Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(34,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.790518980011\) |
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: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 34.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.34 |
Dual form | 99.2.e.a.67.1 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | −0.986869 | − | 0.161521i | \(-0.948360\pi\) |
0.633316 | + | 0.773893i | \(0.281693\pi\) | |||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | 0.732294 | − | 0.680989i | \(-0.238450\pi\) |
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | −2.00000 | + | 3.46410i | −0.755929 | + | 1.30931i | 0.188982 | + | 0.981981i | \(0.439481\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | −1.50000 | − | 0.866025i | −0.433013 | − | 0.250000i | ||||
\(13\) | 1.00000 | + | 1.73205i | 0.277350 | + | 0.480384i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | −2.00000 | − | 3.46410i | −0.534522 | − | 0.925820i | ||||
\(15\) | 1.50000 | + | 0.866025i | 0.387298 | + | 0.223607i | ||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 1.50000 | + | 2.59808i | 0.353553 | + | 0.612372i | ||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | − | 6.92820i | − | 1.51186i | ||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 4.50000 | − | 2.59808i | 0.918559 | − | 0.530330i | ||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −4.00000 | −0.755929 | ||||||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | −1.50000 | + | 0.866025i | −0.273861 | + | 0.158114i | ||||
\(31\) | −3.50000 | − | 6.06218i | −0.628619 | − | 1.08880i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | −2.50000 | − | 4.33013i | −0.441942 | − | 0.765466i | ||||
\(33\) | − | 1.73205i | − | 0.301511i | ||||||
\(34\) | −2.00000 | + | 3.46410i | −0.342997 | + | 0.594089i | ||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | −3.00000 | + | 5.19615i | −0.486664 | + | 0.842927i | ||||
\(39\) | −3.00000 | − | 1.73205i | −0.480384 | − | 0.277350i | ||||
\(40\) | 1.50000 | + | 2.59808i | 0.237171 | + | 0.410792i | ||||
\(41\) | 1.00000 | + | 1.73205i | 0.156174 | + | 0.270501i | 0.933486 | − | 0.358614i | \(-0.116751\pi\) |
−0.777312 | + | 0.629115i | \(0.783417\pi\) | |||||||
\(42\) | 6.00000 | + | 3.46410i | 0.925820 | + | 0.534522i | ||||
\(43\) | −3.00000 | + | 5.19615i | −0.457496 | + | 0.792406i | −0.998828 | − | 0.0484030i | \(-0.984587\pi\) |
0.541332 | + | 0.840809i | \(0.317920\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 3.50000 | − | 6.06218i | 0.510527 | − | 0.884260i | −0.489398 | − | 0.872060i | \(-0.662783\pi\) |
0.999926 | − | 0.0121990i | \(-0.00388317\pi\) | |||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | −4.50000 | − | 7.79423i | −0.642857 | − | 1.11346i | ||||
\(50\) | 2.00000 | + | 3.46410i | 0.282843 | + | 0.489898i | ||||
\(51\) | −6.00000 | + | 3.46410i | −0.840168 | + | 0.485071i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | −4.50000 | − | 2.59808i | −0.612372 | − | 0.353553i | ||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 6.00000 | − | 10.3923i | 0.801784 | − | 1.38873i | ||||
\(57\) | −9.00000 | + | 5.19615i | −1.19208 | + | 0.688247i | ||||
\(58\) | −3.00000 | − | 5.19615i | −0.393919 | − | 0.682288i | ||||
\(59\) | 3.50000 | + | 6.06218i | 0.455661 | + | 0.789228i | 0.998726 | − | 0.0504625i | \(-0.0160695\pi\) |
−0.543065 | + | 0.839691i | \(0.682736\pi\) | |||||||
\(60\) | 1.73205i | 0.223607i | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 7.00000 | 0.889001 | ||||||||
\(63\) | 6.00000 | + | 10.3923i | 0.755929 | + | 1.30931i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 1.00000 | − | 1.73205i | 0.124035 | − | 0.214834i | ||||
\(66\) | 1.50000 | + | 0.866025i | 0.184637 | + | 0.106600i | ||||
\(67\) | −5.50000 | − | 9.52628i | −0.671932 | − | 1.16382i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.305424 | − | 0.952217i | \(-0.401202\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | −6.00000 | − | 3.46410i | −0.722315 | − | 0.417029i | ||||
\(70\) | −2.00000 | + | 3.46410i | −0.239046 | + | 0.414039i | ||||
\(71\) | 9.00000 | 1.06810 | 0.534052 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534052 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(72\) | −4.50000 | + | 7.79423i | −0.530330 | + | 0.918559i | ||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | −1.50000 | + | 2.59808i | −0.174371 | + | 0.302020i | ||||
\(75\) | 6.92820i | 0.800000i | ||||||||
\(76\) | 3.00000 | + | 5.19615i | 0.344124 | + | 0.596040i | ||||
\(77\) | −2.00000 | − | 3.46410i | −0.227921 | − | 0.394771i | ||||
\(78\) | 3.00000 | − | 1.73205i | 0.339683 | − | 0.196116i | ||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | 6.00000 | − | 10.3923i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621783\pi\) | |||||||
\(84\) | 6.00000 | − | 3.46410i | 0.654654 | − | 0.377964i | ||||
\(85\) | −2.00000 | − | 3.46410i | −0.216930 | − | 0.375735i | ||||
\(86\) | −3.00000 | − | 5.19615i | −0.323498 | − | 0.560316i | ||||
\(87\) | − | 10.3923i | − | 1.11417i | ||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 1.50000 | − | 2.59808i | 0.158114 | − | 0.273861i | ||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | −2.00000 | + | 3.46410i | −0.208514 | + | 0.361158i | ||||
\(93\) | 10.5000 | + | 6.06218i | 1.08880 | + | 0.628619i | ||||
\(94\) | 3.50000 | + | 6.06218i | 0.360997 | + | 0.625266i | ||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 7.50000 | + | 4.33013i | 0.765466 | + | 0.441942i | ||||
\(97\) | 9.50000 | − | 16.4545i | 0.964579 | − | 1.67070i | 0.253837 | − | 0.967247i | \(-0.418307\pi\) |
0.710742 | − | 0.703452i | \(-0.248359\pi\) | |||||||
\(98\) | 9.00000 | 0.909137 | ||||||||
\(99\) | 1.50000 | + | 2.59808i | 0.150756 | + | 0.261116i | ||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 2.00000 | − | 3.46410i | 0.199007 | − | 0.344691i | −0.749199 | − | 0.662344i | \(-0.769562\pi\) |
0.948207 | + | 0.317653i | \(0.102895\pi\) | |||||||
\(102\) | − | 6.92820i | − | 0.685994i | ||||||
\(103\) | 6.50000 | + | 11.2583i | 0.640464 | + | 1.10932i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) |
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | −3.00000 | − | 5.19615i | −0.294174 | − | 0.509525i | ||||
\(105\) | −6.00000 | + | 3.46410i | −0.585540 | + | 0.338062i | ||||
\(106\) | 4.50000 | − | 7.79423i | 0.437079 | − | 0.757042i | ||||
\(107\) | −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 | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −0.500000 | + | 0.866025i | −0.0476731 | + | 0.0825723i | ||||
\(111\) | −4.50000 | + | 2.59808i | −0.427121 | + | 0.246598i | ||||
\(112\) | 2.00000 | + | 3.46410i | 0.188982 | + | 0.327327i | ||||
\(113\) | 7.50000 | + | 12.9904i | 0.705541 | + | 1.22203i | 0.966496 | + | 0.256681i | \(0.0826291\pi\) |
−0.260955 | + | 0.965351i | \(0.584038\pi\) | |||||||
\(114\) | − | 10.3923i | − | 0.973329i | ||||||
\(115\) | 2.00000 | − | 3.46410i | 0.186501 | − | 0.323029i | ||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 6.00000 | 0.554700 | ||||||||
\(118\) | −7.00000 | −0.644402 | ||||||||
\(119\) | −8.00000 | + | 13.8564i | −0.733359 | + | 1.27021i | ||||
\(120\) | −4.50000 | − | 2.59808i | −0.410792 | − | 0.237171i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00000 | − | 1.73205i | −0.270501 | − | 0.156174i | ||||
\(124\) | 3.50000 | − | 6.06218i | 0.314309 | − | 0.544400i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | −12.0000 | −1.06904 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 1.50000 | − | 2.59808i | 0.132583 | − | 0.229640i | ||||
\(129\) | − | 10.3923i | − | 0.914991i | ||||||
\(130\) | 1.00000 | + | 1.73205i | 0.0877058 | + | 0.151911i | ||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 1.50000 | − | 0.866025i | 0.130558 | − | 0.0753778i | ||||
\(133\) | −12.0000 | + | 20.7846i | −1.04053 | + | 1.80225i | ||||
\(134\) | 11.0000 | 0.950255 | ||||||||
\(135\) | 4.50000 | − | 2.59808i | 0.387298 | − | 0.223607i | ||||
\(136\) | −12.0000 | −1.02899 | ||||||||
\(137\) | −2.50000 | + | 4.33013i | −0.213589 | + | 0.369948i | −0.952835 | − | 0.303488i | \(-0.901849\pi\) |
0.739246 | + | 0.673436i | \(0.235182\pi\) | |||||||
\(138\) | 6.00000 | − | 3.46410i | 0.510754 | − | 0.294884i | ||||
\(139\) | 1.00000 | + | 1.73205i | 0.0848189 | + | 0.146911i | 0.905314 | − | 0.424743i | \(-0.139635\pi\) |
−0.820495 | + | 0.571654i | \(0.806302\pi\) | |||||||
\(140\) | 2.00000 | + | 3.46410i | 0.169031 | + | 0.292770i | ||||
\(141\) | 12.1244i | 1.02105i | ||||||||
\(142\) | −4.50000 | + | 7.79423i | −0.377632 | + | 0.654077i | ||||
\(143\) | −2.00000 | −0.167248 | ||||||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | −2.00000 | + | 3.46410i | −0.165521 | + | 0.286691i | ||||
\(147\) | 13.5000 | + | 7.79423i | 1.11346 | + | 0.642857i | ||||
\(148\) | 1.50000 | + | 2.59808i | 0.123299 | + | 0.213561i | ||||
\(149\) | 2.00000 | + | 3.46410i | 0.163846 | + | 0.283790i | 0.936245 | − | 0.351348i | \(-0.114277\pi\) |
−0.772399 | + | 0.635138i | \(0.780943\pi\) | |||||||
\(150\) | −6.00000 | − | 3.46410i | −0.489898 | − | 0.282843i | ||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | −18.0000 | −1.45999 | ||||||||
\(153\) | 6.00000 | − | 10.3923i | 0.485071 | − | 0.840168i | ||||
\(154\) | 4.00000 | 0.322329 | ||||||||
\(155\) | −3.50000 | + | 6.06218i | −0.281127 | + | 0.486926i | ||||
\(156\) | − | 3.46410i | − | 0.277350i | ||||||
\(157\) | 3.50000 | + | 6.06218i | 0.279330 | + | 0.483814i | 0.971219 | − | 0.238190i | \(-0.0765542\pi\) |
−0.691888 | + | 0.722005i | \(0.743221\pi\) | |||||||
\(158\) | −4.00000 | − | 6.92820i | −0.318223 | − | 0.551178i | ||||
\(159\) | 13.5000 | − | 7.79423i | 1.07062 | − | 0.618123i | ||||
\(160\) | −2.50000 | + | 4.33013i | −0.197642 | + | 0.342327i | ||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | −11.0000 | −0.861586 | −0.430793 | − | 0.902451i | \(-0.641766\pi\) | ||||
−0.430793 | + | 0.902451i | \(0.641766\pi\) | |||||||
\(164\) | −1.00000 | + | 1.73205i | −0.0780869 | + | 0.135250i | ||||
\(165\) | −1.50000 | + | 0.866025i | −0.116775 | + | 0.0674200i | ||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | −6.00000 | − | 10.3923i | −0.464294 | − | 0.804181i | 0.534875 | − | 0.844931i | \(-0.320359\pi\) |
−0.999169 | + | 0.0407502i | \(0.987025\pi\) | |||||||
\(168\) | 20.7846i | 1.60357i | ||||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 9.00000 | − | 15.5885i | 0.688247 | − | 1.19208i | ||||
\(172\) | −6.00000 | −0.457496 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 9.00000 | + | 5.19615i | 0.682288 | + | 0.393919i | ||||
\(175\) | 8.00000 | + | 13.8564i | 0.604743 | + | 1.04745i | ||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | −10.5000 | − | 6.06218i | −0.789228 | − | 0.455661i | ||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | −1.50000 | − | 2.59808i | −0.111803 | − | 0.193649i | ||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 4.00000 | − | 6.92820i | 0.296500 | − | 0.513553i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00000 | − | 10.3923i | −0.442326 | − | 0.766131i | ||||
\(185\) | −1.50000 | − | 2.59808i | −0.110282 | − | 0.191014i | ||||
\(186\) | −10.5000 | + | 6.06218i | −0.769897 | + | 0.444500i | ||||
\(187\) | −2.00000 | + | 3.46410i | −0.146254 | + | 0.253320i | ||||
\(188\) | 7.00000 | 0.510527 | ||||||||
\(189\) | −18.0000 | − | 10.3923i | −1.30931 | − | 0.755929i | ||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | 6.50000 | − | 11.2583i | 0.470323 | − | 0.814624i | −0.529101 | − | 0.848559i | \(-0.677471\pi\) |
0.999424 | + | 0.0339349i | \(0.0108039\pi\) | |||||||
\(192\) | −10.5000 | + | 6.06218i | −0.757772 | + | 0.437500i | ||||
\(193\) | −2.00000 | − | 3.46410i | −0.143963 | − | 0.249351i | 0.785022 | − | 0.619467i | \(-0.212651\pi\) |
−0.928986 | + | 0.370116i | \(0.879318\pi\) | |||||||
\(194\) | 9.50000 | + | 16.4545i | 0.682060 | + | 1.18136i | ||||
\(195\) | 3.46410i | 0.248069i | ||||||||
\(196\) | 4.50000 | − | 7.79423i | 0.321429 | − | 0.556731i | ||||
\(197\) | 16.0000 | 1.13995 | 0.569976 | − | 0.821661i | \(-0.306952\pi\) | ||||
0.569976 | + | 0.821661i | \(0.306952\pi\) | |||||||
\(198\) | −3.00000 | −0.213201 | ||||||||
\(199\) | −3.00000 | −0.212664 | −0.106332 | − | 0.994331i | \(-0.533911\pi\) | ||||
−0.106332 | + | 0.994331i | \(0.533911\pi\) | |||||||
\(200\) | −6.00000 | + | 10.3923i | −0.424264 | + | 0.734847i | ||||
\(201\) | 16.5000 | + | 9.52628i | 1.16382 | + | 0.671932i | ||||
\(202\) | 2.00000 | + | 3.46410i | 0.140720 | + | 0.243733i | ||||
\(203\) | −12.0000 | − | 20.7846i | −0.842235 | − | 1.45879i | ||||
\(204\) | −6.00000 | − | 3.46410i | −0.420084 | − | 0.242536i | ||||
\(205\) | 1.00000 | − | 1.73205i | 0.0698430 | − | 0.120972i | ||||
\(206\) | −13.0000 | −0.905753 | ||||||||
\(207\) | 12.0000 | 0.834058 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −3.00000 | + | 5.19615i | −0.207514 | + | 0.359425i | ||||
\(210\) | − | 6.92820i | − | 0.478091i | ||||||
\(211\) | −3.00000 | − | 5.19615i | −0.206529 | − | 0.357718i | 0.744090 | − | 0.668079i | \(-0.232883\pi\) |
−0.950619 | + | 0.310361i | \(0.899550\pi\) | |||||||
\(212\) | −4.50000 | − | 7.79423i | −0.309061 | − | 0.535310i | ||||
\(213\) | −13.5000 | + | 7.79423i | −0.925005 | + | 0.534052i | ||||
\(214\) | 9.00000 | − | 15.5885i | 0.615227 | − | 1.06561i | ||||
\(215\) | 6.00000 | 0.409197 | ||||||||
\(216\) | − | 15.5885i | − | 1.06066i | ||||||
\(217\) | 28.0000 | 1.90076 | ||||||||
\(218\) | 1.00000 | − | 1.73205i | 0.0677285 | − | 0.117309i | ||||
\(219\) | −6.00000 | + | 3.46410i | −0.405442 | + | 0.234082i | ||||
\(220\) | 0.500000 | + | 0.866025i | 0.0337100 | + | 0.0583874i | ||||
\(221\) | 4.00000 | + | 6.92820i | 0.269069 | + | 0.466041i | ||||
\(222\) | − | 5.19615i | − | 0.348743i | ||||||
\(223\) | −8.00000 | + | 13.8564i | −0.535720 | + | 0.927894i | 0.463409 | + | 0.886145i | \(0.346626\pi\) |
−0.999128 | + | 0.0417488i | \(0.986707\pi\) | |||||||
\(224\) | 20.0000 | 1.33631 | ||||||||
\(225\) | −6.00000 | − | 10.3923i | −0.400000 | − | 0.692820i | ||||
\(226\) | −15.0000 | −0.997785 | ||||||||
\(227\) | 9.00000 | − | 15.5885i | 0.597351 | − | 1.03464i | −0.395860 | − | 0.918311i | \(-0.629553\pi\) |
0.993210 | − | 0.116331i | \(-0.0371134\pi\) | |||||||
\(228\) | −9.00000 | − | 5.19615i | −0.596040 | − | 0.344124i | ||||
\(229\) | 3.00000 | + | 5.19615i | 0.198246 | + | 0.343371i | 0.947960 | − | 0.318390i | \(-0.103142\pi\) |
−0.749714 | + | 0.661762i | \(0.769809\pi\) | |||||||
\(230\) | 2.00000 | + | 3.46410i | 0.131876 | + | 0.228416i | ||||
\(231\) | 6.00000 | + | 3.46410i | 0.394771 | + | 0.227921i | ||||
\(232\) | 9.00000 | − | 15.5885i | 0.590879 | − | 1.02343i | ||||
\(233\) | 24.0000 | 1.57229 | 0.786146 | − | 0.618041i | \(-0.212073\pi\) | ||||
0.786146 | + | 0.618041i | \(0.212073\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | −7.00000 | −0.456630 | ||||||||
\(236\) | −3.50000 | + | 6.06218i | −0.227831 | + | 0.394614i | ||||
\(237\) | − | 13.8564i | − | 0.900070i | ||||||
\(238\) | −8.00000 | − | 13.8564i | −0.518563 | − | 0.898177i | ||||
\(239\) | −3.00000 | − | 5.19615i | −0.194054 | − | 0.336111i | 0.752536 | − | 0.658551i | \(-0.228830\pi\) |
−0.946590 | + | 0.322440i | \(0.895497\pi\) | |||||||
\(240\) | 1.50000 | − | 0.866025i | 0.0968246 | − | 0.0559017i | ||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.50000 | + | 7.79423i | −0.287494 | + | 0.497955i | ||||
\(246\) | 3.00000 | − | 1.73205i | 0.191273 | − | 0.110432i | ||||
\(247\) | 6.00000 | + | 10.3923i | 0.381771 | + | 0.661247i | ||||
\(248\) | 10.5000 | + | 18.1865i | 0.666751 | + | 1.15485i | ||||
\(249\) | 20.7846i | 1.31717i | ||||||||
\(250\) | 4.50000 | − | 7.79423i | 0.284605 | − | 0.492950i | ||||
\(251\) | 28.0000 | 1.76734 | 0.883672 | − | 0.468106i | \(-0.155064\pi\) | ||||
0.883672 | + | 0.468106i | \(0.155064\pi\) | |||||||
\(252\) | −6.00000 | + | 10.3923i | −0.377964 | + | 0.654654i | ||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | −1.00000 | + | 1.73205i | −0.0627456 | + | 0.108679i | ||||
\(255\) | 6.00000 | + | 3.46410i | 0.375735 | + | 0.216930i | ||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | −11.0000 | − | 19.0526i | −0.686161 | − | 1.18847i | −0.973070 | − | 0.230508i | \(-0.925961\pi\) |
0.286909 | − | 0.957958i | \(-0.407372\pi\) | |||||||
\(258\) | 9.00000 | + | 5.19615i | 0.560316 | + | 0.323498i | ||||
\(259\) | −6.00000 | + | 10.3923i | −0.372822 | + | 0.645746i | ||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 9.00000 | + | 15.5885i | 0.557086 | + | 0.964901i | ||||
\(262\) | −6.00000 | −0.370681 | ||||||||
\(263\) | 8.00000 | − | 13.8564i | 0.493301 | − | 0.854423i | −0.506669 | − | 0.862141i | \(-0.669123\pi\) |
0.999970 | + | 0.00771799i | \(0.00245674\pi\) | |||||||
\(264\) | 5.19615i | 0.319801i | ||||||||
\(265\) | 4.50000 | + | 7.79423i | 0.276433 | + | 0.478796i | ||||
\(266\) | −12.0000 | − | 20.7846i | −0.735767 | − | 1.27439i | ||||
\(267\) | −9.00000 | + | 5.19615i | −0.550791 | + | 0.317999i | ||||
\(268\) | 5.50000 | − | 9.52628i | 0.335966 | − | 0.581910i | ||||
\(269\) | −17.0000 | −1.03651 | −0.518254 | − | 0.855227i | \(-0.673418\pi\) | ||||
−0.518254 | + | 0.855227i | \(0.673418\pi\) | |||||||
\(270\) | 5.19615i | 0.316228i | ||||||||
\(271\) | −22.0000 | −1.33640 | −0.668202 | − | 0.743980i | \(-0.732936\pi\) | ||||
−0.668202 | + | 0.743980i | \(0.732936\pi\) | |||||||
\(272\) | 2.00000 | − | 3.46410i | 0.121268 | − | 0.210042i | ||||
\(273\) | 12.0000 | − | 6.92820i | 0.726273 | − | 0.419314i | ||||
\(274\) | −2.50000 | − | 4.33013i | −0.151031 | − | 0.261593i | ||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | − | 6.92820i | − | 0.417029i | ||||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | −2.00000 | −0.119952 | ||||||||
\(279\) | −21.0000 | −1.25724 | ||||||||
\(280\) | −12.0000 | −0.717137 | ||||||||
\(281\) | −3.00000 | + | 5.19615i | −0.178965 | + | 0.309976i | −0.941526 | − | 0.336939i | \(-0.890608\pi\) |
0.762561 | + | 0.646916i | \(0.223942\pi\) | |||||||
\(282\) | −10.5000 | − | 6.06218i | −0.625266 | − | 0.360997i | ||||
\(283\) | −14.0000 | − | 24.2487i | −0.832214 | − | 1.44144i | −0.896279 | − | 0.443491i | \(-0.853740\pi\) |
0.0640654 | − | 0.997946i | \(-0.479593\pi\) | |||||||
\(284\) | 4.50000 | + | 7.79423i | 0.267026 | + | 0.462502i | ||||
\(285\) | 9.00000 | + | 5.19615i | 0.533114 | + | 0.307794i | ||||
\(286\) | 1.00000 | − | 1.73205i | 0.0591312 | − | 0.102418i | ||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | −15.0000 | −0.883883 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −3.00000 | + | 5.19615i | −0.176166 | + | 0.305129i | ||||
\(291\) | 32.9090i | 1.92916i | ||||||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | −6.00000 | − | 10.3923i | −0.350524 | − | 0.607125i | 0.635818 | − | 0.771839i | \(-0.280663\pi\) |
−0.986341 | + | 0.164714i | \(0.947330\pi\) | |||||||
\(294\) | −13.5000 | + | 7.79423i | −0.787336 | + | 0.454569i | ||||
\(295\) | 3.50000 | − | 6.06218i | 0.203778 | − | 0.352954i | ||||
\(296\) | −9.00000 | −0.523114 | ||||||||
\(297\) | −4.50000 | − | 2.59808i | −0.261116 | − | 0.150756i | ||||
\(298\) | −4.00000 | −0.231714 | ||||||||
\(299\) | −4.00000 | + | 6.92820i | −0.231326 | + | 0.400668i | ||||
\(300\) | −6.00000 | + | 3.46410i | −0.346410 | + | 0.200000i | ||||
\(301\) | −12.0000 | − | 20.7846i | −0.691669 | − | 1.19800i | ||||
\(302\) | 8.00000 | + | 13.8564i | 0.460348 | + | 0.797347i | ||||
\(303\) | 6.92820i | 0.398015i | ||||||||
\(304\) | 3.00000 | − | 5.19615i | 0.172062 | − | 0.298020i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.00000 | + | 10.3923i | 0.342997 | + | 0.594089i | ||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 2.00000 | − | 3.46410i | 0.113961 | − | 0.197386i | ||||
\(309\) | −19.5000 | − | 11.2583i | −1.10932 | − | 0.640464i | ||||
\(310\) | −3.50000 | − | 6.06218i | −0.198787 | − | 0.344309i | ||||
\(311\) | 10.5000 | + | 18.1865i | 0.595400 | + | 1.03126i | 0.993490 | + | 0.113917i | \(0.0363399\pi\) |
−0.398090 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(312\) | 9.00000 | + | 5.19615i | 0.509525 | + | 0.294174i | ||||
\(313\) | −7.00000 | + | 12.1244i | −0.395663 | + | 0.685309i | −0.993186 | − | 0.116543i | \(-0.962819\pi\) |
0.597522 | + | 0.801852i | \(0.296152\pi\) | |||||||
\(314\) | −7.00000 | −0.395033 | ||||||||
\(315\) | 6.00000 | − | 10.3923i | 0.338062 | − | 0.585540i | ||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −11.0000 | + | 19.0526i | −0.617822 | + | 1.07010i | 0.372061 | + | 0.928208i | \(0.378651\pi\) |
−0.989882 | + | 0.141890i | \(0.954682\pi\) | |||||||
\(318\) | 15.5885i | 0.874157i | ||||||||
\(319\) | −3.00000 | − | 5.19615i | −0.167968 | − | 0.290929i | ||||
\(320\) | −3.50000 | − | 6.06218i | −0.195656 | − | 0.338886i | ||||
\(321\) | 27.0000 | − | 15.5885i | 1.50699 | − | 0.870063i | ||||
\(322\) | 8.00000 | − | 13.8564i | 0.445823 | − | 0.772187i | ||||
\(323\) | 24.0000 | 1.33540 | ||||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | 8.00000 | 0.443760 | ||||||||
\(326\) | 5.50000 | − | 9.52628i | 0.304617 | − | 0.527612i | ||||
\(327\) | 3.00000 | − | 1.73205i | 0.165900 | − | 0.0957826i | ||||
\(328\) | −3.00000 | − | 5.19615i | −0.165647 | − | 0.286910i | ||||
\(329\) | 14.0000 | + | 24.2487i | 0.771845 | + | 1.33687i | ||||
\(330\) | − | 1.73205i | − | 0.0953463i | ||||||
\(331\) | −0.500000 | + | 0.866025i | −0.0274825 | + | 0.0476011i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
0.851957 | + | 0.523612i | \(0.175416\pi\) | |||||||
\(332\) | 12.0000 | 0.658586 | ||||||||
\(333\) | 4.50000 | − | 7.79423i | 0.246598 | − | 0.427121i | ||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | −5.50000 | + | 9.52628i | −0.300497 | + | 0.520476i | ||||
\(336\) | −6.00000 | − | 3.46410i | −0.327327 | − | 0.188982i | ||||
\(337\) | 11.0000 | + | 19.0526i | 0.599208 | + | 1.03786i | 0.992938 | + | 0.118633i | \(0.0378512\pi\) |
−0.393730 | + | 0.919226i | \(0.628816\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | −22.5000 | − | 12.9904i | −1.22203 | − | 0.705541i | ||||
\(340\) | 2.00000 | − | 3.46410i | 0.108465 | − | 0.187867i | ||||
\(341\) | 7.00000 | 0.379071 | ||||||||
\(342\) | 9.00000 | + | 15.5885i | 0.486664 | + | 0.842927i | ||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 9.00000 | − | 15.5885i | 0.485247 | − | 0.840473i | ||||
\(345\) | 6.92820i | 0.373002i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.00000 | − | 3.46410i | −0.107366 | − | 0.185963i | 0.807337 | − | 0.590091i | \(-0.200908\pi\) |
−0.914702 | + | 0.404128i | \(0.867575\pi\) | |||||||
\(348\) | 9.00000 | − | 5.19615i | 0.482451 | − | 0.278543i | ||||
\(349\) | −15.0000 | + | 25.9808i | −0.802932 | + | 1.39072i | 0.114747 | + | 0.993395i | \(0.463394\pi\) |
−0.917679 | + | 0.397324i | \(0.869939\pi\) | |||||||
\(350\) | −16.0000 | −0.855236 | ||||||||
\(351\) | −9.00000 | + | 5.19615i | −0.480384 | + | 0.277350i | ||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | 9.00000 | − | 15.5885i | 0.479022 | − | 0.829690i | −0.520689 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240566i | \(0.00765819\pi\) | |||||||
\(354\) | 10.5000 | − | 6.06218i | 0.558069 | − | 0.322201i | ||||
\(355\) | −4.50000 | − | 7.79423i | −0.238835 | − | 0.413675i | ||||
\(356\) | 3.00000 | + | 5.19615i | 0.159000 | + | 0.275396i | ||||
\(357\) | − | 27.7128i | − | 1.46672i | ||||||
\(358\) | 4.50000 | − | 7.79423i | 0.237832 | − | 0.411938i | ||||
\(359\) | −32.0000 | −1.68890 | −0.844448 | − | 0.535638i | \(-0.820071\pi\) | ||||
−0.844448 | + | 0.535638i | \(0.820071\pi\) | |||||||
\(360\) | 9.00000 | 0.474342 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −3.50000 | + | 6.06218i | −0.183956 | + | 0.318621i | ||||
\(363\) | 1.50000 | + | 0.866025i | 0.0787296 | + | 0.0454545i | ||||
\(364\) | −4.00000 | − | 6.92820i | −0.209657 | − | 0.363137i | ||||
\(365\) | −2.00000 | − | 3.46410i | −0.104685 | − | 0.181319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.50000 | − | 9.52628i | 0.287098 | − | 0.497268i | −0.686018 | − | 0.727585i | \(-0.740643\pi\) |
0.973116 | + | 0.230317i | \(0.0739762\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 3.00000 | 0.155963 | ||||||||
\(371\) | 18.0000 | − | 31.1769i | 0.934513 | − | 1.61862i | ||||
\(372\) | 12.1244i | 0.628619i | ||||||||
\(373\) | −5.00000 | − | 8.66025i | −0.258890 | − | 0.448411i | 0.707055 | − | 0.707159i | \(-0.250023\pi\) |
−0.965945 | + | 0.258748i | \(0.916690\pi\) | |||||||
\(374\) | −2.00000 | − | 3.46410i | −0.103418 | − | 0.179124i | ||||
\(375\) | 13.5000 | − | 7.79423i | 0.697137 | − | 0.402492i | ||||
\(376\) | −10.5000 | + | 18.1865i | −0.541496 | + | 0.937899i | ||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 18.0000 | − | 10.3923i | 0.925820 | − | 0.534522i | ||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 3.00000 | − | 5.19615i | 0.153897 | − | 0.266557i | ||||
\(381\) | −3.00000 | + | 1.73205i | −0.153695 | + | 0.0887357i | ||||
\(382\) | 6.50000 | + | 11.2583i | 0.332569 | + | 0.576026i | ||||
\(383\) | −14.5000 | − | 25.1147i | −0.740915 | − | 1.28330i | −0.952079 | − | 0.305852i | \(-0.901059\pi\) |
0.211164 | − | 0.977451i | \(-0.432275\pi\) | |||||||
\(384\) | 5.19615i | 0.265165i | ||||||||
\(385\) | −2.00000 | + | 3.46410i | −0.101929 | + | 0.176547i | ||||
\(386\) | 4.00000 | 0.203595 | ||||||||
\(387\) | 9.00000 | + | 15.5885i | 0.457496 | + | 0.792406i | ||||
\(388\) | 19.0000 | 0.964579 | ||||||||
\(389\) | −16.5000 | + | 28.5788i | −0.836583 | + | 1.44900i | 0.0561516 | + | 0.998422i | \(0.482117\pi\) |
−0.892735 | + | 0.450582i | \(0.851216\pi\) | |||||||
\(390\) | −3.00000 | − | 1.73205i | −0.151911 | − | 0.0877058i | ||||
\(391\) | 8.00000 | + | 13.8564i | 0.404577 | + | 0.700749i | ||||
\(392\) | 13.5000 | + | 23.3827i | 0.681853 | + | 1.18100i | ||||
\(393\) | −9.00000 | − | 5.19615i | −0.453990 | − | 0.262111i | ||||
\(394\) | −8.00000 | + | 13.8564i | −0.403034 | + | 0.698076i | ||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | −1.50000 | + | 2.59808i | −0.0753778 | + | 0.130558i | ||||
\(397\) | 13.0000 | 0.652451 | 0.326226 | − | 0.945292i | \(-0.394223\pi\) | ||||
0.326226 | + | 0.945292i | \(0.394223\pi\) | |||||||
\(398\) | 1.50000 | − | 2.59808i | 0.0751882 | − | 0.130230i | ||||
\(399\) | − | 41.5692i | − | 2.08106i | ||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −8.50000 | − | 14.7224i | −0.424470 | − | 0.735203i | 0.571901 | − | 0.820323i | \(-0.306206\pi\) |
−0.996371 | + | 0.0851195i | \(0.972873\pi\) | |||||||
\(402\) | −16.5000 | + | 9.52628i | −0.822945 | + | 0.475128i | ||||
\(403\) | 7.00000 | − | 12.1244i | 0.348695 | − | 0.603957i | ||||
\(404\) | 4.00000 | 0.199007 | ||||||||
\(405\) | −4.50000 | + | 7.79423i | −0.223607 | + | 0.387298i | ||||
\(406\) | 24.0000 | 1.19110 | ||||||||
\(407\) | −1.50000 | + | 2.59808i | −0.0743522 | + | 0.128782i | ||||
\(408\) | 18.0000 | − | 10.3923i | 0.891133 | − | 0.514496i | ||||
\(409\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(410\) | 1.00000 | + | 1.73205i | 0.0493865 | + | 0.0855399i | ||||
\(411\) | − | 8.66025i | − | 0.427179i | ||||||
\(412\) | −6.50000 | + | 11.2583i | −0.320232 | + | 0.554658i | ||||
\(413\) | −28.0000 | −1.37779 | ||||||||
\(414\) | −6.00000 | + | 10.3923i | −0.294884 | + | 0.510754i | ||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 5.00000 | − | 8.66025i | 0.245145 | − | 0.424604i | ||||
\(417\) | −3.00000 | − | 1.73205i | −0.146911 | − | 0.0848189i | ||||
\(418\) | −3.00000 | − | 5.19615i | −0.146735 | − | 0.254152i | ||||
\(419\) | −2.50000 | − | 4.33013i | −0.122133 | − | 0.211541i | 0.798476 | − | 0.602027i | \(-0.205640\pi\) |
−0.920609 | + | 0.390487i | \(0.872307\pi\) | |||||||
\(420\) | −6.00000 | − | 3.46410i | −0.292770 | − | 0.169031i | ||||
\(421\) | −6.50000 | + | 11.2583i | −0.316791 | + | 0.548697i | −0.979817 | − | 0.199899i | \(-0.935939\pi\) |
0.663026 | + | 0.748596i | \(0.269272\pi\) | |||||||
\(422\) | 6.00000 | 0.292075 | ||||||||
\(423\) | −10.5000 | − | 18.1865i | −0.510527 | − | 0.884260i | ||||
\(424\) | 27.0000 | 1.31124 | ||||||||
\(425\) | 8.00000 | − | 13.8564i | 0.388057 | − | 0.672134i | ||||
\(426\) | − | 15.5885i | − | 0.755263i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.00000 | − | 15.5885i | −0.435031 | − | 0.753497i | ||||
\(429\) | 3.00000 | − | 1.73205i | 0.144841 | − | 0.0836242i | ||||
\(430\) | −3.00000 | + | 5.19615i | −0.144673 | + | 0.250581i | ||||
\(431\) | −30.0000 | −1.44505 | −0.722525 | − | 0.691345i | \(-0.757018\pi\) | ||||
−0.722525 | + | 0.691345i | \(0.757018\pi\) | |||||||
\(432\) | 4.50000 | + | 2.59808i | 0.216506 | + | 0.125000i | ||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | −14.0000 | + | 24.2487i | −0.672022 | + | 1.16398i | ||||
\(435\) | −9.00000 | + | 5.19615i | −0.431517 | + | 0.249136i | ||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | 12.0000 | + | 20.7846i | 0.574038 | + | 0.994263i | ||||
\(438\) | − | 6.92820i | − | 0.331042i | ||||||
\(439\) | 7.00000 | − | 12.1244i | 0.334092 | − | 0.578664i | −0.649218 | − | 0.760602i | \(-0.724904\pi\) |
0.983310 | + | 0.181938i | \(0.0582371\pi\) | |||||||
\(440\) | −3.00000 | −0.143019 | ||||||||
\(441\) | −27.0000 | −1.28571 | ||||||||
\(442\) | −8.00000 | −0.380521 | ||||||||
\(443\) | −0.500000 | + | 0.866025i | −0.0237557 | + | 0.0411461i | −0.877659 | − | 0.479286i | \(-0.840896\pi\) |
0.853903 | + | 0.520432i | \(0.174229\pi\) | |||||||
\(444\) | −4.50000 | − | 2.59808i | −0.213561 | − | 0.123299i | ||||
\(445\) | −3.00000 | − | 5.19615i | −0.142214 | − | 0.246321i | ||||
\(446\) | −8.00000 | − | 13.8564i | −0.378811 | − | 0.656120i | ||||
\(447\) | −6.00000 | − | 3.46410i | −0.283790 | − | 0.163846i | ||||
\(448\) | −14.0000 | + | 24.2487i | −0.661438 | + | 1.14564i | ||||
\(449\) | 23.0000 | 1.08544 | 0.542719 | − | 0.839915i | \(-0.317395\pi\) | ||||
0.542719 | + | 0.839915i | \(0.317395\pi\) | |||||||
\(450\) | 12.0000 | 0.565685 | ||||||||
\(451\) | −2.00000 | −0.0941763 | ||||||||
\(452\) | −7.50000 | + | 12.9904i | −0.352770 | + | 0.611016i | ||||
\(453\) | 27.7128i | 1.30206i | ||||||||
\(454\) | 9.00000 | + | 15.5885i | 0.422391 | + | 0.731603i | ||||
\(455\) | 4.00000 | + | 6.92820i | 0.187523 | + | 0.324799i | ||||
\(456\) | 27.0000 | − | 15.5885i | 1.26439 | − | 0.729996i | ||||
\(457\) | 3.00000 | − | 5.19615i | 0.140334 | − | 0.243066i | −0.787288 | − | 0.616585i | \(-0.788516\pi\) |
0.927622 | + | 0.373519i | \(0.121849\pi\) | |||||||
\(458\) | −6.00000 | −0.280362 | ||||||||
\(459\) | 20.7846i | 0.970143i | ||||||||
\(460\) | 4.00000 | 0.186501 | ||||||||
\(461\) | 6.00000 | − | 10.3923i | 0.279448 | − | 0.484018i | −0.691800 | − | 0.722089i | \(-0.743182\pi\) |
0.971248 | + | 0.238071i | \(0.0765153\pi\) | |||||||
\(462\) | −6.00000 | + | 3.46410i | −0.279145 | + | 0.161165i | ||||
\(463\) | 4.00000 | + | 6.92820i | 0.185896 | + | 0.321981i | 0.943878 | − | 0.330294i | \(-0.107148\pi\) |
−0.757982 | + | 0.652275i | \(0.773815\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | − | 12.1244i | − | 0.562254i | ||||||
\(466\) | −12.0000 | + | 20.7846i | −0.555889 | + | 0.962828i | ||||
\(467\) | 27.0000 | 1.24941 | 0.624705 | − | 0.780860i | \(-0.285219\pi\) | ||||
0.624705 | + | 0.780860i | \(0.285219\pi\) | |||||||
\(468\) | 3.00000 | + | 5.19615i | 0.138675 | + | 0.240192i | ||||
\(469\) | 44.0000 | 2.03173 | ||||||||
\(470\) | 3.50000 | − | 6.06218i | 0.161443 | − | 0.279627i | ||||
\(471\) | −10.5000 | − | 6.06218i | −0.483814 | − | 0.279330i | ||||
\(472\) | −10.5000 | − | 18.1865i | −0.483302 | − | 0.837103i | ||||
\(473\) | −3.00000 | − | 5.19615i | −0.137940 | − | 0.238919i | ||||
\(474\) | 12.0000 | + | 6.92820i | 0.551178 | + | 0.318223i | ||||
\(475\) | 12.0000 | − | 20.7846i | 0.550598 | − | 0.953663i | ||||
\(476\) | −16.0000 | −0.733359 | ||||||||
\(477\) | −13.5000 | + | 23.3827i | −0.618123 | + | 1.07062i | ||||
\(478\) | 6.00000 | 0.274434 | ||||||||
\(479\) | 2.00000 | − | 3.46410i | 0.0913823 | − | 0.158279i | −0.816711 | − | 0.577047i | \(-0.804205\pi\) |
0.908093 | + | 0.418769i | \(0.137538\pi\) | |||||||
\(480\) | − | 8.66025i | − | 0.395285i | ||||||
\(481\) | 3.00000 | + | 5.19615i | 0.136788 | + | 0.236924i | ||||
\(482\) | −5.00000 | − | 8.66025i | −0.227744 | − | 0.394464i | ||||
\(483\) | 24.0000 | − | 13.8564i | 1.09204 | − | 0.630488i | ||||
\(484\) | 0.500000 | − | 0.866025i | 0.0227273 | − | 0.0393648i | ||||
\(485\) | −19.0000 | −0.862746 | ||||||||
\(486\) | −13.5000 | + | 7.79423i | −0.612372 | + | 0.353553i | ||||
\(487\) | −37.0000 | −1.67663 | −0.838315 | − | 0.545186i | \(-0.816459\pi\) | ||||
−0.838315 | + | 0.545186i | \(0.816459\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.5000 | − | 9.52628i | 0.746156 | − | 0.430793i | ||||
\(490\) | −4.50000 | − | 7.79423i | −0.203289 | − | 0.352107i | ||||
\(491\) | 4.00000 | + | 6.92820i | 0.180517 | + | 0.312665i | 0.942057 | − | 0.335453i | \(-0.108889\pi\) |
−0.761539 | + | 0.648119i | \(0.775556\pi\) | |||||||
\(492\) | − | 3.46410i | − | 0.156174i | ||||||
\(493\) | −12.0000 | + | 20.7846i | −0.540453 | + | 0.936092i | ||||
\(494\) | −12.0000 | −0.539906 | ||||||||
\(495\) | 1.50000 | − | 2.59808i | 0.0674200 | − | 0.116775i | ||||
\(496\) | −7.00000 | −0.314309 | ||||||||
\(497\) | −18.0000 | + | 31.1769i | −0.807410 | + | 1.39848i | ||||
\(498\) | −18.0000 | − | 10.3923i | −0.806599 | − | 0.465690i | ||||
\(499\) | 12.5000 | + | 21.6506i | 0.559577 | + | 0.969216i | 0.997532 | + | 0.0702185i | \(0.0223697\pi\) |
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(500\) | −4.50000 | − | 7.79423i | −0.201246 | − | 0.348569i | ||||
\(501\) | 18.0000 | + | 10.3923i | 0.804181 | + | 0.464294i | ||||
\(502\) | −14.0000 | + | 24.2487i | −0.624851 | + | 1.08227i | ||||
\(503\) | −14.0000 | −0.624229 | −0.312115 | − | 0.950044i | \(-0.601037\pi\) | ||||
−0.312115 | + | 0.950044i | \(0.601037\pi\) | |||||||
\(504\) | −18.0000 | − | 31.1769i | −0.801784 | − | 1.38873i | ||||
\(505\) | −4.00000 | −0.177998 | ||||||||
\(506\) | 2.00000 | − | 3.46410i | 0.0889108 | − | 0.153998i | ||||
\(507\) | 15.5885i | 0.692308i | ||||||||
\(508\) | 1.00000 | + | 1.73205i | 0.0443678 | + | 0.0768473i | ||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | −6.00000 | + | 3.46410i | −0.265684 | + | 0.153393i | ||||
\(511\) | −8.00000 | + | 13.8564i | −0.353899 | + | 0.612971i | ||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 31.1769i | 1.37649i | ||||||||
\(514\) | 22.0000 | 0.970378 | ||||||||
\(515\) | 6.50000 | − | 11.2583i | 0.286424 | − | 0.496101i | ||||
\(516\) | 9.00000 | − | 5.19615i | 0.396203 | − | 0.228748i | ||||
\(517\) | 3.50000 | + | 6.06218i | 0.153930 | + | 0.266614i | ||||
\(518\) | −6.00000 | − | 10.3923i | −0.263625 | − | 0.456612i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.00000 | + | 5.19615i | −0.131559 | + | 0.227866i | ||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | −18.0000 | −0.787839 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | −3.00000 | + | 5.19615i | −0.131056 | + | 0.226995i | ||||
\(525\) | −24.0000 | − | 13.8564i | −1.04745 | − | 0.604743i | ||||
\(526\) | 8.00000 | + | 13.8564i | 0.348817 | + | 0.604168i | ||||
\(527\) | −14.0000 | − | 24.2487i | −0.609850 | − | 1.05629i | ||||
\(528\) | −1.50000 | − | 0.866025i | −0.0652791 | − | 0.0376889i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −9.00000 | −0.390935 | ||||||||
\(531\) | 21.0000 | 0.911322 | ||||||||
\(532\) | −24.0000 | −1.04053 | ||||||||
\(533\) | −2.00000 | + | 3.46410i | −0.0866296 | + | 0.150047i | ||||
\(534\) | − | 10.3923i | − | 0.449719i | ||||||
\(535\) | 9.00000 | + | 15.5885i | 0.389104 | + | 0.673948i | ||||
\(536\) | 16.5000 | + | 28.5788i | 0.712691 | + | 1.23442i | ||||
\(537\) | 13.5000 | − | 7.79423i | 0.582568 | − | 0.336346i | ||||
\(538\) | 8.50000 | − | 14.7224i | 0.366461 | − | 0.634729i | ||||
\(539\) | 9.00000 | 0.387657 | ||||||||
\(540\) | 4.50000 | + | 2.59808i | 0.193649 | + | 0.111803i | ||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 11.0000 | − | 19.0526i | 0.472490 | − | 0.818377i | ||||
\(543\) | −10.5000 | + | 6.06218i | −0.450598 | + | 0.260153i | ||||
\(544\) | −10.0000 | − | 17.3205i | −0.428746 | − | 0.742611i | ||||
\(545\) | 1.00000 | + | 1.73205i | 0.0428353 | + | 0.0741929i | ||||
\(546\) | 13.8564i | 0.592999i | ||||||||
\(547\) | 11.0000 | − | 19.0526i | 0.470326 | − | 0.814629i | −0.529098 | − | 0.848561i | \(-0.677470\pi\) |
0.999424 | + | 0.0339321i | \(0.0108030\pi\) | |||||||
\(548\) | −5.00000 | −0.213589 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.00000 | −0.170561 | ||||||||
\(551\) | −18.0000 | + | 31.1769i | −0.766826 | + | 1.32818i | ||||
\(552\) | 18.0000 | + | 10.3923i | 0.766131 | + | 0.442326i | ||||
\(553\) | −16.0000 | − | 27.7128i | −0.680389 | − | 1.17847i | ||||
\(554\) | 1.00000 | + | 1.73205i | 0.0424859 | + | 0.0735878i | ||||
\(555\) | 4.50000 | + | 2.59808i | 0.191014 | + | 0.110282i | ||||
\(556\) | −1.00000 | + | 1.73205i | −0.0424094 | + | 0.0734553i | ||||
\(557\) | 40.0000 | 1.69485 | 0.847427 | − | 0.530912i | \(-0.178150\pi\) | ||||
0.847427 | + | 0.530912i | \(0.178150\pi\) | |||||||
\(558\) | 10.5000 | − | 18.1865i | 0.444500 | − | 0.769897i | ||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 2.00000 | − | 3.46410i | 0.0845154 | − | 0.146385i | ||||
\(561\) | − | 6.92820i | − | 0.292509i | ||||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | 7.00000 | + | 12.1244i | 0.295015 | + | 0.510981i | 0.974988 | − | 0.222256i | \(-0.0713421\pi\) |
−0.679974 | + | 0.733237i | \(0.738009\pi\) | |||||||
\(564\) | −10.5000 | + | 6.06218i | −0.442130 | + | 0.255264i | ||||
\(565\) | 7.50000 | − | 12.9904i | 0.315527 | − | 0.546509i | ||||
\(566\) | 28.0000 | 1.17693 | ||||||||
\(567\) | 36.0000 | 1.51186 | ||||||||
\(568\) | −27.0000 | −1.13289 | ||||||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | −9.00000 | + | 5.19615i | −0.376969 | + | 0.217643i | ||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | −1.00000 | − | 1.73205i | −0.0418121 | − | 0.0724207i | ||||
\(573\) | 22.5167i | 0.940647i | ||||||||
\(574\) | 4.00000 | − | 6.92820i | 0.166957 | − | 0.289178i | ||||
\(575\) | 16.0000 | 0.667246 | ||||||||
\(576\) | 10.5000 | − | 18.1865i | 0.437500 | − | 0.757772i | ||||
\(577\) | −3.00000 | −0.124892 | −0.0624458 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624458 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | 6.00000 | + | 3.46410i | 0.249351 | + | 0.143963i | ||||
\(580\) | 3.00000 | + | 5.19615i | 0.124568 | + | 0.215758i | ||||
\(581\) | 24.0000 | + | 41.5692i | 0.995688 | + | 1.72458i | ||||
\(582\) | −28.5000 | − | 16.4545i | −1.18136 | − | 0.682060i | ||||
\(583\) | 4.50000 | − | 7.79423i | 0.186371 | − | 0.322804i | ||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | −3.00000 | − | 5.19615i | −0.124035 | − | 0.214834i | ||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 2.50000 | − | 4.33013i | 0.103186 | − | 0.178723i | −0.809810 | − | 0.586693i | \(-0.800430\pi\) |
0.912996 | + | 0.407969i | \(0.133763\pi\) | |||||||
\(588\) | 15.5885i | 0.642857i | ||||||||
\(589\) | −21.0000 | − | 36.3731i | −0.865290 | − | 1.49873i | ||||
\(590\) | 3.50000 | + | 6.06218i | 0.144093 | + | 0.249576i | ||||
\(591\) | −24.0000 | + | 13.8564i | −0.987228 | + | 0.569976i | ||||
\(592\) | 1.50000 | − | 2.59808i | 0.0616496 | − | 0.106780i | ||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 4.50000 | − | 2.59808i | 0.184637 | − | 0.106600i | ||||
\(595\) | 16.0000 | 0.655936 | ||||||||
\(596\) | −2.00000 | + | 3.46410i | −0.0819232 | + | 0.141895i | ||||
\(597\) | 4.50000 | − | 2.59808i | 0.184173 | − | 0.106332i | ||||
\(598\) | −4.00000 | − | 6.92820i | −0.163572 | − | 0.283315i | ||||
\(599\) | −2.00000 | − | 3.46410i | −0.0817178 | − | 0.141539i | 0.822270 | − | 0.569097i | \(-0.192707\pi\) |
−0.903988 | + | 0.427558i | \(0.859374\pi\) | |||||||
\(600\) | − | 20.7846i | − | 0.848528i | ||||||
\(601\) | −1.00000 | + | 1.73205i | −0.0407909 | + | 0.0706518i | −0.885700 | − | 0.464258i | \(-0.846321\pi\) |
0.844909 | + | 0.534910i | \(0.179654\pi\) | |||||||
\(602\) | 24.0000 | 0.978167 | ||||||||
\(603\) | −33.0000 | −1.34386 | ||||||||
\(604\) | 16.0000 | 0.651031 | ||||||||
\(605\) | −0.500000 | + | 0.866025i | −0.0203279 | + | 0.0352089i | ||||
\(606\) | −6.00000 | − | 3.46410i | −0.243733 | − | 0.140720i | ||||
\(607\) | −4.00000 | − | 6.92820i | −0.162355 | − | 0.281207i | 0.773358 | − | 0.633970i | \(-0.218576\pi\) |
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(608\) | −15.0000 | − | 25.9808i | −0.608330 | − | 1.05366i | ||||
\(609\) | 36.0000 | + | 20.7846i | 1.45879 | + | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.0000 | 0.566379 | ||||||||
\(612\) | 12.0000 | 0.485071 | ||||||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 14.0000 | − | 24.2487i | 0.564994 | − | 0.978598i | ||||
\(615\) | 3.46410i | 0.139686i | ||||||||
\(616\) | 6.00000 | + | 10.3923i | 0.241747 | + | 0.418718i | ||||
\(617\) | 7.50000 | + | 12.9904i | 0.301939 | + | 0.522973i | 0.976575 | − | 0.215177i | \(-0.0690329\pi\) |
−0.674636 | + | 0.738150i | \(0.735700\pi\) | |||||||
\(618\) | 19.5000 | − | 11.2583i | 0.784405 | − | 0.452876i | ||||
\(619\) | 12.5000 | − | 21.6506i | 0.502417 | − | 0.870212i | −0.497579 | − | 0.867419i | \(-0.665777\pi\) |
0.999996 | − | 0.00279365i | \(-0.000889247\pi\) | |||||||
\(620\) | −7.00000 | −0.281127 | ||||||||
\(621\) | −18.0000 | + | 10.3923i | −0.722315 | + | 0.417029i | ||||
\(622\) | −21.0000 | −0.842023 | ||||||||
\(623\) | −12.0000 | + | 20.7846i | −0.480770 | + | 0.832718i | ||||
\(624\) | −3.00000 | + | 1.73205i | −0.120096 | + | 0.0693375i | ||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | −7.00000 | − | 12.1244i | −0.279776 | − | 0.484587i | ||||
\(627\) | − | 10.3923i | − | 0.415029i | ||||||
\(628\) | −3.50000 | + | 6.06218i | −0.139665 | + | 0.241907i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 6.00000 | + | 10.3923i | 0.239046 | + | 0.414039i | ||||
\(631\) | 37.0000 | 1.47295 | 0.736473 | − | 0.676467i | \(-0.236490\pi\) | ||||
0.736473 | + | 0.676467i | \(0.236490\pi\) | |||||||
\(632\) | 12.0000 | − | 20.7846i | 0.477334 | − | 0.826767i | ||||
\(633\) | 9.00000 | + | 5.19615i | 0.357718 | + | 0.206529i | ||||
\(634\) | −11.0000 | − | 19.0526i | −0.436866 | − | 0.756674i | ||||
\(635\) | −1.00000 | − | 1.73205i | −0.0396838 | − | 0.0687343i | ||||
\(636\) | 13.5000 | + | 7.79423i | 0.535310 | + | 0.309061i | ||||
\(637\) | 9.00000 | − | 15.5885i | 0.356593 | − | 0.617637i | ||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | 13.5000 | − | 23.3827i | 0.534052 | − | 0.925005i | ||||
\(640\) | −3.00000 | −0.118585 | ||||||||
\(641\) | 15.0000 | − | 25.9808i | 0.592464 | − | 1.02618i | −0.401435 | − | 0.915888i | \(-0.631488\pi\) |
0.993899 | − | 0.110291i | \(-0.0351782\pi\) | |||||||
\(642\) | 31.1769i | 1.23045i | ||||||||
\(643\) | 8.00000 | + | 13.8564i | 0.315489 | + | 0.546443i | 0.979541 | − | 0.201243i | \(-0.0644981\pi\) |
−0.664052 | + | 0.747686i | \(0.731165\pi\) | |||||||
\(644\) | −8.00000 | − | 13.8564i | −0.315244 | − | 0.546019i | ||||
\(645\) | −9.00000 | + | 5.19615i | −0.354375 | + | 0.204598i | ||||
\(646\) | −12.0000 | + | 20.7846i | −0.472134 | + | 0.817760i | ||||
\(647\) | 32.0000 | 1.25805 | 0.629025 | − | 0.777385i | \(-0.283454\pi\) | ||||
0.629025 | + | 0.777385i | \(0.283454\pi\) | |||||||
\(648\) | 13.5000 | + | 23.3827i | 0.530330 | + | 0.918559i | ||||
\(649\) | −7.00000 | −0.274774 | ||||||||
\(650\) | −4.00000 | + | 6.92820i | −0.156893 | + | 0.271746i | ||||
\(651\) | −42.0000 | + | 24.2487i | −1.64611 | + | 0.950382i | ||||
\(652\) | −5.50000 | − | 9.52628i | −0.215397 | − | 0.373078i | ||||
\(653\) | −15.5000 | − | 26.8468i | −0.606562 | − | 1.05060i | −0.991803 | − | 0.127780i | \(-0.959215\pi\) |
0.385241 | − | 0.922816i | \(-0.374118\pi\) | |||||||
\(654\) | 3.46410i | 0.135457i | ||||||||
\(655\) | 3.00000 | − | 5.19615i | 0.117220 | − | 0.203030i | ||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | 6.00000 | − | 10.3923i | 0.234082 | − | 0.405442i | ||||
\(658\) | −28.0000 | −1.09155 | ||||||||
\(659\) | −17.0000 | + | 29.4449i | −0.662226 | + | 1.14701i | 0.317803 | + | 0.948157i | \(0.397055\pi\) |
−0.980029 | + | 0.198852i | \(0.936279\pi\) | |||||||
\(660\) | −1.50000 | − | 0.866025i | −0.0583874 | − | 0.0337100i | ||||
\(661\) | −24.5000 | − | 42.4352i | −0.952940 | − | 1.65054i | −0.739014 | − | 0.673690i | \(-0.764708\pi\) |
−0.213925 | − | 0.976850i | \(-0.568625\pi\) | |||||||
\(662\) | −0.500000 | − | 0.866025i | −0.0194331 | − | 0.0336590i | ||||
\(663\) | −12.0000 | − | 6.92820i | −0.466041 | − | 0.269069i | ||||
\(664\) | −18.0000 | + | 31.1769i | −0.698535 | + | 1.20990i | ||||
\(665\) | 24.0000 | 0.930680 | ||||||||
\(666\) | 4.50000 | + | 7.79423i | 0.174371 | + | 0.302020i | ||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | 6.00000 | − | 10.3923i | 0.232147 | − | 0.402090i | ||||
\(669\) | − | 27.7128i | − | 1.07144i | ||||||
\(670\) | −5.50000 | − | 9.52628i | −0.212484 | − | 0.368032i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −30.0000 | + | 17.3205i | −1.15728 | + | 0.668153i | ||||
\(673\) | 11.0000 | − | 19.0526i | 0.424019 | − | 0.734422i | −0.572309 | − | 0.820038i | \(-0.693952\pi\) |
0.996328 | + | 0.0856156i | \(0.0272857\pi\) | |||||||
\(674\) | −22.0000 | −0.847408 | ||||||||
\(675\) | 18.0000 | + | 10.3923i | 0.692820 | + | 0.400000i | ||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 22.5000 | − | 12.9904i | 0.864107 | − | 0.498893i | ||||
\(679\) | 38.0000 | + | 65.8179i | 1.45831 | + | 2.52586i | ||||
\(680\) | 6.00000 | + | 10.3923i | 0.230089 | + | 0.398527i | ||||
\(681\) | 31.1769i | 1.19470i | ||||||||
\(682\) | −3.50000 | + | 6.06218i | −0.134022 | + | 0.232133i | ||||
\(683\) | 5.00000 | 0.191320 | 0.0956598 | − | 0.995414i | \(-0.469504\pi\) | ||||
0.0956598 | + | 0.995414i | \(0.469504\pi\) | |||||||
\(684\) | 18.0000 | 0.688247 | ||||||||
\(685\) | 5.00000 | 0.191040 | ||||||||
\(686\) | −4.00000 | + | 6.92820i | −0.152721 | + | 0.264520i | ||||
\(687\) | −9.00000 | − | 5.19615i | −0.343371 | − | 0.198246i | ||||
\(688\) | 3.00000 | + | 5.19615i | 0.114374 | + | 0.198101i | ||||
\(689\) | −9.00000 | − | 15.5885i | −0.342873 | − | 0.593873i | ||||
\(690\) | −6.00000 | − | 3.46410i | −0.228416 | − | 0.131876i | ||||
\(691\) | −17.5000 | + | 30.3109i | −0.665731 | + | 1.15308i | 0.313355 | + | 0.949636i | \(0.398547\pi\) |
−0.979086 | + | 0.203445i | \(0.934786\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.0000 | −0.455842 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | 1.00000 | − | 1.73205i | 0.0379322 | − | 0.0657004i | ||||
\(696\) | 31.1769i | 1.18176i | ||||||||
\(697\) | 4.00000 | + | 6.92820i | 0.151511 | + | 0.262424i | ||||
\(698\) | −15.0000 | − | 25.9808i | −0.567758 | − | 0.983386i | ||||
\(699\) | −36.0000 | + | 20.7846i | −1.36165 | + | 0.786146i | ||||
\(700\) | −8.00000 | + | 13.8564i | −0.302372 | + | 0.523723i | ||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | − | 10.3923i | − | 0.392232i | ||||||
\(703\) | 18.0000 | 0.678883 | ||||||||
\(704\) | −3.50000 | + | 6.06218i | −0.131911 | + | 0.228477i | ||||
\(705\) | 10.5000 | − | 6.06218i | 0.395453 | − | 0.228315i | ||||
\(706\) | 9.00000 | + | 15.5885i | 0.338719 | + | 0.586679i | ||||
\(707\) | 8.00000 | + | 13.8564i | 0.300871 | + | 0.521124i | ||||
\(708\) | − | 12.1244i | − | 0.455661i | ||||||
\(709\) | 6.50000 | − | 11.2583i | 0.244113 | − | 0.422815i | −0.717769 | − | 0.696281i | \(-0.754837\pi\) |
0.961882 | + | 0.273466i | \(0.0881700\pi\) | |||||||
\(710\) | 9.00000 | 0.337764 | ||||||||
\(711\) | 12.0000 | + | 20.7846i | 0.450035 | + | 0.779484i | ||||
\(712\) | −18.0000 | −0.674579 | ||||||||
\(713\) | 14.0000 | − | 24.2487i | 0.524304 | − | 0.908121i | ||||
\(714\) | 24.0000 | + | 13.8564i | 0.898177 | + | 0.518563i | ||||
\(715\) | 1.00000 | + | 1.73205i | 0.0373979 | + | 0.0647750i | ||||
\(716\) | −4.50000 | − | 7.79423i | −0.168173 | − | 0.291284i | ||||
\(717\) | 9.00000 | + | 5.19615i | 0.336111 | + | 0.194054i | ||||
\(718\) | 16.0000 | − | 27.7128i | 0.597115 | − | 1.03423i | ||||
\(719\) | −15.0000 | −0.559406 | −0.279703 | − | 0.960087i | \(-0.590236\pi\) | ||||
−0.279703 | + | 0.960087i | \(0.590236\pi\) | |||||||
\(720\) | −1.50000 | + | 2.59808i | −0.0559017 | + | 0.0968246i | ||||
\(721\) | −52.0000 | −1.93658 | ||||||||
\(722\) | −8.50000 | + | 14.7224i | −0.316337 | + | 0.547912i | ||||
\(723\) | − | 17.3205i | − | 0.644157i | ||||||
\(724\) | 3.50000 | + | 6.06218i | 0.130076 | + | 0.225299i | ||||
\(725\) | 12.0000 | + | 20.7846i | 0.445669 | + | 0.771921i | ||||
\(726\) | −1.50000 | + | 0.866025i | −0.0556702 | + | 0.0321412i | ||||
\(727\) | 16.5000 | − | 28.5788i | 0.611951 | − | 1.05993i | −0.378960 | − | 0.925413i | \(-0.623718\pi\) |
0.990911 | − | 0.134517i | \(-0.0429484\pi\) | |||||||
\(728\) | 24.0000 | 0.889499 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 4.00000 | 0.148047 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.00000 | + | 5.19615i | 0.110808 | + | 0.191924i | 0.916096 | − | 0.400959i | \(-0.131323\pi\) |
−0.805289 | + | 0.592883i | \(0.797990\pi\) | |||||||
\(734\) | 5.50000 | + | 9.52628i | 0.203009 | + | 0.351621i | ||||
\(735\) | − | 15.5885i | − | 0.574989i | ||||||
\(736\) | 10.0000 | − | 17.3205i | 0.368605 | − | 0.638442i | ||||
\(737\) | 11.0000 | 0.405190 | ||||||||
\(738\) | −3.00000 | + | 5.19615i | −0.110432 | + | 0.191273i | ||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 1.50000 | − | 2.59808i | 0.0551411 | − | 0.0955072i | ||||
\(741\) | −18.0000 | − | 10.3923i | −0.661247 | − | 0.381771i | ||||
\(742\) | 18.0000 | + | 31.1769i | 0.660801 | + | 1.14454i | ||||
\(743\) | 25.0000 | + | 43.3013i | 0.917161 | + | 1.58857i | 0.803706 | + | 0.595026i | \(0.202858\pi\) |
0.113455 | + | 0.993543i | \(0.463808\pi\) | |||||||
\(744\) | −31.5000 | − | 18.1865i | −1.15485 | − | 0.666751i | ||||
\(745\) | 2.00000 | − | 3.46410i | 0.0732743 | − | 0.126915i | ||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | −18.0000 | − | 31.1769i | −0.658586 | − | 1.14070i | ||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | 36.0000 | − | 62.3538i | 1.31541 | − | 2.27836i | ||||
\(750\) | 15.5885i | 0.569210i | ||||||||
\(751\) | 5.50000 | + | 9.52628i | 0.200698 | + | 0.347619i | 0.948753 | − | 0.316017i | \(-0.102346\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(752\) | −3.50000 | − | 6.06218i | −0.127632 | − | 0.221065i | ||||
\(753\) | −42.0000 | + | 24.2487i | −1.53057 | + | 0.883672i | ||||
\(754\) | 6.00000 | − | 10.3923i | 0.218507 | − | 0.378465i | ||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | − | 20.7846i | − | 0.755929i | ||||||
\(757\) | −19.0000 | −0.690567 | −0.345283 | − | 0.938498i | \(-0.612217\pi\) | ||||
−0.345283 | + | 0.938498i | \(0.612217\pi\) | |||||||
\(758\) | −8.00000 | + | 13.8564i | −0.290573 | + | 0.503287i | ||||
\(759\) | 6.00000 | − | 3.46410i | 0.217786 | − | 0.125739i | ||||
\(760\) | 9.00000 | + | 15.5885i | 0.326464 | + | 0.565453i | ||||
\(761\) | −18.0000 | − | 31.1769i | −0.652499 | − | 1.13016i | −0.982514 | − | 0.186187i | \(-0.940387\pi\) |
0.330015 | − | 0.943976i | \(-0.392946\pi\) | |||||||
\(762\) | − | 3.46410i | − | 0.125491i | ||||||
\(763\) | 4.00000 | − | 6.92820i | 0.144810 | − | 0.250818i | ||||
\(764\) | 13.0000 | 0.470323 | ||||||||
\(765\) | −12.0000 | −0.433861 | ||||||||
\(766\) | 29.0000 | 1.04781 | ||||||||
\(767\) | −7.00000 | + | 12.1244i | −0.252755 | + | 0.437785i | ||||
\(768\) | −25.5000 | − | 14.7224i | −0.920152 | − | 0.531250i | ||||
\(769\) | 8.00000 | + | 13.8564i | 0.288487 | + | 0.499675i | 0.973449 | − | 0.228904i | \(-0.0735143\pi\) |
−0.684962 | + | 0.728579i | \(0.740181\pi\) | |||||||
\(770\) | −2.00000 | − | 3.46410i | −0.0720750 | − | 0.124838i | ||||
\(771\) | 33.0000 | + | 19.0526i | 1.18847 | + | 0.686161i | ||||
\(772\) | 2.00000 | − | 3.46410i | 0.0719816 | − | 0.124676i | ||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | −18.0000 | −0.646997 | ||||||||
\(775\) | −28.0000 | −1.00579 | ||||||||
\(776\) | −28.5000 | + | 49.3634i | −1.02309 | + | 1.77204i | ||||
\(777\) | − | 20.7846i | − | 0.745644i | ||||||
\(778\) | −16.5000 | − | 28.5788i | −0.591554 | − | 1.02460i | ||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | −3.00000 | + | 1.73205i | −0.107417 | + | 0.0620174i | ||||
\(781\) | −4.50000 | + | 7.79423i | −0.161023 | + | 0.278899i | ||||
\(782\) | −16.0000 | −0.572159 | ||||||||
\(783\) | −27.0000 | − | 15.5885i | −0.964901 | − | 0.557086i | ||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | 3.50000 | − | 6.06218i | 0.124920 | − | 0.216368i | ||||
\(786\) | 9.00000 | − | 5.19615i | 0.321019 | − | 0.185341i | ||||
\(787\) | 7.00000 | + | 12.1244i | 0.249523 | + | 0.432187i | 0.963394 | − | 0.268091i | \(-0.0863928\pi\) |
−0.713871 | + | 0.700278i | \(0.753059\pi\) | |||||||
\(788\) | 8.00000 | + | 13.8564i | 0.284988 | + | 0.493614i | ||||
\(789\) | 27.7128i | 0.986602i | ||||||||
\(790\) | −4.00000 | + | 6.92820i | −0.142314 | + | 0.246494i | ||||
\(791\) | −60.0000 | −2.13335 | ||||||||
\(792\) | −4.50000 | − | 7.79423i | −0.159901 | − | 0.276956i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −6.50000 | + | 11.2583i | −0.230676 | + | 0.399543i | ||||
\(795\) | −13.5000 | − | 7.79423i | −0.478796 | − | 0.276433i | ||||
\(796\) | −1.50000 | − | 2.59808i | −0.0531661 | − | 0.0920864i | ||||
\(797\) | −2.50000 | − | 4.33013i | −0.0885545 | − | 0.153381i | 0.818346 | − | 0.574726i | \(-0.194891\pi\) |
−0.906900 | + | 0.421345i | \(0.861558\pi\) | |||||||
\(798\) | 36.0000 | + | 20.7846i | 1.27439 | + | 0.735767i | ||||
\(799\) | 14.0000 | − | 24.2487i | 0.495284 | − | 0.857858i | ||||
\(800\) | −20.0000 | −0.707107 | ||||||||
\(801\) | 9.00000 | − | 15.5885i | 0.317999 | − | 0.550791i | ||||
\(802\) | 17.0000 | 0.600291 | ||||||||
\(803\) | −2.00000 | + | 3.46410i | −0.0705785 | + | 0.122245i | ||||
\(804\) | 19.0526i | 0.671932i | ||||||||
\(805\) | 8.00000 | + | 13.8564i | 0.281963 | + | 0.488374i | ||||
\(806\) | 7.00000 | + | 12.1244i | 0.246564 | + | 0.427062i | ||||
\(807\) | 25.5000 | − | 14.7224i | 0.897643 | − | 0.518254i | ||||
\(808\) | −6.00000 | + | 10.3923i | −0.211079 | + | 0.365600i | ||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | −4.50000 | − | 7.79423i | −0.158114 | − | 0.273861i | ||||
\(811\) | −14.0000 | −0.491606 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(812\) | 12.0000 | − | 20.7846i | 0.421117 | − | 0.729397i | ||||
\(813\) | 33.0000 | − | 19.0526i | 1.15736 | − | 0.668202i | ||||
\(814\) | −1.50000 | − | 2.59808i | −0.0525750 | − | 0.0910625i | ||||
\(815\) | 5.50000 | + | 9.52628i | 0.192657 | + | 0.333691i | ||||
\(816\) | 6.92820i | 0.242536i | ||||||||
\(817\) | −18.0000 | + | 31.1769i | −0.629740 | + | 1.09074i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.0000 | + | 20.7846i | −0.419314 | + | 0.726273i | ||||
\(820\) | 2.00000 | 0.0698430 | ||||||||
\(821\) | 10.0000 | − | 17.3205i | 0.349002 | − | 0.604490i | −0.637070 | − | 0.770806i | \(-0.719854\pi\) |
0.986073 | + | 0.166316i | \(0.0531872\pi\) | |||||||
\(822\) | 7.50000 | + | 4.33013i | 0.261593 | + | 0.151031i | ||||
\(823\) | 12.0000 | + | 20.7846i | 0.418294 | + | 0.724506i | 0.995768 | − | 0.0919029i | \(-0.0292950\pi\) |
−0.577474 | + | 0.816409i | \(0.695962\pi\) | |||||||
\(824\) | −19.5000 | − | 33.7750i | −0.679315 | − | 1.17661i | ||||
\(825\) | −6.00000 | − | 3.46410i | −0.208893 | − | 0.120605i | ||||
\(826\) | 14.0000 | − | 24.2487i | 0.487122 | − | 0.843721i | ||||
\(827\) | −40.0000 | −1.39094 | −0.695468 | − | 0.718557i | \(-0.744803\pi\) | ||||
−0.695468 | + | 0.718557i | \(0.744803\pi\) | |||||||
\(828\) | 6.00000 | + | 10.3923i | 0.208514 | + | 0.361158i | ||||
\(829\) | 25.0000 | 0.868286 | 0.434143 | − | 0.900844i | \(-0.357051\pi\) | ||||
0.434143 | + | 0.900844i | \(0.357051\pi\) | |||||||
\(830\) | 6.00000 | − | 10.3923i | 0.208263 | − | 0.360722i | ||||
\(831\) | 3.46410i | 0.120168i | ||||||||
\(832\) | 7.00000 | + | 12.1244i | 0.242681 | + | 0.420336i | ||||
\(833\) | −18.0000 | − | 31.1769i | −0.623663 | − | 1.08022i | ||||
\(834\) | 3.00000 | − | 1.73205i | 0.103882 | − | 0.0599760i | ||||
\(835\) | −6.00000 | + | 10.3923i | −0.207639 | + | 0.359641i | ||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | 31.5000 | − | 18.1865i | 1.08880 | − | 0.628619i | ||||
\(838\) | 5.00000 | 0.172722 | ||||||||
\(839\) | −8.00000 | + | 13.8564i | −0.276191 | + | 0.478376i | −0.970435 | − | 0.241363i | \(-0.922405\pi\) |
0.694244 | + | 0.719740i | \(0.255739\pi\) | |||||||
\(840\) | 18.0000 | − | 10.3923i | 0.621059 | − | 0.358569i | ||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −6.50000 | − | 11.2583i | −0.224005 | − | 0.387988i | ||||
\(843\) | − | 10.3923i | − | 0.357930i | ||||||
\(844\) | 3.00000 | − | 5.19615i | 0.103264 | − | 0.178859i | ||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 21.0000 | 0.721995 | ||||||||
\(847\) | 4.00000 | 0.137442 | ||||||||
\(848\) | −4.50000 | + | 7.79423i | −0.154531 | + | 0.267655i | ||||
\(849\) | 42.0000 | + | 24.2487i | 1.44144 | + | 0.832214i | ||||
\(850\) | 8.00000 | + | 13.8564i | 0.274398 | + | 0.475271i | ||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | −13.5000 | − | 7.79423i | −0.462502 | − | 0.267026i | ||||
\(853\) | −1.00000 | + | 1.73205i | −0.0342393 | + | 0.0593043i | −0.882637 | − | 0.470055i | \(-0.844234\pi\) |
0.848398 | + | 0.529359i | \(0.177568\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.0000 | −0.615587 | ||||||||
\(856\) | 54.0000 | 1.84568 | ||||||||
\(857\) | −19.0000 | + | 32.9090i | −0.649028 | + | 1.12415i | 0.334328 | + | 0.942457i | \(0.391491\pi\) |
−0.983355 | + | 0.181692i | \(0.941843\pi\) | |||||||
\(858\) | 3.46410i | 0.118262i | ||||||||
\(859\) | −7.50000 | − | 12.9904i | −0.255897 | − | 0.443226i | 0.709242 | − | 0.704965i | \(-0.249037\pi\) |
−0.965139 | + | 0.261739i | \(0.915704\pi\) | |||||||
\(860\) | 3.00000 | + | 5.19615i | 0.102299 | + | 0.177187i | ||||
\(861\) | 12.0000 | − | 6.92820i | 0.408959 | − | 0.236113i | ||||
\(862\) | 15.0000 | − | 25.9808i | 0.510902 | − | 0.884908i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 22.5000 | − | 12.9904i | 0.765466 | − | 0.441942i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.00000 | − | 12.1244i | 0.237870 | − | 0.412002i | ||||
\(867\) | 1.50000 | − | 0.866025i | 0.0509427 | − | 0.0294118i | ||||
\(868\) | 14.0000 | + | 24.2487i | 0.475191 | + | 0.823055i | ||||
\(869\) | −4.00000 | − | 6.92820i | −0.135691 | − | 0.235023i | ||||
\(870\) | − | 10.3923i | − | 0.352332i | ||||||
\(871\) | 11.0000 | − | 19.0526i | 0.372721 | − | 0.645571i | ||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | −28.5000 | − | 49.3634i | −0.964579 | − | 1.67070i | ||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | 18.0000 | − | 31.1769i | 0.608511 | − | 1.05397i | ||||
\(876\) | −6.00000 | − | 3.46410i | −0.202721 | − | 0.117041i | ||||
\(877\) | 9.00000 | + | 15.5885i | 0.303908 | + | 0.526385i | 0.977018 | − | 0.213158i | \(-0.0683750\pi\) |
−0.673109 | + | 0.739543i | \(0.735042\pi\) | |||||||
\(878\) | 7.00000 | + | 12.1244i | 0.236239 | + | 0.409177i | ||||
\(879\) | 18.0000 | + | 10.3923i | 0.607125 | + | 0.350524i | ||||
\(880\) | 0.500000 | − | 0.866025i | 0.0168550 | − | 0.0291937i | ||||
\(881\) | −7.00000 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(882\) | 13.5000 | − | 23.3827i | 0.454569 | − | 0.787336i | ||||
\(883\) | −5.00000 | −0.168263 | −0.0841317 | − | 0.996455i | \(-0.526812\pi\) | ||||
−0.0841317 | + | 0.996455i | \(0.526812\pi\) | |||||||
\(884\) | −4.00000 | + | 6.92820i | −0.134535 | + | 0.233021i | ||||
\(885\) | 12.1244i | 0.407556i | ||||||||
\(886\) | −0.500000 | − | 0.866025i | −0.0167978 | − | 0.0290947i | ||||
\(887\) | −4.00000 | − | 6.92820i | −0.134307 | − | 0.232626i | 0.791026 | − | 0.611783i | \(-0.209547\pi\) |
−0.925332 | + | 0.379157i | \(0.876214\pi\) | |||||||
\(888\) | 13.5000 | − | 7.79423i | 0.453030 | − | 0.261557i | ||||
\(889\) | −4.00000 | + | 6.92820i | −0.134156 | + | 0.232364i | ||||
\(890\) | 6.00000 | 0.201120 | ||||||||
\(891\) | 9.00000 | 0.301511 | ||||||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | 21.0000 | − | 36.3731i | 0.702738 | − | 1.21718i | ||||
\(894\) | 6.00000 | − | 3.46410i | 0.200670 | − | 0.115857i | ||||
\(895\) | 4.50000 | + | 7.79423i | 0.150418 | + | 0.260532i | ||||
\(896\) | 6.00000 | + | 10.3923i | 0.200446 | + | 0.347183i | ||||
\(897\) | − | 13.8564i | − | 0.462652i | ||||||
\(898\) | −11.5000 | + | 19.9186i | −0.383760 | + | 0.664692i | ||||
\(899\) | 42.0000 | 1.40078 | ||||||||
\(900\) | 6.00000 | − | 10.3923i | 0.200000 | − | 0.346410i | ||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 1.00000 | − | 1.73205i | 0.0332964 | − | 0.0576710i | ||||
\(903\) | 36.0000 | + | 20.7846i | 1.19800 | + | 0.691669i | ||||
\(904\) | −22.5000 | − | 38.9711i | −0.748339 | − | 1.29616i | ||||
\(905\) | −3.50000 | − | 6.06218i | −0.116344 | − | 0.201514i | ||||
\(906\) | −24.0000 | − | 13.8564i | −0.797347 | − | 0.460348i | ||||
\(907\) | −6.00000 | + | 10.3923i | −0.199227 | + | 0.345071i | −0.948278 | − | 0.317441i | \(-0.897176\pi\) |
0.749051 | + | 0.662512i | \(0.230510\pi\) | |||||||
\(908\) | 18.0000 | 0.597351 | ||||||||
\(909\) | −6.00000 | − | 10.3923i | −0.199007 | − | 0.344691i | ||||
\(910\) | −8.00000 | −0.265197 | ||||||||
\(911\) | −13.5000 | + | 23.3827i | −0.447275 | + | 0.774703i | −0.998208 | − | 0.0598468i | \(-0.980939\pi\) |
0.550933 | + | 0.834550i | \(0.314272\pi\) | |||||||
\(912\) | 10.3923i | 0.344124i | ||||||||
\(913\) | 6.00000 | + | 10.3923i | 0.198571 | + | 0.343935i | ||||
\(914\) | 3.00000 | + | 5.19615i | 0.0992312 | + | 0.171873i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.00000 | + | 5.19615i | −0.0991228 | + | 0.171686i | ||||
\(917\) | −24.0000 | −0.792550 | ||||||||
\(918\) | −18.0000 | − | 10.3923i | −0.594089 | − | 0.342997i | ||||
\(919\) | 52.0000 | 1.71532 | 0.857661 | − | 0.514216i | \(-0.171917\pi\) | ||||
0.857661 | + | 0.514216i | \(0.171917\pi\) | |||||||
\(920\) | −6.00000 | + | 10.3923i | −0.197814 | + | 0.342624i | ||||
\(921\) | 42.0000 | − | 24.2487i | 1.38395 | − | 0.799022i | ||||
\(922\) | 6.00000 | + | 10.3923i | 0.197599 | + | 0.342252i | ||||
\(923\) | 9.00000 | + | 15.5885i | 0.296239 | + | 0.513100i | ||||
\(924\) | 6.92820i | 0.227921i | ||||||||
\(925\) | 6.00000 | − | 10.3923i | 0.197279 | − | 0.341697i | ||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | 39.0000 | 1.28093 | ||||||||
\(928\) | 30.0000 | 0.984798 | ||||||||
\(929\) | −10.5000 | + | 18.1865i | −0.344494 | + | 0.596681i | −0.985262 | − | 0.171054i | \(-0.945283\pi\) |
0.640768 | + | 0.767735i | \(0.278616\pi\) | |||||||
\(930\) | 10.5000 | + | 6.06218i | 0.344309 | + | 0.198787i | ||||
\(931\) | −27.0000 | − | 46.7654i | −0.884889 | − | 1.53267i | ||||
\(932\) | 12.0000 | + | 20.7846i | 0.393073 | + | 0.680823i | ||||
\(933\) | −31.5000 | − | 18.1865i | −1.03126 | − | 0.595400i | ||||
\(934\) | −13.5000 | + | 23.3827i | −0.441733 | + | 0.765105i | ||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | −18.0000 | −0.588348 | ||||||||
\(937\) | 14.0000 | 0.457360 | 0.228680 | − | 0.973502i | \(-0.426559\pi\) | ||||
0.228680 | + | 0.973502i | \(0.426559\pi\) | |||||||
\(938\) | −22.0000 | + | 38.1051i | −0.718325 | + | 1.24418i | ||||
\(939\) | − | 24.2487i | − | 0.791327i | ||||||
\(940\) | −3.50000 | − | 6.06218i | −0.114157 | − | 0.197726i | ||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 10.5000 | − | 6.06218i | 0.342108 | − | 0.197516i | ||||
\(943\) | −4.00000 | + | 6.92820i | −0.130258 | + | 0.225613i | ||||
\(944\) | 7.00000 | 0.227831 | ||||||||
\(945\) | 20.7846i | 0.676123i | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | −7.50000 | + | 12.9904i | −0.243717 | + | 0.422131i | −0.961770 | − | 0.273858i | \(-0.911700\pi\) |
0.718053 | + | 0.695988i | \(0.245034\pi\) | |||||||
\(948\) | 12.0000 | − | 6.92820i | 0.389742 | − | 0.225018i | ||||
\(949\) | 4.00000 | + | 6.92820i | 0.129845 | + | 0.224899i | ||||
\(950\) | 12.0000 | + | 20.7846i | 0.389331 | + | 0.674342i | ||||
\(951\) | − | 38.1051i | − | 1.23564i | ||||||
\(952\) | 24.0000 | − | 41.5692i | 0.777844 | − | 1.34727i | ||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | −13.5000 | − | 23.3827i | −0.437079 | − | 0.757042i | ||||
\(955\) | −13.0000 | −0.420670 | ||||||||
\(956\) | 3.00000 | − | 5.19615i | 0.0970269 | − | 0.168056i | ||||
\(957\) | 9.00000 | + | 5.19615i | 0.290929 | + | 0.167968i | ||||
\(958\) | 2.00000 | + | 3.46410i | 0.0646171 | + | 0.111920i | ||||
\(959\) | −10.0000 | − | 17.3205i | −0.322917 | − | 0.559308i | ||||
\(960\) | 10.5000 | + | 6.06218i | 0.338886 | + | 0.195656i | ||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | −6.00000 | −0.193448 | ||||||||
\(963\) | −27.0000 | + | 46.7654i | −0.870063 | + | 1.50699i | ||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | −2.00000 | + | 3.46410i | −0.0643823 | + | 0.111513i | ||||
\(966\) | 27.7128i | 0.891645i | ||||||||
\(967\) | 25.0000 | + | 43.3013i | 0.803946 | + | 1.39247i | 0.917000 | + | 0.398886i | \(0.130603\pi\) |
−0.113055 | + | 0.993589i | \(0.536064\pi\) | |||||||
\(968\) | 1.50000 | + | 2.59808i | 0.0482118 | + | 0.0835053i | ||||
\(969\) | −36.0000 | + | 20.7846i | −1.15649 | + | 0.667698i | ||||
\(970\) | 9.50000 | − | 16.4545i | 0.305027 | − | 0.528322i | ||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 18.5000 | − | 32.0429i | 0.592778 | − | 1.02672i | ||||
\(975\) | −12.0000 | + | 6.92820i | −0.384308 | + | 0.221880i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | 19.0526i | 0.609234i | ||||||||
\(979\) | −3.00000 | + | 5.19615i | −0.0958804 | + | 0.166070i | ||||
\(980\) | −9.00000 | −0.287494 | ||||||||
\(981\) | −3.00000 | + | 5.19615i | −0.0957826 | + | 0.165900i | ||||
\(982\) | −8.00000 | −0.255290 | ||||||||
\(983\) | −1.50000 | + | 2.59808i | −0.0478426 | + | 0.0828658i | −0.888955 | − | 0.457995i | \(-0.848568\pi\) |
0.841112 | + | 0.540860i | \(0.181901\pi\) | |||||||
\(984\) | 9.00000 | + | 5.19615i | 0.286910 | + | 0.165647i | ||||
\(985\) | −8.00000 | − | 13.8564i | −0.254901 | − | 0.441502i | ||||
\(986\) | −12.0000 | − | 20.7846i | −0.382158 | − | 0.661917i | ||||
\(987\) | −42.0000 | − | 24.2487i | −1.33687 | − | 0.771845i | ||||
\(988\) | −6.00000 | + | 10.3923i | −0.190885 | + | 0.330623i | ||||
\(989\) | −24.0000 | −0.763156 | ||||||||
\(990\) | 1.50000 | + | 2.59808i | 0.0476731 | + | 0.0825723i | ||||
\(991\) | −44.0000 | −1.39771 | −0.698853 | − | 0.715265i | \(-0.746306\pi\) | ||||
−0.698853 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(992\) | −17.5000 | + | 30.3109i | −0.555626 | + | 0.962372i | ||||
\(993\) | − | 1.73205i | − | 0.0549650i | ||||||
\(994\) | −18.0000 | − | 31.1769i | −0.570925 | − | 0.988872i | ||||
\(995\) | 1.50000 | + | 2.59808i | 0.0475532 | + | 0.0823646i | ||||
\(996\) | −18.0000 | + | 10.3923i | −0.570352 | + | 0.329293i | ||||
\(997\) | 2.00000 | − | 3.46410i | 0.0633406 | − | 0.109709i | −0.832616 | − | 0.553851i | \(-0.813158\pi\) |
0.895957 | + | 0.444141i | \(0.146491\pi\) | |||||||
\(998\) | −25.0000 | −0.791361 | ||||||||
\(999\) | 15.5885i | 0.493197i |
(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 | 99.2.e.a.34.1 | ✓ | 2 | |
3.2 | odd | 2 | 297.2.e.c.100.1 | 2 | |||
9.2 | odd | 6 | 891.2.a.c.1.1 | 1 | |||
9.4 | even | 3 | inner | 99.2.e.a.67.1 | yes | 2 | |
9.5 | odd | 6 | 297.2.e.c.199.1 | 2 | |||
9.7 | even | 3 | 891.2.a.g.1.1 | 1 | |||
11.10 | odd | 2 | 1089.2.e.c.727.1 | 2 | |||
99.43 | odd | 6 | 9801.2.a.c.1.1 | 1 | |||
99.65 | even | 6 | 9801.2.a.i.1.1 | 1 | |||
99.76 | odd | 6 | 1089.2.e.c.364.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.e.a.34.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.2.e.a.67.1 | yes | 2 | 9.4 | even | 3 | inner | |
297.2.e.c.100.1 | 2 | 3.2 | odd | 2 | |||
297.2.e.c.199.1 | 2 | 9.5 | odd | 6 | |||
891.2.a.c.1.1 | 1 | 9.2 | odd | 6 | |||
891.2.a.g.1.1 | 1 | 9.7 | even | 3 | |||
1089.2.e.c.364.1 | 2 | 99.76 | odd | 6 | |||
1089.2.e.c.727.1 | 2 | 11.10 | odd | 2 | |||
9801.2.a.c.1.1 | 1 | 99.43 | odd | 6 | |||
9801.2.a.i.1.1 | 1 | 99.65 | even | 6 |