Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1201,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, 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("2100.1201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1201 |
Dual form | 2100.2.q.a.1801.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | + | 0.866025i | 0.114708 | + | 0.198680i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | − | 1.73205i | 0.436436 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50000 | − | 4.33013i | 0.449013 | − | 0.777714i | −0.549309 | − | 0.835619i | \(-0.685109\pi\) |
0.998322 | + | 0.0579057i | \(0.0184423\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | + | 1.73205i | 0.174078 | + | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50000 | − | 4.33013i | −0.410997 | − | 0.711868i | 0.584002 | − | 0.811752i | \(-0.301486\pi\) |
−0.994999 | + | 0.0998840i | \(0.968153\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.00000 | 1.37249 | 0.686244 | − | 0.727372i | \(-0.259258\pi\) | ||||
0.686244 | + | 0.727372i | \(0.259258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | + | 12.1244i | 0.896258 | + | 1.55236i | 0.832240 | + | 0.554416i | \(0.187058\pi\) |
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.500000 | + | 2.59808i | 0.0629941 | + | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50000 | − | 7.79423i | 0.549762 | − | 0.952217i | −0.448528 | − | 0.893769i | \(-0.648052\pi\) |
0.998290 | − | 0.0584478i | \(-0.0186151\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.500000 | − | 0.866025i | 0.0585206 | − | 0.101361i | −0.835281 | − | 0.549823i | \(-0.814695\pi\) |
0.893801 | + | 0.448463i | \(0.148028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | + | 3.46410i | −0.455842 | + | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | + | 2.59808i | 0.168763 | + | 0.292306i | 0.937985 | − | 0.346675i | \(-0.112689\pi\) |
−0.769222 | + | 0.638982i | \(0.779356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.0000 | 1.97576 | 0.987878 | − | 0.155230i | \(-0.0496119\pi\) | ||||
0.987878 | + | 0.155230i | \(0.0496119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | + | 3.46410i | 0.212000 | + | 0.367194i | 0.952340 | − | 0.305038i | \(-0.0986691\pi\) |
−0.740341 | + | 0.672232i | \(0.765336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | + | 0.866025i | 0.262071 | + | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.50000 | + | 4.33013i | 0.259238 | + | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.500000 | − | 0.866025i | −0.0492665 | − | 0.0853320i | 0.840341 | − | 0.542059i | \(-0.182355\pi\) |
−0.889607 | + | 0.456727i | \(0.849022\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00000 | + | 3.46410i | 0.193347 | + | 0.334887i | 0.946357 | − | 0.323122i | \(-0.104732\pi\) |
−0.753010 | + | 0.658009i | \(0.771399\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.50000 | + | 11.2583i | −0.622587 | + | 1.07835i | 0.366415 | + | 0.930451i | \(0.380585\pi\) |
−0.989002 | + | 0.147901i | \(0.952748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00000 | 0.474579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.00000 | − | 6.92820i | 0.733359 | − | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | 0.798621 | 0.399310 | − | 0.916816i | \(-0.369250\pi\) | ||||
0.399310 | + | 0.916816i | \(0.369250\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.50000 | + | 7.79423i | −0.396203 | + | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.500000 | − | 2.59808i | −0.0433555 | − | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.00000 | − | 13.8564i | 0.683486 | − | 1.18383i | −0.290424 | − | 0.956898i | \(-0.593796\pi\) |
0.973910 | − | 0.226935i | \(-0.0728704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0000 | −1.10265 | −0.551323 | − | 0.834292i | \(-0.685877\pi\) | ||||
−0.551323 | + | 0.834292i | \(0.685877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | + | 1.73205i | −0.0836242 | + | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.50000 | + | 2.59808i | −0.536111 | + | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | − | 10.3923i | −0.491539 | − | 0.851371i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0000 | + | 19.0526i | −0.877896 | + | 1.52056i | −0.0242497 | + | 0.999706i | \(0.507720\pi\) |
−0.853646 | + | 0.520854i | \(0.825614\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | + | 10.3923i | 0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | − | 10.3923i | −0.157622 | − | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | + | 10.3923i | 0.469956 | + | 0.813988i | 0.999410 | − | 0.0343508i | \(-0.0109363\pi\) |
−0.529454 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.00000 | −0.154765 | −0.0773823 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773823 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | − | 0.866025i | 0.0382360 | − | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.00000 | − | 13.8564i | −0.608229 | − | 1.05348i | −0.991532 | − | 0.129861i | \(-0.958547\pi\) |
0.383304 | − | 0.923622i | \(-0.374786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | + | 6.92820i | 0.300658 | + | 0.520756i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.0000 | − | 22.5167i | 0.971666 | − | 1.68297i | 0.281139 | − | 0.959667i | \(-0.409288\pi\) |
0.690526 | − | 0.723307i | \(-0.257379\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0000 | 1.26360 | 0.631800 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631800 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0000 | −1.03491 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | + | 6.92820i | 0.292509 | + | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50000 | − | 0.866025i | −0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.00000 | + | 8.66025i | 0.361787 | + | 0.626634i | 0.988255 | − | 0.152813i | \(-0.0488333\pi\) |
−0.626468 | + | 0.779447i | \(0.715500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.50000 | + | 14.7224i | −0.611843 | + | 1.05974i | 0.379086 | + | 0.925361i | \(0.376238\pi\) |
−0.990930 | + | 0.134382i | \(0.957095\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | − | 13.8564i | 0.567105 | − | 0.982255i | −0.429745 | − | 0.902950i | \(-0.641397\pi\) |
0.996850 | − | 0.0793045i | \(-0.0252700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.50000 | + | 7.79423i | 0.317406 | + | 0.549762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | − | 3.46410i | 0.139010 | − | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.0000 | −1.92760 | −0.963800 | − | 0.266627i | \(-0.914091\pi\) | ||||
−0.963800 | + | 0.266627i | \(0.914091\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.00000 | + | 1.73205i | −0.0685189 | + | 0.118678i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0000 | + | 8.66025i | −0.678844 | + | 0.587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.500000 | + | 0.866025i | 0.0337869 | + | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | − | 3.46410i | 0.134535 | − | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.00000 | − | 15.5885i | 0.597351 | − | 1.03464i | −0.395860 | − | 0.918311i | \(-0.629553\pi\) |
0.993210 | − | 0.116331i | \(-0.0371134\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | − | 0.866025i | −0.0330409 | − | 0.0572286i | 0.849032 | − | 0.528341i | \(-0.177186\pi\) |
−0.882073 | + | 0.471113i | \(0.843853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | − | 5.19615i | −0.0657952 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.00000 | − | 1.73205i | −0.0655122 | − | 0.113470i | 0.831409 | − | 0.555661i | \(-0.187535\pi\) |
−0.896921 | + | 0.442191i | \(0.854201\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.00000 | −0.194871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.0000 | 1.68180 | 0.840900 | − | 0.541190i | \(-0.182026\pi\) | ||||
0.840900 | + | 0.541190i | \(0.182026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.00000 | − | 15.5885i | 0.579741 | − | 1.00414i | −0.415768 | − | 0.909471i | \(-0.636487\pi\) |
0.995509 | − | 0.0946700i | \(-0.0301796\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.500000 | − | 0.866025i | −0.0318142 | − | 0.0551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.00000 | + | 15.5885i | −0.570352 | + | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.00000 | + | 12.1244i | 0.436648 | + | 0.756297i | 0.997429 | − | 0.0716680i | \(-0.0228322\pi\) |
−0.560781 | + | 0.827964i | \(0.689499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50000 | + | 12.9904i | 0.155342 | + | 0.807183i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.00000 | −0.244796 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.00000 | − | 15.5885i | 0.548740 | − | 0.950445i | −0.449622 | − | 0.893219i | \(-0.648441\pi\) |
0.998361 | − | 0.0572259i | \(-0.0182255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | + | 1.73205i | −0.121046 | + | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.50000 | − | 4.33013i | 0.150210 | − | 0.260172i | −0.781094 | − | 0.624413i | \(-0.785338\pi\) |
0.931305 | + | 0.364241i | \(0.118672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.00000 | −0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0000 | −1.19310 | −0.596550 | − | 0.802576i | \(-0.703462\pi\) | ||||
−0.596550 | + | 0.802576i | \(0.703462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5000 | + | 21.6506i | −0.743048 | + | 1.28700i | 0.208053 | + | 0.978117i | \(0.433287\pi\) |
−0.951101 | + | 0.308879i | \(0.900046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.00000 | − | 1.73205i | −0.295141 | − | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | − | 8.66025i | 0.293105 | − | 0.507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | − | 1.73205i | 0.0580259 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.00000 | − | 3.46410i | −0.115663 | − | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.5000 | − | 7.79423i | −1.29688 | − | 0.449252i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | − | 5.19615i | −0.172345 | − | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0000 | 1.08439 | 0.542194 | − | 0.840254i | \(-0.317594\pi\) | ||||
0.542194 | + | 0.840254i | \(0.317594\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0000 | + | 22.5167i | −0.737162 | + | 1.27680i | 0.216606 | + | 0.976259i | \(0.430501\pi\) |
−0.953768 | + | 0.300544i | \(0.902832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.50000 | + | 16.4545i | 0.536972 | + | 0.930062i | 0.999065 | + | 0.0432311i | \(0.0137652\pi\) |
−0.462093 | + | 0.886831i | \(0.652902\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.00000 | − | 3.46410i | −0.112331 | − | 0.194563i | 0.804379 | − | 0.594117i | \(-0.202498\pi\) |
−0.916710 | + | 0.399554i | \(0.869165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.50000 | − | 11.2583i | −0.359451 | − | 0.622587i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.00000 | + | 5.19615i | 0.0551318 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.500000 | − | 0.866025i | −0.0274825 | − | 0.0476011i | 0.851957 | − | 0.523612i | \(-0.175416\pi\) |
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.50000 | + | 4.33013i | −0.136999 | + | 0.237289i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.00000 | 0.381314 | 0.190657 | − | 0.981657i | \(-0.438938\pi\) | ||||
0.190657 | + | 0.981657i | \(0.438938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.00000 | + | 12.1244i | −0.380188 | + | 0.658505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.00000 | − | 8.66025i | −0.270765 | − | 0.468979i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | − | 20.7846i | 0.644194 | − | 1.11578i | −0.340293 | − | 0.940319i | \(-0.610526\pi\) |
0.984487 | − | 0.175457i | \(-0.0561403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0000 | − | 25.9808i | 0.798369 | − | 1.38282i | −0.122308 | − | 0.992492i | \(-0.539030\pi\) |
0.920677 | − | 0.390324i | \(-0.127637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.00000 | + | 10.3923i | 0.105851 | + | 0.550019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.00000 | − | 13.8564i | −0.422224 | − | 0.731313i | 0.573933 | − | 0.818902i | \(-0.305417\pi\) |
−0.996157 | + | 0.0875892i | \(0.972084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.500000 | − | 0.866025i | 0.0260998 | − | 0.0452062i | −0.852680 | − | 0.522433i | \(-0.825025\pi\) |
0.878780 | + | 0.477227i | \(0.158358\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | − | 1.73205i | −0.0520579 | − | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | + | 20.7846i | −1.24602 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.5000 | − | 21.6506i | −0.647225 | − | 1.12103i | −0.983783 | − | 0.179364i | \(-0.942596\pi\) |
0.336557 | − | 0.941663i | \(-0.390737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0000 | −0.565032 | −0.282516 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282516 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.50000 | + | 7.79423i | −0.230542 | + | 0.399310i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0000 | − | 31.1769i | −0.919757 | − | 1.59307i | −0.799783 | − | 0.600289i | \(-0.795052\pi\) |
−0.119974 | − | 0.992777i | \(-0.538281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.50000 | − | 7.79423i | −0.228748 | − | 0.396203i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0000 | + | 25.9808i | −0.760530 | + | 1.31728i | 0.182047 | + | 0.983290i | \(0.441728\pi\) |
−0.942578 | + | 0.333987i | \(0.891606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.0000 | −0.907980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.5000 | + | 26.8468i | 0.777923 | + | 1.34740i | 0.933137 | + | 0.359521i | \(0.117060\pi\) |
−0.155214 | + | 0.987881i | \(0.549607\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.50000 | + | 0.866025i | 0.125157 | + | 0.0433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | − | 10.3923i | −0.299626 | − | 0.518967i | 0.676425 | − | 0.736512i | \(-0.263528\pi\) |
−0.976050 | + | 0.217545i | \(0.930195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.50000 | + | 4.33013i | −0.124534 | + | 0.215699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50000 | + | 11.2583i | −0.321404 | + | 0.556689i | −0.980778 | − | 0.195127i | \(-0.937488\pi\) |
0.659374 | + | 0.751815i | \(0.270822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.00000 | + | 13.8564i | 0.394611 | + | 0.683486i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.0000 | + | 13.8564i | −0.787309 | + | 0.681829i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.50000 | − | 11.2583i | 0.318306 | − | 0.551323i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.0000 | −1.70580 | −0.852898 | − | 0.522078i | \(-0.825157\pi\) | ||||
−0.852898 | + | 0.522078i | \(0.825157\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.00000 | + | 1.73205i | −0.0486217 | + | 0.0842152i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.00000 | − | 36.3731i | −0.338754 | − | 1.76022i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00000 | − | 1.73205i | −0.0482805 | − | 0.0836242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | − | 25.9808i | 0.722525 | − | 1.25145i | −0.237460 | − | 0.971397i | \(-0.576315\pi\) |
0.959985 | − | 0.280052i | \(-0.0903517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.0000 | −1.29754 | −0.648769 | − | 0.760986i | \(-0.724716\pi\) | ||||
−0.648769 | + | 0.760986i | \(0.724716\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00000 | + | 3.46410i | −0.0956730 | + | 0.165710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | − | 6.92820i | −0.190910 | − | 0.330665i | 0.754642 | − | 0.656136i | \(-0.227810\pi\) |
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.00000 | − | 3.46410i | −0.0950229 | − | 0.164584i | 0.814595 | − | 0.580030i | \(-0.196959\pi\) |
−0.909618 | + | 0.415445i | \(0.863626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | − | 3.46410i | 0.0941763 | − | 0.163118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.00000 | + | 13.8564i | 0.375873 | + | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | + | 0.866025i | 0.0233890 | + | 0.0405110i | 0.877483 | − | 0.479608i | \(-0.159221\pi\) |
−0.854094 | + | 0.520119i | \(0.825888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.0000 | −0.745194 | −0.372597 | − | 0.927993i | \(-0.621533\pi\) | ||||
−0.372597 | + | 0.927993i | \(0.621533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.0000 | −1.90543 | −0.952716 | − | 0.303863i | \(-0.901724\pi\) | ||||
−0.952716 | + | 0.303863i | \(0.901724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0000 | + | 29.4449i | 0.786666 | + | 1.36255i | 0.927999 | + | 0.372584i | \(0.121528\pi\) |
−0.141332 | + | 0.989962i | \(0.545139\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.0000 | + | 15.5885i | −0.831163 | + | 0.719808i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.0000 | − | 19.0526i | −0.506853 | − | 0.877896i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.00000 | − | 15.5885i | 0.413820 | − | 0.716758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | + | 4.33013i | 0.113990 | + | 0.197437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0000 | + | 3.46410i | 0.455016 | + | 0.157622i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5000 | − | 28.5788i | 0.747686 | − | 1.29503i | −0.201243 | − | 0.979541i | \(-0.564498\pi\) |
0.948929 | − | 0.315489i | \(-0.102169\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.00000 | − | 1.73205i | −0.224281 | − | 0.0776931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50000 | + | 4.33013i | 0.111915 | + | 0.193843i | 0.916542 | − | 0.399937i | \(-0.130968\pi\) |
−0.804627 | + | 0.593780i | \(0.797635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | − | 1.73205i | 0.0446767 | − | 0.0773823i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.0000 | −0.445878 | −0.222939 | − | 0.974832i | \(-0.571565\pi\) | ||||
−0.222939 | + | 0.974832i | \(0.571565\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.0000 | − | 22.5167i | −0.576215 | − | 0.998033i | −0.995908 | − | 0.0903676i | \(-0.971196\pi\) |
0.419694 | − | 0.907666i | \(-0.362138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | + | 1.73205i | −0.0884748 | + | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.500000 | + | 0.866025i | 0.0220755 | + | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.00000 | −0.175920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0000 | 0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | + | 31.1769i | −0.788594 | + | 1.36589i | 0.138234 | + | 0.990400i | \(0.455857\pi\) |
−0.926828 | + | 0.375486i | \(0.877476\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5000 | + | 25.1147i | 0.634041 | + | 1.09819i | 0.986718 | + | 0.162446i | \(0.0519382\pi\) |
−0.352677 | + | 0.935745i | \(0.614728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0000 | + | 17.3205i | 0.435607 | + | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.00000 | −0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.0000 | + | 22.5167i | 0.560991 | + | 0.971666i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.0000 | − | 5.19615i | 0.559950 | − | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.5000 | + | 26.8468i | 0.666397 | + | 1.15423i | 0.978905 | + | 0.204318i | \(0.0654977\pi\) |
−0.312507 | + | 0.949915i | \(0.601169\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.50000 | + | 14.7224i | −0.364770 | + | 0.631800i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.00000 | − | 12.1244i | 0.298753 | − | 0.517455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.50000 | − | 7.79423i | −0.0637865 | − | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.00000 | + | 1.73205i | −0.0423714 | + | 0.0733893i | −0.886433 | − | 0.462856i | \(-0.846825\pi\) |
0.844062 | + | 0.536246i | \(0.180158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.00000 | −0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0000 | + | 25.9808i | −0.632175 | + | 1.09496i | 0.354932 | + | 0.934892i | \(0.384504\pi\) |
−0.987106 | + | 0.160066i | \(0.948829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.00000 | − | 1.73205i | 0.0839921 | − | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.50000 | − | 4.33013i | 0.104622 | − | 0.181210i | −0.808962 | − | 0.587861i | \(-0.799970\pi\) |
0.913584 | + | 0.406651i | \(0.133303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.0000 | −0.417756 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.50000 | + | 11.2583i | −0.270599 | + | 0.468690i | −0.969015 | − | 0.247001i | \(-0.920555\pi\) |
0.698417 | + | 0.715691i | \(0.253888\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.50000 | − | 14.7224i | −0.353248 | − | 0.611843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.0000 | − | 15.5885i | −1.86691 | − | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | − | 20.7846i | −0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0000 | 1.48588 | 0.742940 | − | 0.669359i | \(-0.233431\pi\) | ||||
0.742940 | + | 0.669359i | \(0.233431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00000 | 0.206021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | − | 10.3923i | 0.246807 | − | 0.427482i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.00000 | + | 13.8564i | 0.327418 | + | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0000 | − | 24.2487i | 0.572024 | − | 0.990775i | −0.424333 | − | 0.905506i | \(-0.639492\pi\) |
0.996358 | − | 0.0852695i | \(-0.0271751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.0000 | 0.938190 | 0.469095 | − | 0.883148i | \(-0.344580\pi\) | ||||
0.469095 | + | 0.883148i | \(0.344580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.00000 | −0.366508 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.50000 | + | 7.79423i | 0.182649 | + | 0.316358i | 0.942782 | − | 0.333410i | \(-0.108199\pi\) |
−0.760133 | + | 0.649768i | \(0.774866\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00000 | + | 1.73205i | 0.0404557 | + | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00000 | − | 1.73205i | 0.0403896 | − | 0.0699569i | −0.845124 | − | 0.534570i | \(-0.820473\pi\) |
0.885514 | + | 0.464614i | \(0.153807\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.0000 | −1.36879 | −0.684394 | − | 0.729112i | \(-0.739933\pi\) | ||||
−0.684394 | + | 0.729112i | \(0.739933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.50000 | − | 9.52628i | 0.221064 | − | 0.382893i | −0.734068 | − | 0.679076i | \(-0.762380\pi\) |
0.955131 | + | 0.296183i | \(0.0957138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | + | 3.46410i | 0.0802572 | + | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00000 | − | 10.3923i | −0.0801283 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.00000 | + | 1.73205i | −0.0399362 | + | 0.0691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.0000 | − | 24.2487i | 0.556450 | − | 0.963800i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.50000 | − | 4.33013i | −0.217918 | − | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −0.0395594 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | − | 31.1769i | 0.710957 | − | 1.23141i | −0.253541 | − | 0.967325i | \(-0.581595\pi\) |
0.964498 | − | 0.264089i | \(-0.0850714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00000 | −0.276053 | −0.138027 | − | 0.990429i | \(-0.544076\pi\) | ||||
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.00000 | + | 12.1244i | −0.275198 | + | 0.476658i | −0.970185 | − | 0.242365i | \(-0.922077\pi\) |
0.694987 | + | 0.719023i | \(0.255410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | − | 13.8564i | −0.314027 | − | 0.543912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.50000 | − | 12.9904i | −0.0979827 | − | 0.509133i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.00000 | + | 12.1244i | 0.273931 | + | 0.474463i | 0.969865 | − | 0.243643i | \(-0.0783426\pi\) |
−0.695934 | + | 0.718106i | \(0.745009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.00000 | −0.0390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.00000 | 0.155818 | 0.0779089 | − | 0.996960i | \(-0.475176\pi\) | ||||
0.0779089 | + | 0.996960i | \(0.475176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5000 | + | 30.3109i | −0.680671 | + | 1.17896i | 0.294105 | + | 0.955773i | \(0.404978\pi\) |
−0.974776 | + | 0.223184i | \(0.928355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.00000 | + | 3.46410i | 0.0776736 | + | 0.134535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.0000 | 1.08093 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0000 | −0.424019 | −0.212009 | − | 0.977268i | \(-0.568001\pi\) | ||||
−0.212009 | + | 0.977268i | \(0.568001\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0000 | + | 20.7846i | 0.461197 | + | 0.798817i | 0.999021 | − | 0.0442400i | \(-0.0140866\pi\) |
−0.537823 | + | 0.843057i | \(0.680753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.0000 | + | 8.66025i | 0.959412 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00000 | + | 15.5885i | 0.344881 | + | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.00000 | + | 13.8564i | −0.306111 | + | 0.530201i | −0.977508 | − | 0.210898i | \(-0.932361\pi\) |
0.671397 | + | 0.741098i | \(0.265695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.00000 | 0.0381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.50000 | + | 9.52628i | 0.209230 | + | 0.362397i | 0.951472 | − | 0.307735i | \(-0.0995710\pi\) |
−0.742242 | + | 0.670132i | \(0.766238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.00000 | + | 1.73205i | 0.189934 | + | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | + | 6.92820i | −0.151511 | + | 0.262424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.00000 | 0.0756469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0000 | 1.35970 | 0.679851 | − | 0.733351i | \(-0.262045\pi\) | ||||
0.679851 | + | 0.733351i | \(0.262045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.50000 | − | 4.33013i | 0.0942893 | − | 0.163314i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | − | 10.3923i | 0.451306 | − | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | + | 22.5167i | 0.488225 | + | 0.845631i | 0.999908 | − | 0.0135434i | \(-0.00431112\pi\) |
−0.511683 | + | 0.859174i | \(0.670978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.50000 | − | 2.59808i | 0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.0000 | 0.749006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.0000 | + | 22.5167i | −0.485494 | + | 0.840900i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.0000 | − | 36.3731i | −0.783168 | − | 1.35649i | −0.930087 | − | 0.367338i | \(-0.880269\pi\) |
0.146920 | − | 0.989148i | \(-0.453064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.500000 | + | 2.59808i | 0.0186210 | + | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.00000 | + | 15.5885i | 0.334714 | + | 0.579741i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.00000 | 0.111264 | 0.0556319 | − | 0.998451i | \(-0.482283\pi\) | ||||
0.0556319 | + | 0.998451i | \(0.482283\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0000 | + | 31.1769i | −0.665754 | + | 1.15312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.50000 | + | 7.79423i | 0.166211 | + | 0.287886i | 0.937085 | − | 0.349102i | \(-0.113513\pi\) |
−0.770873 | + | 0.636988i | \(0.780180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.00000 | − | 15.5885i | −0.331519 | − | 0.574208i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.50000 | + | 12.9904i | −0.275892 | + | 0.477859i | −0.970360 | − | 0.241665i | \(-0.922307\pi\) |
0.694468 | + | 0.719524i | \(0.255640\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.00000 | 0.0367359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000 | 0.220119 | 0.110059 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110059 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.00000 | − | 15.5885i | −0.329293 | − | 0.570352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.00000 | − | 10.3923i | −0.0730784 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.5000 | − | 26.8468i | −0.565603 | − | 0.979653i | −0.996993 | − | 0.0774878i | \(-0.975310\pi\) |
0.431390 | − | 0.902165i | \(-0.358023\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.00000 | + | 3.46410i | −0.0728841 | + | 0.126239i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.00000 | + | 6.92820i | −0.145191 | + | 0.251478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0000 | − | 17.3205i | −0.362500 | − | 0.627868i | 0.625872 | − | 0.779926i | \(-0.284743\pi\) |
−0.988372 | + | 0.152058i | \(0.951410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.0000 | − | 22.5167i | 0.941263 | − | 0.815158i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | + | 6.92820i | −0.144432 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0000 | 1.11789 | 0.558944 | − | 0.829205i | \(-0.311207\pi\) | ||||
0.558944 | + | 0.829205i | \(0.311207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.00000 | + | 12.1244i | −0.251773 | + | 0.436083i | −0.964014 | − | 0.265852i | \(-0.914347\pi\) |
0.712241 | + | 0.701935i | \(0.247680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.5000 | − | 4.33013i | −0.448435 | − | 0.155342i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00000 | + | 1.73205i | 0.0358287 | + | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | − | 3.46410i | 0.0715656 | − | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.00000 | + | 13.8564i | −0.285169 | + | 0.493928i | −0.972650 | − | 0.232275i | \(-0.925383\pi\) |
0.687481 | + | 0.726202i | \(0.258716\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.00000 | + | 10.3923i | 0.213606 | + | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.0000 | − | 12.1244i | −1.24446 | − | 0.431092i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.00000 | − | 12.1244i | −0.248577 | − | 0.430548i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.0000 | −0.425062 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | − | 3.46410i | 0.0706665 | − | 0.122398i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.00000 | − | 1.73205i | −0.0352892 | − | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.00000 | + | 15.5885i | 0.316815 | + | 0.548740i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.0000 | + | 39.8372i | −0.808637 | + | 1.40060i | 0.105171 | + | 0.994454i | \(0.466461\pi\) |
−0.913808 | + | 0.406146i | \(0.866872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.0000 | 1.68551 | 0.842754 | − | 0.538299i | \(-0.180933\pi\) | ||||
0.842754 | + | 0.538299i | \(0.180933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.50000 | + | 7.79423i | 0.157435 | + | 0.272686i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.500000 | − | 2.59808i | −0.0174714 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.0000 | + | 43.3013i | 0.872506 | + | 1.51122i | 0.859396 | + | 0.511311i | \(0.170840\pi\) |
0.0131101 | + | 0.999914i | \(0.495827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.00000 | −0.208640 | −0.104320 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104320 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.50000 | + | 4.33013i | −0.0868286 | + | 0.150392i | −0.906169 | − | 0.422916i | \(-0.861007\pi\) |
0.819340 | + | 0.573307i | \(0.194340\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.50000 | + | 4.33013i | 0.0867240 | + | 0.150210i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.0000 | + | 10.3923i | −0.900847 | + | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.50000 | − | 4.33013i | 0.0864126 | − | 0.149671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.0000 | −1.65714 | −0.828572 | − | 0.559883i | \(-0.810846\pi\) | ||||
−0.828572 | + | 0.559883i | \(0.810846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.0000 | − | 17.3205i | 0.344418 | − | 0.596550i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.50000 | − | 18.1865i | −0.120261 | − | 0.624897i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.5000 | − | 21.6506i | −0.428999 | − | 0.743048i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.0000 | − | 17.3205i | 0.342796 | − | 0.593739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.0000 | 0.992941 | 0.496471 | − | 0.868054i | \(-0.334629\pi\) | ||||
0.496471 | + | 0.868054i | \(0.334629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0000 | − | 38.1051i | 0.751506 | − | 1.30165i | −0.195587 | − | 0.980686i | \(-0.562661\pi\) |
0.947093 | − | 0.320960i | \(-0.104005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | − | 6.92820i | −0.136478 | − | 0.236387i | 0.789683 | − | 0.613515i | \(-0.210245\pi\) |
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.00000 | − | 3.46410i | 0.136320 | − | 0.118056i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.0000 | + | 25.9808i | 0.510606 | + | 0.884395i | 0.999924 | + | 0.0122903i | \(0.00391222\pi\) |
−0.489319 | + | 0.872105i | \(0.662754\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.00000 | 0.203536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.50000 | + | 7.79423i | −0.152477 | + | 0.264097i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.00000 | + | 8.66025i | 0.169224 | + | 0.293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0000 | − | 19.0526i | −0.371444 | − | 0.643359i | 0.618344 | − | 0.785907i | \(-0.287804\pi\) |
−0.989788 | + | 0.142548i | \(0.954470\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.0000 | 0.808581 | 0.404290 | − | 0.914631i | \(-0.367519\pi\) | ||||
0.404290 | + | 0.914631i | \(0.367519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00000 | −0.0336527 | −0.0168263 | − | 0.999858i | \(-0.505356\pi\) | ||||
−0.0168263 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.0000 | + | 19.0526i | 0.369344 | + | 0.639722i | 0.989463 | − | 0.144785i | \(-0.0462491\pi\) |
−0.620119 | + | 0.784508i | \(0.712916\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.5000 | − | 7.79423i | −0.754626 | − | 0.261410i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | + | 1.73205i | 0.0335013 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.00000 | − | 1.73205i | 0.0334637 | − | 0.0579609i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.00000 | 0.133556 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000 | + | 41.5692i | 0.799556 | + | 1.38487i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.0000 | − | 15.5885i | 0.599002 | − | 0.518751i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.50000 | − | 7.79423i | 0.149420 | − | 0.258803i | −0.781593 | − | 0.623788i | \(-0.785593\pi\) |
0.931013 | + | 0.364985i | \(0.118926\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | − | 31.1769i | 0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.00000 | − | 46.7654i | −0.297206 | − | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.50000 | + | 9.52628i | 0.181428 | + | 0.314243i | 0.942367 | − | 0.334581i | \(-0.108595\pi\) |
−0.760939 | + | 0.648824i | \(0.775261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.50000 | + | 16.4545i | −0.313036 | + | 0.542194i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.00000 | −0.0658308 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.500000 | + | 0.866025i | −0.0164222 | + | 0.0284440i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.00000 | + | 12.1244i | 0.229663 | + | 0.397787i | 0.957708 | − | 0.287742i | \(-0.0929044\pi\) |
−0.728046 | + | 0.685529i | \(0.759571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | + | 6.92820i | −0.0327737 | + | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.0000 | − | 22.5167i | −0.425601 | − | 0.737162i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.0000 | 0.686040 | 0.343020 | − | 0.939328i | \(-0.388550\pi\) | ||||
0.343020 | + | 0.939328i | \(0.388550\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.0000 | −0.620042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.0000 | − | 41.5692i | 0.782378 | − | 1.35512i | −0.148176 | − | 0.988961i | \(-0.547340\pi\) |
0.930553 | − | 0.366157i | \(-0.119327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.00000 | + | 6.92820i | 0.130258 | + | 0.225613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.00000 | − | 15.5885i | −0.292461 | − | 0.506557i | 0.681930 | − | 0.731417i | \(-0.261141\pi\) |
−0.974391 | + | 0.224860i | \(0.927807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.500000 | + | 0.866025i | −0.0162307 | + | 0.0281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00000 | 0.129709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.0000 | + | 27.7128i | −1.03333 | + | 0.894893i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.00000 | − | 3.46410i | 0.0644491 | − | 0.111629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.0000 | −1.18984 | −0.594920 | − | 0.803785i | \(-0.702816\pi\) | ||||
−0.594920 | + | 0.803785i | \(0.702816\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.00000 | − | 3.46410i | 0.0642493 | − | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | + | 31.1769i | 0.577647 | + | 1.00051i | 0.995748 | + | 0.0921142i | \(0.0293625\pi\) |
−0.418101 | + | 0.908401i | \(0.637304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.5000 | + | 11.2583i | 1.04190 | + | 0.360925i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | 0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.0000 | 0.415058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.00000 | + | 13.8564i | −0.255160 | + | 0.441951i | −0.964939 | − | 0.262474i | \(-0.915462\pi\) |
0.709779 | + | 0.704425i | \(0.248795\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.00000 | − | 1.73205i | −0.159152 | − | 0.0551318i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0000 | + | 31.1769i | 0.572367 | + | 0.991368i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.5000 | − | 45.8993i | 0.841800 | − | 1.45804i | −0.0465710 | − | 0.998915i | \(-0.514829\pi\) |
0.888371 | − | 0.459126i | \(-0.151837\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.00000 | 0.0317340 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.50000 | − | 9.52628i | 0.174187 | − | 0.301700i | −0.765693 | − | 0.643206i | \(-0.777604\pi\) |
0.939880 | + | 0.341506i | \(0.110937\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.50000 | − | 4.33013i | −0.0790965 | − | 0.136999i |
(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 | 2100.2.q.a.1201.1 | 2 | ||
5.2 | odd | 4 | 2100.2.bc.c.949.2 | 4 | |||
5.3 | odd | 4 | 2100.2.bc.c.949.1 | 4 | |||
5.4 | even | 2 | 420.2.q.a.361.1 | yes | 2 | ||
7.2 | even | 3 | inner | 2100.2.q.a.1801.1 | 2 | ||
15.14 | odd | 2 | 1260.2.s.d.361.1 | 2 | |||
20.19 | odd | 2 | 1680.2.bg.a.1201.1 | 2 | |||
35.2 | odd | 12 | 2100.2.bc.c.1549.1 | 4 | |||
35.4 | even | 6 | 2940.2.a.d.1.1 | 1 | |||
35.9 | even | 6 | 420.2.q.a.121.1 | ✓ | 2 | ||
35.19 | odd | 6 | 2940.2.q.h.961.1 | 2 | |||
35.23 | odd | 12 | 2100.2.bc.c.1549.2 | 4 | |||
35.24 | odd | 6 | 2940.2.a.h.1.1 | 1 | |||
35.34 | odd | 2 | 2940.2.q.h.361.1 | 2 | |||
105.44 | odd | 6 | 1260.2.s.d.541.1 | 2 | |||
105.59 | even | 6 | 8820.2.a.y.1.1 | 1 | |||
105.74 | odd | 6 | 8820.2.a.j.1.1 | 1 | |||
140.79 | odd | 6 | 1680.2.bg.a.961.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.a.121.1 | ✓ | 2 | 35.9 | even | 6 | ||
420.2.q.a.361.1 | yes | 2 | 5.4 | even | 2 | ||
1260.2.s.d.361.1 | 2 | 15.14 | odd | 2 | |||
1260.2.s.d.541.1 | 2 | 105.44 | odd | 6 | |||
1680.2.bg.a.961.1 | 2 | 140.79 | odd | 6 | |||
1680.2.bg.a.1201.1 | 2 | 20.19 | odd | 2 | |||
2100.2.q.a.1201.1 | 2 | 1.1 | even | 1 | trivial | ||
2100.2.q.a.1801.1 | 2 | 7.2 | even | 3 | inner | ||
2100.2.bc.c.949.1 | 4 | 5.3 | odd | 4 | |||
2100.2.bc.c.949.2 | 4 | 5.2 | odd | 4 | |||
2100.2.bc.c.1549.1 | 4 | 35.2 | odd | 12 | |||
2100.2.bc.c.1549.2 | 4 | 35.23 | odd | 12 | |||
2940.2.a.d.1.1 | 1 | 35.4 | even | 6 | |||
2940.2.a.h.1.1 | 1 | 35.24 | odd | 6 | |||
2940.2.q.h.361.1 | 2 | 35.34 | odd | 2 | |||
2940.2.q.h.961.1 | 2 | 35.19 | odd | 6 | |||
8820.2.a.j.1.1 | 1 | 105.74 | odd | 6 | |||
8820.2.a.y.1.1 | 1 | 105.59 | even | 6 |