Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1425,2,Mod(1,1425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1425, 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("1425.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1425 = 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1425.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: | \(11.3786822880\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.523976\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1425.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.523976 | −0.370507 | −0.185254 | − | 0.982691i | \(-0.559311\pi\) | ||||
−0.185254 | + | 0.982691i | \(0.559311\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.72545 | −0.862724 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.523976 | 0.213912 | ||||||||
\(7\) | 3.20147 | 1.21004 | 0.605021 | − | 0.796209i | \(-0.293165\pi\) | ||||
0.605021 | + | 0.796209i | \(0.293165\pi\) | |||||||
\(8\) | 1.95205 | 0.690153 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20147 | 0.663769 | 0.331884 | − | 0.943320i | \(-0.392316\pi\) | ||||
0.331884 | + | 0.943320i | \(0.392316\pi\) | |||||||
\(12\) | 1.72545 | 0.498094 | ||||||||
\(13\) | −3.04795 | −0.845350 | −0.422675 | − | 0.906281i | \(-0.638909\pi\) | ||||
−0.422675 | + | 0.906281i | \(0.638909\pi\) | |||||||
\(14\) | −1.67750 | −0.448330 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.42807 | 0.607018 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −0.523976 | −0.123502 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.20147 | −0.698619 | ||||||||
\(22\) | −1.15352 | −0.245931 | ||||||||
\(23\) | −3.24943 | −0.677552 | −0.338776 | − | 0.940867i | \(-0.610013\pi\) | ||||
−0.338776 | + | 0.940867i | \(0.610013\pi\) | |||||||
\(24\) | −1.95205 | −0.398460 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.59706 | 0.313208 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −5.52398 | −1.04393 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.24943 | −0.224403 | −0.112202 | − | 0.993685i | \(-0.535790\pi\) | ||||
−0.112202 | + | 0.993685i | \(0.535790\pi\) | |||||||
\(32\) | −5.17635 | −0.915057 | ||||||||
\(33\) | −2.20147 | −0.383227 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.72545 | −0.287575 | ||||||||
\(37\) | 3.45090 | 0.567324 | 0.283662 | − | 0.958924i | \(-0.408451\pi\) | ||||
0.283662 | + | 0.958924i | \(0.408451\pi\) | |||||||
\(38\) | −0.523976 | −0.0850002 | ||||||||
\(39\) | 3.04795 | 0.488063 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.55646 | 1.33630 | 0.668148 | − | 0.744029i | \(-0.267087\pi\) | ||||
0.668148 | + | 0.744029i | \(0.267087\pi\) | |||||||
\(42\) | 1.67750 | 0.258843 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −3.79853 | −0.572650 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.70262 | 0.251038 | ||||||||
\(47\) | −3.35499 | −0.489376 | −0.244688 | − | 0.969602i | \(-0.578686\pi\) | ||||
−0.244688 | + | 0.969602i | \(0.578686\pi\) | |||||||
\(48\) | −2.42807 | −0.350462 | ||||||||
\(49\) | 3.24943 | 0.464204 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.25909 | 0.729304 | ||||||||
\(53\) | −0.904094 | −0.124187 | −0.0620935 | − | 0.998070i | \(-0.519778\pi\) | ||||
−0.0620935 | + | 0.998070i | \(0.519778\pi\) | |||||||
\(54\) | 0.523976 | 0.0713042 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.24943 | 0.835115 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | −1.57193 | −0.206404 | ||||||||
\(59\) | 11.2015 | 1.45831 | 0.729154 | − | 0.684350i | \(-0.239914\pi\) | ||||
0.729154 | + | 0.684350i | \(0.239914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.40294 | 0.435702 | 0.217851 | − | 0.975982i | \(-0.430095\pi\) | ||||
0.217851 | + | 0.975982i | \(0.430095\pi\) | |||||||
\(62\) | 0.654669 | 0.0831431 | ||||||||
\(63\) | 3.20147 | 0.403348 | ||||||||
\(64\) | −2.14386 | −0.267982 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.15352 | 0.141988 | ||||||||
\(67\) | 2.29738 | 0.280669 | 0.140335 | − | 0.990104i | \(-0.455182\pi\) | ||||
0.140335 | + | 0.990104i | \(0.455182\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.24943 | 0.391185 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.29738 | 0.866039 | 0.433020 | − | 0.901384i | \(-0.357448\pi\) | ||||
0.433020 | + | 0.901384i | \(0.357448\pi\) | |||||||
\(72\) | 1.95205 | 0.230051 | ||||||||
\(73\) | −1.09591 | −0.128266 | −0.0641330 | − | 0.997941i | \(-0.520428\pi\) | ||||
−0.0641330 | + | 0.997941i | \(0.520428\pi\) | |||||||
\(74\) | −1.80819 | −0.210198 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.72545 | −0.197923 | ||||||||
\(77\) | 7.04795 | 0.803189 | ||||||||
\(78\) | −1.59706 | −0.180831 | ||||||||
\(79\) | 13.5565 | 1.52522 | 0.762611 | − | 0.646858i | \(-0.223917\pi\) | ||||
0.762611 | + | 0.646858i | \(0.223917\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.48339 | −0.495107 | ||||||||
\(83\) | 8.20147 | 0.900229 | 0.450114 | − | 0.892971i | \(-0.351383\pi\) | ||||
0.450114 | + | 0.892971i | \(0.351383\pi\) | |||||||
\(84\) | 5.52398 | 0.602715 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.19181 | 0.452015 | ||||||||
\(87\) | −3.00000 | −0.321634 | ||||||||
\(88\) | 4.29738 | 0.458102 | ||||||||
\(89\) | −7.40294 | −0.784711 | −0.392355 | − | 0.919814i | \(-0.628340\pi\) | ||||
−0.392355 | + | 0.919814i | \(0.628340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.75794 | −1.02291 | ||||||||
\(92\) | 5.60672 | 0.584541 | ||||||||
\(93\) | 1.24943 | 0.129559 | ||||||||
\(94\) | 1.75794 | 0.181317 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.17635 | 0.528309 | ||||||||
\(97\) | 7.14386 | 0.725349 | 0.362674 | − | 0.931916i | \(-0.381864\pi\) | ||||
0.362674 | + | 0.931916i | \(0.381864\pi\) | |||||||
\(98\) | −1.70262 | −0.171991 | ||||||||
\(99\) | 2.20147 | 0.221256 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7579 | 1.36897 | 0.684483 | − | 0.729029i | \(-0.260028\pi\) | ||||
0.684483 | + | 0.729029i | \(0.260028\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.20147 | 0.611049 | 0.305525 | − | 0.952184i | \(-0.401168\pi\) | ||||
0.305525 | + | 0.952184i | \(0.401168\pi\) | |||||||
\(104\) | −5.94975 | −0.583421 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.473724 | 0.0460122 | ||||||||
\(107\) | 15.6044 | 1.50854 | 0.754268 | − | 0.656567i | \(-0.227992\pi\) | ||||
0.754268 | + | 0.656567i | \(0.227992\pi\) | |||||||
\(108\) | 1.72545 | 0.166031 | ||||||||
\(109\) | 7.45090 | 0.713667 | 0.356833 | − | 0.934168i | \(-0.383856\pi\) | ||||
0.356833 | + | 0.934168i | \(0.383856\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.45090 | −0.327545 | ||||||||
\(112\) | 7.77340 | 0.734517 | ||||||||
\(113\) | 15.2494 | 1.43455 | 0.717273 | − | 0.696793i | \(-0.245390\pi\) | ||||
0.717273 | + | 0.696793i | \(0.245390\pi\) | |||||||
\(114\) | 0.523976 | 0.0490749 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.17635 | −0.480612 | ||||||||
\(117\) | −3.04795 | −0.281783 | ||||||||
\(118\) | −5.86931 | −0.540314 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.15352 | −0.559411 | ||||||||
\(122\) | −1.78306 | −0.161431 | ||||||||
\(123\) | −8.55646 | −0.771510 | ||||||||
\(124\) | 2.15582 | 0.193598 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.67750 | −0.149443 | ||||||||
\(127\) | −14.0553 | −1.24721 | −0.623604 | − | 0.781741i | \(-0.714332\pi\) | ||||
−0.623604 | + | 0.781741i | \(0.714332\pi\) | |||||||
\(128\) | 11.4760 | 1.01435 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.34763 | 0.379854 | 0.189927 | − | 0.981798i | \(-0.439175\pi\) | ||||
0.189927 | + | 0.981798i | \(0.439175\pi\) | |||||||
\(132\) | 3.79853 | 0.330619 | ||||||||
\(133\) | 3.20147 | 0.277603 | ||||||||
\(134\) | −1.20377 | −0.103990 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.7077 | 1.68374 | 0.841871 | − | 0.539680i | \(-0.181455\pi\) | ||||
0.841871 | + | 0.539680i | \(0.181455\pi\) | |||||||
\(138\) | −1.70262 | −0.144937 | ||||||||
\(139\) | −15.9115 | −1.34959 | −0.674796 | − | 0.738004i | \(-0.735768\pi\) | ||||
−0.674796 | + | 0.738004i | \(0.735768\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.35499 | 0.282541 | ||||||||
\(142\) | −3.82365 | −0.320874 | ||||||||
\(143\) | −6.70998 | −0.561117 | ||||||||
\(144\) | 2.42807 | 0.202339 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.574229 | 0.0475235 | ||||||||
\(147\) | −3.24943 | −0.268008 | ||||||||
\(148\) | −5.95435 | −0.489444 | ||||||||
\(149\) | −15.8538 | −1.29880 | −0.649399 | − | 0.760448i | \(-0.724979\pi\) | ||||
−0.649399 | + | 0.760448i | \(0.724979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.9018 | 1.53821 | 0.769103 | − | 0.639125i | \(-0.220703\pi\) | ||||
0.769103 | + | 0.639125i | \(0.220703\pi\) | |||||||
\(152\) | 1.95205 | 0.158332 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.69296 | −0.297587 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.25909 | −0.421064 | ||||||||
\(157\) | −14.4606 | −1.15408 | −0.577039 | − | 0.816717i | \(-0.695792\pi\) | ||||
−0.577039 | + | 0.816717i | \(0.695792\pi\) | |||||||
\(158\) | −7.10327 | −0.565106 | ||||||||
\(159\) | 0.904094 | 0.0716994 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.4029 | −0.819867 | ||||||||
\(162\) | −0.523976 | −0.0411675 | ||||||||
\(163\) | −22.0074 | −1.72375 | −0.861875 | − | 0.507121i | \(-0.830710\pi\) | ||||
−0.861875 | + | 0.507121i | \(0.830710\pi\) | |||||||
\(164\) | −14.7637 | −1.15285 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.29738 | −0.333541 | ||||||||
\(167\) | −3.10557 | −0.240316 | −0.120158 | − | 0.992755i | \(-0.538340\pi\) | ||||
−0.120158 | + | 0.992755i | \(0.538340\pi\) | |||||||
\(168\) | −6.24943 | −0.482154 | ||||||||
\(169\) | −3.70998 | −0.285383 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 13.8036 | 1.05251 | ||||||||
\(173\) | 15.9977 | 1.21628 | 0.608141 | − | 0.793829i | \(-0.291915\pi\) | ||||
0.608141 | + | 0.793829i | \(0.291915\pi\) | |||||||
\(174\) | 1.57193 | 0.119168 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.34533 | 0.402919 | ||||||||
\(177\) | −11.2015 | −0.841954 | ||||||||
\(178\) | 3.87897 | 0.290741 | ||||||||
\(179\) | 2.89443 | 0.216340 | 0.108170 | − | 0.994132i | \(-0.465501\pi\) | ||||
0.108170 | + | 0.994132i | \(0.465501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.90179 | 0.513006 | 0.256503 | − | 0.966543i | \(-0.417430\pi\) | ||||
0.256503 | + | 0.966543i | \(0.417430\pi\) | |||||||
\(182\) | 5.11293 | 0.378995 | ||||||||
\(183\) | −3.40294 | −0.251553 | ||||||||
\(184\) | −6.34303 | −0.467614 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.654669 | −0.0480027 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.78887 | 0.422196 | ||||||||
\(189\) | −3.20147 | −0.232873 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.24943 | −0.669265 | −0.334632 | − | 0.942349i | \(-0.608612\pi\) | ||||
−0.334632 | + | 0.942349i | \(0.608612\pi\) | |||||||
\(192\) | 2.14386 | 0.154720 | ||||||||
\(193\) | 1.19411 | 0.0859540 | 0.0429770 | − | 0.999076i | \(-0.486316\pi\) | ||||
0.0429770 | + | 0.999076i | \(0.486316\pi\) | |||||||
\(194\) | −3.74321 | −0.268747 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.60672 | −0.400480 | ||||||||
\(197\) | −17.4509 | −1.24332 | −0.621662 | − | 0.783285i | \(-0.713542\pi\) | ||||
−0.621662 | + | 0.783285i | \(0.713542\pi\) | |||||||
\(198\) | −1.15352 | −0.0819771 | ||||||||
\(199\) | 2.79853 | 0.198382 | 0.0991912 | − | 0.995068i | \(-0.468374\pi\) | ||||
0.0991912 | + | 0.995068i | \(0.468374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.29738 | −0.162045 | ||||||||
\(202\) | −7.20883 | −0.507212 | ||||||||
\(203\) | 9.60442 | 0.674098 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.24943 | −0.226398 | ||||||||
\(207\) | −3.24943 | −0.225851 | ||||||||
\(208\) | −7.40065 | −0.513142 | ||||||||
\(209\) | 2.20147 | 0.152279 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.2471 | −1.80693 | −0.903463 | − | 0.428665i | \(-0.858984\pi\) | ||||
−0.903463 | + | 0.428665i | \(0.858984\pi\) | |||||||
\(212\) | 1.55997 | 0.107139 | ||||||||
\(213\) | −7.29738 | −0.500008 | ||||||||
\(214\) | −8.17635 | −0.558924 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.95205 | −0.132820 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | −3.90409 | −0.264419 | ||||||||
\(219\) | 1.09591 | 0.0740544 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.80819 | 0.121358 | ||||||||
\(223\) | 13.2494 | 0.887247 | 0.443624 | − | 0.896213i | \(-0.353693\pi\) | ||||
0.443624 | + | 0.896213i | \(0.353693\pi\) | |||||||
\(224\) | −16.5719 | −1.10726 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.99034 | −0.531509 | ||||||||
\(227\) | −7.29738 | −0.484344 | −0.242172 | − | 0.970233i | \(-0.577860\pi\) | ||||
−0.242172 | + | 0.970233i | \(0.577860\pi\) | |||||||
\(228\) | 1.72545 | 0.114271 | ||||||||
\(229\) | 15.8635 | 1.04829 | 0.524145 | − | 0.851629i | \(-0.324385\pi\) | ||||
0.524145 | + | 0.851629i | \(0.324385\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.04795 | −0.463721 | ||||||||
\(232\) | 5.85614 | 0.384475 | ||||||||
\(233\) | 8.64501 | 0.566353 | 0.283177 | − | 0.959068i | \(-0.408612\pi\) | ||||
0.283177 | + | 0.959068i | \(0.408612\pi\) | |||||||
\(234\) | 1.59706 | 0.104403 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −19.3276 | −1.25812 | ||||||||
\(237\) | −13.5565 | −0.880587 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.7579 | 1.66614 | 0.833071 | − | 0.553166i | \(-0.186580\pi\) | ||||
0.833071 | + | 0.553166i | \(0.186580\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.59706 | 0.618201 | 0.309100 | − | 0.951029i | \(-0.399972\pi\) | ||||
0.309100 | + | 0.951029i | \(0.399972\pi\) | |||||||
\(242\) | 3.22430 | 0.207266 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.87161 | −0.375891 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.48339 | 0.285850 | ||||||||
\(247\) | −3.04795 | −0.193937 | ||||||||
\(248\) | −2.43894 | −0.154873 | ||||||||
\(249\) | −8.20147 | −0.519747 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.6118 | 1.11165 | 0.555823 | − | 0.831301i | \(-0.312403\pi\) | ||||
0.555823 | + | 0.831301i | \(0.312403\pi\) | |||||||
\(252\) | −5.52398 | −0.347978 | ||||||||
\(253\) | −7.15352 | −0.449738 | ||||||||
\(254\) | 7.36465 | 0.462099 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.72545 | −0.107841 | ||||||||
\(257\) | −0.692961 | −0.0432257 | −0.0216129 | − | 0.999766i | \(-0.506880\pi\) | ||||
−0.0216129 | + | 0.999766i | \(0.506880\pi\) | |||||||
\(258\) | −4.19181 | −0.260971 | ||||||||
\(259\) | 11.0480 | 0.686486 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | −2.27806 | −0.140739 | ||||||||
\(263\) | 23.5062 | 1.44946 | 0.724728 | − | 0.689036i | \(-0.241966\pi\) | ||||
0.724728 | + | 0.689036i | \(0.241966\pi\) | |||||||
\(264\) | −4.29738 | −0.264485 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.67750 | −0.102854 | ||||||||
\(267\) | 7.40294 | 0.453053 | ||||||||
\(268\) | −3.96401 | −0.242140 | ||||||||
\(269\) | −10.6141 | −0.647152 | −0.323576 | − | 0.946202i | \(-0.604885\pi\) | ||||
−0.323576 | + | 0.946202i | \(0.604885\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.2974 | 0.929250 | 0.464625 | − | 0.885508i | \(-0.346189\pi\) | ||||
0.464625 | + | 0.885508i | \(0.346189\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.75794 | 0.590577 | ||||||||
\(274\) | −10.3264 | −0.623838 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.60672 | −0.337485 | ||||||||
\(277\) | −19.5948 | −1.17733 | −0.588667 | − | 0.808375i | \(-0.700347\pi\) | ||||
−0.588667 | + | 0.808375i | \(0.700347\pi\) | |||||||
\(278\) | 8.33723 | 0.500034 | ||||||||
\(279\) | −1.24943 | −0.0748011 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.5542 | −1.82271 | −0.911354 | − | 0.411623i | \(-0.864962\pi\) | ||||
−0.911354 | + | 0.411623i | \(0.864962\pi\) | |||||||
\(282\) | −1.75794 | −0.104684 | ||||||||
\(283\) | 8.61408 | 0.512054 | 0.256027 | − | 0.966670i | \(-0.417586\pi\) | ||||
0.256027 | + | 0.966670i | \(0.417586\pi\) | |||||||
\(284\) | −12.5913 | −0.747153 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.51587 | 0.207898 | ||||||||
\(287\) | 27.3933 | 1.61697 | ||||||||
\(288\) | −5.17635 | −0.305019 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.14386 | −0.418780 | ||||||||
\(292\) | 1.89093 | 0.110658 | ||||||||
\(293\) | 29.5565 | 1.72671 | 0.863354 | − | 0.504600i | \(-0.168360\pi\) | ||||
0.863354 | + | 0.504600i | \(0.168360\pi\) | |||||||
\(294\) | 1.70262 | 0.0992989 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.73631 | 0.391540 | ||||||||
\(297\) | −2.20147 | −0.127742 | ||||||||
\(298\) | 8.30704 | 0.481214 | ||||||||
\(299\) | 9.90409 | 0.572769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.6118 | −1.47624 | ||||||||
\(302\) | −9.90409 | −0.569917 | ||||||||
\(303\) | −13.7579 | −0.790373 | ||||||||
\(304\) | 2.42807 | 0.139259 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9115 | −0.965188 | −0.482594 | − | 0.875844i | \(-0.660305\pi\) | ||||
−0.482594 | + | 0.875844i | \(0.660305\pi\) | |||||||
\(308\) | −12.1609 | −0.692931 | ||||||||
\(309\) | −6.20147 | −0.352789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.0959 | 0.799305 | 0.399653 | − | 0.916667i | \(-0.369131\pi\) | ||||
0.399653 | + | 0.916667i | \(0.369131\pi\) | |||||||
\(312\) | 5.94975 | 0.336838 | ||||||||
\(313\) | 4.05531 | 0.229220 | 0.114610 | − | 0.993411i | \(-0.463438\pi\) | ||||
0.114610 | + | 0.993411i | \(0.463438\pi\) | |||||||
\(314\) | 7.57699 | 0.427594 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.3910 | −1.31585 | ||||||||
\(317\) | −21.9977 | −1.23551 | −0.617757 | − | 0.786369i | \(-0.711958\pi\) | ||||
−0.617757 | + | 0.786369i | \(0.711958\pi\) | |||||||
\(318\) | −0.473724 | −0.0265651 | ||||||||
\(319\) | 6.60442 | 0.369776 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.6044 | −0.870954 | ||||||||
\(322\) | 5.45090 | 0.303767 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.72545 | −0.0958583 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.5313 | 0.638662 | ||||||||
\(327\) | −7.45090 | −0.412036 | ||||||||
\(328\) | 16.7026 | 0.922248 | ||||||||
\(329\) | −10.7409 | −0.592166 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4583 | 0.684768 | 0.342384 | − | 0.939560i | \(-0.388766\pi\) | ||||
0.342384 | + | 0.939560i | \(0.388766\pi\) | |||||||
\(332\) | −14.1512 | −0.776649 | ||||||||
\(333\) | 3.45090 | 0.189108 | ||||||||
\(334\) | 1.62724 | 0.0890388 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.77340 | −0.424074 | ||||||||
\(337\) | −20.4989 | −1.11664 | −0.558322 | − | 0.829624i | \(-0.688555\pi\) | ||||
−0.558322 | + | 0.829624i | \(0.688555\pi\) | |||||||
\(338\) | 1.94394 | 0.105737 | ||||||||
\(339\) | −15.2494 | −0.828235 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.75057 | −0.148952 | ||||||||
\(342\) | −0.523976 | −0.0283334 | ||||||||
\(343\) | −12.0074 | −0.648337 | ||||||||
\(344\) | −15.6164 | −0.841979 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.38242 | −0.450642 | ||||||||
\(347\) | 4.45320 | 0.239060 | 0.119530 | − | 0.992831i | \(-0.461861\pi\) | ||||
0.119530 | + | 0.992831i | \(0.461861\pi\) | |||||||
\(348\) | 5.17635 | 0.277481 | ||||||||
\(349\) | −9.30704 | −0.498194 | −0.249097 | − | 0.968478i | \(-0.580134\pi\) | ||||
−0.249097 | + | 0.968478i | \(0.580134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.04795 | 0.162688 | ||||||||
\(352\) | −11.3956 | −0.607387 | ||||||||
\(353\) | 16.6141 | 0.884278 | 0.442139 | − | 0.896947i | \(-0.354220\pi\) | ||||
0.442139 | + | 0.896947i | \(0.354220\pi\) | |||||||
\(354\) | 5.86931 | 0.311950 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.7734 | 0.676989 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.51661 | −0.0801556 | ||||||||
\(359\) | 29.9497 | 1.58069 | 0.790344 | − | 0.612664i | \(-0.209902\pi\) | ||||
0.790344 | + | 0.612664i | \(0.209902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −3.61638 | −0.190073 | ||||||||
\(363\) | 6.15352 | 0.322976 | ||||||||
\(364\) | 16.8368 | 0.882489 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.78306 | 0.0932022 | ||||||||
\(367\) | 28.1106 | 1.46736 | 0.733681 | − | 0.679494i | \(-0.237800\pi\) | ||||
0.733681 | + | 0.679494i | \(0.237800\pi\) | |||||||
\(368\) | −7.88983 | −0.411286 | ||||||||
\(369\) | 8.55646 | 0.445432 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.89443 | −0.150271 | ||||||||
\(372\) | −2.15582 | −0.111774 | ||||||||
\(373\) | −10.5948 | −0.548576 | −0.274288 | − | 0.961648i | \(-0.588442\pi\) | ||||
−0.274288 | + | 0.961648i | \(0.588442\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.54910 | −0.337744 | ||||||||
\(377\) | −9.14386 | −0.470933 | ||||||||
\(378\) | 1.67750 | 0.0862811 | ||||||||
\(379\) | 3.04795 | 0.156563 | 0.0782814 | − | 0.996931i | \(-0.475057\pi\) | ||||
0.0782814 | + | 0.996931i | \(0.475057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.0553 | 0.720076 | ||||||||
\(382\) | 4.84648 | 0.247968 | ||||||||
\(383\) | 16.6021 | 0.848329 | 0.424164 | − | 0.905585i | \(-0.360568\pi\) | ||||
0.424164 | + | 0.905585i | \(0.360568\pi\) | |||||||
\(384\) | −11.4760 | −0.585633 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.625686 | −0.0318466 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | −12.3264 | −0.625776 | ||||||||
\(389\) | 7.25909 | 0.368050 | 0.184025 | − | 0.982922i | \(-0.441087\pi\) | ||||
0.184025 | + | 0.982922i | \(0.441087\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.34303 | 0.320371 | ||||||||
\(393\) | −4.34763 | −0.219309 | ||||||||
\(394\) | 9.14386 | 0.460661 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.79853 | −0.190883 | ||||||||
\(397\) | −20.2664 | −1.01714 | −0.508572 | − | 0.861020i | \(-0.669826\pi\) | ||||
−0.508572 | + | 0.861020i | \(0.669826\pi\) | |||||||
\(398\) | −1.46636 | −0.0735021 | ||||||||
\(399\) | −3.20147 | −0.160274 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.24943 | −0.162269 | −0.0811343 | − | 0.996703i | \(-0.525854\pi\) | ||||
−0.0811343 | + | 0.996703i | \(0.525854\pi\) | |||||||
\(402\) | 1.20377 | 0.0600387 | ||||||||
\(403\) | 3.80819 | 0.189699 | ||||||||
\(404\) | −23.7386 | −1.18104 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.03249 | −0.249758 | ||||||||
\(407\) | 7.59706 | 0.376572 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.0457 | 1.68345 | 0.841725 | − | 0.539907i | \(-0.181541\pi\) | ||||
0.841725 | + | 0.539907i | \(0.181541\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.7077 | −0.972108 | ||||||||
\(412\) | −10.7003 | −0.527167 | ||||||||
\(413\) | 35.8612 | 1.76461 | ||||||||
\(414\) | 1.70262 | 0.0836793 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.7773 | 0.773544 | ||||||||
\(417\) | 15.9115 | 0.779187 | ||||||||
\(418\) | −1.15352 | −0.0564205 | ||||||||
\(419\) | 26.2568 | 1.28273 | 0.641364 | − | 0.767237i | \(-0.278369\pi\) | ||||
0.641364 | + | 0.767237i | \(0.278369\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7579 | −0.573047 | −0.286523 | − | 0.958073i | \(-0.592500\pi\) | ||||
−0.286523 | + | 0.958073i | \(0.592500\pi\) | |||||||
\(422\) | 13.7529 | 0.669479 | ||||||||
\(423\) | −3.35499 | −0.163125 | ||||||||
\(424\) | −1.76483 | −0.0857080 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.82365 | 0.185257 | ||||||||
\(427\) | 10.8944 | 0.527219 | ||||||||
\(428\) | −26.9246 | −1.30145 | ||||||||
\(429\) | 6.70998 | 0.323961 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.0051 | −1.30079 | −0.650394 | − | 0.759597i | \(-0.725396\pi\) | ||||
−0.650394 | + | 0.759597i | \(0.725396\pi\) | |||||||
\(432\) | −2.42807 | −0.116821 | ||||||||
\(433\) | −14.6597 | −0.704502 | −0.352251 | − | 0.935906i | \(-0.614584\pi\) | ||||
−0.352251 | + | 0.935906i | \(0.614584\pi\) | |||||||
\(434\) | 2.09591 | 0.100607 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.8561 | −0.615698 | ||||||||
\(437\) | −3.24943 | −0.155441 | ||||||||
\(438\) | −0.574229 | −0.0274377 | ||||||||
\(439\) | −22.7653 | −1.08653 | −0.543264 | − | 0.839562i | \(-0.682812\pi\) | ||||
−0.543264 | + | 0.839562i | \(0.682812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.24943 | 0.154735 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39.3601 | −1.87005 | −0.935026 | − | 0.354578i | \(-0.884624\pi\) | ||||
−0.935026 | + | 0.354578i | \(0.884624\pi\) | |||||||
\(444\) | 5.95435 | 0.282581 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.94239 | −0.328732 | ||||||||
\(447\) | 15.8538 | 0.749861 | ||||||||
\(448\) | −6.86350 | −0.324270 | ||||||||
\(449\) | −12.3047 | −0.580697 | −0.290348 | − | 0.956921i | \(-0.593771\pi\) | ||||
−0.290348 | + | 0.956921i | \(0.593771\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.8368 | 0.886991 | ||||||||
\(452\) | −26.3121 | −1.23762 | ||||||||
\(453\) | −18.9018 | −0.888084 | ||||||||
\(454\) | 3.82365 | 0.179453 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.95205 | −0.0914130 | ||||||||
\(457\) | 3.15122 | 0.147408 | 0.0737039 | − | 0.997280i | \(-0.476518\pi\) | ||||
0.0737039 | + | 0.997280i | \(0.476518\pi\) | |||||||
\(458\) | −8.31210 | −0.388399 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.0457 | −1.49251 | −0.746257 | − | 0.665657i | \(-0.768151\pi\) | ||||
−0.746257 | + | 0.665657i | \(0.768151\pi\) | |||||||
\(462\) | 3.69296 | 0.171812 | ||||||||
\(463\) | 19.0936 | 0.887355 | 0.443678 | − | 0.896186i | \(-0.353674\pi\) | ||||
0.443678 | + | 0.896186i | \(0.353674\pi\) | |||||||
\(464\) | 7.28421 | 0.338161 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.52978 | −0.209838 | ||||||||
\(467\) | 0.105567 | 0.00488505 | 0.00244252 | − | 0.999997i | \(-0.499223\pi\) | ||||
0.00244252 | + | 0.999997i | \(0.499223\pi\) | |||||||
\(468\) | 5.25909 | 0.243101 | ||||||||
\(469\) | 7.35499 | 0.339622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4606 | 0.666307 | ||||||||
\(472\) | 21.8658 | 1.00646 | ||||||||
\(473\) | −17.6118 | −0.809790 | ||||||||
\(474\) | 7.10327 | 0.326264 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.904094 | −0.0413956 | ||||||||
\(478\) | −13.4966 | −0.617318 | ||||||||
\(479\) | −29.2951 | −1.33853 | −0.669263 | − | 0.743025i | \(-0.733390\pi\) | ||||
−0.669263 | + | 0.743025i | \(0.733390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5182 | −0.479587 | ||||||||
\(482\) | −5.02863 | −0.229048 | ||||||||
\(483\) | 10.4029 | 0.473350 | ||||||||
\(484\) | 10.6176 | 0.482617 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.523976 | 0.0237681 | ||||||||
\(487\) | −6.24206 | −0.282855 | −0.141427 | − | 0.989949i | \(-0.545169\pi\) | ||||
−0.141427 | + | 0.989949i | \(0.545169\pi\) | |||||||
\(488\) | 6.64271 | 0.300701 | ||||||||
\(489\) | 22.0074 | 0.995207 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.5182 | −0.655196 | −0.327598 | − | 0.944817i | \(-0.606239\pi\) | ||||
−0.327598 | + | 0.944817i | \(0.606239\pi\) | |||||||
\(492\) | 14.7637 | 0.665601 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.59706 | 0.0718549 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.03369 | −0.136217 | ||||||||
\(497\) | 23.3624 | 1.04794 | ||||||||
\(498\) | 4.29738 | 0.192570 | ||||||||
\(499\) | 0.913756 | 0.0409053 | 0.0204527 | − | 0.999791i | \(-0.493489\pi\) | ||||
0.0204527 | + | 0.999791i | \(0.493489\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.10557 | 0.138746 | ||||||||
\(502\) | −9.22816 | −0.411873 | ||||||||
\(503\) | 27.8538 | 1.24194 | 0.620971 | − | 0.783834i | \(-0.286739\pi\) | ||||
0.620971 | + | 0.783834i | \(0.286739\pi\) | |||||||
\(504\) | 6.24943 | 0.278372 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.74828 | 0.166631 | ||||||||
\(507\) | 3.70998 | 0.164766 | ||||||||
\(508\) | 24.2517 | 1.07600 | ||||||||
\(509\) | −31.5136 | −1.39681 | −0.698407 | − | 0.715701i | \(-0.746108\pi\) | ||||
−0.698407 | + | 0.715701i | \(0.746108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.50851 | −0.155207 | ||||||||
\(512\) | −22.0480 | −0.974391 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0.363095 | 0.0160154 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.8036 | −0.607669 | ||||||||
\(517\) | −7.38592 | −0.324832 | ||||||||
\(518\) | −5.78887 | −0.254348 | ||||||||
\(519\) | −15.9977 | −0.702221 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.49885 | −0.416152 | −0.208076 | − | 0.978113i | \(-0.566720\pi\) | ||||
−0.208076 | + | 0.978113i | \(0.566720\pi\) | |||||||
\(522\) | −1.57193 | −0.0688015 | ||||||||
\(523\) | 23.9691 | 1.04809 | 0.524047 | − | 0.851689i | \(-0.324422\pi\) | ||||
0.524047 | + | 0.851689i | \(0.324422\pi\) | |||||||
\(524\) | −7.50161 | −0.327709 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.3167 | −0.537034 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −5.34533 | −0.232626 | ||||||||
\(529\) | −12.4412 | −0.540923 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2015 | 0.486102 | ||||||||
\(532\) | −5.52398 | −0.239495 | ||||||||
\(533\) | −26.0797 | −1.12964 | ||||||||
\(534\) | −3.87897 | −0.167859 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.48459 | 0.193705 | ||||||||
\(537\) | −2.89443 | −0.124904 | ||||||||
\(538\) | 5.56153 | 0.239774 | ||||||||
\(539\) | 7.15352 | 0.308124 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.9401 | 0.943278 | 0.471639 | − | 0.881792i | \(-0.343663\pi\) | ||||
0.471639 | + | 0.881792i | \(0.343663\pi\) | |||||||
\(542\) | −8.01546 | −0.344294 | ||||||||
\(543\) | −6.90179 | −0.296184 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.11293 | −0.218813 | ||||||||
\(547\) | 39.0074 | 1.66783 | 0.833917 | − | 0.551890i | \(-0.186093\pi\) | ||||
0.833917 | + | 0.551890i | \(0.186093\pi\) | |||||||
\(548\) | −34.0046 | −1.45260 | ||||||||
\(549\) | 3.40294 | 0.145234 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | 0.127804 | ||||||||
\(552\) | 6.34303 | 0.269977 | ||||||||
\(553\) | 43.4006 | 1.84558 | ||||||||
\(554\) | 10.2672 | 0.436211 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.4544 | 1.16433 | ||||||||
\(557\) | 26.0959 | 1.10572 | 0.552860 | − | 0.833274i | \(-0.313537\pi\) | ||||
0.552860 | + | 0.833274i | \(0.313537\pi\) | |||||||
\(558\) | 0.654669 | 0.0277144 | ||||||||
\(559\) | 24.3836 | 1.03132 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.0097 | 0.675327 | ||||||||
\(563\) | −20.8944 | −0.880595 | −0.440298 | − | 0.897852i | \(-0.645127\pi\) | ||||
−0.440298 | + | 0.897852i | \(0.645127\pi\) | |||||||
\(564\) | −5.78887 | −0.243755 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.51357 | −0.189720 | ||||||||
\(567\) | 3.20147 | 0.134449 | ||||||||
\(568\) | 14.2448 | 0.597700 | ||||||||
\(569\) | −39.8419 | −1.67026 | −0.835129 | − | 0.550054i | \(-0.814607\pi\) | ||||
−0.835129 | + | 0.550054i | \(0.814607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.7173 | 0.699599 | 0.349800 | − | 0.936825i | \(-0.386250\pi\) | ||||
0.349800 | + | 0.936825i | \(0.386250\pi\) | |||||||
\(572\) | 11.5777 | 0.484089 | ||||||||
\(573\) | 9.24943 | 0.386400 | ||||||||
\(574\) | −14.3534 | −0.599101 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.14386 | −0.0893274 | ||||||||
\(577\) | −36.0360 | −1.50020 | −0.750099 | − | 0.661326i | \(-0.769994\pi\) | ||||
−0.750099 | + | 0.661326i | \(0.769994\pi\) | |||||||
\(578\) | 8.90760 | 0.370507 | ||||||||
\(579\) | −1.19411 | −0.0496255 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.2568 | 1.08932 | ||||||||
\(582\) | 3.74321 | 0.155161 | ||||||||
\(583\) | −1.99034 | −0.0824314 | ||||||||
\(584\) | −2.13926 | −0.0885232 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.4869 | −0.639758 | ||||||||
\(587\) | −3.95941 | −0.163422 | −0.0817111 | − | 0.996656i | \(-0.526038\pi\) | ||||
−0.0817111 | + | 0.996656i | \(0.526038\pi\) | |||||||
\(588\) | 5.60672 | 0.231217 | ||||||||
\(589\) | −1.24943 | −0.0514817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.4509 | 0.717834 | ||||||||
\(592\) | 8.37902 | 0.344376 | ||||||||
\(593\) | −21.1439 | −0.868274 | −0.434137 | − | 0.900847i | \(-0.642947\pi\) | ||||
−0.434137 | + | 0.900847i | \(0.642947\pi\) | |||||||
\(594\) | 1.15352 | 0.0473295 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 27.3550 | 1.12050 | ||||||||
\(597\) | −2.79853 | −0.114536 | ||||||||
\(598\) | −5.18951 | −0.212215 | ||||||||
\(599\) | 4.19181 | 0.171273 | 0.0856364 | − | 0.996326i | \(-0.472708\pi\) | ||||
0.0856364 | + | 0.996326i | \(0.472708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.54910 | −0.185562 | −0.0927809 | − | 0.995687i | \(-0.529576\pi\) | ||||
−0.0927809 | + | 0.995687i | \(0.529576\pi\) | |||||||
\(602\) | 13.4200 | 0.546957 | ||||||||
\(603\) | 2.29738 | 0.0935565 | ||||||||
\(604\) | −32.6141 | −1.32705 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.20883 | 0.292839 | ||||||||
\(607\) | 34.6044 | 1.40455 | 0.702275 | − | 0.711906i | \(-0.252168\pi\) | ||||
0.702275 | + | 0.711906i | \(0.252168\pi\) | |||||||
\(608\) | −5.17635 | −0.209929 | ||||||||
\(609\) | −9.60442 | −0.389191 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2259 | 0.413694 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.13420 | −0.166979 | −0.0834893 | − | 0.996509i | \(-0.526606\pi\) | ||||
−0.0834893 | + | 0.996509i | \(0.526606\pi\) | |||||||
\(614\) | 8.86120 | 0.357609 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.7579 | 0.554323 | ||||||||
\(617\) | 17.2398 | 0.694047 | 0.347023 | − | 0.937856i | \(-0.387192\pi\) | ||||
0.347023 | + | 0.937856i | \(0.387192\pi\) | |||||||
\(618\) | 3.24943 | 0.130711 | ||||||||
\(619\) | −39.0244 | −1.56852 | −0.784261 | − | 0.620431i | \(-0.786958\pi\) | ||||
−0.784261 | + | 0.620431i | \(0.786958\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.24943 | 0.130395 | ||||||||
\(622\) | −7.38592 | −0.296148 | ||||||||
\(623\) | −23.7003 | −0.949533 | ||||||||
\(624\) | 7.40065 | 0.296263 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.12489 | −0.0849276 | ||||||||
\(627\) | −2.20147 | −0.0879183 | ||||||||
\(628\) | 24.9510 | 0.995651 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0959 | 1.35734 | 0.678668 | − | 0.734445i | \(-0.262557\pi\) | ||||
0.678668 | + | 0.734445i | \(0.262557\pi\) | |||||||
\(632\) | 26.4629 | 1.05264 | ||||||||
\(633\) | 26.2471 | 1.04323 | ||||||||
\(634\) | 11.5263 | 0.457767 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.55997 | −0.0618568 | ||||||||
\(637\) | −9.90409 | −0.392415 | ||||||||
\(638\) | −3.46056 | −0.137005 | ||||||||
\(639\) | 7.29738 | 0.288680 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.8036 | 1.09818 | 0.549088 | − | 0.835765i | \(-0.314975\pi\) | ||||
0.549088 | + | 0.835765i | \(0.314975\pi\) | |||||||
\(642\) | 8.17635 | 0.322695 | ||||||||
\(643\) | −40.2185 | −1.58606 | −0.793031 | − | 0.609181i | \(-0.791498\pi\) | ||||
−0.793031 | + | 0.609181i | \(0.791498\pi\) | |||||||
\(644\) | 17.9497 | 0.707319 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.1512 | −0.792226 | −0.396113 | − | 0.918202i | \(-0.629641\pi\) | ||||
−0.396113 | + | 0.918202i | \(0.629641\pi\) | |||||||
\(648\) | 1.95205 | 0.0766837 | ||||||||
\(649\) | 24.6597 | 0.967979 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | 37.9726 | 1.48712 | ||||||||
\(653\) | −26.7556 | −1.04703 | −0.523514 | − | 0.852017i | \(-0.675379\pi\) | ||||
−0.523514 | + | 0.852017i | \(0.675379\pi\) | |||||||
\(654\) | 3.90409 | 0.152662 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20.7757 | 0.811155 | ||||||||
\(657\) | −1.09591 | −0.0427553 | ||||||||
\(658\) | 5.62799 | 0.219402 | ||||||||
\(659\) | 17.6118 | 0.686057 | 0.343029 | − | 0.939325i | \(-0.388547\pi\) | ||||
0.343029 | + | 0.939325i | \(0.388547\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.5159 | 0.447916 | 0.223958 | − | 0.974599i | \(-0.428102\pi\) | ||||
0.223958 | + | 0.974599i | \(0.428102\pi\) | |||||||
\(662\) | −6.52783 | −0.253711 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.0097 | 0.621295 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.80819 | −0.0700659 | ||||||||
\(667\) | −9.74828 | −0.377455 | ||||||||
\(668\) | 5.35850 | 0.207326 | ||||||||
\(669\) | −13.2494 | −0.512252 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.49149 | 0.289206 | ||||||||
\(672\) | 16.5719 | 0.639276 | ||||||||
\(673\) | 7.85384 | 0.302743 | 0.151372 | − | 0.988477i | \(-0.451631\pi\) | ||||
0.151372 | + | 0.988477i | \(0.451631\pi\) | |||||||
\(674\) | 10.7409 | 0.413725 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.40139 | 0.246207 | ||||||||
\(677\) | −43.5136 | −1.67236 | −0.836181 | − | 0.548453i | \(-0.815217\pi\) | ||||
−0.836181 | + | 0.548453i | \(0.815217\pi\) | |||||||
\(678\) | 7.99034 | 0.306867 | ||||||||
\(679\) | 22.8709 | 0.877703 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.29738 | 0.279636 | ||||||||
\(682\) | 1.44124 | 0.0551878 | ||||||||
\(683\) | 4.60212 | 0.176095 | 0.0880476 | − | 0.996116i | \(-0.471937\pi\) | ||||
0.0880476 | + | 0.996116i | \(0.471937\pi\) | |||||||
\(684\) | −1.72545 | −0.0659742 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.29157 | 0.240213 | ||||||||
\(687\) | −15.8635 | −0.605230 | ||||||||
\(688\) | −19.4246 | −0.740555 | ||||||||
\(689\) | 2.75564 | 0.104981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5948 | 1.08780 | 0.543898 | − | 0.839151i | \(-0.316948\pi\) | ||||
0.543898 | + | 0.839151i | \(0.316948\pi\) | |||||||
\(692\) | −27.6032 | −1.04932 | ||||||||
\(693\) | 7.04795 | 0.267730 | ||||||||
\(694\) | −2.33337 | −0.0885735 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.85614 | −0.221976 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 4.87667 | 0.184585 | ||||||||
\(699\) | −8.64501 | −0.326984 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.2111 | −0.687825 | −0.343913 | − | 0.939002i | \(-0.611752\pi\) | ||||
−0.343913 | + | 0.939002i | \(0.611752\pi\) | |||||||
\(702\) | −1.59706 | −0.0602770 | ||||||||
\(703\) | 3.45090 | 0.130153 | ||||||||
\(704\) | −4.71964 | −0.177878 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.70538 | −0.327631 | ||||||||
\(707\) | 44.0457 | 1.65651 | ||||||||
\(708\) | 19.3276 | 0.726374 | ||||||||
\(709\) | −10.6930 | −0.401583 | −0.200791 | − | 0.979634i | \(-0.564351\pi\) | ||||
−0.200791 | + | 0.979634i | \(0.564351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.5565 | 0.508407 | ||||||||
\(712\) | −14.4509 | −0.541570 | ||||||||
\(713\) | 4.05991 | 0.152045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.99420 | −0.186642 | ||||||||
\(717\) | −25.7579 | −0.961948 | ||||||||
\(718\) | −15.6930 | −0.585656 | ||||||||
\(719\) | −41.9548 | −1.56465 | −0.782325 | − | 0.622870i | \(-0.785966\pi\) | ||||
−0.782325 | + | 0.622870i | \(0.785966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8538 | 0.739396 | ||||||||
\(722\) | −0.523976 | −0.0195004 | ||||||||
\(723\) | −9.59706 | −0.356918 | ||||||||
\(724\) | −11.9087 | −0.442583 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.22430 | −0.119665 | ||||||||
\(727\) | 28.4103 | 1.05368 | 0.526840 | − | 0.849964i | \(-0.323377\pi\) | ||||
0.526840 | + | 0.849964i | \(0.323377\pi\) | |||||||
\(728\) | −19.0480 | −0.705964 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 5.87161 | 0.217021 | ||||||||
\(733\) | −14.6930 | −0.542697 | −0.271348 | − | 0.962481i | \(-0.587470\pi\) | ||||
−0.271348 | + | 0.962481i | \(0.587470\pi\) | |||||||
\(734\) | −14.7293 | −0.543669 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.8201 | 0.619999 | ||||||||
\(737\) | 5.05761 | 0.186300 | ||||||||
\(738\) | −4.48339 | −0.165036 | ||||||||
\(739\) | 14.4103 | 0.530092 | 0.265046 | − | 0.964236i | \(-0.414613\pi\) | ||||
0.265046 | + | 0.964236i | \(0.414613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.04795 | 0.111969 | ||||||||
\(742\) | 1.51661 | 0.0556767 | ||||||||
\(743\) | −31.5851 | −1.15874 | −0.579372 | − | 0.815063i | \(-0.696702\pi\) | ||||
−0.579372 | + | 0.815063i | \(0.696702\pi\) | |||||||
\(744\) | 2.43894 | 0.0894158 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.55140 | 0.203251 | ||||||||
\(747\) | 8.20147 | 0.300076 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.9571 | 1.82539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.4509 | 0.928716 | 0.464358 | − | 0.885647i | \(-0.346285\pi\) | ||||
0.464358 | + | 0.885647i | \(0.346285\pi\) | |||||||
\(752\) | −8.14616 | −0.297060 | ||||||||
\(753\) | −17.6118 | −0.641809 | ||||||||
\(754\) | 4.79117 | 0.174484 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.52398 | 0.200905 | ||||||||
\(757\) | −14.0170 | −0.509457 | −0.254729 | − | 0.967013i | \(-0.581986\pi\) | ||||
−0.254729 | + | 0.967013i | \(0.581986\pi\) | |||||||
\(758\) | −1.59706 | −0.0580077 | ||||||||
\(759\) | 7.15352 | 0.259656 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.2738 | −1.71367 | −0.856837 | − | 0.515587i | \(-0.827574\pi\) | ||||
−0.856837 | + | 0.515587i | \(0.827574\pi\) | |||||||
\(762\) | −7.36465 | −0.266793 | ||||||||
\(763\) | 23.8538 | 0.863567 | ||||||||
\(764\) | 15.9594 | 0.577391 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.69912 | −0.314312 | ||||||||
\(767\) | −34.1416 | −1.23278 | ||||||||
\(768\) | 1.72545 | 0.0622618 | ||||||||
\(769\) | 26.0936 | 0.940960 | 0.470480 | − | 0.882411i | \(-0.344081\pi\) | ||||
0.470480 | + | 0.882411i | \(0.344081\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.692961 | 0.0249564 | ||||||||
\(772\) | −2.06038 | −0.0741546 | ||||||||
\(773\) | −23.6501 | −0.850634 | −0.425317 | − | 0.905044i | \(-0.639837\pi\) | ||||
−0.425317 | + | 0.905044i | \(0.639837\pi\) | |||||||
\(774\) | 4.19181 | 0.150672 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.9451 | 0.500602 | ||||||||
\(777\) | −11.0480 | −0.396343 | ||||||||
\(778\) | −3.80359 | −0.136365 | ||||||||
\(779\) | 8.55646 | 0.306567 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0650 | 0.574850 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.00000 | −0.107211 | ||||||||
\(784\) | 7.88983 | 0.281780 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.27806 | 0.0812556 | ||||||||
\(787\) | 22.8156 | 0.813287 | 0.406643 | − | 0.913587i | \(-0.366699\pi\) | ||||
0.406643 | + | 0.913587i | \(0.366699\pi\) | |||||||
\(788\) | 30.1106 | 1.07265 | ||||||||
\(789\) | −23.5062 | −0.836843 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.8206 | 1.73586 | ||||||||
\(792\) | 4.29738 | 0.152701 | ||||||||
\(793\) | −10.3720 | −0.368321 | ||||||||
\(794\) | 10.6191 | 0.376859 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.82872 | −0.171149 | ||||||||
\(797\) | −0.748275 | −0.0265053 | −0.0132526 | − | 0.999912i | \(-0.504219\pi\) | ||||
−0.0132526 | + | 0.999912i | \(0.504219\pi\) | |||||||
\(798\) | 1.67750 | 0.0593827 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.40294 | −0.261570 | ||||||||
\(802\) | 1.70262 | 0.0601217 | ||||||||
\(803\) | −2.41261 | −0.0851390 | ||||||||
\(804\) | 3.96401 | 0.139800 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.99540 | −0.0702850 | ||||||||
\(807\) | 10.6141 | 0.373633 | ||||||||
\(808\) | 26.8561 | 0.944796 | ||||||||
\(809\) | 50.1563 | 1.76340 | 0.881700 | − | 0.471810i | \(-0.156399\pi\) | ||||
0.881700 | + | 0.471810i | \(0.156399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.9903 | 0.982874 | 0.491437 | − | 0.870913i | \(-0.336472\pi\) | ||||
0.491437 | + | 0.870913i | \(0.336472\pi\) | |||||||
\(812\) | −16.5719 | −0.581561 | ||||||||
\(813\) | −15.2974 | −0.536502 | ||||||||
\(814\) | −3.98068 | −0.139523 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | −17.8391 | −0.623730 | ||||||||
\(819\) | −9.75794 | −0.340970 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.3218 | −1.47704 | −0.738520 | − | 0.674232i | \(-0.764475\pi\) | ||||
−0.738520 | + | 0.674232i | \(0.764475\pi\) | |||||||
\(822\) | 10.3264 | 0.360173 | ||||||||
\(823\) | −35.6044 | −1.24109 | −0.620546 | − | 0.784170i | \(-0.713089\pi\) | ||||
−0.620546 | + | 0.784170i | \(0.713089\pi\) | |||||||
\(824\) | 12.1056 | 0.421717 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.7904 | −0.653802 | ||||||||
\(827\) | −51.4154 | −1.78789 | −0.893944 | − | 0.448179i | \(-0.852073\pi\) | ||||
−0.893944 | + | 0.448179i | \(0.852073\pi\) | |||||||
\(828\) | 5.60672 | 0.194847 | ||||||||
\(829\) | −26.9520 | −0.936083 | −0.468042 | − | 0.883706i | \(-0.655040\pi\) | ||||
−0.468042 | + | 0.883706i | \(0.655040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.5948 | 0.679735 | ||||||||
\(832\) | 6.53438 | 0.226539 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.33723 | −0.288695 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.79853 | −0.131375 | ||||||||
\(837\) | 1.24943 | 0.0431865 | ||||||||
\(838\) | −13.7579 | −0.475260 | ||||||||
\(839\) | 34.7026 | 1.19807 | 0.599034 | − | 0.800724i | \(-0.295552\pi\) | ||||
0.599034 | + | 0.800724i | \(0.295552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 6.16088 | 0.212318 | ||||||||
\(843\) | 30.5542 | 1.05234 | ||||||||
\(844\) | 45.2881 | 1.55888 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.75794 | 0.0604391 | ||||||||
\(847\) | −19.7003 | −0.676911 | ||||||||
\(848\) | −2.19521 | −0.0753837 | ||||||||
\(849\) | −8.61408 | −0.295634 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.2134 | −0.384392 | ||||||||
\(852\) | 12.5913 | 0.431369 | ||||||||
\(853\) | 0.134197 | 0.00459483 | 0.00229741 | − | 0.999997i | \(-0.499269\pi\) | ||||
0.00229741 | + | 0.999997i | \(0.499269\pi\) | |||||||
\(854\) | −5.70843 | −0.195338 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.4606 | 1.04112 | ||||||||
\(857\) | 30.5371 | 1.04313 | 0.521564 | − | 0.853212i | \(-0.325349\pi\) | ||||
0.521564 | + | 0.853212i | \(0.325349\pi\) | |||||||
\(858\) | −3.51587 | −0.120030 | ||||||||
\(859\) | −57.1010 | −1.94826 | −0.974130 | − | 0.225989i | \(-0.927439\pi\) | ||||
−0.974130 | + | 0.225989i | \(0.927439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.3933 | −0.933561 | ||||||||
\(862\) | 14.1500 | 0.481951 | ||||||||
\(863\) | −0.376261 | −0.0128081 | −0.00640403 | − | 0.999979i | \(-0.502038\pi\) | ||||
−0.00640403 | + | 0.999979i | \(0.502038\pi\) | |||||||
\(864\) | 5.17635 | 0.176103 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.68135 | 0.261023 | ||||||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | 6.90179 | 0.234262 | ||||||||
\(869\) | 29.8442 | 1.01239 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.00230 | −0.237264 | ||||||||
\(872\) | 14.5445 | 0.492539 | ||||||||
\(873\) | 7.14386 | 0.241783 | ||||||||
\(874\) | 1.70262 | 0.0575921 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.89093 | −0.0638886 | ||||||||
\(877\) | 5.54680 | 0.187302 | 0.0936511 | − | 0.995605i | \(-0.470146\pi\) | ||||
0.0936511 | + | 0.995605i | \(0.470146\pi\) | |||||||
\(878\) | 11.9285 | 0.402567 | ||||||||
\(879\) | −29.5565 | −0.996915 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.3357 | 0.449290 | 0.224645 | − | 0.974441i | \(-0.427878\pi\) | ||||
0.224645 | + | 0.974441i | \(0.427878\pi\) | |||||||
\(882\) | −1.70262 | −0.0573303 | ||||||||
\(883\) | −11.6044 | −0.390520 | −0.195260 | − | 0.980752i | \(-0.562555\pi\) | ||||
−0.195260 | + | 0.980752i | \(0.562555\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.6237 | 0.692868 | ||||||||
\(887\) | 33.2282 | 1.11569 | 0.557846 | − | 0.829944i | \(-0.311628\pi\) | ||||
0.557846 | + | 0.829944i | \(0.311628\pi\) | |||||||
\(888\) | −6.73631 | −0.226056 | ||||||||
\(889\) | −44.9977 | −1.50917 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.20147 | 0.0737521 | ||||||||
\(892\) | −22.8612 | −0.765450 | ||||||||
\(893\) | −3.35499 | −0.112271 | ||||||||
\(894\) | −8.30704 | −0.277829 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 36.7402 | 1.22740 | ||||||||
\(897\) | −9.90409 | −0.330688 | ||||||||
\(898\) | 6.44739 | 0.215152 | ||||||||
\(899\) | −3.74828 | −0.125012 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −9.87005 | −0.328637 | ||||||||
\(903\) | 25.6118 | 0.852307 | ||||||||
\(904\) | 29.7676 | 0.990056 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.90409 | 0.329041 | ||||||||
\(907\) | −18.9018 | −0.627624 | −0.313812 | − | 0.949485i | \(-0.601606\pi\) | ||||
−0.313812 | + | 0.949485i | \(0.601606\pi\) | |||||||
\(908\) | 12.5913 | 0.417855 | ||||||||
\(909\) | 13.7579 | 0.456322 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.3910 | −0.344269 | −0.172134 | − | 0.985073i | \(-0.555066\pi\) | ||||
−0.172134 | + | 0.985073i | \(0.555066\pi\) | |||||||
\(912\) | −2.42807 | −0.0804015 | ||||||||
\(913\) | 18.0553 | 0.597544 | ||||||||
\(914\) | −1.65116 | −0.0546157 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.3717 | −0.904385 | ||||||||
\(917\) | 13.9188 | 0.459640 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.894433 | −0.0295046 | −0.0147523 | − | 0.999891i | \(-0.504696\pi\) | ||||
−0.0147523 | + | 0.999891i | \(0.504696\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.9115 | 0.557251 | ||||||||
\(922\) | 16.7912 | 0.552988 | ||||||||
\(923\) | −22.2421 | −0.732106 | ||||||||
\(924\) | 12.1609 | 0.400064 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.0046 | −0.328772 | ||||||||
\(927\) | 6.20147 | 0.203683 | ||||||||
\(928\) | −15.5290 | −0.509766 | ||||||||
\(929\) | −3.69296 | −0.121162 | −0.0605811 | − | 0.998163i | \(-0.519295\pi\) | ||||
−0.0605811 | + | 0.998163i | \(0.519295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.24943 | 0.106496 | ||||||||
\(932\) | −14.9165 | −0.488607 | ||||||||
\(933\) | −14.0959 | −0.461479 | ||||||||
\(934\) | −0.0553145 | −0.00180995 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.94975 | −0.194474 | ||||||||
\(937\) | 16.2494 | 0.530846 | 0.265423 | − | 0.964132i | \(-0.414488\pi\) | ||||
0.265423 | + | 0.964132i | \(0.414488\pi\) | |||||||
\(938\) | −3.85384 | −0.125832 | ||||||||
\(939\) | −4.05531 | −0.132340 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.1535 | 0.428792 | 0.214396 | − | 0.976747i | \(-0.431222\pi\) | ||||
0.214396 | + | 0.976747i | \(0.431222\pi\) | |||||||
\(942\) | −7.57699 | −0.246872 | ||||||||
\(943\) | −27.8036 | −0.905409 | ||||||||
\(944\) | 27.1980 | 0.885218 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.22816 | 0.300033 | ||||||||
\(947\) | 40.5136 | 1.31651 | 0.658257 | − | 0.752793i | \(-0.271294\pi\) | ||||
0.658257 | + | 0.752793i | \(0.271294\pi\) | |||||||
\(948\) | 23.3910 | 0.759704 | ||||||||
\(949\) | 3.34027 | 0.108430 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.9977 | 0.713324 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6884 | 1.44760 | 0.723799 | − | 0.690011i | \(-0.242394\pi\) | ||||
0.723799 | + | 0.690011i | \(0.242394\pi\) | |||||||
\(954\) | 0.473724 | 0.0153374 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −44.4440 | −1.43742 | ||||||||
\(957\) | −6.60442 | −0.213490 | ||||||||
\(958\) | 15.3499 | 0.495934 | ||||||||
\(959\) | 63.0936 | 2.03740 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4389 | −0.949643 | ||||||||
\(962\) | 5.51127 | 0.177691 | ||||||||
\(963\) | 15.6044 | 0.502845 | ||||||||
\(964\) | −16.5592 | −0.533337 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.45090 | −0.175380 | ||||||||
\(967\) | 38.3910 | 1.23457 | 0.617285 | − | 0.786739i | \(-0.288232\pi\) | ||||
0.617285 | + | 0.786739i | \(0.288232\pi\) | |||||||
\(968\) | −12.0120 | −0.386079 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.6980 | −0.407499 | −0.203749 | − | 0.979023i | \(-0.565313\pi\) | ||||
−0.203749 | + | 0.979023i | \(0.565313\pi\) | |||||||
\(972\) | 1.72545 | 0.0553438 | ||||||||
\(973\) | −50.9401 | −1.63306 | ||||||||
\(974\) | 3.27069 | 0.104800 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.26259 | 0.264479 | ||||||||
\(977\) | 3.48183 | 0.111394 | 0.0556968 | − | 0.998448i | \(-0.482262\pi\) | ||||
0.0556968 | + | 0.998448i | \(0.482262\pi\) | |||||||
\(978\) | −11.5313 | −0.368732 | ||||||||
\(979\) | −16.2974 | −0.520866 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.45090 | 0.237889 | ||||||||
\(982\) | 7.60718 | 0.242755 | ||||||||
\(983\) | −10.1152 | −0.322626 | −0.161313 | − | 0.986903i | \(-0.551573\pi\) | ||||
−0.161313 | + | 0.986903i | \(0.551573\pi\) | |||||||
\(984\) | −16.7026 | −0.532460 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.7409 | 0.341887 | ||||||||
\(988\) | 5.25909 | 0.167314 | ||||||||
\(989\) | 25.9954 | 0.826606 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7985 | 0.755985 | 0.377993 | − | 0.925809i | \(-0.376614\pi\) | ||||
0.377993 | + | 0.925809i | \(0.376614\pi\) | |||||||
\(992\) | 6.46746 | 0.205342 | ||||||||
\(993\) | −12.4583 | −0.395351 | ||||||||
\(994\) | −12.2413 | −0.388271 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.1512 | 0.448399 | ||||||||
\(997\) | 38.9571 | 1.23378 | 0.616892 | − | 0.787048i | \(-0.288392\pi\) | ||||
0.616892 | + | 0.787048i | \(0.288392\pi\) | |||||||
\(998\) | −0.478786 | −0.0151557 | ||||||||
\(999\) | −3.45090 | −0.109182 |
(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 | 1425.2.a.u.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 4275.2.a.be.1.2 | 3 | |||
5.2 | odd | 4 | 1425.2.c.p.799.3 | 6 | |||
5.3 | odd | 4 | 1425.2.c.p.799.4 | 6 | |||
5.4 | even | 2 | 1425.2.a.v.1.2 | yes | 3 | ||
15.14 | odd | 2 | 4275.2.a.bh.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1425.2.a.u.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1425.2.a.v.1.2 | yes | 3 | 5.4 | even | 2 | ||
1425.2.c.p.799.3 | 6 | 5.2 | odd | 4 | |||
1425.2.c.p.799.4 | 6 | 5.3 | odd | 4 | |||
4275.2.a.be.1.2 | 3 | 3.2 | odd | 2 | |||
4275.2.a.bh.1.2 | 3 | 15.14 | odd | 2 |