Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,3,Mod(13,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("21.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.d (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: | \(0.572208555157\) |
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: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.13 |
Dual form | 21.3.d.a.13.2 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.500000 | 0.250000 | − | 0.968246i | \(-0.419569\pi\) | ||||
0.250000 | + | 0.968246i | \(0.419569\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | 6.92820i | 1.38564i | 0.721110 | + | 0.692820i | \(0.243632\pi\) | ||||
−0.721110 | + | 0.692820i | \(0.756368\pi\) | |||||||
\(6\) | − | 1.73205i | − | 0.288675i | ||||||
\(7\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(8\) | −7.00000 | −0.875000 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 6.92820i | 0.692820i | ||||||||
\(11\) | 10.0000 | 0.909091 | 0.454545 | − | 0.890724i | \(-0.349802\pi\) | ||||
0.454545 | + | 0.890724i | \(0.349802\pi\) | |||||||
\(12\) | 5.19615i | 0.433013i | ||||||||
\(13\) | − | 6.92820i | − | 0.532939i | −0.963843 | − | 0.266469i | \(-0.914143\pi\) | ||
0.963843 | − | 0.266469i | \(-0.0858571\pi\) | |||||||
\(14\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(15\) | 12.0000 | 0.800000 | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −3.00000 | −0.166667 | ||||||||
\(19\) | 20.7846i | 1.09393i | 0.837157 | + | 0.546963i | \(0.184216\pi\) | ||||
−0.837157 | + | 0.546963i | \(0.815784\pi\) | |||||||
\(20\) | − | 20.7846i | − | 1.03923i | ||||||
\(21\) | −12.0000 | − | 1.73205i | −0.571429 | − | 0.0824786i | ||||
\(22\) | 10.0000 | 0.454545 | ||||||||
\(23\) | −14.0000 | −0.608696 | −0.304348 | − | 0.952561i | \(-0.598439\pi\) | ||||
−0.304348 | + | 0.952561i | \(0.598439\pi\) | |||||||
\(24\) | 12.1244i | 0.505181i | ||||||||
\(25\) | −23.0000 | −0.920000 | ||||||||
\(26\) | − | 6.92820i | − | 0.266469i | ||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −3.00000 | + | 20.7846i | −0.107143 | + | 0.742307i | ||||
\(29\) | −38.0000 | −1.31034 | −0.655172 | − | 0.755479i | \(-0.727404\pi\) | ||||
−0.655172 | + | 0.755479i | \(0.727404\pi\) | |||||||
\(30\) | 12.0000 | 0.400000 | ||||||||
\(31\) | − | 27.7128i | − | 0.893962i | −0.894544 | − | 0.446981i | \(-0.852499\pi\) | ||
0.894544 | − | 0.446981i | \(-0.147501\pi\) | |||||||
\(32\) | 33.0000 | 1.03125 | ||||||||
\(33\) | − | 17.3205i | − | 0.524864i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 48.0000 | + | 6.92820i | 1.37143 | + | 0.197949i | ||||
\(36\) | 9.00000 | 0.250000 | ||||||||
\(37\) | 26.0000 | 0.702703 | 0.351351 | − | 0.936244i | \(-0.385722\pi\) | ||||
0.351351 | + | 0.936244i | \(0.385722\pi\) | |||||||
\(38\) | 20.7846i | 0.546963i | ||||||||
\(39\) | −12.0000 | −0.307692 | ||||||||
\(40\) | − | 48.4974i | − | 1.21244i | ||||||
\(41\) | 69.2820i | 1.68981i | 0.534920 | + | 0.844903i | \(0.320342\pi\) | ||||
−0.534920 | + | 0.844903i | \(0.679658\pi\) | |||||||
\(42\) | −12.0000 | − | 1.73205i | −0.285714 | − | 0.0412393i | ||||
\(43\) | 26.0000 | 0.604651 | 0.302326 | − | 0.953205i | \(-0.402237\pi\) | ||||
0.302326 | + | 0.953205i | \(0.402237\pi\) | |||||||
\(44\) | −30.0000 | −0.681818 | ||||||||
\(45\) | − | 20.7846i | − | 0.461880i | ||||||
\(46\) | −14.0000 | −0.304348 | ||||||||
\(47\) | − | 27.7128i | − | 0.589634i | −0.955554 | − | 0.294817i | \(-0.904741\pi\) | ||
0.955554 | − | 0.294817i | \(-0.0952587\pi\) | |||||||
\(48\) | − | 8.66025i | − | 0.180422i | ||||||
\(49\) | −47.0000 | − | 13.8564i | −0.959184 | − | 0.282784i | ||||
\(50\) | −23.0000 | −0.460000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 20.7846i | 0.399704i | ||||||||
\(53\) | 10.0000 | 0.188679 | 0.0943396 | − | 0.995540i | \(-0.469926\pi\) | ||||
0.0943396 | + | 0.995540i | \(0.469926\pi\) | |||||||
\(54\) | 5.19615i | 0.0962250i | ||||||||
\(55\) | 69.2820i | 1.25967i | ||||||||
\(56\) | −7.00000 | + | 48.4974i | −0.125000 | + | 0.866025i | ||||
\(57\) | 36.0000 | 0.631579 | ||||||||
\(58\) | −38.0000 | −0.655172 | ||||||||
\(59\) | − | 76.2102i | − | 1.29170i | −0.763465 | − | 0.645849i | \(-0.776503\pi\) | ||
0.763465 | − | 0.645849i | \(-0.223497\pi\) | |||||||
\(60\) | −36.0000 | −0.600000 | ||||||||
\(61\) | − | 34.6410i | − | 0.567886i | −0.958841 | − | 0.283943i | \(-0.908357\pi\) | ||
0.958841 | − | 0.283943i | \(-0.0916426\pi\) | |||||||
\(62\) | − | 27.7128i | − | 0.446981i | ||||||
\(63\) | −3.00000 | + | 20.7846i | −0.0476190 | + | 0.329914i | ||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | 48.0000 | 0.738462 | ||||||||
\(66\) | − | 17.3205i | − | 0.262432i | ||||||
\(67\) | 74.0000 | 1.10448 | 0.552239 | − | 0.833686i | \(-0.313774\pi\) | ||||
0.552239 | + | 0.833686i | \(0.313774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.2487i | 0.351431i | ||||||||
\(70\) | 48.0000 | + | 6.92820i | 0.685714 | + | 0.0989743i | ||||
\(71\) | −62.0000 | −0.873239 | −0.436620 | − | 0.899646i | \(-0.643824\pi\) | ||||
−0.436620 | + | 0.899646i | \(0.643824\pi\) | |||||||
\(72\) | 21.0000 | 0.291667 | ||||||||
\(73\) | 41.5692i | 0.569441i | 0.958611 | + | 0.284721i | \(0.0919009\pi\) | ||||
−0.958611 | + | 0.284721i | \(0.908099\pi\) | |||||||
\(74\) | 26.0000 | 0.351351 | ||||||||
\(75\) | 39.8372i | 0.531162i | ||||||||
\(76\) | − | 62.3538i | − | 0.820445i | ||||||
\(77\) | 10.0000 | − | 69.2820i | 0.129870 | − | 0.899767i | ||||
\(78\) | −12.0000 | −0.153846 | ||||||||
\(79\) | −46.0000 | −0.582278 | −0.291139 | − | 0.956681i | \(-0.594034\pi\) | ||||
−0.291139 | + | 0.956681i | \(0.594034\pi\) | |||||||
\(80\) | 34.6410i | 0.433013i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 69.2820i | 0.844903i | ||||||||
\(83\) | − | 90.0666i | − | 1.08514i | −0.840011 | − | 0.542570i | \(-0.817451\pi\) | ||
0.840011 | − | 0.542570i | \(-0.182549\pi\) | |||||||
\(84\) | 36.0000 | + | 5.19615i | 0.428571 | + | 0.0618590i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 26.0000 | 0.302326 | ||||||||
\(87\) | 65.8179i | 0.756528i | ||||||||
\(88\) | −70.0000 | −0.795455 | ||||||||
\(89\) | 41.5692i | 0.467070i | 0.972348 | + | 0.233535i | \(0.0750293\pi\) | ||||
−0.972348 | + | 0.233535i | \(0.924971\pi\) | |||||||
\(90\) | − | 20.7846i | − | 0.230940i | ||||||
\(91\) | −48.0000 | − | 6.92820i | −0.527473 | − | 0.0761341i | ||||
\(92\) | 42.0000 | 0.456522 | ||||||||
\(93\) | −48.0000 | −0.516129 | ||||||||
\(94\) | − | 27.7128i | − | 0.294817i | ||||||
\(95\) | −144.000 | −1.51579 | ||||||||
\(96\) | − | 57.1577i | − | 0.595392i | ||||||
\(97\) | − | 55.4256i | − | 0.571398i | −0.958319 | − | 0.285699i | \(-0.907774\pi\) | ||
0.958319 | − | 0.285699i | \(-0.0922258\pi\) | |||||||
\(98\) | −47.0000 | − | 13.8564i | −0.479592 | − | 0.141392i | ||||
\(99\) | −30.0000 | −0.303030 | ||||||||
\(100\) | 69.0000 | 0.690000 | ||||||||
\(101\) | 117.779i | 1.16613i | 0.812424 | + | 0.583067i | \(0.198147\pi\) | ||||
−0.812424 | + | 0.583067i | \(0.801853\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 96.9948i | 0.941698i | 0.882214 | + | 0.470849i | \(0.156052\pi\) | ||||
−0.882214 | + | 0.470849i | \(0.843948\pi\) | |||||||
\(104\) | 48.4974i | 0.466321i | ||||||||
\(105\) | 12.0000 | − | 83.1384i | 0.114286 | − | 0.791795i | ||||
\(106\) | 10.0000 | 0.0943396 | ||||||||
\(107\) | 10.0000 | 0.0934579 | 0.0467290 | − | 0.998908i | \(-0.485120\pi\) | ||||
0.0467290 | + | 0.998908i | \(0.485120\pi\) | |||||||
\(108\) | − | 15.5885i | − | 0.144338i | ||||||
\(109\) | 74.0000 | 0.678899 | 0.339450 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339450 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(110\) | 69.2820i | 0.629837i | ||||||||
\(111\) | − | 45.0333i | − | 0.405706i | ||||||
\(112\) | 5.00000 | − | 34.6410i | 0.0446429 | − | 0.309295i | ||||
\(113\) | 178.000 | 1.57522 | 0.787611 | − | 0.616173i | \(-0.211318\pi\) | ||||
0.787611 | + | 0.616173i | \(0.211318\pi\) | |||||||
\(114\) | 36.0000 | 0.315789 | ||||||||
\(115\) | − | 96.9948i | − | 0.843433i | ||||||
\(116\) | 114.000 | 0.982759 | ||||||||
\(117\) | 20.7846i | 0.177646i | ||||||||
\(118\) | − | 76.2102i | − | 0.645849i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −84.0000 | −0.700000 | ||||||||
\(121\) | −21.0000 | −0.173554 | ||||||||
\(122\) | − | 34.6410i | − | 0.283943i | ||||||
\(123\) | 120.000 | 0.975610 | ||||||||
\(124\) | 83.1384i | 0.670471i | ||||||||
\(125\) | 13.8564i | 0.110851i | ||||||||
\(126\) | −3.00000 | + | 20.7846i | −0.0238095 | + | 0.164957i | ||||
\(127\) | −190.000 | −1.49606 | −0.748031 | − | 0.663663i | \(-0.769001\pi\) | ||||
−0.748031 | + | 0.663663i | \(0.769001\pi\) | |||||||
\(128\) | −119.000 | −0.929688 | ||||||||
\(129\) | − | 45.0333i | − | 0.349096i | ||||||
\(130\) | 48.0000 | 0.369231 | ||||||||
\(131\) | 48.4974i | 0.370209i | 0.982719 | + | 0.185105i | \(0.0592624\pi\) | ||||
−0.982719 | + | 0.185105i | \(0.940738\pi\) | |||||||
\(132\) | 51.9615i | 0.393648i | ||||||||
\(133\) | 144.000 | + | 20.7846i | 1.08271 | + | 0.156275i | ||||
\(134\) | 74.0000 | 0.552239 | ||||||||
\(135\) | −36.0000 | −0.266667 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −206.000 | −1.50365 | −0.751825 | − | 0.659363i | \(-0.770826\pi\) | ||||
−0.751825 | + | 0.659363i | \(0.770826\pi\) | |||||||
\(138\) | 24.2487i | 0.175715i | ||||||||
\(139\) | 117.779i | 0.847334i | 0.905818 | + | 0.423667i | \(0.139257\pi\) | ||||
−0.905818 | + | 0.423667i | \(0.860743\pi\) | |||||||
\(140\) | −144.000 | − | 20.7846i | −1.02857 | − | 0.148461i | ||||
\(141\) | −48.0000 | −0.340426 | ||||||||
\(142\) | −62.0000 | −0.436620 | ||||||||
\(143\) | − | 69.2820i | − | 0.484490i | ||||||
\(144\) | −15.0000 | −0.104167 | ||||||||
\(145\) | − | 263.272i | − | 1.81567i | ||||||
\(146\) | 41.5692i | 0.284721i | ||||||||
\(147\) | −24.0000 | + | 81.4064i | −0.163265 | + | 0.553785i | ||||
\(148\) | −78.0000 | −0.527027 | ||||||||
\(149\) | 106.000 | 0.711409 | 0.355705 | − | 0.934598i | \(-0.384241\pi\) | ||||
0.355705 | + | 0.934598i | \(0.384241\pi\) | |||||||
\(150\) | 39.8372i | 0.265581i | ||||||||
\(151\) | −46.0000 | −0.304636 | −0.152318 | − | 0.988332i | \(-0.548674\pi\) | ||||
−0.152318 | + | 0.988332i | \(0.548674\pi\) | |||||||
\(152\) | − | 145.492i | − | 0.957186i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.0000 | − | 69.2820i | 0.0649351 | − | 0.449883i | ||||
\(155\) | 192.000 | 1.23871 | ||||||||
\(156\) | 36.0000 | 0.230769 | ||||||||
\(157\) | 242.487i | 1.54450i | 0.635316 | + | 0.772252i | \(0.280870\pi\) | ||||
−0.635316 | + | 0.772252i | \(0.719130\pi\) | |||||||
\(158\) | −46.0000 | −0.291139 | ||||||||
\(159\) | − | 17.3205i | − | 0.108934i | ||||||
\(160\) | 228.631i | 1.42894i | ||||||||
\(161\) | −14.0000 | + | 96.9948i | −0.0869565 | + | 0.602452i | ||||
\(162\) | 9.00000 | 0.0555556 | ||||||||
\(163\) | 170.000 | 1.04294 | 0.521472 | − | 0.853268i | \(-0.325383\pi\) | ||||
0.521472 | + | 0.853268i | \(0.325383\pi\) | |||||||
\(164\) | − | 207.846i | − | 1.26735i | ||||||
\(165\) | 120.000 | 0.727273 | ||||||||
\(166\) | − | 90.0666i | − | 0.542570i | ||||||
\(167\) | − | 96.9948i | − | 0.580807i | −0.956904 | − | 0.290404i | \(-0.906210\pi\) | ||
0.956904 | − | 0.290404i | \(-0.0937896\pi\) | |||||||
\(168\) | 84.0000 | + | 12.1244i | 0.500000 | + | 0.0721688i | ||||
\(169\) | 121.000 | 0.715976 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 62.3538i | − | 0.364642i | ||||||
\(172\) | −78.0000 | −0.453488 | ||||||||
\(173\) | − | 173.205i | − | 1.00119i | −0.865683 | − | 0.500593i | \(-0.833115\pi\) | ||
0.865683 | − | 0.500593i | \(-0.166885\pi\) | |||||||
\(174\) | 65.8179i | 0.378264i | ||||||||
\(175\) | −23.0000 | + | 159.349i | −0.131429 | + | 0.910564i | ||||
\(176\) | 50.0000 | 0.284091 | ||||||||
\(177\) | −132.000 | −0.745763 | ||||||||
\(178\) | 41.5692i | 0.233535i | ||||||||
\(179\) | −38.0000 | −0.212291 | −0.106145 | − | 0.994351i | \(-0.533851\pi\) | ||||
−0.106145 | + | 0.994351i | \(0.533851\pi\) | |||||||
\(180\) | 62.3538i | 0.346410i | ||||||||
\(181\) | − | 187.061i | − | 1.03349i | −0.856140 | − | 0.516744i | \(-0.827144\pi\) | ||
0.856140 | − | 0.516744i | \(-0.172856\pi\) | |||||||
\(182\) | −48.0000 | − | 6.92820i | −0.263736 | − | 0.0380671i | ||||
\(183\) | −60.0000 | −0.327869 | ||||||||
\(184\) | 98.0000 | 0.532609 | ||||||||
\(185\) | 180.133i | 0.973693i | ||||||||
\(186\) | −48.0000 | −0.258065 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 83.1384i | 0.442226i | ||||||||
\(189\) | 36.0000 | + | 5.19615i | 0.190476 | + | 0.0274929i | ||||
\(190\) | −144.000 | −0.757895 | ||||||||
\(191\) | 82.0000 | 0.429319 | 0.214660 | − | 0.976689i | \(-0.431136\pi\) | ||||
0.214660 | + | 0.976689i | \(0.431136\pi\) | |||||||
\(192\) | − | 22.5167i | − | 0.117274i | ||||||
\(193\) | 50.0000 | 0.259067 | 0.129534 | − | 0.991575i | \(-0.458652\pi\) | ||||
0.129534 | + | 0.991575i | \(0.458652\pi\) | |||||||
\(194\) | − | 55.4256i | − | 0.285699i | ||||||
\(195\) | − | 83.1384i | − | 0.426351i | ||||||
\(196\) | 141.000 | + | 41.5692i | 0.719388 | + | 0.212088i | ||||
\(197\) | −278.000 | −1.41117 | −0.705584 | − | 0.708627i | \(-0.749315\pi\) | ||||
−0.705584 | + | 0.708627i | \(0.749315\pi\) | |||||||
\(198\) | −30.0000 | −0.151515 | ||||||||
\(199\) | − | 290.985i | − | 1.46223i | −0.682252 | − | 0.731117i | \(-0.738999\pi\) | ||
0.682252 | − | 0.731117i | \(-0.261001\pi\) | |||||||
\(200\) | 161.000 | 0.805000 | ||||||||
\(201\) | − | 128.172i | − | 0.637670i | ||||||
\(202\) | 117.779i | 0.583067i | ||||||||
\(203\) | −38.0000 | + | 263.272i | −0.187192 | + | 1.29691i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −480.000 | −2.34146 | ||||||||
\(206\) | 96.9948i | 0.470849i | ||||||||
\(207\) | 42.0000 | 0.202899 | ||||||||
\(208\) | − | 34.6410i | − | 0.166543i | ||||||
\(209\) | 207.846i | 0.994479i | ||||||||
\(210\) | 12.0000 | − | 83.1384i | 0.0571429 | − | 0.395897i | ||||
\(211\) | 74.0000 | 0.350711 | 0.175355 | − | 0.984505i | \(-0.443893\pi\) | ||||
0.175355 | + | 0.984505i | \(0.443893\pi\) | |||||||
\(212\) | −30.0000 | −0.141509 | ||||||||
\(213\) | 107.387i | 0.504165i | ||||||||
\(214\) | 10.0000 | 0.0467290 | ||||||||
\(215\) | 180.133i | 0.837829i | ||||||||
\(216\) | − | 36.3731i | − | 0.168394i | ||||||
\(217\) | −192.000 | − | 27.7128i | −0.884793 | − | 0.127709i | ||||
\(218\) | 74.0000 | 0.339450 | ||||||||
\(219\) | 72.0000 | 0.328767 | ||||||||
\(220\) | − | 207.846i | − | 0.944755i | ||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 45.0333i | − | 0.202853i | ||||||
\(223\) | − | 304.841i | − | 1.36700i | −0.729951 | − | 0.683500i | \(-0.760457\pi\) | ||
0.729951 | − | 0.683500i | \(-0.239543\pi\) | |||||||
\(224\) | 33.0000 | − | 228.631i | 0.147321 | − | 1.02067i | ||||
\(225\) | 69.0000 | 0.306667 | ||||||||
\(226\) | 178.000 | 0.787611 | ||||||||
\(227\) | − | 6.92820i | − | 0.0305207i | −0.999884 | − | 0.0152604i | \(-0.995142\pi\) | ||
0.999884 | − | 0.0152604i | \(-0.00485771\pi\) | |||||||
\(228\) | −108.000 | −0.473684 | ||||||||
\(229\) | 284.056i | 1.24042i | 0.784436 | + | 0.620210i | \(0.212953\pi\) | ||||
−0.784436 | + | 0.620210i | \(0.787047\pi\) | |||||||
\(230\) | − | 96.9948i | − | 0.421717i | ||||||
\(231\) | −120.000 | − | 17.3205i | −0.519481 | − | 0.0749806i | ||||
\(232\) | 266.000 | 1.14655 | ||||||||
\(233\) | 178.000 | 0.763948 | 0.381974 | − | 0.924173i | \(-0.375244\pi\) | ||||
0.381974 | + | 0.924173i | \(0.375244\pi\) | |||||||
\(234\) | 20.7846i | 0.0888231i | ||||||||
\(235\) | 192.000 | 0.817021 | ||||||||
\(236\) | 228.631i | 0.968774i | ||||||||
\(237\) | 79.6743i | 0.336179i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 34.0000 | 0.142259 | 0.0711297 | − | 0.997467i | \(-0.477340\pi\) | ||||
0.0711297 | + | 0.997467i | \(0.477340\pi\) | |||||||
\(240\) | 60.0000 | 0.250000 | ||||||||
\(241\) | 193.990i | 0.804936i | 0.915434 | + | 0.402468i | \(0.131848\pi\) | ||||
−0.915434 | + | 0.402468i | \(0.868152\pi\) | |||||||
\(242\) | −21.0000 | −0.0867769 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 103.923i | 0.425914i | ||||||||
\(245\) | 96.0000 | − | 325.626i | 0.391837 | − | 1.32908i | ||||
\(246\) | 120.000 | 0.487805 | ||||||||
\(247\) | 144.000 | 0.582996 | ||||||||
\(248\) | 193.990i | 0.782216i | ||||||||
\(249\) | −156.000 | −0.626506 | ||||||||
\(250\) | 13.8564i | 0.0554256i | ||||||||
\(251\) | − | 187.061i | − | 0.745265i | −0.927979 | − | 0.372632i | \(-0.878455\pi\) | ||
0.927979 | − | 0.372632i | \(-0.121545\pi\) | |||||||
\(252\) | 9.00000 | − | 62.3538i | 0.0357143 | − | 0.247436i | ||||
\(253\) | −140.000 | −0.553360 | ||||||||
\(254\) | −190.000 | −0.748031 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | − | 138.564i | − | 0.539160i | −0.962978 | − | 0.269580i | \(-0.913115\pi\) | ||
0.962978 | − | 0.269580i | \(-0.0868848\pi\) | |||||||
\(258\) | − | 45.0333i | − | 0.174548i | ||||||
\(259\) | 26.0000 | − | 180.133i | 0.100386 | − | 0.695495i | ||||
\(260\) | −144.000 | −0.553846 | ||||||||
\(261\) | 114.000 | 0.436782 | ||||||||
\(262\) | 48.4974i | 0.185105i | ||||||||
\(263\) | −62.0000 | −0.235741 | −0.117871 | − | 0.993029i | \(-0.537607\pi\) | ||||
−0.117871 | + | 0.993029i | \(0.537607\pi\) | |||||||
\(264\) | 121.244i | 0.459256i | ||||||||
\(265\) | 69.2820i | 0.261442i | ||||||||
\(266\) | 144.000 | + | 20.7846i | 0.541353 | + | 0.0781376i | ||||
\(267\) | 72.0000 | 0.269663 | ||||||||
\(268\) | −222.000 | −0.828358 | ||||||||
\(269\) | − | 228.631i | − | 0.849928i | −0.905210 | − | 0.424964i | \(-0.860287\pi\) | ||
0.905210 | − | 0.424964i | \(-0.139713\pi\) | |||||||
\(270\) | −36.0000 | −0.133333 | ||||||||
\(271\) | 332.554i | 1.22714i | 0.789642 | + | 0.613568i | \(0.210266\pi\) | ||||
−0.789642 | + | 0.613568i | \(0.789734\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | + | 83.1384i | −0.0439560 | + | 0.304536i | ||||
\(274\) | −206.000 | −0.751825 | ||||||||
\(275\) | −230.000 | −0.836364 | ||||||||
\(276\) | − | 72.7461i | − | 0.263573i | ||||||
\(277\) | 26.0000 | 0.0938628 | 0.0469314 | − | 0.998898i | \(-0.485056\pi\) | ||||
0.0469314 | + | 0.998898i | \(0.485056\pi\) | |||||||
\(278\) | 117.779i | 0.423667i | ||||||||
\(279\) | 83.1384i | 0.297987i | ||||||||
\(280\) | −336.000 | − | 48.4974i | −1.20000 | − | 0.173205i | ||||
\(281\) | −494.000 | −1.75801 | −0.879004 | − | 0.476815i | \(-0.841791\pi\) | ||||
−0.879004 | + | 0.476815i | \(0.841791\pi\) | |||||||
\(282\) | −48.0000 | −0.170213 | ||||||||
\(283\) | 200.918i | 0.709957i | 0.934874 | + | 0.354979i | \(0.115512\pi\) | ||||
−0.934874 | + | 0.354979i | \(0.884488\pi\) | |||||||
\(284\) | 186.000 | 0.654930 | ||||||||
\(285\) | 249.415i | 0.875141i | ||||||||
\(286\) | − | 69.2820i | − | 0.242245i | ||||||
\(287\) | 480.000 | + | 69.2820i | 1.67247 | + | 0.241401i | ||||
\(288\) | −99.0000 | −0.343750 | ||||||||
\(289\) | 289.000 | 1.00000 | ||||||||
\(290\) | − | 263.272i | − | 0.907834i | ||||||
\(291\) | −96.0000 | −0.329897 | ||||||||
\(292\) | − | 124.708i | − | 0.427081i | ||||||
\(293\) | − | 491.902i | − | 1.67885i | −0.543477 | − | 0.839424i | \(-0.682893\pi\) | ||
0.543477 | − | 0.839424i | \(-0.317107\pi\) | |||||||
\(294\) | −24.0000 | + | 81.4064i | −0.0816327 | + | 0.276892i | ||||
\(295\) | 528.000 | 1.78983 | ||||||||
\(296\) | −182.000 | −0.614865 | ||||||||
\(297\) | 51.9615i | 0.174955i | ||||||||
\(298\) | 106.000 | 0.355705 | ||||||||
\(299\) | 96.9948i | 0.324397i | ||||||||
\(300\) | − | 119.512i | − | 0.398372i | ||||||
\(301\) | 26.0000 | − | 180.133i | 0.0863787 | − | 0.598449i | ||||
\(302\) | −46.0000 | −0.152318 | ||||||||
\(303\) | 204.000 | 0.673267 | ||||||||
\(304\) | 103.923i | 0.341852i | ||||||||
\(305\) | 240.000 | 0.786885 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7846i | 0.0677023i | 0.999427 | + | 0.0338512i | \(0.0107772\pi\) | ||||
−0.999427 | + | 0.0338512i | \(0.989223\pi\) | |||||||
\(308\) | −30.0000 | + | 207.846i | −0.0974026 | + | 0.674825i | ||||
\(309\) | 168.000 | 0.543689 | ||||||||
\(310\) | 192.000 | 0.619355 | ||||||||
\(311\) | − | 13.8564i | − | 0.0445544i | −0.999752 | − | 0.0222772i | \(-0.992908\pi\) | ||
0.999752 | − | 0.0222772i | \(-0.00709163\pi\) | |||||||
\(312\) | 84.0000 | 0.269231 | ||||||||
\(313\) | − | 263.272i | − | 0.841124i | −0.907264 | − | 0.420562i | \(-0.861833\pi\) | ||
0.907264 | − | 0.420562i | \(-0.138167\pi\) | |||||||
\(314\) | 242.487i | 0.772252i | ||||||||
\(315\) | −144.000 | − | 20.7846i | −0.457143 | − | 0.0659829i | ||||
\(316\) | 138.000 | 0.436709 | ||||||||
\(317\) | 250.000 | 0.788644 | 0.394322 | − | 0.918972i | \(-0.370980\pi\) | ||||
0.394322 | + | 0.918972i | \(0.370980\pi\) | |||||||
\(318\) | − | 17.3205i | − | 0.0544670i | ||||||
\(319\) | −380.000 | −1.19122 | ||||||||
\(320\) | 90.0666i | 0.281458i | ||||||||
\(321\) | − | 17.3205i | − | 0.0539580i | ||||||
\(322\) | −14.0000 | + | 96.9948i | −0.0434783 | + | 0.301226i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −27.0000 | −0.0833333 | ||||||||
\(325\) | 159.349i | 0.490304i | ||||||||
\(326\) | 170.000 | 0.521472 | ||||||||
\(327\) | − | 128.172i | − | 0.391963i | ||||||
\(328\) | − | 484.974i | − | 1.47858i | ||||||
\(329\) | −192.000 | − | 27.7128i | −0.583587 | − | 0.0842335i | ||||
\(330\) | 120.000 | 0.363636 | ||||||||
\(331\) | −646.000 | −1.95166 | −0.975831 | − | 0.218527i | \(-0.929875\pi\) | ||||
−0.975831 | + | 0.218527i | \(0.929875\pi\) | |||||||
\(332\) | 270.200i | 0.813855i | ||||||||
\(333\) | −78.0000 | −0.234234 | ||||||||
\(334\) | − | 96.9948i | − | 0.290404i | ||||||
\(335\) | 512.687i | 1.53041i | ||||||||
\(336\) | −60.0000 | − | 8.66025i | −0.178571 | − | 0.0257746i | ||||
\(337\) | 146.000 | 0.433234 | 0.216617 | − | 0.976257i | \(-0.430498\pi\) | ||||
0.216617 | + | 0.976257i | \(0.430498\pi\) | |||||||
\(338\) | 121.000 | 0.357988 | ||||||||
\(339\) | − | 308.305i | − | 0.909454i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 277.128i | − | 0.812692i | ||||||
\(342\) | − | 62.3538i | − | 0.182321i | ||||||
\(343\) | −143.000 | + | 311.769i | −0.416910 | + | 0.908948i | ||||
\(344\) | −182.000 | −0.529070 | ||||||||
\(345\) | −168.000 | −0.486957 | ||||||||
\(346\) | − | 173.205i | − | 0.500593i | ||||||
\(347\) | 106.000 | 0.305476 | 0.152738 | − | 0.988267i | \(-0.451191\pi\) | ||||
0.152738 | + | 0.988267i | \(0.451191\pi\) | |||||||
\(348\) | − | 197.454i | − | 0.567396i | ||||||
\(349\) | 630.466i | 1.80649i | 0.429121 | + | 0.903247i | \(0.358823\pi\) | ||||
−0.429121 | + | 0.903247i | \(0.641177\pi\) | |||||||
\(350\) | −23.0000 | + | 159.349i | −0.0657143 | + | 0.455282i | ||||
\(351\) | 36.0000 | 0.102564 | ||||||||
\(352\) | 330.000 | 0.937500 | ||||||||
\(353\) | 304.841i | 0.863572i | 0.901976 | + | 0.431786i | \(0.142116\pi\) | ||||
−0.901976 | + | 0.431786i | \(0.857884\pi\) | |||||||
\(354\) | −132.000 | −0.372881 | ||||||||
\(355\) | − | 429.549i | − | 1.21000i | ||||||
\(356\) | − | 124.708i | − | 0.350302i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.0000 | −0.106145 | ||||||||
\(359\) | −494.000 | −1.37604 | −0.688022 | − | 0.725690i | \(-0.741521\pi\) | ||||
−0.688022 | + | 0.725690i | \(0.741521\pi\) | |||||||
\(360\) | 145.492i | 0.404145i | ||||||||
\(361\) | −71.0000 | −0.196676 | ||||||||
\(362\) | − | 187.061i | − | 0.516744i | ||||||
\(363\) | 36.3731i | 0.100201i | ||||||||
\(364\) | 144.000 | + | 20.7846i | 0.395604 | + | 0.0571006i | ||||
\(365\) | −288.000 | −0.789041 | ||||||||
\(366\) | −60.0000 | −0.163934 | ||||||||
\(367\) | − | 554.256i | − | 1.51024i | −0.655589 | − | 0.755118i | \(-0.727580\pi\) | ||
0.655589 | − | 0.755118i | \(-0.272420\pi\) | |||||||
\(368\) | −70.0000 | −0.190217 | ||||||||
\(369\) | − | 207.846i | − | 0.563269i | ||||||
\(370\) | 180.133i | 0.486847i | ||||||||
\(371\) | 10.0000 | − | 69.2820i | 0.0269542 | − | 0.186744i | ||||
\(372\) | 144.000 | 0.387097 | ||||||||
\(373\) | 218.000 | 0.584450 | 0.292225 | − | 0.956350i | \(-0.405604\pi\) | ||||
0.292225 | + | 0.956350i | \(0.405604\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.0000 | 0.0640000 | ||||||||
\(376\) | 193.990i | 0.515930i | ||||||||
\(377\) | 263.272i | 0.698333i | ||||||||
\(378\) | 36.0000 | + | 5.19615i | 0.0952381 | + | 0.0137464i | ||||
\(379\) | −550.000 | −1.45119 | −0.725594 | − | 0.688123i | \(-0.758435\pi\) | ||||
−0.725594 | + | 0.688123i | \(0.758435\pi\) | |||||||
\(380\) | 432.000 | 1.13684 | ||||||||
\(381\) | 329.090i | 0.863752i | ||||||||
\(382\) | 82.0000 | 0.214660 | ||||||||
\(383\) | − | 55.4256i | − | 0.144714i | −0.997379 | − | 0.0723572i | \(-0.976948\pi\) | ||
0.997379 | − | 0.0723572i | \(-0.0230522\pi\) | |||||||
\(384\) | 206.114i | 0.536755i | ||||||||
\(385\) | 480.000 | + | 69.2820i | 1.24675 | + | 0.179953i | ||||
\(386\) | 50.0000 | 0.129534 | ||||||||
\(387\) | −78.0000 | −0.201550 | ||||||||
\(388\) | 166.277i | 0.428549i | ||||||||
\(389\) | 394.000 | 1.01285 | 0.506427 | − | 0.862283i | \(-0.330966\pi\) | ||||
0.506427 | + | 0.862283i | \(0.330966\pi\) | |||||||
\(390\) | − | 83.1384i | − | 0.213175i | ||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 329.000 | + | 96.9948i | 0.839286 | + | 0.247436i | ||||
\(393\) | 84.0000 | 0.213740 | ||||||||
\(394\) | −278.000 | −0.705584 | ||||||||
\(395\) | − | 318.697i | − | 0.806829i | ||||||
\(396\) | 90.0000 | 0.227273 | ||||||||
\(397\) | 103.923i | 0.261771i | 0.991397 | + | 0.130885i | \(0.0417820\pi\) | ||||
−0.991397 | + | 0.130885i | \(0.958218\pi\) | |||||||
\(398\) | − | 290.985i | − | 0.731117i | ||||||
\(399\) | 36.0000 | − | 249.415i | 0.0902256 | − | 0.625101i | ||||
\(400\) | −115.000 | −0.287500 | ||||||||
\(401\) | 178.000 | 0.443890 | 0.221945 | − | 0.975059i | \(-0.428759\pi\) | ||||
0.221945 | + | 0.975059i | \(0.428759\pi\) | |||||||
\(402\) | − | 128.172i | − | 0.318835i | ||||||
\(403\) | −192.000 | −0.476427 | ||||||||
\(404\) | − | 353.338i | − | 0.874600i | ||||||
\(405\) | 62.3538i | 0.153960i | ||||||||
\(406\) | −38.0000 | + | 263.272i | −0.0935961 | + | 0.648453i | ||||
\(407\) | 260.000 | 0.638821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 651.251i | − | 1.59230i | −0.605099 | − | 0.796150i | \(-0.706866\pi\) | ||
0.605099 | − | 0.796150i | \(-0.293134\pi\) | |||||||
\(410\) | −480.000 | −1.17073 | ||||||||
\(411\) | 356.802i | 0.868133i | ||||||||
\(412\) | − | 290.985i | − | 0.706273i | ||||||
\(413\) | −528.000 | − | 76.2102i | −1.27845 | − | 0.184528i | ||||
\(414\) | 42.0000 | 0.101449 | ||||||||
\(415\) | 624.000 | 1.50361 | ||||||||
\(416\) | − | 228.631i | − | 0.549593i | ||||||
\(417\) | 204.000 | 0.489209 | ||||||||
\(418\) | 207.846i | 0.497239i | ||||||||
\(419\) | 713.605i | 1.70311i | 0.524262 | + | 0.851557i | \(0.324341\pi\) | ||||
−0.524262 | + | 0.851557i | \(0.675659\pi\) | |||||||
\(420\) | −36.0000 | + | 249.415i | −0.0857143 | + | 0.593846i | ||||
\(421\) | 602.000 | 1.42993 | 0.714964 | − | 0.699161i | \(-0.246443\pi\) | ||||
0.714964 | + | 0.699161i | \(0.246443\pi\) | |||||||
\(422\) | 74.0000 | 0.175355 | ||||||||
\(423\) | 83.1384i | 0.196545i | ||||||||
\(424\) | −70.0000 | −0.165094 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 107.387i | 0.252083i | ||||||||
\(427\) | −240.000 | − | 34.6410i | −0.562061 | − | 0.0811265i | ||||
\(428\) | −30.0000 | −0.0700935 | ||||||||
\(429\) | −120.000 | −0.279720 | ||||||||
\(430\) | 180.133i | 0.418915i | ||||||||
\(431\) | 34.0000 | 0.0788863 | 0.0394432 | − | 0.999222i | \(-0.487442\pi\) | ||||
0.0394432 | + | 0.999222i | \(0.487442\pi\) | |||||||
\(432\) | 25.9808i | 0.0601407i | ||||||||
\(433\) | 415.692i | 0.960028i | 0.877261 | + | 0.480014i | \(0.159368\pi\) | ||||
−0.877261 | + | 0.480014i | \(0.840632\pi\) | |||||||
\(434\) | −192.000 | − | 27.7128i | −0.442396 | − | 0.0638544i | ||||
\(435\) | −456.000 | −1.04828 | ||||||||
\(436\) | −222.000 | −0.509174 | ||||||||
\(437\) | − | 290.985i | − | 0.665869i | ||||||
\(438\) | 72.0000 | 0.164384 | ||||||||
\(439\) | − | 96.9948i | − | 0.220945i | −0.993879 | − | 0.110472i | \(-0.964764\pi\) | ||
0.993879 | − | 0.110472i | \(-0.0352364\pi\) | |||||||
\(440\) | − | 484.974i | − | 1.10221i | ||||||
\(441\) | 141.000 | + | 41.5692i | 0.319728 | + | 0.0942613i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −470.000 | −1.06095 | −0.530474 | − | 0.847701i | \(-0.677986\pi\) | ||||
−0.530474 | + | 0.847701i | \(0.677986\pi\) | |||||||
\(444\) | 135.100i | 0.304279i | ||||||||
\(445\) | −288.000 | −0.647191 | ||||||||
\(446\) | − | 304.841i | − | 0.683500i | ||||||
\(447\) | − | 183.597i | − | 0.410732i | ||||||
\(448\) | 13.0000 | − | 90.0666i | 0.0290179 | − | 0.201042i | ||||
\(449\) | 514.000 | 1.14477 | 0.572383 | − | 0.819986i | \(-0.306019\pi\) | ||||
0.572383 | + | 0.819986i | \(0.306019\pi\) | |||||||
\(450\) | 69.0000 | 0.153333 | ||||||||
\(451\) | 692.820i | 1.53619i | ||||||||
\(452\) | −534.000 | −1.18142 | ||||||||
\(453\) | 79.6743i | 0.175882i | ||||||||
\(454\) | − | 6.92820i | − | 0.0152604i | ||||||
\(455\) | 48.0000 | − | 332.554i | 0.105495 | − | 0.730887i | ||||
\(456\) | −252.000 | −0.552632 | ||||||||
\(457\) | −478.000 | −1.04595 | −0.522976 | − | 0.852347i | \(-0.675178\pi\) | ||||
−0.522976 | + | 0.852347i | \(0.675178\pi\) | |||||||
\(458\) | 284.056i | 0.620210i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 290.985i | 0.632575i | ||||||||
\(461\) | − | 672.036i | − | 1.45778i | −0.684632 | − | 0.728889i | \(-0.740037\pi\) | ||
0.684632 | − | 0.728889i | \(-0.259963\pi\) | |||||||
\(462\) | −120.000 | − | 17.3205i | −0.259740 | − | 0.0374903i | ||||
\(463\) | −430.000 | −0.928726 | −0.464363 | − | 0.885645i | \(-0.653717\pi\) | ||||
−0.464363 | + | 0.885645i | \(0.653717\pi\) | |||||||
\(464\) | −190.000 | −0.409483 | ||||||||
\(465\) | − | 332.554i | − | 0.715169i | ||||||
\(466\) | 178.000 | 0.381974 | ||||||||
\(467\) | 852.169i | 1.82477i | 0.409330 | + | 0.912387i | \(0.365763\pi\) | ||||
−0.409330 | + | 0.912387i | \(0.634237\pi\) | |||||||
\(468\) | − | 62.3538i | − | 0.133235i | ||||||
\(469\) | 74.0000 | − | 512.687i | 0.157783 | − | 1.09315i | ||||
\(470\) | 192.000 | 0.408511 | ||||||||
\(471\) | 420.000 | 0.891720 | ||||||||
\(472\) | 533.472i | 1.13024i | ||||||||
\(473\) | 260.000 | 0.549683 | ||||||||
\(474\) | 79.6743i | 0.168089i | ||||||||
\(475\) | − | 478.046i | − | 1.00641i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.0000 | −0.0628931 | ||||||||
\(478\) | 34.0000 | 0.0711297 | ||||||||
\(479\) | 387.979i | 0.809978i | 0.914322 | + | 0.404989i | \(0.132725\pi\) | ||||
−0.914322 | + | 0.404989i | \(0.867275\pi\) | |||||||
\(480\) | 396.000 | 0.825000 | ||||||||
\(481\) | − | 180.133i | − | 0.374497i | ||||||
\(482\) | 193.990i | 0.402468i | ||||||||
\(483\) | 168.000 | + | 24.2487i | 0.347826 | + | 0.0502044i | ||||
\(484\) | 63.0000 | 0.130165 | ||||||||
\(485\) | 384.000 | 0.791753 | ||||||||
\(486\) | − | 15.5885i | − | 0.0320750i | ||||||
\(487\) | 818.000 | 1.67967 | 0.839836 | − | 0.542841i | \(-0.182651\pi\) | ||||
0.839836 | + | 0.542841i | \(0.182651\pi\) | |||||||
\(488\) | 242.487i | 0.496900i | ||||||||
\(489\) | − | 294.449i | − | 0.602144i | ||||||
\(490\) | 96.0000 | − | 325.626i | 0.195918 | − | 0.664542i | ||||
\(491\) | 490.000 | 0.997963 | 0.498982 | − | 0.866613i | \(-0.333707\pi\) | ||||
0.498982 | + | 0.866613i | \(0.333707\pi\) | |||||||
\(492\) | −360.000 | −0.731707 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 144.000 | 0.291498 | ||||||||
\(495\) | − | 207.846i | − | 0.419891i | ||||||
\(496\) | − | 138.564i | − | 0.279363i | ||||||
\(497\) | −62.0000 | + | 429.549i | −0.124748 | + | 0.864283i | ||||
\(498\) | −156.000 | −0.313253 | ||||||||
\(499\) | 554.000 | 1.11022 | 0.555110 | − | 0.831777i | \(-0.312676\pi\) | ||||
0.555110 | + | 0.831777i | \(0.312676\pi\) | |||||||
\(500\) | − | 41.5692i | − | 0.0831384i | ||||||
\(501\) | −168.000 | −0.335329 | ||||||||
\(502\) | − | 187.061i | − | 0.372632i | ||||||
\(503\) | − | 290.985i | − | 0.578498i | −0.957254 | − | 0.289249i | \(-0.906594\pi\) | ||
0.957254 | − | 0.289249i | \(-0.0934056\pi\) | |||||||
\(504\) | 21.0000 | − | 145.492i | 0.0416667 | − | 0.288675i | ||||
\(505\) | −816.000 | −1.61584 | ||||||||
\(506\) | −140.000 | −0.276680 | ||||||||
\(507\) | − | 209.578i | − | 0.413369i | ||||||
\(508\) | 570.000 | 1.12205 | ||||||||
\(509\) | 963.020i | 1.89198i | 0.324189 | + | 0.945992i | \(0.394909\pi\) | ||||
−0.324189 | + | 0.945992i | \(0.605091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 288.000 | + | 41.5692i | 0.563601 | + | 0.0813488i | ||||
\(512\) | 305.000 | 0.595703 | ||||||||
\(513\) | −108.000 | −0.210526 | ||||||||
\(514\) | − | 138.564i | − | 0.269580i | ||||||
\(515\) | −672.000 | −1.30485 | ||||||||
\(516\) | 135.100i | 0.261822i | ||||||||
\(517\) | − | 277.128i | − | 0.536031i | ||||||
\(518\) | 26.0000 | − | 180.133i | 0.0501931 | − | 0.347748i | ||||
\(519\) | −300.000 | −0.578035 | ||||||||
\(520\) | −336.000 | −0.646154 | ||||||||
\(521\) | 124.708i | 0.239362i | 0.992812 | + | 0.119681i | \(0.0381872\pi\) | ||||
−0.992812 | + | 0.119681i | \(0.961813\pi\) | |||||||
\(522\) | 114.000 | 0.218391 | ||||||||
\(523\) | 62.3538i | 0.119223i | 0.998222 | + | 0.0596117i | \(0.0189862\pi\) | ||||
−0.998222 | + | 0.0596117i | \(0.981014\pi\) | |||||||
\(524\) | − | 145.492i | − | 0.277657i | ||||||
\(525\) | 276.000 | + | 39.8372i | 0.525714 | + | 0.0758803i | ||||
\(526\) | −62.0000 | −0.117871 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | − | 86.6025i | − | 0.164020i | ||||||
\(529\) | −333.000 | −0.629490 | ||||||||
\(530\) | 69.2820i | 0.130721i | ||||||||
\(531\) | 228.631i | 0.430566i | ||||||||
\(532\) | −432.000 | − | 62.3538i | −0.812030 | − | 0.117206i | ||||
\(533\) | 480.000 | 0.900563 | ||||||||
\(534\) | 72.0000 | 0.134831 | ||||||||
\(535\) | 69.2820i | 0.129499i | ||||||||
\(536\) | −518.000 | −0.966418 | ||||||||
\(537\) | 65.8179i | 0.122566i | ||||||||
\(538\) | − | 228.631i | − | 0.424964i | ||||||
\(539\) | −470.000 | − | 138.564i | −0.871985 | − | 0.257076i | ||||
\(540\) | 108.000 | 0.200000 | ||||||||
\(541\) | −118.000 | −0.218115 | −0.109057 | − | 0.994035i | \(-0.534783\pi\) | ||||
−0.109057 | + | 0.994035i | \(0.534783\pi\) | |||||||
\(542\) | 332.554i | 0.613568i | ||||||||
\(543\) | −324.000 | −0.596685 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 512.687i | 0.940710i | ||||||||
\(546\) | −12.0000 | + | 83.1384i | −0.0219780 | + | 0.152268i | ||||
\(547\) | −406.000 | −0.742230 | −0.371115 | − | 0.928587i | \(-0.621024\pi\) | ||||
−0.371115 | + | 0.928587i | \(0.621024\pi\) | |||||||
\(548\) | 618.000 | 1.12774 | ||||||||
\(549\) | 103.923i | 0.189295i | ||||||||
\(550\) | −230.000 | −0.418182 | ||||||||
\(551\) | − | 789.815i | − | 1.43342i | ||||||
\(552\) | − | 169.741i | − | 0.307502i | ||||||
\(553\) | −46.0000 | + | 318.697i | −0.0831826 | + | 0.576306i | ||||
\(554\) | 26.0000 | 0.0469314 | ||||||||
\(555\) | 312.000 | 0.562162 | ||||||||
\(556\) | − | 353.338i | − | 0.635501i | ||||||
\(557\) | −998.000 | −1.79174 | −0.895871 | − | 0.444315i | \(-0.853447\pi\) | ||||
−0.895871 | + | 0.444315i | \(0.853447\pi\) | |||||||
\(558\) | 83.1384i | 0.148994i | ||||||||
\(559\) | − | 180.133i | − | 0.322242i | ||||||
\(560\) | 240.000 | + | 34.6410i | 0.428571 | + | 0.0618590i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −494.000 | −0.879004 | ||||||||
\(563\) | − | 367.195i | − | 0.652211i | −0.945333 | − | 0.326105i | \(-0.894264\pi\) | ||
0.945333 | − | 0.326105i | \(-0.105736\pi\) | |||||||
\(564\) | 144.000 | 0.255319 | ||||||||
\(565\) | 1233.22i | 2.18269i | ||||||||
\(566\) | 200.918i | 0.354979i | ||||||||
\(567\) | 9.00000 | − | 62.3538i | 0.0158730 | − | 0.109971i | ||||
\(568\) | 434.000 | 0.764085 | ||||||||
\(569\) | −62.0000 | −0.108963 | −0.0544815 | − | 0.998515i | \(-0.517351\pi\) | ||||
−0.0544815 | + | 0.998515i | \(0.517351\pi\) | |||||||
\(570\) | 249.415i | 0.437571i | ||||||||
\(571\) | 410.000 | 0.718039 | 0.359019 | − | 0.933330i | \(-0.383111\pi\) | ||||
0.359019 | + | 0.933330i | \(0.383111\pi\) | |||||||
\(572\) | 207.846i | 0.363367i | ||||||||
\(573\) | − | 142.028i | − | 0.247868i | ||||||
\(574\) | 480.000 | + | 69.2820i | 0.836237 | + | 0.120700i | ||||
\(575\) | 322.000 | 0.560000 | ||||||||
\(576\) | −39.0000 | −0.0677083 | ||||||||
\(577\) | − | 831.384i | − | 1.44087i | −0.693520 | − | 0.720437i | \(-0.743941\pi\) | ||
0.693520 | − | 0.720437i | \(-0.256059\pi\) | |||||||
\(578\) | 289.000 | 0.500000 | ||||||||
\(579\) | − | 86.6025i | − | 0.149573i | ||||||
\(580\) | 789.815i | 1.36175i | ||||||||
\(581\) | −624.000 | − | 90.0666i | −1.07401 | − | 0.155020i | ||||
\(582\) | −96.0000 | −0.164948 | ||||||||
\(583\) | 100.000 | 0.171527 | ||||||||
\(584\) | − | 290.985i | − | 0.498261i | ||||||
\(585\) | −144.000 | −0.246154 | ||||||||
\(586\) | − | 491.902i | − | 0.839424i | ||||||
\(587\) | − | 547.328i | − | 0.932416i | −0.884675 | − | 0.466208i | \(-0.845620\pi\) | ||
0.884675 | − | 0.466208i | \(-0.154380\pi\) | |||||||
\(588\) | 72.0000 | − | 244.219i | 0.122449 | − | 0.415339i | ||||
\(589\) | 576.000 | 0.977929 | ||||||||
\(590\) | 528.000 | 0.894915 | ||||||||
\(591\) | 481.510i | 0.814738i | ||||||||
\(592\) | 130.000 | 0.219595 | ||||||||
\(593\) | − | 997.661i | − | 1.68240i | −0.540727 | − | 0.841198i | \(-0.681851\pi\) | ||
0.540727 | − | 0.841198i | \(-0.318149\pi\) | |||||||
\(594\) | 51.9615i | 0.0874773i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −318.000 | −0.533557 | ||||||||
\(597\) | −504.000 | −0.844221 | ||||||||
\(598\) | 96.9948i | 0.162199i | ||||||||
\(599\) | 1186.00 | 1.97997 | 0.989983 | − | 0.141184i | \(-0.0450911\pi\) | ||||
0.989983 | + | 0.141184i | \(0.0450911\pi\) | |||||||
\(600\) | − | 278.860i | − | 0.464767i | ||||||
\(601\) | 401.836i | 0.668612i | 0.942465 | + | 0.334306i | \(0.108502\pi\) | ||||
−0.942465 | + | 0.334306i | \(0.891498\pi\) | |||||||
\(602\) | 26.0000 | − | 180.133i | 0.0431894 | − | 0.299225i | ||||
\(603\) | −222.000 | −0.368159 | ||||||||
\(604\) | 138.000 | 0.228477 | ||||||||
\(605\) | − | 145.492i | − | 0.240483i | ||||||
\(606\) | 204.000 | 0.336634 | ||||||||
\(607\) | 138.564i | 0.228277i | 0.993465 | + | 0.114138i | \(0.0364107\pi\) | ||||
−0.993465 | + | 0.114138i | \(0.963589\pi\) | |||||||
\(608\) | 685.892i | 1.12811i | ||||||||
\(609\) | 456.000 | + | 65.8179i | 0.748768 | + | 0.108075i | ||||
\(610\) | 240.000 | 0.393443 | ||||||||
\(611\) | −192.000 | −0.314239 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0000 | 0.0424144 | 0.0212072 | − | 0.999775i | \(-0.493249\pi\) | ||||
0.0212072 | + | 0.999775i | \(0.493249\pi\) | |||||||
\(614\) | 20.7846i | 0.0338512i | ||||||||
\(615\) | 831.384i | 1.35184i | ||||||||
\(616\) | −70.0000 | + | 484.974i | −0.113636 | + | 0.787296i | ||||
\(617\) | −734.000 | −1.18963 | −0.594814 | − | 0.803864i | \(-0.702774\pi\) | ||||
−0.594814 | + | 0.803864i | \(0.702774\pi\) | |||||||
\(618\) | 168.000 | 0.271845 | ||||||||
\(619\) | 838.313i | 1.35430i | 0.735844 | + | 0.677151i | \(0.236785\pi\) | ||||
−0.735844 | + | 0.677151i | \(0.763215\pi\) | |||||||
\(620\) | −576.000 | −0.929032 | ||||||||
\(621\) | − | 72.7461i | − | 0.117144i | ||||||
\(622\) | − | 13.8564i | − | 0.0222772i | ||||||
\(623\) | 288.000 | + | 41.5692i | 0.462279 | + | 0.0667243i | ||||
\(624\) | −60.0000 | −0.0961538 | ||||||||
\(625\) | −671.000 | −1.07360 | ||||||||
\(626\) | − | 263.272i | − | 0.420562i | ||||||
\(627\) | 360.000 | 0.574163 | ||||||||
\(628\) | − | 727.461i | − | 1.15838i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −144.000 | − | 20.7846i | −0.228571 | − | 0.0329914i | ||||
\(631\) | −286.000 | −0.453249 | −0.226624 | − | 0.973982i | \(-0.572769\pi\) | ||||
−0.226624 | + | 0.973982i | \(0.572769\pi\) | |||||||
\(632\) | 322.000 | 0.509494 | ||||||||
\(633\) | − | 128.172i | − | 0.202483i | ||||||
\(634\) | 250.000 | 0.394322 | ||||||||
\(635\) | − | 1316.36i | − | 2.07301i | ||||||
\(636\) | 51.9615i | 0.0817005i | ||||||||
\(637\) | −96.0000 | + | 325.626i | −0.150706 | + | 0.511186i | ||||
\(638\) | −380.000 | −0.595611 | ||||||||
\(639\) | 186.000 | 0.291080 | ||||||||
\(640\) | − | 824.456i | − | 1.28821i | ||||||
\(641\) | 658.000 | 1.02652 | 0.513261 | − | 0.858233i | \(-0.328437\pi\) | ||||
0.513261 | + | 0.858233i | \(0.328437\pi\) | |||||||
\(642\) | − | 17.3205i | − | 0.0269790i | ||||||
\(643\) | 325.626i | 0.506416i | 0.967412 | + | 0.253208i | \(0.0814857\pi\) | ||||
−0.967412 | + | 0.253208i | \(0.918514\pi\) | |||||||
\(644\) | 42.0000 | − | 290.985i | 0.0652174 | − | 0.451839i | ||||
\(645\) | 312.000 | 0.483721 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 457.261i | 0.706741i | 0.935483 | + | 0.353370i | \(0.114964\pi\) | ||||
−0.935483 | + | 0.353370i | \(0.885036\pi\) | |||||||
\(648\) | −63.0000 | −0.0972222 | ||||||||
\(649\) | − | 762.102i | − | 1.17427i | ||||||
\(650\) | 159.349i | 0.245152i | ||||||||
\(651\) | −48.0000 | + | 332.554i | −0.0737327 | + | 0.510835i | ||||
\(652\) | −510.000 | −0.782209 | ||||||||
\(653\) | −614.000 | −0.940276 | −0.470138 | − | 0.882593i | \(-0.655796\pi\) | ||||
−0.470138 | + | 0.882593i | \(0.655796\pi\) | |||||||
\(654\) | − | 128.172i | − | 0.195981i | ||||||
\(655\) | −336.000 | −0.512977 | ||||||||
\(656\) | 346.410i | 0.528064i | ||||||||
\(657\) | − | 124.708i | − | 0.189814i | ||||||
\(658\) | −192.000 | − | 27.7128i | −0.291793 | − | 0.0421167i | ||||
\(659\) | 442.000 | 0.670713 | 0.335357 | − | 0.942091i | \(-0.391143\pi\) | ||||
0.335357 | + | 0.942091i | \(0.391143\pi\) | |||||||
\(660\) | −360.000 | −0.545455 | ||||||||
\(661\) | 34.6410i | 0.0524070i | 0.999657 | + | 0.0262035i | \(0.00834179\pi\) | ||||
−0.999657 | + | 0.0262035i | \(0.991658\pi\) | |||||||
\(662\) | −646.000 | −0.975831 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 630.466i | 0.949498i | ||||||||
\(665\) | −144.000 | + | 997.661i | −0.216541 | + | 1.50024i | ||||
\(666\) | −78.0000 | −0.117117 | ||||||||
\(667\) | 532.000 | 0.797601 | ||||||||
\(668\) | 290.985i | 0.435606i | ||||||||
\(669\) | −528.000 | −0.789238 | ||||||||
\(670\) | 512.687i | 0.765205i | ||||||||
\(671\) | − | 346.410i | − | 0.516260i | ||||||
\(672\) | −396.000 | − | 57.1577i | −0.589286 | − | 0.0850561i | ||||
\(673\) | 386.000 | 0.573551 | 0.286776 | − | 0.957998i | \(-0.407417\pi\) | ||||
0.286776 | + | 0.957998i | \(0.407417\pi\) | |||||||
\(674\) | 146.000 | 0.216617 | ||||||||
\(675\) | − | 119.512i | − | 0.177054i | ||||||
\(676\) | −363.000 | −0.536982 | ||||||||
\(677\) | 782.887i | 1.15641i | 0.815893 | + | 0.578203i | \(0.196246\pi\) | ||||
−0.815893 | + | 0.578203i | \(0.803754\pi\) | |||||||
\(678\) | − | 308.305i | − | 0.454727i | ||||||
\(679\) | −384.000 | − | 55.4256i | −0.565538 | − | 0.0816283i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.0176211 | ||||||||
\(682\) | − | 277.128i | − | 0.406346i | ||||||
\(683\) | 298.000 | 0.436310 | 0.218155 | − | 0.975914i | \(-0.429996\pi\) | ||||
0.218155 | + | 0.975914i | \(0.429996\pi\) | |||||||
\(684\) | 187.061i | 0.273482i | ||||||||
\(685\) | − | 1427.21i | − | 2.08352i | ||||||
\(686\) | −143.000 | + | 311.769i | −0.208455 | + | 0.454474i | ||||
\(687\) | 492.000 | 0.716157 | ||||||||
\(688\) | 130.000 | 0.188953 | ||||||||
\(689\) | − | 69.2820i | − | 0.100554i | ||||||
\(690\) | −168.000 | −0.243478 | ||||||||
\(691\) | − | 866.025i | − | 1.25329i | −0.779304 | − | 0.626646i | \(-0.784427\pi\) | ||
0.779304 | − | 0.626646i | \(-0.215573\pi\) | |||||||
\(692\) | 519.615i | 0.750889i | ||||||||
\(693\) | −30.0000 | + | 207.846i | −0.0432900 | + | 0.299922i | ||||
\(694\) | 106.000 | 0.152738 | ||||||||
\(695\) | −816.000 | −1.17410 | ||||||||
\(696\) | − | 460.726i | − | 0.661962i | ||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 630.466i | 0.903247i | ||||||||
\(699\) | − | 308.305i | − | 0.441066i | ||||||
\(700\) | 69.0000 | − | 478.046i | 0.0985714 | − | 0.682923i | ||||
\(701\) | 154.000 | 0.219686 | 0.109843 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109843 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(702\) | 36.0000 | 0.0512821 | ||||||||
\(703\) | 540.400i | 0.768705i | ||||||||
\(704\) | 130.000 | 0.184659 | ||||||||
\(705\) | − | 332.554i | − | 0.471707i | ||||||
\(706\) | 304.841i | 0.431786i | ||||||||
\(707\) | 816.000 | + | 117.779i | 1.15417 | + | 0.166590i | ||||
\(708\) | 396.000 | 0.559322 | ||||||||
\(709\) | 890.000 | 1.25529 | 0.627645 | − | 0.778500i | \(-0.284019\pi\) | ||||
0.627645 | + | 0.778500i | \(0.284019\pi\) | |||||||
\(710\) | − | 429.549i | − | 0.604998i | ||||||
\(711\) | 138.000 | 0.194093 | ||||||||
\(712\) | − | 290.985i | − | 0.408686i | ||||||
\(713\) | 387.979i | 0.544151i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 480.000 | 0.671329 | ||||||||
\(716\) | 114.000 | 0.159218 | ||||||||
\(717\) | − | 58.8897i | − | 0.0821335i | ||||||
\(718\) | −494.000 | −0.688022 | ||||||||
\(719\) | − | 83.1384i | − | 0.115631i | −0.998327 | − | 0.0578153i | \(-0.981587\pi\) | ||
0.998327 | − | 0.0578153i | \(-0.0184135\pi\) | |||||||
\(720\) | − | 103.923i | − | 0.144338i | ||||||
\(721\) | 672.000 | + | 96.9948i | 0.932039 | + | 0.134528i | ||||
\(722\) | −71.0000 | −0.0983380 | ||||||||
\(723\) | 336.000 | 0.464730 | ||||||||
\(724\) | 561.184i | 0.775117i | ||||||||
\(725\) | 874.000 | 1.20552 | ||||||||
\(726\) | 36.3731i | 0.0501006i | ||||||||
\(727\) | 235.559i | 0.324015i | 0.986790 | + | 0.162008i | \(0.0517969\pi\) | ||||
−0.986790 | + | 0.162008i | \(0.948203\pi\) | |||||||
\(728\) | 336.000 | + | 48.4974i | 0.461538 | + | 0.0666173i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −288.000 | −0.394521 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 180.000 | 0.245902 | ||||||||
\(733\) | 76.2102i | 0.103970i | 0.998648 | + | 0.0519852i | \(0.0165549\pi\) | ||||
−0.998648 | + | 0.0519852i | \(0.983445\pi\) | |||||||
\(734\) | − | 554.256i | − | 0.755118i | ||||||
\(735\) | −564.000 | − | 166.277i | −0.767347 | − | 0.226227i | ||||
\(736\) | −462.000 | −0.627717 | ||||||||
\(737\) | 740.000 | 1.00407 | ||||||||
\(738\) | − | 207.846i | − | 0.281634i | ||||||
\(739\) | −982.000 | −1.32882 | −0.664411 | − | 0.747367i | \(-0.731318\pi\) | ||||
−0.664411 | + | 0.747367i | \(0.731318\pi\) | |||||||
\(740\) | − | 540.400i | − | 0.730270i | ||||||
\(741\) | − | 249.415i | − | 0.336593i | ||||||
\(742\) | 10.0000 | − | 69.2820i | 0.0134771 | − | 0.0933720i | ||||
\(743\) | −686.000 | −0.923284 | −0.461642 | − | 0.887066i | \(-0.652740\pi\) | ||||
−0.461642 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(744\) | 336.000 | 0.451613 | ||||||||
\(745\) | 734.390i | 0.985758i | ||||||||
\(746\) | 218.000 | 0.292225 | ||||||||
\(747\) | 270.200i | 0.361713i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.0000 | − | 69.2820i | 0.0133511 | − | 0.0924994i | ||||
\(750\) | 24.0000 | 0.0320000 | ||||||||
\(751\) | 290.000 | 0.386152 | 0.193076 | − | 0.981184i | \(-0.438154\pi\) | ||||
0.193076 | + | 0.981184i | \(0.438154\pi\) | |||||||
\(752\) | − | 138.564i | − | 0.184261i | ||||||
\(753\) | −324.000 | −0.430279 | ||||||||
\(754\) | 263.272i | 0.349167i | ||||||||
\(755\) | − | 318.697i | − | 0.422116i | ||||||
\(756\) | −108.000 | − | 15.5885i | −0.142857 | − | 0.0206197i | ||||
\(757\) | −358.000 | −0.472919 | −0.236460 | − | 0.971641i | \(-0.575987\pi\) | ||||
−0.236460 | + | 0.971641i | \(0.575987\pi\) | |||||||
\(758\) | −550.000 | −0.725594 | ||||||||
\(759\) | 242.487i | 0.319482i | ||||||||
\(760\) | 1008.00 | 1.32632 | ||||||||
\(761\) | 651.251i | 0.855783i | 0.903830 | + | 0.427892i | \(0.140744\pi\) | ||||
−0.903830 | + | 0.427892i | \(0.859256\pi\) | |||||||
\(762\) | 329.090i | 0.431876i | ||||||||
\(763\) | 74.0000 | − | 512.687i | 0.0969856 | − | 0.671936i | ||||
\(764\) | −246.000 | −0.321990 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 55.4256i | − | 0.0723572i | ||||||
\(767\) | −528.000 | −0.688396 | ||||||||
\(768\) | 296.181i | 0.385652i | ||||||||
\(769\) | − | 775.959i | − | 1.00905i | −0.863397 | − | 0.504525i | \(-0.831668\pi\) | ||
0.863397 | − | 0.504525i | \(-0.168332\pi\) | |||||||
\(770\) | 480.000 | + | 69.2820i | 0.623377 | + | 0.0899767i | ||||
\(771\) | −240.000 | −0.311284 | ||||||||
\(772\) | −150.000 | −0.194301 | ||||||||
\(773\) | 228.631i | 0.295771i | 0.989005 | + | 0.147885i | \(0.0472467\pi\) | ||||
−0.989005 | + | 0.147885i | \(0.952753\pi\) | |||||||
\(774\) | −78.0000 | −0.100775 | ||||||||
\(775\) | 637.395i | 0.822445i | ||||||||
\(776\) | 387.979i | 0.499973i | ||||||||
\(777\) | −312.000 | − | 45.0333i | −0.401544 | − | 0.0579579i | ||||
\(778\) | 394.000 | 0.506427 | ||||||||
\(779\) | −1440.00 | −1.84852 | ||||||||
\(780\) | 249.415i | 0.319763i | ||||||||
\(781\) | −620.000 | −0.793854 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 197.454i | − | 0.252176i | ||||||
\(784\) | −235.000 | − | 69.2820i | −0.299745 | − | 0.0883699i | ||||
\(785\) | −1680.00 | −2.14013 | ||||||||
\(786\) | 84.0000 | 0.106870 | ||||||||
\(787\) | 76.2102i | 0.0968364i | 0.998827 | + | 0.0484182i | \(0.0154180\pi\) | ||||
−0.998827 | + | 0.0484182i | \(0.984582\pi\) | |||||||
\(788\) | 834.000 | 1.05838 | ||||||||
\(789\) | 107.387i | 0.136105i | ||||||||
\(790\) | − | 318.697i | − | 0.403414i | ||||||
\(791\) | 178.000 | − | 1233.22i | 0.225032 | − | 1.55906i | ||||
\(792\) | 210.000 | 0.265152 | ||||||||
\(793\) | −240.000 | −0.302648 | ||||||||
\(794\) | 103.923i | 0.130885i | ||||||||
\(795\) | 120.000 | 0.150943 | ||||||||
\(796\) | 872.954i | 1.09668i | ||||||||
\(797\) | − | 866.025i | − | 1.08661i | −0.839537 | − | 0.543303i | \(-0.817173\pi\) | ||
0.839537 | − | 0.543303i | \(-0.182827\pi\) | |||||||
\(798\) | 36.0000 | − | 249.415i | 0.0451128 | − | 0.312551i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −759.000 | −0.948750 | ||||||||
\(801\) | − | 124.708i | − | 0.155690i | ||||||
\(802\) | 178.000 | 0.221945 | ||||||||
\(803\) | 415.692i | 0.517674i | ||||||||
\(804\) | 384.515i | 0.478253i | ||||||||
\(805\) | −672.000 | − | 96.9948i | −0.834783 | − | 0.120490i | ||||
\(806\) | −192.000 | −0.238213 | ||||||||
\(807\) | −396.000 | −0.490706 | ||||||||
\(808\) | − | 824.456i | − | 1.02037i | ||||||
\(809\) | 802.000 | 0.991347 | 0.495674 | − | 0.868509i | \(-0.334921\pi\) | ||||
0.495674 | + | 0.868509i | \(0.334921\pi\) | |||||||
\(810\) | 62.3538i | 0.0769800i | ||||||||
\(811\) | 893.738i | 1.10202i | 0.834499 | + | 0.551010i | \(0.185757\pi\) | ||||
−0.834499 | + | 0.551010i | \(0.814243\pi\) | |||||||
\(812\) | 114.000 | − | 789.815i | 0.140394 | − | 0.972679i | ||||
\(813\) | 576.000 | 0.708487 | ||||||||
\(814\) | 260.000 | 0.319410 | ||||||||
\(815\) | 1177.79i | 1.44515i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 540.400i | 0.661444i | ||||||||
\(818\) | − | 651.251i | − | 0.796150i | ||||||
\(819\) | 144.000 | + | 20.7846i | 0.175824 | + | 0.0253780i | ||||
\(820\) | 1440.00 | 1.75610 | ||||||||
\(821\) | 1450.00 | 1.76614 | 0.883069 | − | 0.469242i | \(-0.155473\pi\) | ||||
0.883069 | + | 0.469242i | \(0.155473\pi\) | |||||||
\(822\) | 356.802i | 0.434066i | ||||||||
\(823\) | −1246.00 | −1.51397 | −0.756987 | − | 0.653430i | \(-0.773329\pi\) | ||||
−0.756987 | + | 0.653430i | \(0.773329\pi\) | |||||||
\(824\) | − | 678.964i | − | 0.823985i | ||||||
\(825\) | 398.372i | 0.482875i | ||||||||
\(826\) | −528.000 | − | 76.2102i | −0.639225 | − | 0.0922642i | ||||
\(827\) | 586.000 | 0.708585 | 0.354293 | − | 0.935135i | \(-0.384722\pi\) | ||||
0.354293 | + | 0.935135i | \(0.384722\pi\) | |||||||
\(828\) | −126.000 | −0.152174 | ||||||||
\(829\) | − | 810.600i | − | 0.977804i | −0.872339 | − | 0.488902i | \(-0.837398\pi\) | ||
0.872339 | − | 0.488902i | \(-0.162602\pi\) | |||||||
\(830\) | 624.000 | 0.751807 | ||||||||
\(831\) | − | 45.0333i | − | 0.0541917i | ||||||
\(832\) | − | 90.0666i | − | 0.108253i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 204.000 | 0.244604 | ||||||||
\(835\) | 672.000 | 0.804790 | ||||||||
\(836\) | − | 623.538i | − | 0.745859i | ||||||
\(837\) | 144.000 | 0.172043 | ||||||||
\(838\) | 713.605i | 0.851557i | ||||||||
\(839\) | 13.8564i | 0.0165154i | 0.999966 | + | 0.00825769i | \(0.00262853\pi\) | ||||
−0.999966 | + | 0.00825769i | \(0.997371\pi\) | |||||||
\(840\) | −84.0000 | + | 581.969i | −0.100000 | + | 0.692820i | ||||
\(841\) | 603.000 | 0.717004 | ||||||||
\(842\) | 602.000 | 0.714964 | ||||||||
\(843\) | 855.633i | 1.01499i | ||||||||
\(844\) | −222.000 | −0.263033 | ||||||||
\(845\) | 838.313i | 0.992086i | ||||||||
\(846\) | 83.1384i | 0.0982724i | ||||||||
\(847\) | −21.0000 | + | 145.492i | −0.0247934 | + | 0.171774i | ||||
\(848\) | 50.0000 | 0.0589623 | ||||||||
\(849\) | 348.000 | 0.409894 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −364.000 | −0.427732 | ||||||||
\(852\) | − | 322.161i | − | 0.378124i | ||||||
\(853\) | − | 242.487i | − | 0.284276i | −0.989847 | − | 0.142138i | \(-0.954602\pi\) | ||
0.989847 | − | 0.142138i | \(-0.0453976\pi\) | |||||||
\(854\) | −240.000 | − | 34.6410i | −0.281030 | − | 0.0405633i | ||||
\(855\) | 432.000 | 0.505263 | ||||||||
\(856\) | −70.0000 | −0.0817757 | ||||||||
\(857\) | − | 1399.50i | − | 1.63302i | −0.577332 | − | 0.816509i | \(-0.695906\pi\) | ||
0.577332 | − | 0.816509i | \(-0.304094\pi\) | |||||||
\(858\) | −120.000 | −0.139860 | ||||||||
\(859\) | − | 297.913i | − | 0.346813i | −0.984850 | − | 0.173407i | \(-0.944522\pi\) | ||
0.984850 | − | 0.173407i | \(-0.0554775\pi\) | |||||||
\(860\) | − | 540.400i | − | 0.628372i | ||||||
\(861\) | 120.000 | − | 831.384i | 0.139373 | − | 0.965603i | ||||
\(862\) | 34.0000 | 0.0394432 | ||||||||
\(863\) | −1070.00 | −1.23986 | −0.619930 | − | 0.784657i | \(-0.712839\pi\) | ||||
−0.619930 | + | 0.784657i | \(0.712839\pi\) | |||||||
\(864\) | 171.473i | 0.198464i | ||||||||
\(865\) | 1200.00 | 1.38728 | ||||||||
\(866\) | 415.692i | 0.480014i | ||||||||
\(867\) | − | 500.563i | − | 0.577350i | ||||||
\(868\) | 576.000 | + | 83.1384i | 0.663594 | + | 0.0957816i | ||||
\(869\) | −460.000 | −0.529344 | ||||||||
\(870\) | −456.000 | −0.524138 | ||||||||
\(871\) | − | 512.687i | − | 0.588619i | ||||||
\(872\) | −518.000 | −0.594037 | ||||||||
\(873\) | 166.277i | 0.190466i | ||||||||
\(874\) | − | 290.985i | − | 0.332934i | ||||||
\(875\) | 96.0000 | + | 13.8564i | 0.109714 | + | 0.0158359i | ||||
\(876\) | −216.000 | −0.246575 | ||||||||
\(877\) | −502.000 | −0.572406 | −0.286203 | − | 0.958169i | \(-0.592393\pi\) | ||||
−0.286203 | + | 0.958169i | \(0.592393\pi\) | |||||||
\(878\) | − | 96.9948i | − | 0.110472i | ||||||
\(879\) | −852.000 | −0.969283 | ||||||||
\(880\) | 346.410i | 0.393648i | ||||||||
\(881\) | 997.661i | 1.13242i | 0.824261 | + | 0.566210i | \(0.191591\pi\) | ||||
−0.824261 | + | 0.566210i | \(0.808409\pi\) | |||||||
\(882\) | 141.000 | + | 41.5692i | 0.159864 | + | 0.0471306i | ||||
\(883\) | −118.000 | −0.133635 | −0.0668177 | − | 0.997765i | \(-0.521285\pi\) | ||||
−0.0668177 | + | 0.997765i | \(0.521285\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 914.523i | − | 1.03336i | ||||||
\(886\) | −470.000 | −0.530474 | ||||||||
\(887\) | − | 512.687i | − | 0.578001i | −0.957329 | − | 0.289001i | \(-0.906677\pi\) | ||
0.957329 | − | 0.289001i | \(-0.0933230\pi\) | |||||||
\(888\) | 315.233i | 0.354992i | ||||||||
\(889\) | −190.000 | + | 1316.36i | −0.213723 | + | 1.48072i | ||||
\(890\) | −288.000 | −0.323596 | ||||||||
\(891\) | 90.0000 | 0.101010 | ||||||||
\(892\) | 914.523i | 1.02525i | ||||||||
\(893\) | 576.000 | 0.645017 | ||||||||
\(894\) | − | 183.597i | − | 0.205366i | ||||||
\(895\) | − | 263.272i | − | 0.294158i | ||||||
\(896\) | −119.000 | + | 824.456i | −0.132812 | + | 0.920152i | ||||
\(897\) | 168.000 | 0.187291 | ||||||||
\(898\) | 514.000 | 0.572383 | ||||||||
\(899\) | 1053.09i | 1.17140i | ||||||||
\(900\) | −207.000 | −0.230000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 692.820i | 0.768093i | ||||||||
\(903\) | −312.000 | − | 45.0333i | −0.345515 | − | 0.0498708i | ||||
\(904\) | −1246.00 | −1.37832 | ||||||||
\(905\) | 1296.00 | 1.43204 | ||||||||
\(906\) | 79.6743i | 0.0879408i | ||||||||
\(907\) | 1466.00 | 1.61632 | 0.808159 | − | 0.588965i | \(-0.200464\pi\) | ||||
0.808159 | + | 0.588965i | \(0.200464\pi\) | |||||||
\(908\) | 20.7846i | 0.0228905i | ||||||||
\(909\) | − | 353.338i | − | 0.388711i | ||||||
\(910\) | 48.0000 | − | 332.554i | 0.0527473 | − | 0.365444i | ||||
\(911\) | −542.000 | −0.594951 | −0.297475 | − | 0.954730i | \(-0.596145\pi\) | ||||
−0.297475 | + | 0.954730i | \(0.596145\pi\) | |||||||
\(912\) | 180.000 | 0.197368 | ||||||||
\(913\) | − | 900.666i | − | 0.986491i | ||||||
\(914\) | −478.000 | −0.522976 | ||||||||
\(915\) | − | 415.692i | − | 0.454308i | ||||||
\(916\) | − | 852.169i | − | 0.930315i | ||||||
\(917\) | 336.000 | + | 48.4974i | 0.366412 | + | 0.0528870i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1630.00 | −1.77367 | −0.886834 | − | 0.462089i | \(-0.847100\pi\) | ||||
−0.886834 | + | 0.462089i | \(0.847100\pi\) | |||||||
\(920\) | 678.964i | 0.738004i | ||||||||
\(921\) | 36.0000 | 0.0390879 | ||||||||
\(922\) | − | 672.036i | − | 0.728889i | ||||||
\(923\) | 429.549i | 0.465383i | ||||||||
\(924\) | 360.000 | + | 51.9615i | 0.389610 | + | 0.0562354i | ||||
\(925\) | −598.000 | −0.646486 | ||||||||
\(926\) | −430.000 | −0.464363 | ||||||||
\(927\) | − | 290.985i | − | 0.313899i | ||||||
\(928\) | −1254.00 | −1.35129 | ||||||||
\(929\) | − | 193.990i | − | 0.208816i | −0.994535 | − | 0.104408i | \(-0.966705\pi\) | ||
0.994535 | − | 0.104408i | \(-0.0332947\pi\) | |||||||
\(930\) | − | 332.554i | − | 0.357585i | ||||||
\(931\) | 288.000 | − | 976.877i | 0.309345 | − | 1.04928i | ||||
\(932\) | −534.000 | −0.572961 | ||||||||
\(933\) | −24.0000 | −0.0257235 | ||||||||
\(934\) | 852.169i | 0.912387i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 145.492i | − | 0.155440i | ||||||
\(937\) | 1205.51i | 1.28656i | 0.765631 | + | 0.643280i | \(0.222427\pi\) | ||||
−0.765631 | + | 0.643280i | \(0.777573\pi\) | |||||||
\(938\) | 74.0000 | − | 512.687i | 0.0788913 | − | 0.546575i | ||||
\(939\) | −456.000 | −0.485623 | ||||||||
\(940\) | −576.000 | −0.612766 | ||||||||
\(941\) | 879.882i | 0.935050i | 0.883980 | + | 0.467525i | \(0.154854\pi\) | ||||
−0.883980 | + | 0.467525i | \(0.845146\pi\) | |||||||
\(942\) | 420.000 | 0.445860 | ||||||||
\(943\) | − | 969.948i | − | 1.02858i | ||||||
\(944\) | − | 381.051i | − | 0.403656i | ||||||
\(945\) | −36.0000 | + | 249.415i | −0.0380952 | + | 0.263932i | ||||
\(946\) | 260.000 | 0.274841 | ||||||||
\(947\) | 1402.00 | 1.48046 | 0.740232 | − | 0.672351i | \(-0.234716\pi\) | ||||
0.740232 | + | 0.672351i | \(0.234716\pi\) | |||||||
\(948\) | − | 239.023i | − | 0.252134i | ||||||
\(949\) | 288.000 | 0.303477 | ||||||||
\(950\) | − | 478.046i | − | 0.503206i | ||||||
\(951\) | − | 433.013i | − | 0.455324i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −110.000 | −0.115425 | −0.0577125 | − | 0.998333i | \(-0.518381\pi\) | ||||
−0.0577125 | + | 0.998333i | \(0.518381\pi\) | |||||||
\(954\) | −30.0000 | −0.0314465 | ||||||||
\(955\) | 568.113i | 0.594882i | ||||||||
\(956\) | −102.000 | −0.106695 | ||||||||
\(957\) | 658.179i | 0.687753i | ||||||||
\(958\) | 387.979i | 0.404989i | ||||||||
\(959\) | −206.000 | + | 1427.21i | −0.214807 | + | 1.48823i | ||||
\(960\) | 156.000 | 0.162500 | ||||||||
\(961\) | 193.000 | 0.200832 | ||||||||
\(962\) | − | 180.133i | − | 0.187249i | ||||||
\(963\) | −30.0000 | −0.0311526 | ||||||||
\(964\) | − | 581.969i | − | 0.603702i | ||||||
\(965\) | 346.410i | 0.358974i | ||||||||
\(966\) | 168.000 | + | 24.2487i | 0.173913 | + | 0.0251022i | ||||
\(967\) | 1202.00 | 1.24302 | 0.621510 | − | 0.783406i | \(-0.286520\pi\) | ||||
0.621510 | + | 0.783406i | \(0.286520\pi\) | |||||||
\(968\) | 147.000 | 0.151860 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 384.000 | 0.395876 | ||||||||
\(971\) | − | 270.200i | − | 0.278270i | −0.990273 | − | 0.139135i | \(-0.955568\pi\) | ||
0.990273 | − | 0.139135i | \(-0.0444322\pi\) | |||||||
\(972\) | 46.7654i | 0.0481125i | ||||||||
\(973\) | 816.000 | + | 117.779i | 0.838643 | + | 0.121048i | ||||
\(974\) | 818.000 | 0.839836 | ||||||||
\(975\) | 276.000 | 0.283077 | ||||||||
\(976\) | − | 173.205i | − | 0.177464i | ||||||
\(977\) | −1310.00 | −1.34084 | −0.670420 | − | 0.741982i | \(-0.733886\pi\) | ||||
−0.670420 | + | 0.741982i | \(0.733886\pi\) | |||||||
\(978\) | − | 294.449i | − | 0.301072i | ||||||
\(979\) | 415.692i | 0.424609i | ||||||||
\(980\) | −288.000 | + | 976.877i | −0.293878 | + | 0.996813i | ||||
\(981\) | −222.000 | −0.226300 | ||||||||
\(982\) | 490.000 | 0.498982 | ||||||||
\(983\) | − | 1565.77i | − | 1.59285i | −0.604736 | − | 0.796426i | \(-0.706721\pi\) | ||
0.604736 | − | 0.796426i | \(-0.293279\pi\) | |||||||
\(984\) | −840.000 | −0.853659 | ||||||||
\(985\) | − | 1926.04i | − | 1.95537i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −48.0000 | + | 332.554i | −0.0486322 | + | 0.336934i | ||||
\(988\) | −432.000 | −0.437247 | ||||||||
\(989\) | −364.000 | −0.368049 | ||||||||
\(990\) | − | 207.846i | − | 0.209946i | ||||||
\(991\) | 818.000 | 0.825429 | 0.412714 | − | 0.910860i | \(-0.364581\pi\) | ||||
0.412714 | + | 0.910860i | \(0.364581\pi\) | |||||||
\(992\) | − | 914.523i | − | 0.921898i | ||||||
\(993\) | 1118.90i | 1.12679i | ||||||||
\(994\) | −62.0000 | + | 429.549i | −0.0623742 | + | 0.432141i | ||||
\(995\) | 2016.00 | 2.02613 | ||||||||
\(996\) | 468.000 | 0.469880 | ||||||||
\(997\) | 173.205i | 0.173726i | 0.996220 | + | 0.0868631i | \(0.0276843\pi\) | ||||
−0.996220 | + | 0.0868631i | \(0.972316\pi\) | |||||||
\(998\) | 554.000 | 0.555110 | ||||||||
\(999\) | 135.100i | 0.135235i |
(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 | 21.3.d.a.13.1 | ✓ | 2 | |
3.2 | odd | 2 | 63.3.d.b.55.1 | 2 | |||
4.3 | odd | 2 | 336.3.f.a.97.2 | 2 | |||
5.2 | odd | 4 | 525.3.e.a.349.3 | 4 | |||
5.3 | odd | 4 | 525.3.e.a.349.2 | 4 | |||
5.4 | even | 2 | 525.3.h.a.76.2 | 2 | |||
7.2 | even | 3 | 147.3.f.d.31.1 | 2 | |||
7.3 | odd | 6 | 147.3.f.d.19.1 | 2 | |||
7.4 | even | 3 | 147.3.f.b.19.1 | 2 | |||
7.5 | odd | 6 | 147.3.f.b.31.1 | 2 | |||
7.6 | odd | 2 | inner | 21.3.d.a.13.2 | yes | 2 | |
8.3 | odd | 2 | 1344.3.f.b.769.1 | 2 | |||
8.5 | even | 2 | 1344.3.f.c.769.2 | 2 | |||
12.11 | even | 2 | 1008.3.f.d.433.1 | 2 | |||
21.2 | odd | 6 | 441.3.m.d.325.1 | 2 | |||
21.5 | even | 6 | 441.3.m.f.325.1 | 2 | |||
21.11 | odd | 6 | 441.3.m.f.19.1 | 2 | |||
21.17 | even | 6 | 441.3.m.d.19.1 | 2 | |||
21.20 | even | 2 | 63.3.d.b.55.2 | 2 | |||
28.27 | even | 2 | 336.3.f.a.97.1 | 2 | |||
35.13 | even | 4 | 525.3.e.a.349.1 | 4 | |||
35.27 | even | 4 | 525.3.e.a.349.4 | 4 | |||
35.34 | odd | 2 | 525.3.h.a.76.1 | 2 | |||
56.13 | odd | 2 | 1344.3.f.c.769.1 | 2 | |||
56.27 | even | 2 | 1344.3.f.b.769.2 | 2 | |||
84.83 | odd | 2 | 1008.3.f.d.433.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.d.a.13.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.3.d.a.13.2 | yes | 2 | 7.6 | odd | 2 | inner | |
63.3.d.b.55.1 | 2 | 3.2 | odd | 2 | |||
63.3.d.b.55.2 | 2 | 21.20 | even | 2 | |||
147.3.f.b.19.1 | 2 | 7.4 | even | 3 | |||
147.3.f.b.31.1 | 2 | 7.5 | odd | 6 | |||
147.3.f.d.19.1 | 2 | 7.3 | odd | 6 | |||
147.3.f.d.31.1 | 2 | 7.2 | even | 3 | |||
336.3.f.a.97.1 | 2 | 28.27 | even | 2 | |||
336.3.f.a.97.2 | 2 | 4.3 | odd | 2 | |||
441.3.m.d.19.1 | 2 | 21.17 | even | 6 | |||
441.3.m.d.325.1 | 2 | 21.2 | odd | 6 | |||
441.3.m.f.19.1 | 2 | 21.11 | odd | 6 | |||
441.3.m.f.325.1 | 2 | 21.5 | even | 6 | |||
525.3.e.a.349.1 | 4 | 35.13 | even | 4 | |||
525.3.e.a.349.2 | 4 | 5.3 | odd | 4 | |||
525.3.e.a.349.3 | 4 | 5.2 | odd | 4 | |||
525.3.e.a.349.4 | 4 | 35.27 | even | 4 | |||
525.3.h.a.76.1 | 2 | 35.34 | odd | 2 | |||
525.3.h.a.76.2 | 2 | 5.4 | even | 2 | |||
1008.3.f.d.433.1 | 2 | 12.11 | even | 2 | |||
1008.3.f.d.433.2 | 2 | 84.83 | odd | 2 | |||
1344.3.f.b.769.1 | 2 | 8.3 | odd | 2 | |||
1344.3.f.b.769.2 | 2 | 56.27 | even | 2 | |||
1344.3.f.c.769.1 | 2 | 56.13 | odd | 2 | |||
1344.3.f.c.769.2 | 2 | 8.5 | even | 2 |