Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.09100\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09100 | −0.771451 | −0.385726 | − | 0.922614i | \(-0.626049\pi\) | ||||
−0.385726 | + | 0.922614i | \(0.626049\pi\) | |||||||
\(3\) | −1.45952 | −0.842654 | −0.421327 | − | 0.906909i | \(-0.638435\pi\) | ||||
−0.421327 | + | 0.906909i | \(0.638435\pi\) | |||||||
\(4\) | −0.809726 | −0.404863 | ||||||||
\(5\) | −1.35087 | −0.604125 | −0.302063 | − | 0.953288i | \(-0.597675\pi\) | ||||
−0.302063 | + | 0.953288i | \(0.597675\pi\) | |||||||
\(6\) | 1.59233 | 0.650066 | ||||||||
\(7\) | −0.216325 | −0.0817633 | −0.0408816 | − | 0.999164i | \(-0.513017\pi\) | ||||
−0.0408816 | + | 0.999164i | \(0.513017\pi\) | |||||||
\(8\) | 3.06540 | 1.08378 | ||||||||
\(9\) | −0.869803 | −0.289934 | ||||||||
\(10\) | 1.47379 | 0.466053 | ||||||||
\(11\) | −6.03107 | −1.81844 | −0.909219 | − | 0.416319i | \(-0.863320\pi\) | ||||
−0.909219 | + | 0.416319i | \(0.863320\pi\) | |||||||
\(12\) | 1.18181 | 0.341159 | ||||||||
\(13\) | −2.87520 | −0.797436 | −0.398718 | − | 0.917073i | \(-0.630545\pi\) | ||||
−0.398718 | + | 0.917073i | \(0.630545\pi\) | |||||||
\(14\) | 0.236010 | 0.0630764 | ||||||||
\(15\) | 1.97161 | 0.509069 | ||||||||
\(16\) | −1.72489 | −0.431223 | ||||||||
\(17\) | 0.282609 | 0.0685429 | 0.0342714 | − | 0.999413i | \(-0.489089\pi\) | ||||
0.0342714 | + | 0.999413i | \(0.489089\pi\) | |||||||
\(18\) | 0.948953 | 0.223670 | ||||||||
\(19\) | 1.13727 | 0.260908 | 0.130454 | − | 0.991454i | \(-0.458356\pi\) | ||||
0.130454 | + | 0.991454i | \(0.458356\pi\) | |||||||
\(20\) | 1.09383 | 0.244588 | ||||||||
\(21\) | 0.315731 | 0.0688981 | ||||||||
\(22\) | 6.57988 | 1.40284 | ||||||||
\(23\) | −3.94262 | −0.822093 | −0.411046 | − | 0.911614i | \(-0.634837\pi\) | ||||
−0.411046 | + | 0.911614i | \(0.634837\pi\) | |||||||
\(24\) | −4.47401 | −0.913254 | ||||||||
\(25\) | −3.17516 | −0.635033 | ||||||||
\(26\) | 3.13683 | 0.615183 | ||||||||
\(27\) | 5.64805 | 1.08697 | ||||||||
\(28\) | 0.175164 | 0.0331029 | ||||||||
\(29\) | −6.90413 | −1.28206 | −0.641032 | − | 0.767514i | \(-0.721494\pi\) | ||||
−0.641032 | + | 0.767514i | \(0.721494\pi\) | |||||||
\(30\) | −2.15103 | −0.392722 | ||||||||
\(31\) | −9.89090 | −1.77646 | −0.888229 | − | 0.459400i | \(-0.848064\pi\) | ||||
−0.888229 | + | 0.459400i | \(0.848064\pi\) | |||||||
\(32\) | −4.24895 | −0.751115 | ||||||||
\(33\) | 8.80247 | 1.53231 | ||||||||
\(34\) | −0.308326 | −0.0528775 | ||||||||
\(35\) | 0.292226 | 0.0493953 | ||||||||
\(36\) | 0.704302 | 0.117384 | ||||||||
\(37\) | −7.54258 | −1.23999 | −0.619996 | − | 0.784605i | \(-0.712866\pi\) | ||||
−0.619996 | + | 0.784605i | \(0.712866\pi\) | |||||||
\(38\) | −1.24076 | −0.201278 | ||||||||
\(39\) | 4.19641 | 0.671963 | ||||||||
\(40\) | −4.14095 | −0.654741 | ||||||||
\(41\) | 5.12997 | 0.801167 | 0.400584 | − | 0.916260i | \(-0.368807\pi\) | ||||
0.400584 | + | 0.916260i | \(0.368807\pi\) | |||||||
\(42\) | −0.344461 | −0.0531516 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 4.88351 | 0.736217 | ||||||||
\(45\) | 1.17499 | 0.175157 | ||||||||
\(46\) | 4.30138 | 0.634205 | ||||||||
\(47\) | 0.462299 | 0.0674332 | 0.0337166 | − | 0.999431i | \(-0.489266\pi\) | ||||
0.0337166 | + | 0.999431i | \(0.489266\pi\) | |||||||
\(48\) | 2.51752 | 0.363372 | ||||||||
\(49\) | −6.95320 | −0.993315 | ||||||||
\(50\) | 3.46409 | 0.489897 | ||||||||
\(51\) | −0.412474 | −0.0577579 | ||||||||
\(52\) | 2.32812 | 0.322852 | ||||||||
\(53\) | 8.35339 | 1.14743 | 0.573713 | − | 0.819057i | \(-0.305503\pi\) | ||||
0.573713 | + | 0.819057i | \(0.305503\pi\) | |||||||
\(54\) | −6.16201 | −0.838543 | ||||||||
\(55\) | 8.14717 | 1.09856 | ||||||||
\(56\) | −0.663124 | −0.0886137 | ||||||||
\(57\) | −1.65987 | −0.219855 | ||||||||
\(58\) | 7.53238 | 0.989050 | ||||||||
\(59\) | −8.35544 | −1.08779 | −0.543893 | − | 0.839155i | \(-0.683050\pi\) | ||||
−0.543893 | + | 0.839155i | \(0.683050\pi\) | |||||||
\(60\) | −1.59647 | −0.206103 | ||||||||
\(61\) | −13.4329 | −1.71990 | −0.859950 | − | 0.510377i | \(-0.829506\pi\) | ||||
−0.859950 | + | 0.510377i | \(0.829506\pi\) | |||||||
\(62\) | 10.7909 | 1.37045 | ||||||||
\(63\) | 0.188160 | 0.0237060 | ||||||||
\(64\) | 8.08538 | 1.01067 | ||||||||
\(65\) | 3.88401 | 0.481752 | ||||||||
\(66\) | −9.60347 | −1.18210 | ||||||||
\(67\) | −6.29357 | −0.768882 | −0.384441 | − | 0.923150i | \(-0.625606\pi\) | ||||
−0.384441 | + | 0.923150i | \(0.625606\pi\) | |||||||
\(68\) | −0.228836 | −0.0277504 | ||||||||
\(69\) | 5.75433 | 0.692740 | ||||||||
\(70\) | −0.318818 | −0.0381060 | ||||||||
\(71\) | 1.47896 | 0.175520 | 0.0877600 | − | 0.996142i | \(-0.472029\pi\) | ||||
0.0877600 | + | 0.996142i | \(0.472029\pi\) | |||||||
\(72\) | −2.66630 | −0.314226 | ||||||||
\(73\) | 0.820130 | 0.0959890 | 0.0479945 | − | 0.998848i | \(-0.484717\pi\) | ||||
0.0479945 | + | 0.998848i | \(0.484717\pi\) | |||||||
\(74\) | 8.22893 | 0.956594 | ||||||||
\(75\) | 4.63421 | 0.535113 | ||||||||
\(76\) | −0.920878 | −0.105632 | ||||||||
\(77\) | 1.30467 | 0.148681 | ||||||||
\(78\) | −4.57827 | −0.518387 | ||||||||
\(79\) | 6.15595 | 0.692599 | 0.346299 | − | 0.938124i | \(-0.387438\pi\) | ||||
0.346299 | + | 0.938124i | \(0.387438\pi\) | |||||||
\(80\) | 2.33010 | 0.260513 | ||||||||
\(81\) | −5.63403 | −0.626003 | ||||||||
\(82\) | −5.59678 | −0.618061 | ||||||||
\(83\) | −7.20537 | −0.790893 | −0.395446 | − | 0.918489i | \(-0.629410\pi\) | ||||
−0.395446 | + | 0.918489i | \(0.629410\pi\) | |||||||
\(84\) | −0.255655 | −0.0278943 | ||||||||
\(85\) | −0.381767 | −0.0414085 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.0767 | 1.08034 | ||||||||
\(88\) | −18.4877 | −1.97079 | ||||||||
\(89\) | −4.43399 | −0.470002 | −0.235001 | − | 0.971995i | \(-0.575509\pi\) | ||||
−0.235001 | + | 0.971995i | \(0.575509\pi\) | |||||||
\(90\) | −1.28191 | −0.135125 | ||||||||
\(91\) | 0.621978 | 0.0652010 | ||||||||
\(92\) | 3.19244 | 0.332835 | ||||||||
\(93\) | 14.4360 | 1.49694 | ||||||||
\(94\) | −0.504367 | −0.0520214 | ||||||||
\(95\) | −1.53630 | −0.157621 | ||||||||
\(96\) | 6.20143 | 0.632930 | ||||||||
\(97\) | −4.46918 | −0.453777 | −0.226888 | − | 0.973921i | \(-0.572855\pi\) | ||||
−0.226888 | + | 0.973921i | \(0.572855\pi\) | |||||||
\(98\) | 7.58592 | 0.766294 | ||||||||
\(99\) | 5.24585 | 0.527228 | ||||||||
\(100\) | 2.57101 | 0.257101 | ||||||||
\(101\) | −2.99466 | −0.297980 | −0.148990 | − | 0.988839i | \(-0.547602\pi\) | ||||
−0.148990 | + | 0.988839i | \(0.547602\pi\) | |||||||
\(102\) | 0.450008 | 0.0445574 | ||||||||
\(103\) | 8.44886 | 0.832491 | 0.416245 | − | 0.909252i | \(-0.363346\pi\) | ||||
0.416245 | + | 0.909252i | \(0.363346\pi\) | |||||||
\(104\) | −8.81364 | −0.864248 | ||||||||
\(105\) | −0.426510 | −0.0416231 | ||||||||
\(106\) | −9.11352 | −0.885183 | ||||||||
\(107\) | 6.26653 | 0.605808 | 0.302904 | − | 0.953021i | \(-0.402044\pi\) | ||||
0.302904 | + | 0.953021i | \(0.402044\pi\) | |||||||
\(108\) | −4.57337 | −0.440073 | ||||||||
\(109\) | 0.212675 | 0.0203705 | 0.0101853 | − | 0.999948i | \(-0.496758\pi\) | ||||
0.0101853 | + | 0.999948i | \(0.496758\pi\) | |||||||
\(110\) | −8.88854 | −0.847489 | ||||||||
\(111\) | 11.0085 | 1.04488 | ||||||||
\(112\) | 0.373138 | 0.0352582 | ||||||||
\(113\) | 11.0725 | 1.04161 | 0.520807 | − | 0.853674i | \(-0.325631\pi\) | ||||
0.520807 | + | 0.853674i | \(0.325631\pi\) | |||||||
\(114\) | 1.81091 | 0.169608 | ||||||||
\(115\) | 5.32595 | 0.496647 | ||||||||
\(116\) | 5.59045 | 0.519060 | ||||||||
\(117\) | 2.50086 | 0.231204 | ||||||||
\(118\) | 9.11576 | 0.839174 | ||||||||
\(119\) | −0.0611356 | −0.00560429 | ||||||||
\(120\) | 6.04379 | 0.551720 | ||||||||
\(121\) | 25.3738 | 2.30671 | ||||||||
\(122\) | 14.6552 | 1.32682 | ||||||||
\(123\) | −7.48729 | −0.675107 | ||||||||
\(124\) | 8.00892 | 0.719222 | ||||||||
\(125\) | 11.0435 | 0.987765 | ||||||||
\(126\) | −0.205282 | −0.0182880 | ||||||||
\(127\) | 7.81423 | 0.693401 | 0.346700 | − | 0.937976i | \(-0.387302\pi\) | ||||
0.346700 | + | 0.937976i | \(0.387302\pi\) | |||||||
\(128\) | −0.323224 | −0.0285692 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.23744 | −0.371648 | ||||||||
\(131\) | 17.9581 | 1.56901 | 0.784505 | − | 0.620123i | \(-0.212917\pi\) | ||||
0.784505 | + | 0.620123i | \(0.212917\pi\) | |||||||
\(132\) | −7.12758 | −0.620376 | ||||||||
\(133\) | −0.246021 | −0.0213327 | ||||||||
\(134\) | 6.86627 | 0.593155 | ||||||||
\(135\) | −7.62976 | −0.656665 | ||||||||
\(136\) | 0.866312 | 0.0742856 | ||||||||
\(137\) | −10.0468 | −0.858359 | −0.429180 | − | 0.903219i | \(-0.641197\pi\) | ||||
−0.429180 | + | 0.903219i | \(0.641197\pi\) | |||||||
\(138\) | −6.27795 | −0.534415 | ||||||||
\(139\) | −12.4203 | −1.05348 | −0.526738 | − | 0.850028i | \(-0.676585\pi\) | ||||
−0.526738 | + | 0.850028i | \(0.676585\pi\) | |||||||
\(140\) | −0.236623 | −0.0199983 | ||||||||
\(141\) | −0.674734 | −0.0568229 | ||||||||
\(142\) | −1.61354 | −0.135405 | ||||||||
\(143\) | 17.3405 | 1.45009 | ||||||||
\(144\) | 1.50032 | 0.125027 | ||||||||
\(145\) | 9.32655 | 0.774528 | ||||||||
\(146\) | −0.894760 | −0.0740508 | ||||||||
\(147\) | 10.1483 | 0.837021 | ||||||||
\(148\) | 6.10742 | 0.502027 | ||||||||
\(149\) | 3.69719 | 0.302886 | 0.151443 | − | 0.988466i | \(-0.451608\pi\) | ||||
0.151443 | + | 0.988466i | \(0.451608\pi\) | |||||||
\(150\) | −5.05591 | −0.412813 | ||||||||
\(151\) | 11.5179 | 0.937316 | 0.468658 | − | 0.883380i | \(-0.344738\pi\) | ||||
0.468658 | + | 0.883380i | \(0.344738\pi\) | |||||||
\(152\) | 3.48620 | 0.282768 | ||||||||
\(153\) | −0.245815 | −0.0198729 | ||||||||
\(154\) | −1.42339 | −0.114700 | ||||||||
\(155\) | 13.3613 | 1.07320 | ||||||||
\(156\) | −3.39794 | −0.272053 | ||||||||
\(157\) | 20.5978 | 1.64388 | 0.821940 | − | 0.569574i | \(-0.192892\pi\) | ||||
0.821940 | + | 0.569574i | \(0.192892\pi\) | |||||||
\(158\) | −6.71612 | −0.534306 | ||||||||
\(159\) | −12.1919 | −0.966883 | ||||||||
\(160\) | 5.73976 | 0.453768 | ||||||||
\(161\) | 0.852888 | 0.0672170 | ||||||||
\(162\) | 6.14671 | 0.482931 | ||||||||
\(163\) | −6.91536 | −0.541653 | −0.270826 | − | 0.962628i | \(-0.587297\pi\) | ||||
−0.270826 | + | 0.962628i | \(0.587297\pi\) | |||||||
\(164\) | −4.15387 | −0.324363 | ||||||||
\(165\) | −11.8909 | −0.925709 | ||||||||
\(166\) | 7.86104 | 0.610135 | ||||||||
\(167\) | 3.55518 | 0.275108 | 0.137554 | − | 0.990494i | \(-0.456076\pi\) | ||||
0.137554 | + | 0.990494i | \(0.456076\pi\) | |||||||
\(168\) | 0.967842 | 0.0746706 | ||||||||
\(169\) | −4.73324 | −0.364095 | ||||||||
\(170\) | 0.416507 | 0.0319446 | ||||||||
\(171\) | −0.989203 | −0.0756463 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.0563 | −1.82897 | −0.914483 | − | 0.404623i | \(-0.867403\pi\) | ||||
−0.914483 | + | 0.404623i | \(0.867403\pi\) | |||||||
\(174\) | −10.9937 | −0.833427 | ||||||||
\(175\) | 0.686868 | 0.0519223 | ||||||||
\(176\) | 10.4030 | 0.784153 | ||||||||
\(177\) | 12.1949 | 0.916627 | ||||||||
\(178\) | 4.83747 | 0.362584 | ||||||||
\(179\) | 5.20188 | 0.388807 | 0.194403 | − | 0.980922i | \(-0.437723\pi\) | ||||
0.194403 | + | 0.980922i | \(0.437723\pi\) | |||||||
\(180\) | −0.951417 | −0.0709145 | ||||||||
\(181\) | −2.77405 | −0.206193 | −0.103097 | − | 0.994671i | \(-0.532875\pi\) | ||||
−0.103097 | + | 0.994671i | \(0.532875\pi\) | |||||||
\(182\) | −0.678576 | −0.0502994 | ||||||||
\(183\) | 19.6055 | 1.44928 | ||||||||
\(184\) | −12.0857 | −0.890970 | ||||||||
\(185\) | 10.1890 | 0.749111 | ||||||||
\(186\) | −15.7496 | −1.15482 | ||||||||
\(187\) | −1.70444 | −0.124641 | ||||||||
\(188\) | −0.374335 | −0.0273012 | ||||||||
\(189\) | −1.22182 | −0.0888741 | ||||||||
\(190\) | 1.67610 | 0.121597 | ||||||||
\(191\) | 3.45560 | 0.250038 | 0.125019 | − | 0.992154i | \(-0.460101\pi\) | ||||
0.125019 | + | 0.992154i | \(0.460101\pi\) | |||||||
\(192\) | −11.8008 | −0.851647 | ||||||||
\(193\) | −18.2577 | −1.31422 | −0.657111 | − | 0.753794i | \(-0.728222\pi\) | ||||
−0.657111 | + | 0.753794i | \(0.728222\pi\) | |||||||
\(194\) | 4.87587 | 0.350067 | ||||||||
\(195\) | −5.66878 | −0.405950 | ||||||||
\(196\) | 5.63019 | 0.402156 | ||||||||
\(197\) | 10.1801 | 0.725299 | 0.362649 | − | 0.931926i | \(-0.381872\pi\) | ||||
0.362649 | + | 0.931926i | \(0.381872\pi\) | |||||||
\(198\) | −5.72321 | −0.406730 | ||||||||
\(199\) | −9.19652 | −0.651924 | −0.325962 | − | 0.945383i | \(-0.605688\pi\) | ||||
−0.325962 | + | 0.945383i | \(0.605688\pi\) | |||||||
\(200\) | −9.73315 | −0.688238 | ||||||||
\(201\) | 9.18559 | 0.647902 | ||||||||
\(202\) | 3.26717 | 0.229877 | ||||||||
\(203\) | 1.49354 | 0.104826 | ||||||||
\(204\) | 0.333991 | 0.0233840 | ||||||||
\(205\) | −6.92990 | −0.484005 | ||||||||
\(206\) | −9.21768 | −0.642226 | ||||||||
\(207\) | 3.42930 | 0.238353 | ||||||||
\(208\) | 4.95941 | 0.343873 | ||||||||
\(209\) | −6.85897 | −0.474445 | ||||||||
\(210\) | 0.465321 | 0.0321102 | ||||||||
\(211\) | 19.0580 | 1.31201 | 0.656005 | − | 0.754756i | \(-0.272245\pi\) | ||||
0.656005 | + | 0.754756i | \(0.272245\pi\) | |||||||
\(212\) | −6.76395 | −0.464550 | ||||||||
\(213\) | −2.15857 | −0.147903 | ||||||||
\(214\) | −6.83676 | −0.467352 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 17.3136 | 1.17804 | ||||||||
\(217\) | 2.13965 | 0.145249 | ||||||||
\(218\) | −0.232027 | −0.0157149 | ||||||||
\(219\) | −1.19700 | −0.0808855 | ||||||||
\(220\) | −6.59697 | −0.444768 | ||||||||
\(221\) | −0.812558 | −0.0546586 | ||||||||
\(222\) | −12.0103 | −0.806078 | ||||||||
\(223\) | 7.29778 | 0.488695 | 0.244348 | − | 0.969688i | \(-0.421426\pi\) | ||||
0.244348 | + | 0.969688i | \(0.421426\pi\) | |||||||
\(224\) | 0.919155 | 0.0614136 | ||||||||
\(225\) | 2.76177 | 0.184118 | ||||||||
\(226\) | −12.0801 | −0.803555 | ||||||||
\(227\) | −15.6379 | −1.03792 | −0.518962 | − | 0.854797i | \(-0.673681\pi\) | ||||
−0.518962 | + | 0.854797i | \(0.673681\pi\) | |||||||
\(228\) | 1.34404 | 0.0890112 | ||||||||
\(229\) | −1.07522 | −0.0710529 | −0.0355264 | − | 0.999369i | \(-0.511311\pi\) | ||||
−0.0355264 | + | 0.999369i | \(0.511311\pi\) | |||||||
\(230\) | −5.81059 | −0.383139 | ||||||||
\(231\) | −1.90420 | −0.125287 | ||||||||
\(232\) | −21.1639 | −1.38948 | ||||||||
\(233\) | 1.33303 | 0.0873298 | 0.0436649 | − | 0.999046i | \(-0.486097\pi\) | ||||
0.0436649 | + | 0.999046i | \(0.486097\pi\) | |||||||
\(234\) | −2.72843 | −0.178363 | ||||||||
\(235\) | −0.624503 | −0.0407381 | ||||||||
\(236\) | 6.76561 | 0.440404 | ||||||||
\(237\) | −8.98473 | −0.583621 | ||||||||
\(238\) | 0.0666987 | 0.00432343 | ||||||||
\(239\) | 14.8772 | 0.962327 | 0.481164 | − | 0.876631i | \(-0.340214\pi\) | ||||
0.481164 | + | 0.876631i | \(0.340214\pi\) | |||||||
\(240\) | −3.40082 | −0.219522 | ||||||||
\(241\) | −23.9040 | −1.53979 | −0.769897 | − | 0.638168i | \(-0.779693\pi\) | ||||
−0.769897 | + | 0.638168i | \(0.779693\pi\) | |||||||
\(242\) | −27.6828 | −1.77952 | ||||||||
\(243\) | −8.72118 | −0.559464 | ||||||||
\(244\) | 10.8769 | 0.696324 | ||||||||
\(245\) | 9.39284 | 0.600087 | ||||||||
\(246\) | 8.16862 | 0.520812 | ||||||||
\(247\) | −3.26988 | −0.208058 | ||||||||
\(248\) | −30.3196 | −1.92530 | ||||||||
\(249\) | 10.5164 | 0.666449 | ||||||||
\(250\) | −12.0485 | −0.762012 | ||||||||
\(251\) | −20.5359 | −1.29622 | −0.648108 | − | 0.761548i | \(-0.724440\pi\) | ||||
−0.648108 | + | 0.761548i | \(0.724440\pi\) | |||||||
\(252\) | −0.152358 | −0.00959767 | ||||||||
\(253\) | 23.7782 | 1.49492 | ||||||||
\(254\) | −8.52530 | −0.534925 | ||||||||
\(255\) | 0.557197 | 0.0348930 | ||||||||
\(256\) | −15.8181 | −0.988633 | ||||||||
\(257\) | 22.8388 | 1.42464 | 0.712322 | − | 0.701853i | \(-0.247644\pi\) | ||||
0.712322 | + | 0.701853i | \(0.247644\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.63165 | 0.101386 | ||||||||
\(260\) | −3.14498 | −0.195043 | ||||||||
\(261\) | 6.00524 | 0.371715 | ||||||||
\(262\) | −19.5923 | −1.21041 | ||||||||
\(263\) | −6.15818 | −0.379730 | −0.189865 | − | 0.981810i | \(-0.560805\pi\) | ||||
−0.189865 | + | 0.981810i | \(0.560805\pi\) | |||||||
\(264\) | 26.9831 | 1.66070 | ||||||||
\(265\) | −11.2843 | −0.693189 | ||||||||
\(266\) | 0.268408 | 0.0164571 | ||||||||
\(267\) | 6.47150 | 0.396049 | ||||||||
\(268\) | 5.09607 | 0.311292 | ||||||||
\(269\) | 15.0181 | 0.915671 | 0.457835 | − | 0.889037i | \(-0.348625\pi\) | ||||
0.457835 | + | 0.889037i | \(0.348625\pi\) | |||||||
\(270\) | 8.32404 | 0.506585 | ||||||||
\(271\) | 3.09449 | 0.187977 | 0.0939886 | − | 0.995573i | \(-0.470038\pi\) | ||||
0.0939886 | + | 0.995573i | \(0.470038\pi\) | |||||||
\(272\) | −0.487471 | −0.0295573 | ||||||||
\(273\) | −0.907789 | −0.0549419 | ||||||||
\(274\) | 10.9611 | 0.662183 | ||||||||
\(275\) | 19.1496 | 1.15477 | ||||||||
\(276\) | −4.65943 | −0.280464 | ||||||||
\(277\) | −15.1134 | −0.908075 | −0.454037 | − | 0.890983i | \(-0.650017\pi\) | ||||
−0.454037 | + | 0.890983i | \(0.650017\pi\) | |||||||
\(278\) | 13.5505 | 0.812706 | ||||||||
\(279\) | 8.60314 | 0.515057 | ||||||||
\(280\) | 0.895791 | 0.0535338 | ||||||||
\(281\) | 11.1617 | 0.665850 | 0.332925 | − | 0.942953i | \(-0.391964\pi\) | ||||
0.332925 | + | 0.942953i | \(0.391964\pi\) | |||||||
\(282\) | 0.736133 | 0.0438361 | ||||||||
\(283\) | −16.0909 | −0.956503 | −0.478252 | − | 0.878223i | \(-0.658729\pi\) | ||||
−0.478252 | + | 0.878223i | \(0.658729\pi\) | |||||||
\(284\) | −1.19755 | −0.0710615 | ||||||||
\(285\) | 2.24226 | 0.132820 | ||||||||
\(286\) | −18.9185 | −1.11867 | ||||||||
\(287\) | −1.10974 | −0.0655060 | ||||||||
\(288\) | 3.69575 | 0.217774 | ||||||||
\(289\) | −16.9201 | −0.995302 | ||||||||
\(290\) | −10.1752 | −0.597510 | ||||||||
\(291\) | 6.52286 | 0.382377 | ||||||||
\(292\) | −0.664080 | −0.0388624 | ||||||||
\(293\) | −14.6854 | −0.857931 | −0.428966 | − | 0.903321i | \(-0.641122\pi\) | ||||
−0.428966 | + | 0.903321i | \(0.641122\pi\) | |||||||
\(294\) | −11.0718 | −0.645721 | ||||||||
\(295\) | 11.2871 | 0.657159 | ||||||||
\(296\) | −23.1210 | −1.34388 | ||||||||
\(297\) | −34.0638 | −1.97658 | ||||||||
\(298\) | −4.03363 | −0.233662 | ||||||||
\(299\) | 11.3358 | 0.655567 | ||||||||
\(300\) | −3.75244 | −0.216647 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.5660 | −0.723094 | ||||||||
\(303\) | 4.37077 | 0.251094 | ||||||||
\(304\) | −1.96167 | −0.112510 | ||||||||
\(305\) | 18.1460 | 1.03904 | ||||||||
\(306\) | 0.268183 | 0.0153310 | ||||||||
\(307\) | 0.0283640 | 0.00161882 | 0.000809410 | − | 1.00000i | \(-0.499742\pi\) | ||||
0.000809410 | 1.00000i | \(0.499742\pi\) | ||||||||
\(308\) | −1.05643 | −0.0601955 | ||||||||
\(309\) | −12.3313 | −0.701501 | ||||||||
\(310\) | −14.5771 | −0.827924 | ||||||||
\(311\) | −10.2776 | −0.582792 | −0.291396 | − | 0.956603i | \(-0.594120\pi\) | ||||
−0.291396 | + | 0.956603i | \(0.594120\pi\) | |||||||
\(312\) | 12.8637 | 0.728262 | ||||||||
\(313\) | −17.9283 | −1.01337 | −0.506683 | − | 0.862132i | \(-0.669129\pi\) | ||||
−0.506683 | + | 0.862132i | \(0.669129\pi\) | |||||||
\(314\) | −22.4721 | −1.26817 | ||||||||
\(315\) | −0.254179 | −0.0143214 | ||||||||
\(316\) | −4.98463 | −0.280407 | ||||||||
\(317\) | −21.7299 | −1.22047 | −0.610237 | − | 0.792219i | \(-0.708926\pi\) | ||||
−0.610237 | + | 0.792219i | \(0.708926\pi\) | |||||||
\(318\) | 13.3014 | 0.745903 | ||||||||
\(319\) | 41.6393 | 2.33135 | ||||||||
\(320\) | −10.9223 | −0.610573 | ||||||||
\(321\) | −9.14612 | −0.510487 | ||||||||
\(322\) | −0.930498 | −0.0518546 | ||||||||
\(323\) | 0.321404 | 0.0178834 | ||||||||
\(324\) | 4.56202 | 0.253446 | ||||||||
\(325\) | 9.12922 | 0.506398 | ||||||||
\(326\) | 7.54464 | 0.417859 | ||||||||
\(327\) | −0.310403 | −0.0171653 | ||||||||
\(328\) | 15.7254 | 0.868292 | ||||||||
\(329\) | −0.100007 | −0.00551356 | ||||||||
\(330\) | 12.9730 | 0.714140 | ||||||||
\(331\) | −13.2271 | −0.727028 | −0.363514 | − | 0.931589i | \(-0.618423\pi\) | ||||
−0.363514 | + | 0.931589i | \(0.618423\pi\) | |||||||
\(332\) | 5.83438 | 0.320203 | ||||||||
\(333\) | 6.56056 | 0.359517 | ||||||||
\(334\) | −3.87869 | −0.212232 | ||||||||
\(335\) | 8.50177 | 0.464501 | ||||||||
\(336\) | −0.544602 | −0.0297105 | ||||||||
\(337\) | −9.43072 | −0.513724 | −0.256862 | − | 0.966448i | \(-0.582689\pi\) | ||||
−0.256862 | + | 0.966448i | \(0.582689\pi\) | |||||||
\(338\) | 5.16395 | 0.280882 | ||||||||
\(339\) | −16.1606 | −0.877721 | ||||||||
\(340\) | 0.309127 | 0.0167648 | ||||||||
\(341\) | 59.6528 | 3.23038 | ||||||||
\(342\) | 1.07922 | 0.0583574 | ||||||||
\(343\) | 3.01843 | 0.162980 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.77332 | −0.418502 | ||||||||
\(346\) | 26.2454 | 1.41096 | ||||||||
\(347\) | 17.4825 | 0.938511 | 0.469256 | − | 0.883062i | \(-0.344522\pi\) | ||||
0.469256 | + | 0.883062i | \(0.344522\pi\) | |||||||
\(348\) | −8.15937 | −0.437388 | ||||||||
\(349\) | −9.33264 | −0.499565 | −0.249782 | − | 0.968302i | \(-0.580359\pi\) | ||||
−0.249782 | + | 0.968302i | \(0.580359\pi\) | |||||||
\(350\) | −0.749371 | −0.0400556 | ||||||||
\(351\) | −16.2393 | −0.866788 | ||||||||
\(352\) | 25.6257 | 1.36586 | ||||||||
\(353\) | 10.3879 | 0.552893 | 0.276447 | − | 0.961029i | \(-0.410843\pi\) | ||||
0.276447 | + | 0.961029i | \(0.410843\pi\) | |||||||
\(354\) | −13.3046 | −0.707133 | ||||||||
\(355\) | −1.99787 | −0.106036 | ||||||||
\(356\) | 3.59032 | 0.190286 | ||||||||
\(357\) | 0.0892285 | 0.00472247 | ||||||||
\(358\) | −5.67524 | −0.299946 | ||||||||
\(359\) | 10.8048 | 0.570253 | 0.285127 | − | 0.958490i | \(-0.407964\pi\) | ||||
0.285127 | + | 0.958490i | \(0.407964\pi\) | |||||||
\(360\) | 3.60181 | 0.189832 | ||||||||
\(361\) | −17.7066 | −0.931927 | ||||||||
\(362\) | 3.02648 | 0.159068 | ||||||||
\(363\) | −37.0336 | −1.94376 | ||||||||
\(364\) | −0.503631 | −0.0263975 | ||||||||
\(365\) | −1.10789 | −0.0579894 | ||||||||
\(366\) | −21.3896 | −1.11805 | ||||||||
\(367\) | 19.3732 | 1.01128 | 0.505638 | − | 0.862746i | \(-0.331257\pi\) | ||||
0.505638 | + | 0.862746i | \(0.331257\pi\) | |||||||
\(368\) | 6.80060 | 0.354506 | ||||||||
\(369\) | −4.46207 | −0.232286 | ||||||||
\(370\) | −11.1162 | −0.577903 | ||||||||
\(371\) | −1.80705 | −0.0938173 | ||||||||
\(372\) | −11.6892 | −0.606055 | ||||||||
\(373\) | −34.3456 | −1.77835 | −0.889175 | − | 0.457568i | \(-0.848721\pi\) | ||||
−0.889175 | + | 0.457568i | \(0.848721\pi\) | |||||||
\(374\) | 1.85954 | 0.0961544 | ||||||||
\(375\) | −16.1183 | −0.832344 | ||||||||
\(376\) | 1.41713 | 0.0730830 | ||||||||
\(377\) | 19.8507 | 1.02236 | ||||||||
\(378\) | 1.33300 | 0.0685620 | ||||||||
\(379\) | 2.58065 | 0.132559 | 0.0662794 | − | 0.997801i | \(-0.478887\pi\) | ||||
0.0662794 | + | 0.997801i | \(0.478887\pi\) | |||||||
\(380\) | 1.24398 | 0.0638150 | ||||||||
\(381\) | −11.4050 | −0.584297 | ||||||||
\(382\) | −3.77004 | −0.192892 | ||||||||
\(383\) | −14.3072 | −0.731065 | −0.365532 | − | 0.930799i | \(-0.619113\pi\) | ||||
−0.365532 | + | 0.930799i | \(0.619113\pi\) | |||||||
\(384\) | 0.471751 | 0.0240739 | ||||||||
\(385\) | −1.76244 | −0.0898222 | ||||||||
\(386\) | 19.9191 | 1.01386 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.61881 | 0.183717 | ||||||||
\(389\) | 15.7874 | 0.800455 | 0.400228 | − | 0.916416i | \(-0.368931\pi\) | ||||
0.400228 | + | 0.916416i | \(0.368931\pi\) | |||||||
\(390\) | 6.18462 | 0.313171 | ||||||||
\(391\) | −1.11422 | −0.0563486 | ||||||||
\(392\) | −21.3144 | −1.07654 | ||||||||
\(393\) | −26.2102 | −1.32213 | ||||||||
\(394\) | −11.1064 | −0.559533 | ||||||||
\(395\) | −8.31586 | −0.418416 | ||||||||
\(396\) | −4.24770 | −0.213455 | ||||||||
\(397\) | −29.1059 | −1.46078 | −0.730391 | − | 0.683029i | \(-0.760662\pi\) | ||||
−0.730391 | + | 0.683029i | \(0.760662\pi\) | |||||||
\(398\) | 10.0334 | 0.502928 | ||||||||
\(399\) | 0.359072 | 0.0179761 | ||||||||
\(400\) | 5.47682 | 0.273841 | ||||||||
\(401\) | 14.3104 | 0.714629 | 0.357314 | − | 0.933984i | \(-0.383692\pi\) | ||||
0.357314 | + | 0.933984i | \(0.383692\pi\) | |||||||
\(402\) | −10.0215 | −0.499825 | ||||||||
\(403\) | 28.4383 | 1.41661 | ||||||||
\(404\) | 2.42485 | 0.120641 | ||||||||
\(405\) | 7.61082 | 0.378185 | ||||||||
\(406\) | −1.62944 | −0.0808680 | ||||||||
\(407\) | 45.4899 | 2.25485 | ||||||||
\(408\) | −1.26440 | −0.0625970 | ||||||||
\(409\) | −30.4520 | −1.50575 | −0.752877 | − | 0.658161i | \(-0.771335\pi\) | ||||
−0.752877 | + | 0.658161i | \(0.771335\pi\) | |||||||
\(410\) | 7.56050 | 0.373387 | ||||||||
\(411\) | 14.6636 | 0.723300 | ||||||||
\(412\) | −6.84126 | −0.337044 | ||||||||
\(413\) | 1.80749 | 0.0889409 | ||||||||
\(414\) | −3.74136 | −0.183878 | ||||||||
\(415\) | 9.73349 | 0.477798 | ||||||||
\(416\) | 12.2166 | 0.598967 | ||||||||
\(417\) | 18.1277 | 0.887716 | ||||||||
\(418\) | 7.48312 | 0.366011 | ||||||||
\(419\) | −35.5658 | −1.73750 | −0.868752 | − | 0.495247i | \(-0.835078\pi\) | ||||
−0.868752 | + | 0.495247i | \(0.835078\pi\) | |||||||
\(420\) | 0.345356 | 0.0168516 | ||||||||
\(421\) | −16.4973 | −0.804028 | −0.402014 | − | 0.915634i | \(-0.631690\pi\) | ||||
−0.402014 | + | 0.915634i | \(0.631690\pi\) | |||||||
\(422\) | −20.7923 | −1.01215 | ||||||||
\(423\) | −0.402109 | −0.0195512 | ||||||||
\(424\) | 25.6065 | 1.24356 | ||||||||
\(425\) | −0.897331 | −0.0435269 | ||||||||
\(426\) | 2.35499 | 0.114100 | ||||||||
\(427\) | 2.90587 | 0.140625 | ||||||||
\(428\) | −5.07417 | −0.245269 | ||||||||
\(429\) | −25.3088 | −1.22192 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.05750 | −0.436285 | −0.218142 | − | 0.975917i | \(-0.570000\pi\) | ||||
−0.218142 | + | 0.975917i | \(0.570000\pi\) | |||||||
\(432\) | −9.74229 | −0.468726 | ||||||||
\(433\) | −17.2817 | −0.830506 | −0.415253 | − | 0.909706i | \(-0.636307\pi\) | ||||
−0.415253 | + | 0.909706i | \(0.636307\pi\) | |||||||
\(434\) | −2.33435 | −0.112053 | ||||||||
\(435\) | −13.6123 | −0.652659 | ||||||||
\(436\) | −0.172208 | −0.00824727 | ||||||||
\(437\) | −4.48383 | −0.214491 | ||||||||
\(438\) | 1.30592 | 0.0623992 | ||||||||
\(439\) | 18.4756 | 0.881791 | 0.440896 | − | 0.897558i | \(-0.354661\pi\) | ||||
0.440896 | + | 0.897558i | \(0.354661\pi\) | |||||||
\(440\) | 24.9743 | 1.19061 | ||||||||
\(441\) | 6.04792 | 0.287996 | ||||||||
\(442\) | 0.886498 | 0.0421664 | ||||||||
\(443\) | −8.94530 | −0.425004 | −0.212502 | − | 0.977161i | \(-0.568161\pi\) | ||||
−0.212502 | + | 0.977161i | \(0.568161\pi\) | |||||||
\(444\) | −8.91390 | −0.423035 | ||||||||
\(445\) | 5.98973 | 0.283940 | ||||||||
\(446\) | −7.96185 | −0.377005 | ||||||||
\(447\) | −5.39612 | −0.255228 | ||||||||
\(448\) | −1.74907 | −0.0826359 | ||||||||
\(449\) | 20.2725 | 0.956718 | 0.478359 | − | 0.878164i | \(-0.341232\pi\) | ||||
0.478359 | + | 0.878164i | \(0.341232\pi\) | |||||||
\(450\) | −3.01308 | −0.142038 | ||||||||
\(451\) | −30.9392 | −1.45687 | ||||||||
\(452\) | −8.96570 | −0.421711 | ||||||||
\(453\) | −16.8106 | −0.789833 | ||||||||
\(454\) | 17.0609 | 0.800708 | ||||||||
\(455\) | −0.840208 | −0.0393896 | ||||||||
\(456\) | −5.08817 | −0.238275 | ||||||||
\(457\) | 10.7619 | 0.503419 | 0.251710 | − | 0.967803i | \(-0.419007\pi\) | ||||
0.251710 | + | 0.967803i | \(0.419007\pi\) | |||||||
\(458\) | 1.17307 | 0.0548138 | ||||||||
\(459\) | 1.59619 | 0.0745039 | ||||||||
\(460\) | −4.31256 | −0.201074 | ||||||||
\(461\) | −8.51750 | −0.396700 | −0.198350 | − | 0.980131i | \(-0.563558\pi\) | ||||
−0.198350 | + | 0.980131i | \(0.563558\pi\) | |||||||
\(462\) | 2.07747 | 0.0966528 | ||||||||
\(463\) | 2.27432 | 0.105697 | 0.0528483 | − | 0.998603i | \(-0.483170\pi\) | ||||
0.0528483 | + | 0.998603i | \(0.483170\pi\) | |||||||
\(464\) | 11.9089 | 0.552856 | ||||||||
\(465\) | −19.5010 | −0.904339 | ||||||||
\(466\) | −1.45433 | −0.0673707 | ||||||||
\(467\) | 30.2512 | 1.39986 | 0.699930 | − | 0.714211i | \(-0.253214\pi\) | ||||
0.699930 | + | 0.714211i | \(0.253214\pi\) | |||||||
\(468\) | −2.02501 | −0.0936060 | ||||||||
\(469\) | 1.36146 | 0.0628663 | ||||||||
\(470\) | 0.681331 | 0.0314275 | ||||||||
\(471\) | −30.0628 | −1.38522 | ||||||||
\(472\) | −25.6128 | −1.17892 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9.80231 | 0.450235 | ||||||||
\(475\) | −3.61102 | −0.165685 | ||||||||
\(476\) | 0.0495030 | 0.00226897 | ||||||||
\(477\) | −7.26580 | −0.332678 | ||||||||
\(478\) | −16.2310 | −0.742389 | ||||||||
\(479\) | 13.5795 | 0.620465 | 0.310233 | − | 0.950661i | \(-0.399593\pi\) | ||||
0.310233 | + | 0.950661i | \(0.399593\pi\) | |||||||
\(480\) | −8.37729 | −0.382369 | ||||||||
\(481\) | 21.6864 | 0.988816 | ||||||||
\(482\) | 26.0792 | 1.18788 | ||||||||
\(483\) | −1.24481 | −0.0566406 | ||||||||
\(484\) | −20.5459 | −0.933902 | ||||||||
\(485\) | 6.03727 | 0.274138 | ||||||||
\(486\) | 9.51478 | 0.431599 | ||||||||
\(487\) | −37.2554 | −1.68820 | −0.844101 | − | 0.536184i | \(-0.819865\pi\) | ||||
−0.844101 | + | 0.536184i | \(0.819865\pi\) | |||||||
\(488\) | −41.1771 | −1.86400 | ||||||||
\(489\) | 10.0931 | 0.456426 | ||||||||
\(490\) | −10.2476 | −0.462938 | ||||||||
\(491\) | −20.5331 | −0.926644 | −0.463322 | − | 0.886190i | \(-0.653343\pi\) | ||||
−0.463322 | + | 0.886190i | \(0.653343\pi\) | |||||||
\(492\) | 6.06265 | 0.273325 | ||||||||
\(493\) | −1.95117 | −0.0878764 | ||||||||
\(494\) | 3.56743 | 0.160506 | ||||||||
\(495\) | −7.08644 | −0.318512 | ||||||||
\(496\) | 17.0608 | 0.766050 | ||||||||
\(497\) | −0.319936 | −0.0143511 | ||||||||
\(498\) | −11.4733 | −0.514133 | ||||||||
\(499\) | −6.97052 | −0.312043 | −0.156022 | − | 0.987754i | \(-0.549867\pi\) | ||||
−0.156022 | + | 0.987754i | \(0.549867\pi\) | |||||||
\(500\) | −8.94224 | −0.399909 | ||||||||
\(501\) | −5.18885 | −0.231821 | ||||||||
\(502\) | 22.4046 | 0.999968 | ||||||||
\(503\) | −12.9747 | −0.578513 | −0.289256 | − | 0.957252i | \(-0.593408\pi\) | ||||
−0.289256 | + | 0.957252i | \(0.593408\pi\) | |||||||
\(504\) | 0.576787 | 0.0256922 | ||||||||
\(505\) | 4.04539 | 0.180017 | ||||||||
\(506\) | −25.9420 | −1.15326 | ||||||||
\(507\) | 6.90825 | 0.306806 | ||||||||
\(508\) | −6.32738 | −0.280732 | ||||||||
\(509\) | 29.8062 | 1.32114 | 0.660568 | − | 0.750766i | \(-0.270315\pi\) | ||||
0.660568 | + | 0.750766i | \(0.270315\pi\) | |||||||
\(510\) | −0.607900 | −0.0269183 | ||||||||
\(511\) | −0.177415 | −0.00784837 | ||||||||
\(512\) | 17.9040 | 0.791251 | ||||||||
\(513\) | 6.42337 | 0.283599 | ||||||||
\(514\) | −24.9170 | −1.09904 | ||||||||
\(515\) | −11.4133 | −0.502929 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.78816 | −0.122623 | ||||||||
\(518\) | −1.78013 | −0.0782143 | ||||||||
\(519\) | 35.1106 | 1.54119 | ||||||||
\(520\) | 11.9060 | 0.522114 | ||||||||
\(521\) | 31.1756 | 1.36583 | 0.682914 | − | 0.730499i | \(-0.260712\pi\) | ||||
0.682914 | + | 0.730499i | \(0.260712\pi\) | |||||||
\(522\) | −6.55169 | −0.286760 | ||||||||
\(523\) | −13.9018 | −0.607884 | −0.303942 | − | 0.952691i | \(-0.598303\pi\) | ||||
−0.303942 | + | 0.952691i | \(0.598303\pi\) | |||||||
\(524\) | −14.5412 | −0.635234 | ||||||||
\(525\) | −1.00250 | −0.0437525 | ||||||||
\(526\) | 6.71856 | 0.292943 | ||||||||
\(527\) | −2.79526 | −0.121764 | ||||||||
\(528\) | −15.1833 | −0.660769 | ||||||||
\(529\) | −7.45576 | −0.324163 | ||||||||
\(530\) | 12.3111 | 0.534762 | ||||||||
\(531\) | 7.26759 | 0.315387 | ||||||||
\(532\) | 0.199209 | 0.00863681 | ||||||||
\(533\) | −14.7497 | −0.638880 | ||||||||
\(534\) | −7.06038 | −0.305533 | ||||||||
\(535\) | −8.46524 | −0.365984 | ||||||||
\(536\) | −19.2923 | −0.833302 | ||||||||
\(537\) | −7.59224 | −0.327630 | ||||||||
\(538\) | −16.3847 | −0.706395 | ||||||||
\(539\) | 41.9353 | 1.80628 | ||||||||
\(540\) | 6.17801 | 0.265859 | ||||||||
\(541\) | −20.7378 | −0.891587 | −0.445793 | − | 0.895136i | \(-0.647078\pi\) | ||||
−0.445793 | + | 0.895136i | \(0.647078\pi\) | |||||||
\(542\) | −3.37608 | −0.145015 | ||||||||
\(543\) | 4.04877 | 0.173750 | ||||||||
\(544\) | −1.20079 | −0.0514836 | ||||||||
\(545\) | −0.287295 | −0.0123064 | ||||||||
\(546\) | 0.990395 | 0.0423850 | ||||||||
\(547\) | 20.4705 | 0.875255 | 0.437627 | − | 0.899156i | \(-0.355819\pi\) | ||||
0.437627 | + | 0.899156i | \(0.355819\pi\) | |||||||
\(548\) | 8.13518 | 0.347518 | ||||||||
\(549\) | 11.6839 | 0.498659 | ||||||||
\(550\) | −20.8922 | −0.890846 | ||||||||
\(551\) | −7.85187 | −0.334501 | ||||||||
\(552\) | 17.6393 | 0.750780 | ||||||||
\(553\) | −1.33169 | −0.0566291 | ||||||||
\(554\) | 16.4886 | 0.700535 | ||||||||
\(555\) | −14.8711 | −0.631241 | ||||||||
\(556\) | 10.0570 | 0.426513 | ||||||||
\(557\) | −17.0851 | −0.723920 | −0.361960 | − | 0.932194i | \(-0.617892\pi\) | ||||
−0.361960 | + | 0.932194i | \(0.617892\pi\) | |||||||
\(558\) | −9.38600 | −0.397341 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.504059 | −0.0213004 | ||||||||
\(561\) | 2.48766 | 0.105029 | ||||||||
\(562\) | −12.1774 | −0.513671 | ||||||||
\(563\) | −11.2648 | −0.474754 | −0.237377 | − | 0.971418i | \(-0.576288\pi\) | ||||
−0.237377 | + | 0.971418i | \(0.576288\pi\) | |||||||
\(564\) | 0.546349 | 0.0230055 | ||||||||
\(565\) | −14.9575 | −0.629266 | ||||||||
\(566\) | 17.5551 | 0.737896 | ||||||||
\(567\) | 1.21878 | 0.0511841 | ||||||||
\(568\) | 4.53360 | 0.190226 | ||||||||
\(569\) | −8.03597 | −0.336885 | −0.168443 | − | 0.985711i | \(-0.553874\pi\) | ||||
−0.168443 | + | 0.985711i | \(0.553874\pi\) | |||||||
\(570\) | −2.44630 | −0.102464 | ||||||||
\(571\) | 29.1124 | 1.21832 | 0.609158 | − | 0.793049i | \(-0.291507\pi\) | ||||
0.609158 | + | 0.793049i | \(0.291507\pi\) | |||||||
\(572\) | −14.0411 | −0.587087 | ||||||||
\(573\) | −5.04351 | −0.210696 | ||||||||
\(574\) | 1.21073 | 0.0505347 | ||||||||
\(575\) | 12.5185 | 0.522056 | ||||||||
\(576\) | −7.03269 | −0.293029 | ||||||||
\(577\) | 7.18569 | 0.299144 | 0.149572 | − | 0.988751i | \(-0.452210\pi\) | ||||
0.149572 | + | 0.988751i | \(0.452210\pi\) | |||||||
\(578\) | 18.4598 | 0.767827 | ||||||||
\(579\) | 26.6475 | 1.10743 | ||||||||
\(580\) | −7.55194 | −0.313577 | ||||||||
\(581\) | 1.55870 | 0.0646660 | ||||||||
\(582\) | −7.11642 | −0.294985 | ||||||||
\(583\) | −50.3799 | −2.08652 | ||||||||
\(584\) | 2.51403 | 0.104031 | ||||||||
\(585\) | −3.37832 | −0.139676 | ||||||||
\(586\) | 16.0217 | 0.661852 | ||||||||
\(587\) | 29.7095 | 1.22624 | 0.613121 | − | 0.789989i | \(-0.289914\pi\) | ||||
0.613121 | + | 0.789989i | \(0.289914\pi\) | |||||||
\(588\) | −8.21737 | −0.338878 | ||||||||
\(589\) | −11.2486 | −0.463492 | ||||||||
\(590\) | −12.3142 | −0.506966 | ||||||||
\(591\) | −14.8580 | −0.611176 | ||||||||
\(592\) | 13.0102 | 0.534714 | ||||||||
\(593\) | −32.2081 | −1.32263 | −0.661314 | − | 0.750109i | \(-0.730001\pi\) | ||||
−0.661314 | + | 0.750109i | \(0.730001\pi\) | |||||||
\(594\) | 37.1635 | 1.52484 | ||||||||
\(595\) | 0.0825859 | 0.00338569 | ||||||||
\(596\) | −2.99371 | −0.122627 | ||||||||
\(597\) | 13.4225 | 0.549346 | ||||||||
\(598\) | −12.3673 | −0.505738 | ||||||||
\(599\) | −15.2252 | −0.622086 | −0.311043 | − | 0.950396i | \(-0.600678\pi\) | ||||
−0.311043 | + | 0.950396i | \(0.600678\pi\) | |||||||
\(600\) | 14.2057 | 0.579946 | ||||||||
\(601\) | 14.8489 | 0.605699 | 0.302849 | − | 0.953038i | \(-0.402062\pi\) | ||||
0.302849 | + | 0.953038i | \(0.402062\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.47417 | 0.222925 | ||||||||
\(604\) | −9.32636 | −0.379484 | ||||||||
\(605\) | −34.2767 | −1.39354 | ||||||||
\(606\) | −4.76849 | −0.193707 | ||||||||
\(607\) | 9.34659 | 0.379367 | 0.189683 | − | 0.981845i | \(-0.439254\pi\) | ||||
0.189683 | + | 0.981845i | \(0.439254\pi\) | |||||||
\(608\) | −4.83221 | −0.195972 | ||||||||
\(609\) | −2.17985 | −0.0883318 | ||||||||
\(610\) | −19.7972 | −0.801566 | ||||||||
\(611\) | −1.32920 | −0.0537737 | ||||||||
\(612\) | 0.199042 | 0.00804581 | ||||||||
\(613\) | 30.8057 | 1.24423 | 0.622116 | − | 0.782925i | \(-0.286273\pi\) | ||||
0.622116 | + | 0.782925i | \(0.286273\pi\) | |||||||
\(614\) | −0.0309450 | −0.00124884 | ||||||||
\(615\) | 10.1143 | 0.407849 | ||||||||
\(616\) | 3.99935 | 0.161138 | ||||||||
\(617\) | −3.84050 | −0.154613 | −0.0773064 | − | 0.997007i | \(-0.524632\pi\) | ||||
−0.0773064 | + | 0.997007i | \(0.524632\pi\) | |||||||
\(618\) | 13.4534 | 0.541174 | ||||||||
\(619\) | 34.1580 | 1.37292 | 0.686462 | − | 0.727166i | \(-0.259163\pi\) | ||||
0.686462 | + | 0.727166i | \(0.259163\pi\) | |||||||
\(620\) | −10.8190 | −0.434500 | ||||||||
\(621\) | −22.2681 | −0.893589 | ||||||||
\(622\) | 11.2129 | 0.449596 | ||||||||
\(623\) | 0.959185 | 0.0384289 | ||||||||
\(624\) | −7.23836 | −0.289766 | ||||||||
\(625\) | 0.957471 | 0.0382988 | ||||||||
\(626\) | 19.5597 | 0.781763 | ||||||||
\(627\) | 10.0108 | 0.399793 | ||||||||
\(628\) | −16.6785 | −0.665546 | ||||||||
\(629\) | −2.13160 | −0.0849926 | ||||||||
\(630\) | 0.277309 | 0.0110483 | ||||||||
\(631\) | 9.20560 | 0.366469 | 0.183235 | − | 0.983069i | \(-0.441343\pi\) | ||||
0.183235 | + | 0.983069i | \(0.441343\pi\) | |||||||
\(632\) | 18.8705 | 0.750627 | ||||||||
\(633\) | −27.8156 | −1.10557 | ||||||||
\(634\) | 23.7073 | 0.941536 | ||||||||
\(635\) | −10.5560 | −0.418901 | ||||||||
\(636\) | 9.87211 | 0.391455 | ||||||||
\(637\) | 19.9918 | 0.792105 | ||||||||
\(638\) | −45.4284 | −1.79853 | ||||||||
\(639\) | −1.28640 | −0.0508893 | ||||||||
\(640\) | 0.436631 | 0.0172594 | ||||||||
\(641\) | −3.38335 | −0.133634 | −0.0668171 | − | 0.997765i | \(-0.521284\pi\) | ||||
−0.0668171 | + | 0.997765i | \(0.521284\pi\) | |||||||
\(642\) | 9.97839 | 0.393816 | ||||||||
\(643\) | 11.3071 | 0.445910 | 0.222955 | − | 0.974829i | \(-0.428430\pi\) | ||||
0.222955 | + | 0.974829i | \(0.428430\pi\) | |||||||
\(644\) | −0.690605 | −0.0272137 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.350651 | −0.0137962 | ||||||||
\(647\) | 22.7411 | 0.894046 | 0.447023 | − | 0.894522i | \(-0.352484\pi\) | ||||
0.447023 | + | 0.894522i | \(0.352484\pi\) | |||||||
\(648\) | −17.2706 | −0.678452 | ||||||||
\(649\) | 50.3923 | 1.97807 | ||||||||
\(650\) | −9.95995 | −0.390662 | ||||||||
\(651\) | −3.12286 | −0.122395 | ||||||||
\(652\) | 5.59954 | 0.219295 | ||||||||
\(653\) | −25.8110 | −1.01006 | −0.505032 | − | 0.863101i | \(-0.668519\pi\) | ||||
−0.505032 | + | 0.863101i | \(0.668519\pi\) | |||||||
\(654\) | 0.338648 | 0.0132422 | ||||||||
\(655\) | −24.2590 | −0.947878 | ||||||||
\(656\) | −8.84866 | −0.345482 | ||||||||
\(657\) | −0.713352 | −0.0278305 | ||||||||
\(658\) | 0.109107 | 0.00425344 | ||||||||
\(659\) | 10.1927 | 0.397053 | 0.198526 | − | 0.980096i | \(-0.436384\pi\) | ||||
0.198526 | + | 0.980096i | \(0.436384\pi\) | |||||||
\(660\) | 9.62841 | 0.374785 | ||||||||
\(661\) | −13.3155 | −0.517913 | −0.258957 | − | 0.965889i | \(-0.583379\pi\) | ||||
−0.258957 | + | 0.965889i | \(0.583379\pi\) | |||||||
\(662\) | 14.4308 | 0.560867 | ||||||||
\(663\) | 1.18594 | 0.0460583 | ||||||||
\(664\) | −22.0874 | −0.857156 | ||||||||
\(665\) | 0.332341 | 0.0128876 | ||||||||
\(666\) | −7.15756 | −0.277350 | ||||||||
\(667\) | 27.2203 | 1.05398 | ||||||||
\(668\) | −2.87872 | −0.111381 | ||||||||
\(669\) | −10.6512 | −0.411801 | ||||||||
\(670\) | −9.27540 | −0.358340 | ||||||||
\(671\) | 81.0145 | 3.12753 | ||||||||
\(672\) | −1.34152 | −0.0517504 | ||||||||
\(673\) | 6.31447 | 0.243405 | 0.121703 | − | 0.992567i | \(-0.461165\pi\) | ||||
0.121703 | + | 0.992567i | \(0.461165\pi\) | |||||||
\(674\) | 10.2889 | 0.396313 | ||||||||
\(675\) | −17.9335 | −0.690260 | ||||||||
\(676\) | 3.83262 | 0.147409 | ||||||||
\(677\) | 26.0519 | 1.00126 | 0.500628 | − | 0.865662i | \(-0.333102\pi\) | ||||
0.500628 | + | 0.865662i | \(0.333102\pi\) | |||||||
\(678\) | 17.6311 | 0.677119 | ||||||||
\(679\) | 0.966797 | 0.0371023 | ||||||||
\(680\) | −1.17027 | −0.0448778 | ||||||||
\(681\) | 22.8238 | 0.874610 | ||||||||
\(682\) | −65.0810 | −2.49208 | ||||||||
\(683\) | −49.2576 | −1.88479 | −0.942395 | − | 0.334503i | \(-0.891431\pi\) | ||||
−0.942395 | + | 0.334503i | \(0.891431\pi\) | |||||||
\(684\) | 0.800983 | 0.0306264 | ||||||||
\(685\) | 13.5719 | 0.518557 | ||||||||
\(686\) | −3.29310 | −0.125731 | ||||||||
\(687\) | 1.56931 | 0.0598730 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.0176 | −0.914999 | ||||||||
\(690\) | 8.48067 | 0.322854 | ||||||||
\(691\) | 49.3631 | 1.87786 | 0.938931 | − | 0.344106i | \(-0.111818\pi\) | ||||
0.938931 | + | 0.344106i | \(0.111818\pi\) | |||||||
\(692\) | 19.4790 | 0.740481 | ||||||||
\(693\) | −1.13481 | −0.0431078 | ||||||||
\(694\) | −19.0734 | −0.724016 | ||||||||
\(695\) | 16.7782 | 0.636432 | ||||||||
\(696\) | 30.8892 | 1.17085 | ||||||||
\(697\) | 1.44978 | 0.0549143 | ||||||||
\(698\) | 10.1819 | 0.385390 | ||||||||
\(699\) | −1.94558 | −0.0735888 | ||||||||
\(700\) | −0.556174 | −0.0210214 | ||||||||
\(701\) | −17.4990 | −0.660929 | −0.330464 | − | 0.943818i | \(-0.607205\pi\) | ||||
−0.330464 | + | 0.943818i | \(0.607205\pi\) | |||||||
\(702\) | 17.7170 | 0.668685 | ||||||||
\(703\) | −8.57797 | −0.323524 | ||||||||
\(704\) | −48.7635 | −1.83784 | ||||||||
\(705\) | 0.911475 | 0.0343281 | ||||||||
\(706\) | −11.3332 | −0.426530 | ||||||||
\(707\) | 0.647821 | 0.0243638 | ||||||||
\(708\) | −9.87455 | −0.371108 | ||||||||
\(709\) | 31.8895 | 1.19763 | 0.598817 | − | 0.800886i | \(-0.295638\pi\) | ||||
0.598817 | + | 0.800886i | \(0.295638\pi\) | |||||||
\(710\) | 2.17967 | 0.0818017 | ||||||||
\(711\) | −5.35447 | −0.200808 | ||||||||
\(712\) | −13.5920 | −0.509381 | ||||||||
\(713\) | 38.9961 | 1.46041 | ||||||||
\(714\) | −0.0973480 | −0.00364316 | ||||||||
\(715\) | −23.4247 | −0.876035 | ||||||||
\(716\) | −4.21210 | −0.157413 | ||||||||
\(717\) | −21.7136 | −0.810909 | ||||||||
\(718\) | −11.7880 | −0.439923 | ||||||||
\(719\) | 43.2301 | 1.61221 | 0.806105 | − | 0.591773i | \(-0.201572\pi\) | ||||
0.806105 | + | 0.591773i | \(0.201572\pi\) | |||||||
\(720\) | −2.02673 | −0.0755317 | ||||||||
\(721\) | −1.82770 | −0.0680672 | ||||||||
\(722\) | 19.3179 | 0.718936 | ||||||||
\(723\) | 34.8884 | 1.29751 | ||||||||
\(724\) | 2.24622 | 0.0834800 | ||||||||
\(725\) | 21.9217 | 0.814153 | ||||||||
\(726\) | 40.4036 | 1.49952 | ||||||||
\(727\) | 4.19063 | 0.155422 | 0.0777109 | − | 0.996976i | \(-0.475239\pi\) | ||||
0.0777109 | + | 0.996976i | \(0.475239\pi\) | |||||||
\(728\) | 1.90661 | 0.0706638 | ||||||||
\(729\) | 29.6308 | 1.09744 | ||||||||
\(730\) | 1.20870 | 0.0447360 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −15.8751 | −0.586760 | ||||||||
\(733\) | −49.2097 | −1.81760 | −0.908802 | − | 0.417228i | \(-0.863002\pi\) | ||||
−0.908802 | + | 0.417228i | \(0.863002\pi\) | |||||||
\(734\) | −21.1362 | −0.780150 | ||||||||
\(735\) | −13.7090 | −0.505665 | ||||||||
\(736\) | 16.7520 | 0.617487 | ||||||||
\(737\) | 37.9570 | 1.39816 | ||||||||
\(738\) | 4.86810 | 0.179197 | ||||||||
\(739\) | 2.50823 | 0.0922666 | 0.0461333 | − | 0.998935i | \(-0.485310\pi\) | ||||
0.0461333 | + | 0.998935i | \(0.485310\pi\) | |||||||
\(740\) | −8.25030 | −0.303287 | ||||||||
\(741\) | 4.77246 | 0.175321 | ||||||||
\(742\) | 1.97148 | 0.0723755 | ||||||||
\(743\) | −17.8168 | −0.653636 | −0.326818 | − | 0.945087i | \(-0.605976\pi\) | ||||
−0.326818 | + | 0.945087i | \(0.605976\pi\) | |||||||
\(744\) | 44.2520 | 1.62236 | ||||||||
\(745\) | −4.99441 | −0.182981 | ||||||||
\(746\) | 37.4710 | 1.37191 | ||||||||
\(747\) | 6.26726 | 0.229307 | ||||||||
\(748\) | 1.38013 | 0.0504624 | ||||||||
\(749\) | −1.35561 | −0.0495328 | ||||||||
\(750\) | 17.5850 | 0.642113 | ||||||||
\(751\) | −38.7221 | −1.41299 | −0.706495 | − | 0.707718i | \(-0.749725\pi\) | ||||
−0.706495 | + | 0.707718i | \(0.749725\pi\) | |||||||
\(752\) | −0.797416 | −0.0290788 | ||||||||
\(753\) | 29.9726 | 1.09226 | ||||||||
\(754\) | −21.6571 | −0.788705 | ||||||||
\(755\) | −15.5592 | −0.566256 | ||||||||
\(756\) | 0.989336 | 0.0359818 | ||||||||
\(757\) | −30.9261 | −1.12403 | −0.562014 | − | 0.827127i | \(-0.689973\pi\) | ||||
−0.562014 | + | 0.827127i | \(0.689973\pi\) | |||||||
\(758\) | −2.81548 | −0.102263 | ||||||||
\(759\) | −34.7048 | −1.25970 | ||||||||
\(760\) | −4.70938 | −0.170827 | ||||||||
\(761\) | 42.9702 | 1.55767 | 0.778834 | − | 0.627231i | \(-0.215812\pi\) | ||||
0.778834 | + | 0.627231i | \(0.215812\pi\) | |||||||
\(762\) | 12.4428 | 0.450757 | ||||||||
\(763\) | −0.0460069 | −0.00166556 | ||||||||
\(764\) | −2.79808 | −0.101231 | ||||||||
\(765\) | 0.332063 | 0.0120057 | ||||||||
\(766\) | 15.6091 | 0.563981 | ||||||||
\(767\) | 24.0236 | 0.867440 | ||||||||
\(768\) | 23.0869 | 0.833075 | ||||||||
\(769\) | 11.5254 | 0.415616 | 0.207808 | − | 0.978170i | \(-0.433367\pi\) | ||||
0.207808 | + | 0.978170i | \(0.433367\pi\) | |||||||
\(770\) | 1.92281 | 0.0692934 | ||||||||
\(771\) | −33.3336 | −1.20048 | ||||||||
\(772\) | 14.7838 | 0.532079 | ||||||||
\(773\) | 24.2393 | 0.871828 | 0.435914 | − | 0.899988i | \(-0.356425\pi\) | ||||
0.435914 | + | 0.899988i | \(0.356425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.4052 | 1.12811 | ||||||||
\(776\) | −13.6998 | −0.491796 | ||||||||
\(777\) | −2.38143 | −0.0854332 | ||||||||
\(778\) | −17.2241 | −0.617512 | ||||||||
\(779\) | 5.83417 | 0.209031 | ||||||||
\(780\) | 4.59016 | 0.164354 | ||||||||
\(781\) | −8.91970 | −0.319172 | ||||||||
\(782\) | 1.21561 | 0.0434702 | ||||||||
\(783\) | −38.9949 | −1.39356 | ||||||||
\(784\) | 11.9935 | 0.428341 | ||||||||
\(785\) | −27.8248 | −0.993109 | ||||||||
\(786\) | 28.5953 | 1.01996 | ||||||||
\(787\) | 10.0588 | 0.358559 | 0.179279 | − | 0.983798i | \(-0.442623\pi\) | ||||
0.179279 | + | 0.983798i | \(0.442623\pi\) | |||||||
\(788\) | −8.24305 | −0.293647 | ||||||||
\(789\) | 8.98799 | 0.319981 | ||||||||
\(790\) | 9.07258 | 0.322788 | ||||||||
\(791\) | −2.39526 | −0.0851658 | ||||||||
\(792\) | 16.0806 | 0.571401 | ||||||||
\(793\) | 38.6221 | 1.37151 | ||||||||
\(794\) | 31.7544 | 1.12692 | ||||||||
\(795\) | 16.4697 | 0.584118 | ||||||||
\(796\) | 7.44666 | 0.263940 | ||||||||
\(797\) | −40.8078 | −1.44549 | −0.722744 | − | 0.691116i | \(-0.757119\pi\) | ||||
−0.722744 | + | 0.691116i | \(0.757119\pi\) | |||||||
\(798\) | −0.391746 | −0.0138677 | ||||||||
\(799\) | 0.130650 | 0.00462206 | ||||||||
\(800\) | 13.4911 | 0.476983 | ||||||||
\(801\) | 3.85670 | 0.136270 | ||||||||
\(802\) | −15.6126 | −0.551302 | ||||||||
\(803\) | −4.94627 | −0.174550 | ||||||||
\(804\) | −7.43781 | −0.262311 | ||||||||
\(805\) | −1.15214 | −0.0406075 | ||||||||
\(806\) | −31.0261 | −1.09285 | ||||||||
\(807\) | −21.9192 | −0.771593 | ||||||||
\(808\) | −9.17984 | −0.322946 | ||||||||
\(809\) | −46.8987 | −1.64887 | −0.824435 | − | 0.565957i | \(-0.808507\pi\) | ||||
−0.824435 | + | 0.565957i | \(0.808507\pi\) | |||||||
\(810\) | −8.30338 | −0.291751 | ||||||||
\(811\) | −34.2713 | −1.20343 | −0.601714 | − | 0.798711i | \(-0.705515\pi\) | ||||
−0.601714 | + | 0.798711i | \(0.705515\pi\) | |||||||
\(812\) | −1.20936 | −0.0424400 | ||||||||
\(813\) | −4.51647 | −0.158400 | ||||||||
\(814\) | −49.6293 | −1.73951 | ||||||||
\(815\) | 9.34172 | 0.327226 | ||||||||
\(816\) | 0.711474 | 0.0249066 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 33.2230 | 1.16162 | ||||||||
\(819\) | −0.540999 | −0.0189040 | ||||||||
\(820\) | 5.61132 | 0.195956 | ||||||||
\(821\) | −18.4513 | −0.643956 | −0.321978 | − | 0.946747i | \(-0.604348\pi\) | ||||
−0.321978 | + | 0.946747i | \(0.604348\pi\) | |||||||
\(822\) | −15.9979 | −0.557991 | ||||||||
\(823\) | 9.18853 | 0.320292 | 0.160146 | − | 0.987093i | \(-0.448803\pi\) | ||||
0.160146 | + | 0.987093i | \(0.448803\pi\) | |||||||
\(824\) | 25.8991 | 0.902240 | ||||||||
\(825\) | −27.9493 | −0.973069 | ||||||||
\(826\) | −1.97197 | −0.0686136 | ||||||||
\(827\) | 36.7050 | 1.27636 | 0.638179 | − | 0.769888i | \(-0.279688\pi\) | ||||
0.638179 | + | 0.769888i | \(0.279688\pi\) | |||||||
\(828\) | −2.77679 | −0.0965003 | ||||||||
\(829\) | −4.54590 | −0.157885 | −0.0789427 | − | 0.996879i | \(-0.525154\pi\) | ||||
−0.0789427 | + | 0.996879i | \(0.525154\pi\) | |||||||
\(830\) | −10.6192 | −0.368598 | ||||||||
\(831\) | 22.0583 | 0.765193 | ||||||||
\(832\) | −23.2471 | −0.805947 | ||||||||
\(833\) | −1.96504 | −0.0680846 | ||||||||
\(834\) | −19.7772 | −0.684830 | ||||||||
\(835\) | −4.80257 | −0.166200 | ||||||||
\(836\) | 5.55388 | 0.192085 | ||||||||
\(837\) | −55.8643 | −1.93095 | ||||||||
\(838\) | 38.8022 | 1.34040 | ||||||||
\(839\) | 24.0212 | 0.829304 | 0.414652 | − | 0.909980i | \(-0.363903\pi\) | ||||
0.414652 | + | 0.909980i | \(0.363903\pi\) | |||||||
\(840\) | −1.30742 | −0.0451104 | ||||||||
\(841\) | 18.6670 | 0.643689 | ||||||||
\(842\) | 17.9985 | 0.620268 | ||||||||
\(843\) | −16.2907 | −0.561081 | ||||||||
\(844\) | −15.4318 | −0.531184 | ||||||||
\(845\) | 6.39396 | 0.219959 | ||||||||
\(846\) | 0.438700 | 0.0150828 | ||||||||
\(847\) | −5.48900 | −0.188604 | ||||||||
\(848\) | −14.4087 | −0.494797 | ||||||||
\(849\) | 23.4849 | 0.806001 | ||||||||
\(850\) | 0.978985 | 0.0335789 | ||||||||
\(851\) | 29.7375 | 1.01939 | ||||||||
\(852\) | 1.74785 | 0.0598803 | ||||||||
\(853\) | −49.7259 | −1.70258 | −0.851292 | − | 0.524693i | \(-0.824180\pi\) | ||||
−0.851292 | + | 0.524693i | \(0.824180\pi\) | |||||||
\(854\) | −3.17029 | −0.108485 | ||||||||
\(855\) | 1.33628 | 0.0456998 | ||||||||
\(856\) | 19.2094 | 0.656565 | ||||||||
\(857\) | −35.3238 | −1.20664 | −0.603320 | − | 0.797499i | \(-0.706156\pi\) | ||||
−0.603320 | + | 0.797499i | \(0.706156\pi\) | |||||||
\(858\) | 27.6119 | 0.942654 | ||||||||
\(859\) | −8.58814 | −0.293024 | −0.146512 | − | 0.989209i | \(-0.546805\pi\) | ||||
−0.146512 | + | 0.989209i | \(0.546805\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.61969 | 0.0551989 | ||||||||
\(862\) | 9.88171 | 0.336572 | ||||||||
\(863\) | −33.8631 | −1.15271 | −0.576357 | − | 0.817198i | \(-0.695526\pi\) | ||||
−0.576357 | + | 0.817198i | \(0.695526\pi\) | |||||||
\(864\) | −23.9983 | −0.816439 | ||||||||
\(865\) | 32.4968 | 1.10493 | ||||||||
\(866\) | 18.8543 | 0.640695 | ||||||||
\(867\) | 24.6953 | 0.838695 | ||||||||
\(868\) | −1.73253 | −0.0588059 | ||||||||
\(869\) | −37.1270 | −1.25945 | ||||||||
\(870\) | 14.8510 | 0.503494 | ||||||||
\(871\) | 18.0953 | 0.613135 | ||||||||
\(872\) | 0.651933 | 0.0220772 | ||||||||
\(873\) | 3.88731 | 0.131566 | ||||||||
\(874\) | 4.89184 | 0.165469 | ||||||||
\(875\) | −2.38900 | −0.0807629 | ||||||||
\(876\) | 0.969238 | 0.0327475 | ||||||||
\(877\) | −18.0007 | −0.607842 | −0.303921 | − | 0.952697i | \(-0.598296\pi\) | ||||
−0.303921 | + | 0.952697i | \(0.598296\pi\) | |||||||
\(878\) | −20.1568 | −0.680259 | ||||||||
\(879\) | 21.4337 | 0.722939 | ||||||||
\(880\) | −14.0530 | −0.473726 | ||||||||
\(881\) | −26.2153 | −0.883215 | −0.441608 | − | 0.897208i | \(-0.645592\pi\) | ||||
−0.441608 | + | 0.897208i | \(0.645592\pi\) | |||||||
\(882\) | −6.59826 | −0.222175 | ||||||||
\(883\) | −49.7624 | −1.67464 | −0.837319 | − | 0.546715i | \(-0.815878\pi\) | ||||
−0.837319 | + | 0.546715i | \(0.815878\pi\) | |||||||
\(884\) | 0.657949 | 0.0221292 | ||||||||
\(885\) | −16.4737 | −0.553758 | ||||||||
\(886\) | 9.75930 | 0.327870 | ||||||||
\(887\) | 8.57645 | 0.287969 | 0.143985 | − | 0.989580i | \(-0.454008\pi\) | ||||
0.143985 | + | 0.989580i | \(0.454008\pi\) | |||||||
\(888\) | 33.7456 | 1.13243 | ||||||||
\(889\) | −1.69042 | −0.0566947 | ||||||||
\(890\) | −6.53477 | −0.219046 | ||||||||
\(891\) | 33.9793 | 1.13835 | ||||||||
\(892\) | −5.90920 | −0.197855 | ||||||||
\(893\) | 0.525759 | 0.0175939 | ||||||||
\(894\) | 5.88715 | 0.196896 | ||||||||
\(895\) | −7.02704 | −0.234888 | ||||||||
\(896\) | 0.0699214 | 0.00233591 | ||||||||
\(897\) | −16.5448 | −0.552416 | ||||||||
\(898\) | −22.1172 | −0.738061 | ||||||||
\(899\) | 68.2881 | 2.27753 | ||||||||
\(900\) | −2.23627 | −0.0745425 | ||||||||
\(901\) | 2.36075 | 0.0786478 | ||||||||
\(902\) | 33.7546 | 1.12391 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 33.9417 | 1.12888 | ||||||||
\(905\) | 3.74736 | 0.124567 | ||||||||
\(906\) | 18.3404 | 0.609318 | ||||||||
\(907\) | −28.1743 | −0.935511 | −0.467756 | − | 0.883858i | \(-0.654937\pi\) | ||||
−0.467756 | + | 0.883858i | \(0.654937\pi\) | |||||||
\(908\) | 12.6624 | 0.420217 | ||||||||
\(909\) | 2.60477 | 0.0863947 | ||||||||
\(910\) | 0.916665 | 0.0303871 | ||||||||
\(911\) | 24.4367 | 0.809623 | 0.404811 | − | 0.914400i | \(-0.367337\pi\) | ||||
0.404811 | + | 0.914400i | \(0.367337\pi\) | |||||||
\(912\) | 2.86310 | 0.0948067 | ||||||||
\(913\) | 43.4561 | 1.43819 | ||||||||
\(914\) | −11.7412 | −0.388363 | ||||||||
\(915\) | −26.4844 | −0.875548 | ||||||||
\(916\) | 0.870637 | 0.0287667 | ||||||||
\(917\) | −3.88480 | −0.128287 | ||||||||
\(918\) | −1.74144 | −0.0574761 | ||||||||
\(919\) | −15.9543 | −0.526284 | −0.263142 | − | 0.964757i | \(-0.584759\pi\) | ||||
−0.263142 | + | 0.964757i | \(0.584759\pi\) | |||||||
\(920\) | 16.3262 | 0.538258 | ||||||||
\(921\) | −0.0413978 | −0.00136410 | ||||||||
\(922\) | 9.29257 | 0.306034 | ||||||||
\(923\) | −4.25230 | −0.139966 | ||||||||
\(924\) | 1.54188 | 0.0507240 | ||||||||
\(925\) | 23.9489 | 0.787436 | ||||||||
\(926\) | −2.48127 | −0.0815398 | ||||||||
\(927\) | −7.34885 | −0.241368 | ||||||||
\(928\) | 29.3353 | 0.962978 | ||||||||
\(929\) | 6.25130 | 0.205099 | 0.102549 | − | 0.994728i | \(-0.467300\pi\) | ||||
0.102549 | + | 0.994728i | \(0.467300\pi\) | |||||||
\(930\) | 21.2756 | 0.697654 | ||||||||
\(931\) | −7.90768 | −0.259164 | ||||||||
\(932\) | −1.07939 | −0.0353566 | ||||||||
\(933\) | 15.0004 | 0.491092 | ||||||||
\(934\) | −33.0040 | −1.07992 | ||||||||
\(935\) | 2.30247 | 0.0752987 | ||||||||
\(936\) | 7.66613 | 0.250575 | ||||||||
\(937\) | 54.0642 | 1.76620 | 0.883101 | − | 0.469184i | \(-0.155452\pi\) | ||||
0.883101 | + | 0.469184i | \(0.155452\pi\) | |||||||
\(938\) | −1.48535 | −0.0484983 | ||||||||
\(939\) | 26.1667 | 0.853917 | ||||||||
\(940\) | 0.505676 | 0.0164933 | ||||||||
\(941\) | 31.2455 | 1.01857 | 0.509287 | − | 0.860597i | \(-0.329909\pi\) | ||||
0.509287 | + | 0.860597i | \(0.329909\pi\) | |||||||
\(942\) | 32.7984 | 1.06863 | ||||||||
\(943\) | −20.2255 | −0.658634 | ||||||||
\(944\) | 14.4122 | 0.469079 | ||||||||
\(945\) | 1.65051 | 0.0536911 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.7946 | −1.26066 | −0.630328 | − | 0.776329i | \(-0.717080\pi\) | ||||
−0.630328 | + | 0.776329i | \(0.717080\pi\) | |||||||
\(948\) | 7.27516 | 0.236286 | ||||||||
\(949\) | −2.35804 | −0.0765451 | ||||||||
\(950\) | 3.93962 | 0.127818 | ||||||||
\(951\) | 31.7152 | 1.02844 | ||||||||
\(952\) | −0.187405 | −0.00607383 | ||||||||
\(953\) | 29.2296 | 0.946839 | 0.473420 | − | 0.880837i | \(-0.343019\pi\) | ||||
0.473420 | + | 0.880837i | \(0.343019\pi\) | |||||||
\(954\) | 7.92697 | 0.256645 | ||||||||
\(955\) | −4.66804 | −0.151054 | ||||||||
\(956\) | −12.0465 | −0.389610 | ||||||||
\(957\) | −60.7734 | −1.96452 | ||||||||
\(958\) | −14.8152 | −0.478659 | ||||||||
\(959\) | 2.17338 | 0.0701823 | ||||||||
\(960\) | 15.9412 | 0.514502 | ||||||||
\(961\) | 66.8300 | 2.15581 | ||||||||
\(962\) | −23.6598 | −0.762823 | ||||||||
\(963\) | −5.45065 | −0.175645 | ||||||||
\(964\) | 19.3557 | 0.623406 | ||||||||
\(965\) | 24.6638 | 0.793954 | ||||||||
\(966\) | 1.35808 | 0.0436955 | ||||||||
\(967\) | 25.5158 | 0.820532 | 0.410266 | − | 0.911966i | \(-0.365436\pi\) | ||||
0.410266 | + | 0.911966i | \(0.365436\pi\) | |||||||
\(968\) | 77.7810 | 2.49998 | ||||||||
\(969\) | −0.469095 | −0.0150695 | ||||||||
\(970\) | −6.58664 | −0.211484 | ||||||||
\(971\) | 20.8009 | 0.667534 | 0.333767 | − | 0.942656i | \(-0.391680\pi\) | ||||
0.333767 | + | 0.942656i | \(0.391680\pi\) | |||||||
\(972\) | 7.06176 | 0.226506 | ||||||||
\(973\) | 2.68683 | 0.0861357 | ||||||||
\(974\) | 40.6455 | 1.30237 | ||||||||
\(975\) | −13.3243 | −0.426718 | ||||||||
\(976\) | 23.1702 | 0.741661 | ||||||||
\(977\) | −18.8229 | −0.602198 | −0.301099 | − | 0.953593i | \(-0.597353\pi\) | ||||
−0.301099 | + | 0.953593i | \(0.597353\pi\) | |||||||
\(978\) | −11.0115 | −0.352110 | ||||||||
\(979\) | 26.7417 | 0.854670 | ||||||||
\(980\) | −7.60562 | −0.242953 | ||||||||
\(981\) | −0.184985 | −0.00590612 | ||||||||
\(982\) | 22.4015 | 0.714861 | ||||||||
\(983\) | 22.2313 | 0.709068 | 0.354534 | − | 0.935043i | \(-0.384640\pi\) | ||||
0.354534 | + | 0.935043i | \(0.384640\pi\) | |||||||
\(984\) | −22.9516 | −0.731669 | ||||||||
\(985\) | −13.7519 | −0.438172 | ||||||||
\(986\) | 2.12872 | 0.0677923 | ||||||||
\(987\) | 0.145962 | 0.00464602 | ||||||||
\(988\) | 2.64771 | 0.0842348 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 7.73128 | 0.245716 | ||||||||
\(991\) | −15.3259 | −0.486842 | −0.243421 | − | 0.969921i | \(-0.578270\pi\) | ||||
−0.243421 | + | 0.969921i | \(0.578270\pi\) | |||||||
\(992\) | 42.0260 | 1.33433 | ||||||||
\(993\) | 19.3052 | 0.612633 | ||||||||
\(994\) | 0.349049 | 0.0110712 | ||||||||
\(995\) | 12.4233 | 0.393844 | ||||||||
\(996\) | −8.51538 | −0.269820 | ||||||||
\(997\) | −7.09424 | −0.224677 | −0.112338 | − | 0.993670i | \(-0.535834\pi\) | ||||
−0.112338 | + | 0.993670i | \(0.535834\pi\) | |||||||
\(998\) | 7.60481 | 0.240726 | ||||||||
\(999\) | −42.6009 | −1.34783 |
(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 | 1849.2.a.o.1.6 | 18 | ||
43.30 | odd | 42 | 43.2.g.a.40.2 | yes | 36 | ||
43.33 | odd | 42 | 43.2.g.a.14.2 | ✓ | 36 | ||
43.42 | odd | 2 | 1849.2.a.n.1.13 | 18 | |||
129.116 | even | 42 | 387.2.y.c.298.2 | 36 | |||
129.119 | even | 42 | 387.2.y.c.100.2 | 36 | |||
172.119 | even | 42 | 688.2.bg.c.401.1 | 36 | |||
172.159 | even | 42 | 688.2.bg.c.513.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.g.a.14.2 | ✓ | 36 | 43.33 | odd | 42 | ||
43.2.g.a.40.2 | yes | 36 | 43.30 | odd | 42 | ||
387.2.y.c.100.2 | 36 | 129.119 | even | 42 | |||
387.2.y.c.298.2 | 36 | 129.116 | even | 42 | |||
688.2.bg.c.401.1 | 36 | 172.119 | even | 42 | |||
688.2.bg.c.513.1 | 36 | 172.159 | even | 42 | |||
1849.2.a.n.1.13 | 18 | 43.42 | odd | 2 | |||
1849.2.a.o.1.6 | 18 | 1.1 | even | 1 | trivial |