Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,52,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 52, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 52);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 52 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
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: | yes |
Analytic conductor: | \(16.4731353414\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 495735060514x^{2} - 23954614981416598x + 48979992255622025570313 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(324949.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.12369e7 | 1.71194 | 0.855970 | − | 0.517026i | \(-0.172961\pi\) | ||||
0.855970 | + | 0.517026i | \(0.172961\pi\) | |||||||
\(3\) | −2.41142e12 | −1.64316 | −0.821581 | − | 0.570092i | \(-0.806907\pi\) | ||||
−0.821581 | + | 0.570092i | \(0.806907\pi\) | |||||||
\(4\) | 4.34763e15 | 1.93074 | ||||||||
\(5\) | 2.42754e17 | 0.364277 | 0.182138 | − | 0.983273i | \(-0.441698\pi\) | ||||
0.182138 | + | 0.983273i | \(0.441698\pi\) | |||||||
\(6\) | −1.95896e20 | −2.81299 | ||||||||
\(7\) | 2.85586e21 | 0.804889 | 0.402445 | − | 0.915444i | \(-0.368161\pi\) | ||||
0.402445 | + | 0.915444i | \(0.368161\pi\) | |||||||
\(8\) | 1.70259e23 | 1.59336 | ||||||||
\(9\) | 3.66124e24 | 1.69998 | ||||||||
\(10\) | 1.97206e25 | 0.623620 | ||||||||
\(11\) | 3.52088e26 | 0.979801 | 0.489900 | − | 0.871778i | \(-0.337033\pi\) | ||||
0.489900 | + | 0.871778i | \(0.337033\pi\) | |||||||
\(12\) | −1.04840e28 | −3.17251 | ||||||||
\(13\) | 3.67432e28 | 1.44418 | 0.722091 | − | 0.691798i | \(-0.243181\pi\) | ||||
0.722091 | + | 0.691798i | \(0.243181\pi\) | |||||||
\(14\) | 2.32001e29 | 1.37792 | ||||||||
\(15\) | −5.85381e29 | −0.598565 | ||||||||
\(16\) | 4.04130e30 | 0.797006 | ||||||||
\(17\) | −6.54277e30 | −0.274988 | −0.137494 | − | 0.990503i | \(-0.543905\pi\) | ||||
−0.137494 | + | 0.990503i | \(0.543905\pi\) | |||||||
\(18\) | 2.97427e32 | 2.91026 | ||||||||
\(19\) | 2.55736e32 | 0.630341 | 0.315170 | − | 0.949035i | \(-0.397938\pi\) | ||||
0.315170 | + | 0.949035i | \(0.397938\pi\) | |||||||
\(20\) | 1.05541e33 | 0.703322 | ||||||||
\(21\) | −6.88666e33 | −1.32256 | ||||||||
\(22\) | 2.86025e34 | 1.67736 | ||||||||
\(23\) | −1.69990e34 | −0.320896 | −0.160448 | − | 0.987044i | \(-0.551294\pi\) | ||||
−0.160448 | + | 0.987044i | \(0.551294\pi\) | |||||||
\(24\) | −4.10565e35 | −2.61815 | ||||||||
\(25\) | −3.85160e35 | −0.867302 | ||||||||
\(26\) | 2.98490e36 | 2.47235 | ||||||||
\(27\) | −3.63531e36 | −1.15018 | ||||||||
\(28\) | 1.24162e37 | 1.55403 | ||||||||
\(29\) | 3.94490e36 | 0.201784 | 0.100892 | − | 0.994897i | \(-0.467830\pi\) | ||||
0.100892 | + | 0.994897i | \(0.467830\pi\) | |||||||
\(30\) | −4.75545e37 | −1.02471 | ||||||||
\(31\) | 9.38800e37 | 0.876698 | 0.438349 | − | 0.898805i | \(-0.355563\pi\) | ||||
0.438349 | + | 0.898805i | \(0.355563\pi\) | |||||||
\(32\) | −5.50861e37 | −0.228938 | ||||||||
\(33\) | −8.49031e38 | −1.60997 | ||||||||
\(34\) | −5.31514e38 | −0.470763 | ||||||||
\(35\) | 6.93270e38 | 0.293202 | ||||||||
\(36\) | 1.59177e40 | 3.28221 | ||||||||
\(37\) | −1.74413e40 | −1.78828 | −0.894140 | − | 0.447787i | \(-0.852212\pi\) | ||||
−0.894140 | + | 0.447787i | \(0.852212\pi\) | |||||||
\(38\) | 2.07752e40 | 1.07911 | ||||||||
\(39\) | −8.86032e40 | −2.37302 | ||||||||
\(40\) | 4.13310e40 | 0.580425 | ||||||||
\(41\) | 2.14671e41 | 1.60615 | 0.803074 | − | 0.595880i | \(-0.203197\pi\) | ||||
0.803074 | + | 0.595880i | \(0.203197\pi\) | |||||||
\(42\) | −5.59451e41 | −2.26415 | ||||||||
\(43\) | −2.13159e41 | −0.473432 | −0.236716 | − | 0.971579i | \(-0.576071\pi\) | ||||
−0.236716 | + | 0.971579i | \(0.576071\pi\) | |||||||
\(44\) | 1.53075e42 | 1.89174 | ||||||||
\(45\) | 8.88780e41 | 0.619263 | ||||||||
\(46\) | −1.38095e42 | −0.549354 | ||||||||
\(47\) | 4.04105e42 | 0.928963 | 0.464481 | − | 0.885583i | \(-0.346241\pi\) | ||||
0.464481 | + | 0.885583i | \(0.346241\pi\) | |||||||
\(48\) | −9.74526e42 | −1.30961 | ||||||||
\(49\) | −4.43335e42 | −0.352153 | ||||||||
\(50\) | −3.12892e43 | −1.48477 | ||||||||
\(51\) | 1.57773e43 | 0.451850 | ||||||||
\(52\) | 1.59746e44 | 2.78833 | ||||||||
\(53\) | −4.94974e42 | −0.0531555 | −0.0265777 | − | 0.999647i | \(-0.508461\pi\) | ||||
−0.0265777 | + | 0.999647i | \(0.508461\pi\) | |||||||
\(54\) | −2.95321e44 | −1.96904 | ||||||||
\(55\) | 8.54708e43 | 0.356919 | ||||||||
\(56\) | 4.86235e44 | 1.28248 | ||||||||
\(57\) | −6.16687e44 | −1.03575 | ||||||||
\(58\) | 3.20472e44 | 0.345443 | ||||||||
\(59\) | −1.20757e45 | −0.841752 | −0.420876 | − | 0.907118i | \(-0.638277\pi\) | ||||
−0.420876 | + | 0.907118i | \(0.638277\pi\) | |||||||
\(60\) | −2.54502e45 | −1.15567 | ||||||||
\(61\) | 2.20569e45 | 0.657104 | 0.328552 | − | 0.944486i | \(-0.393439\pi\) | ||||
0.328552 | + | 0.944486i | \(0.393439\pi\) | |||||||
\(62\) | 7.62652e45 | 1.50085 | ||||||||
\(63\) | 1.04560e46 | 1.36830 | ||||||||
\(64\) | −1.35752e46 | −1.18893 | ||||||||
\(65\) | 8.91957e45 | 0.526082 | ||||||||
\(66\) | −6.89726e46 | −2.75617 | ||||||||
\(67\) | 4.56801e46 | 1.24400 | 0.621999 | − | 0.783018i | \(-0.286321\pi\) | ||||
0.621999 | + | 0.783018i | \(0.286321\pi\) | |||||||
\(68\) | −2.84456e46 | −0.530930 | ||||||||
\(69\) | 4.09917e46 | 0.527284 | ||||||||
\(70\) | 5.63191e46 | 0.501945 | ||||||||
\(71\) | −1.91444e47 | −1.18838 | −0.594189 | − | 0.804326i | \(-0.702527\pi\) | ||||
−0.594189 | + | 0.804326i | \(0.702527\pi\) | |||||||
\(72\) | 6.23358e47 | 2.70869 | ||||||||
\(73\) | −8.49448e46 | −0.259659 | −0.129830 | − | 0.991536i | \(-0.541443\pi\) | ||||
−0.129830 | + | 0.991536i | \(0.541443\pi\) | |||||||
\(74\) | −1.41688e48 | −3.06143 | ||||||||
\(75\) | 9.28780e47 | 1.42512 | ||||||||
\(76\) | 1.11185e48 | 1.21702 | ||||||||
\(77\) | 1.00551e48 | 0.788631 | ||||||||
\(78\) | −7.19785e48 | −4.06247 | ||||||||
\(79\) | 2.35655e48 | 0.961139 | 0.480570 | − | 0.876957i | \(-0.340430\pi\) | ||||
0.480570 | + | 0.876957i | \(0.340430\pi\) | |||||||
\(80\) | 9.81042e47 | 0.290331 | ||||||||
\(81\) | 8.81070e47 | 0.189951 | ||||||||
\(82\) | 1.74392e49 | 2.74963 | ||||||||
\(83\) | 5.38960e48 | 0.623828 | 0.311914 | − | 0.950110i | \(-0.399030\pi\) | ||||
0.311914 | + | 0.950110i | \(0.399030\pi\) | |||||||
\(84\) | −2.99406e49 | −2.55352 | ||||||||
\(85\) | −1.58828e48 | −0.100172 | ||||||||
\(86\) | −1.73164e49 | −0.810487 | ||||||||
\(87\) | −9.51281e48 | −0.331564 | ||||||||
\(88\) | 5.99461e49 | 1.56118 | ||||||||
\(89\) | −7.58432e49 | −1.48071 | −0.740357 | − | 0.672213i | \(-0.765344\pi\) | ||||
−0.740357 | + | 0.672213i | \(0.765344\pi\) | |||||||
\(90\) | 7.22017e49 | 1.06014 | ||||||||
\(91\) | 1.04933e50 | 1.16241 | ||||||||
\(92\) | −7.39055e49 | −0.619565 | ||||||||
\(93\) | −2.26384e50 | −1.44056 | ||||||||
\(94\) | 3.28282e50 | 1.59033 | ||||||||
\(95\) | 6.20810e49 | 0.229619 | ||||||||
\(96\) | 1.32835e50 | 0.376182 | ||||||||
\(97\) | −8.33376e50 | −1.81201 | −0.906007 | − | 0.423263i | \(-0.860885\pi\) | ||||
−0.906007 | + | 0.423263i | \(0.860885\pi\) | |||||||
\(98\) | −3.60151e50 | −0.602865 | ||||||||
\(99\) | 1.28908e51 | 1.66564 | ||||||||
\(100\) | −1.67453e51 | −1.67453 | ||||||||
\(101\) | 3.60874e50 | 0.280001 | 0.140001 | − | 0.990151i | \(-0.455290\pi\) | ||||
0.140001 | + | 0.990151i | \(0.455290\pi\) | |||||||
\(102\) | 1.28170e51 | 0.773540 | ||||||||
\(103\) | −5.92261e50 | −0.278717 | −0.139359 | − | 0.990242i | \(-0.544504\pi\) | ||||
−0.139359 | + | 0.990242i | \(0.544504\pi\) | |||||||
\(104\) | 6.25586e51 | 2.30111 | ||||||||
\(105\) | −1.67176e51 | −0.481779 | ||||||||
\(106\) | −4.02102e50 | −0.0909989 | ||||||||
\(107\) | −2.68636e51 | −0.478495 | −0.239247 | − | 0.970959i | \(-0.576901\pi\) | ||||
−0.239247 | + | 0.970959i | \(0.576901\pi\) | |||||||
\(108\) | −1.58050e52 | −2.22069 | ||||||||
\(109\) | −1.08273e52 | −1.20267 | −0.601335 | − | 0.798997i | \(-0.705364\pi\) | ||||
−0.601335 | + | 0.798997i | \(0.705364\pi\) | |||||||
\(110\) | 6.94338e51 | 0.611023 | ||||||||
\(111\) | 4.20583e52 | 2.93843 | ||||||||
\(112\) | 1.15414e52 | 0.641502 | ||||||||
\(113\) | −1.18691e52 | −0.525915 | −0.262958 | − | 0.964807i | \(-0.584698\pi\) | ||||
−0.262958 | + | 0.964807i | \(0.584698\pi\) | |||||||
\(114\) | −5.00977e52 | −1.77314 | ||||||||
\(115\) | −4.12658e51 | −0.116895 | ||||||||
\(116\) | 1.71510e52 | 0.389592 | ||||||||
\(117\) | 1.34526e53 | 2.45508 | ||||||||
\(118\) | −9.80988e52 | −1.44103 | ||||||||
\(119\) | −1.86852e52 | −0.221335 | ||||||||
\(120\) | −9.96663e52 | −0.953733 | ||||||||
\(121\) | −5.16394e51 | −0.0399903 | ||||||||
\(122\) | 1.79184e53 | 1.12492 | ||||||||
\(123\) | −5.17662e53 | −2.63916 | ||||||||
\(124\) | 4.08156e53 | 1.69267 | ||||||||
\(125\) | −2.01304e53 | −0.680215 | ||||||||
\(126\) | 8.49410e53 | 2.34244 | ||||||||
\(127\) | 2.91976e53 | 0.658190 | 0.329095 | − | 0.944297i | \(-0.393256\pi\) | ||||
0.329095 | + | 0.944297i | \(0.393256\pi\) | |||||||
\(128\) | −9.78766e53 | −1.80644 | ||||||||
\(129\) | 5.14015e53 | 0.777925 | ||||||||
\(130\) | 7.24598e53 | 0.900620 | ||||||||
\(131\) | −1.12031e54 | −1.14530 | −0.572651 | − | 0.819799i | \(-0.694085\pi\) | ||||
−0.572651 | + | 0.819799i | \(0.694085\pi\) | |||||||
\(132\) | −3.69127e54 | −3.10843 | ||||||||
\(133\) | 7.30346e53 | 0.507355 | ||||||||
\(134\) | 3.71091e54 | 2.12965 | ||||||||
\(135\) | −8.82487e53 | −0.418984 | ||||||||
\(136\) | −1.11396e54 | −0.438156 | ||||||||
\(137\) | 3.16309e54 | 1.03214 | 0.516068 | − | 0.856548i | \(-0.327395\pi\) | ||||
0.516068 | + | 0.856548i | \(0.327395\pi\) | |||||||
\(138\) | 3.33004e54 | 0.902678 | ||||||||
\(139\) | −8.65660e53 | −0.195196 | −0.0975978 | − | 0.995226i | \(-0.531116\pi\) | ||||
−0.0975978 | + | 0.995226i | \(0.531116\pi\) | |||||||
\(140\) | 3.01408e54 | 0.566097 | ||||||||
\(141\) | −9.74464e54 | −1.52644 | ||||||||
\(142\) | −1.55523e55 | −2.03443 | ||||||||
\(143\) | 1.29368e55 | 1.41501 | ||||||||
\(144\) | 1.47962e55 | 1.35489 | ||||||||
\(145\) | 9.57641e53 | 0.0735053 | ||||||||
\(146\) | −6.90065e54 | −0.444521 | ||||||||
\(147\) | 1.06906e55 | 0.578645 | ||||||||
\(148\) | −7.58285e55 | −3.45270 | ||||||||
\(149\) | −6.45813e54 | −0.247661 | −0.123830 | − | 0.992303i | \(-0.539518\pi\) | ||||
−0.123830 | + | 0.992303i | \(0.539518\pi\) | |||||||
\(150\) | 7.54512e55 | 2.43972 | ||||||||
\(151\) | 2.64453e55 | 0.721832 | 0.360916 | − | 0.932598i | \(-0.382464\pi\) | ||||
0.360916 | + | 0.932598i | \(0.382464\pi\) | |||||||
\(152\) | 4.35414e55 | 1.00436 | ||||||||
\(153\) | −2.39546e55 | −0.467474 | ||||||||
\(154\) | 8.16847e55 | 1.35009 | ||||||||
\(155\) | 2.27898e55 | 0.319361 | ||||||||
\(156\) | −3.85214e56 | −4.58168 | ||||||||
\(157\) | −1.74550e55 | −0.176392 | −0.0881962 | − | 0.996103i | \(-0.528110\pi\) | ||||
−0.0881962 | + | 0.996103i | \(0.528110\pi\) | |||||||
\(158\) | 1.91439e56 | 1.64541 | ||||||||
\(159\) | 1.19359e55 | 0.0873430 | ||||||||
\(160\) | −1.33724e55 | −0.0833967 | ||||||||
\(161\) | −4.85467e55 | −0.258286 | ||||||||
\(162\) | 7.15754e55 | 0.325185 | ||||||||
\(163\) | −2.44447e56 | −0.949296 | −0.474648 | − | 0.880176i | \(-0.657425\pi\) | ||||
−0.474648 | + | 0.880176i | \(0.657425\pi\) | |||||||
\(164\) | 9.33311e56 | 3.10105 | ||||||||
\(165\) | −2.06106e56 | −0.586475 | ||||||||
\(166\) | 4.37834e56 | 1.06796 | ||||||||
\(167\) | −7.65512e56 | −1.60207 | −0.801036 | − | 0.598616i | \(-0.795718\pi\) | ||||
−0.801036 | + | 0.598616i | \(0.795718\pi\) | |||||||
\(168\) | −1.17251e57 | −2.10732 | ||||||||
\(169\) | 7.02756e56 | 1.08566 | ||||||||
\(170\) | −1.29027e56 | −0.171488 | ||||||||
\(171\) | 9.36311e56 | 1.07157 | ||||||||
\(172\) | −9.26736e56 | −0.914073 | ||||||||
\(173\) | 6.79321e56 | 0.577963 | 0.288981 | − | 0.957335i | \(-0.406683\pi\) | ||||
0.288981 | + | 0.957335i | \(0.406683\pi\) | |||||||
\(174\) | −7.72791e56 | −0.567618 | ||||||||
\(175\) | −1.09996e57 | −0.698082 | ||||||||
\(176\) | 1.42289e57 | 0.780907 | ||||||||
\(177\) | 2.91194e57 | 1.38313 | ||||||||
\(178\) | −6.16126e57 | −2.53489 | ||||||||
\(179\) | 2.98876e57 | 1.06596 | 0.532978 | − | 0.846129i | \(-0.321073\pi\) | ||||
0.532978 | + | 0.846129i | \(0.321073\pi\) | |||||||
\(180\) | 3.86409e57 | 1.19563 | ||||||||
\(181\) | −1.29245e57 | −0.347223 | −0.173611 | − | 0.984814i | \(-0.555544\pi\) | ||||
−0.173611 | + | 0.984814i | \(0.555544\pi\) | |||||||
\(182\) | 8.52446e57 | 1.98997 | ||||||||
\(183\) | −5.31885e57 | −1.07973 | ||||||||
\(184\) | −2.89423e57 | −0.511304 | ||||||||
\(185\) | −4.23395e57 | −0.651429 | ||||||||
\(186\) | −1.83907e58 | −2.46614 | ||||||||
\(187\) | −2.30363e57 | −0.269434 | ||||||||
\(188\) | 1.75690e58 | 1.79358 | ||||||||
\(189\) | −1.03819e58 | −0.925767 | ||||||||
\(190\) | 5.04327e57 | 0.393093 | ||||||||
\(191\) | 2.79327e58 | 1.90442 | 0.952209 | − | 0.305446i | \(-0.0988057\pi\) | ||||
0.952209 | + | 0.305446i | \(0.0988057\pi\) | |||||||
\(192\) | 3.27355e58 | 1.95361 | ||||||||
\(193\) | 1.88817e58 | 0.987027 | 0.493514 | − | 0.869738i | \(-0.335712\pi\) | ||||
0.493514 | + | 0.869738i | \(0.335712\pi\) | |||||||
\(194\) | −6.77008e58 | −3.10206 | ||||||||
\(195\) | −2.15088e58 | −0.864437 | ||||||||
\(196\) | −1.92746e58 | −0.679915 | ||||||||
\(197\) | −3.18961e58 | −0.988209 | −0.494104 | − | 0.869403i | \(-0.664504\pi\) | ||||
−0.494104 | + | 0.869403i | \(0.664504\pi\) | |||||||
\(198\) | 1.04721e59 | 2.85148 | ||||||||
\(199\) | 4.26943e58 | 1.02239 | 0.511195 | − | 0.859465i | \(-0.329203\pi\) | ||||
0.511195 | + | 0.859465i | \(0.329203\pi\) | |||||||
\(200\) | −6.55768e58 | −1.38193 | ||||||||
\(201\) | −1.10154e59 | −2.04409 | ||||||||
\(202\) | 2.93163e58 | 0.479346 | ||||||||
\(203\) | 1.12661e58 | 0.162414 | ||||||||
\(204\) | 6.85941e58 | 0.872403 | ||||||||
\(205\) | 5.21123e58 | 0.585082 | ||||||||
\(206\) | −4.81134e58 | −0.477147 | ||||||||
\(207\) | −6.22374e58 | −0.545517 | ||||||||
\(208\) | 1.48490e59 | 1.15102 | ||||||||
\(209\) | 9.00417e58 | 0.617609 | ||||||||
\(210\) | −1.35809e59 | −0.824776 | ||||||||
\(211\) | −1.08128e59 | −0.581748 | −0.290874 | − | 0.956761i | \(-0.593946\pi\) | ||||
−0.290874 | + | 0.956761i | \(0.593946\pi\) | |||||||
\(212\) | −2.15197e58 | −0.102629 | ||||||||
\(213\) | 4.61652e59 | 1.95270 | ||||||||
\(214\) | −2.18231e59 | −0.819154 | ||||||||
\(215\) | −5.17452e58 | −0.172460 | ||||||||
\(216\) | −6.18944e59 | −1.83266 | ||||||||
\(217\) | 2.68108e59 | 0.705645 | ||||||||
\(218\) | −8.79580e59 | −2.05890 | ||||||||
\(219\) | 2.04837e59 | 0.426662 | ||||||||
\(220\) | 3.71596e59 | 0.689116 | ||||||||
\(221\) | −2.40402e59 | −0.397133 | ||||||||
\(222\) | 3.41669e60 | 5.03042 | ||||||||
\(223\) | −6.98254e59 | −0.916726 | −0.458363 | − | 0.888765i | \(-0.651564\pi\) | ||||
−0.458363 | + | 0.888765i | \(0.651564\pi\) | |||||||
\(224\) | −1.57318e59 | −0.184270 | ||||||||
\(225\) | −1.41016e60 | −1.47440 | ||||||||
\(226\) | −9.64205e59 | −0.900335 | ||||||||
\(227\) | 1.84393e60 | 1.53846 | 0.769228 | − | 0.638975i | \(-0.220641\pi\) | ||||
0.769228 | + | 0.638975i | \(0.220641\pi\) | |||||||
\(228\) | −2.68113e60 | −1.99976 | ||||||||
\(229\) | 3.39685e59 | 0.226606 | 0.113303 | − | 0.993560i | \(-0.463857\pi\) | ||||
0.113303 | + | 0.993560i | \(0.463857\pi\) | |||||||
\(230\) | −3.35231e59 | −0.200117 | ||||||||
\(231\) | −2.42471e60 | −1.29585 | ||||||||
\(232\) | 6.71655e59 | 0.321516 | ||||||||
\(233\) | −1.17691e60 | −0.504854 | −0.252427 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252427 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(234\) | 1.09284e61 | 4.20295 | ||||||||
\(235\) | 9.80980e59 | 0.338400 | ||||||||
\(236\) | −5.25005e60 | −1.62520 | ||||||||
\(237\) | −5.68263e60 | −1.57931 | ||||||||
\(238\) | −1.51793e60 | −0.378912 | ||||||||
\(239\) | 5.07807e60 | 1.13907 | 0.569537 | − | 0.821966i | \(-0.307122\pi\) | ||||
0.569537 | + | 0.821966i | \(0.307122\pi\) | |||||||
\(240\) | −2.36570e60 | −0.477060 | ||||||||
\(241\) | 4.94984e60 | 0.897752 | 0.448876 | − | 0.893594i | \(-0.351824\pi\) | ||||
0.448876 | + | 0.893594i | \(0.351824\pi\) | |||||||
\(242\) | −4.19503e59 | −0.0684609 | ||||||||
\(243\) | 5.70472e60 | 0.838059 | ||||||||
\(244\) | 9.58954e60 | 1.26870 | ||||||||
\(245\) | −1.07621e60 | −0.128281 | ||||||||
\(246\) | −4.20532e61 | −4.51808 | ||||||||
\(247\) | 9.39657e60 | 0.910327 | ||||||||
\(248\) | 1.59839e61 | 1.39690 | ||||||||
\(249\) | −1.29966e61 | −1.02505 | ||||||||
\(250\) | −1.63533e61 | −1.16449 | ||||||||
\(251\) | −1.18124e60 | −0.0759731 | −0.0379866 | − | 0.999278i | \(-0.512094\pi\) | ||||
−0.0379866 | + | 0.999278i | \(0.512094\pi\) | |||||||
\(252\) | 4.54587e61 | 2.64182 | ||||||||
\(253\) | −5.98515e60 | −0.314414 | ||||||||
\(254\) | 2.37192e61 | 1.12678 | ||||||||
\(255\) | 3.83001e60 | 0.164598 | ||||||||
\(256\) | −4.89432e61 | −1.90359 | ||||||||
\(257\) | 2.72008e61 | 0.957827 | 0.478914 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478914 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(258\) | 4.17570e61 | 1.33176 | ||||||||
\(259\) | −4.98099e61 | −1.43937 | ||||||||
\(260\) | 3.87790e61 | 1.01572 | ||||||||
\(261\) | 1.44432e61 | 0.343029 | ||||||||
\(262\) | −9.10105e61 | −1.96069 | ||||||||
\(263\) | −2.48007e61 | −0.484834 | −0.242417 | − | 0.970172i | \(-0.577940\pi\) | ||||
−0.242417 | + | 0.970172i | \(0.577940\pi\) | |||||||
\(264\) | −1.44555e62 | −2.56527 | ||||||||
\(265\) | −1.20157e60 | −0.0193633 | ||||||||
\(266\) | 5.93310e61 | 0.868560 | ||||||||
\(267\) | 1.82890e62 | 2.43305 | ||||||||
\(268\) | 1.98600e62 | 2.40183 | ||||||||
\(269\) | −6.54289e61 | −0.719592 | −0.359796 | − | 0.933031i | \(-0.617154\pi\) | ||||
−0.359796 | + | 0.933031i | \(0.617154\pi\) | |||||||
\(270\) | −7.16905e61 | −0.717275 | ||||||||
\(271\) | −6.85359e60 | −0.0624024 | −0.0312012 | − | 0.999513i | \(-0.509933\pi\) | ||||
−0.0312012 | + | 0.999513i | \(0.509933\pi\) | |||||||
\(272\) | −2.64413e61 | −0.219167 | ||||||||
\(273\) | −2.53038e62 | −1.91002 | ||||||||
\(274\) | 2.56959e62 | 1.76695 | ||||||||
\(275\) | −1.35610e62 | −0.849784 | ||||||||
\(276\) | 1.78217e62 | 1.01805 | ||||||||
\(277\) | −2.43203e62 | −1.26688 | −0.633438 | − | 0.773793i | \(-0.718357\pi\) | ||||
−0.633438 | + | 0.773793i | \(0.718357\pi\) | |||||||
\(278\) | −7.03235e61 | −0.334163 | ||||||||
\(279\) | 3.43717e62 | 1.49037 | ||||||||
\(280\) | 1.18035e62 | 0.467178 | ||||||||
\(281\) | 2.21655e62 | 0.801062 | 0.400531 | − | 0.916283i | \(-0.368826\pi\) | ||||
0.400531 | + | 0.916283i | \(0.368826\pi\) | |||||||
\(282\) | −7.91624e62 | −2.61317 | ||||||||
\(283\) | 1.63167e62 | 0.492127 | 0.246063 | − | 0.969254i | \(-0.420863\pi\) | ||||
0.246063 | + | 0.969254i | \(0.420863\pi\) | |||||||
\(284\) | −8.32329e62 | −2.29444 | ||||||||
\(285\) | −1.49703e62 | −0.377300 | ||||||||
\(286\) | 1.05095e63 | 2.42241 | ||||||||
\(287\) | 6.13070e62 | 1.29277 | ||||||||
\(288\) | −2.01683e62 | −0.389190 | ||||||||
\(289\) | −5.23295e62 | −0.924381 | ||||||||
\(290\) | 7.77958e61 | 0.125837 | ||||||||
\(291\) | 2.00962e63 | 2.97743 | ||||||||
\(292\) | −3.69309e62 | −0.501334 | ||||||||
\(293\) | −7.35742e62 | −0.915380 | −0.457690 | − | 0.889112i | \(-0.651323\pi\) | ||||
−0.457690 | + | 0.889112i | \(0.651323\pi\) | |||||||
\(294\) | 8.68475e62 | 0.990605 | ||||||||
\(295\) | −2.93141e62 | −0.306631 | ||||||||
\(296\) | −2.96954e63 | −2.84938 | ||||||||
\(297\) | −1.27995e63 | −1.12695 | ||||||||
\(298\) | −5.24638e62 | −0.423980 | ||||||||
\(299\) | −6.24599e62 | −0.463432 | ||||||||
\(300\) | 4.03800e63 | 2.75153 | ||||||||
\(301\) | −6.08751e62 | −0.381060 | ||||||||
\(302\) | 2.14833e63 | 1.23573 | ||||||||
\(303\) | −8.70217e62 | −0.460088 | ||||||||
\(304\) | 1.03351e63 | 0.502386 | ||||||||
\(305\) | 5.35441e62 | 0.239368 | ||||||||
\(306\) | −1.94600e63 | −0.800288 | ||||||||
\(307\) | −2.33959e63 | −0.885341 | −0.442671 | − | 0.896684i | \(-0.645969\pi\) | ||||
−0.442671 | + | 0.896684i | \(0.645969\pi\) | |||||||
\(308\) | 4.37160e63 | 1.52264 | ||||||||
\(309\) | 1.42819e63 | 0.457977 | ||||||||
\(310\) | 1.85137e63 | 0.546726 | ||||||||
\(311\) | 5.85752e63 | 1.59340 | 0.796698 | − | 0.604378i | \(-0.206578\pi\) | ||||
0.796698 | + | 0.604378i | \(0.206578\pi\) | |||||||
\(312\) | −1.50855e64 | −3.78109 | ||||||||
\(313\) | −5.58306e63 | −1.28971 | −0.644855 | − | 0.764305i | \(-0.723082\pi\) | ||||
−0.644855 | + | 0.764305i | \(0.723082\pi\) | |||||||
\(314\) | −1.41799e63 | −0.301973 | ||||||||
\(315\) | 2.53823e63 | 0.498438 | ||||||||
\(316\) | 1.02454e64 | 1.85571 | ||||||||
\(317\) | −2.94076e63 | −0.491414 | −0.245707 | − | 0.969344i | \(-0.579020\pi\) | ||||
−0.245707 | + | 0.969344i | \(0.579020\pi\) | |||||||
\(318\) | 9.69634e62 | 0.149526 | ||||||||
\(319\) | 1.38895e63 | 0.197708 | ||||||||
\(320\) | −3.29544e63 | −0.433101 | ||||||||
\(321\) | 6.47792e63 | 0.786244 | ||||||||
\(322\) | −3.94379e63 | −0.442169 | ||||||||
\(323\) | −1.67322e63 | −0.173336 | ||||||||
\(324\) | 3.83057e63 | 0.366746 | ||||||||
\(325\) | −1.41520e64 | −1.25254 | ||||||||
\(326\) | −1.98582e64 | −1.62514 | ||||||||
\(327\) | 2.61092e64 | 1.97618 | ||||||||
\(328\) | 3.65497e64 | 2.55918 | ||||||||
\(329\) | 1.15406e64 | 0.747712 | ||||||||
\(330\) | −1.67434e64 | −1.00401 | ||||||||
\(331\) | 8.27822e63 | 0.459540 | 0.229770 | − | 0.973245i | \(-0.426203\pi\) | ||||
0.229770 | + | 0.973245i | \(0.426203\pi\) | |||||||
\(332\) | 2.34320e64 | 1.20445 | ||||||||
\(333\) | −6.38568e64 | −3.04004 | ||||||||
\(334\) | −6.21878e64 | −2.74265 | ||||||||
\(335\) | 1.10890e64 | 0.453159 | ||||||||
\(336\) | −2.78311e64 | −1.05409 | ||||||||
\(337\) | 2.46670e63 | 0.0866070 | 0.0433035 | − | 0.999062i | \(-0.486212\pi\) | ||||
0.0433035 | + | 0.999062i | \(0.486212\pi\) | |||||||
\(338\) | 5.70897e64 | 1.85858 | ||||||||
\(339\) | 2.86212e64 | 0.864164 | ||||||||
\(340\) | −6.90527e63 | −0.193405 | ||||||||
\(341\) | 3.30540e64 | 0.858989 | ||||||||
\(342\) | 7.60630e64 | 1.83446 | ||||||||
\(343\) | −4.86141e64 | −1.08833 | ||||||||
\(344\) | −3.62922e64 | −0.754350 | ||||||||
\(345\) | 9.95091e63 | 0.192077 | ||||||||
\(346\) | 5.51860e64 | 0.989437 | ||||||||
\(347\) | 1.55920e64 | 0.259717 | 0.129858 | − | 0.991533i | \(-0.458548\pi\) | ||||
0.129858 | + | 0.991533i | \(0.458548\pi\) | |||||||
\(348\) | −4.13582e64 | −0.640163 | ||||||||
\(349\) | −5.23164e64 | −0.752644 | −0.376322 | − | 0.926489i | \(-0.622811\pi\) | ||||
−0.376322 | + | 0.926489i | \(0.622811\pi\) | |||||||
\(350\) | −8.93573e64 | −1.19507 | ||||||||
\(351\) | −1.33573e65 | −1.66107 | ||||||||
\(352\) | −1.93951e64 | −0.224313 | ||||||||
\(353\) | 1.78259e65 | 1.91777 | 0.958885 | − | 0.283795i | \(-0.0915934\pi\) | ||||
0.958885 | + | 0.283795i | \(0.0915934\pi\) | |||||||
\(354\) | 2.36557e65 | 2.36784 | ||||||||
\(355\) | −4.64739e64 | −0.432898 | ||||||||
\(356\) | −3.29738e65 | −2.85887 | ||||||||
\(357\) | 4.50578e64 | 0.363689 | ||||||||
\(358\) | 2.42798e65 | 1.82485 | ||||||||
\(359\) | −1.48533e65 | −1.03972 | −0.519858 | − | 0.854253i | \(-0.674015\pi\) | ||||
−0.519858 | + | 0.854253i | \(0.674015\pi\) | |||||||
\(360\) | 1.51323e65 | 0.986711 | ||||||||
\(361\) | −9.92004e64 | −0.602670 | ||||||||
\(362\) | −1.04994e65 | −0.594425 | ||||||||
\(363\) | 1.24524e64 | 0.0657105 | ||||||||
\(364\) | 4.56211e65 | 2.24430 | ||||||||
\(365\) | −2.06207e64 | −0.0945879 | ||||||||
\(366\) | −4.32086e65 | −1.84843 | ||||||||
\(367\) | 8.05130e64 | 0.321278 | 0.160639 | − | 0.987013i | \(-0.448644\pi\) | ||||
0.160639 | + | 0.987013i | \(0.448644\pi\) | |||||||
\(368\) | −6.86982e64 | −0.255756 | ||||||||
\(369\) | 7.85962e65 | 2.73042 | ||||||||
\(370\) | −3.43953e65 | −1.11521 | ||||||||
\(371\) | −1.41357e64 | −0.0427843 | ||||||||
\(372\) | −9.84233e65 | −2.78133 | ||||||||
\(373\) | 2.25234e64 | 0.0594372 | 0.0297186 | − | 0.999558i | \(-0.490539\pi\) | ||||
0.0297186 | + | 0.999558i | \(0.490539\pi\) | |||||||
\(374\) | −1.87140e65 | −0.461254 | ||||||||
\(375\) | 4.85427e65 | 1.11770 | ||||||||
\(376\) | 6.88024e65 | 1.48018 | ||||||||
\(377\) | 1.44948e65 | 0.291413 | ||||||||
\(378\) | −8.43395e65 | −1.58486 | ||||||||
\(379\) | −1.01382e66 | −1.78098 | −0.890491 | − | 0.455001i | \(-0.849639\pi\) | ||||
−0.890491 | + | 0.455001i | \(0.849639\pi\) | |||||||
\(380\) | 2.69905e65 | 0.443333 | ||||||||
\(381\) | −7.04075e65 | −1.08151 | ||||||||
\(382\) | 2.26917e66 | 3.26025 | ||||||||
\(383\) | −3.69389e65 | −0.496496 | −0.248248 | − | 0.968697i | \(-0.579855\pi\) | ||||
−0.248248 | + | 0.968697i | \(0.579855\pi\) | |||||||
\(384\) | 2.36021e66 | 2.96828 | ||||||||
\(385\) | 2.44092e65 | 0.287280 | ||||||||
\(386\) | 1.53389e66 | 1.68973 | ||||||||
\(387\) | −7.80425e65 | −0.804825 | ||||||||
\(388\) | −3.62321e66 | −3.49852 | ||||||||
\(389\) | −1.20048e66 | −1.08552 | −0.542762 | − | 0.839887i | \(-0.682621\pi\) | ||||
−0.542762 | + | 0.839887i | \(0.682621\pi\) | |||||||
\(390\) | −1.74731e66 | −1.47986 | ||||||||
\(391\) | 1.11221e65 | 0.0882426 | ||||||||
\(392\) | −7.54816e65 | −0.561108 | ||||||||
\(393\) | 2.70153e66 | 1.88192 | ||||||||
\(394\) | −2.59114e66 | −1.69175 | ||||||||
\(395\) | 5.72063e65 | 0.350121 | ||||||||
\(396\) | 5.60443e66 | 3.21591 | ||||||||
\(397\) | −2.17708e66 | −1.17143 | −0.585714 | − | 0.810518i | \(-0.699186\pi\) | ||||
−0.585714 | + | 0.810518i | \(0.699186\pi\) | |||||||
\(398\) | 3.46835e66 | 1.75027 | ||||||||
\(399\) | −1.76117e66 | −0.833666 | ||||||||
\(400\) | −1.55655e66 | −0.691245 | ||||||||
\(401\) | 4.28565e66 | 1.78581 | 0.892905 | − | 0.450245i | \(-0.148663\pi\) | ||||
0.892905 | + | 0.450245i | \(0.148663\pi\) | |||||||
\(402\) | −8.94854e66 | −3.49935 | ||||||||
\(403\) | 3.44945e66 | 1.26611 | ||||||||
\(404\) | 1.56895e66 | 0.540609 | ||||||||
\(405\) | 2.13883e65 | 0.0691949 | ||||||||
\(406\) | 9.15221e65 | 0.278043 | ||||||||
\(407\) | −6.14088e66 | −1.75216 | ||||||||
\(408\) | 2.68623e66 | 0.719962 | ||||||||
\(409\) | 7.61605e66 | 1.91772 | 0.958860 | − | 0.283878i | \(-0.0916211\pi\) | ||||
0.958860 | + | 0.283878i | \(0.0916211\pi\) | |||||||
\(410\) | 4.23344e66 | 1.00162 | ||||||||
\(411\) | −7.62752e66 | −1.69597 | ||||||||
\(412\) | −2.57493e66 | −0.538129 | ||||||||
\(413\) | −3.44863e66 | −0.677517 | ||||||||
\(414\) | −5.05598e66 | −0.933891 | ||||||||
\(415\) | 1.30835e66 | 0.227246 | ||||||||
\(416\) | −2.02404e66 | −0.330628 | ||||||||
\(417\) | 2.08747e66 | 0.320738 | ||||||||
\(418\) | 7.31471e66 | 1.05731 | ||||||||
\(419\) | 3.51155e66 | 0.477574 | 0.238787 | − | 0.971072i | \(-0.423250\pi\) | ||||
0.238787 | + | 0.971072i | \(0.423250\pi\) | |||||||
\(420\) | −7.26821e66 | −0.930188 | ||||||||
\(421\) | −3.18883e66 | −0.384094 | −0.192047 | − | 0.981386i | \(-0.561513\pi\) | ||||
−0.192047 | + | 0.981386i | \(0.561513\pi\) | |||||||
\(422\) | −8.78397e66 | −0.995917 | ||||||||
\(423\) | 1.47952e67 | 1.57922 | ||||||||
\(424\) | −8.42737e65 | −0.0846960 | ||||||||
\(425\) | 2.52001e66 | 0.238498 | ||||||||
\(426\) | 3.75031e67 | 3.34290 | ||||||||
\(427\) | 6.29914e66 | 0.528896 | ||||||||
\(428\) | −1.16793e67 | −0.923847 | ||||||||
\(429\) | −3.11961e67 | −2.32509 | ||||||||
\(430\) | −4.20362e66 | −0.295242 | ||||||||
\(431\) | −2.27664e66 | −0.150704 | −0.0753519 | − | 0.997157i | \(-0.524008\pi\) | ||||
−0.0753519 | + | 0.997157i | \(0.524008\pi\) | |||||||
\(432\) | −1.46914e67 | −0.916700 | ||||||||
\(433\) | −2.96559e66 | −0.174449 | −0.0872247 | − | 0.996189i | \(-0.527800\pi\) | ||||
−0.0872247 | + | 0.996189i | \(0.527800\pi\) | |||||||
\(434\) | 2.17802e67 | 1.20802 | ||||||||
\(435\) | −2.30927e66 | −0.120781 | ||||||||
\(436\) | −4.70733e67 | −2.32204 | ||||||||
\(437\) | −4.34727e66 | −0.202274 | ||||||||
\(438\) | 1.66404e67 | 0.730420 | ||||||||
\(439\) | 3.03815e67 | 1.25824 | 0.629121 | − | 0.777307i | \(-0.283415\pi\) | ||||
0.629121 | + | 0.777307i | \(0.283415\pi\) | |||||||
\(440\) | 1.45522e67 | 0.568701 | ||||||||
\(441\) | −1.62315e67 | −0.598653 | ||||||||
\(442\) | −1.95295e67 | −0.679867 | ||||||||
\(443\) | −1.74549e67 | −0.573619 | −0.286810 | − | 0.957988i | \(-0.592595\pi\) | ||||
−0.286810 | + | 0.957988i | \(0.592595\pi\) | |||||||
\(444\) | 1.82854e68 | 5.67334 | ||||||||
\(445\) | −1.84112e67 | −0.539390 | ||||||||
\(446\) | −5.67240e67 | −1.56938 | ||||||||
\(447\) | 1.55732e67 | 0.406946 | ||||||||
\(448\) | −3.87689e67 | −0.956960 | ||||||||
\(449\) | −2.54711e67 | −0.593972 | −0.296986 | − | 0.954882i | \(-0.595981\pi\) | ||||
−0.296986 | + | 0.954882i | \(0.595981\pi\) | |||||||
\(450\) | −1.14557e68 | −2.52408 | ||||||||
\(451\) | 7.55832e67 | 1.57370 | ||||||||
\(452\) | −5.16023e67 | −1.01540 | ||||||||
\(453\) | −6.37706e67 | −1.18609 | ||||||||
\(454\) | 1.49795e68 | 2.63374 | ||||||||
\(455\) | 2.54730e67 | 0.423437 | ||||||||
\(456\) | −1.04996e68 | −1.65033 | ||||||||
\(457\) | 8.96015e67 | 1.33184 | 0.665920 | − | 0.746023i | \(-0.268039\pi\) | ||||
0.665920 | + | 0.746023i | \(0.268039\pi\) | |||||||
\(458\) | 2.75949e67 | 0.387935 | ||||||||
\(459\) | 2.37850e67 | 0.316286 | ||||||||
\(460\) | −1.79409e67 | −0.225693 | ||||||||
\(461\) | 8.19688e67 | 0.975607 | 0.487804 | − | 0.872953i | \(-0.337798\pi\) | ||||
0.487804 | + | 0.872953i | \(0.337798\pi\) | |||||||
\(462\) | −1.96976e68 | −2.21841 | ||||||||
\(463\) | −1.13766e68 | −1.21254 | −0.606269 | − | 0.795259i | \(-0.707335\pi\) | ||||
−0.606269 | + | 0.795259i | \(0.707335\pi\) | |||||||
\(464\) | 1.59425e67 | 0.160823 | ||||||||
\(465\) | −5.49556e67 | −0.524761 | ||||||||
\(466\) | −9.56082e67 | −0.864280 | ||||||||
\(467\) | 2.22344e67 | 0.190303 | 0.0951516 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951516 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(468\) | 5.84868e68 | 4.74011 | ||||||||
\(469\) | 1.30456e68 | 1.00128 | ||||||||
\(470\) | 7.96918e67 | 0.579319 | ||||||||
\(471\) | 4.20914e67 | 0.289841 | ||||||||
\(472\) | −2.05599e68 | −1.34122 | ||||||||
\(473\) | −7.50507e67 | −0.463869 | ||||||||
\(474\) | −4.61639e68 | −2.70368 | ||||||||
\(475\) | −9.84993e67 | −0.546696 | ||||||||
\(476\) | −8.12364e67 | −0.427340 | ||||||||
\(477\) | −1.81222e67 | −0.0903632 | ||||||||
\(478\) | 4.12527e68 | 1.95003 | ||||||||
\(479\) | −1.15577e68 | −0.517983 | −0.258992 | − | 0.965880i | \(-0.583390\pi\) | ||||
−0.258992 | + | 0.965880i | \(0.583390\pi\) | |||||||
\(480\) | 3.22464e67 | 0.137034 | ||||||||
\(481\) | −6.40851e68 | −2.58260 | ||||||||
\(482\) | 4.02110e68 | 1.53690 | ||||||||
\(483\) | 1.17066e68 | 0.424405 | ||||||||
\(484\) | −2.24509e67 | −0.0772107 | ||||||||
\(485\) | −2.02305e68 | −0.660074 | ||||||||
\(486\) | 4.63434e68 | 1.43471 | ||||||||
\(487\) | 2.20619e66 | 0.00648118 | 0.00324059 | − | 0.999995i | \(-0.498968\pi\) | ||||
0.00324059 | + | 0.999995i | \(0.498968\pi\) | |||||||
\(488\) | 3.75539e68 | 1.04701 | ||||||||
\(489\) | 5.89465e68 | 1.55985 | ||||||||
\(490\) | −8.74282e67 | −0.219610 | ||||||||
\(491\) | 7.91071e68 | 1.88642 | 0.943208 | − | 0.332202i | \(-0.107792\pi\) | ||||
0.943208 | + | 0.332202i | \(0.107792\pi\) | |||||||
\(492\) | −2.25060e69 | −5.09552 | ||||||||
\(493\) | −2.58106e67 | −0.0554883 | ||||||||
\(494\) | 7.63348e68 | 1.55842 | ||||||||
\(495\) | 3.12929e68 | 0.606754 | ||||||||
\(496\) | 3.79397e68 | 0.698734 | ||||||||
\(497\) | −5.46737e68 | −0.956512 | ||||||||
\(498\) | −1.05580e69 | −1.75482 | ||||||||
\(499\) | −9.62285e68 | −1.51964 | −0.759819 | − | 0.650135i | \(-0.774712\pi\) | ||||
−0.759819 | + | 0.650135i | \(0.774712\pi\) | |||||||
\(500\) | −8.75194e68 | −1.31332 | ||||||||
\(501\) | 1.84597e69 | 2.63246 | ||||||||
\(502\) | −9.59607e67 | −0.130061 | ||||||||
\(503\) | 5.82620e67 | 0.0750588 | 0.0375294 | − | 0.999296i | \(-0.488051\pi\) | ||||
0.0375294 | + | 0.999296i | \(0.488051\pi\) | |||||||
\(504\) | 1.78022e69 | 2.18019 | ||||||||
\(505\) | 8.76036e67 | 0.101998 | ||||||||
\(506\) | −4.86215e68 | −0.538258 | ||||||||
\(507\) | −1.69464e69 | −1.78391 | ||||||||
\(508\) | 1.26940e69 | 1.27079 | ||||||||
\(509\) | 5.13252e68 | 0.488683 | 0.244342 | − | 0.969689i | \(-0.421428\pi\) | ||||
0.244342 | + | 0.969689i | \(0.421428\pi\) | |||||||
\(510\) | 3.11138e68 | 0.281783 | ||||||||
\(511\) | −2.42590e68 | −0.208997 | ||||||||
\(512\) | −1.77201e69 | −1.45239 | ||||||||
\(513\) | −9.29681e68 | −0.725005 | ||||||||
\(514\) | 2.20971e69 | 1.63974 | ||||||||
\(515\) | −1.43774e68 | −0.101530 | ||||||||
\(516\) | 2.23475e69 | 1.50197 | ||||||||
\(517\) | 1.42280e69 | 0.910199 | ||||||||
\(518\) | −4.04640e69 | −2.46411 | ||||||||
\(519\) | −1.63813e69 | −0.949686 | ||||||||
\(520\) | 1.51863e69 | 0.838240 | ||||||||
\(521\) | 1.75529e69 | 0.922545 | 0.461272 | − | 0.887259i | \(-0.347393\pi\) | ||||
0.461272 | + | 0.887259i | \(0.347393\pi\) | |||||||
\(522\) | 1.17332e69 | 0.587245 | ||||||||
\(523\) | 3.31068e68 | 0.157806 | 0.0789032 | − | 0.996882i | \(-0.474858\pi\) | ||||
0.0789032 | + | 0.996882i | \(0.474858\pi\) | |||||||
\(524\) | −4.87069e69 | −2.21128 | ||||||||
\(525\) | 2.65246e69 | 1.14706 | ||||||||
\(526\) | −2.01473e69 | −0.830006 | ||||||||
\(527\) | −6.14235e68 | −0.241082 | ||||||||
\(528\) | −3.43119e69 | −1.28316 | ||||||||
\(529\) | −2.51724e69 | −0.897026 | ||||||||
\(530\) | −9.76118e67 | −0.0331488 | ||||||||
\(531\) | −4.42118e69 | −1.43096 | ||||||||
\(532\) | 3.17527e69 | 0.979568 | ||||||||
\(533\) | 7.88771e69 | 2.31957 | ||||||||
\(534\) | 1.48574e70 | 4.16524 | ||||||||
\(535\) | −6.52124e68 | −0.174304 | ||||||||
\(536\) | 7.77744e69 | 1.98214 | ||||||||
\(537\) | −7.20716e69 | −1.75154 | ||||||||
\(538\) | −5.31524e69 | −1.23190 | ||||||||
\(539\) | −1.56093e69 | −0.345040 | ||||||||
\(540\) | −3.83673e69 | −0.808947 | ||||||||
\(541\) | −8.41369e69 | −1.69222 | −0.846109 | − | 0.533009i | \(-0.821061\pi\) | ||||
−0.846109 | + | 0.533009i | \(0.821061\pi\) | |||||||
\(542\) | −5.56764e68 | −0.106829 | ||||||||
\(543\) | 3.11662e69 | 0.570543 | ||||||||
\(544\) | 3.60415e68 | 0.0629552 | ||||||||
\(545\) | −2.62838e69 | −0.438104 | ||||||||
\(546\) | −2.05560e70 | −3.26984 | ||||||||
\(547\) | 1.11230e70 | 1.68867 | 0.844334 | − | 0.535817i | \(-0.179996\pi\) | ||||
0.844334 | + | 0.535817i | \(0.179996\pi\) | |||||||
\(548\) | 1.37519e70 | 1.99278 | ||||||||
\(549\) | 8.07556e69 | 1.11706 | ||||||||
\(550\) | −1.10165e70 | −1.45478 | ||||||||
\(551\) | 1.00885e69 | 0.127193 | ||||||||
\(552\) | 6.97920e69 | 0.840155 | ||||||||
\(553\) | 6.72997e69 | 0.773611 | ||||||||
\(554\) | −1.97570e70 | −2.16882 | ||||||||
\(555\) | 1.02098e70 | 1.07040 | ||||||||
\(556\) | −3.76357e69 | −0.376871 | ||||||||
\(557\) | −1.12523e70 | −1.07630 | −0.538152 | − | 0.842848i | \(-0.680877\pi\) | ||||
−0.538152 | + | 0.842848i | \(0.680877\pi\) | |||||||
\(558\) | 2.79225e70 | 2.55142 | ||||||||
\(559\) | −7.83214e69 | −0.683722 | ||||||||
\(560\) | 2.80171e69 | 0.233684 | ||||||||
\(561\) | 5.55501e69 | 0.442723 | ||||||||
\(562\) | 1.80065e70 | 1.37137 | ||||||||
\(563\) | −2.06561e68 | −0.0150344 | −0.00751718 | − | 0.999972i | \(-0.502393\pi\) | ||||
−0.00751718 | + | 0.999972i | \(0.502393\pi\) | |||||||
\(564\) | −4.23661e70 | −2.94715 | ||||||||
\(565\) | −2.88126e69 | −0.191579 | ||||||||
\(566\) | 1.32551e70 | 0.842491 | ||||||||
\(567\) | 2.51621e69 | 0.152890 | ||||||||
\(568\) | −3.25951e70 | −1.89352 | ||||||||
\(569\) | 1.15170e70 | 0.639698 | 0.319849 | − | 0.947469i | \(-0.396368\pi\) | ||||
0.319849 | + | 0.947469i | \(0.396368\pi\) | |||||||
\(570\) | −1.21614e70 | −0.645915 | ||||||||
\(571\) | 2.10280e70 | 1.06801 | 0.534007 | − | 0.845480i | \(-0.320686\pi\) | ||||
0.534007 | + | 0.845480i | \(0.320686\pi\) | |||||||
\(572\) | 5.62447e70 | 2.73201 | ||||||||
\(573\) | −6.73574e70 | −3.12927 | ||||||||
\(574\) | 4.98039e70 | 2.21315 | ||||||||
\(575\) | 6.54734e69 | 0.278314 | ||||||||
\(576\) | −4.97021e70 | −2.02116 | ||||||||
\(577\) | 5.78798e68 | 0.0225187 | 0.0112594 | − | 0.999937i | \(-0.496416\pi\) | ||||
0.0112594 | + | 0.999937i | \(0.496416\pi\) | |||||||
\(578\) | −4.25108e70 | −1.58248 | ||||||||
\(579\) | −4.55316e70 | −1.62185 | ||||||||
\(580\) | 4.16347e69 | 0.141919 | ||||||||
\(581\) | 1.53919e70 | 0.502113 | ||||||||
\(582\) | 1.63255e71 | 5.09718 | ||||||||
\(583\) | −1.74274e69 | −0.0520818 | ||||||||
\(584\) | −1.44626e70 | −0.413732 | ||||||||
\(585\) | 3.26566e70 | 0.894328 | ||||||||
\(586\) | −5.97694e70 | −1.56707 | ||||||||
\(587\) | −3.63201e70 | −0.911748 | −0.455874 | − | 0.890044i | \(-0.650673\pi\) | ||||
−0.455874 | + | 0.890044i | \(0.650673\pi\) | |||||||
\(588\) | 4.64790e70 | 1.11721 | ||||||||
\(589\) | 2.40085e70 | 0.552619 | ||||||||
\(590\) | −2.38139e70 | −0.524933 | ||||||||
\(591\) | 7.69148e70 | 1.62379 | ||||||||
\(592\) | −7.04857e70 | −1.42527 | ||||||||
\(593\) | −2.80060e70 | −0.542447 | −0.271223 | − | 0.962516i | \(-0.587428\pi\) | ||||
−0.271223 | + | 0.962516i | \(0.587428\pi\) | |||||||
\(594\) | −1.03979e71 | −1.92927 | ||||||||
\(595\) | −4.53591e69 | −0.0806272 | ||||||||
\(596\) | −2.80776e70 | −0.478167 | ||||||||
\(597\) | −1.02954e71 | −1.67995 | ||||||||
\(598\) | −5.07405e70 | −0.793367 | ||||||||
\(599\) | 4.36080e70 | 0.653404 | 0.326702 | − | 0.945127i | \(-0.394063\pi\) | ||||
0.326702 | + | 0.945127i | \(0.394063\pi\) | |||||||
\(600\) | 1.58133e71 | 2.27073 | ||||||||
\(601\) | 3.82831e70 | 0.526875 | 0.263437 | − | 0.964676i | \(-0.415144\pi\) | ||||
0.263437 | + | 0.964676i | \(0.415144\pi\) | |||||||
\(602\) | −4.94530e70 | −0.652352 | ||||||||
\(603\) | 1.67246e71 | 2.11477 | ||||||||
\(604\) | 1.14974e71 | 1.39367 | ||||||||
\(605\) | −1.25357e69 | −0.0145675 | ||||||||
\(606\) | −7.06937e70 | −0.787642 | ||||||||
\(607\) | −2.49833e70 | −0.266894 | −0.133447 | − | 0.991056i | \(-0.542605\pi\) | ||||
−0.133447 | + | 0.991056i | \(0.542605\pi\) | |||||||
\(608\) | −1.40875e70 | −0.144309 | ||||||||
\(609\) | −2.71672e70 | −0.266872 | ||||||||
\(610\) | 4.34976e70 | 0.409783 | ||||||||
\(611\) | 1.48481e71 | 1.34159 | ||||||||
\(612\) | −1.04146e71 | −0.902570 | ||||||||
\(613\) | −1.99012e71 | −1.65439 | −0.827193 | − | 0.561919i | \(-0.810063\pi\) | ||||
−0.827193 | + | 0.561919i | \(0.810063\pi\) | |||||||
\(614\) | −1.90061e71 | −1.51565 | ||||||||
\(615\) | −1.25664e71 | −0.961384 | ||||||||
\(616\) | 1.71197e71 | 1.25658 | ||||||||
\(617\) | 5.04536e70 | 0.355321 | 0.177660 | − | 0.984092i | \(-0.443147\pi\) | ||||
0.177660 | + | 0.984092i | \(0.443147\pi\) | |||||||
\(618\) | 1.16021e71 | 0.784029 | ||||||||
\(619\) | −8.80938e70 | −0.571260 | −0.285630 | − | 0.958340i | \(-0.592203\pi\) | ||||
−0.285630 | + | 0.958340i | \(0.592203\pi\) | |||||||
\(620\) | 9.90814e70 | 0.616601 | ||||||||
\(621\) | 6.17968e70 | 0.369088 | ||||||||
\(622\) | 4.75846e71 | 2.72780 | ||||||||
\(623\) | −2.16597e71 | −1.19181 | ||||||||
\(624\) | −3.58072e71 | −1.89131 | ||||||||
\(625\) | 1.22178e71 | 0.619516 | ||||||||
\(626\) | −4.53551e71 | −2.20790 | ||||||||
\(627\) | −2.17128e71 | −1.01483 | ||||||||
\(628\) | −7.58881e70 | −0.340567 | ||||||||
\(629\) | 1.14115e71 | 0.491756 | ||||||||
\(630\) | 2.06198e71 | 0.853296 | ||||||||
\(631\) | 3.58339e71 | 1.42411 | 0.712057 | − | 0.702121i | \(-0.247764\pi\) | ||||
0.712057 | + | 0.702121i | \(0.247764\pi\) | |||||||
\(632\) | 4.01224e71 | 1.53144 | ||||||||
\(633\) | 2.60741e71 | 0.955906 | ||||||||
\(634\) | −2.38898e71 | −0.841271 | ||||||||
\(635\) | 7.08782e70 | 0.239763 | ||||||||
\(636\) | 5.18928e70 | 0.168636 | ||||||||
\(637\) | −1.62895e71 | −0.508573 | ||||||||
\(638\) | 1.12834e71 | 0.338465 | ||||||||
\(639\) | −7.00922e71 | −2.02022 | ||||||||
\(640\) | −2.37599e71 | −0.658046 | ||||||||
\(641\) | 6.07769e71 | 1.61755 | 0.808777 | − | 0.588116i | \(-0.200130\pi\) | ||||
0.808777 | + | 0.588116i | \(0.200130\pi\) | |||||||
\(642\) | 5.26246e71 | 1.34600 | ||||||||
\(643\) | −7.85977e71 | −1.93210 | −0.966050 | − | 0.258353i | \(-0.916820\pi\) | ||||
−0.966050 | + | 0.258353i | \(0.916820\pi\) | |||||||
\(644\) | −2.11063e71 | −0.498681 | ||||||||
\(645\) | 1.24779e71 | 0.283380 | ||||||||
\(646\) | −1.35927e71 | −0.296741 | ||||||||
\(647\) | 5.80462e71 | 1.21819 | 0.609095 | − | 0.793098i | \(-0.291533\pi\) | ||||
0.609095 | + | 0.793098i | \(0.291533\pi\) | |||||||
\(648\) | 1.50010e71 | 0.302662 | ||||||||
\(649\) | −4.25169e71 | −0.824750 | ||||||||
\(650\) | −1.14966e72 | −2.14428 | ||||||||
\(651\) | −6.46519e71 | −1.15949 | ||||||||
\(652\) | −1.06277e72 | −1.83284 | ||||||||
\(653\) | 9.50695e71 | 1.57672 | 0.788361 | − | 0.615213i | \(-0.210930\pi\) | ||||
0.788361 | + | 0.615213i | \(0.210930\pi\) | |||||||
\(654\) | 2.12103e72 | 3.38310 | ||||||||
\(655\) | −2.71960e71 | −0.417207 | ||||||||
\(656\) | 8.67551e71 | 1.28011 | ||||||||
\(657\) | −3.11003e71 | −0.441416 | ||||||||
\(658\) | 9.37526e71 | 1.28004 | ||||||||
\(659\) | 5.24300e71 | 0.688655 | 0.344327 | − | 0.938850i | \(-0.388107\pi\) | ||||
0.344327 | + | 0.938850i | \(0.388107\pi\) | |||||||
\(660\) | −8.96072e71 | −1.13233 | ||||||||
\(661\) | 1.48904e71 | 0.181038 | 0.0905189 | − | 0.995895i | \(-0.471147\pi\) | ||||
0.0905189 | + | 0.995895i | \(0.471147\pi\) | |||||||
\(662\) | 6.72497e71 | 0.786704 | ||||||||
\(663\) | 5.79710e71 | 0.652553 | ||||||||
\(664\) | 9.17627e71 | 0.993986 | ||||||||
\(665\) | 1.77294e71 | 0.184817 | ||||||||
\(666\) | −5.18753e72 | −5.20437 | ||||||||
\(667\) | −6.70595e70 | −0.0647518 | ||||||||
\(668\) | −3.32817e72 | −3.09318 | ||||||||
\(669\) | 1.68378e72 | 1.50633 | ||||||||
\(670\) | 9.00838e71 | 0.775781 | ||||||||
\(671\) | 7.76598e71 | 0.643831 | ||||||||
\(672\) | 3.79359e71 | 0.302785 | ||||||||
\(673\) | −5.12793e70 | −0.0394056 | −0.0197028 | − | 0.999806i | \(-0.506272\pi\) | ||||
−0.0197028 | + | 0.999806i | \(0.506272\pi\) | |||||||
\(674\) | 2.00387e71 | 0.148266 | ||||||||
\(675\) | 1.40018e72 | 0.997554 | ||||||||
\(676\) | 3.05533e72 | 2.09612 | ||||||||
\(677\) | −2.88331e72 | −1.90494 | −0.952468 | − | 0.304639i | \(-0.901464\pi\) | ||||
−0.952468 | + | 0.304639i | \(0.901464\pi\) | |||||||
\(678\) | 2.32510e72 | 1.47940 | ||||||||
\(679\) | −2.38000e72 | −1.45847 | ||||||||
\(680\) | −2.70419e71 | −0.159610 | ||||||||
\(681\) | −4.44648e72 | −2.52793 | ||||||||
\(682\) | 2.68521e72 | 1.47054 | ||||||||
\(683\) | 1.21910e72 | 0.643150 | 0.321575 | − | 0.946884i | \(-0.395788\pi\) | ||||
0.321575 | + | 0.946884i | \(0.395788\pi\) | |||||||
\(684\) | 4.07073e72 | 2.06891 | ||||||||
\(685\) | 7.67852e71 | 0.375983 | ||||||||
\(686\) | −3.94926e72 | −1.86316 | ||||||||
\(687\) | −8.19121e71 | −0.372350 | ||||||||
\(688\) | −8.61439e71 | −0.377328 | ||||||||
\(689\) | −1.81869e71 | −0.0767661 | ||||||||
\(690\) | 8.08381e71 | 0.328824 | ||||||||
\(691\) | −1.39481e72 | −0.546794 | −0.273397 | − | 0.961901i | \(-0.588147\pi\) | ||||
−0.273397 | + | 0.961901i | \(0.588147\pi\) | |||||||
\(692\) | 2.95344e72 | 1.11589 | ||||||||
\(693\) | 3.68142e72 | 1.34066 | ||||||||
\(694\) | 1.26665e72 | 0.444619 | ||||||||
\(695\) | −2.10143e71 | −0.0711052 | ||||||||
\(696\) | −1.61964e72 | −0.528302 | ||||||||
\(697\) | −1.40454e72 | −0.441672 | ||||||||
\(698\) | −4.25002e72 | −1.28848 | ||||||||
\(699\) | 2.83801e72 | 0.829557 | ||||||||
\(700\) | −4.78222e72 | −1.34781 | ||||||||
\(701\) | 5.63382e72 | 1.53106 | 0.765532 | − | 0.643397i | \(-0.222476\pi\) | ||||
0.765532 | + | 0.643397i | \(0.222476\pi\) | |||||||
\(702\) | −1.08511e73 | −2.84365 | ||||||||
\(703\) | −4.46038e72 | −1.12723 | ||||||||
\(704\) | −4.77967e72 | −1.16492 | ||||||||
\(705\) | −2.36555e72 | −0.556045 | ||||||||
\(706\) | 1.44812e73 | 3.28311 | ||||||||
\(707\) | 1.03060e72 | 0.225370 | ||||||||
\(708\) | 1.26601e73 | 2.67047 | ||||||||
\(709\) | 3.78104e72 | 0.769365 | 0.384682 | − | 0.923049i | \(-0.374311\pi\) | ||||
0.384682 | + | 0.923049i | \(0.374311\pi\) | |||||||
\(710\) | −3.77539e72 | −0.741095 | ||||||||
\(711\) | 8.62789e72 | 1.63392 | ||||||||
\(712\) | −1.29130e73 | −2.35932 | ||||||||
\(713\) | −1.59587e72 | −0.281329 | ||||||||
\(714\) | 3.66036e72 | 0.622614 | ||||||||
\(715\) | 3.14047e72 | 0.515455 | ||||||||
\(716\) | 1.29940e73 | 2.05808 | ||||||||
\(717\) | −1.22453e73 | −1.87168 | ||||||||
\(718\) | −1.20664e73 | −1.77993 | ||||||||
\(719\) | 6.26463e72 | 0.891885 | 0.445943 | − | 0.895062i | \(-0.352869\pi\) | ||||
0.445943 | + | 0.895062i | \(0.352869\pi\) | |||||||
\(720\) | 3.59183e72 | 0.493556 | ||||||||
\(721\) | −1.69141e72 | −0.224336 | ||||||||
\(722\) | −8.05873e72 | −1.03173 | ||||||||
\(723\) | −1.19361e73 | −1.47515 | ||||||||
\(724\) | −5.61907e72 | −0.670396 | ||||||||
\(725\) | −1.51942e72 | −0.175008 | ||||||||
\(726\) | 1.01160e72 | 0.112492 | ||||||||
\(727\) | 1.48516e73 | 1.59457 | 0.797287 | − | 0.603600i | \(-0.206267\pi\) | ||||
0.797287 | + | 0.603600i | \(0.206267\pi\) | |||||||
\(728\) | 1.78658e73 | 1.85214 | ||||||||
\(729\) | −1.56540e73 | −1.56702 | ||||||||
\(730\) | −1.67516e72 | −0.161929 | ||||||||
\(731\) | 1.39465e72 | 0.130188 | ||||||||
\(732\) | −2.31244e73 | −2.08467 | ||||||||
\(733\) | 5.93373e72 | 0.516627 | 0.258313 | − | 0.966061i | \(-0.416833\pi\) | ||||
0.258313 | + | 0.966061i | \(0.416833\pi\) | |||||||
\(734\) | 6.54063e72 | 0.550009 | ||||||||
\(735\) | 2.59520e72 | 0.210787 | ||||||||
\(736\) | 9.36409e71 | 0.0734652 | ||||||||
\(737\) | 1.60834e73 | 1.21887 | ||||||||
\(738\) | 6.38491e73 | 4.67431 | ||||||||
\(739\) | 1.50074e72 | 0.106138 | 0.0530692 | − | 0.998591i | \(-0.483100\pi\) | ||||
0.0530692 | + | 0.998591i | \(0.483100\pi\) | |||||||
\(740\) | −1.84077e73 | −1.25774 | ||||||||
\(741\) | −2.26591e73 | −1.49581 | ||||||||
\(742\) | −1.14834e72 | −0.0732441 | ||||||||
\(743\) | −2.89489e73 | −1.78409 | −0.892047 | − | 0.451943i | \(-0.850731\pi\) | ||||
−0.892047 | + | 0.451943i | \(0.850731\pi\) | |||||||
\(744\) | −3.85438e73 | −2.29533 | ||||||||
\(745\) | −1.56774e72 | −0.0902170 | ||||||||
\(746\) | 1.82973e72 | 0.101753 | ||||||||
\(747\) | 1.97326e73 | 1.06050 | ||||||||
\(748\) | −1.00153e73 | −0.520205 | ||||||||
\(749\) | −7.67184e72 | −0.385135 | ||||||||
\(750\) | 3.94346e73 | 1.91344 | ||||||||
\(751\) | 1.40821e73 | 0.660462 | 0.330231 | − | 0.943900i | \(-0.392873\pi\) | ||||
0.330231 | + | 0.943900i | \(0.392873\pi\) | |||||||
\(752\) | 1.63311e73 | 0.740389 | ||||||||
\(753\) | 2.84847e72 | 0.124836 | ||||||||
\(754\) | 1.17752e73 | 0.498882 | ||||||||
\(755\) | 6.41970e72 | 0.262946 | ||||||||
\(756\) | −4.51368e73 | −1.78741 | ||||||||
\(757\) | −9.83514e72 | −0.376561 | −0.188281 | − | 0.982115i | \(-0.560291\pi\) | ||||
−0.188281 | + | 0.982115i | \(0.560291\pi\) | |||||||
\(758\) | −8.23593e73 | −3.04893 | ||||||||
\(759\) | 1.44327e73 | 0.516633 | ||||||||
\(760\) | 1.05698e73 | 0.365866 | ||||||||
\(761\) | 4.56710e73 | 1.52873 | 0.764367 | − | 0.644782i | \(-0.223052\pi\) | ||||
0.764367 | + | 0.644782i | \(0.223052\pi\) | |||||||
\(762\) | −5.71968e73 | −1.85148 | ||||||||
\(763\) | −3.09213e73 | −0.968016 | ||||||||
\(764\) | 1.21441e74 | 3.67693 | ||||||||
\(765\) | −5.81508e72 | −0.170290 | ||||||||
\(766\) | −3.00081e73 | −0.849971 | ||||||||
\(767\) | −4.43698e73 | −1.21564 | ||||||||
\(768\) | 1.18022e74 | 3.12791 | ||||||||
\(769\) | 3.75294e73 | 0.962167 | 0.481083 | − | 0.876675i | \(-0.340243\pi\) | ||||
0.481083 | + | 0.876675i | \(0.340243\pi\) | |||||||
\(770\) | 1.98293e73 | 0.491806 | ||||||||
\(771\) | −6.55925e73 | −1.57386 | ||||||||
\(772\) | 8.20906e73 | 1.90569 | ||||||||
\(773\) | 3.47460e73 | 0.780419 | 0.390210 | − | 0.920726i | \(-0.372403\pi\) | ||||
0.390210 | + | 0.920726i | \(0.372403\pi\) | |||||||
\(774\) | −6.33993e73 | −1.37781 | ||||||||
\(775\) | −3.61588e73 | −0.760362 | ||||||||
\(776\) | −1.41890e74 | −2.88720 | ||||||||
\(777\) | 1.20112e74 | 2.36511 | ||||||||
\(778\) | −9.75230e73 | −1.85835 | ||||||||
\(779\) | 5.48992e73 | 1.01242 | ||||||||
\(780\) | −9.35123e73 | −1.66900 | ||||||||
\(781\) | −6.74052e73 | −1.16437 | ||||||||
\(782\) | 9.03522e72 | 0.151066 | ||||||||
\(783\) | −1.43410e73 | −0.232088 | ||||||||
\(784\) | −1.79165e73 | −0.280668 | ||||||||
\(785\) | −4.23728e72 | −0.0642556 | ||||||||
\(786\) | 2.19464e74 | 3.22173 | ||||||||
\(787\) | −5.13224e72 | −0.0729376 | −0.0364688 | − | 0.999335i | \(-0.511611\pi\) | ||||
−0.0364688 | + | 0.999335i | \(0.511611\pi\) | |||||||
\(788\) | −1.38672e74 | −1.90797 | ||||||||
\(789\) | 5.98049e73 | 0.796660 | ||||||||
\(790\) | 4.64726e73 | 0.599385 | ||||||||
\(791\) | −3.38963e73 | −0.423304 | ||||||||
\(792\) | 2.19477e74 | 2.65397 | ||||||||
\(793\) | 8.10443e73 | 0.948978 | ||||||||
\(794\) | −1.76859e74 | −2.00541 | ||||||||
\(795\) | 2.89749e72 | 0.0318170 | ||||||||
\(796\) | 1.85619e74 | 1.97397 | ||||||||
\(797\) | −5.49546e73 | −0.566001 | −0.283000 | − | 0.959120i | \(-0.591330\pi\) | ||||
−0.283000 | + | 0.959120i | \(0.591330\pi\) | |||||||
\(798\) | −1.43072e74 | −1.42719 | ||||||||
\(799\) | −2.64396e73 | −0.255454 | ||||||||
\(800\) | 2.12169e73 | 0.198558 | ||||||||
\(801\) | −2.77680e74 | −2.51719 | ||||||||
\(802\) | 3.48153e74 | 3.05720 | ||||||||
\(803\) | −2.99081e73 | −0.254414 | ||||||||
\(804\) | −4.78908e74 | −3.94659 | ||||||||
\(805\) | −1.17849e73 | −0.0940874 | ||||||||
\(806\) | 2.80223e74 | 2.16750 | ||||||||
\(807\) | 1.57776e74 | 1.18241 | ||||||||
\(808\) | 6.14420e73 | 0.446144 | ||||||||
\(809\) | 2.78397e73 | 0.195874 | 0.0979372 | − | 0.995193i | \(-0.468776\pi\) | ||||
0.0979372 | + | 0.995193i | \(0.468776\pi\) | |||||||
\(810\) | 1.73752e73 | 0.118457 | ||||||||
\(811\) | −2.13458e74 | −1.41020 | −0.705099 | − | 0.709109i | \(-0.749098\pi\) | ||||
−0.705099 | + | 0.709109i | \(0.749098\pi\) | |||||||
\(812\) | 4.89807e73 | 0.313579 | ||||||||
\(813\) | 1.65269e73 | 0.102537 | ||||||||
\(814\) | −4.98866e74 | −2.99959 | ||||||||
\(815\) | −5.93406e73 | −0.345806 | ||||||||
\(816\) | 6.37610e73 | 0.360127 | ||||||||
\(817\) | −5.45124e73 | −0.298424 | ||||||||
\(818\) | 6.18704e74 | 3.28302 | ||||||||
\(819\) | 3.84186e74 | 1.97607 | ||||||||
\(820\) | 2.26565e74 | 1.12964 | ||||||||
\(821\) | −1.21993e74 | −0.589639 | −0.294819 | − | 0.955553i | \(-0.595259\pi\) | ||||
−0.294819 | + | 0.955553i | \(0.595259\pi\) | |||||||
\(822\) | −6.19636e74 | −2.90339 | ||||||||
\(823\) | −9.32706e72 | −0.0423691 | −0.0211845 | − | 0.999776i | \(-0.506744\pi\) | ||||
−0.0211845 | + | 0.999776i | \(0.506744\pi\) | |||||||
\(824\) | −1.00838e74 | −0.444098 | ||||||||
\(825\) | 3.27012e74 | 1.39633 | ||||||||
\(826\) | −2.80156e74 | −1.15987 | ||||||||
\(827\) | 2.77630e73 | 0.111449 | 0.0557244 | − | 0.998446i | \(-0.482253\pi\) | ||||
0.0557244 | + | 0.998446i | \(0.482253\pi\) | |||||||
\(828\) | −2.70585e74 | −1.05325 | ||||||||
\(829\) | 3.61616e74 | 1.36492 | 0.682461 | − | 0.730922i | \(-0.260910\pi\) | ||||
0.682461 | + | 0.730922i | \(0.260910\pi\) | |||||||
\(830\) | 1.06286e74 | 0.389032 | ||||||||
\(831\) | 5.86463e74 | 2.08168 | ||||||||
\(832\) | −4.98797e74 | −1.71704 | ||||||||
\(833\) | 2.90064e73 | 0.0968380 | ||||||||
\(834\) | 1.69579e74 | 0.549084 | ||||||||
\(835\) | −1.85831e74 | −0.583598 | ||||||||
\(836\) | 3.91468e74 | 1.19244 | ||||||||
\(837\) | −3.41283e74 | −1.00836 | ||||||||
\(838\) | 2.85267e74 | 0.817578 | ||||||||
\(839\) | −4.79920e74 | −1.33425 | −0.667127 | − | 0.744944i | \(-0.732476\pi\) | ||||
−0.667127 | + | 0.744944i | \(0.732476\pi\) | |||||||
\(840\) | −2.84633e74 | −0.767649 | ||||||||
\(841\) | −3.66644e74 | −0.959283 | ||||||||
\(842\) | −2.59050e74 | −0.657546 | ||||||||
\(843\) | −5.34502e74 | −1.31627 | ||||||||
\(844\) | −4.70100e74 | −1.12320 | ||||||||
\(845\) | 1.70597e74 | 0.395481 | ||||||||
\(846\) | 1.20192e75 | 2.70353 | ||||||||
\(847\) | −1.47475e73 | −0.0321877 | ||||||||
\(848\) | −2.00034e73 | −0.0423652 | ||||||||
\(849\) | −3.93463e74 | −0.808644 | ||||||||
\(850\) | 2.04718e74 | 0.408294 | ||||||||
\(851\) | 2.96486e74 | 0.573852 | ||||||||
\(852\) | 2.00709e75 | 3.77014 | ||||||||
\(853\) | 6.60846e74 | 1.20476 | 0.602379 | − | 0.798210i | \(-0.294220\pi\) | ||||
0.602379 | + | 0.798210i | \(0.294220\pi\) | |||||||
\(854\) | 5.11723e74 | 0.905438 | ||||||||
\(855\) | 2.27293e74 | 0.390347 | ||||||||
\(856\) | −4.57376e74 | −0.762416 | ||||||||
\(857\) | −2.87199e74 | −0.464699 | −0.232349 | − | 0.972632i | \(-0.574641\pi\) | ||||
−0.232349 | + | 0.972632i | \(0.574641\pi\) | |||||||
\(858\) | −2.53428e75 | −3.98041 | ||||||||
\(859\) | 7.69360e74 | 1.17302 | 0.586508 | − | 0.809944i | \(-0.300502\pi\) | ||||
0.586508 | + | 0.809944i | \(0.300502\pi\) | |||||||
\(860\) | −2.24969e74 | −0.332975 | ||||||||
\(861\) | −1.47837e75 | −2.12423 | ||||||||
\(862\) | −1.84947e74 | −0.257996 | ||||||||
\(863\) | −8.71585e74 | −1.18041 | −0.590207 | − | 0.807252i | \(-0.700954\pi\) | ||||
−0.590207 | + | 0.807252i | \(0.700954\pi\) | |||||||
\(864\) | 2.00255e74 | 0.263320 | ||||||||
\(865\) | 1.64908e74 | 0.210538 | ||||||||
\(866\) | −2.40915e74 | −0.298647 | ||||||||
\(867\) | 1.26188e75 | 1.51891 | ||||||||
\(868\) | 1.16563e75 | 1.36241 | ||||||||
\(869\) | 8.29714e74 | 0.941725 | ||||||||
\(870\) | −1.87598e74 | −0.206770 | ||||||||
\(871\) | 1.67843e75 | 1.79656 | ||||||||
\(872\) | −1.84345e75 | −1.91629 | ||||||||
\(873\) | −3.05118e75 | −3.08039 | ||||||||
\(874\) | −3.53158e74 | −0.346280 | ||||||||
\(875\) | −5.74894e74 | −0.547498 | ||||||||
\(876\) | 8.90557e74 | 0.823772 | ||||||||
\(877\) | 1.44865e75 | 1.30159 | 0.650797 | − | 0.759252i | \(-0.274435\pi\) | ||||
0.650797 | + | 0.759252i | \(0.274435\pi\) | |||||||
\(878\) | 2.46810e75 | 2.15403 | ||||||||
\(879\) | 1.77418e75 | 1.50412 | ||||||||
\(880\) | 3.45413e74 | 0.284466 | ||||||||
\(881\) | −1.16519e75 | −0.932207 | −0.466103 | − | 0.884730i | \(-0.654343\pi\) | ||||
−0.466103 | + | 0.884730i | \(0.654343\pi\) | |||||||
\(882\) | −1.31860e75 | −1.02486 | ||||||||
\(883\) | −1.52991e75 | −1.15523 | −0.577615 | − | 0.816309i | \(-0.696016\pi\) | ||||
−0.577615 | + | 0.816309i | \(0.696016\pi\) | |||||||
\(884\) | −1.04518e75 | −0.766759 | ||||||||
\(885\) | 7.06886e74 | 0.503844 | ||||||||
\(886\) | −1.41799e75 | −0.982001 | ||||||||
\(887\) | −2.18618e75 | −1.47107 | −0.735535 | − | 0.677487i | \(-0.763069\pi\) | ||||
−0.735535 | + | 0.677487i | \(0.763069\pi\) | |||||||
\(888\) | 7.16080e75 | 4.68199 | ||||||||
\(889\) | 8.33840e74 | 0.529770 | ||||||||
\(890\) | −1.49567e75 | −0.923403 | ||||||||
\(891\) | 3.10214e74 | 0.186115 | ||||||||
\(892\) | −3.03575e75 | −1.76996 | ||||||||
\(893\) | 1.03344e75 | 0.585563 | ||||||||
\(894\) | 1.26512e75 | 0.696667 | ||||||||
\(895\) | 7.25535e74 | 0.388303 | ||||||||
\(896\) | −2.79521e75 | −1.45399 | ||||||||
\(897\) | 1.50617e75 | 0.761493 | ||||||||
\(898\) | −2.06919e75 | −1.01684 | ||||||||
\(899\) | 3.70348e74 | 0.176904 | ||||||||
\(900\) | −6.13086e75 | −2.84667 | ||||||||
\(901\) | 3.23850e73 | 0.0146171 | ||||||||
\(902\) | 6.14014e75 | 2.69409 | ||||||||
\(903\) | 1.46795e75 | 0.626144 | ||||||||
\(904\) | −2.02081e75 | −0.837975 | ||||||||
\(905\) | −3.13746e74 | −0.126485 | ||||||||
\(906\) | −5.18052e75 | −2.03051 | ||||||||
\(907\) | −3.40042e75 | −1.29583 | −0.647914 | − | 0.761714i | \(-0.724358\pi\) | ||||
−0.647914 | + | 0.761714i | \(0.724358\pi\) | |||||||
\(908\) | 8.01672e75 | 2.97035 | ||||||||
\(909\) | 1.32124e75 | 0.475997 | ||||||||
\(910\) | 2.06935e75 | 0.724899 | ||||||||
\(911\) | −4.11484e74 | −0.140163 | −0.0700817 | − | 0.997541i | \(-0.522326\pi\) | ||||
−0.0700817 | + | 0.997541i | \(0.522326\pi\) | |||||||
\(912\) | −2.49222e75 | −0.825501 | ||||||||
\(913\) | 1.89761e75 | 0.611228 | ||||||||
\(914\) | 7.27895e75 | 2.28003 | ||||||||
\(915\) | −1.29117e75 | −0.393320 | ||||||||
\(916\) | 1.47682e75 | 0.437516 | ||||||||
\(917\) | −3.19944e75 | −0.921841 | ||||||||
\(918\) | 1.93222e75 | 0.541462 | ||||||||
\(919\) | −4.75576e75 | −1.29621 | −0.648104 | − | 0.761552i | \(-0.724438\pi\) | ||||
−0.648104 | + | 0.761552i | \(0.724438\pi\) | |||||||
\(920\) | −7.02587e74 | −0.186256 | ||||||||
\(921\) | 5.64172e75 | 1.45476 | ||||||||
\(922\) | 6.65889e75 | 1.67018 | ||||||||
\(923\) | −7.03428e75 | −1.71623 | ||||||||
\(924\) | −1.05417e76 | −2.50194 | ||||||||
\(925\) | 6.71770e75 | 1.55098 | ||||||||
\(926\) | −9.24196e75 | −2.07579 | ||||||||
\(927\) | −2.16841e75 | −0.473814 | ||||||||
\(928\) | −2.17309e74 | −0.0461960 | ||||||||
\(929\) | 7.98781e75 | 1.65207 | 0.826033 | − | 0.563622i | \(-0.190593\pi\) | ||||
0.826033 | + | 0.563622i | \(0.190593\pi\) | |||||||
\(930\) | −4.46442e75 | −0.898359 | ||||||||
\(931\) | −1.13377e75 | −0.221977 | ||||||||
\(932\) | −5.11675e75 | −0.974740 | ||||||||
\(933\) | −1.41249e76 | −2.61821 | ||||||||
\(934\) | 1.80626e75 | 0.325787 | ||||||||
\(935\) | −5.59216e74 | −0.0981484 | ||||||||
\(936\) | 2.29042e76 | 3.91183 | ||||||||
\(937\) | −3.77230e75 | −0.626970 | −0.313485 | − | 0.949593i | \(-0.601497\pi\) | ||||
−0.313485 | + | 0.949593i | \(0.601497\pi\) | |||||||
\(938\) | 1.05978e76 | 1.71413 | ||||||||
\(939\) | 1.34631e76 | 2.11920 | ||||||||
\(940\) | 4.26494e75 | 0.653360 | ||||||||
\(941\) | −1.08168e75 | −0.161274 | −0.0806371 | − | 0.996744i | \(-0.525695\pi\) | ||||
−0.0806371 | + | 0.996744i | \(0.525695\pi\) | |||||||
\(942\) | 3.41937e75 | 0.496191 | ||||||||
\(943\) | −3.64920e75 | −0.515406 | ||||||||
\(944\) | −4.88014e75 | −0.670882 | ||||||||
\(945\) | −2.52025e75 | −0.337235 | ||||||||
\(946\) | −6.09688e75 | −0.794116 | ||||||||
\(947\) | 2.23798e75 | 0.283747 | 0.141873 | − | 0.989885i | \(-0.454687\pi\) | ||||
0.141873 | + | 0.989885i | \(0.454687\pi\) | |||||||
\(948\) | −2.47060e76 | −3.04922 | ||||||||
\(949\) | −3.12115e75 | −0.374995 | ||||||||
\(950\) | −8.00178e75 | −0.935911 | ||||||||
\(951\) | 7.09139e75 | 0.807473 | ||||||||
\(952\) | −3.18132e75 | −0.352667 | ||||||||
\(953\) | 1.63024e76 | 1.75947 | 0.879737 | − | 0.475461i | \(-0.157719\pi\) | ||||
0.879737 | + | 0.475461i | \(0.157719\pi\) | |||||||
\(954\) | −1.47219e75 | −0.154696 | ||||||||
\(955\) | 6.78078e75 | 0.693735 | ||||||||
\(956\) | 2.20776e76 | 2.19925 | ||||||||
\(957\) | −3.34935e75 | −0.324867 | ||||||||
\(958\) | −9.38912e75 | −0.886756 | ||||||||
\(959\) | 9.03332e75 | 0.830755 | ||||||||
\(960\) | 7.94668e75 | 0.711655 | ||||||||
\(961\) | −2.65345e75 | −0.231401 | ||||||||
\(962\) | −5.20607e76 | −4.42126 | ||||||||
\(963\) | −9.83538e75 | −0.813431 | ||||||||
\(964\) | 2.15201e76 | 1.73332 | ||||||||
\(965\) | 4.58360e75 | 0.359551 | ||||||||
\(966\) | 9.51011e75 | 0.726556 | ||||||||
\(967\) | −1.19422e76 | −0.888609 | −0.444305 | − | 0.895876i | \(-0.646549\pi\) | ||||
−0.444305 | + | 0.895876i | \(0.646549\pi\) | |||||||
\(968\) | −8.79207e74 | −0.0637191 | ||||||||
\(969\) | 4.03484e75 | 0.284820 | ||||||||
\(970\) | −1.64347e76 | −1.13001 | ||||||||
\(971\) | −9.57238e75 | −0.641106 | −0.320553 | − | 0.947231i | \(-0.603869\pi\) | ||||
−0.320553 | + | 0.947231i | \(0.603869\pi\) | |||||||
\(972\) | 2.48020e76 | 1.61807 | ||||||||
\(973\) | −2.47220e75 | −0.157111 | ||||||||
\(974\) | 1.79224e74 | 0.0110954 | ||||||||
\(975\) | 3.41264e76 | 2.05813 | ||||||||
\(976\) | 8.91387e75 | 0.523716 | ||||||||
\(977\) | −3.03295e75 | −0.173602 | −0.0868008 | − | 0.996226i | \(-0.527664\pi\) | ||||
−0.0868008 | + | 0.996226i | \(0.527664\pi\) | |||||||
\(978\) | 4.78863e76 | 2.67036 | ||||||||
\(979\) | −2.67035e76 | −1.45081 | ||||||||
\(980\) | −4.67898e75 | −0.247677 | ||||||||
\(981\) | −3.96415e76 | −2.04451 | ||||||||
\(982\) | 6.42642e76 | 3.22943 | ||||||||
\(983\) | 7.25776e75 | 0.355376 | 0.177688 | − | 0.984087i | \(-0.443138\pi\) | ||||
0.177688 | + | 0.984087i | \(0.443138\pi\) | |||||||
\(984\) | −8.81365e76 | −4.20514 | ||||||||
\(985\) | −7.74291e75 | −0.359981 | ||||||||
\(986\) | −2.09677e75 | −0.0949926 | ||||||||
\(987\) | −2.78293e76 | −1.22861 | ||||||||
\(988\) | 4.08528e76 | 1.75760 | ||||||||
\(989\) | 3.62349e75 | 0.151922 | ||||||||
\(990\) | 2.54214e76 | 1.03873 | ||||||||
\(991\) | −1.83886e74 | −0.00732268 | −0.00366134 | − | 0.999993i | \(-0.501165\pi\) | ||||
−0.00366134 | + | 0.999993i | \(0.501165\pi\) | |||||||
\(992\) | −5.17148e75 | −0.200709 | ||||||||
\(993\) | −1.99622e76 | −0.755098 | ||||||||
\(994\) | −4.44152e76 | −1.63749 | ||||||||
\(995\) | 1.03642e76 | 0.372433 | ||||||||
\(996\) | −5.65043e76 | −1.97910 | ||||||||
\(997\) | 4.30923e76 | 1.47120 | 0.735602 | − | 0.677414i | \(-0.236900\pi\) | ||||
0.735602 | + | 0.677414i | \(0.236900\pi\) | |||||||
\(998\) | −7.81731e76 | −2.60153 | ||||||||
\(999\) | 6.34047e76 | 2.05684 |
(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 | 1.52.a.a.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 9.52.a.b.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.52.a.a.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.52.a.b.1.1 | 4 | 3.2 | odd | 2 |