Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(506,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.506");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.c (of order \(2\), degree \(1\), 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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 506.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.506 |
Dual form | 845.2.c.e.506.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205i | 1.22474i | 0.790569 | + | 0.612372i | \(0.209785\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | −0.732051 | −0.422650 | −0.211325 | − | 0.977416i | \(-0.567778\pi\) | ||||
−0.211325 | + | 0.977416i | \(0.567778\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | − 1.26795i | − 0.517638i | ||||||||
\(7\) | − 2.00000i | − 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | 1.26795i | 0.382301i | 0.981561 | + | 0.191151i | \(0.0612219\pi\) | ||||
−0.981561 | + | 0.191151i | \(0.938778\pi\) | |||||||
\(12\) | 0.732051 | 0.211325 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | 0.732051i | 0.189015i | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | − 4.26795i | − 1.00597i | ||||||||
\(19\) | 4.19615i | 0.962663i | 0.876539 | + | 0.481332i | \(0.159847\pi\) | ||||
−0.876539 | + | 0.481332i | \(0.840153\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 1.46410i | 0.319493i | ||||||||
\(22\) | −2.19615 | −0.468221 | ||||||||
\(23\) | −4.73205 | −0.986701 | −0.493350 | − | 0.869831i | \(-0.664228\pi\) | ||||
−0.493350 | + | 0.869831i | \(0.664228\pi\) | |||||||
\(24\) | − 1.26795i | − 0.258819i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | −9.46410 | −1.75744 | −0.878720 | − | 0.477338i | \(-0.841602\pi\) | ||||
−0.878720 | + | 0.477338i | \(0.841602\pi\) | |||||||
\(30\) | −1.26795 | −0.231495 | ||||||||
\(31\) | − 0.196152i | − 0.0352300i | −0.999845 | − | 0.0176150i | \(-0.994393\pi\) | ||||
0.999845 | − | 0.0176150i | \(-0.00560732\pi\) | |||||||
\(32\) | − 5.19615i | − 0.918559i | ||||||||
\(33\) | − 0.928203i | − 0.161579i | ||||||||
\(34\) | − 6.00000i | − 1.02899i | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 2.46410 | 0.410684 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | −7.26795 | −1.17902 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | − 3.46410i | − 0.541002i | −0.962720 | − | 0.270501i | \(-0.912811\pi\) | ||||
0.962720 | − | 0.270501i | \(-0.0871893\pi\) | |||||||
\(42\) | −2.53590 | −0.391298 | ||||||||
\(43\) | −10.1962 | −1.55490 | −0.777449 | − | 0.628946i | \(-0.783487\pi\) | ||||
−0.777449 | + | 0.628946i | \(0.783487\pi\) | |||||||
\(44\) | − 1.26795i | − 0.191151i | ||||||||
\(45\) | 2.46410i | 0.367327i | ||||||||
\(46\) | − 8.19615i | − 1.20846i | ||||||||
\(47\) | − 6.00000i | − 0.875190i | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||||
0.899172 | − | 0.437595i | \(-0.144170\pi\) | |||||||
\(48\) | 3.66025 | 0.528312 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | − 1.73205i | − 0.244949i | ||||||||
\(51\) | 2.53590 | 0.355097 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3923 | −1.42749 | −0.713746 | − | 0.700404i | \(-0.753003\pi\) | ||||
−0.713746 | + | 0.700404i | \(0.753003\pi\) | |||||||
\(54\) | 6.92820i | 0.942809i | ||||||||
\(55\) | 1.26795 | 0.170970 | ||||||||
\(56\) | 3.46410 | 0.462910 | ||||||||
\(57\) | − 3.07180i | − 0.406869i | ||||||||
\(58\) | − 16.3923i | − 2.15242i | ||||||||
\(59\) | 15.1244i | 1.96902i | 0.175319 | + | 0.984512i | \(0.443904\pi\) | ||||
−0.175319 | + | 0.984512i | \(0.556096\pi\) | |||||||
\(60\) | − 0.732051i | − 0.0945074i | ||||||||
\(61\) | 12.3923 | 1.58667 | 0.793336 | − | 0.608784i | \(-0.208342\pi\) | ||||
0.793336 | + | 0.608784i | \(0.208342\pi\) | |||||||
\(62\) | 0.339746 | 0.0431478 | ||||||||
\(63\) | 4.92820i | 0.620895i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.60770 | 0.197894 | ||||||||
\(67\) | − 14.3923i | − 1.75830i | −0.476545 | − | 0.879150i | \(-0.658111\pi\) | ||||
0.476545 | − | 0.879150i | \(-0.341889\pi\) | |||||||
\(68\) | 3.46410 | 0.420084 | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | − 3.46410i | − 0.414039i | ||||||||
\(71\) | 1.26795i | 0.150478i | 0.997166 | + | 0.0752389i | \(0.0239720\pi\) | ||||
−0.997166 | + | 0.0752389i | \(0.976028\pi\) | |||||||
\(72\) | − 4.26795i | − 0.502983i | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | −6.92820 | −0.805387 | ||||||||
\(75\) | 0.732051 | 0.0845299 | ||||||||
\(76\) | − 4.19615i | − 0.481332i | ||||||||
\(77\) | 2.53590 | 0.288992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3923 | 1.39424 | 0.697122 | − | 0.716953i | \(-0.254464\pi\) | ||||
0.697122 | + | 0.716953i | \(0.254464\pi\) | |||||||
\(80\) | 5.00000i | 0.559017i | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | − 6.00000i | − 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | − 1.46410i | − 0.159747i | ||||||||
\(85\) | 3.46410i | 0.375735i | ||||||||
\(86\) | − 17.6603i | − 1.90435i | ||||||||
\(87\) | 6.92820 | 0.742781 | ||||||||
\(88\) | −2.19615 | −0.234111 | ||||||||
\(89\) | − 0.928203i | − 0.0983893i | −0.998789 | − | 0.0491947i | \(-0.984335\pi\) | ||||
0.998789 | − | 0.0491947i | \(-0.0156655\pi\) | |||||||
\(90\) | −4.26795 | −0.449881 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.73205 | 0.493350 | ||||||||
\(93\) | 0.143594i | 0.0148900i | ||||||||
\(94\) | 10.3923 | 1.07188 | ||||||||
\(95\) | 4.19615 | 0.430516 | ||||||||
\(96\) | 3.80385i | 0.388229i | ||||||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | 5.19615i | 0.524891i | ||||||||
\(99\) | − 3.12436i | − 0.314010i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.9282 | −1.28640 | −0.643202 | − | 0.765696i | \(-0.722395\pi\) | ||||
−0.643202 | + | 0.765696i | \(0.722395\pi\) | |||||||
\(102\) | 4.39230i | 0.434903i | ||||||||
\(103\) | −10.1962 | −1.00466 | −0.502328 | − | 0.864677i | \(-0.667523\pi\) | ||||
−0.502328 | + | 0.864677i | \(0.667523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.46410 | 0.142882 | ||||||||
\(106\) | − 18.0000i | − 1.74831i | ||||||||
\(107\) | 0.339746 | 0.0328445 | 0.0164222 | − | 0.999865i | \(-0.494772\pi\) | ||||
0.0164222 | + | 0.999865i | \(0.494772\pi\) | |||||||
\(108\) | −4.00000 | −0.384900 | ||||||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 2.19615i | 0.209395i | ||||||||
\(111\) | − 2.92820i | − 0.277933i | ||||||||
\(112\) | 10.0000i | 0.944911i | ||||||||
\(113\) | 15.4641 | 1.45474 | 0.727370 | − | 0.686245i | \(-0.240742\pi\) | ||||
0.727370 | + | 0.686245i | \(0.240742\pi\) | |||||||
\(114\) | 5.32051 | 0.498311 | ||||||||
\(115\) | 4.73205i | 0.441266i | ||||||||
\(116\) | 9.46410 | 0.878720 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −26.1962 | −2.41155 | ||||||||
\(119\) | 6.92820i | 0.635107i | ||||||||
\(120\) | −1.26795 | −0.115747 | ||||||||
\(121\) | 9.39230 | 0.853846 | ||||||||
\(122\) | 21.4641i | 1.94327i | ||||||||
\(123\) | 2.53590i | 0.228654i | ||||||||
\(124\) | 0.196152i | 0.0176150i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −8.53590 | −0.760438 | ||||||||
\(127\) | −5.80385 | −0.515008 | −0.257504 | − | 0.966277i | \(-0.582900\pi\) | ||||
−0.257504 | + | 0.966277i | \(0.582900\pi\) | |||||||
\(128\) | − 12.1244i | − 1.07165i | ||||||||
\(129\) | 7.46410 | 0.657178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0.928203i | 0.0807897i | ||||||||
\(133\) | 8.39230 | 0.727705 | ||||||||
\(134\) | 24.9282 | 2.15347 | ||||||||
\(135\) | − 4.00000i | − 0.344265i | ||||||||
\(136\) | − 6.00000i | − 0.514496i | ||||||||
\(137\) | 12.9282i | 1.10453i | 0.833668 | + | 0.552265i | \(0.186237\pi\) | ||||
−0.833668 | + | 0.552265i | \(0.813763\pi\) | |||||||
\(138\) | 6.00000i | 0.510754i | ||||||||
\(139\) | −8.39230 | −0.711826 | −0.355913 | − | 0.934519i | \(-0.615830\pi\) | ||||
−0.355913 | + | 0.934519i | \(0.615830\pi\) | |||||||
\(140\) | 2.00000 | 0.169031 | ||||||||
\(141\) | 4.39230i | 0.369899i | ||||||||
\(142\) | −2.19615 | −0.184297 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.3205 | 1.02671 | ||||||||
\(145\) | 9.46410i | 0.785951i | ||||||||
\(146\) | −6.92820 | −0.573382 | ||||||||
\(147\) | −2.19615 | −0.181136 | ||||||||
\(148\) | − 4.00000i | − 0.328798i | ||||||||
\(149\) | 19.8564i | 1.62670i | 0.581775 | + | 0.813350i | \(0.302359\pi\) | ||||
−0.581775 | + | 0.813350i | \(0.697641\pi\) | |||||||
\(150\) | 1.26795i | 0.103528i | ||||||||
\(151\) | 12.1962i | 0.992509i | 0.868177 | + | 0.496254i | \(0.165292\pi\) | ||||
−0.868177 | + | 0.496254i | \(0.834708\pi\) | |||||||
\(152\) | −7.26795 | −0.589509 | ||||||||
\(153\) | 8.53590 | 0.690086 | ||||||||
\(154\) | 4.39230i | 0.353942i | ||||||||
\(155\) | −0.196152 | −0.0157553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 21.4641i | 1.70759i | ||||||||
\(159\) | 7.60770 | 0.603329 | ||||||||
\(160\) | −5.19615 | −0.410792 | ||||||||
\(161\) | 9.46410i | 0.745876i | ||||||||
\(162\) | 7.73205i | 0.607487i | ||||||||
\(163\) | − 6.39230i | − 0.500684i | −0.968157 | − | 0.250342i | \(-0.919457\pi\) | ||||
0.968157 | − | 0.250342i | \(-0.0805431\pi\) | |||||||
\(164\) | 3.46410i | 0.270501i | ||||||||
\(165\) | −0.928203 | −0.0722605 | ||||||||
\(166\) | 10.3923 | 0.806599 | ||||||||
\(167\) | − 12.9282i | − 1.00041i | −0.865906 | − | 0.500207i | \(-0.833257\pi\) | ||||
0.865906 | − | 0.500207i | \(-0.166743\pi\) | |||||||
\(168\) | −2.53590 | −0.195649 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.00000 | −0.460179 | ||||||||
\(171\) | − 10.3397i | − 0.790700i | ||||||||
\(172\) | 10.1962 | 0.777449 | ||||||||
\(173\) | −15.4641 | −1.17571 | −0.587857 | − | 0.808965i | \(-0.700028\pi\) | ||||
−0.587857 | + | 0.808965i | \(0.700028\pi\) | |||||||
\(174\) | 12.0000i | 0.909718i | ||||||||
\(175\) | 2.00000i | 0.151186i | ||||||||
\(176\) | − 6.33975i | − 0.477876i | ||||||||
\(177\) | − 11.0718i | − 0.832207i | ||||||||
\(178\) | 1.60770 | 0.120502 | ||||||||
\(179\) | 5.07180 | 0.379084 | 0.189542 | − | 0.981873i | \(-0.439300\pi\) | ||||
0.189542 | + | 0.981873i | \(0.439300\pi\) | |||||||
\(180\) | − 2.46410i | − 0.183663i | ||||||||
\(181\) | 20.3923 | 1.51575 | 0.757874 | − | 0.652401i | \(-0.226238\pi\) | ||||
0.757874 | + | 0.652401i | \(0.226238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.07180 | −0.670607 | ||||||||
\(184\) | − 8.19615i | − 0.604228i | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | −0.248711 | −0.0182364 | ||||||||
\(187\) | − 4.39230i | − 0.321197i | ||||||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | − 8.00000i | − 0.581914i | ||||||||
\(190\) | 7.26795i | 0.527272i | ||||||||
\(191\) | −18.9282 | −1.36960 | −0.684798 | − | 0.728733i | \(-0.740110\pi\) | ||||
−0.684798 | + | 0.728733i | \(0.740110\pi\) | |||||||
\(192\) | 0.732051 | 0.0528312 | ||||||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | −3.46410 | −0.248708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 0.928203i | 0.0661317i | 0.999453 | + | 0.0330659i | \(0.0105271\pi\) | ||||
−0.999453 | + | 0.0330659i | \(0.989473\pi\) | |||||||
\(198\) | 5.41154 | 0.384582 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | − 1.73205i | − 0.122474i | ||||||||
\(201\) | 10.5359i | 0.743145i | ||||||||
\(202\) | − 22.3923i | − 1.57552i | ||||||||
\(203\) | 18.9282i | 1.32850i | ||||||||
\(204\) | −2.53590 | −0.177548 | ||||||||
\(205\) | −3.46410 | −0.241943 | ||||||||
\(206\) | − 17.6603i | − 1.23045i | ||||||||
\(207\) | 11.6603 | 0.810444 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.32051 | −0.368027 | ||||||||
\(210\) | 2.53590i | 0.174994i | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 10.3923 | 0.713746 | ||||||||
\(213\) | − 0.928203i | − 0.0635994i | ||||||||
\(214\) | 0.588457i | 0.0402261i | ||||||||
\(215\) | 10.1962i | 0.695372i | ||||||||
\(216\) | 6.92820i | 0.471405i | ||||||||
\(217\) | −0.392305 | −0.0266314 | ||||||||
\(218\) | −3.46410 | −0.234619 | ||||||||
\(219\) | − 2.92820i | − 0.197870i | ||||||||
\(220\) | −1.26795 | −0.0854851 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.07180 | 0.340397 | ||||||||
\(223\) | 2.00000i | 0.133930i | 0.997755 | + | 0.0669650i | \(0.0213316\pi\) | ||||
−0.997755 | + | 0.0669650i | \(0.978668\pi\) | |||||||
\(224\) | −10.3923 | −0.694365 | ||||||||
\(225\) | 2.46410 | 0.164273 | ||||||||
\(226\) | 26.7846i | 1.78169i | ||||||||
\(227\) | 3.46410i | 0.229920i | 0.993370 | + | 0.114960i | \(0.0366741\pi\) | ||||
−0.993370 | + | 0.114960i | \(0.963326\pi\) | |||||||
\(228\) | 3.07180i | 0.203435i | ||||||||
\(229\) | 14.3923i | 0.951070i | 0.879697 | + | 0.475535i | \(0.157746\pi\) | ||||
−0.879697 | + | 0.475535i | \(0.842254\pi\) | |||||||
\(230\) | −8.19615 | −0.540438 | ||||||||
\(231\) | −1.85641 | −0.122143 | ||||||||
\(232\) | − 16.3923i | − 1.07621i | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | − 15.1244i | − 0.984512i | ||||||||
\(237\) | −9.07180 | −0.589277 | ||||||||
\(238\) | −12.0000 | −0.777844 | ||||||||
\(239\) | − 3.80385i | − 0.246050i | −0.992404 | − | 0.123025i | \(-0.960740\pi\) | ||||
0.992404 | − | 0.123025i | \(-0.0392596\pi\) | |||||||
\(240\) | − 3.66025i | − 0.236268i | ||||||||
\(241\) | − 18.3923i | − 1.18475i | −0.805661 | − | 0.592376i | \(-0.798190\pi\) | ||||
0.805661 | − | 0.592376i | \(-0.201810\pi\) | |||||||
\(242\) | 16.2679i | 1.04574i | ||||||||
\(243\) | −15.2679 | −0.979439 | ||||||||
\(244\) | −12.3923 | −0.793336 | ||||||||
\(245\) | − 3.00000i | − 0.191663i | ||||||||
\(246\) | −4.39230 | −0.280043 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.339746 | 0.0215739 | ||||||||
\(249\) | 4.39230i | 0.278351i | ||||||||
\(250\) | −1.73205 | −0.109545 | ||||||||
\(251\) | 14.5359 | 0.917498 | 0.458749 | − | 0.888566i | \(-0.348298\pi\) | ||||
0.458749 | + | 0.888566i | \(0.348298\pi\) | |||||||
\(252\) | − 4.92820i | − 0.310448i | ||||||||
\(253\) | − 6.00000i | − 0.377217i | ||||||||
\(254\) | − 10.0526i | − 0.630754i | ||||||||
\(255\) | − 2.53590i | − 0.158804i | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 7.85641 | 0.490069 | 0.245035 | − | 0.969514i | \(-0.421201\pi\) | ||||
0.245035 | + | 0.969514i | \(0.421201\pi\) | |||||||
\(258\) | 12.9282i | 0.804875i | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.3205 | 1.44350 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.73205 | 0.291791 | 0.145895 | − | 0.989300i | \(-0.453394\pi\) | ||||
0.145895 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(264\) | 1.60770 | 0.0989468 | ||||||||
\(265\) | 10.3923i | 0.638394i | ||||||||
\(266\) | 14.5359i | 0.891253i | ||||||||
\(267\) | 0.679492i | 0.0415842i | ||||||||
\(268\) | 14.3923i | 0.879150i | ||||||||
\(269\) | 7.85641 | 0.479014 | 0.239507 | − | 0.970895i | \(-0.423014\pi\) | ||||
0.239507 | + | 0.970895i | \(0.423014\pi\) | |||||||
\(270\) | 6.92820 | 0.421637 | ||||||||
\(271\) | 20.9808i | 1.27449i | 0.770661 | + | 0.637245i | \(0.219926\pi\) | ||||
−0.770661 | + | 0.637245i | \(0.780074\pi\) | |||||||
\(272\) | 17.3205 | 1.05021 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.3923 | −1.35277 | ||||||||
\(275\) | − 1.26795i | − 0.0764602i | ||||||||
\(276\) | −3.46410 | −0.208514 | ||||||||
\(277\) | 5.60770 | 0.336934 | 0.168467 | − | 0.985707i | \(-0.446118\pi\) | ||||
0.168467 | + | 0.985707i | \(0.446118\pi\) | |||||||
\(278\) | − 14.5359i | − 0.871805i | ||||||||
\(279\) | 0.483340i | 0.0289368i | ||||||||
\(280\) | − 3.46410i | − 0.207020i | ||||||||
\(281\) | − 1.60770i | − 0.0959071i | −0.998850 | − | 0.0479535i | \(-0.984730\pi\) | ||||
0.998850 | − | 0.0479535i | \(-0.0152699\pi\) | |||||||
\(282\) | −7.60770 | −0.453032 | ||||||||
\(283\) | −1.41154 | −0.0839075 | −0.0419538 | − | 0.999120i | \(-0.513358\pi\) | ||||
−0.0419538 | + | 0.999120i | \(0.513358\pi\) | |||||||
\(284\) | − 1.26795i | − 0.0752389i | ||||||||
\(285\) | −3.07180 | −0.181958 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.92820 | −0.408959 | ||||||||
\(288\) | 12.8038i | 0.754474i | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | −16.3923 | −0.962589 | ||||||||
\(291\) | − 1.46410i | − 0.0858272i | ||||||||
\(292\) | − 4.00000i | − 0.234082i | ||||||||
\(293\) | 18.9282i | 1.10580i | 0.833248 | + | 0.552899i | \(0.186478\pi\) | ||||
−0.833248 | + | 0.552899i | \(0.813522\pi\) | |||||||
\(294\) | − 3.80385i | − 0.221845i | ||||||||
\(295\) | 15.1244 | 0.880574 | ||||||||
\(296\) | −6.92820 | −0.402694 | ||||||||
\(297\) | 5.07180i | 0.294295i | ||||||||
\(298\) | −34.3923 | −1.99229 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.732051 | −0.0422650 | ||||||||
\(301\) | 20.3923i | 1.17539i | ||||||||
\(302\) | −21.1244 | −1.21557 | ||||||||
\(303\) | 9.46410 | 0.543698 | ||||||||
\(304\) | − 20.9808i | − 1.20333i | ||||||||
\(305\) | − 12.3923i | − 0.709581i | ||||||||
\(306\) | 14.7846i | 0.845180i | ||||||||
\(307\) | − 22.7846i | − 1.30039i | −0.759769 | − | 0.650193i | \(-0.774688\pi\) | ||||
0.759769 | − | 0.650193i | \(-0.225312\pi\) | |||||||
\(308\) | −2.53590 | −0.144496 | ||||||||
\(309\) | 7.46410 | 0.424618 | ||||||||
\(310\) | − 0.339746i | − 0.0192963i | ||||||||
\(311\) | −4.39230 | −0.249065 | −0.124532 | − | 0.992216i | \(-0.539743\pi\) | ||||
−0.124532 | + | 0.992216i | \(0.539743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.39230 | 0.361314 | 0.180657 | − | 0.983546i | \(-0.442178\pi\) | ||||
0.180657 | + | 0.983546i | \(0.442178\pi\) | |||||||
\(314\) | − 17.3205i | − 0.977453i | ||||||||
\(315\) | 4.92820 | 0.277673 | ||||||||
\(316\) | −12.3923 | −0.697122 | ||||||||
\(317\) | 24.0000i | 1.34797i | 0.738743 | + | 0.673987i | \(0.235420\pi\) | ||||
−0.738743 | + | 0.673987i | \(0.764580\pi\) | |||||||
\(318\) | 13.1769i | 0.738925i | ||||||||
\(319\) | − 12.0000i | − 0.671871i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −0.248711 | −0.0138817 | ||||||||
\(322\) | −16.3923 | −0.913507 | ||||||||
\(323\) | − 14.5359i | − 0.808799i | ||||||||
\(324\) | −4.46410 | −0.248006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.0718 | 0.613210 | ||||||||
\(327\) | − 1.46410i | − 0.0809650i | ||||||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | − 1.60770i | − 0.0885007i | ||||||||
\(331\) | − 28.5885i | − 1.57136i | −0.618631 | − | 0.785682i | \(-0.712312\pi\) | ||||
0.618631 | − | 0.785682i | \(-0.287688\pi\) | |||||||
\(332\) | 6.00000i | 0.329293i | ||||||||
\(333\) | − 9.85641i | − 0.540128i | ||||||||
\(334\) | 22.3923 | 1.22525 | ||||||||
\(335\) | −14.3923 | −0.786336 | ||||||||
\(336\) | − 7.32051i | − 0.399366i | ||||||||
\(337\) | 5.60770 | 0.305471 | 0.152735 | − | 0.988267i | \(-0.451192\pi\) | ||||
0.152735 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.3205 | −0.614846 | ||||||||
\(340\) | − 3.46410i | − 0.187867i | ||||||||
\(341\) | 0.248711 | 0.0134685 | ||||||||
\(342\) | 17.9090 | 0.968406 | ||||||||
\(343\) | − 20.0000i | − 1.07990i | ||||||||
\(344\) | − 17.6603i | − 0.952177i | ||||||||
\(345\) | − 3.46410i | − 0.186501i | ||||||||
\(346\) | − 26.7846i | − 1.43995i | ||||||||
\(347\) | 11.6603 | 0.625955 | 0.312978 | − | 0.949761i | \(-0.398674\pi\) | ||||
0.312978 | + | 0.949761i | \(0.398674\pi\) | |||||||
\(348\) | −6.92820 | −0.371391 | ||||||||
\(349\) | − 6.39230i | − 0.342172i | −0.985256 | − | 0.171086i | \(-0.945272\pi\) | ||||
0.985256 | − | 0.171086i | \(-0.0547276\pi\) | |||||||
\(350\) | −3.46410 | −0.185164 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.58846 | 0.351166 | ||||||||
\(353\) | 27.7128i | 1.47500i | 0.675345 | + | 0.737502i | \(0.263995\pi\) | ||||
−0.675345 | + | 0.737502i | \(0.736005\pi\) | |||||||
\(354\) | 19.1769 | 1.01924 | ||||||||
\(355\) | 1.26795 | 0.0672958 | ||||||||
\(356\) | 0.928203i | 0.0491947i | ||||||||
\(357\) | − 5.07180i | − 0.268428i | ||||||||
\(358\) | 8.78461i | 0.464281i | ||||||||
\(359\) | − 8.19615i | − 0.432576i | −0.976330 | − | 0.216288i | \(-0.930605\pi\) | ||||
0.976330 | − | 0.216288i | \(-0.0693951\pi\) | |||||||
\(360\) | −4.26795 | −0.224941 | ||||||||
\(361\) | 1.39230 | 0.0732792 | ||||||||
\(362\) | 35.3205i | 1.85640i | ||||||||
\(363\) | −6.87564 | −0.360878 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | 0.209370 | ||||||||
\(366\) | − 15.7128i | − 0.821322i | ||||||||
\(367\) | 22.1962 | 1.15863 | 0.579315 | − | 0.815104i | \(-0.303320\pi\) | ||||
0.579315 | + | 0.815104i | \(0.303320\pi\) | |||||||
\(368\) | 23.6603 | 1.23338 | ||||||||
\(369\) | 8.53590i | 0.444361i | ||||||||
\(370\) | 6.92820i | 0.360180i | ||||||||
\(371\) | 20.7846i | 1.07908i | ||||||||
\(372\) | − 0.143594i | − 0.00744498i | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 7.60770 | 0.393385 | ||||||||
\(375\) | − 0.732051i | − 0.0378029i | ||||||||
\(376\) | 10.3923 | 0.535942 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 13.8564 | 0.712697 | ||||||||
\(379\) | − 32.9808i | − 1.69411i | −0.531507 | − | 0.847054i | \(-0.678374\pi\) | ||||
0.531507 | − | 0.847054i | \(-0.321626\pi\) | |||||||
\(380\) | −4.19615 | −0.215258 | ||||||||
\(381\) | 4.24871 | 0.217668 | ||||||||
\(382\) | − 32.7846i | − 1.67741i | ||||||||
\(383\) | − 0.928203i | − 0.0474290i | −0.999719 | − | 0.0237145i | \(-0.992451\pi\) | ||||
0.999719 | − | 0.0237145i | \(-0.00754926\pi\) | |||||||
\(384\) | 8.87564i | 0.452933i | ||||||||
\(385\) | − 2.53590i | − 0.129241i | ||||||||
\(386\) | −17.3205 | −0.881591 | ||||||||
\(387\) | 25.1244 | 1.27714 | ||||||||
\(388\) | − 2.00000i | − 0.101535i | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3923 | 0.828994 | ||||||||
\(392\) | 5.19615i | 0.262445i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.60770 | −0.0809945 | ||||||||
\(395\) | − 12.3923i | − 0.623525i | ||||||||
\(396\) | 3.12436i | 0.157005i | ||||||||
\(397\) | 12.7846i | 0.641641i | 0.947140 | + | 0.320821i | \(0.103959\pi\) | ||||
−0.947140 | + | 0.320821i | \(0.896041\pi\) | |||||||
\(398\) | − 34.6410i | − 1.73640i | ||||||||
\(399\) | −6.14359 | −0.307564 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | 23.0718i | 1.15215i | 0.817397 | + | 0.576075i | \(0.195416\pi\) | ||||
−0.817397 | + | 0.576075i | \(0.804584\pi\) | |||||||
\(402\) | −18.2487 | −0.910163 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.9282 | 0.643202 | ||||||||
\(405\) | − 4.46410i | − 0.221823i | ||||||||
\(406\) | −32.7846 | −1.62707 | ||||||||
\(407\) | −5.07180 | −0.251400 | ||||||||
\(408\) | 4.39230i | 0.217451i | ||||||||
\(409\) | − 38.3923i | − 1.89838i | −0.314708 | − | 0.949189i | \(-0.601906\pi\) | ||||
0.314708 | − | 0.949189i | \(-0.398094\pi\) | |||||||
\(410\) | − 6.00000i | − 0.296319i | ||||||||
\(411\) | − 9.46410i | − 0.466830i | ||||||||
\(412\) | 10.1962 | 0.502328 | ||||||||
\(413\) | 30.2487 | 1.48844 | ||||||||
\(414\) | 20.1962i | 0.992587i | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.14359 | 0.300853 | ||||||||
\(418\) | − 9.21539i | − 0.450739i | ||||||||
\(419\) | −9.46410 | −0.462352 | −0.231176 | − | 0.972912i | \(-0.574257\pi\) | ||||
−0.231176 | + | 0.972912i | \(0.574257\pi\) | |||||||
\(420\) | −1.46410 | −0.0714408 | ||||||||
\(421\) | 10.7846i | 0.525610i | 0.964849 | + | 0.262805i | \(0.0846475\pi\) | ||||
−0.964849 | + | 0.262805i | \(0.915352\pi\) | |||||||
\(422\) | 13.8564i | 0.674519i | ||||||||
\(423\) | 14.7846i | 0.718852i | ||||||||
\(424\) | − 18.0000i | − 0.874157i | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 1.60770 | 0.0778931 | ||||||||
\(427\) | − 24.7846i | − 1.19941i | ||||||||
\(428\) | −0.339746 | −0.0164222 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.6603 | −0.851653 | ||||||||
\(431\) | 19.5167i | 0.940084i | 0.882644 | + | 0.470042i | \(0.155761\pi\) | ||||
−0.882644 | + | 0.470042i | \(0.844239\pi\) | |||||||
\(432\) | −20.0000 | −0.962250 | ||||||||
\(433\) | 6.78461 | 0.326048 | 0.163024 | − | 0.986622i | \(-0.447875\pi\) | ||||
0.163024 | + | 0.986622i | \(0.447875\pi\) | |||||||
\(434\) | − 0.679492i | − 0.0326167i | ||||||||
\(435\) | − 6.92820i | − 0.332182i | ||||||||
\(436\) | − 2.00000i | − 0.0957826i | ||||||||
\(437\) | − 19.8564i | − 0.949861i | ||||||||
\(438\) | 5.07180 | 0.242340 | ||||||||
\(439\) | −32.0000 | −1.52728 | −0.763638 | − | 0.645644i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(440\) | 2.19615i | 0.104697i | ||||||||
\(441\) | −7.39230 | −0.352015 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.9808 | 1.66199 | 0.830993 | − | 0.556283i | \(-0.187773\pi\) | ||||
0.830993 | + | 0.556283i | \(0.187773\pi\) | |||||||
\(444\) | 2.92820i | 0.138966i | ||||||||
\(445\) | −0.928203 | −0.0440011 | ||||||||
\(446\) | −3.46410 | −0.164030 | ||||||||
\(447\) | − 14.5359i | − 0.687524i | ||||||||
\(448\) | 2.00000i | 0.0944911i | ||||||||
\(449\) | − 27.4641i | − 1.29611i | −0.761593 | − | 0.648056i | \(-0.775582\pi\) | ||||
0.761593 | − | 0.648056i | \(-0.224418\pi\) | |||||||
\(450\) | 4.26795i | 0.201193i | ||||||||
\(451\) | 4.39230 | 0.206826 | ||||||||
\(452\) | −15.4641 | −0.727370 | ||||||||
\(453\) | − 8.92820i | − 0.419484i | ||||||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.32051 | 0.249156 | ||||||||
\(457\) | − 30.7846i | − 1.44004i | −0.693952 | − | 0.720022i | \(-0.744132\pi\) | ||||
0.693952 | − | 0.720022i | \(-0.255868\pi\) | |||||||
\(458\) | −24.9282 | −1.16482 | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | − 4.73205i | − 0.220633i | ||||||||
\(461\) | 3.46410i | 0.161339i | 0.996741 | + | 0.0806696i | \(0.0257059\pi\) | ||||
−0.996741 | + | 0.0806696i | \(0.974294\pi\) | |||||||
\(462\) | − 3.21539i | − 0.149593i | ||||||||
\(463\) | − 18.3923i | − 0.854763i | −0.904071 | − | 0.427381i | \(-0.859436\pi\) | ||||
0.904071 | − | 0.427381i | \(-0.140564\pi\) | |||||||
\(464\) | 47.3205 | 2.19680 | ||||||||
\(465\) | 0.143594 | 0.00665899 | ||||||||
\(466\) | 10.3923i | 0.481414i | ||||||||
\(467\) | −38.1962 | −1.76751 | −0.883754 | − | 0.467953i | \(-0.844992\pi\) | ||||
−0.883754 | + | 0.467953i | \(0.844992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.7846 | −1.32915 | ||||||||
\(470\) | − 10.3923i | − 0.479361i | ||||||||
\(471\) | 7.32051 | 0.337311 | ||||||||
\(472\) | −26.1962 | −1.20578 | ||||||||
\(473\) | − 12.9282i | − 0.594439i | ||||||||
\(474\) | − 15.7128i | − 0.721713i | ||||||||
\(475\) | − 4.19615i | − 0.192533i | ||||||||
\(476\) | − 6.92820i | − 0.317554i | ||||||||
\(477\) | 25.6077 | 1.17250 | ||||||||
\(478\) | 6.58846 | 0.301349 | ||||||||
\(479\) | − 18.3397i | − 0.837964i | −0.907994 | − | 0.418982i | \(-0.862387\pi\) | ||||
0.907994 | − | 0.418982i | \(-0.137613\pi\) | |||||||
\(480\) | 3.80385 | 0.173621 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 31.8564 | 1.45102 | ||||||||
\(483\) | − 6.92820i | − 0.315244i | ||||||||
\(484\) | −9.39230 | −0.426923 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | − 26.4449i | − 1.19956i | ||||||||
\(487\) | − 5.60770i | − 0.254109i | −0.991896 | − | 0.127054i | \(-0.959448\pi\) | ||||
0.991896 | − | 0.127054i | \(-0.0405523\pi\) | |||||||
\(488\) | 21.4641i | 0.971634i | ||||||||
\(489\) | 4.67949i | 0.211614i | ||||||||
\(490\) | 5.19615 | 0.234738 | ||||||||
\(491\) | 9.46410 | 0.427109 | 0.213554 | − | 0.976931i | \(-0.431496\pi\) | ||||
0.213554 | + | 0.976931i | \(0.431496\pi\) | |||||||
\(492\) | − 2.53590i | − 0.114327i | ||||||||
\(493\) | 32.7846 | 1.47654 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.12436 | −0.140429 | ||||||||
\(496\) | 0.980762i | 0.0440375i | ||||||||
\(497\) | 2.53590 | 0.113751 | ||||||||
\(498\) | −7.60770 | −0.340909 | ||||||||
\(499\) | 12.9808i | 0.581099i | 0.956860 | + | 0.290549i | \(0.0938380\pi\) | ||||
−0.956860 | + | 0.290549i | \(0.906162\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | 9.46410i | 0.422825i | ||||||||
\(502\) | 25.1769i | 1.12370i | ||||||||
\(503\) | −25.5167 | −1.13773 | −0.568866 | − | 0.822430i | \(-0.692618\pi\) | ||||
−0.568866 | + | 0.822430i | \(0.692618\pi\) | |||||||
\(504\) | −8.53590 | −0.380219 | ||||||||
\(505\) | 12.9282i | 0.575297i | ||||||||
\(506\) | 10.3923 | 0.461994 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.80385 | 0.257504 | ||||||||
\(509\) | 32.5359i | 1.44213i | 0.692868 | + | 0.721064i | \(0.256347\pi\) | ||||
−0.692868 | + | 0.721064i | \(0.743653\pi\) | |||||||
\(510\) | 4.39230 | 0.194495 | ||||||||
\(511\) | 8.00000 | 0.353899 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 16.7846i | 0.741059i | ||||||||
\(514\) | 13.6077i | 0.600210i | ||||||||
\(515\) | 10.1962i | 0.449296i | ||||||||
\(516\) | −7.46410 | −0.328589 | ||||||||
\(517\) | 7.60770 | 0.334586 | ||||||||
\(518\) | 13.8564i | 0.608816i | ||||||||
\(519\) | 11.3205 | 0.496915 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.60770 | −0.333299 | −0.166650 | − | 0.986016i | \(-0.553295\pi\) | ||||
−0.166650 | + | 0.986016i | \(0.553295\pi\) | |||||||
\(522\) | 40.3923i | 1.76792i | ||||||||
\(523\) | −13.8038 | −0.603600 | −0.301800 | − | 0.953371i | \(-0.597588\pi\) | ||||
−0.301800 | + | 0.953371i | \(0.597588\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.46410i | − 0.0638986i | ||||||||
\(526\) | 8.19615i | 0.357369i | ||||||||
\(527\) | 0.679492i | 0.0295991i | ||||||||
\(528\) | 4.64102i | 0.201974i | ||||||||
\(529\) | −0.607695 | −0.0264215 | ||||||||
\(530\) | −18.0000 | −0.781870 | ||||||||
\(531\) | − 37.2679i | − 1.61729i | ||||||||
\(532\) | −8.39230 | −0.363853 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.17691 | −0.0509301 | ||||||||
\(535\) | − 0.339746i | − 0.0146885i | ||||||||
\(536\) | 24.9282 | 1.07673 | ||||||||
\(537\) | −3.71281 | −0.160220 | ||||||||
\(538\) | 13.6077i | 0.586669i | ||||||||
\(539\) | 3.80385i | 0.163843i | ||||||||
\(540\) | 4.00000i | 0.172133i | ||||||||
\(541\) | 5.60770i | 0.241094i | 0.992708 | + | 0.120547i | \(0.0384648\pi\) | ||||
−0.992708 | + | 0.120547i | \(0.961535\pi\) | |||||||
\(542\) | −36.3397 | −1.56093 | ||||||||
\(543\) | −14.9282 | −0.640631 | ||||||||
\(544\) | 18.0000i | 0.771744i | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.80385 | −0.0771270 | −0.0385635 | − | 0.999256i | \(-0.512278\pi\) | ||||
−0.0385635 | + | 0.999256i | \(0.512278\pi\) | |||||||
\(548\) | − 12.9282i | − 0.552265i | ||||||||
\(549\) | −30.5359 | −1.30324 | ||||||||
\(550\) | 2.19615 | 0.0936443 | ||||||||
\(551\) | − 39.7128i | − 1.69182i | ||||||||
\(552\) | 6.00000i | 0.255377i | ||||||||
\(553\) | − 24.7846i | − 1.05395i | ||||||||
\(554\) | 9.71281i | 0.412658i | ||||||||
\(555\) | −2.92820 | −0.124295 | ||||||||
\(556\) | 8.39230 | 0.355913 | ||||||||
\(557\) | 25.8564i | 1.09557i | 0.836619 | + | 0.547786i | \(0.184529\pi\) | ||||
−0.836619 | + | 0.547786i | \(0.815471\pi\) | |||||||
\(558\) | −0.837169 | −0.0354402 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.0000 | 0.422577 | ||||||||
\(561\) | 3.21539i | 0.135754i | ||||||||
\(562\) | 2.78461 | 0.117462 | ||||||||
\(563\) | −16.0526 | −0.676535 | −0.338267 | − | 0.941050i | \(-0.609841\pi\) | ||||
−0.338267 | + | 0.941050i | \(0.609841\pi\) | |||||||
\(564\) | − 4.39230i | − 0.184949i | ||||||||
\(565\) | − 15.4641i | − 0.650580i | ||||||||
\(566\) | − 2.44486i | − 0.102765i | ||||||||
\(567\) | − 8.92820i | − 0.374949i | ||||||||
\(568\) | −2.19615 | −0.0921485 | ||||||||
\(569\) | 9.46410 | 0.396756 | 0.198378 | − | 0.980126i | \(-0.436433\pi\) | ||||
0.198378 | + | 0.980126i | \(0.436433\pi\) | |||||||
\(570\) | − 5.32051i | − 0.222852i | ||||||||
\(571\) | −15.6077 | −0.653162 | −0.326581 | − | 0.945169i | \(-0.605897\pi\) | ||||
−0.326581 | + | 0.945169i | \(0.605897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8564 | 0.578860 | ||||||||
\(574\) | − 12.0000i | − 0.500870i | ||||||||
\(575\) | 4.73205 | 0.197340 | ||||||||
\(576\) | 2.46410 | 0.102671 | ||||||||
\(577\) | − 4.00000i | − 0.166522i | −0.996528 | − | 0.0832611i | \(-0.973466\pi\) | ||||
0.996528 | − | 0.0832611i | \(-0.0265335\pi\) | |||||||
\(578\) | − 8.66025i | − 0.360219i | ||||||||
\(579\) | − 7.32051i | − 0.304230i | ||||||||
\(580\) | − 9.46410i | − 0.392975i | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 2.53590 | 0.105116 | ||||||||
\(583\) | − 13.1769i | − 0.545732i | ||||||||
\(584\) | −6.92820 | −0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.7846 | −1.35432 | ||||||||
\(587\) | − 15.4641i | − 0.638272i | −0.947709 | − | 0.319136i | \(-0.896607\pi\) | ||||
0.947709 | − | 0.319136i | \(-0.103393\pi\) | |||||||
\(588\) | 2.19615 | 0.0905678 | ||||||||
\(589\) | 0.823085 | 0.0339146 | ||||||||
\(590\) | 26.1962i | 1.07848i | ||||||||
\(591\) | − 0.679492i | − 0.0279506i | ||||||||
\(592\) | − 20.0000i | − 0.821995i | ||||||||
\(593\) | 14.7846i | 0.607131i | 0.952811 | + | 0.303566i | \(0.0981771\pi\) | ||||
−0.952811 | + | 0.303566i | \(0.901823\pi\) | |||||||
\(594\) | −8.78461 | −0.360437 | ||||||||
\(595\) | 6.92820 | 0.284029 | ||||||||
\(596\) | − 19.8564i | − 0.813350i | ||||||||
\(597\) | 14.6410 | 0.599217 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.3923 | −1.16008 | −0.580039 | − | 0.814589i | \(-0.696963\pi\) | ||||
−0.580039 | + | 0.814589i | \(0.696963\pi\) | |||||||
\(600\) | 1.26795i | 0.0517638i | ||||||||
\(601\) | −39.5692 | −1.61406 | −0.807031 | − | 0.590509i | \(-0.798927\pi\) | ||||
−0.807031 | + | 0.590509i | \(0.798927\pi\) | |||||||
\(602\) | −35.3205 | −1.43956 | ||||||||
\(603\) | 35.4641i | 1.44421i | ||||||||
\(604\) | − 12.1962i | − 0.496254i | ||||||||
\(605\) | − 9.39230i | − 0.381851i | ||||||||
\(606\) | 16.3923i | 0.665892i | ||||||||
\(607\) | −26.9808 | −1.09512 | −0.547558 | − | 0.836768i | \(-0.684442\pi\) | ||||
−0.547558 | + | 0.836768i | \(0.684442\pi\) | |||||||
\(608\) | 21.8038 | 0.884263 | ||||||||
\(609\) | − 13.8564i | − 0.561490i | ||||||||
\(610\) | 21.4641 | 0.869056 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8.53590 | −0.345043 | ||||||||
\(613\) | 26.0000i | 1.05013i | 0.851062 | + | 0.525065i | \(0.175959\pi\) | ||||
−0.851062 | + | 0.525065i | \(0.824041\pi\) | |||||||
\(614\) | 39.4641 | 1.59264 | ||||||||
\(615\) | 2.53590 | 0.102257 | ||||||||
\(616\) | 4.39230i | 0.176971i | ||||||||
\(617\) | − 21.7128i | − 0.874125i | −0.899431 | − | 0.437062i | \(-0.856019\pi\) | ||||
0.899431 | − | 0.437062i | \(-0.143981\pi\) | |||||||
\(618\) | 12.9282i | 0.520049i | ||||||||
\(619\) | 44.9808i | 1.80793i | 0.427607 | + | 0.903965i | \(0.359357\pi\) | ||||
−0.427607 | + | 0.903965i | \(0.640643\pi\) | |||||||
\(620\) | 0.196152 | 0.00787767 | ||||||||
\(621\) | −18.9282 | −0.759563 | ||||||||
\(622\) | − 7.60770i | − 0.305041i | ||||||||
\(623\) | −1.85641 | −0.0743754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.0718i | 0.442518i | ||||||||
\(627\) | 3.89488 | 0.155547 | ||||||||
\(628\) | 10.0000 | 0.399043 | ||||||||
\(629\) | − 13.8564i | − 0.552491i | ||||||||
\(630\) | 8.53590i | 0.340078i | ||||||||
\(631\) | − 16.1962i | − 0.644759i | −0.946611 | − | 0.322379i | \(-0.895517\pi\) | ||||
0.946611 | − | 0.322379i | \(-0.104483\pi\) | |||||||
\(632\) | 21.4641i | 0.853796i | ||||||||
\(633\) | −5.85641 | −0.232771 | ||||||||
\(634\) | −41.5692 | −1.65092 | ||||||||
\(635\) | 5.80385i | 0.230319i | ||||||||
\(636\) | −7.60770 | −0.301665 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.7846 | 0.822871 | ||||||||
\(639\) | − 3.12436i | − 0.123598i | ||||||||
\(640\) | −12.1244 | −0.479257 | ||||||||
\(641\) | 0.928203 | 0.0366618 | 0.0183309 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183309 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(642\) | − 0.430781i | − 0.0170016i | ||||||||
\(643\) | 34.7846i | 1.37177i | 0.727709 | + | 0.685886i | \(0.240585\pi\) | ||||
−0.727709 | + | 0.685886i | \(0.759415\pi\) | |||||||
\(644\) | − 9.46410i | − 0.372938i | ||||||||
\(645\) | − 7.46410i | − 0.293899i | ||||||||
\(646\) | 25.1769 | 0.990572 | ||||||||
\(647\) | 16.0526 | 0.631091 | 0.315546 | − | 0.948910i | \(-0.397812\pi\) | ||||
0.315546 | + | 0.948910i | \(0.397812\pi\) | |||||||
\(648\) | 7.73205i | 0.303744i | ||||||||
\(649\) | −19.1769 | −0.752760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.287187 | 0.0112557 | ||||||||
\(652\) | 6.39230i | 0.250342i | ||||||||
\(653\) | −19.8564 | −0.777041 | −0.388521 | − | 0.921440i | \(-0.627014\pi\) | ||||
−0.388521 | + | 0.921440i | \(0.627014\pi\) | |||||||
\(654\) | 2.53590 | 0.0991615 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17.3205i | 0.676252i | ||||||||
\(657\) | − 9.85641i | − 0.384535i | ||||||||
\(658\) | − 20.7846i | − 0.810268i | ||||||||
\(659\) | −14.5359 | −0.566238 | −0.283119 | − | 0.959085i | \(-0.591369\pi\) | ||||
−0.283119 | + | 0.959085i | \(0.591369\pi\) | |||||||
\(660\) | 0.928203 | 0.0361303 | ||||||||
\(661\) | 30.7846i | 1.19738i | 0.800980 | + | 0.598691i | \(0.204312\pi\) | ||||
−0.800980 | + | 0.598691i | \(0.795688\pi\) | |||||||
\(662\) | 49.5167 | 1.92452 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.3923 | 0.403300 | ||||||||
\(665\) | − 8.39230i | − 0.325440i | ||||||||
\(666\) | 17.0718 | 0.661519 | ||||||||
\(667\) | 44.7846 | 1.73407 | ||||||||
\(668\) | 12.9282i | 0.500207i | ||||||||
\(669\) | − 1.46410i | − 0.0566054i | ||||||||
\(670\) | − 24.9282i | − 0.963061i | ||||||||
\(671\) | 15.7128i | 0.606586i | ||||||||
\(672\) | 7.60770 | 0.293473 | ||||||||
\(673\) | −6.39230 | −0.246405 | −0.123203 | − | 0.992382i | \(-0.539317\pi\) | ||||
−0.123203 | + | 0.992382i | \(0.539317\pi\) | |||||||
\(674\) | 9.71281i | 0.374124i | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3923 | −0.399409 | −0.199704 | − | 0.979856i | \(-0.563998\pi\) | ||||
−0.199704 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(678\) | − 19.6077i | − 0.753029i | ||||||||
\(679\) | 4.00000 | 0.153506 | ||||||||
\(680\) | −6.00000 | −0.230089 | ||||||||
\(681\) | − 2.53590i | − 0.0971758i | ||||||||
\(682\) | 0.430781i | 0.0164954i | ||||||||
\(683\) | − 39.4641i | − 1.51005i | −0.655695 | − | 0.755026i | \(-0.727624\pi\) | ||||
0.655695 | − | 0.755026i | \(-0.272376\pi\) | |||||||
\(684\) | 10.3397i | 0.395350i | ||||||||
\(685\) | 12.9282 | 0.493961 | ||||||||
\(686\) | 34.6410 | 1.32260 | ||||||||
\(687\) | − 10.5359i | − 0.401970i | ||||||||
\(688\) | 50.9808 | 1.94362 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 6.00000 | 0.228416 | ||||||||
\(691\) | 45.7654i | 1.74100i | 0.492171 | + | 0.870498i | \(0.336203\pi\) | ||||
−0.492171 | + | 0.870498i | \(0.663797\pi\) | |||||||
\(692\) | 15.4641 | 0.587857 | ||||||||
\(693\) | −6.24871 | −0.237369 | ||||||||
\(694\) | 20.1962i | 0.766635i | ||||||||
\(695\) | 8.39230i | 0.318338i | ||||||||
\(696\) | 12.0000i | 0.454859i | ||||||||
\(697\) | 12.0000i | 0.454532i | ||||||||
\(698\) | 11.0718 | 0.419074 | ||||||||
\(699\) | −4.39230 | −0.166132 | ||||||||
\(700\) | − 2.00000i | − 0.0755929i | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.7846 | −0.633044 | ||||||||
\(704\) | − 1.26795i | − 0.0477876i | ||||||||
\(705\) | 4.39230 | 0.165424 | ||||||||
\(706\) | −48.0000 | −1.80650 | ||||||||
\(707\) | 25.8564i | 0.972430i | ||||||||
\(708\) | 11.0718i | 0.416104i | ||||||||
\(709\) | − 9.60770i | − 0.360825i | −0.983591 | − | 0.180412i | \(-0.942257\pi\) | ||||
0.983591 | − | 0.180412i | \(-0.0577432\pi\) | |||||||
\(710\) | 2.19615i | 0.0824201i | ||||||||
\(711\) | −30.5359 | −1.14519 | ||||||||
\(712\) | 1.60770 | 0.0602509 | ||||||||
\(713\) | 0.928203i | 0.0347615i | ||||||||
\(714\) | 8.78461 | 0.328756 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.07180 | −0.189542 | ||||||||
\(717\) | 2.78461i | 0.103993i | ||||||||
\(718\) | 14.1962 | 0.529796 | ||||||||
\(719\) | −1.85641 | −0.0692323 | −0.0346161 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346161 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(720\) | − 12.3205i | − 0.459158i | ||||||||
\(721\) | 20.3923i | 0.759449i | ||||||||
\(722\) | 2.41154i | 0.0897483i | ||||||||
\(723\) | 13.4641i | 0.500735i | ||||||||
\(724\) | −20.3923 | −0.757874 | ||||||||
\(725\) | 9.46410 | 0.351488 | ||||||||
\(726\) | − 11.9090i | − 0.441983i | ||||||||
\(727\) | −13.4115 | −0.497407 | −0.248703 | − | 0.968580i | \(-0.580004\pi\) | ||||
−0.248703 | + | 0.968580i | \(0.580004\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 6.92820i | 0.256424i | ||||||||
\(731\) | 35.3205 | 1.30638 | ||||||||
\(732\) | 9.07180 | 0.335303 | ||||||||
\(733\) | 38.0000i | 1.40356i | 0.712393 | + | 0.701781i | \(0.247612\pi\) | ||||
−0.712393 | + | 0.701781i | \(0.752388\pi\) | |||||||
\(734\) | 38.4449i | 1.41903i | ||||||||
\(735\) | 2.19615i | 0.0810063i | ||||||||
\(736\) | 24.5885i | 0.906343i | ||||||||
\(737\) | 18.2487 | 0.672200 | ||||||||
\(738\) | −14.7846 | −0.544229 | ||||||||
\(739\) | 7.80385i | 0.287069i | 0.989645 | + | 0.143535i | \(0.0458468\pi\) | ||||
−0.989645 | + | 0.143535i | \(0.954153\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36.0000 | −1.32160 | ||||||||
\(743\) | − 43.8564i | − 1.60894i | −0.593996 | − | 0.804468i | \(-0.702451\pi\) | ||||
0.593996 | − | 0.804468i | \(-0.297549\pi\) | |||||||
\(744\) | −0.248711 | −0.00911820 | ||||||||
\(745\) | 19.8564 | 0.727482 | ||||||||
\(746\) | − 17.3205i | − 0.634149i | ||||||||
\(747\) | 14.7846i | 0.540941i | ||||||||
\(748\) | 4.39230i | 0.160599i | ||||||||
\(749\) | − 0.679492i | − 0.0248281i | ||||||||
\(750\) | 1.26795 | 0.0462990 | ||||||||
\(751\) | −15.6077 | −0.569533 | −0.284766 | − | 0.958597i | \(-0.591916\pi\) | ||||
−0.284766 | + | 0.958597i | \(0.591916\pi\) | |||||||
\(752\) | 30.0000i | 1.09399i | ||||||||
\(753\) | −10.6410 | −0.387780 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.1962 | 0.443863 | ||||||||
\(756\) | 8.00000i | 0.290957i | ||||||||
\(757\) | 18.3923 | 0.668480 | 0.334240 | − | 0.942488i | \(-0.391520\pi\) | ||||
0.334240 | + | 0.942488i | \(0.391520\pi\) | |||||||
\(758\) | 57.1244 | 2.07485 | ||||||||
\(759\) | 4.39230i | 0.159431i | ||||||||
\(760\) | 7.26795i | 0.263636i | ||||||||
\(761\) | − 7.85641i | − 0.284795i | −0.989810 | − | 0.142397i | \(-0.954519\pi\) | ||||
0.989810 | − | 0.142397i | \(-0.0454810\pi\) | |||||||
\(762\) | 7.35898i | 0.266588i | ||||||||
\(763\) | 4.00000 | 0.144810 | ||||||||
\(764\) | 18.9282 | 0.684798 | ||||||||
\(765\) | − 8.53590i | − 0.308616i | ||||||||
\(766\) | 1.60770 | 0.0580884 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13.9090 | −0.501897 | ||||||||
\(769\) | − 6.78461i | − 0.244659i | −0.992490 | − | 0.122330i | \(-0.960963\pi\) | ||||
0.992490 | − | 0.122330i | \(-0.0390365\pi\) | |||||||
\(770\) | 4.39230 | 0.158288 | ||||||||
\(771\) | −5.75129 | −0.207128 | ||||||||
\(772\) | − 10.0000i | − 0.359908i | ||||||||
\(773\) | − 6.92820i | − 0.249190i | −0.992208 | − | 0.124595i | \(-0.960237\pi\) | ||||
0.992208 | − | 0.124595i | \(-0.0397632\pi\) | |||||||
\(774\) | 43.5167i | 1.56417i | ||||||||
\(775\) | 0.196152i | 0.00704600i | ||||||||
\(776\) | −3.46410 | −0.124354 | ||||||||
\(777\) | −5.85641 | −0.210097 | ||||||||
\(778\) | − 10.3923i | − 0.372582i | ||||||||
\(779\) | 14.5359 | 0.520803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.60770 | −0.0575279 | ||||||||
\(782\) | 28.3923i | 1.01531i | ||||||||
\(783\) | −37.8564 | −1.35288 | ||||||||
\(784\) | −15.0000 | −0.535714 | ||||||||
\(785\) | 10.0000i | 0.356915i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.5692i | 1.83824i | 0.393973 | + | 0.919122i | \(0.371100\pi\) | ||||
−0.393973 | + | 0.919122i | \(0.628900\pi\) | |||||||
\(788\) | − 0.928203i | − 0.0330659i | ||||||||
\(789\) | −3.46410 | −0.123325 | ||||||||
\(790\) | 21.4641 | 0.763658 | ||||||||
\(791\) | − 30.9282i | − 1.09968i | ||||||||
\(792\) | 5.41154 | 0.192291 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −22.1436 | −0.785847 | ||||||||
\(795\) | − 7.60770i | − 0.269817i | ||||||||
\(796\) | 20.0000 | 0.708881 | ||||||||
\(797\) | −28.6410 | −1.01452 | −0.507258 | − | 0.861794i | \(-0.669341\pi\) | ||||
−0.507258 | + | 0.861794i | \(0.669341\pi\) | |||||||
\(798\) | − 10.6410i | − 0.376688i | ||||||||
\(799\) | 20.7846i | 0.735307i | ||||||||
\(800\) | 5.19615i | 0.183712i | ||||||||
\(801\) | 2.28719i | 0.0808138i | ||||||||
\(802\) | −39.9615 | −1.41109 | ||||||||
\(803\) | −5.07180 | −0.178980 | ||||||||
\(804\) | − 10.5359i | − 0.371572i | ||||||||
\(805\) | 9.46410 | 0.333566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.75129 | −0.202455 | ||||||||
\(808\) | − 22.3923i | − 0.787759i | ||||||||
\(809\) | −9.46410 | −0.332740 | −0.166370 | − | 0.986063i | \(-0.553205\pi\) | ||||
−0.166370 | + | 0.986063i | \(0.553205\pi\) | |||||||
\(810\) | 7.73205 | 0.271677 | ||||||||
\(811\) | 28.1962i | 0.990101i | 0.868864 | + | 0.495050i | \(0.164850\pi\) | ||||
−0.868864 | + | 0.495050i | \(0.835150\pi\) | |||||||
\(812\) | − 18.9282i | − 0.664250i | ||||||||
\(813\) | − 15.3590i | − 0.538663i | ||||||||
\(814\) | − 8.78461i | − 0.307900i | ||||||||
\(815\) | −6.39230 | −0.223913 | ||||||||
\(816\) | −12.6795 | −0.443871 | ||||||||
\(817\) | − 42.7846i | − 1.49684i | ||||||||
\(818\) | 66.4974 | 2.32503 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.46410 | 0.120972 | ||||||||
\(821\) | − 40.6410i | − 1.41838i | −0.705017 | − | 0.709191i | \(-0.749061\pi\) | ||||
0.705017 | − | 0.709191i | \(-0.250939\pi\) | |||||||
\(822\) | 16.3923 | 0.571747 | ||||||||
\(823\) | 46.5885 | 1.62397 | 0.811986 | − | 0.583677i | \(-0.198387\pi\) | ||||
0.811986 | + | 0.583677i | \(0.198387\pi\) | |||||||
\(824\) | − 17.6603i | − 0.615224i | ||||||||
\(825\) | 0.928203i | 0.0323159i | ||||||||
\(826\) | 52.3923i | 1.82296i | ||||||||
\(827\) | − 18.0000i | − 0.625921i | −0.949766 | − | 0.312961i | \(-0.898679\pi\) | ||||
0.949766 | − | 0.312961i | \(-0.101321\pi\) | |||||||
\(828\) | −11.6603 | −0.405222 | ||||||||
\(829\) | 20.3923 | 0.708254 | 0.354127 | − | 0.935197i | \(-0.384778\pi\) | ||||
0.354127 | + | 0.935197i | \(0.384778\pi\) | |||||||
\(830\) | − 10.3923i | − 0.360722i | ||||||||
\(831\) | −4.10512 | −0.142405 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.3923 | −0.360072 | ||||||||
\(834\) | 10.6410i | 0.368468i | ||||||||
\(835\) | −12.9282 | −0.447399 | ||||||||
\(836\) | 5.32051 | 0.184014 | ||||||||
\(837\) | − 0.784610i | − 0.0271201i | ||||||||
\(838\) | − 16.3923i | − 0.566263i | ||||||||
\(839\) | − 17.6603i | − 0.609700i | −0.952400 | − | 0.304850i | \(-0.901394\pi\) | ||||
0.952400 | − | 0.304850i | \(-0.0986063\pi\) | |||||||
\(840\) | 2.53590i | 0.0874968i | ||||||||
\(841\) | 60.5692 | 2.08859 | ||||||||
\(842\) | −18.6795 | −0.643738 | ||||||||
\(843\) | 1.17691i | 0.0405351i | ||||||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.6077 | −0.880411 | ||||||||
\(847\) | − 18.7846i | − 0.645447i | ||||||||
\(848\) | 51.9615 | 1.78437 | ||||||||
\(849\) | 1.03332 | 0.0354635 | ||||||||
\(850\) | 6.00000i | 0.205798i | ||||||||
\(851\) | − 18.9282i | − 0.648850i | ||||||||
\(852\) | 0.928203i | 0.0317997i | ||||||||
\(853\) | − 8.00000i | − 0.273915i | −0.990577 | − | 0.136957i | \(-0.956268\pi\) | ||||
0.990577 | − | 0.136957i | \(-0.0437323\pi\) | |||||||
\(854\) | 42.9282 | 1.46897 | ||||||||
\(855\) | −10.3397 | −0.353612 | ||||||||
\(856\) | 0.588457i | 0.0201131i | ||||||||
\(857\) | −47.5692 | −1.62493 | −0.812467 | − | 0.583007i | \(-0.801876\pi\) | ||||
−0.812467 | + | 0.583007i | \(0.801876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.1769 | 1.54142 | 0.770708 | − | 0.637188i | \(-0.219903\pi\) | ||||
0.770708 | + | 0.637188i | \(0.219903\pi\) | |||||||
\(860\) | − 10.1962i | − 0.347686i | ||||||||
\(861\) | 5.07180 | 0.172846 | ||||||||
\(862\) | −33.8038 | −1.15136 | ||||||||
\(863\) | 2.78461i | 0.0947892i | 0.998876 | + | 0.0473946i | \(0.0150918\pi\) | ||||
−0.998876 | + | 0.0473946i | \(0.984908\pi\) | |||||||
\(864\) | − 20.7846i | − 0.707107i | ||||||||
\(865\) | 15.4641i | 0.525795i | ||||||||
\(866\) | 11.7513i | 0.399325i | ||||||||
\(867\) | 3.66025 | 0.124309 | ||||||||
\(868\) | 0.392305 | 0.0133157 | ||||||||
\(869\) | 15.7128i | 0.533021i | ||||||||
\(870\) | 12.0000 | 0.406838 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.46410 | −0.117309 | ||||||||
\(873\) | − 4.92820i | − 0.166794i | ||||||||
\(874\) | 34.3923 | 1.16334 | ||||||||
\(875\) | 2.00000 | 0.0676123 | ||||||||
\(876\) | 2.92820i | 0.0989348i | ||||||||
\(877\) | 2.00000i | 0.0675352i | 0.999430 | + | 0.0337676i | \(0.0107506\pi\) | ||||
−0.999430 | + | 0.0337676i | \(0.989249\pi\) | |||||||
\(878\) | − 55.4256i | − 1.87052i | ||||||||
\(879\) | − 13.8564i | − 0.467365i | ||||||||
\(880\) | −6.33975 | −0.213713 | ||||||||
\(881\) | 12.6795 | 0.427183 | 0.213591 | − | 0.976923i | \(-0.431484\pi\) | ||||
0.213591 | + | 0.976923i | \(0.431484\pi\) | |||||||
\(882\) | − 12.8038i | − 0.431128i | ||||||||
\(883\) | −34.1962 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.0718 | −0.372174 | ||||||||
\(886\) | 60.5885i | 2.03551i | ||||||||
\(887\) | 17.9090 | 0.601324 | 0.300662 | − | 0.953731i | \(-0.402792\pi\) | ||||
0.300662 | + | 0.953731i | \(0.402792\pi\) | |||||||
\(888\) | 5.07180 | 0.170198 | ||||||||
\(889\) | 11.6077i | 0.389310i | ||||||||
\(890\) | − 1.60770i | − 0.0538901i | ||||||||
\(891\) | 5.66025i | 0.189626i | ||||||||
\(892\) | − 2.00000i | − 0.0669650i | ||||||||
\(893\) | 25.1769 | 0.842513 | ||||||||
\(894\) | 25.1769 | 0.842042 | ||||||||
\(895\) | − 5.07180i | − 0.169531i | ||||||||
\(896\) | −24.2487 | −0.810093 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 47.5692 | 1.58741 | ||||||||
\(899\) | 1.85641i | 0.0619146i | ||||||||
\(900\) | −2.46410 | −0.0821367 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 7.60770i | 0.253309i | ||||||||
\(903\) | − 14.9282i | − 0.496779i | ||||||||
\(904\) | 26.7846i | 0.890843i | ||||||||
\(905\) | − 20.3923i | − 0.677863i | ||||||||
\(906\) | 15.4641 | 0.513760 | ||||||||
\(907\) | −39.7654 | −1.32039 | −0.660194 | − | 0.751095i | \(-0.729526\pi\) | ||||
−0.660194 | + | 0.751095i | \(0.729526\pi\) | |||||||
\(908\) | − 3.46410i | − 0.114960i | ||||||||
\(909\) | 31.8564 | 1.05661 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 15.3590i | 0.508587i | ||||||||
\(913\) | 7.60770 | 0.251778 | ||||||||
\(914\) | 53.3205 | 1.76369 | ||||||||
\(915\) | 9.07180i | 0.299904i | ||||||||
\(916\) | − 14.3923i | − 0.475535i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − 24.0000i | − 0.792118i | ||||||||
\(919\) | −53.1769 | −1.75414 | −0.877072 | − | 0.480358i | \(-0.840507\pi\) | ||||
−0.877072 | + | 0.480358i | \(0.840507\pi\) | |||||||
\(920\) | −8.19615 | −0.270219 | ||||||||
\(921\) | 16.6795i | 0.549608i | ||||||||
\(922\) | −6.00000 | −0.197599 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.85641 | 0.0610713 | ||||||||
\(925\) | − 4.00000i | − 0.131519i | ||||||||
\(926\) | 31.8564 | 1.04687 | ||||||||
\(927\) | 25.1244 | 0.825192 | ||||||||
\(928\) | 49.1769i | 1.61431i | ||||||||
\(929\) | 51.4641i | 1.68848i | 0.535963 | + | 0.844241i | \(0.319948\pi\) | ||||
−0.535963 | + | 0.844241i | \(0.680052\pi\) | |||||||
\(930\) | 0.248711i | 0.00815557i | ||||||||
\(931\) | 12.5885i | 0.412570i | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 3.21539 | 0.105267 | ||||||||
\(934\) | − 66.1577i | − 2.16475i | ||||||||
\(935\) | −4.39230 | −0.143644 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.78461 | −0.221644 | −0.110822 | − | 0.993840i | \(-0.535348\pi\) | ||||
−0.110822 | + | 0.993840i | \(0.535348\pi\) | |||||||
\(938\) | − 49.8564i | − 1.62787i | ||||||||
\(939\) | −4.67949 | −0.152709 | ||||||||
\(940\) | 6.00000 | 0.195698 | ||||||||
\(941\) | − 31.1769i | − 1.01634i | −0.861257 | − | 0.508169i | \(-0.830322\pi\) | ||||
0.861257 | − | 0.508169i | \(-0.169678\pi\) | |||||||
\(942\) | 12.6795i | 0.413120i | ||||||||
\(943\) | 16.3923i | 0.533807i | ||||||||
\(944\) | − 75.6218i | − 2.46128i | ||||||||
\(945\) | −8.00000 | −0.260240 | ||||||||
\(946\) | 22.3923 | 0.728037 | ||||||||
\(947\) | 28.6410i | 0.930708i | 0.885125 | + | 0.465354i | \(0.154073\pi\) | ||||
−0.885125 | + | 0.465354i | \(0.845927\pi\) | |||||||
\(948\) | 9.07180 | 0.294638 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.26795 | 0.235803 | ||||||||
\(951\) | − 17.5692i | − 0.569721i | ||||||||
\(952\) | −12.0000 | −0.388922 | ||||||||
\(953\) | 12.9282 | 0.418786 | 0.209393 | − | 0.977832i | \(-0.432851\pi\) | ||||
0.209393 | + | 0.977832i | \(0.432851\pi\) | |||||||
\(954\) | 44.3538i | 1.43601i | ||||||||
\(955\) | 18.9282i | 0.612502i | ||||||||
\(956\) | 3.80385i | 0.123025i | ||||||||
\(957\) | 8.78461i | 0.283966i | ||||||||
\(958\) | 31.7654 | 1.02629 | ||||||||
\(959\) | 25.8564 | 0.834947 | ||||||||
\(960\) | − 0.732051i | − 0.0236268i | ||||||||
\(961\) | 30.9615 | 0.998759 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.837169 | −0.0269774 | ||||||||
\(964\) | 18.3923i | 0.592376i | ||||||||
\(965\) | 10.0000 | 0.321911 | ||||||||
\(966\) | 12.0000 | 0.386094 | ||||||||
\(967\) | − 29.6077i | − 0.952119i | −0.879413 | − | 0.476060i | \(-0.842065\pi\) | ||||
0.879413 | − | 0.476060i | \(-0.157935\pi\) | |||||||
\(968\) | 16.2679i | 0.522872i | ||||||||
\(969\) | 10.6410i | 0.341839i | ||||||||
\(970\) | 3.46410i | 0.111226i | ||||||||
\(971\) | 5.07180 | 0.162762 | 0.0813809 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813809 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(972\) | 15.2679 | 0.489720 | ||||||||
\(973\) | 16.7846i | 0.538090i | ||||||||
\(974\) | 9.71281 | 0.311219 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.9615 | −1.98334 | ||||||||
\(977\) | 39.7128i | 1.27053i | 0.772296 | + | 0.635263i | \(0.219108\pi\) | ||||
−0.772296 | + | 0.635263i | \(0.780892\pi\) | |||||||
\(978\) | −8.10512 | −0.259173 | ||||||||
\(979\) | 1.17691 | 0.0376144 | ||||||||
\(980\) | 3.00000i | 0.0958315i | ||||||||
\(981\) | − 4.92820i | − 0.157345i | ||||||||
\(982\) | 16.3923i | 0.523099i | ||||||||
\(983\) | 13.6077i | 0.434018i | 0.976170 | + | 0.217009i | \(0.0696301\pi\) | ||||
−0.976170 | + | 0.217009i | \(0.930370\pi\) | |||||||
\(984\) | −4.39230 | −0.140022 | ||||||||
\(985\) | 0.928203 | 0.0295750 | ||||||||
\(986\) | 56.7846i | 1.80839i | ||||||||
\(987\) | 8.78461 | 0.279617 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.2487 | 1.53422 | ||||||||
\(990\) | − 5.41154i | − 0.171990i | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | −1.01924 | −0.0323608 | ||||||||
\(993\) | 20.9282i | 0.664136i | ||||||||
\(994\) | 4.39230i | 0.139315i | ||||||||
\(995\) | 20.0000i | 0.634043i | ||||||||
\(996\) | − 4.39230i | − 0.139176i | ||||||||
\(997\) | 54.3923 | 1.72262 | 0.861311 | − | 0.508078i | \(-0.169644\pi\) | ||||
0.861311 | + | 0.508078i | \(0.169644\pi\) | |||||||
\(998\) | −22.4833 | −0.711698 | ||||||||
\(999\) | 16.0000i | 0.506218i |
(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 | 845.2.c.e.506.3 | 4 | ||
13.2 | odd | 12 | 845.2.e.e.191.1 | 4 | |||
13.3 | even | 3 | 845.2.m.a.316.2 | 4 | |||
13.4 | even | 6 | 845.2.m.a.361.2 | 4 | |||
13.5 | odd | 4 | 65.2.a.c.1.2 | ✓ | 2 | ||
13.6 | odd | 12 | 845.2.e.e.146.1 | 4 | |||
13.7 | odd | 12 | 845.2.e.f.146.2 | 4 | |||
13.8 | odd | 4 | 845.2.a.d.1.1 | 2 | |||
13.9 | even | 3 | 845.2.m.c.361.2 | 4 | |||
13.10 | even | 6 | 845.2.m.c.316.2 | 4 | |||
13.11 | odd | 12 | 845.2.e.f.191.2 | 4 | |||
13.12 | even | 2 | inner | 845.2.c.e.506.1 | 4 | ||
39.5 | even | 4 | 585.2.a.k.1.1 | 2 | |||
39.8 | even | 4 | 7605.2.a.be.1.2 | 2 | |||
52.31 | even | 4 | 1040.2.a.h.1.2 | 2 | |||
65.18 | even | 4 | 325.2.b.e.274.2 | 4 | |||
65.34 | odd | 4 | 4225.2.a.w.1.2 | 2 | |||
65.44 | odd | 4 | 325.2.a.g.1.1 | 2 | |||
65.57 | even | 4 | 325.2.b.e.274.3 | 4 | |||
91.83 | even | 4 | 3185.2.a.k.1.2 | 2 | |||
104.5 | odd | 4 | 4160.2.a.y.1.2 | 2 | |||
104.83 | even | 4 | 4160.2.a.bj.1.1 | 2 | |||
143.109 | even | 4 | 7865.2.a.h.1.1 | 2 | |||
156.83 | odd | 4 | 9360.2.a.cm.1.2 | 2 | |||
195.44 | even | 4 | 2925.2.a.z.1.2 | 2 | |||
195.83 | odd | 4 | 2925.2.c.v.2224.3 | 4 | |||
195.122 | odd | 4 | 2925.2.c.v.2224.2 | 4 | |||
260.239 | even | 4 | 5200.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.c.1.2 | ✓ | 2 | 13.5 | odd | 4 | ||
325.2.a.g.1.1 | 2 | 65.44 | odd | 4 | |||
325.2.b.e.274.2 | 4 | 65.18 | even | 4 | |||
325.2.b.e.274.3 | 4 | 65.57 | even | 4 | |||
585.2.a.k.1.1 | 2 | 39.5 | even | 4 | |||
845.2.a.d.1.1 | 2 | 13.8 | odd | 4 | |||
845.2.c.e.506.1 | 4 | 13.12 | even | 2 | inner | ||
845.2.c.e.506.3 | 4 | 1.1 | even | 1 | trivial | ||
845.2.e.e.146.1 | 4 | 13.6 | odd | 12 | |||
845.2.e.e.191.1 | 4 | 13.2 | odd | 12 | |||
845.2.e.f.146.2 | 4 | 13.7 | odd | 12 | |||
845.2.e.f.191.2 | 4 | 13.11 | odd | 12 | |||
845.2.m.a.316.2 | 4 | 13.3 | even | 3 | |||
845.2.m.a.361.2 | 4 | 13.4 | even | 6 | |||
845.2.m.c.316.2 | 4 | 13.10 | even | 6 | |||
845.2.m.c.361.2 | 4 | 13.9 | even | 3 | |||
1040.2.a.h.1.2 | 2 | 52.31 | even | 4 | |||
2925.2.a.z.1.2 | 2 | 195.44 | even | 4 | |||
2925.2.c.v.2224.2 | 4 | 195.122 | odd | 4 | |||
2925.2.c.v.2224.3 | 4 | 195.83 | odd | 4 | |||
3185.2.a.k.1.2 | 2 | 91.83 | even | 4 | |||
4160.2.a.y.1.2 | 2 | 104.5 | odd | 4 | |||
4160.2.a.bj.1.1 | 2 | 104.83 | even | 4 | |||
4225.2.a.w.1.2 | 2 | 65.34 | odd | 4 | |||
5200.2.a.ca.1.1 | 2 | 260.239 | even | 4 | |||
7605.2.a.be.1.2 | 2 | 39.8 | even | 4 | |||
7865.2.a.h.1.1 | 2 | 143.109 | even | 4 | |||
9360.2.a.cm.1.2 | 2 | 156.83 | odd | 4 |