Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7942,2,Mod(1,7942)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7942, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7942.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7942 = 2 \cdot 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7942.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: | \(63.4171892853\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7942.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.61803 | 0.934172 | 0.467086 | − | 0.884212i | \(-0.345304\pi\) | ||||
0.467086 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.85410 | −1.27639 | −0.638197 | − | 0.769873i | \(-0.720319\pi\) | ||||
−0.638197 | + | 0.769873i | \(0.720319\pi\) | |||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | −2.85410 | −0.902546 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | 5.23607 | 1.45222 | 0.726112 | − | 0.687576i | \(-0.241325\pi\) | ||||
0.726112 | + | 0.687576i | \(0.241325\pi\) | |||||||
\(14\) | 3.23607 | 0.864876 | ||||||||
\(15\) | −4.61803 | −1.19237 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.47214 | 1.56972 | 0.784862 | − | 0.619671i | \(-0.212734\pi\) | ||||
0.784862 | + | 0.619671i | \(0.212734\pi\) | |||||||
\(18\) | −0.381966 | −0.0900303 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.85410 | −0.638197 | ||||||||
\(21\) | 5.23607 | 1.14260 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.85410 | −0.595121 | −0.297561 | − | 0.954703i | \(-0.596173\pi\) | ||||
−0.297561 | + | 0.954703i | \(0.596173\pi\) | |||||||
\(24\) | 1.61803 | 0.330280 | ||||||||
\(25\) | 3.14590 | 0.629180 | ||||||||
\(26\) | 5.23607 | 1.02688 | ||||||||
\(27\) | −5.47214 | −1.05311 | ||||||||
\(28\) | 3.23607 | 0.611559 | ||||||||
\(29\) | 10.4721 | 1.94463 | 0.972313 | − | 0.233681i | \(-0.0750770\pi\) | ||||
0.972313 | + | 0.233681i | \(0.0750770\pi\) | |||||||
\(30\) | −4.61803 | −0.843134 | ||||||||
\(31\) | −6.09017 | −1.09383 | −0.546913 | − | 0.837189i | \(-0.684197\pi\) | ||||
−0.546913 | + | 0.837189i | \(0.684197\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.61803 | 0.281664 | ||||||||
\(34\) | 6.47214 | 1.10996 | ||||||||
\(35\) | −9.23607 | −1.56118 | ||||||||
\(36\) | −0.381966 | −0.0636610 | ||||||||
\(37\) | 5.38197 | 0.884790 | 0.442395 | − | 0.896820i | \(-0.354129\pi\) | ||||
0.442395 | + | 0.896820i | \(0.354129\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.47214 | 1.35663 | ||||||||
\(40\) | −2.85410 | −0.451273 | ||||||||
\(41\) | −10.9443 | −1.70921 | −0.854604 | − | 0.519280i | \(-0.826200\pi\) | ||||
−0.854604 | + | 0.519280i | \(0.826200\pi\) | |||||||
\(42\) | 5.23607 | 0.807943 | ||||||||
\(43\) | −3.23607 | −0.493496 | −0.246748 | − | 0.969080i | \(-0.579362\pi\) | ||||
−0.246748 | + | 0.969080i | \(0.579362\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.09017 | 0.162513 | ||||||||
\(46\) | −2.85410 | −0.420814 | ||||||||
\(47\) | 3.09017 | 0.450748 | 0.225374 | − | 0.974272i | \(-0.427640\pi\) | ||||
0.225374 | + | 0.974272i | \(0.427640\pi\) | |||||||
\(48\) | 1.61803 | 0.233543 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 3.14590 | 0.444897 | ||||||||
\(51\) | 10.4721 | 1.46639 | ||||||||
\(52\) | 5.23607 | 0.726112 | ||||||||
\(53\) | −1.14590 | −0.157401 | −0.0787006 | − | 0.996898i | \(-0.525077\pi\) | ||||
−0.0787006 | + | 0.996898i | \(0.525077\pi\) | |||||||
\(54\) | −5.47214 | −0.744663 | ||||||||
\(55\) | −2.85410 | −0.384847 | ||||||||
\(56\) | 3.23607 | 0.432438 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.4721 | 1.37506 | ||||||||
\(59\) | 7.85410 | 1.02252 | 0.511258 | − | 0.859427i | \(-0.329179\pi\) | ||||
0.511258 | + | 0.859427i | \(0.329179\pi\) | |||||||
\(60\) | −4.61803 | −0.596186 | ||||||||
\(61\) | 6.94427 | 0.889123 | 0.444561 | − | 0.895748i | \(-0.353360\pi\) | ||||
0.444561 | + | 0.895748i | \(0.353360\pi\) | |||||||
\(62\) | −6.09017 | −0.773452 | ||||||||
\(63\) | −1.23607 | −0.155730 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −14.9443 | −1.85361 | ||||||||
\(66\) | 1.61803 | 0.199166 | ||||||||
\(67\) | −4.14590 | −0.506502 | −0.253251 | − | 0.967401i | \(-0.581500\pi\) | ||||
−0.253251 | + | 0.967401i | \(0.581500\pi\) | |||||||
\(68\) | 6.47214 | 0.784862 | ||||||||
\(69\) | −4.61803 | −0.555946 | ||||||||
\(70\) | −9.23607 | −1.10392 | ||||||||
\(71\) | 1.52786 | 0.181324 | 0.0906621 | − | 0.995882i | \(-0.471102\pi\) | ||||
0.0906621 | + | 0.995882i | \(0.471102\pi\) | |||||||
\(72\) | −0.381966 | −0.0450151 | ||||||||
\(73\) | −5.70820 | −0.668095 | −0.334047 | − | 0.942556i | \(-0.608415\pi\) | ||||
−0.334047 | + | 0.942556i | \(0.608415\pi\) | |||||||
\(74\) | 5.38197 | 0.625641 | ||||||||
\(75\) | 5.09017 | 0.587762 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23607 | 0.368784 | ||||||||
\(78\) | 8.47214 | 0.959280 | ||||||||
\(79\) | 16.4721 | 1.85326 | 0.926630 | − | 0.375974i | \(-0.122692\pi\) | ||||
0.926630 | + | 0.375974i | \(0.122692\pi\) | |||||||
\(80\) | −2.85410 | −0.319098 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | −10.9443 | −1.20859 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 5.23607 | 0.571302 | ||||||||
\(85\) | −18.4721 | −2.00358 | ||||||||
\(86\) | −3.23607 | −0.348954 | ||||||||
\(87\) | 16.9443 | 1.81662 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −1.85410 | −0.196534 | −0.0982672 | − | 0.995160i | \(-0.531330\pi\) | ||||
−0.0982672 | + | 0.995160i | \(0.531330\pi\) | |||||||
\(90\) | 1.09017 | 0.114914 | ||||||||
\(91\) | 16.9443 | 1.77624 | ||||||||
\(92\) | −2.85410 | −0.297561 | ||||||||
\(93\) | −9.85410 | −1.02182 | ||||||||
\(94\) | 3.09017 | 0.318727 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.61803 | 0.165140 | ||||||||
\(97\) | −16.4721 | −1.67249 | −0.836246 | − | 0.548354i | \(-0.815254\pi\) | ||||
−0.836246 | + | 0.548354i | \(0.815254\pi\) | |||||||
\(98\) | 3.47214 | 0.350739 | ||||||||
\(99\) | −0.381966 | −0.0383890 | ||||||||
\(100\) | 3.14590 | 0.314590 | ||||||||
\(101\) | 10.7639 | 1.07105 | 0.535526 | − | 0.844519i | \(-0.320114\pi\) | ||||
0.535526 | + | 0.844519i | \(0.320114\pi\) | |||||||
\(102\) | 10.4721 | 1.03690 | ||||||||
\(103\) | −0.944272 | −0.0930419 | −0.0465209 | − | 0.998917i | \(-0.514813\pi\) | ||||
−0.0465209 | + | 0.998917i | \(0.514813\pi\) | |||||||
\(104\) | 5.23607 | 0.513439 | ||||||||
\(105\) | −14.9443 | −1.45841 | ||||||||
\(106\) | −1.14590 | −0.111299 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | −5.47214 | −0.526557 | ||||||||
\(109\) | −10.1803 | −0.975100 | −0.487550 | − | 0.873095i | \(-0.662109\pi\) | ||||
−0.487550 | + | 0.873095i | \(0.662109\pi\) | |||||||
\(110\) | −2.85410 | −0.272128 | ||||||||
\(111\) | 8.70820 | 0.826546 | ||||||||
\(112\) | 3.23607 | 0.305780 | ||||||||
\(113\) | 14.7984 | 1.39211 | 0.696057 | − | 0.717987i | \(-0.254936\pi\) | ||||
0.696057 | + | 0.717987i | \(0.254936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.14590 | 0.759609 | ||||||||
\(116\) | 10.4721 | 0.972313 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 7.85410 | 0.723029 | ||||||||
\(119\) | 20.9443 | 1.91996 | ||||||||
\(120\) | −4.61803 | −0.421567 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.94427 | 0.628705 | ||||||||
\(123\) | −17.7082 | −1.59669 | ||||||||
\(124\) | −6.09017 | −0.546913 | ||||||||
\(125\) | 5.29180 | 0.473313 | ||||||||
\(126\) | −1.23607 | −0.110118 | ||||||||
\(127\) | −9.41641 | −0.835571 | −0.417786 | − | 0.908546i | \(-0.637194\pi\) | ||||
−0.417786 | + | 0.908546i | \(0.637194\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.23607 | −0.461010 | ||||||||
\(130\) | −14.9443 | −1.31070 | ||||||||
\(131\) | −17.4164 | −1.52168 | −0.760839 | − | 0.648940i | \(-0.775212\pi\) | ||||
−0.760839 | + | 0.648940i | \(0.775212\pi\) | |||||||
\(132\) | 1.61803 | 0.140832 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.14590 | −0.358151 | ||||||||
\(135\) | 15.6180 | 1.34419 | ||||||||
\(136\) | 6.47214 | 0.554981 | ||||||||
\(137\) | 13.8541 | 1.18364 | 0.591818 | − | 0.806072i | \(-0.298410\pi\) | ||||
0.591818 | + | 0.806072i | \(0.298410\pi\) | |||||||
\(138\) | −4.61803 | −0.393113 | ||||||||
\(139\) | 13.4164 | 1.13796 | 0.568982 | − | 0.822350i | \(-0.307337\pi\) | ||||
0.568982 | + | 0.822350i | \(0.307337\pi\) | |||||||
\(140\) | −9.23607 | −0.780590 | ||||||||
\(141\) | 5.00000 | 0.421076 | ||||||||
\(142\) | 1.52786 | 0.128216 | ||||||||
\(143\) | 5.23607 | 0.437862 | ||||||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | −29.8885 | −2.48211 | ||||||||
\(146\) | −5.70820 | −0.472414 | ||||||||
\(147\) | 5.61803 | 0.463368 | ||||||||
\(148\) | 5.38197 | 0.442395 | ||||||||
\(149\) | −18.7639 | −1.53720 | −0.768601 | − | 0.639729i | \(-0.779047\pi\) | ||||
−0.768601 | + | 0.639729i | \(0.779047\pi\) | |||||||
\(150\) | 5.09017 | 0.415611 | ||||||||
\(151\) | −16.4721 | −1.34048 | −0.670242 | − | 0.742143i | \(-0.733810\pi\) | ||||
−0.670242 | + | 0.742143i | \(0.733810\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.47214 | −0.199860 | ||||||||
\(154\) | 3.23607 | 0.260770 | ||||||||
\(155\) | 17.3820 | 1.39615 | ||||||||
\(156\) | 8.47214 | 0.678314 | ||||||||
\(157\) | 15.5623 | 1.24201 | 0.621004 | − | 0.783808i | \(-0.286725\pi\) | ||||
0.621004 | + | 0.783808i | \(0.286725\pi\) | |||||||
\(158\) | 16.4721 | 1.31045 | ||||||||
\(159\) | −1.85410 | −0.147040 | ||||||||
\(160\) | −2.85410 | −0.225637 | ||||||||
\(161\) | −9.23607 | −0.727904 | ||||||||
\(162\) | −7.70820 | −0.605614 | ||||||||
\(163\) | 3.14590 | 0.246406 | 0.123203 | − | 0.992382i | \(-0.460683\pi\) | ||||
0.123203 | + | 0.992382i | \(0.460683\pi\) | |||||||
\(164\) | −10.9443 | −0.854604 | ||||||||
\(165\) | −4.61803 | −0.359513 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | 25.2361 | 1.95283 | 0.976413 | − | 0.215912i | \(-0.0692725\pi\) | ||||
0.976413 | + | 0.215912i | \(0.0692725\pi\) | |||||||
\(168\) | 5.23607 | 0.403971 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | −18.4721 | −1.41675 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.23607 | −0.246748 | ||||||||
\(173\) | 15.2361 | 1.15838 | 0.579188 | − | 0.815194i | \(-0.303370\pi\) | ||||
0.579188 | + | 0.815194i | \(0.303370\pi\) | |||||||
\(174\) | 16.9443 | 1.28454 | ||||||||
\(175\) | 10.1803 | 0.769561 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 12.7082 | 0.955207 | ||||||||
\(178\) | −1.85410 | −0.138971 | ||||||||
\(179\) | −12.0902 | −0.903662 | −0.451831 | − | 0.892104i | \(-0.649229\pi\) | ||||
−0.451831 | + | 0.892104i | \(0.649229\pi\) | |||||||
\(180\) | 1.09017 | 0.0812565 | ||||||||
\(181\) | −1.67376 | −0.124410 | −0.0622049 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622049 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(182\) | 16.9443 | 1.25599 | ||||||||
\(183\) | 11.2361 | 0.830594 | ||||||||
\(184\) | −2.85410 | −0.210407 | ||||||||
\(185\) | −15.3607 | −1.12934 | ||||||||
\(186\) | −9.85410 | −0.722538 | ||||||||
\(187\) | 6.47214 | 0.473289 | ||||||||
\(188\) | 3.09017 | 0.225374 | ||||||||
\(189\) | −17.7082 | −1.28808 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.38197 | −0.244710 | −0.122355 | − | 0.992486i | \(-0.539045\pi\) | ||||
−0.122355 | + | 0.992486i | \(0.539045\pi\) | |||||||
\(192\) | 1.61803 | 0.116772 | ||||||||
\(193\) | −23.8885 | −1.71954 | −0.859768 | − | 0.510686i | \(-0.829392\pi\) | ||||
−0.859768 | + | 0.510686i | \(0.829392\pi\) | |||||||
\(194\) | −16.4721 | −1.18263 | ||||||||
\(195\) | −24.1803 | −1.73159 | ||||||||
\(196\) | 3.47214 | 0.248010 | ||||||||
\(197\) | −13.5279 | −0.963820 | −0.481910 | − | 0.876221i | \(-0.660057\pi\) | ||||
−0.481910 | + | 0.876221i | \(0.660057\pi\) | |||||||
\(198\) | −0.381966 | −0.0271451 | ||||||||
\(199\) | 6.67376 | 0.473090 | 0.236545 | − | 0.971620i | \(-0.423985\pi\) | ||||
0.236545 | + | 0.971620i | \(0.423985\pi\) | |||||||
\(200\) | 3.14590 | 0.222449 | ||||||||
\(201\) | −6.70820 | −0.473160 | ||||||||
\(202\) | 10.7639 | 0.757348 | ||||||||
\(203\) | 33.8885 | 2.37851 | ||||||||
\(204\) | 10.4721 | 0.733196 | ||||||||
\(205\) | 31.2361 | 2.18162 | ||||||||
\(206\) | −0.944272 | −0.0657905 | ||||||||
\(207\) | 1.09017 | 0.0757720 | ||||||||
\(208\) | 5.23607 | 0.363056 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −14.9443 | −1.03125 | ||||||||
\(211\) | −6.94427 | −0.478063 | −0.239032 | − | 0.971012i | \(-0.576830\pi\) | ||||
−0.239032 | + | 0.971012i | \(0.576830\pi\) | |||||||
\(212\) | −1.14590 | −0.0787006 | ||||||||
\(213\) | 2.47214 | 0.169388 | ||||||||
\(214\) | 6.00000 | 0.410152 | ||||||||
\(215\) | 9.23607 | 0.629895 | ||||||||
\(216\) | −5.47214 | −0.372332 | ||||||||
\(217\) | −19.7082 | −1.33788 | ||||||||
\(218\) | −10.1803 | −0.689500 | ||||||||
\(219\) | −9.23607 | −0.624116 | ||||||||
\(220\) | −2.85410 | −0.192424 | ||||||||
\(221\) | 33.8885 | 2.27959 | ||||||||
\(222\) | 8.70820 | 0.584456 | ||||||||
\(223\) | 9.56231 | 0.640339 | 0.320170 | − | 0.947360i | \(-0.396260\pi\) | ||||
0.320170 | + | 0.947360i | \(0.396260\pi\) | |||||||
\(224\) | 3.23607 | 0.216219 | ||||||||
\(225\) | −1.20163 | −0.0801084 | ||||||||
\(226\) | 14.7984 | 0.984373 | ||||||||
\(227\) | 22.3607 | 1.48413 | 0.742065 | − | 0.670328i | \(-0.233846\pi\) | ||||
0.742065 | + | 0.670328i | \(0.233846\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.61803 | −0.239086 | −0.119543 | − | 0.992829i | \(-0.538143\pi\) | ||||
−0.119543 | + | 0.992829i | \(0.538143\pi\) | |||||||
\(230\) | 8.14590 | 0.537125 | ||||||||
\(231\) | 5.23607 | 0.344508 | ||||||||
\(232\) | 10.4721 | 0.687529 | ||||||||
\(233\) | 1.52786 | 0.100094 | 0.0500469 | − | 0.998747i | \(-0.484063\pi\) | ||||
0.0500469 | + | 0.998747i | \(0.484063\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | −8.81966 | −0.575331 | ||||||||
\(236\) | 7.85410 | 0.511258 | ||||||||
\(237\) | 26.6525 | 1.73126 | ||||||||
\(238\) | 20.9443 | 1.35762 | ||||||||
\(239\) | 19.7082 | 1.27482 | 0.637409 | − | 0.770526i | \(-0.280006\pi\) | ||||
0.637409 | + | 0.770526i | \(0.280006\pi\) | |||||||
\(240\) | −4.61803 | −0.298093 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | 6.94427 | 0.444561 | ||||||||
\(245\) | −9.90983 | −0.633116 | ||||||||
\(246\) | −17.7082 | −1.12903 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.09017 | −0.386726 | ||||||||
\(249\) | 9.70820 | 0.615232 | ||||||||
\(250\) | 5.29180 | 0.334683 | ||||||||
\(251\) | 4.14590 | 0.261687 | 0.130843 | − | 0.991403i | \(-0.458231\pi\) | ||||
0.130843 | + | 0.991403i | \(0.458231\pi\) | |||||||
\(252\) | −1.23607 | −0.0778650 | ||||||||
\(253\) | −2.85410 | −0.179436 | ||||||||
\(254\) | −9.41641 | −0.590838 | ||||||||
\(255\) | −29.8885 | −1.87169 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.9443 | 1.68074 | 0.840369 | − | 0.542015i | \(-0.182338\pi\) | ||||
0.840369 | + | 0.542015i | \(0.182338\pi\) | |||||||
\(258\) | −5.23607 | −0.325983 | ||||||||
\(259\) | 17.4164 | 1.08220 | ||||||||
\(260\) | −14.9443 | −0.926804 | ||||||||
\(261\) | −4.00000 | −0.247594 | ||||||||
\(262\) | −17.4164 | −1.07599 | ||||||||
\(263\) | 29.2361 | 1.80277 | 0.901387 | − | 0.433015i | \(-0.142550\pi\) | ||||
0.901387 | + | 0.433015i | \(0.142550\pi\) | |||||||
\(264\) | 1.61803 | 0.0995831 | ||||||||
\(265\) | 3.27051 | 0.200906 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.00000 | −0.183597 | ||||||||
\(268\) | −4.14590 | −0.253251 | ||||||||
\(269\) | −19.5623 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(270\) | 15.6180 | 0.950483 | ||||||||
\(271\) | −20.7639 | −1.26132 | −0.630660 | − | 0.776060i | \(-0.717216\pi\) | ||||
−0.630660 | + | 0.776060i | \(0.717216\pi\) | |||||||
\(272\) | 6.47214 | 0.392431 | ||||||||
\(273\) | 27.4164 | 1.65932 | ||||||||
\(274\) | 13.8541 | 0.836957 | ||||||||
\(275\) | 3.14590 | 0.189705 | ||||||||
\(276\) | −4.61803 | −0.277973 | ||||||||
\(277\) | 13.7082 | 0.823646 | 0.411823 | − | 0.911264i | \(-0.364892\pi\) | ||||
0.411823 | + | 0.911264i | \(0.364892\pi\) | |||||||
\(278\) | 13.4164 | 0.804663 | ||||||||
\(279\) | 2.32624 | 0.139268 | ||||||||
\(280\) | −9.23607 | −0.551961 | ||||||||
\(281\) | 11.2361 | 0.670288 | 0.335144 | − | 0.942167i | \(-0.391215\pi\) | ||||
0.335144 | + | 0.942167i | \(0.391215\pi\) | |||||||
\(282\) | 5.00000 | 0.297746 | ||||||||
\(283\) | 16.9443 | 1.00723 | 0.503616 | − | 0.863927i | \(-0.332003\pi\) | ||||
0.503616 | + | 0.863927i | \(0.332003\pi\) | |||||||
\(284\) | 1.52786 | 0.0906621 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.23607 | 0.309615 | ||||||||
\(287\) | −35.4164 | −2.09056 | ||||||||
\(288\) | −0.381966 | −0.0225076 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | −29.8885 | −1.75512 | ||||||||
\(291\) | −26.6525 | −1.56240 | ||||||||
\(292\) | −5.70820 | −0.334047 | ||||||||
\(293\) | −23.4164 | −1.36800 | −0.684001 | − | 0.729481i | \(-0.739761\pi\) | ||||
−0.684001 | + | 0.729481i | \(0.739761\pi\) | |||||||
\(294\) | 5.61803 | 0.327650 | ||||||||
\(295\) | −22.4164 | −1.30513 | ||||||||
\(296\) | 5.38197 | 0.312820 | ||||||||
\(297\) | −5.47214 | −0.317526 | ||||||||
\(298\) | −18.7639 | −1.08697 | ||||||||
\(299\) | −14.9443 | −0.864250 | ||||||||
\(300\) | 5.09017 | 0.293881 | ||||||||
\(301\) | −10.4721 | −0.603604 | ||||||||
\(302\) | −16.4721 | −0.947865 | ||||||||
\(303\) | 17.4164 | 1.00055 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.8197 | −1.13487 | ||||||||
\(306\) | −2.47214 | −0.141323 | ||||||||
\(307\) | 2.58359 | 0.147453 | 0.0737267 | − | 0.997278i | \(-0.476511\pi\) | ||||
0.0737267 | + | 0.997278i | \(0.476511\pi\) | |||||||
\(308\) | 3.23607 | 0.184392 | ||||||||
\(309\) | −1.52786 | −0.0869171 | ||||||||
\(310\) | 17.3820 | 0.987229 | ||||||||
\(311\) | −30.5066 | −1.72987 | −0.864935 | − | 0.501884i | \(-0.832640\pi\) | ||||
−0.864935 | + | 0.501884i | \(0.832640\pi\) | |||||||
\(312\) | 8.47214 | 0.479640 | ||||||||
\(313\) | 3.52786 | 0.199407 | 0.0997033 | − | 0.995017i | \(-0.468211\pi\) | ||||
0.0997033 | + | 0.995017i | \(0.468211\pi\) | |||||||
\(314\) | 15.5623 | 0.878232 | ||||||||
\(315\) | 3.52786 | 0.198773 | ||||||||
\(316\) | 16.4721 | 0.926630 | ||||||||
\(317\) | 9.41641 | 0.528878 | 0.264439 | − | 0.964402i | \(-0.414813\pi\) | ||||
0.264439 | + | 0.964402i | \(0.414813\pi\) | |||||||
\(318\) | −1.85410 | −0.103973 | ||||||||
\(319\) | 10.4721 | 0.586327 | ||||||||
\(320\) | −2.85410 | −0.159549 | ||||||||
\(321\) | 9.70820 | 0.541859 | ||||||||
\(322\) | −9.23607 | −0.514706 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | 16.4721 | 0.913710 | ||||||||
\(326\) | 3.14590 | 0.174235 | ||||||||
\(327\) | −16.4721 | −0.910911 | ||||||||
\(328\) | −10.9443 | −0.604296 | ||||||||
\(329\) | 10.0000 | 0.551318 | ||||||||
\(330\) | −4.61803 | −0.254214 | ||||||||
\(331\) | −7.14590 | −0.392774 | −0.196387 | − | 0.980526i | \(-0.562921\pi\) | ||||
−0.196387 | + | 0.980526i | \(0.562921\pi\) | |||||||
\(332\) | 6.00000 | 0.329293 | ||||||||
\(333\) | −2.05573 | −0.112653 | ||||||||
\(334\) | 25.2361 | 1.38086 | ||||||||
\(335\) | 11.8328 | 0.646496 | ||||||||
\(336\) | 5.23607 | 0.285651 | ||||||||
\(337\) | −3.88854 | −0.211822 | −0.105911 | − | 0.994376i | \(-0.533776\pi\) | ||||
−0.105911 | + | 0.994376i | \(0.533776\pi\) | |||||||
\(338\) | 14.4164 | 0.784149 | ||||||||
\(339\) | 23.9443 | 1.30047 | ||||||||
\(340\) | −18.4721 | −1.00179 | ||||||||
\(341\) | −6.09017 | −0.329801 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | −3.23607 | −0.174477 | ||||||||
\(345\) | 13.1803 | 0.709606 | ||||||||
\(346\) | 15.2361 | 0.819096 | ||||||||
\(347\) | −12.9443 | −0.694885 | −0.347442 | − | 0.937701i | \(-0.612950\pi\) | ||||
−0.347442 | + | 0.937701i | \(0.612950\pi\) | |||||||
\(348\) | 16.9443 | 0.908308 | ||||||||
\(349\) | 17.8885 | 0.957552 | 0.478776 | − | 0.877937i | \(-0.341081\pi\) | ||||
0.478776 | + | 0.877937i | \(0.341081\pi\) | |||||||
\(350\) | 10.1803 | 0.544162 | ||||||||
\(351\) | −28.6525 | −1.52936 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −21.8541 | −1.16318 | −0.581588 | − | 0.813483i | \(-0.697568\pi\) | ||||
−0.581588 | + | 0.813483i | \(0.697568\pi\) | |||||||
\(354\) | 12.7082 | 0.675433 | ||||||||
\(355\) | −4.36068 | −0.231441 | ||||||||
\(356\) | −1.85410 | −0.0982672 | ||||||||
\(357\) | 33.8885 | 1.79357 | ||||||||
\(358\) | −12.0902 | −0.638985 | ||||||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 1.09017 | 0.0574570 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −1.67376 | −0.0879710 | ||||||||
\(363\) | 1.61803 | 0.0849248 | ||||||||
\(364\) | 16.9443 | 0.888121 | ||||||||
\(365\) | 16.2918 | 0.852752 | ||||||||
\(366\) | 11.2361 | 0.587319 | ||||||||
\(367\) | −9.20163 | −0.480321 | −0.240160 | − | 0.970733i | \(-0.577200\pi\) | ||||
−0.240160 | + | 0.970733i | \(0.577200\pi\) | |||||||
\(368\) | −2.85410 | −0.148780 | ||||||||
\(369\) | 4.18034 | 0.217620 | ||||||||
\(370\) | −15.3607 | −0.798564 | ||||||||
\(371\) | −3.70820 | −0.192520 | ||||||||
\(372\) | −9.85410 | −0.510911 | ||||||||
\(373\) | 1.34752 | 0.0697722 | 0.0348861 | − | 0.999391i | \(-0.488893\pi\) | ||||
0.0348861 | + | 0.999391i | \(0.488893\pi\) | |||||||
\(374\) | 6.47214 | 0.334666 | ||||||||
\(375\) | 8.56231 | 0.442156 | ||||||||
\(376\) | 3.09017 | 0.159363 | ||||||||
\(377\) | 54.8328 | 2.82403 | ||||||||
\(378\) | −17.7082 | −0.910812 | ||||||||
\(379\) | 30.8328 | 1.58378 | 0.791888 | − | 0.610667i | \(-0.209099\pi\) | ||||
0.791888 | + | 0.610667i | \(0.209099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.2361 | −0.780567 | ||||||||
\(382\) | −3.38197 | −0.173036 | ||||||||
\(383\) | 6.85410 | 0.350228 | 0.175114 | − | 0.984548i | \(-0.443971\pi\) | ||||
0.175114 | + | 0.984548i | \(0.443971\pi\) | |||||||
\(384\) | 1.61803 | 0.0825700 | ||||||||
\(385\) | −9.23607 | −0.470714 | ||||||||
\(386\) | −23.8885 | −1.21589 | ||||||||
\(387\) | 1.23607 | 0.0628329 | ||||||||
\(388\) | −16.4721 | −0.836246 | ||||||||
\(389\) | −3.79837 | −0.192585 | −0.0962926 | − | 0.995353i | \(-0.530698\pi\) | ||||
−0.0962926 | + | 0.995353i | \(0.530698\pi\) | |||||||
\(390\) | −24.1803 | −1.22442 | ||||||||
\(391\) | −18.4721 | −0.934176 | ||||||||
\(392\) | 3.47214 | 0.175369 | ||||||||
\(393\) | −28.1803 | −1.42151 | ||||||||
\(394\) | −13.5279 | −0.681524 | ||||||||
\(395\) | −47.0132 | −2.36549 | ||||||||
\(396\) | −0.381966 | −0.0191945 | ||||||||
\(397\) | −16.3820 | −0.822187 | −0.411094 | − | 0.911593i | \(-0.634853\pi\) | ||||
−0.411094 | + | 0.911593i | \(0.634853\pi\) | |||||||
\(398\) | 6.67376 | 0.334525 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.14590 | 0.157295 | ||||||||
\(401\) | 13.9787 | 0.698064 | 0.349032 | − | 0.937111i | \(-0.386511\pi\) | ||||
0.349032 | + | 0.937111i | \(0.386511\pi\) | |||||||
\(402\) | −6.70820 | −0.334575 | ||||||||
\(403\) | −31.8885 | −1.58848 | ||||||||
\(404\) | 10.7639 | 0.535526 | ||||||||
\(405\) | 22.0000 | 1.09319 | ||||||||
\(406\) | 33.8885 | 1.68186 | ||||||||
\(407\) | 5.38197 | 0.266774 | ||||||||
\(408\) | 10.4721 | 0.518448 | ||||||||
\(409\) | −15.7082 | −0.776721 | −0.388360 | − | 0.921508i | \(-0.626958\pi\) | ||||
−0.388360 | + | 0.921508i | \(0.626958\pi\) | |||||||
\(410\) | 31.2361 | 1.54264 | ||||||||
\(411\) | 22.4164 | 1.10572 | ||||||||
\(412\) | −0.944272 | −0.0465209 | ||||||||
\(413\) | 25.4164 | 1.25066 | ||||||||
\(414\) | 1.09017 | 0.0535789 | ||||||||
\(415\) | −17.1246 | −0.840614 | ||||||||
\(416\) | 5.23607 | 0.256719 | ||||||||
\(417\) | 21.7082 | 1.06306 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.673762 | −0.0329154 | −0.0164577 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164577 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(420\) | −14.9443 | −0.729206 | ||||||||
\(421\) | 33.4508 | 1.63029 | 0.815147 | − | 0.579254i | \(-0.196656\pi\) | ||||
0.815147 | + | 0.579254i | \(0.196656\pi\) | |||||||
\(422\) | −6.94427 | −0.338042 | ||||||||
\(423\) | −1.18034 | −0.0573901 | ||||||||
\(424\) | −1.14590 | −0.0556497 | ||||||||
\(425\) | 20.3607 | 0.987638 | ||||||||
\(426\) | 2.47214 | 0.119775 | ||||||||
\(427\) | 22.4721 | 1.08750 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 8.47214 | 0.409039 | ||||||||
\(430\) | 9.23607 | 0.445403 | ||||||||
\(431\) | −14.7639 | −0.711154 | −0.355577 | − | 0.934647i | \(-0.615716\pi\) | ||||
−0.355577 | + | 0.934647i | \(0.615716\pi\) | |||||||
\(432\) | −5.47214 | −0.263278 | ||||||||
\(433\) | −9.79837 | −0.470880 | −0.235440 | − | 0.971889i | \(-0.575653\pi\) | ||||
−0.235440 | + | 0.971889i | \(0.575653\pi\) | |||||||
\(434\) | −19.7082 | −0.946024 | ||||||||
\(435\) | −48.3607 | −2.31872 | ||||||||
\(436\) | −10.1803 | −0.487550 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −9.23607 | −0.441316 | ||||||||
\(439\) | 7.34752 | 0.350678 | 0.175339 | − | 0.984508i | \(-0.443898\pi\) | ||||
0.175339 | + | 0.984508i | \(0.443898\pi\) | |||||||
\(440\) | −2.85410 | −0.136064 | ||||||||
\(441\) | −1.32624 | −0.0631542 | ||||||||
\(442\) | 33.8885 | 1.61191 | ||||||||
\(443\) | 15.2705 | 0.725524 | 0.362762 | − | 0.931882i | \(-0.381834\pi\) | ||||
0.362762 | + | 0.931882i | \(0.381834\pi\) | |||||||
\(444\) | 8.70820 | 0.413273 | ||||||||
\(445\) | 5.29180 | 0.250855 | ||||||||
\(446\) | 9.56231 | 0.452788 | ||||||||
\(447\) | −30.3607 | −1.43601 | ||||||||
\(448\) | 3.23607 | 0.152890 | ||||||||
\(449\) | 5.56231 | 0.262501 | 0.131251 | − | 0.991349i | \(-0.458101\pi\) | ||||
0.131251 | + | 0.991349i | \(0.458101\pi\) | |||||||
\(450\) | −1.20163 | −0.0566452 | ||||||||
\(451\) | −10.9443 | −0.515346 | ||||||||
\(452\) | 14.7984 | 0.696057 | ||||||||
\(453\) | −26.6525 | −1.25224 | ||||||||
\(454\) | 22.3607 | 1.04944 | ||||||||
\(455\) | −48.3607 | −2.26718 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.76393 | −0.222847 | −0.111424 | − | 0.993773i | \(-0.535541\pi\) | ||||
−0.111424 | + | 0.993773i | \(0.535541\pi\) | |||||||
\(458\) | −3.61803 | −0.169060 | ||||||||
\(459\) | −35.4164 | −1.65310 | ||||||||
\(460\) | 8.14590 | 0.379804 | ||||||||
\(461\) | −20.6525 | −0.961882 | −0.480941 | − | 0.876753i | \(-0.659705\pi\) | ||||
−0.480941 | + | 0.876753i | \(0.659705\pi\) | |||||||
\(462\) | 5.23607 | 0.243604 | ||||||||
\(463\) | −39.1591 | −1.81988 | −0.909938 | − | 0.414745i | \(-0.863871\pi\) | ||||
−0.909938 | + | 0.414745i | \(0.863871\pi\) | |||||||
\(464\) | 10.4721 | 0.486157 | ||||||||
\(465\) | 28.1246 | 1.30425 | ||||||||
\(466\) | 1.52786 | 0.0707769 | ||||||||
\(467\) | 1.61803 | 0.0748737 | 0.0374368 | − | 0.999299i | \(-0.488081\pi\) | ||||
0.0374368 | + | 0.999299i | \(0.488081\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | −13.4164 | −0.619512 | ||||||||
\(470\) | −8.81966 | −0.406821 | ||||||||
\(471\) | 25.1803 | 1.16025 | ||||||||
\(472\) | 7.85410 | 0.361514 | ||||||||
\(473\) | −3.23607 | −0.148795 | ||||||||
\(474\) | 26.6525 | 1.22419 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 20.9443 | 0.959979 | ||||||||
\(477\) | 0.437694 | 0.0200406 | ||||||||
\(478\) | 19.7082 | 0.901432 | ||||||||
\(479\) | −17.1246 | −0.782443 | −0.391222 | − | 0.920296i | \(-0.627947\pi\) | ||||
−0.391222 | + | 0.920296i | \(0.627947\pi\) | |||||||
\(480\) | −4.61803 | −0.210783 | ||||||||
\(481\) | 28.1803 | 1.28491 | ||||||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | −14.9443 | −0.679988 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 47.0132 | 2.13476 | ||||||||
\(486\) | 3.94427 | 0.178916 | ||||||||
\(487\) | −10.8541 | −0.491846 | −0.245923 | − | 0.969289i | \(-0.579091\pi\) | ||||
−0.245923 | + | 0.969289i | \(0.579091\pi\) | |||||||
\(488\) | 6.94427 | 0.314352 | ||||||||
\(489\) | 5.09017 | 0.230185 | ||||||||
\(490\) | −9.90983 | −0.447680 | ||||||||
\(491\) | 22.9443 | 1.03546 | 0.517730 | − | 0.855544i | \(-0.326777\pi\) | ||||
0.517730 | + | 0.855544i | \(0.326777\pi\) | |||||||
\(492\) | −17.7082 | −0.798347 | ||||||||
\(493\) | 67.7771 | 3.05253 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.09017 | 0.0489995 | ||||||||
\(496\) | −6.09017 | −0.273457 | ||||||||
\(497\) | 4.94427 | 0.221781 | ||||||||
\(498\) | 9.70820 | 0.435035 | ||||||||
\(499\) | −2.03444 | −0.0910741 | −0.0455371 | − | 0.998963i | \(-0.514500\pi\) | ||||
−0.0455371 | + | 0.998963i | \(0.514500\pi\) | |||||||
\(500\) | 5.29180 | 0.236656 | ||||||||
\(501\) | 40.8328 | 1.82428 | ||||||||
\(502\) | 4.14590 | 0.185040 | ||||||||
\(503\) | 4.76393 | 0.212413 | 0.106207 | − | 0.994344i | \(-0.466130\pi\) | ||||
0.106207 | + | 0.994344i | \(0.466130\pi\) | |||||||
\(504\) | −1.23607 | −0.0550588 | ||||||||
\(505\) | −30.7214 | −1.36708 | ||||||||
\(506\) | −2.85410 | −0.126880 | ||||||||
\(507\) | 23.3262 | 1.03595 | ||||||||
\(508\) | −9.41641 | −0.417786 | ||||||||
\(509\) | 16.4721 | 0.730115 | 0.365057 | − | 0.930985i | \(-0.381049\pi\) | ||||
0.365057 | + | 0.930985i | \(0.381049\pi\) | |||||||
\(510\) | −29.8885 | −1.32349 | ||||||||
\(511\) | −18.4721 | −0.817159 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.9443 | 1.18846 | ||||||||
\(515\) | 2.69505 | 0.118758 | ||||||||
\(516\) | −5.23607 | −0.230505 | ||||||||
\(517\) | 3.09017 | 0.135906 | ||||||||
\(518\) | 17.4164 | 0.765233 | ||||||||
\(519\) | 24.6525 | 1.08212 | ||||||||
\(520\) | −14.9443 | −0.655350 | ||||||||
\(521\) | 26.0000 | 1.13908 | 0.569540 | − | 0.821963i | \(-0.307121\pi\) | ||||
0.569540 | + | 0.821963i | \(0.307121\pi\) | |||||||
\(522\) | −4.00000 | −0.175075 | ||||||||
\(523\) | −1.23607 | −0.0540495 | −0.0270247 | − | 0.999635i | \(-0.508603\pi\) | ||||
−0.0270247 | + | 0.999635i | \(0.508603\pi\) | |||||||
\(524\) | −17.4164 | −0.760839 | ||||||||
\(525\) | 16.4721 | 0.718903 | ||||||||
\(526\) | 29.2361 | 1.27475 | ||||||||
\(527\) | −39.4164 | −1.71701 | ||||||||
\(528\) | 1.61803 | 0.0704159 | ||||||||
\(529\) | −14.8541 | −0.645831 | ||||||||
\(530\) | 3.27051 | 0.142062 | ||||||||
\(531\) | −3.00000 | −0.130189 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −57.3050 | −2.48215 | ||||||||
\(534\) | −3.00000 | −0.129823 | ||||||||
\(535\) | −17.1246 | −0.740362 | ||||||||
\(536\) | −4.14590 | −0.179076 | ||||||||
\(537\) | −19.5623 | −0.844176 | ||||||||
\(538\) | −19.5623 | −0.843391 | ||||||||
\(539\) | 3.47214 | 0.149555 | ||||||||
\(540\) | 15.6180 | 0.672093 | ||||||||
\(541\) | −8.83282 | −0.379752 | −0.189876 | − | 0.981808i | \(-0.560809\pi\) | ||||
−0.189876 | + | 0.981808i | \(0.560809\pi\) | |||||||
\(542\) | −20.7639 | −0.891887 | ||||||||
\(543\) | −2.70820 | −0.116220 | ||||||||
\(544\) | 6.47214 | 0.277491 | ||||||||
\(545\) | 29.0557 | 1.24461 | ||||||||
\(546\) | 27.4164 | 1.17331 | ||||||||
\(547\) | −14.7639 | −0.631260 | −0.315630 | − | 0.948882i | \(-0.602216\pi\) | ||||
−0.315630 | + | 0.948882i | \(0.602216\pi\) | |||||||
\(548\) | 13.8541 | 0.591818 | ||||||||
\(549\) | −2.65248 | −0.113205 | ||||||||
\(550\) | 3.14590 | 0.134142 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −4.61803 | −0.196557 | ||||||||
\(553\) | 53.3050 | 2.26676 | ||||||||
\(554\) | 13.7082 | 0.582406 | ||||||||
\(555\) | −24.8541 | −1.05500 | ||||||||
\(556\) | 13.4164 | 0.568982 | ||||||||
\(557\) | −46.1803 | −1.95672 | −0.978362 | − | 0.206901i | \(-0.933662\pi\) | ||||
−0.978362 | + | 0.206901i | \(0.933662\pi\) | |||||||
\(558\) | 2.32624 | 0.0984775 | ||||||||
\(559\) | −16.9443 | −0.716666 | ||||||||
\(560\) | −9.23607 | −0.390295 | ||||||||
\(561\) | 10.4721 | 0.442134 | ||||||||
\(562\) | 11.2361 | 0.473965 | ||||||||
\(563\) | 4.36068 | 0.183781 | 0.0918904 | − | 0.995769i | \(-0.470709\pi\) | ||||
0.0918904 | + | 0.995769i | \(0.470709\pi\) | |||||||
\(564\) | 5.00000 | 0.210538 | ||||||||
\(565\) | −42.2361 | −1.77688 | ||||||||
\(566\) | 16.9443 | 0.712221 | ||||||||
\(567\) | −24.9443 | −1.04756 | ||||||||
\(568\) | 1.52786 | 0.0641078 | ||||||||
\(569\) | −7.05573 | −0.295792 | −0.147896 | − | 0.989003i | \(-0.547250\pi\) | ||||
−0.147896 | + | 0.989003i | \(0.547250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8328 | −0.620734 | −0.310367 | − | 0.950617i | \(-0.600452\pi\) | ||||
−0.310367 | + | 0.950617i | \(0.600452\pi\) | |||||||
\(572\) | 5.23607 | 0.218931 | ||||||||
\(573\) | −5.47214 | −0.228602 | ||||||||
\(574\) | −35.4164 | −1.47825 | ||||||||
\(575\) | −8.97871 | −0.374438 | ||||||||
\(576\) | −0.381966 | −0.0159153 | ||||||||
\(577\) | −19.6869 | −0.819577 | −0.409789 | − | 0.912181i | \(-0.634398\pi\) | ||||
−0.409789 | + | 0.912181i | \(0.634398\pi\) | |||||||
\(578\) | 24.8885 | 1.03523 | ||||||||
\(579\) | −38.6525 | −1.60634 | ||||||||
\(580\) | −29.8885 | −1.24105 | ||||||||
\(581\) | 19.4164 | 0.805528 | ||||||||
\(582\) | −26.6525 | −1.10478 | ||||||||
\(583\) | −1.14590 | −0.0474582 | ||||||||
\(584\) | −5.70820 | −0.236207 | ||||||||
\(585\) | 5.70820 | 0.236005 | ||||||||
\(586\) | −23.4164 | −0.967323 | ||||||||
\(587\) | −45.4508 | −1.87596 | −0.937979 | − | 0.346693i | \(-0.887305\pi\) | ||||
−0.937979 | + | 0.346693i | \(0.887305\pi\) | |||||||
\(588\) | 5.61803 | 0.231684 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −22.4164 | −0.922869 | ||||||||
\(591\) | −21.8885 | −0.900374 | ||||||||
\(592\) | 5.38197 | 0.221197 | ||||||||
\(593\) | 5.59675 | 0.229831 | 0.114915 | − | 0.993375i | \(-0.463340\pi\) | ||||
0.114915 | + | 0.993375i | \(0.463340\pi\) | |||||||
\(594\) | −5.47214 | −0.224524 | ||||||||
\(595\) | −59.7771 | −2.45062 | ||||||||
\(596\) | −18.7639 | −0.768601 | ||||||||
\(597\) | 10.7984 | 0.441948 | ||||||||
\(598\) | −14.9443 | −0.611117 | ||||||||
\(599\) | 8.03444 | 0.328278 | 0.164139 | − | 0.986437i | \(-0.447515\pi\) | ||||
0.164139 | + | 0.986437i | \(0.447515\pi\) | |||||||
\(600\) | 5.09017 | 0.207805 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | −10.4721 | −0.426812 | ||||||||
\(603\) | 1.58359 | 0.0644889 | ||||||||
\(604\) | −16.4721 | −0.670242 | ||||||||
\(605\) | −2.85410 | −0.116036 | ||||||||
\(606\) | 17.4164 | 0.707493 | ||||||||
\(607\) | 41.7771 | 1.69568 | 0.847840 | − | 0.530252i | \(-0.177903\pi\) | ||||
0.847840 | + | 0.530252i | \(0.177903\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 54.8328 | 2.22194 | ||||||||
\(610\) | −19.8197 | −0.802475 | ||||||||
\(611\) | 16.1803 | 0.654586 | ||||||||
\(612\) | −2.47214 | −0.0999302 | ||||||||
\(613\) | −39.2361 | −1.58473 | −0.792365 | − | 0.610047i | \(-0.791150\pi\) | ||||
−0.792365 | + | 0.610047i | \(0.791150\pi\) | |||||||
\(614\) | 2.58359 | 0.104265 | ||||||||
\(615\) | 50.5410 | 2.03801 | ||||||||
\(616\) | 3.23607 | 0.130385 | ||||||||
\(617\) | −14.9656 | −0.602491 | −0.301245 | − | 0.953547i | \(-0.597402\pi\) | ||||
−0.301245 | + | 0.953547i | \(0.597402\pi\) | |||||||
\(618\) | −1.52786 | −0.0614597 | ||||||||
\(619\) | −17.9656 | −0.722097 | −0.361048 | − | 0.932547i | \(-0.617581\pi\) | ||||
−0.361048 | + | 0.932547i | \(0.617581\pi\) | |||||||
\(620\) | 17.3820 | 0.698077 | ||||||||
\(621\) | 15.6180 | 0.626730 | ||||||||
\(622\) | −30.5066 | −1.22320 | ||||||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 8.47214 | 0.339157 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | 3.52786 | 0.141002 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.5623 | 0.621004 | ||||||||
\(629\) | 34.8328 | 1.38888 | ||||||||
\(630\) | 3.52786 | 0.140553 | ||||||||
\(631\) | 23.9787 | 0.954578 | 0.477289 | − | 0.878747i | \(-0.341620\pi\) | ||||
0.477289 | + | 0.878747i | \(0.341620\pi\) | |||||||
\(632\) | 16.4721 | 0.655226 | ||||||||
\(633\) | −11.2361 | −0.446594 | ||||||||
\(634\) | 9.41641 | 0.373973 | ||||||||
\(635\) | 26.8754 | 1.06652 | ||||||||
\(636\) | −1.85410 | −0.0735199 | ||||||||
\(637\) | 18.1803 | 0.720331 | ||||||||
\(638\) | 10.4721 | 0.414596 | ||||||||
\(639\) | −0.583592 | −0.0230865 | ||||||||
\(640\) | −2.85410 | −0.112818 | ||||||||
\(641\) | −5.97871 | −0.236145 | −0.118072 | − | 0.993005i | \(-0.537672\pi\) | ||||
−0.118072 | + | 0.993005i | \(0.537672\pi\) | |||||||
\(642\) | 9.70820 | 0.383152 | ||||||||
\(643\) | −28.1459 | −1.10997 | −0.554983 | − | 0.831862i | \(-0.687275\pi\) | ||||
−0.554983 | + | 0.831862i | \(0.687275\pi\) | |||||||
\(644\) | −9.23607 | −0.363952 | ||||||||
\(645\) | 14.9443 | 0.588430 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.7426 | 0.461651 | 0.230826 | − | 0.972995i | \(-0.425857\pi\) | ||||
0.230826 | + | 0.972995i | \(0.425857\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | 7.85410 | 0.308300 | ||||||||
\(650\) | 16.4721 | 0.646090 | ||||||||
\(651\) | −31.8885 | −1.24981 | ||||||||
\(652\) | 3.14590 | 0.123203 | ||||||||
\(653\) | −46.6180 | −1.82430 | −0.912152 | − | 0.409851i | \(-0.865581\pi\) | ||||
−0.912152 | + | 0.409851i | \(0.865581\pi\) | |||||||
\(654\) | −16.4721 | −0.644111 | ||||||||
\(655\) | 49.7082 | 1.94226 | ||||||||
\(656\) | −10.9443 | −0.427302 | ||||||||
\(657\) | 2.18034 | 0.0850632 | ||||||||
\(658\) | 10.0000 | 0.389841 | ||||||||
\(659\) | 9.88854 | 0.385203 | 0.192601 | − | 0.981277i | \(-0.438308\pi\) | ||||
0.192601 | + | 0.981277i | \(0.438308\pi\) | |||||||
\(660\) | −4.61803 | −0.179757 | ||||||||
\(661\) | −19.7984 | −0.770067 | −0.385034 | − | 0.922902i | \(-0.625810\pi\) | ||||
−0.385034 | + | 0.922902i | \(0.625810\pi\) | |||||||
\(662\) | −7.14590 | −0.277733 | ||||||||
\(663\) | 54.8328 | 2.12953 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.05573 | −0.0796578 | ||||||||
\(667\) | −29.8885 | −1.15729 | ||||||||
\(668\) | 25.2361 | 0.976413 | ||||||||
\(669\) | 15.4721 | 0.598187 | ||||||||
\(670\) | 11.8328 | 0.457142 | ||||||||
\(671\) | 6.94427 | 0.268081 | ||||||||
\(672\) | 5.23607 | 0.201986 | ||||||||
\(673\) | −29.8885 | −1.15212 | −0.576059 | − | 0.817408i | \(-0.695410\pi\) | ||||
−0.576059 | + | 0.817408i | \(0.695410\pi\) | |||||||
\(674\) | −3.88854 | −0.149781 | ||||||||
\(675\) | −17.2148 | −0.662597 | ||||||||
\(676\) | 14.4164 | 0.554477 | ||||||||
\(677\) | −24.8328 | −0.954403 | −0.477201 | − | 0.878794i | \(-0.658349\pi\) | ||||
−0.477201 | + | 0.878794i | \(0.658349\pi\) | |||||||
\(678\) | 23.9443 | 0.919574 | ||||||||
\(679\) | −53.3050 | −2.04566 | ||||||||
\(680\) | −18.4721 | −0.708374 | ||||||||
\(681\) | 36.1803 | 1.38643 | ||||||||
\(682\) | −6.09017 | −0.233205 | ||||||||
\(683\) | 38.9230 | 1.48935 | 0.744673 | − | 0.667429i | \(-0.232605\pi\) | ||||
0.744673 | + | 0.667429i | \(0.232605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.5410 | −1.51078 | ||||||||
\(686\) | −11.4164 | −0.435880 | ||||||||
\(687\) | −5.85410 | −0.223348 | ||||||||
\(688\) | −3.23607 | −0.123374 | ||||||||
\(689\) | −6.00000 | −0.228582 | ||||||||
\(690\) | 13.1803 | 0.501767 | ||||||||
\(691\) | 26.3820 | 1.00362 | 0.501809 | − | 0.864979i | \(-0.332668\pi\) | ||||
0.501809 | + | 0.864979i | \(0.332668\pi\) | |||||||
\(692\) | 15.2361 | 0.579188 | ||||||||
\(693\) | −1.23607 | −0.0469543 | ||||||||
\(694\) | −12.9443 | −0.491358 | ||||||||
\(695\) | −38.2918 | −1.45249 | ||||||||
\(696\) | 16.9443 | 0.642271 | ||||||||
\(697\) | −70.8328 | −2.68298 | ||||||||
\(698\) | 17.8885 | 0.677091 | ||||||||
\(699\) | 2.47214 | 0.0935048 | ||||||||
\(700\) | 10.1803 | 0.384781 | ||||||||
\(701\) | 36.6525 | 1.38434 | 0.692172 | − | 0.721732i | \(-0.256654\pi\) | ||||
0.692172 | + | 0.721732i | \(0.256654\pi\) | |||||||
\(702\) | −28.6525 | −1.08142 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −14.2705 | −0.537458 | ||||||||
\(706\) | −21.8541 | −0.822490 | ||||||||
\(707\) | 34.8328 | 1.31002 | ||||||||
\(708\) | 12.7082 | 0.477604 | ||||||||
\(709\) | −16.8328 | −0.632170 | −0.316085 | − | 0.948731i | \(-0.602368\pi\) | ||||
−0.316085 | + | 0.948731i | \(0.602368\pi\) | |||||||
\(710\) | −4.36068 | −0.163653 | ||||||||
\(711\) | −6.29180 | −0.235961 | ||||||||
\(712\) | −1.85410 | −0.0694854 | ||||||||
\(713\) | 17.3820 | 0.650960 | ||||||||
\(714\) | 33.8885 | 1.26825 | ||||||||
\(715\) | −14.9443 | −0.558884 | ||||||||
\(716\) | −12.0902 | −0.451831 | ||||||||
\(717\) | 31.8885 | 1.19090 | ||||||||
\(718\) | −18.0000 | −0.671754 | ||||||||
\(719\) | −20.9787 | −0.782374 | −0.391187 | − | 0.920311i | \(-0.627935\pi\) | ||||
−0.391187 | + | 0.920311i | \(0.627935\pi\) | |||||||
\(720\) | 1.09017 | 0.0406282 | ||||||||
\(721\) | −3.05573 | −0.113801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.1803 | −0.601753 | ||||||||
\(724\) | −1.67376 | −0.0622049 | ||||||||
\(725\) | 32.9443 | 1.22352 | ||||||||
\(726\) | 1.61803 | 0.0600509 | ||||||||
\(727\) | −19.1591 | −0.710570 | −0.355285 | − | 0.934758i | \(-0.615616\pi\) | ||||
−0.355285 | + | 0.934758i | \(0.615616\pi\) | |||||||
\(728\) | 16.9443 | 0.627996 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 16.2918 | 0.602986 | ||||||||
\(731\) | −20.9443 | −0.774652 | ||||||||
\(732\) | 11.2361 | 0.415297 | ||||||||
\(733\) | 18.0689 | 0.667389 | 0.333695 | − | 0.942681i | \(-0.391705\pi\) | ||||
0.333695 | + | 0.942681i | \(0.391705\pi\) | |||||||
\(734\) | −9.20163 | −0.339638 | ||||||||
\(735\) | −16.0344 | −0.591439 | ||||||||
\(736\) | −2.85410 | −0.105204 | ||||||||
\(737\) | −4.14590 | −0.152716 | ||||||||
\(738\) | 4.18034 | 0.153880 | ||||||||
\(739\) | 15.8197 | 0.581936 | 0.290968 | − | 0.956733i | \(-0.406023\pi\) | ||||
0.290968 | + | 0.956733i | \(0.406023\pi\) | |||||||
\(740\) | −15.3607 | −0.564670 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.70820 | −0.136132 | ||||||||
\(743\) | 24.1803 | 0.887091 | 0.443545 | − | 0.896252i | \(-0.353721\pi\) | ||||
0.443545 | + | 0.896252i | \(0.353721\pi\) | |||||||
\(744\) | −9.85410 | −0.361269 | ||||||||
\(745\) | 53.5542 | 1.96207 | ||||||||
\(746\) | 1.34752 | 0.0493364 | ||||||||
\(747\) | −2.29180 | −0.0838524 | ||||||||
\(748\) | 6.47214 | 0.236645 | ||||||||
\(749\) | 19.4164 | 0.709460 | ||||||||
\(750\) | 8.56231 | 0.312651 | ||||||||
\(751\) | −29.3262 | −1.07013 | −0.535065 | − | 0.844811i | \(-0.679713\pi\) | ||||
−0.535065 | + | 0.844811i | \(0.679713\pi\) | |||||||
\(752\) | 3.09017 | 0.112687 | ||||||||
\(753\) | 6.70820 | 0.244461 | ||||||||
\(754\) | 54.8328 | 1.99689 | ||||||||
\(755\) | 47.0132 | 1.71098 | ||||||||
\(756\) | −17.7082 | −0.644041 | ||||||||
\(757\) | −33.0557 | −1.20143 | −0.600715 | − | 0.799463i | \(-0.705118\pi\) | ||||
−0.600715 | + | 0.799463i | \(0.705118\pi\) | |||||||
\(758\) | 30.8328 | 1.11990 | ||||||||
\(759\) | −4.61803 | −0.167624 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.9443 | −1.04923 | −0.524615 | − | 0.851340i | \(-0.675791\pi\) | ||||
−0.524615 | + | 0.851340i | \(0.675791\pi\) | |||||||
\(762\) | −15.2361 | −0.551945 | ||||||||
\(763\) | −32.9443 | −1.19266 | ||||||||
\(764\) | −3.38197 | −0.122355 | ||||||||
\(765\) | 7.05573 | 0.255100 | ||||||||
\(766\) | 6.85410 | 0.247649 | ||||||||
\(767\) | 41.1246 | 1.48492 | ||||||||
\(768\) | 1.61803 | 0.0583858 | ||||||||
\(769\) | −44.3607 | −1.59969 | −0.799844 | − | 0.600209i | \(-0.795084\pi\) | ||||
−0.799844 | + | 0.600209i | \(0.795084\pi\) | |||||||
\(770\) | −9.23607 | −0.332845 | ||||||||
\(771\) | 43.5967 | 1.57010 | ||||||||
\(772\) | −23.8885 | −0.859768 | ||||||||
\(773\) | 46.3262 | 1.66624 | 0.833119 | − | 0.553093i | \(-0.186553\pi\) | ||||
0.833119 | + | 0.553093i | \(0.186553\pi\) | |||||||
\(774\) | 1.23607 | 0.0444295 | ||||||||
\(775\) | −19.1591 | −0.688214 | ||||||||
\(776\) | −16.4721 | −0.591315 | ||||||||
\(777\) | 28.1803 | 1.01096 | ||||||||
\(778\) | −3.79837 | −0.136178 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −24.1803 | −0.865795 | ||||||||
\(781\) | 1.52786 | 0.0546713 | ||||||||
\(782\) | −18.4721 | −0.660562 | ||||||||
\(783\) | −57.3050 | −2.04791 | ||||||||
\(784\) | 3.47214 | 0.124005 | ||||||||
\(785\) | −44.4164 | −1.58529 | ||||||||
\(786\) | −28.1803 | −1.00516 | ||||||||
\(787\) | 15.5967 | 0.555964 | 0.277982 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277982 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(788\) | −13.5279 | −0.481910 | ||||||||
\(789\) | 47.3050 | 1.68410 | ||||||||
\(790\) | −47.0132 | −1.67265 | ||||||||
\(791\) | 47.8885 | 1.70272 | ||||||||
\(792\) | −0.381966 | −0.0135726 | ||||||||
\(793\) | 36.3607 | 1.29121 | ||||||||
\(794\) | −16.3820 | −0.581374 | ||||||||
\(795\) | 5.29180 | 0.187681 | ||||||||
\(796\) | 6.67376 | 0.236545 | ||||||||
\(797\) | −9.90983 | −0.351024 | −0.175512 | − | 0.984477i | \(-0.556158\pi\) | ||||
−0.175512 | + | 0.984477i | \(0.556158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.0000 | 0.707549 | ||||||||
\(800\) | 3.14590 | 0.111224 | ||||||||
\(801\) | 0.708204 | 0.0250232 | ||||||||
\(802\) | 13.9787 | 0.493606 | ||||||||
\(803\) | −5.70820 | −0.201438 | ||||||||
\(804\) | −6.70820 | −0.236580 | ||||||||
\(805\) | 26.3607 | 0.929092 | ||||||||
\(806\) | −31.8885 | −1.12323 | ||||||||
\(807\) | −31.6525 | −1.11422 | ||||||||
\(808\) | 10.7639 | 0.378674 | ||||||||
\(809\) | −23.0557 | −0.810596 | −0.405298 | − | 0.914185i | \(-0.632832\pi\) | ||||
−0.405298 | + | 0.914185i | \(0.632832\pi\) | |||||||
\(810\) | 22.0000 | 0.773001 | ||||||||
\(811\) | 17.8885 | 0.628152 | 0.314076 | − | 0.949398i | \(-0.398305\pi\) | ||||
0.314076 | + | 0.949398i | \(0.398305\pi\) | |||||||
\(812\) | 33.8885 | 1.18925 | ||||||||
\(813\) | −33.5967 | −1.17829 | ||||||||
\(814\) | 5.38197 | 0.188638 | ||||||||
\(815\) | −8.97871 | −0.314511 | ||||||||
\(816\) | 10.4721 | 0.366598 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −15.7082 | −0.549224 | ||||||||
\(819\) | −6.47214 | −0.226155 | ||||||||
\(820\) | 31.2361 | 1.09081 | ||||||||
\(821\) | −5.23607 | −0.182740 | −0.0913700 | − | 0.995817i | \(-0.529125\pi\) | ||||
−0.0913700 | + | 0.995817i | \(0.529125\pi\) | |||||||
\(822\) | 22.4164 | 0.781862 | ||||||||
\(823\) | −21.1459 | −0.737100 | −0.368550 | − | 0.929608i | \(-0.620146\pi\) | ||||
−0.368550 | + | 0.929608i | \(0.620146\pi\) | |||||||
\(824\) | −0.944272 | −0.0328953 | ||||||||
\(825\) | 5.09017 | 0.177217 | ||||||||
\(826\) | 25.4164 | 0.884350 | ||||||||
\(827\) | −52.6525 | −1.83091 | −0.915453 | − | 0.402425i | \(-0.868167\pi\) | ||||
−0.915453 | + | 0.402425i | \(0.868167\pi\) | |||||||
\(828\) | 1.09017 | 0.0378860 | ||||||||
\(829\) | −23.3050 | −0.809414 | −0.404707 | − | 0.914446i | \(-0.632627\pi\) | ||||
−0.404707 | + | 0.914446i | \(0.632627\pi\) | |||||||
\(830\) | −17.1246 | −0.594404 | ||||||||
\(831\) | 22.1803 | 0.769427 | ||||||||
\(832\) | 5.23607 | 0.181528 | ||||||||
\(833\) | 22.4721 | 0.778613 | ||||||||
\(834\) | 21.7082 | 0.751694 | ||||||||
\(835\) | −72.0263 | −2.49257 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 33.3262 | 1.15192 | ||||||||
\(838\) | −0.673762 | −0.0232747 | ||||||||
\(839\) | 22.4508 | 0.775089 | 0.387545 | − | 0.921851i | \(-0.373323\pi\) | ||||
0.387545 | + | 0.921851i | \(0.373323\pi\) | |||||||
\(840\) | −14.9443 | −0.515626 | ||||||||
\(841\) | 80.6656 | 2.78157 | ||||||||
\(842\) | 33.4508 | 1.15279 | ||||||||
\(843\) | 18.1803 | 0.626164 | ||||||||
\(844\) | −6.94427 | −0.239032 | ||||||||
\(845\) | −41.1459 | −1.41546 | ||||||||
\(846\) | −1.18034 | −0.0405809 | ||||||||
\(847\) | 3.23607 | 0.111193 | ||||||||
\(848\) | −1.14590 | −0.0393503 | ||||||||
\(849\) | 27.4164 | 0.940929 | ||||||||
\(850\) | 20.3607 | 0.698366 | ||||||||
\(851\) | −15.3607 | −0.526557 | ||||||||
\(852\) | 2.47214 | 0.0846940 | ||||||||
\(853\) | −36.8328 | −1.26113 | −0.630566 | − | 0.776136i | \(-0.717177\pi\) | ||||
−0.630566 | + | 0.776136i | \(0.717177\pi\) | |||||||
\(854\) | 22.4721 | 0.768981 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | 0.205076 | ||||||||
\(857\) | −54.5410 | −1.86309 | −0.931543 | − | 0.363632i | \(-0.881537\pi\) | ||||
−0.931543 | + | 0.363632i | \(0.881537\pi\) | |||||||
\(858\) | 8.47214 | 0.289234 | ||||||||
\(859\) | 13.0344 | 0.444729 | 0.222365 | − | 0.974964i | \(-0.428622\pi\) | ||||
0.222365 | + | 0.974964i | \(0.428622\pi\) | |||||||
\(860\) | 9.23607 | 0.314947 | ||||||||
\(861\) | −57.3050 | −1.95295 | ||||||||
\(862\) | −14.7639 | −0.502862 | ||||||||
\(863\) | 10.4934 | 0.357200 | 0.178600 | − | 0.983922i | \(-0.442843\pi\) | ||||
0.178600 | + | 0.983922i | \(0.442843\pi\) | |||||||
\(864\) | −5.47214 | −0.186166 | ||||||||
\(865\) | −43.4853 | −1.47854 | ||||||||
\(866\) | −9.79837 | −0.332962 | ||||||||
\(867\) | 40.2705 | 1.36766 | ||||||||
\(868\) | −19.7082 | −0.668940 | ||||||||
\(869\) | 16.4721 | 0.558779 | ||||||||
\(870\) | −48.3607 | −1.63958 | ||||||||
\(871\) | −21.7082 | −0.735554 | ||||||||
\(872\) | −10.1803 | −0.344750 | ||||||||
\(873\) | 6.29180 | 0.212945 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.1246 | 0.578918 | ||||||||
\(876\) | −9.23607 | −0.312058 | ||||||||
\(877\) | 13.3050 | 0.449276 | 0.224638 | − | 0.974442i | \(-0.427880\pi\) | ||||
0.224638 | + | 0.974442i | \(0.427880\pi\) | |||||||
\(878\) | 7.34752 | 0.247967 | ||||||||
\(879\) | −37.8885 | −1.27795 | ||||||||
\(880\) | −2.85410 | −0.0962118 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | −1.32624 | −0.0446568 | ||||||||
\(883\) | 33.6180 | 1.13134 | 0.565668 | − | 0.824633i | \(-0.308618\pi\) | ||||
0.565668 | + | 0.824633i | \(0.308618\pi\) | |||||||
\(884\) | 33.8885 | 1.13980 | ||||||||
\(885\) | −36.2705 | −1.21922 | ||||||||
\(886\) | 15.2705 | 0.513023 | ||||||||
\(887\) | −1.70820 | −0.0573559 | −0.0286779 | − | 0.999589i | \(-0.509130\pi\) | ||||
−0.0286779 | + | 0.999589i | \(0.509130\pi\) | |||||||
\(888\) | 8.70820 | 0.292228 | ||||||||
\(889\) | −30.4721 | −1.02200 | ||||||||
\(890\) | 5.29180 | 0.177381 | ||||||||
\(891\) | −7.70820 | −0.258235 | ||||||||
\(892\) | 9.56231 | 0.320170 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −30.3607 | −1.01541 | ||||||||
\(895\) | 34.5066 | 1.15343 | ||||||||
\(896\) | 3.23607 | 0.108109 | ||||||||
\(897\) | −24.1803 | −0.807358 | ||||||||
\(898\) | 5.56231 | 0.185617 | ||||||||
\(899\) | −63.7771 | −2.12708 | ||||||||
\(900\) | −1.20163 | −0.0400542 | ||||||||
\(901\) | −7.41641 | −0.247076 | ||||||||
\(902\) | −10.9443 | −0.364404 | ||||||||
\(903\) | −16.9443 | −0.563870 | ||||||||
\(904\) | 14.7984 | 0.492187 | ||||||||
\(905\) | 4.77709 | 0.158796 | ||||||||
\(906\) | −26.6525 | −0.885469 | ||||||||
\(907\) | 13.4377 | 0.446191 | 0.223096 | − | 0.974797i | \(-0.428384\pi\) | ||||
0.223096 | + | 0.974797i | \(0.428384\pi\) | |||||||
\(908\) | 22.3607 | 0.742065 | ||||||||
\(909\) | −4.11146 | −0.136368 | ||||||||
\(910\) | −48.3607 | −1.60314 | ||||||||
\(911\) | 16.3820 | 0.542759 | 0.271379 | − | 0.962472i | \(-0.412520\pi\) | ||||
0.271379 | + | 0.962472i | \(0.412520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | −4.76393 | −0.157577 | ||||||||
\(915\) | −32.0689 | −1.06016 | ||||||||
\(916\) | −3.61803 | −0.119543 | ||||||||
\(917\) | −56.3607 | −1.86119 | ||||||||
\(918\) | −35.4164 | −1.16892 | ||||||||
\(919\) | −49.0132 | −1.61679 | −0.808397 | − | 0.588637i | \(-0.799665\pi\) | ||||
−0.808397 | + | 0.588637i | \(0.799665\pi\) | |||||||
\(920\) | 8.14590 | 0.268562 | ||||||||
\(921\) | 4.18034 | 0.137747 | ||||||||
\(922\) | −20.6525 | −0.680153 | ||||||||
\(923\) | 8.00000 | 0.263323 | ||||||||
\(924\) | 5.23607 | 0.172254 | ||||||||
\(925\) | 16.9311 | 0.556692 | ||||||||
\(926\) | −39.1591 | −1.28685 | ||||||||
\(927\) | 0.360680 | 0.0118463 | ||||||||
\(928\) | 10.4721 | 0.343765 | ||||||||
\(929\) | 42.3394 | 1.38911 | 0.694555 | − | 0.719439i | \(-0.255601\pi\) | ||||
0.694555 | + | 0.719439i | \(0.255601\pi\) | |||||||
\(930\) | 28.1246 | 0.922242 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.52786 | 0.0500469 | ||||||||
\(933\) | −49.3607 | −1.61600 | ||||||||
\(934\) | 1.61803 | 0.0529437 | ||||||||
\(935\) | −18.4721 | −0.604103 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | 10.1803 | 0.332577 | 0.166289 | − | 0.986077i | \(-0.446822\pi\) | ||||
0.166289 | + | 0.986077i | \(0.446822\pi\) | |||||||
\(938\) | −13.4164 | −0.438061 | ||||||||
\(939\) | 5.70820 | 0.186280 | ||||||||
\(940\) | −8.81966 | −0.287666 | ||||||||
\(941\) | −6.58359 | −0.214619 | −0.107309 | − | 0.994226i | \(-0.534224\pi\) | ||||
−0.107309 | + | 0.994226i | \(0.534224\pi\) | |||||||
\(942\) | 25.1803 | 0.820420 | ||||||||
\(943\) | 31.2361 | 1.01719 | ||||||||
\(944\) | 7.85410 | 0.255629 | ||||||||
\(945\) | 50.5410 | 1.64410 | ||||||||
\(946\) | −3.23607 | −0.105214 | ||||||||
\(947\) | −54.8328 | −1.78183 | −0.890914 | − | 0.454173i | \(-0.849935\pi\) | ||||
−0.890914 | + | 0.454173i | \(0.849935\pi\) | |||||||
\(948\) | 26.6525 | 0.865632 | ||||||||
\(949\) | −29.8885 | −0.970223 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.2361 | 0.494063 | ||||||||
\(952\) | 20.9443 | 0.678808 | ||||||||
\(953\) | 0.583592 | 0.0189044 | 0.00945220 | − | 0.999955i | \(-0.496991\pi\) | ||||
0.00945220 | + | 0.999955i | \(0.496991\pi\) | |||||||
\(954\) | 0.437694 | 0.0141709 | ||||||||
\(955\) | 9.65248 | 0.312347 | ||||||||
\(956\) | 19.7082 | 0.637409 | ||||||||
\(957\) | 16.9443 | 0.547731 | ||||||||
\(958\) | −17.1246 | −0.553271 | ||||||||
\(959\) | 44.8328 | 1.44773 | ||||||||
\(960\) | −4.61803 | −0.149046 | ||||||||
\(961\) | 6.09017 | 0.196457 | ||||||||
\(962\) | 28.1803 | 0.908571 | ||||||||
\(963\) | −2.29180 | −0.0738521 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | 68.1803 | 2.19480 | ||||||||
\(966\) | −14.9443 | −0.480824 | ||||||||
\(967\) | −55.9574 | −1.79947 | −0.899735 | − | 0.436437i | \(-0.856240\pi\) | ||||
−0.899735 | + | 0.436437i | \(0.856240\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 47.0132 | 1.50950 | ||||||||
\(971\) | −31.2705 | −1.00352 | −0.501759 | − | 0.865007i | \(-0.667314\pi\) | ||||
−0.501759 | + | 0.865007i | \(0.667314\pi\) | |||||||
\(972\) | 3.94427 | 0.126513 | ||||||||
\(973\) | 43.4164 | 1.39187 | ||||||||
\(974\) | −10.8541 | −0.347788 | ||||||||
\(975\) | 26.6525 | 0.853562 | ||||||||
\(976\) | 6.94427 | 0.222281 | ||||||||
\(977\) | −2.14590 | −0.0686534 | −0.0343267 | − | 0.999411i | \(-0.510929\pi\) | ||||
−0.0343267 | + | 0.999411i | \(0.510929\pi\) | |||||||
\(978\) | 5.09017 | 0.162766 | ||||||||
\(979\) | −1.85410 | −0.0592574 | ||||||||
\(980\) | −9.90983 | −0.316558 | ||||||||
\(981\) | 3.88854 | 0.124152 | ||||||||
\(982\) | 22.9443 | 0.732181 | ||||||||
\(983\) | −61.6312 | −1.96573 | −0.982865 | − | 0.184328i | \(-0.940989\pi\) | ||||
−0.982865 | + | 0.184328i | \(0.940989\pi\) | |||||||
\(984\) | −17.7082 | −0.564517 | ||||||||
\(985\) | 38.6099 | 1.23021 | ||||||||
\(986\) | 67.7771 | 2.15846 | ||||||||
\(987\) | 16.1803 | 0.515026 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.23607 | 0.293690 | ||||||||
\(990\) | 1.09017 | 0.0346479 | ||||||||
\(991\) | −18.6738 | −0.593192 | −0.296596 | − | 0.955003i | \(-0.595851\pi\) | ||||
−0.296596 | + | 0.955003i | \(0.595851\pi\) | |||||||
\(992\) | −6.09017 | −0.193363 | ||||||||
\(993\) | −11.5623 | −0.366919 | ||||||||
\(994\) | 4.94427 | 0.156823 | ||||||||
\(995\) | −19.0476 | −0.603849 | ||||||||
\(996\) | 9.70820 | 0.307616 | ||||||||
\(997\) | −26.0689 | −0.825610 | −0.412805 | − | 0.910819i | \(-0.635451\pi\) | ||||
−0.412805 | + | 0.910819i | \(0.635451\pi\) | |||||||
\(998\) | −2.03444 | −0.0643991 | ||||||||
\(999\) | −29.4508 | −0.931784 |
(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 | 7942.2.a.z.1.2 | yes | 2 | |
19.18 | odd | 2 | 7942.2.a.u.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7942.2.a.u.1.1 | ✓ | 2 | 19.18 | odd | 2 | ||
7942.2.a.z.1.2 | yes | 2 | 1.1 | even | 1 | trivial |