Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 608) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.577 |
Dual form | 1216.2.i.j.961.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | + | 2.59808i | 0.866025 | + | 1.50000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | + | 1.73205i | 0.447214 | + | 0.774597i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | + | 5.19615i | −1.00000 | + | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | + | 5.19615i | −0.774597 | + | 1.34164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | + | 2.59808i | −0.802955 | + | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | − | 5.19615i | −0.654654 | − | 1.13389i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.00000 | −1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.50000 | + | 7.79423i | 0.783349 | + | 1.35680i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | − | 3.46410i | −0.338062 | − | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | 0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.0000 | −1.78885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.00000 | + | 8.66025i | −0.729325 | + | 1.26323i | 0.227844 | + | 0.973698i | \(0.426832\pi\) |
−0.957169 | + | 0.289530i | \(0.906501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.00000 | + | 15.5885i | −1.26025 | + | 2.18282i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | + | 5.19615i | 0.404520 | + | 0.700649i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.0000 | − | 5.19615i | −1.58944 | − | 0.688247i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | − | 12.1244i | 0.896258 | − | 1.55236i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.00000 | − | 10.3923i | 0.755929 | − | 1.30931i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.0000 | 1.44463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | + | 1.73205i | 0.118678 | + | 0.205557i | 0.919244 | − | 0.393688i | \(-0.128801\pi\) |
−0.800566 | + | 0.599245i | \(0.795468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000 | 0.346410 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | −0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.0000 | 1.64646 | 0.823232 | − | 0.567705i | \(-0.192169\pi\) | ||||
0.823232 | + | 0.567705i | \(0.192169\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | + | 10.3923i | −0.650791 | + | 1.12720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.0000 | −1.92980 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | − | 15.5885i | 0.953998 | − | 1.65237i | 0.217354 | − | 0.976093i | \(-0.430258\pi\) |
0.736644 | − | 0.676280i | \(-0.236409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | + | 3.46410i | −0.209657 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.0000 | − | 20.7846i | −1.24434 | − | 2.15526i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | − | 3.46410i | −0.820783 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.50000 | + | 2.59808i | 0.152302 | + | 0.263795i | 0.932073 | − | 0.362270i | \(-0.117998\pi\) |
−0.779771 | + | 0.626064i | \(0.784665\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.00000 | + | 15.5885i | −0.904534 | + | 1.56670i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00000 | − | 1.73205i | 0.0995037 | − | 0.172345i | −0.811976 | − | 0.583691i | \(-0.801608\pi\) |
0.911479 | + | 0.411346i | \(0.134941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0000 | −0.985329 | −0.492665 | − | 0.870219i | \(-0.663977\pi\) | ||||
−0.492665 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | − | 10.3923i | 0.585540 | − | 1.01419i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | + | 13.8564i | 0.766261 | + | 1.32720i | 0.939577 | + | 0.342337i | \(0.111218\pi\) |
−0.173316 | + | 0.984866i | \(0.555448\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | + | 20.7846i | 1.13899 | + | 1.97279i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.0000 | 1.41108 | 0.705541 | − | 0.708669i | \(-0.250704\pi\) | ||||
0.705541 | + | 0.708669i | \(0.250704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | + | 10.3923i | 0.554700 | + | 0.960769i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | − | 10.3923i | −0.550019 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.50000 | + | 7.79423i | −0.405751 | + | 0.702782i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | + | 1.73205i | −0.0887357 | + | 0.153695i | −0.906977 | − | 0.421180i | \(-0.861616\pi\) |
0.818241 | + | 0.574875i | \(0.194949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | − | 20.7846i | 1.05654 | − | 1.82998i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.500000 | − | 0.866025i | −0.0436852 | − | 0.0756650i | 0.843356 | − | 0.537355i | \(-0.180577\pi\) |
−0.887041 | + | 0.461690i | \(0.847243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.00000 | − | 5.19615i | 0.606977 | − | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.00000 | − | 15.5885i | −0.774597 | − | 1.34164i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.50000 | + | 14.7224i | −0.726204 | + | 1.25782i | 0.232273 | + | 0.972651i | \(0.425384\pi\) |
−0.958477 | + | 0.285171i | \(0.907949\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.50000 | + | 6.06218i | −0.296866 | + | 0.514187i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) |
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.0000 | −2.52646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | − | 5.19615i | 0.250873 | − | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | −0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.50000 | − | 7.79423i | −0.371154 | − | 0.642857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −36.0000 | −2.91043 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | − | 13.8564i | −0.642575 | − | 1.11297i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | + | 17.3205i | 0.798087 | + | 1.38233i | 0.920860 | + | 0.389892i | \(0.127488\pi\) |
−0.122774 | + | 0.992435i | \(0.539179\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | + | 6.92820i | −0.315244 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0000 | 1.33154 | 0.665771 | − | 0.746156i | \(-0.268103\pi\) | ||||
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.00000 | + | 15.5885i | −0.700649 | + | 1.21356i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | + | 10.3923i | −0.464294 | + | 0.804181i | −0.999169 | − | 0.0407502i | \(-0.987025\pi\) |
0.534875 | + | 0.844931i | \(0.320359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 25.9808i | −0.229416 | − | 1.98680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | + | 1.73205i | −0.0755929 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.50000 | − | 7.79423i | 0.338241 | − | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.0000 | −1.42013 | −0.710063 | − | 0.704138i | \(-0.751334\pi\) | ||||
−0.710063 | + | 0.704138i | \(0.751334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | + | 10.3923i | −0.445976 | + | 0.772454i | −0.998120 | − | 0.0612954i | \(-0.980477\pi\) |
0.552143 | + | 0.833749i | \(0.313810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 42.0000 | 3.10473 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | + | 13.8564i | 0.588172 | + | 1.01874i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | + | 15.5885i | 0.658145 | + | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.0000 | 1.30931 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0000 | 1.44715 | 0.723575 | − | 0.690246i | \(-0.242498\pi\) | ||||
0.723575 | + | 0.690246i | \(0.242498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.00000 | − | 8.66025i | −0.359908 | − | 0.623379i | 0.628037 | − | 0.778183i | \(-0.283859\pi\) |
−0.987945 | + | 0.154805i | \(0.950525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.00000 | + | 10.3923i | 0.429669 | + | 0.744208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00000 | − | 8.66025i | 0.354441 | − | 0.613909i | −0.632581 | − | 0.774494i | \(-0.718005\pi\) |
0.987022 | + | 0.160585i | \(0.0513380\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.0000 | 1.48123 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.00000 | − | 10.3923i | 0.421117 | − | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | + | 5.19615i | −0.209529 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.0000 | + | 20.7846i | 0.834058 | + | 1.44463i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5000 | + | 7.79423i | −0.726300 | + | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | + | 5.19615i | −0.205557 | + | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | − | 13.8564i | 0.545595 | − | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.5000 | − | 28.5788i | 1.11497 | − | 1.93118i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | + | 13.8564i | 0.535720 | + | 0.927894i | 0.999128 | + | 0.0417488i | \(0.0132929\pi\) |
−0.463409 | + | 0.886145i | \(0.653374\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | + | 5.19615i | 0.200000 | + | 0.346410i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0000 | 0.730096 | 0.365048 | − | 0.930989i | \(-0.381053\pi\) | ||||
0.365048 | + | 0.930989i | \(0.381053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.0000 | 1.32164 | 0.660819 | − | 0.750546i | \(-0.270209\pi\) | ||||
0.660819 | + | 0.750546i | \(0.270209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.00000 | − | 15.5885i | −0.592157 | − | 1.02565i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.50000 | − | 6.06218i | −0.229293 | − | 0.397146i | 0.728306 | − | 0.685252i | \(-0.240308\pi\) |
−0.957599 | + | 0.288106i | \(0.906975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.0000 | −1.30466 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.00000 | + | 10.3923i | −0.389742 | + | 0.675053i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.50000 | + | 11.2583i | −0.418702 | + | 0.725213i | −0.995809 | − | 0.0914555i | \(-0.970848\pi\) |
0.577107 | + | 0.816668i | \(0.304181\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | − | 5.19615i | −0.191663 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | + | 8.66025i | 0.0636285 | + | 0.551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.5000 | + | 38.9711i | 1.42588 | + | 2.46970i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.500000 | + | 0.866025i | −0.0315597 | + | 0.0546630i | −0.881374 | − | 0.472419i | \(-0.843381\pi\) |
0.849814 | + | 0.527082i | \(0.176714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 10.3923i | 0.377217 | − | 0.653359i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.0000 | −2.25441 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.50000 | + | 6.06218i | −0.218324 | + | 0.378148i | −0.954296 | − | 0.298864i | \(-0.903392\pi\) |
0.735972 | + | 0.677012i | \(0.236726\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.0000 | − | 31.1769i | −1.11417 | − | 1.92980i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0000 | − | 22.5167i | −0.801614 | − | 1.38844i | −0.918553 | − | 0.395298i | \(-0.870641\pi\) |
0.116939 | − | 0.993139i | \(-0.462692\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 54.0000 | 3.30475 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0000 | − | 25.9808i | −0.911185 | − | 1.57822i | −0.812393 | − | 0.583111i | \(-0.801835\pi\) |
−0.0987925 | − | 0.995108i | \(-0.531498\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | −0.726273 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.50000 | − | 2.59808i | 0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0000 | 1.08152 | 0.540758 | − | 0.841178i | \(-0.318138\pi\) | ||||
0.540758 | + | 0.841178i | \(0.318138\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.0000 | − | 41.5692i | 1.43684 | − | 2.48868i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.50000 | − | 14.7224i | 0.507067 | − | 0.878267i | −0.492899 | − | 0.870087i | \(-0.664063\pi\) |
0.999967 | − | 0.00818015i | \(-0.00260385\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.50000 | − | 7.79423i | −0.267497 | − | 0.463319i | 0.700718 | − | 0.713439i | \(-0.252863\pi\) |
−0.968215 | + | 0.250120i | \(0.919530\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 25.9808i | −0.177705 | − | 1.53897i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.00000 | − | 5.19615i | −0.177084 | − | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.50000 | + | 7.79423i | −0.263795 | + | 0.456906i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | − | 5.19615i | 0.174667 | − | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.0000 | −1.56670 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.00000 | − | 6.92820i | −0.231326 | − | 0.400668i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 13.8564i | 0.461112 | + | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.0000 | 1.60328 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.50000 | − | 7.79423i | −0.256829 | − | 0.444840i | 0.708562 | − | 0.705649i | \(-0.249344\pi\) |
−0.965391 | + | 0.260808i | \(0.916011\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0000 | − | 25.9808i | −0.853320 | − | 1.47799i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | + | 0.866025i | −0.0282617 | + | 0.0489506i | −0.879810 | − | 0.475325i | \(-0.842331\pi\) |
0.851549 | + | 0.524276i | \(0.175664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.0000 | 1.35225 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.0000 | − | 22.5167i | 0.730153 | − | 1.26466i | −0.226665 | − | 0.973973i | \(-0.572782\pi\) |
0.956818 | − | 0.290689i | \(-0.0938844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | + | 10.3923i | 0.334887 | + | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.0000 | − | 10.3923i | −1.33540 | − | 0.578243i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | − | 1.73205i | −0.0554700 | − | 0.0960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.0000 | + | 41.5692i | −1.32720 | + | 2.29878i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0000 | − | 17.3205i | 0.551318 | − | 0.954911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.0000 | 1.37412 | 0.687062 | − | 0.726599i | \(-0.258900\pi\) | ||||
0.687062 | + | 0.726599i | \(0.258900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.0000 | + | 41.5692i | −1.31519 | + | 2.27798i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.0000 | 0.764902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5000 | − | 26.8468i | −0.844339 | − | 1.46244i | −0.886194 | − | 0.463314i | \(-0.846660\pi\) |
0.0418554 | − | 0.999124i | \(-0.486673\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.5000 | + | 38.9711i | 1.22203 | + | 2.11662i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | + | 20.7846i | 0.646058 | + | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.50000 | − | 6.06218i | −0.187890 | − | 0.325435i | 0.756657 | − | 0.653812i | \(-0.226831\pi\) |
−0.944547 | + | 0.328378i | \(0.893498\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0000 | 0.856460 | 0.428230 | − | 0.903670i | \(-0.359137\pi\) | ||||
0.428230 | + | 0.903670i | \(0.359137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | + | 15.5885i | −0.480384 | + | 0.832050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.0000 | −1.33062 | −0.665308 | − | 0.746569i | \(-0.731700\pi\) | ||||
−0.665308 | + | 0.746569i | \(0.731700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.00000 | + | 3.46410i | −0.106149 | + | 0.183855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.0000 | − | 31.1769i | 0.952661 | − | 1.65006i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0000 | − | 20.7846i | −0.633336 | − | 1.09697i | −0.986865 | − | 0.161546i | \(-0.948352\pi\) |
0.353529 | − | 0.935423i | \(-0.384981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 18.1865i | 0.289474 | − | 0.957186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00000 | − | 5.19615i | −0.157459 | − | 0.272727i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.0000 | − | 19.0526i | 0.575766 | − | 0.997257i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | − | 3.46410i | 0.104399 | − | 0.180825i | −0.809093 | − | 0.587680i | \(-0.800041\pi\) |
0.913493 | + | 0.406855i | \(0.133375\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.0000 | −0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | + | 3.46410i | −0.103835 | + | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.0000 | −1.24267 | −0.621336 | − | 0.783544i | \(-0.713410\pi\) | ||||
−0.621336 | + | 0.783544i | \(0.713410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.0000 | + | 31.1769i | 0.929516 | + | 1.60997i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000 | + | 10.3923i | 0.309016 | + | 0.535231i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | −0.307389 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.00000 | + | 5.19615i | 0.153293 | + | 0.265511i | 0.932436 | − | 0.361335i | \(-0.117679\pi\) |
−0.779143 | + | 0.626846i | \(0.784346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 10.3923i | −0.305788 | − | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 48.0000 | 2.43998 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.00000 | − | 13.8564i | 0.405616 | − | 0.702548i | −0.588777 | − | 0.808296i | \(-0.700390\pi\) |
0.994393 | + | 0.105748i | \(0.0337237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.50000 | − | 2.59808i | 0.0756650 | − | 0.131056i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.00000 | + | 6.92820i | −0.201262 | + | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | − | 6.92820i | −0.200754 | − | 0.347717i | 0.748017 | − | 0.663679i | \(-0.231006\pi\) |
−0.948772 | + | 0.315963i | \(0.897673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.0000 | + | 10.3923i | 1.20150 | + | 0.520266i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | + | 2.59808i | 0.0749064 | + | 0.129742i | 0.901046 | − | 0.433724i | \(-0.142801\pi\) |
−0.826139 | + | 0.563466i | \(0.809468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | + | 13.8564i | −0.398508 | + | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.00000 | − | 15.5885i | 0.447214 | − | 0.774597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50000 | + | 4.33013i | −0.123617 | + | 0.214111i | −0.921192 | − | 0.389109i | \(-0.872783\pi\) |
0.797574 | + | 0.603220i | \(0.206116\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −51.0000 | −2.51564 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.00000 | + | 5.19615i | 0.147620 | + | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0000 | + | 25.9808i | 0.736321 | + | 1.27535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.0000 | −1.02837 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | − | 10.3923i | −0.292422 | − | 0.506490i | 0.681960 | − | 0.731390i | \(-0.261128\pi\) |
−0.974382 | + | 0.224900i | \(0.927795\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.0000 | − | 51.9615i | −1.45865 | − | 2.52646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | 0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.0000 | + | 24.2487i | −0.677507 | + | 1.17348i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.0000 | 0.869048 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.0000 | − | 22.5167i | 0.626188 | − | 1.08459i | −0.362122 | − | 0.932131i | \(-0.617948\pi\) |
0.988310 | − | 0.152459i | \(-0.0487191\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00000 | + | 12.1244i | −0.336399 | + | 0.582659i | −0.983752 | − | 0.179530i | \(-0.942542\pi\) |
0.647354 | + | 0.762190i | \(0.275876\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0000 | − | 31.1769i | −0.863034 | − | 1.49482i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000 | + | 17.3205i | 0.0956730 | + | 0.828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.00000 | − | 3.46410i | −0.0954548 | − | 0.165333i | 0.814344 | − | 0.580383i | \(-0.197097\pi\) |
−0.909798 | + | 0.415051i | \(0.863764\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | − | 15.5885i | 0.428571 | − | 0.742307i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.50000 | − | 2.59808i | 0.0712672 | − | 0.123438i | −0.828190 | − | 0.560448i | \(-0.810629\pi\) |
0.899457 | + | 0.437009i | \(0.143962\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.0000 | 1.70656 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.0000 | 0.991051 | 0.495526 | − | 0.868593i | \(-0.334975\pi\) | ||||
0.495526 | + | 0.868593i | \(0.334975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.50000 | + | 7.79423i | 0.211897 | + | 0.367016i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.00000 | −0.375046 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00000 | −0.327446 | −0.163723 | − | 0.986506i | \(-0.552350\pi\) | ||||
−0.163723 | + | 0.986506i | \(0.552350\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.0000 | − | 46.7654i | −1.26025 | − | 2.18282i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.00000 | − | 15.5885i | −0.419172 | − | 0.726027i | 0.576685 | − | 0.816967i | \(-0.304346\pi\) |
−0.995856 | + | 0.0909401i | \(0.971013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0000 | 0.464739 | 0.232370 | − | 0.972628i | \(-0.425352\pi\) | ||||
0.232370 | + | 0.972628i | \(0.425352\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.0000 | − | 41.5692i | 1.11297 | − | 1.92773i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0000 | 0.971764 | 0.485882 | − | 0.874024i | \(-0.338498\pi\) | ||||
0.485882 | + | 0.874024i | \(0.338498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.00000 | + | 12.1244i | −0.323230 | + | 0.559851i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.0000 | + | 51.9615i | −1.38233 | + | 2.39426i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.0000 | − | 20.7846i | −0.551761 | − | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.500000 | + | 4.33013i | 0.0229416 | + | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | + | 10.3923i | 0.274721 | + | 0.475831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0000 | − | 24.2487i | 0.639676 | − | 1.10795i | −0.345827 | − | 0.938298i | \(-0.612402\pi\) |
0.985504 | − | 0.169654i | \(-0.0542649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | − | 13.8564i | 0.364769 | − | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.0000 | −1.09204 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.00000 | + | 5.19615i | −0.136223 | + | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.5000 | + | 44.1673i | 1.15315 | + | 1.99731i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.0000 | − | 24.2487i | −0.631811 | − | 1.09433i | −0.987181 | − | 0.159603i | \(-0.948978\pi\) |
0.355370 | − | 0.934726i | \(-0.384355\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.0000 | −1.62136 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −36.0000 | −1.61808 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.00000 | − | 3.46410i | −0.0897123 | − | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.500000 | + | 0.866025i | 0.0223831 | + | 0.0387686i | 0.877000 | − | 0.480490i | \(-0.159541\pi\) |
−0.854617 | + | 0.519259i | \(0.826208\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.0000 | −1.60836 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.0000 | + | 31.1769i | −0.802580 | + | 1.39011i | 0.115332 | + | 0.993327i | \(0.463207\pi\) |
−0.917912 | + | 0.396783i | \(0.870127\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.5000 | + | 23.3827i | −0.599556 | + | 1.03846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.0000 | + | 17.3205i | −0.443242 | + | 0.767718i | −0.997928 | − | 0.0643419i | \(-0.979505\pi\) |
0.554686 | + | 0.832060i | \(0.312839\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0000 | + | 19.0526i | 0.486611 | + | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31.5000 | − | 23.3827i | 1.39076 | − | 1.03237i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0000 | − | 17.3205i | −0.440653 | − | 0.763233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0000 | + | 25.9808i | −0.659699 | + | 1.14263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.00000 | + | 15.5885i | −0.395056 | + | 0.684257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.00000 | + | 13.8564i | −0.349816 | + | 0.605898i | −0.986216 | − | 0.165460i | \(-0.947089\pi\) |
0.636401 | + | 0.771358i | \(0.280422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.00000 | −0.261861 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.0000 | − | 41.5692i | −1.04546 | − | 1.81078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0000 | 0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | 0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | + | 6.92820i | 0.172935 | + | 0.299532i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.5000 | − | 49.3634i | −1.22987 | − | 2.13019i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.00000 | −0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | − | 34.6410i | 0.859867 | − | 1.48933i | −0.0121878 | − | 0.999926i | \(-0.503880\pi\) |
0.872055 | − | 0.489408i | \(-0.162787\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36.0000 | −1.54491 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.0000 | + | 27.7128i | −0.685365 | + | 1.18709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | + | 27.7128i | −0.684111 | + | 1.18491i | 0.289605 | + | 0.957146i | \(0.406476\pi\) |
−0.973715 | + | 0.227768i | \(0.926857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 42.0000 | + | 72.7461i | 1.79252 | + | 3.10473i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | − | 25.9808i | −0.127804 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | − | 6.92820i | −0.170097 | − | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.0000 | + | 41.5692i | −1.01874 | + | 1.76452i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.00000 | + | 13.8564i | −0.338971 | + | 0.587115i | −0.984239 | − | 0.176841i | \(-0.943412\pi\) |
0.645269 | + | 0.763956i | \(0.276745\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.0000 | + | 46.7654i | −1.13994 | + | 1.97444i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.0000 | 0.800755 | 0.400377 | − | 0.916350i | \(-0.368879\pi\) | ||||
0.400377 | + | 0.916350i | \(0.368879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.0000 | + | 25.9808i | 0.631055 | + | 1.09302i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.00000 | + | 15.5885i | 0.377964 | + | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0000 | 0.544033 | 0.272017 | − | 0.962293i | \(-0.412309\pi\) | ||||
0.272017 | + | 0.962293i | \(0.412309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.0000 | + | 51.9615i | 1.25327 | + | 2.17072i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.00000 | − | 3.46410i | −0.0834058 | − | 0.144463i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.0000 | −1.87337 | −0.936687 | − | 0.350167i | \(-0.886125\pi\) | ||||
−0.936687 | + | 0.350167i | \(0.886125\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.0000 | − | 25.9808i | 0.623379 | − | 1.07972i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.0000 | −1.24461 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00000 | − | 5.19615i | 0.124247 | − | 0.215203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0000 | + | 20.7846i | −0.496139 | + | 0.859338i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | − | 20.7846i | −0.495293 | − | 0.857873i | 0.504692 | − | 0.863299i | \(-0.331606\pi\) |
−0.999985 | + | 0.00542667i | \(0.998273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000 | − | 20.7846i | 1.15372 | − | 0.856415i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | − | 31.1769i | −0.740421 | − | 1.28245i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.50000 | − | 7.79423i | 0.184793 | − | 0.320071i | −0.758714 | − | 0.651424i | \(-0.774172\pi\) |
0.943507 | + | 0.331353i | \(0.107505\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | − | 20.7846i | 0.491952 | − | 0.852086i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.0000 | 1.22782 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | − | 10.3923i | 0.245153 | − | 0.424618i | −0.717021 | − | 0.697051i | \(-0.754495\pi\) |
0.962175 | + | 0.272433i | \(0.0878284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0000 | 0.448699 | 0.224350 | − | 0.974509i | \(-0.427974\pi\) | ||||
0.224350 | + | 0.974509i | \(0.427974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.0000 | + | 36.3731i | 0.855186 | + | 1.48123i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.00000 | − | 3.46410i | −0.0813116 | − | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0000 | −0.568242 | −0.284121 | − | 0.958788i | \(-0.591702\pi\) | ||||
−0.284121 | + | 0.958788i | \(0.591702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 36.0000 | 1.45879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.0000 | + | 17.3205i | 0.404557 | + | 0.700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.0000 | − | 36.3731i | −0.848182 | − | 1.46909i | −0.882829 | − | 0.469695i | \(-0.844364\pi\) |
0.0346469 | − | 0.999400i | \(-0.488969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0000 | −0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.50000 | − | 7.79423i | 0.181163 | − | 0.313784i | −0.761114 | − | 0.648618i | \(-0.775347\pi\) |
0.942277 | + | 0.334835i | \(0.108680\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.0000 | 1.60774 | 0.803868 | − | 0.594808i | \(-0.202772\pi\) | ||||
0.803868 | + | 0.594808i | \(0.202772\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | + | 31.1769i | −0.722315 | + | 1.25109i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.0000 | + | 31.1769i | −0.721155 | + | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −36.0000 | − | 15.5885i | −1.43770 | − | 0.622543i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.0000 | + | 41.5692i | 0.956943 | + | 1.65747i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00000 | − | 1.73205i | 0.0398094 | − | 0.0689519i | −0.845434 | − | 0.534080i | \(-0.820658\pi\) |
0.885244 | + | 0.465128i | \(0.153992\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.00000 | + | 10.3923i | −0.238479 | + | 0.413057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | −0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | + | 5.19615i | −0.118864 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.5000 | − | 32.0429i | −0.730706 | − | 1.26562i | −0.956582 | − | 0.291464i | \(-0.905858\pi\) |
0.225876 | − | 0.974156i | \(-0.427476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.500000 | − | 0.866025i | −0.0197181 | − | 0.0341527i | 0.855998 | − | 0.516979i | \(-0.172944\pi\) |
−0.875716 | + | 0.482826i | \(0.839610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.0000 | 1.89000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0000 | −0.707653 | −0.353827 | − | 0.935311i | \(-0.615120\pi\) | ||||
−0.353827 | + | 0.935311i | \(0.615120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.50000 | − | 7.79423i | −0.176640 | − | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.0000 | + | 41.5692i | 0.940634 | + | 1.62923i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.00000 | −0.156532 | −0.0782660 | − | 0.996933i | \(-0.524938\pi\) | ||||
−0.0782660 | + | 0.996933i | \(0.524938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00000 | − | 1.73205i | 0.0390732 | − | 0.0676768i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 66.0000 | 2.57491 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | + | 31.1769i | −0.701180 | + | 1.21448i | 0.266872 | + | 0.963732i | \(0.414010\pi\) |
−0.968052 | + | 0.250748i | \(0.919323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.00000 | + | 5.19615i | −0.116686 | + | 0.202107i | −0.918453 | − | 0.395531i | \(-0.870561\pi\) |
0.801766 | + | 0.597638i | \(0.203894\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.0000 | + | 31.1769i | 0.699062 | + | 1.21081i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000 | + | 6.92820i | 0.620453 | + | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.0000 | + | 41.5692i | −0.927894 | + | 1.60716i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.0000 | − | 36.3731i | 0.810696 | − | 1.40417i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0000 | −0.848038 | −0.424019 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424019 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.50000 | + | 7.79423i | −0.173205 | + | 0.300000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.0000 | −0.999261 | −0.499631 | − | 0.866239i | \(-0.666531\pi\) | ||||
−0.499631 | + | 0.866239i | \(0.666531\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.00000 | − | 5.19615i | −0.115129 | − | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.5000 | + | 28.5788i | 0.632281 | + | 1.09514i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.0000 | −1.68361 | −0.841807 | − | 0.539779i | \(-0.818508\pi\) | ||||
−0.841807 | + | 0.539779i | \(0.818508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.0000 | −1.29907 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.0000 | + | 51.9615i | 1.14457 | + | 1.98246i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | − | 3.46410i | −0.0761939 | − | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000 | 0.456502 | 0.228251 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228251 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.0000 | − | 31.1769i | 0.683763 | − | 1.18431i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.0000 | −0.531050 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5000 | − | 18.1865i | 0.397146 | − | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.00000 | − | 12.1244i | −0.264386 | − | 0.457931i | 0.703016 | − | 0.711174i | \(-0.251836\pi\) |
−0.967403 | + | 0.253243i | \(0.918503\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.0000 | + | 20.7846i | −1.05604 | + | 0.783906i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30.0000 | − | 51.9615i | −1.12987 | − | 1.95698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.00000 | + | 3.46410i | −0.0752177 | + | 0.130281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.0000 | −0.900070 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | + | 27.7128i | −0.599205 | + | 1.03785i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000 | + | 20.7846i | 0.448148 | + | 0.776215i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.0000 | + | 39.8372i | 0.857755 | + | 1.48568i | 0.874065 | + | 0.485809i | \(0.161475\pi\) |
−0.0163099 | + | 0.999867i | \(0.505192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0000 | 0.744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −39.0000 | −1.45043 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0000 | + | 38.1051i | 0.815935 | + | 1.41324i | 0.908655 | + | 0.417548i | \(0.137111\pi\) |
−0.0927199 | + | 0.995692i | \(0.529556\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | − | 41.5692i | 0.887672 | − | 1.53749i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.0000 | −1.32969 | −0.664845 | − | 0.746981i | \(-0.731502\pi\) | ||||
−0.664845 | + | 0.746981i | \(0.731502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.00000 | − | 15.5885i | 0.331970 | − | 0.574989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5000 | − | 18.1865i | 0.386772 | − | 0.669910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.50000 | + | 11.2583i | 0.239106 | + | 0.414144i | 0.960458 | − | 0.278425i | \(-0.0898122\pi\) |
−0.721352 | + | 0.692569i | \(0.756479\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.0000 | + | 15.5885i | −0.771454 | + | 0.572656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0000 | + | 20.7846i | 0.440237 | + | 0.762513i | 0.997707 | − | 0.0676840i | \(-0.0215610\pi\) |
−0.557470 | + | 0.830197i | \(0.688228\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.0000 | + | 77.9423i | −1.64646 | + | 2.85176i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.0000 | − | 19.0526i | 0.401396 | − | 0.695238i | −0.592499 | − | 0.805571i | \(-0.701859\pi\) |
0.993895 | + | 0.110333i | \(0.0351919\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.00000 | −0.109326 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.00000 | − | 12.1244i | −0.254419 | − | 0.440667i | 0.710318 | − | 0.703881i | \(-0.248551\pi\) |
−0.964738 | + | 0.263213i | \(0.915218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.0000 | 1.30672 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | 0.761249 | 0.380625 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | − | 27.7128i | −0.579239 | − | 1.00327i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −36.0000 | − | 62.3538i | −1.30158 | − | 2.25441i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00000 | − | 1.73205i | 0.0360609 | − | 0.0624593i | −0.847432 | − | 0.530904i | \(-0.821852\pi\) |
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.0000 | −0.756297 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.00000 | − | 12.1244i | 0.251773 | − | 0.436083i | −0.712241 | − | 0.701935i | \(-0.752320\pi\) |
0.964014 | + | 0.265852i | \(0.0856532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | + | 6.92820i | −0.143684 | + | 0.248868i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.0000 | − | 41.5692i | −0.860995 | − | 1.49129i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0000 | − | 5.19615i | −0.429945 | − | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.00000 | + | 5.19615i | 0.107348 | + | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.0000 | − | 46.7654i | 0.964901 | − | 1.67126i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0000 | + | 34.6410i | −0.713831 | + | 1.23639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.0000 | −1.24762 | −0.623808 | − | 0.781578i | \(-0.714415\pi\) | ||||
−0.623808 | + | 0.781578i | \(0.714415\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 39.0000 | − | 67.5500i | 1.38844 | − | 2.40484i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0000 | −1.06668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0000 | − | 24.2487i | −0.497155 | − | 0.861097i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.00000 | + | 10.3923i | 0.212798 | + | 0.368577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.00000 | 0.141687 | 0.0708436 | − | 0.997487i | \(-0.477431\pi\) | ||||
0.0708436 | + | 0.997487i | \(0.477431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.0000 | −2.12265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 54.0000 | + | 93.5307i | 1.90800 | + | 3.30475i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.5000 | − | 28.5788i | −0.582272 | − | 1.00853i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.0000 | −0.563926 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0000 | −0.386739 | −0.193370 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193370 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0000 | − | 17.3205i | 0.351147 | − | 0.608205i | −0.635303 | − | 0.772263i | \(-0.719125\pi\) |
0.986451 | + | 0.164057i | \(0.0524582\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.0000 | − | 77.9423i | 1.57822 | − | 2.73356i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.0000 | + | 29.4449i | 0.595484 | + | 1.03141i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.0000 | + | 13.8564i | 1.11954 | + | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.0000 | − | 20.7846i | −0.419314 | − | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | + | 15.5885i | −0.314102 | + | 0.544041i | −0.979246 | − | 0.202674i | \(-0.935037\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.00000 | + | 5.19615i | −0.104573 | + | 0.181126i | −0.913564 | − | 0.406695i | \(-0.866681\pi\) |
0.808990 | + | 0.587822i | \(0.200014\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.00000 | 0.313340 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.50000 | − | 12.9904i | 0.260801 | − | 0.451720i | −0.705654 | − | 0.708556i | \(-0.749347\pi\) |
0.966455 | + | 0.256836i | \(0.0826802\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.0000 | −1.11141 | −0.555703 | − | 0.831381i | \(-0.687551\pi\) | ||||
−0.555703 | + | 0.831381i | \(0.687551\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.0000 | + | 46.7654i | 0.936620 | + | 1.62227i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.00000 | − | 15.5885i | −0.311832 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0000 | −0.830554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 72.0000 | 2.48868 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0000 | − | 22.5167i | −0.448810 | − | 0.777361i | 0.549499 | − | 0.835494i | \(-0.314819\pi\) |
−0.998309 | + | 0.0581329i | \(0.981485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 51.0000 | 1.75653 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | + | 15.5885i | −0.309609 | + | 0.536259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.00000 | 0.137442 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5000 | − | 23.3827i | 0.463319 | − | 0.802492i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.0000 | − | 27.7128i | 0.548473 | − | 0.949983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0000 | + | 22.5167i | 0.445112 | + | 0.770956i | 0.998060 | − | 0.0622597i | \(-0.0198307\pi\) |
−0.552948 | + | 0.833215i | \(0.686497\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 42.0000 | − | 31.1769i | 1.43637 | − | 1.06623i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.50000 | − | 11.2583i | −0.222036 | − | 0.384577i | 0.733390 | − | 0.679808i | \(-0.237937\pi\) |
−0.955426 | + | 0.295231i | \(0.904604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.500000 | + | 0.866025i | −0.0170598 | + | 0.0295484i | −0.874429 | − | 0.485153i | \(-0.838764\pi\) |
0.857369 | + | 0.514701i | \(0.172097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.00000 | − | 15.5885i | 0.306719 | − | 0.531253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.00000 | −0.272323 | −0.136162 | − | 0.990687i | \(-0.543477\pi\) | ||||
−0.136162 | + | 0.990687i | \(0.543477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | + | 10.3923i | −0.204006 | + | 0.353349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −57.0000 | −1.93582 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.00000 | + | 10.3923i | 0.203536 | + | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.00000 | − | 12.1244i | −0.237186 | − | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.0000 | −0.609208 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.0000 | −0.811348 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0000 | − | 39.8372i | −0.776655 | − | 1.34521i | −0.933860 | − | 0.357640i | \(-0.883582\pi\) |
0.157205 | − | 0.987566i | \(-0.449752\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.0000 | − | 36.3731i | −0.708312 | − | 1.22683i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.0000 | −1.24656 | −0.623281 | − | 0.781998i | \(-0.714201\pi\) | ||||
−0.623281 | + | 0.781998i | \(0.714201\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.50000 | − | 9.52628i | 0.185090 | − | 0.320585i | −0.758517 | − | 0.651653i | \(-0.774076\pi\) |
0.943607 | + | 0.331068i | \(0.107409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.0000 | 0.605063 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | − | 3.46410i | 0.0670778 | − | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | − | 23.3827i | −0.452267 | − | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.00000 | − | 43.3013i | −0.167319 | − | 1.44902i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.0000 | − | 32.9090i | −0.635100 | − | 1.10003i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | − | 20.7846i | 0.400668 | − | 0.693978i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.0000 | − | 41.5692i | 0.800445 | − | 1.38641i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0000 | + | 41.5692i | −0.798670 | + | 1.38334i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.0000 | −0.797787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.50000 | + | 2.59808i | 0.0498067 | + | 0.0862677i | 0.889854 | − | 0.456246i | \(-0.150806\pi\) |
−0.840047 | + | 0.542513i | \(0.817473\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | + | 10.3923i | 0.199007 | + | 0.344691i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.0000 | 1.48928 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 42.0000 | + | 72.7461i | 1.38848 | + | 2.40491i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.00000 | + | 1.73205i | 0.0330229 | + | 0.0571974i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0000 | −0.461817 | −0.230909 | − | 0.972975i | \(-0.574170\pi\) | ||||
−0.230909 | + | 0.972975i | \(0.574170\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.5000 | − | 23.3827i | 0.444840 | − | 0.770486i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.00000 | 0.131662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | − | 6.92820i | 0.131519 | − | 0.227798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.0000 | − | 51.9615i | 0.985329 | − | 1.70664i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.50000 | − | 4.33013i | −0.0820223 | − | 0.142067i | 0.822096 | − | 0.569349i | \(-0.192805\pi\) |
−0.904118 | + | 0.427282i | \(0.859471\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5000 | − | 7.79423i | 0.344124 | − | 0.255446i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.0000 | − | 31.1769i | −0.589294 | − | 1.02069i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.0000 | + | 31.1769i | −0.588663 | + | 1.01959i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.50000 | + | 6.06218i | −0.114340 | + | 0.198043i | −0.917516 | − | 0.397699i | \(-0.869809\pi\) |
0.803176 | + | 0.595742i | \(0.203142\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.00000 | −0.0979013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0000 | − | 46.7654i | 0.880175 | − | 1.52451i | 0.0290288 | − | 0.999579i | \(-0.490759\pi\) |
0.851146 | − | 0.524929i | \(-0.175908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.0000 | 0.390774 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.0000 | + | 31.1769i | 0.585540 | + | 1.01419i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.0000 | + | 24.2487i | 0.454939 | + | 0.787977i | 0.998685 | − | 0.0512727i | \(-0.0163278\pi\) |
−0.543746 | + | 0.839250i | \(0.682994\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.0000 | −0.714150 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 78.0000 | 2.52932 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.50000 | + | 2.59808i | 0.0485898 | + | 0.0841599i | 0.889297 | − | 0.457329i | \(-0.151194\pi\) |
−0.840708 | + | 0.541489i | \(0.817861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.0000 | + | 34.6410i | 0.647185 | + | 1.12096i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −54.0000 | −1.74557 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.0000 | − | 29.4449i | 0.548959 | − | 0.950824i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | + | 20.7846i | −0.386695 | + | 0.669775i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.0000 | − | 17.3205i | 0.321911 | − | 0.557567i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.00000 | − | 12.1244i | −0.225105 | − | 0.389893i | 0.731246 | − | 0.682114i | \(-0.238939\pi\) |
−0.956351 | + | 0.292221i | \(0.905606\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.00000 | − | 77.9423i | −0.289122 | − | 2.50387i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.5000 | + | 47.6314i | 0.882517 | + | 1.52856i | 0.848533 | + | 0.529142i | \(0.177486\pi\) |
0.0339836 | + | 0.999422i | \(0.489181\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.00000 | − | 12.1244i | 0.224410 | − | 0.388689i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00000 | − | 5.19615i | 0.0960769 | − | 0.166410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −59.0000 | −1.88758 | −0.943789 | − | 0.330550i | \(-0.892766\pi\) | ||||
−0.943789 | + | 0.330550i | \(0.892766\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0000 | − | 46.7654i | 0.862924 | − | 1.49463i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −96.0000 | −3.06504 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.00000 | − | 10.3923i | −0.191370 | − | 0.331463i | 0.754334 | − | 0.656490i | \(-0.227960\pi\) |
−0.945705 | + | 0.325027i | \(0.894626\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0000 | − | 20.7846i | −0.382352 | − | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 60.0000 | 1.90982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32.0000 | −1.01754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | + | 13.8564i | 0.254128 | + | 0.440163i | 0.964658 | − | 0.263504i | \(-0.0848781\pi\) |
−0.710530 | + | 0.703667i | \(0.751545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 37.5000 | + | 64.9519i | 1.19003 | + | 2.06119i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.0000 | 0.634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.0000 | − | 29.4449i | 0.538395 | − | 0.932528i | −0.460595 | − | 0.887610i | \(-0.652364\pi\) |
0.998991 | − | 0.0449179i | \(-0.0143026\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −72.0000 | −2.27798 |
(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 | 1216.2.i.j.577.1 | 2 | ||
4.3 | odd | 2 | 1216.2.i.a.577.1 | 2 | |||
8.3 | odd | 2 | 608.2.i.b.577.1 | yes | 2 | ||
8.5 | even | 2 | 608.2.i.a.577.1 | yes | 2 | ||
19.11 | even | 3 | inner | 1216.2.i.j.961.1 | 2 | ||
76.11 | odd | 6 | 1216.2.i.a.961.1 | 2 | |||
152.11 | odd | 6 | 608.2.i.b.353.1 | yes | 2 | ||
152.125 | even | 6 | 608.2.i.a.353.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.i.a.353.1 | ✓ | 2 | 152.125 | even | 6 | ||
608.2.i.a.577.1 | yes | 2 | 8.5 | even | 2 | ||
608.2.i.b.353.1 | yes | 2 | 152.11 | odd | 6 | ||
608.2.i.b.577.1 | yes | 2 | 8.3 | odd | 2 | ||
1216.2.i.a.577.1 | 2 | 4.3 | odd | 2 | |||
1216.2.i.a.961.1 | 2 | 76.11 | odd | 6 | |||
1216.2.i.j.577.1 | 2 | 1.1 | even | 1 | trivial | ||
1216.2.i.j.961.1 | 2 | 19.11 | even | 3 | inner |