Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), 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: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.11337408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 18x^{4} + 81x^{2} + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(-0.391571i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.961 |
Dual form | 1960.2.q.w.361.3 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.29211 | + | 2.23800i | 0.746002 | + | 1.29211i | 0.949725 | + | 0.313084i | \(0.101362\pi\) |
−0.203724 | + | 0.979028i | \(0.565304\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.83911 | + | 3.18543i | −0.613037 | + | 1.06181i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.839111 | − | 1.45338i | −0.253001 | − | 0.438211i | 0.711349 | − | 0.702839i | \(-0.248084\pi\) |
−0.964351 | + | 0.264627i | \(0.914751\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.84667 | 1.34422 | 0.672112 | − | 0.740449i | \(-0.265387\pi\) | ||||
0.672112 | + | 0.740449i | \(0.265387\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.58423 | 0.667244 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.42334 | − | 5.92939i | 0.785367 | − | 1.36030i | −0.143412 | − | 0.989663i | \(-0.545808\pi\) |
0.928779 | − | 0.370633i | \(-0.120859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.13122 | − | 1.95934i | 0.235876 | − | 0.408550i | −0.723651 | − | 0.690166i | \(-0.757537\pi\) |
0.959527 | + | 0.281617i | \(0.0908706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.75268 | −0.337303 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.32178 | 0.616839 | 0.308419 | − | 0.951250i | \(-0.400200\pi\) | ||||
0.308419 | + | 0.951250i | \(0.400200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.58423 | + | 7.94011i | 0.823351 | + | 1.42609i | 0.903173 | + | 0.429277i | \(0.141232\pi\) |
−0.0798217 | + | 0.996809i | \(0.525435\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.16845 | − | 3.75587i | 0.377479 | − | 0.653813i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.42334 | − | 2.46529i | 0.233995 | − | 0.405291i | −0.724985 | − | 0.688765i | \(-0.758153\pi\) |
0.958980 | + | 0.283473i | \(0.0914867\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.26245 | + | 10.8469i | 1.00279 | + | 1.73689i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.52489 | −1.48754 | −0.743769 | − | 0.668437i | \(-0.766964\pi\) | ||||
−0.743769 | + | 0.668437i | \(0.766964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.58423 | 1.00408 | 0.502042 | − | 0.864843i | \(-0.332582\pi\) | ||||
0.502042 | + | 0.864843i | \(0.332582\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.83911 | + | 3.18543i | 0.274158 | + | 0.474856i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.10156 | + | 10.5682i | −0.890004 | + | 1.54153i | −0.0501344 | + | 0.998742i | \(0.515965\pi\) |
−0.839869 | + | 0.542789i | \(0.817368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.58423 | + | 4.47601i | −0.361864 | + | 0.626767i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.74511 | − | 6.48673i | −0.514431 | − | 0.891021i | −0.999860 | − | 0.0167445i | \(-0.994670\pi\) |
0.485429 | − | 0.874276i | \(-0.338664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.67822 | −0.226291 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.6933 | 2.34354 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | + | 6.92820i | 0.520756 | + | 0.901975i | 0.999709 | + | 0.0241347i | \(0.00768307\pi\) |
−0.478953 | + | 0.877841i | \(0.658984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.24511 | + | 5.62070i | −0.415494 | + | 0.719657i | −0.995480 | − | 0.0949692i | \(-0.969725\pi\) |
0.579986 | + | 0.814627i | \(0.303058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.42334 | − | 4.19734i | 0.300578 | − | 0.520616i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.87634 | + | 4.98196i | 0.351401 | + | 0.608644i | 0.986495 | − | 0.163791i | \(-0.0523722\pi\) |
−0.635094 | + | 0.772434i | \(0.719039\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.84667 | 0.703857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.84667 | − | 10.1267i | −0.684301 | − | 1.18524i | −0.973656 | − | 0.228022i | \(-0.926774\pi\) |
0.289355 | − | 0.957222i | \(-0.406559\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.29211 | − | 2.23800i | 0.149200 | − | 0.258423i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.84667 | + | 4.93058i | −0.320276 | + | 0.554734i | −0.980545 | − | 0.196295i | \(-0.937109\pi\) |
0.660269 | + | 0.751029i | \(0.270442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.25268 | + | 5.63380i | 0.361408 | + | 0.625978i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.5842 | 1.38130 | 0.690649 | − | 0.723190i | \(-0.257325\pi\) | ||||
0.690649 | + | 0.723190i | \(0.257325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.29211 | + | 7.43416i | 0.460163 | + | 0.797025i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.92334 | + | 5.06337i | −0.309873 | + | 0.536716i | −0.978334 | − | 0.207031i | \(-0.933620\pi\) |
0.668461 | + | 0.743747i | \(0.266953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.8467 | + | 20.5190i | −1.22844 | + | 2.12773i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.42334 | − | 5.92939i | −0.351227 | − | 0.608343i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.17287 | 0.620397 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.50756 | − | 14.7355i | −0.846534 | − | 1.46624i | −0.884282 | − | 0.466953i | \(-0.845352\pi\) |
0.0377483 | − | 0.999287i | \(-0.487981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.55456 | − | 6.15668i | 0.350241 | − | 0.606635i | −0.636050 | − | 0.771648i | \(-0.719433\pi\) |
0.986292 | + | 0.165012i | \(0.0527663\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.876338 | − | 1.51786i | 0.0847188 | − | 0.146737i | −0.820553 | − | 0.571571i | \(-0.806334\pi\) |
0.905271 | + | 0.424834i | \(0.139667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.77001 | − | 16.9222i | −0.935797 | − | 1.62085i | −0.773206 | − | 0.634154i | \(-0.781348\pi\) |
−0.162591 | − | 0.986694i | \(-0.551985\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.35644 | 0.698243 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3369 | 0.972414 | 0.486207 | − | 0.873844i | \(-0.338380\pi\) | ||||
0.486207 | + | 0.873844i | \(0.338380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.13122 | − | 1.95934i | −0.105487 | − | 0.182709i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.91357 | + | 15.4387i | −0.824059 | + | 1.42731i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.09179 | − | 7.08718i | 0.371981 | − | 0.644289i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.3072 | − | 21.3168i | −1.10971 | − | 1.92207i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.1836 | −1.70227 | −0.851133 | − | 0.524949i | \(-0.824084\pi\) | ||||
−0.851133 | + | 0.524949i | \(0.824084\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.50756 | + | 14.7355i | 0.749049 | + | 1.29739i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.91357 | + | 15.4387i | −0.778782 | + | 1.34889i | 0.153862 | + | 0.988092i | \(0.450829\pi\) |
−0.932644 | + | 0.360797i | \(0.882505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.876338 | + | 1.51786i | −0.0754232 | + | 0.130637i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | − | 3.46410i | −0.170872 | − | 0.295958i | 0.767853 | − | 0.640626i | \(-0.221325\pi\) |
−0.938725 | + | 0.344668i | \(0.887992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.16845 | 0.438382 | 0.219191 | − | 0.975682i | \(-0.429658\pi\) | ||||
0.219191 | + | 0.975682i | \(0.429658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.5356 | −2.65578 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.06689 | − | 7.04407i | −0.340091 | − | 0.589054i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.66089 | − | 2.87674i | 0.137929 | − | 0.238901i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.398443 | + | 0.690123i | −0.0326417 | + | 0.0565371i | −0.881885 | − | 0.471465i | \(-0.843725\pi\) |
0.849243 | + | 0.528002i | \(0.177059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.26245 | + | 14.3110i | 0.672388 | + | 1.16461i | 0.977225 | + | 0.212206i | \(0.0680648\pi\) |
−0.304837 | + | 0.952405i | \(0.598602\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.35644 | −0.594733 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.16845 | 0.736428 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.10156 | + | 7.10411i | 0.327340 | + | 0.566969i | 0.981983 | − | 0.188969i | \(-0.0605145\pi\) |
−0.654643 | + | 0.755938i | \(0.727181\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.67822 | − | 16.7632i | 0.767533 | − | 1.32941i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.84667 | + | 3.19853i | −0.144643 | + | 0.250528i | −0.929240 | − | 0.369478i | \(-0.879537\pi\) |
0.784597 | + | 0.620006i | \(0.212870\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.16845 | − | 3.75587i | −0.168814 | − | 0.292394i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.262447 | 0.0203087 | 0.0101544 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101544 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4902 | 0.806941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.5918 | + | 21.8096i | 0.962918 | + | 1.66782i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.42334 | + | 16.3217i | −0.716443 | + | 1.24092i | 0.245957 | + | 0.969281i | \(0.420898\pi\) |
−0.962400 | + | 0.271635i | \(0.912436\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.3369 | + | 17.9040i | −0.776969 | + | 1.34575i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00756 | + | 10.4054i | 0.449026 | + | 0.777736i | 0.998323 | − | 0.0578912i | \(-0.0184376\pi\) |
−0.549297 | + | 0.835627i | \(0.685104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.03466 | 0.448553 | 0.224276 | − | 0.974526i | \(-0.427998\pi\) | ||||
0.224276 | + | 0.974526i | \(0.427998\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.7722 | −1.23984 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.42334 | − | 2.46529i | −0.104646 | − | 0.181252i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.67822 | − | 2.90676i | 0.122724 | − | 0.212564i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.41577 | + | 2.45219i | −0.102442 | + | 0.177434i | −0.912690 | − | 0.408652i | \(-0.865999\pi\) |
0.810248 | + | 0.586087i | \(0.199332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.49023 | − | 11.2414i | −0.467177 | − | 0.809174i | 0.532120 | − | 0.846669i | \(-0.321396\pi\) |
−0.999297 | + | 0.0374948i | \(0.988062\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.5249 | 0.896926 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.84667 | −0.345311 | −0.172656 | − | 0.984982i | \(-0.555235\pi\) | ||||
−0.172656 | + | 0.984982i | \(0.555235\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.69334 | − | 13.3253i | −0.545367 | − | 0.944603i | −0.998584 | − | 0.0532026i | \(-0.983057\pi\) |
0.453217 | − | 0.891400i | \(-0.350276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.43311 | + | 12.8745i | −0.524291 | + | 0.908098i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.76245 | + | 8.24880i | −0.332624 | + | 0.576121i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.16089 | + | 7.20687i | 0.289202 | + | 0.500912i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.4902 | −0.794796 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.18357 | 0.632223 | 0.316112 | − | 0.948722i | \(-0.397623\pi\) | ||||
0.316112 | + | 0.948722i | \(0.397623\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.29211 | − | 5.70211i | 0.224520 | − | 0.388880i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.1091 | − | 26.1698i | 1.02098 | − | 1.76839i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.84667 | + | 8.39468i | 0.326022 | + | 0.564687i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9805 | 0.869236 | 0.434618 | − | 0.900615i | \(-0.356883\pi\) | ||||
0.434618 | + | 0.900615i | \(0.356883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.67822 | 0.245215 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0151 | − | 19.0788i | −0.731099 | − | 1.26630i | −0.956414 | − | 0.292015i | \(-0.905674\pi\) |
0.225314 | − | 0.974286i | \(-0.427659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.15333 | − | 3.72967i | 0.142296 | − | 0.246464i | −0.786065 | − | 0.618144i | \(-0.787885\pi\) |
0.928361 | + | 0.371680i | \(0.121218\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.10156 | + | 10.5682i | 0.398022 | + | 0.689394i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7129 | −0.955705 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.8618 | 0.702591 | 0.351296 | − | 0.936265i | \(-0.385741\pi\) | ||||
0.351296 | + | 0.936265i | \(0.385741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.101557 | + | 0.175902i | 0.00654187 | + | 0.0113309i | 0.869278 | − | 0.494324i | \(-0.164584\pi\) |
−0.862736 | + | 0.505655i | \(0.831251\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0347 | + | 19.1126i | −0.707874 | + | 1.22607i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.5918 | − | 28.7378i | 1.05571 | − | 1.82854i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.2602 | + | 28.1636i | 1.03045 | + | 1.78479i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.03466 | −0.317785 | −0.158893 | − | 0.987296i | \(-0.550792\pi\) | ||||
−0.158893 | + | 0.987296i | \(0.550792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.79689 | −0.238708 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.58423 | + | 4.47601i | 0.161830 | + | 0.280299i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.6933 | − | 20.2535i | 0.729411 | − | 1.26338i | −0.227722 | − | 0.973726i | \(-0.573128\pi\) |
0.957133 | − | 0.289650i | \(-0.0935390\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.10912 | + | 10.5813i | −0.378145 | + | 0.654966i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5546 | − | 23.4772i | −0.835810 | − | 1.44767i | −0.893369 | − | 0.449323i | \(-0.851665\pi\) |
0.0575594 | − | 0.998342i | \(-0.481668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.49023 | −0.460121 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.1091 | −0.924663 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.24511 | + | 5.62070i | 0.197858 | + | 0.342700i | 0.947834 | − | 0.318765i | \(-0.103268\pi\) |
−0.749976 | + | 0.661466i | \(0.769935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6933 | + | 20.2535i | −0.710320 | + | 1.23031i | 0.254417 | + | 0.967095i | \(0.418116\pi\) |
−0.964737 | + | 0.263216i | \(0.915217\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.839111 | + | 1.45338i | −0.0506003 | + | 0.0876422i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.83155 | − | 3.17234i | −0.110047 | − | 0.190607i | 0.805742 | − | 0.592267i | \(-0.201767\pi\) |
−0.915789 | + | 0.401660i | \(0.868434\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −33.7236 | −2.01898 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8965 | 0.828993 | 0.414497 | − | 0.910051i | \(-0.363958\pi\) | ||||
0.414497 | + | 0.910051i | \(0.363958\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.1685 | − | 17.6123i | −0.604452 | − | 1.04694i | −0.992138 | − | 0.125150i | \(-0.960059\pi\) |
0.387686 | − | 0.921791i | \(-0.373274\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.84667 | − | 15.3229i | 0.524032 | − | 0.907649i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.58423 | + | 4.47601i | 0.151490 | + | 0.262388i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.8467 | −1.10103 | −0.550517 | − | 0.834824i | \(-0.685569\pi\) | ||||
−0.550517 | + | 0.834824i | \(0.685569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.47069 | + | 2.54731i | 0.0853380 | + | 0.147810i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.48267 | − | 9.49626i | 0.317071 | − | 0.549183i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.9855 | − | 38.0799i | 1.26303 | − | 2.18763i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.24511 | + | 5.62070i | 0.185815 | + | 0.321841i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.39623 | 0.136760 | 0.0683802 | − | 0.997659i | \(-0.478217\pi\) | ||||
0.0683802 | + | 0.997659i | \(0.478217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.3716 | 1.04512 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.83155 | − | 4.90439i | −0.160562 | − | 0.278102i | 0.774508 | − | 0.632564i | \(-0.217997\pi\) |
−0.935071 | + | 0.354462i | \(0.884664\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.8618 | − | 25.7414i | 0.840038 | − | 1.45499i | −0.0498231 | − | 0.998758i | \(-0.515866\pi\) |
0.889861 | − | 0.456231i | \(-0.150801\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.52489 | + | 16.4976i | −0.534971 | + | 0.926597i | 0.464193 | + | 0.885734i | \(0.346344\pi\) |
−0.999165 | + | 0.0408636i | \(0.986989\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.78734 | − | 4.82781i | −0.156061 | − | 0.270306i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.52931 | 0.252801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.6933 | 0.761918 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.42334 | − | 4.19734i | −0.134422 | − | 0.232827i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.2479 | − | 43.7307i | 1.39621 | − | 2.41831i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.16089 | + | 2.01072i | −0.0638083 | + | 0.110519i | −0.896165 | − | 0.443722i | \(-0.853658\pi\) |
0.832356 | + | 0.554241i | \(0.186991\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.23534 | + | 9.06788i | 0.286895 | + | 0.496917i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.75268 | 0.314302 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.4062 | −0.893704 | −0.446852 | − | 0.894608i | \(-0.647455\pi\) | ||||
−0.446852 | + | 0.894608i | \(0.647455\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.3564 | + | 23.1340i | 0.725422 | + | 1.25647i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.69334 | − | 13.3253i | 0.416618 | − | 0.721603i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.92334 | − | 5.06337i | 0.157387 | − | 0.272602i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.29211 | − | 3.97006i | −0.123047 | − | 0.213124i | 0.797921 | − | 0.602762i | \(-0.205933\pi\) |
−0.920968 | + | 0.389639i | \(0.872600\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3716 | −0.662235 | −0.331117 | − | 0.943590i | \(-0.607426\pi\) | ||||
−0.331117 | + | 0.943590i | \(0.607426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.49465 | −0.453411 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.69334 | + | 16.7894i | 0.515925 | + | 0.893608i | 0.999829 | + | 0.0184869i | \(0.00588489\pi\) |
−0.483904 | + | 0.875121i | \(0.660782\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.90600 | − | 8.49745i | 0.258929 | − | 0.448478i | −0.707026 | − | 0.707187i | \(-0.749964\pi\) |
0.965955 | + | 0.258709i | \(0.0832971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9385 | − | 24.1421i | −0.733603 | − | 1.27064i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.1482 | 1.10999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.6933 | −0.612058 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.35901 | − | 11.0141i | −0.331937 | − | 0.574933i | 0.650954 | − | 0.759117i | \(-0.274369\pi\) |
−0.982892 | + | 0.184184i | \(0.941036\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.5173 | − | 30.3409i | 0.911916 | − | 1.57948i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.20311 | − | 14.2082i | 0.424741 | − | 0.735673i | −0.571655 | − | 0.820494i | \(-0.693698\pi\) |
0.996396 | + | 0.0848208i | \(0.0270318\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.29211 | − | 2.23800i | −0.0667244 | − | 0.115570i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.0996 | 0.829170 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4707 | 0.743309 | 0.371655 | − | 0.928371i | \(-0.378791\pi\) | ||||
0.371655 | + | 0.928371i | \(0.378791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.7873 | − | 42.9329i | −1.26989 | − | 2.19952i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.77478 | + | 3.07401i | −0.0906871 | + | 0.157075i | −0.907800 | − | 0.419402i | \(-0.862240\pi\) |
0.817113 | + | 0.576477i | \(0.195573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.1091 | + | 20.9736i | −0.615541 | + | 1.06615i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.49023 | − | 7.77731i | −0.227664 | − | 0.394325i | 0.729452 | − | 0.684032i | \(-0.239775\pi\) |
−0.957115 | + | 0.289707i | \(0.906442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.52489 | 0.228834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −46.0693 | −2.32389 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.84667 | + | 4.93058i | 0.143232 | + | 0.248084i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0498 | + | 24.3349i | −0.705139 | + | 1.22134i | 0.261503 | + | 0.965203i | \(0.415782\pi\) |
−0.966642 | + | 0.256133i | \(0.917551\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3467 | − | 23.1171i | 0.666501 | − | 1.15441i | −0.312375 | − | 0.949959i | \(-0.601125\pi\) |
0.978876 | − | 0.204455i | \(-0.0655421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.2182 | + | 38.4831i | 1.10677 | + | 1.91698i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.50535 | 0.323254 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.77735 | −0.236804 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0325 | + | 24.3049i | 0.693860 | + | 1.20180i | 0.970563 | + | 0.240846i | \(0.0774248\pi\) |
−0.276703 | + | 0.960955i | \(0.589242\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.16845 | − | 8.95202i | 0.254941 | − | 0.441571i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.29211 | − | 10.8983i | 0.308868 | − | 0.534974i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.67822 | + | 11.5670i | 0.327034 | + | 0.566439i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.8769 | 0.922198 | 0.461099 | − | 0.887349i | \(-0.347455\pi\) | ||||
0.461099 | + | 0.887349i | \(0.347455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.1836 | −1.37358 | −0.686792 | − | 0.726854i | \(-0.740982\pi\) | ||||
−0.686792 | + | 0.726854i | \(0.740982\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.4429 | − | 38.8722i | −1.09121 | − | 1.89003i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.5098 | − | 18.2035i | 0.507416 | − | 0.878871i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.41577 | − | 2.45219i | −0.0681955 | − | 0.118118i | 0.829912 | − | 0.557895i | \(-0.188391\pi\) |
−0.898107 | + | 0.439777i | \(0.855057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.33690 | 0.112304 | 0.0561522 | − | 0.998422i | \(-0.482117\pi\) | ||||
0.0561522 | + | 0.998422i | \(0.482117\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.58423 | 0.411582 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.74511 | − | 13.4149i | −0.370499 | − | 0.641723i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.03466 | + | 5.25619i | −0.144837 | + | 0.250864i | −0.929312 | − | 0.369296i | \(-0.879599\pi\) |
0.784475 | + | 0.620160i | \(0.212932\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.80188 | + | 10.0492i | −0.275656 | + | 0.477450i | −0.970300 | − | 0.241903i | \(-0.922228\pi\) |
0.694645 | + | 0.719353i | \(0.255562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.92334 | + | 5.06337i | 0.138579 | + | 0.240027i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.05933 | −0.0974031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.13821 | 0.195294 | 0.0976470 | − | 0.995221i | \(-0.468868\pi\) | ||||
0.0976470 | + | 0.995221i | \(0.468868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.99244 | + | 13.8433i | 0.376349 | + | 0.651856i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.3520 | + | 36.9828i | −1.00321 | + | 1.73760i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.32178 | − | 10.9496i | 0.295720 | − | 0.512203i | −0.679432 | − | 0.733739i | \(-0.737774\pi\) |
0.975152 | + | 0.221536i | \(0.0711070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.75268 | − | 3.03572i | −0.0818079 | − | 0.141695i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.7129 | −0.964695 | −0.482348 | − | 0.875980i | \(-0.660216\pi\) | ||||
−0.482348 | + | 0.875980i | \(0.660216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.3811 | −0.761295 | −0.380647 | − | 0.924720i | \(-0.624299\pi\) | ||||
−0.380647 | + | 0.924720i | \(0.624299\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.8467 | + | 20.5190i | 0.549376 | + | 0.951548i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.861215 | + | 1.49167i | −0.0398523 | + | 0.0690262i | −0.885264 | − | 0.465090i | \(-0.846022\pi\) |
0.845411 | + | 0.534116i | \(0.179355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5993 | + | 18.3586i | −0.488392 | + | 0.845920i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.52489 | − | 9.56940i | −0.254035 | − | 0.440001i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.84667 | −0.314147 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.5507 | 1.26146 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.890881 | − | 1.54305i | −0.0407054 | − | 0.0705038i | 0.844955 | − | 0.534838i | \(-0.179627\pi\) |
−0.885660 | + | 0.464334i | \(0.846294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.89844 | − | 11.9485i | 0.314542 | − | 0.544803i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.50977 | + | 9.54320i | 0.249672 | + | 0.432444i | 0.963435 | − | 0.267943i | \(-0.0863440\pi\) |
−0.713763 | + | 0.700387i | \(0.753011\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.54443 | −0.431614 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.9311 | −0.944608 | −0.472304 | − | 0.881436i | \(-0.656578\pi\) | ||||
−0.472304 | + | 0.881436i | \(0.656578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.32178 | + | 5.75349i | 0.149605 | + | 0.259124i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.08643 | − | 5.34586i | 0.138725 | − | 0.240279i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.75268 | − | 6.49983i | 0.167993 | − | 0.290972i | −0.769721 | − | 0.638380i | \(-0.779605\pi\) |
0.937714 | + | 0.347408i | \(0.112938\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.339111 | + | 0.587357i | 0.0151503 | + | 0.0262412i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.5842 | −0.917805 | −0.458903 | − | 0.888487i | \(-0.651757\pi\) | ||||
−0.458903 | + | 0.888487i | \(0.651757\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0151 | −0.757163 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.5546 | + | 23.4772i | 0.601979 | + | 1.04266i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.82934 | − | 11.8288i | 0.302705 | − | 0.524301i | −0.674043 | − | 0.738693i | \(-0.735444\pi\) |
0.976748 | + | 0.214392i | \(0.0687769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.00000 | + | 10.3923i | −0.264906 | + | 0.458831i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.55456 | − | 6.15668i | −0.156633 | − | 0.271296i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.4795 | 0.900688 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.7040 | −2.13787 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0820 | − | 36.5151i | −0.923620 | − | 1.59976i | −0.793766 | − | 0.608224i | \(-0.791882\pi\) |
−0.129854 | − | 0.991533i | \(-0.541451\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.3218 | + | 26.5381i | −0.669975 | + | 1.16043i | 0.307936 | + | 0.951407i | \(0.400362\pi\) |
−0.977911 | + | 0.209023i | \(0.932972\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.16845 | + | 15.8802i | −0.399384 | + | 0.691753i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.94067 | + | 15.4857i | 0.388725 | + | 0.673291i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.4258 | −1.27697 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.1640 | −1.99959 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.876338 | − | 1.51786i | −0.0378874 | − | 0.0656229i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.5249 | + | 26.8899i | −0.669949 | + | 1.16038i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.8445 | − | 29.1755i | 0.724200 | − | 1.25435i | −0.235102 | − | 0.971971i | \(-0.575543\pi\) |
0.959302 | − | 0.282381i | \(-0.0911241\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.79747 | + | 13.5056i | 0.334621 | + | 0.579581i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.5400 | −0.837002 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.03979 | −0.129972 | −0.0649861 | − | 0.997886i | \(-0.520700\pi\) | ||||
−0.0649861 | + | 0.997886i | \(0.520700\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.9363 | − | 20.6742i | −0.509427 | − | 0.882353i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3716 | − | 19.6961i | 0.484445 | − | 0.839083i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.67822 | − | 6.37087i | 0.156132 | − | 0.270428i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.08202 | − | 15.7305i | −0.384817 | − | 0.666523i | 0.606926 | − | 0.794758i | \(-0.292402\pi\) |
−0.991744 | + | 0.128235i | \(0.959069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.9116 | 1.34972 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.67380 | 0.366208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4952 | − | 32.0347i | −0.779481 | − | 1.35010i | −0.932241 | − | 0.361837i | \(-0.882150\pi\) |
0.152760 | − | 0.988263i | \(-0.451184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.16845 | − | 8.95202i | 0.217438 | − | 0.376614i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.3047 | + | 28.2405i | −0.683527 | + | 1.18390i | 0.290370 | + | 0.956915i | \(0.406222\pi\) |
−0.973897 | + | 0.226990i | \(0.927112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2182 | − | 35.0190i | −0.846107 | − | 1.46550i | −0.884656 | − | 0.466243i | \(-0.845607\pi\) |
0.0385496 | − | 0.999257i | \(-0.487726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.31736 | −0.305687 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.26245 | −0.0943505 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0151 | − | 32.9352i | −0.791610 | − | 1.37111i | −0.924970 | − | 0.380041i | \(-0.875910\pi\) |
0.133360 | − | 0.991068i | \(-0.457423\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.7722 | − | 29.0503i | 0.697030 | − | 1.20729i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.28513 | + | 10.8862i | −0.260304 | + | 0.450859i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.91357 | + | 15.4387i | 0.368531 | + | 0.638314i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.0302 | −1.40458 | −0.702289 | − | 0.711892i | \(-0.747839\pi\) | ||||
−0.702289 | + | 0.711892i | \(0.747839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 62.7734 | 2.58653 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.26245 | − | 10.8469i | −0.257603 | − | 0.446181i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.8618 | + | 29.2055i | −0.692431 | + | 1.19933i | 0.278608 | + | 0.960405i | \(0.410127\pi\) |
−0.971039 | + | 0.238921i | \(0.923206\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.8813 | − | 34.4355i | 0.813689 | − | 1.40935i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.15333 | − | 5.46172i | −0.128841 | − | 0.223160i | 0.794387 | − | 0.607413i | \(-0.207793\pi\) |
−0.923228 | + | 0.384253i | \(0.874459\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2871 | 0.460411 | 0.230206 | − | 0.973142i | \(-0.426060\pi\) | ||||
0.230206 | + | 0.973142i | \(0.426060\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.1596 | −0.861686 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.09179 | − | 7.08718i | −0.166355 | − | 0.288135i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.73057 | + | 13.3897i | −0.313774 | + | 0.543473i | −0.979176 | − | 0.203012i | \(-0.934927\pi\) |
0.665402 | + | 0.746485i | \(0.268260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.5722 | + | 51.2206i | −1.19637 | + | 2.07217i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0820 | + | 19.1946i | 0.447598 | + | 0.775263i | 0.998229 | − | 0.0594857i | \(-0.0189461\pi\) |
−0.550631 | + | 0.834749i | \(0.685613\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.6145 | −0.992551 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.9805 | −0.603091 | −0.301545 | − | 0.953452i | \(-0.597502\pi\) | ||||
−0.301545 | + | 0.953452i | \(0.597502\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8196 | + | 20.4721i | 0.475069 | + | 0.822843i | 0.999592 | − | 0.0285529i | \(-0.00908990\pi\) |
−0.524524 | + | 0.851396i | \(0.675757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.98267 | + | 3.43408i | −0.0795617 | + | 0.137805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.8467 | − | 25.7152i | −0.592919 | − | 1.02697i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.69334 | 0.227008 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7818 | −0.548643 | −0.274322 | − | 0.961638i | \(-0.588453\pi\) | ||||
−0.274322 | + | 0.961638i | \(0.588453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.8662 | + | 20.5529i | 0.471640 | + | 0.816904i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.59179 | + | 16.6135i | −0.380638 | + | 0.659285i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9309 | − | 37.9854i | −0.866218 | − | 1.50033i | −0.865832 | − | 0.500334i | \(-0.833210\pi\) |
−0.000386062 | − | 1.00000i | \(-0.500123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.04979 | −0.278016 | −0.139008 | − | 0.990291i | \(-0.544391\pi\) | ||||
−0.139008 | + | 0.990291i | \(0.544391\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0151 | 0.669970 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.2403 | − | 21.2009i | −0.481217 | − | 0.833493i | 0.518550 | − | 0.855047i | \(-0.326472\pi\) |
−0.999768 | + | 0.0215540i | \(0.993139\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.71288 | − | 11.6271i | 0.263504 | − | 0.456402i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.408213 | + | 0.707046i | −0.0159746 | + | 0.0276688i | −0.873902 | − | 0.486102i | \(-0.838418\pi\) |
0.857928 | + | 0.513771i | \(0.171752\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.91357 | + | 15.4387i | 0.348282 | + | 0.603242i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 43.0107 | 1.67801 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.2871 | 0.829228 | 0.414614 | − | 0.909997i | \(-0.363917\pi\) | ||||
0.414614 | + | 0.909997i | \(0.363917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9731 | + | 22.4701i | 0.504596 | + | 0.873986i | 0.999986 | + | 0.00531513i | \(0.00169187\pi\) |
−0.495390 | + | 0.868671i | \(0.664975\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.5249 | + | 21.6938i | −0.486427 | + | 0.842515i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.75767 | − | 6.50848i | 0.145498 | − | 0.252009i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.7722 | + | 29.0503i | 0.648451 | + | 1.12315i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.8920 | 0.420483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0693 | 0.850710 | 0.425355 | − | 0.905027i | \(-0.360149\pi\) | ||||
0.425355 | + | 0.905027i | \(0.360149\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.876338 | + | 1.51786i | 0.0337303 | + | 0.0584225i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.74511 | − | 4.75468i | 0.105503 | − | 0.182737i | −0.808440 | − | 0.588578i | \(-0.799688\pi\) |
0.913944 | + | 0.405841i | \(0.133021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.4656 | − | 49.3038i | 1.09080 | − | 1.88933i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.61389 | − | 16.6517i | −0.367865 | − | 0.637161i | 0.621366 | − | 0.783520i | \(-0.286578\pi\) |
−0.989232 | + | 0.146359i | \(0.953245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.00000 | −0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.1294 | 0.424612 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.1513 | − | 31.4390i | −0.691511 | − | 1.19773i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.10912 | − | 12.3134i | 0.270444 | − | 0.468422i | −0.698532 | − | 0.715579i | \(-0.746163\pi\) |
0.968975 | + | 0.247157i | \(0.0794963\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.58423 | − | 4.47601i | 0.0980253 | − | 0.169785i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.52489 | − | 16.4976i | −0.360781 | − | 0.624891i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −46.5161 | −1.75940 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.1533 | 0.534564 | 0.267282 | − | 0.963618i | \(-0.413875\pi\) | ||||
0.267282 | + | 0.963618i | \(0.413875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.74511 | − | 16.8790i | −0.367544 | − | 0.636605i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.7678 | + | 27.3106i | −0.593850 | + | 1.02858i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.52268 | + | 14.7617i | −0.320076 | + | 0.554388i | −0.980503 | − | 0.196502i | \(-0.937042\pi\) |
0.660427 | + | 0.750890i | \(0.270375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.4707 | − | 18.1358i | −0.392682 | − | 0.680144i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7431 | 0.776836 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.13379 | −0.304186 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.0347 | + | 24.3088i | 0.524134 | + | 0.907827i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.75268 | + | 9.96393i | −0.214539 | + | 0.371592i | −0.953130 | − | 0.302562i | \(-0.902158\pi\) |
0.738591 | + | 0.674154i | \(0.235491\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.262447 | + | 0.454571i | −0.00976049 | + | 0.0169057i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.66089 | − | 2.87674i | −0.0616839 | − | 0.106840i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4114 | −0.608664 | −0.304332 | − | 0.952566i | \(-0.598433\pi\) | ||||
−0.304332 | + | 0.952566i | \(0.598433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.5161 | −1.38948 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.58423 | + | 11.4042i | 0.243526 | + | 0.421800i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.55712 | + | 7.89317i | −0.168321 | + | 0.291541i | −0.937830 | − | 0.347096i | \(-0.887168\pi\) |
0.769509 | + | 0.638637i | \(0.220501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.82713 | − | 8.36084i | 0.177810 | − | 0.307975i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.4978 | + | 30.3071i | 0.643667 | + | 1.11486i | 0.984608 | + | 0.174779i | \(0.0559210\pi\) |
−0.340941 | + | 0.940085i | \(0.610746\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 85.7538 | 3.15025 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.5305 | −1.59698 | −0.798489 | − | 0.602009i | \(-0.794367\pi\) | ||||
−0.798489 | + | 0.602009i | \(0.794367\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.398443 | + | 0.690123i | 0.0145978 | + | 0.0252842i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.1438 | + | 40.0862i | −0.846787 | + | 1.46668i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.15333 | + | 5.46172i | −0.115067 | + | 0.199301i | −0.917806 | − | 0.397028i | \(-0.870041\pi\) |
0.802740 | + | 0.596329i | \(0.203375\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.50535 | − | 11.2676i | −0.237068 | − | 0.410614i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.5249 | 0.601402 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.3369 | 0.884540 | 0.442270 | − | 0.896882i | \(-0.354173\pi\) | ||||
0.442270 | + | 0.896882i | \(0.354173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.90600 | − | 8.49745i | −0.178077 | − | 0.308438i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.1016 | + | 24.4246i | −0.511181 | + | 0.885392i | 0.488735 | + | 0.872432i | \(0.337459\pi\) |
−0.999916 | + | 0.0129592i | \(0.995875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.67822 | + | 6.37087i | −0.132986 | + | 0.230339i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.3867 | + | 33.5787i | 0.700013 | + | 1.21246i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.8965 | 1.51082 | 0.755412 | − | 0.655250i | \(-0.227437\pi\) | ||||
0.755412 | + | 0.655250i | \(0.227437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.4365 | 2.17657 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.9287 | + | 34.5175i | 0.716785 | + | 1.24151i | 0.962267 | + | 0.272107i | \(0.0877205\pi\) |
−0.245482 | + | 0.969401i | \(0.578946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.58423 | − | 7.94011i | 0.164670 | − | 0.285217i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.6069 | + | 56.4768i | −1.16826 | + | 2.02349i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.82200 | −0.208061 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.20311 | 0.292782 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.6637 | + | 30.5944i | 0.629642 | + | 1.09057i | 0.987623 | + | 0.156843i | \(0.0501318\pi\) |
−0.357981 | + | 0.933729i | \(0.616535\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35.0280 | − | 60.6703i | 1.24703 | − | 2.15992i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.7280 | + | 27.2417i | −0.558518 | + | 0.967381i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.67822 | − | 16.7632i | −0.343251 | − | 0.594528i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.6933 | −1.05179 | −0.525896 | − | 0.850549i | \(-0.676270\pi\) | ||||
−0.525896 | + | 0.850549i | \(0.676270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.4062 | −0.863430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.7527 | − | 18.6242i | −0.379927 | − | 0.658053i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.81201 | + | 16.9949i | −0.346258 | + | 0.599737i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.38611 | + | 14.5252i | −0.295205 | + | 0.511310i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.82178 | + | 17.0118i | 0.345315 | + | 0.598104i | 0.985411 | − | 0.170191i | \(-0.0544386\pi\) |
−0.640096 | + | 0.768295i | \(0.721105\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.252452 | −0.00886479 | −0.00443239 | − | 0.999990i | \(-0.501411\pi\) | ||||
−0.00443239 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −60.4365 | −2.11960 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.84667 | + | 3.19853i | 0.0646861 | + | 0.112040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.5400 | − | 39.0405i | 0.788575 | − | 1.36585i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3867 | + | 38.7749i | −0.781301 | + | 1.35325i | 0.149883 | + | 0.988704i | \(0.452110\pi\) |
−0.931184 | + | 0.364549i | \(0.881223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.64856 | − | 2.85538i | −0.0574650 | − | 0.0995323i | 0.835862 | − | 0.548940i | \(-0.184968\pi\) |
−0.893327 | + | 0.449408i | \(0.851635\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.33690 | −0.150992 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.41577 | 0.327419 | 0.163709 | − | 0.986509i | \(-0.447654\pi\) | ||||
0.163709 | + | 0.986509i | \(0.447654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.35644 | − | 4.08148i | −0.0818426 | − | 0.141756i | 0.822199 | − | 0.569200i | \(-0.192747\pi\) |
−0.904041 | + | 0.427445i | \(0.859414\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.73314 | − | 8.19803i | 0.164191 | − | 0.284387i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.131223 | − | 0.227285i | 0.00454117 | − | 0.00786554i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.03466 | − | 13.9164i | −0.277719 | − | 0.481023i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1880 | −0.766015 | −0.383007 | − | 0.923745i | \(-0.625112\pi\) | ||||
−0.383007 | + | 0.923745i | \(0.625112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9658 | −0.619510 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.9558 | + | 31.1003i | 0.618430 | + | 1.07115i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.24511 | − | 9.08481i | 0.180437 | − | 0.312527i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.2776 | − | 45.5141i | 0.901844 | − | 1.56204i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.22022 | − | 5.57759i | −0.110388 | − | 0.191197i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.9267 | −1.36706 | −0.683532 | − | 0.729920i | \(-0.739557\pi\) | ||||
−0.683532 | + | 0.729920i | \(0.739557\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.1836 | 0.861260 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.812009 | − | 1.40644i | −0.0277377 | − | 0.0480431i | 0.851823 | − | 0.523829i | \(-0.175497\pi\) |
−0.879561 | + | 0.475786i | \(0.842164\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | − | 6.92820i | 0.136478 | − | 0.236387i | −0.789683 | − | 0.613515i | \(-0.789755\pi\) |
0.926161 | + | 0.377128i | \(0.123088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.11168 | + | 15.7819i | −0.310165 | + | 0.537222i | −0.978398 | − | 0.206730i | \(-0.933718\pi\) |
0.668233 | + | 0.743952i | \(0.267051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.42334 | + | 16.3217i | 0.320403 | + | 0.554954i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.5949 | 1.14094 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.55469 | 0.324121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.9407 | + | 24.1459i | 0.472362 | + | 0.818154i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.67822 | + | 6.37087i | −0.124489 | + | 0.215621i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.4385 | − | 44.0607i | 0.858996 | − | 1.48782i | −0.0138922 | − | 0.999903i | \(-0.504422\pi\) |
0.872888 | − | 0.487921i | \(-0.162244\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.3520 | − | 42.1789i | −0.821373 | − | 1.42266i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1187 | 0.644124 | 0.322062 | − | 0.946719i | \(-0.395624\pi\) | ||||
0.322062 | + | 0.946719i | \(0.395624\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.3174 | 1.32313 | 0.661567 | − | 0.749886i | \(-0.269892\pi\) | ||||
0.661567 | + | 0.749886i | \(0.269892\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.3369 | + | 17.9040i | 0.347471 | + | 0.601838i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.5199 | − | 23.4171i | 0.453954 | − | 0.786271i | −0.544674 | − | 0.838648i | \(-0.683346\pi\) |
0.998627 | + | 0.0523772i | \(0.0166798\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.45871 | − | 9.45476i | 0.182874 | − | 0.316746i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.7754 | + | 72.3570i | 1.39796 | + | 2.42134i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0151 | 0.401621 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.3369 | 0.946142 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.2278 | + | 26.3753i | 0.507875 | + | 0.879665i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.49023 | − | 12.9735i | 0.249536 | − | 0.432209i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.01733 | − | 5.22617i | 0.100299 | − | 0.173724i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.4012 | − | 28.4078i | −0.544594 | − | 0.943264i | −0.998632 | − | 0.0522823i | \(-0.983350\pi\) |
0.454038 | − | 0.890982i | \(-0.349983\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 62.5854 | 2.07583 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.18799 | 0.205017 | 0.102509 | − | 0.994732i | \(-0.467313\pi\) | ||||
0.102509 | + | 0.994732i | \(0.467313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5596 | − | 18.2897i | −0.349470 | − | 0.605300i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.38611 | + | 14.5252i | −0.277236 | + | 0.480187i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.8965 | − | 41.3899i | 0.788271 | − | 1.36533i | −0.138754 | − | 0.990327i | \(-0.544310\pi\) |
0.927025 | − | 0.374999i | \(-0.122357\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.09620 | + | 5.36278i | 0.102023 | + | 0.176710i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.84667 | −0.0935980 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.0745 | + | 22.6456i | 0.429421 | + | 0.743780i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.9309 | + | 34.5213i | −0.653912 | + | 1.13261i | 0.328254 | + | 0.944590i | \(0.393540\pi\) |
−0.982165 | + | 0.188018i | \(0.939794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.31736 | − | 12.6740i | 0.239560 | − | 0.414929i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.67822 | − | 2.90676i | −0.0548837 | − | 0.0950614i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.406229 | −0.0132709 | −0.00663546 | − | 0.999978i | \(-0.502112\pi\) | ||||
−0.00663546 | + | 0.999978i | \(0.502112\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 76.8125 | 2.50668 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.8271 | + | 29.1454i | 0.548549 | + | 0.950114i | 0.998374 | + | 0.0569979i | \(0.0181528\pi\) |
−0.449825 | + | 0.893116i | \(0.648514\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.7748 | + | 18.6625i | −0.350875 | + | 0.607734i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.92055 | + | 5.05854i | −0.0949050 | + | 0.164380i | −0.909569 | − | 0.415553i | \(-0.863588\pi\) |
0.814664 | + | 0.579933i | \(0.196921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.3369 | − | 49.0810i | −0.919855 | − | 1.59324i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49.2289 | −1.59636 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.0605 | 1.03854 | 0.519271 | − | 0.854610i | \(-0.326204\pi\) | ||||
0.519271 | + | 0.854610i | \(0.326204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.41577 | + | 2.45219i | 0.0458134 | + | 0.0793511i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.20311 | − | 12.4762i | 0.232844 | − | 0.403297i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5302 | + | 45.9517i | −0.855814 | + | 1.48231i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.22337 | + | 5.58303i | 0.103872 | + | 0.179911i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.9805 | −0.417856 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0896 | 0.774669 | 0.387334 | − | 0.921939i | \(-0.373396\pi\) | ||||
0.387334 | + | 0.921939i | \(0.373396\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.6933 | + | 30.6458i | 0.568392 | + | 0.984484i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.23534 | − | 15.9961i | 0.296376 | − | 0.513339i | −0.678928 | − | 0.734205i | \(-0.737555\pi\) |
0.975304 | + | 0.220866i | \(0.0708884\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.26245 | − | 10.8469i | 0.200559 | − | 0.347378i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.1685 | − | 21.0764i | −0.389303 | − | 0.674293i | 0.603053 | − | 0.797701i | \(-0.293951\pi\) |
−0.992356 | + | 0.123408i | \(0.960618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.81201 | 0.313593 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 71.8725 | 2.29471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.33434 | + | 7.50729i | 0.138244 | + | 0.239445i | 0.926832 | − | 0.375476i | \(-0.122521\pi\) |
−0.788588 | + | 0.614922i | \(0.789188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.42334 | + | 4.19734i | −0.0772139 | + | 0.133738i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.44823 | − | 12.9007i | 0.236840 | − | 0.410219i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7527 | + | 48.0690i | 0.881593 | + | 1.52696i | 0.849570 | + | 0.527476i | \(0.176862\pi\) |
0.0320231 | + | 0.999487i | \(0.489805\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.00000 | −0.190404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.3867 | −0.487791 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.5596 | − | 30.4140i | −0.556117 | − | 0.963222i | −0.997816 | − | 0.0660591i | \(-0.978957\pi\) |
0.441699 | − | 0.897163i | \(-0.354376\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.49465 | + | 4.32086i | −0.0789271 | + | 0.136706i |
(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 | 1960.2.q.w.961.3 | 6 | ||
7.2 | even | 3 | 1960.2.a.v.1.1 | 3 | |||
7.3 | odd | 6 | 280.2.q.e.81.1 | ✓ | 6 | ||
7.4 | even | 3 | inner | 1960.2.q.w.361.3 | 6 | ||
7.5 | odd | 6 | 1960.2.a.w.1.3 | 3 | |||
7.6 | odd | 2 | 280.2.q.e.121.1 | yes | 6 | ||
21.17 | even | 6 | 2520.2.bi.q.361.1 | 6 | |||
21.20 | even | 2 | 2520.2.bi.q.1801.1 | 6 | |||
28.3 | even | 6 | 560.2.q.l.81.3 | 6 | |||
28.19 | even | 6 | 3920.2.a.cc.1.1 | 3 | |||
28.23 | odd | 6 | 3920.2.a.cb.1.3 | 3 | |||
28.27 | even | 2 | 560.2.q.l.401.3 | 6 | |||
35.3 | even | 12 | 1400.2.bh.i.249.2 | 12 | |||
35.9 | even | 6 | 9800.2.a.cf.1.3 | 3 | |||
35.13 | even | 4 | 1400.2.bh.i.849.5 | 12 | |||
35.17 | even | 12 | 1400.2.bh.i.249.5 | 12 | |||
35.19 | odd | 6 | 9800.2.a.ce.1.1 | 3 | |||
35.24 | odd | 6 | 1400.2.q.j.1201.3 | 6 | |||
35.27 | even | 4 | 1400.2.bh.i.849.2 | 12 | |||
35.34 | odd | 2 | 1400.2.q.j.401.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.e.81.1 | ✓ | 6 | 7.3 | odd | 6 | ||
280.2.q.e.121.1 | yes | 6 | 7.6 | odd | 2 | ||
560.2.q.l.81.3 | 6 | 28.3 | even | 6 | |||
560.2.q.l.401.3 | 6 | 28.27 | even | 2 | |||
1400.2.q.j.401.3 | 6 | 35.34 | odd | 2 | |||
1400.2.q.j.1201.3 | 6 | 35.24 | odd | 6 | |||
1400.2.bh.i.249.2 | 12 | 35.3 | even | 12 | |||
1400.2.bh.i.249.5 | 12 | 35.17 | even | 12 | |||
1400.2.bh.i.849.2 | 12 | 35.27 | even | 4 | |||
1400.2.bh.i.849.5 | 12 | 35.13 | even | 4 | |||
1960.2.a.v.1.1 | 3 | 7.2 | even | 3 | |||
1960.2.a.w.1.3 | 3 | 7.5 | odd | 6 | |||
1960.2.q.w.361.3 | 6 | 7.4 | even | 3 | inner | ||
1960.2.q.w.961.3 | 6 | 1.1 | even | 1 | trivial | ||
2520.2.bi.q.361.1 | 6 | 21.17 | even | 6 | |||
2520.2.bi.q.1801.1 | 6 | 21.20 | even | 2 | |||
3920.2.a.cb.1.3 | 3 | 28.23 | odd | 6 | |||
3920.2.a.cc.1.1 | 3 | 28.19 | even | 6 | |||
9800.2.a.ce.1.1 | 3 | 35.19 | odd | 6 | |||
9800.2.a.cf.1.3 | 3 | 35.9 | even | 6 |