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 | 569.5 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.569 |
Dual form | 570.2.c.e.569.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | \(0.153195\pi\) | ||||
−0.886405 | + | 0.462910i | \(0.846805\pi\) | |||||||
\(8\) | − | 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 | ||||||||
\(15\) | 1.03528 | + | 3.73205i | 0.267307 | + | 0.963611i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.92820 | 1.68034 | 0.840168 | − | 0.542326i | \(-0.182456\pi\) | ||||
0.840168 | + | 0.542326i | \(0.182456\pi\) | |||||||
\(18\) | −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 | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | −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 | \(-0.426968\pi\) | ||||
0.227429 | + | 0.973795i | \(0.426968\pi\) | |||||||
\(30\) | −3.73205 | + | 1.03528i | −0.681376 | + | 0.189015i | ||||
\(31\) | 6.92820i | 1.24434i | 0.782881 | + | 0.622171i | \(0.213749\pi\) | ||||
−0.782881 | + | 0.622171i | \(0.786251\pi\) | |||||||
\(32\) | 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 | \(-0.0943788\pi\) | ||||
0.956365 | + | 0.292174i | \(0.0943788\pi\) | |||||||
\(42\) | 3.46410 | + | 2.44949i | 0.534522 | + | 0.377964i | ||||
\(43\) | 7.34847i | 1.12063i | 0.828279 | + | 0.560316i | \(0.189320\pi\) | ||||
−0.828279 | + | 0.560316i | \(0.810680\pi\) | |||||||
\(44\) | 1.41421i | 0.213201i | ||||||||
\(45\) | 2.26795 | − | 6.31319i | 0.338086 | − | 0.941115i | ||||
\(46\) | 3.46410i | 0.510754i | ||||||||
\(47\) | −3.46410 | −0.505291 | −0.252646 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252646 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(48\) | −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 | ||||||||
\(57\) | −7.38891 | − | 1.55051i | −0.978684 | − | 0.205370i | ||||
\(58\) | 2.44949i | 0.321634i | ||||||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | −1.03528 | − | 3.73205i | −0.133654 | − | 0.481806i | ||||
\(61\) | −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 | \(-0.593888\pi\) | ||||
−0.290701 | + | 0.956814i | \(0.593888\pi\) | |||||||
\(72\) | 2.82843 | − | 1.00000i | 0.333333 | − | 0.117851i | ||||
\(73\) | − | 14.6969i | − | 1.72015i | −0.510171 | − | 0.860073i | \(-0.670418\pi\) | ||
0.510171 | − | 0.860073i | \(-0.329582\pi\) | |||||||
\(74\) | 4.24264i | 0.493197i | ||||||||
\(75\) | 3.48477 | − | 7.92820i | 0.402386 | − | 0.915470i | ||||
\(76\) | −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 | \(0.198754\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | −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 | \(-0.306807\pi\) | ||||
0.570352 | + | 0.821401i | \(0.306807\pi\) | |||||||
\(84\) | −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 | \(-0.541441\pi\) | ||||
−0.129823 | + | 0.991537i | \(0.541441\pi\) | |||||||
\(90\) | 6.31319 | + | 2.26795i | 0.665469 | + | 0.239063i | ||||
\(91\) | − | 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 | ||||||||
\(105\) | −9.14162 | + | 2.53590i | −0.892131 | + | 0.247478i | ||||
\(106\) | 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 | \(0.107656\pi\) | ||||
−0.943349 | + | 0.331801i | \(0.892344\pi\) | |||||||
\(110\) | −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 | \(-0.321383\pi\) | |||||||
\(114\) | 1.55051 | − | 7.38891i | 0.145219 | − | 0.692034i | ||||
\(115\) | −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 | ||||||||
\(120\) | 3.73205 | − | 1.03528i | 0.340688 | − | 0.0945074i | ||||
\(121\) | 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 | ||||||||
\(135\) | −9.52056 | + | 6.66025i | −0.819399 | + | 0.573223i | ||||
\(136\) | − | 6.92820i | − | 0.594089i | ||||||
\(137\) | −17.3205 | −1.47979 | −0.739895 | − | 0.672722i | \(-0.765125\pi\) | ||||
−0.739895 | + | 0.672722i | \(0.765125\pi\) | |||||||
\(138\) | 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 | \(0.846619\pi\) | |||||||
\(150\) | 7.92820 | + | 3.48477i | 0.647335 | + | 0.284530i | ||||
\(151\) | 13.8564i | 1.12762i | 0.825905 | + | 0.563809i | \(0.190665\pi\) | ||||
−0.825905 | + | 0.563809i | \(0.809335\pi\) | |||||||
\(152\) | −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 | \(-0.800517\pi\) | ||
0.809970 | − | 0.586472i | \(-0.199483\pi\) | |||||||
\(158\) | −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 | \(0.159235\pi\) | ||||
−0.877461 | + | 0.479647i | \(0.840765\pi\) | |||||||
\(164\) | −12.2474 | −0.956365 | ||||||||
\(165\) | 5.27792 | − | 1.46410i | 0.410885 | − | 0.113980i | ||||
\(166\) | 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 | ||||
\(171\) | 8.89898 | + | 9.58166i | 0.680522 | + | 0.732728i | ||||
\(172\) | − | 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 | \(-0.558608\pi\) | ||||
−0.183083 | + | 0.983097i | \(0.558608\pi\) | |||||||
\(180\) | −2.26795 | + | 6.31319i | −0.169043 | + | 0.470558i | ||||
\(181\) | − | 13.8564i | − | 1.02994i | −0.857209 | − | 0.514969i | \(-0.827803\pi\) | ||
0.857209 | − | 0.514969i | \(-0.172197\pi\) | |||||||
\(182\) | 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 | ||||||||
\(195\) | −4.39230 | − | 15.8338i | −0.314539 | − | 1.13388i | ||||
\(196\) | −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 | ||||
\(210\) | −2.53590 | − | 9.14162i | −0.174994 | − | 0.630832i | ||||
\(211\) | 3.46410i | 0.238479i | 0.992866 | + | 0.119239i | \(0.0380456\pi\) | ||||
−0.992866 | + | 0.119239i | \(0.961954\pi\) | |||||||
\(212\) | 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 | ||||||||
\(225\) | −12.8564 | + | 7.72741i | −0.857094 | + | 0.515160i | ||||
\(226\) | 18.0000 | 1.19734 | ||||||||
\(227\) | 12.0000i | 0.796468i | 0.917284 | + | 0.398234i | \(0.130377\pi\) | ||||
−0.917284 | + | 0.398234i | \(0.869623\pi\) | |||||||
\(228\) | 7.38891 | + | 1.55051i | 0.489342 | + | 0.102685i | ||||
\(229\) | 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 | \(-0.610566\pi\) | ||||
−0.340411 | + | 0.940277i | \(0.610566\pi\) | |||||||
\(234\) | 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 | \(0.985436\pi\) | |||||||
\(240\) | 1.03528 | + | 3.73205i | 0.0668268 | + | 0.240903i | ||||
\(241\) | 13.8564i | 0.892570i | 0.894891 | + | 0.446285i | \(0.147253\pi\) | ||||
−0.894891 | + | 0.446285i | \(0.852747\pi\) | |||||||
\(242\) | 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 | ||||||||
\(255\) | 7.17260 | + | 25.8564i | 0.449166 | + | 1.61919i | ||||
\(256\) | 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 | \(-0.534061\pi\) | ||||
−0.106803 | + | 0.994280i | \(0.534061\pi\) | |||||||
\(264\) | 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 | \(-0.324918\pi\) | ||||
0.522718 | + | 0.852506i | \(0.324918\pi\) | |||||||
\(270\) | −6.66025 | − | 9.52056i | −0.405330 | − | 0.579403i | ||||
\(271\) | 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 | \(0.200361\pi\) | ||||
−0.808350 | + | 0.588702i | \(0.799639\pi\) | |||||||
\(278\) | 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 | \(-0.429660\pi\) | ||||
0.219186 | + | 0.975683i | \(0.429660\pi\) | |||||||
\(282\) | −3.46410 | + | 4.89898i | −0.206284 | + | 0.291730i | ||||
\(283\) | 12.2474i | 0.728035i | 0.931392 | + | 0.364018i | \(0.118595\pi\) | ||||
−0.931392 | + | 0.364018i | \(0.881405\pi\) | |||||||
\(284\) | 4.89898 | 0.290701 | ||||||||
\(285\) | 10.6052 | + | 13.1351i | 0.628198 | + | 0.778053i | ||||
\(286\) | −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 | ||||||||
\(300\) | −3.48477 | + | 7.92820i | −0.201193 | + | 0.457735i | ||||
\(301\) | −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 | \(0.0442131\pi\) | ||||
−0.990369 | + | 0.138453i | \(0.955787\pi\) | |||||||
\(314\) | 14.6969 | 0.829396 | ||||||||
\(315\) | 15.4641 | + | 5.55532i | 0.871303 | + | 0.313007i | ||||
\(316\) | − | 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 | ||||||
\(330\) | 1.46410 | + | 5.27792i | 0.0805961 | + | 0.290540i | ||||
\(331\) | − | 6.92820i | − | 0.380808i | −0.981706 | − | 0.190404i | \(-0.939020\pi\) | ||
0.981706 | − | 0.190404i | \(-0.0609799\pi\) | |||||||
\(332\) | −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 | ||||||||
\(342\) | −9.58166 | + | 8.89898i | −0.518117 | + | 0.481202i | ||||
\(343\) | 19.5959i | 1.05808i | ||||||||
\(344\) | 7.34847 | 0.396203 | ||||||||
\(345\) | 3.58630 | + | 12.9282i | 0.193080 | + | 0.696031i | ||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | −24.2487 | −1.30174 | −0.650870 | − | 0.759190i | \(-0.725596\pi\) | ||||
−0.650870 | + | 0.759190i | \(0.725596\pi\) | |||||||
\(348\) | 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 | \(-0.347513\pi\) | ||||
0.460939 | + | 0.887432i | \(0.347513\pi\) | |||||||
\(354\) | −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 | \(-0.161237\pi\) | |||||||
\(360\) | −6.31319 | − | 2.26795i | −0.332734 | − | 0.119531i | ||||
\(361\) | 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 | \(-0.687709\pi\) | ||
0.556115 | − | 0.831105i | \(-0.312291\pi\) | |||||||
\(368\) | 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 | ||||||||
\(375\) | −17.2480 | + | 8.80385i | −0.890681 | + | 0.454629i | ||||
\(376\) | 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 | \(-0.820757\pi\) | ||
0.845600 | − | 0.533817i | \(-0.179243\pi\) | |||||||
\(380\) | 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 | \(-0.167374\pi\) | |||||||
\(390\) | 15.8338 | − | 4.39230i | 0.801773 | − | 0.222413i | ||||
\(391\) | 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 | \(0.163641\pi\) | ||||
−0.870739 | + | 0.491745i | \(0.836359\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 3.79796 | − | 18.0990i | 0.190136 | − | 0.906086i | ||||
\(400\) | 1.00000 | + | 4.89898i | 0.0500000 | + | 0.244949i | ||||
\(401\) | 22.0454 | 1.10090 | 0.550448 | − | 0.834870i | \(-0.314457\pi\) | ||||
0.550448 | + | 0.834870i | \(0.314457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 29.3939i | − | 1.46421i | ||||||
\(404\) | − | 2.82843i | − | 0.140720i | ||||||
\(405\) | 20.1244 | + | 0.101536i | 0.999987 | + | 0.00504536i | ||||
\(406\) | −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 | \(-0.828213\pi\) | ||
0.857870 | − | 0.513866i | \(-0.171787\pi\) | |||||||
\(410\) | 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 | \(0.922259\pi\) | |||||||
\(420\) | 9.14162 | − | 2.53590i | 0.446065 | − | 0.123739i | ||||
\(421\) | 13.8564i | 0.675320i | 0.941268 | + | 0.337660i | \(0.109635\pi\) | ||||
−0.941268 | + | 0.337660i | \(0.890365\pi\) | |||||||
\(422\) | −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 | \(-0.656450\pi\) | ||||
−0.471951 | + | 0.881625i | \(0.656450\pi\) | |||||||
\(432\) | 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 | ||||||
\(435\) | 2.53590 | + | 9.14162i | 0.121587 | + | 0.438307i | ||||
\(436\) | − | 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 | \(0.0263436\pi\) | ||||
−0.996577 | + | 0.0826663i | \(0.973656\pi\) | |||||||
\(440\) | 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 | \(-0.365019\pi\) | ||||
0.411461 | + | 0.911427i | \(0.365019\pi\) | |||||||
\(444\) | 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 | \(-0.406678\pi\) | ||||
0.288996 | + | 0.957330i | \(0.406678\pi\) | |||||||
\(450\) | −7.72741 | − | 12.8564i | −0.364273 | − | 0.606057i | ||||
\(451\) | − | 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 | ||||
\(456\) | −1.55051 | + | 7.38891i | −0.0726093 | + | 0.346017i | ||||
\(457\) | 24.4949i | 1.14582i | 0.819617 | + | 0.572911i | \(0.194186\pi\) | ||||
−0.819617 | + | 0.572911i | \(0.805814\pi\) | |||||||
\(458\) | 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 | \(-0.908141\pi\) | ||
0.958648 | − | 0.284594i | \(-0.0918587\pi\) | |||||||
\(464\) | 2.44949 | 0.113715 | ||||||||
\(465\) | −25.8564 | + | 7.17260i | −1.19906 | + | 0.332622i | ||||
\(466\) | − | 10.3923i | − | 0.481414i | ||||||
\(467\) | 24.2487 | 1.12210 | 0.561048 | − | 0.827783i | \(-0.310398\pi\) | ||||
0.561048 | + | 0.827783i | \(0.310398\pi\) | |||||||
\(468\) | 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 | \(-0.0726171\pi\) | |||||||
\(480\) | −3.73205 | + | 1.03528i | −0.170344 | + | 0.0472537i | ||||
\(481\) | −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 | ||||
\(495\) | −8.92820 | − | 3.20736i | −0.401293 | − | 0.144160i | ||||
\(496\) | 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 | \(-0.626192\pi\) | ||||
−0.386142 | + | 0.922440i | \(0.626192\pi\) | |||||||
\(504\) | 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 | \(-0.337518\pi\) | ||||
0.488573 | + | 0.872523i | \(0.337518\pi\) | |||||||
\(510\) | −25.8564 | + | 7.17260i | −1.14494 | + | 0.317608i | ||||
\(511\) | 36.0000 | 1.59255 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −3.00340 | − | 22.4495i | −0.132603 | − | 0.991169i | ||||
\(514\) | −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 | \(-0.660421\pi\) | ||||
−0.482913 | + | 0.875668i | \(0.660421\pi\) | |||||||
\(522\) | −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 | ||||||
\(525\) | 19.4201 | + | 8.53590i | 0.847561 | + | 0.372537i | ||||
\(526\) | − | 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 | ||||||
\(540\) | 9.52056 | − | 6.66025i | 0.409700 | − | 0.286612i | ||||
\(541\) | −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 | ||||||||
\(555\) | 4.39230 | + | 15.8338i | 0.186443 | + | 0.672105i | ||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | −10.3923 | −0.440336 | −0.220168 | − | 0.975462i | \(-0.570661\pi\) | ||||
−0.220168 | + | 0.975462i | \(0.570661\pi\) | |||||||
\(558\) | −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 | \(-0.929446\pi\) | ||||
−0.975536 | + | 0.219842i | \(0.929446\pi\) | |||||||
\(570\) | −13.1351 | + | 10.6052i | −0.550167 | + | 0.444203i | ||||
\(571\) | 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 | \(-0.829694\pi\) | ||
0.860253 | − | 0.509868i | \(-0.170306\pi\) | |||||||
\(578\) | 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 | ||||||||
\(585\) | −9.62209 | + | 26.7846i | −0.397825 | + | 1.10741i | ||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −3.46410 | −0.142979 | −0.0714894 | − | 0.997441i | \(-0.522775\pi\) | ||||
−0.0714894 | + | 0.997441i | \(0.522775\pi\) | |||||||
\(588\) | 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 | \(-0.522659\pi\) | ||||
−0.0711268 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(594\) | 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 | \(-0.531911\pi\) | ||||
−0.100083 | + | 0.994979i | \(0.531911\pi\) | |||||||
\(600\) | −7.92820 | − | 3.48477i | −0.323668 | − | 0.142265i | ||||
\(601\) | − | 6.92820i | − | 0.282607i | −0.989966 | − | 0.141304i | \(-0.954871\pi\) | ||
0.989966 | − | 0.141304i | \(-0.0451294\pi\) | |||||||
\(602\) | − | 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 | \(-0.650421\pi\) | ||
0.455168 | − | 0.890406i | \(-0.349579\pi\) | |||||||
\(614\) | − | 25.4558i | − | 1.02731i | ||||||
\(615\) | 12.6795 | + | 45.7081i | 0.511286 | + | 1.84313i | ||||
\(616\) | − | 3.46410i | − | 0.139573i | ||||||
\(617\) | −20.7846 | −0.836757 | −0.418378 | − | 0.908273i | \(-0.637401\pi\) | ||||
−0.418378 | + | 0.908273i | \(0.637401\pi\) | |||||||
\(618\) | 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 | ||||||||
\(627\) | −2.19275 | + | 10.4495i | −0.0875701 | + | 0.417312i | ||||
\(628\) | 14.6969i | 0.586472i | ||||||||
\(629\) | 29.3939 | 1.17201 | ||||||||
\(630\) | −5.55532 | + | 15.4641i | −0.221329 | + | 0.616105i | ||||
\(631\) | −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 | \(-0.577762\pi\) | ||||
−0.241873 | + | 0.970308i | \(0.577762\pi\) | |||||||
\(642\) | 25.4558 | + | 18.0000i | 1.00466 | + | 0.710403i | ||||
\(643\) | 7.34847i | 0.289795i | 0.989447 | + | 0.144898i | \(0.0462853\pi\) | ||||
−0.989447 | + | 0.144898i | \(0.953715\pi\) | |||||||
\(644\) | − | 8.48528i | − | 0.334367i | ||||||
\(645\) | −27.4249 | + | 7.60770i | −1.07985 | + | 0.299553i | ||||
\(646\) | 12.0000 | + | 27.7128i | 0.472134 | + | 1.09035i | ||||
\(647\) | −10.3923 | −0.408564 | −0.204282 | − | 0.978912i | \(-0.565486\pi\) | ||||
−0.204282 | + | 0.978912i | \(0.565486\pi\) | |||||||
\(648\) | 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 | \(-0.171231\pi\) | ||||
0.858767 | + | 0.512366i | \(0.171231\pi\) | |||||||
\(660\) | −5.27792 | + | 1.46410i | −0.205443 | + | 0.0569901i | ||||
\(661\) | − | 48.4974i | − | 1.88633i | −0.332323 | − | 0.943166i | \(-0.607832\pi\) | ||
0.332323 | − | 0.943166i | \(-0.392168\pi\) | |||||||
\(662\) | 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 | ||||||||
\(675\) | 25.9091 | + | 1.92820i | 0.997242 | + | 0.0742166i | ||||
\(676\) | −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 | \(0.888091\pi\) | |||||||
\(684\) | −8.89898 | − | 9.58166i | −0.340261 | − | 0.366364i | ||||
\(685\) | 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 | ||||||||
\(690\) | −12.9282 | + | 3.58630i | −0.492168 | + | 0.136528i | ||||
\(691\) | −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 | ||||||||
\(705\) | −3.58630 | − | 12.9282i | −0.135068 | − | 0.486904i | ||||
\(706\) | 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 | \(0.957907\pi\) | |||||||
\(720\) | 2.26795 | − | 6.31319i | 0.0845215 | − | 0.235279i | ||||
\(721\) | 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 | \(0.201070\pi\) | ||||
−0.807036 | + | 0.590503i | \(0.798930\pi\) | |||||||
\(728\) | −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 | \(0.0288382\pi\) | ||||
−0.995899 | + | 0.0904740i | \(0.971162\pi\) | |||||||
\(734\) | 31.8434 | 1.17536 | ||||||||
\(735\) | 1.03528 | + | 3.73205i | 0.0381867 | + | 0.137659i | ||||
\(736\) | 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 | ||||
\(741\) | 31.3485 | + | 6.57826i | 1.15161 | + | 0.241658i | ||||
\(742\) | 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 | ||||||||
\(750\) | −8.80385 | − | 17.2480i | −0.321471 | − | 0.629807i | ||||
\(751\) | 41.5692i | 1.51688i | 0.651741 | + | 0.758441i | \(0.274039\pi\) | ||||
−0.651741 | + | 0.758441i | \(0.725961\pi\) | |||||||
\(752\) | −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 | \(-0.943019\pi\) | ||
0.984020 | − | 0.178056i | \(-0.0569810\pi\) | |||||||
\(758\) | 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 | ||||||||
\(765\) | 15.7128 | − | 43.7391i | 0.568098 | − | 1.58139i | ||||
\(766\) | 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 | ||||
\(780\) | 4.39230 | + | 15.8338i | 0.157270 | + | 0.566939i | ||||
\(781\) | 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 | ||||||||
\(795\) | 22.3923 | − | 6.21166i | 0.794173 | − | 0.220305i | ||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | − | 6.00000i | − | 0.212531i | −0.994338 | − | 0.106265i | \(-0.966111\pi\) | ||
0.994338 | − | 0.106265i | \(-0.0338893\pi\) | |||||||
\(798\) | 18.0990 | + | 3.79796i | 0.640699 | + | 0.134446i | ||||
\(799\) | −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 | \(-0.292811\pi\) | |||||||
\(810\) | −0.101536 | + | 20.1244i | −0.00356761 | + | 0.707098i | ||||
\(811\) | 38.1051i | 1.33805i | 0.743239 | + | 0.669026i | \(0.233288\pi\) | ||||
−0.743239 | + | 0.669026i | \(0.766712\pi\) | |||||||
\(812\) | − | 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 | \(0.439370\pi\) | ||||
−0.189326 | + | 0.981914i | \(0.560630\pi\) | |||||||
\(824\) | − | 8.48528i | − | 0.295599i | ||||||
\(825\) | −11.2122 | − | 4.92820i | −0.390358 | − | 0.171578i | ||||
\(826\) | 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 | \(-0.840182\pi\) | ||
0.876582 | − | 0.481253i | \(-0.159818\pi\) | |||||||
\(830\) | 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 | \(-0.880387\pi\) | ||||
−0.930224 | + | 0.366993i | \(0.880387\pi\) | |||||||
\(840\) | 2.53590 | + | 9.14162i | 0.0874968 | + | 0.315416i | ||||
\(841\) | −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 | \(0.234114\pi\) | ||||
−0.741501 | + | 0.670951i | \(0.765886\pi\) | |||||||
\(854\) | 19.5959 | 0.670559 | ||||||||
\(855\) | −1.86297 | − | 29.1810i | −0.0637124 | − | 0.997968i | ||||
\(856\) | 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 | ||||||||
\(870\) | −9.14162 | + | 2.53590i | −0.309930 | + | 0.0859750i | ||||
\(871\) | 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 | \(-0.850220\pi\) | ||
0.891320 | − | 0.453375i | \(-0.149780\pi\) | |||||||
\(884\) | 29.3939 | 0.988623 | ||||||||
\(885\) | −5.07180 | − | 18.2832i | −0.170487 | − | 0.614584i | ||||
\(886\) | 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 | ||||||||
\(900\) | 12.8564 | − | 7.72741i | 0.428547 | − | 0.257580i | ||||
\(901\) | − | 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 | \(-0.801377\pi\) | ||||
−0.811552 | + | 0.584280i | \(0.801377\pi\) | |||||||
\(912\) | −7.38891 | − | 1.55051i | −0.244671 | − | 0.0513425i | ||||
\(913\) | − | 14.6969i | − | 0.486398i | ||||||
\(914\) | −24.4949 | −0.810219 | ||||||||
\(915\) | −8.28221 | − | 29.8564i | −0.273801 | − | 0.987022i | ||||
\(916\) | −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 | \(-0.0147745\pi\) | |||||||
\(930\) | −7.17260 | − | 25.8564i | −0.235199 | − | 0.847865i | ||||
\(931\) | 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 | \(0.103712\pi\) | ||||
−0.947389 | + | 0.320085i | \(0.896288\pi\) | |||||||
\(938\) | 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 | \(-0.816530\pi\) | ||||
−0.838436 | + | 0.544999i | \(0.816530\pi\) | |||||||
\(942\) | −20.7846 | − | 14.6969i | −0.677199 | − | 0.478852i | ||||
\(943\) | 42.4264 | 1.38159 | ||||||||
\(944\) | −4.89898 | −0.159448 | ||||||||
\(945\) | −16.3142 | − | 23.3205i | −0.530702 | − | 0.758616i | ||||
\(946\) | 10.3923i | 0.337883i | ||||||||
\(947\) | 3.46410 | 0.112568 | 0.0562841 | − | 0.998415i | \(-0.482075\pi\) | ||||
0.0562841 | + | 0.998415i | \(0.482075\pi\) | |||||||
\(948\) | −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 | ||||||
\(960\) | −1.03528 | − | 3.73205i | −0.0334134 | − | 0.120451i | ||||
\(961\) | −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 | \(0.0125399\pi\) | ||||
−0.999224 | + | 0.0393851i | \(0.987460\pi\) | |||||||
\(968\) | − | 9.00000i | − | 0.289271i | ||||||
\(969\) | −51.1918 | − | 10.7423i | −1.64452 | − | 0.345091i | ||||
\(970\) | 18.0000 | − | 22.0454i | 0.577945 | − | 0.707835i | ||||
\(971\) | −4.89898 | −0.157216 | −0.0786079 | − | 0.996906i | \(-0.525048\pi\) | ||||
−0.0786079 | + | 0.996906i | \(0.525048\pi\) | |||||||
\(972\) | −15.5563 | + | 1.00000i | −0.498970 | + | 0.0320750i | ||||
\(973\) | 9.79796i | 0.314108i | ||||||||
\(974\) | − | 33.9411i | − | 1.08754i | ||||||
\(975\) | −14.7846 | + | 33.6365i | −0.473486 | + | 1.07723i | ||||
\(976\) | −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 | ||||||||
\(990\) | 3.20736 | − | 8.92820i | 0.101937 | − | 0.283757i | ||||
\(991\) | − | 38.1051i | − | 1.21045i | −0.796055 | − | 0.605224i | \(-0.793083\pi\) | ||
0.796055 | − | 0.605224i | \(-0.206917\pi\) | |||||||
\(992\) | −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 | \(0.0247181\pi\) | ||||
−0.996986 | + | 0.0775761i | \(0.975282\pi\) | |||||||
\(998\) | − | 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.569.5 | yes | 8 | |
3.2 | odd | 2 | inner | 570.2.c.e.569.2 | yes | 8 | |
5.4 | even | 2 | inner | 570.2.c.e.569.4 | yes | 8 | |
15.14 | odd | 2 | inner | 570.2.c.e.569.7 | yes | 8 | |
19.18 | odd | 2 | inner | 570.2.c.e.569.3 | yes | 8 | |
57.56 | even | 2 | inner | 570.2.c.e.569.8 | yes | 8 | |
95.94 | odd | 2 | inner | 570.2.c.e.569.6 | yes | 8 | |
285.284 | even | 2 | inner | 570.2.c.e.569.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.c.e.569.1 | ✓ | 8 | 285.284 | even | 2 | inner | |
570.2.c.e.569.2 | yes | 8 | 3.2 | odd | 2 | inner | |
570.2.c.e.569.3 | yes | 8 | 19.18 | odd | 2 | inner | |
570.2.c.e.569.4 | yes | 8 | 5.4 | even | 2 | inner | |
570.2.c.e.569.5 | yes | 8 | 1.1 | even | 1 | trivial | |
570.2.c.e.569.6 | yes | 8 | 95.94 | odd | 2 | inner | |
570.2.c.e.569.7 | yes | 8 | 15.14 | odd | 2 | inner | |
570.2.c.e.569.8 | yes | 8 | 57.56 | even | 2 | inner |