Properties

Label 5.26.b.a.4.8
Level $5$
Weight $26$
Character 5.4
Analytic conductor $19.800$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5,26,Mod(4,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 26, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.4");
 
S:= CuspForms(chi, 26);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 5.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.7998389976\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 71168091 x^{10} + \cdots + 10\!\cdots\!36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{44}\cdot 3^{20}\cdot 5^{29} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.8
Root \(1460.97i\) of defining polynomial
Character \(\chi\) \(=\) 5.4
Dual form 5.26.b.a.4.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2921.94i q^{2} -1.33312e6i q^{3} +2.50167e7 q^{4} +(-5.18558e8 + 1.70647e8i) q^{5} +3.89530e9 q^{6} +4.60230e10i q^{7} +1.71141e11i q^{8} -9.29927e11 q^{9} +O(q^{10})\) \(q+2921.94i q^{2} -1.33312e6i q^{3} +2.50167e7 q^{4} +(-5.18558e8 + 1.70647e8i) q^{5} +3.89530e9 q^{6} +4.60230e10i q^{7} +1.71141e11i q^{8} -9.29927e11 q^{9} +(-4.98620e11 - 1.51520e12i) q^{10} +1.55304e13 q^{11} -3.33503e13i q^{12} -6.93016e13i q^{13} -1.34476e14 q^{14} +(2.27493e14 + 6.91302e14i) q^{15} +3.39357e14 q^{16} +1.00732e15i q^{17} -2.71719e15i q^{18} +9.85510e15 q^{19} +(-1.29726e16 + 4.26903e15i) q^{20} +6.13543e16 q^{21} +4.53789e16i q^{22} +3.90157e16i q^{23} +2.28152e17 q^{24} +(2.39782e17 - 1.76981e17i) q^{25} +2.02495e17 q^{26} +1.10167e17i q^{27} +1.15134e18i q^{28} +2.60223e18 q^{29} +(-2.01994e18 + 6.64722e17i) q^{30} -3.55337e18 q^{31} +6.73413e18i q^{32} -2.07039e19i q^{33} -2.94331e18 q^{34} +(-7.85368e18 - 2.38656e19i) q^{35} -2.32637e19 q^{36} +5.55139e19i q^{37} +2.87960e19i q^{38} -9.23875e19 q^{39} +(-2.92047e19 - 8.87467e19i) q^{40} +1.48547e20 q^{41} +1.79273e20i q^{42} -2.65747e20i q^{43} +3.88520e20 q^{44} +(4.82222e20 - 1.58689e20i) q^{45} -1.14002e20 q^{46} +1.37381e21i q^{47} -4.52404e20i q^{48} -7.77046e20 q^{49} +(5.17127e20 + 7.00630e20i) q^{50} +1.34288e21 q^{51} -1.73370e21i q^{52} -1.71008e21i q^{53} -3.21902e20 q^{54} +(-8.05343e21 + 2.65022e21i) q^{55} -7.87643e21 q^{56} -1.31381e22i q^{57} +7.60356e21i q^{58} +5.13294e21 q^{59} +(5.69114e21 + 1.72941e22i) q^{60} -9.68041e19 q^{61} -1.03827e22i q^{62} -4.27980e22i q^{63} -8.28978e21 q^{64} +(1.18261e22 + 3.59369e22i) q^{65} +6.04957e22 q^{66} +9.29203e22i q^{67} +2.51997e22i q^{68} +5.20127e22 q^{69} +(6.97338e22 - 2.29480e22i) q^{70} -6.03387e22 q^{71} -1.59149e23i q^{72} -3.38440e22i q^{73} -1.62208e23 q^{74} +(-2.35937e23 - 3.19659e23i) q^{75} +2.46542e23 q^{76} +7.14756e23i q^{77} -2.69951e23i q^{78} -5.76376e23 q^{79} +(-1.75976e23 + 5.79103e22i) q^{80} -6.41050e23 q^{81} +4.34044e23i q^{82} -2.45821e23i q^{83} +1.53488e24 q^{84} +(-1.71895e23 - 5.22352e23i) q^{85} +7.76495e23 q^{86} -3.46909e24i q^{87} +2.65789e24i q^{88} +1.04517e24 q^{89} +(4.63680e23 + 1.40902e24i) q^{90} +3.18946e24 q^{91} +9.76045e23i q^{92} +4.73708e24i q^{93} -4.01417e24 q^{94} +(-5.11044e24 + 1.68174e24i) q^{95} +8.97742e24 q^{96} -8.72407e24i q^{97} -2.27048e24i q^{98} -1.44422e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9} + 4435846671960 q^{10} - 1090673824176 q^{11} - 890646861445848 q^{14} + 443085522435120 q^{15} + 22\!\cdots\!32 q^{16}+ \cdots - 10\!\cdots\!72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2921.94i 0.504424i 0.967672 + 0.252212i \(0.0811581\pi\)
−0.967672 + 0.252212i \(0.918842\pi\)
\(3\) 1.33312e6i 1.44829i −0.689650 0.724143i \(-0.742235\pi\)
0.689650 0.724143i \(-0.257765\pi\)
\(4\) 2.50167e7 0.745556
\(5\) −5.18558e8 + 1.70647e8i −0.949888 + 0.312589i
\(6\) 3.89530e9 0.730551
\(7\) 4.60230e10i 1.25675i 0.777910 + 0.628375i \(0.216280\pi\)
−0.777910 + 0.628375i \(0.783720\pi\)
\(8\) 1.71141e11i 0.880501i
\(9\) −9.29927e11 −1.09753
\(10\) −4.98620e11 1.51520e12i −0.157678 0.479147i
\(11\) 1.55304e13 1.49202 0.746010 0.665935i \(-0.231967\pi\)
0.746010 + 0.665935i \(0.231967\pi\)
\(12\) 3.33503e13i 1.07978i
\(13\) 6.93016e13i 0.824995i −0.910959 0.412497i \(-0.864657\pi\)
0.910959 0.412497i \(-0.135343\pi\)
\(14\) −1.34476e14 −0.633936
\(15\) 2.27493e14 + 6.91302e14i 0.452718 + 1.37571i
\(16\) 3.39357e14 0.301410
\(17\) 1.00732e15i 0.419328i 0.977773 + 0.209664i \(0.0672370\pi\)
−0.977773 + 0.209664i \(0.932763\pi\)
\(18\) 2.71719e15i 0.553623i
\(19\) 9.85510e15 1.02151 0.510753 0.859728i \(-0.329367\pi\)
0.510753 + 0.859728i \(0.329367\pi\)
\(20\) −1.29726e16 + 4.26903e15i −0.708195 + 0.233053i
\(21\) 6.13543e16 1.82014
\(22\) 4.53789e16i 0.752611i
\(23\) 3.90157e16i 0.371229i 0.982623 + 0.185614i \(0.0594275\pi\)
−0.982623 + 0.185614i \(0.940572\pi\)
\(24\) 2.28152e17 1.27522
\(25\) 2.39782e17 1.76981e17i 0.804576 0.593849i
\(26\) 2.02495e17 0.416148
\(27\) 1.10167e17i 0.141256i
\(28\) 1.15134e18i 0.936978i
\(29\) 2.60223e18 1.36575 0.682874 0.730536i \(-0.260730\pi\)
0.682874 + 0.730536i \(0.260730\pi\)
\(30\) −2.01994e18 + 6.64722e17i −0.693942 + 0.228362i
\(31\) −3.55337e18 −0.810251 −0.405126 0.914261i \(-0.632772\pi\)
−0.405126 + 0.914261i \(0.632772\pi\)
\(32\) 6.73413e18i 1.03254i
\(33\) 2.07039e19i 2.16087i
\(34\) −2.94331e18 −0.211519
\(35\) −7.85368e18 2.38656e19i −0.392846 1.19377i
\(36\) −2.32637e19 −0.818272
\(37\) 5.55139e19i 1.38637i 0.720758 + 0.693187i \(0.243794\pi\)
−0.720758 + 0.693187i \(0.756206\pi\)
\(38\) 2.87960e19i 0.515273i
\(39\) −9.23875e19 −1.19483
\(40\) −2.92047e19 8.87467e19i −0.275235 0.836378i
\(41\) 1.48547e20 1.02817 0.514085 0.857739i \(-0.328132\pi\)
0.514085 + 0.857739i \(0.328132\pi\)
\(42\) 1.79273e20i 0.918121i
\(43\) 2.65747e20i 1.01417i −0.861895 0.507087i \(-0.830722\pi\)
0.861895 0.507087i \(-0.169278\pi\)
\(44\) 3.88520e20 1.11238
\(45\) 4.82222e20 1.58689e20i 1.04253 0.343077i
\(46\) −1.14002e20 −0.187257
\(47\) 1.37381e21i 1.72465i 0.506352 + 0.862327i \(0.330994\pi\)
−0.506352 + 0.862327i \(0.669006\pi\)
\(48\) 4.52404e20i 0.436527i
\(49\) −7.77046e20 −0.579423
\(50\) 5.17127e20 + 7.00630e20i 0.299552 + 0.405848i
\(51\) 1.34288e21 0.607307
\(52\) 1.73370e21i 0.615080i
\(53\) 1.71008e21i 0.478153i −0.971001 0.239077i \(-0.923155\pi\)
0.971001 0.239077i \(-0.0768447\pi\)
\(54\) −3.21902e20 −0.0712529
\(55\) −8.05343e21 + 2.65022e21i −1.41725 + 0.466389i
\(56\) −7.87643e21 −1.10657
\(57\) 1.31381e22i 1.47943i
\(58\) 7.60356e21i 0.688917i
\(59\) 5.13294e21 0.375592 0.187796 0.982208i \(-0.439866\pi\)
0.187796 + 0.982208i \(0.439866\pi\)
\(60\) 5.69114e21 + 1.72941e22i 0.337527 + 1.02567i
\(61\) −9.68041e19 −0.00466951 −0.00233475 0.999997i \(-0.500743\pi\)
−0.00233475 + 0.999997i \(0.500743\pi\)
\(62\) 1.03827e22i 0.408711i
\(63\) 4.27980e22i 1.37933i
\(64\) −8.28978e21 −0.219429
\(65\) 1.18261e22 + 3.59369e22i 0.257884 + 0.783653i
\(66\) 6.04957e22 1.09000
\(67\) 9.29203e22i 1.38732i 0.720304 + 0.693658i \(0.244002\pi\)
−0.720304 + 0.693658i \(0.755998\pi\)
\(68\) 2.51997e22i 0.312633i
\(69\) 5.20127e22 0.537646
\(70\) 6.97338e22 2.29480e22i 0.602168 0.198161i
\(71\) −6.03387e22 −0.436381 −0.218191 0.975906i \(-0.570015\pi\)
−0.218191 + 0.975906i \(0.570015\pi\)
\(72\) 1.59149e23i 0.966379i
\(73\) 3.38440e22i 0.172960i −0.996254 0.0864801i \(-0.972438\pi\)
0.996254 0.0864801i \(-0.0275619\pi\)
\(74\) −1.62208e23 −0.699321
\(75\) −2.35937e23 3.19659e23i −0.860064 1.16526i
\(76\) 2.46542e23 0.761590
\(77\) 7.14756e23i 1.87510i
\(78\) 2.69951e23i 0.602701i
\(79\) −5.76376e23 −1.09741 −0.548703 0.836018i \(-0.684878\pi\)
−0.548703 + 0.836018i \(0.684878\pi\)
\(80\) −1.75976e23 + 5.79103e22i −0.286305 + 0.0942173i
\(81\) −6.41050e23 −0.892954
\(82\) 4.34044e23i 0.518634i
\(83\) 2.45821e23i 0.252431i −0.992003 0.126216i \(-0.959717\pi\)
0.992003 0.126216i \(-0.0402831\pi\)
\(84\) 1.53488e24 1.35701
\(85\) −1.71895e23 5.22352e23i −0.131077 0.398315i
\(86\) 7.76495e23 0.511574
\(87\) 3.46909e24i 1.97800i
\(88\) 2.65789e24i 1.31372i
\(89\) 1.04517e24 0.448553 0.224276 0.974526i \(-0.427998\pi\)
0.224276 + 0.974526i \(0.427998\pi\)
\(90\) 4.63680e23 + 1.40902e24i 0.173056 + 0.525880i
\(91\) 3.18946e24 1.03681
\(92\) 9.76045e23i 0.276772i
\(93\) 4.73708e24i 1.17348i
\(94\) −4.01417e24 −0.869958
\(95\) −5.11044e24 + 1.68174e24i −0.970317 + 0.319312i
\(96\) 8.97742e24 1.49541
\(97\) 8.72407e24i 1.27665i −0.769766 0.638326i \(-0.779627\pi\)
0.769766 0.638326i \(-0.220373\pi\)
\(98\) 2.27048e24i 0.292275i
\(99\) −1.44422e25 −1.63754
\(100\) 5.99857e24 4.42748e24i 0.599857 0.442748i
\(101\) −5.47037e24 −0.483058 −0.241529 0.970394i \(-0.577649\pi\)
−0.241529 + 0.970394i \(0.577649\pi\)
\(102\) 3.92380e24i 0.306341i
\(103\) 1.52638e25i 1.05487i −0.849596 0.527434i \(-0.823154\pi\)
0.849596 0.527434i \(-0.176846\pi\)
\(104\) 1.18604e25 0.726409
\(105\) −3.18158e25 + 1.04699e25i −1.72893 + 0.568954i
\(106\) 4.99674e24 0.241192
\(107\) 2.40394e25i 1.03187i 0.856627 + 0.515937i \(0.172556\pi\)
−0.856627 + 0.515937i \(0.827444\pi\)
\(108\) 2.75603e24i 0.105314i
\(109\) −2.25515e25 −0.767970 −0.383985 0.923339i \(-0.625449\pi\)
−0.383985 + 0.923339i \(0.625449\pi\)
\(110\) −7.74378e24 2.35316e25i −0.235258 0.714897i
\(111\) 7.40069e25 2.00787
\(112\) 1.56182e25i 0.378797i
\(113\) 1.47234e25i 0.319541i −0.987154 0.159771i \(-0.948925\pi\)
0.987154 0.159771i \(-0.0510755\pi\)
\(114\) 3.83886e25 0.746262
\(115\) −6.65792e24 2.02319e25i −0.116042 0.352626i
\(116\) 6.50992e25 1.01824
\(117\) 6.44454e25i 0.905459i
\(118\) 1.49981e25i 0.189458i
\(119\) −4.63597e25 −0.526991
\(120\) −1.18310e26 + 3.89335e25i −1.21131 + 0.398619i
\(121\) 1.32847e26 1.22612
\(122\) 2.82856e23i 0.00235541i
\(123\) 1.98031e26i 1.48908i
\(124\) −8.88937e25 −0.604088
\(125\) −9.41399e25 + 1.32693e26i −0.578627 + 0.815592i
\(126\) 1.25053e26 0.695766
\(127\) 2.67225e26i 1.34689i −0.739240 0.673443i \(-0.764815\pi\)
0.739240 0.673443i \(-0.235185\pi\)
\(128\) 2.01738e26i 0.921854i
\(129\) −3.54273e26 −1.46881
\(130\) −1.05005e26 + 3.45552e25i −0.395294 + 0.130083i
\(131\) 1.69205e26 0.578790 0.289395 0.957210i \(-0.406546\pi\)
0.289395 + 0.957210i \(0.406546\pi\)
\(132\) 5.17944e26i 1.61105i
\(133\) 4.53561e26i 1.28378i
\(134\) −2.71507e26 −0.699796
\(135\) −1.87997e25 5.71282e25i −0.0441550 0.134177i
\(136\) −1.72393e26 −0.369219
\(137\) 6.29711e26i 1.23065i 0.788274 + 0.615325i \(0.210975\pi\)
−0.788274 + 0.615325i \(0.789025\pi\)
\(138\) 1.51978e26i 0.271202i
\(139\) 9.76873e26 1.59277 0.796385 0.604790i \(-0.206743\pi\)
0.796385 + 0.604790i \(0.206743\pi\)
\(140\) −1.96473e26 5.97039e26i −0.292889 0.890025i
\(141\) 1.83145e27 2.49779
\(142\) 1.76306e26i 0.220122i
\(143\) 1.07628e27i 1.23091i
\(144\) −3.15577e26 −0.330807
\(145\) −1.34941e27 + 4.44063e26i −1.29731 + 0.426918i
\(146\) 9.88901e25 0.0872453
\(147\) 1.03590e27i 0.839170i
\(148\) 1.38878e27i 1.03362i
\(149\) 8.38306e26 0.573554 0.286777 0.957997i \(-0.407416\pi\)
0.286777 + 0.957997i \(0.407416\pi\)
\(150\) 9.34025e26 6.89394e26i 0.587784 0.433837i
\(151\) −1.30894e27 −0.758068 −0.379034 0.925383i \(-0.623744\pi\)
−0.379034 + 0.925383i \(0.623744\pi\)
\(152\) 1.68661e27i 0.899437i
\(153\) 9.36730e26i 0.460226i
\(154\) −2.08847e27 −0.945845
\(155\) 1.84263e27 6.06373e26i 0.769649 0.253276i
\(156\) −2.31123e27 −0.890811
\(157\) 1.73490e27i 0.617344i −0.951168 0.308672i \(-0.900115\pi\)
0.951168 0.308672i \(-0.0998846\pi\)
\(158\) 1.68413e27i 0.553558i
\(159\) −2.27974e27 −0.692503
\(160\) −1.14916e27 3.49204e27i −0.322760 0.980797i
\(161\) −1.79562e27 −0.466542
\(162\) 1.87311e27i 0.450428i
\(163\) 2.32016e27i 0.516623i −0.966062 0.258311i \(-0.916834\pi\)
0.966062 0.258311i \(-0.0831661\pi\)
\(164\) 3.71615e27 0.766558
\(165\) 3.53307e27 + 1.07362e28i 0.675464 + 2.05259i
\(166\) 7.18275e26 0.127333
\(167\) 1.85957e27i 0.305814i 0.988241 + 0.152907i \(0.0488635\pi\)
−0.988241 + 0.152907i \(0.951137\pi\)
\(168\) 1.05002e28i 1.60263i
\(169\) 2.25370e27 0.319384
\(170\) 1.52628e27 5.02268e26i 0.200920 0.0661186i
\(171\) −9.16452e27 −1.12114
\(172\) 6.64811e27i 0.756123i
\(173\) 1.33577e28i 1.41304i −0.707691 0.706522i \(-0.750263\pi\)
0.707691 0.706522i \(-0.249737\pi\)
\(174\) 1.01365e28 0.997749
\(175\) 8.14519e27 + 1.10355e28i 0.746321 + 1.01115i
\(176\) 5.27035e27 0.449709
\(177\) 6.84283e27i 0.543964i
\(178\) 3.05393e27i 0.226261i
\(179\) 9.48628e27 0.655289 0.327644 0.944801i \(-0.393745\pi\)
0.327644 + 0.944801i \(0.393745\pi\)
\(180\) 1.20636e28 3.96988e27i 0.777267 0.255783i
\(181\) −3.16510e28 −1.90285 −0.951427 0.307876i \(-0.900382\pi\)
−0.951427 + 0.307876i \(0.900382\pi\)
\(182\) 9.31942e27i 0.522994i
\(183\) 1.29052e26i 0.00676278i
\(184\) −6.67720e27 −0.326867
\(185\) −9.47329e27 2.87872e28i −0.433365 1.31690i
\(186\) −1.38415e28 −0.591930
\(187\) 1.56440e28i 0.625646i
\(188\) 3.43681e28i 1.28583i
\(189\) −5.07023e27 −0.177523
\(190\) −4.91395e27 1.49324e28i −0.161069 0.489452i
\(191\) −3.69520e28 −1.13428 −0.567141 0.823621i \(-0.691951\pi\)
−0.567141 + 0.823621i \(0.691951\pi\)
\(192\) 1.10513e28i 0.317796i
\(193\) 4.44096e28i 1.19677i −0.801209 0.598385i \(-0.795809\pi\)
0.801209 0.598385i \(-0.204191\pi\)
\(194\) 2.54912e28 0.643974
\(195\) 4.79083e28 1.57656e28i 1.13495 0.373490i
\(196\) −1.94391e28 −0.431992
\(197\) 1.61228e28i 0.336211i 0.985769 + 0.168106i \(0.0537650\pi\)
−0.985769 + 0.168106i \(0.946235\pi\)
\(198\) 4.21991e28i 0.826016i
\(199\) −8.59811e28 −1.58030 −0.790150 0.612913i \(-0.789998\pi\)
−0.790150 + 0.612913i \(0.789998\pi\)
\(200\) 3.02887e28 + 4.10367e28i 0.522885 + 0.708430i
\(201\) 1.23874e29 2.00923
\(202\) 1.59841e28i 0.243666i
\(203\) 1.19762e29i 1.71641i
\(204\) 3.35943e28 0.452781
\(205\) −7.70301e28 + 2.53491e28i −0.976647 + 0.321395i
\(206\) 4.46000e28 0.532102
\(207\) 3.62818e28i 0.407436i
\(208\) 2.35180e28i 0.248661i
\(209\) 1.53054e29 1.52411
\(210\) −3.05925e28 9.29637e28i −0.286994 0.872112i
\(211\) −4.71369e28 −0.416707 −0.208353 0.978054i \(-0.566810\pi\)
−0.208353 + 0.978054i \(0.566810\pi\)
\(212\) 4.27805e28i 0.356490i
\(213\) 8.04388e28i 0.632005i
\(214\) −7.02417e28 −0.520502
\(215\) 4.53489e28 + 1.37805e29i 0.317019 + 0.963351i
\(216\) −1.88542e28 −0.124376
\(217\) 1.63537e29i 1.01828i
\(218\) 6.58941e28i 0.387383i
\(219\) −4.51182e28 −0.250496
\(220\) −2.01470e29 + 6.62997e28i −1.05664 + 0.347719i
\(221\) 6.98085e28 0.345943
\(222\) 2.16244e29i 1.01282i
\(223\) 9.50446e28i 0.420840i −0.977611 0.210420i \(-0.932517\pi\)
0.977611 0.210420i \(-0.0674831\pi\)
\(224\) −3.09925e29 −1.29765
\(225\) −2.22980e29 + 1.64579e29i −0.883049 + 0.651769i
\(226\) 4.30208e28 0.161184
\(227\) 3.76543e29i 1.33503i −0.744596 0.667516i \(-0.767358\pi\)
0.744596 0.667516i \(-0.232642\pi\)
\(228\) 3.28671e29i 1.10300i
\(229\) −8.92811e28 −0.283672 −0.141836 0.989890i \(-0.545301\pi\)
−0.141836 + 0.989890i \(0.545301\pi\)
\(230\) 5.91165e28 1.94540e28i 0.177873 0.0585345i
\(231\) 9.52857e29 2.71568
\(232\) 4.45349e29i 1.20254i
\(233\) 5.97595e28i 0.152918i 0.997073 + 0.0764589i \(0.0243614\pi\)
−0.997073 + 0.0764589i \(0.975639\pi\)
\(234\) −1.88306e29 −0.456736
\(235\) −2.34436e29 7.12398e29i −0.539108 1.63823i
\(236\) 1.28409e29 0.280024
\(237\) 7.68380e29i 1.58936i
\(238\) 1.35460e29i 0.265827i
\(239\) 4.35621e29 0.811214 0.405607 0.914048i \(-0.367060\pi\)
0.405607 + 0.914048i \(0.367060\pi\)
\(240\) 7.72015e28 + 2.34598e29i 0.136454 + 0.414652i
\(241\) −3.34058e29 −0.560543 −0.280271 0.959921i \(-0.590424\pi\)
−0.280271 + 0.959921i \(0.590424\pi\)
\(242\) 3.88170e29i 0.618486i
\(243\) 9.47942e29i 1.43451i
\(244\) −2.42172e27 −0.00348138
\(245\) 4.02944e29 1.32601e29i 0.550387 0.181121i
\(246\) 5.78634e29 0.751131
\(247\) 6.82974e29i 0.842737i
\(248\) 6.08129e29i 0.713427i
\(249\) −3.27710e29 −0.365593
\(250\) −3.87721e29 2.75071e29i −0.411405 0.291874i
\(251\) 2.73598e29 0.276179 0.138090 0.990420i \(-0.455904\pi\)
0.138090 + 0.990420i \(0.455904\pi\)
\(252\) 1.07067e30i 1.02836i
\(253\) 6.05930e29i 0.553881i
\(254\) 7.80815e29 0.679402
\(255\) −6.96359e29 + 2.29158e29i −0.576874 + 0.189838i
\(256\) −8.67624e29 −0.684435
\(257\) 8.97420e29i 0.674267i −0.941457 0.337133i \(-0.890543\pi\)
0.941457 0.337133i \(-0.109457\pi\)
\(258\) 1.03516e30i 0.740905i
\(259\) −2.55492e30 −1.74233
\(260\) 2.95850e29 + 8.99023e29i 0.192267 + 0.584257i
\(261\) −2.41989e30 −1.49895
\(262\) 4.94405e29i 0.291956i
\(263\) 1.70766e30i 0.961510i 0.876855 + 0.480755i \(0.159637\pi\)
−0.876855 + 0.480755i \(0.840363\pi\)
\(264\) 3.54330e30 1.90265
\(265\) 2.91819e29 + 8.86774e29i 0.149465 + 0.454192i
\(266\) −1.32528e30 −0.647569
\(267\) 1.39334e30i 0.649633i
\(268\) 2.32456e30i 1.03432i
\(269\) 3.03624e29 0.128953 0.0644766 0.997919i \(-0.479462\pi\)
0.0644766 + 0.997919i \(0.479462\pi\)
\(270\) 1.66925e29 5.49317e28i 0.0676823 0.0222729i
\(271\) 1.57356e30 0.609210 0.304605 0.952479i \(-0.401476\pi\)
0.304605 + 0.952479i \(0.401476\pi\)
\(272\) 3.41840e29i 0.126390i
\(273\) 4.25195e30i 1.50160i
\(274\) −1.83998e30 −0.620770
\(275\) 3.72392e30 2.74859e30i 1.20044 0.886035i
\(276\) 1.30119e30 0.400845
\(277\) 1.53940e30i 0.453267i −0.973980 0.226633i \(-0.927228\pi\)
0.973980 0.226633i \(-0.0727719\pi\)
\(278\) 2.85436e30i 0.803432i
\(279\) 3.30438e30 0.889278
\(280\) 4.08439e30 1.34409e30i 1.05112 0.345902i
\(281\) −6.95030e30 −1.71070 −0.855351 0.518049i \(-0.826659\pi\)
−0.855351 + 0.518049i \(0.826659\pi\)
\(282\) 5.35139e30i 1.25995i
\(283\) 2.34367e28i 0.00527917i 0.999997 + 0.00263958i \(0.000840206\pi\)
−0.999997 + 0.00263958i \(0.999160\pi\)
\(284\) −1.50947e30 −0.325347
\(285\) 2.24197e30 + 6.81285e30i 0.462454 + 1.40530i
\(286\) 3.14483e30 0.620900
\(287\) 6.83656e30i 1.29215i
\(288\) 6.26225e30i 1.13325i
\(289\) 4.75594e30 0.824164
\(290\) −1.29752e30 3.94289e30i −0.215348 0.654394i
\(291\) −1.16302e31 −1.84896
\(292\) 8.46666e29i 0.128951i
\(293\) 1.03650e31i 1.51260i −0.654226 0.756299i \(-0.727006\pi\)
0.654226 0.756299i \(-0.272994\pi\)
\(294\) −3.02683e30 −0.423298
\(295\) −2.66173e30 + 8.75920e29i −0.356770 + 0.117406i
\(296\) −9.50073e30 −1.22070
\(297\) 1.71095e30i 0.210756i
\(298\) 2.44948e30i 0.289315i
\(299\) 2.70385e30 0.306262
\(300\) −5.90237e30 7.99682e30i −0.641226 0.868764i
\(301\) 1.22305e31 1.27456
\(302\) 3.82465e30i 0.382388i
\(303\) 7.29268e30i 0.699607i
\(304\) 3.34440e30 0.307892
\(305\) 5.01986e28 1.65193e28i 0.00443551 0.00145964i
\(306\) 2.73707e30 0.232150
\(307\) 6.56613e30i 0.534663i −0.963605 0.267331i \(-0.913858\pi\)
0.963605 0.267331i \(-0.0861418\pi\)
\(308\) 1.78808e31i 1.39799i
\(309\) −2.03486e31 −1.52775
\(310\) 1.77178e30 + 5.38406e30i 0.127758 + 0.388230i
\(311\) 1.09459e31 0.758138 0.379069 0.925368i \(-0.376244\pi\)
0.379069 + 0.925368i \(0.376244\pi\)
\(312\) 1.58113e31i 1.05205i
\(313\) 1.19799e30i 0.0765861i −0.999267 0.0382930i \(-0.987808\pi\)
0.999267 0.0382930i \(-0.0121920\pi\)
\(314\) 5.06926e30 0.311404
\(315\) 7.30335e30 + 2.21933e31i 0.431162 + 1.31021i
\(316\) −1.44190e31 −0.818177
\(317\) 8.57599e30i 0.467782i −0.972263 0.233891i \(-0.924854\pi\)
0.972263 0.233891i \(-0.0751459\pi\)
\(318\) 6.66126e30i 0.349315i
\(319\) 4.04137e31 2.03772
\(320\) 4.29874e30 1.41463e30i 0.208433 0.0685910i
\(321\) 3.20475e31 1.49445
\(322\) 5.24669e30i 0.235335i
\(323\) 9.92719e30i 0.428346i
\(324\) −1.60370e31 −0.665747
\(325\) −1.22651e31 1.66173e31i −0.489923 0.663771i
\(326\) 6.77938e30 0.260597
\(327\) 3.00639e31i 1.11224i
\(328\) 2.54225e31i 0.905305i
\(329\) −6.32266e31 −2.16746
\(330\) −3.13705e31 + 1.03234e31i −1.03537 + 0.340721i
\(331\) 4.51780e31 1.43575 0.717873 0.696174i \(-0.245116\pi\)
0.717873 + 0.696174i \(0.245116\pi\)
\(332\) 6.14964e30i 0.188202i
\(333\) 5.16239e31i 1.52159i
\(334\) −5.43356e30 −0.154260
\(335\) −1.58566e31 4.81846e31i −0.433660 1.31780i
\(336\) 2.08210e31 0.548606
\(337\) 3.65657e31i 0.928325i 0.885750 + 0.464163i \(0.153645\pi\)
−0.885750 + 0.464163i \(0.846355\pi\)
\(338\) 6.58518e30i 0.161105i
\(339\) −1.96281e31 −0.462787
\(340\) −4.30026e30 1.30675e31i −0.0977255 0.296966i
\(341\) −5.51854e31 −1.20891
\(342\) 2.67782e31i 0.565529i
\(343\) 2.59580e31i 0.528561i
\(344\) 4.54802e31 0.892981
\(345\) −2.69716e31 + 8.87582e30i −0.510703 + 0.168062i
\(346\) 3.90304e31 0.712774
\(347\) 1.69385e31i 0.298370i −0.988809 0.149185i \(-0.952335\pi\)
0.988809 0.149185i \(-0.0476651\pi\)
\(348\) 8.67853e31i 1.47471i
\(349\) −2.49178e31 −0.408500 −0.204250 0.978919i \(-0.565476\pi\)
−0.204250 + 0.978919i \(0.565476\pi\)
\(350\) −3.22451e31 + 2.37997e31i −0.510050 + 0.376462i
\(351\) 7.63478e30 0.116535
\(352\) 1.04584e32i 1.54057i
\(353\) 5.75445e31i 0.818125i 0.912506 + 0.409063i \(0.134144\pi\)
−0.912506 + 0.409063i \(0.865856\pi\)
\(354\) 1.99943e31 0.274389
\(355\) 3.12891e31 1.02966e31i 0.414514 0.136408i
\(356\) 2.61468e31 0.334421
\(357\) 6.18031e31i 0.763234i
\(358\) 2.77183e31i 0.330544i
\(359\) 6.95546e31 0.801024 0.400512 0.916292i \(-0.368832\pi\)
0.400512 + 0.916292i \(0.368832\pi\)
\(360\) 2.71583e31 + 8.25280e31i 0.302079 + 0.917952i
\(361\) 4.04645e30 0.0434745
\(362\) 9.24823e31i 0.959846i
\(363\) 1.77101e32i 1.77577i
\(364\) 7.97899e31 0.773002
\(365\) 5.77538e30 + 1.75501e31i 0.0540654 + 0.164293i
\(366\) −3.77081e29 −0.00341131
\(367\) 1.92271e32i 1.68107i −0.541754 0.840537i \(-0.682240\pi\)
0.541754 0.840537i \(-0.317760\pi\)
\(368\) 1.32403e31i 0.111892i
\(369\) −1.38138e32 −1.12845
\(370\) 8.41145e31 2.76804e31i 0.664277 0.218600i
\(371\) 7.87028e31 0.600919
\(372\) 1.18506e32i 0.874892i
\(373\) 2.12399e32i 1.51632i 0.652068 + 0.758161i \(0.273902\pi\)
−0.652068 + 0.758161i \(0.726098\pi\)
\(374\) −4.57109e31 −0.315591
\(375\) 1.76896e32 + 1.25500e32i 1.18121 + 0.838018i
\(376\) −2.35115e32 −1.51856
\(377\) 1.80339e32i 1.12674i
\(378\) 1.48149e31i 0.0895471i
\(379\) −2.03719e32 −1.19136 −0.595679 0.803223i \(-0.703117\pi\)
−0.595679 + 0.803223i \(0.703117\pi\)
\(380\) −1.27846e32 + 4.20717e31i −0.723425 + 0.238065i
\(381\) −3.56244e32 −1.95068
\(382\) 1.07972e32i 0.572160i
\(383\) 3.00431e32i 1.54085i 0.637531 + 0.770424i \(0.279956\pi\)
−0.637531 + 0.770424i \(0.720044\pi\)
\(384\) 2.68941e32 1.33511
\(385\) −1.21971e32 3.70643e32i −0.586135 1.78113i
\(386\) 1.29762e32 0.603680
\(387\) 2.47125e32i 1.11309i
\(388\) 2.18247e32i 0.951815i
\(389\) 1.14176e32 0.482177 0.241088 0.970503i \(-0.422496\pi\)
0.241088 + 0.970503i \(0.422496\pi\)
\(390\) 4.60663e31 + 1.39985e32i 0.188398 + 0.572498i
\(391\) −3.93011e31 −0.155667
\(392\) 1.32985e32i 0.510183i
\(393\) 2.25570e32i 0.838253i
\(394\) −4.71098e31 −0.169593
\(395\) 2.98885e32 9.83568e31i 1.04241 0.343037i
\(396\) −3.61295e32 −1.22088
\(397\) 1.58269e32i 0.518221i 0.965848 + 0.259111i \(0.0834294\pi\)
−0.965848 + 0.259111i \(0.916571\pi\)
\(398\) 2.51232e32i 0.797142i
\(399\) 6.04652e32 1.85928
\(400\) 8.13718e31 6.00597e31i 0.242507 0.178992i
\(401\) −1.50822e32 −0.435671 −0.217836 0.975985i \(-0.569900\pi\)
−0.217836 + 0.975985i \(0.569900\pi\)
\(402\) 3.61953e32i 1.01351i
\(403\) 2.46254e32i 0.668453i
\(404\) −1.36851e32 −0.360147
\(405\) 3.32422e32 1.09393e32i 0.848207 0.279128i
\(406\) −3.49938e32 −0.865797
\(407\) 8.62154e32i 2.06850i
\(408\) 2.29821e32i 0.534735i
\(409\) −4.78027e31 −0.107873 −0.0539363 0.998544i \(-0.517177\pi\)
−0.0539363 + 0.998544i \(0.517177\pi\)
\(410\) −7.40684e31 2.25077e32i −0.162119 0.492645i
\(411\) 8.39483e32 1.78233
\(412\) 3.81851e32i 0.786464i
\(413\) 2.36233e32i 0.472025i
\(414\) 1.06013e32 0.205521
\(415\) 4.19487e31 + 1.27473e32i 0.0789073 + 0.239782i
\(416\) 4.66686e32 0.851840
\(417\) 1.30229e33i 2.30679i
\(418\) 4.47214e32i 0.768797i
\(419\) −5.50053e32 −0.917760 −0.458880 0.888498i \(-0.651749\pi\)
−0.458880 + 0.888498i \(0.651749\pi\)
\(420\) −7.95926e32 + 2.61923e32i −1.28901 + 0.424187i
\(421\) −6.24373e32 −0.981563 −0.490781 0.871283i \(-0.663289\pi\)
−0.490781 + 0.871283i \(0.663289\pi\)
\(422\) 1.37731e32i 0.210197i
\(423\) 1.27754e33i 1.89286i
\(424\) 2.92665e32 0.421014
\(425\) 1.78276e32 + 2.41537e32i 0.249018 + 0.337381i
\(426\) −2.35037e32 −0.318799
\(427\) 4.45521e30i 0.00586841i
\(428\) 6.01387e32i 0.769319i
\(429\) −1.43482e33 −1.78271
\(430\) −4.02658e32 + 1.32507e32i −0.485938 + 0.159912i
\(431\) 9.95413e32 1.16691 0.583455 0.812146i \(-0.301701\pi\)
0.583455 + 0.812146i \(0.301701\pi\)
\(432\) 3.73861e31i 0.0425758i
\(433\) 1.01179e33i 1.11942i −0.828688 0.559711i \(-0.810912\pi\)
0.828688 0.559711i \(-0.189088\pi\)
\(434\) 4.77845e32 0.513648
\(435\) 5.91990e32 + 1.79893e33i 0.618299 + 1.87887i
\(436\) −5.64164e32 −0.572565
\(437\) 3.84504e32i 0.379213i
\(438\) 1.31833e32i 0.126356i
\(439\) −1.31957e33 −1.22921 −0.614606 0.788834i \(-0.710685\pi\)
−0.614606 + 0.788834i \(0.710685\pi\)
\(440\) −4.53562e32 1.37827e33i −0.410656 1.24789i
\(441\) 7.22596e32 0.635936
\(442\) 2.03976e32i 0.174502i
\(443\) 7.07458e32i 0.588375i 0.955748 + 0.294188i \(0.0950490\pi\)
−0.955748 + 0.294188i \(0.904951\pi\)
\(444\) 1.85141e33 1.49698
\(445\) −5.41984e32 + 1.78356e32i −0.426075 + 0.140213i
\(446\) 2.77715e32 0.212282
\(447\) 1.11757e33i 0.830671i
\(448\) 3.81520e32i 0.275767i
\(449\) −1.43255e32 −0.100701 −0.0503503 0.998732i \(-0.516034\pi\)
−0.0503503 + 0.998732i \(0.516034\pi\)
\(450\) −4.80891e32 6.51534e32i −0.328768 0.445432i
\(451\) 2.30699e33 1.53405
\(452\) 3.68330e32i 0.238236i
\(453\) 1.74498e33i 1.09790i
\(454\) 1.10024e33 0.673423
\(455\) −1.65392e33 + 5.44273e32i −0.984857 + 0.324096i
\(456\) 2.24846e33 1.30264
\(457\) 2.29124e33i 1.29157i 0.763519 + 0.645785i \(0.223470\pi\)
−0.763519 + 0.645785i \(0.776530\pi\)
\(458\) 2.60874e32i 0.143091i
\(459\) −1.10973e32 −0.0592325
\(460\) −1.66559e32 5.06136e32i −0.0865158 0.262902i
\(461\) −5.28423e30 −0.00267129 −0.00133564 0.999999i \(-0.500425\pi\)
−0.00133564 + 0.999999i \(0.500425\pi\)
\(462\) 2.78419e33i 1.36985i
\(463\) 9.84320e32i 0.471383i −0.971828 0.235692i \(-0.924264\pi\)
0.971828 0.235692i \(-0.0757355\pi\)
\(464\) 8.83085e32 0.411650
\(465\) −8.08369e32 2.45645e33i −0.366816 1.11467i
\(466\) −1.74614e32 −0.0771355
\(467\) 2.70720e33i 1.16428i −0.813087 0.582142i \(-0.802215\pi\)
0.813087 0.582142i \(-0.197785\pi\)
\(468\) 1.61221e33i 0.675070i
\(469\) −4.27647e33 −1.74351
\(470\) 2.08158e33 6.85007e32i 0.826363 0.271939i
\(471\) −2.31283e33 −0.894092
\(472\) 8.78457e32i 0.330709i
\(473\) 4.12715e33i 1.51317i
\(474\) −2.24516e33 −0.801711
\(475\) 2.36308e33 1.74416e33i 0.821879 0.606621i
\(476\) −1.15977e33 −0.392901
\(477\) 1.59025e33i 0.524789i
\(478\) 1.27286e33i 0.409196i
\(479\) −6.97657e32 −0.218498 −0.109249 0.994014i \(-0.534845\pi\)
−0.109249 + 0.994014i \(0.534845\pi\)
\(480\) −4.65532e33 + 1.53197e33i −1.42048 + 0.467450i
\(481\) 3.84720e33 1.14375
\(482\) 9.76097e32i 0.282752i
\(483\) 2.39378e33i 0.675687i
\(484\) 3.32339e33 0.914142
\(485\) 1.48874e33 + 4.52394e33i 0.399067 + 1.21268i
\(486\) −2.76983e33 −0.723602
\(487\) 2.67547e33i 0.681222i −0.940204 0.340611i \(-0.889366\pi\)
0.940204 0.340611i \(-0.110634\pi\)
\(488\) 1.65672e31i 0.00411151i
\(489\) −3.09306e33 −0.748218
\(490\) 3.87451e32 + 1.17738e33i 0.0913620 + 0.277629i
\(491\) −6.76932e33 −1.55606 −0.778030 0.628227i \(-0.783781\pi\)
−0.778030 + 0.628227i \(0.783781\pi\)
\(492\) 4.95408e33i 1.11020i
\(493\) 2.62127e33i 0.572697i
\(494\) 1.99561e33 0.425097
\(495\) 7.48910e33 2.46451e33i 1.55548 0.511877i
\(496\) −1.20586e33 −0.244218
\(497\) 2.77696e33i 0.548423i
\(498\) 9.57548e32i 0.184414i
\(499\) 9.92600e33 1.86431 0.932153 0.362064i \(-0.117928\pi\)
0.932153 + 0.362064i \(0.117928\pi\)
\(500\) −2.35507e33 + 3.31954e33i −0.431399 + 0.608070i
\(501\) 2.47904e33 0.442906
\(502\) 7.99436e32i 0.139312i
\(503\) 5.51083e33i 0.936736i 0.883534 + 0.468368i \(0.155158\pi\)
−0.883534 + 0.468368i \(0.844842\pi\)
\(504\) 7.32451e33 1.21450
\(505\) 2.83671e33 9.33503e32i 0.458852 0.150999i
\(506\) −1.77049e33 −0.279391
\(507\) 3.00446e33i 0.462559i
\(508\) 6.68509e33i 1.00418i
\(509\) −3.51385e33 −0.515004 −0.257502 0.966278i \(-0.582899\pi\)
−0.257502 + 0.966278i \(0.582899\pi\)
\(510\) −6.69585e32 2.03472e33i −0.0957587 0.290989i
\(511\) 1.55760e33 0.217368
\(512\) 4.23405e33i 0.576609i
\(513\) 1.08571e33i 0.144294i
\(514\) 2.62221e33 0.340117
\(515\) 2.60473e33 + 7.91519e33i 0.329740 + 1.00201i
\(516\) −8.86274e33 −1.09508
\(517\) 2.13358e34i 2.57322i
\(518\) 7.46531e33i 0.878873i
\(519\) −1.78075e34 −2.04649
\(520\) −6.15029e33 + 2.02393e33i −0.690007 + 0.227067i
\(521\) −4.44244e33 −0.486575 −0.243288 0.969954i \(-0.578226\pi\)
−0.243288 + 0.969954i \(0.578226\pi\)
\(522\) 7.07076e33i 0.756109i
\(523\) 3.50209e33i 0.365642i −0.983146 0.182821i \(-0.941477\pi\)
0.983146 0.182821i \(-0.0585229\pi\)
\(524\) 4.23294e33 0.431520
\(525\) 1.47117e34 1.08585e34i 1.46444 1.08089i
\(526\) −4.98967e33 −0.485009
\(527\) 3.57937e33i 0.339761i
\(528\) 7.02603e33i 0.651307i
\(529\) 9.52354e33 0.862189
\(530\) −2.59110e33 + 8.52678e32i −0.229106 + 0.0753940i
\(531\) −4.77326e33 −0.412224
\(532\) 1.13466e34i 0.957129i
\(533\) 1.02945e34i 0.848235i
\(534\) 4.07127e33 0.327691
\(535\) −4.10225e33 1.24658e34i −0.322552 0.980165i
\(536\) −1.59025e34 −1.22153
\(537\) 1.26464e34i 0.949046i
\(538\) 8.87170e32i 0.0650472i
\(539\) −1.20678e34 −0.864510
\(540\) −4.70308e32 1.42916e33i −0.0329200 0.100037i
\(541\) 8.58091e33 0.586905 0.293452 0.955974i \(-0.405196\pi\)
0.293452 + 0.955974i \(0.405196\pi\)
\(542\) 4.59784e33i 0.307300i
\(543\) 4.21947e34i 2.75588i
\(544\) −6.78339e33 −0.432973
\(545\) 1.16943e34 3.84835e33i 0.729486 0.240059i
\(546\) 1.24239e34 0.757445
\(547\) 7.19024e33i 0.428452i −0.976784 0.214226i \(-0.931277\pi\)
0.976784 0.214226i \(-0.0687229\pi\)
\(548\) 1.57533e34i 0.917518i
\(549\) 9.00208e31 0.00512494
\(550\) 8.03120e33 + 1.08811e34i 0.446938 + 0.605533i
\(551\) 2.56452e34 1.39512
\(552\) 8.90153e33i 0.473398i
\(553\) 2.65265e34i 1.37917i
\(554\) 4.49803e33 0.228639
\(555\) −3.83769e34 + 1.26291e34i −1.90725 + 0.627637i
\(556\) 2.44381e34 1.18750
\(557\) 6.67160e33i 0.316986i 0.987360 + 0.158493i \(0.0506635\pi\)
−0.987360 + 0.158493i \(0.949336\pi\)
\(558\) 9.65520e33i 0.448573i
\(559\) −1.84167e34 −0.836687
\(560\) −2.66520e33 8.09896e33i −0.118408 0.359815i
\(561\) 2.08554e34 0.906114
\(562\) 2.03083e34i 0.862920i
\(563\) 2.00429e34i 0.832925i −0.909153 0.416462i \(-0.863270\pi\)
0.909153 0.416462i \(-0.136730\pi\)
\(564\) 4.58169e34 1.86224
\(565\) 2.51250e33 + 7.63493e33i 0.0998851 + 0.303529i
\(566\) −6.84805e31 −0.00266294
\(567\) 2.95030e34i 1.12222i
\(568\) 1.03264e34i 0.384234i
\(569\) 1.35074e34 0.491664 0.245832 0.969312i \(-0.420939\pi\)
0.245832 + 0.969312i \(0.420939\pi\)
\(570\) −1.99067e34 + 6.55090e33i −0.708866 + 0.233273i
\(571\) −4.31121e34 −1.50192 −0.750961 0.660346i \(-0.770410\pi\)
−0.750961 + 0.660346i \(0.770410\pi\)
\(572\) 2.69250e34i 0.917711i
\(573\) 4.92616e34i 1.64276i
\(574\) −1.99760e34 −0.651794
\(575\) 6.90504e33 + 9.35528e33i 0.220454 + 0.298682i
\(576\) 7.70889e33 0.240830
\(577\) 3.54921e34i 1.08501i 0.840052 + 0.542505i \(0.182524\pi\)
−0.840052 + 0.542505i \(0.817476\pi\)
\(578\) 1.38966e34i 0.415728i
\(579\) −5.92034e34 −1.73326
\(580\) −3.37578e34 + 1.11090e34i −0.967216 + 0.318291i
\(581\) 1.13134e34 0.317243
\(582\) 3.39829e34i 0.932659i
\(583\) 2.65582e34i 0.713414i
\(584\) 5.79211e33 0.152292
\(585\) −1.09974e34 3.34187e34i −0.283036 0.860085i
\(586\) 3.02859e34 0.762991
\(587\) 1.24414e34i 0.306827i 0.988162 + 0.153413i \(0.0490266\pi\)
−0.988162 + 0.153413i \(0.950973\pi\)
\(588\) 2.59147e34i 0.625648i
\(589\) −3.50189e34 −0.827677
\(590\) −2.55939e33 7.77741e33i −0.0592223 0.179964i
\(591\) 2.14937e34 0.486930
\(592\) 1.88390e34i 0.417867i
\(593\) 8.64628e34i 1.87778i −0.344212 0.938892i \(-0.611854\pi\)
0.344212 0.938892i \(-0.388146\pi\)
\(594\) −4.99928e33 −0.106311
\(595\) 2.40402e34 7.91114e33i 0.500583 0.164732i
\(596\) 2.09717e34 0.427617
\(597\) 1.14623e35i 2.28873i
\(598\) 7.90049e33i 0.154486i
\(599\) −1.88641e34 −0.361243 −0.180622 0.983553i \(-0.557811\pi\)
−0.180622 + 0.983553i \(0.557811\pi\)
\(600\) 5.47069e34 4.03786e34i 1.02601 0.757287i
\(601\) 7.66027e33 0.140706 0.0703531 0.997522i \(-0.477587\pi\)
0.0703531 + 0.997522i \(0.477587\pi\)
\(602\) 3.57366e34i 0.642921i
\(603\) 8.64091e34i 1.52263i
\(604\) −3.27454e34 −0.565182
\(605\) −6.88888e34 + 2.26699e34i −1.16468 + 0.383272i
\(606\) −2.13088e34 −0.352899
\(607\) 3.80410e34i 0.617154i −0.951199 0.308577i \(-0.900147\pi\)
0.951199 0.308577i \(-0.0998527\pi\)
\(608\) 6.63655e34i 1.05475i
\(609\) 1.59658e35 2.48585
\(610\) 4.82685e31 + 1.46677e32i 0.000736276 + 0.00223738i
\(611\) 9.52069e34 1.42283
\(612\) 2.34339e34i 0.343125i
\(613\) 2.90088e34i 0.416172i 0.978111 + 0.208086i \(0.0667234\pi\)
−0.978111 + 0.208086i \(0.933277\pi\)
\(614\) 1.91858e34 0.269697
\(615\) 3.37934e34 + 1.02691e35i 0.465471 + 1.41446i
\(616\) −1.22324e35 −1.65102
\(617\) 4.91805e34i 0.650472i 0.945633 + 0.325236i \(0.105444\pi\)
−0.945633 + 0.325236i \(0.894556\pi\)
\(618\) 5.94573e34i 0.770635i
\(619\) 2.55433e34 0.324447 0.162223 0.986754i \(-0.448133\pi\)
0.162223 + 0.986754i \(0.448133\pi\)
\(620\) 4.60966e34 1.51694e34i 0.573816 0.188831i
\(621\) −4.29826e33 −0.0524382
\(622\) 3.19834e34i 0.382424i
\(623\) 4.81020e34i 0.563719i
\(624\) −3.13523e34 −0.360133
\(625\) 2.61734e34 8.48738e34i 0.294686 0.955594i
\(626\) 3.50046e33 0.0386319
\(627\) 2.04039e35i 2.20734i
\(628\) 4.34014e34i 0.460265i
\(629\) −5.59201e34 −0.581346
\(630\) −6.48474e34 + 2.13400e34i −0.660900 + 0.217489i
\(631\) −1.79226e35 −1.79075 −0.895375 0.445314i \(-0.853092\pi\)
−0.895375 + 0.445314i \(0.853092\pi\)
\(632\) 9.86417e34i 0.966267i
\(633\) 6.28393e34i 0.603510i
\(634\) 2.50585e34 0.235961
\(635\) 4.56011e34 + 1.38572e35i 0.421021 + 1.27939i
\(636\) −5.70316e34 −0.516299
\(637\) 5.38505e34i 0.478021i
\(638\) 1.18086e35i 1.02788i
\(639\) 5.61106e34 0.478943
\(640\) −3.44259e34 1.04613e35i −0.288161 0.875659i
\(641\) −1.08126e35 −0.887575 −0.443787 0.896132i \(-0.646365\pi\)
−0.443787 + 0.896132i \(0.646365\pi\)
\(642\) 9.36407e34i 0.753836i
\(643\) 1.53840e35i 1.21459i 0.794475 + 0.607297i \(0.207746\pi\)
−0.794475 + 0.607297i \(0.792254\pi\)
\(644\) −4.49205e34 −0.347833
\(645\) 1.83711e35 6.04556e34i 1.39521 0.459135i
\(646\) −2.90066e34 −0.216068
\(647\) 2.04770e35i 1.49611i −0.663639 0.748053i \(-0.730989\pi\)
0.663639 0.748053i \(-0.269011\pi\)
\(648\) 1.09710e35i 0.786247i
\(649\) 7.97166e34 0.560390
\(650\) 4.85547e34 3.58377e34i 0.334822 0.247129i
\(651\) −2.18015e35 −1.47477
\(652\) 5.80429e34i 0.385171i
\(653\) 6.07692e33i 0.0395611i 0.999804 + 0.0197806i \(0.00629676\pi\)
−0.999804 + 0.0197806i \(0.993703\pi\)
\(654\) −8.78449e34 −0.561041
\(655\) −8.77424e34 + 2.88743e34i −0.549786 + 0.180923i
\(656\) 5.04104e34 0.309900
\(657\) 3.14725e34i 0.189829i
\(658\) 1.84744e35i 1.09332i
\(659\) 1.25296e35 0.727559 0.363780 0.931485i \(-0.381486\pi\)
0.363780 + 0.931485i \(0.381486\pi\)
\(660\) 8.83857e34 + 2.68584e35i 0.503597 + 1.53032i
\(661\) 3.27675e35 1.83200 0.915998 0.401183i \(-0.131401\pi\)
0.915998 + 0.401183i \(0.131401\pi\)
\(662\) 1.32007e35i 0.724225i
\(663\) 9.30633e34i 0.501025i
\(664\) 4.20702e34 0.222266
\(665\) −7.73988e34 2.35198e35i −0.401295 1.21945i
\(666\) 1.50842e35 0.767528
\(667\) 1.01528e35i 0.507005i
\(668\) 4.65204e34i 0.228001i
\(669\) −1.26706e35 −0.609496
\(670\) 1.40792e35 4.63319e34i 0.664728 0.218749i
\(671\) −1.50341e33 −0.00696699
\(672\) 4.13168e35i 1.87936i
\(673\) 2.70609e35i 1.20824i 0.796892 + 0.604122i \(0.206476\pi\)
−0.796892 + 0.604122i \(0.793524\pi\)
\(674\) −1.06843e35 −0.468270
\(675\) 1.94975e34 + 2.64162e34i 0.0838846 + 0.113651i
\(676\) 5.63802e34 0.238119
\(677\) 5.21912e33i 0.0216391i 0.999941 + 0.0108196i \(0.00344404\pi\)
−0.999941 + 0.0108196i \(0.996556\pi\)
\(678\) 5.73520e34i 0.233441i
\(679\) 4.01507e35 1.60443
\(680\) 8.93960e34 2.94184e34i 0.350717 0.115414i
\(681\) −5.01978e35 −1.93351
\(682\) 1.61248e35i 0.609804i
\(683\) 3.69358e34i 0.137148i 0.997646 + 0.0685739i \(0.0218449\pi\)
−0.997646 + 0.0685739i \(0.978155\pi\)
\(684\) −2.29266e35 −0.835870
\(685\) −1.07458e35 3.26542e35i −0.384688 1.16898i
\(686\) −7.58477e34 −0.266619
\(687\) 1.19023e35i 0.410838i
\(688\) 9.01830e34i 0.305681i
\(689\) −1.18511e35 −0.394474
\(690\) −2.59346e34 7.88095e34i −0.0847746 0.257611i
\(691\) 1.05074e35 0.337304 0.168652 0.985676i \(-0.446059\pi\)
0.168652 + 0.985676i \(0.446059\pi\)
\(692\) 3.34166e35i 1.05350i
\(693\) 6.64671e35i 2.05798i
\(694\) 4.94932e34 0.150505
\(695\) −5.06566e35 + 1.66700e35i −1.51295 + 0.497882i
\(696\) 5.93705e35 1.74163
\(697\) 1.49633e35i 0.431141i
\(698\) 7.28083e34i 0.206057i
\(699\) 7.96667e34 0.221469
\(700\) 2.03766e35 + 2.76072e35i 0.556424 + 0.753870i
\(701\) −1.02093e35 −0.273855 −0.136928 0.990581i \(-0.543723\pi\)
−0.136928 + 0.990581i \(0.543723\pi\)
\(702\) 2.23083e34i 0.0587832i
\(703\) 5.47095e35i 1.41619i
\(704\) −1.28744e35 −0.327392
\(705\) −9.49714e35 + 3.12532e35i −2.37262 + 0.780782i
\(706\) −1.68141e35 −0.412682
\(707\) 2.51763e35i 0.607084i
\(708\) 1.71185e35i 0.405556i
\(709\) −2.46590e35 −0.573981 −0.286990 0.957933i \(-0.592655\pi\)
−0.286990 + 0.957933i \(0.592655\pi\)
\(710\) 3.00861e34 + 9.14249e34i 0.0688076 + 0.209091i
\(711\) 5.35988e35 1.20444
\(712\) 1.78872e35i 0.394951i
\(713\) 1.38637e35i 0.300789i
\(714\) −1.80585e35 −0.384994
\(715\) 1.83664e35 + 5.58115e35i 0.384768 + 1.16923i
\(716\) 2.37315e35 0.488555
\(717\) 5.80736e35i 1.17487i
\(718\) 2.03234e35i 0.404056i
\(719\) −8.52137e34 −0.166494 −0.0832470 0.996529i \(-0.526529\pi\)
−0.0832470 + 0.996529i \(0.526529\pi\)
\(720\) 1.63645e35 5.38523e34i 0.314230 0.103407i
\(721\) 7.02487e35 1.32571
\(722\) 1.18235e34i 0.0219296i
\(723\) 4.45340e35i 0.811827i
\(724\) −7.91804e35 −1.41868
\(725\) 6.23969e35 4.60545e35i 1.09885 0.811049i
\(726\) 5.17478e35 0.895744
\(727\) 9.18354e35i 1.56254i −0.624196 0.781268i \(-0.714573\pi\)
0.624196 0.781268i \(-0.285427\pi\)
\(728\) 5.45849e35i 0.912915i
\(729\) 7.20568e35 1.18463
\(730\) −5.12803e34 + 1.68753e34i −0.0828733 + 0.0272719i
\(731\) 2.67691e35 0.425271
\(732\) 3.22845e33i 0.00504203i
\(733\) 2.21685e35i 0.340358i −0.985413 0.170179i \(-0.945565\pi\)
0.985413 0.170179i \(-0.0544347\pi\)
\(734\) 5.61803e35 0.847975
\(735\) −1.76773e35 5.37173e35i −0.262315 0.797118i
\(736\) −2.62737e35 −0.383308
\(737\) 1.44309e36i 2.06990i
\(738\) 4.03630e35i 0.569218i
\(739\) 6.47256e35 0.897472 0.448736 0.893664i \(-0.351874\pi\)
0.448736 + 0.893664i \(0.351874\pi\)
\(740\) −2.36990e35 7.20161e35i −0.323098 0.981823i
\(741\) −9.10488e35 −1.22052
\(742\) 2.29965e35i 0.303119i
\(743\) 3.13033e35i 0.405723i 0.979207 + 0.202861i \(0.0650241\pi\)
−0.979207 + 0.202861i \(0.934976\pi\)
\(744\) −8.10711e35 −1.03325
\(745\) −4.34711e35 + 1.43054e35i −0.544813 + 0.179287i
\(746\) −6.20616e35 −0.764870
\(747\) 2.28596e35i 0.277052i
\(748\) 3.91362e35i 0.466454i
\(749\) −1.10636e36 −1.29681
\(750\) −3.66704e35 + 5.16880e35i −0.422717 + 0.595832i
\(751\) 1.24295e36 1.40914 0.704569 0.709635i \(-0.251140\pi\)
0.704569 + 0.709635i \(0.251140\pi\)
\(752\) 4.66210e35i 0.519827i
\(753\) 3.64739e35i 0.399987i
\(754\) 5.26938e35 0.568353
\(755\) 6.78763e35 2.23367e35i 0.720080 0.236964i
\(756\) −1.26841e35 −0.132354
\(757\) 2.50689e35i 0.257298i 0.991690 + 0.128649i \(0.0410641\pi\)
−0.991690 + 0.128649i \(0.958936\pi\)
\(758\) 5.95255e35i 0.600950i
\(759\) 8.07779e35 0.802178
\(760\) −2.87816e35 8.74608e35i −0.281154 0.854365i
\(761\) −1.75153e36 −1.68309 −0.841547 0.540183i \(-0.818355\pi\)
−0.841547 + 0.540183i \(0.818355\pi\)
\(762\) 1.04092e36i 0.983968i
\(763\) 1.03789e36i 0.965147i
\(764\) −9.24418e35 −0.845670
\(765\) 1.59850e35 + 4.85749e35i 0.143862 + 0.437164i
\(766\) −8.77841e35 −0.777242
\(767\) 3.55721e35i 0.309861i
\(768\) 1.15665e36i 0.991257i
\(769\) 1.03505e36 0.872731 0.436366 0.899769i \(-0.356265\pi\)
0.436366 + 0.899769i \(0.356265\pi\)
\(770\) 1.08300e36 3.56392e35i 0.898447 0.295661i
\(771\) −1.19637e36 −0.976531
\(772\) 1.11098e36i 0.892258i
\(773\) 8.74798e35i 0.691296i −0.938364 0.345648i \(-0.887659\pi\)
0.938364 0.345648i \(-0.112341\pi\)
\(774\) −7.22084e35 −0.561469
\(775\) −8.52037e35 + 6.28879e35i −0.651909 + 0.481167i
\(776\) 1.49305e36 1.12409
\(777\) 3.40602e36i 2.52339i
\(778\) 3.33616e35i 0.243222i
\(779\) 1.46394e36 1.05028
\(780\) 1.19851e36 3.94405e35i 0.846171 0.278458i
\(781\) −9.37084e35 −0.651090
\(782\) 1.14836e35i 0.0785221i
\(783\) 2.86681e35i 0.192920i
\(784\) −2.63696e35 −0.174644
\(785\) 2.96055e35 + 8.99644e35i 0.192975 + 0.586408i
\(786\) 6.59103e35 0.422835
\(787\) 5.62209e35i 0.354988i −0.984122 0.177494i \(-0.943201\pi\)
0.984122 0.177494i \(-0.0567990\pi\)
\(788\) 4.03339e35i 0.250664i
\(789\) 2.27652e36 1.39254
\(790\) 2.87393e35 + 8.73322e35i 0.173036 + 0.525819i
\(791\) 6.77614e35 0.401584
\(792\) 2.47165e36i 1.44186i
\(793\) 6.70868e33i 0.00385232i
\(794\) −4.62453e35 −0.261403
\(795\) 1.18218e36 3.89031e35i 0.657800 0.216469i
\(796\) −2.15096e36 −1.17820
\(797\) 1.39898e36i 0.754369i −0.926138 0.377184i \(-0.876892\pi\)
0.926138 0.377184i \(-0.123108\pi\)
\(798\) 1.76676e36i 0.937866i
\(799\) −1.38386e36 −0.723196
\(800\) 1.19181e36 + 1.61473e36i 0.613173 + 0.830757i
\(801\) −9.71936e35 −0.492301
\(802\) 4.40692e35i 0.219763i
\(803\) 5.25611e35i 0.258060i
\(804\) 3.09892e36 1.49799
\(805\) 9.31134e35 3.06417e35i 0.443163 0.145836i
\(806\) −7.19540e35 −0.337184
\(807\) 4.04768e35i 0.186761i
\(808\) 9.36206e35i 0.425333i
\(809\) −1.99727e36 −0.893469 −0.446734 0.894667i \(-0.647413\pi\)
−0.446734 + 0.894667i \(0.647413\pi\)
\(810\) 3.19640e35 + 9.71316e35i 0.140799 + 0.427856i
\(811\) −1.75537e36 −0.761393 −0.380696 0.924700i \(-0.624316\pi\)
−0.380696 + 0.924700i \(0.624316\pi\)
\(812\) 2.99606e36i 1.27968i
\(813\) 2.09775e36i 0.882310i
\(814\) −2.51916e36 −1.04340
\(815\) 3.95929e35 + 1.20314e36i 0.161491 + 0.490734i
\(816\) 4.55714e35 0.183048
\(817\) 2.61896e36i 1.03598i
\(818\) 1.39677e35i 0.0544136i
\(819\) −2.96597e36 −1.13794
\(820\) −1.92704e36 + 6.34150e35i −0.728145 + 0.239618i
\(821\) 1.90029e36 0.707181 0.353591 0.935400i \(-0.384961\pi\)
0.353591 + 0.935400i \(0.384961\pi\)
\(822\) 2.45292e36i 0.899052i
\(823\) 1.45322e35i 0.0524606i −0.999656 0.0262303i \(-0.991650\pi\)
0.999656 0.0262303i \(-0.00835033\pi\)
\(824\) 2.61227e36 0.928813
\(825\) −3.66420e36 4.96444e36i −1.28323 1.73859i
\(826\) −6.90259e35 −0.238101
\(827\) 1.69798e36i 0.576918i 0.957492 + 0.288459i \(0.0931428\pi\)
−0.957492 + 0.288459i \(0.906857\pi\)
\(828\) 9.07651e35i 0.303766i
\(829\) 1.42211e35 0.0468816 0.0234408 0.999725i \(-0.492538\pi\)
0.0234408 + 0.999725i \(0.492538\pi\)
\(830\) −3.72467e35 + 1.22571e35i −0.120952 + 0.0398028i
\(831\) −2.05221e36 −0.656460
\(832\) 5.74495e35i 0.181027i
\(833\) 7.82730e35i 0.242968i
\(834\) 3.80521e36 1.16360
\(835\) −3.17330e35 9.64297e35i −0.0955940 0.290489i
\(836\) 3.82890e36 1.13631
\(837\) 3.91466e35i 0.114453i
\(838\) 1.60722e36i 0.462941i
\(839\) −1.73838e36 −0.493311 −0.246656 0.969103i \(-0.579332\pi\)
−0.246656 + 0.969103i \(0.579332\pi\)
\(840\) −1.79184e36 5.44499e36i −0.500965 1.52232i
\(841\) 3.14124e36 0.865269
\(842\) 1.82438e36i 0.495124i
\(843\) 9.26560e36i 2.47759i
\(844\) −1.17921e36 −0.310678
\(845\) −1.16868e36 + 3.84588e35i −0.303379 + 0.0998359i
\(846\) 3.73289e36 0.954807
\(847\) 6.11400e36i 1.54093i
\(848\) 5.80326e35i 0.144120i
\(849\) 3.12439e34 0.00764574
\(850\) −7.05755e35 + 5.20910e35i −0.170183 + 0.125611i
\(851\) −2.16592e36 −0.514662
\(852\) 2.01231e36i 0.471195i
\(853\) 5.78242e36i 1.33428i 0.744933 + 0.667139i \(0.232481\pi\)
−0.744933 + 0.667139i \(0.767519\pi\)
\(854\) 1.30179e34 0.00296017
\(855\) 4.75234e36 1.56390e36i 1.06495 0.350455i
\(856\) −4.11413e36 −0.908566
\(857\) 4.03252e36i 0.877640i −0.898575 0.438820i \(-0.855397\pi\)
0.898575 0.438820i \(-0.144603\pi\)
\(858\) 4.19244e36i 0.899241i
\(859\) 5.20623e36 1.10055 0.550274 0.834984i \(-0.314523\pi\)
0.550274 + 0.834984i \(0.314523\pi\)
\(860\) 1.13448e36 + 3.44743e36i 0.236356 + 0.718232i
\(861\) 9.11398e36 1.87141
\(862\) 2.90853e36i 0.588618i
\(863\) 5.25366e36i 1.04792i −0.851744 0.523958i \(-0.824455\pi\)
0.851744 0.523958i \(-0.175545\pi\)
\(864\) −7.41882e35 −0.145852
\(865\) 2.27945e36 + 6.92676e36i 0.441702 + 1.34223i
\(866\) 2.95640e36 0.564664
\(867\) 6.34025e36i 1.19363i
\(868\) 4.09115e36i 0.759188i
\(869\) −8.95135e36 −1.63735
\(870\) −5.25635e36 + 1.72976e36i −0.947750 + 0.311885i
\(871\) 6.43952e36 1.14453
\(872\) 3.85949e36i 0.676199i
\(873\) 8.11275e36i 1.40117i
\(874\) −1.12350e36 −0.191284
\(875\) −6.10693e36 4.33260e36i −1.02500 0.727190i
\(876\) −1.12871e36 −0.186759
\(877\) 8.98820e36i 1.46615i −0.680149 0.733074i \(-0.738085\pi\)
0.680149 0.733074i \(-0.261915\pi\)
\(878\) 3.85571e36i 0.620045i
\(879\) −1.38178e37 −2.19067
\(880\) −2.73299e36 + 8.99370e35i −0.427173 + 0.140574i
\(881\) 7.27878e36 1.12166 0.560828 0.827933i \(-0.310483\pi\)
0.560828 + 0.827933i \(0.310483\pi\)
\(882\) 2.11138e36i 0.320782i
\(883\) 1.06302e37i 1.59233i −0.605078 0.796166i \(-0.706858\pi\)
0.605078 0.796166i \(-0.293142\pi\)
\(884\) 1.74638e36 0.257920
\(885\) 1.16771e36 + 3.54841e36i 0.170037 + 0.516705i
\(886\) −2.06715e36 −0.296791
\(887\) 7.11036e36i 1.00658i 0.864119 + 0.503288i \(0.167876\pi\)
−0.864119 + 0.503288i \(0.832124\pi\)
\(888\) 1.26656e37i 1.76793i
\(889\) 1.22985e37 1.69270
\(890\) −5.21145e35 1.58364e36i −0.0707267 0.214923i
\(891\) −9.95577e36 −1.33230
\(892\) 2.37770e36i 0.313760i
\(893\) 1.35390e37i 1.76174i
\(894\) 3.26546e36 0.419011
\(895\) −4.91919e36 + 1.61880e36i −0.622451 + 0.204836i
\(896\) −9.28457e36 −1.15854
\(897\) 3.60456e36i 0.443555i
\(898\) 4.18583e35i 0.0507958i
\(899\) −9.24670e36 −1.10660
\(900\) −5.57823e36 + 4.11723e36i −0.658362 + 0.485930i
\(901\) 1.72259e36 0.200503
\(902\) 6.74089e36i 0.773812i
\(903\) 1.63047e37i 1.84593i
\(904\) 2.51978e36 0.281356
\(905\) 1.64129e37 5.40115e36i 1.80750 0.594811i
\(906\) −5.09872e36 −0.553808
\(907\) 2.31903e35i 0.0248437i 0.999923 + 0.0124218i \(0.00395409\pi\)
−0.999923 + 0.0124218i \(0.996046\pi\)
\(908\) 9.41987e36i 0.995341i
\(909\) 5.08705e36 0.530173
\(910\) −1.59033e36 4.83266e36i −0.163482 0.496786i
\(911\) 1.71872e37 1.74271 0.871353 0.490656i \(-0.163243\pi\)
0.871353 + 0.490656i \(0.163243\pi\)
\(912\) 4.45849e36i 0.445915i
\(913\) 3.81771e36i 0.376632i
\(914\) −6.69486e36 −0.651500
\(915\) −2.20223e34 6.69209e34i −0.00211397 0.00642389i
\(916\) −2.23352e36 −0.211493
\(917\) 7.78730e36i 0.727395i
\(918\) 3.24257e35i 0.0298783i
\(919\) 1.57745e37 1.43387 0.716937 0.697138i \(-0.245543\pi\)
0.716937 + 0.697138i \(0.245543\pi\)
\(920\) 3.46252e36 1.13944e36i 0.310488 0.102175i
\(921\) −8.75346e36 −0.774344
\(922\) 1.54402e34i 0.00134746i
\(923\) 4.18156e36i 0.360012i
\(924\) 2.38373e37 2.02469
\(925\) 9.82491e36 + 1.33113e37i 0.823297 + 1.11544i
\(926\) 2.87612e36 0.237777
\(927\) 1.41943e37i 1.15775i
\(928\) 1.75238e37i 1.41019i
\(929\) −2.16681e37 −1.72038 −0.860189 0.509975i \(-0.829655\pi\)
−0.860189 + 0.509975i \(0.829655\pi\)
\(930\) 7.17761e36 2.36201e36i 0.562268 0.185031i
\(931\) −7.65786e36 −0.591884
\(932\) 1.49499e36i 0.114009i
\(933\) 1.45923e37i 1.09800i
\(934\) 7.91026e36 0.587293
\(935\) −2.66961e36 8.11234e36i −0.195570 0.594294i
\(936\) −1.10293e37 −0.797258
\(937\) 2.38865e37i 1.70376i 0.523740 + 0.851878i \(0.324536\pi\)
−0.523740 + 0.851878i \(0.675464\pi\)
\(938\) 1.24956e37i 0.879470i
\(939\) −1.59707e36 −0.110919
\(940\) −5.86481e36 1.78219e37i −0.401935 1.22139i
\(941\) −2.60228e37 −1.75989 −0.879943 0.475080i \(-0.842419\pi\)
−0.879943 + 0.475080i \(0.842419\pi\)
\(942\) 6.75794e36i 0.451002i
\(943\) 5.79566e36i 0.381686i
\(944\) 1.74190e36 0.113207
\(945\) 2.62921e36 8.65220e35i 0.168627 0.0554918i
\(946\) 1.20593e37 0.763278
\(947\) 6.01381e36i 0.375643i −0.982203 0.187821i \(-0.939857\pi\)
0.982203 0.187821i \(-0.0601426\pi\)
\(948\) 1.92223e37i 1.18495i
\(949\) −2.34544e36 −0.142691
\(950\) 5.09634e36 + 6.90477e36i 0.305994 + 0.414576i
\(951\) −1.14328e37 −0.677482
\(952\) 7.93405e36i 0.464016i
\(953\) 7.32290e36i 0.422690i 0.977412 + 0.211345i \(0.0677843\pi\)
−0.977412 + 0.211345i \(0.932216\pi\)
\(954\) −4.64660e36 −0.264716
\(955\) 1.91618e37 6.30575e36i 1.07744 0.354564i
\(956\) 1.08978e37 0.604805
\(957\) 5.38764e37i 2.95121i
\(958\) 2.03851e36i 0.110216i
\(959\) −2.89812e37 −1.54662
\(960\) −1.88587e36 5.73074e36i −0.0993394 0.301870i
\(961\) −6.60632e36 −0.343493
\(962\) 1.12413e37i 0.576936i
\(963\) 2.23549e37i 1.13252i
\(964\) −8.35703e36 −0.417916
\(965\) 7.57837e36 + 2.30290e37i 0.374097 + 1.13680i
\(966\) −6.99448e36 −0.340833
\(967\) 1.82355e37i 0.877174i −0.898689 0.438587i \(-0.855479\pi\)
0.898689 0.438587i \(-0.144521\pi\)
\(968\) 2.27355e37i 1.07960i
\(969\) 1.32342e37 0.620368
\(970\) −1.32187e37 + 4.34999e36i −0.611704 + 0.201299i
\(971\) −1.93748e37 −0.885111 −0.442555 0.896741i \(-0.645928\pi\)
−0.442555 + 0.896741i \(0.645928\pi\)
\(972\) 2.37144e37i 1.06951i
\(973\) 4.49586e37i 2.00171i
\(974\) 7.81757e36 0.343625
\(975\) −2.21529e37 + 1.63508e37i −0.961331 + 0.709548i
\(976\) −3.28512e34 −0.00140743
\(977\) 4.13548e37i 1.74922i −0.484828 0.874610i \(-0.661118\pi\)
0.484828 0.874610i \(-0.338882\pi\)
\(978\) 9.03774e36i 0.377419i
\(979\) 1.62320e37 0.669249
\(980\) 1.00803e37 3.31723e36i 0.410344 0.135036i
\(981\) 2.09713e37 0.842872
\(982\) 1.97795e37i 0.784915i
\(983\) 8.53182e36i 0.334289i −0.985932 0.167145i \(-0.946545\pi\)
0.985932 0.167145i \(-0.0534547\pi\)
\(984\) 3.38913e37 1.31114
\(985\) −2.75131e36 8.36061e36i −0.105096 0.319363i
\(986\) −7.65918e36 −0.288882
\(987\) 8.42888e37i 3.13910i
\(988\) 1.70858e37i 0.628308i
\(989\) 1.03683e37 0.376490
\(990\) 7.20115e36 + 2.18827e37i 0.258203 + 0.784623i
\(991\) 9.57286e36 0.338939 0.169469 0.985535i \(-0.445795\pi\)
0.169469 + 0.985535i \(0.445795\pi\)
\(992\) 2.39289e37i 0.836617i
\(993\) 6.02279e37i 2.07937i
\(994\) 8.11412e36 0.276638
\(995\) 4.45862e37 1.46724e37i 1.50111 0.493985i
\(996\) −8.19822e36 −0.272570
\(997\) 3.61670e37i 1.18747i 0.804660 + 0.593736i \(0.202347\pi\)
−0.804660 + 0.593736i \(0.797653\pi\)
\(998\) 2.90032e37i 0.940402i
\(999\) −6.11583e36 −0.195833
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 5.26.b.a.4.8 yes 12
3.2 odd 2 45.26.b.b.19.5 12
5.2 odd 4 25.26.a.f.1.5 12
5.3 odd 4 25.26.a.f.1.8 12
5.4 even 2 inner 5.26.b.a.4.5 12
15.14 odd 2 45.26.b.b.19.8 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.26.b.a.4.5 12 5.4 even 2 inner
5.26.b.a.4.8 yes 12 1.1 even 1 trivial
25.26.a.f.1.5 12 5.2 odd 4
25.26.a.f.1.8 12 5.3 odd 4
45.26.b.b.19.5 12 3.2 odd 2
45.26.b.b.19.8 12 15.14 odd 2