Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(104,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11, 9, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.104");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.cs (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 524.2 | ||
Character | \(\chi\) | \(=\) | 945.524 |
Dual form | 945.2.cs.a.734.2 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{13}{18}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(3\) | −0.306808 | − | 1.70466i | −0.177136 | − | 0.984186i | ||||
\(4\) | −0.347296 | − | 1.96962i | −0.173648 | − | 0.984808i | ||||
\(5\) | 0.764780 | − | 2.10122i | 0.342020 | − | 0.939693i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.459430 | + | 2.60556i | −0.173648 | + | 0.984808i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.81174 | + | 1.04601i | −0.937246 | + | 0.348669i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.890490 | − | 2.44660i | −0.268493 | − | 0.737678i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.730034 | − | 0.683411i | \(-0.239504\pi\) | |||||||
\(12\) | −3.25097 | + | 1.19632i | −0.938475 | + | 0.345347i | ||||
\(13\) | −0.146967 | + | 0.123320i | −0.0407614 | + | 0.0342029i | −0.662941 | − | 0.748672i | \(-0.730692\pi\) |
0.622179 | + | 0.782875i | \(0.286247\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.81650 | − | 0.659021i | −0.985417 | − | 0.170158i | ||||
\(16\) | −3.75877 | + | 1.36808i | −0.939693 | + | 0.342020i | ||||
\(17\) | −7.10570 | + | 4.10248i | −1.72339 | + | 0.994997i | −0.811742 | + | 0.584016i | \(0.801481\pi\) |
−0.911644 | + | 0.410982i | \(0.865186\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | −4.40419 | − | 0.776578i | −0.984808 | − | 0.173648i | ||||
\(21\) | 4.58255 | − | 0.0162334i | 0.999994 | − | 0.00354242i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.83022 | − | 3.21394i | −0.766044 | − | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.64575 | + | 4.47214i | 0.509175 | + | 0.860663i | ||||
\(28\) | 5.29150 | 1.00000 | ||||||||
\(29\) | 6.91142 | − | 8.23672i | 1.28342 | − | 1.52952i | 0.597365 | − | 0.801970i | \(-0.296214\pi\) |
0.686055 | − | 0.727550i | \(-0.259341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.89741 | + | 2.26862i | −0.678453 | + | 0.394916i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.12348 | + | 2.95804i | 0.866025 | + | 0.500000i | ||||
\(36\) | 3.03674 | + | 5.17477i | 0.506123 | + | 0.862461i | ||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.255310 | + | 0.212694i | 0.0408823 | + | 0.0340583i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(44\) | −4.50960 | + | 2.60362i | −0.679847 | + | 0.392510i | ||||
\(45\) | 0.0475262 | + | 6.70804i | 0.00708479 | + | 0.999975i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.67301 | − | 1.35296i | −1.11922 | − | 0.197349i | −0.416724 | − | 0.909033i | \(-0.636822\pi\) |
−0.702500 | + | 0.711684i | \(0.747933\pi\) | |||||||
\(48\) | 3.48533 | + | 5.98769i | 0.503065 | + | 0.864249i | ||||
\(49\) | −6.57785 | − | 2.39414i | −0.939693 | − | 0.342020i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.17342 | + | 10.8541i | 1.28454 | + | 1.51988i | ||||
\(52\) | 0.293934 | + | 0.246640i | 0.0407614 | + | 0.0342029i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.82187 | −0.785020 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(60\) | 0.0274394 | + | 7.74592i | 0.00354242 | + | 0.999994i | ||||
\(61\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.43363 | − | 7.80671i | −0.180621 | − | 0.983553i | ||||
\(64\) | 4.00000 | + | 6.92820i | 0.500000 | + | 0.866025i | ||||
\(65\) | 0.146725 | + | 0.403123i | 0.0181990 | + | 0.0500012i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(68\) | 10.5481 | + | 12.5707i | 1.27914 | + | 1.52442i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.45506 | − | 4.88153i | 1.00343 | − | 0.579331i | 0.0941692 | − | 0.995556i | \(-0.469981\pi\) |
0.909262 | + | 0.416225i | \(0.136647\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.52515 | + | 13.0339i | −0.880752 | + | 1.52551i | −0.0302463 | + | 0.999542i | \(0.509629\pi\) |
−0.850506 | + | 0.525965i | \(0.823704\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.30353 | + | 7.51529i | −0.496929 | + | 0.867791i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.78387 | − | 1.19618i | 0.773094 | − | 0.136317i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.32613 | − | 7.82555i | −1.04927 | − | 0.880443i | −0.0562544 | − | 0.998416i | \(-0.517916\pi\) |
−0.993017 | + | 0.117973i | \(0.962360\pi\) | |||||||
\(80\) | 8.94427i | 1.00000i | ||||||||
\(81\) | 6.81174 | − | 5.88220i | 0.756860 | − | 0.653577i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.9632 | − | 13.0654i | 1.20336 | − | 1.43411i | 0.332136 | − | 0.943231i | \(-0.392231\pi\) |
0.871227 | − | 0.490881i | \(-0.163325\pi\) | |||||||
\(84\) | −1.62348 | − | 9.02022i | −0.177136 | − | 0.984186i | ||||
\(85\) | 3.18590 | + | 18.0681i | 0.345559 | + | 1.95976i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.1613 | − | 9.25455i | −1.73267 | − | 0.992191i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.253796 | − | 0.439588i | −0.0266051 | − | 0.0460814i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.18582 | − | 1.15954i | 0.323471 | − | 0.117734i | −0.175180 | − | 0.984536i | \(-0.556051\pi\) |
0.498652 | + | 0.866802i | \(0.333829\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.06298 | + | 5.94774i | 0.508849 | + | 0.597770i | ||||
\(100\) | −5.00000 | + | 8.66025i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.1343 | − | 5.50842i | −1.49122 | − | 0.542761i | −0.537452 | − | 0.843294i | \(-0.680613\pi\) |
−0.953771 | + | 0.300533i | \(0.902835\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.47053 | − | 9.64134i | 0.338689 | − | 0.940898i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 7.88953 | − | 6.76427i | 0.759170 | − | 0.650892i | ||||
\(109\) | −16.4069 | −1.57149 | −0.785747 | − | 0.618548i | \(-0.787721\pi\) | ||||
−0.785747 | + | 0.618548i | \(0.787721\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.83772 | − | 10.4222i | −0.173648 | − | 0.984808i | ||||
\(113\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −18.6235 | − | 10.7523i | −1.72915 | − | 0.998323i | ||||
\(117\) | 0.284240 | − | 0.500473i | 0.0262780 | − | 0.0462687i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.42467 | − | 20.3991i | −0.680618 | − | 1.86998i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.23361 | − | 2.71332i | 0.293964 | − | 0.246666i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.68246 | + | 5.59017i | −0.866025 | + | 0.500000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(132\) | 5.82187 | + | 6.88852i | 0.506728 | + | 0.599569i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.4203 | − | 2.13910i | 0.982907 | − | 0.184104i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(140\) | 4.04684 | − | 11.1186i | 0.342020 | − | 0.939693i | ||||
\(141\) | 0.0478051 | + | 13.4950i | 0.00402592 | + | 1.13648i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.432588 | + | 0.249755i | 0.0361748 | + | 0.0208855i | ||||
\(144\) | 9.13765 | − | 7.77838i | 0.761471 | − | 0.648199i | ||||
\(145\) | −12.0214 | − | 20.8217i | −0.998323 | − | 1.72915i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.06306 | + | 11.9475i | −0.170158 | + | 0.985417i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.9747 | − | 15.4627i | −1.06293 | − | 1.26675i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
−0.100582 | − | 0.994929i | \(-0.532070\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51705 | + | 0.552160i | −0.123455 | + | 0.0449341i | −0.403009 | − | 0.915196i | \(-0.632036\pi\) |
0.279554 | + | 0.960130i | \(0.409814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.6881 | − | 18.9677i | 1.26831 | − | 1.53345i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.330257 | − | 0.576730i | 0.0264417 | − | 0.0461753i | ||||
\(157\) | 23.3401 | + | 8.49510i | 1.86274 | + | 0.677983i | 0.976788 | + | 0.214210i | \(0.0687178\pi\) |
0.885954 | + | 0.463772i | \(0.153504\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.78619 | + | 9.92431i | 0.139055 | + | 0.772606i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.18939 | − | 22.5002i | 0.633714 | − | 1.74111i | −0.0369115 | − | 0.999319i | \(-0.511752\pi\) |
0.670625 | − | 0.741796i | \(-0.266026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.25103 | + | 12.7663i | −0.173157 | + | 0.982019i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.14105 | − | 14.1249i | −0.390867 | − | 1.07390i | −0.966607 | − | 0.256265i | \(-0.917508\pi\) |
0.575740 | − | 0.817633i | \(-0.304714\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.1338 | − | 8.50328i | 0.766044 | − | 0.642788i | ||||
\(176\) | 6.69429 | + | 7.97795i | 0.504601 | + | 0.601360i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.7377 | − | 9.66354i | 1.25104 | − | 0.722287i | 0.279722 | − | 0.960081i | \(-0.409758\pi\) |
0.971316 | + | 0.237794i | \(0.0764244\pi\) | |||||||
\(180\) | 13.1957 | − | 2.42328i | 0.983553 | − | 0.180621i | ||||
\(181\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.3647 | + | 13.7316i | 1.19670 | + | 1.00415i | ||||
\(188\) | 15.5828i | 1.13649i | ||||||||
\(189\) | −12.8679 | + | 4.83902i | −0.936005 | + | 0.351987i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.80278 | + | 4.53198i | −0.275160 | + | 0.327923i | −0.885872 | − | 0.463930i | \(-0.846439\pi\) |
0.610712 | + | 0.791853i | \(0.290883\pi\) | |||||||
\(192\) | 10.5830 | − | 8.94427i | 0.763763 | − | 0.645497i | ||||
\(193\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.642171 | − | 0.373797i | 0.0459869 | − | 0.0267682i | ||||
\(196\) | −2.43107 | + | 13.7873i | −0.173648 | + | 0.984808i | ||||
\(197\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.2859 | + | 21.7923i | 1.28342 | + | 1.52952i | ||||
\(204\) | 18.1926 | − | 21.8377i | 1.27374 | − | 1.52895i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.383704 | − | 0.664595i | 0.0266051 | − | 0.0460814i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.1776 | − | 7.34403i | −1.38908 | − | 0.505584i | −0.464162 | − | 0.885750i | \(-0.653645\pi\) |
−0.924918 | + | 0.380166i | \(0.875867\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.9154 | − | 12.9153i | −0.747913 | − | 0.884943i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.5272 | + | 8.82891i | 1.65740 | + | 0.596603i | ||||
\(220\) | 2.02191 | + | 11.4668i | 0.136317 | + | 0.773094i | ||||
\(221\) | 0.538387 | − | 1.47921i | 0.0362158 | − | 0.0995022i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.02474 | + | 11.4829i | −0.135587 | + | 0.768950i | 0.838863 | + | 0.544343i | \(0.183221\pi\) |
−0.974449 | + | 0.224607i | \(0.927890\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.1314 | + | 5.03031i | 0.942092 | + | 0.335354i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2710 | − | 28.2195i | −0.681713 | − | 1.87299i | −0.418306 | − | 0.908306i | \(-0.637376\pi\) |
−0.263407 | − | 0.964685i | \(-0.584846\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.12043 | − | 11.1972i | −0.271104 | − | 0.736722i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.71103 | + | 15.0879i | −0.568245 | + | 0.984229i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.4786 | + | 18.2988i | −0.680657 | + | 1.18864i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.88969 | + | 1.21484i | −0.445657 | + | 0.0785813i | −0.391973 | − | 0.919977i | \(-0.628207\pi\) |
−0.0536837 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(240\) | 15.2470 | − | 2.74417i | 0.984186 | − | 0.177136i | ||||
\(241\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.1170 | − | 9.80700i | −0.777309 | − | 0.629119i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0612 | + | 11.9905i | −0.642788 | + | 0.766044i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.6356 | − | 14.6799i | −1.62459 | − | 0.930301i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | −14.8783 | + | 5.53495i | −0.937246 | + | 0.348669i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 29.8226 | − | 10.9743i | 1.86756 | − | 0.687238i | ||||
\(256\) | 12.2567 | − | 10.2846i | 0.766044 | − | 0.642788i | ||||
\(257\) | 4.27863 | + | 5.09908i | 0.266894 | + | 0.318072i | 0.882801 | − | 0.469747i | \(-0.155655\pi\) |
−0.615907 | + | 0.787819i | \(0.711210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.743040 | − | 0.428994i | 0.0460814 | − | 0.0266051i | ||||
\(261\) | −10.8174 | + | 30.3889i | −0.669583 | + | 1.88102i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 21.0962 | − | 25.1415i | 1.27914 | − | 1.52442i | ||||
\(273\) | −0.671482 | + | 0.567506i | −0.0406400 | + | 0.0343470i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.45245 | + | 12.2330i | −0.268493 | + | 0.737678i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7638 | + | 29.5734i | 0.642116 | + | 1.76420i | 0.644974 | + | 0.764204i | \(0.276868\pi\) |
−0.00285781 | + | 0.999996i | \(0.500910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.6555 | − | 21.5275i | 1.52506 | − | 1.27968i | 0.701036 | − | 0.713126i | \(-0.252721\pi\) |
0.824025 | − | 0.566553i | \(-0.191723\pi\) | |||||||
\(284\) | −12.5511 | − | 14.9579i | −0.744774 | − | 0.887587i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.1607 | − | 43.5796i | 1.48004 | − | 2.56350i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.95407 | − | 5.07499i | −0.173170 | − | 0.297501i | ||||
\(292\) | 28.2853 | + | 10.2950i | 1.65527 | + | 0.602470i | ||||
\(293\) | −8.19677 | + | 1.44531i | −0.478860 | + | 0.0844360i | −0.407868 | − | 0.913041i | \(-0.633728\pi\) |
−0.0709922 | + | 0.997477i | \(0.522617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.58551 | − | 10.4555i | 0.498182 | − | 0.606689i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 16.2968 | + | 5.86627i | 0.940898 | + | 0.338689i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.3299 | − | 26.5522i | −0.874926 | − | 1.51542i | −0.856842 | − | 0.515579i | \(-0.827577\pi\) |
−0.0180837 | − | 0.999836i | \(-0.505757\pi\) | |||||||
\(308\) | −4.71203 | − | 12.9462i | −0.268493 | − | 0.737678i | ||||
\(309\) | −4.74668 | + | 27.4888i | −0.270029 | + | 1.56378i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.0514 | + | 10.9378i | −1.69861 | + | 0.618242i | −0.995666 | − | 0.0930055i | \(-0.970353\pi\) |
−0.702941 | + | 0.711248i | \(0.748130\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.5000 | − | 2.95804i | −0.986013 | − | 0.166667i | ||||
\(316\) | −12.1744 | + | 21.0867i | −0.684863 | + | 1.18622i | ||||
\(317\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.3065 | − | 9.57478i | −1.47288 | − | 0.536085i | ||||
\(320\) | 17.6168 | − | 3.10631i | 0.984808 | − | 0.173648i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −13.9514 | − | 11.3736i | −0.775075 | − | 0.631869i | ||||
\(325\) | 0.959261 | 0.0532102 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.03376 | + | 27.9682i | 0.278368 | + | 1.54664i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.05042 | − | 19.3709i | 0.388702 | − | 1.06795i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.82903 | + | 33.0580i | −0.320392 | + | 1.81703i | 0.219860 | + | 0.975531i | \(0.429440\pi\) |
−0.540252 | + | 0.841503i | \(0.681671\pi\) | |||||||
\(332\) | −29.5412 | − | 17.0556i | −1.62129 | − | 0.936050i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −17.2025 | + | 6.33031i | −0.938475 | + | 0.345347i | ||||
\(337\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 34.4808 | − | 12.5500i | 1.86998 | − | 0.680618i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.26013 | − | 16.0390i | 0.500000 | − | 0.866025i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(348\) | −12.6151 | + | 35.0456i | −0.676243 | + | 1.87864i | ||||
\(349\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.940343 | − | 0.330983i | −0.0501918 | − | 0.0176666i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.5979 | + | 26.9311i | −1.20276 | + | 1.43340i | −0.330887 | + | 0.943670i | \(0.607348\pi\) |
−0.871876 | + | 0.489726i | \(0.837097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.79089 | − | 21.4992i | −0.201200 | − | 1.14106i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −32.4956 | + | 18.9152i | −1.71985 | + | 1.00110i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.8765 | + | 12.6304i | 1.15460 | + | 0.666608i | 0.950004 | − | 0.312239i | \(-0.101079\pi\) |
0.204595 | + | 0.978847i | \(0.434412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | − | 16.4545i | −0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.61739 | − | 4.67974i | −0.294836 | − | 0.245623i | ||||
\(364\) | −0.777678 | + | 0.652549i | −0.0407614 | + | 0.0342029i | ||||
\(365\) | 21.6321 | + | 25.7801i | 1.13227 | + | 1.34939i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.92780 | − | 2.52151i | 0.361628 | − | 0.131622i | −0.154815 | − | 0.987944i | \(-0.549478\pi\) |
0.516443 | + | 0.856322i | \(0.327256\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.5000 | + | 14.7902i | 0.645497 | + | 0.763763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.06285i | 0.106242i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5600 | 0.542430 | 0.271215 | − | 0.962519i | \(-0.412575\pi\) | ||||
0.271215 | + | 0.962519i | \(0.412575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.22207 | − | 8.85257i | 0.164640 | − | 0.452345i | −0.829748 | − | 0.558138i | \(-0.811516\pi\) |
0.994388 | + | 0.105793i | \(0.0337381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.67474 | − | 15.1692i | 0.136317 | − | 0.773094i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.39028 | − | 5.87214i | −0.172115 | − | 0.298113i | ||||
\(389\) | 6.46352 | + | 17.7584i | 0.327714 | + | 0.900386i | 0.988689 | + | 0.149979i | \(0.0479205\pi\) |
−0.660976 | + | 0.750407i | \(0.729857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.5756 | + | 13.6114i | −1.18622 | + | 0.684863i | ||||
\(396\) | 9.95640 | − | 12.0378i | 0.500328 | − | 0.604920i | ||||
\(397\) | −0.115521 | + | 0.200088i | −0.00579782 | + | 0.0100421i | −0.868910 | − | 0.494971i | \(-0.835179\pi\) |
0.863112 | + | 0.505013i | \(0.168512\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.7939 | + | 6.84040i | 0.939693 | + | 0.342020i | ||||
\(401\) | 29.1310 | − | 5.13658i | 1.45473 | − | 0.256509i | 0.610300 | − | 0.792170i | \(-0.291049\pi\) |
0.844433 | + | 0.535662i | \(0.179938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.15028 | − | 18.8115i | −0.355301 | − | 0.934752i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.59340 | + | 31.7217i | −0.275567 | + | 1.56282i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.0688 | − | 33.0281i | −0.936050 | − | 1.62129i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(420\) | −20.1950 | − | 3.48721i | −0.985417 | − | 0.170158i | ||||
\(421\) | 37.3547 | − | 13.5960i | 1.82055 | − | 0.662628i | 0.825372 | − | 0.564590i | \(-0.190966\pi\) |
0.995183 | − | 0.0980380i | \(-0.0312567\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.9897 | − | 4.22186i | 1.11780 | − | 0.205274i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 40.4015 | + | 7.12388i | 1.95976 | + | 0.345559i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.293026 | − | 0.814042i | 0.0141474 | − | 0.0393023i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 39.9411i | − | 1.92390i | −0.273231 | − | 0.961948i | \(-0.588092\pi\) | ||
0.273231 | − | 0.961948i | \(-0.411908\pi\) | |||||||
\(432\) | −16.0630 | − | 13.1901i | −0.772832 | − | 0.634611i | ||||
\(433\) | −40.1484 | −1.92941 | −0.964703 | − | 0.263339i | \(-0.915176\pi\) | ||||
−0.964703 | + | 0.263339i | \(0.915176\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.8056 | + | 26.8807i | −1.52496 | + | 1.28883i | ||||
\(436\) | 5.69805 | + | 32.3152i | 0.272887 | + | 1.54762i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.9995 | − | 0.148781i | 0.999975 | − | 0.00708479i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.3778 | + | 26.8615i | −1.05844 | + | 1.27051i | ||||
\(448\) | −19.8895 | + | 7.23920i | −0.939693 | + | 0.342020i | ||||
\(449\) | −24.6822 | + | 14.2503i | −1.16482 | + | 0.672511i | −0.952455 | − | 0.304679i | \(-0.901451\pi\) |
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.40669 | + | 2.41664i | 0.0660919 | + | 0.113544i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.11777 | + | 0.197093i | −0.0524018 | + | 0.00923985i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −37.1468 | − | 20.9235i | −1.73386 | − | 0.976627i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(464\) | −14.7100 | + | 40.4153i | −0.682893 | + | 1.87623i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1585 | + | 7.59708i | 0.608904 | + | 0.351551i | 0.772536 | − | 0.634970i | \(-0.218988\pi\) |
−0.163632 | + | 0.986521i | \(0.552321\pi\) | |||||||
\(468\) | −1.08445 | − | 0.386030i | −0.0501289 | − | 0.0178443i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.32034 | − | 42.3933i | 0.337303 | − | 1.95338i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −37.5998 | + | 21.7083i | −1.72339 | + | 0.994997i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.46722 | − | 5.42664i | −0.293964 | − | 0.246666i | ||||
\(485\) | − | 7.58090i | − | 0.344231i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.3672 | − | 36.7261i | 0.603254 | − | 1.65743i | −0.141380 | − | 0.989955i | \(-0.545154\pi\) |
0.744635 | − | 0.667472i | \(-0.232624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.3196 | + | 86.8816i | −0.689959 | + | 3.91295i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.3696 | − | 6.08971i | 0.735757 | − | 0.273712i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.83460 | + | 24.2729i | 0.396286 | + | 1.08879i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8433 | − | 15.8114i | 0.843542 | − | 0.707816i | −0.114816 | − | 0.993387i | \(-0.536628\pi\) |
0.958358 | + | 0.285571i | \(0.0921833\pi\) | |||||||
\(500\) | 14.3732 | + | 17.1293i | 0.642788 | + | 0.766044i | ||||
\(501\) | −40.8677 | − | 7.05690i | −1.82583 | − | 0.315279i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.39864 | − | 0.807506i | 0.0623624 | − | 0.0360049i | −0.468495 | − | 0.883466i | \(-0.655203\pi\) |
0.530857 | + | 0.847461i | \(0.321870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.4528 | − | 0.0795375i | 0.997162 | − | 0.00353239i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.5034 | − | 25.5954i | −1.34939 | − | 1.13227i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.1488 | + | 27.5876i | −1.02006 | + | 1.21566i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.52259 | + | 19.9776i | 0.154923 | + | 0.878613i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.5009 | + | 13.0974i | −0.987679 | + | 0.574911i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.9920 | − | 38.0913i | −0.961644 | − | 1.66562i | −0.718372 | − | 0.695659i | \(-0.755112\pi\) |
−0.243272 | − | 0.969958i | \(-0.578221\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.6043 | − | 14.6658i | −0.768317 | − | 0.640070i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 11.5458 | − | 13.8592i | 0.502468 | − | 0.603144i | ||||
\(529\) | 21.6129 | − | 7.86646i | 0.939693 | − | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.6083 | − | 25.5673i | −0.932468 | − | 1.10331i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.2253i | 0.785020i | ||||||||
\(540\) | −8.17944 | − | 21.7508i | −0.351987 | − | 0.936005i | ||||
\(541\) | 34.3365 | 1.47624 | 0.738121 | − | 0.674668i | \(-0.235713\pi\) | ||||
0.738121 | + | 0.674668i | \(0.235713\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.5477 | + | 34.4744i | −0.537482 | + | 1.47672i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.6746 | − | 20.7045i | 1.04927 | − | 0.880443i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −23.3048 | − | 4.10927i | −0.984808 | − | 0.173648i | ||||
\(561\) | 18.3869 | − | 32.1092i | 0.776296 | − | 1.35565i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.0436 | + | 4.06321i | −0.971173 | + | 0.171244i | −0.636658 | − | 0.771146i | \(-0.719684\pi\) |
−0.334515 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(564\) | 26.5633 | − | 4.78092i | 1.11852 | − | 0.201313i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.1969 | + | 20.4508i | 0.512221 | + | 0.858854i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.08090 | − | 10.8222i | 0.380691 | − | 0.453690i | −0.541341 | − | 0.840803i | \(-0.682083\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.11345 | − | 17.6573i | −0.130294 | − | 0.738933i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.847728 | − | 0.530431i | \(-0.177970\pi\) | |||||||
\(572\) | 0.341685 | − | 0.938771i | 0.0142866 | − | 0.0392520i | ||||
\(573\) | 8.89221 | + | 5.09201i | 0.371478 | + | 0.212722i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −18.4939 | − | 15.2963i | −0.770579 | − | 0.637344i | ||||
\(577\) | 21.8961 | + | 37.9252i | 0.911547 | + | 1.57885i | 0.811880 | + | 0.583825i | \(0.198444\pi\) |
0.0996670 | + | 0.995021i | \(0.468222\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −36.8357 | + | 30.9088i | −1.52952 | + | 1.28342i | ||||
\(581\) | 29.0058 | + | 34.5678i | 1.20336 | + | 1.43411i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.834221 | − | 0.980001i | −0.0344908 | − | 0.0405180i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.2124 | − | 6.38523i | −1.49465 | − | 0.263546i | −0.634232 | − | 0.773142i | \(-0.718684\pi\) |
−0.860414 | + | 0.509596i | \(0.829795\pi\) | |||||||
\(588\) | 24.2486 | − | 0.0858990i | 0.999994 | − | 0.00354242i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.8642i | 1.71916i | 0.511003 | + | 0.859579i | \(0.329274\pi\) | ||||
−0.511003 | + | 0.859579i | \(0.670726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −48.5412 | −1.98999 | ||||||||
\(596\) | −25.9494 | + | 30.9253i | −1.06293 | + | 1.26675i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.3241 | + | 44.8502i | −0.666987 | + | 1.83253i | −0.124975 | + | 0.992160i | \(0.539885\pi\) |
−0.542012 | + | 0.840371i | \(0.682337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.61441 | + | 2.79624i | 0.0656893 | + | 0.113777i | ||||
\(605\) | −3.22827 | − | 8.86961i | −0.131248 | − | 0.360601i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.5784 | − | 25.6584i | 1.24114 | − | 1.04144i | 0.243706 | − | 0.969849i | \(-0.421637\pi\) |
0.997434 | − | 0.0715913i | \(-0.0228077\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.5382 | − | 37.8573i | 1.27799 | − | 1.53406i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.29453 | − | 0.747397i | 0.0523710 | − | 0.0302364i | ||||
\(612\) | −42.8075 | − | 24.3122i | −1.73039 | − | 0.982763i | ||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.25063 | − | 0.450182i | −0.0500654 | − | 0.0180217i | ||||
\(625\) | 4.34120 | + | 24.6202i | 0.173648 | + | 0.984808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.62615 | − | 48.9213i | 0.344221 | − | 1.95217i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.1179 | + | 43.5055i | 0.999928 | + | 1.73193i | 0.510357 | + | 0.859962i | \(0.329513\pi\) |
0.489570 | + | 0.871964i | \(0.337154\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.32845 | + | 36.6491i | −0.251533 | + | 1.45667i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.26197 | − | 0.459321i | 0.0500012 | − | 0.0181990i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.6673 | + | 22.5696i | −0.738467 | + | 0.892841i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.6564 | + | 6.81617i | 1.52684 | + | 0.269223i | 0.873116 | − | 0.487513i | \(-0.162096\pi\) |
0.653722 | + | 0.756735i | \(0.273207\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.2329 | + | 15.3715i | 1.66550 | + | 0.606194i | 0.991213 | − | 0.132273i | \(-0.0422275\pi\) |
0.674290 | + | 0.738467i | \(0.264450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 50.1875i | − | 1.97307i | −0.163543 | − | 0.986536i | \(-0.552292\pi\) | ||
0.163543 | − | 0.986536i | \(-0.447708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.52515 | − | 44.5194i | 0.293584 | − | 1.73687i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.7622 | − | 35.0638i | −0.497144 | − | 1.36589i | −0.894023 | − | 0.448022i | \(-0.852129\pi\) |
0.396878 | − | 0.917871i | \(-0.370093\pi\) | |||||||
\(660\) | 18.9267 | − | 6.96479i | 0.736722 | − | 0.271104i | ||||
\(661\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.68673 | − | 0.463935i | −0.104344 | − | 0.0180177i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −47.1608 | − | 8.31572i | −1.82471 | − | 0.321745i | ||||
\(669\) | 20.1956 | − | 0.0715417i | 0.780808 | − | 0.00276596i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.23935 | − | 25.6326i | 0.163173 | − | 0.986598i | ||||
\(676\) | 25.9264 | 0.997169 | ||||||||
\(677\) | 29.3197 | − | 34.9418i | 1.12685 | − | 1.34292i | 0.194690 | − | 0.980865i | \(-0.437630\pi\) |
0.932156 | − | 0.362058i | \(-0.117926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.55760 | + | 8.83357i | 0.0597751 | + | 0.339001i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −44.9534 | + | 26.1666i | −1.72262 | + | 1.00271i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(692\) | −26.0352 | + | 15.0314i | −0.989709 | + | 0.571409i | ||||
\(693\) | −17.8233 | + | 10.4593i | −0.677049 | + | 0.397317i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −20.2676 | − | 17.0066i | −0.766044 | − | 0.642788i | ||||
\(701\) | 52.9359i | 1.99936i | 0.0253058 | + | 0.999680i | \(0.491944\pi\) | ||||
−0.0253058 | + | 0.999680i | \(0.508056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 13.3886 | − | 15.9559i | 0.504601 | − | 0.601360i | ||||
\(705\) | 28.3924 | + | 10.2202i | 1.06932 | + | 0.384917i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.92032 | + | 44.9183i | −0.297454 | + | 1.68694i | 0.359605 | + | 0.933105i | \(0.382911\pi\) |
−0.657059 | + | 0.753839i | \(0.728200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.4082 | + | 12.2482i | 1.29041 | + | 0.459343i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.855623 | − | 0.717953i | 0.0319985 | − | 0.0268499i | ||||
\(716\) | −24.8464 | − | 29.6108i | −0.928554 | − | 1.10661i | ||||
\(717\) | 4.18470 | + | 11.3719i | 0.156280 | + | 0.424690i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | −9.35577 | − | 25.1489i | −0.348669 | − | 0.937246i | ||||
\(721\) | 21.3056 | − | 36.9024i | 0.793463 | − | 1.37432i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −52.9446 | + | 9.33556i | −1.96631 | + | 0.346714i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.7818 | + | 33.3809i | 1.47543 | + | 1.23803i | 0.910909 | + | 0.412608i | \(0.135382\pi\) |
0.564517 | + | 0.825421i | \(0.309062\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | + | 23.6643i | −0.481481 | + | 0.876456i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.33817 | − | 7.58914i | −0.0494264 | − | 0.280311i | 0.950070 | − | 0.312036i | \(-0.101011\pi\) |
−0.999497 | + | 0.0317250i | \(0.989900\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23.5266 | + | 13.4722i | 0.867791 | + | 0.496929i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.8056 | + | 44.6967i | 0.949276 | + | 1.64419i | 0.746955 | + | 0.664875i | \(0.231515\pi\) |
0.202321 | + | 0.979319i | \(0.435152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −42.4132 | + | 15.4371i | −1.55390 | + | 0.565573i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.1590 | + | 48.2040i | −0.627816 | + | 1.76369i | ||||
\(748\) | 21.3626 | − | 37.0011i | 0.781093 | − | 1.35289i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.2224 | + | 13.5479i | 1.35827 | + | 0.494368i | 0.915518 | − | 0.402278i | \(-0.131781\pi\) |
0.442748 | + | 0.896646i | \(0.354004\pi\) | |||||||
\(752\) | 30.6921 | − | 5.41184i | 1.11922 | − | 0.197349i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.60992i | 0.131379i | ||||||||
\(756\) | 14.0000 | + | 23.6643i | 0.509175 | + | 0.860663i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.53781 | − | 42.7490i | 0.272887 | − | 1.54762i | ||||
\(764\) | 10.2470 | + | 5.91608i | 0.370722 | + | 0.214036i | ||||
\(765\) | −27.8573 | − | 47.4703i | −1.00718 | − | 1.71629i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −21.2922 | − | 17.7381i | −0.768317 | − | 0.640070i | ||||
\(769\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.37948 | − | 8.85805i | 0.265765 | − | 0.319015i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.2767 | − | 10.5521i | 0.657367 | − | 0.379531i | −0.133906 | − | 0.990994i | \(-0.542752\pi\) |
0.791273 | + | 0.611463i | \(0.209419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.959261 | − | 1.13501i | −0.0343470 | − | 0.0406400i | ||||
\(781\) | −19.4723 | − | 16.3392i | −0.696773 | − | 0.584662i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 55.1216 | + | 9.11653i | 1.96989 | + | 0.325798i | ||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 35.7001 | − | 42.5457i | 1.27419 | − | 1.51852i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.37961 | + | 24.8380i | 0.156116 | + | 0.885378i | 0.957758 | + | 0.287574i | \(0.0928488\pi\) |
−0.801642 | + | 0.597804i | \(0.796040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.2467 | − | 28.8961i | −0.858863 | − | 1.02355i | −0.999439 | − | 0.0334835i | \(-0.989340\pi\) |
0.140576 | − | 0.990070i | \(-0.455105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.0726 | − | 21.8647i | 2.12522 | − | 0.773516i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.5899 | + | 6.80444i | 1.36181 | + | 0.240124i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.5987i | 1.60317i | 0.597884 | + | 0.801583i | \(0.296008\pi\) | ||||
−0.597884 | + | 0.801583i | \(0.703992\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 36.5718 | − | 43.5846i | 1.28342 | − | 1.52952i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −49.3301 | − | 28.2482i | −1.72690 | − | 0.988886i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.17342 | + | 0.970534i | 0.0410027 | + | 0.0339132i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.9812 | + | 30.1706i | 0.383247 | + | 1.05296i | 0.969981 | + | 0.243182i | \(0.0781913\pi\) |
−0.586734 | + | 0.809780i | \(0.699586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22.2192 | + | 3.83673i | 0.773572 | + | 0.133578i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.44226 | − | 0.524938i | −0.0500012 | − | 0.0181990i | ||||
\(833\) | 56.5621 | − | 9.97343i | 1.95976 | − | 0.345559i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.0146 | − | 34.4154i | −1.41937 | − | 1.19099i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0399 | − | 85.2955i | −0.518617 | − | 2.94122i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47.1102 | − | 27.4220i | 1.62256 | − | 0.944465i | ||||
\(844\) | −7.45733 | + | 42.2926i | −0.256692 | + | 1.45577i | ||||
\(845\) | 25.1031 | + | 14.4933i | 0.863573 | + | 0.498584i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.58409 | + | 9.67193i | 0.191872 | + | 0.332332i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44.5684 | − | 37.1291i | −1.52959 | − | 1.27427i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −21.6473 | + | 25.9846i | −0.741625 | + | 0.890219i | ||||
\(853\) | 52.6443 | − | 19.1609i | 1.80251 | − | 0.656058i | 0.804430 | − | 0.594048i | \(-0.202471\pi\) |
0.998075 | − | 0.0620108i | \(-0.0197513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.2042 | − | 6.91277i | −1.33919 | − | 0.236136i | −0.542263 | − | 0.840209i | \(-0.682432\pi\) |
−0.796929 | + | 0.604073i | \(0.793543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.6113 | −1.14282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −82.0079 | − | 29.5199i | −2.78513 | − | 1.00255i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.8412 | + | 29.7859i | −0.367761 | + | 1.01042i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.74481 | + | 6.59273i | −0.262122 | + | 0.223130i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1171 | − | 27.7965i | −0.342020 | − | 0.939693i | ||||
\(876\) | 8.87134 | − | 51.3755i | 0.299735 | − | 1.73582i | ||||
\(877\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.97860 | + | 13.5293i | 0.167924 | + | 0.456331i | ||||
\(880\) | 21.8831 | − | 7.96478i | 0.737678 | − | 0.268493i | ||||
\(881\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(884\) | −3.10045 | − | 0.546693i | −0.104279 | − | 0.0183873i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.9998 | − | 4.05549i | 0.772259 | − | 0.136170i | 0.226385 | − | 0.974038i | \(-0.427309\pi\) |
0.545873 | + | 0.837868i | \(0.316198\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.4572 | − | 11.4276i | −0.685341 | − | 0.382838i | ||||
\(892\) | 23.3200 | 0.780813 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.50449 | − | 42.5601i | −0.250848 | − | 1.42263i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | − | 29.5804i | 0.166667 | − | 0.986013i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(908\) | −52.0144 | + | 30.0305i | −1.72616 | + | 0.996598i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.7903 | − | 10.3663i | −1.94781 | − | 0.343451i | −0.999673 | − | 0.0255863i | \(-0.991855\pi\) |
−0.948136 | − | 0.317865i | \(-0.897034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.7283 | − | 15.1879i | −1.38101 | − | 0.502645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −60.6113 | −1.99938 | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) | ||||
−0.999691 | + | 0.0248659i | \(0.992084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −40.5592 | + | 34.2788i | −1.33647 | + | 1.12952i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.640626 | + | 1.76010i | −0.0210864 | + | 0.0579345i | ||||
\(924\) | −20.6232 | + | 12.0044i | −0.678453 | + | 0.394916i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 48.3154 | − | 0.342313i | 1.58689 | − | 0.0112430i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.3684 | − | 23.8841i | 1.35289 | − | 0.781093i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.1518 | − | 36.6360i | 0.690999 | − | 1.19685i | −0.280512 | − | 0.959851i | \(-0.590504\pi\) |
0.971511 | − | 0.236995i | \(-0.0761625\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.8653 | + | 47.8717i | 0.909350 | + | 1.56223i | ||||
\(940\) | 32.7428 | + | 11.9174i | 1.06795 | + | 0.388702i | ||||
\(941\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.326685 | + | 30.7391i | 0.0106271 | + | 0.999944i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(948\) | 39.6808 | + | 14.2837i | 1.28877 | + | 0.463911i | ||||
\(949\) | −0.501397 | − | 2.84357i | −0.0162760 | − | 0.0923060i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.61438 | + | 11.4564i | 0.214036 | + | 0.370722i | ||||
\(956\) | 4.78553 | + | 13.1481i | 0.154775 | + | 0.425241i | ||||
\(957\) | −8.25071 | + | 47.7813i | −0.266708 | + | 1.54455i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.7002 | − | 29.0776i | −0.345347 | − | 0.938475i | ||||
\(961\) | −29.1305 | + | 10.6026i | −0.939693 | + | 0.342020i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −15.1078 | + | 27.2719i | −0.484583 | + | 0.874745i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.294309 | − | 1.63521i | −0.00942543 | − | 0.0523688i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 27.1109 | + | 15.6525i | 0.866025 | + | 0.500000i | ||||
\(981\) | 46.1318 | − | 17.1617i | 1.47288 | − | 0.547931i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.59871 | − | 12.6348i | −0.146676 | − | 0.402989i | 0.844498 | − | 0.535559i | \(-0.179899\pi\) |
−0.991174 | + | 0.132570i | \(0.957677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.1839 | − | 6.07544i | −1.11992 | − | 0.193383i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.50881 | − | 14.7377i | 0.270291 | − | 0.468158i | −0.698645 | − | 0.715468i | \(-0.746213\pi\) |
0.968936 | + | 0.247310i | \(0.0795467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 58.1412 | − | 0.205961i | 1.84505 | − | 0.00653599i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −20.0106 | + | 55.5906i | −0.634060 | + | 1.76146i | ||||
\(997\) | 14.1873 | + | 11.9046i | 0.449318 | + | 0.377022i | 0.839183 | − | 0.543850i | \(-0.183034\pi\) |
−0.389865 | + | 0.920872i | \(0.627478\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.cs.a.524.2 | ✓ | 24 | |
5.4 | even | 2 | inner | 945.2.cs.a.524.3 | yes | 24 | |
7.6 | odd | 2 | inner | 945.2.cs.a.524.3 | yes | 24 | |
27.5 | odd | 18 | inner | 945.2.cs.a.734.2 | yes | 24 | |
35.34 | odd | 2 | CM | 945.2.cs.a.524.2 | ✓ | 24 | |
135.59 | odd | 18 | inner | 945.2.cs.a.734.3 | yes | 24 | |
189.167 | even | 18 | inner | 945.2.cs.a.734.3 | yes | 24 | |
945.734 | even | 18 | inner | 945.2.cs.a.734.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.cs.a.524.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
945.2.cs.a.524.2 | ✓ | 24 | 35.34 | odd | 2 | CM | |
945.2.cs.a.524.3 | yes | 24 | 5.4 | even | 2 | inner | |
945.2.cs.a.524.3 | yes | 24 | 7.6 | odd | 2 | inner | |
945.2.cs.a.734.2 | yes | 24 | 27.5 | odd | 18 | inner | |
945.2.cs.a.734.2 | yes | 24 | 945.734 | even | 18 | inner | |
945.2.cs.a.734.3 | yes | 24 | 135.59 | odd | 18 | inner | |
945.2.cs.a.734.3 | yes | 24 | 189.167 | even | 18 | inner |