Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(160,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("483.160");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.h (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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 17x^{10} + 92x^{8} + 180x^{6} + 92x^{4} + 17x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 160.12 | ||
Root | \(1.77931i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.160 |
Dual form | 483.2.h.c.160.10 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.51820 | 1.78064 | 0.890318 | − | 0.455340i | \(-0.150482\pi\) | ||||
0.890318 | + | 0.455340i | \(0.150482\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 4.34132 | 2.17066 | ||||||||
\(5\) | 1.21729 | 0.544390 | 0.272195 | − | 0.962242i | \(-0.412250\pi\) | ||||
0.272195 | + | 0.962242i | \(0.412250\pi\) | |||||||
\(6\) | 2.51820i | 1.02805i | ||||||||
\(7\) | −2.34908 | + | 1.21729i | −0.887871 | + | 0.460093i | ||||
\(8\) | 5.89592 | 2.08452 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 3.06538 | 0.969360 | ||||||||
\(11\) | − | 1.13179i | − | 0.341248i | −0.985336 | − | 0.170624i | \(-0.945422\pi\) | ||
0.985336 | − | 0.170624i | \(-0.0545784\pi\) | |||||||
\(12\) | 4.34132i | 1.25323i | ||||||||
\(13\) | − | 0.518199i | − | 0.143722i | −0.997415 | − | 0.0718612i | \(-0.977106\pi\) | ||
0.997415 | − | 0.0718612i | \(-0.0228939\pi\) | |||||||
\(14\) | −5.91546 | + | 3.06538i | −1.58097 | + | 0.819259i | ||||
\(15\) | 1.21729i | 0.314304i | ||||||||
\(16\) | 6.16445 | 1.54111 | ||||||||
\(17\) | 3.06538 | 0.743465 | 0.371732 | − | 0.928340i | \(-0.378764\pi\) | ||||
0.371732 | + | 0.928340i | \(0.378764\pi\) | |||||||
\(18\) | −2.51820 | −0.593545 | ||||||||
\(19\) | −1.13179 | −0.259651 | −0.129825 | − | 0.991537i | \(-0.541442\pi\) | ||||
−0.129825 | + | 0.991537i | \(0.541442\pi\) | |||||||
\(20\) | 5.28466 | 1.18169 | ||||||||
\(21\) | −1.21729 | − | 2.34908i | −0.265635 | − | 0.512612i | ||||
\(22\) | − | 2.85008i | − | 0.607639i | ||||||
\(23\) | −0.341325 | − | 4.78367i | −0.0711711 | − | 0.997464i | ||||
\(24\) | 5.89592i | 1.20350i | ||||||||
\(25\) | −3.51820 | −0.703640 | ||||||||
\(26\) | − | 1.30493i | − | 0.255917i | ||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −10.1981 | + | 5.28466i | −1.92727 | + | 0.998707i | ||||
\(29\) | −2.17687 | −0.404235 | −0.202118 | − | 0.979361i | \(-0.564782\pi\) | ||||
−0.202118 | + | 0.979361i | \(0.564782\pi\) | |||||||
\(30\) | 3.06538i | 0.559660i | ||||||||
\(31\) | − | 6.85952i | − | 1.23201i | −0.787744 | − | 0.616003i | \(-0.788751\pi\) | ||
0.787744 | − | 0.616003i | \(-0.211249\pi\) | |||||||
\(32\) | 3.73147 | 0.659637 | ||||||||
\(33\) | 1.13179 | 0.197020 | ||||||||
\(34\) | 7.71925 | 1.32384 | ||||||||
\(35\) | −2.85952 | + | 1.48180i | −0.483348 | + | 0.250470i | ||||
\(36\) | −4.34132 | −0.723554 | ||||||||
\(37\) | 10.1981i | 1.67656i | 0.545237 | + | 0.838282i | \(0.316440\pi\) | ||||
−0.545237 | + | 0.838282i | \(0.683560\pi\) | |||||||
\(38\) | −2.85008 | −0.462344 | ||||||||
\(39\) | 0.518199 | 0.0829782 | ||||||||
\(40\) | 7.17706 | 1.13479 | ||||||||
\(41\) | 5.00000i | 0.780869i | 0.920631 | + | 0.390434i | \(0.127675\pi\) | ||||
−0.920631 | + | 0.390434i | \(0.872325\pi\) | |||||||
\(42\) | −3.06538 | − | 5.91546i | −0.472999 | − | 0.912776i | ||||
\(43\) | − | 6.71726i | − | 1.02437i | −0.858874 | − | 0.512186i | \(-0.828836\pi\) | ||
0.858874 | − | 0.512186i | \(-0.171164\pi\) | |||||||
\(44\) | − | 4.91348i | − | 0.740734i | ||||||
\(45\) | −1.21729 | −0.181463 | ||||||||
\(46\) | −0.859523 | − | 12.0462i | −0.126730 | − | 1.77612i | ||||
\(47\) | − | 4.21327i | − | 0.614569i | −0.951618 | − | 0.307284i | \(-0.900580\pi\) | ||
0.951618 | − | 0.307284i | \(-0.0994203\pi\) | |||||||
\(48\) | 6.16445i | 0.889762i | ||||||||
\(49\) | 4.03640 | − | 5.71905i | 0.576628 | − | 0.817007i | ||||
\(50\) | −8.85952 | −1.25293 | ||||||||
\(51\) | 3.06538i | 0.429240i | ||||||||
\(52\) | − | 2.24967i | − | 0.311973i | ||||||
\(53\) | 5.41447i | 0.743735i | 0.928286 | + | 0.371867i | \(0.121282\pi\) | ||||
−0.928286 | + | 0.371867i | \(0.878718\pi\) | |||||||
\(54\) | − | 2.51820i | − | 0.342683i | ||||||
\(55\) | − | 1.37772i | − | 0.185772i | ||||||
\(56\) | −13.8500 | + | 7.17706i | −1.85079 | + | 0.959075i | ||||
\(57\) | − | 1.13179i | − | 0.149910i | ||||||
\(58\) | −5.48180 | −0.719796 | ||||||||
\(59\) | 0.200848i | 0.0261482i | 0.999915 | + | 0.0130741i | \(0.00416173\pi\) | ||||
−0.999915 | + | 0.0130741i | \(0.995838\pi\) | |||||||
\(60\) | 5.28466i | 0.682247i | ||||||||
\(61\) | 6.21627 | 0.795912 | 0.397956 | − | 0.917405i | \(-0.369720\pi\) | ||||
0.397956 | + | 0.917405i | \(0.369720\pi\) | |||||||
\(62\) | − | 17.2736i | − | 2.19375i | ||||||
\(63\) | 2.34908 | − | 1.21729i | 0.295957 | − | 0.153364i | ||||
\(64\) | −2.93232 | −0.366540 | ||||||||
\(65\) | − | 0.630799i | − | 0.0782410i | ||||||
\(66\) | 2.85008 | 0.350820 | ||||||||
\(67\) | − | 3.65188i | − | 0.446148i | −0.974802 | − | 0.223074i | \(-0.928391\pi\) | ||
0.974802 | − | 0.223074i | \(-0.0716091\pi\) | |||||||
\(68\) | 13.3078 | 1.61381 | ||||||||
\(69\) | 4.78367 | − | 0.341325i | 0.575886 | − | 0.0410907i | ||||
\(70\) | −7.20085 | + | 3.73147i | −0.860666 | + | 0.445996i | ||||
\(71\) | 2.16445 | 0.256873 | 0.128437 | − | 0.991718i | \(-0.459004\pi\) | ||||
0.128437 | + | 0.991718i | \(0.459004\pi\) | |||||||
\(72\) | −5.89592 | −0.694841 | ||||||||
\(73\) | 10.2248i | 1.19672i | 0.801226 | + | 0.598362i | \(0.204182\pi\) | ||||
−0.801226 | + | 0.598362i | \(0.795818\pi\) | |||||||
\(74\) | 25.6809i | 2.98535i | ||||||||
\(75\) | − | 3.51820i | − | 0.406247i | ||||||
\(76\) | −4.91348 | −0.563614 | ||||||||
\(77\) | 1.37772 | + | 2.65868i | 0.157006 | + | 0.302984i | ||||
\(78\) | 1.30493 | 0.147754 | ||||||||
\(79\) | 8.59454i | 0.966961i | 0.875355 | + | 0.483481i | \(0.160628\pi\) | ||||
−0.875355 | + | 0.483481i | \(0.839372\pi\) | |||||||
\(80\) | 7.50394 | 0.838966 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.5910i | 1.39044i | ||||||||
\(83\) | −11.6307 | −1.27664 | −0.638320 | − | 0.769771i | \(-0.720370\pi\) | ||||
−0.638320 | + | 0.769771i | \(0.720370\pi\) | |||||||
\(84\) | −5.28466 | − | 10.1981i | −0.576604 | − | 1.11271i | ||||
\(85\) | 3.73147 | 0.404735 | ||||||||
\(86\) | − | 16.9154i | − | 1.82403i | ||||||
\(87\) | − | 2.17687i | − | 0.233385i | ||||||
\(88\) | − | 6.67296i | − | 0.711340i | ||||||
\(89\) | 5.11366 | 0.542047 | 0.271024 | − | 0.962573i | \(-0.412638\pi\) | ||||
0.271024 | + | 0.962573i | \(0.412638\pi\) | |||||||
\(90\) | −3.06538 | −0.323120 | ||||||||
\(91\) | 0.630799 | + | 1.21729i | 0.0661257 | + | 0.127607i | ||||
\(92\) | −1.48180 | − | 20.7675i | −0.154488 | − | 2.16516i | ||||
\(93\) | 6.85952 | 0.711299 | ||||||||
\(94\) | − | 10.6099i | − | 1.09432i | ||||||
\(95\) | −1.37772 | −0.141351 | ||||||||
\(96\) | 3.73147i | 0.380842i | ||||||||
\(97\) | −18.1619 | −1.84406 | −0.922030 | − | 0.387119i | \(-0.873470\pi\) | ||||
−0.922030 | + | 0.387119i | \(0.873470\pi\) | |||||||
\(98\) | 10.1645 | − | 14.4017i | 1.02676 | − | 1.45479i | ||||
\(99\) | 1.13179i | 0.113749i | ||||||||
\(100\) | −15.2736 | −1.52736 | ||||||||
\(101\) | 8.88350i | 0.883941i | 0.897030 | + | 0.441971i | \(0.145720\pi\) | ||||
−0.897030 | + | 0.441971i | \(0.854280\pi\) | |||||||
\(102\) | 7.71925i | 0.764319i | ||||||||
\(103\) | 11.5009 | 1.13322 | 0.566610 | − | 0.823986i | \(-0.308255\pi\) | ||||
0.566610 | + | 0.823986i | \(0.308255\pi\) | |||||||
\(104\) | − | 3.05526i | − | 0.299593i | ||||||
\(105\) | −1.48180 | − | 2.85952i | −0.144609 | − | 0.279061i | ||||
\(106\) | 13.6347i | 1.32432i | ||||||||
\(107\) | − | 2.67908i | − | 0.258996i | −0.991580 | − | 0.129498i | \(-0.958663\pi\) | ||
0.991580 | − | 0.129498i | \(-0.0413366\pi\) | |||||||
\(108\) | − | 4.34132i | − | 0.417744i | ||||||
\(109\) | − | 17.7464i | − | 1.69980i | −0.526948 | − | 0.849898i | \(-0.676664\pi\) | ||
0.526948 | − | 0.849898i | \(-0.323336\pi\) | |||||||
\(110\) | − | 3.46938i | − | 0.330792i | ||||||
\(111\) | −10.1981 | −0.967965 | ||||||||
\(112\) | −14.4808 | + | 7.50394i | −1.36831 | + | 0.709056i | ||||
\(113\) | 2.21928i | 0.208772i | 0.994537 | + | 0.104386i | \(0.0332878\pi\) | ||||
−0.994537 | + | 0.104386i | \(0.966712\pi\) | |||||||
\(114\) | − | 2.85008i | − | 0.266934i | ||||||
\(115\) | −0.415492 | − | 5.82313i | −0.0387448 | − | 0.543009i | ||||
\(116\) | −9.45052 | −0.877458 | ||||||||
\(117\) | 0.518199i | 0.0479075i | ||||||||
\(118\) | 0.505775i | 0.0465604i | ||||||||
\(119\) | −7.20085 | + | 3.73147i | −0.660101 | + | 0.342063i | ||||
\(120\) | 7.17706i | 0.655173i | ||||||||
\(121\) | 9.71905 | 0.883550 | ||||||||
\(122\) | 15.6538 | 1.41723 | ||||||||
\(123\) | −5.00000 | −0.450835 | ||||||||
\(124\) | − | 29.7794i | − | 2.67427i | ||||||
\(125\) | −10.3691 | −0.927444 | ||||||||
\(126\) | 5.91546 | − | 3.06538i | 0.526991 | − | 0.273086i | ||||
\(127\) | −2.73147 | −0.242379 | −0.121189 | − | 0.992629i | \(-0.538671\pi\) | ||||
−0.121189 | + | 0.992629i | \(0.538671\pi\) | |||||||
\(128\) | −14.8471 | −1.31231 | ||||||||
\(129\) | 6.71726 | 0.591422 | ||||||||
\(130\) | − | 1.58848i | − | 0.139319i | ||||||
\(131\) | 18.7190i | 1.63549i | 0.575580 | + | 0.817745i | \(0.304776\pi\) | ||||
−0.575580 | + | 0.817745i | \(0.695224\pi\) | |||||||
\(132\) | 4.91348 | 0.427663 | ||||||||
\(133\) | 2.65868 | − | 1.37772i | 0.230536 | − | 0.119464i | ||||
\(134\) | − | 9.19615i | − | 0.794427i | ||||||
\(135\) | − | 1.21729i | − | 0.104768i | ||||||
\(136\) | 18.0733 | 1.54977 | ||||||||
\(137\) | 12.3027i | 1.05109i | 0.850765 | + | 0.525547i | \(0.176139\pi\) | ||||
−0.850765 | + | 0.525547i | \(0.823861\pi\) | |||||||
\(138\) | 12.0462 | − | 0.859523i | 1.02544 | − | 0.0731675i | ||||
\(139\) | − | 13.7794i | − | 1.16876i | −0.811482 | − | 0.584378i | \(-0.801339\pi\) | ||
0.811482 | − | 0.584378i | \(-0.198661\pi\) | |||||||
\(140\) | −12.4141 | + | 6.43298i | −1.04918 | + | 0.543686i | ||||
\(141\) | 4.21327 | 0.354821 | ||||||||
\(142\) | 5.45052 | 0.457397 | ||||||||
\(143\) | −0.586493 | −0.0490450 | ||||||||
\(144\) | −6.16445 | −0.513704 | ||||||||
\(145\) | −2.64989 | −0.220062 | ||||||||
\(146\) | 25.7481i | 2.13093i | ||||||||
\(147\) | 5.71905 | + | 4.03640i | 0.471699 | + | 0.332916i | ||||
\(148\) | 44.2734i | 3.63925i | ||||||||
\(149\) | − | 8.46473i | − | 0.693458i | −0.937965 | − | 0.346729i | \(-0.887292\pi\) | ||
0.937965 | − | 0.346729i | \(-0.112708\pi\) | |||||||
\(150\) | − | 8.85952i | − | 0.723377i | ||||||
\(151\) | 17.5786 | 1.43052 | 0.715262 | − | 0.698857i | \(-0.246307\pi\) | ||||
0.715262 | + | 0.698857i | \(0.246307\pi\) | |||||||
\(152\) | −6.67296 | −0.541248 | ||||||||
\(153\) | −3.06538 | −0.247822 | ||||||||
\(154\) | 3.46938 | + | 6.69507i | 0.279570 | + | 0.539504i | ||||
\(155\) | − | 8.35005i | − | 0.670692i | ||||||
\(156\) | 2.24967 | 0.180118 | ||||||||
\(157\) | 18.6337 | 1.48713 | 0.743565 | − | 0.668664i | \(-0.233133\pi\) | ||||
0.743565 | + | 0.668664i | \(0.233133\pi\) | |||||||
\(158\) | 21.6428i | 1.72181i | ||||||||
\(159\) | −5.41447 | −0.429395 | ||||||||
\(160\) | 4.54229 | 0.359100 | ||||||||
\(161\) | 6.62493 | + | 10.8218i | 0.522117 | + | 0.852874i | ||||
\(162\) | 2.51820 | 0.197848 | ||||||||
\(163\) | 7.23725 | 0.566865 | 0.283432 | − | 0.958992i | \(-0.408527\pi\) | ||||
0.283432 | + | 0.958992i | \(0.408527\pi\) | |||||||
\(164\) | 21.7066i | 1.69500i | ||||||||
\(165\) | 1.37772 | 0.107256 | ||||||||
\(166\) | −29.2885 | −2.27323 | ||||||||
\(167\) | 17.8282i | 1.37959i | 0.724004 | + | 0.689795i | \(0.242299\pi\) | ||||
−0.724004 | + | 0.689795i | \(0.757701\pi\) | |||||||
\(168\) | −7.17706 | − | 13.8500i | −0.553722 | − | 1.06855i | ||||
\(169\) | 12.7315 | 0.979344 | ||||||||
\(170\) | 9.39658 | 0.720685 | ||||||||
\(171\) | 1.13179 | 0.0865503 | ||||||||
\(172\) | − | 29.1618i | − | 2.22357i | ||||||
\(173\) | 20.2248i | 1.53766i | 0.639450 | + | 0.768832i | \(0.279162\pi\) | ||||
−0.639450 | + | 0.768832i | \(0.720838\pi\) | |||||||
\(174\) | − | 5.48180i | − | 0.415574i | ||||||
\(175\) | 8.26455 | − | 4.28268i | 0.624741 | − | 0.323740i | ||||
\(176\) | − | 6.97688i | − | 0.525902i | ||||||
\(177\) | −0.200848 | −0.0150967 | ||||||||
\(178\) | 12.8772 | 0.965188 | ||||||||
\(179\) | −10.4141 | −0.778388 | −0.389194 | − | 0.921156i | \(-0.627246\pi\) | ||||
−0.389194 | + | 0.921156i | \(0.627246\pi\) | |||||||
\(180\) | −5.28466 | −0.393895 | ||||||||
\(181\) | −14.0653 | −1.04547 | −0.522734 | − | 0.852496i | \(-0.675088\pi\) | ||||
−0.522734 | + | 0.852496i | \(0.675088\pi\) | |||||||
\(182\) | 1.58848 | + | 3.06538i | 0.117746 | + | 0.227221i | ||||
\(183\) | 6.21627i | 0.459520i | ||||||||
\(184\) | −2.01242 | − | 28.2041i | −0.148358 | − | 2.07924i | ||||
\(185\) | 12.4141i | 0.912704i | ||||||||
\(186\) | 17.2736 | 1.26656 | ||||||||
\(187\) | − | 3.46938i | − | 0.253706i | ||||||
\(188\) | − | 18.2912i | − | 1.33402i | ||||||
\(189\) | 1.21729 | + | 2.34908i | 0.0885450 | + | 0.170871i | ||||
\(190\) | −3.46938 | −0.251695 | ||||||||
\(191\) | 12.3319i | 0.892306i | 0.894957 | + | 0.446153i | \(0.147206\pi\) | ||||
−0.894957 | + | 0.446153i | \(0.852794\pi\) | |||||||
\(192\) | − | 2.93232i | − | 0.211622i | ||||||
\(193\) | −3.17687 | −0.228676 | −0.114338 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114338 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(194\) | −45.7352 | −3.28360 | ||||||||
\(195\) | 0.630799 | 0.0451725 | ||||||||
\(196\) | 17.5233 | − | 24.8282i | 1.25167 | − | 1.77345i | ||||
\(197\) | 16.5661 | 1.18029 | 0.590145 | − | 0.807298i | \(-0.299071\pi\) | ||||
0.590145 | + | 0.807298i | \(0.299071\pi\) | |||||||
\(198\) | 2.85008i | 0.202546i | ||||||||
\(199\) | 9.28165 | 0.657959 | 0.328980 | − | 0.944337i | \(-0.393295\pi\) | ||||
0.328980 | + | 0.944337i | \(0.393295\pi\) | |||||||
\(200\) | −20.7430 | −1.46675 | ||||||||
\(201\) | 3.65188 | 0.257584 | ||||||||
\(202\) | 22.3704i | 1.57398i | ||||||||
\(203\) | 5.11366 | − | 2.64989i | 0.358909 | − | 0.185986i | ||||
\(204\) | 13.3078i | 0.931734i | ||||||||
\(205\) | 6.08646i | 0.425097i | ||||||||
\(206\) | 28.9616 | 2.01785 | ||||||||
\(207\) | 0.341325 | + | 4.78367i | 0.0237237 | + | 0.332488i | ||||
\(208\) | − | 3.19441i | − | 0.221493i | ||||||
\(209\) | 1.28095i | 0.0886054i | ||||||||
\(210\) | −3.73147 | − | 7.20085i | −0.257496 | − | 0.496906i | ||||
\(211\) | 7.96360 | 0.548237 | 0.274119 | − | 0.961696i | \(-0.411614\pi\) | ||||
0.274119 | + | 0.961696i | \(0.411614\pi\) | |||||||
\(212\) | 23.5060i | 1.61440i | ||||||||
\(213\) | 2.16445i | 0.148306i | ||||||||
\(214\) | − | 6.74645i | − | 0.461178i | ||||||
\(215\) | − | 8.17687i | − | 0.557658i | ||||||
\(216\) | − | 5.89592i | − | 0.401167i | ||||||
\(217\) | 8.35005 | + | 16.1136i | 0.566838 | + | 1.09386i | ||||
\(218\) | − | 44.6889i | − | 3.02672i | ||||||
\(219\) | −10.2248 | −0.690929 | ||||||||
\(220\) | − | 5.98114i | − | 0.403248i | ||||||
\(221\) | − | 1.58848i | − | 0.106853i | ||||||
\(222\) | −25.6809 | −1.72359 | ||||||||
\(223\) | − | 21.0968i | − | 1.41274i | −0.707841 | − | 0.706372i | \(-0.750331\pi\) | ||
0.707841 | − | 0.706372i | \(-0.249669\pi\) | |||||||
\(224\) | −8.76554 | + | 4.54229i | −0.585672 | + | 0.303495i | ||||
\(225\) | 3.51820 | 0.234547 | ||||||||
\(226\) | 5.58858i | 0.371747i | ||||||||
\(227\) | 24.8791 | 1.65129 | 0.825643 | − | 0.564193i | \(-0.190812\pi\) | ||||
0.825643 | + | 0.564193i | \(0.190812\pi\) | |||||||
\(228\) | − | 4.91348i | − | 0.325403i | ||||||
\(229\) | −19.5090 | −1.28919 | −0.644595 | − | 0.764524i | \(-0.722974\pi\) | ||||
−0.644595 | + | 0.764524i | \(0.722974\pi\) | |||||||
\(230\) | −1.04629 | − | 14.6638i | −0.0689904 | − | 0.966902i | ||||
\(231\) | −2.65868 | + | 1.37772i | −0.174928 | + | 0.0906475i | ||||
\(232\) | −12.8347 | −0.842638 | ||||||||
\(233\) | −8.34132 | −0.546458 | −0.273229 | − | 0.961949i | \(-0.588092\pi\) | ||||
−0.273229 | + | 0.961949i | \(0.588092\pi\) | |||||||
\(234\) | 1.30493i | 0.0853058i | ||||||||
\(235\) | − | 5.12878i | − | 0.334565i | ||||||
\(236\) | 0.871947i | 0.0567589i | ||||||||
\(237\) | −8.59454 | −0.558275 | ||||||||
\(238\) | −18.1332 | + | 9.39658i | −1.17540 | + | 0.609090i | ||||
\(239\) | −21.3777 | −1.38281 | −0.691405 | − | 0.722467i | \(-0.743008\pi\) | ||||
−0.691405 | + | 0.722467i | \(0.743008\pi\) | |||||||
\(240\) | 7.50394i | 0.484377i | ||||||||
\(241\) | 8.86616 | 0.571120 | 0.285560 | − | 0.958361i | \(-0.407820\pi\) | ||||
0.285560 | + | 0.958361i | \(0.407820\pi\) | |||||||
\(242\) | 24.4745 | 1.57328 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 26.9868 | 1.72766 | ||||||||
\(245\) | 4.91348 | − | 6.96175i | 0.313911 | − | 0.444770i | ||||
\(246\) | −12.5910 | −0.802772 | ||||||||
\(247\) | 0.586493i | 0.0373177i | ||||||||
\(248\) | − | 40.4432i | − | 2.56815i | ||||||
\(249\) | − | 11.6307i | − | 0.737068i | ||||||
\(250\) | −26.1116 | −1.65144 | ||||||||
\(251\) | −13.0925 | −0.826393 | −0.413196 | − | 0.910642i | \(-0.635588\pi\) | ||||
−0.413196 | + | 0.910642i | \(0.635588\pi\) | |||||||
\(252\) | 10.1981 | − | 5.28466i | 0.642422 | − | 0.332902i | ||||
\(253\) | −5.41412 | + | 0.386309i | −0.340383 | + | 0.0242870i | ||||
\(254\) | −6.87838 | −0.431588 | ||||||||
\(255\) | 3.73147i | 0.233674i | ||||||||
\(256\) | −31.5233 | −1.97021 | ||||||||
\(257\) | − | 13.9075i | − | 0.867524i | −0.901027 | − | 0.433762i | \(-0.857186\pi\) | ||
0.901027 | − | 0.433762i | \(-0.142814\pi\) | |||||||
\(258\) | 16.9154 | 1.05311 | ||||||||
\(259\) | −12.4141 | − | 23.9563i | −0.771376 | − | 1.48857i | ||||
\(260\) | − | 2.73851i | − | 0.169835i | ||||||
\(261\) | 2.17687 | 0.134745 | ||||||||
\(262\) | 47.1383i | 2.91221i | ||||||||
\(263\) | 23.7917i | 1.46706i | 0.679659 | + | 0.733528i | \(0.262128\pi\) | ||||
−0.679659 | + | 0.733528i | \(0.737872\pi\) | |||||||
\(264\) | 6.67296 | 0.410692 | ||||||||
\(265\) | 6.59099i | 0.404882i | ||||||||
\(266\) | 6.69507 | − | 3.46938i | 0.410501 | − | 0.212721i | ||||
\(267\) | 5.11366i | 0.312951i | ||||||||
\(268\) | − | 15.8540i | − | 0.968436i | ||||||
\(269\) | − | 5.76275i | − | 0.351361i | −0.984447 | − | 0.175681i | \(-0.943787\pi\) | ||
0.984447 | − | 0.175681i | \(-0.0562126\pi\) | |||||||
\(270\) | − | 3.06538i | − | 0.186553i | ||||||
\(271\) | − | 11.5422i | − | 0.701137i | −0.936537 | − | 0.350569i | \(-0.885988\pi\) | ||
0.936537 | − | 0.350569i | \(-0.114012\pi\) | |||||||
\(272\) | 18.8964 | 1.14576 | ||||||||
\(273\) | −1.21729 | + | 0.630799i | −0.0736739 | + | 0.0381777i | ||||
\(274\) | 30.9807i | 1.87161i | ||||||||
\(275\) | 3.98187i | 0.240116i | ||||||||
\(276\) | 20.7675 | − | 1.48180i | 1.25005 | − | 0.0891940i | ||||
\(277\) | 24.5713 | 1.47634 | 0.738172 | − | 0.674613i | \(-0.235689\pi\) | ||||
0.738172 | + | 0.674613i | \(0.235689\pi\) | |||||||
\(278\) | − | 34.6993i | − | 2.08113i | ||||||
\(279\) | 6.85952i | 0.410669i | ||||||||
\(280\) | −16.8595 | + | 8.73658i | −1.00755 | + | 0.522111i | ||||
\(281\) | − | 16.7001i | − | 0.996244i | −0.867107 | − | 0.498122i | \(-0.834023\pi\) | ||
0.867107 | − | 0.498122i | \(-0.165977\pi\) | |||||||
\(282\) | 10.6099 | 0.631808 | ||||||||
\(283\) | −12.2172 | −0.726239 | −0.363120 | − | 0.931743i | \(-0.618288\pi\) | ||||
−0.363120 | + | 0.931743i | \(0.618288\pi\) | |||||||
\(284\) | 9.39658 | 0.557585 | ||||||||
\(285\) | − | 1.37772i | − | 0.0816092i | ||||||
\(286\) | −1.47691 | −0.0873313 | ||||||||
\(287\) | −6.08646 | − | 11.7454i | −0.359273 | − | 0.693310i | ||||
\(288\) | −3.73147 | −0.219879 | ||||||||
\(289\) | −7.60342 | −0.447260 | ||||||||
\(290\) | −6.67296 | −0.391849 | ||||||||
\(291\) | − | 18.1619i | − | 1.06467i | ||||||
\(292\) | 44.3893i | 2.59769i | ||||||||
\(293\) | −22.0582 | −1.28866 | −0.644328 | − | 0.764749i | \(-0.722863\pi\) | ||||
−0.644328 | + | 0.764749i | \(0.722863\pi\) | |||||||
\(294\) | 14.4017 | + | 10.1645i | 0.839924 | + | 0.592803i | ||||
\(295\) | 0.244491i | 0.0142348i | ||||||||
\(296\) | 60.1274i | 3.49484i | ||||||||
\(297\) | −1.13179 | −0.0656732 | ||||||||
\(298\) | − | 21.3159i | − | 1.23480i | ||||||
\(299\) | −2.47889 | + | 0.176874i | −0.143358 | + | 0.0102289i | ||||
\(300\) | − | 15.2736i | − | 0.881824i | ||||||
\(301\) | 8.17687 | + | 15.7794i | 0.471307 | + | 0.909511i | ||||
\(302\) | 44.2663 | 2.54724 | ||||||||
\(303\) | −8.88350 | −0.510344 | ||||||||
\(304\) | −6.97688 | −0.400151 | ||||||||
\(305\) | 7.56702 | 0.433286 | ||||||||
\(306\) | −7.71925 | −0.441280 | ||||||||
\(307\) | 20.0167i | 1.14241i | 0.820807 | + | 0.571206i | \(0.193524\pi\) | ||||
−0.820807 | + | 0.571206i | \(0.806476\pi\) | |||||||
\(308\) | 5.98114 | + | 11.5422i | 0.340807 | + | 0.657676i | ||||
\(309\) | 11.5009i | 0.654265i | ||||||||
\(310\) | − | 21.0271i | − | 1.19426i | ||||||
\(311\) | − | 15.7430i | − | 0.892705i | −0.894857 | − | 0.446352i | \(-0.852723\pi\) | ||
0.894857 | − | 0.446352i | \(-0.147277\pi\) | |||||||
\(312\) | 3.05526 | 0.172970 | ||||||||
\(313\) | 8.46473 | 0.478455 | 0.239227 | − | 0.970964i | \(-0.423106\pi\) | ||||
0.239227 | + | 0.970964i | \(0.423106\pi\) | |||||||
\(314\) | 46.9233 | 2.64804 | ||||||||
\(315\) | 2.85952 | − | 1.48180i | 0.161116 | − | 0.0834900i | ||||
\(316\) | 37.3117i | 2.09895i | ||||||||
\(317\) | 28.1083 | 1.57872 | 0.789360 | − | 0.613930i | \(-0.210412\pi\) | ||||
0.789360 | + | 0.613930i | \(0.210412\pi\) | |||||||
\(318\) | −13.6347 | −0.764597 | ||||||||
\(319\) | 2.46377i | 0.137945i | ||||||||
\(320\) | −3.56949 | −0.199541 | ||||||||
\(321\) | 2.67908 | 0.149531 | ||||||||
\(322\) | 16.6829 | + | 27.2513i | 0.929701 | + | 1.51866i | ||||
\(323\) | −3.46938 | −0.193041 | ||||||||
\(324\) | 4.34132 | 0.241185 | ||||||||
\(325\) | 1.82313i | 0.101129i | ||||||||
\(326\) | 18.2248 | 1.00938 | ||||||||
\(327\) | 17.7464 | 0.981377 | ||||||||
\(328\) | 29.4796i | 1.62774i | ||||||||
\(329\) | 5.12878 | + | 9.89733i | 0.282759 | + | 0.545658i | ||||
\(330\) | 3.46938 | 0.190983 | ||||||||
\(331\) | −9.22482 | −0.507042 | −0.253521 | − | 0.967330i | \(-0.581589\pi\) | ||||
−0.253521 | + | 0.967330i | \(0.581589\pi\) | |||||||
\(332\) | −50.4928 | −2.77115 | ||||||||
\(333\) | − | 10.1981i | − | 0.558855i | ||||||
\(334\) | 44.8950i | 2.45655i | ||||||||
\(335\) | − | 4.44540i | − | 0.242878i | ||||||
\(336\) | −7.50394 | − | 14.4808i | −0.409374 | − | 0.789993i | ||||
\(337\) | − | 14.0794i | − | 0.766953i | −0.923551 | − | 0.383476i | \(-0.874727\pi\) | ||
0.923551 | − | 0.383476i | \(-0.125273\pi\) | |||||||
\(338\) | 32.0604 | 1.74385 | ||||||||
\(339\) | −2.21928 | −0.120535 | ||||||||
\(340\) | 16.1995 | 0.878543 | ||||||||
\(341\) | −7.76355 | −0.420420 | ||||||||
\(342\) | 2.85008 | 0.154115 | ||||||||
\(343\) | −2.52009 | + | 18.3480i | −0.136072 | + | 0.990699i | ||||
\(344\) | − | 39.6044i | − | 2.13533i | ||||||
\(345\) | 5.82313 | − | 0.415492i | 0.313507 | − | 0.0223693i | ||||
\(346\) | 50.9301i | 2.73802i | ||||||||
\(347\) | −4.50578 | −0.241883 | −0.120941 | − | 0.992660i | \(-0.538591\pi\) | ||||
−0.120941 | + | 0.992660i | \(0.538591\pi\) | |||||||
\(348\) | − | 9.45052i | − | 0.506601i | ||||||
\(349\) | − | 11.8522i | − | 0.634434i | −0.948353 | − | 0.317217i | \(-0.897252\pi\) | ||
0.948353 | − | 0.317217i | \(-0.102748\pi\) | |||||||
\(350\) | 20.8118 | − | 10.7846i | 1.11244 | − | 0.576463i | ||||
\(351\) | −0.518199 | −0.0276594 | ||||||||
\(352\) | − | 4.22325i | − | 0.225100i | ||||||
\(353\) | − | 24.0167i | − | 1.27828i | −0.769091 | − | 0.639139i | \(-0.779291\pi\) | ||
0.769091 | − | 0.639139i | \(-0.220709\pi\) | |||||||
\(354\) | −0.505775 | −0.0268817 | ||||||||
\(355\) | 2.63477 | 0.139839 | ||||||||
\(356\) | 22.2001 | 1.17660 | ||||||||
\(357\) | −3.73147 | − | 7.20085i | −0.197490 | − | 0.381109i | ||||
\(358\) | −26.2248 | −1.38602 | ||||||||
\(359\) | 1.21729i | 0.0642462i | 0.999484 | + | 0.0321231i | \(0.0102269\pi\) | ||||
−0.999484 | + | 0.0321231i | \(0.989773\pi\) | |||||||
\(360\) | −7.17706 | −0.378264 | ||||||||
\(361\) | −17.7190 | −0.932581 | ||||||||
\(362\) | −35.4193 | −1.86160 | ||||||||
\(363\) | 9.71905i | 0.510118i | ||||||||
\(364\) | 2.73851 | + | 5.28466i | 0.143537 | + | 0.276992i | ||||
\(365\) | 12.4466i | 0.651485i | ||||||||
\(366\) | 15.6538i | 0.818237i | ||||||||
\(367\) | −10.7434 | −0.560803 | −0.280401 | − | 0.959883i | \(-0.590468\pi\) | ||||
−0.280401 | + | 0.959883i | \(0.590468\pi\) | |||||||
\(368\) | −2.10408 | − | 29.4887i | −0.109683 | − | 1.53720i | ||||
\(369\) | − | 5.00000i | − | 0.260290i | ||||||
\(370\) | 31.2612i | 1.62519i | ||||||||
\(371\) | −6.59099 | − | 12.7190i | −0.342187 | − | 0.660340i | ||||
\(372\) | 29.7794 | 1.54399 | ||||||||
\(373\) | − | 28.3308i | − | 1.46691i | −0.679735 | − | 0.733457i | \(-0.737905\pi\) | ||
0.679735 | − | 0.733457i | \(-0.262095\pi\) | |||||||
\(374\) | − | 8.73658i | − | 0.451758i | ||||||
\(375\) | − | 10.3691i | − | 0.535460i | ||||||
\(376\) | − | 24.8411i | − | 1.28108i | ||||||
\(377\) | 1.12805i | 0.0580977i | ||||||||
\(378\) | 3.06538 | + | 5.91546i | 0.157666 | + | 0.304259i | ||||
\(379\) | − | 4.86917i | − | 0.250112i | −0.992150 | − | 0.125056i | \(-0.960089\pi\) | ||
0.992150 | − | 0.125056i | \(-0.0399111\pi\) | |||||||
\(380\) | −5.98114 | −0.306826 | ||||||||
\(381\) | − | 2.73147i | − | 0.139937i | ||||||
\(382\) | 31.0542i | 1.58887i | ||||||||
\(383\) | 34.6326 | 1.76964 | 0.884822 | − | 0.465930i | \(-0.154280\pi\) | ||||
0.884822 | + | 0.465930i | \(0.154280\pi\) | |||||||
\(384\) | − | 14.8471i | − | 0.757663i | ||||||
\(385\) | 1.67709 | + | 3.23639i | 0.0854725 | + | 0.164941i | ||||
\(386\) | −8.00000 | −0.407189 | ||||||||
\(387\) | 6.71726i | 0.341458i | ||||||||
\(388\) | −78.8466 | −4.00283 | ||||||||
\(389\) | 11.6307i | 0.589702i | 0.955543 | + | 0.294851i | \(0.0952700\pi\) | ||||
−0.955543 | + | 0.294851i | \(0.904730\pi\) | |||||||
\(390\) | 1.58848 | 0.0804357 | ||||||||
\(391\) | −1.04629 | − | 14.6638i | −0.0529132 | − | 0.741580i | ||||
\(392\) | 23.7983 | − | 33.7190i | 1.20199 | − | 1.70307i | ||||
\(393\) | −18.7190 | −0.944251 | ||||||||
\(394\) | 41.7168 | 2.10166 | ||||||||
\(395\) | 10.4621i | 0.526404i | ||||||||
\(396\) | 4.91348i | 0.246911i | ||||||||
\(397\) | 27.5109i | 1.38073i | 0.723460 | + | 0.690366i | \(0.242550\pi\) | ||||
−0.723460 | + | 0.690366i | \(0.757450\pi\) | |||||||
\(398\) | 23.3731 | 1.17159 | ||||||||
\(399\) | 1.37772 | + | 2.65868i | 0.0689724 | + | 0.133100i | ||||
\(400\) | −21.6878 | −1.08439 | ||||||||
\(401\) | − | 15.1679i | − | 0.757450i | −0.925509 | − | 0.378725i | \(-0.876363\pi\) | ||
0.925509 | − | 0.378725i | \(-0.123637\pi\) | |||||||
\(402\) | 9.19615 | 0.458662 | ||||||||
\(403\) | −3.55460 | −0.177067 | ||||||||
\(404\) | 38.5661i | 1.91874i | ||||||||
\(405\) | 1.21729 | 0.0604878 | ||||||||
\(406\) | 12.8772 | − | 6.67296i | 0.639085 | − | 0.331173i | ||||
\(407\) | 11.5422 | 0.572124 | ||||||||
\(408\) | 18.0733i | 0.894760i | ||||||||
\(409\) | − | 23.2861i | − | 1.15142i | −0.817653 | − | 0.575711i | \(-0.804725\pi\) | ||
0.817653 | − | 0.575711i | \(-0.195275\pi\) | |||||||
\(410\) | 15.3269i | 0.756943i | ||||||||
\(411\) | −12.3027 | −0.606849 | ||||||||
\(412\) | 49.9293 | 2.45984 | ||||||||
\(413\) | −0.244491 | − | 0.471809i | −0.0120306 | − | 0.0232162i | ||||
\(414\) | 0.859523 | + | 12.0462i | 0.0422433 | + | 0.592040i | ||||
\(415\) | −14.1580 | −0.694990 | ||||||||
\(416\) | − | 1.93364i | − | 0.0948046i | ||||||
\(417\) | 13.7794 | 0.674781 | ||||||||
\(418\) | 3.22569i | 0.157774i | ||||||||
\(419\) | 5.31385 | 0.259598 | 0.129799 | − | 0.991540i | \(-0.458567\pi\) | ||||
0.129799 | + | 0.991540i | \(0.458567\pi\) | |||||||
\(420\) | −6.43298 | − | 12.4141i | −0.313897 | − | 0.605747i | ||||
\(421\) | 16.1136i | 0.785329i | 0.919682 | + | 0.392664i | \(0.128447\pi\) | ||||
−0.919682 | + | 0.392664i | \(0.871553\pi\) | |||||||
\(422\) | 20.0539 | 0.976210 | ||||||||
\(423\) | 4.21327i | 0.204856i | ||||||||
\(424\) | 31.9233i | 1.55033i | ||||||||
\(425\) | −10.7846 | −0.523132 | ||||||||
\(426\) | 5.45052i | 0.264078i | ||||||||
\(427\) | −14.6025 | + | 7.56702i | −0.706667 | + | 0.366194i | ||||
\(428\) | − | 11.6307i | − | 0.562193i | ||||||
\(429\) | − | 0.586493i | − | 0.0283162i | ||||||
\(430\) | − | 20.5910i | − | 0.992986i | ||||||
\(431\) | − | 11.4274i | − | 0.550441i | −0.961381 | − | 0.275220i | \(-0.911249\pi\) | ||
0.961381 | − | 0.275220i | \(-0.0887508\pi\) | |||||||
\(432\) | − | 6.16445i | − | 0.296587i | ||||||
\(433\) | −13.5351 | −0.650458 | −0.325229 | − | 0.945635i | \(-0.605441\pi\) | ||||
−0.325229 | + | 0.945635i | \(0.605441\pi\) | |||||||
\(434\) | 21.0271 | + | 40.5772i | 1.00933 | + | 1.94777i | ||||
\(435\) | − | 2.64989i | − | 0.127053i | ||||||
\(436\) | − | 77.0428i | − | 3.68968i | ||||||
\(437\) | 0.386309 | + | 5.41412i | 0.0184796 | + | 0.258992i | ||||
\(438\) | −25.7481 | −1.23029 | ||||||||
\(439\) | − | 36.0415i | − | 1.72017i | −0.510153 | − | 0.860084i | \(-0.670411\pi\) | ||
0.510153 | − | 0.860084i | \(-0.329589\pi\) | |||||||
\(440\) | − | 8.12294i | − | 0.387246i | ||||||
\(441\) | −4.03640 | + | 5.71905i | −0.192209 | + | 0.272336i | ||||
\(442\) | − | 4.00010i | − | 0.190266i | ||||||
\(443\) | −32.8034 | −1.55854 | −0.779268 | − | 0.626691i | \(-0.784409\pi\) | ||||
−0.779268 | + | 0.626691i | \(0.784409\pi\) | |||||||
\(444\) | −44.2734 | −2.10112 | ||||||||
\(445\) | 6.22482 | 0.295085 | ||||||||
\(446\) | − | 53.1259i | − | 2.51558i | ||||||
\(447\) | 8.46473 | 0.400368 | ||||||||
\(448\) | 6.88826 | − | 3.56949i | 0.325440 | − | 0.168643i | ||||
\(449\) | −20.7430 | −0.978924 | −0.489462 | − | 0.872025i | \(-0.662807\pi\) | ||||
−0.489462 | + | 0.872025i | \(0.662807\pi\) | |||||||
\(450\) | 8.85952 | 0.417642 | ||||||||
\(451\) | 5.65896 | 0.266470 | ||||||||
\(452\) | 9.63461i | 0.453174i | ||||||||
\(453\) | 17.5786i | 0.825913i | ||||||||
\(454\) | 62.6506 | 2.94034 | ||||||||
\(455\) | 0.767868 | + | 1.48180i | 0.0359982 | + | 0.0694679i | ||||
\(456\) | − | 6.67296i | − | 0.312490i | ||||||
\(457\) | 3.13887i | 0.146830i | 0.997301 | + | 0.0734152i | \(0.0233898\pi\) | ||||
−0.997301 | + | 0.0734152i | \(0.976610\pi\) | |||||||
\(458\) | −49.1275 | −2.29558 | ||||||||
\(459\) | − | 3.06538i | − | 0.143080i | ||||||
\(460\) | −1.80379 | − | 25.2801i | −0.0841019 | − | 1.17869i | ||||
\(461\) | − | 39.0094i | − | 1.81685i | −0.418051 | − | 0.908423i | \(-0.637287\pi\) | ||
0.418051 | − | 0.908423i | \(-0.362713\pi\) | |||||||
\(462\) | −6.69507 | + | 3.46938i | −0.311483 | + | 0.161410i | ||||
\(463\) | −20.2299 | −0.940165 | −0.470082 | − | 0.882623i | \(-0.655776\pi\) | ||||
−0.470082 | + | 0.882623i | \(0.655776\pi\) | |||||||
\(464\) | −13.4192 | −0.622972 | ||||||||
\(465\) | 8.35005 | 0.387224 | ||||||||
\(466\) | −21.0051 | −0.973043 | ||||||||
\(467\) | −12.4617 | −0.576660 | −0.288330 | − | 0.957531i | \(-0.593100\pi\) | ||||
−0.288330 | + | 0.957531i | \(0.593100\pi\) | |||||||
\(468\) | 2.24967i | 0.103991i | ||||||||
\(469\) | 4.44540 | + | 8.57857i | 0.205270 | + | 0.396122i | ||||
\(470\) | − | 12.9153i | − | 0.595738i | ||||||
\(471\) | 18.6337i | 0.858595i | ||||||||
\(472\) | 1.18418i | 0.0545065i | ||||||||
\(473\) | −7.60254 | −0.349565 | ||||||||
\(474\) | −21.6428 | −0.994085 | ||||||||
\(475\) | 3.98187 | 0.182701 | ||||||||
\(476\) | −31.2612 | + | 16.1995i | −1.43286 | + | 0.742504i | ||||
\(477\) | − | 5.41447i | − | 0.247912i | ||||||
\(478\) | −53.8334 | −2.46228 | ||||||||
\(479\) | −25.2363 | −1.15307 | −0.576537 | − | 0.817071i | \(-0.695596\pi\) | ||||
−0.576537 | + | 0.817071i | \(0.695596\pi\) | |||||||
\(480\) | 4.54229i | 0.207326i | ||||||||
\(481\) | 5.28466 | 0.240960 | ||||||||
\(482\) | 22.3268 | 1.01696 | ||||||||
\(483\) | −10.8218 | + | 6.62493i | −0.492407 | + | 0.301445i | ||||
\(484\) | 42.1935 | 1.91789 | ||||||||
\(485\) | −22.1083 | −1.00389 | ||||||||
\(486\) | 2.51820i | 0.114228i | ||||||||
\(487\) | −19.0531 | −0.863377 | −0.431688 | − | 0.902023i | \(-0.642082\pi\) | ||||
−0.431688 | + | 0.902023i | \(0.642082\pi\) | |||||||
\(488\) | 36.6506 | 1.65910 | ||||||||
\(489\) | 7.23725i | 0.327280i | ||||||||
\(490\) | 12.3731 | − | 17.5311i | 0.558960 | − | 0.791973i | ||||
\(491\) | −12.8471 | −0.579782 | −0.289891 | − | 0.957060i | \(-0.593619\pi\) | ||||
−0.289891 | + | 0.957060i | \(0.593619\pi\) | |||||||
\(492\) | −21.7066 | −0.978610 | ||||||||
\(493\) | −6.67296 | −0.300535 | ||||||||
\(494\) | 1.47691i | 0.0664492i | ||||||||
\(495\) | 1.37772i | 0.0619240i | ||||||||
\(496\) | − | 42.2852i | − | 1.89866i | ||||||
\(497\) | −5.08448 | + | 2.63477i | −0.228070 | + | 0.118186i | ||||
\(498\) | − | 29.2885i | − | 1.31245i | ||||||
\(499\) | −8.62228 | −0.385986 | −0.192993 | − | 0.981200i | \(-0.561819\pi\) | ||||
−0.192993 | + | 0.981200i | \(0.561819\pi\) | |||||||
\(500\) | −45.0158 | −2.01317 | ||||||||
\(501\) | −17.8282 | −0.796507 | ||||||||
\(502\) | −32.9696 | −1.47150 | ||||||||
\(503\) | 3.30988 | 0.147580 | 0.0737900 | − | 0.997274i | \(-0.476491\pi\) | ||||
0.0737900 | + | 0.997274i | \(0.476491\pi\) | |||||||
\(504\) | 13.8500 | − | 7.17706i | 0.616929 | − | 0.319692i | ||||
\(505\) | 10.8138i | 0.481208i | ||||||||
\(506\) | −13.6338 | + | 0.972802i | −0.606098 | + | 0.0432463i | ||||
\(507\) | 12.7315i | 0.565424i | ||||||||
\(508\) | −11.8582 | −0.526122 | ||||||||
\(509\) | − | 8.92077i | − | 0.395406i | −0.980262 | − | 0.197703i | \(-0.936652\pi\) | ||
0.980262 | − | 0.197703i | \(-0.0633482\pi\) | |||||||
\(510\) | 9.39658i | 0.416088i | ||||||||
\(511\) | −12.4466 | − | 24.0190i | −0.550605 | − | 1.06254i | ||||
\(512\) | −49.6878 | −2.19591 | ||||||||
\(513\) | 1.13179i | 0.0499698i | ||||||||
\(514\) | − | 35.0218i | − | 1.54474i | ||||||
\(515\) | 14.0000 | 0.616914 | ||||||||
\(516\) | 29.1618 | 1.28378 | ||||||||
\(517\) | −4.76855 | −0.209720 | ||||||||
\(518\) | −31.2612 | − | 60.3267i | −1.37354 | − | 2.65060i | ||||
\(519\) | −20.2248 | −0.887771 | ||||||||
\(520\) | − | 3.71914i | − | 0.163095i | ||||||
\(521\) | 42.6255 | 1.86746 | 0.933729 | − | 0.357980i | \(-0.116535\pi\) | ||||
0.933729 | + | 0.357980i | \(0.116535\pi\) | |||||||
\(522\) | 5.48180 | 0.239932 | ||||||||
\(523\) | 20.5553 | 0.898819 | 0.449410 | − | 0.893326i | \(-0.351634\pi\) | ||||
0.449410 | + | 0.893326i | \(0.351634\pi\) | |||||||
\(524\) | 81.2655i | 3.55010i | ||||||||
\(525\) | 4.28268 | + | 8.26455i | 0.186911 | + | 0.360694i | ||||
\(526\) | 59.9121i | 2.61229i | ||||||||
\(527\) | − | 21.0271i | − | 0.915954i | ||||||
\(528\) | 6.97688 | 0.303630 | ||||||||
\(529\) | −22.7670 | + | 3.26557i | −0.989869 | + | 0.141981i | ||||
\(530\) | 16.5974i | 0.720946i | ||||||||
\(531\) | − | 0.200848i | − | 0.00871606i | ||||||
\(532\) | 11.5422 | − | 5.98114i | 0.500417 | − | 0.259315i | ||||
\(533\) | 2.59099 | 0.112228 | ||||||||
\(534\) | 12.8772i | 0.557252i | ||||||||
\(535\) | − | 3.26122i | − | 0.140995i | ||||||
\(536\) | − | 21.5312i | − | 0.930005i | ||||||
\(537\) | − | 10.4141i | − | 0.449402i | ||||||
\(538\) | − | 14.5118i | − | 0.625646i | ||||||
\(539\) | −6.47277 | − | 4.56836i | −0.278802 | − | 0.196773i | ||||
\(540\) | − | 5.28466i | − | 0.227416i | ||||||
\(541\) | 5.98027 | 0.257112 | 0.128556 | − | 0.991702i | \(-0.458966\pi\) | ||||
0.128556 | + | 0.991702i | \(0.458966\pi\) | |||||||
\(542\) | − | 29.0655i | − | 1.24847i | ||||||
\(543\) | − | 14.0653i | − | 0.603601i | ||||||
\(544\) | 11.4384 | 0.490417 | ||||||||
\(545\) | − | 21.6025i | − | 0.925351i | ||||||
\(546\) | −3.06538 | + | 1.58848i | −0.131186 | + | 0.0679806i | ||||
\(547\) | 4.06037 | 0.173609 | 0.0868045 | − | 0.996225i | \(-0.472334\pi\) | ||||
0.0868045 | + | 0.996225i | \(0.472334\pi\) | |||||||
\(548\) | 53.4102i | 2.28157i | ||||||||
\(549\) | −6.21627 | −0.265304 | ||||||||
\(550\) | 10.0271i | 0.427559i | ||||||||
\(551\) | 2.46377 | 0.104960 | ||||||||
\(552\) | 28.2041 | − | 2.01242i | 1.20045 | − | 0.0856544i | ||||
\(553\) | −10.4621 | − | 20.1893i | −0.444892 | − | 0.858536i | ||||
\(554\) | 61.8753 | 2.62883 | ||||||||
\(555\) | −12.4141 | −0.526950 | ||||||||
\(556\) | − | 59.8209i | − | 2.53697i | ||||||
\(557\) | − | 2.49295i | − | 0.105630i | −0.998604 | − | 0.0528149i | \(-0.983181\pi\) | ||
0.998604 | − | 0.0528149i | \(-0.0168193\pi\) | |||||||
\(558\) | 17.2736i | 0.731252i | ||||||||
\(559\) | −3.48088 | −0.147225 | ||||||||
\(560\) | −17.6274 | + | 9.13449i | −0.744893 | + | 0.386003i | ||||
\(561\) | 3.46938 | 0.146477 | ||||||||
\(562\) | − | 42.0542i | − | 1.77395i | ||||||
\(563\) | 0.846107 | 0.0356592 | 0.0178296 | − | 0.999841i | \(-0.494324\pi\) | ||||
0.0178296 | + | 0.999841i | \(0.494324\pi\) | |||||||
\(564\) | 18.2912 | 0.770198 | ||||||||
\(565\) | 2.70151i | 0.113653i | ||||||||
\(566\) | −30.7654 | −1.29317 | ||||||||
\(567\) | −2.34908 | + | 1.21729i | −0.0986523 | + | 0.0511215i | ||||
\(568\) | 12.7614 | 0.535458 | ||||||||
\(569\) | − | 40.2916i | − | 1.68911i | −0.535469 | − | 0.844555i | \(-0.679865\pi\) | ||
0.535469 | − | 0.844555i | \(-0.320135\pi\) | |||||||
\(570\) | − | 3.46938i | − | 0.145316i | ||||||
\(571\) | 38.1275i | 1.59559i | 0.602930 | + | 0.797794i | \(0.294000\pi\) | ||||
−0.602930 | + | 0.797794i | \(0.706000\pi\) | |||||||
\(572\) | −2.54616 | −0.106460 | ||||||||
\(573\) | −12.3319 | −0.515173 | ||||||||
\(574\) | −15.3269 | − | 29.5773i | −0.639733 | − | 1.23453i | ||||
\(575\) | 1.20085 | + | 16.8299i | 0.0500788 | + | 0.701855i | ||||
\(576\) | 2.93232 | 0.122180 | ||||||||
\(577\) | 23.7918i | 0.990467i | 0.868760 | + | 0.495234i | \(0.164918\pi\) | ||||
−0.868760 | + | 0.495234i | \(0.835082\pi\) | |||||||
\(578\) | −19.1469 | −0.796407 | ||||||||
\(579\) | − | 3.17687i | − | 0.132026i | ||||||
\(580\) | −11.5040 | −0.477679 | ||||||||
\(581\) | 27.3216 | − | 14.1580i | 1.13349 | − | 0.587373i | ||||
\(582\) | − | 45.7352i | − | 1.89579i | ||||||
\(583\) | 6.12805 | 0.253798 | ||||||||
\(584\) | 60.2847i | 2.49460i | ||||||||
\(585\) | 0.630799i | 0.0260803i | ||||||||
\(586\) | −55.5470 | −2.29463 | ||||||||
\(587\) | − | 16.3049i | − | 0.672976i | −0.941688 | − | 0.336488i | \(-0.890761\pi\) | ||
0.941688 | − | 0.336488i | \(-0.109239\pi\) | |||||||
\(588\) | 24.8282 | + | 17.5233i | 1.02390 | + | 0.722649i | ||||
\(589\) | 7.76355i | 0.319892i | ||||||||
\(590\) | 0.615677i | 0.0253470i | ||||||||
\(591\) | 16.5661i | 0.681440i | ||||||||
\(592\) | 62.8659i | 2.58377i | ||||||||
\(593\) | − | 3.57346i | − | 0.146744i | −0.997305 | − | 0.0733721i | \(-0.976624\pi\) | ||
0.997305 | − | 0.0733721i | \(-0.0233761\pi\) | |||||||
\(594\) | −2.85008 | −0.116940 | ||||||||
\(595\) | −8.76554 | + | 4.54229i | −0.359352 | + | 0.186216i | ||||
\(596\) | − | 36.7481i | − | 1.50526i | ||||||
\(597\) | 9.28165i | 0.379873i | ||||||||
\(598\) | −6.24234 | + | 0.445404i | −0.255268 | + | 0.0182139i | ||||
\(599\) | −16.3100 | −0.666410 | −0.333205 | − | 0.942854i | \(-0.608130\pi\) | ||||
−0.333205 | + | 0.942854i | \(0.608130\pi\) | |||||||
\(600\) | − | 20.7430i | − | 0.846830i | ||||||
\(601\) | 21.8771i | 0.892384i | 0.894937 | + | 0.446192i | \(0.147220\pi\) | ||||
−0.894937 | + | 0.446192i | \(0.852780\pi\) | |||||||
\(602\) | 20.5910 | + | 39.7357i | 0.839226 | + | 1.61951i | ||||
\(603\) | 3.65188i | 0.148716i | ||||||||
\(604\) | 76.3143 | 3.10518 | ||||||||
\(605\) | 11.8309 | 0.480995 | ||||||||
\(606\) | −22.3704 | −0.908736 | ||||||||
\(607\) | − | 17.8355i | − | 0.723923i | −0.932193 | − | 0.361961i | \(-0.882107\pi\) | ||
0.932193 | − | 0.361961i | \(-0.117893\pi\) | |||||||
\(608\) | −4.22325 | −0.171275 | ||||||||
\(609\) | 2.64989 | + | 5.11366i | 0.107379 | + | 0.207216i | ||||
\(610\) | 19.0553 | 0.771525 | ||||||||
\(611\) | −2.18331 | −0.0883273 | ||||||||
\(612\) | −13.3078 | −0.537937 | ||||||||
\(613\) | − | 28.6488i | − | 1.15711i | −0.815642 | − | 0.578557i | \(-0.803616\pi\) | ||
0.815642 | − | 0.578557i | \(-0.196384\pi\) | |||||||
\(614\) | 50.4059i | 2.03422i | ||||||||
\(615\) | −6.08646 | −0.245430 | ||||||||
\(616\) | 8.12294 | + | 15.6753i | 0.327283 | + | 0.631577i | ||||
\(617\) | 30.6387i | 1.23347i | 0.787171 | + | 0.616734i | \(0.211545\pi\) | ||||
−0.787171 | + | 0.616734i | \(0.788455\pi\) | |||||||
\(618\) | 28.9616i | 1.16501i | ||||||||
\(619\) | 27.1135 | 1.08979 | 0.544893 | − | 0.838506i | \(-0.316570\pi\) | ||||
0.544893 | + | 0.838506i | \(0.316570\pi\) | |||||||
\(620\) | − | 36.2503i | − | 1.45585i | ||||||
\(621\) | −4.78367 | + | 0.341325i | −0.191962 | + | 0.0136969i | ||||
\(622\) | − | 39.6441i | − | 1.58958i | ||||||
\(623\) | −12.0124 | + | 6.22482i | −0.481268 | + | 0.249392i | ||||
\(624\) | 3.19441 | 0.127879 | ||||||||
\(625\) | 4.96872 | 0.198749 | ||||||||
\(626\) | 21.3159 | 0.851954 | ||||||||
\(627\) | −1.28095 | −0.0511563 | ||||||||
\(628\) | 80.8949 | 3.22806 | ||||||||
\(629\) | 31.2612i | 1.24647i | ||||||||
\(630\) | 7.20085 | − | 3.73147i | 0.286889 | − | 0.148665i | ||||
\(631\) | − | 39.5904i | − | 1.57607i | −0.615631 | − | 0.788034i | \(-0.711099\pi\) | ||
0.615631 | − | 0.788034i | \(-0.288901\pi\) | |||||||
\(632\) | 50.6727i | 2.01565i | ||||||||
\(633\) | 7.96360i | 0.316525i | ||||||||
\(634\) | 70.7823 | 2.81113 | ||||||||
\(635\) | −3.32500 | −0.131949 | ||||||||
\(636\) | −23.5060 | −0.932072 | ||||||||
\(637\) | −2.96360 | − | 2.09166i | −0.117422 | − | 0.0828744i | ||||
\(638\) | 6.20426i | 0.245629i | ||||||||
\(639\) | −2.16445 | −0.0856243 | ||||||||
\(640\) | −18.0733 | −0.714409 | ||||||||
\(641\) | 27.2725i | 1.07720i | 0.842562 | + | 0.538600i | \(0.181047\pi\) | ||||
−0.842562 | + | 0.538600i | \(0.818953\pi\) | |||||||
\(642\) | 6.74645 | 0.266261 | ||||||||
\(643\) | −32.3127 | −1.27429 | −0.637144 | − | 0.770745i | \(-0.719884\pi\) | ||||
−0.637144 | + | 0.770745i | \(0.719884\pi\) | |||||||
\(644\) | 28.7610 | + | 46.9807i | 1.13334 | + | 1.85130i | ||||
\(645\) | 8.17687 | 0.321964 | ||||||||
\(646\) | −8.73658 | −0.343736 | ||||||||
\(647\) | 1.89168i | 0.0743696i | 0.999308 | + | 0.0371848i | \(0.0118390\pi\) | ||||
−0.999308 | + | 0.0371848i | \(0.988161\pi\) | |||||||
\(648\) | 5.89592 | 0.231614 | ||||||||
\(649\) | 0.227318 | 0.00892302 | ||||||||
\(650\) | 4.59099i | 0.180074i | ||||||||
\(651\) | −16.1136 | + | 8.35005i | −0.631542 | + | 0.327264i | ||||
\(652\) | 31.4192 | 1.23047 | ||||||||
\(653\) | 39.2903 | 1.53755 | 0.768774 | − | 0.639520i | \(-0.220867\pi\) | ||||
0.768774 | + | 0.639520i | \(0.220867\pi\) | |||||||
\(654\) | 44.6889 | 1.74748 | ||||||||
\(655\) | 22.7866i | 0.890344i | ||||||||
\(656\) | 30.8223i | 1.20341i | ||||||||
\(657\) | − | 10.2248i | − | 0.398908i | ||||||
\(658\) | 12.9153 | + | 24.9234i | 0.503491 | + | 0.971617i | ||||
\(659\) | − | 22.8600i | − | 0.890501i | −0.895406 | − | 0.445251i | \(-0.853115\pi\) | ||
0.895406 | − | 0.445251i | \(-0.146885\pi\) | |||||||
\(660\) | 5.98114 | 0.232816 | ||||||||
\(661\) | 46.0209 | 1.79001 | 0.895003 | − | 0.446060i | \(-0.147173\pi\) | ||||
0.895003 | + | 0.446060i | \(0.147173\pi\) | |||||||
\(662\) | −23.2299 | −0.902857 | ||||||||
\(663\) | 1.58848 | 0.0616914 | ||||||||
\(664\) | −68.5739 | −2.66118 | ||||||||
\(665\) | 3.23639 | − | 1.67709i | 0.125502 | − | 0.0650348i | ||||
\(666\) | − | 25.6809i | − | 0.995116i | ||||||
\(667\) | 0.743021 | + | 10.4134i | 0.0287699 | + | 0.403210i | ||||
\(668\) | 77.3982i | 2.99463i | ||||||||
\(669\) | 21.0968 | 0.815648 | ||||||||
\(670\) | − | 11.1944i | − | 0.432478i | ||||||
\(671\) | − | 7.03552i | − | 0.271603i | ||||||
\(672\) | −4.54229 | − | 8.76554i | −0.175223 | − | 0.338138i | ||||
\(673\) | −11.6347 | −0.448485 | −0.224242 | − | 0.974533i | \(-0.571991\pi\) | ||||
−0.224242 | + | 0.974533i | \(0.571991\pi\) | |||||||
\(674\) | − | 35.4547i | − | 1.36566i | ||||||
\(675\) | 3.51820i | 0.135416i | ||||||||
\(676\) | 55.2714 | 2.12582 | ||||||||
\(677\) | 36.8519 | 1.41633 | 0.708166 | − | 0.706046i | \(-0.249523\pi\) | ||||
0.708166 | + | 0.706046i | \(0.249523\pi\) | |||||||
\(678\) | −5.58858 | −0.214628 | ||||||||
\(679\) | 42.6638 | − | 22.1083i | 1.63729 | − | 0.848439i | ||||
\(680\) | 22.0005 | 0.843679 | ||||||||
\(681\) | 24.8791i | 0.953371i | ||||||||
\(682\) | −19.5502 | −0.748615 | ||||||||
\(683\) | −20.6034 | −0.788368 | −0.394184 | − | 0.919032i | \(-0.628973\pi\) | ||||
−0.394184 | + | 0.919032i | \(0.628973\pi\) | |||||||
\(684\) | 4.91348 | 0.187871 | ||||||||
\(685\) | 14.9760i | 0.572205i | ||||||||
\(686\) | −6.34608 | + | 46.2039i | −0.242294 | + | 1.76407i | ||||
\(687\) | − | 19.5090i | − | 0.744314i | ||||||
\(688\) | − | 41.4082i | − | 1.57867i | ||||||
\(689\) | 2.80577 | 0.106891 | ||||||||
\(690\) | 14.6638 | − | 1.04629i | 0.558241 | − | 0.0398316i | ||||
\(691\) | 27.9314i | 1.06256i | 0.847196 | + | 0.531281i | \(0.178289\pi\) | ||||
−0.847196 | + | 0.531281i | \(0.821711\pi\) | |||||||
\(692\) | 87.8025i | 3.33775i | ||||||||
\(693\) | −1.37772 | − | 2.65868i | −0.0523353 | − | 0.100995i | ||||
\(694\) | −11.3464 | −0.430705 | ||||||||
\(695\) | − | 16.7736i | − | 0.636258i | ||||||
\(696\) | − | 12.8347i | − | 0.486497i | ||||||
\(697\) | 15.3269i | 0.580549i | ||||||||
\(698\) | − | 29.8462i | − | 1.12970i | ||||||
\(699\) | − | 8.34132i | − | 0.315498i | ||||||
\(700\) | 35.8791 | − | 18.5925i | 1.35610 | − | 0.702730i | ||||
\(701\) | 45.7180i | 1.72675i | 0.504566 | + | 0.863373i | \(0.331653\pi\) | ||||
−0.504566 | + | 0.863373i | \(0.668347\pi\) | |||||||
\(702\) | −1.30493 | −0.0492513 | ||||||||
\(703\) | − | 11.5422i | − | 0.435321i | ||||||
\(704\) | 3.31877i | 0.125081i | ||||||||
\(705\) | 5.12878 | 0.193161 | ||||||||
\(706\) | − | 60.4787i | − | 2.27615i | ||||||
\(707\) | −10.8138 | − | 20.8681i | −0.406695 | − | 0.784825i | ||||
\(708\) | −0.871947 | −0.0327698 | ||||||||
\(709\) | 15.4536i | 0.580373i | 0.956970 | + | 0.290186i | \(0.0937173\pi\) | ||||
−0.956970 | + | 0.290186i | \(0.906283\pi\) | |||||||
\(710\) | 6.63487 | 0.249002 | ||||||||
\(711\) | − | 8.59454i | − | 0.322320i | ||||||
\(712\) | 30.1497 | 1.12991 | ||||||||
\(713\) | −32.8137 | + | 2.34132i | −1.22888 | + | 0.0876833i | ||||
\(714\) | −9.39658 | − | 18.1332i | −0.351658 | − | 0.678617i | ||||
\(715\) | −0.713934 | −0.0266996 | ||||||||
\(716\) | −45.2111 | −1.68962 | ||||||||
\(717\) | − | 21.3777i | − | 0.798366i | ||||||
\(718\) | 3.06538i | 0.114399i | ||||||||
\(719\) | 23.3820i | 0.872000i | 0.899947 | + | 0.436000i | \(0.143605\pi\) | ||||
−0.899947 | + | 0.436000i | \(0.856395\pi\) | |||||||
\(720\) | −7.50394 | −0.279655 | ||||||||
\(721\) | −27.0167 | + | 14.0000i | −1.00615 | + | 0.521387i | ||||
\(722\) | −44.6201 | −1.66059 | ||||||||
\(723\) | 8.86616i | 0.329736i | ||||||||
\(724\) | −61.0621 | −2.26936 | ||||||||
\(725\) | 7.65868 | 0.284436 | ||||||||
\(726\) | 24.4745i | 0.908334i | ||||||||
\(727\) | −0.447787 | −0.0166075 | −0.00830376 | − | 0.999966i | \(-0.502643\pi\) | ||||
−0.00830376 | + | 0.999966i | \(0.502643\pi\) | |||||||
\(728\) | 3.71914 | + | 7.17706i | 0.137841 | + | 0.266000i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 31.3430i | 1.16006i | ||||||||
\(731\) | − | 20.5910i | − | 0.761585i | ||||||
\(732\) | 26.9868i | 0.997463i | ||||||||
\(733\) | 19.9959 | 0.738566 | 0.369283 | − | 0.929317i | \(-0.379603\pi\) | ||||
0.369283 | + | 0.929317i | \(0.379603\pi\) | |||||||
\(734\) | −27.0541 | −0.998585 | ||||||||
\(735\) | 6.96175 | + | 4.91348i | 0.256788 | + | 0.181236i | ||||
\(736\) | −1.27364 | − | 17.8501i | −0.0469471 | − | 0.657964i | ||||
\(737\) | −4.13317 | −0.152247 | ||||||||
\(738\) | − | 12.5910i | − | 0.463481i | ||||||
\(739\) | −18.8449 | −0.693221 | −0.346610 | − | 0.938009i | \(-0.612667\pi\) | ||||
−0.346610 | + | 0.938009i | \(0.612667\pi\) | |||||||
\(740\) | 53.8937i | 1.98117i | ||||||||
\(741\) | −0.586493 | −0.0215454 | ||||||||
\(742\) | −16.5974 | − | 32.0291i | −0.609311 | − | 1.17582i | ||||
\(743\) | − | 4.81285i | − | 0.176566i | −0.996095 | − | 0.0882832i | \(-0.971862\pi\) | ||
0.996095 | − | 0.0882832i | \(-0.0281381\pi\) | |||||||
\(744\) | 40.4432 | 1.48272 | ||||||||
\(745\) | − | 10.3041i | − | 0.377511i | ||||||
\(746\) | − | 71.3427i | − | 2.61204i | ||||||
\(747\) | 11.6307 | 0.425546 | ||||||||
\(748\) | − | 15.0617i | − | 0.550710i | ||||||
\(749\) | 3.26122 | + | 6.29338i | 0.119162 | + | 0.229955i | ||||
\(750\) | − | 26.1116i | − | 0.953459i | ||||||
\(751\) | − | 40.5772i | − | 1.48068i | −0.672230 | − | 0.740342i | \(-0.734663\pi\) | ||
0.672230 | − | 0.740342i | \(-0.265337\pi\) | |||||||
\(752\) | − | 25.9725i | − | 0.947120i | ||||||
\(753\) | − | 13.0925i | − | 0.477118i | ||||||
\(754\) | 2.84066i | 0.103451i | ||||||||
\(755\) | 21.3983 | 0.778763 | ||||||||
\(756\) | 5.28466 | + | 10.1981i | 0.192201 | + | 0.370903i | ||||
\(757\) | − | 39.0471i | − | 1.41919i | −0.704609 | − | 0.709596i | \(-0.748877\pi\) | ||
0.704609 | − | 0.709596i | \(-0.251123\pi\) | |||||||
\(758\) | − | 12.2615i | − | 0.445359i | ||||||
\(759\) | −0.386309 | − | 5.41412i | −0.0140221 | − | 0.196520i | ||||
\(760\) | −8.12294 | −0.294650 | ||||||||
\(761\) | − | 40.8959i | − | 1.48248i | −0.671242 | − | 0.741238i | \(-0.734239\pi\) | ||
0.671242 | − | 0.741238i | \(-0.265761\pi\) | |||||||
\(762\) | − | 6.87838i | − | 0.249178i | ||||||
\(763\) | 21.6025 | + | 41.6878i | 0.782065 | + | 1.50920i | ||||
\(764\) | 53.5369i | 1.93690i | ||||||||
\(765\) | −3.73147 | −0.134912 | ||||||||
\(766\) | 87.2118 | 3.15109 | ||||||||
\(767\) | 0.104079 | 0.00375808 | ||||||||
\(768\) | − | 31.5233i | − | 1.13750i | ||||||
\(769\) | −28.8730 | −1.04119 | −0.520594 | − | 0.853804i | \(-0.674289\pi\) | ||||
−0.520594 | + | 0.853804i | \(0.674289\pi\) | |||||||
\(770\) | 4.22325 | + | 8.14986i | 0.152195 | + | 0.293701i | ||||
\(771\) | 13.9075 | 0.500865 | ||||||||
\(772\) | −13.7918 | −0.496379 | ||||||||
\(773\) | −23.7213 | −0.853195 | −0.426598 | − | 0.904442i | \(-0.640288\pi\) | ||||
−0.426598 | + | 0.904442i | \(0.640288\pi\) | |||||||
\(774\) | 16.9154i | 0.608012i | ||||||||
\(775\) | 24.1332i | 0.866889i | ||||||||
\(776\) | −107.081 | −3.84398 | ||||||||
\(777\) | 23.9563 | − | 12.4141i | 0.859427 | − | 0.445354i | ||||
\(778\) | 29.2885i | 1.05004i | ||||||||
\(779\) | − | 5.65896i | − | 0.202753i | ||||||
\(780\) | 2.73851 | 0.0980542 | ||||||||
\(781\) | − | 2.44971i | − | 0.0876574i | ||||||
\(782\) | −2.63477 | − | 36.9263i | −0.0942192 | − | 1.32048i | ||||
\(783\) | 2.17687i | 0.0777951i | ||||||||
\(784\) | 24.8822 | − | 35.2548i | 0.888649 | − | 1.25910i | ||||
\(785\) | 22.6826 | 0.809578 | ||||||||
\(786\) | −47.1383 | −1.68137 | ||||||||
\(787\) | −33.2615 | −1.18564 | −0.592822 | − | 0.805334i | \(-0.701986\pi\) | ||||
−0.592822 | + | 0.805334i | \(0.701986\pi\) | |||||||
\(788\) | 71.9190 | 2.56201 | ||||||||
\(789\) | −23.7917 | −0.847005 | ||||||||
\(790\) | 26.3456i | 0.937333i | ||||||||
\(791\) | −2.70151 | − | 5.21327i | −0.0960547 | − | 0.185363i | ||||
\(792\) | 6.67296i | 0.237113i | ||||||||
\(793\) | − | 3.22126i | − | 0.114390i | ||||||
\(794\) | 69.2779i | 2.45858i | ||||||||
\(795\) | −6.59099 | −0.233758 | ||||||||
\(796\) | 40.2947 | 1.42821 | ||||||||
\(797\) | −9.62571 | −0.340960 | −0.170480 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170480 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(798\) | 3.46938 | + | 6.69507i | 0.122815 | + | 0.237003i | ||||
\(799\) | − | 12.9153i | − | 0.456910i | ||||||
\(800\) | −13.1281 | −0.464147 | ||||||||
\(801\) | −5.11366 | −0.180682 | ||||||||
\(802\) | − | 38.1959i | − | 1.34874i | ||||||
\(803\) | 11.5724 | 0.408380 | ||||||||
\(804\) | 15.8540 | 0.559127 | ||||||||
\(805\) | 8.06447 | + | 13.1732i | 0.284235 | + | 0.464296i | ||||
\(806\) | −8.95118 | −0.315292 | ||||||||
\(807\) | 5.76275 | 0.202859 | ||||||||
\(808\) | 52.3764i | 1.84260i | ||||||||
\(809\) | 20.6869 | 0.727312 | 0.363656 | − | 0.931533i | \(-0.381528\pi\) | ||||
0.363656 | + | 0.931533i | \(0.381528\pi\) | |||||||
\(810\) | 3.06538 | 0.107707 | ||||||||
\(811\) | 2.81158i | 0.0987278i | 0.998781 | + | 0.0493639i | \(0.0157194\pi\) | ||||
−0.998781 | + | 0.0493639i | \(0.984281\pi\) | |||||||
\(812\) | 22.2001 | − | 11.5040i | 0.779070 | − | 0.403713i | ||||
\(813\) | 11.5422 | 0.404802 | ||||||||
\(814\) | 29.0655 | 1.01874 | ||||||||
\(815\) | 8.80985 | 0.308595 | ||||||||
\(816\) | 18.8964i | 0.661507i | ||||||||
\(817\) | 7.60254i | 0.265979i | ||||||||
\(818\) | − | 58.6389i | − | 2.05026i | ||||||
\(819\) | −0.630799 | − | 1.21729i | −0.0220419 | − | 0.0425356i | ||||
\(820\) | 26.4233i | 0.922742i | ||||||||
\(821\) | 39.1092 | 1.36492 | 0.682460 | − | 0.730923i | \(-0.260910\pi\) | ||||
0.682460 | + | 0.730923i | \(0.260910\pi\) | |||||||
\(822\) | −30.9807 | −1.08058 | ||||||||
\(823\) | 34.8689 | 1.21545 | 0.607726 | − | 0.794147i | \(-0.292082\pi\) | ||||
0.607726 | + | 0.794147i | \(0.292082\pi\) | |||||||
\(824\) | 67.8086 | 2.36222 | ||||||||
\(825\) | −3.98187 | −0.138631 | ||||||||
\(826\) | −0.615677 | − | 1.18811i | −0.0214221 | − | 0.0413396i | ||||
\(827\) | 56.4343i | 1.96241i | 0.192957 | + | 0.981207i | \(0.438192\pi\) | ||||
−0.192957 | + | 0.981207i | \(0.561808\pi\) | |||||||
\(828\) | 1.48180 | + | 20.7675i | 0.0514962 | + | 0.721719i | ||||
\(829\) | 49.9687i | 1.73549i | 0.497014 | + | 0.867743i | \(0.334430\pi\) | ||||
−0.497014 | + | 0.867743i | \(0.665570\pi\) | |||||||
\(830\) | −35.6527 | −1.23752 | ||||||||
\(831\) | 24.5713i | 0.852368i | ||||||||
\(832\) | 1.51952i | 0.0526800i | ||||||||
\(833\) | 12.3731 | − | 17.5311i | 0.428703 | − | 0.607416i | ||||
\(834\) | 34.6993 | 1.20154 | ||||||||
\(835\) | 21.7022i | 0.751035i | ||||||||
\(836\) | 5.56103i | 0.192332i | ||||||||
\(837\) | −6.85952 | −0.237100 | ||||||||
\(838\) | 13.3813 | 0.462250 | ||||||||
\(839\) | −10.4958 | −0.362356 | −0.181178 | − | 0.983450i | \(-0.557991\pi\) | ||||
−0.181178 | + | 0.983450i | \(0.557991\pi\) | |||||||
\(840\) | −8.73658 | − | 16.8595i | −0.301441 | − | 0.581709i | ||||
\(841\) | −24.2612 | −0.836594 | ||||||||
\(842\) | 40.5772i | 1.39838i | ||||||||
\(843\) | 16.7001 | 0.575182 | ||||||||
\(844\) | 34.5726 | 1.19004 | ||||||||
\(845\) | 15.4979 | 0.533145 | ||||||||
\(846\) | 10.6099i | 0.364774i | ||||||||
\(847\) | −22.8309 | + | 11.8309i | −0.784478 | + | 0.406515i | ||||
\(848\) | 33.3772i | 1.14618i | ||||||||
\(849\) | − | 12.2172i | − | 0.419294i | ||||||
\(850\) | −27.1578 | −0.931506 | ||||||||
\(851\) | 48.7845 | − | 3.48088i | 1.67231 | − | 0.119323i | ||||
\(852\) | 9.39658i | 0.321922i | ||||||||
\(853\) | 40.7803i | 1.39629i | 0.715956 | + | 0.698145i | \(0.245991\pi\) | ||||
−0.715956 | + | 0.698145i | \(0.754009\pi\) | |||||||
\(854\) | −36.7721 | + | 19.0553i | −1.25832 | + | 0.652058i | ||||
\(855\) | 1.37772 | 0.0471171 | ||||||||
\(856\) | − | 15.7956i | − | 0.539883i | ||||||
\(857\) | − | 22.6150i | − | 0.772513i | −0.922392 | − | 0.386256i | \(-0.873768\pi\) | ||
0.922392 | − | 0.386256i | \(-0.126232\pi\) | |||||||
\(858\) | − | 1.47691i | − | 0.0504208i | ||||||
\(859\) | − | 35.5983i | − | 1.21460i | −0.794473 | − | 0.607299i | \(-0.792253\pi\) | ||
0.794473 | − | 0.607299i | \(-0.207747\pi\) | |||||||
\(860\) | − | 35.4985i | − | 1.21049i | ||||||
\(861\) | 11.7454 | − | 6.08646i | 0.400283 | − | 0.207426i | ||||
\(862\) | − | 28.7766i | − | 0.980134i | ||||||
\(863\) | 34.8282 | 1.18557 | 0.592784 | − | 0.805362i | \(-0.298029\pi\) | ||||
0.592784 | + | 0.805362i | \(0.298029\pi\) | |||||||
\(864\) | − | 3.73147i | − | 0.126947i | ||||||
\(865\) | 24.6195i | 0.837089i | ||||||||
\(866\) | −34.0842 | −1.15823 | ||||||||
\(867\) | − | 7.60342i | − | 0.258226i | ||||||
\(868\) | 36.2503 | + | 69.9544i | 1.23041 | + | 2.37441i | ||||
\(869\) | 9.72723 | 0.329974 | ||||||||
\(870\) | − | 6.67296i | − | 0.226234i | ||||||
\(871\) | −1.89240 | −0.0641215 | ||||||||
\(872\) | − | 104.631i | − | 3.54326i | ||||||
\(873\) | 18.1619 | 0.614686 | ||||||||
\(874\) | 0.972802 | + | 13.6338i | 0.0329055 | + | 0.461171i | ||||
\(875\) | 24.3580 | − | 12.6223i | 0.823450 | − | 0.426711i | ||||
\(876\) | −44.3893 | −1.49977 | ||||||||
\(877\) | 45.2350 | 1.52748 | 0.763740 | − | 0.645525i | \(-0.223361\pi\) | ||||
0.763740 | + | 0.645525i | \(0.223361\pi\) | |||||||
\(878\) | − | 90.7597i | − | 3.06299i | ||||||
\(879\) | − | 22.0582i | − | 0.744006i | ||||||
\(880\) | − | 8.49290i | − | 0.286296i | ||||||
\(881\) | −47.2653 | −1.59241 | −0.796205 | − | 0.605027i | \(-0.793162\pi\) | ||||
−0.796205 | + | 0.605027i | \(0.793162\pi\) | |||||||
\(882\) | −10.1645 | + | 14.4017i | −0.342255 | + | 0.484930i | ||||
\(883\) | 3.85865 | 0.129854 | 0.0649270 | − | 0.997890i | \(-0.479319\pi\) | ||||
0.0649270 | + | 0.997890i | \(0.479319\pi\) | |||||||
\(884\) | − | 6.89610i | − | 0.231941i | ||||||
\(885\) | −0.244491 | −0.00821847 | ||||||||
\(886\) | −82.6055 | −2.77518 | ||||||||
\(887\) | 41.3944i | 1.38989i | 0.719064 | + | 0.694944i | \(0.244571\pi\) | ||||
−0.719064 | + | 0.694944i | \(0.755429\pi\) | |||||||
\(888\) | −60.1274 | −2.01774 | ||||||||
\(889\) | 6.41645 | − | 3.32500i | 0.215201 | − | 0.111517i | ||||
\(890\) | 15.6753 | 0.525439 | ||||||||
\(891\) | − | 1.13179i | − | 0.0379165i | ||||||
\(892\) | − | 91.5879i | − | 3.06659i | ||||||
\(893\) | 4.76855i | 0.159573i | ||||||||
\(894\) | 21.3159 | 0.712910 | ||||||||
\(895\) | −12.6770 | −0.423746 | ||||||||
\(896\) | 34.8771 | − | 18.0733i | 1.16516 | − | 0.603785i | ||||
\(897\) | −0.176874 | − | 2.47889i | −0.00590565 | − | 0.0827678i | ||||
\(898\) | −52.2350 | −1.74311 | ||||||||
\(899\) | 14.9323i | 0.498021i | ||||||||
\(900\) | 15.2736 | 0.509121 | ||||||||
\(901\) | 16.5974i | 0.552941i | ||||||||
\(902\) | 14.2504 | 0.474486 | ||||||||
\(903\) | −15.7794 | + | 8.17687i | −0.525106 | + | 0.272109i | ||||
\(904\) | 13.0847i | 0.435190i | ||||||||
\(905\) | −17.1216 | −0.569142 | ||||||||
\(906\) | 44.2663i | 1.47065i | ||||||||
\(907\) | − | 22.9335i | − | 0.761496i | −0.924679 | − | 0.380748i | \(-0.875667\pi\) | ||
0.924679 | − | 0.380748i | \(-0.124333\pi\) | |||||||
\(908\) | 108.008 | 3.58439 | ||||||||
\(909\) | − | 8.88350i | − | 0.294647i | ||||||
\(910\) | 1.93364 | + | 3.73147i | 0.0640996 | + | 0.123697i | ||||
\(911\) | 7.56337i | 0.250586i | 0.992120 | + | 0.125293i | \(0.0399870\pi\) | ||||
−0.992120 | + | 0.125293i | \(0.960013\pi\) | |||||||
\(912\) | − | 6.97688i | − | 0.231027i | ||||||
\(913\) | 13.1636i | 0.435651i | ||||||||
\(914\) | 7.90431i | 0.261451i | ||||||||
\(915\) | 7.56702i | 0.250158i | ||||||||
\(916\) | −84.6948 | −2.79840 | ||||||||
\(917\) | −22.7866 | − | 43.9726i | −0.752478 | − | 1.45210i | ||||
\(918\) | − | 7.71925i | − | 0.254773i | ||||||
\(919\) | 27.9586i | 0.922269i | 0.887330 | + | 0.461134i | \(0.152557\pi\) | ||||
−0.887330 | + | 0.461134i | \(0.847443\pi\) | |||||||
\(920\) | −2.44971 | − | 34.3327i | −0.0807645 | − | 1.13192i | ||||
\(921\) | −20.0167 | −0.659571 | ||||||||
\(922\) | − | 98.2333i | − | 3.23514i | ||||||
\(923\) | − | 1.12162i | − | 0.0369184i | ||||||
\(924\) | −11.5422 | + | 5.98114i | −0.379710 | + | 0.196765i | ||||
\(925\) | − | 35.8791i | − | 1.17970i | ||||||
\(926\) | −50.9430 | −1.67409 | ||||||||
\(927\) | −11.5009 | −0.377740 | ||||||||
\(928\) | −8.12294 | −0.266649 | ||||||||
\(929\) | − | 11.3298i | − | 0.371718i | −0.982576 | − | 0.185859i | \(-0.940493\pi\) | ||
0.982576 | − | 0.185859i | \(-0.0595067\pi\) | |||||||
\(930\) | 21.0271 | 0.689505 | ||||||||
\(931\) | −4.56836 | + | 6.47277i | −0.149722 | + | 0.212137i | ||||
\(932\) | −36.2124 | −1.18618 | ||||||||
\(933\) | 15.7430 | 0.515403 | ||||||||
\(934\) | −31.3811 | −1.02682 | ||||||||
\(935\) | − | 4.22325i | − | 0.138115i | ||||||
\(936\) | 3.05526i | 0.0998642i | ||||||||
\(937\) | 7.75154 | 0.253232 | 0.126616 | − | 0.991952i | \(-0.459588\pi\) | ||||
0.126616 | + | 0.991952i | \(0.459588\pi\) | |||||||
\(938\) | 11.1944 | + | 21.6025i | 0.365510 | + | 0.705348i | ||||
\(939\) | 8.46473i | 0.276236i | ||||||||
\(940\) | − | 22.2657i | − | 0.726228i | ||||||
\(941\) | 4.38019 | 0.142790 | 0.0713950 | − | 0.997448i | \(-0.477255\pi\) | ||||
0.0713950 | + | 0.997448i | \(0.477255\pi\) | |||||||
\(942\) | 46.9233i | 1.52884i | ||||||||
\(943\) | 23.9183 | − | 1.70662i | 0.778889 | − | 0.0555753i | ||||
\(944\) | 1.23812i | 0.0402973i | ||||||||
\(945\) | 1.48180 | + | 2.85952i | 0.0482030 | + | 0.0930203i | ||||
\(946\) | −19.1447 | −0.622448 | ||||||||
\(947\) | 4.60985 | 0.149800 | 0.0749001 | − | 0.997191i | \(-0.476136\pi\) | ||||
0.0749001 | + | 0.997191i | \(0.476136\pi\) | |||||||
\(948\) | −37.3117 | −1.21183 | ||||||||
\(949\) | 5.29849 | 0.171996 | ||||||||
\(950\) | 10.0271 | 0.325323 | ||||||||
\(951\) | 28.1083i | 0.911475i | ||||||||
\(952\) | −42.4556 | + | 22.0005i | −1.37599 | + | 0.713039i | ||||
\(953\) | 2.26047i | 0.0732239i | 0.999330 | + | 0.0366119i | \(0.0116565\pi\) | ||||
−0.999330 | + | 0.0366119i | \(0.988343\pi\) | |||||||
\(954\) | − | 13.6347i | − | 0.441440i | ||||||
\(955\) | 15.0116i | 0.485762i | ||||||||
\(956\) | −92.8076 | −3.00161 | ||||||||
\(957\) | −2.46377 | −0.0796423 | ||||||||
\(958\) | −63.5499 | −2.05321 | ||||||||
\(959\) | −14.9760 | − | 28.9002i | −0.483601 | − | 0.933235i | ||||
\(960\) | − | 3.56949i | − | 0.115205i | ||||||
\(961\) | −16.0531 | −0.517841 | ||||||||
\(962\) | 13.3078 | 0.429062 | ||||||||
\(963\) | 2.67908i | 0.0863320i | ||||||||
\(964\) | 38.4909 | 1.23971 | ||||||||
\(965\) | −3.86719 | −0.124489 | ||||||||
\(966\) | −27.2513 | + | 16.6829i | −0.876797 | + | 0.536763i | ||||
\(967\) | 33.1820 | 1.06706 | 0.533530 | − | 0.845781i | \(-0.320865\pi\) | ||||
0.533530 | + | 0.845781i | \(0.320865\pi\) | |||||||
\(968\) | 57.3027 | 1.84178 | ||||||||
\(969\) | − | 3.46938i | − | 0.111452i | ||||||
\(970\) | −55.6731 | −1.78756 | ||||||||
\(971\) | 13.1660 | 0.422517 | 0.211259 | − | 0.977430i | \(-0.432244\pi\) | ||||
0.211259 | + | 0.977430i | \(0.432244\pi\) | |||||||
\(972\) | 4.34132i | 0.139248i | ||||||||
\(973\) | 16.7736 | + | 32.3690i | 0.537736 | + | 1.03770i | ||||
\(974\) | −47.9794 | −1.53736 | ||||||||
\(975\) | −1.82313 | −0.0583868 | ||||||||
\(976\) | 38.3199 | 1.22659 | ||||||||
\(977\) | − | 24.5200i | − | 0.784463i | −0.919866 | − | 0.392232i | \(-0.871703\pi\) | ||
0.919866 | − | 0.392232i | \(-0.128297\pi\) | |||||||
\(978\) | 18.2248i | 0.582766i | ||||||||
\(979\) | − | 5.78760i | − | 0.184973i | ||||||
\(980\) | 21.3310 | − | 30.2232i | 0.681394 | − | 0.965446i | ||||
\(981\) | 17.7464i | 0.566598i | ||||||||
\(982\) | −32.3516 | −1.03238 | ||||||||
\(983\) | −47.6949 | −1.52123 | −0.760615 | − | 0.649203i | \(-0.775103\pi\) | ||||
−0.760615 | + | 0.649203i | \(0.775103\pi\) | |||||||
\(984\) | −29.4796 | −0.939775 | ||||||||
\(985\) | 20.1658 | 0.642537 | ||||||||
\(986\) | −16.8038 | −0.535143 | ||||||||
\(987\) | −9.89733 | + | 5.12878i | −0.315036 | + | 0.163251i | ||||
\(988\) | 2.54616i | 0.0810041i | ||||||||
\(989\) | −32.1332 | + | 2.29277i | −1.02178 | + | 0.0729058i | ||||
\(990\) | 3.46938i | 0.110264i | ||||||||
\(991\) | 15.9512 | 0.506706 | 0.253353 | − | 0.967374i | \(-0.418467\pi\) | ||||
0.253353 | + | 0.967374i | \(0.418467\pi\) | |||||||
\(992\) | − | 25.5961i | − | 0.812677i | ||||||
\(993\) | − | 9.22482i | − | 0.292741i | ||||||
\(994\) | −12.8037 | + | 6.63487i | −0.406110 | + | 0.210445i | ||||
\(995\) | 11.2985 | 0.358186 | ||||||||
\(996\) | − | 50.4928i | − | 1.59993i | ||||||
\(997\) | 27.8959i | 0.883473i | 0.897145 | + | 0.441736i | \(0.145637\pi\) | ||||
−0.897145 | + | 0.441736i | \(0.854363\pi\) | |||||||
\(998\) | −21.7126 | −0.687301 | ||||||||
\(999\) | 10.1981 | 0.322655 |
(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 | 483.2.h.c.160.12 | yes | 12 | |
3.2 | odd | 2 | 1449.2.h.e.1126.2 | 12 | |||
7.6 | odd | 2 | inner | 483.2.h.c.160.9 | ✓ | 12 | |
21.20 | even | 2 | 1449.2.h.e.1126.4 | 12 | |||
23.22 | odd | 2 | inner | 483.2.h.c.160.11 | yes | 12 | |
69.68 | even | 2 | 1449.2.h.e.1126.3 | 12 | |||
161.160 | even | 2 | inner | 483.2.h.c.160.10 | yes | 12 | |
483.482 | odd | 2 | 1449.2.h.e.1126.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.h.c.160.9 | ✓ | 12 | 7.6 | odd | 2 | inner | |
483.2.h.c.160.10 | yes | 12 | 161.160 | even | 2 | inner | |
483.2.h.c.160.11 | yes | 12 | 23.22 | odd | 2 | inner | |
483.2.h.c.160.12 | yes | 12 | 1.1 | even | 1 | trivial | |
1449.2.h.e.1126.1 | 12 | 483.482 | odd | 2 | |||
1449.2.h.e.1126.2 | 12 | 3.2 | odd | 2 | |||
1449.2.h.e.1126.3 | 12 | 69.68 | even | 2 | |||
1449.2.h.e.1126.4 | 12 | 21.20 | even | 2 |