Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,7,Mod(18,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, 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("19.18");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.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: | \(4.37102758878\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 483x^{6} + 75582x^{4} + 4242376x^{2} + 71047680 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 29 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 18.8 | ||
Root | \(14.9269i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 19.18 |
Dual form | 19.7.b.b.18.1 |
$q$-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 \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 14.9269i | 1.86587i | 0.360047 | + | 0.932934i | \(0.382761\pi\) | ||||
−0.360047 | + | 0.932934i | \(0.617239\pi\) | |||||||
\(3\) | 33.0827i | 1.22529i | 0.790360 | + | 0.612643i | \(0.209894\pi\) | ||||
−0.790360 | + | 0.612643i | \(0.790106\pi\) | |||||||
\(4\) | −158.814 | −2.48146 | ||||||||
\(5\) | 159.622 | 1.27698 | 0.638489 | − | 0.769631i | \(-0.279560\pi\) | ||||
0.638489 | + | 0.769631i | \(0.279560\pi\) | |||||||
\(6\) | −493.824 | −2.28622 | ||||||||
\(7\) | 445.794 | 1.29969 | 0.649845 | − | 0.760067i | \(-0.274834\pi\) | ||||
0.649845 | + | 0.760067i | \(0.274834\pi\) | |||||||
\(8\) | − | 1415.28i | − | 2.76422i | ||||||
\(9\) | −365.466 | −0.501325 | ||||||||
\(10\) | 2382.67i | 2.38267i | ||||||||
\(11\) | −1700.61 | −1.27770 | −0.638848 | − | 0.769333i | \(-0.720589\pi\) | ||||
−0.638848 | + | 0.769333i | \(0.720589\pi\) | |||||||
\(12\) | − | 5253.99i | − | 3.04050i | ||||||
\(13\) | − | 439.288i | − | 0.199949i | −0.994990 | − | 0.0999746i | \(-0.968124\pi\) | ||
0.994990 | − | 0.0999746i | \(-0.0318762\pi\) | |||||||
\(14\) | 6654.34i | 2.42505i | ||||||||
\(15\) | 5280.74i | 1.56466i | ||||||||
\(16\) | 10961.7 | 2.67620 | ||||||||
\(17\) | 569.044 | 0.115824 | 0.0579121 | − | 0.998322i | \(-0.481556\pi\) | ||||
0.0579121 | + | 0.998322i | \(0.481556\pi\) | |||||||
\(18\) | − | 5455.29i | − | 0.935407i | ||||||
\(19\) | 6482.51 | − | 2241.20i | 0.945110 | − | 0.326754i | ||||
\(20\) | −25350.2 | −3.16878 | ||||||||
\(21\) | 14748.1i | 1.59249i | ||||||||
\(22\) | − | 25385.0i | − | 2.38401i | ||||||
\(23\) | −2746.30 | −0.225717 | −0.112859 | − | 0.993611i | \(-0.536001\pi\) | ||||
−0.112859 | + | 0.993611i | \(0.536001\pi\) | |||||||
\(24\) | 46821.3 | 3.38695 | ||||||||
\(25\) | 9854.28 | 0.630674 | ||||||||
\(26\) | 6557.23 | 0.373079 | ||||||||
\(27\) | 12026.7i | 0.611019i | ||||||||
\(28\) | −70798.1 | −3.22513 | ||||||||
\(29\) | − | 26932.8i | − | 1.10430i | −0.833745 | − | 0.552150i | \(-0.813807\pi\) | ||
0.833745 | − | 0.552150i | \(-0.186193\pi\) | |||||||
\(30\) | −78825.3 | −2.91946 | ||||||||
\(31\) | 29892.3i | 1.00340i | 0.865041 | + | 0.501701i | \(0.167292\pi\) | ||||
−0.865041 | + | 0.501701i | \(0.832708\pi\) | |||||||
\(32\) | 73047.0i | 2.22922i | ||||||||
\(33\) | − | 56260.9i | − | 1.56554i | ||||||
\(34\) | 8494.09i | 0.216113i | ||||||||
\(35\) | 71158.6 | 1.65968 | ||||||||
\(36\) | 58041.0 | 1.24402 | ||||||||
\(37\) | − | 52516.0i | − | 1.03678i | −0.855144 | − | 0.518390i | \(-0.826532\pi\) | ||
0.855144 | − | 0.518390i | \(-0.173468\pi\) | |||||||
\(38\) | 33454.3 | + | 96764.0i | 0.609679 | + | 1.76345i | ||||
\(39\) | 14532.9 | 0.244995 | ||||||||
\(40\) | − | 225910.i | − | 3.52984i | ||||||
\(41\) | 27399.8i | 0.397554i | 0.980045 | + | 0.198777i | \(0.0636970\pi\) | ||||
−0.980045 | + | 0.198777i | \(0.936303\pi\) | |||||||
\(42\) | −220144. | −2.97138 | ||||||||
\(43\) | 67448.4 | 0.848332 | 0.424166 | − | 0.905584i | \(-0.360567\pi\) | ||||
0.424166 | + | 0.905584i | \(0.360567\pi\) | |||||||
\(44\) | 270081. | 3.17056 | ||||||||
\(45\) | −58336.5 | −0.640181 | ||||||||
\(46\) | − | 40993.9i | − | 0.421159i | ||||||
\(47\) | −66319.6 | −0.638776 | −0.319388 | − | 0.947624i | \(-0.603477\pi\) | ||||
−0.319388 | + | 0.947624i | \(0.603477\pi\) | |||||||
\(48\) | 362643.i | 3.27911i | ||||||||
\(49\) | 81083.1 | 0.689195 | ||||||||
\(50\) | 147094.i | 1.17675i | ||||||||
\(51\) | 18825.5i | 0.141918i | ||||||||
\(52\) | 69765.0i | 0.496167i | ||||||||
\(53\) | − | 59959.3i | − | 0.402744i | −0.979515 | − | 0.201372i | \(-0.935460\pi\) | ||
0.979515 | − | 0.201372i | \(-0.0645399\pi\) | |||||||
\(54\) | −179522. | −1.14008 | ||||||||
\(55\) | −271456. | −1.63159 | ||||||||
\(56\) | − | 630922.i | − | 3.59262i | ||||||
\(57\) | 74145.1 | + | 214459.i | 0.400367 | + | 1.15803i | ||||
\(58\) | 402024. | 2.06048 | ||||||||
\(59\) | 396359.i | 1.92989i | 0.262452 | + | 0.964945i | \(0.415469\pi\) | ||||
−0.262452 | + | 0.964945i | \(0.584531\pi\) | |||||||
\(60\) | − | 838654.i | − | 3.88266i | ||||||
\(61\) | −73557.7 | −0.324070 | −0.162035 | − | 0.986785i | \(-0.551806\pi\) | ||||
−0.162035 | + | 0.986785i | \(0.551806\pi\) | |||||||
\(62\) | −446201. | −1.87222 | ||||||||
\(63\) | −162922. | −0.651567 | ||||||||
\(64\) | −388819. | −1.48323 | ||||||||
\(65\) | − | 70120.2i | − | 0.255331i | ||||||
\(66\) | 839803. | 2.92110 | ||||||||
\(67\) | − | 160211.i | − | 0.532681i | −0.963879 | − | 0.266341i | \(-0.914185\pi\) | ||
0.963879 | − | 0.266341i | \(-0.0858146\pi\) | |||||||
\(68\) | −90372.0 | −0.287413 | ||||||||
\(69\) | − | 90855.2i | − | 0.276568i | ||||||
\(70\) | 1.06218e6i | 3.09674i | ||||||||
\(71\) | − | 259957.i | − | 0.726317i | −0.931727 | − | 0.363158i | \(-0.881698\pi\) | ||
0.931727 | − | 0.363158i | \(-0.118302\pi\) | |||||||
\(72\) | 517236.i | 1.38577i | ||||||||
\(73\) | 291024. | 0.748101 | 0.374051 | − | 0.927408i | \(-0.377969\pi\) | ||||
0.374051 | + | 0.927408i | \(0.377969\pi\) | |||||||
\(74\) | 783903. | 1.93449 | ||||||||
\(75\) | 326006.i | 0.772755i | ||||||||
\(76\) | −1.02951e6 | + | 355934.i | −2.34525 | + | 0.810827i | ||||
\(77\) | −758123. | −1.66061 | ||||||||
\(78\) | 216931.i | 0.457128i | ||||||||
\(79\) | − | 917363.i | − | 1.86063i | −0.366761 | − | 0.930315i | \(-0.619533\pi\) | ||
0.366761 | − | 0.930315i | \(-0.380467\pi\) | |||||||
\(80\) | 1.74973e6 | 3.41745 | ||||||||
\(81\) | −664300. | −1.25000 | ||||||||
\(82\) | −408996. | −0.741784 | ||||||||
\(83\) | 681097. | 1.19117 | 0.595586 | − | 0.803291i | \(-0.296920\pi\) | ||||
0.595586 | + | 0.803291i | \(0.296920\pi\) | |||||||
\(84\) | − | 2.34219e6i | − | 3.95171i | ||||||
\(85\) | 90832.1 | 0.147905 | ||||||||
\(86\) | 1.00680e6i | 1.58288i | ||||||||
\(87\) | 891010. | 1.35308 | ||||||||
\(88\) | 2.40684e6i | 3.53183i | ||||||||
\(89\) | − | 242644.i | − | 0.344191i | −0.985080 | − | 0.172095i | \(-0.944946\pi\) | ||
0.985080 | − | 0.172095i | \(-0.0550537\pi\) | |||||||
\(90\) | − | 870786.i | − | 1.19449i | ||||||
\(91\) | − | 195832.i | − | 0.259872i | ||||||
\(92\) | 436151. | 0.560110 | ||||||||
\(93\) | −988920. | −1.22945 | ||||||||
\(94\) | − | 989949.i | − | 1.19187i | ||||||
\(95\) | 1.03475e6 | − | 357746.i | 1.20688 | − | 0.417257i | ||||
\(96\) | −2.41659e6 | −2.73143 | ||||||||
\(97\) | − | 1.24569e6i | − | 1.36488i | −0.730941 | − | 0.682440i | \(-0.760919\pi\) | ||
0.730941 | − | 0.682440i | \(-0.239081\pi\) | |||||||
\(98\) | 1.21032e6i | 1.28595i | ||||||||
\(99\) | 621516. | 0.640541 | ||||||||
\(100\) | −1.56499e6 | −1.56499 | ||||||||
\(101\) | −1.34311e6 | −1.30361 | −0.651807 | − | 0.758385i | \(-0.725989\pi\) | ||||
−0.651807 | + | 0.758385i | \(0.725989\pi\) | |||||||
\(102\) | −281007. | −0.264800 | ||||||||
\(103\) | 1.37650e6i | 1.25969i | 0.776719 | + | 0.629847i | \(0.216883\pi\) | ||||
−0.776719 | + | 0.629847i | \(0.783117\pi\) | |||||||
\(104\) | −621715. | −0.552703 | ||||||||
\(105\) | 2.35412e6i | 2.03358i | ||||||||
\(106\) | 895009. | 0.751466 | ||||||||
\(107\) | 920616.i | 0.751497i | 0.926722 | + | 0.375748i | \(0.122614\pi\) | ||||
−0.926722 | + | 0.375748i | \(0.877386\pi\) | |||||||
\(108\) | − | 1.91000e6i | − | 1.51622i | ||||||
\(109\) | 385747.i | 0.297868i | 0.988847 | + | 0.148934i | \(0.0475841\pi\) | ||||
−0.988847 | + | 0.148934i | \(0.952416\pi\) | |||||||
\(110\) | − | 4.05200e6i | − | 3.04433i | ||||||
\(111\) | 1.73737e6 | 1.27035 | ||||||||
\(112\) | 4.88666e6 | 3.47823 | ||||||||
\(113\) | − | 620853.i | − | 0.430282i | −0.976583 | − | 0.215141i | \(-0.930979\pi\) | ||
0.976583 | − | 0.215141i | \(-0.0690212\pi\) | |||||||
\(114\) | −3.20122e6 | + | 1.10676e6i | −2.16073 | + | 0.747031i | ||||
\(115\) | −438371. | −0.288236 | ||||||||
\(116\) | 4.27729e6i | 2.74028i | ||||||||
\(117\) | 160545.i | 0.100240i | ||||||||
\(118\) | −5.91643e6 | −3.60092 | ||||||||
\(119\) | 253676. | 0.150536 | ||||||||
\(120\) | 7.47372e6 | 4.32507 | ||||||||
\(121\) | 1.12052e6 | 0.632506 | ||||||||
\(122\) | − | 1.09799e6i | − | 0.604671i | ||||||
\(123\) | −906461. | −0.487118 | ||||||||
\(124\) | − | 4.74731e6i | − | 2.48990i | ||||||
\(125\) | −921136. | −0.471622 | ||||||||
\(126\) | − | 2.43193e6i | − | 1.21574i | ||||||
\(127\) | − | 1.13559e6i | − | 0.554385i | −0.960814 | − | 0.277193i | \(-0.910596\pi\) | ||
0.960814 | − | 0.277193i | \(-0.0894041\pi\) | |||||||
\(128\) | − | 1.12887e6i | − | 0.538288i | ||||||
\(129\) | 2.23138e6i | 1.03945i | ||||||||
\(130\) | 1.04668e6 | 0.476414 | ||||||||
\(131\) | −370425. | −0.164773 | −0.0823866 | − | 0.996600i | \(-0.526254\pi\) | ||||
−0.0823866 | + | 0.996600i | \(0.526254\pi\) | |||||||
\(132\) | 8.93500e6i | 3.88484i | ||||||||
\(133\) | 2.88986e6 | − | 999114.i | 1.22835 | − | 0.424679i | ||||
\(134\) | 2.39146e6 | 0.993913 | ||||||||
\(135\) | 1.91973e6i | 0.780258i | ||||||||
\(136\) | − | 805356.i | − | 0.320163i | ||||||
\(137\) | −2.35314e6 | −0.915136 | −0.457568 | − | 0.889175i | \(-0.651279\pi\) | ||||
−0.457568 | + | 0.889175i | \(0.651279\pi\) | |||||||
\(138\) | 1.35619e6 | 0.516040 | ||||||||
\(139\) | 2.91982e6 | 1.08720 | 0.543602 | − | 0.839343i | \(-0.317060\pi\) | ||||
0.543602 | + | 0.839343i | \(0.317060\pi\) | |||||||
\(140\) | −1.13010e7 | −4.11843 | ||||||||
\(141\) | − | 2.19403e6i | − | 0.782683i | ||||||
\(142\) | 3.88036e6 | 1.35521 | ||||||||
\(143\) | 747059.i | 0.255474i | ||||||||
\(144\) | −4.00613e6 | −1.34165 | ||||||||
\(145\) | − | 4.29907e6i | − | 1.41017i | ||||||
\(146\) | 4.34410e6i | 1.39586i | ||||||||
\(147\) | 2.68245e6i | 0.844461i | ||||||||
\(148\) | 8.34026e6i | 2.57273i | ||||||||
\(149\) | −1.34951e6 | −0.407961 | −0.203980 | − | 0.978975i | \(-0.565388\pi\) | ||||
−0.203980 | + | 0.978975i | \(0.565388\pi\) | |||||||
\(150\) | −4.86628e6 | −1.44186 | ||||||||
\(151\) | − | 5.87074e6i | − | 1.70515i | −0.522607 | − | 0.852574i | \(-0.675040\pi\) | ||
0.522607 | − | 0.852574i | \(-0.324960\pi\) | |||||||
\(152\) | −3.17193e6 | − | 9.17455e6i | −0.903218 | − | 2.61249i | ||||
\(153\) | −207966. | −0.0580656 | ||||||||
\(154\) | − | 1.13165e7i | − | 3.09848i | ||||||
\(155\) | 4.77148e6i | 1.28132i | ||||||||
\(156\) | −2.30802e6 | −0.607946 | ||||||||
\(157\) | −673724. | −0.174094 | −0.0870469 | − | 0.996204i | \(-0.527743\pi\) | ||||
−0.0870469 | + | 0.996204i | \(0.527743\pi\) | |||||||
\(158\) | 1.36934e7 | 3.47169 | ||||||||
\(159\) | 1.98362e6 | 0.493476 | ||||||||
\(160\) | 1.16599e7i | 2.84666i | ||||||||
\(161\) | −1.22429e6 | −0.293363 | ||||||||
\(162\) | − | 9.91597e6i | − | 2.33233i | ||||||
\(163\) | −4.36326e6 | −1.00751 | −0.503754 | − | 0.863847i | \(-0.668048\pi\) | ||||
−0.503754 | + | 0.863847i | \(0.668048\pi\) | |||||||
\(164\) | − | 4.35147e6i | − | 0.986517i | ||||||
\(165\) | − | 8.98049e6i | − | 1.99916i | ||||||
\(166\) | 1.01667e7i | 2.22257i | ||||||||
\(167\) | − | 2.14529e6i | − | 0.460613i | −0.973118 | − | 0.230306i | \(-0.926027\pi\) | ||
0.973118 | − | 0.230306i | \(-0.0739728\pi\) | |||||||
\(168\) | 2.08726e7 | 4.40199 | ||||||||
\(169\) | 4.63383e6 | 0.960020 | ||||||||
\(170\) | 1.35585e6i | 0.275971i | ||||||||
\(171\) | −2.36914e6 | + | 819084.i | −0.473807 | + | 0.163810i | ||||
\(172\) | −1.07117e7 | −2.10511 | ||||||||
\(173\) | 3.44402e6i | 0.665161i | 0.943075 | + | 0.332581i | \(0.107919\pi\) | ||||
−0.943075 | + | 0.332581i | \(0.892081\pi\) | |||||||
\(174\) | 1.33001e7i | 2.52468i | ||||||||
\(175\) | 4.39297e6 | 0.819680 | ||||||||
\(176\) | −1.86416e7 | −3.41937 | ||||||||
\(177\) | −1.31126e7 | −2.36467 | ||||||||
\(178\) | 3.62193e6 | 0.642214 | ||||||||
\(179\) | 9.69997e6i | 1.69126i | 0.533767 | + | 0.845632i | \(0.320776\pi\) | ||||
−0.533767 | + | 0.845632i | \(0.679224\pi\) | |||||||
\(180\) | 9.26464e6 | 1.58859 | ||||||||
\(181\) | 6.17944e6i | 1.04211i | 0.853523 | + | 0.521055i | \(0.174461\pi\) | ||||
−0.853523 | + | 0.521055i | \(0.825539\pi\) | |||||||
\(182\) | 2.92317e6 | 0.484887 | ||||||||
\(183\) | − | 2.43349e6i | − | 0.397078i | ||||||
\(184\) | 3.88679e6i | 0.623932i | ||||||||
\(185\) | − | 8.38272e6i | − | 1.32395i | ||||||
\(186\) | − | 1.47616e7i | − | 2.29400i | ||||||
\(187\) | −967724. | −0.147988 | ||||||||
\(188\) | 1.05325e7 | 1.58510 | ||||||||
\(189\) | 5.36142e6i | 0.794136i | ||||||||
\(190\) | 5.34005e6 | + | 1.54457e7i | 0.778547 | + | 2.25189i | ||||
\(191\) | 6.71701e6 | 0.963998 | 0.481999 | − | 0.876172i | \(-0.339911\pi\) | ||||
0.481999 | + | 0.876172i | \(0.339911\pi\) | |||||||
\(192\) | − | 1.28632e7i | − | 1.81738i | ||||||
\(193\) | − | 5.48205e6i | − | 0.762555i | −0.924461 | − | 0.381278i | \(-0.875484\pi\) | ||
0.924461 | − | 0.381278i | \(-0.124516\pi\) | |||||||
\(194\) | 1.85943e7 | 2.54669 | ||||||||
\(195\) | 2.31977e6 | 0.312853 | ||||||||
\(196\) | −1.28771e7 | −1.71021 | ||||||||
\(197\) | −8.07614e6 | −1.05634 | −0.528172 | − | 0.849137i | \(-0.677122\pi\) | ||||
−0.528172 | + | 0.849137i | \(0.677122\pi\) | |||||||
\(198\) | 9.27734e6i | 1.19516i | ||||||||
\(199\) | −7.76482e6 | −0.985309 | −0.492654 | − | 0.870225i | \(-0.663973\pi\) | ||||
−0.492654 | + | 0.870225i | \(0.663973\pi\) | |||||||
\(200\) | − | 1.39465e7i | − | 1.74332i | ||||||
\(201\) | 5.30021e6 | 0.652687 | ||||||||
\(202\) | − | 2.00486e7i | − | 2.43237i | ||||||
\(203\) | − | 1.20065e7i | − | 1.43525i | ||||||
\(204\) | − | 2.98975e6i | − | 0.352164i | ||||||
\(205\) | 4.37363e6i | 0.507668i | ||||||||
\(206\) | −2.05470e7 | −2.35042 | ||||||||
\(207\) | 1.00368e6 | 0.113158 | ||||||||
\(208\) | − | 4.81535e6i | − | 0.535104i | ||||||
\(209\) | −1.10242e7 | + | 3.81142e6i | −1.20756 | + | 0.417492i | ||||
\(210\) | −3.51398e7 | −3.79439 | ||||||||
\(211\) | 6.10034e6i | 0.649392i | 0.945818 | + | 0.324696i | \(0.105262\pi\) | ||||
−0.945818 | + | 0.324696i | \(0.894738\pi\) | |||||||
\(212\) | 9.52235e6i | 0.999394i | ||||||||
\(213\) | 8.60008e6 | 0.889946 | ||||||||
\(214\) | −1.37420e7 | −1.40219 | ||||||||
\(215\) | 1.07663e7 | 1.08330 | ||||||||
\(216\) | 1.70211e7 | 1.68899 | ||||||||
\(217\) | 1.33258e7i | 1.30411i | ||||||||
\(218\) | −5.75803e6 | −0.555782 | ||||||||
\(219\) | 9.62787e6i | 0.916638i | ||||||||
\(220\) | 4.31109e7 | 4.04873 | ||||||||
\(221\) | − | 249974.i | − | 0.0231589i | ||||||
\(222\) | 2.59337e7i | 2.37031i | ||||||||
\(223\) | 3.09709e6i | 0.279279i | 0.990202 | + | 0.139640i | \(0.0445944\pi\) | ||||
−0.990202 | + | 0.139640i | \(0.955406\pi\) | |||||||
\(224\) | 3.25639e7i | 2.89729i | ||||||||
\(225\) | −3.60140e6 | −0.316173 | ||||||||
\(226\) | 9.26744e6 | 0.802850 | ||||||||
\(227\) | 1.26462e6i | 0.108114i | 0.998538 | + | 0.0540569i | \(0.0172152\pi\) | ||||
−0.998538 | + | 0.0540569i | \(0.982785\pi\) | |||||||
\(228\) | −1.17753e7 | − | 3.40590e7i | −0.993495 | − | 2.87361i | ||||
\(229\) | 1.06635e7 | 0.887958 | 0.443979 | − | 0.896037i | \(-0.353566\pi\) | ||||
0.443979 | + | 0.896037i | \(0.353566\pi\) | |||||||
\(230\) | − | 6.54355e6i | − | 0.537811i | ||||||
\(231\) | − | 2.50808e7i | − | 2.03472i | ||||||
\(232\) | −3.81174e7 | −3.05252 | ||||||||
\(233\) | 2.85242e6 | 0.225500 | 0.112750 | − | 0.993623i | \(-0.464034\pi\) | ||||
0.112750 | + | 0.993623i | \(0.464034\pi\) | |||||||
\(234\) | −2.39645e6 | −0.187034 | ||||||||
\(235\) | −1.05861e7 | −0.815703 | ||||||||
\(236\) | − | 6.29472e7i | − | 4.78895i | ||||||
\(237\) | 3.03489e7 | 2.27980 | ||||||||
\(238\) | 3.78661e6i | 0.280879i | ||||||||
\(239\) | −1.78416e7 | −1.30689 | −0.653445 | − | 0.756974i | \(-0.726677\pi\) | ||||
−0.653445 | + | 0.756974i | \(0.726677\pi\) | |||||||
\(240\) | 5.78859e7i | 4.18735i | ||||||||
\(241\) | − | 5.72052e6i | − | 0.408681i | −0.978900 | − | 0.204340i | \(-0.934495\pi\) | ||
0.978900 | − | 0.204340i | \(-0.0655049\pi\) | |||||||
\(242\) | 1.67260e7i | 1.18017i | ||||||||
\(243\) | − | 1.32094e7i | − | 0.920586i | ||||||
\(244\) | 1.16820e7 | 0.804167 | ||||||||
\(245\) | 1.29427e7 | 0.880087 | ||||||||
\(246\) | − | 1.35307e7i | − | 0.908897i | ||||||
\(247\) | −984535. | − | 2.84769e6i | −0.0653341 | − | 0.188974i | ||||
\(248\) | 4.23060e7 | 2.77362 | ||||||||
\(249\) | 2.25325e7i | 1.45953i | ||||||||
\(250\) | − | 1.37498e7i | − | 0.879984i | ||||||
\(251\) | 7.46125e6 | 0.471835 | 0.235918 | − | 0.971773i | \(-0.424190\pi\) | ||||
0.235918 | + | 0.971773i | \(0.424190\pi\) | |||||||
\(252\) | 2.58743e7 | 1.61684 | ||||||||
\(253\) | 4.67040e6 | 0.288398 | ||||||||
\(254\) | 1.69509e7 | 1.03441 | ||||||||
\(255\) | 3.00497e6i | 0.181226i | ||||||||
\(256\) | −8.03380e6 | −0.478852 | ||||||||
\(257\) | 8.46675e6i | 0.498790i | 0.968402 | + | 0.249395i | \(0.0802317\pi\) | ||||
−0.968402 | + | 0.249395i | \(0.919768\pi\) | |||||||
\(258\) | −3.33076e7 | −1.93948 | ||||||||
\(259\) | − | 2.34113e7i | − | 1.34749i | ||||||
\(260\) | 1.11360e7i | 0.633594i | ||||||||
\(261\) | 9.84302e6i | 0.553614i | ||||||||
\(262\) | − | 5.52932e6i | − | 0.307445i | ||||||
\(263\) | −3.14002e7 | −1.72610 | −0.863049 | − | 0.505121i | \(-0.831448\pi\) | ||||
−0.863049 | + | 0.505121i | \(0.831448\pi\) | |||||||
\(264\) | −7.96248e7 | −4.32750 | ||||||||
\(265\) | − | 9.57083e6i | − | 0.514295i | ||||||
\(266\) | 1.49137e7 | + | 4.31368e7i | 0.792394 | + | 2.29194i | ||||
\(267\) | 8.02731e6 | 0.421732 | ||||||||
\(268\) | 2.54437e7i | 1.32183i | ||||||||
\(269\) | − | 6.30864e6i | − | 0.324100i | −0.986783 | − | 0.162050i | \(-0.948189\pi\) | ||
0.986783 | − | 0.162050i | \(-0.0518105\pi\) | |||||||
\(270\) | −2.86557e7 | −1.45586 | ||||||||
\(271\) | 1.43606e7 | 0.721545 | 0.360772 | − | 0.932654i | \(-0.382513\pi\) | ||||
0.360772 | + | 0.932654i | \(0.382513\pi\) | |||||||
\(272\) | 6.23769e6 | 0.309968 | ||||||||
\(273\) | 6.47865e6 | 0.318417 | ||||||||
\(274\) | − | 3.51252e7i | − | 1.70752i | ||||||
\(275\) | −1.67583e7 | −0.805809 | ||||||||
\(276\) | 1.44291e7i | 0.686294i | ||||||||
\(277\) | 9.38558e6 | 0.441593 | 0.220796 | − | 0.975320i | \(-0.429134\pi\) | ||||
0.220796 | + | 0.975320i | \(0.429134\pi\) | |||||||
\(278\) | 4.35839e7i | 2.02858i | ||||||||
\(279\) | − | 1.09246e7i | − | 0.503030i | ||||||
\(280\) | − | 1.00709e8i | − | 4.58770i | ||||||
\(281\) | − | 3.93600e7i | − | 1.77393i | −0.461837 | − | 0.886965i | \(-0.652810\pi\) | ||
0.461837 | − | 0.886965i | \(-0.347190\pi\) | |||||||
\(282\) | 3.27502e7 | 1.46038 | ||||||||
\(283\) | −2.61094e7 | −1.15196 | −0.575980 | − | 0.817464i | \(-0.695379\pi\) | ||||
−0.575980 | + | 0.817464i | \(0.695379\pi\) | |||||||
\(284\) | 4.12847e7i | 1.80233i | ||||||||
\(285\) | 1.18352e7 | + | 3.42324e7i | 0.511259 | + | 1.47878i | ||||
\(286\) | −1.11513e7 | −0.476681 | ||||||||
\(287\) | 1.22147e7i | 0.516698i | ||||||||
\(288\) | − | 2.66962e7i | − | 1.11756i | ||||||
\(289\) | −2.38138e7 | −0.986585 | ||||||||
\(290\) | 6.41720e7 | 2.63119 | ||||||||
\(291\) | 4.12108e7 | 1.67237 | ||||||||
\(292\) | −4.62186e7 | −1.85639 | ||||||||
\(293\) | 1.58306e7i | 0.629354i | 0.949199 | + | 0.314677i | \(0.101896\pi\) | ||||
−0.949199 | + | 0.314677i | \(0.898104\pi\) | |||||||
\(294\) | −4.00408e7 | −1.57565 | ||||||||
\(295\) | 6.32677e7i | 2.46443i | ||||||||
\(296\) | −7.43248e7 | −2.86588 | ||||||||
\(297\) | − | 2.04527e7i | − | 0.780697i | ||||||
\(298\) | − | 2.01441e7i | − | 0.761201i | ||||||
\(299\) | 1.20642e6i | 0.0451320i | ||||||||
\(300\) | − | 5.17742e7i | − | 1.91756i | ||||||
\(301\) | 3.00681e7 | 1.10257 | ||||||||
\(302\) | 8.76322e7 | 3.18158 | ||||||||
\(303\) | − | 4.44339e7i | − | 1.59730i | ||||||
\(304\) | 7.10593e7 | − | 2.45674e7i | 2.52930 | − | 0.874458i | ||||
\(305\) | −1.17414e7 | −0.413830 | ||||||||
\(306\) | − | 3.10430e6i | − | 0.108343i | ||||||
\(307\) | 5.21895e7i | 1.80371i | 0.432034 | + | 0.901857i | \(0.357796\pi\) | ||||
−0.432034 | + | 0.901857i | \(0.642204\pi\) | |||||||
\(308\) | 1.20400e8 | 4.12074 | ||||||||
\(309\) | −4.55384e7 | −1.54349 | ||||||||
\(310\) | −7.12237e7 | −2.39078 | ||||||||
\(311\) | −5.40593e7 | −1.79717 | −0.898585 | − | 0.438800i | \(-0.855404\pi\) | ||||
−0.898585 | + | 0.438800i | \(0.855404\pi\) | |||||||
\(312\) | − | 2.05680e7i | − | 0.677219i | ||||||
\(313\) | 2.48919e7 | 0.811754 | 0.405877 | − | 0.913928i | \(-0.366966\pi\) | ||||
0.405877 | + | 0.913928i | \(0.366966\pi\) | |||||||
\(314\) | − | 1.00566e7i | − | 0.324836i | ||||||
\(315\) | −2.60061e7 | −0.832038 | ||||||||
\(316\) | 1.45690e8i | 4.61709i | ||||||||
\(317\) | − | 3.78290e7i | − | 1.18754i | −0.804636 | − | 0.593769i | \(-0.797639\pi\) | ||
0.804636 | − | 0.593769i | \(-0.202361\pi\) | |||||||
\(318\) | 2.96093e7i | 0.920761i | ||||||||
\(319\) | 4.58022e7i | 1.41096i | ||||||||
\(320\) | −6.20642e7 | −1.89405 | ||||||||
\(321\) | −3.04565e7 | −0.920798 | ||||||||
\(322\) | − | 1.82748e7i | − | 0.547376i | ||||||
\(323\) | 3.68883e6 | − | 1.27534e6i | 0.109466 | − | 0.0378460i | ||||
\(324\) | 1.05500e8 | 3.10183 | ||||||||
\(325\) | − | 4.32887e6i | − | 0.126103i | ||||||
\(326\) | − | 6.51302e7i | − | 1.87988i | ||||||
\(327\) | −1.27616e7 | −0.364973 | ||||||||
\(328\) | 3.87784e7 | 1.09893 | ||||||||
\(329\) | −2.95649e7 | −0.830211 | ||||||||
\(330\) | 1.34051e8 | 3.73018 | ||||||||
\(331\) | − | 6.04318e7i | − | 1.66641i | −0.552964 | − | 0.833205i | \(-0.686503\pi\) | ||
0.552964 | − | 0.833205i | \(-0.313497\pi\) | |||||||
\(332\) | −1.08168e8 | −2.95585 | ||||||||
\(333\) | 1.91928e7i | 0.519764i | ||||||||
\(334\) | 3.20226e7 | 0.859442 | ||||||||
\(335\) | − | 2.55732e7i | − | 0.680222i | ||||||
\(336\) | 1.61664e8i | 4.26182i | ||||||||
\(337\) | 5.31644e7i | 1.38909i | 0.719449 | + | 0.694546i | \(0.244395\pi\) | ||||
−0.719449 | + | 0.694546i | \(0.755605\pi\) | |||||||
\(338\) | 6.91690e7i | 1.79127i | ||||||||
\(339\) | 2.05395e7 | 0.527219 | ||||||||
\(340\) | −1.44254e7 | −0.367021 | ||||||||
\(341\) | − | 5.08353e7i | − | 1.28204i | ||||||
\(342\) | −1.22264e7 | − | 3.53640e7i | −0.305648 | − | 0.884062i | ||||
\(343\) | −1.63009e7 | −0.403950 | ||||||||
\(344\) | − | 9.54582e7i | − | 2.34497i | ||||||
\(345\) | − | 1.45025e7i | − | 0.353172i | ||||||
\(346\) | −5.14087e7 | −1.24110 | ||||||||
\(347\) | −1.73896e7 | −0.416200 | −0.208100 | − | 0.978108i | \(-0.566728\pi\) | ||||
−0.208100 | + | 0.978108i | \(0.566728\pi\) | |||||||
\(348\) | −1.41505e8 | −3.35763 | ||||||||
\(349\) | 5.87325e7 | 1.38166 | 0.690832 | − | 0.723015i | \(-0.257244\pi\) | ||||
0.690832 | + | 0.723015i | \(0.257244\pi\) | |||||||
\(350\) | 6.55737e7i | 1.52942i | ||||||||
\(351\) | 5.28319e6 | 0.122173 | ||||||||
\(352\) | − | 1.24225e8i | − | 2.84826i | ||||||
\(353\) | 7.21844e7 | 1.64104 | 0.820520 | − | 0.571618i | \(-0.193684\pi\) | ||||
0.820520 | + | 0.571618i | \(0.193684\pi\) | |||||||
\(354\) | − | 1.95731e8i | − | 4.41216i | ||||||
\(355\) | − | 4.14949e7i | − | 0.927491i | ||||||
\(356\) | 3.85351e7i | 0.854097i | ||||||||
\(357\) | 8.39230e6i | 0.184449i | ||||||||
\(358\) | −1.44791e8 | −3.15567 | ||||||||
\(359\) | 2.58410e6 | 0.0558504 | 0.0279252 | − | 0.999610i | \(-0.491110\pi\) | ||||
0.0279252 | + | 0.999610i | \(0.491110\pi\) | |||||||
\(360\) | 8.25624e7i | 1.76960i | ||||||||
\(361\) | 3.69999e7 | − | 2.90572e7i | 0.786464 | − | 0.617636i | ||||
\(362\) | −9.22401e7 | −1.94444 | ||||||||
\(363\) | 3.70700e7i | 0.775001i | ||||||||
\(364\) | 3.11008e7i | 0.644863i | ||||||||
\(365\) | 4.64539e7 | 0.955309 | ||||||||
\(366\) | 3.63245e7 | 0.740895 | ||||||||
\(367\) | 2.11836e7 | 0.428551 | 0.214275 | − | 0.976773i | \(-0.431261\pi\) | ||||
0.214275 | + | 0.976773i | \(0.431261\pi\) | |||||||
\(368\) | −3.01042e7 | −0.604065 | ||||||||
\(369\) | − | 1.00137e7i | − | 0.199304i | ||||||
\(370\) | 1.25128e8 | 2.47031 | ||||||||
\(371\) | − | 2.67295e7i | − | 0.523442i | ||||||
\(372\) | 1.57054e8 | 3.05084 | ||||||||
\(373\) | − | 5.14538e6i | − | 0.0991496i | −0.998770 | − | 0.0495748i | \(-0.984213\pi\) | ||
0.998770 | − | 0.0495748i | \(-0.0157866\pi\) | |||||||
\(374\) | − | 1.44452e7i | − | 0.276126i | ||||||
\(375\) | − | 3.04737e7i | − | 0.577871i | ||||||
\(376\) | 9.38607e7i | 1.76571i | ||||||||
\(377\) | −1.18313e7 | −0.220804 | ||||||||
\(378\) | −8.00297e7 | −1.48175 | ||||||||
\(379\) | 7.33294e7i | 1.34698i | 0.739197 | + | 0.673489i | \(0.235205\pi\) | ||||
−0.739197 | + | 0.673489i | \(0.764795\pi\) | |||||||
\(380\) | −1.64333e8 | + | 5.68150e7i | −2.99484 | + | 1.03541i | ||||
\(381\) | 3.75685e7 | 0.679281 | ||||||||
\(382\) | 1.00265e8i | 1.79869i | ||||||||
\(383\) | 110690.i | 0.00197020i | 1.00000 | 0.000985101i | \(0.000313567\pi\) | |||||
−1.00000 | 0.000985101i | \(0.999686\pi\) | ||||||||
\(384\) | 3.73462e7 | 0.659557 | ||||||||
\(385\) | −1.21013e8 | −2.12056 | ||||||||
\(386\) | 8.18303e7 | 1.42283 | ||||||||
\(387\) | −2.46501e7 | −0.425290 | ||||||||
\(388\) | 1.97833e8i | 3.38690i | ||||||||
\(389\) | 5.72855e7 | 0.973186 | 0.486593 | − | 0.873629i | \(-0.338239\pi\) | ||||
0.486593 | + | 0.873629i | \(0.338239\pi\) | |||||||
\(390\) | 3.46270e7i | 0.583743i | ||||||||
\(391\) | −1.56277e6 | −0.0261435 | ||||||||
\(392\) | − | 1.14755e8i | − | 1.90508i | ||||||
\(393\) | − | 1.22547e7i | − | 0.201894i | ||||||
\(394\) | − | 1.20552e8i | − | 1.97100i | ||||||
\(395\) | − | 1.46432e8i | − | 2.37598i | ||||||
\(396\) | −9.87053e7 | −1.58948 | ||||||||
\(397\) | −8.20397e7 | −1.31115 | −0.655575 | − | 0.755130i | \(-0.727574\pi\) | ||||
−0.655575 | + | 0.755130i | \(0.727574\pi\) | |||||||
\(398\) | − | 1.15905e8i | − | 1.83846i | ||||||
\(399\) | 3.30534e7 | + | 9.56044e7i | 0.520353 | + | 1.50508i | ||||
\(400\) | 1.08020e8 | 1.68781 | ||||||||
\(401\) | 6.27155e6i | 0.0972617i | 0.998817 | + | 0.0486309i | \(0.0154858\pi\) | ||||
−0.998817 | + | 0.0486309i | \(0.984514\pi\) | |||||||
\(402\) | 7.91159e7i | 1.21783i | ||||||||
\(403\) | 1.31314e7 | 0.200629 | ||||||||
\(404\) | 2.13305e8 | 3.23487 | ||||||||
\(405\) | −1.06037e8 | −1.59622 | ||||||||
\(406\) | 1.79220e8 | 2.67798 | ||||||||
\(407\) | 8.93094e7i | 1.32469i | ||||||||
\(408\) | 2.66434e7 | 0.392291 | ||||||||
\(409\) | 2.96714e7i | 0.433678i | 0.976207 | + | 0.216839i | \(0.0695747\pi\) | ||||
−0.976207 | + | 0.216839i | \(0.930425\pi\) | |||||||
\(410\) | −6.52849e7 | −0.947242 | ||||||||
\(411\) | − | 7.78482e7i | − | 1.12130i | ||||||
\(412\) | − | 2.18607e8i | − | 3.12589i | ||||||
\(413\) | 1.76694e8i | 2.50826i | ||||||||
\(414\) | 1.49819e7i | 0.211138i | ||||||||
\(415\) | 1.08718e8 | 1.52110 | ||||||||
\(416\) | 3.20887e7 | 0.445730 | ||||||||
\(417\) | 9.65955e7i | 1.33214i | ||||||||
\(418\) | −5.68928e7 | − | 1.64558e8i | −0.778984 | − | 2.25315i | ||||
\(419\) | 6.59835e7 | 0.897002 | 0.448501 | − | 0.893782i | \(-0.351958\pi\) | ||||
0.448501 | + | 0.893782i | \(0.351958\pi\) | |||||||
\(420\) | − | 3.73867e8i | − | 5.04625i | ||||||
\(421\) | 1.93760e7i | 0.259668i | 0.991536 | + | 0.129834i | \(0.0414444\pi\) | ||||
−0.991536 | + | 0.129834i | \(0.958556\pi\) | |||||||
\(422\) | −9.10595e7 | −1.21168 | ||||||||
\(423\) | 2.42376e7 | 0.320234 | ||||||||
\(424\) | −8.48590e7 | −1.11327 | ||||||||
\(425\) | 5.60752e6 | 0.0730472 | ||||||||
\(426\) | 1.28373e8i | 1.66052i | ||||||||
\(427\) | −3.27916e7 | −0.421190 | ||||||||
\(428\) | − | 1.46206e8i | − | 1.86481i | ||||||
\(429\) | −2.47148e7 | −0.313029 | ||||||||
\(430\) | 1.60707e8i | 2.02130i | ||||||||
\(431\) | 1.45675e8i | 1.81951i | 0.415147 | + | 0.909755i | \(0.363730\pi\) | ||||
−0.415147 | + | 0.909755i | \(0.636270\pi\) | |||||||
\(432\) | 1.31833e8i | 1.63521i | ||||||||
\(433\) | − | 9.54378e7i | − | 1.17559i | −0.809009 | − | 0.587796i | \(-0.799996\pi\) | ||
0.809009 | − | 0.587796i | \(-0.200004\pi\) | |||||||
\(434\) | −1.98914e8 | −2.43330 | ||||||||
\(435\) | 1.42225e8 | 1.72786 | ||||||||
\(436\) | − | 6.12619e7i | − | 0.739148i | ||||||
\(437\) | −1.78029e7 | + | 6.15503e6i | −0.213328 | + | 0.0737540i | ||||
\(438\) | −1.43715e8 | −1.71033 | ||||||||
\(439\) | − | 1.14060e7i | − | 0.134816i | −0.997726 | − | 0.0674078i | \(-0.978527\pi\) | ||
0.997726 | − | 0.0674078i | \(-0.0214729\pi\) | |||||||
\(440\) | 3.84185e8i | 4.51007i | ||||||||
\(441\) | −2.96331e7 | −0.345511 | ||||||||
\(442\) | 3.73135e6 | 0.0432115 | ||||||||
\(443\) | 1.16201e7 | 0.133659 | 0.0668294 | − | 0.997764i | \(-0.478712\pi\) | ||||
0.0668294 | + | 0.997764i | \(0.478712\pi\) | |||||||
\(444\) | −2.75918e8 | −3.15233 | ||||||||
\(445\) | − | 3.87313e7i | − | 0.439524i | ||||||
\(446\) | −4.62301e7 | −0.521099 | ||||||||
\(447\) | − | 4.46456e7i | − | 0.499869i | ||||||
\(448\) | −1.73333e8 | −1.92774 | ||||||||
\(449\) | − | 2.46346e7i | − | 0.272148i | −0.990699 | − | 0.136074i | \(-0.956551\pi\) | ||
0.990699 | − | 0.136074i | \(-0.0434486\pi\) | |||||||
\(450\) | − | 5.37579e7i | − | 0.589936i | ||||||
\(451\) | − | 4.65965e7i | − | 0.507954i | ||||||
\(452\) | 9.86000e7i | 1.06773i | ||||||||
\(453\) | 1.94220e8 | 2.08929 | ||||||||
\(454\) | −1.88769e7 | −0.201726 | ||||||||
\(455\) | − | 3.12592e7i | − | 0.331851i | ||||||
\(456\) | 3.03519e8 | − | 1.04936e8i | 3.20104 | − | 1.10670i | ||||
\(457\) | −2.23961e7 | −0.234652 | −0.117326 | − | 0.993093i | \(-0.537432\pi\) | ||||
−0.117326 | + | 0.993093i | \(0.537432\pi\) | |||||||
\(458\) | 1.59173e8i | 1.65681i | ||||||||
\(459\) | 6.84372e6i | 0.0707708i | ||||||||
\(460\) | 6.96194e7 | 0.715248 | ||||||||
\(461\) | −6.33431e7 | −0.646541 | −0.323271 | − | 0.946307i | \(-0.604782\pi\) | ||||
−0.323271 | + | 0.946307i | \(0.604782\pi\) | |||||||
\(462\) | 3.74379e8 | 3.79652 | ||||||||
\(463\) | −1.35759e8 | −1.36781 | −0.683903 | − | 0.729573i | \(-0.739719\pi\) | ||||
−0.683903 | + | 0.729573i | \(0.739719\pi\) | |||||||
\(464\) | − | 2.95229e8i | − | 2.95533i | ||||||
\(465\) | −1.57854e8 | −1.56999 | ||||||||
\(466\) | 4.25780e7i | 0.420753i | ||||||||
\(467\) | −1.60120e8 | −1.57215 | −0.786075 | − | 0.618131i | \(-0.787890\pi\) | ||||
−0.786075 | + | 0.618131i | \(0.787890\pi\) | |||||||
\(468\) | − | 2.54967e7i | − | 0.248741i | ||||||
\(469\) | − | 7.14210e7i | − | 0.692321i | ||||||
\(470\) | − | 1.58018e8i | − | 1.52199i | ||||||
\(471\) | − | 2.22886e7i | − | 0.213315i | ||||||
\(472\) | 5.60958e8 | 5.33463 | ||||||||
\(473\) | −1.14704e8 | −1.08391 | ||||||||
\(474\) | 4.53016e8i | 4.25381i | ||||||||
\(475\) | 6.38804e7 | − | 2.20854e7i | 0.596056 | − | 0.206075i | ||||
\(476\) | −4.02873e7 | −0.373548 | ||||||||
\(477\) | 2.19131e7i | 0.201906i | ||||||||
\(478\) | − | 2.66320e8i | − | 2.43849i | ||||||
\(479\) | 1.15981e8 | 1.05531 | 0.527654 | − | 0.849460i | \(-0.323072\pi\) | ||||
0.527654 | + | 0.849460i | \(0.323072\pi\) | |||||||
\(480\) | −3.85742e8 | −3.48797 | ||||||||
\(481\) | −2.30697e7 | −0.207303 | ||||||||
\(482\) | 8.53898e7 | 0.762544 | ||||||||
\(483\) | − | 4.05027e7i | − | 0.359453i | ||||||
\(484\) | −1.77954e8 | −1.56954 | ||||||||
\(485\) | − | 1.98840e8i | − | 1.74292i | ||||||
\(486\) | 1.97176e8 | 1.71769 | ||||||||
\(487\) | − | 9.87991e7i | − | 0.855394i | −0.903922 | − | 0.427697i | \(-0.859325\pi\) | ||
0.903922 | − | 0.427697i | \(-0.140675\pi\) | |||||||
\(488\) | 1.04105e8i | 0.895799i | ||||||||
\(489\) | − | 1.44349e8i | − | 1.23449i | ||||||
\(490\) | 1.93195e8i | 1.64213i | ||||||||
\(491\) | −1.66715e8 | −1.40841 | −0.704206 | − | 0.709996i | \(-0.748697\pi\) | ||||
−0.704206 | + | 0.709996i | \(0.748697\pi\) | |||||||
\(492\) | 1.43958e8 | 1.20876 | ||||||||
\(493\) | − | 1.53259e7i | − | 0.127905i | ||||||
\(494\) | 4.25073e7 | − | 1.46961e7i | 0.352600 | − | 0.121905i | ||||
\(495\) | 9.92078e7 | 0.817957 | ||||||||
\(496\) | 3.27671e8i | 2.68530i | ||||||||
\(497\) | − | 1.15887e8i | − | 0.943987i | ||||||
\(498\) | −3.36342e8 | −2.72328 | ||||||||
\(499\) | 1.89230e8 | 1.52296 | 0.761479 | − | 0.648189i | \(-0.224473\pi\) | ||||
0.761479 | + | 0.648189i | \(0.224473\pi\) | |||||||
\(500\) | 1.46289e8 | 1.17031 | ||||||||
\(501\) | 7.09719e7 | 0.564382 | ||||||||
\(502\) | 1.11374e8i | 0.880383i | ||||||||
\(503\) | 1.32915e8 | 1.04441 | 0.522203 | − | 0.852821i | \(-0.325110\pi\) | ||||
0.522203 | + | 0.852821i | \(0.325110\pi\) | |||||||
\(504\) | 2.30581e8i | 1.80107i | ||||||||
\(505\) | −2.14391e8 | −1.66469 | ||||||||
\(506\) | 6.97148e7i | 0.538113i | ||||||||
\(507\) | 1.53300e8i | 1.17630i | ||||||||
\(508\) | 1.80348e8i | 1.37569i | ||||||||
\(509\) | 1.41670e8i | 1.07430i | 0.843488 | + | 0.537148i | \(0.180499\pi\) | ||||
−0.843488 | + | 0.537148i | \(0.819501\pi\) | |||||||
\(510\) | −4.48551e7 | −0.338143 | ||||||||
\(511\) | 1.29737e8 | 0.972300 | ||||||||
\(512\) | − | 1.92168e8i | − | 1.43176i | ||||||
\(513\) | 2.69543e7 | + | 7.79631e7i | 0.199653 | + | 0.577480i | ||||
\(514\) | −1.26383e8 | −0.930676 | ||||||||
\(515\) | 2.19720e8i | 1.60860i | ||||||||
\(516\) | − | 3.54373e8i | − | 2.57936i | ||||||
\(517\) | 1.12784e8 | 0.816161 | ||||||||
\(518\) | 3.49459e8 | 2.51424 | ||||||||
\(519\) | −1.13937e8 | −0.815013 | ||||||||
\(520\) | −9.92396e7 | −0.705789 | ||||||||
\(521\) | − | 6.06347e7i | − | 0.428754i | −0.976751 | − | 0.214377i | \(-0.931228\pi\) | ||
0.976751 | − | 0.214377i | \(-0.0687721\pi\) | |||||||
\(522\) | −1.46926e8 | −1.03297 | ||||||||
\(523\) | 7.90109e7i | 0.552309i | 0.961113 | + | 0.276154i | \(0.0890601\pi\) | ||||
−0.961113 | + | 0.276154i | \(0.910940\pi\) | |||||||
\(524\) | 5.88286e7 | 0.408879 | ||||||||
\(525\) | 1.45332e8i | 1.00434i | ||||||||
\(526\) | − | 4.68709e8i | − | 3.22067i | ||||||
\(527\) | 1.70101e7i | 0.116218i | ||||||||
\(528\) | − | 6.16715e8i | − | 4.18970i | ||||||
\(529\) | −1.40494e8 | −0.949052 | ||||||||
\(530\) | 1.42863e8 | 0.959606 | ||||||||
\(531\) | − | 1.44856e8i | − | 0.967502i | ||||||
\(532\) | −4.58949e8 | + | 1.58673e8i | −3.04811 | + | 1.05382i | ||||
\(533\) | 1.20364e7 | 0.0794907 | ||||||||
\(534\) | 1.19823e8i | 0.786896i | ||||||||
\(535\) | 1.46951e8i | 0.959645i | ||||||||
\(536\) | −2.26743e8 | −1.47245 | ||||||||
\(537\) | −3.20901e8 | −2.07228 | ||||||||
\(538\) | 9.41687e7 | 0.604727 | ||||||||
\(539\) | −1.37891e8 | −0.880581 | ||||||||
\(540\) | − | 3.04879e8i | − | 1.93618i | ||||||
\(541\) | 1.11613e8 | 0.704895 | 0.352448 | − | 0.935832i | \(-0.385349\pi\) | ||||
0.352448 | + | 0.935832i | \(0.385349\pi\) | |||||||
\(542\) | 2.14359e8i | 1.34631i | ||||||||
\(543\) | −2.04433e8 | −1.27688 | ||||||||
\(544\) | 4.15669e7i | 0.258197i | ||||||||
\(545\) | 6.15738e7i | 0.380370i | ||||||||
\(546\) | 9.67065e7i | 0.594125i | ||||||||
\(547\) | 1.81019e8i | 1.10602i | 0.833176 | + | 0.553008i | \(0.186520\pi\) | ||||
−0.833176 | + | 0.553008i | \(0.813480\pi\) | |||||||
\(548\) | 3.73710e8 | 2.27088 | ||||||||
\(549\) | 2.68828e7 | 0.162464 | ||||||||
\(550\) | − | 2.50150e8i | − | 1.50353i | ||||||
\(551\) | −6.03618e7 | − | 1.74592e8i | −0.360834 | − | 1.04368i | ||||
\(552\) | −1.28585e8 | −0.764495 | ||||||||
\(553\) | − | 4.08955e8i | − | 2.41824i | ||||||
\(554\) | 1.40098e8i | 0.823954i | ||||||||
\(555\) | 2.77323e8 | 1.62221 | ||||||||
\(556\) | −4.63707e8 | −2.69786 | ||||||||
\(557\) | 2.25990e8 | 1.30775 | 0.653873 | − | 0.756604i | \(-0.273143\pi\) | ||||
0.653873 | + | 0.756604i | \(0.273143\pi\) | |||||||
\(558\) | 1.63071e8 | 0.938589 | ||||||||
\(559\) | − | 2.96293e7i | − | 0.169623i | ||||||
\(560\) | 7.80020e8 | 4.44162 | ||||||||
\(561\) | − | 3.20149e7i | − | 0.181328i | ||||||
\(562\) | 5.87525e8 | 3.30992 | ||||||||
\(563\) | 3.26109e8i | 1.82742i | 0.406370 | + | 0.913709i | \(0.366794\pi\) | ||||
−0.406370 | + | 0.913709i | \(0.633206\pi\) | |||||||
\(564\) | 3.48442e8i | 1.94220i | ||||||||
\(565\) | − | 9.91020e7i | − | 0.549461i | ||||||
\(566\) | − | 3.89733e8i | − | 2.14941i | ||||||
\(567\) | −2.96141e8 | −1.62461 | ||||||||
\(568\) | −3.67911e8 | −2.00770 | ||||||||
\(569\) | 1.86517e8i | 1.01247i | 0.862396 | + | 0.506234i | \(0.168963\pi\) | ||||
−0.862396 | + | 0.506234i | \(0.831037\pi\) | |||||||
\(570\) | −5.10985e8 | + | 1.76664e8i | −2.75921 | + | 0.953943i | ||||
\(571\) | 8.66919e7 | 0.465662 | 0.232831 | − | 0.972517i | \(-0.425201\pi\) | ||||
0.232831 | + | 0.972517i | \(0.425201\pi\) | |||||||
\(572\) | − | 1.18643e8i | − | 0.633950i | ||||||
\(573\) | 2.22217e8i | 1.18117i | ||||||||
\(574\) | −1.82328e8 | −0.964090 | ||||||||
\(575\) | −2.70628e7 | −0.142354 | ||||||||
\(576\) | 1.42100e8 | 0.743579 | ||||||||
\(577\) | −1.74442e8 | −0.908079 | −0.454039 | − | 0.890982i | \(-0.650017\pi\) | ||||
−0.454039 | + | 0.890982i | \(0.650017\pi\) | |||||||
\(578\) | − | 3.55467e8i | − | 1.84084i | ||||||
\(579\) | 1.81361e8 | 0.934348 | ||||||||
\(580\) | 6.82751e8i | 3.49928i | ||||||||
\(581\) | 3.03629e8 | 1.54816 | ||||||||
\(582\) | 6.15151e8i | 3.12042i | ||||||||
\(583\) | 1.01967e8i | 0.514584i | ||||||||
\(584\) | − | 4.11880e8i | − | 2.06791i | ||||||
\(585\) | 2.56266e7i | 0.128004i | ||||||||
\(586\) | −2.36303e8 | −1.17429 | ||||||||
\(587\) | −6.77908e6 | −0.0335164 | −0.0167582 | − | 0.999860i | \(-0.505335\pi\) | ||||
−0.0167582 | + | 0.999860i | \(0.505335\pi\) | |||||||
\(588\) | − | 4.26010e8i | − | 2.09550i | ||||||
\(589\) | 6.69948e7 | + | 1.93777e8i | 0.327865 | + | 0.948324i | ||||
\(590\) | −9.44394e8 | −4.59830 | ||||||||
\(591\) | − | 2.67181e8i | − | 1.29432i | ||||||
\(592\) | − | 5.75665e8i | − | 2.77463i | ||||||
\(593\) | 4.99086e7 | 0.239338 | 0.119669 | − | 0.992814i | \(-0.461817\pi\) | ||||
0.119669 | + | 0.992814i | \(0.461817\pi\) | |||||||
\(594\) | 3.05297e8 | 1.45668 | ||||||||
\(595\) | 4.04924e7 | 0.192231 | ||||||||
\(596\) | 2.14321e8 | 1.01234 | ||||||||
\(597\) | − | 2.56881e8i | − | 1.20728i | ||||||
\(598\) | −1.80082e7 | −0.0842104 | ||||||||
\(599\) | − | 1.34986e8i | − | 0.628072i | −0.949411 | − | 0.314036i | \(-0.898319\pi\) | ||
0.949411 | − | 0.314036i | \(-0.101681\pi\) | |||||||
\(600\) | 4.61390e8 | 2.13606 | ||||||||
\(601\) | 9.31195e7i | 0.428960i | 0.976728 | + | 0.214480i | \(0.0688057\pi\) | ||||
−0.976728 | + | 0.214480i | \(0.931194\pi\) | |||||||
\(602\) | 4.48824e8i | 2.05725i | ||||||||
\(603\) | 5.85516e7i | 0.267047i | ||||||||
\(604\) | 9.32354e8i | 4.23126i | ||||||||
\(605\) | 1.78860e8 | 0.807697 | ||||||||
\(606\) | 6.63262e8 | 2.98035 | ||||||||
\(607\) | − | 2.08533e8i | − | 0.932415i | −0.884675 | − | 0.466207i | \(-0.845620\pi\) | ||
0.884675 | − | 0.466207i | \(-0.154380\pi\) | |||||||
\(608\) | 1.63713e8 | + | 4.73528e8i | 0.728405 | + | 2.10685i | ||||
\(609\) | 3.97207e8 | 1.75859 | ||||||||
\(610\) | − | 1.75264e8i | − | 0.772152i | ||||||
\(611\) | 2.91334e7i | 0.127723i | ||||||||
\(612\) | 3.30279e7 | 0.144088 | ||||||||
\(613\) | 3.14675e8 | 1.36609 | 0.683047 | − | 0.730374i | \(-0.260654\pi\) | ||||
0.683047 | + | 0.730374i | \(0.260654\pi\) | |||||||
\(614\) | −7.79029e8 | −3.36549 | ||||||||
\(615\) | −1.44691e8 | −0.622039 | ||||||||
\(616\) | 1.07295e9i | 4.59028i | ||||||||
\(617\) | −4.21738e7 | −0.179551 | −0.0897753 | − | 0.995962i | \(-0.528615\pi\) | ||||
−0.0897753 | + | 0.995962i | \(0.528615\pi\) | |||||||
\(618\) | − | 6.79750e8i | − | 2.87994i | ||||||
\(619\) | −2.07102e7 | −0.0873198 | −0.0436599 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436599 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(620\) | − | 7.57777e8i | − | 3.17955i | ||||||
\(621\) | − | 3.30290e7i | − | 0.137918i | ||||||
\(622\) | − | 8.06940e8i | − | 3.35328i | ||||||
\(623\) | − | 1.08169e8i | − | 0.447341i | ||||||
\(624\) | 1.59305e8 | 0.655655 | ||||||||
\(625\) | −3.01007e8 | −1.23292 | ||||||||
\(626\) | 3.71559e8i | 1.51463i | ||||||||
\(627\) | −1.26092e8 | − | 3.64712e8i | −0.511547 | − | 1.47961i | ||||
\(628\) | 1.06997e8 | 0.432007 | ||||||||
\(629\) | − | 2.98839e7i | − | 0.120084i | ||||||
\(630\) | − | 3.88191e8i | − | 1.55247i | ||||||
\(631\) | 2.34658e8 | 0.934000 | 0.467000 | − | 0.884257i | \(-0.345335\pi\) | ||||
0.467000 | + | 0.884257i | \(0.345335\pi\) | |||||||
\(632\) | −1.29832e9 | −5.14318 | ||||||||
\(633\) | −2.01816e8 | −0.795691 | ||||||||
\(634\) | 5.64672e8 | 2.21579 | ||||||||
\(635\) | − | 1.81266e8i | − | 0.707938i | ||||||
\(636\) | −3.15025e8 | −1.22454 | ||||||||
\(637\) | − | 3.56189e7i | − | 0.137804i | ||||||
\(638\) | −6.83687e8 | −2.63266 | ||||||||
\(639\) | 9.50054e7i | 0.364121i | ||||||||
\(640\) | − | 1.80193e8i | − | 0.687382i | ||||||
\(641\) | 4.48685e8i | 1.70360i | 0.523868 | + | 0.851799i | \(0.324488\pi\) | ||||
−0.523868 | + | 0.851799i | \(0.675512\pi\) | |||||||
\(642\) | − | 4.54622e8i | − | 1.71809i | ||||||
\(643\) | −2.63984e7 | −0.0992991 | −0.0496495 | − | 0.998767i | \(-0.515810\pi\) | ||||
−0.0496495 | + | 0.998767i | \(0.515810\pi\) | |||||||
\(644\) | 1.94433e8 | 0.727969 | ||||||||
\(645\) | 3.56177e8i | 1.32735i | ||||||||
\(646\) | 1.90370e7 | + | 5.50630e7i | 0.0706156 | + | 0.204250i | ||||
\(647\) | 2.06171e8 | 0.761229 | 0.380614 | − | 0.924734i | \(-0.375713\pi\) | ||||
0.380614 | + | 0.924734i | \(0.375713\pi\) | |||||||
\(648\) | 9.40170e8i | 3.45526i | ||||||||
\(649\) | − | 6.74053e8i | − | 2.46581i | ||||||
\(650\) | 6.46168e7 | 0.235291 | ||||||||
\(651\) | −4.40854e8 | −1.59791 | ||||||||
\(652\) | 6.92946e8 | 2.50010 | ||||||||
\(653\) | −1.04864e8 | −0.376606 | −0.188303 | − | 0.982111i | \(-0.560299\pi\) | ||||
−0.188303 | + | 0.982111i | \(0.560299\pi\) | |||||||
\(654\) | − | 1.90491e8i | − | 0.680991i | ||||||
\(655\) | −5.91281e7 | −0.210412 | ||||||||
\(656\) | 3.00349e8i | 1.06393i | ||||||||
\(657\) | −1.06359e8 | −0.375042 | ||||||||
\(658\) | − | 4.41313e8i | − | 1.54906i | ||||||
\(659\) | 1.00063e8i | 0.349638i | 0.984601 | + | 0.174819i | \(0.0559340\pi\) | ||||
−0.984601 | + | 0.174819i | \(0.944066\pi\) | |||||||
\(660\) | 1.42622e9i | 4.96085i | ||||||||
\(661\) | 3.79284e8i | 1.31329i | 0.754201 | + | 0.656644i | \(0.228024\pi\) | ||||
−0.754201 | + | 0.656644i | \(0.771976\pi\) | |||||||
\(662\) | 9.02063e8 | 3.10930 | ||||||||
\(663\) | 8.26983e6 | 0.0283763 | ||||||||
\(664\) | − | 9.63942e8i | − | 3.29266i | ||||||
\(665\) | 4.61286e8 | − | 1.59481e8i | 1.56858 | − | 0.542305i | ||||
\(666\) | −2.86490e8 | −0.969811 | ||||||||
\(667\) | 7.39656e7i | 0.249260i | ||||||||
\(668\) | 3.40701e8i | 1.14299i | ||||||||
\(669\) | −1.02460e8 | −0.342197 | ||||||||
\(670\) | 3.81730e8 | 1.26921 | ||||||||
\(671\) | 1.25093e8 | 0.414063 | ||||||||
\(672\) | −1.07730e9 | −3.55001 | ||||||||
\(673\) | 3.66445e8i | 1.20216i | 0.799187 | + | 0.601082i | \(0.205264\pi\) | ||||
−0.799187 | + | 0.601082i | \(0.794736\pi\) | |||||||
\(674\) | −7.93581e8 | −2.59186 | ||||||||
\(675\) | 1.18514e8i | 0.385354i | ||||||||
\(676\) | −7.35916e8 | −2.38226 | ||||||||
\(677\) | 2.76020e8i | 0.889560i | 0.895640 | + | 0.444780i | \(0.146718\pi\) | ||||
−0.895640 | + | 0.444780i | \(0.853282\pi\) | |||||||
\(678\) | 3.06592e8i | 0.983721i | ||||||||
\(679\) | − | 5.55321e8i | − | 1.77392i | ||||||
\(680\) | − | 1.28553e8i | − | 0.408841i | ||||||
\(681\) | −4.18370e7 | −0.132470 | ||||||||
\(682\) | 7.58816e8 | 2.39212 | ||||||||
\(683\) | − | 1.05100e8i | − | 0.329868i | −0.986305 | − | 0.164934i | \(-0.947259\pi\) | ||
0.986305 | − | 0.164934i | \(-0.0527412\pi\) | |||||||
\(684\) | 3.76251e8 | − | 1.30082e8i | 1.17574 | − | 0.406488i | ||||
\(685\) | −3.75613e8 | −1.16861 | ||||||||
\(686\) | − | 2.43322e8i | − | 0.753718i | ||||||
\(687\) | 3.52777e8i | 1.08800i | ||||||||
\(688\) | 7.39349e8 | 2.27031 | ||||||||
\(689\) | −2.63394e7 | −0.0805283 | ||||||||
\(690\) | 2.16478e8 | 0.658972 | ||||||||
\(691\) | −3.03677e8 | −0.920402 | −0.460201 | − | 0.887815i | \(-0.652223\pi\) | ||||
−0.460201 | + | 0.887815i | \(0.652223\pi\) | |||||||
\(692\) | − | 5.46957e8i | − | 1.65057i | ||||||
\(693\) | 2.77068e8 | 0.832505 | ||||||||
\(694\) | − | 2.59574e8i | − | 0.776574i | ||||||
\(695\) | 4.66068e8 | 1.38834 | ||||||||
\(696\) | − | 1.26103e9i | − | 3.74021i | ||||||
\(697\) | 1.55917e7i | 0.0460464i | ||||||||
\(698\) | 8.76697e8i | 2.57800i | ||||||||
\(699\) | 9.43659e7i | 0.276302i | ||||||||
\(700\) | −6.97664e8 | −2.03401 | ||||||||
\(701\) | −4.26003e8 | −1.23668 | −0.618342 | − | 0.785909i | \(-0.712195\pi\) | ||||
−0.618342 | + | 0.785909i | \(0.712195\pi\) | |||||||
\(702\) | 7.88618e7i | 0.227958i | ||||||||
\(703\) | −1.17699e8 | − | 3.40435e8i | −0.338772 | − | 0.979870i | ||||
\(704\) | 6.61231e8 | 1.89511 | ||||||||
\(705\) | − | 3.50217e8i | − | 0.999469i | ||||||
\(706\) | 1.07749e9i | 3.06196i | ||||||||
\(707\) | −5.98752e8 | −1.69429 | ||||||||
\(708\) | 2.08246e9 | 5.86783 | ||||||||
\(709\) | 4.72028e8 | 1.32443 | 0.662216 | − | 0.749313i | \(-0.269616\pi\) | ||||
0.662216 | + | 0.749313i | \(0.269616\pi\) | |||||||
\(710\) | 6.19392e8 | 1.73058 | ||||||||
\(711\) | 3.35265e8i | 0.932781i | ||||||||
\(712\) | −3.43408e8 | −0.951417 | ||||||||
\(713\) | − | 8.20935e7i | − | 0.226485i | ||||||
\(714\) | −1.25271e8 | −0.344158 | ||||||||
\(715\) | 1.19247e8i | 0.326235i | ||||||||
\(716\) | − | 1.54049e9i | − | 4.19681i | ||||||
\(717\) | − | 5.90247e8i | − | 1.60131i | ||||||
\(718\) | 3.85728e7i | 0.104210i | ||||||||
\(719\) | 7.72222e7 | 0.207757 | 0.103879 | − | 0.994590i | \(-0.466875\pi\) | ||||
0.103879 | + | 0.994590i | \(0.466875\pi\) | |||||||
\(720\) | −6.39468e8 | −1.71325 | ||||||||
\(721\) | 6.13636e8i | 1.63721i | ||||||||
\(722\) | 4.33736e8 | + | 5.52295e8i | 1.15243 | + | 1.46744i | ||||
\(723\) | 1.89250e8 | 0.500751 | ||||||||
\(724\) | − | 9.81379e8i | − | 2.58596i | ||||||
\(725\) | − | 2.65403e8i | − | 0.696453i | ||||||
\(726\) | −5.53341e8 | −1.44605 | ||||||||
\(727\) | −4.32964e8 | −1.12680 | −0.563402 | − | 0.826183i | \(-0.690508\pi\) | ||||
−0.563402 | + | 0.826183i | \(0.690508\pi\) | |||||||
\(728\) | −2.77157e8 | −0.718342 | ||||||||
\(729\) | −4.72721e7 | −0.122018 | ||||||||
\(730\) | 6.93415e8i | 1.78248i | ||||||||
\(731\) | 3.83811e7 | 0.0982574 | ||||||||
\(732\) | 3.86471e8i | 0.985335i | ||||||||
\(733\) | −4.94099e8 | −1.25459 | −0.627296 | − | 0.778781i | \(-0.715838\pi\) | ||||
−0.627296 | + | 0.778781i | \(0.715838\pi\) | |||||||
\(734\) | 3.16207e8i | 0.799619i | ||||||||
\(735\) | 4.28179e8i | 1.07836i | ||||||||
\(736\) | − | 2.00609e8i | − | 0.503173i | ||||||
\(737\) | 2.72457e8i | 0.680605i | ||||||||
\(738\) | 1.49474e8 | 0.371875 | ||||||||
\(739\) | −6.00444e8 | −1.48778 | −0.743890 | − | 0.668302i | \(-0.767022\pi\) | ||||
−0.743890 | + | 0.668302i | \(0.767022\pi\) | |||||||
\(740\) | 1.33129e9i | 3.28532i | ||||||||
\(741\) | 9.42093e7 | − | 3.25711e7i | 0.231547 | − | 0.0800530i | ||||
\(742\) | 3.98989e8 | 0.976674 | ||||||||
\(743\) | − | 1.76594e8i | − | 0.430536i | −0.976555 | − | 0.215268i | \(-0.930937\pi\) | ||
0.976555 | − | 0.215268i | \(-0.0690625\pi\) | |||||||
\(744\) | 1.39960e9i | 3.39848i | ||||||||
\(745\) | −2.15412e8 | −0.520957 | ||||||||
\(746\) | 7.68048e7 | 0.185000 | ||||||||
\(747\) | −2.48918e8 | −0.597165 | ||||||||
\(748\) | 1.53688e8 | 0.367227 | ||||||||
\(749\) | 4.10405e8i | 0.976713i | ||||||||
\(750\) | 4.54879e8 | 1.07823 | ||||||||
\(751\) | − | 4.85737e8i | − | 1.14678i | −0.819281 | − | 0.573392i | \(-0.805627\pi\) | ||
0.819281 | − | 0.573392i | \(-0.194373\pi\) | |||||||
\(752\) | −7.26976e8 | −1.70949 | ||||||||
\(753\) | 2.46838e8i | 0.578133i | ||||||||
\(754\) | − | 1.76605e8i | − | 0.411991i | ||||||
\(755\) | − | 9.37101e8i | − | 2.17744i | ||||||
\(756\) | − | 8.51467e8i | − | 1.97062i | ||||||
\(757\) | 6.87374e8 | 1.58455 | 0.792274 | − | 0.610166i | \(-0.208897\pi\) | ||||
0.792274 | + | 0.610166i | \(0.208897\pi\) | |||||||
\(758\) | −1.09458e9 | −2.51328 | ||||||||
\(759\) | 1.54510e8i | 0.353370i | ||||||||
\(760\) | −5.06310e8 | − | 1.46446e9i | −1.15339 | − | 3.33609i | ||||
\(761\) | 7.71555e8 | 1.75070 | 0.875352 | − | 0.483485i | \(-0.160629\pi\) | ||||
0.875352 | + | 0.483485i | \(0.160629\pi\) | |||||||
\(762\) | 5.60783e8i | 1.26745i | ||||||||
\(763\) | 1.71964e8i | 0.387136i | ||||||||
\(764\) | −1.06675e9 | −2.39213 | ||||||||
\(765\) | −3.31960e7 | −0.0741485 | ||||||||
\(766\) | −1.65226e6 | −0.00367614 | ||||||||
\(767\) | 1.74116e8 | 0.385880 | ||||||||
\(768\) | − | 2.65780e8i | − | 0.586730i | ||||||
\(769\) | −1.01084e8 | −0.222281 | −0.111141 | − | 0.993805i | \(-0.535450\pi\) | ||||
−0.111141 | + | 0.993805i | \(0.535450\pi\) | |||||||
\(770\) | − | 1.80636e9i | − | 3.95669i | ||||||
\(771\) | −2.80103e8 | −0.611160 | ||||||||
\(772\) | 8.70625e8i | 1.89225i | ||||||||
\(773\) | − | 4.04573e8i | − | 0.875909i | −0.898997 | − | 0.437954i | \(-0.855703\pi\) | ||
0.898997 | − | 0.437954i | \(-0.144297\pi\) | |||||||
\(774\) | − | 3.67951e8i | − | 0.793536i | ||||||
\(775\) | 2.94567e8i | 0.632819i | ||||||||
\(776\) | −1.76300e9 | −3.77282 | ||||||||
\(777\) | 7.74510e8 | 1.65106 | ||||||||
\(778\) | 8.55097e8i | 1.81584i | ||||||||
\(779\) | 6.14086e7 | + | 1.77620e8i | 0.129902 | + | 0.375732i | ||||
\(780\) | −3.68411e8 | −0.776334 | ||||||||
\(781\) | 4.42086e8i | 0.928012i | ||||||||
\(782\) | − | 2.33274e7i | − | 0.0487804i | ||||||
\(783\) | 3.23912e8 | 0.674749 | ||||||||
\(784\) | 8.88809e8 | 1.84442 | ||||||||
\(785\) | −1.07541e8 | −0.222314 | ||||||||
\(786\) | 1.82925e8 | 0.376708 | ||||||||
\(787\) | 4.48190e8i | 0.919470i | 0.888056 | + | 0.459735i | \(0.152056\pi\) | ||||
−0.888056 | + | 0.459735i | \(0.847944\pi\) | |||||||
\(788\) | 1.28260e9 | 2.62128 | ||||||||
\(789\) | − | 1.03880e9i | − | 2.11496i | ||||||
\(790\) | 2.18578e9 | 4.43327 | ||||||||
\(791\) | − | 2.76772e8i | − | 0.559234i | ||||||
\(792\) | − | 8.79619e8i | − | 1.77059i | ||||||
\(793\) | 3.23130e7i | 0.0647975i | ||||||||
\(794\) | − | 1.22460e9i | − | 2.44643i | ||||||
\(795\) | 3.16629e8 | 0.630158 | ||||||||
\(796\) | 1.23316e9 | 2.44501 | ||||||||
\(797\) | − | 8.28284e8i | − | 1.63608i | −0.575162 | − | 0.818040i | \(-0.695061\pi\) | ||
0.575162 | − | 0.818040i | \(-0.304939\pi\) | |||||||
\(798\) | −1.42708e9 | + | 4.93387e8i | −2.80828 | + | 0.970909i | ||||
\(799\) | −3.77388e7 | −0.0739856 | ||||||||
\(800\) | 7.19825e8i | 1.40591i | ||||||||
\(801\) | 8.86780e7i | 0.172551i | ||||||||
\(802\) | −9.36151e7 | −0.181478 | ||||||||
\(803\) | −4.94919e8 | −0.955846 | ||||||||
\(804\) | −8.41746e8 | −1.61962 | ||||||||
\(805\) | −1.95423e8 | −0.374618 | ||||||||
\(806\) | 1.96011e8i | 0.374348i | ||||||||
\(807\) | 2.08707e8 | 0.397115 | ||||||||
\(808\) | 1.90088e9i | 3.60347i | ||||||||
\(809\) | 5.49140e8 | 1.03714 | 0.518570 | − | 0.855035i | \(-0.326464\pi\) | ||||
0.518570 | + | 0.855035i | \(0.326464\pi\) | |||||||
\(810\) | − | 1.58281e9i | − | 2.97834i | ||||||
\(811\) | 4.97409e8i | 0.932505i | 0.884652 | + | 0.466252i | \(0.154396\pi\) | ||||
−0.884652 | + | 0.466252i | \(0.845604\pi\) | |||||||
\(812\) | 1.90679e9i | 3.56152i | ||||||||
\(813\) | 4.75086e8i | 0.884099i | ||||||||
\(814\) | −1.33312e9 | −2.47169 | ||||||||
\(815\) | −6.96474e8 | −1.28657 | ||||||||
\(816\) | 2.06360e8i | 0.379800i | ||||||||
\(817\) | 4.37234e8 | − | 1.51166e8i | 0.801767 | − | 0.277196i | ||||
\(818\) | −4.42903e8 | −0.809186 | ||||||||
\(819\) | 7.15700e7i | 0.130280i | ||||||||
\(820\) | − | 6.94592e8i | − | 1.25976i | ||||||
\(821\) | −2.38989e8 | −0.431865 | −0.215932 | − | 0.976408i | \(-0.569279\pi\) | ||||
−0.215932 | + | 0.976408i | \(0.569279\pi\) | |||||||
\(822\) | 1.16204e9 | 2.09220 | ||||||||
\(823\) | −6.68644e8 | −1.19949 | −0.599743 | − | 0.800193i | \(-0.704731\pi\) | ||||
−0.599743 | + | 0.800193i | \(0.704731\pi\) | |||||||
\(824\) | 1.94813e9 | 3.48207 | ||||||||
\(825\) | − | 5.54410e8i | − | 0.987346i | ||||||
\(826\) | −2.63751e9 | −4.68008 | ||||||||
\(827\) | 2.00405e8i | 0.354317i | 0.984182 | + | 0.177158i | \(0.0566905\pi\) | ||||
−0.984182 | + | 0.177158i | \(0.943310\pi\) | |||||||
\(828\) | −1.59398e8 | −0.280797 | ||||||||
\(829\) | 5.83575e8i | 1.02431i | 0.858892 | + | 0.512157i | \(0.171154\pi\) | ||||
−0.858892 | + | 0.512157i | \(0.828846\pi\) | |||||||
\(830\) | 1.62283e9i | 2.83817i | ||||||||
\(831\) | 3.10501e8i | 0.541077i | ||||||||
\(832\) | 1.70804e8i | 0.296570i | ||||||||
\(833\) | 4.61398e7 | 0.0798254 | ||||||||
\(834\) | −1.44188e9 | −2.48559 | ||||||||
\(835\) | − | 3.42435e8i | − | 0.588192i | ||||||
\(836\) | 1.75080e9 | − | 6.05305e8i | 2.99652 | − | 1.03599i | ||||
\(837\) | −3.59506e8 | −0.613098 | ||||||||
\(838\) | 9.84932e8i | 1.67369i | ||||||||
\(839\) | 2.41664e8i | 0.409190i | 0.978847 | + | 0.204595i | \(0.0655878\pi\) | ||||
−0.978847 | + | 0.204595i | \(0.934412\pi\) | |||||||
\(840\) | 3.33174e9 | 5.62125 | ||||||||
\(841\) | −1.30551e8 | −0.219479 | ||||||||
\(842\) | −2.89225e8 | −0.484506 | ||||||||
\(843\) | 1.30214e9 | 2.17357 | ||||||||
\(844\) | − | 9.68818e8i | − | 1.61144i | ||||||
\(845\) | 7.39663e8 | 1.22593 | ||||||||
\(846\) | 3.61793e8i | 0.597515i | ||||||||
\(847\) | 4.99522e8 | 0.822062 | ||||||||
\(848\) | − | 6.57256e8i | − | 1.07782i | ||||||
\(849\) | − | 8.63770e8i | − | 1.41148i | ||||||
\(850\) | 8.37031e7i | 0.136296i | ||||||||
\(851\) | 1.44225e8i | 0.234019i | ||||||||
\(852\) | −1.36581e9 | −2.20837 | ||||||||
\(853\) | 3.27850e8 | 0.528236 | 0.264118 | − | 0.964490i | \(-0.414919\pi\) | ||||
0.264118 | + | 0.964490i | \(0.414919\pi\) | |||||||
\(854\) | − | 4.89478e8i | − | 0.785886i | ||||||
\(855\) | −3.78167e8 | + | 1.30744e8i | −0.605042 | + | 0.209182i | ||||
\(856\) | 1.30293e9 | 2.07730 | ||||||||
\(857\) | − | 5.60607e8i | − | 0.890668i | −0.895364 | − | 0.445334i | \(-0.853085\pi\) | ||
0.895364 | − | 0.445334i | \(-0.146915\pi\) | |||||||
\(858\) | − | 3.68916e8i | − | 0.584071i | ||||||
\(859\) | 1.07374e9 | 1.69402 | 0.847010 | − | 0.531576i | \(-0.178400\pi\) | ||||
0.847010 | + | 0.531576i | \(0.178400\pi\) | |||||||
\(860\) | −1.70983e9 | −2.68818 | ||||||||
\(861\) | −4.04095e8 | −0.633102 | ||||||||
\(862\) | −2.17449e9 | −3.39496 | ||||||||
\(863\) | − | 5.66605e8i | − | 0.881552i | −0.897617 | − | 0.440776i | \(-0.854703\pi\) | ||
0.897617 | − | 0.440776i | \(-0.145297\pi\) | |||||||
\(864\) | −8.78513e8 | −1.36209 | ||||||||
\(865\) | 5.49742e8i | 0.849397i | ||||||||
\(866\) | 1.42459e9 | 2.19350 | ||||||||
\(867\) | − | 7.87824e8i | − | 1.20885i | ||||||
\(868\) | − | 2.11632e9i | − | 3.23611i | ||||||
\(869\) | 1.56008e9i | 2.37732i | ||||||||
\(870\) | 2.12298e9i | 3.22396i | ||||||||
\(871\) | −7.03788e7 | −0.106509 | ||||||||
\(872\) | 5.45940e8 | 0.823370 | ||||||||
\(873\) | 4.55257e8i | 0.684249i | ||||||||
\(874\) | −9.18757e7 | − | 2.65743e8i | −0.137615 | − | 0.398041i | ||||
\(875\) | −4.10637e8 | −0.612962 | ||||||||
\(876\) | − | 1.52904e9i | − | 2.27460i | ||||||
\(877\) | − | 2.64799e8i | − | 0.392571i | −0.980547 | − | 0.196285i | \(-0.937112\pi\) | ||
0.980547 | − | 0.196285i | \(-0.0628879\pi\) | |||||||
\(878\) | 1.70257e8 | 0.251548 | ||||||||
\(879\) | −5.23720e8 | −0.771139 | ||||||||
\(880\) | −2.97562e9 | −4.36646 | ||||||||
\(881\) | −3.11993e8 | −0.456265 | −0.228133 | − | 0.973630i | \(-0.573262\pi\) | ||||
−0.228133 | + | 0.973630i | \(0.573262\pi\) | |||||||
\(882\) | − | 4.42332e8i | − | 0.644677i | ||||||
\(883\) | 7.80065e8 | 1.13305 | 0.566525 | − | 0.824045i | \(-0.308288\pi\) | ||||
0.566525 | + | 0.824045i | \(0.308288\pi\) | |||||||
\(884\) | 3.96994e7i | 0.0574681i | ||||||||
\(885\) | −2.09307e9 | −3.01963 | ||||||||
\(886\) | 1.73452e8i | 0.249390i | ||||||||
\(887\) | 2.78539e8i | 0.399131i | 0.979885 | + | 0.199565i | \(0.0639530\pi\) | ||||
−0.979885 | + | 0.199565i | \(0.936047\pi\) | |||||||
\(888\) | − | 2.45887e9i | − | 3.51153i | ||||||
\(889\) | − | 5.06241e8i | − | 0.720529i | ||||||
\(890\) | 5.78141e8 | 0.820094 | ||||||||
\(891\) | 1.12972e9 | 1.59712 | ||||||||
\(892\) | − | 4.91860e8i | − | 0.693022i | ||||||
\(893\) | −4.29917e8 | + | 1.48636e8i | −0.603713 | + | 0.208722i | ||||
\(894\) | 6.66422e8 | 0.932689 | ||||||||
\(895\) | 1.54833e9i | 2.15971i | ||||||||
\(896\) | − | 5.03244e8i | − | 0.699608i | ||||||
\(897\) | −3.99116e7 | −0.0552996 | ||||||||
\(898\) | 3.67719e8 | 0.507793 | ||||||||
\(899\) | 8.05084e8 | 1.10806 | ||||||||
\(900\) | 5.71952e8 | 0.784571 | ||||||||
\(901\) | − | 3.41195e7i | − | 0.0466474i | ||||||
\(902\) | 6.95544e8 | 0.947774 | ||||||||
\(903\) | 9.94733e8i | 1.35096i | ||||||||
\(904\) | −8.78680e8 | −1.18939 | ||||||||
\(905\) | 9.86376e8i | 1.33075i | ||||||||
\(906\) | 2.89911e9i | 3.89835i | ||||||||
\(907\) | − | 1.08363e9i | − | 1.45231i | −0.687533 | − | 0.726153i | \(-0.741307\pi\) | ||
0.687533 | − | 0.726153i | \(-0.258693\pi\) | |||||||
\(908\) | − | 2.00838e8i | − | 0.268281i | ||||||
\(909\) | 4.90863e8 | 0.653534 | ||||||||
\(910\) | 4.66604e8 | 0.619190 | ||||||||
\(911\) | 3.58900e8i | 0.474699i | 0.971424 | + | 0.237350i | \(0.0762787\pi\) | ||||
−0.971424 | + | 0.237350i | \(0.923721\pi\) | |||||||
\(912\) | 8.12757e8 | + | 2.35084e9i | 1.07146 | + | 3.09912i | ||||
\(913\) | −1.15828e9 | −1.52196 | ||||||||
\(914\) | − | 3.34305e8i | − | 0.437829i | ||||||
\(915\) | − | 3.88439e8i | − | 0.507060i | ||||||
\(916\) | −1.69351e9 | −2.20344 | ||||||||
\(917\) | −1.65133e8 | −0.214154 | ||||||||
\(918\) | −1.02156e8 | −0.132049 | ||||||||
\(919\) | 3.96276e8 | 0.510565 | 0.255282 | − | 0.966867i | \(-0.417832\pi\) | ||||
0.255282 | + | 0.966867i | \(0.417832\pi\) | |||||||
\(920\) | 6.20418e8i | 0.796747i | ||||||||
\(921\) | −1.72657e9 | −2.21007 | ||||||||
\(922\) | − | 9.45518e8i | − | 1.20636i | ||||||
\(923\) | −1.14196e8 | −0.145226 | ||||||||
\(924\) | 3.98317e9i | 5.04908i | ||||||||
\(925\) | − | 5.17507e8i | − | 0.653870i | ||||||
\(926\) | − | 2.02646e9i | − | 2.55215i | ||||||
\(927\) | − | 5.03065e8i | − | 0.631517i | ||||||
\(928\) | 1.96736e9 | 2.46173 | ||||||||
\(929\) | 7.38996e8 | 0.921711 | 0.460855 | − | 0.887475i | \(-0.347543\pi\) | ||||
0.460855 | + | 0.887475i | \(0.347543\pi\) | |||||||
\(930\) | − | 2.35627e9i | − | 2.92939i | ||||||
\(931\) | 5.25622e8 | − | 1.81724e8i | 0.651365 | − | 0.225197i | ||||
\(932\) | −4.53004e8 | −0.559569 | ||||||||
\(933\) | − | 1.78843e9i | − | 2.20205i | ||||||
\(934\) | − | 2.39010e9i | − | 2.93342i | ||||||
\(935\) | −1.54470e8 | −0.188977 | ||||||||
\(936\) | 2.27216e8 | 0.277084 | ||||||||
\(937\) | −2.42474e8 | −0.294745 | −0.147372 | − | 0.989081i | \(-0.547082\pi\) | ||||
−0.147372 | + | 0.989081i | \(0.547082\pi\) | |||||||
\(938\) | 1.06610e9 | 1.29178 | ||||||||
\(939\) | 8.23490e8i | 0.994630i | ||||||||
\(940\) | 1.68122e9 | 2.02414 | ||||||||
\(941\) | 7.76759e8i | 0.932218i | 0.884727 | + | 0.466109i | \(0.154345\pi\) | ||||
−0.884727 | + | 0.466109i | \(0.845655\pi\) | |||||||
\(942\) | 3.32701e8 | 0.398017 | ||||||||
\(943\) | − | 7.52483e7i | − | 0.0897350i | ||||||
\(944\) | 4.34477e9i | 5.16477i | ||||||||
\(945\) | 8.55803e8i | 1.01409i | ||||||||
\(946\) | − | 1.71217e9i | − | 2.02243i | ||||||
\(947\) | −7.91274e8 | −0.931702 | −0.465851 | − | 0.884863i | \(-0.654252\pi\) | ||||
−0.465851 | + | 0.884863i | \(0.654252\pi\) | |||||||
\(948\) | −4.81982e9 | −5.65725 | ||||||||
\(949\) | − | 1.27844e8i | − | 0.149582i | ||||||
\(950\) | 3.29668e8 | + | 9.53539e8i | 0.384509 | + | 1.11216i | ||||
\(951\) | 1.25149e9 | 1.45507 | ||||||||
\(952\) | − | 3.59023e8i | − | 0.416113i | ||||||
\(953\) | − | 1.79542e8i | − | 0.207437i | −0.994607 | − | 0.103718i | \(-0.966926\pi\) | ||
0.994607 | − | 0.103718i | \(-0.0330741\pi\) | |||||||
\(954\) | −3.27095e8 | −0.376729 | ||||||||
\(955\) | 1.07219e9 | 1.23100 | ||||||||
\(956\) | 2.83348e9 | 3.24300 | ||||||||
\(957\) | −1.51526e9 | −1.72883 | ||||||||
\(958\) | 1.73124e9i | 1.96906i | ||||||||
\(959\) | −1.04901e9 | −1.18939 | ||||||||
\(960\) | − | 2.05325e9i | − | 2.32075i | ||||||
\(961\) | −6.04825e6 | −0.00681490 | ||||||||
\(962\) | − | 3.44360e8i | − | 0.386801i | ||||||
\(963\) | − | 3.36454e8i | − | 0.376744i | ||||||
\(964\) | 9.08496e8i | 1.01413i | ||||||||
\(965\) | − | 8.75058e8i | − | 0.973767i | ||||||
\(966\) | 6.04581e8 | 0.670692 | ||||||||
\(967\) | −7.59012e8 | −0.839400 | −0.419700 | − | 0.907663i | \(-0.637865\pi\) | ||||
−0.419700 | + | 0.907663i | \(0.637865\pi\) | |||||||
\(968\) | − | 1.58585e9i | − | 1.74838i | ||||||
\(969\) | 4.21918e7 | + | 1.22037e8i | 0.0463721 | + | 0.134128i | ||||
\(970\) | 2.96807e9 | 3.25206 | ||||||||
\(971\) | − | 9.72178e8i | − | 1.06191i | −0.847400 | − | 0.530956i | \(-0.821833\pi\) | ||
0.847400 | − | 0.530956i | \(-0.178167\pi\) | |||||||
\(972\) | 2.09783e9i | 2.28440i | ||||||||
\(973\) | 1.30164e9 | 1.41303 | ||||||||
\(974\) | 1.47477e9 | 1.59605 | ||||||||
\(975\) | 1.43211e8 | 0.154512 | ||||||||
\(976\) | −8.06318e8 | −0.867275 | ||||||||
\(977\) | − | 3.54587e8i | − | 0.380224i | −0.981762 | − | 0.190112i | \(-0.939115\pi\) | ||
0.981762 | − | 0.190112i | \(-0.0608851\pi\) | |||||||
\(978\) | 2.15468e9 | 2.30339 | ||||||||
\(979\) | 4.12643e8i | 0.439771i | ||||||||
\(980\) | −2.05547e9 | −2.18390 | ||||||||
\(981\) | − | 1.40977e8i | − | 0.149329i | ||||||
\(982\) | − | 2.48854e9i | − | 2.62791i | ||||||
\(983\) | − | 7.87276e8i | − | 0.828832i | −0.910088 | − | 0.414416i | \(-0.863986\pi\) | ||
0.910088 | − | 0.414416i | \(-0.136014\pi\) | |||||||
\(984\) | 1.28290e9i | 1.34650i | ||||||||
\(985\) | −1.28913e9 | −1.34893 | ||||||||
\(986\) | 2.28769e8 | 0.238653 | ||||||||
\(987\) | − | 9.78086e8i | − | 1.01725i | ||||||
\(988\) | 1.56358e8 | + | 4.52252e8i | 0.162124 | + | 0.468932i | ||||
\(989\) | −1.85234e8 | −0.191483 | ||||||||
\(990\) | 1.48087e9i | 1.52620i | ||||||||
\(991\) | 1.87947e8i | 0.193114i | 0.995327 | + | 0.0965571i | \(0.0307830\pi\) | ||||
−0.995327 | + | 0.0965571i | \(0.969217\pi\) | |||||||
\(992\) | −2.18355e9 | −2.23680 | ||||||||
\(993\) | 1.99925e9 | 2.04183 | ||||||||
\(994\) | 1.72984e9 | 1.76136 | ||||||||
\(995\) | −1.23944e9 | −1.25822 | ||||||||
\(996\) | − | 3.57847e9i | − | 3.62176i | ||||||
\(997\) | −3.26970e8 | −0.329930 | −0.164965 | − | 0.986299i | \(-0.552751\pi\) | ||||
−0.164965 | + | 0.986299i | \(0.552751\pi\) | |||||||
\(998\) | 2.82462e9i | 2.84164i | ||||||||
\(999\) | 6.31594e8 | 0.633492 |
(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 | 19.7.b.b.18.8 | yes | 8 | |
3.2 | odd | 2 | 171.7.c.d.37.1 | 8 | |||
4.3 | odd | 2 | 304.7.e.d.113.2 | 8 | |||
19.18 | odd | 2 | inner | 19.7.b.b.18.1 | ✓ | 8 | |
57.56 | even | 2 | 171.7.c.d.37.8 | 8 | |||
76.75 | even | 2 | 304.7.e.d.113.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.7.b.b.18.1 | ✓ | 8 | 19.18 | odd | 2 | inner | |
19.7.b.b.18.8 | yes | 8 | 1.1 | even | 1 | trivial | |
171.7.c.d.37.1 | 8 | 3.2 | odd | 2 | |||
171.7.c.d.37.8 | 8 | 57.56 | even | 2 | |||
304.7.e.d.113.2 | 8 | 4.3 | odd | 2 | |||
304.7.e.d.113.7 | 8 | 76.75 | even | 2 |