Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(20.2899871536\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.236068 | 0.0746512 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | −0.618034 | −0.165177 | ||||||||
\(15\) | −0.381966 | −0.0986232 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −4.23607 | −1.02740 | −0.513699 | − | 0.857971i | \(-0.671725\pi\) | ||||
−0.513699 | + | 0.857971i | \(0.671725\pi\) | |||||||
\(18\) | −0.618034 | −0.145672 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0.618034 | 0.138197 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.23607 | −0.674767 | −0.337383 | − | 0.941367i | \(-0.609542\pi\) | ||||
−0.337383 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | 0.618034 | 0.121206 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.61803 | −0.305780 | ||||||||
\(29\) | 6.70820 | 1.24568 | 0.622841 | − | 0.782348i | \(-0.285978\pi\) | ||||
0.622841 | + | 0.782348i | \(0.285978\pi\) | |||||||
\(30\) | 0.236068 | 0.0430999 | ||||||||
\(31\) | −10.2361 | −1.83845 | −0.919226 | − | 0.393730i | \(-0.871184\pi\) | ||||
−0.919226 | + | 0.393730i | \(0.871184\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.61803 | 0.448989 | ||||||||
\(35\) | −0.381966 | −0.0645640 | ||||||||
\(36\) | −1.61803 | −0.269672 | ||||||||
\(37\) | 6.94427 | 1.14163 | 0.570816 | − | 0.821078i | \(-0.306627\pi\) | ||||
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −0.854102 | −0.135045 | ||||||||
\(41\) | 5.09017 | 0.794951 | 0.397475 | − | 0.917613i | \(-0.369886\pi\) | ||||
0.397475 | + | 0.917613i | \(0.369886\pi\) | |||||||
\(42\) | −0.618034 | −0.0953647 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.381966 | −0.0569401 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | −7.32624 | −1.06864 | −0.534321 | − | 0.845282i | \(-0.679433\pi\) | ||||
−0.534321 | + | 0.845282i | \(0.679433\pi\) | |||||||
\(48\) | 1.85410 | 0.267617 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | −4.23607 | −0.593168 | ||||||||
\(52\) | 1.61803 | 0.224381 | ||||||||
\(53\) | 7.61803 | 1.04642 | 0.523209 | − | 0.852205i | \(-0.324735\pi\) | ||||
0.523209 | + | 0.852205i | \(0.324735\pi\) | |||||||
\(54\) | −0.618034 | −0.0841038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.14590 | −0.544383 | ||||||||
\(59\) | −4.14590 | −0.539750 | −0.269875 | − | 0.962895i | \(-0.586982\pi\) | ||||
−0.269875 | + | 0.962895i | \(0.586982\pi\) | |||||||
\(60\) | 0.618034 | 0.0797878 | ||||||||
\(61\) | −5.76393 | −0.737996 | −0.368998 | − | 0.929430i | \(-0.620299\pi\) | ||||
−0.368998 | + | 0.929430i | \(0.620299\pi\) | |||||||
\(62\) | 6.32624 | 0.803433 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0.381966 | 0.0473771 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.23607 | −1.12837 | −0.564183 | − | 0.825650i | \(-0.690809\pi\) | ||||
−0.564183 | + | 0.825650i | \(0.690809\pi\) | |||||||
\(68\) | 6.85410 | 0.831182 | ||||||||
\(69\) | −3.23607 | −0.389577 | ||||||||
\(70\) | 0.236068 | 0.0282155 | ||||||||
\(71\) | −7.47214 | −0.886779 | −0.443390 | − | 0.896329i | \(-0.646224\pi\) | ||||
−0.443390 | + | 0.896329i | \(0.646224\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | 11.5623 | 1.35327 | 0.676633 | − | 0.736321i | \(-0.263438\pi\) | ||||
0.676633 | + | 0.736321i | \(0.263438\pi\) | |||||||
\(74\) | −4.29180 | −0.498911 | ||||||||
\(75\) | −4.85410 | −0.560503 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.618034 | 0.0699786 | ||||||||
\(79\) | 10.8541 | 1.22118 | 0.610591 | − | 0.791946i | \(-0.290932\pi\) | ||||
0.610591 | + | 0.791946i | \(0.290932\pi\) | |||||||
\(80\) | −0.708204 | −0.0791796 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.14590 | −0.347406 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | −1.61803 | −0.176542 | ||||||||
\(85\) | 1.61803 | 0.175500 | ||||||||
\(86\) | 0.618034 | 0.0666443 | ||||||||
\(87\) | 6.70820 | 0.719195 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.38197 | −0.676487 | −0.338244 | − | 0.941059i | \(-0.609833\pi\) | ||||
−0.338244 | + | 0.941059i | \(0.609833\pi\) | |||||||
\(90\) | 0.236068 | 0.0248837 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 5.23607 | 0.545898 | ||||||||
\(93\) | −10.2361 | −1.06143 | ||||||||
\(94\) | 4.52786 | 0.467014 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.61803 | −0.573388 | ||||||||
\(97\) | −17.0000 | −1.72609 | −0.863044 | − | 0.505128i | \(-0.831445\pi\) | ||||
−0.863044 | + | 0.505128i | \(0.831445\pi\) | |||||||
\(98\) | −0.618034 | −0.0624309 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.85410 | 0.785410 | ||||||||
\(101\) | −4.18034 | −0.415959 | −0.207980 | − | 0.978133i | \(-0.566689\pi\) | ||||
−0.207980 | + | 0.978133i | \(0.566689\pi\) | |||||||
\(102\) | 2.61803 | 0.259224 | ||||||||
\(103\) | −12.7082 | −1.25218 | −0.626088 | − | 0.779752i | \(-0.715345\pi\) | ||||
−0.626088 | + | 0.779752i | \(0.715345\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | −0.381966 | −0.0372761 | ||||||||
\(106\) | −4.70820 | −0.457301 | ||||||||
\(107\) | 15.7639 | 1.52396 | 0.761978 | − | 0.647602i | \(-0.224228\pi\) | ||||
0.761978 | + | 0.647602i | \(0.224228\pi\) | |||||||
\(108\) | −1.61803 | −0.155695 | ||||||||
\(109\) | −7.56231 | −0.724338 | −0.362169 | − | 0.932113i | \(-0.617964\pi\) | ||||
−0.362169 | + | 0.932113i | \(0.617964\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.94427 | 0.659121 | ||||||||
\(112\) | 1.85410 | 0.175196 | ||||||||
\(113\) | −11.6525 | −1.09617 | −0.548086 | − | 0.836422i | \(-0.684643\pi\) | ||||
−0.548086 | + | 0.836422i | \(0.684643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.23607 | 0.115264 | ||||||||
\(116\) | −10.8541 | −1.00778 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 2.56231 | 0.235879 | ||||||||
\(119\) | −4.23607 | −0.388320 | ||||||||
\(120\) | −0.854102 | −0.0779685 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.56231 | 0.322516 | ||||||||
\(123\) | 5.09017 | 0.458965 | ||||||||
\(124\) | 16.5623 | 1.48734 | ||||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | −0.618034 | −0.0550588 | ||||||||
\(127\) | −7.32624 | −0.650098 | −0.325049 | − | 0.945697i | \(-0.605381\pi\) | ||||
−0.325049 | + | 0.945697i | \(0.605381\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | −1.00000 | −0.0880451 | ||||||||
\(130\) | −0.236068 | −0.0207045 | ||||||||
\(131\) | −3.32624 | −0.290615 | −0.145307 | − | 0.989387i | \(-0.546417\pi\) | ||||
−0.145307 | + | 0.989387i | \(0.546417\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.70820 | 0.493114 | ||||||||
\(135\) | −0.381966 | −0.0328744 | ||||||||
\(136\) | −9.47214 | −0.812229 | ||||||||
\(137\) | −3.05573 | −0.261068 | −0.130534 | − | 0.991444i | \(-0.541669\pi\) | ||||
−0.130534 | + | 0.991444i | \(0.541669\pi\) | |||||||
\(138\) | 2.00000 | 0.170251 | ||||||||
\(139\) | −17.5623 | −1.48962 | −0.744808 | − | 0.667279i | \(-0.767459\pi\) | ||||
−0.744808 | + | 0.667279i | \(0.767459\pi\) | |||||||
\(140\) | 0.618034 | 0.0522334 | ||||||||
\(141\) | −7.32624 | −0.616981 | ||||||||
\(142\) | 4.61803 | 0.387537 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | −2.56231 | −0.212788 | ||||||||
\(146\) | −7.14590 | −0.591399 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −11.2361 | −0.923599 | ||||||||
\(149\) | −13.0902 | −1.07239 | −0.536194 | − | 0.844095i | \(-0.680139\pi\) | ||||
−0.536194 | + | 0.844095i | \(0.680139\pi\) | |||||||
\(150\) | 3.00000 | 0.244949 | ||||||||
\(151\) | −21.0902 | −1.71629 | −0.858147 | − | 0.513404i | \(-0.828384\pi\) | ||||
−0.858147 | + | 0.513404i | \(0.828384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.23607 | −0.342466 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.90983 | 0.314045 | ||||||||
\(156\) | 1.61803 | 0.129546 | ||||||||
\(157\) | −1.67376 | −0.133581 | −0.0667904 | − | 0.997767i | \(-0.521276\pi\) | ||||
−0.0667904 | + | 0.997767i | \(0.521276\pi\) | |||||||
\(158\) | −6.70820 | −0.533676 | ||||||||
\(159\) | 7.61803 | 0.604149 | ||||||||
\(160\) | 2.14590 | 0.169648 | ||||||||
\(161\) | −3.23607 | −0.255038 | ||||||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | 6.03444 | 0.472654 | 0.236327 | − | 0.971674i | \(-0.424056\pi\) | ||||
0.236327 | + | 0.971674i | \(0.424056\pi\) | |||||||
\(164\) | −8.23607 | −0.643129 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.70820 | 0.287812 | ||||||||
\(167\) | 9.38197 | 0.725998 | 0.362999 | − | 0.931789i | \(-0.381753\pi\) | ||||
0.362999 | + | 0.931789i | \(0.381753\pi\) | |||||||
\(168\) | 2.23607 | 0.172516 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.61803 | 0.123374 | ||||||||
\(173\) | −14.6180 | −1.11139 | −0.555694 | − | 0.831387i | \(-0.687547\pi\) | ||||
−0.555694 | + | 0.831387i | \(0.687547\pi\) | |||||||
\(174\) | −4.14590 | −0.314300 | ||||||||
\(175\) | −4.85410 | −0.366936 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.14590 | −0.311625 | ||||||||
\(178\) | 3.94427 | 0.295636 | ||||||||
\(179\) | −2.23607 | −0.167132 | −0.0835658 | − | 0.996502i | \(-0.526631\pi\) | ||||
−0.0835658 | + | 0.996502i | \(0.526631\pi\) | |||||||
\(180\) | 0.618034 | 0.0460655 | ||||||||
\(181\) | −0.236068 | −0.0175468 | −0.00877340 | − | 0.999962i | \(-0.502793\pi\) | ||||
−0.00877340 | + | 0.999962i | \(0.502793\pi\) | |||||||
\(182\) | 0.618034 | 0.0458117 | ||||||||
\(183\) | −5.76393 | −0.426082 | ||||||||
\(184\) | −7.23607 | −0.533450 | ||||||||
\(185\) | −2.65248 | −0.195014 | ||||||||
\(186\) | 6.32624 | 0.463862 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.8541 | 0.864549 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.76393 | 0.706493 | 0.353247 | − | 0.935530i | \(-0.385078\pi\) | ||||
0.353247 | + | 0.935530i | \(0.385078\pi\) | |||||||
\(192\) | −0.236068 | −0.0170367 | ||||||||
\(193\) | 5.05573 | 0.363919 | 0.181960 | − | 0.983306i | \(-0.441756\pi\) | ||||
0.181960 | + | 0.983306i | \(0.441756\pi\) | |||||||
\(194\) | 10.5066 | 0.754328 | ||||||||
\(195\) | 0.381966 | 0.0273532 | ||||||||
\(196\) | −1.61803 | −0.115574 | ||||||||
\(197\) | −9.23607 | −0.658043 | −0.329021 | − | 0.944323i | \(-0.606719\pi\) | ||||
−0.329021 | + | 0.944323i | \(0.606719\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.56231 | −0.536078 | −0.268039 | − | 0.963408i | \(-0.586376\pi\) | ||||
−0.268039 | + | 0.963408i | \(0.586376\pi\) | |||||||
\(200\) | −10.8541 | −0.767501 | ||||||||
\(201\) | −9.23607 | −0.651462 | ||||||||
\(202\) | 2.58359 | 0.181781 | ||||||||
\(203\) | 6.70820 | 0.470824 | ||||||||
\(204\) | 6.85410 | 0.479883 | ||||||||
\(205\) | −1.94427 | −0.135794 | ||||||||
\(206\) | 7.85410 | 0.547221 | ||||||||
\(207\) | −3.23607 | −0.224922 | ||||||||
\(208\) | −1.85410 | −0.128559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.236068 | 0.0162902 | ||||||||
\(211\) | 5.29180 | 0.364302 | 0.182151 | − | 0.983271i | \(-0.441694\pi\) | ||||
0.182151 | + | 0.983271i | \(0.441694\pi\) | |||||||
\(212\) | −12.3262 | −0.846569 | ||||||||
\(213\) | −7.47214 | −0.511982 | ||||||||
\(214\) | −9.74265 | −0.665994 | ||||||||
\(215\) | 0.381966 | 0.0260499 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −10.2361 | −0.694870 | ||||||||
\(218\) | 4.67376 | 0.316547 | ||||||||
\(219\) | 11.5623 | 0.781308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.23607 | 0.284949 | ||||||||
\(222\) | −4.29180 | −0.288046 | ||||||||
\(223\) | −12.7082 | −0.851004 | −0.425502 | − | 0.904957i | \(-0.639903\pi\) | ||||
−0.425502 | + | 0.904957i | \(0.639903\pi\) | |||||||
\(224\) | −5.61803 | −0.375371 | ||||||||
\(225\) | −4.85410 | −0.323607 | ||||||||
\(226\) | 7.20163 | 0.479045 | ||||||||
\(227\) | 18.9787 | 1.25966 | 0.629831 | − | 0.776732i | \(-0.283124\pi\) | ||||
0.629831 | + | 0.776732i | \(0.283124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.7082 | −0.773700 | −0.386850 | − | 0.922143i | \(-0.626437\pi\) | ||||
−0.386850 | + | 0.922143i | \(0.626437\pi\) | |||||||
\(230\) | −0.763932 | −0.0503722 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.0000 | 0.984798 | ||||||||
\(233\) | 6.23607 | 0.408538 | 0.204269 | − | 0.978915i | \(-0.434518\pi\) | ||||
0.204269 | + | 0.978915i | \(0.434518\pi\) | |||||||
\(234\) | 0.618034 | 0.0404021 | ||||||||
\(235\) | 2.79837 | 0.182546 | ||||||||
\(236\) | 6.70820 | 0.436667 | ||||||||
\(237\) | 10.8541 | 0.705050 | ||||||||
\(238\) | 2.61803 | 0.169702 | ||||||||
\(239\) | 19.1459 | 1.23845 | 0.619223 | − | 0.785215i | \(-0.287448\pi\) | ||||
0.619223 | + | 0.785215i | \(0.287448\pi\) | |||||||
\(240\) | −0.708204 | −0.0457144 | ||||||||
\(241\) | −24.7082 | −1.59160 | −0.795798 | − | 0.605563i | \(-0.792948\pi\) | ||||
−0.795798 | + | 0.605563i | \(0.792948\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.32624 | 0.597051 | ||||||||
\(245\) | −0.381966 | −0.0244029 | ||||||||
\(246\) | −3.14590 | −0.200575 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −22.8885 | −1.45342 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | −2.32624 | −0.147124 | ||||||||
\(251\) | 26.5967 | 1.67877 | 0.839386 | − | 0.543536i | \(-0.182915\pi\) | ||||
0.839386 | + | 0.543536i | \(0.182915\pi\) | |||||||
\(252\) | −1.61803 | −0.101927 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.52786 | 0.284103 | ||||||||
\(255\) | 1.61803 | 0.101325 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 26.9443 | 1.68074 | 0.840369 | − | 0.542015i | \(-0.182338\pi\) | ||||
0.840369 | + | 0.542015i | \(0.182338\pi\) | |||||||
\(258\) | 0.618034 | 0.0384771 | ||||||||
\(259\) | 6.94427 | 0.431496 | ||||||||
\(260\) | −0.618034 | −0.0383288 | ||||||||
\(261\) | 6.70820 | 0.415227 | ||||||||
\(262\) | 2.05573 | 0.127003 | ||||||||
\(263\) | 0.708204 | 0.0436697 | 0.0218349 | − | 0.999762i | \(-0.493049\pi\) | ||||
0.0218349 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.90983 | −0.178749 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.38197 | −0.390570 | ||||||||
\(268\) | 14.9443 | 0.912867 | ||||||||
\(269\) | 23.9443 | 1.45991 | 0.729954 | − | 0.683496i | \(-0.239541\pi\) | ||||
0.729954 | + | 0.683496i | \(0.239541\pi\) | |||||||
\(270\) | 0.236068 | 0.0143666 | ||||||||
\(271\) | −6.41641 | −0.389769 | −0.194885 | − | 0.980826i | \(-0.562433\pi\) | ||||
−0.194885 | + | 0.980826i | \(0.562433\pi\) | |||||||
\(272\) | −7.85410 | −0.476225 | ||||||||
\(273\) | −1.00000 | −0.0605228 | ||||||||
\(274\) | 1.88854 | 0.114091 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.23607 | 0.315174 | ||||||||
\(277\) | −25.4164 | −1.52712 | −0.763562 | − | 0.645735i | \(-0.776551\pi\) | ||||
−0.763562 | + | 0.645735i | \(0.776551\pi\) | |||||||
\(278\) | 10.8541 | 0.650986 | ||||||||
\(279\) | −10.2361 | −0.612817 | ||||||||
\(280\) | −0.854102 | −0.0510424 | ||||||||
\(281\) | 15.6180 | 0.931694 | 0.465847 | − | 0.884865i | \(-0.345750\pi\) | ||||
0.465847 | + | 0.884865i | \(0.345750\pi\) | |||||||
\(282\) | 4.52786 | 0.269630 | ||||||||
\(283\) | 7.29180 | 0.433452 | 0.216726 | − | 0.976232i | \(-0.430462\pi\) | ||||
0.216726 | + | 0.976232i | \(0.430462\pi\) | |||||||
\(284\) | 12.0902 | 0.717420 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.09017 | 0.300463 | ||||||||
\(288\) | −5.61803 | −0.331046 | ||||||||
\(289\) | 0.944272 | 0.0555454 | ||||||||
\(290\) | 1.58359 | 0.0929917 | ||||||||
\(291\) | −17.0000 | −0.996558 | ||||||||
\(292\) | −18.7082 | −1.09481 | ||||||||
\(293\) | −13.2361 | −0.773259 | −0.386630 | − | 0.922235i | \(-0.626361\pi\) | ||||
−0.386630 | + | 0.922235i | \(0.626361\pi\) | |||||||
\(294\) | −0.618034 | −0.0360445 | ||||||||
\(295\) | 1.58359 | 0.0922003 | ||||||||
\(296\) | 15.5279 | 0.902539 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.09017 | 0.468651 | ||||||||
\(299\) | 3.23607 | 0.187147 | ||||||||
\(300\) | 7.85410 | 0.453457 | ||||||||
\(301\) | −1.00000 | −0.0576390 | ||||||||
\(302\) | 13.0344 | 0.750048 | ||||||||
\(303\) | −4.18034 | −0.240154 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.20163 | 0.126065 | ||||||||
\(306\) | 2.61803 | 0.149663 | ||||||||
\(307\) | 19.1803 | 1.09468 | 0.547340 | − | 0.836910i | \(-0.315640\pi\) | ||||
0.547340 | + | 0.836910i | \(0.315640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.7082 | −0.722944 | ||||||||
\(310\) | −2.41641 | −0.137243 | ||||||||
\(311\) | 16.7984 | 0.952548 | 0.476274 | − | 0.879297i | \(-0.341987\pi\) | ||||
0.476274 | + | 0.879297i | \(0.341987\pi\) | |||||||
\(312\) | −2.23607 | −0.126592 | ||||||||
\(313\) | −15.7984 | −0.892977 | −0.446488 | − | 0.894789i | \(-0.647326\pi\) | ||||
−0.446488 | + | 0.894789i | \(0.647326\pi\) | |||||||
\(314\) | 1.03444 | 0.0583769 | ||||||||
\(315\) | −0.381966 | −0.0215213 | ||||||||
\(316\) | −17.5623 | −0.987957 | ||||||||
\(317\) | 25.3607 | 1.42440 | 0.712199 | − | 0.701978i | \(-0.247699\pi\) | ||||
0.712199 | + | 0.701978i | \(0.247699\pi\) | |||||||
\(318\) | −4.70820 | −0.264023 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.0901699 | 0.00504065 | ||||||||
\(321\) | 15.7639 | 0.879857 | ||||||||
\(322\) | 2.00000 | 0.111456 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.61803 | −0.0898908 | ||||||||
\(325\) | 4.85410 | 0.269257 | ||||||||
\(326\) | −3.72949 | −0.206557 | ||||||||
\(327\) | −7.56231 | −0.418196 | ||||||||
\(328\) | 11.3820 | 0.628464 | ||||||||
\(329\) | −7.32624 | −0.403909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.7082 | −0.808436 | −0.404218 | − | 0.914663i | \(-0.632456\pi\) | ||||
−0.404218 | + | 0.914663i | \(0.632456\pi\) | |||||||
\(332\) | 9.70820 | 0.532807 | ||||||||
\(333\) | 6.94427 | 0.380544 | ||||||||
\(334\) | −5.79837 | −0.317273 | ||||||||
\(335\) | 3.52786 | 0.192748 | ||||||||
\(336\) | 1.85410 | 0.101150 | ||||||||
\(337\) | 1.29180 | 0.0703686 | 0.0351843 | − | 0.999381i | \(-0.488798\pi\) | ||||
0.0351843 | + | 0.999381i | \(0.488798\pi\) | |||||||
\(338\) | 7.41641 | 0.403399 | ||||||||
\(339\) | −11.6525 | −0.632876 | ||||||||
\(340\) | −2.61803 | −0.141983 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.23607 | −0.120561 | ||||||||
\(345\) | 1.23607 | 0.0665477 | ||||||||
\(346\) | 9.03444 | 0.485695 | ||||||||
\(347\) | −25.4164 | −1.36442 | −0.682212 | − | 0.731154i | \(-0.738982\pi\) | ||||
−0.682212 | + | 0.731154i | \(0.738982\pi\) | |||||||
\(348\) | −10.8541 | −0.581841 | ||||||||
\(349\) | 34.9230 | 1.86938 | 0.934692 | − | 0.355458i | \(-0.115675\pi\) | ||||
0.934692 | + | 0.355458i | \(0.115675\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.4721 | −1.35574 | −0.677872 | − | 0.735179i | \(-0.737098\pi\) | ||||
−0.677872 | + | 0.735179i | \(0.737098\pi\) | |||||||
\(354\) | 2.56231 | 0.136185 | ||||||||
\(355\) | 2.85410 | 0.151480 | ||||||||
\(356\) | 10.3262 | 0.547290 | ||||||||
\(357\) | −4.23607 | −0.224196 | ||||||||
\(358\) | 1.38197 | 0.0730392 | ||||||||
\(359\) | −33.2148 | −1.75301 | −0.876505 | − | 0.481394i | \(-0.840131\pi\) | ||||
−0.876505 | + | 0.481394i | \(0.840131\pi\) | |||||||
\(360\) | −0.854102 | −0.0450151 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0.145898 | 0.00766823 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.61803 | 0.0848080 | ||||||||
\(365\) | −4.41641 | −0.231165 | ||||||||
\(366\) | 3.56231 | 0.186205 | ||||||||
\(367\) | 11.2918 | 0.589427 | 0.294713 | − | 0.955586i | \(-0.404776\pi\) | ||||
0.294713 | + | 0.955586i | \(0.404776\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 5.09017 | 0.264984 | ||||||||
\(370\) | 1.63932 | 0.0852242 | ||||||||
\(371\) | 7.61803 | 0.395509 | ||||||||
\(372\) | 16.5623 | 0.858716 | ||||||||
\(373\) | 30.1803 | 1.56268 | 0.781339 | − | 0.624106i | \(-0.214537\pi\) | ||||
0.781339 | + | 0.624106i | \(0.214537\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.76393 | 0.194369 | ||||||||
\(376\) | −16.3820 | −0.844835 | ||||||||
\(377\) | −6.70820 | −0.345490 | ||||||||
\(378\) | −0.618034 | −0.0317882 | ||||||||
\(379\) | −10.8541 | −0.557538 | −0.278769 | − | 0.960358i | \(-0.589926\pi\) | ||||
−0.278769 | + | 0.960358i | \(0.589926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.32624 | −0.375335 | ||||||||
\(382\) | −6.03444 | −0.308749 | ||||||||
\(383\) | −7.90983 | −0.404173 | −0.202087 | − | 0.979368i | \(-0.564772\pi\) | ||||
−0.202087 | + | 0.979368i | \(0.564772\pi\) | |||||||
\(384\) | 11.3820 | 0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.12461 | −0.159039 | ||||||||
\(387\) | −1.00000 | −0.0508329 | ||||||||
\(388\) | 27.5066 | 1.39643 | ||||||||
\(389\) | 20.6525 | 1.04712 | 0.523561 | − | 0.851988i | \(-0.324603\pi\) | ||||
0.523561 | + | 0.851988i | \(0.324603\pi\) | |||||||
\(390\) | −0.236068 | −0.0119538 | ||||||||
\(391\) | 13.7082 | 0.693254 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | −3.32624 | −0.167787 | ||||||||
\(394\) | 5.70820 | 0.287575 | ||||||||
\(395\) | −4.14590 | −0.208603 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.6869 | 1.28919 | 0.644595 | − | 0.764524i | \(-0.277026\pi\) | ||||
0.644595 | + | 0.764524i | \(0.277026\pi\) | |||||||
\(398\) | 4.67376 | 0.234275 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.00000 | −0.450000 | ||||||||
\(401\) | 11.6738 | 0.582960 | 0.291480 | − | 0.956577i | \(-0.405852\pi\) | ||||
0.291480 | + | 0.956577i | \(0.405852\pi\) | |||||||
\(402\) | 5.70820 | 0.284699 | ||||||||
\(403\) | 10.2361 | 0.509895 | ||||||||
\(404\) | 6.76393 | 0.336518 | ||||||||
\(405\) | −0.381966 | −0.0189800 | ||||||||
\(406\) | −4.14590 | −0.205757 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.47214 | −0.468941 | ||||||||
\(409\) | −26.3820 | −1.30450 | −0.652252 | − | 0.758002i | \(-0.726176\pi\) | ||||
−0.652252 | + | 0.758002i | \(0.726176\pi\) | |||||||
\(410\) | 1.20163 | 0.0593441 | ||||||||
\(411\) | −3.05573 | −0.150728 | ||||||||
\(412\) | 20.5623 | 1.01303 | ||||||||
\(413\) | −4.14590 | −0.204006 | ||||||||
\(414\) | 2.00000 | 0.0982946 | ||||||||
\(415\) | 2.29180 | 0.112500 | ||||||||
\(416\) | 5.61803 | 0.275447 | ||||||||
\(417\) | −17.5623 | −0.860030 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.3262 | −0.748736 | −0.374368 | − | 0.927280i | \(-0.622140\pi\) | ||||
−0.374368 | + | 0.927280i | \(0.622140\pi\) | |||||||
\(420\) | 0.618034 | 0.0301570 | ||||||||
\(421\) | 2.72949 | 0.133027 | 0.0665136 | − | 0.997786i | \(-0.478812\pi\) | ||||
0.0665136 | + | 0.997786i | \(0.478812\pi\) | |||||||
\(422\) | −3.27051 | −0.159206 | ||||||||
\(423\) | −7.32624 | −0.356214 | ||||||||
\(424\) | 17.0344 | 0.827266 | ||||||||
\(425\) | 20.5623 | 0.997418 | ||||||||
\(426\) | 4.61803 | 0.223744 | ||||||||
\(427\) | −5.76393 | −0.278936 | ||||||||
\(428\) | −25.5066 | −1.23291 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.236068 | −0.0113842 | ||||||||
\(431\) | −37.7984 | −1.82068 | −0.910342 | − | 0.413857i | \(-0.864181\pi\) | ||||
−0.910342 | + | 0.413857i | \(0.864181\pi\) | |||||||
\(432\) | 1.85410 | 0.0892055 | ||||||||
\(433\) | −2.58359 | −0.124160 | −0.0620798 | − | 0.998071i | \(-0.519773\pi\) | ||||
−0.0620798 | + | 0.998071i | \(0.519773\pi\) | |||||||
\(434\) | 6.32624 | 0.303669 | ||||||||
\(435\) | −2.56231 | −0.122853 | ||||||||
\(436\) | 12.2361 | 0.586001 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −7.14590 | −0.341444 | ||||||||
\(439\) | 0.527864 | 0.0251936 | 0.0125968 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125968 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −2.61803 | −0.124527 | ||||||||
\(443\) | −36.6525 | −1.74141 | −0.870706 | − | 0.491804i | \(-0.836338\pi\) | ||||
−0.870706 | + | 0.491804i | \(0.836338\pi\) | |||||||
\(444\) | −11.2361 | −0.533240 | ||||||||
\(445\) | 2.43769 | 0.115558 | ||||||||
\(446\) | 7.85410 | 0.371903 | ||||||||
\(447\) | −13.0902 | −0.619144 | ||||||||
\(448\) | −0.236068 | −0.0111532 | ||||||||
\(449\) | 15.6525 | 0.738686 | 0.369343 | − | 0.929293i | \(-0.379583\pi\) | ||||
0.369343 | + | 0.929293i | \(0.379583\pi\) | |||||||
\(450\) | 3.00000 | 0.141421 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 18.8541 | 0.886822 | ||||||||
\(453\) | −21.0902 | −0.990903 | ||||||||
\(454\) | −11.7295 | −0.550492 | ||||||||
\(455\) | 0.381966 | 0.0179068 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2705 | 0.573990 | 0.286995 | − | 0.957932i | \(-0.407344\pi\) | ||||
0.286995 | + | 0.957932i | \(0.407344\pi\) | |||||||
\(458\) | 7.23607 | 0.338119 | ||||||||
\(459\) | −4.23607 | −0.197723 | ||||||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | 23.1803 | 1.07962 | 0.539808 | − | 0.841788i | \(-0.318497\pi\) | ||||
0.539808 | + | 0.841788i | \(0.318497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.9230 | −1.66948 | −0.834741 | − | 0.550642i | \(-0.814383\pi\) | ||||
−0.834741 | + | 0.550642i | \(0.814383\pi\) | |||||||
\(464\) | 12.4377 | 0.577405 | ||||||||
\(465\) | 3.90983 | 0.181314 | ||||||||
\(466\) | −3.85410 | −0.178538 | ||||||||
\(467\) | 31.9443 | 1.47820 | 0.739102 | − | 0.673593i | \(-0.235250\pi\) | ||||
0.739102 | + | 0.673593i | \(0.235250\pi\) | |||||||
\(468\) | 1.61803 | 0.0747936 | ||||||||
\(469\) | −9.23607 | −0.426482 | ||||||||
\(470\) | −1.72949 | −0.0797754 | ||||||||
\(471\) | −1.67376 | −0.0771229 | ||||||||
\(472\) | −9.27051 | −0.426710 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.70820 | −0.308118 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.85410 | 0.314157 | ||||||||
\(477\) | 7.61803 | 0.348806 | ||||||||
\(478\) | −11.8328 | −0.541220 | ||||||||
\(479\) | 21.5066 | 0.982661 | 0.491330 | − | 0.870973i | \(-0.336511\pi\) | ||||
0.491330 | + | 0.870973i | \(0.336511\pi\) | |||||||
\(480\) | 2.14590 | 0.0979464 | ||||||||
\(481\) | −6.94427 | −0.316632 | ||||||||
\(482\) | 15.2705 | 0.695553 | ||||||||
\(483\) | −3.23607 | −0.147246 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.49342 | 0.294851 | ||||||||
\(486\) | −0.618034 | −0.0280346 | ||||||||
\(487\) | 16.6180 | 0.753035 | 0.376518 | − | 0.926410i | \(-0.377121\pi\) | ||||
0.376518 | + | 0.926410i | \(0.377121\pi\) | |||||||
\(488\) | −12.8885 | −0.583437 | ||||||||
\(489\) | 6.03444 | 0.272887 | ||||||||
\(490\) | 0.236068 | 0.0106645 | ||||||||
\(491\) | 3.70820 | 0.167349 | 0.0836745 | − | 0.996493i | \(-0.473334\pi\) | ||||
0.0836745 | + | 0.996493i | \(0.473334\pi\) | |||||||
\(492\) | −8.23607 | −0.371311 | ||||||||
\(493\) | −28.4164 | −1.27981 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.9787 | −0.852169 | ||||||||
\(497\) | −7.47214 | −0.335171 | ||||||||
\(498\) | 3.70820 | 0.166169 | ||||||||
\(499\) | −5.00000 | −0.223831 | −0.111915 | − | 0.993718i | \(-0.535699\pi\) | ||||
−0.111915 | + | 0.993718i | \(0.535699\pi\) | |||||||
\(500\) | −6.09017 | −0.272361 | ||||||||
\(501\) | 9.38197 | 0.419155 | ||||||||
\(502\) | −16.4377 | −0.733650 | ||||||||
\(503\) | −32.3050 | −1.44041 | −0.720203 | − | 0.693763i | \(-0.755951\pi\) | ||||
−0.720203 | + | 0.693763i | \(0.755951\pi\) | |||||||
\(504\) | 2.23607 | 0.0996024 | ||||||||
\(505\) | 1.59675 | 0.0710543 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0000 | −0.532939 | ||||||||
\(508\) | 11.8541 | 0.525941 | ||||||||
\(509\) | 41.8328 | 1.85421 | 0.927103 | − | 0.374805i | \(-0.122291\pi\) | ||||
0.927103 | + | 0.374805i | \(0.122291\pi\) | |||||||
\(510\) | −1.00000 | −0.0442807 | ||||||||
\(511\) | 11.5623 | 0.511486 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.6525 | −0.734509 | ||||||||
\(515\) | 4.85410 | 0.213897 | ||||||||
\(516\) | 1.61803 | 0.0712300 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.29180 | −0.188571 | ||||||||
\(519\) | −14.6180 | −0.641660 | ||||||||
\(520\) | 0.854102 | 0.0374548 | ||||||||
\(521\) | −19.1803 | −0.840306 | −0.420153 | − | 0.907453i | \(-0.638024\pi\) | ||||
−0.420153 | + | 0.907453i | \(0.638024\pi\) | |||||||
\(522\) | −4.14590 | −0.181461 | ||||||||
\(523\) | 20.3050 | 0.887874 | 0.443937 | − | 0.896058i | \(-0.353581\pi\) | ||||
0.443937 | + | 0.896058i | \(0.353581\pi\) | |||||||
\(524\) | 5.38197 | 0.235112 | ||||||||
\(525\) | −4.85410 | −0.211850 | ||||||||
\(526\) | −0.437694 | −0.0190844 | ||||||||
\(527\) | 43.3607 | 1.88882 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.5279 | −0.544690 | ||||||||
\(530\) | 1.79837 | 0.0781164 | ||||||||
\(531\) | −4.14590 | −0.179917 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.09017 | −0.220480 | ||||||||
\(534\) | 3.94427 | 0.170685 | ||||||||
\(535\) | −6.02129 | −0.260323 | ||||||||
\(536\) | −20.6525 | −0.892051 | ||||||||
\(537\) | −2.23607 | −0.0964935 | ||||||||
\(538\) | −14.7984 | −0.638003 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.618034 | 0.0265959 | ||||||||
\(541\) | 20.0902 | 0.863744 | 0.431872 | − | 0.901935i | \(-0.357853\pi\) | ||||
0.431872 | + | 0.901935i | \(0.357853\pi\) | |||||||
\(542\) | 3.96556 | 0.170335 | ||||||||
\(543\) | −0.236068 | −0.0101306 | ||||||||
\(544\) | 23.7984 | 1.02035 | ||||||||
\(545\) | 2.88854 | 0.123732 | ||||||||
\(546\) | 0.618034 | 0.0264494 | ||||||||
\(547\) | 22.5967 | 0.966167 | 0.483084 | − | 0.875574i | \(-0.339517\pi\) | ||||
0.483084 | + | 0.875574i | \(0.339517\pi\) | |||||||
\(548\) | 4.94427 | 0.211209 | ||||||||
\(549\) | −5.76393 | −0.245999 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −7.23607 | −0.307988 | ||||||||
\(553\) | 10.8541 | 0.461563 | ||||||||
\(554\) | 15.7082 | 0.667378 | ||||||||
\(555\) | −2.65248 | −0.112591 | ||||||||
\(556\) | 28.4164 | 1.20512 | ||||||||
\(557\) | 0.763932 | 0.0323688 | 0.0161844 | − | 0.999869i | \(-0.494848\pi\) | ||||
0.0161844 | + | 0.999869i | \(0.494848\pi\) | |||||||
\(558\) | 6.32624 | 0.267811 | ||||||||
\(559\) | 1.00000 | 0.0422955 | ||||||||
\(560\) | −0.708204 | −0.0299271 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.65248 | −0.407165 | ||||||||
\(563\) | −45.0689 | −1.89943 | −0.949713 | − | 0.313120i | \(-0.898626\pi\) | ||||
−0.949713 | + | 0.313120i | \(0.898626\pi\) | |||||||
\(564\) | 11.8541 | 0.499148 | ||||||||
\(565\) | 4.45085 | 0.187249 | ||||||||
\(566\) | −4.50658 | −0.189426 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −16.7082 | −0.701061 | ||||||||
\(569\) | 39.0689 | 1.63785 | 0.818926 | − | 0.573899i | \(-0.194570\pi\) | ||||
0.818926 | + | 0.573899i | \(0.194570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.76393 | 0.407894 | ||||||||
\(574\) | −3.14590 | −0.131307 | ||||||||
\(575\) | 15.7082 | 0.655077 | ||||||||
\(576\) | −0.236068 | −0.00983617 | ||||||||
\(577\) | −9.43769 | −0.392896 | −0.196448 | − | 0.980514i | \(-0.562941\pi\) | ||||
−0.196448 | + | 0.980514i | \(0.562941\pi\) | |||||||
\(578\) | −0.583592 | −0.0242742 | ||||||||
\(579\) | 5.05573 | 0.210109 | ||||||||
\(580\) | 4.14590 | 0.172149 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 10.5066 | 0.435512 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 25.8541 | 1.06985 | ||||||||
\(585\) | 0.381966 | 0.0157924 | ||||||||
\(586\) | 8.18034 | 0.337927 | ||||||||
\(587\) | 35.8885 | 1.48128 | 0.740639 | − | 0.671903i | \(-0.234523\pi\) | ||||
0.740639 | + | 0.671903i | \(0.234523\pi\) | |||||||
\(588\) | −1.61803 | −0.0667266 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.978714 | −0.0402930 | ||||||||
\(591\) | −9.23607 | −0.379921 | ||||||||
\(592\) | 12.8754 | 0.529175 | ||||||||
\(593\) | −23.8885 | −0.980985 | −0.490492 | − | 0.871445i | \(-0.663183\pi\) | ||||
−0.490492 | + | 0.871445i | \(0.663183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.61803 | 0.0663329 | ||||||||
\(596\) | 21.1803 | 0.867581 | ||||||||
\(597\) | −7.56231 | −0.309505 | ||||||||
\(598\) | −2.00000 | −0.0817861 | ||||||||
\(599\) | 31.5066 | 1.28732 | 0.643662 | − | 0.765310i | \(-0.277414\pi\) | ||||
0.643662 | + | 0.765310i | \(0.277414\pi\) | |||||||
\(600\) | −10.8541 | −0.443117 | ||||||||
\(601\) | −14.8328 | −0.605043 | −0.302522 | − | 0.953143i | \(-0.597828\pi\) | ||||
−0.302522 | + | 0.953143i | \(0.597828\pi\) | |||||||
\(602\) | 0.618034 | 0.0251892 | ||||||||
\(603\) | −9.23607 | −0.376122 | ||||||||
\(604\) | 34.1246 | 1.38851 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.58359 | 0.104951 | ||||||||
\(607\) | −16.1459 | −0.655342 | −0.327671 | − | 0.944792i | \(-0.606264\pi\) | ||||
−0.327671 | + | 0.944792i | \(0.606264\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.70820 | 0.271830 | ||||||||
\(610\) | −1.36068 | −0.0550923 | ||||||||
\(611\) | 7.32624 | 0.296388 | ||||||||
\(612\) | 6.85410 | 0.277061 | ||||||||
\(613\) | 34.4508 | 1.39146 | 0.695728 | − | 0.718305i | \(-0.255082\pi\) | ||||
0.695728 | + | 0.718305i | \(0.255082\pi\) | |||||||
\(614\) | −11.8541 | −0.478393 | ||||||||
\(615\) | −1.94427 | −0.0784006 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.0902 | −0.406215 | −0.203107 | − | 0.979156i | \(-0.565104\pi\) | ||||
−0.203107 | + | 0.979156i | \(0.565104\pi\) | |||||||
\(618\) | 7.85410 | 0.315938 | ||||||||
\(619\) | 35.1246 | 1.41178 | 0.705889 | − | 0.708323i | \(-0.250548\pi\) | ||||
0.705889 | + | 0.708323i | \(0.250548\pi\) | |||||||
\(620\) | −6.32624 | −0.254068 | ||||||||
\(621\) | −3.23607 | −0.129859 | ||||||||
\(622\) | −10.3820 | −0.416279 | ||||||||
\(623\) | −6.38197 | −0.255688 | ||||||||
\(624\) | −1.85410 | −0.0742235 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 9.76393 | 0.390245 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.70820 | 0.108069 | ||||||||
\(629\) | −29.4164 | −1.17291 | ||||||||
\(630\) | 0.236068 | 0.00940517 | ||||||||
\(631\) | −9.18034 | −0.365464 | −0.182732 | − | 0.983163i | \(-0.558494\pi\) | ||||
−0.182732 | + | 0.983163i | \(0.558494\pi\) | |||||||
\(632\) | 24.2705 | 0.965429 | ||||||||
\(633\) | 5.29180 | 0.210330 | ||||||||
\(634\) | −15.6738 | −0.622485 | ||||||||
\(635\) | 2.79837 | 0.111050 | ||||||||
\(636\) | −12.3262 | −0.488767 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.47214 | −0.295593 | ||||||||
\(640\) | −4.34752 | −0.171851 | ||||||||
\(641\) | 27.9787 | 1.10509 | 0.552546 | − | 0.833482i | \(-0.313656\pi\) | ||||
0.552546 | + | 0.833482i | \(0.313656\pi\) | |||||||
\(642\) | −9.74265 | −0.384512 | ||||||||
\(643\) | −16.0000 | −0.630978 | −0.315489 | − | 0.948929i | \(-0.602169\pi\) | ||||
−0.315489 | + | 0.948929i | \(0.602169\pi\) | |||||||
\(644\) | 5.23607 | 0.206330 | ||||||||
\(645\) | 0.381966 | 0.0150399 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.34752 | 0.0922907 | 0.0461453 | − | 0.998935i | \(-0.485306\pi\) | ||||
0.0461453 | + | 0.998935i | \(0.485306\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.00000 | −0.117670 | ||||||||
\(651\) | −10.2361 | −0.401183 | ||||||||
\(652\) | −9.76393 | −0.382385 | ||||||||
\(653\) | 0.708204 | 0.0277142 | 0.0138571 | − | 0.999904i | \(-0.495589\pi\) | ||||
0.0138571 | + | 0.999904i | \(0.495589\pi\) | |||||||
\(654\) | 4.67376 | 0.182759 | ||||||||
\(655\) | 1.27051 | 0.0496429 | ||||||||
\(656\) | 9.43769 | 0.368480 | ||||||||
\(657\) | 11.5623 | 0.451089 | ||||||||
\(658\) | 4.52786 | 0.176515 | ||||||||
\(659\) | 41.8328 | 1.62958 | 0.814788 | − | 0.579760i | \(-0.196854\pi\) | ||||
0.814788 | + | 0.579760i | \(0.196854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.00000 | −0.116686 | −0.0583432 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583432 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(662\) | 9.09017 | 0.353299 | ||||||||
\(663\) | 4.23607 | 0.164515 | ||||||||
\(664\) | −13.4164 | −0.520658 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.29180 | −0.166304 | ||||||||
\(667\) | −21.7082 | −0.840545 | ||||||||
\(668\) | −15.1803 | −0.587345 | ||||||||
\(669\) | −12.7082 | −0.491328 | ||||||||
\(670\) | −2.18034 | −0.0842339 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −5.61803 | −0.216720 | ||||||||
\(673\) | −7.58359 | −0.292326 | −0.146163 | − | 0.989261i | \(-0.546692\pi\) | ||||
−0.146163 | + | 0.989261i | \(0.546692\pi\) | |||||||
\(674\) | −0.798374 | −0.0307522 | ||||||||
\(675\) | −4.85410 | −0.186834 | ||||||||
\(676\) | 19.4164 | 0.746785 | ||||||||
\(677\) | 23.4508 | 0.901289 | 0.450645 | − | 0.892703i | \(-0.351194\pi\) | ||||
0.450645 | + | 0.892703i | \(0.351194\pi\) | |||||||
\(678\) | 7.20163 | 0.276577 | ||||||||
\(679\) | −17.0000 | −0.652400 | ||||||||
\(680\) | 3.61803 | 0.138745 | ||||||||
\(681\) | 18.9787 | 0.727266 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.3050 | −1.23611 | −0.618057 | − | 0.786133i | \(-0.712080\pi\) | ||||
−0.618057 | + | 0.786133i | \(0.712080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.16718 | 0.0445958 | ||||||||
\(686\) | −0.618034 | −0.0235966 | ||||||||
\(687\) | −11.7082 | −0.446696 | ||||||||
\(688\) | −1.85410 | −0.0706870 | ||||||||
\(689\) | −7.61803 | −0.290224 | ||||||||
\(690\) | −0.763932 | −0.0290824 | ||||||||
\(691\) | 14.5623 | 0.553976 | 0.276988 | − | 0.960873i | \(-0.410664\pi\) | ||||
0.276988 | + | 0.960873i | \(0.410664\pi\) | |||||||
\(692\) | 23.6525 | 0.899132 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.7082 | 0.596275 | ||||||||
\(695\) | 6.70820 | 0.254457 | ||||||||
\(696\) | 15.0000 | 0.568574 | ||||||||
\(697\) | −21.5623 | −0.816731 | ||||||||
\(698\) | −21.5836 | −0.816951 | ||||||||
\(699\) | 6.23607 | 0.235870 | ||||||||
\(700\) | 7.85410 | 0.296857 | ||||||||
\(701\) | 27.0000 | 1.01978 | 0.509888 | − | 0.860241i | \(-0.329687\pi\) | ||||
0.509888 | + | 0.860241i | \(0.329687\pi\) | |||||||
\(702\) | 0.618034 | 0.0233262 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.79837 | 0.105393 | ||||||||
\(706\) | 15.7426 | 0.592482 | ||||||||
\(707\) | −4.18034 | −0.157218 | ||||||||
\(708\) | 6.70820 | 0.252110 | ||||||||
\(709\) | −50.6525 | −1.90229 | −0.951147 | − | 0.308739i | \(-0.900093\pi\) | ||||
−0.951147 | + | 0.308739i | \(0.900093\pi\) | |||||||
\(710\) | −1.76393 | −0.0661992 | ||||||||
\(711\) | 10.8541 | 0.407061 | ||||||||
\(712\) | −14.2705 | −0.534810 | ||||||||
\(713\) | 33.1246 | 1.24053 | ||||||||
\(714\) | 2.61803 | 0.0979775 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.61803 | 0.135212 | ||||||||
\(717\) | 19.1459 | 0.715017 | ||||||||
\(718\) | 20.5279 | 0.766093 | ||||||||
\(719\) | −8.61803 | −0.321398 | −0.160699 | − | 0.987003i | \(-0.551375\pi\) | ||||
−0.160699 | + | 0.987003i | \(0.551375\pi\) | |||||||
\(720\) | −0.708204 | −0.0263932 | ||||||||
\(721\) | −12.7082 | −0.473278 | ||||||||
\(722\) | 11.7426 | 0.437016 | ||||||||
\(723\) | −24.7082 | −0.918908 | ||||||||
\(724\) | 0.381966 | 0.0141957 | ||||||||
\(725\) | −32.5623 | −1.20933 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.1459 | 0.821346 | 0.410673 | − | 0.911783i | \(-0.365294\pi\) | ||||
0.410673 | + | 0.911783i | \(0.365294\pi\) | |||||||
\(728\) | −2.23607 | −0.0828742 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.72949 | 0.101023 | ||||||||
\(731\) | 4.23607 | 0.156677 | ||||||||
\(732\) | 9.32624 | 0.344708 | ||||||||
\(733\) | 4.12461 | 0.152346 | 0.0761730 | − | 0.997095i | \(-0.475730\pi\) | ||||
0.0761730 | + | 0.997095i | \(0.475730\pi\) | |||||||
\(734\) | −6.97871 | −0.257589 | ||||||||
\(735\) | −0.381966 | −0.0140890 | ||||||||
\(736\) | 18.1803 | 0.670136 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.14590 | −0.115802 | ||||||||
\(739\) | 42.6869 | 1.57026 | 0.785132 | − | 0.619329i | \(-0.212595\pi\) | ||||
0.785132 | + | 0.619329i | \(0.212595\pi\) | |||||||
\(740\) | 4.29180 | 0.157770 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.70820 | −0.172844 | ||||||||
\(743\) | 25.9098 | 0.950539 | 0.475270 | − | 0.879840i | \(-0.342350\pi\) | ||||
0.475270 | + | 0.879840i | \(0.342350\pi\) | |||||||
\(744\) | −22.8885 | −0.839135 | ||||||||
\(745\) | 5.00000 | 0.183186 | ||||||||
\(746\) | −18.6525 | −0.682916 | ||||||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.7639 | 0.576002 | ||||||||
\(750\) | −2.32624 | −0.0849422 | ||||||||
\(751\) | −28.8541 | −1.05290 | −0.526451 | − | 0.850206i | \(-0.676477\pi\) | ||||
−0.526451 | + | 0.850206i | \(0.676477\pi\) | |||||||
\(752\) | −13.5836 | −0.495343 | ||||||||
\(753\) | 26.5967 | 0.969239 | ||||||||
\(754\) | 4.14590 | 0.150985 | ||||||||
\(755\) | 8.05573 | 0.293178 | ||||||||
\(756\) | −1.61803 | −0.0588473 | ||||||||
\(757\) | 45.2361 | 1.64413 | 0.822066 | − | 0.569392i | \(-0.192821\pi\) | ||||
0.822066 | + | 0.569392i | \(0.192821\pi\) | |||||||
\(758\) | 6.70820 | 0.243653 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0901699 | 0.00326866 | 0.00163433 | − | 0.999999i | \(-0.499480\pi\) | ||||
0.00163433 | + | 0.999999i | \(0.499480\pi\) | |||||||
\(762\) | 4.52786 | 0.164027 | ||||||||
\(763\) | −7.56231 | −0.273774 | ||||||||
\(764\) | −15.7984 | −0.571565 | ||||||||
\(765\) | 1.61803 | 0.0585001 | ||||||||
\(766\) | 4.88854 | 0.176630 | ||||||||
\(767\) | 4.14590 | 0.149700 | ||||||||
\(768\) | −6.56231 | −0.236797 | ||||||||
\(769\) | 44.4721 | 1.60371 | 0.801853 | − | 0.597521i | \(-0.203848\pi\) | ||||
0.801853 | + | 0.597521i | \(0.203848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.9443 | 0.970374 | ||||||||
\(772\) | −8.18034 | −0.294417 | ||||||||
\(773\) | 10.5836 | 0.380665 | 0.190333 | − | 0.981720i | \(-0.439043\pi\) | ||||
0.190333 | + | 0.981720i | \(0.439043\pi\) | |||||||
\(774\) | 0.618034 | 0.0222148 | ||||||||
\(775\) | 49.6869 | 1.78481 | ||||||||
\(776\) | −38.0132 | −1.36459 | ||||||||
\(777\) | 6.94427 | 0.249124 | ||||||||
\(778\) | −12.7639 | −0.457609 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.618034 | −0.0221292 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.47214 | −0.302963 | ||||||||
\(783\) | 6.70820 | 0.239732 | ||||||||
\(784\) | 1.85410 | 0.0662179 | ||||||||
\(785\) | 0.639320 | 0.0228183 | ||||||||
\(786\) | 2.05573 | 0.0733254 | ||||||||
\(787\) | −32.8541 | −1.17112 | −0.585561 | − | 0.810628i | \(-0.699126\pi\) | ||||
−0.585561 | + | 0.810628i | \(0.699126\pi\) | |||||||
\(788\) | 14.9443 | 0.532368 | ||||||||
\(789\) | 0.708204 | 0.0252127 | ||||||||
\(790\) | 2.56231 | 0.0911628 | ||||||||
\(791\) | −11.6525 | −0.414314 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.76393 | 0.204683 | ||||||||
\(794\) | −15.8754 | −0.563396 | ||||||||
\(795\) | −2.90983 | −0.103201 | ||||||||
\(796\) | 12.2361 | 0.433696 | ||||||||
\(797\) | −32.4508 | −1.14947 | −0.574734 | − | 0.818340i | \(-0.694894\pi\) | ||||
−0.574734 | + | 0.818340i | \(0.694894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.0344 | 1.09792 | ||||||||
\(800\) | 27.2705 | 0.964158 | ||||||||
\(801\) | −6.38197 | −0.225496 | ||||||||
\(802\) | −7.21478 | −0.254763 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 14.9443 | 0.527044 | ||||||||
\(805\) | 1.23607 | 0.0435657 | ||||||||
\(806\) | −6.32624 | −0.222832 | ||||||||
\(807\) | 23.9443 | 0.842878 | ||||||||
\(808\) | −9.34752 | −0.328845 | ||||||||
\(809\) | 30.9787 | 1.08915 | 0.544577 | − | 0.838711i | \(-0.316690\pi\) | ||||
0.544577 | + | 0.838711i | \(0.316690\pi\) | |||||||
\(810\) | 0.236068 | 0.00829458 | ||||||||
\(811\) | −23.1246 | −0.812015 | −0.406007 | − | 0.913870i | \(-0.633079\pi\) | ||||
−0.406007 | + | 0.913870i | \(0.633079\pi\) | |||||||
\(812\) | −10.8541 | −0.380904 | ||||||||
\(813\) | −6.41641 | −0.225033 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.30495 | −0.0807389 | ||||||||
\(816\) | −7.85410 | −0.274949 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 16.3050 | 0.570089 | ||||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | 3.14590 | 0.109860 | ||||||||
\(821\) | 5.81966 | 0.203108 | 0.101554 | − | 0.994830i | \(-0.467619\pi\) | ||||
0.101554 | + | 0.994830i | \(0.467619\pi\) | |||||||
\(822\) | 1.88854 | 0.0658705 | ||||||||
\(823\) | −26.2492 | −0.914990 | −0.457495 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457495 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(824\) | −28.4164 | −0.989932 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.56231 | 0.0891540 | ||||||||
\(827\) | 5.11146 | 0.177743 | 0.0888714 | − | 0.996043i | \(-0.471674\pi\) | ||||
0.0888714 | + | 0.996043i | \(0.471674\pi\) | |||||||
\(828\) | 5.23607 | 0.181966 | ||||||||
\(829\) | 37.6869 | 1.30892 | 0.654460 | − | 0.756096i | \(-0.272896\pi\) | ||||
0.654460 | + | 0.756096i | \(0.272896\pi\) | |||||||
\(830\) | −1.41641 | −0.0491642 | ||||||||
\(831\) | −25.4164 | −0.881685 | ||||||||
\(832\) | 0.236068 | 0.00818418 | ||||||||
\(833\) | −4.23607 | −0.146771 | ||||||||
\(834\) | 10.8541 | 0.375847 | ||||||||
\(835\) | −3.58359 | −0.124015 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.2361 | −0.353810 | ||||||||
\(838\) | 9.47214 | 0.327210 | ||||||||
\(839\) | 29.0689 | 1.00357 | 0.501785 | − | 0.864993i | \(-0.332677\pi\) | ||||
0.501785 | + | 0.864993i | \(0.332677\pi\) | |||||||
\(840\) | −0.854102 | −0.0294693 | ||||||||
\(841\) | 16.0000 | 0.551724 | ||||||||
\(842\) | −1.68692 | −0.0581350 | ||||||||
\(843\) | 15.6180 | 0.537914 | ||||||||
\(844\) | −8.56231 | −0.294727 | ||||||||
\(845\) | 4.58359 | 0.157680 | ||||||||
\(846\) | 4.52786 | 0.155671 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 14.1246 | 0.485041 | ||||||||
\(849\) | 7.29180 | 0.250254 | ||||||||
\(850\) | −12.7082 | −0.435888 | ||||||||
\(851\) | −22.4721 | −0.770335 | ||||||||
\(852\) | 12.0902 | 0.414202 | ||||||||
\(853\) | 9.20163 | 0.315058 | 0.157529 | − | 0.987514i | \(-0.449647\pi\) | ||||
0.157529 | + | 0.987514i | \(0.449647\pi\) | |||||||
\(854\) | 3.56231 | 0.121900 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.2492 | 1.20479 | ||||||||
\(857\) | −54.2361 | −1.85267 | −0.926334 | − | 0.376702i | \(-0.877058\pi\) | ||||
−0.926334 | + | 0.376702i | \(0.877058\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.8328 | −1.42732 | −0.713659 | − | 0.700494i | \(-0.752963\pi\) | ||||
−0.713659 | + | 0.700494i | \(0.752963\pi\) | |||||||
\(860\) | −0.618034 | −0.0210748 | ||||||||
\(861\) | 5.09017 | 0.173473 | ||||||||
\(862\) | 23.3607 | 0.795668 | ||||||||
\(863\) | 31.3607 | 1.06753 | 0.533765 | − | 0.845633i | \(-0.320777\pi\) | ||||
0.533765 | + | 0.845633i | \(0.320777\pi\) | |||||||
\(864\) | −5.61803 | −0.191129 | ||||||||
\(865\) | 5.58359 | 0.189848 | ||||||||
\(866\) | 1.59675 | 0.0542597 | ||||||||
\(867\) | 0.944272 | 0.0320692 | ||||||||
\(868\) | 16.5623 | 0.562161 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.58359 | 0.0536888 | ||||||||
\(871\) | 9.23607 | 0.312952 | ||||||||
\(872\) | −16.9098 | −0.572639 | ||||||||
\(873\) | −17.0000 | −0.575363 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.76393 | 0.127244 | ||||||||
\(876\) | −18.7082 | −0.632092 | ||||||||
\(877\) | 41.7426 | 1.40955 | 0.704774 | − | 0.709431i | \(-0.251048\pi\) | ||||
0.704774 | + | 0.709431i | \(0.251048\pi\) | |||||||
\(878\) | −0.326238 | −0.0110100 | ||||||||
\(879\) | −13.2361 | −0.446441 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.9443 | −0.402413 | −0.201206 | − | 0.979549i | \(-0.564486\pi\) | ||||
−0.201206 | + | 0.979549i | \(0.564486\pi\) | |||||||
\(882\) | −0.618034 | −0.0208103 | ||||||||
\(883\) | −33.0344 | −1.11170 | −0.555849 | − | 0.831283i | \(-0.687607\pi\) | ||||
−0.555849 | + | 0.831283i | \(0.687607\pi\) | |||||||
\(884\) | −6.85410 | −0.230528 | ||||||||
\(885\) | 1.58359 | 0.0532319 | ||||||||
\(886\) | 22.6525 | 0.761025 | ||||||||
\(887\) | −21.4721 | −0.720964 | −0.360482 | − | 0.932766i | \(-0.617388\pi\) | ||||
−0.360482 | + | 0.932766i | \(0.617388\pi\) | |||||||
\(888\) | 15.5279 | 0.521081 | ||||||||
\(889\) | −7.32624 | −0.245714 | ||||||||
\(890\) | −1.50658 | −0.0505006 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.5623 | 0.688477 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 8.09017 | 0.270576 | ||||||||
\(895\) | 0.854102 | 0.0285495 | ||||||||
\(896\) | 11.3820 | 0.380245 | ||||||||
\(897\) | 3.23607 | 0.108049 | ||||||||
\(898\) | −9.67376 | −0.322818 | ||||||||
\(899\) | −68.6656 | −2.29013 | ||||||||
\(900\) | 7.85410 | 0.261803 | ||||||||
\(901\) | −32.2705 | −1.07509 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.00000 | −0.0332779 | ||||||||
\(904\) | −26.0557 | −0.866601 | ||||||||
\(905\) | 0.0901699 | 0.00299735 | ||||||||
\(906\) | 13.0344 | 0.433040 | ||||||||
\(907\) | 18.9787 | 0.630178 | 0.315089 | − | 0.949062i | \(-0.397966\pi\) | ||||
0.315089 | + | 0.949062i | \(0.397966\pi\) | |||||||
\(908\) | −30.7082 | −1.01909 | ||||||||
\(909\) | −4.18034 | −0.138653 | ||||||||
\(910\) | −0.236068 | −0.00782558 | ||||||||
\(911\) | −32.6738 | −1.08253 | −0.541265 | − | 0.840852i | \(-0.682054\pi\) | ||||
−0.541265 | + | 0.840852i | \(0.682054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −7.58359 | −0.250843 | ||||||||
\(915\) | 2.20163 | 0.0727835 | ||||||||
\(916\) | 18.9443 | 0.625936 | ||||||||
\(917\) | −3.32624 | −0.109842 | ||||||||
\(918\) | 2.61803 | 0.0864080 | ||||||||
\(919\) | −16.5836 | −0.547042 | −0.273521 | − | 0.961866i | \(-0.588188\pi\) | ||||
−0.273521 | + | 0.961866i | \(0.588188\pi\) | |||||||
\(920\) | 2.76393 | 0.0911241 | ||||||||
\(921\) | 19.1803 | 0.632014 | ||||||||
\(922\) | −14.3262 | −0.471810 | ||||||||
\(923\) | 7.47214 | 0.245948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.7082 | −1.10832 | ||||||||
\(926\) | 22.2016 | 0.729591 | ||||||||
\(927\) | −12.7082 | −0.417392 | ||||||||
\(928\) | −37.6869 | −1.23713 | ||||||||
\(929\) | −15.7771 | −0.517629 | −0.258815 | − | 0.965927i | \(-0.583332\pi\) | ||||
−0.258815 | + | 0.965927i | \(0.583332\pi\) | |||||||
\(930\) | −2.41641 | −0.0792371 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.0902 | −0.330515 | ||||||||
\(933\) | 16.7984 | 0.549954 | ||||||||
\(934\) | −19.7426 | −0.645999 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.23607 | −0.0730882 | ||||||||
\(937\) | −7.00000 | −0.228680 | −0.114340 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114340 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(938\) | 5.70820 | 0.186379 | ||||||||
\(939\) | −15.7984 | −0.515560 | ||||||||
\(940\) | −4.52786 | −0.147683 | ||||||||
\(941\) | −54.1803 | −1.76623 | −0.883114 | − | 0.469158i | \(-0.844558\pi\) | ||||
−0.883114 | + | 0.469158i | \(0.844558\pi\) | |||||||
\(942\) | 1.03444 | 0.0337039 | ||||||||
\(943\) | −16.4721 | −0.536407 | ||||||||
\(944\) | −7.68692 | −0.250188 | ||||||||
\(945\) | −0.381966 | −0.0124254 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.618034 | −0.0200834 | −0.0100417 | − | 0.999950i | \(-0.503196\pi\) | ||||
−0.0100417 | + | 0.999950i | \(0.503196\pi\) | |||||||
\(948\) | −17.5623 | −0.570397 | ||||||||
\(949\) | −11.5623 | −0.375328 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.3607 | 0.822376 | ||||||||
\(952\) | −9.47214 | −0.306994 | ||||||||
\(953\) | 19.2016 | 0.622002 | 0.311001 | − | 0.950410i | \(-0.399336\pi\) | ||||
0.311001 | + | 0.950410i | \(0.399336\pi\) | |||||||
\(954\) | −4.70820 | −0.152434 | ||||||||
\(955\) | −3.72949 | −0.120683 | ||||||||
\(956\) | −30.9787 | −1.00192 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.2918 | −0.429438 | ||||||||
\(959\) | −3.05573 | −0.0986746 | ||||||||
\(960\) | 0.0901699 | 0.00291022 | ||||||||
\(961\) | 73.7771 | 2.37991 | ||||||||
\(962\) | 4.29180 | 0.138373 | ||||||||
\(963\) | 15.7639 | 0.507986 | ||||||||
\(964\) | 39.9787 | 1.28763 | ||||||||
\(965\) | −1.93112 | −0.0621648 | ||||||||
\(966\) | 2.00000 | 0.0643489 | ||||||||
\(967\) | 36.2918 | 1.16707 | 0.583533 | − | 0.812090i | \(-0.301670\pi\) | ||||
0.583533 | + | 0.812090i | \(0.301670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.01316 | −0.128855 | ||||||||
\(971\) | −24.7082 | −0.792924 | −0.396462 | − | 0.918051i | \(-0.629762\pi\) | ||||
−0.396462 | + | 0.918051i | \(0.629762\pi\) | |||||||
\(972\) | −1.61803 | −0.0518985 | ||||||||
\(973\) | −17.5623 | −0.563022 | ||||||||
\(974\) | −10.2705 | −0.329088 | ||||||||
\(975\) | 4.85410 | 0.155456 | ||||||||
\(976\) | −10.6869 | −0.342080 | ||||||||
\(977\) | 33.0000 | 1.05576 | 0.527882 | − | 0.849318i | \(-0.322986\pi\) | ||||
0.527882 | + | 0.849318i | \(0.322986\pi\) | |||||||
\(978\) | −3.72949 | −0.119256 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.618034 | 0.0197424 | ||||||||
\(981\) | −7.56231 | −0.241446 | ||||||||
\(982\) | −2.29180 | −0.0731342 | ||||||||
\(983\) | −29.9443 | −0.955074 | −0.477537 | − | 0.878612i | \(-0.658470\pi\) | ||||
−0.477537 | + | 0.878612i | \(0.658470\pi\) | |||||||
\(984\) | 11.3820 | 0.362844 | ||||||||
\(985\) | 3.52786 | 0.112407 | ||||||||
\(986\) | 17.5623 | 0.559298 | ||||||||
\(987\) | −7.32624 | −0.233197 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.23607 | 0.102901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.6312 | 1.06833 | 0.534165 | − | 0.845380i | \(-0.320626\pi\) | ||||
0.534165 | + | 0.845380i | \(0.320626\pi\) | |||||||
\(992\) | 57.5066 | 1.82584 | ||||||||
\(993\) | −14.7082 | −0.466751 | ||||||||
\(994\) | 4.61803 | 0.146475 | ||||||||
\(995\) | 2.88854 | 0.0915730 | ||||||||
\(996\) | 9.70820 | 0.307616 | ||||||||
\(997\) | 1.41641 | 0.0448581 | 0.0224290 | − | 0.999748i | \(-0.492860\pi\) | ||||
0.0224290 | + | 0.999748i | \(0.492860\pi\) | |||||||
\(998\) | 3.09017 | 0.0978176 | ||||||||
\(999\) | 6.94427 | 0.219707 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2541.2.a.bb.1.1 | 2 | ||
3.2 | odd | 2 | 7623.2.a.ba.1.2 | 2 | |||
11.5 | even | 5 | 231.2.j.d.190.1 | yes | 4 | ||
11.9 | even | 5 | 231.2.j.d.169.1 | ✓ | 4 | ||
11.10 | odd | 2 | 2541.2.a.s.1.2 | 2 | |||
33.5 | odd | 10 | 693.2.m.b.190.1 | 4 | |||
33.20 | odd | 10 | 693.2.m.b.631.1 | 4 | |||
33.32 | even | 2 | 7623.2.a.bp.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.d.169.1 | ✓ | 4 | 11.9 | even | 5 | ||
231.2.j.d.190.1 | yes | 4 | 11.5 | even | 5 | ||
693.2.m.b.190.1 | 4 | 33.5 | odd | 10 | |||
693.2.m.b.631.1 | 4 | 33.20 | odd | 10 | |||
2541.2.a.s.1.2 | 2 | 11.10 | odd | 2 | |||
2541.2.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7623.2.a.ba.1.2 | 2 | 3.2 | odd | 2 | |||
7623.2.a.bp.1.1 | 2 | 33.32 | even | 2 |