Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,9,Mod(37,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.37");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.4803871823\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 46118 x^{10} + 738386961 x^{8} + 5214446299656 x^{6} + \cdots + 92\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{21} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.5 | ||
Root | \(63.2768i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.37 |
Dual form | 38.9.b.a.37.8 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 11.3137i | − | 0.707107i | ||||||
\(3\) | 76.0047i | 0.938330i | 0.883110 | + | 0.469165i | \(0.155445\pi\) | ||||
−0.883110 | + | 0.469165i | \(0.844555\pi\) | |||||||
\(4\) | −128.000 | −0.500000 | ||||||||
\(5\) | 1155.75 | 1.84919 | 0.924597 | − | 0.380946i | \(-0.124401\pi\) | ||||
0.924597 | + | 0.380946i | \(0.124401\pi\) | |||||||
\(6\) | 859.895 | 0.663500 | ||||||||
\(7\) | −2869.50 | −1.19513 | −0.597563 | − | 0.801822i | \(-0.703864\pi\) | ||||
−0.597563 | + | 0.801822i | \(0.703864\pi\) | |||||||
\(8\) | 1448.15i | 0.353553i | ||||||||
\(9\) | 784.279 | 0.119537 | ||||||||
\(10\) | − | 13075.8i | − | 1.30758i | ||||||
\(11\) | −4907.91 | −0.335217 | −0.167608 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167608 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(12\) | − | 9728.61i | − | 0.469165i | ||||||
\(13\) | 41678.7i | 1.45929i | 0.683828 | + | 0.729644i | \(0.260314\pi\) | ||||
−0.683828 | + | 0.729644i | \(0.739686\pi\) | |||||||
\(14\) | 32464.7i | 0.845082i | ||||||||
\(15\) | 87842.2i | 1.73516i | ||||||||
\(16\) | 16384.0 | 0.250000 | ||||||||
\(17\) | 51317.5 | 0.614426 | 0.307213 | − | 0.951641i | \(-0.400604\pi\) | ||||
0.307213 | + | 0.951641i | \(0.400604\pi\) | |||||||
\(18\) | − | 8873.11i | − | 0.0845251i | ||||||
\(19\) | 94212.1 | + | 90042.5i | 0.722923 | + | 0.690929i | ||||
\(20\) | −147936. | −0.924597 | ||||||||
\(21\) | − | 218095.i | − | 1.12142i | ||||||
\(22\) | 55526.7i | 0.237034i | ||||||||
\(23\) | −88541.5 | −0.316399 | −0.158200 | − | 0.987407i | \(-0.550569\pi\) | ||||
−0.158200 | + | 0.987407i | \(0.550569\pi\) | |||||||
\(24\) | −110067. | −0.331750 | ||||||||
\(25\) | 945126. | 2.41952 | ||||||||
\(26\) | 471541. | 1.03187 | ||||||||
\(27\) | 558276.i | 1.05049i | ||||||||
\(28\) | 367296. | 0.597563 | ||||||||
\(29\) | 180690.i | 0.255471i | 0.991808 | + | 0.127736i | \(0.0407709\pi\) | ||||
−0.991808 | + | 0.127736i | \(0.959229\pi\) | |||||||
\(30\) | 993821. | 1.22694 | ||||||||
\(31\) | 888002.i | 0.961539i | 0.876847 | + | 0.480770i | \(0.159643\pi\) | ||||
−0.876847 | + | 0.480770i | \(0.840357\pi\) | |||||||
\(32\) | − | 185364.i | − | 0.176777i | ||||||
\(33\) | − | 373025.i | − | 0.314544i | ||||||
\(34\) | − | 580591.i | − | 0.434465i | ||||||
\(35\) | −3.31641e6 | −2.21002 | ||||||||
\(36\) | −100388. | −0.0597683 | ||||||||
\(37\) | 2.53247e6i | 1.35125i | 0.737243 | + | 0.675627i | \(0.236127\pi\) | ||||
−0.737243 | + | 0.675627i | \(0.763873\pi\) | |||||||
\(38\) | 1.01871e6 | − | 1.06589e6i | 0.488560 | − | 0.511184i | ||||
\(39\) | −3.16778e6 | −1.36929 | ||||||||
\(40\) | 1.67370e6i | 0.653789i | ||||||||
\(41\) | − | 3.37210e6i | − | 1.19334i | −0.802485 | − | 0.596672i | \(-0.796489\pi\) | ||
0.802485 | − | 0.596672i | \(-0.203511\pi\) | |||||||
\(42\) | −2.46747e6 | −0.792966 | ||||||||
\(43\) | 3.46074e6 | 1.01227 | 0.506134 | − | 0.862455i | \(-0.331074\pi\) | ||||
0.506134 | + | 0.862455i | \(0.331074\pi\) | |||||||
\(44\) | 628213. | 0.167608 | ||||||||
\(45\) | 906428. | 0.221046 | ||||||||
\(46\) | 1.00173e6i | 0.223728i | ||||||||
\(47\) | −5.32862e6 | −1.09200 | −0.546001 | − | 0.837785i | \(-0.683850\pi\) | ||||
−0.546001 | + | 0.837785i | \(0.683850\pi\) | |||||||
\(48\) | 1.24526e6i | 0.234583i | ||||||||
\(49\) | 2.46922e6 | 0.428327 | ||||||||
\(50\) | − | 1.06929e7i | − | 1.71086i | ||||||
\(51\) | 3.90037e6i | 0.576535i | ||||||||
\(52\) | − | 5.33487e6i | − | 0.729644i | ||||||
\(53\) | − | 7.74166e6i | − | 0.981139i | −0.871402 | − | 0.490569i | \(-0.836789\pi\) | ||
0.871402 | − | 0.490569i | \(-0.163211\pi\) | |||||||
\(54\) | 6.31617e6 | 0.742812 | ||||||||
\(55\) | −5.67230e6 | −0.619881 | ||||||||
\(56\) | − | 4.15548e6i | − | 0.422541i | ||||||
\(57\) | −6.84366e6 | + | 7.16056e6i | −0.648319 | + | 0.678341i | ||||
\(58\) | 2.04428e6 | 0.180646 | ||||||||
\(59\) | − | 1.04388e7i | − | 0.861473i | −0.902478 | − | 0.430737i | \(-0.858254\pi\) | ||
0.902478 | − | 0.430737i | \(-0.141746\pi\) | |||||||
\(60\) | − | 1.12438e7i | − | 0.867578i | ||||||
\(61\) | −1.38848e7 | −1.00281 | −0.501406 | − | 0.865212i | \(-0.667184\pi\) | ||||
−0.501406 | + | 0.865212i | \(0.667184\pi\) | |||||||
\(62\) | 1.00466e7 | 0.679911 | ||||||||
\(63\) | −2.25049e6 | −0.142861 | ||||||||
\(64\) | −2.09715e6 | −0.125000 | ||||||||
\(65\) | 4.81700e7i | 2.69851i | ||||||||
\(66\) | −4.22029e6 | −0.222416 | ||||||||
\(67\) | − | 1.81780e7i | − | 0.902082i | −0.892503 | − | 0.451041i | \(-0.851053\pi\) | ||
0.892503 | − | 0.451041i | \(-0.148947\pi\) | |||||||
\(68\) | −6.56864e6 | −0.307213 | ||||||||
\(69\) | − | 6.72957e6i | − | 0.296887i | ||||||
\(70\) | 3.75209e7i | 1.56272i | ||||||||
\(71\) | − | 1.83448e7i | − | 0.721904i | −0.932584 | − | 0.360952i | \(-0.882452\pi\) | ||
0.932584 | − | 0.360952i | \(-0.117548\pi\) | |||||||
\(72\) | 1.13576e6i | 0.0422626i | ||||||||
\(73\) | 4.49830e7 | 1.58401 | 0.792004 | − | 0.610516i | \(-0.209038\pi\) | ||||
0.792004 | + | 0.610516i | \(0.209038\pi\) | |||||||
\(74\) | 2.86516e7 | 0.955481 | ||||||||
\(75\) | 7.18340e7i | 2.27031i | ||||||||
\(76\) | −1.20591e7 | − | 1.15254e7i | −0.361462 | − | 0.345464i | ||||
\(77\) | 1.40832e7 | 0.400627 | ||||||||
\(78\) | 3.58393e7i | 0.968236i | ||||||||
\(79\) | − | 5.30791e7i | − | 1.36275i | −0.731935 | − | 0.681374i | \(-0.761383\pi\) | ||
0.731935 | − | 0.681374i | \(-0.238617\pi\) | |||||||
\(80\) | 1.89358e7 | 0.462299 | ||||||||
\(81\) | −3.72860e7 | −0.866174 | ||||||||
\(82\) | −3.81510e7 | −0.843822 | ||||||||
\(83\) | 1.92972e7 | 0.406613 | 0.203307 | − | 0.979115i | \(-0.434831\pi\) | ||||
0.203307 | + | 0.979115i | \(0.434831\pi\) | |||||||
\(84\) | 2.79162e7i | 0.560712i | ||||||||
\(85\) | 5.93100e7 | 1.13619 | ||||||||
\(86\) | − | 3.91539e7i | − | 0.715782i | ||||||
\(87\) | −1.37333e7 | −0.239717 | ||||||||
\(88\) | − | 7.10741e6i | − | 0.118517i | ||||||
\(89\) | 2.43432e7i | 0.387987i | 0.981003 | + | 0.193993i | \(0.0621440\pi\) | ||||
−0.981003 | + | 0.193993i | \(0.937856\pi\) | |||||||
\(90\) | − | 1.02551e7i | − | 0.156303i | ||||||
\(91\) | − | 1.19597e8i | − | 1.74403i | ||||||
\(92\) | 1.13333e7 | 0.158200 | ||||||||
\(93\) | −6.74923e7 | −0.902241 | ||||||||
\(94\) | 6.02865e7i | 0.772162i | ||||||||
\(95\) | 1.08885e8 | + | 1.04066e8i | 1.33683 | + | 1.27766i | ||||
\(96\) | 1.40885e7 | 0.165875 | ||||||||
\(97\) | 7.02129e7i | 0.793103i | 0.918012 | + | 0.396552i | \(0.129793\pi\) | ||||
−0.918012 | + | 0.396552i | \(0.870207\pi\) | |||||||
\(98\) | − | 2.79360e7i | − | 0.302873i | ||||||
\(99\) | −3.84917e6 | −0.0400707 | ||||||||
\(100\) | −1.20976e8 | −1.20976 | ||||||||
\(101\) | 1.09928e8 | 1.05638 | 0.528192 | − | 0.849125i | \(-0.322870\pi\) | ||||
0.528192 | + | 0.849125i | \(0.322870\pi\) | |||||||
\(102\) | 4.41277e7 | 0.407671 | ||||||||
\(103\) | 1.98935e8i | 1.76751i | 0.467946 | + | 0.883757i | \(0.344994\pi\) | ||||
−0.467946 | + | 0.883757i | \(0.655006\pi\) | |||||||
\(104\) | −6.03572e7 | −0.515936 | ||||||||
\(105\) | − | 2.52063e8i | − | 2.07373i | ||||||
\(106\) | −8.75869e7 | −0.693770 | ||||||||
\(107\) | − | 1.82276e8i | − | 1.39057i | −0.718732 | − | 0.695287i | \(-0.755277\pi\) | ||
0.718732 | − | 0.695287i | \(-0.244723\pi\) | |||||||
\(108\) | − | 7.14593e7i | − | 0.525247i | ||||||
\(109\) | − | 1.88301e8i | − | 1.33397i | −0.745070 | − | 0.666987i | \(-0.767584\pi\) | ||
0.745070 | − | 0.666987i | \(-0.232416\pi\) | |||||||
\(110\) | 6.41748e7i | 0.438322i | ||||||||
\(111\) | −1.92480e8 | −1.26792 | ||||||||
\(112\) | −4.70139e7 | −0.298782 | ||||||||
\(113\) | − | 1.54544e8i | − | 0.947847i | −0.880566 | − | 0.473923i | \(-0.842837\pi\) | ||
0.880566 | − | 0.473923i | \(-0.157163\pi\) | |||||||
\(114\) | 8.10125e7 | + | 7.74271e7i | 0.479659 | + | 0.458431i | ||||
\(115\) | −1.02332e8 | −0.585084 | ||||||||
\(116\) | − | 2.31283e7i | − | 0.127736i | ||||||
\(117\) | 3.26877e7i | 0.174438i | ||||||||
\(118\) | −1.18101e8 | −0.609153 | ||||||||
\(119\) | −1.47255e8 | −0.734317 | ||||||||
\(120\) | −1.27209e8 | −0.613470 | ||||||||
\(121\) | −1.90271e8 | −0.887630 | ||||||||
\(122\) | 1.57088e8i | 0.709096i | ||||||||
\(123\) | 2.56296e8 | 1.11975 | ||||||||
\(124\) | − | 1.13664e8i | − | 0.480770i | ||||||
\(125\) | 6.40862e8 | 2.62497 | ||||||||
\(126\) | 2.54614e7i | 0.101018i | ||||||||
\(127\) | − | 4.44809e6i | − | 0.0170985i | −0.999963 | − | 0.00854926i | \(-0.997279\pi\) | ||
0.999963 | − | 0.00854926i | \(-0.00272135\pi\) | |||||||
\(128\) | 2.37266e7i | 0.0883883i | ||||||||
\(129\) | 2.63033e8i | 0.949842i | ||||||||
\(130\) | 5.44982e8 | 1.90813 | ||||||||
\(131\) | −4.41022e8 | −1.49753 | −0.748764 | − | 0.662837i | \(-0.769352\pi\) | ||||
−0.748764 | + | 0.662837i | \(0.769352\pi\) | |||||||
\(132\) | 4.77471e7i | 0.157272i | ||||||||
\(133\) | −2.70341e8 | − | 2.58377e8i | −0.863984 | − | 0.825747i | ||||
\(134\) | −2.05660e8 | −0.637868 | ||||||||
\(135\) | 6.45226e8i | 1.94257i | ||||||||
\(136\) | 7.43157e7i | 0.217232i | ||||||||
\(137\) | −5.19418e8 | −1.47447 | −0.737233 | − | 0.675639i | \(-0.763868\pi\) | ||||
−0.737233 | + | 0.675639i | \(0.763868\pi\) | |||||||
\(138\) | −7.61364e7 | −0.209931 | ||||||||
\(139\) | 2.29949e8 | 0.615987 | 0.307994 | − | 0.951388i | \(-0.400342\pi\) | ||||
0.307994 | + | 0.951388i | \(0.400342\pi\) | |||||||
\(140\) | 4.24501e8 | 1.10501 | ||||||||
\(141\) | − | 4.05000e8i | − | 1.02466i | ||||||
\(142\) | −2.07548e8 | −0.510463 | ||||||||
\(143\) | − | 2.04555e8i | − | 0.489178i | ||||||
\(144\) | 1.28496e7 | 0.0298841 | ||||||||
\(145\) | 2.08832e8i | 0.472417i | ||||||||
\(146\) | − | 5.08925e8i | − | 1.12006i | ||||||
\(147\) | 1.87672e8i | 0.401912i | ||||||||
\(148\) | − | 3.24156e8i | − | 0.675627i | ||||||
\(149\) | 9.23988e8 | 1.87465 | 0.937327 | − | 0.348451i | \(-0.113292\pi\) | ||||
0.937327 | + | 0.348451i | \(0.113292\pi\) | |||||||
\(150\) | 8.12709e8 | 1.60535 | ||||||||
\(151\) | 5.06741e8i | 0.974717i | 0.873202 | + | 0.487358i | \(0.162039\pi\) | ||||
−0.873202 | + | 0.487358i | \(0.837961\pi\) | |||||||
\(152\) | −1.30395e8 | + | 1.36434e8i | −0.244280 | + | 0.255592i | ||||
\(153\) | 4.02472e7 | 0.0734464 | ||||||||
\(154\) | − | 1.59334e8i | − | 0.283286i | ||||||
\(155\) | 1.02631e9i | 1.77807i | ||||||||
\(156\) | 4.05476e8 | 0.684647 | ||||||||
\(157\) | 5.44968e7 | 0.0896958 | 0.0448479 | − | 0.998994i | \(-0.485720\pi\) | ||||
0.0448479 | + | 0.998994i | \(0.485720\pi\) | |||||||
\(158\) | −6.00522e8 | −0.963608 | ||||||||
\(159\) | 5.88403e8 | 0.920632 | ||||||||
\(160\) | − | 2.14234e8i | − | 0.326895i | ||||||
\(161\) | 2.54070e8 | 0.378137 | ||||||||
\(162\) | 4.21843e8i | 0.612478i | ||||||||
\(163\) | 1.07938e8 | 0.152905 | 0.0764527 | − | 0.997073i | \(-0.475641\pi\) | ||||
0.0764527 | + | 0.997073i | \(0.475641\pi\) | |||||||
\(164\) | 4.31629e8i | 0.596672i | ||||||||
\(165\) | − | 4.31122e8i | − | 0.581653i | ||||||
\(166\) | − | 2.18323e8i | − | 0.287519i | ||||||
\(167\) | 5.79071e8i | 0.744502i | 0.928132 | + | 0.372251i | \(0.121414\pi\) | ||||
−0.928132 | + | 0.372251i | \(0.878586\pi\) | |||||||
\(168\) | 3.15836e8 | 0.396483 | ||||||||
\(169\) | −9.21383e8 | −1.12952 | ||||||||
\(170\) | − | 6.71016e8i | − | 0.803410i | ||||||
\(171\) | 7.38886e7 | + | 7.06185e7i | 0.0864157 | + | 0.0825912i | ||||
\(172\) | −4.42975e8 | −0.506134 | ||||||||
\(173\) | − | 1.19382e9i | − | 1.33277i | −0.745608 | − | 0.666385i | \(-0.767841\pi\) | ||
0.745608 | − | 0.666385i | \(-0.232159\pi\) | |||||||
\(174\) | 1.55375e8i | 0.169505i | ||||||||
\(175\) | −2.71204e9 | −2.89163 | ||||||||
\(176\) | −8.04112e7 | −0.0838042 | ||||||||
\(177\) | 7.93397e8 | 0.808346 | ||||||||
\(178\) | 2.75411e8 | 0.274348 | ||||||||
\(179\) | − | 1.06451e9i | − | 1.03690i | −0.855108 | − | 0.518450i | \(-0.826509\pi\) | ||
0.855108 | − | 0.518450i | \(-0.173491\pi\) | |||||||
\(180\) | −1.16023e8 | −0.110523 | ||||||||
\(181\) | 1.76596e9i | 1.64539i | 0.568486 | + | 0.822693i | \(0.307529\pi\) | ||||
−0.568486 | + | 0.822693i | \(0.692471\pi\) | |||||||
\(182\) | −1.35309e9 | −1.23322 | ||||||||
\(183\) | − | 1.05531e9i | − | 0.940969i | ||||||
\(184\) | − | 1.28222e8i | − | 0.111864i | ||||||
\(185\) | 2.92689e9i | 2.49873i | ||||||||
\(186\) | 7.63589e8i | 0.637981i | ||||||||
\(187\) | −2.51862e8 | −0.205966 | ||||||||
\(188\) | 6.82063e8 | 0.546001 | ||||||||
\(189\) | − | 1.60197e9i | − | 1.25547i | ||||||
\(190\) | 1.17738e9 | − | 1.23190e9i | 0.903443 | − | 0.945278i | ||||
\(191\) | −2.47773e8 | −0.186175 | −0.0930874 | − | 0.995658i | \(-0.529674\pi\) | ||||
−0.0930874 | + | 0.995658i | \(0.529674\pi\) | |||||||
\(192\) | − | 1.59393e8i | − | 0.117291i | ||||||
\(193\) | − | 1.04978e9i | − | 0.756607i | −0.925682 | − | 0.378304i | \(-0.876508\pi\) | ||
0.925682 | − | 0.378304i | \(-0.123492\pi\) | |||||||
\(194\) | 7.94368e8 | 0.560809 | ||||||||
\(195\) | −3.66115e9 | −2.53209 | ||||||||
\(196\) | −3.16060e8 | −0.214163 | ||||||||
\(197\) | −4.22634e8 | −0.280608 | −0.140304 | − | 0.990108i | \(-0.544808\pi\) | ||||
−0.140304 | + | 0.990108i | \(0.544808\pi\) | |||||||
\(198\) | 4.35484e7i | 0.0283342i | ||||||||
\(199\) | 1.95755e9 | 1.24825 | 0.624124 | − | 0.781325i | \(-0.285456\pi\) | ||||
0.624124 | + | 0.781325i | \(0.285456\pi\) | |||||||
\(200\) | 1.36869e9i | 0.855430i | ||||||||
\(201\) | 1.38161e9 | 0.846450 | ||||||||
\(202\) | − | 1.24369e9i | − | 0.746976i | ||||||
\(203\) | − | 5.18490e8i | − | 0.305321i | ||||||
\(204\) | − | 4.99248e8i | − | 0.288267i | ||||||
\(205\) | − | 3.89730e9i | − | 2.20673i | ||||||
\(206\) | 2.25070e9 | 1.24982 | ||||||||
\(207\) | −6.94413e7 | −0.0378213 | ||||||||
\(208\) | 6.82864e8i | 0.364822i | ||||||||
\(209\) | −4.62384e8 | − | 4.41921e8i | −0.242336 | − | 0.231611i | ||||
\(210\) | −2.85177e9 | −1.46635 | ||||||||
\(211\) | − | 2.40016e9i | − | 1.21091i | −0.795881 | − | 0.605453i | \(-0.792992\pi\) | ||
0.795881 | − | 0.605453i | \(-0.207008\pi\) | |||||||
\(212\) | 9.90932e8i | 0.490569i | ||||||||
\(213\) | 1.39429e9 | 0.677384 | ||||||||
\(214\) | −2.06222e9 | −0.983284 | ||||||||
\(215\) | 3.99974e9 | 1.87188 | ||||||||
\(216\) | −8.08470e8 | −0.371406 | ||||||||
\(217\) | − | 2.54812e9i | − | 1.14916i | ||||||
\(218\) | −2.13039e9 | −0.943262 | ||||||||
\(219\) | 3.41892e9i | 1.48632i | ||||||||
\(220\) | 7.26055e8 | 0.309941 | ||||||||
\(221\) | 2.13885e9i | 0.896624i | ||||||||
\(222\) | 2.17766e9i | 0.896557i | ||||||||
\(223\) | − | 1.31765e8i | − | 0.0532819i | −0.999645 | − | 0.0266409i | \(-0.991519\pi\) | ||
0.999645 | − | 0.0266409i | \(-0.00848107\pi\) | |||||||
\(224\) | 5.31901e8i | 0.211270i | ||||||||
\(225\) | 7.41243e8 | 0.289221 | ||||||||
\(226\) | −1.74846e9 | −0.670229 | ||||||||
\(227\) | 2.48274e9i | 0.935035i | 0.883984 | + | 0.467517i | \(0.154851\pi\) | ||||
−0.883984 | + | 0.467517i | \(0.845149\pi\) | |||||||
\(228\) | 8.75988e8 | − | 9.16552e8i | 0.324160 | − | 0.339170i | ||||
\(229\) | 3.34493e9 | 1.21631 | 0.608156 | − | 0.793818i | \(-0.291910\pi\) | ||||
0.608156 | + | 0.793818i | \(0.291910\pi\) | |||||||
\(230\) | 1.15775e9i | 0.413717i | ||||||||
\(231\) | 1.07039e9i | 0.375920i | ||||||||
\(232\) | −2.61667e8 | −0.0903228 | ||||||||
\(233\) | 1.23387e9 | 0.418644 | 0.209322 | − | 0.977847i | \(-0.432874\pi\) | ||||
0.209322 | + | 0.977847i | \(0.432874\pi\) | |||||||
\(234\) | 3.69820e8 | 0.123346 | ||||||||
\(235\) | −6.15854e9 | −2.01932 | ||||||||
\(236\) | 1.33616e9i | 0.430737i | ||||||||
\(237\) | 4.03427e9 | 1.27871 | ||||||||
\(238\) | 1.66601e9i | 0.519240i | ||||||||
\(239\) | 1.00656e9 | 0.308496 | 0.154248 | − | 0.988032i | \(-0.450705\pi\) | ||||
0.154248 | + | 0.988032i | \(0.450705\pi\) | |||||||
\(240\) | 1.43921e9i | 0.433789i | ||||||||
\(241\) | 2.78434e9i | 0.825380i | 0.910871 | + | 0.412690i | \(0.135411\pi\) | ||||
−0.910871 | + | 0.412690i | \(0.864589\pi\) | |||||||
\(242\) | 2.15267e9i | 0.627649i | ||||||||
\(243\) | 8.28939e8i | 0.237737i | ||||||||
\(244\) | 1.77725e9 | 0.501406 | ||||||||
\(245\) | 2.85379e9 | 0.792060 | ||||||||
\(246\) | − | 2.89966e9i | − | 0.791783i | ||||||
\(247\) | −3.75285e9 | + | 3.92664e9i | −1.00826 | + | 1.05495i | ||||
\(248\) | −1.28596e9 | −0.339955 | ||||||||
\(249\) | 1.46668e9i | 0.381537i | ||||||||
\(250\) | − | 7.25053e9i | − | 1.85614i | ||||||
\(251\) | −3.39707e9 | −0.855873 | −0.427936 | − | 0.903809i | \(-0.640759\pi\) | ||||
−0.427936 | + | 0.903809i | \(0.640759\pi\) | |||||||
\(252\) | 2.88062e8 | 0.0714306 | ||||||||
\(253\) | 4.34554e8 | 0.106062 | ||||||||
\(254\) | −5.03244e7 | −0.0120905 | ||||||||
\(255\) | 4.50784e9i | 1.06612i | ||||||||
\(256\) | 2.68435e8 | 0.0625000 | ||||||||
\(257\) | − | 1.08377e9i | − | 0.248430i | −0.992255 | − | 0.124215i | \(-0.960359\pi\) | ||
0.992255 | − | 0.124215i | \(-0.0396412\pi\) | |||||||
\(258\) | 2.97588e9 | 0.671640 | ||||||||
\(259\) | − | 7.26691e9i | − | 1.61492i | ||||||
\(260\) | − | 6.16576e9i | − | 1.34925i | ||||||
\(261\) | 1.41712e8i | 0.0305382i | ||||||||
\(262\) | 4.98959e9i | 1.05891i | ||||||||
\(263\) | 3.42971e9 | 0.716860 | 0.358430 | − | 0.933557i | \(-0.383312\pi\) | ||||
0.358430 | + | 0.933557i | \(0.383312\pi\) | |||||||
\(264\) | 5.40197e8 | 0.111208 | ||||||||
\(265\) | − | 8.94740e9i | − | 1.81432i | ||||||
\(266\) | −2.92320e9 | + | 3.05856e9i | −0.583891 | + | 0.610929i | ||||
\(267\) | −1.85020e9 | −0.364060 | ||||||||
\(268\) | 2.32678e9i | 0.451041i | ||||||||
\(269\) | − | 3.38539e9i | − | 0.646547i | −0.946306 | − | 0.323273i | \(-0.895217\pi\) | ||
0.946306 | − | 0.323273i | \(-0.104783\pi\) | |||||||
\(270\) | 7.29990e9 | 1.37360 | ||||||||
\(271\) | 2.23995e9 | 0.415299 | 0.207650 | − | 0.978203i | \(-0.433419\pi\) | ||||
0.207650 | + | 0.978203i | \(0.433419\pi\) | |||||||
\(272\) | 8.40786e8 | 0.153607 | ||||||||
\(273\) | 9.08994e9 | 1.63648 | ||||||||
\(274\) | 5.87654e9i | 1.04260i | ||||||||
\(275\) | −4.63859e9 | −0.811065 | ||||||||
\(276\) | 8.61386e8i | 0.148444i | ||||||||
\(277\) | −7.70540e9 | −1.30881 | −0.654404 | − | 0.756145i | \(-0.727081\pi\) | ||||
−0.654404 | + | 0.756145i | \(0.727081\pi\) | |||||||
\(278\) | − | 2.60157e9i | − | 0.435569i | ||||||
\(279\) | 6.96441e8i | 0.114939i | ||||||||
\(280\) | − | 4.80268e9i | − | 0.781361i | ||||||
\(281\) | − | 9.53553e9i | − | 1.52939i | −0.644390 | − | 0.764697i | \(-0.722888\pi\) | ||
0.644390 | − | 0.764697i | \(-0.277112\pi\) | |||||||
\(282\) | −4.58206e9 | −0.724543 | ||||||||
\(283\) | 9.62545e9 | 1.50064 | 0.750318 | − | 0.661077i | \(-0.229900\pi\) | ||||
0.750318 | + | 0.661077i | \(0.229900\pi\) | |||||||
\(284\) | 2.34813e9i | 0.360952i | ||||||||
\(285\) | −7.90953e9 | + | 8.27580e9i | −1.19887 | + | 1.25438i | ||||
\(286\) | −2.31428e9 | −0.345901 | ||||||||
\(287\) | 9.67625e9i | 1.42620i | ||||||||
\(288\) | − | 1.45377e8i | − | 0.0211313i | ||||||
\(289\) | −4.34227e9 | −0.622481 | ||||||||
\(290\) | 2.36266e9 | 0.334049 | ||||||||
\(291\) | −5.33651e9 | −0.744193 | ||||||||
\(292\) | −5.75783e9 | −0.792004 | ||||||||
\(293\) | 1.32147e9i | 0.179303i | 0.995973 | + | 0.0896515i | \(0.0285753\pi\) | ||||
−0.995973 | + | 0.0896515i | \(0.971425\pi\) | |||||||
\(294\) | 2.12327e9 | 0.284195 | ||||||||
\(295\) | − | 1.20646e10i | − | 1.59303i | ||||||
\(296\) | −3.66741e9 | −0.477741 | ||||||||
\(297\) | − | 2.73997e9i | − | 0.352144i | ||||||
\(298\) | − | 1.04537e10i | − | 1.32558i | ||||||
\(299\) | − | 3.69029e9i | − | 0.461717i | ||||||
\(300\) | − | 9.19476e9i | − | 1.13516i | ||||||
\(301\) | −9.93060e9 | −1.20979 | ||||||||
\(302\) | 5.73312e9 | 0.689229 | ||||||||
\(303\) | 8.35503e9i | 0.991237i | ||||||||
\(304\) | 1.54357e9 | + | 1.47526e9i | 0.180731 | + | 0.172732i | ||||
\(305\) | −1.60473e10 | −1.85440 | ||||||||
\(306\) | − | 4.55346e8i | − | 0.0519344i | ||||||
\(307\) | 6.27589e9i | 0.706516i | 0.935526 | + | 0.353258i | \(0.114926\pi\) | ||||
−0.935526 | + | 0.353258i | \(0.885074\pi\) | |||||||
\(308\) | −1.80265e9 | −0.200313 | ||||||||
\(309\) | −1.51200e10 | −1.65851 | ||||||||
\(310\) | 1.16113e10 | 1.25729 | ||||||||
\(311\) | −6.55650e7 | −0.00700859 | −0.00350429 | − | 0.999994i | \(-0.501115\pi\) | ||||
−0.00350429 | + | 0.999994i | \(0.501115\pi\) | |||||||
\(312\) | − | 4.58743e9i | − | 0.484118i | ||||||
\(313\) | 4.03513e9 | 0.420417 | 0.210208 | − | 0.977657i | \(-0.432586\pi\) | ||||
0.210208 | + | 0.977657i | \(0.432586\pi\) | |||||||
\(314\) | − | 6.16561e8i | − | 0.0634245i | ||||||
\(315\) | −2.60099e9 | −0.264178 | ||||||||
\(316\) | 6.79413e9i | 0.681374i | ||||||||
\(317\) | 9.49658e8i | 0.0940438i | 0.998894 | + | 0.0470219i | \(0.0149731\pi\) | ||||
−0.998894 | + | 0.0470219i | \(0.985027\pi\) | |||||||
\(318\) | − | 6.65702e9i | − | 0.650985i | ||||||
\(319\) | − | 8.86811e8i | − | 0.0856384i | ||||||
\(320\) | −2.42378e9 | −0.231149 | ||||||||
\(321\) | 1.38538e10 | 1.30482 | ||||||||
\(322\) | − | 2.87447e9i | − | 0.267383i | ||||||
\(323\) | 4.83473e9 | + | 4.62075e9i | 0.444183 | + | 0.424525i | ||||
\(324\) | 4.77260e9 | 0.433087 | ||||||||
\(325\) | 3.93916e10i | 3.53078i | ||||||||
\(326\) | − | 1.22118e9i | − | 0.108120i | ||||||
\(327\) | 1.43118e10 | 1.25171 | ||||||||
\(328\) | 4.88333e9 | 0.421911 | ||||||||
\(329\) | 1.52905e10 | 1.30508 | ||||||||
\(330\) | −4.87759e9 | −0.411291 | ||||||||
\(331\) | − | 6.32042e9i | − | 0.526543i | −0.964722 | − | 0.263272i | \(-0.915198\pi\) | ||
0.964722 | − | 0.263272i | \(-0.0848015\pi\) | |||||||
\(332\) | −2.47004e9 | −0.203307 | ||||||||
\(333\) | 1.98616e9i | 0.161524i | ||||||||
\(334\) | 6.55144e9 | 0.526443 | ||||||||
\(335\) | − | 2.10091e10i | − | 1.66812i | ||||||
\(336\) | − | 3.57328e9i | − | 0.280356i | ||||||
\(337\) | 6.66861e9i | 0.517030i | 0.966007 | + | 0.258515i | \(0.0832332\pi\) | ||||
−0.966007 | + | 0.258515i | \(0.916767\pi\) | |||||||
\(338\) | 1.04243e10i | 0.798691i | ||||||||
\(339\) | 1.17461e10 | 0.889393 | ||||||||
\(340\) | −7.59168e9 | −0.568097 | ||||||||
\(341\) | − | 4.35823e9i | − | 0.322324i | ||||||
\(342\) | 7.98957e8 | − | 8.35954e8i | 0.0584008 | − | 0.0611051i | ||||
\(343\) | 9.45667e9 | 0.683222 | ||||||||
\(344\) | 5.01169e9i | 0.357891i | ||||||||
\(345\) | − | 7.77768e9i | − | 0.549002i | ||||||
\(346\) | −1.35066e10 | −0.942411 | ||||||||
\(347\) | 2.52011e10 | 1.73821 | 0.869103 | − | 0.494632i | \(-0.164697\pi\) | ||||
0.869103 | + | 0.494632i | \(0.164697\pi\) | |||||||
\(348\) | 1.75786e9 | 0.119858 | ||||||||
\(349\) | −2.93228e10 | −1.97653 | −0.988267 | − | 0.152736i | \(-0.951192\pi\) | ||||
−0.988267 | + | 0.152736i | \(0.951192\pi\) | |||||||
\(350\) | 3.06832e10i | 2.04469i | ||||||||
\(351\) | −2.32682e10 | −1.53297 | ||||||||
\(352\) | 9.09749e8i | 0.0592585i | ||||||||
\(353\) | −4.05561e9 | −0.261191 | −0.130595 | − | 0.991436i | \(-0.541689\pi\) | ||||
−0.130595 | + | 0.991436i | \(0.541689\pi\) | |||||||
\(354\) | − | 8.97626e9i | − | 0.571587i | ||||||
\(355\) | − | 2.12019e10i | − | 1.33494i | ||||||
\(356\) | − | 3.11592e9i | − | 0.193993i | ||||||
\(357\) | − | 1.11921e10i | − | 0.689032i | ||||||
\(358\) | −1.20435e10 | −0.733199 | ||||||||
\(359\) | −9.40026e9 | −0.565929 | −0.282965 | − | 0.959130i | \(-0.591318\pi\) | ||||
−0.282965 | + | 0.959130i | \(0.591318\pi\) | |||||||
\(360\) | 1.31265e9i | 0.0781517i | ||||||||
\(361\) | 7.68260e8 | + | 1.69662e10i | 0.0452355 | + | 0.998976i | ||||
\(362\) | 1.99796e10 | 1.16346 | ||||||||
\(363\) | − | 1.44615e10i | − | 0.832890i | ||||||
\(364\) | 1.53084e10i | 0.872016i | ||||||||
\(365\) | 5.19890e10 | 2.92914 | ||||||||
\(366\) | −1.19395e10 | −0.665366 | ||||||||
\(367\) | −2.66414e9 | −0.146856 | −0.0734281 | − | 0.997301i | \(-0.523394\pi\) | ||||
−0.0734281 | + | 0.997301i | \(0.523394\pi\) | |||||||
\(368\) | −1.45066e9 | −0.0790998 | ||||||||
\(369\) | − | 2.64467e9i | − | 0.142648i | ||||||
\(370\) | 3.31140e10 | 1.76687 | ||||||||
\(371\) | 2.22147e10i | 1.17258i | ||||||||
\(372\) | 8.63902e9 | 0.451121 | ||||||||
\(373\) | − | 1.71702e10i | − | 0.887035i | −0.896266 | − | 0.443517i | \(-0.853730\pi\) | ||
0.896266 | − | 0.443517i | \(-0.146270\pi\) | |||||||
\(374\) | 2.84949e9i | 0.145640i | ||||||||
\(375\) | 4.87086e10i | 2.46309i | ||||||||
\(376\) | − | 7.71667e9i | − | 0.386081i | ||||||
\(377\) | −7.53093e9 | −0.372806 | ||||||||
\(378\) | −1.81242e10 | −0.887754 | ||||||||
\(379\) | 9.05015e9i | 0.438631i | 0.975654 | + | 0.219315i | \(0.0703823\pi\) | ||||
−0.975654 | + | 0.219315i | \(0.929618\pi\) | |||||||
\(380\) | −1.39373e10 | − | 1.33205e10i | −0.668413 | − | 0.638831i | ||||
\(381\) | 3.38076e8 | 0.0160441 | ||||||||
\(382\) | 2.80323e9i | 0.131645i | ||||||||
\(383\) | 9.57995e9i | 0.445213i | 0.974908 | + | 0.222607i | \(0.0714566\pi\) | ||||
−0.974908 | + | 0.222607i | \(0.928543\pi\) | |||||||
\(384\) | −1.80333e9 | −0.0829375 | ||||||||
\(385\) | 1.62767e10 | 0.740837 | ||||||||
\(386\) | −1.18769e10 | −0.535002 | ||||||||
\(387\) | 2.71419e9 | 0.121003 | ||||||||
\(388\) | − | 8.98725e9i | − | 0.396552i | ||||||
\(389\) | −2.19375e10 | −0.958053 | −0.479026 | − | 0.877800i | \(-0.659010\pi\) | ||||
−0.479026 | + | 0.877800i | \(0.659010\pi\) | |||||||
\(390\) | 4.14212e10i | 1.79046i | ||||||||
\(391\) | −4.54373e9 | −0.194404 | ||||||||
\(392\) | 3.57581e9i | 0.151436i | ||||||||
\(393\) | − | 3.35197e10i | − | 1.40517i | ||||||
\(394\) | 4.78156e9i | 0.198420i | ||||||||
\(395\) | − | 6.13460e10i | − | 2.51999i | ||||||
\(396\) | 4.92694e8 | 0.0200353 | ||||||||
\(397\) | 5.05069e9 | 0.203324 | 0.101662 | − | 0.994819i | \(-0.467584\pi\) | ||||
0.101662 | + | 0.994819i | \(0.467584\pi\) | |||||||
\(398\) | − | 2.21472e10i | − | 0.882644i | ||||||
\(399\) | 1.96379e10 | − | 2.05472e10i | 0.774823 | − | 0.810703i | ||||
\(400\) | 1.54849e10 | 0.604880 | ||||||||
\(401\) | − | 2.54035e10i | − | 0.982464i | −0.871029 | − | 0.491232i | \(-0.836547\pi\) | ||
0.871029 | − | 0.491232i | \(-0.163453\pi\) | |||||||
\(402\) | − | 1.56311e10i | − | 0.598531i | ||||||
\(403\) | −3.70108e10 | −1.40316 | ||||||||
\(404\) | −1.40707e10 | −0.528192 | ||||||||
\(405\) | −4.30931e10 | −1.60173 | ||||||||
\(406\) | −5.86604e9 | −0.215894 | ||||||||
\(407\) | − | 1.24291e10i | − | 0.452963i | ||||||
\(408\) | −5.64834e9 | −0.203836 | ||||||||
\(409\) | 4.77621e10i | 1.70683i | 0.521231 | + | 0.853415i | \(0.325473\pi\) | ||||
−0.521231 | + | 0.853415i | \(0.674527\pi\) | |||||||
\(410\) | −4.40929e10 | −1.56039 | ||||||||
\(411\) | − | 3.94782e10i | − | 1.38354i | ||||||
\(412\) | − | 2.54637e10i | − | 0.883757i | ||||||
\(413\) | 2.99541e10i | 1.02957i | ||||||||
\(414\) | 7.85638e8i | 0.0267437i | ||||||||
\(415\) | 2.23026e10 | 0.751907 | ||||||||
\(416\) | 7.72572e9 | 0.257968 | ||||||||
\(417\) | 1.74772e10i | 0.578000i | ||||||||
\(418\) | −4.99976e9 | + | 5.23128e9i | −0.163774 | + | 0.171357i | ||||
\(419\) | −3.91913e10 | −1.27155 | −0.635775 | − | 0.771874i | \(-0.719320\pi\) | ||||
−0.635775 | + | 0.771874i | \(0.719320\pi\) | |||||||
\(420\) | 3.22641e10i | 1.03686i | ||||||||
\(421\) | 1.27758e10i | 0.406685i | 0.979108 | + | 0.203342i | \(0.0651805\pi\) | ||||
−0.979108 | + | 0.203342i | \(0.934820\pi\) | |||||||
\(422\) | −2.71547e10 | −0.856240 | ||||||||
\(423\) | −4.17913e9 | −0.130534 | ||||||||
\(424\) | 1.12111e10 | 0.346885 | ||||||||
\(425\) | 4.85015e10 | 1.48662 | ||||||||
\(426\) | − | 1.57746e10i | − | 0.478983i | ||||||
\(427\) | 3.98424e10 | 1.19849 | ||||||||
\(428\) | 2.33313e10i | 0.695287i | ||||||||
\(429\) | 1.55472e10 | 0.459010 | ||||||||
\(430\) | − | 4.52519e10i | − | 1.32362i | ||||||
\(431\) | − | 3.52399e10i | − | 1.02123i | −0.859808 | − | 0.510617i | \(-0.829417\pi\) | ||
0.859808 | − | 0.510617i | \(-0.170583\pi\) | |||||||
\(432\) | 9.14679e9i | 0.262624i | ||||||||
\(433\) | 8.20445e9i | 0.233398i | 0.993167 | + | 0.116699i | \(0.0372313\pi\) | ||||
−0.993167 | + | 0.116699i | \(0.962769\pi\) | |||||||
\(434\) | −2.88287e10 | −0.812580 | ||||||||
\(435\) | −1.58722e10 | −0.443283 | ||||||||
\(436\) | 2.41026e10i | 0.666987i | ||||||||
\(437\) | −8.34168e9 | − | 7.97250e9i | −0.228732 | − | 0.218609i | ||||
\(438\) | 3.86807e10 | 1.05099 | ||||||||
\(439\) | − | 6.65038e7i | − | 0.00179056i | −1.00000 | 0.000895279i | \(-0.999715\pi\) | |||
1.00000 | 0.000895279i | \(-0.000284976\pi\) | ||||||||
\(440\) | − | 8.21437e9i | − | 0.219161i | ||||||
\(441\) | 1.93656e9 | 0.0512007 | ||||||||
\(442\) | 2.41983e10 | 0.634009 | ||||||||
\(443\) | 8.14225e9 | 0.211412 | 0.105706 | − | 0.994397i | \(-0.466290\pi\) | ||||
0.105706 | + | 0.994397i | \(0.466290\pi\) | |||||||
\(444\) | 2.46374e10 | 0.633961 | ||||||||
\(445\) | 2.81345e10i | 0.717463i | ||||||||
\(446\) | −1.49075e9 | −0.0376760 | ||||||||
\(447\) | 7.02275e10i | 1.75904i | ||||||||
\(448\) | 6.01777e9 | 0.149391 | ||||||||
\(449\) | − | 9.39424e9i | − | 0.231141i | −0.993299 | − | 0.115570i | \(-0.963130\pi\) | ||
0.993299 | − | 0.115570i | \(-0.0368695\pi\) | |||||||
\(450\) | − | 8.38620e9i | − | 0.204510i | ||||||
\(451\) | 1.65500e10i | 0.400029i | ||||||||
\(452\) | 1.97816e10i | 0.473923i | ||||||||
\(453\) | −3.85147e10 | −0.914606 | ||||||||
\(454\) | 2.80890e10 | 0.661169 | ||||||||
\(455\) | − | 1.38224e11i | − | 3.22506i | ||||||
\(456\) | −1.03696e10 | − | 9.91067e9i | −0.239830 | − | 0.229215i | ||||
\(457\) | −3.13612e10 | −0.718998 | −0.359499 | − | 0.933145i | \(-0.617052\pi\) | ||||
−0.359499 | + | 0.933145i | \(0.617052\pi\) | |||||||
\(458\) | − | 3.78435e10i | − | 0.860062i | ||||||
\(459\) | 2.86493e10i | 0.645451i | ||||||||
\(460\) | 1.30984e10 | 0.292542 | ||||||||
\(461\) | 2.63379e9 | 0.0583146 | 0.0291573 | − | 0.999575i | \(-0.490718\pi\) | ||||
0.0291573 | + | 0.999575i | \(0.490718\pi\) | |||||||
\(462\) | 1.21101e10 | 0.265816 | ||||||||
\(463\) | 8.85572e10 | 1.92708 | 0.963540 | − | 0.267563i | \(-0.0862182\pi\) | ||||
0.963540 | + | 0.267563i | \(0.0862182\pi\) | |||||||
\(464\) | 2.96043e9i | 0.0638679i | ||||||||
\(465\) | −7.80041e10 | −1.66842 | ||||||||
\(466\) | − | 1.39596e10i | − | 0.296026i | ||||||
\(467\) | 3.29979e10 | 0.693775 | 0.346887 | − | 0.937907i | \(-0.387239\pi\) | ||||
0.346887 | + | 0.937907i | \(0.387239\pi\) | |||||||
\(468\) | − | 4.18403e9i | − | 0.0872191i | ||||||
\(469\) | 5.21616e10i | 1.07810i | ||||||||
\(470\) | 6.96759e10i | 1.42788i | ||||||||
\(471\) | 4.14201e9i | 0.0841643i | ||||||||
\(472\) | 1.51170e10 | 0.304577 | ||||||||
\(473\) | −1.69850e10 | −0.339330 | ||||||||
\(474\) | − | 4.56425e10i | − | 0.904183i | ||||||
\(475\) | 8.90422e10 | + | 8.51015e10i | 1.74913 | + | 1.67172i | ||||
\(476\) | 1.88487e10 | 0.367158 | ||||||||
\(477\) | − | 6.07162e9i | − | 0.117282i | ||||||
\(478\) | − | 1.13880e10i | − | 0.218140i | ||||||
\(479\) | −4.27389e10 | −0.811860 | −0.405930 | − | 0.913904i | \(-0.633052\pi\) | ||||
−0.405930 | + | 0.913904i | \(0.633052\pi\) | |||||||
\(480\) | 1.62828e10 | 0.306735 | ||||||||
\(481\) | −1.05550e11 | −1.97187 | ||||||||
\(482\) | 3.15012e10 | 0.583632 | ||||||||
\(483\) | 1.93105e10i | 0.354817i | ||||||||
\(484\) | 2.43547e10 | 0.443815 | ||||||||
\(485\) | 8.11483e10i | 1.46660i | ||||||||
\(486\) | 9.37837e9 | 0.168106 | ||||||||
\(487\) | − | 2.99875e10i | − | 0.533119i | −0.963818 | − | 0.266559i | \(-0.914113\pi\) | ||
0.963818 | − | 0.266559i | \(-0.0858869\pi\) | |||||||
\(488\) | − | 2.01073e10i | − | 0.354548i | ||||||
\(489\) | 8.20378e9i | 0.143476i | ||||||||
\(490\) | − | 3.22870e10i | − | 0.560071i | ||||||
\(491\) | 1.26087e10 | 0.216942 | 0.108471 | − | 0.994100i | \(-0.465405\pi\) | ||||
0.108471 | + | 0.994100i | \(0.465405\pi\) | |||||||
\(492\) | −3.28059e10 | −0.559875 | ||||||||
\(493\) | 9.27256e9i | 0.156968i | ||||||||
\(494\) | 4.44248e10 | + | 4.24587e10i | 0.745964 | + | 0.712950i | ||||
\(495\) | −4.44867e9 | −0.0740985 | ||||||||
\(496\) | 1.45490e10i | 0.240385i | ||||||||
\(497\) | 5.26403e10i | 0.862766i | ||||||||
\(498\) | 1.65936e10 | 0.269788 | ||||||||
\(499\) | 3.70124e10 | 0.596960 | 0.298480 | − | 0.954416i | \(-0.403520\pi\) | ||||
0.298480 | + | 0.954416i | \(0.403520\pi\) | |||||||
\(500\) | −8.20304e10 | −1.31249 | ||||||||
\(501\) | −4.40121e10 | −0.698589 | ||||||||
\(502\) | 3.84334e10i | 0.605193i | ||||||||
\(503\) | −2.48541e10 | −0.388264 | −0.194132 | − | 0.980975i | \(-0.562189\pi\) | ||||
−0.194132 | + | 0.980975i | \(0.562189\pi\) | |||||||
\(504\) | − | 3.25905e9i | − | 0.0505091i | ||||||
\(505\) | 1.27049e11 | 1.95346 | ||||||||
\(506\) | − | 4.91642e9i | − | 0.0749974i | ||||||
\(507\) | − | 7.00295e10i | − | 1.05986i | ||||||
\(508\) | 5.69355e8i | 0.00854926i | ||||||||
\(509\) | − | 4.24098e10i | − | 0.631822i | −0.948789 | − | 0.315911i | \(-0.897690\pi\) | ||
0.948789 | − | 0.315911i | \(-0.102310\pi\) | |||||||
\(510\) | 5.10004e10 | 0.753864 | ||||||||
\(511\) | −1.29079e11 | −1.89309 | ||||||||
\(512\) | − | 3.03700e9i | − | 0.0441942i | ||||||
\(513\) | −5.02686e10 | + | 5.25963e10i | −0.725817 | + | 0.759427i | ||||
\(514\) | −1.22614e10 | −0.175666 | ||||||||
\(515\) | 2.29919e11i | 3.26848i | ||||||||
\(516\) | − | 3.36682e10i | − | 0.474921i | ||||||
\(517\) | 2.61524e10 | 0.366057 | ||||||||
\(518\) | −8.22157e10 | −1.14192 | ||||||||
\(519\) | 9.07362e10 | 1.25058 | ||||||||
\(520\) | −6.97576e10 | −0.954066 | ||||||||
\(521\) | − | 6.28514e10i | − | 0.853030i | −0.904481 | − | 0.426515i | \(-0.859741\pi\) | ||
0.904481 | − | 0.426515i | \(-0.140259\pi\) | |||||||
\(522\) | 1.60328e9 | 0.0215938 | ||||||||
\(523\) | − | 2.26507e10i | − | 0.302743i | −0.988477 | − | 0.151372i | \(-0.951631\pi\) | ||
0.988477 | − | 0.151372i | \(-0.0483690\pi\) | |||||||
\(524\) | 5.64508e10 | 0.748764 | ||||||||
\(525\) | − | 2.06128e11i | − | 2.71331i | ||||||
\(526\) | − | 3.88027e10i | − | 0.506896i | ||||||
\(527\) | 4.55700e10i | 0.590795i | ||||||||
\(528\) | − | 6.11163e9i | − | 0.0786360i | ||||||
\(529\) | −7.04714e10 | −0.899891 | ||||||||
\(530\) | −1.01228e11 | −1.28292 | ||||||||
\(531\) | − | 8.18692e9i | − | 0.102978i | ||||||
\(532\) | 3.46037e10 | + | 3.30722e10i | 0.431992 | + | 0.412873i | ||||
\(533\) | 1.40545e11 | 1.74143 | ||||||||
\(534\) | 2.09326e10i | 0.257429i | ||||||||
\(535\) | − | 2.10665e11i | − | 2.57144i | ||||||
\(536\) | 2.63245e10 | 0.318934 | ||||||||
\(537\) | 8.09076e10 | 0.972954 | ||||||||
\(538\) | −3.83013e10 | −0.457178 | ||||||||
\(539\) | −1.21187e10 | −0.143582 | ||||||||
\(540\) | − | 8.25889e10i | − | 0.971285i | ||||||
\(541\) | 6.24255e10 | 0.728740 | 0.364370 | − | 0.931254i | \(-0.381284\pi\) | ||||
0.364370 | + | 0.931254i | \(0.381284\pi\) | |||||||
\(542\) | − | 2.53421e10i | − | 0.293661i | ||||||
\(543\) | −1.34222e11 | −1.54392 | ||||||||
\(544\) | − | 9.51240e9i | − | 0.108616i | ||||||
\(545\) | − | 2.17629e11i | − | 2.46678i | ||||||
\(546\) | − | 1.02841e11i | − | 1.15716i | ||||||
\(547\) | − | 5.38177e10i | − | 0.601141i | −0.953760 | − | 0.300570i | \(-0.902823\pi\) | ||
0.953760 | − | 0.300570i | \(-0.0971770\pi\) | |||||||
\(548\) | 6.64855e10 | 0.737233 | ||||||||
\(549\) | −1.08895e10 | −0.119873 | ||||||||
\(550\) | 5.24797e10i | 0.573509i | ||||||||
\(551\) | −1.62698e10 | + | 1.70232e10i | −0.176513 | + | 0.184686i | ||||
\(552\) | 9.74546e9 | 0.104965 | ||||||||
\(553\) | 1.52310e11i | 1.62866i | ||||||||
\(554\) | 8.71767e10i | 0.925467i | ||||||||
\(555\) | −2.22458e11 | −2.34464 | ||||||||
\(556\) | −2.94334e10 | −0.307994 | ||||||||
\(557\) | 3.66646e10 | 0.380913 | 0.190457 | − | 0.981696i | \(-0.439003\pi\) | ||||
0.190457 | + | 0.981696i | \(0.439003\pi\) | |||||||
\(558\) | 7.87934e9 | 0.0812742 | ||||||||
\(559\) | 1.44239e11i | 1.47719i | ||||||||
\(560\) | −5.43361e10 | −0.552505 | ||||||||
\(561\) | − | 1.91427e10i | − | 0.193264i | ||||||
\(562\) | −1.07882e11 | −1.08145 | ||||||||
\(563\) | 1.94465e11i | 1.93557i | 0.251780 | + | 0.967784i | \(0.418984\pi\) | ||||
−0.251780 | + | 0.967784i | \(0.581016\pi\) | |||||||
\(564\) | 5.18401e10i | 0.512329i | ||||||||
\(565\) | − | 1.78614e11i | − | 1.75275i | ||||||
\(566\) | − | 1.08900e11i | − | 1.06111i | ||||||
\(567\) | 1.06992e11 | 1.03519 | ||||||||
\(568\) | 2.65661e10 | 0.255231 | ||||||||
\(569\) | − | 1.32228e11i | − | 1.26146i | −0.776003 | − | 0.630730i | \(-0.782756\pi\) | ||
0.776003 | − | 0.630730i | \(-0.217244\pi\) | |||||||
\(570\) | 9.36300e10 | + | 8.94862e10i | 0.886983 | + | 0.847728i | ||||
\(571\) | 3.62336e10 | 0.340853 | 0.170426 | − | 0.985370i | \(-0.445485\pi\) | ||||
0.170426 | + | 0.985370i | \(0.445485\pi\) | |||||||
\(572\) | 2.61831e10i | 0.244589i | ||||||||
\(573\) | − | 1.88319e10i | − | 0.174693i | ||||||
\(574\) | 1.09474e11 | 1.00847 | ||||||||
\(575\) | −8.36829e10 | −0.765535 | ||||||||
\(576\) | −1.64475e9 | −0.0149421 | ||||||||
\(577\) | 9.54873e10 | 0.861475 | 0.430737 | − | 0.902477i | \(-0.358254\pi\) | ||||
0.430737 | + | 0.902477i | \(0.358254\pi\) | |||||||
\(578\) | 4.91272e10i | 0.440160i | ||||||||
\(579\) | 7.97885e10 | 0.709947 | ||||||||
\(580\) | − | 2.67305e10i | − | 0.236208i | ||||||
\(581\) | −5.53732e10 | −0.485954 | ||||||||
\(582\) | 6.03757e10i | 0.526224i | ||||||||
\(583\) | 3.79954e10i | 0.328894i | ||||||||
\(584\) | 6.51424e10i | 0.560031i | ||||||||
\(585\) | 3.77788e10i | 0.322570i | ||||||||
\(586\) | 1.49507e10 | 0.126786 | ||||||||
\(587\) | −1.95703e10 | −0.164833 | −0.0824167 | − | 0.996598i | \(-0.526264\pi\) | ||||
−0.0824167 | + | 0.996598i | \(0.526264\pi\) | |||||||
\(588\) | − | 2.40221e10i | − | 0.200956i | ||||||
\(589\) | −7.99579e10 | + | 8.36605e10i | −0.664355 | + | 0.695119i | ||||
\(590\) | −1.36495e11 | −1.12644 | ||||||||
\(591\) | − | 3.21222e10i | − | 0.263303i | ||||||
\(592\) | 4.14920e10i | 0.337814i | ||||||||
\(593\) | 7.21741e10 | 0.583664 | 0.291832 | − | 0.956470i | \(-0.405735\pi\) | ||||
0.291832 | + | 0.956470i | \(0.405735\pi\) | |||||||
\(594\) | −3.09992e10 | −0.249003 | ||||||||
\(595\) | −1.70190e11 | −1.35789 | ||||||||
\(596\) | −1.18270e11 | −0.937327 | ||||||||
\(597\) | 1.48783e11i | 1.17127i | ||||||||
\(598\) | −4.17509e10 | −0.326484 | ||||||||
\(599\) | − | 2.60479e10i | − | 0.202332i | −0.994870 | − | 0.101166i | \(-0.967743\pi\) | ||
0.994870 | − | 0.101166i | \(-0.0322573\pi\) | |||||||
\(600\) | −1.04027e11 | −0.802676 | ||||||||
\(601\) | − | 2.01515e11i | − | 1.54458i | −0.635270 | − | 0.772290i | \(-0.719111\pi\) | ||
0.635270 | − | 0.772290i | \(-0.280889\pi\) | |||||||
\(602\) | 1.12352e11i | 0.855450i | ||||||||
\(603\) | − | 1.42566e10i | − | 0.107832i | ||||||
\(604\) | − | 6.48629e10i | − | 0.487358i | ||||||
\(605\) | −2.19905e11 | −1.64140 | ||||||||
\(606\) | 9.45263e10 | 0.700910 | ||||||||
\(607\) | 1.85499e11i | 1.36643i | 0.730219 | + | 0.683213i | \(0.239418\pi\) | ||||
−0.730219 | + | 0.683213i | \(0.760582\pi\) | |||||||
\(608\) | 1.66906e10 | − | 1.74635e10i | 0.122140 | − | 0.127796i | ||||
\(609\) | 3.94077e10 | 0.286492 | ||||||||
\(610\) | 1.81554e11i | 1.31126i | ||||||||
\(611\) | − | 2.22090e11i | − | 1.59354i | ||||||
\(612\) | −5.15165e9 | −0.0367232 | ||||||||
\(613\) | 1.64157e10 | 0.116257 | 0.0581283 | − | 0.998309i | \(-0.481487\pi\) | ||||
0.0581283 | + | 0.998309i | \(0.481487\pi\) | |||||||
\(614\) | 7.10036e10 | 0.499582 | ||||||||
\(615\) | 2.96213e11 | 2.07064 | ||||||||
\(616\) | 2.03947e10i | 0.141643i | ||||||||
\(617\) | 2.57869e11 | 1.77934 | 0.889669 | − | 0.456606i | \(-0.150935\pi\) | ||||
0.889669 | + | 0.456606i | \(0.150935\pi\) | |||||||
\(618\) | 1.71064e11i | 1.17274i | ||||||||
\(619\) | 1.58897e11 | 1.08231 | 0.541155 | − | 0.840923i | \(-0.317987\pi\) | ||||
0.541155 | + | 0.840923i | \(0.317987\pi\) | |||||||
\(620\) | − | 1.31367e11i | − | 0.889037i | ||||||
\(621\) | − | 4.94306e10i | − | 0.332376i | ||||||
\(622\) | 7.41783e8i | 0.00495582i | ||||||||
\(623\) | − | 6.98527e10i | − | 0.463693i | ||||||
\(624\) | −5.19009e10 | −0.342323 | ||||||||
\(625\) | 3.71485e11 | 2.43456 | ||||||||
\(626\) | − | 4.56522e10i | − | 0.297279i | ||||||
\(627\) | 3.35881e10 | − | 3.51434e10i | 0.217328 | − | 0.227391i | ||||
\(628\) | −6.97559e9 | −0.0448479 | ||||||||
\(629\) | 1.29960e11i | 0.830246i | ||||||||
\(630\) | 2.94269e10i | 0.186802i | ||||||||
\(631\) | −2.87396e11 | −1.81285 | −0.906427 | − | 0.422363i | \(-0.861201\pi\) | ||||
−0.906427 | + | 0.422363i | \(0.861201\pi\) | |||||||
\(632\) | 7.68668e10 | 0.481804 | ||||||||
\(633\) | 1.82424e11 | 1.13623 | ||||||||
\(634\) | 1.07442e10 | 0.0664990 | ||||||||
\(635\) | − | 5.14086e9i | − | 0.0316185i | ||||||
\(636\) | −7.53155e10 | −0.460316 | ||||||||
\(637\) | 1.02914e11i | 0.625052i | ||||||||
\(638\) | −1.00331e10 | −0.0605555 | ||||||||
\(639\) | − | 1.43874e10i | − | 0.0862939i | ||||||
\(640\) | 2.74219e10i | 0.163447i | ||||||||
\(641\) | 2.16808e11i | 1.28423i | 0.766608 | + | 0.642116i | \(0.221943\pi\) | ||||
−0.766608 | + | 0.642116i | \(0.778057\pi\) | |||||||
\(642\) | − | 1.56738e11i | − | 0.922645i | ||||||
\(643\) | 1.00531e11 | 0.588107 | 0.294054 | − | 0.955789i | \(-0.404996\pi\) | ||||
0.294054 | + | 0.955789i | \(0.404996\pi\) | |||||||
\(644\) | −3.25209e10 | −0.189069 | ||||||||
\(645\) | 3.04000e11i | 1.75644i | ||||||||
\(646\) | 5.22779e10 | − | 5.46987e10i | 0.300184 | − | 0.314085i | ||||
\(647\) | 1.18417e11 | 0.675766 | 0.337883 | − | 0.941188i | \(-0.390289\pi\) | ||||
0.337883 | + | 0.941188i | \(0.390289\pi\) | |||||||
\(648\) | − | 5.39959e10i | − | 0.306239i | ||||||
\(649\) | 5.12326e10i | 0.288780i | ||||||||
\(650\) | 4.45665e11 | 2.49664 | ||||||||
\(651\) | 1.93669e11 | 1.07829 | ||||||||
\(652\) | −1.38160e10 | −0.0764527 | ||||||||
\(653\) | −1.42936e11 | −0.786119 | −0.393059 | − | 0.919513i | \(-0.628583\pi\) | ||||
−0.393059 | + | 0.919513i | \(0.628583\pi\) | |||||||
\(654\) | − | 1.61919e11i | − | 0.885091i | ||||||
\(655\) | −5.09709e11 | −2.76922 | ||||||||
\(656\) | − | 5.52486e10i | − | 0.298336i | ||||||
\(657\) | 3.52793e10 | 0.189347 | ||||||||
\(658\) | − | 1.72992e11i | − | 0.922831i | ||||||
\(659\) | − | 1.65523e11i | − | 0.877641i | −0.898575 | − | 0.438821i | \(-0.855396\pi\) | ||
0.898575 | − | 0.438821i | \(-0.144604\pi\) | |||||||
\(660\) | 5.51836e10i | 0.290827i | ||||||||
\(661\) | − | 1.29844e11i | − | 0.680165i | −0.940396 | − | 0.340083i | \(-0.889545\pi\) | ||
0.940396 | − | 0.340083i | \(-0.110455\pi\) | |||||||
\(662\) | −7.15074e10 | −0.372322 | ||||||||
\(663\) | −1.62562e11 | −0.841329 | ||||||||
\(664\) | 2.79453e10i | 0.143759i | ||||||||
\(665\) | −3.12446e11 | − | 2.98618e11i | −1.59768 | − | 1.52697i | ||||
\(666\) | 2.24709e10 | 0.114215 | ||||||||
\(667\) | − | 1.59986e10i | − | 0.0808310i | ||||||
\(668\) | − | 7.41211e10i | − | 0.372251i | ||||||
\(669\) | 1.00147e10 | 0.0499960 | ||||||||
\(670\) | −2.37691e11 | −1.17954 | ||||||||
\(671\) | 6.81453e10 | 0.336160 | ||||||||
\(672\) | −4.04270e10 | −0.198241 | ||||||||
\(673\) | − | 4.76706e10i | − | 0.232376i | −0.993227 | − | 0.116188i | \(-0.962933\pi\) | ||
0.993227 | − | 0.116188i | \(-0.0370674\pi\) | |||||||
\(674\) | 7.54468e10 | 0.365596 | ||||||||
\(675\) | 5.27641e11i | 2.54170i | ||||||||
\(676\) | 1.17937e11 | 0.564760 | ||||||||
\(677\) | 2.95654e11i | 1.40744i | 0.710480 | + | 0.703718i | \(0.248478\pi\) | ||||
−0.710480 | + | 0.703718i | \(0.751522\pi\) | |||||||
\(678\) | − | 1.32892e11i | − | 0.628896i | ||||||
\(679\) | − | 2.01476e11i | − | 0.947858i | ||||||
\(680\) | 8.58901e10i | 0.401705i | ||||||||
\(681\) | −1.88700e11 | −0.877371 | ||||||||
\(682\) | −4.93078e10 | −0.227918 | ||||||||
\(683\) | − | 1.73886e11i | − | 0.799064i | −0.916719 | − | 0.399532i | \(-0.869173\pi\) | ||
0.916719 | − | 0.399532i | \(-0.130827\pi\) | |||||||
\(684\) | −9.45774e9 | − | 9.03916e9i | −0.0432079 | − | 0.0412956i | ||||
\(685\) | −6.00315e11 | −2.72657 | ||||||||
\(686\) | − | 1.06990e11i | − | 0.483111i | ||||||
\(687\) | 2.54230e11i | 1.14130i | ||||||||
\(688\) | 5.67008e10 | 0.253067 | ||||||||
\(689\) | 3.22662e11 | 1.43176 | ||||||||
\(690\) | −8.79944e10 | −0.388203 | ||||||||
\(691\) | −3.55302e11 | −1.55842 | −0.779211 | − | 0.626761i | \(-0.784380\pi\) | ||||
−0.779211 | + | 0.626761i | \(0.784380\pi\) | |||||||
\(692\) | 1.52809e11i | 0.666385i | ||||||||
\(693\) | 1.10452e10 | 0.0478895 | ||||||||
\(694\) | − | 2.85118e11i | − | 1.22910i | ||||||
\(695\) | 2.65763e11 | 1.13908 | ||||||||
\(696\) | − | 1.98880e10i | − | 0.0847526i | ||||||
\(697\) | − | 1.73048e11i | − | 0.733222i | ||||||
\(698\) | 3.31750e11i | 1.39762i | ||||||||
\(699\) | 9.37799e10i | 0.392827i | ||||||||
\(700\) | 3.47141e11 | 1.44582 | ||||||||
\(701\) | 3.34079e11 | 1.38350 | 0.691748 | − | 0.722139i | \(-0.256841\pi\) | ||||
0.691748 | + | 0.722139i | \(0.256841\pi\) | |||||||
\(702\) | 2.63250e11i | 1.08398i | ||||||||
\(703\) | −2.28030e11 | + | 2.38589e11i | −0.933620 | + | 0.976853i | ||||
\(704\) | 1.02926e10 | 0.0419021 | ||||||||
\(705\) | − | 4.68078e11i | − | 1.89479i | ||||||
\(706\) | 4.58840e10i | 0.184690i | ||||||||
\(707\) | −3.15437e11 | −1.26251 | ||||||||
\(708\) | −1.01555e11 | −0.404173 | ||||||||
\(709\) | 3.05528e11 | 1.20911 | 0.604556 | − | 0.796563i | \(-0.293351\pi\) | ||||
0.604556 | + | 0.796563i | \(0.293351\pi\) | |||||||
\(710\) | −2.39872e11 | −0.943945 | ||||||||
\(711\) | − | 4.16289e10i | − | 0.162898i | ||||||
\(712\) | −3.52527e10 | −0.137174 | ||||||||
\(713\) | − | 7.86250e10i | − | 0.304230i | ||||||
\(714\) | −1.26624e11 | −0.487219 | ||||||||
\(715\) | − | 2.36414e11i | − | 0.904585i | ||||||
\(716\) | 1.36257e11i | 0.518450i | ||||||||
\(717\) | 7.65036e10i | 0.289471i | ||||||||
\(718\) | 1.06352e11i | 0.400172i | ||||||||
\(719\) | 9.46989e10 | 0.354347 | 0.177174 | − | 0.984180i | \(-0.443305\pi\) | ||||
0.177174 | + | 0.984180i | \(0.443305\pi\) | |||||||
\(720\) | 1.48509e10 | 0.0552616 | ||||||||
\(721\) | − | 5.70844e11i | − | 2.11240i | ||||||
\(722\) | 1.91950e11 | − | 8.69187e9i | 0.706383 | − | 0.0319863i | ||||
\(723\) | −2.11623e11 | −0.774479 | ||||||||
\(724\) | − | 2.26044e11i | − | 0.822693i | ||||||
\(725\) | 1.70775e11i | 0.618119i | ||||||||
\(726\) | −1.63613e11 | −0.588942 | ||||||||
\(727\) | −2.03292e11 | −0.727752 | −0.363876 | − | 0.931447i | \(-0.618547\pi\) | ||||
−0.363876 | + | 0.931447i | \(0.618547\pi\) | |||||||
\(728\) | 1.73195e11 | 0.616609 | ||||||||
\(729\) | −3.07637e11 | −1.08925 | ||||||||
\(730\) | − | 5.88188e11i | − | 2.07121i | ||||||
\(731\) | 1.77597e11 | 0.621964 | ||||||||
\(732\) | 1.35080e11i | 0.470485i | ||||||||
\(733\) | −2.58631e11 | −0.895912 | −0.447956 | − | 0.894056i | \(-0.647848\pi\) | ||||
−0.447956 | + | 0.894056i | \(0.647848\pi\) | |||||||
\(734\) | 3.01413e10i | 0.103843i | ||||||||
\(735\) | 2.16902e11i | 0.743214i | ||||||||
\(736\) | 1.64124e10i | 0.0559320i | ||||||||
\(737\) | 8.92158e10i | 0.302393i | ||||||||
\(738\) | −2.99210e10 | −0.100868 | ||||||||
\(739\) | −7.22594e10 | −0.242280 | −0.121140 | − | 0.992635i | \(-0.538655\pi\) | ||||
−0.121140 | + | 0.992635i | \(0.538655\pi\) | |||||||
\(740\) | − | 3.74642e11i | − | 1.24937i | ||||||
\(741\) | −2.98443e11 | − | 2.85235e11i | −0.989894 | − | 0.946084i | ||||
\(742\) | 2.51330e11 | 0.829143 | ||||||||
\(743\) | − | 4.17980e11i | − | 1.37151i | −0.727830 | − | 0.685757i | \(-0.759471\pi\) | ||
0.727830 | − | 0.685757i | \(-0.240529\pi\) | |||||||
\(744\) | − | 9.77394e10i | − | 0.318990i | ||||||
\(745\) | 1.06790e12 | 3.46660 | ||||||||
\(746\) | −1.94259e11 | −0.627228 | ||||||||
\(747\) | 1.51344e10 | 0.0486051 | ||||||||
\(748\) | 3.22383e10 | 0.102983 | ||||||||
\(749\) | 5.23040e11i | 1.66191i | ||||||||
\(750\) | 5.51075e11 | 1.74167 | ||||||||
\(751\) | − | 1.85959e11i | − | 0.584599i | −0.956327 | − | 0.292299i | \(-0.905580\pi\) | ||
0.956327 | − | 0.292299i | \(-0.0944204\pi\) | |||||||
\(752\) | −8.73041e10 | −0.273000 | ||||||||
\(753\) | − | 2.58193e11i | − | 0.803091i | ||||||
\(754\) | 8.52027e10i | 0.263614i | ||||||||
\(755\) | 5.85665e11i | 1.80244i | ||||||||
\(756\) | 2.05052e11i | 0.627737i | ||||||||
\(757\) | −4.78405e11 | −1.45684 | −0.728421 | − | 0.685130i | \(-0.759746\pi\) | ||||
−0.728421 | + | 0.685130i | \(0.759746\pi\) | |||||||
\(758\) | 1.02391e11 | 0.310159 | ||||||||
\(759\) | 3.30282e10i | 0.0995216i | ||||||||
\(760\) | −1.50704e11 | + | 1.57683e11i | −0.451722 | + | 0.472639i | ||||
\(761\) | 2.99794e10 | 0.0893891 | 0.0446946 | − | 0.999001i | \(-0.485769\pi\) | ||||
0.0446946 | + | 0.999001i | \(0.485769\pi\) | |||||||
\(762\) | − | 3.82489e9i | − | 0.0113449i | ||||||
\(763\) | 5.40330e11i | 1.59427i | ||||||||
\(764\) | 3.17150e10 | 0.0930874 | ||||||||
\(765\) | 4.65156e10 | 0.135817 | ||||||||
\(766\) | 1.08385e11 | 0.314813 | ||||||||
\(767\) | 4.35075e11 | 1.25714 | ||||||||
\(768\) | 2.04024e10i | 0.0586456i | ||||||||
\(769\) | −1.36083e11 | −0.389134 | −0.194567 | − | 0.980889i | \(-0.562330\pi\) | ||||
−0.194567 | + | 0.980889i | \(0.562330\pi\) | |||||||
\(770\) | − | 1.84149e11i | − | 0.523851i | ||||||
\(771\) | 8.23714e10 | 0.233109 | ||||||||
\(772\) | 1.34372e11i | 0.378304i | ||||||||
\(773\) | 3.83430e11i | 1.07391i | 0.843611 | + | 0.536955i | \(0.180425\pi\) | ||||
−0.843611 | + | 0.536955i | \(0.819575\pi\) | |||||||
\(774\) | − | 3.07076e10i | − | 0.0855621i | ||||||
\(775\) | 8.39273e11i | 2.32647i | ||||||||
\(776\) | −1.01679e11 | −0.280404 | ||||||||
\(777\) | 5.52320e11 | 1.51533 | ||||||||
\(778\) | 2.48195e11i | 0.677446i | ||||||||
\(779\) | 3.03633e11 | − | 3.17693e11i | 0.824515 | − | 0.862696i | ||||
\(780\) | 4.68627e11 | 1.26604 | ||||||||
\(781\) | 9.00346e10i | 0.241994i | ||||||||
\(782\) | 5.14064e10i | 0.137464i | ||||||||
\(783\) | −1.00875e11 | −0.268371 | ||||||||
\(784\) | 4.04557e10 | 0.107082 | ||||||||
\(785\) | 6.29845e10 | 0.165865 | ||||||||
\(786\) | −3.79232e11 | −0.993609 | ||||||||
\(787\) | − | 6.40375e11i | − | 1.66930i | −0.550778 | − | 0.834652i | \(-0.685669\pi\) | ||
0.550778 | − | 0.834652i | \(-0.314331\pi\) | |||||||
\(788\) | 5.40972e10 | 0.140304 | ||||||||
\(789\) | 2.60674e11i | 0.672651i | ||||||||
\(790\) | −6.94051e11 | −1.78190 | ||||||||
\(791\) | 4.43464e11i | 1.13280i | ||||||||
\(792\) | − | 5.57420e9i | − | 0.0141671i | ||||||
\(793\) | − | 5.78700e11i | − | 1.46339i | ||||||
\(794\) | − | 5.71420e10i | − | 0.143772i | ||||||
\(795\) | 6.80044e11 | 1.70243 | ||||||||
\(796\) | −2.50567e11 | −0.624124 | ||||||||
\(797\) | − | 2.74440e11i | − | 0.680165i | −0.940396 | − | 0.340083i | \(-0.889545\pi\) | ||
0.940396 | − | 0.340083i | \(-0.110455\pi\) | |||||||
\(798\) | −2.32465e11 | − | 2.22177e11i | −0.573253 | − | 0.547883i | ||||
\(799\) | −2.73451e11 | −0.670954 | ||||||||
\(800\) | − | 1.75192e11i | − | 0.427715i | ||||||
\(801\) | 1.90918e10i | 0.0463786i | ||||||||
\(802\) | −2.87408e11 | −0.694707 | ||||||||
\(803\) | −2.20773e11 | −0.530986 | ||||||||
\(804\) | −1.76846e11 | −0.423225 | ||||||||
\(805\) | 2.93640e11 | 0.699249 | ||||||||
\(806\) | 4.18729e11i | 0.992185i | ||||||||
\(807\) | 2.57306e11 | 0.606674 | ||||||||
\(808\) | 1.59192e11i | 0.373488i | ||||||||
\(809\) | −3.21744e11 | −0.751133 | −0.375567 | − | 0.926795i | \(-0.622552\pi\) | ||||
−0.375567 | + | 0.926795i | \(0.622552\pi\) | |||||||
\(810\) | 4.87543e11i | 1.13259i | ||||||||
\(811\) | − | 5.63846e11i | − | 1.30340i | −0.758478 | − | 0.651699i | \(-0.774056\pi\) | ||
0.758478 | − | 0.651699i | \(-0.225944\pi\) | |||||||
\(812\) | 6.63667e10i | 0.152660i | ||||||||
\(813\) | 1.70247e11i | 0.389688i | ||||||||
\(814\) | −1.40620e11 | −0.320293 | ||||||||
\(815\) | 1.24749e11 | 0.282752 | ||||||||
\(816\) | 6.39037e10i | 0.144134i | ||||||||
\(817\) | 3.26044e11 | + | 3.11614e11i | 0.731792 | + | 0.699405i | ||||
\(818\) | 5.40367e11 | 1.20691 | ||||||||
\(819\) | − | 9.37974e10i | − | 0.208476i | ||||||
\(820\) | 4.98854e11i | 1.10336i | ||||||||
\(821\) | −6.95776e11 | −1.53143 | −0.765714 | − | 0.643181i | \(-0.777614\pi\) | ||||
−0.765714 | + | 0.643181i | \(0.777614\pi\) | |||||||
\(822\) | −4.46645e11 | −0.978307 | ||||||||
\(823\) | 6.32636e11 | 1.37897 | 0.689485 | − | 0.724300i | \(-0.257837\pi\) | ||||
0.689485 | + | 0.724300i | \(0.257837\pi\) | |||||||
\(824\) | −2.88089e11 | −0.624911 | ||||||||
\(825\) | − | 3.52555e11i | − | 0.761046i | ||||||
\(826\) | 3.38892e11 | 0.728015 | ||||||||
\(827\) | − | 7.69772e11i | − | 1.64566i | −0.568287 | − | 0.822830i | \(-0.692394\pi\) | ||
0.568287 | − | 0.822830i | \(-0.307606\pi\) | |||||||
\(828\) | 8.88848e9 | 0.0189106 | ||||||||
\(829\) | 4.60248e11i | 0.974482i | 0.873268 | + | 0.487241i | \(0.161997\pi\) | ||||
−0.873268 | + | 0.487241i | \(0.838003\pi\) | |||||||
\(830\) | − | 2.52326e11i | − | 0.531678i | ||||||
\(831\) | − | 5.85647e11i | − | 1.22809i | ||||||
\(832\) | − | 8.74066e10i | − | 0.182411i | ||||||
\(833\) | 1.26714e11 | 0.263175 | ||||||||
\(834\) | 1.97732e11 | 0.408707 | ||||||||
\(835\) | 6.69260e11i | 1.37673i | ||||||||
\(836\) | 5.91852e10 | + | 5.65658e10i | 0.121168 | + | 0.115805i | ||||
\(837\) | −4.95750e11 | −1.01009 | ||||||||
\(838\) | 4.43399e11i | 0.899122i | ||||||||
\(839\) | − | 5.13894e11i | − | 1.03711i | −0.855044 | − | 0.518556i | \(-0.826470\pi\) | ||
0.855044 | − | 0.518556i | \(-0.173530\pi\) | |||||||
\(840\) | 3.65026e11 | 0.733174 | ||||||||
\(841\) | 4.67597e11 | 0.934734 | ||||||||
\(842\) | 1.44541e11 | 0.287570 | ||||||||
\(843\) | 7.24746e11 | 1.43508 | ||||||||
\(844\) | 3.07220e11i | 0.605453i | ||||||||
\(845\) | −1.06489e12 | −2.08870 | ||||||||
\(846\) | 4.72814e10i | 0.0923016i | ||||||||
\(847\) | 5.45983e11 | 1.06083 | ||||||||
\(848\) | − | 1.26839e11i | − | 0.245285i | ||||||
\(849\) | 7.31580e11i | 1.40809i | ||||||||
\(850\) | − | 5.48732e11i | − | 1.05120i | ||||||
\(851\) | − | 2.24229e11i | − | 0.427536i | ||||||
\(852\) | −1.78469e11 | −0.338692 | ||||||||
\(853\) | −7.41234e10 | −0.140010 | −0.0700050 | − | 0.997547i | \(-0.522302\pi\) | ||||
−0.0700050 | + | 0.997547i | \(0.522302\pi\) | |||||||
\(854\) | − | 4.50765e11i | − | 0.847459i | ||||||
\(855\) | 8.53965e10 | + | 8.16171e10i | 0.159800 | + | 0.152727i | ||||
\(856\) | 2.63964e11 | 0.491642 | ||||||||
\(857\) | 8.78805e11i | 1.62918i | 0.580037 | + | 0.814590i | \(0.303038\pi\) | ||||
−0.580037 | + | 0.814590i | \(0.696962\pi\) | |||||||
\(858\) | − | 1.75896e11i | − | 0.324569i | ||||||
\(859\) | −4.07221e11 | −0.747923 | −0.373962 | − | 0.927444i | \(-0.622001\pi\) | ||||
−0.373962 | + | 0.927444i | \(0.622001\pi\) | |||||||
\(860\) | −5.11967e11 | −0.935941 | ||||||||
\(861\) | −7.35441e11 | −1.33824 | ||||||||
\(862\) | −3.98694e11 | −0.722122 | ||||||||
\(863\) | 1.98526e11i | 0.357911i | 0.983857 | + | 0.178955i | \(0.0572717\pi\) | ||||
−0.983857 | + | 0.178955i | \(0.942728\pi\) | |||||||
\(864\) | 1.03484e11 | 0.185703 | ||||||||
\(865\) | − | 1.37976e12i | − | 2.46455i | ||||||
\(866\) | 9.28227e10 | 0.165038 | ||||||||
\(867\) | − | 3.30033e11i | − | 0.584092i | ||||||
\(868\) | 3.26159e11i | 0.574580i | ||||||||
\(869\) | 2.60508e11i | 0.456816i | ||||||||
\(870\) | 1.79574e11i | 0.313448i | ||||||||
\(871\) | 7.57634e11 | 1.31640 | ||||||||
\(872\) | 2.72689e11 | 0.471631 | ||||||||
\(873\) | 5.50665e10i | 0.0948048i | ||||||||
\(874\) | −9.01985e10 | + | 9.43753e10i | −0.154580 | + | 0.161738i | ||||
\(875\) | −1.83895e12 | −3.13717 | ||||||||
\(876\) | − | 4.37622e11i | − | 0.743161i | ||||||
\(877\) | − | 9.45892e11i | − | 1.59898i | −0.600679 | − | 0.799490i | \(-0.705103\pi\) | ||
0.600679 | − | 0.799490i | \(-0.294897\pi\) | |||||||
\(878\) | −7.52405e8 | −0.00126612 | ||||||||
\(879\) | −1.00438e11 | −0.168245 | ||||||||
\(880\) | −9.29350e10 | −0.154970 | ||||||||
\(881\) | −8.71114e11 | −1.44601 | −0.723005 | − | 0.690843i | \(-0.757240\pi\) | ||||
−0.723005 | + | 0.690843i | \(0.757240\pi\) | |||||||
\(882\) | − | 2.19096e10i | − | 0.0362044i | ||||||
\(883\) | −7.40621e11 | −1.21830 | −0.609148 | − | 0.793056i | \(-0.708489\pi\) | ||||
−0.609148 | + | 0.793056i | \(0.708489\pi\) | |||||||
\(884\) | − | 2.73772e11i | − | 0.448312i | ||||||
\(885\) | 9.16966e11 | 1.49479 | ||||||||
\(886\) | − | 9.21191e10i | − | 0.149491i | ||||||
\(887\) | 1.27828e11i | 0.206506i | 0.994655 | + | 0.103253i | \(0.0329251\pi\) | ||||
−0.994655 | + | 0.103253i | \(0.967075\pi\) | |||||||
\(888\) | − | 2.78740e11i | − | 0.448278i | ||||||
\(889\) | 1.27638e10i | 0.0204349i | ||||||||
\(890\) | 3.18306e11 | 0.507323 | ||||||||
\(891\) | 1.82996e11 | 0.290356 | ||||||||
\(892\) | 1.68659e10i | 0.0266409i | ||||||||
\(893\) | −5.02020e11 | − | 4.79802e11i | −0.789433 | − | 0.754495i | ||||
\(894\) | 7.94533e11 | 1.24383 | ||||||||
\(895\) | − | 1.23030e12i | − | 1.91743i | ||||||
\(896\) | − | 6.80833e10i | − | 0.105635i | ||||||
\(897\) | 2.80480e11 | 0.433243 | ||||||||
\(898\) | −1.06284e11 | −0.163441 | ||||||||
\(899\) | −1.60453e11 | −0.245646 | ||||||||
\(900\) | −9.48790e10 | −0.144611 | ||||||||
\(901\) | − | 3.97282e11i | − | 0.602837i | ||||||
\(902\) | 1.87242e11 | 0.282863 | ||||||||
\(903\) | − | 7.54773e11i | − | 1.13518i | ||||||
\(904\) | 2.23804e11 | 0.335114 | ||||||||
\(905\) | 2.04101e12i | 3.04264i | ||||||||
\(906\) | 4.35745e11i | 0.646724i | ||||||||
\(907\) | − | 4.56362e9i | − | 0.00674343i | −0.999994 | − | 0.00337171i | \(-0.998927\pi\) | ||
0.999994 | − | 0.00337171i | \(-0.00107325\pi\) | |||||||
\(908\) | − | 3.17791e11i | − | 0.467517i | ||||||
\(909\) | 8.62140e10 | 0.126276 | ||||||||
\(910\) | −1.56382e12 | −2.28046 | ||||||||
\(911\) | 7.74104e11i | 1.12390i | 0.827173 | + | 0.561948i | \(0.189948\pi\) | ||||
−0.827173 | + | 0.561948i | \(0.810052\pi\) | |||||||
\(912\) | −1.12126e11 | + | 1.17319e11i | −0.162080 | + | 0.169585i | ||||
\(913\) | −9.47088e10 | −0.136304 | ||||||||
\(914\) | 3.54811e11i | 0.508408i | ||||||||
\(915\) | − | 1.21967e12i | − | 1.74004i | ||||||
\(916\) | −4.28151e11 | −0.608156 | ||||||||
\(917\) | 1.26551e12 | 1.78973 | ||||||||
\(918\) | 3.24130e11 | 0.456403 | ||||||||
\(919\) | 1.28875e12 | 1.80678 | 0.903391 | − | 0.428818i | \(-0.141070\pi\) | ||||
0.903391 | + | 0.428818i | \(0.141070\pi\) | |||||||
\(920\) | − | 1.48192e11i | − | 0.206858i | ||||||
\(921\) | −4.76998e11 | −0.662945 | ||||||||
\(922\) | − | 2.97979e10i | − | 0.0412346i | ||||||
\(923\) | 7.64587e11 | 1.05346 | ||||||||
\(924\) | − | 1.37010e11i | − | 0.187960i | ||||||
\(925\) | 2.39350e12i | 3.26939i | ||||||||
\(926\) | − | 1.00191e12i | − | 1.36265i | ||||||
\(927\) | 1.56021e11i | 0.211283i | ||||||||
\(928\) | 3.34934e10 | 0.0451614 | ||||||||
\(929\) | −7.44599e11 | −0.999677 | −0.499838 | − | 0.866119i | \(-0.666607\pi\) | ||||
−0.499838 | + | 0.866119i | \(0.666607\pi\) | |||||||
\(930\) | 8.82515e11i | 1.17975i | ||||||||
\(931\) | 2.32630e11 | + | 2.22335e11i | 0.309647 | + | 0.295943i | ||||
\(932\) | −1.57935e11 | −0.209322 | ||||||||
\(933\) | − | 4.98325e9i | − | 0.00657637i | ||||||
\(934\) | − | 3.73328e11i | − | 0.490573i | ||||||
\(935\) | −2.91088e11 | −0.380871 | ||||||||
\(936\) | −4.73369e10 | −0.0616732 | ||||||||
\(937\) | 5.69314e11 | 0.738573 | 0.369287 | − | 0.929316i | \(-0.379602\pi\) | ||||
0.369287 | + | 0.929316i | \(0.379602\pi\) | |||||||
\(938\) | 5.90141e11 | 0.762333 | ||||||||
\(939\) | 3.06689e11i | 0.394490i | ||||||||
\(940\) | 7.88293e11 | 1.00966 | ||||||||
\(941\) | 1.43384e11i | 0.182869i | 0.995811 | + | 0.0914347i | \(0.0291453\pi\) | ||||
−0.995811 | + | 0.0914347i | \(0.970855\pi\) | |||||||
\(942\) | 4.68615e10 | 0.0595131 | ||||||||
\(943\) | 2.98571e11i | 0.377573i | ||||||||
\(944\) | − | 1.71029e11i | − | 0.215368i | ||||||
\(945\) | − | 1.85147e12i | − | 2.32162i | ||||||
\(946\) | 1.92164e11i | 0.239942i | ||||||||
\(947\) | −6.81778e11 | −0.847702 | −0.423851 | − | 0.905732i | \(-0.639322\pi\) | ||||
−0.423851 | + | 0.905732i | \(0.639322\pi\) | |||||||
\(948\) | −5.16386e11 | −0.639354 | ||||||||
\(949\) | 1.87483e12i | 2.31152i | ||||||||
\(950\) | 9.62813e11 | − | 1.00740e12i | 1.18208 | − | 1.23682i | ||||
\(951\) | −7.21785e10 | −0.0882442 | ||||||||
\(952\) | − | 2.13249e11i | − | 0.259620i | ||||||
\(953\) | 1.16217e12i | 1.40896i | 0.709725 | + | 0.704479i | \(0.248819\pi\) | ||||
−0.709725 | + | 0.704479i | \(0.751181\pi\) | |||||||
\(954\) | −6.86926e10 | −0.0829309 | ||||||||
\(955\) | −2.86363e11 | −0.344274 | ||||||||
\(956\) | −1.28840e11 | −0.154248 | ||||||||
\(957\) | 6.74018e10 | 0.0803571 | ||||||||
\(958\) | 4.83535e11i | 0.574072i | ||||||||
\(959\) | 1.49047e12 | 1.76217 | ||||||||
\(960\) | − | 1.84219e11i | − | 0.216894i | ||||||
\(961\) | 6.43439e10 | 0.0754421 | ||||||||
\(962\) | 1.19416e12i | 1.39432i | ||||||||
\(963\) | − | 1.42955e11i | − | 0.166224i | ||||||
\(964\) | − | 3.56396e11i | − | 0.412690i | ||||||
\(965\) | − | 1.21328e12i | − | 1.39911i | ||||||
\(966\) | 2.18473e11 | 0.250894 | ||||||||
\(967\) | −1.33496e11 | −0.152673 | −0.0763364 | − | 0.997082i | \(-0.524322\pi\) | ||||
−0.0763364 | + | 0.997082i | \(0.524322\pi\) | |||||||
\(968\) | − | 2.75542e11i | − | 0.313824i | ||||||
\(969\) | −3.51199e11 | + | 3.67462e11i | −0.398344 | + | 0.416790i | ||||
\(970\) | 9.18088e11 | 1.03704 | ||||||||
\(971\) | 7.76210e11i | 0.873177i | 0.899661 | + | 0.436589i | \(0.143813\pi\) | ||||
−0.899661 | + | 0.436589i | \(0.856187\pi\) | |||||||
\(972\) | − | 1.06104e11i | − | 0.118869i | ||||||
\(973\) | −6.59838e11 | −0.736183 | ||||||||
\(974\) | −3.39270e11 | −0.376972 | ||||||||
\(975\) | −2.99395e12 | −3.31303 | ||||||||
\(976\) | −2.27488e11 | −0.250703 | ||||||||
\(977\) | − | 5.28023e10i | − | 0.0579528i | −0.999580 | − | 0.0289764i | \(-0.990775\pi\) | ||
0.999580 | − | 0.0289764i | \(-0.00922477\pi\) | |||||||
\(978\) | 9.28152e10 | 0.101453 | ||||||||
\(979\) | − | 1.19474e11i | − | 0.130060i | ||||||
\(980\) | −3.65285e11 | −0.396030 | ||||||||
\(981\) | − | 1.47681e11i | − | 0.159459i | ||||||
\(982\) | − | 1.42651e11i | − | 0.153401i | ||||||
\(983\) | 3.57496e11i | 0.382875i | 0.981505 | + | 0.191438i | \(0.0613150\pi\) | ||||
−0.981505 | + | 0.191438i | \(0.938685\pi\) | |||||||
\(984\) | 3.71156e11i | 0.395892i | ||||||||
\(985\) | −4.88458e11 | −0.518898 | ||||||||
\(986\) | 1.04907e11 | 0.110993 | ||||||||
\(987\) | 1.16215e12i | 1.22460i | ||||||||
\(988\) | 4.80365e11 | − | 5.02609e11i | 0.504132 | − | 0.527476i | ||||
\(989\) | −3.06420e11 | −0.320281 | ||||||||
\(990\) | 5.03309e10i | 0.0523955i | ||||||||
\(991\) | 1.23547e12i | 1.28097i | 0.767972 | + | 0.640484i | \(0.221266\pi\) | ||||
−0.767972 | + | 0.640484i | \(0.778734\pi\) | |||||||
\(992\) | 1.64603e11 | 0.169978 | ||||||||
\(993\) | 4.80382e11 | 0.494071 | ||||||||
\(994\) | 5.95557e11 | 0.610068 | ||||||||
\(995\) | 2.26243e12 | 2.30825 | ||||||||
\(996\) | − | 1.87735e11i | − | 0.190769i | ||||||
\(997\) | −5.40410e11 | −0.546944 | −0.273472 | − | 0.961880i | \(-0.588172\pi\) | ||||
−0.273472 | + | 0.961880i | \(0.588172\pi\) | |||||||
\(998\) | − | 4.18748e11i | − | 0.422115i | ||||||
\(999\) | −1.41382e12 | −1.41949 |
(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 | 38.9.b.a.37.5 | ✓ | 12 | |
3.2 | odd | 2 | 342.9.d.a.37.7 | 12 | |||
4.3 | odd | 2 | 304.9.e.e.113.3 | 12 | |||
19.18 | odd | 2 | inner | 38.9.b.a.37.8 | yes | 12 | |
57.56 | even | 2 | 342.9.d.a.37.1 | 12 | |||
76.75 | even | 2 | 304.9.e.e.113.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.9.b.a.37.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
38.9.b.a.37.8 | yes | 12 | 19.18 | odd | 2 | inner | |
304.9.e.e.113.3 | 12 | 4.3 | odd | 2 | |||
304.9.e.e.113.10 | 12 | 76.75 | even | 2 | |||
342.9.d.a.37.1 | 12 | 57.56 | even | 2 | |||
342.9.d.a.37.7 | 12 | 3.2 | odd | 2 |