Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14348 | −1.51567 | −0.757833 | − | 0.652449i | \(-0.773742\pi\) | ||||
−0.757833 | + | 0.652449i | \(0.773742\pi\) | |||||||
\(3\) | 2.01146 | 1.16132 | 0.580659 | − | 0.814147i | \(-0.302795\pi\) | ||||
0.580659 | + | 0.814147i | \(0.302795\pi\) | |||||||
\(4\) | 2.59449 | 1.29724 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −4.31152 | −1.76017 | ||||||||
\(7\) | −3.47503 | −1.31344 | −0.656718 | − | 0.754136i | \(-0.728056\pi\) | ||||
−0.656718 | + | 0.754136i | \(0.728056\pi\) | |||||||
\(8\) | −1.27427 | −0.450521 | ||||||||
\(9\) | 1.04598 | 0.348661 | ||||||||
\(10\) | −2.14348 | −0.677826 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 5.21871 | 1.50651 | ||||||||
\(13\) | 6.08523 | 1.68774 | 0.843869 | − | 0.536549i | \(-0.180272\pi\) | ||||
0.843869 | + | 0.536549i | \(0.180272\pi\) | |||||||
\(14\) | 7.44863 | 1.99073 | ||||||||
\(15\) | 2.01146 | 0.519357 | ||||||||
\(16\) | −2.45761 | −0.614403 | ||||||||
\(17\) | −0.860759 | −0.208765 | −0.104382 | − | 0.994537i | \(-0.533287\pi\) | ||||
−0.104382 | + | 0.994537i | \(0.533287\pi\) | |||||||
\(18\) | −2.24204 | −0.528453 | ||||||||
\(19\) | 5.32833 | 1.22240 | 0.611201 | − | 0.791475i | \(-0.290687\pi\) | ||||
0.611201 | + | 0.791475i | \(0.290687\pi\) | |||||||
\(20\) | 2.59449 | 0.580145 | ||||||||
\(21\) | −6.98989 | −1.52532 | ||||||||
\(22\) | −2.14348 | −0.456990 | ||||||||
\(23\) | 5.95868 | 1.24247 | 0.621235 | − | 0.783624i | \(-0.286631\pi\) | ||||
0.621235 | + | 0.783624i | \(0.286631\pi\) | |||||||
\(24\) | −2.56314 | −0.523199 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −13.0435 | −2.55805 | ||||||||
\(27\) | −3.93043 | −0.756412 | ||||||||
\(28\) | −9.01591 | −1.70385 | ||||||||
\(29\) | 5.45897 | 1.01371 | 0.506853 | − | 0.862033i | \(-0.330809\pi\) | ||||
0.506853 | + | 0.862033i | \(0.330809\pi\) | |||||||
\(30\) | −4.31152 | −0.787172 | ||||||||
\(31\) | −4.31699 | −0.775355 | −0.387677 | − | 0.921795i | \(-0.626723\pi\) | ||||
−0.387677 | + | 0.921795i | \(0.626723\pi\) | |||||||
\(32\) | 7.81637 | 1.38175 | ||||||||
\(33\) | 2.01146 | 0.350151 | ||||||||
\(34\) | 1.84501 | 0.316417 | ||||||||
\(35\) | −3.47503 | −0.587387 | ||||||||
\(36\) | 2.71379 | 0.452298 | ||||||||
\(37\) | 6.22550 | 1.02347 | 0.511733 | − | 0.859145i | \(-0.329004\pi\) | ||||
0.511733 | + | 0.859145i | \(0.329004\pi\) | |||||||
\(38\) | −11.4211 | −1.85275 | ||||||||
\(39\) | 12.2402 | 1.96000 | ||||||||
\(40\) | −1.27427 | −0.201479 | ||||||||
\(41\) | 7.88150 | 1.23088 | 0.615442 | − | 0.788182i | \(-0.288978\pi\) | ||||
0.615442 | + | 0.788182i | \(0.288978\pi\) | |||||||
\(42\) | 14.9826 | 2.31187 | ||||||||
\(43\) | 7.05333 | 1.07562 | 0.537812 | − | 0.843065i | \(-0.319251\pi\) | ||||
0.537812 | + | 0.843065i | \(0.319251\pi\) | |||||||
\(44\) | 2.59449 | 0.391134 | ||||||||
\(45\) | 1.04598 | 0.155926 | ||||||||
\(46\) | −12.7723 | −1.88317 | ||||||||
\(47\) | −9.39039 | −1.36973 | −0.684865 | − | 0.728670i | \(-0.740139\pi\) | ||||
−0.684865 | + | 0.728670i | \(0.740139\pi\) | |||||||
\(48\) | −4.94340 | −0.713518 | ||||||||
\(49\) | 5.07581 | 0.725116 | ||||||||
\(50\) | −2.14348 | −0.303133 | ||||||||
\(51\) | −1.73138 | −0.242442 | ||||||||
\(52\) | 15.7880 | 2.18941 | ||||||||
\(53\) | −13.5459 | −1.86068 | −0.930338 | − | 0.366704i | \(-0.880486\pi\) | ||||
−0.930338 | + | 0.366704i | \(0.880486\pi\) | |||||||
\(54\) | 8.42479 | 1.14647 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 4.42811 | 0.591731 | ||||||||
\(57\) | 10.7177 | 1.41960 | ||||||||
\(58\) | −11.7012 | −1.53644 | ||||||||
\(59\) | −13.0360 | −1.69715 | −0.848574 | − | 0.529077i | \(-0.822538\pi\) | ||||
−0.848574 | + | 0.529077i | \(0.822538\pi\) | |||||||
\(60\) | 5.21871 | 0.673733 | ||||||||
\(61\) | −7.65313 | −0.979883 | −0.489941 | − | 0.871755i | \(-0.662982\pi\) | ||||
−0.489941 | + | 0.871755i | \(0.662982\pi\) | |||||||
\(62\) | 9.25337 | 1.17518 | ||||||||
\(63\) | −3.63482 | −0.457944 | ||||||||
\(64\) | −11.8390 | −1.47987 | ||||||||
\(65\) | 6.08523 | 0.754780 | ||||||||
\(66\) | −4.31152 | −0.530711 | ||||||||
\(67\) | −4.95049 | −0.604799 | −0.302400 | − | 0.953181i | \(-0.597788\pi\) | ||||
−0.302400 | + | 0.953181i | \(0.597788\pi\) | |||||||
\(68\) | −2.23323 | −0.270819 | ||||||||
\(69\) | 11.9857 | 1.44290 | ||||||||
\(70\) | 7.44863 | 0.890282 | ||||||||
\(71\) | 9.98830 | 1.18539 | 0.592696 | − | 0.805426i | \(-0.298063\pi\) | ||||
0.592696 | + | 0.805426i | \(0.298063\pi\) | |||||||
\(72\) | −1.33286 | −0.157079 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −13.3442 | −1.55123 | ||||||||
\(75\) | 2.01146 | 0.232264 | ||||||||
\(76\) | 13.8243 | 1.58575 | ||||||||
\(77\) | −3.47503 | −0.396016 | ||||||||
\(78\) | −26.2366 | −2.97071 | ||||||||
\(79\) | −14.0370 | −1.57928 | −0.789640 | − | 0.613570i | \(-0.789733\pi\) | ||||
−0.789640 | + | 0.613570i | \(0.789733\pi\) | |||||||
\(80\) | −2.45761 | −0.274770 | ||||||||
\(81\) | −11.0439 | −1.22710 | ||||||||
\(82\) | −16.8938 | −1.86561 | ||||||||
\(83\) | −15.5205 | −1.70360 | −0.851800 | − | 0.523867i | \(-0.824489\pi\) | ||||
−0.851800 | + | 0.523867i | \(0.824489\pi\) | |||||||
\(84\) | −18.1352 | −1.97871 | ||||||||
\(85\) | −0.860759 | −0.0933624 | ||||||||
\(86\) | −15.1186 | −1.63029 | ||||||||
\(87\) | 10.9805 | 1.17723 | ||||||||
\(88\) | −1.27427 | −0.135837 | ||||||||
\(89\) | 16.0682 | 1.70322 | 0.851612 | − | 0.524172i | \(-0.175625\pi\) | ||||
0.851612 | + | 0.524172i | \(0.175625\pi\) | |||||||
\(90\) | −2.24204 | −0.236331 | ||||||||
\(91\) | −21.1463 | −2.21674 | ||||||||
\(92\) | 15.4597 | 1.61179 | ||||||||
\(93\) | −8.68347 | −0.900434 | ||||||||
\(94\) | 20.1281 | 2.07605 | ||||||||
\(95\) | 5.32833 | 0.546675 | ||||||||
\(96\) | 15.7223 | 1.60465 | ||||||||
\(97\) | −0.440714 | −0.0447477 | −0.0223738 | − | 0.999750i | \(-0.507122\pi\) | ||||
−0.0223738 | + | 0.999750i | \(0.507122\pi\) | |||||||
\(98\) | −10.8799 | −1.09903 | ||||||||
\(99\) | 1.04598 | 0.105125 | ||||||||
\(100\) | 2.59449 | 0.259449 | ||||||||
\(101\) | 11.1222 | 1.10670 | 0.553350 | − | 0.832949i | \(-0.313349\pi\) | ||||
0.553350 | + | 0.832949i | \(0.313349\pi\) | |||||||
\(102\) | 3.71118 | 0.367461 | ||||||||
\(103\) | 9.81539 | 0.967139 | 0.483570 | − | 0.875306i | \(-0.339340\pi\) | ||||
0.483570 | + | 0.875306i | \(0.339340\pi\) | |||||||
\(104\) | −7.75421 | −0.760362 | ||||||||
\(105\) | −6.98989 | −0.682143 | ||||||||
\(106\) | 29.0354 | 2.82016 | ||||||||
\(107\) | 10.8099 | 1.04503 | 0.522516 | − | 0.852629i | \(-0.324993\pi\) | ||||
0.522516 | + | 0.852629i | \(0.324993\pi\) | |||||||
\(108\) | −10.1975 | −0.981251 | ||||||||
\(109\) | 15.0083 | 1.43754 | 0.718770 | − | 0.695248i | \(-0.244706\pi\) | ||||
0.718770 | + | 0.695248i | \(0.244706\pi\) | |||||||
\(110\) | −2.14348 | −0.204372 | ||||||||
\(111\) | 12.5224 | 1.18857 | ||||||||
\(112\) | 8.54027 | 0.806980 | ||||||||
\(113\) | 14.5182 | 1.36575 | 0.682877 | − | 0.730534i | \(-0.260729\pi\) | ||||
0.682877 | + | 0.730534i | \(0.260729\pi\) | |||||||
\(114\) | −22.9732 | −2.15164 | ||||||||
\(115\) | 5.95868 | 0.555650 | ||||||||
\(116\) | 14.1632 | 1.31502 | ||||||||
\(117\) | 6.36504 | 0.588448 | ||||||||
\(118\) | 27.9424 | 2.57231 | ||||||||
\(119\) | 2.99116 | 0.274199 | ||||||||
\(120\) | −2.56314 | −0.233982 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 16.4043 | 1.48517 | ||||||||
\(123\) | 15.8533 | 1.42945 | ||||||||
\(124\) | −11.2004 | −1.00582 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.79114 | 0.694090 | ||||||||
\(127\) | −3.43377 | −0.304698 | −0.152349 | − | 0.988327i | \(-0.548684\pi\) | ||||
−0.152349 | + | 0.988327i | \(0.548684\pi\) | |||||||
\(128\) | 9.74379 | 0.861238 | ||||||||
\(129\) | 14.1875 | 1.24914 | ||||||||
\(130\) | −13.0435 | −1.14399 | ||||||||
\(131\) | −0.970461 | −0.0847896 | −0.0423948 | − | 0.999101i | \(-0.513499\pi\) | ||||
−0.0423948 | + | 0.999101i | \(0.513499\pi\) | |||||||
\(132\) | 5.21871 | 0.454231 | ||||||||
\(133\) | −18.5161 | −1.60555 | ||||||||
\(134\) | 10.6113 | 0.916673 | ||||||||
\(135\) | −3.93043 | −0.338278 | ||||||||
\(136\) | 1.09684 | 0.0940529 | ||||||||
\(137\) | −11.3261 | −0.967651 | −0.483825 | − | 0.875165i | \(-0.660753\pi\) | ||||
−0.483825 | + | 0.875165i | \(0.660753\pi\) | |||||||
\(138\) | −25.6910 | −2.18696 | ||||||||
\(139\) | 17.3886 | 1.47488 | 0.737440 | − | 0.675413i | \(-0.236035\pi\) | ||||
0.737440 | + | 0.675413i | \(0.236035\pi\) | |||||||
\(140\) | −9.01591 | −0.761983 | ||||||||
\(141\) | −18.8884 | −1.59069 | ||||||||
\(142\) | −21.4097 | −1.79666 | ||||||||
\(143\) | 6.08523 | 0.508872 | ||||||||
\(144\) | −2.57062 | −0.214218 | ||||||||
\(145\) | 5.45897 | 0.453343 | ||||||||
\(146\) | −2.14348 | −0.177395 | ||||||||
\(147\) | 10.2098 | 0.842090 | ||||||||
\(148\) | 16.1520 | 1.32768 | ||||||||
\(149\) | 7.51945 | 0.616017 | 0.308009 | − | 0.951384i | \(-0.400337\pi\) | ||||
0.308009 | + | 0.951384i | \(0.400337\pi\) | |||||||
\(150\) | −4.31152 | −0.352034 | ||||||||
\(151\) | 13.8880 | 1.13019 | 0.565095 | − | 0.825026i | \(-0.308839\pi\) | ||||
0.565095 | + | 0.825026i | \(0.308839\pi\) | |||||||
\(152\) | −6.78971 | −0.550719 | ||||||||
\(153\) | −0.900338 | −0.0727880 | ||||||||
\(154\) | 7.44863 | 0.600228 | ||||||||
\(155\) | −4.31699 | −0.346749 | ||||||||
\(156\) | 31.7571 | 2.54260 | ||||||||
\(157\) | −6.26466 | −0.499974 | −0.249987 | − | 0.968249i | \(-0.580426\pi\) | ||||
−0.249987 | + | 0.968249i | \(0.580426\pi\) | |||||||
\(158\) | 30.0879 | 2.39366 | ||||||||
\(159\) | −27.2471 | −2.16084 | ||||||||
\(160\) | 7.81637 | 0.617938 | ||||||||
\(161\) | −20.7066 | −1.63191 | ||||||||
\(162\) | 23.6723 | 1.85987 | ||||||||
\(163\) | 2.44872 | 0.191798 | 0.0958991 | − | 0.995391i | \(-0.469427\pi\) | ||||
0.0958991 | + | 0.995391i | \(0.469427\pi\) | |||||||
\(164\) | 20.4484 | 1.59676 | ||||||||
\(165\) | 2.01146 | 0.156592 | ||||||||
\(166\) | 33.2679 | 2.58209 | ||||||||
\(167\) | 2.54186 | 0.196695 | 0.0983476 | − | 0.995152i | \(-0.468644\pi\) | ||||
0.0983476 | + | 0.995152i | \(0.468644\pi\) | |||||||
\(168\) | 8.90698 | 0.687188 | ||||||||
\(169\) | 24.0300 | 1.84846 | ||||||||
\(170\) | 1.84501 | 0.141506 | ||||||||
\(171\) | 5.57334 | 0.426204 | ||||||||
\(172\) | 18.2998 | 1.39534 | ||||||||
\(173\) | 0.678878 | 0.0516141 | 0.0258071 | − | 0.999667i | \(-0.491784\pi\) | ||||
0.0258071 | + | 0.999667i | \(0.491784\pi\) | |||||||
\(174\) | −23.5365 | −1.78429 | ||||||||
\(175\) | −3.47503 | −0.262687 | ||||||||
\(176\) | −2.45761 | −0.185250 | ||||||||
\(177\) | −26.2215 | −1.97093 | ||||||||
\(178\) | −34.4418 | −2.58152 | ||||||||
\(179\) | 14.0497 | 1.05012 | 0.525060 | − | 0.851065i | \(-0.324043\pi\) | ||||
0.525060 | + | 0.851065i | \(0.324043\pi\) | |||||||
\(180\) | 2.71379 | 0.202274 | ||||||||
\(181\) | 6.22283 | 0.462539 | 0.231270 | − | 0.972890i | \(-0.425712\pi\) | ||||
0.231270 | + | 0.972890i | \(0.425712\pi\) | |||||||
\(182\) | 45.3266 | 3.35983 | ||||||||
\(183\) | −15.3940 | −1.13796 | ||||||||
\(184\) | −7.59295 | −0.559760 | ||||||||
\(185\) | 6.22550 | 0.457708 | ||||||||
\(186\) | 18.6128 | 1.36476 | ||||||||
\(187\) | −0.860759 | −0.0629449 | ||||||||
\(188\) | −24.3632 | −1.77687 | ||||||||
\(189\) | 13.6584 | 0.993500 | ||||||||
\(190\) | −11.4211 | −0.828577 | ||||||||
\(191\) | 25.8029 | 1.86703 | 0.933515 | − | 0.358539i | \(-0.116725\pi\) | ||||
0.933515 | + | 0.358539i | \(0.116725\pi\) | |||||||
\(192\) | −23.8136 | −1.71860 | ||||||||
\(193\) | 21.1940 | 1.52558 | 0.762788 | − | 0.646649i | \(-0.223830\pi\) | ||||
0.762788 | + | 0.646649i | \(0.223830\pi\) | |||||||
\(194\) | 0.944659 | 0.0678226 | ||||||||
\(195\) | 12.2402 | 0.876540 | ||||||||
\(196\) | 13.1691 | 0.940651 | ||||||||
\(197\) | 8.94792 | 0.637513 | 0.318757 | − | 0.947837i | \(-0.396735\pi\) | ||||
0.318757 | + | 0.947837i | \(0.396735\pi\) | |||||||
\(198\) | −2.24204 | −0.159335 | ||||||||
\(199\) | 1.97787 | 0.140208 | 0.0701039 | − | 0.997540i | \(-0.477667\pi\) | ||||
0.0701039 | + | 0.997540i | \(0.477667\pi\) | |||||||
\(200\) | −1.27427 | −0.0901043 | ||||||||
\(201\) | −9.95773 | −0.702364 | ||||||||
\(202\) | −23.8401 | −1.67739 | ||||||||
\(203\) | −18.9701 | −1.33144 | ||||||||
\(204\) | −4.49205 | −0.314507 | ||||||||
\(205\) | 7.88150 | 0.550468 | ||||||||
\(206\) | −21.0390 | −1.46586 | ||||||||
\(207\) | 6.23267 | 0.433201 | ||||||||
\(208\) | −14.9551 | −1.03695 | ||||||||
\(209\) | 5.32833 | 0.368568 | ||||||||
\(210\) | 14.9826 | 1.03390 | ||||||||
\(211\) | −20.0443 | −1.37991 | −0.689954 | − | 0.723853i | \(-0.742369\pi\) | ||||
−0.689954 | + | 0.723853i | \(0.742369\pi\) | |||||||
\(212\) | −35.1447 | −2.41375 | ||||||||
\(213\) | 20.0911 | 1.37662 | ||||||||
\(214\) | −23.1707 | −1.58392 | ||||||||
\(215\) | 7.05333 | 0.481033 | ||||||||
\(216\) | 5.00842 | 0.340780 | ||||||||
\(217\) | 15.0017 | 1.01838 | ||||||||
\(218\) | −32.1700 | −2.17883 | ||||||||
\(219\) | 2.01146 | 0.135922 | ||||||||
\(220\) | 2.59449 | 0.174920 | ||||||||
\(221\) | −5.23791 | −0.352340 | ||||||||
\(222\) | −26.8414 | −1.80147 | ||||||||
\(223\) | −5.44124 | −0.364372 | −0.182186 | − | 0.983264i | \(-0.558317\pi\) | ||||
−0.182186 | + | 0.983264i | \(0.558317\pi\) | |||||||
\(224\) | −27.1621 | −1.81484 | ||||||||
\(225\) | 1.04598 | 0.0697321 | ||||||||
\(226\) | −31.1193 | −2.07003 | ||||||||
\(227\) | −21.1635 | −1.40467 | −0.702335 | − | 0.711846i | \(-0.747859\pi\) | ||||
−0.702335 | + | 0.711846i | \(0.747859\pi\) | |||||||
\(228\) | 27.8070 | 1.84157 | ||||||||
\(229\) | −3.73849 | −0.247046 | −0.123523 | − | 0.992342i | \(-0.539419\pi\) | ||||
−0.123523 | + | 0.992342i | \(0.539419\pi\) | |||||||
\(230\) | −12.7723 | −0.842179 | ||||||||
\(231\) | −6.98989 | −0.459901 | ||||||||
\(232\) | −6.95618 | −0.456696 | ||||||||
\(233\) | 14.5831 | 0.955371 | 0.477686 | − | 0.878531i | \(-0.341476\pi\) | ||||
0.477686 | + | 0.878531i | \(0.341476\pi\) | |||||||
\(234\) | −13.6433 | −0.891891 | ||||||||
\(235\) | −9.39039 | −0.612562 | ||||||||
\(236\) | −33.8218 | −2.20161 | ||||||||
\(237\) | −28.2348 | −1.83405 | ||||||||
\(238\) | −6.41148 | −0.415594 | ||||||||
\(239\) | 19.1418 | 1.23818 | 0.619090 | − | 0.785320i | \(-0.287502\pi\) | ||||
0.619090 | + | 0.785320i | \(0.287502\pi\) | |||||||
\(240\) | −4.94340 | −0.319095 | ||||||||
\(241\) | −15.2597 | −0.982964 | −0.491482 | − | 0.870888i | \(-0.663545\pi\) | ||||
−0.491482 | + | 0.870888i | \(0.663545\pi\) | |||||||
\(242\) | −2.14348 | −0.137788 | ||||||||
\(243\) | −10.4230 | −0.668637 | ||||||||
\(244\) | −19.8559 | −1.27115 | ||||||||
\(245\) | 5.07581 | 0.324282 | ||||||||
\(246\) | −33.9813 | −2.16657 | ||||||||
\(247\) | 32.4241 | 2.06310 | ||||||||
\(248\) | 5.50100 | 0.349314 | ||||||||
\(249\) | −31.2190 | −1.97842 | ||||||||
\(250\) | −2.14348 | −0.135565 | ||||||||
\(251\) | 15.8773 | 1.00217 | 0.501083 | − | 0.865399i | \(-0.332935\pi\) | ||||
0.501083 | + | 0.865399i | \(0.332935\pi\) | |||||||
\(252\) | −9.43048 | −0.594064 | ||||||||
\(253\) | 5.95868 | 0.374619 | ||||||||
\(254\) | 7.36020 | 0.461820 | ||||||||
\(255\) | −1.73138 | −0.108423 | ||||||||
\(256\) | 2.79235 | 0.174522 | ||||||||
\(257\) | 22.9203 | 1.42973 | 0.714865 | − | 0.699262i | \(-0.246488\pi\) | ||||
0.714865 | + | 0.699262i | \(0.246488\pi\) | |||||||
\(258\) | −30.4106 | −1.89328 | ||||||||
\(259\) | −21.6338 | −1.34426 | ||||||||
\(260\) | 15.7880 | 0.979133 | ||||||||
\(261\) | 5.70998 | 0.353439 | ||||||||
\(262\) | 2.08016 | 0.128513 | ||||||||
\(263\) | −12.2937 | −0.758062 | −0.379031 | − | 0.925384i | \(-0.623743\pi\) | ||||
−0.379031 | + | 0.925384i | \(0.623743\pi\) | |||||||
\(264\) | −2.56314 | −0.157750 | ||||||||
\(265\) | −13.5459 | −0.832119 | ||||||||
\(266\) | 39.6888 | 2.43348 | ||||||||
\(267\) | 32.3206 | 1.97799 | ||||||||
\(268\) | −12.8440 | −0.784571 | ||||||||
\(269\) | −11.6500 | −0.710311 | −0.355156 | − | 0.934807i | \(-0.615572\pi\) | ||||
−0.355156 | + | 0.934807i | \(0.615572\pi\) | |||||||
\(270\) | 8.42479 | 0.512716 | ||||||||
\(271\) | 20.2070 | 1.22749 | 0.613743 | − | 0.789506i | \(-0.289663\pi\) | ||||
0.613743 | + | 0.789506i | \(0.289663\pi\) | |||||||
\(272\) | 2.11541 | 0.128266 | ||||||||
\(273\) | −42.5351 | −2.57434 | ||||||||
\(274\) | 24.2771 | 1.46663 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 31.0966 | 1.87180 | ||||||||
\(277\) | −23.0018 | −1.38204 | −0.691022 | − | 0.722834i | \(-0.742839\pi\) | ||||
−0.691022 | + | 0.722834i | \(0.742839\pi\) | |||||||
\(278\) | −37.2720 | −2.23542 | ||||||||
\(279\) | −4.51550 | −0.270336 | ||||||||
\(280\) | 4.42811 | 0.264630 | ||||||||
\(281\) | 29.5901 | 1.76519 | 0.882597 | − | 0.470130i | \(-0.155793\pi\) | ||||
0.882597 | + | 0.470130i | \(0.155793\pi\) | |||||||
\(282\) | 40.4869 | 2.41096 | ||||||||
\(283\) | 0.968632 | 0.0575792 | 0.0287896 | − | 0.999585i | \(-0.490835\pi\) | ||||
0.0287896 | + | 0.999585i | \(0.490835\pi\) | |||||||
\(284\) | 25.9145 | 1.53774 | ||||||||
\(285\) | 10.7177 | 0.634864 | ||||||||
\(286\) | −13.0435 | −0.771281 | ||||||||
\(287\) | −27.3884 | −1.61669 | ||||||||
\(288\) | 8.17578 | 0.481762 | ||||||||
\(289\) | −16.2591 | −0.956417 | ||||||||
\(290\) | −11.7012 | −0.687116 | ||||||||
\(291\) | −0.886479 | −0.0519663 | ||||||||
\(292\) | 2.59449 | 0.151831 | ||||||||
\(293\) | −10.2420 | −0.598346 | −0.299173 | − | 0.954199i | \(-0.596711\pi\) | ||||
−0.299173 | + | 0.954199i | \(0.596711\pi\) | |||||||
\(294\) | −21.8845 | −1.27633 | ||||||||
\(295\) | −13.0360 | −0.758988 | ||||||||
\(296\) | −7.93294 | −0.461093 | ||||||||
\(297\) | −3.93043 | −0.228067 | ||||||||
\(298\) | −16.1178 | −0.933677 | ||||||||
\(299\) | 36.2599 | 2.09697 | ||||||||
\(300\) | 5.21871 | 0.301303 | ||||||||
\(301\) | −24.5105 | −1.41276 | ||||||||
\(302\) | −29.7686 | −1.71299 | ||||||||
\(303\) | 22.3719 | 1.28523 | ||||||||
\(304\) | −13.0950 | −0.751048 | ||||||||
\(305\) | −7.65313 | −0.438217 | ||||||||
\(306\) | 1.92985 | 0.110322 | ||||||||
\(307\) | −0.187378 | −0.0106942 | −0.00534711 | − | 0.999986i | \(-0.501702\pi\) | ||||
−0.00534711 | + | 0.999986i | \(0.501702\pi\) | |||||||
\(308\) | −9.01591 | −0.513729 | ||||||||
\(309\) | 19.7433 | 1.12316 | ||||||||
\(310\) | 9.25337 | 0.525556 | ||||||||
\(311\) | 8.39962 | 0.476299 | 0.238149 | − | 0.971229i | \(-0.423459\pi\) | ||||
0.238149 | + | 0.971229i | \(0.423459\pi\) | |||||||
\(312\) | −15.5973 | −0.883023 | ||||||||
\(313\) | 11.0663 | 0.625504 | 0.312752 | − | 0.949835i | \(-0.398749\pi\) | ||||
0.312752 | + | 0.949835i | \(0.398749\pi\) | |||||||
\(314\) | 13.4281 | 0.757793 | ||||||||
\(315\) | −3.63482 | −0.204799 | ||||||||
\(316\) | −36.4187 | −2.04871 | ||||||||
\(317\) | −13.5612 | −0.761672 | −0.380836 | − | 0.924643i | \(-0.624364\pi\) | ||||
−0.380836 | + | 0.924643i | \(0.624364\pi\) | |||||||
\(318\) | 58.4035 | 3.27511 | ||||||||
\(319\) | 5.45897 | 0.305644 | ||||||||
\(320\) | −11.8390 | −0.661818 | ||||||||
\(321\) | 21.7437 | 1.21361 | ||||||||
\(322\) | 44.3840 | 2.47342 | ||||||||
\(323\) | −4.58641 | −0.255194 | ||||||||
\(324\) | −28.6532 | −1.59184 | ||||||||
\(325\) | 6.08523 | 0.337548 | ||||||||
\(326\) | −5.24876 | −0.290702 | ||||||||
\(327\) | 30.1887 | 1.66944 | ||||||||
\(328\) | −10.0431 | −0.554539 | ||||||||
\(329\) | 32.6319 | 1.79905 | ||||||||
\(330\) | −4.31152 | −0.237341 | ||||||||
\(331\) | −17.4635 | −0.959880 | −0.479940 | − | 0.877301i | \(-0.659341\pi\) | ||||
−0.479940 | + | 0.877301i | \(0.659341\pi\) | |||||||
\(332\) | −40.2678 | −2.20998 | ||||||||
\(333\) | 6.51176 | 0.356842 | ||||||||
\(334\) | −5.44842 | −0.298124 | ||||||||
\(335\) | −4.95049 | −0.270474 | ||||||||
\(336\) | 17.1784 | 0.937161 | ||||||||
\(337\) | −10.5428 | −0.574303 | −0.287152 | − | 0.957885i | \(-0.592708\pi\) | ||||
−0.287152 | + | 0.957885i | \(0.592708\pi\) | |||||||
\(338\) | −51.5077 | −2.80165 | ||||||||
\(339\) | 29.2027 | 1.58607 | ||||||||
\(340\) | −2.23323 | −0.121114 | ||||||||
\(341\) | −4.31699 | −0.233778 | ||||||||
\(342\) | −11.9463 | −0.645983 | ||||||||
\(343\) | 6.68661 | 0.361043 | ||||||||
\(344\) | −8.98783 | −0.484591 | ||||||||
\(345\) | 11.9857 | 0.645286 | ||||||||
\(346\) | −1.45516 | −0.0782298 | ||||||||
\(347\) | −4.89240 | −0.262638 | −0.131319 | − | 0.991340i | \(-0.541921\pi\) | ||||
−0.131319 | + | 0.991340i | \(0.541921\pi\) | |||||||
\(348\) | 28.4888 | 1.52716 | ||||||||
\(349\) | −20.6715 | −1.10652 | −0.553261 | − | 0.833008i | \(-0.686617\pi\) | ||||
−0.553261 | + | 0.833008i | \(0.686617\pi\) | |||||||
\(350\) | 7.44863 | 0.398146 | ||||||||
\(351\) | −23.9176 | −1.27663 | ||||||||
\(352\) | 7.81637 | 0.416614 | ||||||||
\(353\) | 10.5329 | 0.560611 | 0.280305 | − | 0.959911i | \(-0.409564\pi\) | ||||
0.280305 | + | 0.959911i | \(0.409564\pi\) | |||||||
\(354\) | 56.2051 | 2.98727 | ||||||||
\(355\) | 9.98830 | 0.530124 | ||||||||
\(356\) | 41.6887 | 2.20950 | ||||||||
\(357\) | 6.01661 | 0.318433 | ||||||||
\(358\) | −30.1151 | −1.59163 | ||||||||
\(359\) | −9.14214 | −0.482504 | −0.241252 | − | 0.970463i | \(-0.577558\pi\) | ||||
−0.241252 | + | 0.970463i | \(0.577558\pi\) | |||||||
\(360\) | −1.33286 | −0.0702479 | ||||||||
\(361\) | 9.39110 | 0.494269 | ||||||||
\(362\) | −13.3385 | −0.701055 | ||||||||
\(363\) | 2.01146 | 0.105574 | ||||||||
\(364\) | −54.8639 | −2.87565 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 32.9966 | 1.72476 | ||||||||
\(367\) | −1.98979 | −0.103866 | −0.0519331 | − | 0.998651i | \(-0.516538\pi\) | ||||
−0.0519331 | + | 0.998651i | \(0.516538\pi\) | |||||||
\(368\) | −14.6441 | −0.763378 | ||||||||
\(369\) | 8.24391 | 0.429161 | ||||||||
\(370\) | −13.3442 | −0.693732 | ||||||||
\(371\) | 47.0724 | 2.44388 | ||||||||
\(372\) | −22.5291 | −1.16808 | ||||||||
\(373\) | −15.4376 | −0.799328 | −0.399664 | − | 0.916662i | \(-0.630873\pi\) | ||||
−0.399664 | + | 0.916662i | \(0.630873\pi\) | |||||||
\(374\) | 1.84501 | 0.0954035 | ||||||||
\(375\) | 2.01146 | 0.103871 | ||||||||
\(376\) | 11.9659 | 0.617092 | ||||||||
\(377\) | 33.2191 | 1.71087 | ||||||||
\(378\) | −29.2764 | −1.50581 | ||||||||
\(379\) | −7.94818 | −0.408271 | −0.204135 | − | 0.978943i | \(-0.565438\pi\) | ||||
−0.204135 | + | 0.978943i | \(0.565438\pi\) | |||||||
\(380\) | 13.8243 | 0.709171 | ||||||||
\(381\) | −6.90690 | −0.353851 | ||||||||
\(382\) | −55.3078 | −2.82979 | ||||||||
\(383\) | 26.8032 | 1.36958 | 0.684789 | − | 0.728741i | \(-0.259894\pi\) | ||||
0.684789 | + | 0.728741i | \(0.259894\pi\) | |||||||
\(384\) | 19.5993 | 1.00017 | ||||||||
\(385\) | −3.47503 | −0.177104 | ||||||||
\(386\) | −45.4288 | −2.31226 | ||||||||
\(387\) | 7.37766 | 0.375028 | ||||||||
\(388\) | −1.14343 | −0.0580486 | ||||||||
\(389\) | −9.55541 | −0.484478 | −0.242239 | − | 0.970217i | \(-0.577882\pi\) | ||||
−0.242239 | + | 0.970217i | \(0.577882\pi\) | |||||||
\(390\) | −26.2366 | −1.32854 | ||||||||
\(391\) | −5.12898 | −0.259384 | ||||||||
\(392\) | −6.46794 | −0.326680 | ||||||||
\(393\) | −1.95205 | −0.0984677 | ||||||||
\(394\) | −19.1797 | −0.966257 | ||||||||
\(395\) | −14.0370 | −0.706276 | ||||||||
\(396\) | 2.71379 | 0.136373 | ||||||||
\(397\) | 18.9457 | 0.950855 | 0.475428 | − | 0.879755i | \(-0.342293\pi\) | ||||
0.475428 | + | 0.879755i | \(0.342293\pi\) | |||||||
\(398\) | −4.23952 | −0.212508 | ||||||||
\(399\) | −37.2444 | −1.86455 | ||||||||
\(400\) | −2.45761 | −0.122881 | ||||||||
\(401\) | 23.2141 | 1.15925 | 0.579627 | − | 0.814882i | \(-0.303198\pi\) | ||||
0.579627 | + | 0.814882i | \(0.303198\pi\) | |||||||
\(402\) | 21.3442 | 1.06455 | ||||||||
\(403\) | −26.2699 | −1.30860 | ||||||||
\(404\) | 28.8564 | 1.43566 | ||||||||
\(405\) | −11.0439 | −0.548774 | ||||||||
\(406\) | 40.6619 | 2.01801 | ||||||||
\(407\) | 6.22550 | 0.308586 | ||||||||
\(408\) | 2.20625 | 0.109225 | ||||||||
\(409\) | 20.7211 | 1.02459 | 0.512295 | − | 0.858809i | \(-0.328795\pi\) | ||||
0.512295 | + | 0.858809i | \(0.328795\pi\) | |||||||
\(410\) | −16.8938 | −0.834326 | ||||||||
\(411\) | −22.7819 | −1.12375 | ||||||||
\(412\) | 25.4659 | 1.25461 | ||||||||
\(413\) | 45.3006 | 2.22910 | ||||||||
\(414\) | −13.3596 | −0.656587 | ||||||||
\(415\) | −15.5205 | −0.761873 | ||||||||
\(416\) | 47.5644 | 2.33204 | ||||||||
\(417\) | 34.9765 | 1.71280 | ||||||||
\(418\) | −11.4211 | −0.558626 | ||||||||
\(419\) | −9.83194 | −0.480322 | −0.240161 | − | 0.970733i | \(-0.577200\pi\) | ||||
−0.240161 | + | 0.970733i | \(0.577200\pi\) | |||||||
\(420\) | −18.1352 | −0.884905 | ||||||||
\(421\) | 1.39939 | 0.0682020 | 0.0341010 | − | 0.999418i | \(-0.489143\pi\) | ||||
0.0341010 | + | 0.999418i | \(0.489143\pi\) | |||||||
\(422\) | 42.9645 | 2.09148 | ||||||||
\(423\) | −9.82218 | −0.477571 | ||||||||
\(424\) | 17.2611 | 0.838274 | ||||||||
\(425\) | −0.860759 | −0.0417529 | ||||||||
\(426\) | −43.0647 | −2.08649 | ||||||||
\(427\) | 26.5948 | 1.28701 | ||||||||
\(428\) | 28.0461 | 1.35566 | ||||||||
\(429\) | 12.2402 | 0.590963 | ||||||||
\(430\) | −15.1186 | −0.729086 | ||||||||
\(431\) | 24.7144 | 1.19045 | 0.595227 | − | 0.803558i | \(-0.297062\pi\) | ||||
0.595227 | + | 0.803558i | \(0.297062\pi\) | |||||||
\(432\) | 9.65949 | 0.464742 | ||||||||
\(433\) | −22.0244 | −1.05843 | −0.529213 | − | 0.848489i | \(-0.677513\pi\) | ||||
−0.529213 | + | 0.848489i | \(0.677513\pi\) | |||||||
\(434\) | −32.1557 | −1.54352 | ||||||||
\(435\) | 10.9805 | 0.526475 | ||||||||
\(436\) | 38.9390 | 1.86484 | ||||||||
\(437\) | 31.7498 | 1.51880 | ||||||||
\(438\) | −4.31152 | −0.206012 | ||||||||
\(439\) | −12.4472 | −0.594071 | −0.297035 | − | 0.954866i | \(-0.595998\pi\) | ||||
−0.297035 | + | 0.954866i | \(0.595998\pi\) | |||||||
\(440\) | −1.27427 | −0.0607483 | ||||||||
\(441\) | 5.30921 | 0.252819 | ||||||||
\(442\) | 11.2273 | 0.534030 | ||||||||
\(443\) | −28.7124 | −1.36416 | −0.682082 | − | 0.731275i | \(-0.738925\pi\) | ||||
−0.682082 | + | 0.731275i | \(0.738925\pi\) | |||||||
\(444\) | 32.4891 | 1.54186 | ||||||||
\(445\) | 16.0682 | 0.761705 | ||||||||
\(446\) | 11.6632 | 0.552266 | ||||||||
\(447\) | 15.1251 | 0.715392 | ||||||||
\(448\) | 41.1407 | 1.94372 | ||||||||
\(449\) | −16.6133 | −0.784031 | −0.392016 | − | 0.919959i | \(-0.628222\pi\) | ||||
−0.392016 | + | 0.919959i | \(0.628222\pi\) | |||||||
\(450\) | −2.24204 | −0.105691 | ||||||||
\(451\) | 7.88150 | 0.371125 | ||||||||
\(452\) | 37.6672 | 1.77171 | ||||||||
\(453\) | 27.9352 | 1.31251 | ||||||||
\(454\) | 45.3634 | 2.12901 | ||||||||
\(455\) | −21.1463 | −0.991355 | ||||||||
\(456\) | −13.6573 | −0.639560 | ||||||||
\(457\) | −7.42305 | −0.347236 | −0.173618 | − | 0.984813i | \(-0.555546\pi\) | ||||
−0.173618 | + | 0.984813i | \(0.555546\pi\) | |||||||
\(458\) | 8.01336 | 0.374440 | ||||||||
\(459\) | 3.38316 | 0.157912 | ||||||||
\(460\) | 15.4597 | 0.720813 | ||||||||
\(461\) | −9.94481 | −0.463176 | −0.231588 | − | 0.972814i | \(-0.574392\pi\) | ||||
−0.231588 | + | 0.972814i | \(0.574392\pi\) | |||||||
\(462\) | 14.9826 | 0.697056 | ||||||||
\(463\) | −37.2609 | −1.73166 | −0.865830 | − | 0.500337i | \(-0.833209\pi\) | ||||
−0.865830 | + | 0.500337i | \(0.833209\pi\) | |||||||
\(464\) | −13.4160 | −0.622824 | ||||||||
\(465\) | −8.68347 | −0.402686 | ||||||||
\(466\) | −31.2585 | −1.44802 | ||||||||
\(467\) | 19.6412 | 0.908885 | 0.454442 | − | 0.890776i | \(-0.349839\pi\) | ||||
0.454442 | + | 0.890776i | \(0.349839\pi\) | |||||||
\(468\) | 16.5140 | 0.763360 | ||||||||
\(469\) | 17.2031 | 0.794365 | ||||||||
\(470\) | 20.1281 | 0.928439 | ||||||||
\(471\) | −12.6011 | −0.580629 | ||||||||
\(472\) | 16.6114 | 0.764601 | ||||||||
\(473\) | 7.05333 | 0.324313 | ||||||||
\(474\) | 60.5206 | 2.77980 | ||||||||
\(475\) | 5.32833 | 0.244481 | ||||||||
\(476\) | 7.76052 | 0.355703 | ||||||||
\(477\) | −14.1688 | −0.648744 | ||||||||
\(478\) | −41.0300 | −1.87667 | ||||||||
\(479\) | −13.9792 | −0.638725 | −0.319362 | − | 0.947633i | \(-0.603469\pi\) | ||||
−0.319362 | + | 0.947633i | \(0.603469\pi\) | |||||||
\(480\) | 15.7223 | 0.717623 | ||||||||
\(481\) | 37.8836 | 1.72734 | ||||||||
\(482\) | 32.7088 | 1.48984 | ||||||||
\(483\) | −41.6505 | −1.89516 | ||||||||
\(484\) | 2.59449 | 0.117931 | ||||||||
\(485\) | −0.440714 | −0.0200118 | ||||||||
\(486\) | 22.3415 | 1.01343 | ||||||||
\(487\) | −5.54233 | −0.251147 | −0.125574 | − | 0.992084i | \(-0.540077\pi\) | ||||
−0.125574 | + | 0.992084i | \(0.540077\pi\) | |||||||
\(488\) | 9.75213 | 0.441458 | ||||||||
\(489\) | 4.92550 | 0.222739 | ||||||||
\(490\) | −10.8799 | −0.491503 | ||||||||
\(491\) | 31.0809 | 1.40266 | 0.701331 | − | 0.712835i | \(-0.252589\pi\) | ||||
0.701331 | + | 0.712835i | \(0.252589\pi\) | |||||||
\(492\) | 41.1313 | 1.85434 | ||||||||
\(493\) | −4.69886 | −0.211626 | ||||||||
\(494\) | −69.5003 | −3.12697 | ||||||||
\(495\) | 1.04598 | 0.0470134 | ||||||||
\(496\) | 10.6095 | 0.476380 | ||||||||
\(497\) | −34.7096 | −1.55694 | ||||||||
\(498\) | 66.9171 | 2.99863 | ||||||||
\(499\) | −5.75541 | −0.257648 | −0.128824 | − | 0.991667i | \(-0.541120\pi\) | ||||
−0.128824 | + | 0.991667i | \(0.541120\pi\) | |||||||
\(500\) | 2.59449 | 0.116029 | ||||||||
\(501\) | 5.11286 | 0.228426 | ||||||||
\(502\) | −34.0326 | −1.51895 | ||||||||
\(503\) | −29.7198 | −1.32514 | −0.662570 | − | 0.749000i | \(-0.730534\pi\) | ||||
−0.662570 | + | 0.749000i | \(0.730534\pi\) | |||||||
\(504\) | 4.63173 | 0.206313 | ||||||||
\(505\) | 11.1222 | 0.494931 | ||||||||
\(506\) | −12.7723 | −0.567797 | ||||||||
\(507\) | 48.3355 | 2.14665 | ||||||||
\(508\) | −8.90887 | −0.395267 | ||||||||
\(509\) | 20.8070 | 0.922254 | 0.461127 | − | 0.887334i | \(-0.347445\pi\) | ||||
0.461127 | + | 0.887334i | \(0.347445\pi\) | |||||||
\(510\) | 3.71118 | 0.164334 | ||||||||
\(511\) | −3.47503 | −0.153726 | ||||||||
\(512\) | −25.4729 | −1.12575 | ||||||||
\(513\) | −20.9427 | −0.924641 | ||||||||
\(514\) | −49.1292 | −2.16699 | ||||||||
\(515\) | 9.81539 | 0.432518 | ||||||||
\(516\) | 36.8093 | 1.62044 | ||||||||
\(517\) | −9.39039 | −0.412989 | ||||||||
\(518\) | 46.3714 | 2.03744 | ||||||||
\(519\) | 1.36554 | 0.0599405 | ||||||||
\(520\) | −7.75421 | −0.340044 | ||||||||
\(521\) | 6.12846 | 0.268493 | 0.134246 | − | 0.990948i | \(-0.457139\pi\) | ||||
0.134246 | + | 0.990948i | \(0.457139\pi\) | |||||||
\(522\) | −12.2392 | −0.535696 | ||||||||
\(523\) | −29.4407 | −1.28735 | −0.643676 | − | 0.765298i | \(-0.722592\pi\) | ||||
−0.643676 | + | 0.765298i | \(0.722592\pi\) | |||||||
\(524\) | −2.51785 | −0.109993 | ||||||||
\(525\) | −6.98989 | −0.305064 | ||||||||
\(526\) | 26.3512 | 1.14897 | ||||||||
\(527\) | 3.71589 | 0.161867 | ||||||||
\(528\) | −4.94340 | −0.215134 | ||||||||
\(529\) | 12.5059 | 0.543733 | ||||||||
\(530\) | 29.0354 | 1.26122 | ||||||||
\(531\) | −13.6355 | −0.591729 | ||||||||
\(532\) | −48.0397 | −2.08279 | ||||||||
\(533\) | 47.9607 | 2.07741 | ||||||||
\(534\) | −69.2783 | −2.99797 | ||||||||
\(535\) | 10.8099 | 0.467353 | ||||||||
\(536\) | 6.30825 | 0.272475 | ||||||||
\(537\) | 28.2604 | 1.21952 | ||||||||
\(538\) | 24.9714 | 1.07659 | ||||||||
\(539\) | 5.07581 | 0.218631 | ||||||||
\(540\) | −10.1975 | −0.438829 | ||||||||
\(541\) | −30.1809 | −1.29758 | −0.648789 | − | 0.760968i | \(-0.724724\pi\) | ||||
−0.648789 | + | 0.760968i | \(0.724724\pi\) | |||||||
\(542\) | −43.3131 | −1.86046 | ||||||||
\(543\) | 12.5170 | 0.537155 | ||||||||
\(544\) | −6.72801 | −0.288461 | ||||||||
\(545\) | 15.0083 | 0.642887 | ||||||||
\(546\) | 91.1729 | 3.90184 | ||||||||
\(547\) | −38.5413 | −1.64791 | −0.823953 | − | 0.566658i | \(-0.808236\pi\) | ||||
−0.823953 | + | 0.566658i | \(0.808236\pi\) | |||||||
\(548\) | −29.3853 | −1.25528 | ||||||||
\(549\) | −8.00503 | −0.341647 | ||||||||
\(550\) | −2.14348 | −0.0913981 | ||||||||
\(551\) | 29.0872 | 1.23916 | ||||||||
\(552\) | −15.2729 | −0.650059 | ||||||||
\(553\) | 48.7788 | 2.07428 | ||||||||
\(554\) | 49.3037 | 2.09472 | ||||||||
\(555\) | 12.5224 | 0.531544 | ||||||||
\(556\) | 45.1144 | 1.91328 | ||||||||
\(557\) | 14.1873 | 0.601135 | 0.300567 | − | 0.953761i | \(-0.402824\pi\) | ||||
0.300567 | + | 0.953761i | \(0.402824\pi\) | |||||||
\(558\) | 9.67885 | 0.409739 | ||||||||
\(559\) | 42.9212 | 1.81537 | ||||||||
\(560\) | 8.54027 | 0.360892 | ||||||||
\(561\) | −1.73138 | −0.0730991 | ||||||||
\(562\) | −63.4256 | −2.67545 | ||||||||
\(563\) | 33.9242 | 1.42973 | 0.714867 | − | 0.699261i | \(-0.246487\pi\) | ||||
0.714867 | + | 0.699261i | \(0.246487\pi\) | |||||||
\(564\) | −49.0058 | −2.06351 | ||||||||
\(565\) | 14.5182 | 0.610783 | ||||||||
\(566\) | −2.07624 | −0.0872708 | ||||||||
\(567\) | 38.3777 | 1.61171 | ||||||||
\(568\) | −12.7278 | −0.534045 | ||||||||
\(569\) | 26.4714 | 1.10974 | 0.554870 | − | 0.831937i | \(-0.312768\pi\) | ||||
0.554870 | + | 0.831937i | \(0.312768\pi\) | |||||||
\(570\) | −22.9732 | −0.962242 | ||||||||
\(571\) | −36.2667 | −1.51771 | −0.758857 | − | 0.651258i | \(-0.774242\pi\) | ||||
−0.758857 | + | 0.651258i | \(0.774242\pi\) | |||||||
\(572\) | 15.7880 | 0.660131 | ||||||||
\(573\) | 51.9015 | 2.16822 | ||||||||
\(574\) | 58.7064 | 2.45036 | ||||||||
\(575\) | 5.95868 | 0.248494 | ||||||||
\(576\) | −12.3833 | −0.515973 | ||||||||
\(577\) | −1.44734 | −0.0602534 | −0.0301267 | − | 0.999546i | \(-0.509591\pi\) | ||||
−0.0301267 | + | 0.999546i | \(0.509591\pi\) | |||||||
\(578\) | 34.8510 | 1.44961 | ||||||||
\(579\) | 42.6309 | 1.77168 | ||||||||
\(580\) | 14.1632 | 0.588096 | ||||||||
\(581\) | 53.9343 | 2.23757 | ||||||||
\(582\) | 1.90015 | 0.0787636 | ||||||||
\(583\) | −13.5459 | −0.561015 | ||||||||
\(584\) | −1.27427 | −0.0527295 | ||||||||
\(585\) | 6.36504 | 0.263162 | ||||||||
\(586\) | 21.9536 | 0.906893 | ||||||||
\(587\) | −17.9532 | −0.741007 | −0.370504 | − | 0.928831i | \(-0.620815\pi\) | ||||
−0.370504 | + | 0.928831i | \(0.620815\pi\) | |||||||
\(588\) | 26.4892 | 1.09240 | ||||||||
\(589\) | −23.0024 | −0.947796 | ||||||||
\(590\) | 27.9424 | 1.15037 | ||||||||
\(591\) | 17.9984 | 0.740356 | ||||||||
\(592\) | −15.2999 | −0.628820 | ||||||||
\(593\) | −1.56421 | −0.0642345 | −0.0321172 | − | 0.999484i | \(-0.510225\pi\) | ||||
−0.0321172 | + | 0.999484i | \(0.510225\pi\) | |||||||
\(594\) | 8.42479 | 0.345673 | ||||||||
\(595\) | 2.99116 | 0.122626 | ||||||||
\(596\) | 19.5091 | 0.799124 | ||||||||
\(597\) | 3.97842 | 0.162826 | ||||||||
\(598\) | −77.7223 | −3.17830 | ||||||||
\(599\) | −8.21802 | −0.335779 | −0.167890 | − | 0.985806i | \(-0.553695\pi\) | ||||
−0.167890 | + | 0.985806i | \(0.553695\pi\) | |||||||
\(600\) | −2.56314 | −0.104640 | ||||||||
\(601\) | 2.34970 | 0.0958463 | 0.0479232 | − | 0.998851i | \(-0.484740\pi\) | ||||
0.0479232 | + | 0.998851i | \(0.484740\pi\) | |||||||
\(602\) | 52.5377 | 2.14128 | ||||||||
\(603\) | −5.17813 | −0.210870 | ||||||||
\(604\) | 36.0323 | 1.46613 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −47.9535 | −1.94798 | ||||||||
\(607\) | 12.6551 | 0.513654 | 0.256827 | − | 0.966457i | \(-0.417323\pi\) | ||||
0.256827 | + | 0.966457i | \(0.417323\pi\) | |||||||
\(608\) | 41.6482 | 1.68906 | ||||||||
\(609\) | −38.1576 | −1.54622 | ||||||||
\(610\) | 16.4043 | 0.664190 | ||||||||
\(611\) | −57.1427 | −2.31175 | ||||||||
\(612\) | −2.33592 | −0.0944238 | ||||||||
\(613\) | 29.8371 | 1.20511 | 0.602555 | − | 0.798078i | \(-0.294150\pi\) | ||||
0.602555 | + | 0.798078i | \(0.294150\pi\) | |||||||
\(614\) | 0.401640 | 0.0162089 | ||||||||
\(615\) | 15.8533 | 0.639269 | ||||||||
\(616\) | 4.42811 | 0.178414 | ||||||||
\(617\) | −1.05710 | −0.0425572 | −0.0212786 | − | 0.999774i | \(-0.506774\pi\) | ||||
−0.0212786 | + | 0.999774i | \(0.506774\pi\) | |||||||
\(618\) | −42.3193 | −1.70233 | ||||||||
\(619\) | −5.05379 | −0.203129 | −0.101565 | − | 0.994829i | \(-0.532385\pi\) | ||||
−0.101565 | + | 0.994829i | \(0.532385\pi\) | |||||||
\(620\) | −11.2004 | −0.449818 | ||||||||
\(621\) | −23.4202 | −0.939820 | ||||||||
\(622\) | −18.0044 | −0.721910 | ||||||||
\(623\) | −55.8374 | −2.23708 | ||||||||
\(624\) | −30.0817 | −1.20423 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −23.7203 | −0.948055 | ||||||||
\(627\) | 10.7177 | 0.428025 | ||||||||
\(628\) | −16.2536 | −0.648588 | ||||||||
\(629\) | −5.35865 | −0.213663 | ||||||||
\(630\) | 7.79114 | 0.310406 | ||||||||
\(631\) | −18.9247 | −0.753380 | −0.376690 | − | 0.926339i | \(-0.622938\pi\) | ||||
−0.376690 | + | 0.926339i | \(0.622938\pi\) | |||||||
\(632\) | 17.8868 | 0.711500 | ||||||||
\(633\) | −40.3184 | −1.60251 | ||||||||
\(634\) | 29.0681 | 1.15444 | ||||||||
\(635\) | −3.43377 | −0.136265 | ||||||||
\(636\) | −70.6923 | −2.80313 | ||||||||
\(637\) | 30.8875 | 1.22381 | ||||||||
\(638\) | −11.7012 | −0.463254 | ||||||||
\(639\) | 10.4476 | 0.413300 | ||||||||
\(640\) | 9.74379 | 0.385157 | ||||||||
\(641\) | 29.9158 | 1.18160 | 0.590801 | − | 0.806817i | \(-0.298812\pi\) | ||||
0.590801 | + | 0.806817i | \(0.298812\pi\) | |||||||
\(642\) | −46.6071 | −1.83943 | ||||||||
\(643\) | 36.0543 | 1.42184 | 0.710922 | − | 0.703271i | \(-0.248278\pi\) | ||||
0.710922 | + | 0.703271i | \(0.248278\pi\) | |||||||
\(644\) | −53.7229 | −2.11698 | ||||||||
\(645\) | 14.1875 | 0.558633 | ||||||||
\(646\) | 9.83085 | 0.386790 | ||||||||
\(647\) | 5.97437 | 0.234877 | 0.117438 | − | 0.993080i | \(-0.462532\pi\) | ||||
0.117438 | + | 0.993080i | \(0.462532\pi\) | |||||||
\(648\) | 14.0728 | 0.552833 | ||||||||
\(649\) | −13.0360 | −0.511709 | ||||||||
\(650\) | −13.0435 | −0.511610 | ||||||||
\(651\) | 30.1753 | 1.18266 | ||||||||
\(652\) | 6.35316 | 0.248809 | ||||||||
\(653\) | 13.0849 | 0.512053 | 0.256027 | − | 0.966670i | \(-0.417587\pi\) | ||||
0.256027 | + | 0.966670i | \(0.417587\pi\) | |||||||
\(654\) | −64.7088 | −2.53031 | ||||||||
\(655\) | −0.970461 | −0.0379191 | ||||||||
\(656\) | −19.3697 | −0.756259 | ||||||||
\(657\) | 1.04598 | 0.0408076 | ||||||||
\(658\) | −69.9456 | −2.72676 | ||||||||
\(659\) | 46.7837 | 1.82244 | 0.911218 | − | 0.411925i | \(-0.135144\pi\) | ||||
0.911218 | + | 0.411925i | \(0.135144\pi\) | |||||||
\(660\) | 5.21871 | 0.203138 | ||||||||
\(661\) | −20.5875 | −0.800759 | −0.400380 | − | 0.916349i | \(-0.631122\pi\) | ||||
−0.400380 | + | 0.916349i | \(0.631122\pi\) | |||||||
\(662\) | 37.4325 | 1.45486 | ||||||||
\(663\) | −10.5359 | −0.409179 | ||||||||
\(664\) | 19.7773 | 0.767508 | ||||||||
\(665\) | −18.5161 | −0.718023 | ||||||||
\(666\) | −13.9578 | −0.540853 | ||||||||
\(667\) | 32.5282 | 1.25950 | ||||||||
\(668\) | 6.59483 | 0.255161 | ||||||||
\(669\) | −10.9448 | −0.423152 | ||||||||
\(670\) | 10.6113 | 0.409949 | ||||||||
\(671\) | −7.65313 | −0.295446 | ||||||||
\(672\) | −54.6355 | −2.10761 | ||||||||
\(673\) | −39.3176 | −1.51558 | −0.757791 | − | 0.652497i | \(-0.773721\pi\) | ||||
−0.757791 | + | 0.652497i | \(0.773721\pi\) | |||||||
\(674\) | 22.5983 | 0.870452 | ||||||||
\(675\) | −3.93043 | −0.151282 | ||||||||
\(676\) | 62.3455 | 2.39791 | ||||||||
\(677\) | −15.1748 | −0.583215 | −0.291607 | − | 0.956538i | \(-0.594190\pi\) | ||||
−0.291607 | + | 0.956538i | \(0.594190\pi\) | |||||||
\(678\) | −62.5953 | −2.40396 | ||||||||
\(679\) | 1.53149 | 0.0587733 | ||||||||
\(680\) | 1.09684 | 0.0420618 | ||||||||
\(681\) | −42.5696 | −1.63127 | ||||||||
\(682\) | 9.25337 | 0.354330 | ||||||||
\(683\) | −33.9264 | −1.29816 | −0.649080 | − | 0.760721i | \(-0.724846\pi\) | ||||
−0.649080 | + | 0.760721i | \(0.724846\pi\) | |||||||
\(684\) | 14.4599 | 0.552890 | ||||||||
\(685\) | −11.3261 | −0.432746 | ||||||||
\(686\) | −14.3326 | −0.547221 | ||||||||
\(687\) | −7.51984 | −0.286900 | ||||||||
\(688\) | −17.3344 | −0.660866 | ||||||||
\(689\) | −82.4300 | −3.14033 | ||||||||
\(690\) | −25.6910 | −0.978038 | ||||||||
\(691\) | 36.9312 | 1.40493 | 0.702465 | − | 0.711718i | \(-0.252083\pi\) | ||||
0.702465 | + | 0.711718i | \(0.252083\pi\) | |||||||
\(692\) | 1.76134 | 0.0669561 | ||||||||
\(693\) | −3.63482 | −0.138075 | ||||||||
\(694\) | 10.4867 | 0.398071 | ||||||||
\(695\) | 17.3886 | 0.659586 | ||||||||
\(696\) | −13.9921 | −0.530369 | ||||||||
\(697\) | −6.78407 | −0.256965 | ||||||||
\(698\) | 44.3089 | 1.67712 | ||||||||
\(699\) | 29.3334 | 1.10949 | ||||||||
\(700\) | −9.01591 | −0.340769 | ||||||||
\(701\) | −29.8280 | −1.12659 | −0.563294 | − | 0.826257i | \(-0.690466\pi\) | ||||
−0.563294 | + | 0.826257i | \(0.690466\pi\) | |||||||
\(702\) | 51.2668 | 1.93494 | ||||||||
\(703\) | 33.1715 | 1.25109 | ||||||||
\(704\) | −11.8390 | −0.446198 | ||||||||
\(705\) | −18.8884 | −0.711379 | ||||||||
\(706\) | −22.5771 | −0.849699 | ||||||||
\(707\) | −38.6499 | −1.45358 | ||||||||
\(708\) | −68.0313 | −2.55677 | ||||||||
\(709\) | 29.7702 | 1.11804 | 0.559021 | − | 0.829153i | \(-0.311177\pi\) | ||||
0.559021 | + | 0.829153i | \(0.311177\pi\) | |||||||
\(710\) | −21.4097 | −0.803490 | ||||||||
\(711\) | −14.6824 | −0.550633 | ||||||||
\(712\) | −20.4752 | −0.767339 | ||||||||
\(713\) | −25.7236 | −0.963355 | ||||||||
\(714\) | −12.8964 | −0.482637 | ||||||||
\(715\) | 6.08523 | 0.227575 | ||||||||
\(716\) | 36.4517 | 1.36226 | ||||||||
\(717\) | 38.5030 | 1.43792 | ||||||||
\(718\) | 19.5959 | 0.731314 | ||||||||
\(719\) | −1.13906 | −0.0424799 | −0.0212399 | − | 0.999774i | \(-0.506761\pi\) | ||||
−0.0212399 | + | 0.999774i | \(0.506761\pi\) | |||||||
\(720\) | −2.57062 | −0.0958013 | ||||||||
\(721\) | −34.1087 | −1.27028 | ||||||||
\(722\) | −20.1296 | −0.749146 | ||||||||
\(723\) | −30.6943 | −1.14153 | ||||||||
\(724\) | 16.1450 | 0.600026 | ||||||||
\(725\) | 5.45897 | 0.202741 | ||||||||
\(726\) | −4.31152 | −0.160016 | ||||||||
\(727\) | −50.2602 | −1.86405 | −0.932024 | − | 0.362397i | \(-0.881958\pi\) | ||||
−0.932024 | + | 0.362397i | \(0.881958\pi\) | |||||||
\(728\) | 26.9461 | 0.998688 | ||||||||
\(729\) | 12.1661 | 0.450595 | ||||||||
\(730\) | −2.14348 | −0.0793336 | ||||||||
\(731\) | −6.07122 | −0.224552 | ||||||||
\(732\) | −39.9395 | −1.47621 | ||||||||
\(733\) | 24.4876 | 0.904468 | 0.452234 | − | 0.891899i | \(-0.350627\pi\) | ||||
0.452234 | + | 0.891899i | \(0.350627\pi\) | |||||||
\(734\) | 4.26507 | 0.157427 | ||||||||
\(735\) | 10.2098 | 0.376594 | ||||||||
\(736\) | 46.5752 | 1.71679 | ||||||||
\(737\) | −4.95049 | −0.182354 | ||||||||
\(738\) | −17.6706 | −0.650464 | ||||||||
\(739\) | 15.5961 | 0.573713 | 0.286856 | − | 0.957974i | \(-0.407390\pi\) | ||||
0.286856 | + | 0.957974i | \(0.407390\pi\) | |||||||
\(740\) | 16.1520 | 0.593758 | ||||||||
\(741\) | 65.2199 | 2.39591 | ||||||||
\(742\) | −100.899 | −3.70410 | ||||||||
\(743\) | 9.05995 | 0.332377 | 0.166189 | − | 0.986094i | \(-0.446854\pi\) | ||||
0.166189 | + | 0.986094i | \(0.446854\pi\) | |||||||
\(744\) | 11.0651 | 0.405665 | ||||||||
\(745\) | 7.51945 | 0.275491 | ||||||||
\(746\) | 33.0901 | 1.21151 | ||||||||
\(747\) | −16.2342 | −0.593978 | ||||||||
\(748\) | −2.23323 | −0.0816549 | ||||||||
\(749\) | −37.5647 | −1.37258 | ||||||||
\(750\) | −4.31152 | −0.157434 | ||||||||
\(751\) | 18.1498 | 0.662295 | 0.331147 | − | 0.943579i | \(-0.392564\pi\) | ||||
0.331147 | + | 0.943579i | \(0.392564\pi\) | |||||||
\(752\) | 23.0779 | 0.841566 | ||||||||
\(753\) | 31.9366 | 1.16383 | ||||||||
\(754\) | −71.2043 | −2.59311 | ||||||||
\(755\) | 13.8880 | 0.505437 | ||||||||
\(756\) | 35.4364 | 1.28881 | ||||||||
\(757\) | −13.4169 | −0.487647 | −0.243823 | − | 0.969820i | \(-0.578402\pi\) | ||||
−0.243823 | + | 0.969820i | \(0.578402\pi\) | |||||||
\(758\) | 17.0367 | 0.618802 | ||||||||
\(759\) | 11.9857 | 0.435052 | ||||||||
\(760\) | −6.78971 | −0.246289 | ||||||||
\(761\) | 40.9690 | 1.48513 | 0.742563 | − | 0.669776i | \(-0.233610\pi\) | ||||
0.742563 | + | 0.669776i | \(0.233610\pi\) | |||||||
\(762\) | 14.8048 | 0.536320 | ||||||||
\(763\) | −52.1544 | −1.88812 | ||||||||
\(764\) | 66.9452 | 2.42199 | ||||||||
\(765\) | −0.900338 | −0.0325518 | ||||||||
\(766\) | −57.4519 | −2.07582 | ||||||||
\(767\) | −79.3273 | −2.86434 | ||||||||
\(768\) | 5.61671 | 0.202675 | ||||||||
\(769\) | 45.1176 | 1.62698 | 0.813492 | − | 0.581576i | \(-0.197564\pi\) | ||||
0.813492 | + | 0.581576i | \(0.197564\pi\) | |||||||
\(770\) | 7.44863 | 0.268430 | ||||||||
\(771\) | 46.1034 | 1.66037 | ||||||||
\(772\) | 54.9875 | 1.97904 | ||||||||
\(773\) | −19.8257 | −0.713081 | −0.356541 | − | 0.934280i | \(-0.616044\pi\) | ||||
−0.356541 | + | 0.934280i | \(0.616044\pi\) | |||||||
\(774\) | −15.8138 | −0.568416 | ||||||||
\(775\) | −4.31699 | −0.155071 | ||||||||
\(776\) | 0.561587 | 0.0201598 | ||||||||
\(777\) | −43.5155 | −1.56111 | ||||||||
\(778\) | 20.4818 | 0.734308 | ||||||||
\(779\) | 41.9952 | 1.50464 | ||||||||
\(780\) | 31.7571 | 1.13709 | ||||||||
\(781\) | 9.98830 | 0.357409 | ||||||||
\(782\) | 10.9939 | 0.393139 | ||||||||
\(783\) | −21.4561 | −0.766779 | ||||||||
\(784\) | −12.4744 | −0.445513 | ||||||||
\(785\) | −6.26466 | −0.223595 | ||||||||
\(786\) | 4.18416 | 0.149244 | ||||||||
\(787\) | −20.0822 | −0.715853 | −0.357926 | − | 0.933750i | \(-0.616516\pi\) | ||||
−0.357926 | + | 0.933750i | \(0.616516\pi\) | |||||||
\(788\) | 23.2153 | 0.827010 | ||||||||
\(789\) | −24.7283 | −0.880352 | ||||||||
\(790\) | 30.0879 | 1.07048 | ||||||||
\(791\) | −50.4510 | −1.79383 | ||||||||
\(792\) | −1.33286 | −0.0473611 | ||||||||
\(793\) | −46.5710 | −1.65379 | ||||||||
\(794\) | −40.6096 | −1.44118 | ||||||||
\(795\) | −27.2471 | −0.966356 | ||||||||
\(796\) | 5.13157 | 0.181884 | ||||||||
\(797\) | −50.2117 | −1.77859 | −0.889294 | − | 0.457336i | \(-0.848804\pi\) | ||||
−0.889294 | + | 0.457336i | \(0.848804\pi\) | |||||||
\(798\) | 79.8325 | 2.82604 | ||||||||
\(799\) | 8.08286 | 0.285951 | ||||||||
\(800\) | 7.81637 | 0.276350 | ||||||||
\(801\) | 16.8070 | 0.593848 | ||||||||
\(802\) | −49.7588 | −1.75704 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −25.8352 | −0.911137 | ||||||||
\(805\) | −20.7066 | −0.729811 | ||||||||
\(806\) | 56.3089 | 1.98339 | ||||||||
\(807\) | −23.4335 | −0.824898 | ||||||||
\(808\) | −14.1726 | −0.498592 | ||||||||
\(809\) | −10.4267 | −0.366585 | −0.183292 | − | 0.983058i | \(-0.558675\pi\) | ||||
−0.183292 | + | 0.983058i | \(0.558675\pi\) | |||||||
\(810\) | 23.6723 | 0.831758 | ||||||||
\(811\) | 51.4982 | 1.80835 | 0.904174 | − | 0.427165i | \(-0.140488\pi\) | ||||
0.904174 | + | 0.427165i | \(0.140488\pi\) | |||||||
\(812\) | −49.2176 | −1.72720 | ||||||||
\(813\) | 40.6456 | 1.42550 | ||||||||
\(814\) | −13.3442 | −0.467714 | ||||||||
\(815\) | 2.44872 | 0.0857748 | ||||||||
\(816\) | 4.25507 | 0.148957 | ||||||||
\(817\) | 37.5825 | 1.31484 | ||||||||
\(818\) | −44.4151 | −1.55294 | ||||||||
\(819\) | −22.1187 | −0.772889 | ||||||||
\(820\) | 20.4484 | 0.714091 | ||||||||
\(821\) | 16.4254 | 0.573249 | 0.286625 | − | 0.958043i | \(-0.407467\pi\) | ||||
0.286625 | + | 0.958043i | \(0.407467\pi\) | |||||||
\(822\) | 48.8325 | 1.70323 | ||||||||
\(823\) | −32.1197 | −1.11962 | −0.559811 | − | 0.828620i | \(-0.689126\pi\) | ||||
−0.559811 | + | 0.828620i | \(0.689126\pi\) | |||||||
\(824\) | −12.5074 | −0.435717 | ||||||||
\(825\) | 2.01146 | 0.0700301 | ||||||||
\(826\) | −97.1007 | −3.37856 | ||||||||
\(827\) | −11.3431 | −0.394438 | −0.197219 | − | 0.980359i | \(-0.563191\pi\) | ||||
−0.197219 | + | 0.980359i | \(0.563191\pi\) | |||||||
\(828\) | 16.1706 | 0.561967 | ||||||||
\(829\) | 6.84713 | 0.237811 | 0.118905 | − | 0.992906i | \(-0.462062\pi\) | ||||
0.118905 | + | 0.992906i | \(0.462062\pi\) | |||||||
\(830\) | 33.2679 | 1.15474 | ||||||||
\(831\) | −46.2672 | −1.60499 | ||||||||
\(832\) | −72.0428 | −2.49763 | ||||||||
\(833\) | −4.36905 | −0.151379 | ||||||||
\(834\) | −74.9712 | −2.59604 | ||||||||
\(835\) | 2.54186 | 0.0879648 | ||||||||
\(836\) | 13.8243 | 0.478123 | ||||||||
\(837\) | 16.9677 | 0.586488 | ||||||||
\(838\) | 21.0745 | 0.728007 | ||||||||
\(839\) | −2.66868 | −0.0921330 | −0.0460665 | − | 0.998938i | \(-0.514669\pi\) | ||||
−0.0460665 | + | 0.998938i | \(0.514669\pi\) | |||||||
\(840\) | 8.90698 | 0.307320 | ||||||||
\(841\) | 0.800348 | 0.0275982 | ||||||||
\(842\) | −2.99955 | −0.103371 | ||||||||
\(843\) | 59.5193 | 2.04995 | ||||||||
\(844\) | −52.0047 | −1.79008 | ||||||||
\(845\) | 24.0300 | 0.826658 | ||||||||
\(846\) | 21.0536 | 0.723838 | ||||||||
\(847\) | −3.47503 | −0.119403 | ||||||||
\(848\) | 33.2906 | 1.14321 | ||||||||
\(849\) | 1.94837 | 0.0668678 | ||||||||
\(850\) | 1.84501 | 0.0632835 | ||||||||
\(851\) | 37.0957 | 1.27163 | ||||||||
\(852\) | 52.1260 | 1.78581 | ||||||||
\(853\) | 47.6656 | 1.63204 | 0.816019 | − | 0.578025i | \(-0.196176\pi\) | ||||
0.816019 | + | 0.578025i | \(0.196176\pi\) | |||||||
\(854\) | −57.0053 | −1.95068 | ||||||||
\(855\) | 5.57334 | 0.190604 | ||||||||
\(856\) | −13.7747 | −0.470809 | ||||||||
\(857\) | −22.7766 | −0.778033 | −0.389016 | − | 0.921231i | \(-0.627185\pi\) | ||||
−0.389016 | + | 0.921231i | \(0.627185\pi\) | |||||||
\(858\) | −26.2366 | −0.895702 | ||||||||
\(859\) | −42.2964 | −1.44313 | −0.721567 | − | 0.692344i | \(-0.756578\pi\) | ||||
−0.721567 | + | 0.692344i | \(0.756578\pi\) | |||||||
\(860\) | 18.2998 | 0.624017 | ||||||||
\(861\) | −55.0908 | −1.87749 | ||||||||
\(862\) | −52.9748 | −1.80433 | ||||||||
\(863\) | −41.6476 | −1.41770 | −0.708850 | − | 0.705359i | \(-0.750786\pi\) | ||||
−0.708850 | + | 0.705359i | \(0.750786\pi\) | |||||||
\(864\) | −30.7217 | −1.04517 | ||||||||
\(865\) | 0.678878 | 0.0230825 | ||||||||
\(866\) | 47.2088 | 1.60422 | ||||||||
\(867\) | −32.7046 | −1.11071 | ||||||||
\(868\) | 38.9216 | 1.32109 | ||||||||
\(869\) | −14.0370 | −0.476171 | ||||||||
\(870\) | −23.5365 | −0.797961 | ||||||||
\(871\) | −30.1249 | −1.02074 | ||||||||
\(872\) | −19.1246 | −0.647642 | ||||||||
\(873\) | −0.460979 | −0.0156018 | ||||||||
\(874\) | −68.0549 | −2.30199 | ||||||||
\(875\) | −3.47503 | −0.117477 | ||||||||
\(876\) | 5.21871 | 0.176324 | ||||||||
\(877\) | −30.5965 | −1.03317 | −0.516586 | − | 0.856236i | \(-0.672797\pi\) | ||||
−0.516586 | + | 0.856236i | \(0.672797\pi\) | |||||||
\(878\) | 26.6802 | 0.900413 | ||||||||
\(879\) | −20.6015 | −0.694871 | ||||||||
\(880\) | −2.45761 | −0.0828461 | ||||||||
\(881\) | 12.0095 | 0.404609 | 0.202304 | − | 0.979323i | \(-0.435157\pi\) | ||||
0.202304 | + | 0.979323i | \(0.435157\pi\) | |||||||
\(882\) | −11.3802 | −0.383190 | ||||||||
\(883\) | −41.1405 | −1.38449 | −0.692245 | − | 0.721663i | \(-0.743378\pi\) | ||||
−0.692245 | + | 0.721663i | \(0.743378\pi\) | |||||||
\(884\) | −13.5897 | −0.457071 | ||||||||
\(885\) | −26.2215 | −0.881426 | ||||||||
\(886\) | 61.5442 | 2.06762 | ||||||||
\(887\) | 29.9927 | 1.00705 | 0.503527 | − | 0.863979i | \(-0.332035\pi\) | ||||
0.503527 | + | 0.863979i | \(0.332035\pi\) | |||||||
\(888\) | −15.9568 | −0.535476 | ||||||||
\(889\) | 11.9324 | 0.400201 | ||||||||
\(890\) | −34.4418 | −1.15449 | ||||||||
\(891\) | −11.0439 | −0.369983 | ||||||||
\(892\) | −14.1172 | −0.472679 | ||||||||
\(893\) | −50.0351 | −1.67436 | ||||||||
\(894\) | −32.4203 | −1.08430 | ||||||||
\(895\) | 14.0497 | 0.469628 | ||||||||
\(896\) | −33.8599 | −1.13118 | ||||||||
\(897\) | 72.9355 | 2.43525 | ||||||||
\(898\) | 35.6103 | 1.18833 | ||||||||
\(899\) | −23.5663 | −0.785981 | ||||||||
\(900\) | 2.71379 | 0.0904595 | ||||||||
\(901\) | 11.6598 | 0.388443 | ||||||||
\(902\) | −16.8938 | −0.562502 | ||||||||
\(903\) | −49.3020 | −1.64067 | ||||||||
\(904\) | −18.5000 | −0.615301 | ||||||||
\(905\) | 6.22283 | 0.206854 | ||||||||
\(906\) | −59.8785 | −1.98933 | ||||||||
\(907\) | −33.8969 | −1.12553 | −0.562764 | − | 0.826618i | \(-0.690262\pi\) | ||||
−0.562764 | + | 0.826618i | \(0.690262\pi\) | |||||||
\(908\) | −54.9084 | −1.82220 | ||||||||
\(909\) | 11.6336 | 0.385863 | ||||||||
\(910\) | 45.3266 | 1.50256 | ||||||||
\(911\) | −37.1666 | −1.23138 | −0.615691 | − | 0.787987i | \(-0.711123\pi\) | ||||
−0.615691 | + | 0.787987i | \(0.711123\pi\) | |||||||
\(912\) | −26.3401 | −0.872206 | ||||||||
\(913\) | −15.5205 | −0.513655 | ||||||||
\(914\) | 15.9111 | 0.526293 | ||||||||
\(915\) | −15.3940 | −0.508909 | ||||||||
\(916\) | −9.69946 | −0.320479 | ||||||||
\(917\) | 3.37238 | 0.111366 | ||||||||
\(918\) | −7.25171 | −0.239342 | ||||||||
\(919\) | −13.0921 | −0.431867 | −0.215934 | − | 0.976408i | \(-0.569279\pi\) | ||||
−0.215934 | + | 0.976408i | \(0.569279\pi\) | |||||||
\(920\) | −7.59295 | −0.250332 | ||||||||
\(921\) | −0.376903 | −0.0124194 | ||||||||
\(922\) | 21.3165 | 0.702020 | ||||||||
\(923\) | 60.7811 | 2.00063 | ||||||||
\(924\) | −18.1352 | −0.596603 | ||||||||
\(925\) | 6.22550 | 0.204693 | ||||||||
\(926\) | 79.8678 | 2.62462 | ||||||||
\(927\) | 10.2667 | 0.337203 | ||||||||
\(928\) | 42.6693 | 1.40069 | ||||||||
\(929\) | −58.1511 | −1.90787 | −0.953937 | − | 0.300006i | \(-0.903011\pi\) | ||||
−0.953937 | + | 0.300006i | \(0.903011\pi\) | |||||||
\(930\) | 18.6128 | 0.610338 | ||||||||
\(931\) | 27.0456 | 0.886383 | ||||||||
\(932\) | 37.8357 | 1.23935 | ||||||||
\(933\) | 16.8955 | 0.553135 | ||||||||
\(934\) | −42.1003 | −1.37757 | ||||||||
\(935\) | −0.860759 | −0.0281498 | ||||||||
\(936\) | −8.11076 | −0.265109 | ||||||||
\(937\) | 14.2872 | 0.466743 | 0.233372 | − | 0.972388i | \(-0.425024\pi\) | ||||
0.233372 | + | 0.972388i | \(0.425024\pi\) | |||||||
\(938\) | −36.8744 | −1.20399 | ||||||||
\(939\) | 22.2594 | 0.726409 | ||||||||
\(940\) | −24.3632 | −0.794641 | ||||||||
\(941\) | −29.1327 | −0.949700 | −0.474850 | − | 0.880067i | \(-0.657498\pi\) | ||||
−0.474850 | + | 0.880067i | \(0.657498\pi\) | |||||||
\(942\) | 27.0102 | 0.880040 | ||||||||
\(943\) | 46.9633 | 1.52934 | ||||||||
\(944\) | 32.0375 | 1.04273 | ||||||||
\(945\) | 13.6584 | 0.444307 | ||||||||
\(946\) | −15.1186 | −0.491550 | ||||||||
\(947\) | 41.1640 | 1.33765 | 0.668825 | − | 0.743420i | \(-0.266798\pi\) | ||||
0.668825 | + | 0.743420i | \(0.266798\pi\) | |||||||
\(948\) | −73.2548 | −2.37921 | ||||||||
\(949\) | 6.08523 | 0.197535 | ||||||||
\(950\) | −11.4211 | −0.370551 | ||||||||
\(951\) | −27.2778 | −0.884544 | ||||||||
\(952\) | −3.81154 | −0.123533 | ||||||||
\(953\) | 39.3961 | 1.27617 | 0.638083 | − | 0.769968i | \(-0.279728\pi\) | ||||
0.638083 | + | 0.769968i | \(0.279728\pi\) | |||||||
\(954\) | 30.3705 | 0.983280 | ||||||||
\(955\) | 25.8029 | 0.834961 | ||||||||
\(956\) | 49.6632 | 1.60622 | ||||||||
\(957\) | 10.9805 | 0.354950 | ||||||||
\(958\) | 29.9640 | 0.968094 | ||||||||
\(959\) | 39.3584 | 1.27095 | ||||||||
\(960\) | −23.8136 | −0.768582 | ||||||||
\(961\) | −12.3636 | −0.398825 | ||||||||
\(962\) | −81.2025 | −2.61807 | ||||||||
\(963\) | 11.3070 | 0.364362 | ||||||||
\(964\) | −39.5911 | −1.27514 | ||||||||
\(965\) | 21.1940 | 0.682258 | ||||||||
\(966\) | 89.2768 | 2.87243 | ||||||||
\(967\) | −55.2335 | −1.77619 | −0.888095 | − | 0.459659i | \(-0.847972\pi\) | ||||
−0.888095 | + | 0.459659i | \(0.847972\pi\) | |||||||
\(968\) | −1.27427 | −0.0409565 | ||||||||
\(969\) | −9.22539 | −0.296362 | ||||||||
\(970\) | 0.944659 | 0.0303312 | ||||||||
\(971\) | 16.2648 | 0.521963 | 0.260982 | − | 0.965344i | \(-0.415954\pi\) | ||||
0.260982 | + | 0.965344i | \(0.415954\pi\) | |||||||
\(972\) | −27.0424 | −0.867385 | ||||||||
\(973\) | −60.4257 | −1.93716 | ||||||||
\(974\) | 11.8799 | 0.380655 | ||||||||
\(975\) | 12.2402 | 0.392000 | ||||||||
\(976\) | 18.8084 | 0.602043 | ||||||||
\(977\) | 7.13298 | 0.228204 | 0.114102 | − | 0.993469i | \(-0.463601\pi\) | ||||
0.114102 | + | 0.993469i | \(0.463601\pi\) | |||||||
\(978\) | −10.5577 | −0.337598 | ||||||||
\(979\) | 16.0682 | 0.513542 | ||||||||
\(980\) | 13.1691 | 0.420672 | ||||||||
\(981\) | 15.6985 | 0.501213 | ||||||||
\(982\) | −66.6212 | −2.12597 | ||||||||
\(983\) | −9.56032 | −0.304927 | −0.152463 | − | 0.988309i | \(-0.548721\pi\) | ||||
−0.152463 | + | 0.988309i | \(0.548721\pi\) | |||||||
\(984\) | −20.2014 | −0.643997 | ||||||||
\(985\) | 8.94792 | 0.285105 | ||||||||
\(986\) | 10.0719 | 0.320754 | ||||||||
\(987\) | 65.6378 | 2.08927 | ||||||||
\(988\) | 84.1239 | 2.67634 | ||||||||
\(989\) | 42.0286 | 1.33643 | ||||||||
\(990\) | −2.24204 | −0.0712566 | ||||||||
\(991\) | 31.1509 | 0.989540 | 0.494770 | − | 0.869024i | \(-0.335252\pi\) | ||||
0.494770 | + | 0.869024i | \(0.335252\pi\) | |||||||
\(992\) | −33.7432 | −1.07135 | ||||||||
\(993\) | −35.1271 | −1.11473 | ||||||||
\(994\) | 74.3992 | 2.35980 | ||||||||
\(995\) | 1.97787 | 0.0627028 | ||||||||
\(996\) | −80.9972 | −2.56649 | ||||||||
\(997\) | 13.1014 | 0.414927 | 0.207463 | − | 0.978243i | \(-0.433479\pi\) | ||||
0.207463 | + | 0.978243i | \(0.433479\pi\) | |||||||
\(998\) | 12.3366 | 0.390508 | ||||||||
\(999\) | −24.4689 | −0.774162 |
(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 | 4015.2.a.h.1.5 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.5 | ✓ | 37 | 1.1 | even | 1 | trivial |