Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(57,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.n (of order \(5\), degree \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 57.3 | ||
Character | \(\chi\) | \(=\) | 1148.57 |
Dual form | 1148.2.n.e.141.3 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | ||||||||
\(3\) | 0.325457 | 0.187903 | 0.0939514 | − | 0.995577i | \(-0.470050\pi\) | ||||
0.0939514 | + | 0.995577i | \(0.470050\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.538931 | + | 0.391556i | 0.241017 | + | 0.175109i | 0.701736 | − | 0.712437i | \(-0.252408\pi\) |
−0.460719 | + | 0.887546i | \(0.652408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89408 | −0.964693 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24816 | + | 3.08647i | −1.28087 | + | 0.930605i | −0.999579 | − | 0.0290186i | \(-0.990762\pi\) |
−0.281289 | + | 0.959623i | \(0.590762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13089 | − | 3.48051i | 0.313651 | − | 0.965320i | −0.662655 | − | 0.748925i | \(-0.730570\pi\) |
0.976306 | − | 0.216395i | \(-0.0694297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.175399 | + | 0.127435i | 0.0452878 | + | 0.0329035i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.83222 | − | 1.33119i | 0.444379 | − | 0.322860i | −0.342993 | − | 0.939338i | \(-0.611441\pi\) |
0.787373 | + | 0.616477i | \(0.211441\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.09763 | − | 6.45584i | −0.481229 | − | 1.48107i | −0.837369 | − | 0.546638i | \(-0.815907\pi\) |
0.356140 | − | 0.934432i | \(-0.384093\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.100572 | − | 0.309528i | −0.0219466 | − | 0.0675446i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.80862 | + | 8.64404i | −0.585637 | + | 1.80241i | 0.0110586 | + | 0.999939i | \(0.496480\pi\) |
−0.596696 | + | 0.802467i | \(0.703520\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.40795 | − | 4.33324i | −0.281591 | − | 0.866648i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.91827 | −0.369171 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.24886 | − | 5.99315i | −1.53177 | − | 1.11290i | −0.955242 | − | 0.295825i | \(-0.904406\pi\) |
−0.576532 | − | 0.817075i | \(-0.695594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.31581 | − | 3.86216i | 0.954748 | − | 0.693665i | 0.00282296 | − | 0.999996i | \(-0.499101\pi\) |
0.951925 | + | 0.306331i | \(0.0991014\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.38259 | + | 1.00451i | −0.240679 | + | 0.174863i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.205853 | − | 0.633552i | 0.0347956 | − | 0.107090i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.58977 | − | 5.51429i | −1.24775 | − | 0.906544i | −0.249662 | − | 0.968333i | \(-0.580320\pi\) |
−0.998089 | + | 0.0617887i | \(0.980320\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.368055 | − | 1.13276i | 0.0589360 | − | 0.181386i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82568 | + | 5.74591i | 0.441298 | + | 0.897361i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.39909 | − | 4.30597i | 0.213360 | − | 0.656654i | −0.785906 | − | 0.618346i | \(-0.787803\pi\) |
0.999266 | − | 0.0383082i | \(-0.0121969\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.55971 | − | 1.13319i | −0.232508 | − | 0.168927i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.991640 | + | 3.05195i | −0.144646 | + | 0.445173i | −0.996965 | − | 0.0778480i | \(-0.975195\pi\) |
0.852320 | + | 0.523021i | \(0.175195\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.596310 | − | 0.433244i | 0.0835001 | − | 0.0606664i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.495136 | + | 0.359737i | 0.0680121 | + | 0.0494137i | 0.621272 | − | 0.783595i | \(-0.286616\pi\) |
−0.553260 | + | 0.833009i | \(0.686616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.49799 | −0.471669 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.682688 | − | 2.10110i | −0.0904243 | − | 0.278297i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.83322 | − | 8.71976i | 0.368854 | − | 1.13522i | −0.578678 | − | 0.815556i | \(-0.696431\pi\) |
0.947532 | − | 0.319660i | \(-0.103569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.66183 | + | 11.2699i | 0.468849 | + | 1.44297i | 0.854077 | + | 0.520147i | \(0.174123\pi\) |
−0.385228 | + | 0.922821i | \(0.625877\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.894319 | + | 2.75243i | 0.112674 | + | 0.346774i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.97229 | − | 1.43295i | 0.244632 | − | 0.177735i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.29526 | + | 6.02686i | 1.01343 | + | 0.736298i | 0.964925 | − | 0.262525i | \(-0.0845552\pi\) |
0.0485023 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.914085 | + | 2.81326i | −0.110043 | + | 0.338677i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.25805 | + | 1.64057i | −0.267981 | + | 0.194699i | −0.713658 | − | 0.700494i | \(-0.752963\pi\) |
0.445677 | + | 0.895194i | \(0.352963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.6036 | −1.47514 | −0.737569 | − | 0.675272i | \(-0.764026\pi\) | ||||
−0.737569 | + | 0.675272i | \(0.764026\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.458229 | − | 1.41028i | −0.0529117 | − | 0.162846i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.24816 | + | 3.08647i | 0.484122 | + | 0.351735i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.25045 | −0.815740 | −0.407870 | − | 0.913040i | \(-0.633728\pi\) | ||||
−0.407870 | + | 0.913040i | \(0.633728\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.05792 | 0.895324 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.91989 | −0.649792 | −0.324896 | − | 0.945750i | \(-0.605329\pi\) | ||||
−0.324896 | + | 0.945750i | \(0.605329\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50868 | 0.163639 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.68465 | − | 1.95051i | −0.287825 | − | 0.209117i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.43556 | − | 7.49588i | −0.258169 | − | 0.794561i | −0.993189 | − | 0.116516i | \(-0.962827\pi\) |
0.735020 | − | 0.678045i | \(-0.237173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.65962 | −0.383633 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.73007 | − | 1.25697i | 0.179400 | − | 0.130342i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.39735 | − | 4.30059i | 0.143365 | − | 0.441231i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.91856 | − | 5.02663i | −0.702474 | − | 0.510377i | 0.178263 | − | 0.983983i | \(-0.442952\pi\) |
−0.880737 | + | 0.473606i | \(0.842952\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.2945 | − | 8.93247i | 1.23564 | − | 0.897747i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.39622 | − | 16.6079i | −0.536944 | − | 1.65254i | −0.739411 | − | 0.673255i | \(-0.764896\pi\) |
0.202467 | − | 0.979289i | \(-0.435104\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.02265 | − | 3.14739i | −0.100765 | − | 0.310121i | 0.887949 | − | 0.459943i | \(-0.152130\pi\) |
−0.988713 | + | 0.149821i | \(0.952130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0669965 | − | 0.206194i | 0.00653819 | − | 0.0201225i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.04265 | + | 12.4420i | 0.390818 | + | 1.20281i | 0.932171 | + | 0.362019i | \(0.117912\pi\) |
−0.541353 | + | 0.840796i | \(0.682088\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.59041 | −0.535464 | −0.267732 | − | 0.963493i | \(-0.586274\pi\) | ||||
−0.267732 | + | 0.963493i | \(0.586274\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.47015 | − | 1.79467i | −0.234456 | − | 0.170342i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.16453 | − | 5.93188i | 0.768055 | − | 0.558024i | −0.133315 | − | 0.991074i | \(-0.542562\pi\) |
0.901370 | + | 0.433049i | \(0.142562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.89828 | + | 3.55881i | −0.456767 | + | 0.331861i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.27287 | + | 10.0729i | −0.302577 | + | 0.931237i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.83222 | − | 1.33119i | −0.167960 | − | 0.122030i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.12137 | − | 15.7620i | 0.465579 | − | 1.43291i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.919639 | + | 1.87005i | 0.0829210 | + | 0.168617i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.96718 | − | 6.05437i | 0.175950 | − | 0.541519i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.787954 | + | 0.572482i | 0.0699196 | + | 0.0507996i | 0.622196 | − | 0.782861i | \(-0.286241\pi\) |
−0.552276 | + | 0.833661i | \(0.686241\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.455345 | − | 1.40141i | 0.0400909 | − | 0.123387i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.73044 | + | 4.88995i | −0.588042 | + | 0.427237i | −0.841614 | − | 0.540079i | \(-0.818394\pi\) |
0.253573 | + | 0.967316i | \(0.418394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.49166 | + | 3.98993i | −0.476187 | + | 0.345970i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.03382 | − | 0.751111i | −0.0889767 | − | 0.0646453i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.7387 | −1.51552 | −0.757759 | − | 0.652535i | \(-0.773706\pi\) | ||||
−0.757759 | + | 0.652535i | \(0.773706\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.75215 | + | 17.7033i | 0.487891 | + | 1.50157i | 0.827750 | + | 0.561097i | \(0.189621\pi\) |
−0.339859 | + | 0.940476i | \(0.610379\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.322736 | + | 0.993280i | −0.0271793 | + | 0.0836493i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.93829 | + | 18.2762i | 0.496585 | + | 1.52833i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.09891 | − | 6.45979i | −0.174305 | − | 0.536456i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.263300 | + | 0.191299i | −0.0217167 | + | 0.0157781i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0184 | + | 8.73187i | 0.984585 | + | 0.715343i | 0.958729 | − | 0.284323i | \(-0.0917687\pi\) |
0.0258564 | + | 0.999666i | \(0.491769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.50768 | + | 4.64015i | −0.122693 | + | 0.377610i | −0.993474 | − | 0.114062i | \(-0.963614\pi\) |
0.870781 | + | 0.491671i | \(0.163614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.30259 | + | 3.85256i | −0.428689 | + | 0.311461i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.37711 | 0.351578 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.338159 | + | 1.04075i | 0.0269880 | + | 0.0830606i | 0.963643 | − | 0.267192i | \(-0.0860958\pi\) |
−0.936655 | + | 0.350253i | \(0.886096\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.161145 | + | 0.117079i | 0.0127797 | + | 0.00928497i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.08888 | 0.716304 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.3161 | 1.04300 | 0.521498 | − | 0.853252i | \(-0.325373\pi\) | ||||
0.521498 | + | 0.853252i | \(0.325373\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.13845 | −0.0886279 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.527389 | 0.0408106 | 0.0204053 | − | 0.999792i | \(-0.493504\pi\) | ||||
0.0204053 | + | 0.999792i | \(0.493504\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.317821 | − | 0.230911i | −0.0244478 | − | 0.0177624i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.07070 | + | 18.6837i | 0.464238 | + | 1.42878i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.24932 | 0.323070 | 0.161535 | − | 0.986867i | \(-0.448356\pi\) | ||||
0.161535 | + | 0.986867i | \(0.448356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.68607 | + | 2.67809i | −0.278641 | + | 0.202444i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.922092 | − | 2.83791i | 0.0693087 | − | 0.213310i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.16036 | − | 1.56959i | −0.161473 | − | 0.117317i | 0.504115 | − | 0.863637i | \(-0.331819\pi\) |
−0.665587 | + | 0.746320i | \(0.731819\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.10339 | − | 3.70783i | 0.379332 | − | 0.275601i | −0.381738 | − | 0.924271i | \(-0.624674\pi\) |
0.761070 | + | 0.648670i | \(0.224674\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.19177 | + | 3.66788i | 0.0880980 | + | 0.271138i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.93121 | − | 5.94365i | −0.141985 | − | 0.436986i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.67490 | + | 11.3102i | −0.268735 | + | 0.827083i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.592778 | + | 1.82438i | 0.0431183 | + | 0.132704i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.98345 | 0.143518 | 0.0717588 | − | 0.997422i | \(-0.477139\pi\) | ||||
0.0717588 | + | 0.997422i | \(0.477139\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.45868 | − | 1.78634i | −0.176980 | − | 0.128583i | 0.495769 | − | 0.868455i | \(-0.334886\pi\) |
−0.672748 | + | 0.739871i | \(0.734886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.641895 | − | 0.466364i | 0.0459670 | − | 0.0333970i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.4089 | − | 10.4687i | 1.02659 | − | 0.745864i | 0.0589700 | − | 0.998260i | \(-0.481218\pi\) |
0.967624 | + | 0.252395i | \(0.0812184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.90080 | − | 12.0054i | 0.276521 | − | 0.851043i | −0.712293 | − | 0.701883i | \(-0.752343\pi\) |
0.988813 | − | 0.149160i | \(-0.0476569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.69975 | + | 1.96149i | 0.190426 | + | 0.138352i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.15078 | + | 9.69711i | −0.221142 | + | 0.680604i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.727000 | + | 4.20307i | −0.0507759 | + | 0.293555i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.12836 | − | 25.0165i | 0.564960 | − | 1.73877i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.8368 | + | 20.9511i | 1.99468 | + | 1.44922i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.52009 | − | 20.0668i | 0.448862 | − | 1.38145i | −0.429331 | − | 0.903147i | \(-0.641251\pi\) |
0.878193 | − | 0.478307i | \(-0.158749\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.734898 | + | 0.533934i | −0.0503544 | + | 0.0365846i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.44004 | − | 1.77280i | 0.166410 | − | 0.120904i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.31581 | − | 3.86216i | −0.360861 | − | 0.262181i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.10193 | −0.277182 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.56118 | − | 7.88249i | −0.172283 | − | 0.530233i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.91413 | + | 27.4349i | −0.596934 | + | 1.83717i | −0.0520819 | + | 0.998643i | \(0.516586\pi\) |
−0.544852 | + | 0.838532i | \(0.683414\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.07473 | + | 12.5407i | 0.271649 | + | 0.836049i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.82138 | + | 8.68331i | 0.187261 | + | 0.576331i | 0.999980 | − | 0.00632511i | \(-0.00201336\pi\) |
−0.812719 | + | 0.582656i | \(0.802013\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.948868 | − | 0.689393i | 0.0627030 | − | 0.0455564i | −0.555992 | − | 0.831187i | \(-0.687662\pi\) |
0.618695 | + | 0.785631i | \(0.287662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.38259 | + | 1.00451i | 0.0909679 | + | 0.0660921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.567505 | + | 1.74660i | −0.0371785 | + | 0.114424i | −0.967923 | − | 0.251246i | \(-0.919160\pi\) |
0.930745 | + | 0.365669i | \(0.119160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.72944 | + | 1.25651i | −0.112816 | + | 0.0819657i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.35971 | −0.153280 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.607947 | − | 1.87107i | −0.0393248 | − | 0.121029i | 0.929467 | − | 0.368905i | \(-0.120267\pi\) |
−0.968792 | + | 0.247876i | \(0.920267\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.1453 | + | 16.0895i | 1.42651 | + | 1.03642i | 0.990654 | + | 0.136399i | \(0.0435530\pi\) |
0.435852 | + | 0.900018i | \(0.356447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.37732 | 0.537405 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.666156 | −0.0425591 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.8418 | −1.58064 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.92667 | −0.122098 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.04562 | − | 6.57203i | −0.570954 | − | 0.414823i | 0.264497 | − | 0.964386i | \(-0.414794\pi\) |
−0.835452 | + | 0.549564i | \(0.814794\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.7481 | − | 45.3899i | −0.927204 | − | 2.85364i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.491010 | 0.0307482 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.7298 | + | 15.0611i | −1.29309 | + | 0.939483i | −0.999863 | − | 0.0165611i | \(-0.994728\pi\) |
−0.293224 | + | 0.956044i | \(0.594728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.89904 | + | 8.92231i | −0.180137 | + | 0.554406i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.8728 | + | 17.3446i | 1.47769 | + | 1.07361i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.78545 | − | 3.47683i | 0.295083 | − | 0.214391i | −0.430386 | − | 0.902645i | \(-0.641623\pi\) |
0.725470 | + | 0.688254i | \(0.241623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.125987 | + | 0.387747i | 0.00773930 | + | 0.0238191i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.792670 | − | 2.43959i | −0.0485106 | − | 0.149300i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.71781 | − | 29.9083i | 0.592505 | − | 1.82354i | 0.0257338 | − | 0.999669i | \(-0.491808\pi\) |
0.566771 | − | 0.823875i | \(-0.308192\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.56247 | + | 17.1195i | 0.337896 | + | 1.03994i | 0.965278 | + | 0.261226i | \(0.0841267\pi\) |
−0.627382 | + | 0.778712i | \(0.715873\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.19105 | −0.0720857 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.3556 | + | 14.0627i | 1.16719 | + | 0.848011i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.1822 | − | 9.57740i | 0.792040 | − | 0.575450i | −0.116528 | − | 0.993187i | \(-0.537177\pi\) |
0.908568 | + | 0.417737i | \(0.137177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.3844 | + | 11.1774i | −0.921038 | + | 0.669173i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.195604 | + | 0.602006i | −0.0116687 | + | 0.0359127i | −0.956721 | − | 0.291006i | \(-0.906010\pi\) |
0.945053 | + | 0.326918i | \(0.106010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.05033 | + | 2.94274i | 0.240767 | + | 0.174927i | 0.701625 | − | 0.712546i | \(-0.252458\pi\) |
−0.460858 | + | 0.887474i | \(0.652458\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.454777 | − | 1.39966i | 0.0269386 | − | 0.0829086i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.59150 | − | 4.46297i | 0.271028 | − | 0.263441i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.66831 | + | 11.2899i | −0.215783 | + | 0.664112i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.25170 | − | 1.63595i | −0.131997 | − | 0.0959013i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.56220 | − | 20.1964i | 0.383368 | − | 1.17988i | −0.554290 | − | 0.832324i | \(-0.687010\pi\) |
0.937657 | − | 0.347561i | \(-0.112990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.94119 | − | 3.58998i | 0.287687 | − | 0.209017i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.14911 | − | 5.92068i | 0.472859 | − | 0.343552i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.9094 | + | 19.5508i | 1.55621 | + | 1.13065i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.52756 | −0.260964 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.75624 | − | 5.40515i | −0.100893 | − | 0.310518i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.43935 | + | 7.50753i | −0.139677 | + | 0.429880i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.699876 | − | 2.15400i | −0.0399440 | − | 0.122935i | 0.929096 | − | 0.369838i | \(-0.120587\pi\) |
−0.969040 | + | 0.246903i | \(0.920587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.332828 | − | 1.02434i | −0.0189339 | − | 0.0582727i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.60844 | + | 2.62169i | −0.204616 | + | 0.148662i | −0.685374 | − | 0.728191i | \(-0.740361\pi\) |
0.480758 | + | 0.876853i | \(0.340361\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.479297 | + | 0.348230i | 0.0270915 | + | 0.0196831i | 0.601249 | − | 0.799062i | \(-0.294670\pi\) |
−0.574157 | + | 0.818745i | \(0.694670\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.595756 | + | 1.83355i | −0.0335670 | + | 0.103309i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.5425 | + | 12.7454i | −0.985285 | + | 0.715851i | −0.958883 | − | 0.283800i | \(-0.908405\pi\) |
−0.0264013 | + | 0.999651i | \(0.508405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 53.5401 | 2.99767 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.31571 | + | 4.04934i | 0.0734358 | + | 0.226012i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.4372 | − | 9.03619i | −0.692027 | − | 0.502787i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.6741 | −0.924913 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.81944 | −0.100615 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.20901 | 0.176919 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.1708 | −1.43848 | −0.719240 | − | 0.694762i | \(-0.755510\pi\) | ||||
−0.719240 | + | 0.694762i | \(0.755510\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.9654 | + | 15.9588i | 1.20370 | + | 0.874537i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.11072 | + | 6.49613i | 0.115321 | + | 0.354921i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0739 | 0.548763 | 0.274381 | − | 0.961621i | \(-0.411527\pi\) | ||||
0.274381 | + | 0.961621i | \(0.411527\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.65721 | − | 1.93057i | 0.144320 | − | 0.104854i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.6620 | + | 32.8142i | −0.577378 | + | 1.77699i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.59418 | + | 1.15824i | −0.0858278 | + | 0.0623575i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.25485 | + | 16.1728i | 0.282095 | + | 0.868200i | 0.987254 | + | 0.159151i | \(0.0508757\pi\) |
−0.705159 | + | 0.709049i | \(0.749124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.300814 | − | 0.925809i | −0.0161022 | − | 0.0495574i | 0.942683 | − | 0.333691i | \(-0.108294\pi\) |
−0.958785 | + | 0.284133i | \(0.908294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.16934 | + | 6.67656i | −0.115791 | + | 0.356368i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.308621 | − | 0.949837i | −0.0164262 | − | 0.0505547i | 0.942507 | − | 0.334185i | \(-0.108461\pi\) |
−0.958934 | + | 0.283630i | \(0.908461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.85931 | −0.0986817 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.596310 | − | 0.433244i | −0.0315601 | − | 0.0229297i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.23584 | + | 2.35098i | −0.170781 | + | 0.124080i | −0.669893 | − | 0.742458i | \(-0.733660\pi\) |
0.499111 | + | 0.866538i | \(0.333660\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.9064 | + | 15.9160i | −1.15297 | + | 0.837682i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.66679 | − | 5.12984i | 0.0874837 | − | 0.269247i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.79246 | − | 4.93501i | −0.355534 | − | 0.258310i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.22453 | − | 22.2348i | 0.377117 | − | 1.16065i | −0.564922 | − | 0.825144i | \(-0.691094\pi\) |
0.942039 | − | 0.335503i | \(-0.108906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.17775 | − | 16.6291i | −0.425716 | − | 0.865677i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.189125 | − | 0.582067i | 0.00981888 | − | 0.0302194i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.21759 | − | 4.51735i | −0.321935 | − | 0.233899i | 0.415066 | − | 0.909791i | \(-0.363759\pi\) |
−0.737001 | + | 0.675892i | \(0.763759\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.640234 | − | 1.97044i | 0.0330615 | − | 0.101753i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.1877 | + | 21.9327i | −1.55475 | + | 1.12959i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.77827 | + | 5.65124i | −0.399543 | + | 0.290285i | −0.769355 | − | 0.638822i | \(-0.779422\pi\) |
0.369812 | + | 0.929107i | \(0.379422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.256445 | + | 0.186318i | 0.0131381 | + | 0.00954539i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.3506 | 1.19316 | 0.596580 | − | 0.802554i | \(-0.296526\pi\) | ||||
0.596580 | + | 0.802554i | \(0.296526\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.08094 | + | 3.32679i | 0.0550897 | + | 0.169549i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.04909 | + | 12.4618i | −0.205827 | + | 0.633469i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.25840 | − | 16.1837i | −0.266612 | − | 0.820546i | −0.991318 | − | 0.131488i | \(-0.958024\pi\) |
0.724706 | − | 0.689058i | \(-0.241976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.36082 | + | 19.5766i | 0.321681 | + | 0.990031i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.19047 | + | 1.59147i | −0.110495 | + | 0.0802791i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.90750 | − | 2.83896i | −0.196607 | − | 0.142844i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.85695 | − | 21.1035i | 0.344140 | − | 1.05916i | −0.617902 | − | 0.786255i | \(-0.712017\pi\) |
0.962042 | − | 0.272900i | \(-0.0879828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.78730 | + | 1.29855i | −0.0894770 | + | 0.0650088i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.4310 | −1.71940 | −0.859701 | − | 0.510798i | \(-0.829350\pi\) | ||||
−0.859701 | + | 0.510798i | \(0.829350\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.43072 | − | 22.8694i | −0.370150 | − | 1.13921i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.34266 | + | 3.15513i | 0.215789 | + | 0.156780i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 49.2622 | 2.44184 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.5815 | −1.36382 | −0.681908 | − | 0.731438i | \(-0.738849\pi\) | ||||
−0.681908 | + | 0.731438i | \(0.738849\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.77318 | −0.284770 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.16850 | −0.451152 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.19041 | − | 2.31797i | −0.156611 | − | 0.113785i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.87208 | + | 5.76166i | 0.0916761 | + | 0.282150i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.9769 | 0.927083 | 0.463542 | − | 0.886075i | \(-0.346578\pi\) | ||||
0.463542 | + | 0.886075i | \(0.346578\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.7214 | − | 15.0550i | 1.00990 | − | 0.733736i | 0.0457127 | − | 0.998955i | \(-0.485444\pi\) |
0.964188 | + | 0.265219i | \(0.0854441\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.86988 | − | 8.83259i | 0.139538 | − | 0.429455i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.34804 | − | 6.06520i | −0.404939 | − | 0.294206i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.58678 | − | 6.96521i | 0.463937 | − | 0.337070i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.93266 | + | 5.94812i | 0.0933097 | + | 0.287178i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.96184 | + | 6.03794i | 0.0944987 | + | 0.290837i | 0.987123 | − | 0.159965i | \(-0.0511381\pi\) |
−0.892624 | + | 0.450802i | \(0.851138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.25809 | − | 25.4158i | 0.396858 | − | 1.22140i | −0.530646 | − | 0.847593i | \(-0.678051\pi\) |
0.927505 | − | 0.373811i | \(-0.121949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.683106 | − | 2.10238i | −0.0327524 | − | 0.100802i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 61.6959 | 2.95132 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.00522 | + | 1.45688i | 0.0957040 | + | 0.0695330i | 0.634608 | − | 0.772834i | \(-0.281162\pi\) |
−0.538904 | + | 0.842367i | \(0.681162\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.34136 | − | 1.70110i | 0.111493 | − | 0.0810046i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.1509 | − | 7.37505i | 0.482283 | − | 0.350399i | −0.319926 | − | 0.947443i | \(-0.603658\pi\) |
0.802209 | + | 0.597043i | \(0.203658\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.62246 | − | 4.99342i | 0.0769120 | − | 0.236711i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.91147 | + | 2.84185i | 0.185006 | + | 0.134415i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.35925 | − | 10.3387i | 0.158533 | − | 0.487913i | −0.839969 | − | 0.542634i | \(-0.817427\pi\) |
0.998502 | + | 0.0547210i | \(0.0174269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.7385 | − | 15.6882i | −1.40033 | − | 0.738727i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.490684 | + | 1.51017i | −0.0230543 | + | 0.0709539i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.97229 | − | 1.43295i | −0.0924622 | − | 0.0671777i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.78856 | − | 5.50463i | 0.0836655 | − | 0.257496i | −0.900469 | − | 0.434920i | \(-0.856777\pi\) |
0.984134 | + | 0.177424i | \(0.0567765\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.51470 | + | 2.55358i | −0.164052 | + | 0.119191i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.70075 | − | 2.68876i | 0.172361 | − | 0.125228i | −0.498260 | − | 0.867028i | \(-0.666028\pi\) |
0.670621 | + | 0.741800i | \(0.266028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3599 | − | 12.6127i | −0.806781 | − | 0.586161i | 0.106115 | − | 0.994354i | \(-0.466159\pi\) |
−0.912896 | + | 0.408193i | \(0.866159\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.42456 | 0.0660625 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.4747 | − | 32.2379i | −0.484713 | − | 1.49179i | −0.832396 | − | 0.554182i | \(-0.813031\pi\) |
0.347682 | − | 0.937612i | \(-0.386969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.16851 | − | 9.75166i | 0.146308 | − | 0.450290i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.110056 | + | 0.338718i | 0.00507112 | + | 0.0156073i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.34666 | + | 22.6107i | 0.337800 | + | 1.03964i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.0213 | + | 18.1790i | −1.14806 | + | 0.834112i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.43296 | − | 1.04111i | −0.0656108 | − | 0.0476690i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.08292 | − | 24.8767i | 0.369318 | − | 1.13664i | −0.577914 | − | 0.816097i | \(-0.696133\pi\) |
0.947233 | − | 0.320547i | \(-0.103867\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.7757 | + | 20.1802i | −1.26646 | + | 0.920140i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.95804 | 0.134596 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.76042 | − | 5.41802i | −0.0799366 | − | 0.246019i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.3953 | − | 18.4508i | −1.15077 | − | 0.836084i | −0.162188 | − | 0.986760i | \(-0.551855\pi\) |
−0.988583 | + | 0.150676i | \(0.951855\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.33382 | 0.195982 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.3875 | −1.55188 | −0.775942 | − | 0.630804i | \(-0.782725\pi\) | ||||
−0.775942 | + | 0.630804i | \(0.782725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.0917 | −1.04000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.1235 | 0.455015 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.25805 | + | 1.64057i | 0.101287 | + | 0.0735895i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.71984 | + | 17.6039i | 0.256055 | + | 0.788057i | 0.993620 | + | 0.112780i | \(0.0359757\pi\) |
−0.737565 | + | 0.675276i | \(0.764024\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.171643 | 0.00766842 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.85203 | + | 4.97829i | −0.305517 | + | 0.221971i | −0.729970 | − | 0.683479i | \(-0.760466\pi\) |
0.424454 | + | 0.905450i | \(0.360466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.59472 | − | 11.0634i | 0.159963 | − | 0.492316i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.103437 | − | 0.0751515i | −0.00459381 | − | 0.00333760i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.8183 | + | 14.3989i | −0.878432 | + | 0.638218i | −0.932836 | − | 0.360301i | \(-0.882674\pi\) |
0.0544041 | + | 0.998519i | \(0.482674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.89472 | + | 11.9867i | 0.172292 | + | 0.530261i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.02382 | + | 12.3840i | 0.177656 | + | 0.546769i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.681243 | − | 2.09665i | 0.0300192 | − | 0.0923895i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.20711 | − | 16.0258i | −0.229008 | − | 0.704816i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.38297 | 0.0607057 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.9805 | + | 23.2352i | 1.40109 | + | 1.01795i | 0.994544 | + | 0.104320i | \(0.0332667\pi\) |
0.406545 | + | 0.913631i | \(0.366733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.4505 | + | 25.0298i | −1.50642 | + | 1.09448i | −0.538681 | + | 0.842510i | \(0.681077\pi\) |
−0.967736 | + | 0.251966i | \(0.918923\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.19966 | + | 0.871603i | −0.0523574 | + | 0.0380399i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.59849 | − | 14.1527i | 0.200313 | − | 0.616501i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −48.2236 | − | 35.0365i | −2.09668 | − | 1.52333i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.19956 | + | 25.2357i | −0.355831 | + | 1.09513i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.1942 | − | 3.33684i | 1.00465 | − | 0.144535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.69304 | + | 8.28832i | −0.116430 | + | 0.358335i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.703105 | − | 0.510836i | −0.0303412 | − | 0.0220442i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.62265 | − | 4.99401i | 0.0698925 | − | 0.215107i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3439 | − | 9.69493i | 0.573700 | − | 0.416817i | −0.262747 | − | 0.964865i | \(-0.584629\pi\) |
0.836447 | + | 0.548047i | \(0.184629\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.66094 | − | 1.20674i | 0.0712776 | − | 0.0517862i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.01284 | − | 2.18896i | −0.129056 | − | 0.0937647i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.0987 | 0.474548 | 0.237274 | − | 0.971443i | \(-0.423746\pi\) | ||||
0.237274 | + | 0.971443i | \(0.423746\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.5976 | − | 32.6161i | −0.452295 | − | 1.39202i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.3877 | + | 65.8247i | −0.911148 | + | 2.80422i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.24051 | + | 6.89559i | 0.0952763 | + | 0.293230i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.628526 | − | 1.93440i | −0.0266794 | − | 0.0821109i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.8372 | − | 7.87365i | 0.459185 | − | 0.333617i | −0.334027 | − | 0.942564i | \(-0.608408\pi\) |
0.793211 | + | 0.608946i | \(0.208408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4047 | − | 9.73912i | −0.566960 | − | 0.411921i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.19602 | + | 3.68098i | −0.0504961 | + | 0.155411i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.99480 | + | 2.90239i | −0.168361 | + | 0.122321i | −0.668775 | − | 0.743465i | \(-0.733181\pi\) |
0.500414 | + | 0.865786i | \(0.333181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.72279 | 0.282830 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.49003 | − | 7.66354i | −0.104572 | − | 0.321838i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.4997 | + | 9.08157i | 0.524015 | + | 0.380719i | 0.818114 | − | 0.575056i | \(-0.195020\pi\) |
−0.294099 | + | 0.955775i | \(0.595020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.5530 | −1.86448 | −0.932242 | − | 0.361835i | \(-0.882150\pi\) | ||||
−0.932242 | + | 0.361835i | \(0.882150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.645529 | 0.0269674 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41.4111 | 1.72696 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.9369 | 1.45444 | 0.727221 | − | 0.686404i | \(-0.240812\pi\) | ||||
0.727221 | + | 0.686404i | \(0.240812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.800195 | − | 0.581376i | −0.0332550 | − | 0.0241611i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.82935 | + | 5.63015i | 0.0758941 | + | 0.233578i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.21373 | −0.133099 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.70795 | + | 4.14707i | −0.235995 | + | 0.171460i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.67954 | − | 17.4798i | 0.234420 | − | 0.721470i | −0.762778 | − | 0.646660i | \(-0.776165\pi\) |
0.997198 | − | 0.0748095i | \(-0.0238349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0841 | − | 26.2166i | −1.48682 | − | 1.08024i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.68949 | − | 3.40712i | 0.192900 | − | 0.140150i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.48060 | − | 7.63450i | −0.101866 | − | 0.313511i | 0.887116 | − | 0.461546i | \(-0.152705\pi\) |
−0.988982 | + | 0.148035i | \(0.952705\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.466207 | − | 1.43484i | −0.0191126 | − | 0.0588226i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.26954 | − | 3.90726i | 0.0519590 | − | 0.159913i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.53189 | + | 13.9477i | 0.185168 | + | 0.569889i | 0.999951 | − | 0.00987721i | \(-0.00314407\pi\) |
−0.814783 | + | 0.579766i | \(0.803144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.1543 | −0.740531 | −0.370265 | − | 0.928926i | \(-0.620733\pi\) | ||||
−0.370265 | + | 0.928926i | \(0.620733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.0071 | − | 17.4422i | −0.977646 | − | 0.710301i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.93177 | − | 6.48931i | 0.363128 | − | 0.263828i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.1307 | − | 10.9931i | 0.614135 | − | 0.446195i | −0.236733 | − | 0.971575i | \(-0.576077\pi\) |
0.850868 | + | 0.525380i | \(0.176077\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.02544 | + | 3.15600i | −0.0415531 | + | 0.127887i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.50092 | + | 6.90282i | 0.384366 | + | 0.279258i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.52444 | − | 26.2355i | 0.344299 | − | 1.05964i | −0.617659 | − | 0.786446i | \(-0.711919\pi\) |
0.961958 | − | 0.273197i | \(-0.0880811\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.236608 | + | 1.36792i | −0.00954094 | + | 0.0551598i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.96214 | − | 15.2719i | 0.199768 | − | 0.614824i | −0.800119 | − | 0.599841i | \(-0.795231\pi\) |
0.999888 | − | 0.0149830i | \(-0.00476941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.6041 | − | 21.5086i | −1.18989 | − | 0.864505i | −0.196637 | − | 0.980476i | \(-0.563002\pi\) |
−0.993253 | + | 0.115971i | \(0.963002\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.38769 | − | 16.5816i | 0.216200 | − | 0.665397i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.37637 | + | 4.63271i | −0.255464 | + | 0.185605i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.9996 | + | 10.8978i | −0.599982 | + | 0.435913i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.38514 | + | 6.81870i | 0.374806 | + | 0.272313i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.2467 | −0.847162 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.95879 | − | 30.6500i | −0.396453 | − | 1.22016i | −0.927824 | − | 0.373018i | \(-0.878323\pi\) |
0.531371 | − | 0.847139i | \(-0.321677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.12201 | − | 6.53088i | 0.0843424 | − | 0.259579i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.200494 | + | 0.617057i | 0.00795636 | + | 0.0244872i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.13089 | + | 3.48051i | 0.0448073 | + | 0.137903i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.53496 | − | 4.74793i | 0.258519 | − | 0.187825i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.9334 | − | 10.1232i | −0.550338 | − | 0.399844i | 0.277572 | − | 0.960705i | \(-0.410470\pi\) |
−0.827910 | + | 0.560861i | \(0.810470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.99168 | − | 15.3628i | 0.196853 | − | 0.605850i | −0.803097 | − | 0.595848i | \(-0.796816\pi\) |
0.999950 | − | 0.0100021i | \(-0.00318382\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.794130 | − | 0.576969i | 0.0312688 | − | 0.0227181i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −50.4766 | −1.98444 | −0.992220 | − | 0.124494i | \(-0.960269\pi\) | ||||
−0.992220 | + | 0.124494i | \(0.960269\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8773 | + | 45.7875i | 0.583984 | + | 1.79732i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.73007 | − | 1.25697i | −0.0678068 | − | 0.0492645i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.3771 | −0.953951 | −0.476976 | − | 0.878917i | \(-0.658267\pi\) | ||||
−0.476976 | + | 0.878917i | \(0.658267\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.54194 | −0.216541 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.4757 | 1.42305 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.3693 | −0.559748 | −0.279874 | − | 0.960037i | \(-0.590293\pi\) | ||||
−0.279874 | + | 0.960037i | \(0.590293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.69198 | − | 5.58855i | −0.299183 | − | 0.217370i | 0.428058 | − | 0.903751i | \(-0.359198\pi\) |
−0.727241 | + | 0.686382i | \(0.759198\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.833553 | − | 2.56541i | −0.0323725 | − | 0.0996324i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.52191 | −0.175352 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 74.9729 | − | 54.4710i | 2.90296 | − | 2.10912i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.90117 | + | 8.92888i | −0.112166 | + | 0.345210i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.3403 | − | 36.5744i | −1.94337 | − | 1.41194i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.4859 | − | 16.3370i | 0.866767 | − | 0.629743i | −0.0629502 | − | 0.998017i | \(-0.520051\pi\) |
0.929718 | + | 0.368273i | \(0.120051\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.70084 | + | 8.31232i | 0.103955 | + | 0.319941i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.95743 | + | 9.10204i | 0.113663 | + | 0.349820i | 0.991666 | − | 0.128836i | \(-0.0411241\pi\) |
−0.878003 | + | 0.478656i | \(0.841124\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.64266 | + | 8.13326i | −0.101416 | + | 0.312126i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.918237 | + | 2.82604i | 0.0351869 | + | 0.108294i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.69887 | 0.179797 | 0.0898987 | − | 0.995951i | \(-0.471346\pi\) | ||||
0.0898987 | + | 0.995951i | \(0.471346\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.55993 | − | 6.94569i | −0.365266 | − | 0.265381i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.308816 | − | 0.224368i | 0.0117821 | − | 0.00856017i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.81201 | − | 1.31650i | 0.0690321 | − | 0.0501547i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0561 | − | 30.9496i | 0.382553 | − | 1.17738i | −0.555686 | − | 0.831392i | \(-0.687544\pi\) |
0.938240 | − | 0.345986i | \(-0.112456\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.2945 | − | 8.93247i | −0.467029 | − | 0.339317i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.83183 | + | 11.7931i | −0.145349 | + | 0.447340i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.8262 | + | 6.76628i | 0.485826 | + | 0.256291i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.184699 | + | 0.568444i | −0.00698594 | + | 0.0215005i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.1805 | + | 11.0292i | 0.573358 | + | 0.416569i | 0.836323 | − | 0.548236i | \(-0.184701\pi\) |
−0.262966 | + | 0.964805i | \(0.584701\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.6789 | + | 60.5653i | −0.742202 | + | 2.28426i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.562858 | + | 0.408940i | −0.0211985 | + | 0.0154016i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.1275 | + | 10.2642i | −0.531319 | + | 0.386026i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.2694 | − | 16.1797i | −0.836346 | − | 0.607641i | 0.0850012 | − | 0.996381i | \(-0.472911\pi\) |
−0.921348 | + | 0.388740i | \(0.872911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.9834 | 0.786938 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.4546 | + | 56.7974i | 0.691130 | + | 2.12708i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.95583 | + | 12.1748i | −0.147940 | + | 0.455311i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.197861 | − | 0.608953i | −0.00738924 | − | 0.0227418i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.5964 | − | 32.6122i | −0.395178 | − | 1.21623i | −0.928823 | − | 0.370523i | \(-0.879178\pi\) |
0.533646 | − | 0.845708i | \(-0.320822\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.67733 | + | 1.94519i | −0.0997089 | + | 0.0724428i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.20736 | + | 5.23645i | 0.268045 | + | 0.194746i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.3557 | + | 44.1823i | −0.533158 | + | 1.64089i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.1552 | − | 19.0028i | 0.970041 | − | 0.704776i | 0.0145803 | − | 0.999894i | \(-0.495359\pi\) |
0.955461 | + | 0.295117i | \(0.0953588\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.4473 | −0.794344 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.16860 | − | 9.75195i | −0.117195 | − | 0.360689i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.98533 | + | 2.89551i | 0.147201 | + | 0.106948i | 0.658949 | − | 0.752188i | \(-0.271002\pi\) |
−0.511747 | + | 0.859136i | \(0.671002\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.216805 | −0.00799698 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −53.8413 | −1.98327 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.8745 | 0.951810 | 0.475905 | − | 0.879497i | \(-0.342121\pi\) | ||||
0.475905 | + | 0.879497i | \(0.342121\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.08493 | −0.297007 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.8721 | − | 15.1644i | −0.765722 | − | 0.556329i | 0.134938 | − | 0.990854i | \(-0.456916\pi\) |
−0.900660 | + | 0.434525i | \(0.856916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.05807 | + | 9.41176i | 0.112039 | + | 0.344820i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.1326 | 0.626850 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5838 | − | 7.68959i | 0.386724 | − | 0.280971i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.93209 | + | 18.2571i | −0.216465 | + | 0.666211i | 0.782581 | + | 0.622548i | \(0.213903\pi\) |
−0.999046 | + | 0.0436623i | \(0.986097\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.94396 | − | 2.13891i | −0.107284 | − | 0.0779463i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.62941 | + | 1.91038i | −0.0956941 | + | 0.0695258i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.40237 | + | 13.5491i | 0.160007 | + | 0.492450i | 0.998634 | − | 0.0522559i | \(-0.0166411\pi\) |
−0.838627 | + | 0.544706i | \(0.816641\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.79987 | − | 14.7725i | −0.174224 | − | 0.536207i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.7771 | + | 36.2461i | −0.426918 | + | 1.31392i | 0.474227 | + | 0.880403i | \(0.342728\pi\) |
−0.901145 | + | 0.433517i | \(0.857272\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.72753 | + | 5.31679i | 0.0625408 | + | 0.192481i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.36623 | −0.157861 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.1452 | − | 19.7221i | −0.980155 | − | 0.712124i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.3236 | + | 28.5702i | −1.41804 | + | 1.03027i | −0.425954 | + | 0.904745i | \(0.640061\pi\) |
−0.992091 | + | 0.125525i | \(0.959939\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.74665 | + | 4.90173i | −0.242975 | + | 0.176531i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.743810 | + | 2.28921i | −0.0267530 | + | 0.0823372i | −0.963542 | − | 0.267559i | \(-0.913783\pi\) |
0.936789 | + | 0.349896i | \(0.113783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.2201 | − | 17.5969i | −0.870012 | − | 0.632100i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.943512 | + | 2.90383i | −0.0338483 | + | 0.104174i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.1674 | − | 30.2949i | 1.11669 | − | 1.08543i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.52898 | − | 13.9388i | 0.162060 | − | 0.498768i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.8235 | + | 11.4965i | 0.565487 | + | 0.410850i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.225266 | + | 0.693299i | −0.00804010 | + | 0.0247449i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.7840 | + | 11.4677i | −0.562639 | + | 0.408781i | −0.832424 | − | 0.554140i | \(-0.813047\pi\) |
0.269785 | + | 0.962921i | \(0.413047\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.55746 | − | 1.13156i | 0.0554470 | − | 0.0402846i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.16453 | − | 5.93188i | −0.290297 | − | 0.210913i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.3662 | 1.53998 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0410033 | + | 0.126195i | 0.00145424 | + | 0.00447568i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.93592 | − | 15.1912i | 0.174839 | − | 0.538100i | −0.824787 | − | 0.565444i | \(-0.808705\pi\) |
0.999626 | + | 0.0273439i | \(0.00870493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.24582 | + | 6.91191i | 0.0794513 | + | 0.244526i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.04869 | + | 21.6936i | 0.249053 | + | 0.766507i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 53.5420 | − | 38.9005i | 1.88946 | − | 1.37277i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.89828 | + | 3.55881i | 0.172642 | + | 0.125432i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.16273 | − | 9.73389i | 0.111333 | − | 0.342649i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9082 | − | 7.92527i | 0.383512 | − | 0.278637i | −0.379280 | − | 0.925282i | \(-0.623828\pi\) |
0.762792 | + | 0.646644i | \(0.223828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9233 | 0.488914 | 0.244457 | − | 0.969660i | \(-0.421390\pi\) | ||||
0.244457 | + | 0.969660i | \(0.421390\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.81035 | + | 5.57168i | 0.0634916 | + | 0.195407i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.17646 | + | 5.21400i | 0.251380 | + | 0.182638i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.7334 | −1.07523 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.5912 | 0.370088 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.8587 | −0.972276 | −0.486138 | − | 0.873882i | \(-0.661595\pi\) | ||||
−0.486138 | + | 0.873882i | \(0.661595\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.91228 | −0.101516 | −0.0507578 | − | 0.998711i | \(-0.516164\pi\) | ||||
−0.0507578 | + | 0.998711i | \(0.516164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.29942 | + | 4.57680i | 0.219318 | + | 0.159344i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.09908 | + | 18.7710i | 0.212086 | + | 0.652733i | 0.999348 | + | 0.0361143i | \(0.0114980\pi\) |
−0.787262 | + | 0.616619i | \(0.788502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.34109 | −0.289698 | −0.144849 | − | 0.989454i | \(-0.546270\pi\) | ||||
−0.144849 | + | 0.989454i | \(0.546270\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.29023 | − | 3.11704i | 0.148826 | − | 0.108129i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.699847 | + | 2.15391i | −0.0242482 | + | 0.0746284i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.284226 | + | 0.206503i | 0.00983606 | + | 0.00714631i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.1972 | + | 7.40867i | −0.352465 | + | 0.256081i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.69668 | + | 5.22184i | 0.0585759 | + | 0.180278i | 0.976063 | − | 0.217487i | \(-0.0697860\pi\) |
−0.917487 | + | 0.397765i | \(0.869786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.1644 | + | 71.2926i | 0.798771 | + | 2.45836i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0636606 | + | 0.195927i | −0.00219259 | + | 0.00674809i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.0808692 | − | 0.248890i | −0.00278199 | − | 0.00856207i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.5731 | −0.569459 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.31821 | + | 0.957735i | 0.0452408 | + | 0.0328694i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 68.9825 | − | 50.1187i | 2.36469 | − | 1.71805i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.0251 | − | 21.0880i | 0.993801 | − | 0.722039i | 0.0330508 | − | 0.999454i | \(-0.489478\pi\) |
0.960750 | + | 0.277415i | \(0.0894777\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.04403 | + | 12.4462i | −0.138303 | + | 0.425653i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.95566 | + | 7.23321i | 0.340079 | + | 0.247082i | 0.744695 | − | 0.667405i | \(-0.232595\pi\) |
−0.404616 | + | 0.914487i | \(0.632595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.44486 | − | 7.52451i | 0.0834175 | − | 0.256733i | −0.900645 | − | 0.434556i | \(-0.856905\pi\) |
0.984063 | + | 0.177823i | \(0.0569054\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.49434 | − | 1.45251i | 0.0509269 | − | 0.0495012i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.17942 | − | 28.2513i | 0.312471 | − | 0.961687i | −0.664312 | − | 0.747455i | \(-0.731275\pi\) |
0.976783 | − | 0.214231i | \(-0.0687247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.29009 | + | 1.66385i | 0.0778654 | + | 0.0565725i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.19388 | + | 3.67438i | −0.0405462 | + | 0.124788i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.8011 | − | 22.3783i | 1.04485 | − | 0.759131i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.3575 | − | 22.0560i | 1.02863 | − | 0.747341i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.0229 | + | 14.5475i | 0.677671 | + | 0.492357i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.36594 | −0.215208 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.14151 | − | 15.8239i | −0.173616 | − | 0.534336i | 0.825951 | − | 0.563742i | \(-0.190639\pi\) |
−0.999568 | + | 0.0294053i | \(0.990639\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.13572 | − | 6.57306i | 0.0720359 | − | 0.221704i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.19118 | + | 3.66609i | 0.0401320 | + | 0.123514i | 0.969115 | − | 0.246608i | \(-0.0793160\pi\) |
−0.928983 | + | 0.370122i | \(0.879316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.95612 | − | 6.02032i | −0.0658287 | − | 0.202600i | 0.912732 | − | 0.408559i | \(-0.133969\pi\) |
−0.978561 | + | 0.205959i | \(0.933969\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.60815 | − | 1.16839i | 0.0540572 | − | 0.0392749i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.2690 | − | 29.2572i | −1.35210 | − | 0.982359i | −0.998904 | − | 0.0468105i | \(-0.985094\pi\) |
−0.353198 | − | 0.935549i | \(-0.614906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.300972 | − | 0.926296i | 0.0100943 | − | 0.0310670i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.2313 | + | 24.8705i | −1.14679 | + | 0.833193i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.7830 | 0.728940 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.549701 | − | 1.69181i | −0.0183745 | − | 0.0565508i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.75787 | + | 6.36296i | 0.292417 | + | 0.212453i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −66.9959 | −2.23444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.38608 | 0.0461769 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.47353 | −0.0490359 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.20220 | 0.139686 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.0248 | + | 26.1735i | 1.19618 | + | 0.869078i | 0.993904 | − | 0.110250i | \(-0.0351653\pi\) |
0.202279 | + | 0.979328i | \(0.435165\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.6171 | + | 48.0644i | 0.517986 | + | 1.59420i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.5429 | −0.548091 | −0.274045 | − | 0.961717i | \(-0.588362\pi\) | ||||
−0.274045 | + | 0.961717i | \(0.588362\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.1486 | − | 18.2715i | 0.832298 | − | 0.604700i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.793902 | + | 2.44338i | −0.0262456 | + | 0.0807757i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.73044 | + | 4.88995i | 0.222259 | + | 0.161481i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.05517 | − | 3.67279i | 0.166755 | − | 0.121154i | −0.501278 | − | 0.865286i | \(-0.667137\pi\) |
0.668033 | + | 0.744132i | \(0.267137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.227780 | − | 0.701033i | −0.00750559 | − | 0.0230998i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.15642 | + | 9.71445i | 0.103895 | + | 0.319755i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.2087 | + | 40.6522i | −0.434299 | + | 1.33664i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.95962 | + | 9.10879i | 0.0972068 | + | 0.299172i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.2468 | 1.05798 | 0.528991 | − | 0.848627i | \(-0.322571\pi\) | ||||
0.528991 | + | 0.848627i | \(0.322571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.49166 | + | 3.98993i | 0.179982 | + | 0.130765i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.17439 | + | 0.853246i | −0.0384479 | + | 0.0279340i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.40909 | + | 4.65648i | −0.209600 | + | 0.152283i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.96352 | − | 12.1985i | 0.129483 | − | 0.398506i | −0.865209 | − | 0.501412i | \(-0.832814\pi\) |
0.994691 | + | 0.102906i | \(0.0328140\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.155991 | + | 0.113334i | 0.00509056 | + | 0.00369851i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.63197 | + | 8.10036i | −0.0857997 | + | 0.264064i | −0.984747 | − | 0.173993i | \(-0.944333\pi\) |
0.898947 | + | 0.438057i | \(0.144333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −57.6041 | + | 8.28723i | −1.87585 | + | 0.269869i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.394882 | + | 1.21532i | −0.0128455 | + | 0.0395345i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.70983 | − | 4.87498i | −0.218040 | − | 0.158415i | 0.473404 | − | 0.880845i | \(-0.343025\pi\) |
−0.691444 | + | 0.722430i | \(0.743025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.2532 | + | 43.8669i | −0.462679 | + | 1.42398i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.70933 | + | 4.14807i | −0.185138 | + | 0.134510i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.89974 | + | 2.83333i | −0.126325 | + | 0.0917806i | −0.649154 | − | 0.760657i | \(-0.724877\pi\) |
0.522829 | + | 0.852438i | \(0.324877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.06894 | + | 0.776633i | 0.0345902 | + | 0.0251313i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.4250 | 0.563270 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.48155 | + | 16.8705i | 0.177009 | + | 0.544776i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.76202 | − | 11.5783i | 0.121356 | − | 0.373494i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.6998 | − | 36.0081i | −0.377019 | − | 1.16035i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.625608 | − | 1.92542i | −0.0201390 | − | 0.0619816i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.57445 | + | 3.32353i | −0.147104 | + | 0.106878i | −0.658903 | − | 0.752228i | \(-0.728979\pi\) |
0.511799 | + | 0.859105i | \(0.328979\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.04779 | − | 2.94089i | −0.130034 | − | 0.0944751i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.00083 | − | 27.7017i | 0.288850 | − | 0.888990i | −0.696368 | − | 0.717685i | \(-0.745202\pi\) |
0.985218 | − | 0.171305i | \(-0.0547983\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0593 | − | 10.9412i | 0.482780 | − | 0.350760i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.42671 | −0.173794 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.33223 | − | 28.7217i | −0.298565 | − | 0.918887i | −0.982001 | − | 0.188877i | \(-0.939515\pi\) |
0.683436 | − | 0.730010i | \(-0.260485\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.4824 | + | 24.3264i | 1.07010 | + | 0.777475i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1791 | 0.516558 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.5835 | −0.433246 | −0.216623 | − | 0.976255i | \(-0.569504\pi\) | ||||
−0.216623 | + | 0.976255i | \(0.569504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.8645 | 0.378035 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.04440 | 0.0332435 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.2914 | + | 24.1876i | 1.05861 | + | 0.769122i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.27646 | + | 25.4723i | 0.262910 | + | 0.809155i | 0.992167 | + | 0.124915i | \(0.0398659\pi\) |
−0.729257 | + | 0.684240i | \(0.760134\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.51749 | −0.270294 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.80307 | − | 4.94272i | 0.215672 | − | 0.156695i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.26423 | − | 28.5124i | 0.293401 | − | 0.902995i | −0.690353 | − | 0.723473i | \(-0.742545\pi\) |
0.983754 | − | 0.179523i | \(-0.0574553\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.5592 | + | 10.5779i | 0.460634 | + | 0.334670i |
(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 | 1148.2.n.e.57.3 | ✓ | 24 | |
41.18 | even | 5 | inner | 1148.2.n.e.141.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.n.e.57.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1148.2.n.e.141.3 | yes | 24 | 41.18 | even | 5 | inner |