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: | \(1\) |
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 | 1.12 | ||
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 | \(-0.422986\pi\) | ||||
0.239592 | + | 0.970874i | \(0.422986\pi\) | |||||||
\(3\) | 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 | \(-0.718641\pi\) | ||||
−0.634128 | + | 0.773228i | \(0.718641\pi\) | |||||||
\(8\) | −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 | \(-0.697179\pi\) | ||||
−0.580593 | + | 0.814194i | \(0.697179\pi\) | |||||||
\(14\) | −2.27391 | −0.607728 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.45549 | 0.363872 | ||||||||
\(17\) | 3.48327 | 0.844818 | 0.422409 | − | 0.906405i | \(-0.361185\pi\) | ||||
0.422409 | + | 0.906405i | \(0.361185\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.07908 | 1.39464 | 0.697318 | − | 0.716762i | \(-0.254377\pi\) | ||||
0.697318 | + | 0.716762i | \(0.254377\pi\) | |||||||
\(20\) | 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 | \(-0.549248\pi\) | ||||
−0.154102 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(30\) | 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 | \(-0.669060\pi\) | ||||
−0.506499 | + | 0.862241i | \(0.669060\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0495959 | −0.00756330 | −0.00378165 | − | 0.999993i | \(-0.501204\pi\) | ||||
−0.00378165 | + | 0.999993i | \(0.501204\pi\) | |||||||
\(44\) | 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 | \(-0.579463\pi\) | ||||
−0.247056 | + | 0.969001i | \(0.579463\pi\) | |||||||
\(62\) | 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 | \(-0.523468\pi\) | ||||
−0.0736591 | + | 0.997283i | \(0.523468\pi\) | |||||||
\(74\) | −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 | \(-0.537820\pi\) | ||||
−0.118535 | + | 0.992950i | \(0.537820\pi\) | |||||||
\(80\) | −0.423248 | −0.0473206 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.39559 | −0.485412 | ||||||||
\(83\) | 9.37527 | 1.02907 | 0.514535 | − | 0.857470i | \(-0.327965\pi\) | ||||
0.514535 | + | 0.857470i | \(0.327965\pi\) | |||||||
\(84\) | 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 | \(-0.562345\pi\) | ||||
−0.194611 | + | 0.980880i | \(0.562345\pi\) | |||||||
\(102\) | 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 | \(-0.402077\pi\) | ||||
0.302804 | + | 0.953053i | \(0.402077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.09153 | −0.296115 | −0.148057 | − | 0.988979i | \(-0.547302\pi\) | ||||
−0.148057 | + | 0.988979i | \(0.547302\pi\) | |||||||
\(110\) | 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 | \(-0.193375\pi\) | ||||
0.821075 | + | 0.570821i | \(0.193375\pi\) | |||||||
\(128\) | −10.8864 | −0.962233 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.825044 | 0.0723612 | ||||||||
\(131\) | −0.864643 | −0.0755442 | −0.0377721 | − | 0.999286i | \(-0.512026\pi\) | ||||
−0.0377721 | + | 0.999286i | \(0.512026\pi\) | |||||||
\(132\) | 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 | \(-0.491009\pi\) | ||||
0.0282434 | + | 0.999601i | \(0.491009\pi\) | |||||||
\(140\) | −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 | \(-0.664363\pi\) | ||||
−0.493720 | + | 0.869621i | \(0.664363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.5049 | −1.66867 | −0.834333 | − | 0.551260i | \(-0.814147\pi\) | ||||
−0.834333 | + | 0.551260i | \(0.814147\pi\) | |||||||
\(152\) | −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 | \(-0.773565\pi\) | ||||
−0.757469 | + | 0.652871i | \(0.773565\pi\) | |||||||
\(168\) | 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 | \(-0.261614\pi\) | ||||
0.680843 | + | 0.732429i | \(0.261614\pi\) | |||||||
\(174\) | 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 | \(-0.661480\pi\) | ||||
−0.485824 | + | 0.874057i | \(0.661480\pi\) | |||||||
\(194\) | 0.666476 | 0.0478502 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.56259 | −0.468756 | ||||||||
\(197\) | 1.70047 | 0.121153 | 0.0605766 | − | 0.998164i | \(-0.480706\pi\) | ||||
0.0605766 | + | 0.998164i | \(0.480706\pi\) | |||||||
\(198\) | 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 | \(-0.380227\pi\) | ||||
0.367461 | + | 0.930039i | \(0.380227\pi\) | |||||||
\(212\) | −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 | \(-0.430946\pi\) | ||||
0.215241 | + | 0.976561i | \(0.430946\pi\) | |||||||
\(228\) | 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 | \(-0.506777\pi\) | ||||
−0.0212876 | + | 0.999773i | \(0.506777\pi\) | |||||||
\(234\) | 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 | \(-0.684498\pi\) | ||||
−0.547703 | + | 0.836673i | \(0.684498\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.4993 | −1.57814 | −0.789069 | − | 0.614305i | \(-0.789437\pi\) | ||||
−0.789069 | + | 0.614305i | \(0.789437\pi\) | |||||||
\(242\) | 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 | \(-0.673089\pi\) | ||||
−0.517371 | + | 0.855761i | \(0.673089\pi\) | |||||||
\(264\) | 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 | \(-0.599331\pi\) | ||||
−0.307018 | + | 0.951704i | \(0.599331\pi\) | |||||||
\(272\) | 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 | \(-0.575025\pi\) | ||||
−0.233520 | + | 0.972352i | \(0.575025\pi\) | |||||||
\(278\) | 0.451306 | 0.0270676 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.34130 | −0.139919 | ||||||||
\(281\) | −32.2904 | −1.92628 | −0.963142 | − | 0.268995i | \(-0.913309\pi\) | ||||
−0.963142 | + | 0.268995i | \(0.913309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5231 | 0.744418 | 0.372209 | − | 0.928149i | \(-0.378600\pi\) | ||||
0.372209 | + | 0.928149i | \(0.378600\pi\) | |||||||
\(284\) | −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 | \(-0.680448\pi\) | ||||
−0.537013 | + | 0.843574i | \(0.680448\pi\) | |||||||
\(294\) | 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 | \(-0.577275\pi\) | ||||
−0.240388 | + | 0.970677i | \(0.577275\pi\) | |||||||
\(308\) | 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 | \(-0.478267\pi\) | ||||
0.0682239 | + | 0.997670i | \(0.478267\pi\) | |||||||
\(338\) | 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 | \(-0.821123\pi\) | ||||
−0.846213 | + | 0.532844i | \(0.821123\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.75192 | 0.468480 | 0.234240 | − | 0.972179i | \(-0.424740\pi\) | ||||
0.234240 | + | 0.972179i | \(0.424740\pi\) | |||||||
\(350\) | 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 | \(-0.354375\pi\) | ||||
0.441702 | + | 0.897162i | \(0.354375\pi\) | |||||||
\(360\) | 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 | \(-0.709754\pi\) | ||||
−0.612296 | + | 0.790629i | \(0.709754\pi\) | |||||||
\(374\) | 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 | \(-0.309939\pi\) | ||||
0.562242 | + | 0.826973i | \(0.309939\pi\) | |||||||
\(410\) | 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 | \(-0.595294\pi\) | ||||
−0.294922 | + | 0.955521i | \(0.595294\pi\) | |||||||
\(432\) | 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 | \(-0.348548\pi\) | ||||
0.458049 | + | 0.888927i | \(0.348548\pi\) | |||||||
\(440\) | 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 | \(-0.352607\pi\) | ||||
0.446678 | + | 0.894695i | \(0.352607\pi\) | |||||||
\(458\) | −17.3757 | −0.811911 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.99784 | 0.139775 | ||||||||
\(461\) | 8.37180 | 0.389914 | 0.194957 | − | 0.980812i | \(-0.437543\pi\) | ||||
0.194957 | + | 0.980812i | \(0.437543\pi\) | |||||||
\(462\) | 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 | \(-0.744601\pi\) | ||||
−0.695012 | + | 0.718999i | \(0.744601\pi\) | |||||||
\(480\) | 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 | \(-0.760631\pi\) | ||||
−0.730325 | + | 0.683100i | \(0.760631\pi\) | |||||||
\(492\) | 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 | \(-0.631776\pi\) | ||||
−0.402263 | + | 0.915524i | \(0.631776\pi\) | |||||||
\(504\) | 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 | \(-0.692764\pi\) | ||||
−0.569243 | + | 0.822170i | \(0.692764\pi\) | |||||||
\(524\) | 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 | \(-0.605400\pi\) | ||||
−0.325106 | + | 0.945678i | \(0.605400\pi\) | |||||||
\(542\) | −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 | \(-0.342260\pi\) | ||||
0.475521 | + | 0.879704i | \(0.342260\pi\) | |||||||
\(548\) | −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 | \(-0.774121\pi\) | ||||
−0.758609 | + | 0.651546i | \(0.774121\pi\) | |||||||
\(558\) | 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 | \(-0.249467\pi\) | ||||
0.708289 | + | 0.705922i | \(0.249467\pi\) | |||||||
\(564\) | 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 | \(-0.658210\pi\) | ||||
−0.476817 | + | 0.879002i | \(0.658210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3194 | 1.47807 | 0.739035 | − | 0.673667i | \(-0.235282\pi\) | ||||
0.739035 | + | 0.673667i | \(0.235282\pi\) | |||||||
\(572\) | 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 | \(-0.564114\pi\) | ||||
−0.200060 | + | 0.979784i | \(0.564114\pi\) | |||||||
\(594\) | 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 | \(-0.356814\pi\) | ||||
0.434815 | + | 0.900520i | \(0.356814\pi\) | |||||||
\(602\) | 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 | \(-0.627006\pi\) | ||||
−0.388497 | + | 0.921450i | \(0.627006\pi\) | |||||||
\(608\) | 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 | \(-0.539013\pi\) | ||||
−0.122257 | + | 0.992498i | \(0.539013\pi\) | |||||||
\(614\) | −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 | \(-0.781683\pi\) | ||||
−0.773873 | + | 0.633341i | \(0.781683\pi\) | |||||||
\(660\) | 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 | \(-0.370635\pi\) | ||||
0.395316 | + | 0.918545i | \(0.370635\pi\) | |||||||
\(674\) | 1.69746 | 0.0653836 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.97745 | −0.268364 | ||||||||
\(677\) | 1.18298 | 0.0454658 | 0.0227329 | − | 0.999742i | \(-0.492763\pi\) | ||||
0.0227329 | + | 0.999742i | \(0.492763\pi\) | |||||||
\(678\) | 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 | \(-0.523417\pi\) | ||||
−0.0735011 | + | 0.997295i | \(0.523417\pi\) | |||||||
\(702\) | 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 | \(-0.594845\pi\) | ||||
−0.293574 | + | 0.955936i | \(0.594845\pi\) | |||||||
\(734\) | −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 | \(-0.732749\pi\) | ||||
−0.667766 | + | 0.744371i | \(0.732749\pi\) | |||||||
\(740\) | −1.13646 | −0.0417771 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.26962 | −0.156743 | ||||||||
\(743\) | 41.8306 | 1.53462 | 0.767308 | − | 0.641279i | \(-0.221596\pi\) | ||||
0.767308 | + | 0.641279i | \(0.221596\pi\) | |||||||
\(744\) | 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 | \(-0.503026\pi\) | ||||
−0.00950543 | + | 0.999955i | \(0.503026\pi\) | |||||||
\(762\) | 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 | \(-0.493144\pi\) | ||||
0.0215374 | + | 0.999768i | \(0.493144\pi\) | |||||||
\(770\) | 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 | \(-0.565752\pi\) | ||||
−0.205101 | + | 0.978741i | \(0.565752\pi\) | |||||||
\(788\) | −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 | \(-0.675096\pi\) | ||||
−0.522757 | + | 0.852482i | \(0.675096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.5904 | −1.00395 | −0.501973 | − | 0.864883i | \(-0.667392\pi\) | ||||
−0.501973 | + | 0.864883i | \(0.667392\pi\) | |||||||
\(812\) | −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 | \(-0.587411\pi\) | ||||
−0.271171 | + | 0.962531i | \(0.587411\pi\) | |||||||
\(822\) | 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 | \(-0.514081\pi\) | ||||
−0.0442236 | + | 0.999022i | \(0.514081\pi\) | |||||||
\(828\) | 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 | \(-0.705298\pi\) | ||||
−0.601170 | + | 0.799121i | \(0.705298\pi\) | |||||||
\(854\) | 8.77534 | 0.300286 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.0314 | −0.513762 | ||||||||
\(857\) | 29.0102 | 0.990971 | 0.495486 | − | 0.868616i | \(-0.334990\pi\) | ||||
0.495486 | + | 0.868616i | \(0.334990\pi\) | |||||||
\(858\) | 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 | \(-0.305212\pi\) | ||||
0.574460 | + | 0.818533i | \(0.305212\pi\) | |||||||
\(878\) | 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 | \(-0.279958\pi\) | ||||
0.637527 | + | 0.770428i | \(0.279958\pi\) | |||||||
\(888\) | 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 | \(-0.558304\pi\) | ||||
−0.182145 | + | 0.983272i | \(0.558304\pi\) | |||||||
\(920\) | 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 | \(-0.619605\pi\) | ||||
−0.366971 | + | 0.930232i | \(0.619605\pi\) | |||||||
\(938\) | 20.3180 | 0.663407 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.604598 | −0.0197198 | ||||||||
\(941\) | −5.21088 | −0.169870 | −0.0849350 | − | 0.996386i | \(-0.527068\pi\) | ||||
−0.0849350 | + | 0.996386i | \(0.527068\pi\) | |||||||
\(942\) | 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 | \(-0.772809\pi\) | ||||
−0.755917 | + | 0.654667i | \(0.772809\pi\) | |||||||
\(954\) | 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 | \(-0.497071\pi\) | ||||
0.00920051 | + | 0.999958i | \(0.497071\pi\) | |||||||
\(968\) | 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 | \(-0.312122\pi\) | ||||
0.556558 | + | 0.830809i | \(0.312122\pi\) | |||||||
\(998\) | 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.cn.1.12 | 18 | ||
3.2 | odd | 2 | 9801.2.a.co.1.7 | 18 | |||
9.2 | odd | 6 | 1089.2.e.o.364.12 | 36 | |||
9.5 | odd | 6 | 1089.2.e.o.727.12 | 36 | |||
11.7 | odd | 10 | 891.2.f.e.82.4 | 36 | |||
11.8 | odd | 10 | 891.2.f.e.163.4 | 36 | |||
11.10 | odd | 2 | 9801.2.a.cp.1.7 | 18 | |||
33.8 | even | 10 | 891.2.f.f.163.6 | 36 | |||
33.29 | even | 10 | 891.2.f.f.82.6 | 36 | |||
33.32 | even | 2 | 9801.2.a.cm.1.12 | 18 | |||
99.7 | odd | 30 | 297.2.n.b.280.4 | 72 | |||
99.29 | even | 30 | 99.2.m.b.49.6 | yes | 72 | ||
99.32 | even | 6 | 1089.2.e.p.727.7 | 36 | |||
99.40 | odd | 30 | 297.2.n.b.181.6 | 72 | |||
99.41 | even | 30 | 99.2.m.b.97.6 | yes | 72 | ||
99.52 | odd | 30 | 297.2.n.b.64.6 | 72 | |||
99.65 | even | 6 | 1089.2.e.p.364.7 | 36 | |||
99.74 | even | 30 | 99.2.m.b.31.4 | yes | 72 | ||
99.85 | odd | 30 | 297.2.n.b.262.4 | 72 | |||
99.95 | even | 30 | 99.2.m.b.16.4 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.16.4 | ✓ | 72 | 99.95 | even | 30 | ||
99.2.m.b.31.4 | yes | 72 | 99.74 | even | 30 | ||
99.2.m.b.49.6 | yes | 72 | 99.29 | even | 30 | ||
99.2.m.b.97.6 | yes | 72 | 99.41 | even | 30 | ||
297.2.n.b.64.6 | 72 | 99.52 | odd | 30 | |||
297.2.n.b.181.6 | 72 | 99.40 | odd | 30 | |||
297.2.n.b.262.4 | 72 | 99.85 | odd | 30 | |||
297.2.n.b.280.4 | 72 | 99.7 | odd | 30 | |||
891.2.f.e.82.4 | 36 | 11.7 | odd | 10 | |||
891.2.f.e.163.4 | 36 | 11.8 | odd | 10 | |||
891.2.f.f.82.6 | 36 | 33.29 | even | 10 | |||
891.2.f.f.163.6 | 36 | 33.8 | even | 10 | |||
1089.2.e.o.364.12 | 36 | 9.2 | odd | 6 | |||
1089.2.e.o.727.12 | 36 | 9.5 | odd | 6 | |||
1089.2.e.p.364.7 | 36 | 99.65 | even | 6 | |||
1089.2.e.p.727.7 | 36 | 99.32 | even | 6 | |||
9801.2.a.cm.1.12 | 18 | 33.32 | even | 2 | |||
9801.2.a.cn.1.12 | 18 | 1.1 | even | 1 | trivial | ||
9801.2.a.co.1.7 | 18 | 3.2 | odd | 2 | |||
9801.2.a.cp.1.7 | 18 | 11.10 | odd | 2 |