Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
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.q (of order \(3\), degree \(2\), 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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 3781.5 | ||
Character | \(\chi\) | \(=\) | 4020.3781 |
Dual form | 4020.2.q.m.841.5 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.436767 | − | 0.756503i | −0.165083 | − | 0.285931i | 0.771602 | − | 0.636106i | \(-0.219456\pi\) |
−0.936685 | + | 0.350174i | \(0.886122\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09530 | + | 1.89712i | 0.330247 | + | 0.572004i | 0.982560 | − | 0.185945i | \(-0.0595347\pi\) |
−0.652313 | + | 0.757949i | \(0.726201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.27391 | + | 2.20647i | −0.353318 | + | 0.611964i | −0.986829 | − | 0.161769i | \(-0.948280\pi\) |
0.633511 | + | 0.773734i | \(0.281613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.07842 | + | 5.33199i | −0.746628 | + | 1.29320i | 0.202803 | + | 0.979220i | \(0.434995\pi\) |
−0.949431 | + | 0.313977i | \(0.898338\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.66901 | + | 2.89081i | −0.382897 | + | 0.663198i | −0.991475 | − | 0.130297i | \(-0.958407\pi\) |
0.608578 | + | 0.793494i | \(0.291740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.436767 | − | 0.756503i | −0.0953104 | − | 0.165083i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.10244 | + | 3.64153i | −0.438389 | + | 0.759312i | −0.997565 | − | 0.0697369i | \(-0.977784\pi\) |
0.559177 | + | 0.829049i | \(0.311117\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.323233 | − | 0.559856i | −0.0600228 | − | 0.103963i | 0.834453 | − | 0.551080i | \(-0.185784\pi\) |
−0.894475 | + | 0.447117i | \(0.852451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.579844 | + | 1.00432i | 0.104143 | + | 0.180381i | 0.913388 | − | 0.407091i | \(-0.133457\pi\) |
−0.809245 | + | 0.587472i | \(0.800123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.09530 | + | 1.89712i | 0.190668 | + | 0.330247i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.436767 | − | 0.756503i | −0.0738271 | − | 0.127872i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.36632 | + | 4.09859i | −0.389021 | + | 0.673805i | −0.992318 | − | 0.123712i | \(-0.960520\pi\) |
0.603297 | + | 0.797517i | \(0.293853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.27391 | + | 2.20647i | −0.203988 | + | 0.353318i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00304 | − | 6.93346i | −0.625169 | − | 1.08283i | −0.988508 | − | 0.151168i | \(-0.951697\pi\) |
0.363339 | − | 0.931657i | \(-0.381637\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.15156 | −1.39560 | −0.697800 | − | 0.716293i | \(-0.745837\pi\) | ||||
−0.697800 | + | 0.716293i | \(0.745837\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.21127 | − | 10.7582i | −0.906006 | − | 1.56925i | −0.819561 | − | 0.572992i | \(-0.805783\pi\) |
−0.0864453 | − | 0.996257i | \(-0.527551\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.11847 | − | 5.40135i | 0.445496 | − | 0.771621i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.07842 | + | 5.33199i | −0.431066 | + | 0.746628i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.66314 | −1.18997 | −0.594987 | − | 0.803735i | \(-0.702843\pi\) | ||||
−0.594987 | + | 0.803735i | \(0.702843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.09530 | + | 1.89712i | 0.147691 | + | 0.255808i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.66901 | + | 2.89081i | −0.221066 | + | 0.382897i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.64380 | −0.474382 | −0.237191 | − | 0.971463i | \(-0.576227\pi\) | ||||
−0.237191 | + | 0.971463i | \(0.576227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.99641 | + | 5.18993i | −0.383651 | + | 0.664502i | −0.991581 | − | 0.129488i | \(-0.958667\pi\) |
0.607930 | + | 0.793990i | \(0.292000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.436767 | − | 0.756503i | −0.0550275 | − | 0.0953104i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.27391 | + | 2.20647i | −0.158009 | + | 0.273679i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.38723 | + | 8.06694i | 0.169477 | + | 0.985534i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.10244 | + | 3.64153i | −0.253104 | + | 0.438389i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.31716 | + | 9.20959i | 0.631031 | + | 1.09298i | 0.987341 | + | 0.158610i | \(0.0507012\pi\) |
−0.356311 | + | 0.934368i | \(0.615965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.0239280 | + | 0.0414445i | −0.00280056 | + | 0.00485071i | −0.867422 | − | 0.497573i | \(-0.834225\pi\) |
0.864622 | + | 0.502423i | \(0.167558\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.956786 | − | 1.65720i | 0.109036 | − | 0.188856i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.57787 | − | 2.73295i | −0.177524 | − | 0.307481i | 0.763508 | − | 0.645799i | \(-0.223475\pi\) |
−0.941032 | + | 0.338318i | \(0.890142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.29548 | + | 3.97588i | −0.251961 | + | 0.436409i | −0.964066 | − | 0.265664i | \(-0.914409\pi\) |
0.712105 | + | 0.702073i | \(0.247742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.07842 | + | 5.33199i | −0.333902 | + | 0.578335i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.323233 | − | 0.559856i | −0.0346542 | − | 0.0600228i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.07807 | −0.326275 | −0.163137 | − | 0.986603i | \(-0.552161\pi\) | ||||
−0.163137 | + | 0.986603i | \(0.552161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.22560 | 0.233306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.579844 | + | 1.00432i | 0.0601270 | + | 0.104143i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.66901 | + | 2.89081i | −0.171237 | + | 0.296591i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.76819 | − | 3.06259i | 0.179532 | − | 0.310959i | −0.762188 | − | 0.647355i | \(-0.775875\pi\) |
0.941720 | + | 0.336397i | \(0.109208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.09530 | + | 1.89712i | 0.110082 | + | 0.190668i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.45576 | − | 2.52145i | −0.144853 | − | 0.250894i | 0.784465 | − | 0.620173i | \(-0.212938\pi\) |
−0.929318 | + | 0.369280i | \(0.879604\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.42216 | + | 5.92736i | 0.337196 | + | 0.584040i | 0.983904 | − | 0.178697i | \(-0.0571883\pi\) |
−0.646708 | + | 0.762737i | \(0.723855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.436767 | − | 0.756503i | −0.0426241 | − | 0.0738271i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.6982 | 1.03423 | 0.517115 | − | 0.855916i | \(-0.327006\pi\) | ||||
0.517115 | + | 0.855916i | \(0.327006\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.25484 | 0.503323 | 0.251661 | − | 0.967815i | \(-0.419023\pi\) | ||||
0.251661 | + | 0.967815i | \(0.419023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.36632 | + | 4.09859i | −0.224602 | + | 0.389021i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.32036 | + | 16.1433i | 0.876786 | + | 1.51864i | 0.854848 | + | 0.518878i | \(0.173650\pi\) |
0.0219375 | + | 0.999759i | \(0.493017\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.10244 | + | 3.64153i | −0.196053 | + | 0.339575i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.27391 | + | 2.20647i | −0.117773 | + | 0.203988i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.37822 | 0.493021 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.10062 | − | 5.37042i | 0.281874 | − | 0.488220i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.00304 | − | 6.93346i | −0.360942 | − | 0.625169i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.10885 | − | 15.7770i | −0.808279 | − | 1.39998i | −0.914055 | − | 0.405591i | \(-0.867066\pi\) |
0.105775 | − | 0.994390i | \(-0.466268\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.15156 | −0.805750 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.92110 | −0.604699 | −0.302350 | − | 0.953197i | \(-0.597771\pi\) | ||||
−0.302350 | + | 0.953197i | \(0.597771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.91588 | 0.252839 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.08824 | 0.263846 | 0.131923 | − | 0.991260i | \(-0.457885\pi\) | ||||
0.131923 | + | 0.991260i | \(0.457885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.25892 | 0.191599 | 0.0957995 | − | 0.995401i | \(-0.469459\pi\) | ||||
0.0957995 | + | 0.995401i | \(0.469459\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.21127 | − | 10.7582i | −0.523083 | − | 0.906006i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.58126 | −0.466728 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.323233 | − | 0.559856i | −0.0268430 | − | 0.0464935i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.11847 | − | 5.40135i | 0.257207 | − | 0.445496i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7007 | 1.04049 | 0.520243 | − | 0.854019i | \(-0.325842\pi\) | ||||
0.520243 | + | 0.854019i | \(0.325842\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.02601 | + | 1.77710i | −0.0834955 | + | 0.144618i | −0.904749 | − | 0.425945i | \(-0.859942\pi\) |
0.821254 | + | 0.570563i | \(0.193275\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.07842 | + | 5.33199i | −0.248876 | + | 0.431066i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.579844 | + | 1.00432i | 0.0465742 | + | 0.0806689i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.88957 | + | 3.27283i | −0.150804 | + | 0.261200i | −0.931523 | − | 0.363682i | \(-0.881520\pi\) |
0.780719 | + | 0.624882i | \(0.214853\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.66314 | −0.687032 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.67311 | 0.289481 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.92924 | + | 13.7338i | 0.621066 | + | 1.07572i | 0.989288 | + | 0.145979i | \(0.0466334\pi\) |
−0.368222 | + | 0.929738i | \(0.620033\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.09530 | + | 1.89712i | 0.0852693 | + | 0.147691i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.55406 | + | 16.5481i | 0.739315 | + | 1.28053i | 0.952804 | + | 0.303586i | \(0.0981839\pi\) |
−0.213489 | + | 0.976945i | \(0.568483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.25433 | + | 5.63666i | 0.250333 | + | 0.433590i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.66901 | + | 2.89081i | −0.127632 | + | 0.221066i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.12739 | + | 7.14884i | −0.313799 | + | 0.543517i | −0.979182 | − | 0.202986i | \(-0.934935\pi\) |
0.665382 | + | 0.746503i | \(0.268269\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.436767 | − | 0.756503i | −0.0330165 | − | 0.0571863i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.64380 | −0.273885 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.75612 | −0.131259 | −0.0656293 | − | 0.997844i | \(-0.520905\pi\) | ||||
−0.0656293 | + | 0.997844i | \(0.520905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.58843 | − | 2.75125i | −0.118067 | − | 0.204499i | 0.800934 | − | 0.598752i | \(-0.204337\pi\) |
−0.919002 | + | 0.394253i | \(0.871003\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.99641 | + | 5.18993i | −0.221501 | + | 0.383651i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.36632 | + | 4.09859i | −0.173976 | + | 0.301335i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4872 | −0.986285 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.436767 | − | 0.756503i | −0.0317701 | − | 0.0550275i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.01274 | + | 10.4144i | −0.435067 | + | 0.753557i | −0.997301 | − | 0.0734204i | \(-0.976609\pi\) |
0.562234 | + | 0.826978i | \(0.309942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.9520 | 1.58014 | 0.790069 | − | 0.613017i | \(-0.210044\pi\) | ||||
0.790069 | + | 0.613017i | \(0.210044\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.27391 | + | 2.20647i | −0.0912263 | + | 0.158009i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.82749 | + | 15.2897i | 0.628933 | + | 1.08934i | 0.987766 | + | 0.155942i | \(0.0498412\pi\) |
−0.358834 | + | 0.933402i | \(0.616825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.39395 | + | 4.14645i | −0.169703 | + | 0.293934i | −0.938315 | − | 0.345781i | \(-0.887614\pi\) |
0.768612 | + | 0.639715i | \(0.220947\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.38723 | + | 8.06694i | 0.0978475 | + | 0.568998i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.282355 | + | 0.489053i | −0.0198174 | + | 0.0343248i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00304 | − | 6.93346i | −0.279584 | − | 0.484254i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.10244 | + | 3.64153i | −0.146130 | + | 0.253104i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.31230 | −0.505802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.86531 | − | 3.23081i | 0.128413 | − | 0.222418i | −0.794649 | − | 0.607070i | \(-0.792345\pi\) |
0.923062 | + | 0.384651i | \(0.125678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.31716 | + | 9.20959i | 0.364326 | + | 0.631031i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.15156 | −0.624131 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.506514 | − | 0.877308i | 0.0343844 | − | 0.0595555i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0239280 | + | 0.0414445i | −0.00161690 | + | 0.00280056i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.84324 | − | 13.5849i | −0.527594 | − | 0.913819i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.6541 | −1.24917 | −0.624584 | − | 0.780958i | \(-0.714731\pi\) | ||||
−0.624584 | + | 0.780958i | \(0.714731\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.43267 | − | 14.6058i | −0.559696 | − | 0.969422i | −0.997522 | − | 0.0703622i | \(-0.977585\pi\) |
0.437825 | − | 0.899060i | \(-0.355749\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.04145 | − | 6.99999i | 0.267066 | − | 0.462573i | −0.701037 | − | 0.713125i | \(-0.747279\pi\) |
0.968103 | + | 0.250553i | \(0.0806124\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.956786 | − | 1.65720i | 0.0629519 | − | 0.109036i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.70411 | − | 4.68365i | −0.177152 | − | 0.306836i | 0.763752 | − | 0.645510i | \(-0.223355\pi\) |
−0.940904 | + | 0.338674i | \(0.890022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.21127 | − | 10.7582i | −0.405178 | − | 0.701789i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.57787 | − | 2.73295i | −0.102494 | − | 0.177524i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.54264 | − | 16.5283i | −0.617262 | − | 1.06913i | −0.989983 | − | 0.141186i | \(-0.954909\pi\) |
0.372721 | − | 0.927943i | \(-0.378425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.37395 | 0.474998 | 0.237499 | − | 0.971388i | \(-0.423672\pi\) | ||||
0.237499 | + | 0.971388i | \(0.423672\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.11847 | − | 5.40135i | 0.199232 | − | 0.345079i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.25232 | − | 7.36524i | −0.270569 | − | 0.468639i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.29548 | + | 3.97588i | −0.145470 | + | 0.251961i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.20657 | + | 12.4821i | −0.454874 | + | 0.787866i | −0.998681 | − | 0.0513449i | \(-0.983649\pi\) |
0.543807 | + | 0.839211i | \(0.316983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.21124 | −0.579106 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.07842 | + | 5.33199i | −0.192778 | + | 0.333902i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.0017 | + | 19.0555i | 0.686268 | + | 1.18865i | 0.973037 | + | 0.230651i | \(0.0740854\pi\) |
−0.286769 | + | 0.958000i | \(0.592581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.13413 | 0.256883 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.323233 | − | 0.559856i | −0.0200076 | − | 0.0346542i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.51723 | −0.340207 | −0.170104 | − | 0.985426i | \(-0.554410\pi\) | ||||
−0.170104 | + | 0.985426i | \(0.554410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.66314 | −0.532173 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.07807 | −0.188375 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.05203 | −0.247057 | −0.123528 | − | 0.992341i | \(-0.539421\pi\) | ||||
−0.123528 | + | 0.992341i | \(0.539421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.3639 | 1.35851 | 0.679256 | − | 0.733902i | \(-0.262303\pi\) | ||||
0.679256 | + | 0.733902i | \(0.262303\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.22560 | 0.134700 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.09530 | + | 1.89712i | 0.0660493 | + | 0.114401i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.341518 | −0.0205198 | −0.0102599 | − | 0.999947i | \(-0.503266\pi\) | ||||
−0.0102599 | + | 0.999947i | \(0.503266\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.579844 | + | 1.00432i | 0.0347144 | + | 0.0601270i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.37905 | + | 11.0488i | −0.380542 | + | 0.659118i | −0.991140 | − | 0.132823i | \(-0.957596\pi\) |
0.610598 | + | 0.791941i | \(0.290929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.8010 | 1.11760 | 0.558802 | − | 0.829301i | \(-0.311261\pi\) | ||||
0.558802 | + | 0.829301i | \(0.311261\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.66901 | + | 2.89081i | −0.0988636 | + | 0.171237i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.49679 | + | 6.05662i | −0.206409 | + | 0.357511i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4534 | − | 18.1058i | −0.614905 | − | 1.06505i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.76819 | − | 3.06259i | 0.103653 | − | 0.179532i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.9116 | −1.04641 | −0.523204 | − | 0.852207i | \(-0.675263\pi\) | ||||
−0.523204 | + | 0.852207i | \(0.675263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.64380 | −0.212150 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.09530 | + | 1.89712i | 0.0635560 | + | 0.110082i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.35662 | − | 9.27793i | −0.309781 | − | 0.536557i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.99710 | + | 6.92318i | 0.230389 | + | 0.399046i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.45576 | − | 2.52145i | −0.0836312 | − | 0.144853i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.99641 | + | 5.18993i | −0.171574 | + | 0.297174i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.6094 | − | 20.1080i | 0.662581 | − | 1.14762i | −0.317354 | − | 0.948307i | \(-0.602794\pi\) |
0.979935 | − | 0.199317i | \(-0.0638722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.42216 | + | 5.92736i | 0.194680 | + | 0.337196i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.428849 | −0.0243178 | −0.0121589 | − | 0.999926i | \(-0.503870\pi\) | ||||
−0.0121589 | + | 0.999926i | \(0.503870\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.4449 | 1.49475 | 0.747377 | − | 0.664401i | \(-0.231313\pi\) | ||||
0.747377 | + | 0.664401i | \(0.231313\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.436767 | − | 0.756503i | −0.0246090 | − | 0.0426241i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.5428 | − | 23.4567i | 0.760637 | − | 1.31746i | −0.181886 | − | 0.983320i | \(-0.558220\pi\) |
0.942523 | − | 0.334142i | \(-0.108446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.708077 | − | 1.22643i | 0.0396447 | − | 0.0686666i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.6982 | 0.597113 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.2758 | − | 17.7983i | −0.571763 | − | 0.990323i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.27391 | + | 2.20647i | −0.0706636 | + | 0.122393i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.25484 | 0.290593 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.42576 | + | 9.39768i | −0.299132 | + | 0.518111i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.07232 | − | 7.05347i | −0.223835 | − | 0.387694i | 0.732134 | − | 0.681160i | \(-0.238524\pi\) |
−0.955969 | + | 0.293467i | \(0.905191\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.36632 | + | 4.09859i | −0.129674 | + | 0.224602i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.38723 | + | 8.06694i | 0.0757923 | + | 0.440744i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.1864 | − | 22.8395i | 0.718307 | − | 1.24414i | −0.243363 | − | 0.969935i | \(-0.578251\pi\) |
0.961670 | − | 0.274209i | \(-0.0884160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.32036 | + | 16.1433i | 0.506212 | + | 0.876786i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.27021 | + | 2.20007i | −0.0687858 | + | 0.119141i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.5629 | −0.624339 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.10244 | + | 3.64153i | −0.113192 | + | 0.196053i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.76820 | + | 9.99082i | 0.309653 | + | 0.536335i | 0.978287 | − | 0.207257i | \(-0.0664536\pi\) |
−0.668633 | + | 0.743592i | \(0.733120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7299 | 0.895528 | 0.447764 | − | 0.894152i | \(-0.352220\pi\) | ||||
0.447764 | + | 0.894152i | \(0.352220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.27391 | + | 2.20647i | −0.0679960 | + | 0.117773i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.8770 | + | 25.7678i | −0.791825 | + | 1.37148i | 0.133011 | + | 0.991115i | \(0.457536\pi\) |
−0.924836 | + | 0.380367i | \(0.875798\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.31716 | + | 9.20959i | 0.282206 | + | 0.488794i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.37822 | 0.284646 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.6130 | 1.29902 | 0.649511 | − | 0.760352i | \(-0.274974\pi\) | ||||
0.649511 | + | 0.760352i | \(0.274974\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.92881 | + | 6.80490i | 0.206779 | + | 0.358152i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.10062 | − | 5.37042i | 0.162740 | − | 0.281874i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0239280 | + | 0.0414445i | −0.00125245 | + | 0.00216930i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.33883 | − | 10.9792i | −0.330884 | − | 0.573108i | 0.651801 | − | 0.758390i | \(-0.274014\pi\) |
−0.982685 | + | 0.185282i | \(0.940680\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.00304 | − | 6.93346i | −0.208390 | − | 0.360942i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.78378 | + | 6.55369i | 0.196444 | + | 0.340251i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.10934 | − | 12.3137i | −0.368108 | − | 0.637581i | 0.621162 | − | 0.783682i | \(-0.286661\pi\) |
−0.989270 | + | 0.146101i | \(0.953328\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.64707 | 0.0848286 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7582 | + | 18.6337i | −0.552610 | + | 0.957148i | 0.445475 | + | 0.895294i | \(0.353035\pi\) |
−0.998085 | + | 0.0618542i | \(0.980299\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.10885 | − | 15.7770i | −0.466660 | − | 0.808279i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.2051 | + | 22.8719i | −0.674750 | + | 1.16870i | 0.301792 | + | 0.953374i | \(0.402415\pi\) |
−0.976542 | + | 0.215328i | \(0.930918\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.956786 | − | 1.65720i | 0.0487623 | − | 0.0844589i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.15156 | −0.465200 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.88730 | + | 15.3933i | −0.450604 | + | 0.780469i | −0.998424 | − | 0.0561275i | \(-0.982125\pi\) |
0.547820 | + | 0.836596i | \(0.315458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.9444 | − | 22.4204i | −0.654626 | − | 1.13385i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.92110 | −0.349123 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.57787 | − | 2.73295i | −0.0793912 | − | 0.137510i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.2842 | 0.716906 | 0.358453 | − | 0.933548i | \(-0.383304\pi\) | ||||
0.358453 | + | 0.933548i | \(0.383304\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.91588 | 0.145976 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.0441 | 1.30058 | 0.650291 | − | 0.759686i | \(-0.274647\pi\) | ||||
0.650291 | + | 0.759686i | \(0.274647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.95467 | −0.147182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.3674 | −0.513892 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.7417 | − | 27.2654i | −0.778376 | − | 1.34819i | −0.932878 | − | 0.360194i | \(-0.882711\pi\) |
0.154502 | − | 0.987993i | \(-0.450623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.08824 | 0.152332 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.59149 | + | 2.75655i | 0.0783122 | + | 0.135641i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.29548 | + | 3.97588i | −0.112680 | + | 0.195168i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.25892 | 0.110620 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.07225 | + | 13.9815i | −0.394355 | + | 0.683043i | −0.993019 | − | 0.117958i | \(-0.962365\pi\) |
0.598664 | + | 0.801001i | \(0.295699\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.98072 | + | 17.2871i | −0.486430 | + | 0.842522i | −0.999878 | − | 0.0155985i | \(-0.995035\pi\) |
0.513448 | + | 0.858121i | \(0.328368\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.21127 | − | 10.7582i | −0.302002 | − | 0.523083i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.07842 | + | 5.33199i | −0.149326 | + | 0.258639i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.23493 | 0.253336 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.58126 | −0.269466 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.43435 | − | 9.41257i | −0.261763 | − | 0.453387i | 0.704947 | − | 0.709260i | \(-0.250971\pi\) |
−0.966711 | + | 0.255872i | \(0.917637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.47684 | + | 4.29001i | 0.119029 | + | 0.206165i | 0.919383 | − | 0.393363i | \(-0.128688\pi\) |
−0.800354 | + | 0.599528i | \(0.795355\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.323233 | − | 0.559856i | −0.0154978 | − | 0.0268430i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.01799 | − | 12.1555i | −0.335716 | − | 0.581477i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.54614 | − | 11.3382i | 0.312430 | − | 0.541145i | −0.666458 | − | 0.745543i | \(-0.732190\pi\) |
0.978888 | + | 0.204398i | \(0.0655237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.11847 | − | 5.40135i | 0.148499 | − | 0.257207i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.60200 | + | 4.50680i | 0.123625 | + | 0.214125i | 0.921195 | − | 0.389102i | \(-0.127215\pi\) |
−0.797570 | + | 0.603227i | \(0.793881\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.07807 | −0.145915 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.7007 | 0.600724 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.41212 | + | 14.5702i | 0.396992 | + | 0.687611i | 0.993353 | − | 0.115105i | \(-0.0367206\pi\) |
−0.596361 | + | 0.802717i | \(0.703387\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.76909 | − | 15.1885i | 0.412920 | − | 0.715199i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.02601 | + | 1.77710i | −0.0482062 | + | 0.0834955i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.22560 | 0.104338 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.9881 | + | 19.0320i | 0.514003 | + | 0.890280i | 0.999868 | + | 0.0162456i | \(0.00517137\pi\) |
−0.485865 | + | 0.874034i | \(0.661495\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.07842 | + | 5.33199i | −0.143689 | + | 0.248876i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.4235 | −1.04437 | −0.522184 | − | 0.852833i | \(-0.674883\pi\) | ||||
−0.522184 | + | 0.852833i | \(0.674883\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.98973 | + | 15.5707i | −0.417788 | + | 0.723630i | −0.995717 | − | 0.0924571i | \(-0.970528\pi\) |
0.577929 | + | 0.816087i | \(0.303861\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.579844 | + | 1.00432i | 0.0268896 | + | 0.0465742i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.89466 | − | 13.6740i | 0.365321 | − | 0.632755i | −0.623506 | − | 0.781818i | \(-0.714292\pi\) |
0.988828 | + | 0.149063i | \(0.0476258\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.49677 | − | 4.57282i | 0.253817 | − | 0.211153i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.88957 | + | 3.27283i | −0.0870667 | + | 0.150804i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.0237 | − | 17.3616i | −0.460892 | − | 0.798288i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.66901 | + | 2.89081i | −0.0765795 | + | 0.132640i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.66314 | −0.396658 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.0622 | − | 20.8924i | 0.551137 | − | 0.954597i | −0.447056 | − | 0.894506i | \(-0.647528\pi\) |
0.998193 | − | 0.0600909i | \(-0.0191391\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.02895 | − | 10.4424i | −0.274896 | − | 0.476134i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.67311 | 0.167132 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.76819 | − | 3.06259i | 0.0802892 | − | 0.139065i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.00357 | − | 12.1305i | 0.317362 | − | 0.549687i | −0.662575 | − | 0.748996i | \(-0.730536\pi\) |
0.979937 | + | 0.199309i | \(0.0638697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.92924 | + | 13.7338i | 0.358572 | + | 0.621066i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.1879 | −0.956196 | −0.478098 | − | 0.878307i | \(-0.658674\pi\) | ||||
−0.478098 | + | 0.878307i | \(0.658674\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.98019 | 0.179259 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.09530 | + | 1.89712i | 0.0492303 | + | 0.0852693i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.64472 | − | 8.04490i | 0.208344 | − | 0.360863i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.14567 | + | 5.44846i | −0.140820 | + | 0.243907i | −0.927805 | − | 0.373064i | \(-0.878307\pi\) |
0.786986 | + | 0.616971i | \(0.211640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.55406 | + | 16.5481i | 0.426844 | + | 0.739315i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.41870 | + | 7.65342i | 0.197020 | + | 0.341249i | 0.947561 | − | 0.319575i | \(-0.103540\pi\) |
−0.750541 | + | 0.660824i | \(0.770207\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.45576 | − | 2.52145i | −0.0647804 | − | 0.112203i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.25433 | + | 5.63666i | 0.144530 | + | 0.250333i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.59211 | −0.114893 | −0.0574466 | − | 0.998349i | \(-0.518296\pi\) | ||||
−0.0574466 | + | 0.998349i | \(0.518296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0418039 | 0.00184929 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.66901 | + | 2.89081i | −0.0736886 | + | 0.127632i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.42216 | + | 5.92736i | 0.150798 | + | 0.261191i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6065 | − | 23.5671i | 0.598411 | − | 1.03648i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.12739 | + | 7.14884i | −0.181172 | + | 0.313799i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.4807 | 1.81730 | 0.908650 | − | 0.417558i | \(-0.137114\pi\) | ||||
0.908650 | + | 0.417558i | \(0.137114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.4360 | + | 31.9321i | −0.806151 | + | 1.39629i | 0.109360 | + | 0.994002i | \(0.465120\pi\) |
−0.915511 | + | 0.402293i | \(0.868213\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.436767 | − | 0.756503i | −0.0190621 | − | 0.0330165i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.14002 | −0.311024 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.65950 | + | 4.60639i | 0.115630 | + | 0.200278i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.64380 | −0.158127 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.3980 | 0.883534 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.6982 | 0.462522 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.75612 | −0.0757822 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.6627 | 0.588494 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.44614 | −0.277141 | −0.138571 | − | 0.990353i | \(-0.544251\pi\) | ||||
−0.138571 | + | 0.990353i | \(0.544251\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.58843 | − | 2.75125i | −0.0681663 | − | 0.118067i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.25484 | 0.225093 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.64619 | − | 8.04744i | −0.198657 | − | 0.344084i | 0.749436 | − | 0.662076i | \(-0.230325\pi\) |
−0.948093 | + | 0.317993i | \(0.896991\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.99641 | + | 5.18993i | −0.127884 | + | 0.221501i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.15792 | 0.0919303 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.37832 | + | 2.38733i | −0.0586123 | + | 0.101519i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.36632 | + | 4.09859i | −0.100445 | + | 0.173976i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.592099 | + | 1.02555i | 0.0250880 | + | 0.0434538i | 0.878297 | − | 0.478116i | \(-0.158680\pi\) |
−0.853209 | + | 0.521570i | \(0.825347\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.6582 | − | 20.1926i | 0.493090 | − | 0.854057i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.4872 | −0.569432 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.1492 | −1.22849 | −0.614245 | − | 0.789115i | \(-0.710540\pi\) | ||||
−0.614245 | + | 0.789115i | \(0.710540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.32036 | + | 16.1433i | 0.392111 | + | 0.679155i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.436767 | − | 0.756503i | −0.0183425 | − | 0.0317701i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.105593 | − | 0.182893i | −0.00442670 | − | 0.00766727i | 0.863804 | − | 0.503829i | \(-0.168076\pi\) |
−0.868230 | + | 0.496161i | \(0.834742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.6012 | − | 20.0939i | −0.485495 | − | 0.840902i | 0.514366 | − | 0.857571i | \(-0.328027\pi\) |
−0.999861 | + | 0.0166686i | \(0.994694\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.01274 | + | 10.4144i | −0.251186 | + | 0.435067i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.10244 | + | 3.64153i | −0.0876778 | + | 0.151862i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.98263 | − | 6.89812i | −0.165799 | − | 0.287173i | 0.771140 | − | 0.636666i | \(-0.219687\pi\) |
−0.936939 | + | 0.349493i | \(0.886354\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.9520 | 0.912294 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.01035 | 0.166378 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.48878 | − | 16.4350i | −0.392985 | − | 0.680670i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.27391 | + | 2.20647i | −0.0526695 | + | 0.0912263i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.9774 | + | 29.4058i | −0.700734 | + | 1.21371i | 0.267476 | + | 0.963565i | \(0.413810\pi\) |
−0.968209 | + | 0.250142i | \(0.919523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.87106 | −0.159504 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.82749 | + | 15.2897i | 0.363114 | + | 0.628933i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.56903 | + | 6.18174i | −0.146563 | + | 0.253854i | −0.929955 | − | 0.367674i | \(-0.880154\pi\) |
0.783392 | + | 0.621528i | \(0.213488\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.37822 | 0.220486 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.39395 | + | 4.14645i | −0.0979780 | + | 0.169703i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.738992 | + | 1.27997i | 0.0301944 | + | 0.0522982i | 0.880728 | − | 0.473623i | \(-0.157054\pi\) |
−0.850533 | + | 0.525921i | \(0.823721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.3549 | − | 35.2556i | 0.830292 | − | 1.43811i | −0.0675147 | − | 0.997718i | \(-0.521507\pi\) |
0.897807 | − | 0.440390i | \(-0.145160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.38723 | + | 8.06694i | 0.0564923 | + | 0.328511i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.10062 | − | 5.37042i | 0.126058 | − | 0.218339i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.1173 | + | 17.5237i | 0.410649 | + | 0.711265i | 0.994961 | − | 0.100264i | \(-0.0319688\pi\) |
−0.584312 | + | 0.811529i | \(0.698635\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.282355 | + | 0.489053i | −0.0114416 | + | 0.0198174i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.6503 | 1.28043 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.2177 | − | 21.1617i | 0.493469 | − | 0.854714i | −0.506503 | − | 0.862238i | \(-0.669062\pi\) |
0.999972 | + | 0.00752486i | \(0.00239526\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.00304 | − | 6.93346i | −0.161418 | − | 0.279584i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.97216 | −0.320947 | −0.160473 | − | 0.987040i | \(-0.551302\pi\) | ||||
−0.160473 | + | 0.987040i | \(0.551302\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.20120 | + | 12.4728i | −0.289441 | + | 0.501326i | −0.973676 | − | 0.227935i | \(-0.926803\pi\) |
0.684236 | + | 0.729261i | \(0.260136\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.10244 | + | 3.64153i | −0.0843680 | + | 0.146130i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.34440 | + | 2.32857i | 0.0538623 | + | 0.0932922i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.31230 | −0.292025 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.5691 | − | 25.2344i | −0.580908 | − | 1.00616i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.54690 | − | 14.8037i | 0.340247 | − | 0.589325i | −0.644232 | − | 0.764830i | \(-0.722823\pi\) |
0.984478 | + | 0.175506i | \(0.0561561\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.86531 | − | 3.23081i | 0.0741395 | − | 0.128413i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.10885 | − | 15.7770i | −0.361474 | − | 0.626091i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.94527 | + | 13.7616i | 0.314803 | + | 0.545255i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.31716 | + | 9.20959i | 0.210344 | + | 0.364326i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.37426 | + | 14.5046i | 0.330763 | + | 0.572899i | 0.982662 | − | 0.185407i | \(-0.0593604\pi\) |
−0.651898 | + | 0.758306i | \(0.726027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9880 | 0.433324 | 0.216662 | − | 0.976247i | \(-0.430483\pi\) | ||||
0.216662 | + | 0.976247i | \(0.430483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.15156 | −0.360342 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.75088 | + | 3.03261i | −0.0688342 | + | 0.119224i | −0.898388 | − | 0.439202i | \(-0.855261\pi\) |
0.829554 | + | 0.558426i | \(0.188595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.99107 | − | 6.91274i | −0.156663 | − | 0.271349i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.506514 | − | 0.877308i | 0.0198518 | − | 0.0343844i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.0009 | + | 34.6426i | −0.782695 | + | 1.35567i | 0.147671 | + | 0.989037i | \(0.452822\pi\) |
−0.930366 | + | 0.366632i | \(0.880511\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.92110 | −0.270430 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.0239280 | + | 0.0414445i | −0.000933520 | + | 0.00161690i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.22357 | + | 15.9757i | 0.359299 | + | 0.622324i | 0.987844 | − | 0.155449i | \(-0.0496824\pi\) |
−0.628545 | + | 0.777773i | \(0.716349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.6127 | 1.85192 | 0.925961 | − | 0.377620i | \(-0.123258\pi\) | ||||
0.925961 | + | 0.377620i | \(0.123258\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.84324 | − | 13.5849i | −0.304606 | − | 0.527594i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.91588 | 0.113073 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.71831 | 0.105253 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.6541 | −0.721208 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.1279 | −0.506797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.55614 | 0.0599848 | 0.0299924 | − | 0.999550i | \(-0.490452\pi\) | ||||
0.0299924 | + | 0.999550i | \(0.490452\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.3586 | − | 33.5302i | −0.744013 | − | 1.28867i | −0.950654 | − | 0.310252i | \(-0.899587\pi\) |
0.206641 | − | 0.978417i | \(-0.433747\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.08914 | −0.118550 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.43267 | − | 14.6058i | −0.323141 | − | 0.559696i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.5183 | + | 32.0747i | −0.708583 | + | 1.22730i | 0.256799 | + | 0.966465i | \(0.417332\pi\) |
−0.965383 | + | 0.260838i | \(0.916001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.08824 | 0.117996 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.04145 | − | 6.99999i | 0.154191 | − | 0.267066i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.0360 | − | 19.1150i | 0.420439 | − | 0.728222i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3993 | − | 24.9404i | −0.547776 | − | 0.948776i | −0.998427 | − | 0.0560758i | \(-0.982141\pi\) |
0.450650 | − | 0.892701i | \(-0.351192\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.956786 | − | 1.65720i | 0.0363453 | − | 0.0629519i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.25892 | 0.0856857 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 49.2922 | 1.86707 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.70411 | − | 4.68365i | −0.102279 | − | 0.177152i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.38903 | + | 11.0661i | 0.241311 | + | 0.417962i | 0.961088 | − | 0.276243i | \(-0.0890894\pi\) |
−0.719777 | + | 0.694205i | \(0.755756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.89884 | − | 13.6812i | −0.297910 | − | 0.515996i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.21127 | − | 10.7582i | −0.233930 | − | 0.405178i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.27166 | + | 2.20257i | −0.0478255 | + | 0.0828363i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.87848 | − | 15.3780i | 0.333438 | − | 0.577532i | −0.649745 | − | 0.760152i | \(-0.725124\pi\) |
0.983184 | + | 0.182620i | \(0.0584578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.57787 | − | 2.73295i | −0.0591747 | − | 0.102494i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.87635 | −0.182621 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.58126 | −0.208727 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.54264 | − | 16.5283i | −0.356376 | − | 0.617262i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.8214 | − | 34.3317i | 0.739215 | − | 1.28036i | −0.213634 | − | 0.976914i | \(-0.568530\pi\) |
0.952849 | − | 0.303444i | \(-0.0981365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.98938 | − | 5.17775i | 0.111330 | − | 0.192830i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.37395 | 0.274240 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.323233 | − | 0.559856i | −0.0120046 | − | 0.0207925i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9401 | − | 29.3411i | 0.628274 | − | 1.08820i | −0.359624 | − | 0.933097i | \(-0.617095\pi\) |
0.987898 | − | 0.155106i | \(-0.0495718\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.1724 | − | 48.7960i | 1.04199 | − | 1.80478i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3172 | − | 29.9943i | −0.639625 | − | 1.10786i | −0.985515 | − | 0.169588i | \(-0.945756\pi\) |
0.345890 | − | 0.938275i | \(-0.387577\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.11847 | − | 5.40135i | 0.115026 | − | 0.199232i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.7846 | + | 11.4675i | −0.507760 | + | 0.422411i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.1097 | + | 17.5106i | −0.371893 | + | 0.644137i | −0.989857 | − | 0.142069i | \(-0.954624\pi\) |
0.617964 | + | 0.786206i | \(0.287958\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.25232 | − | 7.36524i | −0.156213 | − | 0.270569i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.1138 | + | 34.8381i | −0.737904 | + | 1.27809i | 0.215533 | + | 0.976496i | \(0.430851\pi\) |
−0.953437 | + | 0.301591i | \(0.902482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.7007 | 0.465319 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.29548 | + | 3.97588i | −0.0839870 | + | 0.145470i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.67261 | − | 8.09319i | −0.170733 | − | 0.295719i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.40388 | −0.233681 | −0.116840 | − | 0.993151i | \(-0.537277\pi\) | ||||
−0.116840 | + | 0.993151i | \(0.537277\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.20657 | + | 12.4821i | −0.262622 | + | 0.454874i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.02601 | + | 1.77710i | −0.0373403 | + | 0.0646754i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.9984 | + | 19.0498i | 0.399743 | + | 0.692375i | 0.993694 | − | 0.112126i | \(-0.0357661\pi\) |
−0.593951 | + | 0.804501i | \(0.702433\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.21124 | −0.334347 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.3840 | −0.775169 | −0.387584 | − | 0.921834i | \(-0.626690\pi\) | ||||
−0.387584 | + | 0.921834i | \(0.626690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.29514 | − | 3.97531i | −0.0830898 | − | 0.143916i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.07842 | + | 5.33199i | −0.111301 | + | 0.192778i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.64186 | − | 8.03993i | 0.167608 | − | 0.290305i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.0411 | + | 20.8559i | 0.434215 | + | 0.752082i | 0.997231 | − | 0.0743638i | \(-0.0236926\pi\) |
−0.563017 | + | 0.826446i | \(0.690359\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0017 | + | 19.0555i | 0.396217 | + | 0.686268i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.30251 | + | 7.45216i | 0.154750 | + | 0.268036i | 0.932968 | − | 0.359959i | \(-0.117209\pi\) |
−0.778218 | + | 0.627995i | \(0.783876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.579844 | + | 1.00432i | 0.0208286 | + | 0.0360762i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.13413 | 0.148311 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.7244 | 0.957503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6478 | + | 20.1746i | −0.416792 | + | 0.721904i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.323233 | − | 0.559856i | −0.0115514 | − | 0.0200076i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.88957 | + | 3.27283i | −0.0674416 | + | 0.116812i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.89857 | + | 11.9487i | −0.245907 | + | 0.425924i | −0.962386 | − | 0.271685i | \(-0.912419\pi\) |
0.716479 | + | 0.697609i | \(0.245753\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.51723 | −0.196419 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.14166 | − | 14.1018i | 0.289484 | − | 0.501401i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.63428 | − | 13.2230i | −0.271101 | − | 0.469561i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.66314 | −0.307250 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.03228 | + | 6.98411i | 0.142831 | + | 0.247390i | 0.928561 | − | 0.371179i | \(-0.121046\pi\) |
−0.785731 | + | 0.618568i | \(0.787713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.4836 | 2.70580 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.07807 | −0.108758 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.104834 | −0.00369950 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.67311 | 0.129460 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.05203 | −0.142638 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.70801 | 0.130367 | 0.0651834 | − | 0.997873i | \(-0.479237\pi\) | ||||
0.0651834 | + | 0.997873i | \(0.479237\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.14352 | + | 1.98064i | 0.0401545 | + | 0.0695497i | 0.885404 | − | 0.464822i | \(-0.153882\pi\) |
−0.845250 | + | 0.534372i | \(0.820548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.3639 | 0.784337 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.92924 | + | 13.7338i | 0.277749 | + | 0.481075i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.2740 | − | 26.4554i | 0.534371 | − | 0.925558i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.22560 | 0.0777688 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2218 | − | 43.6854i | 0.880245 | − | 1.52463i | 0.0291776 | − | 0.999574i | \(-0.490711\pi\) |
0.851068 | − | 0.525056i | \(-0.175956\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.17792 | − | 3.77226i | 0.0759174 | − | 0.131493i | −0.825567 | − | 0.564303i | \(-0.809145\pi\) |
0.901485 | + | 0.432811i | \(0.142478\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.09530 | + | 1.89712i | 0.0381336 | + | 0.0660493i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.15215 | − | 10.6558i | 0.213931 | − | 0.370540i | −0.739010 | − | 0.673694i | \(-0.764706\pi\) |
0.952941 | + | 0.303155i | \(0.0980398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.4404 | −1.68241 | −0.841203 | − | 0.540720i | \(-0.818152\pi\) | ||||
−0.841203 | + | 0.540720i | \(0.818152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.341518 | −0.0118471 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.1999 | + | 33.2553i | 0.665238 | + | 1.15223i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.55406 | + | 16.5481i | 0.330632 | + | 0.572671i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.579844 | + | 1.00432i | 0.0200423 | + | 0.0347144i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0058 | − | 34.6511i | −0.690678 | − | 1.19629i | −0.971616 | − | 0.236564i | \(-0.923979\pi\) |
0.280938 | − | 0.959726i | \(-0.409354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2910 | − | 24.7528i | 0.492795 | − | 0.853545i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.37905 | + | 11.0488i | −0.219706 | + | 0.380542i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.25433 | + | 5.63666i | 0.111952 | + | 0.193907i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.41699 | −0.186130 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.8010 | 0.645249 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.95011 | − | 17.2341i | −0.341085 | − | 0.590777i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.94990 | + | 15.5017i | −0.306439 | + | 0.530767i | −0.977581 | − | 0.210561i | \(-0.932471\pi\) |
0.671142 | + | 0.741329i | \(0.265804\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.66901 | + | 2.89081i | −0.0570790 | + | 0.0988636i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.32144 | 0.0792990 | 0.0396495 | − | 0.999214i | \(-0.487376\pi\) | ||||
0.0396495 | + | 0.999214i | \(0.487376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.11931 | − | 10.5989i | −0.208788 | − | 0.361631i | 0.742545 | − | 0.669796i | \(-0.233619\pi\) |
−0.951333 | + | 0.308165i | \(0.900285\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.49679 | + | 6.05662i | −0.119170 | + | 0.206409i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.5235 | −1.41348 | −0.706738 | − | 0.707476i | \(-0.749834\pi\) | ||||
−0.706738 | + | 0.707476i | \(0.749834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.12739 | + | 7.14884i | −0.140335 | + | 0.243068i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.4534 | − | 18.1058i | −0.355016 | − | 0.614905i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.45649 | − | 5.98682i | 0.117254 | − | 0.203089i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.5667 | − | 7.21565i | −0.662991 | − | 0.244493i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.76819 | − | 3.06259i | 0.0598440 | − | 0.103653i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.436767 | − | 0.756503i | −0.0147654 | − | 0.0255745i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.09708 | − | 15.7566i | 0.307187 | − | 0.532063i | −0.670559 | − | 0.741856i | \(-0.733946\pi\) |
0.977746 | + | 0.209793i | \(0.0672791\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.9116 | −0.604144 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.77004 | + | 8.26195i | −0.160707 | + | 0.278352i | −0.935122 | − | 0.354325i | \(-0.884711\pi\) |
0.774416 | + | 0.632677i | \(0.218044\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.9079 | − | 41.4098i | −0.804566 | − | 1.39355i | −0.916584 | − | 0.399843i | \(-0.869065\pi\) |
0.112017 | − | 0.993706i | \(-0.464269\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.64380 | −0.122485 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.6204 | − | 40.9117i | 0.793095 | − | 1.37368i | −0.130947 | − | 0.991389i | \(-0.541802\pi\) |
0.924042 | − | 0.382291i | \(-0.124865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.95689 | + | 13.7817i | −0.266866 | + | 0.462225i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.09530 | + | 1.89712i | 0.0366941 | + | 0.0635560i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.4667 | 1.38763 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.75612 | −0.0587007 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.35662 | − | 9.27793i | −0.178852 | − | 0.309781i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.374849 | − | 0.649258i | 0.0125019 | − | 0.0216540i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.6688 | − | 46.1918i | 0.888467 | − | 1.53887i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.99710 | + | 6.92318i | 0.133015 | + | 0.230389i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.58843 | − | 2.75125i | −0.0528014 | − | 0.0914546i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.5111 | − | 30.3302i | −0.581448 | − | 1.00710i | −0.995308 | − | 0.0967570i | \(-0.969153\pi\) |
0.413860 | − | 0.910341i | \(-0.364180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.45576 | − | 2.52145i | −0.0482845 | − | 0.0836312i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.8606 | −1.35377 | −0.676886 | − | 0.736088i | \(-0.736671\pi\) | ||||
−0.676886 | + | 0.736088i | \(0.736671\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0570 | −0.332837 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.99641 | + | 5.18993i | −0.0990581 | + | 0.171574i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.02291 | + | 5.23583i | 0.0998252 | + | 0.172902i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.3055 | + | 35.1701i | −0.669816 | + | 1.16016i | 0.308139 | + | 0.951341i | \(0.400294\pi\) |
−0.977955 | + | 0.208814i | \(0.933040\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.6094 | − | 20.1080i | 0.382541 | − | 0.662581i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.0942 | −0.891818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.36632 | + | 4.09859i | −0.0778043 | + | 0.134761i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.42216 | + | 5.92736i | 0.112399 | + | 0.194680i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.4723 | 1.16381 | 0.581905 | − | 0.813257i | \(-0.302308\pi\) | ||||
0.581905 | + | 0.813257i | \(0.302308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.4095 | + | 18.0298i | 0.341158 | + | 0.590903i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.428849 | −0.0140399 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.4872 | −0.441080 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.2336 | 0.661002 | 0.330501 | − | 0.943806i | \(-0.392782\pi\) | ||||
0.330501 | + | 0.943806i | \(0.392782\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.4449 | 0.862996 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.2172 | 0.561264 | 0.280632 | − | 0.959815i | \(-0.409456\pi\) | ||||
0.280632 | + | 0.959815i | \(0.409456\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.6646 | 1.09627 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.436767 | − | 0.756503i | −0.0142080 | − | 0.0246090i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.7168 | −1.61558 | −0.807789 | − | 0.589471i | \(-0.799336\pi\) | ||||
−0.807789 | + | 0.589471i | \(0.799336\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0609640 | − | 0.105593i | −0.00197898 | − | 0.00342769i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.5428 | − | 23.4567i | 0.439154 | − | 0.760637i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.3052 | −0.981682 | −0.490841 | − | 0.871249i | \(-0.663310\pi\) | ||||
−0.490841 | + | 0.871249i | \(0.663310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.01274 | + | 10.4144i | −0.194568 | + | 0.337001i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.708077 | − | 1.22643i | 0.0228889 | − | 0.0396447i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.34884 | − | 2.33626i | −0.0435564 | − | 0.0754418i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8276 | − | 25.6821i | 0.478308 | − | 0.828455i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.6982 | 0.344743 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.9520 | 0.706660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.0317 | − | 36.4280i | −0.676334 | − | 1.17145i | −0.976077 | − | 0.217425i | \(-0.930234\pi\) |
0.299743 | − | 0.954020i | \(-0.403099\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.2758 | − | 17.7983i | −0.330108 | − | 0.571763i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.3806 | + | 35.3003i | 0.654045 | + | 1.13284i | 0.982132 | + | 0.188192i | \(0.0602628\pi\) |
−0.328087 | + | 0.944648i | \(0.606404\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.986622 | − | 1.70888i | −0.0316296 | − | 0.0547842i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.27391 | + | 2.20647i | −0.0407976 | + | 0.0706636i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.1615 | + | 45.3131i | −0.836981 | + | 1.44969i | 0.0554256 | + | 0.998463i | \(0.482348\pi\) |
−0.892407 | + | 0.451231i | \(0.850985\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.37143 | − | 5.83948i | −0.107751 | − | 0.186631i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.25484 | 0.167774 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.7056 | 1.13883 | 0.569416 | − | 0.822049i | \(-0.307169\pi\) | ||||
0.569416 | + | 0.822049i | \(0.307169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.82749 | + | 15.2897i | 0.281267 | + | 0.487169i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.42576 | + | 9.39768i | −0.172704 | + | 0.299132i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.2406 | − | 33.3257i | 0.611815 | − | 1.05969i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.6689 | −0.751867 | −0.375933 | − | 0.926647i | \(-0.622678\pi\) | ||||
−0.375933 | + | 0.926647i | \(0.622678\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.07232 | − | 7.05347i | −0.129231 | − | 0.223835i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.39395 | + | 4.14645i | −0.0758935 | + | 0.131451i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.6861 | 1.32021 | 0.660106 | − | 0.751173i | \(-0.270511\pi\) | ||||
0.660106 | + | 0.751173i | \(0.270511\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.36632 | + | 4.09859i | −0.0748672 | + | 0.129674i |
(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.q.m.3781.5 | yes | 24 | |
67.37 | even | 3 | inner | 4020.2.q.m.841.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.m.841.5 | ✓ | 24 | 67.37 | even | 3 | inner | |
4020.2.q.m.3781.5 | yes | 24 | 1.1 | even | 1 | trivial |