Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4275,2,Mod(1,4275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4275.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: | \(34.1360468641\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.552409\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4275.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14243 | −1.51493 | −0.757465 | − | 0.652876i | \(-0.773562\pi\) | ||||
−0.757465 | + | 0.652876i | \(0.773562\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.59002 | 1.29501 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.10482 | −1.17351 | −0.586756 | − | 0.809764i | \(-0.699595\pi\) | ||||
−0.586756 | + | 0.809764i | \(0.699595\pi\) | |||||||
\(8\) | −1.26409 | −0.446923 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.10482 | 0.333115 | 0.166558 | − | 0.986032i | \(-0.446735\pi\) | ||||
0.166558 | + | 0.986032i | \(0.446735\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.77353 | −0.491888 | −0.245944 | − | 0.969284i | \(-0.579098\pi\) | ||||
−0.245944 | + | 0.969284i | \(0.579098\pi\) | |||||||
\(14\) | 6.65187 | 1.77779 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.47182 | −0.617955 | ||||||||
\(17\) | 7.75669 | 1.88127 | 0.940637 | − | 0.339415i | \(-0.110229\pi\) | ||||
0.940637 | + | 0.339415i | \(0.110229\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.36700 | −0.504647 | ||||||||
\(23\) | −6.65187 | −1.38701 | −0.693505 | − | 0.720451i | \(-0.743935\pi\) | ||||
−0.693505 | + | 0.720451i | \(0.743935\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.79966 | 0.745175 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.04156 | −1.51971 | ||||||||
\(29\) | −7.75669 | −1.44038 | −0.720191 | − | 0.693776i | \(-0.755946\pi\) | ||||
−0.720191 | + | 0.693776i | \(0.755946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.57664 | 1.18120 | 0.590600 | − | 0.806965i | \(-0.298891\pi\) | ||||
0.590600 | + | 0.806965i | \(0.298891\pi\) | |||||||
\(32\) | 7.82389 | 1.38308 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.6182 | −2.85000 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.40652 | 0.231231 | 0.115616 | − | 0.993294i | \(-0.463116\pi\) | ||||
0.115616 | + | 0.993294i | \(0.463116\pi\) | |||||||
\(38\) | −2.14243 | −0.347549 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.81995 | −0.440402 | −0.220201 | − | 0.975454i | \(-0.570671\pi\) | ||||
−0.220201 | + | 0.975454i | \(0.570671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.10482 | −0.473480 | −0.236740 | − | 0.971573i | \(-0.576079\pi\) | ||||
−0.236740 | + | 0.971573i | \(0.576079\pi\) | |||||||
\(44\) | 2.86151 | 0.431389 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.2512 | 2.10122 | ||||||||
\(47\) | 1.46492 | 0.213680 | 0.106840 | − | 0.994276i | \(-0.465927\pi\) | ||||
0.106840 | + | 0.994276i | \(0.465927\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.63990 | 0.377129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.59348 | −0.637001 | ||||||||
\(53\) | −2.59348 | −0.356241 | −0.178121 | − | 0.984009i | \(-0.557002\pi\) | ||||
−0.178121 | + | 0.984009i | \(0.557002\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.92477 | 0.524469 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 16.6182 | 2.18208 | ||||||||
\(59\) | 5.38969 | 0.701678 | 0.350839 | − | 0.936436i | \(-0.385897\pi\) | ||||
0.350839 | + | 0.936436i | \(0.385897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.07523 | 0.521780 | 0.260890 | − | 0.965369i | \(-0.415984\pi\) | ||||
0.260890 | + | 0.965369i | \(0.415984\pi\) | |||||||
\(62\) | −14.0900 | −1.78943 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.8185 | −1.47732 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.8151 | 1.93212 | 0.966060 | − | 0.258318i | \(-0.0831681\pi\) | ||||
0.966060 | + | 0.258318i | \(0.0831681\pi\) | |||||||
\(68\) | 20.0900 | 2.43627 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.14638 | −0.848119 | −0.424059 | − | 0.905634i | \(-0.639395\pi\) | ||||
−0.424059 | + | 0.905634i | \(0.639395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.243310 | −0.0284773 | −0.0142387 | − | 0.999899i | \(-0.504532\pi\) | ||||
−0.0142387 | + | 0.999899i | \(0.504532\pi\) | |||||||
\(74\) | −3.01339 | −0.350299 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.59002 | 0.297096 | ||||||||
\(77\) | −3.43026 | −0.390915 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.38969 | −1.05642 | −0.528211 | − | 0.849113i | \(-0.677137\pi\) | ||||
−0.528211 | + | 0.849113i | \(0.677137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.04156 | 0.667178 | ||||||||
\(83\) | 8.86151 | 0.972677 | 0.486338 | − | 0.873771i | \(-0.338332\pi\) | ||||
0.486338 | + | 0.873771i | \(0.338332\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.65187 | 0.717290 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.39659 | −0.148877 | ||||||||
\(89\) | −0.813048 | −0.0861829 | −0.0430914 | − | 0.999071i | \(-0.513721\pi\) | ||||
−0.0430914 | + | 0.999071i | \(0.513721\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.50648 | 0.577236 | ||||||||
\(92\) | −17.2285 | −1.79620 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.13849 | −0.323711 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.19689 | −0.324595 | −0.162297 | − | 0.986742i | \(-0.551890\pi\) | ||||
−0.162297 | + | 0.986742i | \(0.551890\pi\) | |||||||
\(98\) | −5.65581 | −0.571323 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.01887 | 0.300389 | 0.150195 | − | 0.988656i | \(-0.452010\pi\) | ||||
0.150195 | + | 0.988656i | \(0.452010\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.05839 | −0.596951 | −0.298476 | − | 0.954417i | \(-0.596478\pi\) | ||||
−0.298476 | + | 0.954417i | \(0.596478\pi\) | |||||||
\(104\) | 2.24190 | 0.219836 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.55635 | 0.539681 | ||||||||
\(107\) | 20.3848 | 1.97068 | 0.985338 | − | 0.170616i | \(-0.0545759\pi\) | ||||
0.985338 | + | 0.170616i | \(0.0545759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.72710 | 0.452774 | 0.226387 | − | 0.974037i | \(-0.427309\pi\) | ||||
0.226387 | + | 0.974037i | \(0.427309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.67456 | 0.725177 | ||||||||
\(113\) | −7.98316 | −0.750993 | −0.375496 | − | 0.926824i | \(-0.622528\pi\) | ||||
−0.375496 | + | 0.926824i | \(0.622528\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −20.0900 | −1.86531 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.5471 | −1.06299 | ||||||||
\(119\) | −24.0831 | −2.20770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.77938 | −0.889034 | ||||||||
\(122\) | −8.73091 | −0.790460 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.0337 | 1.52967 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.63503 | −0.411293 | −0.205646 | − | 0.978626i | \(-0.565930\pi\) | ||||
−0.205646 | + | 0.978626i | \(0.565930\pi\) | |||||||
\(128\) | 9.67265 | 0.854950 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5134 | −1.35541 | −0.677705 | − | 0.735334i | \(-0.737025\pi\) | ||||
−0.677705 | + | 0.735334i | \(0.737025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.10482 | −0.269222 | ||||||||
\(134\) | −33.8828 | −2.92703 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.80515 | −0.840785 | ||||||||
\(137\) | −0.813048 | −0.0694634 | −0.0347317 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347317 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7687 | −1.08302 | −0.541512 | − | 0.840693i | \(-0.682148\pi\) | ||||
−0.541512 | + | 0.840693i | \(0.682148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.3106 | 1.28484 | ||||||||
\(143\) | −1.95942 | −0.163855 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.521277 | 0.0431412 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.64293 | 0.299447 | ||||||||
\(149\) | 13.7982 | 1.13040 | 0.565198 | − | 0.824955i | \(-0.308800\pi\) | ||||
0.565198 | + | 0.824955i | \(0.308800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.02269 | 0.408740 | 0.204370 | − | 0.978894i | \(-0.434485\pi\) | ||||
0.204370 | + | 0.978894i | \(0.434485\pi\) | |||||||
\(152\) | −1.26409 | −0.102531 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.34911 | 0.592208 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.18695 | −0.573581 | −0.286791 | − | 0.957993i | \(-0.592588\pi\) | ||||
−0.286791 | + | 0.957993i | \(0.592588\pi\) | |||||||
\(158\) | 20.1168 | 1.60041 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.6529 | 1.62767 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.25528 | −0.568277 | −0.284139 | − | 0.958783i | \(-0.591708\pi\) | ||||
−0.284139 | + | 0.958783i | \(0.591708\pi\) | |||||||
\(164\) | −7.30374 | −0.570326 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.9852 | −1.47354 | ||||||||
\(167\) | −7.33129 | −0.567312 | −0.283656 | − | 0.958926i | \(-0.591547\pi\) | ||||
−0.283656 | + | 0.958926i | \(0.591547\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.85461 | −0.758047 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.04156 | −0.613163 | ||||||||
\(173\) | −5.77353 | −0.438953 | −0.219477 | − | 0.975618i | \(-0.570435\pi\) | ||||
−0.219477 | + | 0.975618i | \(0.570435\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.73091 | −0.205850 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.74190 | 0.130561 | ||||||||
\(179\) | 4.48379 | 0.335134 | 0.167567 | − | 0.985861i | \(-0.446409\pi\) | ||||
0.167567 | + | 0.985861i | \(0.446409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.73400 | −0.203217 | −0.101608 | − | 0.994824i | \(-0.532399\pi\) | ||||
−0.101608 | + | 0.994824i | \(0.532399\pi\) | |||||||
\(182\) | −11.7973 | −0.874471 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.40856 | 0.619887 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.56974 | 0.626681 | ||||||||
\(188\) | 3.79418 | 0.276719 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.7230 | 1.28239 | 0.641196 | − | 0.767377i | \(-0.278438\pi\) | ||||
0.641196 | + | 0.767377i | \(0.278438\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.5371 | 0.974423 | 0.487212 | − | 0.873284i | \(-0.338014\pi\) | ||||
0.487212 | + | 0.873284i | \(0.338014\pi\) | |||||||
\(194\) | 6.84912 | 0.491738 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.83741 | 0.488386 | ||||||||
\(197\) | −21.5134 | −1.53276 | −0.766382 | − | 0.642385i | \(-0.777945\pi\) | ||||
−0.766382 | + | 0.642385i | \(0.777945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.09410 | 0.502888 | 0.251444 | − | 0.967872i | \(-0.419095\pi\) | ||||
0.251444 | + | 0.967872i | \(0.419095\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.46774 | −0.455068 | ||||||||
\(203\) | 24.0831 | 1.69030 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.9797 | 0.904339 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.38384 | 0.303964 | ||||||||
\(209\) | 1.10482 | 0.0764219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0604 | 0.761431 | 0.380716 | − | 0.924692i | \(-0.375678\pi\) | ||||
0.380716 | + | 0.924692i | \(0.375678\pi\) | |||||||
\(212\) | −6.71717 | −0.461337 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −43.6731 | −2.98543 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.4193 | −1.38615 | ||||||||
\(218\) | −10.1275 | −0.685921 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.7567 | −0.925375 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6350 | 0.846104 | 0.423052 | − | 0.906105i | \(-0.360959\pi\) | ||||
0.423052 | + | 0.906105i | \(0.360959\pi\) | |||||||
\(224\) | −24.2918 | −1.62306 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.1034 | 1.13770 | ||||||||
\(227\) | −6.62813 | −0.439925 | −0.219962 | − | 0.975508i | \(-0.570593\pi\) | ||||
−0.219962 | + | 0.975508i | \(0.570593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0752308 | −0.00497139 | −0.00248570 | − | 0.999997i | \(-0.500791\pi\) | ||||
−0.00248570 | + | 0.999997i | \(0.500791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.80515 | 0.643740 | ||||||||
\(233\) | 9.51338 | 0.623242 | 0.311621 | − | 0.950206i | \(-0.399128\pi\) | ||||
0.311621 | + | 0.950206i | \(0.399128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.9594 | 0.908681 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 51.5965 | 3.34450 | ||||||||
\(239\) | 2.92984 | 0.189515 | 0.0947577 | − | 0.995500i | \(-0.469792\pi\) | ||||
0.0947577 | + | 0.995500i | \(0.469792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.42743 | −0.607274 | −0.303637 | − | 0.952788i | \(-0.598201\pi\) | ||||
−0.303637 | + | 0.952788i | \(0.598201\pi\) | |||||||
\(242\) | 20.9517 | 1.34682 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.5549 | 0.675711 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.77353 | −0.112847 | ||||||||
\(248\) | −8.31346 | −0.527905 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.9298 | 0.942363 | 0.471181 | − | 0.882036i | \(-0.343828\pi\) | ||||
0.471181 | + | 0.882036i | \(0.343828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.34911 | −0.462035 | ||||||||
\(254\) | 9.93026 | 0.623080 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.91405 | 0.182128 | ||||||||
\(257\) | −15.1295 | −0.943755 | −0.471877 | − | 0.881664i | \(-0.656424\pi\) | ||||
−0.471877 | + | 0.881664i | \(0.656424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.36700 | −0.271352 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 33.2364 | 2.05335 | ||||||||
\(263\) | −15.2216 | −0.938605 | −0.469302 | − | 0.883038i | \(-0.655495\pi\) | ||||
−0.469302 | + | 0.883038i | \(0.655495\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.65187 | 0.407852 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 40.9615 | 2.50212 | ||||||||
\(269\) | −11.5203 | −0.702404 | −0.351202 | − | 0.936300i | \(-0.614227\pi\) | ||||
−0.351202 | + | 0.936300i | \(0.614227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.16118 | 0.131282 | 0.0656411 | − | 0.997843i | \(-0.479091\pi\) | ||||
0.0656411 | + | 0.997843i | \(0.479091\pi\) | |||||||
\(272\) | −19.1731 | −1.16254 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.74190 | 0.105232 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.4205 | −1.40720 | −0.703602 | − | 0.710595i | \(-0.748426\pi\) | ||||
−0.703602 | + | 0.710595i | \(0.748426\pi\) | |||||||
\(278\) | 27.3560 | 1.64070 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.6824 | −1.53209 | −0.766043 | − | 0.642789i | \(-0.777777\pi\) | ||||
−0.766043 | + | 0.642789i | \(0.777777\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.38587 | −0.439045 | −0.219522 | − | 0.975607i | \(-0.570450\pi\) | ||||
−0.219522 | + | 0.975607i | \(0.570450\pi\) | |||||||
\(284\) | −18.5093 | −1.09832 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.19794 | 0.248229 | ||||||||
\(287\) | 8.75543 | 0.516817 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.1662 | 2.53919 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.630180 | −0.0368785 | ||||||||
\(293\) | −24.1522 | −1.41099 | −0.705494 | − | 0.708716i | \(-0.749275\pi\) | ||||
−0.705494 | + | 0.708716i | \(0.749275\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.77797 | −0.103343 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −29.5618 | −1.71247 | ||||||||
\(299\) | 11.7973 | 0.682253 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.63990 | 0.555635 | ||||||||
\(302\) | −10.7608 | −0.619213 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.47182 | −0.141769 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.38482 | −0.250255 | −0.125127 | − | 0.992141i | \(-0.539934\pi\) | ||||
−0.125127 | + | 0.992141i | \(0.539934\pi\) | |||||||
\(308\) | −8.88447 | −0.506239 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7123 | 0.890963 | 0.445481 | − | 0.895291i | \(-0.353033\pi\) | ||||
0.445481 | + | 0.895291i | \(0.353033\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.7794 | −1.40061 | −0.700307 | − | 0.713842i | \(-0.746953\pi\) | ||||
−0.700307 | + | 0.713842i | \(0.746953\pi\) | |||||||
\(314\) | 15.3976 | 0.868935 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.3195 | −1.36808 | ||||||||
\(317\) | −27.3798 | −1.53780 | −0.768900 | − | 0.639369i | \(-0.779196\pi\) | ||||
−0.768900 | + | 0.639369i | \(0.779196\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.56974 | −0.479813 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −44.2474 | −2.46581 | ||||||||
\(323\) | 7.75669 | 0.431594 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.5440 | 0.860900 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.56467 | 0.196826 | ||||||||
\(329\) | −4.54831 | −0.250756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.70033 | 0.258354 | 0.129177 | − | 0.991622i | \(-0.458767\pi\) | ||||
0.129177 | + | 0.991622i | \(0.458767\pi\) | |||||||
\(332\) | 22.9515 | 1.25963 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.7068 | 0.859439 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6360 | 1.12412 | 0.562058 | − | 0.827098i | \(-0.310010\pi\) | ||||
0.562058 | + | 0.827098i | \(0.310010\pi\) | |||||||
\(338\) | 21.1128 | 1.14839 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.26600 | 0.393476 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5373 | 0.730947 | ||||||||
\(344\) | 3.92477 | 0.211609 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.3694 | 0.664983 | ||||||||
\(347\) | 30.0148 | 1.61128 | 0.805639 | − | 0.592407i | \(-0.201822\pi\) | ||||
0.805639 | + | 0.592407i | \(0.201822\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.7340 | −0.788693 | −0.394347 | − | 0.918962i | \(-0.629029\pi\) | ||||
−0.394347 | + | 0.918962i | \(0.629029\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.64399 | 0.460726 | ||||||||
\(353\) | −29.6302 | −1.57705 | −0.788527 | − | 0.615000i | \(-0.789156\pi\) | ||||
−0.788527 | + | 0.615000i | \(0.789156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.10581 | −0.111608 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.60623 | −0.507705 | ||||||||
\(359\) | −21.7577 | −1.14833 | −0.574163 | − | 0.818741i | \(-0.694672\pi\) | ||||
−0.574163 | + | 0.818741i | \(0.694672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 5.85742 | 0.307859 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.2619 | 0.747527 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.0347 | −1.56780 | −0.783898 | − | 0.620889i | \(-0.786772\pi\) | ||||
−0.783898 | + | 0.620889i | \(0.786772\pi\) | |||||||
\(368\) | 16.4422 | 0.857111 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.05227 | 0.418053 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.3055 | 1.93161 | 0.965803 | − | 0.259277i | \(-0.0834843\pi\) | ||||
0.965803 | + | 0.259277i | \(0.0834843\pi\) | |||||||
\(374\) | −18.3601 | −0.949378 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.85179 | −0.0954987 | ||||||||
\(377\) | 13.7567 | 0.708506 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.7794 | −0.759166 | −0.379583 | − | 0.925158i | \(-0.623932\pi\) | ||||
−0.379583 | + | 0.925158i | \(0.623932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −37.9704 | −1.94273 | ||||||||
\(383\) | −29.0020 | −1.48193 | −0.740967 | − | 0.671541i | \(-0.765633\pi\) | ||||
−0.740967 | + | 0.671541i | \(0.765633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −29.0024 | −1.47618 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.28001 | −0.420354 | ||||||||
\(389\) | −21.1987 | −1.07481 | −0.537407 | − | 0.843323i | \(-0.680596\pi\) | ||||
−0.537407 | + | 0.843323i | \(0.680596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.5965 | −2.60935 | ||||||||
\(392\) | −3.33707 | −0.168548 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 46.0910 | 2.32203 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3856 | −0.521238 | −0.260619 | − | 0.965442i | \(-0.583927\pi\) | ||||
−0.260619 | + | 0.965442i | \(0.583927\pi\) | |||||||
\(398\) | −15.1987 | −0.761840 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.6638 | −1.28159 | −0.640796 | − | 0.767712i | \(-0.721395\pi\) | ||||
−0.640796 | + | 0.767712i | \(0.721395\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.6638 | −0.581017 | ||||||||
\(404\) | 7.81896 | 0.389008 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −51.5965 | −2.56069 | ||||||||
\(407\) | 1.55395 | 0.0770266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.71611 | 0.282644 | 0.141322 | − | 0.989964i | \(-0.454865\pi\) | ||||
0.141322 | + | 0.989964i | \(0.454865\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.6914 | −0.773059 | ||||||||
\(413\) | −16.7340 | −0.823427 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −13.8759 | −0.680321 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.36700 | −0.115774 | ||||||||
\(419\) | −15.4303 | −0.753818 | −0.376909 | − | 0.926250i | \(-0.623013\pi\) | ||||
−0.376909 | + | 0.926250i | \(0.623013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.18005 | −0.0575121 | −0.0287561 | − | 0.999586i | \(-0.509155\pi\) | ||||
−0.0287561 | + | 0.999586i | \(0.509155\pi\) | |||||||
\(422\) | −23.6962 | −1.15352 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.27839 | 0.159213 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.6529 | −0.612315 | ||||||||
\(428\) | 52.7972 | 2.55205 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0255 | 0.675585 | 0.337792 | − | 0.941221i | \(-0.390320\pi\) | ||||
0.337792 | + | 0.941221i | \(0.390320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.5894 | −1.22975 | −0.614874 | − | 0.788625i | \(-0.710793\pi\) | ||||
−0.614874 | + | 0.788625i | \(0.710793\pi\) | |||||||
\(434\) | 43.7470 | 2.09992 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.2433 | 0.586348 | ||||||||
\(437\) | −6.65187 | −0.318202 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.9732 | −1.04873 | −0.524363 | − | 0.851495i | \(-0.675696\pi\) | ||||
−0.524363 | + | 0.851495i | \(0.675696\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 29.4728 | 1.40188 | ||||||||
\(443\) | −19.3721 | −0.920395 | −0.460197 | − | 0.887817i | \(-0.652221\pi\) | ||||
−0.460197 | + | 0.887817i | \(0.652221\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −27.0697 | −1.28179 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 36.6944 | 1.73365 | ||||||||
\(449\) | 19.1841 | 0.905355 | 0.452677 | − | 0.891674i | \(-0.350469\pi\) | ||||
0.452677 | + | 0.891674i | \(0.350469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.11553 | −0.146705 | ||||||||
\(452\) | −20.6766 | −0.972545 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.2003 | 0.666455 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.36010 | −0.391069 | −0.195534 | − | 0.980697i | \(-0.562644\pi\) | ||||
−0.195534 | + | 0.980697i | \(0.562644\pi\) | |||||||
\(458\) | 0.161177 | 0.00753131 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.0268 | 1.16561 | 0.582806 | − | 0.812611i | \(-0.301955\pi\) | ||||
0.582806 | + | 0.812611i | \(0.301955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.3749 | −1.50459 | −0.752294 | − | 0.658827i | \(-0.771053\pi\) | ||||
−0.752294 | + | 0.658827i | \(0.771053\pi\) | |||||||
\(464\) | 19.1731 | 0.890091 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.3818 | −0.944168 | ||||||||
\(467\) | 15.2216 | 0.704372 | 0.352186 | − | 0.935930i | \(-0.385438\pi\) | ||||
0.352186 | + | 0.935930i | \(0.385438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −49.1030 | −2.26736 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.81305 | −0.313596 | ||||||||
\(473\) | −3.43026 | −0.157724 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −62.3759 | −2.85899 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.27698 | −0.287103 | ||||||||
\(479\) | 20.0485 | 0.916038 | 0.458019 | − | 0.888943i | \(-0.348559\pi\) | ||||
0.458019 | + | 0.888943i | \(0.348559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.49451 | −0.113740 | ||||||||
\(482\) | 20.1977 | 0.919978 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.3288 | −1.15131 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6508 | 1.43424 | 0.717118 | − | 0.696952i | \(-0.245461\pi\) | ||||
0.717118 | + | 0.696952i | \(0.245461\pi\) | |||||||
\(488\) | −5.15146 | −0.233195 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.8033 | −1.11936 | −0.559679 | − | 0.828710i | \(-0.689076\pi\) | ||||
−0.559679 | + | 0.828710i | \(0.689076\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.1662 | −2.70975 | ||||||||
\(494\) | 3.79966 | 0.170955 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.2563 | −0.729928 | ||||||||
\(497\) | 22.1882 | 0.995277 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.0237 | −1.47834 | −0.739171 | − | 0.673518i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673518i | \(0.764783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −31.9862 | −1.42761 | ||||||||
\(503\) | −3.54396 | −0.158017 | −0.0790087 | − | 0.996874i | \(-0.525175\pi\) | ||||
−0.0790087 | + | 0.996874i | \(0.525175\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.7450 | 0.699950 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.0049 | −0.532629 | ||||||||
\(509\) | 2.11679 | 0.0938250 | 0.0469125 | − | 0.998899i | \(-0.485062\pi\) | ||||
0.0469125 | + | 0.998899i | \(0.485062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.755435 | 0.0334185 | ||||||||
\(512\) | −25.5885 | −1.13086 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.4140 | 1.42972 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.61847 | 0.0711802 | ||||||||
\(518\) | 9.35601 | 0.411080 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.60748 | 0.377101 | 0.188550 | − | 0.982064i | \(-0.439621\pi\) | ||||
0.188550 | + | 0.982064i | \(0.439621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.8349 | −1.61068 | −0.805340 | − | 0.592814i | \(-0.798017\pi\) | ||||
−0.805340 | + | 0.592814i | \(0.798017\pi\) | |||||||
\(524\) | −40.1800 | −1.75527 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.6113 | 1.42192 | ||||||||
\(527\) | 51.0130 | 2.22216 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2474 | 0.923799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.04156 | −0.348646 | ||||||||
\(533\) | 5.00125 | 0.216628 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.9917 | −0.863509 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.6814 | 1.06409 | ||||||||
\(539\) | 2.91661 | 0.125627 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0079 | −1.37613 | −0.688063 | − | 0.725651i | \(-0.741539\pi\) | ||||
−0.688063 | + | 0.725651i | \(0.741539\pi\) | |||||||
\(542\) | −4.63018 | −0.198883 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 60.6875 | 2.60196 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6240 | −0.753550 | −0.376775 | − | 0.926305i | \(-0.622967\pi\) | ||||
−0.376775 | + | 0.926305i | \(0.622967\pi\) | |||||||
\(548\) | −2.10581 | −0.0899559 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.75669 | −0.330446 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.1533 | 1.23972 | ||||||||
\(554\) | 50.1769 | 2.13181 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −33.0711 | −1.40253 | ||||||||
\(557\) | −34.6865 | −1.46972 | −0.734858 | − | 0.678221i | \(-0.762751\pi\) | ||||
−0.734858 | + | 0.678221i | \(0.762751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.50648 | 0.232899 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 55.0229 | 2.32100 | ||||||||
\(563\) | 13.5073 | 0.569263 | 0.284632 | − | 0.958637i | \(-0.408129\pi\) | ||||
0.284632 | + | 0.958637i | \(0.408129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.8238 | 0.665122 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.03366 | 0.379044 | ||||||||
\(569\) | −32.3588 | −1.35655 | −0.678276 | − | 0.734807i | \(-0.737273\pi\) | ||||
−0.678276 | + | 0.734807i | \(0.737273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.93293 | −0.373831 | −0.186916 | − | 0.982376i | \(-0.559849\pi\) | ||||
−0.186916 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(572\) | −5.07496 | −0.212195 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.7579 | −0.782941 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.9059 | −0.620541 | −0.310270 | − | 0.950648i | \(-0.600420\pi\) | ||||
−0.310270 | + | 0.950648i | \(0.600420\pi\) | |||||||
\(578\) | −92.4808 | −3.84669 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.5134 | −1.14145 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.86532 | −0.118669 | ||||||||
\(584\) | 0.307566 | 0.0127272 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 51.7446 | 2.13755 | ||||||||
\(587\) | 7.37207 | 0.304278 | 0.152139 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152139 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.57664 | 0.270986 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.47668 | −0.142890 | ||||||||
\(593\) | −17.6853 | −0.726247 | −0.363124 | − | 0.931741i | \(-0.618290\pi\) | ||||
−0.363124 | + | 0.931741i | \(0.618290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 35.7378 | 1.46388 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −25.2749 | −1.03357 | ||||||||
\(599\) | −5.30657 | −0.216821 | −0.108410 | − | 0.994106i | \(-0.534576\pi\) | ||||
−0.108410 | + | 0.994106i | \(0.534576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.7875 | 1.78613 | 0.893065 | − | 0.449927i | \(-0.148550\pi\) | ||||
0.893065 | + | 0.449927i | \(0.148550\pi\) | |||||||
\(602\) | −20.6529 | −0.841747 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.0089 | 0.529324 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.24535 | 0.294080 | 0.147040 | − | 0.989131i | \(-0.453025\pi\) | ||||
0.147040 | + | 0.989131i | \(0.453025\pi\) | |||||||
\(608\) | 7.82389 | 0.317301 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.59807 | −0.105107 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.8962 | −0.843988 | −0.421994 | − | 0.906599i | \(-0.638670\pi\) | ||||
−0.421994 | + | 0.906599i | \(0.638670\pi\) | |||||||
\(614\) | 9.39419 | 0.379119 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.33616 | 0.174709 | ||||||||
\(617\) | −22.0494 | −0.887677 | −0.443839 | − | 0.896107i | \(-0.646384\pi\) | ||||
−0.443839 | + | 0.896107i | \(0.646384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0484607 | −0.00194780 | −0.000973900 | − | 1.00000i | \(-0.500310\pi\) | ||||
−0.000973900 | 1.00000i | \(0.500310\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −33.6626 | −1.34975 | ||||||||
\(623\) | 2.52437 | 0.101137 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 53.0882 | 2.12183 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.6144 | −0.742795 | ||||||||
\(629\) | 10.9100 | 0.435009 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.6182 | −1.29851 | −0.649255 | − | 0.760571i | \(-0.724919\pi\) | ||||
−0.649255 | + | 0.760571i | \(0.724919\pi\) | |||||||
\(632\) | 11.8694 | 0.472140 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 58.6593 | 2.32966 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.68193 | −0.185505 | ||||||||
\(638\) | 18.3601 | 0.726883 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.4136 | 0.529806 | 0.264903 | − | 0.964275i | \(-0.414660\pi\) | ||||
0.264903 | + | 0.964275i | \(0.414660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.8052 | −0.938783 | −0.469392 | − | 0.882990i | \(-0.655527\pi\) | ||||
−0.469392 | + | 0.882990i | \(0.655527\pi\) | |||||||
\(644\) | 53.4914 | 2.10786 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.6182 | −0.653834 | ||||||||
\(647\) | −48.4580 | −1.90508 | −0.952540 | − | 0.304412i | \(-0.901540\pi\) | ||||
−0.952540 | + | 0.304412i | \(0.901540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.95463 | 0.233740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.7914 | −0.735926 | ||||||||
\(653\) | 22.2351 | 0.870128 | 0.435064 | − | 0.900399i | \(-0.356726\pi\) | ||||
0.435064 | + | 0.900399i | \(0.356726\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.97041 | 0.272149 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.74445 | 0.379878 | ||||||||
\(659\) | 10.7072 | 0.417095 | 0.208547 | − | 0.978012i | \(-0.433126\pi\) | ||||
0.208547 | + | 0.978012i | \(0.433126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.7980 | −1.74244 | −0.871220 | − | 0.490893i | \(-0.836670\pi\) | ||||
−0.871220 | + | 0.490893i | \(0.836670\pi\) | |||||||
\(662\) | −10.0702 | −0.391388 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.2017 | −0.434712 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.5965 | 1.99782 | ||||||||
\(668\) | −18.9882 | −0.734677 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.50239 | 0.173813 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.2772 | 1.66821 | 0.834106 | − | 0.551604i | \(-0.185984\pi\) | ||||
0.834106 | + | 0.551604i | \(0.185984\pi\) | |||||||
\(674\) | −44.2113 | −1.70296 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.5237 | −0.981680 | ||||||||
\(677\) | 11.5330 | 0.443251 | 0.221625 | − | 0.975132i | \(-0.428864\pi\) | ||||
0.221625 | + | 0.975132i | \(0.428864\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.92575 | 0.380915 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.5669 | −0.596088 | ||||||||
\(683\) | 0.916090 | 0.0350532 | 0.0175266 | − | 0.999846i | \(-0.494421\pi\) | ||||
0.0175266 | + | 0.999846i | \(0.494421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −29.0028 | −1.10733 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.67456 | 0.292590 | ||||||||
\(689\) | 4.59960 | 0.175231 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8278 | 0.564077 | 0.282039 | − | 0.959403i | \(-0.408989\pi\) | ||||
0.282039 | + | 0.959403i | \(0.408989\pi\) | |||||||
\(692\) | −14.9536 | −0.568450 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −64.3047 | −2.44097 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.8735 | −0.828517 | ||||||||
\(698\) | 31.5666 | 1.19481 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.1722 | −1.36620 | −0.683102 | − | 0.730323i | \(-0.739369\pi\) | ||||
−0.683102 | + | 0.730323i | \(0.739369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.40652 | 0.0530481 | ||||||||
\(704\) | −13.0573 | −0.492117 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 63.4807 | 2.38913 | ||||||||
\(707\) | −9.37305 | −0.352510 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.4331 | 0.391823 | 0.195911 | − | 0.980622i | \(-0.437234\pi\) | ||||
0.195911 | + | 0.980622i | \(0.437234\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.02777 | 0.0385171 | ||||||||
\(713\) | −43.7470 | −1.63834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.6131 | 0.434003 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 46.6144 | 1.73963 | ||||||||
\(719\) | −7.73373 | −0.288420 | −0.144210 | − | 0.989547i | \(-0.546064\pi\) | ||||
−0.144210 | + | 0.989547i | \(0.546064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8102 | 0.700529 | ||||||||
\(722\) | −2.14243 | −0.0797331 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.08114 | −0.263168 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.5241 | 1.46587 | 0.732934 | − | 0.680300i | \(-0.238151\pi\) | ||||
0.732934 | + | 0.680300i | \(0.238151\pi\) | |||||||
\(728\) | −6.96068 | −0.257980 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.0831 | −0.890746 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.7498 | −1.87449 | −0.937243 | − | 0.348677i | \(-0.886631\pi\) | ||||
−0.937243 | + | 0.348677i | \(0.886631\pi\) | |||||||
\(734\) | 64.3473 | 2.37510 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −52.0435 | −1.91835 | ||||||||
\(737\) | 17.4728 | 0.643619 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.419276 | 0.0154233 | 0.00771165 | − | 0.999970i | \(-0.497545\pi\) | ||||
0.00771165 | + | 0.999970i | \(0.497545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.2515 | −0.633321 | ||||||||
\(743\) | 19.5511 | 0.717259 | 0.358630 | − | 0.933480i | \(-0.383244\pi\) | ||||
0.358630 | + | 0.933480i | \(0.383244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −79.9246 | −2.92625 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22.1958 | 0.811560 | ||||||||
\(749\) | −63.2912 | −2.31261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.76768 | 0.319937 | 0.159969 | − | 0.987122i | \(-0.448861\pi\) | ||||
0.159969 | + | 0.987122i | \(0.448861\pi\) | |||||||
\(752\) | −3.62102 | −0.132045 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −29.4728 | −1.07334 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0535 | 1.74653 | 0.873267 | − | 0.487241i | \(-0.161997\pi\) | ||||
0.873267 | + | 0.487241i | \(0.161997\pi\) | |||||||
\(758\) | 31.6638 | 1.15008 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.3947 | −1.06556 | −0.532779 | − | 0.846254i | \(-0.678852\pi\) | ||||
−0.532779 | + | 0.846254i | \(0.678852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.6768 | −0.531336 | ||||||||
\(764\) | 45.9031 | 1.66071 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 62.1350 | 2.24503 | ||||||||
\(767\) | −9.55875 | −0.345146 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3790 | −0.482458 | −0.241229 | − | 0.970468i | \(-0.577551\pi\) | ||||
−0.241229 | + | 0.970468i | \(0.577551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 35.0615 | 1.26189 | ||||||||
\(773\) | 0.133625 | 0.00480617 | 0.00240309 | − | 0.999997i | \(-0.499235\pi\) | ||||
0.00240309 | + | 0.999997i | \(0.499235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.04115 | 0.145069 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 45.4167 | 1.62827 | ||||||||
\(779\) | −2.81995 | −0.101035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.89545 | −0.282522 | ||||||||
\(782\) | 110.542 | 3.95298 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.52536 | −0.233049 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.84060 | 0.172549 | 0.0862744 | − | 0.996271i | \(-0.472504\pi\) | ||||
0.0862744 | + | 0.996271i | \(0.472504\pi\) | |||||||
\(788\) | −55.7202 | −1.98495 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.7863 | 0.881299 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.22753 | −0.256657 | ||||||||
\(794\) | 22.2505 | 0.789640 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.3739 | 0.651246 | ||||||||
\(797\) | 11.6993 | 0.414410 | 0.207205 | − | 0.978298i | \(-0.433563\pi\) | ||||
0.207205 | + | 0.978298i | \(0.433563\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.3629 | 0.401991 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 54.9831 | 1.94152 | ||||||||
\(803\) | −0.268814 | −0.00948624 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.9890 | 0.880200 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.81613 | −0.134251 | ||||||||
\(809\) | 33.1987 | 1.16720 | 0.583601 | − | 0.812040i | \(-0.301643\pi\) | ||||
0.583601 | + | 0.812040i | \(0.301643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.5766 | −0.933232 | −0.466616 | − | 0.884460i | \(-0.654527\pi\) | ||||
−0.466616 | + | 0.884460i | \(0.654527\pi\) | |||||||
\(812\) | 62.3759 | 2.18896 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.32924 | −0.116690 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.10482 | −0.108624 | ||||||||
\(818\) | −12.2464 | −0.428185 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.5807 | −0.892773 | −0.446387 | − | 0.894840i | \(-0.647289\pi\) | ||||
−0.446387 | + | 0.894840i | \(0.647289\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.9783 | −0.452395 | −0.226198 | − | 0.974081i | \(-0.572629\pi\) | ||||
−0.226198 | + | 0.974081i | \(0.572629\pi\) | |||||||
\(824\) | 7.65835 | 0.266791 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 35.8515 | 1.24743 | ||||||||
\(827\) | −12.5167 | −0.435248 | −0.217624 | − | 0.976033i | \(-0.569831\pi\) | ||||
−0.217624 | + | 0.976033i | \(0.569831\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.4391 | −0.675149 | −0.337574 | − | 0.941299i | \(-0.609606\pi\) | ||||
−0.337574 | + | 0.941299i | \(0.609606\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.9605 | 0.726674 | ||||||||
\(833\) | 20.4769 | 0.709482 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.86151 | 0.0989673 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.0583 | 1.14198 | ||||||||
\(839\) | 43.9972 | 1.51895 | 0.759475 | − | 0.650536i | \(-0.225456\pi\) | ||||
0.759475 | + | 0.650536i | \(0.225456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.1662 | 1.07470 | ||||||||
\(842\) | 2.52818 | 0.0871268 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.6468 | 0.986063 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.3632 | 1.04329 | ||||||||
\(848\) | 6.41061 | 0.220141 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.35601 | −0.320720 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.30374 | −0.113118 | −0.0565590 | − | 0.998399i | \(-0.518013\pi\) | ||||
−0.0565590 | + | 0.998399i | \(0.518013\pi\) | |||||||
\(854\) | 27.1079 | 0.927614 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.7682 | −0.880740 | ||||||||
\(857\) | 6.02374 | 0.205767 | 0.102883 | − | 0.994693i | \(-0.467193\pi\) | ||||
0.102883 | + | 0.994693i | \(0.467193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.0158 | −1.22884 | −0.614421 | − | 0.788978i | \(-0.710610\pi\) | ||||
−0.614421 | + | 0.788978i | \(0.710610\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.0487 | −1.02346 | ||||||||
\(863\) | 29.9250 | 1.01866 | 0.509329 | − | 0.860572i | \(-0.329894\pi\) | ||||
0.509329 | + | 0.860572i | \(0.329894\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 54.8236 | 1.86298 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −52.8864 | −1.79508 | ||||||||
\(869\) | −10.3739 | −0.351911 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.0485 | −0.950386 | ||||||||
\(872\) | −5.97548 | −0.202355 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.2512 | 0.482054 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.618980 | −0.0209015 | −0.0104507 | − | 0.999945i | \(-0.503327\pi\) | ||||
−0.0104507 | + | 0.999945i | \(0.503327\pi\) | |||||||
\(878\) | 47.0762 | 1.58874 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.2423 | 0.715672 | 0.357836 | − | 0.933784i | \(-0.383515\pi\) | ||||
0.357836 | + | 0.933784i | \(0.383515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.8971 | 1.64552 | 0.822760 | − | 0.568389i | \(-0.192433\pi\) | ||||
0.822760 | + | 0.568389i | \(0.192433\pi\) | |||||||
\(884\) | −35.6302 | −1.19837 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 41.5034 | 1.39433 | ||||||||
\(887\) | 58.2797 | 1.95684 | 0.978421 | − | 0.206622i | \(-0.0662469\pi\) | ||||
0.978421 | + | 0.206622i | \(0.0662469\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3909 | 0.482657 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 32.7251 | 1.09572 | ||||||||
\(893\) | 1.46492 | 0.0490216 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −30.0318 | −1.00329 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41.1007 | −1.37155 | ||||||||
\(899\) | −51.0130 | −1.70138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.1168 | −0.670187 | ||||||||
\(902\) | 6.67483 | 0.222247 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.0914 | 0.335636 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.5154 | 1.21247 | 0.606237 | − | 0.795284i | \(-0.292678\pi\) | ||||
0.606237 | + | 0.795284i | \(0.292678\pi\) | |||||||
\(908\) | −17.1670 | −0.569708 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.62735 | −0.219574 | −0.109787 | − | 0.993955i | \(-0.535017\pi\) | ||||
−0.109787 | + | 0.993955i | \(0.535017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.79036 | 0.324014 | ||||||||
\(914\) | 17.9110 | 0.592442 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.194850 | −0.00643802 | ||||||||
\(917\) | 48.1662 | 1.59059 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.91688 | 0.261154 | 0.130577 | − | 0.991438i | \(-0.458317\pi\) | ||||
0.130577 | + | 0.991438i | \(0.458317\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −53.6182 | −1.76582 | ||||||||
\(923\) | 12.6743 | 0.417179 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 69.3611 | 2.27935 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −60.6875 | −1.99217 | ||||||||
\(929\) | −35.8597 | −1.17652 | −0.588259 | − | 0.808673i | \(-0.700186\pi\) | ||||
−0.588259 | + | 0.808673i | \(0.700186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.63990 | 0.0865192 | ||||||||
\(932\) | 24.6399 | 0.807106 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.6113 | −1.06707 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.4420 | 0.373793 | 0.186896 | − | 0.982380i | \(-0.440157\pi\) | ||||
0.186896 | + | 0.982380i | \(0.440157\pi\) | |||||||
\(938\) | 105.200 | 3.43490 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.360100 | 0.0117389 | 0.00586945 | − | 0.999983i | \(-0.498132\pi\) | ||||
0.00586945 | + | 0.999983i | \(0.498132\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.7579 | 0.610843 | ||||||||
\(944\) | −13.3223 | −0.433605 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.34911 | 0.238940 | ||||||||
\(947\) | 2.63807 | 0.0857256 | 0.0428628 | − | 0.999081i | \(-0.486352\pi\) | ||||
0.0428628 | + | 0.999081i | \(0.486352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.431517 | 0.0140076 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 30.4432 | 0.986670 | ||||||||
\(953\) | 10.4430 | 0.338282 | 0.169141 | − | 0.985592i | \(-0.445901\pi\) | ||||
0.169141 | + | 0.985592i | \(0.445901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.58835 | 0.245425 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −42.9525 | −1.38773 | ||||||||
\(959\) | 2.52437 | 0.0815160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2522 | 0.395232 | ||||||||
\(962\) | 5.34432 | 0.172308 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24.4173 | −0.786428 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.2732 | −1.06999 | −0.534996 | − | 0.844854i | \(-0.679687\pi\) | ||||
−0.534996 | + | 0.844854i | \(0.679687\pi\) | |||||||
\(968\) | 12.3620 | 0.397330 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.5657 | −0.756258 | −0.378129 | − | 0.925753i | \(-0.623432\pi\) | ||||
−0.378129 | + | 0.925753i | \(0.623432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.6444 | 1.27094 | ||||||||
\(974\) | −67.8098 | −2.17277 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0732 | −0.322437 | ||||||||
\(977\) | 0.402439 | 0.0128752 | 0.00643759 | − | 0.999979i | \(-0.497951\pi\) | ||||
0.00643759 | + | 0.999979i | \(0.497951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.898271 | −0.0287089 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 53.1395 | 1.69575 | ||||||||
\(983\) | 11.4927 | 0.366561 | 0.183281 | − | 0.983061i | \(-0.441328\pi\) | ||||
0.183281 | + | 0.983061i | \(0.441328\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 128.902 | 4.10508 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.59348 | −0.146138 | ||||||||
\(989\) | 20.6529 | 0.656723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.05761 | 0.192426 | 0.0962132 | − | 0.995361i | \(-0.469327\pi\) | ||||
0.0962132 | + | 0.995361i | \(0.469327\pi\) | |||||||
\(992\) | 51.4549 | 1.63370 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −47.5368 | −1.50777 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.1086 | 1.52362 | 0.761808 | − | 0.647803i | \(-0.224312\pi\) | ||||
0.761808 | + | 0.647803i | \(0.224312\pi\) | |||||||
\(998\) | 70.7510 | 2.23959 | ||||||||
\(999\) | 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 | 4275.2.a.bo.1.2 | 4 | ||
3.2 | odd | 2 | 475.2.a.i.1.3 | 4 | |||
5.4 | even | 2 | 855.2.a.m.1.3 | 4 | |||
12.11 | even | 2 | 7600.2.a.cf.1.1 | 4 | |||
15.2 | even | 4 | 475.2.b.e.324.7 | 8 | |||
15.8 | even | 4 | 475.2.b.e.324.2 | 8 | |||
15.14 | odd | 2 | 95.2.a.b.1.2 | ✓ | 4 | ||
57.56 | even | 2 | 9025.2.a.bf.1.2 | 4 | |||
60.59 | even | 2 | 1520.2.a.t.1.4 | 4 | |||
105.104 | even | 2 | 4655.2.a.y.1.2 | 4 | |||
120.29 | odd | 2 | 6080.2.a.cc.1.4 | 4 | |||
120.59 | even | 2 | 6080.2.a.ch.1.1 | 4 | |||
285.284 | even | 2 | 1805.2.a.p.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.a.b.1.2 | ✓ | 4 | 15.14 | odd | 2 | ||
475.2.a.i.1.3 | 4 | 3.2 | odd | 2 | |||
475.2.b.e.324.2 | 8 | 15.8 | even | 4 | |||
475.2.b.e.324.7 | 8 | 15.2 | even | 4 | |||
855.2.a.m.1.3 | 4 | 5.4 | even | 2 | |||
1520.2.a.t.1.4 | 4 | 60.59 | even | 2 | |||
1805.2.a.p.1.3 | 4 | 285.284 | even | 2 | |||
4275.2.a.bo.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4655.2.a.y.1.2 | 4 | 105.104 | even | 2 | |||
6080.2.a.cc.1.4 | 4 | 120.29 | odd | 2 | |||
6080.2.a.ch.1.1 | 4 | 120.59 | even | 2 | |||
7600.2.a.cf.1.1 | 4 | 12.11 | even | 2 | |||
9025.2.a.bf.1.2 | 4 | 57.56 | even | 2 |