Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(689,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.n (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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 689.13 | ||
Character | \(\chi\) | \(=\) | 1380.689 |
Dual form | 1380.2.n.a.689.15 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.888021 | − | 1.48708i | −0.512699 | − | 0.858568i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.29815 | + | 1.82066i | −0.580552 | + | 0.814223i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.470527 | 0.177843 | 0.0889213 | − | 0.996039i | \(-0.471658\pi\) | ||||
0.0889213 | + | 0.996039i | \(0.471658\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.42284 | + | 2.64112i | −0.474279 | + | 0.880375i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.71789 | −0.819475 | −0.409737 | − | 0.912204i | \(-0.634380\pi\) | ||||
−0.409737 | + | 0.912204i | \(0.634380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.59395i | − | 0.719432i | −0.933062 | − | 0.359716i | \(-0.882874\pi\) | ||
0.933062 | − | 0.359716i | \(-0.117126\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.86026 | + | 0.313680i | 0.996715 | + | 0.0809919i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.294363i | 0.0713936i | 0.999363 | + | 0.0356968i | \(0.0113651\pi\) | ||||
−0.999363 | + | 0.0356968i | \(0.988635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.759425i | 0.174224i | 0.996199 | + | 0.0871120i | \(0.0277638\pi\) | ||||
−0.996199 | + | 0.0871120i | \(0.972236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.417838 | − | 0.699714i | −0.0911798 | − | 0.152690i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.33187 | + | 3.44944i | 0.694743 | + | 0.719258i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.62959 | − | 4.72699i | −0.325919 | − | 0.945398i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19108 | − | 0.229499i | 0.999024 | − | 0.0441670i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.71717i | − | 1.24735i | −0.781685 | − | 0.623674i | \(-0.785639\pi\) | ||
0.781685 | − | 0.623674i | \(-0.214361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.75201 | 0.494276 | 0.247138 | − | 0.968980i | \(-0.420510\pi\) | ||||
0.247138 | + | 0.968980i | \(0.420510\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.41354 | + | 4.04173i | 0.420144 | + | 0.703575i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.610817 | + | 0.856670i | −0.103247 | + | 0.144804i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9455 | 1.79942 | 0.899711 | − | 0.436487i | \(-0.143777\pi\) | ||||
0.899711 | + | 0.436487i | \(0.143777\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.85742 | + | 2.30348i | −0.617681 | + | 0.368852i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.64338i | − | 0.256653i | −0.991732 | − | 0.128327i | \(-0.959039\pi\) | ||
0.991732 | − | 0.128327i | \(-0.0409606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.08303 | 0.470157 | 0.235079 | − | 0.971976i | \(-0.424465\pi\) | ||||
0.235079 | + | 0.971976i | \(0.424465\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.96152 | − | 6.01908i | −0.441478 | − | 0.897272i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.53862 | 1.39135 | 0.695675 | − | 0.718357i | \(-0.255105\pi\) | ||||
0.695675 | + | 0.718357i | \(0.255105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77860 | −0.968372 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.437743 | − | 0.261401i | 0.0612963 | − | 0.0366035i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.10802i | − | 0.289558i | −0.989464 | − | 0.144779i | \(-0.953753\pi\) | ||
0.989464 | − | 0.144779i | \(-0.0462472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.52824 | − | 4.94835i | 0.475748 | − | 0.667235i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.12933 | − | 0.674385i | 0.149583 | − | 0.0893245i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.16407i | 0.672304i | 0.941808 | + | 0.336152i | \(0.109126\pi\) | ||||
−0.941808 | + | 0.336152i | \(0.890874\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.99054i | − | 1.15112i | −0.817759 | − | 0.575560i | \(-0.804784\pi\) | ||
0.817759 | − | 0.575560i | \(-0.195216\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.669483 | + | 1.24272i | −0.0843470 | + | 0.156568i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.72269 | + | 3.36734i | 0.585778 | + | 0.417668i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.92409 | 1.21242 | 0.606210 | − | 0.795304i | \(-0.292689\pi\) | ||||
0.606210 | + | 0.795304i | \(0.292689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.17084 | − | 8.01795i | 0.261338 | − | 0.965247i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.98391i | − | 0.354124i | −0.984200 | − | 0.177062i | \(-0.943341\pi\) | ||
0.984200 | − | 0.177062i | \(-0.0566594\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.50311i | − | 0.995214i | −0.867403 | − | 0.497607i | \(-0.834212\pi\) | ||
0.867403 | − | 0.497607i | \(-0.165788\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.58232 | + | 6.62101i | −0.644590 | + | 0.764528i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.27884 | −0.145738 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.8177i | 1.66712i | 0.552431 | + | 0.833559i | \(0.313700\pi\) | ||||
−0.552431 | + | 0.833559i | \(0.686300\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.95108 | − | 7.51577i | −0.550119 | − | 0.835086i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.6851i | − | 1.17284i | −0.810008 | − | 0.586419i | \(-0.800537\pi\) | ||
0.810008 | − | 0.586419i | \(-0.199463\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.535935 | − | 0.382129i | −0.0581303 | − | 0.0414477i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.98899 | + | 5.96499i | −1.07093 | + | 0.639514i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.27339 | 0.876977 | 0.438489 | − | 0.898737i | \(-0.355514\pi\) | ||||
0.438489 | + | 0.898737i | \(0.355514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.22052i | − | 0.127946i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.44385 | − | 4.09248i | −0.253415 | − | 0.424370i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.38265 | − | 0.985850i | −0.141857 | − | 0.101146i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.506765 | −0.0514542 | −0.0257271 | − | 0.999669i | \(-0.508190\pi\) | ||||
−0.0257271 | + | 0.999669i | \(0.508190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.86711 | − | 7.17828i | 0.388659 | − | 0.721445i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.25035i | − | 0.621933i | −0.950421 | − | 0.310966i | \(-0.899347\pi\) | ||
0.950421 | − | 0.310966i | \(-0.100653\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.74406 | −0.171847 | −0.0859237 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859237 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.81636 | + | 0.147595i | 0.177258 | + | 0.0144038i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.93391i | − | 0.670326i | −0.942160 | − | 0.335163i | \(-0.891209\pi\) | ||
0.942160 | − | 0.335163i | \(-0.108791\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.9349i | − | 1.43050i | −0.698868 | − | 0.715250i | \(-0.746313\pi\) | ||
0.698868 | − | 0.715250i | \(-0.253687\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.71980 | − | 16.2768i | −0.922562 | − | 1.54493i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.96261i | 0.654987i | 0.944853 | + | 0.327494i | \(0.106204\pi\) | ||||
−0.944853 | + | 0.327494i | \(0.893796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6055 | + | 1.58829i | −0.988971 | + | 0.148109i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.85094 | + | 3.69076i | 0.633370 | + | 0.341211i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.138506i | 0.0126968i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.61308 | −0.328461 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.44385 | + | 1.45936i | −0.220354 | + | 0.131586i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7217 | + | 3.16943i | 0.958977 | + | 0.283482i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.91915i | − | 0.525239i | −0.964899 | − | 0.262620i | \(-0.915414\pi\) | ||
0.964899 | − | 0.262620i | \(-0.0845865\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.73779 | − | 4.58472i | −0.241049 | − | 0.403662i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.5848i | − | 0.924800i | −0.886671 | − | 0.462400i | \(-0.846988\pi\) | ||
0.886671 | − | 0.462400i | \(-0.153012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.357330i | 0.0309845i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.32099 | + | 9.74911i | −0.544024 | + | 0.839070i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.04370i | 0.516348i | 0.966098 | + | 0.258174i | \(0.0831207\pi\) | ||||
−0.966098 | + | 0.258174i | \(0.916879\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4216 | 1.22322 | 0.611611 | − | 0.791159i | \(-0.290522\pi\) | ||||
0.611611 | + | 0.791159i | \(0.290522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.47049 | − | 14.1847i | −0.713344 | − | 1.19457i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.05006i | 0.589556i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.2297 | + | 8.71992i | 1.01562 | + | 0.724150i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.01955 | + | 10.0804i | 0.496484 | + | 0.831413i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.83274 | 0.150144 | 0.0750721 | − | 0.997178i | \(-0.476081\pi\) | ||||
0.0750721 | + | 0.997178i | \(0.476081\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6590 | 1.51845 | 0.759223 | − | 0.650831i | \(-0.225579\pi\) | ||||
0.759223 | + | 0.650831i | \(0.225579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.777450 | − | 0.418831i | −0.0628531 | − | 0.0338605i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.57254 | + | 5.01048i | −0.286953 | + | 0.402451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.11927 | −0.248944 | −0.124472 | − | 0.992223i | \(-0.539724\pi\) | ||||
−0.124472 | + | 0.992223i | \(0.539724\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.13480 | + | 1.87196i | −0.248605 | + | 0.148456i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.56774 | + | 1.62306i | 0.123555 | + | 0.127915i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.25275i | − | 0.0981226i | −0.998796 | − | 0.0490613i | \(-0.984377\pi\) | ||
0.998796 | − | 0.0490613i | \(-0.0156230\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.4918 | − | 0.852548i | −0.816782 | − | 0.0663708i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.4752 | −1.58442 | −0.792209 | − | 0.610250i | \(-0.791069\pi\) | ||||
−0.792209 | + | 0.610250i | \(0.791069\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.27143 | 0.482418 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00574 | − | 1.08054i | −0.153382 | − | 0.0826307i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.44210 | 0.413756 | 0.206878 | − | 0.978367i | \(-0.433670\pi\) | ||||
0.206878 | + | 0.978367i | \(0.433670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.766768 | − | 2.22418i | −0.0579622 | − | 0.168132i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.67940 | − | 4.58580i | 0.577219 | − | 0.344690i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.2700i | 0.991845i | 0.868367 | + | 0.495923i | \(0.165170\pi\) | ||||
−0.868367 | + | 0.495923i | \(0.834830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7821i | 1.39606i | 0.716069 | + | 0.698029i | \(0.245940\pi\) | ||||
−0.716069 | + | 0.698029i | \(0.754060\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3697 | + | 7.98379i | −0.988315 | + | 0.590179i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.2089 | + | 19.9279i | −1.04466 | + | 1.46513i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.800047i | − | 0.0585053i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.44255 | − | 0.107985i | 0.177669 | − | 0.00785478i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.8404 | −1.29088 | −0.645441 | − | 0.763810i | \(-0.723327\pi\) | ||||
−0.645441 | + | 0.763810i | \(0.723327\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.93881i | − | 0.499466i | −0.968315 | − | 0.249733i | \(-0.919657\pi\) | ||
0.968315 | − | 0.249733i | \(-0.0803429\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.813670 | − | 10.0133i | 0.0582681 | − | 0.717068i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.71610 | 0.478502 | 0.239251 | − | 0.970958i | \(-0.423098\pi\) | ||||
0.239251 | + | 0.970958i | \(0.423098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1393i | 1.28586i | 0.765924 | + | 0.642931i | \(0.222282\pi\) | ||||
−0.765924 | + | 0.642931i | \(0.777718\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.81281 | − | 14.7580i | −0.621607 | − | 1.04095i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 3.16061i | − | 0.221831i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.99204 | + | 2.13336i | 0.208973 | + | 0.149001i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.8511 | + | 3.89189i | −0.962719 | + | 0.270505i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.06403i | − | 0.142772i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.85377 | 0.402990 | 0.201495 | − | 0.979489i | \(-0.435420\pi\) | ||||
0.201495 | + | 0.979489i | \(0.435420\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.43732 | + | 2.64977i | −0.304040 | + | 0.181559i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00224 | + | 5.61314i | −0.272951 | + | 0.382813i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.29490 | 0.0879034 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.6448 | + | 7.55095i | −0.854459 | + | 0.510246i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.763563 | 0.0513628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4919i | 1.43921i | 0.694386 | + | 0.719603i | \(0.255676\pi\) | ||||
−0.694386 | + | 0.719603i | \(0.744324\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.8032 | + | 2.42177i | 0.986881 | + | 0.161452i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.82471i | 0.253855i | 0.991912 | + | 0.126928i | \(0.0405116\pi\) | ||||
−0.991912 | + | 0.126928i | \(0.959488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.876625i | 0.0579290i | 0.999580 | + | 0.0289645i | \(0.00922098\pi\) | ||||
−0.999580 | + | 0.0289645i | \(0.990779\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.13564 | + | 1.90174i | 0.0747195 | + | 0.125126i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.23404 | 0.342894 | 0.171447 | − | 0.985193i | \(-0.445156\pi\) | ||||
0.171447 | + | 0.985193i | \(0.445156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.3826 | + | 17.3666i | −0.807751 | + | 1.13287i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.0351 | − | 13.1584i | 1.43133 | − | 0.854730i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7332i | 0.823643i | 0.911265 | + | 0.411821i | \(0.135107\pi\) | ||||
−0.911265 | + | 0.411821i | \(0.864893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.343898i | − | 0.0221524i | −0.999939 | − | 0.0110762i | \(-0.996474\pi\) | ||
0.999939 | − | 0.0110762i | \(-0.00352574\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.77992 | + | 14.0368i | −0.434932 | + | 0.900463i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.79967 | − | 12.3415i | 0.562190 | − | 0.788471i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.96991 | 0.125342 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.8896 | + | 9.48856i | −1.00696 | + | 0.601313i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3426 | −1.09466 | −0.547329 | − | 0.836918i | \(-0.684355\pi\) | ||||
−0.547329 | + | 0.836918i | \(0.684355\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.05565 | − | 9.37520i | −0.569324 | − | 0.589414i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0923360 | + | 1.13632i | −0.00578230 | + | 0.0711591i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.0455 | 1.18803 | 0.594013 | − | 0.804456i | \(-0.297543\pi\) | ||||
0.594013 | + | 0.804456i | \(0.297543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.15014 | 0.320014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.7409 | + | 9.55743i | 1.09813 | + | 0.591590i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.0915i | − | 1.11557i | −0.829985 | − | 0.557786i | \(-0.811651\pi\) | ||
0.829985 | − | 0.557786i | \(-0.188349\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.83798 | + | 2.73653i | 0.235765 | + | 0.168104i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.34694 | − | 12.3032i | −0.449626 | − | 0.752945i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.39246i | 0.450726i | 0.974275 | + | 0.225363i | \(0.0723568\pi\) | ||||
−0.974275 | + | 0.225363i | \(0.927643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.1023 | 1.64635 | 0.823175 | − | 0.567788i | \(-0.192201\pi\) | ||||
0.823175 | + | 0.567788i | \(0.192201\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.81502 | + | 1.08385i | −0.109850 | + | 0.0655976i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.42905 | + | 12.8474i | 0.267082 | + | 0.774729i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8783i | 1.07420i | 0.843517 | + | 0.537102i | \(0.180481\pi\) | ||||
−0.843517 | + | 0.537102i | \(0.819519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.91567 | + | 7.26841i | −0.234425 | + | 0.435149i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.7140 | −1.47431 | −0.737156 | − | 0.675722i | \(-0.763832\pi\) | ||||
−0.737156 | + | 0.675722i | \(0.763832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.9367 | 0.828452 | 0.414226 | − | 0.910174i | \(-0.364052\pi\) | ||||
0.414226 | + | 0.910174i | \(0.364052\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.238217 | + | 2.93158i | −0.0141107 | + | 0.173652i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.773257i | − | 0.0456439i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9134 | 0.994903 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.450019 | + | 0.753603i | 0.0263806 | + | 0.0441770i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.6494i | − | 1.14793i | −0.818881 | − | 0.573964i | \(-0.805405\pi\) | ||
0.818881 | − | 0.573964i | \(-0.194595\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.40200 | − | 6.70376i | −0.547406 | − | 0.390308i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.1088 | + | 0.623752i | −0.818675 | + | 0.0361937i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.94767 | − | 8.64270i | 0.517457 | − | 0.499820i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.45065 | 0.0836140 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.29479 | + | 5.55044i | −0.533972 | + | 0.318864i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.3687 | + | 11.6711i | 0.937269 | + | 0.668285i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.855496i | 0.0488258i | 0.999702 | + | 0.0244129i | \(0.00777163\pi\) | ||||
−0.999702 | + | 0.0244129i | \(0.992228\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.54876 | + | 2.59356i | 0.0881061 | + | 0.147543i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 25.5437i | − | 1.44845i | −0.689563 | − | 0.724225i | \(-0.742198\pi\) | ||
0.689563 | − | 0.724225i | \(-0.257802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7271 | 1.00200 | 0.500998 | − | 0.865448i | \(-0.332966\pi\) | ||||
0.500998 | + | 0.865448i | \(0.332966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.39348 | − | 2.83214i | −0.0785136 | − | 0.159573i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.1134 | −0.905019 | −0.452510 | − | 0.891760i | \(-0.649471\pi\) | ||||
−0.452510 | + | 0.891760i | \(0.649471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.2565i | 1.02217i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3113 | + | 6.15746i | −0.575521 | + | 0.343676i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.223547 | −0.0124385 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.2616 | + | 4.22708i | −0.680149 | + | 0.234476i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.2094 | + | 13.2625i | −1.22818 | + | 0.733417i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.48818 | 0.247441 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.40122 | 0.351843 | 0.175921 | − | 0.984404i | \(-0.443710\pi\) | ||||
0.175921 | + | 0.984404i | \(0.443710\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.5736 | + | 28.9083i | −0.853427 | + | 1.58417i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.8830 | + | 18.0684i | −0.703873 | + | 0.987181i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.5553 | 0.956296 | 0.478148 | − | 0.878279i | \(-0.341308\pi\) | ||||
0.478148 | + | 0.878279i | \(0.341308\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.3540 | − | 6.18295i | 0.562351 | − | 0.335812i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.47967 | −0.405047 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.48321 | −0.350060 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.7799 | + | 14.3609i | 0.634206 | + | 0.773164i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.89843 | 0.209279 | 0.104639 | − | 0.994510i | \(-0.466631\pi\) | ||||
0.104639 | + | 0.994510i | \(0.466631\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.1848 | −1.24105 | −0.620527 | − | 0.784185i | \(-0.713081\pi\) | ||||
−0.620527 | + | 0.784185i | \(0.713081\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.595307 | − | 13.4654i | −0.0317752 | − | 0.718730i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.37228 | 0.498836 | 0.249418 | − | 0.968396i | \(-0.419761\pi\) | ||||
0.249418 | + | 0.968396i | \(0.419761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.43267 | + | 3.87357i | 0.288336 | + | 0.205588i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.205970 | − | 0.122996i | 0.0109011 | − | 0.00650966i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0966 | 1.27177 | 0.635884 | − | 0.771785i | \(-0.280636\pi\) | ||||
0.635884 | + | 0.771785i | \(0.280636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4233 | 0.969646 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.20849 | + | 5.37295i | 0.168402 | + | 0.282007i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.4813 | + | 11.0384i | 0.810326 | + | 0.577774i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.9693 | −1.92978 | −0.964891 | − | 0.262651i | \(-0.915403\pi\) | ||||
−0.964891 | + | 0.262651i | \(0.915403\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.34038 | + | 2.33826i | 0.225951 | + | 0.121725i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.991879i | − | 0.0514958i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.2888 | −1.51652 | −0.758260 | − | 0.651953i | \(-0.773950\pi\) | ||||
−0.758260 | + | 0.651953i | \(0.773950\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.80789 | − | 18.7586i | −0.248278 | − | 0.968689i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.4240 | −0.897381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.9410i | 0.716103i | 0.933702 | + | 0.358052i | \(0.116559\pi\) | ||||
−0.933702 | + | 0.358052i | \(0.883441\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.80227 | + | 5.25633i | −0.450954 | + | 0.269290i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 17.7556i | − | 0.907268i | −0.891188 | − | 0.453634i | \(-0.850127\pi\) | ||
0.891188 | − | 0.453634i | \(-0.149873\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.66013 | − | 2.32833i | 0.0846082 | − | 0.118663i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.38664 | + | 8.14266i | −0.222986 | + | 0.413915i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.3747 | −1.28655 | −0.643275 | − | 0.765635i | \(-0.722425\pi\) | ||||
−0.643275 | + | 0.765635i | \(0.722425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.01539 | + | 0.980780i | −0.0513505 | + | 0.0496002i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.7405 | + | 9.39955i | −0.794004 | + | 0.474145i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.9779 | − | 19.2356i | −1.35741 | − | 0.967849i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.8480i | − | 0.644821i | −0.946600 | − | 0.322411i | \(-0.895507\pi\) | ||
0.946600 | − | 0.322411i | \(-0.104493\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.531380 | − | 0.317317i | 0.0266023 | − | 0.0158857i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.59631 | 0.129653 | 0.0648267 | − | 0.997897i | \(-0.479351\pi\) | ||||
0.0648267 | + | 0.997897i | \(0.479351\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.13858i | − | 0.355598i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.1109 | + | 0.742416i | 0.999319 | + | 0.0368909i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.7485 | −1.47458 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.62758 | −0.179372 | −0.0896860 | − | 0.995970i | \(-0.528586\pi\) | ||||
−0.0896860 | + | 0.995970i | \(0.528586\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.98748 | − | 5.36693i | 0.443320 | − | 0.264731i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.42984i | 0.119564i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.4538 | + | 13.8709i | 0.954951 | + | 0.680893i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.8067 | − | 21.4461i | −0.627145 | − | 1.05022i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.394895 | 0.0192919 | 0.00964595 | − | 0.999953i | \(-0.496930\pi\) | ||||
0.00964595 | + | 0.999953i | \(0.496930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.7426i | − | 1.25462i | −0.778771 | − | 0.627308i | \(-0.784157\pi\) | ||
0.778771 | − | 0.627308i | \(-0.215843\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.5719 | + | 25.1927i | −0.659888 | + | 1.22491i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.39145 | − | 0.479692i | 0.0674954 | − | 0.0232685i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.23029i | − | 0.204718i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.4840 | − | 6.26061i | 0.506174 | − | 0.302265i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.6918 | −1.62288 | −0.811439 | − | 0.584438i | \(-0.801315\pi\) | ||||
−0.811439 | + | 0.584438i | \(0.801315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.89010 | 0.235003 | 0.117502 | − | 0.993073i | \(-0.462511\pi\) | ||||
0.117502 | + | 0.993073i | \(0.462511\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.10704 | − | 25.9300i | 0.101025 | − | 1.24325i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.61959 | + | 2.53030i | −0.125312 | + | 0.121041i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.2938 | −1.01630 | −0.508150 | − | 0.861269i | \(-0.669670\pi\) | ||||
−0.508150 | + | 0.861269i | \(0.669670\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.64484 | − | 17.9031i | 0.459278 | − | 0.852530i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.9103 | 1.65864 | 0.829320 | − | 0.558774i | \(-0.188728\pi\) | ||||
0.829320 | + | 0.558774i | \(0.188728\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.7401 | + | 15.0630i | −0.509131 | + | 0.714055i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.62752 | − | 2.72544i | −0.0769789 | − | 0.128909i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.02761i | 0.237268i | 0.992938 | + | 0.118634i | \(0.0378515\pi\) | ||||
−0.992938 | + | 0.118634i | \(0.962149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.46653i | 0.210321i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.5696 | − | 27.7474i | −0.778506 | − | 1.30369i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.22216 | + | 1.58443i | 0.104176 | + | 0.0742791i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.7256 | −1.25017 | −0.625086 | − | 0.780556i | \(-0.714936\pi\) | ||||
−0.625086 | + | 0.780556i | \(0.714936\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0675560 | + | 1.52806i | 0.00315324 | + | 0.0713239i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 41.7818i | − | 1.94597i | −0.230866 | − | 0.972986i | \(-0.574156\pi\) | ||
0.230866 | − | 0.972986i | \(-0.425844\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.5946i | 0.492375i | 0.969222 | + | 0.246187i | \(0.0791778\pi\) | ||||
−0.969222 | + | 0.246187i | \(0.920822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.6235 | + | 0.863253i | 0.492653 | + | 0.0400324i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.92981i | − | 0.0893009i | −0.999003 | − | 0.0446504i | \(-0.985783\pi\) | ||
0.999003 | − | 0.0446504i | \(-0.0142174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.66956 | 0.215620 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.76997 | + | 4.63861i | 0.127634 | + | 0.213736i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.37933 | −0.385282 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.58979 | − | 1.23755i | 0.164711 | − | 0.0567828i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.56753 | + | 2.99936i | 0.254920 | + | 0.137331i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.45475 | −0.0664692 | −0.0332346 | − | 0.999448i | \(-0.510581\pi\) | ||||
−0.0332346 | + | 0.999448i | \(0.510581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 28.3919i | − | 1.29456i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.02144 | − | 3.77266i | 0.0464771 | − | 0.171662i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.657860 | − | 0.922647i | 0.0298719 | − | 0.0418952i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.4249i | 0.608341i | 0.952618 | + | 0.304171i | \(0.0983793\pi\) | ||||
−0.952618 | + | 0.304171i | \(0.901621\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.86294 | + | 1.11247i | −0.0842450 | + | 0.0503074i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.32212i | 0.104796i | 0.998626 | + | 0.0523980i | \(0.0166864\pi\) | ||||
−0.998626 | + | 0.0523980i | \(0.983314\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.97729 | 0.0890526 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.04910 | + | 16.3592i | 0.361780 | + | 0.735292i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.40401i | − | 0.0629784i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.57904 | −0.339284 | −0.169642 | − | 0.985506i | \(-0.554261\pi\) | ||||
−0.169642 | + | 0.985506i | \(0.554261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.1824 | + | 30.4483i | 0.812330 | + | 1.36033i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 33.5867i | − | 1.49756i | −0.662821 | − | 0.748778i | \(-0.730641\pi\) | ||
0.662821 | − | 0.748778i | \(-0.269359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.3797 | + | 8.11391i | 0.506392 | + | 0.361064i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.56917 | − | 9.32615i | −0.247335 | − | 0.414189i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 19.8690i | − | 0.880677i | −0.897832 | − | 0.440338i | \(-0.854858\pi\) | ||
0.897832 | − | 0.440338i | \(-0.145142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.00095i | − | 0.176992i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.174287 | + | 3.94224i | 0.00769495 | + | 0.174054i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.26406 | − | 3.17534i | 0.0997664 | − | 0.139922i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.9249 | −1.14018 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.83271 | − | 8.09287i | −0.212132 | − | 0.355237i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3058 | 0.714368 | 0.357184 | − | 0.934034i | \(-0.383737\pi\) | ||||
0.357184 | + | 0.934034i | \(0.383737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.3526 | 1.80822 | 0.904112 | − | 0.427295i | \(-0.140534\pi\) | ||||
0.904112 | + | 0.427295i | \(0.140534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.62663 | + | 3.11537i | −0.114636 | + | 0.135966i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.810093i | 0.0352882i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.797293 | + | 22.9862i | −0.0346649 | + | 0.999399i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.6389 | − | 7.34762i | −0.591880 | − | 0.318860i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.26285 | −0.184645 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6243 | + | 9.00128i | 0.545795 | + | 0.389159i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.7336 | − | 11.7840i | 0.851567 | − | 0.508518i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.4235 | 0.793556 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3949 | −0.575893 | −0.287947 | − | 0.957646i | \(-0.592973\pi\) | ||||
−0.287947 | + | 0.957646i | \(0.592973\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.9305 | − | 16.6789i | 1.19861 | − | 0.715758i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.1913 | + | 19.3878i | 1.16475 | + | 0.830480i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.9768i | − | 0.811387i | −0.914009 | − | 0.405694i | \(-0.867030\pi\) | ||
0.914009 | − | 0.405694i | \(-0.132970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.7451 | + | 12.7921i | 1.01342 | + | 0.545952i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.10118 | 0.217318 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.97212i | 0.296485i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42.2523 | + | 3.43337i | 1.79351 | + | 0.145739i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.4609i | 1.71438i | 0.514998 | + | 0.857192i | \(0.327793\pi\) | ||||
−0.514998 | + | 0.857192i | \(0.672207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.99721i | − | 0.338246i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.18974 | + | 0.710459i | −0.0502307 | + | 0.0299956i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.62726i | − | 0.110726i | −0.998466 | − | 0.0553629i | \(-0.982368\pi\) | ||
0.998466 | − | 0.0553629i | \(-0.0176316\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.6765 | − | 9.03854i | −0.533306 | − | 0.380254i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.32962 | − | 3.53638i | −0.0978347 | − | 0.148514i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −45.1617 | −1.89327 | −0.946637 | − | 0.322300i | \(-0.895544\pi\) | ||||
−0.946637 | + | 0.322300i | \(0.895544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 12.0554i | − | 0.504504i | −0.967662 | − | 0.252252i | \(-0.918829\pi\) | ||
0.967662 | − | 0.252252i | \(-0.0811711\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.8426 | + | 26.5301i | 0.661835 | + | 1.10831i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8759 | − | 21.3709i | 0.453556 | − | 0.891228i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.8658i | − | 0.910287i | −0.890418 | − | 0.455144i | \(-0.849588\pi\) | ||
0.890418 | − | 0.455144i | \(-0.150412\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.3186 | + | 6.16181i | −0.428826 | + | 0.256076i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.02761i | − | 0.208581i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.72935i | 0.237286i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.6132 | + | 7.68204i | −0.645526 | + | 0.317613i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.5450 | 0.682886 | 0.341443 | − | 0.939902i | \(-0.389084\pi\) | ||||
0.341443 | + | 0.939902i | \(0.389084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.08995i | 0.0861148i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.96404 | − | 9.98741i | −0.245328 | − | 0.410827i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.6571 | 0.725089 | 0.362545 | − | 0.931966i | \(-0.381908\pi\) | ||||
0.362545 | + | 0.931966i | \(0.381908\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.252172 | − | 0.179802i | −0.0103381 | − | 0.00737117i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.9747 | − | 16.1081i | 1.10400 | − | 0.659261i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0528i | 1.30964i | 0.755784 | + | 0.654821i | \(0.227256\pi\) | ||||
−0.755784 | + | 0.654821i | \(0.772744\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.6282 | −1.04540 | −0.522698 | − | 0.852518i | \(-0.675074\pi\) | ||||
−0.522698 | + | 0.852518i | \(0.675074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.1204 | + | 26.2108i | −0.575025 | + | 1.06738i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.69033 | − | 6.57818i | 0.190689 | − | 0.267441i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.1937i | − | 0.981992i | −0.871162 | − | 0.490996i | \(-0.836633\pi\) | ||
0.871162 | − | 0.490996i | \(-0.163367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.70009 | + | 2.80669i | −0.190457 | + | 0.113733i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 24.7427i | − | 1.00098i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.9078 | 0.804067 | 0.402033 | − | 0.915625i | \(-0.368304\pi\) | ||||
0.402033 | + | 0.915625i | \(0.368304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.515497 | − | 6.34388i | 0.0207868 | − | 0.255810i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.9069i | 1.60659i | 0.595581 | + | 0.803295i | \(0.296922\pi\) | ||||
−0.595581 | + | 0.803295i | \(0.703078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 41.3469i | − | 1.66187i | −0.556369 | − | 0.830935i | \(-0.687806\pi\) | ||
0.556369 | − | 0.830935i | \(-0.312194\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0876 | + | 17.1417i | 0.725832 | + | 0.687872i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.89285 | 0.155964 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.6889 | + | 15.4061i | −0.787554 | + | 0.616245i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.06939 | + | 1.83291i | −0.122580 | + | 0.0731992i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.22194i | 0.128467i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.27753i | 0.289714i | 0.989453 | + | 0.144857i | \(0.0462722\pi\) | ||||
−0.989453 | + | 0.144857i | \(0.953728\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.19828 | − | 8.70505i | −0.206613 | − | 0.345995i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7767 | + | 7.68396i | 0.427662 | + | 0.304929i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.5833i | 0.696678i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.88087 | + | 4.24561i | 0.311762 | + | 0.167954i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.9598 | 0.630373 | 0.315187 | − | 0.949030i | \(-0.397933\pi\) | ||||
0.315187 | + | 0.949030i | \(0.397933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.7217 | −0.422822 | −0.211411 | − | 0.977397i | \(-0.567806\pi\) | ||||
−0.211411 | + | 0.977397i | \(0.567806\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.9013 | + | 0.967085i | 0.468613 | + | 0.0380789i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.95520 | −0.155495 | −0.0777475 | − | 0.996973i | \(-0.524773\pi\) | ||||
−0.0777475 | + | 0.996973i | \(0.524773\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.0354i | − | 0.550936i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.14990 | − | 1.92562i | −0.0450680 | − | 0.0754711i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.4228 | 0.799207 | 0.399603 | − | 0.916688i | \(-0.369148\pi\) | ||||
0.399603 | + | 0.916688i | \(0.369148\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.2713 | + | 13.7407i | 0.752994 | + | 0.536895i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.4578 | + | 12.0985i | 0.876161 | + | 0.472009i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.9648 | 1.20622 | 0.603109 | − | 0.797659i | \(-0.293929\pi\) | ||||
0.603109 | + | 0.797659i | \(0.293929\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 30.2091i | − | 1.17500i | −0.809225 | − | 0.587499i | \(-0.800113\pi\) | ||
0.809225 | − | 0.587499i | \(-0.199887\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.678061 | − | 1.13548i | −0.0263337 | − | 0.0440985i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.650576 | − | 0.463870i | −0.0252283 | − | 0.0179881i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.1705 | − | 22.3807i | 0.897165 | − | 0.866585i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.9603 | − | 19.0853i | 1.23566 | − | 0.737880i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.4353i | 0.943314i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 34.6381i | − | 1.33520i | −0.744520 | − | 0.667601i | \(-0.767321\pi\) | ||
0.744520 | − | 0.667601i | \(-0.232679\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.54419 | − | 24.1642i | −0.367356 | − | 0.930080i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4.28688i | − | 0.164758i | −0.996601 | − | 0.0823791i | \(-0.973748\pi\) | ||
0.996601 | − | 0.0823791i | \(-0.0262518\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.238447 | −0.00915076 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.68767 | − | 3.39643i | 0.217952 | − | 0.130151i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3046 | 1.35089 | 0.675447 | − | 0.737409i | \(-0.263951\pi\) | ||||
0.675447 | + | 0.737409i | \(0.263951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.0035 | − | 7.84565i | −0.420422 | − | 0.299767i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.30362 | − | 0.778462i | 0.0497360 | − | 0.0297002i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.46808 | −0.208317 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.9438 | −1.44345 | −0.721725 | − | 0.692180i | \(-0.756651\pi\) | ||||
−0.721725 | + | 0.692180i | \(0.756651\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.81958 | − | 3.37758i | 0.0691202 | − | 0.128304i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.7214 | + | 26.2567i | −0.710144 | + | 0.995975i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.483752 | 0.0183234 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.64794 | − | 7.78346i | −0.175801 | − | 0.294398i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0595 | −0.417712 | −0.208856 | − | 0.977946i | \(-0.566974\pi\) | ||||
−0.208856 | + | 0.977946i | \(0.566974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.31225i | 0.313502i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36.8215 | + | 2.99208i | 1.38678 | + | 0.112688i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2.94096i | − | 0.110606i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 31.1952i | − | 1.17156i | −0.810470 | − | 0.585781i | \(-0.800788\pi\) | ||
0.810470 | − | 0.585781i | \(-0.199212\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.1353 | − | 21.0831i | −1.46769 | − | 0.790678i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.16935 | + | 9.49291i | 0.343395 | + | 0.355512i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.8358 | − | 9.15207i | −0.480030 | − | 0.342268i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.9353 | − | 11.3074i | 0.707153 | − | 0.422281i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.6275i | 1.06763i | 0.845602 | + | 0.533813i | \(0.179242\pi\) | ||||
−0.845602 | + | 0.533813i | \(0.820758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.820628 | −0.0305618 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.511406 | + | 0.305389i | −0.0190194 | + | 0.0113575i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −31.7520 | + | 10.9462i | −1.17924 | + | 0.406533i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0328 | 1.18803 | 0.594015 | − | 0.804454i | \(-0.297542\pi\) | ||||
0.594015 | + | 0.804454i | \(0.297542\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.8947 | − | 2.38269i | 0.996099 | − | 0.0882478i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.907531i | 0.0335662i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.5996 | −0.391503 | −0.195752 | − | 0.980653i | \(-0.562715\pi\) | ||||
−0.195752 | + | 0.980653i | \(0.562715\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.1672 | − | 2.12631i | −0.965191 | − | 0.0784303i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.9726 | −0.993548 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.8330 | 0.803140 | 0.401570 | − | 0.915828i | \(-0.368465\pi\) | ||||
0.401570 | + | 0.915828i | \(0.368465\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.74932 | − | 2.92942i | −0.0642629 | − | 0.107615i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.424532i | 0.0155746i | 0.999970 | + | 0.00778728i | \(0.00247879\pi\) | ||||
−0.999970 | + | 0.00778728i | \(0.997521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.37918 | + | 3.33680i | −0.0871666 | + | 0.122251i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.2206 | + | 15.2031i | 1.03254 | + | 0.556252i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3.26259i | − | 0.119213i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3391i | 1.32603i | 0.748605 | + | 0.663016i | \(0.230724\pi\) | ||||
−0.748605 | + | 0.663016i | \(0.769276\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.4006 | + | 25.7900i | 0.561230 | + | 0.939838i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.2222 | + | 33.9716i | −0.881537 | + | 1.23635i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.12855 | 0.113709 | 0.0568545 | − | 0.998382i | \(-0.481893\pi\) | ||||
0.0568545 | + | 0.998382i | \(0.481893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.90010 | + | 21.7919i | −0.214160 | + | 0.790996i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.0859i | 1.41686i | 0.705779 | + | 0.708432i | \(0.250597\pi\) | ||||
−0.705779 | + | 0.708432i | \(0.749403\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 7.02726i | − | 0.254404i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.77180 | − | 0.871764i | 0.0640595 | − | 0.0315187i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.3953 | 0.483677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 45.8619i | − | 1.65382i | −0.562334 | − | 0.826910i | \(-0.690096\pi\) | ||
0.562334 | − | 0.826910i | \(-0.309904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.9128 | − | 28.3222i | −0.609100 | − | 1.02000i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 36.9125i | − | 1.32765i | −0.747888 | − | 0.663825i | \(-0.768932\pi\) | ||
0.747888 | − | 0.663825i | \(-0.231068\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.48466 | − | 13.0087i | −0.161094 | − | 0.467288i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.57343 | − | 7.65868i | −0.164071 | − | 0.274754i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.24803 | 0.0447152 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.10993i | 0.290196i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.54158 | − | 34.8694i | −0.0550916 | − | 1.24613i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.04929 | − | 5.67912i | 0.144525 | − | 0.202696i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.3328 | −0.546557 | −0.273278 | − | 0.961935i | \(-0.588108\pi\) | ||||
−0.273278 | + | 0.961935i | \(0.588108\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.9036 | + | 16.0657i | −0.957795 | + | 0.571953i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.27610i | 0.116485i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.3210 | −0.828152 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.661243 | − | 8.13749i | 0.0234519 | − | 0.288607i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 45.0345i | − | 1.59520i | −0.603185 | − | 0.797601i | \(-0.706102\pi\) | ||
0.603185 | − | 0.797601i | \(-0.293898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.80782i | 0.0993335i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.7717 | + | 21.8510i | −0.415932 | + | 0.772069i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.1105i | 0.815553i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.99019 | + | 0.747333i | −0.175881 | + | 0.0263400i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.9932 | − | 6.56466i | 0.386979 | − | 0.231087i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 24.1332i | − | 0.848479i | −0.905550 | − | 0.424240i | \(-0.860541\pi\) | ||
0.905550 | − | 0.424240i | \(-0.139459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.67375 | 0.199232 | 0.0996161 | − | 0.995026i | \(-0.468239\pi\) | ||||
0.0996161 | + | 0.995026i | \(0.468239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.0674 | − | 40.3034i | −0.844082 | − | 1.41350i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.28082 | + | 1.62626i | 0.0798937 | + | 0.0569653i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.34133i | 0.0819127i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.22355 | + | 1.73660i | 0.112640 | + | 0.0606819i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.4857i | − | 0.365952i | −0.983117 | − | 0.182976i | \(-0.941427\pi\) | ||
0.983117 | − | 0.182976i | \(-0.0585731\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.66303i | 0.162543i | 0.996692 | + | 0.0812715i | \(0.0258981\pi\) | ||||
−0.996692 | + | 0.0812715i | \(0.974102\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.1721 | − | 17.9952i | 0.528225 | − | 0.626511i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.9806i | 1.73800i | 0.494816 | + | 0.868998i | \(0.335236\pi\) | ||||
−0.494816 | + | 0.868998i | \(0.664764\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.39168 | −0.221992 | −0.110996 | − | 0.993821i | \(-0.535404\pi\) | ||||
−0.110996 | + | 0.993821i | \(0.535404\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.5866 | − | 15.8763i | 0.922277 | − | 0.550744i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.99537i | − | 0.0691356i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.5799 | − | 37.2783i | 0.919837 | − | 1.29007i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.2859 | − | 0.631583i | 0.493794 | − | 0.0218307i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.0331 | 0.933285 | 0.466642 | − | 0.884446i | \(-0.345464\pi\) | ||||
0.466642 | + | 0.884446i | \(0.345464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1204 | −0.555875 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.9465 | + | 36.7518i | 0.755879 | + | 1.26580i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.14129 | + | 11.4181i | −0.280069 | + | 0.392796i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.70005 | −0.0584145 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.3761 | − | 20.7251i | −0.424747 | − | 0.711283i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.4688 | + | 37.7557i | 1.25014 | + | 1.29425i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.4110i | 1.58908i | 0.607211 | + | 0.794541i | \(0.292288\pi\) | ||||
−0.607211 | + | 0.794541i | \(0.707712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.57104 | − | 2.24905i | 0.156326 | − | 0.0769161i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.0436 | −0.684676 | −0.342338 | − | 0.939577i | \(-0.611219\pi\) | ||||
−0.342338 | + | 0.939577i | \(0.611219\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.2450 | −1.68022 | −0.840108 | − | 0.542419i | \(-0.817509\pi\) | ||||
−0.840108 | + | 0.542419i | \(0.817509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.14990 | + | 0.686668i | −0.0391884 | + | 0.0234016i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.42611 | −0.286828 | −0.143414 | − | 0.989663i | \(-0.545808\pi\) | ||||
−0.143414 | + | 0.989663i | \(0.545808\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.06469 | + | 9.90821i | −0.240207 | + | 0.336889i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.0194 | − | 25.1516i | −0.510086 | − | 0.854192i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 40.2728i | − | 1.36616i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 25.7426i | − | 0.872254i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.721044 | − | 1.33843i | 0.0244036 | − | 0.0452990i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.04485 | + | 1.49130i | 0.170547 | + | 0.0504152i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.9659i | 0.944341i | 0.881507 | + | 0.472170i | \(0.156529\pi\) | ||||
−0.881507 | + | 0.472170i | \(0.843471\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.2202 | + | 17.4491i | −0.985575 | + | 0.588542i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.2217 | 1.69201 | 0.846006 | − | 0.533174i | \(-0.179001\pi\) | ||||
0.846006 | + | 0.533174i | \(0.179001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.4586i | − | 1.12597i | −0.826467 | − | 0.562986i | \(-0.809653\pi\) | ||
0.826467 | − | 0.562986i | \(-0.190347\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.61987 | + | 19.9346i | −0.0544512 | + | 0.670096i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.9037 | 1.54129 | 0.770647 | − | 0.637262i | \(-0.219933\pi\) | ||||
0.770647 | + | 0.637262i | \(0.219933\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.78512i | − | 0.0934100i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.4565 | + | 20.4270i | 0.450809 | + | 0.684332i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.24386i | 0.242407i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.1601 | − | 17.2265i | −0.807583 | − | 0.575818i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.7981 | − | 5.63104i | −0.694430 | − | 0.188015i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 18.4857i | − | 0.616534i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.620523 | 0.0206726 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.28821 | − | 2.15724i | −0.0428689 | − | 0.0717883i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −34.1957 | − | 24.3820i | −1.13670 | − | 0.810485i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.2790 | −0.772967 | −0.386483 | − | 0.922296i | \(-0.626310\pi\) | ||||
−0.386483 | + | 0.922296i | \(0.626310\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.5079 | + | 8.89322i | 0.547534 | + | 0.294969i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.7049 | 0.984167 | 0.492083 | − | 0.870548i | \(-0.336236\pi\) | ||||
0.492083 | + | 0.870548i | \(0.336236\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.0408i | 0.961110i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.82015 | − | 34.7058i | 0.0932314 | − | 1.14734i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.98045i | − | 0.164469i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.3966i | 0.606848i | 0.952856 | + | 0.303424i | \(0.0981298\pi\) | ||||
−0.952856 | + | 0.303424i | \(0.901870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.27219 | − | 0.759699i | 0.0419202 | − | 0.0250329i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.74010 | −0.254768 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.8366 | − | 51.7390i | −0.586465 | − | 1.70117i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.48151 | − | 4.60628i | 0.0815036 | − | 0.151290i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19.5644i | − | 0.641888i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) | ||
0.947098 | − | 0.320944i | \(-0.104000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5.14784i | − | 0.168714i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37.9856 | + | 22.6834i | −1.24359 | + | 0.742620i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.45661 | + | 1.03858i | 0.0476363 | + | 0.0339653i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.72907 | −0.317835 | −0.158917 | − | 0.987292i | \(-0.550800\pi\) | ||||
−0.158917 | + | 0.987292i | \(0.550800\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.7421 | − | 26.3617i | −0.513723 | − | 0.860282i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7025 | −0.674883 | −0.337441 | − | 0.941347i | \(-0.609561\pi\) | ||||
−0.337441 | + | 0.941347i | \(0.609561\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.66875 | − | 5.47554i | 0.184600 | − | 0.178308i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.97420 | + | 4.58722i | −0.0967506 | + | 0.149222i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.15842 | 0.135130 | 0.0675652 | − | 0.997715i | \(-0.478477\pi\) | ||||
0.0675652 | + | 0.997715i | \(0.478477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.0566 | −0.715989 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.3091 | + | 23.9620i | 0.464003 | + | 0.777021i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.6049i | − | 0.440705i | −0.975420 | − | 0.220352i | \(-0.929279\pi\) | ||
0.975420 | − | 0.220352i | \(-0.0707208\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.1595 | − | 32.4812i | 0.749425 | − | 1.05107i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.1490 | − | 16.2122i | 0.877602 | − | 0.524065i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.84372i | 0.0918286i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4264 | −0.755691 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.3133 | + | 9.86581i | 0.590138 | + | 0.317921i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.6332 | + | 9.00764i | 0.406677 | + | 0.289966i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.31539i | 0.203089i | 0.994831 | + | 0.101545i | \(0.0323784\pi\) | ||||
−0.994831 | + | 0.101545i | \(0.967622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.198514 | + | 0.332433i | 0.00637720 | + | 0.0106793i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0773 | −0.387578 | −0.193789 | − | 0.981043i | \(-0.562078\pi\) | ||||
−0.193789 | + | 0.981043i | \(0.562078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.78574 | 0.217541 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.1746 | + | 14.4802i | 0.550026 | + | 0.463739i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 15.8674i | − | 0.507642i | −0.967251 | − | 0.253821i | \(-0.918313\pi\) | ||
0.967251 | − | 0.253821i | \(-0.0816874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.4861 | −0.718660 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.4448 | + | 21.2499i | 1.25938 | + | 0.678456i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 27.6415i | − | 0.881628i | −0.897599 | − | 0.440814i | \(-0.854690\pi\) | ||
0.897599 | − | 0.440814i | \(-0.145310\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.71853 | + | 12.2277i | −0.277796 | + | 0.389608i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.98560 | − | 6.67430i | −0.126863 | − | 0.212445i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.2722 | + | 10.6347i | 0.326638 | + | 0.338165i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.6111 | 0.686499 | 0.343249 | − | 0.939244i | \(-0.388472\pi\) | ||||
0.343249 | + | 0.939244i | \(0.388472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.68442 | − | 9.51915i | −0.180390 | − | 0.302081i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.0255 | − | 23.5476i | −1.04698 | − | 0.746510i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.7984i | 1.57713i | 0.614950 | + | 0.788566i | \(0.289176\pi\) | ||||
−0.614950 | + | 0.788566i | \(0.710824\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 56.8187 | − | 2.51197i | 1.79767 | − | 0.0794751i |
(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 | 1380.2.n.a.689.13 | ✓ | 48 | |
3.2 | odd | 2 | inner | 1380.2.n.a.689.34 | yes | 48 | |
5.4 | even | 2 | inner | 1380.2.n.a.689.35 | yes | 48 | |
15.14 | odd | 2 | inner | 1380.2.n.a.689.16 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.n.a.689.14 | yes | 48 | |
69.68 | even | 2 | inner | 1380.2.n.a.689.33 | yes | 48 | |
115.114 | odd | 2 | inner | 1380.2.n.a.689.36 | yes | 48 | |
345.344 | even | 2 | inner | 1380.2.n.a.689.15 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.n.a.689.13 | ✓ | 48 | 1.1 | even | 1 | trivial | |
1380.2.n.a.689.14 | yes | 48 | 23.22 | odd | 2 | inner | |
1380.2.n.a.689.15 | yes | 48 | 345.344 | even | 2 | inner | |
1380.2.n.a.689.16 | yes | 48 | 15.14 | odd | 2 | inner | |
1380.2.n.a.689.33 | yes | 48 | 69.68 | even | 2 | inner | |
1380.2.n.a.689.34 | yes | 48 | 3.2 | odd | 2 | inner | |
1380.2.n.a.689.35 | yes | 48 | 5.4 | even | 2 | inner | |
1380.2.n.a.689.36 | yes | 48 | 115.114 | odd | 2 | inner |