Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(401,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.6 | ||
Character | \(\chi\) | \(=\) | 4020.401 |
Dual form | 4020.2.f.b.401.5 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.65640 | + | 0.506295i | −0.956324 | + | 0.292310i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.66467i | 1.76308i | 0.472108 | + | 0.881540i | \(0.343493\pi\) | ||||
−0.472108 | + | 0.881540i | \(0.656507\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.48733 | − | 1.67726i | 0.829110 | − | 0.559085i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.85459 | 0.559179 | 0.279590 | − | 0.960120i | \(-0.409802\pi\) | ||||
0.279590 | + | 0.960120i | \(0.409802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.81559i | − | 1.61295i | −0.591266 | − | 0.806477i | \(-0.701372\pi\) | ||
0.591266 | − | 0.806477i | \(-0.298628\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.65640 | + | 0.506295i | −0.427681 | + | 0.130725i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.48476i | − | 0.602642i | −0.953523 | − | 0.301321i | \(-0.902572\pi\) | ||
0.953523 | − | 0.301321i | \(-0.0974276\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.91357 | −1.12725 | −0.563625 | − | 0.826031i | \(-0.690594\pi\) | ||||
−0.563625 | + | 0.826031i | \(0.690594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.36170 | − | 7.72657i | −0.515366 | − | 1.68608i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.23397i | − | 0.882845i | −0.897299 | − | 0.441422i | \(-0.854474\pi\) | ||
0.897299 | − | 0.441422i | \(-0.145526\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.27083 | + | 4.03753i | −0.629472 | + | 0.777024i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.15242i | 0.399695i | 0.979827 | + | 0.199847i | \(0.0640446\pi\) | ||||
−0.979827 | + | 0.199847i | \(0.935955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.26861i | 1.12588i | 0.826499 | + | 0.562938i | \(0.190329\pi\) | ||||
−0.826499 | + | 0.562938i | \(0.809671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.07194 | + | 0.938969i | −0.534756 | + | 0.163453i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.66467i | 0.788474i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.13976 | −1.00937 | −0.504685 | − | 0.863303i | \(-0.668392\pi\) | ||||
−0.504685 | + | 0.863303i | \(0.668392\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.94440 | + | 9.63295i | 0.471482 | + | 1.54251i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.27504 | −0.979996 | −0.489998 | − | 0.871724i | \(-0.663002\pi\) | ||||
−0.489998 | + | 0.871724i | \(0.663002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.35463i | 0.664075i | 0.943266 | + | 0.332037i | \(0.107736\pi\) | ||||
−0.943266 | + | 0.332037i | \(0.892264\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.48733 | − | 1.67726i | 0.370789 | − | 0.250031i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.64731i | 0.386151i | 0.981184 | + | 0.193075i | \(0.0618462\pi\) | ||||
−0.981184 | + | 0.193075i | \(0.938154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.7592 | −2.10845 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.25802 | + | 4.11575i | 0.176158 | + | 0.576321i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.24742 | 0.308707 | 0.154353 | − | 0.988016i | \(-0.450671\pi\) | ||||
0.154353 | + | 0.988016i | \(0.450671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.85459 | 0.250072 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.13884 | − | 2.48772i | 1.07802 | − | 0.329506i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.02689i | 1.04501i | 0.852635 | + | 0.522506i | \(0.175003\pi\) | ||||
−0.852635 | + | 0.522506i | \(0.824997\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.752813i | 0.0963879i | 0.998838 | + | 0.0481939i | \(0.0153466\pi\) | ||||
−0.998838 | + | 0.0481939i | \(0.984653\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.82385 | + | 11.6026i | 0.985713 | + | 1.46179i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.81559i | − | 0.721335i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.18218 | + | 0.228007i | −0.999612 | + | 0.0278555i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.14364 | + | 7.01316i | 0.258064 | + | 0.844285i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.41023i | − | 0.879433i | −0.898137 | − | 0.439716i | \(-0.855079\pi\) | ||
0.898137 | − | 0.439716i | \(-0.144921\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.4070 | −1.33508 | −0.667541 | − | 0.744573i | \(-0.732653\pi\) | ||||
−0.667541 | + | 0.744573i | \(0.732653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.65640 | + | 0.506295i | −0.191265 | + | 0.0584619i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.65104i | 0.985878i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.19579i | 0.809590i | 0.914407 | + | 0.404795i | \(0.132657\pi\) | ||||
−0.914407 | + | 0.404795i | \(0.867343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.37362 | − | 8.34378i | 0.374847 | − | 0.927087i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.4884i | − | 1.37078i | −0.728174 | − | 0.685392i | \(-0.759631\pi\) | ||
0.728174 | − | 0.685392i | \(-0.240369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.48476i | − | 0.269510i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.08976 | − | 3.56527i | −0.116835 | − | 0.382237i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.65585i | 0.917518i | 0.888561 | + | 0.458759i | \(0.151706\pi\) | ||||
−0.888561 | + | 0.458759i | \(0.848294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.1278 | 2.84377 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.17377 | − | 10.3833i | −0.329104 | − | 1.07670i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.91357 | −0.504121 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0915269i | 0.00929315i | 0.999989 | + | 0.00464657i | \(0.00147906\pi\) | ||||
−0.999989 | + | 0.00464657i | \(0.998521\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.61297 | − | 3.11062i | 0.463621 | − | 0.312629i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9663 | 1.48920 | 0.744601 | − | 0.667510i | \(-0.232640\pi\) | ||||
0.744601 | + | 0.667510i | \(0.232640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.38243 | −0.333281 | −0.166640 | − | 0.986018i | \(-0.553292\pi\) | ||||
−0.166640 | + | 0.986018i | \(0.553292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.36170 | − | 7.72657i | −0.230479 | − | 0.754036i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.57713i | − | 0.925856i | −0.886396 | − | 0.462928i | \(-0.846799\pi\) | ||
0.886396 | − | 0.462928i | \(-0.153201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.60653i | − | 0.153878i | −0.997036 | − | 0.0769389i | \(-0.975485\pi\) | ||
0.997036 | − | 0.0769389i | \(-0.0245146\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.1699 | − | 3.10853i | 0.965285 | − | 0.295049i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9965 | −1.12853 | −0.564267 | − | 0.825592i | \(-0.690841\pi\) | ||||
−0.564267 | + | 0.825592i | \(0.690841\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.23397i | − | 0.394820i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.75423 | − | 14.4653i | −0.901779 | − | 1.33732i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.5906 | 1.06251 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.56051 | −0.687319 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3940 | − | 3.17702i | 0.937193 | − | 0.286462i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.0413 | −1.60090 | −0.800452 | − | 0.599397i | \(-0.795407\pi\) | ||||
−0.800452 | + | 0.599397i | \(0.795407\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.20473 | − | 7.21301i | −0.194115 | − | 0.635070i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2675i | 1.33393i | 0.745091 | + | 0.666963i | \(0.232406\pi\) | ||||
−0.745091 | + | 0.666963i | \(0.767594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 22.9202i | − | 1.98743i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.27083 | + | 4.03753i | −0.281508 | + | 0.347495i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.32666 | −0.198780 | −0.0993901 | − | 0.995049i | \(-0.531689\pi\) | ||||
−0.0993901 | + | 0.995049i | \(0.531689\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.57809i | − | 0.303490i | −0.988420 | − | 0.151745i | \(-0.951511\pi\) | ||
0.988420 | − | 0.151745i | \(-0.0484892\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.34032 | − | 4.38502i | −0.112876 | − | 0.369285i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 10.7855i | − | 0.901930i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.15242i | 0.178749i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.4471 | − | 7.47250i | 2.01636 | − | 0.616322i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9654i | 0.898318i | 0.893452 | + | 0.449159i | \(0.148276\pi\) | ||||
−0.893452 | + | 0.449159i | \(0.851724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.63035 | −0.132676 | −0.0663379 | − | 0.997797i | \(-0.521132\pi\) | ||||
−0.0663379 | + | 0.997797i | \(0.521132\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.16757 | − | 6.18041i | −0.336928 | − | 0.499656i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.26861i | 0.503507i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6770 | 0.931925 | 0.465963 | − | 0.884804i | \(-0.345708\pi\) | ||||
0.465963 | + | 0.884804i | \(0.345708\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.72263 | + | 1.13786i | −0.295224 | + | 0.0902380i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.7501 | 1.55653 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.29655 | −0.101554 | −0.0507768 | − | 0.998710i | \(-0.516170\pi\) | ||||
−0.0507768 | + | 0.998710i | \(0.516170\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.07194 | + | 0.938969i | −0.239150 | + | 0.0730986i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.36731i | 0.647482i | 0.946146 | + | 0.323741i | \(0.104941\pi\) | ||||
−0.946146 | + | 0.323741i | \(0.895059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.8211 | −1.60162 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.2217 | + | 8.24131i | −0.934614 | + | 0.630229i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4609i | 1.09944i | 0.835347 | + | 0.549722i | \(0.185267\pi\) | ||||
−0.835347 | + | 0.549722i | \(0.814733\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.66467i | 0.352616i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.06398 | − | 13.2958i | −0.305467 | − | 0.999370i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.3463 | −1.29652 | −0.648262 | − | 0.761417i | \(-0.724504\pi\) | ||||
−0.648262 | + | 0.761417i | \(0.724504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0961398 | −0.00714602 | −0.00357301 | − | 0.999994i | \(-0.501137\pi\) | ||||
−0.00357301 | + | 0.999994i | \(0.501137\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.381146 | − | 1.24696i | −0.0281751 | − | 0.0921780i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.13976 | −0.451404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.60820i | − | 0.336985i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.8338 | − | 15.2574i | −1.36996 | − | 1.10981i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.4064 | −1.98306 | −0.991531 | − | 0.129874i | \(-0.958543\pi\) | ||||
−0.991531 | + | 0.129874i | \(0.958543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.74008 | 0.701106 | 0.350553 | − | 0.936543i | \(-0.385994\pi\) | ||||
0.350553 | + | 0.936543i | \(0.385994\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.94440 | + | 9.63295i | 0.210853 | + | 0.689830i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.56079 | −0.324943 | −0.162471 | − | 0.986713i | \(-0.551947\pi\) | ||||
−0.162471 | + | 0.986713i | \(0.551947\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.49985 | −0.531651 | −0.265825 | − | 0.964021i | \(-0.585644\pi\) | ||||
−0.265825 | + | 0.964021i | \(0.585644\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.4375 | − | 4.52027i | 0.947810 | − | 0.318835i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0403 | −0.704694 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.27504 | −0.438267 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.10146 | − | 10.5313i | −0.493586 | − | 0.731975i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.11264 | −0.630334 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.7738 | −1.22360 | −0.611799 | − | 0.791013i | \(-0.709554\pi\) | ||||
−0.611799 | + | 0.791013i | \(0.709554\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.75177 | + | 12.2743i | 0.257067 | + | 0.841022i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.35463i | 0.296983i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.2410 | −1.98501 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.8945 | − | 5.77529i | 1.27677 | − | 0.390258i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.4503 | −0.972034 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.8007 | −1.39292 | −0.696460 | − | 0.717596i | \(-0.745243\pi\) | ||||
−0.696460 | + | 0.717596i | \(0.745243\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.48733 | − | 1.67726i | 0.165822 | − | 0.111817i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 28.9431i | − | 1.92102i | −0.278247 | − | 0.960510i | \(-0.589753\pi\) | ||
0.278247 | − | 0.960510i | \(-0.410247\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.77352i | 0.117198i | 0.998282 | + | 0.0585988i | \(0.0186633\pi\) | ||||
−0.998282 | + | 0.0585988i | \(0.981337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.37998 | − | 14.3296i | −0.288182 | − | 0.942818i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.1983 | −0.930160 | −0.465080 | − | 0.885269i | \(-0.653974\pi\) | ||||
−0.465080 | + | 0.885269i | \(0.653974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.64731i | 0.172692i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.64320 | − | 11.9191i | −0.236651 | − | 0.774230i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.7153 | 0.757799 | 0.378900 | − | 0.925438i | \(-0.376303\pi\) | ||||
0.378900 | + | 0.925438i | \(0.376303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.4018 | 1.76510 | 0.882551 | − | 0.470216i | \(-0.155824\pi\) | ||||
0.882551 | + | 0.470216i | \(0.155824\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.36366 | + | 15.5287i | −0.0874787 | + | 0.996166i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.7592 | −0.942929 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.5753i | 1.81820i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.32283 | + | 20.6859i | 0.400693 | + | 1.31091i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.0033 | 1.38883 | 0.694417 | − | 0.719573i | \(-0.255662\pi\) | ||||
0.694417 | + | 0.719573i | \(0.255662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.85227i | − | 0.493668i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.25802 | + | 4.11575i | 0.0787803 | + | 0.257738i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.73411i | − | 0.170549i | −0.996357 | − | 0.0852746i | \(-0.972823\pi\) | ||
0.996357 | − | 0.0852746i | \(-0.0271768\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 28.6400i | − | 1.77960i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.61016 | + | 5.35378i | 0.223463 | + | 0.331391i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 30.0129i | − | 1.85068i | −0.379144 | − | 0.925338i | \(-0.623781\pi\) | ||
0.379144 | − | 0.925338i | \(-0.376219\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.24742 | 0.138058 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.38242 | − | 14.3376i | −0.268199 | − | 0.877444i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.75306i | − | 0.167857i | −0.996472 | − | 0.0839285i | \(-0.973253\pi\) | ||
0.996472 | − | 0.0839285i | \(-0.0267467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.2052i | 1.53111i | 0.643372 | + | 0.765554i | \(0.277535\pi\) | ||||
−0.643372 | + | 0.765554i | \(0.722465\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −44.9346 | + | 13.7347i | −2.71956 | + | 0.831261i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.85459 | 0.111836 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8472 | −1.07234 | −0.536169 | − | 0.844111i | \(-0.680129\pi\) | ||||
−0.536169 | + | 0.844111i | \(0.680129\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.5141 | + | 15.5921i | 0.629461 | + | 0.933475i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.62012 | −0.454578 | −0.227289 | − | 0.973827i | \(-0.572986\pi\) | ||||
−0.227289 | + | 0.973827i | \(0.572986\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.9886 | 1.36653 | 0.683265 | − | 0.730171i | \(-0.260560\pi\) | ||||
0.683265 | + | 0.730171i | \(0.260560\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.13884 | − | 2.48772i | 0.482103 | − | 0.147360i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 29.2710i | − | 1.72781i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8260 | 0.636823 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0463396 | − | 0.151605i | −0.00271648 | − | 0.00888726i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3.48606i | − | 0.203658i | −0.994802 | − | 0.101829i | \(-0.967531\pi\) | ||
0.994802 | − | 0.101829i | \(-0.0324694\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.02689i | 0.467344i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.06604 | + | 7.48796i | −0.351987 | + | 0.434495i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.6230 | −1.42399 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.3129 | −1.17082 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −24.7902 | + | 7.57736i | −1.42416 | + | 0.435308i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.752813i | 0.0431060i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.0950 | 1.20396 | 0.601979 | − | 0.798512i | \(-0.294379\pi\) | ||||
0.601979 | + | 0.798512i | \(0.294379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.60266 | − | 1.71251i | 0.318724 | − | 0.0974212i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.2041 | 0.975553 | 0.487776 | − | 0.872969i | \(-0.337808\pi\) | ||||
0.487776 | + | 0.872969i | \(0.337808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.74318i | − | 0.155054i | −0.996990 | − | 0.0775269i | \(-0.975298\pi\) | ||
0.996990 | − | 0.0775269i | \(-0.0247024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.82385 | + | 11.6026i | 0.440824 | + | 0.653732i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 12.6964i | − | 0.713101i | −0.934276 | − | 0.356551i | \(-0.883953\pi\) | ||
0.934276 | − | 0.356551i | \(-0.116047\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.99185i | 0.223501i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.84885 | + | 15.8636i | 0.270637 | + | 0.885418i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.2090i | 0.679328i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.81559i | − | 0.322591i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.813379 | + | 2.66106i | 0.0449799 | + | 0.147157i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.3489 | −0.680815 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6.01948i | − | 0.330861i | −0.986221 | − | 0.165430i | \(-0.947099\pi\) | ||
0.986221 | − | 0.165430i | \(-0.0529013\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.2716 | + | 10.2980i | −0.836880 | + | 0.564325i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.18218 | + | 0.228007i | −0.447040 | + | 0.0124573i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.3648i | 1.76302i | 0.472165 | + | 0.881510i | \(0.343473\pi\) | ||||
−0.472165 | + | 0.881510i | \(0.656527\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.8710 | − | 6.07376i | 1.07924 | − | 0.329881i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6257i | 0.629566i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 36.1940i | − | 1.95429i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.14364 | + | 7.01316i | 0.115410 | + | 0.377576i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.6844 | −1.37881 | −0.689406 | − | 0.724375i | \(-0.742128\pi\) | ||||
−0.689406 | + | 0.724375i | \(0.742128\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.1555 | −1.45360 | −0.726800 | − | 0.686849i | \(-0.758993\pi\) | ||||
−0.726800 | + | 0.686849i | \(0.758993\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.4806 | + | 19.0218i | 1.25330 | + | 1.01531i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.6584 | −1.41888 | −0.709441 | − | 0.704765i | \(-0.751052\pi\) | ||||
−0.709441 | + | 0.704765i | \(0.751052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.41023i | − | 0.393294i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.1986 | + | 5.86825i | −1.01610 | + | 0.310581i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 20.8930i | − | 1.10269i | −0.834277 | − | 0.551346i | \(-0.814115\pi\) | ||
0.834277 | − | 0.551346i | \(-0.185885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.14315 | 0.270692 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.5232 | − | 3.82785i | 0.657299 | − | 0.200910i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.4070 | −0.597067 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.1786i | 0.896714i | 0.893855 | + | 0.448357i | \(0.147991\pi\) | ||||
−0.893855 | + | 0.448357i | \(0.852009\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.6081 | + | 10.5248i | −0.812524 | + | 0.547901i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4835i | 0.544275i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5.24645i | − | 0.271651i | −0.990733 | − | 0.135825i | \(-0.956631\pi\) | ||
0.990733 | − | 0.135825i | \(-0.0433686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.65640 | + | 0.506295i | −0.0855362 | + | 0.0261450i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.5176 | 0.644689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 0.138169i | − | 0.00709728i | −0.999994 | − | 0.00354864i | \(-0.998870\pi\) | ||
0.999994 | − | 0.00354864i | \(-0.00112957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.8836 | − | 9.13421i | 1.53098 | − | 0.467960i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.63739 | 0.441350 | 0.220675 | − | 0.975347i | \(-0.429174\pi\) | ||||
0.220675 | + | 0.975347i | \(0.429174\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.65104i | 0.440898i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.30383 | + | 10.8314i | 0.371274 | + | 0.550591i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 23.0040i | − | 1.16635i | −0.812347 | − | 0.583174i | \(-0.801810\pi\) | ||
0.812347 | − | 0.583174i | \(-0.198190\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.5204 | −0.532039 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.72985 | − | 25.2891i | −0.389919 | − | 1.27566i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.19579i | 0.362060i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.9997 | 0.853189 | 0.426594 | − | 0.904443i | \(-0.359713\pi\) | ||||
0.426594 | + | 0.904443i | \(0.359713\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.6044 | + | 37.9650i | 0.580946 | + | 1.90063i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6389 | 0.531279 | 0.265639 | − | 0.964072i | \(-0.414417\pi\) | ||||
0.265639 | + | 0.964072i | \(0.414417\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.4557 | 1.81599 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.37362 | − | 8.34378i | 0.167637 | − | 0.414606i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.3867 | −0.564419 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.8187i | − | 0.831629i | −0.909449 | − | 0.415815i | \(-0.863497\pi\) | ||
0.909449 | − | 0.415815i | \(-0.136503\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.85389 | − | 1.17798i | 0.190098 | − | 0.0581054i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −37.4428 | −1.84244 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 12.4884i | − | 0.613033i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.81157 | + | 5.92675i | 0.0887130 | + | 0.290234i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.3818i | 0.800304i | 0.916449 | + | 0.400152i | \(0.131043\pi\) | ||||
−0.916449 | + | 0.400152i | \(0.868957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4074 | 1.28702 | 0.643509 | − | 0.765439i | \(-0.277478\pi\) | ||||
0.643509 | + | 0.765439i | \(0.277478\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.44022 | + | 6.58475i | 0.215891 | + | 0.320161i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2.48476i | − | 0.120528i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.51163 | −0.169940 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.46065 | + | 17.8651i | 0.263643 | + | 0.862537i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.53866i | 0.314956i | 0.987522 | + | 0.157478i | \(0.0503363\pi\) | ||||
−0.987522 | + | 0.157478i | \(0.949664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2765i | 0.541916i | 0.962591 | + | 0.270958i | \(0.0873404\pi\) | ||||
−0.962591 | + | 0.270958i | \(0.912660\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.08976 | − | 3.56527i | −0.0522500 | − | 0.170942i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.8039i | 0.995186i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.07504 | 0.337673 | 0.168837 | − | 0.985644i | \(-0.445999\pi\) | ||||
0.168837 | + | 0.985644i | \(0.445999\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.7110 | + | 24.7549i | −1.74814 | + | 1.17881i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.56348 | 0.359352 | 0.179676 | − | 0.983726i | \(-0.442495\pi\) | ||||
0.179676 | + | 0.983726i | \(0.442495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.65585i | 0.410327i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.55171 | − | 18.1631i | −0.262587 | − | 0.859083i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 21.6674i | − | 1.02255i | −0.859418 | − | 0.511273i | \(-0.829174\pi\) | ||
0.859418 | − | 0.511273i | \(-0.170826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.6376 | −0.547993 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.70051 | − | 0.825438i | 0.126881 | − | 0.0387824i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.1278 | 1.27177 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.2853 | −1.55702 | −0.778511 | − | 0.627631i | \(-0.784025\pi\) | ||||
−0.778511 | + | 0.627631i | \(0.784025\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.0323 | + | 8.12722i | 0.468267 | + | 0.379346i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 37.0985i | − | 1.72785i | −0.503619 | − | 0.863926i | \(-0.667999\pi\) | ||
0.503619 | − | 0.863926i | \(-0.332001\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.6282i | − | 1.23752i | −0.785581 | − | 0.618759i | \(-0.787636\pi\) | ||
0.785581 | − | 0.618759i | \(-0.212364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.17377 | − | 10.3833i | −0.147180 | − | 0.481516i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 21.3309i | − | 0.987077i | −0.869724 | − | 0.493538i | \(-0.835703\pi\) | ||
0.869724 | − | 0.493538i | \(-0.164297\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.06358 | − | 38.1672i | −0.0491115 | − | 1.76240i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.3418 | + | 5.91200i | −0.891222 | + | 0.272411i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.07604i | 0.371337i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.91357 | −0.225450 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.59007 | − | 3.76950i | 0.255952 | − | 0.172593i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 36.4557i | − | 1.66570i | −0.553496 | − | 0.832852i | \(-0.686706\pi\) | ||
0.553496 | − | 0.832852i | \(-0.313294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.7063i | 1.62807i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −32.7141 | + | 9.99939i | −1.48854 | + | 0.454988i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0915269i | 0.00415602i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.07562i | − | 0.275313i | −0.990480 | − | 0.137656i | \(-0.956043\pi\) | ||
0.990480 | − | 0.137656i | \(-0.0439569\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.14761 | − | 0.656437i | 0.0971182 | − | 0.0296851i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 44.1905i | 1.99429i | 0.0755275 | + | 0.997144i | \(0.475936\pi\) | ||||
−0.0755275 | + | 0.997144i | \(0.524064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.34824 | 0.240873 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.61297 | − | 3.11062i | 0.207338 | − | 0.139812i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.5663 | 1.55051 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 10.8944i | − | 0.487703i | −0.969813 | − | 0.243851i | \(-0.921589\pi\) | ||
0.969813 | − | 0.243851i | \(-0.0784109\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.23633 | − | 13.8596i | −0.189265 | − | 0.619202i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.22373 | 0.322090 | 0.161045 | − | 0.986947i | \(-0.448514\pi\) | ||||
0.161045 | + | 0.986947i | \(0.448514\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.9663 | 0.665991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.4880 | − | 10.5416i | 1.53167 | − | 0.468169i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.1181i | − | 0.714423i | −0.934024 | − | 0.357212i | \(-0.883728\pi\) | ||
0.934024 | − | 0.357212i | \(-0.116272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 53.2097i | − | 2.35386i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.0714 | − | 19.8387i | 0.709572 | − | 0.875900i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.38243 | −0.149048 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.90967i | 0.215927i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.32150 | − | 23.9531i | −0.321378 | − | 1.05143i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.0366 | −1.75403 | −0.877017 | − | 0.480460i | \(-0.840470\pi\) | ||||
−0.877017 | + | 0.480460i | \(0.840470\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.70290 | 0.249370 | 0.124685 | − | 0.992196i | \(-0.460208\pi\) | ||||
0.124685 | + | 0.992196i | \(0.460208\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.36170 | − | 7.72657i | −0.103073 | − | 0.337215i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.5760 | 0.678500 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.07346 | 0.220585 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.4632 | + | 19.9655i | 0.584251 | + | 0.866431i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.4930i | 1.58069i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9.57713i | − | 0.414055i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.7325 | − | 8.78236i | 1.23990 | − | 0.378987i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.3722 | −1.17900 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.7799i | 0.936389i | 0.883625 | + | 0.468195i | \(0.155095\pi\) | ||||
−0.883625 | + | 0.468195i | \(0.844905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.159246 | − | 0.0486751i | 0.00683391 | − | 0.00208885i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.60653i | − | 0.0688162i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.43896i | 0.189796i | 0.995487 | + | 0.0948981i | \(0.0302525\pi\) | ||||
−0.995487 | + | 0.0948981i | \(0.969747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.26266 | + | 1.87250i | 0.0538891 | + | 0.0799162i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.5761i | − | 0.450556i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.5660 | −1.42737 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.1699 | − | 3.10853i | 0.431689 | − | 0.131950i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.31693i | 0.394771i | 0.980326 | + | 0.197386i | \(0.0632451\pi\) | ||||
−0.980326 | + | 0.197386i | \(0.936755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.3247 | 1.07112 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.33311 | + | 7.63302i | 0.0985039 | + | 0.322266i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.4048 | −1.82929 | −0.914647 | − | 0.404253i | \(-0.867532\pi\) | ||||
−0.914647 | + | 0.404253i | \(0.867532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.9965 | −0.504696 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 38.9210 | + | 15.7369i | 1.63453 | + | 0.660886i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 28.8447i | − | 1.20923i | −0.796517 | − | 0.604617i | \(-0.793326\pi\) | ||
0.796517 | − | 0.604617i | \(-0.206674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.4854 | 1.10838 | 0.554189 | − | 0.832391i | \(-0.313028\pi\) | ||||
0.554189 | + | 0.832391i | \(0.313028\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 45.3961 | − | 13.8758i | 1.89645 | − | 0.579668i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.23397i | − | 0.176569i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 7.95947i | − | 0.331357i | −0.986180 | − | 0.165678i | \(-0.947019\pi\) | ||
0.986180 | − | 0.165678i | \(-0.0529814\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.1335 | + | 4.93135i | −0.670484 | + | 0.204940i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 58.2545 | 2.41680 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.16803 | 0.172622 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.75423 | − | 14.4653i | −0.403288 | − | 0.598066i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.0836 | 1.40678 | 0.703390 | − | 0.710804i | \(-0.251669\pi\) | ||||
0.703390 | + | 0.710804i | \(0.251669\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 30.8012i | − | 1.26914i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.55450 | − | 2.30911i | 0.310750 | − | 0.0949839i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.7130 | −0.932712 | −0.466356 | − | 0.884597i | \(-0.654433\pi\) | ||||
−0.466356 | + | 0.884597i | \(0.654433\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.5906 | 0.475167 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.4228 | − | 3.79714i | 0.508430 | − | 0.155407i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.0904 | −1.39289 | −0.696447 | − | 0.717608i | \(-0.745237\pi\) | ||||
−0.696447 | + | 0.717608i | \(0.745237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.6322 | 1.24951 | 0.624756 | − | 0.780820i | \(-0.285198\pi\) | ||||
0.624756 | + | 0.780820i | \(0.285198\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.9693 | + | 14.2907i | −0.813215 | + | 0.581964i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.56051 | −0.307378 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.3533 | 1.06965 | 0.534825 | − | 0.844963i | \(-0.320378\pi\) | ||||
0.534825 | + | 0.844963i | \(0.320378\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.6308 | − | 5.08338i | 0.673916 | − | 0.205989i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.3957 | 0.622843 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.43510 | 0.0579633 | 0.0289817 | − | 0.999580i | \(-0.490774\pi\) | ||||
0.0289817 | + | 0.999580i | \(0.490774\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.3940 | − | 3.17702i | 0.419126 | − | 0.128110i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.43295i | − | 0.299239i | −0.988744 | − | 0.149620i | \(-0.952195\pi\) | ||
0.988744 | − | 0.149620i | \(-0.0478049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.974193 | 0.0391561 | 0.0195781 | − | 0.999808i | \(-0.493768\pi\) | ||||
0.0195781 | + | 0.999808i | \(0.493768\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.0948 | + | 13.8486i | 0.685991 | + | 0.555726i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −40.3767 | −1.61766 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.0942 | − | 4.61369i | 0.602804 | − | 0.184253i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.2558i | 0.608289i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.9821i | 1.91014i | 0.296382 | + | 0.955070i | \(0.404220\pi\) | ||||
−0.296382 | + | 0.955070i | \(0.595780\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.4405 | − | 8.99879i | 1.17016 | − | 0.357670i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.0413 | −0.715946 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 85.8333i | 3.40084i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4289 | − | 18.4317i | −0.491678 | − | 0.729147i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2638 | −0.523888 | −0.261944 | − | 0.965083i | \(-0.584364\pi\) | ||||
−0.261944 | + | 0.965083i | \(0.584364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.43363 | −0.214282 | −0.107141 | − | 0.994244i | \(-0.534170\pi\) | ||||
−0.107141 | + | 0.994244i | \(0.534170\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.20473 | − | 7.21301i | −0.0868111 | − | 0.284012i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.91923 | −0.389965 | −0.194983 | − | 0.980807i | \(-0.562465\pi\) | ||||
−0.194983 | + | 0.980807i | \(0.562465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8866i | 0.584349i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 48.4349 | − | 14.8046i | 1.89831 | − | 0.580238i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.30639 | 0.0511230 | 0.0255615 | − | 0.999673i | \(-0.491863\pi\) | ||||
0.0255615 | + | 0.999673i | \(0.491863\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.2675i | 0.596549i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.3729 | + | 19.1324i | −1.10693 | + | 0.746425i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 7.09051i | − | 0.276207i | −0.990418 | − | 0.138103i | \(-0.955899\pi\) | ||
0.990418 | − | 0.138103i | \(-0.0441006\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.7859i | − | 1.31412i | −0.753839 | − | 0.657060i | \(-0.771800\pi\) | ||
0.753839 | − | 0.657060i | \(-0.228200\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.9355 | − | 7.31613i | 0.929579 | − | 0.284135i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 22.9202i | − | 0.888807i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.11330 | 0.352868 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.4544 | − | 10.5313i | 1.33208 | − | 0.407164i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.39616i | 0.0538981i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.9854i | 0.539097i | 0.962987 | + | 0.269548i | \(0.0868744\pi\) | ||||
−0.962987 | + | 0.269548i | \(0.913126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.27083 | + | 4.03753i | −0.125894 | + | 0.155405i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.35018 | 0.320924 | 0.160462 | − | 0.987042i | \(-0.448702\pi\) | ||||
0.160462 | + | 0.987042i | \(0.448702\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.426943 | −0.0163846 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.6537 | + | 47.9413i | 0.561533 | + | 1.83712i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.6554 | −1.17300 | −0.586498 | − | 0.809951i | \(-0.699494\pi\) | ||||
−0.586498 | + | 0.809951i | \(0.699494\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.32666 | −0.0888972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.897926 | − | 2.93767i | −0.0342580 | − | 0.112079i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13.0701i | − | 0.497930i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0932 | −0.764382 | −0.382191 | − | 0.924083i | \(-0.624830\pi\) | ||||
−0.382191 | + | 0.924083i | \(0.624830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.5100 | + | 21.5180i | 0.551190 | + | 0.817401i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.57809i | − | 0.135725i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5919i | 0.590587i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.5180 | − | 7.18852i | 0.889534 | − | 0.271895i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.865169 | 0.0326770 | 0.0163385 | − | 0.999867i | \(-0.494799\pi\) | ||||
0.0163385 | + | 0.999867i | \(0.494799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.1681 | 1.13781 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.34032 | − | 4.38502i | −0.0504795 | − | 0.165149i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 69.8128i | 2.62558i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.6220 | −1.63826 | −0.819130 | − | 0.573608i | \(-0.805543\pi\) | ||||
−0.819130 | + | 0.573608i | \(0.805543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0692 | + | 17.8983i | 0.452630 | + | 0.671239i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.5411 | 0.993973 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 10.7855i | − | 0.403355i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.4052 | + | 5.93140i | −0.724701 | + | 0.221512i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.3270i | 1.09371i | 0.837226 | + | 0.546857i | \(0.184176\pi\) | ||||
−0.837226 | + | 0.546857i | \(0.815824\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 15.7779i | − | 0.587601i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −45.3883 | + | 13.8734i | −1.68801 | + | 0.515957i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.15242i | 0.0799389i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.6139i | 1.20958i | 0.796383 | + | 0.604792i | \(0.206744\pi\) | ||||
−0.796383 | + | 0.604792i | \(0.793256\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.60334 | − | 26.4122i | −0.207531 | − | 0.978228i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.8202 | 0.400199 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.2144i | 0.451150i | 0.974226 | + | 0.225575i | \(0.0724260\pi\) | ||||
−0.974226 | + | 0.225575i | \(0.927574\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.4471 | − | 7.47250i | 0.901746 | − | 0.275627i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.1746 | + | 0.422859i | −0.558962 | + | 0.0155762i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.9114i | 1.98316i | 0.129489 | + | 0.991581i | \(0.458666\pi\) | ||||
−0.129489 | + | 0.991581i | \(0.541334\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.4675 | − | 47.3321i | −0.531478 | − | 1.73879i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.5913i | 1.78264i | 0.453373 | + | 0.891321i | \(0.350221\pi\) | ||||
−0.453373 | + | 0.891321i | \(0.649779\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.9654i | 0.401740i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.9463 | − | 31.0629i | −0.766385 | − | 1.13653i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 44.6742 | 1.63236 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.20564 | −0.226447 | −0.113223 | − | 0.993570i | \(-0.536118\pi\) | ||||
−0.113223 | + | 0.993570i | \(0.536118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.4462 | + | 11.1401i | −1.32817 | + | 0.405970i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.63035 | −0.0593345 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 15.9766i | − | 0.580679i | −0.956924 | − | 0.290339i | \(-0.906232\pi\) | ||
0.956924 | − | 0.290339i | \(-0.0937682\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.97557 | + | 13.0065i | 0.144304 | + | 0.472107i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.6989i | 1.36658i | 0.730145 | + | 0.683292i | \(0.239452\pi\) | ||||
−0.730145 | + | 0.683292i | \(0.760548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.49394 | 0.271299 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.16757 | − | 6.18041i | −0.150679 | − | 0.223453i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.6811 | 1.68556 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.1126i | 0.364669i | 0.983237 | + | 0.182334i | \(0.0583653\pi\) | ||||
−0.983237 | + | 0.182334i | \(0.941635\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.38427 | + | 4.52879i | 0.0498532 | + | 0.163100i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.3296i | 0.839106i | 0.907731 | + | 0.419553i | \(0.137813\pi\) | ||||
−0.907731 | + | 0.419553i | \(0.862187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.26861i | 0.225175i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.5003 | + | 47.4393i | 0.520195 | + | 1.70188i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.8328 | 1.10470 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 13.7429i | − | 0.491760i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.69047 | − | 7.04020i | −0.310572 | − | 0.251596i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.6770 | 0.416770 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 37.3847i | − | 1.33262i | −0.745675 | − | 0.666310i | \(-0.767873\pi\) | ||
0.745675 | − | 0.666310i | \(-0.232127\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.1954 | + | 49.7134i | 0.540970 | + | 1.76985i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 55.9597i | − | 1.98970i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.37805 | 0.155469 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.72263 | + | 1.13786i | −0.132028 | + | 0.0403557i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.7033i | 1.01672i | 0.861144 | + | 0.508361i | \(0.169748\pi\) | ||||
−0.861144 | + | 0.508361i | \(0.830252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.57793 | 0.232710 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.5181 | + | 21.5300i | 0.512971 | + | 0.760724i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.1552 | −0.746550 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.7501 | 0.696100 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.39386 | + | 4.56017i | 0.0490662 | + | 0.160526i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.1622 | 1.65814 | 0.829068 | − | 0.559148i | \(-0.188872\pi\) | ||||
0.829068 | + | 0.559148i | \(0.188872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.04581i | 0.177182i | 0.996068 | + | 0.0885911i | \(0.0282364\pi\) | ||||
−0.996068 | + | 0.0885911i | \(0.971764\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.7613 | − | 41.7499i | −0.447558 | − | 1.46423i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.29655 | −0.0454162 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 21.3968i | − | 0.748578i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 67.4758 | − | 45.5003i | 2.35780 | − | 1.58991i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 26.9863i | − | 0.941827i | −0.882179 | − | 0.470914i | \(-0.843924\pi\) | ||
0.882179 | − | 0.470914i | \(-0.156076\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.79168 | −0.132170 | −0.0660848 | − | 0.997814i | \(-0.521051\pi\) | ||||
−0.0660848 | + | 0.997814i | \(0.521051\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.07194 | + | 0.938969i | −0.106951 | + | 0.0326907i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.7113i | 0.407243i | 0.979050 | + | 0.203621i | \(0.0652711\pi\) | ||||
−0.979050 | + | 0.203621i | \(0.934729\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.7941 | 0.374894 | 0.187447 | − | 0.982275i | \(-0.439979\pi\) | ||||
0.187447 | + | 0.982275i | \(0.439979\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.5622 | − | 9.03598i | 1.02550 | − | 0.313455i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.6730i | 1.27064i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.36731i | 0.289563i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.3097 | − | 20.5036i | −0.874832 | − | 0.708707i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.7995i | 1.30498i | 0.757796 | + | 0.652492i | \(0.226276\pi\) | ||||
−0.757796 | + | 0.652492i | \(0.773724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.3671 | 0.840244 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.6220 | − | 3.85803i | 0.434724 | − | 0.132878i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.8211 | −0.716266 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 35.2673i | − | 1.21180i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.0783 | + | 11.6390i | −1.30684 | + | 0.399450i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.9956i | 0.891118i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.9904 | 0.650219 | 0.325109 | − | 0.945676i | \(-0.394599\pi\) | ||||
0.325109 | + | 0.945676i | \(0.394599\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.2217 | + | 8.24131i | −0.417972 | + | 0.281847i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.7014 | −1.25370 | −0.626848 | − | 0.779142i | \(-0.715655\pi\) | ||||
−0.626848 | + | 0.779142i | \(0.715655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.4450 | 1.27761 | 0.638804 | − | 0.769370i | \(-0.279430\pi\) | ||||
0.638804 | + | 0.769370i | \(0.279430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.8198 | + | 48.4845i | 0.505056 | + | 1.65235i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 27.3882i | − | 0.932307i | −0.884704 | − | 0.466153i | \(-0.845639\pi\) | ||
0.884704 | − | 0.466153i | \(-0.154361\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.4609i | 0.491687i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.9322 | + | 5.48115i | −0.609009 | + | 0.186149i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3452i | 0.452706i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.32599 | + | 47.5842i | 0.0449296 | + | 1.61233i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.153514 | + | 0.227658i | 0.00519566 | + | 0.00770504i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.66467i | 0.157695i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.6724 | 1.81239 | 0.906194 | − | 0.422861i | \(-0.138974\pi\) | ||||
0.906194 | + | 0.422861i | \(0.138974\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.76498 | + | 5.77431i | 0.0595311 | + | 0.194763i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.1960i | − | 0.511965i | −0.966681 | − | 0.255983i | \(-0.917601\pi\) | ||
0.966681 | − | 0.255983i | \(-0.0823990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.2856i | 1.79320i | 0.442839 | + | 0.896601i | \(0.353971\pi\) | ||||
−0.442839 | + | 0.896601i | \(0.646029\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.06398 | − | 13.2958i | −0.136609 | − | 0.446932i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.4042i | 0.852988i | 0.904490 | + | 0.426494i | \(0.140252\pi\) | ||||
−0.904490 | + | 0.426494i | \(0.859748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 84.1566i | − | 2.82252i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.25668 | − | 15.4743i | 0.209607 | − | 0.518407i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 13.0078i | − | 0.435288i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.3463 | −0.579823 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.7856 | − | 12.4665i | 1.36179 | − | 0.416245i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.4927 | −0.450006 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.58429i | − | 0.186040i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.6463 | − | 10.2843i | 1.11968 | − | 0.342241i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0961398 | −0.00319580 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.2592 | 1.60242 | 0.801210 | − | 0.598383i | \(-0.204190\pi\) | ||||
0.801210 | + | 0.598383i | \(0.204190\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.2261 | − | 25.1023i | 1.23471 | − | 0.832591i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.6148i | 0.484210i | 0.970250 | + | 0.242105i | \(0.0778378\pi\) | ||||
−0.970250 | + | 0.242105i | \(0.922162\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.1609i | − | 0.766513i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.381146 | − | 1.24696i | −0.0126003 | − | 0.0412233i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −71.2178 | −2.35182 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.67252i | − | 0.121145i | −0.998164 | − | 0.0605727i | \(-0.980707\pi\) | ||
0.998164 | − | 0.0605727i | \(-0.0192927\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34.9419 | + | 10.6803i | −1.15137 | + | 0.351929i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43.0949 | −1.41848 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.13976 | −0.201874 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.41322 | + | 5.67320i | −0.276326 | + | 0.186332i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.4217 | 1.29338 | 0.646692 | − | 0.762751i | \(-0.276152\pi\) | ||||
0.646692 | + | 0.762751i | \(0.276152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 72.5202 | 2.37675 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.4968 | + | 8.71034i | −0.932944 | + | 0.285164i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 4.60820i | − | 0.150704i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 47.8618i | − | 1.56358i | −0.623545 | − | 0.781788i | \(-0.714308\pi\) | ||
0.623545 | − | 0.781788i | \(-0.285692\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.38886 | + | 4.54381i | 0.0453238 | + | 0.148282i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.3746 | 1.28358 | 0.641788 | − | 0.766882i | \(-0.278193\pi\) | ||||
0.641788 | + | 0.766882i | \(0.278193\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.5683i | 0.865184i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.8338 | − | 15.2574i | −0.612663 | − | 0.496322i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 23.2261i | − | 0.754746i | −0.926061 | − | 0.377373i | \(-0.876827\pi\) | ||
0.926061 | − | 0.377373i | \(-0.123173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 66.3381i | 2.15343i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.42813 | + | 21.0303i | 0.208446 | + | 0.681956i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.1506i | 1.36539i | 0.730702 | + | 0.682696i | \(0.239193\pi\) | ||||
−0.730702 | + | 0.682696i | \(0.760807\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.4064 | −0.886852 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.02106 | − | 6.61211i | −0.0653315 | − | 0.213739i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 10.8531i | − | 0.350466i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.29547 | −0.267596 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.0633 | − | 23.8215i | −0.517633 | − | 0.767637i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.74008 | 0.313544 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4938 | −0.787669 | −0.393834 | − | 0.919181i | \(-0.628852\pi\) | ||||
−0.393834 | + | 0.919181i | \(0.628852\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.18137 | − | 20.2230i | −0.198574 | − | 0.649657i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.2521i | 0.874561i | 0.899325 | + | 0.437280i | \(0.144058\pi\) | ||||
−0.899325 | + | 0.437280i | \(0.855942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6906 | 0.535077 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.94440 | + | 9.63295i | 0.0942964 | + | 0.308501i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8133i | 0.825841i | 0.910767 | + | 0.412920i | \(0.135491\pi\) | ||||
−0.910767 | + | 0.412920i | \(0.864509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0530i | 0.513057i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.69456 | − | 3.99597i | −0.0860308 | − | 0.127582i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.2340 | −1.47464 | −0.737318 | − | 0.675545i | \(-0.763908\pi\) | ||||
−0.737318 | + | 0.675545i | \(0.763908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.56079 | −0.145319 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.4547 | − | 6.25217i | 0.651079 | − | 0.199009i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.4374 | 0.586275 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 48.2546i | − | 1.53286i | −0.642328 | − | 0.766429i | \(-0.722031\pi\) | ||
0.642328 | − | 0.766429i | \(-0.277969\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.04764 | + | 9.97068i | 0.0967138 | + | 0.316410i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.49985 | −0.237761 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.02279 | 0.190744 | 0.0953718 | − | 0.995442i | \(-0.469596\pi\) | ||||
0.0953718 | + | 0.995442i | \(0.469596\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.0821 | − | 24.7895i | 0.635370 | − | 0.784305i |
(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 | 4020.2.f.b.401.6 | yes | 46 | |
3.2 | odd | 2 | 4020.2.f.a.401.42 | yes | 46 | ||
67.66 | odd | 2 | 4020.2.f.a.401.41 | ✓ | 46 | ||
201.200 | even | 2 | inner | 4020.2.f.b.401.5 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.f.a.401.41 | ✓ | 46 | 67.66 | odd | 2 | ||
4020.2.f.a.401.42 | yes | 46 | 3.2 | odd | 2 | ||
4020.2.f.b.401.5 | yes | 46 | 201.200 | even | 2 | inner | |
4020.2.f.b.401.6 | yes | 46 | 1.1 | even | 1 | trivial |