Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(569,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 569.6 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.569 |
Dual form | 570.2.c.e.569.2 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.41421 | − | 1.00000i | −0.816497 | − | 0.577350i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.73205 | − | 1.41421i | 0.774597 | − | 0.632456i | ||||
\(6\) | 1.00000 | − | 1.41421i | 0.408248 | − | 0.577350i | ||||
\(7\) | − | 2.44949i | − | 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 1.41421 | + | 1.73205i | 0.447214 | + | 0.547723i | ||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 1.41421 | + | 1.00000i | 0.408248 | + | 0.288675i | ||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 2.44949 | 0.654654 | ||||||||
\(15\) | −3.86370 | + | 0.267949i | −0.997604 | + | 0.0691842i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.92820 | −1.68034 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | −2.82843 | + | 1.00000i | −0.666667 | + | 0.235702i | ||||
\(19\) | 4.00000 | + | 1.73205i | 0.917663 | + | 0.397360i | ||||
\(20\) | −1.73205 | + | 1.41421i | −0.387298 | + | 0.316228i | ||||
\(21\) | −2.44949 | + | 3.46410i | −0.534522 | + | 0.755929i | ||||
\(22\) | 1.41421 | 0.301511 | ||||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | −1.00000 | + | 1.41421i | −0.204124 | + | 0.288675i | ||||
\(25\) | 1.00000 | − | 4.89898i | 0.200000 | − | 0.979796i | ||||
\(26\) | − | 4.24264i | − | 0.832050i | ||||||
\(27\) | 1.41421 | − | 5.00000i | 0.272166 | − | 0.962250i | ||||
\(28\) | 2.44949i | 0.462910i | ||||||||
\(29\) | −2.44949 | −0.454859 | −0.227429 | − | 0.973795i | \(-0.573032\pi\) | ||||
−0.227429 | + | 0.973795i | \(0.573032\pi\) | |||||||
\(30\) | −0.267949 | − | 3.86370i | −0.0489206 | − | 0.705412i | ||||
\(31\) | − | 6.92820i | − | 1.24434i | −0.782881 | − | 0.622171i | \(-0.786251\pi\) | ||
0.782881 | − | 0.622171i | \(-0.213749\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −1.41421 | + | 2.00000i | −0.246183 | + | 0.348155i | ||||
\(34\) | − | 6.92820i | − | 1.18818i | ||||||
\(35\) | −3.46410 | − | 4.24264i | −0.585540 | − | 0.717137i | ||||
\(36\) | −1.00000 | − | 2.82843i | −0.166667 | − | 0.471405i | ||||
\(37\) | 4.24264 | 0.697486 | 0.348743 | − | 0.937218i | \(-0.386609\pi\) | ||||
0.348743 | + | 0.937218i | \(0.386609\pi\) | |||||||
\(38\) | −1.73205 | + | 4.00000i | −0.280976 | + | 0.648886i | ||||
\(39\) | 6.00000 | + | 4.24264i | 0.960769 | + | 0.679366i | ||||
\(40\) | −1.41421 | − | 1.73205i | −0.223607 | − | 0.273861i | ||||
\(41\) | −12.2474 | −1.91273 | −0.956365 | − | 0.292174i | \(-0.905621\pi\) | ||||
−0.956365 | + | 0.292174i | \(0.905621\pi\) | |||||||
\(42\) | −3.46410 | − | 2.44949i | −0.534522 | − | 0.377964i | ||||
\(43\) | − | 7.34847i | − | 1.12063i | −0.828279 | − | 0.560316i | \(-0.810680\pi\) | ||
0.828279 | − | 0.560316i | \(-0.189320\pi\) | |||||||
\(44\) | 1.41421i | 0.213201i | ||||||||
\(45\) | 5.73205 | + | 3.48477i | 0.854484 | + | 0.519478i | ||||
\(46\) | − | 3.46410i | − | 0.510754i | ||||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | −1.41421 | − | 1.00000i | −0.204124 | − | 0.144338i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.89898 | + | 1.00000i | 0.692820 | + | 0.141421i | ||||
\(51\) | 9.79796 | + | 6.92820i | 1.37199 | + | 0.970143i | ||||
\(52\) | 4.24264 | 0.588348 | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 5.00000 | + | 1.41421i | 0.680414 | + | 0.192450i | ||||
\(55\) | −2.00000 | − | 2.44949i | −0.269680 | − | 0.330289i | ||||
\(56\) | −2.44949 | −0.327327 | ||||||||
\(57\) | −3.92480 | − | 6.44949i | −0.519853 | − | 0.854256i | ||||
\(58\) | − | 2.44949i | − | 0.321634i | ||||||
\(59\) | 4.89898 | 0.637793 | 0.318896 | − | 0.947790i | \(-0.396688\pi\) | ||||
0.318896 | + | 0.947790i | \(0.396688\pi\) | |||||||
\(60\) | 3.86370 | − | 0.267949i | 0.498802 | − | 0.0345921i | ||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 6.92820 | 0.879883 | ||||||||
\(63\) | 6.92820 | − | 2.44949i | 0.872872 | − | 0.308607i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −7.34847 | + | 6.00000i | −0.911465 | + | 0.744208i | ||||
\(66\) | −2.00000 | − | 1.41421i | −0.246183 | − | 0.174078i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 6.92820 | 0.840168 | ||||||||
\(69\) | 4.89898 | + | 3.46410i | 0.589768 | + | 0.417029i | ||||
\(70\) | 4.24264 | − | 3.46410i | 0.507093 | − | 0.414039i | ||||
\(71\) | 4.89898 | 0.581402 | 0.290701 | − | 0.956814i | \(-0.406112\pi\) | ||||
0.290701 | + | 0.956814i | \(0.406112\pi\) | |||||||
\(72\) | 2.82843 | − | 1.00000i | 0.333333 | − | 0.117851i | ||||
\(73\) | 14.6969i | 1.72015i | 0.510171 | + | 0.860073i | \(0.329582\pi\) | ||||
−0.510171 | + | 0.860073i | \(0.670418\pi\) | |||||||
\(74\) | 4.24264i | 0.493197i | ||||||||
\(75\) | −6.31319 | + | 5.92820i | −0.728985 | + | 0.684530i | ||||
\(76\) | −4.00000 | − | 1.73205i | −0.458831 | − | 0.198680i | ||||
\(77\) | −3.46410 | −0.394771 | ||||||||
\(78\) | −4.24264 | + | 6.00000i | −0.480384 | + | 0.679366i | ||||
\(79\) | − | 10.3923i | − | 1.16923i | −0.811312 | − | 0.584613i | \(-0.801246\pi\) | ||
0.811312 | − | 0.584613i | \(-0.198754\pi\) | |||||||
\(80\) | 1.73205 | − | 1.41421i | 0.193649 | − | 0.158114i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | − | 12.2474i | − | 1.35250i | ||||||
\(83\) | −10.3923 | −1.14070 | −0.570352 | − | 0.821401i | \(-0.693193\pi\) | ||||
−0.570352 | + | 0.821401i | \(0.693193\pi\) | |||||||
\(84\) | 2.44949 | − | 3.46410i | 0.267261 | − | 0.377964i | ||||
\(85\) | −12.0000 | + | 9.79796i | −1.30158 | + | 1.06274i | ||||
\(86\) | 7.34847 | 0.792406 | ||||||||
\(87\) | 3.46410 | + | 2.44949i | 0.371391 | + | 0.262613i | ||||
\(88\) | −1.41421 | −0.150756 | ||||||||
\(89\) | 2.44949 | 0.259645 | 0.129823 | − | 0.991537i | \(-0.458559\pi\) | ||||
0.129823 | + | 0.991537i | \(0.458559\pi\) | |||||||
\(90\) | −3.48477 | + | 5.73205i | −0.367327 | + | 0.604211i | ||||
\(91\) | 10.3923i | 1.08941i | ||||||||
\(92\) | 3.46410 | 0.361158 | ||||||||
\(93\) | −6.92820 | + | 9.79796i | −0.718421 | + | 1.01600i | ||||
\(94\) | 3.46410i | 0.357295i | ||||||||
\(95\) | 9.37769 | − | 2.65685i | 0.962131 | − | 0.272587i | ||||
\(96\) | 1.00000 | − | 1.41421i | 0.102062 | − | 0.144338i | ||||
\(97\) | 12.7279 | 1.29232 | 0.646162 | − | 0.763200i | \(-0.276373\pi\) | ||||
0.646162 | + | 0.763200i | \(0.276373\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 4.00000 | − | 1.41421i | 0.402015 | − | 0.142134i | ||||
\(100\) | −1.00000 | + | 4.89898i | −0.100000 | + | 0.489898i | ||||
\(101\) | 2.82843i | 0.281439i | 0.990050 | + | 0.140720i | \(0.0449416\pi\) | ||||
−0.990050 | + | 0.140720i | \(0.955058\pi\) | |||||||
\(102\) | −6.92820 | + | 9.79796i | −0.685994 | + | 0.970143i | ||||
\(103\) | 8.48528 | 0.836080 | 0.418040 | − | 0.908429i | \(-0.362717\pi\) | ||||
0.418040 | + | 0.908429i | \(0.362717\pi\) | |||||||
\(104\) | 4.24264i | 0.416025i | ||||||||
\(105\) | 0.656339 | + | 9.46410i | 0.0640521 | + | 0.923602i | ||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 18.0000i | 1.74013i | 0.492941 | + | 0.870063i | \(0.335922\pi\) | ||||
−0.492941 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(108\) | −1.41421 | + | 5.00000i | −0.136083 | + | 0.481125i | ||||
\(109\) | − | 6.92820i | − | 0.663602i | −0.943349 | − | 0.331801i | \(-0.892344\pi\) | ||
0.943349 | − | 0.331801i | \(-0.107656\pi\) | |||||||
\(110\) | 2.44949 | − | 2.00000i | 0.233550 | − | 0.190693i | ||||
\(111\) | −6.00000 | − | 4.24264i | −0.569495 | − | 0.402694i | ||||
\(112\) | − | 2.44949i | − | 0.231455i | ||||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | 6.44949 | − | 3.92480i | 0.604050 | − | 0.367592i | ||||
\(115\) | −6.00000 | + | 4.89898i | −0.559503 | + | 0.456832i | ||||
\(116\) | 2.44949 | 0.227429 | ||||||||
\(117\) | −4.24264 | − | 12.0000i | −0.392232 | − | 1.10940i | ||||
\(118\) | 4.89898i | 0.450988i | ||||||||
\(119\) | 16.9706i | 1.55569i | ||||||||
\(120\) | 0.267949 | + | 3.86370i | 0.0244603 | + | 0.352706i | ||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | − | 8.00000i | − | 0.724286i | ||||||
\(123\) | 17.3205 | + | 12.2474i | 1.56174 | + | 1.10432i | ||||
\(124\) | 6.92820i | 0.622171i | ||||||||
\(125\) | −5.19615 | − | 9.89949i | −0.464758 | − | 0.885438i | ||||
\(126\) | 2.44949 | + | 6.92820i | 0.218218 | + | 0.617213i | ||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −7.34847 | + | 10.3923i | −0.646997 | + | 0.914991i | ||||
\(130\) | −6.00000 | − | 7.34847i | −0.526235 | − | 0.644503i | ||||
\(131\) | 1.41421i | 0.123560i | 0.998090 | + | 0.0617802i | \(0.0196778\pi\) | ||||
−0.998090 | + | 0.0617802i | \(0.980322\pi\) | |||||||
\(132\) | 1.41421 | − | 2.00000i | 0.123091 | − | 0.174078i | ||||
\(133\) | 4.24264 | − | 9.79796i | 0.367884 | − | 0.849591i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.62158 | − | 10.6603i | −0.397762 | − | 0.917489i | ||||
\(136\) | 6.92820i | 0.594089i | ||||||||
\(137\) | 17.3205 | 1.47979 | 0.739895 | − | 0.672722i | \(-0.234875\pi\) | ||||
0.739895 | + | 0.672722i | \(0.234875\pi\) | |||||||
\(138\) | −3.46410 | + | 4.89898i | −0.294884 | + | 0.417029i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 3.46410 | + | 4.24264i | 0.292770 | + | 0.358569i | ||||
\(141\) | −4.89898 | − | 3.46410i | −0.412568 | − | 0.291730i | ||||
\(142\) | 4.89898i | 0.411113i | ||||||||
\(143\) | 6.00000i | 0.501745i | ||||||||
\(144\) | 1.00000 | + | 2.82843i | 0.0833333 | + | 0.235702i | ||||
\(145\) | −4.24264 | + | 3.46410i | −0.352332 | + | 0.287678i | ||||
\(146\) | −14.6969 | −1.21633 | ||||||||
\(147\) | −1.41421 | − | 1.00000i | −0.116642 | − | 0.0824786i | ||||
\(148\) | −4.24264 | −0.348743 | ||||||||
\(149\) | 11.3137i | 0.926855i | 0.886135 | + | 0.463428i | \(0.153381\pi\) | ||||
−0.886135 | + | 0.463428i | \(0.846619\pi\) | |||||||
\(150\) | −5.92820 | − | 6.31319i | −0.484036 | − | 0.515470i | ||||
\(151\) | − | 13.8564i | − | 1.12762i | −0.825905 | − | 0.563809i | \(-0.809335\pi\) | ||
0.825905 | − | 0.563809i | \(-0.190665\pi\) | |||||||
\(152\) | 1.73205 | − | 4.00000i | 0.140488 | − | 0.324443i | ||||
\(153\) | −6.92820 | − | 19.5959i | −0.560112 | − | 1.58424i | ||||
\(154\) | − | 3.46410i | − | 0.279145i | ||||||
\(155\) | −9.79796 | − | 12.0000i | −0.786991 | − | 0.963863i | ||||
\(156\) | −6.00000 | − | 4.24264i | −0.480384 | − | 0.339683i | ||||
\(157\) | 14.6969i | 1.17294i | 0.809970 | + | 0.586472i | \(0.199483\pi\) | ||||
−0.809970 | + | 0.586472i | \(0.800517\pi\) | |||||||
\(158\) | 10.3923 | 0.826767 | ||||||||
\(159\) | −6.00000 | + | 8.48528i | −0.475831 | + | 0.672927i | ||||
\(160\) | 1.41421 | + | 1.73205i | 0.111803 | + | 0.136931i | ||||
\(161\) | 8.48528i | 0.668734i | ||||||||
\(162\) | −5.65685 | − | 7.00000i | −0.444444 | − | 0.549972i | ||||
\(163\) | − | 12.2474i | − | 0.959294i | −0.877461 | − | 0.479647i | \(-0.840765\pi\) | ||
0.877461 | − | 0.479647i | \(-0.159235\pi\) | |||||||
\(164\) | 12.2474 | 0.956365 | ||||||||
\(165\) | 0.378937 | + | 5.46410i | 0.0295002 | + | 0.425380i | ||||
\(166\) | − | 10.3923i | − | 0.806599i | ||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 3.46410 | + | 2.44949i | 0.267261 | + | 0.188982i | ||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | −9.79796 | − | 12.0000i | −0.751469 | − | 0.920358i | ||||
\(171\) | −0.898979 | + | 13.0458i | −0.0687467 | + | 0.997634i | ||||
\(172\) | 7.34847i | 0.560316i | ||||||||
\(173\) | − | 6.00000i | − | 0.456172i | −0.973641 | − | 0.228086i | \(-0.926753\pi\) | ||
0.973641 | − | 0.228086i | \(-0.0732467\pi\) | |||||||
\(174\) | −2.44949 | + | 3.46410i | −0.185695 | + | 0.262613i | ||||
\(175\) | −12.0000 | − | 2.44949i | −0.907115 | − | 0.185164i | ||||
\(176\) | − | 1.41421i | − | 0.106600i | ||||||
\(177\) | −6.92820 | − | 4.89898i | −0.520756 | − | 0.368230i | ||||
\(178\) | 2.44949i | 0.183597i | ||||||||
\(179\) | 4.89898 | 0.366167 | 0.183083 | − | 0.983097i | \(-0.441392\pi\) | ||||
0.183083 | + | 0.983097i | \(0.441392\pi\) | |||||||
\(180\) | −5.73205 | − | 3.48477i | −0.427242 | − | 0.259739i | ||||
\(181\) | 13.8564i | 1.02994i | 0.857209 | + | 0.514969i | \(0.172197\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827803\pi\) | |||||||
\(182\) | −10.3923 | −0.770329 | ||||||||
\(183\) | 11.3137 | + | 8.00000i | 0.836333 | + | 0.591377i | ||||
\(184\) | 3.46410i | 0.255377i | ||||||||
\(185\) | 7.34847 | − | 6.00000i | 0.540270 | − | 0.441129i | ||||
\(186\) | −9.79796 | − | 6.92820i | −0.718421 | − | 0.508001i | ||||
\(187\) | 9.79796i | 0.716498i | ||||||||
\(188\) | −3.46410 | −0.252646 | ||||||||
\(189\) | −12.2474 | − | 3.46410i | −0.890871 | − | 0.251976i | ||||
\(190\) | 2.65685 | + | 9.37769i | 0.192748 | + | 0.680329i | ||||
\(191\) | − | 24.0416i | − | 1.73959i | −0.493412 | − | 0.869796i | \(-0.664251\pi\) | ||
0.493412 | − | 0.869796i | \(-0.335749\pi\) | |||||||
\(192\) | 1.41421 | + | 1.00000i | 0.102062 | + | 0.0721688i | ||||
\(193\) | 12.7279 | 0.916176 | 0.458088 | − | 0.888907i | \(-0.348534\pi\) | ||||
0.458088 | + | 0.888907i | \(0.348534\pi\) | |||||||
\(194\) | 12.7279i | 0.913812i | ||||||||
\(195\) | 16.3923 | − | 1.13681i | 1.17388 | − | 0.0814088i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 1.41421 | + | 4.00000i | 0.100504 | + | 0.284268i | ||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | −4.89898 | − | 1.00000i | −0.346410 | − | 0.0707107i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.82843 | −0.199007 | ||||||||
\(203\) | 6.00000i | 0.421117i | ||||||||
\(204\) | −9.79796 | − | 6.92820i | −0.685994 | − | 0.485071i | ||||
\(205\) | −21.2132 | + | 17.3205i | −1.48159 | + | 1.20972i | ||||
\(206\) | 8.48528i | 0.591198i | ||||||||
\(207\) | −3.46410 | − | 9.79796i | −0.240772 | − | 0.681005i | ||||
\(208\) | −4.24264 | −0.294174 | ||||||||
\(209\) | 2.44949 | − | 5.65685i | 0.169435 | − | 0.391293i | ||||
\(210\) | −9.46410 | + | 0.656339i | −0.653085 | + | 0.0452917i | ||||
\(211\) | − | 3.46410i | − | 0.238479i | −0.992866 | − | 0.119239i | \(-0.961954\pi\) | ||
0.992866 | − | 0.119239i | \(-0.0380456\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | −6.92820 | − | 4.89898i | −0.474713 | − | 0.335673i | ||||
\(214\) | −18.0000 | −1.23045 | ||||||||
\(215\) | −10.3923 | − | 12.7279i | −0.708749 | − | 0.868037i | ||||
\(216\) | −5.00000 | − | 1.41421i | −0.340207 | − | 0.0962250i | ||||
\(217\) | −16.9706 | −1.15204 | ||||||||
\(218\) | 6.92820 | 0.469237 | ||||||||
\(219\) | 14.6969 | − | 20.7846i | 0.993127 | − | 1.40449i | ||||
\(220\) | 2.00000 | + | 2.44949i | 0.134840 | + | 0.165145i | ||||
\(221\) | 29.3939 | 1.97725 | ||||||||
\(222\) | 4.24264 | − | 6.00000i | 0.284747 | − | 0.402694i | ||||
\(223\) | 25.4558 | 1.70465 | 0.852325 | − | 0.523013i | \(-0.175192\pi\) | ||||
0.852325 | + | 0.523013i | \(0.175192\pi\) | |||||||
\(224\) | 2.44949 | 0.163663 | ||||||||
\(225\) | 14.8564 | − | 2.07055i | 0.990427 | − | 0.138037i | ||||
\(226\) | 18.0000 | 1.19734 | ||||||||
\(227\) | 12.0000i | 0.796468i | 0.917284 | + | 0.398234i | \(0.130377\pi\) | ||||
−0.917284 | + | 0.398234i | \(0.869623\pi\) | |||||||
\(228\) | 3.92480 | + | 6.44949i | 0.259926 | + | 0.427128i | ||||
\(229\) | 28.0000 | 1.85029 | 0.925146 | − | 0.379611i | \(-0.123942\pi\) | ||||
0.925146 | + | 0.379611i | \(0.123942\pi\) | |||||||
\(230\) | −4.89898 | − | 6.00000i | −0.323029 | − | 0.395628i | ||||
\(231\) | 4.89898 | + | 3.46410i | 0.322329 | + | 0.227921i | ||||
\(232\) | 2.44949i | 0.160817i | ||||||||
\(233\) | 10.3923 | 0.680823 | 0.340411 | − | 0.940277i | \(-0.389434\pi\) | ||||
0.340411 | + | 0.940277i | \(0.389434\pi\) | |||||||
\(234\) | 12.0000 | − | 4.24264i | 0.784465 | − | 0.277350i | ||||
\(235\) | 6.00000 | − | 4.89898i | 0.391397 | − | 0.319574i | ||||
\(236\) | −4.89898 | −0.318896 | ||||||||
\(237\) | −10.3923 | + | 14.6969i | −0.675053 | + | 0.954669i | ||||
\(238\) | −16.9706 | −1.10004 | ||||||||
\(239\) | 1.41421i | 0.0914779i | 0.998953 | + | 0.0457389i | \(0.0145642\pi\) | ||||
−0.998953 | + | 0.0457389i | \(0.985436\pi\) | |||||||
\(240\) | −3.86370 | + | 0.267949i | −0.249401 | + | 0.0172960i | ||||
\(241\) | − | 13.8564i | − | 0.892570i | −0.894891 | − | 0.446285i | \(-0.852747\pi\) | ||
0.894891 | − | 0.446285i | \(-0.147253\pi\) | |||||||
\(242\) | 9.00000i | 0.578542i | ||||||||
\(243\) | 15.5563 | − | 1.00000i | 0.997940 | − | 0.0641500i | ||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 1.73205 | − | 1.41421i | 0.110657 | − | 0.0903508i | ||||
\(246\) | −12.2474 | + | 17.3205i | −0.780869 | + | 1.10432i | ||||
\(247\) | −16.9706 | − | 7.34847i | −1.07981 | − | 0.467572i | ||||
\(248\) | −6.92820 | −0.439941 | ||||||||
\(249\) | 14.6969 | + | 10.3923i | 0.931381 | + | 0.658586i | ||||
\(250\) | 9.89949 | − | 5.19615i | 0.626099 | − | 0.328634i | ||||
\(251\) | 1.41421i | 0.0892644i | 0.999003 | + | 0.0446322i | \(0.0142116\pi\) | ||||
−0.999003 | + | 0.0446322i | \(0.985788\pi\) | |||||||
\(252\) | −6.92820 | + | 2.44949i | −0.436436 | + | 0.154303i | ||||
\(253\) | 4.89898i | 0.307996i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 26.7685 | − | 1.85641i | 1.67631 | − | 0.116253i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | −10.3923 | − | 7.34847i | −0.646997 | − | 0.457496i | ||||
\(259\) | − | 10.3923i | − | 0.645746i | ||||||
\(260\) | 7.34847 | − | 6.00000i | 0.455733 | − | 0.372104i | ||||
\(261\) | −2.44949 | − | 6.92820i | −0.151620 | − | 0.428845i | ||||
\(262\) | −1.41421 | −0.0873704 | ||||||||
\(263\) | 3.46410 | 0.213606 | 0.106803 | − | 0.994280i | \(-0.465939\pi\) | ||||
0.106803 | + | 0.994280i | \(0.465939\pi\) | |||||||
\(264\) | 2.00000 | + | 1.41421i | 0.123091 | + | 0.0870388i | ||||
\(265\) | −8.48528 | − | 10.3923i | −0.521247 | − | 0.638394i | ||||
\(266\) | 9.79796 | + | 4.24264i | 0.600751 | + | 0.260133i | ||||
\(267\) | −3.46410 | − | 2.44949i | −0.212000 | − | 0.149906i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.1464 | −1.04544 | −0.522718 | − | 0.852506i | \(-0.675082\pi\) | ||||
−0.522718 | + | 0.852506i | \(0.675082\pi\) | |||||||
\(270\) | 10.6603 | − | 4.62158i | 0.648762 | − | 0.281260i | ||||
\(271\) | 4.00000 | 0.242983 | 0.121491 | − | 0.992592i | \(-0.461232\pi\) | ||||
0.121491 | + | 0.992592i | \(0.461232\pi\) | |||||||
\(272\) | −6.92820 | −0.420084 | ||||||||
\(273\) | 10.3923 | − | 14.6969i | 0.628971 | − | 0.889499i | ||||
\(274\) | 17.3205i | 1.04637i | ||||||||
\(275\) | −6.92820 | − | 1.41421i | −0.417786 | − | 0.0852803i | ||||
\(276\) | −4.89898 | − | 3.46410i | −0.294884 | − | 0.208514i | ||||
\(277\) | − | 19.5959i | − | 1.17740i | −0.808350 | − | 0.588702i | \(-0.799639\pi\) | ||
0.808350 | − | 0.588702i | \(-0.200361\pi\) | |||||||
\(278\) | 4.00000i | 0.239904i | ||||||||
\(279\) | 19.5959 | − | 6.92820i | 1.17318 | − | 0.414781i | ||||
\(280\) | −4.24264 | + | 3.46410i | −0.253546 | + | 0.207020i | ||||
\(281\) | −7.34847 | −0.438373 | −0.219186 | − | 0.975683i | \(-0.570340\pi\) | ||||
−0.219186 | + | 0.975683i | \(0.570340\pi\) | |||||||
\(282\) | 3.46410 | − | 4.89898i | 0.206284 | − | 0.291730i | ||||
\(283\) | − | 12.2474i | − | 0.728035i | −0.931392 | − | 0.364018i | \(-0.881405\pi\) | ||
0.931392 | − | 0.364018i | \(-0.118595\pi\) | |||||||
\(284\) | −4.89898 | −0.290701 | ||||||||
\(285\) | −15.9189 | − | 5.62033i | −0.942955 | − | 0.332920i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 30.0000i | 1.77084i | ||||||||
\(288\) | −2.82843 | + | 1.00000i | −0.166667 | + | 0.0589256i | ||||
\(289\) | 31.0000 | 1.82353 | ||||||||
\(290\) | −3.46410 | − | 4.24264i | −0.203419 | − | 0.249136i | ||||
\(291\) | −18.0000 | − | 12.7279i | −1.05518 | − | 0.746124i | ||||
\(292\) | − | 14.6969i | − | 0.860073i | ||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 1.00000 | − | 1.41421i | 0.0583212 | − | 0.0824786i | ||||
\(295\) | 8.48528 | − | 6.92820i | 0.494032 | − | 0.403376i | ||||
\(296\) | − | 4.24264i | − | 0.246598i | ||||||
\(297\) | −7.07107 | − | 2.00000i | −0.410305 | − | 0.116052i | ||||
\(298\) | −11.3137 | −0.655386 | ||||||||
\(299\) | 14.6969 | 0.849946 | ||||||||
\(300\) | 6.31319 | − | 5.92820i | 0.364492 | − | 0.342265i | ||||
\(301\) | −18.0000 | −1.03750 | ||||||||
\(302\) | 13.8564 | 0.797347 | ||||||||
\(303\) | 2.82843 | − | 4.00000i | 0.162489 | − | 0.229794i | ||||
\(304\) | 4.00000 | + | 1.73205i | 0.229416 | + | 0.0993399i | ||||
\(305\) | −13.8564 | + | 11.3137i | −0.793416 | + | 0.647821i | ||||
\(306\) | 19.5959 | − | 6.92820i | 1.12022 | − | 0.396059i | ||||
\(307\) | −25.4558 | −1.45284 | −0.726421 | − | 0.687250i | \(-0.758818\pi\) | ||||
−0.726421 | + | 0.687250i | \(0.758818\pi\) | |||||||
\(308\) | 3.46410 | 0.197386 | ||||||||
\(309\) | −12.0000 | − | 8.48528i | −0.682656 | − | 0.482711i | ||||
\(310\) | 12.0000 | − | 9.79796i | 0.681554 | − | 0.556487i | ||||
\(311\) | − | 26.8701i | − | 1.52366i | −0.647776 | − | 0.761831i | \(-0.724301\pi\) | ||
0.647776 | − | 0.761831i | \(-0.275699\pi\) | |||||||
\(312\) | 4.24264 | − | 6.00000i | 0.240192 | − | 0.339683i | ||||
\(313\) | − | 4.89898i | − | 0.276907i | −0.990369 | − | 0.138453i | \(-0.955787\pi\) | ||
0.990369 | − | 0.138453i | \(-0.0442131\pi\) | |||||||
\(314\) | −14.6969 | −0.829396 | ||||||||
\(315\) | 8.53590 | − | 14.0406i | 0.480943 | − | 0.791098i | ||||
\(316\) | 10.3923i | 0.584613i | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | −8.48528 | − | 6.00000i | −0.475831 | − | 0.336463i | ||||
\(319\) | 3.46410i | 0.193952i | ||||||||
\(320\) | −1.73205 | + | 1.41421i | −0.0968246 | + | 0.0790569i | ||||
\(321\) | 18.0000 | − | 25.4558i | 1.00466 | − | 1.42081i | ||||
\(322\) | −8.48528 | −0.472866 | ||||||||
\(323\) | −27.7128 | − | 12.0000i | −1.54198 | − | 0.667698i | ||||
\(324\) | 7.00000 | − | 5.65685i | 0.388889 | − | 0.314270i | ||||
\(325\) | −4.24264 | + | 20.7846i | −0.235339 | + | 1.15292i | ||||
\(326\) | 12.2474 | 0.678323 | ||||||||
\(327\) | −6.92820 | + | 9.79796i | −0.383131 | + | 0.541828i | ||||
\(328\) | 12.2474i | 0.676252i | ||||||||
\(329\) | − | 8.48528i | − | 0.467809i | ||||||
\(330\) | −5.46410 | + | 0.378937i | −0.300789 | + | 0.0208598i | ||||
\(331\) | 6.92820i | 0.380808i | 0.981706 | + | 0.190404i | \(0.0609799\pi\) | ||||
−0.981706 | + | 0.190404i | \(0.939020\pi\) | |||||||
\(332\) | 10.3923 | 0.570352 | ||||||||
\(333\) | 4.24264 | + | 12.0000i | 0.232495 | + | 0.657596i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.44949 | + | 3.46410i | −0.133631 | + | 0.188982i | ||||
\(337\) | 4.24264 | 0.231111 | 0.115556 | − | 0.993301i | \(-0.463135\pi\) | ||||
0.115556 | + | 0.993301i | \(0.463135\pi\) | |||||||
\(338\) | 5.00000i | 0.271964i | ||||||||
\(339\) | −18.0000 | + | 25.4558i | −0.977626 | + | 1.38257i | ||||
\(340\) | 12.0000 | − | 9.79796i | 0.650791 | − | 0.531369i | ||||
\(341\) | −9.79796 | −0.530589 | ||||||||
\(342\) | −13.0458 | − | 0.898979i | −0.705434 | − | 0.0486112i | ||||
\(343\) | − | 19.5959i | − | 1.05808i | ||||||
\(344\) | −7.34847 | −0.396203 | ||||||||
\(345\) | 13.3843 | − | 0.928203i | 0.720584 | − | 0.0499728i | ||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | 24.2487 | 1.30174 | 0.650870 | − | 0.759190i | \(-0.274404\pi\) | ||||
0.650870 | + | 0.759190i | \(0.274404\pi\) | |||||||
\(348\) | −3.46410 | − | 2.44949i | −0.185695 | − | 0.131306i | ||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 2.44949 | − | 12.0000i | 0.130931 | − | 0.641427i | ||||
\(351\) | −6.00000 | + | 21.2132i | −0.320256 | + | 1.13228i | ||||
\(352\) | 1.41421 | 0.0753778 | ||||||||
\(353\) | −17.3205 | −0.921878 | −0.460939 | − | 0.887432i | \(-0.652487\pi\) | ||||
−0.460939 | + | 0.887432i | \(0.652487\pi\) | |||||||
\(354\) | 4.89898 | − | 6.92820i | 0.260378 | − | 0.368230i | ||||
\(355\) | 8.48528 | − | 6.92820i | 0.450352 | − | 0.367711i | ||||
\(356\) | −2.44949 | −0.129823 | ||||||||
\(357\) | 16.9706 | − | 24.0000i | 0.898177 | − | 1.27021i | ||||
\(358\) | 4.89898i | 0.258919i | ||||||||
\(359\) | − | 18.3848i | − | 0.970311i | −0.874428 | − | 0.485156i | \(-0.838763\pi\) | ||
0.874428 | − | 0.485156i | \(-0.161237\pi\) | |||||||
\(360\) | 3.48477 | − | 5.73205i | 0.183663 | − | 0.302106i | ||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | −13.8564 | −0.728277 | ||||||||
\(363\) | −12.7279 | − | 9.00000i | −0.668043 | − | 0.472377i | ||||
\(364\) | − | 10.3923i | − | 0.544705i | ||||||
\(365\) | 20.7846 | + | 25.4558i | 1.08792 | + | 1.33242i | ||||
\(366\) | −8.00000 | + | 11.3137i | −0.418167 | + | 0.591377i | ||||
\(367\) | 31.8434i | 1.66221i | 0.556115 | + | 0.831105i | \(0.312291\pi\) | ||||
−0.556115 | + | 0.831105i | \(0.687709\pi\) | |||||||
\(368\) | −3.46410 | −0.180579 | ||||||||
\(369\) | −12.2474 | − | 34.6410i | −0.637577 | − | 1.80334i | ||||
\(370\) | 6.00000 | + | 7.34847i | 0.311925 | + | 0.382029i | ||||
\(371\) | −14.6969 | −0.763027 | ||||||||
\(372\) | 6.92820 | − | 9.79796i | 0.359211 | − | 0.508001i | ||||
\(373\) | 12.7279 | 0.659027 | 0.329513 | − | 0.944151i | \(-0.393115\pi\) | ||||
0.329513 | + | 0.944151i | \(0.393115\pi\) | |||||||
\(374\) | −9.79796 | −0.506640 | ||||||||
\(375\) | −2.55103 | + | 19.1962i | −0.131734 | + | 0.991285i | ||||
\(376\) | − | 3.46410i | − | 0.178647i | ||||||
\(377\) | 10.3923 | 0.535231 | ||||||||
\(378\) | 3.46410 | − | 12.2474i | 0.178174 | − | 0.629941i | ||||
\(379\) | 20.7846i | 1.06763i | 0.845600 | + | 0.533817i | \(0.179243\pi\) | ||||
−0.845600 | + | 0.533817i | \(0.820757\pi\) | |||||||
\(380\) | −9.37769 | + | 2.65685i | −0.481065 | + | 0.136294i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.0416 | 1.23008 | ||||||||
\(383\) | − | 6.00000i | − | 0.306586i | −0.988181 | − | 0.153293i | \(-0.951012\pi\) | ||
0.988181 | − | 0.153293i | \(-0.0489878\pi\) | |||||||
\(384\) | −1.00000 | + | 1.41421i | −0.0510310 | + | 0.0721688i | ||||
\(385\) | −6.00000 | + | 4.89898i | −0.305788 | + | 0.249675i | ||||
\(386\) | 12.7279i | 0.647834i | ||||||||
\(387\) | 20.7846 | − | 7.34847i | 1.05654 | − | 0.373544i | ||||
\(388\) | −12.7279 | −0.646162 | ||||||||
\(389\) | − | 19.7990i | − | 1.00385i | −0.864912 | − | 0.501924i | \(-0.832626\pi\) | ||
0.864912 | − | 0.501924i | \(-0.167374\pi\) | |||||||
\(390\) | 1.13681 | + | 16.3923i | 0.0575647 | + | 0.830057i | ||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | 1.41421 | − | 2.00000i | 0.0713376 | − | 0.100887i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.6969 | − | 18.0000i | −0.739483 | − | 0.905678i | ||||
\(396\) | −4.00000 | + | 1.41421i | −0.201008 | + | 0.0710669i | ||||
\(397\) | − | 19.5959i | − | 0.983491i | −0.870739 | − | 0.491745i | \(-0.836359\pi\) | ||
0.870739 | − | 0.491745i | \(-0.163641\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | −15.7980 | + | 9.61377i | −0.790887 | + | 0.481290i | ||||
\(400\) | 1.00000 | − | 4.89898i | 0.0500000 | − | 0.244949i | ||||
\(401\) | −22.0454 | −1.10090 | −0.550448 | − | 0.834870i | \(-0.685543\pi\) | ||||
−0.550448 | + | 0.834870i | \(0.685543\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.3939i | 1.46421i | ||||||||
\(404\) | − | 2.82843i | − | 0.140720i | ||||||
\(405\) | −4.12436 | + | 19.6975i | −0.204941 | + | 0.978774i | ||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | − | 6.00000i | − | 0.297409i | ||||||
\(408\) | 6.92820 | − | 9.79796i | 0.342997 | − | 0.485071i | ||||
\(409\) | 20.7846i | 1.02773i | 0.857870 | + | 0.513866i | \(0.171787\pi\) | ||||
−0.857870 | + | 0.513866i | \(0.828213\pi\) | |||||||
\(410\) | −17.3205 | − | 21.2132i | −0.855399 | − | 1.04765i | ||||
\(411\) | −24.4949 | − | 17.3205i | −1.20824 | − | 0.854358i | ||||
\(412\) | −8.48528 | −0.418040 | ||||||||
\(413\) | − | 12.0000i | − | 0.590481i | ||||||
\(414\) | 9.79796 | − | 3.46410i | 0.481543 | − | 0.170251i | ||||
\(415\) | −18.0000 | + | 14.6969i | −0.883585 | + | 0.721444i | ||||
\(416\) | − | 4.24264i | − | 0.208013i | ||||||
\(417\) | −5.65685 | − | 4.00000i | −0.277017 | − | 0.195881i | ||||
\(418\) | 5.65685 | + | 2.44949i | 0.276686 | + | 0.119808i | ||||
\(419\) | 9.89949i | 0.483622i | 0.970323 | + | 0.241811i | \(0.0777414\pi\) | ||||
−0.970323 | + | 0.241811i | \(0.922259\pi\) | |||||||
\(420\) | −0.656339 | − | 9.46410i | −0.0320261 | − | 0.461801i | ||||
\(421\) | − | 13.8564i | − | 0.675320i | −0.941268 | − | 0.337660i | \(-0.890365\pi\) | ||
0.941268 | − | 0.337660i | \(-0.109635\pi\) | |||||||
\(422\) | 3.46410 | 0.168630 | ||||||||
\(423\) | 3.46410 | + | 9.79796i | 0.168430 | + | 0.476393i | ||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −6.92820 | + | 33.9411i | −0.336067 | + | 1.64639i | ||||
\(426\) | 4.89898 | − | 6.92820i | 0.237356 | − | 0.335673i | ||||
\(427\) | 19.5959i | 0.948313i | ||||||||
\(428\) | − | 18.0000i | − | 0.870063i | ||||||
\(429\) | 6.00000 | − | 8.48528i | 0.289683 | − | 0.409673i | ||||
\(430\) | 12.7279 | − | 10.3923i | 0.613795 | − | 0.501161i | ||||
\(431\) | 19.5959 | 0.943902 | 0.471951 | − | 0.881625i | \(-0.343550\pi\) | ||||
0.471951 | + | 0.881625i | \(0.343550\pi\) | |||||||
\(432\) | 1.41421 | − | 5.00000i | 0.0680414 | − | 0.240563i | ||||
\(433\) | −38.1838 | −1.83499 | −0.917497 | − | 0.397742i | \(-0.869794\pi\) | ||||
−0.917497 | + | 0.397742i | \(0.869794\pi\) | |||||||
\(434\) | − | 16.9706i | − | 0.814613i | ||||||
\(435\) | 9.46410 | − | 0.656339i | 0.453769 | − | 0.0314690i | ||||
\(436\) | 6.92820i | 0.331801i | ||||||||
\(437\) | −13.8564 | − | 6.00000i | −0.662842 | − | 0.287019i | ||||
\(438\) | 20.7846 | + | 14.6969i | 0.993127 | + | 0.702247i | ||||
\(439\) | − | 3.46410i | − | 0.165333i | −0.996577 | − | 0.0826663i | \(-0.973656\pi\) | ||
0.996577 | − | 0.0826663i | \(-0.0263436\pi\) | |||||||
\(440\) | −2.44949 | + | 2.00000i | −0.116775 | + | 0.0953463i | ||||
\(441\) | 1.00000 | + | 2.82843i | 0.0476190 | + | 0.134687i | ||||
\(442\) | 29.3939i | 1.39812i | ||||||||
\(443\) | −17.3205 | −0.822922 | −0.411461 | − | 0.911427i | \(-0.634981\pi\) | ||||
−0.411461 | + | 0.911427i | \(0.634981\pi\) | |||||||
\(444\) | 6.00000 | + | 4.24264i | 0.284747 | + | 0.201347i | ||||
\(445\) | 4.24264 | − | 3.46410i | 0.201120 | − | 0.164214i | ||||
\(446\) | 25.4558i | 1.20537i | ||||||||
\(447\) | 11.3137 | − | 16.0000i | 0.535120 | − | 0.756774i | ||||
\(448\) | 2.44949i | 0.115728i | ||||||||
\(449\) | −12.2474 | −0.577993 | −0.288996 | − | 0.957330i | \(-0.593322\pi\) | ||||
−0.288996 | + | 0.957330i | \(0.593322\pi\) | |||||||
\(450\) | 2.07055 | + | 14.8564i | 0.0976068 | + | 0.700338i | ||||
\(451\) | 17.3205i | 0.815591i | ||||||||
\(452\) | 18.0000i | 0.846649i | ||||||||
\(453\) | −13.8564 | + | 19.5959i | −0.651031 | + | 0.920697i | ||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | 14.6969 | + | 18.0000i | 0.689003 | + | 0.843853i | ||||
\(456\) | −6.44949 | + | 3.92480i | −0.302025 | + | 0.183796i | ||||
\(457\) | − | 24.4949i | − | 1.14582i | −0.819617 | − | 0.572911i | \(-0.805814\pi\) | ||
0.819617 | − | 0.572911i | \(-0.194186\pi\) | |||||||
\(458\) | 28.0000i | 1.30835i | ||||||||
\(459\) | −9.79796 | + | 34.6410i | −0.457330 | + | 1.61690i | ||||
\(460\) | 6.00000 | − | 4.89898i | 0.279751 | − | 0.228416i | ||||
\(461\) | 22.6274i | 1.05386i | 0.849907 | + | 0.526932i | \(0.176658\pi\) | ||||
−0.849907 | + | 0.526932i | \(0.823342\pi\) | |||||||
\(462\) | −3.46410 | + | 4.89898i | −0.161165 | + | 0.227921i | ||||
\(463\) | 12.2474i | 0.569187i | 0.958648 | + | 0.284594i | \(0.0918587\pi\) | ||||
−0.958648 | + | 0.284594i | \(0.908141\pi\) | |||||||
\(464\) | −2.44949 | −0.113715 | ||||||||
\(465\) | 1.85641 | + | 26.7685i | 0.0860888 | + | 1.24136i | ||||
\(466\) | 10.3923i | 0.481414i | ||||||||
\(467\) | −24.2487 | −1.12210 | −0.561048 | − | 0.827783i | \(-0.689602\pi\) | ||||
−0.561048 | + | 0.827783i | \(0.689602\pi\) | |||||||
\(468\) | 4.24264 | + | 12.0000i | 0.196116 | + | 0.554700i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.89898 | + | 6.00000i | 0.225973 | + | 0.276759i | ||||
\(471\) | 14.6969 | − | 20.7846i | 0.677199 | − | 0.957704i | ||||
\(472\) | − | 4.89898i | − | 0.225494i | ||||||
\(473\) | −10.3923 | −0.477839 | ||||||||
\(474\) | −14.6969 | − | 10.3923i | −0.675053 | − | 0.477334i | ||||
\(475\) | 12.4853 | − | 17.8639i | 0.572864 | − | 0.819650i | ||||
\(476\) | − | 16.9706i | − | 0.777844i | ||||||
\(477\) | 16.9706 | − | 6.00000i | 0.777029 | − | 0.274721i | ||||
\(478\) | −1.41421 | −0.0646846 | ||||||||
\(479\) | − | 9.89949i | − | 0.452319i | −0.974090 | − | 0.226160i | \(-0.927383\pi\) | ||
0.974090 | − | 0.226160i | \(-0.0726171\pi\) | |||||||
\(480\) | −0.267949 | − | 3.86370i | −0.0122302 | − | 0.176353i | ||||
\(481\) | −18.0000 | −0.820729 | ||||||||
\(482\) | 13.8564 | 0.631142 | ||||||||
\(483\) | 8.48528 | − | 12.0000i | 0.386094 | − | 0.546019i | ||||
\(484\) | −9.00000 | −0.409091 | ||||||||
\(485\) | 22.0454 | − | 18.0000i | 1.00103 | − | 0.817338i | ||||
\(486\) | 1.00000 | + | 15.5563i | 0.0453609 | + | 0.705650i | ||||
\(487\) | −33.9411 | −1.53802 | −0.769010 | − | 0.639237i | \(-0.779250\pi\) | ||||
−0.769010 | + | 0.639237i | \(0.779250\pi\) | |||||||
\(488\) | 8.00000i | 0.362143i | ||||||||
\(489\) | −12.2474 | + | 17.3205i | −0.553849 | + | 0.783260i | ||||
\(490\) | 1.41421 | + | 1.73205i | 0.0638877 | + | 0.0782461i | ||||
\(491\) | − | 7.07107i | − | 0.319113i | −0.987189 | − | 0.159556i | \(-0.948994\pi\) | ||
0.987189 | − | 0.159556i | \(-0.0510064\pi\) | |||||||
\(492\) | −17.3205 | − | 12.2474i | −0.780869 | − | 0.552158i | ||||
\(493\) | 16.9706 | 0.764316 | ||||||||
\(494\) | 7.34847 | − | 16.9706i | 0.330623 | − | 0.763542i | ||||
\(495\) | 4.92820 | − | 8.10634i | 0.221506 | − | 0.364353i | ||||
\(496\) | − | 6.92820i | − | 0.311086i | ||||||
\(497\) | − | 12.0000i | − | 0.538274i | ||||||
\(498\) | −10.3923 | + | 14.6969i | −0.465690 | + | 0.658586i | ||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 5.19615 | + | 9.89949i | 0.232379 | + | 0.442719i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.41421 | −0.0631194 | ||||||||
\(503\) | 17.3205 | 0.772283 | 0.386142 | − | 0.922440i | \(-0.373808\pi\) | ||||
0.386142 | + | 0.922440i | \(0.373808\pi\) | |||||||
\(504\) | −2.44949 | − | 6.92820i | −0.109109 | − | 0.308607i | ||||
\(505\) | 4.00000 | + | 4.89898i | 0.177998 | + | 0.218002i | ||||
\(506\) | −4.89898 | −0.217786 | ||||||||
\(507\) | −7.07107 | − | 5.00000i | −0.314037 | − | 0.222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.0454 | −0.977146 | −0.488573 | − | 0.872523i | \(-0.662482\pi\) | ||||
−0.488573 | + | 0.872523i | \(0.662482\pi\) | |||||||
\(510\) | 1.85641 | + | 26.7685i | 0.0822031 | + | 1.18533i | ||||
\(511\) | 36.0000 | 1.59255 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 14.3171 | − | 17.5505i | 0.632116 | − | 0.774874i | ||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | 14.6969 | − | 12.0000i | 0.647624 | − | 0.528783i | ||||
\(516\) | 7.34847 | − | 10.3923i | 0.323498 | − | 0.457496i | ||||
\(517\) | − | 4.89898i | − | 0.215457i | ||||||
\(518\) | 10.3923 | 0.456612 | ||||||||
\(519\) | −6.00000 | + | 8.48528i | −0.263371 | + | 0.372463i | ||||
\(520\) | 6.00000 | + | 7.34847i | 0.263117 | + | 0.322252i | ||||
\(521\) | 22.0454 | 0.965827 | 0.482913 | − | 0.875668i | \(-0.339579\pi\) | ||||
0.482913 | + | 0.875668i | \(0.339579\pi\) | |||||||
\(522\) | 6.92820 | − | 2.44949i | 0.303239 | − | 0.107211i | ||||
\(523\) | −16.9706 | −0.742071 | −0.371035 | − | 0.928619i | \(-0.620997\pi\) | ||||
−0.371035 | + | 0.928619i | \(0.620997\pi\) | |||||||
\(524\) | − | 1.41421i | − | 0.0617802i | ||||||
\(525\) | 14.5211 | + | 15.4641i | 0.633752 | + | 0.674909i | ||||
\(526\) | 3.46410i | 0.151042i | ||||||||
\(527\) | 48.0000i | 2.09091i | ||||||||
\(528\) | −1.41421 | + | 2.00000i | −0.0615457 | + | 0.0870388i | ||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 10.3923 | − | 8.48528i | 0.451413 | − | 0.368577i | ||||
\(531\) | 4.89898 | + | 13.8564i | 0.212598 | + | 0.601317i | ||||
\(532\) | −4.24264 | + | 9.79796i | −0.183942 | + | 0.424795i | ||||
\(533\) | 51.9615 | 2.25070 | ||||||||
\(534\) | 2.44949 | − | 3.46410i | 0.106000 | − | 0.149906i | ||||
\(535\) | 25.4558 | + | 31.1769i | 1.10055 | + | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.92820 | − | 4.89898i | −0.298974 | − | 0.211407i | ||||
\(538\) | − | 17.1464i | − | 0.739235i | ||||||
\(539\) | − | 1.41421i | − | 0.0609145i | ||||||
\(540\) | 4.62158 | + | 10.6603i | 0.198881 | + | 0.458744i | ||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 4.00000i | 0.171815i | ||||||||
\(543\) | 13.8564 | − | 19.5959i | 0.594635 | − | 0.840941i | ||||
\(544\) | − | 6.92820i | − | 0.297044i | ||||||
\(545\) | −9.79796 | − | 12.0000i | −0.419698 | − | 0.514024i | ||||
\(546\) | 14.6969 | + | 10.3923i | 0.628971 | + | 0.444750i | ||||
\(547\) | 25.4558 | 1.08841 | 0.544207 | − | 0.838951i | \(-0.316831\pi\) | ||||
0.544207 | + | 0.838951i | \(0.316831\pi\) | |||||||
\(548\) | −17.3205 | −0.739895 | ||||||||
\(549\) | −8.00000 | − | 22.6274i | −0.341432 | − | 0.965715i | ||||
\(550\) | 1.41421 | − | 6.92820i | 0.0603023 | − | 0.295420i | ||||
\(551\) | −9.79796 | − | 4.24264i | −0.417407 | − | 0.180743i | ||||
\(552\) | 3.46410 | − | 4.89898i | 0.147442 | − | 0.208514i | ||||
\(553\) | −25.4558 | −1.08249 | ||||||||
\(554\) | 19.5959 | 0.832551 | ||||||||
\(555\) | −16.3923 | + | 1.13681i | −0.695815 | + | 0.0482550i | ||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 10.3923 | 0.440336 | 0.220168 | − | 0.975462i | \(-0.429339\pi\) | ||||
0.220168 | + | 0.975462i | \(0.429339\pi\) | |||||||
\(558\) | 6.92820 | + | 19.5959i | 0.293294 | + | 0.829561i | ||||
\(559\) | 31.1769i | 1.31864i | ||||||||
\(560\) | −3.46410 | − | 4.24264i | −0.146385 | − | 0.179284i | ||||
\(561\) | 9.79796 | − | 13.8564i | 0.413670 | − | 0.585018i | ||||
\(562\) | − | 7.34847i | − | 0.309976i | ||||||
\(563\) | − | 36.0000i | − | 1.51722i | −0.651546 | − | 0.758610i | \(-0.725879\pi\) | ||
0.651546 | − | 0.758610i | \(-0.274121\pi\) | |||||||
\(564\) | 4.89898 | + | 3.46410i | 0.206284 | + | 0.145865i | ||||
\(565\) | −25.4558 | − | 31.1769i | −1.07094 | − | 1.31162i | ||||
\(566\) | 12.2474 | 0.514799 | ||||||||
\(567\) | 13.8564 | + | 17.1464i | 0.581914 | + | 0.720082i | ||||
\(568\) | − | 4.89898i | − | 0.205557i | ||||||
\(569\) | 46.5403 | 1.95107 | 0.975536 | − | 0.219842i | \(-0.0705541\pi\) | ||||
0.975536 | + | 0.219842i | \(0.0705541\pi\) | |||||||
\(570\) | 5.62033 | − | 15.9189i | 0.235410 | − | 0.666770i | ||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | − | 6.00000i | − | 0.250873i | ||||||
\(573\) | −24.0416 | + | 34.0000i | −1.00435 | + | 1.42037i | ||||
\(574\) | −30.0000 | −1.25218 | ||||||||
\(575\) | −3.46410 | + | 16.9706i | −0.144463 | + | 0.707721i | ||||
\(576\) | −1.00000 | − | 2.82843i | −0.0416667 | − | 0.117851i | ||||
\(577\) | 24.4949i | 1.01974i | 0.860253 | + | 0.509868i | \(0.170306\pi\) | ||||
−0.860253 | + | 0.509868i | \(0.829694\pi\) | |||||||
\(578\) | 31.0000i | 1.28943i | ||||||||
\(579\) | −18.0000 | − | 12.7279i | −0.748054 | − | 0.528954i | ||||
\(580\) | 4.24264 | − | 3.46410i | 0.176166 | − | 0.143839i | ||||
\(581\) | 25.4558i | 1.05609i | ||||||||
\(582\) | 12.7279 | − | 18.0000i | 0.527589 | − | 0.746124i | ||||
\(583\) | −8.48528 | −0.351424 | ||||||||
\(584\) | 14.6969 | 0.608164 | ||||||||
\(585\) | −24.3190 | − | 14.7846i | −1.00547 | − | 0.611268i | ||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 3.46410 | 0.142979 | 0.0714894 | − | 0.997441i | \(-0.477225\pi\) | ||||
0.0714894 | + | 0.997441i | \(0.477225\pi\) | |||||||
\(588\) | 1.41421 | + | 1.00000i | 0.0583212 | + | 0.0412393i | ||||
\(589\) | 12.0000 | − | 27.7128i | 0.494451 | − | 1.14189i | ||||
\(590\) | 6.92820 | + | 8.48528i | 0.285230 | + | 0.349334i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.24264 | 0.174371 | ||||||||
\(593\) | 3.46410 | 0.142254 | 0.0711268 | − | 0.997467i | \(-0.477341\pi\) | ||||
0.0711268 | + | 0.997467i | \(0.477341\pi\) | |||||||
\(594\) | 2.00000 | − | 7.07107i | 0.0820610 | − | 0.290129i | ||||
\(595\) | 24.0000 | + | 29.3939i | 0.983904 | + | 1.20503i | ||||
\(596\) | − | 11.3137i | − | 0.463428i | ||||||
\(597\) | 22.6274 | + | 16.0000i | 0.926079 | + | 0.654836i | ||||
\(598\) | 14.6969i | 0.601003i | ||||||||
\(599\) | 4.89898 | 0.200167 | 0.100083 | − | 0.994979i | \(-0.468089\pi\) | ||||
0.100083 | + | 0.994979i | \(0.468089\pi\) | |||||||
\(600\) | 5.92820 | + | 6.31319i | 0.242018 | + | 0.257735i | ||||
\(601\) | 6.92820i | 0.282607i | 0.989966 | + | 0.141304i | \(0.0451294\pi\) | ||||
−0.989966 | + | 0.141304i | \(0.954871\pi\) | |||||||
\(602\) | − | 18.0000i | − | 0.733625i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.8564i | 0.563809i | ||||||||
\(605\) | 15.5885 | − | 12.7279i | 0.633761 | − | 0.517464i | ||||
\(606\) | 4.00000 | + | 2.82843i | 0.162489 | + | 0.114897i | ||||
\(607\) | 16.9706 | 0.688814 | 0.344407 | − | 0.938820i | \(-0.388080\pi\) | ||||
0.344407 | + | 0.938820i | \(0.388080\pi\) | |||||||
\(608\) | −1.73205 | + | 4.00000i | −0.0702439 | + | 0.162221i | ||||
\(609\) | 6.00000 | − | 8.48528i | 0.243132 | − | 0.343841i | ||||
\(610\) | −11.3137 | − | 13.8564i | −0.458079 | − | 0.561029i | ||||
\(611\) | −14.6969 | −0.594574 | ||||||||
\(612\) | 6.92820 | + | 19.5959i | 0.280056 | + | 0.792118i | ||||
\(613\) | 44.0908i | 1.78081i | 0.455168 | + | 0.890406i | \(0.349579\pi\) | ||||
−0.455168 | + | 0.890406i | \(0.650421\pi\) | |||||||
\(614\) | − | 25.4558i | − | 1.02731i | ||||||
\(615\) | 47.3205 | − | 3.28169i | 1.90815 | − | 0.132331i | ||||
\(616\) | 3.46410i | 0.139573i | ||||||||
\(617\) | 20.7846 | 0.836757 | 0.418378 | − | 0.908273i | \(-0.362599\pi\) | ||||
0.418378 | + | 0.908273i | \(0.362599\pi\) | |||||||
\(618\) | 8.48528 | − | 12.0000i | 0.341328 | − | 0.482711i | ||||
\(619\) | 16.0000 | 0.643094 | 0.321547 | − | 0.946894i | \(-0.395797\pi\) | ||||
0.321547 | + | 0.946894i | \(0.395797\pi\) | |||||||
\(620\) | 9.79796 | + | 12.0000i | 0.393496 | + | 0.481932i | ||||
\(621\) | −4.89898 | + | 17.3205i | −0.196589 | + | 0.695048i | ||||
\(622\) | 26.8701 | 1.07739 | ||||||||
\(623\) | − | 6.00000i | − | 0.240385i | ||||||
\(624\) | 6.00000 | + | 4.24264i | 0.240192 | + | 0.169842i | ||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | 4.89898 | 0.195803 | ||||||||
\(627\) | −9.12096 | + | 5.55051i | −0.364256 | + | 0.221666i | ||||
\(628\) | − | 14.6969i | − | 0.586472i | ||||||
\(629\) | −29.3939 | −1.17201 | ||||||||
\(630\) | 14.0406 | + | 8.53590i | 0.559391 | + | 0.340078i | ||||
\(631\) | −44.0000 | −1.75161 | −0.875806 | − | 0.482663i | \(-0.839670\pi\) | ||||
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | −10.3923 | −0.413384 | ||||||||
\(633\) | −3.46410 | + | 4.89898i | −0.137686 | + | 0.194717i | ||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.00000 | − | 8.48528i | 0.237915 | − | 0.336463i | ||||
\(637\) | −4.24264 | −0.168100 | ||||||||
\(638\) | −3.46410 | −0.137145 | ||||||||
\(639\) | 4.89898 | + | 13.8564i | 0.193801 | + | 0.548151i | ||||
\(640\) | −1.41421 | − | 1.73205i | −0.0559017 | − | 0.0684653i | ||||
\(641\) | 12.2474 | 0.483745 | 0.241873 | − | 0.970308i | \(-0.422238\pi\) | ||||
0.241873 | + | 0.970308i | \(0.422238\pi\) | |||||||
\(642\) | 25.4558 | + | 18.0000i | 1.00466 | + | 0.710403i | ||||
\(643\) | − | 7.34847i | − | 0.289795i | −0.989447 | − | 0.144898i | \(-0.953715\pi\) | ||
0.989447 | − | 0.144898i | \(-0.0462853\pi\) | |||||||
\(644\) | − | 8.48528i | − | 0.334367i | ||||||
\(645\) | 1.96902 | + | 28.3923i | 0.0775299 | + | 1.11795i | ||||
\(646\) | 12.0000 | − | 27.7128i | 0.472134 | − | 1.09035i | ||||
\(647\) | 10.3923 | 0.408564 | 0.204282 | − | 0.978912i | \(-0.434514\pi\) | ||||
0.204282 | + | 0.978912i | \(0.434514\pi\) | |||||||
\(648\) | 5.65685 | + | 7.00000i | 0.222222 | + | 0.274986i | ||||
\(649\) | − | 6.92820i | − | 0.271956i | ||||||
\(650\) | −20.7846 | − | 4.24264i | −0.815239 | − | 0.166410i | ||||
\(651\) | 24.0000 | + | 16.9706i | 0.940634 | + | 0.665129i | ||||
\(652\) | 12.2474i | 0.479647i | ||||||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | −9.79796 | − | 6.92820i | −0.383131 | − | 0.270914i | ||||
\(655\) | 2.00000 | + | 2.44949i | 0.0781465 | + | 0.0957095i | ||||
\(656\) | −12.2474 | −0.478183 | ||||||||
\(657\) | −41.5692 | + | 14.6969i | −1.62177 | + | 0.573382i | ||||
\(658\) | 8.48528 | 0.330791 | ||||||||
\(659\) | −44.0908 | −1.71753 | −0.858767 | − | 0.512366i | \(-0.828769\pi\) | ||||
−0.858767 | + | 0.512366i | \(0.828769\pi\) | |||||||
\(660\) | −0.378937 | − | 5.46410i | −0.0147501 | − | 0.212690i | ||||
\(661\) | 48.4974i | 1.88633i | 0.332323 | + | 0.943166i | \(0.392168\pi\) | ||||
−0.332323 | + | 0.943166i | \(0.607832\pi\) | |||||||
\(662\) | −6.92820 | −0.269272 | ||||||||
\(663\) | −41.5692 | − | 29.3939i | −1.61441 | − | 1.14156i | ||||
\(664\) | 10.3923i | 0.403300i | ||||||||
\(665\) | −6.50794 | − | 22.9706i | −0.252367 | − | 0.890760i | ||||
\(666\) | −12.0000 | + | 4.24264i | −0.464991 | + | 0.164399i | ||||
\(667\) | 8.48528 | 0.328551 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36.0000 | − | 25.4558i | −1.39184 | − | 0.984180i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.3137i | 0.436761i | ||||||||
\(672\) | −3.46410 | − | 2.44949i | −0.133631 | − | 0.0944911i | ||||
\(673\) | −12.7279 | −0.490625 | −0.245313 | − | 0.969444i | \(-0.578891\pi\) | ||||
−0.245313 | + | 0.969444i | \(0.578891\pi\) | |||||||
\(674\) | 4.24264i | 0.163420i | ||||||||
\(675\) | −23.0807 | − | 11.9282i | −0.888376 | − | 0.459117i | ||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | − | 30.0000i | − | 1.15299i | −0.817099 | − | 0.576497i | \(-0.804419\pi\) | ||
0.817099 | − | 0.576497i | \(-0.195581\pi\) | |||||||
\(678\) | −25.4558 | − | 18.0000i | −0.977626 | − | 0.691286i | ||||
\(679\) | − | 31.1769i | − | 1.19646i | ||||||
\(680\) | 9.79796 | + | 12.0000i | 0.375735 | + | 0.460179i | ||||
\(681\) | 12.0000 | − | 16.9706i | 0.459841 | − | 0.650313i | ||||
\(682\) | − | 9.79796i | − | 0.375183i | ||||||
\(683\) | 18.0000i | 0.688751i | 0.938832 | + | 0.344375i | \(0.111909\pi\) | ||||
−0.938832 | + | 0.344375i | \(0.888091\pi\) | |||||||
\(684\) | 0.898979 | − | 13.0458i | 0.0343733 | − | 0.498817i | ||||
\(685\) | 30.0000 | − | 24.4949i | 1.14624 | − | 0.935902i | ||||
\(686\) | 19.5959 | 0.748176 | ||||||||
\(687\) | −39.5980 | − | 28.0000i | −1.51076 | − | 1.06827i | ||||
\(688\) | − | 7.34847i | − | 0.280158i | ||||||
\(689\) | 25.4558i | 0.969790i | ||||||||
\(690\) | 0.928203 | + | 13.3843i | 0.0353361 | + | 0.509530i | ||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 6.00000i | 0.228086i | ||||||||
\(693\) | −3.46410 | − | 9.79796i | −0.131590 | − | 0.372194i | ||||
\(694\) | 24.2487i | 0.920468i | ||||||||
\(695\) | 6.92820 | − | 5.65685i | 0.262802 | − | 0.214577i | ||||
\(696\) | 2.44949 | − | 3.46410i | 0.0928477 | − | 0.131306i | ||||
\(697\) | 84.8528 | 3.21403 | ||||||||
\(698\) | − | 22.0000i | − | 0.832712i | ||||||
\(699\) | −14.6969 | − | 10.3923i | −0.555889 | − | 0.393073i | ||||
\(700\) | 12.0000 | + | 2.44949i | 0.453557 | + | 0.0925820i | ||||
\(701\) | 28.2843i | 1.06828i | 0.845395 | + | 0.534141i | \(0.179365\pi\) | ||||
−0.845395 | + | 0.534141i | \(0.820635\pi\) | |||||||
\(702\) | −21.2132 | − | 6.00000i | −0.800641 | − | 0.226455i | ||||
\(703\) | 16.9706 | + | 7.34847i | 0.640057 | + | 0.277153i | ||||
\(704\) | 1.41421i | 0.0533002i | ||||||||
\(705\) | −13.3843 | + | 0.928203i | −0.504080 | + | 0.0349582i | ||||
\(706\) | − | 17.3205i | − | 0.651866i | ||||||
\(707\) | 6.92820 | 0.260562 | ||||||||
\(708\) | 6.92820 | + | 4.89898i | 0.260378 | + | 0.184115i | ||||
\(709\) | −16.0000 | −0.600893 | −0.300446 | − | 0.953799i | \(-0.597136\pi\) | ||||
−0.300446 | + | 0.953799i | \(0.597136\pi\) | |||||||
\(710\) | 6.92820 | + | 8.48528i | 0.260011 | + | 0.318447i | ||||
\(711\) | 29.3939 | − | 10.3923i | 1.10236 | − | 0.389742i | ||||
\(712\) | − | 2.44949i | − | 0.0917985i | ||||||
\(713\) | 24.0000i | 0.898807i | ||||||||
\(714\) | 24.0000 | + | 16.9706i | 0.898177 | + | 0.635107i | ||||
\(715\) | 8.48528 | + | 10.3923i | 0.317332 | + | 0.388650i | ||||
\(716\) | −4.89898 | −0.183083 | ||||||||
\(717\) | 1.41421 | − | 2.00000i | 0.0528148 | − | 0.0746914i | ||||
\(718\) | 18.3848 | 0.686114 | ||||||||
\(719\) | 7.07107i | 0.263706i | 0.991269 | + | 0.131853i | \(0.0420927\pi\) | ||||
−0.991269 | + | 0.131853i | \(0.957907\pi\) | |||||||
\(720\) | 5.73205 | + | 3.48477i | 0.213621 | + | 0.129870i | ||||
\(721\) | − | 20.7846i | − | 0.774059i | ||||||
\(722\) | −13.8564 | + | 13.0000i | −0.515682 | + | 0.483810i | ||||
\(723\) | −13.8564 | + | 19.5959i | −0.515325 | + | 0.728780i | ||||
\(724\) | − | 13.8564i | − | 0.514969i | ||||||
\(725\) | −2.44949 | + | 12.0000i | −0.0909718 | + | 0.445669i | ||||
\(726\) | 9.00000 | − | 12.7279i | 0.334021 | − | 0.472377i | ||||
\(727\) | − | 31.8434i | − | 1.18101i | −0.807036 | − | 0.590503i | \(-0.798930\pi\) | ||
0.807036 | − | 0.590503i | \(-0.201070\pi\) | |||||||
\(728\) | 10.3923 | 0.385164 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | −25.4558 | + | 20.7846i | −0.942163 | + | 0.769273i | ||||
\(731\) | 50.9117i | 1.88304i | ||||||||
\(732\) | −11.3137 | − | 8.00000i | −0.418167 | − | 0.295689i | ||||
\(733\) | − | 4.89898i | − | 0.180948i | −0.995899 | − | 0.0904740i | \(-0.971162\pi\) | ||
0.995899 | − | 0.0904740i | \(-0.0288382\pi\) | |||||||
\(734\) | −31.8434 | −1.17536 | ||||||||
\(735\) | −3.86370 | + | 0.267949i | −0.142515 | + | 0.00988345i | ||||
\(736\) | − | 3.46410i | − | 0.127688i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 34.6410 | − | 12.2474i | 1.27515 | − | 0.450835i | ||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | −7.34847 | + | 6.00000i | −0.270135 | + | 0.220564i | ||||
\(741\) | 16.6515 | + | 27.3629i | 0.611709 | + | 1.00520i | ||||
\(742\) | − | 14.6969i | − | 0.539542i | ||||||
\(743\) | − | 30.0000i | − | 1.10059i | −0.834969 | − | 0.550297i | \(-0.814515\pi\) | ||
0.834969 | − | 0.550297i | \(-0.185485\pi\) | |||||||
\(744\) | 9.79796 | + | 6.92820i | 0.359211 | + | 0.254000i | ||||
\(745\) | 16.0000 | + | 19.5959i | 0.586195 | + | 0.717939i | ||||
\(746\) | 12.7279i | 0.466002i | ||||||||
\(747\) | −10.3923 | − | 29.3939i | −0.380235 | − | 1.07547i | ||||
\(748\) | − | 9.79796i | − | 0.358249i | ||||||
\(749\) | 44.0908 | 1.61104 | ||||||||
\(750\) | −19.1962 | − | 2.55103i | −0.700944 | − | 0.0931503i | ||||
\(751\) | − | 41.5692i | − | 1.51688i | −0.651741 | − | 0.758441i | \(-0.725961\pi\) | ||
0.651741 | − | 0.758441i | \(-0.274039\pi\) | |||||||
\(752\) | 3.46410 | 0.126323 | ||||||||
\(753\) | 1.41421 | − | 2.00000i | 0.0515368 | − | 0.0728841i | ||||
\(754\) | 10.3923i | 0.378465i | ||||||||
\(755\) | −19.5959 | − | 24.0000i | −0.713168 | − | 0.873449i | ||||
\(756\) | 12.2474 | + | 3.46410i | 0.445435 | + | 0.125988i | ||||
\(757\) | 9.79796i | 0.356113i | 0.984020 | + | 0.178056i | \(0.0569810\pi\) | ||||
−0.984020 | + | 0.178056i | \(0.943019\pi\) | |||||||
\(758\) | −20.7846 | −0.754931 | ||||||||
\(759\) | 4.89898 | − | 6.92820i | 0.177822 | − | 0.251478i | ||||
\(760\) | −2.65685 | − | 9.37769i | −0.0963742 | − | 0.340165i | ||||
\(761\) | − | 14.1421i | − | 0.512652i | −0.966590 | − | 0.256326i | \(-0.917488\pi\) | ||
0.966590 | − | 0.256326i | \(-0.0825121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.9706 | −0.614376 | ||||||||
\(764\) | 24.0416i | 0.869796i | ||||||||
\(765\) | −39.7128 | − | 24.1432i | −1.43582 | − | 0.872898i | ||||
\(766\) | 6.00000 | 0.216789 | ||||||||
\(767\) | −20.7846 | −0.750489 | ||||||||
\(768\) | −1.41421 | − | 1.00000i | −0.0510310 | − | 0.0360844i | ||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | −4.89898 | − | 6.00000i | −0.176547 | − | 0.216225i | ||||
\(771\) | 6.00000 | − | 8.48528i | 0.216085 | − | 0.305590i | ||||
\(772\) | −12.7279 | −0.458088 | ||||||||
\(773\) | 18.0000i | 0.647415i | 0.946157 | + | 0.323708i | \(0.104929\pi\) | ||||
−0.946157 | + | 0.323708i | \(0.895071\pi\) | |||||||
\(774\) | 7.34847 | + | 20.7846i | 0.264135 | + | 0.747087i | ||||
\(775\) | −33.9411 | − | 6.92820i | −1.21920 | − | 0.248868i | ||||
\(776\) | − | 12.7279i | − | 0.456906i | ||||||
\(777\) | −10.3923 | + | 14.6969i | −0.372822 | + | 0.527250i | ||||
\(778\) | 19.7990 | 0.709828 | ||||||||
\(779\) | −48.9898 | − | 21.2132i | −1.75524 | − | 0.760042i | ||||
\(780\) | −16.3923 | + | 1.13681i | −0.586939 | + | 0.0407044i | ||||
\(781\) | − | 6.92820i | − | 0.247911i | ||||||
\(782\) | 24.0000i | 0.858238i | ||||||||
\(783\) | −3.46410 | + | 12.2474i | −0.123797 | + | 0.437688i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 20.7846 | + | 25.4558i | 0.741835 | + | 0.908558i | ||||
\(786\) | 2.00000 | + | 1.41421i | 0.0713376 | + | 0.0504433i | ||||
\(787\) | −50.9117 | −1.81481 | −0.907403 | − | 0.420262i | \(-0.861938\pi\) | ||||
−0.907403 | + | 0.420262i | \(0.861938\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.89898 | − | 3.46410i | −0.174408 | − | 0.123325i | ||||
\(790\) | 18.0000 | − | 14.6969i | 0.640411 | − | 0.522894i | ||||
\(791\) | −44.0908 | −1.56769 | ||||||||
\(792\) | −1.41421 | − | 4.00000i | −0.0502519 | − | 0.142134i | ||||
\(793\) | 33.9411 | 1.20528 | ||||||||
\(794\) | 19.5959 | 0.695433 | ||||||||
\(795\) | 1.60770 | + | 23.1822i | 0.0570191 | + | 0.822189i | ||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | − | 6.00000i | − | 0.212531i | −0.994338 | − | 0.106265i | \(-0.966111\pi\) | ||
0.994338 | − | 0.106265i | \(-0.0338893\pi\) | |||||||
\(798\) | −9.61377 | − | 15.7980i | −0.340324 | − | 0.559242i | ||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 4.89898 | + | 1.00000i | 0.173205 | + | 0.0353553i | ||||
\(801\) | 2.44949 | + | 6.92820i | 0.0865485 | + | 0.244796i | ||||
\(802\) | − | 22.0454i | − | 0.778450i | ||||||
\(803\) | 20.7846 | 0.733473 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0000 | + | 14.6969i | 0.422944 | + | 0.517999i | ||||
\(806\) | −29.3939 | −1.03536 | ||||||||
\(807\) | 24.2487 | + | 17.1464i | 0.853595 | + | 0.603583i | ||||
\(808\) | 2.82843 | 0.0995037 | ||||||||
\(809\) | − | 45.2548i | − | 1.59108i | −0.605904 | − | 0.795538i | \(-0.707189\pi\) | ||
0.605904 | − | 0.795538i | \(-0.292811\pi\) | |||||||
\(810\) | −19.6975 | − | 4.12436i | −0.692098 | − | 0.144915i | ||||
\(811\) | − | 38.1051i | − | 1.33805i | −0.743239 | − | 0.669026i | \(-0.766712\pi\) | ||
0.743239 | − | 0.669026i | \(-0.233288\pi\) | |||||||
\(812\) | − | 6.00000i | − | 0.210559i | ||||||
\(813\) | −5.65685 | − | 4.00000i | −0.198395 | − | 0.140286i | ||||
\(814\) | 6.00000 | 0.210300 | ||||||||
\(815\) | −17.3205 | − | 21.2132i | −0.606711 | − | 0.743066i | ||||
\(816\) | 9.79796 | + | 6.92820i | 0.342997 | + | 0.242536i | ||||
\(817\) | 12.7279 | − | 29.3939i | 0.445294 | − | 1.02836i | ||||
\(818\) | −20.7846 | −0.726717 | ||||||||
\(819\) | −29.3939 | + | 10.3923i | −1.02711 | + | 0.363137i | ||||
\(820\) | 21.2132 | − | 17.3205i | 0.740797 | − | 0.604858i | ||||
\(821\) | 14.1421i | 0.493564i | 0.969071 | + | 0.246782i | \(0.0793731\pi\) | ||||
−0.969071 | + | 0.246782i | \(0.920627\pi\) | |||||||
\(822\) | 17.3205 | − | 24.4949i | 0.604122 | − | 0.854358i | ||||
\(823\) | − | 56.3383i | − | 1.96383i | −0.189326 | − | 0.981914i | \(-0.560630\pi\) | ||
0.189326 | − | 0.981914i | \(-0.439370\pi\) | |||||||
\(824\) | − | 8.48528i | − | 0.295599i | ||||||
\(825\) | 8.38375 | + | 8.92820i | 0.291885 | + | 0.310840i | ||||
\(826\) | 12.0000 | 0.417533 | ||||||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 3.46410 | + | 9.79796i | 0.120386 | + | 0.340503i | ||||
\(829\) | 27.7128i | 0.962506i | 0.876582 | + | 0.481253i | \(0.159818\pi\) | ||||
−0.876582 | + | 0.481253i | \(0.840182\pi\) | |||||||
\(830\) | −14.6969 | − | 18.0000i | −0.510138 | − | 0.624789i | ||||
\(831\) | −19.5959 | + | 27.7128i | −0.679775 | + | 0.961347i | ||||
\(832\) | 4.24264 | 0.147087 | ||||||||
\(833\) | −6.92820 | −0.240048 | ||||||||
\(834\) | 4.00000 | − | 5.65685i | 0.138509 | − | 0.195881i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.44949 | + | 5.65685i | −0.0847174 | + | 0.195646i | ||||
\(837\) | −34.6410 | − | 9.79796i | −1.19737 | − | 0.338667i | ||||
\(838\) | −9.89949 | −0.341972 | ||||||||
\(839\) | 53.8888 | 1.86045 | 0.930224 | − | 0.366993i | \(-0.119613\pi\) | ||||
0.930224 | + | 0.366993i | \(0.119613\pi\) | |||||||
\(840\) | 9.46410 | − | 0.656339i | 0.326543 | − | 0.0226458i | ||||
\(841\) | −23.0000 | −0.793103 | ||||||||
\(842\) | 13.8564 | 0.477523 | ||||||||
\(843\) | 10.3923 | + | 7.34847i | 0.357930 | + | 0.253095i | ||||
\(844\) | 3.46410i | 0.119239i | ||||||||
\(845\) | 8.66025 | − | 7.07107i | 0.297922 | − | 0.243252i | ||||
\(846\) | −9.79796 | + | 3.46410i | −0.336861 | + | 0.119098i | ||||
\(847\) | − | 22.0454i | − | 0.757489i | ||||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −12.2474 | + | 17.3205i | −0.420331 | + | 0.594438i | ||||
\(850\) | −33.9411 | − | 6.92820i | −1.16417 | − | 0.237635i | ||||
\(851\) | −14.6969 | −0.503805 | ||||||||
\(852\) | 6.92820 | + | 4.89898i | 0.237356 | + | 0.167836i | ||||
\(853\) | − | 39.1918i | − | 1.34190i | −0.741501 | − | 0.670951i | \(-0.765886\pi\) | ||
0.741501 | − | 0.670951i | \(-0.234114\pi\) | |||||||
\(854\) | −19.5959 | −0.670559 | ||||||||
\(855\) | 16.8924 | + | 23.8673i | 0.577708 | + | 0.816243i | ||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | − | 54.0000i | − | 1.84460i | −0.386469 | − | 0.922302i | \(-0.626305\pi\) | ||
0.386469 | − | 0.922302i | \(-0.373695\pi\) | |||||||
\(858\) | 8.48528 | + | 6.00000i | 0.289683 | + | 0.204837i | ||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 10.3923 | + | 12.7279i | 0.354375 | + | 0.434019i | ||||
\(861\) | 30.0000 | − | 42.4264i | 1.02240 | − | 1.44589i | ||||
\(862\) | 19.5959i | 0.667440i | ||||||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | 5.00000 | + | 1.41421i | 0.170103 | + | 0.0481125i | ||||
\(865\) | −8.48528 | − | 10.3923i | −0.288508 | − | 0.353349i | ||||
\(866\) | − | 38.1838i | − | 1.29754i | ||||||
\(867\) | −43.8406 | − | 31.0000i | −1.48891 | − | 1.05282i | ||||
\(868\) | 16.9706 | 0.576018 | ||||||||
\(869\) | −14.6969 | −0.498559 | ||||||||
\(870\) | 0.656339 | + | 9.46410i | 0.0222520 | + | 0.320863i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.92820 | −0.234619 | ||||||||
\(873\) | 12.7279 | + | 36.0000i | 0.430775 | + | 1.21842i | ||||
\(874\) | 6.00000 | − | 13.8564i | 0.202953 | − | 0.468700i | ||||
\(875\) | −24.2487 | + | 12.7279i | −0.819756 | + | 0.430282i | ||||
\(876\) | −14.6969 | + | 20.7846i | −0.496564 | + | 0.702247i | ||||
\(877\) | 4.24264 | 0.143264 | 0.0716319 | − | 0.997431i | \(-0.477179\pi\) | ||||
0.0716319 | + | 0.997431i | \(0.477179\pi\) | |||||||
\(878\) | 3.46410 | 0.116908 | ||||||||
\(879\) | 6.00000 | − | 8.48528i | 0.202375 | − | 0.286201i | ||||
\(880\) | −2.00000 | − | 2.44949i | −0.0674200 | − | 0.0825723i | ||||
\(881\) | − | 56.5685i | − | 1.90584i | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||
0.303218 | − | 0.952921i | \(-0.401939\pi\) | |||||||
\(882\) | −2.82843 | + | 1.00000i | −0.0952381 | + | 0.0336718i | ||||
\(883\) | 26.9444i | 0.906751i | 0.891320 | + | 0.453375i | \(0.149780\pi\) | ||||
−0.891320 | + | 0.453375i | \(0.850220\pi\) | |||||||
\(884\) | −29.3939 | −0.988623 | ||||||||
\(885\) | −18.9282 | + | 1.31268i | −0.636265 | + | 0.0441252i | ||||
\(886\) | − | 17.3205i | − | 0.581894i | ||||||
\(887\) | − | 6.00000i | − | 0.201460i | −0.994914 | − | 0.100730i | \(-0.967882\pi\) | ||
0.994914 | − | 0.100730i | \(-0.0321179\pi\) | |||||||
\(888\) | −4.24264 | + | 6.00000i | −0.142374 | + | 0.201347i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.46410 | + | 4.24264i | 0.116117 | + | 0.142214i | ||||
\(891\) | 8.00000 | + | 9.89949i | 0.268010 | + | 0.331646i | ||||
\(892\) | −25.4558 | −0.852325 | ||||||||
\(893\) | 13.8564 | + | 6.00000i | 0.463687 | + | 0.200782i | ||||
\(894\) | 16.0000 | + | 11.3137i | 0.535120 | + | 0.378387i | ||||
\(895\) | 8.48528 | − | 6.92820i | 0.283632 | − | 0.231584i | ||||
\(896\) | −2.44949 | −0.0818317 | ||||||||
\(897\) | −20.7846 | − | 14.6969i | −0.693978 | − | 0.490716i | ||||
\(898\) | − | 12.2474i | − | 0.408703i | ||||||
\(899\) | 16.9706i | 0.566000i | ||||||||
\(900\) | −14.8564 | + | 2.07055i | −0.495214 | + | 0.0690184i | ||||
\(901\) | 41.5692i | 1.38487i | ||||||||
\(902\) | −17.3205 | −0.576710 | ||||||||
\(903\) | 25.4558 | + | 18.0000i | 0.847117 | + | 0.599002i | ||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 19.5959 | + | 24.0000i | 0.651390 | + | 0.797787i | ||||
\(906\) | −19.5959 | − | 13.8564i | −0.651031 | − | 0.460348i | ||||
\(907\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | − | 12.0000i | − | 0.398234i | ||||||
\(909\) | −8.00000 | + | 2.82843i | −0.265343 | + | 0.0938130i | ||||
\(910\) | −18.0000 | + | 14.6969i | −0.596694 | + | 0.487199i | ||||
\(911\) | 48.9898 | 1.62310 | 0.811552 | − | 0.584280i | \(-0.198623\pi\) | ||||
0.811552 | + | 0.584280i | \(0.198623\pi\) | |||||||
\(912\) | −3.92480 | − | 6.44949i | −0.129963 | − | 0.213564i | ||||
\(913\) | 14.6969i | 0.486398i | ||||||||
\(914\) | 24.4949 | 0.810219 | ||||||||
\(915\) | 30.9096 | − | 2.14359i | 1.02184 | − | 0.0708650i | ||||
\(916\) | −28.0000 | −0.925146 | ||||||||
\(917\) | 3.46410 | 0.114395 | ||||||||
\(918\) | −34.6410 | − | 9.79796i | −1.14332 | − | 0.323381i | ||||
\(919\) | 56.0000 | 1.84727 | 0.923635 | − | 0.383274i | \(-0.125203\pi\) | ||||
0.923635 | + | 0.383274i | \(0.125203\pi\) | |||||||
\(920\) | 4.89898 | + | 6.00000i | 0.161515 | + | 0.197814i | ||||
\(921\) | 36.0000 | + | 25.4558i | 1.18624 | + | 0.838799i | ||||
\(922\) | −22.6274 | −0.745194 | ||||||||
\(923\) | −20.7846 | −0.684134 | ||||||||
\(924\) | −4.89898 | − | 3.46410i | −0.161165 | − | 0.113961i | ||||
\(925\) | 4.24264 | − | 20.7846i | 0.139497 | − | 0.683394i | ||||
\(926\) | −12.2474 | −0.402476 | ||||||||
\(927\) | 8.48528 | + | 24.0000i | 0.278693 | + | 0.788263i | ||||
\(928\) | − | 2.44949i | − | 0.0804084i | ||||||
\(929\) | − | 2.82843i | − | 0.0927977i | −0.998923 | − | 0.0463988i | \(-0.985225\pi\) | ||
0.998923 | − | 0.0463988i | \(-0.0147745\pi\) | |||||||
\(930\) | −26.7685 | + | 1.85641i | −0.877774 | + | 0.0608740i | ||||
\(931\) | 4.00000 | + | 1.73205i | 0.131095 | + | 0.0567657i | ||||
\(932\) | −10.3923 | −0.340411 | ||||||||
\(933\) | −26.8701 | + | 38.0000i | −0.879686 | + | 1.24406i | ||||
\(934\) | − | 24.2487i | − | 0.793442i | ||||||
\(935\) | 13.8564 | + | 16.9706i | 0.453153 | + | 0.554997i | ||||
\(936\) | −12.0000 | + | 4.24264i | −0.392232 | + | 0.138675i | ||||
\(937\) | − | 19.5959i | − | 0.640171i | −0.947389 | − | 0.320085i | \(-0.896288\pi\) | ||
0.947389 | − | 0.320085i | \(-0.103712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.89898 | + | 6.92820i | −0.159872 | + | 0.226093i | ||||
\(940\) | −6.00000 | + | 4.89898i | −0.195698 | + | 0.159787i | ||||
\(941\) | 51.4393 | 1.67687 | 0.838436 | − | 0.544999i | \(-0.183470\pi\) | ||||
0.838436 | + | 0.544999i | \(0.183470\pi\) | |||||||
\(942\) | 20.7846 | + | 14.6969i | 0.677199 | + | 0.478852i | ||||
\(943\) | 42.4264 | 1.38159 | ||||||||
\(944\) | 4.89898 | 0.159448 | ||||||||
\(945\) | −26.1122 | + | 11.3205i | −0.849429 | + | 0.368256i | ||||
\(946\) | − | 10.3923i | − | 0.337883i | ||||||
\(947\) | −3.46410 | −0.112568 | −0.0562841 | − | 0.998415i | \(-0.517925\pi\) | ||||
−0.0562841 | + | 0.998415i | \(0.517925\pi\) | |||||||
\(948\) | 10.3923 | − | 14.6969i | 0.337526 | − | 0.477334i | ||||
\(949\) | − | 62.3538i | − | 2.02409i | ||||||
\(950\) | 17.8639 | + | 12.4853i | 0.579580 | + | 0.405076i | ||||
\(951\) | 18.0000 | − | 25.4558i | 0.583690 | − | 0.825462i | ||||
\(952\) | 16.9706 | 0.550019 | ||||||||
\(953\) | 54.0000i | 1.74923i | 0.484817 | + | 0.874616i | \(0.338886\pi\) | ||||
−0.484817 | + | 0.874616i | \(0.661114\pi\) | |||||||
\(954\) | 6.00000 | + | 16.9706i | 0.194257 | + | 0.549442i | ||||
\(955\) | −34.0000 | − | 41.6413i | −1.10021 | − | 1.34748i | ||||
\(956\) | − | 1.41421i | − | 0.0457389i | ||||||
\(957\) | 3.46410 | − | 4.89898i | 0.111979 | − | 0.158362i | ||||
\(958\) | 9.89949 | 0.319838 | ||||||||
\(959\) | − | 42.4264i | − | 1.37002i | ||||||
\(960\) | 3.86370 | − | 0.267949i | 0.124700 | − | 0.00864802i | ||||
\(961\) | −17.0000 | −0.548387 | ||||||||
\(962\) | − | 18.0000i | − | 0.580343i | ||||||
\(963\) | −50.9117 | + | 18.0000i | −1.64061 | + | 0.580042i | ||||
\(964\) | 13.8564i | 0.446285i | ||||||||
\(965\) | 22.0454 | − | 18.0000i | 0.709667 | − | 0.579441i | ||||
\(966\) | 12.0000 | + | 8.48528i | 0.386094 | + | 0.273009i | ||||
\(967\) | − | 2.44949i | − | 0.0787703i | −0.999224 | − | 0.0393851i | \(-0.987460\pi\) | ||
0.999224 | − | 0.0393851i | \(-0.0125399\pi\) | |||||||
\(968\) | − | 9.00000i | − | 0.289271i | ||||||
\(969\) | 27.1918 | + | 44.6834i | 0.873528 | + | 1.43544i | ||||
\(970\) | 18.0000 | + | 22.0454i | 0.577945 | + | 0.707835i | ||||
\(971\) | 4.89898 | 0.157216 | 0.0786079 | − | 0.996906i | \(-0.474952\pi\) | ||||
0.0786079 | + | 0.996906i | \(0.474952\pi\) | |||||||
\(972\) | −15.5563 | + | 1.00000i | −0.498970 | + | 0.0320750i | ||||
\(973\) | − | 9.79796i | − | 0.314108i | ||||||
\(974\) | − | 33.9411i | − | 1.08754i | ||||||
\(975\) | 26.7846 | − | 25.1512i | 0.857794 | − | 0.805484i | ||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 30.0000i | 0.959785i | 0.877327 | + | 0.479893i | \(0.159324\pi\) | ||||
−0.877327 | + | 0.479893i | \(0.840676\pi\) | |||||||
\(978\) | −17.3205 | − | 12.2474i | −0.553849 | − | 0.391630i | ||||
\(979\) | − | 3.46410i | − | 0.110713i | ||||||
\(980\) | −1.73205 | + | 1.41421i | −0.0553283 | + | 0.0451754i | ||||
\(981\) | 19.5959 | − | 6.92820i | 0.625650 | − | 0.221201i | ||||
\(982\) | 7.07107 | 0.225647 | ||||||||
\(983\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(984\) | 12.2474 | − | 17.3205i | 0.390434 | − | 0.552158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16.9706i | 0.540453i | ||||||||
\(987\) | −8.48528 | + | 12.0000i | −0.270089 | + | 0.381964i | ||||
\(988\) | 16.9706 | + | 7.34847i | 0.539906 | + | 0.233786i | ||||
\(989\) | 25.4558i | 0.809449i | ||||||||
\(990\) | 8.10634 | + | 4.92820i | 0.257637 | + | 0.156629i | ||||
\(991\) | 38.1051i | 1.21045i | 0.796055 | + | 0.605224i | \(0.206917\pi\) | ||||
−0.796055 | + | 0.605224i | \(0.793083\pi\) | |||||||
\(992\) | 6.92820 | 0.219971 | ||||||||
\(993\) | 6.92820 | − | 9.79796i | 0.219860 | − | 0.310929i | ||||
\(994\) | 12.0000 | 0.380617 | ||||||||
\(995\) | −27.7128 | + | 22.6274i | −0.878555 | + | 0.717337i | ||||
\(996\) | −14.6969 | − | 10.3923i | −0.465690 | − | 0.329293i | ||||
\(997\) | − | 4.89898i | − | 0.155152i | −0.996986 | − | 0.0775761i | \(-0.975282\pi\) | ||
0.996986 | − | 0.0775761i | \(-0.0247181\pi\) | |||||||
\(998\) | − | 20.0000i | − | 0.633089i | ||||||
\(999\) | 6.00000 | − | 21.2132i | 0.189832 | − | 0.671156i |
(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 | 570.2.c.e.569.6 | yes | 8 | |
3.2 | odd | 2 | inner | 570.2.c.e.569.1 | ✓ | 8 | |
5.4 | even | 2 | inner | 570.2.c.e.569.3 | yes | 8 | |
15.14 | odd | 2 | inner | 570.2.c.e.569.8 | yes | 8 | |
19.18 | odd | 2 | inner | 570.2.c.e.569.4 | yes | 8 | |
57.56 | even | 2 | inner | 570.2.c.e.569.7 | yes | 8 | |
95.94 | odd | 2 | inner | 570.2.c.e.569.5 | yes | 8 | |
285.284 | even | 2 | inner | 570.2.c.e.569.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.c.e.569.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
570.2.c.e.569.2 | yes | 8 | 285.284 | even | 2 | inner | |
570.2.c.e.569.3 | yes | 8 | 5.4 | even | 2 | inner | |
570.2.c.e.569.4 | yes | 8 | 19.18 | odd | 2 | inner | |
570.2.c.e.569.5 | yes | 8 | 95.94 | odd | 2 | inner | |
570.2.c.e.569.6 | yes | 8 | 1.1 | even | 1 | trivial | |
570.2.c.e.569.7 | yes | 8 | 57.56 | even | 2 | inner | |
570.2.c.e.569.8 | yes | 8 | 15.14 | odd | 2 | inner |