Properties

Label 8.12.b.a.5.9
Level $8$
Weight $12$
Character 8.5
Analytic conductor $6.147$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8,12,Mod(5,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.5");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.14674544448\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - 48 x^{8} + 8836 x^{7} - 92554 x^{6} - 2200342 x^{5} - 88894588 x^{4} + \cdots + 34431558027300 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{45}\cdot 3^{2}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.9
Root \(20.8472 - 5.89062i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.12.b.a.5.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(43.6944 - 11.7812i) q^{2} +381.717i q^{3} +(1770.40 - 1029.55i) q^{4} +8937.55i q^{5} +(4497.10 + 16678.9i) q^{6} +10175.0 q^{7} +(65227.5 - 65843.1i) q^{8} +31439.0 q^{9} +(105295. + 390521. i) q^{10} +408594. i q^{11} +(392996. + 675794. i) q^{12} -1.94255e6i q^{13} +(444591. - 119874. i) q^{14} -3.41162e6 q^{15} +(2.07436e6 - 3.64544e6i) q^{16} -9.64991e6 q^{17} +(1.37371e6 - 370391. i) q^{18} -1.27489e7i q^{19} +(9.20165e6 + 1.58231e7i) q^{20} +3.88398e6i q^{21} +(4.81374e6 + 1.78533e7i) q^{22} +2.34581e7 q^{23} +(2.51334e7 + 2.48984e7i) q^{24} -3.10517e7 q^{25} +(-2.28857e7 - 8.48786e7i) q^{26} +7.96209e7i q^{27} +(1.80139e7 - 1.04757e7i) q^{28} -4.83134e7i q^{29} +(-1.49069e8 + 4.01931e7i) q^{30} +2.63557e8 q^{31} +(4.76903e7 - 1.83724e8i) q^{32} -1.55967e8 q^{33} +(-4.21647e8 + 1.13688e8i) q^{34} +9.09397e7i q^{35} +(5.56598e7 - 3.23680e7i) q^{36} -7.91290e7i q^{37} +(-1.50198e8 - 5.57057e8i) q^{38} +7.41505e8 q^{39} +(5.88476e8 + 5.82974e8i) q^{40} -6.96380e8 q^{41} +(4.57581e7 + 1.69708e8i) q^{42} +4.03606e8i q^{43} +(4.20667e8 + 7.23376e8i) q^{44} +2.80988e8i q^{45} +(1.02499e9 - 2.76365e8i) q^{46} -5.59625e8 q^{47} +(1.39153e9 + 7.91820e8i) q^{48} -1.87380e9 q^{49} +(-1.35679e9 + 3.65828e8i) q^{50} -3.68354e9i q^{51} +(-1.99995e9 - 3.43910e9i) q^{52} -2.88775e9i q^{53} +(9.38032e8 + 3.47899e9i) q^{54} -3.65183e9 q^{55} +(6.63690e8 - 6.69954e8i) q^{56} +4.86648e9 q^{57} +(-5.69191e8 - 2.11102e9i) q^{58} +9.84523e9i q^{59} +(-6.03994e9 + 3.51243e9i) q^{60} +5.65364e9i q^{61} +(1.15160e10 - 3.10503e9i) q^{62} +3.19892e8 q^{63} +(-8.06933e7 - 8.58956e9i) q^{64} +1.73617e10 q^{65} +(-6.81489e9 + 1.83749e9i) q^{66} -1.28196e10i q^{67} +(-1.70842e10 + 9.93505e9i) q^{68} +8.95435e9i q^{69} +(1.07138e9 + 3.97356e9i) q^{70} -3.63445e9 q^{71} +(2.05069e9 - 2.07004e9i) q^{72} -2.56732e9 q^{73} +(-9.32237e8 - 3.45749e9i) q^{74} -1.18530e10i q^{75} +(-1.31256e10 - 2.25707e10i) q^{76} +4.15744e9i q^{77} +(3.23996e10 - 8.73585e9i) q^{78} -2.59475e10 q^{79} +(3.25813e10 + 1.85397e10i) q^{80} -2.48233e10 q^{81} +(-3.04279e10 + 8.20422e9i) q^{82} +3.80496e10i q^{83} +(3.99874e9 + 6.87621e9i) q^{84} -8.62466e10i q^{85} +(4.75498e9 + 1.76353e10i) q^{86} +1.84420e10 q^{87} +(2.69031e10 + 2.66515e10i) q^{88} -2.00557e10 q^{89} +(3.31039e9 + 1.22776e10i) q^{90} -1.97655e10i q^{91} +(4.15303e10 - 2.41512e10i) q^{92} +1.00604e11i q^{93} +(-2.44525e10 + 6.59307e9i) q^{94} +1.13944e11 q^{95} +(7.01305e10 + 1.82042e10i) q^{96} -6.90643e10 q^{97} +(-8.18744e10 + 2.20756e10i) q^{98} +1.28458e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18}+ \cdots - 6194726778 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 43.6944 11.7812i 0.965519 0.260331i
\(3\) 381.717i 0.906932i 0.891274 + 0.453466i \(0.149813\pi\)
−0.891274 + 0.453466i \(0.850187\pi\)
\(4\) 1770.40 1029.55i 0.864455 0.502709i
\(5\) 8937.55i 1.27904i 0.768775 + 0.639519i \(0.220867\pi\)
−0.768775 + 0.639519i \(0.779133\pi\)
\(6\) 4497.10 + 16678.9i 0.236103 + 0.875661i
\(7\) 10175.0 0.228821 0.114410 0.993434i \(-0.463502\pi\)
0.114410 + 0.993434i \(0.463502\pi\)
\(8\) 65227.5 65843.1i 0.703778 0.710420i
\(9\) 31439.0 0.177474
\(10\) 105295. + 390521.i 0.332973 + 1.23494i
\(11\) 408594.i 0.764948i 0.923966 + 0.382474i \(0.124928\pi\)
−0.923966 + 0.382474i \(0.875072\pi\)
\(12\) 392996. + 675794.i 0.455923 + 0.784002i
\(13\) 1.94255e6i 1.45106i −0.688193 0.725528i \(-0.741596\pi\)
0.688193 0.725528i \(-0.258404\pi\)
\(14\) 444591. 119874.i 0.220931 0.0595692i
\(15\) −3.41162e6 −1.16000
\(16\) 2.07436e6 3.64544e6i 0.494567 0.869140i
\(17\) −9.64991e6 −1.64837 −0.824184 0.566322i \(-0.808366\pi\)
−0.824184 + 0.566322i \(0.808366\pi\)
\(18\) 1.37371e6 370391.i 0.171355 0.0462020i
\(19\) 1.27489e7i 1.18121i −0.806959 0.590607i \(-0.798888\pi\)
0.806959 0.590607i \(-0.201112\pi\)
\(20\) 9.20165e6 + 1.58231e7i 0.642985 + 1.10567i
\(21\) 3.88398e6i 0.207525i
\(22\) 4.81374e6 + 1.78533e7i 0.199140 + 0.738572i
\(23\) 2.34581e7 0.759957 0.379979 0.924995i \(-0.375931\pi\)
0.379979 + 0.924995i \(0.375931\pi\)
\(24\) 2.51334e7 + 2.48984e7i 0.644303 + 0.638279i
\(25\) −3.10517e7 −0.635939
\(26\) −2.28857e7 8.48786e7i −0.377755 1.40102i
\(27\) 7.96209e7i 1.06789i
\(28\) 1.80139e7 1.04757e7i 0.197805 0.115030i
\(29\) 4.83134e7i 0.437400i −0.975792 0.218700i \(-0.929818\pi\)
0.975792 0.218700i \(-0.0701815\pi\)
\(30\) −1.49069e8 + 4.01931e7i −1.12000 + 0.301984i
\(31\) 2.63557e8 1.65343 0.826714 0.562622i \(-0.190207\pi\)
0.826714 + 0.562622i \(0.190207\pi\)
\(32\) 4.76903e7 1.83724e8i 0.251250 0.967922i
\(33\) −1.55967e8 −0.693756
\(34\) −4.21647e8 + 1.13688e8i −1.59153 + 0.429121i
\(35\) 9.09397e7i 0.292671i
\(36\) 5.56598e7 3.23680e7i 0.153419 0.0892179i
\(37\) 7.91290e7i 0.187597i −0.995591 0.0937985i \(-0.970099\pi\)
0.995591 0.0937985i \(-0.0299010\pi\)
\(38\) −1.50198e8 5.57057e8i −0.307507 1.14048i
\(39\) 7.41505e8 1.31601
\(40\) 5.88476e8 + 5.82974e8i 0.908655 + 0.900159i
\(41\) −6.96380e8 −0.938718 −0.469359 0.883008i \(-0.655515\pi\)
−0.469359 + 0.883008i \(0.655515\pi\)
\(42\) 4.57581e7 + 1.69708e8i 0.0540252 + 0.200369i
\(43\) 4.03606e8i 0.418679i 0.977843 + 0.209339i \(0.0671314\pi\)
−0.977843 + 0.209339i \(0.932869\pi\)
\(44\) 4.20667e8 + 7.23376e8i 0.384546 + 0.661263i
\(45\) 2.80988e8i 0.226996i
\(46\) 1.02499e9 2.76365e8i 0.733753 0.197840i
\(47\) −5.59625e8 −0.355925 −0.177963 0.984037i \(-0.556951\pi\)
−0.177963 + 0.984037i \(0.556951\pi\)
\(48\) 1.39153e9 + 7.91820e8i 0.788251 + 0.448538i
\(49\) −1.87380e9 −0.947641
\(50\) −1.35679e9 + 3.65828e8i −0.614012 + 0.165555i
\(51\) 3.68354e9i 1.49496i
\(52\) −1.99995e9 3.43910e9i −0.729459 1.25437i
\(53\) 2.88775e9i 0.948510i −0.880388 0.474255i \(-0.842717\pi\)
0.880388 0.474255i \(-0.157283\pi\)
\(54\) 9.38032e8 + 3.47899e9i 0.278005 + 1.03107i
\(55\) −3.65183e9 −0.978397
\(56\) 6.63690e8 6.69954e8i 0.161039 0.162559i
\(57\) 4.86648e9 1.07128
\(58\) −5.69191e8 2.11102e9i −0.113869 0.422318i
\(59\) 9.84523e9i 1.79283i 0.443213 + 0.896417i \(0.353839\pi\)
−0.443213 + 0.896417i \(0.646161\pi\)
\(60\) −6.03994e9 + 3.51243e9i −1.00277 + 0.583143i
\(61\) 5.65364e9i 0.857066i 0.903526 + 0.428533i \(0.140969\pi\)
−0.903526 + 0.428533i \(0.859031\pi\)
\(62\) 1.15160e10 3.10503e9i 1.59642 0.430439i
\(63\) 3.19892e8 0.0406098
\(64\) −8.06933e7 8.58956e9i −0.00939394 0.999956i
\(65\) 1.73617e10 1.85596
\(66\) −6.81489e9 + 1.83749e9i −0.669834 + 0.180606i
\(67\) 1.28196e10i 1.16001i −0.814613 0.580005i \(-0.803051\pi\)
0.814613 0.580005i \(-0.196949\pi\)
\(68\) −1.70842e10 + 9.93505e9i −1.42494 + 0.828650i
\(69\) 8.95435e9i 0.689230i
\(70\) 1.07138e9 + 3.97356e9i 0.0761913 + 0.282579i
\(71\) −3.63445e9 −0.239066 −0.119533 0.992830i \(-0.538140\pi\)
−0.119533 + 0.992830i \(0.538140\pi\)
\(72\) 2.05069e9 2.07004e9i 0.124902 0.126081i
\(73\) −2.56732e9 −0.144945 −0.0724727 0.997370i \(-0.523089\pi\)
−0.0724727 + 0.997370i \(0.523089\pi\)
\(74\) −9.32237e8 3.45749e9i −0.0488373 0.181129i
\(75\) 1.18530e10i 0.576754i
\(76\) −1.31256e10 2.25707e10i −0.593807 1.02111i
\(77\) 4.15744e9i 0.175036i
\(78\) 3.23996e10 8.73585e9i 1.27063 0.342598i
\(79\) −2.59475e10 −0.948739 −0.474370 0.880326i \(-0.657324\pi\)
−0.474370 + 0.880326i \(0.657324\pi\)
\(80\) 3.25813e10 + 1.85397e10i 1.11166 + 0.632570i
\(81\) −2.48233e10 −0.791029
\(82\) −3.04279e10 + 8.20422e9i −0.906350 + 0.244377i
\(83\) 3.80496e10i 1.06028i 0.847910 + 0.530140i \(0.177860\pi\)
−0.847910 + 0.530140i \(0.822140\pi\)
\(84\) 3.99874e9 + 6.87621e9i 0.104325 + 0.179396i
\(85\) 8.62466e10i 2.10833i
\(86\) 4.75498e9 + 1.76353e10i 0.108995 + 0.404243i
\(87\) 1.84420e10 0.396692
\(88\) 2.69031e10 + 2.66515e10i 0.543434 + 0.538353i
\(89\) −2.00557e10 −0.380709 −0.190354 0.981715i \(-0.560964\pi\)
−0.190354 + 0.981715i \(0.560964\pi\)
\(90\) 3.31039e9 + 1.22776e10i 0.0590942 + 0.219169i
\(91\) 1.97655e10i 0.332032i
\(92\) 4.15303e10 2.41512e10i 0.656949 0.382038i
\(93\) 1.00604e11i 1.49955i
\(94\) −2.44525e10 + 6.59307e9i −0.343653 + 0.0926584i
\(95\) 1.13944e11 1.51082
\(96\) 7.01305e10 + 1.82042e10i 0.877840 + 0.227866i
\(97\) −6.90643e10 −0.816600 −0.408300 0.912848i \(-0.633878\pi\)
−0.408300 + 0.912848i \(0.633878\pi\)
\(98\) −8.18744e10 + 2.20756e10i −0.914966 + 0.246700i
\(99\) 1.28458e10i 0.135758i
\(100\) −5.49741e10 + 3.19693e10i −0.549741 + 0.319693i
\(101\) 3.00032e10i 0.284053i −0.989863 0.142027i \(-0.954638\pi\)
0.989863 0.142027i \(-0.0453619\pi\)
\(102\) −4.33966e10 1.60950e11i −0.389184 1.44341i
\(103\) 4.46196e10 0.379246 0.189623 0.981857i \(-0.439273\pi\)
0.189623 + 0.981857i \(0.439273\pi\)
\(104\) −1.27904e11 1.26708e11i −1.03086 1.02122i
\(105\) −3.47132e10 −0.265432
\(106\) −3.40212e10 1.26178e11i −0.246927 0.915805i
\(107\) 1.84556e10i 0.127209i −0.997975 0.0636044i \(-0.979740\pi\)
0.997975 0.0636044i \(-0.0202596\pi\)
\(108\) 8.19736e10 + 1.40961e11i 0.536838 + 0.923143i
\(109\) 9.05577e8i 0.00563741i −0.999996 0.00281871i \(-0.999103\pi\)
0.999996 0.00281871i \(-0.000897223\pi\)
\(110\) −1.59564e11 + 4.30230e10i −0.944662 + 0.254707i
\(111\) 3.02049e10 0.170138
\(112\) 2.11067e10 3.70924e10i 0.113167 0.198877i
\(113\) 1.77827e11 0.907957 0.453978 0.891013i \(-0.350004\pi\)
0.453978 + 0.891013i \(0.350004\pi\)
\(114\) 2.12638e11 5.73332e10i 1.03434 0.278888i
\(115\) 2.09658e11i 0.972014i
\(116\) −4.97410e10 8.55342e10i −0.219885 0.378112i
\(117\) 6.10719e10i 0.257525i
\(118\) 1.15989e11 + 4.30182e11i 0.466730 + 1.73102i
\(119\) −9.81879e10 −0.377181
\(120\) −2.22531e11 + 2.24631e11i −0.816383 + 0.824088i
\(121\) 1.18363e11 0.414855
\(122\) 6.66069e10 + 2.47033e11i 0.223121 + 0.827514i
\(123\) 2.65820e11i 0.851353i
\(124\) 4.66603e11 2.71345e11i 1.42932 0.831194i
\(125\) 1.58877e11i 0.465648i
\(126\) 1.39775e10 3.76873e9i 0.0392095 0.0105720i
\(127\) −5.40179e11 −1.45083 −0.725417 0.688310i \(-0.758353\pi\)
−0.725417 + 0.688310i \(0.758353\pi\)
\(128\) −1.04721e11 3.74365e11i −0.269390 0.963031i
\(129\) −1.54063e11 −0.379713
\(130\) 7.58607e11 2.04542e11i 1.79196 0.483163i
\(131\) 2.23934e11i 0.507141i −0.967317 0.253570i \(-0.918395\pi\)
0.967317 0.253570i \(-0.0816049\pi\)
\(132\) −2.76125e11 + 1.60576e11i −0.599721 + 0.348757i
\(133\) 1.29720e11i 0.270286i
\(134\) −1.51030e11 5.60143e11i −0.301986 1.12001i
\(135\) −7.11616e11 −1.36587
\(136\) −6.29439e11 + 6.35380e11i −1.16008 + 1.17103i
\(137\) 3.35319e11 0.593602 0.296801 0.954939i \(-0.404080\pi\)
0.296801 + 0.954939i \(0.404080\pi\)
\(138\) 1.05493e11 + 3.91255e11i 0.179428 + 0.665465i
\(139\) 2.72700e10i 0.0445763i 0.999752 + 0.0222881i \(0.00709512\pi\)
−0.999752 + 0.0222881i \(0.992905\pi\)
\(140\) 9.36269e10 + 1.61000e11i 0.147128 + 0.253001i
\(141\) 2.13618e11i 0.322800i
\(142\) −1.58805e11 + 4.28184e10i −0.230823 + 0.0622363i
\(143\) 7.93714e11 1.10998
\(144\) 6.52159e10 1.14609e11i 0.0877728 0.154250i
\(145\) 4.31803e11 0.559451
\(146\) −1.12178e11 + 3.02462e10i −0.139948 + 0.0377338i
\(147\) 7.15260e11i 0.859446i
\(148\) −8.14671e10 1.40090e11i −0.0943068 0.162169i
\(149\) 1.14880e12i 1.28151i 0.767747 + 0.640753i \(0.221378\pi\)
−0.767747 + 0.640753i \(0.778622\pi\)
\(150\) −1.39643e11 5.17909e11i −0.150147 0.556867i
\(151\) 4.51160e11 0.467689 0.233845 0.972274i \(-0.424869\pi\)
0.233845 + 0.972274i \(0.424869\pi\)
\(152\) −8.39428e11 8.31579e11i −0.839158 0.831312i
\(153\) −3.03384e11 −0.292543
\(154\) 4.89798e10 + 1.81657e11i 0.0455673 + 0.169001i
\(155\) 2.35556e12i 2.11480i
\(156\) 1.31276e12 7.63416e11i 1.13763 0.661570i
\(157\) 8.98082e10i 0.0751395i −0.999294 0.0375697i \(-0.988038\pi\)
0.999294 0.0375697i \(-0.0119616\pi\)
\(158\) −1.13376e12 + 3.05694e11i −0.916026 + 0.246986i
\(159\) 1.10230e12 0.860234
\(160\) 1.64204e12 + 4.26235e11i 1.23801 + 0.321358i
\(161\) 2.38686e11 0.173894
\(162\) −1.08464e12 + 2.92449e11i −0.763754 + 0.205929i
\(163\) 3.45737e11i 0.235350i −0.993052 0.117675i \(-0.962456\pi\)
0.993052 0.117675i \(-0.0375441\pi\)
\(164\) −1.23287e12 + 7.16957e11i −0.811480 + 0.471902i
\(165\) 1.39396e12i 0.887340i
\(166\) 4.48271e11 + 1.66255e12i 0.276024 + 1.02372i
\(167\) 6.61651e11 0.394174 0.197087 0.980386i \(-0.436852\pi\)
0.197087 + 0.980386i \(0.436852\pi\)
\(168\) 2.55733e11 + 2.53342e11i 0.147430 + 0.146051i
\(169\) −1.98134e12 −1.10556
\(170\) −1.01609e12 3.76849e12i −0.548863 2.03563i
\(171\) 4.00813e11i 0.209635i
\(172\) 4.15532e11 + 7.14546e11i 0.210474 + 0.361929i
\(173\) 2.94318e12i 1.44399i −0.691900 0.721993i \(-0.743226\pi\)
0.691900 0.721993i \(-0.256774\pi\)
\(174\) 8.05814e11 2.17270e11i 0.383014 0.103271i
\(175\) −3.15952e11 −0.145516
\(176\) 1.48950e12 + 8.47571e11i 0.664846 + 0.378318i
\(177\) −3.75809e12 −1.62598
\(178\) −8.76322e11 + 2.36281e11i −0.367582 + 0.0991103i
\(179\) 8.70295e11i 0.353977i −0.984213 0.176988i \(-0.943364\pi\)
0.984213 0.176988i \(-0.0566355\pi\)
\(180\) 2.89291e11 + 4.97462e11i 0.114113 + 0.196228i
\(181\) 4.02698e12i 1.54080i 0.637559 + 0.770401i \(0.279944\pi\)
−0.637559 + 0.770401i \(0.720056\pi\)
\(182\) −2.32862e11 8.63641e11i −0.0864382 0.320583i
\(183\) −2.15809e12 −0.777301
\(184\) 1.53011e12 1.54455e12i 0.534841 0.539889i
\(185\) 7.07219e11 0.239944
\(186\) 1.18524e12 + 4.39585e12i 0.390379 + 1.44784i
\(187\) 3.94289e12i 1.26092i
\(188\) −9.90762e11 + 5.76161e11i −0.307681 + 0.178927i
\(189\) 8.10143e11i 0.244355i
\(190\) 4.97872e12 1.34240e12i 1.45872 0.393313i
\(191\) 5.16393e12 1.46993 0.734965 0.678105i \(-0.237199\pi\)
0.734965 + 0.678105i \(0.237199\pi\)
\(192\) 3.27878e12 3.08020e10i 0.906892 0.00851966i
\(193\) 2.61981e12 0.704214 0.352107 0.935960i \(-0.385465\pi\)
0.352107 + 0.935960i \(0.385465\pi\)
\(194\) −3.01773e12 + 8.13663e11i −0.788443 + 0.212586i
\(195\) 6.62724e12i 1.68323i
\(196\) −3.31738e12 + 1.92916e12i −0.819193 + 0.476388i
\(197\) 9.51398e11i 0.228453i 0.993455 + 0.114227i \(0.0364390\pi\)
−0.993455 + 0.114227i \(0.963561\pi\)
\(198\) 1.51339e11 + 5.61289e11i 0.0353421 + 0.131077i
\(199\) −7.34864e12 −1.66923 −0.834613 0.550837i \(-0.814309\pi\)
−0.834613 + 0.550837i \(0.814309\pi\)
\(200\) −2.02543e12 + 2.04454e12i −0.447560 + 0.451784i
\(201\) 4.89344e12 1.05205
\(202\) −3.53475e11 1.31097e12i −0.0739479 0.274259i
\(203\) 4.91589e11i 0.100086i
\(204\) −3.79238e12 6.52135e12i −0.751529 1.29232i
\(205\) 6.22393e12i 1.20066i
\(206\) 1.94963e12 5.25674e11i 0.366169 0.0987294i
\(207\) 7.37499e11 0.134873
\(208\) −7.08145e12 4.02956e12i −1.26117 0.717644i
\(209\) 5.20912e12 0.903567
\(210\) −1.51678e12 + 4.08965e11i −0.256280 + 0.0691003i
\(211\) 6.80722e11i 0.112051i −0.998429 0.0560256i \(-0.982157\pi\)
0.998429 0.0560256i \(-0.0178428\pi\)
\(212\) −2.97308e12 5.11248e12i −0.476825 0.819945i
\(213\) 1.38733e12i 0.216817i
\(214\) −2.17430e11 8.06406e11i −0.0331164 0.122823i
\(215\) −3.60725e12 −0.535506
\(216\) 5.24248e12 + 5.19347e12i 0.758650 + 0.751557i
\(217\) 2.68170e12 0.378339
\(218\) −1.06688e10 3.95687e10i −0.00146759 0.00544303i
\(219\) 9.79991e11i 0.131456i
\(220\) −6.46521e12 + 3.75973e12i −0.845781 + 0.491850i
\(221\) 1.87454e13i 2.39187i
\(222\) 1.31979e12 3.55851e11i 0.164271 0.0442922i
\(223\) −1.19442e12 −0.145037 −0.0725187 0.997367i \(-0.523104\pi\)
−0.0725187 + 0.997367i \(0.523104\pi\)
\(224\) 4.85249e11 1.86939e12i 0.0574911 0.221481i
\(225\) −9.76236e11 −0.112863
\(226\) 7.77003e12 2.09502e12i 0.876650 0.236369i
\(227\) 5.02675e12i 0.553535i −0.960937 0.276768i \(-0.910737\pi\)
0.960937 0.276768i \(-0.0892632\pi\)
\(228\) 8.61564e12 5.01028e12i 0.926074 0.538543i
\(229\) 2.86620e12i 0.300754i −0.988629 0.150377i \(-0.951951\pi\)
0.988629 0.150377i \(-0.0480487\pi\)
\(230\) 2.47003e12 + 9.16087e12i 0.253046 + 0.938499i
\(231\) −1.58697e12 −0.158746
\(232\) −3.18110e12 3.15136e12i −0.310737 0.307832i
\(233\) −9.05833e12 −0.864153 −0.432077 0.901837i \(-0.642219\pi\)
−0.432077 + 0.901837i \(0.642219\pi\)
\(234\) −7.19503e11 2.66850e12i −0.0670417 0.248645i
\(235\) 5.00168e12i 0.455242i
\(236\) 1.01361e13 + 1.74300e13i 0.901274 + 1.54982i
\(237\) 9.90461e12i 0.860442i
\(238\) −4.29026e12 + 1.15678e12i −0.364176 + 0.0981919i
\(239\) 1.48753e13 1.23389 0.616947 0.787005i \(-0.288369\pi\)
0.616947 + 0.787005i \(0.288369\pi\)
\(240\) −7.07693e12 + 1.24368e13i −0.573698 + 1.00820i
\(241\) 1.65832e12 0.131394 0.0656969 0.997840i \(-0.479073\pi\)
0.0656969 + 0.997840i \(0.479073\pi\)
\(242\) 5.17180e12 1.39446e12i 0.400551 0.108000i
\(243\) 4.62911e12i 0.350480i
\(244\) 5.82070e12 + 1.00092e13i 0.430855 + 0.740896i
\(245\) 1.67472e13i 1.21207i
\(246\) −3.13169e12 1.16149e13i −0.221634 0.821998i
\(247\) −2.47654e13 −1.71401
\(248\) 1.71912e13 1.73534e13i 1.16365 1.17463i
\(249\) −1.45242e13 −0.961601
\(250\) 1.87177e12 + 6.94206e12i 0.121223 + 0.449592i
\(251\) 1.60614e13i 1.01760i 0.860883 + 0.508802i \(0.169912\pi\)
−0.860883 + 0.508802i \(0.830088\pi\)
\(252\) 5.66339e11 3.29345e11i 0.0351054 0.0204149i
\(253\) 9.58481e12i 0.581327i
\(254\) −2.36028e13 + 6.36398e12i −1.40081 + 0.377697i
\(255\) 3.29218e13 1.91211
\(256\) −8.98623e12 1.51239e13i −0.510808 0.859695i
\(257\) −2.90477e13 −1.61614 −0.808072 0.589084i \(-0.799489\pi\)
−0.808072 + 0.589084i \(0.799489\pi\)
\(258\) −6.73171e12 + 1.81506e12i −0.366621 + 0.0988512i
\(259\) 8.05138e11i 0.0429261i
\(260\) 3.07372e13 1.78747e13i 1.60439 0.933006i
\(261\) 1.51892e12i 0.0776271i
\(262\) −2.63822e12 9.78468e12i −0.132024 0.489654i
\(263\) −7.15627e12 −0.350695 −0.175348 0.984507i \(-0.556105\pi\)
−0.175348 + 0.984507i \(0.556105\pi\)
\(264\) −1.01733e13 + 1.02694e13i −0.488250 + 0.492858i
\(265\) 2.58094e13 1.21318
\(266\) −1.52827e12 5.66806e12i −0.0703639 0.260967i
\(267\) 7.65561e12i 0.345277i
\(268\) −1.31984e13 2.26958e13i −0.583147 1.00278i
\(269\) 9.77777e12i 0.423255i −0.977350 0.211627i \(-0.932124\pi\)
0.977350 0.211627i \(-0.0678764\pi\)
\(270\) −3.10936e13 + 8.38371e12i −1.31878 + 0.355579i
\(271\) 3.73866e13 1.55376 0.776882 0.629647i \(-0.216800\pi\)
0.776882 + 0.629647i \(0.216800\pi\)
\(272\) −2.00174e13 + 3.51781e13i −0.815228 + 1.43266i
\(273\) 7.54482e12 0.301130
\(274\) 1.46516e13 3.95048e12i 0.573134 0.154533i
\(275\) 1.26875e13i 0.486460i
\(276\) 9.21894e12 + 1.58528e13i 0.346482 + 0.595808i
\(277\) 2.28097e13i 0.840391i 0.907433 + 0.420196i \(0.138039\pi\)
−0.907433 + 0.420196i \(0.861961\pi\)
\(278\) 3.21274e11 + 1.19155e12i 0.0116046 + 0.0430392i
\(279\) 8.28598e12 0.293441
\(280\) 5.98775e12 + 5.93176e12i 0.207919 + 0.205975i
\(281\) −8.47235e12 −0.288482 −0.144241 0.989543i \(-0.546074\pi\)
−0.144241 + 0.989543i \(0.546074\pi\)
\(282\) −2.51669e12 9.33393e12i −0.0840349 0.311670i
\(283\) 5.48093e13i 1.79485i 0.441163 + 0.897427i \(0.354566\pi\)
−0.441163 + 0.897427i \(0.645434\pi\)
\(284\) −6.43445e12 + 3.74185e12i −0.206662 + 0.120181i
\(285\) 4.34944e13i 1.37021i
\(286\) 3.46809e13 9.35093e12i 1.07171 0.288963i
\(287\) −7.08567e12 −0.214798
\(288\) 1.49934e12 5.77610e12i 0.0445903 0.171781i
\(289\) 5.88488e13 1.71712
\(290\) 1.88674e13 5.08718e12i 0.540161 0.145642i
\(291\) 2.63630e13i 0.740601i
\(292\) −4.54520e12 + 2.64318e12i −0.125299 + 0.0728655i
\(293\) 5.59919e13i 1.51479i −0.652955 0.757396i \(-0.726471\pi\)
0.652955 0.757396i \(-0.273529\pi\)
\(294\) −8.42665e12 3.12529e13i −0.223740 0.829812i
\(295\) −8.79923e13 −2.29310
\(296\) −5.21010e12 5.16138e12i −0.133273 0.132027i
\(297\) −3.25326e13 −0.816879
\(298\) 1.35343e13 + 5.01962e13i 0.333616 + 1.23732i
\(299\) 4.55685e13i 1.10274i
\(300\) −1.22032e13 2.09846e13i −0.289940 0.498578i
\(301\) 4.10670e12i 0.0958025i
\(302\) 1.97132e13 5.31522e12i 0.451563 0.121754i
\(303\) 1.14527e13 0.257617
\(304\) −4.64754e13 2.64459e13i −1.02664 0.584189i
\(305\) −5.05297e13 −1.09622
\(306\) −1.32562e13 + 3.57423e12i −0.282456 + 0.0761580i
\(307\) 3.49392e13i 0.731226i −0.930767 0.365613i \(-0.880859\pi\)
0.930767 0.365613i \(-0.119141\pi\)
\(308\) 4.28029e12 + 7.36036e12i 0.0879922 + 0.151311i
\(309\) 1.70321e13i 0.343950i
\(310\) 2.77514e13 + 1.02925e14i 0.550548 + 2.04188i
\(311\) −8.77394e13 −1.71006 −0.855032 0.518575i \(-0.826463\pi\)
−0.855032 + 0.518575i \(0.826463\pi\)
\(312\) 4.83665e13 4.88230e13i 0.926178 0.934919i
\(313\) 9.47630e13 1.78297 0.891487 0.453046i \(-0.149663\pi\)
0.891487 + 0.453046i \(0.149663\pi\)
\(314\) −1.05805e12 3.92412e12i −0.0195611 0.0725486i
\(315\) 2.85905e12i 0.0519415i
\(316\) −4.59376e13 + 2.67142e13i −0.820143 + 0.476940i
\(317\) 7.45724e13i 1.30844i −0.756306 0.654218i \(-0.772998\pi\)
0.756306 0.654218i \(-0.227002\pi\)
\(318\) 4.81645e13 1.29865e13i 0.830573 0.223946i
\(319\) 1.97405e13 0.334588
\(320\) 7.67696e13 7.21201e11i 1.27898 0.0120152i
\(321\) 7.04482e12 0.115370
\(322\) 1.04293e13 2.81202e12i 0.167898 0.0452700i
\(323\) 1.23026e14i 1.94707i
\(324\) −4.39473e13 + 2.55568e13i −0.683809 + 0.397658i
\(325\) 6.03196e13i 0.922783i
\(326\) −4.07321e12 1.51068e13i −0.0612688 0.227235i
\(327\) 3.45674e11 0.00511275
\(328\) −4.54231e13 + 4.58518e13i −0.660649 + 0.666884i
\(329\) −5.69419e12 −0.0814431
\(330\) −1.64226e13 6.09085e13i −0.231002 0.856744i
\(331\) 9.05611e13i 1.25282i −0.779495 0.626409i \(-0.784524\pi\)
0.779495 0.626409i \(-0.215476\pi\)
\(332\) 3.91739e13 + 6.73631e13i 0.533012 + 0.916564i
\(333\) 2.48774e12i 0.0332936i
\(334\) 2.89105e13 7.79507e12i 0.380583 0.102616i
\(335\) 1.14575e14 1.48370
\(336\) 1.41588e13 + 8.05677e12i 0.180368 + 0.102635i
\(337\) 3.77207e13 0.472733 0.236366 0.971664i \(-0.424043\pi\)
0.236366 + 0.971664i \(0.424043\pi\)
\(338\) −8.65737e13 + 2.33427e13i −1.06744 + 0.287812i
\(339\) 6.78794e13i 0.823455i
\(340\) −8.87950e13 1.52691e14i −1.05988 1.82255i
\(341\) 1.07688e14i 1.26479i
\(342\) −4.72208e12 1.75133e13i −0.0545745 0.202407i
\(343\) −3.91852e13 −0.445661
\(344\) 2.65747e13 + 2.63262e13i 0.297438 + 0.294657i
\(345\) −8.00299e13 −0.881551
\(346\) −3.46743e13 1.28601e14i −0.375915 1.39420i
\(347\) 4.95297e13i 0.528510i −0.964453 0.264255i \(-0.914874\pi\)
0.964453 0.264255i \(-0.0851261\pi\)
\(348\) 3.26499e13 1.89870e13i 0.342922 0.199421i
\(349\) 4.22844e13i 0.437160i −0.975819 0.218580i \(-0.929858\pi\)
0.975819 0.218580i \(-0.0701425\pi\)
\(350\) −1.38053e13 + 3.72230e12i −0.140499 + 0.0378824i
\(351\) 1.54668e14 1.54957
\(352\) 7.50684e13 + 1.94860e13i 0.740410 + 0.192193i
\(353\) −5.42310e13 −0.526607 −0.263304 0.964713i \(-0.584812\pi\)
−0.263304 + 0.964713i \(0.584812\pi\)
\(354\) −1.64208e14 + 4.42750e13i −1.56991 + 0.423293i
\(355\) 3.24831e13i 0.305775i
\(356\) −3.55067e13 + 2.06483e13i −0.329106 + 0.191386i
\(357\) 3.74800e13i 0.342078i
\(358\) −1.02532e13 3.80270e13i −0.0921512 0.341771i
\(359\) 1.11001e14 0.982441 0.491220 0.871035i \(-0.336551\pi\)
0.491220 + 0.871035i \(0.336551\pi\)
\(360\) 1.85011e13 + 1.83281e13i 0.161263 + 0.159755i
\(361\) −4.60446e13 −0.395266
\(362\) 4.74428e13 + 1.75956e14i 0.401119 + 1.48767i
\(363\) 4.51812e13i 0.376245i
\(364\) −2.03495e13 3.49929e13i −0.166915 0.287027i
\(365\) 2.29456e13i 0.185391i
\(366\) −9.42966e13 + 2.54250e13i −0.750499 + 0.202356i
\(367\) −1.37111e14 −1.07500 −0.537502 0.843262i \(-0.680632\pi\)
−0.537502 + 0.843262i \(0.680632\pi\)
\(368\) 4.86605e13 8.55149e13i 0.375849 0.660509i
\(369\) −2.18935e13 −0.166598
\(370\) 3.09015e13 8.33192e12i 0.231670 0.0624648i
\(371\) 2.93829e13i 0.217039i
\(372\) 1.03577e14 + 1.78110e14i 0.753837 + 1.29629i
\(373\) 1.24348e14i 0.891744i −0.895097 0.445872i \(-0.852894\pi\)
0.895097 0.445872i \(-0.147106\pi\)
\(374\) −4.64521e13 1.72282e14i −0.328255 1.21744i
\(375\) −6.06463e13 −0.422311
\(376\) −3.65029e13 + 3.68474e13i −0.250492 + 0.252856i
\(377\) −9.38512e13 −0.634691
\(378\) 9.54449e12 + 3.53987e13i 0.0636133 + 0.235930i
\(379\) 2.76010e14i 1.81305i 0.422157 + 0.906523i \(0.361273\pi\)
−0.422157 + 0.906523i \(0.638727\pi\)
\(380\) 2.01727e14 1.17311e14i 1.30603 0.759502i
\(381\) 2.06196e14i 1.31581i
\(382\) 2.25635e14 6.08374e13i 1.41925 0.382668i
\(383\) 1.30866e14 0.811396 0.405698 0.914007i \(-0.367028\pi\)
0.405698 + 0.914007i \(0.367028\pi\)
\(384\) 1.42902e14 3.99740e13i 0.873404 0.244318i
\(385\) −3.71574e13 −0.223878
\(386\) 1.14471e14 3.08646e13i 0.679933 0.183329i
\(387\) 1.26890e13i 0.0743047i
\(388\) −1.22272e14 + 7.11051e13i −0.705914 + 0.410512i
\(389\) 2.65449e14i 1.51098i 0.655161 + 0.755489i \(0.272601\pi\)
−0.655161 + 0.755489i \(0.727399\pi\)
\(390\) 7.80771e13 + 2.89573e14i 0.438196 + 1.62519i
\(391\) −2.26368e14 −1.25269
\(392\) −1.22223e14 + 1.23377e14i −0.666929 + 0.673223i
\(393\) 8.54795e13 0.459942
\(394\) 1.12086e13 + 4.15708e13i 0.0594735 + 0.220576i
\(395\) 2.31907e14i 1.21347i
\(396\) 1.32254e13 + 2.27422e13i 0.0682470 + 0.117357i
\(397\) 2.55728e14i 1.30146i 0.759309 + 0.650730i \(0.225537\pi\)
−0.759309 + 0.650730i \(0.774463\pi\)
\(398\) −3.21095e14 + 8.65761e13i −1.61167 + 0.434551i
\(399\) 4.95165e13 0.245131
\(400\) −6.44125e13 + 1.13197e14i −0.314514 + 0.552720i
\(401\) 4.93538e13 0.237698 0.118849 0.992912i \(-0.462079\pi\)
0.118849 + 0.992912i \(0.462079\pi\)
\(402\) 2.13816e14 5.76508e13i 1.01577 0.273881i
\(403\) 5.11973e14i 2.39922i
\(404\) −3.08898e13 5.31178e13i −0.142796 0.245551i
\(405\) 2.21860e14i 1.01176i
\(406\) −5.79153e12 2.14797e13i −0.0260555 0.0966351i
\(407\) 3.23316e13 0.143502
\(408\) −2.42535e14 2.40268e14i −1.06205 1.05212i
\(409\) 2.01464e14 0.870400 0.435200 0.900334i \(-0.356678\pi\)
0.435200 + 0.900334i \(0.356678\pi\)
\(410\) −7.33256e13 2.71951e14i −0.312568 1.15926i
\(411\) 1.27997e14i 0.538357i
\(412\) 7.89947e13 4.59380e13i 0.327841 0.190650i
\(413\) 1.00175e14i 0.410238i
\(414\) 3.22246e13 8.68865e12i 0.130222 0.0351116i
\(415\) −3.40070e14 −1.35614
\(416\) −3.56893e14 9.26409e13i −1.40451 0.364577i
\(417\) −1.04094e13 −0.0404276
\(418\) 2.27610e14 6.13699e13i 0.872411 0.235226i
\(419\) 3.36722e14i 1.27378i 0.770954 + 0.636891i \(0.219780\pi\)
−0.770954 + 0.636891i \(0.780220\pi\)
\(420\) −6.14565e13 + 3.57390e13i −0.229455 + 0.133435i
\(421\) 1.20703e12i 0.00444800i 0.999998 + 0.00222400i \(0.000707922\pi\)
−0.999998 + 0.00222400i \(0.999292\pi\)
\(422\) −8.01975e12 2.97438e13i −0.0291704 0.108188i
\(423\) −1.75941e13 −0.0631675
\(424\) −1.90138e14 1.88360e14i −0.673841 0.667540i
\(425\) 2.99646e14 1.04826
\(426\) −1.63445e13 6.06187e13i −0.0564441 0.209341i
\(427\) 5.75259e13i 0.196115i
\(428\) −1.90009e13 3.26739e13i −0.0639491 0.109966i
\(429\) 3.02974e14i 1.00668i
\(430\) −1.57617e14 + 4.24979e13i −0.517042 + 0.139409i
\(431\) −1.87948e13 −0.0608714 −0.0304357 0.999537i \(-0.509689\pi\)
−0.0304357 + 0.999537i \(0.509689\pi\)
\(432\) 2.90253e14 + 1.65163e14i 0.928145 + 0.528142i
\(433\) 3.13621e14 0.990197 0.495098 0.868837i \(-0.335132\pi\)
0.495098 + 0.868837i \(0.335132\pi\)
\(434\) 1.17175e14 3.15937e13i 0.365294 0.0984934i
\(435\) 1.64827e14i 0.507384i
\(436\) −9.32336e11 1.60324e12i −0.00283398 0.00487329i
\(437\) 2.99065e14i 0.897672i
\(438\) −1.15455e13 4.28201e13i −0.0342220 0.126923i
\(439\) 4.95205e14 1.44954 0.724771 0.688990i \(-0.241946\pi\)
0.724771 + 0.688990i \(0.241946\pi\)
\(440\) −2.38199e14 + 2.40448e14i −0.688574 + 0.695073i
\(441\) −5.89103e13 −0.168182
\(442\) 2.20845e14 + 8.19071e14i 0.622679 + 2.30940i
\(443\) 2.99673e14i 0.834500i 0.908792 + 0.417250i \(0.137006\pi\)
−0.908792 + 0.417250i \(0.862994\pi\)
\(444\) 5.34749e13 3.10974e13i 0.147077 0.0855299i
\(445\) 1.79249e14i 0.486941i
\(446\) −5.21894e13 + 1.40717e13i −0.140036 + 0.0377577i
\(447\) −4.38517e14 −1.16224
\(448\) −8.21055e11 8.73988e13i −0.00214953 0.228811i
\(449\) 2.49937e14 0.646362 0.323181 0.946337i \(-0.395248\pi\)
0.323181 + 0.946337i \(0.395248\pi\)
\(450\) −4.26561e13 + 1.15013e13i −0.108971 + 0.0293817i
\(451\) 2.84536e14i 0.718070i
\(452\) 3.14825e14 1.83081e14i 0.784888 0.456438i
\(453\) 1.72215e14i 0.424162i
\(454\) −5.92214e13 2.19641e14i −0.144102 0.534449i
\(455\) 1.76655e14 0.424681
\(456\) 3.17428e14 3.20424e14i 0.753943 0.761059i
\(457\) −7.22584e14 −1.69570 −0.847851 0.530235i \(-0.822104\pi\)
−0.847851 + 0.530235i \(0.822104\pi\)
\(458\) −3.37674e13 1.25237e14i −0.0782955 0.290383i
\(459\) 7.68334e14i 1.76027i
\(460\) 2.15853e14 + 3.71179e14i 0.488641 + 0.840263i
\(461\) 2.69171e13i 0.0602107i 0.999547 + 0.0301054i \(0.00958428\pi\)
−0.999547 + 0.0301054i \(0.990416\pi\)
\(462\) −6.93416e13 + 1.86964e13i −0.153272 + 0.0413265i
\(463\) −6.06138e13 −0.132396 −0.0661982 0.997806i \(-0.521087\pi\)
−0.0661982 + 0.997806i \(0.521087\pi\)
\(464\) −1.76123e14 1.00219e14i −0.380161 0.216323i
\(465\) −8.99156e14 −1.91798
\(466\) −3.95799e14 + 1.06718e14i −0.834357 + 0.224966i
\(467\) 2.97151e13i 0.0619063i 0.999521 + 0.0309531i \(0.00985426\pi\)
−0.999521 + 0.0309531i \(0.990146\pi\)
\(468\) −6.28765e13 1.08122e14i −0.129460 0.222619i
\(469\) 1.30439e14i 0.265434i
\(470\) −5.89259e13 2.18545e14i −0.118514 0.439545i
\(471\) 3.42813e13 0.0681464
\(472\) 6.48241e14 + 6.42179e14i 1.27366 + 1.26176i
\(473\) −1.64911e14 −0.320267
\(474\) −1.16689e14 4.32776e14i −0.224000 0.830774i
\(475\) 3.95876e14i 0.751180i
\(476\) −1.73832e14 + 1.01089e14i −0.326056 + 0.189612i
\(477\) 9.07879e13i 0.168336i
\(478\) 6.49968e14 1.75250e14i 1.19135 0.321221i
\(479\) 1.21025e14 0.219296 0.109648 0.993970i \(-0.465028\pi\)
0.109648 + 0.993970i \(0.465028\pi\)
\(480\) −1.62701e14 + 6.26795e14i −0.291450 + 1.12279i
\(481\) −1.53712e14 −0.272214
\(482\) 7.24594e13 1.95371e13i 0.126863 0.0342059i
\(483\) 9.11106e13i 0.157710i
\(484\) 2.09550e14 1.21860e14i 0.358624 0.208552i
\(485\) 6.17266e14i 1.04446i
\(486\) 5.45366e13 + 2.02266e14i 0.0912408 + 0.338395i
\(487\) 6.01563e14 0.995111 0.497556 0.867432i \(-0.334231\pi\)
0.497556 + 0.867432i \(0.334231\pi\)
\(488\) 3.72253e14 + 3.68773e14i 0.608877 + 0.603184i
\(489\) 1.31974e14 0.213446
\(490\) −1.97302e14 7.31757e14i −0.315539 1.17028i
\(491\) 8.74926e13i 0.138364i −0.997604 0.0691820i \(-0.977961\pi\)
0.997604 0.0691820i \(-0.0220389\pi\)
\(492\) −2.73675e14 4.70609e14i −0.427983 0.735957i
\(493\) 4.66220e14i 0.720995i
\(494\) −1.08211e15 + 2.91767e14i −1.65491 + 0.446209i
\(495\) −1.14810e14 −0.173640
\(496\) 5.46713e14 9.60781e14i 0.817730 1.43706i
\(497\) −3.69806e13 −0.0547033
\(498\) −6.34625e14 + 1.71113e14i −0.928445 + 0.250335i
\(499\) 8.99853e14i 1.30202i 0.759068 + 0.651011i \(0.225655\pi\)
−0.759068 + 0.651011i \(0.774345\pi\)
\(500\) 1.63572e14 + 2.81277e14i 0.234085 + 0.402532i
\(501\) 2.52564e14i 0.357489i
\(502\) 1.89224e14 + 7.01796e14i 0.264914 + 0.982517i
\(503\) 6.87292e14 0.951738 0.475869 0.879516i \(-0.342134\pi\)
0.475869 + 0.879516i \(0.342134\pi\)
\(504\) 2.08658e13 2.10627e13i 0.0285803 0.0288500i
\(505\) 2.68155e14 0.363315
\(506\) 1.12921e14 + 4.18803e14i 0.151338 + 0.561283i
\(507\) 7.56313e14i 1.00267i
\(508\) −9.56336e14 + 5.56141e14i −1.25418 + 0.729347i
\(509\) 1.78689e14i 0.231819i 0.993260 + 0.115910i \(0.0369783\pi\)
−0.993260 + 0.115910i \(0.963022\pi\)
\(510\) 1.43850e15 3.87860e14i 1.84618 0.497781i
\(511\) −2.61225e13 −0.0331666
\(512\) −5.70826e14 5.54962e14i −0.717000 0.697073i
\(513\) 1.01508e15 1.26141
\(514\) −1.26922e15 + 3.42218e14i −1.56042 + 0.420732i
\(515\) 3.98790e14i 0.485070i
\(516\) −2.72754e14 + 1.58616e14i −0.328245 + 0.190885i
\(517\) 2.28659e14i 0.272264i
\(518\) −9.48553e12 3.51800e13i −0.0111750 0.0414460i
\(519\) 1.12346e15 1.30960
\(520\) 1.13246e15 1.14315e15i 1.30618 1.31851i
\(521\) 3.87660e14 0.442429 0.221215 0.975225i \(-0.428998\pi\)
0.221215 + 0.975225i \(0.428998\pi\)
\(522\) −1.78948e13 6.63685e13i −0.0202088 0.0749505i
\(523\) 3.70738e14i 0.414293i 0.978310 + 0.207146i \(0.0664177\pi\)
−0.978310 + 0.207146i \(0.933582\pi\)
\(524\) −2.30551e14 3.96454e14i −0.254944 0.438400i
\(525\) 1.20604e14i 0.131973i
\(526\) −3.12689e14 + 8.43097e13i −0.338603 + 0.0912969i
\(527\) −2.54330e15 −2.72546
\(528\) −3.23532e14 + 5.68568e14i −0.343108 + 0.602971i
\(529\) −4.02529e14 −0.422465
\(530\) 1.12773e15 3.04067e14i 1.17135 0.315829i
\(531\) 3.09524e14i 0.318182i
\(532\) −1.33553e14 2.29658e14i −0.135875 0.233651i
\(533\) 1.35275e15i 1.36213i
\(534\) −9.01925e13 3.34507e14i −0.0898863 0.333372i
\(535\) 1.64948e14 0.162705
\(536\) −8.44079e14 8.36187e14i −0.824094 0.816388i
\(537\) 3.32207e14 0.321033
\(538\) −1.15194e14 4.27234e14i −0.110186 0.408661i
\(539\) 7.65621e14i 0.724896i
\(540\) −1.25985e15 + 7.32643e14i −1.18073 + 0.686636i
\(541\) 1.32152e15i 1.22599i −0.790086 0.612995i \(-0.789964\pi\)
0.790086 0.612995i \(-0.210036\pi\)
\(542\) 1.63359e15 4.40460e14i 1.50019 0.404493i
\(543\) −1.53717e15 −1.39740
\(544\) −4.60207e14 + 1.77292e15i −0.414152 + 1.59549i
\(545\) 8.09364e12 0.00721046
\(546\) 3.29667e14 8.88874e13i 0.290747 0.0783936i
\(547\) 1.58642e15i 1.38513i −0.721357 0.692563i \(-0.756481\pi\)
0.721357 0.692563i \(-0.243519\pi\)
\(548\) 5.93651e14 3.45228e14i 0.513143 0.298409i
\(549\) 1.77745e14i 0.152107i
\(550\) −1.49475e14 5.54375e14i −0.126641 0.469687i
\(551\) −6.15943e14 −0.516662
\(552\) 5.89582e14 + 5.84069e14i 0.489643 + 0.485064i
\(553\) −2.64016e14 −0.217091
\(554\) 2.68727e14 + 9.96658e14i 0.218780 + 0.811414i
\(555\) 2.69958e14i 0.217613i
\(556\) 2.80758e13 + 4.82789e13i 0.0224089 + 0.0385342i
\(557\) 1.21582e15i 0.960869i −0.877031 0.480435i \(-0.840479\pi\)
0.877031 0.480435i \(-0.159521\pi\)
\(558\) 3.62051e14 9.76191e13i 0.283323 0.0763918i
\(559\) 7.84025e14 0.607526
\(560\) 3.31515e14 + 1.88642e14i 0.254372 + 0.144745i
\(561\) 1.50507e15 1.14356
\(562\) −3.70194e14 + 9.98148e13i −0.278535 + 0.0751009i
\(563\) 2.27297e15i 1.69355i −0.531951 0.846775i \(-0.678541\pi\)
0.531951 0.846775i \(-0.321459\pi\)
\(564\) −2.19931e14 3.78191e14i −0.162275 0.279046i
\(565\) 1.58933e15i 1.16131i
\(566\) 6.45722e14 + 2.39486e15i 0.467256 + 1.73297i
\(567\) −2.52578e14 −0.181004
\(568\) −2.37066e14 + 2.39304e14i −0.168249 + 0.169837i
\(569\) −3.01866e14 −0.212176 −0.106088 0.994357i \(-0.533833\pi\)
−0.106088 + 0.994357i \(0.533833\pi\)
\(570\) 5.12418e14 + 1.90046e15i 0.356708 + 1.32296i
\(571\) 2.23731e15i 1.54251i 0.636529 + 0.771253i \(0.280370\pi\)
−0.636529 + 0.771253i \(0.719630\pi\)
\(572\) 1.40519e15 8.17167e14i 0.959530 0.557998i
\(573\) 1.97116e15i 1.33313i
\(574\) −3.09604e14 + 8.34780e13i −0.207392 + 0.0559186i
\(575\) −7.28414e14 −0.483287
\(576\) −2.53692e12 2.70047e14i −0.00166718 0.177466i
\(577\) −1.67626e15 −1.09113 −0.545564 0.838069i \(-0.683684\pi\)
−0.545564 + 0.838069i \(0.683684\pi\)
\(578\) 2.57137e15 6.93312e14i 1.65791 0.447019i
\(579\) 1.00003e15i 0.638675i
\(580\) 7.64467e14 4.44563e14i 0.483620 0.281241i
\(581\) 3.87155e14i 0.242614i
\(582\) −3.10589e14 1.15192e15i −0.192801 0.715064i
\(583\) 1.17991e15 0.725561
\(584\) −1.67460e14 + 1.69040e14i −0.102009 + 0.102972i
\(585\) 5.45833e14 0.329384
\(586\) −6.59654e14 2.44653e15i −0.394348 1.46256i
\(587\) 1.50304e15i 0.890144i 0.895495 + 0.445072i \(0.146822\pi\)
−0.895495 + 0.445072i \(0.853178\pi\)
\(588\) −7.36395e14 1.26630e15i −0.432052 0.742953i
\(589\) 3.36007e15i 1.95305i
\(590\) −3.84477e15 + 1.03666e15i −2.21403 + 0.596966i
\(591\) −3.63165e14 −0.207192
\(592\) −2.88460e14 1.64142e14i −0.163048 0.0927792i
\(593\) −1.38749e14 −0.0777015 −0.0388507 0.999245i \(-0.512370\pi\)
−0.0388507 + 0.999245i \(0.512370\pi\)
\(594\) −1.42149e15 + 3.83274e14i −0.788713 + 0.212659i
\(595\) 8.77560e14i 0.482429i
\(596\) 1.18275e15 + 2.03384e15i 0.644225 + 1.10780i
\(597\) 2.80510e15i 1.51387i
\(598\) −5.36853e14 1.99109e15i −0.287077 1.06472i
\(599\) 1.44893e15 0.767717 0.383859 0.923392i \(-0.374595\pi\)
0.383859 + 0.923392i \(0.374595\pi\)
\(600\) −7.80437e14 7.73140e14i −0.409738 0.405906i
\(601\) −7.86748e13 −0.0409285 −0.0204643 0.999791i \(-0.506514\pi\)
−0.0204643 + 0.999791i \(0.506514\pi\)
\(602\) 4.83820e13 + 1.79440e14i 0.0249404 + 0.0924992i
\(603\) 4.03034e14i 0.205872i
\(604\) 7.98735e14 4.64491e14i 0.404296 0.235112i
\(605\) 1.05788e15i 0.530616i
\(606\) 5.00421e14 1.34927e14i 0.248734 0.0670657i
\(607\) 1.57249e15 0.774550 0.387275 0.921964i \(-0.373416\pi\)
0.387275 + 0.921964i \(0.373416\pi\)
\(608\) −2.34228e15 6.08000e14i −1.14332 0.296779i
\(609\) 1.87648e14 0.0907713
\(610\) −2.20787e15 + 5.95303e14i −1.05842 + 0.285380i
\(611\) 1.08710e15i 0.516467i
\(612\) −5.37112e14 + 3.12348e14i −0.252890 + 0.147064i
\(613\) 8.60982e14i 0.401755i 0.979616 + 0.200878i \(0.0643794\pi\)
−0.979616 + 0.200878i \(0.935621\pi\)
\(614\) −4.11627e14 1.52665e15i −0.190361 0.706013i
\(615\) 2.37578e15 1.08891
\(616\) 2.73739e14 + 2.71179e14i 0.124349 + 0.123186i
\(617\) −9.54957e14 −0.429947 −0.214974 0.976620i \(-0.568967\pi\)
−0.214974 + 0.976620i \(0.568967\pi\)
\(618\) 2.00659e14 + 7.44206e14i 0.0895409 + 0.332090i
\(619\) 1.65458e13i 0.00731793i 0.999993 + 0.00365896i \(0.00116469\pi\)
−0.999993 + 0.00365896i \(0.998835\pi\)
\(620\) 2.42516e15 + 4.17029e15i 1.06313 + 1.82815i
\(621\) 1.86775e15i 0.811550i
\(622\) −3.83372e15 + 1.03368e15i −1.65110 + 0.445183i
\(623\) −2.04067e14 −0.0871141
\(624\) 1.53815e15 2.70311e15i 0.650854 1.14380i
\(625\) −2.93617e15 −1.23152
\(626\) 4.14062e15 1.11643e15i 1.72150 0.464164i
\(627\) 1.98841e15i 0.819474i
\(628\) −9.24620e13 1.58997e14i −0.0377733 0.0649547i
\(629\) 7.63587e14i 0.309229i
\(630\) 3.36832e13 + 1.24925e14i 0.0135220 + 0.0501505i
\(631\) 2.66470e15 1.06044 0.530221 0.847859i \(-0.322109\pi\)
0.530221 + 0.847859i \(0.322109\pi\)
\(632\) −1.69249e15 + 1.70847e15i −0.667702 + 0.674004i
\(633\) 2.59843e14 0.101623
\(634\) −8.78556e14 3.25840e15i −0.340626 1.26332i
\(635\) 4.82788e15i 1.85567i
\(636\) 1.95152e15 1.13487e15i 0.743634 0.432448i
\(637\) 3.63994e15i 1.37508i
\(638\) 8.62551e14 2.32568e14i 0.323051 0.0871036i
\(639\) −1.14264e14 −0.0424281
\(640\) 3.34591e15 9.35954e14i 1.23175 0.344560i
\(641\) 2.68473e15 0.979901 0.489951 0.871750i \(-0.337015\pi\)
0.489951 + 0.871750i \(0.337015\pi\)
\(642\) 3.07819e14 8.29967e13i 0.111392 0.0300343i
\(643\) 4.42246e14i 0.158673i −0.996848 0.0793367i \(-0.974720\pi\)
0.996848 0.0793367i \(-0.0252802\pi\)
\(644\) 4.22571e14 2.45739e14i 0.150324 0.0874182i
\(645\) 1.37695e15i 0.485668i
\(646\) 1.44940e15 + 5.37554e15i 0.506884 + 1.87994i
\(647\) −3.79844e15 −1.31714 −0.658570 0.752520i \(-0.728838\pi\)
−0.658570 + 0.752520i \(0.728838\pi\)
\(648\) −1.61916e15 + 1.63444e15i −0.556708 + 0.561963i
\(649\) −4.02270e15 −1.37142
\(650\) 7.10639e14 + 2.63563e15i 0.240229 + 0.890965i
\(651\) 1.02365e15i 0.343128i
\(652\) −3.55953e14 6.12094e14i −0.118313 0.203449i
\(653\) 5.25844e15i 1.73314i −0.499052 0.866572i \(-0.666318\pi\)
0.499052 0.866572i \(-0.333682\pi\)
\(654\) 1.51040e13 4.07247e12i 0.00493646 0.00133101i
\(655\) 2.00142e15 0.648652
\(656\) −1.44454e15 + 2.53861e15i −0.464258 + 0.815877i
\(657\) −8.07141e13 −0.0257241
\(658\) −2.48804e14 + 6.70846e13i −0.0786349 + 0.0212022i
\(659\) 3.68455e15i 1.15482i 0.816454 + 0.577410i \(0.195937\pi\)
−0.816454 + 0.577410i \(0.804063\pi\)
\(660\) −1.43515e15 2.46788e15i −0.446074 0.767066i
\(661\) 1.45382e15i 0.448130i −0.974574 0.224065i \(-0.928067\pi\)
0.974574 0.224065i \(-0.0719327\pi\)
\(662\) −1.06692e15 3.95702e15i −0.326147 1.20962i
\(663\) −7.15546e15 −2.16927
\(664\) 2.50530e15 + 2.48188e15i 0.753244 + 0.746201i
\(665\) 1.15938e15 0.345707
\(666\) −2.93086e13 1.08700e14i −0.00866737 0.0321457i
\(667\) 1.13334e15i 0.332405i
\(668\) 1.17139e15 6.81202e14i 0.340746 0.198155i
\(669\) 4.55930e14i 0.131539i
\(670\) 5.00631e15 1.34984e15i 1.43254 0.386252i
\(671\) −2.31004e15 −0.655611
\(672\) 7.13579e14 + 1.85228e14i 0.200868 + 0.0521406i
\(673\) 4.59102e15 1.28182 0.640909 0.767617i \(-0.278557\pi\)
0.640909 + 0.767617i \(0.278557\pi\)
\(674\) 1.64818e15 4.44397e14i 0.456432 0.123067i
\(675\) 2.47237e15i 0.679113i
\(676\) −3.50778e15 + 2.03989e15i −0.955709 + 0.555776i
\(677\) 2.08953e15i 0.564691i −0.959313 0.282345i \(-0.908888\pi\)
0.959313 0.282345i \(-0.0911124\pi\)
\(678\) 7.99704e14 + 2.96595e15i 0.214371 + 0.795062i
\(679\) −7.02730e14 −0.186855
\(680\) −5.67874e15 5.62564e15i −1.49780 1.48379i
\(681\) 1.91880e15 0.502019
\(682\) 1.26869e15 + 4.70535e15i 0.329263 + 1.22118i
\(683\) 3.35863e14i 0.0864667i 0.999065 + 0.0432333i \(0.0137659\pi\)
−0.999065 + 0.0432333i \(0.986234\pi\)
\(684\) −4.12657e14 7.09602e14i −0.105385 0.181220i
\(685\) 2.99693e15i 0.759240i
\(686\) −1.71218e15 + 4.61650e14i −0.430294 + 0.116019i
\(687\) 1.09408e15 0.272763
\(688\) 1.47132e15 + 8.37225e14i 0.363891 + 0.207065i
\(689\) −5.60960e15 −1.37634
\(690\) −3.49686e15 + 9.42852e14i −0.851155 + 0.229495i
\(691\) 6.13314e14i 0.148099i −0.997255 0.0740497i \(-0.976408\pi\)
0.997255 0.0740497i \(-0.0235923\pi\)
\(692\) −3.03015e15 5.21062e15i −0.725906 1.24826i
\(693\) 1.30706e14i 0.0310644i
\(694\) −5.83521e14 2.16417e15i −0.137588 0.510287i
\(695\) −2.43727e14 −0.0570148
\(696\) 1.20293e15 1.21428e15i 0.279183 0.281818i
\(697\) 6.72000e15 1.54735
\(698\) −4.98163e14 1.84759e15i −0.113806 0.422087i
\(699\) 3.45772e15i 0.783728i
\(700\) −5.59362e14 + 3.25288e14i −0.125792 + 0.0731524i
\(701\) 7.14041e15i 1.59321i 0.604498 + 0.796606i \(0.293374\pi\)
−0.604498 + 0.796606i \(0.706626\pi\)
\(702\) 6.75811e15 1.82218e15i 1.49614 0.403400i
\(703\) −1.00881e15 −0.221592
\(704\) 3.50964e15 3.29708e13i 0.764914 0.00718587i
\(705\) 1.90923e15 0.412874
\(706\) −2.36959e15 + 6.38909e14i −0.508450 + 0.137092i
\(707\) 3.05283e14i 0.0649973i
\(708\) −6.65335e15 + 3.86914e15i −1.40559 + 0.817394i
\(709\) 1.70696e15i 0.357823i 0.983865 + 0.178911i \(0.0572576\pi\)
−0.983865 + 0.178911i \(0.942742\pi\)
\(710\) −3.82691e14 1.41933e15i −0.0796027 0.295231i
\(711\) −8.15765e14 −0.168377
\(712\) −1.30818e15 + 1.32053e15i −0.267934 + 0.270463i
\(713\) 6.18254e15 1.25653
\(714\) −4.41561e14 1.63767e15i −0.0890534 0.330282i
\(715\) 7.09386e15i 1.41971i
\(716\) −8.96011e14 1.54077e15i −0.177947 0.305997i
\(717\) 5.67816e15i 1.11906i
\(718\) 4.85011e15 1.30773e15i 0.948566 0.255760i
\(719\) 7.81443e15 1.51666 0.758330 0.651870i \(-0.226015\pi\)
0.758330 + 0.651870i \(0.226015\pi\)
\(720\) 1.02432e15 + 5.82871e14i 0.197292 + 0.112265i
\(721\) 4.54005e14 0.0867793
\(722\) −2.01189e15 + 5.42463e14i −0.381637 + 0.102900i
\(723\) 6.33009e14i 0.119165i
\(724\) 4.14597e15 + 7.12938e15i 0.774576 + 1.33196i
\(725\) 1.50021e15i 0.278160i
\(726\) 5.32290e14 + 1.97417e15i 0.0979484 + 0.363272i
\(727\) 9.77013e12 0.00178427 0.000892136 1.00000i \(-0.499716\pi\)
0.000892136 1.00000i \(0.499716\pi\)
\(728\) −1.30142e15 1.28925e15i −0.235882 0.233677i
\(729\) −6.16439e15 −1.10889
\(730\) −2.70327e14 1.00259e15i −0.0482630 0.178998i
\(731\) 3.89476e15i 0.690137i
\(732\) −3.82070e15 + 2.22186e15i −0.671942 + 0.390756i
\(733\) 1.07577e16i 1.87780i −0.344191 0.938900i \(-0.611847\pi\)
0.344191 0.938900i \(-0.388153\pi\)
\(734\) −5.99100e15 + 1.61534e15i −1.03794 + 0.279857i
\(735\) 6.39267e15 1.09926
\(736\) 1.11872e15 4.30981e15i 0.190939 0.735580i
\(737\) 5.23799e15 0.887346
\(738\) −9.56624e14 + 2.57933e14i −0.160854 + 0.0433707i
\(739\) 1.55149e14i 0.0258944i −0.999916 0.0129472i \(-0.995879\pi\)
0.999916 0.0129472i \(-0.00412133\pi\)
\(740\) 1.25206e15 7.28117e14i 0.207421 0.120622i
\(741\) 9.45339e15i 1.55449i
\(742\) −3.46167e14 1.28387e15i −0.0565020 0.209555i
\(743\) −6.27422e15 −1.01653 −0.508266 0.861200i \(-0.669713\pi\)
−0.508266 + 0.861200i \(0.669713\pi\)
\(744\) 6.62410e15 + 6.56216e15i 1.06531 + 1.05535i
\(745\) −1.02675e16 −1.63910
\(746\) −1.46497e15 5.43332e15i −0.232149 0.860996i
\(747\) 1.19624e15i 0.188172i
\(748\) −4.05940e15 6.98051e15i −0.633874 1.09000i
\(749\) 1.87786e14i 0.0291080i
\(750\) −2.64990e15 + 7.14488e14i −0.407749 + 0.109941i
\(751\) −6.57869e15 −1.00489 −0.502447 0.864608i \(-0.667567\pi\)
−0.502447 + 0.864608i \(0.667567\pi\)
\(752\) −1.16086e15 + 2.04008e15i −0.176029 + 0.309349i
\(753\) −6.13093e15 −0.922898
\(754\) −4.10077e15 + 1.10568e15i −0.612806 + 0.165230i
\(755\) 4.03226e15i 0.598192i
\(756\) 8.34082e14 + 1.43428e15i 0.122840 + 0.211234i
\(757\) 2.54343e15i 0.371871i 0.982562 + 0.185935i \(0.0595315\pi\)
−0.982562 + 0.185935i \(0.940468\pi\)
\(758\) 3.25174e15 + 1.20601e16i 0.471992 + 1.75053i
\(759\) −3.65869e15 −0.527225
\(760\) 7.43228e15 7.50243e15i 1.06328 1.07332i
\(761\) −5.98810e15 −0.850498 −0.425249 0.905076i \(-0.639813\pi\)
−0.425249 + 0.905076i \(0.639813\pi\)
\(762\) −2.42924e15 9.00960e15i −0.342545 1.27044i
\(763\) 9.21426e12i 0.00128996i
\(764\) 9.14224e15 5.31651e15i 1.27069 0.738947i
\(765\) 2.71151e15i 0.374173i
\(766\) 5.71810e15 1.54176e15i 0.783418 0.211232i
\(767\) 1.91249e16 2.60150
\(768\) 5.77306e15 3.43020e15i 0.779685 0.463268i
\(769\) −7.50045e15 −1.00576 −0.502878 0.864358i \(-0.667725\pi\)
−0.502878 + 0.864358i \(0.667725\pi\)
\(770\) −1.62357e15 + 4.37760e14i −0.216158 + 0.0582823i
\(771\) 1.10880e16i 1.46573i
\(772\) 4.63813e15 2.69722e15i 0.608762 0.354015i
\(773\) 6.98863e15i 0.910762i 0.890297 + 0.455381i \(0.150497\pi\)
−0.890297 + 0.455381i \(0.849503\pi\)
\(774\) 1.49492e14 + 5.54437e14i 0.0193438 + 0.0717426i
\(775\) −8.18390e15 −1.05148
\(776\) −4.50489e15 + 4.54741e15i −0.574705 + 0.580129i
\(777\) 3.07335e14 0.0389311
\(778\) 3.12732e15 + 1.15986e16i 0.393355 + 1.45888i
\(779\) 8.87809e15i 1.10883i
\(780\) 6.82307e15 + 1.17329e16i 0.846173 + 1.45507i
\(781\) 1.48501e15i 0.182873i
\(782\) −9.89103e15 + 2.66690e15i −1.20950 + 0.326114i
\(783\) 3.84675e15 0.467094
\(784\) −3.88693e15 + 6.83080e15i −0.468672 + 0.823632i
\(785\) 8.02666e14 0.0961063
\(786\) 3.73498e15 1.00705e15i 0.444083 0.119737i
\(787\) 2.82969e15i 0.334102i −0.985948 0.167051i \(-0.946576\pi\)
0.985948 0.167051i \(-0.0534244\pi\)
\(788\) 9.79510e14 + 1.68436e15i 0.114846 + 0.197488i
\(789\) 2.73167e15i 0.318057i
\(790\) −2.73216e15 1.01331e16i −0.315905 1.17163i
\(791\) 1.80939e15 0.207759
\(792\) 8.45806e14 + 8.37897e14i 0.0964456 + 0.0955438i
\(793\) 1.09825e16 1.24365
\(794\) 3.01280e15 + 1.11739e16i 0.338811 + 1.25659i
\(795\) 9.85189e15i 1.10027i
\(796\) −1.30101e16 + 7.56578e15i −1.44297 + 0.839136i
\(797\) 7.15437e15i 0.788044i −0.919101 0.394022i \(-0.871083\pi\)
0.919101 0.394022i \(-0.128917\pi\)
\(798\) 2.16359e15 5.83366e14i 0.236679 0.0638153i
\(799\) 5.40033e15 0.586696
\(800\) −1.48087e15 + 5.70494e15i −0.159779 + 0.615540i
\(801\) −6.30532e14 −0.0675660
\(802\) 2.15648e15 5.81449e14i 0.229502 0.0618803i
\(803\) 1.04899e15i 0.110876i
\(804\) 8.66337e15 5.03804e15i 0.909450 0.528875i
\(805\) 2.13327e15i 0.222417i
\(806\) −6.03168e15 2.23704e16i −0.624591 2.31649i
\(807\) 3.73234e15 0.383864
\(808\) −1.97550e15 1.95703e15i −0.201797 0.199910i
\(809\) −6.06373e15 −0.615209 −0.307605 0.951514i \(-0.599527\pi\)
−0.307605 + 0.951514i \(0.599527\pi\)
\(810\) −2.61378e15 9.69403e15i −0.263392 0.976870i
\(811\) 1.25004e16i 1.25115i −0.780164 0.625576i \(-0.784864\pi\)
0.780164 0.625576i \(-0.215136\pi\)
\(812\) −5.06115e14 8.70312e14i −0.0503142 0.0865200i
\(813\) 1.42711e16i 1.40916i
\(814\) 1.41271e15 3.80906e14i 0.138554 0.0373580i
\(815\) 3.09004e15 0.301021
\(816\) −1.34281e16 7.64099e15i −1.29933 0.739356i
\(817\) 5.14554e15 0.494549
\(818\) 8.80284e15 2.37349e15i 0.840388 0.226592i
\(819\) 6.21407e14i 0.0589271i
\(820\) −6.40784e15 1.10189e16i −0.603581 1.03791i
\(821\) 9.11023e15i 0.852397i 0.904630 + 0.426198i \(0.140147\pi\)
−0.904630 + 0.426198i \(0.859853\pi\)
\(822\) 1.50796e15 + 5.59276e15i 0.140151 + 0.519794i
\(823\) −1.90354e16 −1.75737 −0.878683 0.477407i \(-0.841577\pi\)
−0.878683 + 0.477407i \(0.841577\pi\)
\(824\) 2.91042e15 2.93789e15i 0.266905 0.269424i
\(825\) 4.84305e15 0.441187
\(826\) 1.18019e15 + 4.37710e15i 0.106798 + 0.396092i
\(827\) 6.03027e15i 0.542071i 0.962569 + 0.271036i \(0.0873661\pi\)
−0.962569 + 0.271036i \(0.912634\pi\)
\(828\) 1.30567e15 7.59291e14i 0.116592 0.0678018i
\(829\) 1.35457e16i 1.20158i −0.799408 0.600788i \(-0.794854\pi\)
0.799408 0.600788i \(-0.205146\pi\)
\(830\) −1.48592e16 + 4.00645e15i −1.30938 + 0.353045i
\(831\) −8.70687e15 −0.762178
\(832\) −1.66857e16 + 1.56751e14i −1.45099 + 0.0136311i
\(833\) 1.80820e16 1.56206
\(834\) −4.54834e14 + 1.22636e14i −0.0390337 + 0.0105246i
\(835\) 5.91354e15i 0.504164i
\(836\) 9.22226e15 5.36305e15i 0.781093 0.454231i
\(837\) 2.09846e16i 1.76568i
\(838\) 3.96701e15 + 1.47129e16i 0.331605 + 1.22986i
\(839\) 5.63944e15 0.468322 0.234161 0.972198i \(-0.424766\pi\)
0.234161 + 0.972198i \(0.424766\pi\)
\(840\) −2.26426e15 + 2.28563e15i −0.186805 + 0.188569i
\(841\) 9.86633e15 0.808682
\(842\) 1.42203e13 + 5.27403e13i 0.00115795 + 0.00429463i
\(843\) 3.23404e15i 0.261634i
\(844\) −7.00837e14 1.20515e15i −0.0563292 0.0968633i
\(845\) 1.77084e16i 1.41406i
\(846\) −7.68762e14 + 2.07280e14i −0.0609895 + 0.0164445i
\(847\) 1.20434e15 0.0949275
\(848\) −1.05271e16 5.99023e15i −0.824388 0.469101i
\(849\) −2.09217e16 −1.62781
\(850\) 1.30929e16 3.53020e15i 1.01212 0.272895i
\(851\) 1.85621e15i 0.142566i
\(852\) −1.42833e15 2.45614e15i −0.108996 0.187428i
\(853\) 2.66012e15i 0.201689i −0.994902 0.100844i \(-0.967846\pi\)
0.994902 0.100844i \(-0.0321544\pi\)
\(854\) 6.77726e14 + 2.51356e15i 0.0510547 + 0.189353i
\(855\) 3.58229e15 0.268131
\(856\) −1.21517e15 1.20381e15i −0.0903717 0.0895267i
\(857\) 6.62417e15 0.489482 0.244741 0.969588i \(-0.421297\pi\)
0.244741 + 0.969588i \(0.421297\pi\)
\(858\) 3.56941e15 + 1.32383e16i 0.262070 + 0.971967i
\(859\) 2.28112e16i 1.66412i −0.554683 0.832062i \(-0.687161\pi\)
0.554683 0.832062i \(-0.312839\pi\)
\(860\) −6.38629e15 + 3.71384e15i −0.462922 + 0.269204i
\(861\) 2.70472e15i 0.194807i
\(862\) −8.21229e14 + 2.21426e14i −0.0587725 + 0.0158467i
\(863\) −2.00538e16 −1.42606 −0.713031 0.701133i \(-0.752678\pi\)
−0.713031 + 0.701133i \(0.752678\pi\)
\(864\) 1.46282e16 + 3.79714e15i 1.03363 + 0.268307i
\(865\) 2.63048e16 1.84691
\(866\) 1.37035e16 3.69484e15i 0.956054 0.257779i
\(867\) 2.24636e16i 1.55731i
\(868\) 4.74769e15 2.76094e15i 0.327057 0.190195i
\(869\) 1.06020e16i 0.725736i
\(870\) 1.94186e15 + 7.20201e15i 0.132088 + 0.489889i
\(871\) −2.49026e16 −1.68324
\(872\) −5.96260e13 5.90685e13i −0.00400493 0.00396748i
\(873\) −2.17131e15 −0.144925
\(874\) −3.52336e15 1.30675e16i −0.233692 0.866720i
\(875\) 1.61658e15i 0.106550i
\(876\) −1.00895e15 1.73498e15i −0.0660840 0.113638i
\(877\) 2.76399e16i 1.79903i 0.436887 + 0.899516i \(0.356081\pi\)
−0.436887 + 0.899516i \(0.643919\pi\)
\(878\) 2.16377e16 5.83413e15i 1.39956 0.377361i
\(879\) 2.13731e16 1.37381
\(880\) −7.57521e15 + 1.33125e16i −0.483883 + 0.850364i
\(881\) −2.51486e16 −1.59642 −0.798208 0.602382i \(-0.794218\pi\)
−0.798208 + 0.602382i \(0.794218\pi\)
\(882\) −2.57405e15 + 6.94036e14i −0.162383 + 0.0437829i
\(883\) 1.31245e16i 0.822810i 0.911453 + 0.411405i \(0.134962\pi\)
−0.911453 + 0.411405i \(0.865038\pi\)
\(884\) 1.92993e16 + 3.31870e16i 1.20242 + 2.06767i
\(885\) 3.35882e16i 2.07969i
\(886\) 3.53051e15 + 1.30940e16i 0.217246 + 0.805726i
\(887\) −5.71207e15 −0.349312 −0.174656 0.984630i \(-0.555881\pi\)
−0.174656 + 0.984630i \(0.555881\pi\)
\(888\) 1.97019e15 1.98878e15i 0.119739 0.120869i
\(889\) −5.49633e15 −0.331981
\(890\) −2.11177e15 7.83218e15i −0.126766 0.470151i
\(891\) 1.01426e16i 0.605096i
\(892\) −2.11460e15 + 1.22971e15i −0.125378 + 0.0729116i
\(893\) 7.13461e15i 0.420424i
\(894\) −1.91608e16 + 5.16628e15i −1.12216 + 0.302567i
\(895\) 7.77831e15 0.452750
\(896\) −1.06554e15 3.80917e15i −0.0616420 0.220362i
\(897\) 1.73943e16 1.00011
\(898\) 1.09208e16 2.94457e15i 0.624075 0.168268i
\(899\) 1.27333e16i 0.723209i
\(900\) −1.72833e15 + 1.00508e15i −0.0975649 + 0.0567372i
\(901\) 2.78665e16i 1.56349i
\(902\) −3.35219e15 1.24327e16i −0.186936 0.693310i
\(903\) −1.56760e15 −0.0868864
\(904\) 1.15992e16 1.17086e16i 0.639000 0.645031i
\(905\) −3.59913e16 −1.97075
\(906\) 2.02891e15 + 7.52485e15i 0.110423 + 0.409537i
\(907\) 1.52922e16i 0.827235i −0.910451 0.413618i \(-0.864265\pi\)
0.910451 0.413618i \(-0.135735\pi\)
\(908\) −5.17529e15 8.89938e15i −0.278267 0.478506i
\(909\) 9.43271e14i 0.0504121i
\(910\) 7.71884e15 2.08121e15i 0.410038 0.110558i
\(911\) −5.29684e14 −0.0279683 −0.0139842 0.999902i \(-0.504451\pi\)
−0.0139842 + 0.999902i \(0.504451\pi\)
\(912\) 1.00948e16 1.77404e16i 0.529820 0.931093i
\(913\) −1.55468e16 −0.811058
\(914\) −3.15729e16 + 8.51294e15i −1.63723 + 0.441444i
\(915\) 1.92881e16i 0.994198i
\(916\) −2.95089e15 5.07433e15i −0.151192 0.259988i
\(917\) 2.27853e15i 0.116044i
\(918\) −9.05193e15 3.35719e16i −0.458254 1.69958i
\(919\) 2.61618e16 1.31654 0.658268 0.752783i \(-0.271289\pi\)
0.658268 + 0.752783i \(0.271289\pi\)
\(920\) 1.38045e16 + 1.36754e16i 0.690539 + 0.684082i
\(921\) 1.33369e16 0.663173
\(922\) 3.17117e14 + 1.17613e15i 0.0156747 + 0.0581346i
\(923\) 7.06011e15i 0.346898i
\(924\) −2.80957e15 + 1.63386e15i −0.137229 + 0.0798030i
\(925\) 2.45709e15i 0.119300i
\(926\) −2.64848e15 + 7.14105e14i −0.127831 + 0.0344669i
\(927\) 1.40280e15 0.0673063
\(928\) −8.87631e15 2.30408e15i −0.423369 0.109896i
\(929\) −2.14173e16 −1.01550 −0.507749 0.861505i \(-0.669522\pi\)
−0.507749 + 0.861505i \(0.669522\pi\)
\(930\) −3.92881e16 + 1.05932e16i −1.85185 + 0.499309i
\(931\) 2.38889e16i 1.11937i
\(932\) −1.60369e16 + 9.32600e15i −0.747022 + 0.434418i
\(933\) 3.34916e16i 1.55091i
\(934\) 3.50081e14 + 1.29838e15i 0.0161161 + 0.0597717i
\(935\) 3.52398e16 1.61276
\(936\) −4.02116e15 3.98356e15i −0.182951 0.181240i
\(937\) 1.84540e16 0.834685 0.417343 0.908749i \(-0.362961\pi\)
0.417343 + 0.908749i \(0.362961\pi\)
\(938\) −1.53673e15 5.69946e15i −0.0691008 0.256282i
\(939\) 3.61727e16i 1.61704i
\(940\) −5.14947e15 8.85499e15i −0.228854 0.393536i
\(941\) 1.10663e16i 0.488946i −0.969656 0.244473i \(-0.921385\pi\)
0.969656 0.244473i \(-0.0786149\pi\)
\(942\) 1.49790e15 4.03877e14i 0.0657967 0.0177406i
\(943\) −1.63357e16 −0.713385
\(944\) 3.58902e16 + 2.04226e16i 1.55822 + 0.886675i
\(945\) −7.24070e15 −0.312540
\(946\) −7.20568e15 + 1.94285e15i −0.309224 + 0.0833756i
\(947\) 1.56625e16i 0.668244i −0.942530 0.334122i \(-0.891560\pi\)
0.942530 0.334122i \(-0.108440\pi\)
\(948\) −1.01973e16 1.75352e16i −0.432552 0.743814i
\(949\) 4.98715e15i 0.210324i
\(950\) 4.66391e15 + 1.72976e16i 0.195556 + 0.725279i
\(951\) 2.84656e16 1.18666
\(952\) −6.40455e15 + 6.46500e15i −0.265452 + 0.267957i
\(953\) 2.46314e16 1.01503 0.507515 0.861643i \(-0.330564\pi\)
0.507515 + 0.861643i \(0.330564\pi\)
\(954\) −1.06959e15 3.96693e15i −0.0438231 0.162532i
\(955\) 4.61529e16i 1.88010i
\(956\) 2.63353e16 1.53149e16i 1.06665 0.620290i
\(957\) 7.53530e15i 0.303448i
\(958\) 5.28812e15 1.42583e15i 0.211734 0.0570895i
\(959\) 3.41188e15 0.135829
\(960\) 2.75295e14 + 2.93043e16i 0.0108970 + 1.15995i
\(961\) 4.40539e16 1.73383
\(962\) −6.71636e15 + 1.81092e15i −0.262828 + 0.0708657i
\(963\) 5.80226e14i 0.0225763i
\(964\) 2.93590e15 1.70732e15i 0.113584 0.0660529i
\(965\) 2.34147e16i 0.900717i
\(966\) 1.07340e15 + 3.98102e15i 0.0410568 + 0.152272i
\(967\) 1.75674e16 0.668130 0.334065 0.942550i \(-0.391579\pi\)
0.334065 + 0.942550i \(0.391579\pi\)
\(968\) 7.72052e15 7.79339e15i 0.291966 0.294721i
\(969\) −4.69611e16 −1.76586
\(970\) −7.27216e15 2.69711e16i −0.271906 1.00845i
\(971\) 1.47579e15i 0.0548679i −0.999624 0.0274339i \(-0.991266\pi\)
0.999624 0.0274339i \(-0.00873359\pi\)
\(972\) 4.76589e15 + 8.19540e15i 0.176189 + 0.302974i
\(973\) 2.77472e14i 0.0102000i
\(974\) 2.62849e16 7.08715e15i 0.960799 0.259058i
\(975\) −2.30250e16 −0.836902
\(976\) 2.06100e16 + 1.17277e16i 0.744910 + 0.423876i
\(977\) −3.43891e16 −1.23595 −0.617975 0.786198i \(-0.712047\pi\)
−0.617975 + 0.786198i \(0.712047\pi\)
\(978\) 5.76651e15 1.55481e15i 0.206086 0.0555667i
\(979\) 8.19463e15i 0.291222i
\(980\) −1.72420e16 2.96492e16i −0.609319 1.04778i
\(981\) 2.84705e13i 0.00100049i
\(982\) −1.03077e15 3.82294e15i −0.0360204 0.133593i
\(983\) −3.64560e16 −1.26685 −0.633424 0.773805i \(-0.718351\pi\)
−0.633424 + 0.773805i \(0.718351\pi\)
\(984\) −1.75024e16 1.73388e16i −0.604819 0.599163i
\(985\) −8.50317e15 −0.292201
\(986\) 5.49264e15 + 2.03712e16i 0.187697 + 0.696135i
\(987\) 2.17357e15i 0.0738634i
\(988\) −4.38448e16 + 2.54972e16i −1.48168 + 0.861647i
\(989\) 9.46782e15i 0.318178i
\(990\) −5.01655e15 + 1.35260e15i −0.167653 + 0.0452040i
\(991\) −1.42245e16 −0.472750 −0.236375 0.971662i \(-0.575959\pi\)
−0.236375 + 0.971662i \(0.575959\pi\)
\(992\) 1.25691e16 4.84217e16i 0.415423 1.60039i
\(993\) 3.45687e16 1.13622
\(994\) −1.61585e15 + 4.35677e14i −0.0528171 + 0.0142410i
\(995\) 6.56789e16i 2.13500i
\(996\) −2.57137e16 + 1.49533e16i −0.831261 + 0.483406i
\(997\) 6.02174e16i 1.93597i −0.251009 0.967985i \(-0.580762\pi\)
0.251009 0.967985i \(-0.419238\pi\)
\(998\) 1.06014e16 + 3.93185e16i 0.338957 + 1.25713i
\(999\) 6.30032e15 0.200333
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 8.12.b.a.5.9 10
3.2 odd 2 72.12.d.b.37.2 10
4.3 odd 2 32.12.b.a.17.3 10
8.3 odd 2 32.12.b.a.17.8 10
8.5 even 2 inner 8.12.b.a.5.10 yes 10
16.3 odd 4 256.12.a.o.1.8 10
16.5 even 4 256.12.a.p.1.8 10
16.11 odd 4 256.12.a.o.1.3 10
16.13 even 4 256.12.a.p.1.3 10
24.5 odd 2 72.12.d.b.37.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.12.b.a.5.9 10 1.1 even 1 trivial
8.12.b.a.5.10 yes 10 8.5 even 2 inner
32.12.b.a.17.3 10 4.3 odd 2
32.12.b.a.17.8 10 8.3 odd 2
72.12.d.b.37.1 10 24.5 odd 2
72.12.d.b.37.2 10 3.2 odd 2
256.12.a.o.1.3 10 16.11 odd 4
256.12.a.o.1.8 10 16.3 odd 4
256.12.a.p.1.3 10 16.13 even 4
256.12.a.p.1.8 10 16.5 even 4