Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.88454\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88454 | −1.33257 | −0.666287 | − | 0.745696i | \(-0.732117\pi\) | ||||
−0.666287 | + | 0.745696i | \(0.732117\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.55150 | 0.775751 | ||||||||
\(5\) | −1.57704 | −0.705275 | −0.352638 | − | 0.935760i | \(-0.614715\pi\) | ||||
−0.352638 | + | 0.935760i | \(0.614715\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47195 | −0.934309 | −0.467154 | − | 0.884176i | \(-0.654721\pi\) | ||||
−0.467154 | + | 0.884176i | \(0.654721\pi\) | |||||||
\(8\) | 0.845212 | 0.298828 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.97201 | 0.939831 | ||||||||
\(11\) | 3.83501 | 1.15630 | 0.578149 | − | 0.815931i | \(-0.303775\pi\) | ||||
0.578149 | + | 0.815931i | \(0.303775\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.18691 | −0.883889 | −0.441945 | − | 0.897042i | \(-0.645711\pi\) | ||||
−0.441945 | + | 0.897042i | \(0.645711\pi\) | |||||||
\(14\) | 4.65849 | 1.24503 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.69584 | −1.17396 | ||||||||
\(17\) | 4.51018 | 1.09388 | 0.546939 | − | 0.837172i | \(-0.315793\pi\) | ||||
0.546939 | + | 0.837172i | \(0.315793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.54355 | 1.04236 | 0.521181 | − | 0.853446i | \(-0.325492\pi\) | ||||
0.521181 | + | 0.853446i | \(0.325492\pi\) | |||||||
\(20\) | −2.44679 | −0.547118 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.22723 | −1.54085 | ||||||||
\(23\) | −1.92415 | −0.401213 | −0.200607 | − | 0.979672i | \(-0.564291\pi\) | ||||
−0.200607 | + | 0.979672i | \(0.564291\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.51293 | −0.502587 | ||||||||
\(26\) | 6.00587 | 1.17785 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.83524 | −0.724791 | ||||||||
\(29\) | 0.0587099 | 0.0109022 | 0.00545108 | − | 0.999985i | \(-0.498265\pi\) | ||||
0.00545108 | + | 0.999985i | \(0.498265\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.58500 | −1.72152 | −0.860758 | − | 0.509014i | \(-0.830010\pi\) | ||||
−0.860758 | + | 0.509014i | \(0.830010\pi\) | |||||||
\(32\) | 7.15910 | 1.26556 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.49962 | −1.45767 | ||||||||
\(35\) | 3.89837 | 0.658945 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.789192 | 0.129742 | 0.0648712 | − | 0.997894i | \(-0.479336\pi\) | ||||
0.0648712 | + | 0.997894i | \(0.479336\pi\) | |||||||
\(38\) | −8.56252 | −1.38902 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.33294 | −0.210756 | ||||||||
\(41\) | 2.07589 | 0.324199 | 0.162100 | − | 0.986774i | \(-0.448173\pi\) | ||||
0.162100 | + | 0.986774i | \(0.448173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.55270 | 0.389283 | 0.194641 | − | 0.980874i | \(-0.437646\pi\) | ||||
0.194641 | + | 0.980874i | \(0.437646\pi\) | |||||||
\(44\) | 5.95002 | 0.897000 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.62615 | 0.534646 | ||||||||
\(47\) | −11.9701 | −1.74601 | −0.873007 | − | 0.487708i | \(-0.837833\pi\) | ||||
−0.873007 | + | 0.487708i | \(0.837833\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.889470 | −0.127067 | ||||||||
\(50\) | 4.73573 | 0.669734 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.94450 | −0.685678 | ||||||||
\(53\) | 0.844934 | 0.116061 | 0.0580303 | − | 0.998315i | \(-0.481518\pi\) | ||||
0.0580303 | + | 0.998315i | \(0.481518\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.04797 | −0.815508 | ||||||||
\(56\) | −2.08932 | −0.279197 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.110641 | −0.0145279 | ||||||||
\(59\) | 1.09245 | 0.142225 | 0.0711123 | − | 0.997468i | \(-0.477345\pi\) | ||||
0.0711123 | + | 0.997468i | \(0.477345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.97957 | 0.381494 | 0.190747 | − | 0.981639i | \(-0.438909\pi\) | ||||
0.190747 | + | 0.981639i | \(0.438909\pi\) | |||||||
\(62\) | 18.0633 | 2.29405 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.09994 | −0.512492 | ||||||||
\(65\) | 5.02589 | 0.623385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.93061 | 0.235862 | 0.117931 | − | 0.993022i | \(-0.462374\pi\) | ||||
0.117931 | + | 0.993022i | \(0.462374\pi\) | |||||||
\(68\) | 6.99755 | 0.848578 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.34665 | −0.878092 | ||||||||
\(71\) | 8.02351 | 0.952215 | 0.476107 | − | 0.879387i | \(-0.342047\pi\) | ||||
0.476107 | + | 0.879387i | \(0.342047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.42371 | −0.751839 | −0.375919 | − | 0.926652i | \(-0.622673\pi\) | ||||
−0.375919 | + | 0.926652i | \(0.622673\pi\) | |||||||
\(74\) | −1.48727 | −0.172891 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.04934 | 0.808614 | ||||||||
\(77\) | −9.47994 | −1.08034 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.18519 | 0.920906 | 0.460453 | − | 0.887684i | \(-0.347687\pi\) | ||||
0.460453 | + | 0.887684i | \(0.347687\pi\) | |||||||
\(80\) | 7.40555 | 0.827966 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.91210 | −0.432019 | ||||||||
\(83\) | 9.82889 | 1.07886 | 0.539431 | − | 0.842030i | \(-0.318640\pi\) | ||||
0.539431 | + | 0.842030i | \(0.318640\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.11274 | −0.771485 | ||||||||
\(86\) | −4.81067 | −0.518748 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.24139 | 0.345534 | ||||||||
\(89\) | −8.85934 | −0.939088 | −0.469544 | − | 0.882909i | \(-0.655582\pi\) | ||||
−0.469544 | + | 0.882909i | \(0.655582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.87787 | 0.825825 | ||||||||
\(92\) | −2.98533 | −0.311242 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 22.5581 | 2.32669 | ||||||||
\(95\) | −7.16538 | −0.735153 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4977 | 1.67508 | 0.837541 | − | 0.546374i | \(-0.183992\pi\) | ||||
0.837541 | + | 0.546374i | \(0.183992\pi\) | |||||||
\(98\) | 1.67625 | 0.169326 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.89882 | −0.389882 | ||||||||
\(101\) | 8.00022 | 0.796052 | 0.398026 | − | 0.917374i | \(-0.369695\pi\) | ||||
0.398026 | + | 0.917374i | \(0.369695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.66612 | −0.459766 | −0.229883 | − | 0.973218i | \(-0.573834\pi\) | ||||
−0.229883 | + | 0.973218i | \(0.573834\pi\) | |||||||
\(104\) | −2.69361 | −0.264130 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.59232 | −0.154659 | ||||||||
\(107\) | 1.59511 | 0.154205 | 0.0771023 | − | 0.997023i | \(-0.475433\pi\) | ||||
0.0771023 | + | 0.997023i | \(0.475433\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.67236 | 0.639096 | 0.319548 | − | 0.947570i | \(-0.396469\pi\) | ||||
0.319548 | + | 0.947570i | \(0.396469\pi\) | |||||||
\(110\) | 11.3977 | 1.08672 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.6079 | 1.09684 | ||||||||
\(113\) | −1.46613 | −0.137922 | −0.0689612 | − | 0.997619i | \(-0.521968\pi\) | ||||
−0.0689612 | + | 0.997619i | \(0.521968\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.03447 | 0.282966 | ||||||||
\(116\) | 0.0910886 | 0.00845736 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.05876 | −0.189525 | ||||||||
\(119\) | −11.1489 | −1.02202 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.70727 | 0.337024 | ||||||||
\(122\) | −5.61512 | −0.508369 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.8712 | −1.33547 | ||||||||
\(125\) | 11.8482 | 1.05974 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0707 | −1.33731 | −0.668655 | − | 0.743572i | \(-0.733130\pi\) | ||||
−0.668655 | + | 0.743572i | \(0.733130\pi\) | |||||||
\(128\) | −6.59168 | −0.582628 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.47151 | −0.830706 | ||||||||
\(131\) | 10.1307 | 0.885122 | 0.442561 | − | 0.896738i | \(-0.354070\pi\) | ||||
0.442561 | + | 0.896738i | \(0.354070\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.2314 | −0.973888 | ||||||||
\(134\) | −3.63832 | −0.314303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.81205 | 0.326881 | ||||||||
\(137\) | 1.49257 | 0.127519 | 0.0637596 | − | 0.997965i | \(-0.479691\pi\) | ||||
0.0637596 | + | 0.997965i | \(0.479691\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.4652 | 1.90547 | 0.952736 | − | 0.303800i | \(-0.0982555\pi\) | ||||
0.952736 | + | 0.303800i | \(0.0982555\pi\) | |||||||
\(140\) | 6.04833 | 0.511177 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.1206 | −1.26890 | ||||||||
\(143\) | −12.2218 | −1.02204 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0925881 | −0.00768902 | ||||||||
\(146\) | 12.1058 | 1.00188 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.22443 | 0.100648 | ||||||||
\(149\) | 11.3282 | 0.928045 | 0.464022 | − | 0.885823i | \(-0.346406\pi\) | ||||
0.464022 | + | 0.885823i | \(0.346406\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2512 | 0.834231 | 0.417116 | − | 0.908853i | \(-0.363041\pi\) | ||||
0.417116 | + | 0.908853i | \(0.363041\pi\) | |||||||
\(152\) | 3.84027 | 0.311487 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 17.8653 | 1.43963 | ||||||||
\(155\) | 15.1160 | 1.21414 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.23497 | −0.178370 | −0.0891849 | − | 0.996015i | \(-0.528426\pi\) | ||||
−0.0891849 | + | 0.996015i | \(0.528426\pi\) | |||||||
\(158\) | −15.4253 | −1.22717 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11.2902 | −0.892569 | ||||||||
\(161\) | 4.75640 | 0.374857 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1937 | −0.876762 | −0.438381 | − | 0.898789i | \(-0.644448\pi\) | ||||
−0.438381 | + | 0.898789i | \(0.644448\pi\) | |||||||
\(164\) | 3.22075 | 0.251498 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.5230 | −1.43766 | ||||||||
\(167\) | 9.54997 | 0.738999 | 0.369499 | − | 0.929231i | \(-0.379529\pi\) | ||||
0.369499 | + | 0.929231i | \(0.379529\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.84362 | −0.218740 | ||||||||
\(170\) | 13.4043 | 1.02806 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.96052 | 0.301987 | ||||||||
\(173\) | −7.16166 | −0.544491 | −0.272246 | − | 0.962228i | \(-0.587766\pi\) | ||||
−0.272246 | + | 0.962228i | \(0.587766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.21184 | 0.469571 | ||||||||
\(176\) | −18.0086 | −1.35745 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.6958 | 1.25140 | ||||||||
\(179\) | −0.114586 | −0.00856454 | −0.00428227 | − | 0.999991i | \(-0.501363\pi\) | ||||
−0.00428227 | + | 0.999991i | \(0.501363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.24629 | −0.166966 | −0.0834828 | − | 0.996509i | \(-0.526604\pi\) | ||||
−0.0834828 | + | 0.996509i | \(0.526604\pi\) | |||||||
\(182\) | −14.8462 | −1.10047 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.62632 | −0.119894 | ||||||||
\(185\) | −1.24459 | −0.0915041 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.2965 | 1.26485 | ||||||||
\(188\) | −18.5716 | −1.35447 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.5035 | 0.979645 | ||||||||
\(191\) | 7.90682 | 0.572117 | 0.286059 | − | 0.958212i | \(-0.407655\pi\) | ||||
0.286059 | + | 0.958212i | \(0.407655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5321 | −0.758120 | −0.379060 | − | 0.925372i | \(-0.623753\pi\) | ||||
−0.379060 | + | 0.925372i | \(0.623753\pi\) | |||||||
\(194\) | −31.0905 | −2.23217 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.38002 | −0.0985726 | ||||||||
\(197\) | 16.5832 | 1.18150 | 0.590751 | − | 0.806854i | \(-0.298832\pi\) | ||||
0.590751 | + | 0.806854i | \(0.298832\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2741 | 0.870089 | 0.435044 | − | 0.900409i | \(-0.356733\pi\) | ||||
0.435044 | + | 0.900409i | \(0.356733\pi\) | |||||||
\(200\) | −2.12396 | −0.150187 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.0768 | −1.06080 | ||||||||
\(203\) | −0.145128 | −0.0101860 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.27377 | −0.228650 | ||||||||
\(206\) | 8.79350 | 0.612672 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.9652 | 1.03765 | ||||||||
\(209\) | 17.4246 | 1.20528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.24295 | −0.0855685 | −0.0427842 | − | 0.999084i | \(-0.513623\pi\) | ||||
−0.0427842 | + | 0.999084i | \(0.513623\pi\) | |||||||
\(212\) | 1.31092 | 0.0900342 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.00605 | −0.205489 | ||||||||
\(215\) | −4.02571 | −0.274551 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.6936 | 1.60843 | ||||||||
\(218\) | −12.5743 | −0.851642 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.38344 | −0.632632 | ||||||||
\(221\) | −14.3735 | −0.966867 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4338 | 1.16745 | 0.583727 | − | 0.811950i | \(-0.301594\pi\) | ||||
0.583727 | + | 0.811950i | \(0.301594\pi\) | |||||||
\(224\) | −17.6969 | −1.18243 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.76299 | 0.183792 | ||||||||
\(227\) | 1.91090 | 0.126831 | 0.0634154 | − | 0.997987i | \(-0.479801\pi\) | ||||
0.0634154 | + | 0.997987i | \(0.479801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7477 | −0.842389 | −0.421195 | − | 0.906970i | \(-0.638389\pi\) | ||||
−0.421195 | + | 0.906970i | \(0.638389\pi\) | |||||||
\(230\) | −5.71859 | −0.377073 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0496223 | 0.00325787 | ||||||||
\(233\) | 9.04128 | 0.592314 | 0.296157 | − | 0.955139i | \(-0.404295\pi\) | ||||
0.296157 | + | 0.955139i | \(0.404295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.8773 | 1.23142 | ||||||||
\(236\) | 1.69494 | 0.110331 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 21.0106 | 1.36192 | ||||||||
\(239\) | 1.00000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.3266 | 1.37377 | 0.686884 | − | 0.726767i | \(-0.258978\pi\) | ||||
0.686884 | + | 0.726767i | \(0.258978\pi\) | |||||||
\(242\) | −6.98650 | −0.449110 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.62281 | 0.295945 | ||||||||
\(245\) | 1.40273 | 0.0896174 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.4799 | −0.921333 | ||||||||
\(248\) | −8.10135 | −0.514437 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −22.3285 | −1.41218 | ||||||||
\(251\) | 29.4696 | 1.86010 | 0.930052 | − | 0.367427i | \(-0.119761\pi\) | ||||
0.930052 | + | 0.367427i | \(0.119761\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.37913 | −0.463922 | ||||||||
\(254\) | 28.4014 | 1.78206 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.6222 | 1.28889 | ||||||||
\(257\) | 6.15087 | 0.383681 | 0.191840 | − | 0.981426i | \(-0.438554\pi\) | ||||
0.191840 | + | 0.981426i | \(0.438554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.95084 | −0.121219 | ||||||||
\(260\) | 7.79769 | 0.483592 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.0917 | −1.17949 | ||||||||
\(263\) | −10.2302 | −0.630823 | −0.315412 | − | 0.948955i | \(-0.602143\pi\) | ||||
−0.315412 | + | 0.948955i | \(0.602143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.33250 | −0.0818547 | ||||||||
\(266\) | 21.1661 | 1.29778 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.99535 | 0.182970 | ||||||||
\(269\) | 27.2980 | 1.66439 | 0.832193 | − | 0.554486i | \(-0.187085\pi\) | ||||
0.832193 | + | 0.554486i | \(0.187085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5829 | 1.31107 | 0.655534 | − | 0.755166i | \(-0.272444\pi\) | ||||
0.655534 | + | 0.755166i | \(0.272444\pi\) | |||||||
\(272\) | −21.1791 | −1.28417 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.81282 | −0.169929 | ||||||||
\(275\) | −9.63712 | −0.581140 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.8035 | −1.00962 | −0.504812 | − | 0.863230i | \(-0.668438\pi\) | ||||
−0.504812 | + | 0.863230i | \(0.668438\pi\) | |||||||
\(278\) | −42.3366 | −2.53918 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.29495 | 0.196911 | ||||||||
\(281\) | 2.74082 | 0.163504 | 0.0817519 | − | 0.996653i | \(-0.473948\pi\) | ||||
0.0817519 | + | 0.996653i | \(0.473948\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.1177 | 1.13643 | 0.568214 | − | 0.822881i | \(-0.307635\pi\) | ||||
0.568214 | + | 0.822881i | \(0.307635\pi\) | |||||||
\(284\) | 12.4485 | 0.738682 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.0325 | 1.36194 | ||||||||
\(287\) | −5.13149 | −0.302902 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.34168 | 0.196569 | ||||||||
\(290\) | 0.174486 | 0.0102462 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.96641 | −0.583240 | ||||||||
\(293\) | 26.6427 | 1.55648 | 0.778241 | − | 0.627966i | \(-0.216112\pi\) | ||||
0.778241 | + | 0.627966i | \(0.216112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.72284 | −0.100307 | ||||||||
\(296\) | 0.667034 | 0.0387706 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.3485 | −1.23669 | ||||||||
\(299\) | 6.13210 | 0.354628 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.31014 | −0.363710 | ||||||||
\(302\) | −19.3188 | −1.11167 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.3358 | −1.22369 | ||||||||
\(305\) | −4.69891 | −0.269059 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0399 | 0.858373 | 0.429186 | − | 0.903216i | \(-0.358800\pi\) | ||||
0.429186 | + | 0.903216i | \(0.358800\pi\) | |||||||
\(308\) | −14.7081 | −0.838075 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −28.4867 | −1.61793 | ||||||||
\(311\) | 13.7719 | 0.780933 | 0.390467 | − | 0.920617i | \(-0.372314\pi\) | ||||
0.390467 | + | 0.920617i | \(0.372314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.15686 | −0.0653898 | −0.0326949 | − | 0.999465i | \(-0.510409\pi\) | ||||
−0.0326949 | + | 0.999465i | \(0.510409\pi\) | |||||||
\(314\) | 4.21189 | 0.237691 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.6993 | 0.714394 | ||||||||
\(317\) | −19.8540 | −1.11511 | −0.557557 | − | 0.830139i | \(-0.688261\pi\) | ||||
−0.557557 | + | 0.830139i | \(0.688261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.225153 | 0.0126061 | ||||||||
\(320\) | 6.46578 | 0.361448 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.96365 | −0.499525 | ||||||||
\(323\) | 20.4922 | 1.14022 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00849 | 0.444231 | ||||||||
\(326\) | 21.0951 | 1.16835 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.75457 | 0.0968797 | ||||||||
\(329\) | 29.5894 | 1.63132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5712 | 0.800904 | 0.400452 | − | 0.916318i | \(-0.368853\pi\) | ||||
0.400452 | + | 0.916318i | \(0.368853\pi\) | |||||||
\(332\) | 15.2496 | 0.836928 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.9973 | −0.984770 | ||||||||
\(335\) | −3.04466 | −0.166347 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.1805 | 0.826933 | 0.413466 | − | 0.910519i | \(-0.364318\pi\) | ||||
0.413466 | + | 0.910519i | \(0.364318\pi\) | |||||||
\(338\) | 5.35892 | 0.291487 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.0354 | −0.598481 | ||||||||
\(341\) | −36.7585 | −1.99059 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5024 | 1.05303 | ||||||||
\(344\) | 2.15757 | 0.116328 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.4965 | 0.725574 | ||||||||
\(347\) | −10.1274 | −0.543667 | −0.271834 | − | 0.962344i | \(-0.587630\pi\) | ||||
−0.271834 | + | 0.962344i | \(0.587630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4379 | 0.772842 | 0.386421 | − | 0.922322i | \(-0.373711\pi\) | ||||
0.386421 | + | 0.922322i | \(0.373711\pi\) | |||||||
\(350\) | −11.7065 | −0.625738 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 27.4552 | 1.46337 | ||||||||
\(353\) | 24.6191 | 1.31034 | 0.655171 | − | 0.755481i | \(-0.272597\pi\) | ||||
0.655171 | + | 0.755481i | \(0.272597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.6534 | −0.671574 | ||||||||
\(356\) | −13.7453 | −0.728499 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.215942 | 0.0114129 | ||||||||
\(359\) | −15.5002 | −0.818070 | −0.409035 | − | 0.912519i | \(-0.634135\pi\) | ||||
−0.409035 | + | 0.912519i | \(0.634135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.64388 | 0.0865198 | ||||||||
\(362\) | 4.23324 | 0.222494 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.2225 | 0.640635 | ||||||||
\(365\) | 10.1305 | 0.530253 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1151 | −0.580205 | −0.290103 | − | 0.956996i | \(-0.593689\pi\) | ||||
−0.290103 | + | 0.956996i | \(0.593689\pi\) | |||||||
\(368\) | 9.03552 | 0.471009 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.34548 | 0.121936 | ||||||||
\(371\) | −2.08863 | −0.108436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.7318 | 1.48767 | 0.743837 | − | 0.668361i | \(-0.233004\pi\) | ||||
0.743837 | + | 0.668361i | \(0.233004\pi\) | |||||||
\(374\) | −32.5961 | −1.68550 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.1172 | −0.521757 | ||||||||
\(377\) | −0.187103 | −0.00963630 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0688 | −1.18496 | −0.592481 | − | 0.805584i | \(-0.701852\pi\) | ||||
−0.592481 | + | 0.805584i | \(0.701852\pi\) | |||||||
\(380\) | −11.1171 | −0.570296 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.9007 | −0.762388 | ||||||||
\(383\) | −25.1173 | −1.28343 | −0.641717 | − | 0.766941i | \(-0.721778\pi\) | ||||
−0.641717 | + | 0.766941i | \(0.721778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.9503 | 0.761936 | ||||||||
\(386\) | 19.8483 | 1.01025 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 25.5962 | 1.29945 | ||||||||
\(389\) | 20.2979 | 1.02915 | 0.514573 | − | 0.857447i | \(-0.327951\pi\) | ||||
0.514573 | + | 0.857447i | \(0.327951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.67826 | −0.438879 | ||||||||
\(392\) | −0.751791 | −0.0379712 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −31.2517 | −1.57444 | ||||||||
\(395\) | −12.9084 | −0.649492 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.09694 | −0.255808 | −0.127904 | − | 0.991787i | \(-0.540825\pi\) | ||||
−0.127904 | + | 0.991787i | \(0.540825\pi\) | |||||||
\(398\) | −23.1311 | −1.15946 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.8003 | 0.590017 | ||||||||
\(401\) | 22.6376 | 1.13047 | 0.565235 | − | 0.824930i | \(-0.308786\pi\) | ||||
0.565235 | + | 0.824930i | \(0.308786\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.5465 | 1.52163 | ||||||||
\(404\) | 12.4124 | 0.617539 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.273500 | 0.0135736 | ||||||||
\(407\) | 3.02656 | 0.150021 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.2093 | −0.603712 | −0.301856 | − | 0.953353i | \(-0.597606\pi\) | ||||
−0.301856 | + | 0.953353i | \(0.597606\pi\) | |||||||
\(410\) | 6.16955 | 0.304693 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.23950 | −0.356665 | ||||||||
\(413\) | −2.70047 | −0.132882 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.5006 | −0.760894 | ||||||||
\(416\) | −22.8154 | −1.11862 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −32.8373 | −1.60613 | ||||||||
\(419\) | −36.9777 | −1.80648 | −0.903239 | − | 0.429137i | \(-0.858818\pi\) | ||||
−0.903239 | + | 0.429137i | \(0.858818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.2814 | −1.13466 | −0.567332 | − | 0.823489i | \(-0.692024\pi\) | ||||
−0.567332 | + | 0.823489i | \(0.692024\pi\) | |||||||
\(422\) | 2.34240 | 0.114026 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.714149 | 0.0346821 | ||||||||
\(425\) | −11.3338 | −0.549769 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.36534 | −0.356434 | ||||||||
\(428\) | 2.47481 | 0.119625 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.58663 | 0.365860 | ||||||||
\(431\) | −34.2064 | −1.64766 | −0.823832 | − | 0.566834i | \(-0.808168\pi\) | ||||
−0.823832 | + | 0.566834i | \(0.808168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.581765 | 0.0279578 | 0.0139789 | − | 0.999902i | \(-0.495550\pi\) | ||||
0.0139789 | + | 0.999902i | \(0.495550\pi\) | |||||||
\(434\) | −44.6516 | −2.14335 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3522 | 0.495780 | ||||||||
\(437\) | −8.74249 | −0.418210 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.5628 | −0.742771 | −0.371386 | − | 0.928479i | \(-0.621117\pi\) | ||||
−0.371386 | + | 0.928479i | \(0.621117\pi\) | |||||||
\(440\) | −5.11182 | −0.243696 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.0875 | 1.28842 | ||||||||
\(443\) | −37.1224 | −1.76374 | −0.881870 | − | 0.471493i | \(-0.843715\pi\) | ||||
−0.881870 | + | 0.471493i | \(0.843715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.9716 | 0.662316 | ||||||||
\(446\) | −32.8548 | −1.55572 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.1348 | 0.478826 | ||||||||
\(449\) | −16.6269 | −0.784670 | −0.392335 | − | 0.919822i | \(-0.628333\pi\) | ||||
−0.392335 | + | 0.919822i | \(0.628333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.96104 | 0.374871 | ||||||||
\(452\) | −2.27471 | −0.106993 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.60117 | −0.169011 | ||||||||
\(455\) | −12.4237 | −0.582434 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.3822 | 0.485659 | 0.242829 | − | 0.970069i | \(-0.421924\pi\) | ||||
0.242829 | + | 0.970069i | \(0.421924\pi\) | |||||||
\(458\) | 24.0235 | 1.12255 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.70799 | 0.219511 | ||||||||
\(461\) | 13.7020 | 0.638164 | 0.319082 | − | 0.947727i | \(-0.396625\pi\) | ||||
0.319082 | + | 0.947727i | \(0.396625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.4574 | −1.92669 | −0.963345 | − | 0.268265i | \(-0.913550\pi\) | ||||
−0.963345 | + | 0.268265i | \(0.913550\pi\) | |||||||
\(464\) | −0.275693 | −0.0127987 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.0387 | −0.789302 | ||||||||
\(467\) | −19.8888 | −0.920345 | −0.460173 | − | 0.887829i | \(-0.652212\pi\) | ||||
−0.460173 | + | 0.887829i | \(0.652212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.77237 | −0.220367 | ||||||||
\(470\) | −35.5751 | −1.64096 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.923350 | 0.0425006 | ||||||||
\(473\) | 9.78961 | 0.450127 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.4176 | −0.523878 | ||||||||
\(476\) | −17.2976 | −0.792833 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.88454 | −0.0861970 | ||||||||
\(479\) | −13.2603 | −0.605878 | −0.302939 | − | 0.953010i | \(-0.597968\pi\) | ||||
−0.302939 | + | 0.953010i | \(0.597968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.51508 | −0.114678 | ||||||||
\(482\) | −40.1909 | −1.83065 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.75184 | 0.261447 | ||||||||
\(485\) | −26.0175 | −1.18139 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.1123 | 1.59109 | 0.795545 | − | 0.605895i | \(-0.207185\pi\) | ||||
0.795545 | + | 0.605895i | \(0.207185\pi\) | |||||||
\(488\) | 2.51837 | 0.114001 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.64351 | −0.119422 | ||||||||
\(491\) | 6.60916 | 0.298267 | 0.149134 | − | 0.988817i | \(-0.452352\pi\) | ||||
0.149134 | + | 0.988817i | \(0.452352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.264792 | 0.0119256 | ||||||||
\(494\) | 27.2880 | 1.22774 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 45.0097 | 2.02099 | ||||||||
\(497\) | −19.8337 | −0.889663 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.6811 | −1.01534 | −0.507672 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507672 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(500\) | 18.3826 | 0.822093 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −55.5367 | −2.47873 | ||||||||
\(503\) | −30.0329 | −1.33910 | −0.669549 | − | 0.742768i | \(-0.733513\pi\) | ||||
−0.669549 | + | 0.742768i | \(0.733513\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.6167 | −0.561436 | ||||||||
\(506\) | 13.9063 | 0.618210 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.3823 | −1.03742 | ||||||||
\(509\) | 39.2106 | 1.73798 | 0.868990 | − | 0.494829i | \(-0.164769\pi\) | ||||
0.868990 | + | 0.494829i | \(0.164769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.8791 | 0.702450 | ||||||||
\(512\) | −25.6800 | −1.13491 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.5916 | −0.511283 | ||||||||
\(515\) | 7.35867 | 0.324262 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.9053 | −2.01891 | ||||||||
\(518\) | 3.67645 | 0.161534 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.24794 | 0.186285 | ||||||||
\(521\) | 34.0212 | 1.49049 | 0.745247 | − | 0.666789i | \(-0.232332\pi\) | ||||
0.745247 | + | 0.666789i | \(0.232332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.3066 | −1.15031 | −0.575153 | − | 0.818046i | \(-0.695058\pi\) | ||||
−0.575153 | + | 0.818046i | \(0.695058\pi\) | |||||||
\(524\) | 15.7178 | 0.686635 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.2793 | 0.840618 | ||||||||
\(527\) | −43.2300 | −1.88313 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2976 | −0.839028 | ||||||||
\(530\) | 2.51115 | 0.109077 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.4256 | −0.755495 | ||||||||
\(533\) | −6.61567 | −0.286556 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.51555 | −0.108757 | ||||||||
\(536\) | 1.63177 | 0.0704819 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −51.4442 | −2.21792 | ||||||||
\(539\) | −3.41112 | −0.146928 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.1226 | 0.693163 | 0.346581 | − | 0.938020i | \(-0.387342\pi\) | ||||
0.346581 | + | 0.938020i | \(0.387342\pi\) | |||||||
\(542\) | −40.6739 | −1.74709 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.2888 | 1.38437 | ||||||||
\(545\) | −10.5226 | −0.450739 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.430130 | −0.0183910 | −0.00919552 | − | 0.999958i | \(-0.502927\pi\) | ||||
−0.00919552 | + | 0.999958i | \(0.502927\pi\) | |||||||
\(548\) | 2.31573 | 0.0989232 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.1616 | 0.774412 | ||||||||
\(551\) | 0.266752 | 0.0113640 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.2334 | −0.860410 | ||||||||
\(554\) | 31.6669 | 1.34540 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 34.8548 | 1.47817 | ||||||||
\(557\) | 13.6791 | 0.579602 | 0.289801 | − | 0.957087i | \(-0.406411\pi\) | ||||
0.289801 | + | 0.957087i | \(0.406411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.13521 | −0.344083 | ||||||||
\(560\) | −18.3061 | −0.773576 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.16520 | −0.217881 | ||||||||
\(563\) | 13.3807 | 0.563931 | 0.281965 | − | 0.959425i | \(-0.409014\pi\) | ||||
0.281965 | + | 0.959425i | \(0.409014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.31216 | 0.0972732 | ||||||||
\(566\) | −36.0281 | −1.51437 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.78156 | 0.284548 | ||||||||
\(569\) | −5.69249 | −0.238641 | −0.119321 | − | 0.992856i | \(-0.538072\pi\) | ||||
−0.119321 | + | 0.992856i | \(0.538072\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9082 | 0.623889 | 0.311944 | − | 0.950100i | \(-0.399020\pi\) | ||||
0.311944 | + | 0.950100i | \(0.399020\pi\) | |||||||
\(572\) | −18.9622 | −0.792848 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.67051 | 0.403639 | ||||||||
\(575\) | 4.83527 | 0.201645 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0799 | −1.08572 | −0.542860 | − | 0.839823i | \(-0.682659\pi\) | ||||
−0.542860 | + | 0.839823i | \(0.682659\pi\) | |||||||
\(578\) | −6.29754 | −0.261943 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.143651 | −0.00596477 | ||||||||
\(581\) | −24.2965 | −1.00799 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.24033 | 0.134201 | ||||||||
\(584\) | −5.42940 | −0.224670 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −50.2093 | −2.07413 | ||||||||
\(587\) | 20.0301 | 0.826729 | 0.413365 | − | 0.910566i | \(-0.364354\pi\) | ||||
0.413365 | + | 0.910566i | \(0.364354\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.5499 | −1.79444 | ||||||||
\(590\) | 3.24676 | 0.133667 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.70592 | −0.152312 | ||||||||
\(593\) | 28.0351 | 1.15126 | 0.575632 | − | 0.817709i | \(-0.304756\pi\) | ||||
0.575632 | + | 0.817709i | \(0.304756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.5823 | 0.720805 | ||||||||
\(596\) | 17.5758 | 0.719932 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.5562 | −0.472568 | ||||||||
\(599\) | 31.5499 | 1.28909 | 0.644547 | − | 0.764564i | \(-0.277046\pi\) | ||||
0.644547 | + | 0.764564i | \(0.277046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.70265 | 0.110243 | 0.0551217 | − | 0.998480i | \(-0.482445\pi\) | ||||
0.0551217 | + | 0.998480i | \(0.482445\pi\) | |||||||
\(602\) | 11.8917 | 0.484670 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.9048 | 0.647156 | ||||||||
\(605\) | −5.84652 | −0.237695 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.4724 | −1.60213 | −0.801067 | − | 0.598575i | \(-0.795734\pi\) | ||||
−0.801067 | + | 0.598575i | \(0.795734\pi\) | |||||||
\(608\) | 32.5277 | 1.31917 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.85529 | 0.358540 | ||||||||
\(611\) | 38.1475 | 1.54328 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.3060 | 0.698982 | 0.349491 | − | 0.936940i | \(-0.386354\pi\) | ||||
0.349491 | + | 0.936940i | \(0.386354\pi\) | |||||||
\(614\) | −28.3434 | −1.14384 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.01256 | −0.322835 | ||||||||
\(617\) | 42.7513 | 1.72110 | 0.860551 | − | 0.509365i | \(-0.170120\pi\) | ||||
0.860551 | + | 0.509365i | \(0.170120\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.29106 | 0.0920853 | 0.0460427 | − | 0.998939i | \(-0.485339\pi\) | ||||
0.0460427 | + | 0.998939i | \(0.485339\pi\) | |||||||
\(620\) | 23.4525 | 0.941873 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −25.9538 | −1.04065 | ||||||||
\(623\) | 21.8998 | 0.877398 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.12049 | −0.244820 | ||||||||
\(626\) | 2.18016 | 0.0871367 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.46756 | −0.138371 | ||||||||
\(629\) | 3.55939 | 0.141922 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.3021 | 1.60440 | 0.802201 | − | 0.597054i | \(-0.203662\pi\) | ||||
0.802201 | + | 0.597054i | \(0.203662\pi\) | |||||||
\(632\) | 6.91822 | 0.275192 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 37.4158 | 1.48597 | ||||||||
\(635\) | 23.7672 | 0.943172 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.83466 | 0.112313 | ||||||||
\(638\) | −0.424310 | −0.0167986 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.3954 | 0.410913 | ||||||||
\(641\) | 12.3428 | 0.487511 | 0.243756 | − | 0.969837i | \(-0.421621\pi\) | ||||
0.243756 | + | 0.969837i | \(0.421621\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.36474 | 0.251001 | 0.125501 | − | 0.992094i | \(-0.459946\pi\) | ||||
0.125501 | + | 0.992094i | \(0.459946\pi\) | |||||||
\(644\) | 7.37958 | 0.290796 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −38.6185 | −1.51942 | ||||||||
\(647\) | −13.9746 | −0.549399 | −0.274700 | − | 0.961530i | \(-0.588578\pi\) | ||||
−0.274700 | + | 0.961530i | \(0.588578\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.18954 | 0.164454 | ||||||||
\(650\) | −15.0923 | −0.591970 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.3671 | −0.680149 | ||||||||
\(653\) | −0.742205 | −0.0290447 | −0.0145224 | − | 0.999895i | \(-0.504623\pi\) | ||||
−0.0145224 | + | 0.999895i | \(0.504623\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.9765 | −0.624255 | ||||||||
\(656\) | −9.74805 | −0.380597 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −55.7625 | −2.17385 | ||||||||
\(659\) | −41.9051 | −1.63239 | −0.816196 | − | 0.577776i | \(-0.803921\pi\) | ||||
−0.816196 | + | 0.577776i | \(0.803921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.6618 | −1.19261 | −0.596304 | − | 0.802759i | \(-0.703365\pi\) | ||||
−0.596304 | + | 0.802759i | \(0.703365\pi\) | |||||||
\(662\) | −27.4600 | −1.06726 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.30750 | 0.322393 | ||||||||
\(665\) | 17.7125 | 0.686859 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.112967 | −0.00437409 | ||||||||
\(668\) | 14.8168 | 0.573279 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.73778 | 0.221670 | ||||||||
\(671\) | 11.4267 | 0.441121 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.2232 | 1.58904 | 0.794519 | − | 0.607240i | \(-0.207723\pi\) | ||||
0.794519 | + | 0.607240i | \(0.207723\pi\) | |||||||
\(674\) | −28.6082 | −1.10195 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.41188 | −0.169688 | ||||||||
\(677\) | −42.5360 | −1.63479 | −0.817395 | − | 0.576078i | \(-0.804583\pi\) | ||||
−0.817395 | + | 0.576078i | \(0.804583\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −40.7814 | −1.56504 | ||||||||
\(680\) | −6.01178 | −0.230541 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 69.2730 | 2.65260 | ||||||||
\(683\) | 32.3571 | 1.23811 | 0.619055 | − | 0.785348i | \(-0.287516\pi\) | ||||
0.619055 | + | 0.785348i | \(0.287516\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.35385 | −0.0899361 | ||||||||
\(686\) | −36.7530 | −1.40324 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.9871 | −0.457003 | ||||||||
\(689\) | −2.69273 | −0.102585 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.4308 | 1.11960 | 0.559801 | − | 0.828627i | \(-0.310878\pi\) | ||||
0.559801 | + | 0.828627i | \(0.310878\pi\) | |||||||
\(692\) | −11.1113 | −0.422390 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.0855 | 0.724476 | ||||||||
\(695\) | −35.4286 | −1.34388 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.36262 | 0.354635 | ||||||||
\(698\) | −27.2088 | −1.02987 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.63769 | 0.364271 | ||||||||
\(701\) | 27.9008 | 1.05380 | 0.526899 | − | 0.849928i | \(-0.323354\pi\) | ||||
0.526899 | + | 0.849928i | \(0.323354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.58574 | 0.135239 | ||||||||
\(704\) | −15.7233 | −0.592594 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −46.3957 | −1.74613 | ||||||||
\(707\) | −19.7761 | −0.743758 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.6158 | −0.511351 | −0.255676 | − | 0.966763i | \(-0.582298\pi\) | ||||
−0.255676 | + | 0.966763i | \(0.582298\pi\) | |||||||
\(710\) | 23.8459 | 0.894921 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.48802 | −0.280625 | ||||||||
\(713\) | 18.4430 | 0.690695 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.2743 | 0.720819 | ||||||||
\(716\) | −0.177780 | −0.00664395 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.2108 | 1.09014 | ||||||||
\(719\) | 42.0015 | 1.56639 | 0.783195 | − | 0.621776i | \(-0.213589\pi\) | ||||
0.783195 | + | 0.621776i | \(0.213589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5344 | 0.429564 | ||||||||
\(722\) | −3.09796 | −0.115294 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.48513 | −0.129524 | ||||||||
\(725\) | −0.147534 | −0.00547928 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.9245 | −1.70324 | −0.851622 | − | 0.524156i | \(-0.824381\pi\) | ||||
−0.851622 | + | 0.524156i | \(0.824381\pi\) | |||||||
\(728\) | 6.65847 | 0.246779 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.0913 | −0.706601 | ||||||||
\(731\) | 11.5131 | 0.425828 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.25611 | 0.0833315 | 0.0416657 | − | 0.999132i | \(-0.486734\pi\) | ||||
0.0416657 | + | 0.999132i | \(0.486734\pi\) | |||||||
\(734\) | 20.9469 | 0.773166 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.7752 | −0.507760 | ||||||||
\(737\) | 7.40390 | 0.272726 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.6417 | −0.428248 | −0.214124 | − | 0.976806i | \(-0.568690\pi\) | ||||
−0.214124 | + | 0.976806i | \(0.568690\pi\) | |||||||
\(740\) | −1.93098 | −0.0709844 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.93612 | 0.144500 | ||||||||
\(743\) | −9.19350 | −0.337277 | −0.168638 | − | 0.985678i | \(-0.553937\pi\) | ||||
−0.168638 | + | 0.985678i | \(0.553937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.8651 | −0.654527 | ||||||||
\(746\) | −54.1463 | −1.98244 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 26.8356 | 0.981208 | ||||||||
\(749\) | −3.94302 | −0.144075 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.6899 | 1.95917 | 0.979586 | − | 0.201027i | \(-0.0644280\pi\) | ||||
0.979586 | + | 0.201027i | \(0.0644280\pi\) | |||||||
\(752\) | 56.2096 | 2.04975 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.352604 | 0.0128411 | ||||||||
\(755\) | −16.1666 | −0.588363 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.7983 | −0.610546 | −0.305273 | − | 0.952265i | \(-0.598748\pi\) | ||||
−0.305273 | + | 0.952265i | \(0.598748\pi\) | |||||||
\(758\) | 43.4741 | 1.57905 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.05627 | −0.219684 | ||||||||
\(761\) | 9.97766 | 0.361690 | 0.180845 | − | 0.983512i | \(-0.442117\pi\) | ||||
0.180845 | + | 0.983512i | \(0.442117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4937 | −0.597113 | ||||||||
\(764\) | 12.2675 | 0.443821 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 47.3347 | 1.71027 | ||||||||
\(767\) | −3.48153 | −0.125711 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −49.8609 | −1.79803 | −0.899016 | − | 0.437917i | \(-0.855716\pi\) | ||||
−0.899016 | + | 0.437917i | \(0.855716\pi\) | |||||||
\(770\) | −28.1744 | −1.01534 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.3406 | −0.588112 | ||||||||
\(773\) | 2.95716 | 0.106362 | 0.0531809 | − | 0.998585i | \(-0.483064\pi\) | ||||
0.0531809 | + | 0.998585i | \(0.483064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.0865 | 0.865211 | ||||||||
\(776\) | 13.9440 | 0.500561 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.2523 | −1.37141 | ||||||||
\(779\) | 9.43191 | 0.337933 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.7702 | 1.10104 | ||||||||
\(782\) | 16.3546 | 0.584838 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.17681 | 0.149172 | ||||||||
\(785\) | 3.52464 | 0.125800 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.9607 | −0.925399 | −0.462699 | − | 0.886515i | \(-0.653119\pi\) | ||||
−0.462699 | + | 0.886515i | \(0.653119\pi\) | |||||||
\(788\) | 25.7288 | 0.916552 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.3264 | 0.865496 | ||||||||
\(791\) | 3.62421 | 0.128862 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.49560 | −0.337199 | ||||||||
\(794\) | 9.60541 | 0.340883 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.0433 | 0.674973 | ||||||||
\(797\) | 5.84720 | 0.207119 | 0.103559 | − | 0.994623i | \(-0.466977\pi\) | ||||
0.103559 | + | 0.994623i | \(0.466977\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53.9871 | −1.90993 | ||||||||
\(800\) | −17.9903 | −0.636055 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −42.6616 | −1.50643 | ||||||||
\(803\) | −24.6350 | −0.869349 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.50106 | −0.264378 | ||||||||
\(806\) | −57.5662 | −2.02768 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.76189 | 0.237882 | ||||||||
\(809\) | 1.10730 | 0.0389306 | 0.0194653 | − | 0.999811i | \(-0.493804\pi\) | ||||
0.0194653 | + | 0.999811i | \(0.493804\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.9703 | −1.08751 | −0.543757 | − | 0.839243i | \(-0.682999\pi\) | ||||
−0.543757 | + | 0.839243i | \(0.682999\pi\) | |||||||
\(812\) | −0.225166 | −0.00790179 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.70367 | −0.199914 | ||||||||
\(815\) | 17.6530 | 0.618358 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5983 | 0.405774 | ||||||||
\(818\) | 23.0090 | 0.804491 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.07926 | −0.177375 | ||||||||
\(821\) | −44.0188 | −1.53627 | −0.768133 | − | 0.640290i | \(-0.778814\pi\) | ||||
−0.768133 | + | 0.640290i | \(0.778814\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.54554 | 0.123590 | 0.0617949 | − | 0.998089i | \(-0.480318\pi\) | ||||
0.0617949 | + | 0.998089i | \(0.480318\pi\) | |||||||
\(824\) | −3.94386 | −0.137391 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.08916 | 0.177075 | ||||||||
\(827\) | 32.6215 | 1.13436 | 0.567180 | − | 0.823594i | \(-0.308034\pi\) | ||||
0.567180 | + | 0.823594i | \(0.308034\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.5811 | 1.51363 | 0.756817 | − | 0.653627i | \(-0.226754\pi\) | ||||
0.756817 | + | 0.653627i | \(0.226754\pi\) | |||||||
\(830\) | 29.2115 | 1.01395 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.0661 | 0.452987 | ||||||||
\(833\) | −4.01167 | −0.138996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.0607 | −0.521197 | ||||||||
\(836\) | 27.0342 | 0.934999 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 69.6861 | 2.40726 | ||||||||
\(839\) | 27.9176 | 0.963822 | 0.481911 | − | 0.876220i | \(-0.339943\pi\) | ||||
0.481911 | + | 0.876220i | \(0.339943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9966 | −0.999881 | ||||||||
\(842\) | 43.8747 | 1.51202 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.92845 | −0.0663799 | ||||||||
\(845\) | 4.48451 | 0.154272 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.16417 | −0.314885 | ||||||||
\(848\) | −3.96768 | −0.136251 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.3590 | 0.732607 | ||||||||
\(851\) | −1.51853 | −0.0520544 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.6342 | 0.535303 | 0.267652 | − | 0.963516i | \(-0.413752\pi\) | ||||
0.267652 | + | 0.963516i | \(0.413752\pi\) | |||||||
\(854\) | 13.8803 | 0.474974 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.34820 | 0.0460806 | ||||||||
\(857\) | 19.1584 | 0.654438 | 0.327219 | − | 0.944949i | \(-0.393889\pi\) | ||||
0.327219 | + | 0.944949i | \(0.393889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.26808 | 0.145625 | 0.0728125 | − | 0.997346i | \(-0.476803\pi\) | ||||
0.0728125 | + | 0.997346i | \(0.476803\pi\) | |||||||
\(860\) | −6.24591 | −0.212984 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 64.4635 | 2.19563 | ||||||||
\(863\) | −23.1367 | −0.787582 | −0.393791 | − | 0.919200i | \(-0.628837\pi\) | ||||
−0.393791 | + | 0.919200i | \(0.628837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.2943 | 0.384016 | ||||||||
\(866\) | −1.09636 | −0.0372559 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 36.7607 | 1.24774 | ||||||||
\(869\) | 31.3902 | 1.06484 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.15268 | −0.208475 | ||||||||
\(872\) | 5.63956 | 0.190980 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.4756 | 0.557295 | ||||||||
\(875\) | −29.2882 | −0.990122 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.378032 | 0.0127652 | 0.00638262 | − | 0.999980i | \(-0.497968\pi\) | ||||
0.00638262 | + | 0.999980i | \(0.497968\pi\) | |||||||
\(878\) | 29.3287 | 0.989797 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 28.4003 | 0.957375 | ||||||||
\(881\) | 3.64768 | 0.122893 | 0.0614467 | − | 0.998110i | \(-0.480429\pi\) | ||||
0.0614467 | + | 0.998110i | \(0.480429\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.3198 | −1.15495 | −0.577477 | − | 0.816407i | \(-0.695963\pi\) | ||||
−0.577477 | + | 0.816407i | \(0.695963\pi\) | |||||||
\(884\) | −22.3005 | −0.750049 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 69.9588 | 2.35031 | ||||||||
\(887\) | 48.0103 | 1.61203 | 0.806014 | − | 0.591896i | \(-0.201620\pi\) | ||||
0.806014 | + | 0.591896i | \(0.201620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.2541 | 1.24946 | ||||||||
\(890\) | −26.3300 | −0.882584 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.0486 | 0.905654 | ||||||||
\(893\) | −54.3866 | −1.81998 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.180707 | 0.00604036 | ||||||||
\(896\) | 16.2943 | 0.544354 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.3340 | 1.04563 | ||||||||
\(899\) | −0.562734 | −0.0187682 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.81080 | 0.126956 | ||||||||
\(902\) | −15.0029 | −0.499543 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.23919 | −0.0412150 | ||||||||
\(905\) | 3.54250 | 0.117757 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.2463 | −0.605857 | −0.302929 | − | 0.953013i | \(-0.597964\pi\) | ||||
−0.302929 | + | 0.953013i | \(0.597964\pi\) | |||||||
\(908\) | 2.96476 | 0.0983891 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 23.4131 | 0.776136 | ||||||||
\(911\) | −3.39432 | −0.112459 | −0.0562294 | − | 0.998418i | \(-0.517908\pi\) | ||||
−0.0562294 | + | 0.998418i | \(0.517908\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.6939 | 1.24748 | ||||||||
\(914\) | −19.5657 | −0.647176 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.7780 | −0.653485 | ||||||||
\(917\) | −25.0425 | −0.826977 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −58.2249 | −1.92066 | −0.960332 | − | 0.278860i | \(-0.910044\pi\) | ||||
−0.960332 | + | 0.278860i | \(0.910044\pi\) | |||||||
\(920\) | 2.56477 | 0.0845580 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25.8220 | −0.850401 | ||||||||
\(923\) | −25.5702 | −0.841653 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.98319 | −0.0652068 | ||||||||
\(926\) | 78.1283 | 2.56746 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.420310 | 0.0137974 | ||||||||
\(929\) | 42.0740 | 1.38040 | 0.690202 | − | 0.723617i | \(-0.257522\pi\) | ||||
0.690202 | + | 0.723617i | \(0.257522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.04136 | −0.132450 | ||||||||
\(932\) | 14.0276 | 0.459489 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.4814 | 1.22643 | ||||||||
\(935\) | −27.2774 | −0.892067 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.9489 | 0.782375 | 0.391188 | − | 0.920311i | \(-0.372064\pi\) | ||||
0.391188 | + | 0.920311i | \(0.372064\pi\) | |||||||
\(938\) | 8.99373 | 0.293656 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.2882 | 0.955276 | ||||||||
\(941\) | −3.92678 | −0.128009 | −0.0640047 | − | 0.997950i | \(-0.520387\pi\) | ||||
−0.0640047 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.99433 | −0.130073 | ||||||||
\(944\) | −5.12996 | −0.166966 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.4489 | −0.599827 | ||||||||
\(947\) | −8.59682 | −0.279359 | −0.139680 | − | 0.990197i | \(-0.544607\pi\) | ||||
−0.139680 | + | 0.990197i | \(0.544607\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.4718 | 0.664542 | ||||||||
\(950\) | 21.5171 | 0.698105 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.42320 | −0.305408 | ||||||||
\(953\) | 10.1361 | 0.328342 | 0.164171 | − | 0.986432i | \(-0.447505\pi\) | ||||
0.164171 | + | 0.986432i | \(0.447505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.4694 | −0.403500 | ||||||||
\(956\) | 1.55150 | 0.0501792 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.9896 | 0.807377 | ||||||||
\(959\) | −3.68957 | −0.119142 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.8722 | 1.96362 | ||||||||
\(962\) | 4.73978 | 0.152817 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 33.0883 | 1.06570 | ||||||||
\(965\) | 16.6096 | 0.534683 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.1978 | 1.19620 | 0.598100 | − | 0.801421i | \(-0.295922\pi\) | ||||
0.598100 | + | 0.801421i | \(0.295922\pi\) | |||||||
\(968\) | 3.13343 | 0.100712 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 49.0311 | 1.57429 | ||||||||
\(971\) | −24.0240 | −0.770967 | −0.385483 | − | 0.922715i | \(-0.625965\pi\) | ||||
−0.385483 | + | 0.922715i | \(0.625965\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −55.5328 | −1.78030 | ||||||||
\(974\) | −66.1706 | −2.12024 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.9916 | −0.447860 | ||||||||
\(977\) | −54.0203 | −1.72826 | −0.864132 | − | 0.503265i | \(-0.832132\pi\) | ||||
−0.864132 | + | 0.503265i | \(0.832132\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.9756 | −1.08587 | ||||||||
\(980\) | 2.17635 | 0.0695208 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.4552 | −0.397463 | ||||||||
\(983\) | −27.5324 | −0.878146 | −0.439073 | − | 0.898451i | \(-0.644693\pi\) | ||||
−0.439073 | + | 0.898451i | \(0.644693\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.1524 | −0.833284 | ||||||||
\(986\) | −0.499012 | −0.0158918 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.4656 | −0.714726 | ||||||||
\(989\) | −4.91178 | −0.156185 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.915480 | −0.0290812 | −0.0145406 | − | 0.999894i | \(-0.504629\pi\) | ||||
−0.0145406 | + | 0.999894i | \(0.504629\pi\) | |||||||
\(992\) | −68.6199 | −2.17868 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 37.3774 | 1.18554 | ||||||||
\(995\) | −19.3568 | −0.613652 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.5160 | 1.88489 | 0.942446 | − | 0.334359i | \(-0.108520\pi\) | ||||
0.942446 | + | 0.334359i | \(0.108520\pi\) | |||||||
\(998\) | 42.7435 | 1.35302 | ||||||||
\(999\) | 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 | 2151.2.a.k.1.4 | yes | 20 | |
3.2 | odd | 2 | 2151.2.a.j.1.17 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.17 | ✓ | 20 | 3.2 | odd | 2 | ||
2151.2.a.k.1.4 | yes | 20 | 1.1 | even | 1 | trivial |