Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 41.5 | ||
Character | \(\chi\) | \(=\) | 76.41 |
Dual form | 76.5.j.a.13.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.65366 | + | 7.29088i | 0.294851 | + | 0.810098i | 0.995339 | + | 0.0964336i | \(0.0307435\pi\) |
−0.700488 | + | 0.713664i | \(0.747034\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.405227 | − | 2.29816i | 0.0162091 | − | 0.0919263i | −0.975630 | − | 0.219422i | \(-0.929583\pi\) |
0.991839 | + | 0.127496i | \(0.0406939\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.2726 | + | 40.3094i | 0.474952 | + | 0.822641i | 0.999588 | − | 0.0286856i | \(-0.00913217\pi\) |
−0.524637 | + | 0.851326i | \(0.675799\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 15.9346 | − | 13.3707i | 0.196723 | − | 0.165070i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −88.3294 | + | 152.991i | −0.729995 | + | 1.26439i | 0.226889 | + | 0.973921i | \(0.427144\pi\) |
−0.956885 | + | 0.290468i | \(0.906189\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.7242 | + | 103.646i | −0.223220 | + | 0.613293i | −0.999861 | − | 0.0166508i | \(-0.994700\pi\) |
0.776641 | + | 0.629943i | \(0.216922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 17.8309 | − | 3.14407i | 0.0792486 | − | 0.0139737i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −57.1483 | − | 47.9531i | −0.197745 | − | 0.165928i | 0.538539 | − | 0.842601i | \(-0.318977\pi\) |
−0.736284 | + | 0.676673i | \(0.763421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −192.492 | + | 305.398i | −0.533218 | + | 0.845978i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −232.133 | + | 276.646i | −0.526379 | + | 0.627314i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 15.6411 | + | 88.7052i | 0.0295673 | + | 0.167685i | 0.996016 | − | 0.0891754i | \(-0.0284232\pi\) |
−0.966449 | + | 0.256860i | \(0.917312\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 582.191 | + | 211.900i | 0.931505 | + | 0.339040i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 684.034 | + | 394.927i | 0.938318 | + | 0.541738i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −121.887 | − | 145.259i | −0.144931 | − | 0.172721i | 0.688696 | − | 0.725051i | \(-0.258184\pi\) |
−0.833626 | + | 0.552329i | \(0.813739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 670.369 | − | 387.038i | 0.697574 | − | 0.402745i | −0.108869 | − | 0.994056i | \(-0.534723\pi\) |
0.806443 | + | 0.591311i | \(0.201390\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1349.84 | − | 238.013i | −1.23952 | − | 0.218561i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 102.068 | − | 37.1497i | 0.0833208 | − | 0.0303263i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1355.70i | − | 0.990283i | −0.868812 | − | 0.495141i | \(-0.835116\pi\) | ||
0.868812 | − | 0.495141i | \(-0.164884\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −855.781 | −0.562644 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −316.776 | − | 870.336i | −0.188445 | − | 0.517749i | 0.809108 | − | 0.587660i | \(-0.199951\pi\) |
−0.997553 | + | 0.0699111i | \(0.977728\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 298.395 | − | 1692.28i | 0.161382 | − | 0.915243i | −0.791335 | − | 0.611383i | \(-0.790613\pi\) |
0.952717 | − | 0.303860i | \(-0.0982754\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −24.2709 | − | 42.0384i | −0.0119856 | − | 0.0207597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1738.43 | − | 1458.72i | 0.786978 | − | 0.660353i | −0.158018 | − | 0.987436i | \(-0.550510\pi\) |
0.944995 | + | 0.327083i | \(0.106066\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 117.269 | − | 203.116i | 0.0488417 | − | 0.0845962i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 197.968 | − | 543.913i | 0.0761123 | − | 0.209117i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1141.83 | + | 201.336i | −0.406491 | + | 0.0716753i | −0.373155 | − | 0.927769i | \(-0.621724\pi\) |
−0.0333356 | + | 0.999444i | \(0.510613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 315.804 | + | 264.991i | 0.104398 | + | 0.0876004i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2737.43 | − | 593.012i | −0.842545 | − | 0.182521i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2592.52 | − | 3089.64i | 0.744763 | − | 0.887574i | −0.252020 | − | 0.967722i | \(-0.581095\pi\) |
0.996783 | + | 0.0801483i | \(0.0255394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 702.333 | + | 3983.13i | 0.188749 | + | 1.07045i | 0.921044 | + | 0.389459i | \(0.127338\pi\) |
−0.732295 | + | 0.680987i | \(0.761551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 909.805 | + | 331.142i | 0.229228 | + | 0.0834321i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 222.909 | + | 128.697i | 0.0527595 | + | 0.0304607i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1781.28 | + | 2122.85i | 0.396811 | + | 0.472900i | 0.927045 | − | 0.374951i | \(-0.122340\pi\) |
−0.530234 | + | 0.847851i | \(0.677896\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −605.233 | + | 349.431i | −0.127123 | + | 0.0733945i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5745.13 | + | 1013.02i | 1.13968 | + | 0.200956i | 0.711466 | − | 0.702721i | \(-0.248032\pi\) |
0.428215 | + | 0.903677i | \(0.359143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4484.03 | + | 1632.05i | −0.841440 | + | 0.306259i | −0.726545 | − | 0.687119i | \(-0.758875\pi\) |
−0.114895 | + | 0.993378i | \(0.536653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4806.99i | 0.854577i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8222.63 | −1.38685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1602.75 | + | 4403.53i | 0.256810 | + | 0.705581i | 0.999359 | + | 0.0357890i | \(0.0113944\pi\) |
−0.742549 | + | 0.669792i | \(0.766383\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −771.592 | + | 4375.92i | −0.117603 | + | 0.666959i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3711.86 | − | 6429.14i | −0.538810 | − | 0.933247i | −0.998968 | − | 0.0454098i | \(-0.985541\pi\) |
0.460158 | − | 0.887837i | \(-0.347793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −133.362 | + | 111.904i | −0.0184584 | + | 0.0154884i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 735.618 | − | 1274.13i | 0.0971883 | − | 0.168335i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1547.47 | + | 4251.63i | −0.195362 | + | 0.536754i | −0.998234 | − | 0.0593976i | \(-0.981082\pi\) |
0.802872 | + | 0.596152i | \(0.203304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5055.87 | + | 891.486i | −0.610538 | + | 0.107654i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4600.78 | + | 3860.51i | 0.531943 | + | 0.446353i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 623.850 | + | 566.132i | 0.0691246 | + | 0.0627293i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3365.63 | − | 4011.01i | 0.357704 | − | 0.426295i | −0.556942 | − | 0.830552i | \(-0.688025\pi\) |
0.914646 | + | 0.404257i | \(0.132470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 638.106 | + | 3618.88i | 0.0651062 | + | 0.369235i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6086.56 | − | 2215.33i | −0.596663 | − | 0.217168i | 0.0259944 | − | 0.999662i | \(-0.491725\pi\) |
−0.622658 | + | 0.782494i | \(0.713947\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12871.6 | + | 7431.44i | 1.21327 | + | 0.700484i | 0.963471 | − | 0.267812i | \(-0.0863007\pi\) |
0.249803 | + | 0.968297i | \(0.419634\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 541.708 | + | 645.583i | 0.0491346 | + | 0.0585563i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13745.2 | + | 7935.81i | −1.20056 | + | 0.693144i | −0.960680 | − | 0.277658i | \(-0.910442\pi\) |
−0.239881 | + | 0.970802i | \(0.577108\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10969.9 | + | 1934.29i | 0.923314 | + | 0.162805i | 0.615043 | − | 0.788493i | \(-0.289139\pi\) |
0.308271 | + | 0.951299i | \(0.400250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9884.23 | − | 3597.56i | 0.802226 | − | 0.291986i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 24537.3i | − | 1.92163i | −0.277193 | − | 0.960814i | \(-0.589404\pi\) | ||
0.277193 | − | 0.960814i | \(-0.410596\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 210.197 | 0.0158939 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 784.706 | + | 2155.96i | 0.0573239 | + | 0.157496i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 602.969 | − | 3419.61i | 0.0425796 | − | 0.241481i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8283.67 | − | 14347.7i | −0.565786 | − | 0.979970i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5504.89 | − | 4619.16i | 0.363864 | − | 0.305318i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1452.15 | − | 2515.20i | 0.0929378 | − | 0.160973i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1306.34 | + | 3589.15i | −0.0809935 | + | 0.222528i | −0.973579 | − | 0.228350i | \(-0.926667\pi\) |
0.892586 | + | 0.450878i | \(0.148889\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13130.1 | − | 2315.19i | 0.789020 | − | 0.139125i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −25945.5 | − | 21770.9i | −1.51189 | − | 1.26862i | −0.859983 | − | 0.510323i | \(-0.829526\pi\) |
−0.651905 | − | 0.758301i | \(-0.726030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16790.2 | − | 651.813i | −0.949189 | − | 0.0368485i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1184.79 | − | 1411.98i | 0.0650092 | − | 0.0774750i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −771.241 | − | 4373.93i | −0.0410912 | − | 0.233040i | 0.957345 | − | 0.288948i | \(-0.0933056\pi\) |
−0.998436 | + | 0.0559085i | \(0.982194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9764.51 | + | 3553.99i | 0.505383 | + | 0.183944i | 0.582114 | − | 0.813107i | \(-0.302226\pi\) |
−0.0767305 | + | 0.997052i | \(0.524448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15248.6 | + | 8803.77i | 0.766992 | + | 0.442823i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12524.8 | − | 14926.5i | −0.612491 | − | 0.729938i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −383.219 | + | 221.252i | −0.0182268 | + | 0.0105233i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1792.08 | + | 315.993i | 0.0829323 | + | 0.0146232i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17999.4 | − | 6551.26i | 0.810748 | − | 0.295088i | 0.0968155 | − | 0.995302i | \(-0.469134\pi\) |
0.713933 | + | 0.700214i | \(0.246912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16772.4i | − | 0.735598i | −0.929905 | − | 0.367799i | \(-0.880111\pi\) | ||
0.929905 | − | 0.367799i | \(-0.119889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1551.80 | −0.0662909 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −617.822 | − | 1697.45i | −0.0257158 | − | 0.0706535i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6522.77 | + | 36992.5i | −0.264626 | + | 1.50077i | 0.505471 | + | 0.862844i | \(0.331319\pi\) |
−0.770097 | + | 0.637926i | \(0.779792\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4497.96 | − | 7790.69i | −0.177918 | − | 0.308164i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3211.64 | + | 2694.89i | −0.123901 | + | 0.103965i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11507.2 | + | 19931.0i | −0.433105 | + | 0.750160i | −0.997139 | − | 0.0755914i | \(-0.975916\pi\) |
0.564034 | + | 0.825752i | \(0.309249\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1093.98 | + | 3005.69i | −0.0401829 | + | 0.110402i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7735.07 | + | 1363.90i | −0.277352 | + | 0.0489046i | −0.310594 | − | 0.950543i | \(-0.600528\pi\) |
0.0332420 | + | 0.999447i | \(0.489417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12559.5 | + | 10538.7i | 0.439744 | + | 0.368989i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1016.11 | + | 7440.14i | 0.0347494 | + | 0.254442i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11562.8 | − | 13780.0i | 0.386341 | − | 0.460424i | −0.537464 | − | 0.843287i | \(-0.680617\pi\) |
0.923805 | + | 0.382863i | \(0.125062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5007.55 | + | 28399.2i | 0.163512 | + | 0.927321i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29405.9 | + | 10702.9i | 0.938616 | + | 0.341628i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19162.8 | + | 11063.7i | 0.598072 | + | 0.345297i | 0.768283 | − | 0.640111i | \(-0.221111\pi\) |
−0.170211 | + | 0.985408i | \(0.554445\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20579.6 | + | 24525.8i | 0.628175 | + | 0.748629i | 0.982453 | − | 0.186511i | \(-0.0597179\pi\) |
−0.354278 | + | 0.935140i | \(0.615273\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27176.8 | + | 15690.5i | −0.811513 | + | 0.468527i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3115.61 | − | 549.365i | −0.0910330 | − | 0.0160516i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12384.3 | − | 4507.51i | 0.354150 | − | 0.128900i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 36764.0i | 1.02920i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −54589.8 | −1.49639 | −0.748196 | − | 0.663478i | \(-0.769080\pi\) | ||||
−0.748196 | + | 0.663478i | \(0.769080\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18704.7 | − | 51390.8i | −0.502154 | − | 1.37966i | −0.889167 | − | 0.457582i | \(-0.848716\pi\) |
0.387013 | − | 0.922074i | \(-0.373507\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −346.786 | + | 1966.72i | −0.00911994 | + | 0.0517218i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3388.48 | + | 5869.03i | 0.0873118 | + | 0.151229i | 0.906374 | − | 0.422476i | \(-0.138839\pi\) |
−0.819062 | + | 0.573705i | \(0.805506\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −49441.1 | + | 41486.0i | −1.24848 | + | 1.04760i | −0.251669 | + | 0.967813i | \(0.580980\pi\) |
−0.996812 | + | 0.0797869i | \(0.974576\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10750.5 | + | 18620.4i | −0.266095 | + | 0.460891i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3018.67 | − | 8293.73i | 0.0732527 | − | 0.201260i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2128.53 | + | 375.318i | −0.0506492 | + | 0.00893083i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1435.29 | + | 1204.35i | 0.0334964 | + | 0.0281068i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29720.5 | − | 56425.1i | −0.680398 | − | 1.29175i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 43222.2 | − | 51510.2i | 0.970827 | − | 1.15699i | −0.0167510 | − | 0.999860i | \(-0.505332\pi\) |
0.987578 | − | 0.157127i | \(-0.0502233\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7859.82 | + | 44575.3i | 0.173242 | + | 0.982505i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3768.22 | − | 1371.52i | −0.0815190 | − | 0.0296705i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31202.5 | + | 18014.8i | 0.662628 | + | 0.382569i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23798.2 | − | 28361.6i | −0.496200 | − | 0.591348i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7126.05 | − | 4114.23i | 0.145903 | − | 0.0842371i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3287.92 | + | 579.750i | 0.0661168 | + | 0.0116582i | 0.206609 | − | 0.978424i | \(-0.433757\pi\) |
−0.140492 | + | 0.990082i | \(0.544868\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12110.2 | − | 4407.76i | 0.239214 | − | 0.0870669i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 74854.6i | 1.45267i | 0.687341 | + | 0.726335i | \(0.258778\pi\) | ||||
−0.687341 | + | 0.726335i | \(0.741222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 69586.5 | 1.32695 | 0.663474 | − | 0.748199i | \(-0.269081\pi\) | ||||
0.663474 | + | 0.748199i | \(0.269081\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21820.1 | − | 59950.2i | −0.408915 | − | 1.12348i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5567.08 | − | 31572.5i | 0.102545 | − | 0.581563i | −0.889627 | − | 0.456688i | \(-0.849036\pi\) |
0.992172 | − | 0.124876i | \(-0.0398532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2647.91 | − | 4586.31i | −0.0479476 | − | 0.0830477i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27852.4 | + | 23371.0i | −0.495869 | + | 0.416083i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12567.6 | − | 21767.7i | 0.220017 | − | 0.381081i | −0.734796 | − | 0.678289i | \(-0.762722\pi\) |
0.954813 | + | 0.297207i | \(0.0960553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10430.9 | − | 28658.6i | 0.179592 | − | 0.493425i | −0.816932 | − | 0.576735i | \(-0.804327\pi\) |
0.996524 | + | 0.0833092i | \(0.0265489\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29054.4 | − | 5123.07i | 0.492038 | − | 0.0867596i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −419.271 | − | 351.810i | −0.00698494 | − | 0.00586106i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24391.8 | − | 31472.0i | −0.399807 | − | 0.515858i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 37024.0 | − | 44123.5i | 0.597152 | − | 0.711658i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7734.70 | + | 43865.7i | 0.122771 | + | 0.696269i | 0.982607 | + | 0.185699i | \(0.0594548\pi\) |
−0.859836 | + | 0.510571i | \(0.829434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14952.7 | − | 5442.33i | −0.233603 | − | 0.0850244i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1169.78 | − | 675.371i | −0.0179896 | − | 0.0103863i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −65549.4 | − | 78118.7i | −0.992436 | − | 1.18274i | −0.983153 | − | 0.182782i | \(-0.941490\pi\) |
−0.00928251 | − | 0.999957i | \(-0.502955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 54647.3 | − | 31550.6i | 0.814647 | − | 0.470337i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3884.43 | − | 684.929i | −0.0570224 | − | 0.0100546i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 113180. | − | 41194.3i | 1.63629 | − | 0.595560i | 0.649904 | − | 0.760017i | \(-0.274809\pi\) |
0.986384 | + | 0.164456i | \(0.0525870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2705.70i | 0.0385290i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35104.6 | −0.492426 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −47107.1 | − | 129426.i | −0.651001 | − | 1.78861i | −0.614013 | − | 0.789296i | \(-0.710446\pi\) |
−0.0369886 | − | 0.999316i | \(-0.511777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15656.1 | + | 88790.1i | −0.213179 | + | 1.20900i | 0.670859 | + | 0.741585i | \(0.265925\pi\) |
−0.884038 | + | 0.467414i | \(0.845186\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19916.3 | − | 34496.0i | −0.267229 | − | 0.462854i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −83843.4 | + | 70352.9i | −1.10867 | + | 0.930287i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −62079.9 | + | 107525.i | −0.809080 | + | 1.40137i | 0.104423 | + | 0.994533i | \(0.466701\pi\) |
−0.913502 | + | 0.406834i | \(0.866633\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5507.09 | − | 15130.6i | 0.0707479 | − | 0.194378i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 47169.6 | − | 8317.28i | 0.597379 | − | 0.105334i | 0.133221 | − | 0.991086i | \(-0.457468\pi\) |
0.464158 | + | 0.885752i | \(0.346357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22734.0 | − | 19076.1i | −0.283860 | − | 0.238187i | 0.489729 | − | 0.871875i | \(-0.337096\pi\) |
−0.773589 | + | 0.633688i | \(0.781540\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2472.11 | + | 6050.74i | −0.0304354 | + | 0.0744935i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27710.5 | − | 33024.1i | 0.336419 | − | 0.400928i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13536.8 | − | 76771.2i | −0.162077 | − | 0.919185i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38175.0 | + | 13894.6i | 0.450810 | + | 0.164081i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 121893. | + | 70375.0i | 1.41986 | + | 0.819754i | 0.996286 | − | 0.0861098i | \(-0.0274436\pi\) |
0.423570 | + | 0.905864i | \(0.360777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6049.93 | − | 7210.03i | −0.0695194 | − | 0.0828500i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −120841. | + | 69767.3i | −1.36993 | + | 0.790932i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9784.03 | − | 1725.19i | −0.109440 | − | 0.0192972i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 75159.4 | − | 27355.8i | 0.829564 | − | 0.301937i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 50255.1i | − | 0.547388i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9438.46 | 0.101462 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33386.2 | − | 91727.9i | −0.354234 | − | 0.973251i | −0.980994 | − | 0.194038i | \(-0.937841\pi\) |
0.626760 | − | 0.779213i | \(-0.284381\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20024.8 | + | 113566.i | −0.209725 | + | 1.18941i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 72667.7 | + | 125864.i | 0.751313 | + | 1.30131i | 0.947187 | + | 0.320682i | \(0.103912\pi\) |
−0.195874 | + | 0.980629i | \(0.562754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −101844. | + | 85457.2i | −1.03955 | + | 0.872288i | −0.991957 | − | 0.126579i | \(-0.959600\pi\) |
−0.0475958 | + | 0.998867i | \(0.515156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1129.69 | − | 1956.69i | 0.0113852 | − | 0.0197197i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −54530.5 | + | 149821.i | −0.542651 | + | 1.49092i | 0.300784 | + | 0.953692i | \(0.402752\pi\) |
−0.843436 | + | 0.537230i | \(0.819471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32989.5 | − | 5816.93i | 0.324186 | − | 0.0571627i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −94334.2 | − | 79155.8i | −0.915502 | − | 0.768197i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25645.4 | − | 8222.39i | 0.245813 | − | 0.0788122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −43925.4 | + | 52348.2i | −0.415861 | + | 0.495604i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15007.7 | + | 85113.1i | 0.140352 | + | 0.795978i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 99258.0 | + | 36127.0i | 0.917010 | + | 0.333764i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 78104.0 | + | 45093.4i | 0.712881 | + | 0.411582i | 0.812127 | − | 0.583481i | \(-0.198310\pi\) |
−0.0992457 | + | 0.995063i | \(0.531643\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18126.6 | − | 21602.5i | −0.163466 | − | 0.194812i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5600.47 | − | 3233.43i | 0.0499039 | − | 0.0288120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9306.78 | − | 1641.04i | −0.0819482 | − | 0.0144497i | 0.132524 | − | 0.991180i | \(-0.457692\pi\) |
−0.214472 | + | 0.976730i | \(0.568803\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 178898. | − | 65113.7i | 1.55671 | − | 0.566595i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 136747.i | 1.17601i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 122672. | 1.04269 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 557.791 | + | 1532.52i | 0.00468634 | + | 0.0128756i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30236.7 | + | 171481.i | −0.251117 | + | 1.42415i | 0.554730 | + | 0.832031i | \(0.312822\pi\) |
−0.805847 | + | 0.592124i | \(0.798289\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −85890.6 | − | 148767.i | −0.705172 | − | 1.22139i | −0.966630 | − | 0.256178i | \(-0.917537\pi\) |
0.261458 | − | 0.965215i | \(-0.415797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −66737.4 | + | 55999.3i | −0.541695 | + | 0.454536i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −52519.6 | + | 90966.6i | −0.421475 | + | 0.730016i | −0.996084 | − | 0.0884119i | \(-0.971821\pi\) |
0.574609 | + | 0.818428i | \(0.305154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4656.17 | − | 12792.7i | 0.0369464 | − | 0.101509i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26532.0 | − | 4678.32i | 0.208178 | − | 0.0367074i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −131354. | − | 110219.i | −1.01919 | − | 0.855200i | −0.0296621 | − | 0.999560i | \(-0.509443\pi\) |
−0.989525 | + | 0.144360i | \(0.953888\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −56214.8 | − | 117573.i | −0.431356 | − | 0.902182i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 82625.6 | − | 98469.4i | 0.627049 | − | 0.747288i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1933.67 | + | 10966.4i | 0.0145143 | + | 0.0823146i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −41854.0 | − | 15233.6i | −0.310745 | − | 0.113102i | 0.181940 | − | 0.983310i | \(-0.441762\pi\) |
−0.492685 | + | 0.870208i | \(0.663985\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16684.7 | − | 9632.92i | −0.122537 | − | 0.0707465i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34689.2 | − | 41341.0i | −0.252027 | − | 0.300354i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −192034. | + | 110871.i | −1.38026 | + | 0.796894i | −0.992190 | − | 0.124736i | \(-0.960192\pi\) |
−0.388070 | + | 0.921630i | \(0.626858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 22191.6 | + | 3912.97i | 0.157807 | + | 0.0278256i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19653.6 | − | 7153.34i | 0.138280 | − | 0.0503299i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 146879.i | − | 1.02254i | −0.859419 | − | 0.511271i | \(-0.829175\pi\) | ||
0.859419 | − | 0.511271i | \(-0.170825\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29634.7 | −0.204150 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −946.882 | − | 2601.54i | −0.00645503 | − | 0.0177351i | 0.936423 | − | 0.350872i | \(-0.114115\pi\) |
−0.942878 | + | 0.333137i | \(0.891893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3332.04 | + | 18896.9i | −0.0224796 | + | 0.127488i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17872.2 | − | 30955.6i | −0.119332 | − | 0.206689i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35161.7 | − | 29504.2i | 0.232365 | − | 0.194977i | −0.519169 | − | 0.854671i | \(-0.673759\pi\) |
0.751534 | + | 0.659694i | \(0.229314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3359.83 | − | 5819.39i | 0.0219768 | − | 0.0380649i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 89878.1 | − | 246938.i | 0.581927 | − | 1.59883i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10769.5 | − | 1898.95i | 0.0690241 | − | 0.0121708i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 91174.4 | + | 76504.4i | 0.578485 | + | 0.485406i | 0.884449 | − | 0.466637i | \(-0.154534\pi\) |
−0.305964 | + | 0.952043i | \(0.598979\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −39803.2 | − | 124145.i | −0.250019 | − | 0.779800i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 130832. | − | 155920.i | 0.813628 | − | 0.969644i | −0.186289 | − | 0.982495i | \(-0.559646\pi\) |
0.999917 | + | 0.0128506i | \(0.00409060\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14825.9 | + | 84082.0i | 0.0912876 | + | 0.517718i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9743.87 | + | 3546.48i | 0.0594048 | + | 0.0216216i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 207410. | + | 119748.i | 1.25210 | + | 0.722902i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −67298.2 | − | 80202.8i | −0.402306 | − | 0.479450i | 0.526416 | − | 0.850227i | \(-0.323536\pi\) |
−0.928722 | + | 0.370778i | \(0.879091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29843.2 | − | 17230.0i | 0.176669 | − | 0.102000i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 184876. | + | 32598.7i | 1.08388 | + | 0.191117i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16279.3 | + | 5925.19i | −0.0945236 | + | 0.0344038i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 80622.9i | 0.463646i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −214521. | −1.22192 | −0.610959 | − | 0.791662i | \(-0.709216\pi\) | ||||
−0.610959 | + | 0.791662i | \(0.709216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −76569.4 | − | 210373.i | −0.432007 | − | 1.18693i | −0.944579 | − | 0.328286i | \(-0.893529\pi\) |
0.512571 | − | 0.858645i | \(-0.328693\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8197.12 | − | 46488.2i | 0.0458122 | − | 0.259814i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23109.9 | − | 40027.6i | −0.127944 | − | 0.221606i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −144212. | + | 121009.i | −0.790946 | + | 0.663682i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 75590.7 | − | 130927.i | 0.410727 | − | 0.711400i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37160.5 | + | 102098.i | −0.200045 | + | 0.549618i | −0.998634 | − | 0.0522588i | \(-0.983358\pi\) |
0.798589 | + | 0.601877i | \(0.205580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 117896. | − | 20788.3i | 0.628818 | − | 0.110878i | 0.149848 | − | 0.988709i | \(-0.452122\pi\) |
0.478970 | + | 0.877832i | \(0.341010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2630.06 | − | 2206.88i | −0.0138991 | − | 0.0116627i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −30101.2 | − | 12298.3i | −0.157623 | − | 0.0643992i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 146363. | − | 174429.i | 0.759456 | − | 0.905084i | −0.238357 | − | 0.971177i | \(-0.576609\pi\) |
0.997813 | + | 0.0660931i | \(0.0210534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −847.169 | − | 4804.53i | −0.00435605 | − | 0.0247044i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −67184.3 | − | 24453.1i | −0.342342 | − | 0.124602i | 0.165127 | − | 0.986272i | \(-0.447197\pi\) |
−0.507469 | + | 0.861670i | \(0.669419\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9143.84 | + | 5279.20i | 0.0461752 | + | 0.0266592i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 95528.8 | + | 113847.i | 0.478101 | + | 0.569778i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14220.1 | + | 8210.00i | −0.0705361 | + | 0.0407240i | −0.534853 | − | 0.844945i | \(-0.679633\pi\) |
0.464317 | + | 0.885669i | \(0.346300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 161134. | + | 28412.3i | 0.792200 | + | 0.139686i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 122285. | − | 44508.2i | 0.595907 | − | 0.216892i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11980.4i | 0.0578695i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −236201. | −1.13097 | −0.565483 | − | 0.824760i | \(-0.691310\pi\) | ||||
−0.565483 | + | 0.824760i | \(0.691310\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20153.4 | − | 55371.0i | −0.0956583 | − | 0.262819i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8044.64 | − | 45623.4i | 0.0378534 | − | 0.214677i | −0.960014 | − | 0.279952i | \(-0.909681\pi\) |
0.997867 | + | 0.0652750i | \(0.0207925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −107047. | − | 185410.i | −0.499358 | − | 0.864913i | 0.500642 | − | 0.865654i | \(-0.333097\pi\) |
−1.00000 | 0.000741640i | \(0.999764\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10736.4 | − | 9008.93i | 0.0496539 | − | 0.0416646i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −90821.3 | + | 157307.i | −0.416441 | + | 0.721298i | −0.995579 | − | 0.0939325i | \(-0.970056\pi\) |
0.579137 | + | 0.815230i | \(0.303390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −44115.6 | + | 121207.i | −0.200561 | + | 0.551037i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −287017. | + | 50608.8i | −1.29380 | + | 0.228131i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 232547. | + | 195130.i | 1.03941 | + | 0.872172i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −176781. | + | 137011.i | −0.783516 | + | 0.607250i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15502.6 | + | 18475.3i | −0.0681348 | + | 0.0811999i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37321.6 | + | 211661.i | 0.162663 | + | 0.922508i | 0.951441 | + | 0.307830i | \(0.0996028\pi\) |
−0.788778 | + | 0.614678i | \(0.789286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 140513. | + | 51142.6i | 0.607333 | + | 0.221051i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28170.7 | − | 16264.4i | −0.120755 | − | 0.0697177i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7854.08 | − | 9360.13i | −0.0333896 | − | 0.0397922i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 127784. | − | 73775.9i | 0.538787 | − | 0.311069i | −0.205800 | − | 0.978594i | \(-0.565980\pi\) |
0.744587 | + | 0.667525i | \(0.232646\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −175851. | − | 31007.2i | −0.735405 | − | 0.129672i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −256367. | + | 93309.9i | −1.06341 | + | 0.387048i | −0.813707 | − | 0.581276i | \(-0.802554\pi\) |
−0.249698 | + | 0.968324i | \(0.580331\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14146.1i | 0.0582028i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8575.33 | 0.0349978 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 92870.0 | + | 255158.i | 0.375978 | + | 1.03299i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29635.6 | − | 168072.i | 0.119018 | − | 0.674985i | −0.865664 | − | 0.500626i | \(-0.833103\pi\) |
0.984682 | − | 0.174360i | \(-0.0557856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30470.3 | − | 52776.1i | −0.121395 | − | 0.210263i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12725.1 | − | 10677.7i | 0.0502952 | − | 0.0422027i | −0.617294 | − | 0.786733i | \(-0.711771\pi\) |
0.667589 | + | 0.744530i | \(0.267326\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7557.61 | + | 13090.2i | −0.0296348 | + | 0.0513290i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −43507.6 | + | 119536.i | −0.169258 | + | 0.465033i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 182544. | − | 32187.4i | 0.704581 | − | 0.124237i | 0.190133 | − | 0.981758i | \(-0.439108\pi\) |
0.514448 | + | 0.857522i | \(0.327997\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −170142. | − | 142766.i | −0.651584 | − | 0.546744i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −252281. | + | 132882.i | −0.958626 | + | 0.504931i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22294.5 | − | 26569.6i | 0.0840590 | − | 0.100178i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 69616.1 | + | 394813.i | 0.260453 | + | 1.47710i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 131152. | + | 47735.5i | 0.486902 | + | 0.177218i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 376417. | + | 217325.i | 1.38674 | + | 0.800633i | 0.992946 | − | 0.118568i | \(-0.0378303\pi\) |
0.393790 | + | 0.919200i | \(0.371164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12503.6 | + | 14901.2i | 0.0457122 | + | 0.0544776i | 0.788416 | − | 0.615142i | \(-0.210901\pi\) |
−0.742704 | + | 0.669620i | \(0.766457\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −193767. | + | 111871.i | −0.703009 | + | 0.405883i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −56870.1 | − | 10027.7i | −0.204768 | − | 0.0361062i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 255341. | − | 92936.4i | 0.912449 | − | 0.332104i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 83896.0i | − | 0.297545i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 102157. | 0.359596 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12667.8 | + | 34804.5i | 0.0442582 | + | 0.121598i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29812.2 | + | 169073.i | −0.103382 | + | 0.586308i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20716.6 | + | 35882.2i | 0.0713084 | + | 0.123510i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 346656. | − | 290879.i | 1.18442 | − | 0.993844i | 0.184477 | − | 0.982837i | \(-0.440941\pi\) |
0.999939 | − | 0.0110070i | \(-0.00350370\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −124204. | + | 215127.i | −0.421245 | + | 0.729617i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8890.60 | − | 24426.7i | 0.0299322 | − | 0.0822379i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −312719. | + | 55140.9i | −1.04515 | + | 0.184289i | −0.669761 | − | 0.742577i | \(-0.733603\pi\) |
−0.375393 | + | 0.926866i | \(0.622492\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 64448.7 | + | 54078.8i | 0.213830 | + | 0.179425i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 67823.9 | − | 9262.78i | 0.223398 | − | 0.0305097i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −140203. | + | 167088.i | −0.458467 | + | 0.546379i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4262.41 | − | 24173.3i | −0.0138379 | − | 0.0784785i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −63243.6 | − | 23018.8i | −0.203848 | − | 0.0741945i | 0.238078 | − | 0.971246i | \(-0.423482\pi\) |
−0.441926 | + | 0.897051i | \(0.645705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 164142. | + | 94767.7i | 0.525288 | + | 0.303275i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 65727.4 | + | 78330.9i | 0.208843 | + | 0.248890i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 178538. | − | 103079.i | 0.563268 | − | 0.325203i | −0.191188 | − | 0.981553i | \(-0.561234\pi\) |
0.754456 | + | 0.656351i | \(0.227901\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56390.5 | − | 9943.17i | −0.176648 | − | 0.0311478i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −194347. | + | 70736.7i | −0.604523 | + | 0.220028i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 532584.i | − | 1.64499i | −0.568771 | − | 0.822496i | \(-0.692581\pi\) | ||
0.568771 | − | 0.822496i | \(-0.307419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −197356. | −0.605309 | −0.302654 | − | 0.953100i | \(-0.597873\pi\) | ||||
−0.302654 | + | 0.953100i | \(0.597873\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −144863. | − | 398008.i | −0.441213 | − | 1.21222i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9690.52 | + | 54957.7i | −0.0293097 | + | 0.166224i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 50452.7 | + | 87386.6i | 0.151542 | + | 0.262478i | 0.931794 | − | 0.362986i | \(-0.118243\pi\) |
−0.780253 | + | 0.625464i | \(0.784910\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 325048. | − | 272748.i | 0.969596 | − | 0.813588i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 172770. | − | 299246.i | 0.511818 | − | 0.886494i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 70054.8 | − | 192474.i | 0.206111 | − | 0.566285i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5272.73 | − | 929.724i | 0.0154072 | − | 0.00271670i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −368685. | − | 309363.i | −1.06999 | − | 0.897826i | −0.0749363 | − | 0.997188i | \(-0.523875\pi\) |
−0.995051 | + | 0.0993621i | \(0.968320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10840.0 | + | 279231.i | −0.0312464 | + | 0.804883i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33798.5 | + | 40279.5i | −0.0967659 | + | 0.115321i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −65332.1 | − | 370517.i | −0.185788 | − | 1.05366i | −0.924939 | − | 0.380116i | \(-0.875884\pi\) |
0.739151 | − | 0.673540i | \(-0.235227\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7614.46 | − | 2771.44i | −0.0215083 | − | 0.00782837i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −433670. | − | 250379.i | −1.21678 | − | 0.702505i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −51498.6 | − | 61373.7i | −0.143530 | − | 0.171052i | 0.689490 | − | 0.724295i | \(-0.257835\pi\) |
−0.833020 | + | 0.553243i | \(0.813390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −206392. | + | 119160.i | −0.571403 | + | 0.329900i | −0.757710 | − | 0.652592i | \(-0.773682\pi\) |
0.186306 | + | 0.982492i | \(0.440348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 56768.0 | + | 10009.7i | 0.156124 | + | 0.0275288i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36330.2 | + | 13223.1i | −0.0992559 | + | 0.0361262i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 46881.4i | − | 0.127240i | −0.997974 | − | 0.0636199i | \(-0.979735\pi\) | ||
0.997974 | − | 0.0636199i | \(-0.0202645\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 68479.1 | 0.184639 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 85610.0 | + | 235212.i | 0.229320 | + | 0.630052i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 62444.3 | − | 354139.i | 0.166177 | − | 0.942438i | −0.781665 | − | 0.623698i | \(-0.785629\pi\) |
0.947842 | − | 0.318740i | \(-0.103260\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8384.81 | − | 14522.9i | −0.0221689 | − | 0.0383976i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34916.8 | + | 29298.6i | −0.0917199 | + | 0.0769622i | −0.687495 | − | 0.726189i | \(-0.741290\pi\) |
0.595775 | + | 0.803152i | \(0.296845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 179541. | − | 310975.i | 0.468579 | − | 0.811603i | −0.530776 | − | 0.847512i | \(-0.678099\pi\) |
0.999355 | + | 0.0359092i | \(0.0114327\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24333.0 | + | 66854.4i | −0.0630976 | + | 0.173359i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −207394. | + | 36569.2i | −0.534343 | + | 0.0942191i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 291437. | + | 244545.i | 0.746079 | + | 0.626034i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 332521. | − | 366422.i | 0.845832 | − | 0.932065i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −65009.9 | + | 77475.8i | −0.164315 | + | 0.195824i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −68745.3 | − | 389874.i | −0.172657 | − | 0.979187i | −0.940814 | − | 0.338925i | \(-0.889937\pi\) |
0.768156 | − | 0.640262i | \(-0.221174\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 490252. | + | 178437.i | 1.22352 | + | 0.445326i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7719.07 | + | 4456.61i | 0.0191433 | + | 0.0110524i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16628.3 | + | 19816.9i | 0.0409798 | + | 0.0488378i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 105091. | − | 60674.4i | 0.257374 | − | 0.148595i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9953.74 | − | 1755.11i | −0.0242254 | − | 0.00427158i | 0.161522 | − | 0.986869i | \(-0.448360\pi\) |
−0.185748 | + | 0.982597i | \(0.559471\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 147595. | − | 53720.0i | 0.356984 | − | 0.129931i | −0.157302 | − | 0.987551i | \(-0.550279\pi\) |
0.514285 | + | 0.857619i | \(0.328057\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 31113.2i | − | 0.0747868i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 63979.4 | 0.152838 | 0.0764190 | − | 0.997076i | \(-0.475651\pi\) | ||||
0.0764190 | + | 0.997076i | \(0.475651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 243692. | + | 669539.i | 0.578565 | + | 1.58959i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −48542.6 | + | 275299.i | −0.114541 | + | 0.649595i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −365655. | − | 633333.i | −0.857522 | − | 1.48527i | −0.874286 | − | 0.485411i | \(-0.838670\pi\) |
0.0167642 | − | 0.999859i | \(-0.494664\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60546.7 | + | 50804.7i | −0.141126 | + | 0.118419i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −49629.5 | + | 85960.8i | −0.114977 | + | 0.199145i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47157.2 | + | 129563.i | −0.108587 | + | 0.298340i | −0.982071 | − | 0.188513i | \(-0.939633\pi\) |
0.873484 | + | 0.486853i | \(0.161855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 474797. | − | 83719.5i | 1.08669 | − | 0.191612i | 0.398517 | − | 0.917161i | \(-0.369525\pi\) |
0.688171 | + | 0.725549i | \(0.258414\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48906.5 | + | 41037.4i | 0.111260 | + | 0.0933582i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8301.81 | + | 38322.4i | −0.0187728 | + | 0.0866581i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10978.8 | − | 13084.0i | 0.0246775 | − | 0.0294095i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4498.16 | + | 25510.3i | 0.0100504 | + | 0.0569985i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −671420. | − | 244377.i | −1.49125 | − | 0.542769i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −680011. | − | 392605.i | −1.50136 | − | 0.866813i | −0.999999 | − | 0.00157637i | \(-0.999498\pi\) |
−0.501365 | − | 0.865236i | \(-0.667168\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 314553. | + | 374869.i | 0.690377 | + | 0.822759i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 139771. | − | 80696.9i | 0.304958 | − | 0.176068i | −0.339710 | − | 0.940530i | \(-0.610329\pi\) |
0.644668 | + | 0.764463i | \(0.276996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 240008. | + | 42320.0i | 0.520579 | + | 0.0917922i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −545756. | + | 198639.i | −1.17681 | + | 0.428322i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 328136.i | 0.703417i | 0.936110 | + | 0.351708i | \(0.114399\pi\) | ||||
−0.936110 | + | 0.351708i | \(0.885601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10364.5 | −0.0220886 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 184659. | + | 507347.i | 0.391253 | + | 1.07496i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22207.0 | − | 125942.i | 0.0467790 | − | 0.265297i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 397198. | + | 687967.i | 0.831862 | + | 1.44083i | 0.896560 | + | 0.442922i | \(0.146058\pi\) |
−0.0646987 | + | 0.997905i | \(0.520609\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −131024. | + | 109942.i | −0.272826 | + | 0.228928i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12124.5 | − | 21000.2i | 0.0251011 | − | 0.0434764i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23632.1 | + | 64928.6i | −0.0486448 | + | 0.133651i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 244964. | − | 43193.8i | 0.501359 | − | 0.0884031i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −94166.3 | − | 79014.9i | −0.191628 | − | 0.160795i | 0.541926 | − | 0.840426i | \(-0.317695\pi\) |
−0.733554 | + | 0.679631i | \(0.762140\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 414027. | + | 260961.i | 0.837757 | + | 0.528037i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26411.6 | − | 31476.1i | 0.0531393 | − | 0.0633290i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −52351.8 | − | 296902.i | −0.104735 | − | 0.593984i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −809937. | − | 294793.i | −1.61124 | − | 0.586442i | −0.629551 | − | 0.776959i | \(-0.716761\pi\) |
−0.981684 | + | 0.190517i | \(0.938984\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 84417.5 | + | 48738.5i | 0.166991 | + | 0.0964124i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 44817.6 | + | 53411.5i | 0.0881595 | + | 0.105064i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39378.8 | + | 22735.4i | −0.0770284 | + | 0.0444724i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 192056. | + | 33864.7i | 0.373585 | + | 0.0658732i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −512487. | + | 186530.i | −0.991346 | + | 0.360821i | −0.786241 | − | 0.617919i | \(-0.787976\pi\) |
−0.205105 | + | 0.978740i | \(0.565754\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 691797.i | 1.33078i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 236627. | 0.452676 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40180.9 | − | 110396.i | −0.0764440 | − | 0.210028i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38500.0 | − | 218344.i | 0.0728437 | − | 0.413117i | −0.926480 | − | 0.376344i | \(-0.877181\pi\) |
0.999324 | − | 0.0367730i | \(-0.0117078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 294411. | + | 509934.i | 0.553986 | + | 0.959532i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −98203.1 | + | 82402.2i | −0.183777 | + | 0.154207i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −77402.2 | + | 134065.i | −0.144061 | + | 0.249521i | −0.929022 | − | 0.370024i | \(-0.879349\pi\) |
0.784961 | + | 0.619545i | \(0.212683\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1452.40 | − | 3990.44i | 0.00268851 | − | 0.00738663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −482117. | + | 85010.2i | −0.887600 | + | 0.156508i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 360117. | + | 302174.i | 0.659409 | + | 0.553310i | 0.909910 | − | 0.414807i | \(-0.136151\pi\) |
−0.250501 | + | 0.968116i | \(0.580595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 164731. | − | 261354.i | 0.300012 | − | 0.475984i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −514022. | + | 612588.i | −0.931117 | + | 1.10966i | 0.0626329 | + | 0.998037i | \(0.480050\pi\) |
−0.993750 | + | 0.111626i | \(0.964394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7761.96 | − | 44020.3i | −0.0139849 | − | 0.0793122i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −145109. | − | 52815.4i | −0.260048 | − | 0.0946498i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −639775. | − | 369374.i | −1.14042 | − | 0.658420i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −502229. | − | 598533.i | −0.890475 | − | 1.06123i | −0.997753 | − | 0.0669978i | \(-0.978658\pi\) |
0.107278 | − | 0.994229i | \(-0.465787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −299294. | + | 172797.i | −0.527847 | + | 0.304753i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38545.6 | − | 6796.62i | −0.0676208 | − | 0.0119234i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −187799. | + | 68353.4i | −0.327719 | + | 0.119280i | −0.500640 | − | 0.865656i | \(-0.666902\pi\) |
0.172920 | + | 0.984936i | \(0.444680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 123460.i | − | 0.214311i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 718953. | 1.24146 | 0.620728 | − | 0.784026i | \(-0.286837\pi\) | ||||
0.620728 | + | 0.784026i | \(0.286837\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 177328. | + | 487206.i | 0.304600 | + | 0.836880i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −628.833 | + | 3566.29i | −0.00107451 | + | 0.00609387i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 222430. | + | 385260.i | 0.378096 | + | 0.654882i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −307970. | + | 258418.i | −0.520782 | + | 0.436988i | −0.864904 | − | 0.501937i | \(-0.832621\pi\) |
0.344122 | + | 0.938925i | \(0.388177\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 395608. | − | 685214.i | 0.665513 | − | 1.15270i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 341555. | − | 938415.i | 0.571612 | − | 1.57049i | −0.230344 | − | 0.973109i | \(-0.573985\pi\) |
0.801956 | − | 0.597383i | \(-0.203793\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 472296. | − | 83278.5i | 0.786340 | − | 0.138653i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 375048. | + | 314702.i | 0.621218 | + | 0.521264i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 326776. | + | 70789.7i | 0.538486 | + | 0.116653i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −662447. | + | 789474.i | −1.08605 | + | 1.29430i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26007.9 | − | 147498.i | −0.0424211 | − | 0.240582i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 82371.3 | + | 29980.7i | 0.133671 | + | 0.0486522i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −113438. | − | 65493.7i | −0.183152 | − | 0.105743i | 0.405621 | − | 0.914041i | \(-0.367055\pi\) |
−0.588773 | + | 0.808299i | \(0.700389\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 600685. | + | 715869.i | 0.964924 | + | 1.14995i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 989082. | − | 571047.i | 1.58081 | − | 0.912681i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −439332. | − | 77466.1i | −0.698629 | − | 0.123187i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19726.9 | + | 7180.01i | −0.0312123 | + | 0.0113603i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 115451.i | − | 0.181753i | −0.995862 | − | 0.0908763i | \(-0.971033\pi\) | ||
0.995862 | − | 0.0908763i | \(-0.0289668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −169299. | −0.265192 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32189.0 | + | 88438.7i | 0.0501699 | + | 0.137841i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 146382. | − | 830175.i | 0.227017 | − | 1.28747i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4891.83 | + | 8472.90i | 0.00754883 | + | 0.0130750i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 818621. | − | 686905.i | 1.25700 | − | 1.05475i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −289577. | + | 501562.i | −0.442453 | + | 0.766351i | −0.997871 | − | 0.0652204i | \(-0.979225\pi\) |
0.555418 | + | 0.831571i | \(0.312558\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −210873. | + | 579369.i | −0.320612 | + | 0.880874i | 0.669777 | + | 0.742563i | \(0.266390\pi\) |
−0.990389 | + | 0.138312i | \(0.955832\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −688904. | + | 121472.i | −1.04226 | + | 0.183779i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41141.6 | + | 34521.9i | 0.0619392 | + | 0.0519732i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 459381. | + | 416880.i | 0.688223 | + | 0.624550i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −68643.4 | + | 81806.0i | −0.102337 | + | 0.121960i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −167837. | − | 951854.i | −0.249002 | − | 1.41216i | −0.811012 | − | 0.585030i | \(-0.801083\pi\) |
0.562010 | − | 0.827130i | \(-0.310028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 454734. | + | 165510.i | 0.671364 | + | 0.244357i | 0.655135 | − | 0.755512i | \(-0.272612\pi\) |
0.0162291 | + | 0.999868i | \(0.494834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −735427. | − | 424599.i | −1.08052 | − | 0.623837i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −415744. | − | 495464.i | −0.607876 | − | 0.724438i | 0.371059 | − | 0.928609i | \(-0.378995\pi\) |
−0.978935 | + | 0.204171i | \(0.934550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 596643. | − | 344472.i | 0.868171 | − | 0.501239i | 0.00143079 | − | 0.999999i | \(-0.499545\pi\) |
0.866740 | + | 0.498760i | \(0.166211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −948695. | − | 167280.i | −1.37380 | − | 0.242238i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16441.7 | + | 5984.31i | −0.0236951 | + | 0.00862430i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18329.1i | 0.0262886i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 611406. | 0.872728 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −229836. | − | 631469.i | −0.326508 | − | 0.897074i | −0.988988 | − | 0.147994i | \(-0.952718\pi\) |
0.662480 | − | 0.749080i | \(-0.269504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 116574. | − | 661126.i | 0.164820 | − | 0.934743i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 185813. | + | 321837.i | 0.261469 | + | 0.452877i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29309.0 | − | 24593.2i | 0.0410477 | − | 0.0344431i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 385566. | − | 667820.i | 0.537442 | − | 0.930877i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 78753.2 | − | 216373.i | 0.109258 | − | 0.300184i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 120257. | − | 21204.6i | 0.166055 | − | 0.0292800i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −404189. | − | 339155.i | −0.555502 | − | 0.466122i | 0.321297 | − | 0.946979i | \(-0.395881\pi\) |
−0.876799 | + | 0.480857i | \(0.840326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17510.4 | + | 679.771i | 0.0239532 | + | 0.000929887i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −111406. | + | 132768.i | −0.151686 | + | 0.180773i | −0.836537 | − | 0.547911i | \(-0.815423\pi\) |
0.684850 | + | 0.728684i | \(0.259868\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −74590.2 | − | 423022.i | −0.101087 | − | 0.573293i | −0.992711 | − | 0.120517i | \(-0.961545\pi\) |
0.891624 | − | 0.452776i | \(-0.149566\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 314309. | + | 114399.i | 0.423985 | + | 0.154318i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −843301. | − | 486880.i | −1.13230 | − | 0.653733i | −0.187786 | − | 0.982210i | \(-0.560131\pi\) |
−0.944512 | + | 0.328477i | \(0.893465\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26983.1 | − | 32157.2i | −0.0360628 | − | 0.0429780i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 523808. | − | 302421.i | 0.696841 | − | 0.402321i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −815271. | − | 143754.i | −1.07960 | − | 0.190362i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −287223. | + | 104541.i | −0.378602 | + | 0.137800i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 108915.i | − | 0.142908i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 135182. | 0.176564 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −115276. | − | 316717.i | −0.149878 | − | 0.411787i | 0.841920 | − | 0.539603i | \(-0.181426\pi\) |
−0.991798 | + | 0.127816i | \(0.959203\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −189633. | + | 1.07546e6i | −0.245434 | + | 1.39193i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −66029.0 | − | 114366.i | −0.0850713 | − | 0.147348i | 0.820350 | − | 0.571861i | \(-0.193778\pi\) |
−0.905422 | + | 0.424514i | \(0.860445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 576917. | − | 484091.i | 0.739932 | − | 0.620877i | −0.192887 | − | 0.981221i | \(-0.561785\pi\) |
0.932819 | + | 0.360344i | \(0.117341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36513.0 | − | 63242.3i | 0.0466187 | − | 0.0807460i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −201026. | + | 552313.i | −0.255508 | + | 0.702002i | 0.743923 | + | 0.668265i | \(0.232963\pi\) |
−0.999431 | + | 0.0337365i | \(0.989259\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −175079. | + | 30871.1i | −0.221528 | + | 0.0390614i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −601322. | − | 504569.i | −0.757446 | − | 0.635572i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 110856. | + | 811706.i | 0.139013 | + | 1.01788i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33191.4 | − | 39555.9i | 0.0414361 | − | 0.0493816i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13385.4 | − | 75912.2i | −0.0166359 | − | 0.0943467i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −137930. | − | 50202.3i | −0.170662 | − | 0.0621160i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 74908.5 | + | 43248.5i | 0.0922745 | + | 0.0532747i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 398895. | + | 475385.i | 0.489197 | + | 0.583002i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 64703.7 | − | 37356.7i | 0.0790009 | − | 0.0456112i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −774708. | − | 136602.i | −0.941724 | − | 0.166051i | −0.318348 | − | 0.947974i | \(-0.603128\pi\) |
−0.623375 | + | 0.781923i | \(0.714239\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −126607. | + | 46081.3i | −0.153226 | + | 0.0557695i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 651620.i | 0.785159i | 0.919718 | + | 0.392580i | \(0.128417\pi\) | ||||
−0.919718 | + | 0.392580i | \(0.871583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.31147e6 | 1.57332 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25046.5 | + | 68814.7i | 0.0299161 | + | 0.0821938i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 273750. | − | 1.55251e6i | 0.325548 | − | 1.84628i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 836911. | + | 1.44957e6i | 0.990942 | + | 1.71636i | 0.611768 | + | 0.791037i | \(0.290459\pi\) |
0.379175 | + | 0.925325i | \(0.376208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 580181. | − | 486830.i | 0.683982 | − | 0.573929i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −321727. | + | 557247.i | −0.377645 | + | 0.654100i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 287272. | − | 789274.i | 0.335746 | − | 0.922453i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 304468. | − | 53685.9i | 0.354309 | − | 0.0624742i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.13934e6 | + | 956016.i | 1.32014 | + | 1.10773i | 0.986275 | + | 0.165108i | \(0.0527973\pi\) |
0.333865 | + | 0.942621i | \(0.391647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39457.8 | + | 74911.8i | 0.0455233 | + | 0.0864272i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −724825. | + | 863813.i | −0.832664 | + | 0.992330i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5340.52 | − | 30287.6i | −0.00610886 | − | 0.0346451i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −142188. | − | 51752.2i | −0.161951 | − | 0.0589454i | 0.259772 | − | 0.965670i | \(-0.416352\pi\) |
−0.421723 | + | 0.906725i | \(0.638575\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −893318. | − | 515757.i | −1.01315 | − | 0.584944i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 875851. | + | 1.04380e6i | 0.989124 | + | 1.17879i | 0.983884 | + | 0.178806i | \(0.0572235\pi\) |
0.00523986 | + | 0.999986i | \(0.498332\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 72248.6 | − | 41712.7i | 0.0812467 | − | 0.0469078i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 84489.4 | + | 14897.8i | 0.0946103 | + | 0.0166824i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −988738. | + | 359871.i | −1.10251 | + | 0.401280i | −0.828240 | − | 0.560374i | \(-0.810657\pi\) |
−0.274267 | + | 0.961654i | \(0.588435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 526322.i | − | 0.584412i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.23703e6 | −1.36779 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 260609. | + | 716017.i | 0.286948 | + | 0.788384i | 0.996489 | + | 0.0837199i | \(0.0266801\pi\) |
−0.709541 | + | 0.704664i | \(0.751098\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22121.3 | + | 125456.i | −0.0242551 | + | 0.137558i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 129953. | + | 225086.i | 0.141894 | + | 0.245768i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 158361. | − | 132881.i | 0.172192 | − | 0.144486i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −162164. | + | 280877.i | −0.175594 | + | 0.304137i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −112917. | + | 310237.i | −0.121761 | + | 0.334535i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −125684. | + | 22161.5i | −0.134966 | + | 0.0237982i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 408657. | + | 342904.i | 0.437025 | + | 0.366708i | 0.834595 | − | 0.550864i | \(-0.185702\pi\) |
−0.397570 | + | 0.917572i | \(0.630146\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 128003. | + | 165158.i | 0.136324 | + | 0.175894i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −710180. | + | 846359.i | −0.753234 | + | 0.897669i | −0.997400 | − | 0.0720641i | \(-0.977041\pi\) |
0.244166 | + | 0.969733i | \(0.421486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 83986.7 | + | 476312.i | 0.0887125 | + | 0.503113i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −498228. | − | 181340.i | −0.524105 | − | 0.190759i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −193555. | − | 111749.i | −0.202775 | − | 0.117072i | 0.395174 | − | 0.918606i | \(-0.370684\pi\) |
−0.597949 | + | 0.801534i | \(0.704018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −513774. | − | 612292.i | −0.536052 | − | 0.638842i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 200664. | − | 115853.i | 0.208512 | − | 0.120384i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 763466. | + | 134620.i | 0.790101 | + | 0.139316i | 0.554115 | − | 0.832440i | \(-0.313057\pi\) |
0.235986 | + | 0.971756i | \(0.424168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14861.1 | − | 5408.98i | 0.0153171 | − | 0.00557498i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 819547.i | 0.841278i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 154782. | 0.158244 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 399466. | + | 1.09753e6i | 0.406755 | + | 1.11755i | 0.958886 | + | 0.283793i | \(0.0915928\pi\) |
−0.552130 | + | 0.833758i | \(0.686185\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −121509. | + | 689109.i | −0.123228 | + | 0.698859i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 75306.5 | + | 130435.i | 0.0760653 | + | 0.131749i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −542528. | + | 455235.i | −0.545798 | + | 0.457979i | −0.873515 | − | 0.486797i | \(-0.838165\pi\) |
0.327717 | + | 0.944776i | \(0.393721\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 535401. | − | 927342.i | 0.536474 | − | 0.929200i |
(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 | 76.5.j.a.41.5 | yes | 42 | |
19.13 | odd | 18 | inner | 76.5.j.a.13.5 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.13.5 | ✓ | 42 | 19.13 | odd | 18 | inner | |
76.5.j.a.41.5 | yes | 42 | 1.1 | even | 1 | trivial |