0.975118i | \(-0.428844\pi\) | ||||
0.221686 | + | 0.975118i | \(0.428844\pi\) | |||||||
\(948\) | 4.93766 | 0.160368 | ||||||||
\(949\) | 9.44825 | 0.306703 | ||||||||
\(950\) | −2.62106 | −0.0850385 | ||||||||
\(951\) | 72.5068 | 2.35119 | ||||||||
\(952\) | 4.44949 | 0.144209 | ||||||||
\(953\) | 6.71082 | 0.217385 | 0.108692 | − | 0.994075i | \(-0.465334\pi\) | ||||
0.108692 | + | 0.994075i | \(0.465334\pi\) | |||||||
\(954\) | −27.6544 | −0.895343 | ||||||||
\(955\) | −7.72208 | −0.249881 | ||||||||
\(956\) | 22.0876 | 0.714364 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.84888 | −0.318203 | ||||||||
\(959\) | −19.2526 | −0.621699 | ||||||||
\(960\) | −2.41421 | −0.0779184 | ||||||||
\(961\) | 72.5692 | 2.34094 | ||||||||
\(962\) | −12.1751 | −0.392542 | ||||||||
\(963\) | −52.2979 | −1.68528 | ||||||||
\(964\) | −0.236073 | −0.00760339 | ||||||||
\(965\) | 3.22678 | 0.103874 | ||||||||
\(966\) | 3.73205 | 0.120077 | ||||||||
\(967\) | −13.8214 | −0.444467 | −0.222233 | − | 0.974994i | \(-0.571335\pi\) | ||||
−0.222233 | + | 0.974994i | \(0.571335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.1555 | 0.904485 | ||||||||
\(970\) | 2.35827 | 0.0757196 | ||||||||
\(971\) | 52.9417 | 1.69898 | 0.849491 | − | 0.527604i | \(-0.176909\pi\) | ||||
0.849491 | + | 0.527604i | \(0.176909\pi\) | |||||||
\(972\) | 21.6569 | 0.694644 | ||||||||
\(973\) | −3.20612 | −0.102783 | ||||||||
\(974\) | 35.0712 | 1.12375 | ||||||||
\(975\) | 6.68092 | 0.213961 | ||||||||
\(976\) | 2.63567 | 0.0843659 | ||||||||
\(977\) | 8.77943 | 0.280879 | 0.140439 | − | 0.990089i | \(-0.455148\pi\) | ||||
0.140439 | + | 0.990089i | \(0.455148\pi\) | |||||||
\(978\) | −35.5040 | −1.13529 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −2.86976 | −0.0916242 | ||||||||
\(982\) | 1.40389 | 0.0448001 | ||||||||
\(983\) | 13.4596 | 0.429295 | 0.214648 | − | 0.976692i | \(-0.431140\pi\) | ||||
0.214648 | + | 0.976692i | \(0.431140\pi\) | |||||||
\(984\) | −11.6070 | −0.370017 | ||||||||
\(985\) | 13.2066 | 0.420798 | ||||||||
\(986\) | 41.5040 | 1.32176 | ||||||||
\(987\) | 29.7972 | 0.948456 | ||||||||
\(988\) | −7.25334 | −0.230759 | ||||||||
\(989\) | 17.2235 | 0.547674 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.1845 | 1.91182 | 0.955912 | − | 0.293653i | \(-0.0948711\pi\) | ||||
0.955912 | + | 0.293653i | \(0.0948711\pi\) | |||||||
\(992\) | 10.1769 | 0.323117 | ||||||||
\(993\) | −23.3636 | −0.741421 | ||||||||
\(994\) | −14.8484 | −0.470961 | ||||||||
\(995\) | 5.99270 | 0.189981 | ||||||||
\(996\) | 10.3196 | 0.326989 | ||||||||
\(997\) | −39.4998 | −1.25097 | −0.625486 | − | 0.780235i | \(-0.715099\pi\) | ||||
−0.625486 | + | 0.780235i | \(0.715099\pi\) | |||||||
\(998\) | 5.73573 | 0.181561 | ||||||||
\(999\) | −1.82237 | −0.0576574 |
(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 | 8470.2.a.cp.1.1 | ✓ | 4 | |
11.10 | odd | 2 | 8470.2.a.cr.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cp.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
8470.2.a.cr.1.2 | yes | 4 | 11.10 | odd | 2 |