Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,7,Mod(6,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.6");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(1.61037858534\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-510}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 510 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 6.2 | ||
Root | \(22.5832i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.6 |
Dual form | 7.7.b.b.6.1 |
$q$-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 \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 45.1664i | 1.67283i | 0.548098 | + | 0.836414i | \(0.315352\pi\) | ||||
−0.548098 | + | 0.836414i | \(0.684648\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 45.1664i | − | 0.361331i | −0.983545 | − | 0.180665i | \(-0.942175\pi\) | ||
0.983545 | − | 0.180665i | \(-0.0578251\pi\) | |||||||
\(6\) | − | 361.331i | − | 1.67283i | ||||||
\(7\) | 133.000 | + | 316.165i | 0.387755 | + | 0.921762i | ||||
\(8\) | 512.000 | 1.00000 | ||||||||
\(9\) | −1311.00 | −1.79835 | ||||||||
\(10\) | 361.331i | 0.361331i | ||||||||
\(11\) | 874.000 | 0.656649 | 0.328325 | − | 0.944565i | \(-0.393516\pi\) | ||||
0.328325 | + | 0.944565i | \(0.393516\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2213.15i | 1.00735i | 0.863893 | + | 0.503676i | \(0.168019\pi\) | ||||
−0.863893 | + | 0.503676i | \(0.831981\pi\) | |||||||
\(14\) | −1064.00 | − | 2529.32i | −0.387755 | − | 0.921762i | ||||
\(15\) | 2040.00 | 0.604444 | ||||||||
\(16\) | −4096.00 | −1.00000 | ||||||||
\(17\) | − | 5961.96i | − | 1.21351i | −0.794890 | − | 0.606753i | \(-0.792472\pi\) | ||
0.794890 | − | 0.606753i | \(-0.207528\pi\) | |||||||
\(18\) | 10488.0 | 1.79835 | ||||||||
\(19\) | 3116.48i | 0.454363i | 0.973852 | + | 0.227182i | \(0.0729511\pi\) | ||||
−0.973852 | + | 0.227182i | \(0.927049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14280.0 | + | 6007.13i | −1.54195 | + | 0.648648i | ||||
\(22\) | −6992.00 | −0.656649 | ||||||||
\(23\) | 4738.00 | 0.389414 | 0.194707 | − | 0.980861i | \(-0.437624\pi\) | ||||
0.194707 | + | 0.980861i | \(0.437624\pi\) | |||||||
\(24\) | 23125.2i | 1.67283i | ||||||||
\(25\) | 13585.0 | 0.869440 | ||||||||
\(26\) | − | 17705.2i | − | 1.00735i | ||||||
\(27\) | − | 26286.8i | − | 1.33551i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11146.0 | 0.457009 | 0.228505 | − | 0.973543i | \(-0.426616\pi\) | ||||
0.228505 | + | 0.973543i | \(0.426616\pi\) | |||||||
\(30\) | −16320.0 | −0.604444 | ||||||||
\(31\) | − | 27461.1i | − | 0.921793i | −0.887454 | − | 0.460897i | \(-0.847528\pi\) | ||
0.887454 | − | 0.460897i | \(-0.152472\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 39475.4i | 1.09846i | ||||||||
\(34\) | 47695.7i | 1.21351i | ||||||||
\(35\) | 14280.0 | − | 6007.13i | 0.333061 | − | 0.140108i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3002.00 | 0.0592660 | 0.0296330 | − | 0.999561i | \(-0.490566\pi\) | ||||
0.0296330 | + | 0.999561i | \(0.490566\pi\) | |||||||
\(38\) | − | 24931.8i | − | 0.454363i | ||||||
\(39\) | −99960.0 | −1.68513 | ||||||||
\(40\) | − | 23125.2i | − | 0.361331i | ||||||
\(41\) | 57541.9i | 0.834897i | 0.908701 | + | 0.417449i | \(0.137076\pi\) | ||||
−0.908701 | + | 0.417449i | \(0.862924\pi\) | |||||||
\(42\) | 114240. | − | 48057.0i | 1.54195 | − | 0.648648i | ||||
\(43\) | 31418.0 | 0.395160 | 0.197580 | − | 0.980287i | \(-0.436692\pi\) | ||||
0.197580 | + | 0.980287i | \(0.436692\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 59213.1i | 0.649801i | ||||||||
\(46\) | −37904.0 | −0.389414 | ||||||||
\(47\) | − | 72446.8i | − | 0.697792i | −0.937161 | − | 0.348896i | \(-0.886557\pi\) | ||
0.937161 | − | 0.348896i | \(-0.113443\pi\) | |||||||
\(48\) | − | 185001.i | − | 1.67283i | ||||||
\(49\) | −82271.0 | + | 84099.8i | −0.699292 | + | 0.714836i | ||||
\(50\) | −108680. | −0.869440 | ||||||||
\(51\) | 269280. | 2.02999 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −76406.0 | −0.513216 | −0.256608 | − | 0.966516i | \(-0.582605\pi\) | ||||
−0.256608 | + | 0.966516i | \(0.582605\pi\) | |||||||
\(54\) | 210295.i | 1.33551i | ||||||||
\(55\) | − | 39475.4i | − | 0.237268i | ||||||
\(56\) | 68096.0 | + | 161876.i | 0.387755 | + | 0.921762i | ||||
\(57\) | −140760. | −0.760072 | ||||||||
\(58\) | −89168.0 | −0.457009 | ||||||||
\(59\) | 113232.i | 0.551332i | 0.961253 | + | 0.275666i | \(0.0888984\pi\) | ||||
−0.961253 | + | 0.275666i | \(0.911102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 275108.i | − | 1.21203i | −0.795452 | − | 0.606016i | \(-0.792767\pi\) | ||
0.795452 | − | 0.606016i | \(-0.207233\pi\) | |||||||
\(62\) | 219689.i | 0.921793i | ||||||||
\(63\) | −174363. | − | 414492.i | −0.697321 | − | 1.65766i | ||||
\(64\) | 262144. | 1.00000 | ||||||||
\(65\) | 99960.0 | 0.363987 | ||||||||
\(66\) | − | 315803.i | − | 1.09846i | ||||||
\(67\) | 495242. | 1.64662 | 0.823309 | − | 0.567593i | \(-0.192125\pi\) | ||||
0.823309 | + | 0.567593i | \(0.192125\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 213998.i | 0.651423i | ||||||||
\(70\) | −114240. | + | 48057.0i | −0.333061 | + | 0.140108i | ||||
\(71\) | −184406. | −0.515229 | −0.257614 | − | 0.966248i | \(-0.582936\pi\) | ||||
−0.257614 | + | 0.966248i | \(0.582936\pi\) | |||||||
\(72\) | −671232. | −1.79835 | ||||||||
\(73\) | − | 60974.6i | − | 0.156740i | −0.996924 | − | 0.0783701i | \(-0.975028\pi\) | ||
0.996924 | − | 0.0783701i | \(-0.0249716\pi\) | |||||||
\(74\) | −24016.0 | −0.0592660 | ||||||||
\(75\) | 613585.i | 1.45442i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 116242. | + | 276328.i | 0.254619 | + | 0.605275i | ||||
\(78\) | 799680. | 1.68513 | ||||||||
\(79\) | −534934. | −1.08497 | −0.542486 | − | 0.840065i | \(-0.682517\pi\) | ||||
−0.542486 | + | 0.840065i | \(0.682517\pi\) | |||||||
\(80\) | 185001.i | 0.361331i | ||||||||
\(81\) | 231561. | 0.435723 | ||||||||
\(82\) | − | 460336.i | − | 0.834897i | ||||||
\(83\) | − | 714848.i | − | 1.25020i | −0.780545 | − | 0.625100i | \(-0.785058\pi\) | ||
0.780545 | − | 0.625100i | \(-0.214942\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −269280. | −0.438478 | ||||||||
\(86\) | −251344. | −0.395160 | ||||||||
\(87\) | 503424.i | 0.764498i | ||||||||
\(88\) | 447488. | 0.656649 | ||||||||
\(89\) | − | 629529.i | − | 0.892988i | −0.894787 | − | 0.446494i | \(-0.852672\pi\) | ||
0.894787 | − | 0.446494i | \(-0.147328\pi\) | |||||||
\(90\) | − | 473705.i | − | 0.649801i | ||||||
\(91\) | −699720. | + | 294349.i | −0.928539 | + | 0.390606i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.24032e6 | 1.54200 | ||||||||
\(94\) | 579575.i | 0.697792i | ||||||||
\(95\) | 140760. | 0.164176 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 814440.i | 0.892368i | 0.894941 | + | 0.446184i | \(0.147217\pi\) | ||||
−0.894941 | + | 0.446184i | \(0.852783\pi\) | |||||||
\(98\) | 658168. | − | 672798.i | 0.699292 | − | 0.714836i | ||||
\(99\) | −1.14581e6 | −1.18089 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.95195e6i | − | 1.89455i | −0.320425 | − | 0.947274i | \(-0.603826\pi\) | ||
0.320425 | − | 0.947274i | \(-0.396174\pi\) | |||||||
\(102\) | −2.15424e6 | −2.02999 | ||||||||
\(103\) | 1.69744e6i | 1.55340i | 0.629871 | + | 0.776700i | \(0.283108\pi\) | ||||
−0.629871 | + | 0.776700i | \(0.716892\pi\) | |||||||
\(104\) | 1.13313e6i | 1.00735i | ||||||||
\(105\) | 271320. | + | 644976.i | 0.234376 | + | 0.557154i | ||||
\(106\) | 611248. | 0.513216 | ||||||||
\(107\) | 1.61603e6 | 1.31916 | 0.659579 | − | 0.751635i | \(-0.270734\pi\) | ||||
0.659579 | + | 0.751635i | \(0.270734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 199226. | 0.153839 | 0.0769195 | − | 0.997037i | \(-0.475492\pi\) | ||||
0.0769195 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(110\) | 315803.i | 0.237268i | ||||||||
\(111\) | 135589.i | 0.0991418i | ||||||||
\(112\) | −544768. | − | 1.29501e6i | −0.387755 | − | 0.921762i | ||||
\(113\) | −1.80762e6 | −1.25277 | −0.626386 | − | 0.779513i | \(-0.715467\pi\) | ||||
−0.626386 | + | 0.779513i | \(0.715467\pi\) | |||||||
\(114\) | 1.12608e6 | 0.760072 | ||||||||
\(115\) | − | 213998.i | − | 0.140707i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.90144e6i | − | 1.81157i | ||||||
\(118\) | − | 905856.i | − | 0.551332i | ||||||
\(119\) | 1.88496e6 | − | 792941.i | 1.11857 | − | 0.470543i | ||||
\(120\) | 1.04448e6 | 0.604444 | ||||||||
\(121\) | −1.00768e6 | −0.568812 | ||||||||
\(122\) | 2.20087e6i | 1.21203i | ||||||||
\(123\) | −2.59896e6 | −1.39664 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.31931e6i | − | 0.675486i | ||||||
\(126\) | 1.39490e6 | + | 3.31593e6i | 0.697321 | + | 1.65766i | ||||
\(127\) | 3.32472e6 | 1.62310 | 0.811548 | − | 0.584286i | \(-0.198625\pi\) | ||||
0.811548 | + | 0.584286i | \(0.198625\pi\) | |||||||
\(128\) | −2.09715e6 | −1.00000 | ||||||||
\(129\) | 1.41904e6i | 0.661035i | ||||||||
\(130\) | −799680. | −0.363987 | ||||||||
\(131\) | 3.13567e6i | 1.39482i | 0.716674 | + | 0.697408i | \(0.245664\pi\) | ||||
−0.716674 | + | 0.697408i | \(0.754336\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −985320. | + | 414492.i | −0.418815 | + | 0.176182i | ||||
\(134\) | −3.96194e6 | −1.64662 | ||||||||
\(135\) | −1.18728e6 | −0.482561 | ||||||||
\(136\) | − | 3.05252e6i | − | 1.21351i | ||||||
\(137\) | 2.12927e6 | 0.828072 | 0.414036 | − | 0.910260i | \(-0.364119\pi\) | ||||
0.414036 | + | 0.910260i | \(0.364119\pi\) | |||||||
\(138\) | − | 1.71199e6i | − | 0.651423i | ||||||
\(139\) | − | 1.68421e6i | − | 0.627121i | −0.949568 | − | 0.313561i | \(-0.898478\pi\) | ||
0.949568 | − | 0.313561i | \(-0.101522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.27216e6 | 1.16729 | ||||||||
\(142\) | 1.47525e6 | 0.515229 | ||||||||
\(143\) | 1.93429e6i | 0.661477i | ||||||||
\(144\) | 5.36986e6 | 1.79835 | ||||||||
\(145\) | − | 503424.i | − | 0.165132i | ||||||
\(146\) | 487797.i | 0.156740i | ||||||||
\(147\) | −3.79848e6 | − | 3.71588e6i | −1.19580 | − | 1.16980i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.59573e6 | −0.784696 | −0.392348 | − | 0.919817i | \(-0.628337\pi\) | ||||
−0.392348 | + | 0.919817i | \(0.628337\pi\) | |||||||
\(150\) | − | 4.90868e6i | − | 1.45442i | ||||||
\(151\) | −1.68557e6 | −0.489570 | −0.244785 | − | 0.969577i | \(-0.578717\pi\) | ||||
−0.244785 | + | 0.969577i | \(0.578717\pi\) | |||||||
\(152\) | 1.59564e6i | 0.454363i | ||||||||
\(153\) | 7.81613e6i | 2.18231i | ||||||||
\(154\) | −929936. | − | 2.21062e6i | −0.254619 | − | 0.605275i | ||||
\(155\) | −1.24032e6 | −0.333072 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.67641e6i | 0.950002i | 0.879985 | + | 0.475001i | \(0.157552\pi\) | ||||
−0.879985 | + | 0.475001i | \(0.842448\pi\) | |||||||
\(158\) | 4.27947e6 | 1.08497 | ||||||||
\(159\) | − | 3.45098e6i | − | 0.858521i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 630154. | + | 1.49799e6i | 0.150997 | + | 0.358947i | ||||
\(162\) | −1.85249e6 | −0.435723 | ||||||||
\(163\) | 1.88191e6 | 0.434547 | 0.217274 | − | 0.976111i | \(-0.430284\pi\) | ||||
0.217274 | + | 0.976111i | \(0.430284\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.78296e6 | 0.396908 | ||||||||
\(166\) | 5.71878e6i | 1.25020i | ||||||||
\(167\) | − | 3.15595e6i | − | 0.677612i | −0.940856 | − | 0.338806i | \(-0.889977\pi\) | ||
0.940856 | − | 0.338806i | \(-0.110023\pi\) | |||||||
\(168\) | −7.31136e6 | + | 3.07565e6i | −1.54195 | + | 0.648648i | ||||
\(169\) | −71231.0 | −0.0147574 | ||||||||
\(170\) | 2.15424e6 | 0.438478 | ||||||||
\(171\) | − | 4.08570e6i | − | 0.817106i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.29477e6i | − | 0.443201i | −0.975138 | − | 0.221600i | \(-0.928872\pi\) | ||
0.975138 | − | 0.221600i | \(-0.0711280\pi\) | |||||||
\(174\) | − | 4.02739e6i | − | 0.764498i | ||||||
\(175\) | 1.80680e6 | + | 4.29509e6i | 0.337130 | + | 0.801417i | ||||
\(176\) | −3.57990e6 | −0.656649 | ||||||||
\(177\) | −5.11428e6 | −0.922284 | ||||||||
\(178\) | 5.03623e6i | 0.892988i | ||||||||
\(179\) | 3.51846e6 | 0.613470 | 0.306735 | − | 0.951795i | \(-0.400763\pi\) | ||||
0.306735 | + | 0.951795i | \(0.400763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.48267e6i | − | 1.26189i | −0.775829 | − | 0.630944i | \(-0.782668\pi\) | ||
0.775829 | − | 0.630944i | \(-0.217332\pi\) | |||||||
\(182\) | 5.59776e6 | − | 2.35479e6i | 0.928539 | − | 0.390606i | ||||
\(183\) | 1.24256e7 | 2.02752 | ||||||||
\(184\) | 2.42586e6 | 0.389414 | ||||||||
\(185\) | − | 135589.i | − | 0.0214146i | ||||||
\(186\) | −9.92256e6 | −1.54200 | ||||||||
\(187\) | − | 5.21075e6i | − | 0.796848i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.31096e6 | − | 3.49615e6i | 1.23102 | − | 0.517850i | ||||
\(190\) | −1.12608e6 | −0.164176 | ||||||||
\(191\) | −7.20028e6 | −1.03335 | −0.516677 | − | 0.856180i | \(-0.672831\pi\) | ||||
−0.516677 | + | 0.856180i | \(0.672831\pi\) | |||||||
\(192\) | 1.18401e7i | 1.67283i | ||||||||
\(193\) | −1.30889e7 | −1.82067 | −0.910335 | − | 0.413872i | \(-0.864176\pi\) | ||||
−0.910335 | + | 0.413872i | \(0.864176\pi\) | |||||||
\(194\) | − | 6.51552e6i | − | 0.892368i | ||||||
\(195\) | 4.51483e6i | 0.608888i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.17476e6 | −1.20004 | −0.600020 | − | 0.799985i | \(-0.704841\pi\) | ||||
−0.600020 | + | 0.799985i | \(0.704841\pi\) | |||||||
\(198\) | 9.16651e6 | 1.18089 | ||||||||
\(199\) | − | 6.78769e6i | − | 0.861317i | −0.902515 | − | 0.430658i | \(-0.858281\pi\) | ||
0.902515 | − | 0.430658i | \(-0.141719\pi\) | |||||||
\(200\) | 6.95552e6 | 0.869440 | ||||||||
\(201\) | 2.23683e7i | 2.75451i | ||||||||
\(202\) | 1.56156e7i | 1.89455i | ||||||||
\(203\) | 1.48242e6 | + | 3.52397e6i | 0.177208 | + | 0.421254i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.59896e6 | 0.301674 | ||||||||
\(206\) | − | 1.35795e7i | − | 1.55340i | ||||||
\(207\) | −6.21152e6 | −0.700304 | ||||||||
\(208\) | − | 9.06507e6i | − | 1.00735i | ||||||
\(209\) | 2.72380e6i | 0.298357i | ||||||||
\(210\) | −2.17056e6 | − | 5.15980e6i | −0.234376 | − | 0.557154i | ||||
\(211\) | 8.40084e6 | 0.894284 | 0.447142 | − | 0.894463i | \(-0.352442\pi\) | ||||
0.447142 | + | 0.894463i | \(0.352442\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.32895e6i | − | 0.861889i | ||||||
\(214\) | −1.29282e7 | −1.31916 | ||||||||
\(215\) | − | 1.41904e6i | − | 0.142784i | ||||||
\(216\) | − | 1.34589e7i | − | 1.33551i | ||||||
\(217\) | 8.68224e6 | − | 3.65233e6i | 0.849675 | − | 0.357430i | ||||
\(218\) | −1.59381e6 | −0.153839 | ||||||||
\(219\) | 2.75400e6 | 0.262199 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.31947e7 | 1.22243 | ||||||||
\(222\) | − | 1.08472e6i | − | 0.0991418i | ||||||
\(223\) | 4.90434e6i | 0.442248i | 0.975246 | + | 0.221124i | \(0.0709726\pi\) | ||||
−0.975246 | + | 0.221124i | \(0.929027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.78099e7 | −1.56356 | ||||||||
\(226\) | 1.44610e7 | 1.25277 | ||||||||
\(227\) | 1.32183e7i | 1.13005i | 0.825075 | + | 0.565023i | \(0.191133\pi\) | ||||
−0.825075 | + | 0.565023i | \(0.808867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 338974.i | − | 0.0282266i | −0.999900 | − | 0.0141133i | \(-0.995507\pi\) | ||
0.999900 | − | 0.0141133i | \(-0.00449256\pi\) | |||||||
\(230\) | 1.71199e6i | 0.140707i | ||||||||
\(231\) | −1.24807e7 | + | 5.25023e6i | −1.01252 | + | 0.425934i | ||||
\(232\) | 5.70675e6 | 0.457009 | ||||||||
\(233\) | 4.84146e6 | 0.382744 | 0.191372 | − | 0.981518i | \(-0.438706\pi\) | ||||
0.191372 | + | 0.981518i | \(0.438706\pi\) | |||||||
\(234\) | 2.32115e7i | 1.81157i | ||||||||
\(235\) | −3.27216e6 | −0.252134 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2.41610e7i | − | 1.81497i | ||||||
\(238\) | −1.50797e7 | + | 6.34352e6i | −1.11857 | + | 0.470543i | ||||
\(239\) | −1.37297e7 | −1.00570 | −0.502850 | − | 0.864374i | \(-0.667715\pi\) | ||||
−0.502850 | + | 0.864374i | \(0.667715\pi\) | |||||||
\(240\) | −8.35584e6 | −0.604444 | ||||||||
\(241\) | 3.66913e6i | 0.262127i | 0.991374 | + | 0.131064i | \(0.0418392\pi\) | ||||
−0.991374 | + | 0.131064i | \(0.958161\pi\) | |||||||
\(242\) | 8.06148e6 | 0.568812 | ||||||||
\(243\) | − | 8.70433e6i | − | 0.606619i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.79848e6 | + | 3.71588e6i | 0.258292 | + | 0.252676i | ||||
\(246\) | 2.07917e7 | 1.39664 | ||||||||
\(247\) | −6.89724e6 | −0.457704 | ||||||||
\(248\) | − | 1.40601e7i | − | 0.921793i | ||||||
\(249\) | 3.22871e7 | 2.09137 | ||||||||
\(250\) | 1.05545e7i | 0.675486i | ||||||||
\(251\) | 1.57289e7i | 0.994664i | 0.867560 | + | 0.497332i | \(0.165687\pi\) | ||||
−0.867560 | + | 0.497332i | \(0.834313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.14101e6 | 0.255708 | ||||||||
\(254\) | −2.65978e7 | −1.62310 | ||||||||
\(255\) | − | 1.21624e7i | − | 0.733498i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.54531e6i | − | 0.444506i | −0.974989 | − | 0.222253i | \(-0.928659\pi\) | ||
0.974989 | − | 0.222253i | \(-0.0713411\pi\) | |||||||
\(258\) | − | 1.13523e7i | − | 0.661035i | ||||||
\(259\) | 399266. | + | 949126.i | 0.0229807 | + | 0.0546292i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.46124e7 | −0.821864 | ||||||||
\(262\) | − | 2.50854e7i | − | 1.39482i | ||||||
\(263\) | −1.32059e7 | −0.725942 | −0.362971 | − | 0.931800i | \(-0.618238\pi\) | ||||
−0.362971 | + | 0.931800i | \(0.618238\pi\) | |||||||
\(264\) | 2.02114e7i | 1.09846i | ||||||||
\(265\) | 3.45098e6i | 0.185441i | ||||||||
\(266\) | 7.88256e6 | − | 3.31593e6i | 0.418815 | − | 0.176182i | ||||
\(267\) | 2.84335e7 | 1.49382 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.59600e7i | 0.819930i | 0.912101 | + | 0.409965i | \(0.134459\pi\) | ||||
−0.912101 | + | 0.409965i | \(0.865541\pi\) | |||||||
\(270\) | 9.49824e6 | 0.482561 | ||||||||
\(271\) | − | 2.48446e7i | − | 1.24831i | −0.781299 | − | 0.624157i | \(-0.785443\pi\) | ||
0.781299 | − | 0.624157i | \(-0.214557\pi\) | |||||||
\(272\) | 2.44202e7i | 1.21351i | ||||||||
\(273\) | −1.32947e7 | − | 3.16038e7i | −0.653416 | − | 1.55329i | ||||
\(274\) | −1.70341e7 | −0.828072 | ||||||||
\(275\) | 1.18733e7 | 0.570917 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.60013e7 | 0.752863 | 0.376432 | − | 0.926444i | \(-0.377151\pi\) | ||||
0.376432 | + | 0.926444i | \(0.377151\pi\) | |||||||
\(278\) | 1.34737e7i | 0.627121i | ||||||||
\(279\) | 3.60016e7i | 1.65771i | ||||||||
\(280\) | 7.31136e6 | − | 3.07565e6i | 0.333061 | − | 0.140108i | ||||
\(281\) | −603566. | −0.0272023 | −0.0136012 | − | 0.999908i | \(-0.504330\pi\) | ||||
−0.0136012 | + | 0.999908i | \(0.504330\pi\) | |||||||
\(282\) | −2.61773e7 | −1.16729 | ||||||||
\(283\) | 2.22195e7i | 0.980334i | 0.871629 | + | 0.490167i | \(0.163064\pi\) | ||||
−0.871629 | + | 0.490167i | \(0.836936\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.35762e6i | 0.274637i | ||||||||
\(286\) | − | 1.54744e7i | − | 0.661477i | ||||||
\(287\) | −1.81927e7 | + | 7.65308e6i | −0.769577 | + | 0.323736i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.14074e7 | −0.472599 | ||||||||
\(290\) | 4.02739e6i | 0.165132i | ||||||||
\(291\) | −3.67853e7 | −1.49278 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.28134e7i | − | 1.70207i | −0.525110 | − | 0.851034i | \(-0.675976\pi\) | ||
0.525110 | − | 0.851034i | \(-0.324024\pi\) | |||||||
\(294\) | 3.03878e7 | + | 2.97271e7i | 1.19580 | + | 1.16980i | ||||
\(295\) | 5.11428e6 | 0.199213 | ||||||||
\(296\) | 1.53702e6 | 0.0592660 | ||||||||
\(297\) | − | 2.29747e7i | − | 0.876961i | ||||||
\(298\) | 2.07659e7 | 0.784696 | ||||||||
\(299\) | 1.04859e7i | 0.392277i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.17859e6 | + | 9.93326e6i | 0.153225 | + | 0.364244i | ||||
\(302\) | 1.34845e7 | 0.489570 | ||||||||
\(303\) | 8.81627e7 | 3.16925 | ||||||||
\(304\) | − | 1.27651e7i | − | 0.454363i | ||||||
\(305\) | −1.24256e7 | −0.437945 | ||||||||
\(306\) | − | 6.25290e7i | − | 2.18231i | ||||||
\(307\) | − | 4.02152e7i | − | 1.38987i | −0.719072 | − | 0.694936i | \(-0.755433\pi\) | ||
0.719072 | − | 0.694936i | \(-0.244567\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.66673e7 | −2.59857 | ||||||||
\(310\) | 9.92256e6 | 0.333072 | ||||||||
\(311\) | 1.47381e7i | 0.489958i | 0.969528 | + | 0.244979i | \(0.0787811\pi\) | ||||
−0.969528 | + | 0.244979i | \(0.921219\pi\) | |||||||
\(312\) | −5.11795e7 | −1.68513 | ||||||||
\(313\) | 4.19490e7i | 1.36801i | 0.729479 | + | 0.684004i | \(0.239763\pi\) | ||||
−0.729479 | + | 0.684004i | \(0.760237\pi\) | |||||||
\(314\) | − | 2.94112e7i | − | 0.950002i | ||||||
\(315\) | −1.87211e7 | + | 7.87534e6i | −0.598962 | + | 0.251964i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.30922e7 | 1.35276 | 0.676380 | − | 0.736553i | \(-0.263548\pi\) | ||||
0.676380 | + | 0.736553i | \(0.263548\pi\) | |||||||
\(318\) | 2.76078e7i | 0.858521i | ||||||||
\(319\) | 9.74160e6 | 0.300095 | ||||||||
\(320\) | − | 1.18401e7i | − | 0.361331i | ||||||
\(321\) | 7.29900e7i | 2.20673i | ||||||||
\(322\) | −5.04123e6 | − | 1.19839e7i | −0.150997 | − | 0.358947i | ||||
\(323\) | 1.85803e7 | 0.551373 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00657e7i | 0.875832i | ||||||||
\(326\) | −1.50553e7 | −0.434547 | ||||||||
\(327\) | 8.99831e6i | 0.257346i | ||||||||
\(328\) | 2.94615e7i | 0.834897i | ||||||||
\(329\) | 2.29051e7 | − | 9.63543e6i | 0.643198 | − | 0.270572i | ||||
\(330\) | −1.42637e7 | −0.396908 | ||||||||
\(331\) | −5.32204e7 | −1.46755 | −0.733777 | − | 0.679390i | \(-0.762244\pi\) | ||||
−0.733777 | + | 0.679390i | \(0.762244\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.93562e6 | −0.106581 | ||||||||
\(334\) | 2.52476e7i | 0.677612i | ||||||||
\(335\) | − | 2.23683e7i | − | 0.594974i | ||||||
\(336\) | 5.84909e7 | − | 2.46052e7i | 1.54195 | − | 0.648648i | ||||
\(337\) | 2.34579e6 | 0.0612913 | 0.0306456 | − | 0.999530i | \(-0.490244\pi\) | ||||
0.0306456 | + | 0.999530i | \(0.490244\pi\) | |||||||
\(338\) | 569848. | 0.0147574 | ||||||||
\(339\) | − | 8.16437e7i | − | 2.09567i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.40010e7i | − | 0.605295i | ||||||
\(342\) | 3.26856e7i | 0.817106i | ||||||||
\(343\) | −3.75314e7 | − | 1.48259e7i | −0.930063 | − | 0.367400i | ||||
\(344\) | 1.60860e7 | 0.395160 | ||||||||
\(345\) | 9.66552e6 | 0.235379 | ||||||||
\(346\) | 1.83581e7i | 0.443201i | ||||||||
\(347\) | −4.80596e7 | −1.15025 | −0.575124 | − | 0.818066i | \(-0.695046\pi\) | ||||
−0.575124 | + | 0.818066i | \(0.695046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.00499e7i | 0.236421i | 0.992989 | + | 0.118211i | \(0.0377158\pi\) | ||||
−0.992989 | + | 0.118211i | \(0.962284\pi\) | |||||||
\(350\) | −1.44544e7 | − | 3.43608e7i | −0.337130 | − | 0.801417i | ||||
\(351\) | 5.81767e7 | 1.34533 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7.65216e7i | − | 1.73964i | −0.493368 | − | 0.869821i | \(-0.664234\pi\) | ||
0.493368 | − | 0.869821i | \(-0.335766\pi\) | |||||||
\(354\) | 4.09142e7 | 0.922284 | ||||||||
\(355\) | 8.32895e6i | 0.186168i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.58142e7 | + | 8.51368e7i | 0.787138 | + | 1.87117i | ||||
\(358\) | −2.81477e7 | −0.613470 | ||||||||
\(359\) | 8.39735e6 | 0.181493 | 0.0907463 | − | 0.995874i | \(-0.471075\pi\) | ||||
0.0907463 | + | 0.995874i | \(0.471075\pi\) | |||||||
\(360\) | 3.03171e7i | 0.649801i | ||||||||
\(361\) | 3.73334e7 | 0.793554 | ||||||||
\(362\) | 5.98613e7i | 1.26189i | ||||||||
\(363\) | − | 4.55135e7i | − | 0.951525i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.75400e6 | −0.0566351 | ||||||||
\(366\) | −9.94051e7 | −2.02752 | ||||||||
\(367\) | − | 3.82776e6i | − | 0.0774366i | −0.999250 | − | 0.0387183i | \(-0.987672\pi\) | ||
0.999250 | − | 0.0387183i | \(-0.0123275\pi\) | |||||||
\(368\) | −1.94068e7 | −0.389414 | ||||||||
\(369\) | − | 7.54375e7i | − | 1.50144i | ||||||
\(370\) | 1.08472e6i | 0.0214146i | ||||||||
\(371\) | −1.01620e7 | − | 2.41569e7i | −0.199002 | − | 0.473063i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.93836e7 | −0.951604 | −0.475802 | − | 0.879552i | \(-0.657842\pi\) | ||||
−0.475802 | + | 0.879552i | \(0.657842\pi\) | |||||||
\(374\) | 4.16860e7i | 0.796848i | ||||||||
\(375\) | 5.95884e7 | 1.12997 | ||||||||
\(376\) | − | 3.70928e7i | − | 0.697792i | ||||||
\(377\) | 2.46678e7i | 0.460369i | ||||||||
\(378\) | −6.64877e7 | + | 2.79692e7i | −1.23102 | + | 0.517850i | ||||
\(379\) | 3.74561e7 | 0.688026 | 0.344013 | − | 0.938965i | \(-0.388214\pi\) | ||||
0.344013 | + | 0.938965i | \(0.388214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50166e8i | 2.71516i | ||||||||
\(382\) | 5.76022e7 | 1.03335 | ||||||||
\(383\) | 5.01003e7i | 0.891752i | 0.895095 | + | 0.445876i | \(0.147108\pi\) | ||||
−0.895095 | + | 0.445876i | \(0.852892\pi\) | |||||||
\(384\) | − | 9.47207e7i | − | 1.67283i | ||||||
\(385\) | 1.24807e7 | − | 5.25023e6i | 0.218704 | − | 0.0920017i | ||||
\(386\) | 1.04711e8 | 1.82067 | ||||||||
\(387\) | −4.11890e7 | −0.710638 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 224986. | 0.00382214 | 0.00191107 | − | 0.999998i | \(-0.499392\pi\) | ||||
0.00191107 | + | 0.999998i | \(0.499392\pi\) | |||||||
\(390\) | − | 3.61186e7i | − | 0.608888i | ||||||
\(391\) | − | 2.82478e7i | − | 0.472557i | ||||||
\(392\) | −4.21228e7 | + | 4.30591e7i | −0.699292 | + | 0.714836i | ||||
\(393\) | −1.41627e8 | −2.33329 | ||||||||
\(394\) | 7.33981e7 | 1.20004 | ||||||||
\(395\) | 2.41610e7i | 0.392034i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 871937.i | 0.0139352i | 0.999976 | + | 0.00696760i | \(0.00221787\pi\) | ||||
−0.999976 | + | 0.00696760i | \(0.997782\pi\) | |||||||
\(398\) | 5.43015e7i | 0.861317i | ||||||||
\(399\) | −1.87211e7 | − | 4.45033e7i | −0.294722 | − | 0.700606i | ||||
\(400\) | −5.56442e7 | −0.869440 | ||||||||
\(401\) | 1.44909e7 | 0.224730 | 0.112365 | − | 0.993667i | \(-0.464157\pi\) | ||||
0.112365 | + | 0.993667i | \(0.464157\pi\) | |||||||
\(402\) | − | 1.78946e8i | − | 2.75451i | ||||||
\(403\) | 6.07757e7 | 0.928570 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.04588e7i | − | 0.157440i | ||||||
\(406\) | −1.18593e7 | − | 2.81918e7i | −0.177208 | − | 0.421254i | ||||
\(407\) | 2.62375e6 | 0.0389170 | ||||||||
\(408\) | 1.37871e8 | 2.02999 | ||||||||
\(409\) | − | 1.04303e8i | − | 1.52450i | −0.647284 | − | 0.762249i | \(-0.724095\pi\) | ||
0.647284 | − | 0.762249i | \(-0.275905\pi\) | |||||||
\(410\) | −2.07917e7 | −0.301674 | ||||||||
\(411\) | 9.61712e7i | 1.38522i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.58000e7 | + | 1.50599e7i | −0.508197 | + | 0.213782i | ||||
\(414\) | 4.96921e7 | 0.700304 | ||||||||
\(415\) | −3.22871e7 | −0.451736 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.60696e7 | 1.04907 | ||||||||
\(418\) | − | 2.17904e7i | − | 0.298357i | ||||||
\(419\) | 8.22075e7i | 1.11756i | 0.829317 | + | 0.558778i | \(0.188730\pi\) | ||||
−0.829317 | + | 0.558778i | \(0.811270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.33780e7 | −0.179285 | −0.0896427 | − | 0.995974i | \(-0.528573\pi\) | ||||
−0.0896427 | + | 0.995974i | \(0.528573\pi\) | |||||||
\(422\) | −6.72067e7 | −0.894284 | ||||||||
\(423\) | 9.49778e7i | 1.25488i | ||||||||
\(424\) | −3.91199e7 | −0.513216 | ||||||||
\(425\) | − | 8.09932e7i | − | 1.05507i | ||||||
\(426\) | 6.66316e7i | 0.861889i | ||||||||
\(427\) | 8.69795e7 | − | 3.65894e7i | 1.11721 | − | 0.469972i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.73650e7 | −1.10654 | ||||||||
\(430\) | 1.13523e7i | 0.142784i | ||||||||
\(431\) | −1.34244e8 | −1.67673 | −0.838367 | − | 0.545106i | \(-0.816490\pi\) | ||||
−0.838367 | + | 0.545106i | \(0.816490\pi\) | |||||||
\(432\) | 1.07671e8i | 1.33551i | ||||||||
\(433\) | 1.03230e8i | 1.27158i | 0.771863 | + | 0.635789i | \(0.219325\pi\) | ||||
−0.771863 | + | 0.635789i | \(0.780675\pi\) | |||||||
\(434\) | −6.94579e7 | + | 2.92187e7i | −0.849675 | + | 0.357430i | ||||
\(435\) | 2.27378e7 | 0.276237 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.47659e7i | 0.176935i | ||||||||
\(438\) | −2.20320e7 | −0.262199 | ||||||||
\(439\) | − | 2.65816e7i | − | 0.314186i | −0.987584 | − | 0.157093i | \(-0.949788\pi\) | ||
0.987584 | − | 0.157093i | \(-0.0502123\pi\) | |||||||
\(440\) | − | 2.02114e7i | − | 0.237268i | ||||||
\(441\) | 1.07857e8 | − | 1.10255e8i | 1.25757 | − | 1.28553i | ||||
\(442\) | −1.05558e8 | −1.22243 | ||||||||
\(443\) | 1.31972e8 | 1.51799 | 0.758996 | − | 0.651096i | \(-0.225690\pi\) | ||||
0.758996 | + | 0.651096i | \(0.225690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.84335e7 | −0.322664 | ||||||||
\(446\) | − | 3.92348e7i | − | 0.442248i | ||||||
\(447\) | − | 1.17240e8i | − | 1.31266i | ||||||
\(448\) | 3.48652e7 | + | 8.28806e7i | 0.387755 | + | 0.921762i | ||||
\(449\) | 1.47766e8 | 1.63244 | 0.816218 | − | 0.577743i | \(-0.196067\pi\) | ||||
0.816218 | + | 0.577743i | \(0.196067\pi\) | |||||||
\(450\) | 1.42479e8 | 1.56356 | ||||||||
\(451\) | 5.02917e7i | 0.548234i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 7.61309e7i | − | 0.818967i | ||||||
\(454\) | − | 1.05746e8i | − | 1.13005i | ||||||
\(455\) | 1.32947e7 | + | 3.16038e7i | 0.141138 | + | 0.335510i | ||||
\(456\) | −7.20691e7 | −0.760072 | ||||||||
\(457\) | −8.22868e7 | −0.862147 | −0.431074 | − | 0.902317i | \(-0.641865\pi\) | ||||
−0.431074 | + | 0.902317i | \(0.641865\pi\) | |||||||
\(458\) | 2.71179e6i | 0.0282266i | ||||||||
\(459\) | −1.56721e8 | −1.62065 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.31884e8i | − | 1.34614i | −0.739580 | − | 0.673068i | \(-0.764976\pi\) | ||
0.739580 | − | 0.673068i | \(-0.235024\pi\) | |||||||
\(462\) | 9.98458e7 | − | 4.20018e7i | 1.01252 | − | 0.425934i | ||||
\(463\) | 1.39927e6 | 0.0140981 | 0.00704904 | − | 0.999975i | \(-0.497756\pi\) | ||||
0.00704904 | + | 0.999975i | \(0.497756\pi\) | |||||||
\(464\) | −4.56540e7 | −0.457009 | ||||||||
\(465\) | − | 5.60207e7i | − | 0.557173i | ||||||
\(466\) | −3.87317e7 | −0.382744 | ||||||||
\(467\) | − | 1.81321e7i | − | 0.178032i | −0.996030 | − | 0.0890158i | \(-0.971628\pi\) | ||
0.996030 | − | 0.0890158i | \(-0.0283722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.58672e7 | + | 1.56578e8i | 0.638485 | + | 1.51779i | ||||
\(470\) | 2.61773e7 | 0.252134 | ||||||||
\(471\) | −1.66050e8 | −1.58919 | ||||||||
\(472\) | 5.79748e7i | 0.551332i | ||||||||
\(473\) | 2.74593e7 | 0.259482 | ||||||||
\(474\) | 1.93288e8i | 1.81497i | ||||||||
\(475\) | 4.23374e7i | 0.395042i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.00168e8 | 0.922943 | ||||||||
\(478\) | 1.09838e8 | 1.00570 | ||||||||
\(479\) | − | 2.89375e7i | − | 0.263303i | −0.991296 | − | 0.131651i | \(-0.957972\pi\) | ||
0.991296 | − | 0.131651i | \(-0.0420279\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.64388e6i | 0.0597017i | ||||||||
\(482\) | − | 2.93531e7i | − | 0.262127i | ||||||
\(483\) | −6.76586e7 | + | 2.84618e7i | −0.600457 | + | 0.252592i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.67853e7 | 0.322440 | ||||||||
\(486\) | 6.96346e7i | 0.606619i | ||||||||
\(487\) | −9.47515e7 | −0.820350 | −0.410175 | − | 0.912007i | \(-0.634532\pi\) | ||||
−0.410175 | + | 0.912007i | \(0.634532\pi\) | |||||||
\(488\) | − | 1.40855e8i | − | 1.21203i | ||||||
\(489\) | 8.49992e7i | 0.726923i | ||||||||
\(490\) | −3.03878e7 | − | 2.97271e7i | −0.258292 | − | 0.252676i | ||||
\(491\) | −2.58834e7 | −0.218663 | −0.109332 | − | 0.994005i | \(-0.534871\pi\) | ||||
−0.109332 | + | 0.994005i | \(0.534871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.64520e7i | − | 0.554584i | ||||||
\(494\) | 5.51779e7 | 0.457704 | ||||||||
\(495\) | 5.17522e7i | 0.426691i | ||||||||
\(496\) | 1.12481e8i | 0.921793i | ||||||||
\(497\) | −2.45260e7 | − | 5.83026e7i | −0.199783 | − | 0.474918i | ||||
\(498\) | −2.58297e8 | −2.09137 | ||||||||
\(499\) | 1.56023e8 | 1.25571 | 0.627853 | − | 0.778332i | \(-0.283934\pi\) | ||||
0.627853 | + | 0.778332i | \(0.283934\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.42543e8 | 1.13353 | ||||||||
\(502\) | − | 1.25831e8i | − | 0.994664i | ||||||
\(503\) | 1.11476e8i | 0.875950i | 0.898987 | + | 0.437975i | \(0.144304\pi\) | ||||
−0.898987 | + | 0.437975i | \(0.855696\pi\) | |||||||
\(504\) | −8.92739e7 | − | 2.12220e8i | −0.697321 | − | 1.65766i | ||||
\(505\) | −8.81627e7 | −0.684559 | ||||||||
\(506\) | −3.31281e7 | −0.255708 | ||||||||
\(507\) | − | 3.21724e6i | − | 0.0246865i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.45421e7i | 0.565260i | 0.959229 | + | 0.282630i | \(0.0912068\pi\) | ||||
−0.959229 | + | 0.282630i | \(0.908793\pi\) | |||||||
\(510\) | 9.72992e7i | 0.733498i | ||||||||
\(511\) | 1.92780e7 | − | 8.10962e6i | 0.144477 | − | 0.0607768i | ||||
\(512\) | 1.34218e8 | 1.00000 | ||||||||
\(513\) | 8.19223e7 | 0.606806 | ||||||||
\(514\) | 6.03625e7i | 0.444506i | ||||||||
\(515\) | 7.66673e7 | 0.561291 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.33185e7i | − | 0.458204i | ||||||
\(518\) | −3.19413e6 | − | 7.59301e6i | −0.0229807 | − | 0.0546292i | ||||
\(519\) | 1.03646e8 | 0.741398 | ||||||||
\(520\) | 5.11795e7 | 0.363987 | ||||||||
\(521\) | − | 1.96232e8i | − | 1.38758i | −0.720179 | − | 0.693789i | \(-0.755940\pi\) | ||
0.720179 | − | 0.693789i | \(-0.244060\pi\) | |||||||
\(522\) | 1.16899e8 | 0.821864 | ||||||||
\(523\) | 4.62080e7i | 0.323007i | 0.986872 | + | 0.161504i | \(0.0516344\pi\) | ||||
−0.986872 | + | 0.161504i | \(0.948366\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.93994e8 | + | 8.16068e7i | −1.34063 | + | 0.563960i | ||||
\(526\) | 1.05648e8 | 0.725942 | ||||||||
\(527\) | −1.63722e8 | −1.11860 | ||||||||
\(528\) | − | 1.61691e8i | − | 1.09846i | ||||||
\(529\) | −1.25587e8 | −0.848357 | ||||||||
\(530\) | − | 2.76078e7i | − | 0.185441i | ||||||
\(531\) | − | 1.48447e8i | − | 0.991490i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.27349e8 | −0.841035 | ||||||||
\(534\) | −2.27468e8 | −1.49382 | ||||||||
\(535\) | − | 7.29900e7i | − | 0.476653i | ||||||
\(536\) | 2.53564e8 | 1.64662 | ||||||||
\(537\) | 1.58916e8i | 1.02623i | ||||||||
\(538\) | − | 1.27680e8i | − | 0.819930i | ||||||
\(539\) | −7.19049e7 | + | 7.35032e7i | −0.459189 | + | 0.469397i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.52906e7 | −0.475498 | −0.237749 | − | 0.971327i | \(-0.576410\pi\) | ||||
−0.237749 | + | 0.971327i | \(0.576410\pi\) | |||||||
\(542\) | 1.98757e8i | 1.24831i | ||||||||
\(543\) | 3.37965e8 | 2.11092 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.99831e6i | − | 0.0555868i | ||||||
\(546\) | 1.06357e8 | + | 2.52830e8i | 0.653416 | + | 1.55329i | ||||
\(547\) | 7.26760e7 | 0.444047 | 0.222023 | − | 0.975041i | \(-0.428734\pi\) | ||||
0.222023 | + | 0.975041i | \(0.428734\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.60667e8i | 2.17966i | ||||||||
\(550\) | −9.49863e7 | −0.570917 | ||||||||
\(551\) | 3.47363e7i | 0.207648i | ||||||||
\(552\) | 1.09567e8i | 0.651423i | ||||||||
\(553\) | −7.11462e7 | − | 1.69127e8i | −0.420704 | − | 1.00009i | ||||
\(554\) | −1.28010e8 | −0.752863 | ||||||||
\(555\) | 6.12408e6 | 0.0358230 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.10741e8 | −1.79818 | −0.899090 | − | 0.437765i | \(-0.855770\pi\) | ||||
−0.899090 | + | 0.437765i | \(0.855770\pi\) | |||||||
\(558\) | − | 2.88013e8i | − | 1.65771i | ||||||
\(559\) | 6.95328e7i | 0.398065i | ||||||||
\(560\) | −5.84909e7 | + | 2.46052e7i | −0.333061 | + | 0.140108i | ||||
\(561\) | 2.35351e8 | 1.33299 | ||||||||
\(562\) | 4.82853e6 | 0.0272023 | ||||||||
\(563\) | 5.66378e7i | 0.317381i | 0.987328 | + | 0.158690i | \(0.0507272\pi\) | ||||
−0.987328 | + | 0.158690i | \(0.949273\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.16437e7i | 0.452665i | ||||||||
\(566\) | − | 1.77756e8i | − | 0.980334i | ||||||
\(567\) | 3.07976e7 | + | 7.32114e7i | 0.168954 | + | 0.401633i | ||||
\(568\) | −9.44159e7 | −0.515229 | ||||||||
\(569\) | 5.17304e7 | 0.280808 | 0.140404 | − | 0.990094i | \(-0.455160\pi\) | ||||
0.140404 | + | 0.990094i | \(0.455160\pi\) | |||||||
\(570\) | − | 5.08609e7i | − | 0.274637i | ||||||
\(571\) | 8.68765e7 | 0.466653 | 0.233326 | − | 0.972398i | \(-0.425039\pi\) | ||||
0.233326 | + | 0.972398i | \(0.425039\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.25210e8i | − | 1.72862i | ||||||
\(574\) | 1.45542e8 | − | 6.12246e7i | 0.769577 | − | 0.323736i | ||||
\(575\) | 6.43657e7 | 0.338572 | ||||||||
\(576\) | −3.43671e8 | −1.79835 | ||||||||
\(577\) | 5.89865e7i | 0.307062i | 0.988144 | + | 0.153531i | \(0.0490644\pi\) | ||||
−0.988144 | + | 0.153531i | \(0.950936\pi\) | |||||||
\(578\) | 9.12591e7 | 0.472599 | ||||||||
\(579\) | − | 5.91178e8i | − | 3.04567i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.26010e8 | − | 9.50748e7i | 1.15239 | − | 0.484771i | ||||
\(582\) | 2.94282e8 | 1.49278 | ||||||||
\(583\) | −6.67788e7 | −0.337003 | ||||||||
\(584\) | − | 3.12190e7i | − | 0.156740i | ||||||
\(585\) | −1.31048e8 | −0.654578 | ||||||||
\(586\) | 3.42507e8i | 1.70207i | ||||||||
\(587\) | 3.10848e8i | 1.53686i | 0.639934 | + | 0.768430i | \(0.278962\pi\) | ||||
−0.639934 | + | 0.768430i | \(0.721038\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.55821e7 | 0.418829 | ||||||||
\(590\) | −4.09142e7 | −0.199213 | ||||||||
\(591\) | − | 4.14390e8i | − | 2.00746i | ||||||
\(592\) | −1.22962e7 | −0.0592660 | ||||||||
\(593\) | 3.46714e8i | 1.66268i | 0.555766 | + | 0.831339i | \(0.312425\pi\) | ||||
−0.555766 | + | 0.831339i | \(0.687575\pi\) | |||||||
\(594\) | 1.83797e8i | 0.876961i | ||||||||
\(595\) | −3.58142e7 | − | 8.51368e7i | −0.170022 | − | 0.404172i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.06575e8 | 1.44083 | ||||||||
\(598\) | − | 8.38873e7i | − | 0.392277i | ||||||
\(599\) | 9.47771e7 | 0.440984 | 0.220492 | − | 0.975389i | \(-0.429234\pi\) | ||||
0.220492 | + | 0.975389i | \(0.429234\pi\) | |||||||
\(600\) | 3.14156e8i | 1.45442i | ||||||||
\(601\) | 2.04951e8i | 0.944119i | 0.881567 | + | 0.472060i | \(0.156489\pi\) | ||||
−0.881567 | + | 0.472060i | \(0.843511\pi\) | |||||||
\(602\) | −3.34288e7 | − | 7.94661e7i | −0.153225 | − | 0.364244i | ||||
\(603\) | −6.49262e8 | −2.96120 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.55135e7i | 0.205529i | ||||||||
\(606\) | −7.05301e8 | −3.16925 | ||||||||
\(607\) | − | 3.28634e8i | − | 1.46942i | −0.678379 | − | 0.734712i | \(-0.737317\pi\) | ||
0.678379 | − | 0.734712i | \(-0.262683\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.59165e8 | + | 6.69554e7i | −0.704686 | + | 0.296438i | ||||
\(610\) | 9.94051e7 | 0.437945 | ||||||||
\(611\) | 1.60336e8 | 0.702922 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.67967e8 | 1.16332 | 0.581660 | − | 0.813432i | \(-0.302403\pi\) | ||||
0.581660 | + | 0.813432i | \(0.302403\pi\) | |||||||
\(614\) | 3.21721e8i | 1.38987i | ||||||||
\(615\) | 1.17386e8i | 0.504649i | ||||||||
\(616\) | 5.95159e7 | + | 1.41480e8i | 0.254619 | + | 0.605275i | ||||
\(617\) | −3.88909e8 | −1.65574 | −0.827870 | − | 0.560921i | \(-0.810447\pi\) | ||||
−0.827870 | + | 0.560921i | \(0.810447\pi\) | |||||||
\(618\) | 6.13338e8 | 2.59857 | ||||||||
\(619\) | 6.30894e7i | 0.266002i | 0.991116 | + | 0.133001i | \(0.0424613\pi\) | ||||
−0.991116 | + | 0.133001i | \(0.957539\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.24547e8i | − | 0.520066i | ||||||
\(622\) | − | 1.17904e8i | − | 0.489958i | ||||||
\(623\) | 1.99035e8 | − | 8.37273e7i | 0.823123 | − | 0.346261i | ||||
\(624\) | 4.09436e8 | 1.68513 | ||||||||
\(625\) | 1.52677e8 | 0.625366 | ||||||||
\(626\) | − | 3.35592e8i | − | 1.36801i | ||||||
\(627\) | −1.23024e8 | −0.499101 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.78978e7i | − | 0.0719197i | ||||||
\(630\) | 1.49769e8 | − | 6.30027e7i | 0.598962 | − | 0.251964i | ||||
\(631\) | −1.30827e8 | −0.520725 | −0.260363 | − | 0.965511i | \(-0.583842\pi\) | ||||
−0.260363 | + | 0.965511i | \(0.583842\pi\) | |||||||
\(632\) | −2.73886e8 | −1.08497 | ||||||||
\(633\) | 3.79435e8i | 1.49598i | ||||||||
\(634\) | −3.44738e8 | −1.35276 | ||||||||
\(635\) | − | 1.50166e8i | − | 0.586475i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.86126e8 | − | 1.82078e8i | −0.720091 | − | 0.704433i | ||||
\(638\) | −7.79328e7 | −0.300095 | ||||||||
\(639\) | 2.41756e8 | 0.926563 | ||||||||
\(640\) | 9.47207e7i | 0.361331i | ||||||||
\(641\) | −7.17536e7 | −0.272439 | −0.136220 | − | 0.990679i | \(-0.543495\pi\) | ||||
−0.136220 | + | 0.990679i | \(0.543495\pi\) | |||||||
\(642\) | − | 5.83920e8i | − | 2.20673i | ||||||
\(643\) | − | 2.56068e8i | − | 0.963214i | −0.876387 | − | 0.481607i | \(-0.840053\pi\) | ||
0.876387 | − | 0.481607i | \(-0.159947\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.40927e7 | 0.238852 | ||||||||
\(646\) | −1.48643e8 | −0.551373 | ||||||||
\(647\) | 4.93122e8i | 1.82071i | 0.413827 | + | 0.910356i | \(0.364192\pi\) | ||||
−0.413827 | + | 0.910356i | \(0.635808\pi\) | |||||||
\(648\) | 1.18559e8 | 0.435723 | ||||||||
\(649\) | 9.89648e7i | 0.362032i | ||||||||
\(650\) | − | 2.40525e8i | − | 0.875832i | ||||||
\(651\) | 1.64963e8 | + | 3.92145e8i | 0.597919 | + | 1.42136i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.55036e8 | 0.556793 | 0.278397 | − | 0.960466i | \(-0.410197\pi\) | ||||
0.278397 | + | 0.960466i | \(0.410197\pi\) | |||||||
\(654\) | − | 7.19865e7i | − | 0.257346i | ||||||
\(655\) | 1.41627e8 | 0.503990 | ||||||||
\(656\) | − | 2.35692e8i | − | 0.834897i | ||||||
\(657\) | 7.99377e7i | 0.281874i | ||||||||
\(658\) | −1.83241e8 | + | 7.70834e7i | −0.643198 | + | 0.270572i | ||||
\(659\) | −3.01683e8 | −1.05413 | −0.527065 | − | 0.849825i | \(-0.676707\pi\) | ||||
−0.527065 | + | 0.849825i | \(0.676707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.80227e8i | − | 0.624044i | −0.950075 | − | 0.312022i | \(-0.898994\pi\) | ||
0.950075 | − | 0.312022i | \(-0.101006\pi\) | |||||||
\(662\) | 4.25763e8 | 1.46755 | ||||||||
\(663\) | 5.95957e8i | 2.04491i | ||||||||
\(664\) | − | 3.66002e8i | − | 1.25020i | ||||||
\(665\) | 1.87211e7 | + | 4.45033e7i | 0.0636599 | + | 0.151331i | ||||
\(666\) | 3.14850e7 | 0.106581 | ||||||||
\(667\) | 5.28097e7 | 0.177966 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.21511e8 | −0.739806 | ||||||||
\(670\) | 1.78946e8i | 0.594974i | ||||||||
\(671\) | − | 2.40445e8i | − | 0.795880i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.06265e8 | 1.33280 | 0.666399 | − | 0.745595i | \(-0.267835\pi\) | ||||
0.666399 | + | 0.745595i | \(0.267835\pi\) | |||||||
\(674\) | −1.87663e7 | −0.0612913 | ||||||||
\(675\) | − | 3.57106e8i | − | 1.16114i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.77837e7i | − | 0.0573133i | −0.999589 | − | 0.0286566i | \(-0.990877\pi\) | ||
0.999589 | − | 0.0286566i | \(-0.00912294\pi\) | |||||||
\(678\) | 6.53150e8i | 2.09567i | ||||||||
\(679\) | −2.57497e8 | + | 1.08320e8i | −0.822551 | + | 0.346020i | ||||
\(680\) | −1.37871e8 | −0.438478 | ||||||||
\(681\) | −5.97020e8 | −1.89037 | ||||||||
\(682\) | 1.92008e8i | 0.605295i | ||||||||
\(683\) | −2.66054e8 | −0.835042 | −0.417521 | − | 0.908667i | \(-0.637101\pi\) | ||||
−0.417521 | + | 0.908667i | \(0.637101\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.61712e7i | − | 0.299208i | ||||||
\(686\) | 3.00251e8 | + | 1.18607e8i | 0.930063 | + | 0.367400i | ||||
\(687\) | 1.53102e7 | 0.0472183 | ||||||||
\(688\) | −1.28688e8 | −0.395160 | ||||||||
\(689\) | − | 1.69098e8i | − | 0.516989i | ||||||
\(690\) | −7.73242e7 | −0.235379 | ||||||||
\(691\) | 2.44451e8i | 0.740898i | 0.928853 | + | 0.370449i | \(0.120796\pi\) | ||||
−0.928853 | + | 0.370449i | \(0.879204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.52393e8 | − | 3.62266e8i | −0.457895 | − | 1.08850i | ||||
\(694\) | 3.84476e8 | 1.15025 | ||||||||
\(695\) | −7.60696e7 | −0.226598 | ||||||||
\(696\) | 2.57753e8i | 0.764498i | ||||||||
\(697\) | 3.43063e8 | 1.01315 | ||||||||
\(698\) | − | 8.03994e7i | − | 0.236421i | ||||||
\(699\) | 2.18671e8i | 0.640265i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.31727e8 | 0.672702 | 0.336351 | − | 0.941737i | \(-0.390807\pi\) | ||||
0.336351 | + | 0.941737i | \(0.390807\pi\) | |||||||
\(702\) | −4.65414e8 | −1.34533 | ||||||||
\(703\) | 9.35567e6i | 0.0269283i | ||||||||
\(704\) | 2.29114e8 | 0.656649 | ||||||||
\(705\) | − | 1.47792e8i | − | 0.421776i | ||||||
\(706\) | 6.12173e8i | 1.73964i | ||||||||
\(707\) | 6.17139e8 | − | 2.59610e8i | 1.74632 | − | 0.734621i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.09705e8 | −0.868979 | −0.434489 | − | 0.900677i | \(-0.643071\pi\) | ||||
−0.434489 | + | 0.900677i | \(0.643071\pi\) | |||||||
\(710\) | − | 6.66316e7i | − | 0.186168i | ||||||
\(711\) | 7.01298e8 | 1.95117 | ||||||||
\(712\) | − | 3.22319e8i | − | 0.892988i | ||||||
\(713\) | − | 1.30111e8i | − | 0.358959i | ||||||
\(714\) | −2.86514e8 | − | 6.81094e8i | −0.787138 | − | 1.87117i | ||||
\(715\) | 8.73650e7 | 0.239012 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.20122e8i | − | 1.68236i | ||||||
\(718\) | −6.71788e7 | −0.181493 | ||||||||
\(719\) | − | 3.85416e8i | − | 1.03692i | −0.855103 | − | 0.518458i | \(-0.826506\pi\) | ||
0.855103 | − | 0.518458i | \(-0.173494\pi\) | |||||||
\(720\) | − | 2.42537e8i | − | 0.649801i | ||||||
\(721\) | −5.36671e8 | + | 2.25760e8i | −1.43187 | + | 0.602339i | ||||
\(722\) | −2.98668e8 | −0.793554 | ||||||||
\(723\) | −1.65721e8 | −0.438494 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.51418e8 | 0.397342 | ||||||||
\(726\) | 3.64108e8i | 0.951525i | ||||||||
\(727\) | 3.13918e8i | 0.816983i | 0.912762 | + | 0.408491i | \(0.133945\pi\) | ||||
−0.912762 | + | 0.408491i | \(0.866055\pi\) | |||||||
\(728\) | −3.58257e8 | + | 1.50707e8i | −0.928539 | + | 0.390606i | ||||
\(729\) | 5.61951e8 | 1.45049 | ||||||||
\(730\) | 2.20320e7 | 0.0566351 | ||||||||
\(731\) | − | 1.87313e8i | − | 0.479530i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.18118e7i | − | 0.182341i | −0.995835 | − | 0.0911704i | \(-0.970939\pi\) | ||
0.995835 | − | 0.0911704i | \(-0.0290608\pi\) | |||||||
\(734\) | 3.06221e7i | 0.0774366i | ||||||||
\(735\) | −1.67833e8 | + | 1.71564e8i | −0.422683 | + | 0.432079i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.32842e8 | 1.08125 | ||||||||
\(738\) | 6.03500e8i | 1.50144i | ||||||||
\(739\) | 2.77815e7 | 0.0688370 | 0.0344185 | − | 0.999408i | \(-0.489042\pi\) | ||||
0.0344185 | + | 0.999408i | \(0.489042\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.11523e8i | − | 0.765660i | ||||||
\(742\) | 8.12960e7 | + | 1.93255e8i | 0.199002 | + | 0.473063i | ||||
\(743\) | −7.03366e8 | −1.71481 | −0.857403 | − | 0.514646i | \(-0.827923\pi\) | ||||
−0.857403 | + | 0.514646i | \(0.827923\pi\) | |||||||
\(744\) | 6.35044e8 | 1.54200 | ||||||||
\(745\) | 1.17240e8i | 0.283535i | ||||||||
\(746\) | 3.95069e8 | 0.951604 | ||||||||
\(747\) | 9.37166e8i | 2.24830i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.14931e8 | + | 5.10930e8i | 0.511510 | + | 1.21595i | ||||
\(750\) | −4.76707e8 | −1.12997 | ||||||||
\(751\) | −3.00617e8 | −0.709731 | −0.354866 | − | 0.934917i | \(-0.615473\pi\) | ||||
−0.354866 | + | 0.934917i | \(0.615473\pi\) | |||||||
\(752\) | 2.96742e8i | 0.697792i | ||||||||
\(753\) | −7.10416e8 | −1.66390 | ||||||||
\(754\) | − | 1.97342e8i | − | 0.460369i | ||||||
\(755\) | 7.61309e7i | 0.176897i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.17057e8 | 0.269841 | 0.134921 | − | 0.990856i | \(-0.456922\pi\) | ||||
0.134921 | + | 0.990856i | \(0.456922\pi\) | |||||||
\(758\) | −2.99649e8 | −0.688026 | ||||||||
\(759\) | 1.87034e8i | 0.427756i | ||||||||
\(760\) | 7.20691e7 | 0.164176 | ||||||||
\(761\) | − | 2.63542e8i | − | 0.597992i | −0.954254 | − | 0.298996i | \(-0.903348\pi\) | ||
0.954254 | − | 0.298996i | \(-0.0966518\pi\) | |||||||
\(762\) | − | 1.20132e9i | − | 2.71516i | ||||||
\(763\) | 2.64971e7 | + | 6.29882e7i | 0.0596519 | + | 0.141803i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.53026e8 | 0.788538 | ||||||||
\(766\) | − | 4.00803e8i | − | 0.891752i | ||||||
\(767\) | −2.50600e8 | −0.555385 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.25689e8i | − | 0.276388i | −0.990405 | − | 0.138194i | \(-0.955870\pi\) | ||
0.990405 | − | 0.138194i | \(-0.0441298\pi\) | |||||||
\(770\) | −9.98458e7 | + | 4.20018e7i | −0.218704 | + | 0.0920017i | ||||
\(771\) | 3.40794e8 | 0.743582 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.58329e8i | − | 0.342786i | −0.985203 | − | 0.171393i | \(-0.945173\pi\) | ||
0.985203 | − | 0.171393i | \(-0.0548268\pi\) | |||||||
\(774\) | 3.29512e8 | 0.710638 | ||||||||
\(775\) | − | 3.73060e8i | − | 0.801444i | ||||||
\(776\) | 4.16993e8i | 0.892368i | ||||||||
\(777\) | −4.28686e7 | + | 1.80334e7i | −0.0913852 | + | 0.0384427i | ||||
\(778\) | −1.79989e6 | −0.00382214 | ||||||||
\(779\) | −1.79328e8 | −0.379347 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.61171e8 | −0.338324 | ||||||||
\(782\) | 2.25982e8i | 0.472557i | ||||||||
\(783\) | − | 2.92993e8i | − | 0.610340i | ||||||
\(784\) | 3.36982e8 | − | 3.44473e8i | 0.699292 | − | 0.714836i | ||||
\(785\) | 1.66050e8 | 0.343265 | ||||||||
\(786\) | 1.13302e9 | 2.33329 | ||||||||
\(787\) | 5.15726e8i | 1.05802i | 0.848615 | + | 0.529012i | \(0.177437\pi\) | ||||
−0.848615 | + | 0.529012i | \(0.822563\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 5.96464e8i | − | 1.21438i | ||||||
\(790\) | − | 1.93288e8i | − | 0.392034i | ||||||
\(791\) | −2.40414e8 | − | 5.71506e8i | −0.485769 | − | 1.15476i | ||||
\(792\) | −5.86657e8 | −1.18089 | ||||||||
\(793\) | 6.08856e8 | 1.22094 | ||||||||
\(794\) | − | 6.97549e6i | − | 0.0139352i | ||||||
\(795\) | −1.55868e8 | −0.310210 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.29429e8i | 1.83587i | 0.396735 | + | 0.917933i | \(0.370143\pi\) | ||||
−0.396735 | + | 0.917933i | \(0.629857\pi\) | |||||||
\(798\) | 1.49769e8 | + | 3.56027e8i | 0.294722 | + | 0.700606i | ||||
\(799\) | −4.31925e8 | −0.846775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.25312e8i | 1.60591i | ||||||||
\(802\) | −1.15927e8 | −0.224730 | ||||||||
\(803\) | − | 5.32918e7i | − | 0.102923i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.76586e7 | − | 2.84618e7i | 0.129699 | − | 0.0545600i | ||||
\(806\) | −4.86205e8 | −0.928570 | ||||||||
\(807\) | −7.20856e8 | −1.37160 | ||||||||
\(808\) | − | 9.99401e8i | − | 1.89455i | ||||||
\(809\) | −6.89731e8 | −1.30267 | −0.651335 | − | 0.758791i | \(-0.725791\pi\) | ||||
−0.651335 | + | 0.758791i | \(0.725791\pi\) | |||||||
\(810\) | 8.36701e7i | 0.157440i | ||||||||
\(811\) | − | 2.85961e7i | − | 0.0536099i | −0.999641 | − | 0.0268049i | \(-0.991467\pi\) | ||
0.999641 | − | 0.0268049i | \(-0.00853330\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.12214e9 | 2.08821 | ||||||||
\(814\) | −2.09900e7 | −0.0389170 | ||||||||
\(815\) | − | 8.49992e7i | − | 0.157015i | ||||||
\(816\) | −1.10297e9 | −2.02999 | ||||||||
\(817\) | 9.79135e7i | 0.179546i | ||||||||
\(818\) | 8.34424e8i | 1.52450i | ||||||||
\(819\) | 9.17333e8 | − | 3.85892e8i | 1.66984 | − | 0.702447i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.51151e8 | −0.453844 | −0.226922 | − | 0.973913i | \(-0.572866\pi\) | ||||
−0.226922 | + | 0.973913i | \(0.572866\pi\) | |||||||
\(822\) | − | 7.69370e8i | − | 1.38522i | ||||||
\(823\) | 2.40085e8 | 0.430691 | 0.215346 | − | 0.976538i | \(-0.430912\pi\) | ||||
0.215346 | + | 0.976538i | \(0.430912\pi\) | |||||||
\(824\) | 8.69090e8i | 1.55340i | ||||||||
\(825\) | 5.36273e8i | 0.955046i | ||||||||
\(826\) | 2.86400e8 | − | 1.20479e8i | 0.508197 | − | 0.213782i | ||||
\(827\) | 9.14380e8 | 1.61663 | 0.808314 | − | 0.588751i | \(-0.200380\pi\) | ||||
0.808314 | + | 0.588751i | \(0.200380\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.22917e8i | − | 0.917845i | −0.888476 | − | 0.458922i | \(-0.848236\pi\) | ||
0.888476 | − | 0.458922i | \(-0.151764\pi\) | |||||||
\(830\) | 2.58297e8 | 0.451736 | ||||||||
\(831\) | 7.22721e8i | 1.25941i | ||||||||
\(832\) | 5.80164e8i | 1.00735i | ||||||||
\(833\) | 5.01399e8 | + | 4.90496e8i | 0.867459 | + | 0.848596i | ||||
\(834\) | −6.08556e8 | −1.04907 | ||||||||
\(835\) | −1.42543e8 | −0.244842 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.21866e8 | −1.23106 | ||||||||
\(838\) | − | 6.57660e8i | − | 1.11756i | ||||||
\(839\) | − | 9.46684e8i | − | 1.60295i | −0.598030 | − | 0.801474i | \(-0.704050\pi\) | ||
0.598030 | − | 0.801474i | \(-0.295950\pi\) | |||||||
\(840\) | 1.38916e8 | + | 3.30228e8i | 0.234376 | + | 0.557154i | ||||
\(841\) | −4.70590e8 | −0.791142 | ||||||||
\(842\) | 1.07024e8 | 0.179285 | ||||||||
\(843\) | − | 2.72609e7i | − | 0.0455048i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.21724e6i | 0.00533229i | ||||||||
\(846\) | − | 7.59822e8i | − | 1.25488i | ||||||
\(847\) | −1.34022e8 | − | 3.18594e8i | −0.220560 | − | 0.524309i | ||||
\(848\) | 3.12959e8 | 0.513216 | ||||||||
\(849\) | −1.00357e9 | −1.63993 | ||||||||
\(850\) | 6.47946e8i | 1.05507i | ||||||||
\(851\) | 1.42235e7 | 0.0230790 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.30334e8i | 0.371117i | 0.982633 | + | 0.185558i | \(0.0594094\pi\) | ||||
−0.982633 | + | 0.185558i | \(0.940591\pi\) | |||||||
\(854\) | −6.95836e8 | + | 2.92715e8i | −1.11721 | + | 0.469972i | ||||
\(855\) | −1.84536e8 | −0.295246 | ||||||||
\(856\) | 8.27405e8 | 1.31916 | ||||||||
\(857\) | 4.34496e7i | 0.0690308i | 0.999404 | + | 0.0345154i | \(0.0109888\pi\) | ||||
−0.999404 | + | 0.0345154i | \(0.989011\pi\) | |||||||
\(858\) | 6.98920e8 | 1.10654 | ||||||||
\(859\) | 1.61129e8i | 0.254211i | 0.991889 | + | 0.127105i | \(0.0405686\pi\) | ||||
−0.991889 | + | 0.127105i | \(0.959431\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.45662e8 | − | 8.21699e8i | −0.541554 | − | 1.28737i | ||||
\(862\) | 1.07396e9 | 1.67673 | ||||||||
\(863\) | 2.56357e8 | 0.398853 | 0.199426 | − | 0.979913i | \(-0.436092\pi\) | ||||
0.199426 | + | 0.979913i | \(0.436092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.03646e8 | −0.160142 | ||||||||
\(866\) | − | 8.25842e8i | − | 1.27158i | ||||||
\(867\) | − | 5.15230e8i | − | 0.790577i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.67532e8 | −0.712447 | ||||||||
\(870\) | −1.81903e8 | −0.276237 | ||||||||
\(871\) | 1.09605e9i | 1.65872i | ||||||||
\(872\) | 1.02004e8 | 0.153839 | ||||||||
\(873\) | − | 1.06773e9i | − | 1.60479i | ||||||
\(874\) | − | 1.18127e8i | − | 0.176935i | ||||||
\(875\) | 4.17119e8 | − | 1.75468e8i | 0.622638 | − | 0.261923i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.47675e8 | 0.367184 | 0.183592 | − | 0.983003i | \(-0.441228\pi\) | ||||
0.183592 | + | 0.983003i | \(0.441228\pi\) | |||||||
\(878\) | 2.12653e8i | 0.314186i | ||||||||
\(879\) | 1.93373e9 | 2.84727 | ||||||||
\(880\) | 1.61691e8i | 0.237268i | ||||||||
\(881\) | − | 1.05612e9i | − | 1.54450i | −0.635320 | − | 0.772249i | \(-0.719132\pi\) | ||
0.635320 | − | 0.772249i | \(-0.280868\pi\) | |||||||
\(882\) | −8.62858e8 | + | 8.82038e8i | −1.25757 | + | 1.28553i | ||||
\(883\) | −5.38572e8 | −0.782278 | −0.391139 | − | 0.920332i | \(-0.627919\pi\) | ||||
−0.391139 | + | 0.920332i | \(0.627919\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.30993e8i | 0.333250i | ||||||||
\(886\) | −1.05577e9 | −1.51799 | ||||||||
\(887\) | − | 1.13395e8i | − | 0.162489i | −0.996694 | − | 0.0812445i | \(-0.974111\pi\) | ||
0.996694 | − | 0.0812445i | \(-0.0258895\pi\) | |||||||
\(888\) | 6.94218e7i | 0.0991418i | ||||||||
\(889\) | 4.42188e8 | + | 1.05116e9i | 0.629364 | + | 1.49611i | ||||
\(890\) | 2.27468e8 | 0.322664 | ||||||||
\(891\) | 2.02384e8 | 0.286117 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.25779e8 | 0.317051 | ||||||||
\(894\) | 9.37919e8i | 1.31266i | ||||||||
\(895\) | − | 1.58916e8i | − | 0.221666i | ||||||
\(896\) | −2.78921e8 | − | 6.63045e8i | −0.387755 | − | 0.921762i | ||||
\(897\) | −4.73610e8 | −0.656212 | ||||||||
\(898\) | −1.18213e9 | −1.63244 | ||||||||
\(899\) | − | 3.06082e8i | − | 0.421268i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.55529e8i | 0.622791i | ||||||||
\(902\) | − | 4.02333e8i | − | 0.548234i | ||||||
\(903\) | −4.48649e8 | + | 1.88732e8i | −0.609317 | + | 0.256320i | ||||
\(904\) | −9.25502e8 | −1.25277 | ||||||||
\(905\) | −3.37965e8 | −0.455959 | ||||||||
\(906\) | 6.09047e8i | 0.818967i | ||||||||
\(907\) | −4.58651e8 | −0.614696 | −0.307348 | − | 0.951597i | \(-0.599442\pi\) | ||||
−0.307348 | + | 0.951597i | \(0.599442\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.55901e9i | 3.40707i | ||||||||
\(910\) | −1.06357e8 | − | 2.52830e8i | −0.141138 | − | 0.335510i | ||||
\(911\) | 6.00692e8 | 0.794505 | 0.397253 | − | 0.917709i | \(-0.369964\pi\) | ||||
0.397253 | + | 0.917709i | \(0.369964\pi\) | |||||||
\(912\) | 5.76553e8 | 0.760072 | ||||||||
\(913\) | − | 6.24777e8i | − | 0.820943i | ||||||
\(914\) | 6.58294e8 | 0.862147 | ||||||||
\(915\) | − | 5.61221e8i | − | 0.732606i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.91389e8 | + | 4.17045e8i | −1.28569 | + | 0.540847i | ||||
\(918\) | 1.25377e9 | 1.62065 | ||||||||
\(919\) | 7.19637e8 | 0.927187 | 0.463593 | − | 0.886048i | \(-0.346560\pi\) | ||||
0.463593 | + | 0.886048i | \(0.346560\pi\) | |||||||
\(920\) | − | 1.09567e8i | − | 0.140707i | ||||||
\(921\) | 1.81637e9 | 2.32502 | ||||||||
\(922\) | 1.05507e9i | 1.34614i | ||||||||
\(923\) | − | 4.08118e8i | − | 0.519016i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.07822e7 | 0.0515282 | ||||||||
\(926\) | −1.11942e7 | −0.0140981 | ||||||||
\(927\) | − | 2.22535e9i | − | 2.79356i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.63919e8i | 0.578622i | 0.957235 | + | 0.289311i | \(0.0934262\pi\) | ||||
−0.957235 | + | 0.289311i | \(0.906574\pi\) | |||||||
\(930\) | 4.48166e8i | 0.557173i | ||||||||
\(931\) | −2.62095e8 | − | 2.56396e8i | −0.324795 | − | 0.317733i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.65664e8 | −0.819616 | ||||||||
\(934\) | 1.45057e8i | 0.178032i | ||||||||
\(935\) | −2.35351e8 | −0.287926 | ||||||||
\(936\) | − | 1.48554e9i | − | 1.81157i | ||||||
\(937\) | − | 1.26911e9i | − | 1.54269i | −0.636417 | − | 0.771345i | \(-0.719584\pi\) | ||
0.636417 | − | 0.771345i | \(-0.280416\pi\) | |||||||
\(938\) | −5.26937e8 | − | 1.25262e9i | −0.638485 | − | 1.51779i | ||||
\(939\) | −1.89468e9 | −2.28844 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.06092e8i | 0.127325i | 0.997971 | + | 0.0636626i | \(0.0202782\pi\) | ||||
−0.997971 | + | 0.0636626i | \(0.979722\pi\) | |||||||
\(942\) | 1.32840e9 | 1.58919 | ||||||||
\(943\) | 2.72634e8i | 0.325121i | ||||||||
\(944\) | − | 4.63799e8i | − | 0.551332i | ||||||
\(945\) | −1.57908e8 | − | 3.75376e8i | −0.187115 | − | 0.444806i | ||||
\(946\) | −2.19675e8 | −0.259482 | ||||||||
\(947\) | 3.60651e8 | 0.424655 | 0.212328 | − | 0.977199i | \(-0.431896\pi\) | ||||
0.212328 | + | 0.977199i | \(0.431896\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.34946e8 | 0.157892 | ||||||||
\(950\) | − | 3.38699e8i | − | 0.395042i | ||||||
\(951\) | 1.94632e9i | 2.26294i | ||||||||
\(952\) | 9.65100e8 | − | 4.05986e8i | 1.11857 | − | 0.470543i | ||||
\(953\) | 1.35809e9 | 1.56910 | 0.784551 | − | 0.620064i | \(-0.212893\pi\) | ||||
0.784551 | + | 0.620064i | \(0.212893\pi\) | |||||||
\(954\) | −8.01346e8 | −0.922943 | ||||||||
\(955\) | 3.25210e8i | 0.373383i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.39993e8i | 0.502007i | ||||||||
\(958\) | 2.31500e8i | 0.263303i | ||||||||
\(959\) | 2.83192e8 | + | 6.73198e8i | 0.321089 | + | 0.763286i | ||||
\(960\) | 5.34774e8 | 0.604444 | ||||||||
\(961\) | 1.33389e8 | 0.150297 | ||||||||
\(962\) | − | 5.31510e7i | − | 0.0597017i | ||||||
\(963\) | −2.11861e9 | −2.37231 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.91178e8i | 0.657864i | ||||||||
\(966\) | 5.41269e8 | − | 2.27694e8i | 0.600457 | − | 0.252592i | ||||
\(967\) | 4.83872e8 | 0.535119 | 0.267560 | − | 0.963541i | \(-0.413783\pi\) | ||||
0.267560 | + | 0.963541i | \(0.413783\pi\) | |||||||
\(968\) | −5.15935e8 | −0.568812 | ||||||||
\(969\) | 8.39205e8i | 0.922353i | ||||||||
\(970\) | −2.94282e8 | −0.322440 | ||||||||
\(971\) | 3.07992e8i | 0.336420i | 0.985751 | + | 0.168210i | \(0.0537987\pi\) | ||||
−0.985751 | + | 0.168210i | \(0.946201\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.32487e8 | − | 2.24000e8i | 0.578057 | − | 0.243169i | ||||
\(974\) | 7.58012e8 | 0.820350 | ||||||||
\(975\) | −1.35796e9 | −1.46512 | ||||||||
\(976\) | 1.12684e9i | 1.21203i | ||||||||
\(977\) | −2.33410e8 | −0.250285 | −0.125143 | − | 0.992139i | \(-0.539939\pi\) | ||||
−0.125143 | + | 0.992139i | \(0.539939\pi\) | |||||||
\(978\) | − | 6.79994e8i | − | 0.726923i | ||||||
\(979\) | − | 5.50208e8i | − | 0.586380i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.61185e8 | −0.276657 | ||||||||
\(982\) | 2.07067e8 | 0.218663 | ||||||||
\(983\) | 6.02617e8i | 0.634426i | 0.948354 | + | 0.317213i | \(0.102747\pi\) | ||||
−0.948354 | + | 0.317213i | \(0.897253\pi\) | |||||||
\(984\) | −1.33067e9 | −1.39664 | ||||||||
\(985\) | 4.14390e8i | 0.433612i | ||||||||
\(986\) | 5.31616e8i | 0.554584i | ||||||||
\(987\) | 4.35197e8 | + | 1.03454e9i | 0.452621 | + | 1.07596i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.48858e8 | 0.153881 | ||||||||
\(990\) | − | 4.14018e8i | − | 0.426691i | ||||||
\(991\) | 1.12772e9 | 1.15873 | 0.579364 | − | 0.815069i | \(-0.303301\pi\) | ||||
0.579364 | + | 0.815069i | \(0.303301\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.40377e9i | − | 2.45497i | ||||||
\(994\) | 1.96208e8 | + | 4.66421e8i | 0.199783 | + | 0.474918i | ||||
\(995\) | −3.06575e8 | −0.311220 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.17224e9i | − | 1.18286i | −0.806357 | − | 0.591429i | \(-0.798564\pi\) | ||
0.806357 | − | 0.591429i | \(-0.201436\pi\) | |||||||
\(998\) | −1.24819e9 | −1.25571 | ||||||||
\(999\) | − | 7.89130e7i | − | 0.0791503i |
(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 | 7.7.b.b.6.2 | yes | 2 | |
3.2 | odd | 2 | 63.7.d.d.55.2 | 2 | |||
4.3 | odd | 2 | 112.7.c.b.97.1 | 2 | |||
5.2 | odd | 4 | 175.7.c.c.174.2 | 4 | |||
5.3 | odd | 4 | 175.7.c.c.174.3 | 4 | |||
5.4 | even | 2 | 175.7.d.e.76.1 | 2 | |||
7.2 | even | 3 | 49.7.d.d.31.1 | 4 | |||
7.3 | odd | 6 | 49.7.d.d.19.1 | 4 | |||
7.4 | even | 3 | 49.7.d.d.19.2 | 4 | |||
7.5 | odd | 6 | 49.7.d.d.31.2 | 4 | |||
7.6 | odd | 2 | inner | 7.7.b.b.6.1 | ✓ | 2 | |
8.3 | odd | 2 | 448.7.c.c.321.2 | 2 | |||
8.5 | even | 2 | 448.7.c.d.321.1 | 2 | |||
21.20 | even | 2 | 63.7.d.d.55.1 | 2 | |||
28.27 | even | 2 | 112.7.c.b.97.2 | 2 | |||
35.13 | even | 4 | 175.7.c.c.174.4 | 4 | |||
35.27 | even | 4 | 175.7.c.c.174.1 | 4 | |||
35.34 | odd | 2 | 175.7.d.e.76.2 | 2 | |||
56.13 | odd | 2 | 448.7.c.d.321.2 | 2 | |||
56.27 | even | 2 | 448.7.c.c.321.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.7.b.b.6.1 | ✓ | 2 | 7.6 | odd | 2 | inner | |
7.7.b.b.6.2 | yes | 2 | 1.1 | even | 1 | trivial | |
49.7.d.d.19.1 | 4 | 7.3 | odd | 6 | |||
49.7.d.d.19.2 | 4 | 7.4 | even | 3 | |||
49.7.d.d.31.1 | 4 | 7.2 | even | 3 | |||
49.7.d.d.31.2 | 4 | 7.5 | odd | 6 | |||
63.7.d.d.55.1 | 2 | 21.20 | even | 2 | |||
63.7.d.d.55.2 | 2 | 3.2 | odd | 2 | |||
112.7.c.b.97.1 | 2 | 4.3 | odd | 2 | |||
112.7.c.b.97.2 | 2 | 28.27 | even | 2 | |||
175.7.c.c.174.1 | 4 | 35.27 | even | 4 | |||
175.7.c.c.174.2 | 4 | 5.2 | odd | 4 | |||
175.7.c.c.174.3 | 4 | 5.3 | odd | 4 | |||
175.7.c.c.174.4 | 4 | 35.13 | even | 4 | |||
175.7.d.e.76.1 | 2 | 5.4 | even | 2 | |||
175.7.d.e.76.2 | 2 | 35.34 | odd | 2 | |||
448.7.c.c.321.1 | 2 | 56.27 | even | 2 | |||
448.7.c.c.321.2 | 2 | 8.3 | odd | 2 | |||
448.7.c.d.321.1 | 2 | 8.5 | even | 2 | |||
448.7.c.d.321.2 | 2 | 56.13 | odd | 2 |