Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(191,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.24 | ||
Character | \(\chi\) | \(=\) | 912.191 |
Dual form | 912.2.d.b.191.23 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 1.72850 | + | 0.110841i | 0.997950 | + | 0.0639940i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.67549i | 1.64373i | 0.569682 | + | 0.821865i | \(0.307066\pi\) | ||||
−0.569682 | + | 0.821865i | \(0.692934\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.87247i | − | 1.84162i | −0.390012 | − | 0.920810i | \(-0.627529\pi\) | ||
0.390012 | − | 0.920810i | \(-0.372471\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.97543 | + | 0.383177i | 0.991810 | + | 0.127726i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.458180 | −0.138146 | −0.0690732 | − | 0.997612i | \(-0.522004\pi\) | ||||
−0.0690732 | + | 0.997612i | \(0.522004\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.96949 | 1.37829 | 0.689144 | − | 0.724624i | \(-0.257987\pi\) | ||||
0.689144 | + | 0.724624i | \(0.257987\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.407395 | + | 6.35309i | −0.105189 | + | 1.64036i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.91518i | 0.949571i | 0.880102 | + | 0.474785i | \(0.157474\pi\) | ||||
−0.880102 | + | 0.474785i | \(0.842526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.540069 | − | 8.42206i | 0.117853 | − | 1.83784i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.77039 | 0.577666 | 0.288833 | − | 0.957379i | \(-0.406733\pi\) | ||||
0.288833 | + | 0.957379i | \(0.406733\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.50924 | −1.70185 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.10056 | + | 0.992121i | 0.981603 | + | 0.190934i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.21341i | − | 0.782412i | −0.920303 | − | 0.391206i | \(-0.872058\pi\) | ||
0.920303 | − | 0.391206i | \(-0.127942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.33770i | − | 0.599468i | −0.954023 | − | 0.299734i | \(-0.903102\pi\) | ||
0.954023 | − | 0.299734i | \(-0.0968979\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.791964 | − | 0.0507851i | −0.137863 | − | 0.00884055i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.9087 | 3.02712 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.65655 | 1.09433 | 0.547165 | − | 0.837025i | \(-0.315707\pi\) | ||||
0.547165 | + | 0.837025i | \(0.315707\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.58977 | + | 0.550823i | 1.37546 | + | 0.0882023i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.60465i | 1.49999i | 0.661441 | + | 0.749997i | \(0.269945\pi\) | ||||
−0.661441 | + | 0.749997i | \(0.730055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.41172i | 0.977779i | 0.872346 | + | 0.488889i | \(0.162598\pi\) | ||||
−0.872346 | + | 0.488889i | \(0.837402\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.40836 | + | 10.9362i | −0.209947 | + | 1.63027i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.8413 | −1.72723 | −0.863613 | − | 0.504155i | \(-0.831804\pi\) | ||||
−0.863613 | + | 0.504155i | \(0.831804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.7409 | −2.39156 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.433962 | + | 6.76739i | −0.0607669 | + | 0.947625i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.95236i | − | 0.542898i | −0.962453 | − | 0.271449i | \(-0.912497\pi\) | ||
0.962453 | − | 0.271449i | \(-0.0875029\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.68404i | − | 0.227075i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.110841 | + | 1.72850i | −0.0146812 | + | 0.228945i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.01813 | −0.262738 | −0.131369 | − | 0.991334i | \(-0.541937\pi\) | ||||
−0.131369 | + | 0.991334i | \(0.541937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.63375 | −0.849364 | −0.424682 | − | 0.905342i | \(-0.639614\pi\) | ||||
−0.424682 | + | 0.905342i | \(0.639614\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.86702 | − | 14.4977i | 0.235222 | − | 1.82654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.2653i | 2.26553i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.01112i | − | 0.123528i | −0.998091 | − | 0.0617639i | \(-0.980327\pi\) | ||
0.998091 | − | 0.0617639i | \(-0.0196726\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.78862 | + | 0.307073i | 0.576482 | + | 0.0369672i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.71670 | 0.678448 | 0.339224 | − | 0.940706i | \(-0.389836\pi\) | ||||
0.339224 | + | 0.940706i | \(0.389836\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.95226 | 1.16482 | 0.582412 | − | 0.812894i | \(-0.302109\pi\) | ||||
0.582412 | + | 0.812894i | \(0.302109\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.7082 | − | 0.943172i | −1.69836 | − | 0.108908i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.23247i | 0.254413i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.29894i | 0.708687i | 0.935115 | + | 0.354343i | \(0.115296\pi\) | ||||
−0.935115 | + | 0.354343i | \(0.884704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.70635 | + | 2.28023i | 0.967372 | + | 0.253359i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6759 | 1.28160 | 0.640799 | − | 0.767709i | \(-0.278603\pi\) | ||||
0.640799 | + | 0.767709i | \(0.278603\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.3902 | −1.56084 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.467019 | − | 7.28289i | 0.0500697 | − | 0.780808i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.1435i | − | 1.49921i | −0.661885 | − | 0.749606i | \(-0.730243\pi\) | ||
0.661885 | − | 0.749606i | \(-0.269757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 24.2137i | − | 2.53828i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.369953 | − | 5.76921i | 0.0383624 | − | 0.598239i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.67549 | −0.377098 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.6574 | −1.28516 | −0.642581 | − | 0.766218i | \(-0.722136\pi\) | ||||
−0.642581 | + | 0.766218i | \(0.722136\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.36328 | − | 0.175564i | −0.137015 | − | 0.0176449i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.76056i | − | 0.772205i | −0.922456 | − | 0.386102i | \(-0.873821\pi\) | ||
0.922456 | − | 0.386102i | \(-0.126179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.92512i | − | 0.879418i | −0.898140 | − | 0.439709i | \(-0.855082\pi\) | ||
0.898140 | − | 0.439709i | \(-0.144918\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.9552 | + | 1.98502i | 3.02092 | + | 0.193718i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.6024 | −1.79836 | −0.899182 | − | 0.437574i | \(-0.855838\pi\) | ||||
−0.899182 | + | 0.437574i | \(0.855838\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.73669 | −0.741040 | −0.370520 | − | 0.928824i | \(-0.620821\pi\) | ||||
−0.370520 | + | 0.928824i | \(0.620821\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.5059 | + | 0.737818i | 1.09209 | + | 0.0700306i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.0995i | − | 0.950085i | −0.879963 | − | 0.475043i | \(-0.842433\pi\) | ||
0.879963 | − | 0.475043i | \(-0.157567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1825i | 0.949527i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.7864 | + | 1.90420i | 1.36700 | + | 0.176043i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.0766 | 1.74875 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7901 | −0.980916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.06459 | + | 16.6016i | −0.0959907 | + | 1.49692i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.8982i | − | 1.15365i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.37994i | 0.388657i | 0.980936 | + | 0.194329i | \(0.0622528\pi\) | ||||
−0.980936 | + | 0.194329i | \(0.937747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.710682 | + | 11.0827i | −0.0625720 | + | 0.975775i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.51958 | −0.482248 | −0.241124 | − | 0.970494i | \(-0.577516\pi\) | ||||
−0.241124 | + | 0.970494i | \(0.577516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.87247 | 0.422496 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.64653 | + | 18.7471i | −0.313844 | + | 1.61349i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.53267i | − | 0.301817i | −0.988548 | − | 0.150908i | \(-0.951780\pi\) | ||
0.988548 | − | 0.150908i | \(-0.0482198\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.97062i | − | 0.167146i | −0.996502 | − | 0.0835729i | \(-0.973367\pi\) | ||
0.996502 | − | 0.0835729i | \(-0.0266331\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.4676 | − | 1.31250i | −1.72369 | − | 0.110532i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.27692 | −0.190406 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.4864 | 1.28607 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −28.9367 | − | 1.85558i | −2.38666 | − | 0.153046i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.83262i | − | 0.805520i | −0.915306 | − | 0.402760i | \(-0.868051\pi\) | ||
0.915306 | − | 0.402760i | \(-0.131949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.90906i | − | 0.725009i | −0.931982 | − | 0.362505i | \(-0.881922\pi\) | ||
0.931982 | − | 0.362505i | \(-0.118078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50021 | + | 11.6493i | −0.121285 | + | 0.941793i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.2677 | 0.985364 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.600145 | −0.0478968 | −0.0239484 | − | 0.999713i | \(-0.507624\pi\) | ||||
−0.0239484 | + | 0.999713i | \(0.507624\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.438083 | − | 6.83165i | 0.0347422 | − | 0.541785i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 13.4986i | − | 1.06384i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.42612i | − | 0.111702i | −0.998439 | − | 0.0558511i | \(-0.982213\pi\) | ||
0.998439 | − | 0.0558511i | \(-0.0177872\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.186660 | − | 2.91086i | 0.0145315 | − | 0.226610i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3789 | −0.880528 | −0.440264 | − | 0.897868i | \(-0.645115\pi\) | ||||
−0.440264 | + | 0.897868i | \(0.645115\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6958 | 0.899679 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.383177 | + | 2.97543i | −0.0293023 | + | 0.227537i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 10.0057i | − | 0.760720i | −0.924838 | − | 0.380360i | \(-0.875800\pi\) | ||
0.924838 | − | 0.380360i | \(-0.124200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 41.4610i | 3.13416i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.48833 | − | 0.223691i | −0.262199 | − | 0.0168136i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.87586 | 0.140208 | 0.0701041 | − | 0.997540i | \(-0.477667\pi\) | ||||
0.0701041 | + | 0.997540i | \(0.477667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.78558 | 0.578698 | 0.289349 | − | 0.957224i | \(-0.406561\pi\) | ||||
0.289349 | + | 0.957224i | \(0.406561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4664 | − | 0.735291i | −0.847624 | − | 0.0543543i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.4661i | 1.79878i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.79386i | − | 0.131180i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.83408 | − | 24.8523i | 0.351627 | − | 1.80774i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0402 | −1.45006 | −0.725030 | − | 0.688717i | \(-0.758174\pi\) | ||||
−0.725030 | + | 0.688717i | \(0.758174\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3016 | 0.813505 | 0.406752 | − | 0.913538i | \(-0.366661\pi\) | ||||
0.406752 | + | 0.913538i | \(0.366661\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.02455 | + | 31.5716i | −0.144981 | + | 2.26089i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.9523i | 0.994059i | 0.867734 | + | 0.497029i | \(0.165576\pi\) | ||||
−0.867734 | + | 0.497029i | \(0.834424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.3458i | − | 1.15873i | −0.815070 | − | 0.579363i | \(-0.803301\pi\) | ||
0.815070 | − | 0.579363i | \(-0.196699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.112073 | − | 1.74772i | 0.00790504 | − | 0.123275i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.5297 | −1.44090 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.3018 | −2.46559 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.24310 | + | 1.06155i | 0.572935 | + | 0.0737828i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.458180i | − | 0.0316930i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.2045i | − | 0.771348i | −0.922635 | − | 0.385674i | \(-0.873969\pi\) | ||
0.922635 | − | 0.385674i | \(-0.126031\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.88133 | + | 0.633645i | 0.677057 | + | 0.0434166i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.5662 | −1.60720 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.2628 | −1.10399 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.2025 | + | 1.10312i | 1.16244 | + | 0.0745418i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.4565i | 1.30878i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.4542i | 1.36971i | 0.728677 | + | 0.684857i | \(0.240135\pi\) | ||||
−0.728677 | + | 0.684857i | \(0.759865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.3186 | − | 3.26055i | −1.68791 | − | 0.217370i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.32690 | −0.0880698 | −0.0440349 | − | 0.999030i | \(-0.514021\pi\) | ||||
−0.0440349 | + | 0.999030i | \(0.514021\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7298 | 0.841209 | 0.420605 | − | 0.907244i | \(-0.361818\pi\) | ||||
0.420605 | + | 0.907244i | \(0.361818\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.247449 | + | 3.85882i | −0.0162809 | + | 0.253892i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.1683i | 1.12473i | 0.826889 | + | 0.562366i | \(0.190109\pi\) | ||||
−0.826889 | + | 0.562366i | \(0.809891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 43.5225i | − | 2.83909i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.698181 | + | 10.8877i | −0.0453517 | + | 0.707234i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.3625 | −0.929032 | −0.464516 | − | 0.885565i | \(-0.653772\pi\) | ||||
−0.464516 | + | 0.885565i | \(0.653772\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.11757 | 0.522899 | 0.261449 | − | 0.965217i | \(-0.415800\pi\) | ||||
0.261449 | + | 0.965217i | \(0.415800\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.7962 | + | 4.90640i | 0.949176 | + | 0.314746i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 61.5311i | − | 3.93108i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.96949i | 0.316201i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.1818 | + | 1.29417i | 1.27897 | + | 0.0820146i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.96058 | −0.249990 | −0.124995 | − | 0.992157i | \(-0.539891\pi\) | ||||
−0.124995 | + | 0.992157i | \(0.539891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.26934 | −0.0798026 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −24.8735 | − | 1.59502i | −1.55764 | − | 0.0998843i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.1159i | 0.755771i | 0.925852 | + | 0.377885i | \(0.123349\pi\) | ||||
−0.925852 | + | 0.377885i | \(0.876651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 32.4338i | − | 2.01534i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.61448 | − | 12.5367i | 0.0999341 | − | 0.776003i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.7968 | −1.46737 | −0.733686 | − | 0.679488i | \(-0.762202\pi\) | ||||
−0.733686 | + | 0.679488i | \(0.762202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.5269 | 0.892378 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.56768 | − | 24.4471i | 0.0959406 | − | 1.49614i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 9.75296i | − | 0.594648i | −0.954777 | − | 0.297324i | \(-0.903906\pi\) | ||
0.954777 | − | 0.297324i | \(-0.0960942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.0706i | − | 0.733239i | −0.930371 | − | 0.366620i | \(-0.880515\pi\) | ||
0.930371 | − | 0.366620i | \(-0.119485\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.68387 | − | 41.8533i | 0.162435 | − | 2.53308i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.89876 | 0.235104 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.0483 | −1.74534 | −0.872672 | − | 0.488306i | \(-0.837615\pi\) | ||||
−0.872672 | + | 0.488306i | \(0.837615\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.27893 | − | 9.93108i | 0.0765675 | − | 0.594558i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.0496i | 1.49433i | 0.664637 | + | 0.747166i | \(0.268586\pi\) | ||||
−0.664637 | + | 0.747166i | \(0.731414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.04411i | − | 0.240397i | −0.992750 | − | 0.120199i | \(-0.961647\pi\) | ||
0.992750 | − | 0.120199i | \(-0.0383532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.35309 | − | 0.407395i | −0.376325 | − | 0.0241320i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 46.7983 | 2.76242 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.67136 | 0.0983151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.8783 | − | 1.40296i | −1.28253 | − | 0.0822427i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 12.1605i | − | 0.710426i | −0.934785 | − | 0.355213i | \(-0.884408\pi\) | ||
0.934785 | − | 0.355213i | \(-0.115592\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.41760i | − | 0.431870i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.33697 | − | 0.454570i | −0.135605 | − | 0.0263768i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.7674 | 0.796191 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.2409 | 1.80070 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.860188 | − | 13.4141i | 0.0494165 | − | 0.770622i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 24.3823i | − | 1.39613i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.2313i | 0.583934i | 0.956428 | + | 0.291967i | \(0.0943097\pi\) | ||||
−0.956428 | + | 0.291967i | \(0.905690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.989268 | − | 15.4271i | 0.0562775 | − | 0.877616i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.47072 | 0.0833970 | 0.0416985 | − | 0.999130i | \(-0.486723\pi\) | ||||
0.0416985 | + | 0.999130i | \(0.486723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.1089 | −0.910527 | −0.455264 | − | 0.890357i | \(-0.650455\pi\) | ||||
−0.455264 | + | 0.890357i | \(0.650455\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 53.2861 | + | 6.86221i | 3.00233 | + | 0.386642i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.4406i | 1.37272i | 0.727260 | + | 0.686362i | \(0.240793\pi\) | ||||
−0.727260 | + | 0.686362i | \(0.759207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.93050i | 0.108087i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.1543 | − | 2.06191i | −1.79468 | − | 0.115085i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.91518 | −0.217847 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −42.2866 | −2.34564 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.3729 | − | 0.857542i | −0.739522 | − | 0.0474222i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 57.6962i | 3.18089i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.4550i | 1.23424i | 0.786870 | + | 0.617119i | \(0.211700\pi\) | ||||
−0.786870 | + | 0.617119i | \(0.788300\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.8061 | + | 2.55064i | 1.08537 | + | 0.139774i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.71636 | 0.203046 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4268 | −0.622460 | −0.311230 | − | 0.950335i | \(-0.600741\pi\) | ||||
−0.311230 | + | 0.950335i | \(0.600741\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.11944 | − | 17.4571i | 0.0607998 | − | 0.948138i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.52927i | 0.0828144i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 47.4623i | 2.56273i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.12864 | + | 17.6005i | −0.0607641 | + | 0.947581i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.80109 | −0.204053 | −0.102027 | − | 0.994782i | \(-0.532533\pi\) | ||||
−0.102027 | + | 0.994782i | \(0.532533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.12591 | 0.488499 | 0.244249 | − | 0.969712i | \(-0.421458\pi\) | ||||
0.244249 | + | 0.969712i | \(0.421458\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.3472 | + | 4.93034i | 1.35293 | + | 0.263162i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 32.0681i | − | 1.70682i | −0.521244 | − | 0.853408i | \(-0.674532\pi\) | ||
0.521244 | − | 0.853408i | \(-0.325468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.0117i | 1.11519i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.9739 | + | 2.11447i | 1.74516 | + | 0.111909i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.5410 | 1.13689 | 0.568445 | − | 0.822721i | \(-0.307545\pi\) | ||||
0.568445 | + | 0.822721i | \(0.307545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.6506 | − | 1.19598i | −0.978905 | − | 0.0627727i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.5795i | 1.91466i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.3688i | − | 1.27204i | −0.771671 | − | 0.636022i | \(-0.780579\pi\) | ||
0.771671 | − | 0.636022i | \(-0.219421\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.68028 | + | 28.5779i | −0.191588 | + | 1.48771i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.2577 | −0.999812 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3460 | 0.949920 | 0.474960 | − | 0.880007i | \(-0.342463\pi\) | ||||
0.474960 | + | 0.880007i | \(0.342463\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.42965 | − | 22.2945i | 0.0738266 | − | 1.15128i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 20.9385i | − | 1.07839i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.29049i | 0.0662881i | 0.999451 | + | 0.0331441i | \(0.0105520\pi\) | ||||
−0.999451 | + | 0.0331441i | \(0.989448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.485477 | + | 7.57073i | −0.0248717 | + | 0.387860i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.9739 | −1.12281 | −0.561407 | − | 0.827540i | \(-0.689740\pi\) | ||||
−0.561407 | + | 0.827540i | \(0.689740\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.20541 | −0.418187 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.45683 | + | 19.0776i | −0.124888 | + | 0.969770i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.1642i | 1.32658i | 0.748364 | + | 0.663288i | \(0.230840\pi\) | ||||
−0.748364 | + | 0.663288i | \(0.769160\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8466i | 0.548535i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.54060 | − | 0.611795i | −0.481260 | − | 0.0308610i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.1517 | −1.16489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3935 | 1.57559 | 0.787797 | − | 0.615935i | \(-0.211222\pi\) | ||||
0.787797 | + | 0.615935i | \(0.211222\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.42206 | + | 0.540069i | 0.421630 | + | 0.0270373i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 13.5738i | − | 0.677841i | −0.940815 | − | 0.338921i | \(-0.889938\pi\) | ||
0.940815 | − | 0.338921i | \(-0.110062\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 16.5867i | − | 0.826240i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.38098 | + | 32.0001i | −0.416454 | + | 1.59010i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.04990 | −0.151178 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.8998 | −0.983980 | −0.491990 | − | 0.870601i | \(-0.663730\pi\) | ||||
−0.491990 | + | 0.870601i | \(0.663730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.391565 | − | 6.10623i | 0.0193145 | − | 0.301198i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.83325i | 0.483863i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 42.9147i | 2.10660i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.218425 | − | 3.40622i | 0.0106963 | − | 0.166803i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.94929 | 0.0952291 | 0.0476146 | − | 0.998866i | \(-0.484838\pi\) | ||||
0.0476146 | + | 0.998866i | \(0.484838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.5881 | −1.29583 | −0.647913 | − | 0.761715i | \(-0.724358\pi\) | ||||
−0.647913 | + | 0.761715i | \(0.724358\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −35.2328 | − | 4.53730i | −1.71308 | − | 0.220611i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 33.3152i | − | 1.61603i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.3227i | 1.56421i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.93566 | − | 0.252376i | −0.190015 | − | 0.0121848i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.7664 | 1.96365 | 0.981825 | − | 0.189789i | \(-0.0607803\pi\) | ||||
0.981825 | + | 0.189789i | \(0.0607803\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 41.5783 | 1.99813 | 0.999063 | − | 0.0432833i | \(-0.0137818\pi\) | ||||
0.999063 | + | 0.0432833i | \(0.0137818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.7682 | + | 1.71652i | 1.28344 | + | 0.0823010i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.77039i | 0.132526i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.5230i | 1.02724i | 0.858019 | + | 0.513619i | \(0.171695\pi\) | ||||
−0.858019 | + | 0.513619i | \(0.828305\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −49.8114 | − | 6.41474i | −2.37197 | − | 0.305464i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5866 | 0.788053 | 0.394026 | − | 0.919099i | \(-0.371082\pi\) | ||||
0.394026 | + | 0.919099i | \(0.371082\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 51.9844 | 2.46430 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.08986 | − | 16.9957i | 0.0515485 | − | 0.803869i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.4916i | 1.39179i | 0.718142 | + | 0.695897i | \(0.244993\pi\) | ||||
−0.718142 | + | 0.695897i | \(0.755007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.40066i | − | 0.207219i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.987489 | − | 15.3993i | 0.0463963 | − | 0.723523i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 88.9972 | 4.17225 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1563 | −0.475090 | −0.237545 | − | 0.971377i | \(-0.576343\pi\) | ||||
−0.237545 | + | 0.971377i | \(0.576343\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.88433 | + | 19.9696i | −0.181305 | + | 0.932102i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.6327i | 0.914385i | 0.889368 | + | 0.457192i | \(0.151145\pi\) | ||||
−0.889368 | + | 0.457192i | \(0.848855\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.8892i | 0.970802i | 0.874292 | + | 0.485401i | \(0.161326\pi\) | ||||
−0.874292 | + | 0.485401i | \(0.838674\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.2047 | + | 1.35976i | 0.983344 | + | 0.0630574i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.59395 | 0.351406 | 0.175703 | − | 0.984443i | \(-0.443780\pi\) | ||||
0.175703 | + | 0.984443i | \(0.443780\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.92664 | −0.227491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.03735 | − | 0.0665207i | −0.0477986 | − | 0.00306511i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.93772i | − | 0.135077i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8.50924i | − | 0.390431i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.51445 | − | 11.7600i | 0.0693421 | − | 0.538452i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.9802 | 0.821538 | 0.410769 | − | 0.911739i | \(-0.365260\pi\) | ||||
0.410769 | + | 0.911739i | \(0.365260\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.0797 | 1.50830 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.49620 | − | 23.3324i | 0.0680795 | − | 1.06166i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 46.5221i | − | 2.11246i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.4070i | 0.607530i | 0.952747 | + | 0.303765i | \(0.0982437\pi\) | ||||
−0.952747 | + | 0.303765i | \(0.901756\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.158072 | − | 2.46505i | 0.00714828 | − | 0.111473i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.3770 | −0.468309 | −0.234155 | − | 0.972199i | \(-0.575232\pi\) | ||||
−0.234155 | + | 0.972199i | \(0.575232\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.4963 | 0.742955 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.645285 | − | 5.01073i | 0.0290034 | − | 0.225216i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 27.8545i | − | 1.24944i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.4778i | 0.469051i | 0.972110 | + | 0.234526i | \(0.0753537\pi\) | ||||
−0.972110 | + | 0.234526i | \(0.924646\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.6685 | − | 1.26125i | −0.878724 | − | 0.0563486i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.24048 | −0.189074 | −0.0945369 | − | 0.995521i | \(-0.530137\pi\) | ||||
−0.0945369 | + | 0.995521i | \(0.530137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.5239 | 1.26930 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.2163 | + | 1.29638i | 0.897835 | + | 0.0575741i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.417908i | 0.0185234i | 0.999957 | + | 0.00926172i | \(0.00294814\pi\) | ||||
−0.999957 | + | 0.00926172i | \(0.997052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 48.4921i | − | 2.14516i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.992121 | + | 5.10056i | −0.0438032 | + | 0.225195i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.8042 | 1.44553 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.42543 | 0.238610 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.10904 | − | 17.2949i | 0.0486816 | − | 0.759161i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.40766i | 0.0616706i | 0.999524 | + | 0.0308353i | \(0.00981674\pi\) | ||||
−0.999524 | + | 0.0308353i | \(0.990183\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 36.8671i | − | 1.61209i | −0.591856 | − | 0.806044i | \(-0.701605\pi\) | ||
0.591856 | − | 0.806044i | \(-0.298395\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.59557 | + | 71.6653i | −0.200567 | + | 3.12773i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.0677 | 0.569237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3249 | −0.666302 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00479 | − | 0.773300i | −0.260586 | − | 0.0335583i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.7302i | 2.06742i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 68.3731i | − | 2.95603i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.24242 | + | 0.207922i | 0.139921 | + | 0.00897248i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.67036 | 0.330386 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.35415 | 0.359173 | 0.179587 | − | 0.983742i | \(-0.442524\pi\) | ||||
0.179587 | + | 0.983742i | \(0.442524\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.4574 | + | 0.862961i | 0.577512 | + | 0.0370332i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 28.4361i | − | 1.21807i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.21551i | − | 0.137485i | −0.997634 | − | 0.0687427i | \(-0.978101\pi\) | ||
0.997634 | − | 0.0687427i | \(-0.0218988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.7382 | − | 2.54190i | −0.842408 | − | 0.108486i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.21341 | 0.179498 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.6914 | 1.30513 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.71185 | + | 42.2897i | −0.115111 | + | 1.79510i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.46405i | 0.146777i | 0.997303 | + | 0.0733883i | \(0.0233812\pi\) | ||||
−0.997303 | + | 0.0733883i | \(0.976619\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.8630i | 1.34766i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.198833 | − | 3.10068i | 0.00839473 | − | 0.130911i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.5544 | −0.866264 | −0.433132 | − | 0.901330i | \(-0.642592\pi\) | ||||
−0.433132 | + | 0.901330i | \(0.642592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.1208 | 1.56168 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.1104 | − | 42.4214i | 0.466591 | − | 1.78153i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.5397i | 1.02876i | 0.857563 | + | 0.514379i | \(0.171978\pi\) | ||||
−0.857563 | + | 0.514379i | \(0.828022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 33.1631i | − | 1.38783i | −0.720056 | − | 0.693916i | \(-0.755884\pi\) | ||
0.720056 | − | 0.693916i | \(-0.244116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.6396 | − | 2.22128i | −1.44709 | − | 0.0927952i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.5739 | −0.983100 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.9733 | 1.41433 | 0.707163 | − | 0.707051i | \(-0.249975\pi\) | ||||
0.707163 | + | 0.707051i | \(0.249975\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.5348 | + | 1.25268i | 0.811837 | + | 0.0520595i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 56.8905i | − | 2.36021i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.81089i | 0.0749995i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.99885 | + | 54.3472i | −0.289367 | + | 2.24698i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.7301 | 1.76366 | 0.881830 | − | 0.471567i | \(-0.156312\pi\) | ||||
0.881830 | + | 0.471567i | \(0.156312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.33770 | 0.137527 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.54648 | + | 24.1165i | −0.0636138 | + | 0.992021i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.6793i | 1.42411i | 0.702125 | + | 0.712054i | \(0.252235\pi\) | ||||
−0.702125 | + | 0.712054i | \(0.747765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 70.1158i | 2.87447i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.81179 | − | 28.2538i | 0.0741516 | − | 1.15635i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.5797 | 0.718288 | 0.359144 | − | 0.933282i | \(-0.383069\pi\) | ||||
0.359144 | + | 0.933282i | \(0.383069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.17032 | −0.374065 | −0.187033 | − | 0.982354i | \(-0.559887\pi\) | ||||
−0.187033 | + | 0.982354i | \(0.559887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.387438 | − | 3.00851i | 0.0157777 | − | 0.122516i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 39.6588i | − | 1.61236i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.7473i | − | 0.557987i | −0.960293 | − | 0.278993i | \(-0.909999\pi\) | ||
0.960293 | − | 0.278993i | \(-0.0900007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −35.4856 | − | 2.27553i | −1.43795 | − | 0.0922093i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −58.8450 | −2.38062 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.1115 | −1.09502 | −0.547511 | − | 0.836799i | \(-0.684425\pi\) | ||||
−0.547511 | + | 0.836799i | \(0.684425\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −61.0192 | − | 3.91289i | −2.46053 | − | 0.157783i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 34.7987i | − | 1.40094i | −0.713681 | − | 0.700471i | \(-0.752973\pi\) | ||
0.713681 | − | 0.700471i | \(-0.247027\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.8015i | − | 0.554728i | −0.960765 | − | 0.277364i | \(-0.910539\pi\) | ||
0.960765 | − | 0.277364i | \(-0.0894608\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.1305 | + | 2.74856i | 0.567039 | + | 0.110296i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −68.9139 | −2.76098 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.86097 | 0.194439 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0507851 | − | 0.791964i | 0.00202816 | − | 0.0316280i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.0616i | 1.03914i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.5490i | − | 1.21614i | −0.793885 | − | 0.608068i | \(-0.791945\pi\) | ||
0.793885 | − | 0.608068i | \(-0.208055\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.24191 | − | 19.3669i | 0.0493616 | − | 0.769766i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.0984 | −0.638847 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −83.1939 | −3.29626 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.0096 | + | 2.19051i | 0.672891 | + | 0.0866553i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.6474i | 0.934014i | 0.884254 | + | 0.467007i | \(0.154668\pi\) | ||||
−0.884254 | + | 0.467007i | \(0.845332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.248940i | 0.00981723i | 0.999988 | + | 0.00490862i | \(0.00156247\pi\) | ||||
−0.999988 | + | 0.00490862i | \(0.998438\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.7343 | − | 2.61210i | −1.60391 | − | 0.102851i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.50401 | −0.0984429 | −0.0492215 | − | 0.998788i | \(-0.515674\pi\) | ||||
−0.0492215 | + | 0.998788i | \(0.515674\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.924665 | 0.0362963 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.1103 | − | 1.80259i | −1.10173 | − | 0.0706489i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.07925i | − | 0.0813672i | −0.999172 | − | 0.0406836i | \(-0.987046\pi\) | ||
0.999172 | − | 0.0406836i | \(-0.0129536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 20.2872i | − | 0.792686i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.6122 | + | 3.81348i | 1.15528 | + | 0.148778i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.2887 | 1.72524 | 0.862622 | − | 0.505849i | \(-0.168821\pi\) | ||||
0.862622 | + | 0.505849i | \(0.168821\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.5567 | −0.838458 | −0.419229 | − | 0.907881i | \(-0.637700\pi\) | ||||
−0.419229 | + | 0.907881i | \(0.637700\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.15657 | + | 33.6305i | −0.0837543 | + | 1.30610i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.9087i | 0.694470i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.6728i | − | 0.451973i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.26716 | + | 35.3551i | −0.0876536 | + | 1.36691i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.03945 | 0.117337 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.09131 | 0.0806139 | 0.0403069 | − | 0.999187i | \(-0.487166\pi\) | ||||
0.0403069 | + | 0.999187i | \(0.487166\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −43.4019 | − | 8.44220i | −1.67054 | − | 0.324940i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.8723i | 1.22495i | 0.790489 | + | 0.612476i | \(0.209826\pi\) | ||||
−0.790489 | + | 0.612476i | \(0.790174\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 61.6727i | 2.36678i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.29356 | − | 0.147075i | −0.0878893 | − | 0.00563594i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.9455 | 0.954512 | 0.477256 | − | 0.878764i | \(-0.341631\pi\) | ||||
0.477256 | + | 0.878764i | \(0.341631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9843 | 0.496105 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.0035 | + | 1.41098i | 0.839485 | + | 0.0538324i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 19.6412i | − | 0.748270i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.21814i | − | 0.350674i | −0.984508 | − | 0.175337i | \(-0.943898\pi\) | ||
0.984508 | − | 0.175337i | \(-0.0561016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.855430 | + | 6.64255i | −0.0324951 | + | 0.252329i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.24299 | 0.274742 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.6039 | −1.42435 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.90295 | + | 29.6754i | −0.0719761 | + | 1.12243i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.80868i | − | 0.181621i | −0.995868 | − | 0.0908106i | \(-0.971054\pi\) | ||
0.995868 | − | 0.0908106i | \(-0.0289458\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.65655i | 0.251057i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.82407 | − | 75.2286i | 0.181685 | − | 2.83327i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.8131 | −1.42211 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.2498 | 1.28628 | 0.643139 | − | 0.765750i | \(-0.277632\pi\) | ||||
0.643139 | + | 0.765750i | \(0.277632\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.41361 | + | 18.7421i | −0.0905175 | + | 0.702882i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.24672i | − | 0.346292i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 8.36880i | − | 0.312976i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.8256 | − | 1.59195i | −0.927128 | − | 0.0594525i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.7212 | 0.549009 | 0.274504 | − | 0.961586i | \(-0.411486\pi\) | ||||
0.274504 | + | 0.961586i | \(0.411486\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.4873 | −1.61955 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.0312 | + | 0.899759i | 0.521827 | + | 0.0334624i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35.8530i | 1.33155i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.15451i | − | 0.339522i | −0.985485 | − | 0.169761i | \(-0.945700\pi\) | ||
0.985485 | − | 0.169761i | \(-0.0542996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.0314 | + | 10.1207i | 0.927089 | + | 0.374842i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.1031 | −0.928470 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.7844 | 1.76496 | 0.882479 | − | 0.470353i | \(-0.155873\pi\) | ||||
0.882479 | + | 0.470353i | \(0.155873\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.82017 | − | 106.357i | 0.251566 | − | 3.92302i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.463274i | 0.0170649i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.8896i | 1.24665i | 0.781963 | + | 0.623325i | \(0.214219\pi\) | ||||
−0.781963 | + | 0.623325i | \(0.785781\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.550823 | + | 8.58977i | −0.0202350 | + | 0.315553i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.8773 | −0.619169 | −0.309584 | − | 0.950872i | \(-0.600190\pi\) | ||||
−0.309584 | + | 0.950872i | \(0.600190\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.1397 | 1.32406 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.7408 | + | 4.47394i | 1.27110 | + | 0.163693i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 90.6397i | 3.31190i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.3239i | 1.69038i | 0.534465 | + | 0.845191i | \(0.320513\pi\) | ||||
−0.534465 | + | 0.845191i | \(0.679487\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.84586 | − | 0.438994i | −0.249477 | − | 0.0159978i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.7452 | 1.19172 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.1404 | −0.732014 | −0.366007 | − | 0.930612i | \(-0.619275\pi\) | ||||
−0.366007 | + | 0.930612i | \(0.619275\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.19405 | − | 0.140695i | −0.0796390 | − | 0.00510689i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 23.5191i | − | 0.852565i | −0.904590 | − | 0.426283i | \(-0.859823\pi\) | ||
0.904590 | − | 0.426283i | \(-0.140177\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.6968i | 1.36471i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −42.8171 | − | 5.51400i | −1.54805 | − | 0.199359i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.0291 | −0.362128 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.43505 | 0.340237 | 0.170118 | − | 0.985424i | \(-0.445585\pi\) | ||||
0.170118 | + | 0.985424i | \(0.445585\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.34294 | + | 20.9424i | −0.0483648 | + | 0.754222i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 30.5433i | − | 1.09857i | −0.835636 | − | 0.549283i | \(-0.814901\pi\) | ||
0.835636 | − | 0.549283i | \(-0.185099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.4013i | 1.02020i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.59500 | − | 56.0619i | 0.128970 | − | 2.01121i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.60465 | −0.344122 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.61928 | −0.0937252 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.18022 | − | 21.4908i | 0.149389 | − | 0.768017i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.20583i | − | 0.0787294i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.32720i | 0.296833i | 0.988925 | + | 0.148416i | \(0.0474175\pi\) | ||||
−0.988925 | + | 0.148416i | \(0.952582\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.1328 | − | 2.63766i | −1.46437 | − | 0.0939031i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −49.2097 | −1.74970 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.9663 | −1.17067 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.1097 | + | 1.61017i | 0.890549 | + | 0.0571069i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4.69531i | − | 0.166317i | −0.996536 | − | 0.0831583i | \(-0.973499\pi\) | ||
0.996536 | − | 0.0831583i | \(-0.0265007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 46.3607i | − | 1.64012i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.41948 | − | 42.0831i | 0.191488 | − | 1.48693i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.55993 | −0.160916 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 49.6141 | 1.74867 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.08103 | − | 16.8580i | 0.0380539 | − | 0.593429i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 29.1013i | − | 1.02315i | −0.859239 | − | 0.511574i | \(-0.829063\pi\) | ||
0.859239 | − | 0.511574i | \(-0.170937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.6250i | 1.63722i | 0.574347 | + | 0.818612i | \(0.305256\pi\) | ||||
−0.574347 | + | 0.818612i | \(0.694744\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.33792 | − | 20.8641i | 0.0469229 | − | 0.731736i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.24169 | 0.183608 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.41172 | −0.224318 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.27813 | − | 72.0461i | 0.324204 | − | 2.51749i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 47.8969i | − | 1.67161i | −0.549024 | − | 0.835806i | \(-0.685001\pi\) | ||
0.549024 | − | 0.835806i | \(-0.314999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.6418i | 0.719528i | 0.933043 | + | 0.359764i | \(0.117143\pi\) | ||||
−0.933043 | + | 0.359764i | \(0.882857\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.73902 | + | 0.432143i | 0.234622 | + | 0.0150453i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.9435 | −0.971691 | −0.485845 | − | 0.874045i | \(-0.661488\pi\) | ||||
−0.485845 | + | 0.874045i | \(0.661488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.10149 | 0.142451 | 0.0712254 | − | 0.997460i | \(-0.477309\pi\) | ||||
0.0712254 | + | 0.997460i | \(0.477309\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.2100 | − | 3.21974i | −1.74177 | − | 0.111692i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 65.5438i | − | 2.27096i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 41.8232i | − | 1.44735i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.31140 | − | 17.0241i | 0.114459 | − | 0.588440i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.4642 | −0.395789 | −0.197894 | − | 0.980223i | \(-0.563410\pi\) | ||||
−0.197894 | + | 0.980223i | \(0.563410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.2471 | 0.387832 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.77652 | + | 43.2982i | −0.0956284 | + | 1.49127i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.9879i | 1.47883i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 52.5743i | 1.80647i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.448253 | − | 6.99025i | 0.0153840 | − | 0.239905i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.4412 | 0.632158 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.34278 | −0.251412 | −0.125706 | − | 0.992068i | \(-0.540120\pi\) | ||||
−0.125706 | + | 0.992068i | \(0.540120\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.9362 | − | 1.40836i | −0.374009 | − | 0.0481651i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 36.6827i | − | 1.25306i | −0.779398 | − | 0.626529i | \(-0.784475\pi\) | ||
0.779398 | − | 0.626529i | \(-0.215525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 21.4036i | − | 0.730283i | −0.930952 | − | 0.365141i | \(-0.881021\pi\) | ||
0.930952 | − | 0.365141i | \(-0.118979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 80.8909 | + | 5.18717i | 2.75676 | + | 0.176778i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.1955 | −1.47039 | −0.735196 | − | 0.677855i | \(-0.762910\pi\) | ||||
−0.735196 | + | 0.677855i | \(0.762910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.7759 | 1.25042 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.88894 | + | 0.185255i | 0.0981136 | + | 0.00629158i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.88605i | − | 0.0979025i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 5.02474i | − | 0.170257i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37.6611 | − | 4.85002i | −1.27464 | − | 0.164148i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −62.8460 | −2.12458 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.5936 | 1.20191 | 0.600955 | − | 0.799283i | \(-0.294787\pi\) | ||||
0.600955 | + | 0.799283i | \(0.294787\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.34788 | − | 21.0195i | 0.0454630 | − | 0.708970i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.10230i | 0.0371376i | 0.999828 | + | 0.0185688i | \(0.00591097\pi\) | ||||
−0.999828 | + | 0.0185688i | \(0.994089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18.7841i | − | 0.632134i | −0.948737 | − | 0.316067i | \(-0.897638\pi\) | ||
0.948737 | − | 0.316067i | \(-0.102362\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.822174 | − | 12.8213i | 0.0276371 | − | 0.430984i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.5227 | −0.823391 | −0.411696 | − | 0.911321i | \(-0.635063\pi\) | ||||
−0.411696 | + | 0.911321i | \(0.635063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.3411 | 0.715758 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.98908 | − | 1.04476i | −0.133639 | − | 0.0350007i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 11.8413i | − | 0.396253i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.89470i | 0.230464i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.7970 | + | 1.52599i | 0.794559 | + | 0.0509515i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.0631 | −0.469031 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4742 | 0.515520 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 53.9999 | + | 3.46277i | 1.79701 | + | 0.115234i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.6158i | 0.951223i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 25.1303i | − | 0.834437i | −0.908806 | − | 0.417218i | \(-0.863005\pi\) | ||
0.908806 | − | 0.417218i | \(-0.136995\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.97367 | − | 23.0910i | 0.0986304 | − | 0.765880i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0888 | −1.32820 | −0.664100 | − | 0.747644i | \(-0.731185\pi\) | ||||
−0.664100 | + | 0.747644i | \(0.731185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.34967 | −0.177048 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.70256 | − | 42.1448i | 0.0893437 | − | 1.39326i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.8940i | 0.888117i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.3270i | 1.75909i | 0.475811 | + | 0.879547i | \(0.342154\pi\) | ||||
−0.475811 | + | 0.879547i | \(0.657846\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.13405 | + | 17.6849i | −0.0373683 | + | 0.582737i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.4091 | 0.935097 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −56.6422 | −1.86238 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.41990 | − | 26.5561i | 0.112324 | − | 0.872215i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.39055i | − | 0.308094i | −0.988064 | − | 0.154047i | \(-0.950769\pi\) | ||
0.988064 | − | 0.154047i | \(-0.0492307\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 16.7409i | − | 0.548662i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.54214 | + | 0.163016i | 0.0832260 | + | 0.00533691i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.59331 | 0.215624 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.7801 | −0.482846 | −0.241423 | − | 0.970420i | \(-0.577614\pi\) | ||||
−0.241423 | + | 0.970420i | \(0.577614\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.8442 | − | 1.78552i | −0.908661 | − | 0.0582683i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.3640i | 0.989837i | 0.868939 | + | 0.494919i | \(0.164802\pi\) | ||||
−0.868939 | + | 0.494919i | \(0.835198\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.6086i | 0.866496i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 91.3444 | + | 17.7676i | 2.97143 | + | 0.577980i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.93072 | −0.127731 | −0.0638656 | − | 0.997959i | \(-0.520343\pi\) | ||||
−0.0638656 | + | 0.997959i | \(0.520343\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.4577 | 1.60546 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.70902 | + | 42.2457i | −0.0878461 | + | 1.36991i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.9232i | 1.51999i | 0.649929 | + | 0.759995i | \(0.274799\pi\) | ||||
−0.649929 | + | 0.759995i | \(0.725201\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 73.6577i | − | 2.38351i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.213979 | + | 3.33687i | −0.00691695 | + | 0.107866i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.2128 | −0.555831 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.8598 | 0.640638 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −55.3502 | − | 7.12803i | −1.78364 | − | 0.229697i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.5388i | 1.33718i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.63554i | − | 0.213385i | −0.994292 | − | 0.106692i | \(-0.965974\pi\) | ||
0.994292 | − | 0.106692i | \(-0.0340260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.76739 | − | 0.433962i | −0.217400 | − | 0.0139409i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.1573 | 1.60962 | 0.804812 | − | 0.593530i | \(-0.202266\pi\) | ||||
0.804812 | + | 0.593530i | \(0.202266\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.60177 | −0.307819 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −73.0924 | − | 4.68708i | −2.34083 | − | 0.150107i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 20.3448i | − | 0.650889i | −0.945561 | − | 0.325444i | \(-0.894486\pi\) | ||
0.945561 | − | 0.325444i | \(-0.105514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.48028i | 0.207111i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.0200 | − | 2.96452i | −0.734971 | − | 0.0946499i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.2578 | −1.66676 | −0.833382 | − | 0.552698i | \(-0.813598\pi\) | ||||
−0.833382 | + | 0.552698i | \(0.813598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.2815 | −1.63396 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.39510 | + | 99.7279i | −0.203558 | + | 3.17437i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.7630i | 0.564830i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.47055i | 0.205544i | 0.994705 | + | 0.102772i | \(0.0327712\pi\) | ||||
−0.994705 | + | 0.102772i | \(0.967229\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.48893 | + | 38.8135i | −0.0789839 | + | 1.23171i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 60.0790 | 1.90463 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1233 | −0.415619 | −0.207810 | − | 0.978169i | \(-0.566633\pi\) | ||||
−0.207810 | + | 0.978169i | \(0.566633\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.9521 | + | 6.60411i | 1.07420 | + | 0.208945i |
(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 | 912.2.d.b.191.24 | yes | 24 | |
3.2 | odd | 2 | inner | 912.2.d.b.191.2 | yes | 24 | |
4.3 | odd | 2 | inner | 912.2.d.b.191.1 | ✓ | 24 | |
12.11 | even | 2 | inner | 912.2.d.b.191.23 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.d.b.191.1 | ✓ | 24 | 4.3 | odd | 2 | inner | |
912.2.d.b.191.2 | yes | 24 | 3.2 | odd | 2 | inner | |
912.2.d.b.191.23 | yes | 24 | 12.11 | even | 2 | inner | |
912.2.d.b.191.24 | yes | 24 | 1.1 | even | 1 | trivial |