Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,2,Mod(4,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.i (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.598878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
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: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-2.35083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.19 |
Dual form | 75.2.i.a.4.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23577 | + | 0.726446i | −1.58093 | + | 0.513675i | −0.962296 | − | 0.272005i | \(-0.912313\pi\) |
−0.618634 | + | 0.785680i | \(0.712313\pi\) | |||||||
\(3\) | −0.587785 | − | 0.809017i | −0.339358 | − | 0.467086i | ||||
\(4\) | 2.85292 | − | 2.07277i | 1.42646 | − | 1.03638i | ||||
\(5\) | 0.725498 | + | 2.11510i | 0.324453 | + | 0.945902i | ||||
\(6\) | 1.90186 | + | 1.38178i | 0.776432 | + | 0.564111i | ||||
\(7\) | 3.48189i | 1.31603i | 0.753005 | + | 0.658015i | \(0.228604\pi\) | ||||
−0.753005 | + | 0.658015i | \(0.771396\pi\) | |||||||
\(8\) | −2.10915 | + | 2.90300i | −0.745698 | + | 1.02637i | ||||
\(9\) | −0.309017 | + | 0.951057i | −0.103006 | + | 0.317019i | ||||
\(10\) | −3.15856 | − | 4.20185i | −0.998823 | − | 1.32874i | ||||
\(11\) | 0.905762 | + | 2.78765i | 0.273097 | + | 0.840508i | 0.989717 | + | 0.143043i | \(0.0456887\pi\) |
−0.716619 | + | 0.697465i | \(0.754311\pi\) | |||||||
\(12\) | −3.35381 | − | 1.08972i | −0.968160 | − | 0.314574i | ||||
\(13\) | 1.78394 | + | 0.579638i | 0.494776 | + | 0.160763i | 0.545768 | − | 0.837937i | \(-0.316238\pi\) |
−0.0509914 | + | 0.998699i | \(0.516238\pi\) | |||||||
\(14\) | −2.52940 | − | 7.78470i | −0.676012 | − | 2.08055i | ||||
\(15\) | 1.28472 | − | 1.83017i | 0.331712 | − | 0.472547i | ||||
\(16\) | 0.427277 | − | 1.31502i | 0.106819 | − | 0.328756i | ||||
\(17\) | 3.98851 | − | 5.48972i | 0.967356 | − | 1.33145i | 0.0239850 | − | 0.999712i | \(-0.492365\pi\) |
0.943371 | − | 0.331739i | \(-0.107635\pi\) | |||||||
\(18\) | − | 2.35083i | − | 0.554096i | ||||||
\(19\) | −2.38620 | − | 1.73367i | −0.547431 | − | 0.397732i | 0.279406 | − | 0.960173i | \(-0.409862\pi\) |
−0.826837 | + | 0.562441i | \(0.809862\pi\) | |||||||
\(20\) | 6.45390 | + | 4.53042i | 1.44314 | + | 1.01303i | ||||
\(21\) | 2.81691 | − | 2.04660i | 0.614699 | − | 0.446605i | ||||
\(22\) | −4.05015 | − | 5.57456i | −0.863496 | − | 1.18850i | ||||
\(23\) | −5.22149 | + | 1.69656i | −1.08876 | + | 0.353758i | −0.797765 | − | 0.602968i | \(-0.793985\pi\) |
−0.290990 | + | 0.956726i | \(0.593985\pi\) | |||||||
\(24\) | 3.58831 | 0.732460 | ||||||||
\(25\) | −3.94730 | + | 3.06900i | −0.789461 | + | 0.613801i | ||||
\(26\) | −4.40956 | −0.864786 | ||||||||
\(27\) | 0.951057 | − | 0.309017i | 0.183031 | − | 0.0594703i | ||||
\(28\) | 7.21714 | + | 9.93354i | 1.36391 | + | 1.87726i | ||||
\(29\) | 2.06779 | − | 1.50234i | 0.383980 | − | 0.278978i | −0.379004 | − | 0.925395i | \(-0.623733\pi\) |
0.762984 | + | 0.646417i | \(0.223733\pi\) | |||||||
\(30\) | −1.54281 | + | 5.02511i | −0.281678 | + | 0.917455i | ||||
\(31\) | −0.338237 | − | 0.245744i | −0.0607492 | − | 0.0441369i | 0.556996 | − | 0.830515i | \(-0.311954\pi\) |
−0.617745 | + | 0.786378i | \(0.711954\pi\) | |||||||
\(32\) | − | 3.92613i | − | 0.694048i | ||||||
\(33\) | 1.72286 | − | 2.37132i | 0.299912 | − | 0.412793i | ||||
\(34\) | −4.92942 | + | 15.1712i | −0.845388 | + | 2.60184i | ||||
\(35\) | −7.36454 | + | 2.52610i | −1.24483 | + | 0.426989i | ||||
\(36\) | 1.08972 | + | 3.35381i | 0.181620 | + | 0.558968i | ||||
\(37\) | 4.98314 | + | 1.61912i | 0.819224 | + | 0.266182i | 0.688500 | − | 0.725237i | \(-0.258270\pi\) |
0.130724 | + | 0.991419i | \(0.458270\pi\) | |||||||
\(38\) | 6.59441 | + | 2.14265i | 1.06975 | + | 0.347584i | ||||
\(39\) | −0.579638 | − | 1.78394i | −0.0928163 | − | 0.285659i | ||||
\(40\) | −7.67033 | − | 2.35495i | −1.21279 | − | 0.372350i | ||||
\(41\) | 0.518744 | − | 1.59653i | 0.0810142 | − | 0.249336i | −0.902343 | − | 0.431019i | \(-0.858154\pi\) |
0.983357 | + | 0.181683i | \(0.0581543\pi\) | |||||||
\(42\) | −4.81121 | + | 6.62206i | −0.742386 | + | 1.02181i | ||||
\(43\) | − | 10.9233i | − | 1.66578i | −0.553436 | − | 0.832892i | \(-0.686684\pi\) | ||
0.553436 | − | 0.832892i | \(-0.313316\pi\) | |||||||
\(44\) | 8.36221 | + | 6.07550i | 1.26065 | + | 0.915916i | ||||
\(45\) | −2.23577 | + | 0.0363878i | −0.333289 | + | 0.00542438i | ||||
\(46\) | 10.4416 | − | 7.58626i | 1.53953 | − | 1.11853i | ||||
\(47\) | 4.40356 | + | 6.06098i | 0.642325 | + | 0.884084i | 0.998737 | − | 0.0502446i | \(-0.0160001\pi\) |
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(48\) | −1.31502 | + | 0.427277i | −0.189807 | + | 0.0616721i | ||||
\(49\) | −5.12353 | −0.731933 | ||||||||
\(50\) | 6.59580 | − | 9.72910i | 0.932788 | − | 1.37590i | ||||
\(51\) | −6.78566 | −0.950183 | ||||||||
\(52\) | 6.29089 | − | 2.04403i | 0.872390 | − | 0.283457i | ||||
\(53\) | 2.18041 | + | 3.00107i | 0.299502 | + | 0.412229i | 0.932071 | − | 0.362275i | \(-0.118000\pi\) |
−0.632570 | + | 0.774504i | \(0.718000\pi\) | |||||||
\(54\) | −1.90186 | + | 1.38178i | −0.258811 | + | 0.188037i | ||||
\(55\) | −5.23903 | + | 3.93821i | −0.706431 | + | 0.531028i | ||||
\(56\) | −10.1079 | − | 7.34383i | −1.35073 | − | 0.981361i | ||||
\(57\) | 2.94950i | 0.390671i | ||||||||
\(58\) | −3.53175 | + | 4.86103i | −0.463741 | + | 0.638285i | ||||
\(59\) | 2.19666 | − | 6.76062i | 0.285981 | − | 0.880158i | −0.700122 | − | 0.714023i | \(-0.746871\pi\) |
0.986103 | − | 0.166135i | \(-0.0531288\pi\) | |||||||
\(60\) | −0.128318 | − | 7.88423i | −0.0165658 | − | 1.01785i | ||||
\(61\) | −1.98917 | − | 6.12204i | −0.254687 | − | 0.783847i | −0.993891 | − | 0.110365i | \(-0.964798\pi\) |
0.739204 | − | 0.673482i | \(-0.235202\pi\) | |||||||
\(62\) | 0.934741 | + | 0.303716i | 0.118712 | + | 0.0385719i | ||||
\(63\) | −3.31147 | − | 1.07596i | −0.417206 | − | 0.135558i | ||||
\(64\) | 3.70667 | + | 11.4080i | 0.463334 | + | 1.42600i | ||||
\(65\) | 0.0682544 | + | 4.19374i | 0.00846591 | + | 0.520170i | ||||
\(66\) | −2.12929 | + | 6.55329i | −0.262098 | + | 0.806654i | ||||
\(67\) | 5.90225 | − | 8.12376i | 0.721075 | − | 0.992475i | −0.278412 | − | 0.960462i | \(-0.589808\pi\) |
0.999487 | − | 0.0320131i | \(-0.0101918\pi\) | |||||||
\(68\) | − | 23.9290i | − | 2.90181i | ||||||
\(69\) | 4.44166 | + | 3.22706i | 0.534713 | + | 0.388492i | ||||
\(70\) | 14.6304 | − | 10.9977i | 1.74866 | − | 1.31448i | ||||
\(71\) | −0.589451 | + | 0.428261i | −0.0699550 | + | 0.0508253i | −0.622213 | − | 0.782848i | \(-0.713766\pi\) |
0.552258 | + | 0.833673i | \(0.313766\pi\) | |||||||
\(72\) | −2.10915 | − | 2.90300i | −0.248566 | − | 0.342122i | ||||
\(73\) | −3.41685 | + | 1.11020i | −0.399912 | + | 0.129939i | −0.502066 | − | 0.864829i | \(-0.667427\pi\) |
0.102154 | + | 0.994769i | \(0.467427\pi\) | |||||||
\(74\) | −12.3174 | −1.43187 | ||||||||
\(75\) | 4.80304 | + | 1.38952i | 0.554608 | + | 0.160448i | ||||
\(76\) | −10.4011 | −1.19309 | ||||||||
\(77\) | −9.70628 | + | 3.15376i | −1.10613 | + | 0.359404i | ||||
\(78\) | 2.59188 | + | 3.56741i | 0.293472 | + | 0.403930i | ||||
\(79\) | 2.48583 | − | 1.80606i | 0.279677 | − | 0.203197i | −0.439099 | − | 0.898439i | \(-0.644702\pi\) |
0.718777 | + | 0.695241i | \(0.244702\pi\) | |||||||
\(80\) | 3.09140 | − | 0.0503134i | 0.345629 | − | 0.00562521i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 3.94632i | 0.435798i | ||||||||
\(83\) | −5.94559 | + | 8.18340i | −0.652613 | + | 0.898245i | −0.999209 | − | 0.0397694i | \(-0.987338\pi\) |
0.346595 | + | 0.938015i | \(0.387338\pi\) | |||||||
\(84\) | 3.79427 | − | 11.6776i | 0.413989 | − | 1.27413i | ||||
\(85\) | 14.5050 | + | 4.45333i | 1.57328 | + | 0.483031i | ||||
\(86\) | 7.93517 | + | 24.4219i | 0.855672 | + | 2.63349i | ||||
\(87\) | −2.43084 | − | 0.789827i | −0.260613 | − | 0.0846784i | ||||
\(88\) | −10.0029 | − | 3.25015i | −1.06632 | − | 0.346467i | ||||
\(89\) | −0.0888461 | − | 0.273440i | −0.00941767 | − | 0.0289846i | 0.946237 | − | 0.323473i | \(-0.104851\pi\) |
−0.955655 | + | 0.294489i | \(0.904851\pi\) | |||||||
\(90\) | 4.97224 | − | 1.70552i | 0.524120 | − | 0.179778i | ||||
\(91\) | −2.01823 | + | 6.21148i | −0.211568 | + | 0.651140i | ||||
\(92\) | −11.3799 | + | 15.6631i | −1.18644 | + | 1.63299i | ||||
\(93\) | 0.418084i | 0.0433533i | ||||||||
\(94\) | −14.2483 | − | 10.3520i | −1.46960 | − | 1.06773i | ||||
\(95\) | 1.93571 | − | 6.30482i | 0.198600 | − | 0.646861i | ||||
\(96\) | −3.17630 | + | 2.30772i | −0.324180 | + | 0.235531i | ||||
\(97\) | 6.11828 | + | 8.42109i | 0.621217 | + | 0.855032i | 0.997441 | − | 0.0714966i | \(-0.0227775\pi\) |
−0.376224 | + | 0.926529i | \(0.622778\pi\) | |||||||
\(98\) | 11.4551 | − | 3.72197i | 1.15714 | − | 0.375976i | ||||
\(99\) | −2.93111 | −0.294587 | ||||||||
\(100\) | −4.90001 | + | 16.9375i | −0.490001 | + | 1.69375i | ||||
\(101\) | 7.65744 | 0.761943 | 0.380972 | − | 0.924587i | \(-0.375590\pi\) | ||||
0.380972 | + | 0.924587i | \(0.375590\pi\) | |||||||
\(102\) | 15.1712 | − | 4.92942i | 1.50217 | − | 0.488085i | ||||
\(103\) | −1.75514 | − | 2.41574i | −0.172939 | − | 0.238030i | 0.713745 | − | 0.700405i | \(-0.246997\pi\) |
−0.886684 | + | 0.462375i | \(0.846997\pi\) | |||||||
\(104\) | −5.44530 | + | 3.95624i | −0.533955 | + | 0.387941i | ||||
\(105\) | 6.37243 | + | 4.47323i | 0.621885 | + | 0.436543i | ||||
\(106\) | −7.05501 | − | 5.12576i | −0.685243 | − | 0.497858i | ||||
\(107\) | − | 7.07213i | − | 0.683689i | −0.939757 | − | 0.341844i | \(-0.888948\pi\) | ||
0.939757 | − | 0.341844i | \(-0.111052\pi\) | |||||||
\(108\) | 2.07277 | − | 2.85292i | 0.199452 | − | 0.274522i | ||||
\(109\) | 4.11060 | − | 12.6511i | 0.393724 | − | 1.21176i | −0.536227 | − | 0.844074i | \(-0.680151\pi\) |
0.929951 | − | 0.367683i | \(-0.119849\pi\) | |||||||
\(110\) | 8.85237 | − | 12.6108i | 0.844041 | − | 1.20239i | ||||
\(111\) | −1.61912 | − | 4.98314i | −0.153680 | − | 0.472979i | ||||
\(112\) | 4.57876 | + | 1.48773i | 0.432653 | + | 0.140577i | ||||
\(113\) | −9.53271 | − | 3.09737i | −0.896762 | − | 0.291376i | −0.175862 | − | 0.984415i | \(-0.556271\pi\) |
−0.720900 | + | 0.693039i | \(0.756271\pi\) | |||||||
\(114\) | −2.14265 | − | 6.59441i | −0.200678 | − | 0.617623i | ||||
\(115\) | −7.37658 | − | 9.81312i | −0.687870 | − | 0.915078i | ||||
\(116\) | 2.78525 | − | 8.57211i | 0.258604 | − | 0.795900i | ||||
\(117\) | −1.10254 | + | 1.51751i | −0.101930 | + | 0.140294i | ||||
\(118\) | 16.7110i | 1.53837i | ||||||||
\(119\) | 19.1146 | + | 13.8875i | 1.75223 | + | 1.27307i | ||||
\(120\) | 2.60331 | + | 7.58963i | 0.237649 | + | 0.692835i | ||||
\(121\) | 1.94861 | − | 1.41575i | 0.177146 | − | 0.128704i | ||||
\(122\) | 8.89467 | + | 12.2425i | 0.805286 | + | 1.10838i | ||||
\(123\) | −1.59653 | + | 0.518744i | −0.143954 | + | 0.0467736i | ||||
\(124\) | −1.47433 | −0.132399 | ||||||||
\(125\) | −9.35502 | − | 6.12239i | −0.836738 | − | 0.547603i | ||||
\(126\) | 8.18532 | 0.729206 | ||||||||
\(127\) | −10.0556 | + | 3.26725i | −0.892286 | + | 0.289921i | −0.719049 | − | 0.694959i | \(-0.755423\pi\) |
−0.173237 | + | 0.984880i | \(0.555423\pi\) | |||||||
\(128\) | −11.9591 | − | 16.4603i | −1.05705 | − | 1.45490i | ||||
\(129\) | −8.83711 | + | 6.42054i | −0.778064 | + | 0.565297i | ||||
\(130\) | −3.19913 | − | 9.32667i | −0.280582 | − | 0.818003i | ||||
\(131\) | 7.30225 | + | 5.30540i | 0.638001 | + | 0.463535i | 0.859163 | − | 0.511703i | \(-0.170985\pi\) |
−0.221162 | + | 0.975237i | \(0.570985\pi\) | |||||||
\(132\) | − | 10.3363i | − | 0.899656i | ||||||
\(133\) | 6.03645 | − | 8.30847i | 0.523427 | − | 0.720435i | ||||
\(134\) | −7.29462 | + | 22.4505i | −0.630159 | + | 1.93943i | ||||
\(135\) | 1.34359 | + | 1.78739i | 0.115638 | + | 0.153834i | ||||
\(136\) | 7.52427 | + | 23.1573i | 0.645200 | + | 1.98572i | ||||
\(137\) | −18.7021 | − | 6.07669i | −1.59783 | − | 0.519167i | −0.631261 | − | 0.775571i | \(-0.717462\pi\) |
−0.966570 | + | 0.256404i | \(0.917462\pi\) | |||||||
\(138\) | −12.2748 | − | 3.98833i | −1.04490 | − | 0.339509i | ||||
\(139\) | 3.60067 | + | 11.0817i | 0.305404 | + | 0.939938i | 0.979526 | + | 0.201318i | \(0.0645224\pi\) |
−0.674122 | + | 0.738620i | \(0.735478\pi\) | |||||||
\(140\) | −15.7744 | + | 22.4717i | −1.33318 | + | 1.89921i | ||||
\(141\) | 2.31509 | − | 7.12511i | 0.194965 | − | 0.600042i | ||||
\(142\) | 1.00677 | − | 1.38570i | 0.0844862 | − | 0.116285i | ||||
\(143\) | 5.49801i | 0.459767i | ||||||||
\(144\) | 1.11863 | + | 0.812729i | 0.0932188 | + | 0.0677275i | ||||
\(145\) | 4.67778 | + | 3.28365i | 0.388469 | + | 0.272692i | ||||
\(146\) | 6.83280 | − | 4.96432i | 0.565486 | − | 0.410850i | ||||
\(147\) | 3.01154 | + | 4.14503i | 0.248387 | + | 0.341876i | ||||
\(148\) | 17.5726 | − | 5.70967i | 1.44446 | − | 0.469332i | ||||
\(149\) | 7.33020 | 0.600513 | 0.300257 | − | 0.953858i | \(-0.402928\pi\) | ||||
0.300257 | + | 0.953858i | \(0.402928\pi\) | |||||||
\(150\) | −11.7479 | + | 0.382503i | −0.959214 | + | 0.0312312i | ||||
\(151\) | −16.7358 | −1.36194 | −0.680968 | − | 0.732313i | \(-0.738441\pi\) | ||||
−0.680968 | + | 0.732313i | \(0.738441\pi\) | |||||||
\(152\) | 10.0657 | − | 3.27055i | 0.816437 | − | 0.265276i | ||||
\(153\) | 3.98851 | + | 5.48972i | 0.322452 | + | 0.443817i | ||||
\(154\) | 19.4100 | − | 14.1022i | 1.56410 | − | 1.13639i | ||||
\(155\) | 0.274382 | − | 0.893692i | 0.0220389 | − | 0.0717831i | ||||
\(156\) | −5.35135 | − | 3.88798i | −0.428451 | − | 0.311288i | ||||
\(157\) | 7.88635i | 0.629399i | 0.949191 | + | 0.314700i | \(0.101904\pi\) | ||||
−0.949191 | + | 0.314700i | \(0.898096\pi\) | |||||||
\(158\) | −4.24574 | + | 5.84375i | −0.337773 | + | 0.464904i | ||||
\(159\) | 1.14631 | − | 3.52797i | 0.0909081 | − | 0.279786i | ||||
\(160\) | 8.30415 | − | 2.84840i | 0.656501 | − | 0.225186i | ||||
\(161\) | −5.90724 | − | 18.1806i | −0.465556 | − | 1.43283i | ||||
\(162\) | 2.23577 | + | 0.726446i | 0.175659 | + | 0.0570750i | ||||
\(163\) | 9.45343 | + | 3.07160i | 0.740450 | + | 0.240587i | 0.654867 | − | 0.755744i | \(-0.272725\pi\) |
0.0855829 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(164\) | −1.82930 | − | 5.63000i | −0.142844 | − | 0.439629i | ||||
\(165\) | 6.26550 | + | 1.92364i | 0.487769 | + | 0.149755i | ||||
\(166\) | 7.34818 | − | 22.6154i | 0.570330 | − | 1.75529i | ||||
\(167\) | 3.27847 | − | 4.51243i | 0.253696 | − | 0.349182i | −0.663106 | − | 0.748526i | \(-0.730762\pi\) |
0.916801 | + | 0.399344i | \(0.130762\pi\) | |||||||
\(168\) | 12.4941i | 0.963939i | ||||||||
\(169\) | −7.67075 | − | 5.57313i | −0.590058 | − | 0.428702i | ||||
\(170\) | −35.6649 | + | 0.580456i | −2.73537 | + | 0.0445190i | ||||
\(171\) | 2.38620 | − | 1.73367i | 0.182477 | − | 0.132577i | ||||
\(172\) | −22.6414 | − | 31.1632i | −1.72639 | − | 2.37617i | ||||
\(173\) | 15.7573 | − | 5.11985i | 1.19800 | − | 0.389255i | 0.358978 | − | 0.933346i | \(-0.383125\pi\) |
0.839026 | + | 0.544091i | \(0.183125\pi\) | |||||||
\(174\) | 6.00857 | 0.455508 | ||||||||
\(175\) | −10.6859 | − | 13.7441i | −0.807780 | − | 1.03895i | ||||
\(176\) | 4.05284 | 0.305494 | ||||||||
\(177\) | −6.76062 | + | 2.19666i | −0.508160 | + | 0.165111i | ||||
\(178\) | 0.397279 | + | 0.546808i | 0.0297773 | + | 0.0409850i | ||||
\(179\) | −4.33650 | + | 3.15065i | −0.324125 | + | 0.235491i | −0.737934 | − | 0.674873i | \(-0.764198\pi\) |
0.413808 | + | 0.910364i | \(0.364198\pi\) | |||||||
\(180\) | −6.30305 | + | 4.73804i | −0.469802 | + | 0.353153i | ||||
\(181\) | 0.265151 | + | 0.192643i | 0.0197085 | + | 0.0143191i | 0.597596 | − | 0.801797i | \(-0.296123\pi\) |
−0.577887 | + | 0.816117i | \(0.696123\pi\) | |||||||
\(182\) | − | 15.3536i | − | 1.13808i | ||||||
\(183\) | −3.78363 | + | 5.20772i | −0.279694 | + | 0.384966i | ||||
\(184\) | 6.08779 | − | 18.7363i | 0.448798 | − | 1.38126i | ||||
\(185\) | 0.190657 | + | 11.7145i | 0.0140174 | + | 0.861269i | ||||
\(186\) | −0.303716 | − | 0.934741i | −0.0222695 | − | 0.0685385i | ||||
\(187\) | 18.9160 | + | 6.14619i | 1.38328 | + | 0.449454i | ||||
\(188\) | 25.1260 | + | 8.16392i | 1.83250 | + | 0.595415i | ||||
\(189\) | 1.07596 | + | 3.31147i | 0.0782647 | + | 0.240874i | ||||
\(190\) | 0.252305 | + | 15.5023i | 0.0183041 | + | 1.12466i | ||||
\(191\) | −1.07226 | + | 3.30009i | −0.0775862 | + | 0.238786i | −0.982326 | − | 0.187179i | \(-0.940065\pi\) |
0.904740 | + | 0.425965i | \(0.140065\pi\) | |||||||
\(192\) | 7.05051 | − | 9.70420i | 0.508827 | − | 0.700340i | ||||
\(193\) | 24.3134i | 1.75012i | 0.484018 | + | 0.875058i | \(0.339177\pi\) | ||||
−0.484018 | + | 0.875058i | \(0.660823\pi\) | |||||||
\(194\) | −19.7966 | − | 14.3830i | −1.42131 | − | 1.03264i | ||||
\(195\) | 3.35269 | − | 2.52024i | 0.240091 | − | 0.180478i | ||||
\(196\) | −14.6170 | + | 10.6199i | −1.04407 | + | 0.758563i | ||||
\(197\) | −8.79098 | − | 12.0997i | −0.626331 | − | 0.862071i | 0.371463 | − | 0.928448i | \(-0.378856\pi\) |
−0.997795 | + | 0.0663764i | \(0.978856\pi\) | |||||||
\(198\) | 6.55329 | − | 2.12929i | 0.465722 | − | 0.151322i | ||||
\(199\) | 11.3251 | 0.802817 | 0.401408 | − | 0.915899i | \(-0.368521\pi\) | ||||
0.401408 | + | 0.915899i | \(0.368521\pi\) | |||||||
\(200\) | −0.583853 | − | 17.9320i | −0.0412846 | − | 1.26799i | ||||
\(201\) | −10.0415 | −0.708274 | ||||||||
\(202\) | −17.1203 | + | 5.56272i | −1.20458 | + | 0.391391i | ||||
\(203\) | 5.23098 | + | 7.19983i | 0.367143 | + | 0.505329i | ||||
\(204\) | −19.3589 | + | 14.0651i | −1.35540 | + | 0.984753i | ||||
\(205\) | 3.75317 | − | 0.0610839i | 0.262133 | − | 0.00426628i | ||||
\(206\) | 5.67900 | + | 4.12603i | 0.395674 | + | 0.287474i | ||||
\(207\) | − | 5.49019i | − | 0.381595i | ||||||
\(208\) | 1.52447 | − | 2.09826i | 0.105703 | − | 0.145488i | ||||
\(209\) | 2.67155 | − | 8.22217i | 0.184795 | − | 0.568739i | ||||
\(210\) | −17.4969 | − | 5.37190i | −1.20740 | − | 0.370696i | ||||
\(211\) | 2.33086 | + | 7.17366i | 0.160463 | + | 0.493855i | 0.998673 | − | 0.0514924i | \(-0.0163978\pi\) |
−0.838210 | + | 0.545347i | \(0.816398\pi\) | |||||||
\(212\) | 12.4410 | + | 4.04234i | 0.854454 | + | 0.277629i | ||||
\(213\) | 0.692941 | + | 0.225150i | 0.0474796 | + | 0.0154270i | ||||
\(214\) | 5.13752 | + | 15.8117i | 0.351194 | + | 1.08086i | ||||
\(215\) | 23.1038 | − | 7.92482i | 1.57567 | − | 0.540468i | ||||
\(216\) | −1.10885 | + | 3.41268i | −0.0754475 | + | 0.232204i | ||||
\(217\) | 0.855651 | − | 1.17770i | 0.0580854 | − | 0.0799477i | ||||
\(218\) | 31.2711i | 2.11795i | ||||||||
\(219\) | 2.90655 | + | 2.11173i | 0.196406 | + | 0.142697i | ||||
\(220\) | −6.78353 | + | 22.0947i | −0.457345 | + | 1.48962i | ||||
\(221\) | 10.2973 | − | 7.48144i | 0.692672 | − | 0.503256i | ||||
\(222\) | 7.23997 | + | 9.96497i | 0.485915 | + | 0.668805i | ||||
\(223\) | −7.41386 | + | 2.40891i | −0.496469 | + | 0.161313i | −0.546540 | − | 0.837433i | \(-0.684055\pi\) |
0.0500709 | + | 0.998746i | \(0.484055\pi\) | |||||||
\(224\) | 13.6703 | 0.913387 | ||||||||
\(225\) | −1.69901 | − | 4.70248i | −0.113268 | − | 0.313499i | ||||
\(226\) | 23.5630 | 1.56739 | ||||||||
\(227\) | 12.2039 | − | 3.96529i | 0.810001 | − | 0.263185i | 0.125403 | − | 0.992106i | \(-0.459978\pi\) |
0.684598 | + | 0.728921i | \(0.259978\pi\) | |||||||
\(228\) | 6.11363 | + | 8.41468i | 0.404885 | + | 0.557276i | ||||
\(229\) | −11.7334 | + | 8.52483i | −0.775366 | + | 0.563337i | −0.903585 | − | 0.428409i | \(-0.859074\pi\) |
0.128218 | + | 0.991746i | \(0.459074\pi\) | |||||||
\(230\) | 23.6211 | + | 16.5812i | 1.55753 | + | 1.09333i | ||||
\(231\) | 8.25665 | + | 5.99881i | 0.543248 | + | 0.394693i | ||||
\(232\) | 9.17148i | 0.602137i | ||||||||
\(233\) | −6.69902 | + | 9.22041i | −0.438867 | + | 0.604049i | −0.969960 | − | 0.243265i | \(-0.921782\pi\) |
0.531093 | + | 0.847314i | \(0.321782\pi\) | |||||||
\(234\) | 1.36263 | − | 4.19374i | 0.0890779 | − | 0.274153i | ||||
\(235\) | −9.62480 | + | 13.7112i | −0.627853 | + | 0.894420i | ||||
\(236\) | −7.74630 | − | 23.8407i | −0.504241 | − | 1.55190i | ||||
\(237\) | −2.92226 | − | 0.949501i | −0.189821 | − | 0.0616767i | ||||
\(238\) | −52.8244 | − | 17.1637i | −3.42410 | − | 1.11256i | ||||
\(239\) | −2.13244 | − | 6.56298i | −0.137936 | − | 0.424524i | 0.858099 | − | 0.513484i | \(-0.171646\pi\) |
−0.996035 | + | 0.0889605i | \(0.971646\pi\) | |||||||
\(240\) | −1.85778 | − | 2.47142i | −0.119919 | − | 0.159529i | ||||
\(241\) | −8.79052 | + | 27.0545i | −0.566247 | + | 1.74273i | 0.0979683 | + | 0.995190i | \(0.468766\pi\) |
−0.664216 | + | 0.747541i | \(0.731234\pi\) | |||||||
\(242\) | −3.32818 | + | 4.58085i | −0.213943 | + | 0.294468i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −18.3645 | − | 13.3426i | −1.17567 | − | 0.854172i | ||||
\(245\) | −3.71712 | − | 10.8368i | −0.237478 | − | 0.692337i | ||||
\(246\) | 3.19264 | − | 2.31959i | 0.203555 | − | 0.147891i | ||||
\(247\) | −3.25193 | − | 4.47590i | −0.206915 | − | 0.284795i | ||||
\(248\) | 1.42679 | − | 0.463592i | 0.0906011 | − | 0.0294381i | ||||
\(249\) | 10.1152 | 0.641028 | ||||||||
\(250\) | 25.3633 | + | 6.89235i | 1.60411 | + | 0.435910i | ||||
\(251\) | −12.3258 | −0.777999 | −0.389000 | − | 0.921238i | \(-0.627179\pi\) | ||||
−0.389000 | + | 0.921238i | \(0.627179\pi\) | |||||||
\(252\) | −11.6776 | + | 3.79427i | −0.735618 | + | 0.239017i | ||||
\(253\) | −9.45885 | − | 13.0190i | −0.594673 | − | 0.818496i | ||||
\(254\) | 20.1084 | − | 14.6096i | 1.26172 | − | 0.916690i | ||||
\(255\) | −4.92299 | − | 14.3524i | −0.308289 | − | 0.898780i | ||||
\(256\) | 19.2870 | + | 14.0128i | 1.20544 | + | 0.875801i | ||||
\(257\) | 20.8274i | 1.29918i | 0.760285 | + | 0.649590i | \(0.225059\pi\) | ||||
−0.760285 | + | 0.649590i | \(0.774941\pi\) | |||||||
\(258\) | 15.0936 | − | 20.7745i | 0.939686 | − | 1.29337i | ||||
\(259\) | −5.63760 | + | 17.3507i | −0.350303 | + | 1.07812i | ||||
\(260\) | 8.88737 | + | 11.8229i | 0.551171 | + | 0.733227i | ||||
\(261\) | 0.789827 | + | 2.43084i | 0.0488891 | + | 0.150465i | ||||
\(262\) | −20.1802 | − | 6.55696i | −1.24674 | − | 0.405090i | ||||
\(263\) | −2.12577 | − | 0.690704i | −0.131080 | − | 0.0425906i | 0.242742 | − | 0.970091i | \(-0.421953\pi\) |
−0.373823 | + | 0.927500i | \(0.621953\pi\) | |||||||
\(264\) | 3.25015 | + | 10.0029i | 0.200033 | + | 0.615638i | ||||
\(265\) | −4.76569 | + | 6.78905i | −0.292754 | + | 0.417048i | ||||
\(266\) | −7.46048 | + | 22.9610i | −0.457431 | + | 1.40783i | ||||
\(267\) | −0.168995 | + | 0.232602i | −0.0103423 | + | 0.0142350i | ||||
\(268\) | − | 35.4104i | − | 2.16303i | ||||||
\(269\) | −15.6170 | − | 11.3464i | −0.952183 | − | 0.691802i | −0.000861106 | − | 1.00000i | \(-0.500274\pi\) |
−0.951322 | + | 0.308198i | \(0.900274\pi\) | |||||||
\(270\) | −4.30241 | − | 3.02015i | −0.261836 | − | 0.183800i | ||||
\(271\) | 9.66058 | − | 7.01882i | 0.586838 | − | 0.426363i | −0.254345 | − | 0.967114i | \(-0.581860\pi\) |
0.841183 | + | 0.540751i | \(0.181860\pi\) | |||||||
\(272\) | −5.51491 | − | 7.59062i | −0.334390 | − | 0.460249i | ||||
\(273\) | 6.21148 | − | 2.01823i | 0.375936 | − | 0.122149i | ||||
\(274\) | 46.2281 | 2.79274 | ||||||||
\(275\) | −12.1306 | − | 8.22391i | −0.731504 | − | 0.495920i | ||||
\(276\) | 19.3606 | 1.16537 | ||||||||
\(277\) | −24.8669 | + | 8.07975i | −1.49411 | + | 0.485465i | −0.938293 | − | 0.345841i | \(-0.887594\pi\) |
−0.555815 | + | 0.831306i | \(0.687594\pi\) | |||||||
\(278\) | −16.1005 | − | 22.1605i | −0.965646 | − | 1.32910i | ||||
\(279\) | 0.338237 | − | 0.245744i | 0.0202497 | − | 0.0147123i | ||||
\(280\) | 8.19967 | − | 26.7072i | 0.490024 | − | 1.59606i | ||||
\(281\) | −8.18876 | − | 5.94948i | −0.488500 | − | 0.354916i | 0.316107 | − | 0.948724i | \(-0.397624\pi\) |
−0.804607 | + | 0.593807i | \(0.797624\pi\) | |||||||
\(282\) | 17.6119i | 1.04877i | ||||||||
\(283\) | 18.7290 | − | 25.7783i | 1.11333 | − | 1.53236i | 0.296903 | − | 0.954907i | \(-0.404046\pi\) |
0.816423 | − | 0.577455i | \(-0.195954\pi\) | |||||||
\(284\) | −0.793970 | + | 2.44359i | −0.0471135 | + | 0.145000i | ||||
\(285\) | −6.23849 | + | 2.13986i | −0.369536 | + | 0.126754i | ||||
\(286\) | −3.99401 | − | 12.2923i | −0.236171 | − | 0.726859i | ||||
\(287\) | 5.55893 | + | 1.80621i | 0.328134 | + | 0.106617i | ||||
\(288\) | 3.73397 | + | 1.21324i | 0.220026 | + | 0.0714908i | ||||
\(289\) | −8.97546 | − | 27.6236i | −0.527968 | − | 1.62492i | ||||
\(290\) | −12.8439 | − | 3.94333i | −0.754217 | − | 0.231560i | ||||
\(291\) | 3.21657 | − | 9.89959i | 0.188559 | − | 0.580324i | ||||
\(292\) | −7.44680 | + | 10.2496i | −0.435791 | + | 0.599815i | ||||
\(293\) | − | 16.6235i | − | 0.971153i | −0.874194 | − | 0.485576i | \(-0.838610\pi\) | ||
0.874194 | − | 0.485576i | \(-0.161390\pi\) | |||||||
\(294\) | −9.74425 | − | 7.07961i | −0.568296 | − | 0.412891i | ||||
\(295\) | 15.8931 | − | 0.258664i | 0.925331 | − | 0.0150600i | ||||
\(296\) | −15.2105 | + | 11.0511i | −0.884094 | + | 0.642332i | ||||
\(297\) | 1.72286 | + | 2.37132i | 0.0999706 | + | 0.137598i | ||||
\(298\) | −16.3886 | + | 5.32499i | −0.949369 | + | 0.308469i | ||||
\(299\) | −10.2982 | −0.595561 | ||||||||
\(300\) | 16.5828 | − | 5.99140i | 0.957411 | − | 0.345914i | ||||
\(301\) | 38.0336 | 2.19222 | ||||||||
\(302\) | 37.4173 | − | 12.1576i | 2.15312 | − | 0.699593i | ||||
\(303\) | −4.50093 | − | 6.19500i | −0.258572 | − | 0.355893i | ||||
\(304\) | −3.29939 | + | 2.39715i | −0.189233 | + | 0.137486i | ||||
\(305\) | 11.5056 | − | 8.64883i | 0.658809 | − | 0.495231i | ||||
\(306\) | −12.9054 | − | 9.37631i | −0.737752 | − | 0.536008i | ||||
\(307\) | − | 14.1643i | − | 0.808402i | −0.914670 | − | 0.404201i | \(-0.867550\pi\) | ||
0.914670 | − | 0.404201i | \(-0.132450\pi\) | |||||||
\(308\) | −21.1542 | + | 29.1163i | −1.20537 | + | 1.65905i | ||||
\(309\) | −0.922731 | + | 2.83987i | −0.0524923 | + | 0.161555i | ||||
\(310\) | 0.0357636 | + | 2.19742i | 0.00203123 | + | 0.124805i | ||||
\(311\) | 4.65070 | + | 14.3134i | 0.263717 | + | 0.811637i | 0.991986 | + | 0.126346i | \(0.0403250\pi\) |
−0.728269 | + | 0.685291i | \(0.759675\pi\) | |||||||
\(312\) | 6.40133 | + | 2.07992i | 0.362404 | + | 0.117752i | ||||
\(313\) | 3.39980 | + | 1.10466i | 0.192168 | + | 0.0624392i | 0.403520 | − | 0.914971i | \(-0.367787\pi\) |
−0.211352 | + | 0.977410i | \(0.567787\pi\) | |||||||
\(314\) | −5.72901 | − | 17.6321i | −0.323307 | − | 0.995036i | ||||
\(315\) | −0.126698 | − | 7.78470i | −0.00713864 | − | 0.438618i | ||||
\(316\) | 3.34832 | − | 10.3051i | 0.188358 | − | 0.579706i | ||||
\(317\) | 7.51306 | − | 10.3408i | 0.421975 | − | 0.580799i | −0.544113 | − | 0.839012i | \(-0.683134\pi\) |
0.966088 | + | 0.258213i | \(0.0831336\pi\) | |||||||
\(318\) | 8.72047i | 0.489020i | ||||||||
\(319\) | 6.06093 | + | 4.40352i | 0.339347 | + | 0.246550i | ||||
\(320\) | −21.4398 | + | 16.1165i | −1.19852 | + | 0.900937i | ||||
\(321\) | −5.72147 | + | 4.15689i | −0.319342 | + | 0.232015i | ||||
\(322\) | 26.4145 | + | 36.3564i | 1.47202 | + | 2.02606i | ||||
\(323\) | −19.0347 | + | 6.18476i | −1.05912 | + | 0.344129i | ||||
\(324\) | −3.52640 | −0.195911 | ||||||||
\(325\) | −8.82067 | + | 3.18692i | −0.489283 | + | 0.176778i | ||||
\(326\) | −23.3671 | −1.29418 | ||||||||
\(327\) | −12.6511 | + | 4.11060i | −0.699608 | + | 0.227317i | ||||
\(328\) | 3.54062 | + | 4.87324i | 0.195498 | + | 0.269080i | ||||
\(329\) | −21.1036 | + | 15.3327i | −1.16348 | + | 0.845318i | ||||
\(330\) | −15.4057 | + | 0.250732i | −0.848054 | + | 0.0138023i | ||||
\(331\) | −3.80646 | − | 2.76555i | −0.209222 | − | 0.152009i | 0.478240 | − | 0.878229i | \(-0.341275\pi\) |
−0.687462 | + | 0.726221i | \(0.741275\pi\) | |||||||
\(332\) | 35.6704i | 1.95767i | ||||||||
\(333\) | −3.07975 | + | 4.23892i | −0.168769 | + | 0.232291i | ||||
\(334\) | −4.05187 | + | 12.4704i | −0.221709 | + | 0.682349i | ||||
\(335\) | 21.4646 | + | 6.59009i | 1.17274 | + | 0.360055i | ||||
\(336\) | −1.48773 | − | 4.57876i | −0.0811624 | − | 0.249792i | ||||
\(337\) | −16.5529 | − | 5.37837i | −0.901694 | − | 0.292978i | −0.178758 | − | 0.983893i | \(-0.557208\pi\) |
−0.722936 | + | 0.690915i | \(0.757208\pi\) | |||||||
\(338\) | 21.1986 | + | 6.88785i | 1.15305 | + | 0.374650i | ||||
\(339\) | 3.09737 | + | 9.53271i | 0.168226 | + | 0.517746i | ||||
\(340\) | 50.6122 | − | 17.3604i | 2.74483 | − | 0.941501i | ||||
\(341\) | 0.378685 | − | 1.16547i | 0.0205069 | − | 0.0631138i | ||||
\(342\) | −4.07557 | + | 5.60954i | −0.220382 | + | 0.303329i | ||||
\(343\) | 6.53364i | 0.352783i | ||||||||
\(344\) | 31.7103 | + | 23.0389i | 1.70970 | + | 1.24217i | ||||
\(345\) | −3.60313 | + | 11.7358i | −0.193986 | + | 0.631833i | ||||
\(346\) | −31.5104 | + | 22.8936i | −1.69401 | + | 1.23077i | ||||
\(347\) | −8.23525 | − | 11.3348i | −0.442091 | − | 0.608486i | 0.528584 | − | 0.848881i | \(-0.322723\pi\) |
−0.970675 | + | 0.240395i | \(0.922723\pi\) | |||||||
\(348\) | −8.57211 | + | 2.78525i | −0.459513 | + | 0.149305i | ||||
\(349\) | −35.9459 | −1.92414 | −0.962069 | − | 0.272806i | \(-0.912048\pi\) | ||||
−0.962069 | + | 0.272806i | \(0.912048\pi\) | |||||||
\(350\) | 33.8756 | + | 22.9658i | 1.81073 | + | 1.22758i | ||||
\(351\) | 1.87575 | 0.100120 | ||||||||
\(352\) | 10.9447 | − | 3.55614i | 0.583352 | − | 0.189543i | ||||
\(353\) | 5.17367 | + | 7.12095i | 0.275367 | + | 0.379010i | 0.924192 | − | 0.381927i | \(-0.124740\pi\) |
−0.648826 | + | 0.760937i | \(0.724740\pi\) | |||||||
\(354\) | 13.5195 | − | 9.82246i | 0.718551 | − | 0.522058i | ||||
\(355\) | −1.33346 | − | 0.936046i | −0.0707728 | − | 0.0496802i | ||||
\(356\) | −0.820248 | − | 0.595945i | −0.0434731 | − | 0.0315850i | ||||
\(357\) | − | 23.6269i | − | 1.25047i | ||||||
\(358\) | 7.40665 | − | 10.1944i | 0.391454 | − | 0.538790i | ||||
\(359\) | −1.86326 | + | 5.73451i | −0.0983389 | + | 0.302656i | −0.988109 | − | 0.153752i | \(-0.950864\pi\) |
0.889771 | + | 0.456408i | \(0.150864\pi\) | |||||||
\(360\) | 4.60995 | − | 6.56720i | 0.242966 | − | 0.346122i | ||||
\(361\) | −3.18301 | − | 9.79630i | −0.167527 | − | 0.515595i | ||||
\(362\) | −0.732762 | − | 0.238089i | −0.0385131 | − | 0.0125137i | ||||
\(363\) | −2.29073 | − | 0.744302i | −0.120232 | − | 0.0390657i | ||||
\(364\) | 7.11710 | + | 21.9042i | 0.373037 | + | 1.14809i | ||||
\(365\) | −4.82711 | − | 6.42153i | −0.252662 | − | 0.336118i | ||||
\(366\) | 4.67621 | − | 14.3919i | 0.244429 | − | 0.752276i | ||||
\(367\) | 16.9084 | − | 23.2724i | 0.882609 | − | 1.21481i | −0.0930825 | − | 0.995658i | \(-0.529672\pi\) |
0.975691 | − | 0.219149i | \(-0.0703280\pi\) | |||||||
\(368\) | 7.59128i | 0.395723i | ||||||||
\(369\) | 1.35809 | + | 0.986709i | 0.0706993 | + | 0.0513660i | ||||
\(370\) | −8.93624 | − | 26.0525i | −0.464573 | − | 1.35440i | ||||
\(371\) | −10.4494 | + | 7.59193i | −0.542505 | + | 0.394153i | ||||
\(372\) | 0.866590 | + | 1.19276i | 0.0449306 | + | 0.0618417i | ||||
\(373\) | 31.9555 | − | 10.3830i | 1.65459 | − | 0.537610i | 0.674866 | − | 0.737940i | \(-0.264201\pi\) |
0.979729 | + | 0.200330i | \(0.0642013\pi\) | |||||||
\(374\) | −46.7568 | −2.41774 | ||||||||
\(375\) | 0.545625 | + | 11.1670i | 0.0281759 | + | 0.576662i | ||||
\(376\) | −26.8828 | −1.38637 | ||||||||
\(377\) | 4.55964 | − | 1.48152i | 0.234833 | − | 0.0763020i | ||||
\(378\) | −4.81121 | − | 6.62206i | −0.247462 | − | 0.340602i | ||||
\(379\) | 3.74901 | − | 2.72381i | 0.192574 | − | 0.139913i | −0.487321 | − | 0.873223i | \(-0.662026\pi\) |
0.679894 | + | 0.733310i | \(0.262026\pi\) | |||||||
\(380\) | −7.54600 | − | 21.9994i | −0.387101 | − | 1.12855i | ||||
\(381\) | 8.55377 | + | 6.21467i | 0.438223 | + | 0.318387i | ||||
\(382\) | − | 8.15718i | − | 0.417358i | ||||||
\(383\) | 7.58581 | − | 10.4410i | 0.387617 | − | 0.533509i | −0.569965 | − | 0.821669i | \(-0.693043\pi\) |
0.957582 | + | 0.288160i | \(0.0930434\pi\) | |||||||
\(384\) | −6.28728 | + | 19.3503i | −0.320846 | + | 0.987464i | ||||
\(385\) | −13.7124 | − | 18.2417i | −0.698849 | − | 0.929683i | ||||
\(386\) | −17.6624 | − | 54.3592i | −0.898991 | − | 2.76681i | ||||
\(387\) | 10.3886 | + | 3.37548i | 0.528085 | + | 0.171585i | ||||
\(388\) | 34.9099 | + | 11.3429i | 1.77228 | + | 0.575849i | ||||
\(389\) | 5.41540 | + | 16.6669i | 0.274571 | + | 0.845044i | 0.989332 | + | 0.145675i | \(0.0465355\pi\) |
−0.714761 | + | 0.699369i | \(0.753465\pi\) | |||||||
\(390\) | −5.66503 | + | 8.07023i | −0.286860 | + | 0.408652i | ||||
\(391\) | −11.5123 | + | 35.4312i | −0.582202 | + | 1.79183i | ||||
\(392\) | 10.8063 | − | 14.8736i | 0.545802 | − | 0.751232i | ||||
\(393\) | − | 9.02608i | − | 0.455305i | ||||||
\(394\) | 28.4444 | + | 20.6661i | 1.43301 | + | 1.04114i | ||||
\(395\) | 5.62346 | + | 3.94748i | 0.282947 | + | 0.198619i | ||||
\(396\) | −8.36221 | + | 6.07550i | −0.420217 | + | 0.305305i | ||||
\(397\) | 15.8805 | + | 21.8577i | 0.797021 | + | 1.09701i | 0.993198 | + | 0.116437i | \(0.0371473\pi\) |
−0.196177 | + | 0.980569i | \(0.562853\pi\) | |||||||
\(398\) | −25.3204 | + | 8.22709i | −1.26920 | + | 0.412387i | ||||
\(399\) | −10.2698 | −0.514134 | ||||||||
\(400\) | 2.34922 | + | 6.50211i | 0.117461 | + | 0.325106i | ||||
\(401\) | −15.9792 | −0.797965 | −0.398983 | − | 0.916958i | \(-0.630637\pi\) | ||||
−0.398983 | + | 0.916958i | \(0.630637\pi\) | |||||||
\(402\) | 22.4505 | − | 7.29462i | 1.11973 | − | 0.363823i | ||||
\(403\) | −0.460953 | − | 0.634447i | −0.0229617 | − | 0.0316041i | ||||
\(404\) | 21.8460 | − | 15.8721i | 1.08688 | − | 0.789665i | ||||
\(405\) | 0.656285 | − | 2.13759i | 0.0326110 | − | 0.106218i | ||||
\(406\) | −16.9256 | − | 12.2971i | −0.840002 | − | 0.610297i | ||||
\(407\) | 15.3578i | 0.761258i | ||||||||
\(408\) | 14.3120 | − | 19.6988i | 0.708550 | − | 0.975235i | ||||
\(409\) | 9.57834 | − | 29.4791i | 0.473618 | − | 1.45765i | −0.374193 | − | 0.927351i | \(-0.622080\pi\) |
0.847812 | − | 0.530297i | \(-0.177920\pi\) | |||||||
\(410\) | −8.34686 | + | 2.86305i | −0.412222 | + | 0.141396i | ||||
\(411\) | 6.07669 | + | 18.7021i | 0.299741 | + | 0.922508i | ||||
\(412\) | −10.0145 | − | 3.25392i | −0.493381 | − | 0.160309i | ||||
\(413\) | 23.5397 | + | 7.64852i | 1.15831 | + | 0.376359i | ||||
\(414\) | 3.98833 | + | 12.2748i | 0.196016 | + | 0.603275i | ||||
\(415\) | −21.6222 | − | 6.63848i | −1.06139 | − | 0.325870i | ||||
\(416\) | 2.27573 | − | 7.00398i | 0.111577 | − | 0.343398i | ||||
\(417\) | 6.84887 | − | 9.42666i | 0.335391 | − | 0.461626i | ||||
\(418\) | 20.3236i | 0.994061i | ||||||||
\(419\) | 20.9660 | + | 15.2327i | 1.02425 | + | 0.744164i | 0.967151 | − | 0.254204i | \(-0.0818135\pi\) |
0.0571034 | + | 0.998368i | \(0.481814\pi\) | |||||||
\(420\) | 27.4520 | − | 0.446789i | 1.33952 | − | 0.0218011i | ||||
\(421\) | −3.17658 | + | 2.30792i | −0.154817 | + | 0.112481i | −0.662497 | − | 0.749065i | \(-0.730503\pi\) |
0.507680 | + | 0.861546i | \(0.330503\pi\) | |||||||
\(422\) | −10.4226 | − | 14.3454i | −0.507362 | − | 0.698324i | ||||
\(423\) | −7.12511 | + | 2.31509i | −0.346434 | + | 0.112563i | ||||
\(424\) | −13.3109 | −0.646436 | ||||||||
\(425\) | 1.10409 | + | 33.9103i | 0.0535564 | + | 1.64489i | ||||
\(426\) | −1.71282 | −0.0829863 | ||||||||
\(427\) | 21.3163 | − | 6.92607i | 1.03157 | − | 0.335176i | ||||
\(428\) | −14.6589 | − | 20.1762i | −0.708563 | − | 0.975254i | ||||
\(429\) | 4.44799 | − | 3.23165i | 0.214751 | − | 0.156026i | ||||
\(430\) | −45.8979 | + | 34.5018i | −2.21339 | + | 1.66382i | ||||
\(431\) | 28.6903 | + | 20.8447i | 1.38196 | + | 1.00406i | 0.996694 | + | 0.0812518i | \(0.0258918\pi\) |
0.385270 | + | 0.922804i | \(0.374108\pi\) | |||||||
\(432\) | − | 1.38270i | − | 0.0665251i | ||||||
\(433\) | −5.93423 | + | 8.16776i | −0.285181 | + | 0.392518i | −0.927441 | − | 0.373969i | \(-0.877997\pi\) |
0.642261 | + | 0.766486i | \(0.277997\pi\) | |||||||
\(434\) | −1.05750 | + | 3.25466i | −0.0507618 | + | 0.156229i | ||||
\(435\) | −0.0930049 | − | 5.71449i | −0.00445924 | − | 0.273989i | ||||
\(436\) | −14.4956 | − | 44.6129i | −0.694214 | − | 2.13657i | ||||
\(437\) | 15.4008 | + | 5.00402i | 0.736719 | + | 0.239375i | ||||
\(438\) | −8.03243 | − | 2.60990i | −0.383804 | − | 0.124706i | ||||
\(439\) | −2.19575 | − | 6.75783i | −0.104798 | − | 0.322534i | 0.884885 | − | 0.465809i | \(-0.154237\pi\) |
−0.989683 | + | 0.143275i | \(0.954237\pi\) | |||||||
\(440\) | −0.382717 | − | 23.5152i | −0.0182453 | − | 1.12104i | ||||
\(441\) | 1.58326 | − | 4.87277i | 0.0753933 | − | 0.232037i | ||||
\(442\) | −17.5876 | + | 24.2072i | −0.836556 | + | 1.15142i | ||||
\(443\) | − | 20.6841i | − | 0.982733i | −0.870953 | − | 0.491366i | \(-0.836498\pi\) | ||
0.870953 | − | 0.491366i | \(-0.163502\pi\) | |||||||
\(444\) | −14.9481 | − | 10.8604i | −0.709406 | − | 0.515414i | ||||
\(445\) | 0.513896 | − | 0.386299i | 0.0243610 | − | 0.0183123i | ||||
\(446\) | 14.8258 | − | 10.7715i | 0.702020 | − | 0.510047i | ||||
\(447\) | −4.30858 | − | 5.93025i | −0.203789 | − | 0.280491i | ||||
\(448\) | −39.7213 | + | 12.9062i | −1.87665 | + | 0.609762i | ||||
\(449\) | −19.4940 | −0.919980 | −0.459990 | − | 0.887924i | \(-0.652147\pi\) | ||||
−0.459990 | + | 0.887924i | \(0.652147\pi\) | |||||||
\(450\) | 7.21471 | + | 9.27944i | 0.340105 | + | 0.437437i | ||||
\(451\) | 4.92042 | 0.231694 | ||||||||
\(452\) | −33.6162 | + | 10.9225i | −1.58117 | + | 0.513754i | ||||
\(453\) | 9.83703 | + | 13.5395i | 0.462184 | + | 0.636142i | ||||
\(454\) | −24.4046 | + | 17.7310i | −1.14536 | + | 0.832155i | ||||
\(455\) | −14.6021 | + | 0.237654i | −0.684559 | + | 0.0111414i | ||||
\(456\) | −8.56240 | − | 6.22095i | −0.400971 | − | 0.291323i | ||||
\(457\) | − | 4.34194i | − | 0.203107i | −0.994830 | − | 0.101554i | \(-0.967619\pi\) | ||
0.994830 | − | 0.101554i | \(-0.0323813\pi\) | |||||||
\(458\) | 20.0404 | − | 27.5833i | 0.936427 | − | 1.28888i | ||||
\(459\) | 2.09688 | − | 6.45355i | 0.0978742 | − | 0.301226i | ||||
\(460\) | −41.3851 | − | 12.7061i | −1.92959 | − | 0.592424i | ||||
\(461\) | 3.64322 | + | 11.2127i | 0.169682 | + | 0.522227i | 0.999351 | − | 0.0360287i | \(-0.0114708\pi\) |
−0.829669 | + | 0.558256i | \(0.811471\pi\) | |||||||
\(462\) | −22.8178 | − | 7.41395i | −1.06158 | − | 0.344928i | ||||
\(463\) | 8.63436 | + | 2.80547i | 0.401273 | + | 0.130381i | 0.502699 | − | 0.864462i | \(-0.332341\pi\) |
−0.101426 | + | 0.994843i | \(0.532341\pi\) | |||||||
\(464\) | −1.09209 | − | 3.36112i | −0.0506991 | − | 0.156036i | ||||
\(465\) | −0.884290 | + | 0.303319i | −0.0410080 | + | 0.0140661i | ||||
\(466\) | 8.27934 | − | 25.4812i | 0.383533 | − | 1.18039i | ||||
\(467\) | −20.5244 | + | 28.2494i | −0.949755 | + | 1.30723i | 0.00188168 | + | 0.999998i | \(0.499401\pi\) |
−0.951636 | + | 0.307227i | \(0.900599\pi\) | |||||||
\(468\) | 6.61463i | 0.305762i | ||||||||
\(469\) | 28.2860 | + | 20.5510i | 1.30613 | + | 0.948956i | ||||
\(470\) | 11.5584 | − | 37.6470i | 0.533150 | − | 1.73653i | ||||
\(471\) | 6.38019 | − | 4.63548i | 0.293984 | − | 0.213592i | ||||
\(472\) | 14.9930 | + | 20.6361i | 0.690109 | + | 0.949854i | ||||
\(473\) | 30.4502 | − | 9.89388i | 1.40010 | − | 0.454921i | ||||
\(474\) | 7.22328 | 0.331776 | ||||||||
\(475\) | 14.7397 | − | 0.479913i | 0.676304 | − | 0.0220199i | ||||
\(476\) | 83.3179 | 3.81887 | ||||||||
\(477\) | −3.52797 | + | 1.14631i | −0.161535 | + | 0.0524858i | ||||
\(478\) | 9.53530 | + | 13.1242i | 0.436135 | + | 0.600288i | ||||
\(479\) | −6.99515 | + | 5.08228i | −0.319617 | + | 0.232215i | −0.736012 | − | 0.676969i | \(-0.763293\pi\) |
0.416395 | + | 0.909184i | \(0.363293\pi\) | |||||||
\(480\) | −7.18546 | − | 5.04396i | −0.327970 | − | 0.230224i | ||||
\(481\) | 7.95113 | + | 5.77684i | 0.362540 | + | 0.263401i | ||||
\(482\) | − | 66.8734i | − | 3.04600i | ||||||
\(483\) | −11.2362 | + | 15.4654i | −0.511267 | + | 0.703698i | ||||
\(484\) | 2.62471 | − | 8.07802i | 0.119305 | − | 0.367183i | ||||
\(485\) | −13.3727 | + | 19.0503i | −0.607221 | + | 0.865028i | ||||
\(486\) | −0.726446 | − | 2.23577i | −0.0329523 | − | 0.101417i | ||||
\(487\) | 2.70539 | + | 0.879035i | 0.122593 | + | 0.0398329i | 0.369671 | − | 0.929163i | \(-0.379470\pi\) |
−0.247078 | + | 0.968996i | \(0.579470\pi\) | |||||||
\(488\) | 21.9678 | + | 7.13776i | 0.994434 | + | 0.323111i | ||||
\(489\) | −3.07160 | − | 9.45343i | −0.138903 | − | 0.427499i | ||||
\(490\) | 16.1830 | + | 21.5283i | 0.731072 | + | 0.972550i | ||||
\(491\) | 11.3731 | − | 35.0028i | 0.513260 | − | 1.57965i | −0.273165 | − | 0.961967i | \(-0.588070\pi\) |
0.786425 | − | 0.617686i | \(-0.211930\pi\) | |||||||
\(492\) | −3.47953 | + | 4.78917i | −0.156869 | + | 0.215912i | ||||
\(493\) | − | 17.3437i | − | 0.781121i | ||||||
\(494\) | 10.5221 | + | 7.64474i | 0.473411 | + | 0.343953i | ||||
\(495\) | −2.12651 | − | 6.19959i | −0.0955797 | − | 0.278651i | ||||
\(496\) | −0.467680 | + | 0.339789i | −0.0209994 | + | 0.0152570i | ||||
\(497\) | −1.49116 | − | 2.05240i | −0.0668876 | − | 0.0920628i | ||||
\(498\) | −22.6154 | + | 7.34818i | −1.01342 | + | 0.329280i | ||||
\(499\) | −5.85775 | −0.262229 | −0.131114 | − | 0.991367i | \(-0.541856\pi\) | ||||
−0.131114 | + | 0.991367i | \(0.541856\pi\) | |||||||
\(500\) | −39.3794 | + | 1.92409i | −1.76110 | + | 0.0860480i | ||||
\(501\) | −5.57767 | −0.249192 | ||||||||
\(502\) | 27.5577 | − | 8.95405i | 1.22996 | − | 0.399639i | ||||
\(503\) | −17.8025 | − | 24.5030i | −0.793773 | − | 1.09253i | −0.993628 | − | 0.112709i | \(-0.964047\pi\) |
0.199855 | − | 0.979825i | \(-0.435953\pi\) | |||||||
\(504\) | 10.1079 | − | 7.34383i | 0.450243 | − | 0.327120i | ||||
\(505\) | 5.55546 | + | 16.1963i | 0.247215 | + | 0.720724i | ||||
\(506\) | 30.6054 | + | 22.2361i | 1.36058 | + | 0.988517i | ||||
\(507\) | 9.48157i | 0.421091i | ||||||||
\(508\) | −21.9154 | + | 30.1640i | −0.972340 | + | 1.33831i | ||||
\(509\) | −4.67944 | + | 14.4018i | −0.207413 | + | 0.638350i | 0.792193 | + | 0.610270i | \(0.208939\pi\) |
−0.999606 | + | 0.0280797i | \(0.991061\pi\) | |||||||
\(510\) | 21.4329 | + | 28.5123i | 0.949064 | + | 1.26255i | ||||
\(511\) | −3.86560 | − | 11.8971i | −0.171004 | − | 0.526296i | ||||
\(512\) | −14.6004 | − | 4.74395i | −0.645251 | − | 0.209655i | ||||
\(513\) | −2.80514 | − | 0.911446i | −0.123850 | − | 0.0402413i | ||||
\(514\) | −15.1300 | − | 46.5654i | −0.667356 | − | 2.05391i | ||||
\(515\) | 3.83619 | − | 5.46491i | 0.169043 | − | 0.240813i | ||||
\(516\) | −11.9033 | + | 36.6345i | −0.524013 | + | 1.61275i | ||||
\(517\) | −12.9073 | + | 17.7654i | −0.567662 | + | 0.781320i | ||||
\(518\) | − | 42.8877i | − | 1.88438i | ||||||
\(519\) | −13.4039 | − | 9.73854i | −0.588368 | − | 0.427474i | ||||
\(520\) | −12.3184 | − | 8.64710i | −0.540197 | − | 0.379201i | ||||
\(521\) | −31.6190 | + | 22.9726i | −1.38525 | + | 1.00645i | −0.388887 | + | 0.921286i | \(0.627140\pi\) |
−0.996367 | + | 0.0851601i | \(0.972860\pi\) | |||||||
\(522\) | −3.53175 | − | 4.86103i | −0.154580 | − | 0.212762i | ||||
\(523\) | −36.8987 | + | 11.9891i | −1.61347 | + | 0.524248i | −0.970388 | − | 0.241550i | \(-0.922344\pi\) |
−0.643081 | + | 0.765798i | \(0.722344\pi\) | |||||||
\(524\) | 31.8296 | 1.39048 | ||||||||
\(525\) | −4.83815 | + | 16.7237i | −0.211154 | + | 0.729880i | ||||
\(526\) | 5.25449 | 0.229107 | ||||||||
\(527\) | −2.69813 | + | 0.876674i | −0.117532 | + | 0.0381885i | ||||
\(528\) | −2.38220 | − | 3.27881i | −0.103672 | − | 0.142692i | ||||
\(529\) | 5.77819 | − | 4.19810i | 0.251226 | − | 0.182526i | ||||
\(530\) | 5.72311 | − | 18.6408i | 0.248596 | − | 0.809704i | ||||
\(531\) | 5.75093 | + | 4.17830i | 0.249569 | + | 0.181323i | ||||
\(532\) | − | 36.2155i | − | 1.57014i | ||||||
\(533\) | 1.85082 | − | 2.54743i | 0.0801678 | − | 0.110341i | ||||
\(534\) | 0.208862 | − | 0.642811i | 0.00903835 | − | 0.0278172i | ||||
\(535\) | 14.9583 | − | 5.13082i | 0.646702 | − | 0.221825i | ||||
\(536\) | 11.1345 | + | 34.2685i | 0.480938 | + | 1.48017i | ||||
\(537\) | 5.09787 | + | 1.65640i | 0.219989 | + | 0.0714788i | ||||
\(538\) | 43.1585 | + | 14.0231i | 1.86070 | + | 0.604577i | ||||
\(539\) | −4.64070 | − | 14.2826i | −0.199889 | − | 0.615196i | ||||
\(540\) | 7.53800 | + | 2.31432i | 0.324384 | + | 0.0995926i | ||||
\(541\) | 4.39669 | − | 13.5316i | 0.189029 | − | 0.581770i | −0.810966 | − | 0.585094i | \(-0.801058\pi\) |
0.999994 | + | 0.00332312i | \(0.00105778\pi\) | |||||||
\(542\) | −16.5001 | + | 22.7104i | −0.708738 | + | 0.975494i | ||||
\(543\) | − | 0.327745i | − | 0.0140649i | ||||||
\(544\) | −21.5533 | − | 15.6594i | −0.924091 | − | 0.671391i | ||||
\(545\) | 29.7406 | − | 0.484037i | 1.27395 | − | 0.0207339i | ||||
\(546\) | −12.4213 | + | 9.02462i | −0.531583 | + | 0.386218i | ||||
\(547\) | −23.1134 | − | 31.8129i | −0.988259 | − | 1.36022i | −0.932259 | − | 0.361790i | \(-0.882166\pi\) |
−0.0559991 | − | 0.998431i | \(-0.517834\pi\) | |||||||
\(548\) | −65.9512 | + | 21.4288i | −2.81730 | + | 0.915395i | ||||
\(549\) | 6.43710 | 0.274729 | ||||||||
\(550\) | 33.0955 | + | 9.57454i | 1.41120 | + | 0.408260i | ||||
\(551\) | −7.53873 | −0.321161 | ||||||||
\(552\) | −18.7363 | + | 6.08779i | −0.797470 | + | 0.259114i | ||||
\(553\) | 6.28849 | + | 8.65537i | 0.267414 | + | 0.368064i | ||||
\(554\) | 49.7272 | − | 36.1290i | 2.11271 | − | 1.53497i | ||||
\(555\) | 9.36518 | − | 7.03987i | 0.397530 | − | 0.298826i | ||||
\(556\) | 33.2422 | + | 24.1519i | 1.40978 | + | 1.02427i | ||||
\(557\) | 35.3849i | 1.49931i | 0.661830 | + | 0.749654i | \(0.269780\pi\) | ||||
−0.661830 | + | 0.749654i | \(0.730220\pi\) | |||||||
\(558\) | −0.577701 | + | 0.795138i | −0.0244561 | + | 0.0336609i | ||||
\(559\) | 6.33154 | − | 19.4865i | 0.267796 | − | 0.824190i | ||||
\(560\) | 0.175185 | + | 10.7639i | 0.00740294 | + | 0.454858i | ||||
\(561\) | −6.14619 | − | 18.9160i | −0.259492 | − | 0.798636i | ||||
\(562\) | 22.6302 | + | 7.35299i | 0.954597 | + | 0.310167i | ||||
\(563\) | −14.3025 | − | 4.64717i | −0.602780 | − | 0.195855i | −0.00830000 | − | 0.999966i | \(-0.502642\pi\) |
−0.594480 | + | 0.804111i | \(0.702642\pi\) | |||||||
\(564\) | −8.16392 | − | 25.1260i | −0.343763 | − | 1.05799i | ||||
\(565\) | −0.364726 | − | 22.4098i | −0.0153441 | − | 0.942786i | ||||
\(566\) | −23.1473 | + | 71.2401i | −0.972954 | + | 2.99444i | ||||
\(567\) | 2.04660 | − | 2.81691i | 0.0859492 | − | 0.118299i | ||||
\(568\) | − | 2.61445i | − | 0.109700i | ||||||
\(569\) | −2.20383 | − | 1.60118i | −0.0923895 | − | 0.0671249i | 0.540632 | − | 0.841260i | \(-0.318185\pi\) |
−0.633021 | + | 0.774135i | \(0.718185\pi\) | |||||||
\(570\) | 12.3934 | − | 9.31616i | 0.519100 | − | 0.390211i | ||||
\(571\) | −10.2127 | + | 7.41997i | −0.427389 | + | 0.310516i | −0.780604 | − | 0.625026i | \(-0.785088\pi\) |
0.353215 | + | 0.935542i | \(0.385088\pi\) | |||||||
\(572\) | 11.3961 | + | 15.6854i | 0.476495 | + | 0.655839i | ||||
\(573\) | 3.30009 | − | 1.07226i | 0.137863 | − | 0.0447944i | ||||
\(574\) | −13.7406 | −0.573522 | ||||||||
\(575\) | 15.4040 | − | 22.7216i | 0.642392 | − | 0.947557i | ||||
\(576\) | −11.9951 | −0.499794 | ||||||||
\(577\) | 22.4301 | − | 7.28797i | 0.933776 | − | 0.303402i | 0.197670 | − | 0.980269i | \(-0.436662\pi\) |
0.736106 | + | 0.676866i | \(0.236662\pi\) | |||||||
\(578\) | 40.1342 | + | 55.2399i | 1.66936 | + | 2.29768i | ||||
\(579\) | 19.6700 | − | 14.2911i | 0.817455 | − | 0.593916i | ||||
\(580\) | 20.1516 | − | 0.327973i | 0.836748 | − | 0.0136183i | ||||
\(581\) | −28.4937 | − | 20.7019i | −1.18212 | − | 0.858858i | ||||
\(582\) | 24.4699i | 1.01431i | ||||||||
\(583\) | −6.39100 | + | 8.79646i | −0.264688 | + | 0.364312i | ||||
\(584\) | 3.98374 | − | 12.2607i | 0.164849 | − | 0.507352i | ||||
\(585\) | −4.00958 | − | 1.23102i | −0.165776 | − | 0.0508966i | ||||
\(586\) | 12.0761 | + | 37.1663i | 0.498857 | + | 1.53532i | ||||
\(587\) | −21.5673 | − | 7.00764i | −0.890177 | − | 0.289236i | −0.172000 | − | 0.985097i | \(-0.555023\pi\) |
−0.718177 | + | 0.695861i | \(0.755023\pi\) | |||||||
\(588\) | 17.1833 | + | 5.58321i | 0.708629 | + | 0.230248i | ||||
\(589\) | 0.381061 | + | 1.17279i | 0.0157013 | + | 0.0483238i | ||||
\(590\) | −35.3454 | + | 12.1238i | −1.45515 | + | 0.499128i | ||||
\(591\) | −4.62169 | + | 14.2241i | −0.190111 | + | 0.585102i | ||||
\(592\) | 4.25837 | − | 5.86114i | 0.175018 | − | 0.240891i | ||||
\(593\) | 8.74287i | 0.359027i | 0.983756 | + | 0.179513i | \(0.0574523\pi\) | ||||
−0.983756 | + | 0.179513i | \(0.942548\pi\) | |||||||
\(594\) | −5.57456 | − | 4.05015i | −0.228727 | − | 0.166180i | ||||
\(595\) | −15.5060 | + | 50.5046i | −0.635683 | + | 2.07049i | ||||
\(596\) | 20.9124 | − | 15.1938i | 0.856607 | − | 0.622362i | ||||
\(597\) | −6.65674 | − | 9.16222i | −0.272442 | − | 0.374985i | ||||
\(598\) | 23.0245 | − | 7.48110i | 0.941540 | − | 0.305925i | ||||
\(599\) | −16.3209 | −0.666854 | −0.333427 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333427 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(600\) | −14.1641 | + | 11.0125i | −0.578249 | + | 0.449585i | ||||
\(601\) | 36.2713 | 1.47954 | 0.739768 | − | 0.672862i | \(-0.234935\pi\) | ||||
0.739768 | + | 0.672862i | \(0.234935\pi\) | |||||||
\(602\) | −85.0344 | + | 27.6294i | −3.46575 | + | 1.12609i | ||||
\(603\) | 5.90225 | + | 8.12376i | 0.240358 | + | 0.330825i | ||||
\(604\) | −47.7457 | + | 34.6893i | −1.94275 | + | 1.41149i | ||||
\(605\) | 4.40816 | + | 3.09438i | 0.179217 | + | 0.125804i | ||||
\(606\) | 14.5634 | + | 10.5809i | 0.591597 | + | 0.429820i | ||||
\(607\) | − | 16.6820i | − | 0.677102i | −0.940948 | − | 0.338551i | \(-0.890063\pi\) | ||
0.940948 | − | 0.338551i | \(-0.109937\pi\) | |||||||
\(608\) | −6.80662 | + | 9.36851i | −0.276045 | + | 0.379943i | ||||
\(609\) | 2.75009 | − | 8.46390i | 0.111439 | − | 0.342975i | ||||
\(610\) | −19.4410 | + | 27.6950i | −0.787142 | + | 1.12134i | ||||
\(611\) | 4.34252 | + | 13.3649i | 0.175679 | + | 0.540686i | ||||
\(612\) | 22.7578 | + | 7.39445i | 0.919929 | + | 0.298903i | ||||
\(613\) | −23.5831 | − | 7.66260i | −0.952511 | − | 0.309490i | −0.208776 | − | 0.977964i | \(-0.566948\pi\) |
−0.743736 | + | 0.668474i | \(0.766948\pi\) | |||||||
\(614\) | 10.2896 | + | 31.6682i | 0.415256 | + | 1.27803i | ||||
\(615\) | −2.25548 | − | 3.00047i | −0.0909495 | − | 0.120991i | ||||
\(616\) | 11.3167 | − | 34.8291i | 0.455961 | − | 1.40330i | ||||
\(617\) | 16.4386 | − | 22.6257i | 0.661791 | − | 0.910877i | −0.337748 | − | 0.941237i | \(-0.609665\pi\) |
0.999539 | + | 0.0303592i | \(0.00966511\pi\) | |||||||
\(618\) | − | 7.01963i | − | 0.282371i | ||||||
\(619\) | 22.0608 | + | 16.0281i | 0.886697 | + | 0.644223i | 0.935015 | − | 0.354609i | \(-0.115386\pi\) |
−0.0483179 | + | 0.998832i | \(0.515386\pi\) | |||||||
\(620\) | −1.06963 | − | 3.11836i | −0.0429572 | − | 0.125236i | ||||
\(621\) | −4.44166 | + | 3.22706i | −0.178238 | + | 0.129497i | ||||
\(622\) | −20.7958 | − | 28.6230i | −0.833836 | − | 1.14768i | ||||
\(623\) | 0.952088 | − | 0.309352i | 0.0381446 | − | 0.0123939i | ||||
\(624\) | −2.59359 | −0.103827 | ||||||||
\(625\) | 6.16242 | − | 24.2286i | 0.246497 | − | 0.969144i | ||||
\(626\) | −8.40365 | −0.335878 | ||||||||
\(627\) | −8.22217 | + | 2.67155i | −0.328362 | + | 0.106691i | ||||
\(628\) | 16.3466 | + | 22.4991i | 0.652299 | + | 0.897812i | ||||
\(629\) | 28.7638 | − | 20.8982i | 1.14689 | − | 0.833264i | ||||
\(630\) | 5.93844 | + | 17.3128i | 0.236593 | + | 0.689758i | ||||
\(631\) | −34.1893 | − | 24.8400i | −1.36105 | − | 0.988863i | −0.998377 | − | 0.0569481i | \(-0.981863\pi\) |
−0.362676 | − | 0.931915i | \(-0.618137\pi\) | |||||||
\(632\) | 11.0256i | 0.438575i | ||||||||
\(633\) | 4.43356 | − | 6.10228i | 0.176218 | − | 0.242544i | ||||
\(634\) | −9.28542 | + | 28.5776i | −0.368771 | + | 1.13496i | ||||
\(635\) | −14.2058 | − | 18.8981i | −0.563742 | − | 0.749949i | ||||
\(636\) | −4.04234 | − | 12.4410i | −0.160289 | − | 0.493319i | ||||
\(637\) | −9.14008 | − | 2.96979i | −0.362143 | − | 0.117667i | ||||
\(638\) | −16.7498 | − | 5.44233i | −0.663130 | − | 0.215464i | ||||
\(639\) | −0.225150 | − | 0.692941i | −0.00890681 | − | 0.0274123i | ||||
\(640\) | 26.1389 | − | 37.2367i | 1.03323 | − | 1.47191i | ||||
\(641\) | 14.1671 | − | 43.6017i | 0.559565 | − | 1.72217i | −0.124006 | − | 0.992281i | \(-0.539574\pi\) |
0.683571 | − | 0.729884i | \(-0.260426\pi\) | |||||||
\(642\) | 9.77215 | − | 13.4502i | 0.385676 | − | 0.530837i | ||||
\(643\) | 46.6710i | 1.84052i | 0.391304 | + | 0.920261i | \(0.372024\pi\) | ||||
−0.391304 | + | 0.920261i | \(0.627976\pi\) | |||||||
\(644\) | −54.5370 | − | 39.6235i | −2.14906 | − | 1.56138i | ||||
\(645\) | −19.9914 | − | 14.0333i | −0.787161 | − | 0.552560i | ||||
\(646\) | 38.0644 | − | 27.6554i | 1.49763 | − | 1.08809i | ||||
\(647\) | 7.12775 | + | 9.81050i | 0.280221 | + | 0.385691i | 0.925807 | − | 0.377997i | \(-0.123387\pi\) |
−0.645586 | + | 0.763687i | \(0.723387\pi\) | |||||||
\(648\) | 3.41268 | − | 1.10885i | 0.134063 | − | 0.0435597i | ||||
\(649\) | 20.8359 | 0.817880 | ||||||||
\(650\) | 17.4059 | − | 13.5330i | 0.682715 | − | 0.530807i | ||||
\(651\) | −1.45572 | −0.0570542 | ||||||||
\(652\) | 33.3366 | − | 10.8317i | 1.30556 | − | 0.424202i | ||||
\(653\) | −1.01109 | − | 1.39164i | −0.0395670 | − | 0.0544593i | 0.788775 | − | 0.614682i | \(-0.210716\pi\) |
−0.828342 | + | 0.560223i | \(0.810716\pi\) | |||||||
\(654\) | 25.2989 | − | 18.3807i | 0.989264 | − | 0.718743i | ||||
\(655\) | −5.92368 | + | 19.2941i | −0.231457 | + | 0.753881i | ||||
\(656\) | −1.87783 | − | 1.36432i | −0.0733168 | − | 0.0532678i | ||||
\(657\) | − | 3.59269i | − | 0.140164i | ||||||
\(658\) | 36.0445 | − | 49.6110i | 1.40516 | − | 1.93404i | ||||
\(659\) | −1.69325 | + | 5.21129i | −0.0659596 | + | 0.203003i | −0.978604 | − | 0.205751i | \(-0.934036\pi\) |
0.912645 | + | 0.408754i | \(0.134036\pi\) | |||||||
\(660\) | 21.8622 | − | 7.49894i | 0.850986 | − | 0.291896i | ||||
\(661\) | 0.246425 | + | 0.758418i | 0.00958482 | + | 0.0294990i | 0.955735 | − | 0.294230i | \(-0.0950633\pi\) |
−0.946150 | + | 0.323729i | \(0.895063\pi\) | |||||||
\(662\) | 10.5194 | + | 3.41796i | 0.408848 | + | 0.132843i | ||||
\(663\) | −12.1052 | − | 3.93322i | −0.470128 | − | 0.152754i | ||||
\(664\) | −11.2163 | − | 34.5201i | −0.435276 | − | 1.33964i | ||||
\(665\) | 21.9527 | + | 6.73993i | 0.851288 | + | 0.261363i | ||||
\(666\) | 3.80628 | − | 11.7145i | 0.147490 | − | 0.453929i | ||||
\(667\) | −8.24814 | + | 11.3526i | −0.319369 | + | 0.439574i | ||||
\(668\) | − | 19.6691i | − | 0.761020i | ||||||
\(669\) | 6.30661 | + | 4.58202i | 0.243827 | + | 0.177151i | ||||
\(670\) | −52.7774 | + | 0.858967i | −2.03897 | + | 0.0331848i | ||||
\(671\) | 15.2644 | − | 11.0902i | 0.589275 | − | 0.428133i | ||||
\(672\) | −8.03522 | − | 11.0595i | −0.309965 | − | 0.426631i | ||||
\(673\) | −48.8158 | + | 15.8612i | −1.88171 | + | 0.611405i | −0.895716 | + | 0.444627i | \(0.853336\pi\) |
−0.985995 | + | 0.166777i | \(0.946664\pi\) | |||||||
\(674\) | 40.9156 | 1.57601 | ||||||||
\(675\) | −2.80573 | + | 4.13858i | −0.107993 | + | 0.159294i | ||||
\(676\) | −33.4358 | −1.28599 | ||||||||
\(677\) | −14.3542 | + | 4.66397i | −0.551678 | + | 0.179251i | −0.571573 | − | 0.820551i | \(-0.693667\pi\) |
0.0198952 | + | 0.999802i | \(0.493667\pi\) | |||||||
\(678\) | −13.8500 | − | 19.0629i | −0.531906 | − | 0.732106i | ||||
\(679\) | −29.3213 | + | 21.3032i | −1.12525 | + | 0.817540i | ||||
\(680\) | −43.5212 | + | 32.7152i | −1.66896 | + | 1.25457i | ||||
\(681\) | −10.3813 | − | 7.54242i | −0.397811 | − | 0.289026i | ||||
\(682\) | 2.88082i | 0.110312i | ||||||||
\(683\) | 6.38347 | − | 8.78610i | 0.244257 | − | 0.336191i | −0.669233 | − | 0.743053i | \(-0.733377\pi\) |
0.913490 | + | 0.406862i | \(0.133377\pi\) | |||||||
\(684\) | 3.21412 | − | 9.89205i | 0.122895 | − | 0.378232i | ||||
\(685\) | −0.715551 | − | 43.9655i | −0.0273398 | − | 1.67984i | ||||
\(686\) | −4.74634 | − | 14.6077i | −0.181216 | − | 0.557726i | ||||
\(687\) | 13.7935 | + | 4.48177i | 0.526253 | + | 0.170990i | ||||
\(688\) | −14.3644 | − | 4.66726i | −0.547636 | − | 0.177938i | ||||
\(689\) | 2.15018 | + | 6.61758i | 0.0819154 | + | 0.252110i | ||||
\(690\) | −0.469640 | − | 28.8560i | −0.0178789 | − | 1.09853i | ||||
\(691\) | 2.60981 | − | 8.03217i | 0.0992818 | − | 0.305558i | −0.889064 | − | 0.457783i | \(-0.848644\pi\) |
0.988346 | + | 0.152225i | \(0.0486438\pi\) | |||||||
\(692\) | 34.3420 | − | 47.2677i | 1.30549 | − | 1.79685i | ||||
\(693\) | − | 10.2058i | − | 0.387686i | ||||||
\(694\) | 26.6463 | + | 19.3597i | 1.01148 | + | 0.734883i | ||||
\(695\) | −20.8267 | + | 15.6555i | −0.790000 | + | 0.593848i | ||||
\(696\) | 7.41988 | − | 5.39086i | 0.281250 | − | 0.204340i | ||||
\(697\) | −6.69548 | − | 9.21553i | −0.253609 | − | 0.349063i | ||||
\(698\) | 80.3668 | − | 26.1127i | 3.04193 | − | 0.988382i | ||||
\(699\) | 11.3970 | 0.431076 | ||||||||
\(700\) | −58.9743 | − | 17.0613i | −2.22902 | − | 0.644855i | ||||
\(701\) | 48.9399 | 1.84843 | 0.924216 | − | 0.381869i | \(-0.124719\pi\) | ||||
0.924216 | + | 0.381869i | \(0.124719\pi\) | |||||||
\(702\) | −4.19374 | + | 1.36263i | −0.158283 | + | 0.0514291i | ||||
\(703\) | −9.08373 | − | 12.5027i | −0.342599 | − | 0.471548i | ||||
\(704\) | −28.4440 | + | 20.6658i | −1.07203 | + | 0.778872i | ||||
\(705\) | 16.7499 | − | 0.272610i | 0.630838 | − | 0.0102671i | ||||
\(706\) | −16.7401 | − | 12.1624i | −0.630023 | − | 0.457739i | ||||
\(707\) | 26.6623i | 1.00274i | ||||||||
\(708\) | −14.7343 | + | 20.2801i | −0.553750 | + | 0.762172i | ||||
\(709\) | −7.65850 | + | 23.5705i | −0.287621 | + | 0.885207i | 0.697980 | + | 0.716118i | \(0.254083\pi\) |
−0.985601 | + | 0.169089i | \(0.945917\pi\) | |||||||
\(710\) | 3.66130 | + | 1.12410i | 0.137406 | + | 0.0421866i | ||||
\(711\) | 0.949501 | + | 2.92226i | 0.0356091 | + | 0.109593i | ||||
\(712\) | 0.981187 | + | 0.318807i | 0.0367716 | + | 0.0119478i | ||||
\(713\) | 2.18302 | + | 0.709306i | 0.0817547 | + | 0.0265637i | ||||
\(714\) | 17.1637 | + | 52.8244i | 0.642334 | + | 1.97690i | ||||
\(715\) | −11.6289 | + | 3.98880i | −0.434895 | + | 0.149173i | ||||
\(716\) | −5.84112 | + | 17.9771i | −0.218293 | + | 0.671836i | ||||
\(717\) | −4.05614 | + | 5.58280i | −0.151479 | + | 0.208494i | ||||
\(718\) | − | 14.1746i | − | 0.528992i | ||||||
\(719\) | −14.7379 | − | 10.7077i | −0.549631 | − | 0.399331i | 0.278018 | − | 0.960576i | \(-0.410322\pi\) |
−0.827650 | + | 0.561245i | \(0.810322\pi\) | |||||||
\(720\) | −0.907443 | + | 2.95564i | −0.0338184 | + | 0.110150i | ||||
\(721\) | 8.41134 | − | 6.11119i | 0.313255 | − | 0.227593i | ||||
\(722\) | 14.2330 | + | 19.5900i | 0.529697 | + | 0.729065i | ||||
\(723\) | 27.0545 | − | 8.79052i | 1.00617 | − | 0.326923i | ||||
\(724\) | 1.15576 | 0.0429534 | ||||||||
\(725\) | −3.55152 | + | 12.2763i | −0.131900 | + | 0.455929i | ||||
\(726\) | 5.66224 | 0.210145 | ||||||||
\(727\) | −15.8540 | + | 5.15129i | −0.587994 | + | 0.191051i | −0.587878 | − | 0.808949i | \(-0.700037\pi\) |
−0.000115145 | 1.00000i | \(0.500037\pi\) | ||||||||
\(728\) | −13.7752 | − | 18.9599i | −0.510542 | − | 0.702701i | ||||
\(729\) | 0.809017 | − | 0.587785i | 0.0299636 | − | 0.0217698i | ||||
\(730\) | 15.4572 | + | 10.8504i | 0.572097 | + | 0.401593i | ||||
\(731\) | −59.9657 | − | 43.5676i | −2.21791 | − | 1.61141i | ||||
\(732\) | 22.6998i | 0.839008i | ||||||||
\(733\) | −11.7935 | + | 16.2324i | −0.435604 | + | 0.599558i | −0.969228 | − | 0.246164i | \(-0.920830\pi\) |
0.533624 | + | 0.845722i | \(0.320830\pi\) | |||||||
\(734\) | −20.8971 | + | 64.3147i | −0.771326 | + | 2.37390i | ||||
\(735\) | −6.58228 | + | 9.37692i | −0.242791 | + | 0.345873i | ||||
\(736\) | 6.66092 | + | 20.5002i | 0.245525 | + | 0.755648i | ||||
\(737\) | 27.9922 | + | 9.09522i | 1.03111 | + | 0.335027i | ||||
\(738\) | −3.75317 | − | 1.21948i | −0.138156 | − | 0.0448896i | ||||
\(739\) | 10.5242 | + | 32.3903i | 0.387140 | + | 1.19149i | 0.934916 | + | 0.354870i | \(0.115475\pi\) |
−0.547776 | + | 0.836625i | \(0.684525\pi\) | |||||||
\(740\) | 24.8254 | + | 33.0254i | 0.912600 | + | 1.21404i | ||||
\(741\) | −1.70964 | + | 5.26174i | −0.0628053 | + | 0.193295i | ||||
\(742\) | 17.8473 | − | 24.5647i | 0.655196 | − | 0.901800i | ||||
\(743\) | 38.5355i | 1.41373i | 0.707348 | + | 0.706865i | \(0.249891\pi\) | ||||
−0.707348 | + | 0.706865i | \(0.750109\pi\) | |||||||
\(744\) | −1.21370 | − | 0.881804i | −0.0444963 | − | 0.0323285i | ||||
\(745\) | 5.31805 | + | 15.5041i | 0.194838 | + | 0.568026i | ||||
\(746\) | −63.9026 | + | 46.4280i | −2.33964 | + | 1.69985i | ||||
\(747\) | −5.94559 | − | 8.18340i | −0.217538 | − | 0.299415i | ||||
\(748\) | 66.7055 | − | 21.6739i | 2.43900 | − | 0.792478i | ||||
\(749\) | 24.6244 | 0.899754 | ||||||||
\(750\) | −9.33213 | − | 24.5705i | −0.340761 | − | 0.897189i | ||||
\(751\) | −36.0351 | −1.31494 | −0.657470 | − | 0.753481i | \(-0.728373\pi\) | ||||
−0.657470 | + | 0.753481i | \(0.728373\pi\) | |||||||
\(752\) | 9.85187 | − | 3.20107i | 0.359261 | − | 0.116731i | ||||
\(753\) | 7.24494 | + | 9.97181i | 0.264020 | + | 0.363393i | ||||
\(754\) | −9.11807 | + | 6.62466i | −0.332060 | + | 0.241256i | ||||
\(755\) | −12.1418 | − | 35.3978i | −0.441884 | − | 1.28826i | ||||
\(756\) | 9.93354 | + | 7.21714i | 0.361279 | + | 0.262485i | ||||
\(757\) | 35.0131i | 1.27257i | 0.771453 | + | 0.636287i | \(0.219530\pi\) | ||||
−0.771453 | + | 0.636287i | \(0.780470\pi\) | |||||||
\(758\) | −6.40322 | + | 8.81328i | −0.232576 | + | 0.320113i | ||||
\(759\) | −4.97281 | + | 15.3047i | −0.180502 | + | 0.555527i | ||||
\(760\) | 14.2202 | + | 18.9172i | 0.515821 | + | 0.686200i | ||||
\(761\) | 9.69007 | + | 29.8230i | 0.351265 | + | 1.08108i | 0.958144 | + | 0.286288i | \(0.0924213\pi\) |
−0.606879 | + | 0.794794i | \(0.707579\pi\) | |||||||
\(762\) | −23.6389 | − | 7.68074i | −0.856347 | − | 0.278244i | ||||
\(763\) | 44.0497 | + | 14.3126i | 1.59471 | + | 0.518152i | ||||
\(764\) | 3.78123 | + | 11.6374i | 0.136800 | + | 0.421027i | ||||
\(765\) | −8.71764 | + | 12.4189i | −0.315187 | + | 0.449006i | ||||
\(766\) | −9.37534 | + | 28.8543i | −0.338745 | + | 1.04255i | ||||
\(767\) | 7.83742 | − | 10.7873i | 0.282993 | − | 0.389506i | ||||
\(768\) | − | 23.8400i | − | 0.860253i | ||||||
\(769\) | 1.94014 | + | 1.40959i | 0.0699633 | + | 0.0508313i | 0.622217 | − | 0.782845i | \(-0.286232\pi\) |
−0.552254 | + | 0.833676i | \(0.686232\pi\) | |||||||
\(770\) | 43.9094 | + | 30.8230i | 1.58239 | + | 1.11078i | ||||
\(771\) | 16.8497 | − | 12.2421i | 0.606829 | − | 0.440887i | ||||
\(772\) | 50.3960 | + | 69.3641i | 1.81379 | + | 2.49647i | ||||
\(773\) | −10.3880 | + | 3.37526i | −0.373630 | + | 0.121400i | −0.489812 | − | 0.871828i | \(-0.662935\pi\) |
0.116182 | + | 0.993228i | \(0.462935\pi\) | |||||||
\(774\) | −25.6788 | −0.923004 | ||||||||
\(775\) | 2.08931 | − | 0.0680264i | 0.0750503 | − | 0.00244358i | ||||
\(776\) | −37.3508 | −1.34082 | ||||||||
\(777\) | 17.3507 | − | 5.63760i | 0.622454 | − | 0.202248i | ||||
\(778\) | −24.2152 | − | 33.3293i | −0.868156 | − | 1.19491i | ||||
\(779\) | −4.00568 | + | 2.91030i | −0.143519 | + | 0.104272i | ||||
\(780\) | 4.34108 | − | 14.1394i | 0.155436 | − | 0.506271i | ||||
\(781\) | −1.72774 | − | 1.25528i | −0.0618236 | − | 0.0449174i | ||||
\(782\) | − | 87.5792i | − | 3.13183i | ||||||
\(783\) | 1.50234 | − | 2.06779i | 0.0536893 | − | 0.0738970i | ||||
\(784\) | −2.18917 | + | 6.73757i | −0.0781846 | + | 0.240627i | ||||
\(785\) | −16.6804 | + | 5.72154i | −0.595350 | + | 0.204210i | ||||
\(786\) | 6.55696 | + | 20.1802i | 0.233879 | + | 0.719806i | ||||
\(787\) | 11.0060 | + | 3.57607i | 0.392321 | + | 0.127473i | 0.498533 | − | 0.866871i | \(-0.333872\pi\) |
−0.106212 | + | 0.994344i | \(0.533872\pi\) | |||||||
\(788\) | −50.1599 | − | 16.2979i | −1.78687 | − | 0.580590i | ||||
\(789\) | 0.690704 | + | 2.12577i | 0.0245897 | + | 0.0756794i | ||||
\(790\) | −15.4404 | − | 4.74053i | −0.549345 | − | 0.168660i | ||||
\(791\) | 10.7847 | − | 33.1918i | 0.383459 | − | 1.18017i | ||||
\(792\) | 6.18216 | − | 8.50901i | 0.219673 | − | 0.302354i | ||||
\(793\) | − | 12.0744i | − | 0.428773i | ||||||
\(794\) | −51.3837 | − | 37.3324i | −1.82354 | − | 1.32488i | ||||
\(795\) | 8.29366 | − | 0.134982i | 0.294146 | − | 0.00478731i | ||||
\(796\) | 32.3096 | − | 23.4743i | 1.14518 | − | 0.832026i | ||||
\(797\) | −12.8680 | − | 17.7113i | −0.455808 | − | 0.627366i | 0.517825 | − | 0.855487i | \(-0.326742\pi\) |
−0.973633 | + | 0.228121i | \(0.926742\pi\) | |||||||
\(798\) | 22.9610 | − | 7.46048i | 0.812810 | − | 0.264098i | ||||
\(799\) | 50.8367 | 1.79847 | ||||||||
\(800\) | 12.0493 | + | 15.4976i | 0.426007 | + | 0.547923i | ||||
\(801\) | 0.287512 | 0.0101587 | ||||||||
\(802\) | 35.7259 | − | 11.6081i | 1.26153 | − | 0.409895i | ||||
\(803\) | −6.18970 | − | 8.51940i | −0.218430 | − | 0.300643i | ||||
\(804\) | −28.6476 | + | 20.8137i | −1.01032 | + | 0.734043i | ||||
\(805\) | 34.1682 | − | 25.6844i | 1.20427 | − | 0.905257i | ||||
\(806\) | 1.49148 | + | 1.08362i | 0.0525350 | + | 0.0381689i | ||||
\(807\) | 19.3036i | 0.679520i | ||||||||
\(808\) | −16.1507 | + | 22.2295i | −0.568180 | + | 0.782033i | ||||
\(809\) | 6.65926 | − | 20.4951i | 0.234127 | − | 0.720570i | −0.763109 | − | 0.646270i | \(-0.776328\pi\) |
0.997236 | − | 0.0742994i | \(-0.0236721\pi\) | |||||||
\(810\) | 0.0855416 | + | 5.25592i | 0.00300563 | + | 0.184674i | ||||
\(811\) | −13.5848 | − | 41.8098i | −0.477028 | − | 1.46814i | −0.843203 | − | 0.537596i | \(-0.819333\pi\) |
0.366175 | − | 0.930546i | \(-0.380667\pi\) | |||||||
\(812\) | 29.8471 | + | 9.69791i | 1.04743 | + | 0.340330i | ||||
\(813\) | −11.3567 | − | 3.69001i | −0.398297 | − | 0.129414i | ||||
\(814\) | −11.1566 | − | 34.3365i | −0.391039 | − | 1.20349i | ||||
\(815\) | 0.361692 | + | 22.2234i | 0.0126695 | + | 0.778452i | ||||
\(816\) | −2.89936 | + | 8.92331i | −0.101498 | + | 0.312378i | ||||
\(817\) | −18.9374 | + | 26.0651i | −0.662535 | + | 0.911901i | ||||
\(818\) | 72.8667i | 2.54772i | ||||||||
\(819\) | −5.28380 | − | 3.83891i | −0.184631 | − | 0.134142i | ||||
\(820\) | 10.5809 | − | 7.95371i | 0.369500 | − | 0.277756i | ||||
\(821\) | −27.1070 | + | 19.6944i | −0.946042 | + | 0.687340i | −0.949867 | − | 0.312653i | \(-0.898782\pi\) |
0.00382568 | + | 0.999993i | \(0.498782\pi\) | |||||||
\(822\) | −27.1722 | − | 37.3993i | −0.947739 | − | 1.30445i | ||||
\(823\) | 53.2458 | − | 17.3006i | 1.85603 | − | 0.603061i | 0.860409 | − | 0.509604i | \(-0.170208\pi\) |
0.995623 | − | 0.0934576i | \(-0.0297920\pi\) | |||||||
\(824\) | 10.7148 | 0.373266 | ||||||||
\(825\) | 0.476920 | + | 14.6478i | 0.0166042 | + | 0.509970i | ||||
\(826\) | −58.1857 | −2.02454 | ||||||||
\(827\) | 38.8126 | − | 12.6110i | 1.34965 | − | 0.438527i | 0.457074 | − | 0.889429i | \(-0.348897\pi\) |
0.892574 | + | 0.450901i | \(0.148897\pi\) | |||||||
\(828\) | −11.3799 | − | 15.6631i | −0.395478 | − | 0.544329i | ||||
\(829\) | 0.0994391 | − | 0.0722468i | 0.00345366 | − | 0.00250923i | −0.586057 | − | 0.810270i | \(-0.699321\pi\) |
0.589511 | + | 0.807761i | \(0.299321\pi\) | |||||||
\(830\) | 53.1649 | − | 0.865274i | 1.84538 | − | 0.0300341i | ||||
\(831\) | 21.1531 | + | 15.3686i | 0.733791 | + | 0.533131i | ||||
\(832\) | 22.4997i | 0.780036i | ||||||||
\(833\) | −20.4353 | + | 28.1267i | −0.708040 | + | 0.974534i | ||||
\(834\) | −8.46455 | + | 26.0512i | −0.293103 | + | 0.902080i | ||||
\(835\) | 11.9228 | + | 3.66054i | 0.412604 | + | 0.126678i | ||||
\(836\) | −9.42094 | − | 28.9947i | −0.325830 | − | 1.00280i | ||||
\(837\) | −0.397622 | − | 0.129195i | −0.0137438 | − | 0.00446564i | ||||
\(838\) | −57.9408 | − | 18.8261i | −2.00153 | − | 0.650337i | ||||
\(839\) | −4.57603 | − | 14.0836i | −0.157982 | − | 0.486219i | 0.840469 | − | 0.541860i | \(-0.182280\pi\) |
−0.998451 | + | 0.0556411i | \(0.982280\pi\) | |||||||
\(840\) | −26.4262 | + | 9.06443i | −0.911792 | + | 0.312753i | ||||
\(841\) | −6.94275 | + | 21.3676i | −0.239405 | + | 0.736813i | ||||
\(842\) | 5.42552 | − | 7.46759i | 0.186976 | − | 0.257350i | ||||
\(843\) | 10.1219i | 0.348616i | ||||||||
\(844\) | 21.5191 | + | 15.6345i | 0.740717 | + | 0.538162i | ||||
\(845\) | 6.22261 | − | 20.2677i | 0.214064 | − | 0.697231i | ||||
\(846\) | 14.2483 | − | 10.3520i | 0.489867 | − | 0.355910i | ||||
\(847\) | 4.92947 | + | 6.78483i | 0.169379 | + | 0.233130i | ||||
\(848\) | 4.87812 | − | 1.58500i | 0.167515 | − | 0.0544290i | ||||
\(849\) | −31.8638 | −1.09356 | ||||||||
\(850\) | −27.1025 | − | 75.0137i | −0.929609 | − | 2.57295i | ||||
\(851\) | −28.7664 | −0.986098 | ||||||||
\(852\) | 2.44359 | − | 0.793970i | 0.0837160 | − | 0.0272010i | ||||
\(853\) | 4.27011 | + | 5.87730i | 0.146206 | + | 0.201235i | 0.875839 | − | 0.482604i | \(-0.160309\pi\) |
−0.729633 | + | 0.683839i | \(0.760309\pi\) | |||||||
\(854\) | −42.6269 | + | 30.9702i | −1.45866 | + | 1.05978i | ||||
\(855\) | 5.39808 | + | 3.78927i | 0.184610 | + | 0.129590i | ||||
\(856\) | 20.5304 | + | 14.9162i | 0.701715 | + | 0.509826i | ||||
\(857\) | − | 26.8175i | − | 0.916068i | −0.888935 | − | 0.458034i | \(-0.848554\pi\) | ||
0.888935 | − | 0.458034i | \(-0.151446\pi\) | |||||||
\(858\) | −7.59706 | + | 10.4565i | −0.259359 | + | 0.356978i | ||||
\(859\) | 6.36691 | − | 19.5953i | 0.217236 | − | 0.668584i | −0.781751 | − | 0.623591i | \(-0.785673\pi\) |
0.998987 | − | 0.0449937i | \(-0.0143268\pi\) | |||||||
\(860\) | 49.4870 | − | 70.4977i | 1.68749 | − | 2.40395i | ||||
\(861\) | −1.80621 | − | 5.55893i | −0.0615554 | − | 0.189448i | ||||
\(862\) | −79.2876 | − | 25.7621i | −2.70055 | − | 0.877461i | ||||
\(863\) | −13.0759 | − | 4.24862i | −0.445109 | − | 0.144625i | 0.0778827 | − | 0.996963i | \(-0.475184\pi\) |
−0.522991 | + | 0.852338i | \(0.675184\pi\) | |||||||
\(864\) | −1.21324 | − | 3.73397i | −0.0412753 | − | 0.127032i | ||||
\(865\) | 22.2609 | + | 29.6138i | 0.756893 | + | 1.00690i | ||||
\(866\) | 7.33413 | − | 22.5721i | 0.249224 | − | 0.767033i | ||||
\(867\) | −17.0723 | + | 23.4981i | −0.579807 | + | 0.798036i | ||||
\(868\) | − | 5.13346i | − | 0.174241i | ||||||
\(869\) | 7.28622 | + | 5.29375i | 0.247168 | + | 0.179578i | ||||
\(870\) | 4.35921 | + | 12.7087i | 0.147791 | + | 0.430866i | ||||
\(871\) | 15.2381 | − | 11.0711i | 0.516324 | − | 0.375131i | ||||
\(872\) | 28.0563 | + | 38.6162i | 0.950107 | + | 1.30771i | ||||
\(873\) | −9.89959 | + | 3.21657i | −0.335050 | + | 0.108864i | ||||
\(874\) | −38.0678 | −1.28766 | ||||||||
\(875\) | 21.3175 | − | 32.5731i | 0.720662 | − | 1.10117i | ||||
\(876\) | 12.6693 | 0.428055 | ||||||||
\(877\) | −20.9641 | + | 6.81166i | −0.707909 | + | 0.230014i | −0.640773 | − | 0.767730i | \(-0.721386\pi\) |
−0.0671357 | + | 0.997744i | \(0.521386\pi\) | |||||||
\(878\) | 9.81840 | + | 13.5139i | 0.331355 | + | 0.456071i | ||||
\(879\) | −13.4487 | + | 9.77103i | −0.453612 | + | 0.329569i | ||||
\(880\) | 2.94033 | + | 8.57216i | 0.0991184 | + | 0.288967i | ||||
\(881\) | 7.31294 | + | 5.31316i | 0.246379 | + | 0.179005i | 0.704121 | − | 0.710080i | \(-0.251341\pi\) |
−0.457741 | + | 0.889085i | \(0.651341\pi\) | |||||||
\(882\) | 12.0446i | 0.405561i | ||||||||
\(883\) | 0.941165 | − | 1.29540i | 0.0316727 | − | 0.0435937i | −0.792887 | − | 0.609369i | \(-0.791423\pi\) |
0.824560 | + | 0.565775i | \(0.191423\pi\) | |||||||
\(884\) | 13.8701 | − | 42.6879i | 0.466503 | − | 1.43575i | ||||
\(885\) | −9.55098 | − | 12.7057i | −0.321053 | − | 0.427098i | ||||
\(886\) | 15.0259 | + | 46.2450i | 0.504805 | + | 1.55363i | ||||
\(887\) | 16.5724 | + | 5.38470i | 0.556447 | + | 0.180801i | 0.573722 | − | 0.819050i | \(-0.305499\pi\) |
−0.0172750 | + | 0.999851i | \(0.505499\pi\) | |||||||
\(888\) | 17.8811 | + | 5.80991i | 0.600049 | + | 0.194968i | ||||
\(889\) | −11.3762 | − | 35.0123i | −0.381545 | − | 1.17427i | ||||
\(890\) | −0.868329 | + | 1.23699i | −0.0291064 | + | 0.0414641i | ||||
\(891\) | 0.905762 | − | 2.78765i | 0.0303442 | − | 0.0933897i | ||||
\(892\) | −16.1580 | + | 22.2396i | −0.541011 | + | 0.744638i | ||||
\(893\) | − | 22.0970i | − | 0.739448i | ||||||
\(894\) | 13.9410 | + | 10.1287i | 0.466257 | + | 0.338756i | ||||
\(895\) | −9.81008 | − | 6.88635i | −0.327915 | − | 0.230185i | ||||
\(896\) | 57.3129 | − | 41.6403i | 1.91469 | − | 1.39110i | ||||
\(897\) | 6.05314 | + | 8.33143i | 0.202108 | + | 0.278178i | ||||
\(898\) | 43.5842 | − | 14.1614i | 1.45442 | − | 0.472571i | ||||
\(899\) | −1.06860 | −0.0356397 | ||||||||
\(900\) | −14.5943 | − | 9.89414i | −0.486476 | − | 0.329805i | ||||
\(901\) | 25.1716 | 0.838588 | ||||||||
\(902\) | −11.0009 | + | 3.57442i | −0.366291 | + | 0.119015i | ||||
\(903\) | −22.3556 | − | 30.7698i | −0.743947 | − | 1.02396i | ||||
\(904\) | 29.0976 | − | 21.1406i | 0.967772 | − | 0.703128i | ||||
\(905\) | −0.215094 | + | 0.700584i | −0.00714996 | + | 0.0232882i | ||||
\(906\) | −31.8291 | − | 23.1252i | −1.05745 | − | 0.768283i | ||||
\(907\) | − | 20.8690i | − | 0.692942i | −0.938061 | − | 0.346471i | \(-0.887380\pi\) | ||
0.938061 | − | 0.346471i | \(-0.112620\pi\) | |||||||
\(908\) | 26.5976 | − | 36.6085i | 0.882673 | − | 1.21489i | ||||
\(909\) | −2.36628 | + | 7.28266i | −0.0784845 | + | 0.241550i | ||||
\(910\) | 32.4744 | − | 11.1390i | 1.07652 | − | 0.369254i | ||||
\(911\) | 15.1958 | + | 46.7680i | 0.503461 | + | 1.54949i | 0.803343 | + | 0.595517i | \(0.203053\pi\) |
−0.299882 | + | 0.953976i | \(0.596947\pi\) | |||||||
\(912\) | 3.87866 | + | 1.26025i | 0.128435 | + | 0.0417312i | ||||
\(913\) | −28.1977 | − | 9.16200i | −0.933209 | − | 0.303218i | ||||
\(914\) | 3.15418 | + | 9.70758i | 0.104331 | + | 0.321098i | ||||
\(915\) | −13.7599 | − | 4.22457i | −0.454887 | − | 0.139660i | ||||
\(916\) | −15.8045 | + | 48.6413i | −0.522196 | + | 1.60715i | ||||
\(917\) | −18.4728 | + | 25.4256i | −0.610025 | + | 0.839627i | ||||
\(918\) | 15.9519i | 0.526492i | ||||||||
\(919\) | −9.05765 | − | 6.58077i | −0.298784 | − | 0.217079i | 0.428285 | − | 0.903644i | \(-0.359118\pi\) |
−0.727069 | + | 0.686564i | \(0.759118\pi\) | |||||||
\(920\) | 44.0458 | − | 0.716859i | 1.45215 | − | 0.0236341i | ||||
\(921\) | −11.4592 | + | 8.32559i | −0.377593 | + | 0.274338i | ||||
\(922\) | −16.2908 | − | 22.4224i | −0.536510 | − | 0.738443i | ||||
\(923\) | −1.29978 | + | 0.422325i | −0.0427829 | + | 0.0139010i | ||||
\(924\) | 35.9897 | 1.18397 | ||||||||
\(925\) | −24.6391 | + | 8.90213i | −0.810128 | + | 0.292700i | ||||
\(926\) | −21.3425 | −0.701357 | ||||||||
\(927\) | 2.83987 | − | 0.922731i | 0.0932737 | − | 0.0303065i | ||||
\(928\) | −5.89838 | − | 8.11842i | −0.193624 | − | 0.266500i | ||||
\(929\) | 39.0181 | − | 28.3483i | 1.28014 | − | 0.930077i | 0.280584 | − | 0.959830i | \(-0.409472\pi\) |
0.999557 | + | 0.0297529i | \(0.00947204\pi\) | |||||||
\(930\) | 1.75673 | − | 1.32054i | 0.0576053 | − | 0.0433023i | ||||
\(931\) | 12.2258 | + | 8.88253i | 0.400683 | + | 0.291113i | ||||
\(932\) | 40.1906i | 1.31649i | ||||||||
\(933\) | 8.84615 | − | 12.1757i | 0.289610 | − | 0.398614i | ||||
\(934\) | 25.3662 | − | 78.0690i | 0.830006 | − | 2.55450i | ||||
\(935\) | 0.723736 | + | 44.4684i | 0.0236687 | + | 1.45427i | ||||
\(936\) | −2.07992 | − | 6.40133i | −0.0679842 | − | 0.209234i | ||||
\(937\) | 48.0661 | + | 15.6176i | 1.57025 | + | 0.510205i | 0.959522 | − | 0.281635i | \(-0.0908768\pi\) |
0.610728 | + | 0.791840i | \(0.290877\pi\) | |||||||
\(938\) | −78.1702 | − | 25.3990i | −2.55235 | − | 0.829308i | ||||
\(939\) | −1.10466 | − | 3.39980i | −0.0360493 | − | 0.110948i | ||||
\(940\) | 0.961330 | + | 59.0669i | 0.0313551 | + | 1.92655i | ||||
\(941\) | −11.7934 | + | 36.2965i | −0.384455 | + | 1.18323i | 0.552420 | + | 0.833566i | \(0.313705\pi\) |
−0.936875 | + | 0.349665i | \(0.886295\pi\) | |||||||
\(942\) | −10.8972 | + | 14.9987i | −0.355051 | + | 0.488686i | ||||
\(943\) | 9.21634i | 0.300125i | ||||||||
\(944\) | −7.95180 | − | 5.77732i | −0.258809 | − | 0.188036i | ||||
\(945\) | −6.22349 | + | 4.67824i | −0.202450 | + | 0.152183i | ||||
\(946\) | −60.8924 | + | 44.2409i | −1.97978 | + | 1.43840i | ||||
\(947\) | −14.4119 | − | 19.8363i | −0.468323 | − | 0.644592i | 0.507885 | − | 0.861425i | \(-0.330427\pi\) |
−0.976209 | + | 0.216833i | \(0.930427\pi\) | |||||||
\(948\) | −10.3051 | + | 3.34832i | −0.334693 | + | 0.108748i | ||||
\(949\) | −6.73897 | −0.218756 | ||||||||
\(950\) | −32.6060 | + | 11.7806i | −1.05788 | + | 0.382212i | ||||
\(951\) | −12.7820 | −0.414484 | ||||||||
\(952\) | −80.6311 | + | 26.1986i | −2.61327 | + | 0.849103i | ||||
\(953\) | 7.64232 | + | 10.5187i | 0.247559 | + | 0.340736i | 0.914655 | − | 0.404236i | \(-0.132463\pi\) |
−0.667096 | + | 0.744972i | \(0.732463\pi\) | |||||||
\(954\) | 7.05501 | − | 5.12576i | 0.228414 | − | 0.165953i | ||||
\(955\) | −7.75794 | + | 0.126263i | −0.251041 | + | 0.00408577i | ||||
\(956\) | −19.6872 | − | 14.3036i | −0.636729 | − | 0.462611i | ||||
\(957\) | − | 7.49172i | − | 0.242173i | ||||||
\(958\) | 11.9476 | − | 16.4444i | 0.386008 | − | 0.531295i | ||||
\(959\) | 21.1583 | − | 65.1187i | 0.683239 | − | 2.10279i | ||||
\(960\) | 25.6405 | + | 7.87217i | 0.827544 | + | 0.254073i | ||||
\(961\) | −9.52551 | − | 29.3165i | −0.307275 | − | 0.945694i | ||||
\(962\) | −21.9735 | − | 7.13962i | −0.708453 | − | 0.230190i | ||||
\(963\) | 6.72600 | + | 2.18541i | 0.216742 | + | 0.0704238i | ||||
\(964\) | 30.9989 | + | 95.4048i | 0.998408 | + | 3.07278i | ||||
\(965\) | −51.4253 | + | 17.6393i | −1.65544 | + | 0.567830i | ||||
\(966\) | 13.8869 | − | 42.7395i | 0.446804 | − | 1.37512i | ||||
\(967\) | −25.4636 | + | 35.0476i | −0.818854 | + | 1.12706i | 0.171043 | + | 0.985264i | \(0.445286\pi\) |
−0.989896 | + | 0.141792i | \(0.954714\pi\) | |||||||
\(968\) | 8.64284i | 0.277791i | ||||||||
\(969\) | 16.1919 | + | 11.7641i | 0.520159 | + | 0.377918i | ||||
\(970\) | 16.0592 | − | 52.3066i | 0.515630 | − | 1.67946i | ||||
\(971\) | 23.8922 | − | 17.3587i | 0.766738 | − | 0.557068i | −0.134231 | − | 0.990950i | \(-0.542857\pi\) |
0.900970 | + | 0.433882i | \(0.142857\pi\) | |||||||
\(972\) | 2.07277 | + | 2.85292i | 0.0664840 | + | 0.0915074i | ||||
\(973\) | −38.5853 | + | 12.5371i | −1.23699 | + | 0.401921i | ||||
\(974\) | −6.68721 | −0.214272 | ||||||||
\(975\) | 7.76293 | + | 5.26285i | 0.248613 | + | 0.168546i | ||||
\(976\) | −8.90056 | −0.284900 | ||||||||
\(977\) | 57.6486 | − | 18.7312i | 1.84434 | − | 0.599263i | 0.846591 | − | 0.532244i | \(-0.178651\pi\) |
0.997752 | − | 0.0670189i | \(-0.0213488\pi\) | |||||||
\(978\) | 13.7348 | + | 18.9044i | 0.439191 | + | 0.604495i | ||||
\(979\) | 0.681782 | − | 0.495343i | 0.0217898 | − | 0.0158312i | ||||
\(980\) | −33.0668 | − | 23.2118i | −1.05628 | − | 0.741473i | ||||
\(981\) | 10.7617 | + | 7.81882i | 0.343594 | + | 0.249636i | ||||
\(982\) | 86.5202i | 2.76097i | ||||||||
\(983\) | 23.6757 | − | 32.5868i | 0.755138 | − | 1.03936i | −0.242465 | − | 0.970160i | \(-0.577956\pi\) |
0.997603 | − | 0.0691986i | \(-0.0220442\pi\) | |||||||
\(984\) | 1.86141 | − | 5.72884i | 0.0593397 | − | 0.182629i | ||||
\(985\) | 19.2143 | − | 27.3722i | 0.612220 | − | 0.872150i | ||||
\(986\) | 12.5993 | + | 38.7766i | 0.401243 | + | 1.23490i | ||||
\(987\) | 24.8088 | + | 8.06087i | 0.789673 | + | 0.256580i | ||||
\(988\) | −18.5550 | − | 6.02888i | −0.590313 | − | 0.191804i | ||||
\(989\) | 18.5320 | + | 57.0357i | 0.589284 | + | 1.81363i | ||||
\(990\) | 9.25807 | + | 12.3161i | 0.294241 | + | 0.391430i | ||||
\(991\) | 11.7889 | − | 36.2824i | 0.374485 | − | 1.15255i | −0.569340 | − | 0.822102i | \(-0.692801\pi\) |
0.943825 | − | 0.330445i | \(-0.107199\pi\) | |||||||
\(992\) | −0.964821 | + | 1.32796i | −0.0306331 | + | 0.0421628i | ||||
\(993\) | 4.70504i | 0.149310i | ||||||||
\(994\) | 4.82485 | + | 3.50546i | 0.153035 | + | 0.111186i | ||||
\(995\) | 8.21636 | + | 23.9538i | 0.260476 | + | 0.759386i | ||||
\(996\) | 28.8580 | − | 20.9665i | 0.914399 | − | 0.664350i | ||||
\(997\) | −15.6220 | − | 21.5018i | −0.494753 | − | 0.680969i | 0.486503 | − | 0.873679i | \(-0.338272\pi\) |
−0.981256 | + | 0.192710i | \(0.938272\pi\) | |||||||
\(998\) | 13.0966 | − | 4.25534i | 0.414565 | − | 0.134700i | ||||
\(999\) | 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 | 75.2.i.a.19.1 | yes | 16 | |
3.2 | odd | 2 | 225.2.m.b.19.4 | 16 | |||
5.2 | odd | 4 | 375.2.g.e.151.1 | 16 | |||
5.3 | odd | 4 | 375.2.g.d.151.4 | 16 | |||
5.4 | even | 2 | 375.2.i.c.349.4 | 16 | |||
25.2 | odd | 20 | 1875.2.a.m.1.2 | 8 | |||
25.3 | odd | 20 | 375.2.g.d.226.4 | 16 | |||
25.4 | even | 10 | inner | 75.2.i.a.4.1 | ✓ | 16 | |
25.11 | even | 5 | 1875.2.b.h.1249.15 | 16 | |||
25.14 | even | 10 | 1875.2.b.h.1249.2 | 16 | |||
25.21 | even | 5 | 375.2.i.c.274.4 | 16 | |||
25.22 | odd | 20 | 375.2.g.e.226.1 | 16 | |||
25.23 | odd | 20 | 1875.2.a.p.1.7 | 8 | |||
75.2 | even | 20 | 5625.2.a.bd.1.7 | 8 | |||
75.23 | even | 20 | 5625.2.a.t.1.2 | 8 | |||
75.29 | odd | 10 | 225.2.m.b.154.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.1 | ✓ | 16 | 25.4 | even | 10 | inner | |
75.2.i.a.19.1 | yes | 16 | 1.1 | even | 1 | trivial | |
225.2.m.b.19.4 | 16 | 3.2 | odd | 2 | |||
225.2.m.b.154.4 | 16 | 75.29 | odd | 10 | |||
375.2.g.d.151.4 | 16 | 5.3 | odd | 4 | |||
375.2.g.d.226.4 | 16 | 25.3 | odd | 20 | |||
375.2.g.e.151.1 | 16 | 5.2 | odd | 4 | |||
375.2.g.e.226.1 | 16 | 25.22 | odd | 20 | |||
375.2.i.c.274.4 | 16 | 25.21 | even | 5 | |||
375.2.i.c.349.4 | 16 | 5.4 | even | 2 | |||
1875.2.a.m.1.2 | 8 | 25.2 | odd | 20 | |||
1875.2.a.p.1.7 | 8 | 25.23 | odd | 20 | |||
1875.2.b.h.1249.2 | 16 | 25.14 | even | 10 | |||
1875.2.b.h.1249.15 | 16 | 25.11 | even | 5 | |||
5625.2.a.t.1.2 | 8 | 75.23 | even | 20 | |||
5625.2.a.bd.1.7 | 8 | 75.2 | even | 20 |