Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.11646 | 0.789458 | 0.394729 | − | 0.918798i | \(-0.370838\pi\) | ||||
0.394729 | + | 0.918798i | \(0.370838\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.753512 | −0.376756 | ||||||||
\(5\) | −0.900581 | −0.402752 | −0.201376 | − | 0.979514i | \(-0.564541\pi\) | ||||
−0.201376 | + | 0.979514i | \(0.564541\pi\) | |||||||
\(6\) | 1.11646 | 0.455794 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.07419 | −1.08689 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00546 | −0.317956 | ||||||||
\(11\) | −4.69451 | −1.41545 | −0.707724 | − | 0.706489i | \(-0.750278\pi\) | ||||
−0.707724 | + | 0.706489i | \(0.750278\pi\) | |||||||
\(12\) | −0.753512 | −0.217520 | ||||||||
\(13\) | 1.15587 | 0.320581 | 0.160290 | − | 0.987070i | \(-0.448757\pi\) | ||||
0.160290 | + | 0.987070i | \(0.448757\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.900581 | −0.232529 | ||||||||
\(16\) | −1.92519 | −0.481299 | ||||||||
\(17\) | 5.04891 | 1.22454 | 0.612271 | − | 0.790648i | \(-0.290256\pi\) | ||||
0.612271 | + | 0.790648i | \(0.290256\pi\) | |||||||
\(18\) | 1.11646 | 0.263153 | ||||||||
\(19\) | 0.849395 | 0.194865 | 0.0974323 | − | 0.995242i | \(-0.468937\pi\) | ||||
0.0974323 | + | 0.995242i | \(0.468937\pi\) | |||||||
\(20\) | 0.678599 | 0.151739 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.24124 | −1.11744 | ||||||||
\(23\) | −1.63546 | −0.341016 | −0.170508 | − | 0.985356i | \(-0.554541\pi\) | ||||
−0.170508 | + | 0.985356i | \(0.554541\pi\) | |||||||
\(24\) | −3.07419 | −0.627517 | ||||||||
\(25\) | −4.18895 | −0.837791 | ||||||||
\(26\) | 1.29048 | 0.253085 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.97364 | 1.48067 | 0.740334 | − | 0.672240i | \(-0.234668\pi\) | ||||
0.740334 | + | 0.672240i | \(0.234668\pi\) | |||||||
\(30\) | −1.00546 | −0.183572 | ||||||||
\(31\) | 2.94278 | 0.528539 | 0.264270 | − | 0.964449i | \(-0.414869\pi\) | ||||
0.264270 | + | 0.964449i | \(0.414869\pi\) | |||||||
\(32\) | 3.99898 | 0.706926 | ||||||||
\(33\) | −4.69451 | −0.817210 | ||||||||
\(34\) | 5.63692 | 0.966724 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.753512 | −0.125585 | ||||||||
\(37\) | 3.09905 | 0.509480 | 0.254740 | − | 0.967010i | \(-0.418010\pi\) | ||||
0.254740 | + | 0.967010i | \(0.418010\pi\) | |||||||
\(38\) | 0.948318 | 0.153837 | ||||||||
\(39\) | 1.15587 | 0.185087 | ||||||||
\(40\) | 2.76856 | 0.437748 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.01389 | −0.459614 | −0.229807 | − | 0.973236i | \(-0.573810\pi\) | ||||
−0.229807 | + | 0.973236i | \(0.573810\pi\) | |||||||
\(44\) | 3.53737 | 0.533279 | ||||||||
\(45\) | −0.900581 | −0.134251 | ||||||||
\(46\) | −1.82593 | −0.269218 | ||||||||
\(47\) | −8.14340 | −1.18784 | −0.593918 | − | 0.804525i | \(-0.702420\pi\) | ||||
−0.593918 | + | 0.804525i | \(0.702420\pi\) | |||||||
\(48\) | −1.92519 | −0.277878 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.67681 | −0.661401 | ||||||||
\(51\) | 5.04891 | 0.706989 | ||||||||
\(52\) | −0.870962 | −0.120781 | ||||||||
\(53\) | −8.01568 | −1.10104 | −0.550519 | − | 0.834822i | \(-0.685570\pi\) | ||||
−0.550519 | + | 0.834822i | \(0.685570\pi\) | |||||||
\(54\) | 1.11646 | 0.151931 | ||||||||
\(55\) | 4.22779 | 0.570075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.849395 | 0.112505 | ||||||||
\(58\) | 8.90226 | 1.16892 | ||||||||
\(59\) | −2.60113 | −0.338638 | −0.169319 | − | 0.985561i | \(-0.554157\pi\) | ||||
−0.169319 | + | 0.985561i | \(0.554157\pi\) | |||||||
\(60\) | 0.678599 | 0.0876067 | ||||||||
\(61\) | −7.31482 | −0.936567 | −0.468283 | − | 0.883578i | \(-0.655127\pi\) | ||||
−0.468283 | + | 0.883578i | \(0.655127\pi\) | |||||||
\(62\) | 3.28551 | 0.417260 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.31510 | 1.03939 | ||||||||
\(65\) | −1.04095 | −0.129114 | ||||||||
\(66\) | −5.24124 | −0.645153 | ||||||||
\(67\) | 0.796475 | 0.0973049 | 0.0486524 | − | 0.998816i | \(-0.484507\pi\) | ||||
0.0486524 | + | 0.998816i | \(0.484507\pi\) | |||||||
\(68\) | −3.80442 | −0.461353 | ||||||||
\(69\) | −1.63546 | −0.196886 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7265 | 1.27300 | 0.636501 | − | 0.771276i | \(-0.280381\pi\) | ||||
0.636501 | + | 0.771276i | \(0.280381\pi\) | |||||||
\(72\) | −3.07419 | −0.362297 | ||||||||
\(73\) | 1.76040 | 0.206040 | 0.103020 | − | 0.994679i | \(-0.467149\pi\) | ||||
0.103020 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(74\) | 3.45997 | 0.402213 | ||||||||
\(75\) | −4.18895 | −0.483699 | ||||||||
\(76\) | −0.640030 | −0.0734164 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.29048 | 0.146119 | ||||||||
\(79\) | 13.8908 | 1.56283 | 0.781417 | − | 0.624009i | \(-0.214497\pi\) | ||||
0.781417 | + | 0.624009i | \(0.214497\pi\) | |||||||
\(80\) | 1.73379 | 0.193844 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.11646 | −0.123293 | ||||||||
\(83\) | 10.3080 | 1.13145 | 0.565725 | − | 0.824594i | \(-0.308596\pi\) | ||||
0.565725 | + | 0.824594i | \(0.308596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.54695 | −0.493186 | ||||||||
\(86\) | −3.36490 | −0.362846 | ||||||||
\(87\) | 7.97364 | 0.854864 | ||||||||
\(88\) | 14.4318 | 1.53844 | ||||||||
\(89\) | 15.1741 | 1.60846 | 0.804228 | − | 0.594321i | \(-0.202579\pi\) | ||||
0.804228 | + | 0.594321i | \(0.202579\pi\) | |||||||
\(90\) | −1.00546 | −0.105985 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.23234 | 0.128480 | ||||||||
\(93\) | 2.94278 | 0.305152 | ||||||||
\(94\) | −9.09180 | −0.937747 | ||||||||
\(95\) | −0.764949 | −0.0784821 | ||||||||
\(96\) | 3.99898 | 0.408144 | ||||||||
\(97\) | −0.878601 | −0.0892084 | −0.0446042 | − | 0.999005i | \(-0.514203\pi\) | ||||
−0.0446042 | + | 0.999005i | \(0.514203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.69451 | −0.471816 | ||||||||
\(100\) | 3.15643 | 0.315643 | ||||||||
\(101\) | 4.56591 | 0.454325 | 0.227162 | − | 0.973857i | \(-0.427055\pi\) | ||||
0.227162 | + | 0.973857i | \(0.427055\pi\) | |||||||
\(102\) | 5.63692 | 0.558138 | ||||||||
\(103\) | −0.218199 | −0.0214998 | −0.0107499 | − | 0.999942i | \(-0.503422\pi\) | ||||
−0.0107499 | + | 0.999942i | \(0.503422\pi\) | |||||||
\(104\) | −3.55336 | −0.348436 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.94920 | −0.869224 | ||||||||
\(107\) | 8.05109 | 0.778328 | 0.389164 | − | 0.921168i | \(-0.372764\pi\) | ||||
0.389164 | + | 0.921168i | \(0.372764\pi\) | |||||||
\(108\) | −0.753512 | −0.0725068 | ||||||||
\(109\) | 15.5123 | 1.48581 | 0.742905 | − | 0.669397i | \(-0.233448\pi\) | ||||
0.742905 | + | 0.669397i | \(0.233448\pi\) | |||||||
\(110\) | 4.72016 | 0.450050 | ||||||||
\(111\) | 3.09905 | 0.294149 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0560 | 1.51042 | 0.755211 | − | 0.655482i | \(-0.227534\pi\) | ||||
0.755211 | + | 0.655482i | \(0.227534\pi\) | |||||||
\(114\) | 0.948318 | 0.0888181 | ||||||||
\(115\) | 1.47286 | 0.137345 | ||||||||
\(116\) | −6.00823 | −0.557850 | ||||||||
\(117\) | 1.15587 | 0.106860 | ||||||||
\(118\) | −2.90406 | −0.267340 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.76856 | 0.252734 | ||||||||
\(121\) | 11.0384 | 1.00349 | ||||||||
\(122\) | −8.16672 | −0.739380 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −2.21742 | −0.199130 | ||||||||
\(125\) | 8.27540 | 0.740174 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.08915 | 0.806532 | 0.403266 | − | 0.915083i | \(-0.367875\pi\) | ||||
0.403266 | + | 0.915083i | \(0.367875\pi\) | |||||||
\(128\) | 1.28554 | 0.113626 | ||||||||
\(129\) | −3.01389 | −0.265358 | ||||||||
\(130\) | −1.16219 | −0.101930 | ||||||||
\(131\) | 20.4776 | 1.78914 | 0.894570 | − | 0.446928i | \(-0.147482\pi\) | ||||
0.894570 | + | 0.446928i | \(0.147482\pi\) | |||||||
\(132\) | 3.53737 | 0.307889 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.889234 | 0.0768181 | ||||||||
\(135\) | −0.900581 | −0.0775096 | ||||||||
\(136\) | −15.5213 | −1.33094 | ||||||||
\(137\) | 20.8453 | 1.78094 | 0.890468 | − | 0.455047i | \(-0.150377\pi\) | ||||
0.890468 | + | 0.455047i | \(0.150377\pi\) | |||||||
\(138\) | −1.82593 | −0.155433 | ||||||||
\(139\) | −0.173141 | −0.0146856 | −0.00734280 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734280 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.14340 | −0.685798 | ||||||||
\(142\) | 11.9757 | 1.00498 | ||||||||
\(143\) | −5.42624 | −0.453765 | ||||||||
\(144\) | −1.92519 | −0.160433 | ||||||||
\(145\) | −7.18090 | −0.596342 | ||||||||
\(146\) | 1.96542 | 0.162660 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.33517 | −0.191950 | ||||||||
\(149\) | 1.04440 | 0.0855607 | 0.0427803 | − | 0.999085i | \(-0.486378\pi\) | ||||
0.0427803 | + | 0.999085i | \(0.486378\pi\) | |||||||
\(150\) | −4.67681 | −0.381860 | ||||||||
\(151\) | −11.9553 | −0.972907 | −0.486453 | − | 0.873707i | \(-0.661710\pi\) | ||||
−0.486453 | + | 0.873707i | \(0.661710\pi\) | |||||||
\(152\) | −2.61120 | −0.211797 | ||||||||
\(153\) | 5.04891 | 0.408180 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.65021 | −0.212870 | ||||||||
\(156\) | −0.870962 | −0.0697328 | ||||||||
\(157\) | −4.18839 | −0.334270 | −0.167135 | − | 0.985934i | \(-0.553452\pi\) | ||||
−0.167135 | + | 0.985934i | \(0.553452\pi\) | |||||||
\(158\) | 15.5085 | 1.23379 | ||||||||
\(159\) | −8.01568 | −0.635685 | ||||||||
\(160\) | −3.60140 | −0.284716 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.11646 | 0.0877176 | ||||||||
\(163\) | 10.8840 | 0.852499 | 0.426250 | − | 0.904606i | \(-0.359834\pi\) | ||||
0.426250 | + | 0.904606i | \(0.359834\pi\) | |||||||
\(164\) | 0.753512 | 0.0588394 | ||||||||
\(165\) | 4.22779 | 0.329133 | ||||||||
\(166\) | 11.5085 | 0.893232 | ||||||||
\(167\) | 12.7952 | 0.990120 | 0.495060 | − | 0.868859i | \(-0.335146\pi\) | ||||
0.495060 | + | 0.868859i | \(0.335146\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6640 | −0.897228 | ||||||||
\(170\) | −5.07650 | −0.389350 | ||||||||
\(171\) | 0.849395 | 0.0649549 | ||||||||
\(172\) | 2.27100 | 0.173162 | ||||||||
\(173\) | 5.07018 | 0.385479 | 0.192739 | − | 0.981250i | \(-0.438263\pi\) | ||||
0.192739 | + | 0.981250i | \(0.438263\pi\) | |||||||
\(174\) | 8.90226 | 0.674879 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.03785 | 0.681253 | ||||||||
\(177\) | −2.60113 | −0.195513 | ||||||||
\(178\) | 16.9414 | 1.26981 | ||||||||
\(179\) | 2.27988 | 0.170406 | 0.0852032 | − | 0.996364i | \(-0.472846\pi\) | ||||
0.0852032 | + | 0.996364i | \(0.472846\pi\) | |||||||
\(180\) | 0.678599 | 0.0505798 | ||||||||
\(181\) | −8.62106 | −0.640798 | −0.320399 | − | 0.947283i | \(-0.603817\pi\) | ||||
−0.320399 | + | 0.947283i | \(0.603817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.31482 | −0.540727 | ||||||||
\(184\) | 5.02771 | 0.370648 | ||||||||
\(185\) | −2.79094 | −0.205194 | ||||||||
\(186\) | 3.28551 | 0.240905 | ||||||||
\(187\) | −23.7022 | −1.73328 | ||||||||
\(188\) | 6.13615 | 0.447525 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.854037 | −0.0619583 | ||||||||
\(191\) | −21.2101 | −1.53471 | −0.767356 | − | 0.641222i | \(-0.778428\pi\) | ||||
−0.767356 | + | 0.641222i | \(0.778428\pi\) | |||||||
\(192\) | 8.31510 | 0.600090 | ||||||||
\(193\) | −11.2364 | −0.808814 | −0.404407 | − | 0.914579i | \(-0.632522\pi\) | ||||
−0.404407 | + | 0.914579i | \(0.632522\pi\) | |||||||
\(194\) | −0.980925 | −0.0704263 | ||||||||
\(195\) | −1.04095 | −0.0745442 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4011 | 1.45352 | 0.726758 | − | 0.686894i | \(-0.241026\pi\) | ||||
0.726758 | + | 0.686894i | \(0.241026\pi\) | |||||||
\(198\) | −5.24124 | −0.372479 | ||||||||
\(199\) | 1.26866 | 0.0899326 | 0.0449663 | − | 0.998989i | \(-0.485682\pi\) | ||||
0.0449663 | + | 0.998989i | \(0.485682\pi\) | |||||||
\(200\) | 12.8777 | 0.910587 | ||||||||
\(201\) | 0.796475 | 0.0561790 | ||||||||
\(202\) | 5.09767 | 0.358670 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.80442 | −0.266363 | ||||||||
\(205\) | 0.900581 | 0.0628993 | ||||||||
\(206\) | −0.243611 | −0.0169732 | ||||||||
\(207\) | −1.63546 | −0.113672 | ||||||||
\(208\) | −2.22527 | −0.154295 | ||||||||
\(209\) | −3.98750 | −0.275821 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.25243 | −0.155064 | −0.0775320 | − | 0.996990i | \(-0.524704\pi\) | ||||
−0.0775320 | + | 0.996990i | \(0.524704\pi\) | |||||||
\(212\) | 6.03991 | 0.414823 | ||||||||
\(213\) | 10.7265 | 0.734969 | ||||||||
\(214\) | 8.98874 | 0.614458 | ||||||||
\(215\) | 2.71425 | 0.185110 | ||||||||
\(216\) | −3.07419 | −0.209172 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.3189 | 1.17298 | ||||||||
\(219\) | 1.76040 | 0.118957 | ||||||||
\(220\) | −3.18569 | −0.214779 | ||||||||
\(221\) | 5.83588 | 0.392564 | ||||||||
\(222\) | 3.45997 | 0.232218 | ||||||||
\(223\) | 4.43952 | 0.297292 | 0.148646 | − | 0.988890i | \(-0.452509\pi\) | ||||
0.148646 | + | 0.988890i | \(0.452509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.18895 | −0.279264 | ||||||||
\(226\) | 17.9259 | 1.19241 | ||||||||
\(227\) | −20.3906 | −1.35337 | −0.676686 | − | 0.736271i | \(-0.736585\pi\) | ||||
−0.676686 | + | 0.736271i | \(0.736585\pi\) | |||||||
\(228\) | −0.640030 | −0.0423870 | ||||||||
\(229\) | 20.3158 | 1.34251 | 0.671254 | − | 0.741227i | \(-0.265756\pi\) | ||||
0.671254 | + | 0.741227i | \(0.265756\pi\) | |||||||
\(230\) | 1.64439 | 0.108428 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.5125 | −1.60932 | ||||||||
\(233\) | 19.5481 | 1.28064 | 0.640319 | − | 0.768109i | \(-0.278802\pi\) | ||||
0.640319 | + | 0.768109i | \(0.278802\pi\) | |||||||
\(234\) | 1.29048 | 0.0843616 | ||||||||
\(235\) | 7.33379 | 0.478404 | ||||||||
\(236\) | 1.95998 | 0.127584 | ||||||||
\(237\) | 13.8908 | 0.902303 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.84235 | −0.183856 | −0.0919280 | − | 0.995766i | \(-0.529303\pi\) | ||||
−0.0919280 | + | 0.995766i | \(0.529303\pi\) | |||||||
\(240\) | 1.73379 | 0.111916 | ||||||||
\(241\) | −27.2252 | −1.75373 | −0.876866 | − | 0.480735i | \(-0.840370\pi\) | ||||
−0.876866 | + | 0.480735i | \(0.840370\pi\) | |||||||
\(242\) | 12.3240 | 0.792217 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.51181 | 0.352857 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.11646 | −0.0711830 | ||||||||
\(247\) | 0.981790 | 0.0624698 | ||||||||
\(248\) | −9.04668 | −0.574465 | ||||||||
\(249\) | 10.3080 | 0.653243 | ||||||||
\(250\) | 9.23917 | 0.584336 | ||||||||
\(251\) | 0.890691 | 0.0562199 | 0.0281100 | − | 0.999605i | \(-0.491051\pi\) | ||||
0.0281100 | + | 0.999605i | \(0.491051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.67767 | 0.482691 | ||||||||
\(254\) | 10.1477 | 0.636723 | ||||||||
\(255\) | −4.54695 | −0.284741 | ||||||||
\(256\) | −15.1949 | −0.949684 | ||||||||
\(257\) | −15.0505 | −0.938822 | −0.469411 | − | 0.882980i | \(-0.655534\pi\) | ||||
−0.469411 | + | 0.882980i | \(0.655534\pi\) | |||||||
\(258\) | −3.36490 | −0.209489 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.784371 | 0.0486447 | ||||||||
\(261\) | 7.97364 | 0.493556 | ||||||||
\(262\) | 22.8625 | 1.41245 | ||||||||
\(263\) | −6.76685 | −0.417262 | −0.208631 | − | 0.977994i | \(-0.566901\pi\) | ||||
−0.208631 | + | 0.977994i | \(0.566901\pi\) | |||||||
\(264\) | 14.4318 | 0.888218 | ||||||||
\(265\) | 7.21877 | 0.443445 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.1741 | 0.928643 | ||||||||
\(268\) | −0.600153 | −0.0366602 | ||||||||
\(269\) | −20.7195 | −1.26329 | −0.631646 | − | 0.775257i | \(-0.717620\pi\) | ||||
−0.631646 | + | 0.775257i | \(0.717620\pi\) | |||||||
\(270\) | −1.00546 | −0.0611906 | ||||||||
\(271\) | −2.59986 | −0.157930 | −0.0789651 | − | 0.996877i | \(-0.525162\pi\) | ||||
−0.0789651 | + | 0.996877i | \(0.525162\pi\) | |||||||
\(272\) | −9.72014 | −0.589370 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.2730 | 1.40597 | ||||||||
\(275\) | 19.6651 | 1.18585 | ||||||||
\(276\) | 1.23234 | 0.0741780 | ||||||||
\(277\) | 17.8530 | 1.07268 | 0.536342 | − | 0.844000i | \(-0.319806\pi\) | ||||
0.536342 | + | 0.844000i | \(0.319806\pi\) | |||||||
\(278\) | −0.193305 | −0.0115937 | ||||||||
\(279\) | 2.94278 | 0.176180 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0898344 | 0.00535907 | 0.00267954 | − | 0.999996i | \(-0.499147\pi\) | ||||
0.00267954 | + | 0.999996i | \(0.499147\pi\) | |||||||
\(282\) | −9.09180 | −0.541409 | ||||||||
\(283\) | −14.7404 | −0.876226 | −0.438113 | − | 0.898920i | \(-0.644353\pi\) | ||||
−0.438113 | + | 0.898920i | \(0.644353\pi\) | |||||||
\(284\) | −8.08256 | −0.479612 | ||||||||
\(285\) | −0.764949 | −0.0453117 | ||||||||
\(286\) | −6.05819 | −0.358229 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.99898 | 0.235642 | ||||||||
\(289\) | 8.49152 | 0.499501 | ||||||||
\(290\) | −8.01721 | −0.470787 | ||||||||
\(291\) | −0.878601 | −0.0515045 | ||||||||
\(292\) | −1.32649 | −0.0776267 | ||||||||
\(293\) | 6.71475 | 0.392280 | 0.196140 | − | 0.980576i | \(-0.437159\pi\) | ||||
0.196140 | + | 0.980576i | \(0.437159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34252 | 0.136387 | ||||||||
\(296\) | −9.52707 | −0.553750 | ||||||||
\(297\) | −4.69451 | −0.272403 | ||||||||
\(298\) | 1.16603 | 0.0675465 | ||||||||
\(299\) | −1.89038 | −0.109323 | ||||||||
\(300\) | 3.15643 | 0.182236 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.3476 | −0.768069 | ||||||||
\(303\) | 4.56591 | 0.262305 | ||||||||
\(304\) | −1.63525 | −0.0937881 | ||||||||
\(305\) | 6.58758 | 0.377204 | ||||||||
\(306\) | 5.63692 | 0.322241 | ||||||||
\(307\) | 2.35297 | 0.134291 | 0.0671455 | − | 0.997743i | \(-0.478611\pi\) | ||||
0.0671455 | + | 0.997743i | \(0.478611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.218199 | −0.0124129 | ||||||||
\(310\) | −2.95886 | −0.168052 | ||||||||
\(311\) | −24.4048 | −1.38387 | −0.691934 | − | 0.721961i | \(-0.743241\pi\) | ||||
−0.691934 | + | 0.721961i | \(0.743241\pi\) | |||||||
\(312\) | −3.55336 | −0.201170 | ||||||||
\(313\) | −8.88540 | −0.502232 | −0.251116 | − | 0.967957i | \(-0.580798\pi\) | ||||
−0.251116 | + | 0.967957i | \(0.580798\pi\) | |||||||
\(314\) | −4.67618 | −0.263892 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.4669 | −0.588808 | ||||||||
\(317\) | −0.0289702 | −0.00162713 | −0.000813564 | − | 1.00000i | \(-0.500259\pi\) | ||||
−0.000813564 | 1.00000i | \(0.500259\pi\) | ||||||||
\(318\) | −8.94920 | −0.501846 | ||||||||
\(319\) | −37.4323 | −2.09581 | ||||||||
\(320\) | −7.48842 | −0.418615 | ||||||||
\(321\) | 8.05109 | 0.449368 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.28852 | 0.238620 | ||||||||
\(324\) | −0.753512 | −0.0418618 | ||||||||
\(325\) | −4.84188 | −0.268579 | ||||||||
\(326\) | 12.1516 | 0.673012 | ||||||||
\(327\) | 15.5123 | 0.857832 | ||||||||
\(328\) | 3.07419 | 0.169744 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.72016 | 0.259836 | ||||||||
\(331\) | 7.32795 | 0.402780 | 0.201390 | − | 0.979511i | \(-0.435454\pi\) | ||||
0.201390 | + | 0.979511i | \(0.435454\pi\) | |||||||
\(332\) | −7.76720 | −0.426281 | ||||||||
\(333\) | 3.09905 | 0.169827 | ||||||||
\(334\) | 14.2853 | 0.781658 | ||||||||
\(335\) | −0.717290 | −0.0391897 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.0551 | 1.90957 | 0.954785 | − | 0.297296i | \(-0.0960847\pi\) | ||||
0.954785 | + | 0.297296i | \(0.0960847\pi\) | |||||||
\(338\) | −13.0224 | −0.708324 | ||||||||
\(339\) | 16.0560 | 0.872042 | ||||||||
\(340\) | 3.42619 | 0.185811 | ||||||||
\(341\) | −13.8149 | −0.748120 | ||||||||
\(342\) | 0.948318 | 0.0512791 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.26528 | 0.499550 | ||||||||
\(345\) | 1.47286 | 0.0792962 | ||||||||
\(346\) | 5.66067 | 0.304319 | ||||||||
\(347\) | −22.7234 | −1.21986 | −0.609929 | − | 0.792456i | \(-0.708802\pi\) | ||||
−0.609929 | + | 0.792456i | \(0.708802\pi\) | |||||||
\(348\) | −6.00823 | −0.322075 | ||||||||
\(349\) | 7.64444 | 0.409197 | 0.204599 | − | 0.978846i | \(-0.434411\pi\) | ||||
0.204599 | + | 0.978846i | \(0.434411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.15587 | 0.0616957 | ||||||||
\(352\) | −18.7732 | −1.00062 | ||||||||
\(353\) | −0.643130 | −0.0342303 | −0.0171152 | − | 0.999854i | \(-0.505448\pi\) | ||||
−0.0171152 | + | 0.999854i | \(0.505448\pi\) | |||||||
\(354\) | −2.90406 | −0.154349 | ||||||||
\(355\) | −9.66009 | −0.512704 | ||||||||
\(356\) | −11.4339 | −0.605996 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.54540 | 0.134529 | ||||||||
\(359\) | −28.7366 | −1.51666 | −0.758330 | − | 0.651871i | \(-0.773984\pi\) | ||||
−0.758330 | + | 0.651871i | \(0.773984\pi\) | |||||||
\(360\) | 2.76856 | 0.145916 | ||||||||
\(361\) | −18.2785 | −0.962028 | ||||||||
\(362\) | −9.62509 | −0.505883 | ||||||||
\(363\) | 11.0384 | 0.579368 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.58539 | −0.0829829 | ||||||||
\(366\) | −8.16672 | −0.426881 | ||||||||
\(367\) | 5.33033 | 0.278241 | 0.139120 | − | 0.990275i | \(-0.455573\pi\) | ||||
0.139120 | + | 0.990275i | \(0.455573\pi\) | |||||||
\(368\) | 3.14857 | 0.164131 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −3.11598 | −0.161992 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.21742 | −0.114968 | ||||||||
\(373\) | 9.39088 | 0.486241 | 0.243121 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243121 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(374\) | −26.4626 | −1.36835 | ||||||||
\(375\) | 8.27540 | 0.427340 | ||||||||
\(376\) | 25.0344 | 1.29105 | ||||||||
\(377\) | 9.21648 | 0.474673 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.32747 | −0.273654 | −0.136827 | − | 0.990595i | \(-0.543690\pi\) | ||||
−0.136827 | + | 0.990595i | \(0.543690\pi\) | |||||||
\(380\) | 0.576398 | 0.0295686 | ||||||||
\(381\) | 9.08915 | 0.465651 | ||||||||
\(382\) | −23.6803 | −1.21159 | ||||||||
\(383\) | −10.5597 | −0.539575 | −0.269788 | − | 0.962920i | \(-0.586953\pi\) | ||||
−0.269788 | + | 0.962920i | \(0.586953\pi\) | |||||||
\(384\) | 1.28554 | 0.0656022 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.5450 | −0.638525 | ||||||||
\(387\) | −3.01389 | −0.153205 | ||||||||
\(388\) | 0.662037 | 0.0336098 | ||||||||
\(389\) | 30.7591 | 1.55955 | 0.779775 | − | 0.626060i | \(-0.215333\pi\) | ||||
0.779775 | + | 0.626060i | \(0.215333\pi\) | |||||||
\(390\) | −1.16219 | −0.0588495 | ||||||||
\(391\) | −8.25728 | −0.417589 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.4776 | 1.03296 | ||||||||
\(394\) | 22.7770 | 1.14749 | ||||||||
\(395\) | −12.5098 | −0.629435 | ||||||||
\(396\) | 3.53737 | 0.177760 | ||||||||
\(397\) | −23.3508 | −1.17194 | −0.585972 | − | 0.810331i | \(-0.699287\pi\) | ||||
−0.585972 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(398\) | 1.41641 | 0.0709980 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.06455 | 0.403228 | ||||||||
\(401\) | 12.0188 | 0.600190 | 0.300095 | − | 0.953909i | \(-0.402982\pi\) | ||||
0.300095 | + | 0.953909i | \(0.402982\pi\) | |||||||
\(402\) | 0.889234 | 0.0443509 | ||||||||
\(403\) | 3.40147 | 0.169439 | ||||||||
\(404\) | −3.44047 | −0.171170 | ||||||||
\(405\) | −0.900581 | −0.0447502 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.5485 | −0.721143 | ||||||||
\(408\) | −15.5213 | −0.768420 | ||||||||
\(409\) | −2.07020 | −0.102365 | −0.0511825 | − | 0.998689i | \(-0.516299\pi\) | ||||
−0.0511825 | + | 0.998689i | \(0.516299\pi\) | |||||||
\(410\) | 1.00546 | 0.0496563 | ||||||||
\(411\) | 20.8453 | 1.02822 | ||||||||
\(412\) | 0.164416 | 0.00810018 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.82593 | −0.0897394 | ||||||||
\(415\) | −9.28318 | −0.455693 | ||||||||
\(416\) | 4.62230 | 0.226627 | ||||||||
\(417\) | −0.173141 | −0.00847873 | ||||||||
\(418\) | −4.45189 | −0.217749 | ||||||||
\(419\) | −37.9166 | −1.85235 | −0.926173 | − | 0.377099i | \(-0.876922\pi\) | ||||
−0.926173 | + | 0.377099i | \(0.876922\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.80911 | −0.478067 | −0.239033 | − | 0.971011i | \(-0.576831\pi\) | ||||
−0.239033 | + | 0.971011i | \(0.576831\pi\) | |||||||
\(422\) | −2.51476 | −0.122416 | ||||||||
\(423\) | −8.14340 | −0.395946 | ||||||||
\(424\) | 24.6417 | 1.19671 | ||||||||
\(425\) | −21.1497 | −1.02591 | ||||||||
\(426\) | 11.9757 | 0.580227 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.06660 | −0.293240 | ||||||||
\(429\) | −5.42624 | −0.261981 | ||||||||
\(430\) | 3.03036 | 0.146137 | ||||||||
\(431\) | −32.4424 | −1.56270 | −0.781348 | − | 0.624096i | \(-0.785467\pi\) | ||||
−0.781348 | + | 0.624096i | \(0.785467\pi\) | |||||||
\(432\) | −1.92519 | −0.0926260 | ||||||||
\(433\) | −34.9870 | −1.68137 | −0.840683 | − | 0.541527i | \(-0.817846\pi\) | ||||
−0.840683 | + | 0.541527i | \(0.817846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.18090 | −0.344298 | ||||||||
\(436\) | −11.6887 | −0.559788 | ||||||||
\(437\) | −1.38915 | −0.0664521 | ||||||||
\(438\) | 1.96542 | 0.0939116 | ||||||||
\(439\) | 20.0625 | 0.957530 | 0.478765 | − | 0.877943i | \(-0.341085\pi\) | ||||
0.478765 | + | 0.877943i | \(0.341085\pi\) | |||||||
\(440\) | −12.9970 | −0.619609 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.51554 | 0.309913 | ||||||||
\(443\) | −12.7373 | −0.605165 | −0.302583 | − | 0.953123i | \(-0.597849\pi\) | ||||
−0.302583 | + | 0.953123i | \(0.597849\pi\) | |||||||
\(444\) | −2.33517 | −0.110822 | ||||||||
\(445\) | −13.6655 | −0.647809 | ||||||||
\(446\) | 4.95655 | 0.234699 | ||||||||
\(447\) | 1.04440 | 0.0493985 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.5999 | 0.972170 | 0.486085 | − | 0.873912i | \(-0.338425\pi\) | ||||
0.486085 | + | 0.873912i | \(0.338425\pi\) | |||||||
\(450\) | −4.67681 | −0.220467 | ||||||||
\(451\) | 4.69451 | 0.221056 | ||||||||
\(452\) | −12.0984 | −0.569061 | ||||||||
\(453\) | −11.9553 | −0.561708 | ||||||||
\(454\) | −22.7653 | −1.06843 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.61120 | −0.122281 | ||||||||
\(457\) | 7.53127 | 0.352298 | 0.176149 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176149 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(458\) | 22.6819 | 1.05985 | ||||||||
\(459\) | 5.04891 | 0.235663 | ||||||||
\(460\) | −1.10982 | −0.0517456 | ||||||||
\(461\) | 14.5150 | 0.676032 | 0.338016 | − | 0.941140i | \(-0.390244\pi\) | ||||
0.338016 | + | 0.941140i | \(0.390244\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.59229 | −0.0739998 | −0.0369999 | − | 0.999315i | \(-0.511780\pi\) | ||||
−0.0369999 | + | 0.999315i | \(0.511780\pi\) | |||||||
\(464\) | −15.3508 | −0.712643 | ||||||||
\(465\) | −2.65021 | −0.122901 | ||||||||
\(466\) | 21.8247 | 1.01101 | ||||||||
\(467\) | 33.8659 | 1.56713 | 0.783565 | − | 0.621310i | \(-0.213399\pi\) | ||||
0.783565 | + | 0.621310i | \(0.213399\pi\) | |||||||
\(468\) | −0.870962 | −0.0402602 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.18790 | 0.377679 | ||||||||
\(471\) | −4.18839 | −0.192991 | ||||||||
\(472\) | 7.99636 | 0.368062 | ||||||||
\(473\) | 14.1487 | 0.650560 | ||||||||
\(474\) | 15.5085 | 0.712330 | ||||||||
\(475\) | −3.55808 | −0.163256 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.01568 | −0.367013 | ||||||||
\(478\) | −3.17337 | −0.145147 | ||||||||
\(479\) | −9.40167 | −0.429573 | −0.214787 | − | 0.976661i | \(-0.568906\pi\) | ||||
−0.214787 | + | 0.976661i | \(0.568906\pi\) | |||||||
\(480\) | −3.60140 | −0.164381 | ||||||||
\(481\) | 3.58209 | 0.163329 | ||||||||
\(482\) | −30.3960 | −1.38450 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.31760 | −0.378073 | ||||||||
\(485\) | 0.791251 | 0.0359289 | ||||||||
\(486\) | 1.11646 | 0.0506438 | ||||||||
\(487\) | 24.6937 | 1.11898 | 0.559488 | − | 0.828838i | \(-0.310998\pi\) | ||||
0.559488 | + | 0.828838i | \(0.310998\pi\) | |||||||
\(488\) | 22.4872 | 1.01795 | ||||||||
\(489\) | 10.8840 | 0.492191 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.9667 | 1.57802 | 0.789012 | − | 0.614378i | \(-0.210593\pi\) | ||||
0.789012 | + | 0.614378i | \(0.210593\pi\) | |||||||
\(492\) | 0.753512 | 0.0339710 | ||||||||
\(493\) | 40.2582 | 1.81314 | ||||||||
\(494\) | 1.09613 | 0.0493173 | ||||||||
\(495\) | 4.22779 | 0.190025 | ||||||||
\(496\) | −5.66543 | −0.254385 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.5085 | 0.515708 | ||||||||
\(499\) | 18.5443 | 0.830155 | 0.415077 | − | 0.909786i | \(-0.363755\pi\) | ||||
0.415077 | + | 0.909786i | \(0.363755\pi\) | |||||||
\(500\) | −6.23561 | −0.278865 | ||||||||
\(501\) | 12.7952 | 0.571646 | ||||||||
\(502\) | 0.994423 | 0.0443833 | ||||||||
\(503\) | 33.0348 | 1.47295 | 0.736473 | − | 0.676466i | \(-0.236490\pi\) | ||||
0.736473 | + | 0.676466i | \(0.236490\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.11197 | −0.182980 | ||||||||
\(506\) | 8.57183 | 0.381064 | ||||||||
\(507\) | −11.6640 | −0.518015 | ||||||||
\(508\) | −6.84879 | −0.303866 | ||||||||
\(509\) | 21.5526 | 0.955302 | 0.477651 | − | 0.878550i | \(-0.341488\pi\) | ||||
0.477651 | + | 0.878550i | \(0.341488\pi\) | |||||||
\(510\) | −5.07650 | −0.224791 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.5356 | −0.863362 | ||||||||
\(513\) | 0.849395 | 0.0375017 | ||||||||
\(514\) | −16.8033 | −0.741161 | ||||||||
\(515\) | 0.196506 | 0.00865908 | ||||||||
\(516\) | 2.27100 | 0.0999754 | ||||||||
\(517\) | 38.2293 | 1.68132 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.07018 | 0.222556 | ||||||||
\(520\) | 3.20009 | 0.140333 | ||||||||
\(521\) | 36.0597 | 1.57981 | 0.789903 | − | 0.613232i | \(-0.210131\pi\) | ||||
0.789903 | + | 0.613232i | \(0.210131\pi\) | |||||||
\(522\) | 8.90226 | 0.389642 | ||||||||
\(523\) | 2.02031 | 0.0883421 | 0.0441710 | − | 0.999024i | \(-0.485935\pi\) | ||||
0.0441710 | + | 0.999024i | \(0.485935\pi\) | |||||||
\(524\) | −15.4302 | −0.674069 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.55494 | −0.329411 | ||||||||
\(527\) | 14.8579 | 0.647218 | ||||||||
\(528\) | 9.03785 | 0.393322 | ||||||||
\(529\) | −20.3253 | −0.883708 | ||||||||
\(530\) | 8.05948 | 0.350081 | ||||||||
\(531\) | −2.60113 | −0.112879 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.15587 | −0.0500663 | ||||||||
\(534\) | 16.9414 | 0.733124 | ||||||||
\(535\) | −7.25066 | −0.313473 | ||||||||
\(536\) | −2.44852 | −0.105760 | ||||||||
\(537\) | 2.27988 | 0.0983842 | ||||||||
\(538\) | −23.1326 | −0.997316 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.678599 | 0.0292022 | ||||||||
\(541\) | 28.2526 | 1.21467 | 0.607337 | − | 0.794444i | \(-0.292238\pi\) | ||||
0.607337 | + | 0.794444i | \(0.292238\pi\) | |||||||
\(542\) | −2.90264 | −0.124679 | ||||||||
\(543\) | −8.62106 | −0.369965 | ||||||||
\(544\) | 20.1905 | 0.865660 | ||||||||
\(545\) | −13.9701 | −0.598413 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.6219 | −1.56584 | −0.782919 | − | 0.622123i | \(-0.786270\pi\) | ||||
−0.782919 | + | 0.622123i | \(0.786270\pi\) | |||||||
\(548\) | −15.7072 | −0.670978 | ||||||||
\(549\) | −7.31482 | −0.312189 | ||||||||
\(550\) | 21.9553 | 0.936179 | ||||||||
\(551\) | 6.77277 | 0.288530 | ||||||||
\(552\) | 5.02771 | 0.213994 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19.9322 | 0.846840 | ||||||||
\(555\) | −2.79094 | −0.118469 | ||||||||
\(556\) | 0.130464 | 0.00553289 | ||||||||
\(557\) | −38.9992 | −1.65245 | −0.826224 | − | 0.563342i | \(-0.809515\pi\) | ||||
−0.826224 | + | 0.563342i | \(0.809515\pi\) | |||||||
\(558\) | 3.28551 | 0.139087 | ||||||||
\(559\) | −3.48366 | −0.147343 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.7022 | −1.00071 | ||||||||
\(562\) | 0.100297 | 0.00423076 | ||||||||
\(563\) | 27.9805 | 1.17924 | 0.589619 | − | 0.807682i | \(-0.299278\pi\) | ||||
0.589619 | + | 0.807682i | \(0.299278\pi\) | |||||||
\(564\) | 6.13615 | 0.258379 | ||||||||
\(565\) | −14.4597 | −0.608325 | ||||||||
\(566\) | −16.4571 | −0.691744 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −32.9754 | −1.38362 | ||||||||
\(569\) | 9.11873 | 0.382277 | 0.191139 | − | 0.981563i | \(-0.438782\pi\) | ||||
0.191139 | + | 0.981563i | \(0.438782\pi\) | |||||||
\(570\) | −0.854037 | −0.0357717 | ||||||||
\(571\) | 21.4215 | 0.896460 | 0.448230 | − | 0.893918i | \(-0.352055\pi\) | ||||
0.448230 | + | 0.893918i | \(0.352055\pi\) | |||||||
\(572\) | 4.08874 | 0.170959 | ||||||||
\(573\) | −21.2101 | −0.886066 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.85086 | 0.285700 | ||||||||
\(576\) | 8.31510 | 0.346462 | ||||||||
\(577\) | −31.0255 | −1.29161 | −0.645805 | − | 0.763502i | \(-0.723478\pi\) | ||||
−0.645805 | + | 0.763502i | \(0.723478\pi\) | |||||||
\(578\) | 9.48047 | 0.394335 | ||||||||
\(579\) | −11.2364 | −0.466969 | ||||||||
\(580\) | 5.41090 | 0.224675 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.980925 | −0.0406606 | ||||||||
\(583\) | 37.6297 | 1.55846 | ||||||||
\(584\) | −5.41182 | −0.223943 | ||||||||
\(585\) | −1.04095 | −0.0430381 | ||||||||
\(586\) | 7.49677 | 0.309689 | ||||||||
\(587\) | −2.11563 | −0.0873215 | −0.0436608 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436608 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.49959 | 0.102994 | ||||||||
\(590\) | 2.61534 | 0.107672 | ||||||||
\(591\) | 20.4011 | 0.839187 | ||||||||
\(592\) | −5.96627 | −0.245212 | ||||||||
\(593\) | 3.84915 | 0.158066 | 0.0790328 | − | 0.996872i | \(-0.474817\pi\) | ||||
0.0790328 | + | 0.996872i | \(0.474817\pi\) | |||||||
\(594\) | −5.24124 | −0.215051 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.786969 | −0.0322355 | ||||||||
\(597\) | 1.26866 | 0.0519226 | ||||||||
\(598\) | −2.11053 | −0.0863061 | ||||||||
\(599\) | 13.0766 | 0.534297 | 0.267148 | − | 0.963655i | \(-0.413919\pi\) | ||||
0.267148 | + | 0.963655i | \(0.413919\pi\) | |||||||
\(600\) | 12.8777 | 0.525728 | ||||||||
\(601\) | 37.2633 | 1.52000 | 0.760001 | − | 0.649922i | \(-0.225199\pi\) | ||||
0.760001 | + | 0.649922i | \(0.225199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.796475 | 0.0324350 | ||||||||
\(604\) | 9.00845 | 0.366549 | ||||||||
\(605\) | −9.94100 | −0.404159 | ||||||||
\(606\) | 5.09767 | 0.207078 | ||||||||
\(607\) | 6.25992 | 0.254082 | 0.127041 | − | 0.991897i | \(-0.459452\pi\) | ||||
0.127041 | + | 0.991897i | \(0.459452\pi\) | |||||||
\(608\) | 3.39671 | 0.137755 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.35479 | 0.297787 | ||||||||
\(611\) | −9.41270 | −0.380797 | ||||||||
\(612\) | −3.80442 | −0.153784 | ||||||||
\(613\) | 9.94899 | 0.401836 | 0.200918 | − | 0.979608i | \(-0.435608\pi\) | ||||
0.200918 | + | 0.979608i | \(0.435608\pi\) | |||||||
\(614\) | 2.62700 | 0.106017 | ||||||||
\(615\) | 0.900581 | 0.0363149 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.0271 | 0.524452 | 0.262226 | − | 0.965007i | \(-0.415543\pi\) | ||||
0.262226 | + | 0.965007i | \(0.415543\pi\) | |||||||
\(618\) | −0.243611 | −0.00979947 | ||||||||
\(619\) | −23.8933 | −0.960354 | −0.480177 | − | 0.877172i | \(-0.659428\pi\) | ||||
−0.480177 | + | 0.877172i | \(0.659428\pi\) | |||||||
\(620\) | 1.99697 | 0.0802002 | ||||||||
\(621\) | −1.63546 | −0.0656286 | ||||||||
\(622\) | −27.2470 | −1.09251 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.22527 | −0.0890822 | ||||||||
\(625\) | 13.4921 | 0.539684 | ||||||||
\(626\) | −9.92021 | −0.396491 | ||||||||
\(627\) | −3.98750 | −0.159245 | ||||||||
\(628\) | 3.15601 | 0.125938 | ||||||||
\(629\) | 15.6468 | 0.623880 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.1911 | −1.08246 | −0.541230 | − | 0.840875i | \(-0.682041\pi\) | ||||
−0.541230 | + | 0.840875i | \(0.682041\pi\) | |||||||
\(632\) | −42.7029 | −1.69863 | ||||||||
\(633\) | −2.25243 | −0.0895262 | ||||||||
\(634\) | −0.0323441 | −0.00128455 | ||||||||
\(635\) | −8.18552 | −0.324832 | ||||||||
\(636\) | 6.03991 | 0.239498 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −41.7918 | −1.65455 | ||||||||
\(639\) | 10.7265 | 0.424334 | ||||||||
\(640\) | −1.15773 | −0.0457632 | ||||||||
\(641\) | −9.85980 | −0.389439 | −0.194719 | − | 0.980859i | \(-0.562380\pi\) | ||||
−0.194719 | + | 0.980859i | \(0.562380\pi\) | |||||||
\(642\) | 8.98874 | 0.354757 | ||||||||
\(643\) | −15.5002 | −0.611270 | −0.305635 | − | 0.952149i | \(-0.598869\pi\) | ||||
−0.305635 | + | 0.952149i | \(0.598869\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.71425 | 0.106874 | ||||||||
\(646\) | 4.78797 | 0.188380 | ||||||||
\(647\) | −39.1567 | −1.53941 | −0.769705 | − | 0.638400i | \(-0.779596\pi\) | ||||
−0.769705 | + | 0.638400i | \(0.779596\pi\) | |||||||
\(648\) | −3.07419 | −0.120766 | ||||||||
\(649\) | 12.2110 | 0.479324 | ||||||||
\(650\) | −5.40578 | −0.212032 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.20122 | −0.321184 | ||||||||
\(653\) | −29.5384 | −1.15593 | −0.577964 | − | 0.816062i | \(-0.696153\pi\) | ||||
−0.577964 | + | 0.816062i | \(0.696153\pi\) | |||||||
\(654\) | 17.3189 | 0.677223 | ||||||||
\(655\) | −18.4418 | −0.720580 | ||||||||
\(656\) | 1.92519 | 0.0751662 | ||||||||
\(657\) | 1.76040 | 0.0686799 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.39226 | −0.365871 | −0.182935 | − | 0.983125i | \(-0.558560\pi\) | ||||
−0.182935 | + | 0.983125i | \(0.558560\pi\) | |||||||
\(660\) | −3.18569 | −0.124003 | ||||||||
\(661\) | −42.1189 | −1.63824 | −0.819118 | − | 0.573625i | \(-0.805537\pi\) | ||||
−0.819118 | + | 0.573625i | \(0.805537\pi\) | |||||||
\(662\) | 8.18137 | 0.317978 | ||||||||
\(663\) | 5.83588 | 0.226647 | ||||||||
\(664\) | −31.6888 | −1.22976 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.45997 | 0.134071 | ||||||||
\(667\) | −13.0405 | −0.504932 | ||||||||
\(668\) | −9.64132 | −0.373034 | ||||||||
\(669\) | 4.43952 | 0.171642 | ||||||||
\(670\) | −0.800827 | −0.0309386 | ||||||||
\(671\) | 34.3395 | 1.32566 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.92211 | −0.112639 | −0.0563195 | − | 0.998413i | \(-0.517937\pi\) | ||||
−0.0563195 | + | 0.998413i | \(0.517937\pi\) | |||||||
\(674\) | 39.1377 | 1.50753 | ||||||||
\(675\) | −4.18895 | −0.161233 | ||||||||
\(676\) | 8.78894 | 0.338036 | ||||||||
\(677\) | 36.7706 | 1.41321 | 0.706604 | − | 0.707609i | \(-0.250226\pi\) | ||||
0.706604 | + | 0.707609i | \(0.250226\pi\) | |||||||
\(678\) | 17.9259 | 0.688441 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.9782 | 0.536040 | ||||||||
\(681\) | −20.3906 | −0.781370 | ||||||||
\(682\) | −15.4238 | −0.590609 | ||||||||
\(683\) | −8.03451 | −0.307432 | −0.153716 | − | 0.988115i | \(-0.549124\pi\) | ||||
−0.153716 | + | 0.988115i | \(0.549124\pi\) | |||||||
\(684\) | −0.640030 | −0.0244721 | ||||||||
\(685\) | −18.7729 | −0.717275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.3158 | 0.775098 | ||||||||
\(688\) | 5.80233 | 0.221212 | ||||||||
\(689\) | −9.26508 | −0.352971 | ||||||||
\(690\) | 1.64439 | 0.0626010 | ||||||||
\(691\) | 6.60782 | 0.251373 | 0.125687 | − | 0.992070i | \(-0.459887\pi\) | ||||
0.125687 | + | 0.992070i | \(0.459887\pi\) | |||||||
\(692\) | −3.82045 | −0.145232 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.3699 | −0.963027 | ||||||||
\(695\) | 0.155927 | 0.00591465 | ||||||||
\(696\) | −24.5125 | −0.929144 | ||||||||
\(697\) | −5.04891 | −0.191241 | ||||||||
\(698\) | 8.53473 | 0.323044 | ||||||||
\(699\) | 19.5481 | 0.739377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.0961 | 0.419094 | 0.209547 | − | 0.977799i | \(-0.432801\pi\) | ||||
0.209547 | + | 0.977799i | \(0.432801\pi\) | |||||||
\(702\) | 1.29048 | 0.0487062 | ||||||||
\(703\) | 2.63232 | 0.0992797 | ||||||||
\(704\) | −39.0353 | −1.47120 | ||||||||
\(705\) | 7.33379 | 0.276206 | ||||||||
\(706\) | −0.718030 | −0.0270234 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.95998 | 0.0736606 | ||||||||
\(709\) | 8.02154 | 0.301255 | 0.150628 | − | 0.988591i | \(-0.451871\pi\) | ||||
0.150628 | + | 0.988591i | \(0.451871\pi\) | |||||||
\(710\) | −10.7851 | −0.404759 | ||||||||
\(711\) | 13.8908 | 0.520945 | ||||||||
\(712\) | −46.6482 | −1.74822 | ||||||||
\(713\) | −4.81280 | −0.180241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.88677 | 0.182755 | ||||||||
\(716\) | −1.71792 | −0.0642017 | ||||||||
\(717\) | −2.84235 | −0.106149 | ||||||||
\(718\) | −32.0833 | −1.19734 | ||||||||
\(719\) | −26.9116 | −1.00363 | −0.501816 | − | 0.864974i | \(-0.667335\pi\) | ||||
−0.501816 | + | 0.864974i | \(0.667335\pi\) | |||||||
\(720\) | 1.73379 | 0.0646147 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −20.4073 | −0.759480 | ||||||||
\(723\) | −27.2252 | −1.01252 | ||||||||
\(724\) | 6.49608 | 0.241425 | ||||||||
\(725\) | −33.4012 | −1.24049 | ||||||||
\(726\) | 12.3240 | 0.457386 | ||||||||
\(727\) | 3.40083 | 0.126130 | 0.0630648 | − | 0.998009i | \(-0.479913\pi\) | ||||
0.0630648 | + | 0.998009i | \(0.479913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.77002 | −0.0655115 | ||||||||
\(731\) | −15.2169 | −0.562816 | ||||||||
\(732\) | 5.51181 | 0.203722 | ||||||||
\(733\) | −31.6864 | −1.17036 | −0.585181 | − | 0.810903i | \(-0.698977\pi\) | ||||
−0.585181 | + | 0.810903i | \(0.698977\pi\) | |||||||
\(734\) | 5.95111 | 0.219659 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.54016 | −0.241073 | ||||||||
\(737\) | −3.73906 | −0.137730 | ||||||||
\(738\) | −1.11646 | −0.0410975 | ||||||||
\(739\) | 2.74615 | 0.101019 | 0.0505095 | − | 0.998724i | \(-0.483915\pi\) | ||||
0.0505095 | + | 0.998724i | \(0.483915\pi\) | |||||||
\(740\) | 2.10301 | 0.0773082 | ||||||||
\(741\) | 0.981790 | 0.0360670 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.91699 | 0.290446 | 0.145223 | − | 0.989399i | \(-0.453610\pi\) | ||||
0.145223 | + | 0.989399i | \(0.453610\pi\) | |||||||
\(744\) | −9.04668 | −0.331667 | ||||||||
\(745\) | −0.940567 | −0.0344597 | ||||||||
\(746\) | 10.4846 | 0.383867 | ||||||||
\(747\) | 10.3080 | 0.377150 | ||||||||
\(748\) | 17.8599 | 0.653022 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.23917 | 0.337367 | ||||||||
\(751\) | −26.8980 | −0.981524 | −0.490762 | − | 0.871294i | \(-0.663281\pi\) | ||||
−0.490762 | + | 0.871294i | \(0.663281\pi\) | |||||||
\(752\) | 15.6776 | 0.571704 | ||||||||
\(753\) | 0.890691 | 0.0324586 | ||||||||
\(754\) | 10.2899 | 0.374734 | ||||||||
\(755\) | 10.7667 | 0.391840 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.1992 | −1.31568 | −0.657842 | − | 0.753156i | \(-0.728530\pi\) | ||||
−0.657842 | + | 0.753156i | \(0.728530\pi\) | |||||||
\(758\) | −5.94792 | −0.216038 | ||||||||
\(759\) | 7.67767 | 0.278682 | ||||||||
\(760\) | 2.35160 | 0.0853015 | ||||||||
\(761\) | 9.07694 | 0.329039 | 0.164519 | − | 0.986374i | \(-0.447393\pi\) | ||||
0.164519 | + | 0.986374i | \(0.447393\pi\) | |||||||
\(762\) | 10.1477 | 0.367612 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15.9821 | 0.578212 | ||||||||
\(765\) | −4.54695 | −0.164395 | ||||||||
\(766\) | −11.7895 | −0.425972 | ||||||||
\(767\) | −3.00656 | −0.108561 | ||||||||
\(768\) | −15.1949 | −0.548300 | ||||||||
\(769\) | −19.5528 | −0.705093 | −0.352547 | − | 0.935794i | \(-0.614684\pi\) | ||||
−0.352547 | + | 0.935794i | \(0.614684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.0505 | −0.542029 | ||||||||
\(772\) | 8.46677 | 0.304726 | ||||||||
\(773\) | 53.8122 | 1.93549 | 0.967746 | − | 0.251928i | \(-0.0810646\pi\) | ||||
0.967746 | + | 0.251928i | \(0.0810646\pi\) | |||||||
\(774\) | −3.36490 | −0.120949 | ||||||||
\(775\) | −12.3272 | −0.442805 | ||||||||
\(776\) | 2.70099 | 0.0969598 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.3414 | 1.23120 | ||||||||
\(779\) | −0.849395 | −0.0304327 | ||||||||
\(780\) | 0.784371 | 0.0280850 | ||||||||
\(781\) | −50.3557 | −1.80187 | ||||||||
\(782\) | −9.21894 | −0.329669 | ||||||||
\(783\) | 7.97364 | 0.284955 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.77199 | 0.134628 | ||||||||
\(786\) | 22.8625 | 0.815479 | ||||||||
\(787\) | 38.1745 | 1.36077 | 0.680387 | − | 0.732853i | \(-0.261812\pi\) | ||||
0.680387 | + | 0.732853i | \(0.261812\pi\) | |||||||
\(788\) | −15.3724 | −0.547621 | ||||||||
\(789\) | −6.76685 | −0.240906 | ||||||||
\(790\) | −13.9667 | −0.496912 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 14.4318 | 0.512813 | ||||||||
\(793\) | −8.45498 | −0.300245 | ||||||||
\(794\) | −26.0703 | −0.925200 | ||||||||
\(795\) | 7.21877 | 0.256023 | ||||||||
\(796\) | −0.955947 | −0.0338827 | ||||||||
\(797\) | −0.638938 | −0.0226323 | −0.0113162 | − | 0.999936i | \(-0.503602\pi\) | ||||
−0.0113162 | + | 0.999936i | \(0.503602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.1153 | −1.45455 | ||||||||
\(800\) | −16.7515 | −0.592256 | ||||||||
\(801\) | 15.1741 | 0.536152 | ||||||||
\(802\) | 13.4185 | 0.473825 | ||||||||
\(803\) | −8.26424 | −0.291639 | ||||||||
\(804\) | −0.600153 | −0.0211658 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.79762 | 0.133765 | ||||||||
\(807\) | −20.7195 | −0.729362 | ||||||||
\(808\) | −14.0365 | −0.493802 | ||||||||
\(809\) | 1.14199 | 0.0401501 | 0.0200750 | − | 0.999798i | \(-0.493609\pi\) | ||||
0.0200750 | + | 0.999798i | \(0.493609\pi\) | |||||||
\(810\) | −1.00546 | −0.0353284 | ||||||||
\(811\) | 1.96493 | 0.0689979 | 0.0344990 | − | 0.999405i | \(-0.489016\pi\) | ||||
0.0344990 | + | 0.999405i | \(0.489016\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.59986 | −0.0911811 | ||||||||
\(814\) | −16.2429 | −0.569312 | ||||||||
\(815\) | −9.80191 | −0.343346 | ||||||||
\(816\) | −9.72014 | −0.340273 | ||||||||
\(817\) | −2.55998 | −0.0895625 | ||||||||
\(818\) | −2.31131 | −0.0808129 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.678599 | −0.0236977 | ||||||||
\(821\) | 7.23373 | 0.252459 | 0.126230 | − | 0.992001i | \(-0.459712\pi\) | ||||
0.126230 | + | 0.992001i | \(0.459712\pi\) | |||||||
\(822\) | 23.2730 | 0.811739 | ||||||||
\(823\) | −16.6287 | −0.579640 | −0.289820 | − | 0.957081i | \(-0.593595\pi\) | ||||
−0.289820 | + | 0.957081i | \(0.593595\pi\) | |||||||
\(824\) | 0.670786 | 0.0233679 | ||||||||
\(825\) | 19.6651 | 0.684651 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.9766 | 0.972842 | 0.486421 | − | 0.873725i | \(-0.338302\pi\) | ||||
0.486421 | + | 0.873725i | \(0.338302\pi\) | |||||||
\(828\) | 1.23234 | 0.0428267 | ||||||||
\(829\) | 22.7571 | 0.790388 | 0.395194 | − | 0.918598i | \(-0.370677\pi\) | ||||
0.395194 | + | 0.918598i | \(0.370677\pi\) | |||||||
\(830\) | −10.3643 | −0.359751 | ||||||||
\(831\) | 17.8530 | 0.619315 | ||||||||
\(832\) | 9.61117 | 0.333207 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.193305 | −0.00669360 | ||||||||
\(835\) | −11.5231 | −0.398773 | ||||||||
\(836\) | 3.00463 | 0.103917 | ||||||||
\(837\) | 2.94278 | 0.101717 | ||||||||
\(838\) | −42.3324 | −1.46235 | ||||||||
\(839\) | 14.9814 | 0.517214 | 0.258607 | − | 0.965983i | \(-0.416737\pi\) | ||||
0.258607 | + | 0.965983i | \(0.416737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.5789 | 1.19238 | ||||||||
\(842\) | −10.9515 | −0.377414 | ||||||||
\(843\) | 0.0898344 | 0.00309406 | ||||||||
\(844\) | 1.69724 | 0.0584213 | ||||||||
\(845\) | 10.5043 | 0.361360 | ||||||||
\(846\) | −9.09180 | −0.312582 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.4317 | 0.529928 | ||||||||
\(849\) | −14.7404 | −0.505890 | ||||||||
\(850\) | −23.6128 | −0.809912 | ||||||||
\(851\) | −5.06836 | −0.173741 | ||||||||
\(852\) | −8.08256 | −0.276904 | ||||||||
\(853\) | −38.1171 | −1.30510 | −0.652552 | − | 0.757744i | \(-0.726301\pi\) | ||||
−0.652552 | + | 0.757744i | \(0.726301\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.764949 | −0.0261607 | ||||||||
\(856\) | −24.7506 | −0.845958 | ||||||||
\(857\) | −29.6584 | −1.01311 | −0.506556 | − | 0.862207i | \(-0.669082\pi\) | ||||
−0.506556 | + | 0.862207i | \(0.669082\pi\) | |||||||
\(858\) | −6.05819 | −0.206823 | ||||||||
\(859\) | 14.7355 | 0.502770 | 0.251385 | − | 0.967887i | \(-0.419114\pi\) | ||||
0.251385 | + | 0.967887i | \(0.419114\pi\) | |||||||
\(860\) | −2.04522 | −0.0697415 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.2207 | −1.23368 | ||||||||
\(863\) | 13.1014 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(864\) | 3.99898 | 0.136048 | ||||||||
\(865\) | −4.56611 | −0.155252 | ||||||||
\(866\) | −39.0616 | −1.32737 | ||||||||
\(867\) | 8.49152 | 0.288387 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −65.2104 | −2.21211 | ||||||||
\(870\) | −8.01721 | −0.271809 | ||||||||
\(871\) | 0.920621 | 0.0311940 | ||||||||
\(872\) | −47.6878 | −1.61491 | ||||||||
\(873\) | −0.878601 | −0.0297361 | ||||||||
\(874\) | −1.55093 | −0.0524611 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.32649 | −0.0448178 | ||||||||
\(877\) | 3.85074 | 0.130030 | 0.0650152 | − | 0.997884i | \(-0.479290\pi\) | ||||
0.0650152 | + | 0.997884i | \(0.479290\pi\) | |||||||
\(878\) | 22.3990 | 0.755930 | ||||||||
\(879\) | 6.71475 | 0.226483 | ||||||||
\(880\) | −8.13931 | −0.274376 | ||||||||
\(881\) | 31.4622 | 1.05999 | 0.529995 | − | 0.848001i | \(-0.322194\pi\) | ||||
0.529995 | + | 0.848001i | \(0.322194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.4706 | −0.688889 | −0.344445 | − | 0.938807i | \(-0.611933\pi\) | ||||
−0.344445 | + | 0.938807i | \(0.611933\pi\) | |||||||
\(884\) | −4.39741 | −0.147901 | ||||||||
\(885\) | 2.34252 | 0.0787431 | ||||||||
\(886\) | −14.2207 | −0.477753 | ||||||||
\(887\) | −21.2614 | −0.713887 | −0.356944 | − | 0.934126i | \(-0.616181\pi\) | ||||
−0.356944 | + | 0.934126i | \(0.616181\pi\) | |||||||
\(888\) | −9.52707 | −0.319707 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −15.2571 | −0.511418 | ||||||||
\(891\) | −4.69451 | −0.157272 | ||||||||
\(892\) | −3.34523 | −0.112007 | ||||||||
\(893\) | −6.91696 | −0.231467 | ||||||||
\(894\) | 1.16603 | 0.0389980 | ||||||||
\(895\) | −2.05322 | −0.0686315 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.89038 | −0.0631178 | ||||||||
\(898\) | 22.9990 | 0.767487 | ||||||||
\(899\) | 23.4647 | 0.782591 | ||||||||
\(900\) | 3.15643 | 0.105214 | ||||||||
\(901\) | −40.4705 | −1.34827 | ||||||||
\(902\) | 5.24124 | 0.174514 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49.3592 | −1.64166 | ||||||||
\(905\) | 7.76396 | 0.258083 | ||||||||
\(906\) | −13.3476 | −0.443445 | ||||||||
\(907\) | 24.4166 | 0.810739 | 0.405370 | − | 0.914153i | \(-0.367143\pi\) | ||||
0.405370 | + | 0.914153i | \(0.367143\pi\) | |||||||
\(908\) | 15.3646 | 0.509891 | ||||||||
\(909\) | 4.56591 | 0.151442 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.2660 | 1.03589 | 0.517944 | − | 0.855415i | \(-0.326698\pi\) | ||||
0.517944 | + | 0.855415i | \(0.326698\pi\) | |||||||
\(912\) | −1.63525 | −0.0541486 | ||||||||
\(913\) | −48.3910 | −1.60151 | ||||||||
\(914\) | 8.40838 | 0.278125 | ||||||||
\(915\) | 6.58758 | 0.217779 | ||||||||
\(916\) | −15.3082 | −0.505798 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.63692 | 0.186046 | ||||||||
\(919\) | 53.3081 | 1.75847 | 0.879237 | − | 0.476385i | \(-0.158053\pi\) | ||||
0.879237 | + | 0.476385i | \(0.158053\pi\) | |||||||
\(920\) | −4.52786 | −0.149279 | ||||||||
\(921\) | 2.35297 | 0.0775330 | ||||||||
\(922\) | 16.2055 | 0.533699 | ||||||||
\(923\) | 12.3984 | 0.408100 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.9818 | −0.426838 | ||||||||
\(926\) | −1.77773 | −0.0584197 | ||||||||
\(927\) | −0.218199 | −0.00716660 | ||||||||
\(928\) | 31.8864 | 1.04672 | ||||||||
\(929\) | 43.0707 | 1.41310 | 0.706552 | − | 0.707662i | \(-0.250250\pi\) | ||||
0.706552 | + | 0.707662i | \(0.250250\pi\) | |||||||
\(930\) | −2.95886 | −0.0970249 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.7297 | −0.482489 | ||||||||
\(933\) | −24.4048 | −0.798977 | ||||||||
\(934\) | 37.8100 | 1.23718 | ||||||||
\(935\) | 21.3457 | 0.698080 | ||||||||
\(936\) | −3.55336 | −0.116145 | ||||||||
\(937\) | −35.0260 | −1.14425 | −0.572125 | − | 0.820166i | \(-0.693881\pi\) | ||||
−0.572125 | + | 0.820166i | \(0.693881\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.88540 | −0.289964 | ||||||||
\(940\) | −5.52610 | −0.180241 | ||||||||
\(941\) | 44.2501 | 1.44251 | 0.721257 | − | 0.692668i | \(-0.243565\pi\) | ||||
0.721257 | + | 0.692668i | \(0.243565\pi\) | |||||||
\(942\) | −4.67618 | −0.152358 | ||||||||
\(943\) | 1.63546 | 0.0532578 | ||||||||
\(944\) | 5.00768 | 0.162986 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.7965 | 0.513590 | ||||||||
\(947\) | −3.06304 | −0.0995353 | −0.0497677 | − | 0.998761i | \(-0.515848\pi\) | ||||
−0.0497677 | + | 0.998761i | \(0.515848\pi\) | |||||||
\(948\) | −10.4669 | −0.339948 | ||||||||
\(949\) | 2.03480 | 0.0660523 | ||||||||
\(950\) | −3.97246 | −0.128884 | ||||||||
\(951\) | −0.0289702 | −0.000939423 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.51397 | −0.113829 | −0.0569143 | − | 0.998379i | \(-0.518126\pi\) | ||||
−0.0569143 | + | 0.998379i | \(0.518126\pi\) | |||||||
\(954\) | −8.94920 | −0.289741 | ||||||||
\(955\) | 19.1014 | 0.618108 | ||||||||
\(956\) | 2.14174 | 0.0692689 | ||||||||
\(957\) | −37.4323 | −1.21002 | ||||||||
\(958\) | −10.4966 | −0.339130 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7.48842 | −0.241688 | ||||||||
\(961\) | −22.3400 | −0.720646 | ||||||||
\(962\) | 3.99927 | 0.128942 | ||||||||
\(963\) | 8.05109 | 0.259443 | ||||||||
\(964\) | 20.5146 | 0.660729 | ||||||||
\(965\) | 10.1193 | 0.325751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.9509 | −0.352158 | −0.176079 | − | 0.984376i | \(-0.556341\pi\) | ||||
−0.176079 | + | 0.984376i | \(0.556341\pi\) | |||||||
\(968\) | −33.9343 | −1.09069 | ||||||||
\(969\) | 4.28852 | 0.137767 | ||||||||
\(970\) | 0.883402 | 0.0283643 | ||||||||
\(971\) | 15.9606 | 0.512199 | 0.256100 | − | 0.966650i | \(-0.417563\pi\) | ||||
0.256100 | + | 0.966650i | \(0.417563\pi\) | |||||||
\(972\) | −0.753512 | −0.0241689 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 27.5695 | 0.883385 | ||||||||
\(975\) | −4.84188 | −0.155064 | ||||||||
\(976\) | 14.0825 | 0.450768 | ||||||||
\(977\) | 43.3664 | 1.38741 | 0.693707 | − | 0.720257i | \(-0.255976\pi\) | ||||
0.693707 | + | 0.720257i | \(0.255976\pi\) | |||||||
\(978\) | 12.1516 | 0.388564 | ||||||||
\(979\) | −71.2352 | −2.27669 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5123 | 0.495270 | ||||||||
\(982\) | 39.0390 | 1.24578 | ||||||||
\(983\) | 4.84144 | 0.154418 | 0.0772089 | − | 0.997015i | \(-0.475399\pi\) | ||||
0.0772089 | + | 0.997015i | \(0.475399\pi\) | |||||||
\(984\) | 3.07419 | 0.0980017 | ||||||||
\(985\) | −18.3728 | −0.585406 | ||||||||
\(986\) | 44.9468 | 1.43140 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.739791 | −0.0235359 | ||||||||
\(989\) | 4.92909 | 0.156736 | ||||||||
\(990\) | 4.72016 | 0.150017 | ||||||||
\(991\) | −3.88753 | −0.123492 | −0.0617458 | − | 0.998092i | \(-0.519667\pi\) | ||||
−0.0617458 | + | 0.998092i | \(0.519667\pi\) | |||||||
\(992\) | 11.7681 | 0.373638 | ||||||||
\(993\) | 7.32795 | 0.232545 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.14253 | −0.0362205 | ||||||||
\(996\) | −7.76720 | −0.246113 | ||||||||
\(997\) | 37.9574 | 1.20212 | 0.601062 | − | 0.799203i | \(-0.294745\pi\) | ||||
0.601062 | + | 0.799203i | \(0.294745\pi\) | |||||||
\(998\) | 20.7040 | 0.655372 | ||||||||
\(999\) | 3.09905 | 0.0980495 |
(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 | 6027.2.a.bo.1.14 | yes | 24 | |
7.6 | odd | 2 | 6027.2.a.bn.1.14 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.14 | ✓ | 24 | 7.6 | odd | 2 | ||
6027.2.a.bo.1.14 | yes | 24 | 1.1 | even | 1 | trivial |