Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,74,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, 74, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 74);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 74 \) |
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: | \(33.7483973737\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots + 17\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-6.50494e8\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28059e10 | 0.131769 | 0.0658846 | − | 0.997827i | \(-0.479013\pi\) | ||||
0.0658846 | + | 0.997827i | \(0.479013\pi\) | |||||||
\(3\) | −4.48831e17 | −1.72646 | −0.863232 | − | 0.504808i | \(-0.831563\pi\) | ||||
−0.863232 | + | 0.504808i | \(0.831563\pi\) | |||||||
\(4\) | −9.28074e21 | −0.982637 | ||||||||
\(5\) | 4.05981e25 | 1.24767 | 0.623837 | − | 0.781555i | \(-0.285573\pi\) | ||||
0.623837 | + | 0.781555i | \(0.285573\pi\) | |||||||
\(6\) | −5.74767e27 | −0.227495 | ||||||||
\(7\) | −7.12492e30 | −1.01555 | −0.507775 | − | 0.861489i | \(-0.669532\pi\) | ||||
−0.507775 | + | 0.861489i | \(0.669532\pi\) | |||||||
\(8\) | −2.39796e32 | −0.261250 | ||||||||
\(9\) | 1.33864e35 | 1.98068 | ||||||||
\(10\) | 5.19894e35 | 0.164405 | ||||||||
\(11\) | 5.42440e37 | 0.529076 | 0.264538 | − | 0.964375i | \(-0.414780\pi\) | ||||
0.264538 | + | 0.964375i | \(0.414780\pi\) | |||||||
\(12\) | 4.16549e39 | 1.69649 | ||||||||
\(13\) | 7.16246e40 | 1.57083 | 0.785416 | − | 0.618968i | \(-0.212449\pi\) | ||||
0.785416 | + | 0.618968i | \(0.212449\pi\) | |||||||
\(14\) | −9.12407e40 | −0.133818 | ||||||||
\(15\) | −1.82217e43 | −2.15406 | ||||||||
\(16\) | 8.45834e43 | 0.948212 | ||||||||
\(17\) | 1.30590e44 | 0.160149 | 0.0800744 | − | 0.996789i | \(-0.474484\pi\) | ||||
0.0800744 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(18\) | 1.71425e45 | 0.260992 | ||||||||
\(19\) | −2.65578e46 | −0.561935 | −0.280968 | − | 0.959717i | \(-0.590655\pi\) | ||||
−0.280968 | + | 0.959717i | \(0.590655\pi\) | |||||||
\(20\) | −3.76781e47 | −1.22601 | ||||||||
\(21\) | 3.19789e48 | 1.75331 | ||||||||
\(22\) | 6.94640e47 | 0.0697159 | ||||||||
\(23\) | −6.34296e49 | −1.25668 | −0.628342 | − | 0.777937i | \(-0.716266\pi\) | ||||
−0.628342 | + | 0.777937i | \(0.716266\pi\) | |||||||
\(24\) | 1.07628e50 | 0.451039 | ||||||||
\(25\) | 5.89418e50 | 0.556690 | ||||||||
\(26\) | 9.17214e50 | 0.206987 | ||||||||
\(27\) | −2.97482e52 | −1.69310 | ||||||||
\(28\) | 6.61246e52 | 0.997918 | ||||||||
\(29\) | 8.00076e52 | 0.335432 | 0.167716 | − | 0.985835i | \(-0.446361\pi\) | ||||
0.167716 | + | 0.985835i | \(0.446361\pi\) | |||||||
\(30\) | −2.33345e53 | −0.283839 | ||||||||
\(31\) | −3.53071e54 | −1.29766 | −0.648829 | − | 0.760934i | \(-0.724741\pi\) | ||||
−0.648829 | + | 0.760934i | \(0.724741\pi\) | |||||||
\(32\) | 3.34797e54 | 0.386195 | ||||||||
\(33\) | −2.43464e55 | −0.913431 | ||||||||
\(34\) | 1.67231e54 | 0.0211027 | ||||||||
\(35\) | −2.89259e56 | −1.26708 | ||||||||
\(36\) | −1.24236e57 | −1.94629 | ||||||||
\(37\) | 1.61097e56 | 0.0928376 | 0.0464188 | − | 0.998922i | \(-0.485219\pi\) | ||||
0.0464188 | + | 0.998922i | \(0.485219\pi\) | |||||||
\(38\) | −3.40096e56 | −0.0740457 | ||||||||
\(39\) | −3.21474e58 | −2.71198 | ||||||||
\(40\) | −9.73526e57 | −0.325955 | ||||||||
\(41\) | 6.62324e58 | 0.900450 | 0.450225 | − | 0.892915i | \(-0.351344\pi\) | ||||
0.450225 | + | 0.892915i | \(0.351344\pi\) | |||||||
\(42\) | 4.09517e58 | 0.231032 | ||||||||
\(43\) | 5.13946e57 | 0.0122834 | 0.00614171 | − | 0.999981i | \(-0.498045\pi\) | ||||
0.00614171 | + | 0.999981i | \(0.498045\pi\) | |||||||
\(44\) | −5.03424e59 | −0.519890 | ||||||||
\(45\) | 5.43465e60 | 2.47124 | ||||||||
\(46\) | −8.12270e59 | −0.165592 | ||||||||
\(47\) | 1.87105e61 | 1.73985 | 0.869927 | − | 0.493181i | \(-0.164166\pi\) | ||||
0.869927 | + | 0.493181i | \(0.164166\pi\) | |||||||
\(48\) | −3.79637e61 | −1.63705 | ||||||||
\(49\) | 1.54278e60 | 0.0313436 | ||||||||
\(50\) | 7.54801e60 | 0.0733545 | ||||||||
\(51\) | −5.86128e61 | −0.276491 | ||||||||
\(52\) | −6.64729e62 | −1.54356 | ||||||||
\(53\) | −2.36299e62 | −0.273774 | −0.136887 | − | 0.990587i | \(-0.543710\pi\) | ||||
−0.136887 | + | 0.990587i | \(0.543710\pi\) | |||||||
\(54\) | −3.80951e62 | −0.223099 | ||||||||
\(55\) | 2.20220e63 | 0.660115 | ||||||||
\(56\) | 1.70853e63 | 0.265313 | ||||||||
\(57\) | 1.19200e64 | 0.970160 | ||||||||
\(58\) | 1.02457e63 | 0.0441996 | ||||||||
\(59\) | −2.19113e64 | −0.506489 | −0.253244 | − | 0.967402i | \(-0.581498\pi\) | ||||
−0.253244 | + | 0.967402i | \(0.581498\pi\) | |||||||
\(60\) | 1.69111e65 | 2.11666 | ||||||||
\(61\) | −1.30217e65 | −0.891513 | −0.445756 | − | 0.895154i | \(-0.647065\pi\) | ||||
−0.445756 | + | 0.895154i | \(0.647065\pi\) | |||||||
\(62\) | −4.52138e64 | −0.170991 | ||||||||
\(63\) | −9.53773e65 | −2.01148 | ||||||||
\(64\) | −7.55994e65 | −0.897324 | ||||||||
\(65\) | 2.90783e66 | 1.95989 | ||||||||
\(66\) | −3.11776e65 | −0.120362 | ||||||||
\(67\) | −5.38484e66 | −1.20072 | −0.600361 | − | 0.799729i | \(-0.704977\pi\) | ||||
−0.600361 | + | 0.799729i | \(0.704977\pi\) | |||||||
\(68\) | −1.21197e66 | −0.157368 | ||||||||
\(69\) | 2.84692e67 | 2.16962 | ||||||||
\(70\) | −3.70420e66 | −0.166962 | ||||||||
\(71\) | 3.88431e67 | 1.04324 | 0.521620 | − | 0.853178i | \(-0.325328\pi\) | ||||
0.521620 | + | 0.853178i | \(0.325328\pi\) | |||||||
\(72\) | −3.21001e67 | −0.517452 | ||||||||
\(73\) | −9.28505e67 | −0.904690 | −0.452345 | − | 0.891843i | \(-0.649412\pi\) | ||||
−0.452345 | + | 0.891843i | \(0.649412\pi\) | |||||||
\(74\) | 2.06298e66 | 0.0122331 | ||||||||
\(75\) | −2.64549e68 | −0.961105 | ||||||||
\(76\) | 2.46476e68 | 0.552178 | ||||||||
\(77\) | −3.86484e68 | −0.537304 | ||||||||
\(78\) | −4.11674e68 | −0.357356 | ||||||||
\(79\) | −4.44441e68 | −0.242340 | −0.121170 | − | 0.992632i | \(-0.538665\pi\) | ||||
−0.121170 | + | 0.992632i | \(0.538665\pi\) | |||||||
\(80\) | 3.43393e69 | 1.18306 | ||||||||
\(81\) | 4.30467e69 | 0.942402 | ||||||||
\(82\) | 8.48163e68 | 0.118652 | ||||||||
\(83\) | 9.20761e69 | 0.827555 | 0.413777 | − | 0.910378i | \(-0.364209\pi\) | ||||
0.413777 | + | 0.910378i | \(0.364209\pi\) | |||||||
\(84\) | −2.96788e70 | −1.72287 | ||||||||
\(85\) | 5.30170e69 | 0.199813 | ||||||||
\(86\) | 6.58152e67 | 0.00161858 | ||||||||
\(87\) | −3.59099e70 | −0.579111 | ||||||||
\(88\) | −1.30075e70 | −0.138221 | ||||||||
\(89\) | −3.27546e70 | −0.230429 | −0.115214 | − | 0.993341i | \(-0.536755\pi\) | ||||
−0.115214 | + | 0.993341i | \(0.536755\pi\) | |||||||
\(90\) | 6.95953e70 | 0.325633 | ||||||||
\(91\) | −5.10320e71 | −1.59526 | ||||||||
\(92\) | 5.88674e71 | 1.23486 | ||||||||
\(93\) | 1.58469e72 | 2.24036 | ||||||||
\(94\) | 2.39603e71 | 0.229259 | ||||||||
\(95\) | −1.07820e72 | −0.701112 | ||||||||
\(96\) | −1.50267e72 | −0.666752 | ||||||||
\(97\) | −2.09156e72 | −0.635773 | −0.317886 | − | 0.948129i | \(-0.602973\pi\) | ||||
−0.317886 | + | 0.948129i | \(0.602973\pi\) | |||||||
\(98\) | 1.97567e70 | 0.00413011 | ||||||||
\(99\) | 7.26133e72 | 1.04793 | ||||||||
\(100\) | −5.47024e72 | −0.547024 | ||||||||
\(101\) | −2.75339e73 | −1.91486 | −0.957430 | − | 0.288664i | \(-0.906789\pi\) | ||||
−0.957430 | + | 0.288664i | \(0.906789\pi\) | |||||||
\(102\) | −7.50587e71 | −0.0364330 | ||||||||
\(103\) | 4.01406e73 | 1.36466 | 0.682332 | − | 0.731043i | \(-0.260966\pi\) | ||||
0.682332 | + | 0.731043i | \(0.260966\pi\) | |||||||
\(104\) | −1.71753e73 | −0.410380 | ||||||||
\(105\) | 1.29828e74 | 2.18756 | ||||||||
\(106\) | −3.02601e72 | −0.0360750 | ||||||||
\(107\) | −1.95235e74 | −1.65215 | −0.826077 | − | 0.563557i | \(-0.809432\pi\) | ||||
−0.826077 | + | 0.563557i | \(0.809432\pi\) | |||||||
\(108\) | 2.76085e74 | 1.66370 | ||||||||
\(109\) | −2.72452e74 | −1.17280 | −0.586398 | − | 0.810023i | \(-0.699454\pi\) | ||||
−0.586398 | + | 0.810023i | \(0.699454\pi\) | |||||||
\(110\) | 2.82011e73 | 0.0869827 | ||||||||
\(111\) | −7.23053e73 | −0.160281 | ||||||||
\(112\) | −6.02650e74 | −0.962958 | ||||||||
\(113\) | 4.60081e74 | 0.531461 | 0.265730 | − | 0.964047i | \(-0.414387\pi\) | ||||
0.265730 | + | 0.964047i | \(0.414387\pi\) | |||||||
\(114\) | 1.52646e74 | 0.127837 | ||||||||
\(115\) | −2.57512e75 | −1.56793 | ||||||||
\(116\) | −7.42530e74 | −0.329608 | ||||||||
\(117\) | 9.58798e75 | 3.11131 | ||||||||
\(118\) | −2.80593e74 | −0.0667396 | ||||||||
\(119\) | −9.30442e74 | −0.162639 | ||||||||
\(120\) | 4.36949e75 | 0.562750 | ||||||||
\(121\) | −7.56913e75 | −0.720078 | ||||||||
\(122\) | −1.66754e75 | −0.117474 | ||||||||
\(123\) | −2.97272e76 | −1.55459 | ||||||||
\(124\) | 3.27676e76 | 1.27513 | ||||||||
\(125\) | −1.90557e76 | −0.553106 | ||||||||
\(126\) | −1.22139e76 | −0.265051 | ||||||||
\(127\) | 5.34262e75 | 0.0868798 | 0.0434399 | − | 0.999056i | \(-0.486168\pi\) | ||||
0.0434399 | + | 0.999056i | \(0.486168\pi\) | |||||||
\(128\) | −4.13018e76 | −0.504435 | ||||||||
\(129\) | −2.30675e75 | −0.0212069 | ||||||||
\(130\) | 3.72372e76 | 0.258252 | ||||||||
\(131\) | 2.08365e77 | 1.09250 | 0.546252 | − | 0.837621i | \(-0.316054\pi\) | ||||
0.546252 | + | 0.837621i | \(0.316054\pi\) | |||||||
\(132\) | 2.25953e77 | 0.897571 | ||||||||
\(133\) | 1.89222e77 | 0.570674 | ||||||||
\(134\) | −6.89575e76 | −0.158218 | ||||||||
\(135\) | −1.20772e78 | −2.11244 | ||||||||
\(136\) | −3.13149e76 | −0.0418389 | ||||||||
\(137\) | 1.66251e76 | 0.0170006 | 0.00850030 | − | 0.999964i | \(-0.497294\pi\) | ||||
0.00850030 | + | 0.999964i | \(0.497294\pi\) | |||||||
\(138\) | 3.64572e77 | 0.285889 | ||||||||
\(139\) | −9.14130e76 | −0.0550767 | −0.0275383 | − | 0.999621i | \(-0.508767\pi\) | ||||
−0.0275383 | + | 0.999621i | \(0.508767\pi\) | |||||||
\(140\) | 2.68454e78 | 1.24508 | ||||||||
\(141\) | −8.39784e78 | −3.00379 | ||||||||
\(142\) | 4.97419e77 | 0.137467 | ||||||||
\(143\) | 3.88520e78 | 0.831090 | ||||||||
\(144\) | 1.13227e79 | 1.87810 | ||||||||
\(145\) | 3.24816e78 | 0.418510 | ||||||||
\(146\) | −1.18903e78 | −0.119210 | ||||||||
\(147\) | −6.92450e77 | −0.0541135 | ||||||||
\(148\) | −1.49510e78 | −0.0912257 | ||||||||
\(149\) | −1.98294e79 | −0.946260 | −0.473130 | − | 0.880993i | \(-0.656876\pi\) | ||||
−0.473130 | + | 0.880993i | \(0.656876\pi\) | |||||||
\(150\) | −3.38778e78 | −0.126644 | ||||||||
\(151\) | −2.17790e79 | −0.638821 | −0.319410 | − | 0.947617i | \(-0.603485\pi\) | ||||
−0.319410 | + | 0.947617i | \(0.603485\pi\) | |||||||
\(152\) | 6.36845e78 | 0.146806 | ||||||||
\(153\) | 1.74813e79 | 0.317203 | ||||||||
\(154\) | −4.94926e78 | −0.0708001 | ||||||||
\(155\) | −1.43340e80 | −1.61905 | ||||||||
\(156\) | 2.98351e80 | 2.66490 | ||||||||
\(157\) | −1.69128e80 | −1.19641 | −0.598204 | − | 0.801344i | \(-0.704119\pi\) | ||||
−0.598204 | + | 0.801344i | \(0.704119\pi\) | |||||||
\(158\) | −5.69145e78 | −0.0319330 | ||||||||
\(159\) | 1.06058e80 | 0.472661 | ||||||||
\(160\) | 1.35921e80 | 0.481846 | ||||||||
\(161\) | 4.51931e80 | 1.27623 | ||||||||
\(162\) | 5.51249e79 | 0.124180 | ||||||||
\(163\) | −4.96403e80 | −0.893279 | −0.446640 | − | 0.894714i | \(-0.647379\pi\) | ||||
−0.446640 | + | 0.894714i | \(0.647379\pi\) | |||||||
\(164\) | −6.14686e80 | −0.884816 | ||||||||
\(165\) | −9.88418e80 | −1.13966 | ||||||||
\(166\) | 1.17911e80 | 0.109046 | ||||||||
\(167\) | 1.76051e80 | 0.130764 | 0.0653818 | − | 0.997860i | \(-0.479173\pi\) | ||||
0.0653818 | + | 0.997860i | \(0.479173\pi\) | |||||||
\(168\) | −7.66840e80 | −0.458053 | ||||||||
\(169\) | 3.05103e81 | 1.46751 | ||||||||
\(170\) | 6.78928e79 | 0.0263292 | ||||||||
\(171\) | −3.55515e81 | −1.11301 | ||||||||
\(172\) | −4.76981e79 | −0.0120701 | ||||||||
\(173\) | 8.57658e81 | 1.75643 | 0.878216 | − | 0.478265i | \(-0.158734\pi\) | ||||
0.878216 | + | 0.478265i | \(0.158734\pi\) | |||||||
\(174\) | −4.59857e80 | −0.0763090 | ||||||||
\(175\) | −4.19956e81 | −0.565347 | ||||||||
\(176\) | 4.58814e81 | 0.501677 | ||||||||
\(177\) | 9.83449e81 | 0.874435 | ||||||||
\(178\) | −4.19450e80 | −0.0303634 | ||||||||
\(179\) | −1.04344e82 | −0.615646 | −0.307823 | − | 0.951444i | \(-0.599600\pi\) | ||||
−0.307823 | + | 0.951444i | \(0.599600\pi\) | |||||||
\(180\) | −5.04376e82 | −2.42833 | ||||||||
\(181\) | −5.37748e81 | −0.211500 | −0.105750 | − | 0.994393i | \(-0.533724\pi\) | ||||
−0.105750 | + | 0.994393i | \(0.533724\pi\) | |||||||
\(182\) | −6.53508e81 | −0.210206 | ||||||||
\(183\) | 5.84453e82 | 1.53916 | ||||||||
\(184\) | 1.52101e82 | 0.328309 | ||||||||
\(185\) | 6.54023e81 | 0.115831 | ||||||||
\(186\) | 2.02934e82 | 0.295210 | ||||||||
\(187\) | 7.08371e81 | 0.0847309 | ||||||||
\(188\) | −1.73647e83 | −1.70964 | ||||||||
\(189\) | 2.11954e83 | 1.71943 | ||||||||
\(190\) | −1.38073e82 | −0.0923849 | ||||||||
\(191\) | 2.08649e82 | 0.115265 | 0.0576325 | − | 0.998338i | \(-0.481645\pi\) | ||||
0.0576325 | + | 0.998338i | \(0.481645\pi\) | |||||||
\(192\) | 3.39314e83 | 1.54920 | ||||||||
\(193\) | −1.09262e83 | −0.412693 | −0.206347 | − | 0.978479i | \(-0.566157\pi\) | ||||
−0.206347 | + | 0.978479i | \(0.566157\pi\) | |||||||
\(194\) | −2.67842e82 | −0.0837752 | ||||||||
\(195\) | −1.30512e84 | −3.38367 | ||||||||
\(196\) | −1.43182e82 | −0.0307993 | ||||||||
\(197\) | 7.56333e83 | 1.35113 | 0.675563 | − | 0.737302i | \(-0.263901\pi\) | ||||
0.675563 | + | 0.737302i | \(0.263901\pi\) | |||||||
\(198\) | 9.29876e82 | 0.138085 | ||||||||
\(199\) | −7.27551e83 | −0.898930 | −0.449465 | − | 0.893298i | \(-0.648385\pi\) | ||||
−0.449465 | + | 0.893298i | \(0.648385\pi\) | |||||||
\(200\) | −1.41340e83 | −0.145435 | ||||||||
\(201\) | 2.41689e84 | 2.07300 | ||||||||
\(202\) | −3.52595e83 | −0.252320 | ||||||||
\(203\) | −5.70048e83 | −0.340648 | ||||||||
\(204\) | 5.43970e83 | 0.271690 | ||||||||
\(205\) | 2.68891e84 | 1.12347 | ||||||||
\(206\) | 5.14035e83 | 0.179820 | ||||||||
\(207\) | −8.49097e84 | −2.48908 | ||||||||
\(208\) | 6.05825e84 | 1.48948 | ||||||||
\(209\) | −1.44060e84 | −0.297307 | ||||||||
\(210\) | 1.66256e84 | 0.288253 | ||||||||
\(211\) | −3.42639e84 | −0.499491 | −0.249745 | − | 0.968312i | \(-0.580347\pi\) | ||||
−0.249745 | + | 0.968312i | \(0.580347\pi\) | |||||||
\(212\) | 2.19303e84 | 0.269021 | ||||||||
\(213\) | −1.74340e85 | −1.80112 | ||||||||
\(214\) | −2.50015e84 | −0.217703 | ||||||||
\(215\) | 2.08653e83 | 0.0153257 | ||||||||
\(216\) | 7.13349e84 | 0.442323 | ||||||||
\(217\) | 2.51560e85 | 1.31784 | ||||||||
\(218\) | −3.48898e84 | −0.154538 | ||||||||
\(219\) | 4.16742e85 | 1.56191 | ||||||||
\(220\) | −2.04381e85 | −0.648653 | ||||||||
\(221\) | 9.35344e84 | 0.251567 | ||||||||
\(222\) | −9.25931e83 | −0.0211201 | ||||||||
\(223\) | −7.17475e85 | −1.38893 | −0.694463 | − | 0.719528i | \(-0.744358\pi\) | ||||
−0.694463 | + | 0.719528i | \(0.744358\pi\) | |||||||
\(224\) | −2.38540e85 | −0.392201 | ||||||||
\(225\) | 7.89021e85 | 1.10262 | ||||||||
\(226\) | 5.89173e84 | 0.0700301 | ||||||||
\(227\) | 5.26645e85 | 0.532813 | 0.266406 | − | 0.963861i | \(-0.414164\pi\) | ||||
0.266406 | + | 0.963861i | \(0.414164\pi\) | |||||||
\(228\) | −1.10626e86 | −0.953315 | ||||||||
\(229\) | −1.96927e86 | −1.44648 | −0.723238 | − | 0.690599i | \(-0.757347\pi\) | ||||
−0.723238 | + | 0.690599i | \(0.757347\pi\) | |||||||
\(230\) | −3.29767e85 | −0.206605 | ||||||||
\(231\) | 1.73466e86 | 0.927636 | ||||||||
\(232\) | −1.91855e85 | −0.0876317 | ||||||||
\(233\) | −2.47311e86 | −0.965499 | −0.482750 | − | 0.875758i | \(-0.660362\pi\) | ||||
−0.482750 | + | 0.875758i | \(0.660362\pi\) | |||||||
\(234\) | 1.22782e86 | 0.409975 | ||||||||
\(235\) | 7.59610e86 | 2.17077 | ||||||||
\(236\) | 2.03353e86 | 0.497695 | ||||||||
\(237\) | 1.99479e86 | 0.418392 | ||||||||
\(238\) | −1.19151e85 | −0.0214308 | ||||||||
\(239\) | −9.15532e85 | −0.141303 | −0.0706513 | − | 0.997501i | \(-0.522508\pi\) | ||||
−0.0706513 | + | 0.997501i | \(0.522508\pi\) | |||||||
\(240\) | −1.54125e87 | −2.04251 | ||||||||
\(241\) | −1.90452e86 | −0.216852 | −0.108426 | − | 0.994104i | \(-0.534581\pi\) | ||||
−0.108426 | + | 0.994104i | \(0.534581\pi\) | |||||||
\(242\) | −9.69291e85 | −0.0948841 | ||||||||
\(243\) | 7.84674e85 | 0.0660786 | ||||||||
\(244\) | 1.20851e87 | 0.876033 | ||||||||
\(245\) | 6.26342e85 | 0.0391065 | ||||||||
\(246\) | −3.80682e86 | −0.204848 | ||||||||
\(247\) | −1.90219e87 | −0.882706 | ||||||||
\(248\) | 8.46649e86 | 0.339014 | ||||||||
\(249\) | −4.13267e87 | −1.42874 | ||||||||
\(250\) | −2.44024e86 | −0.0728823 | ||||||||
\(251\) | 6.30464e87 | 1.62768 | 0.813841 | − | 0.581087i | \(-0.197373\pi\) | ||||
0.813841 | + | 0.581087i | \(0.197373\pi\) | |||||||
\(252\) | 8.85173e87 | 1.97655 | ||||||||
\(253\) | −3.44067e87 | −0.664882 | ||||||||
\(254\) | 6.84168e85 | 0.0114481 | ||||||||
\(255\) | −2.37957e87 | −0.344971 | ||||||||
\(256\) | 6.61125e87 | 0.830855 | ||||||||
\(257\) | −6.84443e87 | −0.746068 | −0.373034 | − | 0.927818i | \(-0.621683\pi\) | ||||
−0.373034 | + | 0.927818i | \(0.621683\pi\) | |||||||
\(258\) | −2.95399e85 | −0.00279441 | ||||||||
\(259\) | −1.14780e87 | −0.0942814 | ||||||||
\(260\) | −2.69868e88 | −1.92586 | ||||||||
\(261\) | 1.07102e88 | 0.664382 | ||||||||
\(262\) | 2.66829e87 | 0.143958 | ||||||||
\(263\) | −7.68237e87 | −0.360670 | −0.180335 | − | 0.983605i | \(-0.557718\pi\) | ||||
−0.180335 | + | 0.983605i | \(0.557718\pi\) | |||||||
\(264\) | 5.83816e87 | 0.238634 | ||||||||
\(265\) | −9.59330e87 | −0.341581 | ||||||||
\(266\) | 2.42316e87 | 0.0751972 | ||||||||
\(267\) | 1.47013e88 | 0.397827 | ||||||||
\(268\) | 4.99753e88 | 1.17987 | ||||||||
\(269\) | −6.48183e87 | −0.133579 | −0.0667897 | − | 0.997767i | \(-0.521276\pi\) | ||||
−0.0667897 | + | 0.997767i | \(0.521276\pi\) | |||||||
\(270\) | −1.54659e88 | −0.278354 | ||||||||
\(271\) | −7.02783e88 | −1.10520 | −0.552602 | − | 0.833445i | \(-0.686365\pi\) | ||||
−0.552602 | + | 0.833445i | \(0.686365\pi\) | |||||||
\(272\) | 1.10457e88 | 0.151855 | ||||||||
\(273\) | 2.29047e89 | 2.75416 | ||||||||
\(274\) | 2.12899e86 | 0.00224016 | ||||||||
\(275\) | 3.19724e88 | 0.294531 | ||||||||
\(276\) | −2.64215e89 | −2.13195 | ||||||||
\(277\) | −2.35295e88 | −0.166380 | −0.0831901 | − | 0.996534i | \(-0.526511\pi\) | ||||
−0.0831901 | + | 0.996534i | \(0.526511\pi\) | |||||||
\(278\) | −1.17062e87 | −0.00725740 | ||||||||
\(279\) | −4.72637e89 | −2.57024 | ||||||||
\(280\) | 6.93630e88 | 0.331024 | ||||||||
\(281\) | 3.29283e89 | 1.37971 | 0.689856 | − | 0.723947i | \(-0.257674\pi\) | ||||
0.689856 | + | 0.723947i | \(0.257674\pi\) | |||||||
\(282\) | −1.07542e89 | −0.395807 | ||||||||
\(283\) | 5.00752e89 | 1.61964 | 0.809819 | − | 0.586680i | \(-0.199565\pi\) | ||||
0.809819 | + | 0.586680i | \(0.199565\pi\) | |||||||
\(284\) | −3.60493e89 | −1.02513 | ||||||||
\(285\) | 4.83929e89 | 1.21044 | ||||||||
\(286\) | 4.97533e88 | 0.109512 | ||||||||
\(287\) | −4.71901e89 | −0.914453 | ||||||||
\(288\) | 4.48174e89 | 0.764928 | ||||||||
\(289\) | −6.47869e89 | −0.974352 | ||||||||
\(290\) | 4.15955e88 | 0.0551467 | ||||||||
\(291\) | 9.38757e89 | 1.09764 | ||||||||
\(292\) | 8.61722e89 | 0.888982 | ||||||||
\(293\) | −6.16045e89 | −0.560976 | −0.280488 | − | 0.959858i | \(-0.590496\pi\) | ||||
−0.280488 | + | 0.959858i | \(0.590496\pi\) | |||||||
\(294\) | −8.86741e87 | −0.00713049 | ||||||||
\(295\) | −8.89559e89 | −0.631933 | ||||||||
\(296\) | −3.86303e88 | −0.0242539 | ||||||||
\(297\) | −1.61366e90 | −0.895780 | ||||||||
\(298\) | −2.53932e89 | −0.124688 | ||||||||
\(299\) | −4.54312e90 | −1.97404 | ||||||||
\(300\) | 2.45522e90 | 0.944417 | ||||||||
\(301\) | −3.66183e88 | −0.0124744 | ||||||||
\(302\) | −2.78898e89 | −0.0841768 | ||||||||
\(303\) | 1.23581e91 | 3.30594 | ||||||||
\(304\) | −2.24635e90 | −0.532834 | ||||||||
\(305\) | −5.28656e90 | −1.11232 | ||||||||
\(306\) | 2.23863e89 | 0.0417975 | ||||||||
\(307\) | 9.29015e90 | 1.53983 | 0.769914 | − | 0.638148i | \(-0.220299\pi\) | ||||
0.769914 | + | 0.638148i | \(0.220299\pi\) | |||||||
\(308\) | 3.58686e90 | 0.527975 | ||||||||
\(309\) | −1.80164e91 | −2.35604 | ||||||||
\(310\) | −1.83560e90 | −0.213341 | ||||||||
\(311\) | 2.50281e90 | 0.258627 | 0.129314 | − | 0.991604i | \(-0.458723\pi\) | ||||
0.129314 | + | 0.991604i | \(0.458723\pi\) | |||||||
\(312\) | 7.70880e90 | 0.708507 | ||||||||
\(313\) | 1.82125e91 | 1.48937 | 0.744684 | − | 0.667417i | \(-0.232600\pi\) | ||||
0.744684 | + | 0.667417i | \(0.232600\pi\) | |||||||
\(314\) | −2.16583e90 | −0.157650 | ||||||||
\(315\) | −3.87214e91 | −2.50967 | ||||||||
\(316\) | 4.12475e90 | 0.238133 | ||||||||
\(317\) | −2.15612e91 | −1.10920 | −0.554601 | − | 0.832117i | \(-0.687129\pi\) | ||||
−0.554601 | + | 0.832117i | \(0.687129\pi\) | |||||||
\(318\) | 1.35817e90 | 0.0622821 | ||||||||
\(319\) | 4.33993e90 | 0.177469 | ||||||||
\(320\) | −3.06919e91 | −1.11957 | ||||||||
\(321\) | 8.76277e91 | 2.85238 | ||||||||
\(322\) | 5.78736e90 | 0.168167 | ||||||||
\(323\) | −3.46818e90 | −0.0899932 | ||||||||
\(324\) | −3.99505e91 | −0.926039 | ||||||||
\(325\) | 4.22168e91 | 0.874466 | ||||||||
\(326\) | −6.35687e90 | −0.117707 | ||||||||
\(327\) | 1.22285e92 | 2.02479 | ||||||||
\(328\) | −1.58822e91 | −0.235243 | ||||||||
\(329\) | −1.33311e92 | −1.76691 | ||||||||
\(330\) | −1.26575e91 | −0.150173 | ||||||||
\(331\) | 2.31408e91 | 0.245842 | 0.122921 | − | 0.992416i | \(-0.460774\pi\) | ||||
0.122921 | + | 0.992416i | \(0.460774\pi\) | |||||||
\(332\) | −8.54535e91 | −0.813186 | ||||||||
\(333\) | 2.15651e91 | 0.183881 | ||||||||
\(334\) | 2.25448e90 | 0.0172306 | ||||||||
\(335\) | −2.18615e92 | −1.49811 | ||||||||
\(336\) | 2.70488e92 | 1.66251 | ||||||||
\(337\) | 2.57115e91 | 0.141787 | 0.0708935 | − | 0.997484i | \(-0.477415\pi\) | ||||
0.0708935 | + | 0.997484i | \(0.477415\pi\) | |||||||
\(338\) | 3.90710e91 | 0.193373 | ||||||||
\(339\) | −2.06499e92 | −0.917548 | ||||||||
\(340\) | −4.92037e91 | −0.196344 | ||||||||
\(341\) | −1.91520e92 | −0.686560 | ||||||||
\(342\) | −4.55267e91 | −0.146661 | ||||||||
\(343\) | 3.39709e92 | 0.983720 | ||||||||
\(344\) | −1.23242e90 | −0.00320905 | ||||||||
\(345\) | 1.15580e93 | 2.70698 | ||||||||
\(346\) | 1.09830e92 | 0.231443 | ||||||||
\(347\) | −5.43093e92 | −1.03003 | −0.515013 | − | 0.857182i | \(-0.672213\pi\) | ||||
−0.515013 | + | 0.857182i | \(0.672213\pi\) | |||||||
\(348\) | 3.33271e92 | 0.569056 | ||||||||
\(349\) | −1.29977e90 | −0.00199866 | −0.000999328 | − | 1.00000i | \(-0.500318\pi\) | ||||
−0.000999328 | 1.00000i | \(0.500318\pi\) | ||||||||
\(350\) | −5.37790e91 | −0.0744953 | ||||||||
\(351\) | −2.13070e93 | −2.65958 | ||||||||
\(352\) | 1.81607e92 | 0.204327 | ||||||||
\(353\) | −1.12268e93 | −1.13888 | −0.569442 | − | 0.822032i | \(-0.692841\pi\) | ||||
−0.569442 | + | 0.822032i | \(0.692841\pi\) | |||||||
\(354\) | 1.25939e92 | 0.115224 | ||||||||
\(355\) | 1.57696e93 | 1.30162 | ||||||||
\(356\) | 3.03987e92 | 0.226428 | ||||||||
\(357\) | 4.17612e92 | 0.280791 | ||||||||
\(358\) | −1.33621e92 | −0.0811231 | ||||||||
\(359\) | 8.79228e91 | 0.0482119 | 0.0241059 | − | 0.999709i | \(-0.492326\pi\) | ||||
0.0241059 | + | 0.999709i | \(0.492326\pi\) | |||||||
\(360\) | −1.30320e93 | −0.645612 | ||||||||
\(361\) | −1.52832e93 | −0.684229 | ||||||||
\(362\) | −6.88633e91 | −0.0278692 | ||||||||
\(363\) | 3.39726e93 | 1.24319 | ||||||||
\(364\) | 4.73614e93 | 1.56756 | ||||||||
\(365\) | −3.76956e93 | −1.12876 | ||||||||
\(366\) | 7.48442e92 | 0.202814 | ||||||||
\(367\) | 3.02870e93 | 0.742925 | 0.371462 | − | 0.928448i | \(-0.378856\pi\) | ||||
0.371462 | + | 0.928448i | \(0.378856\pi\) | |||||||
\(368\) | −5.36509e93 | −1.19160 | ||||||||
\(369\) | 8.86616e93 | 1.78350 | ||||||||
\(370\) | 8.37533e91 | 0.0152630 | ||||||||
\(371\) | 1.68361e93 | 0.278032 | ||||||||
\(372\) | −1.47071e94 | −2.20146 | ||||||||
\(373\) | −1.41066e94 | −1.91448 | −0.957239 | − | 0.289297i | \(-0.906579\pi\) | ||||
−0.957239 | + | 0.289297i | \(0.906579\pi\) | |||||||
\(374\) | 9.07129e91 | 0.0111649 | ||||||||
\(375\) | 8.55278e93 | 0.954918 | ||||||||
\(376\) | −4.48669e93 | −0.454537 | ||||||||
\(377\) | 5.73051e93 | 0.526907 | ||||||||
\(378\) | 2.71425e93 | 0.226568 | ||||||||
\(379\) | 3.09449e93 | 0.234562 | 0.117281 | − | 0.993099i | \(-0.462582\pi\) | ||||
0.117281 | + | 0.993099i | \(0.462582\pi\) | |||||||
\(380\) | 1.00065e94 | 0.688938 | ||||||||
\(381\) | −2.39794e93 | −0.149995 | ||||||||
\(382\) | 2.67192e92 | 0.0151884 | ||||||||
\(383\) | −5.62498e93 | −0.290647 | −0.145323 | − | 0.989384i | \(-0.546422\pi\) | ||||
−0.145323 | + | 0.989384i | \(0.546422\pi\) | |||||||
\(384\) | 1.85375e94 | 0.870889 | ||||||||
\(385\) | −1.56905e94 | −0.670380 | ||||||||
\(386\) | −1.39919e93 | −0.0543802 | ||||||||
\(387\) | 6.87991e92 | 0.0243295 | ||||||||
\(388\) | 1.94112e94 | 0.624734 | ||||||||
\(389\) | 4.55175e94 | 1.33358 | 0.666789 | − | 0.745247i | \(-0.267668\pi\) | ||||
0.666789 | + | 0.745247i | \(0.267668\pi\) | |||||||
\(390\) | −1.67132e94 | −0.445863 | ||||||||
\(391\) | −8.28326e93 | −0.201256 | ||||||||
\(392\) | −3.69953e92 | −0.00818852 | ||||||||
\(393\) | −9.35208e94 | −1.88617 | ||||||||
\(394\) | 9.68549e93 | 0.178037 | ||||||||
\(395\) | −1.80435e94 | −0.302362 | ||||||||
\(396\) | −6.73906e94 | −1.02973 | ||||||||
\(397\) | 6.04038e94 | 0.841804 | 0.420902 | − | 0.907106i | \(-0.361714\pi\) | ||||
0.420902 | + | 0.907106i | \(0.361714\pi\) | |||||||
\(398\) | −9.31691e93 | −0.118451 | ||||||||
\(399\) | −8.49290e94 | −0.985247 | ||||||||
\(400\) | 4.98550e94 | 0.527860 | ||||||||
\(401\) | 1.81150e95 | 1.75093 | 0.875465 | − | 0.483281i | \(-0.160555\pi\) | ||||
0.875465 | + | 0.483281i | \(0.160555\pi\) | |||||||
\(402\) | 3.09503e94 | 0.273158 | ||||||||
\(403\) | −2.52886e95 | −2.03840 | ||||||||
\(404\) | 2.55535e95 | 1.88161 | ||||||||
\(405\) | 1.74762e95 | 1.17581 | ||||||||
\(406\) | −7.29995e93 | −0.0448869 | ||||||||
\(407\) | 8.73853e93 | 0.0491182 | ||||||||
\(408\) | 1.40551e94 | 0.0722334 | ||||||||
\(409\) | −2.92901e95 | −1.37664 | −0.688318 | − | 0.725409i | \(-0.741651\pi\) | ||||
−0.688318 | + | 0.725409i | \(0.741651\pi\) | |||||||
\(410\) | 3.44338e94 | 0.148038 | ||||||||
\(411\) | −7.46188e93 | −0.0293509 | ||||||||
\(412\) | −3.72535e95 | −1.34097 | ||||||||
\(413\) | 1.56116e95 | 0.514365 | ||||||||
\(414\) | −1.08734e95 | −0.327984 | ||||||||
\(415\) | 3.73812e95 | 1.03252 | ||||||||
\(416\) | 2.39797e95 | 0.606648 | ||||||||
\(417\) | 4.10290e94 | 0.0950878 | ||||||||
\(418\) | −1.84481e94 | −0.0391758 | ||||||||
\(419\) | −8.12273e95 | −1.58085 | −0.790424 | − | 0.612560i | \(-0.790140\pi\) | ||||
−0.790424 | + | 0.612560i | \(0.790140\pi\) | |||||||
\(420\) | −1.20490e96 | −2.14958 | ||||||||
\(421\) | −1.37700e95 | −0.225236 | −0.112618 | − | 0.993638i | \(-0.535924\pi\) | ||||
−0.112618 | + | 0.993638i | \(0.535924\pi\) | |||||||
\(422\) | −4.38779e94 | −0.0658175 | ||||||||
\(423\) | 2.50467e96 | 3.44609 | ||||||||
\(424\) | 5.66635e94 | 0.0715236 | ||||||||
\(425\) | 7.69720e94 | 0.0891532 | ||||||||
\(426\) | −2.23257e95 | −0.237331 | ||||||||
\(427\) | 9.27784e95 | 0.905377 | ||||||||
\(428\) | 1.81193e96 | 1.62347 | ||||||||
\(429\) | −1.74380e96 | −1.43485 | ||||||||
\(430\) | 2.67198e93 | 0.00201945 | ||||||||
\(431\) | 2.16300e95 | 0.150189 | 0.0750943 | − | 0.997176i | \(-0.476074\pi\) | ||||
0.0750943 | + | 0.997176i | \(0.476074\pi\) | |||||||
\(432\) | −2.51620e96 | −1.60542 | ||||||||
\(433\) | −1.06805e96 | −0.626299 | −0.313149 | − | 0.949704i | \(-0.601384\pi\) | ||||
−0.313149 | + | 0.949704i | \(0.601384\pi\) | |||||||
\(434\) | 3.22145e95 | 0.173650 | ||||||||
\(435\) | −1.45788e96 | −0.722542 | ||||||||
\(436\) | 2.52855e96 | 1.15243 | ||||||||
\(437\) | 1.68455e96 | 0.706175 | ||||||||
\(438\) | 5.33674e95 | 0.205812 | ||||||||
\(439\) | −4.18327e96 | −1.48443 | −0.742217 | − | 0.670160i | \(-0.766225\pi\) | ||||
−0.742217 | + | 0.670160i | \(0.766225\pi\) | |||||||
\(440\) | −5.28079e95 | −0.172455 | ||||||||
\(441\) | 2.06524e95 | 0.0620814 | ||||||||
\(442\) | 1.19779e95 | 0.0331487 | ||||||||
\(443\) | −1.44956e96 | −0.369403 | −0.184701 | − | 0.982795i | \(-0.559132\pi\) | ||||
−0.184701 | + | 0.982795i | \(0.559132\pi\) | |||||||
\(444\) | 6.71047e95 | 0.157498 | ||||||||
\(445\) | −1.32977e96 | −0.287500 | ||||||||
\(446\) | −9.18788e95 | −0.183018 | ||||||||
\(447\) | 8.90005e96 | 1.63368 | ||||||||
\(448\) | 5.38640e96 | 0.911278 | ||||||||
\(449\) | −8.52316e95 | −0.132926 | −0.0664629 | − | 0.997789i | \(-0.521171\pi\) | ||||
−0.0664629 | + | 0.997789i | \(0.521171\pi\) | |||||||
\(450\) | 1.01041e96 | 0.145292 | ||||||||
\(451\) | 3.59271e96 | 0.476407 | ||||||||
\(452\) | −4.26990e96 | −0.522233 | ||||||||
\(453\) | 9.77509e96 | 1.10290 | ||||||||
\(454\) | 6.74414e95 | 0.0702083 | ||||||||
\(455\) | −2.07180e97 | −1.99036 | ||||||||
\(456\) | −2.85836e96 | −0.253455 | ||||||||
\(457\) | −1.28421e97 | −1.05122 | −0.525610 | − | 0.850726i | \(-0.676163\pi\) | ||||
−0.525610 | + | 0.850726i | \(0.676163\pi\) | |||||||
\(458\) | −2.52182e96 | −0.190601 | ||||||||
\(459\) | −3.88481e96 | −0.271148 | ||||||||
\(460\) | 2.38991e97 | 1.54071 | ||||||||
\(461\) | −2.16592e97 | −1.28991 | −0.644954 | − | 0.764221i | \(-0.723124\pi\) | ||||
−0.644954 | + | 0.764221i | \(0.723124\pi\) | |||||||
\(462\) | 2.22138e96 | 0.122234 | ||||||||
\(463\) | −7.61030e96 | −0.386986 | −0.193493 | − | 0.981102i | \(-0.561982\pi\) | ||||
−0.193493 | + | 0.981102i | \(0.561982\pi\) | |||||||
\(464\) | 6.76731e96 | 0.318061 | ||||||||
\(465\) | 6.43356e97 | 2.79524 | ||||||||
\(466\) | −3.16703e96 | −0.127223 | ||||||||
\(467\) | −2.32926e97 | −0.865270 | −0.432635 | − | 0.901569i | \(-0.642416\pi\) | ||||
−0.432635 | + | 0.901569i | \(0.642416\pi\) | |||||||
\(468\) | −8.89836e97 | −3.05729 | ||||||||
\(469\) | 3.83666e97 | 1.21939 | ||||||||
\(470\) | 9.72746e96 | 0.286040 | ||||||||
\(471\) | 7.59101e97 | 2.06555 | ||||||||
\(472\) | 5.25424e96 | 0.132320 | ||||||||
\(473\) | 2.78785e95 | 0.00649887 | ||||||||
\(474\) | 2.55450e96 | 0.0551311 | ||||||||
\(475\) | −1.56537e97 | −0.312824 | ||||||||
\(476\) | 8.63519e96 | 0.159815 | ||||||||
\(477\) | −3.16320e97 | −0.542258 | ||||||||
\(478\) | −1.17242e96 | −0.0186193 | ||||||||
\(479\) | 2.29746e97 | 0.338066 | 0.169033 | − | 0.985610i | \(-0.445936\pi\) | ||||
0.169033 | + | 0.985610i | \(0.445936\pi\) | |||||||
\(480\) | −6.10057e97 | −0.831889 | ||||||||
\(481\) | 1.15385e97 | 0.145832 | ||||||||
\(482\) | −2.43890e96 | −0.0285745 | ||||||||
\(483\) | −2.02841e98 | −2.20336 | ||||||||
\(484\) | 7.02471e97 | 0.707575 | ||||||||
\(485\) | −8.49134e97 | −0.793237 | ||||||||
\(486\) | 1.00484e96 | 0.00870711 | ||||||||
\(487\) | 9.83578e97 | 0.790682 | 0.395341 | − | 0.918534i | \(-0.370626\pi\) | ||||
0.395341 | + | 0.918534i | \(0.370626\pi\) | |||||||
\(488\) | 3.12254e97 | 0.232908 | ||||||||
\(489\) | 2.22801e98 | 1.54221 | ||||||||
\(490\) | 8.02084e95 | 0.00515303 | ||||||||
\(491\) | −1.73954e98 | −1.03743 | −0.518716 | − | 0.854947i | \(-0.673590\pi\) | ||||
−0.518716 | + | 0.854947i | \(0.673590\pi\) | |||||||
\(492\) | 2.75890e98 | 1.52760 | ||||||||
\(493\) | 1.04482e97 | 0.0537190 | ||||||||
\(494\) | −2.43592e97 | −0.116313 | ||||||||
\(495\) | 2.94797e98 | 1.30747 | ||||||||
\(496\) | −2.98639e98 | −1.23046 | ||||||||
\(497\) | −2.76754e98 | −1.05946 | ||||||||
\(498\) | −5.29223e97 | −0.188264 | ||||||||
\(499\) | −4.48498e97 | −0.148283 | −0.0741413 | − | 0.997248i | \(-0.523622\pi\) | ||||
−0.0741413 | + | 0.997248i | \(0.523622\pi\) | |||||||
\(500\) | 1.76851e98 | 0.543503 | ||||||||
\(501\) | −7.90172e97 | −0.225759 | ||||||||
\(502\) | 8.07363e97 | 0.214478 | ||||||||
\(503\) | 7.59682e98 | 1.87672 | 0.938362 | − | 0.345655i | \(-0.112343\pi\) | ||||
0.938362 | + | 0.345655i | \(0.112343\pi\) | |||||||
\(504\) | 2.28711e98 | 0.525499 | ||||||||
\(505\) | −1.11782e99 | −2.38912 | ||||||||
\(506\) | −4.40608e97 | −0.0876109 | ||||||||
\(507\) | −1.36940e99 | −2.53361 | ||||||||
\(508\) | −4.95835e97 | −0.0853713 | ||||||||
\(509\) | 1.10612e98 | 0.177257 | 0.0886284 | − | 0.996065i | \(-0.471752\pi\) | ||||
0.0886284 | + | 0.996065i | \(0.471752\pi\) | |||||||
\(510\) | −3.04724e97 | −0.0454565 | ||||||||
\(511\) | 6.61553e98 | 0.918759 | ||||||||
\(512\) | 4.74747e98 | 0.613916 | ||||||||
\(513\) | 7.90047e98 | 0.951413 | ||||||||
\(514\) | −8.76488e97 | −0.0983087 | ||||||||
\(515\) | 1.62964e99 | 1.70265 | ||||||||
\(516\) | 2.14084e97 | 0.0208387 | ||||||||
\(517\) | 1.01493e99 | 0.920516 | ||||||||
\(518\) | −1.46986e97 | −0.0124234 | ||||||||
\(519\) | −3.84944e99 | −3.03242 | ||||||||
\(520\) | −6.97284e98 | −0.512021 | ||||||||
\(521\) | 1.94380e99 | 1.33068 | 0.665341 | − | 0.746540i | \(-0.268286\pi\) | ||||
0.665341 | + | 0.746540i | \(0.268286\pi\) | |||||||
\(522\) | 1.37153e98 | 0.0875451 | ||||||||
\(523\) | 3.22586e98 | 0.192014 | 0.0960072 | − | 0.995381i | \(-0.469393\pi\) | ||||
0.0960072 | + | 0.995381i | \(0.469393\pi\) | |||||||
\(524\) | −1.93378e99 | −1.07353 | ||||||||
\(525\) | 1.88489e99 | 0.976051 | ||||||||
\(526\) | −9.83793e97 | −0.0475252 | ||||||||
\(527\) | −4.61075e98 | −0.207818 | ||||||||
\(528\) | −2.05930e99 | −0.866126 | ||||||||
\(529\) | 1.47571e99 | 0.579255 | ||||||||
\(530\) | −1.22850e98 | −0.0450098 | ||||||||
\(531\) | −2.93315e99 | −1.00319 | ||||||||
\(532\) | −1.75613e99 | −0.560765 | ||||||||
\(533\) | 4.74387e99 | 1.41446 | ||||||||
\(534\) | 1.88262e98 | 0.0524213 | ||||||||
\(535\) | −7.92619e99 | −2.06135 | ||||||||
\(536\) | 1.29126e99 | 0.313689 | ||||||||
\(537\) | 4.68327e99 | 1.06289 | ||||||||
\(538\) | −8.30054e97 | −0.0176016 | ||||||||
\(539\) | 8.36867e97 | 0.0165831 | ||||||||
\(540\) | 1.12086e100 | 2.07576 | ||||||||
\(541\) | 2.75772e99 | 0.477364 | 0.238682 | − | 0.971098i | \(-0.423285\pi\) | ||||
0.238682 | + | 0.971098i | \(0.423285\pi\) | |||||||
\(542\) | −8.99974e98 | −0.145632 | ||||||||
\(543\) | 2.41358e99 | 0.365148 | ||||||||
\(544\) | 4.37210e98 | 0.0618487 | ||||||||
\(545\) | −1.10610e100 | −1.46327 | ||||||||
\(546\) | 2.93315e99 | 0.362913 | ||||||||
\(547\) | 2.20581e99 | 0.255288 | 0.127644 | − | 0.991820i | \(-0.459258\pi\) | ||||
0.127644 | + | 0.991820i | \(0.459258\pi\) | |||||||
\(548\) | −1.54294e98 | −0.0167054 | ||||||||
\(549\) | −1.74314e100 | −1.76580 | ||||||||
\(550\) | 4.09434e98 | 0.0388102 | ||||||||
\(551\) | −2.12483e99 | −0.188491 | ||||||||
\(552\) | −6.82679e99 | −0.566814 | ||||||||
\(553\) | 3.16661e99 | 0.246109 | ||||||||
\(554\) | −3.01316e98 | −0.0219238 | ||||||||
\(555\) | −2.93546e99 | −0.199978 | ||||||||
\(556\) | 8.48380e98 | 0.0541204 | ||||||||
\(557\) | 3.12775e100 | 1.86860 | 0.934302 | − | 0.356482i | \(-0.116024\pi\) | ||||
0.934302 | + | 0.356482i | \(0.116024\pi\) | |||||||
\(558\) | −6.05251e99 | −0.338678 | ||||||||
\(559\) | 3.68112e98 | 0.0192952 | ||||||||
\(560\) | −2.44665e100 | −1.20146 | ||||||||
\(561\) | −3.17939e99 | −0.146285 | ||||||||
\(562\) | 4.21674e99 | 0.181803 | ||||||||
\(563\) | −3.06947e100 | −1.24024 | −0.620122 | − | 0.784505i | \(-0.712917\pi\) | ||||
−0.620122 | + | 0.784505i | \(0.712917\pi\) | |||||||
\(564\) | 7.79382e100 | 2.95164 | ||||||||
\(565\) | 1.86784e100 | 0.663090 | ||||||||
\(566\) | 6.41256e99 | 0.213418 | ||||||||
\(567\) | −3.06704e100 | −0.957058 | ||||||||
\(568\) | −9.31441e99 | −0.272547 | ||||||||
\(569\) | 5.43050e99 | 0.149019 | 0.0745095 | − | 0.997220i | \(-0.476261\pi\) | ||||
0.0745095 | + | 0.997220i | \(0.476261\pi\) | |||||||
\(570\) | 6.19713e99 | 0.159499 | ||||||||
\(571\) | 5.10752e100 | 1.23308 | 0.616541 | − | 0.787323i | \(-0.288534\pi\) | ||||
0.616541 | + | 0.787323i | \(0.288534\pi\) | |||||||
\(572\) | −3.60575e100 | −0.816660 | ||||||||
\(573\) | −9.36481e99 | −0.199001 | ||||||||
\(574\) | −6.04309e99 | −0.120497 | ||||||||
\(575\) | −3.73866e100 | −0.699583 | ||||||||
\(576\) | −1.01201e101 | −1.77731 | ||||||||
\(577\) | 1.75584e100 | 0.289447 | 0.144723 | − | 0.989472i | \(-0.453771\pi\) | ||||
0.144723 | + | 0.989472i | \(0.453771\pi\) | |||||||
\(578\) | −8.29652e99 | −0.128390 | ||||||||
\(579\) | 4.90402e100 | 0.712500 | ||||||||
\(580\) | −3.01454e100 | −0.411243 | ||||||||
\(581\) | −6.56035e100 | −0.840424 | ||||||||
\(582\) | 1.20216e100 | 0.144635 | ||||||||
\(583\) | −1.28178e100 | −0.144847 | ||||||||
\(584\) | 2.22652e100 | 0.236351 | ||||||||
\(585\) | 3.89254e101 | 3.88190 | ||||||||
\(586\) | −7.88898e99 | −0.0739193 | ||||||||
\(587\) | −1.85514e101 | −1.63337 | −0.816687 | − | 0.577081i | \(-0.804192\pi\) | ||||
−0.816687 | + | 0.577081i | \(0.804192\pi\) | |||||||
\(588\) | 6.42645e99 | 0.0531739 | ||||||||
\(589\) | 9.37680e100 | 0.729200 | ||||||||
\(590\) | −1.13916e100 | −0.0832693 | ||||||||
\(591\) | −3.39466e101 | −2.33267 | ||||||||
\(592\) | 1.36261e100 | 0.0880298 | ||||||||
\(593\) | 2.31200e101 | 1.40440 | 0.702202 | − | 0.711978i | \(-0.252200\pi\) | ||||
0.702202 | + | 0.711978i | \(0.252200\pi\) | |||||||
\(594\) | −2.06643e100 | −0.118036 | ||||||||
\(595\) | −3.77742e100 | −0.202921 | ||||||||
\(596\) | 1.84031e101 | 0.929830 | ||||||||
\(597\) | 3.26548e101 | 1.55197 | ||||||||
\(598\) | −5.81785e100 | −0.260117 | ||||||||
\(599\) | −2.30638e101 | −0.970178 | −0.485089 | − | 0.874465i | \(-0.661213\pi\) | ||||
−0.485089 | + | 0.874465i | \(0.661213\pi\) | |||||||
\(600\) | 6.34378e100 | 0.251089 | ||||||||
\(601\) | −3.98037e101 | −1.48254 | −0.741269 | − | 0.671209i | \(-0.765775\pi\) | ||||
−0.741269 | + | 0.671209i | \(0.765775\pi\) | |||||||
\(602\) | −4.68928e98 | −0.00164375 | ||||||||
\(603\) | −7.20839e101 | −2.37824 | ||||||||
\(604\) | 2.02125e101 | 0.627729 | ||||||||
\(605\) | −3.07292e101 | −0.898423 | ||||||||
\(606\) | 1.58256e101 | 0.435620 | ||||||||
\(607\) | 2.03446e101 | 0.527306 | 0.263653 | − | 0.964618i | \(-0.415073\pi\) | ||||
0.263653 | + | 0.964618i | \(0.415073\pi\) | |||||||
\(608\) | −8.89148e100 | −0.217017 | ||||||||
\(609\) | 2.55856e101 | 0.588117 | ||||||||
\(610\) | −6.76989e100 | −0.146569 | ||||||||
\(611\) | 1.34013e102 | 2.73302 | ||||||||
\(612\) | −1.62240e101 | −0.311695 | ||||||||
\(613\) | 8.11549e101 | 1.46895 | 0.734476 | − | 0.678635i | \(-0.237428\pi\) | ||||
0.734476 | + | 0.678635i | \(0.237428\pi\) | |||||||
\(614\) | 1.18968e101 | 0.202902 | ||||||||
\(615\) | −1.20687e102 | −1.93963 | ||||||||
\(616\) | 9.26772e100 | 0.140371 | ||||||||
\(617\) | −4.85215e101 | −0.692669 | −0.346335 | − | 0.938111i | \(-0.612574\pi\) | ||||
−0.346335 | + | 0.938111i | \(0.612574\pi\) | |||||||
\(618\) | −2.30715e101 | −0.310453 | ||||||||
\(619\) | −1.16809e102 | −1.48173 | −0.740864 | − | 0.671655i | \(-0.765584\pi\) | ||||
−0.740864 | + | 0.671655i | \(0.765584\pi\) | |||||||
\(620\) | 1.33030e102 | 1.59094 | ||||||||
\(621\) | 1.88692e102 | 2.12769 | ||||||||
\(622\) | 3.20507e100 | 0.0340791 | ||||||||
\(623\) | 2.33374e101 | 0.234012 | ||||||||
\(624\) | −2.71913e102 | −2.57154 | ||||||||
\(625\) | −1.39770e102 | −1.24679 | ||||||||
\(626\) | 2.33227e101 | 0.196253 | ||||||||
\(627\) | 6.46587e101 | 0.513289 | ||||||||
\(628\) | 1.56964e102 | 1.17563 | ||||||||
\(629\) | 2.10376e100 | 0.0148678 | ||||||||
\(630\) | −4.95861e101 | −0.330697 | ||||||||
\(631\) | −2.95061e102 | −1.85712 | −0.928559 | − | 0.371185i | \(-0.878952\pi\) | ||||
−0.928559 | + | 0.371185i | \(0.878952\pi\) | |||||||
\(632\) | 1.06575e101 | 0.0633115 | ||||||||
\(633\) | 1.53787e102 | 0.862353 | ||||||||
\(634\) | −2.76110e101 | −0.146159 | ||||||||
\(635\) | 2.16901e101 | 0.108398 | ||||||||
\(636\) | −9.84300e101 | −0.464454 | ||||||||
\(637\) | 1.10501e101 | 0.0492355 | ||||||||
\(638\) | 5.55765e100 | 0.0233850 | ||||||||
\(639\) | 5.19971e102 | 2.06632 | ||||||||
\(640\) | −1.67678e102 | −0.629370 | ||||||||
\(641\) | 4.29395e102 | 1.52244 | 0.761218 | − | 0.648496i | \(-0.224602\pi\) | ||||
0.761218 | + | 0.648496i | \(0.224602\pi\) | |||||||
\(642\) | 1.12215e102 | 0.375856 | ||||||||
\(643\) | 1.03978e102 | 0.329034 | 0.164517 | − | 0.986374i | \(-0.447393\pi\) | ||||
0.164517 | + | 0.986374i | \(0.447393\pi\) | |||||||
\(644\) | −4.19426e102 | −1.25407 | ||||||||
\(645\) | −9.36499e100 | −0.0264593 | ||||||||
\(646\) | −4.44130e100 | −0.0118583 | ||||||||
\(647\) | −9.92922e101 | −0.250558 | −0.125279 | − | 0.992122i | \(-0.539983\pi\) | ||||
−0.125279 | + | 0.992122i | \(0.539983\pi\) | |||||||
\(648\) | −1.03224e102 | −0.246203 | ||||||||
\(649\) | −1.18856e102 | −0.267971 | ||||||||
\(650\) | 5.40623e101 | 0.115228 | ||||||||
\(651\) | −1.12908e103 | −2.27520 | ||||||||
\(652\) | 4.60699e102 | 0.877769 | ||||||||
\(653\) | −2.55572e102 | −0.460450 | −0.230225 | − | 0.973137i | \(-0.573946\pi\) | ||||
−0.230225 | + | 0.973137i | \(0.573946\pi\) | |||||||
\(654\) | 1.56596e102 | 0.266805 | ||||||||
\(655\) | 8.45924e102 | 1.36309 | ||||||||
\(656\) | 5.60216e102 | 0.853818 | ||||||||
\(657\) | −1.24294e103 | −1.79190 | ||||||||
\(658\) | −1.70716e102 | −0.232824 | ||||||||
\(659\) | −9.61531e102 | −1.24064 | −0.620320 | − | 0.784349i | \(-0.712997\pi\) | ||||
−0.620320 | + | 0.784349i | \(0.712997\pi\) | |||||||
\(660\) | 9.17326e102 | 1.11988 | ||||||||
\(661\) | 8.19473e102 | 0.946633 | 0.473316 | − | 0.880893i | \(-0.343057\pi\) | ||||
0.473316 | + | 0.880893i | \(0.343057\pi\) | |||||||
\(662\) | 2.96337e101 | 0.0323944 | ||||||||
\(663\) | −4.19812e102 | −0.434321 | ||||||||
\(664\) | −2.20795e102 | −0.216199 | ||||||||
\(665\) | 7.68208e102 | 0.712015 | ||||||||
\(666\) | 2.76160e101 | 0.0242299 | ||||||||
\(667\) | −5.07485e102 | −0.421532 | ||||||||
\(668\) | −1.63388e102 | −0.128493 | ||||||||
\(669\) | 3.22025e103 | 2.39793 | ||||||||
\(670\) | −2.79955e102 | −0.197405 | ||||||||
\(671\) | −7.06347e102 | −0.471678 | ||||||||
\(672\) | 1.07064e103 | 0.677121 | ||||||||
\(673\) | 9.08707e102 | 0.544344 | 0.272172 | − | 0.962249i | \(-0.412258\pi\) | ||||
0.272172 | + | 0.962249i | \(0.412258\pi\) | |||||||
\(674\) | 3.29258e101 | 0.0186831 | ||||||||
\(675\) | −1.75341e103 | −0.942533 | ||||||||
\(676\) | −2.83158e103 | −1.44203 | ||||||||
\(677\) | −2.19434e103 | −1.05881 | −0.529405 | − | 0.848369i | \(-0.677585\pi\) | ||||
−0.529405 | + | 0.848369i | \(0.677585\pi\) | |||||||
\(678\) | −2.64439e102 | −0.120904 | ||||||||
\(679\) | 1.49022e103 | 0.645659 | ||||||||
\(680\) | −1.27133e102 | −0.0522013 | ||||||||
\(681\) | −2.36375e103 | −0.919882 | ||||||||
\(682\) | −2.45257e102 | −0.0904675 | ||||||||
\(683\) | −3.52716e103 | −1.23330 | −0.616651 | − | 0.787236i | \(-0.711511\pi\) | ||||
−0.616651 | + | 0.787236i | \(0.711511\pi\) | |||||||
\(684\) | 3.29944e103 | 1.09369 | ||||||||
\(685\) | 6.74950e101 | 0.0212112 | ||||||||
\(686\) | 4.35026e102 | 0.129624 | ||||||||
\(687\) | 8.83872e103 | 2.49729 | ||||||||
\(688\) | 4.34713e101 | 0.0116473 | ||||||||
\(689\) | −1.69248e103 | −0.430053 | ||||||||
\(690\) | 1.48010e103 | 0.356696 | ||||||||
\(691\) | 5.99882e103 | 1.37125 | 0.685626 | − | 0.727954i | \(-0.259528\pi\) | ||||
0.685626 | + | 0.727954i | \(0.259528\pi\) | |||||||
\(692\) | −7.95970e103 | −1.72593 | ||||||||
\(693\) | −5.17364e103 | −1.06423 | ||||||||
\(694\) | −6.95477e102 | −0.135726 | ||||||||
\(695\) | −3.71120e102 | −0.0687177 | ||||||||
\(696\) | 8.61105e102 | 0.151293 | ||||||||
\(697\) | 8.64928e102 | 0.144206 | ||||||||
\(698\) | −1.66446e100 | −0.000263361 0 | ||||||||
\(699\) | 1.11001e104 | 1.66690 | ||||||||
\(700\) | 3.89750e103 | 0.555531 | ||||||||
\(701\) | 8.24063e103 | 1.11494 | 0.557472 | − | 0.830196i | \(-0.311771\pi\) | ||||
0.557472 | + | 0.830196i | \(0.311771\pi\) | |||||||
\(702\) | −2.72854e103 | −0.350450 | ||||||||
\(703\) | −4.27838e102 | −0.0521687 | ||||||||
\(704\) | −4.10081e103 | −0.474753 | ||||||||
\(705\) | −3.40937e104 | −3.74776 | ||||||||
\(706\) | −1.43769e103 | −0.150070 | ||||||||
\(707\) | 1.96177e104 | 1.94464 | ||||||||
\(708\) | −9.12713e103 | −0.859252 | ||||||||
\(709\) | −1.70430e104 | −1.52391 | −0.761953 | − | 0.647632i | \(-0.775760\pi\) | ||||
−0.761953 | + | 0.647632i | \(0.775760\pi\) | |||||||
\(710\) | 2.01943e103 | 0.171514 | ||||||||
\(711\) | −5.94949e103 | −0.479998 | ||||||||
\(712\) | 7.85440e102 | 0.0601996 | ||||||||
\(713\) | 2.23952e104 | 1.63075 | ||||||||
\(714\) | 5.34787e102 | 0.0369995 | ||||||||
\(715\) | 1.57732e104 | 1.03693 | ||||||||
\(716\) | 9.68387e103 | 0.604956 | ||||||||
\(717\) | 4.10919e103 | 0.243954 | ||||||||
\(718\) | 1.12593e102 | 0.00635284 | ||||||||
\(719\) | −3.17489e104 | −1.70265 | −0.851323 | − | 0.524642i | \(-0.824199\pi\) | ||||
−0.851323 | + | 0.524642i | \(0.824199\pi\) | |||||||
\(720\) | 4.59681e104 | 2.34326 | ||||||||
\(721\) | −2.85999e104 | −1.38588 | ||||||||
\(722\) | −1.95714e103 | −0.0901602 | ||||||||
\(723\) | 8.54810e103 | 0.374388 | ||||||||
\(724\) | 4.99070e103 | 0.207828 | ||||||||
\(725\) | 4.71580e103 | 0.186732 | ||||||||
\(726\) | 4.35048e103 | 0.163814 | ||||||||
\(727\) | −2.53957e102 | −0.00909398 | −0.00454699 | − | 0.999990i | \(-0.501447\pi\) | ||||
−0.00454699 | + | 0.999990i | \(0.501447\pi\) | |||||||
\(728\) | 1.22372e104 | 0.416762 | ||||||||
\(729\) | −3.26150e104 | −1.05648 | ||||||||
\(730\) | −4.82724e103 | −0.148736 | ||||||||
\(731\) | 6.71162e101 | 0.00196717 | ||||||||
\(732\) | −5.42416e104 | −1.51244 | ||||||||
\(733\) | 5.13601e104 | 1.36248 | 0.681242 | − | 0.732059i | \(-0.261440\pi\) | ||||
0.681242 | + | 0.732059i | \(0.261440\pi\) | |||||||
\(734\) | 3.87851e103 | 0.0978946 | ||||||||
\(735\) | −2.81122e103 | −0.0675160 | ||||||||
\(736\) | −2.12360e104 | −0.485326 | ||||||||
\(737\) | −2.92095e104 | −0.635274 | ||||||||
\(738\) | 1.13539e104 | 0.235010 | ||||||||
\(739\) | −8.61961e104 | −1.69811 | −0.849054 | − | 0.528306i | \(-0.822828\pi\) | ||||
−0.849054 | + | 0.528306i | \(0.822828\pi\) | |||||||
\(740\) | −6.06982e103 | −0.113820 | ||||||||
\(741\) | 8.53764e104 | 1.52396 | ||||||||
\(742\) | 2.15601e103 | 0.0366360 | ||||||||
\(743\) | 8.31834e104 | 1.34569 | 0.672845 | − | 0.739784i | \(-0.265072\pi\) | ||||
0.672845 | + | 0.739784i | \(0.265072\pi\) | |||||||
\(744\) | −3.80003e104 | −0.585295 | ||||||||
\(745\) | −8.05036e104 | −1.18062 | ||||||||
\(746\) | −1.80647e104 | −0.252269 | ||||||||
\(747\) | 1.23257e105 | 1.63912 | ||||||||
\(748\) | −6.57421e103 | −0.0832597 | ||||||||
\(749\) | 1.39104e105 | 1.67785 | ||||||||
\(750\) | 1.09526e104 | 0.125829 | ||||||||
\(751\) | 8.23505e104 | 0.901174 | 0.450587 | − | 0.892733i | \(-0.351215\pi\) | ||||
0.450587 | + | 0.892733i | \(0.351215\pi\) | |||||||
\(752\) | 1.58259e105 | 1.64975 | ||||||||
\(753\) | −2.82972e105 | −2.81013 | ||||||||
\(754\) | 7.33841e103 | 0.0694301 | ||||||||
\(755\) | −8.84186e104 | −0.797040 | ||||||||
\(756\) | −1.96709e105 | −1.68958 | ||||||||
\(757\) | −2.18065e104 | −0.178479 | −0.0892394 | − | 0.996010i | \(-0.528444\pi\) | ||||
−0.0892394 | + | 0.996010i | \(0.528444\pi\) | |||||||
\(758\) | 3.96275e103 | 0.0309080 | ||||||||
\(759\) | 1.54428e105 | 1.14789 | ||||||||
\(760\) | 2.58547e104 | 0.183166 | ||||||||
\(761\) | −2.07078e105 | −1.39828 | −0.699140 | − | 0.714985i | \(-0.746433\pi\) | ||||
−0.699140 | + | 0.714985i | \(0.746433\pi\) | |||||||
\(762\) | −3.07076e103 | −0.0197647 | ||||||||
\(763\) | 1.94120e105 | 1.19103 | ||||||||
\(764\) | −1.93641e104 | −0.113264 | ||||||||
\(765\) | 7.09709e104 | 0.395766 | ||||||||
\(766\) | −7.20327e103 | −0.0382983 | ||||||||
\(767\) | −1.56939e105 | −0.795609 | ||||||||
\(768\) | −2.96734e105 | −1.43444 | ||||||||
\(769\) | 1.22335e105 | 0.563947 | 0.281973 | − | 0.959422i | \(-0.409011\pi\) | ||||
0.281973 | + | 0.959422i | \(0.409011\pi\) | |||||||
\(770\) | −2.00931e104 | −0.0883354 | ||||||||
\(771\) | 3.07200e105 | 1.28806 | ||||||||
\(772\) | 1.01403e105 | 0.405528 | ||||||||
\(773\) | −8.34378e104 | −0.318281 | −0.159141 | − | 0.987256i | \(-0.550872\pi\) | ||||
−0.159141 | + | 0.987256i | \(0.550872\pi\) | |||||||
\(774\) | 8.81032e102 | 0.00320587 | ||||||||
\(775\) | −2.08107e105 | −0.722393 | ||||||||
\(776\) | 5.01547e104 | 0.166096 | ||||||||
\(777\) | 5.15170e104 | 0.162773 | ||||||||
\(778\) | 5.82891e104 | 0.175724 | ||||||||
\(779\) | −1.75899e105 | −0.505995 | ||||||||
\(780\) | 1.21125e106 | 3.32492 | ||||||||
\(781\) | 2.10700e105 | 0.551953 | ||||||||
\(782\) | −1.06074e104 | −0.0265194 | ||||||||
\(783\) | −2.38008e105 | −0.567921 | ||||||||
\(784\) | 1.30494e104 | 0.0297203 | ||||||||
\(785\) | −6.86630e105 | −1.49273 | ||||||||
\(786\) | −1.19761e105 | −0.248539 | ||||||||
\(787\) | −2.99942e105 | −0.594236 | −0.297118 | − | 0.954841i | \(-0.596026\pi\) | ||||
−0.297118 | + | 0.954841i | \(0.596026\pi\) | |||||||
\(788\) | −7.01933e105 | −1.32767 | ||||||||
\(789\) | 3.44809e105 | 0.622684 | ||||||||
\(790\) | −2.31062e104 | −0.0398419 | ||||||||
\(791\) | −3.27804e105 | −0.539726 | ||||||||
\(792\) | −1.74124e105 | −0.273772 | ||||||||
\(793\) | −9.32671e105 | −1.40042 | ||||||||
\(794\) | 7.73522e104 | 0.110924 | ||||||||
\(795\) | 4.30577e105 | 0.589727 | ||||||||
\(796\) | 6.75221e105 | 0.883322 | ||||||||
\(797\) | 1.44943e106 | 1.81121 | 0.905604 | − | 0.424124i | \(-0.139418\pi\) | ||||
0.905604 | + | 0.424124i | \(0.139418\pi\) | |||||||
\(798\) | −1.08759e105 | −0.129825 | ||||||||
\(799\) | 2.44340e105 | 0.278635 | ||||||||
\(800\) | 1.97335e105 | 0.214991 | ||||||||
\(801\) | −4.38467e105 | −0.456405 | ||||||||
\(802\) | 2.31978e105 | 0.230719 | ||||||||
\(803\) | −5.03658e105 | −0.478650 | ||||||||
\(804\) | −2.24305e106 | −2.03701 | ||||||||
\(805\) | 1.83476e106 | 1.59231 | ||||||||
\(806\) | −3.23842e105 | −0.268599 | ||||||||
\(807\) | 2.90925e105 | 0.230620 | ||||||||
\(808\) | 6.60250e105 | 0.500258 | ||||||||
\(809\) | 1.25435e106 | 0.908442 | 0.454221 | − | 0.890889i | \(-0.349918\pi\) | ||||
0.454221 | + | 0.890889i | \(0.349918\pi\) | |||||||
\(810\) | 2.23797e105 | 0.154936 | ||||||||
\(811\) | −1.31775e106 | −0.872112 | −0.436056 | − | 0.899920i | \(-0.643625\pi\) | ||||
−0.436056 | + | 0.899920i | \(0.643625\pi\) | |||||||
\(812\) | 5.29047e105 | 0.334734 | ||||||||
\(813\) | 3.15431e106 | 1.90809 | ||||||||
\(814\) | 1.11904e104 | 0.00647226 | ||||||||
\(815\) | −2.01531e106 | −1.11452 | ||||||||
\(816\) | −4.95767e105 | −0.262172 | ||||||||
\(817\) | −1.36493e104 | −0.00690248 | ||||||||
\(818\) | −3.75084e105 | −0.181398 | ||||||||
\(819\) | −6.83136e106 | −3.15969 | ||||||||
\(820\) | −2.49551e106 | −1.10396 | ||||||||
\(821\) | 2.12804e106 | 0.900439 | 0.450219 | − | 0.892918i | \(-0.351346\pi\) | ||||
0.450219 | + | 0.892918i | \(0.351346\pi\) | |||||||
\(822\) | −9.55558e103 | −0.00386755 | ||||||||
\(823\) | 2.97912e106 | 1.15344 | 0.576720 | − | 0.816942i | \(-0.304333\pi\) | ||||
0.576720 | + | 0.816942i | \(0.304333\pi\) | |||||||
\(824\) | −9.62555e105 | −0.356519 | ||||||||
\(825\) | −1.43502e106 | −0.508498 | ||||||||
\(826\) | 1.99920e105 | 0.0677775 | ||||||||
\(827\) | 3.05296e106 | 0.990306 | 0.495153 | − | 0.868806i | \(-0.335112\pi\) | ||||
0.495153 | + | 0.868806i | \(0.335112\pi\) | |||||||
\(828\) | 7.88025e106 | 2.44587 | ||||||||
\(829\) | −3.55563e106 | −1.05603 | −0.528015 | − | 0.849235i | \(-0.677064\pi\) | ||||
−0.528015 | + | 0.849235i | \(0.677064\pi\) | |||||||
\(830\) | 4.78698e105 | 0.136054 | ||||||||
\(831\) | 1.05608e106 | 0.287249 | ||||||||
\(832\) | −5.41477e106 | −1.40954 | ||||||||
\(833\) | 2.01472e104 | 0.00501963 | ||||||||
\(834\) | 5.25411e104 | 0.0125296 | ||||||||
\(835\) | 7.14734e105 | 0.163150 | ||||||||
\(836\) | 1.33699e106 | 0.292144 | ||||||||
\(837\) | 1.05032e107 | 2.19707 | ||||||||
\(838\) | −1.04019e106 | −0.208307 | ||||||||
\(839\) | 1.13258e106 | 0.217148 | 0.108574 | − | 0.994088i | \(-0.465372\pi\) | ||||
0.108574 | + | 0.994088i | \(0.465372\pi\) | |||||||
\(840\) | −3.11323e106 | −0.571501 | ||||||||
\(841\) | −5.04911e106 | −0.887485 | ||||||||
\(842\) | −1.76337e105 | −0.0296792 | ||||||||
\(843\) | −1.47792e107 | −2.38202 | ||||||||
\(844\) | 3.17995e106 | 0.490818 | ||||||||
\(845\) | 1.23866e107 | 1.83098 | ||||||||
\(846\) | 3.20744e106 | 0.454088 | ||||||||
\(847\) | 5.39294e106 | 0.731276 | ||||||||
\(848\) | −1.99870e106 | −0.259596 | ||||||||
\(849\) | −2.24753e107 | −2.79625 | ||||||||
\(850\) | 9.85692e104 | 0.0117476 | ||||||||
\(851\) | −1.02183e106 | −0.116668 | ||||||||
\(852\) | 1.61800e107 | 1.76984 | ||||||||
\(853\) | −9.81188e106 | −1.02828 | −0.514141 | − | 0.857706i | \(-0.671889\pi\) | ||||
−0.514141 | + | 0.857706i | \(0.671889\pi\) | |||||||
\(854\) | 1.18811e106 | 0.119301 | ||||||||
\(855\) | −1.44332e107 | −1.38868 | ||||||||
\(856\) | 4.68166e106 | 0.431626 | ||||||||
\(857\) | −7.41614e106 | −0.655206 | −0.327603 | − | 0.944815i | \(-0.606241\pi\) | ||||
−0.327603 | + | 0.944815i | \(0.606241\pi\) | |||||||
\(858\) | −2.23308e106 | −0.189068 | ||||||||
\(859\) | 8.57042e106 | 0.695427 | 0.347714 | − | 0.937601i | \(-0.386958\pi\) | ||||
0.347714 | + | 0.937601i | \(0.386958\pi\) | |||||||
\(860\) | −1.93645e105 | −0.0150596 | ||||||||
\(861\) | 2.11804e107 | 1.57877 | ||||||||
\(862\) | 2.76991e105 | 0.0197902 | ||||||||
\(863\) | 7.22821e106 | 0.495036 | 0.247518 | − | 0.968883i | \(-0.420385\pi\) | ||||
0.247518 | + | 0.968883i | \(0.420385\pi\) | |||||||
\(864\) | −9.95960e106 | −0.653868 | ||||||||
\(865\) | 3.48193e107 | 2.19145 | ||||||||
\(866\) | −1.36772e106 | −0.0825269 | ||||||||
\(867\) | 2.90784e107 | 1.68218 | ||||||||
\(868\) | −2.33467e107 | −1.29496 | ||||||||
\(869\) | −2.41083e106 | −0.128217 | ||||||||
\(870\) | −1.86694e106 | −0.0952087 | ||||||||
\(871\) | −3.85687e107 | −1.88613 | ||||||||
\(872\) | 6.53327e106 | 0.306393 | ||||||||
\(873\) | −2.79985e107 | −1.25926 | ||||||||
\(874\) | 2.15721e106 | 0.0930520 | ||||||||
\(875\) | 1.35770e107 | 0.561708 | ||||||||
\(876\) | −3.86768e107 | −1.53480 | ||||||||
\(877\) | 1.98341e107 | 0.754967 | 0.377483 | − | 0.926016i | \(-0.376790\pi\) | ||||
0.377483 | + | 0.926016i | \(0.376790\pi\) | |||||||
\(878\) | −5.35703e106 | −0.195602 | ||||||||
\(879\) | 2.76500e107 | 0.968504 | ||||||||
\(880\) | 1.86270e107 | 0.625929 | ||||||||
\(881\) | −3.33655e107 | −1.07567 | −0.537833 | − | 0.843052i | \(-0.680757\pi\) | ||||
−0.537833 | + | 0.843052i | \(0.680757\pi\) | |||||||
\(882\) | 2.64471e105 | 0.00818042 | ||||||||
\(883\) | −4.17223e106 | −0.123823 | −0.0619116 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619116 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(884\) | −8.68068e106 | −0.247199 | ||||||||
\(885\) | 3.99262e107 | 1.09101 | ||||||||
\(886\) | −1.85628e106 | −0.0486759 | ||||||||
\(887\) | −5.76985e107 | −1.45195 | −0.725976 | − | 0.687720i | \(-0.758612\pi\) | ||||
−0.725976 | + | 0.687720i | \(0.758612\pi\) | |||||||
\(888\) | 1.73385e106 | 0.0418734 | ||||||||
\(889\) | −3.80658e106 | −0.0882308 | ||||||||
\(890\) | −1.70289e106 | −0.0378836 | ||||||||
\(891\) | 2.33502e107 | 0.498603 | ||||||||
\(892\) | 6.65870e107 | 1.36481 | ||||||||
\(893\) | −4.96909e107 | −0.977685 | ||||||||
\(894\) | 1.13973e107 | 0.215269 | ||||||||
\(895\) | −4.23616e107 | −0.768125 | ||||||||
\(896\) | 2.94272e107 | 0.512279 | ||||||||
\(897\) | 2.03909e108 | 3.40811 | ||||||||
\(898\) | −1.09146e106 | −0.0175155 | ||||||||
\(899\) | −2.82484e107 | −0.435276 | ||||||||
\(900\) | −7.32270e107 | −1.08348 | ||||||||
\(901\) | −3.08582e106 | −0.0438446 | ||||||||
\(902\) | 4.60077e106 | 0.0627757 | ||||||||
\(903\) | 1.64354e106 | 0.0215367 | ||||||||
\(904\) | −1.10325e107 | −0.138844 | ||||||||
\(905\) | −2.18316e107 | −0.263883 | ||||||||
\(906\) | 1.25178e107 | 0.145328 | ||||||||
\(907\) | −1.62085e107 | −0.180749 | −0.0903746 | − | 0.995908i | \(-0.528806\pi\) | ||||
−0.0903746 | + | 0.995908i | \(0.528806\pi\) | |||||||
\(908\) | −4.88766e107 | −0.523561 | ||||||||
\(909\) | −3.68581e108 | −3.79272 | ||||||||
\(910\) | −2.65312e107 | −0.262268 | ||||||||
\(911\) | 7.78998e107 | 0.739802 | 0.369901 | − | 0.929071i | \(-0.379392\pi\) | ||||
0.369901 | + | 0.929071i | \(0.379392\pi\) | |||||||
\(912\) | 1.00823e108 | 0.919918 | ||||||||
\(913\) | 4.99457e107 | 0.437840 | ||||||||
\(914\) | −1.64454e107 | −0.138518 | ||||||||
\(915\) | 2.37277e108 | 1.92038 | ||||||||
\(916\) | 1.82763e108 | 1.42136 | ||||||||
\(917\) | −1.48459e108 | −1.10949 | ||||||||
\(918\) | −4.97483e106 | −0.0357290 | ||||||||
\(919\) | 1.01773e107 | 0.0702448 | 0.0351224 | − | 0.999383i | \(-0.488818\pi\) | ||||
0.0351224 | + | 0.999383i | \(0.488818\pi\) | |||||||
\(920\) | 6.17504e107 | 0.409623 | ||||||||
\(921\) | −4.16971e108 | −2.65846 | ||||||||
\(922\) | −2.77365e107 | −0.169970 | ||||||||
\(923\) | 2.78212e108 | 1.63875 | ||||||||
\(924\) | −1.60989e108 | −0.911529 | ||||||||
\(925\) | 9.49534e106 | 0.0516818 | ||||||||
\(926\) | −9.74564e106 | −0.0509929 | ||||||||
\(927\) | 5.37340e108 | 2.70296 | ||||||||
\(928\) | 2.67863e107 | 0.129542 | ||||||||
\(929\) | −1.93150e108 | −0.898092 | −0.449046 | − | 0.893509i | \(-0.648236\pi\) | ||||
−0.449046 | + | 0.893509i | \(0.648236\pi\) | |||||||
\(930\) | 8.23873e107 | 0.368326 | ||||||||
\(931\) | −4.09730e106 | −0.0176130 | ||||||||
\(932\) | 2.29523e108 | 0.948735 | ||||||||
\(933\) | −1.12334e108 | −0.446511 | ||||||||
\(934\) | −2.98281e107 | −0.114016 | ||||||||
\(935\) | 2.87585e107 | 0.105717 | ||||||||
\(936\) | −2.29916e108 | −0.812831 | ||||||||
\(937\) | 3.17605e108 | 1.07992 | 0.539960 | − | 0.841691i | \(-0.318439\pi\) | ||||
0.539960 | + | 0.841691i | \(0.318439\pi\) | |||||||
\(938\) | 4.91317e107 | 0.160679 | ||||||||
\(939\) | −8.17436e108 | −2.57134 | ||||||||
\(940\) | −7.04975e108 | −2.13308 | ||||||||
\(941\) | 2.32516e108 | 0.676756 | 0.338378 | − | 0.941010i | \(-0.390122\pi\) | ||||
0.338378 | + | 0.941010i | \(0.390122\pi\) | |||||||
\(942\) | 9.72094e107 | 0.272176 | ||||||||
\(943\) | −4.20110e108 | −1.13158 | ||||||||
\(944\) | −1.85333e108 | −0.480259 | ||||||||
\(945\) | 8.60492e108 | 2.14529 | ||||||||
\(946\) | 3.57008e105 | 0.000856350 0 | ||||||||
\(947\) | 6.27531e108 | 1.44831 | 0.724154 | − | 0.689638i | \(-0.242230\pi\) | ||||
0.724154 | + | 0.689638i | \(0.242230\pi\) | |||||||
\(948\) | −1.85132e108 | −0.411127 | ||||||||
\(949\) | −6.65038e108 | −1.42112 | ||||||||
\(950\) | −2.00459e107 | −0.0412205 | ||||||||
\(951\) | 9.67736e108 | 1.91500 | ||||||||
\(952\) | 2.23116e107 | 0.0424895 | ||||||||
\(953\) | −1.78151e107 | −0.0326511 | −0.0163255 | − | 0.999867i | \(-0.505197\pi\) | ||||
−0.0163255 | + | 0.999867i | \(0.505197\pi\) | |||||||
\(954\) | −4.05075e107 | −0.0714529 | ||||||||
\(955\) | 8.47075e107 | 0.143813 | ||||||||
\(956\) | 8.49682e107 | 0.138849 | ||||||||
\(957\) | −1.94790e108 | −0.306394 | ||||||||
\(958\) | 2.94209e107 | 0.0445467 | ||||||||
\(959\) | −1.18453e107 | −0.0172650 | ||||||||
\(960\) | 1.37755e109 | 1.93289 | ||||||||
\(961\) | 5.06299e108 | 0.683917 | ||||||||
\(962\) | 1.47760e107 | 0.0192162 | ||||||||
\(963\) | −2.61351e109 | −3.27238 | ||||||||
\(964\) | 1.76754e108 | 0.213087 | ||||||||
\(965\) | −4.43584e108 | −0.514907 | ||||||||
\(966\) | −2.59755e108 | −0.290335 | ||||||||
\(967\) | 9.41056e108 | 1.01286 | 0.506430 | − | 0.862281i | \(-0.330965\pi\) | ||||
0.506430 | + | 0.862281i | \(0.330965\pi\) | |||||||
\(968\) | 1.81504e108 | 0.188121 | ||||||||
\(969\) | 1.55663e108 | 0.155370 | ||||||||
\(970\) | −1.08739e108 | −0.104524 | ||||||||
\(971\) | 5.54960e107 | 0.0513759 | 0.0256879 | − | 0.999670i | \(-0.491822\pi\) | ||||
0.0256879 | + | 0.999670i | \(0.491822\pi\) | |||||||
\(972\) | −7.28236e107 | −0.0649312 | ||||||||
\(973\) | 6.51310e107 | 0.0559331 | ||||||||
\(974\) | 1.25956e108 | 0.104187 | ||||||||
\(975\) | −1.89482e109 | −1.50973 | ||||||||
\(976\) | −1.10142e109 | −0.845343 | ||||||||
\(977\) | 1.67241e109 | 1.23649 | 0.618245 | − | 0.785985i | \(-0.287844\pi\) | ||||
0.618245 | + | 0.785985i | \(0.287844\pi\) | |||||||
\(978\) | 2.85316e108 | 0.203216 | ||||||||
\(979\) | −1.77674e108 | −0.121914 | ||||||||
\(980\) | −5.81292e107 | −0.0384275 | ||||||||
\(981\) | −3.64716e109 | −2.32293 | ||||||||
\(982\) | −2.22763e108 | −0.136701 | ||||||||
\(983\) | 2.14789e108 | 0.127002 | 0.0635008 | − | 0.997982i | \(-0.479773\pi\) | ||||
0.0635008 | + | 0.997982i | \(0.479773\pi\) | |||||||
\(984\) | 7.12845e108 | 0.406138 | ||||||||
\(985\) | 3.07057e109 | 1.68576 | ||||||||
\(986\) | 1.33798e107 | 0.00707851 | ||||||||
\(987\) | 5.98340e109 | 3.05051 | ||||||||
\(988\) | 1.76538e109 | 0.867379 | ||||||||
\(989\) | −3.25994e107 | −0.0154364 | ||||||||
\(990\) | 3.77512e108 | 0.172285 | ||||||||
\(991\) | −2.88916e109 | −1.27082 | −0.635410 | − | 0.772175i | \(-0.719169\pi\) | ||||
−0.635410 | + | 0.772175i | \(0.719169\pi\) | |||||||
\(992\) | −1.18207e109 | −0.501150 | ||||||||
\(993\) | −1.03863e109 | −0.424437 | ||||||||
\(994\) | −3.54407e108 | −0.139605 | ||||||||
\(995\) | −2.95372e109 | −1.12157 | ||||||||
\(996\) | 3.83542e109 | 1.40394 | ||||||||
\(997\) | −2.76095e109 | −0.974284 | −0.487142 | − | 0.873323i | \(-0.661961\pi\) | ||||
−0.487142 | + | 0.873323i | \(0.661961\pi\) | |||||||
\(998\) | −5.74340e107 | −0.0195391 | ||||||||
\(999\) | −4.79234e108 | −0.157184 |
(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 | 1.74.a.a.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 9.74.a.a.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.74.a.a.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.74.a.a.1.2 | 5 | 3.2 | odd | 2 |