Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(101,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.d (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: | \(4.08720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.1 | ||
Root | \(1.58114 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.101 |
Dual form | 150.3.d.c.101.3 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | −2.58114 | + | 1.52896i | −0.860380 | + | 0.509654i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.16228 | + | 3.65028i | 0.360380 | + | 0.608380i | ||||
\(7\) | 7.48683 | 1.06955 | 0.534774 | − | 0.844995i | \(-0.320397\pi\) | ||||
0.534774 | + | 0.844995i | \(0.320397\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 4.32456 | − | 7.89292i | 0.480506 | − | 0.876991i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 8.48528i | − | 0.771389i | −0.922627 | − | 0.385695i | \(-0.873962\pi\) | ||
0.922627 | − | 0.385695i | \(-0.126038\pi\) | |||||||
\(12\) | 5.16228 | − | 3.05792i | 0.430190 | − | 0.254827i | ||||
\(13\) | 10.0000 | 0.769231 | 0.384615 | − | 0.923077i | \(-0.374334\pi\) | ||||
0.384615 | + | 0.923077i | \(0.374334\pi\) | |||||||
\(14\) | − | 10.5880i | − | 0.756284i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 30.3870i | − | 1.78747i | −0.448596 | − | 0.893734i | \(-0.648076\pi\) | ||
0.448596 | − | 0.893734i | \(-0.351924\pi\) | |||||||
\(18\) | −11.1623 | − | 6.11584i | −0.620127 | − | 0.339769i | ||||
\(19\) | 26.9737 | 1.41967 | 0.709833 | − | 0.704370i | \(-0.248770\pi\) | ||||
0.709833 | + | 0.704370i | \(0.248770\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −19.3246 | + | 11.4471i | −0.920217 | + | 0.545099i | ||||
\(22\) | −12.0000 | −0.545455 | ||||||||
\(23\) | 9.17377i | 0.398859i | 0.979912 | + | 0.199430i | \(0.0639090\pi\) | ||||
−0.979912 | + | 0.199430i | \(0.936091\pi\) | |||||||
\(24\) | −4.32456 | − | 7.30056i | −0.180190 | − | 0.304190i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 14.1421i | − | 0.543928i | ||||||
\(27\) | 0.905694 | + | 26.9848i | 0.0335442 | + | 0.999437i | ||||
\(28\) | −14.9737 | −0.534774 | ||||||||
\(29\) | 26.8328i | 0.925270i | 0.886549 | + | 0.462635i | \(0.153096\pi\) | ||||
−0.886549 | + | 0.462635i | \(0.846904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 0.258065 | 0.129032 | − | 0.991640i | \(-0.458813\pi\) | ||||
0.129032 | + | 0.991640i | \(0.458813\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 12.9737 | + | 21.9017i | 0.393141 | + | 0.663688i | ||||
\(34\) | −42.9737 | −1.26393 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.64911 | + | 15.7858i | −0.240253 | + | 0.438496i | ||||
\(37\) | −15.9473 | −0.431009 | −0.215504 | − | 0.976503i | \(-0.569140\pi\) | ||||
−0.215504 | + | 0.976503i | \(0.569140\pi\) | |||||||
\(38\) | − | 38.1465i | − | 1.00386i | ||||||
\(39\) | −25.8114 | + | 15.2896i | −0.661830 | + | 0.392041i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 47.3575i | − | 1.15506i | −0.816369 | − | 0.577531i | \(-0.804016\pi\) | ||
0.816369 | − | 0.577531i | \(-0.195984\pi\) | |||||||
\(42\) | 16.1886 | + | 27.3290i | 0.385443 | + | 0.650692i | ||||
\(43\) | 14.4605 | 0.336291 | 0.168145 | − | 0.985762i | \(-0.446222\pi\) | ||||
0.168145 | + | 0.985762i | \(0.446222\pi\) | |||||||
\(44\) | 16.9706i | 0.385695i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.9737 | 0.282036 | ||||||||
\(47\) | 45.8688i | 0.975933i | 0.872862 | + | 0.487966i | \(0.162261\pi\) | ||||
−0.872862 | + | 0.487966i | \(0.837739\pi\) | |||||||
\(48\) | −10.3246 | + | 6.11584i | −0.215095 | + | 0.127413i | ||||
\(49\) | 7.05267 | 0.143932 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 46.4605 | + | 78.4330i | 0.910990 | + | 1.53790i | ||||
\(52\) | −20.0000 | −0.384615 | ||||||||
\(53\) | − | 30.3870i | − | 0.573339i | −0.958030 | − | 0.286670i | \(-0.907452\pi\) | ||
0.958030 | − | 0.286670i | \(-0.0925482\pi\) | |||||||
\(54\) | 38.1623 | − | 1.28084i | 0.706709 | − | 0.0237194i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 21.1760i | 0.378142i | ||||||||
\(57\) | −69.6228 | + | 41.2417i | −1.22145 | + | 0.723538i | ||||
\(58\) | 37.9473 | 0.654264 | ||||||||
\(59\) | 24.0789i | 0.408116i | 0.978959 | + | 0.204058i | \(0.0654132\pi\) | ||||
−0.978959 | + | 0.204058i | \(0.934587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −53.9473 | −0.884382 | −0.442191 | − | 0.896921i | \(-0.645799\pi\) | ||||
−0.442191 | + | 0.896921i | \(0.645799\pi\) | |||||||
\(62\) | − | 11.3137i | − | 0.182479i | ||||||
\(63\) | 32.3772 | − | 59.0930i | 0.513924 | − | 0.937984i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 30.9737 | − | 18.3475i | 0.469298 | − | 0.277993i | ||||
\(67\) | 110.460 | 1.64866 | 0.824332 | − | 0.566107i | \(-0.191551\pi\) | ||||
0.824332 | + | 0.566107i | \(0.191551\pi\) | |||||||
\(68\) | 60.7739i | 0.893734i | ||||||||
\(69\) | −14.0263 | − | 23.6788i | −0.203280 | − | 0.343171i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 15.5936i | − | 0.219628i | −0.993952 | − | 0.109814i | \(-0.964974\pi\) | ||
0.993952 | − | 0.109814i | \(-0.0350255\pi\) | |||||||
\(72\) | 22.3246 | + | 12.2317i | 0.310063 | + | 0.169885i | ||||
\(73\) | −87.9473 | −1.20476 | −0.602379 | − | 0.798210i | \(-0.705780\pi\) | ||||
−0.602379 | + | 0.798210i | \(0.705780\pi\) | |||||||
\(74\) | 22.5529i | 0.304769i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −53.9473 | −0.709833 | ||||||||
\(77\) | − | 63.5279i | − | 0.825037i | ||||||
\(78\) | 21.6228 | + | 36.5028i | 0.277215 | + | 0.467985i | ||||
\(79\) | −46.9737 | −0.594603 | −0.297302 | − | 0.954784i | \(-0.596087\pi\) | ||||
−0.297302 | + | 0.954784i | \(0.596087\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −43.5964 | − | 68.2668i | −0.538228 | − | 0.842799i | ||||
\(82\) | −66.9737 | −0.816752 | ||||||||
\(83\) | 26.1443i | 0.314992i | 0.987520 | + | 0.157496i | \(0.0503421\pi\) | ||||
−0.987520 | + | 0.157496i | \(0.949658\pi\) | |||||||
\(84\) | 38.6491 | − | 22.8942i | 0.460108 | − | 0.272549i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 20.4502i | − | 0.237793i | ||||||
\(87\) | −41.0263 | − | 69.2592i | −0.471567 | − | 0.796083i | ||||
\(88\) | 24.0000 | 0.272727 | ||||||||
\(89\) | − | 60.7739i | − | 0.682853i | −0.939908 | − | 0.341427i | \(-0.889090\pi\) | ||
0.939908 | − | 0.341427i | \(-0.110910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 74.8683 | 0.822729 | ||||||||
\(92\) | − | 18.3475i | − | 0.199430i | ||||||
\(93\) | −20.6491 | + | 12.2317i | −0.222033 | + | 0.131524i | ||||
\(94\) | 64.8683 | 0.690089 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.64911 | + | 14.6011i | 0.0900949 | + | 0.152095i | ||||
\(97\) | −36.0527 | −0.371677 | −0.185838 | − | 0.982580i | \(-0.559500\pi\) | ||||
−0.185838 | + | 0.982580i | \(0.559500\pi\) | |||||||
\(98\) | − | 9.97398i | − | 0.101775i | ||||||
\(99\) | −66.9737 | − | 36.6951i | −0.676502 | − | 0.370657i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 48.1577i | 0.476809i | 0.971166 | + | 0.238405i | \(0.0766245\pi\) | ||||
−0.971166 | + | 0.238405i | \(0.923376\pi\) | |||||||
\(102\) | 110.921 | − | 65.7051i | 1.08746 | − | 0.644167i | ||||
\(103\) | −140.408 | −1.36318 | −0.681591 | − | 0.731733i | \(-0.738712\pi\) | ||||
−0.681591 | + | 0.731733i | \(0.738712\pi\) | |||||||
\(104\) | 28.2843i | 0.271964i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −42.9737 | −0.405412 | ||||||||
\(107\) | − | 43.1149i | − | 0.402943i | −0.979494 | − | 0.201471i | \(-0.935428\pi\) | ||
0.979494 | − | 0.201471i | \(-0.0645723\pi\) | |||||||
\(108\) | −1.81139 | − | 53.9696i | −0.0167721 | − | 0.499719i | ||||
\(109\) | 133.842 | 1.22791 | 0.613954 | − | 0.789342i | \(-0.289578\pi\) | ||||
0.613954 | + | 0.789342i | \(0.289578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 41.1623 | − | 24.3829i | 0.370831 | − | 0.219665i | ||||
\(112\) | 29.9473 | 0.267387 | ||||||||
\(113\) | 7.90852i | 0.0699869i | 0.999388 | + | 0.0349935i | \(0.0111410\pi\) | ||||
−0.999388 | + | 0.0349935i | \(0.988859\pi\) | |||||||
\(114\) | 58.3246 | + | 98.4615i | 0.511619 | + | 0.863697i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 53.6656i | − | 0.462635i | ||||||
\(117\) | 43.2456 | − | 78.9292i | 0.369620 | − | 0.674609i | ||||
\(118\) | 34.0527 | 0.288582 | ||||||||
\(119\) | − | 227.502i | − | 1.91178i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000 | 0.404959 | ||||||||
\(122\) | 76.2930i | 0.625353i | ||||||||
\(123\) | 72.4078 | + | 122.236i | 0.588682 | + | 0.993792i | ||||
\(124\) | −16.0000 | −0.129032 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −83.5701 | − | 45.7883i | −0.663255 | − | 0.363399i | ||||
\(127\) | 134.460 | 1.05874 | 0.529372 | − | 0.848390i | \(-0.322428\pi\) | ||||
0.529372 | + | 0.848390i | \(0.322428\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | −37.3246 | + | 22.1095i | −0.289338 | + | 0.171392i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 220.394i | 1.68240i | 0.540727 | + | 0.841198i | \(0.318149\pi\) | ||||
−0.540727 | + | 0.841198i | \(0.681851\pi\) | |||||||
\(132\) | −25.9473 | − | 43.8034i | −0.196571 | − | 0.331844i | ||||
\(133\) | 201.947 | 1.51840 | ||||||||
\(134\) | − | 156.215i | − | 1.16578i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 85.9473 | 0.631966 | ||||||||
\(137\) | 95.5153i | 0.697192i | 0.937273 | + | 0.348596i | \(0.113341\pi\) | ||||
−0.937273 | + | 0.348596i | \(0.886659\pi\) | |||||||
\(138\) | −33.4868 | + | 19.8362i | −0.242658 | + | 0.143741i | ||||
\(139\) | −76.8157 | −0.552631 | −0.276315 | − | 0.961067i | \(-0.589113\pi\) | ||||
−0.276315 | + | 0.961067i | \(0.589113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −70.1317 | − | 118.394i | −0.497388 | − | 0.839673i | ||||
\(142\) | −22.0527 | −0.155300 | ||||||||
\(143\) | − | 84.8528i | − | 0.593376i | ||||||
\(144\) | 17.2982 | − | 31.5717i | 0.120127 | − | 0.219248i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 124.376i | 0.851893i | ||||||||
\(147\) | −18.2039 | + | 10.7833i | −0.123836 | + | 0.0733555i | ||||
\(148\) | 31.8947 | 0.215504 | ||||||||
\(149\) | 276.237i | 1.85394i | 0.375139 | + | 0.926969i | \(0.377595\pi\) | ||||
−0.375139 | + | 0.926969i | \(0.622405\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0527 | 0.119554 | 0.0597770 | − | 0.998212i | \(-0.480961\pi\) | ||||
0.0597770 | + | 0.998212i | \(0.480961\pi\) | |||||||
\(152\) | 76.2930i | 0.501928i | ||||||||
\(153\) | −239.842 | − | 131.410i | −1.56759 | − | 0.858890i | ||||
\(154\) | −89.8420 | −0.583390 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 51.6228 | − | 30.5792i | 0.330915 | − | 0.196021i | ||||
\(157\) | −103.842 | −0.661414 | −0.330707 | − | 0.943733i | \(-0.607287\pi\) | ||||
−0.330707 | + | 0.943733i | \(0.607287\pi\) | |||||||
\(158\) | 66.4308i | 0.420448i | ||||||||
\(159\) | 46.4605 | + | 78.4330i | 0.292204 | + | 0.493289i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 68.6825i | 0.426599i | ||||||||
\(162\) | −96.5438 | + | 61.6547i | −0.595949 | + | 0.380584i | ||||
\(163\) | 11.3815 | 0.0698251 | 0.0349126 | − | 0.999390i | \(-0.488885\pi\) | ||||
0.0349126 | + | 0.999390i | \(0.488885\pi\) | |||||||
\(164\) | 94.7151i | 0.577531i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 36.9737 | 0.222733 | ||||||||
\(167\) | 252.270i | 1.51060i | 0.655382 | + | 0.755298i | \(0.272508\pi\) | ||||
−0.655382 | + | 0.755298i | \(0.727492\pi\) | |||||||
\(168\) | −32.3772 | − | 54.6581i | −0.192722 | − | 0.325346i | ||||
\(169\) | −69.0000 | −0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 116.649 | − | 212.901i | 0.682159 | − | 1.24504i | ||||
\(172\) | −28.9210 | −0.168145 | ||||||||
\(173\) | 11.8160i | 0.0683005i | 0.999417 | + | 0.0341502i | \(0.0108725\pi\) | ||||
−0.999417 | + | 0.0341502i | \(0.989128\pi\) | |||||||
\(174\) | −97.9473 | + | 58.0200i | −0.562916 | + | 0.333448i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 33.9411i | − | 0.192847i | ||||||
\(177\) | −36.8157 | − | 62.1509i | −0.207998 | − | 0.351135i | ||||
\(178\) | −85.9473 | −0.482850 | ||||||||
\(179\) | 69.0358i | 0.385675i | 0.981231 | + | 0.192837i | \(0.0617690\pi\) | ||||
−0.981231 | + | 0.192837i | \(0.938231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −189.684 | −1.04798 | −0.523989 | − | 0.851725i | \(-0.675557\pi\) | ||||
−0.523989 | + | 0.851725i | \(0.675557\pi\) | |||||||
\(182\) | − | 105.880i | − | 0.581757i | ||||||
\(183\) | 139.246 | − | 82.4834i | 0.760905 | − | 0.450729i | ||||
\(184\) | −25.9473 | −0.141018 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 17.2982 | + | 29.2023i | 0.0930012 | + | 0.157001i | ||||
\(187\) | −257.842 | −1.37883 | ||||||||
\(188\) | − | 91.7377i | − | 0.487966i | ||||||
\(189\) | 6.78078 | + | 202.031i | 0.0358771 | + | 1.06895i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 108.708i | − | 0.569153i | −0.958653 | − | 0.284577i | \(-0.908147\pi\) | ||
0.958653 | − | 0.284577i | \(-0.0918530\pi\) | |||||||
\(192\) | 20.6491 | − | 12.2317i | 0.107547 | − | 0.0637067i | ||||
\(193\) | 167.947 | 0.870193 | 0.435097 | − | 0.900384i | \(-0.356714\pi\) | ||||
0.435097 | + | 0.900384i | \(0.356714\pi\) | |||||||
\(194\) | 50.9862i | 0.262815i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.1053 | −0.0719660 | ||||||||
\(197\) | 171.659i | 0.871367i | 0.900100 | + | 0.435684i | \(0.143493\pi\) | ||||
−0.900100 | + | 0.435684i | \(0.856507\pi\) | |||||||
\(198\) | −51.8947 | + | 94.7151i | −0.262094 | + | 0.478359i | ||||
\(199\) | 35.0790 | 0.176276 | 0.0881382 | − | 0.996108i | \(-0.471908\pi\) | ||||
0.0881382 | + | 0.996108i | \(0.471908\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −285.114 | + | 168.890i | −1.41848 | + | 0.840248i | ||||
\(202\) | 68.1053 | 0.337155 | ||||||||
\(203\) | 200.893i | 0.989620i | ||||||||
\(204\) | −92.9210 | − | 156.866i | −0.455495 | − | 0.768951i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 198.567i | 0.963916i | ||||||||
\(207\) | 72.4078 | + | 39.6725i | 0.349796 | + | 0.191654i | ||||
\(208\) | 40.0000 | 0.192308 | ||||||||
\(209\) | − | 228.879i | − | 1.09512i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −58.1580 | −0.275630 | −0.137815 | − | 0.990458i | \(-0.544008\pi\) | ||||
−0.137815 | + | 0.990458i | \(0.544008\pi\) | |||||||
\(212\) | 60.7739i | 0.286670i | ||||||||
\(213\) | 23.8420 | + | 40.2492i | 0.111934 | + | 0.188963i | ||||
\(214\) | −60.9737 | −0.284924 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −76.3246 | + | 2.56169i | −0.353354 | + | 0.0118597i | ||||
\(217\) | 59.8947 | 0.276012 | ||||||||
\(218\) | − | 189.281i | − | 0.868262i | ||||||
\(219\) | 227.004 | − | 134.468i | 1.03655 | − | 0.614009i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 303.870i | − | 1.37498i | ||||||
\(222\) | −34.4826 | − | 58.2123i | −0.155327 | − | 0.262217i | ||||
\(223\) | −99.3815 | −0.445657 | −0.222828 | − | 0.974858i | \(-0.571529\pi\) | ||||
−0.222828 | + | 0.974858i | \(0.571529\pi\) | |||||||
\(224\) | − | 42.3519i | − | 0.189071i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.1843 | 0.0494882 | ||||||||
\(227\) | − | 216.951i | − | 0.955733i | −0.878432 | − | 0.477867i | \(-0.841410\pi\) | ||
0.878432 | − | 0.477867i | \(-0.158590\pi\) | |||||||
\(228\) | 139.246 | − | 82.4834i | 0.610726 | − | 0.361769i | ||||
\(229\) | 325.684 | 1.42220 | 0.711100 | − | 0.703090i | \(-0.248197\pi\) | ||||
0.711100 | + | 0.703090i | \(0.248197\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 97.1317 | + | 163.974i | 0.420483 | + | 0.709845i | ||||
\(232\) | −75.8947 | −0.327132 | ||||||||
\(233\) | − | 51.7119i | − | 0.221939i | −0.993824 | − | 0.110970i | \(-0.964604\pi\) | ||
0.993824 | − | 0.110970i | \(-0.0353957\pi\) | |||||||
\(234\) | −111.623 | − | 61.1584i | −0.477020 | − | 0.261361i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 48.1577i | − | 0.204058i | ||||||
\(237\) | 121.246 | − | 71.8209i | 0.511585 | − | 0.303042i | ||||
\(238\) | −321.737 | −1.35183 | ||||||||
\(239\) | 410.047i | 1.71568i | 0.513917 | + | 0.857840i | \(0.328194\pi\) | ||||
−0.513917 | + | 0.857840i | \(0.671806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 445.526 | 1.84866 | 0.924328 | − | 0.381599i | \(-0.124627\pi\) | ||||
0.924328 | + | 0.381599i | \(0.124627\pi\) | |||||||
\(242\) | − | 69.2965i | − | 0.286349i | ||||||
\(243\) | 216.906 | + | 109.549i | 0.892616 | + | 0.450818i | ||||
\(244\) | 107.895 | 0.442191 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 172.868 | − | 102.400i | 0.702717 | − | 0.416261i | ||||
\(247\) | 269.737 | 1.09205 | ||||||||
\(248\) | 22.6274i | 0.0912396i | ||||||||
\(249\) | −39.9737 | − | 67.4821i | −0.160537 | − | 0.271013i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 237.364i | 0.945675i | 0.881150 | + | 0.472838i | \(0.156770\pi\) | ||||
−0.881150 | + | 0.472838i | \(0.843230\pi\) | |||||||
\(252\) | −64.7544 | + | 118.186i | −0.256962 | + | 0.468992i | ||||
\(253\) | 77.8420 | 0.307676 | ||||||||
\(254\) | − | 190.156i | − | 0.748645i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 318.887i | − | 1.24080i | −0.784284 | − | 0.620402i | \(-0.786970\pi\) | ||
0.784284 | − | 0.620402i | \(-0.213030\pi\) | |||||||
\(258\) | 31.2676 | + | 52.7849i | 0.121192 | + | 0.204593i | ||||
\(259\) | −119.395 | −0.460985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 211.789 | + | 116.040i | 0.811453 | + | 0.444598i | ||||
\(262\) | 311.684 | 1.18963 | ||||||||
\(263\) | − | 36.2300i | − | 0.137757i | −0.997625 | − | 0.0688784i | \(-0.978058\pi\) | ||
0.997625 | − | 0.0688784i | \(-0.0219420\pi\) | |||||||
\(264\) | −61.9473 | + | 36.6951i | −0.234649 | + | 0.138996i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 285.597i | − | 1.07367i | ||||||
\(267\) | 92.9210 | + | 156.866i | 0.348019 | + | 0.587513i | ||||
\(268\) | −220.921 | −0.824332 | ||||||||
\(269\) | − | 528.041i | − | 1.96298i | −0.191518 | − | 0.981489i | \(-0.561341\pi\) | ||
0.191518 | − | 0.981489i | \(-0.438659\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −475.895 | −1.75607 | −0.878034 | − | 0.478597i | \(-0.841145\pi\) | ||||
−0.878034 | + | 0.478597i | \(0.841145\pi\) | |||||||
\(272\) | − | 121.548i | − | 0.446867i | ||||||
\(273\) | −193.246 | + | 114.471i | −0.707859 | + | 0.419307i | ||||
\(274\) | 135.079 | 0.492989 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 28.0527 | + | 47.3575i | 0.101640 | + | 0.171585i | ||||
\(277\) | −188.158 | −0.679271 | −0.339635 | − | 0.940557i | \(-0.610304\pi\) | ||||
−0.339635 | + | 0.940557i | \(0.610304\pi\) | |||||||
\(278\) | 108.634i | 0.390769i | ||||||||
\(279\) | 34.5964 | − | 63.1434i | 0.124002 | − | 0.226320i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4322i | 0.0869473i | 0.999055 | + | 0.0434736i | \(0.0138424\pi\) | ||||
−0.999055 | + | 0.0434736i | \(0.986158\pi\) | |||||||
\(282\) | −167.434 | + | 99.1812i | −0.593738 | + | 0.351706i | ||||
\(283\) | −198.460 | −0.701274 | −0.350637 | − | 0.936511i | \(-0.614035\pi\) | ||||
−0.350637 | + | 0.936511i | \(0.614035\pi\) | |||||||
\(284\) | 31.1872i | 0.109814i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −120.000 | −0.419580 | ||||||||
\(287\) | − | 354.558i | − | 1.23539i | ||||||
\(288\) | −44.6491 | − | 24.4634i | −0.155032 | − | 0.0849423i | ||||
\(289\) | −634.368 | −2.19504 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 93.0569 | − | 55.1231i | 0.319783 | − | 0.189427i | ||||
\(292\) | 175.895 | 0.602379 | ||||||||
\(293\) | 513.825i | 1.75367i | 0.480794 | + | 0.876834i | \(0.340349\pi\) | ||||
−0.480794 | + | 0.876834i | \(0.659651\pi\) | |||||||
\(294\) | 15.2498 | + | 25.7442i | 0.0518702 | + | 0.0875654i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 45.1059i | − | 0.152385i | ||||||
\(297\) | 228.974 | − | 7.68507i | 0.770955 | − | 0.0258757i | ||||
\(298\) | 390.658 | 1.31093 | ||||||||
\(299\) | 91.7377i | 0.306815i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 108.263 | 0.359679 | ||||||||
\(302\) | − | 25.5303i | − | 0.0845375i | ||||||
\(303\) | −73.6313 | − | 124.302i | −0.243008 | − | 0.410237i | ||||
\(304\) | 107.895 | 0.354917 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −185.842 | + | 339.188i | −0.607327 | + | 1.10846i | ||||
\(307\) | 11.3815 | 0.0370733 | 0.0185366 | − | 0.999828i | \(-0.494099\pi\) | ||||
0.0185366 | + | 0.999828i | \(0.494099\pi\) | |||||||
\(308\) | 127.056i | 0.412519i | ||||||||
\(309\) | 362.412 | − | 214.678i | 1.17285 | − | 0.694751i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 518.756i | − | 1.66802i | −0.551746 | − | 0.834012i | \(-0.686038\pi\) | ||
0.551746 | − | 0.834012i | \(-0.313962\pi\) | |||||||
\(312\) | −43.2456 | − | 73.0056i | −0.138608 | − | 0.233992i | ||||
\(313\) | 46.3160 | 0.147974 | 0.0739872 | − | 0.997259i | \(-0.476428\pi\) | ||||
0.0739872 | + | 0.997259i | \(0.476428\pi\) | |||||||
\(314\) | 146.855i | 0.467690i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 93.9473 | 0.297302 | ||||||||
\(317\) | − | 39.0957i | − | 0.123330i | −0.998097 | − | 0.0616651i | \(-0.980359\pi\) | ||
0.998097 | − | 0.0616651i | \(-0.0196411\pi\) | |||||||
\(318\) | 110.921 | − | 65.7051i | 0.348808 | − | 0.206620i | ||||
\(319\) | 227.684 | 0.713743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 65.9210 | + | 111.286i | 0.205361 | + | 0.346684i | ||||
\(322\) | 97.1317 | 0.301651 | ||||||||
\(323\) | − | 819.648i | − | 2.53761i | ||||||
\(324\) | 87.1929 | + | 136.534i | 0.269114 | + | 0.421400i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 16.0959i | − | 0.0493738i | ||||||
\(327\) | −345.465 | + | 204.639i | −1.05647 | + | 0.625808i | ||||
\(328\) | 133.947 | 0.408376 | ||||||||
\(329\) | 343.412i | 1.04381i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −445.421 | −1.34568 | −0.672841 | − | 0.739787i | \(-0.734926\pi\) | ||||
−0.672841 | + | 0.739787i | \(0.734926\pi\) | |||||||
\(332\) | − | 52.2887i | − | 0.157496i | ||||||
\(333\) | −68.9651 | + | 125.871i | −0.207102 | + | 0.377991i | ||||
\(334\) | 356.763 | 1.06815 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −77.2982 | + | 45.7883i | −0.230054 | + | 0.136275i | ||||
\(337\) | −325.684 | −0.966421 | −0.483211 | − | 0.875504i | \(-0.660529\pi\) | ||||
−0.483211 | + | 0.875504i | \(0.660529\pi\) | |||||||
\(338\) | 97.5807i | 0.288700i | ||||||||
\(339\) | −12.0918 | − | 20.4130i | −0.0356691 | − | 0.0602153i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 67.8823i | − | 0.199068i | ||||||
\(342\) | −301.088 | − | 164.967i | −0.880373 | − | 0.482359i | ||||
\(343\) | −314.053 | −0.915605 | ||||||||
\(344\) | 40.9005i | 0.118897i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.7103 | 0.0482957 | ||||||||
\(347\) | 51.8236i | 0.149348i | 0.997208 | + | 0.0746738i | \(0.0237916\pi\) | ||||
−0.997208 | + | 0.0746738i | \(0.976208\pi\) | |||||||
\(348\) | 82.0527 | + | 138.518i | 0.235784 | + | 0.398042i | ||||
\(349\) | −97.5787 | −0.279595 | −0.139798 | − | 0.990180i | \(-0.544645\pi\) | ||||
−0.139798 | + | 0.990180i | \(0.544645\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.05694 | + | 269.848i | 0.0258033 | + | 0.768798i | ||||
\(352\) | −48.0000 | −0.136364 | ||||||||
\(353\) | − | 569.797i | − | 1.61416i | −0.590445 | − | 0.807078i | \(-0.701048\pi\) | ||
0.590445 | − | 0.807078i | \(-0.298952\pi\) | |||||||
\(354\) | −87.8947 | + | 52.0652i | −0.248290 | + | 0.147077i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 121.548i | 0.341427i | ||||||||
\(357\) | 347.842 | + | 587.215i | 0.974347 | + | 1.64486i | ||||
\(358\) | 97.6313 | 0.272713 | ||||||||
\(359\) | − | 274.283i | − | 0.764019i | −0.924158 | − | 0.382010i | \(-0.875232\pi\) | ||
0.924158 | − | 0.382010i | \(-0.124768\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 366.579 | 1.01545 | ||||||||
\(362\) | 268.254i | 0.741032i | ||||||||
\(363\) | −126.476 | + | 74.9191i | −0.348418 | + | 0.206389i | ||||
\(364\) | −149.737 | −0.411364 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −116.649 | − | 196.923i | −0.318713 | − | 0.538041i | ||||
\(367\) | −461.828 | −1.25839 | −0.629194 | − | 0.777248i | \(-0.716615\pi\) | ||||
−0.629194 | + | 0.777248i | \(0.716615\pi\) | |||||||
\(368\) | 36.6951i | 0.0997149i | ||||||||
\(369\) | −373.789 | − | 204.800i | −1.01298 | − | 0.555014i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 227.502i | − | 0.613213i | ||||||
\(372\) | 41.2982 | − | 24.4634i | 0.111017 | − | 0.0657618i | ||||
\(373\) | 491.947 | 1.31889 | 0.659447 | − | 0.751751i | \(-0.270791\pi\) | ||||
0.659447 | + | 0.751751i | \(0.270791\pi\) | |||||||
\(374\) | 364.644i | 0.974983i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −129.737 | −0.345044 | ||||||||
\(377\) | 268.328i | 0.711746i | ||||||||
\(378\) | 285.715 | − | 9.58947i | 0.755859 | − | 0.0253690i | ||||
\(379\) | −258.763 | −0.682752 | −0.341376 | − | 0.939927i | \(-0.610893\pi\) | ||||
−0.341376 | + | 0.939927i | \(0.610893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −347.061 | + | 205.585i | −0.910922 | + | 0.539593i | ||||
\(382\) | −153.737 | −0.402452 | ||||||||
\(383\) | 522.422i | 1.36402i | 0.731341 | + | 0.682012i | \(0.238895\pi\) | ||||
−0.731341 | + | 0.682012i | \(0.761105\pi\) | |||||||
\(384\) | −17.2982 | − | 29.2023i | −0.0450475 | − | 0.0760475i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 237.513i | − | 0.615320i | ||||||
\(387\) | 62.5352 | − | 114.136i | 0.161590 | − | 0.294924i | ||||
\(388\) | 72.1053 | 0.185838 | ||||||||
\(389\) | 610.847i | 1.57030i | 0.619306 | + | 0.785150i | \(0.287414\pi\) | ||||
−0.619306 | + | 0.785150i | \(0.712586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 278.763 | 0.712949 | ||||||||
\(392\) | 19.9480i | 0.0508876i | ||||||||
\(393\) | −336.974 | − | 568.867i | −0.857439 | − | 1.44750i | ||||
\(394\) | 242.763 | 0.616150 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 133.947 | + | 73.3901i | 0.338251 | + | 0.185329i | ||||
\(397\) | 214.000 | 0.539043 | 0.269521 | − | 0.962994i | \(-0.413135\pi\) | ||||
0.269521 | + | 0.962994i | \(0.413135\pi\) | |||||||
\(398\) | − | 49.6092i | − | 0.124646i | ||||||
\(399\) | −521.254 | + | 308.770i | −1.30640 | + | 0.773859i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 454.557i | 1.13356i | 0.823869 | + | 0.566780i | \(0.191811\pi\) | ||||
−0.823869 | + | 0.566780i | \(0.808189\pi\) | |||||||
\(402\) | 238.846 | + | 403.212i | 0.594145 | + | 1.00301i | ||||
\(403\) | 80.0000 | 0.198511 | ||||||||
\(404\) | − | 96.3155i | − | 0.238405i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 284.105 | 0.699767 | ||||||||
\(407\) | 135.318i | 0.332476i | ||||||||
\(408\) | −221.842 | + | 131.410i | −0.543730 | + | 0.322084i | ||||
\(409\) | −573.842 | −1.40304 | −0.701518 | − | 0.712651i | \(-0.747494\pi\) | ||||
−0.701518 | + | 0.712651i | \(0.747494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −146.039 | − | 246.538i | −0.355326 | − | 0.599850i | ||||
\(412\) | 280.816 | 0.681591 | ||||||||
\(413\) | 180.274i | 0.436500i | ||||||||
\(414\) | 56.1053 | − | 102.400i | 0.135520 | − | 0.247343i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 56.5685i | − | 0.135982i | ||||||
\(417\) | 198.272 | − | 117.448i | 0.475472 | − | 0.281650i | ||||
\(418\) | −323.684 | −0.774364 | ||||||||
\(419\) | 97.9159i | 0.233690i | 0.993150 | + | 0.116845i | \(0.0372780\pi\) | ||||
−0.993150 | + | 0.116845i | \(0.962722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 717.315 | 1.70384 | 0.851918 | − | 0.523675i | \(-0.175439\pi\) | ||||
0.851918 | + | 0.523675i | \(0.175439\pi\) | |||||||
\(422\) | 82.2478i | 0.194900i | ||||||||
\(423\) | 362.039 | + | 198.362i | 0.855885 | + | 0.468942i | ||||
\(424\) | 85.9473 | 0.202706 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 56.9210 | − | 33.7177i | 0.133617 | − | 0.0791495i | ||||
\(427\) | −403.895 | −0.945889 | ||||||||
\(428\) | 86.2298i | 0.201471i | ||||||||
\(429\) | 129.737 | + | 219.017i | 0.302416 | + | 0.510529i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 293.077i | 0.679994i | 0.940427 | + | 0.339997i | \(0.110426\pi\) | ||||
−0.940427 | + | 0.339997i | \(0.889574\pi\) | |||||||
\(432\) | 3.62278 | + | 107.939i | 0.00838606 | + | 0.249859i | ||||
\(433\) | −487.526 | −1.12593 | −0.562963 | − | 0.826482i | \(-0.690339\pi\) | ||||
−0.562963 | + | 0.826482i | \(0.690339\pi\) | |||||||
\(434\) | − | 84.7038i | − | 0.195170i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −267.684 | −0.613954 | ||||||||
\(437\) | 247.450i | 0.566247i | ||||||||
\(438\) | −190.167 | − | 321.033i | −0.434170 | − | 0.732951i | ||||
\(439\) | 257.237 | 0.585961 | 0.292981 | − | 0.956118i | \(-0.405353\pi\) | ||||
0.292981 | + | 0.956118i | \(0.405353\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.4997 | − | 55.6662i | 0.0691602 | − | 0.126227i | ||||
\(442\) | −429.737 | −0.972255 | ||||||||
\(443\) | 293.096i | 0.661615i | 0.943698 | + | 0.330808i | \(0.107321\pi\) | ||||
−0.943698 | + | 0.330808i | \(0.892679\pi\) | |||||||
\(444\) | −82.3246 | + | 48.7657i | −0.185416 | + | 0.109833i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 140.547i | 0.315127i | ||||||||
\(447\) | −422.355 | − | 713.005i | −0.944866 | − | 1.59509i | ||||
\(448\) | −59.8947 | −0.133693 | ||||||||
\(449\) | − | 585.614i | − | 1.30426i | −0.758106 | − | 0.652132i | \(-0.773875\pi\) | ||
0.758106 | − | 0.652132i | \(-0.226125\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −401.842 | −0.891002 | ||||||||
\(452\) | − | 15.8170i | − | 0.0349935i | ||||||
\(453\) | −46.5964 | + | 27.6018i | −0.102862 | + | 0.0609312i | ||||
\(454\) | −306.816 | −0.675805 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −116.649 | − | 196.923i | −0.255809 | − | 0.431849i | ||||
\(457\) | 813.052 | 1.77911 | 0.889554 | − | 0.456831i | \(-0.151016\pi\) | ||||
0.889554 | + | 0.456831i | \(0.151016\pi\) | |||||||
\(458\) | − | 460.587i | − | 1.00565i | ||||||
\(459\) | 819.986 | − | 27.5213i | 1.78646 | − | 0.0599593i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 554.074i | 1.20190i | 0.799288 | + | 0.600948i | \(0.205210\pi\) | ||||
−0.799288 | + | 0.600948i | \(0.794790\pi\) | |||||||
\(462\) | 231.895 | − | 137.365i | 0.501937 | − | 0.297327i | ||||
\(463\) | 449.723 | 0.971324 | 0.485662 | − | 0.874147i | \(-0.338579\pi\) | ||||
0.485662 | + | 0.874147i | \(0.338579\pi\) | |||||||
\(464\) | 107.331i | 0.231317i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −73.1317 | −0.156935 | ||||||||
\(467\) | 30.7221i | 0.0657862i | 0.999459 | + | 0.0328931i | \(0.0104721\pi\) | ||||
−0.999459 | + | 0.0328931i | \(0.989528\pi\) | |||||||
\(468\) | −86.4911 | + | 157.858i | −0.184810 | + | 0.337304i | ||||
\(469\) | 826.999 | 1.76332 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 268.031 | − | 158.770i | 0.569067 | − | 0.337092i | ||||
\(472\) | −68.1053 | −0.144291 | ||||||||
\(473\) | − | 122.701i | − | 0.259411i | ||||||
\(474\) | −101.570 | − | 171.467i | −0.214283 | − | 0.361745i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 455.004i | 0.955891i | ||||||||
\(477\) | −239.842 | − | 131.410i | −0.502813 | − | 0.275493i | ||||
\(478\) | 579.895 | 1.21317 | ||||||||
\(479\) | − | 735.242i | − | 1.53495i | −0.641078 | − | 0.767476i | \(-0.721512\pi\) | ||
0.641078 | − | 0.767476i | \(-0.278488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −159.473 | −0.331545 | ||||||||
\(482\) | − | 630.069i | − | 1.30720i | ||||||
\(483\) | −105.013 | − | 177.279i | −0.217418 | − | 0.367037i | ||||
\(484\) | −98.0000 | −0.202479 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 154.925 | − | 306.751i | 0.318776 | − | 0.631175i | ||||
\(487\) | 92.6185 | 0.190182 | 0.0950909 | − | 0.995469i | \(-0.469686\pi\) | ||||
0.0950909 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(488\) | − | 152.586i | − | 0.312676i | ||||||
\(489\) | −29.3772 | + | 17.4019i | −0.0600761 | + | 0.0355866i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 898.323i | − | 1.82958i | −0.403933 | − | 0.914789i | \(-0.632357\pi\) | ||
0.403933 | − | 0.914789i | \(-0.367643\pi\) | |||||||
\(492\) | −144.816 | − | 244.473i | −0.294341 | − | 0.496896i | ||||
\(493\) | 815.368 | 1.65389 | ||||||||
\(494\) | − | 381.465i | − | 0.772197i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 0.0645161 | ||||||||
\(497\) | − | 116.747i | − | 0.234903i | ||||||
\(498\) | −95.4342 | + | 56.5313i | −0.191635 | + | 0.113517i | ||||
\(499\) | 136.921 | 0.274391 | 0.137195 | − | 0.990544i | \(-0.456191\pi\) | ||||
0.137195 | + | 0.990544i | \(0.456191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −385.710 | − | 651.143i | −0.769881 | − | 1.29969i | ||||
\(502\) | 335.684 | 0.668693 | ||||||||
\(503\) | 443.077i | 0.880868i | 0.897785 | + | 0.440434i | \(0.145175\pi\) | ||||
−0.897785 | + | 0.440434i | \(0.854825\pi\) | |||||||
\(504\) | 167.140 | + | 91.5766i | 0.331627 | + | 0.181700i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 110.085i | − | 0.217560i | ||||||
\(507\) | 178.099 | − | 105.498i | 0.351279 | − | 0.208083i | ||||
\(508\) | −268.921 | −0.529372 | ||||||||
\(509\) | 213.062i | 0.418590i | 0.977853 | + | 0.209295i | \(0.0671168\pi\) | ||||
−0.977853 | + | 0.209295i | \(0.932883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −658.447 | −1.28855 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 24.4299 | + | 727.879i | 0.0476216 | + | 1.41887i | ||||
\(514\) | −450.974 | −0.877381 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 74.6491 | − | 44.2191i | 0.144669 | − | 0.0856959i | ||||
\(517\) | 389.210 | 0.752824 | ||||||||
\(518\) | 168.850i | 0.325965i | ||||||||
\(519\) | −18.0662 | − | 30.4987i | −0.0348096 | − | 0.0587643i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.20085i | 0.00614366i | 0.999995 | + | 0.00307183i | \(0.000977795\pi\) | ||||
−0.999995 | + | 0.00307183i | \(0.999022\pi\) | |||||||
\(522\) | 164.105 | − | 299.515i | 0.314378 | − | 0.573784i | ||||
\(523\) | −966.644 | −1.84827 | −0.924134 | − | 0.382069i | \(-0.875212\pi\) | ||||
−0.924134 | + | 0.382069i | \(0.875212\pi\) | |||||||
\(524\) | − | 440.788i | − | 0.841198i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −51.2370 | −0.0974088 | ||||||||
\(527\) | − | 243.096i | − | 0.461282i | ||||||
\(528\) | 51.8947 | + | 87.6068i | 0.0982853 | + | 0.165922i | ||||
\(529\) | 444.842 | 0.840911 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 190.053 | + | 104.130i | 0.357915 | + | 0.196102i | ||||
\(532\) | −403.895 | −0.759200 | ||||||||
\(533\) | − | 473.575i | − | 0.888509i | ||||||
\(534\) | 221.842 | − | 131.410i | 0.415434 | − | 0.246086i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 312.429i | 0.582891i | ||||||||
\(537\) | −105.553 | − | 178.191i | −0.196561 | − | 0.331827i | ||||
\(538\) | −746.763 | −1.38804 | ||||||||
\(539\) | − | 59.8439i | − | 0.111028i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −186.105 | −0.344002 | −0.172001 | − | 0.985097i | \(-0.555023\pi\) | ||||
−0.172001 | + | 0.985097i | \(0.555023\pi\) | |||||||
\(542\) | 673.017i | 1.24173i | ||||||||
\(543\) | 489.601 | − | 290.019i | 0.901659 | − | 0.534106i | ||||
\(544\) | −171.895 | −0.315983 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 161.886 | + | 273.290i | 0.296495 | + | 0.500532i | ||||
\(547\) | 309.434 | 0.565693 | 0.282847 | − | 0.959165i | \(-0.408721\pi\) | ||||
0.282847 | + | 0.959165i | \(0.408721\pi\) | |||||||
\(548\) | − | 191.031i | − | 0.348596i | ||||||
\(549\) | −233.298 | + | 425.802i | −0.424951 | + | 0.775596i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 723.779i | 1.31357i | ||||||||
\(552\) | 66.9737 | − | 39.6725i | 0.121329 | − | 0.0718704i | ||||
\(553\) | −351.684 | −0.635957 | ||||||||
\(554\) | 266.096i | 0.480317i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 153.631 | 0.276315 | ||||||||
\(557\) | − | 4.00106i | − | 0.00718323i | −0.999994 | − | 0.00359161i | \(-0.998857\pi\) | ||
0.999994 | − | 0.00359161i | \(-0.00114325\pi\) | |||||||
\(558\) | −89.2982 | − | 48.9268i | −0.160033 | − | 0.0876824i | ||||
\(559\) | 144.605 | 0.258685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 665.526 | − | 394.230i | 1.18632 | − | 0.702728i | ||||
\(562\) | 34.5523 | 0.0614810 | ||||||||
\(563\) | 166.970i | 0.296572i | 0.988945 | + | 0.148286i | \(0.0473756\pi\) | ||||
−0.988945 | + | 0.148286i | \(0.952624\pi\) | |||||||
\(564\) | 140.263 | + | 236.788i | 0.248694 | + | 0.419836i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 280.666i | 0.495875i | ||||||||
\(567\) | −326.399 | − | 511.102i | −0.575660 | − | 0.901414i | ||||
\(568\) | 44.1053 | 0.0776502 | ||||||||
\(569\) | − | 156.289i | − | 0.274673i | −0.990524 | − | 0.137337i | \(-0.956146\pi\) | ||
0.990524 | − | 0.137337i | \(-0.0438542\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −144.105 | −0.252374 | −0.126187 | − | 0.992006i | \(-0.540274\pi\) | ||||
−0.126187 | + | 0.992006i | \(0.540274\pi\) | |||||||
\(572\) | 169.706i | 0.296688i | ||||||||
\(573\) | 166.211 | + | 280.591i | 0.290071 | + | 0.489688i | ||||
\(574\) | −501.421 | −0.873555 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −34.5964 | + | 63.1434i | −0.0600633 | + | 0.109624i | ||||
\(577\) | −532.947 | −0.923651 | −0.461826 | − | 0.886971i | \(-0.652805\pi\) | ||||
−0.461826 | + | 0.886971i | \(0.652805\pi\) | |||||||
\(578\) | 897.132i | 1.55213i | ||||||||
\(579\) | −433.495 | + | 256.785i | −0.748697 | + | 0.443497i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 195.738i | 0.336899i | ||||||||
\(582\) | −77.9559 | − | 131.602i | −0.133945 | − | 0.226121i | ||||
\(583\) | −257.842 | −0.442268 | ||||||||
\(584\) | − | 248.753i | − | 0.425946i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 726.658 | 1.24003 | ||||||||
\(587\) | 190.342i | 0.324262i | 0.986769 | + | 0.162131i | \(0.0518368\pi\) | ||||
−0.986769 | + | 0.162131i | \(0.948163\pi\) | |||||||
\(588\) | 36.4078 | − | 21.5665i | 0.0619181 | − | 0.0366777i | ||||
\(589\) | 215.789 | 0.366366 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −262.460 | − | 443.077i | −0.444096 | − | 0.749707i | ||||
\(592\) | −63.7893 | −0.107752 | ||||||||
\(593\) | 345.719i | 0.583001i | 0.956571 | + | 0.291500i | \(0.0941544\pi\) | ||||
−0.956571 | + | 0.291500i | \(0.905846\pi\) | |||||||
\(594\) | −10.8683 | − | 323.818i | −0.0182969 | − | 0.545148i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 552.473i | − | 0.926969i | ||||||
\(597\) | −90.5438 | + | 53.6344i | −0.151665 | + | 0.0898399i | ||||
\(598\) | 129.737 | 0.216951 | ||||||||
\(599\) | 704.055i | 1.17538i | 0.809085 | + | 0.587692i | \(0.199963\pi\) | ||||
−0.809085 | + | 0.587692i | \(0.800037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 338.474 | 0.563185 | 0.281592 | − | 0.959534i | \(-0.409137\pi\) | ||||
0.281592 | + | 0.959534i | \(0.409137\pi\) | |||||||
\(602\) | − | 153.107i | − | 0.254331i | ||||||
\(603\) | 477.693 | − | 871.856i | 0.792193 | − | 1.44586i | ||||
\(604\) | −36.1053 | −0.0597770 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −175.789 | + | 104.130i | −0.290081 | + | 0.171832i | ||||
\(607\) | 816.513 | 1.34516 | 0.672581 | − | 0.740024i | \(-0.265186\pi\) | ||||
0.672581 | + | 0.740024i | \(0.265186\pi\) | |||||||
\(608\) | − | 152.586i | − | 0.250964i | ||||||
\(609\) | −307.157 | − | 518.532i | −0.504363 | − | 0.851449i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 458.688i | 0.750717i | ||||||||
\(612\) | 479.684 | + | 262.820i | 0.783797 | + | 0.429445i | ||||
\(613\) | 229.263 | 0.374001 | 0.187001 | − | 0.982360i | \(-0.440123\pi\) | ||||
0.187001 | + | 0.982360i | \(0.440123\pi\) | |||||||
\(614\) | − | 16.0959i | − | 0.0262148i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 179.684 | 0.291695 | ||||||||
\(617\) | 1072.25i | 1.73785i | 0.494945 | + | 0.868924i | \(0.335188\pi\) | ||||
−0.494945 | + | 0.868924i | \(0.664812\pi\) | |||||||
\(618\) | −303.601 | − | 512.528i | −0.491263 | − | 0.829334i | ||||
\(619\) | −80.7103 | −0.130388 | −0.0651941 | − | 0.997873i | \(-0.520767\pi\) | ||||
−0.0651941 | + | 0.997873i | \(0.520767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −247.552 | + | 8.30863i | −0.398635 | + | 0.0133794i | ||||
\(622\) | −733.631 | −1.17947 | ||||||||
\(623\) | − | 455.004i | − | 0.730344i | ||||||
\(624\) | −103.246 | + | 61.1584i | −0.165458 | + | 0.0980103i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 65.5007i | − | 0.104634i | ||||||
\(627\) | 349.947 | + | 590.769i | 0.558130 | + | 0.942215i | ||||
\(628\) | 207.684 | 0.330707 | ||||||||
\(629\) | 484.591i | 0.770415i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 492.894 | 0.781131 | 0.390566 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390566 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(632\) | − | 132.862i | − | 0.210224i | ||||||
\(633\) | 150.114 | − | 88.9213i | 0.237147 | − | 0.140476i | ||||
\(634\) | −55.2897 | −0.0872077 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −92.9210 | − | 156.866i | −0.146102 | − | 0.246645i | ||||
\(637\) | 70.5267 | 0.110717 | ||||||||
\(638\) | − | 321.994i | − | 0.504692i | ||||||
\(639\) | −123.079 | − | 67.4353i | −0.192612 | − | 0.105533i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 65.4816i | 0.102155i | 0.998695 | + | 0.0510777i | \(0.0162656\pi\) | ||||
−0.998695 | + | 0.0510777i | \(0.983734\pi\) | |||||||
\(642\) | 157.381 | − | 93.2264i | 0.245143 | − | 0.145212i | ||||
\(643\) | 428.619 | 0.666592 | 0.333296 | − | 0.942822i | \(-0.391839\pi\) | ||||
0.333296 | + | 0.942822i | \(0.391839\pi\) | |||||||
\(644\) | − | 137.365i | − | 0.213300i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1159.16 | −1.79436 | ||||||||
\(647\) | 462.801i | 0.715303i | 0.933855 | + | 0.357652i | \(0.116422\pi\) | ||||
−0.933855 | + | 0.357652i | \(0.883578\pi\) | |||||||
\(648\) | 193.088 | − | 123.309i | 0.297975 | − | 0.190292i | ||||
\(649\) | 204.316 | 0.314817 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −154.596 | + | 91.5766i | −0.237475 | + | 0.140671i | ||||
\(652\) | −22.7630 | −0.0349126 | ||||||||
\(653\) | 425.064i | 0.650941i | 0.945552 | + | 0.325470i | \(0.105523\pi\) | ||||
−0.945552 | + | 0.325470i | \(0.894477\pi\) | |||||||
\(654\) | 289.404 | + | 488.561i | 0.442513 | + | 0.747035i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 189.430i | − | 0.288765i | ||||||
\(657\) | −380.333 | + | 694.161i | −0.578894 | + | 1.05656i | ||||
\(658\) | 485.658 | 0.738083 | ||||||||
\(659\) | 182.769i | 0.277343i | 0.990338 | + | 0.138671i | \(0.0442831\pi\) | ||||
−0.990338 | + | 0.138671i | \(0.955717\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −482.053 | −0.729278 | −0.364639 | − | 0.931149i | \(-0.618808\pi\) | ||||
−0.364639 | + | 0.931149i | \(0.618808\pi\) | |||||||
\(662\) | 629.920i | 0.951541i | ||||||||
\(663\) | 464.605 | + | 784.330i | 0.700762 | + | 1.18300i | ||||
\(664\) | −73.9473 | −0.111366 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 178.009 | + | 97.5314i | 0.267280 | + | 0.146444i | ||||
\(667\) | −246.158 | −0.369052 | ||||||||
\(668\) | − | 504.539i | − | 0.755298i | ||||||
\(669\) | 256.517 | − | 151.950i | 0.383434 | − | 0.227131i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 457.758i | 0.682203i | ||||||||
\(672\) | 64.7544 | + | 109.316i | 0.0963608 | + | 0.162673i | ||||
\(673\) | −184.579 | −0.274264 | −0.137132 | − | 0.990553i | \(-0.543788\pi\) | ||||
−0.137132 | + | 0.990553i | \(0.543788\pi\) | |||||||
\(674\) | 460.587i | 0.683363i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 138.000 | 0.204142 | ||||||||
\(677\) | − | 1065.85i | − | 1.57437i | −0.616715 | − | 0.787187i | \(-0.711537\pi\) | ||
0.616715 | − | 0.787187i | \(-0.288463\pi\) | |||||||
\(678\) | −28.8683 | + | 17.1004i | −0.0425787 | + | 0.0252219i | ||||
\(679\) | −269.920 | −0.397526 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 331.710 | + | 559.982i | 0.487093 | + | 0.822293i | ||||
\(682\) | −96.0000 | −0.140762 | ||||||||
\(683\) | − | 788.926i | − | 1.15509i | −0.816359 | − | 0.577545i | \(-0.804011\pi\) | ||
0.816359 | − | 0.577545i | \(-0.195989\pi\) | |||||||
\(684\) | −233.298 | + | 425.802i | −0.341079 | + | 0.622518i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 444.138i | 0.647431i | ||||||||
\(687\) | −840.636 | + | 497.958i | −1.22363 | + | 0.724830i | ||||
\(688\) | 57.8420 | 0.0840727 | ||||||||
\(689\) | − | 303.870i | − | 0.441030i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 932.000 | 1.34877 | 0.674385 | − | 0.738380i | \(-0.264409\pi\) | ||||
0.674385 | + | 0.738380i | \(0.264409\pi\) | |||||||
\(692\) | − | 23.6320i | − | 0.0341502i | ||||||
\(693\) | −501.421 | − | 274.730i | −0.723551 | − | 0.396436i | ||||
\(694\) | 73.2897 | 0.105605 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 195.895 | − | 116.040i | 0.281458 | − | 0.166724i | ||||
\(697\) | −1439.05 | −2.06464 | ||||||||
\(698\) | 137.997i | 0.197704i | ||||||||
\(699\) | 79.0655 | + | 133.476i | 0.113112 | + | 0.190952i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1352.75i | − | 1.92974i | −0.262721 | − | 0.964872i | \(-0.584620\pi\) | ||
0.262721 | − | 0.964872i | \(-0.415380\pi\) | |||||||
\(702\) | 381.623 | − | 12.8084i | 0.543622 | − | 0.0182457i | ||||
\(703\) | −430.158 | −0.611889 | ||||||||
\(704\) | 67.8823i | 0.0964237i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −805.815 | −1.14138 | ||||||||
\(707\) | 360.549i | 0.509970i | ||||||||
\(708\) | 73.6313 | + | 124.302i | 0.103999 | + | 0.175568i | ||||
\(709\) | −269.473 | −0.380075 | −0.190038 | − | 0.981777i | \(-0.560861\pi\) | ||||
−0.190038 | + | 0.981777i | \(0.560861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −203.140 | + | 370.759i | −0.285711 | + | 0.521462i | ||||
\(712\) | 171.895 | 0.241425 | ||||||||
\(713\) | 73.3901i | 0.102931i | ||||||||
\(714\) | 830.447 | − | 491.923i | 1.16309 | − | 0.688968i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 138.072i | − | 0.192837i | ||||||
\(717\) | −626.947 | − | 1058.39i | −0.874403 | − | 1.47614i | ||||
\(718\) | −387.895 | −0.540243 | ||||||||
\(719\) | 537.103i | 0.747014i | 0.927627 | + | 0.373507i | \(0.121845\pi\) | ||||
−0.927627 | + | 0.373507i | \(0.878155\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1051.21 | −1.45799 | ||||||||
\(722\) | − | 518.421i | − | 0.718034i | ||||||
\(723\) | −1149.96 | + | 681.192i | −1.59055 | + | 0.942174i | ||||
\(724\) | 379.368 | 0.523989 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 105.952 | + | 178.864i | 0.145939 | + | 0.246369i | ||||
\(727\) | 1117.83 | 1.53759 | 0.768795 | − | 0.639495i | \(-0.220856\pi\) | ||||
0.768795 | + | 0.639495i | \(0.220856\pi\) | |||||||
\(728\) | 211.760i | 0.290879i | ||||||||
\(729\) | −727.359 | + | 48.8800i | −0.997750 | + | 0.0670507i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 439.411i | − | 0.601109i | ||||||
\(732\) | −278.491 | + | 164.967i | −0.380452 | + | 0.225364i | ||||
\(733\) | −7.52599 | −0.0102674 | −0.00513369 | − | 0.999987i | \(-0.501634\pi\) | ||||
−0.00513369 | + | 0.999987i | \(0.501634\pi\) | |||||||
\(734\) | 653.124i | 0.889815i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 51.8947 | 0.0705091 | ||||||||
\(737\) | − | 937.288i | − | 1.27176i | ||||||
\(738\) | −289.631 | + | 528.618i | −0.392454 | + | 0.716284i | ||||
\(739\) | −823.079 | −1.11377 | −0.556887 | − | 0.830588i | \(-0.688004\pi\) | ||||
−0.556887 | + | 0.830588i | \(0.688004\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −696.228 | + | 412.417i | −0.939579 | + | 0.556568i | ||||
\(742\) | −321.737 | −0.433607 | ||||||||
\(743\) | − | 3.21898i | − | 0.00433241i | −0.999998 | − | 0.00216620i | \(-0.999310\pi\) | ||
0.999998 | − | 0.00216620i | \(-0.000689524\pi\) | |||||||
\(744\) | −34.5964 | − | 58.4045i | −0.0465006 | − | 0.0785007i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 695.719i | − | 0.932599i | ||||||
\(747\) | 206.355 | + | 113.063i | 0.276245 | + | 0.151356i | ||||
\(748\) | 515.684 | 0.689417 | ||||||||
\(749\) | − | 322.794i | − | 0.430967i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1185.63 | 1.57874 | 0.789368 | − | 0.613920i | \(-0.210408\pi\) | ||||
0.789368 | + | 0.613920i | \(0.210408\pi\) | |||||||
\(752\) | 183.475i | 0.243983i | ||||||||
\(753\) | −362.921 | − | 612.671i | −0.481967 | − | 0.813639i | ||||
\(754\) | 379.473 | 0.503280 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.5616 | − | 404.061i | −0.0179386 | − | 0.534473i | ||||
\(757\) | 863.315 | 1.14044 | 0.570221 | − | 0.821491i | \(-0.306857\pi\) | ||||
0.570221 | + | 0.821491i | \(0.306857\pi\) | |||||||
\(758\) | 365.946i | 0.482779i | ||||||||
\(759\) | −200.921 | + | 119.017i | −0.264718 | + | 0.156808i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 570.597i | − | 0.749800i | −0.927065 | − | 0.374900i | \(-0.877677\pi\) | ||
0.927065 | − | 0.374900i | \(-0.122323\pi\) | |||||||
\(762\) | 290.741 | + | 490.819i | 0.381550 | + | 0.644119i | ||||
\(763\) | 1002.05 | 1.31331 | ||||||||
\(764\) | 217.416i | 0.284577i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 738.816 | 0.964511 | ||||||||
\(767\) | 240.789i | 0.313936i | ||||||||
\(768\) | −41.2982 | + | 24.4634i | −0.0537737 | + | 0.0318534i | ||||
\(769\) | −741.684 | −0.964479 | −0.482239 | − | 0.876040i | \(-0.660176\pi\) | ||||
−0.482239 | + | 0.876040i | \(0.660176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 487.565 | + | 823.090i | 0.632380 | + | 1.06756i | ||||
\(772\) | −335.895 | −0.435097 | ||||||||
\(773\) | − | 623.203i | − | 0.806214i | −0.915153 | − | 0.403107i | \(-0.867930\pi\) | ||
0.915153 | − | 0.403107i | \(-0.132070\pi\) | |||||||
\(774\) | −161.412 | − | 88.4382i | −0.208543 | − | 0.114261i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 101.972i | − | 0.131408i | ||||||
\(777\) | 308.175 | − | 182.550i | 0.396622 | − | 0.234943i | ||||
\(778\) | 863.868 | 1.11037 | ||||||||
\(779\) | − | 1277.41i | − | 1.63980i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −132.316 | −0.169419 | ||||||||
\(782\) | − | 394.230i | − | 0.504131i | ||||||
\(783\) | −724.078 | + | 24.3023i | −0.924749 | + | 0.0310375i | ||||
\(784\) | 28.2107 | 0.0359830 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −804.500 | + | 476.553i | −1.02354 | + | 0.606301i | ||||
\(787\) | −335.303 | −0.426052 | −0.213026 | − | 0.977046i | \(-0.568332\pi\) | ||||
−0.213026 | + | 0.977046i | \(0.568332\pi\) | |||||||
\(788\) | − | 343.319i | − | 0.435684i | ||||||
\(789\) | 55.3943 | + | 93.5147i | 0.0702083 | + | 0.118523i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 59.2098i | 0.0748543i | ||||||||
\(792\) | 103.789 | − | 189.430i | 0.131047 | − | 0.239179i | ||||
\(793\) | −539.473 | −0.680294 | ||||||||
\(794\) | − | 302.642i | − | 0.381161i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −70.1580 | −0.0881382 | ||||||||
\(797\) | − | 550.520i | − | 0.690740i | −0.938467 | − | 0.345370i | \(-0.887753\pi\) | ||
0.938467 | − | 0.345370i | \(-0.112247\pi\) | |||||||
\(798\) | 436.666 | + | 737.165i | 0.547201 | + | 0.923765i | ||||
\(799\) | 1393.81 | 1.74445 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −479.684 | − | 262.820i | −0.598856 | − | 0.328115i | ||||
\(802\) | 642.841 | 0.801548 | ||||||||
\(803\) | 746.258i | 0.929337i | ||||||||
\(804\) | 570.228 | − | 337.780i | 0.709239 | − | 0.420124i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 113.137i | − | 0.140369i | ||||||
\(807\) | 807.354 | + | 1362.95i | 1.00044 | + | 1.68891i | ||||
\(808\) | −136.211 | −0.168578 | ||||||||
\(809\) | − | 560.288i | − | 0.692569i | −0.938130 | − | 0.346284i | \(-0.887443\pi\) | ||
0.938130 | − | 0.346284i | \(-0.112557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −237.842 | −0.293270 | −0.146635 | − | 0.989191i | \(-0.546844\pi\) | ||||
−0.146635 | + | 0.989191i | \(0.546844\pi\) | |||||||
\(812\) | − | 401.786i | − | 0.494810i | ||||||
\(813\) | 1228.35 | − | 727.624i | 1.51089 | − | 0.894987i | ||||
\(814\) | 191.368 | 0.235096 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 185.842 | + | 313.732i | 0.227748 | + | 0.384475i | ||||
\(817\) | 390.053 | 0.477421 | ||||||||
\(818\) | 811.535i | 0.992097i | ||||||||
\(819\) | 323.772 | − | 590.930i | 0.395326 | − | 0.721526i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 65.4816i | 0.0797584i | 0.999205 | + | 0.0398792i | \(0.0126973\pi\) | ||||
−0.999205 | + | 0.0398792i | \(0.987303\pi\) | |||||||
\(822\) | −348.658 | + | 206.531i | −0.424158 | + | 0.251254i | ||||
\(823\) | −521.512 | −0.633673 | −0.316836 | − | 0.948480i | \(-0.602621\pi\) | ||||
−0.316836 | + | 0.948480i | \(0.602621\pi\) | |||||||
\(824\) | − | 397.133i | − | 0.481958i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 254.947 | 0.308652 | ||||||||
\(827\) | − | 987.512i | − | 1.19409i | −0.802208 | − | 0.597045i | \(-0.796342\pi\) | ||
0.802208 | − | 0.597045i | \(-0.203658\pi\) | |||||||
\(828\) | −144.816 | − | 79.3449i | −0.174898 | − | 0.0958272i | ||||
\(829\) | 333.631 | 0.402450 | 0.201225 | − | 0.979545i | \(-0.435508\pi\) | ||||
0.201225 | + | 0.979545i | \(0.435508\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 485.662 | − | 287.686i | 0.584431 | − | 0.346193i | ||||
\(832\) | −80.0000 | −0.0961538 | ||||||||
\(833\) | − | 214.309i | − | 0.257274i | ||||||
\(834\) | −166.097 | − | 280.399i | −0.199157 | − | 0.336210i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 457.758i | 0.547558i | ||||||||
\(837\) | 7.24555 | + | 215.878i | 0.00865657 | + | 0.257919i | ||||
\(838\) | 138.474 | 0.165243 | ||||||||
\(839\) | − | 129.363i | − | 0.154187i | −0.997024 | − | 0.0770934i | \(-0.975436\pi\) | ||
0.997024 | − | 0.0770934i | \(-0.0245640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 121.000 | 0.143876 | ||||||||
\(842\) | − | 1014.44i | − | 1.20479i | ||||||
\(843\) | −37.3559 | − | 63.0629i | −0.0443130 | − | 0.0748077i | ||||
\(844\) | 116.316 | 0.137815 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 280.527 | − | 512.001i | 0.331592 | − | 0.605202i | ||||
\(847\) | 366.855 | 0.433123 | ||||||||
\(848\) | − | 121.548i | − | 0.143335i | ||||||
\(849\) | 512.254 | − | 303.438i | 0.603362 | − | 0.357407i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 146.297i | − | 0.171912i | ||||||
\(852\) | −47.6840 | − | 80.4984i | −0.0559671 | − | 0.0944817i | ||||
\(853\) | −1080.42 | −1.26661 | −0.633306 | − | 0.773902i | \(-0.718303\pi\) | ||||
−0.633306 | + | 0.773902i | \(0.718303\pi\) | |||||||
\(854\) | 571.193i | 0.668845i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 121.947 | 0.142462 | ||||||||
\(857\) | − | 702.548i | − | 0.819776i | −0.912136 | − | 0.409888i | \(-0.865568\pi\) | ||
0.912136 | − | 0.409888i | \(-0.134432\pi\) | |||||||
\(858\) | 309.737 | − | 183.475i | 0.360998 | − | 0.213841i | ||||
\(859\) | −281.132 | −0.327278 | −0.163639 | − | 0.986520i | \(-0.552323\pi\) | ||||
−0.163639 | + | 0.986520i | \(0.552323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 542.105 | + | 915.163i | 0.629623 | + | 1.06291i | ||||
\(862\) | 414.474 | 0.480828 | ||||||||
\(863\) | − | 419.221i | − | 0.485772i | −0.970055 | − | 0.242886i | \(-0.921906\pi\) | ||
0.970055 | − | 0.242886i | \(-0.0780941\pi\) | |||||||
\(864\) | 152.649 | − | 5.12338i | 0.176677 | − | 0.00592984i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 689.466i | 0.796150i | ||||||||
\(867\) | 1637.39 | − | 969.924i | 1.88857 | − | 1.11871i | ||||
\(868\) | −119.789 | −0.138006 | ||||||||
\(869\) | 398.585i | 0.458671i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1104.60 | 1.26820 | ||||||||
\(872\) | 378.562i | 0.434131i | ||||||||
\(873\) | −155.912 | + | 284.561i | −0.178593 | + | 0.325958i | ||||
\(874\) | 349.947 | 0.400397 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −454.009 | + | 268.936i | −0.518275 | + | 0.307005i | ||||
\(877\) | −1079.42 | −1.23081 | −0.615405 | − | 0.788211i | \(-0.711008\pi\) | ||||
−0.615405 | + | 0.788211i | \(0.711008\pi\) | |||||||
\(878\) | − | 363.788i | − | 0.414337i | ||||||
\(879\) | −785.618 | − | 1326.25i | −0.893763 | − | 1.50882i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 748.212i | − | 0.849275i | −0.905363 | − | 0.424638i | \(-0.860401\pi\) | ||
0.905363 | − | 0.424638i | \(-0.139599\pi\) | |||||||
\(882\) | −78.7238 | − | 43.1330i | −0.0892561 | − | 0.0489037i | ||||
\(883\) | 875.749 | 0.991788 | 0.495894 | − | 0.868383i | \(-0.334840\pi\) | ||||
0.495894 | + | 0.868383i | \(0.334840\pi\) | |||||||
\(884\) | 607.739i | 0.687488i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 414.500 | 0.467833 | ||||||||
\(887\) | − | 1015.05i | − | 1.14436i | −0.820127 | − | 0.572182i | \(-0.806097\pi\) | ||
0.820127 | − | 0.572182i | \(-0.193903\pi\) | |||||||
\(888\) | 68.9651 | + | 116.425i | 0.0776634 | + | 0.131109i | ||||
\(889\) | 1006.68 | 1.13238 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −579.263 | + | 369.928i | −0.650126 | + | 0.415183i | ||||
\(892\) | 198.763 | 0.222828 | ||||||||
\(893\) | 1237.25i | 1.38550i | ||||||||
\(894\) | −1008.34 | + | 597.300i | −1.12790 | + | 0.668121i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 84.7038i | 0.0945355i | ||||||||
\(897\) | −140.263 | − | 236.788i | −0.156369 | − | 0.263977i | ||||
\(898\) | −828.184 | −0.922254 | ||||||||
\(899\) | 214.663i | 0.238779i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −923.368 | −1.02483 | ||||||||
\(902\) | 568.290i | 0.630034i | ||||||||
\(903\) | −279.443 | + | 165.530i | −0.309460 | + | 0.183312i | ||||
\(904\) | −22.3687 | −0.0247441 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 39.0349 | + | 65.8973i | 0.0430849 | + | 0.0727343i | ||||
\(907\) | −1504.70 | −1.65898 | −0.829491 | − | 0.558520i | \(-0.811369\pi\) | ||||
−0.829491 | + | 0.558520i | \(0.811369\pi\) | |||||||
\(908\) | 433.903i | 0.477867i | ||||||||
\(909\) | 380.105 | + | 208.261i | 0.418158 | + | 0.229110i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1002.19i | − | 1.10010i | −0.835131 | − | 0.550051i | \(-0.814608\pi\) | ||
0.835131 | − | 0.550051i | \(-0.185392\pi\) | |||||||
\(912\) | −278.491 | + | 164.967i | −0.305363 | + | 0.180885i | ||||
\(913\) | 221.842 | 0.242981 | ||||||||
\(914\) | − | 1149.83i | − | 1.25802i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −651.368 | −0.711100 | ||||||||
\(917\) | 1650.05i | 1.79940i | ||||||||
\(918\) | −38.9210 | − | 1159.64i | −0.0423976 | − | 1.26322i | ||||
\(919\) | −780.289 | −0.849063 | −0.424532 | − | 0.905413i | \(-0.639561\pi\) | ||||
−0.424532 | + | 0.905413i | \(0.639561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.3772 | + | 17.4019i | −0.0318971 | + | 0.0188945i | ||||
\(922\) | 783.579 | 0.849868 | ||||||||
\(923\) | − | 155.936i | − | 0.168945i | ||||||
\(924\) | −194.263 | − | 327.949i | −0.210242 | − | 0.354923i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 636.005i | − | 0.686830i | ||||||
\(927\) | −607.201 | + | 1108.23i | −0.655018 | + | 1.19550i | ||||
\(928\) | 151.789 | 0.163566 | ||||||||
\(929\) | 1093.84i | 1.17744i | 0.808339 | + | 0.588718i | \(0.200367\pi\) | ||||
−0.808339 | + | 0.588718i | \(0.799633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 190.236 | 0.204335 | ||||||||
\(932\) | 103.424i | 0.110970i | ||||||||
\(933\) | 793.157 | + | 1338.98i | 0.850115 | + | 1.43513i | ||||
\(934\) | 43.4477 | 0.0465179 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 223.246 | + | 122.317i | 0.238510 | + | 0.130680i | ||||
\(937\) | 407.947 | 0.435376 | 0.217688 | − | 0.976018i | \(-0.430148\pi\) | ||||
0.217688 | + | 0.976018i | \(0.430148\pi\) | |||||||
\(938\) | − | 1169.55i | − | 1.24686i | ||||||
\(939\) | −119.548 | + | 70.8154i | −0.127314 | + | 0.0754157i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 671.008i | 0.713079i | 0.934280 | + | 0.356540i | \(0.116044\pi\) | ||||
−0.934280 | + | 0.356540i | \(0.883956\pi\) | |||||||
\(942\) | −224.535 | − | 379.053i | −0.238360 | − | 0.402391i | ||||
\(943\) | 434.447 | 0.460707 | ||||||||
\(944\) | 96.3155i | 0.102029i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −173.526 | −0.183431 | ||||||||
\(947\) | 1608.13i | 1.69813i | 0.528290 | + | 0.849064i | \(0.322833\pi\) | ||||
−0.528290 | + | 0.849064i | \(0.677167\pi\) | |||||||
\(948\) | −242.491 | + | 143.642i | −0.255792 | + | 0.151521i | ||||
\(949\) | −879.473 | −0.926737 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 59.7758 | + | 100.911i | 0.0628557 | + | 0.106111i | ||||
\(952\) | 643.473 | 0.675917 | ||||||||
\(953\) | 695.440i | 0.729737i | 0.931059 | + | 0.364869i | \(0.118886\pi\) | ||||
−0.931059 | + | 0.364869i | \(0.881114\pi\) | |||||||
\(954\) | −185.842 | + | 339.188i | −0.194803 | + | 0.355543i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 820.095i | − | 0.857840i | ||||||
\(957\) | −587.684 | + | 348.120i | −0.614090 | + | 0.363762i | ||||
\(958\) | −1039.79 | −1.08538 | ||||||||
\(959\) | 715.107i | 0.745680i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −897.000 | −0.933403 | ||||||||
\(962\) | 225.529i | 0.234438i | ||||||||
\(963\) | −340.302 | − | 186.453i | −0.353377 | − | 0.193617i | ||||
\(964\) | −891.052 | −0.924328 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −250.710 | + | 148.511i | −0.259534 | + | 0.153738i | ||||
\(967\) | 1030.07 | 1.06522 | 0.532609 | − | 0.846361i | \(-0.321212\pi\) | ||||
0.532609 | + | 0.846361i | \(0.321212\pi\) | |||||||
\(968\) | 138.593i | 0.143175i | ||||||||
\(969\) | 1253.21 | + | 2115.63i | 1.29330 | + | 2.18331i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1165.24i | 1.20004i | 0.799986 | + | 0.600019i | \(0.204840\pi\) | ||||
−0.799986 | + | 0.600019i | \(0.795160\pi\) | |||||||
\(972\) | −433.811 | − | 219.097i | −0.446308 | − | 0.225409i | ||||
\(973\) | −575.106 | −0.591065 | ||||||||
\(974\) | − | 130.982i | − | 0.134479i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −215.789 | −0.221096 | ||||||||
\(977\) | − | 726.440i | − | 0.743541i | −0.928325 | − | 0.371771i | \(-0.878751\pi\) | ||
0.928325 | − | 0.371771i | \(-0.121249\pi\) | |||||||
\(978\) | 24.6100 | + | 41.5457i | 0.0251636 | + | 0.0424802i | ||||
\(979\) | −515.684 | −0.526746 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 578.807 | − | 1056.40i | 0.590017 | − | 1.07686i | ||||
\(982\) | −1270.42 | −1.29371 | ||||||||
\(983\) | − | 1024.21i | − | 1.04192i | −0.853581 | − | 0.520960i | \(-0.825574\pi\) | ||
0.853581 | − | 0.520960i | \(-0.174426\pi\) | |||||||
\(984\) | −345.737 | + | 204.800i | −0.351358 | + | 0.208130i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1153.10i | − | 1.16948i | ||||||
\(987\) | −525.064 | − | 886.395i | −0.531980 | − | 0.898070i | ||||
\(988\) | −539.473 | −0.546026 | ||||||||
\(989\) | 132.657i | 0.134133i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1797.89 | −1.81422 | −0.907111 | − | 0.420892i | \(-0.861717\pi\) | ||||
−0.907111 | + | 0.420892i | \(0.861717\pi\) | |||||||
\(992\) | − | 45.2548i | − | 0.0456198i | ||||||
\(993\) | 1149.69 | − | 681.031i | 1.15780 | − | 0.685832i | ||||
\(994\) | −165.105 | −0.166101 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 79.9473 | + | 134.964i | 0.0802684 | + | 0.135506i | ||||
\(997\) | −901.368 | −0.904080 | −0.452040 | − | 0.891998i | \(-0.649304\pi\) | ||||
−0.452040 | + | 0.891998i | \(0.649304\pi\) | |||||||
\(998\) | − | 193.636i | − | 0.194024i | ||||||
\(999\) | −14.4434 | − | 430.336i | −0.0144579 | − | 0.430766i |
(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 | 150.3.d.c.101.1 | 4 | ||
3.2 | odd | 2 | inner | 150.3.d.c.101.3 | 4 | ||
4.3 | odd | 2 | 1200.3.l.u.401.3 | 4 | |||
5.2 | odd | 4 | 150.3.b.b.149.8 | 8 | |||
5.3 | odd | 4 | 150.3.b.b.149.1 | 8 | |||
5.4 | even | 2 | 30.3.d.a.11.4 | yes | 4 | ||
12.11 | even | 2 | 1200.3.l.u.401.4 | 4 | |||
15.2 | even | 4 | 150.3.b.b.149.2 | 8 | |||
15.8 | even | 4 | 150.3.b.b.149.7 | 8 | |||
15.14 | odd | 2 | 30.3.d.a.11.2 | ✓ | 4 | ||
20.3 | even | 4 | 1200.3.c.k.449.6 | 8 | |||
20.7 | even | 4 | 1200.3.c.k.449.3 | 8 | |||
20.19 | odd | 2 | 240.3.l.c.161.2 | 4 | |||
40.19 | odd | 2 | 960.3.l.f.641.3 | 4 | |||
40.29 | even | 2 | 960.3.l.e.641.2 | 4 | |||
45.4 | even | 6 | 810.3.h.a.431.2 | 8 | |||
45.14 | odd | 6 | 810.3.h.a.431.3 | 8 | |||
45.29 | odd | 6 | 810.3.h.a.701.2 | 8 | |||
45.34 | even | 6 | 810.3.h.a.701.3 | 8 | |||
60.23 | odd | 4 | 1200.3.c.k.449.4 | 8 | |||
60.47 | odd | 4 | 1200.3.c.k.449.5 | 8 | |||
60.59 | even | 2 | 240.3.l.c.161.1 | 4 | |||
120.29 | odd | 2 | 960.3.l.e.641.1 | 4 | |||
120.59 | even | 2 | 960.3.l.f.641.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.3.d.a.11.2 | ✓ | 4 | 15.14 | odd | 2 | ||
30.3.d.a.11.4 | yes | 4 | 5.4 | even | 2 | ||
150.3.b.b.149.1 | 8 | 5.3 | odd | 4 | |||
150.3.b.b.149.2 | 8 | 15.2 | even | 4 | |||
150.3.b.b.149.7 | 8 | 15.8 | even | 4 | |||
150.3.b.b.149.8 | 8 | 5.2 | odd | 4 | |||
150.3.d.c.101.1 | 4 | 1.1 | even | 1 | trivial | ||
150.3.d.c.101.3 | 4 | 3.2 | odd | 2 | inner | ||
240.3.l.c.161.1 | 4 | 60.59 | even | 2 | |||
240.3.l.c.161.2 | 4 | 20.19 | odd | 2 | |||
810.3.h.a.431.2 | 8 | 45.4 | even | 6 | |||
810.3.h.a.431.3 | 8 | 45.14 | odd | 6 | |||
810.3.h.a.701.2 | 8 | 45.29 | odd | 6 | |||
810.3.h.a.701.3 | 8 | 45.34 | even | 6 | |||
960.3.l.e.641.1 | 4 | 120.29 | odd | 2 | |||
960.3.l.e.641.2 | 4 | 40.29 | even | 2 | |||
960.3.l.f.641.3 | 4 | 40.19 | odd | 2 | |||
960.3.l.f.641.4 | 4 | 120.59 | even | 2 | |||
1200.3.c.k.449.3 | 8 | 20.7 | even | 4 | |||
1200.3.c.k.449.4 | 8 | 60.23 | odd | 4 | |||
1200.3.c.k.449.5 | 8 | 60.47 | odd | 4 | |||
1200.3.c.k.449.6 | 8 | 20.3 | even | 4 | |||
1200.3.l.u.401.3 | 4 | 4.3 | odd | 2 | |||
1200.3.l.u.401.4 | 4 | 12.11 | even | 2 |