Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.z (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1849.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1849 |
Dual form | 1950.2.z.e.1699.2 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −1.73205 | − | 1.00000i | −0.654654 | − | 0.377964i | 0.135583 | − | 0.990766i | \(-0.456709\pi\) |
−0.790237 | + | 0.612801i | \(0.790043\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −3.46410 | − | 1.00000i | −0.960769 | − | 0.277350i | ||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.73205 | − | 1.00000i | −0.420084 | − | 0.242536i | 0.275029 | − | 0.961436i | \(-0.411312\pi\) |
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 4.33013 | + | 2.50000i | 0.923186 | + | 0.533002i | ||||
\(23\) | −0.866025 | + | 0.500000i | −0.180579 | + | 0.104257i | −0.587565 | − | 0.809177i | \(-0.699913\pi\) |
0.406986 | + | 0.913434i | \(0.366580\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.50000 | + | 0.866025i | −0.686406 | + | 0.169842i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.73205 | + | 1.00000i | −0.327327 | + | 0.188982i | ||||
\(29\) | 2.50000 | + | 4.33013i | 0.464238 | + | 0.804084i | 0.999167 | − | 0.0408130i | \(-0.0129948\pi\) |
−0.534928 | + | 0.844897i | \(0.679661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.0000 | −1.97566 | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −4.33013 | − | 2.50000i | −0.753778 | − | 0.435194i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −2.59808 | + | 1.50000i | −0.427121 | + | 0.246598i | −0.698119 | − | 0.715981i | \(-0.745980\pi\) |
0.270998 | + | 0.962580i | \(0.412646\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | 3.50000 | − | 0.866025i | 0.560449 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | + | 1.73205i | 0.156174 | + | 0.270501i | 0.933486 | − | 0.358614i | \(-0.116751\pi\) |
−0.777312 | + | 0.629115i | \(0.783417\pi\) | |||||||
\(42\) | 1.73205 | − | 1.00000i | 0.267261 | − | 0.154303i | ||||
\(43\) | 9.52628 | + | 5.50000i | 1.45274 | + | 0.838742i | 0.998636 | − | 0.0522047i | \(-0.0166248\pi\) |
0.454108 | + | 0.890947i | \(0.349958\pi\) | |||||||
\(44\) | 5.00000 | 0.753778 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | − | 9.00000i | − | 1.31278i | −0.754420 | − | 0.656392i | \(-0.772082\pi\) | ||
0.754420 | − | 0.656392i | \(-0.227918\pi\) | |||||||
\(48\) | 0.866025 | + | 0.500000i | 0.125000 | + | 0.0721688i | ||||
\(49\) | −1.50000 | − | 2.59808i | −0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | −2.59808 | + | 2.50000i | −0.360288 | + | 0.346688i | ||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | + | 1.73205i | −0.133631 | + | 0.231455i | ||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | 4.33013 | + | 2.50000i | 0.568574 | + | 0.328266i | ||||
\(59\) | −7.50000 | + | 12.9904i | −0.976417 | + | 1.69120i | −0.301239 | + | 0.953549i | \(0.597400\pi\) |
−0.675178 | + | 0.737655i | \(0.735933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | −9.52628 | + | 5.50000i | −1.20984 | + | 0.698501i | ||||
\(63\) | −1.73205 | + | 1.00000i | −0.218218 | + | 0.125988i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.00000 | −0.615457 | ||||||||
\(67\) | −13.8564 | + | 8.00000i | −1.69283 | + | 0.977356i | −0.740613 | + | 0.671932i | \(0.765465\pi\) |
−0.952217 | + | 0.305424i | \(0.901202\pi\) | |||||||
\(68\) | −1.73205 | + | 1.00000i | −0.210042 | + | 0.121268i | ||||
\(69\) | 0.500000 | − | 0.866025i | 0.0601929 | − | 0.104257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | −1.50000 | + | 2.59808i | −0.174371 | + | 0.302020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | + | 1.73205i | 0.114708 | + | 0.198680i | ||||
\(77\) | − | 10.0000i | − | 1.13961i | ||||||
\(78\) | 2.59808 | − | 2.50000i | 0.294174 | − | 0.283069i | ||||
\(79\) | 11.0000 | 1.23760 | 0.618798 | − | 0.785550i | \(-0.287620\pi\) | ||||
0.618798 | + | 0.785550i | \(0.287620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.73205 | + | 1.00000i | 0.191273 | + | 0.110432i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 1.00000 | − | 1.73205i | 0.109109 | − | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.0000 | 1.18616 | ||||||||
\(87\) | −4.33013 | − | 2.50000i | −0.464238 | − | 0.268028i | ||||
\(88\) | 4.33013 | − | 2.50000i | 0.461593 | − | 0.266501i | ||||
\(89\) | 1.00000 | + | 1.73205i | 0.106000 | + | 0.183597i | 0.914146 | − | 0.405385i | \(-0.132862\pi\) |
−0.808146 | + | 0.588982i | \(0.799529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | + | 5.19615i | 0.524142 | + | 0.544705i | ||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 9.52628 | − | 5.50000i | 0.987829 | − | 0.570323i | ||||
\(94\) | −4.50000 | − | 7.79423i | −0.464140 | − | 0.803913i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.73205 | − | 1.00000i | −0.175863 | − | 0.101535i | 0.409484 | − | 0.912317i | \(-0.365709\pi\) |
−0.585348 | + | 0.810782i | \(0.699042\pi\) | |||||||
\(98\) | −2.59808 | − | 1.50000i | −0.262445 | − | 0.151523i | ||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | 1.73205 | − | 1.00000i | 0.171499 | − | 0.0990148i | ||||
\(103\) | 10.0000i | 0.985329i | 0.870219 | + | 0.492665i | \(0.163977\pi\) | ||||
−0.870219 | + | 0.492665i | \(0.836023\pi\) | |||||||
\(104\) | −1.00000 | + | 3.46410i | −0.0980581 | + | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | −8.66025 | + | 5.00000i | −0.837218 | + | 0.483368i | −0.856318 | − | 0.516449i | \(-0.827253\pi\) |
0.0190994 | + | 0.999818i | \(0.493920\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.50000 | − | 2.59808i | 0.142374 | − | 0.246598i | ||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | −9.52628 | − | 5.50000i | −0.896157 | − | 0.517396i | −0.0202056 | − | 0.999796i | \(-0.506432\pi\) |
−0.875951 | + | 0.482399i | \(0.839765\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.00000 | 0.464238 | ||||||||
\(117\) | −2.59808 | + | 2.50000i | −0.240192 | + | 0.231125i | ||||
\(118\) | 15.0000i | 1.38086i | ||||||||
\(119\) | 2.00000 | + | 3.46410i | 0.183340 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 10.0000i | 0.905357i | ||||||||
\(123\) | −1.73205 | − | 1.00000i | −0.156174 | − | 0.0901670i | ||||
\(124\) | −5.50000 | + | 9.52628i | −0.493915 | + | 0.855485i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.00000 | + | 1.73205i | −0.0890871 | + | 0.154303i | ||||
\(127\) | −1.73205 | + | 1.00000i | −0.153695 | + | 0.0887357i | −0.574875 | − | 0.818241i | \(-0.694949\pi\) |
0.421180 | + | 0.906977i | \(0.361616\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −11.0000 | −0.968496 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | −0.0873704 | −0.0436852 | − | 0.999045i | \(-0.513910\pi\) | ||||
−0.0436852 | + | 0.999045i | \(0.513910\pi\) | |||||||
\(132\) | −4.33013 | + | 2.50000i | −0.376889 | + | 0.217597i | ||||
\(133\) | 3.46410 | − | 2.00000i | 0.300376 | − | 0.173422i | ||||
\(134\) | −8.00000 | + | 13.8564i | −0.691095 | + | 1.19701i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | + | 1.73205i | −0.0857493 | + | 0.148522i | ||||
\(137\) | −9.52628 | − | 5.50000i | −0.813885 | − | 0.469897i | 0.0344182 | − | 0.999408i | \(-0.489042\pi\) |
−0.848303 | + | 0.529511i | \(0.822376\pi\) | |||||||
\(138\) | − | 1.00000i | − | 0.0851257i | ||||||
\(139\) | 1.00000 | − | 1.73205i | 0.0848189 | − | 0.146911i | −0.820495 | − | 0.571654i | \(-0.806302\pi\) |
0.905314 | + | 0.424743i | \(0.139635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.50000 | + | 7.79423i | 0.378968 | + | 0.656392i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.33013 | − | 17.5000i | −0.362103 | − | 1.46342i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.00000 | − | 5.19615i | −0.248282 | − | 0.430037i | ||||
\(147\) | 2.59808 | + | 1.50000i | 0.214286 | + | 0.123718i | ||||
\(148\) | 3.00000i | 0.246598i | ||||||||
\(149\) | 8.50000 | − | 14.7224i | 0.696347 | − | 1.20611i | −0.273377 | − | 0.961907i | \(-0.588141\pi\) |
0.969724 | − | 0.244202i | \(-0.0785259\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 1.73205 | + | 1.00000i | 0.140488 | + | 0.0811107i | ||||
\(153\) | −1.73205 | + | 1.00000i | −0.140028 | + | 0.0808452i | ||||
\(154\) | −5.00000 | − | 8.66025i | −0.402911 | − | 0.697863i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00000 | − | 3.46410i | 0.0800641 | − | 0.277350i | ||||
\(157\) | 7.00000i | 0.558661i | 0.960195 | + | 0.279330i | \(0.0901125\pi\) | ||||
−0.960195 | + | 0.279330i | \(0.909888\pi\) | |||||||
\(158\) | 9.52628 | − | 5.50000i | 0.757870 | − | 0.437557i | ||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 12.9904 | + | 7.50000i | 1.01749 | + | 0.587445i | 0.913375 | − | 0.407120i | \(-0.133467\pi\) |
0.104111 | + | 0.994566i | \(0.466800\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | −2.59808 | + | 1.50000i | −0.201045 | + | 0.116073i | −0.597143 | − | 0.802135i | \(-0.703697\pi\) |
0.396098 | + | 0.918208i | \(0.370364\pi\) | |||||||
\(168\) | − | 2.00000i | − | 0.154303i | ||||||
\(169\) | 11.0000 | + | 6.92820i | 0.846154 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 9.52628 | − | 5.50000i | 0.726372 | − | 0.419371i | ||||
\(173\) | −17.3205 | − | 10.0000i | −1.31685 | − | 0.760286i | −0.333633 | − | 0.942703i | \(-0.608275\pi\) |
−0.983221 | + | 0.182417i | \(0.941608\pi\) | |||||||
\(174\) | −5.00000 | −0.379049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.50000 | − | 4.33013i | 0.188445 | − | 0.326396i | ||||
\(177\) | − | 15.0000i | − | 1.12747i | ||||||
\(178\) | 1.73205 | + | 1.00000i | 0.129823 | + | 0.0749532i | ||||
\(179\) | −6.50000 | − | 11.2583i | −0.485833 | − | 0.841487i | 0.514035 | − | 0.857769i | \(-0.328150\pi\) |
−0.999867 | + | 0.0162823i | \(0.994817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 6.92820 | + | 2.00000i | 0.513553 | + | 0.148250i | ||||
\(183\) | − | 10.0000i | − | 0.739221i | ||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.50000 | − | 9.52628i | 0.403280 | − | 0.698501i | ||||
\(187\) | − | 10.0000i | − | 0.731272i | ||||||
\(188\) | −7.79423 | − | 4.50000i | −0.568453 | − | 0.328196i | ||||
\(189\) | 1.00000 | − | 1.73205i | 0.0727393 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −20.7846 | + | 12.0000i | −1.49611 | + | 0.863779i | −0.999990 | − | 0.00447566i | \(-0.998575\pi\) |
−0.496119 | + | 0.868255i | \(0.665242\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 6.92820 | − | 4.00000i | 0.493614 | − | 0.284988i | −0.232458 | − | 0.972606i | \(-0.574677\pi\) |
0.726073 | + | 0.687618i | \(0.241344\pi\) | |||||||
\(198\) | 4.33013 | − | 2.50000i | 0.307729 | − | 0.177667i | ||||
\(199\) | 12.0000 | − | 20.7846i | 0.850657 | − | 1.47338i | −0.0299585 | − | 0.999551i | \(-0.509538\pi\) |
0.880616 | − | 0.473831i | \(-0.157129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | − | 13.8564i | 0.564276 | − | 0.977356i | ||||
\(202\) | −1.73205 | − | 1.00000i | −0.121867 | − | 0.0703598i | ||||
\(203\) | − | 10.0000i | − | 0.701862i | ||||||
\(204\) | 1.00000 | − | 1.73205i | 0.0700140 | − | 0.121268i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.00000 | + | 8.66025i | 0.348367 | + | 0.603388i | ||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 0.866025 | + | 3.50000i | 0.0600481 | + | 0.242681i | ||||
\(209\) | −10.0000 | −0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 5.19615 | + | 3.00000i | 0.356873 | + | 0.206041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.00000 | + | 8.66025i | −0.341793 | + | 0.592003i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 19.0526 | + | 11.0000i | 1.29337 | + | 0.746729i | ||||
\(218\) | 1.73205 | − | 1.00000i | 0.117309 | − | 0.0677285i | ||||
\(219\) | 3.00000 | + | 5.19615i | 0.202721 | + | 0.351123i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.00000 | + | 5.19615i | 0.336336 | + | 0.349531i | ||||
\(222\) | − | 3.00000i | − | 0.201347i | ||||||
\(223\) | 22.5167 | − | 13.0000i | 1.50783 | − | 0.870544i | 0.507869 | − | 0.861435i | \(-0.330434\pi\) |
0.999959 | − | 0.00910984i | \(-0.00289979\pi\) | |||||||
\(224\) | 1.00000 | + | 1.73205i | 0.0668153 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0000 | −0.731709 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | −1.73205 | − | 1.00000i | −0.114708 | − | 0.0662266i | ||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.00000 | + | 8.66025i | 0.328976 | + | 0.569803i | ||||
\(232\) | 4.33013 | − | 2.50000i | 0.284287 | − | 0.164133i | ||||
\(233\) | 1.00000i | 0.0655122i | 0.999463 | + | 0.0327561i | \(0.0104285\pi\) | ||||
−0.999463 | + | 0.0327561i | \(0.989572\pi\) | |||||||
\(234\) | −1.00000 | + | 3.46410i | −0.0653720 | + | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.50000 | + | 12.9904i | 0.488208 | + | 0.845602i | ||||
\(237\) | −9.52628 | + | 5.50000i | −0.618798 | + | 0.357263i | ||||
\(238\) | 3.46410 | + | 2.00000i | 0.224544 | + | 0.129641i | ||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | − | 6.06218i | 0.225455 | − | 0.390499i | −0.731001 | − | 0.682376i | \(-0.760947\pi\) |
0.956456 | + | 0.291877i | \(0.0942799\pi\) | |||||||
\(242\) | 14.0000i | 0.899954i | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 5.00000 | + | 8.66025i | 0.320092 | + | 0.554416i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 5.19615 | − | 5.00000i | 0.330623 | − | 0.318142i | ||||
\(248\) | 11.0000i | 0.698501i | ||||||||
\(249\) | −3.00000 | − | 5.19615i | −0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.5000 | + | 21.6506i | −0.788993 | + | 1.36658i | 0.137591 | + | 0.990489i | \(0.456064\pi\) |
−0.926584 | + | 0.376087i | \(0.877269\pi\) | |||||||
\(252\) | 2.00000i | 0.125988i | ||||||||
\(253\) | −4.33013 | − | 2.50000i | −0.272233 | − | 0.157174i | ||||
\(254\) | −1.00000 | + | 1.73205i | −0.0627456 | + | 0.108679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.7224 | − | 8.50000i | 0.918360 | − | 0.530215i | 0.0352486 | − | 0.999379i | \(-0.488778\pi\) |
0.883112 | + | 0.469163i | \(0.155444\pi\) | |||||||
\(258\) | −9.52628 | + | 5.50000i | −0.593080 | + | 0.342415i | ||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | −0.866025 | + | 0.500000i | −0.0535032 | + | 0.0308901i | ||||
\(263\) | 18.1865 | − | 10.5000i | 1.12143 | − | 0.647458i | 0.179664 | − | 0.983728i | \(-0.442499\pi\) |
0.941766 | + | 0.336270i | \(0.109166\pi\) | |||||||
\(264\) | −2.50000 | + | 4.33013i | −0.153864 | + | 0.266501i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.00000 | − | 3.46410i | 0.122628 | − | 0.212398i | ||||
\(267\) | −1.73205 | − | 1.00000i | −0.106000 | − | 0.0611990i | ||||
\(268\) | 16.0000i | 0.977356i | ||||||||
\(269\) | 7.00000 | − | 12.1244i | 0.426798 | − | 0.739235i | −0.569789 | − | 0.821791i | \(-0.692975\pi\) |
0.996586 | + | 0.0825561i | \(0.0263084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.50000 | + | 11.2583i | 0.394847 | + | 0.683895i | 0.993082 | − | 0.117426i | \(-0.0374643\pi\) |
−0.598235 | + | 0.801321i | \(0.704131\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | −6.92820 | − | 2.00000i | −0.419314 | − | 0.121046i | ||||
\(274\) | −11.0000 | −0.664534 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.500000 | − | 0.866025i | −0.0300965 | − | 0.0521286i | ||||
\(277\) | −9.52628 | − | 5.50000i | −0.572379 | − | 0.330463i | 0.185720 | − | 0.982603i | \(-0.440538\pi\) |
−0.758099 | + | 0.652140i | \(0.773872\pi\) | |||||||
\(278\) | − | 2.00000i | − | 0.119952i | ||||||
\(279\) | −5.50000 | + | 9.52628i | −0.329276 | + | 0.570323i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 7.79423 | + | 4.50000i | 0.464140 | + | 0.267971i | ||||
\(283\) | 16.4545 | − | 9.50000i | 0.978117 | − | 0.564716i | 0.0764162 | − | 0.997076i | \(-0.475652\pi\) |
0.901701 | + | 0.432360i | \(0.142319\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.5000 | − | 12.9904i | −0.739140 | − | 0.768137i | ||||
\(287\) | − | 4.00000i | − | 0.236113i | ||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000 | 0.117242 | ||||||||
\(292\) | −5.19615 | − | 3.00000i | −0.304082 | − | 0.175562i | ||||
\(293\) | −5.19615 | − | 3.00000i | −0.303562 | − | 0.175262i | 0.340480 | − | 0.940252i | \(-0.389411\pi\) |
−0.644042 | + | 0.764990i | \(0.722744\pi\) | |||||||
\(294\) | 3.00000 | 0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.50000 | + | 2.59808i | 0.0871857 | + | 0.151010i | ||||
\(297\) | −4.33013 | + | 2.50000i | −0.251259 | + | 0.145065i | ||||
\(298\) | − | 17.0000i | − | 0.984784i | ||||||
\(299\) | 3.50000 | − | 0.866025i | 0.202410 | − | 0.0500835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0000 | − | 19.0526i | −0.634029 | − | 1.09817i | ||||
\(302\) | 6.92820 | − | 4.00000i | 0.398673 | − | 0.230174i | ||||
\(303\) | 1.73205 | + | 1.00000i | 0.0995037 | + | 0.0574485i | ||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | + | 1.73205i | −0.0571662 | + | 0.0990148i | ||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −8.66025 | − | 5.00000i | −0.493464 | − | 0.284901i | ||||
\(309\) | −5.00000 | − | 8.66025i | −0.284440 | − | 0.492665i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0000 | 1.13410 | 0.567048 | − | 0.823685i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823685i | \(0.308085\pi\) | |||||||
\(312\) | −0.866025 | − | 3.50000i | −0.0490290 | − | 0.198148i | ||||
\(313\) | 20.0000i | 1.13047i | 0.824931 | + | 0.565233i | \(0.191214\pi\) | ||||
−0.824931 | + | 0.565233i | \(0.808786\pi\) | |||||||
\(314\) | 3.50000 | + | 6.06218i | 0.197516 | + | 0.342108i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.50000 | − | 9.52628i | 0.309399 | − | 0.535895i | ||||
\(317\) | − | 16.0000i | − | 0.898650i | −0.893368 | − | 0.449325i | \(-0.851665\pi\) | ||
0.893368 | − | 0.449325i | \(-0.148335\pi\) | |||||||
\(318\) | −5.19615 | − | 3.00000i | −0.291386 | − | 0.168232i | ||||
\(319\) | −12.5000 | + | 21.6506i | −0.699866 | + | 1.21220i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.00000 | − | 8.66025i | 0.279073 | − | 0.483368i | ||||
\(322\) | 1.73205 | − | 1.00000i | 0.0965234 | − | 0.0557278i | ||||
\(323\) | 3.46410 | − | 2.00000i | 0.192748 | − | 0.111283i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.0000 | 0.830773 | ||||||||
\(327\) | −1.73205 | + | 1.00000i | −0.0957826 | + | 0.0553001i | ||||
\(328\) | 1.73205 | − | 1.00000i | 0.0956365 | − | 0.0552158i | ||||
\(329\) | −9.00000 | + | 15.5885i | −0.496186 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | 5.19615 | + | 3.00000i | 0.285176 | + | 0.164646i | ||||
\(333\) | 3.00000i | 0.164399i | ||||||||
\(334\) | −1.50000 | + | 2.59808i | −0.0820763 | + | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.00000 | − | 1.73205i | −0.0545545 | − | 0.0944911i | ||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | 12.9904 | + | 0.500000i | 0.706584 | + | 0.0271964i | ||||
\(339\) | 11.0000 | 0.597438 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.5000 | − | 47.6314i | −1.48921 | − | 2.57938i | ||||
\(342\) | 1.73205 | + | 1.00000i | 0.0936586 | + | 0.0540738i | ||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 5.50000 | − | 9.52628i | 0.296540 | − | 0.513623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.0000 | −1.07521 | ||||||||
\(347\) | 29.4449 | + | 17.0000i | 1.58068 | + | 0.912608i | 0.994760 | + | 0.102241i | \(0.0326014\pi\) |
0.585923 | + | 0.810366i | \(0.300732\pi\) | |||||||
\(348\) | −4.33013 | + | 2.50000i | −0.232119 | + | 0.134014i | ||||
\(349\) | 10.0000 | + | 17.3205i | 0.535288 | + | 0.927146i | 0.999149 | + | 0.0412379i | \(0.0131301\pi\) |
−0.463862 | + | 0.885908i | \(0.653537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | − | 3.46410i | 0.0533761 | − | 0.184900i | ||||
\(352\) | − | 5.00000i | − | 0.266501i | ||||||
\(353\) | −15.5885 | + | 9.00000i | −0.829690 | + | 0.479022i | −0.853746 | − | 0.520689i | \(-0.825675\pi\) |
0.0240566 | + | 0.999711i | \(0.492342\pi\) | |||||||
\(354\) | −7.50000 | − | 12.9904i | −0.398621 | − | 0.690431i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | −3.46410 | − | 2.00000i | −0.183340 | − | 0.105851i | ||||
\(358\) | −11.2583 | − | 6.50000i | −0.595021 | − | 0.343536i | ||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | −13.8564 | + | 8.00000i | −0.728277 | + | 0.420471i | ||||
\(363\) | − | 14.0000i | − | 0.734809i | ||||||
\(364\) | 7.00000 | − | 1.73205i | 0.366900 | − | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.00000 | − | 8.66025i | −0.261354 | − | 0.452679i | ||||
\(367\) | 13.8564 | − | 8.00000i | 0.723299 | − | 0.417597i | −0.0926670 | − | 0.995697i | \(-0.529539\pi\) |
0.815966 | + | 0.578101i | \(0.196206\pi\) | |||||||
\(368\) | 0.866025 | + | 0.500000i | 0.0451447 | + | 0.0260643i | ||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | − | 10.3923i | 0.311504 | − | 0.539542i | ||||
\(372\) | − | 11.0000i | − | 0.570323i | ||||||
\(373\) | 16.4545 | + | 9.50000i | 0.851981 | + | 0.491891i | 0.861319 | − | 0.508065i | \(-0.169639\pi\) |
−0.00933789 | + | 0.999956i | \(0.502972\pi\) | |||||||
\(374\) | −5.00000 | − | 8.66025i | −0.258544 | − | 0.447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | −4.33013 | − | 17.5000i | −0.223013 | − | 0.901296i | ||||
\(378\) | − | 2.00000i | − | 0.102869i | ||||||
\(379\) | −1.00000 | − | 1.73205i | −0.0513665 | − | 0.0889695i | 0.839199 | − | 0.543825i | \(-0.183024\pi\) |
−0.890565 | + | 0.454855i | \(0.849691\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.00000 | − | 1.73205i | 0.0512316 | − | 0.0887357i | ||||
\(382\) | 4.00000i | 0.204658i | ||||||||
\(383\) | −26.8468 | − | 15.5000i | −1.37181 | − | 0.792013i | −0.380651 | − | 0.924719i | \(-0.624300\pi\) |
−0.991155 | + | 0.132706i | \(0.957633\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.0000 | + | 20.7846i | −0.610784 | + | 1.05791i | ||||
\(387\) | 9.52628 | − | 5.50000i | 0.484248 | − | 0.279581i | ||||
\(388\) | −1.73205 | + | 1.00000i | −0.0879316 | + | 0.0507673i | ||||
\(389\) | −5.00000 | −0.253510 | −0.126755 | − | 0.991934i | \(-0.540456\pi\) | ||||
−0.126755 | + | 0.991934i | \(0.540456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | −2.59808 | + | 1.50000i | −0.131223 | + | 0.0757614i | ||||
\(393\) | 0.866025 | − | 0.500000i | 0.0436852 | − | 0.0252217i | ||||
\(394\) | 4.00000 | − | 6.92820i | 0.201517 | − | 0.349038i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.50000 | − | 4.33013i | 0.125630 | − | 0.217597i | ||||
\(397\) | 2.59808 | + | 1.50000i | 0.130394 | + | 0.0752828i | 0.563778 | − | 0.825926i | \(-0.309347\pi\) |
−0.433384 | + | 0.901209i | \(0.642681\pi\) | |||||||
\(398\) | − | 24.0000i | − | 1.20301i | ||||||
\(399\) | −2.00000 | + | 3.46410i | −0.100125 | + | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0000 | − | 31.1769i | −0.898877 | − | 1.55690i | −0.828932 | − | 0.559350i | \(-0.811051\pi\) |
−0.0699455 | − | 0.997551i | \(-0.522283\pi\) | |||||||
\(402\) | − | 16.0000i | − | 0.798007i | ||||||
\(403\) | 38.1051 | + | 11.0000i | 1.89815 | + | 0.547949i | ||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.00000 | − | 8.66025i | −0.248146 | − | 0.429801i | ||||
\(407\) | −12.9904 | − | 7.50000i | −0.643909 | − | 0.371761i | ||||
\(408\) | − | 2.00000i | − | 0.0990148i | ||||||
\(409\) | 15.0000 | − | 25.9808i | 0.741702 | − | 1.28467i | −0.210017 | − | 0.977698i | \(-0.567352\pi\) |
0.951720 | − | 0.306968i | \(-0.0993146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0000 | 0.542590 | ||||||||
\(412\) | 8.66025 | + | 5.00000i | 0.426660 | + | 0.246332i | ||||
\(413\) | 25.9808 | − | 15.0000i | 1.27843 | − | 0.738102i | ||||
\(414\) | 0.500000 | + | 0.866025i | 0.0245737 | + | 0.0425628i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | + | 2.59808i | 0.122573 | + | 0.127381i | ||||
\(417\) | 2.00000i | 0.0979404i | ||||||||
\(418\) | −8.66025 | + | 5.00000i | −0.423587 | + | 0.244558i | ||||
\(419\) | −2.00000 | − | 3.46410i | −0.0977064 | − | 0.169232i | 0.813029 | − | 0.582224i | \(-0.197817\pi\) |
−0.910735 | + | 0.412991i | \(0.864484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | −0.779792 | −0.389896 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389896 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(422\) | 3.46410 | + | 2.00000i | 0.168630 | + | 0.0973585i | ||||
\(423\) | −7.79423 | − | 4.50000i | −0.378968 | − | 0.218797i | ||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.3205 | − | 10.0000i | 0.838198 | − | 0.483934i | ||||
\(428\) | 10.0000i | 0.483368i | ||||||||
\(429\) | 12.5000 | + | 12.9904i | 0.603506 | + | 0.627182i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.0000 | − | 34.6410i | −0.963366 | − | 1.66860i | −0.713942 | − | 0.700205i | \(-0.753092\pi\) |
−0.249424 | − | 0.968394i | \(-0.580241\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | −24.2487 | − | 14.0000i | −1.16532 | − | 0.672797i | −0.212746 | − | 0.977108i | \(-0.568241\pi\) |
−0.952573 | + | 0.304311i | \(0.901574\pi\) | |||||||
\(434\) | 22.0000 | 1.05603 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | − | 2.00000i | − | 0.0956730i | ||||||
\(438\) | 5.19615 | + | 3.00000i | 0.248282 | + | 0.143346i | ||||
\(439\) | −2.00000 | − | 3.46410i | −0.0954548 | − | 0.165333i | 0.814344 | − | 0.580383i | \(-0.197097\pi\) |
−0.909798 | + | 0.415051i | \(0.863764\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 6.92820 | + | 2.00000i | 0.329541 | + | 0.0951303i | ||||
\(443\) | 20.0000i | 0.950229i | 0.879924 | + | 0.475114i | \(0.157593\pi\) | ||||
−0.879924 | + | 0.475114i | \(0.842407\pi\) | |||||||
\(444\) | −1.50000 | − | 2.59808i | −0.0711868 | − | 0.123299i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.0000 | − | 22.5167i | 0.615568 | − | 1.06619i | ||||
\(447\) | 17.0000i | 0.804072i | ||||||||
\(448\) | 1.73205 | + | 1.00000i | 0.0818317 | + | 0.0472456i | ||||
\(449\) | 6.00000 | − | 10.3923i | 0.283158 | − | 0.490443i | −0.689003 | − | 0.724758i | \(-0.741951\pi\) |
0.972161 | + | 0.234315i | \(0.0752847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00000 | + | 8.66025i | −0.235441 | + | 0.407795i | ||||
\(452\) | −9.52628 | + | 5.50000i | −0.448078 | + | 0.258698i | ||||
\(453\) | −6.92820 | + | 4.00000i | −0.325515 | + | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −32.9090 | + | 19.0000i | −1.53942 | + | 0.888783i | −0.540544 | + | 0.841316i | \(0.681781\pi\) |
−0.998873 | + | 0.0474665i | \(0.984885\pi\) | |||||||
\(458\) | −8.66025 | + | 5.00000i | −0.404667 | + | 0.233635i | ||||
\(459\) | 1.00000 | − | 1.73205i | 0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.5000 | − | 33.7750i | 0.908206 | − | 1.57306i | 0.0916500 | − | 0.995791i | \(-0.470786\pi\) |
0.816556 | − | 0.577267i | \(-0.195881\pi\) | |||||||
\(462\) | 8.66025 | + | 5.00000i | 0.402911 | + | 0.232621i | ||||
\(463\) | 14.0000i | 0.650635i | 0.945605 | + | 0.325318i | \(0.105471\pi\) | ||||
−0.945605 | + | 0.325318i | \(0.894529\pi\) | |||||||
\(464\) | 2.50000 | − | 4.33013i | 0.116060 | − | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.500000 | + | 0.866025i | 0.0231621 | + | 0.0401179i | ||||
\(467\) | − | 6.00000i | − | 0.277647i | −0.990317 | − | 0.138823i | \(-0.955668\pi\) | ||
0.990317 | − | 0.138823i | \(-0.0443321\pi\) | |||||||
\(468\) | 0.866025 | + | 3.50000i | 0.0400320 | + | 0.161788i | ||||
\(469\) | 32.0000 | 1.47762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.50000 | − | 6.06218i | −0.161271 | − | 0.279330i | ||||
\(472\) | 12.9904 | + | 7.50000i | 0.597931 | + | 0.345215i | ||||
\(473\) | 55.0000i | 2.52890i | ||||||||
\(474\) | −5.50000 | + | 9.52628i | −0.252623 | + | 0.437557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 5.19615 | + | 3.00000i | 0.237915 | + | 0.137361i | ||||
\(478\) | 17.3205 | − | 10.0000i | 0.792222 | − | 0.457389i | ||||
\(479\) | −12.0000 | − | 20.7846i | −0.548294 | − | 0.949673i | −0.998392 | − | 0.0566937i | \(-0.981944\pi\) |
0.450098 | − | 0.892979i | \(-0.351389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | − | 2.59808i | 0.478759 | − | 0.118462i | ||||
\(482\) | − | 7.00000i | − | 0.318841i | ||||||
\(483\) | −1.73205 | + | 1.00000i | −0.0788110 | + | 0.0455016i | ||||
\(484\) | 7.00000 | + | 12.1244i | 0.318182 | + | 0.551107i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 1.73205 | + | 1.00000i | 0.0784867 | + | 0.0453143i | 0.538730 | − | 0.842479i | \(-0.318904\pi\) |
−0.460243 | + | 0.887793i | \(0.652238\pi\) | |||||||
\(488\) | 8.66025 | + | 5.00000i | 0.392031 | + | 0.226339i | ||||
\(489\) | −15.0000 | −0.678323 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00000 | + | 13.8564i | 0.361035 | + | 0.625331i | 0.988131 | − | 0.153611i | \(-0.0490902\pi\) |
−0.627096 | + | 0.778942i | \(0.715757\pi\) | |||||||
\(492\) | −1.73205 | + | 1.00000i | −0.0780869 | + | 0.0450835i | ||||
\(493\) | − | 10.0000i | − | 0.450377i | ||||||
\(494\) | 2.00000 | − | 6.92820i | 0.0899843 | − | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.50000 | + | 9.52628i | 0.246957 | + | 0.427743i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.19615 | − | 3.00000i | −0.232845 | − | 0.134433i | ||||
\(499\) | −28.0000 | −1.25345 | −0.626726 | − | 0.779240i | \(-0.715605\pi\) | ||||
−0.626726 | + | 0.779240i | \(0.715605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50000 | − | 2.59808i | 0.0670151 | − | 0.116073i | ||||
\(502\) | 25.0000i | 1.11580i | ||||||||
\(503\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(504\) | 1.00000 | + | 1.73205i | 0.0445435 | + | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.00000 | −0.222277 | ||||||||
\(507\) | −12.9904 | − | 0.500000i | −0.576923 | − | 0.0222058i | ||||
\(508\) | 2.00000i | 0.0887357i | ||||||||
\(509\) | 14.5000 | + | 25.1147i | 0.642701 | + | 1.11319i | 0.984827 | + | 0.173537i | \(0.0555197\pi\) |
−0.342126 | + | 0.939654i | \(0.611147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | + | 10.3923i | −0.265424 | + | 0.459728i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.73205 | − | 1.00000i | −0.0764719 | − | 0.0441511i | ||||
\(514\) | 8.50000 | − | 14.7224i | 0.374919 | − | 0.649379i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.50000 | + | 9.52628i | −0.242124 | + | 0.419371i | ||||
\(517\) | 38.9711 | − | 22.5000i | 1.71395 | − | 0.989549i | ||||
\(518\) | 5.19615 | − | 3.00000i | 0.228306 | − | 0.131812i | ||||
\(519\) | 20.0000 | 0.877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 4.33013 | − | 2.50000i | 0.189525 | − | 0.109422i | ||||
\(523\) | −26.8468 | + | 15.5000i | −1.17393 | + | 0.677768i | −0.954602 | − | 0.297884i | \(-0.903719\pi\) |
−0.219326 | + | 0.975652i | \(0.570386\pi\) | |||||||
\(524\) | −0.500000 | + | 0.866025i | −0.0218426 | + | 0.0378325i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.5000 | − | 18.1865i | 0.457822 | − | 0.792971i | ||||
\(527\) | 19.0526 | + | 11.0000i | 0.829943 | + | 0.479168i | ||||
\(528\) | 5.00000i | 0.217597i | ||||||||
\(529\) | −11.0000 | + | 19.0526i | −0.478261 | + | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.50000 | + | 12.9904i | 0.325472 | + | 0.563735i | ||||
\(532\) | − | 4.00000i | − | 0.173422i | ||||||
\(533\) | −1.73205 | − | 7.00000i | −0.0750234 | − | 0.303204i | ||||
\(534\) | −2.00000 | −0.0865485 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.00000 | + | 13.8564i | 0.345547 | + | 0.598506i | ||||
\(537\) | 11.2583 | + | 6.50000i | 0.485833 | + | 0.280496i | ||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | 7.50000 | − | 12.9904i | 0.323048 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(542\) | 11.2583 | + | 6.50000i | 0.483587 | + | 0.279199i | ||||
\(543\) | 13.8564 | − | 8.00000i | 0.594635 | − | 0.343313i | ||||
\(544\) | 1.00000 | + | 1.73205i | 0.0428746 | + | 0.0742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.00000 | + | 1.73205i | −0.299572 | + | 0.0741249i | ||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | −9.52628 | + | 5.50000i | −0.406942 | + | 0.234948i | ||||
\(549\) | 5.00000 | + | 8.66025i | 0.213395 | + | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.0000 | −0.426014 | ||||||||
\(552\) | −0.866025 | − | 0.500000i | −0.0368605 | − | 0.0212814i | ||||
\(553\) | −19.0526 | − | 11.0000i | −0.810197 | − | 0.467768i | ||||
\(554\) | −11.0000 | −0.467345 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | − | 1.73205i | −0.0424094 | − | 0.0734553i | ||||
\(557\) | −22.5167 | + | 13.0000i | −0.954062 | + | 0.550828i | −0.894340 | − | 0.447387i | \(-0.852355\pi\) |
−0.0597213 | + | 0.998215i | \(0.519021\pi\) | |||||||
\(558\) | 11.0000i | 0.465667i | ||||||||
\(559\) | −27.5000 | − | 28.5788i | −1.16313 | − | 1.20876i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.00000 | + | 8.66025i | 0.211100 | + | 0.365636i | ||||
\(562\) | −8.66025 | + | 5.00000i | −0.365311 | + | 0.210912i | ||||
\(563\) | −10.3923 | − | 6.00000i | −0.437983 | − | 0.252870i | 0.264758 | − | 0.964315i | \(-0.414708\pi\) |
−0.702742 | + | 0.711445i | \(0.748041\pi\) | |||||||
\(564\) | 9.00000 | 0.378968 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.50000 | − | 16.4545i | 0.399315 | − | 0.691633i | ||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0000 | − | 19.0526i | −0.461144 | − | 0.798725i | 0.537874 | − | 0.843025i | \(-0.319228\pi\) |
−0.999018 | + | 0.0443003i | \(0.985894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | −17.3205 | − | 5.00000i | −0.724207 | − | 0.209061i | ||||
\(573\) | − | 4.00000i | − | 0.167102i | ||||||
\(574\) | −2.00000 | − | 3.46410i | −0.0834784 | − | 0.144589i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 22.0000i | 0.915872i | 0.888985 | + | 0.457936i | \(0.151411\pi\) | ||||
−0.888985 | + | 0.457936i | \(0.848589\pi\) | |||||||
\(578\) | −11.2583 | − | 6.50000i | −0.468285 | − | 0.270364i | ||||
\(579\) | 12.0000 | − | 20.7846i | 0.498703 | − | 0.863779i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | − | 10.3923i | 0.248922 | − | 0.431145i | ||||
\(582\) | 1.73205 | − | 1.00000i | 0.0717958 | − | 0.0414513i | ||||
\(583\) | −25.9808 | + | 15.0000i | −1.07601 | + | 0.621237i | ||||
\(584\) | −6.00000 | −0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 15.5885 | − | 9.00000i | 0.643404 | − | 0.371470i | −0.142520 | − | 0.989792i | \(-0.545521\pi\) |
0.785925 | + | 0.618322i | \(0.212187\pi\) | |||||||
\(588\) | 2.59808 | − | 1.50000i | 0.107143 | − | 0.0618590i | ||||
\(589\) | 11.0000 | − | 19.0526i | 0.453247 | − | 0.785047i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.00000 | + | 6.92820i | −0.164538 | + | 0.284988i | ||||
\(592\) | 2.59808 | + | 1.50000i | 0.106780 | + | 0.0616496i | ||||
\(593\) | 31.0000i | 1.27302i | 0.771270 | + | 0.636509i | \(0.219622\pi\) | ||||
−0.771270 | + | 0.636509i | \(0.780378\pi\) | |||||||
\(594\) | −2.50000 | + | 4.33013i | −0.102576 | + | 0.177667i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.50000 | − | 14.7224i | −0.348174 | − | 0.603054i | ||||
\(597\) | 24.0000i | 0.982255i | ||||||||
\(598\) | 2.59808 | − | 2.50000i | 0.106243 | − | 0.102233i | ||||
\(599\) | −42.0000 | −1.71607 | −0.858037 | − | 0.513588i | \(-0.828316\pi\) | ||||
−0.858037 | + | 0.513588i | \(0.828316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.50000 | + | 2.59808i | 0.0611863 | + | 0.105978i | 0.894996 | − | 0.446074i | \(-0.147178\pi\) |
−0.833810 | + | 0.552052i | \(0.813845\pi\) | |||||||
\(602\) | −19.0526 | − | 11.0000i | −0.776524 | − | 0.448327i | ||||
\(603\) | 16.0000i | 0.651570i | ||||||||
\(604\) | 4.00000 | − | 6.92820i | 0.162758 | − | 0.281905i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.00000 | 0.0812444 | ||||||||
\(607\) | 15.5885 | + | 9.00000i | 0.632716 | + | 0.365299i | 0.781803 | − | 0.623525i | \(-0.214300\pi\) |
−0.149087 | + | 0.988824i | \(0.547634\pi\) | |||||||
\(608\) | 1.73205 | − | 1.00000i | 0.0702439 | − | 0.0405554i | ||||
\(609\) | 5.00000 | + | 8.66025i | 0.202610 | + | 0.350931i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.00000 | + | 31.1769i | −0.364101 | + | 1.26128i | ||||
\(612\) | 2.00000i | 0.0808452i | ||||||||
\(613\) | −25.1147 | + | 14.5000i | −1.01437 | + | 0.585649i | −0.912470 | − | 0.409145i | \(-0.865827\pi\) |
−0.101905 | + | 0.994794i | \(0.532494\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.0000 | −0.402911 | ||||||||
\(617\) | 35.5070 | + | 20.5000i | 1.42946 | + | 0.825299i | 0.997078 | − | 0.0763917i | \(-0.0243399\pi\) |
0.432382 | + | 0.901691i | \(0.357673\pi\) | |||||||
\(618\) | −8.66025 | − | 5.00000i | −0.348367 | − | 0.201129i | ||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | 17.3205 | − | 10.0000i | 0.694489 | − | 0.400963i | ||||
\(623\) | − | 4.00000i | − | 0.160257i | ||||||
\(624\) | −2.50000 | − | 2.59808i | −0.100080 | − | 0.104006i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.0000 | + | 17.3205i | 0.399680 | + | 0.692267i | ||||
\(627\) | 8.66025 | − | 5.00000i | 0.345857 | − | 0.199681i | ||||
\(628\) | 6.06218 | + | 3.50000i | 0.241907 | + | 0.139665i | ||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | + | 34.6410i | −0.796187 | + | 1.37904i | 0.125895 | + | 0.992044i | \(0.459820\pi\) |
−0.922082 | + | 0.386994i | \(0.873514\pi\) | |||||||
\(632\) | − | 11.0000i | − | 0.437557i | ||||||
\(633\) | −3.46410 | − | 2.00000i | −0.137686 | − | 0.0794929i | ||||
\(634\) | −8.00000 | − | 13.8564i | −0.317721 | − | 0.550308i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 2.59808 | + | 10.5000i | 0.102940 | + | 0.416025i | ||||
\(638\) | 25.0000i | 0.989759i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | − | 25.9808i | 0.592464 | − | 1.02618i | −0.401435 | − | 0.915888i | \(-0.631488\pi\) |
0.993899 | − | 0.110291i | \(-0.0351782\pi\) | |||||||
\(642\) | − | 10.0000i | − | 0.394669i | ||||||
\(643\) | −6.92820 | − | 4.00000i | −0.273222 | − | 0.157745i | 0.357129 | − | 0.934055i | \(-0.383756\pi\) |
−0.630351 | + | 0.776310i | \(0.717089\pi\) | |||||||
\(644\) | 1.00000 | − | 1.73205i | 0.0394055 | − | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.00000 | − | 3.46410i | 0.0786889 | − | 0.136293i | ||||
\(647\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −75.0000 | −2.94401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.0000 | −0.862248 | ||||||||
\(652\) | 12.9904 | − | 7.50000i | 0.508743 | − | 0.293723i | ||||
\(653\) | 29.4449 | − | 17.0000i | 1.15227 | − | 0.665261i | 0.202828 | − | 0.979214i | \(-0.434987\pi\) |
0.949439 | + | 0.313953i | \(0.101653\pi\) | |||||||
\(654\) | −1.00000 | + | 1.73205i | −0.0391031 | + | 0.0677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.00000 | − | 1.73205i | 0.0390434 | − | 0.0676252i | ||||
\(657\) | −5.19615 | − | 3.00000i | −0.202721 | − | 0.117041i | ||||
\(658\) | 18.0000i | 0.701713i | ||||||||
\(659\) | −19.5000 | + | 33.7750i | −0.759612 | + | 1.31569i | 0.183436 | + | 0.983032i | \(0.441278\pi\) |
−0.943049 | + | 0.332655i | \(0.892055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | − | 27.7128i | −0.622328 | − | 1.07790i | −0.989051 | − | 0.147573i | \(-0.952854\pi\) |
0.366723 | − | 0.930330i | \(-0.380480\pi\) | |||||||
\(662\) | − | 28.0000i | − | 1.08825i | ||||||
\(663\) | −6.92820 | − | 2.00000i | −0.269069 | − | 0.0776736i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.50000 | + | 2.59808i | 0.0581238 | + | 0.100673i | ||||
\(667\) | −4.33013 | − | 2.50000i | −0.167663 | − | 0.0968004i | ||||
\(668\) | 3.00000i | 0.116073i | ||||||||
\(669\) | −13.0000 | + | 22.5167i | −0.502609 | + | 0.870544i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.0000 | −1.93023 | ||||||||
\(672\) | −1.73205 | − | 1.00000i | −0.0668153 | − | 0.0385758i | ||||
\(673\) | 6.92820 | − | 4.00000i | 0.267063 | − | 0.154189i | −0.360489 | − | 0.932763i | \(-0.617390\pi\) |
0.627552 | + | 0.778575i | \(0.284057\pi\) | |||||||
\(674\) | 1.00000 | + | 1.73205i | 0.0385186 | + | 0.0667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.5000 | − | 6.06218i | 0.442308 | − | 0.233161i | ||||
\(677\) | 4.00000i | 0.153732i | 0.997041 | + | 0.0768662i | \(0.0244914\pi\) | ||||
−0.997041 | + | 0.0768662i | \(0.975509\pi\) | |||||||
\(678\) | 9.52628 | − | 5.50000i | 0.365855 | − | 0.211226i | ||||
\(679\) | 2.00000 | + | 3.46410i | 0.0767530 | + | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −47.6314 | − | 27.5000i | −1.82390 | − | 1.05303i | ||||
\(683\) | 10.3923 | + | 6.00000i | 0.397650 | + | 0.229584i | 0.685470 | − | 0.728101i | \(-0.259597\pi\) |
−0.287819 | + | 0.957685i | \(0.592930\pi\) | |||||||
\(684\) | 2.00000 | 0.0764719 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.0000 | + | 17.3205i | 0.381802 | + | 0.661300i | ||||
\(687\) | 8.66025 | − | 5.00000i | 0.330409 | − | 0.190762i | ||||
\(688\) | − | 11.0000i | − | 0.419371i | ||||||
\(689\) | 6.00000 | − | 20.7846i | 0.228582 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0000 | + | 25.9808i | 0.570627 | + | 0.988355i | 0.996502 | + | 0.0835727i | \(0.0266331\pi\) |
−0.425875 | + | 0.904782i | \(0.640034\pi\) | |||||||
\(692\) | −17.3205 | + | 10.0000i | −0.658427 | + | 0.380143i | ||||
\(693\) | −8.66025 | − | 5.00000i | −0.328976 | − | 0.189934i | ||||
\(694\) | 34.0000 | 1.29062 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.50000 | + | 4.33013i | −0.0947623 | + | 0.164133i | ||||
\(697\) | − | 4.00000i | − | 0.151511i | ||||||
\(698\) | 17.3205 | + | 10.0000i | 0.655591 | + | 0.378506i | ||||
\(699\) | −0.500000 | − | 0.866025i | −0.0189117 | − | 0.0327561i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0000 | 0.491003 | 0.245502 | − | 0.969396i | \(-0.421047\pi\) | ||||
0.245502 | + | 0.969396i | \(0.421047\pi\) | |||||||
\(702\) | −0.866025 | − | 3.50000i | −0.0326860 | − | 0.132099i | ||||
\(703\) | − | 6.00000i | − | 0.226294i | ||||||
\(704\) | −2.50000 | − | 4.33013i | −0.0942223 | − | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 15.5885i | −0.338719 | + | 0.586679i | ||||
\(707\) | 4.00000i | 0.150435i | ||||||||
\(708\) | −12.9904 | − | 7.50000i | −0.488208 | − | 0.281867i | ||||
\(709\) | −4.00000 | + | 6.92820i | −0.150223 | + | 0.260194i | −0.931309 | − | 0.364229i | \(-0.881333\pi\) |
0.781086 | + | 0.624423i | \(0.214666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.50000 | − | 9.52628i | 0.206266 | − | 0.357263i | ||||
\(712\) | 1.73205 | − | 1.00000i | 0.0649113 | − | 0.0374766i | ||||
\(713\) | 9.52628 | − | 5.50000i | 0.356762 | − | 0.205977i | ||||
\(714\) | −4.00000 | −0.149696 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.0000 | −0.485833 | ||||||||
\(717\) | −17.3205 | + | 10.0000i | −0.646846 | + | 0.373457i | ||||
\(718\) | −10.3923 | + | 6.00000i | −0.387837 | + | 0.223918i | ||||
\(719\) | 12.0000 | − | 20.7846i | 0.447524 | − | 0.775135i | −0.550700 | − | 0.834703i | \(-0.685639\pi\) |
0.998224 | + | 0.0595683i | \(0.0189724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0000 | − | 17.3205i | 0.372419 | − | 0.645049i | ||||
\(722\) | 12.9904 | + | 7.50000i | 0.483452 | + | 0.279121i | ||||
\(723\) | 7.00000i | 0.260333i | ||||||||
\(724\) | −8.00000 | + | 13.8564i | −0.297318 | + | 0.514969i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.00000 | − | 12.1244i | −0.259794 | − | 0.449977i | ||||
\(727\) | 40.0000i | 1.48352i | 0.670667 | + | 0.741759i | \(0.266008\pi\) | ||||
−0.670667 | + | 0.741759i | \(0.733992\pi\) | |||||||
\(728\) | 5.19615 | − | 5.00000i | 0.192582 | − | 0.185312i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0000 | − | 19.0526i | −0.406850 | − | 0.704684i | ||||
\(732\) | −8.66025 | − | 5.00000i | −0.320092 | − | 0.184805i | ||||
\(733\) | 6.00000i | 0.221615i | 0.993842 | + | 0.110808i | \(0.0353437\pi\) | ||||
−0.993842 | + | 0.110808i | \(0.964656\pi\) | |||||||
\(734\) | 8.00000 | − | 13.8564i | 0.295285 | − | 0.511449i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −69.2820 | − | 40.0000i | −2.55204 | − | 1.47342i | ||||
\(738\) | 1.73205 | − | 1.00000i | 0.0637577 | − | 0.0368105i | ||||
\(739\) | 22.0000 | + | 38.1051i | 0.809283 | + | 1.40172i | 0.913361 | + | 0.407150i | \(0.133477\pi\) |
−0.104078 | + | 0.994569i | \(0.533189\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | + | 6.92820i | −0.0734718 | + | 0.254514i | ||||
\(742\) | − | 12.0000i | − | 0.440534i | ||||||
\(743\) | 44.1673 | − | 25.5000i | 1.62034 | − | 0.935504i | 0.633513 | − | 0.773732i | \(-0.281612\pi\) |
0.986828 | − | 0.161772i | \(-0.0517209\pi\) | |||||||
\(744\) | −5.50000 | − | 9.52628i | −0.201640 | − | 0.349250i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.0000 | 0.695639 | ||||||||
\(747\) | 5.19615 | + | 3.00000i | 0.190117 | + | 0.109764i | ||||
\(748\) | −8.66025 | − | 5.00000i | −0.316650 | − | 0.182818i | ||||
\(749\) | 20.0000 | 0.730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.5000 | + | 19.9186i | 0.419641 | + | 0.726839i | 0.995903 | − | 0.0904254i | \(-0.0288227\pi\) |
−0.576262 | + | 0.817265i | \(0.695489\pi\) | |||||||
\(752\) | −7.79423 | + | 4.50000i | −0.284226 | + | 0.164098i | ||||
\(753\) | − | 25.0000i | − | 0.911051i | ||||||
\(754\) | −12.5000 | − | 12.9904i | −0.455223 | − | 0.473082i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.00000 | − | 1.73205i | −0.0363696 | − | 0.0629941i | ||||
\(757\) | −8.66025 | + | 5.00000i | −0.314762 | + | 0.181728i | −0.649056 | − | 0.760741i | \(-0.724836\pi\) |
0.334293 | + | 0.942469i | \(0.391502\pi\) | |||||||
\(758\) | −1.73205 | − | 1.00000i | −0.0629109 | − | 0.0363216i | ||||
\(759\) | 5.00000 | 0.181489 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0000 | + | 17.3205i | −0.362500 | + | 0.627868i | −0.988372 | − | 0.152058i | \(-0.951410\pi\) |
0.625872 | + | 0.779926i | \(0.284743\pi\) | |||||||
\(762\) | − | 2.00000i | − | 0.0724524i | ||||||
\(763\) | −3.46410 | − | 2.00000i | −0.125409 | − | 0.0724049i | ||||
\(764\) | 2.00000 | + | 3.46410i | 0.0723575 | + | 0.125327i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.0000 | −1.12008 | ||||||||
\(767\) | 38.9711 | − | 37.5000i | 1.40717 | − | 1.35405i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 21.5000 | + | 37.2391i | 0.775310 | + | 1.34288i | 0.934620 | + | 0.355647i | \(0.115740\pi\) |
−0.159310 | + | 0.987229i | \(0.550927\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.50000 | + | 14.7224i | −0.306120 | + | 0.530215i | ||||
\(772\) | 24.0000i | 0.863779i | ||||||||
\(773\) | −27.7128 | − | 16.0000i | −0.996761 | − | 0.575480i | −0.0894724 | − | 0.995989i | \(-0.528518\pi\) |
−0.907288 | + | 0.420509i | \(0.861851\pi\) | |||||||
\(774\) | 5.50000 | − | 9.52628i | 0.197693 | − | 0.342415i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.00000 | + | 1.73205i | −0.0358979 | + | 0.0621770i | ||||
\(777\) | −5.19615 | + | 3.00000i | −0.186411 | + | 0.107624i | ||||
\(778\) | −4.33013 | + | 2.50000i | −0.155243 | + | 0.0896293i | ||||
\(779\) | −4.00000 | −0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.73205 | − | 1.00000i | 0.0619380 | − | 0.0357599i | ||||
\(783\) | −4.33013 | + | 2.50000i | −0.154746 | + | 0.0893427i | ||||
\(784\) | −1.50000 | + | 2.59808i | −0.0535714 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.500000 | − | 0.866025i | 0.0178344 | − | 0.0308901i | ||||
\(787\) | −26.8468 | − | 15.5000i | −0.956985 | − | 0.552515i | −0.0617409 | − | 0.998092i | \(-0.519665\pi\) |
−0.895244 | + | 0.445577i | \(0.852999\pi\) | |||||||
\(788\) | − | 8.00000i | − | 0.284988i | ||||||
\(789\) | −10.5000 | + | 18.1865i | −0.373810 | + | 0.647458i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.0000 | + | 19.0526i | 0.391115 | + | 0.677431i | ||||
\(792\) | − | 5.00000i | − | 0.177667i | ||||||
\(793\) | 25.9808 | − | 25.0000i | 0.922604 | − | 0.887776i | ||||
\(794\) | 3.00000 | 0.106466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.0000 | − | 20.7846i | −0.425329 | − | 0.736691i | ||||
\(797\) | 10.3923 | + | 6.00000i | 0.368114 | + | 0.212531i | 0.672634 | − | 0.739975i | \(-0.265163\pi\) |
−0.304520 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(798\) | 4.00000i | 0.141598i | ||||||||
\(799\) | −9.00000 | + | 15.5885i | −0.318397 | + | 0.551480i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | −31.1769 | − | 18.0000i | −1.10090 | − | 0.635602i | ||||
\(803\) | 25.9808 | − | 15.0000i | 0.916841 | − | 0.529339i | ||||
\(804\) | −8.00000 | − | 13.8564i | −0.282138 | − | 0.488678i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 38.5000 | − | 9.52628i | 1.35610 | − | 0.335549i | ||||
\(807\) | 14.0000i | 0.492823i | ||||||||
\(808\) | −1.73205 | + | 1.00000i | −0.0609333 | + | 0.0351799i | ||||
\(809\) | −15.0000 | − | 25.9808i | −0.527372 | − | 0.913435i | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
0.472119 | − | 0.881535i | \(-0.343489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −8.66025 | − | 5.00000i | −0.303915 | − | 0.175466i | ||||
\(813\) | −11.2583 | − | 6.50000i | −0.394847 | − | 0.227965i | ||||
\(814\) | −15.0000 | −0.525750 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.00000 | − | 1.73205i | −0.0350070 | − | 0.0606339i | ||||
\(817\) | −19.0526 | + | 11.0000i | −0.666565 | + | 0.384841i | ||||
\(818\) | − | 30.0000i | − | 1.04893i | ||||||
\(819\) | 7.00000 | − | 1.73205i | 0.244600 | − | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5000 | + | 44.1673i | 0.889956 | + | 1.54145i | 0.839926 | + | 0.542702i | \(0.182599\pi\) |
0.0500305 | + | 0.998748i | \(0.484068\pi\) | |||||||
\(822\) | 9.52628 | − | 5.50000i | 0.332267 | − | 0.191835i | ||||
\(823\) | 1.73205 | + | 1.00000i | 0.0603755 | + | 0.0348578i | 0.529884 | − | 0.848070i | \(-0.322235\pi\) |
−0.469508 | + | 0.882928i | \(0.655569\pi\) | |||||||
\(824\) | 10.0000 | 0.348367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0000 | − | 25.9808i | 0.521917 | − | 0.903986i | ||||
\(827\) | 50.0000i | 1.73867i | 0.494223 | + | 0.869335i | \(0.335453\pi\) | ||||
−0.494223 | + | 0.869335i | \(0.664547\pi\) | |||||||
\(828\) | 0.866025 | + | 0.500000i | 0.0300965 | + | 0.0173762i | ||||
\(829\) | 7.00000 | + | 12.1244i | 0.243120 | + | 0.421096i | 0.961601 | − | 0.274450i | \(-0.0884958\pi\) |
−0.718481 | + | 0.695546i | \(0.755162\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0000 | 0.381586 | ||||||||
\(832\) | 3.46410 | + | 1.00000i | 0.120096 | + | 0.0346688i | ||||
\(833\) | 6.00000i | 0.207888i | ||||||||
\(834\) | 1.00000 | + | 1.73205i | 0.0346272 | + | 0.0599760i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.00000 | + | 8.66025i | −0.172929 | + | 0.299521i | ||||
\(837\) | − | 11.0000i | − | 0.380216i | ||||||
\(838\) | −3.46410 | − | 2.00000i | −0.119665 | − | 0.0690889i | ||||
\(839\) | −27.0000 | + | 46.7654i | −0.932144 | + | 1.61452i | −0.152493 | + | 0.988304i | \(0.548730\pi\) |
−0.779650 | + | 0.626215i | \(0.784603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | −13.8564 | + | 8.00000i | −0.477523 | + | 0.275698i | ||||
\(843\) | 8.66025 | − | 5.00000i | 0.298275 | − | 0.172209i | ||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 24.2487 | − | 14.0000i | 0.833196 | − | 0.481046i | ||||
\(848\) | 5.19615 | − | 3.00000i | 0.178437 | − | 0.103020i | ||||
\(849\) | −9.50000 | + | 16.4545i | −0.326039 | + | 0.564716i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.50000 | − | 2.59808i | 0.0514193 | − | 0.0890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 49.0000i | − | 1.67773i | −0.544341 | − | 0.838864i | \(-0.683220\pi\) | ||
0.544341 | − | 0.838864i | \(-0.316780\pi\) | |||||||
\(854\) | 10.0000 | − | 17.3205i | 0.342193 | − | 0.592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.00000 | + | 8.66025i | 0.170896 | + | 0.296001i | ||||
\(857\) | 25.0000i | 0.853984i | 0.904255 | + | 0.426992i | \(0.140427\pi\) | ||||
−0.904255 | + | 0.426992i | \(0.859573\pi\) | |||||||
\(858\) | 17.3205 | + | 5.00000i | 0.591312 | + | 0.170697i | ||||
\(859\) | 50.0000 | 1.70598 | 0.852989 | − | 0.521929i | \(-0.174787\pi\) | ||||
0.852989 | + | 0.521929i | \(0.174787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.00000 | + | 3.46410i | 0.0681598 | + | 0.118056i | ||||
\(862\) | −34.6410 | − | 20.0000i | −1.17988 | − | 0.681203i | ||||
\(863\) | 39.0000i | 1.32758i | 0.747921 | + | 0.663788i | \(0.231052\pi\) | ||||
−0.747921 | + | 0.663788i | \(0.768948\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.0000 | −0.951479 | ||||||||
\(867\) | 11.2583 | + | 6.50000i | 0.382353 | + | 0.220752i | ||||
\(868\) | 19.0526 | − | 11.0000i | 0.646686 | − | 0.373364i | ||||
\(869\) | 27.5000 | + | 47.6314i | 0.932874 | + | 1.61578i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.0000 | − | 13.8564i | 1.89749 | − | 0.469506i | ||||
\(872\) | − | 2.00000i | − | 0.0677285i | ||||||
\(873\) | −1.73205 | + | 1.00000i | −0.0586210 | + | 0.0338449i | ||||
\(874\) | −1.00000 | − | 1.73205i | −0.0338255 | − | 0.0585875i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | −16.4545 | − | 9.50000i | −0.555628 | − | 0.320792i | 0.195761 | − | 0.980652i | \(-0.437282\pi\) |
−0.751389 | + | 0.659860i | \(0.770616\pi\) | |||||||
\(878\) | −3.46410 | − | 2.00000i | −0.116908 | − | 0.0674967i | ||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.00000 | + | 15.5885i | 0.303218 | + | 0.525188i | 0.976863 | − | 0.213866i | \(-0.0686057\pi\) |
−0.673645 | + | 0.739055i | \(0.735272\pi\) | |||||||
\(882\) | −2.59808 | + | 1.50000i | −0.0874818 | + | 0.0505076i | ||||
\(883\) | − | 1.00000i | − | 0.0336527i | −0.999858 | − | 0.0168263i | \(-0.994644\pi\) | ||
0.999858 | − | 0.0168263i | \(-0.00535624\pi\) | |||||||
\(884\) | 7.00000 | − | 1.73205i | 0.235435 | − | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.0000 | + | 17.3205i | 0.335957 | + | 0.581894i | ||||
\(887\) | −2.59808 | + | 1.50000i | −0.0872349 | + | 0.0503651i | −0.542983 | − | 0.839744i | \(-0.682705\pi\) |
0.455748 | + | 0.890109i | \(0.349372\pi\) | |||||||
\(888\) | −2.59808 | − | 1.50000i | −0.0871857 | − | 0.0503367i | ||||
\(889\) | 4.00000 | 0.134156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | − | 26.0000i | − | 0.870544i | ||||||
\(893\) | 15.5885 | + | 9.00000i | 0.521648 | + | 0.301174i | ||||
\(894\) | 8.50000 | + | 14.7224i | 0.284283 | + | 0.492392i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | −2.59808 | + | 2.50000i | −0.0867472 | + | 0.0834726i | ||||
\(898\) | − | 12.0000i | − | 0.400445i | ||||||
\(899\) | −27.5000 | − | 47.6314i | −0.917176 | − | 1.58860i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | − | 10.3923i | 0.199889 | − | 0.346218i | ||||
\(902\) | 10.0000i | 0.332964i | ||||||||
\(903\) | 19.0526 | + | 11.0000i | 0.634029 | + | 0.366057i | ||||
\(904\) | −5.50000 | + | 9.52628i | −0.182927 | + | 0.316839i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.00000 | + | 6.92820i | −0.132891 | + | 0.230174i | ||||
\(907\) | −16.4545 | + | 9.50000i | −0.546362 | + | 0.315442i | −0.747653 | − | 0.664089i | \(-0.768820\pi\) |
0.201291 | + | 0.979531i | \(0.435486\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0000 | −0.596367 | −0.298183 | − | 0.954509i | \(-0.596381\pi\) | ||||
−0.298183 | + | 0.954509i | \(0.596381\pi\) | |||||||
\(912\) | −1.73205 | + | 1.00000i | −0.0573539 | + | 0.0331133i | ||||
\(913\) | −25.9808 | + | 15.0000i | −0.859838 | + | 0.496428i | ||||
\(914\) | −19.0000 | + | 32.9090i | −0.628464 | + | 1.08853i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.00000 | + | 8.66025i | −0.165205 | + | 0.286143i | ||||
\(917\) | 1.73205 | + | 1.00000i | 0.0571974 | + | 0.0330229i | ||||
\(918\) | − | 2.00000i | − | 0.0660098i | ||||||
\(919\) | −8.00000 | + | 13.8564i | −0.263896 | + | 0.457081i | −0.967274 | − | 0.253735i | \(-0.918341\pi\) |
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 39.0000i | − | 1.28440i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 10.0000 | 0.328976 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.00000 | + | 12.1244i | 0.230034 | + | 0.398431i | ||||
\(927\) | 8.66025 | + | 5.00000i | 0.284440 | + | 0.164222i | ||||
\(928\) | − | 5.00000i | − | 0.164133i | ||||||
\(929\) | −8.00000 | + | 13.8564i | −0.262471 | + | 0.454614i | −0.966898 | − | 0.255163i | \(-0.917871\pi\) |
0.704427 | + | 0.709777i | \(0.251204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | 0.866025 | + | 0.500000i | 0.0283676 | + | 0.0163780i | ||||
\(933\) | −17.3205 | + | 10.0000i | −0.567048 | + | 0.327385i | ||||
\(934\) | −3.00000 | − | 5.19615i | −0.0981630 | − | 0.170023i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.50000 | + | 2.59808i | 0.0817151 | + | 0.0849208i | ||||
\(937\) | 50.0000i | 1.63343i | 0.577042 | + | 0.816714i | \(0.304207\pi\) | ||||
−0.577042 | + | 0.816714i | \(0.695793\pi\) | |||||||
\(938\) | 27.7128 | − | 16.0000i | 0.904855 | − | 0.522419i | ||||
\(939\) | −10.0000 | − | 17.3205i | −0.326338 | − | 0.565233i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.0000 | −1.62995 | −0.814977 | − | 0.579494i | \(-0.803250\pi\) | ||||
−0.814977 | + | 0.579494i | \(0.803250\pi\) | |||||||
\(942\) | −6.06218 | − | 3.50000i | −0.197516 | − | 0.114036i | ||||
\(943\) | −1.73205 | − | 1.00000i | −0.0564033 | − | 0.0325645i | ||||
\(944\) | 15.0000 | 0.488208 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.5000 | + | 47.6314i | 0.894102 | + | 1.54863i | ||||
\(947\) | −6.92820 | + | 4.00000i | −0.225136 | + | 0.129983i | −0.608326 | − | 0.793687i | \(-0.708159\pi\) |
0.383190 | + | 0.923670i | \(0.374825\pi\) | |||||||
\(948\) | 11.0000i | 0.357263i | ||||||||
\(949\) | −6.00000 | + | 20.7846i | −0.194768 | + | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.00000 | + | 13.8564i | 0.259418 | + | 0.449325i | ||||
\(952\) | 3.46410 | − | 2.00000i | 0.112272 | − | 0.0648204i | ||||
\(953\) | 44.1673 | + | 25.5000i | 1.43072 | + | 0.826026i | 0.997176 | − | 0.0751066i | \(-0.0239297\pi\) |
0.433544 | + | 0.901133i | \(0.357263\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.0000 | − | 17.3205i | 0.323423 | − | 0.560185i | ||||
\(957\) | − | 25.0000i | − | 0.808135i | ||||||
\(958\) | −20.7846 | − | 12.0000i | −0.671520 | − | 0.387702i | ||||
\(959\) | 11.0000 | + | 19.0526i | 0.355209 | + | 0.615239i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 90.0000 | 2.90323 | ||||||||
\(962\) | 7.79423 | − | 7.50000i | 0.251296 | − | 0.241810i | ||||
\(963\) | 10.0000i | 0.322245i | ||||||||
\(964\) | −3.50000 | − | 6.06218i | −0.112727 | − | 0.195250i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.00000 | + | 1.73205i | −0.0321745 | + | 0.0557278i | ||||
\(967\) | − | 20.0000i | − | 0.643157i | −0.946883 | − | 0.321578i | \(-0.895787\pi\) | ||
0.946883 | − | 0.321578i | \(-0.104213\pi\) | |||||||
\(968\) | 12.1244 | + | 7.00000i | 0.389692 | + | 0.224989i | ||||
\(969\) | −2.00000 | + | 3.46410i | −0.0642493 | + | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0000 | + | 41.5692i | −0.770197 | + | 1.33402i | 0.167258 | + | 0.985913i | \(0.446509\pi\) |
−0.937455 | + | 0.348107i | \(0.886825\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −3.46410 | + | 2.00000i | −0.111054 | + | 0.0641171i | ||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 18.1865 | − | 10.5000i | 0.581839 | − | 0.335925i | −0.180025 | − | 0.983662i | \(-0.557618\pi\) |
0.761864 | + | 0.647737i | \(0.224285\pi\) | |||||||
\(978\) | −12.9904 | + | 7.50000i | −0.415387 | + | 0.239824i | ||||
\(979\) | −5.00000 | + | 8.66025i | −0.159801 | + | 0.276783i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.00000 | − | 1.73205i | 0.0319275 | − | 0.0553001i | ||||
\(982\) | 13.8564 | + | 8.00000i | 0.442176 | + | 0.255290i | ||||
\(983\) | − | 3.00000i | − | 0.0956851i | −0.998855 | − | 0.0478426i | \(-0.984765\pi\) | ||
0.998855 | − | 0.0478426i | \(-0.0152346\pi\) | |||||||
\(984\) | −1.00000 | + | 1.73205i | −0.0318788 | + | 0.0552158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.00000 | − | 8.66025i | −0.159232 | − | 0.275799i | ||||
\(987\) | − | 18.0000i | − | 0.572946i | ||||||
\(988\) | −1.73205 | − | 7.00000i | −0.0551039 | − | 0.222700i | ||||
\(989\) | −11.0000 | −0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.50000 | + | 14.7224i | 0.270011 | + | 0.467673i | 0.968864 | − | 0.247592i | \(-0.0796392\pi\) |
−0.698853 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(992\) | 9.52628 | + | 5.50000i | 0.302460 | + | 0.174625i | ||||
\(993\) | 28.0000i | 0.888553i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | −1.73205 | − | 1.00000i | −0.0548546 | − | 0.0316703i | 0.472322 | − | 0.881426i | \(-0.343416\pi\) |
−0.527176 | + | 0.849756i | \(0.676749\pi\) | |||||||
\(998\) | −24.2487 | + | 14.0000i | −0.767580 | + | 0.443162i | ||||
\(999\) | −1.50000 | − | 2.59808i | −0.0474579 | − | 0.0821995i |
(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 | 1950.2.z.e.1849.2 | 4 | ||
5.2 | odd | 4 | 390.2.i.f.211.1 | yes | 2 | ||
5.3 | odd | 4 | 1950.2.i.d.601.1 | 2 | |||
5.4 | even | 2 | inner | 1950.2.z.e.1849.1 | 4 | ||
13.9 | even | 3 | inner | 1950.2.z.e.1699.1 | 4 | ||
15.2 | even | 4 | 1170.2.i.a.991.1 | 2 | |||
65.2 | even | 12 | 5070.2.b.h.1351.2 | 2 | |||
65.9 | even | 6 | inner | 1950.2.z.e.1699.2 | 4 | ||
65.22 | odd | 12 | 390.2.i.f.61.1 | ✓ | 2 | ||
65.37 | even | 12 | 5070.2.b.h.1351.1 | 2 | |||
65.42 | odd | 12 | 5070.2.a.d.1.1 | 1 | |||
65.48 | odd | 12 | 1950.2.i.d.451.1 | 2 | |||
65.62 | odd | 12 | 5070.2.a.p.1.1 | 1 | |||
195.152 | even | 12 | 1170.2.i.a.451.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.f.61.1 | ✓ | 2 | 65.22 | odd | 12 | ||
390.2.i.f.211.1 | yes | 2 | 5.2 | odd | 4 | ||
1170.2.i.a.451.1 | 2 | 195.152 | even | 12 | |||
1170.2.i.a.991.1 | 2 | 15.2 | even | 4 | |||
1950.2.i.d.451.1 | 2 | 65.48 | odd | 12 | |||
1950.2.i.d.601.1 | 2 | 5.3 | odd | 4 | |||
1950.2.z.e.1699.1 | 4 | 13.9 | even | 3 | inner | ||
1950.2.z.e.1699.2 | 4 | 65.9 | even | 6 | inner | ||
1950.2.z.e.1849.1 | 4 | 5.4 | even | 2 | inner | ||
1950.2.z.e.1849.2 | 4 | 1.1 | even | 1 | trivial | ||
5070.2.a.d.1.1 | 1 | 65.42 | odd | 12 | |||
5070.2.a.p.1.1 | 1 | 65.62 | odd | 12 | |||
5070.2.b.h.1351.1 | 2 | 65.37 | even | 12 | |||
5070.2.b.h.1351.2 | 2 | 65.2 | even | 12 |