Properties

Label 36.33.d.b.19.5
Level $36$
Weight $33$
Character 36.19
Analytic conductor $233.520$
Analytic rank $0$
Dimension $14$
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] = [36,33,Mod(19,36)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(36, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 33, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("36.19");
 
S:= CuspForms(chi, 33);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 33 \)
Character orbit: \([\chi]\) \(=\) 36.d (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: \(233.519958512\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} + \cdots + 14\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{182}\cdot 3^{29}\cdot 5^{6} \)
Twist minimal: no (minimal twist has level 4)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.5
Root \(-1.70126e9 - 1.38274e12i\) of defining polynomial
Character \(\chi\) \(=\) 36.19
Dual form 36.33.d.b.19.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-32011.4 - 57186.0i) q^{2} +(-2.24550e9 + 3.66121e9i) q^{4} +4.45746e10 q^{5} +4.42477e13i q^{7} +(2.81252e14 + 1.12108e13i) q^{8} +O(q^{10})\) \(q+(-32011.4 - 57186.0i) q^{2} +(-2.24550e9 + 3.66121e9i) q^{4} +4.45746e10 q^{5} +4.42477e13i q^{7} +(2.81252e14 + 1.12108e13i) q^{8} +(-1.42690e15 - 2.54904e15i) q^{10} +2.28722e16i q^{11} -7.09707e17 q^{13} +(2.53035e18 - 1.41643e18i) q^{14} +(-8.36217e18 - 1.64425e19i) q^{16} +5.13492e19 q^{17} -9.08704e19i q^{19} +(-1.00093e20 + 1.63197e20i) q^{20} +(1.30797e21 - 7.32171e20i) q^{22} +3.40920e21i q^{23} -2.12962e22 q^{25} +(2.27187e22 + 4.05853e22i) q^{26} +(-1.62000e23 - 9.93584e22i) q^{28} +9.75903e22 q^{29} -8.90972e23i q^{31} +(-6.72597e23 + 1.00455e24i) q^{32} +(-1.64376e24 - 2.93645e24i) q^{34} +1.97232e24i q^{35} -1.36985e25 q^{37} +(-5.19651e24 + 2.90889e24i) q^{38} +(1.25367e25 + 4.99716e23i) q^{40} -9.45224e25 q^{41} +2.05450e26i q^{43} +(-8.37398e25 - 5.13596e25i) q^{44} +(1.94959e26 - 1.09133e26i) q^{46} -6.70394e25i q^{47} -8.53431e26 q^{49} +(6.81721e26 + 1.21784e27i) q^{50} +(1.59365e27 - 2.59839e27i) q^{52} +3.12663e27 q^{53} +1.01952e27i q^{55} +(-4.96051e26 + 1.24447e28i) q^{56} +(-3.12400e27 - 5.58079e27i) q^{58} -4.03005e28i q^{59} -4.61340e28 q^{61} +(-5.09511e28 + 2.85213e28i) q^{62} +(7.89768e28 + 6.30610e27i) q^{64} -3.16349e28 q^{65} +2.83386e29i q^{67} +(-1.15305e29 + 1.88000e29i) q^{68} +(1.12789e29 - 6.31369e28i) q^{70} +3.78115e29i q^{71} -8.28433e29 q^{73} +(4.38508e29 + 7.83360e29i) q^{74} +(3.32696e29 + 2.04050e29i) q^{76} -1.01204e30 q^{77} -3.22124e30i q^{79} +(-3.72740e29 - 7.32919e29i) q^{80} +(3.02580e30 + 5.40536e30i) q^{82} +3.96300e29i q^{83} +2.28887e30 q^{85} +(1.17489e31 - 6.57676e30i) q^{86} +(-2.56415e29 + 6.43284e30i) q^{88} -1.44641e31 q^{89} -3.14029e31i q^{91} +(-1.24818e31 - 7.65538e30i) q^{92} +(-3.83372e30 + 2.14603e30i) q^{94} -4.05052e30i q^{95} +5.69349e30 q^{97} +(2.73195e31 + 4.88043e31i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8} + 31\!\cdots\!00 q^{10}+ \cdots + 46\!\cdots\!00 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32011.4 57186.0i −0.488456 0.872589i
\(3\) 0 0
\(4\) −2.24550e9 + 3.66121e9i −0.522822 + 0.852442i
\(5\) 4.45746e10 0.292124 0.146062 0.989275i \(-0.453340\pi\)
0.146062 + 0.989275i \(0.453340\pi\)
\(6\) 0 0
\(7\) 4.42477e13i 1.33144i 0.746201 + 0.665721i \(0.231876\pi\)
−0.746201 + 0.665721i \(0.768124\pi\)
\(8\) 2.81252e14 + 1.12108e13i 0.999207 + 0.0398287i
\(9\) 0 0
\(10\) −1.42690e15 2.54904e15i −0.142690 0.254904i
\(11\) 2.28722e16i 0.497765i 0.968534 + 0.248883i \(0.0800633\pi\)
−0.968534 + 0.248883i \(0.919937\pi\)
\(12\) 0 0
\(13\) −7.09707e17 −1.06656 −0.533280 0.845939i \(-0.679041\pi\)
−0.533280 + 0.845939i \(0.679041\pi\)
\(14\) 2.53035e18 1.41643e18i 1.16180 0.650350i
\(15\) 0 0
\(16\) −8.36217e18 1.64425e19i −0.453314 0.891351i
\(17\) 5.13492e19 1.05524 0.527619 0.849481i \(-0.323085\pi\)
0.527619 + 0.849481i \(0.323085\pi\)
\(18\) 0 0
\(19\) 9.08704e19i 0.315039i −0.987516 0.157520i \(-0.949650\pi\)
0.987516 0.157520i \(-0.0503498\pi\)
\(20\) −1.00093e20 + 1.63197e20i −0.152729 + 0.249019i
\(21\) 0 0
\(22\) 1.30797e21 7.32171e20i 0.434344 0.243136i
\(23\) 3.40920e21i 0.555914i 0.960594 + 0.277957i \(0.0896573\pi\)
−0.960594 + 0.277957i \(0.910343\pi\)
\(24\) 0 0
\(25\) −2.12962e22 −0.914663
\(26\) 2.27187e22 + 4.05853e22i 0.520967 + 0.930668i
\(27\) 0 0
\(28\) −1.62000e23 9.93584e22i −1.13498 0.696107i
\(29\) 9.75903e22 0.389977 0.194988 0.980806i \(-0.437533\pi\)
0.194988 + 0.980806i \(0.437533\pi\)
\(30\) 0 0
\(31\) 8.90972e23i 1.22483i −0.790535 0.612416i \(-0.790198\pi\)
0.790535 0.612416i \(-0.209802\pi\)
\(32\) −6.72597e23 + 1.00455e24i −0.556359 + 0.830942i
\(33\) 0 0
\(34\) −1.64376e24 2.93645e24i −0.515437 0.920789i
\(35\) 1.97232e24i 0.388946i
\(36\) 0 0
\(37\) −1.36985e25 −1.11031 −0.555155 0.831747i \(-0.687341\pi\)
−0.555155 + 0.831747i \(0.687341\pi\)
\(38\) −5.19651e24 + 2.90889e24i −0.274900 + 0.153883i
\(39\) 0 0
\(40\) 1.25367e25 + 4.99716e23i 0.291892 + 0.0116349i
\(41\) −9.45224e25 −1.48249 −0.741247 0.671232i \(-0.765765\pi\)
−0.741247 + 0.671232i \(0.765765\pi\)
\(42\) 0 0
\(43\) 2.05450e26i 1.50387i 0.659235 + 0.751937i \(0.270880\pi\)
−0.659235 + 0.751937i \(0.729120\pi\)
\(44\) −8.37398e25 5.13596e25i −0.424316 0.260243i
\(45\) 0 0
\(46\) 1.94959e26 1.09133e26i 0.485084 0.271539i
\(47\) 6.70394e25i 0.118240i −0.998251 0.0591200i \(-0.981171\pi\)
0.998251 0.0591200i \(-0.0188295\pi\)
\(48\) 0 0
\(49\) −8.53431e26 −0.772736
\(50\) 6.81721e26 + 1.21784e27i 0.446773 + 0.798125i
\(51\) 0 0
\(52\) 1.59365e27 2.59839e27i 0.557621 0.909180i
\(53\) 3.12663e27 0.806609 0.403305 0.915066i \(-0.367861\pi\)
0.403305 + 0.915066i \(0.367861\pi\)
\(54\) 0 0
\(55\) 1.01952e27i 0.145409i
\(56\) −4.96051e26 + 1.24447e28i −0.0530296 + 1.33038i
\(57\) 0 0
\(58\) −3.12400e27 5.58079e27i −0.190486 0.340289i
\(59\) 4.03005e28i 1.86930i −0.355572 0.934649i \(-0.615714\pi\)
0.355572 0.934649i \(-0.384286\pi\)
\(60\) 0 0
\(61\) −4.61340e28 −1.25529 −0.627644 0.778500i \(-0.715981\pi\)
−0.627644 + 0.778500i \(0.715981\pi\)
\(62\) −5.09511e28 + 2.85213e28i −1.06878 + 0.598276i
\(63\) 0 0
\(64\) 7.89768e28 + 6.30610e27i 0.996827 + 0.0795942i
\(65\) −3.16349e28 −0.311568
\(66\) 0 0
\(67\) 2.83386e29i 1.71863i 0.511448 + 0.859314i \(0.329109\pi\)
−0.511448 + 0.859314i \(0.670891\pi\)
\(68\) −1.15305e29 + 1.88000e29i −0.551702 + 0.899529i
\(69\) 0 0
\(70\) 1.12789e29 6.31369e28i 0.339390 0.189983i
\(71\) 3.78115e29i 0.906756i 0.891318 + 0.453378i \(0.149781\pi\)
−0.891318 + 0.453378i \(0.850219\pi\)
\(72\) 0 0
\(73\) −8.28433e29 −1.27377 −0.636886 0.770958i \(-0.719778\pi\)
−0.636886 + 0.770958i \(0.719778\pi\)
\(74\) 4.38508e29 + 7.83360e29i 0.542337 + 0.968845i
\(75\) 0 0
\(76\) 3.32696e29 + 2.04050e29i 0.268553 + 0.164710i
\(77\) −1.01204e30 −0.662745
\(78\) 0 0
\(79\) 3.22124e30i 1.39955i −0.714362 0.699776i \(-0.753283\pi\)
0.714362 0.699776i \(-0.246717\pi\)
\(80\) −3.72740e29 7.32919e29i −0.132424 0.260385i
\(81\) 0 0
\(82\) 3.02580e30 + 5.40536e30i 0.724133 + 1.29361i
\(83\) 3.96300e29i 0.0781223i 0.999237 + 0.0390611i \(0.0124367\pi\)
−0.999237 + 0.0390611i \(0.987563\pi\)
\(84\) 0 0
\(85\) 2.28887e30 0.308261
\(86\) 1.17489e31 6.57676e30i 1.31226 0.734576i
\(87\) 0 0
\(88\) −2.56415e29 + 6.43284e30i −0.0198253 + 0.497370i
\(89\) −1.44641e31 −0.933363 −0.466682 0.884425i \(-0.654551\pi\)
−0.466682 + 0.884425i \(0.654551\pi\)
\(90\) 0 0
\(91\) 3.14029e31i 1.42006i
\(92\) −1.24818e31 7.65538e30i −0.473884 0.290644i
\(93\) 0 0
\(94\) −3.83372e30 + 2.14603e30i −0.103175 + 0.0577550i
\(95\) 4.05052e30i 0.0920307i
\(96\) 0 0
\(97\) 5.69349e30 0.0926896 0.0463448 0.998926i \(-0.485243\pi\)
0.0463448 + 0.998926i \(0.485243\pi\)
\(98\) 2.73195e31 + 4.88043e31i 0.377447 + 0.674280i
\(99\) 0 0
\(100\) 4.78206e31 7.79697e31i 0.478206 0.779697i
\(101\) 1.45062e32 1.23712 0.618559 0.785738i \(-0.287717\pi\)
0.618559 + 0.785738i \(0.287717\pi\)
\(102\) 0 0
\(103\) 2.12151e32i 1.32206i 0.750362 + 0.661028i \(0.229879\pi\)
−0.750362 + 0.661028i \(0.770121\pi\)
\(104\) −1.99606e32 7.95637e30i −1.06571 0.0424797i
\(105\) 0 0
\(106\) −1.00088e32 1.78800e32i −0.393993 0.703838i
\(107\) 4.23255e32i 1.43371i −0.697222 0.716855i \(-0.745581\pi\)
0.697222 0.716855i \(-0.254419\pi\)
\(108\) 0 0
\(109\) 4.59934e32 1.15844 0.579218 0.815173i \(-0.303358\pi\)
0.579218 + 0.815173i \(0.303358\pi\)
\(110\) 5.83022e31 3.26362e31i 0.126883 0.0710260i
\(111\) 0 0
\(112\) 7.27544e32 3.70007e32i 1.18678 0.603561i
\(113\) 5.97121e32 0.844904 0.422452 0.906385i \(-0.361170\pi\)
0.422452 + 0.906385i \(0.361170\pi\)
\(114\) 0 0
\(115\) 1.51964e32i 0.162396i
\(116\) −2.19139e32 + 3.57298e32i −0.203888 + 0.332432i
\(117\) 0 0
\(118\) −2.30462e33 + 1.29008e33i −1.63113 + 0.913069i
\(119\) 2.27208e33i 1.40499i
\(120\) 0 0
\(121\) 1.58824e33 0.752230
\(122\) 1.47681e33 + 2.63822e33i 0.613153 + 1.09535i
\(123\) 0 0
\(124\) 3.26203e33 + 2.00068e33i 1.04410 + 0.640370i
\(125\) −1.98710e33 −0.559320
\(126\) 0 0
\(127\) 3.79574e33i 0.828775i −0.910101 0.414387i \(-0.863996\pi\)
0.910101 0.414387i \(-0.136004\pi\)
\(128\) −2.16754e33 4.71823e33i −0.417453 0.908699i
\(129\) 0 0
\(130\) 1.01268e33 + 1.80907e33i 0.152187 + 0.271871i
\(131\) 2.68711e33i 0.357227i −0.983919 0.178614i \(-0.942839\pi\)
0.983919 0.178614i \(-0.0571612\pi\)
\(132\) 0 0
\(133\) 4.02081e33 0.419457
\(134\) 1.62057e34 9.07160e33i 1.49966 0.839474i
\(135\) 0 0
\(136\) 1.44420e34 + 5.75664e32i 1.05440 + 0.0420288i
\(137\) 1.03106e34 0.669509 0.334755 0.942305i \(-0.391347\pi\)
0.334755 + 0.942305i \(0.391347\pi\)
\(138\) 0 0
\(139\) 4.16304e33i 0.214375i −0.994239 0.107188i \(-0.965815\pi\)
0.994239 0.107188i \(-0.0341845\pi\)
\(140\) −7.22109e33 4.42886e33i −0.331554 0.203350i
\(141\) 0 0
\(142\) 2.16229e34 1.21040e34i 0.791225 0.442910i
\(143\) 1.62325e34i 0.530896i
\(144\) 0 0
\(145\) 4.35005e33 0.113922
\(146\) 2.65193e34 + 4.73748e34i 0.622181 + 1.11148i
\(147\) 0 0
\(148\) 3.07600e34 5.01530e34i 0.580495 0.946475i
\(149\) 6.24485e34 1.05814 0.529069 0.848579i \(-0.322541\pi\)
0.529069 + 0.848579i \(0.322541\pi\)
\(150\) 0 0
\(151\) 2.99336e34i 0.409759i 0.978787 + 0.204879i \(0.0656802\pi\)
−0.978787 + 0.204879i \(0.934320\pi\)
\(152\) 1.01873e33 2.55575e34i 0.0125476 0.314789i
\(153\) 0 0
\(154\) 3.23969e34 + 5.78745e34i 0.323722 + 0.578304i
\(155\) 3.97147e34i 0.357803i
\(156\) 0 0
\(157\) 1.31988e35 0.968593 0.484297 0.874904i \(-0.339076\pi\)
0.484297 + 0.874904i \(0.339076\pi\)
\(158\) −1.84210e35 + 1.03116e35i −1.22123 + 0.683619i
\(159\) 0 0
\(160\) −2.99807e34 + 4.47773e34i −0.162526 + 0.242738i
\(161\) −1.50849e35 −0.740167
\(162\) 0 0
\(163\) 1.20065e35i 0.483522i 0.970336 + 0.241761i \(0.0777250\pi\)
−0.970336 + 0.241761i \(0.922275\pi\)
\(164\) 2.12250e35 3.46066e35i 0.775081 1.26374i
\(165\) 0 0
\(166\) 2.26628e34 1.26861e34i 0.0681686 0.0381593i
\(167\) 6.52369e35i 1.78250i 0.453511 + 0.891251i \(0.350171\pi\)
−0.453511 + 0.891251i \(0.649829\pi\)
\(168\) 0 0
\(169\) 6.09044e34 0.137550
\(170\) −7.32700e34 1.30891e35i −0.150572 0.268985i
\(171\) 0 0
\(172\) −7.52197e35 4.61340e35i −1.28197 0.786259i
\(173\) 2.42455e35 0.376611 0.188305 0.982111i \(-0.439701\pi\)
0.188305 + 0.982111i \(0.439701\pi\)
\(174\) 0 0
\(175\) 9.42306e35i 1.21782i
\(176\) 3.76076e35 1.91261e35i 0.443683 0.225644i
\(177\) 0 0
\(178\) 4.63016e35 + 8.27143e35i 0.455907 + 0.814442i
\(179\) 2.94586e35i 0.265194i −0.991170 0.132597i \(-0.957668\pi\)
0.991170 0.132597i \(-0.0423316\pi\)
\(180\) 0 0
\(181\) −8.89528e35 −0.670351 −0.335176 0.942156i \(-0.608796\pi\)
−0.335176 + 0.942156i \(0.608796\pi\)
\(182\) −1.79580e36 + 1.00525e36i −1.23913 + 0.693637i
\(183\) 0 0
\(184\) −3.82198e34 + 9.58844e35i −0.0221413 + 0.555473i
\(185\) −6.10604e35 −0.324349
\(186\) 0 0
\(187\) 1.17447e36i 0.525261i
\(188\) 2.45445e35 + 1.50537e35i 0.100793 + 0.0618185i
\(189\) 0 0
\(190\) −2.31633e35 + 1.29663e35i −0.0803049 + 0.0449529i
\(191\) 6.11925e36i 1.95058i −0.220924 0.975291i \(-0.570907\pi\)
0.220924 0.975291i \(-0.429093\pi\)
\(192\) 0 0
\(193\) −7.19445e36 −1.94125 −0.970623 0.240607i \(-0.922653\pi\)
−0.970623 + 0.240607i \(0.922653\pi\)
\(194\) −1.82257e35 3.25588e35i −0.0452748 0.0808799i
\(195\) 0 0
\(196\) 1.91638e36 3.12459e36i 0.404003 0.658712i
\(197\) −8.26602e35 −0.160634 −0.0803169 0.996769i \(-0.525593\pi\)
−0.0803169 + 0.996769i \(0.525593\pi\)
\(198\) 0 0
\(199\) 1.58369e36i 0.261831i −0.991394 0.130916i \(-0.958208\pi\)
0.991394 0.130916i \(-0.0417917\pi\)
\(200\) −5.98958e36 2.38747e35i −0.913938 0.0364298i
\(201\) 0 0
\(202\) −4.64364e36 8.29550e36i −0.604277 1.07950i
\(203\) 4.31814e36i 0.519231i
\(204\) 0 0
\(205\) −4.21330e36 −0.433073
\(206\) 1.21321e37 6.79126e36i 1.15361 0.645765i
\(207\) 0 0
\(208\) 5.93469e36 + 1.16694e37i 0.483487 + 0.950679i
\(209\) 2.07840e36 0.156816
\(210\) 0 0
\(211\) 3.90069e36i 0.252710i −0.991985 0.126355i \(-0.959672\pi\)
0.991985 0.126355i \(-0.0403278\pi\)
\(212\) −7.02087e36 + 1.14473e37i −0.421713 + 0.687588i
\(213\) 0 0
\(214\) −2.42042e37 + 1.35490e37i −1.25104 + 0.700304i
\(215\) 9.15787e36i 0.439318i
\(216\) 0 0
\(217\) 3.94234e37 1.63079
\(218\) −1.47232e37 2.63018e37i −0.565844 1.01084i
\(219\) 0 0
\(220\) −3.73267e36 2.28933e36i −0.123953 0.0760232i
\(221\) −3.64428e37 −1.12548
\(222\) 0 0
\(223\) 1.06246e37i 0.284076i −0.989861 0.142038i \(-0.954635\pi\)
0.989861 0.142038i \(-0.0453655\pi\)
\(224\) −4.44489e37 2.97609e37i −1.10635 0.740759i
\(225\) 0 0
\(226\) −1.91147e37 3.41469e37i −0.412698 0.737253i
\(227\) 9.86501e36i 0.198465i 0.995064 + 0.0992325i \(0.0316388\pi\)
−0.995064 + 0.0992325i \(0.968361\pi\)
\(228\) 0 0
\(229\) −2.89076e37 −0.505410 −0.252705 0.967543i \(-0.581320\pi\)
−0.252705 + 0.967543i \(0.581320\pi\)
\(230\) 8.69021e36 4.86458e36i 0.141705 0.0793232i
\(231\) 0 0
\(232\) 2.74474e37 + 1.09406e36i 0.389667 + 0.0155323i
\(233\) 5.22180e37 0.692031 0.346015 0.938229i \(-0.387535\pi\)
0.346015 + 0.938229i \(0.387535\pi\)
\(234\) 0 0
\(235\) 2.98826e36i 0.0345408i
\(236\) 1.47549e38 + 9.04950e37i 1.59347 + 0.977310i
\(237\) 0 0
\(238\) 1.29931e38 7.27326e37i 1.22598 0.686274i
\(239\) 2.02819e38i 1.78955i −0.446522 0.894773i \(-0.647337\pi\)
0.446522 0.894773i \(-0.352663\pi\)
\(240\) 0 0
\(241\) 2.98788e37 0.230723 0.115361 0.993324i \(-0.463197\pi\)
0.115361 + 0.993324i \(0.463197\pi\)
\(242\) −5.08419e37 9.08251e37i −0.367431 0.656387i
\(243\) 0 0
\(244\) 1.03594e38 1.68906e38i 0.656293 1.07006i
\(245\) −3.80413e37 −0.225735
\(246\) 0 0
\(247\) 6.44914e37i 0.336009i
\(248\) 9.98849e36 2.50587e38i 0.0487835 1.22386i
\(249\) 0 0
\(250\) 6.36100e37 + 1.13634e38i 0.273203 + 0.488056i
\(251\) 4.02684e38i 1.62250i −0.584698 0.811251i \(-0.698787\pi\)
0.584698 0.811251i \(-0.301213\pi\)
\(252\) 0 0
\(253\) −7.79759e37 −0.276715
\(254\) −2.17063e38 + 1.21507e38i −0.723180 + 0.404820i
\(255\) 0 0
\(256\) −2.00431e38 + 2.74990e38i −0.589013 + 0.808124i
\(257\) −2.02522e38 −0.559167 −0.279583 0.960121i \(-0.590196\pi\)
−0.279583 + 0.960121i \(0.590196\pi\)
\(258\) 0 0
\(259\) 6.06126e38i 1.47831i
\(260\) 7.10363e37 1.15822e38i 0.162895 0.265594i
\(261\) 0 0
\(262\) −1.53665e38 + 8.60182e37i −0.311713 + 0.174490i
\(263\) 4.37514e38i 0.835027i 0.908671 + 0.417513i \(0.137098\pi\)
−0.908671 + 0.417513i \(0.862902\pi\)
\(264\) 0 0
\(265\) 1.39369e38 0.235630
\(266\) −1.28712e38 2.29934e38i −0.204886 0.366013i
\(267\) 0 0
\(268\) −1.03754e39 6.36345e38i −1.46503 0.898537i
\(269\) −9.84294e38 −1.30945 −0.654724 0.755868i \(-0.727215\pi\)
−0.654724 + 0.755868i \(0.727215\pi\)
\(270\) 0 0
\(271\) 5.82572e38i 0.688400i −0.938896 0.344200i \(-0.888150\pi\)
0.938896 0.344200i \(-0.111850\pi\)
\(272\) −4.29390e38 8.44310e38i −0.478354 0.940588i
\(273\) 0 0
\(274\) −3.30058e38 5.89624e38i −0.327026 0.584206i
\(275\) 4.87090e38i 0.455288i
\(276\) 0 0
\(277\) −7.68908e38 −0.640027 −0.320013 0.947413i \(-0.603687\pi\)
−0.320013 + 0.947413i \(0.603687\pi\)
\(278\) −2.38068e38 + 1.33265e38i −0.187061 + 0.104713i
\(279\) 0 0
\(280\) −2.21113e37 + 5.54719e38i −0.0154912 + 0.388638i
\(281\) 3.37707e38 0.223480 0.111740 0.993737i \(-0.464358\pi\)
0.111740 + 0.993737i \(0.464358\pi\)
\(282\) 0 0
\(283\) 2.20946e39i 1.30528i 0.757668 + 0.652641i \(0.226339\pi\)
−0.757668 + 0.652641i \(0.773661\pi\)
\(284\) −1.38436e39 8.49059e38i −0.772956 0.474072i
\(285\) 0 0
\(286\) −9.28273e38 + 5.19627e38i −0.463254 + 0.259319i
\(287\) 4.18240e39i 1.97385i
\(288\) 0 0
\(289\) 2.68825e38 0.113528
\(290\) −1.39251e38 2.48762e38i −0.0556457 0.0994067i
\(291\) 0 0
\(292\) 1.86025e39 3.03307e39i 0.665956 1.08582i
\(293\) −2.28152e39 −0.773291 −0.386646 0.922228i \(-0.626366\pi\)
−0.386646 + 0.922228i \(0.626366\pi\)
\(294\) 0 0
\(295\) 1.79638e39i 0.546067i
\(296\) −3.85272e39 1.53571e38i −1.10943 0.0442222i
\(297\) 0 0
\(298\) −1.99907e39 3.57118e39i −0.516853 0.923319i
\(299\) 2.41953e39i 0.592916i
\(300\) 0 0
\(301\) −9.09070e39 −2.00232
\(302\) 1.71178e39 9.58218e38i 0.357551 0.200149i
\(303\) 0 0
\(304\) −1.49414e39 + 7.59874e38i −0.280811 + 0.142812i
\(305\) −2.05641e39 −0.366700
\(306\) 0 0
\(307\) 9.88725e39i 1.58804i −0.607892 0.794020i \(-0.707984\pi\)
0.607892 0.794020i \(-0.292016\pi\)
\(308\) 2.27254e39 3.70529e39i 0.346498 0.564952i
\(309\) 0 0
\(310\) −2.27113e39 + 1.27133e39i −0.312215 + 0.174771i
\(311\) 2.75970e39i 0.360326i 0.983637 + 0.180163i \(0.0576625\pi\)
−0.983637 + 0.180163i \(0.942337\pi\)
\(312\) 0 0
\(313\) 3.86301e39 0.455215 0.227607 0.973753i \(-0.426910\pi\)
0.227607 + 0.973753i \(0.426910\pi\)
\(314\) −4.22514e39 7.54789e39i −0.473115 0.845183i
\(315\) 0 0
\(316\) 1.17936e40 + 7.23330e39i 1.19304 + 0.731717i
\(317\) −2.74902e39 −0.264381 −0.132190 0.991224i \(-0.542201\pi\)
−0.132190 + 0.991224i \(0.542201\pi\)
\(318\) 0 0
\(319\) 2.23210e39i 0.194117i
\(320\) 3.52036e39 + 2.81092e38i 0.291197 + 0.0232514i
\(321\) 0 0
\(322\) 4.82890e39 + 8.62647e39i 0.361539 + 0.645861i
\(323\) 4.66612e39i 0.332442i
\(324\) 0 0
\(325\) 1.51140e40 0.975543
\(326\) 6.86606e39 3.84347e39i 0.421916 0.236179i
\(327\) 0 0
\(328\) −2.65846e40 1.05967e39i −1.48132 0.0590458i
\(329\) 2.96634e39 0.157430
\(330\) 0 0
\(331\) 2.88587e39i 0.139005i 0.997582 + 0.0695023i \(0.0221411\pi\)
−0.997582 + 0.0695023i \(0.977859\pi\)
\(332\) −1.45094e39 8.89894e38i −0.0665947 0.0408441i
\(333\) 0 0
\(334\) 3.73064e40 2.08833e40i 1.55539 0.870673i
\(335\) 1.26318e40i 0.502053i
\(336\) 0 0
\(337\) −3.46962e39 −0.125373 −0.0626865 0.998033i \(-0.519967\pi\)
−0.0626865 + 0.998033i \(0.519967\pi\)
\(338\) −1.94964e39 3.48288e39i −0.0671873 0.120025i
\(339\) 0 0
\(340\) −5.13967e39 + 8.38003e39i −0.161166 + 0.262774i
\(341\) 2.03785e40 0.609679
\(342\) 0 0
\(343\) 1.11060e40i 0.302589i
\(344\) −2.30326e39 + 5.77832e40i −0.0598973 + 1.50268i
\(345\) 0 0
\(346\) −7.76132e39 1.38650e40i −0.183958 0.328626i
\(347\) 6.04708e39i 0.136859i −0.997656 0.0684296i \(-0.978201\pi\)
0.997656 0.0684296i \(-0.0217989\pi\)
\(348\) 0 0
\(349\) 2.56362e40 0.529232 0.264616 0.964354i \(-0.414755\pi\)
0.264616 + 0.964354i \(0.414755\pi\)
\(350\) −5.38867e40 + 3.01646e40i −1.06266 + 0.594851i
\(351\) 0 0
\(352\) −2.29762e40 1.53837e40i −0.413614 0.276936i
\(353\) 6.22211e40 1.07039 0.535195 0.844728i \(-0.320238\pi\)
0.535195 + 0.844728i \(0.320238\pi\)
\(354\) 0 0
\(355\) 1.68543e40i 0.264885i
\(356\) 3.24792e40 5.29560e40i 0.487983 0.795638i
\(357\) 0 0
\(358\) −1.68462e40 + 9.43012e39i −0.231405 + 0.129535i
\(359\) 6.52926e40i 0.857735i −0.903367 0.428867i \(-0.858913\pi\)
0.903367 0.428867i \(-0.141087\pi\)
\(360\) 0 0
\(361\) 7.49410e40 0.900750
\(362\) 2.84751e40 + 5.08685e40i 0.327437 + 0.584941i
\(363\) 0 0
\(364\) 1.14973e41 + 7.05153e40i 1.21052 + 0.742440i
\(365\) −3.69271e40 −0.372100
\(366\) 0 0
\(367\) 2.37914e39i 0.0219666i −0.999940 0.0109833i \(-0.996504\pi\)
0.999940 0.0109833i \(-0.00349617\pi\)
\(368\) 5.60559e40 2.85083e40i 0.495514 0.252004i
\(369\) 0 0
\(370\) 1.95463e40 + 3.49180e40i 0.158430 + 0.283023i
\(371\) 1.38346e41i 1.07395i
\(372\) 0 0
\(373\) −1.72340e41 −1.22756 −0.613782 0.789476i \(-0.710352\pi\)
−0.613782 + 0.789476i \(0.710352\pi\)
\(374\) 6.71630e40 3.75964e40i 0.458337 0.256567i
\(375\) 0 0
\(376\) 7.51564e38 1.88549e40i 0.00470935 0.118146i
\(377\) −6.92605e40 −0.415933
\(378\) 0 0
\(379\) 1.76915e41i 0.976199i −0.872788 0.488099i \(-0.837690\pi\)
0.872788 0.488099i \(-0.162310\pi\)
\(380\) 1.48298e40 + 9.09545e39i 0.0784508 + 0.0481157i
\(381\) 0 0
\(382\) −3.49935e41 + 1.95886e41i −1.70206 + 0.952773i
\(383\) 4.14172e41i 1.93197i 0.258600 + 0.965984i \(0.416739\pi\)
−0.258600 + 0.965984i \(0.583261\pi\)
\(384\) 0 0
\(385\) −4.51113e40 −0.193604
\(386\) 2.30304e41 + 4.11421e41i 0.948212 + 1.69391i
\(387\) 0 0
\(388\) −1.27848e40 + 2.08451e40i −0.0484602 + 0.0790125i
\(389\) −9.84662e40 −0.358174 −0.179087 0.983833i \(-0.557314\pi\)
−0.179087 + 0.983833i \(0.557314\pi\)
\(390\) 0 0
\(391\) 1.75060e41i 0.586622i
\(392\) −2.40029e41 9.56762e39i −0.772122 0.0307770i
\(393\) 0 0
\(394\) 2.64607e40 + 4.72701e40i 0.0784625 + 0.140167i
\(395\) 1.43585e41i 0.408843i
\(396\) 0 0
\(397\) 2.57975e40 0.0677530 0.0338765 0.999426i \(-0.489215\pi\)
0.0338765 + 0.999426i \(0.489215\pi\)
\(398\) −9.05649e40 + 5.06962e40i −0.228471 + 0.127893i
\(399\) 0 0
\(400\) 1.78082e41 + 3.50163e41i 0.414630 + 0.815286i
\(401\) 1.27557e41 0.285360 0.142680 0.989769i \(-0.454428\pi\)
0.142680 + 0.989769i \(0.454428\pi\)
\(402\) 0 0
\(403\) 6.32329e41i 1.30636i
\(404\) −3.25737e41 + 5.31102e41i −0.646793 + 1.05457i
\(405\) 0 0
\(406\) 2.46937e41 1.38230e41i 0.453075 0.253621i
\(407\) 3.13314e41i 0.552674i
\(408\) 0 0
\(409\) 7.78521e41 1.26969 0.634844 0.772640i \(-0.281064\pi\)
0.634844 + 0.772640i \(0.281064\pi\)
\(410\) 1.34874e41 + 2.40942e41i 0.211537 + 0.377894i
\(411\) 0 0
\(412\) −7.76729e41 4.76386e41i −1.12698 0.691200i
\(413\) 1.78321e42 2.48886
\(414\) 0 0
\(415\) 1.76649e40i 0.0228214i
\(416\) 4.77346e41 7.12934e41i 0.593390 0.886250i
\(417\) 0 0
\(418\) −6.65327e40 1.18856e41i −0.0765975 0.136836i
\(419\) 4.49421e41i 0.498000i 0.968503 + 0.249000i \(0.0801019\pi\)
−0.968503 + 0.249000i \(0.919898\pi\)
\(420\) 0 0
\(421\) −4.94700e40 −0.0507959 −0.0253979 0.999677i \(-0.508085\pi\)
−0.0253979 + 0.999677i \(0.508085\pi\)
\(422\) −2.23065e41 + 1.24867e41i −0.220512 + 0.123438i
\(423\) 0 0
\(424\) 8.79371e41 + 3.50520e40i 0.805969 + 0.0321262i
\(425\) −1.09354e42 −0.965188
\(426\) 0 0
\(427\) 2.04132e42i 1.67134i
\(428\) 1.54963e42 + 9.50421e41i 1.22216 + 0.749576i
\(429\) 0 0
\(430\) 5.23702e41 2.93157e41i 0.383344 0.214587i
\(431\) 2.94290e41i 0.207558i −0.994600 0.103779i \(-0.966907\pi\)
0.994600 0.103779i \(-0.0330934\pi\)
\(432\) 0 0
\(433\) 1.53346e42 1.00431 0.502153 0.864779i \(-0.332542\pi\)
0.502153 + 0.864779i \(0.332542\pi\)
\(434\) −1.26200e42 2.25447e42i −0.796570 1.42301i
\(435\) 0 0
\(436\) −1.03278e42 + 1.68392e42i −0.605656 + 0.987499i
\(437\) 3.09796e41 0.175135
\(438\) 0 0
\(439\) 1.32023e42i 0.693771i −0.937907 0.346886i \(-0.887239\pi\)
0.937907 0.346886i \(-0.112761\pi\)
\(440\) −1.14296e40 + 2.86741e41i −0.00579146 + 0.145294i
\(441\) 0 0
\(442\) 1.16659e42 + 2.08402e42i 0.549745 + 0.982077i
\(443\) 1.15073e42i 0.523016i −0.965201 0.261508i \(-0.915780\pi\)
0.965201 0.261508i \(-0.0842198\pi\)
\(444\) 0 0
\(445\) −6.44731e41 −0.272658
\(446\) −6.07577e41 + 3.40108e41i −0.247881 + 0.138758i
\(447\) 0 0
\(448\) −2.79030e41 + 3.49454e42i −0.105975 + 1.32722i
\(449\) −2.92673e42 −1.07261 −0.536303 0.844025i \(-0.680180\pi\)
−0.536303 + 0.844025i \(0.680180\pi\)
\(450\) 0 0
\(451\) 2.16193e42i 0.737934i
\(452\) −1.34084e42 + 2.18619e42i −0.441734 + 0.720231i
\(453\) 0 0
\(454\) 5.64140e41 3.15793e41i 0.173178 0.0969414i
\(455\) 1.39977e42i 0.414835i
\(456\) 0 0
\(457\) 3.62955e42 1.00275 0.501376 0.865230i \(-0.332827\pi\)
0.501376 + 0.865230i \(0.332827\pi\)
\(458\) 9.25372e41 + 1.65311e42i 0.246870 + 0.441015i
\(459\) 0 0
\(460\) −5.56372e41 3.41236e41i −0.138433 0.0849042i
\(461\) 5.81945e42 1.39852 0.699258 0.714870i \(-0.253514\pi\)
0.699258 + 0.714870i \(0.253514\pi\)
\(462\) 0 0
\(463\) 2.14237e42i 0.480396i −0.970724 0.240198i \(-0.922788\pi\)
0.970724 0.240198i \(-0.0772123\pi\)
\(464\) −8.16066e41 1.60463e42i −0.176782 0.347606i
\(465\) 0 0
\(466\) −1.67157e42 2.98614e42i −0.338026 0.603858i
\(467\) 2.32316e42i 0.453951i −0.973900 0.226975i \(-0.927116\pi\)
0.973900 0.226975i \(-0.0728837\pi\)
\(468\) 0 0
\(469\) −1.25392e43 −2.28825
\(470\) −1.70886e41 + 9.56584e40i −0.0301399 + 0.0168716i
\(471\) 0 0
\(472\) 4.51800e41 1.13346e43i 0.0744517 1.86781i
\(473\) −4.69910e42 −0.748576
\(474\) 0 0
\(475\) 1.93519e42i 0.288155i
\(476\) −8.31857e42 5.10197e42i −1.19767 0.734559i
\(477\) 0 0
\(478\) −1.15984e43 + 6.49253e42i −1.56154 + 0.874114i
\(479\) 1.10819e43i 1.44294i −0.692447 0.721469i \(-0.743467\pi\)
0.692447 0.721469i \(-0.256533\pi\)
\(480\) 0 0
\(481\) 9.72190e42 1.18421
\(482\) −9.56464e41 1.70865e42i −0.112698 0.201326i
\(483\) 0 0
\(484\) −3.56640e42 + 5.81488e42i −0.393282 + 0.641232i
\(485\) 2.53785e41 0.0270769
\(486\) 0 0
\(487\) 7.03406e42i 0.702656i −0.936252 0.351328i \(-0.885730\pi\)
0.936252 0.351328i \(-0.114270\pi\)
\(488\) −1.29753e43 5.17198e41i −1.25429 0.0499965i
\(489\) 0 0
\(490\) 1.21776e42 + 2.17543e42i 0.110261 + 0.196974i
\(491\) 8.92602e42i 0.782265i −0.920334 0.391132i \(-0.872083\pi\)
0.920334 0.391132i \(-0.127917\pi\)
\(492\) 0 0
\(493\) 5.01118e42 0.411518
\(494\) 3.68800e42 2.06446e42i 0.293197 0.164125i
\(495\) 0 0
\(496\) −1.46498e43 + 7.45045e42i −1.09176 + 0.555234i
\(497\) −1.67307e43 −1.20729
\(498\) 0 0
\(499\) 2.62413e43i 1.77573i −0.460102 0.887866i \(-0.652187\pi\)
0.460102 0.887866i \(-0.347813\pi\)
\(500\) 4.46205e42 7.27520e42i 0.292425 0.476787i
\(501\) 0 0
\(502\) −2.30279e43 + 1.28905e43i −1.41578 + 0.792520i
\(503\) 4.05670e42i 0.241593i −0.992677 0.120797i \(-0.961455\pi\)
0.992677 0.120797i \(-0.0385449\pi\)
\(504\) 0 0
\(505\) 6.46608e42 0.361392
\(506\) 2.49612e42 + 4.45913e42i 0.135163 + 0.241458i
\(507\) 0 0
\(508\) 1.38970e43 + 8.52334e42i 0.706482 + 0.433302i
\(509\) 2.68863e43 1.32449 0.662243 0.749289i \(-0.269605\pi\)
0.662243 + 0.749289i \(0.269605\pi\)
\(510\) 0 0
\(511\) 3.66563e43i 1.69595i
\(512\) 2.21417e43 + 2.65899e42i 0.992866 + 0.119233i
\(513\) 0 0
\(514\) 6.48300e42 + 1.15814e43i 0.273128 + 0.487923i
\(515\) 9.45655e42i 0.386204i
\(516\) 0 0
\(517\) 1.53334e42 0.0588558
\(518\) −3.46619e43 + 1.94030e43i −1.28996 + 0.722090i
\(519\) 0 0
\(520\) −8.89737e42 3.54652e41i −0.311321 0.0124093i
\(521\) −3.82848e43 −1.29904 −0.649520 0.760344i \(-0.725030\pi\)
−0.649520 + 0.760344i \(0.725030\pi\)
\(522\) 0 0
\(523\) 1.05305e43i 0.336065i 0.985781 + 0.168033i \(0.0537414\pi\)
−0.985781 + 0.168033i \(0.946259\pi\)
\(524\) 9.83807e42 + 6.03392e42i 0.304516 + 0.186766i
\(525\) 0 0
\(526\) 2.50197e43 1.40055e43i 0.728635 0.407873i
\(527\) 4.57506e43i 1.29249i
\(528\) 0 0
\(529\) 2.59862e43 0.690960
\(530\) −4.46139e42 7.96993e42i −0.115095 0.205608i
\(531\) 0 0
\(532\) −9.02874e42 + 1.47210e43i −0.219301 + 0.357562i
\(533\) 6.70832e43 1.58117
\(534\) 0 0
\(535\) 1.88664e43i 0.418822i
\(536\) −3.17698e42 + 7.97029e43i −0.0684507 + 1.71726i
\(537\) 0 0
\(538\) 3.15087e43 + 5.62878e43i 0.639608 + 1.14261i
\(539\) 1.95198e43i 0.384641i
\(540\) 0 0
\(541\) 1.27835e43 0.237408 0.118704 0.992930i \(-0.462126\pi\)
0.118704 + 0.992930i \(0.462126\pi\)
\(542\) −3.33149e43 + 1.86490e43i −0.600690 + 0.336253i
\(543\) 0 0
\(544\) −3.45373e43 + 5.15827e43i −0.587091 + 0.876842i
\(545\) 2.05014e43 0.338407
\(546\) 0 0
\(547\) 1.15299e43i 0.179485i 0.995965 + 0.0897424i \(0.0286044\pi\)
−0.995965 + 0.0897424i \(0.971396\pi\)
\(548\) −2.31526e43 + 3.77494e43i −0.350034 + 0.570718i
\(549\) 0 0
\(550\) −2.78547e43 + 1.55924e43i −0.397279 + 0.222388i
\(551\) 8.86807e42i 0.122858i
\(552\) 0 0
\(553\) 1.42532e44 1.86342
\(554\) 2.46138e43 + 4.39707e43i 0.312625 + 0.558480i
\(555\) 0 0
\(556\) 1.52418e43 + 9.34813e42i 0.182742 + 0.112080i
\(557\) 6.49038e43 0.756114 0.378057 0.925782i \(-0.376592\pi\)
0.378057 + 0.925782i \(0.376592\pi\)
\(558\) 0 0
\(559\) 1.45809e44i 1.60397i
\(560\) 3.24300e43 1.64929e43i 0.346688 0.176315i
\(561\) 0 0
\(562\) −1.08105e43 1.93121e43i −0.109160 0.195006i
\(563\) 1.15419e44i 1.13277i 0.824140 + 0.566387i \(0.191659\pi\)
−0.824140 + 0.566387i \(0.808341\pi\)
\(564\) 0 0
\(565\) 2.66164e43 0.246817
\(566\) 1.26350e44 7.07281e43i 1.13897 0.637572i
\(567\) 0 0
\(568\) −4.23896e42 + 1.06345e44i −0.0361149 + 0.906036i
\(569\) 1.20494e44 0.998091 0.499045 0.866576i \(-0.333684\pi\)
0.499045 + 0.866576i \(0.333684\pi\)
\(570\) 0 0
\(571\) 1.72878e44i 1.35382i −0.736064 0.676911i \(-0.763318\pi\)
0.736064 0.676911i \(-0.236682\pi\)
\(572\) 5.94307e43 + 3.64502e43i 0.452558 + 0.277564i
\(573\) 0 0
\(574\) −2.39175e44 + 1.33885e44i −1.72236 + 0.964140i
\(575\) 7.26030e43i 0.508474i
\(576\) 0 0
\(577\) 1.82754e44 1.21075 0.605375 0.795941i \(-0.293023\pi\)
0.605375 + 0.795941i \(0.293023\pi\)
\(578\) −8.60547e42 1.53730e43i −0.0554535 0.0990635i
\(579\) 0 0
\(580\) −9.76805e42 + 1.59264e43i −0.0595608 + 0.0971116i
\(581\) −1.75354e43 −0.104015
\(582\) 0 0
\(583\) 7.15129e43i 0.401502i
\(584\) −2.32998e44 9.28738e42i −1.27276 0.0507327i
\(585\) 0 0
\(586\) 7.30348e43 + 1.30471e44i 0.377718 + 0.674765i
\(587\) 1.97836e44i 0.995624i 0.867285 + 0.497812i \(0.165863\pi\)
−0.867285 + 0.497812i \(0.834137\pi\)
\(588\) 0 0
\(589\) −8.09630e43 −0.385871
\(590\) −1.02728e44 + 5.75047e43i −0.476492 + 0.266730i
\(591\) 0 0
\(592\) 1.14549e44 + 2.25237e44i 0.503319 + 0.989676i
\(593\) −6.82693e43 −0.291978 −0.145989 0.989286i \(-0.546636\pi\)
−0.145989 + 0.989286i \(0.546636\pi\)
\(594\) 0 0
\(595\) 1.01277e44i 0.410431i
\(596\) −1.40228e44 + 2.28637e44i −0.553218 + 0.902000i
\(597\) 0 0
\(598\) −1.38363e44 + 7.74528e43i −0.517371 + 0.289613i
\(599\) 2.54468e44i 0.926413i −0.886250 0.463206i \(-0.846699\pi\)
0.886250 0.463206i \(-0.153301\pi\)
\(600\) 0 0
\(601\) −4.10791e44 −1.41785 −0.708924 0.705285i \(-0.750819\pi\)
−0.708924 + 0.705285i \(0.750819\pi\)
\(602\) 2.91006e44 + 5.19861e44i 0.978045 + 1.74720i
\(603\) 0 0
\(604\) −1.09593e44 6.72161e43i −0.349295 0.214231i
\(605\) 7.07953e43 0.219745
\(606\) 0 0
\(607\) 6.36172e44i 1.87308i −0.350565 0.936538i \(-0.614010\pi\)
0.350565 0.936538i \(-0.385990\pi\)
\(608\) 9.12836e43 + 6.11192e43i 0.261780 + 0.175275i
\(609\) 0 0
\(610\) 6.58285e43 + 1.17598e44i 0.179117 + 0.319979i
\(611\) 4.75783e43i 0.126110i
\(612\) 0 0
\(613\) 5.83540e43 0.146792 0.0733961 0.997303i \(-0.476616\pi\)
0.0733961 + 0.997303i \(0.476616\pi\)
\(614\) −5.65412e44 + 3.16505e44i −1.38571 + 0.775687i
\(615\) 0 0
\(616\) −2.84638e44 1.13458e43i −0.662219 0.0263963i
\(617\) 2.60007e44 0.589417 0.294709 0.955587i \(-0.404777\pi\)
0.294709 + 0.955587i \(0.404777\pi\)
\(618\) 0 0
\(619\) 1.93411e44i 0.416324i 0.978094 + 0.208162i \(0.0667481\pi\)
−0.978094 + 0.208162i \(0.933252\pi\)
\(620\) 1.45404e44 + 8.91796e43i 0.305007 + 0.187067i
\(621\) 0 0
\(622\) 1.57816e44 8.83419e43i 0.314416 0.176003i
\(623\) 6.40002e44i 1.24272i
\(624\) 0 0
\(625\) 4.07266e44 0.751273
\(626\) −1.23660e44 2.20910e44i −0.222352 0.397215i
\(627\) 0 0
\(628\) −2.96381e44 + 4.83237e44i −0.506402 + 0.825669i
\(629\) −7.03405e44 −1.17164
\(630\) 0 0
\(631\) 6.02399e44i 0.953707i −0.878983 0.476853i \(-0.841777\pi\)
0.878983 0.476853i \(-0.158223\pi\)
\(632\) 3.61126e43 9.05978e44i 0.0557423 1.39844i
\(633\) 0 0
\(634\) 8.80001e43 + 1.57205e44i 0.129138 + 0.230696i
\(635\) 1.69194e44i 0.242105i
\(636\) 0 0
\(637\) 6.05685e44 0.824169
\(638\) 1.27645e44 7.14528e43i 0.169384 0.0948174i
\(639\) 0 0
\(640\) −9.66173e43 2.10313e44i −0.121948 0.265453i
\(641\) 1.17050e45 1.44093 0.720465 0.693491i \(-0.243928\pi\)
0.720465 + 0.693491i \(0.243928\pi\)
\(642\) 0 0
\(643\) 6.41412e44i 0.751210i −0.926780 0.375605i \(-0.877435\pi\)
0.926780 0.375605i \(-0.122565\pi\)
\(644\) 3.38733e44 5.52291e44i 0.386976 0.630949i
\(645\) 0 0
\(646\) −2.66837e44 + 1.49369e44i −0.290085 + 0.162383i
\(647\) 6.68917e44i 0.709421i −0.934976 0.354710i \(-0.884579\pi\)
0.934976 0.354710i \(-0.115421\pi\)
\(648\) 0 0
\(649\) 9.21761e44 0.930471
\(650\) −4.83822e44 8.64311e44i −0.476510 0.851248i
\(651\) 0 0
\(652\) −4.39585e44 2.69608e44i −0.412175 0.252796i
\(653\) −9.73888e44 −0.891042 −0.445521 0.895271i \(-0.646982\pi\)
−0.445521 + 0.895271i \(0.646982\pi\)
\(654\) 0 0
\(655\) 1.19777e44i 0.104355i
\(656\) 7.90412e44 + 1.55419e45i 0.672036 + 1.32142i
\(657\) 0 0
\(658\) −9.49568e43 1.69633e44i −0.0768974 0.137371i
\(659\) 1.33156e45i 1.05243i 0.850352 + 0.526215i \(0.176389\pi\)
−0.850352 + 0.526215i \(0.823611\pi\)
\(660\) 0 0
\(661\) 1.18916e45 0.895398 0.447699 0.894184i \(-0.352244\pi\)
0.447699 + 0.894184i \(0.352244\pi\)
\(662\) 1.65031e44 9.23808e43i 0.121294 0.0678975i
\(663\) 0 0
\(664\) −4.44284e42 + 1.11460e44i −0.00311151 + 0.0780603i
\(665\) 1.79226e44 0.122533
\(666\) 0 0
\(667\) 3.32705e44i 0.216793i
\(668\) −2.38846e45 1.46490e45i −1.51948 0.931931i
\(669\) 0 0
\(670\) 7.22364e44 4.04363e44i 0.438086 0.245231i
\(671\) 1.05518e45i 0.624839i
\(672\) 0 0
\(673\) −3.07010e45 −1.73345 −0.866726 0.498784i \(-0.833780\pi\)
−0.866726 + 0.498784i \(0.833780\pi\)
\(674\) 1.11068e44 + 1.98414e44i 0.0612392 + 0.109399i
\(675\) 0 0
\(676\) −1.36761e44 + 2.22984e44i −0.0719144 + 0.117254i
\(677\) 1.15491e44 0.0593100 0.0296550 0.999560i \(-0.490559\pi\)
0.0296550 + 0.999560i \(0.490559\pi\)
\(678\) 0 0
\(679\) 2.51924e44i 0.123411i
\(680\) 6.43748e44 + 2.56600e43i 0.308016 + 0.0122776i
\(681\) 0 0
\(682\) −6.52344e44 1.16536e45i −0.297801 0.531999i
\(683\) 4.36205e45i 1.94518i −0.232530 0.972589i \(-0.574700\pi\)
0.232530 0.972589i \(-0.425300\pi\)
\(684\) 0 0
\(685\) 4.59593e44 0.195580
\(686\) 6.35110e44 3.55520e44i 0.264036 0.147801i
\(687\) 0 0
\(688\) 3.37812e45 1.71801e45i 1.34048 0.681727i
\(689\) −2.21899e45 −0.860297
\(690\) 0 0
\(691\) 1.13389e43i 0.00419684i 0.999998 + 0.00209842i \(0.000667948\pi\)
−0.999998 + 0.00209842i \(0.999332\pi\)
\(692\) −5.44433e44 + 8.87677e44i −0.196900 + 0.321039i
\(693\) 0 0
\(694\) −3.45808e44 + 1.93576e44i −0.119422 + 0.0668496i
\(695\) 1.85566e44i 0.0626242i
\(696\) 0 0
\(697\) −4.85365e45 −1.56439
\(698\) −8.20650e44 1.46603e45i −0.258506 0.461802i
\(699\) 0 0
\(700\) 3.44998e45 + 2.11595e45i 1.03812 + 0.636704i
\(701\) −2.51171e45 −0.738722 −0.369361 0.929286i \(-0.620423\pi\)
−0.369361 + 0.929286i \(0.620423\pi\)
\(702\) 0 0
\(703\) 1.24479e45i 0.349792i
\(704\) −1.44234e44 + 1.80637e45i −0.0396192 + 0.496186i
\(705\) 0 0
\(706\) −1.99179e45 3.55817e45i −0.522838 0.934011i
\(707\) 6.41865e45i 1.64715i
\(708\) 0 0
\(709\) 2.49801e45 0.612710 0.306355 0.951917i \(-0.400891\pi\)
0.306355 + 0.951917i \(0.400891\pi\)
\(710\) 9.63831e44 5.39531e44i 0.231136 0.129385i
\(711\) 0 0
\(712\) −4.06805e45 1.62154e44i −0.932623 0.0371746i
\(713\) 3.03750e45 0.680901
\(714\) 0 0
\(715\) 7.23559e44i 0.155088i
\(716\) 1.07854e45 + 6.61494e44i 0.226062 + 0.138649i
\(717\) 0 0
\(718\) −3.73382e45 + 2.09011e45i −0.748450 + 0.418965i
\(719\) 1.24854e45i 0.244759i 0.992483 + 0.122380i \(0.0390526\pi\)
−0.992483 + 0.122380i \(0.960947\pi\)
\(720\) 0 0
\(721\) −9.38719e45 −1.76024
\(722\) −2.39897e45 4.28557e45i −0.439976 0.785984i
\(723\) 0 0
\(724\) 1.99744e45 3.25675e45i 0.350474 0.571435i
\(725\) −2.07830e45 −0.356697
\(726\) 0 0
\(727\) 2.70587e45i 0.444382i 0.975003 + 0.222191i \(0.0713209\pi\)
−0.975003 + 0.222191i \(0.928679\pi\)
\(728\) 3.52051e44 8.83211e45i 0.0565592 1.41894i
\(729\) 0 0
\(730\) 1.18209e45 + 2.11171e45i 0.181754 + 0.324690i
\(731\) 1.05497e46i 1.58695i
\(732\) 0 0
\(733\) 1.08091e46 1.55642 0.778212 0.628002i \(-0.216127\pi\)
0.778212 + 0.628002i \(0.216127\pi\)
\(734\) −1.36054e44 + 7.61598e43i −0.0191678 + 0.0107297i
\(735\) 0 0
\(736\) −3.42471e45 2.29302e45i −0.461932 0.309288i
\(737\) −6.48166e45 −0.855473
\(738\) 0 0
\(739\) 1.01661e46i 1.28482i 0.766360 + 0.642412i \(0.222066\pi\)
−0.766360 + 0.642412i \(0.777934\pi\)
\(740\) 1.37111e45 2.23555e45i 0.169577 0.276488i
\(741\) 0 0
\(742\) 7.91147e45 4.42867e45i 0.937119 0.524578i
\(743\) 1.12410e46i 1.30312i −0.758596 0.651562i \(-0.774114\pi\)
0.758596 0.651562i \(-0.225886\pi\)
\(744\) 0 0
\(745\) 2.78362e45 0.309108
\(746\) 5.51684e45 + 9.85541e45i 0.599610 + 1.07116i
\(747\) 0 0
\(748\) −4.29997e45 2.63727e45i −0.447754 0.274618i
\(749\) 1.87281e46 1.90890
\(750\) 0 0
\(751\) 2.21834e45i 0.216665i 0.994115 + 0.108332i \(0.0345511\pi\)
−0.994115 + 0.108332i \(0.965449\pi\)
\(752\) −1.10230e45 + 5.60595e44i −0.105393 + 0.0535999i
\(753\) 0 0
\(754\) 2.21713e45 + 3.96073e45i 0.203165 + 0.362939i
\(755\) 1.33428e45i 0.119700i
\(756\) 0 0
\(757\) −1.67388e46 −1.43943 −0.719716 0.694268i \(-0.755728\pi\)
−0.719716 + 0.694268i \(0.755728\pi\)
\(758\) −1.01171e46 + 5.66331e45i −0.851820 + 0.476830i
\(759\) 0 0
\(760\) 4.54094e43 1.13921e45i 0.00366546 0.0919577i
\(761\) 1.04245e46 0.823948 0.411974 0.911196i \(-0.364839\pi\)
0.411974 + 0.911196i \(0.364839\pi\)
\(762\) 0 0
\(763\) 2.03510e46i 1.54239i
\(764\) 2.24039e46 + 1.37408e46i 1.66276 + 1.01981i
\(765\) 0 0
\(766\) 2.36848e46 1.32582e46i 1.68581 0.943681i
\(767\) 2.86016e46i 1.99372i
\(768\) 0 0
\(769\) −6.62732e45 −0.443115 −0.221557 0.975147i \(-0.571114\pi\)
−0.221557 + 0.975147i \(0.571114\pi\)
\(770\) 1.44408e45 + 2.57974e45i 0.0945669 + 0.168937i
\(771\) 0 0
\(772\) 1.61552e46 2.63404e46i 1.01493 1.65480i
\(773\) −3.08742e46 −1.89987 −0.949934 0.312451i \(-0.898850\pi\)
−0.949934 + 0.312451i \(0.898850\pi\)
\(774\) 0 0
\(775\) 1.89743e46i 1.12031i
\(776\) 1.60130e45 + 6.38285e43i 0.0926161 + 0.00369171i
\(777\) 0 0
\(778\) 3.15204e45 + 5.63089e45i 0.174952 + 0.312538i
\(779\) 8.58929e45i 0.467044i
\(780\) 0 0
\(781\) −8.64831e45 −0.451351
\(782\) 1.00110e46 5.60391e45i 0.511880 0.286539i
\(783\) 0 0
\(784\) 7.13653e45 + 1.40326e46i 0.350292 + 0.688779i
\(785\) 5.88333e45 0.282950
\(786\) 0 0
\(787\) 1.29987e46i 0.600213i 0.953906 + 0.300107i \(0.0970222\pi\)
−0.953906 + 0.300107i \(0.902978\pi\)
\(788\) 1.85614e45 3.02636e45i 0.0839829 0.136931i
\(789\) 0 0
\(790\) −8.21107e45 + 4.59637e45i −0.356752 + 0.199702i
\(791\) 2.64212e46i 1.12494i
\(792\) 0 0
\(793\) 3.27416e46 1.33884
\(794\) −8.25814e44 1.47525e45i −0.0330944 0.0591205i
\(795\) 0 0
\(796\) 5.79822e45 + 3.55618e45i 0.223196 + 0.136891i
\(797\) 9.76951e44 0.0368587 0.0184293 0.999830i \(-0.494133\pi\)
0.0184293 + 0.999830i \(0.494133\pi\)
\(798\) 0 0
\(799\) 3.44242e45i 0.124771i
\(800\) 1.43237e46 2.13930e46i 0.508881 0.760032i
\(801\) 0 0
\(802\) −4.08327e45 7.29445e45i −0.139386 0.249002i
\(803\) 1.89481e46i 0.634039i
\(804\) 0 0
\(805\) −6.72405e45 −0.216221
\(806\) 3.61603e46 2.02417e46i 1.13991 0.638098i
\(807\) 0 0
\(808\) 4.07989e46 + 1.62626e45i 1.23614 + 0.0492728i
\(809\) −1.11267e46 −0.330515 −0.165258 0.986250i \(-0.552846\pi\)
−0.165258 + 0.986250i \(0.552846\pi\)
\(810\) 0 0
\(811\) 3.33104e46i 0.951145i −0.879677 0.475573i \(-0.842241\pi\)
0.879677 0.475573i \(-0.157759\pi\)
\(812\) −1.58096e46 9.69641e45i −0.442614 0.271465i
\(813\) 0 0
\(814\) −1.79172e46 + 1.00296e46i −0.482257 + 0.269957i
\(815\) 5.35187e45i 0.141249i
\(816\) 0 0
\(817\) 1.86694e46 0.473780
\(818\) −2.49216e46 4.45205e46i −0.620186 1.10792i
\(819\) 0 0
\(820\) 9.46099e45 1.54258e46i 0.226420 0.369169i
\(821\) 3.68247e46 0.864269 0.432134 0.901809i \(-0.357761\pi\)
0.432134 + 0.901809i \(0.357761\pi\)
\(822\) 0 0
\(823\) 4.28307e46i 0.966848i 0.875386 + 0.483424i \(0.160607\pi\)
−0.875386 + 0.483424i \(0.839393\pi\)
\(824\) −2.37838e45 + 5.96678e46i −0.0526557 + 1.32101i
\(825\) 0 0
\(826\) −5.70829e46 1.01974e47i −1.21570 2.17175i
\(827\) 2.53823e45i 0.0530203i 0.999649 + 0.0265102i \(0.00843944\pi\)
−0.999649 + 0.0265102i \(0.991561\pi\)
\(828\) 0 0
\(829\) −3.61887e46 −0.727278 −0.363639 0.931540i \(-0.618466\pi\)
−0.363639 + 0.931540i \(0.618466\pi\)
\(830\) 1.01019e45 5.65480e44i 0.0199137 0.0111472i
\(831\) 0 0
\(832\) −5.60504e46 4.47548e45i −1.06318 0.0848920i
\(833\) −4.38229e46 −0.815420
\(834\) 0 0
\(835\) 2.90791e46i 0.520712i
\(836\) −4.66707e45 + 7.60947e45i −0.0819867 + 0.133676i
\(837\) 0 0
\(838\) 2.57006e46 1.43866e46i 0.434549 0.243251i
\(839\) 1.24041e46i 0.205767i −0.994693 0.102883i \(-0.967193\pi\)
0.994693 0.102883i \(-0.0328068\pi\)
\(840\) 0 0
\(841\) −5.30994e46 −0.847918
\(842\) 1.58361e45 + 2.82899e45i 0.0248115 + 0.0443239i
\(843\) 0 0
\(844\) 1.42812e46 + 8.75901e45i 0.215420 + 0.132122i
\(845\) 2.71479e45 0.0401818
\(846\) 0 0
\(847\) 7.02760e46i 1.00155i
\(848\) −2.61454e46 5.14098e46i −0.365647 0.718972i
\(849\) 0 0
\(850\) 3.50058e46 + 6.25352e46i 0.471452 + 0.842212i
\(851\) 4.67009e46i 0.617237i
\(852\) 0 0
\(853\) −8.73958e46 −1.11252 −0.556258 0.831010i \(-0.687763\pi\)
−0.556258 + 0.831010i \(0.687763\pi\)
\(854\) −1.16735e47 + 6.53457e46i −1.45840 + 0.816377i
\(855\) 0 0
\(856\) 4.74502e45 1.19041e47i 0.0571028 1.43257i
\(857\) −1.34006e47 −1.58282 −0.791412 0.611283i \(-0.790654\pi\)
−0.791412 + 0.611283i \(0.790654\pi\)
\(858\) 0 0
\(859\) 1.58120e46i 0.179927i 0.995945 + 0.0899637i \(0.0286751\pi\)
−0.995945 + 0.0899637i \(0.971325\pi\)
\(860\) −3.35289e46 2.05640e46i −0.374493 0.229685i
\(861\) 0 0
\(862\) −1.68293e46 + 9.42064e45i −0.181113 + 0.101383i
\(863\) 6.77128e46i 0.715316i −0.933853 0.357658i \(-0.883575\pi\)
0.933853 0.357658i \(-0.116425\pi\)
\(864\) 0 0
\(865\) 1.08073e46 0.110017
\(866\) −4.90882e46 8.76923e46i −0.490559 0.876346i
\(867\) 0 0
\(868\) −8.85255e46 + 1.44337e47i −0.852614 + 1.39016i
\(869\) 7.36767e46 0.696648
\(870\) 0 0
\(871\) 2.01121e47i 1.83302i
\(872\) 1.29357e47 + 5.15622e45i 1.15752 + 0.0461390i
\(873\) 0 0
\(874\) −9.91701e45 1.77160e46i −0.0855456 0.152821i
\(875\) 8.79247e46i 0.744701i
\(876\) 0 0
\(877\) −8.77276e46 −0.716378 −0.358189 0.933649i \(-0.616606\pi\)
−0.358189 + 0.933649i \(0.616606\pi\)
\(878\) −7.54985e46 + 4.22624e46i −0.605377 + 0.338877i
\(879\) 0 0
\(880\) 1.67635e46 8.52539e45i 0.129611 0.0659161i
\(881\) 7.45226e43 0.000565814 0.000282907 1.00000i \(-0.499910\pi\)
0.000282907 1.00000i \(0.499910\pi\)
\(882\) 0 0
\(883\) 2.02137e47i 1.48004i −0.672584 0.740021i \(-0.734815\pi\)
0.672584 0.740021i \(-0.265185\pi\)
\(884\) 8.18326e46 1.33425e47i 0.588423 0.959402i
\(885\) 0 0
\(886\) −6.58058e46 + 3.68366e46i −0.456378 + 0.255470i
\(887\) 1.65088e47i 1.12445i 0.826985 + 0.562223i \(0.190054\pi\)
−0.826985 + 0.562223i \(0.809946\pi\)
\(888\) 0 0
\(889\) 1.67953e47 1.10346
\(890\) 2.06388e46 + 3.68696e46i 0.133181 + 0.237918i
\(891\) 0 0
\(892\) 3.88988e46 + 2.38576e46i 0.242158 + 0.148521i
\(893\) −6.09190e45 −0.0372503
\(894\) 0 0
\(895\) 1.31311e46i 0.0774696i
\(896\) 2.08771e47 9.59086e46i 1.20988 0.555814i
\(897\) 0 0
\(898\) 9.36887e46 + 1.67368e47i 0.523921 + 0.935945i
\(899\) 8.69502e46i 0.477656i
\(900\) 0 0
\(901\) 1.60550e47 0.851165
\(902\) −1.23632e47 + 6.92066e46i −0.643913 + 0.360448i
\(903\) 0 0
\(904\) 1.67941e47 + 6.69419e45i 0.844233 + 0.0336514i
\(905\) −3.96504e46 −0.195826
\(906\) 0 0
\(907\) 9.68064e46i 0.461517i −0.973011 0.230758i \(-0.925879\pi\)
0.973011 0.230758i \(-0.0741207\pi\)
\(908\) −3.61179e46 2.21519e46i −0.169180 0.103762i
\(909\) 0 0
\(910\) −8.00473e46 + 4.48087e46i −0.361980 + 0.202628i
\(911\) 7.98730e46i 0.354900i −0.984130 0.177450i \(-0.943215\pi\)
0.984130 0.177450i \(-0.0567848\pi\)
\(912\) 0 0
\(913\) −9.06425e45 −0.0388866
\(914\) −1.16187e47 2.07559e47i −0.489800 0.874990i
\(915\) 0 0
\(916\) 6.49120e46 1.05837e47i 0.264239 0.430833i
\(917\) 1.18898e47 0.475627
\(918\) 0 0
\(919\) 1.59603e47i 0.616585i 0.951292 + 0.308292i \(0.0997575\pi\)
−0.951292 + 0.308292i \(0.900242\pi\)
\(920\) −1.70363e45 + 4.27401e46i −0.00646802 + 0.162267i
\(921\) 0 0
\(922\) −1.86289e47 3.32791e47i −0.683113 1.22033i
\(923\) 2.68351e47i 0.967109i
\(924\) 0 0
\(925\) 2.91725e47 1.01556
\(926\) −1.22514e47 + 6.85804e46i −0.419188 + 0.234652i
\(927\) 0 0
\(928\) −6.56389e46 + 9.80340e46i −0.216967 + 0.324048i
\(929\) −2.29442e46 −0.0745455 −0.0372728 0.999305i \(-0.511867\pi\)
−0.0372728 + 0.999305i \(0.511867\pi\)
\(930\) 0 0
\(931\) 7.75516e46i 0.243442i
\(932\) −1.17256e47 + 1.91181e47i −0.361809 + 0.589916i
\(933\) 0 0
\(934\) −1.32852e47 + 7.43676e46i −0.396112 + 0.221735i
\(935\) 5.23514e46i 0.153441i
\(936\) 0 0
\(937\) −1.64376e46 −0.0465591 −0.0232795 0.999729i \(-0.507411\pi\)
−0.0232795 + 0.999729i \(0.507411\pi\)
\(938\) 4.01397e47 + 7.17066e47i 1.11771 + 1.99670i
\(939\) 0 0
\(940\) 1.09406e46 + 6.71014e45i 0.0294440 + 0.0180587i
\(941\) 5.50564e47 1.45671 0.728356 0.685199i \(-0.240285\pi\)
0.728356 + 0.685199i \(0.240285\pi\)
\(942\) 0 0
\(943\) 3.22246e47i 0.824139i
\(944\) −6.62642e47 + 3.37000e47i −1.66620 + 0.847379i
\(945\) 0 0
\(946\) 1.50425e47 + 2.68722e47i 0.365646 + 0.653199i
\(947\) 5.04243e46i 0.120515i −0.998183 0.0602574i \(-0.980808\pi\)
0.998183 0.0602574i \(-0.0191922\pi\)
\(948\) 0 0
\(949\) 5.87945e47 1.35855
\(950\) 1.10666e47 6.19483e46i 0.251441 0.140751i
\(951\) 0 0
\(952\) −2.54718e46 + 6.39027e47i −0.0559588 + 1.40387i
\(953\) 3.90363e47 0.843299 0.421650 0.906759i \(-0.361451\pi\)
0.421650 + 0.906759i \(0.361451\pi\)
\(954\) 0 0
\(955\) 2.72763e47i 0.569812i
\(956\) 7.42564e47 + 4.55431e47i 1.52548 + 0.935614i
\(957\) 0 0
\(958\) −6.33732e47 + 3.54749e47i −1.25909 + 0.704811i
\(959\) 4.56222e47i 0.891412i
\(960\) 0 0
\(961\) −2.64686e47 −0.500215
\(962\) −3.11212e47 5.55956e47i −0.578436 1.03333i
\(963\) 0 0
\(964\) −6.70930e46 + 1.09393e47i −0.120627 + 0.196678i
\(965\) −3.20690e47 −0.567085
\(966\) 0 0
\(967\) 2.20852e47i 0.377814i −0.981995 0.188907i \(-0.939506\pi\)
0.981995 0.188907i \(-0.0604944\pi\)
\(968\) 4.46695e47 + 1.78054e46i 0.751633 + 0.0299603i
\(969\) 0 0
\(970\) −8.12403e45 1.45130e46i −0.0132259 0.0236270i
\(971\) 1.34172e47i 0.214860i 0.994213 + 0.107430i \(0.0342622\pi\)
−0.994213 + 0.107430i \(0.965738\pi\)
\(972\) 0 0
\(973\) 1.84205e47 0.285428
\(974\) −4.02250e47 + 2.25170e47i −0.613130 + 0.343216i
\(975\) 0 0
\(976\) 3.85780e47 + 7.58559e47i 0.569040 + 1.11890i
\(977\) −3.59875e47 −0.522202 −0.261101 0.965312i \(-0.584085\pi\)
−0.261101 + 0.965312i \(0.584085\pi\)
\(978\) 0 0
\(979\) 3.30825e47i 0.464596i
\(980\) 8.54220e46 1.39277e47i 0.118019 0.192426i
\(981\) 0 0
\(982\) −5.10443e47 + 2.85735e47i −0.682596 + 0.382102i
\(983\) 5.51865e46i 0.0726067i −0.999341 0.0363034i \(-0.988442\pi\)
0.999341 0.0363034i \(-0.0115583\pi\)
\(984\) 0 0
\(985\) −3.68455e46 −0.0469250
\(986\) −1.60415e47 2.86569e47i −0.201008 0.359086i
\(987\) 0 0
\(988\) −2.36116e47 1.44816e47i −0.286428 0.175673i
\(989\) −7.00422e47 −0.836025
\(990\) 0 0
\(991\) 3.22322e47i 0.372488i 0.982504 + 0.186244i \(0.0596314\pi\)
−0.982504 + 0.186244i \(0.940369\pi\)
\(992\) 8.95023e47 + 5.99265e47i 1.01776 + 0.681447i
\(993\) 0 0
\(994\) 5.35574e47 + 9.56762e47i 0.589708 + 1.05347i
\(995\) 7.05924e46i 0.0764872i
\(996\) 0 0
\(997\) −4.66475e47 −0.489447 −0.244724 0.969593i \(-0.578697\pi\)
−0.244724 + 0.969593i \(0.578697\pi\)
\(998\) −1.50064e48 + 8.40023e47i −1.54948 + 0.867366i
\(999\) 0 0
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 36.33.d.b.19.5 14
3.2 odd 2 4.33.b.b.3.10 yes 14
4.3 odd 2 inner 36.33.d.b.19.6 14
12.11 even 2 4.33.b.b.3.9 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4.33.b.b.3.9 14 12.11 even 2
4.33.b.b.3.10 yes 14 3.2 odd 2
36.33.d.b.19.5 14 1.1 even 1 trivial
36.33.d.b.19.6 14 4.3 odd 2 inner