Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), not 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 226.4 | ||
Root | \(-2.35083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.226 |
Dual form | 375.2.g.d.151.4 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.726446 | − | 2.23577i | 0.513675 | − | 1.58093i | −0.272005 | − | 0.962296i | \(-0.587687\pi\) |
0.785680 | − | 0.618634i | \(-0.212313\pi\) | |||||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | ||||
\(4\) | −2.85292 | − | 2.07277i | −1.42646 | − | 1.03638i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.90186 | − | 1.38178i | 0.776432 | − | 0.564111i | ||||
\(7\) | 3.48189 | 1.31603 | 0.658015 | − | 0.753005i | \(-0.271396\pi\) | ||||
0.658015 | + | 0.753005i | \(0.271396\pi\) | |||||||
\(8\) | −2.90300 | + | 2.10915i | −1.02637 | + | 0.745698i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.905762 | − | 2.78765i | 0.273097 | − | 0.840508i | −0.716619 | − | 0.697465i | \(-0.754311\pi\) |
0.989717 | − | 0.143043i | \(-0.0456887\pi\) | |||||||
\(12\) | −1.08972 | − | 3.35381i | −0.314574 | − | 0.968160i | ||||
\(13\) | −0.579638 | − | 1.78394i | −0.160763 | − | 0.494776i | 0.837937 | − | 0.545768i | \(-0.183762\pi\) |
−0.998699 | + | 0.0509914i | \(0.983762\pi\) | |||||||
\(14\) | 2.52940 | − | 7.78470i | 0.676012 | − | 2.08055i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.427277 | + | 1.31502i | 0.106819 | + | 0.328756i | ||||
\(17\) | −5.48972 | + | 3.98851i | −1.33145 | + | 0.967356i | −0.331739 | + | 0.943371i | \(0.607635\pi\) |
−0.999712 | + | 0.0239850i | \(0.992365\pi\) | |||||||
\(18\) | 2.35083 | 0.554096 | ||||||||
\(19\) | 2.38620 | − | 1.73367i | 0.547431 | − | 0.397732i | −0.279406 | − | 0.960173i | \(-0.590138\pi\) |
0.826837 | + | 0.562441i | \(0.190138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.81691 | + | 2.04660i | 0.614699 | + | 0.446605i | ||||
\(22\) | −5.57456 | − | 4.05015i | −1.18850 | − | 0.863496i | ||||
\(23\) | −1.69656 | + | 5.22149i | −0.353758 | + | 1.08876i | 0.602968 | + | 0.797765i | \(0.293985\pi\) |
−0.956726 | + | 0.290990i | \(0.906015\pi\) | |||||||
\(24\) | −3.58831 | −0.732460 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.40956 | −0.864786 | ||||||||
\(27\) | −0.309017 | + | 0.951057i | −0.0594703 | + | 0.183031i | ||||
\(28\) | −9.93354 | − | 7.21714i | −1.87726 | − | 1.36391i | ||||
\(29\) | −2.06779 | − | 1.50234i | −0.383980 | − | 0.278978i | 0.379004 | − | 0.925395i | \(-0.376267\pi\) |
−0.762984 | + | 0.646417i | \(0.776267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.338237 | + | 0.245744i | −0.0607492 | + | 0.0441369i | −0.617745 | − | 0.786378i | \(-0.711954\pi\) |
0.556996 | + | 0.830515i | \(0.311954\pi\) | |||||||
\(32\) | −3.92613 | −0.694048 | ||||||||
\(33\) | 2.37132 | − | 1.72286i | 0.412793 | − | 0.299912i | ||||
\(34\) | 4.92942 | + | 15.1712i | 0.845388 | + | 2.60184i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.08972 | − | 3.35381i | 0.181620 | − | 0.558968i | ||||
\(37\) | 1.61912 | + | 4.98314i | 0.266182 | + | 0.819224i | 0.991419 | + | 0.130724i | \(0.0417303\pi\) |
−0.725237 | + | 0.688500i | \(0.758270\pi\) | |||||||
\(38\) | −2.14265 | − | 6.59441i | −0.347584 | − | 1.06975i | ||||
\(39\) | 0.579638 | − | 1.78394i | 0.0928163 | − | 0.285659i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.518744 | + | 1.59653i | 0.0810142 | + | 0.249336i | 0.983357 | − | 0.181683i | \(-0.0581543\pi\) |
−0.902343 | + | 0.431019i | \(0.858154\pi\) | |||||||
\(42\) | 6.62206 | − | 4.81121i | 1.02181 | − | 0.742386i | ||||
\(43\) | 10.9233 | 1.66578 | 0.832892 | − | 0.553436i | \(-0.186684\pi\) | ||||
0.832892 | + | 0.553436i | \(0.186684\pi\) | |||||||
\(44\) | −8.36221 | + | 6.07550i | −1.26065 | + | 0.915916i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.4416 | + | 7.58626i | 1.53953 | + | 1.11853i | ||||
\(47\) | 6.06098 | + | 4.40356i | 0.884084 | + | 0.642325i | 0.934329 | − | 0.356412i | \(-0.116000\pi\) |
−0.0502446 | + | 0.998737i | \(0.516000\pi\) | |||||||
\(48\) | −0.427277 | + | 1.31502i | −0.0616721 | + | 0.189807i | ||||
\(49\) | 5.12353 | 0.731933 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.78566 | −0.950183 | ||||||||
\(52\) | −2.04403 | + | 6.29089i | −0.283457 | + | 0.872390i | ||||
\(53\) | −3.00107 | − | 2.18041i | −0.412229 | − | 0.299502i | 0.362275 | − | 0.932071i | \(-0.382000\pi\) |
−0.774504 | + | 0.632570i | \(0.782000\pi\) | |||||||
\(54\) | 1.90186 | + | 1.38178i | 0.258811 | + | 0.188037i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.1079 | + | 7.34383i | −1.35073 | + | 0.981361i | ||||
\(57\) | 2.94950 | 0.390671 | ||||||||
\(58\) | −4.86103 | + | 3.53175i | −0.638285 | + | 0.463741i | ||||
\(59\) | −2.19666 | − | 6.76062i | −0.285981 | − | 0.880158i | −0.986103 | − | 0.166135i | \(-0.946871\pi\) |
0.700122 | − | 0.714023i | \(-0.253129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.98917 | + | 6.12204i | −0.254687 | + | 0.783847i | 0.739204 | + | 0.673482i | \(0.235202\pi\) |
−0.993891 | + | 0.110365i | \(0.964798\pi\) | |||||||
\(62\) | 0.303716 | + | 0.934741i | 0.0385719 | + | 0.118712i | ||||
\(63\) | 1.07596 | + | 3.31147i | 0.135558 | + | 0.417206i | ||||
\(64\) | −3.70667 | + | 11.4080i | −0.463334 | + | 1.42600i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.12929 | − | 6.55329i | −0.262098 | − | 0.806654i | ||||
\(67\) | −8.12376 | + | 5.90225i | −0.992475 | + | 0.721075i | −0.960462 | − | 0.278412i | \(-0.910192\pi\) |
−0.0320131 | + | 0.999487i | \(0.510192\pi\) | |||||||
\(68\) | 23.9290 | 2.90181 | ||||||||
\(69\) | −4.44166 | + | 3.22706i | −0.534713 | + | 0.388492i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.589451 | − | 0.428261i | −0.0699550 | − | 0.0508253i | 0.552258 | − | 0.833673i | \(-0.313766\pi\) |
−0.622213 | + | 0.782848i | \(0.713766\pi\) | |||||||
\(72\) | −2.90300 | − | 2.10915i | −0.342122 | − | 0.248566i | ||||
\(73\) | −1.11020 | + | 3.41685i | −0.129939 | + | 0.399912i | −0.994769 | − | 0.102154i | \(-0.967427\pi\) |
0.864829 | + | 0.502066i | \(0.167427\pi\) | |||||||
\(74\) | 12.3174 | 1.43187 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.4011 | −1.19309 | ||||||||
\(77\) | 3.15376 | − | 9.70628i | 0.359404 | − | 1.10613i | ||||
\(78\) | −3.56741 | − | 2.59188i | −0.403930 | − | 0.293472i | ||||
\(79\) | −2.48583 | − | 1.80606i | −0.279677 | − | 0.203197i | 0.439099 | − | 0.898439i | \(-0.355298\pi\) |
−0.718777 | + | 0.695241i | \(0.755298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 3.94632 | 0.435798 | ||||||||
\(83\) | −8.18340 | + | 5.94559i | −0.898245 | + | 0.652613i | −0.938015 | − | 0.346595i | \(-0.887338\pi\) |
0.0397694 | + | 0.999209i | \(0.487338\pi\) | |||||||
\(84\) | −3.79427 | − | 11.6776i | −0.413989 | − | 1.27413i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.93517 | − | 24.4219i | 0.855672 | − | 2.63349i | ||||
\(87\) | −0.789827 | − | 2.43084i | −0.0846784 | − | 0.260613i | ||||
\(88\) | 3.25015 | + | 10.0029i | 0.346467 | + | 1.06632i | ||||
\(89\) | 0.0888461 | − | 0.273440i | 0.00941767 | − | 0.0289846i | −0.946237 | − | 0.323473i | \(-0.895149\pi\) |
0.955655 | + | 0.294489i | \(0.0951494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.01823 | − | 6.21148i | −0.211568 | − | 0.651140i | ||||
\(92\) | 15.6631 | − | 11.3799i | 1.63299 | − | 1.18644i | ||||
\(93\) | −0.418084 | −0.0433533 | ||||||||
\(94\) | 14.2483 | − | 10.3520i | 1.46960 | − | 1.06773i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.17630 | − | 2.30772i | −0.324180 | − | 0.235531i | ||||
\(97\) | 8.42109 | + | 6.11828i | 0.855032 | + | 0.621217i | 0.926529 | − | 0.376224i | \(-0.122778\pi\) |
−0.0714966 | + | 0.997441i | \(0.522778\pi\) | |||||||
\(98\) | 3.72197 | − | 11.4551i | 0.375976 | − | 1.15714i | ||||
\(99\) | 2.93111 | 0.294587 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.65744 | 0.761943 | 0.380972 | − | 0.924587i | \(-0.375590\pi\) | ||||
0.380972 | + | 0.924587i | \(0.375590\pi\) | |||||||
\(102\) | −4.92942 | + | 15.1712i | −0.488085 | + | 1.50217i | ||||
\(103\) | 2.41574 | + | 1.75514i | 0.238030 | + | 0.172939i | 0.700405 | − | 0.713745i | \(-0.253003\pi\) |
−0.462375 | + | 0.886684i | \(0.653003\pi\) | |||||||
\(104\) | 5.44530 | + | 3.95624i | 0.533955 | + | 0.387941i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.05501 | + | 5.12576i | −0.685243 | + | 0.497858i | ||||
\(107\) | −7.07213 | −0.683689 | −0.341844 | − | 0.939757i | \(-0.611052\pi\) | ||||
−0.341844 | + | 0.939757i | \(0.611052\pi\) | |||||||
\(108\) | 2.85292 | − | 2.07277i | 0.274522 | − | 0.199452i | ||||
\(109\) | −4.11060 | − | 12.6511i | −0.393724 | − | 1.21176i | −0.929951 | − | 0.367683i | \(-0.880151\pi\) |
0.536227 | − | 0.844074i | \(-0.319849\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.61912 | + | 4.98314i | −0.153680 | + | 0.472979i | ||||
\(112\) | 1.48773 | + | 4.57876i | 0.140577 | + | 0.432653i | ||||
\(113\) | 3.09737 | + | 9.53271i | 0.291376 | + | 0.896762i | 0.984415 | + | 0.175862i | \(0.0562713\pi\) |
−0.693039 | + | 0.720900i | \(0.743729\pi\) | |||||||
\(114\) | 2.14265 | − | 6.59441i | 0.200678 | − | 0.617623i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.78525 | + | 8.57211i | 0.258604 | + | 0.795900i | ||||
\(117\) | 1.51751 | − | 1.10254i | 0.140294 | − | 0.101930i | ||||
\(118\) | −16.7110 | −1.53837 | ||||||||
\(119\) | −19.1146 | + | 13.8875i | −1.75223 | + | 1.27307i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.94861 | + | 1.41575i | 0.177146 | + | 0.128704i | ||||
\(122\) | 12.2425 | + | 8.89467i | 1.10838 | + | 0.805286i | ||||
\(123\) | −0.518744 | + | 1.59653i | −0.0467736 | + | 0.143954i | ||||
\(124\) | 1.47433 | 0.132399 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.18532 | 0.729206 | ||||||||
\(127\) | 3.26725 | − | 10.0556i | 0.289921 | − | 0.892286i | −0.694959 | − | 0.719049i | \(-0.744577\pi\) |
0.984880 | − | 0.173237i | \(-0.0554225\pi\) | |||||||
\(128\) | 16.4603 | + | 11.9591i | 1.45490 | + | 1.05705i | ||||
\(129\) | 8.83711 | + | 6.42054i | 0.778064 | + | 0.565297i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.30225 | − | 5.30540i | 0.638001 | − | 0.463535i | −0.221162 | − | 0.975237i | \(-0.570985\pi\) |
0.859163 | + | 0.511703i | \(0.170985\pi\) | |||||||
\(132\) | −10.3363 | −0.899656 | ||||||||
\(133\) | 8.30847 | − | 6.03645i | 0.720435 | − | 0.523427i | ||||
\(134\) | 7.29462 | + | 22.4505i | 0.630159 | + | 1.93943i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.52427 | − | 23.1573i | 0.645200 | − | 1.98572i | ||||
\(137\) | −6.07669 | − | 18.7021i | −0.519167 | − | 1.59783i | −0.775571 | − | 0.631261i | \(-0.782538\pi\) |
0.256404 | − | 0.966570i | \(-0.417462\pi\) | |||||||
\(138\) | 3.98833 | + | 12.2748i | 0.339509 | + | 1.04490i | ||||
\(139\) | −3.60067 | + | 11.0817i | −0.305404 | + | 0.939938i | 0.674122 | + | 0.738620i | \(0.264522\pi\) |
−0.979526 | + | 0.201318i | \(0.935478\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.31509 | + | 7.12511i | 0.194965 | + | 0.600042i | ||||
\(142\) | −1.38570 | + | 1.00677i | −0.116285 | + | 0.0844862i | ||||
\(143\) | −5.49801 | −0.459767 | ||||||||
\(144\) | −1.11863 | + | 0.812729i | −0.0932188 | + | 0.0677275i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.83280 | + | 4.96432i | 0.565486 | + | 0.410850i | ||||
\(147\) | 4.14503 | + | 3.01154i | 0.341876 | + | 0.248387i | ||||
\(148\) | 5.70967 | − | 17.5726i | 0.469332 | − | 1.44446i | ||||
\(149\) | −7.33020 | −0.600513 | −0.300257 | − | 0.953858i | \(-0.597072\pi\) | ||||
−0.300257 | + | 0.953858i | \(0.597072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7358 | −1.36194 | −0.680968 | − | 0.732313i | \(-0.738441\pi\) | ||||
−0.680968 | + | 0.732313i | \(0.738441\pi\) | |||||||
\(152\) | −3.27055 | + | 10.0657i | −0.265276 | + | 0.816437i | ||||
\(153\) | −5.48972 | − | 3.98851i | −0.443817 | − | 0.322452i | ||||
\(154\) | −19.4100 | − | 14.1022i | −1.56410 | − | 1.13639i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.35135 | + | 3.88798i | −0.428451 | + | 0.311288i | ||||
\(157\) | 7.88635 | 0.629399 | 0.314700 | − | 0.949191i | \(-0.398096\pi\) | ||||
0.314700 | + | 0.949191i | \(0.398096\pi\) | |||||||
\(158\) | −5.84375 | + | 4.24574i | −0.464904 | + | 0.337773i | ||||
\(159\) | −1.14631 | − | 3.52797i | −0.0909081 | − | 0.279786i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.90724 | + | 18.1806i | −0.465556 | + | 1.43283i | ||||
\(162\) | 0.726446 | + | 2.23577i | 0.0570750 | + | 0.175659i | ||||
\(163\) | −3.07160 | − | 9.45343i | −0.240587 | − | 0.740450i | −0.996331 | − | 0.0855829i | \(-0.972725\pi\) |
0.755744 | − | 0.654867i | \(-0.227275\pi\) | |||||||
\(164\) | 1.82930 | − | 5.63000i | 0.142844 | − | 0.439629i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.34818 | + | 22.6154i | 0.570330 | + | 1.75529i | ||||
\(167\) | −4.51243 | + | 3.27847i | −0.349182 | + | 0.253696i | −0.748526 | − | 0.663106i | \(-0.769238\pi\) |
0.399344 | + | 0.916801i | \(0.369238\pi\) | |||||||
\(168\) | −12.4941 | −0.963939 | ||||||||
\(169\) | 7.67075 | − | 5.57313i | 0.590058 | − | 0.428702i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.38620 | + | 1.73367i | 0.182477 | + | 0.132577i | ||||
\(172\) | −31.1632 | − | 22.6414i | −2.37617 | − | 1.72639i | ||||
\(173\) | 5.11985 | − | 15.7573i | 0.389255 | − | 1.19800i | −0.544091 | − | 0.839026i | \(-0.683125\pi\) |
0.933346 | − | 0.358978i | \(-0.116875\pi\) | |||||||
\(174\) | −6.00857 | −0.455508 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.05284 | 0.305494 | ||||||||
\(177\) | 2.19666 | − | 6.76062i | 0.165111 | − | 0.508160i | ||||
\(178\) | −0.546808 | − | 0.397279i | −0.0409850 | − | 0.0297773i | ||||
\(179\) | 4.33650 | + | 3.15065i | 0.324125 | + | 0.235491i | 0.737934 | − | 0.674873i | \(-0.235802\pi\) |
−0.413808 | + | 0.910364i | \(0.635802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.265151 | − | 0.192643i | 0.0197085 | − | 0.0143191i | −0.577887 | − | 0.816117i | \(-0.696123\pi\) |
0.597596 | + | 0.801797i | \(0.296123\pi\) | |||||||
\(182\) | −15.3536 | −1.13808 | ||||||||
\(183\) | −5.20772 | + | 3.78363i | −0.384966 | + | 0.279694i | ||||
\(184\) | −6.08779 | − | 18.7363i | −0.448798 | − | 1.38126i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.303716 | + | 0.934741i | −0.0222695 | + | 0.0685385i | ||||
\(187\) | 6.14619 | + | 18.9160i | 0.449454 | + | 1.38328i | ||||
\(188\) | −8.16392 | − | 25.1260i | −0.595415 | − | 1.83250i | ||||
\(189\) | −1.07596 | + | 3.31147i | −0.0782647 | + | 0.240874i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.07226 | − | 3.30009i | −0.0775862 | − | 0.238786i | 0.904740 | − | 0.425965i | \(-0.140065\pi\) |
−0.982326 | + | 0.187179i | \(0.940065\pi\) | |||||||
\(192\) | −9.70420 | + | 7.05051i | −0.700340 | + | 0.508827i | ||||
\(193\) | −24.3134 | −1.75012 | −0.875058 | − | 0.484018i | \(-0.839177\pi\) | ||||
−0.875058 | + | 0.484018i | \(0.839177\pi\) | |||||||
\(194\) | 19.7966 | − | 14.3830i | 1.42131 | − | 1.03264i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.6170 | − | 10.6199i | −1.04407 | − | 0.758563i | ||||
\(197\) | −12.0997 | − | 8.79098i | −0.862071 | − | 0.626331i | 0.0663764 | − | 0.997795i | \(-0.478856\pi\) |
−0.928448 | + | 0.371463i | \(0.878856\pi\) | |||||||
\(198\) | 2.12929 | − | 6.55329i | 0.151322 | − | 0.465722i | ||||
\(199\) | −11.3251 | −0.802817 | −0.401408 | − | 0.915899i | \(-0.631479\pi\) | ||||
−0.401408 | + | 0.915899i | \(0.631479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.0415 | −0.708274 | ||||||||
\(202\) | 5.56272 | − | 17.1203i | 0.391391 | − | 1.20458i | ||||
\(203\) | −7.19983 | − | 5.23098i | −0.505329 | − | 0.367143i | ||||
\(204\) | 19.3589 | + | 14.0651i | 1.35540 | + | 0.984753i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.67900 | − | 4.12603i | 0.395674 | − | 0.287474i | ||||
\(207\) | −5.49019 | −0.381595 | ||||||||
\(208\) | 2.09826 | − | 1.52447i | 0.145488 | − | 0.105703i | ||||
\(209\) | −2.67155 | − | 8.22217i | −0.184795 | − | 0.568739i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.33086 | − | 7.17366i | 0.160463 | − | 0.493855i | −0.838210 | − | 0.545347i | \(-0.816398\pi\) |
0.998673 | + | 0.0514924i | \(0.0163978\pi\) | |||||||
\(212\) | 4.04234 | + | 12.4410i | 0.277629 | + | 0.854454i | ||||
\(213\) | −0.225150 | − | 0.692941i | −0.0154270 | − | 0.0474796i | ||||
\(214\) | −5.13752 | + | 15.8117i | −0.351194 | + | 1.08086i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.10885 | − | 3.41268i | −0.0754475 | − | 0.232204i | ||||
\(217\) | −1.17770 | + | 0.855651i | −0.0799477 | + | 0.0580854i | ||||
\(218\) | −31.2711 | −2.11795 | ||||||||
\(219\) | −2.90655 | + | 2.11173i | −0.196406 | + | 0.142697i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.2973 | + | 7.48144i | 0.692672 | + | 0.503256i | ||||
\(222\) | 9.96497 | + | 7.23997i | 0.668805 | + | 0.485915i | ||||
\(223\) | −2.40891 | + | 7.41386i | −0.161313 | + | 0.496469i | −0.998746 | − | 0.0500709i | \(-0.984055\pi\) |
0.837433 | + | 0.546540i | \(0.184055\pi\) | |||||||
\(224\) | −13.6703 | −0.913387 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.5630 | 1.56739 | ||||||||
\(227\) | −3.96529 | + | 12.2039i | −0.263185 | + | 0.810001i | 0.728921 | + | 0.684598i | \(0.240022\pi\) |
−0.992106 | + | 0.125403i | \(0.959978\pi\) | |||||||
\(228\) | −8.41468 | − | 6.11363i | −0.557276 | − | 0.404885i | ||||
\(229\) | 11.7334 | + | 8.52483i | 0.775366 | + | 0.563337i | 0.903585 | − | 0.428409i | \(-0.140926\pi\) |
−0.128218 | + | 0.991746i | \(0.540926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.25665 | − | 5.99881i | 0.543248 | − | 0.394693i | ||||
\(232\) | 9.17148 | 0.602137 | ||||||||
\(233\) | −9.22041 | + | 6.69902i | −0.604049 | + | 0.438867i | −0.847314 | − | 0.531093i | \(-0.821782\pi\) |
0.243265 | + | 0.969960i | \(0.421782\pi\) | |||||||
\(234\) | −1.36263 | − | 4.19374i | −0.0890779 | − | 0.274153i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.74630 | + | 23.8407i | −0.504241 | + | 1.55190i | ||||
\(237\) | −0.949501 | − | 2.92226i | −0.0616767 | − | 0.189821i | ||||
\(238\) | 17.1637 | + | 52.8244i | 1.11256 | + | 3.42410i | ||||
\(239\) | 2.13244 | − | 6.56298i | 0.137936 | − | 0.424524i | −0.858099 | − | 0.513484i | \(-0.828354\pi\) |
0.996035 | + | 0.0889605i | \(0.0283545\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.79052 | − | 27.0545i | −0.566247 | − | 1.74273i | −0.664216 | − | 0.747541i | \(-0.731234\pi\) |
0.0979683 | − | 0.995190i | \(-0.468766\pi\) | |||||||
\(242\) | 4.58085 | − | 3.32818i | 0.294468 | − | 0.213943i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 18.3645 | − | 13.3426i | 1.17567 | − | 0.854172i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.19264 | + | 2.31959i | 0.203555 | + | 0.147891i | ||||
\(247\) | −4.47590 | − | 3.25193i | −0.284795 | − | 0.206915i | ||||
\(248\) | 0.463592 | − | 1.42679i | 0.0294381 | − | 0.0906011i | ||||
\(249\) | −10.1152 | −0.641028 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3258 | −0.777999 | −0.389000 | − | 0.921238i | \(-0.627179\pi\) | ||||
−0.389000 | + | 0.921238i | \(0.627179\pi\) | |||||||
\(252\) | 3.79427 | − | 11.6776i | 0.239017 | − | 0.735618i | ||||
\(253\) | 13.0190 | + | 9.45885i | 0.818496 | + | 0.594673i | ||||
\(254\) | −20.1084 | − | 14.6096i | −1.26172 | − | 0.916690i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.2870 | − | 14.0128i | 1.20544 | − | 0.875801i | ||||
\(257\) | 20.8274 | 1.29918 | 0.649590 | − | 0.760285i | \(-0.274941\pi\) | ||||
0.649590 | + | 0.760285i | \(0.274941\pi\) | |||||||
\(258\) | 20.7745 | − | 15.0936i | 1.29337 | − | 0.939686i | ||||
\(259\) | 5.63760 | + | 17.3507i | 0.350303 | + | 1.07812i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.789827 | − | 2.43084i | 0.0488891 | − | 0.150465i | ||||
\(262\) | −6.55696 | − | 20.1802i | −0.405090 | − | 1.24674i | ||||
\(263\) | 0.690704 | + | 2.12577i | 0.0425906 | + | 0.131080i | 0.970091 | − | 0.242742i | \(-0.0780469\pi\) |
−0.927500 | + | 0.373823i | \(0.878047\pi\) | |||||||
\(264\) | −3.25015 | + | 10.0029i | −0.200033 | + | 0.615638i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.46048 | − | 22.9610i | −0.457431 | − | 1.40783i | ||||
\(267\) | 0.232602 | − | 0.168995i | 0.0142350 | − | 0.0103423i | ||||
\(268\) | 35.4104 | 2.16303 | ||||||||
\(269\) | 15.6170 | − | 11.3464i | 0.952183 | − | 0.691802i | 0.000861106 | − | 1.00000i | \(-0.499726\pi\) |
0.951322 | + | 0.308198i | \(0.0997259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.66058 | + | 7.01882i | 0.586838 | + | 0.426363i | 0.841183 | − | 0.540751i | \(-0.181860\pi\) |
−0.254345 | + | 0.967114i | \(0.581860\pi\) | |||||||
\(272\) | −7.59062 | − | 5.51491i | −0.460249 | − | 0.334390i | ||||
\(273\) | 2.01823 | − | 6.21148i | 0.122149 | − | 0.375936i | ||||
\(274\) | −46.2281 | −2.79274 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 19.3606 | 1.16537 | ||||||||
\(277\) | 8.07975 | − | 24.8669i | 0.485465 | − | 1.49411i | −0.345841 | − | 0.938293i | \(-0.612406\pi\) |
0.831306 | − | 0.555815i | \(-0.187594\pi\) | |||||||
\(278\) | 22.1605 | + | 16.1005i | 1.32910 | + | 0.965646i | ||||
\(279\) | −0.338237 | − | 0.245744i | −0.0202497 | − | 0.0147123i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.18876 | + | 5.94948i | −0.488500 | + | 0.354916i | −0.804607 | − | 0.593807i | \(-0.797624\pi\) |
0.316107 | + | 0.948724i | \(0.397624\pi\) | |||||||
\(282\) | 17.6119 | 1.04877 | ||||||||
\(283\) | 25.7783 | − | 18.7290i | 1.53236 | − | 1.11333i | 0.577455 | − | 0.816423i | \(-0.304046\pi\) |
0.954907 | − | 0.296903i | \(-0.0959540\pi\) | |||||||
\(284\) | 0.793970 | + | 2.44359i | 0.0471135 | + | 0.145000i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.99401 | + | 12.2923i | −0.236171 | + | 0.726859i | ||||
\(287\) | 1.80621 | + | 5.55893i | 0.106617 | + | 0.328134i | ||||
\(288\) | −1.21324 | − | 3.73397i | −0.0714908 | − | 0.220026i | ||||
\(289\) | 8.97546 | − | 27.6236i | 0.527968 | − | 1.62492i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.21657 | + | 9.89959i | 0.188559 | + | 0.580324i | ||||
\(292\) | 10.2496 | − | 7.44680i | 0.599815 | − | 0.435791i | ||||
\(293\) | 16.6235 | 0.971153 | 0.485576 | − | 0.874194i | \(-0.338610\pi\) | ||||
0.485576 | + | 0.874194i | \(0.338610\pi\) | |||||||
\(294\) | 9.74425 | − | 7.07961i | 0.568296 | − | 0.412891i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.2105 | − | 11.0511i | −0.884094 | − | 0.642332i | ||||
\(297\) | 2.37132 | + | 1.72286i | 0.137598 | + | 0.0999706i | ||||
\(298\) | −5.32499 | + | 16.3886i | −0.308469 | + | 0.949369i | ||||
\(299\) | 10.2982 | 0.595561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.0336 | 2.19222 | ||||||||
\(302\) | −12.1576 | + | 37.4173i | −0.699593 | + | 2.15312i | ||||
\(303\) | 6.19500 | + | 4.50093i | 0.355893 | + | 0.258572i | ||||
\(304\) | 3.29939 | + | 2.39715i | 0.189233 | + | 0.137486i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.9054 | + | 9.37631i | −0.737752 | + | 0.536008i | ||||
\(307\) | −14.1643 | −0.808402 | −0.404201 | − | 0.914670i | \(-0.632450\pi\) | ||||
−0.404201 | + | 0.914670i | \(0.632450\pi\) | |||||||
\(308\) | −29.1163 | + | 21.1542i | −1.65905 | + | 1.20537i | ||||
\(309\) | 0.922731 | + | 2.83987i | 0.0524923 | + | 0.161555i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.65070 | − | 14.3134i | 0.263717 | − | 0.811637i | −0.728269 | − | 0.685291i | \(-0.759675\pi\) |
0.991986 | − | 0.126346i | \(-0.0403250\pi\) | |||||||
\(312\) | 2.07992 | + | 6.40133i | 0.117752 | + | 0.362404i | ||||
\(313\) | −1.10466 | − | 3.39980i | −0.0624392 | − | 0.192168i | 0.914971 | − | 0.403520i | \(-0.132213\pi\) |
−0.977410 | + | 0.211352i | \(0.932213\pi\) | |||||||
\(314\) | 5.72901 | − | 17.6321i | 0.323307 | − | 0.995036i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.34832 | + | 10.3051i | 0.188358 | + | 0.579706i | ||||
\(317\) | −10.3408 | + | 7.51306i | −0.580799 | + | 0.421975i | −0.839012 | − | 0.544113i | \(-0.816866\pi\) |
0.258213 | + | 0.966088i | \(0.416866\pi\) | |||||||
\(318\) | −8.72047 | −0.489020 | ||||||||
\(319\) | −6.06093 | + | 4.40352i | −0.339347 | + | 0.246550i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.72147 | − | 4.15689i | −0.319342 | − | 0.232015i | ||||
\(322\) | 36.3564 | + | 26.4145i | 2.02606 | + | 1.47202i | ||||
\(323\) | −6.18476 | + | 19.0347i | −0.344129 | + | 1.05912i | ||||
\(324\) | 3.52640 | 0.195911 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.3671 | −1.29418 | ||||||||
\(327\) | 4.11060 | − | 12.6511i | 0.227317 | − | 0.699608i | ||||
\(328\) | −4.87324 | − | 3.54062i | −0.269080 | − | 0.195498i | ||||
\(329\) | 21.1036 | + | 15.3327i | 1.16348 | + | 0.845318i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.80646 | + | 2.76555i | −0.209222 | + | 0.152009i | −0.687462 | − | 0.726221i | \(-0.741275\pi\) |
0.478240 | + | 0.878229i | \(0.341275\pi\) | |||||||
\(332\) | 35.6704 | 1.95767 | ||||||||
\(333\) | −4.23892 | + | 3.07975i | −0.232291 | + | 0.168769i | ||||
\(334\) | 4.05187 | + | 12.4704i | 0.221709 | + | 0.682349i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.48773 | + | 4.57876i | −0.0811624 | + | 0.249792i | ||||
\(337\) | −5.37837 | − | 16.5529i | −0.292978 | − | 0.901694i | −0.983893 | − | 0.178758i | \(-0.942792\pi\) |
0.690915 | − | 0.722936i | \(-0.257208\pi\) | |||||||
\(338\) | −6.88785 | − | 21.1986i | −0.374650 | − | 1.15305i | ||||
\(339\) | −3.09737 | + | 9.53271i | −0.168226 | + | 0.517746i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.378685 | + | 1.16547i | 0.0205069 | + | 0.0631138i | ||||
\(342\) | 5.60954 | − | 4.07557i | 0.303329 | − | 0.220382i | ||||
\(343\) | −6.53364 | −0.352783 | ||||||||
\(344\) | −31.7103 | + | 23.0389i | −1.70970 | + | 1.24217i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.5104 | − | 22.8936i | −1.69401 | − | 1.23077i | ||||
\(347\) | −11.3348 | − | 8.23525i | −0.608486 | − | 0.442091i | 0.240395 | − | 0.970675i | \(-0.422723\pi\) |
−0.848881 | + | 0.528584i | \(0.822723\pi\) | |||||||
\(348\) | −2.78525 | + | 8.57211i | −0.149305 | + | 0.459513i | ||||
\(349\) | 35.9459 | 1.92414 | 0.962069 | − | 0.272806i | \(-0.0879518\pi\) | ||||
0.962069 | + | 0.272806i | \(0.0879518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.87575 | 0.100120 | ||||||||
\(352\) | −3.55614 | + | 10.9447i | −0.189543 | + | 0.583352i | ||||
\(353\) | −7.12095 | − | 5.17367i | −0.379010 | − | 0.275367i | 0.381927 | − | 0.924192i | \(-0.375260\pi\) |
−0.760937 | + | 0.648826i | \(0.775260\pi\) | |||||||
\(354\) | −13.5195 | − | 9.82246i | −0.718551 | − | 0.522058i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.820248 | + | 0.595945i | −0.0434731 | + | 0.0315850i | ||||
\(357\) | −23.6269 | −1.25047 | ||||||||
\(358\) | 10.1944 | − | 7.40665i | 0.538790 | − | 0.391454i | ||||
\(359\) | 1.86326 | + | 5.73451i | 0.0983389 | + | 0.302656i | 0.988109 | − | 0.153752i | \(-0.0491357\pi\) |
−0.889771 | + | 0.456408i | \(0.849136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.18301 | + | 9.79630i | −0.167527 | + | 0.515595i | ||||
\(362\) | −0.238089 | − | 0.732762i | −0.0125137 | − | 0.0385131i | ||||
\(363\) | 0.744302 | + | 2.29073i | 0.0390657 | + | 0.120232i | ||||
\(364\) | −7.11710 | + | 21.9042i | −0.373037 | + | 1.14809i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.67621 | + | 14.3919i | 0.244429 | + | 0.752276i | ||||
\(367\) | −23.2724 | + | 16.9084i | −1.21481 | + | 0.882609i | −0.995658 | − | 0.0930825i | \(-0.970328\pi\) |
−0.219149 | + | 0.975691i | \(0.570328\pi\) | |||||||
\(368\) | −7.59128 | −0.395723 | ||||||||
\(369\) | −1.35809 | + | 0.986709i | −0.0706993 | + | 0.0513660i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4494 | − | 7.59193i | −0.542505 | − | 0.394153i | ||||
\(372\) | 1.19276 | + | 0.866590i | 0.0618417 | + | 0.0449306i | ||||
\(373\) | 10.3830 | − | 31.9555i | 0.537610 | − | 1.65459i | −0.200330 | − | 0.979729i | \(-0.564201\pi\) |
0.737940 | − | 0.674866i | \(-0.235799\pi\) | |||||||
\(374\) | 46.7568 | 2.41774 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.8828 | −1.38637 | ||||||||
\(377\) | −1.48152 | + | 4.55964i | −0.0763020 | + | 0.234833i | ||||
\(378\) | 6.62206 | + | 4.81121i | 0.340602 | + | 0.247462i | ||||
\(379\) | −3.74901 | − | 2.72381i | −0.192574 | − | 0.139913i | 0.487321 | − | 0.873223i | \(-0.337974\pi\) |
−0.679894 | + | 0.733310i | \(0.737974\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.55377 | − | 6.21467i | 0.438223 | − | 0.318387i | ||||
\(382\) | −8.15718 | −0.417358 | ||||||||
\(383\) | 10.4410 | − | 7.58581i | 0.533509 | − | 0.387617i | −0.288160 | − | 0.957582i | \(-0.593043\pi\) |
0.821669 | + | 0.569965i | \(0.193043\pi\) | |||||||
\(384\) | 6.28728 | + | 19.3503i | 0.320846 | + | 0.987464i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.6624 | + | 54.3592i | −0.898991 | + | 2.76681i | ||||
\(387\) | 3.37548 | + | 10.3886i | 0.171585 | + | 0.528085i | ||||
\(388\) | −11.3429 | − | 34.9099i | −0.575849 | − | 1.77228i | ||||
\(389\) | −5.41540 | + | 16.6669i | −0.274571 | + | 0.845044i | 0.714761 | + | 0.699369i | \(0.246535\pi\) |
−0.989332 | + | 0.145675i | \(0.953465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5123 | − | 35.4312i | −0.582202 | − | 1.79183i | ||||
\(392\) | −14.8736 | + | 10.8063i | −0.751232 | + | 0.545802i | ||||
\(393\) | 9.02608 | 0.455305 | ||||||||
\(394\) | −28.4444 | + | 20.6661i | −1.43301 | + | 1.04114i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.36221 | − | 6.07550i | −0.420217 | − | 0.305305i | ||||
\(397\) | 21.8577 | + | 15.8805i | 1.09701 | + | 0.797021i | 0.980569 | − | 0.196177i | \(-0.0628527\pi\) |
0.116437 | + | 0.993198i | \(0.462853\pi\) | |||||||
\(398\) | −8.22709 | + | 25.3204i | −0.412387 | + | 1.26920i | ||||
\(399\) | 10.2698 | 0.514134 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.9792 | −0.797965 | −0.398983 | − | 0.916958i | \(-0.630637\pi\) | ||||
−0.398983 | + | 0.916958i | \(0.630637\pi\) | |||||||
\(402\) | −7.29462 | + | 22.4505i | −0.363823 | + | 1.11973i | ||||
\(403\) | 0.634447 | + | 0.460953i | 0.0316041 | + | 0.0229617i | ||||
\(404\) | −21.8460 | − | 15.8721i | −1.08688 | − | 0.789665i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.9256 | + | 12.2971i | −0.840002 | + | 0.610297i | ||||
\(407\) | 15.3578 | 0.761258 | ||||||||
\(408\) | 19.6988 | − | 14.3120i | 0.975235 | − | 0.708550i | ||||
\(409\) | −9.57834 | − | 29.4791i | −0.473618 | − | 1.45765i | −0.847812 | − | 0.530297i | \(-0.822080\pi\) |
0.374193 | − | 0.927351i | \(-0.377920\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.07669 | − | 18.7021i | 0.299741 | − | 0.922508i | ||||
\(412\) | −3.25392 | − | 10.0145i | −0.160309 | − | 0.493381i | ||||
\(413\) | −7.64852 | − | 23.5397i | −0.376359 | − | 1.15831i | ||||
\(414\) | −3.98833 | + | 12.2748i | −0.196016 | + | 0.603275i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.27573 | + | 7.00398i | 0.111577 | + | 0.343398i | ||||
\(417\) | −9.42666 | + | 6.84887i | −0.461626 | + | 0.335391i | ||||
\(418\) | −20.3236 | −0.994061 | ||||||||
\(419\) | −20.9660 | + | 15.2327i | −1.02425 | + | 0.744164i | −0.967151 | − | 0.254204i | \(-0.918186\pi\) |
−0.0571034 | + | 0.998368i | \(0.518186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.17658 | − | 2.30792i | −0.154817 | − | 0.112481i | 0.507680 | − | 0.861546i | \(-0.330503\pi\) |
−0.662497 | + | 0.749065i | \(0.730503\pi\) | |||||||
\(422\) | −14.3454 | − | 10.4226i | −0.698324 | − | 0.507362i | ||||
\(423\) | −2.31509 | + | 7.12511i | −0.112563 | + | 0.346434i | ||||
\(424\) | 13.3109 | 0.646436 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.71282 | −0.0829863 | ||||||||
\(427\) | −6.92607 | + | 21.3163i | −0.335176 | + | 1.03157i | ||||
\(428\) | 20.1762 | + | 14.6589i | 0.975254 | + | 0.708563i | ||||
\(429\) | −4.44799 | − | 3.23165i | −0.214751 | − | 0.156026i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.6903 | − | 20.8447i | 1.38196 | − | 1.00406i | 0.385270 | − | 0.922804i | \(-0.374108\pi\) |
0.996694 | − | 0.0812518i | \(-0.0258918\pi\) | |||||||
\(432\) | −1.38270 | −0.0665251 | ||||||||
\(433\) | −8.16776 | + | 5.93423i | −0.392518 | + | 0.285181i | −0.766486 | − | 0.642261i | \(-0.777997\pi\) |
0.373969 | + | 0.927441i | \(0.377997\pi\) | |||||||
\(434\) | 1.05750 | + | 3.25466i | 0.0507618 | + | 0.156229i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.4956 | + | 44.6129i | −0.694214 | + | 2.13657i | ||||
\(437\) | 5.00402 | + | 15.4008i | 0.239375 | + | 0.736719i | ||||
\(438\) | 2.60990 | + | 8.03243i | 0.124706 | + | 0.383804i | ||||
\(439\) | 2.19575 | − | 6.75783i | 0.104798 | − | 0.322534i | −0.884885 | − | 0.465809i | \(-0.845763\pi\) |
0.989683 | + | 0.143275i | \(0.0457634\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.58326 | + | 4.87277i | 0.0753933 | + | 0.232037i | ||||
\(442\) | 24.2072 | − | 17.5876i | 1.15142 | − | 0.836556i | ||||
\(443\) | 20.6841 | 0.982733 | 0.491366 | − | 0.870953i | \(-0.336498\pi\) | ||||
0.491366 | + | 0.870953i | \(0.336498\pi\) | |||||||
\(444\) | 14.9481 | − | 10.8604i | 0.709406 | − | 0.515414i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.8258 | + | 10.7715i | 0.702020 | + | 0.510047i | ||||
\(447\) | −5.93025 | − | 4.30858i | −0.280491 | − | 0.203789i | ||||
\(448\) | −12.9062 | + | 39.7213i | −0.609762 | + | 1.87665i | ||||
\(449\) | 19.4940 | 0.919980 | 0.459990 | − | 0.887924i | \(-0.347853\pi\) | ||||
0.459990 | + | 0.887924i | \(0.347853\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92042 | 0.231694 | ||||||||
\(452\) | 10.9225 | − | 33.6162i | 0.513754 | − | 1.58117i | ||||
\(453\) | −13.5395 | − | 9.83703i | −0.636142 | − | 0.462184i | ||||
\(454\) | 24.4046 | + | 17.7310i | 1.14536 | + | 0.832155i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.56240 | + | 6.22095i | −0.400971 | + | 0.291323i | ||||
\(457\) | −4.34194 | −0.203107 | −0.101554 | − | 0.994830i | \(-0.532381\pi\) | ||||
−0.101554 | + | 0.994830i | \(0.532381\pi\) | |||||||
\(458\) | 27.5833 | − | 20.0404i | 1.28888 | − | 0.936427i | ||||
\(459\) | −2.09688 | − | 6.45355i | −0.0978742 | − | 0.301226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.64322 | − | 11.2127i | 0.169682 | − | 0.522227i | −0.829669 | − | 0.558256i | \(-0.811471\pi\) |
0.999351 | + | 0.0360287i | \(0.0114708\pi\) | |||||||
\(462\) | −7.41395 | − | 22.8178i | −0.344928 | − | 1.06158i | ||||
\(463\) | −2.80547 | − | 8.63436i | −0.130381 | − | 0.401273i | 0.864462 | − | 0.502699i | \(-0.167659\pi\) |
−0.994843 | + | 0.101426i | \(0.967659\pi\) | |||||||
\(464\) | 1.09209 | − | 3.36112i | 0.0506991 | − | 0.156036i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.27934 | + | 25.4812i | 0.383533 | + | 1.18039i | ||||
\(467\) | 28.2494 | − | 20.5244i | 1.30723 | − | 0.949755i | 0.307227 | − | 0.951636i | \(-0.400599\pi\) |
0.999998 | + | 0.00188168i | \(0.000598959\pi\) | |||||||
\(468\) | −6.61463 | −0.305762 | ||||||||
\(469\) | −28.2860 | + | 20.5510i | −1.30613 | + | 0.948956i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.38019 | + | 4.63548i | 0.293984 | + | 0.213592i | ||||
\(472\) | 20.6361 | + | 14.9930i | 0.949854 | + | 0.690109i | ||||
\(473\) | 9.89388 | − | 30.4502i | 0.454921 | − | 1.40010i | ||||
\(474\) | −7.22328 | −0.331776 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 83.3179 | 3.81887 | ||||||||
\(477\) | 1.14631 | − | 3.52797i | 0.0524858 | − | 0.161535i | ||||
\(478\) | −13.1242 | − | 9.53530i | −0.600288 | − | 0.436135i | ||||
\(479\) | 6.99515 | + | 5.08228i | 0.319617 | + | 0.232215i | 0.736012 | − | 0.676969i | \(-0.236707\pi\) |
−0.416395 | + | 0.909184i | \(0.636707\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.95113 | − | 5.77684i | 0.362540 | − | 0.263401i | ||||
\(482\) | −66.8734 | −3.04600 | ||||||||
\(483\) | −15.4654 | + | 11.2362i | −0.703698 | + | 0.511267i | ||||
\(484\) | −2.62471 | − | 8.07802i | −0.119305 | − | 0.367183i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.726446 | + | 2.23577i | −0.0329523 | + | 0.101417i | ||||
\(487\) | 0.879035 | + | 2.70539i | 0.0398329 | + | 0.122593i | 0.968996 | − | 0.247078i | \(-0.0794704\pi\) |
−0.929163 | + | 0.369671i | \(0.879470\pi\) | |||||||
\(488\) | −7.13776 | − | 21.9678i | −0.323111 | − | 0.994434i | ||||
\(489\) | 3.07160 | − | 9.45343i | 0.138903 | − | 0.427499i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3731 | + | 35.0028i | 0.513260 | + | 1.57965i | 0.786425 | + | 0.617686i | \(0.211930\pi\) |
−0.273165 | + | 0.961967i | \(0.588070\pi\) | |||||||
\(492\) | 4.78917 | − | 3.47953i | 0.215912 | − | 0.156869i | ||||
\(493\) | 17.3437 | 0.781121 | ||||||||
\(494\) | −10.5221 | + | 7.64474i | −0.473411 | + | 0.343953i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.467680 | − | 0.339789i | −0.0209994 | − | 0.0152570i | ||||
\(497\) | −2.05240 | − | 1.49116i | −0.0920628 | − | 0.0668876i | ||||
\(498\) | −7.34818 | + | 22.6154i | −0.329280 | + | 1.01342i | ||||
\(499\) | 5.85775 | 0.262229 | 0.131114 | − | 0.991367i | \(-0.458144\pi\) | ||||
0.131114 | + | 0.991367i | \(0.458144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.57767 | −0.249192 | ||||||||
\(502\) | −8.95405 | + | 27.5577i | −0.399639 | + | 1.22996i | ||||
\(503\) | 24.5030 | + | 17.8025i | 1.09253 | + | 0.793773i | 0.979825 | − | 0.199855i | \(-0.0640472\pi\) |
0.112709 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(504\) | −10.1079 | − | 7.34383i | −0.450243 | − | 0.327120i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 30.6054 | − | 22.2361i | 1.36058 | − | 0.988517i | ||||
\(507\) | 9.48157 | 0.421091 | ||||||||
\(508\) | −30.1640 | + | 21.9154i | −1.33831 | + | 0.972340i | ||||
\(509\) | 4.67944 | + | 14.4018i | 0.207413 | + | 0.638350i | 0.999606 | + | 0.0280797i | \(0.00893923\pi\) |
−0.792193 | + | 0.610270i | \(0.791061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.86560 | + | 11.8971i | −0.171004 | + | 0.526296i | ||||
\(512\) | −4.74395 | − | 14.6004i | −0.209655 | − | 0.645251i | ||||
\(513\) | 0.911446 | + | 2.80514i | 0.0402413 | + | 0.123850i | ||||
\(514\) | 15.1300 | − | 46.5654i | 0.667356 | − | 2.05391i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.9033 | − | 36.6345i | −0.524013 | − | 1.61275i | ||||
\(517\) | 17.7654 | − | 12.9073i | 0.781320 | − | 0.567662i | ||||
\(518\) | 42.8877 | 1.88438 | ||||||||
\(519\) | 13.4039 | − | 9.73854i | 0.588368 | − | 0.427474i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.6190 | − | 22.9726i | −1.38525 | − | 1.00645i | −0.996367 | − | 0.0851601i | \(-0.972860\pi\) |
−0.388887 | − | 0.921286i | \(-0.627140\pi\) | |||||||
\(522\) | −4.86103 | − | 3.53175i | −0.212762 | − | 0.154580i | ||||
\(523\) | −11.9891 | + | 36.8987i | −0.524248 | + | 1.61347i | 0.241550 | + | 0.970388i | \(0.422344\pi\) |
−0.765798 | + | 0.643081i | \(0.777656\pi\) | |||||||
\(524\) | −31.8296 | −1.39048 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.25449 | 0.229107 | ||||||||
\(527\) | 0.876674 | − | 2.69813i | 0.0381885 | − | 0.117532i | ||||
\(528\) | 3.27881 | + | 2.38220i | 0.142692 | + | 0.103672i | ||||
\(529\) | −5.77819 | − | 4.19810i | −0.251226 | − | 0.182526i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.75093 | − | 4.17830i | 0.249569 | − | 0.181323i | ||||
\(532\) | −36.2155 | −1.57014 | ||||||||
\(533\) | 2.54743 | − | 1.85082i | 0.110341 | − | 0.0801678i | ||||
\(534\) | −0.208862 | − | 0.642811i | −0.00903835 | − | 0.0278172i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.1345 | − | 34.2685i | 0.480938 | − | 1.48017i | ||||
\(537\) | 1.65640 | + | 5.09787i | 0.0714788 | + | 0.219989i | ||||
\(538\) | −14.0231 | − | 43.1585i | −0.604577 | − | 1.86070i | ||||
\(539\) | 4.64070 | − | 14.2826i | 0.199889 | − | 0.615196i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.39669 | + | 13.5316i | 0.189029 | + | 0.581770i | 0.999994 | − | 0.00332312i | \(-0.00105778\pi\) |
−0.810966 | + | 0.585094i | \(0.801058\pi\) | |||||||
\(542\) | 22.7104 | − | 16.5001i | 0.975494 | − | 0.708738i | ||||
\(543\) | 0.327745 | 0.0140649 | ||||||||
\(544\) | 21.5533 | − | 15.6594i | 0.924091 | − | 0.671391i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.4213 | − | 9.02462i | −0.531583 | − | 0.386218i | ||||
\(547\) | −31.8129 | − | 23.1134i | −1.36022 | − | 0.988259i | −0.998431 | − | 0.0559991i | \(-0.982166\pi\) |
−0.361790 | − | 0.932259i | \(-0.617834\pi\) | |||||||
\(548\) | −21.4288 | + | 65.9512i | −0.915395 | + | 2.81730i | ||||
\(549\) | −6.43710 | −0.274729 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.53873 | −0.321161 | ||||||||
\(552\) | 6.08779 | − | 18.7363i | 0.259114 | − | 0.797470i | ||||
\(553\) | −8.65537 | − | 6.28849i | −0.368064 | − | 0.267414i | ||||
\(554\) | −49.7272 | − | 36.1290i | −2.11271 | − | 1.53497i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 33.2422 | − | 24.1519i | 1.40978 | − | 1.02427i | ||||
\(557\) | 35.3849 | 1.49931 | 0.749654 | − | 0.661830i | \(-0.230220\pi\) | ||||
0.749654 | + | 0.661830i | \(0.230220\pi\) | |||||||
\(558\) | −0.795138 | + | 0.577701i | −0.0336609 | + | 0.0244561i | ||||
\(559\) | −6.33154 | − | 19.4865i | −0.267796 | − | 0.824190i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.14619 | + | 18.9160i | −0.259492 | + | 0.798636i | ||||
\(562\) | 7.35299 | + | 22.6302i | 0.310167 | + | 0.954597i | ||||
\(563\) | 4.64717 | + | 14.3025i | 0.195855 | + | 0.602780i | 0.999966 | + | 0.00830000i | \(0.00264200\pi\) |
−0.804111 | + | 0.594480i | \(0.797358\pi\) | |||||||
\(564\) | 8.16392 | − | 25.1260i | 0.343763 | − | 1.05799i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.1473 | − | 71.2401i | −0.972954 | − | 2.99444i | ||||
\(567\) | −2.81691 | + | 2.04660i | −0.118299 | + | 0.0859492i | ||||
\(568\) | 2.61445 | 0.109700 | ||||||||
\(569\) | 2.20383 | − | 1.60118i | 0.0923895 | − | 0.0671249i | −0.540632 | − | 0.841260i | \(-0.681815\pi\) |
0.633021 | + | 0.774135i | \(0.281815\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.2127 | − | 7.41997i | −0.427389 | − | 0.310516i | 0.353215 | − | 0.935542i | \(-0.385088\pi\) |
−0.780604 | + | 0.625026i | \(0.785088\pi\) | |||||||
\(572\) | 15.6854 | + | 11.3961i | 0.655839 | + | 0.476495i | ||||
\(573\) | 1.07226 | − | 3.30009i | 0.0447944 | − | 0.137863i | ||||
\(574\) | 13.7406 | 0.573522 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.9951 | −0.499794 | ||||||||
\(577\) | −7.28797 | + | 22.4301i | −0.303402 | + | 0.933776i | 0.676866 | + | 0.736106i | \(0.263338\pi\) |
−0.980269 | + | 0.197670i | \(0.936662\pi\) | |||||||
\(578\) | −55.2399 | − | 40.1342i | −2.29768 | − | 1.66936i | ||||
\(579\) | −19.6700 | − | 14.2911i | −0.817455 | − | 0.593916i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.4937 | + | 20.7019i | −1.18212 | + | 0.858858i | ||||
\(582\) | 24.4699 | 1.01431 | ||||||||
\(583\) | −8.79646 | + | 6.39100i | −0.364312 | + | 0.264688i | ||||
\(584\) | −3.98374 | − | 12.2607i | −0.164849 | − | 0.507352i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0761 | − | 37.1663i | 0.498857 | − | 1.53532i | ||||
\(587\) | −7.00764 | − | 21.5673i | −0.289236 | − | 0.890177i | −0.985097 | − | 0.172000i | \(-0.944977\pi\) |
0.695861 | − | 0.718177i | \(-0.255023\pi\) | |||||||
\(588\) | −5.58321 | − | 17.1833i | −0.230248 | − | 0.708629i | ||||
\(589\) | −0.381061 | + | 1.17279i | −0.0157013 | + | 0.0483238i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.62169 | − | 14.2241i | −0.190111 | − | 0.585102i | ||||
\(592\) | −5.86114 | + | 4.25837i | −0.240891 | + | 0.175018i | ||||
\(593\) | −8.74287 | −0.359027 | −0.179513 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179513 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(594\) | 5.57456 | − | 4.05015i | 0.228727 | − | 0.166180i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.9124 | + | 15.1938i | 0.856607 | + | 0.622362i | ||||
\(597\) | −9.16222 | − | 6.65674i | −0.374985 | − | 0.272442i | ||||
\(598\) | 7.48110 | − | 23.0245i | 0.305925 | − | 0.941540i | ||||
\(599\) | 16.3209 | 0.666854 | 0.333427 | − | 0.942776i | \(-0.391795\pi\) | ||||
0.333427 | + | 0.942776i | \(0.391795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2713 | 1.47954 | 0.739768 | − | 0.672862i | \(-0.234935\pi\) | ||||
0.739768 | + | 0.672862i | \(0.234935\pi\) | |||||||
\(602\) | 27.6294 | − | 85.0344i | 1.12609 | − | 3.46575i | ||||
\(603\) | −8.12376 | − | 5.90225i | −0.330825 | − | 0.240358i | ||||
\(604\) | 47.7457 | + | 34.6893i | 1.94275 | + | 1.41149i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.5634 | − | 10.5809i | 0.591597 | − | 0.429820i | ||||
\(607\) | −16.6820 | −0.677102 | −0.338551 | − | 0.940948i | \(-0.609937\pi\) | ||||
−0.338551 | + | 0.940948i | \(0.609937\pi\) | |||||||
\(608\) | −9.36851 | + | 6.80662i | −0.379943 | + | 0.276045i | ||||
\(609\) | −2.75009 | − | 8.46390i | −0.111439 | − | 0.342975i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.34252 | − | 13.3649i | 0.175679 | − | 0.540686i | ||||
\(612\) | 7.39445 | + | 22.7578i | 0.298903 | + | 0.919929i | ||||
\(613\) | 7.66260 | + | 23.5831i | 0.309490 | + | 0.952511i | 0.977964 | + | 0.208776i | \(0.0669479\pi\) |
−0.668474 | + | 0.743736i | \(0.733052\pi\) | |||||||
\(614\) | −10.2896 | + | 31.6682i | −0.415256 | + | 1.27803i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3167 | + | 34.8291i | 0.455961 | + | 1.40330i | ||||
\(617\) | −22.6257 | + | 16.4386i | −0.910877 | + | 0.661791i | −0.941237 | − | 0.337748i | \(-0.890335\pi\) |
0.0303592 | + | 0.999539i | \(0.490335\pi\) | |||||||
\(618\) | 7.01963 | 0.282371 | ||||||||
\(619\) | −22.0608 | + | 16.0281i | −0.886697 | + | 0.644223i | −0.935015 | − | 0.354609i | \(-0.884614\pi\) |
0.0483179 | + | 0.998832i | \(0.484614\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.44166 | − | 3.22706i | −0.178238 | − | 0.129497i | ||||
\(622\) | −28.6230 | − | 20.7958i | −1.14768 | − | 0.833836i | ||||
\(623\) | 0.309352 | − | 0.952088i | 0.0123939 | − | 0.0381446i | ||||
\(624\) | 2.59359 | 0.103827 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.40365 | −0.335878 | ||||||||
\(627\) | 2.67155 | − | 8.22217i | 0.106691 | − | 0.328362i | ||||
\(628\) | −22.4991 | − | 16.3466i | −0.897812 | − | 0.652299i | ||||
\(629\) | −28.7638 | − | 20.8982i | −1.14689 | − | 0.833264i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.1893 | + | 24.8400i | −1.36105 | + | 0.988863i | −0.362676 | + | 0.931915i | \(0.618137\pi\) |
−0.998377 | + | 0.0569481i | \(0.981863\pi\) | |||||||
\(632\) | 11.0256 | 0.438575 | ||||||||
\(633\) | 6.10228 | − | 4.43356i | 0.242544 | − | 0.176218i | ||||
\(634\) | 9.28542 | + | 28.5776i | 0.368771 | + | 1.13496i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.04234 | + | 12.4410i | −0.160289 | + | 0.493319i | ||||
\(637\) | −2.96979 | − | 9.14008i | −0.117667 | − | 0.362143i | ||||
\(638\) | 5.44233 | + | 16.7498i | 0.215464 | + | 0.663130i | ||||
\(639\) | 0.225150 | − | 0.692941i | 0.00890681 | − | 0.0274123i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.1671 | + | 43.6017i | 0.559565 | + | 1.72217i | 0.683571 | + | 0.729884i | \(0.260426\pi\) |
−0.124006 | + | 0.992281i | \(0.539574\pi\) | |||||||
\(642\) | −13.4502 | + | 9.77215i | −0.530837 | + | 0.385676i | ||||
\(643\) | −46.6710 | −1.84052 | −0.920261 | − | 0.391304i | \(-0.872024\pi\) | ||||
−0.920261 | + | 0.391304i | \(0.872024\pi\) | |||||||
\(644\) | 54.5370 | − | 39.6235i | 2.14906 | − | 1.56138i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 38.0644 | + | 27.6554i | 1.49763 | + | 1.08809i | ||||
\(647\) | 9.81050 | + | 7.12775i | 0.385691 | + | 0.280221i | 0.763687 | − | 0.645586i | \(-0.223387\pi\) |
−0.377997 | + | 0.925807i | \(0.623387\pi\) | |||||||
\(648\) | 1.10885 | − | 3.41268i | 0.0435597 | − | 0.134063i | ||||
\(649\) | −20.8359 | −0.817880 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.45572 | −0.0570542 | ||||||||
\(652\) | −10.8317 | + | 33.3366i | −0.424202 | + | 1.30556i | ||||
\(653\) | 1.39164 | + | 1.01109i | 0.0544593 | + | 0.0395670i | 0.614682 | − | 0.788775i | \(-0.289284\pi\) |
−0.560223 | + | 0.828342i | \(0.689284\pi\) | |||||||
\(654\) | −25.2989 | − | 18.3807i | −0.989264 | − | 0.718743i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.87783 | + | 1.36432i | −0.0733168 | + | 0.0532678i | ||||
\(657\) | −3.59269 | −0.140164 | ||||||||
\(658\) | 49.6110 | − | 36.0445i | 1.93404 | − | 1.40516i | ||||
\(659\) | 1.69325 | + | 5.21129i | 0.0659596 | + | 0.203003i | 0.978604 | − | 0.205751i | \(-0.0659636\pi\) |
−0.912645 | + | 0.408754i | \(0.865964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.246425 | − | 0.758418i | 0.00958482 | − | 0.0294990i | −0.946150 | − | 0.323729i | \(-0.895063\pi\) |
0.955735 | + | 0.294230i | \(0.0950633\pi\) | |||||||
\(662\) | 3.41796 | + | 10.5194i | 0.132843 | + | 0.408848i | ||||
\(663\) | 3.93322 | + | 12.1052i | 0.152754 | + | 0.470128i | ||||
\(664\) | 11.2163 | − | 34.5201i | 0.435276 | − | 1.33964i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.80628 | + | 11.7145i | 0.147490 | + | 0.453929i | ||||
\(667\) | 11.3526 | − | 8.24814i | 0.439574 | − | 0.319369i | ||||
\(668\) | 19.6691 | 0.761020 | ||||||||
\(669\) | −6.30661 | + | 4.58202i | −0.243827 | + | 0.177151i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.2644 | + | 11.0902i | 0.589275 | + | 0.428133i | ||||
\(672\) | −11.0595 | − | 8.03522i | −0.426631 | − | 0.309965i | ||||
\(673\) | −15.8612 | + | 48.8158i | −0.611405 | + | 1.88171i | −0.166777 | + | 0.985995i | \(0.553336\pi\) |
−0.444627 | + | 0.895716i | \(0.646664\pi\) | |||||||
\(674\) | −40.9156 | −1.57601 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33.4358 | −1.28599 | ||||||||
\(677\) | 4.66397 | − | 14.3542i | 0.179251 | − | 0.551678i | −0.820551 | − | 0.571573i | \(-0.806333\pi\) |
0.999802 | + | 0.0198952i | \(0.00633326\pi\) | |||||||
\(678\) | 19.0629 | + | 13.8500i | 0.732106 | + | 0.531906i | ||||
\(679\) | 29.3213 | + | 21.3032i | 1.12525 | + | 0.817540i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.3813 | + | 7.54242i | −0.397811 | + | 0.289026i | ||||
\(682\) | 2.88082 | 0.110312 | ||||||||
\(683\) | 8.78610 | − | 6.38347i | 0.336191 | − | 0.244257i | −0.406862 | − | 0.913490i | \(-0.633377\pi\) |
0.743053 | + | 0.669233i | \(0.233377\pi\) | |||||||
\(684\) | −3.21412 | − | 9.89205i | −0.122895 | − | 0.378232i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.74634 | + | 14.6077i | −0.181216 | + | 0.557726i | ||||
\(687\) | 4.48177 | + | 13.7935i | 0.170990 | + | 0.526253i | ||||
\(688\) | 4.66726 | + | 14.3644i | 0.177938 | + | 0.547636i | ||||
\(689\) | −2.15018 | + | 6.61758i | −0.0819154 | + | 0.252110i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.60981 | + | 8.03217i | 0.0992818 | + | 0.305558i | 0.988346 | − | 0.152225i | \(-0.0486438\pi\) |
−0.889064 | + | 0.457783i | \(0.848644\pi\) | |||||||
\(692\) | −47.2677 | + | 34.3420i | −1.79685 | + | 1.30549i | ||||
\(693\) | 10.2058 | 0.387686 | ||||||||
\(694\) | −26.6463 | + | 19.3597i | −1.01148 | + | 0.734883i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.41988 | + | 5.39086i | 0.281250 | + | 0.204340i | ||||
\(697\) | −9.21553 | − | 6.69548i | −0.349063 | − | 0.253609i | ||||
\(698\) | 26.1127 | − | 80.3668i | 0.988382 | − | 3.04193i | ||||
\(699\) | −11.3970 | −0.431076 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.9399 | 1.84843 | 0.924216 | − | 0.381869i | \(-0.124719\pi\) | ||||
0.924216 | + | 0.381869i | \(0.124719\pi\) | |||||||
\(702\) | 1.36263 | − | 4.19374i | 0.0514291 | − | 0.158283i | ||||
\(703\) | 12.5027 | + | 9.08373i | 0.471548 | + | 0.342599i | ||||
\(704\) | 28.4440 | + | 20.6658i | 1.07203 | + | 0.778872i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.7401 | + | 12.1624i | −0.630023 | + | 0.457739i | ||||
\(707\) | 26.6623 | 1.00274 | ||||||||
\(708\) | −20.2801 | + | 14.7343i | −0.762172 | + | 0.553750i | ||||
\(709\) | 7.65850 | + | 23.5705i | 0.287621 | + | 0.885207i | 0.985601 | + | 0.169089i | \(0.0540826\pi\) |
−0.697980 | + | 0.716118i | \(0.745917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.949501 | − | 2.92226i | 0.0356091 | − | 0.109593i | ||||
\(712\) | 0.318807 | + | 0.981187i | 0.0119478 | + | 0.0367716i | ||||
\(713\) | −0.709306 | − | 2.18302i | −0.0265637 | − | 0.0817547i | ||||
\(714\) | −17.1637 | + | 52.8244i | −0.642334 | + | 1.97690i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.84112 | − | 17.9771i | −0.218293 | − | 0.671836i | ||||
\(717\) | 5.58280 | − | 4.05614i | 0.208494 | − | 0.151479i | ||||
\(718\) | 14.1746 | 0.528992 | ||||||||
\(719\) | 14.7379 | − | 10.7077i | 0.549631 | − | 0.399331i | −0.278018 | − | 0.960576i | \(-0.589678\pi\) |
0.827650 | + | 0.561245i | \(0.189678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.41134 | + | 6.11119i | 0.313255 | + | 0.227593i | ||||
\(722\) | 19.5900 | + | 14.2330i | 0.729065 | + | 0.529697i | ||||
\(723\) | 8.79052 | − | 27.0545i | 0.326923 | − | 1.00617i | ||||
\(724\) | −1.15576 | −0.0429534 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.66224 | 0.210145 | ||||||||
\(727\) | 5.15129 | − | 15.8540i | 0.191051 | − | 0.587994i | −0.808949 | − | 0.587878i | \(-0.799963\pi\) |
1.00000 | 0.000115145i | \(-3.66518e-5\pi\) | ||||||||
\(728\) | 18.9599 | + | 13.7752i | 0.702701 | + | 0.510542i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59.9657 | + | 43.5676i | −2.21791 | + | 1.61141i | ||||
\(732\) | 22.6998 | 0.839008 | ||||||||
\(733\) | −16.2324 | + | 11.7935i | −0.599558 | + | 0.435604i | −0.845722 | − | 0.533624i | \(-0.820830\pi\) |
0.246164 | + | 0.969228i | \(0.420830\pi\) | |||||||
\(734\) | 20.8971 | + | 64.3147i | 0.771326 | + | 2.37390i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.66092 | − | 20.5002i | 0.245525 | − | 0.755648i | ||||
\(737\) | 9.09522 | + | 27.9922i | 0.335027 | + | 1.03111i | ||||
\(738\) | 1.21948 | + | 3.75317i | 0.0448896 | + | 0.138156i | ||||
\(739\) | −10.5242 | + | 32.3903i | −0.387140 | + | 1.19149i | 0.547776 | + | 0.836625i | \(0.315475\pi\) |
−0.934916 | + | 0.354870i | \(0.884525\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.70964 | − | 5.26174i | −0.0628053 | − | 0.193295i | ||||
\(742\) | −24.5647 | + | 17.8473i | −0.901800 | + | 0.655196i | ||||
\(743\) | −38.5355 | −1.41373 | −0.706865 | − | 0.707348i | \(-0.749891\pi\) | ||||
−0.706865 | + | 0.707348i | \(0.749891\pi\) | |||||||
\(744\) | 1.21370 | − | 0.881804i | 0.0444963 | − | 0.0323285i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −63.9026 | − | 46.4280i | −2.33964 | − | 1.69985i | ||||
\(747\) | −8.18340 | − | 5.94559i | −0.299415 | − | 0.217538i | ||||
\(748\) | 21.6739 | − | 66.7055i | 0.792478 | − | 2.43900i | ||||
\(749\) | −24.6244 | −0.899754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0351 | −1.31494 | −0.657470 | − | 0.753481i | \(-0.728373\pi\) | ||||
−0.657470 | + | 0.753481i | \(0.728373\pi\) | |||||||
\(752\) | −3.20107 | + | 9.85187i | −0.116731 | + | 0.359261i | ||||
\(753\) | −9.97181 | − | 7.24494i | −0.363393 | − | 0.264020i | ||||
\(754\) | 9.11807 | + | 6.62466i | 0.332060 | + | 0.241256i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.93354 | − | 7.21714i | 0.361279 | − | 0.262485i | ||||
\(757\) | 35.0131 | 1.27257 | 0.636287 | − | 0.771453i | \(-0.280470\pi\) | ||||
0.636287 | + | 0.771453i | \(0.280470\pi\) | |||||||
\(758\) | −8.81328 | + | 6.40322i | −0.320113 | + | 0.232576i | ||||
\(759\) | 4.97281 | + | 15.3047i | 0.180502 | + | 0.555527i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.69007 | − | 29.8230i | 0.351265 | − | 1.08108i | −0.606879 | − | 0.794794i | \(-0.707579\pi\) |
0.958144 | − | 0.286288i | \(-0.0924213\pi\) | |||||||
\(762\) | −7.68074 | − | 23.6389i | −0.278244 | − | 0.856347i | ||||
\(763\) | −14.3126 | − | 44.0497i | −0.518152 | − | 1.59471i | ||||
\(764\) | −3.78123 | + | 11.6374i | −0.136800 | + | 0.421027i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.37534 | − | 28.8543i | −0.338745 | − | 1.04255i | ||||
\(767\) | −10.7873 | + | 7.83742i | −0.389506 | + | 0.282993i | ||||
\(768\) | 23.8400 | 0.860253 | ||||||||
\(769\) | −1.94014 | + | 1.40959i | −0.0699633 | + | 0.0508313i | −0.622217 | − | 0.782845i | \(-0.713768\pi\) |
0.552254 | + | 0.833676i | \(0.313768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.8497 | + | 12.2421i | 0.606829 | + | 0.440887i | ||||
\(772\) | 69.3641 | + | 50.3960i | 2.49647 | + | 1.81379i | ||||
\(773\) | −3.37526 | + | 10.3880i | −0.121400 | + | 0.373630i | −0.993228 | − | 0.116182i | \(-0.962935\pi\) |
0.871828 | + | 0.489812i | \(0.162935\pi\) | |||||||
\(774\) | 25.6788 | 0.923004 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −37.3508 | −1.34082 | ||||||||
\(777\) | −5.63760 | + | 17.3507i | −0.202248 | + | 0.622454i | ||||
\(778\) | 33.3293 | + | 24.2152i | 1.19491 | + | 0.868156i | ||||
\(779\) | 4.00568 | + | 2.91030i | 0.143519 | + | 0.104272i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.72774 | + | 1.25528i | −0.0618236 | + | 0.0449174i | ||||
\(782\) | −87.5792 | −3.13183 | ||||||||
\(783\) | 2.06779 | − | 1.50234i | 0.0738970 | − | 0.0536893i | ||||
\(784\) | 2.18917 | + | 6.73757i | 0.0781846 | + | 0.240627i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.55696 | − | 20.1802i | 0.233879 | − | 0.719806i | ||||
\(787\) | 3.57607 | + | 11.0060i | 0.127473 | + | 0.392321i | 0.994344 | − | 0.106212i | \(-0.0338722\pi\) |
−0.866871 | + | 0.498533i | \(0.833872\pi\) | |||||||
\(788\) | 16.2979 | + | 50.1599i | 0.580590 | + | 1.78687i | ||||
\(789\) | −0.690704 | + | 2.12577i | −0.0245897 | + | 0.0756794i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7847 | + | 33.1918i | 0.383459 | + | 1.18017i | ||||
\(792\) | −8.50901 | + | 6.18216i | −0.302354 | + | 0.219673i | ||||
\(793\) | 12.0744 | 0.428773 | ||||||||
\(794\) | 51.3837 | − | 37.3324i | 1.82354 | − | 1.32488i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32.3096 | + | 23.4743i | 1.14518 | + | 0.832026i | ||||
\(797\) | −17.7113 | − | 12.8680i | −0.627366 | − | 0.455808i | 0.228121 | − | 0.973633i | \(-0.426742\pi\) |
−0.855487 | + | 0.517825i | \(0.826742\pi\) | |||||||
\(798\) | 7.46048 | − | 22.9610i | 0.264098 | − | 0.812810i | ||||
\(799\) | −50.8367 | −1.79847 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.287512 | 0.0101587 | ||||||||
\(802\) | −11.6081 | + | 35.7259i | −0.409895 | + | 1.26153i | ||||
\(803\) | 8.51940 | + | 6.18970i | 0.300643 | + | 0.218430i | ||||
\(804\) | 28.6476 | + | 20.8137i | 1.01032 | + | 0.734043i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.49148 | − | 1.08362i | 0.0525350 | − | 0.0381689i | ||||
\(807\) | 19.3036 | 0.679520 | ||||||||
\(808\) | −22.2295 | + | 16.1507i | −0.782033 | + | 0.568180i | ||||
\(809\) | −6.65926 | − | 20.4951i | −0.234127 | − | 0.720570i | −0.997236 | − | 0.0742994i | \(-0.976328\pi\) |
0.763109 | − | 0.646270i | \(-0.223672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5848 | + | 41.8098i | −0.477028 | + | 1.46814i | 0.366175 | + | 0.930546i | \(0.380667\pi\) |
−0.843203 | + | 0.537596i | \(0.819333\pi\) | |||||||
\(812\) | 9.69791 | + | 29.8471i | 0.340330 | + | 1.04743i | ||||
\(813\) | 3.69001 | + | 11.3567i | 0.129414 | + | 0.398297i | ||||
\(814\) | 11.1566 | − | 34.3365i | 0.391039 | − | 1.20349i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.89936 | − | 8.92331i | −0.101498 | − | 0.312378i | ||||
\(817\) | 26.0651 | − | 18.9374i | 0.911901 | − | 0.662535i | ||||
\(818\) | −72.8667 | −2.54772 | ||||||||
\(819\) | 5.28380 | − | 3.83891i | 0.184631 | − | 0.134142i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.1070 | − | 19.6944i | −0.946042 | − | 0.687340i | 0.00382568 | − | 0.999993i | \(-0.498782\pi\) |
−0.949867 | + | 0.312653i | \(0.898782\pi\) | |||||||
\(822\) | −37.3993 | − | 27.1722i | −1.30445 | − | 0.947739i | ||||
\(823\) | 17.3006 | − | 53.2458i | 0.603061 | − | 1.85603i | 0.0934576 | − | 0.995623i | \(-0.470208\pi\) |
0.509604 | − | 0.860409i | \(-0.329792\pi\) | |||||||
\(824\) | −10.7148 | −0.373266 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58.1857 | −2.02454 | ||||||||
\(827\) | −12.6110 | + | 38.8126i | −0.438527 | + | 1.34965i | 0.450901 | + | 0.892574i | \(0.351103\pi\) |
−0.889429 | + | 0.457074i | \(0.848897\pi\) | |||||||
\(828\) | 15.6631 | + | 11.3799i | 0.544329 | + | 0.395478i | ||||
\(829\) | −0.0994391 | − | 0.0722468i | −0.00345366 | − | 0.00250923i | 0.586057 | − | 0.810270i | \(-0.300679\pi\) |
−0.589511 | + | 0.807761i | \(0.700679\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1531 | − | 15.3686i | 0.733791 | − | 0.533131i | ||||
\(832\) | 22.4997 | 0.780036 | ||||||||
\(833\) | −28.1267 | + | 20.4353i | −0.974534 | + | 0.708040i | ||||
\(834\) | 8.46455 | + | 26.0512i | 0.293103 | + | 0.902080i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.42094 | + | 28.9947i | −0.325830 | + | 1.00280i | ||||
\(837\) | −0.129195 | − | 0.397622i | −0.00446564 | − | 0.0137438i | ||||
\(838\) | 18.8261 | + | 57.9408i | 0.650337 | + | 2.00153i | ||||
\(839\) | 4.57603 | − | 14.0836i | 0.157982 | − | 0.486219i | −0.840469 | − | 0.541860i | \(-0.817720\pi\) |
0.998451 | + | 0.0556411i | \(0.0177203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.94275 | − | 21.3676i | −0.239405 | − | 0.736813i | ||||
\(842\) | −7.46759 | + | 5.42552i | −0.257350 | + | 0.186976i | ||||
\(843\) | −10.1219 | −0.348616 | ||||||||
\(844\) | −21.5191 | + | 15.6345i | −0.740717 | + | 0.538162i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.2483 | + | 10.3520i | 0.489867 | + | 0.355910i | ||||
\(847\) | 6.78483 | + | 4.92947i | 0.233130 | + | 0.169379i | ||||
\(848\) | 1.58500 | − | 4.87812i | 0.0544290 | − | 0.167515i | ||||
\(849\) | 31.8638 | 1.09356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.7664 | −0.986098 | ||||||||
\(852\) | −0.793970 | + | 2.44359i | −0.0272010 | + | 0.0837160i | ||||
\(853\) | −5.87730 | − | 4.27011i | −0.201235 | − | 0.146206i | 0.482604 | − | 0.875839i | \(-0.339691\pi\) |
−0.683839 | + | 0.729633i | \(0.739691\pi\) | |||||||
\(854\) | 42.6269 | + | 30.9702i | 1.45866 | + | 1.05978i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.5304 | − | 14.9162i | 0.701715 | − | 0.509826i | ||||
\(857\) | −26.8175 | −0.916068 | −0.458034 | − | 0.888935i | \(-0.651446\pi\) | ||||
−0.458034 | + | 0.888935i | \(0.651446\pi\) | |||||||
\(858\) | −10.4565 | + | 7.59706i | −0.356978 | + | 0.259359i | ||||
\(859\) | −6.36691 | − | 19.5953i | −0.217236 | − | 0.668584i | −0.998987 | − | 0.0449937i | \(-0.985673\pi\) |
0.781751 | − | 0.623591i | \(-0.214327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.80621 | + | 5.55893i | −0.0615554 | + | 0.189448i | ||||
\(862\) | −25.7621 | − | 79.2876i | −0.877461 | − | 2.70055i | ||||
\(863\) | 4.24862 | + | 13.0759i | 0.144625 | + | 0.445109i | 0.996963 | − | 0.0778827i | \(-0.0248160\pi\) |
−0.852338 | + | 0.522991i | \(0.824816\pi\) | |||||||
\(864\) | 1.21324 | − | 3.73397i | 0.0412753 | − | 0.127032i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.33413 | + | 22.5721i | 0.249224 | + | 0.767033i | ||||
\(867\) | 23.4981 | − | 17.0723i | 0.798036 | − | 0.579807i | ||||
\(868\) | 5.13346 | 0.174241 | ||||||||
\(869\) | −7.28622 | + | 5.29375i | −0.247168 | + | 0.179578i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2381 | + | 11.0711i | 0.516324 | + | 0.375131i | ||||
\(872\) | 38.6162 | + | 28.0563i | 1.30771 | + | 0.950107i | ||||
\(873\) | −3.21657 | + | 9.89959i | −0.108864 | + | 0.335050i | ||||
\(874\) | 38.0678 | 1.28766 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.6693 | 0.428055 | ||||||||
\(877\) | 6.81166 | − | 20.9641i | 0.230014 | − | 0.707909i | −0.767730 | − | 0.640773i | \(-0.778614\pi\) |
0.997744 | − | 0.0671357i | \(-0.0213861\pi\) | |||||||
\(878\) | −13.5139 | − | 9.81840i | −0.456071 | − | 0.331355i | ||||
\(879\) | 13.4487 | + | 9.77103i | 0.453612 | + | 0.329569i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.31294 | − | 5.31316i | 0.246379 | − | 0.179005i | −0.457741 | − | 0.889085i | \(-0.651341\pi\) |
0.704121 | + | 0.710080i | \(0.251341\pi\) | |||||||
\(882\) | 12.0446 | 0.405561 | ||||||||
\(883\) | 1.29540 | − | 0.941165i | 0.0435937 | − | 0.0316727i | −0.565775 | − | 0.824560i | \(-0.691423\pi\) |
0.609369 | + | 0.792887i | \(0.291423\pi\) | |||||||
\(884\) | −13.8701 | − | 42.6879i | −0.466503 | − | 1.43575i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.0259 | − | 46.2450i | 0.504805 | − | 1.55363i | ||||
\(887\) | 5.38470 | + | 16.5724i | 0.180801 | + | 0.556447i | 0.999851 | − | 0.0172750i | \(-0.00549908\pi\) |
−0.819050 | + | 0.573722i | \(0.805499\pi\) | |||||||
\(888\) | −5.80991 | − | 17.8811i | −0.194968 | − | 0.600049i | ||||
\(889\) | 11.3762 | − | 35.0123i | 0.381545 | − | 1.17427i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.905762 | + | 2.78765i | 0.0303442 | + | 0.0933897i | ||||
\(892\) | 22.2396 | − | 16.1580i | 0.744638 | − | 0.541011i | ||||
\(893\) | 22.0970 | 0.739448 | ||||||||
\(894\) | −13.9410 | + | 10.1287i | −0.466257 | + | 0.338756i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 57.3129 | + | 41.6403i | 1.91469 | + | 1.39110i | ||||
\(897\) | 8.33143 | + | 6.05314i | 0.278178 | + | 0.202108i | ||||
\(898\) | 14.1614 | − | 43.5842i | 0.472571 | − | 1.45442i | ||||
\(899\) | 1.06860 | 0.0356397 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.1716 | 0.838588 | ||||||||
\(902\) | 3.57442 | − | 11.0009i | 0.119015 | − | 0.366291i | ||||
\(903\) | 30.7698 | + | 22.3556i | 1.02396 | + | 0.743947i | ||||
\(904\) | −29.0976 | − | 21.1406i | −0.967772 | − | 0.703128i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −31.8291 | + | 23.1252i | −1.05745 | + | 0.768283i | ||||
\(907\) | −20.8690 | −0.692942 | −0.346471 | − | 0.938061i | \(-0.612620\pi\) | ||||
−0.346471 | + | 0.938061i | \(0.612620\pi\) | |||||||
\(908\) | 36.6085 | − | 26.5976i | 1.21489 | − | 0.882673i | ||||
\(909\) | 2.36628 | + | 7.28266i | 0.0784845 | + | 0.241550i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.1958 | − | 46.7680i | 0.503461 | − | 1.54949i | −0.299882 | − | 0.953976i | \(-0.596947\pi\) |
0.803343 | − | 0.595517i | \(-0.203053\pi\) | |||||||
\(912\) | 1.26025 | + | 3.87866i | 0.0417312 | + | 0.128435i | ||||
\(913\) | 9.16200 | + | 28.1977i | 0.303218 | + | 0.933209i | ||||
\(914\) | −3.15418 | + | 9.70758i | −0.104331 | + | 0.321098i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.8045 | − | 48.6413i | −0.522196 | − | 1.60715i | ||||
\(917\) | 25.4256 | − | 18.4728i | 0.839627 | − | 0.610025i | ||||
\(918\) | −15.9519 | −0.526492 | ||||||||
\(919\) | 9.05765 | − | 6.58077i | 0.298784 | − | 0.217079i | −0.428285 | − | 0.903644i | \(-0.640882\pi\) |
0.727069 | + | 0.686564i | \(0.240882\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4592 | − | 8.32559i | −0.377593 | − | 0.274338i | ||||
\(922\) | −22.4224 | − | 16.2908i | −0.738443 | − | 0.536510i | ||||
\(923\) | −0.422325 | + | 1.29978i | −0.0139010 | + | 0.0427829i | ||||
\(924\) | −35.9897 | −1.18397 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.3425 | −0.701357 | ||||||||
\(927\) | −0.922731 | + | 2.83987i | −0.0303065 | + | 0.0932737i | ||||
\(928\) | 8.11842 | + | 5.89838i | 0.266500 | + | 0.193624i | ||||
\(929\) | −39.0181 | − | 28.3483i | −1.28014 | − | 0.930077i | −0.280584 | − | 0.959830i | \(-0.590528\pi\) |
−0.999557 | + | 0.0297529i | \(0.990528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.2258 | − | 8.88253i | 0.400683 | − | 0.291113i | ||||
\(932\) | 40.1906 | 1.31649 | ||||||||
\(933\) | 12.1757 | − | 8.84615i | 0.398614 | − | 0.289610i | ||||
\(934\) | −25.3662 | − | 78.0690i | −0.830006 | − | 2.55450i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.07992 | + | 6.40133i | −0.0679842 | + | 0.209234i | ||||
\(937\) | 15.6176 | + | 48.0661i | 0.510205 | + | 1.57025i | 0.791840 | + | 0.610728i | \(0.209123\pi\) |
−0.281635 | + | 0.959522i | \(0.590877\pi\) | |||||||
\(938\) | 25.3990 | + | 78.1702i | 0.829308 | + | 2.55235i | ||||
\(939\) | 1.10466 | − | 3.39980i | 0.0360493 | − | 0.110948i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7934 | − | 36.2965i | −0.384455 | − | 1.18323i | −0.936875 | − | 0.349665i | \(-0.886295\pi\) |
0.552420 | − | 0.833566i | \(-0.313705\pi\) | |||||||
\(942\) | 14.9987 | − | 10.8972i | 0.488686 | − | 0.355051i | ||||
\(943\) | −9.21634 | −0.300125 | ||||||||
\(944\) | 7.95180 | − | 5.77732i | 0.258809 | − | 0.188036i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −60.8924 | − | 44.2409i | −1.97978 | − | 1.43840i | ||||
\(947\) | −19.8363 | − | 14.4119i | −0.644592 | − | 0.468323i | 0.216833 | − | 0.976209i | \(-0.430427\pi\) |
−0.861425 | + | 0.507885i | \(0.830427\pi\) | |||||||
\(948\) | −3.34832 | + | 10.3051i | −0.108748 | + | 0.334693i | ||||
\(949\) | 6.73897 | 0.218756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.7820 | −0.414484 | ||||||||
\(952\) | 26.1986 | − | 80.6311i | 0.849103 | − | 2.61327i | ||||
\(953\) | −10.5187 | − | 7.64232i | −0.340736 | − | 0.247559i | 0.404236 | − | 0.914655i | \(-0.367537\pi\) |
−0.744972 | + | 0.667096i | \(0.767537\pi\) | |||||||
\(954\) | −7.05501 | − | 5.12576i | −0.228414 | − | 0.165953i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −19.6872 | + | 14.3036i | −0.636729 | + | 0.462611i | ||||
\(957\) | −7.49172 | −0.242173 | ||||||||
\(958\) | 16.4444 | − | 11.9476i | 0.531295 | − | 0.386008i | ||||
\(959\) | −21.1583 | − | 65.1187i | −0.683239 | − | 2.10279i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.52551 | + | 29.3165i | −0.307275 | + | 0.945694i | ||||
\(962\) | −7.13962 | − | 21.9735i | −0.230190 | − | 0.708453i | ||||
\(963\) | −2.18541 | − | 6.72600i | −0.0704238 | − | 0.216742i | ||||
\(964\) | −30.9989 | + | 95.4048i | −0.998408 | + | 3.07278i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.8869 | + | 42.7395i | 0.446804 | + | 1.37512i | ||||
\(967\) | 35.0476 | − | 25.4636i | 1.12706 | − | 0.818854i | 0.141792 | − | 0.989896i | \(-0.454714\pi\) |
0.985264 | + | 0.171043i | \(0.0547136\pi\) | |||||||
\(968\) | −8.64284 | −0.277791 | ||||||||
\(969\) | −16.1919 | + | 11.7641i | −0.520159 | + | 0.377918i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8922 | + | 17.3587i | 0.766738 | + | 0.557068i | 0.900970 | − | 0.433882i | \(-0.142857\pi\) |
−0.134231 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(972\) | 2.85292 | + | 2.07277i | 0.0915074 | + | 0.0664840i | ||||
\(973\) | −12.5371 | + | 38.5853i | −0.401921 | + | 1.23699i | ||||
\(974\) | 6.68721 | 0.214272 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.90056 | −0.284900 | ||||||||
\(977\) | −18.7312 | + | 57.6486i | −0.599263 | + | 1.84434i | −0.0670189 | + | 0.997752i | \(0.521349\pi\) |
−0.532244 | + | 0.846591i | \(0.678651\pi\) | |||||||
\(978\) | −18.9044 | − | 13.7348i | −0.604495 | − | 0.439191i | ||||
\(979\) | −0.681782 | − | 0.495343i | −0.0217898 | − | 0.0158312i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.7617 | − | 7.81882i | 0.343594 | − | 0.249636i | ||||
\(982\) | 86.5202 | 2.76097 | ||||||||
\(983\) | 32.5868 | − | 23.6757i | 1.03936 | − | 0.755138i | 0.0691986 | − | 0.997603i | \(-0.477956\pi\) |
0.970160 | + | 0.242465i | \(0.0779558\pi\) | |||||||
\(984\) | −1.86141 | − | 5.72884i | −0.0593397 | − | 0.182629i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.5993 | − | 38.7766i | 0.401243 | − | 1.23490i | ||||
\(987\) | 8.06087 | + | 24.8088i | 0.256580 | + | 0.789673i | ||||
\(988\) | 6.02888 | + | 18.5550i | 0.191804 | + | 0.590313i | ||||
\(989\) | −18.5320 | + | 57.0357i | −0.589284 | + | 1.81363i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.7889 | + | 36.2824i | 0.374485 | + | 1.15255i | 0.943825 | + | 0.330445i | \(0.107199\pi\) |
−0.569340 | + | 0.822102i | \(0.692801\pi\) | |||||||
\(992\) | 1.32796 | − | 0.964821i | 0.0421628 | − | 0.0306331i | ||||
\(993\) | −4.70504 | −0.149310 | ||||||||
\(994\) | −4.82485 | + | 3.50546i | −0.153035 | + | 0.111186i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 28.8580 | + | 20.9665i | 0.914399 | + | 0.664350i | ||||
\(997\) | −21.5018 | − | 15.6220i | −0.680969 | − | 0.494753i | 0.192710 | − | 0.981256i | \(-0.438272\pi\) |
−0.873679 | + | 0.486503i | \(0.838272\pi\) | |||||||
\(998\) | 4.25534 | − | 13.0966i | 0.134700 | − | 0.414565i | ||||
\(999\) | −5.23959 | −0.165773 |
(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 | 375.2.g.d.226.4 | 16 | ||
5.2 | odd | 4 | 375.2.i.c.274.4 | 16 | |||
5.3 | odd | 4 | 75.2.i.a.4.1 | ✓ | 16 | ||
5.4 | even | 2 | 375.2.g.e.226.1 | 16 | |||
15.8 | even | 4 | 225.2.m.b.154.4 | 16 | |||
25.6 | even | 5 | inner | 375.2.g.d.151.4 | 16 | ||
25.8 | odd | 20 | 375.2.i.c.349.4 | 16 | |||
25.9 | even | 10 | 1875.2.a.m.1.2 | 8 | |||
25.12 | odd | 20 | 1875.2.b.h.1249.15 | 16 | |||
25.13 | odd | 20 | 1875.2.b.h.1249.2 | 16 | |||
25.16 | even | 5 | 1875.2.a.p.1.7 | 8 | |||
25.17 | odd | 20 | 75.2.i.a.19.1 | yes | 16 | ||
25.19 | even | 10 | 375.2.g.e.151.1 | 16 | |||
75.17 | even | 20 | 225.2.m.b.19.4 | 16 | |||
75.41 | odd | 10 | 5625.2.a.t.1.2 | 8 | |||
75.59 | odd | 10 | 5625.2.a.bd.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.1 | ✓ | 16 | 5.3 | odd | 4 | ||
75.2.i.a.19.1 | yes | 16 | 25.17 | odd | 20 | ||
225.2.m.b.19.4 | 16 | 75.17 | even | 20 | |||
225.2.m.b.154.4 | 16 | 15.8 | even | 4 | |||
375.2.g.d.151.4 | 16 | 25.6 | even | 5 | inner | ||
375.2.g.d.226.4 | 16 | 1.1 | even | 1 | trivial | ||
375.2.g.e.151.1 | 16 | 25.19 | even | 10 | |||
375.2.g.e.226.1 | 16 | 5.4 | even | 2 | |||
375.2.i.c.274.4 | 16 | 5.2 | odd | 4 | |||
375.2.i.c.349.4 | 16 | 25.8 | odd | 20 | |||
1875.2.a.m.1.2 | 8 | 25.9 | even | 10 | |||
1875.2.a.p.1.7 | 8 | 25.16 | even | 5 | |||
1875.2.b.h.1249.2 | 16 | 25.13 | odd | 20 | |||
1875.2.b.h.1249.15 | 16 | 25.12 | odd | 20 | |||
5625.2.a.t.1.2 | 8 | 75.41 | odd | 10 | |||
5625.2.a.bd.1.7 | 8 | 75.59 | odd | 10 |