Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,3,Mod(391,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.391");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.0545988610\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.7 | ||
Root | \(1.72286 + 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.391 |
Dual form | 1470.3.f.a.391.6 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − 2.23607i | − 0.447214i | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | − 3.16228i | − 0.316228i | ||||||||
\(11\) | 11.5848 | 1.05316 | 0.526582 | − | 0.850125i | \(-0.323473\pi\) | ||||
0.526582 | + | 0.850125i | \(0.323473\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 7.86371i | 0.604901i | 0.953165 | + | 0.302451i | \(0.0978047\pi\) | ||||
−0.953165 | + | 0.302451i | \(0.902195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 27.6066i | 1.62392i | 0.583715 | + | 0.811959i | \(0.301599\pi\) | ||||
−0.583715 | + | 0.811959i | \(0.698401\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | − 31.4250i | − 1.65395i | −0.562240 | − | 0.826974i | \(-0.690060\pi\) | ||||
0.562240 | − | 0.826974i | \(-0.309940\pi\) | |||||||
\(20\) | − 4.47214i | − 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 16.3834 | 0.744699 | ||||||||
\(23\) | 18.1592 | 0.789530 | 0.394765 | − | 0.918782i | \(-0.370826\pi\) | ||||
0.394765 | + | 0.918782i | \(0.370826\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 11.1210i | 0.427730i | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.30331 | −0.0794244 | −0.0397122 | − | 0.999211i | \(-0.512644\pi\) | ||||
−0.0397122 | + | 0.999211i | \(0.512644\pi\) | |||||||
\(30\) | 5.47723 | 0.182574 | ||||||||
\(31\) | − 5.26382i | − 0.169801i | −0.996389 | − | 0.0849003i | \(-0.972943\pi\) | ||||
0.996389 | − | 0.0849003i | \(-0.0270572\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 20.0655i | 0.608044i | ||||||||
\(34\) | 39.0416i | 1.14828i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 1.98628 | 0.0536834 | 0.0268417 | − | 0.999640i | \(-0.491455\pi\) | ||||
0.0268417 | + | 0.999640i | \(0.491455\pi\) | |||||||
\(38\) | − 44.4417i | − 1.16952i | ||||||||
\(39\) | −13.6204 | −0.349240 | ||||||||
\(40\) | − 6.32456i | − 0.158114i | ||||||||
\(41\) | 22.1905i | 0.541233i | 0.962687 | + | 0.270616i | \(0.0872275\pi\) | ||||
−0.962687 | + | 0.270616i | \(0.912773\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 49.8368 | 1.15900 | 0.579498 | − | 0.814974i | \(-0.303249\pi\) | ||||
0.579498 | + | 0.814974i | \(0.303249\pi\) | |||||||
\(44\) | 23.1696 | 0.526582 | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | 25.6810 | 0.558282 | ||||||||
\(47\) | 76.6670i | 1.63121i | 0.578607 | + | 0.815606i | \(0.303596\pi\) | ||||
−0.578607 | + | 0.815606i | \(0.696404\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | −47.8160 | −0.937569 | ||||||||
\(52\) | 15.7274i | 0.302451i | ||||||||
\(53\) | 57.0954 | 1.07727 | 0.538636 | − | 0.842539i | \(-0.318940\pi\) | ||||
0.538636 | + | 0.842539i | \(0.318940\pi\) | |||||||
\(54\) | − 7.34847i | − 0.136083i | ||||||||
\(55\) | − 25.9044i | − 0.470989i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 54.4297 | 0.954908 | ||||||||
\(58\) | −3.25737 | −0.0561616 | ||||||||
\(59\) | − 70.3495i | − 1.19236i | −0.802849 | − | 0.596182i | \(-0.796684\pi\) | ||||
0.802849 | − | 0.596182i | \(-0.203316\pi\) | |||||||
\(60\) | 7.74597 | 0.129099 | ||||||||
\(61\) | 67.6181i | 1.10849i | 0.832352 | + | 0.554247i | \(0.186994\pi\) | ||||
−0.832352 | + | 0.554247i | \(0.813006\pi\) | |||||||
\(62\) | − 7.44416i | − 0.120067i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 17.5838 | 0.270520 | ||||||||
\(66\) | 28.3768i | 0.429952i | ||||||||
\(67\) | 98.1647 | 1.46514 | 0.732572 | − | 0.680689i | \(-0.238320\pi\) | ||||
0.732572 | + | 0.680689i | \(0.238320\pi\) | |||||||
\(68\) | 55.2132i | 0.811959i | ||||||||
\(69\) | 31.4526i | 0.455835i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −34.2597 | −0.482531 | −0.241266 | − | 0.970459i | \(-0.577563\pi\) | ||||
−0.241266 | + | 0.970459i | \(0.577563\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | 19.4915i | 0.267006i | 0.991048 | + | 0.133503i | \(0.0426226\pi\) | ||||
−0.991048 | + | 0.133503i | \(0.957377\pi\) | |||||||
\(74\) | 2.80903 | 0.0379599 | ||||||||
\(75\) | − 8.66025i | − 0.115470i | ||||||||
\(76\) | − 62.8501i | − 0.826974i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −19.2621 | −0.246950 | ||||||||
\(79\) | 90.4285 | 1.14466 | 0.572332 | − | 0.820022i | \(-0.306039\pi\) | ||||
0.572332 | + | 0.820022i | \(0.306039\pi\) | |||||||
\(80\) | − 8.94427i | − 0.111803i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 31.3822i | 0.382709i | ||||||||
\(83\) | − 133.803i | − 1.61209i | −0.591854 | − | 0.806045i | \(-0.701604\pi\) | ||||
0.591854 | − | 0.806045i | \(-0.298396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 61.7302 | 0.726238 | ||||||||
\(86\) | 70.4799 | 0.819534 | ||||||||
\(87\) | − 3.98945i | − 0.0458557i | ||||||||
\(88\) | 32.7667 | 0.372349 | ||||||||
\(89\) | 11.0647i | 0.124323i | 0.998066 | + | 0.0621613i | \(0.0197993\pi\) | ||||
−0.998066 | + | 0.0621613i | \(0.980201\pi\) | |||||||
\(90\) | 9.48683i | 0.105409i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 36.3184 | 0.394765 | ||||||||
\(93\) | 9.11720 | 0.0980344 | ||||||||
\(94\) | 108.424i | 1.15344i | ||||||||
\(95\) | −70.2685 | −0.739668 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 72.3112i | 0.745476i | 0.927937 | + | 0.372738i | \(0.121581\pi\) | ||||
−0.927937 | + | 0.372738i | \(0.878419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −34.7544 | −0.351054 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | 50.6533i | 0.501518i | 0.968050 | + | 0.250759i | \(0.0806801\pi\) | ||||
−0.968050 | + | 0.250759i | \(0.919320\pi\) | |||||||
\(102\) | −67.6221 | −0.662962 | ||||||||
\(103\) | 197.965i | 1.92199i | 0.276572 | + | 0.960993i | \(0.410802\pi\) | ||||
−0.276572 | + | 0.960993i | \(0.589198\pi\) | |||||||
\(104\) | 22.2419i | 0.213865i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 80.7451 | 0.761746 | ||||||||
\(107\) | 147.936 | 1.38258 | 0.691289 | − | 0.722579i | \(-0.257043\pi\) | ||||
0.691289 | + | 0.722579i | \(0.257043\pi\) | |||||||
\(108\) | − 10.3923i | − 0.0962250i | ||||||||
\(109\) | −54.3219 | −0.498366 | −0.249183 | − | 0.968456i | \(-0.580162\pi\) | ||||
−0.249183 | + | 0.968456i | \(0.580162\pi\) | |||||||
\(110\) | − 36.6343i | − 0.333039i | ||||||||
\(111\) | 3.44035i | 0.0309941i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 47.7883 | 0.422906 | 0.211453 | − | 0.977388i | \(-0.432181\pi\) | ||||
0.211453 | + | 0.977388i | \(0.432181\pi\) | |||||||
\(114\) | 76.9753 | 0.675222 | ||||||||
\(115\) | − 40.6052i | − 0.353089i | ||||||||
\(116\) | −4.60662 | −0.0397122 | ||||||||
\(117\) | − 23.5911i | − 0.201634i | ||||||||
\(118\) | − 99.4892i | − 0.843129i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.9545 | 0.0912871 | ||||||||
\(121\) | 13.2074 | 0.109152 | ||||||||
\(122\) | 95.6265i | 0.783824i | ||||||||
\(123\) | −38.4351 | −0.312481 | ||||||||
\(124\) | − 10.5276i | − 0.0849003i | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −101.973 | −0.802940 | −0.401470 | − | 0.915872i | \(-0.631501\pi\) | ||||
−0.401470 | + | 0.915872i | \(0.631501\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 86.3199i | 0.669147i | ||||||||
\(130\) | 24.8673 | 0.191287 | ||||||||
\(131\) | 74.5980i | 0.569450i | 0.958609 | + | 0.284725i | \(0.0919023\pi\) | ||||
−0.958609 | + | 0.284725i | \(0.908098\pi\) | |||||||
\(132\) | 40.1309i | 0.304022i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 138.826 | 1.03601 | ||||||||
\(135\) | −11.6190 | −0.0860663 | ||||||||
\(136\) | 78.0833i | 0.574142i | ||||||||
\(137\) | −246.899 | −1.80218 | −0.901091 | − | 0.433630i | \(-0.857233\pi\) | ||||
−0.901091 | + | 0.433630i | \(0.857233\pi\) | |||||||
\(138\) | 44.4807i | 0.322324i | ||||||||
\(139\) | 155.917i | 1.12170i | 0.827916 | + | 0.560852i | \(0.189526\pi\) | ||||
−0.827916 | + | 0.560852i | \(0.810474\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −132.791 | −0.941781 | ||||||||
\(142\) | −48.4506 | −0.341201 | ||||||||
\(143\) | 91.0995i | 0.637060i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 5.15035i | 0.0355197i | ||||||||
\(146\) | 27.5651i | 0.188802i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.97257 | 0.0268417 | ||||||||
\(149\) | 163.090 | 1.09457 | 0.547283 | − | 0.836948i | \(-0.315662\pi\) | ||||
0.547283 | + | 0.836948i | \(0.315662\pi\) | |||||||
\(150\) | − 12.2474i | − 0.0816497i | ||||||||
\(151\) | −75.0299 | −0.496887 | −0.248443 | − | 0.968646i | \(-0.579919\pi\) | ||||
−0.248443 | + | 0.968646i | \(0.579919\pi\) | |||||||
\(152\) | − 88.8834i | − 0.584759i | ||||||||
\(153\) | − 82.8198i | − 0.541306i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.7703 | −0.0759371 | ||||||||
\(156\) | −27.2407 | −0.174620 | ||||||||
\(157\) | − 224.731i | − 1.43140i | −0.698405 | − | 0.715702i | \(-0.746107\pi\) | ||||
0.698405 | − | 0.715702i | \(-0.253893\pi\) | |||||||
\(158\) | 127.885 | 0.809400 | ||||||||
\(159\) | 98.8922i | 0.621963i | ||||||||
\(160\) | − 12.6491i | − 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −230.117 | −1.41176 | −0.705882 | − | 0.708330i | \(-0.749449\pi\) | ||||
−0.705882 | + | 0.708330i | \(0.749449\pi\) | |||||||
\(164\) | 44.3811i | 0.270616i | ||||||||
\(165\) | 44.8677 | 0.271926 | ||||||||
\(166\) | − 189.227i | − 1.13992i | ||||||||
\(167\) | − 277.788i | − 1.66340i | −0.555223 | − | 0.831702i | \(-0.687367\pi\) | ||||
0.555223 | − | 0.831702i | \(-0.312633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 107.162 | 0.634095 | ||||||||
\(170\) | 87.2997 | 0.513528 | ||||||||
\(171\) | 94.2751i | 0.551316i | ||||||||
\(172\) | 99.6736 | 0.579498 | ||||||||
\(173\) | − 126.065i | − 0.728702i | −0.931262 | − | 0.364351i | \(-0.881291\pi\) | ||||
0.931262 | − | 0.364351i | \(-0.118709\pi\) | |||||||
\(174\) | − 5.64193i | − 0.0324249i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 46.3392 | 0.263291 | ||||||||
\(177\) | 121.849 | 0.688412 | ||||||||
\(178\) | 15.6479i | 0.0879093i | ||||||||
\(179\) | 77.1069 | 0.430765 | 0.215382 | − | 0.976530i | \(-0.430900\pi\) | ||||
0.215382 | + | 0.976530i | \(0.430900\pi\) | |||||||
\(180\) | 13.4164i | 0.0745356i | ||||||||
\(181\) | − 212.012i | − 1.17134i | −0.810551 | − | 0.585668i | \(-0.800832\pi\) | ||||
0.810551 | − | 0.585668i | \(-0.199168\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −117.118 | −0.639989 | ||||||||
\(184\) | 51.3619 | 0.279141 | ||||||||
\(185\) | − 4.44147i | − 0.0240079i | ||||||||
\(186\) | 12.8937 | 0.0693208 | ||||||||
\(187\) | 319.817i | 1.71025i | ||||||||
\(188\) | 153.334i | 0.815606i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −99.3747 | −0.523025 | ||||||||
\(191\) | 165.696 | 0.867518 | 0.433759 | − | 0.901029i | \(-0.357187\pi\) | ||||
0.433759 | + | 0.901029i | \(0.357187\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −105.299 | −0.545593 | −0.272796 | − | 0.962072i | \(-0.587949\pi\) | ||||
−0.272796 | + | 0.962072i | \(0.587949\pi\) | |||||||
\(194\) | 102.263i | 0.527131i | ||||||||
\(195\) | 30.4560i | 0.156185i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 244.736 | 1.24231 | 0.621156 | − | 0.783687i | \(-0.286663\pi\) | ||||
0.621156 | + | 0.783687i | \(0.286663\pi\) | |||||||
\(198\) | −49.1501 | −0.248233 | ||||||||
\(199\) | 97.9667i | 0.492295i | 0.969232 | + | 0.246147i | \(0.0791647\pi\) | ||||
−0.969232 | + | 0.246147i | \(0.920835\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | 170.026i | 0.845902i | ||||||||
\(202\) | 71.6346i | 0.354627i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −95.6321 | −0.468785 | ||||||||
\(205\) | 49.6196 | 0.242047 | ||||||||
\(206\) | 279.964i | 1.35905i | ||||||||
\(207\) | −54.4776 | −0.263177 | ||||||||
\(208\) | 31.4549i | 0.151225i | ||||||||
\(209\) | − 364.052i | − 1.74188i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −388.914 | −1.84319 | −0.921597 | − | 0.388149i | \(-0.873114\pi\) | ||||
−0.921597 | + | 0.388149i | \(0.873114\pi\) | |||||||
\(212\) | 114.191 | 0.538636 | ||||||||
\(213\) | − 59.3396i | − 0.278590i | ||||||||
\(214\) | 209.213 | 0.977630 | ||||||||
\(215\) | − 111.439i | − 0.518319i | ||||||||
\(216\) | − 14.6969i | − 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −76.8228 | −0.352398 | ||||||||
\(219\) | −33.7602 | −0.154156 | ||||||||
\(220\) | − 51.8088i | − 0.235494i | ||||||||
\(221\) | −217.090 | −0.982310 | ||||||||
\(222\) | 4.86538i | 0.0219161i | ||||||||
\(223\) | 251.913i | 1.12965i | 0.825210 | + | 0.564827i | \(0.191057\pi\) | ||||
−0.825210 | + | 0.564827i | \(0.808943\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 67.5829 | 0.299039 | ||||||||
\(227\) | 267.822i | 1.17983i | 0.807465 | + | 0.589916i | \(0.200839\pi\) | ||||
−0.807465 | + | 0.589916i | \(0.799161\pi\) | |||||||
\(228\) | 108.859 | 0.477454 | ||||||||
\(229\) | − 345.529i | − 1.50886i | −0.656379 | − | 0.754431i | \(-0.727913\pi\) | ||||
0.656379 | − | 0.754431i | \(-0.272087\pi\) | |||||||
\(230\) | − 57.4244i | − 0.249671i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.51474 | −0.0280808 | ||||||||
\(233\) | −288.064 | −1.23633 | −0.618164 | − | 0.786049i | \(-0.712123\pi\) | ||||
−0.618164 | + | 0.786049i | \(0.712123\pi\) | |||||||
\(234\) | − 33.3629i | − 0.142577i | ||||||||
\(235\) | 171.433 | 0.729500 | ||||||||
\(236\) | − 140.699i | − 0.596182i | ||||||||
\(237\) | 156.627i | 0.660872i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −188.810 | −0.789999 | −0.395000 | − | 0.918681i | \(-0.629255\pi\) | ||||
−0.395000 | + | 0.918681i | \(0.629255\pi\) | |||||||
\(240\) | 15.4919 | 0.0645497 | ||||||||
\(241\) | 97.8480i | 0.406008i | 0.979178 | + | 0.203004i | \(0.0650705\pi\) | ||||
−0.979178 | + | 0.203004i | \(0.934929\pi\) | |||||||
\(242\) | 18.6782 | 0.0771824 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 135.236i | 0.554247i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −54.3555 | −0.220957 | ||||||||
\(247\) | 247.117 | 1.00048 | ||||||||
\(248\) | − 14.8883i | − 0.0600336i | ||||||||
\(249\) | 231.754 | 0.930741 | ||||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | − 241.345i | − 0.961533i | −0.876849 | − | 0.480767i | \(-0.840358\pi\) | ||||
0.876849 | − | 0.480767i | \(-0.159642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 210.370 | 0.831504 | ||||||||
\(254\) | −144.212 | −0.567764 | ||||||||
\(255\) | 106.920i | 0.419294i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 12.5639i | 0.0488869i | 0.999701 | + | 0.0244435i | \(0.00778137\pi\) | ||||
−0.999701 | + | 0.0244435i | \(0.992219\pi\) | |||||||
\(258\) | 122.075i | 0.473158i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 35.1676 | 0.135260 | ||||||||
\(261\) | 6.90993 | 0.0264748 | ||||||||
\(262\) | 105.497i | 0.402662i | ||||||||
\(263\) | −212.481 | −0.807911 | −0.403956 | − | 0.914779i | \(-0.632365\pi\) | ||||
−0.403956 | + | 0.914779i | \(0.632365\pi\) | |||||||
\(264\) | 56.7537i | 0.214976i | ||||||||
\(265\) | − 127.669i | − 0.481771i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.1646 | −0.0717777 | ||||||||
\(268\) | 196.329 | 0.732572 | ||||||||
\(269\) | − 334.597i | − 1.24385i | −0.783075 | − | 0.621927i | \(-0.786350\pi\) | ||||
0.783075 | − | 0.621927i | \(-0.213650\pi\) | |||||||
\(270\) | −16.4317 | −0.0608581 | ||||||||
\(271\) | 182.350i | 0.672879i | 0.941705 | + | 0.336440i | \(0.109223\pi\) | ||||
−0.941705 | + | 0.336440i | \(0.890777\pi\) | |||||||
\(272\) | 110.426i | 0.405979i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −349.168 | −1.27434 | ||||||||
\(275\) | −57.9240 | −0.210633 | ||||||||
\(276\) | 62.9053i | 0.227918i | ||||||||
\(277\) | 166.761 | 0.602026 | 0.301013 | − | 0.953620i | \(-0.402675\pi\) | ||||
0.301013 | + | 0.953620i | \(0.402675\pi\) | |||||||
\(278\) | 220.500i | 0.793164i | ||||||||
\(279\) | 15.7915i | 0.0566002i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 38.3085 | 0.136329 | 0.0681647 | − | 0.997674i | \(-0.478286\pi\) | ||||
0.0681647 | + | 0.997674i | \(0.478286\pi\) | |||||||
\(282\) | −187.795 | −0.665940 | ||||||||
\(283\) | − 385.496i | − 1.36218i | −0.732201 | − | 0.681088i | \(-0.761507\pi\) | ||||
0.732201 | − | 0.681088i | \(-0.238493\pi\) | |||||||
\(284\) | −68.5194 | −0.241266 | ||||||||
\(285\) | − 121.709i | − 0.427048i | ||||||||
\(286\) | 128.834i | 0.450469i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −473.125 | −1.63711 | ||||||||
\(290\) | 7.28370i | 0.0251162i | ||||||||
\(291\) | −125.247 | −0.430401 | ||||||||
\(292\) | 38.9829i | 0.133503i | ||||||||
\(293\) | 90.9844i | 0.310527i | 0.987873 | + | 0.155264i | \(0.0496227\pi\) | ||||
−0.987873 | + | 0.155264i | \(0.950377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −157.306 | −0.533242 | ||||||||
\(296\) | 5.61806 | 0.0189799 | ||||||||
\(297\) | − 60.1964i | − 0.202681i | ||||||||
\(298\) | 230.645 | 0.773975 | ||||||||
\(299\) | 142.799i | 0.477588i | ||||||||
\(300\) | − 17.3205i | − 0.0577350i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −106.108 | −0.351352 | ||||||||
\(303\) | −87.7341 | −0.289551 | ||||||||
\(304\) | − 125.700i | − 0.413487i | ||||||||
\(305\) | 151.199 | 0.495734 | ||||||||
\(306\) | − 117.125i | − 0.382761i | ||||||||
\(307\) | − 508.077i | − 1.65497i | −0.561485 | − | 0.827487i | \(-0.689770\pi\) | ||||
0.561485 | − | 0.827487i | \(-0.310230\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −342.885 | −1.10966 | ||||||||
\(310\) | −16.6457 | −0.0536956 | ||||||||
\(311\) | 104.321i | 0.335437i | 0.985835 | + | 0.167719i | \(0.0536400\pi\) | ||||
−0.985835 | + | 0.167719i | \(0.946360\pi\) | |||||||
\(312\) | −38.5242 | −0.123475 | ||||||||
\(313\) | − 265.869i | − 0.849420i | −0.905329 | − | 0.424710i | \(-0.860376\pi\) | ||||
0.905329 | − | 0.424710i | \(-0.139624\pi\) | |||||||
\(314\) | − 317.817i | − 1.01216i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 180.857 | 0.572332 | ||||||||
\(317\) | −10.7223 | −0.0338242 | −0.0169121 | − | 0.999857i | \(-0.505384\pi\) | ||||
−0.0169121 | + | 0.999857i | \(0.505384\pi\) | |||||||
\(318\) | 139.855i | 0.439795i | ||||||||
\(319\) | −26.6834 | −0.0836469 | ||||||||
\(320\) | − 17.8885i | − 0.0559017i | ||||||||
\(321\) | 256.232i | 0.798231i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 867.538 | 2.68588 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | − 39.3186i | − 0.120980i | ||||||||
\(326\) | −325.435 | −0.998267 | ||||||||
\(327\) | − 94.0883i | − 0.287732i | ||||||||
\(328\) | 62.7643i | 0.191355i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 63.4525 | 0.192280 | ||||||||
\(331\) | −352.921 | −1.06623 | −0.533113 | − | 0.846044i | \(-0.678978\pi\) | ||||
−0.533113 | + | 0.846044i | \(0.678978\pi\) | |||||||
\(332\) | − 267.607i | − 0.806045i | ||||||||
\(333\) | −5.95885 | −0.0178945 | ||||||||
\(334\) | − 392.852i | − 1.17620i | ||||||||
\(335\) | − 219.503i | − 0.655233i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 220.634 | 0.654699 | 0.327349 | − | 0.944903i | \(-0.393845\pi\) | ||||
0.327349 | + | 0.944903i | \(0.393845\pi\) | |||||||
\(338\) | 151.550 | 0.448373 | ||||||||
\(339\) | 82.7718i | 0.244165i | ||||||||
\(340\) | 123.460 | 0.363119 | ||||||||
\(341\) | − 60.9802i | − 0.178828i | ||||||||
\(342\) | 133.325i | 0.389839i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 140.960 | 0.409767 | ||||||||
\(345\) | 70.3302 | 0.203856 | ||||||||
\(346\) | − 178.283i | − 0.515270i | ||||||||
\(347\) | −256.009 | −0.737777 | −0.368888 | − | 0.929474i | \(-0.620262\pi\) | ||||
−0.368888 | + | 0.929474i | \(0.620262\pi\) | |||||||
\(348\) | − 7.97889i | − 0.0229279i | ||||||||
\(349\) | − 407.250i | − 1.16691i | −0.812147 | − | 0.583453i | \(-0.801701\pi\) | ||||
0.812147 | − | 0.583453i | \(-0.198299\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 40.8611 | 0.116413 | ||||||||
\(352\) | 65.5335 | 0.186175 | ||||||||
\(353\) | − 583.238i | − 1.65223i | −0.563501 | − | 0.826116i | \(-0.690546\pi\) | ||||
0.563501 | − | 0.826116i | \(-0.309454\pi\) | |||||||
\(354\) | 172.320 | 0.486781 | ||||||||
\(355\) | 76.6071i | 0.215795i | ||||||||
\(356\) | 22.1294i | 0.0621613i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 109.046 | 0.304597 | ||||||||
\(359\) | 691.528 | 1.92626 | 0.963131 | − | 0.269032i | \(-0.0867038\pi\) | ||||
0.963131 | + | 0.269032i | \(0.0867038\pi\) | |||||||
\(360\) | 18.9737i | 0.0527046i | ||||||||
\(361\) | −626.532 | −1.73555 | ||||||||
\(362\) | − 299.830i | − 0.828260i | ||||||||
\(363\) | 22.8760i | 0.0630192i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43.5842 | 0.119409 | ||||||||
\(366\) | −165.630 | −0.452541 | ||||||||
\(367\) | 229.727i | 0.625959i | 0.949760 | + | 0.312980i | \(0.101327\pi\) | ||||
−0.949760 | + | 0.312980i | \(0.898673\pi\) | |||||||
\(368\) | 72.6368 | 0.197382 | ||||||||
\(369\) | − 66.5716i | − 0.180411i | ||||||||
\(370\) | − 6.28118i | − 0.0169762i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 18.2344 | 0.0490172 | ||||||||
\(373\) | −404.609 | −1.08474 | −0.542371 | − | 0.840139i | \(-0.682473\pi\) | ||||
−0.542371 | + | 0.840139i | \(0.682473\pi\) | |||||||
\(374\) | 452.289i | 1.20933i | ||||||||
\(375\) | −19.3649 | −0.0516398 | ||||||||
\(376\) | 216.847i | 0.576721i | ||||||||
\(377\) | − 18.1126i | − 0.0480439i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 265.866 | 0.701493 | 0.350746 | − | 0.936471i | \(-0.385928\pi\) | ||||
0.350746 | + | 0.936471i | \(0.385928\pi\) | |||||||
\(380\) | −140.537 | −0.369834 | ||||||||
\(381\) | − 176.623i | − 0.463578i | ||||||||
\(382\) | 234.329 | 0.613428 | ||||||||
\(383\) | − 306.404i | − 0.800010i | −0.916513 | − | 0.400005i | \(-0.869008\pi\) | ||||
0.916513 | − | 0.400005i | \(-0.130992\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −148.916 | −0.385792 | ||||||||
\(387\) | −149.510 | −0.386332 | ||||||||
\(388\) | 144.622i | 0.372738i | ||||||||
\(389\) | 106.354 | 0.273405 | 0.136702 | − | 0.990612i | \(-0.456350\pi\) | ||||
0.136702 | + | 0.990612i | \(0.456350\pi\) | |||||||
\(390\) | 43.0713i | 0.110439i | ||||||||
\(391\) | 501.314i | 1.28213i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −129.207 | −0.328772 | ||||||||
\(394\) | 346.108 | 0.878448 | ||||||||
\(395\) | − 202.204i | − 0.511909i | ||||||||
\(396\) | −69.5088 | −0.175527 | ||||||||
\(397\) | 217.827i | 0.548682i | 0.961633 | + | 0.274341i | \(0.0884597\pi\) | ||||
−0.961633 | + | 0.274341i | \(0.911540\pi\) | |||||||
\(398\) | 138.546i | 0.348105i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 61.9814 | 0.154567 | 0.0772836 | − | 0.997009i | \(-0.475375\pi\) | ||||
0.0772836 | + | 0.997009i | \(0.475375\pi\) | |||||||
\(402\) | 240.453i | 0.598143i | ||||||||
\(403\) | 41.3932 | 0.102713 | ||||||||
\(404\) | 101.307i | 0.250759i | ||||||||
\(405\) | − 20.1246i | − 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.0107 | 0.0565373 | ||||||||
\(408\) | −135.244 | −0.331481 | ||||||||
\(409\) | − 434.360i | − 1.06201i | −0.847370 | − | 0.531003i | \(-0.821815\pi\) | ||||
0.847370 | − | 0.531003i | \(-0.178185\pi\) | |||||||
\(410\) | 70.1726 | 0.171153 | ||||||||
\(411\) | − 427.642i | − 1.04049i | ||||||||
\(412\) | 395.929i | 0.960993i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −77.0429 | −0.186094 | ||||||||
\(415\) | −299.194 | −0.720949 | ||||||||
\(416\) | 44.4839i | 0.106932i | ||||||||
\(417\) | −270.056 | −0.647616 | ||||||||
\(418\) | − 514.848i | − 1.23169i | ||||||||
\(419\) | 457.221i | 1.09122i | 0.838040 | + | 0.545609i | \(0.183702\pi\) | ||||
−0.838040 | + | 0.545609i | \(0.816298\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −653.149 | −1.55142 | −0.775712 | − | 0.631088i | \(-0.782609\pi\) | ||||
−0.775712 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(422\) | −550.007 | −1.30333 | ||||||||
\(423\) | − 230.001i | − 0.543738i | ||||||||
\(424\) | 161.490 | 0.380873 | ||||||||
\(425\) | − 138.033i | − 0.324784i | ||||||||
\(426\) | − 83.9188i | − 0.196993i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 295.872 | 0.691289 | ||||||||
\(429\) | −157.789 | −0.367807 | ||||||||
\(430\) | − 157.598i | − 0.366507i | ||||||||
\(431\) | −470.256 | −1.09108 | −0.545540 | − | 0.838085i | \(-0.683676\pi\) | ||||
−0.545540 | + | 0.838085i | \(0.683676\pi\) | |||||||
\(432\) | − 20.7846i | − 0.0481125i | ||||||||
\(433\) | 32.0299i | 0.0739719i | 0.999316 | + | 0.0369860i | \(0.0117757\pi\) | ||||
−0.999316 | + | 0.0369860i | \(0.988224\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.92068 | −0.0205073 | ||||||||
\(436\) | −108.644 | −0.249183 | ||||||||
\(437\) | − 570.653i | − 1.30584i | ||||||||
\(438\) | −47.7441 | −0.109005 | ||||||||
\(439\) | − 382.239i | − 0.870703i | −0.900260 | − | 0.435352i | \(-0.856624\pi\) | ||||
0.900260 | − | 0.435352i | \(-0.143376\pi\) | |||||||
\(440\) | − 73.2687i | − 0.166520i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −307.012 | −0.694598 | ||||||||
\(443\) | 123.742 | 0.279326 | 0.139663 | − | 0.990199i | \(-0.455398\pi\) | ||||
0.139663 | + | 0.990199i | \(0.455398\pi\) | |||||||
\(444\) | 6.88069i | 0.0154971i | ||||||||
\(445\) | 24.7414 | 0.0555987 | ||||||||
\(446\) | 356.258i | 0.798785i | ||||||||
\(447\) | 282.481i | 0.631948i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −266.985 | −0.594622 | −0.297311 | − | 0.954781i | \(-0.596090\pi\) | ||||
−0.297311 | + | 0.954781i | \(0.596090\pi\) | |||||||
\(450\) | 21.2132 | 0.0471405 | ||||||||
\(451\) | 257.073i | 0.570006i | ||||||||
\(452\) | 95.5767 | 0.211453 | ||||||||
\(453\) | − 129.956i | − 0.286878i | ||||||||
\(454\) | 378.757i | 0.834267i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 153.951 | 0.337611 | ||||||||
\(457\) | −449.340 | −0.983238 | −0.491619 | − | 0.870810i | \(-0.663595\pi\) | ||||
−0.491619 | + | 0.870810i | \(0.663595\pi\) | |||||||
\(458\) | − 488.652i | − 1.06693i | ||||||||
\(459\) | 143.448 | 0.312523 | ||||||||
\(460\) | − 81.2104i | − 0.176544i | ||||||||
\(461\) | − 105.528i | − 0.228912i | −0.993428 | − | 0.114456i | \(-0.963487\pi\) | ||||
0.993428 | − | 0.114456i | \(-0.0365125\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 588.555 | 1.27118 | 0.635588 | − | 0.772028i | \(-0.280758\pi\) | ||||
0.635588 | + | 0.772028i | \(0.280758\pi\) | |||||||
\(464\) | −9.21323 | −0.0198561 | ||||||||
\(465\) | − 20.3867i | − 0.0438423i | ||||||||
\(466\) | −407.385 | −0.874216 | ||||||||
\(467\) | − 365.657i | − 0.782992i | −0.920180 | − | 0.391496i | \(-0.871958\pi\) | ||||
0.920180 | − | 0.391496i | \(-0.128042\pi\) | |||||||
\(468\) | − 47.1823i | − 0.100817i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 242.442 | 0.515835 | ||||||||
\(471\) | 389.245 | 0.826422 | ||||||||
\(472\) | − 198.978i | − 0.421565i | ||||||||
\(473\) | 577.349 | 1.22061 | ||||||||
\(474\) | 221.504i | 0.467307i | ||||||||
\(475\) | 157.125i | 0.330790i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −171.286 | −0.359091 | ||||||||
\(478\) | −267.017 | −0.558614 | ||||||||
\(479\) | − 487.176i | − 1.01707i | −0.861042 | − | 0.508535i | \(-0.830187\pi\) | ||||
0.861042 | − | 0.508535i | \(-0.169813\pi\) | |||||||
\(480\) | 21.9089 | 0.0456435 | ||||||||
\(481\) | 15.6196i | 0.0324731i | ||||||||
\(482\) | 138.378i | 0.287091i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 26.4149 | 0.0545762 | ||||||||
\(485\) | 161.693 | 0.333387 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | −195.774 | −0.402000 | −0.201000 | − | 0.979591i | \(-0.564419\pi\) | ||||
−0.201000 | + | 0.979591i | \(0.564419\pi\) | |||||||
\(488\) | 191.253i | 0.391912i | ||||||||
\(489\) | − 398.575i | − 0.815082i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −349.221 | −0.711244 | −0.355622 | − | 0.934630i | \(-0.615731\pi\) | ||||
−0.355622 | + | 0.934630i | \(0.615731\pi\) | |||||||
\(492\) | −76.8703 | −0.156240 | ||||||||
\(493\) | − 63.5865i | − 0.128979i | ||||||||
\(494\) | 349.477 | 0.707443 | ||||||||
\(495\) | 77.7132i | 0.156996i | ||||||||
\(496\) | − 21.0553i | − 0.0424501i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 327.750 | 0.658133 | ||||||||
\(499\) | −335.439 | −0.672222 | −0.336111 | − | 0.941822i | \(-0.609112\pi\) | ||||
−0.336111 | + | 0.941822i | \(0.609112\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | 481.144 | 0.960366 | ||||||||
\(502\) | − 341.313i | − 0.679907i | ||||||||
\(503\) | − 523.663i | − 1.04108i | −0.853837 | − | 0.520540i | \(-0.825731\pi\) | ||||
0.853837 | − | 0.520540i | \(-0.174269\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 113.264 | 0.224286 | ||||||||
\(506\) | 297.509 | 0.587962 | ||||||||
\(507\) | 185.610i | 0.366095i | ||||||||
\(508\) | −203.947 | −0.401470 | ||||||||
\(509\) | 482.354i | 0.947651i | 0.880619 | + | 0.473825i | \(0.157127\pi\) | ||||
−0.880619 | + | 0.473825i | \(0.842873\pi\) | |||||||
\(510\) | 151.208i | 0.296485i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −163.289 | −0.318303 | ||||||||
\(514\) | 17.7681i | 0.0345683i | ||||||||
\(515\) | 442.662 | 0.859538 | ||||||||
\(516\) | 172.640i | 0.334573i | ||||||||
\(517\) | 888.171i | 1.71793i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 218.352 | 0.420716 | ||||||||
\(520\) | 49.7345 | 0.0956433 | ||||||||
\(521\) | − 71.3039i | − 0.136860i | −0.997656 | − | 0.0684298i | \(-0.978201\pi\) | ||||
0.997656 | − | 0.0684298i | \(-0.0217989\pi\) | |||||||
\(522\) | 9.77211 | 0.0187205 | ||||||||
\(523\) | 602.128i | 1.15130i | 0.817697 | + | 0.575648i | \(0.195250\pi\) | ||||
−0.817697 | + | 0.575648i | \(0.804750\pi\) | |||||||
\(524\) | 149.196i | 0.284725i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −300.493 | −0.571279 | ||||||||
\(527\) | 145.316 | 0.275742 | ||||||||
\(528\) | 80.2618i | 0.152011i | ||||||||
\(529\) | −199.244 | −0.376643 | ||||||||
\(530\) | − 180.552i | − 0.340663i | ||||||||
\(531\) | 211.049i | 0.397455i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −174.500 | −0.327392 | ||||||||
\(534\) | −27.1029 | −0.0507545 | ||||||||
\(535\) | − 330.794i | − 0.618307i | ||||||||
\(536\) | 277.652 | 0.518007 | ||||||||
\(537\) | 133.553i | 0.248702i | ||||||||
\(538\) | − 473.191i | − 0.879537i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −23.2379 | −0.0430331 | ||||||||
\(541\) | −603.314 | −1.11518 | −0.557591 | − | 0.830116i | \(-0.688274\pi\) | ||||
−0.557591 | + | 0.830116i | \(0.688274\pi\) | |||||||
\(542\) | 257.882i | 0.475798i | ||||||||
\(543\) | 367.215 | 0.676271 | ||||||||
\(544\) | 156.167i | 0.287071i | ||||||||
\(545\) | 121.468i | 0.222876i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −879.935 | −1.60866 | −0.804328 | − | 0.594185i | \(-0.797475\pi\) | ||||
−0.804328 | + | 0.594185i | \(0.797475\pi\) | |||||||
\(548\) | −493.798 | −0.901091 | ||||||||
\(549\) | − 202.854i | − 0.369498i | ||||||||
\(550\) | −81.9169 | −0.148940 | ||||||||
\(551\) | 72.3815i | 0.131364i | ||||||||
\(552\) | 88.9615i | 0.161162i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 235.836 | 0.425697 | ||||||||
\(555\) | 7.69285 | 0.0138610 | ||||||||
\(556\) | 311.834i | 0.560852i | ||||||||
\(557\) | −882.807 | −1.58493 | −0.792466 | − | 0.609916i | \(-0.791203\pi\) | ||||
−0.792466 | + | 0.609916i | \(0.791203\pi\) | |||||||
\(558\) | 22.3325i | 0.0400224i | ||||||||
\(559\) | 391.903i | 0.701078i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −553.939 | −0.987414 | ||||||||
\(562\) | 54.1765 | 0.0963994 | ||||||||
\(563\) | − 521.156i | − 0.925676i | −0.886443 | − | 0.462838i | \(-0.846831\pi\) | ||||
0.886443 | − | 0.462838i | \(-0.153169\pi\) | |||||||
\(564\) | −265.582 | −0.470891 | ||||||||
\(565\) | − 106.858i | − 0.189129i | ||||||||
\(566\) | − 545.174i | − 0.963204i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −96.9011 | −0.170601 | ||||||||
\(569\) | 244.801 | 0.430230 | 0.215115 | − | 0.976589i | \(-0.430987\pi\) | ||||
0.215115 | + | 0.976589i | \(0.430987\pi\) | |||||||
\(570\) | − 172.122i | − 0.301968i | ||||||||
\(571\) | −416.253 | −0.728989 | −0.364495 | − | 0.931205i | \(-0.618758\pi\) | ||||
−0.364495 | + | 0.931205i | \(0.618758\pi\) | |||||||
\(572\) | 182.199i | 0.318530i | ||||||||
\(573\) | 286.994i | 0.500862i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −90.7959 | −0.157906 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 773.568i | 1.34067i | 0.742058 | + | 0.670336i | \(0.233850\pi\) | ||||
−0.742058 | + | 0.670336i | \(0.766150\pi\) | |||||||
\(578\) | −669.099 | −1.15761 | ||||||||
\(579\) | − 182.384i | − 0.314998i | ||||||||
\(580\) | 10.3007i | 0.0177598i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −177.125 | −0.304339 | ||||||||
\(583\) | 661.439 | 1.13454 | ||||||||
\(584\) | 55.1302i | 0.0944010i | ||||||||
\(585\) | −52.7514 | −0.0901733 | ||||||||
\(586\) | 128.671i | 0.219576i | ||||||||
\(587\) | − 633.860i | − 1.07983i | −0.841720 | − | 0.539915i | \(-0.818456\pi\) | ||||
0.841720 | − | 0.539915i | \(-0.181544\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −165.416 | −0.280841 | ||||||||
\(590\) | −222.465 | −0.377059 | ||||||||
\(591\) | 423.894i | 0.717250i | ||||||||
\(592\) | 7.94514 | 0.0134208 | ||||||||
\(593\) | − 92.8412i | − 0.156562i | −0.996931 | − | 0.0782809i | \(-0.975057\pi\) | ||||
0.996931 | − | 0.0782809i | \(-0.0249431\pi\) | |||||||
\(594\) | − 85.1305i | − 0.143317i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 326.181 | 0.547283 | ||||||||
\(597\) | −169.683 | −0.284227 | ||||||||
\(598\) | 201.948i | 0.337705i | ||||||||
\(599\) | −615.361 | −1.02731 | −0.513657 | − | 0.857996i | \(-0.671709\pi\) | ||||
−0.513657 | + | 0.857996i | \(0.671709\pi\) | |||||||
\(600\) | − 24.4949i | − 0.0408248i | ||||||||
\(601\) | 821.399i | 1.36672i | 0.730081 | + | 0.683360i | \(0.239482\pi\) | ||||
−0.730081 | + | 0.683360i | \(0.760518\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −294.494 | −0.488381 | ||||||||
\(604\) | −150.060 | −0.248443 | ||||||||
\(605\) | − 29.5328i | − 0.0488145i | ||||||||
\(606\) | −124.075 | −0.204744 | ||||||||
\(607\) | 1004.56i | 1.65497i | 0.561490 | + | 0.827483i | \(0.310228\pi\) | ||||
−0.561490 | + | 0.827483i | \(0.689772\pi\) | |||||||
\(608\) | − 177.767i | − 0.292380i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 213.827 | 0.350537 | ||||||||
\(611\) | −602.887 | −0.986722 | ||||||||
\(612\) | − 165.640i | − 0.270653i | ||||||||
\(613\) | 1113.75 | 1.81688 | 0.908438 | − | 0.418019i | \(-0.137276\pi\) | ||||
0.908438 | + | 0.418019i | \(0.137276\pi\) | |||||||
\(614\) | − 718.529i | − 1.17024i | ||||||||
\(615\) | 85.9436i | 0.139746i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −463.256 | −0.750820 | −0.375410 | − | 0.926859i | \(-0.622498\pi\) | ||||
−0.375410 | + | 0.926859i | \(0.622498\pi\) | |||||||
\(618\) | −484.912 | −0.784648 | ||||||||
\(619\) | 561.311i | 0.906802i | 0.891307 | + | 0.453401i | \(0.149790\pi\) | ||||
−0.891307 | + | 0.453401i | \(0.850210\pi\) | |||||||
\(620\) | −23.5405 | −0.0379686 | ||||||||
\(621\) | − 94.3579i | − 0.151945i | ||||||||
\(622\) | 147.532i | 0.237190i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −54.4814 | −0.0873100 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − 375.995i | − 0.600631i | ||||||||
\(627\) | 630.557 | 1.00567 | ||||||||
\(628\) | − 449.461i | − 0.715702i | ||||||||
\(629\) | 54.8346i | 0.0871774i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 244.533 | 0.387533 | 0.193767 | − | 0.981048i | \(-0.437930\pi\) | ||||
0.193767 | + | 0.981048i | \(0.437930\pi\) | |||||||
\(632\) | 255.770 | 0.404700 | ||||||||
\(633\) | − 673.618i | − 1.06417i | ||||||||
\(634\) | −15.1636 | −0.0239173 | ||||||||
\(635\) | 228.019i | 0.359086i | ||||||||
\(636\) | 197.784i | 0.310982i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.7360 | −0.0591473 | ||||||||
\(639\) | 102.779 | 0.160844 | ||||||||
\(640\) | − 25.2982i | − 0.0395285i | ||||||||
\(641\) | 651.769 | 1.01680 | 0.508400 | − | 0.861121i | \(-0.330237\pi\) | ||||
0.508400 | + | 0.861121i | \(0.330237\pi\) | |||||||
\(642\) | 362.367i | 0.564435i | ||||||||
\(643\) | − 76.4894i | − 0.118957i | −0.998230 | − | 0.0594786i | \(-0.981056\pi\) | ||||
0.998230 | − | 0.0594786i | \(-0.0189438\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 193.017 | 0.299251 | ||||||||
\(646\) | 1226.88 | 1.89920 | ||||||||
\(647\) | 163.891i | 0.253309i | 0.991947 | + | 0.126654i | \(0.0404239\pi\) | ||||
−0.991947 | + | 0.126654i | \(0.959576\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | − 814.985i | − 1.25575i | ||||||||
\(650\) | − 55.6049i | − 0.0855459i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −460.235 | −0.705882 | ||||||||
\(653\) | −1114.86 | −1.70729 | −0.853647 | − | 0.520852i | \(-0.825614\pi\) | ||||
−0.853647 | + | 0.520852i | \(0.825614\pi\) | |||||||
\(654\) | − 133.061i | − 0.203457i | ||||||||
\(655\) | 166.806 | 0.254666 | ||||||||
\(656\) | 88.7622i | 0.135308i | ||||||||
\(657\) | − 58.4744i | − 0.0890021i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1164.66 | 1.76732 | 0.883660 | − | 0.468130i | \(-0.155072\pi\) | ||||
0.883660 | + | 0.468130i | \(0.155072\pi\) | |||||||
\(660\) | 89.7354 | 0.135963 | ||||||||
\(661\) | 625.948i | 0.946971i | 0.880802 | + | 0.473485i | \(0.157004\pi\) | ||||
−0.880802 | + | 0.473485i | \(0.842996\pi\) | |||||||
\(662\) | −499.105 | −0.753936 | ||||||||
\(663\) | − 376.012i | − 0.567137i | ||||||||
\(664\) | − 378.453i | − 0.569960i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.42709 | −0.0126533 | ||||||||
\(667\) | −41.8262 | −0.0627080 | ||||||||
\(668\) | − 555.577i | − 0.831702i | ||||||||
\(669\) | −436.326 | −0.652206 | ||||||||
\(670\) | − 310.424i | − 0.463319i | ||||||||
\(671\) | 783.342i | 1.16743i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.0207 | −0.0564943 | −0.0282471 | − | 0.999601i | \(-0.508993\pi\) | ||||
−0.0282471 | + | 0.999601i | \(0.508993\pi\) | |||||||
\(674\) | 312.023 | 0.462942 | ||||||||
\(675\) | 25.9808i | 0.0384900i | ||||||||
\(676\) | 214.324 | 0.317047 | ||||||||
\(677\) | − 781.713i | − 1.15467i | −0.816506 | − | 0.577336i | \(-0.804092\pi\) | ||||
0.816506 | − | 0.577336i | \(-0.195908\pi\) | |||||||
\(678\) | 117.057i | 0.172651i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 174.599 | 0.256764 | ||||||||
\(681\) | −463.881 | −0.681176 | ||||||||
\(682\) | − 86.2391i | − 0.126450i | ||||||||
\(683\) | −134.438 | −0.196834 | −0.0984172 | − | 0.995145i | \(-0.531378\pi\) | ||||
−0.0984172 | + | 0.995145i | \(0.531378\pi\) | |||||||
\(684\) | 188.550i | 0.275658i | ||||||||
\(685\) | 552.083i | 0.805960i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 598.474 | 0.871142 | ||||||||
\(688\) | 199.347 | 0.289749 | ||||||||
\(689\) | 448.982i | 0.651643i | ||||||||
\(690\) | 99.4620 | 0.144148 | ||||||||
\(691\) | 454.089i | 0.657148i | 0.944478 | + | 0.328574i | \(0.106568\pi\) | ||||
−0.944478 | + | 0.328574i | \(0.893432\pi\) | |||||||
\(692\) | − 252.131i | − 0.364351i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −362.051 | −0.521687 | ||||||||
\(695\) | 348.641 | 0.501641 | ||||||||
\(696\) | − 11.2839i | − 0.0162124i | ||||||||
\(697\) | −612.605 | −0.878917 | ||||||||
\(698\) | − 575.939i | − 0.825127i | ||||||||
\(699\) | − 498.942i | − 0.713794i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 982.015 | 1.40088 | 0.700439 | − | 0.713713i | \(-0.252988\pi\) | ||||
0.700439 | + | 0.713713i | \(0.252988\pi\) | |||||||
\(702\) | 57.7863 | 0.0823166 | ||||||||
\(703\) | − 62.4191i | − 0.0887896i | ||||||||
\(704\) | 92.6784 | 0.131645 | ||||||||
\(705\) | 296.930i | 0.421177i | ||||||||
\(706\) | − 824.822i | − 1.16830i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 243.698 | 0.344206 | ||||||||
\(709\) | −333.072 | −0.469778 | −0.234889 | − | 0.972022i | \(-0.575473\pi\) | ||||
−0.234889 | + | 0.972022i | \(0.575473\pi\) | |||||||
\(710\) | 108.339i | 0.152590i | ||||||||
\(711\) | −271.285 | −0.381555 | ||||||||
\(712\) | 31.2957i | 0.0439547i | ||||||||
\(713\) | − 95.5866i | − 0.134063i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 203.705 | 0.284902 | ||||||||
\(716\) | 154.214 | 0.215382 | ||||||||
\(717\) | − 327.028i | − 0.456106i | ||||||||
\(718\) | 977.969 | 1.36207 | ||||||||
\(719\) | − 1219.05i | − 1.69547i | −0.530416 | − | 0.847737i | \(-0.677964\pi\) | ||||
0.530416 | − | 0.847737i | \(-0.322036\pi\) | |||||||
\(720\) | 26.8328i | 0.0372678i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −886.051 | −1.22722 | ||||||||
\(723\) | −169.478 | −0.234409 | ||||||||
\(724\) | − 424.024i | − 0.585668i | ||||||||
\(725\) | 11.5165 | 0.0158849 | ||||||||
\(726\) | 32.3515i | 0.0445613i | ||||||||
\(727\) | 215.108i | 0.295885i | 0.988996 | + | 0.147942i | \(0.0472650\pi\) | ||||
−0.988996 | + | 0.147942i | \(0.952735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 61.6374 | 0.0844348 | ||||||||
\(731\) | 1375.83i | 1.88211i | ||||||||
\(732\) | −234.236 | −0.319995 | ||||||||
\(733\) | 749.455i | 1.02245i | 0.859447 | + | 0.511225i | \(0.170808\pi\) | ||||
−0.859447 | + | 0.511225i | \(0.829192\pi\) | |||||||
\(734\) | 324.883i | 0.442620i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 102.724 | 0.139570 | ||||||||
\(737\) | 1137.22 | 1.54304 | ||||||||
\(738\) | − 94.1465i | − 0.127570i | ||||||||
\(739\) | −934.204 | −1.26415 | −0.632073 | − | 0.774909i | \(-0.717796\pi\) | ||||
−0.632073 | + | 0.774909i | \(0.717796\pi\) | |||||||
\(740\) | − 8.88294i | − 0.0120040i | ||||||||
\(741\) | 428.020i | 0.577625i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1232.47 | 1.65878 | 0.829389 | − | 0.558671i | \(-0.188689\pi\) | ||||
0.829389 | + | 0.558671i | \(0.188689\pi\) | |||||||
\(744\) | 25.7873 | 0.0346604 | ||||||||
\(745\) | − 364.681i | − 0.489505i | ||||||||
\(746\) | −572.203 | −0.767028 | ||||||||
\(747\) | 401.410i | 0.537363i | ||||||||
\(748\) | 639.634i | 0.855125i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −27.3861 | −0.0365148 | ||||||||
\(751\) | 786.706 | 1.04754 | 0.523772 | − | 0.851858i | \(-0.324524\pi\) | ||||
0.523772 | + | 0.851858i | \(0.324524\pi\) | |||||||
\(752\) | 306.668i | 0.407803i | ||||||||
\(753\) | 418.022 | 0.555142 | ||||||||
\(754\) | − 25.6150i | − 0.0339722i | ||||||||
\(755\) | 167.772i | 0.222214i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1303.18 | 1.72151 | 0.860753 | − | 0.509023i | \(-0.169993\pi\) | ||||
0.860753 | + | 0.509023i | \(0.169993\pi\) | |||||||
\(758\) | 375.991 | 0.496030 | ||||||||
\(759\) | 364.372i | 0.480069i | ||||||||
\(760\) | −198.749 | −0.261512 | ||||||||
\(761\) | − 694.880i | − 0.913114i | −0.889694 | − | 0.456557i | \(-0.849082\pi\) | ||||
0.889694 | − | 0.456557i | \(-0.150918\pi\) | |||||||
\(762\) | − 249.783i | − 0.327799i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 331.392 | 0.433759 | ||||||||
\(765\) | −185.191 | −0.242079 | ||||||||
\(766\) | − 433.320i | − 0.565692i | ||||||||
\(767\) | 553.209 | 0.721263 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | 263.988i | 0.343287i | 0.985159 | + | 0.171644i | \(0.0549077\pi\) | ||||
−0.985159 | + | 0.171644i | \(0.945092\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7614 | −0.0282249 | ||||||||
\(772\) | −210.599 | −0.272796 | ||||||||
\(773\) | − 157.360i | − 0.203571i | −0.994806 | − | 0.101786i | \(-0.967544\pi\) | ||||
0.994806 | − | 0.101786i | \(-0.0324556\pi\) | |||||||
\(774\) | −211.440 | −0.273178 | ||||||||
\(775\) | 26.3191i | 0.0339601i | ||||||||
\(776\) | 204.527i | 0.263566i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 150.408 | 0.193326 | ||||||||
\(779\) | 697.338 | 0.895171 | ||||||||
\(780\) | 60.9121i | 0.0780924i | ||||||||
\(781\) | −396.892 | −0.508184 | ||||||||
\(782\) | 708.964i | 0.906604i | ||||||||
\(783\) | 11.9683i | 0.0152852i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −502.513 | −0.640144 | ||||||||
\(786\) | −182.727 | −0.232477 | ||||||||
\(787\) | 982.258i | 1.24810i | 0.781383 | + | 0.624052i | \(0.214515\pi\) | ||||
−0.781383 | + | 0.624052i | \(0.785485\pi\) | |||||||
\(788\) | 489.471 | 0.621156 | ||||||||
\(789\) | − 368.027i | − 0.466448i | ||||||||
\(790\) | − 285.960i | − 0.361975i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −98.3002 | −0.124116 | ||||||||
\(793\) | −531.730 | −0.670529 | ||||||||
\(794\) | 308.053i | 0.387977i | ||||||||
\(795\) | 221.130 | 0.278150 | ||||||||
\(796\) | 195.933i | 0.246147i | ||||||||
\(797\) | − 946.927i | − 1.18811i | −0.804423 | − | 0.594057i | \(-0.797525\pi\) | ||||
0.804423 | − | 0.594057i | \(-0.202475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2116.52 | −2.64896 | ||||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | − 33.1941i | − 0.0414408i | ||||||||
\(802\) | 87.6550 | 0.109295 | ||||||||
\(803\) | 225.805i | 0.281201i | ||||||||
\(804\) | 340.052i | 0.422951i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 58.5388 | 0.0726287 | ||||||||
\(807\) | 579.538 | 0.718139 | ||||||||
\(808\) | 143.269i | 0.177313i | ||||||||
\(809\) | 429.136 | 0.530452 | 0.265226 | − | 0.964186i | \(-0.414553\pi\) | ||||
0.265226 | + | 0.964186i | \(0.414553\pi\) | |||||||
\(810\) | − 28.4605i | − 0.0351364i | ||||||||
\(811\) | − 948.404i | − 1.16943i | −0.811241 | − | 0.584713i | \(-0.801207\pi\) | ||||
0.811241 | − | 0.584713i | \(-0.198793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −315.840 | −0.388487 | ||||||||
\(814\) | 32.5420 | 0.0399779 | ||||||||
\(815\) | 514.558i | 0.631360i | ||||||||
\(816\) | −191.264 | −0.234392 | ||||||||
\(817\) | − 1566.12i | − 1.91692i | ||||||||
\(818\) | − 614.278i | − 0.750952i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 99.2391 | 0.121023 | ||||||||
\(821\) | −403.768 | −0.491800 | −0.245900 | − | 0.969295i | \(-0.579083\pi\) | ||||
−0.245900 | + | 0.969295i | \(0.579083\pi\) | |||||||
\(822\) | − 604.776i | − 0.735738i | ||||||||
\(823\) | 866.028 | 1.05228 | 0.526141 | − | 0.850397i | \(-0.323638\pi\) | ||||
0.526141 | + | 0.850397i | \(0.323638\pi\) | |||||||
\(824\) | 559.928i | 0.679525i | ||||||||
\(825\) | − 100.327i | − 0.121609i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −363.528 | −0.439574 | −0.219787 | − | 0.975548i | \(-0.570536\pi\) | ||||
−0.219787 | + | 0.975548i | \(0.570536\pi\) | |||||||
\(828\) | −108.955 | −0.131588 | ||||||||
\(829\) | 240.890i | 0.290579i | 0.989389 | + | 0.145290i | \(0.0464114\pi\) | ||||
−0.989389 | + | 0.145290i | \(0.953589\pi\) | |||||||
\(830\) | −423.124 | −0.509788 | ||||||||
\(831\) | 288.839i | 0.347580i | ||||||||
\(832\) | 62.9097i | 0.0756126i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −381.917 | −0.457934 | ||||||||
\(835\) | −621.154 | −0.743897 | ||||||||
\(836\) | − 728.105i | − 0.870939i | ||||||||
\(837\) | −27.3516 | −0.0326781 | ||||||||
\(838\) | 646.607i | 0.771608i | ||||||||
\(839\) | − 214.638i | − 0.255826i | −0.991785 | − | 0.127913i | \(-0.959172\pi\) | ||||
0.991785 | − | 0.127913i | \(-0.0408278\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −835.695 | −0.993692 | ||||||||
\(842\) | −923.692 | −1.09702 | ||||||||
\(843\) | 66.3523i | 0.0787098i | ||||||||
\(844\) | −777.827 | −0.921597 | ||||||||
\(845\) | − 239.621i | − 0.283576i | ||||||||
\(846\) | − 325.271i | − 0.384481i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 228.382 | 0.269318 | ||||||||
\(849\) | 667.699 | 0.786453 | ||||||||
\(850\) | − 195.208i | − 0.229657i | ||||||||
\(851\) | 36.0693 | 0.0423846 | ||||||||
\(852\) | − 118.679i | − 0.139295i | ||||||||
\(853\) | − 1388.39i | − 1.62765i | −0.581110 | − | 0.813825i | \(-0.697382\pi\) | ||||
0.581110 | − | 0.813825i | \(-0.302618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 210.805 | 0.246556 | ||||||||
\(856\) | 418.426 | 0.488815 | ||||||||
\(857\) | 1096.98i | 1.28002i | 0.768366 | + | 0.640011i | \(0.221070\pi\) | ||||
−0.768366 | + | 0.640011i | \(0.778930\pi\) | |||||||
\(858\) | −223.147 | −0.260078 | ||||||||
\(859\) | 270.552i | 0.314961i | 0.987522 | + | 0.157481i | \(0.0503372\pi\) | ||||
−0.987522 | + | 0.157481i | \(0.949663\pi\) | |||||||
\(860\) | − 222.877i | − 0.259159i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −665.042 | −0.771511 | ||||||||
\(863\) | 268.214 | 0.310792 | 0.155396 | − | 0.987852i | \(-0.450335\pi\) | ||||
0.155396 | + | 0.987852i | \(0.450335\pi\) | |||||||
\(864\) | − 29.3939i | − 0.0340207i | ||||||||
\(865\) | −281.891 | −0.325885 | ||||||||
\(866\) | 45.2970i | 0.0523061i | ||||||||
\(867\) | − 819.476i | − 0.945186i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1047.60 | 1.20552 | ||||||||
\(870\) | −12.6157 | −0.0145009 | ||||||||
\(871\) | 771.939i | 0.886268i | ||||||||
\(872\) | −153.646 | −0.176199 | ||||||||
\(873\) | − 216.934i | − 0.248492i | ||||||||
\(874\) | − 807.025i | − 0.923370i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −67.5204 | −0.0770781 | ||||||||
\(877\) | 507.411 | 0.578575 | 0.289288 | − | 0.957242i | \(-0.406582\pi\) | ||||
0.289288 | + | 0.957242i | \(0.406582\pi\) | |||||||
\(878\) | − 540.567i | − 0.615680i | ||||||||
\(879\) | −157.590 | −0.179283 | ||||||||
\(880\) | − 103.618i | − 0.117747i | ||||||||
\(881\) | 833.545i | 0.946135i | 0.881026 | + | 0.473067i | \(0.156853\pi\) | ||||
−0.881026 | + | 0.473067i | \(0.843147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1350.99 | −1.53000 | −0.765002 | − | 0.644028i | \(-0.777262\pi\) | ||||
−0.765002 | + | 0.644028i | \(0.777262\pi\) | |||||||
\(884\) | −434.181 | −0.491155 | ||||||||
\(885\) | − 272.463i | − 0.307867i | ||||||||
\(886\) | 174.997 | 0.197514 | ||||||||
\(887\) | − 374.129i | − 0.421792i | −0.977509 | − | 0.210896i | \(-0.932362\pi\) | ||||
0.977509 | − | 0.210896i | \(-0.0676381\pi\) | |||||||
\(888\) | 9.73077i | 0.0109581i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 34.9897 | 0.0393142 | ||||||||
\(891\) | 104.263 | 0.117018 | ||||||||
\(892\) | 503.825i | 0.564827i | ||||||||
\(893\) | 2409.26 | 2.69794 | ||||||||
\(894\) | 399.488i | 0.446855i | ||||||||
\(895\) | − 172.416i | − 0.192644i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −247.335 | −0.275735 | ||||||||
\(898\) | −377.574 | −0.420461 | ||||||||
\(899\) | 12.1242i | 0.0134863i | ||||||||
\(900\) | 30.0000 | 0.0333333 | ||||||||
\(901\) | 1576.21i | 1.74940i | ||||||||
\(902\) | 363.556i | 0.403055i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 135.166 | 0.149520 | ||||||||
\(905\) | −474.073 | −0.523837 | ||||||||
\(906\) | − 183.785i | − 0.202853i | ||||||||
\(907\) | −357.516 | −0.394174 | −0.197087 | − | 0.980386i | \(-0.563148\pi\) | ||||
−0.197087 | + | 0.980386i | \(0.563148\pi\) | |||||||
\(908\) | 535.644i | 0.589916i | ||||||||
\(909\) | − 151.960i | − 0.167173i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1503.55 | −1.65044 | −0.825219 | − | 0.564813i | \(-0.808948\pi\) | ||||
−0.825219 | + | 0.564813i | \(0.808948\pi\) | |||||||
\(912\) | 217.719 | 0.238727 | ||||||||
\(913\) | − 1550.09i | − 1.69779i | ||||||||
\(914\) | −635.462 | −0.695254 | ||||||||
\(915\) | 261.884i | 0.286212i | ||||||||
\(916\) | − 691.059i | − 0.754431i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 202.866 | 0.220987 | ||||||||
\(919\) | −624.998 | −0.680085 | −0.340043 | − | 0.940410i | \(-0.610442\pi\) | ||||
−0.340043 | + | 0.940410i | \(0.610442\pi\) | |||||||
\(920\) | − 114.849i | − 0.124836i | ||||||||
\(921\) | 880.015 | 0.955499 | ||||||||
\(922\) | − 149.240i | − 0.161865i | ||||||||
\(923\) | − 269.409i | − 0.291884i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.93142 | −0.0107367 | ||||||||
\(926\) | 832.342 | 0.898858 | ||||||||
\(927\) | − 593.894i | − 0.640662i | ||||||||
\(928\) | −13.0295 | −0.0140404 | ||||||||
\(929\) | 1088.75i | 1.17196i | 0.810327 | + | 0.585978i | \(0.199290\pi\) | ||||
−0.810327 | + | 0.585978i | \(0.800710\pi\) | |||||||
\(930\) | − 28.8311i | − 0.0310012i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −576.129 | −0.618164 | ||||||||
\(933\) | −180.689 | −0.193665 | ||||||||
\(934\) | − 517.117i | − 0.553659i | ||||||||
\(935\) | 715.132 | 0.764847 | ||||||||
\(936\) | − 66.7258i | − 0.0712883i | ||||||||
\(937\) | 252.836i | 0.269835i | 0.990857 | + | 0.134918i | \(0.0430770\pi\) | ||||
−0.990857 | + | 0.134918i | \(0.956923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 460.498 | 0.490413 | ||||||||
\(940\) | 342.865 | 0.364750 | ||||||||
\(941\) | − 383.664i | − 0.407719i | −0.979000 | − | 0.203859i | \(-0.934651\pi\) | ||||
0.979000 | − | 0.203859i | \(-0.0653486\pi\) | |||||||
\(942\) | 550.475 | 0.584369 | ||||||||
\(943\) | 402.962i | 0.427319i | ||||||||
\(944\) | − 281.398i | − 0.298091i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 816.495 | 0.863103 | ||||||||
\(947\) | −281.784 | −0.297554 | −0.148777 | − | 0.988871i | \(-0.547534\pi\) | ||||
−0.148777 | + | 0.988871i | \(0.547534\pi\) | |||||||
\(948\) | 313.253i | 0.330436i | ||||||||
\(949\) | −153.275 | −0.161512 | ||||||||
\(950\) | 222.208i | 0.233904i | ||||||||
\(951\) | − 18.5715i | − 0.0195284i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −332.322 | −0.348711 | −0.174356 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174356 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(954\) | −242.235 | −0.253915 | ||||||||
\(955\) | − 370.507i | − 0.387966i | ||||||||
\(956\) | −377.620 | −0.395000 | ||||||||
\(957\) | − 46.2169i | − 0.0482935i | ||||||||
\(958\) | − 688.971i | − 0.719177i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.9839 | 0.0322749 | ||||||||
\(961\) | 933.292 | 0.971168 | ||||||||
\(962\) | 22.0894i | 0.0229620i | ||||||||
\(963\) | −443.807 | −0.460859 | ||||||||
\(964\) | 195.696i | 0.203004i | ||||||||
\(965\) | 235.457i | 0.243997i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1155.53 | 1.19496 | 0.597482 | − | 0.801882i | \(-0.296168\pi\) | ||||
0.597482 | + | 0.801882i | \(0.296168\pi\) | |||||||
\(968\) | 37.3563 | 0.0385912 | ||||||||
\(969\) | 1502.62i | 1.55069i | ||||||||
\(970\) | 228.668 | 0.235740 | ||||||||
\(971\) | 1510.28i | 1.55539i | 0.628645 | + | 0.777693i | \(0.283610\pi\) | ||||
−0.628645 | + | 0.777693i | \(0.716390\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −276.866 | −0.284257 | ||||||||
\(975\) | 68.1018 | 0.0698480 | ||||||||
\(976\) | 270.473i | 0.277124i | ||||||||
\(977\) | 801.616 | 0.820487 | 0.410244 | − | 0.911976i | \(-0.365444\pi\) | ||||
0.410244 | + | 0.911976i | \(0.365444\pi\) | |||||||
\(978\) | − 563.670i | − 0.576350i | ||||||||
\(979\) | 128.182i | 0.130932i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 162.966 | 0.166122 | ||||||||
\(982\) | −493.873 | −0.502926 | ||||||||
\(983\) | − 1094.79i | − 1.11372i | −0.830605 | − | 0.556862i | \(-0.812005\pi\) | ||||
0.830605 | − | 0.556862i | \(-0.187995\pi\) | |||||||
\(984\) | −108.711 | −0.110479 | ||||||||
\(985\) | − 547.245i | − 0.555579i | ||||||||
\(986\) | − 89.9249i | − 0.0912018i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 494.235 | 0.500238 | ||||||||
\(989\) | 904.996 | 0.915062 | ||||||||
\(990\) | 109.903i | 0.111013i | ||||||||
\(991\) | 43.9925 | 0.0443920 | 0.0221960 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221960 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(992\) | − 29.7766i | − 0.0300168i | ||||||||
\(993\) | − 611.277i | − 0.615586i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 219.060 | 0.220161 | ||||||||
\(996\) | 463.509 | 0.465370 | ||||||||
\(997\) | 12.2561i | 0.0122929i | 0.999981 | + | 0.00614647i | \(0.00195649\pi\) | ||||
−0.999981 | + | 0.00614647i | \(0.998044\pi\) | |||||||
\(998\) | −474.382 | −0.475333 | ||||||||
\(999\) | − 10.3210i | − 0.0103314i |
(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 | 1470.3.f.a.391.7 | 8 | ||
7.4 | even | 3 | 210.3.o.a.61.2 | yes | 8 | ||
7.5 | odd | 6 | 210.3.o.a.31.2 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 1470.3.f.a.391.6 | 8 | ||
21.5 | even | 6 | 630.3.v.b.451.3 | 8 | |||
21.11 | odd | 6 | 630.3.v.b.271.3 | 8 | |||
35.4 | even | 6 | 1050.3.p.b.901.3 | 8 | |||
35.12 | even | 12 | 1050.3.q.c.199.7 | 16 | |||
35.18 | odd | 12 | 1050.3.q.c.649.7 | 16 | |||
35.19 | odd | 6 | 1050.3.p.b.451.3 | 8 | |||
35.32 | odd | 12 | 1050.3.q.c.649.2 | 16 | |||
35.33 | even | 12 | 1050.3.q.c.199.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.a.31.2 | ✓ | 8 | 7.5 | odd | 6 | ||
210.3.o.a.61.2 | yes | 8 | 7.4 | even | 3 | ||
630.3.v.b.271.3 | 8 | 21.11 | odd | 6 | |||
630.3.v.b.451.3 | 8 | 21.5 | even | 6 | |||
1050.3.p.b.451.3 | 8 | 35.19 | odd | 6 | |||
1050.3.p.b.901.3 | 8 | 35.4 | even | 6 | |||
1050.3.q.c.199.2 | 16 | 35.33 | even | 12 | |||
1050.3.q.c.199.7 | 16 | 35.12 | even | 12 | |||
1050.3.q.c.649.2 | 16 | 35.32 | odd | 12 | |||
1050.3.q.c.649.7 | 16 | 35.18 | odd | 12 | |||
1470.3.f.a.391.6 | 8 | 7.6 | odd | 2 | inner | ||
1470.3.f.a.391.7 | 8 | 1.1 | even | 1 | trivial |