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 | 33.7 | ||
Character | \(\chi\) | \(=\) | 76.33 |
Dual form | 76.5.j.a.53.7 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 14.9907 | + | 2.64326i | 1.66563 | + | 0.293695i | 0.925494 | − | 0.378763i | \(-0.123651\pi\) |
0.740135 | + | 0.672459i | \(0.234762\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.74782 | + | 1.46659i | 0.0699127 | + | 0.0586637i | 0.677074 | − | 0.735915i | \(-0.263248\pi\) |
−0.607162 | + | 0.794578i | \(0.707692\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.6416 | + | 39.2164i | 0.462074 | + | 0.800335i | 0.999064 | − | 0.0432534i | \(-0.0137723\pi\) |
−0.536991 | + | 0.843588i | \(0.680439\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 141.618 | + | 51.5447i | 1.74837 | + | 0.636354i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 51.9608 | − | 89.9988i | 0.429428 | − | 0.743791i | −0.567394 | − | 0.823446i | \(-0.692048\pi\) |
0.996823 | + | 0.0796549i | \(0.0253818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −220.896 | + | 38.9500i | −1.30708 | + | 0.230473i | −0.783440 | − | 0.621467i | \(-0.786537\pi\) |
−0.523639 | + | 0.851940i | \(0.675426\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 22.3243 | + | 26.6051i | 0.0992193 | + | 0.118245i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −69.3454 | + | 25.2397i | −0.239950 | + | 0.0873345i | −0.459196 | − | 0.888335i | \(-0.651862\pi\) |
0.219246 | + | 0.975670i | \(0.429640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 340.990 | + | 118.520i | 0.944570 | + | 0.328309i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 235.753 | + | 647.727i | 0.534588 | + | 1.46877i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 547.158 | − | 459.120i | 1.03432 | − | 0.867901i | 0.0429653 | − | 0.999077i | \(-0.486320\pi\) |
0.991359 | + | 0.131175i | \(0.0418751\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −107.626 | − | 610.378i | −0.172202 | − | 0.976605i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 918.911 | + | 530.533i | 1.26051 | + | 0.727755i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −295.925 | + | 813.048i | −0.351873 | + | 0.966763i | 0.629895 | + | 0.776680i | \(0.283098\pi\) |
−0.981768 | + | 0.190083i | \(0.939124\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −723.951 | + | 417.974i | −0.753331 | + | 0.434936i | −0.826896 | − | 0.562354i | \(-0.809896\pi\) |
0.0735650 | + | 0.997290i | \(0.476562\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1016.82 | − | 1211.79i | 0.933716 | − | 1.11276i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17.9411 | + | 101.749i | −0.0146458 | + | 0.0830605i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 603.379i | − | 0.440744i | −0.975416 | − | 0.220372i | \(-0.929273\pi\) | ||
0.975416 | − | 0.220372i | \(-0.0707272\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3414.34 | −2.24480 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1040.36 | − | 183.444i | −0.618894 | − | 0.109128i | −0.144594 | − | 0.989491i | \(-0.546188\pi\) |
−0.474300 | + | 0.880363i | \(0.657299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2617.31 | − | 2196.19i | −1.41553 | − | 1.18777i | −0.953685 | − | 0.300808i | \(-0.902744\pi\) |
−0.461844 | − | 0.886961i | \(-0.652812\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 171.927 | + | 297.786i | 0.0849022 | + | 0.147055i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1022.17 | − | 372.038i | −0.462728 | − | 0.168419i | 0.100128 | − | 0.994975i | \(-0.468075\pi\) |
−0.562855 | + | 0.826555i | \(0.690297\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 175.216 | − | 303.482i | 0.0729761 | − | 0.126398i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1106.25 | + | 195.061i | −0.425317 | + | 0.0749948i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1040.77 | − | 1240.34i | −0.370512 | − | 0.441559i | 0.548284 | − | 0.836292i | \(-0.315281\pi\) |
−0.918796 | + | 0.394734i | \(0.870837\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 222.810 | − | 81.0960i | 0.0736560 | − | 0.0268086i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4798.38 | + | 2678.01i | 1.47688 | + | 0.824257i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −653.388 | − | 1795.17i | −0.187701 | − | 0.515705i | 0.809772 | − | 0.586744i | \(-0.199591\pi\) |
−0.997474 | + | 0.0710395i | \(0.977368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2687.88 | − | 2255.40i | 0.722355 | − | 0.606128i | −0.205680 | − | 0.978619i | \(-0.565941\pi\) |
0.928036 | + | 0.372491i | \(0.121496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1185.06 | + | 6720.80i | 0.298578 | + | 1.69332i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −443.210 | − | 255.888i | −0.104902 | − | 0.0605651i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1445.83 | + | 3972.38i | −0.322082 | + | 0.884914i | 0.667967 | + | 0.744191i | \(0.267165\pi\) |
−0.990049 | + | 0.140723i | \(0.955057\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9415.82 | − | 5436.23i | 1.97770 | − | 1.14182i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3642.09 | + | 4340.47i | −0.722493 | + | 0.861033i | −0.994870 | − | 0.101157i | \(-0.967746\pi\) |
0.272378 | + | 0.962190i | \(0.412190\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −337.943 | + | 1916.57i | −0.0634159 | + | 0.359649i | 0.936543 | + | 0.350553i | \(0.114007\pi\) |
−0.999959 | + | 0.00909602i | \(0.997105\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 9434.45i | − | 1.67724i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4705.90 | 0.793710 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6050.83 | − | 1066.92i | −0.969529 | − | 0.170954i | −0.333611 | − | 0.942711i | \(-0.608267\pi\) |
−0.635918 | + | 0.771757i | \(0.719378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3021.46 | + | 2535.30i | 0.460518 | + | 0.386420i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3629.32 | + | 6286.16i | 0.526828 | + | 0.912493i | 0.999511 | + | 0.0312603i | \(0.00995207\pi\) |
−0.472683 | + | 0.881232i | \(0.656715\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −158.219 | − | 57.5872i | −0.0218989 | − | 0.00797054i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6585.21 | + | 11405.9i | −0.870023 | + | 1.50692i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10477.3 | − | 1847.43i | 1.32272 | − | 0.233232i | 0.532697 | − | 0.846306i | \(-0.321178\pi\) |
0.790025 | + | 0.613074i | \(0.210067\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6528.93 | − | 7780.87i | −0.788423 | − | 0.939605i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11957.3 | + | 4352.11i | −1.38251 | + | 0.503192i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 422.168 | + | 707.244i | 0.0467776 | + | 0.0783650i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4970.62 | − | 13656.7i | −0.528284 | − | 1.45145i | −0.861090 | − | 0.508452i | \(-0.830218\pi\) |
0.332807 | − | 0.942995i | \(-0.392004\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11997.5 | − | 10067.1i | 1.22411 | − | 1.02715i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3332.38 | + | 18898.8i | 0.326672 | + | 1.85265i | 0.497659 | + | 0.867373i | \(0.334193\pi\) |
−0.170987 | + | 0.985273i | \(0.554696\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16336.7 | + | 9432.00i | 1.53989 | + | 0.889056i | 0.998844 | + | 0.0480638i | \(0.0153051\pi\) |
0.541047 | + | 0.840993i | \(0.318028\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −537.898 | + | 1477.86i | −0.0487890 | + | 0.134047i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19063.0 | − | 11006.0i | 1.66503 | − | 0.961307i | 0.694777 | − | 0.719225i | \(-0.255503\pi\) |
0.970256 | − | 0.242082i | \(-0.0778301\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2125.72 | − | 2533.33i | 0.178918 | − | 0.213226i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1594.89 | − | 9045.04i | 0.129444 | − | 0.734116i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 22240.3i | 1.74174i | 0.491512 | + | 0.870871i | \(0.336444\pi\) | ||||
−0.491512 | + | 0.870871i | \(0.663556\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1629.67 | 0.123227 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −33290.5 | − | 5870.02i | −2.43192 | − | 0.428813i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2559.90 | − | 2148.01i | −0.180771 | − | 0.151685i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1920.65 | + | 3326.66i | 0.131183 | + | 0.227216i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15110.8 | − | 5499.88i | −0.998796 | − | 0.363532i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1420.07 | − | 2459.63i | 0.0908845 | − | 0.157416i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18978.7 | + | 3346.45i | −1.17668 | + | 0.207480i | −0.727594 | − | 0.686008i | \(-0.759361\pi\) |
−0.449086 | + | 0.893489i | \(0.648250\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −33430.1 | − | 39840.5i | −2.00890 | − | 2.39412i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8075.04 | + | 2939.07i | −0.470546 | + | 0.171265i | −0.566400 | − | 0.824131i | \(-0.691664\pi\) |
0.0958537 | + | 0.995395i | \(0.469442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3072.64 | + | 16055.9i | 0.173703 | + | 0.907676i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 828.012 | + | 2274.94i | 0.0454327 | + | 0.124825i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 27262.3 | − | 22875.8i | 1.45252 | − | 1.21881i | 0.521800 | − | 0.853068i | \(-0.325261\pi\) |
0.930718 | − | 0.365739i | \(-0.119184\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1315.13 | − | 7458.49i | −0.0680675 | − | 0.386030i | −0.999742 | − | 0.0227348i | \(-0.992763\pi\) |
0.931674 | − | 0.363295i | \(-0.118348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14339.5 | − | 8278.94i | −0.721269 | − | 0.416425i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7972.50 | + | 21904.3i | −0.389872 | + | 1.07117i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1709.63 | + | 987.057i | −0.0813143 | + | 0.0469468i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3428.78 | − | 4086.26i | 0.158674 | − | 0.189100i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3595.41 | + | 20390.6i | −0.161948 | + | 0.918452i | 0.790208 | + | 0.612839i | \(0.209973\pi\) |
−0.952156 | + | 0.305613i | \(0.901139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15854.9i | − | 0.695359i | −0.937613 | − | 0.347679i | \(-0.886970\pi\) | ||
0.937613 | − | 0.347679i | \(-0.113030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11121.5 | −0.475096 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1878.33 | − | 331.201i | −0.0781824 | − | 0.0137857i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 153.155 | + | 128.512i | 0.00621343 | + | 0.00521369i | 0.645889 | − | 0.763431i | \(-0.276487\pi\) |
−0.639676 | + | 0.768645i | \(0.720931\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12323.3 | − | 21344.5i | −0.487451 | − | 0.844290i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30393.6 | + | 11062.3i | 1.17255 | + | 0.426772i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4690.34 | + | 8123.92i | −0.176534 | + | 0.305767i | −0.940691 | − | 0.339264i | \(-0.889822\pi\) |
0.764157 | + | 0.645031i | \(0.223155\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3554.42 | − | 626.740i | 0.130557 | − | 0.0230207i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 32828.4 | + | 39123.3i | 1.17711 | + | 1.40282i | 0.896525 | + | 0.442994i | \(0.146084\pi\) |
0.280584 | + | 0.959830i | \(0.409472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20439.5 | − | 7439.38i | 0.715645 | − | 0.260474i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 42181.2 | + | 34360.7i | 1.44254 | + | 1.17509i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12496.4 | + | 34333.7i | 0.417536 | + | 1.14717i | 0.953095 | + | 0.302673i | \(0.0978789\pi\) |
−0.535558 | + | 0.844498i | \(0.679899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21500.0 | − | 18040.7i | 0.702041 | − | 0.589083i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5049.62 | − | 28637.8i | −0.161180 | − | 0.914099i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18153.5 | + | 10480.9i | 0.566570 | + | 0.327110i | 0.755778 | − | 0.654827i | \(-0.227259\pi\) |
−0.189208 | + | 0.981937i | \(0.560592\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1559.86 | − | 4285.68i | 0.0476133 | − | 0.130816i | −0.913607 | − | 0.406599i | \(-0.866715\pi\) |
0.961220 | + | 0.275782i | \(0.0889369\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 46254.8 | − | 26705.2i | 1.38119 | − | 0.797432i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 884.911 | − | 1054.60i | 0.0258557 | − | 0.0308136i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1331.71 | + | 7552.48i | −0.0380825 | + | 0.215976i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 48048.5i | 1.34511i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −30053.3 | −0.823806 | −0.411903 | − | 0.911228i | \(-0.635136\pi\) | ||||
−0.411903 | + | 0.911228i | \(0.635136\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2660.50 | + | 469.117i | 0.0714246 | + | 0.0125941i | 0.209246 | − | 0.977863i | \(-0.432899\pi\) |
−0.137822 | + | 0.990457i | \(0.544010\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5967.64 | − | 5007.44i | −0.156940 | − | 0.131688i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21955.7 | − | 38028.4i | −0.565738 | − | 0.979886i | −0.996981 | − | 0.0776504i | \(-0.975258\pi\) |
0.431243 | − | 0.902236i | \(-0.358075\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −66862.0 | − | 24335.8i | −1.68839 | − | 0.614524i | −0.693969 | − | 0.720005i | \(-0.744140\pi\) |
−0.994421 | + | 0.105481i | \(0.966362\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −32173.9 | + | 55726.9i | −0.796365 | + | 1.37934i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −38585.0 | + | 6803.58i | −0.936325 | + | 0.165099i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1549.32 | − | 1846.41i | −0.0368667 | − | 0.0439360i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 101152. | − | 36816.5i | 2.36067 | − | 0.859214i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28384.7 | − | 24530.3i | 0.649819 | − | 0.561578i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5157.13 | + | 14169.1i | 0.115836 | + | 0.318256i | 0.984039 | − | 0.177952i | \(-0.0569473\pi\) |
−0.868203 | + | 0.496209i | \(0.834725\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −66070.2 | + | 55439.5i | −1.45629 | + | 1.22197i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1353.67 | − | 7677.06i | −0.0292844 | − | 0.166080i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32782.8 | − | 18927.2i | −0.696189 | − | 0.401945i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10132.0 | + | 27837.4i | −0.211255 | + | 0.580417i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14335.1 | − | 8276.36i | 0.293505 | − | 0.169455i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7463.74 | − | 8894.94i | 0.150088 | − | 0.178868i | −0.685762 | − | 0.727826i | \(-0.740531\pi\) |
0.835850 | + | 0.548958i | \(0.184975\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16220.0 | − | 91988.0i | 0.320394 | − | 1.81705i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 47690.9i | 0.925515i | 0.886485 | + | 0.462757i | \(0.153140\pi\) | ||||
−0.886485 | + | 0.462757i | \(0.846860\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19081.8 | 0.363872 | 0.181936 | − | 0.983310i | \(-0.441764\pi\) | ||||
0.181936 | + | 0.983310i | \(0.441764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 70544.6 | + | 12438.9i | 1.32203 | + | 0.233109i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 43461.8 | + | 36468.8i | 0.800564 | + | 0.671753i | 0.948336 | − | 0.317269i | \(-0.102766\pi\) |
−0.147772 | + | 0.989021i | \(0.547210\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1240.93 | − | 2149.35i | −0.0224705 | − | 0.0389200i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −87885.7 | − | 31987.8i | −1.56467 | − | 0.569492i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 39853.0 | − | 69027.3i | 0.697694 | − | 1.20844i | −0.271571 | − | 0.962419i | \(-0.587543\pi\) |
0.969264 | − | 0.246022i | \(-0.0791236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29149.5 | + | 5139.84i | −0.501876 | + | 0.0884943i | −0.418854 | − | 0.908053i | \(-0.637568\pi\) |
−0.0830218 | + | 0.996548i | \(0.526457\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16653.1 | − | 19846.4i | −0.282022 | − | 0.336101i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 751.329 | − | 273.462i | 0.0125169 | − | 0.00455579i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −79939.8 | − | 12899.0i | −1.31029 | − | 0.211428i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 37789.9 | + | 103827.i | 0.609505 | + | 1.67460i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −84937.6 | + | 71271.1i | −1.34819 | + | 1.13127i | −0.368756 | + | 0.929526i | \(0.620216\pi\) |
−0.979438 | + | 0.201743i | \(0.935339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12889.5 | − | 73099.7i | −0.201369 | − | 1.14202i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2219.60 | − | 1281.48i | −0.0341345 | − | 0.0197076i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19104.6 | − | 52489.5i | 0.289249 | − | 0.794705i | −0.706923 | − | 0.707290i | \(-0.749917\pi\) |
0.996172 | − | 0.0874145i | \(-0.0278604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23662.4 | − | 13661.5i | 0.352743 | − | 0.203656i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −83816.6 | + | 99888.7i | −1.23041 | + | 1.46634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17609.9 | − | 99870.8i | 0.254593 | − | 1.44387i | −0.542524 | − | 0.840040i | \(-0.682531\pi\) |
0.797116 | − | 0.603826i | \(-0.206358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3694.27i | − | 0.0526062i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 161945. | 2.27166 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −41529.3 | − | 7322.74i | −0.573919 | − | 0.101197i | −0.120847 | − | 0.992671i | \(-0.538561\pi\) |
−0.453072 | + | 0.891474i | \(0.649672\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31060.4 | + | 26062.8i | 0.422930 | + | 0.354880i | 0.829276 | − | 0.558839i | \(-0.188753\pi\) |
−0.406346 | + | 0.913719i | \(0.633197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −77306.0 | − | 133898.i | −1.03726 | − | 1.79659i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −60525.6 | − | 22029.5i | −0.800339 | − | 0.291299i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −48837.0 | + | 84588.2i | −0.636487 | + | 1.10243i | 0.349711 | + | 0.936858i | \(0.386280\pi\) |
−0.986198 | + | 0.165570i | \(0.947054\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −124069. | + | 21876.7i | −1.59387 | + | 0.281043i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2277.32 | + | 2714.00i | 0.0288411 | + | 0.0343714i | 0.780272 | − | 0.625440i | \(-0.215081\pi\) |
−0.751431 | + | 0.659812i | \(0.770636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12326.9 | + | 4486.61i | −0.153915 | + | 0.0560203i | −0.417829 | − | 0.908526i | \(-0.637209\pi\) |
0.263914 | + | 0.964546i | \(0.414987\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4459.14 | + | 11717.9i | 0.0548987 | + | 0.144265i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16361.4 | − | 44952.6i | −0.198636 | − | 0.545747i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −59809.0 | + | 50185.8i | −0.716096 | + | 0.600876i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −38414.8 | − | 217861.i | −0.453641 | − | 2.57273i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 71409.0 | + | 41228.0i | 0.831797 | + | 0.480238i | 0.854468 | − | 0.519505i | \(-0.173883\pi\) |
−0.0226704 | + | 0.999743i | \(0.507217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1490.78 | − | 4095.88i | 0.0171305 | − | 0.0470655i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 95494.7 | − | 55133.9i | 1.08260 | − | 0.625037i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −102982. | + | 122730.i | −1.15192 | + | 1.37280i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26866.4 | − | 152367.i | 0.296535 | − | 1.68173i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 292114.i | 3.18176i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8005.69 | 0.0860595 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 67311.4 | + | 11868.8i | 0.714187 | + | 0.125930i | 0.518924 | − | 0.854821i | \(-0.326333\pi\) |
0.195263 | + | 0.980751i | \(0.437444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 219967. | + | 184574.i | 2.30377 | + | 1.93310i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −39321.7 | − | 68107.2i | −0.406548 | − | 0.704162i | 0.587952 | − | 0.808896i | \(-0.299934\pi\) |
−0.994500 | + | 0.104734i | \(0.966601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 54369.8 | + | 19789.0i | 0.554970 | + | 0.201992i | 0.604253 | − | 0.796792i | \(-0.293472\pi\) |
−0.0492835 | + | 0.998785i | \(0.515694\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7785.41 | + | 13484.7i | −0.0784622 | + | 0.135900i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20211.3 | − | 3563.80i | 0.201130 | − | 0.0354646i | −0.0721755 | − | 0.997392i | \(-0.522994\pi\) |
0.273305 | + | 0.961927i | \(0.411883\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 57796.8 | + | 68879.5i | 0.567966 | + | 0.676875i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 314858. | − | 114599.i | 3.05566 | − | 1.11217i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26637.5 | + | 387.671i | −0.255322 | + | 0.00371585i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 47548.4 | + | 130638.i | 0.450163 | + | 1.23681i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 38562.2 | − | 32357.5i | 0.360634 | − | 0.302608i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8553.48 | − | 48509.2i | −0.0790226 | − | 0.448159i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −74022.2 | − | 42736.8i | −0.675626 | − | 0.390073i | 0.122579 | − | 0.992459i | \(-0.460883\pi\) |
−0.798205 | + | 0.602386i | \(0.794217\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31101.0 | − | 85449.2i | 0.280469 | − | 0.770583i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8352.91 | + | 4822.55i | −0.0744300 | + | 0.0429722i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 106192. | − | 126555.i | 0.935043 | − | 1.11434i | −0.0582025 | − | 0.998305i | \(-0.518537\pi\) |
0.993245 | − | 0.116036i | \(-0.0370187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −58786.8 | + | 333397.i | −0.511541 | + | 2.90109i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 86873.0i | 0.747095i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 124594. | 1.05903 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24429.9 | + | 4307.65i | 0.205250 | + | 0.0361911i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −78074.5 | − | 65512.3i | −0.648411 | − | 0.544081i | 0.258178 | − | 0.966097i | \(-0.416878\pi\) |
−0.906588 | + | 0.422016i | \(0.861322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15832.1 | + | 27422.1i | 0.129984 | + | 0.225138i | 0.923670 | − | 0.383189i | \(-0.125174\pi\) |
−0.793686 | + | 0.608327i | \(0.791841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −223648. | − | 81401.3i | −1.81531 | − | 0.660720i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24201.5 | − | 41918.2i | 0.194219 | − | 0.336397i | −0.752425 | − | 0.658678i | \(-0.771116\pi\) |
0.946644 | + | 0.322280i | \(0.104449\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12731.4 | + | 2244.89i | −0.101023 | + | 0.0178131i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −32696.8 | − | 38966.6i | −0.256548 | − | 0.305743i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5651.88 | + | 2057.12i | −0.0438535 | + | 0.0159614i | −0.363854 | − | 0.931456i | \(-0.618539\pi\) |
0.320000 | + | 0.947417i | \(0.396317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 102227. | + | 80828.0i | 0.784426 | + | 0.620223i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19998.6 | + | 54945.6i | 0.151770 | + | 0.416984i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3401.49 | + | 2854.19i | −0.0255320 | + | 0.0214239i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1654.48 | + | 9383.00i | 0.0122837 | + | 0.0696642i | 0.990333 | − | 0.138707i | \(-0.0442948\pi\) |
−0.978050 | + | 0.208372i | \(0.933184\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −137878. | − | 79603.9i | −1.01261 | − | 0.584631i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25077.0 | − | 68898.4i | 0.182191 | − | 0.500566i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −102897. | + | 59407.9i | −0.739583 | + | 0.426998i | −0.821918 | − | 0.569606i | \(-0.807096\pi\) |
0.0823346 | + | 0.996605i | \(0.473762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27789.2 | − | 33117.9i | 0.197612 | − | 0.235505i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 33700.6 | − | 191126.i | 0.237113 | − | 1.34473i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 198715.i | 1.38341i | 0.722178 | + | 0.691707i | \(0.243141\pi\) | ||||
−0.722178 | + | 0.691707i | \(0.756859\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −293348. | −2.02085 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −105698. | − | 18637.4i | −0.720557 | − | 0.127054i | −0.198668 | − | 0.980067i | \(-0.563662\pi\) |
−0.521889 | + | 0.853013i | \(0.674773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8225.06 | + | 6901.64i | 0.0554904 | + | 0.0465619i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −257456. | − | 445927.i | −1.71902 | − | 2.97744i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −62934.1 | − | 22906.1i | −0.415898 | − | 0.151375i | 0.125591 | − | 0.992082i | \(-0.459917\pi\) |
−0.541489 | + | 0.840708i | \(0.682139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26354.9 | + | 45647.9i | −0.172388 | + | 0.298585i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −128819. | + | 22714.2i | −0.834054 | + | 0.147066i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9011.00 | − | 10738.9i | −0.0577536 | − | 0.0688280i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 75943.7 | − | 27641.3i | 0.481849 | − | 0.175379i | −0.0896634 | − | 0.995972i | \(-0.528579\pi\) |
0.571512 | + | 0.820593i | \(0.306357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3621.07 | + | 248810.i | 0.0227453 | + | 1.56287i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 59805.6 | + | 164315.i | 0.371923 | + | 1.02185i | 0.974617 | + | 0.223878i | \(0.0718719\pi\) |
−0.602694 | + | 0.797973i | \(0.705906\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 143638. | − | 120527.i | 0.884423 | − | 0.742119i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1562.70 | + | 8862.49i | 0.00952719 | + | 0.0540314i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −54303.3 | − | 31352.1i | −0.327822 | − | 0.189268i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −73359.1 | + | 201552.i | −0.438538 | + | 1.20487i | 0.501905 | + | 0.864923i | \(0.332633\pi\) |
−0.940443 | + | 0.339951i | \(0.889590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 469146. | − | 270862.i | 2.77731 | − | 1.60348i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 55606.3 | − | 66269.0i | 0.326005 | − | 0.388517i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2875.86 | + | 16309.8i | −0.0166983 | + | 0.0947005i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 115284.i | − | 0.662974i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 55056.9 | 0.313606 | 0.156803 | − | 0.987630i | \(-0.449881\pi\) | ||||
0.156803 | + | 0.987630i | \(0.449881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −118222. | − | 20845.8i | −0.667015 | − | 0.117613i | −0.170120 | − | 0.985423i | \(-0.554416\pi\) |
−0.496895 | + | 0.867811i | \(0.665527\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −125580. | − | 105374.i | −0.701844 | − | 0.588917i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22869.1 | + | 39610.5i | 0.126611 | + | 0.219297i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 149307. | + | 54343.2i | 0.818887 | + | 0.298050i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −177412. | + | 307286.i | −0.963979 | + | 1.66966i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −50451.8 | + | 8896.02i | −0.271595 | + | 0.0478896i | −0.307787 | − | 0.951455i | \(-0.599588\pi\) |
0.0361916 | + | 0.999345i | \(0.488477\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −98086.0 | − | 116894.i | −0.523156 | − | 0.623473i | 0.438168 | − | 0.898893i | \(-0.355628\pi\) |
−0.961324 | + | 0.275420i | \(0.911183\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −28237.6 | + | 10277.6i | −0.149227 | + | 0.0543144i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 240990. | − | 91706.2i | 1.26193 | − | 0.480215i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1574.10 | + | 4324.80i | 0.00816776 | + | 0.0224407i | 0.943710 | − | 0.330775i | \(-0.107310\pi\) |
−0.935542 | + | 0.353216i | \(0.885088\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 40456.5 | − | 33947.1i | 0.208023 | − | 0.174552i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19737.6 | − | 111938.i | −0.100574 | − | 0.570386i | −0.992896 | − | 0.118986i | \(-0.962036\pi\) |
0.892321 | − | 0.451401i | \(-0.149075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21021.8 | + | 12136.9i | 0.106157 | + | 0.0612900i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −107795. | + | 296164.i | −0.539490 | + | 1.48224i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −143782. | + | 83012.8i | −0.713203 | + | 0.411768i | −0.812246 | − | 0.583315i | \(-0.801755\pi\) |
0.0990431 | + | 0.995083i | \(0.468422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −70567.6 | + | 84099.2i | −0.346939 | + | 0.413465i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 41908.5 | − | 237675.i | 0.204224 | − | 1.15821i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 23174.8i | − | 0.111942i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24060.3 | 0.115205 | 0.0576023 | − | 0.998340i | \(-0.481654\pi\) | ||||
0.0576023 | + | 0.998340i | \(0.481654\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −77112.8 | − | 13597.1i | −0.366017 | − | 0.0645386i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −57941.6 | − | 48618.7i | −0.272639 | − | 0.228771i | 0.496209 | − | 0.868203i | \(-0.334725\pi\) |
−0.768848 | + | 0.639432i | \(0.779170\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 90196.5 | + | 156225.i | 0.420754 | + | 0.728767i | 0.996013 | − | 0.0892042i | \(-0.0284324\pi\) |
−0.575260 | + | 0.817971i | \(0.695099\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27282.0 | − | 9929.83i | −0.126174 | − | 0.0459236i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 42977.3 | − | 74438.9i | 0.197063 | − | 0.341324i | −0.750512 | − | 0.660857i | \(-0.770193\pi\) |
0.947575 | + | 0.319534i | \(0.103526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −188518. | + | 33240.9i | −0.857053 | + | 0.151122i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1956.20 | + | 2331.31i | 0.00881803 | + | 0.0105089i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −333652. | + | 121439.i | −1.49132 | + | 0.542796i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35642.4 | − | 220889.i | 0.157972 | − | 0.979008i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −83458.4 | − | 229300.i | −0.366803 | − | 1.00778i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 252890. | − | 212200.i | 1.10220 | − | 0.924857i | 0.104631 | − | 0.994511i | \(-0.466634\pi\) |
0.997571 | + | 0.0696541i | \(0.0221895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23501.6 | + | 133284.i | 0.101580 | + | 0.576088i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 426379. | + | 246170.i | 1.82768 | + | 1.05521i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11341.0 | − | 31159.2i | 0.0482136 | − | 0.132466i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 383052. | − | 221155.i | 1.61510 | − | 0.932480i | 0.626941 | − | 0.779067i | \(-0.284307\pi\) |
0.988162 | − | 0.153413i | \(-0.0490265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −91784.9 | + | 109385.i | −0.383843 | + | 0.457446i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25947.9 | + | 147158.i | −0.107631 | + | 0.610408i | 0.882505 | + | 0.470302i | \(0.155855\pi\) |
−0.990137 | + | 0.140105i | \(0.955256\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 63850.2i | − | 0.262705i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 35733.9 | 0.145838 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −252680. | − | 44554.4i | −1.02296 | − | 0.180375i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 81269.1 | + | 68192.9i | 0.326381 | + | 0.273866i | 0.791223 | − | 0.611528i | \(-0.209445\pi\) |
−0.464843 | + | 0.885393i | \(0.653889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 388706. | + | 673258.i | 1.54862 | + | 2.68229i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −377464. | − | 137385.i | −1.49190 | − | 0.543006i | −0.537949 | − | 0.842977i | \(-0.680801\pi\) |
−0.953948 | + | 0.299971i | \(0.903023\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21892.5 | + | 37919.0i | −0.0858446 | + | 0.148687i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 326066. | − | 57494.3i | 1.26850 | − | 0.223671i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −303927. | − | 362206.i | −1.17310 | − | 1.39804i | −0.899908 | − | 0.436080i | \(-0.856366\pi\) |
−0.273188 | − | 0.961961i | \(-0.588078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −82812.7 | + | 30141.3i | −0.317143 | + | 0.115431i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 250461. | + | 289816.i | 0.951710 | + | 1.10125i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14720.7 | + | 40444.7i | 0.0555026 | + | 0.152492i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −86595.5 | + | 72662.2i | −0.323977 | + | 0.271849i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 96577.0 | + | 547716.i | 0.358541 | + | 2.03339i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 190978. | + | 110261.i | 0.703569 | + | 0.406206i | 0.808675 | − | 0.588255i | \(-0.200185\pi\) |
−0.105106 | + | 0.994461i | \(0.533518\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −52251.1 | + | 143559.i | −0.191026 | + | 0.524839i | −0.997820 | − | 0.0659933i | \(-0.978978\pi\) |
0.806794 | + | 0.590833i | \(0.201201\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 369985. | − | 213611.i | 1.34235 | − | 0.775006i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39653.2 | − | 47256.9i | 0.142777 | − | 0.170155i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39996.6 | − | 226832.i | 0.142926 | − | 0.810575i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 287906.i | − | 1.02109i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 236957. | 0.834094 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49459.9 | + | 8721.11i | 0.172801 | + | 0.0304694i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 244429. | + | 205100.i | 0.847625 | + | 0.711242i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18208.7 | − | 31538.4i | −0.0626759 | − | 0.108558i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 46433.1 | + | 16900.3i | 0.158647 | + | 0.0577430i | 0.420123 | − | 0.907467i | \(-0.361987\pi\) |
−0.261476 | + | 0.965210i | \(0.584209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34711.4 | − | 60122.0i | 0.117726 | − | 0.203908i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7430.74 | − | 1310.24i | 0.0250172 | − | 0.00441121i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −250370. | − | 298379.i | −0.836773 | − | 0.997227i | −0.999944 | − | 0.0106295i | \(-0.996616\pi\) |
0.163170 | − | 0.986598i | \(-0.447828\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 496906. | − | 180859.i | 1.64866 | − | 0.600061i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −197270. | + | 242168.i | −0.649766 | + | 0.797652i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −95159.5 | − | 261449.i | −0.311173 | − | 0.854941i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16053.0 | − | 13470.0i | 0.0521158 | − | 0.0437303i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39569.2 | + | 224408.i | 0.127540 | + | 0.723316i | 0.979767 | + | 0.200143i | \(0.0641406\pi\) |
−0.852227 | + | 0.523173i | \(0.824748\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 663696. | + | 383185.i | 2.12396 | + | 1.22627i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39926.3 | + | 109697.i | −0.126862 | + | 0.348552i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 55165.1 | − | 31849.6i | 0.174040 | − | 0.100482i | −0.410450 | − | 0.911883i | \(-0.634628\pi\) |
0.584489 | + | 0.811401i | \(0.301295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32617.5 | + | 38872.0i | −0.102177 | + | 0.121770i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −31014.9 | + | 175894.i | −0.0964726 | + | 0.547123i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 158917.i | − | 0.490848i | −0.969416 | − | 0.245424i | \(-0.921073\pi\) | ||
0.969416 | − | 0.245424i | \(-0.0789271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −529437. | −1.62384 | −0.811918 | − | 0.583772i | \(-0.801576\pi\) | ||||
−0.811918 | + | 0.583772i | \(0.801576\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −450518. | − | 79438.5i | −1.37216 | − | 0.241948i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −339125. | − | 284560.i | −1.02571 | − | 0.860672i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −178205. | − | 308660.i | −0.535264 | − | 0.927104i | −0.999151 | − | 0.0412098i | \(-0.986879\pi\) |
0.463887 | − | 0.885895i | \(-0.346455\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 38642.6 | + | 14064.7i | 0.115268 | + | 0.0419541i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −164347. | + | 284658.i | −0.486866 | + | 0.843277i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −165708. | + | 29218.8i | −0.487536 | + | 0.0859657i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −49576.8 | − | 59083.4i | −0.144866 | − | 0.172645i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −486773. | + | 177171.i | −1.41270 | + | 0.514181i | −0.931922 | − | 0.362660i | \(-0.881869\pi\) |
−0.480780 | + | 0.876841i | \(0.659646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −296398. | + | 56722.2i | −0.854368 | + | 0.163502i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −228612. | − | 628105.i | −0.654521 | − | 1.79828i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 246993. | − | 207252.i | 0.702385 | − | 0.589371i | −0.220066 | − | 0.975485i | \(-0.570627\pi\) |
0.922451 | + | 0.386114i | \(0.126183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1323.98 | − | 7508.67i | −0.00373979 | − | 0.0212094i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −937979. | − | 541542.i | −2.63175 | − | 1.51944i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 73922.5 | − | 203100.i | 0.206026 | − | 0.566053i | −0.793044 | − | 0.609165i | \(-0.791505\pi\) |
0.999070 | + | 0.0431116i | \(0.0137271\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −289330. | + | 167045.i | −0.801022 | + | 0.462470i | −0.843828 | − | 0.536613i | \(-0.819703\pi\) |
0.0428067 | + | 0.999083i | \(0.486370\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −409510. | + | 488035.i | −1.12624 | + | 1.34220i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1521.92 | + | 8631.21i | −0.00415795 | + | 0.0235809i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 313650.i | − | 0.851271i | −0.904895 | − | 0.425636i | \(-0.860051\pi\) | ||
0.904895 | − | 0.425636i | \(-0.139949\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −596399. | −1.60806 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 240284. | + | 42368.5i | 0.643638 | + | 0.113491i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 59956.8 | + | 50309.7i | 0.159557 | + | 0.133885i | 0.719071 | − | 0.694937i | \(-0.244568\pi\) |
−0.559514 | + | 0.828821i | \(0.689012\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18344.8 | − | 31774.2i | −0.0485024 | − | 0.0840086i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 360615. | + | 131253.i | 0.947269 | + | 0.344778i | 0.769032 | − | 0.639210i | \(-0.220738\pi\) |
0.178237 | + | 0.983988i | \(0.442961\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 267081. | − | 462598.i | 0.697046 | − | 1.20732i | −0.272440 | − | 0.962173i | \(-0.587831\pi\) |
0.969486 | − | 0.245146i | \(-0.0788360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 746367. | − | 131605.i | 1.93539 | − | 0.341262i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 309672. | + | 369053.i | 0.797859 | + | 0.950851i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −357921. | + | 130272.i | −0.916277 | + | 0.333498i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 490346. | − | 292697.i | 1.24729 | − | 0.744531i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15229.1 | + | 41841.6i | 0.0384922 | + | 0.105756i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 307667. | − | 258163.i | 0.772720 | − | 0.648389i | −0.168684 | − | 0.985670i | \(-0.553952\pi\) |
0.941404 | + | 0.337281i | \(0.109507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39856.2 | + | 226036.i | 0.0994691 | + | 0.564117i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38079.1 | − | 21985.0i | −0.0944364 | − | 0.0545229i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26883.8 | + | 73862.7i | −0.0662541 | + | 0.182032i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −739512. | + | 426958.i | −1.81111 | + | 1.04564i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 322528. | − | 384374.i | 0.784967 | − | 0.935487i | −0.214179 | − | 0.976794i | \(-0.568708\pi\) |
0.999146 | + | 0.0413071i | \(0.0131522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −94880.3 | + | 538093.i | −0.229485 | + | 1.30147i | 0.624438 | + | 0.781074i | \(0.285328\pi\) |
−0.853923 | + | 0.520399i | \(0.825783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 118662.i | − | 0.285229i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 761998. | 1.82031 | 0.910155 | − | 0.414268i | \(-0.135962\pi\) | ||||
0.910155 | + | 0.414268i | \(0.135962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −195513. | − | 34474.3i | −0.464181 | − | 0.0818476i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −441407. | − | 370384.i | −1.04154 | − | 0.873958i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 168084. | + | 291130.i | 0.394185 | + | 0.682748i | 0.992997 | − | 0.118141i | \(-0.0376936\pi\) |
−0.598812 | + | 0.800890i | \(0.704360\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18424.1 | − | 6705.83i | −0.0429442 | − | 0.0156304i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −146648. | + | 254002.i | −0.339739 | + | 0.588445i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −446874. | + | 78796.0i | −1.02900 | + | 0.181440i | −0.662565 | − | 0.749004i | \(-0.730532\pi\) |
−0.366433 | + | 0.930444i | \(0.619421\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −57916.7 | − | 69022.4i | −0.132556 | − | 0.157975i | 0.695683 | − | 0.718349i | \(-0.255102\pi\) |
−0.828240 | + | 0.560374i | \(0.810657\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 236769. | − | 86176.7i | 0.538638 | − | 0.196048i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18177.0 | + | 32569.0i | −0.0411036 | + | 0.0736481i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 211369. | + | 580730.i | 0.475104 | + | 1.30534i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 135398. | − | 113612.i | 0.302524 | − | 0.253848i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −63318.8 | − | 359099.i | −0.140633 | − | 0.797570i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −182103. | − | 105137.i | −0.402056 | − | 0.232127i | 0.285315 | − | 0.958434i | \(-0.407902\pi\) |
−0.687371 | + | 0.726307i | \(0.741235\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 224927. | − | 617982.i | 0.493667 | − | 1.35634i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 197145. | − | 113821.i | 0.430138 | − | 0.248340i | −0.269268 | − | 0.963065i | \(-0.586782\pi\) |
0.699405 | + | 0.714725i | \(0.253448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 423023. | − | 504139.i | 0.917538 | − | 1.09348i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −126059. | + | 714917.i | −0.271819 | + | 1.54156i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 517412.i | 1.10916i | 0.832130 | + | 0.554581i | \(0.187121\pi\) | ||||
−0.832130 | + | 0.554581i | \(0.812879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 81199.0 | 0.173049 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 286049. | + | 50438.2i | 0.606076 | + | 0.106868i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 278213. | + | 233448.i | 0.586056 | + | 0.491759i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 151640. | + | 262647.i | 0.317582 | + | 0.550069i | 0.979983 | − | 0.199081i | \(-0.0637957\pi\) |
−0.662401 | + | 0.749150i | \(0.730462\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 666440. | + | 242564.i | 1.38770 | + | 0.505080i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8639.96 | − | 14964.8i | 0.0178872 | − | 0.0309815i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 76774.3 | − | 13537.4i | 0.158034 | − | 0.0278656i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 555125. | + | 661572.i | 1.13615 | + | 1.35401i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −161694. | + | 58851.8i | −0.329047 | + | 0.119763i | −0.501261 | − | 0.865296i | \(-0.667130\pi\) |
0.172214 | + | 0.985060i | \(0.444908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 71512.3 | − | 205746.i | 0.144701 | − | 0.416314i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12921.1 | − | 35500.3i | −0.0259968 | − | 0.0714257i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −665694. | + | 558584.i | −1.33179 | + | 1.11751i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −153332. | − | 869587.i | −0.305028 | − | 1.72990i | −0.623374 | − | 0.781924i | \(-0.714239\pi\) |
0.318347 | − | 0.947974i | \(-0.396872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −801911. | − | 462983.i | −1.58631 | − | 0.915854i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −204216. | + | 561078.i | −0.401708 | + | 1.10368i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −46059.1 | + | 26592.2i | −0.0900956 | + | 0.0520167i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 779879. | − | 929424.i | 1.51701 | − | 1.80790i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 82145.5 | − | 465870.i | 0.158901 | − | 0.901171i | −0.796232 | − | 0.604992i | \(-0.793176\pi\) |
0.955132 | − | 0.296179i | \(-0.0957125\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 854222.i | 1.64324i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −450556. | −0.861929 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 528116. | + | 93121.1i | 1.00474 | + | 0.177163i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −333613. | − | 279935.i | −0.631210 | − | 0.529648i | 0.270094 | − | 0.962834i | \(-0.412945\pi\) |
−0.901305 | + | 0.433185i | \(0.857390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −356923. | − | 618210.i | −0.671614 | − | 1.16327i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 236930. | + | 86235.3i | 0.443389 | + | 0.161380i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 298467. | − | 516959.i | 0.555505 | − | 0.962162i | −0.442359 | − | 0.896838i | \(-0.645858\pi\) |
0.997864 | − | 0.0653246i | \(-0.0208083\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11985.7 | − | 2113.41i | 0.0221866 | − | 0.00391209i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 282383. | + | 336531.i | 0.519880 | + | 0.619569i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −581638. | + | 211699.i | −1.06504 | + | 0.387641i | −0.814318 | − | 0.580419i | \(-0.802889\pi\) |
−0.250718 | + | 0.968060i | \(0.580667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.16425e6 | − | 404666.i | −2.12037 | − | 0.736988i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 212892. | + | 584915.i | 0.385639 | + | 1.05953i | 0.968944 | + | 0.247281i | \(0.0795370\pi\) |
−0.583305 | + | 0.812253i | \(0.698241\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36188.8 | + | 30366.0i | −0.0652020 | + | 0.0547110i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 189958. | + | 1.07730e6i | 0.340421 | + | 1.93062i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 863232. | + | 498387.i | 1.53874 | + | 0.888389i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 60368.6 | − | 165861.i | 0.107036 | − | 0.294080i | −0.874599 | − | 0.484847i | \(-0.838875\pi\) |
0.981635 | + | 0.190767i | \(0.0610975\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.46166e6 | + | 843889.i | −2.57784 | + | 1.48832i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23252.6 | − | 27711.4i | 0.0407923 | − | 0.0486144i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48880.6 | − | 277216.i | 0.0852992 | − | 0.483756i | −0.911992 | − | 0.410207i | \(-0.865456\pi\) |
0.997292 | − | 0.0735486i | \(-0.0234324\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.12988e6i | − | 1.96133i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 877643. | 1.51547 | 0.757737 | − | 0.652560i | \(-0.226305\pi\) | ||||
0.757737 | + | 0.652560i | \(0.226305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 147478. | + | 26004.4i | 0.253325 | + | 0.0446680i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19438.4 | − | 16310.7i | −0.0332152 | − | 0.0278709i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 214253. | + | 371097.i | 0.364196 | + | 0.630807i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 802513. | + | 292091.i | 1.35706 | + | 0.493930i | 0.915145 | − | 0.403126i | \(-0.132076\pi\) |
0.441917 | + | 0.897056i | \(0.354298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 425134. | − | 736353.i | 0.715182 | − | 1.23873i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 772475. | − | 136208.i | 1.29278 | − | 0.227953i | 0.515384 | − | 0.856960i | \(-0.327649\pi\) |
0.777400 | + | 0.629007i | \(0.216538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 333038. | + | 396899.i | 0.554486 | + | 0.660810i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 390825. | − | 142249.i | 0.647352 | − | 0.235617i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −333011. | − | 185856.i | −0.548761 | − | 0.306267i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 201391. | + | 553318.i | 0.330170 | + | 0.907136i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −703278. | + | 590120.i | −1.14711 | + | 0.962536i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 79.2117 | + | 449.232i | 0.000128543 | + | 0.000729006i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 70058.3 | + | 40448.2i | 0.113112 | + | 0.0653054i | 0.555489 | − | 0.831524i | \(-0.312531\pi\) |
−0.442377 | + | 0.896829i | \(0.645865\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 527968. | − | 1.45058e6i | 0.848113 | − | 2.33017i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −872185. | + | 503556.i | −1.39398 | + | 0.804813i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −505896. | + | 602903.i | −0.804479 | + | 0.958741i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9764.90 | − | 55379.5i | 0.0154502 | − | 0.0876223i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 217329.i | − | 0.342138i | −0.985259 | − | 0.171069i | \(-0.945278\pi\) | ||
0.985259 | − | 0.171069i | \(-0.0547220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 80272.6 | 0.125740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.57900e6 | + | 278420.i | 2.46102 | + | 0.433945i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 154929. | + | 130001.i | 0.240272 | + | 0.201612i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36898.4 | + | 63909.9i | 0.0569398 | + | 0.0986226i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −603196. | − | 219545.i | −0.926214 | − | 0.337114i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 132242. | − | 229051.i | 0.202057 | − | 0.349973i | −0.747134 | − | 0.664673i | \(-0.768571\pi\) |
0.949191 | + | 0.314700i | \(0.101904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26180.5 | − | 4616.33i | 0.0398049 | − | 0.00701868i | −0.153710 | − | 0.988116i | \(-0.549122\pi\) |
0.193515 | + | 0.981097i | \(0.438011\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 396725. | + | 472799.i | 0.600218 | + | 0.715312i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20112.3 | + | 7320.29i | −0.0302794 | + | 0.0110208i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −632185. | − | 1.05908e6i | −0.947110 | − | 1.58666i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −523550. | − | 1.43844e6i | −0.780531 | − | 2.14449i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −209659. | + | 175925.i | −0.311049 | + | 0.261001i | −0.784925 | − | 0.619590i | \(-0.787299\pi\) |
0.473877 | + | 0.880591i | \(0.342854\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −111480. | − | 632237.i | −0.164588 | − | 0.933427i | −0.949488 | − | 0.313804i | \(-0.898397\pi\) |
0.784900 | − | 0.619623i | \(-0.212715\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −849089. | − | 490222.i | −1.24751 | − | 0.720252i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −209840. | + | 576530.i | −0.306815 | + | 0.842968i | 0.686457 | + | 0.727170i | \(0.259165\pi\) |
−0.993273 | + | 0.115798i | \(0.963057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20876.8 | − | 12053.2i | 0.0303777 | − | 0.0175386i | −0.484734 | − | 0.874661i | \(-0.661084\pi\) |
0.515112 | + | 0.857123i | \(0.327750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −955687. | + | 1.13894e6i | −1.38393 | + | 1.64930i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4490.60 | + | 25467.5i | −0.00647165 | + | 0.0367025i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 116526.i | 0.167129i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −886996. | −1.26611 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −158732. | − | 27988.7i | −0.225496 | − | 0.0397611i | 0.0597582 | − | 0.998213i | \(-0.480967\pi\) |
−0.285255 | + | 0.958452i | \(0.592078\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31666.3 | − | 26571.2i | −0.0447719 | − | 0.0375681i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26964.7 | + | 46704.2i | 0.0379438 | + | 0.0657205i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46635.1 | + | 16973.8i | 0.0653130 | + | 0.0237720i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −86973.2 | + | 150642.i | −0.121232 | + | 0.209981i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −196647. | + | 34674.2i | −0.272817 | + | 0.0481051i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −277023. | − | 330143.i | −0.382522 | − | 0.455873i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −177828. | + | 64724.0i | −0.244400 | + | 0.0889543i | −0.461316 | − | 0.887236i | \(-0.652622\pi\) |
0.216916 | + | 0.976190i | \(0.430400\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 23331.8 | + | 121919.i | 0.0319166 | + | 0.166778i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −305096. | − | 838245.i | −0.415408 | − | 1.14133i | −0.954274 | − | 0.298933i | \(-0.903369\pi\) |
0.538866 | − | 0.842392i | \(-0.318853\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −745497. | + | 625546.i | −1.01032 | + | 0.847760i | −0.988381 | − | 0.151999i | \(-0.951429\pi\) |
−0.0219409 | + | 0.999759i | \(0.506985\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −126447. | − | 717117.i | −0.170570 | − | 0.967350i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8871.54 | + | 5121.99i | 0.0119118 | + | 0.00687728i | 0.505944 | − | 0.862566i | \(-0.331144\pi\) |
−0.494032 | + | 0.869444i | \(0.664478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28512.0 | + | 78336.2i | −0.0381062 | + | 0.104696i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.02923e6 | + | 594227.i | −1.36922 | + | 0.790522i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −410428. | + | 489129.i | −0.543497 | + | 0.647715i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 164654. | − | 933799.i | 0.217038 | − | 1.23088i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.19024e6i | − | 2.87384i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 128611. | 0.167981 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 731216. | + | 128933.i | 0.950706 | + | 0.167635i | 0.627433 | − | 0.778671i | \(-0.284106\pi\) |
0.323273 | + | 0.946306i | \(0.395217\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 961491. | + | 806787.i | 1.24442 | + | 1.04419i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 428429. | + | 742061.i | 0.551985 | + | 0.956066i | 0.998131 | + | 0.0611060i | \(0.0194628\pi\) |
−0.446146 | + | 0.894960i | \(0.647204\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −652614. | − | 237532.i | −0.837018 | − | 0.304650i | −0.112282 | − | 0.993676i | \(-0.535816\pi\) |
−0.724736 | + | 0.689027i | \(0.758038\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33174.2 | − | 57459.4i | 0.0423559 | − | 0.0733626i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −114060. | + | 20111.9i | −0.144973 | + | 0.0255627i | −0.245664 | − | 0.969355i | \(-0.579006\pi\) |
0.100691 | + | 0.994918i | \(0.467895\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −560943. | − | 668506.i | −0.709766 | − | 0.845867i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 385171. | − | 140191.i | 0.485175 | − | 0.176589i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −304454. | − | 248008.i | −0.381785 | − | 0.311002i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16357.7 | + | 44942.5i | 0.0204210 | + | 0.0561062i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.86818e6 | + | 1.56759e6i | −2.32185 | + | 1.94826i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −125597. | − | 712296.i | −0.155403 | − | 0.881335i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 103478. | + | 59743.2i | 0.127467 | + | 0.0735934i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 805489. | − | 2.21306e6i | 0.987834 | − | 2.71405i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9011.69 | − | 5202.90i | 0.0110029 | − | 0.00635256i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 559305. | − | 666554.i | 0.679883 | − | 0.810253i | −0.310210 | − | 0.950668i | \(-0.600399\pi\) |
0.990093 | + | 0.140415i | \(0.0448437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −502211. | + | 2.84818e6i | −0.607797 | + | 3.44699i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 363042.i | 0.437442i | 0.975787 | + | 0.218721i | \(0.0701884\pi\) | ||||
−0.975787 | + | 0.218721i | \(0.929812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 754329. | 0.904939 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 120011. | + | 21161.1i | 0.143343 | + | 0.0252753i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −298092. | − | 250129.i | −0.354496 | − | 0.297457i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 190974. | + | 330777.i | 0.226123 | + | 0.391656i | 0.956656 | − | 0.291221i | \(-0.0940617\pi\) |
−0.730533 | + | 0.682877i | \(0.760728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 977669. | + | 355843.i | 1.15258 | + | 0.419506i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 635462. | − | 1.10065e6i | 0.745910 | − | 1.29195i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −368289. | + | 64939.3i | −0.430433 | + | 0.0758970i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.82740e6 | + | 2.17781e6i | 2.12654 | + | 2.53431i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 938767. | − | 341683.i | 1.08774 | − | 0.395906i | 0.264959 | − | 0.964260i | \(-0.414642\pi\) |
0.822785 | + | 0.568353i | \(0.192419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 95715.3 | − | 82717.8i | 0.110429 | − | 0.0954333i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −409434. | − | 1.12491e6i | −0.470349 | − | 1.29227i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13404.0 | + | 11247.3i | −0.0153324 | + | 0.0128654i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 194823. | + | 1.10490e6i | 0.221902 | + | 1.25847i | 0.868519 | + | 0.495655i | \(0.165072\pi\) |
−0.646617 | + | 0.762815i | \(0.723817\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 762732. | + | 440363.i | 0.865049 | + | 0.499436i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −365334. | + | 1.00375e6i | −0.412582 | + | 1.13356i | 0.543230 | + | 0.839584i | \(0.317201\pi\) |
−0.955813 | + | 0.293977i | \(0.905021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −653464. | + | 377277.i | −0.734849 | + | 0.424265i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −70467.6 | + | 83980.0i | −0.0789089 | + | 0.0940399i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 292348. | − | 1.65799e6i | 0.325987 | − | 1.84877i | −0.176657 | − | 0.984273i | \(-0.556528\pi\) |
0.502644 | − | 0.864493i | \(-0.332361\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 436527.i | − | 0.484706i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 312401. | 0.345423 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11284.1 | + | 1989.69i | 0.0124246 | + | 0.00219079i | 0.179857 | − | 0.983693i | \(-0.442436\pi\) |
−0.167432 | + | 0.985884i | \(0.553548\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52527.6 | − | 44075.9i | −0.0575945 | − | 0.0483275i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 684345. | + | 1.18532e6i | 0.747225 | + | 1.29423i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.51437e6 | + | 551185.i | 1.64662 | + | 0.599322i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −112357. | + | 194607.i | −0.121661 | + | 0.210723i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.26696e6 | − | 576052.i | 3.52282 | − | 0.621169i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3962.06 | + | 4721.79i | 0.00425467 | + | 0.00507052i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.39440e6 | + | 507520.i | −1.49120 | + | 0.542751i | −0.953764 | − | 0.300556i | \(-0.902828\pi\) |
−0.537432 | + | 0.843307i | \(0.680605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −400338. | − | 64598.3i | −0.426363 | − | 0.0687976i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 427600. | + | 1.17482e6i | 0.453523 | + | 1.24604i | 0.930229 | + | 0.366981i | \(0.119608\pi\) |
−0.476706 | + | 0.879063i | \(0.658169\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 262718. | − | 220447.i | 0.277501 | − | 0.232851i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 367472. | + | 2.08404e6i | 0.386558 | + | 2.19228i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36995.9 | + | 21359.6i | 0.0387583 | + | 0.0223771i | 0.519254 | − | 0.854620i | \(-0.326210\pi\) |
−0.480496 | + | 0.876997i | \(0.659543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 378142. | − | 1.03894e6i | 0.394539 | − | 1.08399i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 431620. | − | 249196.i | 0.448501 | − | 0.258942i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 398552. | − | 474975.i | 0.412456 | − | 0.491546i | −0.519320 | − | 0.854580i | \(-0.673815\pi\) |
0.931776 | + | 0.363034i | \(0.118259\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17397.6 | − | 98666.8i | 0.0179315 | − | 0.101695i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 749794.i | − | 0.769675i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.44039e6 | −2.49498 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −782007. | − | 137889.i | −0.796276 | − | 0.140405i | −0.239313 | − | 0.970942i | \(-0.576922\pi\) |
−0.556963 | + | 0.830538i | \(0.688033\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −996677. | − | 836312.i | −1.01078 | − | 0.848144i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −81171.8 | − | 140594.i | −0.0819897 | − | 0.142010i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −422163. | − | 153655.i | −0.424707 | − | 0.154581i | 0.120819 | − | 0.992675i | \(-0.461448\pi\) |
−0.545526 | + | 0.838094i | \(0.683670\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 320113. | − | 554451.i | 0.320754 | − | 0.555562i |
(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.33.7 | ✓ | 42 | |
19.15 | odd | 18 | inner | 76.5.j.a.53.7 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.33.7 | ✓ | 42 | 1.1 | even | 1 | trivial | |
76.5.j.a.53.7 | yes | 42 | 19.15 | odd | 18 | inner |