Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,2,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (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: | \(1.95633484952\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 116.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.116 |
Dual form | 245.2.e.c.226.1 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | −1.50000 | + | 2.59808i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | −6.00000 | −2.44949 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | −1.00000 | + | 1.73205i | −0.316228 | + | 0.547723i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | −3.00000 | − | 5.19615i | −0.866025 | − | 1.50000i | ||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | −0.774597 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 6.00000 | − | 10.3923i | 1.41421 | − | 2.44949i | ||||
\(19\) | −3.00000 | − | 5.19615i | −0.688247 | − | 1.19208i | −0.972404 | − | 0.233301i | \(-0.925047\pi\) |
0.284157 | − | 0.958778i | \(-0.408286\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 3.00000 | + | 5.19615i | 0.588348 | + | 1.01905i | ||||
\(27\) | 9.00000 | 1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | −3.00000 | − | 5.19615i | −0.547723 | − | 0.948683i | ||||
\(31\) | −3.00000 | + | 5.19615i | −0.538816 | + | 0.933257i | 0.460152 | + | 0.887840i | \(0.347795\pi\) |
−0.998968 | + | 0.0454165i | \(0.985539\pi\) | |||||||
\(32\) | −4.00000 | + | 6.92820i | −0.707107 | + | 1.22474i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.0000 | 2.00000 | ||||||||
\(37\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(38\) | 6.00000 | − | 10.3923i | 0.973329 | − | 1.68585i | ||||
\(39\) | −4.50000 | + | 7.79423i | −0.720577 | + | 1.24808i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | 3.00000 | − | 5.19615i | 0.447214 | − | 0.774597i | ||||
\(46\) | −4.00000 | + | 6.92820i | −0.589768 | + | 1.02151i | ||||
\(47\) | 4.50000 | + | 7.79423i | 0.656392 | + | 1.13691i | 0.981543 | + | 0.191243i | \(0.0612518\pi\) |
−0.325150 | + | 0.945662i | \(0.605415\pi\) | |||||||
\(48\) | −12.0000 | −1.73205 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | −0.282843 | ||||||||
\(51\) | 4.50000 | + | 7.79423i | 0.630126 | + | 1.09141i | ||||
\(52\) | −3.00000 | + | 5.19615i | −0.416025 | + | 0.720577i | ||||
\(53\) | 5.00000 | − | 8.66025i | 0.686803 | − | 1.18958i | −0.286064 | − | 0.958211i | \(-0.592347\pi\) |
0.972867 | − | 0.231367i | \(-0.0743197\pi\) | |||||||
\(54\) | 9.00000 | + | 15.5885i | 1.22474 | + | 2.12132i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.0000 | 2.38416 | ||||||||
\(58\) | −1.00000 | − | 1.73205i | −0.131306 | − | 0.227429i | ||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 3.00000 | − | 5.19615i | 0.387298 | − | 0.670820i | ||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | −12.0000 | −1.52400 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 1.50000 | + | 2.59808i | 0.186052 | + | 0.322252i | ||||
\(66\) | 3.00000 | − | 5.19615i | 0.369274 | − | 0.639602i | ||||
\(67\) | 7.00000 | − | 12.1244i | 0.855186 | − | 1.48123i | −0.0212861 | − | 0.999773i | \(-0.506776\pi\) |
0.876472 | − | 0.481452i | \(-0.159891\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | −12.0000 | −1.44463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | + | 5.19615i | −0.351123 | + | 0.608164i | −0.986447 | − | 0.164083i | \(-0.947534\pi\) |
0.635323 | + | 0.772246i | \(0.280867\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.50000 | − | 2.59808i | −0.173205 | − | 0.300000i | ||||
\(76\) | 12.0000 | 1.37649 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −18.0000 | −2.03810 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | −2.00000 | + | 3.46410i | −0.223607 | + | 0.387298i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 6.00000 | + | 10.3923i | 0.662589 | + | 1.14764i | ||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | 0.325396 | ||||||||
\(86\) | −6.00000 | − | 10.3923i | −0.646997 | − | 1.12063i | ||||
\(87\) | 1.50000 | − | 2.59808i | 0.160817 | − | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | − | 10.3923i | −0.635999 | − | 1.10158i | −0.986303 | − | 0.164946i | \(-0.947255\pi\) |
0.350304 | − | 0.936636i | \(-0.386078\pi\) | |||||||
\(90\) | 12.0000 | 1.26491 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | −9.00000 | − | 15.5885i | −0.933257 | − | 1.61645i | ||||
\(94\) | −9.00000 | + | 15.5885i | −0.928279 | + | 1.60783i | ||||
\(95\) | 3.00000 | − | 5.19615i | 0.307794 | − | 0.533114i | ||||
\(96\) | −12.0000 | − | 20.7846i | −1.22474 | − | 2.12132i | ||||
\(97\) | −15.0000 | −1.52302 | −0.761510 | − | 0.648154i | \(-0.775541\pi\) | ||||
−0.761510 | + | 0.648154i | \(0.775541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | −1.00000 | − | 1.73205i | −0.100000 | − | 0.173205i | ||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | −9.00000 | + | 15.5885i | −0.891133 | + | 1.54349i | ||||
\(103\) | 4.50000 | + | 7.79423i | 0.443398 | + | 0.767988i | 0.997939 | − | 0.0641683i | \(-0.0204394\pi\) |
−0.554541 | + | 0.832156i | \(0.687106\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20.0000 | 1.94257 | ||||||||
\(107\) | 1.00000 | + | 1.73205i | 0.0966736 | + | 0.167444i | 0.910306 | − | 0.413936i | \(-0.135846\pi\) |
−0.813632 | + | 0.581380i | \(0.802513\pi\) | |||||||
\(108\) | −9.00000 | + | 15.5885i | −0.866025 | + | 1.50000i | ||||
\(109\) | 7.50000 | − | 12.9904i | 0.718370 | − | 1.24425i | −0.243276 | − | 0.969957i | \(-0.578222\pi\) |
0.961645 | − | 0.274296i | \(-0.0884447\pi\) | |||||||
\(110\) | −1.00000 | − | 1.73205i | −0.0953463 | − | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 18.0000 | + | 31.1769i | 1.68585 | + | 2.91999i | ||||
\(115\) | −2.00000 | + | 3.46410i | −0.186501 | + | 0.323029i | ||||
\(116\) | 1.00000 | − | 1.73205i | 0.0928477 | − | 0.160817i | ||||
\(117\) | −9.00000 | − | 15.5885i | −0.832050 | − | 1.44115i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.00000 | + | 15.5885i | −0.811503 | + | 1.40556i | ||||
\(124\) | −6.00000 | − | 10.3923i | −0.538816 | − | 0.933257i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.00000 | − | 15.5885i | 0.792406 | − | 1.37249i | ||||
\(130\) | −3.00000 | + | 5.19615i | −0.263117 | + | 0.455733i | ||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | 6.00000 | 0.522233 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 28.0000 | 2.41883 | ||||||||
\(135\) | 4.50000 | + | 7.79423i | 0.387298 | + | 0.670820i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.00000 | + | 6.92820i | −0.341743 | + | 0.591916i | −0.984757 | − | 0.173939i | \(-0.944351\pi\) |
0.643013 | + | 0.765855i | \(0.277684\pi\) | |||||||
\(138\) | −12.0000 | − | 20.7846i | −1.02151 | − | 1.76930i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.0000 | −2.27381 | ||||||||
\(142\) | −8.00000 | − | 13.8564i | −0.671345 | − | 1.16280i | ||||
\(143\) | −1.50000 | + | 2.59808i | −0.125436 | + | 0.217262i | ||||
\(144\) | 12.0000 | − | 20.7846i | 1.00000 | − | 1.73205i | ||||
\(145\) | −0.500000 | − | 0.866025i | −0.0415227 | − | 0.0719195i | ||||
\(146\) | −12.0000 | −0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | − | 8.66025i | −0.409616 | − | 0.709476i | 0.585231 | − | 0.810867i | \(-0.301004\pi\) |
−0.994847 | + | 0.101391i | \(0.967671\pi\) | |||||||
\(150\) | 3.00000 | − | 5.19615i | 0.244949 | − | 0.424264i | ||||
\(151\) | −7.50000 | + | 12.9904i | −0.610341 | + | 1.05714i | 0.380841 | + | 0.924640i | \(0.375634\pi\) |
−0.991183 | + | 0.132502i | \(0.957699\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.0000 | −1.45521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | −9.00000 | − | 15.5885i | −0.720577 | − | 1.24808i | ||||
\(157\) | −9.00000 | + | 15.5885i | −0.718278 | + | 1.24409i | 0.243403 | + | 0.969925i | \(0.421736\pi\) |
−0.961681 | + | 0.274169i | \(0.911597\pi\) | |||||||
\(158\) | −1.00000 | + | 1.73205i | −0.0795557 | + | 0.137795i | ||||
\(159\) | 15.0000 | + | 25.9808i | 1.18958 | + | 2.06041i | ||||
\(160\) | −8.00000 | −0.632456 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −18.0000 | −1.41421 | ||||||||
\(163\) | −8.00000 | − | 13.8564i | −0.626608 | − | 1.08532i | −0.988227 | − | 0.152992i | \(-0.951109\pi\) |
0.361619 | − | 0.932326i | \(-0.382224\pi\) | |||||||
\(164\) | −6.00000 | + | 10.3923i | −0.468521 | + | 0.811503i | ||||
\(165\) | 1.50000 | − | 2.59808i | 0.116775 | − | 0.202260i | ||||
\(166\) | 12.0000 | + | 20.7846i | 0.931381 | + | 1.61320i | ||||
\(167\) | 3.00000 | 0.232147 | 0.116073 | − | 0.993241i | \(-0.462969\pi\) | ||||
0.116073 | + | 0.993241i | \(0.462969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 3.00000 | + | 5.19615i | 0.230089 | + | 0.398527i | ||||
\(171\) | −18.0000 | + | 31.1769i | −1.37649 | + | 2.38416i | ||||
\(172\) | 6.00000 | − | 10.3923i | 0.457496 | − | 0.792406i | ||||
\(173\) | 1.50000 | + | 2.59808i | 0.114043 | + | 0.197528i | 0.917397 | − | 0.397974i | \(-0.130287\pi\) |
−0.803354 | + | 0.595502i | \(0.796953\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 9.00000 | + | 15.5885i | 0.676481 | + | 1.17170i | ||||
\(178\) | 12.0000 | − | 20.7846i | 0.899438 | − | 1.55787i | ||||
\(179\) | −2.00000 | + | 3.46410i | −0.149487 | + | 0.258919i | −0.931038 | − | 0.364922i | \(-0.881096\pi\) |
0.781551 | + | 0.623841i | \(0.214429\pi\) | |||||||
\(180\) | 6.00000 | + | 10.3923i | 0.447214 | + | 0.774597i | ||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 18.0000 | − | 31.1769i | 1.31982 | − | 2.28600i | ||||
\(187\) | 1.50000 | + | 2.59808i | 0.109691 | + | 0.189990i | ||||
\(188\) | −18.0000 | −1.31278 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | 0.870572 | ||||||||
\(191\) | −8.50000 | − | 14.7224i | −0.615038 | − | 1.06528i | −0.990378 | − | 0.138390i | \(-0.955807\pi\) |
0.375339 | − | 0.926887i | \(-0.377526\pi\) | |||||||
\(192\) | 12.0000 | − | 20.7846i | 0.866025 | − | 1.50000i | ||||
\(193\) | −6.00000 | + | 10.3923i | −0.431889 | + | 0.748054i | −0.997036 | − | 0.0769360i | \(-0.975486\pi\) |
0.565147 | + | 0.824991i | \(0.308820\pi\) | |||||||
\(194\) | −15.0000 | − | 25.9808i | −1.07694 | − | 1.86531i | ||||
\(195\) | −9.00000 | −0.644503 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 6.00000 | + | 10.3923i | 0.426401 | + | 0.738549i | ||||
\(199\) | −3.00000 | + | 5.19615i | −0.212664 | + | 0.368345i | −0.952548 | − | 0.304390i | \(-0.901547\pi\) |
0.739883 | + | 0.672735i | \(0.234881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.0000 | + | 36.3731i | 1.48123 | + | 2.56556i | ||||
\(202\) | 36.0000 | 2.53295 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −18.0000 | −1.26025 | ||||||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | −9.00000 | + | 15.5885i | −0.627060 | + | 1.08610i | ||||
\(207\) | 12.0000 | − | 20.7846i | 0.834058 | − | 1.44463i | ||||
\(208\) | 6.00000 | + | 10.3923i | 0.416025 | + | 0.720577i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0000 | 1.03264 | 0.516321 | − | 0.856395i | \(-0.327301\pi\) | ||||
0.516321 | + | 0.856395i | \(0.327301\pi\) | |||||||
\(212\) | 10.0000 | + | 17.3205i | 0.686803 | + | 1.18958i | ||||
\(213\) | 12.0000 | − | 20.7846i | 0.822226 | − | 1.42414i | ||||
\(214\) | −2.00000 | + | 3.46410i | −0.136717 | + | 0.236801i | ||||
\(215\) | −3.00000 | − | 5.19615i | −0.204598 | − | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 30.0000 | 2.03186 | ||||||||
\(219\) | −9.00000 | − | 15.5885i | −0.608164 | − | 1.05337i | ||||
\(220\) | 1.00000 | − | 1.73205i | 0.0674200 | − | 0.116775i | ||||
\(221\) | 4.50000 | − | 7.79423i | 0.302703 | − | 0.524297i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.00000 | 0.200895 | 0.100447 | − | 0.994942i | \(-0.467973\pi\) | ||||
0.100447 | + | 0.994942i | \(0.467973\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.00000 | 0.400000 | ||||||||
\(226\) | 8.00000 | + | 13.8564i | 0.532152 | + | 0.921714i | ||||
\(227\) | −1.50000 | + | 2.59808i | −0.0995585 | + | 0.172440i | −0.911502 | − | 0.411296i | \(-0.865076\pi\) |
0.811943 | + | 0.583736i | \(0.198410\pi\) | |||||||
\(228\) | −18.0000 | + | 31.1769i | −1.19208 | + | 2.06474i | ||||
\(229\) | 3.00000 | + | 5.19615i | 0.198246 | + | 0.343371i | 0.947960 | − | 0.318390i | \(-0.103142\pi\) |
−0.749714 | + | 0.661762i | \(0.769809\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | + | 6.92820i | 0.262049 | + | 0.453882i | 0.966786 | − | 0.255586i | \(-0.0822686\pi\) |
−0.704737 | + | 0.709468i | \(0.748935\pi\) | |||||||
\(234\) | 18.0000 | − | 31.1769i | 1.17670 | − | 2.03810i | ||||
\(235\) | −4.50000 | + | 7.79423i | −0.293548 | + | 0.508439i | ||||
\(236\) | 6.00000 | + | 10.3923i | 0.390567 | + | 0.676481i | ||||
\(237\) | −3.00000 | −0.194871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.00000 | 0.452792 | 0.226396 | − | 0.974035i | \(-0.427306\pi\) | ||||
0.226396 | + | 0.974035i | \(0.427306\pi\) | |||||||
\(240\) | −6.00000 | − | 10.3923i | −0.387298 | − | 0.670820i | ||||
\(241\) | 12.0000 | − | 20.7846i | 0.772988 | − | 1.33885i | −0.162930 | − | 0.986638i | \(-0.552095\pi\) |
0.935918 | − | 0.352217i | \(-0.114572\pi\) | |||||||
\(242\) | −10.0000 | + | 17.3205i | −0.642824 | + | 1.11340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −36.0000 | −2.29528 | ||||||||
\(247\) | −9.00000 | − | 15.5885i | −0.572656 | − | 0.991870i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.0000 | + | 31.1769i | −1.14070 | + | 1.97576i | ||||
\(250\) | −1.00000 | − | 1.73205i | −0.0632456 | − | 0.109545i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | −2.00000 | − | 3.46410i | −0.125491 | − | 0.217357i | ||||
\(255\) | −4.50000 | + | 7.79423i | −0.281801 | + | 0.488094i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | 36.0000 | 2.24126 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.00000 | −0.372104 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | 12.0000 | − | 20.7846i | 0.741362 | − | 1.28408i | ||||
\(263\) | 5.00000 | − | 8.66025i | 0.308313 | − | 0.534014i | −0.669680 | − | 0.742650i | \(-0.733569\pi\) |
0.977993 | + | 0.208635i | \(0.0669022\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000 | 0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.0000 | 2.20316 | ||||||||
\(268\) | 14.0000 | + | 24.2487i | 0.855186 | + | 1.48123i | ||||
\(269\) | −12.0000 | + | 20.7846i | −0.731653 | + | 1.26726i | 0.224523 | + | 0.974469i | \(0.427917\pi\) |
−0.956176 | + | 0.292791i | \(0.905416\pi\) | |||||||
\(270\) | −9.00000 | + | 15.5885i | −0.547723 | + | 0.948683i | ||||
\(271\) | −12.0000 | − | 20.7846i | −0.728948 | − | 1.26258i | −0.957328 | − | 0.289003i | \(-0.906676\pi\) |
0.228380 | − | 0.973572i | \(-0.426657\pi\) | |||||||
\(272\) | 12.0000 | 0.727607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | 12.0000 | − | 20.7846i | 0.722315 | − | 1.25109i | ||||
\(277\) | 14.0000 | − | 24.2487i | 0.841178 | − | 1.45696i | −0.0477206 | − | 0.998861i | \(-0.515196\pi\) |
0.888899 | − | 0.458103i | \(-0.151471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 36.0000 | 2.15526 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.00000 | −0.298275 | −0.149137 | − | 0.988816i | \(-0.547650\pi\) | ||||
−0.149137 | + | 0.988816i | \(0.547650\pi\) | |||||||
\(282\) | −27.0000 | − | 46.7654i | −1.60783 | − | 2.78484i | ||||
\(283\) | −10.5000 | + | 18.1865i | −0.624160 | + | 1.08108i | 0.364542 | + | 0.931187i | \(0.381225\pi\) |
−0.988703 | + | 0.149890i | \(0.952108\pi\) | |||||||
\(284\) | 8.00000 | − | 13.8564i | 0.474713 | − | 0.822226i | ||||
\(285\) | 9.00000 | + | 15.5885i | 0.533114 | + | 0.923381i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 48.0000 | 2.82843 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 1.00000 | − | 1.73205i | 0.0587220 | − | 0.101710i | ||||
\(291\) | 22.5000 | − | 38.9711i | 1.31897 | − | 2.28453i | ||||
\(292\) | −6.00000 | − | 10.3923i | −0.351123 | − | 0.608164i | ||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.50000 | + | 7.79423i | −0.261116 | + | 0.452267i | ||||
\(298\) | 10.0000 | − | 17.3205i | 0.579284 | − | 1.00335i | ||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 6.00000 | 0.346410 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −30.0000 | −1.72631 | ||||||||
\(303\) | 27.0000 | + | 46.7654i | 1.55111 | + | 2.68660i | ||||
\(304\) | 12.0000 | − | 20.7846i | 0.688247 | − | 1.19208i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −18.0000 | − | 31.1769i | −1.02899 | − | 1.78227i | ||||
\(307\) | −3.00000 | −0.171219 | −0.0856095 | − | 0.996329i | \(-0.527284\pi\) | ||||
−0.0856095 | + | 0.996329i | \(0.527284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.0000 | −1.53598 | ||||||||
\(310\) | −6.00000 | − | 10.3923i | −0.340777 | − | 0.590243i | ||||
\(311\) | 3.00000 | − | 5.19615i | 0.170114 | − | 0.294647i | −0.768345 | − | 0.640036i | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.50000 | − | 2.59808i | −0.0847850 | − | 0.146852i | 0.820515 | − | 0.571626i | \(-0.193687\pi\) |
−0.905300 | + | 0.424774i | \(0.860354\pi\) | |||||||
\(314\) | −36.0000 | −2.03160 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | 11.0000 | + | 19.0526i | 0.617822 | + | 1.07010i | 0.989882 | + | 0.141890i | \(0.0453179\pi\) |
−0.372061 | + | 0.928208i | \(0.621349\pi\) | |||||||
\(318\) | −30.0000 | + | 51.9615i | −1.68232 | + | 2.91386i | ||||
\(319\) | 0.500000 | − | 0.866025i | 0.0279946 | − | 0.0484881i | ||||
\(320\) | −4.00000 | − | 6.92820i | −0.223607 | − | 0.387298i | ||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0000 | −1.00155 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.500000 | − | 0.866025i | ||||
\(325\) | −1.50000 | + | 2.59808i | −0.0832050 | + | 0.144115i | ||||
\(326\) | 16.0000 | − | 27.7128i | 0.886158 | − | 1.53487i | ||||
\(327\) | 22.5000 | + | 38.9711i | 1.24425 | + | 2.15511i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.00000 | 0.330289 | ||||||||
\(331\) | −6.00000 | − | 10.3923i | −0.329790 | − | 0.571213i | 0.652680 | − | 0.757634i | \(-0.273645\pi\) |
−0.982470 | + | 0.186421i | \(0.940311\pi\) | |||||||
\(332\) | −12.0000 | + | 20.7846i | −0.658586 | + | 1.14070i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.00000 | + | 5.19615i | 0.164153 | + | 0.284321i | ||||
\(335\) | 14.0000 | 0.764902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.0000 | −1.30736 | −0.653682 | − | 0.756770i | \(-0.726776\pi\) | ||||
−0.653682 | + | 0.756770i | \(0.726776\pi\) | |||||||
\(338\) | −4.00000 | − | 6.92820i | −0.217571 | − | 0.376845i | ||||
\(339\) | −12.0000 | + | 20.7846i | −0.651751 | + | 1.12887i | ||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | −72.0000 | −3.89331 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.00000 | − | 10.3923i | −0.323029 | − | 0.559503i | ||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | −8.00000 | + | 13.8564i | −0.429463 | + | 0.743851i | −0.996826 | − | 0.0796169i | \(-0.974630\pi\) |
0.567363 | + | 0.823468i | \(0.307964\pi\) | |||||||
\(348\) | 3.00000 | + | 5.19615i | 0.160817 | + | 0.278543i | ||||
\(349\) | −30.0000 | −1.60586 | −0.802932 | − | 0.596071i | \(-0.796728\pi\) | ||||
−0.802932 | + | 0.596071i | \(0.796728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.0000 | 1.44115 | ||||||||
\(352\) | −4.00000 | − | 6.92820i | −0.213201 | − | 0.369274i | ||||
\(353\) | 1.50000 | − | 2.59808i | 0.0798369 | − | 0.138282i | −0.823343 | − | 0.567545i | \(-0.807893\pi\) |
0.903179 | + | 0.429263i | \(0.141227\pi\) | |||||||
\(354\) | −18.0000 | + | 31.1769i | −0.956689 | + | 1.65703i | ||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | 24.0000 | 1.27200 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.00000 | −0.422813 | ||||||||
\(359\) | −16.0000 | − | 27.7128i | −0.844448 | − | 1.46263i | −0.886100 | − | 0.463494i | \(-0.846596\pi\) |
0.0416523 | − | 0.999132i | \(-0.486738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | −6.00000 | − | 10.3923i | −0.315353 | − | 0.546207i | ||||
\(363\) | −30.0000 | −1.57459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5000 | − | 28.5788i | 0.861293 | − | 1.49180i | −0.00938849 | − | 0.999956i | \(-0.502988\pi\) |
0.870681 | − | 0.491847i | \(-0.163678\pi\) | |||||||
\(368\) | −8.00000 | + | 13.8564i | −0.417029 | + | 0.722315i | ||||
\(369\) | −18.0000 | − | 31.1769i | −0.937043 | − | 1.62301i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 36.0000 | 1.86651 | ||||||||
\(373\) | −2.00000 | − | 3.46410i | −0.103556 | − | 0.179364i | 0.809591 | − | 0.586994i | \(-0.199689\pi\) |
−0.913147 | + | 0.407630i | \(0.866355\pi\) | |||||||
\(374\) | −3.00000 | + | 5.19615i | −0.155126 | + | 0.268687i | ||||
\(375\) | 1.50000 | − | 2.59808i | 0.0774597 | − | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | 6.00000 | + | 10.3923i | 0.307794 | + | 0.533114i | ||||
\(381\) | 3.00000 | − | 5.19615i | 0.153695 | − | 0.266207i | ||||
\(382\) | 17.0000 | − | 29.4449i | 0.869796 | − | 1.50653i | ||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.0000 | −1.22157 | ||||||||
\(387\) | 18.0000 | + | 31.1769i | 0.914991 | + | 1.58481i | ||||
\(388\) | 15.0000 | − | 25.9808i | 0.761510 | − | 1.31897i | ||||
\(389\) | −6.50000 | + | 11.2583i | −0.329563 | + | 0.570820i | −0.982425 | − | 0.186657i | \(-0.940235\pi\) |
0.652862 | + | 0.757477i | \(0.273568\pi\) | |||||||
\(390\) | −9.00000 | − | 15.5885i | −0.455733 | − | 0.789352i | ||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.0000 | 1.81596 | ||||||||
\(394\) | −2.00000 | − | 3.46410i | −0.100759 | − | 0.174519i | ||||
\(395\) | −0.500000 | + | 0.866025i | −0.0251577 | + | 0.0435745i | ||||
\(396\) | −6.00000 | + | 10.3923i | −0.301511 | + | 0.522233i | ||||
\(397\) | −4.50000 | − | 7.79423i | −0.225849 | − | 0.391181i | 0.730725 | − | 0.682672i | \(-0.239182\pi\) |
−0.956574 | + | 0.291491i | \(0.905849\pi\) | |||||||
\(398\) | −12.0000 | −0.601506 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 9.50000 | + | 16.4545i | 0.474407 | + | 0.821698i | 0.999571 | − | 0.0293039i | \(-0.00932905\pi\) |
−0.525163 | + | 0.851002i | \(0.675996\pi\) | |||||||
\(402\) | −42.0000 | + | 72.7461i | −2.09477 | + | 3.62825i | ||||
\(403\) | −9.00000 | + | 15.5885i | −0.448322 | + | 0.776516i | ||||
\(404\) | 18.0000 | + | 31.1769i | 0.895533 | + | 1.55111i | ||||
\(405\) | −9.00000 | −0.447214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0000 | + | 25.9808i | −0.741702 | + | 1.28467i | 0.210017 | + | 0.977698i | \(0.432648\pi\) |
−0.951720 | + | 0.306968i | \(0.900685\pi\) | |||||||
\(410\) | −6.00000 | + | 10.3923i | −0.296319 | + | 0.513239i | ||||
\(411\) | −12.0000 | − | 20.7846i | −0.591916 | − | 1.02523i | ||||
\(412\) | −18.0000 | −0.886796 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 48.0000 | 2.35907 | ||||||||
\(415\) | 6.00000 | + | 10.3923i | 0.294528 | + | 0.510138i | ||||
\(416\) | −12.0000 | + | 20.7846i | −0.588348 | + | 1.01905i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | + | 10.3923i | 0.293470 | + | 0.508304i | ||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.00000 | 0.0487370 | 0.0243685 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243685 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(422\) | 15.0000 | + | 25.9808i | 0.730189 | + | 1.26472i | ||||
\(423\) | 27.0000 | − | 46.7654i | 1.31278 | − | 2.27381i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.50000 | + | 2.59808i | 0.0727607 | + | 0.126025i | ||||
\(426\) | 48.0000 | 2.32561 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | −4.50000 | − | 7.79423i | −0.217262 | − | 0.376309i | ||||
\(430\) | 6.00000 | − | 10.3923i | 0.289346 | − | 0.501161i | ||||
\(431\) | −2.50000 | + | 4.33013i | −0.120421 | + | 0.208575i | −0.919934 | − | 0.392074i | \(-0.871758\pi\) |
0.799513 | + | 0.600649i | \(0.205091\pi\) | |||||||
\(432\) | 18.0000 | + | 31.1769i | 0.866025 | + | 1.50000i | ||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.00000 | 0.143839 | ||||||||
\(436\) | 15.0000 | + | 25.9808i | 0.718370 | + | 1.24425i | ||||
\(437\) | 12.0000 | − | 20.7846i | 0.574038 | − | 0.994263i | ||||
\(438\) | 18.0000 | − | 31.1769i | 0.860073 | − | 1.48969i | ||||
\(439\) | −6.00000 | − | 10.3923i | −0.286364 | − | 0.495998i | 0.686575 | − | 0.727059i | \(-0.259113\pi\) |
−0.972939 | + | 0.231062i | \(0.925780\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.0000 | 0.856173 | ||||||||
\(443\) | −17.0000 | − | 29.4449i | −0.807694 | − | 1.39897i | −0.914457 | − | 0.404683i | \(-0.867382\pi\) |
0.106763 | − | 0.994285i | \(-0.465952\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | 3.00000 | + | 5.19615i | 0.142054 | + | 0.246045i | ||||
\(447\) | 30.0000 | 1.41895 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.0000 | 1.08544 | 0.542719 | − | 0.839915i | \(-0.317395\pi\) | ||||
0.542719 | + | 0.839915i | \(0.317395\pi\) | |||||||
\(450\) | 6.00000 | + | 10.3923i | 0.282843 | + | 0.489898i | ||||
\(451\) | −3.00000 | + | 5.19615i | −0.141264 | + | 0.244677i | ||||
\(452\) | −8.00000 | + | 13.8564i | −0.376288 | + | 0.651751i | ||||
\(453\) | −22.5000 | − | 38.9711i | −1.05714 | − | 1.83102i | ||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.00000 | − | 5.19615i | −0.140334 | − | 0.243066i | 0.787288 | − | 0.616585i | \(-0.211484\pi\) |
−0.927622 | + | 0.373519i | \(0.878151\pi\) | |||||||
\(458\) | −6.00000 | + | 10.3923i | −0.280362 | + | 0.485601i | ||||
\(459\) | 13.5000 | − | 23.3827i | 0.630126 | − | 1.09141i | ||||
\(460\) | −4.00000 | − | 6.92820i | −0.186501 | − | 0.323029i | ||||
\(461\) | 36.0000 | 1.67669 | 0.838344 | − | 0.545142i | \(-0.183524\pi\) | ||||
0.838344 | + | 0.545142i | \(0.183524\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | −2.00000 | − | 3.46410i | −0.0928477 | − | 0.160817i | ||||
\(465\) | 9.00000 | − | 15.5885i | 0.417365 | − | 0.722897i | ||||
\(466\) | −8.00000 | + | 13.8564i | −0.370593 | + | 0.641886i | ||||
\(467\) | 7.50000 | + | 12.9904i | 0.347059 | + | 0.601123i | 0.985726 | − | 0.168360i | \(-0.0538472\pi\) |
−0.638667 | + | 0.769483i | \(0.720514\pi\) | |||||||
\(468\) | 36.0000 | 1.66410 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −18.0000 | −0.830278 | ||||||||
\(471\) | −27.0000 | − | 46.7654i | −1.24409 | − | 2.15483i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 5.19615i | 0.137940 | − | 0.238919i | ||||
\(474\) | −3.00000 | − | 5.19615i | −0.137795 | − | 0.238667i | ||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −60.0000 | −2.74721 | ||||||||
\(478\) | 7.00000 | + | 12.1244i | 0.320173 | + | 0.554555i | ||||
\(479\) | 12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | \(-0.648611\pi\) |
0.998392 | − | 0.0566937i | \(-0.0180558\pi\) | |||||||
\(480\) | 12.0000 | − | 20.7846i | 0.547723 | − | 0.948683i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 48.0000 | 2.18634 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.0000 | −0.909091 | ||||||||
\(485\) | −7.50000 | − | 12.9904i | −0.340557 | − | 0.589863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0000 | + | 31.1769i | −0.815658 | + | 1.41276i | 0.0931967 | + | 0.995648i | \(0.470291\pi\) |
−0.908855 | + | 0.417113i | \(0.863042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 48.0000 | 2.17064 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.0000 | 1.03798 | 0.518988 | − | 0.854782i | \(-0.326309\pi\) | ||||
0.518988 | + | 0.854782i | \(0.326309\pi\) | |||||||
\(492\) | −18.0000 | − | 31.1769i | −0.811503 | − | 1.40556i | ||||
\(493\) | −1.50000 | + | 2.59808i | −0.0675566 | + | 0.117011i | ||||
\(494\) | 18.0000 | − | 31.1769i | 0.809858 | − | 1.40272i | ||||
\(495\) | 3.00000 | + | 5.19615i | 0.134840 | + | 0.233550i | ||||
\(496\) | −24.0000 | −1.07763 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −72.0000 | −3.22640 | ||||||||
\(499\) | 13.5000 | + | 23.3827i | 0.604343 | + | 1.04675i | 0.992155 | + | 0.125014i | \(0.0398977\pi\) |
−0.387812 | + | 0.921739i | \(0.626769\pi\) | |||||||
\(500\) | 1.00000 | − | 1.73205i | 0.0447214 | − | 0.0774597i | ||||
\(501\) | −4.50000 | + | 7.79423i | −0.201045 | + | 0.348220i | ||||
\(502\) | −12.0000 | − | 20.7846i | −0.535586 | − | 0.927663i | ||||
\(503\) | 9.00000 | 0.401290 | 0.200645 | − | 0.979664i | \(-0.435696\pi\) | ||||
0.200645 | + | 0.979664i | \(0.435696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | −4.00000 | − | 6.92820i | −0.177822 | − | 0.307996i | ||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 2.00000 | − | 3.46410i | 0.0887357 | − | 0.153695i | ||||
\(509\) | 12.0000 | + | 20.7846i | 0.531891 | + | 0.921262i | 0.999307 | + | 0.0372243i | \(0.0118516\pi\) |
−0.467416 | + | 0.884037i | \(0.654815\pi\) | |||||||
\(510\) | −18.0000 | −0.797053 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −32.0000 | −1.41421 | ||||||||
\(513\) | −27.0000 | − | 46.7654i | −1.19208 | − | 2.06474i | ||||
\(514\) | 18.0000 | − | 31.1769i | 0.793946 | − | 1.37515i | ||||
\(515\) | −4.50000 | + | 7.79423i | −0.198294 | + | 0.343455i | ||||
\(516\) | 18.0000 | + | 31.1769i | 0.792406 | + | 1.37249i | ||||
\(517\) | −9.00000 | −0.395820 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.00000 | −0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | −6.00000 | + | 10.3923i | −0.262613 | + | 0.454859i | ||||
\(523\) | −12.0000 | − | 20.7846i | −0.524723 | − | 0.908848i | −0.999586 | − | 0.0287874i | \(-0.990835\pi\) |
0.474862 | − | 0.880060i | \(-0.342498\pi\) | |||||||
\(524\) | 24.0000 | 1.04844 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.0000 | 0.872041 | ||||||||
\(527\) | 9.00000 | + | 15.5885i | 0.392046 | + | 0.679044i | ||||
\(528\) | 6.00000 | − | 10.3923i | 0.261116 | − | 0.452267i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 10.0000 | + | 17.3205i | 0.434372 | + | 0.752355i | ||||
\(531\) | −36.0000 | −1.56227 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.0000 | 0.779667 | ||||||||
\(534\) | 36.0000 | + | 62.3538i | 1.55787 | + | 2.69831i | ||||
\(535\) | −1.00000 | + | 1.73205i | −0.0432338 | + | 0.0748831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | − | 10.3923i | −0.258919 | − | 0.448461i | ||||
\(538\) | −48.0000 | −2.06943 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −18.0000 | −0.774597 | ||||||||
\(541\) | −5.50000 | − | 9.52628i | −0.236463 | − | 0.409567i | 0.723234 | − | 0.690604i | \(-0.242655\pi\) |
−0.959697 | + | 0.281037i | \(0.909322\pi\) | |||||||
\(542\) | 24.0000 | − | 41.5692i | 1.03089 | − | 1.78555i | ||||
\(543\) | 9.00000 | − | 15.5885i | 0.386227 | − | 0.668965i | ||||
\(544\) | 12.0000 | + | 20.7846i | 0.514496 | + | 0.891133i | ||||
\(545\) | 15.0000 | 0.642529 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | −8.00000 | − | 13.8564i | −0.341743 | − | 0.591916i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | − | 1.73205i | 0.0426401 | − | 0.0738549i | ||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 56.0000 | 2.37921 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.00000 | + | 3.46410i | −0.0847427 | + | 0.146779i | −0.905282 | − | 0.424812i | \(-0.860340\pi\) |
0.820539 | + | 0.571591i | \(0.193674\pi\) | |||||||
\(558\) | 36.0000 | + | 62.3538i | 1.52400 | + | 2.63965i | ||||
\(559\) | −18.0000 | −0.761319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | −5.00000 | − | 8.66025i | −0.210912 | − | 0.365311i | ||||
\(563\) | −6.00000 | + | 10.3923i | −0.252870 | + | 0.437983i | −0.964315 | − | 0.264758i | \(-0.914708\pi\) |
0.711445 | + | 0.702742i | \(0.248041\pi\) | |||||||
\(564\) | 27.0000 | − | 46.7654i | 1.13691 | − | 1.96918i | ||||
\(565\) | 4.00000 | + | 6.92820i | 0.168281 | + | 0.291472i | ||||
\(566\) | −42.0000 | −1.76539 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.0000 | + | 32.9090i | 0.796521 | + | 1.37962i | 0.921869 | + | 0.387503i | \(0.126662\pi\) |
−0.125347 | + | 0.992113i | \(0.540004\pi\) | |||||||
\(570\) | −18.0000 | + | 31.1769i | −0.753937 | + | 1.30586i | ||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | −3.00000 | − | 5.19615i | −0.125436 | − | 0.217262i | ||||
\(573\) | 51.0000 | 2.13056 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 24.0000 | + | 41.5692i | 1.00000 | + | 1.73205i | ||||
\(577\) | −7.50000 | + | 12.9904i | −0.312229 | + | 0.540797i | −0.978845 | − | 0.204605i | \(-0.934409\pi\) |
0.666616 | + | 0.745402i | \(0.267742\pi\) | |||||||
\(578\) | −8.00000 | + | 13.8564i | −0.332756 | + | 0.576351i | ||||
\(579\) | −18.0000 | − | 31.1769i | −0.748054 | − | 1.29567i | ||||
\(580\) | 2.00000 | 0.0830455 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 90.0000 | 3.73062 | ||||||||
\(583\) | 5.00000 | + | 8.66025i | 0.207079 | + | 0.358671i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.00000 | − | 15.5885i | 0.372104 | − | 0.644503i | ||||
\(586\) | 9.00000 | + | 15.5885i | 0.371787 | + | 0.643953i | ||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.0000 | 1.48335 | ||||||||
\(590\) | 6.00000 | + | 10.3923i | 0.247016 | + | 0.427844i | ||||
\(591\) | 3.00000 | − | 5.19615i | 0.123404 | − | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.5000 | + | 38.9711i | 0.923964 | + | 1.60035i | 0.793219 | + | 0.608937i | \(0.208404\pi\) |
0.130746 | + | 0.991416i | \(0.458263\pi\) | |||||||
\(594\) | −18.0000 | −0.738549 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.0000 | 0.819232 | ||||||||
\(597\) | −9.00000 | − | 15.5885i | −0.368345 | − | 0.637993i | ||||
\(598\) | −12.0000 | + | 20.7846i | −0.490716 | + | 0.849946i | ||||
\(599\) | −8.50000 | + | 14.7224i | −0.347301 | + | 0.601542i | −0.985769 | − | 0.168106i | \(-0.946235\pi\) |
0.638468 | + | 0.769648i | \(0.279568\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0000 | −1.22373 | −0.611863 | − | 0.790964i | \(-0.709580\pi\) | ||||
−0.611863 | + | 0.790964i | \(0.709580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −84.0000 | −3.42074 | ||||||||
\(604\) | −15.0000 | − | 25.9808i | −0.610341 | − | 1.05714i | ||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | −54.0000 | + | 93.5307i | −2.19360 | + | 3.79943i | ||||
\(607\) | −10.5000 | − | 18.1865i | −0.426182 | − | 0.738169i | 0.570348 | − | 0.821403i | \(-0.306808\pi\) |
−0.996530 | + | 0.0832344i | \(0.973475\pi\) | |||||||
\(608\) | 48.0000 | 1.94666 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.5000 | + | 23.3827i | 0.546152 | + | 0.945962i | ||||
\(612\) | 18.0000 | − | 31.1769i | 0.727607 | − | 1.26025i | ||||
\(613\) | 1.00000 | − | 1.73205i | 0.0403896 | − | 0.0699569i | −0.845124 | − | 0.534570i | \(-0.820473\pi\) |
0.885514 | + | 0.464614i | \(0.153807\pi\) | |||||||
\(614\) | −3.00000 | − | 5.19615i | −0.121070 | − | 0.209700i | ||||
\(615\) | −18.0000 | −0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.00000 | 0.161034 | 0.0805170 | − | 0.996753i | \(-0.474343\pi\) | ||||
0.0805170 | + | 0.996753i | \(0.474343\pi\) | |||||||
\(618\) | −27.0000 | − | 46.7654i | −1.08610 | − | 1.88118i | ||||
\(619\) | 12.0000 | − | 20.7846i | 0.482321 | − | 0.835404i | −0.517473 | − | 0.855699i | \(-0.673127\pi\) |
0.999794 | + | 0.0202954i | \(0.00646066\pi\) | |||||||
\(620\) | 6.00000 | − | 10.3923i | 0.240966 | − | 0.417365i | ||||
\(621\) | 18.0000 | + | 31.1769i | 0.722315 | + | 1.25109i | ||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −36.0000 | −1.44115 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 3.00000 | − | 5.19615i | 0.119904 | − | 0.207680i | ||||
\(627\) | −9.00000 | + | 15.5885i | −0.359425 | + | 0.622543i | ||||
\(628\) | −18.0000 | − | 31.1769i | −0.718278 | − | 1.24409i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.0000 | −0.437903 | −0.218952 | − | 0.975736i | \(-0.570264\pi\) | ||||
−0.218952 | + | 0.975736i | \(0.570264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.5000 | + | 38.9711i | −0.894295 | + | 1.54896i | ||||
\(634\) | −22.0000 | + | 38.1051i | −0.873732 | + | 1.51335i | ||||
\(635\) | −1.00000 | − | 1.73205i | −0.0396838 | − | 0.0687343i | ||||
\(636\) | −60.0000 | −2.37915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | 24.0000 | + | 41.5692i | 0.949425 | + | 1.64445i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.00000 | − | 1.73205i | 0.0394976 | − | 0.0684119i | −0.845601 | − | 0.533816i | \(-0.820758\pi\) |
0.885098 | + | 0.465404i | \(0.154091\pi\) | |||||||
\(642\) | −6.00000 | − | 10.3923i | −0.236801 | − | 0.410152i | ||||
\(643\) | 27.0000 | 1.06478 | 0.532388 | − | 0.846500i | \(-0.321295\pi\) | ||||
0.532388 | + | 0.846500i | \(0.321295\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.0000 | 0.708749 | ||||||||
\(646\) | −18.0000 | − | 31.1769i | −0.708201 | − | 1.22664i | ||||
\(647\) | −6.00000 | + | 10.3923i | −0.235884 | + | 0.408564i | −0.959529 | − | 0.281609i | \(-0.909132\pi\) |
0.723645 | + | 0.690172i | \(0.242465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000 | + | 5.19615i | 0.117760 | + | 0.203967i | ||||
\(650\) | −6.00000 | −0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.0000 | 1.25322 | ||||||||
\(653\) | −7.00000 | − | 12.1244i | −0.273931 | − | 0.474463i | 0.695934 | − | 0.718106i | \(-0.254991\pi\) |
−0.969865 | + | 0.243643i | \(0.921657\pi\) | |||||||
\(654\) | −45.0000 | + | 77.9423i | −1.75964 | + | 3.04778i | ||||
\(655\) | 6.00000 | − | 10.3923i | 0.234439 | − | 0.406061i | ||||
\(656\) | 12.0000 | + | 20.7846i | 0.468521 | + | 0.811503i | ||||
\(657\) | 36.0000 | 1.40449 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.0000 | −0.740135 | −0.370067 | − | 0.929005i | \(-0.620665\pi\) | ||||
−0.370067 | + | 0.929005i | \(0.620665\pi\) | |||||||
\(660\) | 3.00000 | + | 5.19615i | 0.116775 | + | 0.202260i | ||||
\(661\) | −6.00000 | + | 10.3923i | −0.233373 | + | 0.404214i | −0.958799 | − | 0.284087i | \(-0.908310\pi\) |
0.725426 | + | 0.688301i | \(0.241643\pi\) | |||||||
\(662\) | 12.0000 | − | 20.7846i | 0.466393 | − | 0.807817i | ||||
\(663\) | 13.5000 | + | 23.3827i | 0.524297 | + | 0.908108i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00000 | − | 3.46410i | −0.0774403 | − | 0.134131i | ||||
\(668\) | −3.00000 | + | 5.19615i | −0.116073 | + | 0.201045i | ||||
\(669\) | −4.50000 | + | 7.79423i | −0.173980 | + | 0.301342i | ||||
\(670\) | 14.0000 | + | 24.2487i | 0.540867 | + | 0.936809i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0000 | 0.462566 | 0.231283 | − | 0.972887i | \(-0.425708\pi\) | ||||
0.231283 | + | 0.972887i | \(0.425708\pi\) | |||||||
\(674\) | −24.0000 | − | 41.5692i | −0.924445 | − | 1.60119i | ||||
\(675\) | −4.50000 | + | 7.79423i | −0.173205 | + | 0.300000i | ||||
\(676\) | 4.00000 | − | 6.92820i | 0.153846 | − | 0.266469i | ||||
\(677\) | 4.50000 | + | 7.79423i | 0.172949 | + | 0.299557i | 0.939450 | − | 0.342687i | \(-0.111337\pi\) |
−0.766501 | + | 0.642244i | \(0.778004\pi\) | |||||||
\(678\) | −48.0000 | −1.84343 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 7.79423i | −0.172440 | − | 0.298675i | ||||
\(682\) | 6.00000 | − | 10.3923i | 0.229752 | − | 0.397942i | ||||
\(683\) | −4.00000 | + | 6.92820i | −0.153056 | + | 0.265100i | −0.932349 | − | 0.361559i | \(-0.882245\pi\) |
0.779294 | + | 0.626659i | \(0.215578\pi\) | |||||||
\(684\) | −36.0000 | − | 62.3538i | −1.37649 | − | 2.38416i | ||||
\(685\) | −8.00000 | −0.305664 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.0000 | −0.686743 | ||||||||
\(688\) | −12.0000 | − | 20.7846i | −0.457496 | − | 0.792406i | ||||
\(689\) | 15.0000 | − | 25.9808i | 0.571454 | − | 0.989788i | ||||
\(690\) | 12.0000 | − | 20.7846i | 0.456832 | − | 0.791257i | ||||
\(691\) | −18.0000 | − | 31.1769i | −0.684752 | − | 1.18603i | −0.973515 | − | 0.228625i | \(-0.926577\pi\) |
0.288762 | − | 0.957401i | \(-0.406756\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.0000 | −1.21470 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | − | 15.5885i | 0.340899 | − | 0.590455i | ||||
\(698\) | −30.0000 | − | 51.9615i | −1.13552 | − | 1.96677i | ||||
\(699\) | −24.0000 | −0.907763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.0000 | 1.77517 | 0.887583 | − | 0.460648i | \(-0.152383\pi\) | ||||
0.887583 | + | 0.460648i | \(0.152383\pi\) | |||||||
\(702\) | 27.0000 | + | 46.7654i | 1.01905 | + | 1.76505i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.00000 | − | 6.92820i | 0.150756 | − | 0.261116i | ||||
\(705\) | −13.5000 | − | 23.3827i | −0.508439 | − | 0.880643i | ||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −36.0000 | −1.35296 | ||||||||
\(709\) | 16.5000 | + | 28.5788i | 0.619671 | + | 1.07330i | 0.989546 | + | 0.144219i | \(0.0460671\pi\) |
−0.369875 | + | 0.929081i | \(0.620600\pi\) | |||||||
\(710\) | 8.00000 | − | 13.8564i | 0.300235 | − | 0.520022i | ||||
\(711\) | 3.00000 | − | 5.19615i | 0.112509 | − | 0.194871i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.0000 | −0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | −0.112194 | ||||||||
\(716\) | −4.00000 | − | 6.92820i | −0.149487 | − | 0.258919i | ||||
\(717\) | −10.5000 | + | 18.1865i | −0.392130 | + | 0.679189i | ||||
\(718\) | 32.0000 | − | 55.4256i | 1.19423 | − | 2.06847i | ||||
\(719\) | 18.0000 | + | 31.1769i | 0.671287 | + | 1.16270i | 0.977539 | + | 0.210752i | \(0.0675914\pi\) |
−0.306253 | + | 0.951950i | \(0.599075\pi\) | |||||||
\(720\) | 24.0000 | 0.894427 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −34.0000 | −1.26535 | ||||||||
\(723\) | 36.0000 | + | 62.3538i | 1.33885 | + | 2.31896i | ||||
\(724\) | 6.00000 | − | 10.3923i | 0.222988 | − | 0.386227i | ||||
\(725\) | 0.500000 | − | 0.866025i | 0.0185695 | − | 0.0321634i | ||||
\(726\) | −30.0000 | − | 51.9615i | −1.11340 | − | 1.92847i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −6.00000 | − | 10.3923i | −0.222070 | − | 0.384636i | ||||
\(731\) | −9.00000 | + | 15.5885i | −0.332877 | + | 0.576560i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.50000 | − | 12.9904i | −0.277019 | − | 0.479811i | 0.693624 | − | 0.720338i | \(-0.256013\pi\) |
−0.970642 | + | 0.240527i | \(0.922680\pi\) | |||||||
\(734\) | 66.0000 | 2.43610 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.0000 | −1.17954 | ||||||||
\(737\) | 7.00000 | + | 12.1244i | 0.257848 | + | 0.446606i | ||||
\(738\) | 36.0000 | − | 62.3538i | 1.32518 | − | 2.29528i | ||||
\(739\) | 21.5000 | − | 37.2391i | 0.790890 | − | 1.36986i | −0.134526 | − | 0.990910i | \(-0.542951\pi\) |
0.925416 | − | 0.378952i | \(-0.123715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 54.0000 | 1.98374 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.0000 | −0.807102 | −0.403551 | − | 0.914957i | \(-0.632224\pi\) | ||||
−0.403551 | + | 0.914957i | \(0.632224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | − | 8.66025i | 0.183186 | − | 0.317287i | ||||
\(746\) | 4.00000 | − | 6.92820i | 0.146450 | − | 0.253660i | ||||
\(747\) | −36.0000 | − | 62.3538i | −1.31717 | − | 2.28141i | ||||
\(748\) | −6.00000 | −0.219382 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.00000 | 0.219089 | ||||||||
\(751\) | −7.50000 | − | 12.9904i | −0.273679 | − | 0.474026i | 0.696122 | − | 0.717923i | \(-0.254907\pi\) |
−0.969801 | + | 0.243898i | \(0.921574\pi\) | |||||||
\(752\) | −18.0000 | + | 31.1769i | −0.656392 | + | 1.13691i | ||||
\(753\) | 18.0000 | − | 31.1769i | 0.655956 | − | 1.13615i | ||||
\(754\) | −3.00000 | − | 5.19615i | −0.109254 | − | 0.189233i | ||||
\(755\) | −15.0000 | −0.545906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0000 | 1.74459 | 0.872295 | − | 0.488980i | \(-0.162631\pi\) | ||||
0.872295 | + | 0.488980i | \(0.162631\pi\) | |||||||
\(758\) | −24.0000 | − | 41.5692i | −0.871719 | − | 1.50986i | ||||
\(759\) | 6.00000 | − | 10.3923i | 0.217786 | − | 0.377217i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | − | 10.3923i | −0.217500 | − | 0.376721i | 0.736543 | − | 0.676391i | \(-0.236457\pi\) |
−0.954043 | + | 0.299670i | \(0.903123\pi\) | |||||||
\(762\) | 12.0000 | 0.434714 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 34.0000 | 1.23008 | ||||||||
\(765\) | −9.00000 | − | 15.5885i | −0.325396 | − | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.00000 | − | 15.5885i | 0.324971 | − | 0.562867i | ||||
\(768\) | −24.0000 | − | 41.5692i | −0.866025 | − | 1.50000i | ||||
\(769\) | 42.0000 | 1.51456 | 0.757279 | − | 0.653091i | \(-0.226528\pi\) | ||||
0.757279 | + | 0.653091i | \(0.226528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.0000 | 1.94476 | ||||||||
\(772\) | −12.0000 | − | 20.7846i | −0.431889 | − | 0.748054i | ||||
\(773\) | −1.50000 | + | 2.59808i | −0.0539513 | + | 0.0934463i | −0.891740 | − | 0.452549i | \(-0.850515\pi\) |
0.837788 | + | 0.545995i | \(0.183848\pi\) | |||||||
\(774\) | −36.0000 | + | 62.3538i | −1.29399 | + | 2.24126i | ||||
\(775\) | −3.00000 | − | 5.19615i | −0.107763 | − | 0.186651i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.0000 | −0.932145 | ||||||||
\(779\) | −18.0000 | − | 31.1769i | −0.644917 | − | 1.11703i | ||||
\(780\) | 9.00000 | − | 15.5885i | 0.322252 | − | 0.558156i | ||||
\(781\) | 4.00000 | − | 6.92820i | 0.143131 | − | 0.247911i | ||||
\(782\) | 12.0000 | + | 20.7846i | 0.429119 | + | 0.743256i | ||||
\(783\) | −9.00000 | −0.321634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.0000 | −0.642448 | ||||||||
\(786\) | 36.0000 | + | 62.3538i | 1.28408 | + | 2.22409i | ||||
\(787\) | −19.5000 | + | 33.7750i | −0.695100 | + | 1.20395i | 0.275047 | + | 0.961431i | \(0.411307\pi\) |
−0.970147 | + | 0.242518i | \(0.922027\pi\) | |||||||
\(788\) | 2.00000 | − | 3.46410i | 0.0712470 | − | 0.123404i | ||||
\(789\) | 15.0000 | + | 25.9808i | 0.534014 | + | 0.924940i | ||||
\(790\) | −2.00000 | −0.0711568 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.00000 | − | 15.5885i | 0.319398 | − | 0.553214i | ||||
\(795\) | −15.0000 | + | 25.9808i | −0.531995 | + | 0.921443i | ||||
\(796\) | −6.00000 | − | 10.3923i | −0.212664 | − | 0.368345i | ||||
\(797\) | −27.0000 | −0.956389 | −0.478195 | − | 0.878254i | \(-0.658709\pi\) | ||||
−0.478195 | + | 0.878254i | \(0.658709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.0000 | 0.955191 | ||||||||
\(800\) | −4.00000 | − | 6.92820i | −0.141421 | − | 0.244949i | ||||
\(801\) | −36.0000 | + | 62.3538i | −1.27200 | + | 2.20316i | ||||
\(802\) | −19.0000 | + | 32.9090i | −0.670913 | + | 1.16206i | ||||
\(803\) | −3.00000 | − | 5.19615i | −0.105868 | − | 0.183368i | ||||
\(804\) | −84.0000 | −2.96245 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.0000 | −1.26805 | ||||||||
\(807\) | −36.0000 | − | 62.3538i | −1.26726 | − | 2.19496i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.5000 | − | 30.3109i | 0.615267 | − | 1.06567i | −0.375070 | − | 0.926996i | \(-0.622381\pi\) |
0.990338 | − | 0.138678i | \(-0.0442852\pi\) | |||||||
\(810\) | −9.00000 | − | 15.5885i | −0.316228 | − | 0.547723i | ||||
\(811\) | 48.0000 | 1.68551 | 0.842754 | − | 0.538299i | \(-0.180933\pi\) | ||||
0.842754 | + | 0.538299i | \(0.180933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 72.0000 | 2.52515 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | − | 13.8564i | 0.280228 | − | 0.485369i | ||||
\(816\) | −18.0000 | + | 31.1769i | −0.630126 | + | 1.09141i | ||||
\(817\) | 18.0000 | + | 31.1769i | 0.629740 | + | 1.09074i | ||||
\(818\) | −60.0000 | −2.09785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0000 | −0.419058 | ||||||||
\(821\) | 11.5000 | + | 19.9186i | 0.401353 | + | 0.695163i | 0.993889 | − | 0.110380i | \(-0.0352068\pi\) |
−0.592537 | + | 0.805543i | \(0.701873\pi\) | |||||||
\(822\) | 24.0000 | − | 41.5692i | 0.837096 | − | 1.44989i | ||||
\(823\) | −25.0000 | + | 43.3013i | −0.871445 | + | 1.50939i | −0.0109433 | + | 0.999940i | \(0.503483\pi\) |
−0.860502 | + | 0.509447i | \(0.829850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.00000 | 0.104447 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.0000 | −0.556375 | −0.278187 | − | 0.960527i | \(-0.589734\pi\) | ||||
−0.278187 | + | 0.960527i | \(0.589734\pi\) | |||||||
\(828\) | 24.0000 | + | 41.5692i | 0.834058 | + | 1.44463i | ||||
\(829\) | −3.00000 | + | 5.19615i | −0.104194 | + | 0.180470i | −0.913409 | − | 0.407044i | \(-0.866560\pi\) |
0.809214 | + | 0.587513i | \(0.199893\pi\) | |||||||
\(830\) | −12.0000 | + | 20.7846i | −0.416526 | + | 0.721444i | ||||
\(831\) | 42.0000 | + | 72.7461i | 1.45696 | + | 2.52354i | ||||
\(832\) | −24.0000 | −0.832050 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50000 | + | 2.59808i | 0.0519096 | + | 0.0899101i | ||||
\(836\) | −6.00000 | + | 10.3923i | −0.207514 | + | 0.359425i | ||||
\(837\) | −27.0000 | + | 46.7654i | −0.933257 | + | 1.61645i | ||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 1.00000 | + | 1.73205i | 0.0344623 | + | 0.0596904i | ||||
\(843\) | 7.50000 | − | 12.9904i | 0.258314 | − | 0.447412i | ||||
\(844\) | −15.0000 | + | 25.9808i | −0.516321 | + | 0.894295i | ||||
\(845\) | −2.00000 | − | 3.46410i | −0.0688021 | − | 0.119169i | ||||
\(846\) | 108.000 | 3.71312 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 40.0000 | 1.37361 | ||||||||
\(849\) | −31.5000 | − | 54.5596i | −1.08108 | − | 1.87248i | ||||
\(850\) | −3.00000 | + | 5.19615i | −0.102899 | + | 0.178227i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 24.0000 | + | 41.5692i | 0.822226 | + | 1.42414i | ||||
\(853\) | 30.0000 | 1.02718 | 0.513590 | − | 0.858036i | \(-0.328315\pi\) | ||||
0.513590 | + | 0.858036i | \(0.328315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −36.0000 | −1.23117 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.0000 | + | 46.7654i | −0.922302 | + | 1.59747i | −0.126459 | + | 0.991972i | \(0.540361\pi\) |
−0.795843 | + | 0.605503i | \(0.792972\pi\) | |||||||
\(858\) | 9.00000 | − | 15.5885i | 0.307255 | − | 0.532181i | ||||
\(859\) | −6.00000 | − | 10.3923i | −0.204717 | − | 0.354581i | 0.745325 | − | 0.666701i | \(-0.232294\pi\) |
−0.950043 | + | 0.312120i | \(0.898961\pi\) | |||||||
\(860\) | 12.0000 | 0.409197 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.0000 | −0.340601 | ||||||||
\(863\) | 17.0000 | + | 29.4449i | 0.578687 | + | 1.00231i | 0.995630 | + | 0.0933825i | \(0.0297679\pi\) |
−0.416944 | + | 0.908932i | \(0.636899\pi\) | |||||||
\(864\) | −36.0000 | + | 62.3538i | −1.22474 | + | 2.12132i | ||||
\(865\) | −1.50000 | + | 2.59808i | −0.0510015 | + | 0.0883372i | ||||
\(866\) | −30.0000 | − | 51.9615i | −1.01944 | − | 1.76572i | ||||
\(867\) | −24.0000 | −0.815083 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.00000 | −0.0339227 | ||||||||
\(870\) | 3.00000 | + | 5.19615i | 0.101710 | + | 0.176166i | ||||
\(871\) | 21.0000 | − | 36.3731i | 0.711558 | − | 1.23245i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 45.0000 | + | 77.9423i | 1.52302 | + | 2.63795i | ||||
\(874\) | 48.0000 | 1.62362 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 36.0000 | 1.21633 | ||||||||
\(877\) | 11.0000 | + | 19.0526i | 0.371444 | + | 0.643359i | 0.989788 | − | 0.142548i | \(-0.0455296\pi\) |
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(878\) | 12.0000 | − | 20.7846i | 0.404980 | − | 0.701447i | ||||
\(879\) | −13.5000 | + | 23.3827i | −0.455344 | + | 0.788678i | ||||
\(880\) | −2.00000 | − | 3.46410i | −0.0674200 | − | 0.116775i | ||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 9.00000 | + | 15.5885i | 0.302703 | + | 0.524297i | ||||
\(885\) | −9.00000 | + | 15.5885i | −0.302532 | + | 0.524000i | ||||
\(886\) | 34.0000 | − | 58.8897i | 1.14225 | − | 1.97844i | ||||
\(887\) | 12.0000 | + | 20.7846i | 0.402921 | + | 0.697879i | 0.994077 | − | 0.108678i | \(-0.0346618\pi\) |
−0.591156 | + | 0.806557i | \(0.701328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.0000 | 0.804482 | ||||||||
\(891\) | −4.50000 | − | 7.79423i | −0.150756 | − | 0.261116i | ||||
\(892\) | −3.00000 | + | 5.19615i | −0.100447 | + | 0.173980i | ||||
\(893\) | 27.0000 | − | 46.7654i | 0.903521 | − | 1.56494i | ||||
\(894\) | 30.0000 | + | 51.9615i | 1.00335 | + | 1.73785i | ||||
\(895\) | −4.00000 | −0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0000 | −1.20201 | ||||||||
\(898\) | 23.0000 | + | 39.8372i | 0.767520 | + | 1.32938i | ||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | −6.00000 | + | 10.3923i | −0.200000 | + | 0.346410i | ||||
\(901\) | −15.0000 | − | 25.9808i | −0.499722 | − | 0.865545i | ||||
\(902\) | −12.0000 | −0.399556 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.00000 | − | 5.19615i | −0.0997234 | − | 0.172726i | ||||
\(906\) | 45.0000 | − | 77.9423i | 1.49502 | − | 2.58946i | ||||
\(907\) | −12.0000 | + | 20.7846i | −0.398453 | + | 0.690142i | −0.993535 | − | 0.113523i | \(-0.963786\pi\) |
0.595082 | + | 0.803665i | \(0.297120\pi\) | |||||||
\(908\) | −3.00000 | − | 5.19615i | −0.0995585 | − | 0.172440i | ||||
\(909\) | −108.000 | −3.58213 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0000 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(912\) | 36.0000 | + | 62.3538i | 1.19208 | + | 2.06474i | ||||
\(913\) | −6.00000 | + | 10.3923i | −0.198571 | + | 0.343935i | ||||
\(914\) | 6.00000 | − | 10.3923i | 0.198462 | − | 0.343747i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.0000 | −0.396491 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 54.0000 | 1.78227 | ||||||||
\(919\) | 4.50000 | + | 7.79423i | 0.148441 | + | 0.257108i | 0.930652 | − | 0.365907i | \(-0.119241\pi\) |
−0.782210 | + | 0.623015i | \(0.785908\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.50000 | − | 7.79423i | 0.148280 | − | 0.256829i | ||||
\(922\) | 36.0000 | + | 62.3538i | 1.18560 | + | 2.05351i | ||||
\(923\) | −24.0000 | −0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.00000 | − | 6.92820i | −0.131448 | − | 0.227675i | ||||
\(927\) | 27.0000 | − | 46.7654i | 0.886796 | − | 1.53598i | ||||
\(928\) | 4.00000 | − | 6.92820i | 0.131306 | − | 0.227429i | ||||
\(929\) | −21.0000 | − | 36.3731i | −0.688988 | − | 1.19336i | −0.972166 | − | 0.234294i | \(-0.924722\pi\) |
0.283178 | − | 0.959067i | \(-0.408611\pi\) | |||||||
\(930\) | 36.0000 | 1.18049 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.0000 | −0.524097 | ||||||||
\(933\) | 9.00000 | + | 15.5885i | 0.294647 | + | 0.510343i | ||||
\(934\) | −15.0000 | + | 25.9808i | −0.490815 | + | 0.850117i | ||||
\(935\) | −1.50000 | + | 2.59808i | −0.0490552 | + | 0.0849662i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.0000 | −0.882052 | −0.441026 | − | 0.897494i | \(-0.645385\pi\) | ||||
−0.441026 | + | 0.897494i | \(0.645385\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.00000 | 0.293704 | ||||||||
\(940\) | −9.00000 | − | 15.5885i | −0.293548 | − | 0.508439i | ||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 54.0000 | − | 93.5307i | 1.75942 | − | 3.04740i | ||||
\(943\) | 12.0000 | + | 20.7846i | 0.390774 | + | 0.676840i | ||||
\(944\) | 24.0000 | 0.781133 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | 1.00000 | + | 1.73205i | 0.0324956 | + | 0.0562841i | 0.881816 | − | 0.471594i | \(-0.156321\pi\) |
−0.849320 | + | 0.527878i | \(0.822988\pi\) | |||||||
\(948\) | 3.00000 | − | 5.19615i | 0.0974355 | − | 0.168763i | ||||
\(949\) | −9.00000 | + | 15.5885i | −0.292152 | + | 0.506023i | ||||
\(950\) | 6.00000 | + | 10.3923i | 0.194666 | + | 0.337171i | ||||
\(951\) | −66.0000 | −2.14020 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.0000 | −1.23094 | −0.615470 | − | 0.788160i | \(-0.711034\pi\) | ||||
−0.615470 | + | 0.788160i | \(0.711034\pi\) | |||||||
\(954\) | −60.0000 | − | 103.923i | −1.94257 | − | 3.36463i | ||||
\(955\) | 8.50000 | − | 14.7224i | 0.275054 | − | 0.476407i | ||||
\(956\) | −7.00000 | + | 12.1244i | −0.226396 | + | 0.392130i | ||||
\(957\) | 1.50000 | + | 2.59808i | 0.0484881 | + | 0.0839839i | ||||
\(958\) | 48.0000 | 1.55081 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 24.0000 | 0.774597 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 24.0000 | + | 41.5692i | 0.772988 | + | 1.33885i | ||||
\(965\) | −12.0000 | −0.386294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0000 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27.0000 | − | 46.7654i | 0.867365 | − | 1.50232i | ||||
\(970\) | 15.0000 | − | 25.9808i | 0.481621 | − | 0.834192i | ||||
\(971\) | 9.00000 | + | 15.5885i | 0.288824 | + | 0.500257i | 0.973529 | − | 0.228562i | \(-0.0734025\pi\) |
−0.684706 | + | 0.728820i | \(0.740069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −72.0000 | −2.30703 | ||||||||
\(975\) | −4.50000 | − | 7.79423i | −0.144115 | − | 0.249615i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.0000 | + | 29.4449i | −0.543878 | + | 0.942025i | 0.454798 | + | 0.890594i | \(0.349711\pi\) |
−0.998677 | + | 0.0514302i | \(0.983622\pi\) | |||||||
\(978\) | 48.0000 | + | 83.1384i | 1.53487 | + | 2.65847i | ||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −90.0000 | −2.87348 | ||||||||
\(982\) | 23.0000 | + | 39.8372i | 0.733959 | + | 1.27126i | ||||
\(983\) | −22.5000 | + | 38.9711i | −0.717639 | + | 1.24299i | 0.244294 | + | 0.969701i | \(0.421444\pi\) |
−0.961933 | + | 0.273285i | \(0.911890\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.00000 | − | 1.73205i | −0.0318626 | − | 0.0551877i | ||||
\(986\) | −6.00000 | −0.191079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 36.0000 | 1.14531 | ||||||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | −6.00000 | + | 10.3923i | −0.190693 | + | 0.330289i | ||||
\(991\) | 18.0000 | − | 31.1769i | 0.571789 | − | 0.990367i | −0.424594 | − | 0.905384i | \(-0.639583\pi\) |
0.996382 | − | 0.0849833i | \(-0.0270837\pi\) | |||||||
\(992\) | −24.0000 | − | 41.5692i | −0.762001 | − | 1.31982i | ||||
\(993\) | 36.0000 | 1.14243 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.00000 | −0.190213 | ||||||||
\(996\) | −36.0000 | − | 62.3538i | −1.14070 | − | 1.97576i | ||||
\(997\) | 1.50000 | − | 2.59808i | 0.0475055 | − | 0.0822819i | −0.841295 | − | 0.540576i | \(-0.818206\pi\) |
0.888800 | + | 0.458295i | \(0.151540\pi\) | |||||||
\(998\) | −27.0000 | + | 46.7654i | −0.854670 | + | 1.48033i | ||||
\(999\) | 0 | 0 |
(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 | 245.2.e.c.116.1 | 2 | ||
7.2 | even | 3 | inner | 245.2.e.c.226.1 | 2 | ||
7.3 | odd | 6 | 245.2.a.a.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 245.2.a.b.1.1 | yes | 1 | ||
7.5 | odd | 6 | 245.2.e.d.226.1 | 2 | |||
7.6 | odd | 2 | 245.2.e.d.116.1 | 2 | |||
21.11 | odd | 6 | 2205.2.a.l.1.1 | 1 | |||
21.17 | even | 6 | 2205.2.a.j.1.1 | 1 | |||
28.3 | even | 6 | 3920.2.a.bj.1.1 | 1 | |||
28.11 | odd | 6 | 3920.2.a.a.1.1 | 1 | |||
35.3 | even | 12 | 1225.2.b.b.99.2 | 2 | |||
35.4 | even | 6 | 1225.2.a.h.1.1 | 1 | |||
35.17 | even | 12 | 1225.2.b.b.99.1 | 2 | |||
35.18 | odd | 12 | 1225.2.b.a.99.2 | 2 | |||
35.24 | odd | 6 | 1225.2.a.j.1.1 | 1 | |||
35.32 | odd | 12 | 1225.2.b.a.99.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.2.a.a.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
245.2.a.b.1.1 | yes | 1 | 7.4 | even | 3 | ||
245.2.e.c.116.1 | 2 | 1.1 | even | 1 | trivial | ||
245.2.e.c.226.1 | 2 | 7.2 | even | 3 | inner | ||
245.2.e.d.116.1 | 2 | 7.6 | odd | 2 | |||
245.2.e.d.226.1 | 2 | 7.5 | odd | 6 | |||
1225.2.a.h.1.1 | 1 | 35.4 | even | 6 | |||
1225.2.a.j.1.1 | 1 | 35.24 | odd | 6 | |||
1225.2.b.a.99.1 | 2 | 35.32 | odd | 12 | |||
1225.2.b.a.99.2 | 2 | 35.18 | odd | 12 | |||
1225.2.b.b.99.1 | 2 | 35.17 | even | 12 | |||
1225.2.b.b.99.2 | 2 | 35.3 | even | 12 | |||
2205.2.a.j.1.1 | 1 | 21.17 | even | 6 | |||
2205.2.a.l.1.1 | 1 | 21.11 | odd | 6 | |||
3920.2.a.a.1.1 | 1 | 28.11 | odd | 6 | |||
3920.2.a.bj.1.1 | 1 | 28.3 | even | 6 |