Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(65,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bn (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.449 |
Dual form | 912.2.bn.f.65.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 1.73205i | 1.34164 | − | 0.774597i | 0.354593 | − | 0.935021i | \(-0.384620\pi\) |
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50000 | + | 2.59808i | 1.24808 | + | 0.720577i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000 | − | 5.19615i | 0.774597 | − | 1.34164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | + | 1.73205i | −0.727607 | + | 0.420084i | −0.817546 | − | 0.575863i | \(-0.804666\pi\) |
0.0899392 | + | 0.995947i | \(0.471333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | + | 0.866025i | −0.327327 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.50000 | − | 6.06218i | 0.700000 | − | 1.21244i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | + | 5.19615i | 0.522233 | + | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00000 | + | 1.73205i | −0.507093 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.19615i | − | 0.854242i | −0.904194 | − | 0.427121i | \(-0.859528\pi\) | ||
0.904194 | − | 0.427121i | \(-0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.00000 | 1.44115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | − | 10.3923i | −0.937043 | − | 1.62301i | −0.770950 | − | 0.636895i | \(-0.780218\pi\) |
−0.166092 | − | 0.986110i | \(-0.553115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 10.3923i | − | 1.54919i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | − | 3.46410i | −0.875190 | − | 0.505291i | −0.00612051 | − | 0.999981i | \(-0.501948\pi\) |
−0.869069 | + | 0.494690i | \(0.835282\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | + | 5.19615i | −0.420084 | + | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | + | 10.3923i | −0.824163 | + | 1.42749i | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | + | 10.3923i | 0.809040 | + | 1.40130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.50000 | − | 6.06218i | 0.596040 | − | 0.802955i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.50000 | + | 2.59808i | −0.188982 | + | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.0000 | 2.23263 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.50000 | − | 4.33013i | −0.916271 | − | 0.529009i | −0.0338274 | − | 0.999428i | \(-0.510770\pi\) |
−0.882443 | + | 0.470418i | \(0.844103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.50000 | + | 6.06218i | 0.409644 | + | 0.709524i | 0.994850 | − | 0.101361i | \(-0.0323196\pi\) |
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 12.1244i | − | 1.40000i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.46410i | − | 0.394771i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.50000 | + | 2.59808i | −0.506290 | + | 0.292306i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.3923i | − | 1.14070i | −0.821401 | − | 0.570352i | \(-0.806807\pi\) | ||
0.821401 | − | 0.570352i | \(-0.193193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | + | 10.3923i | −0.650791 | + | 1.12720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3923i | 1.11417i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.50000 | − | 2.59808i | −0.471728 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.00000 | − | 12.1244i | 0.923381 | − | 1.24393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | − | 3.46410i | 0.609208 | − | 0.351726i | −0.163448 | − | 0.986552i | \(-0.552261\pi\) |
0.772655 | + | 0.634826i | \(0.218928\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.00000 | + | 5.19615i | 0.904534 | + | 0.522233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | + | 5.19615i | 0.895533 | + | 0.517036i | 0.875748 | − | 0.482768i | \(-0.160368\pi\) |
0.0197851 | + | 0.999804i | \(0.493702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.66025i | 0.853320i | 0.904412 | + | 0.426660i | \(0.140310\pi\) | ||||
−0.904412 | + | 0.426660i | \(0.859690\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.00000 | + | 5.19615i | −0.292770 | + | 0.507093i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.0000 | 1.74013 | 0.870063 | − | 0.492941i | \(-0.164078\pi\) | ||||
0.870063 | + | 0.492941i | \(0.164078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.50000 | − | 7.79423i | −0.427121 | − | 0.739795i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.5000 | − | 7.79423i | 1.24808 | − | 0.720577i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | − | 1.73205i | 0.275010 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.0000 | − | 10.3923i | −1.62301 | − | 0.937043i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | + | 5.19615i | 0.798621 | + | 0.461084i | 0.842989 | − | 0.537931i | \(-0.180794\pi\) |
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.50000 | − | 0.866025i | −0.132068 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | + | 1.73205i | −0.262111 | + | 0.151330i | −0.625297 | − | 0.780387i | \(-0.715022\pi\) |
0.363186 | + | 0.931717i | \(0.381689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 1.73205i | −0.346844 | + | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.00000 | − | 15.5885i | −0.774597 | − | 1.34164i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | − | 1.73205i | −0.256307 | − | 0.147979i | 0.366342 | − | 0.930480i | \(-0.380610\pi\) |
−0.622649 | + | 0.782501i | \(0.713943\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.0000 | −1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.00000 | + | 15.5885i | −0.752618 | + | 1.30357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.7846i | 1.72607i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.00000 | + | 5.19615i | −0.742307 | + | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0000 | − | 8.66025i | 1.22885 | − | 0.709476i | 0.262059 | − | 0.965052i | \(-0.415599\pi\) |
0.966789 | + | 0.255576i | \(0.0822652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.46410i | 0.281905i | 0.990016 | + | 0.140952i | \(0.0450164\pi\) | ||||
−0.990016 | + | 0.140952i | \(0.954984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.3923i | 0.840168i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00000 | − | 5.19615i | −0.240966 | − | 0.417365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.50000 | − | 6.06218i | −0.279330 | − | 0.483814i | 0.691888 | − | 0.722005i | \(-0.256779\pi\) |
−0.971219 | + | 0.238190i | \(0.923446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.7846i | 1.64833i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.0000 | + | 10.3923i | 1.40130 | + | 0.809040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | + | 10.3923i | −0.464294 | + | 0.804181i | −0.999169 | − | 0.0407502i | \(-0.987025\pi\) |
0.534875 | + | 0.844931i | \(0.320359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | + | 12.1244i | 0.538462 | + | 0.932643i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | − | 12.9904i | 0.114708 | − | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.50000 | + | 6.06218i | −0.264575 | + | 0.458258i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | − | 3.46410i | −0.445976 | − | 0.257485i | 0.260153 | − | 0.965567i | \(-0.416227\pi\) |
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.1244i | 0.896258i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.00000 | − | 15.5885i | −0.661693 | − | 1.14609i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | − | 10.3923i | −0.438763 | − | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.19615i | 0.377964i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3205i | 1.25327i | 0.779314 | + | 0.626634i | \(0.215568\pi\) | ||||
−0.779314 | + | 0.626634i | \(0.784432\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5000 | + | 6.06218i | −0.755807 | + | 0.436365i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 27.0000 | − | 15.5885i | 1.93351 | − | 1.11631i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5000 | + | 21.6506i | −0.886102 | + | 1.53477i | −0.0416556 | + | 0.999132i | \(0.513263\pi\) |
−0.844446 | + | 0.535641i | \(0.820070\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.0000 | −1.05802 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000 | − | 5.19615i | 0.210559 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −36.0000 | − | 20.7846i | −2.51435 | − | 1.45166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | + | 13.8564i | 0.415029 | + | 0.958468i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5000 | − | 11.2583i | 1.34244 | − | 0.775055i | 0.355271 | − | 0.934763i | \(-0.384389\pi\) |
0.987164 | + | 0.159708i | \(0.0510552\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.00000 | + | 5.19615i | 0.616670 | + | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | − | 1.73205i | −0.204598 | − | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.73205i | 0.117579i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5000 | + | 6.06218i | 0.709524 | + | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0000 | −1.21081 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.5000 | + | 9.52628i | −1.10492 | + | 0.637927i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) |
−0.167412 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.5000 | − | 18.1865i | −0.700000 | − | 1.21244i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.0000 | −1.19470 | −0.597351 | − | 0.801980i | \(-0.703780\pi\) | ||||
−0.597351 | + | 0.801980i | \(0.703780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | 0.859064 | 0.429532 | − | 0.903052i | \(-0.358679\pi\) | ||||
0.429532 | + | 0.903052i | \(0.358679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 5.19615i | −0.197386 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0000 | − | 8.66025i | 0.982683 | − | 0.567352i | 0.0796037 | − | 0.996827i | \(-0.474635\pi\) |
0.903079 | + | 0.429474i | \(0.141301\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0000 | −1.56559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.50000 | + | 7.79423i | −0.292306 | + | 0.506290i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 24.2487i | − | 1.56852i | −0.620433 | − | 0.784259i | \(-0.713043\pi\) | ||
0.620433 | − | 0.784259i | \(-0.286957\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.50000 | − | 0.866025i | −0.0966235 | − | 0.0557856i | 0.450910 | − | 0.892570i | \(-0.351100\pi\) |
−0.547533 | + | 0.836784i | \(0.684433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.0000 | + | 10.3923i | −1.14998 | + | 0.663940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.5000 | + | 2.59808i | 1.43164 | + | 0.165312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.00000 | − | 15.5885i | −0.570352 | − | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.00000 | + | 3.46410i | 0.378717 | + | 0.218652i | 0.677260 | − | 0.735744i | \(-0.263167\pi\) |
−0.298543 | + | 0.954396i | \(0.596501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.7846i | 1.30158i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.19615i | 0.322873i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | + | 15.5885i | 0.557086 | + | 0.964901i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.0000 | − | 12.1244i | 1.29492 | − | 0.747620i | 0.315394 | − | 0.948961i | \(-0.397863\pi\) |
0.979521 | + | 0.201341i | \(0.0645299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.5692i | 2.55358i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | + | 6.92820i | 0.242983 | + | 0.420858i | 0.961563 | − | 0.274586i | \(-0.0885408\pi\) |
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.00000 | −0.544705 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.0000 | + | 12.1244i | 1.26635 | + | 0.731126i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.50000 | − | 2.59808i | −0.269408 | − | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | + | 5.19615i | −0.178965 | + | 0.309976i | −0.941526 | − | 0.336939i | \(-0.890608\pi\) |
0.762561 | + | 0.646916i | \(0.223942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | − | 24.2487i | −0.832214 | − | 1.44144i | −0.896279 | − | 0.443491i | \(-0.853740\pi\) |
0.0640654 | − | 0.997946i | \(-0.479593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.00000 | − | 25.9808i | 0.177705 | − | 1.53897i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | + | 10.3923i | 0.354169 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.50000 | + | 4.33013i | −0.147059 | + | 0.254713i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 10.3923i | 0.351726 | − | 0.609208i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.0000 | 1.04447 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | + | 0.866025i | 0.0288195 | + | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.0000 | 1.03407 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.2487i | 1.38848i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.0000 | + | 15.5885i | −1.54097 | + | 0.889680i | −0.542194 | + | 0.840254i | \(0.682406\pi\) |
−0.998778 | + | 0.0494267i | \(0.984261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.50000 | + | 12.9904i | 0.426660 | + | 0.738997i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 13.8564i | − | 0.785725i | −0.919597 | − | 0.392862i | \(-0.871485\pi\) | ||
0.919597 | − | 0.392862i | \(-0.128515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.00000 | − | 12.1244i | 0.395663 | − | 0.685309i | −0.597522 | − | 0.801852i | \(-0.703848\pi\) |
0.993186 | + | 0.116543i | \(0.0371814\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.3923i | 0.585540i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | − | 5.19615i | 0.168497 | − | 0.291845i | −0.769395 | − | 0.638774i | \(-0.779442\pi\) |
0.937892 | + | 0.346929i | \(0.112775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | − | 10.3923i | −1.00781 | − | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.0000 | − | 15.5885i | 1.50699 | − | 0.870063i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.00000 | + | 12.1244i | −0.500773 | + | 0.674617i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.5000 | − | 18.1865i | 1.74731 | − | 1.00881i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.00000 | + | 3.46410i | 0.330791 | + | 0.190982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.19615i | 0.285606i | 0.989751 | + | 0.142803i | \(0.0456116\pi\) | ||||
−0.989751 | + | 0.142803i | \(0.954388\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.5000 | − | 7.79423i | −0.739795 | − | 0.427121i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.0000 | −1.63908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.50000 | − | 0.866025i | 0.0817102 | − | 0.0471754i | −0.458588 | − | 0.888649i | \(-0.651645\pi\) |
0.540298 | + | 0.841473i | \(0.318311\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0000 | + | 10.3923i | −0.977626 | + | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.0000 | + | 12.1244i | −1.12734 | + | 0.650870i | −0.943264 | − | 0.332043i | \(-0.892262\pi\) |
−0.184075 | + | 0.982912i | \(0.558929\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.00000 | −0.374701 | −0.187351 | − | 0.982293i | \(-0.559990\pi\) | ||||
−0.187351 | + | 0.982293i | \(0.559990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.5000 | − | 23.3827i | 0.720577 | − | 1.24808i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.3923i | − | 0.553127i | −0.960996 | − | 0.276563i | \(-0.910804\pi\) | ||
0.960996 | − | 0.276563i | \(-0.0891955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | + | 10.3923i | 0.955341 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.00000 | − | 5.19615i | 0.158777 | − | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | − | 3.46410i | 0.316668 | − | 0.182828i | −0.333238 | − | 0.942843i | \(-0.608141\pi\) |
0.649906 | + | 0.760014i | \(0.274808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.50000 | + | 0.866025i | −0.0787296 | + | 0.0454545i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.0000 | + | 12.1244i | 1.09919 | + | 0.634618i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.50000 | − | 14.7224i | 0.443696 | − | 0.768505i | −0.554264 | − | 0.832341i | \(-0.687000\pi\) |
0.997960 | + | 0.0638362i | \(0.0203335\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.0000 | −1.87409 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | − | 10.3923i | 0.311504 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.92820i | 0.358729i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) | ||||
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | − | 10.3923i | −0.309839 | − | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.0000 | + | 15.5885i | −1.39057 | + | 0.802846i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1244i | 0.622786i | 0.950281 | + | 0.311393i | \(0.100796\pi\) | ||||
−0.950281 | + | 0.311393i | \(0.899204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0000 | 0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.00000 | − | 5.19615i | −0.153293 | − | 0.265511i | 0.779143 | − | 0.626846i | \(-0.215654\pi\) |
−0.932436 | + | 0.361335i | \(0.882321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 10.3923i | −0.305788 | − | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | −0.152499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.0000 | − | 13.8564i | −1.21685 | − | 0.702548i | −0.252606 | − | 0.967569i | \(-0.581288\pi\) |
−0.964242 | + | 0.265022i | \(0.914621\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.00000 | + | 5.19615i | −0.151330 | + | 0.262111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.00000 | + | 15.5885i | −0.452839 | + | 0.784340i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.5000 | − | 25.1147i | −0.727734 | − | 1.26047i | −0.957839 | − | 0.287307i | \(-0.907240\pi\) |
0.230105 | − | 0.973166i | \(-0.426093\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.50000 | + | 6.06218i | −0.225282 | + | 0.303488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | − | 20.7846i | −0.599251 | − | 1.03793i | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.50000 | − | 7.79423i | 0.224161 | − | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.0000 | − | 15.5885i | −1.34164 | − | 0.774597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.0000 | 0.892227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.0000 | + | 17.3205i | 1.48340 | + | 0.856444i | 0.999822 | − | 0.0188549i | \(-0.00600205\pi\) |
0.483582 | + | 0.875299i | \(0.339335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | − | 31.1769i | −0.883585 | − | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.66025i | 0.424094i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 10.3923i | − | 0.507697i | −0.967244 | − | 0.253849i | \(-0.918303\pi\) | ||
0.967244 | − | 0.253849i | \(-0.0816965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0000 | − | 6.92820i | 0.584844 | − | 0.337660i | −0.178212 | − | 0.983992i | \(-0.557031\pi\) |
0.763056 | + | 0.646332i | \(0.223698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.0000 | + | 10.3923i | −0.875190 | + | 0.505291i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.2487i | 1.17624i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.50000 | − | 6.06218i | 0.169377 | − | 0.293369i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.1769i | 1.50524i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | − | 10.3923i | 0.289010 | − | 0.500580i | −0.684564 | − | 0.728953i | \(-0.740007\pi\) |
0.973574 | + | 0.228373i | \(0.0733406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.5000 | − | 9.52628i | −0.792939 | − | 0.457804i | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) |
−0.840996 | + | 0.541041i | \(0.818030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.0000 | + | 31.1769i | 0.863034 | + | 1.49482i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.50000 | − | 4.33013i | 0.357955 | − | 0.206666i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.668184 | + | 0.743996i | \(0.267072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.00000 | + | 15.5885i | −0.428571 | + | 0.742307i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.0000 | + | 12.1244i | 0.997740 | + | 0.576046i | 0.907579 | − | 0.419882i | \(-0.137928\pi\) |
0.0901612 | + | 0.995927i | \(0.471262\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.0000 | − | 25.9808i | 0.709476 | − | 1.22885i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0000 | − | 20.7846i | 1.69517 | − | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.00000 | + | 5.19615i | 0.140952 | + | 0.244137i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.0000 | −0.843853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0000 | 0.795226 | 0.397613 | − | 0.917553i | \(-0.369839\pi\) | ||||
0.397613 | + | 0.917553i | \(0.369839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.00000 | + | 15.5885i | 0.420084 | + | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | − | 3.46410i | 0.279448 | − | 0.161339i | −0.353726 | − | 0.935349i | \(-0.615085\pi\) |
0.633173 | + | 0.774010i | \(0.281752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0000 | 0.883005 | 0.441502 | − | 0.897260i | \(-0.354446\pi\) | ||||
0.441502 | + | 0.897260i | \(0.354446\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.00000 | − | 5.19615i | −0.417365 | − | 0.240966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 27.7128i | − | 1.28240i | −0.767375 | − | 0.641198i | \(-0.778438\pi\) | ||
0.767375 | − | 0.641198i | \(-0.221562\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.50000 | + | 4.33013i | 0.346318 | + | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5000 | − | 6.06218i | −0.483814 | − | 0.279330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 1.73205i | 0.137940 | − | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.50000 | − | 30.3109i | 0.160591 | − | 1.39076i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000 | + | 31.1769i | 0.824163 | + | 1.42749i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.00000 | − | 5.19615i | −0.411220 | − | 0.237418i | 0.280094 | − | 0.959973i | \(-0.409635\pi\) |
−0.691314 | + | 0.722554i | \(0.742968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.5000 | − | 23.3827i | 0.615547 | − | 1.06616i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0000 | − | 20.7846i | 0.544892 | − | 0.943781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.46410i | 0.156973i | 0.996915 | + | 0.0784867i | \(0.0250088\pi\) | ||||
−0.996915 | + | 0.0784867i | \(0.974991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.5000 | − | 9.52628i | 0.746156 | − | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.00000 | − | 5.19615i | 0.406164 | − | 0.234499i | −0.282976 | − | 0.959127i | \(-0.591322\pi\) |
0.689140 | + | 0.724628i | \(0.257988\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 20.7846i | − | 0.936092i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 36.0000 | 1.61808 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00000 | − | 5.19615i | −0.134568 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5000 | + | 26.8468i | 0.693875 | + | 1.20183i | 0.970558 | + | 0.240866i | \(0.0774314\pi\) |
−0.276683 | + | 0.960961i | \(0.589235\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.7846i | 0.928588i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.0000 | + | 15.5885i | 1.20387 | + | 0.695055i | 0.961414 | − | 0.275107i | \(-0.0887134\pi\) |
0.242457 | + | 0.970162i | \(0.422047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.0000 | + | 12.1244i | 0.932643 | + | 0.538462i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.50000 | − | 6.06218i | −0.154831 | − | 0.268175i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.00000 | − | 20.7846i | −0.397360 | − | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.0000 | + | 25.9808i | 0.660979 | + | 1.14485i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000 | − | 20.7846i | 0.527759 | − | 0.914106i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000 | + | 5.19615i | 0.395056 | + | 0.228086i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.50000 | + | 2.59808i | 0.196771 | + | 0.113606i | 0.595149 | − | 0.803616i | \(-0.297093\pi\) |
−0.398377 | + | 0.917222i | \(0.630427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.1244i | 0.529150i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 62.3538i | − | 2.70084i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 54.0000 | − | 31.1769i | 2.33462 | − | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.0000 | + | 10.3923i | −0.776757 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 20.7846i | − | 0.895257i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.50000 | − | 11.2583i | 0.279457 | − | 0.484033i | −0.691793 | − | 0.722096i | \(-0.743179\pi\) |
0.971250 | + | 0.238062i | \(0.0765123\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.0000 | −0.514969 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.5000 | − | 12.9904i | −0.962031 | − | 0.555429i | −0.0652331 | − | 0.997870i | \(-0.520779\pi\) |
−0.896797 | + | 0.442441i | \(0.854112\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5000 | + | 18.1865i | 0.448129 | + | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | + | 25.9808i | −0.127804 | + | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.50000 | − | 2.59808i | 0.191359 | − | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.0000 | − | 15.5885i | −1.14609 | − | 0.661693i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.00000 | − | 1.73205i | −0.127114 | − | 0.0733893i | 0.435095 | − | 0.900385i | \(-0.356715\pi\) |
−0.562209 | + | 0.826995i | \(0.690048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.19615i | − | 0.219774i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | − | 10.3923i | −0.759961 | − | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | −0.758610 | −0.379305 | − | 0.925272i | \(-0.623837\pi\) | ||||
−0.379305 | + | 0.925272i | \(0.623837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.0000 | + | 20.7846i | −1.51453 | + | 0.874415i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.50000 | + | 7.79423i | 0.188982 | + | 0.327327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.00000 | −0.209243 | −0.104622 | − | 0.994512i | \(-0.533363\pi\) | ||||
−0.104622 | + | 0.994512i | \(0.533363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.0000 | + | 25.9808i | 0.626634 | + | 1.08536i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.0000 | −1.58196 | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.5000 | + | 18.1865i | −0.436365 | + | 0.755807i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3923i | 0.431145i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0000 | − | 20.7846i | −1.49097 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.0000 | − | 46.7654i | 1.11631 | − | 1.93351i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.00000 | + | 3.46410i | −0.247647 | + | 0.142979i | −0.618686 | − | 0.785638i | \(-0.712335\pi\) |
0.371040 | + | 0.928617i | \(0.379001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00000 | − | 6.92820i | −0.123613 | − | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.0000 | − | 20.7846i | −1.47834 | − | 0.853522i | −0.478643 | − | 0.878010i | \(-0.658871\pi\) |
−0.999700 | + | 0.0244882i | \(0.992204\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | − | 10.3923i | 0.245976 | − | 0.426043i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 43.3013i | 1.77220i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.0000 | + | 25.9808i | −0.612883 | + | 1.06155i | 0.377869 | + | 0.925859i | \(0.376657\pi\) |
−0.990752 | + | 0.135686i | \(0.956676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.73205i | − | 0.0706518i | −0.999376 | − | 0.0353259i | \(-0.988753\pi\) | ||
0.999376 | − | 0.0353259i | \(-0.0112469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.5000 | + | 12.9904i | −0.916271 | + | 0.529009i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.00000 | + | 1.73205i | −0.121967 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9090i | 1.33573i | 0.744281 | + | 0.667867i | \(0.232792\pi\) | ||||
−0.744281 | + | 0.667867i | \(0.767208\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 10.3923i | − | 0.421117i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.0000 | − | 31.1769i | −0.728202 | − | 1.26128i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0000 | + | 32.9090i | 0.767403 | + | 1.32918i | 0.938967 | + | 0.344008i | \(0.111785\pi\) |
−0.171564 | + | 0.985173i | \(0.554882\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −72.0000 | −2.90332 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.0000 | + | 19.0526i | 1.32853 | + | 0.767027i | 0.985072 | − | 0.172141i | \(-0.0550685\pi\) |
0.343458 | + | 0.939168i | \(0.388402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0000 | 0.683288 | 0.341644 | − | 0.939829i | \(-0.389016\pi\) | ||||
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.0000 | + | 15.5885i | 0.838659 | + | 0.622543i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.00000 | + | 15.5885i | 0.358854 | + | 0.621552i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.50000 | − | 11.2583i | 0.258761 | − | 0.448187i | −0.707149 | − | 0.707064i | \(-0.750019\pi\) |
0.965910 | + | 0.258877i | \(0.0833525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.5000 | − | 33.7750i | 0.775055 | − | 1.34244i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.0000 | 1.42862 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.0000 | − | 15.5885i | −1.06978 | − | 0.617637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.0000 | 0.712069 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0000 | + | 20.7846i | 0.473972 | + | 0.820943i | 0.999556 | − | 0.0297987i | \(-0.00948663\pi\) |
−0.525584 | + | 0.850741i | \(0.676153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.50000 | + | 4.33013i | 0.0985904 | + | 0.170764i | 0.911101 | − | 0.412182i | \(-0.135233\pi\) |
−0.812511 | + | 0.582946i | \(0.801900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 38.1051i | − | 1.49807i | −0.662532 | − | 0.749033i | \(-0.730518\pi\) | ||
0.662532 | − | 0.749033i | \(-0.269482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.50000 | + | 2.59808i | 0.0587896 | + | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 17.3205i | − | 0.677804i | −0.940822 | − | 0.338902i | \(-0.889945\pi\) | ||
0.940822 | − | 0.338902i | \(-0.110055\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.00000 | + | 10.3923i | −0.234439 | + | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.0000 | 0.819288 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.00000 | − | 5.19615i | 0.116863 | − | 0.202413i | −0.801660 | − | 0.597781i | \(-0.796049\pi\) |
0.918523 | + | 0.395367i | \(0.129383\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0000 | − | 6.92820i | −0.466746 | − | 0.269476i | 0.248131 | − | 0.968727i | \(-0.420184\pi\) |
−0.714877 | + | 0.699251i | \(0.753517\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.0000 | + | 15.5885i | −1.04859 | + | 0.605406i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.00000 | + | 12.1244i | −0.349005 | + | 0.470162i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.5000 | + | 28.5788i | −0.637927 | + | 1.10492i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.0000 | − | 12.1244i | −0.810696 | − | 0.468056i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.1244i | 0.467360i | 0.972314 | + | 0.233680i | \(0.0750767\pi\) | ||||
−0.972314 | + | 0.233680i | \(0.924923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −31.5000 | − | 18.1865i | −1.21244 | − | 0.700000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.0000 | −1.38359 | −0.691796 | − | 0.722093i | \(-0.743180\pi\) | ||||
−0.691796 | + | 0.722093i | \(0.743180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00000 | + | 3.46410i | −0.230259 | + | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.0000 | + | 15.5885i | −1.03464 | + | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0000 | 1.14792 | 0.573959 | − | 0.818884i | \(-0.305407\pi\) | ||||
0.573959 | + | 0.818884i | \(0.305407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.5000 | − | 11.2583i | 0.743971 | − | 0.429532i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −54.0000 | + | 31.1769i | −2.05724 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.00000 | − | 5.19615i | −0.341882 | − | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.3205i | 0.657004i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.0000 | + | 20.7846i | 1.36360 | + | 0.787273i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.0000 | − | 25.9808i | 0.567352 | − | 0.982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.00000 | + | 5.19615i | −0.339925 | + | 0.196256i | −0.660239 | − | 0.751056i | \(-0.729545\pi\) |
0.320314 | + | 0.947312i | \(0.396212\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.00000 | − | 20.7846i | −0.339441 | − | 0.783906i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −36.0000 | + | 20.7846i | −1.35584 | + | 0.782794i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.00000 | − | 5.19615i | −0.338480 | − | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.50000 | − | 11.2583i | 0.244113 | − | 0.422815i | −0.717769 | − | 0.696281i | \(-0.754837\pi\) |
0.961882 | + | 0.273466i | \(0.0881700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.5885i | 0.584613i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.3538i | 2.33190i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.0000 | − | 36.3731i | −0.784259 | − | 1.35838i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | + | 13.8564i | −0.895049 | + | 0.516757i | −0.875591 | − | 0.483054i | \(-0.839528\pi\) |
−0.0194584 | + | 0.999811i | \(0.506194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 8.66025i | − | 0.322525i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.00000 | −0.111571 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.0000 | + | 36.3731i | 0.779920 | + | 1.35086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.5000 | − | 32.0429i | −0.686127 | − | 1.18841i | −0.973081 | − | 0.230463i | \(-0.925976\pi\) |
0.286954 | − | 0.957944i | \(-0.407357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | + | 1.73205i | 0.110959 | + | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.0000 | + | 31.1769i | −0.663940 | + | 1.14998i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.0000 | − | 25.9808i | 0.552532 | − | 0.957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.5000 | + | 21.6506i | 0.459820 | + | 0.796431i | 0.998951 | − | 0.0457903i | \(-0.0145806\pi\) |
−0.539131 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.0000 | − | 15.5885i | 1.32249 | − | 0.572656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | + | 5.19615i | 0.110059 | + | 0.190628i | 0.915794 | − | 0.401648i | \(-0.131563\pi\) |
−0.805735 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.0000 | − | 51.9615i | 1.09911 | − | 1.90372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.0000 | − | 15.5885i | −0.987878 | − | 0.570352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | −0.657706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.5000 | − | 18.1865i | −1.14945 | − | 0.663636i | −0.200698 | − | 0.979653i | \(-0.564321\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000 | 0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.00000 | + | 10.3923i | 0.218362 | + | 0.378215i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.50000 | − | 11.2583i | −0.236247 | − | 0.409191i | 0.723388 | − | 0.690442i | \(-0.242584\pi\) |
−0.959634 | + | 0.281251i | \(0.909251\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.7128i | 1.00459i | 0.864697 | + | 0.502294i | \(0.167511\pi\) | ||||
−0.864697 | + | 0.502294i | \(0.832489\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.0000 | + | 31.1769i | 0.650791 | + | 1.12720i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.5000 | + | 32.0429i | −0.667127 | + | 1.15550i | 0.311577 | + | 0.950221i | \(0.399143\pi\) |
−0.978704 | + | 0.205277i | \(0.934190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.0000 | + | 20.7846i | −0.431610 | + | 0.747570i | −0.997012 | − | 0.0772449i | \(-0.975388\pi\) |
0.565402 | + | 0.824815i | \(0.308721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.5000 | − | 6.06218i | −0.377171 | − | 0.217760i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.50000 | + | 7.79423i | 0.161437 | + | 0.279616i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.0000 | − | 31.1769i | −1.50481 | − | 1.11703i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | + | 10.3923i | −0.644091 | + | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.0000 | + | 15.5885i | 0.964901 | + | 0.557086i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.0000 | − | 12.1244i | −0.749522 | − | 0.432737i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.9808i | − | 0.926114i | −0.886328 | − | 0.463057i | \(-0.846752\pi\) | ||
0.886328 | − | 0.463057i | \(-0.153248\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.0000 | − | 36.3731i | 0.747620 | − | 1.29492i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | 0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.5000 | + | 18.1865i | −1.11860 | + | 0.645823i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36.0000 | + | 62.3538i | 1.27679 | + | 2.21146i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.0000 | + | 12.1244i | −0.741074 | + | 0.427859i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.46410i | − | 0.121791i | −0.998144 | − | 0.0608957i | \(-0.980604\pi\) | ||
0.998144 | − | 0.0608957i | \(-0.0193957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0000 | + | 15.5885i | 0.948098 | + | 0.547385i | 0.892490 | − | 0.451068i | \(-0.148957\pi\) |
0.0556086 | + | 0.998453i | \(0.482290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0000 | + | 6.92820i | 0.420858 | + | 0.242983i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.0000 | − | 19.0526i | 1.15594 | − | 0.667382i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.50000 | − | 2.59808i | −0.122449 | − | 0.0908952i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.5000 | + | 7.79423i | −0.471728 | + | 0.272352i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0000 | − | 12.1244i | −0.732905 | − | 0.423143i | 0.0865789 | − | 0.996245i | \(-0.472407\pi\) |
−0.819484 | + | 0.573102i | \(0.805740\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | − | 34.6410i | 0.697156 | − | 1.20751i | −0.272292 | − | 0.962215i | \(-0.587782\pi\) |
0.969448 | − | 0.245295i | \(-0.0788849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.0000 | 1.46225 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.00000 | − | 5.19615i | 0.104320 | − | 0.180688i | −0.809140 | − | 0.587616i | \(-0.800067\pi\) |
0.913460 | + | 0.406928i | \(0.133400\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.2295i | 1.74454i | 0.489023 | + | 0.872271i | \(0.337353\pi\) | ||||
−0.489023 | + | 0.872271i | \(0.662647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.00000 | + | 1.73205i | −0.104069 | + | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | − | 10.3923i | 0.623663 | − | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.5692i | 1.43856i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.00000 | −0.311086 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.0000 | + | 46.7654i | 0.932144 | + | 1.61452i | 0.779650 | + | 0.626215i | \(0.215397\pi\) |
0.152493 | + | 0.988304i | \(0.451270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.3923i | 0.357930i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.0000 | + | 24.2487i | 1.44484 | + | 0.834181i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −42.0000 | − | 24.2487i | −1.44144 | − | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.50000 | − | 4.33013i | −0.0855984 | − | 0.148261i | 0.820048 | − | 0.572295i | \(-0.193947\pi\) |
−0.905646 | + | 0.424034i | \(0.860614\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.0000 | − | 41.5692i | −0.615587 | − | 1.42164i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.5000 | + | 30.3109i | −0.597092 | + | 1.03419i | 0.396156 | + | 0.918183i | \(0.370344\pi\) |
−0.993248 | + | 0.116011i | \(0.962989\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0000 | + | 10.3923i | 0.613438 | + | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0000 | + | 10.3923i | 0.612018 | + | 0.353349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.66025i | 0.294118i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.00000 | − | 15.5885i | −0.305304 | − | 0.528802i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.5000 | − | 38.9711i | −0.762383 | − | 1.32049i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 20.7846i | − | 0.703452i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.92820i | 0.234216i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.50000 | − | 2.59808i | 0.151954 | − | 0.0877308i | −0.422095 | − | 0.906552i | \(-0.638705\pi\) |
0.574049 | + | 0.818821i | \(0.305372\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 38.1051i | − | 1.28379i | −0.766791 | − | 0.641897i | \(-0.778148\pi\) | ||
0.766791 | − | 0.641897i | \(-0.221852\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.50000 | − | 11.2583i | 0.218742 | − | 0.378873i | −0.735681 | − | 0.677328i | \(-0.763138\pi\) |
0.954424 | + | 0.298455i | \(0.0964712\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.00000 | − | 5.19615i | −0.301850 | − | 0.174273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.0000 | − | 15.5885i | 0.904534 | − | 0.522233i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.0000 | − | 3.46410i | −1.00391 | − | 0.115922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.0000 | + | 20.7846i | −1.20335 | + | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.00000 | + | 5.19615i | 0.300167 | + | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 41.5692i | − | 1.38487i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.50000 | + | 0.866025i | 0.0499169 | + | 0.0288195i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.0000 | −0.797787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.0000 | + | 12.1244i | −0.697294 | + | 0.402583i | −0.806339 | − | 0.591454i | \(-0.798554\pi\) |
0.109045 | + | 0.994037i | \(0.465221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.0000 | − | 15.5885i | 0.895533 | − | 0.517036i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.0000 | 1.19143 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.0000 | + | 36.3731i | 0.694239 | + | 1.20246i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.00000 | − | 1.73205i | 0.0990687 | − | 0.0571974i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.0000 | 1.74831 | 0.874154 | − | 0.485648i | \(-0.161416\pi\) | ||||
0.874154 | + | 0.485648i | \(0.161416\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.0000 | + | 46.7654i | −0.889680 | + | 1.54097i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.1769i | 1.02620i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.5000 | − | 18.1865i | −1.03571 | − | 0.597970i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.5000 | + | 12.9904i | 0.738997 | + | 0.426660i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.0000 | − | 25.9808i | 1.47640 | − | 0.852401i | 0.476757 | − | 0.879035i | \(-0.341812\pi\) |
0.999645 | + | 0.0266341i | \(0.00847889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0000 | + | 10.3923i | −0.786568 | + | 0.340594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.0000 | − | 20.7846i | −1.17733 | − | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.5000 | + | 19.9186i | −0.375689 | + | 0.650712i | −0.990430 | − | 0.138017i | \(-0.955927\pi\) |
0.614741 | + | 0.788729i | \(0.289260\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 24.2487i | − | 0.791327i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | \(-0.961269\pi\) |
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.00000 | + | 15.5885i | 0.292770 | + | 0.507093i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0000 | − | 15.5885i | 0.877382 | − | 0.506557i | 0.00758776 | − | 0.999971i | \(-0.497585\pi\) |
0.869794 | + | 0.493414i | \(0.164251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.3731i | 1.18072i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 10.3923i | − | 0.336994i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.00000 | − | 5.19615i | −0.0971795 | − | 0.168320i | 0.813337 | − | 0.581793i | \(-0.197649\pi\) |
−0.910516 | + | 0.413473i | \(0.864315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.0000 | + | 51.9615i | 0.970777 | + | 1.68144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.0000 | −1.16371 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.00000 | + | 1.73205i | 0.0968751 | + | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.0000 | − | 46.7654i | 0.870063 | − | 1.50699i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.0000 | + | 36.3731i | −0.676014 | + | 1.17089i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.5000 | − | 25.1147i | −0.466289 | − | 0.807635i | 0.532970 | − | 0.846134i | \(-0.321076\pi\) |
−0.999259 | + | 0.0384986i | \(0.987742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.00000 | + | 25.9808i | −0.0963739 | + | 0.834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0000 | − | 41.5692i | −0.770197 | − | 1.33402i | −0.937455 | − | 0.348107i | \(-0.886825\pi\) |
0.167258 | − | 0.985913i | \(-0.446509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50000 | − | 4.33013i | 0.0801463 | − | 0.138817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 31.5000 | − | 54.5596i | 1.00881 | − | 1.74731i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0000 | 0.383914 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.0000 | − | 36.3731i | −0.669796 | − | 1.16012i | −0.977961 | − | 0.208788i | \(-0.933048\pi\) |
0.308165 | − | 0.951333i | \(-0.400285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.0000 | 0.381964 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.5000 | + | 18.1865i | −1.00063 | + | 0.577714i | −0.908435 | − | 0.418027i | \(-0.862722\pi\) |
−0.0921957 | + | 0.995741i | \(0.529389\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.50000 | + | 7.79423i | 0.142803 | + | 0.247342i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 86.6025i | 2.74549i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5000 | − | 45.8993i | 0.839263 | − | 1.45365i | −0.0512480 | − | 0.998686i | \(-0.516320\pi\) |
0.890511 | − | 0.454961i | \(-0.150347\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.0000 | −0.854242 |
(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 | 912.2.bn.f.449.1 | 2 | ||
3.2 | odd | 2 | 912.2.bn.c.449.1 | 2 | |||
4.3 | odd | 2 | 114.2.h.b.107.1 | yes | 2 | ||
12.11 | even | 2 | 114.2.h.c.107.1 | yes | 2 | ||
19.8 | odd | 6 | 912.2.bn.c.65.1 | 2 | |||
57.8 | even | 6 | inner | 912.2.bn.f.65.1 | 2 | ||
76.27 | even | 6 | 114.2.h.c.65.1 | yes | 2 | ||
228.179 | odd | 6 | 114.2.h.b.65.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.h.b.65.1 | ✓ | 2 | 228.179 | odd | 6 | ||
114.2.h.b.107.1 | yes | 2 | 4.3 | odd | 2 | ||
114.2.h.c.65.1 | yes | 2 | 76.27 | even | 6 | ||
114.2.h.c.107.1 | yes | 2 | 12.11 | even | 2 | ||
912.2.bn.c.65.1 | 2 | 19.8 | odd | 6 | |||
912.2.bn.c.449.1 | 2 | 3.2 | odd | 2 | |||
912.2.bn.f.65.1 | 2 | 57.8 | even | 6 | inner | ||
912.2.bn.f.449.1 | 2 | 1.1 | even | 1 | trivial |