Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,2,Mod(65,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("114.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.h (of order \(6\), 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: | \(0.910294583043\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.107 |
Dual form | 114.2.h.b.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 \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 3.00000 | − | 1.73205i | 1.34164 | − | 0.774597i | 0.354593 | − | 0.935021i | \(-0.384620\pi\) |
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | −3.00000 | − | 1.73205i | −0.948683 | − | 0.547723i | ||||
\(11\) | − | 3.46410i | − | 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | 4.50000 | + | 2.59808i | 1.24808 | + | 0.720577i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −0.500000 | − | 0.866025i | −0.133631 | − | 0.231455i | ||||
\(15\) | −3.00000 | + | 5.19615i | −0.774597 | + | 1.34164i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | + | 1.73205i | −0.727607 | + | 0.420084i | −0.817546 | − | 0.575863i | \(-0.804666\pi\) |
0.0899392 | + | 0.995947i | \(0.471333\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | −4.00000 | + | 1.73205i | −0.917663 | + | 0.397360i | ||||
\(20\) | 3.46410i | 0.774597i | ||||||||
\(21\) | −1.50000 | + | 0.866025i | −0.327327 | + | 0.188982i | ||||
\(22\) | −3.00000 | + | 1.73205i | −0.639602 | + | 0.369274i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | −1.50000 | + | 0.866025i | −0.306186 | + | 0.176777i | ||||
\(25\) | 3.50000 | − | 6.06218i | 0.700000 | − | 1.21244i | ||||
\(26\) | − | 5.19615i | − | 1.01905i | ||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −0.500000 | + | 0.866025i | −0.0944911 | + | 0.163663i | ||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 6.00000 | 1.09545 | ||||||||
\(31\) | 1.73205i | 0.311086i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 3.00000 | + | 5.19615i | 0.522233 | + | 0.904534i | ||||
\(34\) | 3.00000 | + | 1.73205i | 0.514496 | + | 0.297044i | ||||
\(35\) | 3.00000 | − | 1.73205i | 0.507093 | − | 0.292770i | ||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | − | 5.19615i | − | 0.854242i | −0.904194 | − | 0.427121i | \(-0.859528\pi\) | ||
0.904194 | − | 0.427121i | \(-0.140472\pi\) | |||||||
\(38\) | 3.50000 | + | 2.59808i | 0.567775 | + | 0.421464i | ||||
\(39\) | −9.00000 | −1.44115 | ||||||||
\(40\) | 3.00000 | − | 1.73205i | 0.474342 | − | 0.273861i | ||||
\(41\) | −6.00000 | − | 10.3923i | −0.937043 | − | 1.62301i | −0.770950 | − | 0.636895i | \(-0.780218\pi\) |
−0.166092 | − | 0.986110i | \(-0.553115\pi\) | |||||||
\(42\) | 1.50000 | + | 0.866025i | 0.231455 | + | 0.133631i | ||||
\(43\) | 0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | 3.00000 | + | 1.73205i | 0.452267 | + | 0.261116i | ||||
\(45\) | − | 10.3923i | − | 1.54919i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | + | 3.46410i | 0.875190 | + | 0.505291i | 0.869069 | − | 0.494690i | \(-0.164718\pi\) |
0.00612051 | + | 0.999981i | \(0.498052\pi\) | |||||||
\(48\) | 1.50000 | + | 0.866025i | 0.216506 | + | 0.125000i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −7.00000 | −0.989949 | ||||||||
\(51\) | 3.00000 | − | 5.19615i | 0.420084 | − | 0.727607i | ||||
\(52\) | −4.50000 | + | 2.59808i | −0.624038 | + | 0.360288i | ||||
\(53\) | −6.00000 | + | 10.3923i | −0.824163 | + | 1.42749i | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | 4.50000 | − | 2.59808i | 0.612372 | − | 0.353553i | ||||
\(55\) | −6.00000 | − | 10.3923i | −0.809040 | − | 1.40130i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 4.50000 | − | 6.06218i | 0.596040 | − | 0.802955i | ||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | −3.00000 | − | 5.19615i | −0.387298 | − | 0.670820i | ||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 1.50000 | − | 0.866025i | 0.190500 | − | 0.109985i | ||||
\(63\) | 1.50000 | − | 2.59808i | 0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 18.0000 | 2.23263 | ||||||||
\(66\) | 3.00000 | − | 5.19615i | 0.369274 | − | 0.639602i | ||||
\(67\) | 7.50000 | + | 4.33013i | 0.916271 | + | 0.529009i | 0.882443 | − | 0.470418i | \(-0.155897\pi\) |
0.0338274 | + | 0.999428i | \(0.489230\pi\) | |||||||
\(68\) | − | 3.46410i | − | 0.420084i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | − | 1.73205i | −0.358569 | − | 0.207020i | ||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | 1.50000 | − | 2.59808i | 0.176777 | − | 0.306186i | ||||
\(73\) | 3.50000 | + | 6.06218i | 0.409644 | + | 0.709524i | 0.994850 | − | 0.101361i | \(-0.0323196\pi\) |
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | −4.50000 | + | 2.59808i | −0.523114 | + | 0.302020i | ||||
\(75\) | 12.1244i | 1.40000i | ||||||||
\(76\) | 0.500000 | − | 4.33013i | 0.0573539 | − | 0.496700i | ||||
\(77\) | − | 3.46410i | − | 0.394771i | ||||||
\(78\) | 4.50000 | + | 7.79423i | 0.509525 | + | 0.882523i | ||||
\(79\) | 4.50000 | − | 2.59808i | 0.506290 | − | 0.292306i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | −3.00000 | − | 1.73205i | −0.335410 | − | 0.193649i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −6.00000 | + | 10.3923i | −0.662589 | + | 1.14764i | ||||
\(83\) | 10.3923i | 1.14070i | 0.821401 | + | 0.570352i | \(0.193193\pi\) | ||||
−0.821401 | + | 0.570352i | \(0.806807\pi\) | |||||||
\(84\) | − | 1.73205i | − | 0.188982i | ||||||
\(85\) | −6.00000 | + | 10.3923i | −0.650791 | + | 1.12720i | ||||
\(86\) | 0.500000 | − | 0.866025i | 0.0539164 | − | 0.0933859i | ||||
\(87\) | − | 10.3923i | − | 1.11417i | ||||||
\(88\) | − | 3.46410i | − | 0.369274i | ||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | −9.00000 | + | 5.19615i | −0.948683 | + | 0.547723i | ||||
\(91\) | 4.50000 | + | 2.59808i | 0.471728 | + | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | − | 6.92820i | − | 0.714590i | ||||||
\(95\) | −9.00000 | + | 12.1244i | −0.923381 | + | 1.24393i | ||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | 6.00000 | − | 3.46410i | 0.609208 | − | 0.351726i | −0.163448 | − | 0.986552i | \(-0.552261\pi\) |
0.772655 | + | 0.634826i | \(0.218928\pi\) | |||||||
\(98\) | 3.00000 | + | 5.19615i | 0.303046 | + | 0.524891i | ||||
\(99\) | −9.00000 | − | 5.19615i | −0.904534 | − | 0.522233i | ||||
\(100\) | 3.50000 | + | 6.06218i | 0.350000 | + | 0.606218i | ||||
\(101\) | 9.00000 | + | 5.19615i | 0.895533 | + | 0.517036i | 0.875748 | − | 0.482768i | \(-0.160368\pi\) |
0.0197851 | + | 0.999804i | \(0.493702\pi\) | |||||||
\(102\) | −6.00000 | −0.594089 | ||||||||
\(103\) | − | 8.66025i | − | 0.853320i | −0.904412 | − | 0.426660i | \(-0.859690\pi\) | ||
0.904412 | − | 0.426660i | \(-0.140310\pi\) | |||||||
\(104\) | 4.50000 | + | 2.59808i | 0.441261 | + | 0.254762i | ||||
\(105\) | −3.00000 | + | 5.19615i | −0.292770 | + | 0.507093i | ||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | −18.0000 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(108\) | −4.50000 | − | 2.59808i | −0.433013 | − | 0.250000i | ||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | −6.00000 | + | 10.3923i | −0.572078 | + | 0.990867i | ||||
\(111\) | 4.50000 | + | 7.79423i | 0.427121 | + | 0.739795i | ||||
\(112\) | −0.500000 | − | 0.866025i | −0.0472456 | − | 0.0818317i | ||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | −7.50000 | − | 0.866025i | −0.702439 | − | 0.0811107i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.00000 | − | 5.19615i | −0.278543 | − | 0.482451i | ||||
\(117\) | 13.5000 | − | 7.79423i | 1.24808 | − | 0.720577i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | + | 1.73205i | −0.275010 | + | 0.158777i | ||||
\(120\) | −3.00000 | + | 5.19615i | −0.273861 | + | 0.474342i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 7.00000 | 0.633750 | ||||||||
\(123\) | 18.0000 | + | 10.3923i | 1.62301 | + | 0.937043i | ||||
\(124\) | −1.50000 | − | 0.866025i | −0.134704 | − | 0.0777714i | ||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | −3.00000 | −0.267261 | ||||||||
\(127\) | −9.00000 | − | 5.19615i | −0.798621 | − | 0.461084i | 0.0443678 | − | 0.999015i | \(-0.485873\pi\) |
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −1.50000 | − | 0.866025i | −0.132068 | − | 0.0762493i | ||||
\(130\) | −9.00000 | − | 15.5885i | −0.789352 | − | 1.36720i | ||||
\(131\) | 3.00000 | − | 1.73205i | 0.262111 | − | 0.151330i | −0.363186 | − | 0.931717i | \(-0.618311\pi\) |
0.625297 | + | 0.780387i | \(0.284978\pi\) | |||||||
\(132\) | −6.00000 | −0.522233 | ||||||||
\(133\) | −4.00000 | + | 1.73205i | −0.346844 | + | 0.150188i | ||||
\(134\) | − | 8.66025i | − | 0.748132i | ||||||
\(135\) | 9.00000 | + | 15.5885i | 0.774597 | + | 1.34164i | ||||
\(136\) | −3.00000 | + | 1.73205i | −0.257248 | + | 0.148522i | ||||
\(137\) | −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 | −0.740308 | − | 0.672268i | \(-0.765320\pi\) |
0.952355 | + | 0.304991i | \(0.0986536\pi\) | |||||||
\(140\) | 3.46410i | 0.292770i | ||||||||
\(141\) | −12.0000 | −1.01058 | ||||||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | 9.00000 | − | 15.5885i | 0.752618 | − | 1.30357i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 20.7846i | 1.72607i | ||||||||
\(146\) | 3.50000 | − | 6.06218i | 0.289662 | − | 0.501709i | ||||
\(147\) | 9.00000 | − | 5.19615i | 0.742307 | − | 0.428571i | ||||
\(148\) | 4.50000 | + | 2.59808i | 0.369898 | + | 0.213561i | ||||
\(149\) | 15.0000 | − | 8.66025i | 1.22885 | − | 0.709476i | 0.262059 | − | 0.965052i | \(-0.415599\pi\) |
0.966789 | + | 0.255576i | \(0.0822652\pi\) | |||||||
\(150\) | 10.5000 | − | 6.06218i | 0.857321 | − | 0.494975i | ||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | −4.00000 | + | 1.73205i | −0.324443 | + | 0.140488i | ||||
\(153\) | 10.3923i | 0.840168i | ||||||||
\(154\) | −3.00000 | + | 1.73205i | −0.241747 | + | 0.139573i | ||||
\(155\) | 3.00000 | + | 5.19615i | 0.240966 | + | 0.417365i | ||||
\(156\) | 4.50000 | − | 7.79423i | 0.360288 | − | 0.624038i | ||||
\(157\) | −3.50000 | − | 6.06218i | −0.279330 | − | 0.483814i | 0.691888 | − | 0.722005i | \(-0.256779\pi\) |
−0.971219 | + | 0.238190i | \(0.923446\pi\) | |||||||
\(158\) | −4.50000 | − | 2.59808i | −0.358001 | − | 0.206692i | ||||
\(159\) | − | 20.7846i | − | 1.64833i | ||||||
\(160\) | 3.46410i | 0.273861i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.50000 | + | 7.79423i | −0.353553 | + | 0.612372i | ||||
\(163\) | −11.0000 | −0.861586 | −0.430793 | − | 0.902451i | \(-0.641766\pi\) | ||||
−0.430793 | + | 0.902451i | \(0.641766\pi\) | |||||||
\(164\) | 12.0000 | 0.937043 | ||||||||
\(165\) | 18.0000 | + | 10.3923i | 1.40130 | + | 0.809040i | ||||
\(166\) | 9.00000 | − | 5.19615i | 0.698535 | − | 0.403300i | ||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | −1.50000 | + | 0.866025i | −0.115728 | + | 0.0668153i | ||||
\(169\) | 7.00000 | + | 12.1244i | 0.538462 | + | 0.932643i | ||||
\(170\) | 12.0000 | 0.920358 | ||||||||
\(171\) | −1.50000 | + | 12.9904i | −0.114708 | + | 0.993399i | ||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | −9.00000 | + | 5.19615i | −0.682288 | + | 0.393919i | ||||
\(175\) | 3.50000 | − | 6.06218i | 0.264575 | − | 0.458258i | ||||
\(176\) | −3.00000 | + | 1.73205i | −0.226134 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 9.00000 | + | 5.19615i | 0.670820 | + | 0.387298i | ||||
\(181\) | −6.00000 | − | 3.46410i | −0.445976 | − | 0.257485i | 0.260153 | − | 0.965567i | \(-0.416227\pi\) |
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | − | 5.19615i | − | 0.385164i | ||||||
\(183\) | − | 12.1244i | − | 0.896258i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.00000 | − | 15.5885i | −0.661693 | − | 1.14609i | ||||
\(186\) | −1.50000 | + | 2.59808i | −0.109985 | + | 0.190500i | ||||
\(187\) | 6.00000 | + | 10.3923i | 0.438763 | + | 0.759961i | ||||
\(188\) | −6.00000 | + | 3.46410i | −0.437595 | + | 0.252646i | ||||
\(189\) | 5.19615i | 0.377964i | ||||||||
\(190\) | 15.0000 | + | 1.73205i | 1.08821 | + | 0.125656i | ||||
\(191\) | − | 17.3205i | − | 1.25327i | −0.779314 | − | 0.626634i | \(-0.784432\pi\) | ||
0.779314 | − | 0.626634i | \(-0.215568\pi\) | |||||||
\(192\) | −1.50000 | + | 0.866025i | −0.108253 | + | 0.0625000i | ||||
\(193\) | −10.5000 | + | 6.06218i | −0.755807 | + | 0.436365i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | −6.00000 | − | 3.46410i | −0.430775 | − | 0.248708i | ||||
\(195\) | −27.0000 | + | 15.5885i | −1.93351 | + | 1.11631i | ||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 10.3923i | 0.738549i | ||||||||
\(199\) | 12.5000 | − | 21.6506i | 0.886102 | − | 1.53477i | 0.0416556 | − | 0.999132i | \(-0.486737\pi\) |
0.844446 | − | 0.535641i | \(-0.179930\pi\) | |||||||
\(200\) | 3.50000 | − | 6.06218i | 0.247487 | − | 0.428661i | ||||
\(201\) | −15.0000 | −1.05802 | ||||||||
\(202\) | − | 10.3923i | − | 0.731200i | ||||||
\(203\) | −3.00000 | + | 5.19615i | −0.210559 | + | 0.364698i | ||||
\(204\) | 3.00000 | + | 5.19615i | 0.210042 | + | 0.363803i | ||||
\(205\) | −36.0000 | − | 20.7846i | −2.51435 | − | 1.45166i | ||||
\(206\) | −7.50000 | + | 4.33013i | −0.522550 | + | 0.301694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.19615i | − | 0.360288i | ||||||
\(209\) | 6.00000 | + | 13.8564i | 0.415029 | + | 0.958468i | ||||
\(210\) | 6.00000 | 0.414039 | ||||||||
\(211\) | −19.5000 | + | 11.2583i | −1.34244 | + | 0.775055i | −0.987164 | − | 0.159708i | \(-0.948945\pi\) |
−0.355271 | + | 0.934763i | \(0.615611\pi\) | |||||||
\(212\) | −6.00000 | − | 10.3923i | −0.412082 | − | 0.713746i | ||||
\(213\) | 9.00000 | + | 5.19615i | 0.616670 | + | 0.356034i | ||||
\(214\) | 9.00000 | + | 15.5885i | 0.615227 | + | 1.06561i | ||||
\(215\) | 3.00000 | + | 1.73205i | 0.204598 | + | 0.118125i | ||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 1.73205i | 0.117579i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5000 | − | 6.06218i | −0.709524 | − | 0.409644i | ||||
\(220\) | 12.0000 | 0.809040 | ||||||||
\(221\) | −18.0000 | −1.21081 | ||||||||
\(222\) | 4.50000 | − | 7.79423i | 0.302020 | − | 0.523114i | ||||
\(223\) | 16.5000 | − | 9.52628i | 1.10492 | − | 0.637927i | 0.167412 | − | 0.985887i | \(-0.446459\pi\) |
0.937509 | + | 0.347960i | \(0.113126\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | −10.5000 | − | 18.1865i | −0.700000 | − | 1.21244i | ||||
\(226\) | 6.00000 | + | 10.3923i | 0.399114 | + | 0.691286i | ||||
\(227\) | 18.0000 | 1.19470 | 0.597351 | − | 0.801980i | \(-0.296220\pi\) | ||||
0.597351 | + | 0.801980i | \(0.296220\pi\) | |||||||
\(228\) | 3.00000 | + | 6.92820i | 0.198680 | + | 0.458831i | ||||
\(229\) | 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 | ||||
\(232\) | −3.00000 | + | 5.19615i | −0.196960 | + | 0.341144i | ||||
\(233\) | 15.0000 | − | 8.66025i | 0.982683 | − | 0.567352i | 0.0796037 | − | 0.996827i | \(-0.474635\pi\) |
0.903079 | + | 0.429474i | \(0.141301\pi\) | |||||||
\(234\) | −13.5000 | − | 7.79423i | −0.882523 | − | 0.509525i | ||||
\(235\) | 24.0000 | 1.56559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.50000 | + | 7.79423i | −0.292306 | + | 0.506290i | ||||
\(238\) | 3.00000 | + | 1.73205i | 0.194461 | + | 0.112272i | ||||
\(239\) | 24.2487i | 1.56852i | 0.620433 | + | 0.784259i | \(0.286957\pi\) | ||||
−0.620433 | + | 0.784259i | \(0.713043\pi\) | |||||||
\(240\) | 6.00000 | 0.387298 | ||||||||
\(241\) | −1.50000 | − | 0.866025i | −0.0966235 | − | 0.0557856i | 0.450910 | − | 0.892570i | \(-0.351100\pi\) |
−0.547533 | + | 0.836784i | \(0.684433\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | −3.50000 | − | 6.06218i | −0.224065 | − | 0.388091i | ||||
\(245\) | −18.0000 | + | 10.3923i | −1.14998 | + | 0.663940i | ||||
\(246\) | − | 20.7846i | − | 1.32518i | ||||||
\(247\) | −22.5000 | − | 2.59808i | −1.43164 | − | 0.165312i | ||||
\(248\) | 1.73205i | 0.109985i | ||||||||
\(249\) | −9.00000 | − | 15.5885i | −0.570352 | − | 0.987878i | ||||
\(250\) | −6.00000 | + | 3.46410i | −0.379473 | + | 0.219089i | ||||
\(251\) | −6.00000 | − | 3.46410i | −0.378717 | − | 0.218652i | 0.298543 | − | 0.954396i | \(-0.403499\pi\) |
−0.677260 | + | 0.735744i | \(0.736833\pi\) | |||||||
\(252\) | 1.50000 | + | 2.59808i | 0.0944911 | + | 0.163663i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.3923i | 0.652071i | ||||||||
\(255\) | − | 20.7846i | − | 1.30158i | ||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 1.73205i | 0.107833i | ||||||||
\(259\) | − | 5.19615i | − | 0.322873i | ||||||
\(260\) | −9.00000 | + | 15.5885i | −0.558156 | + | 0.966755i | ||||
\(261\) | 9.00000 | + | 15.5885i | 0.557086 | + | 0.964901i | ||||
\(262\) | −3.00000 | − | 1.73205i | −0.185341 | − | 0.107006i | ||||
\(263\) | −21.0000 | + | 12.1244i | −1.29492 | + | 0.747620i | −0.979521 | − | 0.201341i | \(-0.935470\pi\) |
−0.315394 | + | 0.948961i | \(0.602137\pi\) | |||||||
\(264\) | 3.00000 | + | 5.19615i | 0.184637 | + | 0.319801i | ||||
\(265\) | 41.5692i | 2.55358i | ||||||||
\(266\) | 3.50000 | + | 2.59808i | 0.214599 | + | 0.159298i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.50000 | + | 4.33013i | −0.458135 | + | 0.264505i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 9.00000 | − | 15.5885i | 0.547723 | − | 0.948683i | ||||
\(271\) | −4.00000 | − | 6.92820i | −0.242983 | − | 0.420858i | 0.718580 | − | 0.695444i | \(-0.244792\pi\) |
−0.961563 | + | 0.274586i | \(0.911459\pi\) | |||||||
\(272\) | 3.00000 | + | 1.73205i | 0.181902 | + | 0.105021i | ||||
\(273\) | −9.00000 | −0.544705 | ||||||||
\(274\) | 3.46410i | 0.209274i | ||||||||
\(275\) | −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 | \(0.519137\pi\) | |||||||
\(278\) | −5.00000 | −0.299880 | ||||||||
\(279\) | 4.50000 | + | 2.59808i | 0.269408 | + | 0.155543i | ||||
\(280\) | 3.00000 | − | 1.73205i | 0.179284 | − | 0.103510i | ||||
\(281\) | −3.00000 | + | 5.19615i | −0.178965 | + | 0.309976i | −0.941526 | − | 0.336939i | \(-0.890608\pi\) |
0.762561 | + | 0.646916i | \(0.223942\pi\) | |||||||
\(282\) | 6.00000 | + | 10.3923i | 0.357295 | + | 0.618853i | ||||
\(283\) | 14.0000 | + | 24.2487i | 0.832214 | + | 1.44144i | 0.896279 | + | 0.443491i | \(0.146260\pi\) |
−0.0640654 | + | 0.997946i | \(0.520407\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 3.00000 | − | 25.9808i | 0.177705 | − | 1.53897i | ||||
\(286\) | −18.0000 | −1.06436 | ||||||||
\(287\) | −6.00000 | − | 10.3923i | −0.354169 | − | 0.613438i | ||||
\(288\) | 1.50000 | + | 2.59808i | 0.0883883 | + | 0.153093i | ||||
\(289\) | −2.50000 | + | 4.33013i | −0.147059 | + | 0.254713i | ||||
\(290\) | 18.0000 | − | 10.3923i | 1.05700 | − | 0.610257i | ||||
\(291\) | −6.00000 | + | 10.3923i | −0.351726 | + | 0.609208i | ||||
\(292\) | −7.00000 | −0.409644 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −9.00000 | − | 5.19615i | −0.524891 | − | 0.303046i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 5.19615i | − | 0.302020i | ||||||
\(297\) | 18.0000 | 1.04447 | ||||||||
\(298\) | −15.0000 | − | 8.66025i | −0.868927 | − | 0.501675i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.5000 | − | 6.06218i | −0.606218 | − | 0.350000i | ||||
\(301\) | 0.500000 | + | 0.866025i | 0.0288195 | + | 0.0499169i | ||||
\(302\) | −3.00000 | + | 1.73205i | −0.172631 | + | 0.0996683i | ||||
\(303\) | −18.0000 | −1.03407 | ||||||||
\(304\) | 3.50000 | + | 2.59808i | 0.200739 | + | 0.149010i | ||||
\(305\) | 24.2487i | 1.38848i | ||||||||
\(306\) | 9.00000 | − | 5.19615i | 0.514496 | − | 0.297044i | ||||
\(307\) | 27.0000 | − | 15.5885i | 1.54097 | − | 0.889680i | 0.542194 | − | 0.840254i | \(-0.317594\pi\) |
0.998778 | − | 0.0494267i | \(-0.0157394\pi\) | |||||||
\(308\) | 3.00000 | + | 1.73205i | 0.170941 | + | 0.0986928i | ||||
\(309\) | 7.50000 | + | 12.9904i | 0.426660 | + | 0.738997i | ||||
\(310\) | 3.00000 | − | 5.19615i | 0.170389 | − | 0.295122i | ||||
\(311\) | 13.8564i | 0.785725i | 0.919597 | + | 0.392862i | \(0.128515\pi\) | ||||
−0.919597 | + | 0.392862i | \(0.871485\pi\) | |||||||
\(312\) | −9.00000 | −0.509525 | ||||||||
\(313\) | 7.00000 | − | 12.1244i | 0.395663 | − | 0.685309i | −0.597522 | − | 0.801852i | \(-0.703848\pi\) |
0.993186 | + | 0.116543i | \(0.0371814\pi\) | |||||||
\(314\) | −3.50000 | + | 6.06218i | −0.197516 | + | 0.342108i | ||||
\(315\) | − | 10.3923i | − | 0.585540i | ||||||
\(316\) | 5.19615i | 0.292306i | ||||||||
\(317\) | 3.00000 | − | 5.19615i | 0.168497 | − | 0.291845i | −0.769395 | − | 0.638774i | \(-0.779442\pi\) |
0.937892 | + | 0.346929i | \(0.112775\pi\) | |||||||
\(318\) | −18.0000 | + | 10.3923i | −1.00939 | + | 0.582772i | ||||
\(319\) | 18.0000 | + | 10.3923i | 1.00781 | + | 0.581857i | ||||
\(320\) | 3.00000 | − | 1.73205i | 0.167705 | − | 0.0968246i | ||||
\(321\) | 27.0000 | − | 15.5885i | 1.50699 | − | 0.870063i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.00000 | − | 12.1244i | 0.500773 | − | 0.674617i | ||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 31.5000 | − | 18.1865i | 1.74731 | − | 1.00881i | ||||
\(326\) | 5.50000 | + | 9.52628i | 0.304617 | + | 0.527612i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.00000 | − | 10.3923i | −0.331295 | − | 0.573819i | ||||
\(329\) | 6.00000 | + | 3.46410i | 0.330791 | + | 0.190982i | ||||
\(330\) | − | 20.7846i | − | 1.14416i | ||||||
\(331\) | − | 5.19615i | − | 0.285606i | −0.989751 | − | 0.142803i | \(-0.954388\pi\) | ||
0.989751 | − | 0.142803i | \(-0.0456116\pi\) | |||||||
\(332\) | −9.00000 | − | 5.19615i | −0.493939 | − | 0.285176i | ||||
\(333\) | −13.5000 | − | 7.79423i | −0.739795 | − | 0.427121i | ||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 30.0000 | 1.63908 | ||||||||
\(336\) | 1.50000 | + | 0.866025i | 0.0818317 | + | 0.0472456i | ||||
\(337\) | 1.50000 | − | 0.866025i | 0.0817102 | − | 0.0471754i | −0.458588 | − | 0.888649i | \(-0.651645\pi\) |
0.540298 | + | 0.841473i | \(0.318311\pi\) | |||||||
\(338\) | 7.00000 | − | 12.1244i | 0.380750 | − | 0.659478i | ||||
\(339\) | 18.0000 | − | 10.3923i | 0.977626 | − | 0.564433i | ||||
\(340\) | −6.00000 | − | 10.3923i | −0.325396 | − | 0.563602i | ||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 12.0000 | − | 5.19615i | 0.648886 | − | 0.280976i | ||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 0.500000 | + | 0.866025i | 0.0269582 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | 21.0000 | − | 12.1244i | 1.12734 | − | 0.650870i | 0.184075 | − | 0.982912i | \(-0.441071\pi\) |
0.943264 | + | 0.332043i | \(0.107738\pi\) | |||||||
\(348\) | 9.00000 | + | 5.19615i | 0.482451 | + | 0.278543i | ||||
\(349\) | −7.00000 | −0.374701 | −0.187351 | − | 0.982293i | \(-0.559990\pi\) | ||||
−0.187351 | + | 0.982293i | \(0.559990\pi\) | |||||||
\(350\) | −7.00000 | −0.374166 | ||||||||
\(351\) | −13.5000 | + | 23.3827i | −0.720577 | + | 1.24808i | ||||
\(352\) | 3.00000 | + | 1.73205i | 0.159901 | + | 0.0923186i | ||||
\(353\) | − | 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 | ||||
\(358\) | −6.00000 | − | 10.3923i | −0.317110 | − | 0.549250i | ||||
\(359\) | −6.00000 | + | 3.46410i | −0.316668 | + | 0.182828i | −0.649906 | − | 0.760014i | \(-0.725192\pi\) |
0.333238 | + | 0.942843i | \(0.391859\pi\) | |||||||
\(360\) | − | 10.3923i | − | 0.547723i | ||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 6.92820i | 0.364138i | ||||||||
\(363\) | 1.50000 | − | 0.866025i | 0.0787296 | − | 0.0454545i | ||||
\(364\) | −4.50000 | + | 2.59808i | −0.235864 | + | 0.136176i | ||||
\(365\) | 21.0000 | + | 12.1244i | 1.09919 | + | 0.634618i | ||||
\(366\) | −10.5000 | + | 6.06218i | −0.548844 | + | 0.316875i | ||||
\(367\) | −8.50000 | + | 14.7224i | −0.443696 | + | 0.768505i | −0.997960 | − | 0.0638362i | \(-0.979666\pi\) |
0.554264 | + | 0.832341i | \(0.313000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.0000 | −1.87409 | ||||||||
\(370\) | −9.00000 | + | 15.5885i | −0.467888 | + | 0.810405i | ||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | 3.00000 | 0.155543 | ||||||||
\(373\) | 6.92820i | 0.358729i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) | ||||
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | 6.00000 | − | 10.3923i | 0.310253 | − | 0.537373i | ||||
\(375\) | 6.00000 | + | 10.3923i | 0.309839 | + | 0.536656i | ||||
\(376\) | 6.00000 | + | 3.46410i | 0.309426 | + | 0.178647i | ||||
\(377\) | −27.0000 | + | 15.5885i | −1.39057 | + | 0.802846i | ||||
\(378\) | 4.50000 | − | 2.59808i | 0.231455 | − | 0.133631i | ||||
\(379\) | − | 12.1244i | − | 0.622786i | −0.950281 | − | 0.311393i | \(-0.899204\pi\) | ||
0.950281 | − | 0.311393i | \(-0.100796\pi\) | |||||||
\(380\) | −6.00000 | − | 13.8564i | −0.307794 | − | 0.710819i | ||||
\(381\) | 18.0000 | 0.922168 | ||||||||
\(382\) | −15.0000 | + | 8.66025i | −0.767467 | + | 0.443097i | ||||
\(383\) | 3.00000 | + | 5.19615i | 0.153293 | + | 0.265511i | 0.932436 | − | 0.361335i | \(-0.117679\pi\) |
−0.779143 | + | 0.626846i | \(0.784346\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | −6.00000 | − | 10.3923i | −0.305788 | − | 0.529641i | ||||
\(386\) | 10.5000 | + | 6.06218i | 0.534436 | + | 0.308557i | ||||
\(387\) | 3.00000 | 0.152499 | ||||||||
\(388\) | 6.92820i | 0.351726i | ||||||||
\(389\) | −24.0000 | − | 13.8564i | −1.21685 | − | 0.702548i | −0.252606 | − | 0.967569i | \(-0.581288\pi\) |
−0.964242 | + | 0.265022i | \(0.914621\pi\) | |||||||
\(390\) | 27.0000 | + | 15.5885i | 1.36720 | + | 0.789352i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.00000 | −0.303046 | ||||||||
\(393\) | −3.00000 | + | 5.19615i | −0.151330 | + | 0.262111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.00000 | − | 15.5885i | 0.452839 | − | 0.784340i | ||||
\(396\) | 9.00000 | − | 5.19615i | 0.452267 | − | 0.261116i | ||||
\(397\) | −14.5000 | − | 25.1147i | −0.727734 | − | 1.26047i | −0.957839 | − | 0.287307i | \(-0.907240\pi\) |
0.230105 | − | 0.973166i | \(-0.426093\pi\) | |||||||
\(398\) | −25.0000 | −1.25314 | ||||||||
\(399\) | 4.50000 | − | 6.06218i | 0.225282 | − | 0.303488i | ||||
\(400\) | −7.00000 | −0.350000 | ||||||||
\(401\) | −12.0000 | − | 20.7846i | −0.599251 | − | 1.03793i | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | 7.50000 | + | 12.9904i | 0.374066 | + | 0.647901i | ||||
\(403\) | −4.50000 | + | 7.79423i | −0.224161 | + | 0.388258i | ||||
\(404\) | −9.00000 | + | 5.19615i | −0.447767 | + | 0.258518i | ||||
\(405\) | −27.0000 | − | 15.5885i | −1.34164 | − | 0.774597i | ||||
\(406\) | 6.00000 | 0.297775 | ||||||||
\(407\) | −18.0000 | −0.892227 | ||||||||
\(408\) | 3.00000 | − | 5.19615i | 0.148522 | − | 0.257248i | ||||
\(409\) | 30.0000 | + | 17.3205i | 1.48340 | + | 0.856444i | 0.999822 | − | 0.0188549i | \(-0.00600205\pi\) |
0.483582 | + | 0.875299i | \(0.339335\pi\) | |||||||
\(410\) | 41.5692i | 2.05296i | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 7.50000 | + | 4.33013i | 0.369498 | + | 0.213330i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | + | 31.1769i | 0.883585 | + | 1.53041i | ||||
\(416\) | −4.50000 | + | 2.59808i | −0.220631 | + | 0.127381i | ||||
\(417\) | 8.66025i | 0.424094i | ||||||||
\(418\) | 9.00000 | − | 12.1244i | 0.440204 | − | 0.593022i | ||||
\(419\) | 10.3923i | 0.507697i | 0.967244 | + | 0.253849i | \(0.0816965\pi\) | ||||
−0.967244 | + | 0.253849i | \(0.918303\pi\) | |||||||
\(420\) | −3.00000 | − | 5.19615i | −0.146385 | − | 0.253546i | ||||
\(421\) | 12.0000 | − | 6.92820i | 0.584844 | − | 0.337660i | −0.178212 | − | 0.983992i | \(-0.557031\pi\) |
0.763056 | + | 0.646332i | \(0.223698\pi\) | |||||||
\(422\) | 19.5000 | + | 11.2583i | 0.949245 | + | 0.548047i | ||||
\(423\) | 18.0000 | − | 10.3923i | 0.875190 | − | 0.505291i | ||||
\(424\) | −6.00000 | + | 10.3923i | −0.291386 | + | 0.504695i | ||||
\(425\) | 24.2487i | 1.17624i | ||||||||
\(426\) | − | 10.3923i | − | 0.503509i | ||||||
\(427\) | −3.50000 | + | 6.06218i | −0.169377 | + | 0.293369i | ||||
\(428\) | 9.00000 | − | 15.5885i | 0.435031 | − | 0.753497i | ||||
\(429\) | 31.1769i | 1.50524i | ||||||||
\(430\) | − | 3.46410i | − | 0.167054i | ||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | 4.50000 | − | 2.59808i | 0.216506 | − | 0.125000i | ||||
\(433\) | −16.5000 | − | 9.52628i | −0.792939 | − | 0.457804i | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) |
−0.840996 | + | 0.541041i | \(0.818030\pi\) | |||||||
\(434\) | 1.50000 | − | 0.866025i | 0.0720023 | − | 0.0415705i | ||||
\(435\) | −18.0000 | − | 31.1769i | −0.863034 | − | 1.49482i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.1244i | 0.579324i | ||||||||
\(439\) | −7.50000 | + | 4.33013i | −0.357955 | + | 0.206666i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) |
0.310228 | + | 0.950662i | \(0.399595\pi\) | |||||||
\(440\) | −6.00000 | − | 10.3923i | −0.286039 | − | 0.495434i | ||||
\(441\) | −9.00000 | + | 15.5885i | −0.428571 | + | 0.742307i | ||||
\(442\) | 9.00000 | + | 15.5885i | 0.428086 | + | 0.741467i | ||||
\(443\) | −21.0000 | − | 12.1244i | −0.997740 | − | 0.576046i | −0.0901612 | − | 0.995927i | \(-0.528738\pi\) |
−0.907579 | + | 0.419882i | \(0.862072\pi\) | |||||||
\(444\) | −9.00000 | −0.427121 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.5000 | − | 9.52628i | −0.781298 | − | 0.451082i | ||||
\(447\) | −15.0000 | + | 25.9808i | −0.709476 | + | 1.22885i | ||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | −10.5000 | + | 18.1865i | −0.494975 | + | 0.857321i | ||||
\(451\) | −36.0000 | + | 20.7846i | −1.69517 | + | 0.978709i | ||||
\(452\) | 6.00000 | − | 10.3923i | 0.282216 | − | 0.488813i | ||||
\(453\) | 3.00000 | + | 5.19615i | 0.140952 | + | 0.244137i | ||||
\(454\) | −9.00000 | − | 15.5885i | −0.422391 | − | 0.731603i | ||||
\(455\) | 18.0000 | 0.843853 | ||||||||
\(456\) | 4.50000 | − | 6.06218i | 0.210732 | − | 0.283887i | ||||
\(457\) | 17.0000 | 0.795226 | 0.397613 | − | 0.917553i | \(-0.369839\pi\) | ||||
0.397613 | + | 0.917553i | \(0.369839\pi\) | |||||||
\(458\) | −6.50000 | − | 11.2583i | −0.303725 | − | 0.526067i | ||||
\(459\) | −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 | \(0.281752\pi\) | |||||||
\(462\) | 3.00000 | − | 5.19615i | 0.139573 | − | 0.241747i | ||||
\(463\) | −19.0000 | −0.883005 | −0.441502 | − | 0.897260i | \(-0.645554\pi\) | ||||
−0.441502 | + | 0.897260i | \(0.645554\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | −9.00000 | − | 5.19615i | −0.417365 | − | 0.240966i | ||||
\(466\) | −15.0000 | − | 8.66025i | −0.694862 | − | 0.401179i | ||||
\(467\) | 27.7128i | 1.28240i | 0.767375 | + | 0.641198i | \(0.221562\pi\) | ||||
−0.767375 | + | 0.641198i | \(0.778438\pi\) | |||||||
\(468\) | 15.5885i | 0.720577i | ||||||||
\(469\) | 7.50000 | + | 4.33013i | 0.346318 | + | 0.199947i | ||||
\(470\) | −12.0000 | − | 20.7846i | −0.553519 | − | 0.958723i | ||||
\(471\) | 10.5000 | + | 6.06218i | 0.483814 | + | 0.279330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 1.73205i | 0.137940 | − | 0.0796398i | ||||
\(474\) | 9.00000 | 0.413384 | ||||||||
\(475\) | −3.50000 | + | 30.3109i | −0.160591 | + | 1.39076i | ||||
\(476\) | − | 3.46410i | − | 0.158777i | ||||||
\(477\) | 18.0000 | + | 31.1769i | 0.824163 | + | 1.42749i | ||||
\(478\) | 21.0000 | − | 12.1244i | 0.960518 | − | 0.554555i | ||||
\(479\) | 9.00000 | + | 5.19615i | 0.411220 | + | 0.237418i | 0.691314 | − | 0.722554i | \(-0.257032\pi\) |
−0.280094 | + | 0.959973i | \(0.590365\pi\) | |||||||
\(480\) | −3.00000 | − | 5.19615i | −0.136931 | − | 0.237171i | ||||
\(481\) | 13.5000 | − | 23.3827i | 0.615547 | − | 1.06616i | ||||
\(482\) | 1.73205i | 0.0788928i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.500000 | − | 0.866025i | 0.0227273 | − | 0.0393648i | ||||
\(485\) | 12.0000 | − | 20.7846i | 0.544892 | − | 0.943781i | ||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | − | 3.46410i | − | 0.156973i | −0.996915 | − | 0.0784867i | \(-0.974991\pi\) | ||
0.996915 | − | 0.0784867i | \(-0.0250088\pi\) | |||||||
\(488\) | −3.50000 | + | 6.06218i | −0.158438 | + | 0.274422i | ||||
\(489\) | 16.5000 | − | 9.52628i | 0.746156 | − | 0.430793i | ||||
\(490\) | 18.0000 | + | 10.3923i | 0.813157 | + | 0.469476i | ||||
\(491\) | −9.00000 | + | 5.19615i | −0.406164 | + | 0.234499i | −0.689140 | − | 0.724628i | \(-0.742012\pi\) |
0.282976 | + | 0.959127i | \(0.408678\pi\) | |||||||
\(492\) | −18.0000 | + | 10.3923i | −0.811503 | + | 0.468521i | ||||
\(493\) | − | 20.7846i | − | 0.936092i | ||||||
\(494\) | 9.00000 | + | 20.7846i | 0.404929 | + | 0.935144i | ||||
\(495\) | −36.0000 | −1.61808 | ||||||||
\(496\) | 1.50000 | − | 0.866025i | 0.0673520 | − | 0.0388857i | ||||
\(497\) | −3.00000 | − | 5.19615i | −0.134568 | − | 0.233079i | ||||
\(498\) | −9.00000 | + | 15.5885i | −0.403300 | + | 0.698535i | ||||
\(499\) | −15.5000 | − | 26.8468i | −0.693875 | − | 1.20183i | −0.970558 | − | 0.240866i | \(-0.922569\pi\) |
0.276683 | − | 0.960961i | \(-0.410765\pi\) | |||||||
\(500\) | 6.00000 | + | 3.46410i | 0.268328 | + | 0.154919i | ||||
\(501\) | 20.7846i | 0.928588i | ||||||||
\(502\) | 6.92820i | 0.309221i | ||||||||
\(503\) | −27.0000 | − | 15.5885i | −1.20387 | − | 0.695055i | −0.242457 | − | 0.970162i | \(-0.577953\pi\) |
−0.961414 | + | 0.275107i | \(0.911287\pi\) | |||||||
\(504\) | 1.50000 | − | 2.59808i | 0.0668153 | − | 0.115728i | ||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.0000 | − | 12.1244i | −0.932643 | − | 0.538462i | ||||
\(508\) | 9.00000 | − | 5.19615i | 0.399310 | − | 0.230542i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | −18.0000 | + | 10.3923i | −0.797053 | + | 0.460179i | ||||
\(511\) | 3.50000 | + | 6.06218i | 0.154831 | + | 0.268175i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.00000 | − | 20.7846i | −0.397360 | − | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0000 | − | 25.9808i | −0.660979 | − | 1.14485i | ||||
\(516\) | 1.50000 | − | 0.866025i | 0.0660338 | − | 0.0381246i | ||||
\(517\) | 12.0000 | − | 20.7846i | 0.527759 | − | 0.914106i | ||||
\(518\) | −4.50000 | + | 2.59808i | −0.197719 | + | 0.114153i | ||||
\(519\) | −9.00000 | − | 5.19615i | −0.395056 | − | 0.228086i | ||||
\(520\) | 18.0000 | 0.789352 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 9.00000 | − | 15.5885i | 0.393919 | − | 0.682288i | ||||
\(523\) | −4.50000 | − | 2.59808i | −0.196771 | − | 0.113606i | 0.398377 | − | 0.917222i | \(-0.369573\pi\) |
−0.595149 | + | 0.803616i | \(0.702907\pi\) | |||||||
\(524\) | 3.46410i | 0.151330i | ||||||||
\(525\) | 12.1244i | 0.529150i | ||||||||
\(526\) | 21.0000 | + | 12.1244i | 0.915644 | + | 0.528647i | ||||
\(527\) | −3.00000 | − | 5.19615i | −0.130682 | − | 0.226348i | ||||
\(528\) | 3.00000 | − | 5.19615i | 0.130558 | − | 0.226134i | ||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | 36.0000 | − | 20.7846i | 1.56374 | − | 0.902826i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.500000 | − | 4.33013i | 0.0216777 | − | 0.187735i | ||||
\(533\) | − | 62.3538i | − | 2.70084i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −54.0000 | + | 31.1769i | −2.33462 | + | 1.34790i | ||||
\(536\) | 7.50000 | + | 4.33013i | 0.323951 | + | 0.187033i | ||||
\(537\) | −18.0000 | + | 10.3923i | −0.776757 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.7846i | 0.895257i | ||||||||
\(540\) | −18.0000 | −0.774597 | ||||||||
\(541\) | 6.50000 | − | 11.2583i | 0.279457 | − | 0.484033i | −0.691793 | − | 0.722096i | \(-0.743179\pi\) |
0.971250 | + | 0.238062i | \(0.0765123\pi\) | |||||||
\(542\) | −4.00000 | + | 6.92820i | −0.171815 | + | 0.297592i | ||||
\(543\) | 12.0000 | 0.514969 | ||||||||
\(544\) | − | 3.46410i | − | 0.148522i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.50000 | + | 7.79423i | 0.192582 | + | 0.333562i | ||||
\(547\) | 22.5000 | + | 12.9904i | 0.962031 | + | 0.555429i | 0.896797 | − | 0.442441i | \(-0.145888\pi\) |
0.0652331 | + | 0.997870i | \(0.479221\pi\) | |||||||
\(548\) | 3.00000 | − | 1.73205i | 0.128154 | − | 0.0739895i | ||||
\(549\) | 10.5000 | + | 18.1865i | 0.448129 | + | 0.776182i | ||||
\(550\) | 24.2487i | 1.03397i | ||||||||
\(551\) | 3.00000 | − | 25.9808i | 0.127804 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.50000 | − | 2.59808i | 0.191359 | − | 0.110481i | ||||
\(554\) | 1.00000 | + | 1.73205i | 0.0424859 | + | 0.0735878i | ||||
\(555\) | 27.0000 | + | 15.5885i | 1.14609 | + | 0.661693i | ||||
\(556\) | 2.50000 | + | 4.33013i | 0.106024 | + | 0.183638i | ||||
\(557\) | −3.00000 | − | 1.73205i | −0.127114 | − | 0.0733893i | 0.435095 | − | 0.900385i | \(-0.356715\pi\) |
−0.562209 | + | 0.826995i | \(0.690048\pi\) | |||||||
\(558\) | − | 5.19615i | − | 0.219971i | ||||||
\(559\) | 5.19615i | 0.219774i | ||||||||
\(560\) | −3.00000 | − | 1.73205i | −0.126773 | − | 0.0731925i | ||||
\(561\) | −18.0000 | − | 10.3923i | −0.759961 | − | 0.438763i | ||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 18.0000 | 0.758610 | 0.379305 | − | 0.925272i | \(-0.376163\pi\) | ||||
0.379305 | + | 0.925272i | \(0.376163\pi\) | |||||||
\(564\) | 6.00000 | − | 10.3923i | 0.252646 | − | 0.437595i | ||||
\(565\) | −36.0000 | + | 20.7846i | −1.51453 | + | 0.874415i | ||||
\(566\) | 14.0000 | − | 24.2487i | 0.588464 | − | 1.01925i | ||||
\(567\) | −4.50000 | − | 7.79423i | −0.188982 | − | 0.327327i | ||||
\(568\) | −3.00000 | − | 5.19615i | −0.125877 | − | 0.218026i | ||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | −24.0000 | + | 10.3923i | −1.00525 | + | 0.435286i | ||||
\(571\) | 5.00000 | 0.209243 | 0.104622 | − | 0.994512i | \(-0.466637\pi\) | ||||
0.104622 | + | 0.994512i | \(0.466637\pi\) | |||||||
\(572\) | 9.00000 | + | 15.5885i | 0.376309 | + | 0.651786i | ||||
\(573\) | 15.0000 | + | 25.9808i | 0.626634 | + | 1.08536i | ||||
\(574\) | −6.00000 | + | 10.3923i | −0.250435 | + | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | −38.0000 | −1.58196 | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | 5.00000 | 0.207973 | ||||||||
\(579\) | 10.5000 | − | 18.1865i | 0.436365 | − | 0.755807i | ||||
\(580\) | −18.0000 | − | 10.3923i | −0.747409 | − | 0.431517i | ||||
\(581\) | 10.3923i | 0.431145i | ||||||||
\(582\) | 12.0000 | 0.497416 | ||||||||
\(583\) | 36.0000 | + | 20.7846i | 1.49097 | + | 0.860811i | ||||
\(584\) | 3.50000 | + | 6.06218i | 0.144831 | + | 0.250855i | ||||
\(585\) | 27.0000 | − | 46.7654i | 1.11631 | − | 1.93351i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.00000 | − | 3.46410i | 0.247647 | − | 0.142979i | −0.371040 | − | 0.928617i | \(-0.620999\pi\) |
0.618686 | + | 0.785638i | \(0.287665\pi\) | |||||||
\(588\) | 10.3923i | 0.428571i | ||||||||
\(589\) | −3.00000 | − | 6.92820i | −0.123613 | − | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.50000 | + | 2.59808i | −0.184949 | + | 0.106780i | ||||
\(593\) | −36.0000 | − | 20.7846i | −1.47834 | − | 0.853522i | −0.478643 | − | 0.878010i | \(-0.658871\pi\) |
−0.999700 | + | 0.0244882i | \(0.992204\pi\) | |||||||
\(594\) | −9.00000 | − | 15.5885i | −0.369274 | − | 0.639602i | ||||
\(595\) | −6.00000 | + | 10.3923i | −0.245976 | + | 0.426043i | ||||
\(596\) | 17.3205i | 0.709476i | ||||||||
\(597\) | 43.3013i | 1.77220i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0000 | − | 25.9808i | 0.612883 | − | 1.06155i | −0.377869 | − | 0.925859i | \(-0.623343\pi\) |
0.990752 | − | 0.135686i | \(-0.0433238\pi\) | |||||||
\(600\) | 12.1244i | 0.494975i | ||||||||
\(601\) | − | 1.73205i | − | 0.0706518i | −0.999376 | − | 0.0353259i | \(-0.988753\pi\) | ||
0.999376 | − | 0.0353259i | \(-0.0112469\pi\) | |||||||
\(602\) | 0.500000 | − | 0.866025i | 0.0203785 | − | 0.0352966i | ||||
\(603\) | 22.5000 | − | 12.9904i | 0.916271 | − | 0.529009i | ||||
\(604\) | 3.00000 | + | 1.73205i | 0.122068 | + | 0.0704761i | ||||
\(605\) | −3.00000 | + | 1.73205i | −0.121967 | + | 0.0704179i | ||||
\(606\) | 9.00000 | + | 15.5885i | 0.365600 | + | 0.633238i | ||||
\(607\) | − | 32.9090i | − | 1.33573i | −0.744281 | − | 0.667867i | \(-0.767208\pi\) | ||
0.744281 | − | 0.667867i | \(-0.232792\pi\) | |||||||
\(608\) | 0.500000 | − | 4.33013i | 0.0202777 | − | 0.175610i | ||||
\(609\) | − | 10.3923i | − | 0.421117i | ||||||
\(610\) | 21.0000 | − | 12.1244i | 0.850265 | − | 0.490901i | ||||
\(611\) | 18.0000 | + | 31.1769i | 0.728202 | + | 1.26128i | ||||
\(612\) | −9.00000 | − | 5.19615i | −0.363803 | − | 0.210042i | ||||
\(613\) | 19.0000 | + | 32.9090i | 0.767403 | + | 1.32918i | 0.938967 | + | 0.344008i | \(0.111785\pi\) |
−0.171564 | + | 0.985173i | \(0.554882\pi\) | |||||||
\(614\) | −27.0000 | − | 15.5885i | −1.08963 | − | 0.629099i | ||||
\(615\) | 72.0000 | 2.90332 | ||||||||
\(616\) | − | 3.46410i | − | 0.139573i | ||||||
\(617\) | 33.0000 | + | 19.0526i | 1.32853 | + | 0.767027i | 0.985072 | − | 0.172141i | \(-0.0550685\pi\) |
0.343458 | + | 0.939168i | \(0.388402\pi\) | |||||||
\(618\) | 7.50000 | − | 12.9904i | 0.301694 | − | 0.522550i | ||||
\(619\) | −17.0000 | −0.683288 | −0.341644 | − | 0.939829i | \(-0.610984\pi\) | ||||
−0.341644 | + | 0.939829i | \(0.610984\pi\) | |||||||
\(620\) | −6.00000 | −0.240966 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | − | 6.92820i | 0.481156 | − | 0.277796i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.50000 | + | 7.79423i | 0.180144 | + | 0.312019i | ||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | −14.0000 | −0.559553 | ||||||||
\(627\) | −21.0000 | − | 15.5885i | −0.838659 | − | 0.622543i | ||||
\(628\) | 7.00000 | 0.279330 | ||||||||
\(629\) | 9.00000 | + | 15.5885i | 0.358854 | + | 0.621552i | ||||
\(630\) | −9.00000 | + | 5.19615i | −0.358569 | + | 0.207020i | ||||
\(631\) | −6.50000 | + | 11.2583i | −0.258761 | + | 0.448187i | −0.965910 | − | 0.258877i | \(-0.916648\pi\) |
0.707149 | + | 0.707064i | \(0.249981\pi\) | |||||||
\(632\) | 4.50000 | − | 2.59808i | 0.179000 | − | 0.103346i | ||||
\(633\) | 19.5000 | − | 33.7750i | 0.775055 | − | 1.34244i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | −36.0000 | −1.42862 | ||||||||
\(636\) | 18.0000 | + | 10.3923i | 0.713746 | + | 0.412082i | ||||
\(637\) | −27.0000 | − | 15.5885i | −1.06978 | − | 0.617637i | ||||
\(638\) | − | 20.7846i | − | 0.822871i | ||||||
\(639\) | −18.0000 | −0.712069 | ||||||||
\(640\) | −3.00000 | − | 1.73205i | −0.118585 | − | 0.0684653i | ||||
\(641\) | 12.0000 | + | 20.7846i | 0.473972 | + | 0.820943i | 0.999556 | − | 0.0297987i | \(-0.00948663\pi\) |
−0.525584 | + | 0.850741i | \(0.676153\pi\) | |||||||
\(642\) | −27.0000 | − | 15.5885i | −1.06561 | − | 0.615227i | ||||
\(643\) | −2.50000 | − | 4.33013i | −0.0985904 | − | 0.170764i | 0.812511 | − | 0.582946i | \(-0.198100\pi\) |
−0.911101 | + | 0.412182i | \(0.864767\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | −15.0000 | − | 1.73205i | −0.590167 | − | 0.0681466i | ||||
\(647\) | 38.1051i | 1.49807i | 0.662532 | + | 0.749033i | \(0.269482\pi\) | ||||
−0.662532 | + | 0.749033i | \(0.730518\pi\) | |||||||
\(648\) | −4.50000 | − | 7.79423i | −0.176777 | − | 0.306186i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −31.5000 | − | 18.1865i | −1.23553 | − | 0.713335i | ||||
\(651\) | −1.50000 | − | 2.59808i | −0.0587896 | − | 0.101827i | ||||
\(652\) | 5.50000 | − | 9.52628i | 0.215397 | − | 0.373078i | ||||
\(653\) | − | 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 | ||||
\(656\) | −6.00000 | + | 10.3923i | −0.234261 | + | 0.405751i | ||||
\(657\) | 21.0000 | 0.819288 | ||||||||
\(658\) | − | 6.92820i | − | 0.270089i | ||||||
\(659\) | −3.00000 | + | 5.19615i | −0.116863 | + | 0.202413i | −0.918523 | − | 0.395367i | \(-0.870617\pi\) |
0.801660 | + | 0.597781i | \(0.203951\pi\) | |||||||
\(660\) | −18.0000 | + | 10.3923i | −0.700649 | + | 0.404520i | ||||
\(661\) | −12.0000 | − | 6.92820i | −0.466746 | − | 0.269476i | 0.248131 | − | 0.968727i | \(-0.420184\pi\) |
−0.714877 | + | 0.699251i | \(0.753517\pi\) | |||||||
\(662\) | −4.50000 | + | 2.59808i | −0.174897 | + | 0.100977i | ||||
\(663\) | 27.0000 | − | 15.5885i | 1.04859 | − | 0.605406i | ||||
\(664\) | 10.3923i | 0.403300i | ||||||||
\(665\) | −9.00000 | + | 12.1244i | −0.349005 | + | 0.470162i | ||||
\(666\) | 15.5885i | 0.604040i | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.00000 | + | 10.3923i | 0.232147 | + | 0.402090i | ||||
\(669\) | −16.5000 | + | 28.5788i | −0.637927 | + | 1.10492i | ||||
\(670\) | −15.0000 | − | 25.9808i | −0.579501 | − | 1.00372i | ||||
\(671\) | 21.0000 | + | 12.1244i | 0.810696 | + | 0.468056i | ||||
\(672\) | − | 1.73205i | − | 0.0668153i | ||||||
\(673\) | 12.1244i | 0.467360i | 0.972314 | + | 0.233680i | \(0.0750767\pi\) | ||||
−0.972314 | + | 0.233680i | \(0.924923\pi\) | |||||||
\(674\) | −1.50000 | − | 0.866025i | −0.0577778 | − | 0.0333581i | ||||
\(675\) | 31.5000 | + | 18.1865i | 1.21244 | + | 0.700000i | ||||
\(676\) | −14.0000 | −0.538462 | ||||||||
\(677\) | −36.0000 | −1.38359 | −0.691796 | − | 0.722093i | \(-0.743180\pi\) | ||||
−0.691796 | + | 0.722093i | \(0.743180\pi\) | |||||||
\(678\) | −18.0000 | − | 10.3923i | −0.691286 | − | 0.399114i | ||||
\(679\) | 6.00000 | − | 3.46410i | 0.230259 | − | 0.132940i | ||||
\(680\) | −6.00000 | + | 10.3923i | −0.230089 | + | 0.398527i | ||||
\(681\) | −27.0000 | + | 15.5885i | −1.03464 | + | 0.597351i | ||||
\(682\) | −3.00000 | − | 5.19615i | −0.114876 | − | 0.198971i | ||||
\(683\) | −30.0000 | −1.14792 | −0.573959 | − | 0.818884i | \(-0.694593\pi\) | ||||
−0.573959 | + | 0.818884i | \(0.694593\pi\) | |||||||
\(684\) | −10.5000 | − | 7.79423i | −0.401478 | − | 0.298020i | ||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 6.50000 | + | 11.2583i | 0.248171 | + | 0.429845i | ||||
\(687\) | −19.5000 | + | 11.2583i | −0.743971 | + | 0.429532i | ||||
\(688\) | 0.500000 | − | 0.866025i | 0.0190623 | − | 0.0330169i | ||||
\(689\) | −54.0000 | + | 31.1769i | −2.05724 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −9.00000 | − | 5.19615i | −0.341882 | − | 0.197386i | ||||
\(694\) | −21.0000 | − | 12.1244i | −0.797149 | − | 0.460234i | ||||
\(695\) | − | 17.3205i | − | 0.657004i | ||||||
\(696\) | − | 10.3923i | − | 0.393919i | ||||||
\(697\) | 36.0000 | + | 20.7846i | 1.36360 | + | 0.787273i | ||||
\(698\) | 3.50000 | + | 6.06218i | 0.132477 | + | 0.229457i | ||||
\(699\) | −15.0000 | + | 25.9808i | −0.567352 | + | 0.982683i | ||||
\(700\) | 3.50000 | + | 6.06218i | 0.132288 | + | 0.229129i | ||||
\(701\) | −9.00000 | + | 5.19615i | −0.339925 | + | 0.196256i | −0.660239 | − | 0.751056i | \(-0.729545\pi\) |
0.320314 | + | 0.947312i | \(0.396212\pi\) | |||||||
\(702\) | 27.0000 | 1.01905 | ||||||||
\(703\) | 9.00000 | + | 20.7846i | 0.339441 | + | 0.783906i | ||||
\(704\) | − | 3.46410i | − | 0.130558i | ||||||
\(705\) | −36.0000 | + | 20.7846i | −1.35584 | + | 0.782794i | ||||
\(706\) | −9.00000 | + | 5.19615i | −0.338719 | + | 0.195560i | ||||
\(707\) | 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 | \(0.0881700\pi\) | |||||||
\(710\) | 20.7846i | 0.780033i | ||||||||
\(711\) | − | 15.5885i | − | 0.584613i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −6.00000 | −0.224544 | ||||||||
\(715\) | − | 62.3538i | − | 2.33190i | ||||||
\(716\) | −6.00000 | + | 10.3923i | −0.224231 | + | 0.388379i | ||||
\(717\) | −21.0000 | − | 36.3731i | −0.784259 | − | 1.35838i | ||||
\(718\) | 6.00000 | + | 3.46410i | 0.223918 | + | 0.129279i | ||||
\(719\) | 24.0000 | − | 13.8564i | 0.895049 | − | 0.516757i | 0.0194584 | − | 0.999811i | \(-0.493806\pi\) |
0.875591 | + | 0.483054i | \(0.160472\pi\) | |||||||
\(720\) | −9.00000 | + | 5.19615i | −0.335410 | + | 0.193649i | ||||
\(721\) | − | 8.66025i | − | 0.322525i | ||||||
\(722\) | −18.5000 | − | 4.33013i | −0.688499 | − | 0.161151i | ||||
\(723\) | 3.00000 | 0.111571 | ||||||||
\(724\) | 6.00000 | − | 3.46410i | 0.222988 | − | 0.128742i | ||||
\(725\) | 21.0000 | + | 36.3731i | 0.779920 | + | 1.35086i | ||||
\(726\) | −1.50000 | − | 0.866025i | −0.0556702 | − | 0.0321412i | ||||
\(727\) | 18.5000 | + | 32.0429i | 0.686127 | + | 1.18841i | 0.973081 | + | 0.230463i | \(0.0740239\pi\) |
−0.286954 | + | 0.957944i | \(0.592643\pi\) | |||||||
\(728\) | 4.50000 | + | 2.59808i | 0.166781 | + | 0.0962911i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | − | 24.2487i | − | 0.897485i | ||||||
\(731\) | −3.00000 | − | 1.73205i | −0.110959 | − | 0.0640622i | ||||
\(732\) | 10.5000 | + | 6.06218i | 0.388091 | + | 0.224065i | ||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 17.0000 | 0.627481 | ||||||||
\(735\) | 18.0000 | − | 31.1769i | 0.663940 | − | 1.14998i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.0000 | − | 25.9808i | 0.552532 | − | 0.957014i | ||||
\(738\) | 18.0000 | + | 31.1769i | 0.662589 | + | 1.14764i | ||||
\(739\) | −12.5000 | − | 21.6506i | −0.459820 | − | 0.796431i | 0.539131 | − | 0.842222i | \(-0.318753\pi\) |
−0.998951 | + | 0.0457903i | \(0.985419\pi\) | |||||||
\(740\) | 18.0000 | 0.661693 | ||||||||
\(741\) | 36.0000 | − | 15.5885i | 1.32249 | − | 0.572656i | ||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | −1.50000 | − | 2.59808i | −0.0549927 | − | 0.0952501i | ||||
\(745\) | 30.0000 | − | 51.9615i | 1.09911 | − | 1.90372i | ||||
\(746\) | 6.00000 | − | 3.46410i | 0.219676 | − | 0.126830i | ||||
\(747\) | 27.0000 | + | 15.5885i | 0.987878 | + | 0.570352i | ||||
\(748\) | −12.0000 | −0.438763 | ||||||||
\(749\) | −18.0000 | −0.657706 | ||||||||
\(750\) | 6.00000 | − | 10.3923i | 0.219089 | − | 0.379473i | ||||
\(751\) | 31.5000 | + | 18.1865i | 1.14945 | + | 0.663636i | 0.948753 | − | 0.316017i | \(-0.102346\pi\) |
0.200698 | + | 0.979653i | \(0.435679\pi\) | |||||||
\(752\) | − | 6.92820i | − | 0.252646i | ||||||
\(753\) | 12.0000 | 0.437304 | ||||||||
\(754\) | 27.0000 | + | 15.5885i | 0.983282 | + | 0.567698i | ||||
\(755\) | −6.00000 | − | 10.3923i | −0.218362 | − | 0.378215i | ||||
\(756\) | −4.50000 | − | 2.59808i | −0.163663 | − | 0.0944911i | ||||
\(757\) | −6.50000 | − | 11.2583i | −0.236247 | − | 0.409191i | 0.723388 | − | 0.690442i | \(-0.242584\pi\) |
−0.959634 | + | 0.281251i | \(0.909251\pi\) | |||||||
\(758\) | −10.5000 | + | 6.06218i | −0.381377 | + | 0.220188i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.00000 | + | 12.1244i | −0.326464 | + | 0.439797i | ||||
\(761\) | 27.7128i | 1.00459i | 0.864697 | + | 0.502294i | \(0.167511\pi\) | ||||
−0.864697 | + | 0.502294i | \(0.832489\pi\) | |||||||
\(762\) | −9.00000 | − | 15.5885i | −0.326036 | − | 0.564710i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15.0000 | + | 8.66025i | 0.542681 | + | 0.313317i | ||||
\(765\) | 18.0000 | + | 31.1769i | 0.650791 | + | 1.12720i | ||||
\(766\) | 3.00000 | − | 5.19615i | 0.108394 | − | 0.187745i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 1.73205i | − | 0.0625000i | ||||||
\(769\) | −18.5000 | + | 32.0429i | −0.667127 | + | 1.15550i | 0.311577 | + | 0.950221i | \(0.399143\pi\) |
−0.978704 | + | 0.205277i | \(0.934190\pi\) | |||||||
\(770\) | −6.00000 | + | 10.3923i | −0.216225 | + | 0.374513i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 12.1244i | − | 0.436365i | ||||||
\(773\) | −12.0000 | + | 20.7846i | −0.431610 | + | 0.747570i | −0.997012 | − | 0.0772449i | \(-0.975388\pi\) |
0.565402 | + | 0.824815i | \(0.308721\pi\) | |||||||
\(774\) | −1.50000 | − | 2.59808i | −0.0539164 | − | 0.0933859i | ||||
\(775\) | 10.5000 | + | 6.06218i | 0.377171 | + | 0.217760i | ||||
\(776\) | 6.00000 | − | 3.46410i | 0.215387 | − | 0.124354i | ||||
\(777\) | 4.50000 | + | 7.79423i | 0.161437 | + | 0.279616i | ||||
\(778\) | 27.7128i | 0.993552i | ||||||||
\(779\) | 42.0000 | + | 31.1769i | 1.50481 | + | 1.11703i | ||||
\(780\) | − | 31.1769i | − | 1.11631i | ||||||
\(781\) | −18.0000 | + | 10.3923i | −0.644091 | + | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.0000 | − | 15.5885i | −0.964901 | − | 0.557086i | ||||
\(784\) | 3.00000 | + | 5.19615i | 0.107143 | + | 0.185577i | ||||
\(785\) | −21.0000 | − | 12.1244i | −0.749522 | − | 0.432737i | ||||
\(786\) | 6.00000 | 0.214013 | ||||||||
\(787\) | 25.9808i | 0.926114i | 0.886328 | + | 0.463057i | \(0.153248\pi\) | ||||
−0.886328 | + | 0.463057i | \(0.846752\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.0000 | − | 36.3731i | 0.747620 | − | 1.29492i | ||||
\(790\) | −18.0000 | −0.640411 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | −9.00000 | − | 5.19615i | −0.319801 | − | 0.184637i | ||||
\(793\) | −31.5000 | + | 18.1865i | −1.11860 | + | 0.645823i | ||||
\(794\) | −14.5000 | + | 25.1147i | −0.514586 | + | 0.891289i | ||||
\(795\) | −36.0000 | − | 62.3538i | −1.27679 | − | 2.21146i | ||||
\(796\) | 12.5000 | + | 21.6506i | 0.443051 | + | 0.767386i | ||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | −7.50000 | − | 0.866025i | −0.265497 | − | 0.0306570i | ||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 3.50000 | + | 6.06218i | 0.123744 | + | 0.214330i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.0000 | + | 20.7846i | −0.423735 | + | 0.733930i | ||||
\(803\) | 21.0000 | − | 12.1244i | 0.741074 | − | 0.427859i | ||||
\(804\) | 7.50000 | − | 12.9904i | 0.264505 | − | 0.458135i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.00000 | 0.317011 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.00000 | + | 5.19615i | 0.316619 | + | 0.182800i | ||||
\(809\) | − | 3.46410i | − | 0.121791i | −0.998144 | − | 0.0608957i | \(-0.980604\pi\) | ||
0.998144 | − | 0.0608957i | \(-0.0193957\pi\) | |||||||
\(810\) | 31.1769i | 1.09545i | ||||||||
\(811\) | −27.0000 | − | 15.5885i | −0.948098 | − | 0.547385i | −0.0556086 | − | 0.998453i | \(-0.517710\pi\) |
−0.892490 | + | 0.451068i | \(0.851043\pi\) | |||||||
\(812\) | −3.00000 | − | 5.19615i | −0.105279 | − | 0.182349i | ||||
\(813\) | 12.0000 | + | 6.92820i | 0.420858 | + | 0.242983i | ||||
\(814\) | 9.00000 | + | 15.5885i | 0.315450 | + | 0.546375i | ||||
\(815\) | −33.0000 | + | 19.0526i | −1.15594 | + | 0.667382i | ||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | −3.50000 | − | 2.59808i | −0.122449 | − | 0.0908952i | ||||
\(818\) | − | 34.6410i | − | 1.21119i | ||||||
\(819\) | 13.5000 | − | 7.79423i | 0.471728 | − | 0.272352i | ||||
\(820\) | 36.0000 | − | 20.7846i | 1.25717 | − | 0.725830i | ||||
\(821\) | −21.0000 | − | 12.1244i | −0.732905 | − | 0.423143i | 0.0865789 | − | 0.996245i | \(-0.472407\pi\) |
−0.819484 | + | 0.573102i | \(0.805740\pi\) | |||||||
\(822\) | −3.00000 | − | 5.19615i | −0.104637 | − | 0.181237i | ||||
\(823\) | −20.0000 | + | 34.6410i | −0.697156 | + | 1.20751i | 0.272292 | + | 0.962215i | \(0.412218\pi\) |
−0.969448 | + | 0.245295i | \(0.921115\pi\) | |||||||
\(824\) | − | 8.66025i | − | 0.301694i | ||||||
\(825\) | 42.0000 | 1.46225 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.00000 | + | 5.19615i | −0.104320 | + | 0.180688i | −0.913460 | − | 0.406928i | \(-0.866600\pi\) |
0.809140 | + | 0.587616i | \(0.199933\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.2295i | 1.74454i | 0.489023 | + | 0.872271i | \(0.337353\pi\) | ||||
−0.489023 | + | 0.872271i | \(0.662647\pi\) | |||||||
\(830\) | 18.0000 | − | 31.1769i | 0.624789 | − | 1.08217i | ||||
\(831\) | 3.00000 | − | 1.73205i | 0.104069 | − | 0.0600842i | ||||
\(832\) | 4.50000 | + | 2.59808i | 0.156009 | + | 0.0900721i | ||||
\(833\) | 18.0000 | − | 10.3923i | 0.623663 | − | 0.360072i | ||||
\(834\) | 7.50000 | − | 4.33013i | 0.259704 | − | 0.149940i | ||||
\(835\) | − | 41.5692i | − | 1.43856i | ||||||
\(836\) | −15.0000 | − | 1.73205i | −0.518786 | − | 0.0599042i | ||||
\(837\) | −9.00000 | −0.311086 | ||||||||
\(838\) | 9.00000 | − | 5.19615i | 0.310900 | − | 0.179498i | ||||
\(839\) | −27.0000 | − | 46.7654i | −0.932144 | − | 1.61452i | −0.779650 | − | 0.626215i | \(-0.784603\pi\) |
−0.152493 | − | 0.988304i | \(-0.548730\pi\) | |||||||
\(840\) | −3.00000 | + | 5.19615i | −0.103510 | + | 0.179284i | ||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −12.0000 | − | 6.92820i | −0.413547 | − | 0.238762i | ||||
\(843\) | − | 10.3923i | − | 0.357930i | ||||||
\(844\) | − | 22.5167i | − | 0.775055i | ||||||
\(845\) | 42.0000 | + | 24.2487i | 1.44484 | + | 0.834181i | ||||
\(846\) | −18.0000 | − | 10.3923i | −0.618853 | − | 0.357295i | ||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 12.0000 | 0.412082 | ||||||||
\(849\) | −42.0000 | − | 24.2487i | −1.44144 | − | 0.832214i | ||||
\(850\) | 21.0000 | − | 12.1244i | 0.720294 | − | 0.415862i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −9.00000 | + | 5.19615i | −0.308335 | + | 0.178017i | ||||
\(853\) | −2.50000 | − | 4.33013i | −0.0855984 | − | 0.148261i | 0.820048 | − | 0.572295i | \(-0.193947\pi\) |
−0.905646 | + | 0.424034i | \(0.860614\pi\) | |||||||
\(854\) | 7.00000 | 0.239535 | ||||||||
\(855\) | 18.0000 | + | 41.5692i | 0.615587 | + | 1.42164i | ||||
\(856\) | −18.0000 | −0.615227 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 27.0000 | − | 15.5885i | 0.921765 | − | 0.532181i | ||||
\(859\) | 17.5000 | − | 30.3109i | 0.597092 | − | 1.03419i | −0.396156 | − | 0.918183i | \(-0.629656\pi\) |
0.993248 | − | 0.116011i | \(-0.0370107\pi\) | |||||||
\(860\) | −3.00000 | + | 1.73205i | −0.102299 | + | 0.0590624i | ||||
\(861\) | 18.0000 | + | 10.3923i | 0.613438 | + | 0.354169i | ||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | −4.50000 | − | 2.59808i | −0.153093 | − | 0.0883883i | ||||
\(865\) | 18.0000 | + | 10.3923i | 0.612018 | + | 0.353349i | ||||
\(866\) | 19.0526i | 0.647432i | ||||||||
\(867\) | − | 8.66025i | − | 0.294118i | ||||||
\(868\) | −1.50000 | − | 0.866025i | −0.0509133 | − | 0.0293948i | ||||
\(869\) | −9.00000 | − | 15.5885i | −0.305304 | − | 0.528802i | ||||
\(870\) | −18.0000 | + | 31.1769i | −0.610257 | + | 1.05700i | ||||
\(871\) | 22.5000 | + | 38.9711i | 0.762383 | + | 1.32049i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 20.7846i | − | 0.703452i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 6.92820i | − | 0.234216i | ||||||
\(876\) | 10.5000 | − | 6.06218i | 0.354762 | − | 0.204822i | ||||
\(877\) | 4.50000 | − | 2.59808i | 0.151954 | − | 0.0877308i | −0.422095 | − | 0.906552i | \(-0.638705\pi\) |
0.574049 | + | 0.818821i | \(0.305372\pi\) | |||||||
\(878\) | 7.50000 | + | 4.33013i | 0.253113 | + | 0.146135i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00000 | + | 10.3923i | −0.202260 | + | 0.350325i | ||||
\(881\) | − | 38.1051i | − | 1.28379i | −0.766791 | − | 0.641897i | \(-0.778148\pi\) | ||
0.766791 | − | 0.641897i | \(-0.221852\pi\) | |||||||
\(882\) | 18.0000 | 0.606092 | ||||||||
\(883\) | −6.50000 | + | 11.2583i | −0.218742 | + | 0.378873i | −0.954424 | − | 0.298455i | \(-0.903529\pi\) |
0.735681 | + | 0.677328i | \(0.236862\pi\) | |||||||
\(884\) | 9.00000 | − | 15.5885i | 0.302703 | − | 0.524297i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.2487i | 0.814651i | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 4.50000 | + | 7.79423i | 0.151010 | + | 0.261557i | ||||
\(889\) | −9.00000 | − | 5.19615i | −0.301850 | − | 0.174273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.0000 | + | 15.5885i | −0.904534 | + | 0.522233i | ||||
\(892\) | 19.0526i | 0.637927i | ||||||||
\(893\) | −30.0000 | − | 3.46410i | −1.00391 | − | 0.115922i | ||||
\(894\) | 30.0000 | 1.00335 | ||||||||
\(895\) | 36.0000 | − | 20.7846i | 1.20335 | − | 0.694753i | ||||
\(896\) | −0.500000 | − | 0.866025i | −0.0167038 | − | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0000 | − | 25.9808i | −0.500556 | − | 0.866989i | ||||
\(899\) | −9.00000 | − | 5.19615i | −0.300167 | − | 0.173301i | ||||
\(900\) | 21.0000 | 0.700000 | ||||||||
\(901\) | − | 41.5692i | − | 1.38487i | ||||||
\(902\) | 36.0000 | + | 20.7846i | 1.19867 | + | 0.692052i | ||||
\(903\) | −1.50000 | − | 0.866025i | −0.0499169 | − | 0.0288195i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | −24.0000 | −0.797787 | ||||||||
\(906\) | 3.00000 | − | 5.19615i | 0.0996683 | − | 0.172631i | ||||
\(907\) | 21.0000 | − | 12.1244i | 0.697294 | − | 0.402583i | −0.109045 | − | 0.994037i | \(-0.534779\pi\) |
0.806339 | + | 0.591454i | \(0.201446\pi\) | |||||||
\(908\) | −9.00000 | + | 15.5885i | −0.298675 | + | 0.517321i | ||||
\(909\) | 27.0000 | − | 15.5885i | 0.895533 | − | 0.517036i | ||||
\(910\) | −9.00000 | − | 15.5885i | −0.298347 | − | 0.516752i | ||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | −7.50000 | − | 0.866025i | −0.248350 | − | 0.0286770i | ||||
\(913\) | 36.0000 | 1.19143 | ||||||||
\(914\) | −8.50000 | − | 14.7224i | −0.281155 | − | 0.486975i | ||||
\(915\) | −21.0000 | − | 36.3731i | −0.694239 | − | 1.20246i | ||||
\(916\) | −6.50000 | + | 11.2583i | −0.214766 | + | 0.371986i | ||||
\(917\) | 3.00000 | − | 1.73205i | 0.0990687 | − | 0.0571974i | ||||
\(918\) | −9.00000 | + | 15.5885i | −0.297044 | + | 0.514496i | ||||
\(919\) | −53.0000 | −1.74831 | −0.874154 | − | 0.485648i | \(-0.838584\pi\) | ||||
−0.874154 | + | 0.485648i | \(0.838584\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.0000 | + | 46.7654i | −0.889680 | + | 1.54097i | ||||
\(922\) | −6.00000 | − | 3.46410i | −0.197599 | − | 0.114084i | ||||
\(923\) | − | 31.1769i | − | 1.02620i | ||||||
\(924\) | −6.00000 | −0.197386 | ||||||||
\(925\) | −31.5000 | − | 18.1865i | −1.03571 | − | 0.597970i | ||||
\(926\) | 9.50000 | + | 16.4545i | 0.312189 | + | 0.540728i | ||||
\(927\) | −22.5000 | − | 12.9904i | −0.738997 | − | 0.426660i | ||||
\(928\) | −3.00000 | − | 5.19615i | −0.0984798 | − | 0.170572i | ||||
\(929\) | 45.0000 | − | 25.9808i | 1.47640 | − | 0.852401i | 0.476757 | − | 0.879035i | \(-0.341812\pi\) |
0.999645 | + | 0.0266341i | \(0.00847889\pi\) | |||||||
\(930\) | 10.3923i | 0.340777i | ||||||||
\(931\) | 24.0000 | − | 10.3923i | 0.786568 | − | 0.340594i | ||||
\(932\) | 17.3205i | 0.567352i | ||||||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | 24.0000 | − | 13.8564i | 0.785304 | − | 0.453395i | ||||
\(935\) | 36.0000 | + | 20.7846i | 1.17733 | + | 0.679729i | ||||
\(936\) | 13.5000 | − | 7.79423i | 0.441261 | − | 0.254762i | ||||
\(937\) | −11.5000 | + | 19.9186i | −0.375689 | + | 0.650712i | −0.990430 | − | 0.138017i | \(-0.955927\pi\) |
0.614741 | + | 0.788729i | \(0.289260\pi\) | |||||||
\(938\) | − | 8.66025i | − | 0.282767i | ||||||
\(939\) | 24.2487i | 0.791327i | ||||||||
\(940\) | −12.0000 | + | 20.7846i | −0.391397 | + | 0.677919i | ||||
\(941\) | −12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | \(-0.961269\pi\) |
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(942\) | − | 12.1244i | − | 0.395033i | ||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.00000 | + | 15.5885i | 0.292770 | + | 0.507093i | ||||
\(946\) | −3.00000 | − | 1.73205i | −0.0975384 | − | 0.0563138i | ||||
\(947\) | −27.0000 | + | 15.5885i | −0.877382 | + | 0.506557i | −0.869794 | − | 0.493414i | \(-0.835749\pi\) |
−0.00758776 | + | 0.999971i | \(0.502415\pi\) | |||||||
\(948\) | −4.50000 | − | 7.79423i | −0.146153 | − | 0.253145i | ||||
\(949\) | 36.3731i | 1.18072i | ||||||||
\(950\) | 28.0000 | − | 12.1244i | 0.908440 | − | 0.393366i | ||||
\(951\) | 10.3923i | 0.336994i | ||||||||
\(952\) | −3.00000 | + | 1.73205i | −0.0972306 | + | 0.0561361i | ||||
\(953\) | −3.00000 | − | 5.19615i | −0.0971795 | − | 0.168320i | 0.813337 | − | 0.581793i | \(-0.197649\pi\) |
−0.910516 | + | 0.413473i | \(0.864315\pi\) | |||||||
\(954\) | 18.0000 | − | 31.1769i | 0.582772 | − | 1.00939i | ||||
\(955\) | −30.0000 | − | 51.9615i | −0.970777 | − | 1.68144i | ||||
\(956\) | −21.0000 | − | 12.1244i | −0.679189 | − | 0.392130i | ||||
\(957\) | −36.0000 | −1.16371 | ||||||||
\(958\) | − | 10.3923i | − | 0.335760i | ||||||
\(959\) | −3.00000 | − | 1.73205i | −0.0968751 | − | 0.0559308i | ||||
\(960\) | −3.00000 | + | 5.19615i | −0.0968246 | + | 0.167705i | ||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | −27.0000 | −0.870515 | ||||||||
\(963\) | −27.0000 | + | 46.7654i | −0.870063 | + | 1.50699i | ||||
\(964\) | 1.50000 | − | 0.866025i | 0.0483117 | − | 0.0278928i | ||||
\(965\) | −21.0000 | + | 36.3731i | −0.676014 | + | 1.17089i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.5000 | + | 25.1147i | 0.466289 | + | 0.807635i | 0.999259 | − | 0.0384986i | \(-0.0122575\pi\) |
−0.532970 | + | 0.846134i | \(0.678924\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −3.00000 | + | 25.9808i | −0.0963739 | + | 0.834622i | ||||
\(970\) | −24.0000 | −0.770594 | ||||||||
\(971\) | 24.0000 | + | 41.5692i | 0.770197 | + | 1.33402i | 0.937455 | + | 0.348107i | \(0.113175\pi\) |
−0.167258 | + | 0.985913i | \(0.553491\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | 2.50000 | − | 4.33013i | 0.0801463 | − | 0.138817i | ||||
\(974\) | −3.00000 | + | 1.73205i | −0.0961262 | + | 0.0554985i | ||||
\(975\) | −31.5000 | + | 54.5596i | −1.00881 | + | 1.74731i | ||||
\(976\) | 7.00000 | 0.224065 | ||||||||
\(977\) | 12.0000 | 0.383914 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(978\) | −16.5000 | − | 9.52628i | −0.527612 | − | 0.304617i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 20.7846i | − | 0.663940i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.00000 | + | 5.19615i | 0.287202 | + | 0.165816i | ||||
\(983\) | 21.0000 | + | 36.3731i | 0.669796 | + | 1.16012i | 0.977961 | + | 0.208788i | \(0.0669518\pi\) |
−0.308165 | + | 0.951333i | \(0.599715\pi\) | |||||||
\(984\) | 18.0000 | + | 10.3923i | 0.573819 | + | 0.331295i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0000 | + | 10.3923i | −0.573237 | + | 0.330958i | ||||
\(987\) | −12.0000 | −0.381964 | ||||||||
\(988\) | 13.5000 | − | 18.1865i | 0.429492 | − | 0.578591i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 18.0000 | + | 31.1769i | 0.572078 | + | 0.990867i | ||||
\(991\) | 31.5000 | − | 18.1865i | 1.00063 | − | 0.577714i | 0.0921957 | − | 0.995741i | \(-0.470611\pi\) |
0.908435 | + | 0.418027i | \(0.137278\pi\) | |||||||
\(992\) | −1.50000 | − | 0.866025i | −0.0476250 | − | 0.0274963i | ||||
\(993\) | 4.50000 | + | 7.79423i | 0.142803 | + | 0.247342i | ||||
\(994\) | −3.00000 | + | 5.19615i | −0.0951542 | + | 0.164812i | ||||
\(995\) | − | 86.6025i | − | 2.74549i | ||||||
\(996\) | 18.0000 | 0.570352 | ||||||||
\(997\) | 26.5000 | − | 45.8993i | 0.839263 | − | 1.45365i | −0.0512480 | − | 0.998686i | \(-0.516320\pi\) |
0.890511 | − | 0.454961i | \(-0.150347\pi\) | |||||||
\(998\) | −15.5000 | + | 26.8468i | −0.490644 | + | 0.849820i | ||||
\(999\) | 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 | 114.2.h.b.107.1 | yes | 2 | |
3.2 | odd | 2 | 114.2.h.c.107.1 | yes | 2 | ||
4.3 | odd | 2 | 912.2.bn.f.449.1 | 2 | |||
12.11 | even | 2 | 912.2.bn.c.449.1 | 2 | |||
19.8 | odd | 6 | 114.2.h.c.65.1 | yes | 2 | ||
57.8 | even | 6 | inner | 114.2.h.b.65.1 | ✓ | 2 | |
76.27 | even | 6 | 912.2.bn.c.65.1 | 2 | |||
228.179 | odd | 6 | 912.2.bn.f.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.h.b.65.1 | ✓ | 2 | 57.8 | even | 6 | inner | |
114.2.h.b.107.1 | yes | 2 | 1.1 | even | 1 | trivial | |
114.2.h.c.65.1 | yes | 2 | 19.8 | odd | 6 | ||
114.2.h.c.107.1 | yes | 2 | 3.2 | odd | 2 | ||
912.2.bn.c.65.1 | 2 | 76.27 | even | 6 | |||
912.2.bn.c.449.1 | 2 | 12.11 | even | 2 | |||
912.2.bn.f.65.1 | 2 | 228.179 | odd | 6 | |||
912.2.bn.f.449.1 | 2 | 4.3 | odd | 2 |