Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-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 | ||||||||
\(3\) | 0.436625 | 0.252086 | 0.126043 | − | 0.992025i | \(-0.459772\pi\) | ||||
0.126043 | + | 0.992025i | \(0.459772\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.0518544 | −0.0231900 | −0.0115950 | − | 0.999933i | \(-0.503691\pi\) | ||||
−0.0115950 | + | 0.999933i | \(0.503691\pi\) | |||||||
\(6\) | 0.436625 | 0.178252 | ||||||||
\(7\) | 0.167384 | 0.0632651 | 0.0316325 | − | 0.999500i | \(-0.489929\pi\) | ||||
0.0316325 | + | 0.999500i | \(0.489929\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.80936 | −0.936453 | ||||||||
\(10\) | −0.0518544 | −0.0163978 | ||||||||
\(11\) | 1.44287 | 0.435043 | 0.217521 | − | 0.976056i | \(-0.430203\pi\) | ||||
0.217521 | + | 0.976056i | \(0.430203\pi\) | |||||||
\(12\) | 0.436625 | 0.126043 | ||||||||
\(13\) | 4.01294 | 1.11299 | 0.556495 | − | 0.830851i | \(-0.312146\pi\) | ||||
0.556495 | + | 0.830851i | \(0.312146\pi\) | |||||||
\(14\) | 0.167384 | 0.0447352 | ||||||||
\(15\) | −0.0226409 | −0.00584586 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.41030 | −0.584584 | −0.292292 | − | 0.956329i | \(-0.594418\pi\) | ||||
−0.292292 | + | 0.956329i | \(0.594418\pi\) | |||||||
\(18\) | −2.80936 | −0.662172 | ||||||||
\(19\) | −2.67873 | −0.614543 | −0.307271 | − | 0.951622i | \(-0.599416\pi\) | ||||
−0.307271 | + | 0.951622i | \(0.599416\pi\) | |||||||
\(20\) | −0.0518544 | −0.0115950 | ||||||||
\(21\) | 0.0730839 | 0.0159482 | ||||||||
\(22\) | 1.44287 | 0.307622 | ||||||||
\(23\) | −6.72568 | −1.40240 | −0.701201 | − | 0.712964i | \(-0.747352\pi\) | ||||
−0.701201 | + | 0.712964i | \(0.747352\pi\) | |||||||
\(24\) | 0.436625 | 0.0891258 | ||||||||
\(25\) | −4.99731 | −0.999462 | ||||||||
\(26\) | 4.01294 | 0.787002 | ||||||||
\(27\) | −2.53651 | −0.488152 | ||||||||
\(28\) | 0.167384 | 0.0316325 | ||||||||
\(29\) | −8.89627 | −1.65200 | −0.825998 | − | 0.563673i | \(-0.809388\pi\) | ||||
−0.825998 | + | 0.563673i | \(0.809388\pi\) | |||||||
\(30\) | −0.0226409 | −0.00413365 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.629995 | 0.109668 | ||||||||
\(34\) | −2.41030 | −0.413363 | ||||||||
\(35\) | −0.00867957 | −0.00146711 | ||||||||
\(36\) | −2.80936 | −0.468226 | ||||||||
\(37\) | −7.01316 | −1.15296 | −0.576478 | − | 0.817113i | \(-0.695573\pi\) | ||||
−0.576478 | + | 0.817113i | \(0.695573\pi\) | |||||||
\(38\) | −2.67873 | −0.434547 | ||||||||
\(39\) | 1.75215 | 0.280569 | ||||||||
\(40\) | −0.0518544 | −0.00819889 | ||||||||
\(41\) | −2.01690 | −0.314986 | −0.157493 | − | 0.987520i | \(-0.550341\pi\) | ||||
−0.157493 | + | 0.987520i | \(0.550341\pi\) | |||||||
\(42\) | 0.0730839 | 0.0112771 | ||||||||
\(43\) | 2.30133 | 0.350949 | 0.175475 | − | 0.984484i | \(-0.443854\pi\) | ||||
0.175475 | + | 0.984484i | \(0.443854\pi\) | |||||||
\(44\) | 1.44287 | 0.217521 | ||||||||
\(45\) | 0.145677 | 0.0217163 | ||||||||
\(46\) | −6.72568 | −0.991648 | ||||||||
\(47\) | 2.67590 | 0.390320 | 0.195160 | − | 0.980771i | \(-0.437477\pi\) | ||||
0.195160 | + | 0.980771i | \(0.437477\pi\) | |||||||
\(48\) | 0.436625 | 0.0630215 | ||||||||
\(49\) | −6.97198 | −0.995998 | ||||||||
\(50\) | −4.99731 | −0.706727 | ||||||||
\(51\) | −1.05240 | −0.147365 | ||||||||
\(52\) | 4.01294 | 0.556495 | ||||||||
\(53\) | −7.23535 | −0.993852 | −0.496926 | − | 0.867793i | \(-0.665538\pi\) | ||||
−0.496926 | + | 0.867793i | \(0.665538\pi\) | |||||||
\(54\) | −2.53651 | −0.345176 | ||||||||
\(55\) | −0.0748193 | −0.0100886 | ||||||||
\(56\) | 0.167384 | 0.0223676 | ||||||||
\(57\) | −1.16960 | −0.154917 | ||||||||
\(58\) | −8.89627 | −1.16814 | ||||||||
\(59\) | 8.40917 | 1.09478 | 0.547390 | − | 0.836877i | \(-0.315621\pi\) | ||||
0.547390 | + | 0.836877i | \(0.315621\pi\) | |||||||
\(60\) | −0.0226409 | −0.00292293 | ||||||||
\(61\) | 2.45239 | 0.313996 | 0.156998 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.156998 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | −0.470241 | −0.0592447 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.208088 | −0.0258102 | ||||||||
\(66\) | 0.629995 | 0.0775470 | ||||||||
\(67\) | −12.3169 | −1.50475 | −0.752374 | − | 0.658737i | \(-0.771091\pi\) | ||||
−0.752374 | + | 0.658737i | \(0.771091\pi\) | |||||||
\(68\) | −2.41030 | −0.292292 | ||||||||
\(69\) | −2.93660 | −0.353526 | ||||||||
\(70\) | −0.00867957 | −0.00103741 | ||||||||
\(71\) | −3.10491 | −0.368485 | −0.184243 | − | 0.982881i | \(-0.558983\pi\) | ||||
−0.184243 | + | 0.982881i | \(0.558983\pi\) | |||||||
\(72\) | −2.80936 | −0.331086 | ||||||||
\(73\) | 5.71496 | 0.668885 | 0.334443 | − | 0.942416i | \(-0.391452\pi\) | ||||
0.334443 | + | 0.942416i | \(0.391452\pi\) | |||||||
\(74\) | −7.01316 | −0.815263 | ||||||||
\(75\) | −2.18195 | −0.251950 | ||||||||
\(76\) | −2.67873 | −0.307271 | ||||||||
\(77\) | 0.241513 | 0.0275230 | ||||||||
\(78\) | 1.75215 | 0.198392 | ||||||||
\(79\) | 10.4456 | 1.17523 | 0.587613 | − | 0.809142i | \(-0.300068\pi\) | ||||
0.587613 | + | 0.809142i | \(0.300068\pi\) | |||||||
\(80\) | −0.0518544 | −0.00579749 | ||||||||
\(81\) | 7.32057 | 0.813396 | ||||||||
\(82\) | −2.01690 | −0.222729 | ||||||||
\(83\) | 8.37850 | 0.919660 | 0.459830 | − | 0.888007i | \(-0.347910\pi\) | ||||
0.459830 | + | 0.888007i | \(0.347910\pi\) | |||||||
\(84\) | 0.0730839 | 0.00797411 | ||||||||
\(85\) | 0.124985 | 0.0135565 | ||||||||
\(86\) | 2.30133 | 0.248159 | ||||||||
\(87\) | −3.88434 | −0.416445 | ||||||||
\(88\) | 1.44287 | 0.153811 | ||||||||
\(89\) | 6.86237 | 0.727409 | 0.363705 | − | 0.931514i | \(-0.381512\pi\) | ||||
0.363705 | + | 0.931514i | \(0.381512\pi\) | |||||||
\(90\) | 0.145677 | 0.0153558 | ||||||||
\(91\) | 0.671700 | 0.0704133 | ||||||||
\(92\) | −6.72568 | −0.701201 | ||||||||
\(93\) | 0.436625 | 0.0452759 | ||||||||
\(94\) | 2.67590 | 0.275998 | ||||||||
\(95\) | 0.138904 | 0.0142512 | ||||||||
\(96\) | 0.436625 | 0.0445629 | ||||||||
\(97\) | −1.00000 | −0.101535 | ||||||||
\(98\) | −6.97198 | −0.704277 | ||||||||
\(99\) | −4.05355 | −0.407397 | ||||||||
\(100\) | −4.99731 | −0.499731 | ||||||||
\(101\) | −8.14646 | −0.810603 | −0.405302 | − | 0.914183i | \(-0.632834\pi\) | ||||
−0.405302 | + | 0.914183i | \(0.632834\pi\) | |||||||
\(102\) | −1.05240 | −0.104203 | ||||||||
\(103\) | −1.69987 | −0.167494 | −0.0837468 | − | 0.996487i | \(-0.526689\pi\) | ||||
−0.0837468 | + | 0.996487i | \(0.526689\pi\) | |||||||
\(104\) | 4.01294 | 0.393501 | ||||||||
\(105\) | −0.00378972 | −0.000369839 0 | ||||||||
\(106\) | −7.23535 | −0.702759 | ||||||||
\(107\) | 8.05896 | 0.779089 | 0.389544 | − | 0.921008i | \(-0.372632\pi\) | ||||
0.389544 | + | 0.921008i | \(0.372632\pi\) | |||||||
\(108\) | −2.53651 | −0.244076 | ||||||||
\(109\) | −8.16312 | −0.781885 | −0.390942 | − | 0.920415i | \(-0.627851\pi\) | ||||
−0.390942 | + | 0.920415i | \(0.627851\pi\) | |||||||
\(110\) | −0.0748193 | −0.00713374 | ||||||||
\(111\) | −3.06212 | −0.290644 | ||||||||
\(112\) | 0.167384 | 0.0158163 | ||||||||
\(113\) | 5.18278 | 0.487555 | 0.243777 | − | 0.969831i | \(-0.421613\pi\) | ||||
0.243777 | + | 0.969831i | \(0.421613\pi\) | |||||||
\(114\) | −1.16960 | −0.109543 | ||||||||
\(115\) | 0.348756 | 0.0325217 | ||||||||
\(116\) | −8.89627 | −0.825998 | ||||||||
\(117\) | −11.2738 | −1.04226 | ||||||||
\(118\) | 8.40917 | 0.774127 | ||||||||
\(119\) | −0.403445 | −0.0369837 | ||||||||
\(120\) | −0.0226409 | −0.00206682 | ||||||||
\(121\) | −8.91812 | −0.810738 | ||||||||
\(122\) | 2.45239 | 0.222029 | ||||||||
\(123\) | −0.880628 | −0.0794036 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 0.518404 | 0.0463675 | ||||||||
\(126\) | −0.470241 | −0.0418924 | ||||||||
\(127\) | −5.95977 | −0.528844 | −0.264422 | − | 0.964407i | \(-0.585181\pi\) | ||||
−0.264422 | + | 0.964407i | \(0.585181\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.00482 | 0.0884694 | ||||||||
\(130\) | −0.208088 | −0.0182506 | ||||||||
\(131\) | 8.22326 | 0.718470 | 0.359235 | − | 0.933247i | \(-0.383038\pi\) | ||||
0.359235 | + | 0.933247i | \(0.383038\pi\) | |||||||
\(132\) | 0.629995 | 0.0548340 | ||||||||
\(133\) | −0.448375 | −0.0388791 | ||||||||
\(134\) | −12.3169 | −1.06402 | ||||||||
\(135\) | 0.131529 | 0.0113202 | ||||||||
\(136\) | −2.41030 | −0.206682 | ||||||||
\(137\) | 6.09300 | 0.520560 | 0.260280 | − | 0.965533i | \(-0.416185\pi\) | ||||
0.260280 | + | 0.965533i | \(0.416185\pi\) | |||||||
\(138\) | −2.93660 | −0.249980 | ||||||||
\(139\) | 11.1137 | 0.942648 | 0.471324 | − | 0.881960i | \(-0.343776\pi\) | ||||
0.471324 | + | 0.881960i | \(0.343776\pi\) | |||||||
\(140\) | −0.00867957 | −0.000733557 0 | ||||||||
\(141\) | 1.16837 | 0.0983942 | ||||||||
\(142\) | −3.10491 | −0.260558 | ||||||||
\(143\) | 5.79016 | 0.484198 | ||||||||
\(144\) | −2.80936 | −0.234113 | ||||||||
\(145\) | 0.461310 | 0.0383097 | ||||||||
\(146\) | 5.71496 | 0.472973 | ||||||||
\(147\) | −3.04414 | −0.251077 | ||||||||
\(148\) | −7.01316 | −0.576478 | ||||||||
\(149\) | 11.4942 | 0.941638 | 0.470819 | − | 0.882230i | \(-0.343959\pi\) | ||||
0.470819 | + | 0.882230i | \(0.343959\pi\) | |||||||
\(150\) | −2.18195 | −0.178156 | ||||||||
\(151\) | −14.5521 | −1.18423 | −0.592116 | − | 0.805852i | \(-0.701707\pi\) | ||||
−0.592116 | + | 0.805852i | \(0.701707\pi\) | |||||||
\(152\) | −2.67873 | −0.217274 | ||||||||
\(153\) | 6.77140 | 0.547435 | ||||||||
\(154\) | 0.241513 | 0.0194617 | ||||||||
\(155\) | −0.0518544 | −0.00416504 | ||||||||
\(156\) | 1.75215 | 0.140284 | ||||||||
\(157\) | 17.1344 | 1.36748 | 0.683739 | − | 0.729727i | \(-0.260353\pi\) | ||||
0.683739 | + | 0.729727i | \(0.260353\pi\) | |||||||
\(158\) | 10.4456 | 0.831010 | ||||||||
\(159\) | −3.15914 | −0.250536 | ||||||||
\(160\) | −0.0518544 | −0.00409945 | ||||||||
\(161\) | −1.12577 | −0.0887230 | ||||||||
\(162\) | 7.32057 | 0.575158 | ||||||||
\(163\) | −17.9962 | −1.40957 | −0.704787 | − | 0.709419i | \(-0.748957\pi\) | ||||
−0.704787 | + | 0.709419i | \(0.748957\pi\) | |||||||
\(164\) | −2.01690 | −0.157493 | ||||||||
\(165\) | −0.0326680 | −0.00254320 | ||||||||
\(166\) | 8.37850 | 0.650298 | ||||||||
\(167\) | −15.8941 | −1.22993 | −0.614963 | − | 0.788556i | \(-0.710829\pi\) | ||||
−0.614963 | + | 0.788556i | \(0.710829\pi\) | |||||||
\(168\) | 0.0730839 | 0.00563855 | ||||||||
\(169\) | 3.10369 | 0.238746 | ||||||||
\(170\) | 0.124985 | 0.00958588 | ||||||||
\(171\) | 7.52551 | 0.575490 | ||||||||
\(172\) | 2.30133 | 0.175475 | ||||||||
\(173\) | 11.2740 | 0.857150 | 0.428575 | − | 0.903506i | \(-0.359016\pi\) | ||||
0.428575 | + | 0.903506i | \(0.359016\pi\) | |||||||
\(174\) | −3.88434 | −0.294471 | ||||||||
\(175\) | −0.836468 | −0.0632310 | ||||||||
\(176\) | 1.44287 | 0.108761 | ||||||||
\(177\) | 3.67166 | 0.275979 | ||||||||
\(178\) | 6.86237 | 0.514356 | ||||||||
\(179\) | −14.9204 | −1.11521 | −0.557603 | − | 0.830108i | \(-0.688279\pi\) | ||||
−0.557603 | + | 0.830108i | \(0.688279\pi\) | |||||||
\(180\) | 0.145677 | 0.0108582 | ||||||||
\(181\) | −18.1697 | −1.35054 | −0.675272 | − | 0.737569i | \(-0.735974\pi\) | ||||
−0.675272 | + | 0.737569i | \(0.735974\pi\) | |||||||
\(182\) | 0.671700 | 0.0497898 | ||||||||
\(183\) | 1.07078 | 0.0791540 | ||||||||
\(184\) | −6.72568 | −0.495824 | ||||||||
\(185\) | 0.363663 | 0.0267370 | ||||||||
\(186\) | 0.436625 | 0.0320149 | ||||||||
\(187\) | −3.47776 | −0.254319 | ||||||||
\(188\) | 2.67590 | 0.195160 | ||||||||
\(189\) | −0.424571 | −0.0308830 | ||||||||
\(190\) | 0.138904 | 0.0100771 | ||||||||
\(191\) | −15.2353 | −1.10239 | −0.551195 | − | 0.834376i | \(-0.685828\pi\) | ||||
−0.551195 | + | 0.834376i | \(0.685828\pi\) | |||||||
\(192\) | 0.436625 | 0.0315107 | ||||||||
\(193\) | −9.63153 | −0.693293 | −0.346646 | − | 0.937996i | \(-0.612680\pi\) | ||||
−0.346646 | + | 0.937996i | \(0.612680\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | −0.0908567 | −0.00650638 | ||||||||
\(196\) | −6.97198 | −0.497999 | ||||||||
\(197\) | −14.4162 | −1.02711 | −0.513557 | − | 0.858055i | \(-0.671673\pi\) | ||||
−0.513557 | + | 0.858055i | \(0.671673\pi\) | |||||||
\(198\) | −4.05355 | −0.288073 | ||||||||
\(199\) | −13.4697 | −0.954840 | −0.477420 | − | 0.878675i | \(-0.658428\pi\) | ||||
−0.477420 | + | 0.878675i | \(0.658428\pi\) | |||||||
\(200\) | −4.99731 | −0.353363 | ||||||||
\(201\) | −5.37787 | −0.379325 | ||||||||
\(202\) | −8.14646 | −0.573183 | ||||||||
\(203\) | −1.48909 | −0.104514 | ||||||||
\(204\) | −1.05240 | −0.0736827 | ||||||||
\(205\) | 0.104585 | 0.00730452 | ||||||||
\(206\) | −1.69987 | −0.118436 | ||||||||
\(207\) | 18.8949 | 1.31328 | ||||||||
\(208\) | 4.01294 | 0.278247 | ||||||||
\(209\) | −3.86507 | −0.267352 | ||||||||
\(210\) | −0.00378972 | −0.000261516 0 | ||||||||
\(211\) | −10.0648 | −0.692891 | −0.346445 | − | 0.938070i | \(-0.612611\pi\) | ||||
−0.346445 | + | 0.938070i | \(0.612611\pi\) | |||||||
\(212\) | −7.23535 | −0.496926 | ||||||||
\(213\) | −1.35568 | −0.0928899 | ||||||||
\(214\) | 8.05896 | 0.550899 | ||||||||
\(215\) | −0.119334 | −0.00813851 | ||||||||
\(216\) | −2.53651 | −0.172588 | ||||||||
\(217\) | 0.167384 | 0.0113627 | ||||||||
\(218\) | −8.16312 | −0.552876 | ||||||||
\(219\) | 2.49530 | 0.168616 | ||||||||
\(220\) | −0.0748193 | −0.00504431 | ||||||||
\(221\) | −9.67240 | −0.650636 | ||||||||
\(222\) | −3.06212 | −0.205516 | ||||||||
\(223\) | 15.0134 | 1.00537 | 0.502685 | − | 0.864470i | \(-0.332346\pi\) | ||||
0.502685 | + | 0.864470i | \(0.332346\pi\) | |||||||
\(224\) | 0.167384 | 0.0111838 | ||||||||
\(225\) | 14.0392 | 0.935949 | ||||||||
\(226\) | 5.18278 | 0.344753 | ||||||||
\(227\) | −6.02369 | −0.399807 | −0.199903 | − | 0.979816i | \(-0.564063\pi\) | ||||
−0.199903 | + | 0.979816i | \(0.564063\pi\) | |||||||
\(228\) | −1.16960 | −0.0774587 | ||||||||
\(229\) | −5.78767 | −0.382460 | −0.191230 | − | 0.981545i | \(-0.561248\pi\) | ||||
−0.191230 | + | 0.981545i | \(0.561248\pi\) | |||||||
\(230\) | 0.348756 | 0.0229963 | ||||||||
\(231\) | 0.105451 | 0.00693816 | ||||||||
\(232\) | −8.89627 | −0.584069 | ||||||||
\(233\) | −9.17116 | −0.600823 | −0.300411 | − | 0.953810i | \(-0.597124\pi\) | ||||
−0.300411 | + | 0.953810i | \(0.597124\pi\) | |||||||
\(234\) | −11.2738 | −0.736991 | ||||||||
\(235\) | −0.138757 | −0.00905151 | ||||||||
\(236\) | 8.40917 | 0.547390 | ||||||||
\(237\) | 4.56083 | 0.296258 | ||||||||
\(238\) | −0.403445 | −0.0261515 | ||||||||
\(239\) | 12.6834 | 0.820424 | 0.410212 | − | 0.911990i | \(-0.365455\pi\) | ||||
0.410212 | + | 0.911990i | \(0.365455\pi\) | |||||||
\(240\) | −0.0226409 | −0.00146147 | ||||||||
\(241\) | −19.0267 | −1.22562 | −0.612810 | − | 0.790230i | \(-0.709961\pi\) | ||||
−0.612810 | + | 0.790230i | \(0.709961\pi\) | |||||||
\(242\) | −8.91812 | −0.573278 | ||||||||
\(243\) | 10.8059 | 0.693198 | ||||||||
\(244\) | 2.45239 | 0.156998 | ||||||||
\(245\) | 0.361528 | 0.0230972 | ||||||||
\(246\) | −0.880628 | −0.0561468 | ||||||||
\(247\) | −10.7496 | −0.683979 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | 3.65827 | 0.231833 | ||||||||
\(250\) | 0.518404 | 0.0327868 | ||||||||
\(251\) | −30.2633 | −1.91020 | −0.955100 | − | 0.296284i | \(-0.904252\pi\) | ||||
−0.955100 | + | 0.296284i | \(0.904252\pi\) | |||||||
\(252\) | −0.470241 | −0.0296224 | ||||||||
\(253\) | −9.70431 | −0.610105 | ||||||||
\(254\) | −5.95977 | −0.373950 | ||||||||
\(255\) | 0.0545715 | 0.00341740 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.99771 | −0.374127 | −0.187063 | − | 0.982348i | \(-0.559897\pi\) | ||||
−0.187063 | + | 0.982348i | \(0.559897\pi\) | |||||||
\(258\) | 1.00482 | 0.0625573 | ||||||||
\(259\) | −1.17389 | −0.0729418 | ||||||||
\(260\) | −0.208088 | −0.0129051 | ||||||||
\(261\) | 24.9928 | 1.54702 | ||||||||
\(262\) | 8.22326 | 0.508035 | ||||||||
\(263\) | 2.57774 | 0.158950 | 0.0794752 | − | 0.996837i | \(-0.474676\pi\) | ||||
0.0794752 | + | 0.996837i | \(0.474676\pi\) | |||||||
\(264\) | 0.629995 | 0.0387735 | ||||||||
\(265\) | 0.375184 | 0.0230474 | ||||||||
\(266\) | −0.448375 | −0.0274917 | ||||||||
\(267\) | 2.99628 | 0.183370 | ||||||||
\(268\) | −12.3169 | −0.752374 | ||||||||
\(269\) | 29.2747 | 1.78491 | 0.892454 | − | 0.451138i | \(-0.148982\pi\) | ||||
0.892454 | + | 0.451138i | \(0.148982\pi\) | |||||||
\(270\) | 0.131529 | 0.00800462 | ||||||||
\(271\) | −3.85462 | −0.234152 | −0.117076 | − | 0.993123i | \(-0.537352\pi\) | ||||
−0.117076 | + | 0.993123i | \(0.537352\pi\) | |||||||
\(272\) | −2.41030 | −0.146146 | ||||||||
\(273\) | 0.293282 | 0.0177502 | ||||||||
\(274\) | 6.09300 | 0.368091 | ||||||||
\(275\) | −7.21049 | −0.434809 | ||||||||
\(276\) | −2.93660 | −0.176763 | ||||||||
\(277\) | −17.9316 | −1.07741 | −0.538703 | − | 0.842496i | \(-0.681086\pi\) | ||||
−0.538703 | + | 0.842496i | \(0.681086\pi\) | |||||||
\(278\) | 11.1137 | 0.666553 | ||||||||
\(279\) | −2.80936 | −0.168192 | ||||||||
\(280\) | −0.00867957 | −0.000518703 0 | ||||||||
\(281\) | −1.64814 | −0.0983200 | −0.0491600 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491600 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(282\) | 1.16837 | 0.0695752 | ||||||||
\(283\) | 14.2618 | 0.847773 | 0.423887 | − | 0.905715i | \(-0.360665\pi\) | ||||
0.423887 | + | 0.905715i | \(0.360665\pi\) | |||||||
\(284\) | −3.10491 | −0.184243 | ||||||||
\(285\) | 0.0606489 | 0.00359253 | ||||||||
\(286\) | 5.79016 | 0.342380 | ||||||||
\(287\) | −0.337595 | −0.0199276 | ||||||||
\(288\) | −2.80936 | −0.165543 | ||||||||
\(289\) | −11.1904 | −0.658262 | ||||||||
\(290\) | 0.461310 | 0.0270891 | ||||||||
\(291\) | −0.436625 | −0.0255954 | ||||||||
\(292\) | 5.71496 | 0.334443 | ||||||||
\(293\) | 10.7623 | 0.628741 | 0.314371 | − | 0.949300i | \(-0.398207\pi\) | ||||
0.314371 | + | 0.949300i | \(0.398207\pi\) | |||||||
\(294\) | −3.04414 | −0.177538 | ||||||||
\(295\) | −0.436052 | −0.0253879 | ||||||||
\(296\) | −7.01316 | −0.407632 | ||||||||
\(297\) | −3.65987 | −0.212367 | ||||||||
\(298\) | 11.4942 | 0.665838 | ||||||||
\(299\) | −26.9898 | −1.56086 | ||||||||
\(300\) | −2.18195 | −0.125975 | ||||||||
\(301\) | 0.385205 | 0.0222028 | ||||||||
\(302\) | −14.5521 | −0.837379 | ||||||||
\(303\) | −3.55695 | −0.204342 | ||||||||
\(304\) | −2.67873 | −0.153636 | ||||||||
\(305\) | −0.127167 | −0.00728157 | ||||||||
\(306\) | 6.77140 | 0.387095 | ||||||||
\(307\) | −8.22255 | −0.469286 | −0.234643 | − | 0.972082i | \(-0.575392\pi\) | ||||
−0.234643 | + | 0.972082i | \(0.575392\pi\) | |||||||
\(308\) | 0.241513 | 0.0137615 | ||||||||
\(309\) | −0.742209 | −0.0422228 | ||||||||
\(310\) | −0.0518544 | −0.00294513 | ||||||||
\(311\) | 5.16135 | 0.292673 | 0.146337 | − | 0.989235i | \(-0.453252\pi\) | ||||
0.146337 | + | 0.989235i | \(0.453252\pi\) | |||||||
\(312\) | 1.75215 | 0.0991961 | ||||||||
\(313\) | 3.16198 | 0.178726 | 0.0893629 | − | 0.995999i | \(-0.471517\pi\) | ||||
0.0893629 | + | 0.995999i | \(0.471517\pi\) | |||||||
\(314\) | 17.1344 | 0.966953 | ||||||||
\(315\) | 0.0243840 | 0.00137388 | ||||||||
\(316\) | 10.4456 | 0.587613 | ||||||||
\(317\) | 19.3097 | 1.08454 | 0.542270 | − | 0.840204i | \(-0.317565\pi\) | ||||
0.542270 | + | 0.840204i | \(0.317565\pi\) | |||||||
\(318\) | −3.15914 | −0.177156 | ||||||||
\(319\) | −12.8362 | −0.718689 | ||||||||
\(320\) | −0.0518544 | −0.00289875 | ||||||||
\(321\) | 3.51875 | 0.196397 | ||||||||
\(322\) | −1.12577 | −0.0627367 | ||||||||
\(323\) | 6.45655 | 0.359252 | ||||||||
\(324\) | 7.32057 | 0.406698 | ||||||||
\(325\) | −20.0539 | −1.11239 | ||||||||
\(326\) | −17.9962 | −0.996719 | ||||||||
\(327\) | −3.56422 | −0.197102 | ||||||||
\(328\) | −2.01690 | −0.111364 | ||||||||
\(329\) | 0.447902 | 0.0246936 | ||||||||
\(330\) | −0.0326680 | −0.00179831 | ||||||||
\(331\) | 7.59645 | 0.417538 | 0.208769 | − | 0.977965i | \(-0.433054\pi\) | ||||
0.208769 | + | 0.977965i | \(0.433054\pi\) | |||||||
\(332\) | 8.37850 | 0.459830 | ||||||||
\(333\) | 19.7025 | 1.07969 | ||||||||
\(334\) | −15.8941 | −0.869688 | ||||||||
\(335\) | 0.638684 | 0.0348950 | ||||||||
\(336\) | 0.0730839 | 0.00398706 | ||||||||
\(337\) | −30.6571 | −1.67000 | −0.834999 | − | 0.550251i | \(-0.814532\pi\) | ||||
−0.834999 | + | 0.550251i | \(0.814532\pi\) | |||||||
\(338\) | 3.10369 | 0.168819 | ||||||||
\(339\) | 2.26293 | 0.122906 | ||||||||
\(340\) | 0.124985 | 0.00677824 | ||||||||
\(341\) | 1.44287 | 0.0781360 | ||||||||
\(342\) | 7.52551 | 0.406933 | ||||||||
\(343\) | −2.33868 | −0.126277 | ||||||||
\(344\) | 2.30133 | 0.124079 | ||||||||
\(345\) | 0.152276 | 0.00819825 | ||||||||
\(346\) | 11.2740 | 0.606096 | ||||||||
\(347\) | 9.15064 | 0.491232 | 0.245616 | − | 0.969367i | \(-0.421010\pi\) | ||||
0.245616 | + | 0.969367i | \(0.421010\pi\) | |||||||
\(348\) | −3.88434 | −0.208222 | ||||||||
\(349\) | 19.1348 | 1.02426 | 0.512131 | − | 0.858908i | \(-0.328856\pi\) | ||||
0.512131 | + | 0.858908i | \(0.328856\pi\) | |||||||
\(350\) | −0.836468 | −0.0447111 | ||||||||
\(351\) | −10.1789 | −0.543308 | ||||||||
\(352\) | 1.44287 | 0.0769054 | ||||||||
\(353\) | 10.3641 | 0.551624 | 0.275812 | − | 0.961212i | \(-0.411053\pi\) | ||||
0.275812 | + | 0.961212i | \(0.411053\pi\) | |||||||
\(354\) | 3.67166 | 0.195146 | ||||||||
\(355\) | 0.161003 | 0.00854516 | ||||||||
\(356\) | 6.86237 | 0.363705 | ||||||||
\(357\) | −0.176154 | −0.00932308 | ||||||||
\(358\) | −14.9204 | −0.788569 | ||||||||
\(359\) | 23.2049 | 1.22471 | 0.612355 | − | 0.790583i | \(-0.290222\pi\) | ||||
0.612355 | + | 0.790583i | \(0.290222\pi\) | |||||||
\(360\) | 0.145677 | 0.00767788 | ||||||||
\(361\) | −11.8244 | −0.622337 | ||||||||
\(362\) | −18.1697 | −0.954978 | ||||||||
\(363\) | −3.89388 | −0.204376 | ||||||||
\(364\) | 0.671700 | 0.0352067 | ||||||||
\(365\) | −0.296345 | −0.0155114 | ||||||||
\(366\) | 1.07078 | 0.0559704 | ||||||||
\(367\) | 6.11685 | 0.319297 | 0.159648 | − | 0.987174i | \(-0.448964\pi\) | ||||
0.159648 | + | 0.987174i | \(0.448964\pi\) | |||||||
\(368\) | −6.72568 | −0.350600 | ||||||||
\(369\) | 5.66618 | 0.294970 | ||||||||
\(370\) | 0.363663 | 0.0189059 | ||||||||
\(371\) | −1.21108 | −0.0628761 | ||||||||
\(372\) | 0.436625 | 0.0226380 | ||||||||
\(373\) | −23.0809 | −1.19509 | −0.597543 | − | 0.801837i | \(-0.703856\pi\) | ||||
−0.597543 | + | 0.801837i | \(0.703856\pi\) | |||||||
\(374\) | −3.47776 | −0.179831 | ||||||||
\(375\) | 0.226348 | 0.0116886 | ||||||||
\(376\) | 2.67590 | 0.137999 | ||||||||
\(377\) | −35.7002 | −1.83865 | ||||||||
\(378\) | −0.424571 | −0.0218376 | ||||||||
\(379\) | 25.9370 | 1.33229 | 0.666146 | − | 0.745821i | \(-0.267943\pi\) | ||||
0.666146 | + | 0.745821i | \(0.267943\pi\) | |||||||
\(380\) | 0.138904 | 0.00712561 | ||||||||
\(381\) | −2.60219 | −0.133314 | ||||||||
\(382\) | −15.2353 | −0.779508 | ||||||||
\(383\) | 7.28337 | 0.372163 | 0.186081 | − | 0.982534i | \(-0.440421\pi\) | ||||
0.186081 | + | 0.982534i | \(0.440421\pi\) | |||||||
\(384\) | 0.436625 | 0.0222814 | ||||||||
\(385\) | −0.0125235 | −0.000638258 0 | ||||||||
\(386\) | −9.63153 | −0.490232 | ||||||||
\(387\) | −6.46526 | −0.328648 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 32.8781 | 1.66699 | 0.833494 | − | 0.552528i | \(-0.186337\pi\) | ||||
0.833494 | + | 0.552528i | \(0.186337\pi\) | |||||||
\(390\) | −0.0908567 | −0.00460071 | ||||||||
\(391\) | 16.2109 | 0.819822 | ||||||||
\(392\) | −6.97198 | −0.352138 | ||||||||
\(393\) | 3.59049 | 0.181116 | ||||||||
\(394\) | −14.4162 | −0.726280 | ||||||||
\(395\) | −0.541652 | −0.0272535 | ||||||||
\(396\) | −4.05355 | −0.203698 | ||||||||
\(397\) | 33.2627 | 1.66940 | 0.834702 | − | 0.550701i | \(-0.185640\pi\) | ||||
0.834702 | + | 0.550701i | \(0.185640\pi\) | |||||||
\(398\) | −13.4697 | −0.675174 | ||||||||
\(399\) | −0.195772 | −0.00980086 | ||||||||
\(400\) | −4.99731 | −0.249866 | ||||||||
\(401\) | 13.1492 | 0.656642 | 0.328321 | − | 0.944566i | \(-0.393517\pi\) | ||||
0.328321 | + | 0.944566i | \(0.393517\pi\) | |||||||
\(402\) | −5.37787 | −0.268224 | ||||||||
\(403\) | 4.01294 | 0.199899 | ||||||||
\(404\) | −8.14646 | −0.405302 | ||||||||
\(405\) | −0.379603 | −0.0188626 | ||||||||
\(406\) | −1.48909 | −0.0739023 | ||||||||
\(407\) | −10.1191 | −0.501585 | ||||||||
\(408\) | −1.05240 | −0.0521015 | ||||||||
\(409\) | 31.2293 | 1.54419 | 0.772095 | − | 0.635507i | \(-0.219209\pi\) | ||||
0.772095 | + | 0.635507i | \(0.219209\pi\) | |||||||
\(410\) | 0.104585 | 0.00516508 | ||||||||
\(411\) | 2.66036 | 0.131226 | ||||||||
\(412\) | −1.69987 | −0.0837468 | ||||||||
\(413\) | 1.40756 | 0.0692614 | ||||||||
\(414\) | 18.8949 | 0.928631 | ||||||||
\(415\) | −0.434462 | −0.0213269 | ||||||||
\(416\) | 4.01294 | 0.196751 | ||||||||
\(417\) | 4.85251 | 0.237628 | ||||||||
\(418\) | −3.86507 | −0.189047 | ||||||||
\(419\) | 24.4159 | 1.19279 | 0.596397 | − | 0.802689i | \(-0.296598\pi\) | ||||
0.596397 | + | 0.802689i | \(0.296598\pi\) | |||||||
\(420\) | −0.00378972 | −0.000184919 0 | ||||||||
\(421\) | −0.0560206 | −0.00273028 | −0.00136514 | − | 0.999999i | \(-0.500435\pi\) | ||||
−0.00136514 | + | 0.999999i | \(0.500435\pi\) | |||||||
\(422\) | −10.0648 | −0.489948 | ||||||||
\(423\) | −7.51756 | −0.365516 | ||||||||
\(424\) | −7.23535 | −0.351380 | ||||||||
\(425\) | 12.0450 | 0.584270 | ||||||||
\(426\) | −1.35568 | −0.0656831 | ||||||||
\(427\) | 0.410490 | 0.0198650 | ||||||||
\(428\) | 8.05896 | 0.389544 | ||||||||
\(429\) | 2.52813 | 0.122059 | ||||||||
\(430\) | −0.119334 | −0.00575479 | ||||||||
\(431\) | 3.31504 | 0.159680 | 0.0798400 | − | 0.996808i | \(-0.474559\pi\) | ||||
0.0798400 | + | 0.996808i | \(0.474559\pi\) | |||||||
\(432\) | −2.53651 | −0.122038 | ||||||||
\(433\) | 28.7140 | 1.37991 | 0.689953 | − | 0.723854i | \(-0.257631\pi\) | ||||
0.689953 | + | 0.723854i | \(0.257631\pi\) | |||||||
\(434\) | 0.167384 | 0.00803467 | ||||||||
\(435\) | 0.201420 | 0.00965734 | ||||||||
\(436\) | −8.16312 | −0.390942 | ||||||||
\(437\) | 18.0163 | 0.861836 | ||||||||
\(438\) | 2.49530 | 0.119230 | ||||||||
\(439\) | 14.8315 | 0.707871 | 0.353936 | − | 0.935270i | \(-0.384843\pi\) | ||||
0.353936 | + | 0.935270i | \(0.384843\pi\) | |||||||
\(440\) | −0.0748193 | −0.00356687 | ||||||||
\(441\) | 19.5868 | 0.932705 | ||||||||
\(442\) | −9.67240 | −0.460069 | ||||||||
\(443\) | −1.91418 | −0.0909452 | −0.0454726 | − | 0.998966i | \(-0.514479\pi\) | ||||
−0.0454726 | + | 0.998966i | \(0.514479\pi\) | |||||||
\(444\) | −3.06212 | −0.145322 | ||||||||
\(445\) | −0.355844 | −0.0168686 | ||||||||
\(446\) | 15.0134 | 0.710904 | ||||||||
\(447\) | 5.01864 | 0.237374 | ||||||||
\(448\) | 0.167384 | 0.00790813 | ||||||||
\(449\) | 24.7797 | 1.16943 | 0.584713 | − | 0.811240i | \(-0.301207\pi\) | ||||
0.584713 | + | 0.811240i | \(0.301207\pi\) | |||||||
\(450\) | 14.0392 | 0.661816 | ||||||||
\(451\) | −2.91013 | −0.137032 | ||||||||
\(452\) | 5.18278 | 0.243777 | ||||||||
\(453\) | −6.35382 | −0.298528 | ||||||||
\(454\) | −6.02369 | −0.282706 | ||||||||
\(455\) | −0.0348306 | −0.00163288 | ||||||||
\(456\) | −1.16960 | −0.0547716 | ||||||||
\(457\) | −37.9094 | −1.77332 | −0.886662 | − | 0.462417i | \(-0.846982\pi\) | ||||
−0.886662 | + | 0.462417i | \(0.846982\pi\) | |||||||
\(458\) | −5.78767 | −0.270440 | ||||||||
\(459\) | 6.11376 | 0.285366 | ||||||||
\(460\) | 0.348756 | 0.0162608 | ||||||||
\(461\) | 11.7897 | 0.549100 | 0.274550 | − | 0.961573i | \(-0.411471\pi\) | ||||
0.274550 | + | 0.961573i | \(0.411471\pi\) | |||||||
\(462\) | 0.105451 | 0.00490602 | ||||||||
\(463\) | 2.21085 | 0.102747 | 0.0513735 | − | 0.998680i | \(-0.483640\pi\) | ||||
0.0513735 | + | 0.998680i | \(0.483640\pi\) | |||||||
\(464\) | −8.89627 | −0.412999 | ||||||||
\(465\) | −0.0226409 | −0.00104995 | ||||||||
\(466\) | −9.17116 | −0.424846 | ||||||||
\(467\) | 2.05186 | 0.0949489 | 0.0474745 | − | 0.998872i | \(-0.484883\pi\) | ||||
0.0474745 | + | 0.998872i | \(0.484883\pi\) | |||||||
\(468\) | −11.2738 | −0.521131 | ||||||||
\(469\) | −2.06164 | −0.0951979 | ||||||||
\(470\) | −0.138757 | −0.00640039 | ||||||||
\(471\) | 7.48134 | 0.344722 | ||||||||
\(472\) | 8.40917 | 0.387063 | ||||||||
\(473\) | 3.32053 | 0.152678 | ||||||||
\(474\) | 4.56083 | 0.209486 | ||||||||
\(475\) | 13.3864 | 0.614212 | ||||||||
\(476\) | −0.403445 | −0.0184919 | ||||||||
\(477\) | 20.3267 | 0.930695 | ||||||||
\(478\) | 12.6834 | 0.580127 | ||||||||
\(479\) | −30.3350 | −1.38604 | −0.693021 | − | 0.720917i | \(-0.743721\pi\) | ||||
−0.693021 | + | 0.720917i | \(0.743721\pi\) | |||||||
\(480\) | −0.0226409 | −0.00103341 | ||||||||
\(481\) | −28.1434 | −1.28323 | ||||||||
\(482\) | −19.0267 | −0.866644 | ||||||||
\(483\) | −0.491539 | −0.0223658 | ||||||||
\(484\) | −8.91812 | −0.405369 | ||||||||
\(485\) | 0.0518544 | 0.00235459 | ||||||||
\(486\) | 10.8059 | 0.490165 | ||||||||
\(487\) | 29.1251 | 1.31979 | 0.659893 | − | 0.751360i | \(-0.270602\pi\) | ||||
0.659893 | + | 0.751360i | \(0.270602\pi\) | |||||||
\(488\) | 2.45239 | 0.111014 | ||||||||
\(489\) | −7.85761 | −0.355334 | ||||||||
\(490\) | 0.361528 | 0.0163322 | ||||||||
\(491\) | −39.9149 | −1.80134 | −0.900668 | − | 0.434508i | \(-0.856922\pi\) | ||||
−0.900668 | + | 0.434508i | \(0.856922\pi\) | |||||||
\(492\) | −0.880628 | −0.0397018 | ||||||||
\(493\) | 21.4427 | 0.965731 | ||||||||
\(494\) | −10.7496 | −0.483647 | ||||||||
\(495\) | 0.210194 | 0.00944752 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −0.519711 | −0.0233122 | ||||||||
\(498\) | 3.65827 | 0.163931 | ||||||||
\(499\) | 24.9423 | 1.11657 | 0.558284 | − | 0.829650i | \(-0.311460\pi\) | ||||
0.558284 | + | 0.829650i | \(0.311460\pi\) | |||||||
\(500\) | 0.518404 | 0.0231837 | ||||||||
\(501\) | −6.93978 | −0.310047 | ||||||||
\(502\) | −30.2633 | −1.35072 | ||||||||
\(503\) | −2.92782 | −0.130545 | −0.0652725 | − | 0.997867i | \(-0.520792\pi\) | ||||
−0.0652725 | + | 0.997867i | \(0.520792\pi\) | |||||||
\(504\) | −0.470241 | −0.0209462 | ||||||||
\(505\) | 0.422430 | 0.0187979 | ||||||||
\(506\) | −9.70431 | −0.431409 | ||||||||
\(507\) | 1.35515 | 0.0601844 | ||||||||
\(508\) | −5.95977 | −0.264422 | ||||||||
\(509\) | −32.7470 | −1.45149 | −0.725743 | − | 0.687966i | \(-0.758504\pi\) | ||||
−0.725743 | + | 0.687966i | \(0.758504\pi\) | |||||||
\(510\) | 0.0545715 | 0.00241647 | ||||||||
\(511\) | 0.956590 | 0.0423171 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.79463 | 0.299990 | ||||||||
\(514\) | −5.99771 | −0.264547 | ||||||||
\(515\) | 0.0881459 | 0.00388417 | ||||||||
\(516\) | 1.00482 | 0.0442347 | ||||||||
\(517\) | 3.86098 | 0.169806 | ||||||||
\(518\) | −1.17389 | −0.0515777 | ||||||||
\(519\) | 4.92254 | 0.216075 | ||||||||
\(520\) | −0.208088 | −0.00912528 | ||||||||
\(521\) | −22.6993 | −0.994472 | −0.497236 | − | 0.867615i | \(-0.665652\pi\) | ||||
−0.497236 | + | 0.867615i | \(0.665652\pi\) | |||||||
\(522\) | 24.9928 | 1.09391 | ||||||||
\(523\) | 8.33624 | 0.364518 | 0.182259 | − | 0.983251i | \(-0.441659\pi\) | ||||
0.182259 | + | 0.983251i | \(0.441659\pi\) | |||||||
\(524\) | 8.22326 | 0.359235 | ||||||||
\(525\) | −0.365223 | −0.0159396 | ||||||||
\(526\) | 2.57774 | 0.112395 | ||||||||
\(527\) | −2.41030 | −0.104994 | ||||||||
\(528\) | 0.629995 | 0.0274170 | ||||||||
\(529\) | 22.2348 | 0.966731 | ||||||||
\(530\) | 0.375184 | 0.0162970 | ||||||||
\(531\) | −23.6244 | −1.02521 | ||||||||
\(532\) | −0.448375 | −0.0194395 | ||||||||
\(533\) | −8.09368 | −0.350576 | ||||||||
\(534\) | 2.99628 | 0.129662 | ||||||||
\(535\) | −0.417892 | −0.0180670 | ||||||||
\(536\) | −12.3169 | −0.532008 | ||||||||
\(537\) | −6.51464 | −0.281127 | ||||||||
\(538\) | 29.2747 | 1.26212 | ||||||||
\(539\) | −10.0597 | −0.433301 | ||||||||
\(540\) | 0.131529 | 0.00566012 | ||||||||
\(541\) | 44.4243 | 1.90995 | 0.954975 | − | 0.296687i | \(-0.0958818\pi\) | ||||
0.954975 | + | 0.296687i | \(0.0958818\pi\) | |||||||
\(542\) | −3.85462 | −0.165570 | ||||||||
\(543\) | −7.93335 | −0.340453 | ||||||||
\(544\) | −2.41030 | −0.103341 | ||||||||
\(545\) | 0.423293 | 0.0181319 | ||||||||
\(546\) | 0.293282 | 0.0125513 | ||||||||
\(547\) | −19.7025 | −0.842416 | −0.421208 | − | 0.906964i | \(-0.638394\pi\) | ||||
−0.421208 | + | 0.906964i | \(0.638394\pi\) | |||||||
\(548\) | 6.09300 | 0.260280 | ||||||||
\(549\) | −6.88964 | −0.294043 | ||||||||
\(550\) | −7.21049 | −0.307456 | ||||||||
\(551\) | 23.8307 | 1.01522 | ||||||||
\(552\) | −2.93660 | −0.124990 | ||||||||
\(553\) | 1.74843 | 0.0743507 | ||||||||
\(554\) | −17.9316 | −0.761841 | ||||||||
\(555\) | 0.158784 | 0.00674002 | ||||||||
\(556\) | 11.1137 | 0.471324 | ||||||||
\(557\) | 18.9453 | 0.802740 | 0.401370 | − | 0.915916i | \(-0.368534\pi\) | ||||
0.401370 | + | 0.915916i | \(0.368534\pi\) | |||||||
\(558\) | −2.80936 | −0.118930 | ||||||||
\(559\) | 9.23510 | 0.390603 | ||||||||
\(560\) | −0.00867957 | −0.000366779 0 | ||||||||
\(561\) | −1.51848 | −0.0641102 | ||||||||
\(562\) | −1.64814 | −0.0695228 | ||||||||
\(563\) | 39.0032 | 1.64379 | 0.821895 | − | 0.569639i | \(-0.192917\pi\) | ||||
0.821895 | + | 0.569639i | \(0.192917\pi\) | |||||||
\(564\) | 1.16837 | 0.0491971 | ||||||||
\(565\) | −0.268750 | −0.0113064 | ||||||||
\(566\) | 14.2618 | 0.599466 | ||||||||
\(567\) | 1.22534 | 0.0514596 | ||||||||
\(568\) | −3.10491 | −0.130279 | ||||||||
\(569\) | −37.2867 | −1.56314 | −0.781569 | − | 0.623818i | \(-0.785580\pi\) | ||||
−0.781569 | + | 0.623818i | \(0.785580\pi\) | |||||||
\(570\) | 0.0606489 | 0.00254030 | ||||||||
\(571\) | −17.3027 | −0.724096 | −0.362048 | − | 0.932159i | \(-0.617922\pi\) | ||||
−0.362048 | + | 0.932159i | \(0.617922\pi\) | |||||||
\(572\) | 5.79016 | 0.242099 | ||||||||
\(573\) | −6.65214 | −0.277897 | ||||||||
\(574\) | −0.337595 | −0.0140910 | ||||||||
\(575\) | 33.6103 | 1.40165 | ||||||||
\(576\) | −2.80936 | −0.117057 | ||||||||
\(577\) | −34.6438 | −1.44224 | −0.721120 | − | 0.692810i | \(-0.756373\pi\) | ||||
−0.721120 | + | 0.692810i | \(0.756373\pi\) | |||||||
\(578\) | −11.1904 | −0.465461 | ||||||||
\(579\) | −4.20537 | −0.174769 | ||||||||
\(580\) | 0.461310 | 0.0191549 | ||||||||
\(581\) | 1.40242 | 0.0581824 | ||||||||
\(582\) | −0.436625 | −0.0180987 | ||||||||
\(583\) | −10.4397 | −0.432368 | ||||||||
\(584\) | 5.71496 | 0.236487 | ||||||||
\(585\) | 0.584595 | 0.0241700 | ||||||||
\(586\) | 10.7623 | 0.444587 | ||||||||
\(587\) | 16.2036 | 0.668795 | 0.334397 | − | 0.942432i | \(-0.391467\pi\) | ||||
0.334397 | + | 0.942432i | \(0.391467\pi\) | |||||||
\(588\) | −3.04414 | −0.125538 | ||||||||
\(589\) | −2.67873 | −0.110375 | ||||||||
\(590\) | −0.436052 | −0.0179520 | ||||||||
\(591\) | −6.29450 | −0.258921 | ||||||||
\(592\) | −7.01316 | −0.288239 | ||||||||
\(593\) | −28.7224 | −1.17949 | −0.589743 | − | 0.807591i | \(-0.700771\pi\) | ||||
−0.589743 | + | 0.807591i | \(0.700771\pi\) | |||||||
\(594\) | −3.65987 | −0.150166 | ||||||||
\(595\) | 0.0209204 | 0.000857652 0 | ||||||||
\(596\) | 11.4942 | 0.470819 | ||||||||
\(597\) | −5.88120 | −0.240702 | ||||||||
\(598\) | −26.9898 | −1.10369 | ||||||||
\(599\) | 29.1516 | 1.19110 | 0.595551 | − | 0.803318i | \(-0.296934\pi\) | ||||
0.595551 | + | 0.803318i | \(0.296934\pi\) | |||||||
\(600\) | −2.18195 | −0.0890779 | ||||||||
\(601\) | 18.9082 | 0.771280 | 0.385640 | − | 0.922649i | \(-0.373981\pi\) | ||||
0.385640 | + | 0.922649i | \(0.373981\pi\) | |||||||
\(602\) | 0.385205 | 0.0156998 | ||||||||
\(603\) | 34.6025 | 1.40912 | ||||||||
\(604\) | −14.5521 | −0.592116 | ||||||||
\(605\) | 0.462443 | 0.0188010 | ||||||||
\(606\) | −3.55695 | −0.144491 | ||||||||
\(607\) | 2.47095 | 0.100293 | 0.0501463 | − | 0.998742i | \(-0.484031\pi\) | ||||
0.0501463 | + | 0.998742i | \(0.484031\pi\) | |||||||
\(608\) | −2.67873 | −0.108637 | ||||||||
\(609\) | −0.650175 | −0.0263464 | ||||||||
\(610\) | −0.127167 | −0.00514885 | ||||||||
\(611\) | 10.7382 | 0.434422 | ||||||||
\(612\) | 6.77140 | 0.273718 | ||||||||
\(613\) | −33.5553 | −1.35529 | −0.677643 | − | 0.735391i | \(-0.736998\pi\) | ||||
−0.677643 | + | 0.735391i | \(0.736998\pi\) | |||||||
\(614\) | −8.22255 | −0.331835 | ||||||||
\(615\) | 0.0456644 | 0.00184137 | ||||||||
\(616\) | 0.241513 | 0.00973085 | ||||||||
\(617\) | −18.1789 | −0.731855 | −0.365927 | − | 0.930643i | \(-0.619248\pi\) | ||||
−0.365927 | + | 0.930643i | \(0.619248\pi\) | |||||||
\(618\) | −0.742209 | −0.0298560 | ||||||||
\(619\) | −7.06561 | −0.283991 | −0.141995 | − | 0.989867i | \(-0.545352\pi\) | ||||
−0.141995 | + | 0.989867i | \(0.545352\pi\) | |||||||
\(620\) | −0.0518544 | −0.00208252 | ||||||||
\(621\) | 17.0598 | 0.684586 | ||||||||
\(622\) | 5.16135 | 0.206951 | ||||||||
\(623\) | 1.14865 | 0.0460196 | ||||||||
\(624\) | 1.75215 | 0.0701422 | ||||||||
\(625\) | 24.9597 | 0.998387 | ||||||||
\(626\) | 3.16198 | 0.126378 | ||||||||
\(627\) | −1.68759 | −0.0673957 | ||||||||
\(628\) | 17.1344 | 0.683739 | ||||||||
\(629\) | 16.9038 | 0.674000 | ||||||||
\(630\) | 0.0243840 | 0.000971483 0 | ||||||||
\(631\) | −35.1955 | −1.40111 | −0.700556 | − | 0.713598i | \(-0.747065\pi\) | ||||
−0.700556 | + | 0.713598i | \(0.747065\pi\) | |||||||
\(632\) | 10.4456 | 0.415505 | ||||||||
\(633\) | −4.39456 | −0.174668 | ||||||||
\(634\) | 19.3097 | 0.766886 | ||||||||
\(635\) | 0.309040 | 0.0122639 | ||||||||
\(636\) | −3.15914 | −0.125268 | ||||||||
\(637\) | −27.9782 | −1.10853 | ||||||||
\(638\) | −12.8362 | −0.508190 | ||||||||
\(639\) | 8.72281 | 0.345069 | ||||||||
\(640\) | −0.0518544 | −0.00204972 | ||||||||
\(641\) | 1.00332 | 0.0396287 | 0.0198144 | − | 0.999804i | \(-0.493692\pi\) | ||||
0.0198144 | + | 0.999804i | \(0.493692\pi\) | |||||||
\(642\) | 3.51875 | 0.138874 | ||||||||
\(643\) | 23.0459 | 0.908840 | 0.454420 | − | 0.890788i | \(-0.349847\pi\) | ||||
0.454420 | + | 0.890788i | \(0.349847\pi\) | |||||||
\(644\) | −1.12577 | −0.0443615 | ||||||||
\(645\) | −0.0521042 | −0.00205160 | ||||||||
\(646\) | 6.45655 | 0.254029 | ||||||||
\(647\) | 13.5997 | 0.534660 | 0.267330 | − | 0.963605i | \(-0.413859\pi\) | ||||
0.267330 | + | 0.963605i | \(0.413859\pi\) | |||||||
\(648\) | 7.32057 | 0.287579 | ||||||||
\(649\) | 12.1334 | 0.476276 | ||||||||
\(650\) | −20.0539 | −0.786579 | ||||||||
\(651\) | 0.0730839 | 0.00286439 | ||||||||
\(652\) | −17.9962 | −0.704787 | ||||||||
\(653\) | −36.2061 | −1.41686 | −0.708428 | − | 0.705784i | \(-0.750595\pi\) | ||||
−0.708428 | + | 0.705784i | \(0.750595\pi\) | |||||||
\(654\) | −3.56422 | −0.139372 | ||||||||
\(655\) | −0.426412 | −0.0166613 | ||||||||
\(656\) | −2.01690 | −0.0787466 | ||||||||
\(657\) | −16.0554 | −0.626379 | ||||||||
\(658\) | 0.447902 | 0.0174610 | ||||||||
\(659\) | 1.77337 | 0.0690807 | 0.0345404 | − | 0.999403i | \(-0.489003\pi\) | ||||
0.0345404 | + | 0.999403i | \(0.489003\pi\) | |||||||
\(660\) | −0.0326680 | −0.00127160 | ||||||||
\(661\) | −10.7087 | −0.416520 | −0.208260 | − | 0.978074i | \(-0.566780\pi\) | ||||
−0.208260 | + | 0.978074i | \(0.566780\pi\) | |||||||
\(662\) | 7.59645 | 0.295244 | ||||||||
\(663\) | −4.22321 | −0.164016 | ||||||||
\(664\) | 8.37850 | 0.325149 | ||||||||
\(665\) | 0.0232502 | 0.000901605 0 | ||||||||
\(666\) | 19.7025 | 0.763455 | ||||||||
\(667\) | 59.8335 | 2.31676 | ||||||||
\(668\) | −15.8941 | −0.614963 | ||||||||
\(669\) | 6.55522 | 0.253439 | ||||||||
\(670\) | 0.638684 | 0.0246745 | ||||||||
\(671\) | 3.53849 | 0.136602 | ||||||||
\(672\) | 0.0730839 | 0.00281927 | ||||||||
\(673\) | 0.333170 | 0.0128428 | 0.00642138 | − | 0.999979i | \(-0.497956\pi\) | ||||
0.00642138 | + | 0.999979i | \(0.497956\pi\) | |||||||
\(674\) | −30.6571 | −1.18087 | ||||||||
\(675\) | 12.6757 | 0.487890 | ||||||||
\(676\) | 3.10369 | 0.119373 | ||||||||
\(677\) | −27.9940 | −1.07590 | −0.537948 | − | 0.842978i | \(-0.680800\pi\) | ||||
−0.537948 | + | 0.842978i | \(0.680800\pi\) | |||||||
\(678\) | 2.26293 | 0.0869074 | ||||||||
\(679\) | −0.167384 | −0.00642359 | ||||||||
\(680\) | 0.124985 | 0.00479294 | ||||||||
\(681\) | −2.63010 | −0.100786 | ||||||||
\(682\) | 1.44287 | 0.0552505 | ||||||||
\(683\) | −4.98843 | −0.190877 | −0.0954385 | − | 0.995435i | \(-0.530425\pi\) | ||||
−0.0954385 | + | 0.995435i | \(0.530425\pi\) | |||||||
\(684\) | 7.52551 | 0.287745 | ||||||||
\(685\) | −0.315948 | −0.0120718 | ||||||||
\(686\) | −2.33868 | −0.0892912 | ||||||||
\(687\) | −2.52704 | −0.0964127 | ||||||||
\(688\) | 2.30133 | 0.0877374 | ||||||||
\(689\) | −29.0350 | −1.10615 | ||||||||
\(690\) | 0.152276 | 0.00579704 | ||||||||
\(691\) | 17.4931 | 0.665470 | 0.332735 | − | 0.943020i | \(-0.392029\pi\) | ||||
0.332735 | + | 0.943020i | \(0.392029\pi\) | |||||||
\(692\) | 11.2740 | 0.428575 | ||||||||
\(693\) | −0.678497 | −0.0257740 | ||||||||
\(694\) | 9.15064 | 0.347354 | ||||||||
\(695\) | −0.576292 | −0.0218600 | ||||||||
\(696\) | −3.88434 | −0.147235 | ||||||||
\(697\) | 4.86133 | 0.184136 | ||||||||
\(698\) | 19.1348 | 0.724262 | ||||||||
\(699\) | −4.00436 | −0.151459 | ||||||||
\(700\) | −0.836468 | −0.0316155 | ||||||||
\(701\) | −7.33980 | −0.277220 | −0.138610 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138610 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(702\) | −10.1789 | −0.384177 | ||||||||
\(703\) | 18.7864 | 0.708541 | ||||||||
\(704\) | 1.44287 | 0.0543803 | ||||||||
\(705\) | −0.0605849 | −0.00228176 | ||||||||
\(706\) | 10.3641 | 0.390057 | ||||||||
\(707\) | −1.36358 | −0.0512829 | ||||||||
\(708\) | 3.67166 | 0.137989 | ||||||||
\(709\) | −8.51845 | −0.319917 | −0.159959 | − | 0.987124i | \(-0.551136\pi\) | ||||
−0.159959 | + | 0.987124i | \(0.551136\pi\) | |||||||
\(710\) | 0.161003 | 0.00604234 | ||||||||
\(711\) | −29.3455 | −1.10054 | ||||||||
\(712\) | 6.86237 | 0.257178 | ||||||||
\(713\) | −6.72568 | −0.251879 | ||||||||
\(714\) | −0.176154 | −0.00659241 | ||||||||
\(715\) | −0.300245 | −0.0112285 | ||||||||
\(716\) | −14.9204 | −0.557603 | ||||||||
\(717\) | 5.53791 | 0.206817 | ||||||||
\(718\) | 23.2049 | 0.866001 | ||||||||
\(719\) | −34.7296 | −1.29519 | −0.647597 | − | 0.761983i | \(-0.724226\pi\) | ||||
−0.647597 | + | 0.761983i | \(0.724226\pi\) | |||||||
\(720\) | 0.145677 | 0.00542908 | ||||||||
\(721\) | −0.284531 | −0.0105965 | ||||||||
\(722\) | −11.8244 | −0.440059 | ||||||||
\(723\) | −8.30756 | −0.308961 | ||||||||
\(724\) | −18.1697 | −0.675272 | ||||||||
\(725\) | 44.4574 | 1.65111 | ||||||||
\(726\) | −3.89388 | −0.144515 | ||||||||
\(727\) | −31.8181 | −1.18007 | −0.590035 | − | 0.807378i | \(-0.700886\pi\) | ||||
−0.590035 | + | 0.807378i | \(0.700886\pi\) | |||||||
\(728\) | 0.671700 | 0.0248949 | ||||||||
\(729\) | −17.2436 | −0.638651 | ||||||||
\(730\) | −0.296345 | −0.0109682 | ||||||||
\(731\) | −5.54690 | −0.205159 | ||||||||
\(732\) | 1.07078 | 0.0395770 | ||||||||
\(733\) | −18.4345 | −0.680892 | −0.340446 | − | 0.940264i | \(-0.610578\pi\) | ||||
−0.340446 | + | 0.940264i | \(0.610578\pi\) | |||||||
\(734\) | 6.11685 | 0.225777 | ||||||||
\(735\) | 0.157852 | 0.00582247 | ||||||||
\(736\) | −6.72568 | −0.247912 | ||||||||
\(737\) | −17.7717 | −0.654629 | ||||||||
\(738\) | 5.66618 | 0.208575 | ||||||||
\(739\) | 38.8606 | 1.42951 | 0.714756 | − | 0.699374i | \(-0.246538\pi\) | ||||
0.714756 | + | 0.699374i | \(0.246538\pi\) | |||||||
\(740\) | 0.363663 | 0.0133685 | ||||||||
\(741\) | −4.69354 | −0.172422 | ||||||||
\(742\) | −1.21108 | −0.0444601 | ||||||||
\(743\) | −22.4650 | −0.824163 | −0.412081 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412081 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(744\) | 0.436625 | 0.0160075 | ||||||||
\(745\) | −0.596022 | −0.0218366 | ||||||||
\(746\) | −23.0809 | −0.845054 | ||||||||
\(747\) | −23.5382 | −0.861218 | ||||||||
\(748\) | −3.47776 | −0.127159 | ||||||||
\(749\) | 1.34894 | 0.0492891 | ||||||||
\(750\) | 0.226348 | 0.00826508 | ||||||||
\(751\) | −50.4571 | −1.84120 | −0.920602 | − | 0.390502i | \(-0.872302\pi\) | ||||
−0.920602 | + | 0.390502i | \(0.872302\pi\) | |||||||
\(752\) | 2.67590 | 0.0975800 | ||||||||
\(753\) | −13.2137 | −0.481534 | ||||||||
\(754\) | −35.7002 | −1.30012 | ||||||||
\(755\) | 0.754590 | 0.0274623 | ||||||||
\(756\) | −0.424571 | −0.0154415 | ||||||||
\(757\) | −4.61135 | −0.167602 | −0.0838012 | − | 0.996482i | \(-0.526706\pi\) | ||||
−0.0838012 | + | 0.996482i | \(0.526706\pi\) | |||||||
\(758\) | 25.9370 | 0.942073 | ||||||||
\(759\) | −4.23715 | −0.153799 | ||||||||
\(760\) | 0.138904 | 0.00503857 | ||||||||
\(761\) | 19.5038 | 0.707013 | 0.353506 | − | 0.935432i | \(-0.384989\pi\) | ||||
0.353506 | + | 0.935432i | \(0.384989\pi\) | |||||||
\(762\) | −2.60219 | −0.0942674 | ||||||||
\(763\) | −1.36637 | −0.0494660 | ||||||||
\(764\) | −15.2353 | −0.551195 | ||||||||
\(765\) | −0.351127 | −0.0126950 | ||||||||
\(766\) | 7.28337 | 0.263159 | ||||||||
\(767\) | 33.7455 | 1.21848 | ||||||||
\(768\) | 0.436625 | 0.0157554 | ||||||||
\(769\) | −6.95524 | −0.250812 | −0.125406 | − | 0.992105i | \(-0.540023\pi\) | ||||
−0.125406 | + | 0.992105i | \(0.540023\pi\) | |||||||
\(770\) | −0.0125235 | −0.000451316 0 | ||||||||
\(771\) | −2.61875 | −0.0943120 | ||||||||
\(772\) | −9.63153 | −0.346646 | ||||||||
\(773\) | 45.3298 | 1.63040 | 0.815199 | − | 0.579180i | \(-0.196627\pi\) | ||||
0.815199 | + | 0.579180i | \(0.196627\pi\) | |||||||
\(774\) | −6.46526 | −0.232389 | ||||||||
\(775\) | −4.99731 | −0.179509 | ||||||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | −0.512549 | −0.0183876 | ||||||||
\(778\) | 32.8781 | 1.17874 | ||||||||
\(779\) | 5.40272 | 0.193572 | ||||||||
\(780\) | −0.0908567 | −0.00325319 | ||||||||
\(781\) | −4.47999 | −0.160307 | ||||||||
\(782\) | 16.2109 | 0.579701 | ||||||||
\(783\) | 22.5655 | 0.806426 | ||||||||
\(784\) | −6.97198 | −0.248999 | ||||||||
\(785\) | −0.888496 | −0.0317118 | ||||||||
\(786\) | 3.59049 | 0.128068 | ||||||||
\(787\) | −42.8113 | −1.52606 | −0.763030 | − | 0.646364i | \(-0.776289\pi\) | ||||
−0.763030 | + | 0.646364i | \(0.776289\pi\) | |||||||
\(788\) | −14.4162 | −0.513557 | ||||||||
\(789\) | 1.12551 | 0.0400691 | ||||||||
\(790\) | −0.541652 | −0.0192711 | ||||||||
\(791\) | 0.867512 | 0.0308452 | ||||||||
\(792\) | −4.05355 | −0.144037 | ||||||||
\(793\) | 9.84130 | 0.349475 | ||||||||
\(794\) | 33.2627 | 1.18045 | ||||||||
\(795\) | 0.163815 | 0.00580992 | ||||||||
\(796\) | −13.4697 | −0.477420 | ||||||||
\(797\) | −19.8725 | −0.703921 | −0.351960 | − | 0.936015i | \(-0.614485\pi\) | ||||
−0.351960 | + | 0.936015i | \(0.614485\pi\) | |||||||
\(798\) | −0.195772 | −0.00693026 | ||||||||
\(799\) | −6.44973 | −0.228175 | ||||||||
\(800\) | −4.99731 | −0.176682 | ||||||||
\(801\) | −19.2788 | −0.681185 | ||||||||
\(802\) | 13.1492 | 0.464316 | ||||||||
\(803\) | 8.24596 | 0.290994 | ||||||||
\(804\) | −5.37787 | −0.189663 | ||||||||
\(805\) | 0.0583760 | 0.00205748 | ||||||||
\(806\) | 4.01294 | 0.141350 | ||||||||
\(807\) | 12.7821 | 0.449950 | ||||||||
\(808\) | −8.14646 | −0.286592 | ||||||||
\(809\) | 51.7677 | 1.82006 | 0.910028 | − | 0.414546i | \(-0.136060\pi\) | ||||
0.910028 | + | 0.414546i | \(0.136060\pi\) | |||||||
\(810\) | −0.379603 | −0.0133379 | ||||||||
\(811\) | 5.52449 | 0.193991 | 0.0969956 | − | 0.995285i | \(-0.469077\pi\) | ||||
0.0969956 | + | 0.995285i | \(0.469077\pi\) | |||||||
\(812\) | −1.48909 | −0.0522568 | ||||||||
\(813\) | −1.68303 | −0.0590263 | ||||||||
\(814\) | −10.1191 | −0.354674 | ||||||||
\(815\) | 0.933183 | 0.0326880 | ||||||||
\(816\) | −1.05240 | −0.0368413 | ||||||||
\(817\) | −6.16464 | −0.215673 | ||||||||
\(818\) | 31.2293 | 1.09191 | ||||||||
\(819\) | −1.88705 | −0.0659388 | ||||||||
\(820\) | 0.104585 | 0.00365226 | ||||||||
\(821\) | 49.7788 | 1.73729 | 0.868646 | − | 0.495433i | \(-0.164990\pi\) | ||||
0.868646 | + | 0.495433i | \(0.164990\pi\) | |||||||
\(822\) | 2.66036 | 0.0927906 | ||||||||
\(823\) | −22.4384 | −0.782154 | −0.391077 | − | 0.920358i | \(-0.627897\pi\) | ||||
−0.391077 | + | 0.920358i | \(0.627897\pi\) | |||||||
\(824\) | −1.69987 | −0.0592179 | ||||||||
\(825\) | −3.14828 | −0.109609 | ||||||||
\(826\) | 1.40756 | 0.0489752 | ||||||||
\(827\) | −32.2015 | −1.11976 | −0.559878 | − | 0.828575i | \(-0.689152\pi\) | ||||
−0.559878 | + | 0.828575i | \(0.689152\pi\) | |||||||
\(828\) | 18.8949 | 0.656641 | ||||||||
\(829\) | −10.9423 | −0.380042 | −0.190021 | − | 0.981780i | \(-0.560856\pi\) | ||||
−0.190021 | + | 0.981780i | \(0.560856\pi\) | |||||||
\(830\) | −0.434462 | −0.0150804 | ||||||||
\(831\) | −7.82940 | −0.271599 | ||||||||
\(832\) | 4.01294 | 0.139124 | ||||||||
\(833\) | 16.8046 | 0.582244 | ||||||||
\(834\) | 4.85251 | 0.168029 | ||||||||
\(835\) | 0.824180 | 0.0285219 | ||||||||
\(836\) | −3.86507 | −0.133676 | ||||||||
\(837\) | −2.53651 | −0.0876747 | ||||||||
\(838\) | 24.4159 | 0.843433 | ||||||||
\(839\) | −9.76043 | −0.336967 | −0.168484 | − | 0.985704i | \(-0.553887\pi\) | ||||
−0.168484 | + | 0.985704i | \(0.553887\pi\) | |||||||
\(840\) | −0.00378972 | −0.000130758 0 | ||||||||
\(841\) | 50.1436 | 1.72909 | ||||||||
\(842\) | −0.0560206 | −0.00193060 | ||||||||
\(843\) | −0.719622 | −0.0247851 | ||||||||
\(844\) | −10.0648 | −0.346445 | ||||||||
\(845\) | −0.160940 | −0.00553650 | ||||||||
\(846\) | −7.51756 | −0.258459 | ||||||||
\(847\) | −1.49275 | −0.0512914 | ||||||||
\(848\) | −7.23535 | −0.248463 | ||||||||
\(849\) | 6.22704 | 0.213712 | ||||||||
\(850\) | 12.0450 | 0.413141 | ||||||||
\(851\) | 47.1683 | 1.61691 | ||||||||
\(852\) | −1.35568 | −0.0464449 | ||||||||
\(853\) | 17.0302 | 0.583104 | 0.291552 | − | 0.956555i | \(-0.405828\pi\) | ||||
0.291552 | + | 0.956555i | \(0.405828\pi\) | |||||||
\(854\) | 0.410490 | 0.0140467 | ||||||||
\(855\) | −0.390230 | −0.0133456 | ||||||||
\(856\) | 8.05896 | 0.275449 | ||||||||
\(857\) | 27.0825 | 0.925119 | 0.462560 | − | 0.886588i | \(-0.346931\pi\) | ||||
0.462560 | + | 0.886588i | \(0.346931\pi\) | |||||||
\(858\) | 2.52813 | 0.0863090 | ||||||||
\(859\) | 40.8937 | 1.39528 | 0.697638 | − | 0.716450i | \(-0.254234\pi\) | ||||
0.697638 | + | 0.716450i | \(0.254234\pi\) | |||||||
\(860\) | −0.119334 | −0.00406925 | ||||||||
\(861\) | −0.147403 | −0.00502347 | ||||||||
\(862\) | 3.31504 | 0.112911 | ||||||||
\(863\) | −28.5694 | −0.972512 | −0.486256 | − | 0.873816i | \(-0.661638\pi\) | ||||
−0.486256 | + | 0.873816i | \(0.661638\pi\) | |||||||
\(864\) | −2.53651 | −0.0862939 | ||||||||
\(865\) | −0.584608 | −0.0198773 | ||||||||
\(866\) | 28.7140 | 0.975741 | ||||||||
\(867\) | −4.88603 | −0.165938 | ||||||||
\(868\) | 0.167384 | 0.00568137 | ||||||||
\(869\) | 15.0717 | 0.511273 | ||||||||
\(870\) | 0.201420 | 0.00682877 | ||||||||
\(871\) | −49.4269 | −1.67477 | ||||||||
\(872\) | −8.16312 | −0.276438 | ||||||||
\(873\) | 2.80936 | 0.0950824 | ||||||||
\(874\) | 18.0163 | 0.609410 | ||||||||
\(875\) | 0.0867724 | 0.00293344 | ||||||||
\(876\) | 2.49530 | 0.0843082 | ||||||||
\(877\) | 45.0926 | 1.52267 | 0.761335 | − | 0.648358i | \(-0.224544\pi\) | ||||
0.761335 | + | 0.648358i | \(0.224544\pi\) | |||||||
\(878\) | 14.8315 | 0.500541 | ||||||||
\(879\) | 4.69910 | 0.158497 | ||||||||
\(880\) | −0.0748193 | −0.00252216 | ||||||||
\(881\) | 17.3979 | 0.586150 | 0.293075 | − | 0.956089i | \(-0.405321\pi\) | ||||
0.293075 | + | 0.956089i | \(0.405321\pi\) | |||||||
\(882\) | 19.5868 | 0.659522 | ||||||||
\(883\) | −57.7910 | −1.94482 | −0.972411 | − | 0.233273i | \(-0.925057\pi\) | ||||
−0.972411 | + | 0.233273i | \(0.925057\pi\) | |||||||
\(884\) | −9.67240 | −0.325318 | ||||||||
\(885\) | −0.190391 | −0.00639994 | ||||||||
\(886\) | −1.91418 | −0.0643080 | ||||||||
\(887\) | −44.1040 | −1.48087 | −0.740435 | − | 0.672128i | \(-0.765380\pi\) | ||||
−0.740435 | + | 0.672128i | \(0.765380\pi\) | |||||||
\(888\) | −3.06212 | −0.102758 | ||||||||
\(889\) | −0.997569 | −0.0334574 | ||||||||
\(890\) | −0.355844 | −0.0119279 | ||||||||
\(891\) | 10.5627 | 0.353862 | ||||||||
\(892\) | 15.0134 | 0.502685 | ||||||||
\(893\) | −7.16801 | −0.239868 | ||||||||
\(894\) | 5.01864 | 0.167848 | ||||||||
\(895\) | 0.773689 | 0.0258616 | ||||||||
\(896\) | 0.167384 | 0.00559189 | ||||||||
\(897\) | −11.7844 | −0.393470 | ||||||||
\(898\) | 24.7797 | 0.826909 | ||||||||
\(899\) | −8.89627 | −0.296707 | ||||||||
\(900\) | 14.0392 | 0.467975 | ||||||||
\(901\) | 17.4394 | 0.580990 | ||||||||
\(902\) | −2.91013 | −0.0968966 | ||||||||
\(903\) | 0.168190 | 0.00559702 | ||||||||
\(904\) | 5.18278 | 0.172377 | ||||||||
\(905\) | 0.942178 | 0.0313191 | ||||||||
\(906\) | −6.35382 | −0.211091 | ||||||||
\(907\) | 45.2316 | 1.50189 | 0.750946 | − | 0.660364i | \(-0.229598\pi\) | ||||
0.750946 | + | 0.660364i | \(0.229598\pi\) | |||||||
\(908\) | −6.02369 | −0.199903 | ||||||||
\(909\) | 22.8863 | 0.759092 | ||||||||
\(910\) | −0.0348306 | −0.00115462 | ||||||||
\(911\) | 38.1427 | 1.26372 | 0.631862 | − | 0.775081i | \(-0.282291\pi\) | ||||
0.631862 | + | 0.775081i | \(0.282291\pi\) | |||||||
\(912\) | −1.16960 | −0.0387294 | ||||||||
\(913\) | 12.0891 | 0.400091 | ||||||||
\(914\) | −37.9094 | −1.25393 | ||||||||
\(915\) | −0.0555244 | −0.00183558 | ||||||||
\(916\) | −5.78767 | −0.191230 | ||||||||
\(917\) | 1.37644 | 0.0454540 | ||||||||
\(918\) | 6.11376 | 0.201784 | ||||||||
\(919\) | −57.3558 | −1.89199 | −0.945997 | − | 0.324175i | \(-0.894913\pi\) | ||||
−0.945997 | + | 0.324175i | \(0.894913\pi\) | |||||||
\(920\) | 0.348756 | 0.0114981 | ||||||||
\(921\) | −3.59017 | −0.118300 | ||||||||
\(922\) | 11.7897 | 0.388272 | ||||||||
\(923\) | −12.4598 | −0.410120 | ||||||||
\(924\) | 0.105451 | 0.00346908 | ||||||||
\(925\) | 35.0469 | 1.15234 | ||||||||
\(926\) | 2.21085 | 0.0726532 | ||||||||
\(927\) | 4.77556 | 0.156850 | ||||||||
\(928\) | −8.89627 | −0.292034 | ||||||||
\(929\) | −32.0799 | −1.05251 | −0.526253 | − | 0.850328i | \(-0.676403\pi\) | ||||
−0.526253 | + | 0.850328i | \(0.676403\pi\) | |||||||
\(930\) | −0.0226409 | −0.000742425 0 | ||||||||
\(931\) | 18.6761 | 0.612083 | ||||||||
\(932\) | −9.17116 | −0.300411 | ||||||||
\(933\) | 2.25358 | 0.0737788 | ||||||||
\(934\) | 2.05186 | 0.0671390 | ||||||||
\(935\) | 0.180337 | 0.00589765 | ||||||||
\(936\) | −11.2738 | −0.368495 | ||||||||
\(937\) | 41.7762 | 1.36477 | 0.682385 | − | 0.730993i | \(-0.260943\pi\) | ||||
0.682385 | + | 0.730993i | \(0.260943\pi\) | |||||||
\(938\) | −2.06164 | −0.0673151 | ||||||||
\(939\) | 1.38060 | 0.0450543 | ||||||||
\(940\) | −0.138757 | −0.00452576 | ||||||||
\(941\) | 54.8678 | 1.78864 | 0.894320 | − | 0.447428i | \(-0.147660\pi\) | ||||
0.894320 | + | 0.447428i | \(0.147660\pi\) | |||||||
\(942\) | 7.48134 | 0.243755 | ||||||||
\(943\) | 13.5650 | 0.441737 | ||||||||
\(944\) | 8.40917 | 0.273695 | ||||||||
\(945\) | 0.0220158 | 0.000716175 0 | ||||||||
\(946\) | 3.32053 | 0.107960 | ||||||||
\(947\) | 11.9073 | 0.386935 | 0.193468 | − | 0.981107i | \(-0.438027\pi\) | ||||
0.193468 | + | 0.981107i | \(0.438027\pi\) | |||||||
\(948\) | 4.56083 | 0.148129 | ||||||||
\(949\) | 22.9338 | 0.744462 | ||||||||
\(950\) | 13.3864 | 0.434314 | ||||||||
\(951\) | 8.43111 | 0.273397 | ||||||||
\(952\) | −0.403445 | −0.0130757 | ||||||||
\(953\) | −22.7050 | −0.735485 | −0.367743 | − | 0.929928i | \(-0.619869\pi\) | ||||
−0.367743 | + | 0.929928i | \(0.619869\pi\) | |||||||
\(954\) | 20.3267 | 0.658101 | ||||||||
\(955\) | 0.790019 | 0.0255644 | ||||||||
\(956\) | 12.6834 | 0.410212 | ||||||||
\(957\) | −5.60461 | −0.181171 | ||||||||
\(958\) | −30.3350 | −0.980080 | ||||||||
\(959\) | 1.01987 | 0.0329332 | ||||||||
\(960\) | −0.0226409 | −0.000730733 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −28.1434 | −0.907379 | ||||||||
\(963\) | −22.6405 | −0.729580 | ||||||||
\(964\) | −19.0267 | −0.612810 | ||||||||
\(965\) | 0.499437 | 0.0160774 | ||||||||
\(966\) | −0.491539 | −0.0158150 | ||||||||
\(967\) | −23.2766 | −0.748526 | −0.374263 | − | 0.927323i | \(-0.622104\pi\) | ||||
−0.374263 | + | 0.927323i | \(0.622104\pi\) | |||||||
\(968\) | −8.91812 | −0.286639 | ||||||||
\(969\) | 2.81909 | 0.0905623 | ||||||||
\(970\) | 0.0518544 | 0.00166494 | ||||||||
\(971\) | −51.7940 | −1.66215 | −0.831075 | − | 0.556160i | \(-0.812274\pi\) | ||||
−0.831075 | + | 0.556160i | \(0.812274\pi\) | |||||||
\(972\) | 10.8059 | 0.346599 | ||||||||
\(973\) | 1.86024 | 0.0596367 | ||||||||
\(974\) | 29.1251 | 0.933229 | ||||||||
\(975\) | −8.75605 | −0.280418 | ||||||||
\(976\) | 2.45239 | 0.0784991 | ||||||||
\(977\) | 19.5000 | 0.623860 | 0.311930 | − | 0.950105i | \(-0.399025\pi\) | ||||
0.311930 | + | 0.950105i | \(0.399025\pi\) | |||||||
\(978\) | −7.85761 | −0.251259 | ||||||||
\(979\) | 9.90152 | 0.316454 | ||||||||
\(980\) | 0.361528 | 0.0115486 | ||||||||
\(981\) | 22.9331 | 0.732198 | ||||||||
\(982\) | −39.9149 | −1.27374 | ||||||||
\(983\) | 19.4762 | 0.621195 | 0.310598 | − | 0.950542i | \(-0.399471\pi\) | ||||
0.310598 | + | 0.950542i | \(0.399471\pi\) | |||||||
\(984\) | −0.880628 | −0.0280734 | ||||||||
\(985\) | 0.747545 | 0.0238188 | ||||||||
\(986\) | 21.4427 | 0.682875 | ||||||||
\(987\) | 0.195565 | 0.00622491 | ||||||||
\(988\) | −10.7496 | −0.341990 | ||||||||
\(989\) | −15.4780 | −0.492172 | ||||||||
\(990\) | 0.210194 | 0.00668041 | ||||||||
\(991\) | 54.2510 | 1.72334 | 0.861671 | − | 0.507468i | \(-0.169418\pi\) | ||||
0.861671 | + | 0.507468i | \(0.169418\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | 3.31680 | 0.105256 | ||||||||
\(994\) | −0.519711 | −0.0164842 | ||||||||
\(995\) | 0.698462 | 0.0221427 | ||||||||
\(996\) | 3.65827 | 0.115917 | ||||||||
\(997\) | −31.1603 | −0.986857 | −0.493428 | − | 0.869786i | \(-0.664256\pi\) | ||||
−0.493428 | + | 0.869786i | \(0.664256\pi\) | |||||||
\(998\) | 24.9423 | 0.789533 | ||||||||
\(999\) | 17.7890 | 0.562818 |
(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 | 6014.2.a.e.1.14 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.e.1.14 | ✓ | 21 | 1.1 | even | 1 | trivial |