Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(81,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.r (of order \(6\), degree \(2\), 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: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 737.21 | ||
Character | \(\chi\) | \(=\) | 1148.737 |
Dual form | 1148.2.r.a.81.21 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.59496 | − | 0.920850i | 0.920850 | − | 0.531653i | 0.0369437 | − | 0.999317i | \(-0.488238\pi\) |
0.883906 | + | 0.467664i | \(0.154904\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.70544 | − | 2.95391i | 0.762697 | − | 1.32103i | −0.178758 | − | 0.983893i | \(-0.557208\pi\) |
0.941456 | − | 0.337137i | \(-0.109459\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.57642 | − | 0.601730i | −0.973794 | − | 0.227432i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.195929 | − | 0.339358i | 0.0653096 | − | 0.113119i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.43105 | + | 2.55827i | −1.33601 | + | 0.771346i | −0.986213 | − | 0.165479i | \(-0.947083\pi\) |
−0.349798 | + | 0.936825i | \(0.613750\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.75965i | − | 1.32009i | −0.751226 | − | 0.660045i | \(-0.770537\pi\) | ||
0.751226 | − | 0.660045i | \(-0.229463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.28183i | − | 1.62196i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.32577 | − | 0.765436i | 0.321547 | − | 0.185645i | −0.330535 | − | 0.943794i | \(-0.607229\pi\) |
0.652082 | + | 0.758148i | \(0.273896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.164258 | − | 0.0948345i | −0.0376834 | − | 0.0217565i | 0.481040 | − | 0.876699i | \(-0.340259\pi\) |
−0.518723 | + | 0.854942i | \(0.673593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.66338 | + | 1.41276i | −1.01763 | + | 0.308289i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.638818 | − | 1.10647i | 0.133203 | − | 0.230714i | −0.791707 | − | 0.610901i | \(-0.790807\pi\) |
0.924909 | + | 0.380187i | \(0.124140\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.31707 | − | 5.74533i | −0.663414 | − | 1.14907i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.80342i | 0.924418i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.12593i | − | 1.13756i | −0.822491 | − | 0.568778i | \(-0.807416\pi\) | ||
0.822491 | − | 0.568778i | \(-0.192584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.46240 | − | 5.99706i | −0.621866 | − | 1.07710i | −0.989138 | − | 0.146990i | \(-0.953041\pi\) |
0.367272 | − | 0.930114i | \(-0.380292\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.71156 | + | 8.16066i | −0.820177 | + | 1.42059i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.17139 | + | 6.58430i | −1.04315 | + | 1.11295i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.21486 | − | 9.03241i | 0.857318 | − | 1.48492i | −0.0171594 | − | 0.999853i | \(-0.505462\pi\) |
0.874478 | − | 0.485066i | \(-0.161204\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.38293 | − | 7.59145i | −0.701830 | − | 1.21560i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.72483 | − | 2.86817i | 0.894068 | − | 0.447932i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.258062 | −0.0393541 | −0.0196771 | − | 0.999806i | \(-0.506264\pi\) | ||||
−0.0196771 | + | 0.999806i | \(0.506264\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.668290 | − | 1.15751i | −0.0996228 | − | 0.172552i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.76284 | − | 1.59513i | −0.403002 | − | 0.232674i | 0.284776 | − | 0.958594i | \(-0.408081\pi\) |
−0.687779 | + | 0.725920i | \(0.741414\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.27584 | + | 3.10061i | 0.896549 | + | 0.442945i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.40970 | − | 2.44168i | 0.197398 | − | 0.341903i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.49774 | + | 3.17412i | −0.755173 | + | 0.435999i | −0.827560 | − | 0.561377i | \(-0.810272\pi\) |
0.0723869 | + | 0.997377i | \(0.476938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.4519i | 2.35321i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.349313 | −0.0462677 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.59384 | + | 9.68881i | 0.728256 | + | 1.26138i | 0.957620 | + | 0.288035i | \(0.0930021\pi\) |
−0.229364 | + | 0.973341i | \(0.573665\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.82916 | + | 11.8285i | −0.874384 | + | 1.51448i | −0.0169675 | + | 0.999856i | \(0.505401\pi\) |
−0.857417 | + | 0.514622i | \(0.827932\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.708996 | + | 0.756433i | −0.0893251 | + | 0.0953016i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.0596 | − | 8.11731i | −1.74388 | − | 1.00683i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.11534 | − | 0.643944i | 0.136261 | − | 0.0786702i | −0.430320 | − | 0.902676i | \(-0.641599\pi\) |
0.566581 | + | 0.824006i | \(0.308266\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.35302i | − | 0.283271i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.74600i | 0.325891i | 0.986635 | + | 0.162945i | \(0.0520994\pi\) | ||||
−0.986635 | + | 0.162945i | \(0.947901\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.22045 | + | 2.11388i | 0.142843 | + | 0.247411i | 0.928566 | − | 0.371167i | \(-0.121042\pi\) |
−0.785723 | + | 0.618578i | \(0.787709\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.5812 | − | 6.10904i | −1.22181 | − | 0.705412i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.9556 | − | 3.92487i | 1.47643 | − | 0.447280i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.75063 | + | 3.89748i | 0.759505 | + | 0.438501i | 0.829118 | − | 0.559074i | \(-0.188843\pi\) |
−0.0696128 | + | 0.997574i | \(0.522176\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.01101 | + | 8.67932i | 0.556779 | + | 0.964369i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.45819 | 0.269821 | 0.134911 | − | 0.990858i | \(-0.456925\pi\) | ||||
0.134911 | + | 0.990858i | \(0.456925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.22163i | − | 0.566365i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.64106 | − | 9.77061i | −0.604785 | − | 1.04752i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.445657 | − | 0.257300i | −0.0472396 | − | 0.0272738i | 0.476194 | − | 0.879340i | \(-0.342016\pi\) |
−0.523434 | + | 0.852066i | \(0.675349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.86402 | + | 12.2628i | −0.300231 | + | 1.28550i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.0448 | − | 6.37671i | −1.14529 | − | 0.661234i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.560266 | + | 0.323469i | −0.0574820 | + | 0.0331873i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9101i | 1.41236i | 0.708031 | + | 0.706181i | \(0.249583\pi\) | ||||
−0.708031 | + | 0.706181i | \(0.750417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00495i | 0.201505i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.12995 | − | 4.69383i | 0.808960 | − | 0.467053i | −0.0376345 | − | 0.999292i | \(-0.511982\pi\) |
0.846595 | + | 0.532238i | \(0.178649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.62327 | − | 13.2039i | 0.751143 | − | 1.30102i | −0.196126 | − | 0.980579i | \(-0.562836\pi\) |
0.947269 | − | 0.320440i | \(-0.103831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.77996 | + | 16.1846i | −0.368886 | + | 1.57946i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.85744 | − | 17.0736i | 0.952955 | − | 1.65057i | 0.213975 | − | 0.976839i | \(-0.431359\pi\) |
0.738980 | − | 0.673727i | \(-0.235308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.91868 | + | 3.41715i | −0.566907 | + | 0.327304i | −0.755913 | − | 0.654672i | \(-0.772807\pi\) |
0.189006 | + | 0.981976i | \(0.439473\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 19.2084i | − | 1.82318i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.53474 | −0.426592 | −0.213296 | − | 0.976988i | \(-0.568420\pi\) | ||||
−0.213296 | + | 0.976988i | \(0.568420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.17894 | − | 3.77403i | −0.203187 | − | 0.351930i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.61523 | − | 0.932553i | −0.149328 | − | 0.0862145i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.87633 | + | 1.17432i | −0.355343 | + | 0.107650i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.58945 | − | 13.1453i | 0.689950 | − | 1.19503i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.48971 | − | 9.84631i | 0.585157 | − | 0.887812i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.57385 | −0.498541 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.1994 | 1.88114 | 0.940572 | − | 0.339595i | \(-0.110290\pi\) | ||||
0.940572 | + | 0.339595i | \(0.110290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.411599 | + | 0.237637i | −0.0362393 | + | 0.0209227i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.56477 | − | 7.90641i | 0.398825 | − | 0.690786i | −0.594756 | − | 0.803906i | \(-0.702751\pi\) |
0.993581 | + | 0.113120i | \(0.0360846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.366133 | + | 0.343172i | 0.0317477 | + | 0.0297568i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.1889 | + | 8.19195i | 1.22118 | + | 0.705051i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.2179 | − | 9.36341i | 1.38559 | − | 0.799970i | 0.392775 | − | 0.919635i | \(-0.371515\pi\) |
0.992814 | + | 0.119664i | \(0.0381818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3534 | −1.13262 | −0.566310 | − | 0.824192i | \(-0.691630\pi\) | ||||
−0.566310 | + | 0.824192i | \(0.691630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.87550 | −0.494806 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.1765 | + | 21.0902i | 1.01825 | + | 1.76365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.0955 | − | 10.4474i | −1.50275 | − | 0.867611i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.8649 | − | 0.833761i | 1.06108 | − | 0.0687675i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.3202 | − | 8.84515i | −1.25508 | − | 0.724623i | −0.282969 | − | 0.959129i | \(-0.591319\pi\) |
−0.972115 | + | 0.234507i | \(0.924653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0218 | + | 9.25017i | −1.30383 | + | 0.752769i | −0.981059 | − | 0.193708i | \(-0.937949\pi\) |
−0.322774 | + | 0.946476i | \(0.604615\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.599883i | − | 0.0484977i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.6197 | −1.89718 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3609 | − | 7.71393i | 1.06632 | − | 0.615638i | 0.139144 | − | 0.990272i | \(-0.455565\pi\) |
0.927173 | + | 0.374634i | \(0.122232\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.84578 | + | 10.1252i | −0.463601 | + | 0.802980i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.31166 | + | 2.46632i | −0.182184 | + | 0.194373i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.08825 | + | 5.34900i | −0.241890 | + | 0.418966i | −0.961253 | − | 0.275669i | \(-0.911101\pi\) |
0.719363 | + | 0.694635i | \(0.244434\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.0706 | + | 27.8351i | 1.25109 | + | 2.16696i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.63626i | 0.281382i | 0.990054 | + | 0.140691i | \(0.0449324\pi\) | ||||
−0.990054 | + | 0.140691i | \(0.955068\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65429 | −0.742638 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0643658 | + | 0.0371616i | −0.00492217 | + | 0.00284182i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.101342 | − | 0.175530i | 0.00770489 | − | 0.0133453i | −0.862147 | − | 0.506658i | \(-0.830881\pi\) |
0.869852 | + | 0.493313i | \(0.164214\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.08901 | + | 16.7983i | 0.384693 | + | 1.26984i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.8439 | + | 10.3022i | 1.34123 | + | 0.774359i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.35919 | − | 4.24883i | 0.550052 | − | 0.317572i | −0.199091 | − | 0.979981i | \(-0.563799\pi\) |
0.749143 | + | 0.662409i | \(0.230466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.61837i | − | 0.120293i | −0.998190 | − | 0.0601463i | \(-0.980843\pi\) | ||
0.998190 | − | 0.0601463i | \(-0.0191567\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.1545i | 1.85948i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.7873 | − | 30.8085i | −1.30775 | − | 2.26509i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.91638 | + | 6.78336i | −0.286394 | + | 0.496049i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.89036 | − | 12.3756i | 0.210243 | − | 0.900192i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.36245 | + | 5.40541i | 0.677443 | + | 0.391122i | 0.798891 | − | 0.601476i | \(-0.205420\pi\) |
−0.121448 | + | 0.992598i | \(0.538754\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.87819 | + | 2.23908i | −0.279158 | + | 0.161172i | −0.633042 | − | 0.774117i | \(-0.718194\pi\) |
0.353884 | + | 0.935289i | \(0.384861\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −29.8993 | −2.14113 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.60990 | −0.542183 | −0.271092 | − | 0.962554i | \(-0.587385\pi\) | ||||
−0.271092 | + | 0.962554i | \(0.587385\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6687 | − | 11.3557i | 1.39428 | − | 0.804987i | 0.400494 | − | 0.916300i | \(-0.368839\pi\) |
0.993785 | + | 0.111312i | \(0.0355054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.18595 | − | 2.05413i | 0.0836505 | − | 0.144887i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.68615 | + | 15.7829i | −0.258717 | + | 1.10775i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.29105 | − | 21.8021i | 0.0901707 | − | 1.52273i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.250326 | − | 0.433577i | −0.0173988 | − | 0.0301357i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.970447 | 0.0671272 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.4213i | − | 0.992801i | −0.868094 | − | 0.496401i | \(-0.834655\pi\) | ||
0.868094 | − | 0.496401i | \(-0.165345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.52866 | + | 4.37976i | 0.173261 | + | 0.300096i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.440111 | + | 0.762294i | −0.0300153 | + | 0.0519880i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.31199 | + | 17.5344i | 0.360601 | + | 1.19031i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.89313 | + | 2.24770i | 0.263073 | + | 0.151885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.64321 | − | 6.31022i | −0.245069 | − | 0.424471i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.76047 | −0.117890 | −0.0589449 | − | 0.998261i | \(-0.518774\pi\) | ||||
−0.0589449 | + | 0.998261i | \(0.518774\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.59964 | −0.173309 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.4360 | − | 6.60259i | 0.759035 | − | 0.438229i | −0.0699142 | − | 0.997553i | \(-0.522273\pi\) |
0.828949 | + | 0.559324i | \(0.188939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.5476 | + | 7.24434i | 0.829167 | + | 0.478720i | 0.853567 | − | 0.520983i | \(-0.174434\pi\) |
−0.0244005 | + | 0.999702i | \(0.507768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.0494 | − | 18.1902i | 1.12177 | − | 1.19683i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5717 | + | 7.83564i | 0.889114 | + | 0.513330i | 0.873653 | − | 0.486550i | \(-0.161745\pi\) |
0.0154613 | + | 0.999880i | \(0.495078\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.42375 | + | 5.44080i | −0.614737 | + | 0.354919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.3560 | 0.932520 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.32274i | 0.603038i | 0.953460 | + | 0.301519i | \(0.0974936\pi\) | ||||
−0.953460 | + | 0.301519i | \(0.902506\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.44115 | + | 4.22819i | 0.157248 | + | 0.272362i | 0.933875 | − | 0.357599i | \(-0.116404\pi\) |
−0.776627 | + | 0.629961i | \(0.783071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.50507 | + | 2.02365i | 0.224850 | + | 0.129817i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.8620 | − | 13.2504i | 1.26894 | − | 0.846536i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.451379 | + | 0.781812i | −0.0287206 | + | 0.0497455i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.92071 | − | 2.26362i | 0.248465 | − | 0.143451i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.3751 | −1.28607 | −0.643033 | − | 0.765838i | \(-0.722324\pi\) | ||||
−0.643033 | + | 0.765838i | \(0.722324\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.53707i | 0.410982i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.80833 | − | 8.32828i | −0.301110 | − | 0.521537i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.1652 | + | 13.3745i | 1.44501 | + | 0.834276i | 0.998178 | − | 0.0603432i | \(-0.0192195\pi\) |
0.446830 | + | 0.894619i | \(0.352553\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.8707 | + | 20.1333i | −1.17257 | + | 1.25102i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.07889 | − | 1.20025i | −0.128680 | − | 0.0742933i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.97787 | + | 1.14192i | −0.121961 | + | 0.0704140i | −0.559739 | − | 0.828669i | \(-0.689099\pi\) |
0.437779 | + | 0.899083i | \(0.355765\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.6531i | 1.33014i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.947740 | −0.0580008 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.06183 | + | 8.76735i | 0.308626 | + | 0.534555i | 0.978062 | − | 0.208314i | \(-0.0667977\pi\) |
−0.669436 | + | 0.742869i | \(0.733464\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.35252 | + | 12.7349i | −0.446634 | + | 0.773592i | −0.998164 | − | 0.0605623i | \(-0.980711\pi\) |
0.551531 | + | 0.834155i | \(0.314044\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.72424 | + | 22.1961i | 0.406970 | + | 1.34337i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 29.3962 | + | 16.9719i | 1.77266 | + | 1.02344i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.66945 | − | 16.7480i | −0.580981 | − | 1.00629i | −0.995363 | − | 0.0961860i | \(-0.969336\pi\) |
0.414382 | − | 0.910103i | \(-0.363998\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.71354 | −0.162455 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.1645i | − | 1.62050i | −0.586084 | − | 0.810250i | \(-0.699331\pi\) | ||
0.586084 | − | 0.810250i | \(-0.300669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1735 | + | 17.6211i | 0.604754 | + | 1.04746i | 0.992090 | + | 0.125526i | \(0.0400620\pi\) |
−0.387336 | + | 0.921939i | \(0.626605\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.595734 | + | 1.03184i | −0.0352882 | + | 0.0611210i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.4754 | + | 3.94479i | −0.972512 | + | 0.232854i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.32822 | + | 12.6928i | −0.431072 | + | 0.746638i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.8092 | + | 22.1861i | 0.750886 | + | 1.30057i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 30.9381i | − | 1.80742i | −0.428141 | − | 0.903712i | \(-0.640831\pi\) | ||
0.428141 | − | 0.903712i | \(-0.359169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.1599 | 2.22175 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.2884 | − | 21.2842i | −0.713046 | − | 1.23503i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.26639 | − | 3.04055i | −0.304563 | − | 0.175840i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.664876 | + | 0.155284i | 0.0383228 | + | 0.00895041i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.64462 | − | 14.9729i | 0.496620 | − | 0.860172i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.2935 | + | 40.3455i | 1.33378 | + | 2.31018i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.7412 | −1.64035 | −0.820173 | − | 0.572115i | \(-0.806123\pi\) | ||||
−0.820173 | + | 0.572115i | \(0.806123\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 28.0796i | − | 1.59739i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0657 | + | 5.81145i | −0.570775 | + | 0.329537i | −0.757459 | − | 0.652883i | \(-0.773559\pi\) |
0.186684 | + | 0.982420i | \(0.440226\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.01385 | + | 1.74004i | 0.170353 | + | 0.0983531i | 0.582752 | − | 0.812650i | \(-0.301976\pi\) |
−0.412399 | + | 0.911003i | \(0.635309\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.02528 | + | 3.38437i | 0.0577682 | + | 0.190687i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.48485 | − | 2.01198i | −0.195729 | − | 0.113004i | 0.398933 | − | 0.916980i | \(-0.369381\pi\) |
−0.594662 | + | 0.803976i | \(0.702714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.6718 | + | 27.1443i | 0.877450 | + | 1.51979i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 36.3089i | − | 2.02656i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.290359 | −0.0161560 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.3458 | + | 15.7881i | −1.51687 | + | 0.875766i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.29337 | + | 10.9004i | −0.348024 | + | 0.602795i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.15840 | + | 5.77220i | 0.339524 | + | 0.318232i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.03234 | − | 3.48277i | −0.331567 | − | 0.191430i | 0.324969 | − | 0.945725i | \(-0.394646\pi\) |
−0.656537 | + | 0.754294i | \(0.727979\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.04348 | − | 3.53942i | −0.111982 | − | 0.193959i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.39284i | − | 0.240006i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7543 | 0.585826 | 0.292913 | − | 0.956139i | \(-0.405375\pi\) | ||||
0.292913 | + | 0.956139i | \(0.405375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.23272 | + | 4.17581i | −0.392827 | + | 0.226799i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.6842 | + | 17.7155i | 1.66164 | + | 0.959348i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.3035 | − | 11.7648i | −0.772314 | − | 0.635241i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.95062 | − | 4.01295i | −0.374209 | − | 0.216050i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.59574 | + | 4.96275i | −0.461443 | + | 0.266414i | −0.712651 | − | 0.701519i | \(-0.752506\pi\) |
0.251208 | + | 0.967933i | \(0.419172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.3844 | −1.62644 | −0.813221 | − | 0.581955i | \(-0.802288\pi\) | ||||
−0.813221 | + | 0.581955i | \(0.802288\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.8626 | 1.22031 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.7103 | + | 25.4790i | 0.782952 | + | 1.35611i | 0.930215 | + | 0.367015i | \(0.119620\pi\) |
−0.147263 | + | 0.989097i | \(0.547046\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.11145 | + | 4.68315i | 0.430511 | + | 0.248556i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.10121 | + | 5.44252i | −0.269985 | + | 0.288049i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.06991 | + | 10.5134i | −0.320358 | + | 0.554876i | −0.980562 | − | 0.196210i | \(-0.937136\pi\) |
0.660204 | + | 0.751086i | \(0.270470\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.48201 | − | 16.4233i | −0.499053 | − | 0.864386i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 27.9550i | − | 1.46726i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.32562 | 0.435783 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.19812 | − | 12.4675i | −0.375739 | − | 0.650799i | 0.614698 | − | 0.788762i | \(-0.289278\pi\) |
−0.990437 | + | 0.137963i | \(0.955944\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.148321 | − | 2.50472i | 0.00772130 | − | 0.130391i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.0744 | − | 4.86971i | 0.834543 | − | 0.252823i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.1621 | + | 17.6013i | −0.526173 | + | 0.911359i | 0.473362 | + | 0.880868i | \(0.343040\pi\) |
−0.999535 | + | 0.0304908i | \(0.990293\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.89006 | + | 5.13268i | −0.459081 | + | 0.265051i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.1573 | −1.50168 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6087 | −1.16133 | −0.580667 | − | 0.814141i | \(-0.697208\pi\) | ||||
−0.580667 | + | 0.814141i | \(0.697208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33.8122 | − | 19.5215i | 1.73225 | − | 1.00012i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.4563 | + | 11.8105i | 1.04527 | + | 0.603487i | 0.921321 | − | 0.388802i | \(-0.127111\pi\) |
0.123948 | + | 0.992289i | \(0.460444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.5013 | − | 44.9634i | 0.535197 | − | 2.29155i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.0505618 | + | 0.0875757i | −0.00257020 | + | 0.00445172i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.7319 | + | 25.5164i | 0.746937 | + | 1.29373i | 0.949284 | + | 0.314420i | \(0.101810\pi\) |
−0.202347 | + | 0.979314i | \(0.564857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.95590i | − | 0.0989140i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 16.8139i | − | 0.848147i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.0256 | − | 13.2939i | 1.15854 | − | 0.668886i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.3328 | − | 7.12036i | −0.618967 | − | 0.357360i | 0.157500 | − | 0.987519i | \(-0.449657\pi\) |
−0.776467 | + | 0.630158i | \(0.782990\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.899976 | + | 0.210192i | 0.0450552 | + | 0.0105228i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.0558 | − | 24.3454i | 0.701914 | − | 1.21575i | −0.265879 | − | 0.964006i | \(-0.585662\pi\) |
0.967794 | − | 0.251745i | \(-0.0810044\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.5439 | + | 16.4798i | −1.42187 | + | 0.820919i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 34.1840 | 1.69861 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 53.3640i | 2.64516i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5848 | − | 21.7975i | −0.622279 | − | 1.07782i | −0.989060 | − | 0.147511i | \(-0.952874\pi\) |
0.366782 | − | 0.930307i | \(-0.380460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.2446 | − | 29.8685i | 0.850613 | − | 1.47331i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.58201 | − | 28.3284i | −0.422293 | − | 1.39395i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.19230 | − | 7.26128i | 0.205792 | − | 0.356442i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.2981 | + | 12.2965i | −1.04297 | + | 0.602161i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.1264 | 0.543560 | 0.271780 | − | 0.962359i | \(-0.412388\pi\) | ||||
0.271780 | + | 0.962359i | \(0.412388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.95239i | 0.0951537i | 0.998868 | + | 0.0475769i | \(0.0151499\pi\) | ||||
−0.998868 | + | 0.0475769i | \(0.984850\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.08264 | + | 0.625063i | −0.0526398 | + | 0.0303916i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.79536 | − | 5.07801i | −0.426638 | − | 0.246319i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.7123 | − | 26.3657i | 1.19591 | − | 1.27593i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 38.8419 | + | 22.4254i | 1.87530 | + | 1.08271i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.546539 | + | 0.946633i | 0.0263258 | + | 0.0455977i | 0.878888 | − | 0.477028i | \(-0.158286\pi\) |
−0.852562 | + | 0.522626i | \(0.824953\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.4234 | −1.41400 | −0.707000 | − | 0.707213i | \(-0.749952\pi\) | ||||
−0.707000 | + | 0.707213i | \(0.749952\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −38.4820 | −1.84507 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.209862 | + | 0.121164i | −0.0100391 | + | 0.00579606i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.3205 | − | 12.3094i | −1.01757 | − | 0.587496i | −0.104174 | − | 0.994559i | \(-0.533220\pi\) |
−0.913400 | + | 0.407063i | \(0.866553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.28184 | − | 1.52226i | 0.108659 | − | 0.0724887i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0496196 | − | 0.0859436i | 0.00235750 | − | 0.00408330i | −0.864844 | − | 0.502040i | \(-0.832583\pi\) |
0.867202 | + | 0.497957i | \(0.165916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.52009 | + | 0.877622i | −0.0720590 | + | 0.0416033i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.5802 | −1.54099 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.6492 | 1.21046 | 0.605229 | − | 0.796051i | \(-0.293081\pi\) | ||||
0.605229 | + | 0.796051i | \(0.293081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0294 | + | 27.3546i | −0.848973 | + | 1.28808i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.0360 | + | 29.5073i | −0.800423 | + | 1.38637i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 31.3390 | + | 29.3737i | 1.46919 | + | 1.37706i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.72041 | − | 4.45738i | −0.361145 | − | 0.208507i | 0.308438 | − | 0.951245i | \(-0.400194\pi\) |
−0.669583 | + | 0.742737i | \(0.733527\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.67671 | + | 6.36824i | 0.171614 | + | 0.297244i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.610615 | −0.0284392 | −0.0142196 | − | 0.999899i | \(-0.504526\pi\) | ||||
−0.0142196 | + | 0.999899i | \(0.504526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3452i | 1.13142i | 0.824606 | + | 0.565708i | \(0.191397\pi\) | ||||
−0.824606 | + | 0.565708i | \(0.808603\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −37.6725 | + | 21.7502i | −1.74702 | + | 1.00864i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.658834 | + | 1.14113i | −0.0304872 | + | 0.0528053i | −0.880866 | − | 0.473365i | \(-0.843039\pi\) |
0.850379 | + | 0.526170i | \(0.176373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.26107 | + | 0.987932i | −0.150582 | + | 0.0456185i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.2067 | − | 24.6068i | 0.654612 | − | 1.13382i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.14349 | − | 0.660192i | 0.0525776 | − | 0.0303557i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.25829i | 0.0577343i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.48761i | 0.113900i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5766 | + | 6.10641i | −0.483258 | + | 0.279009i | −0.721773 | − | 0.692130i | \(-0.756673\pi\) |
0.238515 | + | 0.971139i | \(0.423339\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.9911 | − | 24.8209i | −1.96023 | − | 1.13174i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.41588 | + | 6.06237i | −0.0644249 | + | 0.275847i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 41.0894 | + | 23.7230i | 1.86577 | + | 1.07720i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.07553 | + | 15.7193i | 0.411252 | + | 0.712309i | 0.995027 | − | 0.0996066i | \(-0.0317584\pi\) |
−0.583775 | + | 0.811915i | \(0.698425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.3752i | 0.514406i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0993 | −0.681423 | −0.340711 | − | 0.940168i | \(-0.610668\pi\) | ||||
−0.340711 | + | 0.940168i | \(0.610668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.68901 | − | 8.12160i | −0.211182 | − | 0.365778i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.92245 | + | 3.41933i | 0.266194 | + | 0.153687i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.65235 | − | 7.07485i | 0.0741181 | − | 0.317350i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.740745 | + | 0.427669i | 0.0331603 | + | 0.0191451i | 0.516489 | − | 0.856294i | \(-0.327239\pi\) |
−0.483328 | + | 0.875439i | \(0.660572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.34844 | + | 5.79968i | 0.149597 | + | 0.259110i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.99714i | 0.267399i | 0.991022 | + | 0.133700i | \(0.0426857\pi\) | ||||
−0.991022 | + | 0.133700i | \(0.957314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 32.0202i | − | 1.42488i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.3982 | + | 8.89015i | −0.683858 | + | 0.394826i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.6136 | + | 18.2521i | 1.40125 | + | 0.809011i | 0.994521 | − | 0.104538i | \(-0.0333365\pi\) |
0.406728 | + | 0.913549i | \(0.366670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.87240 | − | 6.18061i | −0.0828301 | − | 0.273414i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.455529 | − | 0.789000i | 0.0201121 | − | 0.0348352i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.0021 | − | 45.0370i | −1.14579 | − | 1.98457i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.3231 | 0.717887 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 0.373283i | − | 0.0163853i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.51297 | + | 1.45086i | −0.110095 | + | 0.0635634i | −0.554036 | − | 0.832492i | \(-0.686913\pi\) |
0.443941 | + | 0.896056i | \(0.353580\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.39878 | − | 14.5471i | 0.367253 | − | 0.636101i | −0.621882 | − | 0.783111i | \(-0.713632\pi\) |
0.989135 | + | 0.147010i | \(0.0469650\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 23.5855 | + | 22.1064i | 1.02936 | + | 0.964804i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.18073 | − | 5.30050i | −0.399919 | − | 0.230893i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6838 | + | 18.5049i | 0.464514 | + | 0.804562i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.38398 | 0.190248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6515 | − | 27.2482i | −0.591311 | − | 1.18025i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.6226 | − | 58.2361i | −1.45363 | − | 2.51776i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.82507 | − | 13.5534i | 0.337677 | − | 0.584873i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −35.7407 | + | 2.31632i | −1.53946 | + | 0.0997710i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.11917 | + | 3.67050i | −0.0911101 | + | 0.157807i | −0.907979 | − | 0.419017i | \(-0.862375\pi\) |
0.816868 | + | 0.576824i | \(0.195708\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.49028 | − | 2.58124i | −0.0639539 | − | 0.110771i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.3110i | 0.998535i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9406i | 1.53671i | 0.640025 | + | 0.768354i | \(0.278924\pi\) | ||||
−0.640025 | + | 0.768354i | \(0.721076\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.67606 | + | 4.63507i | 0.114211 | + | 0.197820i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.580949 | + | 1.00623i | −0.0247493 | + | 0.0428670i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0472 | − | 14.1036i | −0.639872 | − | 0.599745i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −56.7400 | − | 32.7589i | −2.40848 | − | 1.39054i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.6477 | − | 17.1171i | 1.25621 | − | 0.725276i | 0.283878 | − | 0.958860i | \(-0.408379\pi\) |
0.972336 | + | 0.233585i | \(0.0750456\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.22829i | 0.0519510i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4256i | 0.609048i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.4007 | − | 18.7066i | 1.36553 | − | 0.788387i | 0.375174 | − | 0.926955i | \(-0.377583\pi\) |
0.990353 | + | 0.138567i | \(0.0442498\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.73373 | + | 13.3952i | −0.325361 | + | 0.563541i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.68784 | − | 25.3768i | −0.322859 | − | 1.06573i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.03775 | + | 10.4577i | −0.253116 | + | 0.438409i | −0.964382 | − | 0.264514i | \(-0.914789\pi\) |
0.711266 | + | 0.702923i | \(0.248122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.9092 | − | 13.8040i | 1.00057 | − | 0.577678i | 0.0921515 | − | 0.995745i | \(-0.470626\pi\) |
0.908416 | + | 0.418067i | \(0.137292\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.9103 | 0.831765 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.47602 | −0.353474 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.2413 | + | 16.8825i | −1.21733 | + | 0.702827i | −0.964347 | − | 0.264643i | \(-0.914746\pi\) |
−0.252986 | + | 0.967470i | \(0.581413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.12371 | + | 7.14247i | −0.171375 | + | 0.296831i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.33332 | − | 1.47917i | −0.262750 | − | 0.0613661i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.2405 | − | 28.1294i | 0.672613 | − | 1.16500i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.50936 | + | 3.18083i | −0.227784 | + | 0.131511i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 5.82279i | − | 0.240332i | −0.992754 | − | 0.120166i | \(-0.961657\pi\) | ||
0.992754 | − | 0.120166i | \(-0.0383427\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31342i | 0.0541186i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1375 | + | 7.00758i | −0.499269 | + | 0.288253i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.3909 | − | 12.9274i | −0.919485 | − | 0.530865i | −0.0360146 | − | 0.999351i | \(-0.511466\pi\) |
−0.883471 | + | 0.468486i | \(0.844800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.14201 | + | 13.4531i | −0.128810 | + | 0.551523i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.9139 | − | 36.2239i | 0.855948 | − | 1.48254i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.49872 | + | 11.2561i | 0.265530 | + | 0.459912i | 0.967702 | − | 0.252095i | \(-0.0811196\pi\) |
−0.702172 | + | 0.712007i | \(0.747786\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1758i | 0.578242i | 0.957293 | + | 0.289121i | \(0.0933631\pi\) | ||||
−0.957293 | + | 0.289121i | \(0.906637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 0.504668i | − | 0.0205517i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.8867 | − | 44.8371i | −1.05245 | − | 1.82289i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.89131 | + | 11.9361i | −0.279710 | + | 0.484472i | −0.971313 | − | 0.237807i | \(-0.923572\pi\) |
0.691603 | + | 0.722278i | \(0.256905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.65446 | + | 28.5675i | 0.350697 | + | 1.15762i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.59226 | + | 13.1502i | −0.307150 | + | 0.531999i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.61166 | + | 9.71967i | 0.226653 | + | 0.392574i | 0.956814 | − | 0.290701i | \(-0.0938885\pi\) |
−0.730161 | + | 0.683275i | \(0.760555\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0173 | − | 35.9624i | −0.726528 | − | 1.45014i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.6837 | −1.67812 | −0.839061 | − | 0.544037i | \(-0.816895\pi\) | ||||
−0.839061 | + | 0.544037i | \(0.816895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.3423 | − | 19.6454i | −0.455884 | − | 0.789614i | 0.542855 | − | 0.839827i | \(-0.317343\pi\) |
−0.998739 | + | 0.0502126i | \(0.984010\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.31481 | + | 3.06851i | 0.213276 | + | 0.123135i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.993374 | + | 0.931078i | 0.0397987 | + | 0.0373029i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.07946 | − | 12.2620i | 0.283178 | − | 0.490479i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.54782 | − | 0.893636i | 0.0618141 | − | 0.0356884i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 15.9666i | − | 0.636629i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.8577 | −1.58671 | −0.793355 | − | 0.608760i | \(-0.791667\pi\) | ||||
−0.793355 | + | 0.608760i | \(0.791667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.2798 | − | 23.0013i | −0.527826 | − | 0.914221i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.1544 | − | 62.6212i | 1.43474 | − | 2.48505i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7578 | − | 29.8708i | 0.584727 | − | 1.18353i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.931879 | + | 0.538021i | 0.0368646 | + | 0.0212838i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.2953 | − | 15.1816i | 1.03860 | − | 0.599637i | 0.119164 | − | 0.992875i | \(-0.461978\pi\) |
0.919437 | + | 0.393238i | \(0.128645\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.9876i | − | 0.433311i | −0.976248 | − | 0.216655i | \(-0.930485\pi\) | ||
0.976248 | − | 0.216655i | \(-0.0695148\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.62110i | 0.0638309i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.76865 | + | 6.52750i | 0.148161 | + | 0.256623i | 0.930548 | − | 0.366170i | \(-0.119331\pi\) |
−0.782387 | + | 0.622793i | \(0.785998\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −49.5731 | − | 28.6211i | −1.94592 | − | 1.12347i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.6189 | + | 23.0750i | 0.964891 | + | 0.904382i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.60476 | − | 4.96796i | −0.336730 | − | 0.194411i | 0.322095 | − | 0.946707i | \(-0.395613\pi\) |
−0.658825 | + | 0.752296i | \(0.728946\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.5699 | − | 26.9678i | −0.608366 | − | 1.05372i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.956484 | 0.0373160 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 17.8545i | − | 0.695512i | −0.937585 | − | 0.347756i | \(-0.886944\pi\) | ||
0.937585 | − | 0.347756i | \(-0.113056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.51574 | + | 6.08944i | 0.136746 | + | 0.236852i | 0.926263 | − | 0.376877i | \(-0.123002\pi\) |
−0.789517 | + | 0.613729i | \(0.789669\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.6215 | − | 6.70970i | −0.451343 | − | 0.260583i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.63812 | − | 0.496264i | 0.0635235 | − | 0.0192443i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.77813 | − | 3.91336i | −0.262450 | − | 0.151526i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.80788 | + | 1.62113i | −0.108559 | + | 0.0626765i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 69.8832i | − | 2.69781i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.4238i | 1.24984i | 0.780687 | + | 0.624922i | \(0.214869\pi\) | ||||
−0.780687 | + | 0.624922i | \(0.785131\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.5972 | − | 15.9333i | 1.06222 | − | 0.613271i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.42214 | − | 4.19527i | 0.0930904 | − | 0.161237i | −0.815720 | − | 0.578447i | \(-0.803659\pi\) |
0.908810 | + | 0.417210i | \(0.136992\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.37015 | − | 35.8383i | 0.321217 | − | 1.37535i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.1600 | − | 21.0617i | 0.465971 | − | 0.807086i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.48589 | + | 2.58993i | −0.171648 | + | 0.0991009i | −0.583363 | − | 0.812212i | \(-0.698263\pi\) |
0.411715 | + | 0.911313i | \(0.364930\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 63.8751i | − | 2.44054i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.6838 | 1.01805 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.1077 | + | 26.1673i | 0.575559 | + | 0.996897i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.34043 | + | 1.35125i | 0.0890341 | + | 0.0514039i | 0.543856 | − | 0.839179i | \(-0.316964\pi\) |
−0.454822 | + | 0.890582i | \(0.650297\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.20644 | − | 5.16559i | 0.0458288 | − | 0.196224i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.7735 | + | 39.4448i | −0.863847 | + | 1.49623i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.39443 | − | 8.18452i | 0.204328 | − | 0.310011i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.8618 | 1.09165 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3659 | 0.504821 | 0.252411 | − | 0.967620i | \(-0.418777\pi\) | ||||
0.252411 | + | 0.967620i | \(0.418777\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.71317 | + | 0.989098i | −0.0646133 | + | 0.0373045i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.0203 | + | 17.3557i | −0.377387 | + | 0.653654i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.7705 | + | 7.20123i | −0.893983 | + | 0.270830i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.19931 | + | 4.15653i | 0.270376 | + | 0.156102i | 0.629058 | − | 0.777358i | \(-0.283441\pi\) |
−0.358683 | + | 0.933460i | \(0.616774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.64528 | − | 1.52726i | 0.0992059 | − | 0.0572766i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.84739 | −0.331337 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 83.0650 | 3.10645 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.58484 | + | 14.8694i | 0.320607 | + | 0.555307i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.6965 | − | 24.6508i | −1.59231 | − | 0.919321i | −0.992910 | − | 0.118872i | \(-0.962072\pi\) |
−0.599401 | − | 0.800449i | \(-0.704595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.5859 | + | 29.4316i | −1.02735 | + | 1.09609i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.78706 | + | 4.49586i | 0.289604 | + | 0.167203i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −35.1955 | + | 20.3201i | −1.30713 | + | 0.754671i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.4294i | 1.27691i | 0.769657 | + | 0.638457i | \(0.220427\pi\) | ||||
−0.769657 | + | 0.638457i | \(0.779573\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.6121 | −0.837487 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.342132 | + | 0.197530i | −0.0126542 | + | 0.00730592i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.9788 | + | 34.6043i | −0.737934 | + | 1.27814i | 0.215491 | + | 0.976506i | \(0.430865\pi\) |
−0.953424 | + | 0.301633i | \(0.902468\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.4775 | − | 39.4238i | 0.718438 | − | 1.45417i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.29476 | + | 5.70669i | −0.121364 | + | 0.210209i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0104 | − | 25.9988i | −0.552168 | − | 0.956382i | −0.998118 | − | 0.0613245i | \(-0.980468\pi\) |
0.445950 | − | 0.895058i | \(-0.352866\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.66261i | 0.0610775i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.7941 | −1.27647 | −0.638237 | − | 0.769840i | \(-0.720336\pi\) | ||||
−0.638237 | + | 0.769840i | \(0.720336\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −52.2556 | + | 30.1698i | −1.91450 | + | 1.10534i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.481630 | − | 0.834208i | 0.0176219 | − | 0.0305221i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.6706 | + | 38.0572i | −1.30337 | + | 1.39058i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.3205 | + | 11.7320i | 0.741504 | + | 0.428108i | 0.822616 | − | 0.568597i | \(-0.192514\pi\) |
−0.0811117 | + | 0.996705i | \(0.525847\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −32.4975 | + | 18.7624i | −1.18427 | + | 0.683741i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.1026i | 2.29654i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.20722i | 0.225605i | 0.993617 | + | 0.112803i | \(0.0359828\pi\) | ||||
−0.993617 | + | 0.112803i | \(0.964017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.01966 | + | 10.4264i | 0.218500 | + | 0.378453i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.2682 | − | 28.1773i | 0.589722 | − | 1.02143i | −0.404547 | − | 0.914517i | \(-0.632571\pi\) |
0.994269 | − | 0.106911i | \(-0.0340958\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.3052 | − | 5.24256i | 0.626490 | − | 0.189793i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.77200 | − | 1.02307i | −0.0640669 | − | 0.0369891i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.1154 | − | 26.6247i | 1.66513 | − | 0.961363i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.156285 | −0.00563579 | −0.00281789 | − | 0.999996i | \(-0.500897\pi\) | ||||
−0.00281789 | + | 0.999996i | \(0.500897\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 49.2635 | 1.77418 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.8986 | + | 8.02434i | −0.499896 | + | 0.288615i | −0.728671 | − | 0.684864i | \(-0.759862\pi\) |
0.228774 | + | 0.973479i | \(0.426528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.9701 | + | 39.7853i | −0.825109 | + | 1.42913i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.5583 | + | 49.4889i | −0.414651 | + | 1.77540i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.21235 | − | 0.0717913i | −0.0434369 | − | 0.00257219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.02501 | − | 12.1677i | −0.251374 | − | 0.435393i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29.4254 | 1.05158 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 52.6226i | − | 1.87818i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2854 | + | 19.5468i | 0.402280 | + | 0.696770i | 0.994001 | − | 0.109373i | \(-0.0348844\pi\) |
−0.591720 | + | 0.806143i | \(0.701551\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.10308 | + | 3.64264i | −0.0748716 | + | 0.129681i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.6834 | + | 2.72869i | 0.415413 | + | 0.0970209i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 56.2993 | + | 32.5044i | 1.99925 | + | 1.15427i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.9393 | + | 34.5359i | 0.707174 | + | 1.22486i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.90336 | −0.350795 | −0.175398 | − | 0.984498i | \(-0.556121\pi\) | ||||
−0.175398 | + | 0.984498i | \(0.556121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.88388 | −0.172779 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.174634 | + | 0.100825i | −0.00617040 | + | 0.00356248i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.8157 | − | 6.24446i | −0.381679 | − | 0.220362i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.34290 | + | 11.0346i | 0.117822 | + | 0.388918i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.1468 | + | 9.32238i | 0.568395 | + | 0.328163i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.0816 | + | 8.13004i | −0.495084 | + | 0.285837i | −0.726681 | − | 0.686975i | \(-0.758938\pi\) |
0.231597 | + | 0.972812i | \(0.425605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.9718 | 1.93032 | 0.965161 | − | 0.261658i | \(-0.0842694\pi\) | ||||
0.965161 | + | 0.261658i | \(0.0842694\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.0823i | 0.949816i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5337 | + | 18.2448i | 0.368978 | + | 0.639088i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0423888 | + | 0.0244732i | 0.00148300 | + | 0.000856209i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.60036 | + | 3.37457i | 0.125807 | + | 0.117917i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.2244 | + | 22.9054i | −0.461536 | + | 0.799404i | −0.999038 | − | 0.0438585i | \(-0.986035\pi\) |
0.537501 | + | 0.843263i | \(0.319368\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.6556 | − | 7.30673i | 0.441147 | − | 0.254696i | −0.262937 | − | 0.964813i | \(-0.584691\pi\) |
0.704084 | + | 0.710117i | \(0.251358\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 62.5142 | 2.17647 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.17588i | − | 0.214756i | −0.994218 | − | 0.107378i | \(-0.965754\pi\) | ||
0.994218 | − | 0.107378i | \(-0.0342455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7767 | + | 23.8620i | 0.478486 | + | 0.828762i | 0.999696 | − | 0.0246664i | \(-0.00785235\pi\) |
−0.521210 | + | 0.853429i | \(0.674519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.8448 | − | 17.8082i | −1.06999 | − | 0.617761i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.6937 | − | 0.693046i | 0.370514 | − | 0.0240126i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.7412 | + | 6.20142i | 0.371714 | + | 0.214609i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.8064 | − | 16.6314i | 0.995694 | − | 0.574864i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.46029i | − | 0.119463i | −0.998214 | − | 0.0597313i | \(-0.980976\pi\) | ||
0.998214 | − | 0.0597313i | \(-0.0190244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.52702 | −0.294035 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.0145 | − | 43.3263i | −0.861544 | − | 1.49224i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.4648 | + | 28.5179i | −0.566408 | + | 0.981047i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.4635 | + | 29.3010i | −0.943657 | + | 1.00679i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.4527 | + | 18.7366i | 1.11378 | + | 0.643039i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.66270 | − | 11.5401i | −0.228394 | − | 0.395591i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.14615 | −0.141961 | −0.0709807 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709807 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.253508i | 0.00866978i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.7915 | + | 36.0119i | 0.710224 | + | 1.23014i | 0.964773 | + | 0.263084i | \(0.0847395\pi\) |
−0.254549 | + | 0.967060i | \(0.581927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.3556 | + | 17.9365i | −0.353330 | + | 0.611986i | −0.986831 | − | 0.161756i | \(-0.948284\pi\) |
0.633501 | + | 0.773742i | \(0.281617\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.6450 | + | 21.4631i | −0.771740 | + | 0.731462i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.6980 | − | 47.9744i | 0.942852 | − | 1.63307i | 0.182857 | − | 0.983139i | \(-0.441465\pi\) |
0.759995 | − | 0.649929i | \(-0.225201\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.345666 | − | 0.598711i | −0.0117530 | − | 0.0203568i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.9927i | 0.916722i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.8831 | −1.35294 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.06495 | − | 5.30865i | −0.103852 | − | 0.179877i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.72053 | + | 2.72540i | 0.159766 | + | 0.0922407i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.3606 | + | 3.35395i | 0.485476 | + | 0.113384i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.1987 | − | 41.9134i | 0.817132 | − | 1.41531i | −0.0906551 | − | 0.995882i | \(-0.528896\pi\) |
0.907787 | − | 0.419432i | \(-0.137771\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.4894 | − | 49.3450i | −0.960922 | − | 1.66437i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.85819 | 0.197367 | 0.0986837 | − | 0.995119i | \(-0.468537\pi\) | ||||
0.0986837 | + | 0.995119i | \(0.468537\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.9837i | 1.41286i | 0.707782 | + | 0.706431i | \(0.249696\pi\) | ||||
−0.707782 | + | 0.706431i | \(0.750304\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 60.8634 | − | 35.1395i | 2.04590 | − | 1.18120i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.21981 | + | 4.74571i | 0.275994 | + | 0.159345i | 0.631608 | − | 0.775287i | \(-0.282395\pi\) |
−0.355614 | + | 0.934633i | \(0.615728\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −54.6185 | − | 12.7563i | −1.83185 | − | 0.427833i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44.4080 | − | 25.6390i | −1.48773 | − | 0.858939i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.302546 | + | 0.524026i | 0.0101243 | + | 0.0175359i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 28.9845i | − | 0.968846i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.1996 | −0.373943 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.7376 | + | 21.2104i | −1.22527 | + | 0.707408i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.85918 | + | 8.41634i | −0.161883 | + | 0.280389i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.20344 | − | 0.364580i | 0.0400481 | − | 0.0121325i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.78053 | − | 2.76004i | −0.158910 | − | 0.0917468i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.96077 | + | 15.5205i | 0.297538 | + | 0.515350i | 0.975572 | − | 0.219680i | \(-0.0705013\pi\) |
−0.678034 | + | 0.735030i | \(0.737168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 3.67862i | − | 0.122012i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.2931 | 0.937393 | 0.468696 | − | 0.883359i | \(-0.344724\pi\) | ||||
0.468696 | + | 0.883359i | \(0.344724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.8924 | + | 6.28870i | −0.360484 | + | 0.208126i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 74.3043 | + | 42.8996i | 2.45642 | + | 1.41822i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.5183 | + | 17.6234i | −0.545481 | + | 0.581977i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.4754 | + | 10.0894i | 0.576459 | + | 0.332819i | 0.759725 | − | 0.650244i | \(-0.225334\pi\) |
−0.183266 | + | 0.983063i | \(0.558667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.8410 | + | 26.4663i | −1.51051 | + | 0.872095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.0700 | 0.430205 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −69.1922 | −2.27503 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.98724 | − | 5.17404i | −0.0981137 | − | 0.169938i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.4259 | + | 19.2984i | 1.09667 | + | 0.633161i | 0.935344 | − | 0.353741i | \(-0.115090\pi\) |
0.161323 | + | 0.986902i | \(0.448424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.736813 | − | 1.10447i | −0.0241481 | − | 0.0361974i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.7029 | + | 18.5380i | −0.350399 | + | 0.606908i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.3583 | + | 23.1373i | 0.436863 | + | 0.756670i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.8589i | 1.89017i | 0.326830 | + | 0.945083i | \(0.394020\pi\) | ||||
−0.326830 | + | 0.945083i | \(0.605980\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.40928 | 0.209159 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.35327 | + | 11.0042i | 0.207111 | + | 0.358726i | 0.950803 | − | 0.309796i | \(-0.100261\pi\) |
−0.743693 | + | 0.668522i | \(0.766927\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.483596 | − | 8.16656i | 0.0157481 | − | 0.265940i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −31.6271 | − | 29.6437i | −1.02883 | − | 0.964311i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.92878 | + | 17.1971i | −0.322642 | + | 0.558832i | −0.981032 | − | 0.193845i | \(-0.937904\pi\) |
0.658390 | + | 0.752677i | \(0.271238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0613 | − | 5.80891i | 0.326605 | − | 0.188565i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.41093 | −0.240316 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.9206 | −1.51991 | −0.759954 | − | 0.649977i | \(-0.774779\pi\) | ||||
−0.759954 | + | 0.649977i | \(0.774779\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.9342 | − | 18.4372i | 1.03337 | − | 0.596615i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 49.9916 | + | 28.8627i | 1.61600 | + | 0.932998i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −47.4183 | + | 14.3653i | −1.53122 | + | 0.463878i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.47649 | + | 14.6817i | −0.273435 | + | 0.473604i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.86271 | − | 6.69041i | −0.124474 | − | 0.215596i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.2745i | 0.491702i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.8051i | − | 0.765522i | −0.923847 | − | 0.382761i | \(-0.874973\pi\) | ||
0.923847 | − | 0.382761i | \(-0.125027\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.463110 | + | 0.267377i | −0.0148772 | + | 0.00858938i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5450 | − | 6.08817i | −0.338406 | − | 0.195379i | 0.321161 | − | 0.947025i | \(-0.395927\pi\) |
−0.659567 | + | 0.751646i | \(0.729260\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.4039 | + | 8.03514i | 1.10294 | + | 0.257595i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29.0769 | + | 50.3627i | −0.931207 | + | 1.61290i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.927717 | + | 0.535618i | −0.0296803 | + | 0.0171359i | −0.514767 | − | 0.857330i | \(-0.672121\pi\) |
0.485086 | + | 0.874466i | \(0.338788\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.63297 | 0.0841501 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.67807i | 0.0855043i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.9128 | − | 27.5618i | −0.507540 | − | 0.879086i | −0.999962 | − | 0.00872886i | \(-0.997221\pi\) |
0.492422 | − | 0.870357i | \(-0.336112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9783 | + | 22.4790i | −0.413521 | + | 0.716240i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.1377 | + | 3.53546i | 0.481839 | + | 0.112535i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.164855 | + | 0.285537i | −0.00524208 | + | 0.00907955i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.4378 | − | 27.3882i | 1.50691 | − | 0.870016i | 0.506945 | − | 0.861978i | \(-0.330775\pi\) |
0.999968 | − | 0.00803788i | \(-0.00255856\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.8284 | −0.407098 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 77.4663i | − | 2.45585i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.8562 | + | 9.15457i | −0.502170 | + | 0.289928i | −0.729609 | − | 0.683864i | \(-0.760298\pi\) |
0.227439 | + | 0.973792i | \(0.426965\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.3864 | + | 25.0492i | 1.37269 | + | 0.792520i |
(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.r.a.737.21 | yes | 56 | |
7.4 | even | 3 | inner | 1148.2.r.a.81.8 | ✓ | 56 | |
41.40 | even | 2 | inner | 1148.2.r.a.737.8 | yes | 56 | |
287.81 | even | 6 | inner | 1148.2.r.a.81.21 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.r.a.81.8 | ✓ | 56 | 7.4 | even | 3 | inner | |
1148.2.r.a.81.21 | yes | 56 | 287.81 | even | 6 | inner | |
1148.2.r.a.737.8 | yes | 56 | 41.40 | even | 2 | inner | |
1148.2.r.a.737.21 | yes | 56 | 1.1 | even | 1 | trivial |