Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9801,2,Mod(1,9801)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9801, 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("9801.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9801 = 3^{4} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9801.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: | \(78.2613790211\) |
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: | \( x^{18} - 2 x^{17} - 22 x^{16} + 42 x^{15} + 198 x^{14} - 357 x^{13} - 944 x^{12} + 1579 x^{11} + \cdots - 55 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.677669\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9801.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.677669 | −0.479184 | −0.239592 | − | 0.970874i | \(-0.577014\pi\) | ||||
−0.239592 | + | 0.970874i | \(0.577014\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.54077 | −0.770383 | ||||||||
\(5\) | −0.290795 | −0.130047 | −0.0650237 | − | 0.997884i | \(-0.520712\pi\) | ||||
−0.0650237 | + | 0.997884i | \(0.520712\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.35549 | 1.26826 | 0.634128 | − | 0.773228i | \(-0.281359\pi\) | ||||
0.634128 | + | 0.773228i | \(0.281359\pi\) | |||||||
\(8\) | 2.39947 | 0.848339 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.197063 | 0.0623166 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.18671 | 1.16119 | 0.580593 | − | 0.814194i | \(-0.302821\pi\) | ||||
0.580593 | + | 0.814194i | \(0.302821\pi\) | |||||||
\(14\) | −2.27391 | −0.607728 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.45549 | 0.363872 | ||||||||
\(17\) | −3.48327 | −0.844818 | −0.422409 | − | 0.906405i | \(-0.638815\pi\) | ||||
−0.422409 | + | 0.906405i | \(0.638815\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.07908 | −1.39464 | −0.697318 | − | 0.716762i | \(-0.745623\pi\) | ||||
−0.697318 | + | 0.716762i | \(0.745623\pi\) | |||||||
\(20\) | 0.448047 | 0.100186 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.69090 | 1.39515 | 0.697575 | − | 0.716512i | \(-0.254262\pi\) | ||||
0.697575 | + | 0.716512i | \(0.254262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.91544 | −0.983088 | ||||||||
\(26\) | −2.83720 | −0.556422 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.17002 | −0.977042 | ||||||||
\(29\) | 1.65973 | 0.308204 | 0.154102 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154102 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.96301 | 0.352567 | 0.176284 | − | 0.984339i | \(-0.443592\pi\) | ||||
0.176284 | + | 0.984339i | \(0.443592\pi\) | |||||||
\(32\) | −5.78527 | −1.02270 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.36050 | 0.404823 | ||||||||
\(35\) | −0.975759 | −0.164933 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.53648 | −0.416995 | −0.208497 | − | 0.978023i | \(-0.566857\pi\) | ||||
−0.208497 | + | 0.978023i | \(0.566857\pi\) | |||||||
\(38\) | 4.11960 | 0.668287 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.697752 | −0.110324 | ||||||||
\(41\) | 6.48635 | 1.01300 | 0.506499 | − | 0.862241i | \(-0.330940\pi\) | ||||
0.506499 | + | 0.862241i | \(0.330940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0495959 | 0.00756330 | 0.00378165 | − | 0.999993i | \(-0.498796\pi\) | ||||
0.00378165 | + | 0.999993i | \(0.498796\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.53422 | −0.668534 | ||||||||
\(47\) | −1.34941 | −0.196831 | −0.0984157 | − | 0.995145i | \(-0.531377\pi\) | ||||
−0.0984157 | + | 0.995145i | \(0.531377\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.25930 | 0.608472 | ||||||||
\(50\) | 3.33104 | 0.471080 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.45074 | −0.894557 | ||||||||
\(53\) | 1.87766 | 0.257916 | 0.128958 | − | 0.991650i | \(-0.458837\pi\) | ||||
0.128958 | + | 0.991650i | \(0.458837\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.05138 | 1.07591 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.12475 | −0.147686 | ||||||||
\(59\) | 14.5741 | 1.89739 | 0.948694 | − | 0.316195i | \(-0.102405\pi\) | ||||
0.948694 | + | 0.316195i | \(0.102405\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.85914 | 0.494113 | 0.247056 | − | 0.969001i | \(-0.420537\pi\) | ||||
0.247056 | + | 0.969001i | \(0.420537\pi\) | |||||||
\(62\) | −1.33027 | −0.168945 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00952 | 0.126190 | ||||||||
\(65\) | −1.21747 | −0.151009 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.93528 | −1.09162 | −0.545809 | − | 0.837909i | \(-0.683778\pi\) | ||||
−0.545809 | + | 0.837909i | \(0.683778\pi\) | |||||||
\(68\) | 5.36690 | 0.650833 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.661241 | 0.0790334 | ||||||||
\(71\) | 11.1283 | 1.32068 | 0.660340 | − | 0.750967i | \(-0.270412\pi\) | ||||
0.660340 | + | 0.750967i | \(0.270412\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.25869 | 0.147318 | 0.0736591 | − | 0.997283i | \(-0.476532\pi\) | ||||
0.0736591 | + | 0.997283i | \(0.476532\pi\) | |||||||
\(74\) | 1.71889 | 0.199817 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.36643 | 1.07440 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.10713 | 0.237071 | 0.118535 | − | 0.992950i | \(-0.462180\pi\) | ||||
0.118535 | + | 0.992950i | \(0.462180\pi\) | |||||||
\(80\) | −0.423248 | −0.0473206 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.39559 | −0.485412 | ||||||||
\(83\) | −9.37527 | −1.02907 | −0.514535 | − | 0.857470i | \(-0.672035\pi\) | ||||
−0.514535 | + | 0.857470i | \(0.672035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.01292 | 0.109866 | ||||||||
\(86\) | −0.0336096 | −0.00362421 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.41413 | 0.891896 | 0.445948 | − | 0.895059i | \(-0.352867\pi\) | ||||
0.445948 | + | 0.895059i | \(0.352867\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.0485 | 1.47268 | ||||||||
\(92\) | −10.3091 | −1.07480 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.914452 | 0.0943185 | ||||||||
\(95\) | 1.76776 | 0.181369 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.983484 | 0.0998577 | 0.0499288 | − | 0.998753i | \(-0.484101\pi\) | ||||
0.0499288 | + | 0.998753i | \(0.484101\pi\) | |||||||
\(98\) | −2.88640 | −0.291570 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.57354 | 0.757354 | ||||||||
\(101\) | 3.91164 | 0.389223 | 0.194611 | − | 0.980880i | \(-0.437655\pi\) | ||||
0.194611 | + | 0.980880i | \(0.437655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4623 | 1.52355 | 0.761775 | − | 0.647842i | \(-0.224328\pi\) | ||||
0.761775 | + | 0.647842i | \(0.224328\pi\) | |||||||
\(104\) | 10.0459 | 0.985079 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.27243 | −0.123589 | ||||||||
\(107\) | −6.26446 | −0.605609 | −0.302804 | − | 0.953053i | \(-0.597923\pi\) | ||||
−0.302804 | + | 0.953053i | \(0.597923\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.09153 | 0.296115 | 0.148057 | − | 0.988979i | \(-0.452698\pi\) | ||||
0.148057 | + | 0.988979i | \(0.452698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.88387 | 0.461482 | ||||||||
\(113\) | −15.9441 | −1.49990 | −0.749948 | − | 0.661497i | \(-0.769921\pi\) | ||||
−0.749948 | + | 0.661497i | \(0.769921\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.94568 | −0.181436 | ||||||||
\(116\) | −2.55725 | −0.237435 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.87642 | −0.909199 | ||||||||
\(119\) | −11.6881 | −1.07144 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.61522 | −0.236771 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.02454 | −0.271611 | ||||||||
\(125\) | 2.88336 | 0.257895 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.5061 | −1.64215 | −0.821075 | − | 0.570821i | \(-0.806625\pi\) | ||||
−0.821075 | + | 0.570821i | \(0.806625\pi\) | |||||||
\(128\) | 10.8864 | 0.962233 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.825044 | 0.0723612 | ||||||||
\(131\) | 0.864643 | 0.0755442 | 0.0377721 | − | 0.999286i | \(-0.487974\pi\) | ||||
0.0377721 | + | 0.999286i | \(0.487974\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.3983 | −1.76875 | ||||||||
\(134\) | 6.05516 | 0.523086 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.35799 | −0.716692 | ||||||||
\(137\) | 12.3782 | 1.05754 | 0.528769 | − | 0.848766i | \(-0.322654\pi\) | ||||
0.528769 | + | 0.848766i | \(0.322654\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.665969 | −0.0564868 | −0.0282434 | − | 0.999601i | \(-0.508991\pi\) | ||||
−0.0282434 | + | 0.999601i | \(0.508991\pi\) | |||||||
\(140\) | 1.50341 | 0.127062 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.54127 | −0.632849 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.482640 | −0.0400811 | ||||||||
\(146\) | −0.852974 | −0.0705926 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.90812 | 0.321245 | ||||||||
\(149\) | 12.0532 | 0.987440 | 0.493720 | − | 0.869621i | \(-0.335637\pi\) | ||||
0.493720 | + | 0.869621i | \(0.335637\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.5049 | 1.66867 | 0.834333 | − | 0.551260i | \(-0.185853\pi\) | ||||
0.834333 | + | 0.551260i | \(0.185853\pi\) | |||||||
\(152\) | −14.5865 | −1.18312 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.570833 | −0.0458504 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.45523 | −0.674801 | −0.337401 | − | 0.941361i | \(-0.609548\pi\) | ||||
−0.337401 | + | 0.941361i | \(0.609548\pi\) | |||||||
\(158\) | −1.42794 | −0.113601 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.68233 | 0.133000 | ||||||||
\(161\) | 22.4513 | 1.76941 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.2731 | −1.82289 | −0.911446 | − | 0.411419i | \(-0.865033\pi\) | ||||
−0.911446 | + | 0.411419i | \(0.865033\pi\) | |||||||
\(164\) | −9.99394 | −0.780395 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.35333 | 0.493114 | ||||||||
\(167\) | 19.5773 | 1.51494 | 0.757469 | − | 0.652871i | \(-0.226435\pi\) | ||||
0.757469 | + | 0.652871i | \(0.226435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.52856 | 0.348351 | ||||||||
\(170\) | −0.686422 | −0.0526462 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0764156 | −0.00582664 | ||||||||
\(173\) | −17.9102 | −1.36169 | −0.680843 | − | 0.732429i | \(-0.738386\pi\) | ||||
−0.680843 | + | 0.732429i | \(0.738386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.4937 | −1.24681 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.70199 | −0.427382 | ||||||||
\(179\) | −9.44944 | −0.706284 | −0.353142 | − | 0.935570i | \(-0.614887\pi\) | ||||
−0.353142 | + | 0.935570i | \(0.614887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0798 | 0.823555 | 0.411777 | − | 0.911284i | \(-0.364908\pi\) | ||||
0.411777 | + | 0.911284i | \(0.364908\pi\) | |||||||
\(182\) | −9.52021 | −0.705685 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.0546 | 1.18356 | ||||||||
\(185\) | 0.737595 | 0.0542291 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.07912 | 0.151636 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.19796 | −0.0869090 | ||||||||
\(191\) | 4.53719 | 0.328300 | 0.164150 | − | 0.986435i | \(-0.447512\pi\) | ||||
0.164150 | + | 0.986435i | \(0.447512\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4986 | 0.971647 | 0.485824 | − | 0.874057i | \(-0.338520\pi\) | ||||
0.485824 | + | 0.874057i | \(0.338520\pi\) | |||||||
\(194\) | −0.666476 | −0.0478502 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.56259 | −0.468756 | ||||||||
\(197\) | −1.70047 | −0.121153 | −0.0605766 | − | 0.998164i | \(-0.519294\pi\) | ||||
−0.0605766 | + | 0.998164i | \(0.519294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1442 | −0.719105 | −0.359552 | − | 0.933125i | \(-0.617071\pi\) | ||||
−0.359552 | + | 0.933125i | \(0.617071\pi\) | |||||||
\(200\) | −11.7944 | −0.833992 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.65080 | −0.186509 | ||||||||
\(203\) | 5.56920 | 0.390881 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.88620 | −0.131738 | ||||||||
\(206\) | −10.4783 | −0.730061 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.09371 | 0.422523 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6754 | −0.734923 | −0.367461 | − | 0.930039i | \(-0.619773\pi\) | ||||
−0.367461 | + | 0.930039i | \(0.619773\pi\) | |||||||
\(212\) | −2.89303 | −0.198694 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.24523 | 0.290198 | ||||||||
\(215\) | −0.0144222 | −0.000983588 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.58686 | 0.447145 | ||||||||
\(218\) | −2.09503 | −0.141893 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.5835 | −0.980990 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.83739 | 0.190006 | 0.0950028 | − | 0.995477i | \(-0.469714\pi\) | ||||
0.0950028 | + | 0.995477i | \(0.469714\pi\) | |||||||
\(224\) | −19.4124 | −1.29705 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.8048 | 0.718726 | ||||||||
\(227\) | −6.48587 | −0.430482 | −0.215241 | − | 0.976561i | \(-0.569054\pi\) | ||||
−0.215241 | + | 0.976561i | \(0.569054\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.6403 | −1.69436 | −0.847181 | − | 0.531305i | \(-0.821702\pi\) | ||||
−0.847181 | + | 0.531305i | \(0.821702\pi\) | |||||||
\(230\) | 1.31853 | 0.0869411 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.98246 | 0.261461 | ||||||||
\(233\) | 0.649882 | 0.0425752 | 0.0212876 | − | 0.999773i | \(-0.493223\pi\) | ||||
0.0212876 | + | 0.999773i | \(0.493223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.392401 | 0.0255974 | ||||||||
\(236\) | −22.4553 | −1.46172 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.92065 | 0.513419 | ||||||||
\(239\) | 16.9346 | 1.09541 | 0.547703 | − | 0.836673i | \(-0.315502\pi\) | ||||
0.547703 | + | 0.836673i | \(0.315502\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4993 | 1.57814 | 0.789069 | − | 0.614305i | \(-0.210563\pi\) | ||||
0.789069 | + | 0.614305i | \(0.210563\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.94603 | −0.380656 | ||||||||
\(245\) | −1.23858 | −0.0791302 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.4513 | −1.61943 | ||||||||
\(248\) | 4.71018 | 0.299096 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.95396 | −0.123579 | ||||||||
\(251\) | −17.8710 | −1.12801 | −0.564005 | − | 0.825771i | \(-0.690740\pi\) | ||||
−0.564005 | + | 0.825771i | \(0.690740\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.5410 | 0.786892 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.39643 | −0.587277 | ||||||||
\(257\) | 1.24675 | 0.0777702 | 0.0388851 | − | 0.999244i | \(-0.487619\pi\) | ||||
0.0388851 | + | 0.999244i | \(0.487619\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.51113 | −0.528856 | ||||||||
\(260\) | 1.87584 | 0.116335 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.585941 | −0.0361996 | ||||||||
\(263\) | 16.7807 | 1.03474 | 0.517371 | − | 0.855761i | \(-0.326911\pi\) | ||||
0.517371 | + | 0.855761i | \(0.326911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.546013 | −0.0335413 | ||||||||
\(266\) | 13.8233 | 0.847559 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.7672 | 0.840964 | ||||||||
\(269\) | −21.9703 | −1.33955 | −0.669777 | − | 0.742563i | \(-0.733610\pi\) | ||||
−0.669777 | + | 0.742563i | \(0.733610\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1083 | 0.614037 | 0.307018 | − | 0.951704i | \(-0.400669\pi\) | ||||
0.307018 | + | 0.951704i | \(0.400669\pi\) | |||||||
\(272\) | −5.06986 | −0.307405 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.38829 | −0.506755 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.77311 | 0.467041 | 0.233520 | − | 0.972352i | \(-0.424975\pi\) | ||||
0.233520 | + | 0.972352i | \(0.424975\pi\) | |||||||
\(278\) | 0.451306 | 0.0270676 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.34130 | −0.139919 | ||||||||
\(281\) | 32.2904 | 1.92628 | 0.963142 | − | 0.268995i | \(-0.0866914\pi\) | ||||
0.963142 | + | 0.268995i | \(0.0866914\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5231 | −0.744418 | −0.372209 | − | 0.928149i | \(-0.621400\pi\) | ||||
−0.372209 | + | 0.928149i | \(0.621400\pi\) | |||||||
\(284\) | −17.1460 | −1.01743 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.7649 | 1.28474 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.86682 | −0.286283 | ||||||||
\(290\) | 0.327070 | 0.0192062 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.93934 | −0.113491 | ||||||||
\(293\) | 18.3844 | 1.07403 | 0.537013 | − | 0.843574i | \(-0.319552\pi\) | ||||
0.537013 | + | 0.843574i | \(0.319552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.23808 | −0.246750 | ||||||||
\(296\) | −6.08619 | −0.353753 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.16810 | −0.473166 | ||||||||
\(299\) | 28.0129 | 1.62003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.166418 | 0.00959220 | ||||||||
\(302\) | −13.8955 | −0.799599 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.84802 | −0.507469 | ||||||||
\(305\) | −1.12222 | −0.0642581 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.42389 | 0.480777 | 0.240388 | − | 0.970677i | \(-0.422725\pi\) | ||||
0.240388 | + | 0.970677i | \(0.422725\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.386836 | 0.0219708 | ||||||||
\(311\) | −11.3034 | −0.640954 | −0.320477 | − | 0.947256i | \(-0.603843\pi\) | ||||
−0.320477 | + | 0.947256i | \(0.603843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.11064 | 0.345394 | 0.172697 | − | 0.984975i | \(-0.444752\pi\) | ||||
0.172697 | + | 0.984975i | \(0.444752\pi\) | |||||||
\(314\) | 5.72985 | 0.323354 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.24660 | −0.182635 | ||||||||
\(317\) | 0.828576 | 0.0465374 | 0.0232687 | − | 0.999729i | \(-0.492593\pi\) | ||||
0.0232687 | + | 0.999729i | \(0.492593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.293564 | −0.0164107 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.2145 | −0.847872 | ||||||||
\(323\) | 21.1751 | 1.17821 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.5795 | −1.14155 | ||||||||
\(326\) | 15.7715 | 0.873501 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.5638 | 0.859365 | ||||||||
\(329\) | −4.52792 | −0.249633 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.18453 | 0.449863 | 0.224931 | − | 0.974375i | \(-0.427784\pi\) | ||||
0.224931 | + | 0.974375i | \(0.427784\pi\) | |||||||
\(332\) | 14.4451 | 0.792777 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.2669 | −0.725935 | ||||||||
\(335\) | 2.59833 | 0.141962 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.50485 | −0.136448 | −0.0682239 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682239 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(338\) | −3.06887 | −0.166924 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.56067 | −0.0846391 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.19637 | −0.496558 | ||||||||
\(344\) | 0.119004 | 0.00641625 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.1372 | 0.652498 | ||||||||
\(347\) | 31.5264 | 1.69243 | 0.846213 | − | 0.532844i | \(-0.178877\pi\) | ||||
0.846213 | + | 0.532844i | \(0.178877\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.75192 | −0.468480 | −0.234240 | − | 0.972179i | \(-0.575260\pi\) | ||||
−0.234240 | + | 0.972179i | \(0.575260\pi\) | |||||||
\(350\) | 11.1773 | 0.597450 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.439863 | −0.0234115 | −0.0117058 | − | 0.999931i | \(-0.503726\pi\) | ||||
−0.0117058 | + | 0.999931i | \(0.503726\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.23604 | −0.171751 | ||||||||
\(356\) | −12.9642 | −0.687101 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.40359 | 0.338440 | ||||||||
\(359\) | −16.7381 | −0.883404 | −0.441702 | − | 0.897162i | \(-0.645625\pi\) | ||||
−0.441702 | + | 0.897162i | \(0.645625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.9552 | 0.945009 | ||||||||
\(362\) | −7.50843 | −0.394634 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.6454 | −1.13453 | ||||||||
\(365\) | −0.366020 | −0.0191584 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7488 | −0.769880 | −0.384940 | − | 0.922942i | \(-0.625778\pi\) | ||||
−0.384940 | + | 0.922942i | \(0.625778\pi\) | |||||||
\(368\) | 9.73853 | 0.507656 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.499845 | −0.0259857 | ||||||||
\(371\) | 6.30046 | 0.327103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.6508 | 1.22459 | 0.612296 | − | 0.790629i | \(-0.290246\pi\) | ||||
0.612296 | + | 0.790629i | \(0.290246\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.23786 | −0.166980 | ||||||||
\(377\) | 6.94880 | 0.357882 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4766 | −0.589514 | −0.294757 | − | 0.955572i | \(-0.595239\pi\) | ||||
−0.294757 | + | 0.955572i | \(0.595239\pi\) | |||||||
\(380\) | −2.72371 | −0.139723 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.07471 | −0.157316 | ||||||||
\(383\) | 7.92867 | 0.405136 | 0.202568 | − | 0.979268i | \(-0.435071\pi\) | ||||
0.202568 | + | 0.979268i | \(0.435071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.14755 | −0.465598 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.51532 | −0.0769286 | ||||||||
\(389\) | −9.05099 | −0.458903 | −0.229452 | − | 0.973320i | \(-0.573693\pi\) | ||||
−0.229452 | + | 0.973320i | \(0.573693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.3062 | −1.17865 | ||||||||
\(392\) | 10.2201 | 0.516191 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.15235 | 0.0580547 | ||||||||
\(395\) | −0.612743 | −0.0308305 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.38182 | 0.270106 | 0.135053 | − | 0.990838i | \(-0.456880\pi\) | ||||
0.135053 | + | 0.990838i | \(0.456880\pi\) | |||||||
\(398\) | 6.87442 | 0.344584 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.15436 | −0.357718 | ||||||||
\(401\) | 15.6683 | 0.782438 | 0.391219 | − | 0.920298i | \(-0.372053\pi\) | ||||
0.391219 | + | 0.920298i | \(0.372053\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.21856 | 0.409396 | ||||||||
\(404\) | −6.02692 | −0.299850 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.77407 | −0.187304 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.7413 | −1.12448 | −0.562242 | − | 0.826973i | \(-0.690061\pi\) | ||||
−0.562242 | + | 0.826973i | \(0.690061\pi\) | |||||||
\(410\) | 1.27822 | 0.0631266 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −23.8238 | −1.17372 | ||||||||
\(413\) | 48.9033 | 2.40637 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.72628 | 0.133828 | ||||||||
\(416\) | −24.2213 | −1.18755 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 39.0263 | 1.90656 | 0.953279 | − | 0.302090i | \(-0.0976844\pi\) | ||||
0.953279 | + | 0.302090i | \(0.0976844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.1875 | 1.17883 | 0.589414 | − | 0.807831i | \(-0.299359\pi\) | ||||
0.589414 | + | 0.807831i | \(0.299359\pi\) | |||||||
\(422\) | 7.23436 | 0.352163 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.50537 | 0.218800 | ||||||||
\(425\) | 17.1218 | 0.830530 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9493 | 0.626661 | ||||||||
\(428\) | 9.65207 | 0.466550 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.00977349 | 0.000471320 0 | ||||||||
\(431\) | 12.2455 | 0.589844 | 0.294922 | − | 0.955521i | \(-0.404706\pi\) | ||||
0.294922 | + | 0.955521i | \(0.404706\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.13183 | −0.342734 | −0.171367 | − | 0.985207i | \(-0.554818\pi\) | ||||
−0.171367 | + | 0.985207i | \(0.554818\pi\) | |||||||
\(434\) | −4.46371 | −0.214265 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.76332 | −0.228122 | ||||||||
\(437\) | −40.6745 | −1.94573 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.1944 | −0.916099 | −0.458049 | − | 0.888927i | \(-0.651452\pi\) | ||||
−0.458049 | + | 0.888927i | \(0.651452\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.88275 | 0.470075 | ||||||||
\(443\) | 9.65055 | 0.458511 | 0.229256 | − | 0.973366i | \(-0.426371\pi\) | ||||
0.229256 | + | 0.973366i | \(0.426371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.44678 | −0.115989 | ||||||||
\(446\) | −1.92281 | −0.0910477 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.38744 | 0.160041 | ||||||||
\(449\) | 15.3818 | 0.725912 | 0.362956 | − | 0.931806i | \(-0.381767\pi\) | ||||
0.362956 | + | 0.931806i | \(0.381767\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 24.5661 | 1.15549 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.39527 | 0.206280 | ||||||||
\(455\) | −4.08522 | −0.191518 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0977 | −0.893355 | −0.446678 | − | 0.894695i | \(-0.647393\pi\) | ||||
−0.446678 | + | 0.894695i | \(0.647393\pi\) | |||||||
\(458\) | 17.3757 | 0.811911 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.99784 | 0.139775 | ||||||||
\(461\) | −8.37180 | −0.389914 | −0.194957 | − | 0.980812i | \(-0.562457\pi\) | ||||
−0.194957 | + | 0.980812i | \(0.562457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.2595 | 1.31333 | 0.656665 | − | 0.754182i | \(-0.271966\pi\) | ||||
0.656665 | + | 0.754182i | \(0.271966\pi\) | |||||||
\(464\) | 2.41571 | 0.112147 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.440405 | −0.0204014 | ||||||||
\(467\) | 8.22408 | 0.380565 | 0.190282 | − | 0.981729i | \(-0.439060\pi\) | ||||
0.190282 | + | 0.981729i | \(0.439060\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.9822 | −1.38445 | ||||||||
\(470\) | −0.265918 | −0.0122659 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.9701 | 1.60963 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.8813 | 1.37105 | ||||||||
\(476\) | 18.0086 | 0.825422 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.4760 | −0.524901 | ||||||||
\(479\) | 30.4221 | 1.39002 | 0.695012 | − | 0.718999i | \(-0.255399\pi\) | ||||
0.695012 | + | 0.718999i | \(0.255399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6195 | −0.484208 | ||||||||
\(482\) | −16.6024 | −0.756219 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.285992 | −0.0129862 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.2893 | −1.01002 | −0.505012 | − | 0.863112i | \(-0.668512\pi\) | ||||
−0.505012 | + | 0.863112i | \(0.668512\pi\) | |||||||
\(488\) | 9.25988 | 0.419175 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.839349 | 0.0379179 | ||||||||
\(491\) | 32.3658 | 1.46065 | 0.730325 | − | 0.683100i | \(-0.239369\pi\) | ||||
0.730325 | + | 0.683100i | \(0.239369\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.78128 | −0.260376 | ||||||||
\(494\) | 17.2476 | 0.776005 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.85714 | 0.128289 | ||||||||
\(497\) | 37.3407 | 1.67496 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.261774 | 0.0117186 | 0.00585931 | − | 0.999983i | \(-0.498135\pi\) | ||||
0.00585931 | + | 0.999983i | \(0.498135\pi\) | |||||||
\(500\) | −4.44258 | −0.198678 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.1106 | 0.540524 | ||||||||
\(503\) | 18.0436 | 0.804525 | 0.402263 | − | 0.915524i | \(-0.368224\pi\) | ||||
0.402263 | + | 0.915524i | \(0.368224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.13748 | −0.0506174 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 28.5135 | 1.26508 | ||||||||
\(509\) | 4.25278 | 0.188501 | 0.0942506 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942506 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.22351 | 0.186837 | ||||||||
\(512\) | −15.4052 | −0.680819 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.844884 | −0.0372662 | ||||||||
\(515\) | −4.49637 | −0.198134 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5.76772 | 0.253419 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.92129 | −0.128107 | ||||||||
\(521\) | −13.7326 | −0.601635 | −0.300817 | − | 0.953682i | \(-0.597259\pi\) | ||||
−0.300817 | + | 0.953682i | \(0.597259\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0362 | 1.13849 | 0.569243 | − | 0.822170i | \(-0.307236\pi\) | ||||
0.569243 | + | 0.822170i | \(0.307236\pi\) | |||||||
\(524\) | −1.33221 | −0.0581979 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.3718 | −0.495832 | ||||||||
\(527\) | −6.83770 | −0.297855 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7682 | 0.946444 | ||||||||
\(530\) | 0.370016 | 0.0160725 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 31.4289 | 1.36262 | ||||||||
\(533\) | 27.1565 | 1.17628 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.82167 | 0.0787578 | ||||||||
\(536\) | −21.4399 | −0.926063 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.8886 | 0.641893 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.1235 | 0.650211 | 0.325106 | − | 0.945678i | \(-0.394600\pi\) | ||||
0.325106 | + | 0.945678i | \(0.394600\pi\) | |||||||
\(542\) | −6.85009 | −0.294237 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.1517 | 0.863996 | ||||||||
\(545\) | −0.899000 | −0.0385089 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2430 | −0.951042 | −0.475521 | − | 0.879704i | \(-0.657740\pi\) | ||||
−0.475521 | + | 0.879704i | \(0.657740\pi\) | |||||||
\(548\) | −19.0718 | −0.814709 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.0896 | −0.429832 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.07046 | 0.300667 | ||||||||
\(554\) | −5.26759 | −0.223798 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.02610 | 0.0435164 | ||||||||
\(557\) | 35.8076 | 1.51722 | 0.758609 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758609 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.207644 | 0.00878239 | ||||||||
\(560\) | −1.42020 | −0.0600146 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.8822 | −0.923044 | ||||||||
\(563\) | −33.6120 | −1.41658 | −0.708289 | − | 0.705922i | \(-0.750533\pi\) | ||||
−0.708289 | + | 0.705922i | \(0.750533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.63646 | 0.195058 | ||||||||
\(566\) | 8.48648 | 0.356713 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.7019 | 1.12039 | ||||||||
\(569\) | 22.7477 | 0.953635 | 0.476817 | − | 0.879002i | \(-0.341790\pi\) | ||||
0.476817 | + | 0.879002i | \(0.341790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.3194 | −1.47807 | −0.739035 | − | 0.673667i | \(-0.764718\pi\) | ||||
−0.739035 | + | 0.673667i | \(0.764718\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.7494 | −0.615627 | ||||||||
\(575\) | −32.8887 | −1.37155 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.5174 | 1.22883 | 0.614413 | − | 0.788984i | \(-0.289393\pi\) | ||||
0.614413 | + | 0.788984i | \(0.289393\pi\) | |||||||
\(578\) | 3.29809 | 0.137182 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.743635 | 0.0308778 | ||||||||
\(581\) | −31.4586 | −1.30512 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.02018 | 0.124976 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.4585 | −0.514657 | ||||||||
\(587\) | 33.0777 | 1.36526 | 0.682632 | − | 0.730762i | \(-0.260835\pi\) | ||||
0.682632 | + | 0.730762i | \(0.260835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.9333 | −0.491703 | ||||||||
\(590\) | 2.87201 | 0.118239 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.69181 | −0.151733 | ||||||||
\(593\) | 9.74358 | 0.400121 | 0.200060 | − | 0.979784i | \(-0.435886\pi\) | ||||
0.200060 | + | 0.979784i | \(0.435886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.39883 | 0.139339 | ||||||||
\(596\) | −18.5712 | −0.760706 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.9835 | −0.776292 | ||||||||
\(599\) | −27.8578 | −1.13824 | −0.569120 | − | 0.822255i | \(-0.692716\pi\) | ||||
−0.569120 | + | 0.822255i | \(0.692716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.3192 | −0.869630 | −0.434815 | − | 0.900520i | \(-0.643186\pi\) | ||||
−0.434815 | + | 0.900520i | \(0.643186\pi\) | |||||||
\(602\) | −0.112777 | −0.00459643 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −31.5933 | −1.28551 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1431 | 0.776994 | 0.388497 | − | 0.921450i | \(-0.372994\pi\) | ||||
0.388497 | + | 0.921450i | \(0.372994\pi\) | |||||||
\(608\) | 35.1691 | 1.42630 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.760492 | 0.0307914 | ||||||||
\(611\) | −5.64959 | −0.228558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.05388 | 0.244514 | 0.122257 | − | 0.992498i | \(-0.460987\pi\) | ||||
0.122257 | + | 0.992498i | \(0.460987\pi\) | |||||||
\(614\) | −5.70860 | −0.230380 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.3264 | 1.22090 | 0.610448 | − | 0.792057i | \(-0.290990\pi\) | ||||
0.610448 | + | 0.792057i | \(0.290990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.66068 | −0.187328 | −0.0936642 | − | 0.995604i | \(-0.529858\pi\) | ||||
−0.0936642 | + | 0.995604i | \(0.529858\pi\) | |||||||
\(620\) | 0.879520 | 0.0353224 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.65993 | 0.307135 | ||||||||
\(623\) | 28.2335 | 1.13115 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.7387 | 0.949549 | ||||||||
\(626\) | −4.14099 | −0.165507 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.0275 | 0.519855 | ||||||||
\(629\) | 8.83525 | 0.352284 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.0740 | 1.95360 | 0.976802 | − | 0.214146i | \(-0.0686968\pi\) | ||||
0.976802 | + | 0.214146i | \(0.0686968\pi\) | |||||||
\(632\) | 5.05599 | 0.201117 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.561500 | −0.0223000 | ||||||||
\(635\) | 5.38147 | 0.213557 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.8325 | 0.706549 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.16571 | −0.125136 | ||||||||
\(641\) | −28.7227 | −1.13448 | −0.567239 | − | 0.823553i | \(-0.691988\pi\) | ||||
−0.567239 | + | 0.823553i | \(0.691988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.0211 | 0.513501 | 0.256751 | − | 0.966478i | \(-0.417348\pi\) | ||||
0.256751 | + | 0.966478i | \(0.417348\pi\) | |||||||
\(644\) | −34.5921 | −1.36312 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.3497 | −0.564581 | ||||||||
\(647\) | −36.6127 | −1.43939 | −0.719696 | − | 0.694289i | \(-0.755719\pi\) | ||||
−0.719696 | + | 0.694289i | \(0.755719\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 13.9461 | 0.547011 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 35.8584 | 1.40432 | ||||||||
\(653\) | 11.6694 | 0.456658 | 0.228329 | − | 0.973584i | \(-0.426674\pi\) | ||||
0.228329 | + | 0.973584i | \(0.426674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.251434 | −0.00982432 | ||||||||
\(656\) | 9.44080 | 0.368601 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.06843 | 0.119620 | ||||||||
\(659\) | 39.7322 | 1.54775 | 0.773873 | − | 0.633341i | \(-0.218317\pi\) | ||||
0.773873 | + | 0.633341i | \(0.218317\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.4819 | 0.835550 | 0.417775 | − | 0.908551i | \(-0.362810\pi\) | ||||
0.417775 | + | 0.908551i | \(0.362810\pi\) | |||||||
\(662\) | −5.54640 | −0.215567 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.4956 | −0.873000 | ||||||||
\(665\) | 5.93171 | 0.230022 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1051 | 0.429990 | ||||||||
\(668\) | −30.1641 | −1.16708 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.76081 | −0.0680260 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.5108 | −0.790632 | −0.395316 | − | 0.918545i | \(-0.629365\pi\) | ||||
−0.395316 | + | 0.918545i | \(0.629365\pi\) | |||||||
\(674\) | 1.69746 | 0.0653836 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.97745 | −0.268364 | ||||||||
\(677\) | −1.18298 | −0.0454658 | −0.0227329 | − | 0.999742i | \(-0.507237\pi\) | ||||
−0.0227329 | + | 0.999742i | \(0.507237\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.30007 | 0.126645 | ||||||||
\(680\) | 2.43046 | 0.0932039 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.06013 | 0.231884 | 0.115942 | − | 0.993256i | \(-0.463011\pi\) | ||||
0.115942 | + | 0.993256i | \(0.463011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.59951 | −0.137530 | ||||||||
\(686\) | 6.23210 | 0.237943 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0721862 | 0.00275207 | ||||||||
\(689\) | 7.86121 | 0.299488 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.8292 | 1.62930 | 0.814650 | − | 0.579953i | \(-0.196929\pi\) | ||||
0.814650 | + | 0.579953i | \(0.196929\pi\) | |||||||
\(692\) | 27.5954 | 1.04902 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.3645 | −0.810984 | ||||||||
\(695\) | 0.193660 | 0.00734596 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.5937 | −0.855798 | ||||||||
\(698\) | 5.93091 | 0.224488 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25.4129 | 0.960518 | ||||||||
\(701\) | 3.89209 | 0.147002 | 0.0735011 | − | 0.997295i | \(-0.476583\pi\) | ||||
0.0735011 | + | 0.997295i | \(0.476583\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.4195 | 0.581556 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.298081 | 0.0112184 | ||||||||
\(707\) | 13.1255 | 0.493634 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.1493 | 0.831833 | 0.415917 | − | 0.909403i | \(-0.363461\pi\) | ||||
0.415917 | + | 0.909403i | \(0.363461\pi\) | |||||||
\(710\) | 2.19296 | 0.0823004 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.1894 | 0.756630 | ||||||||
\(713\) | 13.1343 | 0.491884 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.5594 | 0.544109 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.3429 | 0.423313 | ||||||||
\(719\) | 37.5592 | 1.40072 | 0.700362 | − | 0.713788i | \(-0.253022\pi\) | ||||
0.700362 | + | 0.713788i | \(0.253022\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.8837 | 1.93225 | ||||||||
\(722\) | −12.1677 | −0.452833 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.0714 | −0.634452 | ||||||||
\(725\) | −8.15829 | −0.302991 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.4777 | −1.05618 | −0.528090 | − | 0.849189i | \(-0.677092\pi\) | ||||
−0.528090 | + | 0.849189i | \(0.677092\pi\) | |||||||
\(728\) | 33.7088 | 1.24933 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.248040 | 0.00918038 | ||||||||
\(731\) | −0.172756 | −0.00638961 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.8964 | 0.587148 | 0.293574 | − | 0.955936i | \(-0.405155\pi\) | ||||
0.293574 | + | 0.955936i | \(0.405155\pi\) | |||||||
\(734\) | 9.99478 | 0.368914 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.7087 | −1.42682 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.3058 | 1.33553 | 0.667766 | − | 0.744371i | \(-0.267251\pi\) | ||||
0.667766 | + | 0.744371i | \(0.267251\pi\) | |||||||
\(740\) | −1.13646 | −0.0417771 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.26962 | −0.156743 | ||||||||
\(743\) | −41.8306 | −1.53462 | −0.767308 | − | 0.641279i | \(-0.778404\pi\) | ||||
−0.767308 | + | 0.641279i | \(0.778404\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.50502 | −0.128414 | ||||||||
\(746\) | −16.0274 | −0.586805 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.0203 | −0.768066 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9957 | 0.656673 | 0.328337 | − | 0.944561i | \(-0.393512\pi\) | ||||
0.328337 | + | 0.944561i | \(0.393512\pi\) | |||||||
\(752\) | −1.96405 | −0.0716214 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.70899 | −0.171491 | ||||||||
\(755\) | −5.96272 | −0.217006 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.2640 | 0.990928 | 0.495464 | − | 0.868628i | \(-0.334998\pi\) | ||||
0.495464 | + | 0.868628i | \(0.334998\pi\) | |||||||
\(758\) | 7.77735 | 0.282486 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.24169 | 0.153862 | ||||||||
\(761\) | 0.524438 | 0.0190109 | 0.00950543 | − | 0.999955i | \(-0.496974\pi\) | ||||
0.00950543 | + | 0.999955i | \(0.496974\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.3736 | 0.375549 | ||||||||
\(764\) | −6.99075 | −0.252916 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.37301 | −0.194135 | ||||||||
\(767\) | 61.0177 | 2.20322 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.19450 | −0.0430748 | −0.0215374 | − | 0.999768i | \(-0.506856\pi\) | ||||
−0.0215374 | + | 0.999768i | \(0.506856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.7981 | −0.748540 | ||||||||
\(773\) | −28.6486 | −1.03042 | −0.515209 | − | 0.857065i | \(-0.672286\pi\) | ||||
−0.515209 | + | 0.857065i | \(0.672286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.64906 | −0.346604 | ||||||||
\(776\) | 2.35984 | 0.0847132 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.13357 | 0.219899 | ||||||||
\(779\) | −39.4310 | −1.41276 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 15.7939 | 0.564789 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.19936 | 0.221406 | ||||||||
\(785\) | 2.45874 | 0.0877561 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.5076 | 0.410202 | 0.205101 | − | 0.978741i | \(-0.434248\pi\) | ||||
0.205101 | + | 0.978741i | \(0.434248\pi\) | |||||||
\(788\) | 2.62002 | 0.0933342 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.415237 | 0.0147735 | ||||||||
\(791\) | −53.5003 | −1.90225 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1571 | 0.573756 | ||||||||
\(794\) | −3.64709 | −0.129430 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.6299 | 0.553986 | ||||||||
\(797\) | −1.34078 | −0.0474930 | −0.0237465 | − | 0.999718i | \(-0.507559\pi\) | ||||
−0.0237465 | + | 0.999718i | \(0.507559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.70036 | 0.166287 | ||||||||
\(800\) | 28.4371 | 1.00540 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.6179 | −0.374932 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.52871 | −0.230107 | ||||||||
\(806\) | −5.56946 | −0.196176 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.38584 | 0.330193 | ||||||||
\(809\) | 29.7375 | 1.04551 | 0.522757 | − | 0.852482i | \(-0.324904\pi\) | ||||
0.522757 | + | 0.852482i | \(0.324904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.5904 | 1.00395 | 0.501973 | − | 0.864883i | \(-0.332608\pi\) | ||||
0.501973 | + | 0.864883i | \(0.332608\pi\) | |||||||
\(812\) | −8.58082 | −0.301128 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.76771 | 0.237062 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.301497 | −0.0105481 | ||||||||
\(818\) | 15.4111 | 0.538835 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.90619 | 0.101488 | ||||||||
\(821\) | 15.5398 | 0.542341 | 0.271171 | − | 0.962531i | \(-0.412589\pi\) | ||||
0.271171 | + | 0.962531i | \(0.412589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.5777 | −1.41445 | −0.707225 | − | 0.706989i | \(-0.750053\pi\) | ||||
−0.707225 | + | 0.706989i | \(0.750053\pi\) | |||||||
\(824\) | 37.1014 | 1.29249 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33.1402 | −1.15310 | ||||||||
\(827\) | 2.54353 | 0.0884472 | 0.0442236 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442236 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.3710 | −0.499127 | −0.249564 | − | 0.968358i | \(-0.580287\pi\) | ||||
−0.249564 | + | 0.968358i | \(0.580287\pi\) | |||||||
\(830\) | −1.84751 | −0.0641282 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.22658 | 0.146530 | ||||||||
\(833\) | −14.8363 | −0.514048 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.69298 | −0.197014 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.4469 | −0.913593 | ||||||||
\(839\) | −37.5810 | −1.29744 | −0.648721 | − | 0.761026i | \(-0.724696\pi\) | ||||
−0.648721 | + | 0.761026i | \(0.724696\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2453 | −0.905010 | ||||||||
\(842\) | −16.3911 | −0.564876 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.4482 | 0.566172 | ||||||||
\(845\) | −1.31688 | −0.0453022 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.73291 | 0.0938484 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.6029 | −0.397977 | ||||||||
\(851\) | −16.9713 | −0.581770 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.1157 | 1.20234 | 0.601170 | − | 0.799121i | \(-0.294702\pi\) | ||||
0.601170 | + | 0.799121i | \(0.294702\pi\) | |||||||
\(854\) | −8.77534 | −0.300286 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.0314 | −0.513762 | ||||||||
\(857\) | −29.0102 | −0.990971 | −0.495486 | − | 0.868616i | \(-0.665010\pi\) | ||||
−0.495486 | + | 0.868616i | \(0.665010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.91781 | −0.133674 | −0.0668370 | − | 0.997764i | \(-0.521291\pi\) | ||||
−0.0668370 | + | 0.997764i | \(0.521291\pi\) | |||||||
\(860\) | 0.0222213 | 0.000757739 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.29838 | −0.282644 | ||||||||
\(863\) | 15.5259 | 0.528507 | 0.264253 | − | 0.964453i | \(-0.414874\pi\) | ||||
0.264253 | + | 0.964453i | \(0.414874\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.20819 | 0.177084 | ||||||||
\(866\) | 4.83302 | 0.164233 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.1488 | −0.344473 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.4095 | −1.26757 | ||||||||
\(872\) | 7.41801 | 0.251206 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 27.5639 | 0.932361 | ||||||||
\(875\) | 9.67508 | 0.327077 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.0243 | −1.14892 | −0.574460 | − | 0.818533i | \(-0.694788\pi\) | ||||
−0.574460 | + | 0.818533i | \(0.694788\pi\) | |||||||
\(878\) | 13.0074 | 0.438980 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.8513 | 0.837261 | 0.418630 | − | 0.908157i | \(-0.362510\pi\) | ||||
0.418630 | + | 0.908157i | \(0.362510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.5034 | 0.790952 | 0.395476 | − | 0.918476i | \(-0.370580\pi\) | ||||
0.395476 | + | 0.918476i | \(0.370580\pi\) | |||||||
\(884\) | 22.4697 | 0.755737 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.53988 | −0.219711 | ||||||||
\(887\) | −37.9743 | −1.27505 | −0.637527 | − | 0.770428i | \(-0.720042\pi\) | ||||
−0.637527 | + | 0.770428i | \(0.720042\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −62.0970 | −2.08266 | ||||||||
\(890\) | 1.65811 | 0.0555800 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.37175 | −0.146377 | ||||||||
\(893\) | 8.20316 | 0.274508 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.74785 | 0.0918504 | ||||||||
\(896\) | 36.5293 | 1.22036 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.4238 | −0.347846 | ||||||||
\(899\) | 3.25806 | 0.108662 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.54039 | −0.217892 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −38.2573 | −1.27242 | ||||||||
\(905\) | −3.22195 | −0.107101 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.3515 | −0.609352 | −0.304676 | − | 0.952456i | \(-0.598548\pi\) | ||||
−0.304676 | + | 0.952456i | \(0.598548\pi\) | |||||||
\(908\) | 9.99321 | 0.331636 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.76843 | 0.0917725 | ||||||||
\(911\) | −2.10960 | −0.0698943 | −0.0349472 | − | 0.999389i | \(-0.511126\pi\) | ||||
−0.0349472 | + | 0.999389i | \(0.511126\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 12.9419 | 0.428082 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 39.5057 | 1.30531 | ||||||||
\(917\) | 2.90130 | 0.0958093 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.0435 | 0.364290 | 0.182145 | − | 0.983272i | \(-0.441696\pi\) | ||||
0.182145 | + | 0.983272i | \(0.441696\pi\) | |||||||
\(920\) | −4.66859 | −0.153919 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.67331 | 0.186841 | ||||||||
\(923\) | 46.5908 | 1.53355 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.4679 | 0.409942 | ||||||||
\(926\) | −19.1506 | −0.629327 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.60197 | −0.315200 | ||||||||
\(929\) | −15.5418 | −0.509912 | −0.254956 | − | 0.966953i | \(-0.582061\pi\) | ||||
−0.254956 | + | 0.966953i | \(0.582061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.8926 | −0.848597 | ||||||||
\(932\) | −1.00132 | −0.0327992 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.57320 | −0.182361 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.4663 | 0.733941 | 0.366971 | − | 0.930232i | \(-0.380395\pi\) | ||||
0.366971 | + | 0.930232i | \(0.380395\pi\) | |||||||
\(938\) | 20.3180 | 0.663407 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.604598 | −0.0197198 | ||||||||
\(941\) | 5.21088 | 0.169870 | 0.0849350 | − | 0.996386i | \(-0.472932\pi\) | ||||
0.0849350 | + | 0.996386i | \(0.472932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.3995 | 1.41328 | ||||||||
\(944\) | 21.2124 | 0.690406 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.6216 | 0.572625 | 0.286312 | − | 0.958136i | \(-0.407570\pi\) | ||||
0.286312 | + | 0.958136i | \(0.407570\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.26977 | 0.171064 | ||||||||
\(950\) | −20.2496 | −0.656985 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −28.0451 | −0.908948 | ||||||||
\(953\) | 46.6714 | 1.51183 | 0.755917 | − | 0.654667i | \(-0.227191\pi\) | ||||
0.755917 | + | 0.654667i | \(0.227191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.31939 | −0.0426945 | ||||||||
\(956\) | −26.0922 | −0.843882 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.6161 | −0.666077 | ||||||||
\(959\) | 41.5348 | 1.34123 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.1466 | −0.875696 | ||||||||
\(962\) | 7.19651 | 0.232025 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.7476 | −1.21577 | ||||||||
\(965\) | −3.92531 | −0.126360 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.572210 | −0.0184010 | −0.00920051 | − | 0.999958i | \(-0.502929\pi\) | ||||
−0.00920051 | + | 0.999958i | \(0.502929\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.193808 | 0.00622280 | ||||||||
\(971\) | −37.1703 | −1.19285 | −0.596426 | − | 0.802668i | \(-0.703413\pi\) | ||||
−0.596426 | + | 0.802668i | \(0.703413\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.23465 | −0.0716397 | ||||||||
\(974\) | 15.1048 | 0.483988 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.61693 | 0.179794 | ||||||||
\(977\) | 16.0481 | 0.513424 | 0.256712 | − | 0.966488i | \(-0.417361\pi\) | ||||
0.256712 | + | 0.966488i | \(0.417361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.90837 | 0.0609605 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.9333 | −0.699920 | ||||||||
\(983\) | −45.8928 | −1.46375 | −0.731877 | − | 0.681437i | \(-0.761355\pi\) | ||||
−0.731877 | + | 0.681437i | \(0.761355\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.494486 | 0.0157556 | ||||||||
\(986\) | 3.91779 | 0.124768 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 39.2145 | 1.24758 | ||||||||
\(989\) | 0.331841 | 0.0105519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.3187 | −0.899573 | −0.449786 | − | 0.893136i | \(-0.648500\pi\) | ||||
−0.449786 | + | 0.893136i | \(0.648500\pi\) | |||||||
\(992\) | −11.3565 | −0.360571 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.3046 | −0.802614 | ||||||||
\(995\) | 2.94989 | 0.0935177 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.1470 | −1.11312 | −0.556558 | − | 0.830809i | \(-0.687878\pi\) | ||||
−0.556558 | + | 0.830809i | \(0.687878\pi\) | |||||||
\(998\) | −0.177396 | −0.00561538 | ||||||||
\(999\) | 0 | 0 |
(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 | 9801.2.a.cp.1.7 | 18 | ||
3.2 | odd | 2 | 9801.2.a.cm.1.12 | 18 | |||
9.2 | odd | 6 | 1089.2.e.p.364.7 | 36 | |||
9.5 | odd | 6 | 1089.2.e.p.727.7 | 36 | |||
11.3 | even | 5 | 891.2.f.e.163.4 | 36 | |||
11.4 | even | 5 | 891.2.f.e.82.4 | 36 | |||
11.10 | odd | 2 | 9801.2.a.cn.1.12 | 18 | |||
33.14 | odd | 10 | 891.2.f.f.163.6 | 36 | |||
33.26 | odd | 10 | 891.2.f.f.82.6 | 36 | |||
33.32 | even | 2 | 9801.2.a.co.1.7 | 18 | |||
99.4 | even | 15 | 297.2.n.b.181.6 | 72 | |||
99.14 | odd | 30 | 99.2.m.b.97.6 | yes | 72 | ||
99.25 | even | 15 | 297.2.n.b.64.6 | 72 | |||
99.32 | even | 6 | 1089.2.e.o.727.12 | 36 | |||
99.47 | odd | 30 | 99.2.m.b.31.4 | yes | 72 | ||
99.58 | even | 15 | 297.2.n.b.262.4 | 72 | |||
99.59 | odd | 30 | 99.2.m.b.16.4 | ✓ | 72 | ||
99.65 | even | 6 | 1089.2.e.o.364.12 | 36 | |||
99.70 | even | 15 | 297.2.n.b.280.4 | 72 | |||
99.92 | odd | 30 | 99.2.m.b.49.6 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.16.4 | ✓ | 72 | 99.59 | odd | 30 | ||
99.2.m.b.31.4 | yes | 72 | 99.47 | odd | 30 | ||
99.2.m.b.49.6 | yes | 72 | 99.92 | odd | 30 | ||
99.2.m.b.97.6 | yes | 72 | 99.14 | odd | 30 | ||
297.2.n.b.64.6 | 72 | 99.25 | even | 15 | |||
297.2.n.b.181.6 | 72 | 99.4 | even | 15 | |||
297.2.n.b.262.4 | 72 | 99.58 | even | 15 | |||
297.2.n.b.280.4 | 72 | 99.70 | even | 15 | |||
891.2.f.e.82.4 | 36 | 11.4 | even | 5 | |||
891.2.f.e.163.4 | 36 | 11.3 | even | 5 | |||
891.2.f.f.82.6 | 36 | 33.26 | odd | 10 | |||
891.2.f.f.163.6 | 36 | 33.14 | odd | 10 | |||
1089.2.e.o.364.12 | 36 | 99.65 | even | 6 | |||
1089.2.e.o.727.12 | 36 | 99.32 | even | 6 | |||
1089.2.e.p.364.7 | 36 | 9.2 | odd | 6 | |||
1089.2.e.p.727.7 | 36 | 9.5 | odd | 6 | |||
9801.2.a.cm.1.12 | 18 | 3.2 | odd | 2 | |||
9801.2.a.cn.1.12 | 18 | 11.10 | odd | 2 | |||
9801.2.a.co.1.7 | 18 | 33.32 | even | 2 | |||
9801.2.a.cp.1.7 | 18 | 1.1 | even | 1 | trivial |