Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(239,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.s (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.5 | ||
Character | \(\chi\) | \(=\) | 1344.239 |
Dual form | 1344.2.s.c.911.5 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −1.26429 | + | 1.18388i | −0.729936 | + | 0.683515i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.84277 | − | 2.84277i | −1.27133 | − | 1.27133i | −0.945393 | − | 0.325932i | \(-0.894322\pi\) |
−0.325932 | − | 0.945393i | \(-0.605678\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.196841 | − | 2.99354i | 0.0656136 | − | 0.997845i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31805 | − | 3.31805i | 1.00043 | − | 1.00043i | 0.000430454 | − | 1.00000i | \(-0.499863\pi\) |
1.00000 | 0.000430454i | \(-0.000137018\pi\) | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.31290 | − | 2.31290i | −0.641484 | − | 0.641484i | 0.309436 | − | 0.950920i | \(-0.399860\pi\) |
−0.950920 | + | 0.309436i | \(0.899860\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.95958 | + | 0.228568i | 1.79696 | + | 0.0590160i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.814979i | − | 0.197661i | −0.995104 | − | 0.0988307i | \(-0.968490\pi\) | ||
0.995104 | − | 0.0988307i | \(-0.0315102\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.39281 | + | 4.39281i | −1.00778 | + | 1.00778i | −0.00780997 | + | 0.999970i | \(0.502486\pi\) |
−0.999970 | + | 0.00780997i | \(0.997514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.26429 | + | 1.18388i | −0.275890 | + | 0.258345i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.30328i | 0.688782i | 0.938826 | + | 0.344391i | \(0.111915\pi\) | ||||
−0.938826 | + | 0.344391i | \(0.888085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.1627i | 2.23254i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.29513 | + | 4.01772i | 0.634149 | + | 0.773211i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.25705 | − | 3.25705i | 0.604818 | − | 0.604818i | −0.336769 | − | 0.941587i | \(-0.609334\pi\) |
0.941587 | + | 0.336769i | \(0.109334\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.89472i | − | 0.699513i | −0.936841 | − | 0.349756i | \(-0.886264\pi\) | ||
0.936841 | − | 0.349756i | \(-0.113736\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.266782 | + | 8.12315i | −0.0464408 | + | 1.41406i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.84277 | − | 2.84277i | −0.480516 | − | 0.480516i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.65469 | + | 3.65469i | −0.600827 | + | 0.600827i | −0.940532 | − | 0.339705i | \(-0.889673\pi\) |
0.339705 | + | 0.940532i | \(0.389673\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.66238 | + | 0.185965i | 0.906707 | + | 0.0297783i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.20387 | 0.500360 | 0.250180 | − | 0.968199i | \(-0.419510\pi\) | ||||
0.250180 | + | 0.968199i | \(0.419510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.63867 | − | 1.63867i | −0.249895 | − | 0.249895i | 0.571033 | − | 0.820927i | \(-0.306543\pi\) |
−0.820927 | + | 0.571033i | \(0.806543\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.06950 | + | 7.95036i | −1.35200 | + | 1.18517i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.70608 | −0.978182 | −0.489091 | − | 0.872233i | \(-0.662671\pi\) | ||||
−0.489091 | + | 0.872233i | \(0.662671\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.964840 | + | 1.03037i | 0.135105 | + | 0.144280i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.69839 | − | 7.69839i | −1.05746 | − | 1.05746i | −0.998246 | − | 0.0592097i | \(-0.981142\pi\) |
−0.0592097 | − | 0.998246i | \(-0.518858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.8649 | −2.54374 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.353196 | − | 10.7543i | 0.0467820 | − | 1.42445i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.31843 | + | 7.31843i | −0.952778 | + | 0.952778i | −0.998934 | − | 0.0461561i | \(-0.985303\pi\) |
0.0461561 | + | 0.998934i | \(0.485303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.54897 | − | 5.54897i | −0.710473 | − | 0.710473i | 0.256161 | − | 0.966634i | \(-0.417542\pi\) |
−0.966634 | + | 0.256161i | \(0.917542\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.196841 | − | 2.99354i | 0.0247996 | − | 0.377150i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.1501i | 1.63107i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0553126 | − | 0.0553126i | 0.00675751 | − | 0.00675751i | −0.703720 | − | 0.710477i | \(-0.748479\pi\) |
0.710477 | + | 0.703720i | \(0.248479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.91070 | − | 4.17629i | −0.470793 | − | 0.502767i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.50772i | − | 0.772325i | −0.922431 | − | 0.386162i | \(-0.873800\pi\) | ||
0.922431 | − | 0.386162i | \(-0.126200\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.05260i | 0.708403i | 0.935169 | + | 0.354201i | \(0.115247\pi\) | ||||
−0.935169 | + | 0.354201i | \(0.884753\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.2153 | − | 14.1128i | −1.52597 | − | 1.62961i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.31805 | − | 3.31805i | 0.378127 | − | 0.378127i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1804i | 1.70792i | 0.520335 | + | 0.853962i | \(0.325807\pi\) | ||||
−0.520335 | + | 0.853962i | \(0.674193\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.92251 | − | 1.17850i | −0.991390 | − | 0.130944i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.25907 | + | 4.25907i | 0.467494 | + | 0.467494i | 0.901102 | − | 0.433608i | \(-0.142760\pi\) |
−0.433608 | + | 0.901102i | \(0.642760\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.31680 | + | 2.31680i | −0.251292 | + | 0.251292i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.261877 | + | 7.97380i | −0.0280762 | + | 0.854881i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.31624 | 0.245521 | 0.122761 | − | 0.992436i | \(-0.460825\pi\) | ||||
0.122761 | + | 0.992436i | \(0.460825\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.31290 | − | 2.31290i | −0.242458 | − | 0.242458i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.61089 | + | 4.92404i | 0.478128 | + | 0.510599i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24.9755 | 2.56243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.2402 | −1.54741 | −0.773703 | − | 0.633549i | \(-0.781598\pi\) | ||||
−0.773703 | + | 0.633549i | \(0.781598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.27958 | − | 10.5858i | −0.932633 | − | 1.06392i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.01023 | − | 1.01023i | −0.100522 | − | 0.100522i | 0.655058 | − | 0.755579i | \(-0.272644\pi\) |
−0.755579 | + | 0.655058i | \(0.772644\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.54554 | −0.546418 | −0.273209 | − | 0.961955i | \(-0.588085\pi\) | ||||
−0.273209 | + | 0.961955i | \(0.588085\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.95958 | + | 0.228568i | 0.679186 | + | 0.0223060i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.92329 | + | 6.92329i | −0.669300 | + | 0.669300i | −0.957554 | − | 0.288254i | \(-0.906925\pi\) |
0.288254 | + | 0.957554i | \(0.406925\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.69753 | + | 1.69753i | 0.162594 | + | 0.162594i | 0.783715 | − | 0.621121i | \(-0.213322\pi\) |
−0.621121 | + | 0.783715i | \(0.713322\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.293849 | − | 8.94729i | 0.0278909 | − | 0.849239i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.05425i | 0.287320i | 0.989627 | + | 0.143660i | \(0.0458871\pi\) | ||||
−0.989627 | + | 0.143660i | \(0.954113\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.39046 | − | 9.39046i | 0.875665 | − | 0.875665i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.37904 | + | 6.46849i | −0.682192 | + | 0.598012i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.814979i | − | 0.0747090i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.0189i | − | 1.00172i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.05061 | + | 3.79301i | −0.365231 | + | 0.342004i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 17.5191 | − | 17.5191i | 1.56695 | − | 1.56695i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00904i | 0.0895376i | 0.998997 | + | 0.0447688i | \(0.0142551\pi\) | ||||
−0.998997 | + | 0.0447688i | \(0.985745\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.01174 | + | 0.131754i | 0.353214 | + | 0.0116003i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.25508 | + | 1.25508i | 0.109657 | + | 0.109657i | 0.759806 | − | 0.650150i | \(-0.225294\pi\) |
−0.650150 | + | 0.759806i | \(0.725294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.39281 | + | 4.39281i | −0.380905 | + | 0.380905i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.05416 | − | 20.7888i | 0.176794 | − | 1.78921i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.70652 | −0.487540 | −0.243770 | − | 0.969833i | \(-0.578384\pi\) | ||||
−0.243770 | + | 0.969833i | \(0.578384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.78446 | + | 6.78446i | 0.575450 | + | 0.575450i | 0.933646 | − | 0.358196i | \(-0.116608\pi\) |
−0.358196 | + | 0.933646i | \(0.616608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.47840 | − | 7.93921i | 0.714010 | − | 0.668602i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.3487 | −1.28352 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.5181 | −1.53784 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.26429 | + | 1.18388i | −0.104277 | + | 0.0976450i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.36672 | + | 4.36672i | 0.357736 | + | 0.357736i | 0.862978 | − | 0.505242i | \(-0.168597\pi\) |
−0.505242 | + | 0.862978i | \(0.668597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.01244 | −0.570664 | −0.285332 | − | 0.958429i | \(-0.592104\pi\) | ||||
−0.285332 | + | 0.958429i | \(0.592104\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.43967 | − | 0.160421i | −0.197235 | − | 0.0129693i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.0718 | + | 11.0718i | −0.889308 | + | 0.889308i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3514 | + | 10.3514i | 0.826129 | + | 0.826129i | 0.986979 | − | 0.160850i | \(-0.0514235\pi\) |
−0.160850 | + | 0.986979i | \(0.551423\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.8470 | + | 0.618976i | 1.49466 | + | 0.0490880i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.30328i | 0.260335i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2691 | + | 11.2691i | −0.882661 | + | 0.882661i | −0.993804 | − | 0.111143i | \(-0.964549\pi\) |
0.111143 | + | 0.993804i | \(0.464549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23.8507 | − | 22.3339i | 1.85677 | − | 1.73869i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.10358i | − | 0.317545i | −0.987315 | − | 0.158772i | \(-0.949246\pi\) | ||
0.987315 | − | 0.158772i | \(-0.0507536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2.30095i | − | 0.176996i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.2853 | + | 14.0147i | 0.939484 | + | 1.07173i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.181676 | + | 0.181676i | −0.0138126 | + | 0.0138126i | −0.713979 | − | 0.700167i | \(-0.753109\pi\) |
0.700167 | + | 0.713979i | \(0.253109\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.1627i | 0.843819i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.588426 | − | 17.9168i | 0.0442288 | − | 1.34671i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.19489 | − | 8.19489i | −0.612515 | − | 0.612515i | 0.331086 | − | 0.943601i | \(-0.392585\pi\) |
−0.943601 | + | 0.331086i | \(0.892585\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1393 | − | 14.1393i | 1.05097 | − | 1.05097i | 0.0523357 | − | 0.998630i | \(-0.483333\pi\) |
0.998630 | − | 0.0523357i | \(-0.0166666\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.5848 | + | 0.446156i | 1.00422 | + | 0.0329808i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.7789 | 1.52769 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.70414 | − | 2.70414i | −0.197746 | − | 0.197746i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.29513 | + | 4.01772i | 0.239686 | + | 0.292246i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.99690 | −0.650993 | −0.325497 | − | 0.945543i | \(-0.605531\pi\) | ||||
−0.325497 | + | 0.945543i | \(0.605531\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.9613 | 1.79676 | 0.898378 | − | 0.439222i | \(-0.144746\pi\) | ||||
0.898378 | + | 0.439222i | \(0.144746\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.5682 | − | 16.6255i | −1.11486 | − | 1.19058i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.68965 | + | 2.68965i | 0.191630 | + | 0.191630i | 0.796400 | − | 0.604770i | \(-0.206735\pi\) |
−0.604770 | + | 0.796400i | \(0.706735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.82077 | 0.412624 | 0.206312 | − | 0.978486i | \(-0.433854\pi\) | ||||
0.206312 | + | 0.978486i | \(0.433854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.00444732 | + | 0.135415i | −0.000313690 | + | 0.00955142i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.25705 | − | 3.25705i | 0.228600 | − | 0.228600i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.10786 | − | 9.10786i | −0.636120 | − | 0.636120i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.88849 | + | 0.650221i | 0.687297 | + | 0.0451935i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.1511i | 2.01643i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.04692 | − | 5.04692i | 0.347444 | − | 0.347444i | −0.511712 | − | 0.859157i | \(-0.670989\pi\) |
0.859157 | + | 0.511712i | \(0.170989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.70439 | + | 8.22763i | 0.527896 | + | 0.563748i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.31671i | 0.635394i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.89472i | − | 0.264391i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.16557 | − | 7.65222i | −0.484204 | − | 0.517089i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.88497 | + | 1.88497i | −0.126797 | + | 0.126797i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.61492i | 0.175108i | 0.996160 | + | 0.0875539i | \(0.0279050\pi\) | ||||
−0.996160 | + | 0.0875539i | \(0.972095\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 33.4159 | + | 2.19727i | 2.22772 | + | 0.146485i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.46915 | + | 1.46915i | 0.0975109 | + | 0.0975109i | 0.754179 | − | 0.656668i | \(-0.228035\pi\) |
−0.656668 | + | 0.754179i | \(0.728035\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.8529 | + | 14.8529i | −0.981505 | + | 0.981505i | −0.999832 | − | 0.0183274i | \(-0.994166\pi\) |
0.0183274 | + | 0.999832i | \(0.494166\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.266782 | + | 8.12315i | −0.0175530 | + | 0.534464i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.3923 | −1.92556 | −0.962778 | − | 0.270295i | \(-0.912879\pi\) | ||||
−0.962778 | + | 0.270295i | \(0.912879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.0638 | + | 19.0638i | 1.24359 | + | 1.24359i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.9718 | − | 19.1923i | −1.16739 | − | 1.24668i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.818139 | −0.0529210 | −0.0264605 | − | 0.999650i | \(-0.508424\pi\) | ||||
−0.0264605 | + | 0.999650i | \(0.508424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.11229 | 0.522558 | 0.261279 | − | 0.965263i | \(-0.415856\pi\) | ||||
0.261279 | + | 0.965263i | \(0.415856\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.6758 | − | 9.07324i | 0.813154 | − | 0.582049i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.84277 | − | 2.84277i | −0.181618 | − | 0.181618i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.3203 | 1.29295 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.4269 | − | 0.342443i | −0.660780 | − | 0.0217015i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.1026 | + | 17.1026i | −1.07951 | + | 1.07951i | −0.0829549 | + | 0.996553i | \(0.526436\pi\) |
−0.996553 | + | 0.0829549i | \(0.973564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.9605 | + | 10.9605i | 0.689078 | + | 0.689078i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.186278 | − | 5.67191i | 0.0116652 | − | 0.355189i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.1523i | − | 1.06993i | −0.844874 | − | 0.534966i | \(-0.820325\pi\) | ||
0.844874 | − | 0.534966i | \(-0.179675\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.65469 | + | 3.65469i | −0.227091 | + | 0.227091i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.10896 | − | 10.3912i | −0.563831 | − | 0.643199i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5.92938i | − | 0.365621i | −0.983148 | − | 0.182811i | \(-0.941480\pi\) | ||
0.983148 | − | 0.182811i | \(-0.0585196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 43.7695i | 2.68874i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.92839 | + | 2.74216i | −0.179215 | + | 0.167818i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.43027 | + | 4.43027i | −0.270119 | + | 0.270119i | −0.829148 | − | 0.559029i | \(-0.811174\pi\) |
0.559029 | + | 0.829148i | \(0.311174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.4128i | − | 0.997006i | −0.866888 | − | 0.498503i | \(-0.833883\pi\) | ||
0.866888 | − | 0.498503i | \(-0.166117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.66238 | + | 0.185965i | 0.342703 | + | 0.0112551i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 37.0383 | + | 37.0383i | 2.23350 | + | 2.23350i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.2225 | + | 20.2225i | −1.21505 | + | 1.21505i | −0.245709 | + | 0.969344i | \(0.579021\pi\) |
−0.969344 | + | 0.245709i | \(0.920979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.6590 | − | 0.766640i | −0.698005 | − | 0.0458976i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.30930 | −0.197416 | −0.0987082 | − | 0.995116i | \(-0.531471\pi\) | ||||
−0.0987082 | + | 0.995116i | \(0.531471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.67402 | − | 2.67402i | −0.158954 | − | 0.158954i | 0.623149 | − | 0.782103i | \(-0.285853\pi\) |
−0.782103 | + | 0.623149i | \(0.785853\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −31.5762 | + | 29.5681i | −1.87041 | + | 1.75146i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.20387 | 0.189118 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3358 | 0.960930 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.2680 | − | 18.0426i | 1.12951 | − | 1.05768i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.59716 | + | 4.59716i | 0.268569 | + | 0.268569i | 0.828523 | − | 0.559954i | \(-0.189181\pi\) |
−0.559954 | + | 0.828523i | \(0.689181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.6092 | 2.42258 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.2644 | + | 2.39759i | 1.40797 | + | 0.139122i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.64017 | − | 7.64017i | 0.441842 | − | 0.441842i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.63867 | − | 1.63867i | −0.0944513 | − | 0.0944513i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.47321 | + | 0.0812257i | 0.142082 | + | 0.00466630i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.5489i | 1.80648i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.2535 | + | 10.2535i | −0.585198 | + | 0.585198i | −0.936327 | − | 0.351129i | \(-0.885798\pi\) |
0.351129 | + | 0.936327i | \(0.385798\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.01115 | − | 6.56527i | 0.398850 | − | 0.373485i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 28.4542i | − | 1.61349i | −0.590901 | − | 0.806744i | \(-0.701228\pi\) | ||
0.590901 | − | 0.806744i | \(-0.298772\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.6568i | − | 1.33716i | −0.743641 | − | 0.668579i | \(-0.766903\pi\) | ||
0.743641 | − | 0.668579i | \(-0.233097\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.06950 | + | 7.95036i | −0.511009 | + | 0.447952i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.31748 | − | 5.31748i | 0.298660 | − | 0.298660i | −0.541829 | − | 0.840489i | \(-0.682268\pi\) |
0.840489 | + | 0.541829i | \(0.182268\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 21.6141i | − | 1.21016i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.556655 | − | 16.9494i | 0.0310695 | − | 0.946023i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.58005 | + | 3.58005i | 0.199199 | + | 0.199199i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.8182 | − | 25.8182i | 1.43214 | − | 1.43214i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.15585 | − | 0.136487i | −0.229819 | − | 0.00754776i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.70608 | −0.369718 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.17926 | − | 6.17926i | −0.339643 | − | 0.339643i | 0.516590 | − | 0.856233i | \(-0.327201\pi\) |
−0.856233 | + | 0.516590i | \(0.827201\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.2210 | + | 11.6598i | 0.560110 | + | 0.638954i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.314482 | −0.0171820 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.191549 | −0.0104343 | −0.00521717 | − | 0.999986i | \(-0.501661\pi\) | ||||
−0.00521717 | + | 0.999986i | \(0.501661\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.61587 | − | 3.86145i | −0.196387 | − | 0.209725i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.9229 | − | 12.9229i | −0.699814 | − | 0.699814i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.755024 | + | 22.9895i | −0.0406491 | + | 1.23771i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.6420 | − | 17.6420i | 0.947073 | − | 0.947073i | −0.0515951 | − | 0.998668i | \(-0.516431\pi\) |
0.998668 | + | 0.0515951i | \(0.0164305\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.44916 | + | 9.44916i | 0.505802 | + | 0.505802i | 0.913235 | − | 0.407433i | \(-0.133576\pi\) |
−0.407433 | + | 0.913235i | \(0.633576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67128 | − | 16.9139i | 0.0892064 | − | 0.902799i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 37.3053i | − | 1.98556i | −0.119950 | − | 0.992780i | \(-0.538274\pi\) | ||
0.119950 | − | 0.992780i | \(-0.461726\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.5000 | + | 18.5000i | −0.981876 | + | 0.981876i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.964840 | + | 1.03037i | 0.0510647 | + | 0.0545328i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 29.6103i | − | 1.56277i | −0.624049 | − | 0.781385i | \(-0.714514\pi\) | ||
0.624049 | − | 0.781385i | \(-0.285486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 19.5935i | − | 1.03124i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.0451 | + | 13.9311i | 0.684692 | + | 0.731193i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.2061 | − | 17.2061i | 0.900611 | − | 0.900611i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.1073i | 1.15399i | 0.816746 | + | 0.576997i | \(0.195776\pi\) | ||||
−0.816746 | + | 0.576997i | \(0.804224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.630652 | − | 9.59089i | 0.0328304 | − | 0.499282i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.69839 | − | 7.69839i | −0.399681 | − | 0.399681i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.9397 | + | 13.9397i | −0.721771 | + | 0.721771i | −0.968966 | − | 0.247195i | \(-0.920491\pi\) |
0.247195 | + | 0.968966i | \(0.420491\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.40859 | + | 42.8897i | −0.0727393 | + | 2.21481i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0665 | −0.775963 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.03251 | + | 6.03251i | 0.309869 | + | 0.309869i | 0.844859 | − | 0.534989i | \(-0.179684\pi\) |
−0.534989 | + | 0.844859i | \(0.679684\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.19458 | − | 1.27571i | −0.0612003 | − | 0.0653567i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.07832 | 0.463880 | 0.231940 | − | 0.972730i | \(-0.425493\pi\) | ||||
0.231940 | + | 0.972730i | \(0.425493\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.8649 | −0.961445 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.22797 | + | 4.58285i | −0.265753 | + | 0.232960i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.6351 | − | 19.6351i | −0.995538 | − | 0.995538i | 0.00445242 | − | 0.999990i | \(-0.498583\pi\) |
−0.999990 | + | 0.00445242i | \(0.998583\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.69210 | 0.136146 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.07264 | − | 0.100912i | −0.154994 | − | 0.00509035i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43.1543 | − | 43.1543i | 2.17133 | − | 2.17133i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.09474 | + | 2.09474i | 0.105132 | + | 0.105132i | 0.757716 | − | 0.652584i | \(-0.226315\pi\) |
−0.652584 | + | 0.757716i | \(0.726315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.353196 | − | 10.7543i | 0.0176819 | − | 0.538391i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.50963i | 0.175263i | 0.996153 | + | 0.0876313i | \(0.0279297\pi\) | ||||
−0.996153 | + | 0.0876313i | \(0.972070\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00812 | + | 9.00812i | −0.448726 | + | 0.448726i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.0144 | + | 28.7148i | 1.09391 | + | 1.42685i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.2529i | 1.20217i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 19.5923i | − | 0.968778i | −0.874853 | − | 0.484389i | \(-0.839042\pi\) | ||
0.874853 | − | 0.484389i | \(-0.160958\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.21467 | − | 6.75585i | 0.355873 | − | 0.333241i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.31843 | + | 7.31843i | −0.360116 | + | 0.360116i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 24.2151i | − | 1.18867i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.6095 | − | 0.545493i | −0.813371 | − | 0.0267129i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.04462 | + | 3.04462i | 0.148739 | + | 0.148739i | 0.777555 | − | 0.628815i | \(-0.216460\pi\) |
−0.628815 | + | 0.777555i | \(0.716460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3941 | − | 25.3941i | 1.23763 | − | 1.23763i | 0.276668 | − | 0.960965i | \(-0.410770\pi\) |
0.960965 | − | 0.276668i | \(-0.0892303\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.32003 | + | 20.0749i | −0.0641821 | + | 0.976074i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.09735 | 0.441286 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.54897 | − | 5.54897i | −0.268534 | − | 0.268534i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.4051 | − | 18.1710i | 0.936888 | − | 0.877306i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.5588 | −1.61647 | −0.808235 | − | 0.588860i | \(-0.799577\pi\) | ||||
−0.808235 | + | 0.588860i | \(0.799577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.2355 | −1.11663 | −0.558313 | − | 0.829631i | \(-0.688551\pi\) | ||||
−0.558313 | + | 0.829631i | \(0.688551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.4121 | − | 21.9232i | 1.12253 | − | 1.05114i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.5107 | − | 14.5107i | −0.694140 | − | 0.694140i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.6659 | −1.32042 | −0.660211 | − | 0.751080i | \(-0.729533\pi\) | ||||
−0.660211 | + | 0.751080i | \(0.729533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.196841 | − | 2.99354i | 0.00937338 | − | 0.142549i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.5742 | − | 20.5742i | 0.977507 | − | 0.977507i | −0.0222452 | − | 0.999753i | \(-0.507081\pi\) |
0.999753 | + | 0.0222452i | \(0.00708144\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.58455 | − | 6.58455i | −0.312137 | − | 0.312137i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.6905 | − | 0.351099i | −0.505642 | − | 0.0166064i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.3315i | 1.71459i | 0.514826 | + | 0.857294i | \(0.327856\pi\) | ||||
−0.514826 | + | 0.857294i | \(0.672144\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.6306 | − | 10.6306i | 0.500575 | − | 0.500575i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.86573 | − | 8.30191i | 0.416549 | − | 0.390058i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.1501i | 0.616487i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.28562i | − | 0.153695i | −0.997043 | − | 0.0768474i | \(-0.975515\pi\) | ||
0.997043 | − | 0.0768474i | \(-0.0244854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.27436 | − | 2.68546i | 0.152834 | − | 0.125347i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0027 | + | 15.0027i | −0.698744 | + | 0.698744i | −0.964140 | − | 0.265396i | \(-0.914497\pi\) |
0.265396 | + | 0.964140i | \(0.414497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.8407i | 1.20092i | 0.799656 | + | 0.600458i | \(0.205015\pi\) | ||||
−0.799656 | + | 0.600458i | \(0.794985\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.890209 | − | 27.1056i | 0.0412824 | − | 1.25699i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.0389 | − | 22.0389i | −1.01984 | − | 1.01984i | −0.999799 | − | 0.0200376i | \(-0.993621\pi\) |
−0.0200376 | − | 0.999799i | \(-0.506379\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0553126 | − | 0.0553126i | 0.00255410 | − | 0.00255410i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.3419 | − | 0.832284i | −1.16769 | − | 0.0383496i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.8744 | −0.500004 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −49.0355 | − | 49.0355i | −2.24990 | − | 2.24990i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.5608 | + | 21.5300i | −1.12456 | + | 0.985793i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.7108 | −0.900608 | −0.450304 | − | 0.892875i | \(-0.648684\pi\) | ||||
−0.450304 | + | 0.892875i | \(0.648684\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9059 | 0.770842 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.91070 | − | 4.17629i | −0.177943 | − | 0.190028i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 43.3243 | + | 43.3243i | 1.96726 | + | 1.96726i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.69188 | −0.167295 | −0.0836475 | − | 0.996495i | \(-0.526657\pi\) | ||||
−0.0836475 | + | 0.996495i | \(0.526657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.906070 | − | 27.5886i | 0.0409739 | − | 1.24760i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5801 | − | 10.5801i | 0.477475 | − | 0.477475i | −0.426848 | − | 0.904323i | \(-0.640376\pi\) |
0.904323 | + | 0.426848i | \(0.140376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.65442 | − | 2.65442i | −0.119549 | − | 0.119549i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.71339 | + | 56.4728i | −0.166904 | + | 2.53826i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.50772i | − | 0.291911i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1727 | − | 29.1727i | 1.30595 | − | 1.30595i | 0.381636 | − | 0.924313i | \(-0.375361\pi\) |
0.924313 | − | 0.381636i | \(-0.124639\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.85816 | + | 5.18810i | 0.217047 | + | 0.231787i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 15.0826i | − | 0.672498i | −0.941773 | − | 0.336249i | \(-0.890842\pi\) | ||
0.941773 | − | 0.336249i | \(-0.109158\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.74369i | 0.255591i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.72405 | + | 2.90906i | 0.120979 | + | 0.129196i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5998 | − | 16.5998i | 0.735773 | − | 0.735773i | −0.235984 | − | 0.971757i | \(-0.575831\pi\) |
0.971757 | + | 0.235984i | \(0.0758312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.05260i | 0.267751i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.1240 | − | 3.17420i | −1.41831 | − | 0.140144i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.7647 | + | 15.7647i | 0.694675 | + | 0.694675i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.2511 | + | 22.2511i | −0.978603 | + | 0.978603i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0146074 | − | 0.444774i | 0.000641193 | − | 0.0195234i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5578 | 0.944465 | 0.472232 | − | 0.881474i | \(-0.343448\pi\) | ||||
0.472232 | + | 0.881474i | \(0.343448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.5106 | + | 25.5106i | 1.11550 | + | 1.11550i | 0.992393 | + | 0.123109i | \(0.0392866\pi\) |
0.123109 | + | 0.992393i | \(0.460713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.2153 | − | 14.1128i | −0.576763 | − | 0.615934i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.17412 | −0.138267 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.0883 | 0.525580 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.4674 | + | 23.3485i | 0.888210 | + | 1.01324i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.41024 | − | 7.41024i | −0.320973 | − | 0.320973i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.3626 | 1.70180 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.0625 | + | 0.658896i | 0.865760 | + | 0.0284335i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.31805 | − | 3.31805i | 0.142919 | − | 0.142919i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.33890 | + | 7.33890i | 0.315524 | + | 0.315524i | 0.847045 | − | 0.531521i | \(-0.178379\pi\) |
−0.531521 | + | 0.847045i | \(0.678379\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.13685 | + | 34.6154i | −0.0487867 | + | 1.48549i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.65138i | − | 0.413420i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.52913 | − | 5.52913i | 0.236408 | − | 0.236408i | −0.578953 | − | 0.815361i | \(-0.696538\pi\) |
0.815361 | + | 0.578953i | \(0.196538\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.7033 | + | 15.5188i | −0.755559 | + | 0.662325i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.6152i | 1.21905i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.1804i | 0.645535i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.2704 | + | 24.5997i | −1.11512 | + | 1.04420i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.8816 | + | 27.8816i | −1.18138 | + | 1.18138i | −0.201995 | + | 0.979386i | \(0.564743\pi\) |
−0.979386 | + | 0.201995i | \(0.935257\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.58017i | 0.320607i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.62020 | + | 0.217422i | 0.279505 | + | 0.00917956i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.04328 | − | 1.04328i | −0.0439691 | − | 0.0439691i | 0.684780 | − | 0.728749i | \(-0.259898\pi\) |
−0.728749 | + | 0.684780i | \(0.759898\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.68253 | − | 8.68253i | 0.365277 | − | 0.365277i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.92251 | − | 1.17850i | −0.374710 | − | 0.0494924i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.1966 | −0.930530 | −0.465265 | − | 0.885171i | \(-0.654041\pi\) | ||||
−0.465265 | + | 0.885171i | \(0.654041\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.44290 | − | 4.44290i | −0.185930 | − | 0.185930i | 0.608004 | − | 0.793934i | \(-0.291970\pi\) |
−0.793934 | + | 0.608004i | \(0.791970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.3747 | − | 10.6513i | 0.475183 | − | 0.444964i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.8735 | −1.53773 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.94900 | −0.122768 | −0.0613842 | − | 0.998114i | \(-0.519551\pi\) | ||||
−0.0613842 | + | 0.998114i | \(0.519551\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.5583 | + | 29.5513i | −1.31152 | + | 1.22811i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.25907 | + | 4.25907i | 0.176696 | + | 0.176696i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.0873 | −2.11582 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 39.3653 | + | 2.58848i | 1.62756 | + | 0.107020i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8692 | + | 13.8692i | −0.572443 | + | 0.572443i | −0.932811 | − | 0.360367i | \(-0.882651\pi\) |
0.360367 | + | 0.932811i | \(0.382651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1088 | + | 17.1088i | 0.704954 | + | 0.704954i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.58472 | − | 0.216257i | −0.270859 | − | 0.00889561i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 22.9708i | − | 0.943296i | −0.881787 | − | 0.471648i | \(-0.843659\pi\) | ||
0.881787 | − | 0.471648i | \(-0.156341\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.31680 | + | 2.31680i | −0.0949794 | + | 0.0949794i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.35912 | + | 6.89111i | −0.301189 | + | 0.282035i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6.85784i | − | 0.280204i | −0.990137 | − | 0.140102i | \(-0.955257\pi\) | ||
0.990137 | − | 0.140102i | \(-0.0447430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.1867i | − | 1.14976i | −0.818237 | − | 0.574881i | \(-0.805048\pi\) | ||
0.818237 | − | 0.574881i | \(-0.194952\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.154693 | − | 0.176468i | −0.00629957 | − | 0.00718634i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.3243 | + | 31.3243i | −1.27351 | + | 1.27351i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.92533i | − | 0.159324i | −0.996822 | − | 0.0796620i | \(-0.974616\pi\) | ||
0.996822 | − | 0.0796620i | \(-0.0253841\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.261877 | + | 7.97380i | −0.0106118 | + | 0.323115i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.5105 | + | 15.5105i | 0.627488 | + | 0.627488i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.4345 | + | 11.4345i | −0.461835 | + | 0.461835i | −0.899257 | − | 0.437421i | \(-0.855892\pi\) |
0.437421 | + | 0.899257i | \(0.355892\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.2976 | + | 0.732302i | 0.899125 | + | 0.0295293i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.5345 | −1.75263 | −0.876316 | − | 0.481738i | \(-0.840006\pi\) | ||||
−0.876316 | + | 0.481738i | \(0.840006\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.4517 | − | 23.4517i | −0.942603 | − | 0.942603i | 0.0558372 | − | 0.998440i | \(-0.482217\pi\) |
−0.998440 | + | 0.0558372i | \(0.982217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.2717 | + | 10.8847i | −0.532574 | + | 0.436790i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.31624 | 0.0927983 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −43.7920 | −1.75168 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −34.5115 | − | 36.8554i | −1.37826 | − | 1.47186i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.97849 | + | 2.97849i | 0.118760 | + | 0.118760i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.1262 | −1.00026 | −0.500129 | − | 0.865951i | \(-0.666714\pi\) | ||||
−0.500129 | + | 0.865951i | \(0.666714\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.405789 | + | 12.3557i | −0.0161287 | + | 0.491096i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.86846 | − | 2.86846i | 0.113831 | − | 0.113831i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.31290 | − | 2.31290i | −0.0916406 | − | 0.0916406i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.4811 | − | 1.28099i | −0.770661 | − | 0.0506750i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 33.0405i | − | 1.30502i | −0.757779 | − | 0.652511i | \(-0.773716\pi\) | ||
0.757779 | − | 0.652511i | \(-0.226284\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.66006 | − | 2.66006i | 0.104902 | − | 0.104902i | −0.652708 | − | 0.757610i | \(-0.726367\pi\) |
0.757610 | + | 0.652708i | \(0.226367\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0299 | − | 11.7790i | −0.434302 | − | 0.463797i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.7484i | 1.44473i | 0.691512 | + | 0.722365i | \(0.256945\pi\) | ||||
−0.691512 | + | 0.722365i | \(0.743055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.5658i | 1.90638i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.61089 | + | 4.92404i | 0.180715 | + | 0.192988i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.7533 | − | 21.7533i | 0.851271 | − | 0.851271i | −0.139019 | − | 0.990290i | \(-0.544395\pi\) |
0.990290 | + | 0.139019i | \(0.0443949\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 7.13579i | − | 0.278818i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.1187 | + | 1.19140i | 0.706876 | + | 0.0464809i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.3925 | + | 11.3925i | 0.443790 | + | 0.443790i | 0.893283 | − | 0.449494i | \(-0.148396\pi\) |
−0.449494 | + | 0.893283i | \(0.648396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7678 | − | 13.7678i | 0.535506 | − | 0.535506i | −0.386700 | − | 0.922206i | \(-0.626385\pi\) |
0.922206 | + | 0.386700i | \(0.126385\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.151558 | − | 4.61472i | 0.00588601 | − | 0.179221i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.9755 | 0.968508 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.7589 | + | 10.7589i | 0.416588 | + | 0.416588i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.09576 | − | 3.30600i | −0.119689 | − | 0.127818i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.8236 | −1.42156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.8933 | 0.921019 | 0.460509 | − | 0.887655i | \(-0.347667\pi\) | ||||
0.460509 | + | 0.887655i | \(0.347667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −44.8486 | + | 36.7825i | −1.72622 | + | 1.41576i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.9999 | + | 30.9999i | 1.19142 | + | 1.19142i | 0.976668 | + | 0.214755i | \(0.0688951\pi\) |
0.214755 | + | 0.976668i | \(0.431105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.2402 | −0.584864 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.59673 | − | 0.118125i | −0.137827 | − | 0.00452654i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.6478 | + | 22.6478i | −0.866595 | + | 0.866595i | −0.992094 | − | 0.125498i | \(-0.959947\pi\) |
0.125498 | + | 0.992094i | \(0.459947\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.2223 | + | 16.2223i | 0.619823 | + | 0.619823i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.19422 | − | 36.3623i | 0.0455623 | − | 1.38731i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.6113i | 1.35668i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.7567 | − | 14.7567i | 0.561372 | − | 0.561372i | −0.368325 | − | 0.929697i | \(-0.620069\pi\) |
0.929697 | + | 0.368325i | \(0.120069\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.27958 | − | 10.5858i | −0.352502 | − | 0.402123i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 38.5733i | − | 1.46317i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.61108i | − | 0.0989019i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 37.1603 | − | 34.7971i | 1.40553 | − | 1.31615i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.8411 | − | 21.8411i | 0.824928 | − | 0.824928i | −0.161882 | − | 0.986810i | \(-0.551756\pi\) |
0.986810 | + | 0.161882i | \(0.0517564\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.1087i | − | 1.21100i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −46.6715 | − | 1.53279i | −1.75775 | − | 0.0577284i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.01023 | − | 1.01023i | −0.0379936 | − | 0.0379936i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.48004 | − | 2.48004i | 0.0931400 | − | 0.0931400i | −0.659002 | − | 0.752142i | \(-0.729021\pi\) |
0.752142 | + | 0.659002i | \(0.229021\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 45.4430 | + | 2.98812i | 1.70424 | + | 0.112063i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.8654 | 0.481811 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.6327 | + | 43.6327i | 1.63177 | + | 1.63177i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.03436 | − | 0.968582i | 0.0386290 | − | 0.0361723i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.4163 | −1.32080 | −0.660402 | − | 0.750912i | \(-0.729614\pi\) | ||||
−0.660402 | + | 0.750912i | \(0.729614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.54554 | −0.206527 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.2563 | + | 9.60400i | −0.381434 | + | 0.357177i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.3574 | + | 36.3574i | 1.35028 | + | 1.35028i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1700 | −0.377184 | −0.188592 | − | 0.982056i | \(-0.560392\pi\) | ||||
−0.188592 | + | 0.982056i | \(0.560392\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.28420 | + | 26.4779i | −0.195711 | + | 0.980662i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.33548 | + | 1.33548i | −0.0493945 | + | 0.0493945i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.9007 | − | 14.9007i | −0.550371 | − | 0.550371i | 0.376177 | − | 0.926548i | \(-0.377239\pi\) |
−0.926548 | + | 0.376177i | \(0.877239\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.95958 | + | 0.228568i | 0.256708 | + | 0.00843086i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.367060i | − | 0.0135208i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.2894 | + | 30.2894i | −1.11421 | + | 1.11421i | −0.121640 | + | 0.992574i | \(0.538815\pi\) |
−0.992574 | + | 0.121640i | \(0.961185\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.6907 | + | 24.0569i | −0.943770 | + | 0.883751i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 0.334889i | − | 0.0122859i | −0.999981 | − | 0.00614294i | \(-0.998045\pi\) | ||
0.999981 | − | 0.00614294i | \(-0.00195537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 24.8272i | − | 0.909597i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.5880 | − | 11.9113i | 0.497161 | − | 0.435813i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.92329 | + | 6.92329i | −0.252972 | + | 0.252972i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 22.8597i | − | 0.834164i | −0.908869 | − | 0.417082i | \(-0.863053\pi\) | ||
0.908869 | − | 0.417082i | \(-0.136947\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.37511 | − | 41.8701i | 0.0501117 | − | 1.52583i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.9348 | + | 19.9348i | 0.725500 | + | 0.725500i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.43514 | − | 5.43514i | 0.197544 | − | 0.197544i | −0.601403 | − | 0.798946i | \(-0.705391\pi\) |
0.798946 | + | 0.601403i | \(0.205391\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −26.8331 | − | 0.881257i | −0.973978 | − | 0.0319876i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.2552 | 0.843000 | 0.421500 | − | 0.906828i | \(-0.361504\pi\) | ||||
0.421500 | + | 0.906828i | \(0.361504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69753 | + | 1.69753i | 0.0614548 | + | 0.0614548i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.47937 | + | 7.39146i | 0.234262 | + | 0.267239i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.8536 | 1.22238 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.2676 | 0.478443 | 0.239221 | − | 0.970965i | \(-0.423108\pi\) | ||||
0.239221 | + | 0.970965i | \(0.423108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.3063 | + | 21.6854i | 0.731314 | + | 0.780981i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.63940 | − | 3.63940i | −0.130900 | − | 0.130900i | 0.638621 | − | 0.769521i | \(-0.279505\pi\) |
−0.769521 | + | 0.638621i | \(0.779505\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.4755 | 1.56169 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.293849 | − | 8.94729i | 0.0105418 | − | 0.320982i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.0740 | + | 14.0740i | −0.504253 | + | 0.504253i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.5930 | − | 21.5930i | −0.772657 | − | 0.772657i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.8183 | + | 2.35351i | 0.851197 | + | 0.0841076i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 58.8531i | − | 2.10056i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.7316 | − | 28.7316i | 1.02417 | − | 1.02417i | 0.0244694 | − | 0.999701i | \(-0.492210\pi\) |
0.999701 | − | 0.0244694i | \(-0.00778964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.01970 | + | 7.49644i | 0.249908 | + | 0.266880i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.05425i | 0.108597i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.6685i | 0.911514i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −51.8180 | − | 55.3372i | −1.83779 | − | 1.96261i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.8804 | − | 28.8804i | 1.02300 | − | 1.02300i | 0.0232677 | − | 0.999729i | \(-0.492593\pi\) |
0.999729 | − | 0.0232677i | \(-0.00740700\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.46531i | 0.193349i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.455931 | − | 6.93376i | 0.0161095 | − | 0.244992i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0828 | + | 20.0828i | 0.708708 | + | 0.708708i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.39046 | − | 9.39046i | 0.330970 | − | 0.330970i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.356209 | − | 10.8461i | 0.0125391 | − | 0.381799i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.8315 | 0.837870 | 0.418935 | − | 0.908016i | \(-0.362403\pi\) | ||||
0.418935 | + | 0.908016i | \(0.362403\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.597878 | − | 0.597878i | −0.0209943 | − | 0.0209943i | 0.696532 | − | 0.717526i | \(-0.254726\pi\) |
−0.717526 | + | 0.696532i | \(0.754726\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.4308 | + | 20.7505i | 0.681469 | + | 0.727750i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 64.0707 | 2.24430 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.3967 | 0.503677 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.37904 | + | 6.46849i | −0.257844 | + | 0.226027i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.64131 | − | 9.64131i | −0.336484 | − | 0.336484i | 0.518558 | − | 0.855042i | \(-0.326469\pi\) |
−0.855042 | + | 0.518558i | \(0.826469\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2582 | −0.392436 | −0.196218 | − | 0.980560i | \(-0.562866\pi\) | ||||
−0.196218 | + | 0.980560i | \(0.562866\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −90.6762 | − | 2.97801i | −3.15694 | − | 0.103681i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4759 | − | 19.4759i | 0.677245 | − | 0.677245i | −0.282131 | − | 0.959376i | \(-0.591041\pi\) |
0.959376 | + | 0.282131i | \(0.0910413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.7146 | − | 31.7146i | −1.10149 | − | 1.10149i | −0.994231 | − | 0.107263i | \(-0.965791\pi\) |
−0.107263 | − | 0.994231i | \(-0.534209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.62596 | − | 49.5081i | 0.0564038 | − | 1.71742i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.814979i | − | 0.0282373i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.6655 | + | 11.6655i | −0.403703 | + | 0.403703i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.6479 | − | 12.8336i | 0.540871 | − | 0.443595i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 26.3441i | − | 0.909498i | −0.890620 | − | 0.454749i | \(-0.849729\pi\) | ||
0.890620 | − | 0.454749i | \(-0.150271\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.78330i | 0.268390i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.18391 | − | 3.91783i | 0.144101 | − | 0.134937i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.54106 | + | 6.54106i | −0.225019 | + | 0.225019i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.0189i | − | 0.378615i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.54647 | + | 0.215000i | 0.224674 | + | 0.00737879i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0725 | − | 12.0725i | −0.413838 | − | 0.413838i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.6622 | + | 33.6622i | −1.15257 | + | 1.15257i | −0.166538 | + | 0.986035i | \(0.553259\pi\) |
−0.986035 | + | 0.166538i | \(0.946741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.91620 | − | 74.7650i | 0.168130 | − | 2.55691i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.7318 | −0.878982 | −0.439491 | − | 0.898247i | \(-0.644841\pi\) | ||||
−0.439491 | + | 0.898247i | \(0.644841\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.5545 | − | 19.5545i | −0.667189 | − | 0.667189i | 0.289875 | − | 0.957064i | \(-0.406386\pi\) |
−0.957064 | + | 0.289875i | \(0.906386\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.05061 | + | 3.79301i | −0.138044 | + | 0.129265i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.8475 | −1.52663 | −0.763314 | − | 0.646028i | \(-0.776429\pi\) | ||||
−0.763314 | + | 0.646028i | \(0.776429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.03293 | 0.0351206 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.6531 | + | 19.3397i | −0.701418 | + | 0.656810i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.3693 | + | 50.3693i | 1.70866 | + | 1.70866i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.255866 | −0.00866968 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.99989 | + | 45.6220i | −0.101531 | + | 1.54407i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.5191 | − | 17.5191i | 0.592253 | − | 0.592253i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.7902 | − | 37.7902i | −1.27608 | − | 1.27608i | −0.942841 | − | 0.333244i | \(-0.891857\pi\) |
−0.333244 | − | 0.942841i | \(-0.608143\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.2546 | − | 0.369627i | −0.379609 | − | 0.0124672i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.93495i | 0.0651903i | 0.999469 | + | 0.0325951i | \(0.0103772\pi\) | ||||
−0.999469 | + | 0.0325951i | \(0.989623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.35788 | + | 3.35788i | −0.113002 | + | 0.113002i | −0.761347 | − | 0.648345i | \(-0.775461\pi\) |
0.648345 | + | 0.761347i | \(0.275461\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −52.6060 | + | 49.2604i | −1.76833 | + | 1.65587i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.6612i | 0.593005i | 0.955032 | + | 0.296502i | \(0.0958202\pi\) | ||||
−0.955032 | + | 0.296502i | \(0.904180\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00904i | 0.0338420i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.5157 | + | 25.6950i | −1.12282 | + | 0.860816i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.4585 | − | 29.4585i | 0.985791 | − | 0.985791i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.5924i | 1.55741i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.614295 | + | 18.7044i | −0.0205107 | + | 0.624523i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.6853 | − | 12.6853i | −0.423078 | − | 0.423078i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.27403 | + | 6.27403i | −0.209018 | + | 0.209018i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.01174 | + | 0.131754i | 0.133502 | + | 0.00438451i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −80.3895 | −2.67224 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.00083 | − | 6.00083i | −0.199254 | − | 0.199254i | 0.600426 | − | 0.799680i | \(-0.294998\pi\) |
−0.799680 | + | 0.600426i | \(0.794998\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.22301 | + | 2.82530i | −0.106900 | + | 0.0937093i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4940 | 0.712127 | 0.356064 | − | 0.934462i | \(-0.384119\pi\) | ||||
0.356064 | + | 0.934462i | \(0.384119\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.2636 | 0.935390 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −37.3502 | − | 39.8868i | −1.23476 | − | 1.31862i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.25508 | + | 1.25508i | 0.0414463 | + | 0.0414463i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.2110 | −0.963582 | −0.481791 | − | 0.876286i | \(-0.660014\pi\) | ||||
−0.481791 | + | 0.876286i | \(0.660014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.824416 | − | 25.1023i | 0.0271654 | − | 0.827150i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.0517 | + | 15.0517i | −0.495434 | + | 0.495434i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.7961 | − | 40.7961i | −1.34137 | − | 1.34137i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.09159 | + | 16.6008i | −0.0358525 | + | 0.545241i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.2301i | 1.22148i | 0.791831 | + | 0.610741i | \(0.209128\pi\) | ||||
−0.791831 | + | 0.610741i | \(0.790872\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.39281 | + | 4.39281i | −0.143968 | + | 0.143968i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.6864 | + | 35.9742i | 1.10284 | + | 1.17774i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.3745i | 0.502800i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.8582i | − | 0.942755i | −0.881931 | − | 0.471378i | \(-0.843757\pi\) | ||
0.881931 | − | 0.471378i | \(-0.156243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.0068 | + | 29.9089i | 0.913969 | + | 0.976041i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.5463 | + | 36.5463i | −1.19138 | + | 1.19138i | −0.214696 | + | 0.976681i | \(0.568876\pi\) |
−0.976681 | + | 0.214696i | \(0.931124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.5833i | 0.344639i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.05416 | − | 20.7888i | 0.0668217 | − | 0.676259i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.9514 | − | 11.9514i | −0.388367 | − | 0.388367i | 0.485738 | − | 0.874105i | \(-0.338551\pi\) |
−0.874105 | + | 0.485738i | \(0.838551\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.9991 | − | 13.9991i | 0.454429 | − | 0.454429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.427543 | + | 13.0181i | −0.0138640 | + | 0.422141i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.5749 | 1.67068 | 0.835338 | − | 0.549737i | \(-0.185272\pi\) | ||||
0.835338 | + | 0.549737i | \(0.185272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.5761 | + | 25.5761i | 0.827624 | + | 0.827624i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.5886 | + | 27.3264i | 0.827161 | + | 0.883337i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.70652 | −0.184273 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.8311 | 0.510682 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.3623 | + | 22.0879i | 0.623942 | + | 0.711773i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −70.9594 | − | 70.9594i | −2.28426 | − | 2.28426i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.76614 | −0.0889531 | −0.0444766 | − | 0.999010i | \(-0.514162\pi\) | ||||
−0.0444766 | + | 0.999010i | \(0.514162\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.76456 | − | 0.287848i | −0.281558 | − | 0.00924700i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.6491 | + | 26.6491i | −0.855210 | + | 0.855210i | −0.990769 | − | 0.135559i | \(-0.956717\pi\) |
0.135559 | + | 0.990769i | \(0.456717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.78446 | + | 6.78446i | 0.217500 | + | 0.217500i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.07587 | + | 63.2074i | −0.0664810 | + | 2.02426i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.9054i | 0.508859i | 0.967091 | + | 0.254429i | \(0.0818877\pi\) | ||||
−0.967091 | + | 0.254429i | \(0.918112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.68542 | − | 7.68542i | 0.245627 | − | 0.245627i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.41576 | − | 4.74748i | 0.172912 | − | 0.151575i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58.2649i | 1.85836i | 0.369625 | + | 0.929181i | \(0.379486\pi\) | ||||
−0.369625 | + | 0.929181i | \(0.620514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 15.2921i | − | 0.487247i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.47840 | − | 7.93921i | 0.269870 | − | 0.252708i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.41298 | − | 5.41298i | 0.172123 | − | 0.172123i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 5.20415i | − | 0.165315i | −0.996578 | − | 0.0826576i | \(-0.973659\pi\) | ||
0.996578 | − | 0.0826576i | \(-0.0263408\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.1279 | + | 0.496833i | 0.480069 | + | 0.0157665i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.5471 | − | 16.5471i | −0.524579 | − | 0.524579i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.8283 | − | 23.8283i | 0.754650 | − | 0.754650i | −0.220693 | − | 0.975343i | \(-0.570832\pi\) |
0.975343 | + | 0.220693i | \(0.0708319\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.7262 | − | 2.64084i | −0.845579 | − | 0.0835525i |
(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 | 1344.2.s.c.239.5 | 40 | ||
3.2 | odd | 2 | inner | 1344.2.s.c.239.6 | 40 | ||
4.3 | odd | 2 | 336.2.s.c.323.11 | yes | 40 | ||
12.11 | even | 2 | 336.2.s.c.323.10 | yes | 40 | ||
16.5 | even | 4 | 336.2.s.c.155.10 | ✓ | 40 | ||
16.11 | odd | 4 | inner | 1344.2.s.c.911.6 | 40 | ||
48.5 | odd | 4 | 336.2.s.c.155.11 | yes | 40 | ||
48.11 | even | 4 | inner | 1344.2.s.c.911.5 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.s.c.155.10 | ✓ | 40 | 16.5 | even | 4 | ||
336.2.s.c.155.11 | yes | 40 | 48.5 | odd | 4 | ||
336.2.s.c.323.10 | yes | 40 | 12.11 | even | 2 | ||
336.2.s.c.323.11 | yes | 40 | 4.3 | odd | 2 | ||
1344.2.s.c.239.5 | 40 | 1.1 | even | 1 | trivial | ||
1344.2.s.c.239.6 | 40 | 3.2 | odd | 2 | inner | ||
1344.2.s.c.911.5 | 40 | 48.11 | even | 4 | inner | ||
1344.2.s.c.911.6 | 40 | 16.11 | odd | 4 | inner |