Properties

Label 5.27.c.a.2.7
Level $5$
Weight $27$
Character 5.2
Analytic conductor $21.415$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5,27,Mod(2,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 27, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.2");
 
S:= CuspForms(chi, 27);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 27 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), 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: \(21.4146460365\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2.7
Character \(\chi\) \(=\) 5.2
Dual form 5.27.c.a.3.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(584.877 + 584.877i) q^{2} +(-2.17135e6 + 2.17135e6i) q^{3} -6.64247e7i q^{4} +(-1.21727e9 + 9.14507e7i) q^{5} -2.53995e9 q^{6} +(-4.74948e10 - 4.74948e10i) q^{7} +(7.81007e10 - 7.81007e10i) q^{8} -6.88765e12i q^{9} +O(q^{10})\) \(q+(584.877 + 584.877i) q^{2} +(-2.17135e6 + 2.17135e6i) q^{3} -6.64247e7i q^{4} +(-1.21727e9 + 9.14507e7i) q^{5} -2.53995e9 q^{6} +(-4.74948e10 - 4.74948e10i) q^{7} +(7.81007e10 - 7.81007e10i) q^{8} -6.88765e12i q^{9} +(-7.65443e11 - 6.58468e11i) q^{10} -1.55936e13 q^{11} +(1.44231e14 + 1.44231e14i) q^{12} +(-2.89952e14 + 2.89952e14i) q^{13} -5.55572e13i q^{14} +(2.44455e15 - 2.84170e15i) q^{15} -4.36633e15 q^{16} +(1.79130e15 + 1.79130e15i) q^{17} +(4.02843e15 - 4.02843e15i) q^{18} +3.35630e16i q^{19} +(6.07459e15 + 8.08570e16i) q^{20} +2.06255e17 q^{21} +(-9.12034e15 - 9.12034e15i) q^{22} +(9.60657e16 - 9.60657e16i) q^{23} +3.39168e17i q^{24} +(1.47339e18 - 2.22641e17i) q^{25} -3.39173e17 q^{26} +(9.43621e18 + 9.43621e18i) q^{27} +(-3.15483e18 + 3.15483e18i) q^{28} -5.76526e18i q^{29} +(3.09181e18 - 2.32280e17i) q^{30} -2.05949e18 q^{31} +(-7.79502e18 - 7.79502e18i) q^{32} +(3.38591e19 - 3.38591e19i) q^{33} +2.09538e18i q^{34} +(6.21575e19 + 5.34706e19i) q^{35} -4.57510e20 q^{36} +(1.41998e20 + 1.41998e20i) q^{37} +(-1.96302e19 + 1.96302e19i) q^{38} -1.25917e21i q^{39} +(-8.79275e19 + 1.02212e20i) q^{40} -1.34542e21 q^{41} +(1.20634e20 + 1.20634e20i) q^{42} +(1.49931e21 - 1.49931e21i) q^{43} +1.03580e21i q^{44} +(6.29880e20 + 8.38414e21i) q^{45} +1.12373e20 q^{46} +(5.76556e20 + 5.76556e20i) q^{47} +(9.48082e21 - 9.48082e21i) q^{48} -4.87598e21i q^{49} +(9.91970e20 + 7.31535e20i) q^{50} -7.77906e21 q^{51} +(1.92600e22 + 1.92600e22i) q^{52} +(-1.74562e22 + 1.74562e22i) q^{53} +1.10380e22i q^{54} +(1.89817e22 - 1.42604e21i) q^{55} -7.41875e21 q^{56} +(-7.28770e22 - 7.28770e22i) q^{57} +(3.37197e21 - 3.37197e21i) q^{58} -7.32328e22i q^{59} +(-1.88759e23 - 1.62379e23i) q^{60} +1.97728e23 q^{61} +(-1.20455e21 - 1.20455e21i) q^{62} +(-3.27127e23 + 3.27127e23i) q^{63} +2.83901e23i q^{64} +(3.26434e23 - 3.79467e23i) q^{65} +3.96069e22 q^{66} +(2.61879e23 + 2.61879e23i) q^{67} +(1.18986e23 - 1.18986e23i) q^{68} +4.17185e23i q^{69} +(5.08075e21 + 6.76283e22i) q^{70} +1.02318e24 q^{71} +(-5.37930e23 - 5.37930e23i) q^{72} +(9.63289e23 - 9.63289e23i) q^{73} +1.66103e23i q^{74} +(-2.71581e24 + 3.68267e24i) q^{75} +2.22941e24 q^{76} +(7.40614e23 + 7.40614e23i) q^{77} +(7.36462e23 - 7.36462e23i) q^{78} -4.00738e24i q^{79} +(5.31501e24 - 3.99304e23i) q^{80} -2.34711e25 q^{81} +(-7.86907e23 - 7.86907e23i) q^{82} +(4.36215e24 - 4.36215e24i) q^{83} -1.37005e25i q^{84} +(-2.34431e24 - 2.01668e24i) q^{85} +1.75382e24 q^{86} +(1.25184e25 + 1.25184e25i) q^{87} +(-1.21787e24 + 1.21787e24i) q^{88} +3.55980e25i q^{89} +(-4.53529e24 + 5.27210e24i) q^{90} +2.75424e25 q^{91} +(-6.38114e24 - 6.38114e24i) q^{92} +(4.47186e24 - 4.47186e24i) q^{93} +6.74429e23i q^{94} +(-3.06936e24 - 4.08553e25i) q^{95} +3.38514e25 q^{96} +(1.59614e25 + 1.59614e25i) q^{97} +(2.85185e24 - 2.85185e24i) q^{98} +1.07403e26i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8} - 1486502924970 q^{10} - 60046450487712 q^{11} + 474303804173880 q^{12} - 175933888149240 q^{13} + 81\!\cdots\!60 q^{15}+ \cdots + 37\!\cdots\!90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 584.877 + 584.877i 0.0713962 + 0.0713962i 0.741903 0.670507i \(-0.233923\pi\)
−0.670507 + 0.741903i \(0.733923\pi\)
\(3\) −2.17135e6 + 2.17135e6i −1.36193 + 1.36193i −0.490464 + 0.871462i \(0.663173\pi\)
−0.871462 + 0.490464i \(0.836827\pi\)
\(4\) 6.64247e7i 0.989805i
\(5\) −1.21727e9 + 9.14507e7i −0.997190 + 0.0749164i
\(6\) −2.53995e9 −0.194472
\(7\) −4.74948e10 4.74948e10i −0.490198 0.490198i 0.418171 0.908368i \(-0.362671\pi\)
−0.908368 + 0.418171i \(0.862671\pi\)
\(8\) 7.81007e10 7.81007e10i 0.142064 0.142064i
\(9\) 6.88765e12i 2.70968i
\(10\) −7.65443e11 6.58468e11i −0.0765443 0.0658468i
\(11\) −1.55936e13 −0.451691 −0.225845 0.974163i \(-0.572514\pi\)
−0.225845 + 0.974163i \(0.572514\pi\)
\(12\) 1.44231e14 + 1.44231e14i 1.34804 + 1.34804i
\(13\) −2.89952e14 + 2.89952e14i −0.957332 + 0.957332i −0.999126 0.0417946i \(-0.986692\pi\)
0.0417946 + 0.999126i \(0.486692\pi\)
\(14\) 5.55572e13i 0.0699964i
\(15\) 2.44455e15 2.84170e15i 1.25607 1.46013i
\(16\) −4.36633e15 −0.969519
\(17\) 1.79130e15 + 1.79130e15i 0.180856 + 0.180856i 0.791729 0.610873i \(-0.209181\pi\)
−0.610873 + 0.791729i \(0.709181\pi\)
\(18\) 4.02843e15 4.02843e15i 0.193461 0.193461i
\(19\) 3.35630e16i 0.798113i 0.916926 + 0.399056i \(0.130662\pi\)
−0.916926 + 0.399056i \(0.869338\pi\)
\(20\) 6.07459e15 + 8.08570e16i 0.0741527 + 0.987024i
\(21\) 2.06255e17 1.33523
\(22\) −9.12034e15 9.12034e15i −0.0322490 0.0322490i
\(23\) 9.60657e16 9.60657e16i 0.190593 0.190593i −0.605359 0.795952i \(-0.706971\pi\)
0.795952 + 0.605359i \(0.206971\pi\)
\(24\) 3.39168e17i 0.386962i
\(25\) 1.47339e18 2.22641e17i 0.988775 0.149412i
\(26\) −3.39173e17 −0.136700
\(27\) 9.43621e18 + 9.43621e18i 2.32846 + 2.32846i
\(28\) −3.15483e18 + 3.15483e18i −0.485200 + 0.485200i
\(29\) 5.76526e18i 0.561882i −0.959725 0.280941i \(-0.909353\pi\)
0.959725 0.280941i \(-0.0906465\pi\)
\(30\) 3.09181e18 2.32280e17i 0.193926 0.0145692i
\(31\) −2.05949e18 −0.0843445 −0.0421722 0.999110i \(-0.513428\pi\)
−0.0421722 + 0.999110i \(0.513428\pi\)
\(32\) −7.79502e18 7.79502e18i −0.211284 0.211284i
\(33\) 3.38591e19 3.38591e19i 0.615169 0.615169i
\(34\) 2.09538e18i 0.0258248i
\(35\) 6.21575e19 + 5.34706e19i 0.525544 + 0.452096i
\(36\) −4.57510e20 −2.68206
\(37\) 1.41998e20 + 1.41998e20i 0.582990 + 0.582990i 0.935724 0.352734i \(-0.114748\pi\)
−0.352734 + 0.935724i \(0.614748\pi\)
\(38\) −1.96302e19 + 1.96302e19i −0.0569822 + 0.0569822i
\(39\) 1.25917e21i 2.60763i
\(40\) −8.79275e19 + 1.02212e20i −0.131022 + 0.152308i
\(41\) −1.34542e21 −1.45435 −0.727175 0.686453i \(-0.759167\pi\)
−0.727175 + 0.686453i \(0.759167\pi\)
\(42\) 1.20634e20 + 1.20634e20i 0.0953299 + 0.0953299i
\(43\) 1.49931e21 1.49931e21i 0.872571 0.872571i −0.120181 0.992752i \(-0.538348\pi\)
0.992752 + 0.120181i \(0.0383476\pi\)
\(44\) 1.03580e21i 0.447086i
\(45\) 6.29880e20 + 8.38414e21i 0.203000 + 2.70207i
\(46\) 1.12373e20 0.0272152
\(47\) 5.76556e20 + 5.76556e20i 0.105577 + 0.105577i 0.757922 0.652345i \(-0.226215\pi\)
−0.652345 + 0.757922i \(0.726215\pi\)
\(48\) 9.48082e21 9.48082e21i 1.32041 1.32041i
\(49\) 4.87598e21i 0.519413i
\(50\) 9.91970e20 + 7.31535e20i 0.0812622 + 0.0599273i
\(51\) −7.77906e21 −0.492623
\(52\) 1.92600e22 + 1.92600e22i 0.947572 + 0.947572i
\(53\) −1.74562e22 + 1.74562e22i −0.670444 + 0.670444i −0.957818 0.287374i \(-0.907218\pi\)
0.287374 + 0.957818i \(0.407218\pi\)
\(54\) 1.10380e22i 0.332486i
\(55\) 1.89817e22 1.42604e21i 0.450421 0.0338391i
\(56\) −7.41875e21 −0.139279
\(57\) −7.28770e22 7.28770e22i −1.08697 1.08697i
\(58\) 3.37197e21 3.37197e21i 0.0401162 0.0401162i
\(59\) 7.32328e22i 0.697637i −0.937190 0.348819i \(-0.886583\pi\)
0.937190 0.348819i \(-0.113417\pi\)
\(60\) −1.88759e23 1.62379e23i −1.44524 1.24326i
\(61\) 1.97728e23 1.22118 0.610591 0.791946i \(-0.290932\pi\)
0.610591 + 0.791946i \(0.290932\pi\)
\(62\) −1.20455e21 1.20455e21i −0.00602187 0.00602187i
\(63\) −3.27127e23 + 3.27127e23i −1.32828 + 1.32828i
\(64\) 2.83901e23i 0.939350i
\(65\) 3.26434e23 3.79467e23i 0.882921 1.02636i
\(66\) 3.96069e22 0.0878414
\(67\) 2.61879e23 + 2.61879e23i 0.477669 + 0.477669i 0.904386 0.426716i \(-0.140330\pi\)
−0.426716 + 0.904386i \(0.640330\pi\)
\(68\) 1.18986e23 1.18986e23i 0.179012 0.179012i
\(69\) 4.17185e23i 0.519147i
\(70\) 5.08075e21 + 6.76283e22i 0.00524388 + 0.0697997i
\(71\) 1.02318e24 0.878198 0.439099 0.898439i \(-0.355298\pi\)
0.439099 + 0.898439i \(0.355298\pi\)
\(72\) −5.37930e23 5.37930e23i −0.384949 0.384949i
\(73\) 9.63289e23 9.63289e23i 0.576182 0.576182i −0.357667 0.933849i \(-0.616428\pi\)
0.933849 + 0.357667i \(0.116428\pi\)
\(74\) 1.66103e23i 0.0832464i
\(75\) −2.71581e24 + 3.68267e24i −1.14315 + 1.55013i
\(76\) 2.22941e24 0.789976
\(77\) 7.40614e23 + 7.40614e23i 0.221418 + 0.221418i
\(78\) 7.36462e23 7.36462e23i 0.186175 0.186175i
\(79\) 4.00738e24i 0.858438i −0.903201 0.429219i \(-0.858789\pi\)
0.903201 0.429219i \(-0.141211\pi\)
\(80\) 5.31501e24 3.99304e23i 0.966795 0.0726329i
\(81\) −2.34711e25 −3.63269
\(82\) −7.86907e23 7.86907e23i −0.103835 0.103835i
\(83\) 4.36215e24 4.36215e24i 0.491683 0.491683i −0.417153 0.908836i \(-0.636972\pi\)
0.908836 + 0.417153i \(0.136972\pi\)
\(84\) 1.37005e25i 1.32161i
\(85\) −2.34431e24 2.01668e24i −0.193896 0.166798i
\(86\) 1.75382e24 0.124596
\(87\) 1.25184e25 + 1.25184e25i 0.765241 + 0.765241i
\(88\) −1.21787e24 + 1.21787e24i −0.0641692 + 0.0641692i
\(89\) 3.55980e25i 1.61941i 0.586839 + 0.809704i \(0.300372\pi\)
−0.586839 + 0.809704i \(0.699628\pi\)
\(90\) −4.53529e24 + 5.27210e24i −0.178424 + 0.207411i
\(91\) 2.75424e25 0.938563
\(92\) −6.38114e24 6.38114e24i −0.188650 0.188650i
\(93\) 4.47186e24 4.47186e24i 0.114871 0.114871i
\(94\) 6.74429e23i 0.0150756i
\(95\) −3.06936e24 4.08553e25i −0.0597917 0.795870i
\(96\) 3.38514e25 0.575507
\(97\) 1.59614e25 + 1.59614e25i 0.237158 + 0.237158i 0.815672 0.578514i \(-0.196367\pi\)
−0.578514 + 0.815672i \(0.696367\pi\)
\(98\) 2.85185e24 2.85185e24i 0.0370841 0.0370841i
\(99\) 1.07403e26i 1.22394i
\(100\) −1.47889e25 9.78695e25i −0.147889 0.978695i
\(101\) 6.33718e25 0.556825 0.278412 0.960462i \(-0.410192\pi\)
0.278412 + 0.960462i \(0.410192\pi\)
\(102\) −4.54980e24 4.54980e24i −0.0351714 0.0351714i
\(103\) −1.35417e26 + 1.35417e26i −0.922122 + 0.922122i −0.997179 0.0750575i \(-0.976086\pi\)
0.0750575 + 0.997179i \(0.476086\pi\)
\(104\) 4.52909e25i 0.272006i
\(105\) −2.51069e26 + 1.88622e25i −1.33147 + 0.100030i
\(106\) −2.04194e25 −0.0957342
\(107\) −2.65446e26 2.65446e26i −1.10151 1.10151i −0.994229 0.107278i \(-0.965786\pi\)
−0.107278 0.994229i \(-0.534214\pi\)
\(108\) 6.26797e26 6.26797e26i 2.30472 2.30472i
\(109\) 8.26937e25i 0.269729i 0.990864 + 0.134865i \(0.0430600\pi\)
−0.990864 + 0.134865i \(0.956940\pi\)
\(110\) 1.19360e25 + 1.02679e25i 0.0345743 + 0.0297424i
\(111\) −6.16656e26 −1.58798
\(112\) 2.07378e26 + 2.07378e26i 0.475256 + 0.475256i
\(113\) −1.45365e26 + 1.45365e26i −0.296784 + 0.296784i −0.839753 0.542969i \(-0.817300\pi\)
0.542969 + 0.839753i \(0.317300\pi\)
\(114\) 8.52482e25i 0.155211i
\(115\) −1.08153e26 + 1.25723e26i −0.175779 + 0.204336i
\(116\) −3.82956e26 −0.556154
\(117\) 1.99709e27 + 1.99709e27i 2.59406 + 2.59406i
\(118\) 4.28322e25 4.28322e25i 0.0498086 0.0498086i
\(119\) 1.70154e26i 0.177310i
\(120\) −3.10172e25 4.12860e26i −0.0289898 0.385875i
\(121\) −9.48658e26 −0.795975
\(122\) 1.15647e26 + 1.15647e26i 0.0871876 + 0.0871876i
\(123\) 2.92138e27 2.92138e27i 1.98071 1.98071i
\(124\) 1.36801e26i 0.0834846i
\(125\) −1.77316e27 + 4.05757e26i −0.974803 + 0.223067i
\(126\) −3.82658e26 −0.189668
\(127\) −1.05974e27 1.05974e27i −0.473970 0.473970i 0.429227 0.903197i \(-0.358786\pi\)
−0.903197 + 0.429227i \(0.858786\pi\)
\(128\) −6.89162e26 + 6.89162e26i −0.278350 + 0.278350i
\(129\) 6.51104e27i 2.37675i
\(130\) 4.12866e26 3.10176e25i 0.136315 0.0102410i
\(131\) 2.18379e27 0.652655 0.326327 0.945257i \(-0.394189\pi\)
0.326327 + 0.945257i \(0.394189\pi\)
\(132\) −2.24908e27 2.24908e27i −0.608898 0.608898i
\(133\) 1.59407e27 1.59407e27i 0.391233 0.391233i
\(134\) 3.06334e26i 0.0682075i
\(135\) −1.23494e28 1.06235e28i −2.49635 2.14748i
\(136\) 2.79803e26 0.0513863
\(137\) 4.23871e27 + 4.23871e27i 0.707728 + 0.707728i 0.966057 0.258329i \(-0.0831720\pi\)
−0.258329 + 0.966057i \(0.583172\pi\)
\(138\) −2.44002e26 + 2.44002e26i −0.0370651 + 0.0370651i
\(139\) 4.44426e27i 0.614621i −0.951609 0.307310i \(-0.900571\pi\)
0.951609 0.307310i \(-0.0994290\pi\)
\(140\) 3.55177e27 4.12879e27i 0.447487 0.520186i
\(141\) −2.50381e27 −0.287576
\(142\) 5.98434e26 + 5.98434e26i 0.0627000 + 0.0627000i
\(143\) 4.52139e27 4.52139e27i 0.432418 0.432418i
\(144\) 3.00737e28i 2.62709i
\(145\) 5.27237e26 + 7.01790e27i 0.0420942 + 0.560303i
\(146\) 1.12681e27 0.0822743
\(147\) 1.05874e28 + 1.05874e28i 0.707401 + 0.707401i
\(148\) 9.43220e27 9.43220e27i 0.577046 0.577046i
\(149\) 1.09366e28i 0.613003i −0.951870 0.306502i \(-0.900842\pi\)
0.951870 0.306502i \(-0.0991585\pi\)
\(150\) −3.74233e27 + 5.65496e26i −0.192290 + 0.0290565i
\(151\) 6.12606e27 0.288723 0.144361 0.989525i \(-0.453887\pi\)
0.144361 + 0.989525i \(0.453887\pi\)
\(152\) 2.62130e27 + 2.62130e27i 0.113383 + 0.113383i
\(153\) 1.23378e28 1.23378e28i 0.490061 0.490061i
\(154\) 8.66336e26i 0.0316167i
\(155\) 2.50696e27 1.88341e26i 0.0841075 0.00631879i
\(156\) −8.36402e28 −2.58104
\(157\) 3.08998e28 + 3.08998e28i 0.877526 + 0.877526i 0.993278 0.115752i \(-0.0369277\pi\)
−0.115752 + 0.993278i \(0.536928\pi\)
\(158\) 2.34383e27 2.34383e27i 0.0612891 0.0612891i
\(159\) 7.58068e28i 1.82619i
\(160\) 1.02015e28 + 8.77580e27i 0.226519 + 0.194862i
\(161\) −9.12524e27 −0.186856
\(162\) −1.37277e28 1.37277e28i −0.259360 0.259360i
\(163\) 9.56786e27 9.56786e27i 0.166869 0.166869i −0.618733 0.785602i \(-0.712354\pi\)
0.785602 + 0.618733i \(0.212354\pi\)
\(164\) 8.93693e28i 1.43952i
\(165\) −3.81193e28 + 4.43122e28i −0.567354 + 0.659527i
\(166\) 5.10264e27 0.0702085
\(167\) −8.26346e28 8.26346e28i −1.05159 1.05159i −0.998595 0.0529990i \(-0.983122\pi\)
−0.0529990 0.998595i \(-0.516878\pi\)
\(168\) 1.61087e28 1.61087e28i 0.189688 0.189688i
\(169\) 7.64109e28i 0.832968i
\(170\) −1.91624e26 2.55065e27i −0.00193470 0.0257522i
\(171\) 2.31170e29 2.16263
\(172\) −9.95910e28 9.95910e28i −0.863675 0.863675i
\(173\) −1.29926e29 + 1.29926e29i −1.04495 + 1.04495i −0.0460131 + 0.998941i \(0.514652\pi\)
−0.998941 + 0.0460131i \(0.985348\pi\)
\(174\) 1.46435e28i 0.109271i
\(175\) −8.05526e28 5.94040e28i −0.557936 0.411454i
\(176\) 6.80867e28 0.437923
\(177\) 1.59014e29 + 1.59014e29i 0.950130 + 0.950130i
\(178\) −2.08205e28 + 2.08205e28i −0.115619 + 0.115619i
\(179\) 1.66199e29i 0.858104i 0.903280 + 0.429052i \(0.141152\pi\)
−0.903280 + 0.429052i \(0.858848\pi\)
\(180\) 5.56914e29 4.18396e28i 2.67452 0.200930i
\(181\) 8.37582e28 0.374288 0.187144 0.982333i \(-0.440077\pi\)
0.187144 + 0.982333i \(0.440077\pi\)
\(182\) 1.61089e28 + 1.61089e28i 0.0670098 + 0.0670098i
\(183\) −4.29336e29 + 4.29336e29i −1.66316 + 1.66316i
\(184\) 1.50056e28i 0.0541529i
\(185\) −1.85837e29 1.59865e29i −0.625027 0.537676i
\(186\) 5.23098e27 0.0164027
\(187\) −2.79328e28 2.79328e28i −0.0816908 0.0816908i
\(188\) 3.82976e28 3.82976e28i 0.104501 0.104501i
\(189\) 8.96341e29i 2.28281i
\(190\) 2.21002e28 2.56906e28i 0.0525531 0.0610909i
\(191\) 1.10097e29 0.244536 0.122268 0.992497i \(-0.460983\pi\)
0.122268 + 0.992497i \(0.460983\pi\)
\(192\) −6.16448e29 6.16448e29i −1.27932 1.27932i
\(193\) 1.04789e29 1.04789e29i 0.203269 0.203269i −0.598130 0.801399i \(-0.704089\pi\)
0.801399 + 0.598130i \(0.204089\pi\)
\(194\) 1.86709e28i 0.0338644i
\(195\) 1.15152e29 + 1.53276e30i 0.195354 + 2.60030i
\(196\) −3.23885e29 −0.514117
\(197\) 1.47531e29 + 1.47531e29i 0.219190 + 0.219190i 0.808157 0.588967i \(-0.200465\pi\)
−0.588967 + 0.808157i \(0.700465\pi\)
\(198\) −6.28177e28 + 6.28177e28i −0.0873845 + 0.0873845i
\(199\) 6.99337e29i 0.911164i −0.890194 0.455582i \(-0.849431\pi\)
0.890194 0.455582i \(-0.150569\pi\)
\(200\) 9.76844e28 1.32461e29i 0.119244 0.161696i
\(201\) −1.13726e30 −1.30110
\(202\) 3.70647e28 + 3.70647e28i 0.0397551 + 0.0397551i
\(203\) −2.73820e29 + 2.73820e29i −0.275433 + 0.275433i
\(204\) 5.16722e29i 0.487601i
\(205\) 1.63775e30 1.23040e29i 1.45026 0.108955i
\(206\) −1.58404e29 −0.131672
\(207\) −6.61667e29 6.61667e29i −0.516446 0.516446i
\(208\) 1.26602e30 1.26602e30i 0.928152 0.928152i
\(209\) 5.23368e29i 0.360500i
\(210\) −1.57877e29 1.35813e29i −0.102204 0.0879203i
\(211\) 2.89924e30 1.76446 0.882231 0.470816i \(-0.156041\pi\)
0.882231 + 0.470816i \(0.156041\pi\)
\(212\) 1.15952e30 + 1.15952e30i 0.663609 + 0.663609i
\(213\) −2.22168e30 + 2.22168e30i −1.19604 + 1.19604i
\(214\) 3.10507e29i 0.157287i
\(215\) −1.68795e30 + 1.96218e30i −0.804749 + 0.935488i
\(216\) 1.47395e30 0.661582
\(217\) 9.78148e28 + 9.78148e28i 0.0413455 + 0.0413455i
\(218\) −4.83657e28 + 4.83657e28i −0.0192576 + 0.0192576i
\(219\) 4.18327e30i 1.56943i
\(220\) −9.47246e28 1.26085e30i −0.0334941 0.445829i
\(221\) −1.03878e30 −0.346277
\(222\) −3.60668e29 3.60668e29i −0.113375 0.113375i
\(223\) 2.69822e30 2.69822e30i 0.800045 0.800045i −0.183057 0.983102i \(-0.558599\pi\)
0.983102 + 0.183057i \(0.0585994\pi\)
\(224\) 7.40445e29i 0.207142i
\(225\) −1.53347e30 1.01482e31i −0.404858 2.67927i
\(226\) −1.70041e29 −0.0423784
\(227\) −1.18064e30 1.18064e30i −0.277832 0.277832i 0.554411 0.832243i \(-0.312943\pi\)
−0.832243 + 0.554411i \(0.812943\pi\)
\(228\) −4.84083e30 + 4.84083e30i −1.07589 + 1.07589i
\(229\) 4.08307e30i 0.857287i −0.903474 0.428643i \(-0.858992\pi\)
0.903474 0.428643i \(-0.141008\pi\)
\(230\) −1.36789e29 + 1.02766e28i −0.0271387 + 0.00203887i
\(231\) −3.21626e30 −0.603109
\(232\) −4.50271e29 4.50271e29i −0.0798234 0.0798234i
\(233\) 2.54161e30 2.54161e30i 0.426072 0.426072i −0.461216 0.887288i \(-0.652587\pi\)
0.887288 + 0.461216i \(0.152587\pi\)
\(234\) 2.33610e30i 0.370412i
\(235\) −7.54553e29 6.49100e29i −0.113190 0.0973709i
\(236\) −4.86447e30 −0.690525
\(237\) 8.70143e30 + 8.70143e30i 1.16913 + 1.16913i
\(238\) 9.95195e28 9.95195e28i 0.0126592 0.0126592i
\(239\) 1.11754e31i 1.34614i 0.739579 + 0.673070i \(0.235025\pi\)
−0.739579 + 0.673070i \(0.764975\pi\)
\(240\) −1.06737e31 + 1.24078e31i −1.21778 + 1.41562i
\(241\) 1.81933e30 0.196648 0.0983241 0.995154i \(-0.468652\pi\)
0.0983241 + 0.995154i \(0.468652\pi\)
\(242\) −5.54848e29 5.54848e29i −0.0568296 0.0568296i
\(243\) 2.69784e31 2.69784e31i 2.61900 2.61900i
\(244\) 1.31340e31i 1.20873i
\(245\) 4.45911e29 + 5.93539e30i 0.0389125 + 0.517953i
\(246\) 3.41730e30 0.282831
\(247\) −9.73166e30 9.73166e30i −0.764058 0.764058i
\(248\) −1.60847e29 + 1.60847e29i −0.0119824 + 0.0119824i
\(249\) 1.89435e31i 1.33927i
\(250\) −1.27440e30 7.99761e29i −0.0855233 0.0536710i
\(251\) −2.40455e31 −1.53206 −0.766029 0.642805i \(-0.777770\pi\)
−0.766029 + 0.642805i \(0.777770\pi\)
\(252\) 2.17293e31 + 2.17293e31i 1.31474 + 1.31474i
\(253\) −1.49801e30 + 1.49801e30i −0.0860890 + 0.0860890i
\(254\) 1.23964e30i 0.0676793i
\(255\) 9.46924e30 7.11401e29i 0.491239 0.0369056i
\(256\) 1.82461e31 0.899603
\(257\) 2.23633e31 + 2.23633e31i 1.04811 + 1.04811i 0.998783 + 0.0493257i \(0.0157072\pi\)
0.0493257 + 0.998783i \(0.484293\pi\)
\(258\) −3.80816e30 + 3.80816e30i −0.169691 + 0.169691i
\(259\) 1.34884e31i 0.571560i
\(260\) −2.52060e31 2.16833e31i −1.01590 0.873920i
\(261\) −3.97091e31 −1.52252
\(262\) 1.27725e30 + 1.27725e30i 0.0465971 + 0.0465971i
\(263\) −8.57416e30 + 8.57416e30i −0.297692 + 0.297692i −0.840109 0.542417i \(-0.817509\pi\)
0.542417 + 0.840109i \(0.317509\pi\)
\(264\) 5.28885e30i 0.174787i
\(265\) 1.96525e31 2.28453e31i 0.618333 0.718787i
\(266\) 1.86467e30 0.0558650
\(267\) −7.72958e31 7.72958e31i −2.20551 2.20551i
\(268\) 1.73952e31 1.73952e31i 0.472800 0.472800i
\(269\) 3.97784e31i 1.03007i 0.857168 + 0.515037i \(0.172222\pi\)
−0.857168 + 0.515037i \(0.827778\pi\)
\(270\) −1.00944e30 1.34363e31i −0.0249087 0.331552i
\(271\) 5.99004e31 1.40873 0.704366 0.709837i \(-0.251231\pi\)
0.704366 + 0.709837i \(0.251231\pi\)
\(272\) −7.82139e30 7.82139e30i −0.175343 0.175343i
\(273\) −5.98041e31 + 5.98041e31i −1.27825 + 1.27825i
\(274\) 4.95825e30i 0.101058i
\(275\) −2.29754e31 + 3.47177e30i −0.446621 + 0.0674879i
\(276\) 2.77114e31 0.513854
\(277\) 3.13521e31 + 3.13521e31i 0.554664 + 0.554664i 0.927783 0.373120i \(-0.121712\pi\)
−0.373120 + 0.927783i \(0.621712\pi\)
\(278\) 2.59935e30 2.59935e30i 0.0438816 0.0438816i
\(279\) 1.41850e31i 0.228547i
\(280\) 9.03065e30 6.78450e29i 0.138888 0.0104343i
\(281\) 6.05769e31 0.889457 0.444728 0.895666i \(-0.353300\pi\)
0.444728 + 0.895666i \(0.353300\pi\)
\(282\) −1.46442e30 1.46442e30i −0.0205318 0.0205318i
\(283\) −2.00009e31 + 2.00009e31i −0.267810 + 0.267810i −0.828217 0.560407i \(-0.810645\pi\)
0.560407 + 0.828217i \(0.310645\pi\)
\(284\) 6.79643e31i 0.869245i
\(285\) 9.53759e31 + 8.20466e31i 1.16535 + 1.00248i
\(286\) 5.28892e30 0.0617459
\(287\) 6.39005e31 + 6.39005e31i 0.712918 + 0.712918i
\(288\) −5.36893e31 + 5.36893e31i −0.572513 + 0.572513i
\(289\) 9.16832e31i 0.934583i
\(290\) −3.79624e30 + 4.41298e30i −0.0369981 + 0.0430088i
\(291\) −6.93155e31 −0.645984
\(292\) −6.39862e31 6.39862e31i −0.570307 0.570307i
\(293\) 1.04124e32 1.04124e32i 0.887710 0.887710i −0.106593 0.994303i \(-0.533994\pi\)
0.994303 + 0.106593i \(0.0339942\pi\)
\(294\) 1.23847e31i 0.101011i
\(295\) 6.69720e30 + 8.91443e31i 0.0522645 + 0.695677i
\(296\) 2.21804e31 0.165644
\(297\) −1.47144e32 1.47144e32i −1.05174 1.05174i
\(298\) 6.39660e30 6.39660e30i 0.0437661 0.0437661i
\(299\) 5.57089e31i 0.364921i
\(300\) 2.44621e32 + 1.80397e32i 1.53432 + 1.13150i
\(301\) −1.42418e32 −0.855464
\(302\) 3.58300e30 + 3.58300e30i 0.0206137 + 0.0206137i
\(303\) −1.37602e32 + 1.37602e32i −0.758353 + 0.758353i
\(304\) 1.46547e32i 0.773786i
\(305\) −2.40689e32 + 1.80824e31i −1.21775 + 0.0914865i
\(306\) 1.44322e31 0.0699769
\(307\) 1.27797e32 + 1.27797e32i 0.593910 + 0.593910i 0.938685 0.344775i \(-0.112045\pi\)
−0.344775 + 0.938685i \(0.612045\pi\)
\(308\) 4.91951e31 4.91951e31i 0.219160 0.219160i
\(309\) 5.88074e32i 2.51172i
\(310\) 1.57642e30 + 1.35610e30i 0.00645609 + 0.00555381i
\(311\) −1.29479e32 −0.508528 −0.254264 0.967135i \(-0.581833\pi\)
−0.254264 + 0.967135i \(0.581833\pi\)
\(312\) −9.83424e31 9.83424e31i −0.370451 0.370451i
\(313\) −3.36725e32 + 3.36725e32i −1.21674 + 1.21674i −0.247979 + 0.968765i \(0.579767\pi\)
−0.968765 + 0.247979i \(0.920233\pi\)
\(314\) 3.61452e31i 0.125304i
\(315\) 3.68287e32 4.28119e32i 1.22504 1.42406i
\(316\) −2.66189e32 −0.849686
\(317\) 1.47703e32 + 1.47703e32i 0.452501 + 0.452501i 0.896184 0.443683i \(-0.146328\pi\)
−0.443683 + 0.896184i \(0.646328\pi\)
\(318\) 4.43377e31 4.43377e31i 0.130383 0.130383i
\(319\) 8.99011e31i 0.253797i
\(320\) −2.59630e31 3.45585e32i −0.0703727 0.936710i
\(321\) 1.15275e33 3.00034
\(322\) −5.33715e30 5.33715e30i −0.0133408 0.0133408i
\(323\) −6.01213e31 + 6.01213e31i −0.144343 + 0.144343i
\(324\) 1.55906e33i 3.59566i
\(325\) −3.62657e32 + 4.91767e32i −0.803549 + 1.08962i
\(326\) 1.11920e31 0.0238276
\(327\) −1.79557e32 1.79557e32i −0.367351 0.367351i
\(328\) −1.05079e32 + 1.05079e32i −0.206611 + 0.206611i
\(329\) 5.47668e31i 0.103507i
\(330\) −4.82124e31 + 3.62208e30i −0.0875946 + 0.00658076i
\(331\) 6.74699e32 1.17855 0.589273 0.807934i \(-0.299414\pi\)
0.589273 + 0.807934i \(0.299414\pi\)
\(332\) −2.89754e32 2.89754e32i −0.486670 0.486670i
\(333\) 9.78034e32 9.78034e32i 1.57972 1.57972i
\(334\) 9.66622e31i 0.150159i
\(335\) −3.42727e32 2.94829e32i −0.512112 0.440542i
\(336\) −9.00579e32 −1.29453
\(337\) 7.95724e31 + 7.95724e31i 0.110046 + 0.110046i 0.759986 0.649940i \(-0.225206\pi\)
−0.649940 + 0.759986i \(0.725206\pi\)
\(338\) 4.46910e31 4.46910e31i 0.0594707 0.0594707i
\(339\) 6.31276e32i 0.808394i
\(340\) −1.33958e32 + 1.55720e32i −0.165098 + 0.191920i
\(341\) 3.21148e31 0.0380976
\(342\) 1.35206e32 + 1.35206e32i 0.154404 + 0.154404i
\(343\) −6.77439e32 + 6.77439e32i −0.744812 + 0.744812i
\(344\) 2.34194e32i 0.247923i
\(345\) −3.81518e31 5.07827e32i −0.0388926 0.517688i
\(346\) −1.51982e32 −0.149211
\(347\) 1.06237e33 + 1.06237e33i 1.00460 + 1.00460i 0.999989 + 0.00461146i \(0.00146788\pi\)
0.00461146 + 0.999989i \(0.498532\pi\)
\(348\) 8.31531e32 8.31531e32i 0.757440 0.757440i
\(349\) 1.25891e33i 1.10475i 0.833597 + 0.552373i \(0.186278\pi\)
−0.833597 + 0.552373i \(0.813722\pi\)
\(350\) −1.23693e31 8.18574e31i −0.0104583 0.0692107i
\(351\) −5.47209e33 −4.45821
\(352\) 1.21552e32 + 1.21552e32i 0.0954352 + 0.0954352i
\(353\) 1.12455e33 1.12455e33i 0.850957 0.850957i −0.139294 0.990251i \(-0.544483\pi\)
0.990251 + 0.139294i \(0.0444832\pi\)
\(354\) 1.86007e32i 0.135671i
\(355\) −1.24549e33 + 9.35704e31i −0.875731 + 0.0657915i
\(356\) 2.36459e33 1.60290
\(357\) 3.69465e32 + 3.69465e32i 0.241483 + 0.241483i
\(358\) −9.72062e31 + 9.72062e31i −0.0612653 + 0.0612653i
\(359\) 2.90240e33i 1.76413i −0.471130 0.882064i \(-0.656154\pi\)
0.471130 0.882064i \(-0.343846\pi\)
\(360\) 7.04002e32 + 6.05614e32i 0.412707 + 0.355029i
\(361\) 6.41977e32 0.363016
\(362\) 4.89882e31 + 4.89882e31i 0.0267227 + 0.0267227i
\(363\) 2.05987e33 2.05987e33i 1.08406 1.08406i
\(364\) 1.82950e33i 0.928995i
\(365\) −1.08449e33 + 1.26068e33i −0.531397 + 0.617728i
\(366\) −5.02218e32 −0.237486
\(367\) 9.90575e32 + 9.90575e32i 0.452094 + 0.452094i 0.896049 0.443955i \(-0.146425\pi\)
−0.443955 + 0.896049i \(0.646425\pi\)
\(368\) −4.19455e32 + 4.19455e32i −0.184784 + 0.184784i
\(369\) 9.26680e33i 3.94082i
\(370\) −1.51903e31 2.02193e32i −0.00623653 0.0830125i
\(371\) 1.65815e33 0.657300
\(372\) −2.97042e32 2.97042e32i −0.113700 0.113700i
\(373\) −2.06595e33 + 2.06595e33i −0.763669 + 0.763669i −0.976984 0.213315i \(-0.931574\pi\)
0.213315 + 0.976984i \(0.431574\pi\)
\(374\) 3.26745e31i 0.0116648i
\(375\) 2.96910e33 4.73118e33i 1.02381 1.63141i
\(376\) 9.00589e31 0.0299975
\(377\) 1.67165e33 + 1.67165e33i 0.537907 + 0.537907i
\(378\) 5.24249e32 5.24249e32i 0.162984 0.162984i
\(379\) 1.23086e33i 0.369742i −0.982763 0.184871i \(-0.940813\pi\)
0.982763 0.184871i \(-0.0591867\pi\)
\(380\) −2.71380e33 + 2.03881e32i −0.787756 + 0.0591822i
\(381\) 4.60213e33 1.29102
\(382\) 6.43934e31 + 6.43934e31i 0.0174589 + 0.0174589i
\(383\) −2.72533e33 + 2.72533e33i −0.714225 + 0.714225i −0.967416 0.253191i \(-0.918520\pi\)
0.253191 + 0.967416i \(0.418520\pi\)
\(384\) 2.99282e33i 0.758185i
\(385\) −9.69259e32 8.33799e32i −0.237383 0.204208i
\(386\) 1.22578e32 0.0290252
\(387\) −1.03267e34 1.03267e34i −2.36439 2.36439i
\(388\) 1.06023e33 1.06023e33i 0.234741 0.234741i
\(389\) 3.51517e33i 0.752665i −0.926485 0.376332i \(-0.877185\pi\)
0.926485 0.376332i \(-0.122815\pi\)
\(390\) −8.29125e32 + 9.63825e32i −0.171704 + 0.199599i
\(391\) 3.44165e32 0.0689395
\(392\) −3.80817e32 3.80817e32i −0.0737901 0.0737901i
\(393\) −4.74177e33 + 4.74177e33i −0.888867 + 0.888867i
\(394\) 1.72575e32i 0.0312987i
\(395\) 3.66478e32 + 4.87808e33i 0.0643111 + 0.856025i
\(396\) 7.13422e33 1.21146
\(397\) 2.77671e33 + 2.77671e33i 0.456303 + 0.456303i 0.897440 0.441137i \(-0.145425\pi\)
−0.441137 + 0.897440i \(0.645425\pi\)
\(398\) 4.09026e32 4.09026e32i 0.0650536 0.0650536i
\(399\) 6.92255e33i 1.06566i
\(400\) −6.43330e33 + 9.72123e32i −0.958637 + 0.144858i
\(401\) −9.69690e33 −1.39880 −0.699401 0.714730i \(-0.746550\pi\)
−0.699401 + 0.714730i \(0.746550\pi\)
\(402\) −6.65157e32 6.65157e32i −0.0928936 0.0928936i
\(403\) 5.97152e32 5.97152e32i 0.0807457 0.0807457i
\(404\) 4.20945e33i 0.551148i
\(405\) 2.85708e34 2.14645e33i 3.62248 0.272148i
\(406\) −3.20302e32 −0.0393297
\(407\) −2.21426e33 2.21426e33i −0.263331 0.263331i
\(408\) −6.07551e32 + 6.07551e32i −0.0699843 + 0.0699843i
\(409\) 1.68312e34i 1.87807i −0.343826 0.939033i \(-0.611723\pi\)
0.343826 0.939033i \(-0.388277\pi\)
\(410\) 1.02984e33 + 8.85918e32i 0.111322 + 0.0957642i
\(411\) −1.84074e34 −1.92774
\(412\) 8.99501e33 + 8.99501e33i 0.912721 + 0.912721i
\(413\) −3.47818e33 + 3.47818e33i −0.341980 + 0.341980i
\(414\) 7.73988e32i 0.0737445i
\(415\) −4.91100e33 + 5.70884e33i −0.453466 + 0.527136i
\(416\) 4.52036e33 0.404538
\(417\) 9.65004e33 + 9.65004e33i 0.837068 + 0.837068i
\(418\) 3.06106e32 3.06106e32i 0.0257383 0.0257383i
\(419\) 9.88043e33i 0.805366i −0.915339 0.402683i \(-0.868078\pi\)
0.915339 0.402683i \(-0.131922\pi\)
\(420\) 1.25292e33 + 1.66772e34i 0.0990105 + 1.31790i
\(421\) 1.54830e34 1.18628 0.593141 0.805098i \(-0.297888\pi\)
0.593141 + 0.805098i \(0.297888\pi\)
\(422\) 1.69570e33 + 1.69570e33i 0.125976 + 0.125976i
\(423\) 3.97112e33 3.97112e33i 0.286080 0.286080i
\(424\) 2.72668e33i 0.190492i
\(425\) 3.03810e33 + 2.24046e33i 0.205847 + 0.151803i
\(426\) −2.59882e33 −0.170785
\(427\) −9.39104e33 9.39104e33i −0.598620 0.598620i
\(428\) −1.76322e34 + 1.76322e34i −1.09028 + 1.09028i
\(429\) 1.96350e34i 1.17784i
\(430\) −2.13488e33 + 1.60388e32i −0.124246 + 0.00933431i
\(431\) 2.61174e34 1.47477 0.737387 0.675470i \(-0.236059\pi\)
0.737387 + 0.675470i \(0.236059\pi\)
\(432\) −4.12016e34 4.12016e34i −2.25749 2.25749i
\(433\) 1.79399e34 1.79399e34i 0.953844 0.953844i −0.0451367 0.998981i \(-0.514372\pi\)
0.998981 + 0.0451367i \(0.0143723\pi\)
\(434\) 1.14419e32i 0.00590382i
\(435\) −1.63831e34 1.40935e34i −0.820420 0.705762i
\(436\) 5.49291e33 0.266979
\(437\) 3.22426e33 + 3.22426e33i 0.152115 + 0.152115i
\(438\) −2.44670e33 + 2.44670e33i −0.112051 + 0.112051i
\(439\) 2.56244e34i 1.13924i −0.821909 0.569619i \(-0.807091\pi\)
0.821909 0.569619i \(-0.192909\pi\)
\(440\) 1.37111e33 1.59386e33i 0.0591815 0.0687962i
\(441\) −3.35840e34 −1.40744
\(442\) −6.07559e32 6.07559e32i −0.0247229 0.0247229i
\(443\) −1.85005e34 + 1.85005e34i −0.731029 + 0.731029i −0.970824 0.239795i \(-0.922920\pi\)
0.239795 + 0.970824i \(0.422920\pi\)
\(444\) 4.09612e34i 1.57179i
\(445\) −3.25547e33 4.33325e34i −0.121320 1.61486i
\(446\) 3.15626e33 0.114240
\(447\) 2.37473e34 + 2.37473e34i 0.834865 + 0.834865i
\(448\) 1.34838e34 1.34838e34i 0.460467 0.460467i
\(449\) 3.29255e33i 0.109227i −0.998508 0.0546134i \(-0.982607\pi\)
0.998508 0.0546134i \(-0.0173926\pi\)
\(450\) 5.03855e33 6.83234e33i 0.162384 0.220195i
\(451\) 2.09800e34 0.656916
\(452\) 9.65582e33 + 9.65582e33i 0.293758 + 0.293758i
\(453\) −1.33018e34 + 1.33018e34i −0.393219 + 0.393219i
\(454\) 1.38106e33i 0.0396722i
\(455\) −3.35266e34 + 2.51877e33i −0.935926 + 0.0703138i
\(456\) −1.13835e34 −0.308840
\(457\) 2.99714e34 + 2.99714e34i 0.790308 + 0.790308i 0.981544 0.191236i \(-0.0612495\pi\)
−0.191236 + 0.981544i \(0.561249\pi\)
\(458\) 2.38810e33 2.38810e33i 0.0612070 0.0612070i
\(459\) 3.38061e34i 0.842229i
\(460\) 8.35115e33 + 7.18403e33i 0.202253 + 0.173987i
\(461\) 4.28219e34 1.00822 0.504108 0.863640i \(-0.331821\pi\)
0.504108 + 0.863640i \(0.331821\pi\)
\(462\) −1.88112e33 1.88112e33i −0.0430597 0.0430597i
\(463\) −2.59467e33 + 2.59467e33i −0.0577469 + 0.0577469i −0.735390 0.677644i \(-0.763001\pi\)
0.677644 + 0.735390i \(0.263001\pi\)
\(464\) 2.51730e34i 0.544756i
\(465\) −5.03452e33 + 5.85243e33i −0.105942 + 0.123154i
\(466\) 2.97306e33 0.0608397
\(467\) −7.71974e33 7.71974e33i −0.153633 0.153633i 0.626106 0.779738i \(-0.284648\pi\)
−0.779738 + 0.626106i \(0.784648\pi\)
\(468\) 1.32656e35 1.32656e35i 2.56762 2.56762i
\(469\) 2.48757e34i 0.468305i
\(470\) −6.16770e31 8.20964e32i −0.00112941 0.0150332i
\(471\) −1.34188e35 −2.39025
\(472\) −5.71954e33 5.71954e33i −0.0991095 0.0991095i
\(473\) −2.33796e34 + 2.33796e34i −0.394132 + 0.394132i
\(474\) 1.01785e34i 0.166942i
\(475\) 7.47250e33 + 4.94514e34i 0.119247 + 0.789154i
\(476\) −1.13025e34 −0.175502
\(477\) 1.20232e35 + 1.20232e35i 1.81669 + 1.81669i
\(478\) −6.53624e33 + 6.53624e33i −0.0961092 + 0.0961092i
\(479\) 9.13862e34i 1.30773i −0.756610 0.653867i \(-0.773146\pi\)
0.756610 0.653867i \(-0.226854\pi\)
\(480\) −4.12064e34 + 3.09574e33i −0.573890 + 0.0431149i
\(481\) −8.23454e34 −1.11623
\(482\) 1.06408e33 + 1.06408e33i 0.0140399 + 0.0140399i
\(483\) 1.98141e34 1.98141e34i 0.254484 0.254484i
\(484\) 6.30143e34i 0.787861i
\(485\) −2.08891e34 1.79697e34i −0.254259 0.218725i
\(486\) 3.15581e34 0.373973
\(487\) −7.26028e33 7.26028e33i −0.0837678 0.0837678i 0.663981 0.747749i \(-0.268865\pi\)
−0.747749 + 0.663981i \(0.768865\pi\)
\(488\) 1.54427e34 1.54427e34i 0.173486 0.173486i
\(489\) 4.15503e34i 0.454526i
\(490\) −3.21067e33 + 3.73228e33i −0.0342016 + 0.0397581i
\(491\) −9.35922e34 −0.970913 −0.485456 0.874261i \(-0.661346\pi\)
−0.485456 + 0.874261i \(0.661346\pi\)
\(492\) −1.94052e35 1.94052e35i −1.96052 1.96052i
\(493\) 1.03273e34 1.03273e34i 0.101619 0.101619i
\(494\) 1.13837e34i 0.109102i
\(495\) −9.82209e33 1.30739e35i −0.0916931 1.22050i
\(496\) 8.99239e33 0.0817736
\(497\) −4.85956e34 4.85956e34i −0.430491 0.430491i
\(498\) −1.10796e34 + 1.10796e34i −0.0956188 + 0.0956188i
\(499\) 3.71291e34i 0.312182i −0.987743 0.156091i \(-0.950111\pi\)
0.987743 0.156091i \(-0.0498893\pi\)
\(500\) 2.69523e34 + 1.17781e35i 0.220793 + 0.964865i
\(501\) 3.58857e35 2.86438
\(502\) −1.40637e34 1.40637e34i −0.109383 0.109383i
\(503\) 6.29619e34 6.29619e34i 0.477193 0.477193i −0.427040 0.904233i \(-0.640444\pi\)
0.904233 + 0.427040i \(0.140444\pi\)
\(504\) 5.10977e34i 0.377403i
\(505\) −7.71408e34 + 5.79540e33i −0.555260 + 0.0417153i
\(506\) −1.75230e33 −0.0122929
\(507\) 1.65915e35 + 1.65915e35i 1.13444 + 1.13444i
\(508\) −7.03929e34 + 7.03929e34i −0.469138 + 0.469138i
\(509\) 2.89188e35i 1.87866i 0.343010 + 0.939332i \(0.388554\pi\)
−0.343010 + 0.939332i \(0.611446\pi\)
\(510\) 5.95443e33 + 5.12226e33i 0.0377075 + 0.0324377i
\(511\) −9.15024e34 −0.564886
\(512\) 5.69206e34 + 5.69206e34i 0.342579 + 0.342579i
\(513\) −3.16708e35 + 3.16708e35i −1.85837 + 1.85837i
\(514\) 2.61596e34i 0.149662i
\(515\) 1.52455e35 1.77223e35i 0.850448 0.988612i
\(516\) 4.32494e35 2.35252
\(517\) −8.99058e33 8.99058e33i −0.0476882 0.0476882i
\(518\) 7.88903e33 7.88903e33i 0.0408072 0.0408072i
\(519\) 5.64230e35i 2.84630i
\(520\) −4.14189e33 5.51314e34i −0.0203777 0.271241i
\(521\) −1.51202e35 −0.725548 −0.362774 0.931877i \(-0.618170\pi\)
−0.362774 + 0.931877i \(0.618170\pi\)
\(522\) −2.32249e34 2.32249e34i −0.108702 0.108702i
\(523\) −1.20055e35 + 1.20055e35i −0.548099 + 0.548099i −0.925891 0.377792i \(-0.876684\pi\)
0.377792 + 0.925891i \(0.376684\pi\)
\(524\) 1.45057e35i 0.646001i
\(525\) 3.03895e35 4.59209e34i 1.32024 0.199498i
\(526\) −1.00297e34 −0.0425081
\(527\) −3.68915e33 3.68915e33i −0.0152542 0.0152542i
\(528\) −1.47840e35 + 1.47840e35i −0.596418 + 0.596418i
\(529\) 2.35595e35i 0.927349i
\(530\) 2.48560e34 1.86737e33i 0.0954652 0.00717207i
\(531\) −5.04402e35 −1.89038
\(532\) −1.05885e35 1.05885e35i −0.387244 0.387244i
\(533\) 3.90108e35 3.90108e35i 1.39229 1.39229i
\(534\) 9.04171e34i 0.314930i
\(535\) 3.47396e35 + 2.98845e35i 1.18093 + 1.01589i
\(536\) 4.09058e34 0.135720
\(537\) −3.60877e35 3.60877e35i −1.16867 1.16867i
\(538\) −2.32655e34 + 2.32655e34i −0.0735433 + 0.0735433i
\(539\) 7.60340e34i 0.234614i
\(540\) −7.05662e35 + 8.20304e35i −2.12558 + 2.47091i
\(541\) 1.60345e35 0.471510 0.235755 0.971812i \(-0.424244\pi\)
0.235755 + 0.971812i \(0.424244\pi\)
\(542\) 3.50344e34 + 3.50344e34i 0.100578 + 0.100578i
\(543\) −1.81868e35 + 1.81868e35i −0.509752 + 0.509752i
\(544\) 2.79264e34i 0.0764239i
\(545\) −7.56240e33 1.00661e35i −0.0202072 0.268971i
\(546\) −6.99562e34 −0.182525
\(547\) 3.88776e34 + 3.88776e34i 0.0990522 + 0.0990522i 0.754896 0.655844i \(-0.227687\pi\)
−0.655844 + 0.754896i \(0.727687\pi\)
\(548\) 2.81555e35 2.81555e35i 0.700512 0.700512i
\(549\) 1.36188e36i 3.30901i
\(550\) −1.54684e34 1.14072e34i −0.0367054 0.0270686i
\(551\) 1.93500e35 0.448445
\(552\) 3.25824e34 + 3.25824e34i 0.0737523 + 0.0737523i
\(553\) −1.90330e35 + 1.90330e35i −0.420804 + 0.420804i
\(554\) 3.66743e34i 0.0792017i
\(555\) 7.50638e35 5.63936e34i 1.58351 0.118966i
\(556\) −2.95209e35 −0.608355
\(557\) −1.15013e35 1.15013e35i −0.231541 0.231541i 0.581795 0.813336i \(-0.302351\pi\)
−0.813336 + 0.581795i \(0.802351\pi\)
\(558\) −8.29649e33 + 8.29649e33i −0.0163174 + 0.0163174i
\(559\) 8.69454e35i 1.67068i
\(560\) −2.71400e35 2.33470e35i −0.509525 0.438316i
\(561\) 1.21304e35 0.222513
\(562\) 3.54300e34 + 3.54300e34i 0.0635038 + 0.0635038i
\(563\) −1.31797e35 + 1.31797e35i −0.230832 + 0.230832i −0.813040 0.582208i \(-0.802189\pi\)
0.582208 + 0.813040i \(0.302189\pi\)
\(564\) 1.66315e35i 0.284644i
\(565\) 1.63655e35 1.90242e35i 0.273716 0.318184i
\(566\) −2.33962e34 −0.0382412
\(567\) 1.11476e36 + 1.11476e36i 1.78074 + 1.78074i
\(568\) 7.99110e34 7.99110e34i 0.124761 0.124761i
\(569\) 7.73690e35i 1.18061i 0.807179 + 0.590307i \(0.200993\pi\)
−0.807179 + 0.590307i \(0.799007\pi\)
\(570\) 7.79601e33 + 1.03770e35i 0.0116278 + 0.154775i
\(571\) −3.49753e35 −0.509908 −0.254954 0.966953i \(-0.582060\pi\)
−0.254954 + 0.966953i \(0.582060\pi\)
\(572\) −3.00332e35 3.00332e35i −0.428009 0.428009i
\(573\) −2.39060e35 + 2.39060e35i −0.333040 + 0.333040i
\(574\) 7.47479e34i 0.101799i
\(575\) 1.20154e35 1.62930e35i 0.159977 0.216930i
\(576\) 1.95541e36 2.54534
\(577\) −6.69537e35 6.69537e35i −0.852096 0.852096i 0.138295 0.990391i \(-0.455838\pi\)
−0.990391 + 0.138295i \(0.955838\pi\)
\(578\) 5.36234e34 5.36234e34i 0.0667256 0.0667256i
\(579\) 4.55067e35i 0.553674i
\(580\) 4.66162e35 3.50216e34i 0.554591 0.0416650i
\(581\) −4.14358e35 −0.482044
\(582\) −4.05411e34 4.05411e34i −0.0461208 0.0461208i
\(583\) 2.72204e35 2.72204e35i 0.302833 0.302833i
\(584\) 1.50467e35i 0.163710i
\(585\) −2.61363e36 2.24836e36i −2.78111 2.39244i
\(586\) 1.21799e35 0.126758
\(587\) 3.03209e34 + 3.03209e34i 0.0308636 + 0.0308636i 0.722370 0.691507i \(-0.243053\pi\)
−0.691507 + 0.722370i \(0.743053\pi\)
\(588\) 7.03268e35 7.03268e35i 0.700189 0.700189i
\(589\) 6.91226e34i 0.0673164i
\(590\) −4.82215e34 + 5.60555e34i −0.0459372 + 0.0534001i
\(591\) −6.40681e35 −0.597042
\(592\) −6.20011e35 6.20011e35i −0.565220 0.565220i
\(593\) −1.06738e36 + 1.06738e36i −0.951935 + 0.951935i −0.998897 0.0469616i \(-0.985046\pi\)
0.0469616 + 0.998897i \(0.485046\pi\)
\(594\) 1.72123e35i 0.150181i
\(595\) 1.55607e34 + 2.07124e35i 0.0132834 + 0.176812i
\(596\) −7.26464e35 −0.606754
\(597\) 1.51850e36 + 1.51850e36i 1.24094 + 1.24094i
\(598\) −3.25829e34 + 3.25829e34i −0.0260540 + 0.0260540i
\(599\) 1.50216e36i 1.17535i 0.809096 + 0.587676i \(0.199957\pi\)
−0.809096 + 0.587676i \(0.800043\pi\)
\(600\) 7.55127e34 + 4.99727e35i 0.0578167 + 0.382619i
\(601\) −1.91246e36 −1.43293 −0.716463 0.697625i \(-0.754240\pi\)
−0.716463 + 0.697625i \(0.754240\pi\)
\(602\) −8.32973e34 8.32973e34i −0.0610768 0.0610768i
\(603\) 1.80373e36 1.80373e36i 1.29433 1.29433i
\(604\) 4.06922e35i 0.285779i
\(605\) 1.15478e36 8.67554e34i 0.793739 0.0596316i
\(606\) −1.60961e35 −0.108287
\(607\) 1.04936e36 + 1.04936e36i 0.690990 + 0.690990i 0.962450 0.271460i \(-0.0875065\pi\)
−0.271460 + 0.962450i \(0.587506\pi\)
\(608\) 2.61624e35 2.61624e35i 0.168629 0.168629i
\(609\) 1.18912e36i 0.750239i
\(610\) −1.51349e35 1.30197e35i −0.0934744 0.0804108i
\(611\) −3.34347e35 −0.202144
\(612\) −8.19536e35 8.19536e35i −0.485065 0.485065i
\(613\) 1.26683e36 1.26683e36i 0.734063 0.734063i −0.237359 0.971422i \(-0.576282\pi\)
0.971422 + 0.237359i \(0.0762819\pi\)
\(614\) 1.49491e35i 0.0848058i
\(615\) −3.28896e36 + 3.82328e36i −1.82676 + 2.12354i
\(616\) 1.15685e35 0.0629112
\(617\) 1.65895e35 + 1.65895e35i 0.0883338 + 0.0883338i 0.749893 0.661559i \(-0.230105\pi\)
−0.661559 + 0.749893i \(0.730105\pi\)
\(618\) 3.43951e35 3.43951e35i 0.179327 0.179327i
\(619\) 2.32624e36i 1.18762i −0.804607 0.593808i \(-0.797624\pi\)
0.804607 0.593808i \(-0.202376\pi\)
\(620\) −1.25105e34 1.66524e35i −0.00625437 0.0832500i
\(621\) 1.81299e36 0.887575
\(622\) −7.57294e34 7.57294e34i −0.0363069 0.0363069i
\(623\) 1.69072e36 1.69072e36i 0.793830 0.793830i
\(624\) 5.49796e36i 2.52815i
\(625\) 2.12131e36 6.56074e35i 0.955352 0.295469i
\(626\) −3.93886e35 −0.173742
\(627\) 1.13641e36 + 1.13641e36i 0.490974 + 0.490974i
\(628\) 2.05251e36 2.05251e36i 0.868580 0.868580i
\(629\) 5.08723e35i 0.210874i
\(630\) 4.65800e35 3.49944e34i 0.189135 0.0142093i
\(631\) 2.11178e36 0.839976 0.419988 0.907530i \(-0.362034\pi\)
0.419988 + 0.907530i \(0.362034\pi\)
\(632\) −3.12980e35 3.12980e35i −0.121953 0.121953i
\(633\) −6.29526e36 + 6.29526e36i −2.40307 + 2.40307i
\(634\) 1.72776e35i 0.0646136i
\(635\) 1.38691e36 + 1.19308e36i 0.508146 + 0.437130i
\(636\) −5.03545e36 −1.80757
\(637\) 1.41380e36 + 1.41380e36i 0.497250 + 0.497250i
\(638\) −5.25811e34 + 5.25811e34i −0.0181201 + 0.0181201i
\(639\) 7.04729e36i 2.37964i
\(640\) 7.75874e35 9.01923e35i 0.256715 0.298421i
\(641\) 8.23577e35 0.267024 0.133512 0.991047i \(-0.457375\pi\)
0.133512 + 0.991047i \(0.457375\pi\)
\(642\) 6.74219e35 + 6.74219e35i 0.214213 + 0.214213i
\(643\) 7.37575e34 7.37575e34i 0.0229648 0.0229648i −0.695531 0.718496i \(-0.744831\pi\)
0.718496 + 0.695531i \(0.244831\pi\)
\(644\) 6.06141e35i 0.184951i
\(645\) −5.95439e35 7.92571e36i −0.178058 2.37007i
\(646\) −7.03272e34 −0.0206111
\(647\) −2.25014e36 2.25014e36i −0.646329 0.646329i 0.305775 0.952104i \(-0.401085\pi\)
−0.952104 + 0.305775i \(0.901085\pi\)
\(648\) −1.83311e36 + 1.83311e36i −0.516076 + 0.516076i
\(649\) 1.14196e36i 0.315116i
\(650\) −4.99733e35 + 7.55137e34i −0.135165 + 0.0204245i
\(651\) −4.24780e35 −0.112619
\(652\) −6.35542e35 6.35542e35i −0.165168 0.165168i
\(653\) −4.31573e36 + 4.31573e36i −1.09947 + 1.09947i −0.104995 + 0.994473i \(0.533483\pi\)
−0.994473 + 0.104995i \(0.966517\pi\)
\(654\) 2.10038e35i 0.0524549i
\(655\) −2.65827e36 + 1.99709e35i −0.650821 + 0.0488946i
\(656\) 5.87456e36 1.41002
\(657\) −6.63479e36 6.63479e36i −1.56127 1.56127i
\(658\) 3.20319e34 3.20319e34i 0.00739002 0.00739002i
\(659\) 3.38273e36i 0.765168i −0.923921 0.382584i \(-0.875034\pi\)
0.923921 0.382584i \(-0.124966\pi\)
\(660\) 2.94343e36 + 2.53207e36i 0.652803 + 0.561570i
\(661\) 8.18651e36 1.78025 0.890123 0.455721i \(-0.150619\pi\)
0.890123 + 0.455721i \(0.150619\pi\)
\(662\) 3.94616e35 + 3.94616e35i 0.0841436 + 0.0841436i
\(663\) 2.25555e36 2.25555e36i 0.471604 0.471604i
\(664\) 6.81374e35i 0.139701i
\(665\) −1.79464e36 + 2.08619e36i −0.360824 + 0.419443i
\(666\) 1.14406e36 0.225571
\(667\) −5.53844e35 5.53844e35i −0.107091 0.107091i
\(668\) −5.48898e36 + 5.48898e36i −1.04087 + 1.04087i
\(669\) 1.17176e37i 2.17920i
\(670\) −2.80144e34 3.72892e35i −0.00510986 0.0680158i
\(671\) −3.08329e36 −0.551596
\(672\) −1.60776e36 1.60776e36i −0.282112 0.282112i
\(673\) 3.37485e36 3.37485e36i 0.580843 0.580843i −0.354292 0.935135i \(-0.615278\pi\)
0.935135 + 0.354292i \(0.115278\pi\)
\(674\) 9.30801e34i 0.0157137i
\(675\) 1.60041e37 + 1.18023e37i 2.65022 + 1.95442i
\(676\) −5.07557e36 −0.824476
\(677\) −2.01599e36 2.01599e36i −0.321244 0.321244i 0.528000 0.849244i \(-0.322942\pi\)
−0.849244 + 0.528000i \(0.822942\pi\)
\(678\) 3.69219e35 3.69219e35i 0.0577162 0.0577162i
\(679\) 1.51617e36i 0.232509i
\(680\) −3.40597e35 + 2.55882e34i −0.0512419 + 0.00384968i
\(681\) 5.12717e36 0.756772
\(682\) 1.87832e34 + 1.87832e34i 0.00272002 + 0.00272002i
\(683\) 3.31684e36 3.31684e36i 0.471255 0.471255i −0.431066 0.902320i \(-0.641862\pi\)
0.902320 + 0.431066i \(0.141862\pi\)
\(684\) 1.53554e37i 2.14058i
\(685\) −5.54730e36 4.77203e36i −0.758759 0.652718i
\(686\) −7.92438e35 −0.106353
\(687\) 8.86578e36 + 8.86578e36i 1.16756 + 1.16756i
\(688\) −6.54646e36 + 6.54646e36i −0.845974 + 0.845974i
\(689\) 1.01229e37i 1.28367i
\(690\) 2.74703e35 3.19331e35i 0.0341841 0.0397377i
\(691\) −9.98786e36 −1.21971 −0.609857 0.792512i \(-0.708773\pi\)
−0.609857 + 0.792512i \(0.708773\pi\)
\(692\) 8.63030e36 + 8.63030e36i 1.03430 + 1.03430i
\(693\) 5.10109e36 5.10109e36i 0.599972 0.599972i
\(694\) 1.24271e36i 0.143449i
\(695\) 4.06431e35 + 5.40988e36i 0.0460452 + 0.612894i
\(696\) 1.95539e36 0.217427
\(697\) −2.41005e36 2.41005e36i −0.263027 0.263027i
\(698\) −7.36305e35 + 7.36305e35i −0.0788747 + 0.0788747i
\(699\) 1.10375e37i 1.16056i
\(700\) −3.94589e36 + 5.35068e36i −0.407259 + 0.552248i
\(701\) −1.70246e36 −0.172481 −0.0862406 0.996274i \(-0.527485\pi\)
−0.0862406 + 0.996274i \(0.527485\pi\)
\(702\) −3.20050e36 3.20050e36i −0.318299 0.318299i
\(703\) −4.76589e36 + 4.76589e36i −0.465291 + 0.465291i
\(704\) 4.42704e36i 0.424296i
\(705\) 3.04782e36 2.28975e35i 0.286768 0.0215442i
\(706\) 1.31545e36 0.121510
\(707\) −3.00983e36 3.00983e36i −0.272954 0.272954i
\(708\) 1.05625e37 1.05625e37i 0.940444 0.940444i
\(709\) 1.99265e36i 0.174193i 0.996200 + 0.0870963i \(0.0277588\pi\)
−0.996200 + 0.0870963i \(0.972241\pi\)
\(710\) −7.83184e35 6.73730e35i −0.0672211 0.0578265i
\(711\) −2.76014e37 −2.32609
\(712\) 2.78023e36 + 2.78023e36i 0.230060 + 0.230060i
\(713\) −1.97846e35 + 1.97846e35i −0.0160755 + 0.0160755i
\(714\) 4.32183e35i 0.0344819i
\(715\) −5.09028e36 + 5.91725e36i −0.398807 + 0.463598i
\(716\) 1.10397e37 0.849356
\(717\) −2.42657e37 2.42657e37i −1.83334 1.83334i
\(718\) 1.69755e36 1.69755e36i 0.125952 0.125952i
\(719\) 9.34472e36i 0.680912i −0.940261 0.340456i \(-0.889419\pi\)
0.940261 0.340456i \(-0.110581\pi\)
\(720\) −2.75026e36 3.66079e37i −0.196812 2.61971i
\(721\) 1.28632e37 0.904044
\(722\) 3.75478e35 + 3.75478e35i 0.0259180 + 0.0259180i
\(723\) −3.95040e36 + 3.95040e36i −0.267820 + 0.267820i
\(724\) 5.56361e36i 0.370472i
\(725\) −1.28358e36 8.49448e36i −0.0839518 0.555575i
\(726\) 2.40954e36 0.154795
\(727\) 2.09778e37 + 2.09778e37i 1.32377 + 1.32377i 0.910697 + 0.413075i \(0.135545\pi\)
0.413075 + 0.910697i \(0.364455\pi\)
\(728\) 2.15108e36 2.15108e36i 0.133336 0.133336i
\(729\) 5.74987e37i 3.50106i
\(730\) −1.37164e36 + 1.03048e35i −0.0820431 + 0.00616370i
\(731\) 5.37141e36 0.315618
\(732\) 2.85185e37 + 2.85185e37i 1.64620 + 1.64620i
\(733\) −1.48463e37 + 1.48463e37i −0.841913 + 0.841913i −0.989108 0.147194i \(-0.952976\pi\)
0.147194 + 0.989108i \(0.452976\pi\)
\(734\) 1.15873e36i 0.0645555i
\(735\) −1.38560e37 1.19196e37i −0.758409 0.652417i
\(736\) −1.49767e36 −0.0805386
\(737\) −4.08363e36 4.08363e36i −0.215759 0.215759i
\(738\) −5.41994e36 + 5.41994e36i −0.281360 + 0.281360i
\(739\) 5.46072e36i 0.278530i −0.990255 0.139265i \(-0.955526\pi\)
0.990255 0.139265i \(-0.0444740\pi\)
\(740\) −1.06190e37 + 1.23441e37i −0.532194 + 0.618655i
\(741\) 4.22617e37 2.08118
\(742\) 9.69816e35 + 9.69816e35i 0.0469287 + 0.0469287i
\(743\) 2.68229e37 2.68229e37i 1.27541 1.27541i 0.332206 0.943207i \(-0.392207\pi\)
0.943207 0.332206i \(-0.107793\pi\)
\(744\) 6.98512e35i 0.0326381i
\(745\) 1.00016e36 + 1.33129e37i 0.0459240 + 0.611281i
\(746\) −2.41666e36 −0.109046
\(747\) −3.00449e37 3.00449e37i −1.33230 1.33230i
\(748\) −1.85543e36 + 1.85543e36i −0.0808579 + 0.0808579i
\(749\) 2.52146e37i 1.07991i
\(750\) 4.50372e36 1.03060e36i 0.189572 0.0433805i
\(751\) −4.40539e36 −0.182249 −0.0911245 0.995840i \(-0.529046\pi\)
−0.0911245 + 0.995840i \(0.529046\pi\)
\(752\) −2.51743e36 2.51743e36i −0.102359 0.102359i
\(753\) 5.22112e37 5.22112e37i 2.08655 2.08655i
\(754\) 1.95542e36i 0.0768090i
\(755\) −7.45709e36 + 5.60233e35i −0.287911 + 0.0216301i
\(756\) −5.95392e37 −2.25954
\(757\) 8.92923e36 + 8.92923e36i 0.333095 + 0.333095i 0.853761 0.520666i \(-0.174316\pi\)
−0.520666 + 0.853761i \(0.674316\pi\)
\(758\) 7.19902e35 7.19902e35i 0.0263982 0.0263982i
\(759\) 6.50540e36i 0.234494i
\(760\) −3.43055e36 2.95111e36i −0.121559 0.104571i
\(761\) 2.83232e37 0.986600 0.493300 0.869859i \(-0.335790\pi\)
0.493300 + 0.869859i \(0.335790\pi\)
\(762\) 2.69168e36 + 2.69168e36i 0.0921741 + 0.0921741i
\(763\) 3.92752e36 3.92752e36i 0.132221 0.132221i
\(764\) 7.31318e36i 0.242043i
\(765\) −1.38902e37 + 1.61468e37i −0.451970 + 0.525397i
\(766\) −3.18797e36 −0.101986
\(767\) 2.12340e37 + 2.12340e37i 0.667870 + 0.667870i
\(768\) −3.96187e37 + 3.96187e37i −1.22519 + 1.22519i
\(769\) 2.43349e37i 0.739923i −0.929047 0.369962i \(-0.879371\pi\)
0.929047 0.369962i \(-0.120629\pi\)
\(770\) −7.92271e34 1.05457e36i −0.00236861 0.0315279i
\(771\) −9.71173e37 −2.85489
\(772\) −6.96058e36 6.96058e36i −0.201197 0.201197i
\(773\) −2.28771e37 + 2.28771e37i −0.650230 + 0.650230i −0.953048 0.302818i \(-0.902073\pi\)
0.302818 + 0.953048i \(0.402073\pi\)
\(774\) 1.20797e37i 0.337616i
\(775\) −3.03442e36 + 4.58526e35i −0.0833977 + 0.0126021i
\(776\) 2.49319e36 0.0673835
\(777\) 2.92879e37 + 2.92879e37i 0.778422 + 0.778422i
\(778\) 2.05594e36 2.05594e36i 0.0537374 0.0537374i
\(779\) 4.51565e37i 1.16073i
\(780\) 1.01813e38 7.64896e36i 2.57379 0.193363i
\(781\) −1.59550e37 −0.396674
\(782\) 2.01294e35 + 2.01294e35i 0.00492202 + 0.00492202i
\(783\) 5.44022e37 5.44022e37i 1.30832 1.30832i
\(784\) 2.12901e37i 0.503581i
\(785\) −4.04393e37 3.47877e37i −0.940801 0.809319i
\(786\) −5.54670e36 −0.126923
\(787\) −3.51698e37 3.51698e37i −0.791586 0.791586i 0.190166 0.981752i \(-0.439097\pi\)
−0.981752 + 0.190166i \(0.939097\pi\)
\(788\) 9.79968e36 9.79968e36i 0.216956 0.216956i
\(789\) 3.72350e37i 0.810868i
\(790\) −2.63873e36 + 3.06742e36i −0.0565253 + 0.0657085i
\(791\) 1.38081e37 0.290965
\(792\) 8.38827e36 + 8.38827e36i 0.173878 + 0.173878i
\(793\) −5.73316e37 + 5.73316e37i −1.16908 + 1.16908i
\(794\) 3.24807e36i 0.0651566i
\(795\) 6.93259e36 + 9.22776e37i 0.136812 + 1.82106i
\(796\) −4.64532e37 −0.901875
\(797\) −1.57853e36 1.57853e36i −0.0301506 0.0301506i 0.691871 0.722021i \(-0.256787\pi\)
−0.722021 + 0.691871i \(0.756787\pi\)
\(798\) −4.04884e36 + 4.04884e36i −0.0760840 + 0.0760840i
\(799\) 2.06557e36i 0.0381884i
\(800\) −1.32206e37 9.74961e36i −0.240481 0.177344i
\(801\) 2.45187e38 4.38808
\(802\) −5.67150e36 5.67150e36i −0.0998690 0.0998690i
\(803\) −1.50211e37 + 1.50211e37i −0.260256 + 0.260256i
\(804\) 7.55421e37i 1.28784i
\(805\) 1.11079e37 8.34510e35i 0.186331 0.0139986i
\(806\) 6.98521e35 0.0115299
\(807\) −8.63729e37 8.63729e37i −1.40288 1.40288i
\(808\) 4.94939e36 4.94939e36i 0.0791050 0.0791050i
\(809\) 8.05592e37i 1.26702i 0.773734 + 0.633511i \(0.218387\pi\)
−0.773734 + 0.633511i \(0.781613\pi\)
\(810\) 1.79658e37 + 1.54550e37i 0.278062 + 0.239201i
\(811\) 1.27337e38 1.93948 0.969739 0.244143i \(-0.0785068\pi\)
0.969739 + 0.244143i \(0.0785068\pi\)
\(812\) 1.81884e37 + 1.81884e37i 0.272625 + 0.272625i
\(813\) −1.30065e38 + 1.30065e38i −1.91859 + 1.91859i
\(814\) 2.59015e36i 0.0376016i
\(815\) −1.07717e37 + 1.25217e37i −0.153899 + 0.178901i
\(816\) 3.39659e37 0.477608
\(817\) 5.03213e37 + 5.03213e37i 0.696410 + 0.696410i
\(818\) 9.84416e36 9.84416e36i 0.134087 0.134087i
\(819\) 1.89702e38i 2.54321i
\(820\) −8.17289e36 1.08787e38i −0.107844 1.43548i
\(821\) −1.02720e38 −1.33412 −0.667061 0.745003i \(-0.732448\pi\)
−0.667061 + 0.745003i \(0.732448\pi\)
\(822\) −1.07661e37 1.07661e37i −0.137634 0.137634i
\(823\) 4.91705e37 4.91705e37i 0.618738 0.618738i −0.326469 0.945208i \(-0.605859\pi\)
0.945208 + 0.326469i \(0.105859\pi\)
\(824\) 2.11523e37i 0.262001i
\(825\) 4.23493e37 5.74261e37i 0.516350 0.700177i
\(826\) −4.06861e36 −0.0488321
\(827\) −5.51949e37 5.51949e37i −0.652119 0.652119i 0.301384 0.953503i \(-0.402552\pi\)
−0.953503 + 0.301384i \(0.902552\pi\)
\(828\) −4.39510e37 + 4.39510e37i −0.511181 + 0.511181i
\(829\) 2.06117e36i 0.0235996i −0.999930 0.0117998i \(-0.996244\pi\)
0.999930 0.0117998i \(-0.00375609\pi\)
\(830\) −6.21131e36 + 4.66640e35i −0.0700112 + 0.00525977i
\(831\) −1.36153e38 −1.51082
\(832\) −8.23176e37 8.23176e37i −0.899269 0.899269i
\(833\) 8.73432e36 8.73432e36i 0.0939386 0.0939386i
\(834\) 1.12882e37i 0.119527i
\(835\) 1.08146e38 + 9.30319e37i 1.12742 + 0.969857i
\(836\) −3.47646e37 −0.356825
\(837\) −1.94337e37 1.94337e37i −0.196393 0.196393i
\(838\) 5.77884e36 5.77884e36i 0.0575000 0.0575000i
\(839\) 9.33800e37i 0.914847i 0.889249 + 0.457424i \(0.151228\pi\)
−0.889249 + 0.457424i \(0.848772\pi\)
\(840\) −1.81355e37 + 2.10818e37i −0.174944 + 0.203366i
\(841\) 7.20423e37 0.684289
\(842\) 9.05566e36 + 9.05566e36i 0.0846960 + 0.0846960i
\(843\) −1.31534e38 + 1.31534e38i −1.21137 + 1.21137i
\(844\) 1.92581e38i 1.74647i
\(845\) 6.98783e36 + 9.30129e37i 0.0624029 + 0.830627i
\(846\) 4.64523e36 0.0408500
\(847\) 4.50563e37 + 4.50563e37i 0.390185 + 0.390185i
\(848\) 7.62193e37 7.62193e37i 0.650008 0.650008i
\(849\) 8.68580e37i 0.729474i
\(850\) 4.66517e35 + 3.08731e36i 0.00385853 + 0.0255349i
\(851\) 2.72824e37 0.222227
\(852\) 1.47574e38 + 1.47574e38i 1.18385 + 1.18385i
\(853\) 1.28609e38 1.28609e38i 1.01610 1.01610i 0.0162296 0.999868i \(-0.494834\pi\)
0.999868 0.0162296i \(-0.00516628\pi\)
\(854\) 1.09852e37i 0.0854783i
\(855\) −2.81397e38 + 2.11407e37i −2.15655 + 0.162017i
\(856\) −4.14631e37 −0.312970
\(857\) −7.53926e37 7.53926e37i −0.560503 0.560503i 0.368947 0.929450i \(-0.379718\pi\)
−0.929450 + 0.368947i \(0.879718\pi\)
\(858\) −1.14841e37 + 1.14841e37i −0.0840934 + 0.0840934i
\(859\) 1.12492e38i 0.811357i 0.914016 + 0.405678i \(0.132965\pi\)
−0.914016 + 0.405678i \(0.867035\pi\)
\(860\) 1.30337e38 + 1.12122e38i 0.925951 + 0.796544i
\(861\) −2.77501e38 −1.94188
\(862\) 1.52755e37 + 1.52755e37i 0.105293 + 0.105293i
\(863\) 7.22473e37 7.22473e37i 0.490547 0.490547i −0.417931 0.908479i \(-0.637245\pi\)
0.908479 + 0.417931i \(0.137245\pi\)
\(864\) 1.47111e38i 0.983934i
\(865\) 1.46274e38 1.70037e38i 0.963733 1.12030i
\(866\) 2.09853e37 0.136202
\(867\) 1.99076e38 + 1.99076e38i 1.27283 + 1.27283i
\(868\) 6.49732e36 6.49732e36i 0.0409240 0.0409240i
\(869\) 6.24895e37i 0.387748i
\(870\) −1.33915e36 1.78251e37i −0.00818616 0.108964i
\(871\) −1.51864e38 −0.914576
\(872\) 6.45844e36 + 6.45844e36i 0.0383189 + 0.0383189i
\(873\) 1.09936e38 1.09936e38i 0.642624 0.642624i
\(874\) 3.77159e36i 0.0217208i
\(875\) 1.03487e38 + 6.49443e37i 0.587193 + 0.368499i
\(876\) 2.77873e38 1.55343
\(877\) 1.27333e38 + 1.27333e38i 0.701370 + 0.701370i 0.964705 0.263334i \(-0.0848222\pi\)
−0.263334 + 0.964705i \(0.584822\pi\)
\(878\) 1.49871e37 1.49871e37i 0.0813372 0.0813372i
\(879\) 4.52178e38i 2.41799i
\(880\) −8.28801e37 + 6.22658e36i −0.436692 + 0.0328076i
\(881\) −7.87063e37 −0.408623 −0.204312 0.978906i \(-0.565496\pi\)
−0.204312 + 0.978906i \(0.565496\pi\)
\(882\) −1.96425e37 1.96425e37i −0.100486 0.100486i
\(883\) −9.98733e36 + 9.98733e36i −0.0503454 + 0.0503454i −0.731831 0.681486i \(-0.761334\pi\)
0.681486 + 0.731831i \(0.261334\pi\)
\(884\) 6.90007e37i 0.342747i
\(885\) −2.08105e38 1.79022e38i −1.01864 0.876280i
\(886\) −2.16410e37 −0.104385
\(887\) −1.82710e38 1.82710e38i −0.868472 0.868472i 0.123832 0.992303i \(-0.460482\pi\)
−0.992303 + 0.123832i \(0.960482\pi\)
\(888\) −4.81613e37 + 4.81613e37i −0.225595 + 0.225595i
\(889\) 1.00664e38i 0.464678i
\(890\) 2.34402e37 2.72483e37i 0.106633 0.123956i
\(891\) 3.65999e38 1.64085
\(892\) −1.79229e38 1.79229e38i −0.791889 0.791889i
\(893\) −1.93510e37 + 1.93510e37i −0.0842624 + 0.0842624i
\(894\) 2.77785e37i 0.119212i
\(895\) −1.51990e37 2.02310e38i −0.0642861 0.855692i
\(896\) 6.54632e37 0.272893
\(897\) −1.20963e38 1.20963e38i −0.496995 0.496995i
\(898\) 1.92573e36 1.92573e36i 0.00779838 0.00779838i
\(899\) 1.18735e37i 0.0473917i
\(900\) −6.74090e38 + 1.01860e38i −2.65195 + 0.400731i
\(901\) −6.25384e37 −0.242507
\(902\) 1.22707e37 + 1.22707e37i 0.0469013 + 0.0469013i
\(903\) 3.09240e38 3.09240e38i 1.16508 1.16508i
\(904\) 2.27062e37i 0.0843248i
\(905\) −1.01957e38 + 7.65974e36i −0.373236 + 0.0280403i
\(906\) −1.55599e37 −0.0561486
\(907\) −1.23099e38 1.23099e38i −0.437886 0.437886i 0.453414 0.891300i \(-0.350206\pi\)
−0.891300 + 0.453414i \(0.850206\pi\)
\(908\) −7.84237e37 + 7.84237e37i −0.274999 + 0.274999i
\(909\) 4.36483e38i 1.50882i
\(910\) −2.10821e37 1.81358e37i −0.0718416 0.0618014i
\(911\) 1.59759e38 0.536693 0.268346 0.963323i \(-0.413523\pi\)
0.268346 + 0.963323i \(0.413523\pi\)
\(912\) 3.18205e38 + 3.18205e38i 1.05384 + 1.05384i
\(913\) −6.80215e37 + 6.80215e37i −0.222089 + 0.222089i
\(914\) 3.50592e37i 0.112850i
\(915\) 4.83356e38 5.61882e38i 1.53389 1.78308i
\(916\) −2.71217e38 −0.848547
\(917\) −1.03718e38 1.03718e38i −0.319930 0.319930i
\(918\) −1.97724e37 + 1.97724e37i −0.0601319 + 0.0601319i
\(919\) 5.38324e38i 1.61414i 0.590453 + 0.807072i \(0.298949\pi\)
−0.590453 + 0.807072i \(0.701051\pi\)
\(920\) 1.37227e36 + 1.82659e37i 0.00405694 + 0.0540008i
\(921\) −5.54983e38 −1.61772
\(922\) 2.50456e37 + 2.50456e37i 0.0719828 + 0.0719828i
\(923\) −2.96672e38 + 2.96672e38i −0.840727 + 0.840727i
\(924\) 2.13639e38i 0.596960i
\(925\) 2.40834e38 + 1.77604e38i 0.663551 + 0.489340i
\(926\) −3.03512e36 −0.00824582
\(927\) 9.32702e38 + 9.32702e38i 2.49866 + 2.49866i
\(928\) −4.49403e37 + 4.49403e37i −0.118717 + 0.118717i
\(929\) 1.50101e38i 0.391003i −0.980703 0.195501i \(-0.937367\pi\)
0.980703 0.195501i \(-0.0626334\pi\)
\(930\) −6.36753e36 + 4.78377e35i −0.0163566 + 0.00122883i
\(931\) 1.63652e38 0.414550
\(932\) −1.68826e38 1.68826e38i −0.421728 0.421728i
\(933\) 2.81144e38 2.81144e38i 0.692577 0.692577i
\(934\) 9.03020e36i 0.0219375i
\(935\) 3.65563e37 + 3.14473e37i 0.0875812 + 0.0753412i
\(936\) 3.11948e38 0.737048
\(937\) 3.00601e37 + 3.00601e37i 0.0700447 + 0.0700447i 0.741261 0.671217i \(-0.234228\pi\)
−0.671217 + 0.741261i \(0.734228\pi\)
\(938\) 1.45492e37 1.45492e37i 0.0334352 0.0334352i
\(939\) 1.46230e39i 3.31423i
\(940\) −4.31162e37 + 5.01209e37i −0.0963782 + 0.112036i
\(941\) −1.25674e38 −0.277064 −0.138532 0.990358i \(-0.544238\pi\)
−0.138532 + 0.990358i \(0.544238\pi\)
\(942\) −7.84838e37 7.84838e37i −0.170655 0.170655i
\(943\) −1.29249e38 + 1.29249e38i −0.277189 + 0.277189i
\(944\) 3.19759e38i 0.676373i
\(945\) 8.19710e37 + 1.09109e39i 0.171020 + 2.27639i
\(946\) −2.73484e37 −0.0562790
\(947\) −4.87143e38 4.87143e38i −0.988796 0.988796i 0.0111424 0.999938i \(-0.496453\pi\)
−0.999938 + 0.0111424i \(0.996453\pi\)
\(948\) 5.77990e38 5.77990e38i 1.15721 1.15721i
\(949\) 5.58615e38i 1.10319i
\(950\) −2.45525e37 + 3.32935e37i −0.0478287 + 0.0648564i
\(951\) −6.41430e38 −1.23254
\(952\) −1.32892e37 1.32892e37i −0.0251894 0.0251894i
\(953\) 6.26048e38 6.26048e38i 1.17058 1.17058i 0.188505 0.982072i \(-0.439636\pi\)
0.982072 0.188505i \(-0.0603640\pi\)
\(954\) 1.40642e38i 0.259409i
\(955\) −1.34018e38 + 1.00685e37i −0.243849 + 0.0183198i
\(956\) 7.42322e38 1.33242
\(957\) −1.95207e38 1.95207e38i −0.345652 0.345652i
\(958\) 5.34497e37 5.34497e37i 0.0933671 0.0933671i
\(959\) 4.02633e38i 0.693853i
\(960\) 8.06760e38 + 6.94011e38i 1.37157 + 1.17989i
\(961\) −5.91975e38 −0.992886
\(962\) −4.81619e37 4.81619e37i −0.0796944 0.0796944i
\(963\) −1.82830e39 + 1.82830e39i −2.98473 + 2.98473i
\(964\) 1.20848e38i 0.194643i
\(965\) −1.17974e38 + 1.37140e38i −0.187470 + 0.217926i
\(966\) 2.31776e37 0.0363384
\(967\) 8.30973e38 + 8.30973e38i 1.28541 + 1.28541i 0.937543 + 0.347870i \(0.113095\pi\)
0.347870 + 0.937543i \(0.386905\pi\)
\(968\) −7.40909e37 + 7.40909e37i −0.113080 + 0.113080i
\(969\) 2.61089e38i 0.393169i
\(970\) −1.70747e36 2.27276e37i −0.00253700 0.0337692i
\(971\) 1.20931e39 1.77291 0.886454 0.462817i \(-0.153161\pi\)
0.886454 + 0.462817i \(0.153161\pi\)
\(972\) −1.79203e39 1.79203e39i −2.59230 2.59230i
\(973\) −2.11079e38 + 2.11079e38i −0.301286 + 0.301286i
\(974\) 8.49275e36i 0.0119614i
\(975\) −2.80344e38 1.85525e39i −0.389610 2.57836i
\(976\) −8.63345e38 −1.18396
\(977\) −4.57714e37 4.57714e37i −0.0619391 0.0619391i 0.675459 0.737398i \(-0.263946\pi\)
−0.737398 + 0.675459i \(0.763946\pi\)
\(978\) −2.43018e37 + 2.43018e37i −0.0324514 + 0.0324514i
\(979\) 5.55101e38i 0.731471i
\(980\) 3.94257e38 2.96195e37i 0.512673 0.0385158i
\(981\) 5.69565e38 0.730881
\(982\) −5.47399e37 5.47399e37i −0.0693194 0.0693194i
\(983\) 6.64842e38 6.64842e38i 0.830850 0.830850i −0.156783 0.987633i \(-0.550112\pi\)
0.987633 + 0.156783i \(0.0501125\pi\)
\(984\) 4.56324e38i 0.562778i
\(985\) −1.93077e38 1.66093e38i −0.234995 0.202153i
\(986\) 1.20804e37 0.0145105
\(987\) 1.18918e38 + 1.18918e38i 0.140969 + 0.140969i
\(988\) −6.46423e38 + 6.46423e38i −0.756269 + 0.756269i
\(989\) 2.88064e38i 0.332612i
\(990\) 7.07215e37 8.22109e37i 0.0805924 0.0936854i
\(991\) 9.14286e38 1.02831 0.514156 0.857697i \(-0.328105\pi\)
0.514156 + 0.857697i \(0.328105\pi\)
\(992\) 1.60537e37 + 1.60537e37i 0.0178207 + 0.0178207i
\(993\) −1.46501e39 + 1.46501e39i −1.60509 + 1.60509i
\(994\) 5.68449e37i 0.0614708i
\(995\) 6.39549e37 + 8.51284e38i 0.0682611 + 0.908603i
\(996\) 1.25832e39 1.32562
\(997\) 1.59901e38 + 1.59901e38i 0.166270 + 0.166270i 0.785338 0.619068i \(-0.212489\pi\)
−0.619068 + 0.785338i \(0.712489\pi\)
\(998\) 2.17160e37 2.17160e37i 0.0222886 0.0222886i
\(999\) 2.67985e39i 2.71493i
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 5.27.c.a.2.7 24
5.2 odd 4 25.27.c.b.18.6 24
5.3 odd 4 inner 5.27.c.a.3.7 yes 24
5.4 even 2 25.27.c.b.7.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.27.c.a.2.7 24 1.1 even 1 trivial
5.27.c.a.3.7 yes 24 5.3 odd 4 inner
25.27.c.b.7.6 24 5.4 even 2
25.27.c.b.18.6 24 5.2 odd 4