Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(671,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.12 | ||
Root | \(2.17840 + 0.583700i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.671 |
Dual form | 960.2.b.c.671.11 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.59470 | + | 0.675970i | 0.920700 | + | 0.390271i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.648061i | 0.244944i | 0.992472 | + | 0.122472i | \(0.0390822\pi\) | ||||
−0.992472 | + | 0.122472i | \(0.960918\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.08613 | + | 2.15594i | 0.695377 | + | 0.718645i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.17226i | 1.25798i | 0.777412 | + | 0.628992i | \(0.216532\pi\) | ||||
−0.777412 | + | 0.628992i | \(0.783468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.847771i | − | 0.235129i | −0.993065 | − | 0.117565i | \(-0.962491\pi\) | ||
0.993065 | − | 0.117565i | \(-0.0375087\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.59470 | − | 0.675970i | −0.411750 | − | 0.174535i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.91469i | 0.706917i | 0.935450 | + | 0.353459i | \(0.114994\pi\) | ||||
−0.935450 | + | 0.353459i | \(0.885006\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.847771 | −0.194492 | −0.0972460 | − | 0.995260i | \(-0.531003\pi\) | ||||
−0.0972460 | + | 0.995260i | \(0.531003\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.438069 | + | 1.03346i | −0.0955946 | + | 0.225520i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.34163 | 0.488263 | 0.244132 | − | 0.969742i | \(-0.421497\pi\) | ||||
0.244132 | + | 0.969742i | \(0.421497\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.86940 | + | 4.84823i | 0.359767 | + | 0.933042i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.87614 | −1.27687 | −0.638433 | − | 0.769677i | \(-0.720417\pi\) | ||||
−0.638433 | + | 0.769677i | \(0.720417\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.17226i | 0.390149i | 0.980788 | + | 0.195075i | \(0.0624949\pi\) | ||||
−0.980788 | + | 0.195075i | \(0.937505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82032 | + | 6.65350i | −0.490955 | + | 1.15823i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.648061i | − | 0.109542i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.53103i | 0.909295i | 0.890671 | + | 0.454647i | \(0.150235\pi\) | ||||
−0.890671 | + | 0.454647i | \(0.849765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.573067 | − | 1.35194i | 0.0917642 | − | 0.216484i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.31187i | − | 0.673401i | −0.941612 | − | 0.336701i | \(-0.890689\pi\) | ||
0.941612 | − | 0.336701i | \(-0.109311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.56819 | 1.45914 | 0.729568 | − | 0.683908i | \(-0.239721\pi\) | ||||
0.729568 | + | 0.683908i | \(0.239721\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.08613 | − | 2.15594i | −0.310982 | − | 0.321388i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9654 | 1.59946 | 0.799732 | − | 0.600357i | \(-0.204975\pi\) | ||||
0.799732 | + | 0.600357i | \(0.204975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.58002 | 0.940002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.97024 | + | 4.64806i | −0.275889 | + | 0.650859i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6406 | −1.59897 | −0.799483 | − | 0.600689i | \(-0.794893\pi\) | ||||
−0.799483 | + | 0.600689i | \(0.794893\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.17226i | − | 0.562587i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.35194 | − | 0.573067i | −0.179069 | − | 0.0759046i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.87614i | 0.895197i | 0.894235 | + | 0.447599i | \(0.147721\pi\) | ||||
−0.894235 | + | 0.447599i | \(0.852279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6907i | 1.36880i | 0.729107 | + | 0.684400i | \(0.239936\pi\) | ||||
−0.729107 | + | 0.684400i | \(0.760064\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.39718 | + | 1.35194i | −0.176028 | + | 0.170328i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.847771i | 0.105153i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.43435 | −0.663911 | −0.331956 | − | 0.943295i | \(-0.607708\pi\) | ||||
−0.331956 | + | 0.943295i | \(0.607708\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.73419 | + | 1.58287i | 0.449544 | + | 0.190555i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3070 | 1.57925 | 0.789625 | − | 0.613590i | \(-0.210275\pi\) | ||||
0.789625 | + | 0.613590i | \(0.210275\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0484 | −1.52720 | −0.763600 | − | 0.645690i | \(-0.776570\pi\) | ||||
−0.763600 | + | 0.645690i | \(0.776570\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.59470 | + | 0.675970i | 0.184140 | + | 0.0780542i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.70388 | −0.308136 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 17.2207i | − | 1.93748i | −0.248087 | − | 0.968738i | \(-0.579802\pi\) | ||
0.248087 | − | 0.968738i | \(-0.420198\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.296122 | + | 8.99513i | −0.0329024 | + | 0.999459i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.6481i | − | 1.16878i | −0.811474 | − | 0.584388i | \(-0.801335\pi\) | ||
0.811474 | − | 0.584388i | \(-0.198665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.91469i | − | 0.316143i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.9654 | − | 4.64806i | −1.17561 | − | 0.498324i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 17.9903i | − | 1.90696i | −0.301451 | − | 0.953482i | \(-0.597471\pi\) | ||
0.301451 | − | 0.953482i | \(-0.402529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.549407 | 0.0575935 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.46838 | + | 3.46410i | −0.152264 | + | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.847771 | 0.0869794 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.70388 | 0.477606 | 0.238803 | − | 0.971068i | \(-0.423245\pi\) | ||||
0.238803 | + | 0.971068i | \(0.423245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.99513 | + | 8.70388i | −0.904044 | + | 0.874773i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.46838 | 0.146109 | 0.0730547 | − | 0.997328i | \(-0.476725\pi\) | ||||
0.0730547 | + | 0.997328i | \(0.476725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.69646i | 0.758355i | 0.925324 | + | 0.379177i | \(0.123793\pi\) | ||||
−0.925324 | + | 0.379177i | \(0.876207\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.438069 | − | 1.03346i | 0.0427512 | − | 0.100856i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.35194i | − | 0.130697i | −0.997863 | − | 0.0653484i | \(-0.979184\pi\) | ||
0.997863 | − | 0.0653484i | \(-0.0208159\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.6189i | − | 1.68758i | −0.536672 | − | 0.843791i | \(-0.680319\pi\) | ||
0.536672 | − | 0.843791i | \(-0.319681\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.73881 | + | 8.82032i | −0.354872 | + | 0.837188i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.59795i | 0.714755i | 0.933960 | + | 0.357377i | \(0.116329\pi\) | ||||
−0.933960 | + | 0.357377i | \(0.883671\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.34163 | −0.218358 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.82774 | − | 1.76856i | 0.168975 | − | 0.163503i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.88890 | −0.173155 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.40776 | −0.582523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.91469 | − | 6.87614i | 0.262809 | − | 0.620001i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6965i | 1.03789i | 0.854807 | + | 0.518946i | \(0.173676\pi\) | ||||
−0.854807 | + | 0.518946i | \(0.826324\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.2584 | + | 6.46781i | 1.34343 | + | 0.569459i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 9.58002i | − | 0.837010i | −0.908214 | − | 0.418505i | \(-0.862554\pi\) | ||
0.908214 | − | 0.418505i | \(-0.137446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.549407i | − | 0.0476396i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.86940 | − | 4.84823i | −0.160893 | − | 0.417269i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.2217i | − | 1.38591i | −0.720979 | − | 0.692956i | \(-0.756308\pi\) | ||
0.720979 | − | 0.692956i | \(-0.243692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.98162 | −0.422535 | −0.211268 | − | 0.977428i | \(-0.567759\pi\) | ||||
−0.211268 | + | 0.977428i | \(0.567759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.4865 | + | 7.41226i | 1.47263 | + | 0.624225i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.53712 | 0.295789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.87614 | 0.571032 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.4931 | + | 4.44789i | 0.865460 | + | 0.366856i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.34452 | 0.192071 | 0.0960353 | − | 0.995378i | \(-0.469384\pi\) | ||||
0.0960353 | + | 0.995378i | \(0.469384\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5800i | 0.942368i | 0.882035 | + | 0.471184i | \(0.156173\pi\) | ||||
−0.882035 | + | 0.471184i | \(0.843827\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.28390 | + | 6.08043i | −0.508023 | + | 0.491574i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.17226i | − | 0.174480i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.39718i | 0.111507i | 0.998445 | + | 0.0557535i | \(0.0177561\pi\) | ||||
−0.998445 | + | 0.0557535i | \(0.982244\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.5633 | − | 7.86872i | −1.47217 | − | 0.624030i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.51752i | 0.119597i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8131 | 0.925277 | 0.462638 | − | 0.886547i | \(-0.346903\pi\) | ||||
0.462638 | + | 0.886547i | \(0.346903\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.82032 | − | 6.65350i | 0.219562 | − | 0.517974i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.28212 | −0.486125 | −0.243062 | − | 0.970011i | \(-0.578152\pi\) | ||||
−0.243062 | + | 0.970011i | \(0.578152\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2813 | 0.944714 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.76856 | − | 1.82774i | −0.135245 | − | 0.139771i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.0968 | 1.22382 | 0.611908 | − | 0.790929i | \(-0.290402\pi\) | ||||
0.611908 | + | 0.790929i | \(0.290402\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.648061i | 0.0489888i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.64806 | + | 10.9654i | −0.349370 | + | 0.824208i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 13.4684i | − | 1.00667i | −0.864090 | − | 0.503337i | \(-0.832105\pi\) | ||
0.864090 | − | 0.503337i | \(-0.167895\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.0621i | − | 0.822236i | −0.911582 | − | 0.411118i | \(-0.865138\pi\) | ||
0.911582 | − | 0.411118i | \(-0.134862\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.22657 | + | 17.0484i | −0.534203 | + | 1.26025i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.53103i | − | 0.406649i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.1609 | −0.889291 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.14195 | + | 1.21149i | −0.228543 | + | 0.0881227i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.14613 | −0.0829314 | −0.0414657 | − | 0.999140i | \(-0.513203\pi\) | ||||
−0.0414657 | + | 0.999140i | \(0.513203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.3929 | −1.25197 | −0.625985 | − | 0.779835i | \(-0.715303\pi\) | ||||
−0.625985 | + | 0.779835i | \(0.715303\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.573067 | + | 1.35194i | −0.0410382 | + | 0.0968144i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4562 | 0.744970 | 0.372485 | − | 0.928038i | \(-0.378506\pi\) | ||||
0.372485 | + | 0.928038i | \(0.378506\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.2839i | − | 1.01256i | −0.862370 | − | 0.506279i | \(-0.831021\pi\) | ||
0.862370 | − | 0.506279i | \(-0.168979\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.66615 | − | 3.67345i | −0.611263 | − | 0.259105i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4.45616i | − | 0.312761i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.31187i | 0.301154i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.88494 | + | 5.04840i | 0.339527 | + | 0.350888i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.53712i | − | 0.244668i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.92211 | 0.614223 | 0.307112 | − | 0.951673i | \(-0.400637\pi\) | ||||
0.307112 | + | 0.951673i | \(0.400637\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.2207 | + | 8.99513i | 1.45402 | + | 0.616336i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.56819 | −0.652545 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.40776 | −0.0955648 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.8083 | − | 8.82032i | −1.40609 | − | 0.596022i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.47099 | 0.166217 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.1042i | 1.14538i | 0.819771 | + | 0.572692i | \(0.194101\pi\) | ||||
−0.819771 | + | 0.572692i | \(0.805899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.08613 | + | 2.15594i | 0.139075 | + | 0.143729i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 13.3519i | − | 0.886199i | −0.896472 | − | 0.443100i | \(-0.853879\pi\) | ||
0.896472 | − | 0.443100i | \(-0.146121\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.9903i | − | 1.18883i | −0.804159 | − | 0.594415i | \(-0.797384\pi\) | ||
0.804159 | − | 0.594415i | \(-0.202616\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.31187 | − | 1.82774i | −0.283700 | − | 0.120256i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.1622i | − | 1.32087i | −0.750884 | − | 0.660434i | \(-0.770372\pi\) | ||
0.750884 | − | 0.660434i | \(-0.229628\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9654 | −0.715302 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.6406 | − | 27.4618i | 0.756141 | − | 1.78383i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.1609 | −0.786621 | −0.393310 | − | 0.919406i | \(-0.628670\pi\) | ||||
−0.393310 | + | 0.919406i | \(0.628670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.51678 | −0.548614 | −0.274307 | − | 0.961642i | \(-0.588448\pi\) | ||||
−0.274307 | + | 0.961642i | \(0.588448\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.55266 | + | 14.1444i | −0.420353 | + | 0.907361i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.58002 | −0.420382 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.718715i | 0.0457308i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.19777 | − | 16.9805i | 0.456140 | − | 1.07609i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.5168i | − | 0.790052i | −0.918670 | − | 0.395026i | \(-0.870736\pi\) | ||
0.918670 | − | 0.395026i | \(-0.129264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.76988i | 0.614227i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.97024 | − | 4.64806i | 0.123382 | − | 0.291073i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.76856i | 0.110320i | 0.998478 | + | 0.0551599i | \(0.0175668\pi\) | ||||
−0.998478 | + | 0.0551599i | \(0.982433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.58444 | −0.222726 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.3445 | − | 14.8245i | −0.887904 | − | 0.917615i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.1018 | 1.85615 | 0.928077 | − | 0.372388i | \(-0.121461\pi\) | ||||
0.928077 | + | 0.372388i | \(0.121461\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6406 | 0.715079 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1609 | − | 28.6890i | 0.744233 | − | 1.75574i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.06324 | −0.186769 | −0.0933844 | − | 0.995630i | \(-0.529769\pi\) | ||||
−0.0933844 | + | 0.995630i | \(0.529769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.76450i | − | 0.532406i | −0.963917 | − | 0.266203i | \(-0.914231\pi\) | ||
0.963917 | − | 0.266203i | \(-0.0857691\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.876139 | + | 0.371382i | 0.0530263 | + | 0.0224771i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.17226i | 0.251597i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.0112i | 1.68303i | 0.540235 | + | 0.841514i | \(0.318335\pi\) | ||||
−0.540235 | + | 0.841514i | \(0.681665\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.68325 | + | 4.53162i | −0.280379 | + | 0.271301i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.1413i | − | 0.604977i | −0.953153 | − | 0.302488i | \(-0.902183\pi\) | ||
0.953153 | − | 0.302488i | \(-0.0978174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.88494 | −0.290380 | −0.145190 | − | 0.989404i | \(-0.546379\pi\) | ||||
−0.145190 | + | 0.989404i | \(0.546379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.35194 | + | 0.573067i | 0.0800820 | + | 0.0339456i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.79436 | 0.164946 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50456 | 0.500268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.50127 | + | 3.17968i | 0.439732 | + | 0.186396i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6.87614i | − | 0.400344i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −20.2281 | + | 7.79963i | −1.17375 | + | 0.452581i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.98516i | − | 0.114805i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.20077i | 0.357407i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.34163 | + | 0.992582i | 0.134523 | + | 0.0570223i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 10.6907i | − | 0.612146i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.42206 | −0.480672 | −0.240336 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240336 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.20257 | + | 12.2735i | −0.295964 | + | 0.698217i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.9307 | −1.24358 | −0.621789 | − | 0.783185i | \(-0.713594\pi\) | ||||
−0.621789 | + | 0.783185i | \(0.713594\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.39718 | − | 1.35194i | 0.0787220 | − | 0.0761731i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.0484 | −0.957533 | −0.478767 | − | 0.877942i | \(-0.658916\pi\) | ||||
−0.478767 | + | 0.877942i | \(0.658916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 28.6890i | − | 1.60628i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.913870 | − | 2.15594i | 0.0510072 | − | 0.120333i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.47099i | − | 0.137490i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.847771i | − | 0.0470259i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.9098 | − | 28.0968i | 0.658615 | − | 1.55376i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.10623i | 0.391779i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.73667 | 0.150421 | 0.0752105 | − | 0.997168i | \(-0.476037\pi\) | ||||
0.0752105 | + | 0.997168i | \(0.476037\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.9245 | + | 11.5384i | −0.653461 | + | 0.632303i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.43435 | 0.296910 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.65548 | 0.308074 | 0.154037 | − | 0.988065i | \(-0.450773\pi\) | ||||
0.154037 | + | 0.988065i | \(0.450773\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.13598 | + | 12.1164i | −0.278948 | + | 0.658075i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.06324 | −0.490802 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.80068i | 0.475192i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.73419 | − | 1.58287i | −0.201042 | − | 0.0852188i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.0558i | 0.861921i | 0.902371 | + | 0.430961i | \(0.141825\pi\) | ||||
−0.902371 | + | 0.430961i | \(0.858175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 25.5152i | − | 1.36580i | −0.730513 | − | 0.682898i | \(-0.760719\pi\) | ||
0.730513 | − | 0.682898i | \(-0.239281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.11019 | − | 1.58482i | 0.219386 | − | 0.0845917i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.2217i | 0.863394i | 0.902019 | + | 0.431697i | \(0.142085\pi\) | ||||
−0.902019 | + | 0.431697i | \(0.857915\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.3070 | −0.706262 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.01223 | − | 1.27684i | −0.159424 | − | 0.0675775i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0769 | 1.21795 | 0.608976 | − | 0.793189i | \(-0.291581\pi\) | ||||
0.608976 | + | 0.793189i | \(0.291581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2813 | −0.962173 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.2184 | − | 4.33145i | −0.536329 | − | 0.227342i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.0484 | 0.682984 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.9293i | 1.04030i | 0.854074 | + | 0.520152i | \(0.174125\pi\) | ||||
−0.854074 | + | 0.520152i | \(0.825875\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.29612 | − | 8.99513i | 0.483937 | − | 0.468268i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.54384i | − | 0.391657i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.9842i | 1.03474i | 0.855762 | + | 0.517370i | \(0.173089\pi\) | ||||
−0.855762 | + | 0.517370i | \(0.826911\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.59470 | − | 0.675970i | −0.0823499 | − | 0.0349069i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.82939i | 0.300229i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8380 | 0.967644 | 0.483822 | − | 0.875166i | \(-0.339248\pi\) | ||||
0.483822 | + | 0.875166i | \(0.339248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.90645 | + | 18.6523i | −0.405060 | + | 0.955588i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.81924 | −0.501740 | −0.250870 | − | 0.968021i | \(-0.580717\pi\) | ||||
−0.250870 | + | 0.968021i | \(0.580717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.70388 | 0.137802 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.9605 | + | 20.6284i | 1.01465 | + | 1.04860i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.09680 | −0.207716 | −0.103858 | − | 0.994592i | \(-0.533119\pi\) | ||||
−0.103858 | + | 0.994592i | \(0.533119\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.82513i | 0.345162i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.47580 | − | 15.2772i | 0.326661 | − | 0.770635i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.2207i | 0.866465i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5.57835i | − | 0.279969i | −0.990154 | − | 0.139985i | \(-0.955295\pi\) | ||
0.990154 | − | 0.139985i | \(-0.0447053\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.371382 | − | 0.876139i | 0.0185924 | − | 0.0438618i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.4084i | 1.46858i | 0.678834 | + | 0.734292i | \(0.262485\pi\) | ||||
−0.678834 | + | 0.734292i | \(0.737515\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.84158 | 0.0917356 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.296122 | − | 8.99513i | 0.0147144 | − | 0.446971i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.0769 | −1.14388 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.172260 | −0.00851773 | −0.00425886 | − | 0.999991i | \(-0.501356\pi\) | ||||
−0.00425886 | + | 0.999991i | \(0.501356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.9654 | − | 25.8687i | 0.540882 | − | 1.27601i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.45616 | −0.219273 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6481i | 0.522693i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.94418 | − | 3.36742i | −0.389028 | − | 0.164903i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.6284i | 1.00776i | 0.863772 | + | 0.503882i | \(0.168095\pi\) | ||||
−0.863772 | + | 0.503882i | \(0.831905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.8393i | − | 1.30807i | −0.756464 | − | 0.654035i | \(-0.773075\pi\) | ||
0.756464 | − | 0.654035i | \(-0.226925\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.8752 | + | 23.6406i | 1.11223 | + | 1.14945i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.91469i | 0.141383i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.92820 | −0.335279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.64064 | + | 2.39099i | 0.272333 | + | 0.115438i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.9658 | 1.20256 | 0.601280 | − | 0.799039i | \(-0.294658\pi\) | ||||
0.601280 | + | 0.799039i | \(0.294658\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5774 | 0.892773 | 0.446387 | − | 0.894840i | \(-0.352711\pi\) | ||||
0.446387 | + | 0.894840i | \(0.352711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.9654 | + | 4.64806i | 0.525749 | + | 0.222857i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.98516 | −0.0949632 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.71610i | − | 0.0819052i | −0.999161 | − | 0.0409526i | \(-0.986961\pi\) | ||
0.999161 | − | 0.0409526i | \(-0.0130393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.7268 | + | 14.1861i | 0.653656 | + | 0.675528i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.7449i | 1.55576i | 0.628416 | + | 0.777878i | \(0.283704\pi\) | ||||
−0.628416 | + | 0.777878i | \(0.716296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.9903i | 0.852820i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.73881 | + | 1.58482i | 0.176839 | + | 0.0749596i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.31187i | 0.203490i | 0.994811 | + | 0.101745i | \(0.0324426\pi\) | ||||
−0.994811 | + | 0.101745i | \(0.967557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.9903 | 0.847128 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.82774 | + | 18.4666i | −0.367779 | + | 0.867639i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.549407 | −0.0257566 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.6555 | 0.638776 | 0.319388 | − | 0.947624i | \(-0.396523\pi\) | ||||
0.319388 | + | 0.947624i | \(0.396523\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.1311 | + | 5.44874i | −0.659584 | + | 0.254325i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.9974 | −0.512199 | −0.256100 | − | 0.966650i | \(-0.582438\pi\) | ||||
−0.256100 | + | 0.966650i | \(0.582438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.24030i | 0.336485i | 0.985746 | + | 0.168243i | \(0.0538092\pi\) | ||||
−0.985746 | + | 0.168243i | \(0.946191\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.46838 | − | 3.46410i | 0.0680946 | − | 0.160644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.6481i | − | 0.492733i | −0.969177 | − | 0.246367i | \(-0.920763\pi\) | ||
0.969177 | − | 0.246367i | \(-0.0792368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.52179i | − | 0.162621i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.944450 | + | 2.22808i | −0.0435179 | + | 0.102664i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 39.9210i | 1.83557i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.847771 | −0.0388984 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.2839 | − | 25.0965i | −1.11188 | − | 1.14909i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.0769 | −1.05441 | −0.527205 | − | 0.849738i | \(-0.676760\pi\) | ||||
−0.527205 | + | 0.849738i | \(0.676760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.68904 | 0.213802 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.02580 | + | 2.41998i | −0.0466753 | + | 0.110113i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.70388 | −0.213592 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.4003i | − | 0.471284i | −0.971840 | − | 0.235642i | \(-0.924281\pi\) | ||
0.971840 | − | 0.235642i | \(-0.0757193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.8384 | + | 7.98533i | 0.851902 | + | 0.361109i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.5168i | 1.64798i | 0.566605 | + | 0.823990i | \(0.308257\pi\) | ||||
−0.566605 | + | 0.823990i | \(0.691743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 20.0418i | − | 0.902639i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.99513 | − | 8.70388i | 0.404301 | − | 0.391210i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.62374i | 0.386828i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.6944 | 1.46360 | 0.731802 | − | 0.681517i | \(-0.238680\pi\) | ||||
0.731802 | + | 0.681517i | \(0.238680\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0181 | − | 4.24652i | −0.447575 | − | 0.189721i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.6242 | −1.00876 | −0.504381 | − | 0.863482i | \(-0.668279\pi\) | ||||
−0.504381 | + | 0.863482i | \(0.668279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.46838 | −0.0653421 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.5850 | + | 8.30178i | 0.869798 | + | 0.368695i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.12386 | 0.227111 | 0.113556 | − | 0.993532i | \(-0.463776\pi\) | ||||
0.113556 | + | 0.993532i | \(0.463776\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.45616i | − | 0.374078i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.58482 | − | 4.11019i | −0.0699717 | − | 0.181469i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.69646i | − | 0.339147i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.7504i | 2.01210i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.6695 | + | 10.8809i | 1.12677 | + | 0.477621i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.9063i | 1.26641i | 0.773986 | + | 0.633203i | \(0.218260\pi\) | ||||
−0.773986 | + | 0.633203i | \(0.781740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.6075 | 0.638741 | 0.319371 | − | 0.947630i | \(-0.396529\pi\) | ||||
0.319371 | + | 0.947630i | \(0.396529\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.438069 | + | 1.03346i | −0.0191189 | + | 0.0451040i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.33148 | −0.275803 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5168 | −0.761599 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.8245 | + | 14.3445i | −0.643329 | + | 0.622499i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.65548 | −0.158336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.35194i | 0.0584494i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.10422 | − | 21.4780i | 0.392876 | − | 0.926845i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.4535i | 1.18251i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.3446i | 1.34761i | 0.738910 | + | 0.673804i | \(0.235341\pi\) | ||||
−0.738910 | + | 0.673804i | \(0.764659\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.47761 | − | 17.6406i | 0.320895 | − | 0.757032i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.6189i | 0.754710i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.5952 | −0.752317 | −0.376158 | − | 0.926555i | \(-0.622755\pi\) | ||||
−0.376158 | + | 0.926555i | \(0.622755\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.0484 | + | 22.3021i | −0.983682 | + | 0.951832i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.82939 | 0.248340 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1600 | 0.474573 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.73881 | − | 8.82032i | 0.158703 | − | 0.374402i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.5678 | −0.786743 | −0.393371 | − | 0.919380i | \(-0.628691\pi\) | ||||
−0.393371 | + | 0.919380i | \(0.628691\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.11164i | − | 0.343086i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.3929 | − | 8.22038i | −0.818770 | − | 0.347065i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.1191i | 0.552902i | 0.961028 | + | 0.276451i | \(0.0891584\pi\) | ||||
−0.961028 | + | 0.276451i | \(0.910842\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 7.59795i | − | 0.319648i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.82939 | − | 0.191905i | −0.244811 | − | 0.00805924i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.8840i | 0.456282i | 0.973628 | + | 0.228141i | \(0.0732647\pi\) | ||||
−0.973628 | + | 0.228141i | \(0.926735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.4592 | 0.521402 | 0.260701 | − | 0.965420i | \(-0.416046\pi\) | ||||
0.260701 | + | 0.965420i | \(0.416046\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.82774 | − | 0.774752i | −0.0763549 | − | 0.0323657i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.34163 | 0.0976526 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.2813 | 0.885951 | 0.442976 | − | 0.896534i | \(-0.353923\pi\) | ||||
0.442976 | + | 0.896534i | \(0.353923\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.7365 | − | 11.7571i | −1.15269 | − | 0.488608i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.90059 | 0.286285 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 48.5678i | − | 2.01147i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.82774 | + | 1.76856i | −0.0755677 | + | 0.0731210i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.9926i | 1.27920i | 0.768708 | + | 0.639600i | \(0.220900\pi\) | ||||
−0.768708 | + | 0.639600i | \(0.779100\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.84158i | − | 0.0758809i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.6744 | + | 7.06804i | 0.685894 | + | 0.290740i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 39.2986i | − | 1.61380i | −0.590689 | − | 0.806899i | \(-0.701144\pi\) | ||
0.590689 | − | 0.806899i | \(-0.298856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.88890 | 0.0774373 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.65548 | − | 22.7785i | 0.395172 | − | 0.932263i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.4084 | −1.20159 | −0.600796 | − | 0.799402i | \(-0.705150\pi\) | ||||
−0.600796 | + | 0.799402i | \(0.705150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3323 | 0.788581 | 0.394290 | − | 0.918986i | \(-0.370990\pi\) | ||||
0.394290 | + | 0.918986i | \(0.370990\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.3368 | − | 11.7161i | −0.461668 | − | 0.477117i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.40776 | 0.260512 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.87133i | 0.197721i | 0.995101 | + | 0.0988606i | \(0.0315198\pi\) | ||||
−0.995101 | + | 0.0988606i | \(0.968480\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.01223 | − | 7.10623i | 0.122062 | − | 0.287959i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 9.29612i | − | 0.376081i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 12.5065i | − | 0.505135i | −0.967579 | − | 0.252567i | \(-0.918725\pi\) | ||
0.967579 | − | 0.252567i | \(-0.0812749\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.91469 | + | 6.87614i | −0.117532 | + | 0.277273i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.4839i | 1.79085i | 0.445207 | + | 0.895427i | \(0.353130\pi\) | ||||
−0.445207 | + | 0.895427i | \(0.646870\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.1074 | 0.567026 | 0.283513 | − | 0.958968i | \(-0.408500\pi\) | ||||
0.283513 | + | 0.958968i | \(0.408500\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.37744 | + | 11.3527i | 0.175661 | + | 0.455570i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.6588 | 0.467099 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.39099 | − | 5.64064i | 0.0954868 | − | 0.225266i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.1213 | −0.642796 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.64325i | 0.344082i | 0.985090 | + | 0.172041i | \(0.0550362\pi\) | ||||
−0.985090 | + | 0.172041i | \(0.944964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.2281 | + | 6.03107i | 0.565515 | + | 0.239714i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 11.6965i | − | 0.464160i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.57835i | − | 0.221022i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.7601 | + | 28.6890i | 1.09817 | + | 1.13492i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 36.0125i | − | 1.42241i | −0.702986 | − | 0.711204i | \(-0.748150\pi\) | ||
0.702986 | − | 0.711204i | \(-0.251850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.5437 | 0.652421 | 0.326210 | − | 0.945297i | \(-0.394228\pi\) | ||||
0.326210 | + | 0.945297i | \(0.394228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.2584 | − | 6.46781i | −0.600799 | − | 0.254670i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.0773 | 1.45766 | 0.728829 | − | 0.684696i | \(-0.240065\pi\) | ||||
0.728829 | + | 0.684696i | \(0.240065\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.6890 | −1.12614 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.24495 | − | 0.951601i | −0.0879865 | − | 0.0372962i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.3929 | −0.524105 | −0.262053 | − | 0.965054i | \(-0.584399\pi\) | ||||
−0.262053 | + | 0.965054i | \(0.584399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.58002i | 0.374322i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.2207 | − | 28.1315i | −1.06198 | − | 1.09751i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 29.6917i | − | 1.15662i | −0.815816 | − | 0.578311i | \(-0.803712\pi\) | ||
0.815816 | − | 0.578311i | \(-0.196288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 44.8296i | − | 1.74367i | −0.489800 | − | 0.871835i | \(-0.662930\pi\) | ||
0.489800 | − | 0.871835i | \(-0.337070\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.94049 | + | 1.67032i | 0.153036 | + | 0.0648697i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.549407i | 0.0213051i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.1014 | −0.623447 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.5619 | + | 27.2761i | −0.447010 | + | 1.05455i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.6043 | −1.72193 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.3929 | −1.28720 | −0.643601 | − | 0.765361i | \(-0.722560\pi\) | ||||
−0.643601 | + | 0.765361i | \(0.722560\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.86940 | + | 4.84823i | 0.0719533 | + | 0.186608i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.2084 | 1.39160 | 0.695802 | − | 0.718234i | \(-0.255049\pi\) | ||||
0.695802 | + | 0.718234i | \(0.255049\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.04840i | 0.116987i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.02551 | − | 21.2923i | 0.345858 | − | 0.815924i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.51197i | 0.325702i | 0.986651 | + | 0.162851i | \(0.0520689\pi\) | ||||
−0.986651 | + | 0.162851i | \(0.947931\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.2217i | 0.619799i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.1609 | − | 28.6890i | 0.463966 | − | 1.09456i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.86860i | 0.375964i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.2937 | −1.83718 | −0.918589 | − | 0.395213i | \(-0.870671\pi\) | ||||
−0.918589 | + | 0.395213i | \(0.870671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.64064 | − | 5.82939i | −0.214270 | − | 0.221440i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.98162 | 0.188964 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5678 | 0.476039 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.6290 | − | 32.1526i | 0.515497 | − | 1.21612i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.0968 | 1.51444 | 0.757218 | − | 0.653163i | \(-0.226558\pi\) | ||||
0.757218 | + | 0.653163i | \(0.226558\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.68904i | − | 0.176851i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.4865 | − | 7.41226i | −0.658579 | − | 0.279162i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.951601i | 0.0357886i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1487i | 0.606476i | 0.952915 | + | 0.303238i | \(0.0980678\pi\) | ||||
−0.952915 | + | 0.303238i | \(0.901932\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.1266 | − | 35.9245i | 1.39236 | − | 1.34728i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.08662i | 0.190496i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.53712 | −0.132281 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.3929 | − | 8.22038i | −0.724242 | − | 0.306996i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.33148 | 0.236124 | 0.118062 | − | 0.993006i | \(-0.462332\pi\) | ||||
0.118062 | + | 0.993006i | \(0.462332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.98777 | −0.185754 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.5817 | − | 5.75709i | −0.505109 | − | 0.214108i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.87614 | −0.255373 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.6965i | 1.32391i | 0.749544 | + | 0.661954i | \(0.230273\pi\) | ||||
−0.749544 | + | 0.661954i | \(0.769727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.0107 | + | 18.1266i | −0.741136 | + | 0.671355i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.8884i | 1.03149i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.0462i | − | 1.14672i | −0.819304 | − | 0.573359i | \(-0.805640\pi\) | ||
0.819304 | − | 0.573359i | \(-0.194360\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.4931 | − | 4.44789i | −0.387046 | − | 0.164063i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 22.6735i | − | 0.835189i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.1671 | −0.410787 | −0.205393 | − | 0.978679i | \(-0.565847\pi\) | ||||
−0.205393 | + | 0.978679i | \(0.565847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.485830 | + | 1.14613i | −0.0178474 | + | 0.0421043i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.4332 | −1.33661 | −0.668303 | − | 0.743889i | \(-0.732979\pi\) | ||||
−0.668303 | + | 0.743889i | \(0.732979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.34452 | −0.0858966 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.9565 | − | 22.2132i | 0.839936 | − | 0.812740i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.876139 | 0.0320134 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 25.4832i | − | 0.929896i | −0.885338 | − | 0.464948i | \(-0.846073\pi\) | ||
0.885338 | − | 0.464948i | \(-0.153927\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.46096 | − | 19.9605i | 0.308335 | − | 0.727401i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 11.5800i | − | 0.421440i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.1599i | 1.60502i | 0.596641 | + | 0.802509i | \(0.296502\pi\) | ||||
−0.596641 | + | 0.802509i | \(0.703498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.60414 | + | 15.5800i | −0.239715 | + | 0.565519i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.33148i | 0.229516i | 0.993393 | + | 0.114758i | \(0.0366092\pi\) | ||||
−0.993393 | + | 0.114758i | \(0.963391\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.4181 | 0.413363 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.28390 | − | 6.08043i | 0.227195 | − | 0.219839i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.82939 | 0.210487 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.9123 | −1.54746 | −0.773729 | − | 0.633517i | \(-0.781611\pi\) | ||||
−0.773729 | + | 0.633517i | \(0.781611\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.19549 | + | 2.82032i | −0.0430546 | + | 0.101571i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.23289 | −0.224181 | −0.112091 | − | 0.993698i | \(-0.535755\pi\) | ||||
−0.112091 | + | 0.993698i | \(0.535755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.17226i | 0.0780299i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.71610 | − | 2.42297i | −0.205064 | − | 0.0869237i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.65548i | 0.130971i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55.5203i | 1.98667i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.8543 | − | 33.3371i | −0.459374 | − | 1.19137i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.39718i | − | 0.0498674i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.8034 | −1.06238 | −0.531188 | − | 0.847254i | \(-0.678254\pi\) | ||||
−0.531188 | + | 0.847254i | \(0.678254\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 48.0032 | + | 20.3479i | 1.70896 | + | 0.724404i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.92393 | −0.175075 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.06324 | 0.321845 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.5633 | + | 7.86872i | 0.658373 | + | 0.279075i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.6110 | 1.82815 | 0.914077 | − | 0.405540i | \(-0.132917\pi\) | ||||
0.914077 | + | 0.405540i | \(0.132917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.9607i | 1.13069i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.7858 | − | 37.5300i | 1.37043 | − | 1.32606i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 54.4413i | − | 1.92119i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.51752i | − | 0.0534854i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.88494 | − | 2.07065i | −0.171958 | − | 0.0728905i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.1959i | 0.534259i | 0.963661 | + | 0.267130i | \(0.0860752\pi\) | ||||
−0.963661 | + | 0.267130i | \(0.913925\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.96933 | −0.279841 | −0.139921 | − | 0.990163i | \(-0.544685\pi\) | ||||
−0.139921 | + | 0.990163i | \(0.544685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.92454 | − | 13.9767i | 0.207783 | − | 0.490186i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.8131 | −0.413796 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.11164 | −0.283790 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.14613 | + | 1.18449i | 0.0400492 | + | 0.0413893i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.5678 | −1.06682 | −0.533412 | − | 0.845856i | \(-0.679090\pi\) | ||||
−0.533412 | + | 0.845856i | \(0.679090\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 28.2739i | − | 0.985565i | −0.870153 | − | 0.492783i | \(-0.835980\pi\) | ||
0.870153 | − | 0.492783i | \(-0.164020\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.82032 | + | 6.65350i | −0.0981910 | + | 0.231645i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29.0894i | − | 1.01154i | −0.862669 | − | 0.505768i | \(-0.831209\pi\) | ||
0.862669 | − | 0.505768i | \(-0.168791\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 30.7325i | − | 1.06738i | −0.845679 | − | 0.533692i | \(-0.820804\pi\) | ||
0.845679 | − | 0.533692i | \(-0.179196\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.9347 | + | 44.6694i | −0.656838 | + | 1.54956i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.1787i | 0.664504i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.28212 | 0.217402 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.5316 | + | 4.06083i | −0.364026 | + | 0.140363i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.5624 | 0.847989 | 0.423994 | − | 0.905665i | \(-0.360628\pi\) | ||||
0.423994 | + | 0.905665i | \(0.360628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.2813 | 0.630389 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.85518 | − | 16.1723i | 0.236105 | − | 0.557002i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.2813 | −0.422489 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.15262i | − | 0.142686i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.79001 | − | 3.30207i | −0.267352 | − | 0.113327i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.9516i | 0.443975i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 55.1746i | − | 1.88914i | −0.328308 | − | 0.944571i | \(-0.606478\pi\) | ||
0.328308 | − | 0.944571i | \(-0.393522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.76856 | + | 1.82774i | 0.0604835 | + | 0.0625074i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.80359i | 0.164088i | 0.996629 | + | 0.0820438i | \(0.0261447\pi\) | ||||
−0.996629 | + | 0.0820438i | \(0.973855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.8529 | 1.05269 | 0.526343 | − | 0.850272i | \(-0.323563\pi\) | ||||
0.526343 | + | 0.850272i | \(0.323563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.45616 | + | 1.88890i | 0.151865 | + | 0.0643735i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.9907 | −1.08897 | −0.544487 | − | 0.838769i | \(-0.683276\pi\) | ||||
−0.544487 | + | 0.838769i | \(0.683276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.0968 | −0.547308 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.5622 | + | 5.74882i | 0.460597 | + | 0.195240i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 71.8491 | 2.43731 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.60708i | 0.156105i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.81290 | + | 10.1413i | 0.332116 | + | 0.343230i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 0.648061i | − | 0.0219085i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 24.1180i | − | 0.814407i | −0.913337 | − | 0.407204i | \(-0.866504\pi\) | ||
0.913337 | − | 0.407204i | \(-0.133496\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.7046 | + | 12.1675i | 0.968182 | + | 0.410398i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.0449i | − | 0.776402i | −0.921575 | − | 0.388201i | \(-0.873097\pi\) | ||
0.921575 | − | 0.388201i | \(-0.126903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.8261 | −1.20565 | −0.602823 | − | 0.797875i | \(-0.705957\pi\) | ||||
−0.602823 | + | 0.797875i | \(0.705957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.64806 | − | 10.9654i | 0.156243 | − | 0.368597i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.8348 | −1.63971 | −0.819856 | − | 0.572570i | \(-0.805946\pi\) | ||||
−0.819856 | + | 0.572570i | \(0.805946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.58002 | −0.254226 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.5300 | − | 1.23550i | −1.25730 | − | 0.0413907i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.29612 | −0.311083 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.4684i | 0.450198i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.34191 | − | 3.16574i | 0.0448051 | − | 0.105701i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.9368i | − | 0.498169i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 33.9289i | − | 1.13034i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.19153 | + | 9.88836i | −0.139485 | + | 0.329064i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.0621i | 0.367715i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.0483 | −1.06415 | −0.532074 | − | 0.846698i | \(-0.678587\pi\) | ||||
−0.532074 | + | 0.846698i | \(0.678587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.06324 | + | 3.16574i | 0.101601 | + | 0.105001i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9658 | −0.827153 | −0.413577 | − | 0.910469i | \(-0.635721\pi\) | ||||
−0.413577 | + | 0.910469i | \(0.635721\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.4265 | 1.47030 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.22657 | − | 17.0484i | 0.238903 | − | 0.563603i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.20843 | 0.205021 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.5652i | 1.23916i | 0.784933 | + | 0.619580i | \(0.212697\pi\) | ||||
−0.784933 | + | 0.619580i | \(0.787303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.4307 | − | 5.69306i | −0.442555 | − | 0.187593i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 11.2813i | − | 0.371328i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.53103i | 0.181859i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.5931 | + | 16.0558i | −0.544988 | + | 0.527342i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 33.2181i | − | 1.08985i | −0.838484 | − | 0.544926i | \(-0.816558\pi\) | ||
0.838484 | − | 0.544926i | \(-0.183442\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.57835 | −0.182823 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.9729 | − | 14.8245i | −1.14496 | − | 0.485333i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.1609 | 0.397703 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0484 | 1.07964 | 0.539822 | − | 0.841779i | \(-0.318492\pi\) | ||||
0.539822 | + | 0.841779i | \(0.318492\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.3258 | − | 9.46357i | −0.728575 | − | 0.308832i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.5652 | 1.55058 | 0.775290 | − | 0.631605i | \(-0.217604\pi\) | ||||
0.775290 | + | 0.631605i | \(0.217604\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 10.0968i | − | 0.328797i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.14195 | − | 1.21149i | 0.102208 | − | 0.0394097i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 0.551262i | − | 0.0179136i | −0.999960 | − | 0.00895681i | \(-0.997149\pi\) | ||
0.999960 | − | 0.00895681i | \(-0.00285108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.0621i | 0.359089i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.1871 | − | 11.5242i | −0.881601 | − | 0.373698i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.1351i | − | 0.360700i | −0.983602 | − | 0.180350i | \(-0.942277\pi\) | ||
0.983602 | − | 0.180350i | \(-0.0577231\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.14613 | 0.0370880 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.3929 | − | 45.7504i | 0.626884 | − | 1.47890i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5126 | 0.339471 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.2813 | 0.847783 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.91469 | − | 2.82032i | 0.0939247 | − | 0.0908836i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.3929 | 0.559898 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.5700i | 1.20817i | 0.796920 | + | 0.604085i | \(0.206461\pi\) | ||||
−0.796920 | + | 0.604085i | \(0.793539\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.67032 | − | 3.94049i | 0.0536583 | − | 0.126587i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 38.2691i | − | 1.22811i | −0.789262 | − | 0.614056i | \(-0.789537\pi\) | ||
0.789262 | − | 0.614056i | \(-0.210463\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 3.22839i | − | 0.103497i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.573067 | − | 1.35194i | 0.0183528 | − | 0.0432967i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 0.120339i | − | 0.00384999i | −0.999998 | − | 0.00192500i | \(-0.999387\pi\) | ||
0.999998 | − | 0.00192500i | \(-0.000612746\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75.0600 | 2.39893 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.9852 | − | 36.7553i | 1.21277 | − | 1.17351i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.8445 | −0.983788 | −0.491894 | − | 0.870655i | \(-0.663695\pi\) | ||||
−0.491894 | + | 0.870655i | \(0.663695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.4562 | −0.333161 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.80359 | + | 11.3323i | −0.152900 | + | 0.360711i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.4051 | 0.712442 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 9.82774i | − | 0.312188i | −0.987742 | − | 0.156094i | \(-0.950110\pi\) | ||
0.987742 | − | 0.156094i | \(-0.0498903\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.36417 | + | 1.84991i | 0.138493 | + | 0.0587050i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.2839i | 0.452830i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.7295i | 1.13156i | 0.824555 | + | 0.565782i | \(0.191426\pi\) | ||||
−0.824555 | + | 0.565782i | \(0.808574\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.8157 | + | 10.3397i | −0.848411 | + | 0.327134i |
(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 | 960.2.b.c.671.12 | yes | 12 | |
3.2 | odd | 2 | 960.2.b.d.671.11 | yes | 12 | ||
4.3 | odd | 2 | inner | 960.2.b.c.671.1 | ✓ | 12 | |
8.3 | odd | 2 | 960.2.b.d.671.12 | yes | 12 | ||
8.5 | even | 2 | 960.2.b.d.671.1 | yes | 12 | ||
12.11 | even | 2 | 960.2.b.d.671.2 | yes | 12 | ||
24.5 | odd | 2 | inner | 960.2.b.c.671.2 | yes | 12 | |
24.11 | even | 2 | inner | 960.2.b.c.671.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
960.2.b.c.671.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
960.2.b.c.671.2 | yes | 12 | 24.5 | odd | 2 | inner | |
960.2.b.c.671.11 | yes | 12 | 24.11 | even | 2 | inner | |
960.2.b.c.671.12 | yes | 12 | 1.1 | even | 1 | trivial | |
960.2.b.d.671.1 | yes | 12 | 8.5 | even | 2 | ||
960.2.b.d.671.2 | yes | 12 | 12.11 | even | 2 | ||
960.2.b.d.671.11 | yes | 12 | 3.2 | odd | 2 | ||
960.2.b.d.671.12 | yes | 12 | 8.3 | odd | 2 |