Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [924,2,Mod(923,924)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(924, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("924.923");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 924.n (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.37817714677\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 8x^{6} + 13x^{4} - 12x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 923.7 | ||
Root | \(-0.965926 - 0.578737i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 924.923 |
Dual form | 924.2.n.b.923.5 |
$q$-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 \(\left(\mathbb{Z}/924\mathbb{Z}\right)^\times\).
\(n\) | \(463\) | \(617\) | \(661\) | \(673\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 1.11803i | 0.612372 | + | 0.790569i | ||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | −0.500000 | + | 1.93649i | −0.250000 | + | 0.968246i | ||||
\(5\) | −1.41421 | −0.632456 | −0.316228 | − | 0.948683i | \(-0.602416\pi\) | ||||
−0.316228 | + | 0.948683i | \(0.602416\pi\) | |||||||
\(6\) | −1.50000 | − | 1.93649i | −0.612372 | − | 0.790569i | ||||
\(7\) | 2.12132 | + | 1.58114i | 0.801784 | + | 0.597614i | ||||
\(8\) | −2.59808 | + | 1.11803i | −0.918559 | + | 0.395285i | ||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | −1.22474 | − | 1.58114i | −0.387298 | − | 0.500000i | ||||
\(11\) | 2.44949 | + | 2.23607i | 0.738549 | + | 0.674200i | ||||
\(12\) | 0.866025 | − | 3.35410i | 0.250000 | − | 0.968246i | ||||
\(13\) | 2.44949 | 0.679366 | 0.339683 | − | 0.940540i | \(-0.389680\pi\) | ||||
0.339683 | + | 0.940540i | \(0.389680\pi\) | |||||||
\(14\) | 0.0693504 | + | 3.74101i | 0.0185347 | + | 0.999828i | ||||
\(15\) | 2.44949 | 0.632456 | ||||||||
\(16\) | −3.50000 | − | 1.93649i | −0.875000 | − | 0.484123i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 2.59808 | + | 3.35410i | 0.612372 | + | 0.790569i | ||||
\(19\) | 6.32456i | 1.45095i | 0.688247 | + | 0.725476i | \(0.258380\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0.707107 | − | 2.73861i | 0.158114 | − | 0.612372i | ||||
\(21\) | −3.67423 | − | 2.73861i | −0.801784 | − | 0.597614i | ||||
\(22\) | −0.378680 | + | 4.67510i | −0.0807348 | + | 0.996736i | ||||
\(23\) | −2.44949 | −0.510754 | −0.255377 | − | 0.966842i | \(-0.582200\pi\) | ||||
−0.255377 | + | 0.966842i | \(0.582200\pi\) | |||||||
\(24\) | 4.50000 | − | 1.93649i | 0.918559 | − | 0.395285i | ||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 2.12132 | + | 2.73861i | 0.416025 | + | 0.537086i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −4.12252 | + | 3.31735i | −0.779083 | + | 0.626920i | ||||
\(29\) | −6.92820 | −1.28654 | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
−0.643268 | + | 0.765641i | \(0.722422\pi\) | |||||||
\(30\) | 2.12132 | + | 2.73861i | 0.387298 | + | 0.500000i | ||||
\(31\) | −3.46410 | −0.622171 | −0.311086 | − | 0.950382i | \(-0.600693\pi\) | ||||
−0.311086 | + | 0.950382i | \(0.600693\pi\) | |||||||
\(32\) | −0.866025 | − | 5.59017i | −0.153093 | − | 0.988212i | ||||
\(33\) | −4.24264 | − | 3.87298i | −0.738549 | − | 0.674200i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00000 | − | 2.23607i | −0.507093 | − | 0.377964i | ||||
\(36\) | −1.50000 | + | 5.80948i | −0.250000 | + | 0.968246i | ||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −7.07107 | + | 5.47723i | −1.14708 | + | 0.888523i | ||||
\(39\) | −4.24264 | −0.679366 | ||||||||
\(40\) | 3.67423 | − | 1.58114i | 0.580948 | − | 0.250000i | ||||
\(41\) | − | 7.74597i | − | 1.20972i | −0.796333 | − | 0.604858i | \(-0.793230\pi\) | ||
0.796333 | − | 0.604858i | \(-0.206770\pi\) | |||||||
\(42\) | −0.120118 | − | 6.47963i | −0.0185347 | − | 0.999828i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −5.55487 | + | 3.62538i | −0.837428 | + | 0.546547i | ||||
\(45\) | −4.24264 | −0.632456 | ||||||||
\(46\) | −2.12132 | − | 2.73861i | −0.312772 | − | 0.403786i | ||||
\(47\) | − | 5.47723i | − | 0.798935i | −0.916747 | − | 0.399468i | \(-0.869195\pi\) | ||
0.916747 | − | 0.399468i | \(-0.130805\pi\) | |||||||
\(48\) | 6.06218 | + | 3.35410i | 0.875000 | + | 0.484123i | ||||
\(49\) | 2.00000 | + | 6.70820i | 0.285714 | + | 0.958315i | ||||
\(50\) | −2.59808 | − | 3.35410i | −0.367423 | − | 0.474342i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.22474 | + | 4.74342i | −0.169842 | + | 0.657794i | ||||
\(53\) | 9.48683i | 1.30312i | 0.758599 | + | 0.651558i | \(0.225884\pi\) | ||||
−0.758599 | + | 0.651558i | \(0.774116\pi\) | |||||||
\(54\) | −4.50000 | − | 5.80948i | −0.612372 | − | 0.790569i | ||||
\(55\) | −3.46410 | − | 3.16228i | −0.467099 | − | 0.426401i | ||||
\(56\) | −7.27912 | − | 1.73621i | −0.972713 | − | 0.232011i | ||||
\(57\) | − | 10.9545i | − | 1.45095i | ||||||
\(58\) | −6.00000 | − | 7.74597i | −0.787839 | − | 1.01710i | ||||
\(59\) | 10.9545i | 1.42615i | 0.701089 | + | 0.713074i | \(0.252698\pi\) | ||||
−0.701089 | + | 0.713074i | \(0.747302\pi\) | |||||||
\(60\) | −1.22474 | + | 4.74342i | −0.158114 | + | 0.612372i | ||||
\(61\) | 7.34847 | 0.940875 | 0.470438 | − | 0.882433i | \(-0.344096\pi\) | ||||
0.470438 | + | 0.882433i | \(0.344096\pi\) | |||||||
\(62\) | −3.00000 | − | 3.87298i | −0.381000 | − | 0.491869i | ||||
\(63\) | 6.36396 | + | 4.74342i | 0.801784 | + | 0.597614i | ||||
\(64\) | 5.50000 | − | 5.80948i | 0.687500 | − | 0.726184i | ||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0.655892 | − | 8.09752i | 0.0807348 | − | 0.996736i | ||||
\(67\) | 7.74597i | 0.946320i | 0.880976 | + | 0.473160i | \(0.156887\pi\) | ||||
−0.880976 | + | 0.473160i | \(0.843113\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.24264 | 0.510754 | ||||||||
\(70\) | −0.0980762 | − | 5.29059i | −0.0117223 | − | 0.632347i | ||||
\(71\) | −12.2474 | −1.45350 | −0.726752 | − | 0.686900i | \(-0.758971\pi\) | ||||
−0.726752 | + | 0.686900i | \(0.758971\pi\) | |||||||
\(72\) | −7.79423 | + | 3.35410i | −0.918559 | + | 0.395285i | ||||
\(73\) | 9.79796 | 1.14676 | 0.573382 | − | 0.819288i | \(-0.305631\pi\) | ||||
0.573382 | + | 0.819288i | \(0.305631\pi\) | |||||||
\(74\) | 1.73205 | + | 2.23607i | 0.201347 | + | 0.259938i | ||||
\(75\) | 5.19615 | 0.600000 | ||||||||
\(76\) | −12.2474 | − | 3.16228i | −1.40488 | − | 0.362738i | ||||
\(77\) | 1.66062 | + | 8.61640i | 0.189245 | + | 0.981930i | ||||
\(78\) | −3.67423 | − | 4.74342i | −0.416025 | − | 0.537086i | ||||
\(79\) | −4.24264 | −0.477334 | −0.238667 | − | 0.971101i | \(-0.576710\pi\) | ||||
−0.238667 | + | 0.971101i | \(0.576710\pi\) | |||||||
\(80\) | 4.94975 | + | 2.73861i | 0.553399 | + | 0.306186i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 8.66025 | − | 6.70820i | 0.956365 | − | 0.740797i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 7.14042 | − | 5.74582i | 0.779083 | − | 0.626920i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0000 | 1.28654 | ||||||||
\(88\) | −8.86396 | − | 3.07086i | −0.944901 | − | 0.327355i | ||||
\(89\) | 2.82843 | 0.299813 | 0.149906 | − | 0.988700i | \(-0.452103\pi\) | ||||
0.149906 | + | 0.988700i | \(0.452103\pi\) | |||||||
\(90\) | −3.67423 | − | 4.74342i | −0.387298 | − | 0.500000i | ||||
\(91\) | 5.19615 | + | 3.87298i | 0.544705 | + | 0.405999i | ||||
\(92\) | 1.22474 | − | 4.74342i | 0.127688 | − | 0.494535i | ||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 6.12372 | − | 4.74342i | 0.631614 | − | 0.489246i | ||||
\(95\) | − | 8.94427i | − | 0.917663i | ||||||
\(96\) | 1.50000 | + | 9.68246i | 0.153093 | + | 0.988212i | ||||
\(97\) | 13.4164i | 1.36223i | 0.732177 | + | 0.681115i | \(0.238505\pi\) | ||||
−0.732177 | + | 0.681115i | \(0.761495\pi\) | |||||||
\(98\) | −5.76795 | + | 8.04554i | −0.582651 | + | 0.812723i | ||||
\(99\) | 7.34847 | + | 6.70820i | 0.738549 | + | 0.674200i | ||||
\(100\) | 1.50000 | − | 5.80948i | 0.150000 | − | 0.580948i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.46410 | −0.341328 | −0.170664 | − | 0.985329i | \(-0.554591\pi\) | ||||
−0.170664 | + | 0.985329i | \(0.554591\pi\) | |||||||
\(104\) | −6.36396 | + | 2.73861i | −0.624038 | + | 0.268543i | ||||
\(105\) | 5.19615 | + | 3.87298i | 0.507093 | + | 0.377964i | ||||
\(106\) | −10.6066 | + | 8.21584i | −1.03020 | + | 0.797993i | ||||
\(107\) | − | 4.47214i | − | 0.432338i | −0.976356 | − | 0.216169i | \(-0.930644\pi\) | ||
0.976356 | − | 0.216169i | \(-0.0693562\pi\) | |||||||
\(108\) | 2.59808 | − | 10.0623i | 0.250000 | − | 0.968246i | ||||
\(109\) | − | 5.47723i | − | 0.524623i | −0.964983 | − | 0.262312i | \(-0.915515\pi\) | ||
0.964983 | − | 0.262312i | \(-0.0844848\pi\) | |||||||
\(110\) | 0.535534 | − | 6.61160i | 0.0510612 | − | 0.630391i | ||||
\(111\) | −3.46410 | −0.328798 | ||||||||
\(112\) | −4.36276 | − | 9.64191i | −0.412242 | − | 0.911074i | ||||
\(113\) | − | 18.9737i | − | 1.78489i | −0.451154 | − | 0.892446i | \(-0.648987\pi\) | ||
0.451154 | − | 0.892446i | \(-0.351013\pi\) | |||||||
\(114\) | 12.2474 | − | 9.48683i | 1.14708 | − | 0.888523i | ||||
\(115\) | 3.46410 | 0.323029 | ||||||||
\(116\) | 3.46410 | − | 13.4164i | 0.321634 | − | 1.24568i | ||||
\(117\) | 7.34847 | 0.679366 | ||||||||
\(118\) | −12.2474 | + | 9.48683i | −1.12747 | + | 0.873334i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.36396 | + | 2.73861i | −0.580948 | + | 0.250000i | ||||
\(121\) | 1.00000 | + | 10.9545i | 0.0909091 | + | 0.995859i | ||||
\(122\) | 6.36396 | + | 8.21584i | 0.576166 | + | 0.743827i | ||||
\(123\) | 13.4164i | 1.20972i | ||||||||
\(124\) | 1.73205 | − | 6.70820i | 0.155543 | − | 0.602414i | ||||
\(125\) | 11.3137 | 1.01193 | ||||||||
\(126\) | 0.208051 | + | 11.2230i | 0.0185347 | + | 0.999828i | ||||
\(127\) | 21.2132 | 1.88237 | 0.941184 | − | 0.337895i | \(-0.109715\pi\) | ||||
0.941184 | + | 0.337895i | \(0.109715\pi\) | |||||||
\(128\) | 11.2583 | + | 1.11803i | 0.995105 | + | 0.0988212i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 3.87298i | −0.263117 | − | 0.339683i | ||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 9.62132 | − | 6.27935i | 0.837428 | − | 0.546547i | ||||
\(133\) | −10.0000 | + | 13.4164i | −0.867110 | + | 1.16335i | ||||
\(134\) | −8.66025 | + | 6.70820i | −0.748132 | + | 0.579501i | ||||
\(135\) | 7.34847 | 0.632456 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 3.67423 | + | 4.74342i | 0.312772 | + | 0.403786i | ||||
\(139\) | − | 12.6491i | − | 1.07288i | −0.843937 | − | 0.536442i | \(-0.819768\pi\) | ||
0.843937 | − | 0.536442i | \(-0.180232\pi\) | |||||||
\(140\) | 5.83013 | − | 4.69144i | 0.492736 | − | 0.396499i | ||||
\(141\) | 9.48683i | 0.798935i | ||||||||
\(142\) | −10.6066 | − | 13.6931i | −0.890086 | − | 1.14910i | ||||
\(143\) | 6.00000 | + | 5.47723i | 0.501745 | + | 0.458029i | ||||
\(144\) | −10.5000 | − | 5.80948i | −0.875000 | − | 0.484123i | ||||
\(145\) | 9.79796 | 0.813676 | ||||||||
\(146\) | 8.48528 | + | 10.9545i | 0.702247 | + | 0.906597i | ||||
\(147\) | −3.46410 | − | 11.6190i | −0.285714 | − | 0.958315i | ||||
\(148\) | −1.00000 | + | 3.87298i | −0.0821995 | + | 0.318357i | ||||
\(149\) | 6.92820 | 0.567581 | 0.283790 | − | 0.958886i | \(-0.408408\pi\) | ||||
0.283790 | + | 0.958886i | \(0.408408\pi\) | |||||||
\(150\) | 4.50000 | + | 5.80948i | 0.367423 | + | 0.474342i | ||||
\(151\) | 12.7279 | 1.03578 | 0.517892 | − | 0.855446i | \(-0.326717\pi\) | ||||
0.517892 | + | 0.855446i | \(0.326717\pi\) | |||||||
\(152\) | −7.07107 | − | 16.4317i | −0.573539 | − | 1.33278i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.19529 | + | 9.31865i | −0.660395 | + | 0.750918i | ||||
\(155\) | 4.89898 | 0.393496 | ||||||||
\(156\) | 2.12132 | − | 8.21584i | 0.169842 | − | 0.657794i | ||||
\(157\) | 13.4164i | 1.07075i | 0.844616 | + | 0.535373i | \(0.179829\pi\) | ||||
−0.844616 | + | 0.535373i | \(0.820171\pi\) | |||||||
\(158\) | −3.67423 | − | 4.74342i | −0.292306 | − | 0.377366i | ||||
\(159\) | − | 16.4317i | − | 1.30312i | ||||||
\(160\) | 1.22474 | + | 7.90569i | 0.0968246 | + | 0.625000i | ||||
\(161\) | −5.19615 | − | 3.87298i | −0.409514 | − | 0.305234i | ||||
\(162\) | 7.79423 | + | 10.0623i | 0.612372 | + | 0.790569i | ||||
\(163\) | 15.4919i | 1.21342i | 0.794923 | + | 0.606711i | \(0.207511\pi\) | ||||
−0.794923 | + | 0.606711i | \(0.792489\pi\) | |||||||
\(164\) | 15.0000 | + | 3.87298i | 1.17130 | + | 0.302429i | ||||
\(165\) | 6.00000 | + | 5.47723i | 0.467099 | + | 0.426401i | ||||
\(166\) | −5.19615 | − | 6.70820i | −0.403300 | − | 0.520658i | ||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 12.6078 | + | 3.00721i | 0.972713 | + | 0.232011i | ||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.9737i | 1.45095i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4919i | 1.17783i | 0.808195 | + | 0.588915i | \(0.200445\pi\) | ||||
−0.808195 | + | 0.588915i | \(0.799555\pi\) | |||||||
\(174\) | 10.3923 | + | 13.4164i | 0.787839 | + | 1.01710i | ||||
\(175\) | −6.36396 | − | 4.74342i | −0.481070 | − | 0.358569i | ||||
\(176\) | −4.24309 | − | 12.5697i | −0.319835 | − | 0.947473i | ||||
\(177\) | − | 18.9737i | − | 1.42615i | ||||||
\(178\) | 2.44949 | + | 3.16228i | 0.183597 | + | 0.237023i | ||||
\(179\) | 14.6969 | 1.09850 | 0.549250 | − | 0.835658i | \(-0.314913\pi\) | ||||
0.549250 | + | 0.835658i | \(0.314913\pi\) | |||||||
\(180\) | 2.12132 | − | 8.21584i | 0.158114 | − | 0.612372i | ||||
\(181\) | − | 13.4164i | − | 0.997234i | −0.866822 | − | 0.498617i | \(-0.833841\pi\) | ||
0.866822 | − | 0.498617i | \(-0.166159\pi\) | |||||||
\(182\) | 0.169873 | + | 9.16358i | 0.0125918 | + | 0.679250i | ||||
\(183\) | −12.7279 | −0.940875 | ||||||||
\(184\) | 6.36396 | − | 2.73861i | 0.469157 | − | 0.201893i | ||||
\(185\) | −2.82843 | −0.207950 | ||||||||
\(186\) | 5.19615 | + | 6.70820i | 0.381000 | + | 0.491869i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.6066 | + | 2.73861i | 0.773566 | + | 0.199734i | ||||
\(189\) | −11.0227 | − | 8.21584i | −0.801784 | − | 0.597614i | ||||
\(190\) | 10.0000 | − | 7.74597i | 0.725476 | − | 0.561951i | ||||
\(191\) | −12.2474 | −0.886194 | −0.443097 | − | 0.896474i | \(-0.646120\pi\) | ||||
−0.443097 | + | 0.896474i | \(0.646120\pi\) | |||||||
\(192\) | −9.52628 | + | 10.0623i | −0.687500 | + | 0.726184i | ||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | −15.0000 | + | 11.6190i | −1.07694 | + | 0.834192i | ||||
\(195\) | 6.00000 | 0.429669 | ||||||||
\(196\) | −13.9904 | + | 0.518881i | −0.999313 | + | 0.0370630i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | −1.13604 | + | 14.0253i | −0.0807348 | + | 0.996736i | ||||
\(199\) | 24.2487 | 1.71895 | 0.859473 | − | 0.511182i | \(-0.170792\pi\) | ||||
0.859473 | + | 0.511182i | \(0.170792\pi\) | |||||||
\(200\) | 7.79423 | − | 3.35410i | 0.551135 | − | 0.237171i | ||||
\(201\) | − | 13.4164i | − | 0.946320i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.6969 | − | 10.9545i | −1.03152 | − | 0.768852i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.9545i | 0.765092i | ||||||||
\(206\) | −3.00000 | − | 3.87298i | −0.209020 | − | 0.269844i | ||||
\(207\) | −7.34847 | −0.510754 | ||||||||
\(208\) | −8.57321 | − | 4.74342i | −0.594445 | − | 0.328897i | ||||
\(209\) | −14.1421 | + | 15.4919i | −0.978232 | + | 1.07160i | ||||
\(210\) | 0.169873 | + | 9.16358i | 0.0117223 | + | 0.632347i | ||||
\(211\) | 8.48528 | 0.584151 | 0.292075 | − | 0.956395i | \(-0.405654\pi\) | ||||
0.292075 | + | 0.956395i | \(0.405654\pi\) | |||||||
\(212\) | −18.3712 | − | 4.74342i | −1.26174 | − | 0.325779i | ||||
\(213\) | 21.2132 | 1.45350 | ||||||||
\(214\) | 5.00000 | − | 3.87298i | 0.341793 | − | 0.264752i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.5000 | − | 5.80948i | 0.918559 | − | 0.395285i | ||||
\(217\) | −7.34847 | − | 5.47723i | −0.498847 | − | 0.371818i | ||||
\(218\) | 6.12372 | − | 4.74342i | 0.414751 | − | 0.321265i | ||||
\(219\) | −16.9706 | −1.14676 | ||||||||
\(220\) | 7.85578 | − | 5.12707i | 0.529636 | − | 0.345667i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.00000 | − | 3.87298i | −0.201347 | − | 0.259938i | ||||
\(223\) | −17.3205 | −1.15987 | −0.579934 | − | 0.814664i | \(-0.696921\pi\) | ||||
−0.579934 | + | 0.814664i | \(0.696921\pi\) | |||||||
\(224\) | 7.00172 | − | 13.2278i | 0.467822 | − | 0.883823i | ||||
\(225\) | −9.00000 | −0.600000 | ||||||||
\(226\) | 21.2132 | − | 16.4317i | 1.41108 | − | 1.09302i | ||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 21.2132 | + | 5.47723i | 1.40488 | + | 0.362738i | ||||
\(229\) | − | 13.4164i | − | 0.886581i | −0.896378 | − | 0.443291i | \(-0.853811\pi\) | ||
0.896378 | − | 0.443291i | \(-0.146189\pi\) | |||||||
\(230\) | 3.00000 | + | 3.87298i | 0.197814 | + | 0.255377i | ||||
\(231\) | −2.87628 | − | 14.9240i | −0.189245 | − | 0.981930i | ||||
\(232\) | 18.0000 | − | 7.74597i | 1.18176 | − | 0.508548i | ||||
\(233\) | 20.7846 | 1.36165 | 0.680823 | − | 0.732448i | \(-0.261622\pi\) | ||||
0.680823 | + | 0.732448i | \(0.261622\pi\) | |||||||
\(234\) | 6.36396 | + | 8.21584i | 0.416025 | + | 0.537086i | ||||
\(235\) | 7.74597i | 0.505291i | ||||||||
\(236\) | −21.2132 | − | 5.47723i | −1.38086 | − | 0.356537i | ||||
\(237\) | 7.34847 | 0.477334 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.94427i | − | 0.578557i | −0.957245 | − | 0.289278i | \(-0.906585\pi\) | ||
0.957245 | − | 0.289278i | \(-0.0934153\pi\) | |||||||
\(240\) | −8.57321 | − | 4.74342i | −0.553399 | − | 0.306186i | ||||
\(241\) | −24.4949 | −1.57786 | −0.788928 | − | 0.614486i | \(-0.789363\pi\) | ||||
−0.788928 | + | 0.614486i | \(0.789363\pi\) | |||||||
\(242\) | −11.3814 | + | 10.6049i | −0.731626 | + | 0.681707i | ||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | −3.67423 | + | 14.2302i | −0.235219 | + | 0.910998i | ||||
\(245\) | −2.82843 | − | 9.48683i | −0.180702 | − | 0.606092i | ||||
\(246\) | −15.0000 | + | 11.6190i | −0.956365 | + | 0.740797i | ||||
\(247\) | 15.4919i | 0.985728i | ||||||||
\(248\) | 9.00000 | − | 3.87298i | 0.571501 | − | 0.245935i | ||||
\(249\) | 10.3923 | 0.658586 | ||||||||
\(250\) | 9.79796 | + | 12.6491i | 0.619677 | + | 0.800000i | ||||
\(251\) | 21.9089i | 1.38288i | 0.722435 | + | 0.691439i | \(0.243023\pi\) | ||||
−0.722435 | + | 0.691439i | \(0.756977\pi\) | |||||||
\(252\) | −12.3676 | + | 9.95205i | −0.779083 | + | 0.626920i | ||||
\(253\) | −6.00000 | − | 5.47723i | −0.377217 | − | 0.344350i | ||||
\(254\) | 18.3712 | + | 23.7171i | 1.15271 | + | 1.48814i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | + | 13.5554i | 0.531250 | + | 0.847215i | ||||
\(257\) | 14.1421 | 0.882162 | 0.441081 | − | 0.897467i | \(-0.354595\pi\) | ||||
0.441081 | + | 0.897467i | \(0.354595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.24264 | + | 3.16228i | 0.263625 | + | 0.196494i | ||||
\(260\) | 1.73205 | − | 6.70820i | 0.107417 | − | 0.416025i | ||||
\(261\) | −20.7846 | −1.28654 | ||||||||
\(262\) | −15.5885 | − | 20.1246i | −0.963058 | − | 1.24330i | ||||
\(263\) | − | 8.94427i | − | 0.551527i | −0.961225 | − | 0.275764i | \(-0.911069\pi\) | ||
0.961225 | − | 0.275764i | \(-0.0889307\pi\) | |||||||
\(264\) | 15.3528 | + | 5.31889i | 0.944901 | + | 0.327355i | ||||
\(265\) | − | 13.4164i | − | 0.824163i | ||||||
\(266\) | −23.6603 | + | 0.438610i | −1.45070 | + | 0.0268929i | ||||
\(267\) | −4.89898 | −0.299813 | ||||||||
\(268\) | −15.0000 | − | 3.87298i | −0.916271 | − | 0.236580i | ||||
\(269\) | 9.89949 | 0.603583 | 0.301791 | − | 0.953374i | \(-0.402415\pi\) | ||||
0.301791 | + | 0.953374i | \(0.402415\pi\) | |||||||
\(270\) | 6.36396 | + | 8.21584i | 0.387298 | + | 0.500000i | ||||
\(271\) | − | 15.8114i | − | 0.960473i | −0.877139 | − | 0.480237i | \(-0.840551\pi\) | ||
0.877139 | − | 0.480237i | \(-0.159449\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.00000 | − | 6.70820i | −0.544705 | − | 0.405999i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.34847 | − | 6.70820i | −0.443129 | − | 0.404520i | ||||
\(276\) | −2.12132 | + | 8.21584i | −0.127688 | + | 0.494535i | ||||
\(277\) | 5.47723i | 0.329095i | 0.986369 | + | 0.164547i | \(0.0526163\pi\) | ||||
−0.986369 | + | 0.164547i | \(0.947384\pi\) | |||||||
\(278\) | 14.1421 | − | 10.9545i | 0.848189 | − | 0.657004i | ||||
\(279\) | −10.3923 | −0.622171 | ||||||||
\(280\) | 10.2942 | + | 2.45537i | 0.615198 | + | 0.146737i | ||||
\(281\) | 3.46410 | 0.206651 | 0.103325 | − | 0.994648i | \(-0.467052\pi\) | ||||
0.103325 | + | 0.994648i | \(0.467052\pi\) | |||||||
\(282\) | −10.6066 | + | 8.21584i | −0.631614 | + | 0.489246i | ||||
\(283\) | 25.2982i | 1.50382i | 0.659264 | + | 0.751912i | \(0.270868\pi\) | ||||
−0.659264 | + | 0.751912i | \(0.729132\pi\) | |||||||
\(284\) | 6.12372 | − | 23.7171i | 0.363376 | − | 1.40735i | ||||
\(285\) | 15.4919i | 0.917663i | ||||||||
\(286\) | −0.927572 | + | 11.4516i | −0.0548485 | + | 0.677149i | ||||
\(287\) | 12.2474 | − | 16.4317i | 0.722944 | − | 0.969931i | ||||
\(288\) | −2.59808 | − | 16.7705i | −0.153093 | − | 0.988212i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 8.48528 | + | 10.9545i | 0.498273 | + | 0.643268i | ||||
\(291\) | − | 23.2379i | − | 1.36223i | ||||||
\(292\) | −4.89898 | + | 18.9737i | −0.286691 | + | 1.11035i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 9.99038 | − | 13.9353i | 0.582651 | − | 0.812723i | ||||
\(295\) | − | 15.4919i | − | 0.901975i | ||||||
\(296\) | −5.19615 | + | 2.23607i | −0.302020 | + | 0.129969i | ||||
\(297\) | −12.7279 | − | 11.6190i | −0.738549 | − | 0.674200i | ||||
\(298\) | 6.00000 | + | 7.74597i | 0.347571 | + | 0.448712i | ||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | −2.59808 | + | 10.0623i | −0.150000 | + | 0.580948i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.0227 | + | 14.2302i | 0.634285 | + | 0.818859i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.2474 | − | 22.1359i | 0.702439 | − | 1.26958i | ||||
\(305\) | −10.3923 | −0.595062 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.2982i | − | 1.44385i | −0.691974 | − | 0.721923i | \(-0.743259\pi\) | ||
0.691974 | − | 0.721923i | \(-0.256741\pi\) | |||||||
\(308\) | −17.5159 | − | 1.09243i | −0.998061 | − | 0.0622467i | ||||
\(309\) | 6.00000 | 0.341328 | ||||||||
\(310\) | 4.24264 | + | 5.47723i | 0.240966 | + | 0.311086i | ||||
\(311\) | 16.4317i | 0.931755i | 0.884849 | + | 0.465877i | \(0.154261\pi\) | ||||
−0.884849 | + | 0.465877i | \(0.845739\pi\) | |||||||
\(312\) | 11.0227 | − | 4.74342i | 0.624038 | − | 0.268543i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | −15.0000 | + | 11.6190i | −0.846499 | + | 0.655695i | ||||
\(315\) | −9.00000 | − | 6.70820i | −0.507093 | − | 0.377964i | ||||
\(316\) | 2.12132 | − | 8.21584i | 0.119334 | − | 0.462177i | ||||
\(317\) | 28.4605i | 1.59850i | 0.600998 | + | 0.799250i | \(0.294770\pi\) | ||||
−0.600998 | + | 0.799250i | \(0.705230\pi\) | |||||||
\(318\) | 18.3712 | − | 14.2302i | 1.03020 | − | 0.797993i | ||||
\(319\) | −16.9706 | − | 15.4919i | −0.950169 | − | 0.867382i | ||||
\(320\) | −7.77817 | + | 8.21584i | −0.434813 | + | 0.459279i | ||||
\(321\) | 7.74597i | 0.432338i | ||||||||
\(322\) | −0.169873 | − | 9.16358i | −0.00946665 | − | 0.510666i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.50000 | + | 17.4284i | −0.250000 | + | 0.968246i | ||||
\(325\) | −7.34847 | −0.407620 | ||||||||
\(326\) | −17.3205 | + | 13.4164i | −0.959294 | + | 0.743066i | ||||
\(327\) | 9.48683i | 0.524623i | ||||||||
\(328\) | 8.66025 | + | 20.1246i | 0.478183 | + | 1.11120i | ||||
\(329\) | 8.66025 | − | 11.6190i | 0.477455 | − | 0.640573i | ||||
\(330\) | −0.927572 | + | 11.4516i | −0.0510612 | + | 0.630391i | ||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 3.00000 | − | 11.6190i | 0.164646 | − | 0.637673i | ||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | 10.3923 | + | 13.4164i | 0.568642 | + | 0.734113i | ||||
\(335\) | − | 10.9545i | − | 0.598506i | ||||||
\(336\) | 7.55652 | + | 16.7003i | 0.412242 | + | 0.911074i | ||||
\(337\) | 10.9545i | 0.596727i | 0.954452 | + | 0.298363i | \(0.0964408\pi\) | ||||
−0.954452 | + | 0.298363i | \(0.903559\pi\) | |||||||
\(338\) | −6.06218 | − | 7.82624i | −0.329739 | − | 0.425691i | ||||
\(339\) | 32.8634i | 1.78489i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.48528 | − | 7.74597i | −0.459504 | − | 0.419468i | ||||
\(342\) | −21.2132 | + | 16.4317i | −1.14708 | + | 0.888523i | ||||
\(343\) | −6.36396 | + | 17.3925i | −0.343622 | + | 0.939108i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.00000 | −0.323029 | ||||||||
\(346\) | −17.3205 | + | 13.4164i | −0.931156 | + | 0.721271i | ||||
\(347\) | 17.8885i | 0.960307i | 0.877184 | + | 0.480154i | \(0.159419\pi\) | ||||
−0.877184 | + | 0.480154i | \(0.840581\pi\) | |||||||
\(348\) | −6.00000 | + | 23.2379i | −0.321634 | + | 1.24568i | ||||
\(349\) | 12.2474 | 0.655591 | 0.327795 | − | 0.944749i | \(-0.393694\pi\) | ||||
0.327795 | + | 0.944749i | \(0.393694\pi\) | |||||||
\(350\) | −0.208051 | − | 11.2230i | −0.0111208 | − | 0.599897i | ||||
\(351\) | −12.7279 | −0.679366 | ||||||||
\(352\) | 10.3787 | − | 15.6296i | 0.553185 | − | 0.833058i | ||||
\(353\) | 22.6274 | 1.20434 | 0.602168 | − | 0.798369i | \(-0.294304\pi\) | ||||
0.602168 | + | 0.798369i | \(0.294304\pi\) | |||||||
\(354\) | 21.2132 | − | 16.4317i | 1.12747 | − | 0.873334i | ||||
\(355\) | 17.3205 | 0.919277 | ||||||||
\(356\) | −1.41421 | + | 5.47723i | −0.0749532 | + | 0.290292i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.7279 | + | 16.4317i | 0.672692 | + | 0.868441i | ||||
\(359\) | 17.8885i | 0.944121i | 0.881566 | + | 0.472061i | \(0.156490\pi\) | ||||
−0.881566 | + | 0.472061i | \(0.843510\pi\) | |||||||
\(360\) | 11.0227 | − | 4.74342i | 0.580948 | − | 0.250000i | ||||
\(361\) | −21.0000 | −1.10526 | ||||||||
\(362\) | 15.0000 | − | 11.6190i | 0.788382 | − | 0.610678i | ||||
\(363\) | −1.73205 | − | 18.9737i | −0.0909091 | − | 0.995859i | ||||
\(364\) | −10.0981 | + | 8.12581i | −0.529283 | + | 0.425908i | ||||
\(365\) | −13.8564 | −0.725277 | ||||||||
\(366\) | −11.0227 | − | 14.2302i | −0.576166 | − | 0.743827i | ||||
\(367\) | 17.3205 | 0.904123 | 0.452062 | − | 0.891987i | \(-0.350689\pi\) | ||||
0.452062 | + | 0.891987i | \(0.350689\pi\) | |||||||
\(368\) | 8.57321 | + | 4.74342i | 0.446910 | + | 0.247268i | ||||
\(369\) | − | 23.2379i | − | 1.20972i | ||||||
\(370\) | −2.44949 | − | 3.16228i | −0.127343 | − | 0.164399i | ||||
\(371\) | −15.0000 | + | 20.1246i | −0.778761 | + | 1.04482i | ||||
\(372\) | −3.00000 | + | 11.6190i | −0.155543 | + | 0.602414i | ||||
\(373\) | − | 5.47723i | − | 0.283600i | −0.989895 | − | 0.141800i | \(-0.954711\pi\) | ||
0.989895 | − | 0.141800i | \(-0.0452890\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.5959 | −1.01193 | ||||||||
\(376\) | 6.12372 | + | 14.2302i | 0.315807 | + | 0.733869i | ||||
\(377\) | −16.9706 | −0.874028 | ||||||||
\(378\) | −0.360355 | − | 19.4389i | −0.0185347 | − | 0.999828i | ||||
\(379\) | − | 15.4919i | − | 0.795767i | −0.917436 | − | 0.397884i | \(-0.869745\pi\) | ||
0.917436 | − | 0.397884i | \(-0.130255\pi\) | |||||||
\(380\) | 17.3205 | + | 4.47214i | 0.888523 | + | 0.229416i | ||||
\(381\) | −36.7423 | −1.88237 | ||||||||
\(382\) | −10.6066 | − | 13.6931i | −0.542681 | − | 0.700598i | ||||
\(383\) | 16.4317i | 0.839619i | 0.907612 | + | 0.419810i | \(0.137903\pi\) | ||||
−0.907612 | + | 0.419810i | \(0.862097\pi\) | |||||||
\(384\) | −19.5000 | − | 1.93649i | −0.995105 | − | 0.0988212i | ||||
\(385\) | −2.34847 | − | 12.1854i | −0.119689 | − | 0.621027i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.9808 | − | 6.70820i | −1.31897 | − | 0.340557i | ||||
\(389\) | − | 28.4605i | − | 1.44300i | −0.692412 | − | 0.721502i | \(-0.743452\pi\) | ||
0.692412 | − | 0.721502i | \(-0.256548\pi\) | |||||||
\(390\) | 5.19615 | + | 6.70820i | 0.263117 | + | 0.339683i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −12.6962 | − | 15.1924i | −0.641253 | − | 0.767330i | ||||
\(393\) | 31.1769 | 1.57267 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | −16.6646 | + | 10.8761i | −0.837428 | + | 0.546547i | ||||
\(397\) | − | 13.4164i | − | 0.673350i | −0.941621 | − | 0.336675i | \(-0.890698\pi\) | ||
0.941621 | − | 0.336675i | \(-0.109302\pi\) | |||||||
\(398\) | 21.0000 | + | 27.1109i | 1.05263 | + | 1.35895i | ||||
\(399\) | 17.3205 | − | 23.2379i | 0.867110 | − | 1.16335i | ||||
\(400\) | 10.5000 | + | 5.80948i | 0.525000 | + | 0.290474i | ||||
\(401\) | 18.9737i | 0.947500i | 0.880659 | + | 0.473750i | \(0.157100\pi\) | ||||
−0.880659 | + | 0.473750i | \(0.842900\pi\) | |||||||
\(402\) | 15.0000 | − | 11.6190i | 0.748132 | − | 0.579501i | ||||
\(403\) | −8.48528 | −0.422682 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.7279 | −0.632456 | ||||||||
\(406\) | −0.480473 | − | 25.9185i | −0.0238455 | − | 1.28631i | ||||
\(407\) | 4.89898 | + | 4.47214i | 0.242833 | + | 0.221676i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | −12.2474 | + | 9.48683i | −0.604858 | + | 0.468521i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.73205 | − | 6.70820i | 0.0853320 | − | 0.330489i | ||||
\(413\) | −17.3205 | + | 23.2379i | −0.852286 | + | 1.14346i | ||||
\(414\) | −6.36396 | − | 8.21584i | −0.312772 | − | 0.403786i | ||||
\(415\) | 8.48528 | 0.416526 | ||||||||
\(416\) | −2.12132 | − | 13.6931i | −0.104006 | − | 0.671358i | ||||
\(417\) | 21.9089i | 1.07288i | ||||||||
\(418\) | −29.5680 | − | 2.39498i | −1.44622 | − | 0.117142i | ||||
\(419\) | − | 21.9089i | − | 1.07032i | −0.844751 | − | 0.535160i | \(-0.820251\pi\) | ||
0.844751 | − | 0.535160i | \(-0.179749\pi\) | |||||||
\(420\) | −10.0981 | + | 8.12581i | −0.492736 | + | 0.396499i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 7.34847 | + | 9.48683i | 0.357718 | + | 0.461812i | ||||
\(423\) | − | 16.4317i | − | 0.798935i | ||||||
\(424\) | −10.6066 | − | 24.6475i | −0.515102 | − | 1.19699i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18.3712 | + | 23.7171i | 0.890086 | + | 1.14910i | ||||
\(427\) | 15.5885 | + | 11.6190i | 0.754378 | + | 0.562280i | ||||
\(428\) | 8.66025 | + | 2.23607i | 0.418609 | + | 0.108084i | ||||
\(429\) | −10.3923 | − | 9.48683i | −0.501745 | − | 0.458029i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.8885i | − | 0.861661i | −0.902433 | − | 0.430830i | \(-0.858221\pi\) | ||
0.902433 | − | 0.430830i | \(-0.141779\pi\) | |||||||
\(432\) | 18.1865 | + | 10.0623i | 0.875000 | + | 0.484123i | ||||
\(433\) | − | 26.8328i | − | 1.28950i | −0.764392 | − | 0.644751i | \(-0.776961\pi\) | ||
0.764392 | − | 0.644751i | \(-0.223039\pi\) | |||||||
\(434\) | −0.240237 | − | 12.9593i | −0.0115317 | − | 0.622064i | ||||
\(435\) | −16.9706 | −0.813676 | ||||||||
\(436\) | 10.6066 | + | 2.73861i | 0.507964 | + | 0.131156i | ||||
\(437\) | − | 15.4919i | − | 0.741080i | ||||||
\(438\) | −14.6969 | − | 18.9737i | −0.702247 | − | 0.906597i | ||||
\(439\) | − | 34.7851i | − | 1.66020i | −0.557615 | − | 0.830100i | \(-0.688283\pi\) | ||
0.557615 | − | 0.830100i | \(-0.311717\pi\) | |||||||
\(440\) | 12.5355 | + | 4.34286i | 0.597608 | + | 0.207037i | ||||
\(441\) | 6.00000 | + | 20.1246i | 0.285714 | + | 0.958315i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.1918 | 1.86206 | 0.931030 | − | 0.364942i | \(-0.118911\pi\) | ||||
0.931030 | + | 0.364942i | \(0.118911\pi\) | |||||||
\(444\) | 1.73205 | − | 6.70820i | 0.0821995 | − | 0.318357i | ||||
\(445\) | −4.00000 | −0.189618 | ||||||||
\(446\) | −15.0000 | − | 19.3649i | −0.710271 | − | 0.916955i | ||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 20.8528 | − | 3.62749i | 0.985204 | − | 0.171383i | ||||
\(449\) | 37.9473i | 1.79085i | 0.445217 | + | 0.895423i | \(0.353127\pi\) | ||||
−0.445217 | + | 0.895423i | \(0.646873\pi\) | |||||||
\(450\) | −7.79423 | − | 10.0623i | −0.367423 | − | 0.474342i | ||||
\(451\) | 17.3205 | − | 18.9737i | 0.815591 | − | 0.893435i | ||||
\(452\) | 36.7423 | + | 9.48683i | 1.72821 | + | 0.446223i | ||||
\(453\) | −22.0454 | −1.03578 | ||||||||
\(454\) | 10.3923 | + | 13.4164i | 0.487735 | + | 0.629663i | ||||
\(455\) | −7.34847 | − | 5.47723i | −0.344502 | − | 0.256776i | ||||
\(456\) | 12.2474 | + | 28.4605i | 0.573539 | + | 1.33278i | ||||
\(457\) | 10.9545i | 0.512428i | 0.966620 | + | 0.256214i | \(0.0824751\pi\) | ||||
−0.966620 | + | 0.256214i | \(0.917525\pi\) | |||||||
\(458\) | 15.0000 | − | 11.6190i | 0.700904 | − | 0.542918i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.73205 | + | 6.70820i | −0.0807573 | + | 0.312772i | ||||
\(461\) | − | 30.9839i | − | 1.44306i | −0.692382 | − | 0.721531i | \(-0.743439\pi\) | ||
0.692382 | − | 0.721531i | \(-0.256561\pi\) | |||||||
\(462\) | 14.1947 | − | 16.1404i | 0.660395 | − | 0.750918i | ||||
\(463\) | − | 7.74597i | − | 0.359986i | −0.983668 | − | 0.179993i | \(-0.942393\pi\) | ||
0.983668 | − | 0.179993i | \(-0.0576074\pi\) | |||||||
\(464\) | 24.2487 | + | 13.4164i | 1.12572 | + | 0.622841i | ||||
\(465\) | −8.48528 | −0.393496 | ||||||||
\(466\) | 18.0000 | + | 23.2379i | 0.833834 | + | 1.07647i | ||||
\(467\) | − | 10.9545i | − | 0.506912i | −0.967347 | − | 0.253456i | \(-0.918433\pi\) | ||
0.967347 | − | 0.253456i | \(-0.0815672\pi\) | |||||||
\(468\) | −3.67423 | + | 14.2302i | −0.169842 | + | 0.657794i | ||||
\(469\) | −12.2474 | + | 16.4317i | −0.565535 | + | 0.758744i | ||||
\(470\) | −8.66025 | + | 6.70820i | −0.399468 | + | 0.309426i | ||||
\(471\) | − | 23.2379i | − | 1.07075i | ||||||
\(472\) | −12.2474 | − | 28.4605i | −0.563735 | − | 1.31000i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.36396 | + | 8.21584i | 0.292306 | + | 0.377366i | ||||
\(475\) | − | 18.9737i | − | 0.870572i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.4605i | 1.30312i | ||||||||
\(478\) | 10.0000 | − | 7.74597i | 0.457389 | − | 0.354292i | ||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | −2.12132 | − | 13.6931i | −0.0968246 | − | 0.625000i | ||||
\(481\) | 4.89898 | 0.223374 | ||||||||
\(482\) | −21.2132 | − | 27.3861i | −0.966235 | − | 1.24740i | ||||
\(483\) | 9.00000 | + | 6.70820i | 0.409514 | + | 0.305234i | ||||
\(484\) | −21.7132 | − | 3.54073i | −0.986964 | − | 0.160942i | ||||
\(485\) | − | 18.9737i | − | 0.861550i | ||||||
\(486\) | −13.5000 | − | 17.4284i | −0.612372 | − | 0.790569i | ||||
\(487\) | 23.2379i | 1.05301i | 0.850172 | + | 0.526505i | \(0.176498\pi\) | ||||
−0.850172 | + | 0.526505i | \(0.823502\pi\) | |||||||
\(488\) | −19.0919 | + | 8.21584i | −0.864249 | + | 0.371914i | ||||
\(489\) | − | 26.8328i | − | 1.21342i | ||||||
\(490\) | 8.15711 | − | 11.3781i | 0.368501 | − | 0.514011i | ||||
\(491\) | 4.47214i | 0.201825i | 0.994895 | + | 0.100912i | \(0.0321762\pi\) | ||||
−0.994895 | + | 0.100912i | \(0.967824\pi\) | |||||||
\(492\) | −25.9808 | − | 6.70820i | −1.17130 | − | 0.302429i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −17.3205 | + | 13.4164i | −0.779287 | + | 0.603633i | ||||
\(495\) | −10.3923 | − | 9.48683i | −0.467099 | − | 0.426401i | ||||
\(496\) | 12.1244 | + | 6.70820i | 0.544400 | + | 0.301207i | ||||
\(497\) | −25.9808 | − | 19.3649i | −1.16540 | − | 0.868635i | ||||
\(498\) | 9.00000 | + | 11.6190i | 0.403300 | + | 0.520658i | ||||
\(499\) | − | 30.9839i | − | 1.38703i | −0.720443 | − | 0.693514i | \(-0.756061\pi\) | ||
0.720443 | − | 0.693514i | \(-0.243939\pi\) | |||||||
\(500\) | −5.65685 | + | 21.9089i | −0.252982 | + | 0.979796i | ||||
\(501\) | −20.7846 | −0.928588 | ||||||||
\(502\) | −24.4949 | + | 18.9737i | −1.09326 | + | 0.846836i | ||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | −21.8374 | − | 5.20863i | −0.972713 | − | 0.232011i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.927572 | − | 11.4516i | 0.0412356 | − | 0.509087i | ||||
\(507\) | 12.1244 | 0.538462 | ||||||||
\(508\) | −10.6066 | + | 41.0792i | −0.470592 | + | 1.82259i | ||||
\(509\) | −24.0416 | −1.06563 | −0.532813 | − | 0.846233i | \(-0.678865\pi\) | ||||
−0.532813 | + | 0.846233i | \(0.678865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.7846 | + | 15.4919i | 0.919457 | + | 0.685323i | ||||
\(512\) | −7.79423 | + | 21.2426i | −0.344459 | + | 0.938801i | ||||
\(513\) | − | 32.8634i | − | 1.45095i | ||||||
\(514\) | 12.2474 | + | 15.8114i | 0.540212 | + | 0.697410i | ||||
\(515\) | 4.89898 | 0.215875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2474 | − | 13.4164i | 0.538642 | − | 0.590053i | ||||
\(518\) | 0.138701 | + | 7.48203i | 0.00609416 | + | 0.328741i | ||||
\(519\) | − | 26.8328i | − | 1.17783i | ||||||
\(520\) | 9.00000 | − | 3.87298i | 0.394676 | − | 0.169842i | ||||
\(521\) | −19.7990 | −0.867409 | −0.433705 | − | 0.901055i | \(-0.642794\pi\) | ||||
−0.433705 | + | 0.901055i | \(0.642794\pi\) | |||||||
\(522\) | −18.0000 | − | 23.2379i | −0.787839 | − | 1.01710i | ||||
\(523\) | 6.32456i | 0.276553i | 0.990394 | + | 0.138277i | \(0.0441563\pi\) | ||||
−0.990394 | + | 0.138277i | \(0.955844\pi\) | |||||||
\(524\) | 9.00000 | − | 34.8569i | 0.393167 | − | 1.52273i | ||||
\(525\) | 11.0227 | + | 8.21584i | 0.481070 | + | 0.358569i | ||||
\(526\) | 10.0000 | − | 7.74597i | 0.436021 | − | 0.337740i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 7.34924 | + | 21.7713i | 0.319835 | + | 0.947473i | ||||
\(529\) | −17.0000 | −0.739130 | ||||||||
\(530\) | 15.0000 | − | 11.6190i | 0.651558 | − | 0.504695i | ||||
\(531\) | 32.8634i | 1.42615i | ||||||||
\(532\) | −20.9808 | − | 26.0731i | −0.909631 | − | 1.13041i | ||||
\(533\) | − | 18.9737i | − | 0.821841i | ||||||
\(534\) | −4.24264 | − | 5.47723i | −0.183597 | − | 0.237023i | ||||
\(535\) | 6.32456i | 0.273434i | ||||||||
\(536\) | −8.66025 | − | 20.1246i | −0.374066 | − | 0.869251i | ||||
\(537\) | −25.4558 | −1.09850 | ||||||||
\(538\) | 8.57321 | + | 11.0680i | 0.369618 | + | 0.477174i | ||||
\(539\) | −10.1010 | + | 20.9038i | −0.435082 | + | 0.900391i | ||||
\(540\) | −3.67423 | + | 14.2302i | −0.158114 | + | 0.612372i | ||||
\(541\) | 38.3406i | 1.64839i | 0.566306 | + | 0.824195i | \(0.308372\pi\) | ||||
−0.566306 | + | 0.824195i | \(0.691628\pi\) | |||||||
\(542\) | 17.6777 | − | 13.6931i | 0.759321 | − | 0.588167i | ||||
\(543\) | 23.2379i | 0.997234i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.74597i | 0.331801i | ||||||||
\(546\) | −0.294229 | − | 15.8718i | −0.0125918 | − | 0.679250i | ||||
\(547\) | 16.9706 | 0.725609 | 0.362804 | − | 0.931865i | \(-0.381819\pi\) | ||||
0.362804 | + | 0.931865i | \(0.381819\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.0454 | 0.940875 | ||||||||
\(550\) | 1.13604 | − | 14.0253i | 0.0484409 | − | 0.598041i | ||||
\(551\) | − | 43.8178i | − | 1.86670i | ||||||
\(552\) | −11.0227 | + | 4.74342i | −0.469157 | + | 0.201893i | ||||
\(553\) | −9.00000 | − | 6.70820i | −0.382719 | − | 0.285262i | ||||
\(554\) | −6.12372 | + | 4.74342i | −0.260172 | + | 0.201528i | ||||
\(555\) | 4.89898 | 0.207950 | ||||||||
\(556\) | 24.4949 | + | 6.32456i | 1.03882 | + | 0.268221i | ||||
\(557\) | 6.92820 | 0.293557 | 0.146779 | − | 0.989169i | \(-0.453109\pi\) | ||||
0.146779 | + | 0.989169i | \(0.453109\pi\) | |||||||
\(558\) | −9.00000 | − | 11.6190i | −0.381000 | − | 0.491869i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 6.16987 | + | 13.6357i | 0.260725 | + | 0.576214i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.00000 | + | 3.87298i | 0.126547 | + | 0.163372i | ||||
\(563\) | −36.0000 | −1.51722 | −0.758610 | − | 0.651546i | \(-0.774121\pi\) | ||||
−0.758610 | + | 0.651546i | \(0.774121\pi\) | |||||||
\(564\) | −18.3712 | − | 4.74342i | −0.773566 | − | 0.199734i | ||||
\(565\) | 26.8328i | 1.12887i | ||||||||
\(566\) | −28.2843 | + | 21.9089i | −1.18888 | + | 0.920900i | ||||
\(567\) | 19.0919 | + | 14.2302i | 0.801784 | + | 0.597614i | ||||
\(568\) | 31.8198 | − | 13.6931i | 1.33513 | − | 0.574548i | ||||
\(569\) | 10.3923 | 0.435668 | 0.217834 | − | 0.975986i | \(-0.430101\pi\) | ||||
0.217834 | + | 0.975986i | \(0.430101\pi\) | |||||||
\(570\) | −17.3205 | + | 13.4164i | −0.725476 | + | 0.561951i | ||||
\(571\) | −8.48528 | −0.355098 | −0.177549 | − | 0.984112i | \(-0.556817\pi\) | ||||
−0.177549 | + | 0.984112i | \(0.556817\pi\) | |||||||
\(572\) | −13.6066 | + | 8.88034i | −0.568921 | + | 0.371306i | ||||
\(573\) | 21.2132 | 0.886194 | ||||||||
\(574\) | 28.9778 | − | 0.537186i | 1.20951 | − | 0.0224217i | ||||
\(575\) | 7.34847 | 0.306452 | ||||||||
\(576\) | 16.5000 | − | 17.4284i | 0.687500 | − | 0.726184i | ||||
\(577\) | 40.2492i | 1.67560i | 0.545979 | + | 0.837799i | \(0.316158\pi\) | ||||
−0.545979 | + | 0.837799i | \(0.683842\pi\) | |||||||
\(578\) | 14.7224 | + | 19.0066i | 0.612372 | + | 0.790569i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.89898 | + | 18.9737i | −0.203419 | + | 0.787839i | ||||
\(581\) | −12.7279 | − | 9.48683i | −0.528043 | − | 0.393580i | ||||
\(582\) | 25.9808 | − | 20.1246i | 1.07694 | − | 0.834192i | ||||
\(583\) | −21.2132 | + | 23.2379i | −0.878561 | + | 0.962415i | ||||
\(584\) | −25.4558 | + | 10.9545i | −1.05337 | + | 0.453298i | ||||
\(585\) | −10.3923 | −0.429669 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.9545i | 0.452139i | 0.974111 | + | 0.226069i | \(0.0725876\pi\) | ||||
−0.974111 | + | 0.226069i | \(0.927412\pi\) | |||||||
\(588\) | 24.2321 | − | 0.898729i | 0.999313 | − | 0.0370630i | ||||
\(589\) | − | 21.9089i | − | 0.902741i | ||||||
\(590\) | 17.3205 | − | 13.4164i | 0.713074 | − | 0.552345i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.00000 | − | 3.87298i | −0.287698 | − | 0.159179i | ||||
\(593\) | 30.9839i | 1.27235i | 0.771543 | + | 0.636177i | \(0.219485\pi\) | ||||
−0.771543 | + | 0.636177i | \(0.780515\pi\) | |||||||
\(594\) | 1.96768 | − | 24.2926i | 0.0807348 | − | 0.996736i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.46410 | + | 13.4164i | −0.141895 | + | 0.549557i | ||||
\(597\) | −42.0000 | −1.71895 | ||||||||
\(598\) | −5.19615 | − | 6.70820i | −0.212486 | − | 0.274319i | ||||
\(599\) | −26.9444 | −1.10092 | −0.550459 | − | 0.834862i | \(-0.685547\pi\) | ||||
−0.550459 | + | 0.834862i | \(0.685547\pi\) | |||||||
\(600\) | −13.5000 | + | 5.80948i | −0.551135 | + | 0.237171i | ||||
\(601\) | 19.5959 | 0.799334 | 0.399667 | − | 0.916660i | \(-0.369126\pi\) | ||||
0.399667 | + | 0.916660i | \(0.369126\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.2379i | 0.946320i | ||||||||
\(604\) | −6.36396 | + | 24.6475i | −0.258946 | + | 1.00289i | ||||
\(605\) | −1.41421 | − | 15.4919i | −0.0574960 | − | 0.629837i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.16228i | 0.128353i | 0.997939 | + | 0.0641764i | \(0.0204420\pi\) | ||||
−0.997939 | + | 0.0641764i | \(0.979558\pi\) | |||||||
\(608\) | 35.3553 | − | 5.47723i | 1.43385 | − | 0.222131i | ||||
\(609\) | 25.4558 | + | 18.9737i | 1.03152 | + | 0.768852i | ||||
\(610\) | −9.00000 | − | 11.6190i | −0.364399 | − | 0.470438i | ||||
\(611\) | − | 13.4164i | − | 0.542770i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 27.3861i | − | 1.10612i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) | ||
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(614\) | 28.2843 | − | 21.9089i | 1.14146 | − | 0.884171i | ||||
\(615\) | − | 18.9737i | − | 0.765092i | ||||||
\(616\) | −13.9478 | − | 20.5294i | −0.561975 | − | 0.827155i | ||||
\(617\) | − | 18.9737i | − | 0.763851i | −0.924193 | − | 0.381926i | \(-0.875261\pi\) | ||
0.924193 | − | 0.381926i | \(-0.124739\pi\) | |||||||
\(618\) | 5.19615 | + | 6.70820i | 0.209020 | + | 0.269844i | ||||
\(619\) | −27.7128 | −1.11387 | −0.556936 | − | 0.830555i | \(-0.688023\pi\) | ||||
−0.556936 | + | 0.830555i | \(0.688023\pi\) | |||||||
\(620\) | −2.44949 | + | 9.48683i | −0.0983739 | + | 0.381000i | ||||
\(621\) | 12.7279 | 0.510754 | ||||||||
\(622\) | −18.3712 | + | 14.2302i | −0.736617 | + | 0.570581i | ||||
\(623\) | 6.00000 | + | 4.47214i | 0.240385 | + | 0.179172i | ||||
\(624\) | 14.8492 | + | 8.21584i | 0.594445 | + | 0.328897i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.4949 | − | 26.8328i | 0.978232 | − | 1.07160i | ||||
\(628\) | −25.9808 | − | 6.70820i | −1.03675 | − | 0.267686i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −0.294229 | − | 15.8718i | −0.0117223 | − | 0.632347i | ||||
\(631\) | 23.2379i | 0.925086i | 0.886597 | + | 0.462543i | \(0.153063\pi\) | ||||
−0.886597 | + | 0.462543i | \(0.846937\pi\) | |||||||
\(632\) | 11.0227 | − | 4.74342i | 0.438460 | − | 0.188683i | ||||
\(633\) | −14.6969 | −0.584151 | ||||||||
\(634\) | −31.8198 | + | 24.6475i | −1.26373 | + | 0.978878i | ||||
\(635\) | −30.0000 | −1.19051 | ||||||||
\(636\) | 31.8198 | + | 8.21584i | 1.26174 | + | 0.325779i | ||||
\(637\) | 4.89898 | + | 16.4317i | 0.194105 | + | 0.651047i | ||||
\(638\) | 2.62357 | − | 32.3901i | 0.103868 | − | 1.28234i | ||||
\(639\) | −36.7423 | −1.45350 | ||||||||
\(640\) | −15.9217 | − | 1.58114i | −0.629360 | − | 0.0625000i | ||||
\(641\) | 18.9737i | 0.749415i | 0.927143 | + | 0.374707i | \(0.122257\pi\) | ||||
−0.927143 | + | 0.374707i | \(0.877743\pi\) | |||||||
\(642\) | −8.66025 | + | 6.70820i | −0.341793 | + | 0.264752i | ||||
\(643\) | −34.6410 | −1.36611 | −0.683054 | − | 0.730368i | \(-0.739349\pi\) | ||||
−0.683054 | + | 0.730368i | \(0.739349\pi\) | |||||||
\(644\) | 10.0981 | − | 8.12581i | 0.397920 | − | 0.320202i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.47723i | 0.215332i | 0.994187 | + | 0.107666i | \(0.0343377\pi\) | ||||
−0.994187 | + | 0.107666i | \(0.965662\pi\) | |||||||
\(648\) | −23.3827 | + | 10.0623i | −0.918559 | + | 0.395285i | ||||
\(649\) | −24.4949 | + | 26.8328i | −0.961509 | + | 1.05328i | ||||
\(650\) | −6.36396 | − | 8.21584i | −0.249615 | − | 0.322252i | ||||
\(651\) | 12.7279 | + | 9.48683i | 0.498847 | + | 0.371818i | ||||
\(652\) | −30.0000 | − | 7.74597i | −1.17489 | − | 0.303355i | ||||
\(653\) | 9.48683i | 0.371248i | 0.982621 | + | 0.185624i | \(0.0594307\pi\) | ||||
−0.982621 | + | 0.185624i | \(0.940569\pi\) | |||||||
\(654\) | −10.6066 | + | 8.21584i | −0.414751 | + | 0.321265i | ||||
\(655\) | 25.4558 | 0.994642 | ||||||||
\(656\) | −15.0000 | + | 27.1109i | −0.585652 | + | 1.05850i | ||||
\(657\) | 29.3939 | 1.14676 | ||||||||
\(658\) | 20.4904 | − | 0.379848i | 0.798798 | − | 0.0148080i | ||||
\(659\) | 49.1935i | 1.91631i | 0.286256 | + | 0.958153i | \(0.407589\pi\) | ||||
−0.286256 | + | 0.958153i | \(0.592411\pi\) | |||||||
\(660\) | −13.6066 | + | 8.88034i | −0.529636 | + | 0.345667i | ||||
\(661\) | − | 13.4164i | − | 0.521838i | −0.965361 | − | 0.260919i | \(-0.915974\pi\) | ||
0.965361 | − | 0.260919i | \(-0.0840255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.5885 | − | 6.70820i | 0.604949 | − | 0.260329i | ||||
\(665\) | 14.1421 | − | 18.9737i | 0.548408 | − | 0.735767i | ||||
\(666\) | 5.19615 | + | 6.70820i | 0.201347 | + | 0.259938i | ||||
\(667\) | 16.9706 | 0.657103 | ||||||||
\(668\) | −6.00000 | + | 23.2379i | −0.232147 | + | 0.899101i | ||||
\(669\) | 30.0000 | 1.15987 | ||||||||
\(670\) | 12.2474 | − | 9.48683i | 0.473160 | − | 0.366508i | ||||
\(671\) | 18.0000 | + | 16.4317i | 0.694882 | + | 0.634338i | ||||
\(672\) | −12.1273 | + | 22.9113i | −0.467822 | + | 0.883823i | ||||
\(673\) | 32.8634i | 1.26679i | 0.773829 | + | 0.633395i | \(0.218339\pi\) | ||||
−0.773829 | + | 0.633395i | \(0.781661\pi\) | |||||||
\(674\) | −12.2474 | + | 9.48683i | −0.471754 | + | 0.365419i | ||||
\(675\) | 15.5885 | 0.600000 | ||||||||
\(676\) | 3.50000 | − | 13.5554i | 0.134615 | − | 0.521363i | ||||
\(677\) | − | 30.9839i | − | 1.19081i | −0.803427 | − | 0.595403i | \(-0.796992\pi\) | ||
0.803427 | − | 0.595403i | \(-0.203008\pi\) | |||||||
\(678\) | −36.7423 | + | 28.4605i | −1.41108 | + | 1.09302i | ||||
\(679\) | −21.2132 | + | 28.4605i | −0.814088 | + | 1.09221i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.7846 | −0.796468 | ||||||||
\(682\) | 1.31178 | − | 16.1950i | 0.0502308 | − | 0.620140i | ||||
\(683\) | −9.79796 | −0.374908 | −0.187454 | − | 0.982273i | \(-0.560024\pi\) | ||||
−0.187454 | + | 0.982273i | \(0.560024\pi\) | |||||||
\(684\) | −36.7423 | − | 9.48683i | −1.40488 | − | 0.362738i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.9568 | + | 7.94725i | −0.952855 | + | 0.303427i | ||||
\(687\) | 23.2379i | 0.886581i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.2379i | 0.885293i | ||||||||
\(690\) | −5.19615 | − | 6.70820i | −0.197814 | − | 0.255377i | ||||
\(691\) | −20.7846 | −0.790684 | −0.395342 | − | 0.918534i | \(-0.629374\pi\) | ||||
−0.395342 | + | 0.918534i | \(0.629374\pi\) | |||||||
\(692\) | −30.0000 | − | 7.74597i | −1.14043 | − | 0.294457i | ||||
\(693\) | 4.98186 | + | 25.8492i | 0.189245 | + | 0.981930i | ||||
\(694\) | −20.0000 | + | 15.4919i | −0.759190 | + | 0.588066i | ||||
\(695\) | 17.8885i | 0.678551i | ||||||||
\(696\) | −31.1769 | + | 13.4164i | −1.18176 | + | 0.508548i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 10.6066 | + | 13.6931i | 0.401466 | + | 0.518290i | ||||
\(699\) | −36.0000 | −1.36165 | ||||||||
\(700\) | 12.3676 | − | 9.95205i | 0.467450 | − | 0.376152i | ||||
\(701\) | 20.7846 | 0.785024 | 0.392512 | − | 0.919747i | \(-0.371606\pi\) | ||||
0.392512 | + | 0.919747i | \(0.371606\pi\) | |||||||
\(702\) | −11.0227 | − | 14.2302i | −0.416025 | − | 0.537086i | ||||
\(703\) | 12.6491i | 0.477070i | ||||||||
\(704\) | 26.4626 | − | 1.93188i | 0.997346 | − | 0.0728103i | ||||
\(705\) | − | 13.4164i | − | 0.505291i | ||||||
\(706\) | 19.5959 | + | 25.2982i | 0.737502 | + | 0.952111i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 36.7423 | + | 9.48683i | 1.38086 | + | 0.356537i | ||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 15.0000 | + | 19.3649i | 0.562940 | + | 0.726752i | ||||
\(711\) | −12.7279 | −0.477334 | ||||||||
\(712\) | −7.34847 | + | 3.16228i | −0.275396 | + | 0.118511i | ||||
\(713\) | 8.48528 | 0.317776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.48528 | − | 7.74597i | −0.317332 | − | 0.289683i | ||||
\(716\) | −7.34847 | + | 28.4605i | −0.274625 | + | 1.06362i | ||||
\(717\) | 15.4919i | 0.578557i | ||||||||
\(718\) | −20.0000 | + | 15.4919i | −0.746393 | + | 0.578154i | ||||
\(719\) | − | 5.47723i | − | 0.204266i | −0.994771 | − | 0.102133i | \(-0.967433\pi\) | ||
0.994771 | − | 0.102133i | \(-0.0325667\pi\) | |||||||
\(720\) | 14.8492 | + | 8.21584i | 0.553399 | + | 0.306186i | ||||
\(721\) | −7.34847 | − | 5.47723i | −0.273671 | − | 0.203983i | ||||
\(722\) | −18.1865 | − | 23.4787i | −0.676833 | − | 0.873787i | ||||
\(723\) | 42.4264 | 1.57786 | ||||||||
\(724\) | 25.9808 | + | 6.70820i | 0.965567 | + | 0.249308i | ||||
\(725\) | 20.7846 | 0.771921 | ||||||||
\(726\) | 19.7132 | − | 18.3682i | 0.731626 | − | 0.681707i | ||||
\(727\) | −10.3923 | −0.385429 | −0.192715 | − | 0.981255i | \(-0.561729\pi\) | ||||
−0.192715 | + | 0.981255i | \(0.561729\pi\) | |||||||
\(728\) | −17.8301 | − | 4.25283i | −0.660828 | − | 0.157620i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −12.0000 | − | 15.4919i | −0.444140 | − | 0.573382i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 6.36396 | − | 24.6475i | 0.235219 | − | 0.910998i | ||||
\(733\) | −22.0454 | −0.814266 | −0.407133 | − | 0.913369i | \(-0.633471\pi\) | ||||
−0.407133 | + | 0.913369i | \(0.633471\pi\) | |||||||
\(734\) | 15.0000 | + | 19.3649i | 0.553660 | + | 0.714772i | ||||
\(735\) | 4.89898 | + | 16.4317i | 0.180702 | + | 0.606092i | ||||
\(736\) | 2.12132 | + | 13.6931i | 0.0781929 | + | 0.504733i | ||||
\(737\) | −17.3205 | + | 18.9737i | −0.638009 | + | 0.698904i | ||||
\(738\) | 25.9808 | − | 20.1246i | 0.956365 | − | 0.740797i | ||||
\(739\) | 25.4558 | 0.936408 | 0.468204 | − | 0.883620i | \(-0.344901\pi\) | ||||
0.468204 | + | 0.883620i | \(0.344901\pi\) | |||||||
\(740\) | 1.41421 | − | 5.47723i | 0.0519875 | − | 0.201347i | ||||
\(741\) | − | 26.8328i | − | 0.985728i | ||||||
\(742\) | −35.4904 | + | 0.657915i | −1.30289 | + | 0.0241528i | ||||
\(743\) | − | 44.7214i | − | 1.64067i | −0.571885 | − | 0.820334i | \(-0.693788\pi\) | ||
0.571885 | − | 0.820334i | \(-0.306212\pi\) | |||||||
\(744\) | −15.5885 | + | 6.70820i | −0.571501 | + | 0.245935i | ||||
\(745\) | −9.79796 | −0.358969 | ||||||||
\(746\) | 6.12372 | − | 4.74342i | 0.224205 | − | 0.173669i | ||||
\(747\) | −18.0000 | −0.658586 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.07107 | − | 9.48683i | 0.258371 | − | 0.346641i | ||||
\(750\) | −16.9706 | − | 21.9089i | −0.619677 | − | 0.800000i | ||||
\(751\) | − | 38.7298i | − | 1.41327i | −0.707577 | − | 0.706636i | \(-0.750212\pi\) | ||
0.707577 | − | 0.706636i | \(-0.249788\pi\) | |||||||
\(752\) | −10.6066 | + | 19.1703i | −0.386783 | + | 0.699069i | ||||
\(753\) | − | 37.9473i | − | 1.38288i | ||||||
\(754\) | −14.6969 | − | 18.9737i | −0.535231 | − | 0.690980i | ||||
\(755\) | −18.0000 | −0.655087 | ||||||||
\(756\) | 21.4213 | − | 17.2375i | 0.779083 | − | 0.626920i | ||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | 17.3205 | − | 13.4164i | 0.629109 | − | 0.487306i | ||||
\(759\) | 10.3923 | + | 9.48683i | 0.377217 | + | 0.344350i | ||||
\(760\) | 10.0000 | + | 23.2379i | 0.362738 | + | 0.842927i | ||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | −31.8198 | − | 41.0792i | −1.15271 | − | 1.48814i | ||||
\(763\) | 8.66025 | − | 11.6190i | 0.313522 | − | 0.420634i | ||||
\(764\) | 6.12372 | − | 23.7171i | 0.221549 | − | 0.858054i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.3712 | + | 14.2302i | −0.663777 | + | 0.514160i | ||||
\(767\) | 26.8328i | 0.968877i | ||||||||
\(768\) | −14.7224 | − | 23.4787i | −0.531250 | − | 0.847215i | ||||
\(769\) | 24.4949 | 0.883309 | 0.441654 | − | 0.897185i | \(-0.354392\pi\) | ||||
0.441654 | + | 0.897185i | \(0.354392\pi\) | |||||||
\(770\) | 11.5899 | − | 13.1786i | 0.417671 | − | 0.474922i | ||||
\(771\) | −24.4949 | −0.882162 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.07107 | −0.254329 | −0.127164 | − | 0.991882i | \(-0.540588\pi\) | ||||
−0.127164 | + | 0.991882i | \(0.540588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3923 | 0.373303 | ||||||||
\(776\) | −15.0000 | − | 34.8569i | −0.538469 | − | 1.25129i | ||||
\(777\) | −7.34847 | − | 5.47723i | −0.263625 | − | 0.196494i | ||||
\(778\) | 31.8198 | − | 24.6475i | 1.14080 | − | 0.883656i | ||||
\(779\) | 48.9898 | 1.75524 | ||||||||
\(780\) | −3.00000 | + | 11.6190i | −0.107417 | + | 0.416025i | ||||
\(781\) | −30.0000 | − | 27.3861i | −1.07348 | − | 0.979953i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 36.0000 | 1.28654 | ||||||||
\(784\) | 5.99038 | − | 27.3517i | 0.213942 | − | 0.976846i | ||||
\(785\) | − | 18.9737i | − | 0.677199i | ||||||
\(786\) | 27.0000 | + | 34.8569i | 0.963058 | + | 1.24330i | ||||
\(787\) | 31.6228i | 1.12723i | 0.826038 | + | 0.563615i | \(0.190590\pi\) | ||||
−0.826038 | + | 0.563615i | \(0.809410\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.4919i | 0.551527i | ||||||||
\(790\) | 5.19615 | + | 6.70820i | 0.184871 | + | 0.238667i | ||||
\(791\) | 30.0000 | − | 40.2492i | 1.06668 | − | 1.43110i | ||||
\(792\) | −26.5919 | − | 9.21259i | −0.944901 | − | 0.327355i | ||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | 15.0000 | − | 11.6190i | 0.532330 | − | 0.412341i | ||||
\(795\) | 23.2379i | 0.824163i | ||||||||
\(796\) | −12.1244 | + | 46.9574i | −0.429736 | + | 1.66436i | ||||
\(797\) | 49.4975 | 1.75329 | 0.876645 | − | 0.481137i | \(-0.159776\pi\) | ||||
0.876645 | + | 0.481137i | \(0.159776\pi\) | |||||||
\(798\) | 40.9808 | − | 0.759695i | 1.45070 | − | 0.0268929i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 2.59808 | + | 16.7705i | 0.0918559 | + | 0.592927i | ||||
\(801\) | 8.48528 | 0.299813 | ||||||||
\(802\) | −21.2132 | + | 16.4317i | −0.749064 | + | 0.580223i | ||||
\(803\) | 24.0000 | + | 21.9089i | 0.846942 | + | 0.773148i | ||||
\(804\) | 25.9808 | + | 6.70820i | 0.916271 | + | 0.236580i | ||||
\(805\) | 7.34847 | + | 5.47723i | 0.259000 | + | 0.193047i | ||||
\(806\) | −7.34847 | − | 9.48683i | −0.258839 | − | 0.334159i | ||||
\(807\) | −17.1464 | −0.603583 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.92820 | 0.243583 | 0.121791 | − | 0.992556i | \(-0.461136\pi\) | ||||
0.121791 | + | 0.992556i | \(0.461136\pi\) | |||||||
\(810\) | −11.0227 | − | 14.2302i | −0.387298 | − | 0.500000i | ||||
\(811\) | − | 6.32456i | − | 0.222085i | −0.993816 | − | 0.111043i | \(-0.964581\pi\) | ||
0.993816 | − | 0.111043i | \(-0.0354190\pi\) | |||||||
\(812\) | 28.5617 | − | 22.9833i | 1.00232 | − | 0.806555i | ||||
\(813\) | 27.3861i | 0.960473i | ||||||||
\(814\) | −0.757359 | + | 9.35021i | −0.0265454 | + | 0.327725i | ||||
\(815\) | − | 21.9089i | − | 0.767435i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.5885 | + | 11.6190i | 0.544705 | + | 0.405999i | ||||
\(820\) | −21.2132 | − | 5.47723i | −0.740797 | − | 0.191273i | ||||
\(821\) | 48.4974 | 1.69257 | 0.846286 | − | 0.532729i | \(-0.178834\pi\) | ||||
0.846286 | + | 0.532729i | \(0.178834\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 38.7298i | − | 1.35004i | −0.737801 | − | 0.675019i | \(-0.764136\pi\) | ||
0.737801 | − | 0.675019i | \(-0.235864\pi\) | |||||||
\(824\) | 9.00000 | − | 3.87298i | 0.313530 | − | 0.134922i | ||||
\(825\) | 12.7279 | + | 11.6190i | 0.443129 | + | 0.404520i | ||||
\(826\) | −40.9808 | + | 0.759695i | −1.42590 | + | 0.0264332i | ||||
\(827\) | 17.8885i | 0.622046i | 0.950402 | + | 0.311023i | \(0.100672\pi\) | ||||
−0.950402 | + | 0.311023i | \(0.899328\pi\) | |||||||
\(828\) | 3.67423 | − | 14.2302i | 0.127688 | − | 0.494535i | ||||
\(829\) | 13.4164i | 0.465971i | 0.972480 | + | 0.232986i | \(0.0748495\pi\) | ||||
−0.972480 | + | 0.232986i | \(0.925151\pi\) | |||||||
\(830\) | 7.34847 | + | 9.48683i | 0.255069 | + | 0.329293i | ||||
\(831\) | − | 9.48683i | − | 0.329095i | ||||||
\(832\) | 13.4722 | − | 14.2302i | 0.467064 | − | 0.493345i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −24.4949 | + | 18.9737i | −0.848189 | + | 0.657004i | ||||
\(835\) | −16.9706 | −0.587291 | ||||||||
\(836\) | −22.9289 | − | 35.1321i | −0.793014 | − | 1.21507i | ||||
\(837\) | 18.0000 | 0.622171 | ||||||||
\(838\) | 24.4949 | − | 18.9737i | 0.846162 | − | 0.655434i | ||||
\(839\) | − | 38.3406i | − | 1.32366i | −0.749652 | − | 0.661832i | \(-0.769779\pi\) | ||
0.749652 | − | 0.661832i | \(-0.230221\pi\) | |||||||
\(840\) | −17.8301 | − | 4.25283i | −0.615198 | − | 0.146737i | ||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | −8.66025 | − | 11.1803i | −0.298452 | − | 0.385300i | ||||
\(843\) | −6.00000 | −0.206651 | ||||||||
\(844\) | −4.24264 | + | 16.4317i | −0.146038 | + | 0.565602i | ||||
\(845\) | 9.89949 | 0.340553 | ||||||||
\(846\) | 18.3712 | − | 14.2302i | 0.631614 | − | 0.489246i | ||||
\(847\) | −15.1992 | + | 24.8190i | −0.522250 | + | 0.852792i | ||||
\(848\) | 18.3712 | − | 33.2039i | 0.630869 | − | 1.14023i | ||||
\(849\) | − | 43.8178i | − | 1.50382i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.89898 | −0.167935 | ||||||||
\(852\) | −10.6066 | + | 41.0792i | −0.363376 | + | 1.40735i | ||||
\(853\) | 22.0454 | 0.754820 | 0.377410 | − | 0.926046i | \(-0.376815\pi\) | ||||
0.377410 | + | 0.926046i | \(0.376815\pi\) | |||||||
\(854\) | 0.509619 | + | 27.4907i | 0.0174388 | + | 0.940713i | ||||
\(855\) | − | 26.8328i | − | 0.917663i | ||||||
\(856\) | 5.00000 | + | 11.6190i | 0.170896 | + | 0.397128i | ||||
\(857\) | 7.74597i | 0.264597i | 0.991210 | + | 0.132299i | \(0.0422358\pi\) | ||||
−0.991210 | + | 0.132299i | \(0.957764\pi\) | |||||||
\(858\) | 1.60660 | − | 19.8348i | 0.0548485 | − | 0.677149i | ||||
\(859\) | −45.0333 | −1.53652 | −0.768259 | − | 0.640140i | \(-0.778876\pi\) | ||||
−0.768259 | + | 0.640140i | \(0.778876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.2132 | + | 28.4605i | −0.722944 | + | 0.969931i | ||||
\(862\) | 20.0000 | − | 15.4919i | 0.681203 | − | 0.527657i | ||||
\(863\) | −51.4393 | −1.75101 | −0.875507 | − | 0.483206i | \(-0.839472\pi\) | ||||
−0.875507 | + | 0.483206i | \(0.839472\pi\) | |||||||
\(864\) | 4.50000 | + | 29.0474i | 0.153093 | + | 0.988212i | ||||
\(865\) | − | 21.9089i | − | 0.744925i | ||||||
\(866\) | 30.0000 | − | 23.2379i | 1.01944 | − | 0.789656i | ||||
\(867\) | −29.4449 | −1.00000 | ||||||||
\(868\) | 14.2808 | − | 11.4916i | 0.484723 | − | 0.390052i | ||||
\(869\) | −10.3923 | − | 9.48683i | −0.352535 | − | 0.321819i | ||||
\(870\) | −14.6969 | − | 18.9737i | −0.498273 | − | 0.643268i | ||||
\(871\) | 18.9737i | 0.642898i | ||||||||
\(872\) | 6.12372 | + | 14.2302i | 0.207375 | + | 0.481897i | ||||
\(873\) | 40.2492i | 1.36223i | ||||||||
\(874\) | 17.3205 | − | 13.4164i | 0.585875 | − | 0.453817i | ||||
\(875\) | 24.0000 | + | 17.8885i | 0.811348 | + | 0.604743i | ||||
\(876\) | 8.48528 | − | 32.8634i | 0.286691 | − | 1.11035i | ||||
\(877\) | − | 49.2950i | − | 1.66457i | −0.554344 | − | 0.832287i | \(-0.687031\pi\) | ||
0.554344 | − | 0.832287i | \(-0.312969\pi\) | |||||||
\(878\) | 38.8909 | − | 30.1247i | 1.31250 | − | 1.01666i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.00063 | + | 17.7762i | 0.202281 | + | 0.599235i | ||||
\(881\) | −5.65685 | −0.190584 | −0.0952921 | − | 0.995449i | \(-0.530379\pi\) | ||||
−0.0952921 | + | 0.995449i | \(0.530379\pi\) | |||||||
\(882\) | −17.3038 | + | 24.1366i | −0.582651 | + | 0.812723i | ||||
\(883\) | 7.74597i | 0.260673i | 0.991470 | + | 0.130336i | \(0.0416057\pi\) | ||||
−0.991470 | + | 0.130336i | \(0.958394\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.8328i | 0.901975i | ||||||||
\(886\) | 33.9411 | + | 43.8178i | 1.14027 | + | 1.47209i | ||||
\(887\) | 48.0000 | 1.61168 | 0.805841 | − | 0.592132i | \(-0.201714\pi\) | ||||
0.805841 | + | 0.592132i | \(0.201714\pi\) | |||||||
\(888\) | 9.00000 | − | 3.87298i | 0.302020 | − | 0.129969i | ||||
\(889\) | 45.0000 | + | 33.5410i | 1.50925 | + | 1.12493i | ||||
\(890\) | −3.46410 | − | 4.47214i | −0.116117 | − | 0.149906i | ||||
\(891\) | 22.0454 | + | 20.1246i | 0.738549 | + | 0.674200i | ||||
\(892\) | 8.66025 | − | 33.5410i | 0.289967 | − | 1.12304i | ||||
\(893\) | 34.6410 | 1.15922 | ||||||||
\(894\) | −10.3923 | − | 13.4164i | −0.347571 | − | 0.448712i | ||||
\(895\) | −20.7846 | −0.694753 | ||||||||
\(896\) | 22.1148 | + | 20.1727i | 0.738802 | + | 0.673922i | ||||
\(897\) | 10.3923 | 0.346989 | ||||||||
\(898\) | −42.4264 | + | 32.8634i | −1.41579 | + | 1.09666i | ||||
\(899\) | 24.0000 | 0.800445 | ||||||||
\(900\) | 4.50000 | − | 17.4284i | 0.150000 | − | 0.580948i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 36.2132 | + | 2.93324i | 1.20577 | + | 0.0976662i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.2132 | + | 49.2950i | 0.705541 | + | 1.63953i | ||||
\(905\) | 18.9737i | 0.630706i | ||||||||
\(906\) | −19.0919 | − | 24.6475i | −0.634285 | − | 0.818859i | ||||
\(907\) | − | 23.2379i | − | 0.771602i | −0.922582 | − | 0.385801i | \(-0.873925\pi\) | ||
0.922582 | − | 0.385801i | \(-0.126075\pi\) | |||||||
\(908\) | −6.00000 | + | 23.2379i | −0.199117 | + | 0.771177i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.240237 | − | 12.9593i | −0.00796377 | − | 0.429595i | ||||
\(911\) | 36.7423 | 1.21733 | 0.608664 | − | 0.793428i | \(-0.291706\pi\) | ||||
0.608664 | + | 0.793428i | \(0.291706\pi\) | |||||||
\(912\) | −21.2132 | + | 38.3406i | −0.702439 | + | 1.26958i | ||||
\(913\) | −14.6969 | − | 13.4164i | −0.486398 | − | 0.444018i | ||||
\(914\) | −12.2474 | + | 9.48683i | −0.405110 | + | 0.313797i | ||||
\(915\) | 18.0000 | 0.595062 | ||||||||
\(916\) | 25.9808 | + | 6.70820i | 0.858429 | + | 0.221645i | ||||
\(917\) | −38.1838 | − | 28.4605i | −1.26094 | − | 0.939848i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.24264 | −0.139952 | −0.0699759 | − | 0.997549i | \(-0.522292\pi\) | ||||
−0.0699759 | + | 0.997549i | \(0.522292\pi\) | |||||||
\(920\) | −9.00000 | + | 3.87298i | −0.296721 | + | 0.127688i | ||||
\(921\) | 43.8178i | 1.44385i | ||||||||
\(922\) | 34.6410 | − | 26.8328i | 1.14084 | − | 0.883692i | ||||
\(923\) | −30.0000 | −0.987462 | ||||||||
\(924\) | 30.3384 | + | 1.89214i | 0.998061 | + | 0.0622467i | ||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 8.66025 | − | 6.70820i | 0.284594 | − | 0.220445i | ||||
\(927\) | −10.3923 | −0.341328 | ||||||||
\(928\) | 6.00000 | + | 38.7298i | 0.196960 | + | 1.27137i | ||||
\(929\) | 45.2548 | 1.48476 | 0.742381 | − | 0.669977i | \(-0.233696\pi\) | ||||
0.742381 | + | 0.669977i | \(0.233696\pi\) | |||||||
\(930\) | −7.34847 | − | 9.48683i | −0.240966 | − | 0.311086i | ||||
\(931\) | −42.4264 | + | 12.6491i | −1.39047 | + | 0.414558i | ||||
\(932\) | −10.3923 | + | 40.2492i | −0.340411 | + | 1.31841i | ||||
\(933\) | − | 28.4605i | − | 0.931755i | ||||||
\(934\) | 12.2474 | − | 9.48683i | 0.400749 | − | 0.310419i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −19.0919 | + | 8.21584i | −0.624038 | + | 0.268543i | ||||
\(937\) | 44.0908 | 1.44038 | 0.720192 | − | 0.693775i | \(-0.244054\pi\) | ||||
0.720192 | + | 0.693775i | \(0.244054\pi\) | |||||||
\(938\) | −28.9778 | + | 0.537186i | −0.946158 | + | 0.0175397i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.0000 | − | 3.87298i | −0.489246 | − | 0.126323i | ||||
\(941\) | 15.4919i | 0.505023i | 0.967594 | + | 0.252511i | \(0.0812565\pi\) | ||||
−0.967594 | + | 0.252511i | \(0.918744\pi\) | |||||||
\(942\) | 25.9808 | − | 20.1246i | 0.846499 | − | 0.655695i | ||||
\(943\) | 18.9737i | 0.617868i | ||||||||
\(944\) | 21.2132 | − | 38.3406i | 0.690431 | − | 1.24788i | ||||
\(945\) | 15.5885 | + | 11.6190i | 0.507093 | + | 0.377964i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.5959 | 0.636782 | 0.318391 | − | 0.947960i | \(-0.396858\pi\) | ||||
0.318391 | + | 0.947960i | \(0.396858\pi\) | |||||||
\(948\) | −3.67423 | + | 14.2302i | −0.119334 | + | 0.462177i | ||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 21.2132 | − | 16.4317i | 0.688247 | − | 0.533114i | ||||
\(951\) | − | 49.2950i | − | 1.59850i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.6410 | −1.12213 | −0.561066 | − | 0.827771i | \(-0.689609\pi\) | ||||
−0.561066 | + | 0.827771i | \(0.689609\pi\) | |||||||
\(954\) | −31.8198 | + | 24.6475i | −1.03020 | + | 0.797993i | ||||
\(955\) | 17.3205 | 0.560478 | ||||||||
\(956\) | 17.3205 | + | 4.47214i | 0.560185 | + | 0.144639i | ||||
\(957\) | 29.3939 | + | 26.8328i | 0.950169 | + | 0.867382i | ||||
\(958\) | 31.1769 | + | 40.2492i | 1.00728 | + | 1.30039i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.4722 | − | 14.2302i | 0.434813 | − | 0.459279i | ||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 4.24264 | + | 5.47723i | 0.136788 | + | 0.176593i | ||||
\(963\) | − | 13.4164i | − | 0.432338i | ||||||
\(964\) | 12.2474 | − | 47.4342i | 0.394464 | − | 1.52775i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.294229 | + | 15.8718i | 0.00946665 | + | 0.510666i | ||||
\(967\) | 4.24264 | 0.136434 | 0.0682171 | − | 0.997671i | \(-0.478269\pi\) | ||||
0.0682171 | + | 0.997671i | \(0.478269\pi\) | |||||||
\(968\) | −14.8455 | − | 27.3425i | −0.477153 | − | 0.878820i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21.2132 | − | 16.4317i | 0.681115 | − | 0.527589i | ||||
\(971\) | 43.8178i | 1.40618i | 0.711101 | + | 0.703090i | \(0.248197\pi\) | ||||
−0.711101 | + | 0.703090i | \(0.751803\pi\) | |||||||
\(972\) | 7.79423 | − | 30.1869i | 0.250000 | − | 0.968246i | ||||
\(973\) | 20.0000 | − | 26.8328i | 0.641171 | − | 0.860221i | ||||
\(974\) | −25.9808 | + | 20.1246i | −0.832477 | + | 0.644834i | ||||
\(975\) | 12.7279 | 0.407620 | ||||||||
\(976\) | −25.7196 | − | 14.2302i | −0.823266 | − | 0.455499i | ||||
\(977\) | 18.9737i | 0.607021i | 0.952828 | + | 0.303511i | \(0.0981588\pi\) | ||||
−0.952828 | + | 0.303511i | \(0.901841\pi\) | |||||||
\(978\) | 30.0000 | − | 23.2379i | 0.959294 | − | 0.743066i | ||||
\(979\) | 6.92820 | + | 6.32456i | 0.221426 | + | 0.202134i | ||||
\(980\) | 19.7854 | − | 0.733809i | 0.632021 | − | 0.0234407i | ||||
\(981\) | − | 16.4317i | − | 0.524623i | ||||||
\(982\) | −5.00000 | + | 3.87298i | −0.159556 | + | 0.123592i | ||||
\(983\) | − | 49.2950i | − | 1.57227i | −0.618057 | − | 0.786134i | \(-0.712080\pi\) | ||
0.618057 | − | 0.786134i | \(-0.287920\pi\) | |||||||
\(984\) | −15.0000 | − | 34.8569i | −0.478183 | − | 1.11120i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.0000 | + | 20.1246i | −0.477455 | + | 0.640573i | ||||
\(988\) | −30.0000 | − | 7.74597i | −0.954427 | − | 0.246432i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 1.60660 | − | 19.8348i | 0.0510612 | − | 0.630391i | ||||
\(991\) | − | 38.7298i | − | 1.23029i | −0.788413 | − | 0.615147i | \(-0.789097\pi\) | ||
0.788413 | − | 0.615147i | \(-0.210903\pi\) | |||||||
\(992\) | 3.00000 | + | 19.3649i | 0.0952501 | + | 0.614837i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.849365 | − | 45.8179i | −0.0269402 | − | 1.45326i | ||||
\(995\) | −34.2929 | −1.08716 | ||||||||
\(996\) | −5.19615 | + | 20.1246i | −0.164646 | + | 0.637673i | ||||
\(997\) | 7.34847 | 0.232728 | 0.116364 | − | 0.993207i | \(-0.462876\pi\) | ||||
0.116364 | + | 0.993207i | \(0.462876\pi\) | |||||||
\(998\) | 34.6410 | − | 26.8328i | 1.09654 | − | 0.849378i | ||||
\(999\) | −10.3923 | −0.328798 |
(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 | 924.2.n.b.923.7 | yes | 8 | |
3.2 | odd | 2 | 924.2.n.c.923.2 | yes | 8 | ||
4.3 | odd | 2 | 924.2.n.c.923.5 | yes | 8 | ||
7.6 | odd | 2 | 924.2.n.c.923.8 | yes | 8 | ||
11.10 | odd | 2 | 924.2.n.c.923.1 | yes | 8 | ||
12.11 | even | 2 | inner | 924.2.n.b.923.4 | yes | 8 | |
21.20 | even | 2 | inner | 924.2.n.b.923.1 | ✓ | 8 | |
28.27 | even | 2 | inner | 924.2.n.b.923.6 | yes | 8 | |
33.32 | even | 2 | inner | 924.2.n.b.923.8 | yes | 8 | |
44.43 | even | 2 | inner | 924.2.n.b.923.3 | yes | 8 | |
77.76 | even | 2 | inner | 924.2.n.b.923.2 | yes | 8 | |
84.83 | odd | 2 | 924.2.n.c.923.3 | yes | 8 | ||
132.131 | odd | 2 | 924.2.n.c.923.6 | yes | 8 | ||
231.230 | odd | 2 | 924.2.n.c.923.7 | yes | 8 | ||
308.307 | odd | 2 | 924.2.n.c.923.4 | yes | 8 | ||
924.923 | even | 2 | inner | 924.2.n.b.923.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
924.2.n.b.923.1 | ✓ | 8 | 21.20 | even | 2 | inner | |
924.2.n.b.923.2 | yes | 8 | 77.76 | even | 2 | inner | |
924.2.n.b.923.3 | yes | 8 | 44.43 | even | 2 | inner | |
924.2.n.b.923.4 | yes | 8 | 12.11 | even | 2 | inner | |
924.2.n.b.923.5 | yes | 8 | 924.923 | even | 2 | inner | |
924.2.n.b.923.6 | yes | 8 | 28.27 | even | 2 | inner | |
924.2.n.b.923.7 | yes | 8 | 1.1 | even | 1 | trivial | |
924.2.n.b.923.8 | yes | 8 | 33.32 | even | 2 | inner | |
924.2.n.c.923.1 | yes | 8 | 11.10 | odd | 2 | ||
924.2.n.c.923.2 | yes | 8 | 3.2 | odd | 2 | ||
924.2.n.c.923.3 | yes | 8 | 84.83 | odd | 2 | ||
924.2.n.c.923.4 | yes | 8 | 308.307 | odd | 2 | ||
924.2.n.c.923.5 | yes | 8 | 4.3 | odd | 2 | ||
924.2.n.c.923.6 | yes | 8 | 132.131 | odd | 2 | ||
924.2.n.c.923.7 | yes | 8 | 231.230 | odd | 2 | ||
924.2.n.c.923.8 | yes | 8 | 7.6 | odd | 2 |