Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.13 | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.l.1084.12 |
$q$-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 \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.244477i | 0.172872i | 0.996257 | + | 0.0864358i | \(0.0275477\pi\) | ||||
−0.996257 | + | 0.0864358i | \(0.972452\pi\) | |||||||
\(3\) | − | 2.73837i | − | 1.58100i | −0.612464 | − | 0.790499i | \(-0.709821\pi\) | ||
0.612464 | − | 0.790499i | \(-0.290179\pi\) | |||||||
\(4\) | 1.94023 | 0.970115 | ||||||||
\(5\) | 0.750459 | + | 2.10637i | 0.335615 | + | 0.941999i | ||||
\(6\) | 0.669469 | 0.273309 | ||||||||
\(7\) | − | 1.94027i | − | 0.733354i | −0.930348 | − | 0.366677i | \(-0.880495\pi\) | ||
0.930348 | − | 0.366677i | \(-0.119505\pi\) | |||||||
\(8\) | 0.963297i | 0.340577i | ||||||||
\(9\) | −4.49866 | −1.49955 | ||||||||
\(10\) | −0.514961 | + | 0.183470i | −0.162845 | + | 0.0580184i | ||||
\(11\) | 4.23333 | 1.27640 | 0.638198 | − | 0.769872i | \(-0.279680\pi\) | ||||
0.638198 | + | 0.769872i | \(0.279680\pi\) | |||||||
\(12\) | − | 5.31307i | − | 1.53375i | ||||||
\(13\) | − | 1.26982i | − | 0.352186i | −0.984374 | − | 0.176093i | \(-0.943654\pi\) | ||
0.984374 | − | 0.176093i | \(-0.0563459\pi\) | |||||||
\(14\) | 0.474352 | 0.126776 | ||||||||
\(15\) | 5.76803 | − | 2.05503i | 1.48930 | − | 0.530607i | ||||
\(16\) | 3.64496 | 0.911239 | ||||||||
\(17\) | − | 2.46021i | − | 0.596689i | −0.954458 | − | 0.298345i | \(-0.903566\pi\) | ||
0.954458 | − | 0.298345i | \(-0.0964345\pi\) | |||||||
\(18\) | − | 1.09982i | − | 0.259230i | ||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.45606 | + | 4.08685i | 0.325586 | + | 0.913848i | ||||
\(21\) | −5.31318 | −1.15943 | ||||||||
\(22\) | 1.03495i | 0.220653i | ||||||||
\(23\) | 5.13716i | 1.07117i | 0.844481 | + | 0.535586i | \(0.179909\pi\) | ||||
−0.844481 | + | 0.535586i | \(0.820091\pi\) | |||||||
\(24\) | 2.63786 | 0.538451 | ||||||||
\(25\) | −3.87362 | + | 3.16149i | −0.774725 | + | 0.632299i | ||||
\(26\) | 0.310443 | 0.0608829 | ||||||||
\(27\) | 4.10387i | 0.789791i | ||||||||
\(28\) | − | 3.76457i | − | 0.711438i | ||||||
\(29\) | 8.64123 | 1.60464 | 0.802318 | − | 0.596897i | \(-0.203600\pi\) | ||||
0.802318 | + | 0.596897i | \(0.203600\pi\) | |||||||
\(30\) | 0.502409 | + | 1.41015i | 0.0917269 | + | 0.257457i | ||||
\(31\) | −5.10084 | −0.916138 | −0.458069 | − | 0.888917i | \(-0.651459\pi\) | ||||
−0.458069 | + | 0.888917i | \(0.651459\pi\) | |||||||
\(32\) | 2.81770i | 0.498104i | ||||||||
\(33\) | − | 11.5924i | − | 2.01798i | ||||||
\(34\) | 0.601466 | 0.103151 | ||||||||
\(35\) | 4.08694 | − | 1.45609i | 0.690819 | − | 0.246125i | ||||
\(36\) | −8.72843 | −1.45474 | ||||||||
\(37\) | − | 11.0305i | − | 1.81341i | −0.421770 | − | 0.906703i | \(-0.638591\pi\) | ||
0.421770 | − | 0.906703i | \(-0.361409\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.47724 | −0.556805 | ||||||||
\(40\) | −2.02906 | + | 0.722915i | −0.320823 | + | 0.114303i | ||||
\(41\) | −2.49838 | −0.390182 | −0.195091 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195091 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(42\) | − | 1.29895i | − | 0.200432i | ||||||
\(43\) | − | 4.46879i | − | 0.681484i | −0.940157 | − | 0.340742i | \(-0.889322\pi\) | ||
0.940157 | − | 0.340742i | \(-0.110678\pi\) | |||||||
\(44\) | 8.21364 | 1.23825 | ||||||||
\(45\) | −3.37606 | − | 9.47585i | −0.503273 | − | 1.41258i | ||||
\(46\) | −1.25592 | −0.185175 | ||||||||
\(47\) | 6.76901i | 0.987362i | 0.869643 | + | 0.493681i | \(0.164349\pi\) | ||||
−0.869643 | + | 0.493681i | \(0.835651\pi\) | |||||||
\(48\) | − | 9.98123i | − | 1.44067i | ||||||
\(49\) | 3.23535 | 0.462192 | ||||||||
\(50\) | −0.772913 | − | 0.947013i | −0.109306 | − | 0.133928i | ||||
\(51\) | −6.73697 | −0.943364 | ||||||||
\(52\) | − | 2.46375i | − | 0.341661i | ||||||
\(53\) | 0.689802i | 0.0947515i | 0.998877 | + | 0.0473758i | \(0.0150858\pi\) | ||||
−0.998877 | + | 0.0473758i | \(0.984914\pi\) | |||||||
\(54\) | −1.00330 | −0.136532 | ||||||||
\(55\) | 3.17694 | + | 8.91697i | 0.428378 | + | 1.20236i | ||||
\(56\) | 1.86906 | 0.249763 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.11258i | 0.277396i | ||||||||
\(59\) | 5.19336 | 0.676118 | 0.338059 | − | 0.941125i | \(-0.390230\pi\) | ||||
0.338059 | + | 0.941125i | \(0.390230\pi\) | |||||||
\(60\) | 11.1913 | − | 3.98724i | 1.44479 | − | 0.514750i | ||||
\(61\) | 2.80281 | 0.358864 | 0.179432 | − | 0.983770i | \(-0.442574\pi\) | ||||
0.179432 | + | 0.983770i | \(0.442574\pi\) | |||||||
\(62\) | − | 1.24704i | − | 0.158374i | ||||||
\(63\) | 8.72862i | 1.09970i | ||||||||
\(64\) | 6.60105 | 0.825131 | ||||||||
\(65\) | 2.67472 | − | 0.952950i | 0.331759 | − | 0.118199i | ||||
\(66\) | 2.83408 | 0.348851 | ||||||||
\(67\) | 5.21227i | 0.636780i | 0.947960 | + | 0.318390i | \(0.103142\pi\) | ||||
−0.947960 | + | 0.318390i | \(0.896858\pi\) | |||||||
\(68\) | − | 4.77338i | − | 0.578858i | ||||||
\(69\) | 14.0674 | 1.69352 | ||||||||
\(70\) | 0.355982 | + | 0.999163i | 0.0425480 | + | 0.119423i | ||||
\(71\) | −0.791916 | −0.0939832 | −0.0469916 | − | 0.998895i | \(-0.514963\pi\) | ||||
−0.0469916 | + | 0.998895i | \(0.514963\pi\) | |||||||
\(72\) | − | 4.33354i | − | 0.510713i | ||||||
\(73\) | − | 1.41576i | − | 0.165702i | −0.996562 | − | 0.0828512i | \(-0.973597\pi\) | ||
0.996562 | − | 0.0828512i | \(-0.0264026\pi\) | |||||||
\(74\) | 2.69671 | 0.313486 | ||||||||
\(75\) | 8.65733 | + | 10.6074i | 0.999663 | + | 1.22484i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 8.21381i | − | 0.936050i | ||||||
\(78\) | − | 0.850107i | − | 0.0962557i | ||||||
\(79\) | −6.06294 | −0.682134 | −0.341067 | − | 0.940039i | \(-0.610788\pi\) | ||||
−0.341067 | + | 0.940039i | \(0.610788\pi\) | |||||||
\(80\) | 2.73539 | + | 7.67764i | 0.305826 | + | 0.858387i | ||||
\(81\) | −2.25806 | −0.250895 | ||||||||
\(82\) | − | 0.610798i | − | 0.0674514i | ||||||
\(83\) | − | 11.8522i | − | 1.30095i | −0.759527 | − | 0.650476i | \(-0.774570\pi\) | ||
0.759527 | − | 0.650476i | \(-0.225430\pi\) | |||||||
\(84\) | −10.3088 | −1.12478 | ||||||||
\(85\) | 5.18213 | − | 1.84629i | 0.562081 | − | 0.200258i | ||||
\(86\) | 1.09252 | 0.117809 | ||||||||
\(87\) | − | 23.6629i | − | 2.53692i | ||||||
\(88\) | 4.07795i | 0.434711i | ||||||||
\(89\) | −2.23291 | −0.236688 | −0.118344 | − | 0.992973i | \(-0.537759\pi\) | ||||
−0.118344 | + | 0.992973i | \(0.537759\pi\) | |||||||
\(90\) | 2.31663 | − | 0.825369i | 0.244194 | − | 0.0870016i | ||||
\(91\) | −2.46380 | −0.258277 | ||||||||
\(92\) | 9.96727i | 1.03916i | ||||||||
\(93\) | 13.9680i | 1.44841i | ||||||||
\(94\) | −1.65487 | −0.170687 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.71591 | 0.787501 | ||||||||
\(97\) | 8.60981i | 0.874194i | 0.899414 | + | 0.437097i | \(0.143993\pi\) | ||||
−0.899414 | + | 0.437097i | \(0.856007\pi\) | |||||||
\(98\) | 0.790969i | 0.0798999i | ||||||||
\(99\) | −19.0443 | −1.91402 | ||||||||
\(100\) | −7.51572 | + | 6.13403i | −0.751572 | + | 0.613403i | ||||
\(101\) | −13.4510 | −1.33842 | −0.669212 | − | 0.743071i | \(-0.733368\pi\) | ||||
−0.669212 | + | 0.743071i | \(0.733368\pi\) | |||||||
\(102\) | − | 1.64704i | − | 0.163081i | ||||||
\(103\) | 4.03579i | 0.397658i | 0.980034 | + | 0.198829i | \(0.0637139\pi\) | ||||
−0.980034 | + | 0.198829i | \(0.936286\pi\) | |||||||
\(104\) | 1.22322 | 0.119946 | ||||||||
\(105\) | −3.98732 | − | 11.1915i | −0.389123 | − | 1.09218i | ||||
\(106\) | −0.168641 | −0.0163798 | ||||||||
\(107\) | − | 16.9589i | − | 1.63948i | −0.572734 | − | 0.819741i | \(-0.694117\pi\) | ||
0.572734 | − | 0.819741i | \(-0.305883\pi\) | |||||||
\(108\) | 7.96246i | 0.766188i | ||||||||
\(109\) | 6.83567 | 0.654739 | 0.327369 | − | 0.944896i | \(-0.393838\pi\) | ||||
0.327369 | + | 0.944896i | \(0.393838\pi\) | |||||||
\(110\) | −2.18000 | + | 0.776689i | −0.207855 | + | 0.0740544i | ||||
\(111\) | −30.2056 | −2.86699 | ||||||||
\(112\) | − | 7.07221i | − | 0.668261i | ||||||
\(113\) | 5.92416i | 0.557298i | 0.960393 | + | 0.278649i | \(0.0898867\pi\) | ||||
−0.960393 | + | 0.278649i | \(0.910113\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.8208 | + | 3.85523i | −1.00904 | + | 0.359502i | ||||
\(116\) | 16.7660 | 1.55668 | ||||||||
\(117\) | 5.71250i | 0.528121i | ||||||||
\(118\) | 1.26966i | 0.116882i | ||||||||
\(119\) | −4.77348 | −0.437584 | ||||||||
\(120\) | 1.97961 | + | 5.55632i | 0.180712 | + | 0.507221i | ||||
\(121\) | 6.92107 | 0.629188 | ||||||||
\(122\) | 0.685224i | 0.0620373i | ||||||||
\(123\) | 6.84150i | 0.616877i | ||||||||
\(124\) | −9.89681 | −0.888759 | ||||||||
\(125\) | −9.56628 | − | 5.78673i | −0.855634 | − | 0.517581i | ||||
\(126\) | −2.13395 | −0.190107 | ||||||||
\(127\) | 19.1802i | 1.70197i | 0.525193 | + | 0.850983i | \(0.323993\pi\) | ||||
−0.525193 | + | 0.850983i | \(0.676007\pi\) | |||||||
\(128\) | 7.24921i | 0.640746i | ||||||||
\(129\) | −12.2372 | −1.07742 | ||||||||
\(130\) | 0.232975 | + | 0.653909i | 0.0204332 | + | 0.0573516i | ||||
\(131\) | −0.307990 | −0.0269092 | −0.0134546 | − | 0.999909i | \(-0.504283\pi\) | ||||
−0.0134546 | + | 0.999909i | \(0.504283\pi\) | |||||||
\(132\) | − | 22.4920i | − | 1.95767i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.27428 | −0.110081 | ||||||||
\(135\) | −8.64429 | + | 3.07979i | −0.743982 | + | 0.265066i | ||||
\(136\) | 2.36992 | 0.203219 | ||||||||
\(137\) | − | 14.4994i | − | 1.23876i | −0.785090 | − | 0.619382i | \(-0.787383\pi\) | ||
0.785090 | − | 0.619382i | \(-0.212617\pi\) | |||||||
\(138\) | 3.43917i | 0.292761i | ||||||||
\(139\) | −15.7973 | −1.33991 | −0.669955 | − | 0.742401i | \(-0.733687\pi\) | ||||
−0.669955 | + | 0.742401i | \(0.733687\pi\) | |||||||
\(140\) | 7.92960 | − | 2.82516i | 0.670174 | − | 0.238769i | ||||
\(141\) | 18.5360 | 1.56102 | ||||||||
\(142\) | − | 0.193606i | − | 0.0162470i | ||||||
\(143\) | − | 5.37558i | − | 0.449529i | ||||||
\(144\) | −16.3974 | −1.36645 | ||||||||
\(145\) | 6.48489 | + | 18.2017i | 0.538540 | + | 1.51157i | ||||
\(146\) | 0.346122 | 0.0286452 | ||||||||
\(147\) | − | 8.85957i | − | 0.730725i | ||||||
\(148\) | − | 21.4017i | − | 1.75921i | ||||||
\(149\) | 12.4650 | 1.02117 | 0.510585 | − | 0.859827i | \(-0.329429\pi\) | ||||
0.510585 | + | 0.859827i | \(0.329429\pi\) | |||||||
\(150\) | −2.59327 | + | 2.11652i | −0.211740 | + | 0.172813i | ||||
\(151\) | −13.8400 | −1.12629 | −0.563143 | − | 0.826360i | \(-0.690408\pi\) | ||||
−0.563143 | + | 0.826360i | \(0.690408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.0677i | 0.894767i | ||||||||
\(154\) | 2.00809 | 0.161816 | ||||||||
\(155\) | −3.82797 | − | 10.7443i | −0.307470 | − | 0.863001i | ||||
\(156\) | −6.74666 | −0.540165 | ||||||||
\(157\) | − | 18.1970i | − | 1.45228i | −0.687549 | − | 0.726138i | \(-0.741313\pi\) | ||
0.687549 | − | 0.726138i | \(-0.258687\pi\) | |||||||
\(158\) | − | 1.48225i | − | 0.117922i | ||||||
\(159\) | 1.88893 | 0.149802 | ||||||||
\(160\) | −5.93514 | + | 2.11457i | −0.469214 | + | 0.167171i | ||||
\(161\) | 9.96748 | 0.785548 | ||||||||
\(162\) | − | 0.552043i | − | 0.0433726i | ||||||
\(163\) | 15.3337i | 1.20103i | 0.799613 | + | 0.600516i | \(0.205038\pi\) | ||||
−0.799613 | + | 0.600516i | \(0.794962\pi\) | |||||||
\(164\) | −4.84744 | −0.378522 | ||||||||
\(165\) | 24.4180 | − | 8.69963i | 1.90094 | − | 0.677265i | ||||
\(166\) | 2.89760 | 0.224897 | ||||||||
\(167\) | 6.21690i | 0.481079i | 0.970639 | + | 0.240539i | \(0.0773243\pi\) | ||||
−0.970639 | + | 0.240539i | \(0.922676\pi\) | |||||||
\(168\) | − | 5.11817i | − | 0.394875i | ||||||
\(169\) | 11.3875 | 0.875965 | ||||||||
\(170\) | 0.451376 | + | 1.26691i | 0.0346189 | + | 0.0971678i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 8.67048i | − | 0.661118i | ||||||
\(173\) | 2.76604i | 0.210298i | 0.994456 | + | 0.105149i | \(0.0335319\pi\) | ||||
−0.994456 | + | 0.105149i | \(0.966468\pi\) | |||||||
\(174\) | 5.78503 | 0.438562 | ||||||||
\(175\) | 6.13416 | + | 7.51588i | 0.463699 | + | 0.568147i | ||||
\(176\) | 15.4303 | 1.16310 | ||||||||
\(177\) | − | 14.2213i | − | 1.06894i | ||||||
\(178\) | − | 0.545896i | − | 0.0409167i | ||||||
\(179\) | −11.3783 | −0.850456 | −0.425228 | − | 0.905086i | \(-0.639806\pi\) | ||||
−0.425228 | + | 0.905086i | \(0.639806\pi\) | |||||||
\(180\) | −6.55033 | − | 18.3853i | −0.488233 | − | 1.37036i | ||||
\(181\) | −3.56654 | −0.265099 | −0.132549 | − | 0.991176i | \(-0.542316\pi\) | ||||
−0.132549 | + | 0.991176i | \(0.542316\pi\) | |||||||
\(182\) | − | 0.602344i | − | 0.0446487i | ||||||
\(183\) | − | 7.67513i | − | 0.567362i | ||||||
\(184\) | −4.94861 | −0.364816 | ||||||||
\(185\) | 23.2344 | − | 8.27795i | 1.70823 | − | 0.608607i | ||||
\(186\) | −3.41485 | −0.250389 | ||||||||
\(187\) | − | 10.4149i | − | 0.761612i | ||||||
\(188\) | 13.1334i | 0.957855i | ||||||||
\(189\) | 7.96263 | 0.579196 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.67323 | −0.627573 | −0.313786 | − | 0.949494i | \(-0.601598\pi\) | ||||
−0.313786 | + | 0.949494i | \(0.601598\pi\) | |||||||
\(192\) | − | 18.0761i | − | 1.30453i | ||||||
\(193\) | − | 0.422110i | − | 0.0303841i | −0.999885 | − | 0.0151921i | \(-0.995164\pi\) | ||
0.999885 | − | 0.0151921i | \(-0.00483597\pi\) | |||||||
\(194\) | −2.10490 | −0.151123 | ||||||||
\(195\) | −2.60953 | − | 7.32438i | −0.186872 | − | 0.524510i | ||||
\(196\) | 6.27732 | 0.448380 | ||||||||
\(197\) | 15.2415i | 1.08591i | 0.839761 | + | 0.542956i | \(0.182695\pi\) | ||||
−0.839761 | + | 0.542956i | \(0.817305\pi\) | |||||||
\(198\) | − | 4.65590i | − | 0.330880i | ||||||
\(199\) | −12.9264 | −0.916331 | −0.458166 | − | 0.888867i | \(-0.651493\pi\) | ||||
−0.458166 | + | 0.888867i | \(0.651493\pi\) | |||||||
\(200\) | −3.04546 | − | 3.73145i | −0.215346 | − | 0.263853i | ||||
\(201\) | 14.2731 | 1.00675 | ||||||||
\(202\) | − | 3.28846i | − | 0.231376i | ||||||
\(203\) | − | 16.7663i | − | 1.17677i | ||||||
\(204\) | −13.0713 | −0.915172 | ||||||||
\(205\) | −1.87493 | − | 5.26253i | −0.130951 | − | 0.367551i | ||||
\(206\) | −0.986659 | −0.0687438 | ||||||||
\(207\) | − | 23.1103i | − | 1.60628i | ||||||
\(208\) | − | 4.62845i | − | 0.320926i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.73608 | − | 0.974809i | 0.188807 | − | 0.0672682i | ||||
\(211\) | 4.44619 | 0.306089 | 0.153044 | − | 0.988219i | \(-0.451092\pi\) | ||||
0.153044 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(212\) | 1.33837i | 0.0919199i | ||||||||
\(213\) | 2.16856i | 0.148587i | ||||||||
\(214\) | 4.14608 | 0.283420 | ||||||||
\(215\) | 9.41294 | − | 3.35364i | 0.641957 | − | 0.228717i | ||||
\(216\) | −3.95325 | −0.268985 | ||||||||
\(217\) | 9.89701i | 0.671853i | ||||||||
\(218\) | 1.67117i | 0.113186i | ||||||||
\(219\) | −3.87688 | −0.261975 | ||||||||
\(220\) | 6.16399 | + | 17.3010i | 0.415576 | + | 1.16643i | ||||
\(221\) | −3.12404 | −0.210146 | ||||||||
\(222\) | − | 7.38459i | − | 0.495621i | ||||||
\(223\) | 9.19893i | 0.616006i | 0.951385 | + | 0.308003i | \(0.0996607\pi\) | ||||
−0.951385 | + | 0.308003i | \(0.900339\pi\) | |||||||
\(224\) | 5.46711 | 0.365287 | ||||||||
\(225\) | 17.4261 | − | 14.2225i | 1.16174 | − | 0.948165i | ||||
\(226\) | −1.44832 | −0.0963411 | ||||||||
\(227\) | − | 0.600308i | − | 0.0398438i | −0.999802 | − | 0.0199219i | \(-0.993658\pi\) | ||
0.999802 | − | 0.0199219i | \(-0.00634176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.11499 | 0.470172 | 0.235086 | − | 0.971975i | \(-0.424463\pi\) | ||||
0.235086 | + | 0.971975i | \(0.424463\pi\) | |||||||
\(230\) | −0.942515 | − | 2.64543i | −0.0621476 | − | 0.174435i | ||||
\(231\) | −22.4924 | −1.47989 | ||||||||
\(232\) | 8.32407i | 0.546502i | ||||||||
\(233\) | 20.1662i | 1.32113i | 0.750767 | + | 0.660567i | \(0.229684\pi\) | ||||
−0.750767 | + | 0.660567i | \(0.770316\pi\) | |||||||
\(234\) | −1.39658 | −0.0912971 | ||||||||
\(235\) | −14.2581 | + | 5.07986i | −0.930094 | + | 0.331374i | ||||
\(236\) | 10.0763 | 0.655912 | ||||||||
\(237\) | 16.6026i | 1.07845i | ||||||||
\(238\) | − | 1.16701i | − | 0.0756459i | ||||||
\(239\) | 11.6342 | 0.752554 | 0.376277 | − | 0.926507i | \(-0.377204\pi\) | ||||
0.376277 | + | 0.926507i | \(0.377204\pi\) | |||||||
\(240\) | 21.0242 | − | 7.49050i | 1.35711 | − | 0.483510i | ||||
\(241\) | −25.5301 | −1.64454 | −0.822269 | − | 0.569100i | \(-0.807292\pi\) | ||||
−0.822269 | + | 0.569100i | \(0.807292\pi\) | |||||||
\(242\) | 1.69205i | 0.108769i | ||||||||
\(243\) | 18.4950i | 1.18646i | ||||||||
\(244\) | 5.43811 | 0.348139 | ||||||||
\(245\) | 2.42799 | + | 6.81485i | 0.155119 | + | 0.435385i | ||||
\(246\) | −1.67259 | −0.106640 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 4.91362i | − | 0.312015i | ||||||
\(249\) | −32.4558 | −2.05680 | ||||||||
\(250\) | 1.41472 | − | 2.33874i | 0.0894750 | − | 0.147915i | ||||
\(251\) | 15.3783 | 0.970669 | 0.485335 | − | 0.874328i | \(-0.338698\pi\) | ||||
0.485335 | + | 0.874328i | \(0.338698\pi\) | |||||||
\(252\) | 16.9355i | 1.06684i | ||||||||
\(253\) | 21.7473i | 1.36724i | ||||||||
\(254\) | −4.68912 | −0.294221 | ||||||||
\(255\) | −5.05582 | − | 14.1906i | −0.316608 | − | 0.888648i | ||||
\(256\) | 11.4298 | 0.714365 | ||||||||
\(257\) | 16.0534i | 1.00139i | 0.865625 | + | 0.500693i | \(0.166921\pi\) | ||||
−0.865625 | + | 0.500693i | \(0.833079\pi\) | |||||||
\(258\) | − | 2.99172i | − | 0.186256i | ||||||
\(259\) | −21.4022 | −1.32987 | ||||||||
\(260\) | 5.18958 | − | 1.84894i | 0.321844 | − | 0.114667i | ||||
\(261\) | −38.8739 | −2.40624 | ||||||||
\(262\) | − | 0.0752965i | − | 0.00465183i | ||||||
\(263\) | 14.2397i | 0.878055i | 0.898474 | + | 0.439027i | \(0.144677\pi\) | ||||
−0.898474 | + | 0.439027i | \(0.855323\pi\) | |||||||
\(264\) | 11.1669 | 0.687277 | ||||||||
\(265\) | −1.45298 | + | 0.517668i | −0.0892559 | + | 0.0318001i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.11453i | 0.374203i | ||||||||
\(268\) | 10.1130i | 0.617750i | ||||||||
\(269\) | 16.2414 | 0.990254 | 0.495127 | − | 0.868821i | \(-0.335121\pi\) | ||||
0.495127 | + | 0.868821i | \(0.335121\pi\) | |||||||
\(270\) | −0.752938 | − | 2.11333i | −0.0458224 | − | 0.128613i | ||||
\(271\) | −5.92530 | −0.359936 | −0.179968 | − | 0.983672i | \(-0.557599\pi\) | ||||
−0.179968 | + | 0.983672i | \(0.557599\pi\) | |||||||
\(272\) | − | 8.96737i | − | 0.543727i | ||||||
\(273\) | 6.74680i | 0.408335i | ||||||||
\(274\) | 3.54476 | 0.214147 | ||||||||
\(275\) | −16.3983 | + | 13.3836i | −0.988856 | + | 0.807064i | ||||
\(276\) | 27.2941 | 1.64291 | ||||||||
\(277\) | 6.30936i | 0.379093i | 0.981872 | + | 0.189546i | \(0.0607017\pi\) | ||||
−0.981872 | + | 0.189546i | \(0.939298\pi\) | |||||||
\(278\) | − | 3.86208i | − | 0.231632i | ||||||
\(279\) | 22.9469 | 1.37380 | ||||||||
\(280\) | 1.40265 | + | 3.93693i | 0.0838244 | + | 0.235277i | ||||
\(281\) | 2.67961 | 0.159852 | 0.0799261 | − | 0.996801i | \(-0.474532\pi\) | ||||
0.0799261 | + | 0.996801i | \(0.474532\pi\) | |||||||
\(282\) | 4.53164i | 0.269855i | ||||||||
\(283\) | − | 31.0643i | − | 1.84658i | −0.384105 | − | 0.923290i | \(-0.625490\pi\) | ||
0.384105 | − | 0.923290i | \(-0.374510\pi\) | |||||||
\(284\) | −1.53650 | −0.0911745 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.31421 | 0.0777107 | ||||||||
\(287\) | 4.84754i | 0.286142i | ||||||||
\(288\) | − | 12.6759i | − | 0.746933i | ||||||
\(289\) | 10.9474 | 0.643962 | ||||||||
\(290\) | −4.44989 | + | 1.58541i | −0.261307 | + | 0.0930983i | ||||
\(291\) | 23.5768 | 1.38210 | ||||||||
\(292\) | − | 2.74690i | − | 0.160750i | ||||||
\(293\) | 0.865650i | 0.0505718i | 0.999680 | + | 0.0252859i | \(0.00804961\pi\) | ||||
−0.999680 | + | 0.0252859i | \(0.991950\pi\) | |||||||
\(294\) | 2.16596 | 0.126322 | ||||||||
\(295\) | 3.89740 | + | 10.9392i | 0.226916 | + | 0.636902i | ||||
\(296\) | 10.6257 | 0.617604 | ||||||||
\(297\) | 17.3730i | 1.00809i | ||||||||
\(298\) | 3.04740i | 0.176531i | ||||||||
\(299\) | 6.52329 | 0.377251 | ||||||||
\(300\) | 16.7972 | + | 20.5808i | 0.969788 | + | 1.18823i | ||||
\(301\) | −8.67067 | −0.499769 | ||||||||
\(302\) | − | 3.38357i | − | 0.194703i | ||||||
\(303\) | 36.8338i | 2.11605i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.10340 | + | 5.90377i | 0.120440 | + | 0.338049i | ||||
\(306\) | −2.70579 | −0.154680 | ||||||||
\(307\) | 8.99201i | 0.513201i | 0.966518 | + | 0.256601i | \(0.0826025\pi\) | ||||
−0.966518 | + | 0.256601i | \(0.917397\pi\) | |||||||
\(308\) | − | 15.9367i | − | 0.908077i | ||||||
\(309\) | 11.0515 | 0.628696 | ||||||||
\(310\) | 2.62673 | − | 0.935852i | 0.149188 | − | 0.0531528i | ||||
\(311\) | −11.4407 | −0.648742 | −0.324371 | − | 0.945930i | \(-0.605153\pi\) | ||||
−0.324371 | + | 0.945930i | \(0.605153\pi\) | |||||||
\(312\) | − | 3.34962i | − | 0.189635i | ||||||
\(313\) | − | 7.86521i | − | 0.444568i | −0.974982 | − | 0.222284i | \(-0.928649\pi\) | ||
0.974982 | − | 0.222284i | \(-0.0713512\pi\) | |||||||
\(314\) | 4.44875 | 0.251057 | ||||||||
\(315\) | −18.3857 | + | 6.55047i | −1.03592 | + | 0.369077i | ||||
\(316\) | −11.7635 | −0.661749 | ||||||||
\(317\) | − | 16.5265i | − | 0.928218i | −0.885778 | − | 0.464109i | \(-0.846375\pi\) | ||
0.885778 | − | 0.464109i | \(-0.153625\pi\) | |||||||
\(318\) | 0.461801i | 0.0258965i | ||||||||
\(319\) | 36.5812 | 2.04815 | ||||||||
\(320\) | 4.95382 | + | 13.9043i | 0.276927 | + | 0.777273i | ||||
\(321\) | −46.4398 | −2.59202 | ||||||||
\(322\) | 2.43682i | 0.135799i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.38115 | −0.243397 | ||||||||
\(325\) | 4.01454 | + | 4.91882i | 0.222687 | + | 0.272847i | ||||
\(326\) | −3.74875 | −0.207624 | ||||||||
\(327\) | − | 18.7186i | − | 1.03514i | ||||||
\(328\) | − | 2.40669i | − | 0.132887i | ||||||
\(329\) | 13.1337 | 0.724085 | ||||||||
\(330\) | 2.12686 | + | 5.96963i | 0.117080 | + | 0.328618i | ||||
\(331\) | −7.91446 | −0.435018 | −0.217509 | − | 0.976058i | \(-0.569793\pi\) | ||||
−0.217509 | + | 0.976058i | \(0.569793\pi\) | |||||||
\(332\) | − | 22.9961i | − | 1.26207i | ||||||
\(333\) | 49.6225i | 2.71930i | ||||||||
\(334\) | −1.51989 | −0.0831648 | ||||||||
\(335\) | −10.9790 | + | 3.91159i | −0.599846 | + | 0.213713i | ||||
\(336\) | −19.3663 | −1.05652 | ||||||||
\(337\) | 19.0361i | 1.03696i | 0.855090 | + | 0.518480i | \(0.173502\pi\) | ||||
−0.855090 | + | 0.518480i | \(0.826498\pi\) | |||||||
\(338\) | 2.78400i | 0.151429i | ||||||||
\(339\) | 16.2225 | 0.881087 | ||||||||
\(340\) | 10.0545 | − | 3.58223i | 0.545283 | − | 0.194274i | ||||
\(341\) | −21.5935 | −1.16936 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.8594i | − | 1.07230i | ||||||
\(344\) | 4.30477 | 0.232098 | ||||||||
\(345\) | 10.5570 | + | 29.6313i | 0.568371 | + | 1.59529i | ||||
\(346\) | −0.676233 | −0.0363545 | ||||||||
\(347\) | − | 5.46420i | − | 0.293334i | −0.989186 | − | 0.146667i | \(-0.953145\pi\) | ||
0.989186 | − | 0.146667i | \(-0.0468545\pi\) | |||||||
\(348\) | − | 45.9114i | − | 2.46111i | ||||||
\(349\) | 6.26435 | 0.335323 | 0.167662 | − | 0.985845i | \(-0.446378\pi\) | ||||
0.167662 | + | 0.985845i | \(0.446378\pi\) | |||||||
\(350\) | −1.83746 | + | 1.49966i | −0.0982165 | + | 0.0801603i | ||||
\(351\) | 5.21120 | 0.278153 | ||||||||
\(352\) | 11.9283i | 0.635779i | ||||||||
\(353\) | 8.29398i | 0.441444i | 0.975337 | + | 0.220722i | \(0.0708414\pi\) | ||||
−0.975337 | + | 0.220722i | \(0.929159\pi\) | |||||||
\(354\) | 3.47679 | 0.184789 | ||||||||
\(355\) | −0.594300 | − | 1.66807i | −0.0315422 | − | 0.0885321i | ||||
\(356\) | −4.33237 | −0.229615 | ||||||||
\(357\) | 13.0715i | 0.691820i | ||||||||
\(358\) | − | 2.78174i | − | 0.147020i | ||||||
\(359\) | −13.0857 | −0.690637 | −0.345318 | − | 0.938486i | \(-0.612229\pi\) | ||||
−0.345318 | + | 0.938486i | \(0.612229\pi\) | |||||||
\(360\) | 9.12806 | − | 3.25215i | 0.481091 | − | 0.171403i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | − | 0.871938i | − | 0.0458281i | ||||||
\(363\) | − | 18.9524i | − | 0.994745i | ||||||
\(364\) | −4.78035 | −0.250558 | ||||||||
\(365\) | 2.98212 | − | 1.06247i | 0.156091 | − | 0.0556123i | ||||
\(366\) | 1.87640 | 0.0980808 | ||||||||
\(367\) | 26.0942i | 1.36211i | 0.732234 | + | 0.681053i | \(0.238478\pi\) | ||||
−0.732234 | + | 0.681053i | \(0.761522\pi\) | |||||||
\(368\) | 18.7247i | 0.976094i | ||||||||
\(369\) | 11.2394 | 0.585099 | ||||||||
\(370\) | 2.02377 | + | 5.68028i | 0.105211 | + | 0.295304i | ||||
\(371\) | 1.33840 | 0.0694864 | ||||||||
\(372\) | 27.1011i | 1.40513i | ||||||||
\(373\) | 27.1969i | 1.40820i | 0.710101 | + | 0.704100i | \(0.248649\pi\) | ||||
−0.710101 | + | 0.704100i | \(0.751351\pi\) | |||||||
\(374\) | 2.54620 | 0.131661 | ||||||||
\(375\) | −15.8462 | + | 26.1960i | −0.818294 | + | 1.35276i | ||||
\(376\) | −6.52057 | −0.336273 | ||||||||
\(377\) | − | 10.9728i | − | 0.565130i | ||||||
\(378\) | 1.94668i | 0.100127i | ||||||||
\(379\) | 13.6999 | 0.703714 | 0.351857 | − | 0.936054i | \(-0.385550\pi\) | ||||
0.351857 | + | 0.936054i | \(0.385550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52.5224 | 2.69080 | ||||||||
\(382\) | − | 2.12041i | − | 0.108490i | ||||||
\(383\) | 10.2515i | 0.523827i | 0.965091 | + | 0.261913i | \(0.0843535\pi\) | ||||
−0.965091 | + | 0.261913i | \(0.915647\pi\) | |||||||
\(384\) | 19.8510 | 1.01302 | ||||||||
\(385\) | 17.3014 | − | 6.16412i | 0.881758 | − | 0.314153i | ||||
\(386\) | 0.103196 | 0.00525255 | ||||||||
\(387\) | 20.1036i | 1.02192i | ||||||||
\(388\) | 16.7050i | 0.848069i | ||||||||
\(389\) | 5.05671 | 0.256385 | 0.128193 | − | 0.991749i | \(-0.459082\pi\) | ||||
0.128193 | + | 0.991749i | \(0.459082\pi\) | |||||||
\(390\) | 1.79064 | − | 0.637971i | 0.0906728 | − | 0.0323049i | ||||
\(391\) | 12.6385 | 0.639157 | ||||||||
\(392\) | 3.11660i | 0.157412i | ||||||||
\(393\) | 0.843389i | 0.0425434i | ||||||||
\(394\) | −3.72620 | −0.187723 | ||||||||
\(395\) | −4.54999 | − | 12.7708i | −0.228935 | − | 0.642570i | ||||
\(396\) | −36.9503 | −1.85682 | ||||||||
\(397\) | 23.8758i | 1.19829i | 0.800640 | + | 0.599146i | \(0.204493\pi\) | ||||
−0.800640 | + | 0.599146i | \(0.795507\pi\) | |||||||
\(398\) | − | 3.16022i | − | 0.158408i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.1192 | + | 11.5235i | −0.705960 | + | 0.576176i | ||||
\(401\) | 24.7655 | 1.23673 | 0.618366 | − | 0.785891i | \(-0.287795\pi\) | ||||
0.618366 | + | 0.785891i | \(0.287795\pi\) | |||||||
\(402\) | 3.48945i | 0.174038i | ||||||||
\(403\) | 6.47717i | 0.322651i | ||||||||
\(404\) | −26.0981 | −1.29843 | ||||||||
\(405\) | −1.69458 | − | 4.75631i | −0.0842042 | − | 0.236343i | ||||
\(406\) | 4.09899 | 0.203429 | ||||||||
\(407\) | − | 46.6958i | − | 2.31463i | ||||||
\(408\) | − | 6.48970i | − | 0.321288i | ||||||
\(409\) | −9.89998 | −0.489523 | −0.244761 | − | 0.969583i | \(-0.578710\pi\) | ||||
−0.244761 | + | 0.969583i | \(0.578710\pi\) | |||||||
\(410\) | 1.28657 | − | 0.458379i | 0.0635392 | − | 0.0226377i | ||||
\(411\) | −39.7046 | −1.95848 | ||||||||
\(412\) | 7.83036i | 0.385774i | ||||||||
\(413\) | − | 10.0765i | − | 0.495833i | ||||||
\(414\) | 5.64995 | 0.277680 | ||||||||
\(415\) | 24.9652 | − | 8.89461i | 1.22549 | − | 0.436619i | ||||
\(416\) | 3.57799 | 0.175425 | ||||||||
\(417\) | 43.2588i | 2.11839i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.00810 | −0.195808 | −0.0979042 | − | 0.995196i | \(-0.531214\pi\) | ||||
−0.0979042 | + | 0.995196i | \(0.531214\pi\) | |||||||
\(420\) | −7.73632 | − | 21.7142i | −0.377494 | − | 1.05954i | ||||
\(421\) | −20.2781 | −0.988294 | −0.494147 | − | 0.869378i | \(-0.664520\pi\) | ||||
−0.494147 | + | 0.869378i | \(0.664520\pi\) | |||||||
\(422\) | 1.08699i | 0.0529140i | ||||||||
\(423\) | − | 30.4515i | − | 1.48060i | ||||||
\(424\) | −0.664484 | −0.0322702 | ||||||||
\(425\) | 7.77795 | + | 9.52994i | 0.377286 | + | 0.462270i | ||||
\(426\) | −0.530163 | −0.0256865 | ||||||||
\(427\) | − | 5.43822i | − | 0.263174i | ||||||
\(428\) | − | 32.9043i | − | 1.59049i | ||||||
\(429\) | −14.7203 | −0.710704 | ||||||||
\(430\) | 0.819890 | + | 2.30125i | 0.0395386 | + | 0.110976i | ||||
\(431\) | −13.4783 | −0.649229 | −0.324615 | − | 0.945846i | \(-0.605235\pi\) | ||||
−0.324615 | + | 0.945846i | \(0.605235\pi\) | |||||||
\(432\) | 14.9584i | 0.719689i | ||||||||
\(433\) | 34.3776i | 1.65208i | 0.563611 | + | 0.826040i | \(0.309412\pi\) | ||||
−0.563611 | + | 0.826040i | \(0.690588\pi\) | |||||||
\(434\) | −2.41959 | −0.116144 | ||||||||
\(435\) | 49.8428 | − | 17.7580i | 2.38978 | − | 0.851431i | ||||
\(436\) | 13.2628 | 0.635172 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 0.947808i | − | 0.0452880i | ||||||
\(439\) | 23.4179 | 1.11768 | 0.558838 | − | 0.829277i | \(-0.311247\pi\) | ||||
0.558838 | + | 0.829277i | \(0.311247\pi\) | |||||||
\(440\) | −8.58969 | + | 3.06034i | −0.409498 | + | 0.145896i | ||||
\(441\) | −14.5547 | −0.693082 | ||||||||
\(442\) | − | 0.763756i | − | 0.0363282i | ||||||
\(443\) | 2.39888i | 0.113974i | 0.998375 | + | 0.0569871i | \(0.0181494\pi\) | ||||
−0.998375 | + | 0.0569871i | \(0.981851\pi\) | |||||||
\(444\) | −58.6059 | −2.78131 | ||||||||
\(445\) | −1.67571 | − | 4.70335i | −0.0794362 | − | 0.222960i | ||||
\(446\) | −2.24893 | −0.106490 | ||||||||
\(447\) | − | 34.1337i | − | 1.61447i | ||||||
\(448\) | − | 12.8078i | − | 0.605113i | ||||||
\(449\) | 38.2019 | 1.80286 | 0.901430 | − | 0.432924i | \(-0.142518\pi\) | ||||
0.901430 | + | 0.432924i | \(0.142518\pi\) | |||||||
\(450\) | 3.47707 | + | 4.26029i | 0.163911 | + | 0.200832i | ||||
\(451\) | −10.5765 | −0.498027 | ||||||||
\(452\) | 11.4942i | 0.540644i | ||||||||
\(453\) | 37.8991i | 1.78065i | ||||||||
\(454\) | 0.146762 | 0.00688786 | ||||||||
\(455\) | −1.84898 | − | 5.18969i | −0.0866816 | − | 0.243296i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.87605i | 0.0877581i | 0.999037 | + | 0.0438790i | \(0.0139716\pi\) | ||||
−0.999037 | + | 0.0438790i | \(0.986028\pi\) | |||||||
\(458\) | 1.73945i | 0.0812793i | ||||||||
\(459\) | 10.0964 | 0.471260 | ||||||||
\(460\) | −20.9948 | + | 7.48003i | −0.978888 | + | 0.348758i | ||||
\(461\) | 16.8204 | 0.783402 | 0.391701 | − | 0.920092i | \(-0.371887\pi\) | ||||
0.391701 | + | 0.920092i | \(0.371887\pi\) | |||||||
\(462\) | − | 5.49889i | − | 0.255831i | ||||||
\(463\) | 24.3641i | 1.13230i | 0.824303 | + | 0.566148i | \(0.191567\pi\) | ||||
−0.824303 | + | 0.566148i | \(0.808433\pi\) | |||||||
\(464\) | 31.4969 | 1.46221 | ||||||||
\(465\) | −29.4218 | + | 10.4824i | −1.36440 | + | 0.486109i | ||||
\(466\) | −4.93019 | −0.228386 | ||||||||
\(467\) | 13.6511i | 0.631696i | 0.948810 | + | 0.315848i | \(0.102289\pi\) | ||||
−0.948810 | + | 0.315848i | \(0.897711\pi\) | |||||||
\(468\) | 11.0836i | 0.512338i | ||||||||
\(469\) | 10.1132 | 0.466985 | ||||||||
\(470\) | −1.24191 | − | 3.48577i | −0.0572851 | − | 0.160787i | ||||
\(471\) | −49.8300 | −2.29604 | ||||||||
\(472\) | 5.00275i | 0.230270i | ||||||||
\(473\) | − | 18.9179i | − | 0.869844i | ||||||
\(474\) | −4.05895 | −0.186434 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.26166 | −0.424507 | ||||||||
\(477\) | − | 3.10318i | − | 0.142085i | ||||||
\(478\) | 2.84430i | 0.130095i | ||||||||
\(479\) | 21.7405 | 0.993351 | 0.496675 | − | 0.867936i | \(-0.334554\pi\) | ||||
0.496675 | + | 0.867936i | \(0.334554\pi\) | |||||||
\(480\) | 5.79047 | + | 16.2526i | 0.264298 | + | 0.741826i | ||||
\(481\) | −14.0068 | −0.638656 | ||||||||
\(482\) | − | 6.24153i | − | 0.284294i | ||||||
\(483\) | − | 27.2946i | − | 1.24195i | ||||||
\(484\) | 13.4285 | 0.610385 | ||||||||
\(485\) | −18.1355 | + | 6.46131i | −0.823490 | + | 0.293393i | ||||
\(486\) | −4.52161 | −0.205104 | ||||||||
\(487\) | 29.2454i | 1.32524i | 0.748957 | + | 0.662618i | \(0.230555\pi\) | ||||
−0.748957 | + | 0.662618i | \(0.769445\pi\) | |||||||
\(488\) | 2.69994i | 0.122221i | ||||||||
\(489\) | 41.9894 | 1.89883 | ||||||||
\(490\) | −1.66608 | + | 0.593589i | −0.0752656 | + | 0.0268156i | ||||
\(491\) | −18.3556 | −0.828375 | −0.414188 | − | 0.910191i | \(-0.635934\pi\) | ||||
−0.414188 | + | 0.910191i | \(0.635934\pi\) | |||||||
\(492\) | 13.2741i | 0.598442i | ||||||||
\(493\) | − | 21.2593i | − | 0.957469i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.2920 | − | 40.1144i | −0.642376 | − | 1.80301i | ||||
\(496\) | −18.5923 | −0.834821 | ||||||||
\(497\) | 1.53653i | 0.0689229i | ||||||||
\(498\) | − | 7.93470i | − | 0.355562i | ||||||
\(499\) | −10.4159 | −0.466279 | −0.233140 | − | 0.972443i | \(-0.574900\pi\) | ||||
−0.233140 | + | 0.972443i | \(0.574900\pi\) | |||||||
\(500\) | −18.5608 | − | 11.2276i | −0.830064 | − | 0.502113i | ||||
\(501\) | 17.0242 | 0.760584 | ||||||||
\(502\) | 3.75964i | 0.167801i | ||||||||
\(503\) | − | 4.35731i | − | 0.194283i | −0.995271 | − | 0.0971413i | \(-0.969030\pi\) | ||
0.995271 | − | 0.0971413i | \(-0.0309699\pi\) | |||||||
\(504\) | −8.40825 | −0.374533 | ||||||||
\(505\) | −10.0944 | − | 28.3328i | −0.449196 | − | 1.26079i | ||||
\(506\) | −5.31672 | −0.236357 | ||||||||
\(507\) | − | 31.1833i | − | 1.38490i | ||||||
\(508\) | 37.2140i | 1.65110i | ||||||||
\(509\) | −38.2608 | −1.69588 | −0.847941 | − | 0.530091i | \(-0.822158\pi\) | ||||
−0.847941 | + | 0.530091i | \(0.822158\pi\) | |||||||
\(510\) | 3.46927 | − | 1.23603i | 0.153622 | − | 0.0547324i | ||||
\(511\) | −2.74696 | −0.121518 | ||||||||
\(512\) | 17.2928i | 0.764239i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.92470 | −0.173111 | ||||||||
\(515\) | −8.50088 | + | 3.02869i | −0.374594 | + | 0.133460i | ||||
\(516\) | −23.7430 | −1.04523 | ||||||||
\(517\) | 28.6555i | 1.26027i | ||||||||
\(518\) | − | 5.23235i | − | 0.229896i | ||||||
\(519\) | 7.57442 | 0.332480 | ||||||||
\(520\) | 0.917974 | + | 2.57655i | 0.0402558 | + | 0.112989i | ||||
\(521\) | 2.48812 | 0.109007 | 0.0545033 | − | 0.998514i | \(-0.482642\pi\) | ||||
0.0545033 | + | 0.998514i | \(0.482642\pi\) | |||||||
\(522\) | − | 9.50379i | − | 0.415970i | ||||||
\(523\) | 19.4533i | 0.850635i | 0.905044 | + | 0.425317i | \(0.139837\pi\) | ||||
−0.905044 | + | 0.425317i | \(0.860163\pi\) | |||||||
\(524\) | −0.597571 | −0.0261050 | ||||||||
\(525\) | 20.5812 | − | 16.7976i | 0.898239 | − | 0.733106i | ||||
\(526\) | −3.48127 | −0.151791 | ||||||||
\(527\) | 12.5492i | 0.546650i | ||||||||
\(528\) | − | 42.2538i | − | 1.83886i | ||||||
\(529\) | −3.39040 | −0.147409 | ||||||||
\(530\) | −0.126558 | − | 0.355221i | −0.00549733 | − | 0.0154298i | ||||
\(531\) | −23.3631 | −1.01387 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.17251i | 0.137417i | ||||||||
\(534\) | −1.49486 | −0.0646891 | ||||||||
\(535\) | 35.7219 | − | 12.7270i | 1.54439 | − | 0.550236i | ||||
\(536\) | −5.02096 | −0.216873 | ||||||||
\(537\) | 31.1580i | 1.34457i | ||||||||
\(538\) | 3.97065i | 0.171187i | ||||||||
\(539\) | 13.6963 | 0.589941 | ||||||||
\(540\) | −16.7719 | + | 5.97550i | −0.721749 | + | 0.257145i | ||||
\(541\) | 14.4565 | 0.621535 | 0.310768 | − | 0.950486i | \(-0.399414\pi\) | ||||
0.310768 | + | 0.950486i | \(0.399414\pi\) | |||||||
\(542\) | − | 1.44860i | − | 0.0622228i | ||||||
\(543\) | 9.76650i | 0.419121i | ||||||||
\(544\) | 6.93215 | 0.297214 | ||||||||
\(545\) | 5.12989 | + | 14.3985i | 0.219740 | + | 0.616763i | ||||
\(546\) | −1.64944 | −0.0705895 | ||||||||
\(547\) | − | 31.3961i | − | 1.34240i | −0.741276 | − | 0.671200i | \(-0.765779\pi\) | ||
0.741276 | − | 0.671200i | \(-0.234221\pi\) | |||||||
\(548\) | − | 28.1321i | − | 1.20174i | ||||||
\(549\) | −12.6089 | −0.538135 | ||||||||
\(550\) | −3.27200 | − | 4.00902i | −0.139518 | − | 0.170945i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 13.5511i | 0.576774i | ||||||||
\(553\) | 11.7637i | 0.500245i | ||||||||
\(554\) | −1.54250 | −0.0655343 | ||||||||
\(555\) | −22.6681 | − | 63.6243i | −0.962206 | − | 2.70070i | ||||
\(556\) | −30.6504 | −1.29987 | ||||||||
\(557\) | − | 30.4484i | − | 1.29014i | −0.764124 | − | 0.645070i | \(-0.776828\pi\) | ||
0.764124 | − | 0.645070i | \(-0.223172\pi\) | |||||||
\(558\) | 5.61000i | 0.237490i | ||||||||
\(559\) | −5.67458 | −0.240009 | ||||||||
\(560\) | 14.8967 | − | 5.30740i | 0.629501 | − | 0.224279i | ||||
\(561\) | −28.5198 | −1.20411 | ||||||||
\(562\) | 0.655104i | 0.0276339i | ||||||||
\(563\) | − | 26.7012i | − | 1.12532i | −0.826687 | − | 0.562661i | \(-0.809777\pi\) | ||
0.826687 | − | 0.562661i | \(-0.190223\pi\) | |||||||
\(564\) | 35.9642 | 1.51437 | ||||||||
\(565\) | −12.4785 | + | 4.44584i | −0.524975 | + | 0.187038i | ||||
\(566\) | 7.59451 | 0.319221 | ||||||||
\(567\) | 4.38124i | 0.183995i | ||||||||
\(568\) | − | 0.762850i | − | 0.0320085i | ||||||
\(569\) | −25.6513 | −1.07536 | −0.537679 | − | 0.843150i | \(-0.680699\pi\) | ||||
−0.537679 | + | 0.843150i | \(0.680699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.93559 | 0.122851 | 0.0614253 | − | 0.998112i | \(-0.480435\pi\) | ||||
0.0614253 | + | 0.998112i | \(0.480435\pi\) | |||||||
\(572\) | − | 10.4299i | − | 0.436095i | ||||||
\(573\) | 23.7505i | 0.992191i | ||||||||
\(574\) | −1.18511 | −0.0494657 | ||||||||
\(575\) | −16.2411 | − | 19.8994i | −0.677301 | − | 0.829863i | ||||
\(576\) | −29.6959 | −1.23733 | ||||||||
\(577\) | − | 17.7732i | − | 0.739908i | −0.929050 | − | 0.369954i | \(-0.879373\pi\) | ||
0.929050 | − | 0.369954i | \(-0.120627\pi\) | |||||||
\(578\) | 2.67638i | 0.111323i | ||||||||
\(579\) | −1.15589 | −0.0480373 | ||||||||
\(580\) | 12.5822 | + | 35.3154i | 0.522446 | + | 1.46639i | ||||
\(581\) | −22.9965 | −0.954057 | ||||||||
\(582\) | 5.76400i | 0.238925i | ||||||||
\(583\) | 2.92016i | 0.120941i | ||||||||
\(584\) | 1.36380 | 0.0564344 | ||||||||
\(585\) | −12.0327 | + | 4.28700i | −0.497490 | + | 0.177246i | ||||
\(586\) | −0.211632 | −0.00874243 | ||||||||
\(587\) | 23.1236i | 0.954415i | 0.878791 | + | 0.477207i | \(0.158351\pi\) | ||||
−0.878791 | + | 0.477207i | \(0.841649\pi\) | |||||||
\(588\) | − | 17.1896i | − | 0.708887i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.67438 | + | 0.952826i | −0.110102 | + | 0.0392272i | ||||
\(591\) | 41.7368 | 1.71682 | ||||||||
\(592\) | − | 40.2058i | − | 1.65245i | ||||||
\(593\) | − | 17.1574i | − | 0.704569i | −0.935893 | − | 0.352284i | \(-0.885405\pi\) | ||
0.935893 | − | 0.352284i | \(-0.114595\pi\) | |||||||
\(594\) | −4.24732 | −0.174269 | ||||||||
\(595\) | −3.58230 | − | 10.0547i | −0.146860 | − | 0.412204i | ||||
\(596\) | 24.1849 | 0.990653 | ||||||||
\(597\) | 35.3973i | 1.44872i | ||||||||
\(598\) | 1.59480i | 0.0652160i | ||||||||
\(599\) | −13.3967 | −0.547376 | −0.273688 | − | 0.961819i | \(-0.588244\pi\) | ||||
−0.273688 | + | 0.961819i | \(0.588244\pi\) | |||||||
\(600\) | −10.2181 | + | 8.33958i | −0.417151 | + | 0.340462i | ||||
\(601\) | −8.26251 | −0.337035 | −0.168517 | − | 0.985699i | \(-0.553898\pi\) | ||||
−0.168517 | + | 0.985699i | \(0.553898\pi\) | |||||||
\(602\) | − | 2.11978i | − | 0.0863958i | ||||||
\(603\) | − | 23.4482i | − | 0.954885i | ||||||
\(604\) | −26.8528 | −1.09263 | ||||||||
\(605\) | 5.19398 | + | 14.5784i | 0.211165 | + | 0.592695i | ||||
\(606\) | −9.00503 | −0.365804 | ||||||||
\(607\) | 23.5191i | 0.954612i | 0.878737 | + | 0.477306i | \(0.158387\pi\) | ||||
−0.878737 | + | 0.477306i | \(0.841613\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −45.9124 | −1.86046 | ||||||||
\(610\) | −1.44334 | + | 0.514233i | −0.0584391 | + | 0.0208207i | ||||
\(611\) | 8.59545 | 0.347735 | ||||||||
\(612\) | 21.4738i | 0.868027i | ||||||||
\(613\) | 29.8313i | 1.20488i | 0.798166 | + | 0.602438i | \(0.205804\pi\) | ||||
−0.798166 | + | 0.602438i | \(0.794196\pi\) | |||||||
\(614\) | −2.19834 | −0.0887179 | ||||||||
\(615\) | −14.4107 | + | 5.13426i | −0.581098 | + | 0.207033i | ||||
\(616\) | 7.91234 | 0.318797 | ||||||||
\(617\) | 11.5902i | 0.466605i | 0.972404 | + | 0.233303i | \(0.0749533\pi\) | ||||
−0.972404 | + | 0.233303i | \(0.925047\pi\) | |||||||
\(618\) | 2.70183i | 0.108684i | ||||||||
\(619\) | −29.6697 | −1.19253 | −0.596264 | − | 0.802789i | \(-0.703349\pi\) | ||||
−0.596264 | + | 0.802789i | \(0.703349\pi\) | |||||||
\(620\) | −7.42714 | − | 20.8464i | −0.298281 | − | 0.837211i | ||||
\(621\) | −21.0823 | −0.846002 | ||||||||
\(622\) | − | 2.79699i | − | 0.112149i | ||||||
\(623\) | 4.33246i | 0.173576i | ||||||||
\(624\) | −12.6744 | −0.507382 | ||||||||
\(625\) | 5.00991 | − | 24.4929i | 0.200397 | − | 0.979715i | ||||
\(626\) | 1.92287 | 0.0768532 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 35.3063i | − | 1.40888i | ||||||
\(629\) | −27.1374 | −1.08204 | ||||||||
\(630\) | −1.60144 | − | 4.49489i | −0.0638029 | − | 0.179081i | ||||
\(631\) | −24.4964 | −0.975187 | −0.487593 | − | 0.873071i | \(-0.662125\pi\) | ||||
−0.487593 | + | 0.873071i | \(0.662125\pi\) | |||||||
\(632\) | − | 5.84041i | − | 0.232319i | ||||||
\(633\) | − | 12.1753i | − | 0.483925i | ||||||
\(634\) | 4.04034 | 0.160463 | ||||||||
\(635\) | −40.4006 | + | 14.3939i | −1.60325 | + | 0.571206i | ||||
\(636\) | 3.66496 | 0.145325 | ||||||||
\(637\) | − | 4.10832i | − | 0.162778i | ||||||
\(638\) | 8.94326i | 0.354067i | ||||||||
\(639\) | 3.56256 | 0.140933 | ||||||||
\(640\) | −15.2696 | + | 5.44024i | −0.603582 | + | 0.215044i | ||||
\(641\) | −12.3802 | −0.488989 | −0.244495 | − | 0.969651i | \(-0.578622\pi\) | ||||
−0.244495 | + | 0.969651i | \(0.578622\pi\) | |||||||
\(642\) | − | 11.3535i | − | 0.448086i | ||||||
\(643\) | − | 45.9092i | − | 1.81048i | −0.424898 | − | 0.905241i | \(-0.639690\pi\) | ||
0.424898 | − | 0.905241i | \(-0.360310\pi\) | |||||||
\(644\) | 19.3392 | 0.762072 | ||||||||
\(645\) | −9.18351 | − | 25.7761i | −0.361600 | − | 1.01493i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.6773i | 1.32399i | 0.749508 | + | 0.661996i | \(0.230290\pi\) | ||||
−0.749508 | + | 0.661996i | \(0.769710\pi\) | |||||||
\(648\) | − | 2.17518i | − | 0.0854491i | ||||||
\(649\) | 21.9852 | 0.862994 | ||||||||
\(650\) | −1.20254 | + | 0.981464i | −0.0471675 | + | 0.0384962i | ||||
\(651\) | 27.1017 | 1.06220 | ||||||||
\(652\) | 29.7510i | 1.16514i | ||||||||
\(653\) | − | 19.6365i | − | 0.768437i | −0.923242 | − | 0.384219i | \(-0.874471\pi\) | ||
0.923242 | − | 0.384219i | \(-0.125529\pi\) | |||||||
\(654\) | 4.57627 | 0.178946 | ||||||||
\(655\) | −0.231134 | − | 0.648742i | −0.00903114 | − | 0.0253484i | ||||
\(656\) | −9.10651 | −0.355549 | ||||||||
\(657\) | 6.36903i | 0.248479i | ||||||||
\(658\) | 3.21090i | 0.125174i | ||||||||
\(659\) | 20.7693 | 0.809059 | 0.404529 | − | 0.914525i | \(-0.367435\pi\) | ||||
0.404529 | + | 0.914525i | \(0.367435\pi\) | |||||||
\(660\) | 47.3765 | − | 16.8793i | 1.84413 | − | 0.657025i | ||||
\(661\) | −13.2561 | −0.515603 | −0.257802 | − | 0.966198i | \(-0.582998\pi\) | ||||
−0.257802 | + | 0.966198i | \(0.582998\pi\) | |||||||
\(662\) | − | 1.93490i | − | 0.0752022i | ||||||
\(663\) | 8.55476i | 0.332239i | ||||||||
\(664\) | 11.4172 | 0.443074 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.1316 | −0.470089 | ||||||||
\(667\) | 44.3914i | 1.71884i | ||||||||
\(668\) | 12.0622i | 0.466702i | ||||||||
\(669\) | 25.1901 | 0.973904 | ||||||||
\(670\) | −0.956296 | − | 2.68411i | −0.0369449 | − | 0.103696i | ||||
\(671\) | 11.8652 | 0.458052 | ||||||||
\(672\) | − | 14.9710i | − | 0.577517i | ||||||
\(673\) | 12.8576i | 0.495624i | 0.968808 | + | 0.247812i | \(0.0797115\pi\) | ||||
−0.968808 | + | 0.247812i | \(0.920289\pi\) | |||||||
\(674\) | −4.65388 | −0.179261 | ||||||||
\(675\) | −12.9744 | − | 15.8969i | −0.499384 | − | 0.611871i | ||||
\(676\) | 22.0945 | 0.849787 | ||||||||
\(677\) | 25.5573i | 0.982245i | 0.871091 | + | 0.491122i | \(0.163413\pi\) | ||||
−0.871091 | + | 0.491122i | \(0.836587\pi\) | |||||||
\(678\) | 3.96604i | 0.152315i | ||||||||
\(679\) | 16.7054 | 0.641093 | ||||||||
\(680\) | 1.77852 | + | 4.99193i | 0.0682033 | + | 0.191432i | ||||
\(681\) | −1.64386 | −0.0629930 | ||||||||
\(682\) | − | 5.27913i | − | 0.202148i | ||||||
\(683\) | − | 22.8692i | − | 0.875064i | −0.899203 | − | 0.437532i | \(-0.855853\pi\) | ||
0.899203 | − | 0.437532i | \(-0.144147\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.5411 | − | 10.8812i | 1.16691 | − | 0.415748i | ||||
\(686\) | 4.85516 | 0.185371 | ||||||||
\(687\) | − | 19.4835i | − | 0.743340i | ||||||
\(688\) | − | 16.2886i | − | 0.620995i | ||||||
\(689\) | 0.875927 | 0.0333701 | ||||||||
\(690\) | −7.24417 | + | 2.58095i | −0.275781 | + | 0.0982552i | ||||
\(691\) | −32.3148 | −1.22931 | −0.614657 | − | 0.788795i | \(-0.710705\pi\) | ||||
−0.614657 | + | 0.788795i | \(0.710705\pi\) | |||||||
\(692\) | 5.36675i | 0.204013i | ||||||||
\(693\) | 36.9511i | 1.40366i | ||||||||
\(694\) | 1.33587 | 0.0507091 | ||||||||
\(695\) | −11.8552 | − | 33.2750i | −0.449695 | − | 1.26219i | ||||
\(696\) | 22.7944 | 0.864018 | ||||||||
\(697\) | 6.14656i | 0.232818i | ||||||||
\(698\) | 1.53149i | 0.0579678i | ||||||||
\(699\) | 55.2226 | 2.08871 | ||||||||
\(700\) | 11.9017 | + | 14.5825i | 0.449841 | + | 0.551168i | ||||
\(701\) | 34.7457 | 1.31233 | 0.656164 | − | 0.754618i | \(-0.272178\pi\) | ||||
0.656164 | + | 0.754618i | \(0.272178\pi\) | |||||||
\(702\) | 1.27402i | 0.0480848i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 27.9444 | 1.05319 | ||||||||
\(705\) | 13.9105 | + | 39.0438i | 0.523901 | + | 1.47048i | ||||
\(706\) | −2.02769 | −0.0763131 | ||||||||
\(707\) | 26.0986i | 0.981539i | ||||||||
\(708\) | − | 27.5927i | − | 1.03700i | ||||||
\(709\) | −8.00778 | −0.300738 | −0.150369 | − | 0.988630i | \(-0.548046\pi\) | ||||
−0.150369 | + | 0.988630i | \(0.548046\pi\) | |||||||
\(710\) | 0.407806 | − | 0.145293i | 0.0153047 | − | 0.00545275i | ||||
\(711\) | 27.2751 | 1.02290 | ||||||||
\(712\) | − | 2.15096i | − | 0.0806105i | ||||||
\(713\) | − | 26.2038i | − | 0.981341i | ||||||
\(714\) | −3.19570 | −0.119596 | ||||||||
\(715\) | 11.3230 | − | 4.03415i | 0.423456 | − | 0.150869i | ||||
\(716\) | −22.0766 | −0.825040 | ||||||||
\(717\) | − | 31.8587i | − | 1.18979i | ||||||
\(718\) | − | 3.19916i | − | 0.119391i | ||||||
\(719\) | −14.2690 | −0.532143 | −0.266071 | − | 0.963953i | \(-0.585726\pi\) | ||||
−0.266071 | + | 0.963953i | \(0.585726\pi\) | |||||||
\(720\) | −12.3056 | − | 34.5391i | −0.458602 | − | 1.28720i | ||||
\(721\) | 7.83053 | 0.291624 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 69.9107i | 2.60001i | ||||||||
\(724\) | −6.91991 | −0.257177 | ||||||||
\(725\) | −33.4729 | + | 27.3192i | −1.24315 | + | 1.01461i | ||||
\(726\) | 4.63344 | 0.171963 | ||||||||
\(727\) | 3.13639i | 0.116322i | 0.998307 | + | 0.0581612i | \(0.0185237\pi\) | ||||
−0.998307 | + | 0.0581612i | \(0.981476\pi\) | |||||||
\(728\) | − | 2.37337i | − | 0.0879631i | ||||||
\(729\) | 43.8720 | 1.62489 | ||||||||
\(730\) | 0.259750 | + | 0.729061i | 0.00961378 | + | 0.0269838i | ||||
\(731\) | −10.9942 | −0.406634 | ||||||||
\(732\) | − | 14.8915i | − | 0.550407i | ||||||
\(733\) | − | 12.4004i | − | 0.458020i | −0.973424 | − | 0.229010i | \(-0.926451\pi\) | ||
0.973424 | − | 0.229010i | \(-0.0735488\pi\) | |||||||
\(734\) | −6.37944 | −0.235469 | ||||||||
\(735\) | 18.6616 | − | 6.64874i | 0.688342 | − | 0.245243i | ||||
\(736\) | −14.4750 | −0.533555 | ||||||||
\(737\) | 22.0653i | 0.812784i | ||||||||
\(738\) | 2.74777i | 0.101147i | ||||||||
\(739\) | 9.34314 | 0.343693 | 0.171846 | − | 0.985124i | \(-0.445027\pi\) | ||||
0.171846 | + | 0.985124i | \(0.445027\pi\) | |||||||
\(740\) | 45.0801 | − | 16.0611i | 1.65718 | − | 0.590419i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.327209i | 0.0120122i | ||||||||
\(743\) | − | 38.3186i | − | 1.40577i | −0.711302 | − | 0.702887i | \(-0.751894\pi\) | ||
0.711302 | − | 0.702887i | \(-0.248106\pi\) | |||||||
\(744\) | −13.4553 | −0.493295 | ||||||||
\(745\) | 9.35445 | + | 26.2559i | 0.342720 | + | 0.961942i | ||||
\(746\) | −6.64901 | −0.243438 | ||||||||
\(747\) | 53.3191i | 1.95084i | ||||||||
\(748\) | − | 20.2073i | − | 0.738852i | ||||||
\(749\) | −32.9050 | −1.20232 | ||||||||
\(750\) | −6.40433 | − | 3.87403i | −0.233853 | − | 0.141460i | ||||
\(751\) | 49.0370 | 1.78939 | 0.894693 | − | 0.446681i | \(-0.147394\pi\) | ||||
0.894693 | + | 0.446681i | \(0.147394\pi\) | |||||||
\(752\) | 24.6728i | 0.899723i | ||||||||
\(753\) | − | 42.1114i | − | 1.53463i | ||||||
\(754\) | 2.68261 | 0.0976949 | ||||||||
\(755\) | −10.3864 | − | 29.1523i | −0.377999 | − | 1.06096i | ||||
\(756\) | 15.4493 | 0.561887 | ||||||||
\(757\) | − | 36.7936i | − | 1.33728i | −0.743584 | − | 0.668642i | \(-0.766876\pi\) | ||
0.743584 | − | 0.668642i | \(-0.233124\pi\) | |||||||
\(758\) | 3.34930i | 0.121652i | ||||||||
\(759\) | 59.5521 | 2.16160 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.255560 | −0.00926406 | −0.00463203 | − | 0.999989i | \(-0.501474\pi\) | ||||
−0.00463203 | + | 0.999989i | \(0.501474\pi\) | |||||||
\(762\) | 12.8405i | 0.465163i | ||||||||
\(763\) | − | 13.2631i | − | 0.480155i | ||||||
\(764\) | −16.8281 | −0.608818 | ||||||||
\(765\) | −23.3126 | + | 8.30582i | −0.842870 | + | 0.300298i | ||||
\(766\) | −2.50626 | −0.0905548 | ||||||||
\(767\) | − | 6.59465i | − | 0.238119i | ||||||
\(768\) | − | 31.2991i | − | 1.12941i | ||||||
\(769\) | 9.45643 | 0.341008 | 0.170504 | − | 0.985357i | \(-0.445460\pi\) | ||||
0.170504 | + | 0.985357i | \(0.445460\pi\) | |||||||
\(770\) | 1.50699 | + | 4.22979i | 0.0543081 | + | 0.152431i | ||||
\(771\) | 43.9602 | 1.58319 | ||||||||
\(772\) | − | 0.818991i | − | 0.0294761i | ||||||
\(773\) | − | 30.2259i | − | 1.08715i | −0.839360 | − | 0.543575i | \(-0.817070\pi\) | ||
0.839360 | − | 0.543575i | \(-0.182930\pi\) | |||||||
\(774\) | −4.91486 | −0.176661 | ||||||||
\(775\) | 19.7587 | − | 16.1263i | 0.709754 | − | 0.579273i | ||||
\(776\) | −8.29381 | −0.297730 | ||||||||
\(777\) | 58.6071i | 2.10252i | ||||||||
\(778\) | 1.23625i | 0.0443217i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −5.06309 | − | 14.2110i | −0.181288 | − | 0.508835i | ||||
\(781\) | −3.35244 | −0.119960 | ||||||||
\(782\) | 3.08983i | 0.110492i | ||||||||
\(783\) | 35.4625i | 1.26733i | ||||||||
\(784\) | 11.7927 | 0.421168 | ||||||||
\(785\) | 38.3296 | − | 13.6561i | 1.36804 | − | 0.487406i | ||||
\(786\) | −0.206190 | −0.00735454 | ||||||||
\(787\) | − | 36.3976i | − | 1.29743i | −0.761030 | − | 0.648717i | \(-0.775306\pi\) | ||
0.761030 | − | 0.648717i | \(-0.224694\pi\) | |||||||
\(788\) | 29.5720i | 1.05346i | ||||||||
\(789\) | 38.9934 | 1.38820 | ||||||||
\(790\) | 3.12217 | − | 1.11237i | 0.111082 | − | 0.0395763i | ||||
\(791\) | 11.4945 | 0.408697 | ||||||||
\(792\) | − | 18.3453i | − | 0.651872i | ||||||
\(793\) | − | 3.55908i | − | 0.126387i | ||||||
\(794\) | −5.83709 | −0.207151 | ||||||||
\(795\) | 1.41756 | + | 3.97879i | 0.0502758 | + | 0.141113i | ||||
\(796\) | −25.0803 | −0.888947 | ||||||||
\(797\) | 19.2118i | 0.680517i | 0.940332 | + | 0.340258i | \(0.110515\pi\) | ||||
−0.940332 | + | 0.340258i | \(0.889485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.6532 | 0.589148 | ||||||||
\(800\) | −8.90815 | − | 10.9147i | −0.314951 | − | 0.385894i | ||||
\(801\) | 10.0451 | 0.354926 | ||||||||
\(802\) | 6.05461i | 0.213796i | ||||||||
\(803\) | − | 5.99338i | − | 0.211502i | ||||||
\(804\) | 27.6931 | 0.976661 | ||||||||
\(805\) | 7.48019 | + | 20.9952i | 0.263642 | + | 0.739985i | ||||
\(806\) | −1.58352 | −0.0557771 | ||||||||
\(807\) | − | 44.4749i | − | 1.56559i | ||||||
\(808\) | − | 12.9573i | − | 0.455837i | ||||||
\(809\) | 43.0501 | 1.51356 | 0.756781 | − | 0.653669i | \(-0.226771\pi\) | ||||
0.756781 | + | 0.653669i | \(0.226771\pi\) | |||||||
\(810\) | 1.16281 | − | 0.414286i | 0.0408570 | − | 0.0145565i | ||||
\(811\) | 31.3282 | 1.10008 | 0.550040 | − | 0.835138i | \(-0.314612\pi\) | ||||
0.550040 | + | 0.835138i | \(0.314612\pi\) | |||||||
\(812\) | − | 32.5305i | − | 1.14160i | ||||||
\(813\) | 16.2257i | 0.569058i | ||||||||
\(814\) | 11.4161 | 0.400133 | ||||||||
\(815\) | −32.2986 | + | 11.5073i | −1.13137 | + | 0.403085i | ||||
\(816\) | −24.5560 | −0.859631 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 2.42032i | − | 0.0846245i | ||||||
\(819\) | 11.0838 | 0.387299 | ||||||||
\(820\) | −3.63781 | − | 10.2105i | −0.127038 | − | 0.356567i | ||||
\(821\) | 17.0708 | 0.595776 | 0.297888 | − | 0.954601i | \(-0.403718\pi\) | ||||
0.297888 | + | 0.954601i | \(0.403718\pi\) | |||||||
\(822\) | − | 9.70686i | − | 0.338566i | ||||||
\(823\) | 36.3136i | 1.26581i | 0.774228 | + | 0.632907i | \(0.218138\pi\) | ||||
−0.774228 | + | 0.632907i | \(0.781862\pi\) | |||||||
\(824\) | −3.88766 | −0.135433 | ||||||||
\(825\) | 36.6493 | + | 44.9046i | 1.27597 | + | 1.56338i | ||||
\(826\) | 2.46348 | 0.0857155 | ||||||||
\(827\) | − | 19.3430i | − | 0.672623i | −0.941751 | − | 0.336311i | \(-0.890821\pi\) | ||
0.941751 | − | 0.336311i | \(-0.109179\pi\) | |||||||
\(828\) | − | 44.8393i | − | 1.55828i | ||||||
\(829\) | −20.1843 | −0.701029 | −0.350514 | − | 0.936557i | \(-0.613993\pi\) | ||||
−0.350514 | + | 0.936557i | \(0.613993\pi\) | |||||||
\(830\) | 2.17453 | + | 6.10343i | 0.0754790 | + | 0.211853i | ||||
\(831\) | 17.2773 | 0.599345 | ||||||||
\(832\) | − | 8.38217i | − | 0.290600i | ||||||
\(833\) | − | 7.95964i | − | 0.275785i | ||||||
\(834\) | −10.5758 | −0.366210 | ||||||||
\(835\) | −13.0951 | + | 4.66553i | −0.453176 | + | 0.161457i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 20.9332i | − | 0.723557i | ||||||
\(838\) | − | 0.979889i | − | 0.0338497i | ||||||
\(839\) | 25.8209 | 0.891437 | 0.445719 | − | 0.895173i | \(-0.352948\pi\) | ||||
0.445719 | + | 0.895173i | \(0.352948\pi\) | |||||||
\(840\) | 10.7808 | − | 3.84097i | 0.371972 | − | 0.132526i | ||||
\(841\) | 45.6708 | 1.57486 | ||||||||
\(842\) | − | 4.95753i | − | 0.170848i | ||||||
\(843\) | − | 7.33776i | − | 0.252726i | ||||||
\(844\) | 8.62664 | 0.296941 | ||||||||
\(845\) | 8.54589 | + | 23.9864i | 0.293987 | + | 0.825158i | ||||
\(846\) | 7.44469 | 0.255954 | ||||||||
\(847\) | − | 13.4288i | − | 0.461418i | ||||||
\(848\) | 2.51430i | 0.0863413i | ||||||||
\(849\) | −85.0654 | −2.91944 | ||||||||
\(850\) | −2.32985 | + | 1.90153i | −0.0799133 | + | 0.0652220i | ||||
\(851\) | 56.6655 | 1.94247 | ||||||||
\(852\) | 4.20750i | 0.144147i | ||||||||
\(853\) | − | 14.3234i | − | 0.490425i | −0.969469 | − | 0.245212i | \(-0.921142\pi\) | ||
0.969469 | − | 0.245212i | \(-0.0788577\pi\) | |||||||
\(854\) | 1.32952 | 0.0454953 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.3365 | 0.558370 | ||||||||
\(857\) | − | 24.2649i | − | 0.828874i | −0.910078 | − | 0.414437i | \(-0.863979\pi\) | ||
0.910078 | − | 0.414437i | \(-0.136021\pi\) | |||||||
\(858\) | − | 3.59878i | − | 0.122860i | ||||||
\(859\) | −40.5232 | −1.38263 | −0.691317 | − | 0.722551i | \(-0.742969\pi\) | ||||
−0.691317 | + | 0.722551i | \(0.742969\pi\) | |||||||
\(860\) | 18.2633 | − | 6.50684i | 0.622773 | − | 0.221881i | ||||
\(861\) | 13.2744 | 0.452389 | ||||||||
\(862\) | − | 3.29515i | − | 0.112233i | ||||||
\(863\) | 22.9160i | 0.780069i | 0.920800 | + | 0.390035i | \(0.127537\pi\) | ||||
−0.920800 | + | 0.390035i | \(0.872463\pi\) | |||||||
\(864\) | −11.5635 | −0.393398 | ||||||||
\(865\) | −5.82631 | + | 2.07580i | −0.198100 | + | 0.0705792i | ||||
\(866\) | −8.40453 | −0.285598 | ||||||||
\(867\) | − | 29.9779i | − | 1.01810i | ||||||
\(868\) | 19.2025i | 0.651775i | ||||||||
\(869\) | −25.6664 | −0.870673 | ||||||||
\(870\) | 4.34143 | + | 12.1854i | 0.147188 | + | 0.413125i | ||||
\(871\) | 6.61866 | 0.224265 | ||||||||
\(872\) | 6.58478i | 0.222989i | ||||||||
\(873\) | − | 38.7326i | − | 1.31090i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.2278 | + | 18.5612i | −0.379570 | + | 0.627483i | ||||
\(876\) | −7.52203 | −0.254146 | ||||||||
\(877\) | − | 49.6951i | − | 1.67808i | −0.544067 | − | 0.839042i | \(-0.683116\pi\) | ||
0.544067 | − | 0.839042i | \(-0.316884\pi\) | |||||||
\(878\) | 5.72515i | 0.193214i | ||||||||
\(879\) | 2.37047 | 0.0799539 | ||||||||
\(880\) | 11.5798 | + | 32.5020i | 0.390355 | + | 1.09564i | ||||
\(881\) | −11.0358 | −0.371804 | −0.185902 | − | 0.982568i | \(-0.559521\pi\) | ||||
−0.185902 | + | 0.982568i | \(0.559521\pi\) | |||||||
\(882\) | − | 3.55830i | − | 0.119814i | ||||||
\(883\) | − | 22.1244i | − | 0.744547i | −0.928123 | − | 0.372273i | \(-0.878578\pi\) | ||
0.928123 | − | 0.372273i | \(-0.121422\pi\) | |||||||
\(884\) | −6.06135 | −0.203865 | ||||||||
\(885\) | 29.9554 | − | 10.6725i | 1.00694 | − | 0.358753i | ||||
\(886\) | −0.586472 | −0.0197029 | ||||||||
\(887\) | 20.0329i | 0.672640i | 0.941748 | + | 0.336320i | \(0.109182\pi\) | ||||
−0.941748 | + | 0.336320i | \(0.890818\pi\) | |||||||
\(888\) | − | 29.0970i | − | 0.976430i | ||||||
\(889\) | 37.2148 | 1.24814 | ||||||||
\(890\) | 1.14986 | − | 0.409673i | 0.0385435 | − | 0.0137323i | ||||
\(891\) | −9.55909 | −0.320242 | ||||||||
\(892\) | 17.8481i | 0.597597i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 8.34491 | 0.279095 | ||||||||
\(895\) | −8.53896 | − | 23.9670i | −0.285426 | − | 0.801129i | ||||
\(896\) | 14.0654 | 0.469893 | ||||||||
\(897\) | − | 17.8632i | − | 0.596433i | ||||||
\(898\) | 9.33951i | 0.311663i | ||||||||
\(899\) | −44.0775 | −1.47007 | ||||||||
\(900\) | 33.8107 | − | 27.5949i | 1.12702 | − | 0.919830i | ||||
\(901\) | 1.69706 | 0.0565372 | ||||||||
\(902\) | − | 2.58571i | − | 0.0860947i | ||||||
\(903\) | 23.7435i | 0.790133i | ||||||||
\(904\) | −5.70673 | −0.189803 | ||||||||
\(905\) | −2.67654 | − | 7.51247i | −0.0889713 | − | 0.249723i | ||||
\(906\) | −9.26546 | −0.307824 | ||||||||
\(907\) | − | 0.681366i | − | 0.0226244i | −0.999936 | − | 0.0113122i | \(-0.996399\pi\) | ||
0.999936 | − | 0.0113122i | \(-0.00360086\pi\) | |||||||
\(908\) | − | 1.16474i | − | 0.0386531i | ||||||
\(909\) | 60.5114 | 2.00704 | ||||||||
\(910\) | 1.26876 | − | 0.452034i | 0.0420590 | − | 0.0149848i | ||||
\(911\) | −28.7169 | −0.951433 | −0.475716 | − | 0.879599i | \(-0.657811\pi\) | ||||
−0.475716 | + | 0.879599i | \(0.657811\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 50.1744i | − | 1.66053i | ||||||
\(914\) | −0.458652 | −0.0151709 | ||||||||
\(915\) | 16.1667 | − | 5.75987i | 0.534455 | − | 0.190416i | ||||
\(916\) | 13.8047 | 0.456121 | ||||||||
\(917\) | 0.597584i | 0.0197340i | ||||||||
\(918\) | 2.46834i | 0.0814674i | ||||||||
\(919\) | −6.91259 | −0.228025 | −0.114013 | − | 0.993479i | \(-0.536370\pi\) | ||||
−0.114013 | + | 0.993479i | \(0.536370\pi\) | |||||||
\(920\) | −3.71373 | − | 10.4236i | −0.122438 | − | 0.343657i | ||||
\(921\) | 24.6234 | 0.811370 | ||||||||
\(922\) | 4.11220i | 0.135428i | ||||||||
\(923\) | 1.00559i | 0.0330995i | ||||||||
\(924\) | −43.6405 | −1.43567 | ||||||||
\(925\) | 34.8729 | + | 42.7281i | 1.14661 | + | 1.40489i | ||||
\(926\) | −5.95647 | −0.195742 | ||||||||
\(927\) | − | 18.1556i | − | 0.596309i | ||||||
\(928\) | 24.3484i | 0.799276i | ||||||||
\(929\) | −40.8302 | −1.33960 | −0.669798 | − | 0.742544i | \(-0.733619\pi\) | ||||
−0.669798 | + | 0.742544i | \(0.733619\pi\) | |||||||
\(930\) | −2.56271 | − | 7.19296i | −0.0840344 | − | 0.235866i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39.1272i | 1.28165i | ||||||||
\(933\) | 31.3288i | 1.02566i | ||||||||
\(934\) | −3.33737 | −0.109202 | ||||||||
\(935\) | 21.9377 | − | 7.81595i | 0.717438 | − | 0.255609i | ||||
\(936\) | −5.50284 | −0.179866 | ||||||||
\(937\) | 14.7439i | 0.481664i | 0.970567 | + | 0.240832i | \(0.0774202\pi\) | ||||
−0.970567 | + | 0.240832i | \(0.922580\pi\) | |||||||
\(938\) | 2.47245i | 0.0807284i | ||||||||
\(939\) | −21.5378 | −0.702861 | ||||||||
\(940\) | −27.6639 | + | 9.85611i | −0.902298 | + | 0.321471i | ||||
\(941\) | 52.2137 | 1.70212 | 0.851059 | − | 0.525071i | \(-0.175961\pi\) | ||||
0.851059 | + | 0.525071i | \(0.175961\pi\) | |||||||
\(942\) | − | 12.1823i | − | 0.396921i | ||||||
\(943\) | − | 12.8346i | − | 0.417952i | ||||||
\(944\) | 18.9296 | 0.616105 | ||||||||
\(945\) | 5.97563 | + | 16.7723i | 0.194387 | + | 0.545602i | ||||
\(946\) | 4.62499 | 0.150371 | ||||||||
\(947\) | 57.3403i | 1.86331i | 0.363343 | + | 0.931655i | \(0.381635\pi\) | ||||
−0.363343 | + | 0.931655i | \(0.618365\pi\) | |||||||
\(948\) | 32.2128i | 1.04622i | ||||||||
\(949\) | −1.79777 | −0.0583580 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.2555 | −1.46751 | ||||||||
\(952\) | − | 4.59828i | − | 0.149031i | ||||||
\(953\) | 9.31765i | 0.301828i | 0.988547 | + | 0.150914i | \(0.0482217\pi\) | ||||
−0.988547 | + | 0.150914i | \(0.951778\pi\) | |||||||
\(954\) | 0.758657 | 0.0245624 | ||||||||
\(955\) | −6.50890 | − | 18.2691i | −0.210623 | − | 0.591173i | ||||
\(956\) | 22.5731 | 0.730065 | ||||||||
\(957\) | − | 100.173i | − | 3.23812i | ||||||
\(958\) | 5.31507i | 0.171722i | ||||||||
\(959\) | −28.1327 | −0.908452 | ||||||||
\(960\) | 38.0750 | − | 13.5654i | 1.22887 | − | 0.437820i | ||||
\(961\) | −4.98144 | −0.160692 | ||||||||
\(962\) | − | 3.42435i | − | 0.110405i | ||||||
\(963\) | 76.2925i | 2.45849i | ||||||||
\(964\) | −49.5343 | −1.59539 | ||||||||
\(965\) | 0.889122 | − | 0.316776i | 0.0286218 | − | 0.0101974i | ||||
\(966\) | 6.67292 | 0.214698 | ||||||||
\(967\) | − | 8.82697i | − | 0.283856i | −0.989877 | − | 0.141928i | \(-0.954670\pi\) | ||
0.989877 | − | 0.141928i | \(-0.0453302\pi\) | |||||||
\(968\) | 6.66705i | 0.214287i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.57964 | − | 4.43371i | −0.0507193 | − | 0.142358i | ||||
\(971\) | −55.9918 | −1.79686 | −0.898431 | − | 0.439114i | \(-0.855292\pi\) | ||||
−0.898431 | + | 0.439114i | \(0.855292\pi\) | |||||||
\(972\) | 35.8846i | 1.15100i | ||||||||
\(973\) | 30.6511i | 0.982628i | ||||||||
\(974\) | −7.14984 | −0.229096 | ||||||||
\(975\) | 13.4695 | − | 10.9933i | 0.431370 | − | 0.352067i | ||||
\(976\) | 10.2161 | 0.327011 | ||||||||
\(977\) | 41.1034i | 1.31501i | 0.753449 | + | 0.657506i | \(0.228389\pi\) | ||||
−0.753449 | + | 0.657506i | \(0.771611\pi\) | |||||||
\(978\) | 10.2655i | 0.328253i | ||||||||
\(979\) | −9.45265 | −0.302108 | ||||||||
\(980\) | 4.71087 | + | 13.2224i | 0.150483 | + | 0.422374i | ||||
\(981\) | −30.7513 | −0.981815 | ||||||||
\(982\) | − | 4.48752i | − | 0.143203i | ||||||
\(983\) | 2.49864i | 0.0796941i | 0.999206 | + | 0.0398471i | \(0.0126871\pi\) | ||||
−0.999206 | + | 0.0398471i | \(0.987313\pi\) | |||||||
\(984\) | −6.59039 | −0.210094 | ||||||||
\(985\) | −32.1043 | + | 11.4381i | −1.02293 | + | 0.364449i | ||||
\(986\) | 5.19741 | 0.165519 | ||||||||
\(987\) | − | 35.9650i | − | 1.14478i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.9569 | 0.729986 | ||||||||
\(990\) | 9.80706 | − | 3.49406i | 0.311689 | − | 0.111048i | ||||
\(991\) | −17.4234 | −0.553471 | −0.276736 | − | 0.960946i | \(-0.589253\pi\) | ||||
−0.276736 | + | 0.960946i | \(0.589253\pi\) | |||||||
\(992\) | − | 14.3727i | − | 0.456332i | ||||||
\(993\) | 21.6727i | 0.687762i | ||||||||
\(994\) | −0.375647 | −0.0119148 | ||||||||
\(995\) | −9.70076 | − | 27.2279i | −0.307535 | − | 0.863183i | ||||
\(996\) | −62.9717 | −1.99533 | ||||||||
\(997\) | 12.8010i | 0.405412i | 0.979240 | + | 0.202706i | \(0.0649736\pi\) | ||||
−0.979240 | + | 0.202706i | \(0.935026\pi\) | |||||||
\(998\) | − | 2.54645i | − | 0.0806065i | ||||||
\(999\) | 45.2679 | 1.43221 |
(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 | 1805.2.b.l.1084.13 | 24 | ||
5.2 | odd | 4 | 9025.2.a.ct.1.12 | 24 | |||
5.3 | odd | 4 | 9025.2.a.ct.1.13 | 24 | |||
5.4 | even | 2 | inner | 1805.2.b.l.1084.12 | 24 | ||
19.3 | odd | 18 | 95.2.p.a.9.5 | yes | 48 | ||
19.13 | odd | 18 | 95.2.p.a.74.4 | yes | 48 | ||
19.18 | odd | 2 | 1805.2.b.k.1084.12 | 24 | |||
57.32 | even | 18 | 855.2.da.b.739.5 | 48 | |||
57.41 | even | 18 | 855.2.da.b.199.4 | 48 | |||
95.3 | even | 36 | 475.2.l.f.351.4 | 48 | |||
95.13 | even | 36 | 475.2.l.f.226.4 | 48 | |||
95.18 | even | 4 | 9025.2.a.cu.1.12 | 24 | |||
95.22 | even | 36 | 475.2.l.f.351.5 | 48 | |||
95.32 | even | 36 | 475.2.l.f.226.5 | 48 | |||
95.37 | even | 4 | 9025.2.a.cu.1.13 | 24 | |||
95.79 | odd | 18 | 95.2.p.a.9.4 | ✓ | 48 | ||
95.89 | odd | 18 | 95.2.p.a.74.5 | yes | 48 | ||
95.94 | odd | 2 | 1805.2.b.k.1084.13 | 24 | |||
285.89 | even | 18 | 855.2.da.b.739.4 | 48 | |||
285.269 | even | 18 | 855.2.da.b.199.5 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.9.4 | ✓ | 48 | 95.79 | odd | 18 | ||
95.2.p.a.9.5 | yes | 48 | 19.3 | odd | 18 | ||
95.2.p.a.74.4 | yes | 48 | 19.13 | odd | 18 | ||
95.2.p.a.74.5 | yes | 48 | 95.89 | odd | 18 | ||
475.2.l.f.226.4 | 48 | 95.13 | even | 36 | |||
475.2.l.f.226.5 | 48 | 95.32 | even | 36 | |||
475.2.l.f.351.4 | 48 | 95.3 | even | 36 | |||
475.2.l.f.351.5 | 48 | 95.22 | even | 36 | |||
855.2.da.b.199.4 | 48 | 57.41 | even | 18 | |||
855.2.da.b.199.5 | 48 | 285.269 | even | 18 | |||
855.2.da.b.739.4 | 48 | 285.89 | even | 18 | |||
855.2.da.b.739.5 | 48 | 57.32 | even | 18 | |||
1805.2.b.k.1084.12 | 24 | 19.18 | odd | 2 | |||
1805.2.b.k.1084.13 | 24 | 95.94 | odd | 2 | |||
1805.2.b.l.1084.12 | 24 | 5.4 | even | 2 | inner | ||
1805.2.b.l.1084.13 | 24 | 1.1 | even | 1 | trivial | ||
9025.2.a.ct.1.12 | 24 | 5.2 | odd | 4 | |||
9025.2.a.ct.1.13 | 24 | 5.3 | odd | 4 | |||
9025.2.a.cu.1.12 | 24 | 95.18 | even | 4 | |||
9025.2.a.cu.1.13 | 24 | 95.37 | even | 4 |