Properties

Label 8.22.b.a.5.19
Level $8$
Weight $22$
Character 8.5
Analytic conductor $22.358$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8,22,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, 22, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.5");
 
S:= CuspForms(chi, 22);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 22 \)
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: \(22.3581875430\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 10 x^{19} + 8499037025 x^{18} - 76491332940 x^{17} + \cdots + 35\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{190}\cdot 3^{14}\cdot 5^{4}\cdot 7^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.19
Root \(0.500000 + 29091.7i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.22.b.a.5.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1444.36 - 104.758i) q^{2} -116367. i q^{3} +(2.07520e6 - 302616. i) q^{4} -3.48989e7i q^{5} +(-1.21903e7 - 1.68076e8i) q^{6} -1.26580e9 q^{7} +(2.96564e9 - 6.54481e8i) q^{8} -3.08088e9 q^{9} +O(q^{10})\) \(q+(1444.36 - 104.758i) q^{2} -116367. i q^{3} +(2.07520e6 - 302616. i) q^{4} -3.48989e7i q^{5} +(-1.21903e7 - 1.68076e8i) q^{6} -1.26580e9 q^{7} +(2.96564e9 - 6.54481e8i) q^{8} -3.08088e9 q^{9} +(-3.65593e9 - 5.04066e10i) q^{10} +3.61925e10i q^{11} +(-3.52145e10 - 2.41485e11i) q^{12} +5.83952e11i q^{13} +(-1.82827e12 + 1.32602e11i) q^{14} -4.06107e12 q^{15} +(4.21489e12 - 1.25598e12i) q^{16} +3.71123e12 q^{17} +(-4.44990e12 + 3.22746e11i) q^{18} -1.39188e13i q^{19} +(-1.05610e13 - 7.24223e13i) q^{20} +1.47297e14i q^{21} +(3.79144e12 + 5.22750e13i) q^{22} +6.23488e12 q^{23} +(-7.61598e13 - 3.45102e14i) q^{24} -7.41095e14 q^{25} +(6.11735e13 + 8.43438e14i) q^{26} -8.58726e14i q^{27} +(-2.62679e15 + 3.83051e14i) q^{28} -3.96616e15i q^{29} +(-5.86565e15 + 4.25429e14i) q^{30} -5.98822e15 q^{31} +(5.95625e15 - 2.25563e15i) q^{32} +4.21160e15 q^{33} +(5.36036e15 - 3.88781e14i) q^{34} +4.41750e16i q^{35} +(-6.39345e15 + 9.32324e14i) q^{36} -3.67235e16i q^{37} +(-1.45810e15 - 2.01037e16i) q^{38} +6.79526e16 q^{39} +(-2.28406e16 - 1.03498e17i) q^{40} +4.32347e16 q^{41} +(1.54305e16 + 2.12750e17i) q^{42} -1.55834e16i q^{43} +(1.09524e16 + 7.51068e16i) q^{44} +1.07519e17i q^{45} +(9.00542e15 - 6.53153e14i) q^{46} +2.82812e17 q^{47} +(-1.46154e17 - 4.90474e17i) q^{48} +1.04370e18 q^{49} +(-1.07041e18 + 7.76355e16i) q^{50} -4.31864e17i q^{51} +(1.76713e17 + 1.21182e18i) q^{52} +3.04645e17i q^{53} +(-8.99582e16 - 1.24031e18i) q^{54} +1.26308e18 q^{55} +(-3.75391e18 + 8.28441e17i) q^{56} -1.61968e18 q^{57} +(-4.15486e17 - 5.72857e18i) q^{58} +2.15723e18i q^{59} +(-8.42755e18 + 1.22895e18i) q^{60} +4.15297e18i q^{61} +(-8.64915e18 + 6.27313e17i) q^{62} +3.89977e18 q^{63} +(8.36668e18 - 3.88191e18i) q^{64} +2.03793e19 q^{65} +(6.08307e18 - 4.41198e17i) q^{66} -2.12477e19i q^{67} +(7.70157e18 - 1.12308e18i) q^{68} -7.25533e17i q^{69} +(4.62767e18 + 6.38046e19i) q^{70} +1.05682e19 q^{71} +(-9.13678e18 + 2.01638e18i) q^{72} +1.19343e19 q^{73} +(-3.84708e18 - 5.30420e19i) q^{74} +8.62388e19i q^{75} +(-4.21204e18 - 2.88843e19i) q^{76} -4.58124e19i q^{77} +(9.81481e19 - 7.11857e18i) q^{78} -1.10112e20 q^{79} +(-4.38323e19 - 1.47095e20i) q^{80} -1.32154e20 q^{81} +(6.24465e19 - 4.52917e18i) q^{82} +4.07937e19i q^{83} +(4.45744e19 + 3.05671e20i) q^{84} -1.29518e20i q^{85} +(-1.63248e18 - 2.25080e19i) q^{86} -4.61530e20 q^{87} +(2.36873e19 + 1.07334e20i) q^{88} +3.12189e20 q^{89} +(1.12635e19 + 1.55297e20i) q^{90} -7.39166e20i q^{91} +(1.29387e19 - 1.88678e18i) q^{92} +6.96830e20i q^{93} +(4.08483e20 - 2.96268e19i) q^{94} -4.85749e20 q^{95} +(-2.62481e20 - 6.93110e20i) q^{96} -3.40413e20 q^{97} +(1.50748e21 - 1.09336e20i) q^{98} -1.11505e20i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9} - 51269339528 q^{10} + 65316900136 q^{12} - 1924309104464 q^{14} - 2285680856096 q^{15} + 7793508571920 q^{16} + 1740714497000 q^{17} - 41325344023822 q^{18} - 78999934156016 q^{20} + 294957216952508 q^{22} + 335749622520224 q^{23} + 786737698607504 q^{24} - 16\!\cdots\!04 q^{25}+ \cdots + 13\!\cdots\!30 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1444.36 104.758i 0.997380 0.0723388i
\(3\) 116367.i 1.13777i −0.822416 0.568887i \(-0.807374\pi\)
0.822416 0.568887i \(-0.192626\pi\)
\(4\) 2.07520e6 302616.i 0.989534 0.144299i
\(5\) 3.48989e7i 1.59818i −0.601209 0.799091i \(-0.705314\pi\)
0.601209 0.799091i \(-0.294686\pi\)
\(6\) −1.21903e7 1.68076e8i −0.0823052 1.13479i
\(7\) −1.26580e9 −1.69370 −0.846848 0.531835i \(-0.821502\pi\)
−0.846848 + 0.531835i \(0.821502\pi\)
\(8\) 2.96564e9 6.54481e8i 0.976503 0.215502i
\(9\) −3.08088e9 −0.294529
\(10\) −3.65593e9 5.04066e10i −0.115611 1.59400i
\(11\) 3.61925e10i 0.420722i 0.977624 + 0.210361i \(0.0674639\pi\)
−0.977624 + 0.210361i \(0.932536\pi\)
\(12\) −3.52145e10 2.41485e11i −0.164179 1.12587i
\(13\) 5.83952e11i 1.17482i 0.809289 + 0.587411i \(0.199853\pi\)
−0.809289 + 0.587411i \(0.800147\pi\)
\(14\) −1.82827e12 + 1.32602e11i −1.68926 + 0.122520i
\(15\) −4.06107e12 −1.81837
\(16\) 4.21489e12 1.25598e12i 0.958356 0.285577i
\(17\) 3.71123e12 0.446483 0.223241 0.974763i \(-0.428336\pi\)
0.223241 + 0.974763i \(0.428336\pi\)
\(18\) −4.44990e12 + 3.22746e11i −0.293758 + 0.0213059i
\(19\) 1.39188e13i 0.520820i −0.965498 0.260410i \(-0.916142\pi\)
0.965498 0.260410i \(-0.0838578\pi\)
\(20\) −1.05610e13 7.24223e13i −0.230616 1.58146i
\(21\) 1.47297e14i 1.92704i
\(22\) 3.79144e12 + 5.22750e13i 0.0304345 + 0.419620i
\(23\) 6.23488e12 0.0313824 0.0156912 0.999877i \(-0.495005\pi\)
0.0156912 + 0.999877i \(0.495005\pi\)
\(24\) −7.61598e13 3.45102e14i −0.245193 1.11104i
\(25\) −7.41095e14 −1.55419
\(26\) 6.11735e13 + 8.43438e14i 0.0849852 + 1.17174i
\(27\) 8.58726e14i 0.802666i
\(28\) −2.62679e15 + 3.83051e14i −1.67597 + 0.244398i
\(29\) 3.96616e15i 1.75062i −0.483564 0.875309i \(-0.660658\pi\)
0.483564 0.875309i \(-0.339342\pi\)
\(30\) −5.86565e15 + 4.25429e14i −1.81361 + 0.131539i
\(31\) −5.98822e15 −1.31220 −0.656100 0.754674i \(-0.727795\pi\)
−0.656100 + 0.754674i \(0.727795\pi\)
\(32\) 5.95625e15 2.25563e15i 0.935187 0.354155i
\(33\) 4.21160e15 0.478686
\(34\) 5.36036e15 3.88781e14i 0.445313 0.0322980i
\(35\) 4.41750e16i 2.70684i
\(36\) −6.39345e15 + 9.32324e14i −0.291447 + 0.0425002i
\(37\) 3.67235e16i 1.25553i −0.778404 0.627764i \(-0.783970\pi\)
0.778404 0.627764i \(-0.216030\pi\)
\(38\) −1.45810e15 2.01037e16i −0.0376755 0.519456i
\(39\) 6.79526e16 1.33668
\(40\) −2.28406e16 1.03498e17i −0.344412 1.56063i
\(41\) 4.32347e16 0.503039 0.251520 0.967852i \(-0.419070\pi\)
0.251520 + 0.967852i \(0.419070\pi\)
\(42\) 1.54305e16 + 2.12750e17i 0.139400 + 1.92199i
\(43\) 1.55834e16i 0.109962i −0.998487 0.0549811i \(-0.982490\pi\)
0.998487 0.0549811i \(-0.0175098\pi\)
\(44\) 1.09524e16 + 7.51068e16i 0.0607096 + 0.416319i
\(45\) 1.07519e17i 0.470712i
\(46\) 9.00542e15 6.53153e14i 0.0313002 0.00227017i
\(47\) 2.82812e17 0.784280 0.392140 0.919906i \(-0.371735\pi\)
0.392140 + 0.919906i \(0.371735\pi\)
\(48\) −1.46154e17 4.90474e17i −0.324922 1.09039i
\(49\) 1.04370e18 1.86860
\(50\) −1.07041e18 + 7.76355e16i −1.55012 + 0.112428i
\(51\) 4.31864e17i 0.507996i
\(52\) 1.76713e17 + 1.21182e18i 0.169525 + 1.16253i
\(53\) 3.04645e17i 0.239275i 0.992818 + 0.119638i \(0.0381733\pi\)
−0.992818 + 0.119638i \(0.961827\pi\)
\(54\) −8.99582e16 1.24031e18i −0.0580639 0.800563i
\(55\) 1.26308e18 0.672391
\(56\) −3.75391e18 + 8.28441e17i −1.65390 + 0.364995i
\(57\) −1.61968e18 −0.592576
\(58\) −4.15486e17 5.72857e18i −0.126638 1.74603i
\(59\) 2.15723e18i 0.549477i 0.961519 + 0.274739i \(0.0885913\pi\)
−0.961519 + 0.274739i \(0.911409\pi\)
\(60\) −8.42755e18 + 1.22895e18i −1.79934 + 0.262388i
\(61\) 4.15297e18i 0.745410i 0.927950 + 0.372705i \(0.121570\pi\)
−0.927950 + 0.372705i \(0.878430\pi\)
\(62\) −8.64915e18 + 6.27313e17i −1.30876 + 0.0949230i
\(63\) 3.89977e18 0.498843
\(64\) 8.36668e18 3.88191e18i 0.907118 0.420877i
\(65\) 2.03793e19 1.87758
\(66\) 6.08307e18 4.41198e17i 0.477432 0.0346276i
\(67\) 2.12477e19i 1.42405i −0.702152 0.712027i \(-0.747777\pi\)
0.702152 0.712027i \(-0.252223\pi\)
\(68\) 7.70157e18 1.12308e18i 0.441810 0.0644268i
\(69\) 7.25533e17i 0.0357061i
\(70\) 4.62767e18 + 6.38046e19i 0.195809 + 2.69974i
\(71\) 1.05682e19 0.385290 0.192645 0.981269i \(-0.438293\pi\)
0.192645 + 0.981269i \(0.438293\pi\)
\(72\) −9.13678e18 + 2.01638e18i −0.287609 + 0.0634717i
\(73\) 1.19343e19 0.325018 0.162509 0.986707i \(-0.448041\pi\)
0.162509 + 0.986707i \(0.448041\pi\)
\(74\) −3.84708e18 5.30420e19i −0.0908234 1.25224i
\(75\) 8.62388e19i 1.76832i
\(76\) −4.21204e18 2.88843e19i −0.0751536 0.515370i
\(77\) 4.58124e19i 0.712575i
\(78\) 9.81481e19 7.11857e18i 1.33318 0.0966940i
\(79\) −1.10112e20 −1.30843 −0.654213 0.756310i \(-0.727000\pi\)
−0.654213 + 0.756310i \(0.727000\pi\)
\(80\) −4.38323e19 1.47095e20i −0.456404 1.53163i
\(81\) −1.32154e20 −1.20778
\(82\) 6.24465e19 4.52917e18i 0.501721 0.0363893i
\(83\) 4.07937e19i 0.288585i 0.989535 + 0.144292i \(0.0460906\pi\)
−0.989535 + 0.144292i \(0.953909\pi\)
\(84\) 4.45744e19 + 3.05671e20i 0.278069 + 1.90687i
\(85\) 1.29518e20i 0.713561i
\(86\) −1.63248e18 2.25080e19i −0.00795453 0.109674i
\(87\) −4.61530e20 −1.99181
\(88\) 2.36873e19 + 1.07334e20i 0.0906665 + 0.410836i
\(89\) 3.12189e20 1.06126 0.530630 0.847603i \(-0.321955\pi\)
0.530630 + 0.847603i \(0.321955\pi\)
\(90\) 1.12635e19 + 1.55297e20i 0.0340507 + 0.469478i
\(91\) 7.39166e20i 1.98979i
\(92\) 1.29387e19 1.88678e18i 0.0310540 0.00452844i
\(93\) 6.96830e20i 1.49299i
\(94\) 4.08483e20 2.96268e19i 0.782225 0.0567339i
\(95\) −4.85749e20 −0.832366
\(96\) −2.62481e20 6.93110e20i −0.402948 1.06403i
\(97\) −3.40413e20 −0.468709 −0.234355 0.972151i \(-0.575298\pi\)
−0.234355 + 0.972151i \(0.575298\pi\)
\(98\) 1.50748e21 1.09336e20i 1.86371 0.135173i
\(99\) 1.11505e20i 0.123915i
\(100\) −1.53792e21 + 2.24267e20i −1.53792 + 0.224267i
\(101\) 6.23301e20i 0.561466i 0.959786 + 0.280733i \(0.0905775\pi\)
−0.959786 + 0.280733i \(0.909423\pi\)
\(102\) −4.52412e19 6.23768e20i −0.0367478 0.506665i
\(103\) 4.80970e20 0.352637 0.176318 0.984333i \(-0.443581\pi\)
0.176318 + 0.984333i \(0.443581\pi\)
\(104\) 3.82185e20 + 1.73179e21i 0.253177 + 1.14722i
\(105\) 5.14050e21 3.07977
\(106\) 3.19140e19 + 4.40018e20i 0.0173089 + 0.238648i
\(107\) 2.85277e21i 1.40196i 0.713180 + 0.700981i \(0.247254\pi\)
−0.713180 + 0.700981i \(0.752746\pi\)
\(108\) −2.59864e20 1.78203e21i −0.115824 0.794266i
\(109\) 3.01847e21i 1.22126i −0.791915 0.610632i \(-0.790916\pi\)
0.791915 0.610632i \(-0.209084\pi\)
\(110\) 1.82434e21 1.32317e20i 0.670629 0.0486399i
\(111\) −4.27340e21 −1.42851
\(112\) −5.33521e21 + 1.58982e21i −1.62316 + 0.483680i
\(113\) 3.95772e21 1.09678 0.548392 0.836221i \(-0.315240\pi\)
0.548392 + 0.836221i \(0.315240\pi\)
\(114\) −2.33941e21 + 1.69674e20i −0.591023 + 0.0428662i
\(115\) 2.17590e20i 0.0501548i
\(116\) −1.20022e21 8.23059e21i −0.252612 1.73230i
\(117\) 1.79909e21i 0.346019i
\(118\) 2.25986e20 + 3.11581e21i 0.0397485 + 0.548038i
\(119\) −4.69768e21 −0.756206
\(120\) −1.20437e22 + 2.65789e21i −1.77565 + 0.391863i
\(121\) 6.09035e21 0.822993
\(122\) 4.35056e20 + 5.99839e21i 0.0539221 + 0.743458i
\(123\) 5.03108e21i 0.572345i
\(124\) −1.24268e22 + 1.81213e21i −1.29847 + 0.189349i
\(125\) 9.22230e21i 0.885695i
\(126\) 5.63268e21 4.08532e20i 0.497536 0.0360857i
\(127\) −2.93164e20 −0.0238326 −0.0119163 0.999929i \(-0.503793\pi\)
−0.0119163 + 0.999929i \(0.503793\pi\)
\(128\) 1.16778e22 6.48335e21i 0.874295 0.485395i
\(129\) −1.81339e21 −0.125112
\(130\) 2.94350e22 2.13489e21i 1.87266 0.135822i
\(131\) 8.08973e21i 0.474882i −0.971402 0.237441i \(-0.923691\pi\)
0.971402 0.237441i \(-0.0763086\pi\)
\(132\) 8.73993e21 1.27450e21i 0.473677 0.0690738i
\(133\) 1.76184e22i 0.882111i
\(134\) −2.22586e21 3.06893e22i −0.103014 1.42032i
\(135\) −2.99686e22 −1.28281
\(136\) 1.10062e22 2.42893e21i 0.435992 0.0962180i
\(137\) 5.33440e22 1.95668 0.978341 0.207002i \(-0.0663707\pi\)
0.978341 + 0.207002i \(0.0663707\pi\)
\(138\) −7.60053e19 1.04793e21i −0.00258293 0.0356125i
\(139\) 3.30872e22i 1.04233i 0.853456 + 0.521164i \(0.174502\pi\)
−0.853456 + 0.521164i \(0.825498\pi\)
\(140\) 1.33681e22 + 9.16721e22i 0.390592 + 2.67851i
\(141\) 3.29100e22i 0.892333i
\(142\) 1.52643e22 1.10710e21i 0.384280 0.0278714i
\(143\) −2.11347e22 −0.494273
\(144\) −1.29856e22 + 3.86952e21i −0.282264 + 0.0841107i
\(145\) −1.38415e23 −2.79781
\(146\) 1.72375e22 1.25021e21i 0.324167 0.0235115i
\(147\) 1.21452e23i 2.12605i
\(148\) −1.11131e22 7.62088e22i −0.181171 1.24239i
\(149\) 4.27336e22i 0.649103i −0.945868 0.324551i \(-0.894787\pi\)
0.945868 0.324551i \(-0.105213\pi\)
\(150\) 9.03419e21 + 1.24560e23i 0.127918 + 1.76368i
\(151\) 4.47213e22 0.590550 0.295275 0.955412i \(-0.404589\pi\)
0.295275 + 0.955412i \(0.404589\pi\)
\(152\) −9.10956e21 4.12781e22i −0.112238 0.508583i
\(153\) −1.14339e22 −0.131502
\(154\) −4.79921e21 6.61696e22i −0.0515468 0.710708i
\(155\) 2.08982e23i 2.09714i
\(156\) 1.41016e23 2.05636e22i 1.32269 0.192881i
\(157\) 1.28304e23i 1.12536i 0.826673 + 0.562682i \(0.190231\pi\)
−0.826673 + 0.562682i \(0.809769\pi\)
\(158\) −1.59041e23 + 1.15351e22i −1.30500 + 0.0946500i
\(159\) 3.54506e22 0.272241
\(160\) −7.87190e22 2.07867e23i −0.566004 1.49460i
\(161\) −7.89211e21 −0.0531522
\(162\) −1.90878e23 + 1.38442e22i −1.20462 + 0.0873695i
\(163\) 4.69745e22i 0.277902i −0.990299 0.138951i \(-0.955627\pi\)
0.990299 0.138951i \(-0.0443731\pi\)
\(164\) 8.97208e22 1.30835e22i 0.497775 0.0725879i
\(165\) 1.46980e23i 0.765028i
\(166\) 4.27346e21 + 5.89209e22i 0.0208759 + 0.287829i
\(167\) 2.00344e23 0.918870 0.459435 0.888211i \(-0.348052\pi\)
0.459435 + 0.888211i \(0.348052\pi\)
\(168\) 9.64030e22 + 4.36830e23i 0.415282 + 1.88176i
\(169\) −9.39356e22 −0.380207
\(170\) −1.35680e22 1.87071e23i −0.0516182 0.711692i
\(171\) 4.28821e22i 0.153397i
\(172\) −4.71578e21 3.23387e22i −0.0158674 0.108811i
\(173\) 2.89286e23i 0.915889i −0.888981 0.457944i \(-0.848586\pi\)
0.888981 0.457944i \(-0.151414\pi\)
\(174\) −6.66615e23 + 4.83488e22i −1.98659 + 0.144085i
\(175\) 9.38077e23 2.63232
\(176\) 4.54570e22 + 1.52547e23i 0.120148 + 0.403201i
\(177\) 2.51030e23 0.625181
\(178\) 4.50913e23 3.27042e22i 1.05848 0.0767703i
\(179\) 1.16861e23i 0.258651i −0.991602 0.129325i \(-0.958719\pi\)
0.991602 0.129325i \(-0.0412811\pi\)
\(180\) 3.25371e22 + 2.23124e23i 0.0679230 + 0.465785i
\(181\) 6.16947e23i 1.21513i 0.794270 + 0.607565i \(0.207854\pi\)
−0.794270 + 0.607565i \(0.792146\pi\)
\(182\) −7.74334e22 1.06762e24i −0.143939 1.98458i
\(183\) 4.83268e23 0.848108
\(184\) 1.84904e22 4.08061e21i 0.0306450 0.00676298i
\(185\) −1.28161e24 −2.00656
\(186\) 7.29984e22 + 1.00647e24i 0.108001 + 1.48908i
\(187\) 1.34319e23i 0.187845i
\(188\) 5.86893e23 8.55836e22i 0.776071 0.113170i
\(189\) 1.08697e24i 1.35947i
\(190\) −7.01597e23 + 5.08860e22i −0.830186 + 0.0602124i
\(191\) −1.50576e24 −1.68618 −0.843091 0.537771i \(-0.819267\pi\)
−0.843091 + 0.537771i \(0.819267\pi\)
\(192\) −4.51725e23 9.73604e23i −0.478863 1.03209i
\(193\) 8.19140e23 0.822255 0.411127 0.911578i \(-0.365135\pi\)
0.411127 + 0.911578i \(0.365135\pi\)
\(194\) −4.91680e23 + 3.56610e22i −0.467481 + 0.0339059i
\(195\) 2.37147e24i 2.13626i
\(196\) 2.16589e24 3.15841e23i 1.84905 0.269637i
\(197\) 1.76115e24i 1.42528i −0.701530 0.712640i \(-0.747499\pi\)
0.701530 0.712640i \(-0.252501\pi\)
\(198\) −1.16810e22 1.61053e23i −0.00896386 0.123590i
\(199\) −1.06899e24 −0.778067 −0.389033 0.921224i \(-0.627191\pi\)
−0.389033 + 0.921224i \(0.627191\pi\)
\(200\) −2.19782e24 + 4.85032e23i −1.51767 + 0.334931i
\(201\) −2.47253e24 −1.62025
\(202\) 6.52956e22 + 9.00271e23i 0.0406158 + 0.559995i
\(203\) 5.02036e24i 2.96501i
\(204\) −1.30689e23 8.96207e23i −0.0733031 0.502680i
\(205\) 1.50884e24i 0.803949i
\(206\) 6.94694e23 5.03854e22i 0.351713 0.0255093i
\(207\) −1.92089e22 −0.00924303
\(208\) 7.33432e23 + 2.46130e24i 0.335502 + 1.12590i
\(209\) 5.03755e23 0.219121
\(210\) 7.42474e24 5.38507e23i 3.07170 0.222787i
\(211\) 1.29339e24i 0.509056i −0.967065 0.254528i \(-0.918080\pi\)
0.967065 0.254528i \(-0.0819200\pi\)
\(212\) 9.21905e22 + 6.32201e23i 0.0345271 + 0.236771i
\(213\) 1.22978e24i 0.438372i
\(214\) 2.98849e23 + 4.12042e24i 0.101416 + 1.39829i
\(215\) −5.43843e23 −0.175740
\(216\) −5.62019e23 2.54667e24i −0.172976 0.783806i
\(217\) 7.57989e24 2.22247
\(218\) −3.16209e23 4.35977e24i −0.0883447 1.21806i
\(219\) 1.38876e24i 0.369798i
\(220\) 2.62114e24 3.82227e23i 0.665353 0.0970250i
\(221\) 2.16718e24i 0.524538i
\(222\) −6.17233e24 + 4.47672e23i −1.42476 + 0.103337i
\(223\) −4.03079e24 −0.887543 −0.443771 0.896140i \(-0.646360\pi\)
−0.443771 + 0.896140i \(0.646360\pi\)
\(224\) −7.53942e24 + 2.85518e24i −1.58392 + 0.599831i
\(225\) 2.28322e24 0.457754
\(226\) 5.71637e24 4.14602e23i 1.09391 0.0793401i
\(227\) 7.81965e23i 0.142862i −0.997446 0.0714309i \(-0.977243\pi\)
0.997446 0.0714309i \(-0.0227565\pi\)
\(228\) −3.36117e24 + 4.90142e23i −0.586374 + 0.0855079i
\(229\) 8.55580e24i 1.42557i 0.701384 + 0.712784i \(0.252566\pi\)
−0.701384 + 0.712784i \(0.747434\pi\)
\(230\) −2.27943e22 3.14279e23i −0.00362814 0.0500234i
\(231\) −5.33104e24 −0.810749
\(232\) −2.59578e24 1.17622e25i −0.377262 1.70948i
\(233\) 3.05921e24 0.424983 0.212491 0.977163i \(-0.431842\pi\)
0.212491 + 0.977163i \(0.431842\pi\)
\(234\) −1.88468e23 2.59853e24i −0.0250306 0.345113i
\(235\) 9.86984e24i 1.25342i
\(236\) 6.52812e23 + 4.47669e24i 0.0792888 + 0.543727i
\(237\) 1.28134e25i 1.48869i
\(238\) −6.78514e24 + 4.92118e23i −0.754224 + 0.0547030i
\(239\) 5.15515e24 0.548357 0.274178 0.961679i \(-0.411594\pi\)
0.274178 + 0.961679i \(0.411594\pi\)
\(240\) −1.71170e25 + 5.10062e24i −1.74265 + 0.519284i
\(241\) 6.86441e24 0.668997 0.334499 0.942396i \(-0.391433\pi\)
0.334499 + 0.942396i \(0.391433\pi\)
\(242\) 8.79667e24 6.38012e23i 0.820837 0.0595343i
\(243\) 6.39579e24i 0.571516i
\(244\) 1.25676e24 + 8.61826e24i 0.107562 + 0.737609i
\(245\) 3.64240e25i 2.98637i
\(246\) −5.27045e23 7.26670e24i −0.0414028 0.570846i
\(247\) 8.12789e24 0.611871
\(248\) −1.77589e25 + 3.91918e24i −1.28137 + 0.282782i
\(249\) 4.74704e24 0.328344
\(250\) 9.66108e23 + 1.33203e25i 0.0640701 + 0.883374i
\(251\) 8.35468e23i 0.0531319i 0.999647 + 0.0265660i \(0.00845720\pi\)
−0.999647 + 0.0265660i \(0.991543\pi\)
\(252\) 8.09283e24 1.18013e24i 0.493622 0.0719823i
\(253\) 2.25656e23i 0.0132033i
\(254\) −4.23435e23 + 3.07112e22i −0.0237702 + 0.00172402i
\(255\) −1.50716e25 −0.811871
\(256\) 1.61878e25 1.05876e25i 0.836892 0.547368i
\(257\) −1.18113e25 −0.586140 −0.293070 0.956091i \(-0.594677\pi\)
−0.293070 + 0.956091i \(0.594677\pi\)
\(258\) −2.61919e24 + 1.89967e23i −0.124784 + 0.00905046i
\(259\) 4.64846e25i 2.12648i
\(260\) 4.22912e25 6.16710e24i 1.85793 0.270932i
\(261\) 1.22193e25i 0.515608i
\(262\) −8.47463e23 1.16845e25i −0.0343524 0.473638i
\(263\) −1.55635e25 −0.606138 −0.303069 0.952969i \(-0.598011\pi\)
−0.303069 + 0.952969i \(0.598011\pi\)
\(264\) 1.24901e25 2.75641e24i 0.467439 0.103158i
\(265\) 1.06318e25 0.382406
\(266\) 1.84566e24 + 2.54473e25i 0.0638109 + 0.879800i
\(267\) 3.63284e25i 1.20747i
\(268\) −6.42990e24 4.40933e25i −0.205489 1.40915i
\(269\) 3.30880e25i 1.01689i 0.861096 + 0.508443i \(0.169779\pi\)
−0.861096 + 0.508443i \(0.830221\pi\)
\(270\) −4.32854e25 + 3.13944e24i −1.27945 + 0.0927968i
\(271\) 5.93487e25 1.68746 0.843731 0.536767i \(-0.180355\pi\)
0.843731 + 0.536767i \(0.180355\pi\)
\(272\) 1.56425e25 4.66123e24i 0.427889 0.127505i
\(273\) −8.60144e25 −2.26393
\(274\) 7.70480e25 5.58821e24i 1.95155 0.141544i
\(275\) 2.68221e25i 0.653881i
\(276\) −2.19558e23 1.50563e24i −0.00515234 0.0353324i
\(277\) 7.26699e25i 1.64179i −0.571080 0.820894i \(-0.693475\pi\)
0.571080 0.820894i \(-0.306525\pi\)
\(278\) 3.46614e24 + 4.77899e25i 0.0754008 + 1.03960i
\(279\) 1.84490e25 0.386481
\(280\) 2.89117e25 + 1.31007e26i 0.583329 + 2.64323i
\(281\) −4.74175e25 −0.921557 −0.460778 0.887515i \(-0.652430\pi\)
−0.460778 + 0.887515i \(0.652430\pi\)
\(282\) −3.44758e24 4.75339e25i −0.0645503 0.889995i
\(283\) 3.08734e25i 0.556964i −0.960441 0.278482i \(-0.910169\pi\)
0.960441 0.278482i \(-0.0898312\pi\)
\(284\) 2.19311e25 3.19810e24i 0.381257 0.0555968i
\(285\) 5.65251e25i 0.947045i
\(286\) −3.05261e25 + 2.21402e24i −0.492978 + 0.0357551i
\(287\) −5.47264e25 −0.851996
\(288\) −1.83505e25 + 6.94933e24i −0.275440 + 0.104309i
\(289\) −5.53187e25 −0.800653
\(290\) −1.99921e26 + 1.45000e25i −2.79048 + 0.202390i
\(291\) 3.96128e25i 0.533285i
\(292\) 2.47662e25 3.61152e24i 0.321617 0.0468997i
\(293\) 1.20855e25i 0.151410i −0.997130 0.0757050i \(-0.975879\pi\)
0.997130 0.0757050i \(-0.0241207\pi\)
\(294\) −1.27231e25 1.75421e26i −0.153796 2.12048i
\(295\) 7.52848e25 0.878165
\(296\) −2.40348e25 1.08909e26i −0.270569 1.22603i
\(297\) 3.10794e25 0.337699
\(298\) −4.47668e24 6.17227e25i −0.0469553 0.647402i
\(299\) 3.64087e24i 0.0368687i
\(300\) 2.60973e25 + 1.78963e26i 0.255165 + 1.74981i
\(301\) 1.97254e25i 0.186242i
\(302\) 6.45937e25 4.68491e24i 0.589003 0.0427197i
\(303\) 7.25315e25 0.638821
\(304\) −1.74817e25 5.86661e25i −0.148734 0.499131i
\(305\) 1.44934e26 1.19130
\(306\) −1.65146e25 + 1.19779e24i −0.131158 + 0.00951271i
\(307\) 1.35933e26i 1.04321i 0.853186 + 0.521607i \(0.174667\pi\)
−0.853186 + 0.521607i \(0.825333\pi\)
\(308\) −1.38636e25 9.50701e25i −0.102824 0.705117i
\(309\) 5.59690e25i 0.401221i
\(310\) 2.18925e25 + 3.01846e26i 0.151704 + 2.09164i
\(311\) 1.63215e26 1.09339 0.546695 0.837332i \(-0.315886\pi\)
0.546695 + 0.837332i \(0.315886\pi\)
\(312\) 2.01523e26 4.44737e25i 1.30527 0.288058i
\(313\) −3.17530e25 −0.198870 −0.0994349 0.995044i \(-0.531703\pi\)
−0.0994349 + 0.995044i \(0.531703\pi\)
\(314\) 1.34408e25 + 1.85317e26i 0.0814075 + 1.12242i
\(315\) 1.36098e26i 0.797242i
\(316\) −2.28504e26 + 3.33216e25i −1.29473 + 0.188804i
\(317\) 2.32784e26i 1.27594i 0.770061 + 0.637971i \(0.220226\pi\)
−0.770061 + 0.637971i \(0.779774\pi\)
\(318\) 5.12034e25 3.71373e24i 0.271528 0.0196936i
\(319\) 1.43545e26 0.736523
\(320\) −1.35474e26 2.91988e26i −0.672639 1.44974i
\(321\) 3.31967e26 1.59512
\(322\) −1.13991e25 + 8.26760e23i −0.0530130 + 0.00384497i
\(323\) 5.16558e25i 0.232537i
\(324\) −2.74247e26 + 3.99920e25i −1.19514 + 0.174281i
\(325\) 4.32764e26i 1.82590i
\(326\) −4.92094e24 6.78481e25i −0.0201031 0.277174i
\(327\) −3.51250e26 −1.38952
\(328\) 1.28219e26 2.82963e25i 0.491220 0.108406i
\(329\) −3.57984e26 −1.32833
\(330\) −1.53973e25 2.12292e26i −0.0553412 0.763024i
\(331\) 3.56656e26i 1.24181i 0.783885 + 0.620906i \(0.213235\pi\)
−0.783885 + 0.620906i \(0.786765\pi\)
\(332\) 1.23448e25 + 8.46553e25i 0.0416424 + 0.285565i
\(333\) 1.13141e26i 0.369790i
\(334\) 2.89369e26 2.09876e25i 0.916462 0.0664700i
\(335\) −7.41521e26 −2.27590
\(336\) 1.85002e26 + 6.20841e26i 0.550319 + 1.84679i
\(337\) 4.72337e26 1.36188 0.680938 0.732341i \(-0.261572\pi\)
0.680938 + 0.732341i \(0.261572\pi\)
\(338\) −1.35677e26 + 9.84049e24i −0.379211 + 0.0275037i
\(339\) 4.60547e26i 1.24789i
\(340\) −3.91942e25 2.68776e26i −0.102966 0.706093i
\(341\) 2.16729e26i 0.552071i
\(342\) 4.49223e24 + 6.19372e25i 0.0110965 + 0.152995i
\(343\) −6.14109e26 −1.47115
\(344\) −1.01990e25 4.62147e25i −0.0236971 0.107378i
\(345\) −2.53203e25 −0.0570648
\(346\) −3.03049e25 4.17833e26i −0.0662543 0.913489i
\(347\) 2.88810e26i 0.612566i 0.951940 + 0.306283i \(0.0990854\pi\)
−0.951940 + 0.306283i \(0.900915\pi\)
\(348\) −9.57768e26 + 1.39666e26i −1.97096 + 0.287415i
\(349\) 6.64002e26i 1.32587i 0.748675 + 0.662937i \(0.230690\pi\)
−0.748675 + 0.662937i \(0.769310\pi\)
\(350\) 1.35492e27 9.82709e25i 2.62543 0.190419i
\(351\) 5.01455e26 0.942990
\(352\) 8.16369e25 + 2.15572e26i 0.149001 + 0.393454i
\(353\) −5.10078e26 −0.903655 −0.451827 0.892105i \(-0.649228\pi\)
−0.451827 + 0.892105i \(0.649228\pi\)
\(354\) 3.62577e26 2.62973e25i 0.623543 0.0452248i
\(355\) 3.68818e26i 0.615763i
\(356\) 6.47855e26 9.44733e25i 1.05015 0.153138i
\(357\) 5.46653e26i 0.860391i
\(358\) −1.22421e25 1.68790e26i −0.0187105 0.257973i
\(359\) 1.14599e26 0.170095 0.0850474 0.996377i \(-0.472896\pi\)
0.0850474 + 0.996377i \(0.472896\pi\)
\(360\) 7.03693e25 + 3.18864e26i 0.101439 + 0.459651i
\(361\) 5.20477e26 0.728746
\(362\) 6.46300e25 + 8.91094e26i 0.0879011 + 1.21195i
\(363\) 7.08715e26i 0.936380i
\(364\) −2.23684e26 1.53392e27i −0.287124 1.96897i
\(365\) 4.16495e26i 0.519439i
\(366\) 6.98013e26 5.06261e25i 0.845886 0.0613512i
\(367\) −1.17521e27 −1.38395 −0.691976 0.721920i \(-0.743260\pi\)
−0.691976 + 0.721920i \(0.743260\pi\)
\(368\) 2.62794e25 7.83089e24i 0.0300755 0.00896208i
\(369\) −1.33201e26 −0.148160
\(370\) −1.85111e27 + 1.34259e26i −2.00131 + 0.145152i
\(371\) 3.85620e26i 0.405259i
\(372\) 2.10872e26 + 1.44606e27i 0.215436 + 1.47736i
\(373\) 6.90947e26i 0.686281i −0.939284 0.343141i \(-0.888509\pi\)
0.939284 0.343141i \(-0.111491\pi\)
\(374\) 1.40709e25 + 1.94005e26i 0.0135885 + 0.187353i
\(375\) 1.07317e27 1.00772
\(376\) 8.38720e26 1.85095e26i 0.765852 0.169014i
\(377\) 2.31605e27 2.05666
\(378\) 1.13869e26 + 1.56998e27i 0.0983426 + 1.35591i
\(379\) 2.25252e27i 1.89216i 0.323938 + 0.946078i \(0.394993\pi\)
−0.323938 + 0.946078i \(0.605007\pi\)
\(380\) −1.00803e27 + 1.46996e26i −0.823655 + 0.120109i
\(381\) 3.41146e25i 0.0271161i
\(382\) −2.17486e27 + 1.57740e26i −1.68176 + 0.121976i
\(383\) 1.60978e27 1.21110 0.605549 0.795808i \(-0.292953\pi\)
0.605549 + 0.795808i \(0.292953\pi\)
\(384\) −7.54447e26 1.35891e27i −0.552269 0.994750i
\(385\) −1.59880e27 −1.13882
\(386\) 1.18313e27 8.58113e25i 0.820101 0.0594810i
\(387\) 4.80106e25i 0.0323871i
\(388\) −7.06427e26 + 1.03015e26i −0.463804 + 0.0676341i
\(389\) 1.52357e27i 0.973627i −0.873506 0.486814i \(-0.838159\pi\)
0.873506 0.486814i \(-0.161841\pi\)
\(390\) −2.48430e26 3.42526e27i −0.154535 2.13067i
\(391\) 2.31391e25 0.0140117
\(392\) 3.09524e27 6.83082e26i 1.82470 0.402688i
\(393\) −9.41376e26 −0.540308
\(394\) −1.84494e26 2.54373e27i −0.103103 1.42155i
\(395\) 3.84278e27i 2.09111i
\(396\) −3.37431e25 2.31395e26i −0.0178807 0.122618i
\(397\) 4.24807e26i 0.219225i −0.993974 0.109613i \(-0.965039\pi\)
0.993974 0.109613i \(-0.0349611\pi\)
\(398\) −1.54401e27 + 1.11985e26i −0.776028 + 0.0562844i
\(399\) 2.05019e27 1.00364
\(400\) −3.12364e27 + 9.30800e26i −1.48947 + 0.443840i
\(401\) −2.90975e27 −1.35157 −0.675787 0.737097i \(-0.736196\pi\)
−0.675787 + 0.737097i \(0.736196\pi\)
\(402\) −3.57122e27 + 2.59016e26i −1.61601 + 0.117207i
\(403\) 3.49684e27i 1.54160i
\(404\) 1.88621e26 + 1.29348e27i 0.0810187 + 0.555590i
\(405\) 4.61204e27i 1.93026i
\(406\) 5.25922e26 + 7.25121e27i 0.214486 + 2.95725i
\(407\) 1.32912e27 0.528228
\(408\) −2.82647e26 1.28075e27i −0.109474 0.496060i
\(409\) −1.94788e27 −0.735304 −0.367652 0.929963i \(-0.619838\pi\)
−0.367652 + 0.929963i \(0.619838\pi\)
\(410\) −1.58063e26 2.17931e27i −0.0581567 0.801843i
\(411\) 6.20748e27i 2.22626i
\(412\) 9.98111e26 1.45549e26i 0.348946 0.0508850i
\(413\) 2.73062e27i 0.930647i
\(414\) −2.77446e25 + 2.01228e24i −0.00921882 + 0.000668630i
\(415\) 1.42366e27 0.461211
\(416\) 1.31718e27 + 3.47817e27i 0.416069 + 1.09868i
\(417\) 3.85025e27 1.18593
\(418\) 7.27603e26 5.27722e25i 0.218546 0.0158509i
\(419\) 1.80593e27i 0.528997i 0.964386 + 0.264498i \(0.0852064\pi\)
−0.964386 + 0.264498i \(0.914794\pi\)
\(420\) 1.06676e28 1.55560e27i 3.04753 0.444406i
\(421\) 1.98240e27i 0.552370i 0.961105 + 0.276185i \(0.0890702\pi\)
−0.961105 + 0.276185i \(0.910930\pi\)
\(422\) −1.35493e26 1.86813e27i −0.0368245 0.507722i
\(423\) −8.71311e26 −0.230993
\(424\) 1.99384e26 + 9.03468e26i 0.0515643 + 0.233653i
\(425\) −2.75038e27 −0.693918
\(426\) −1.28830e26 1.77625e27i −0.0317113 0.437224i
\(427\) 5.25682e27i 1.26250i
\(428\) 8.63293e26 + 5.92007e27i 0.202301 + 1.38729i
\(429\) 2.45937e27i 0.562371i
\(430\) −7.85505e26 + 5.69718e25i −0.175279 + 0.0127128i
\(431\) −5.89168e27 −1.28300 −0.641501 0.767122i \(-0.721688\pi\)
−0.641501 + 0.767122i \(0.721688\pi\)
\(432\) −1.07854e27 3.61944e27i −0.229223 0.769240i
\(433\) −2.46636e27 −0.511604 −0.255802 0.966729i \(-0.582340\pi\)
−0.255802 + 0.966729i \(0.582340\pi\)
\(434\) 1.09481e28 7.94052e26i 2.21665 0.160771i
\(435\) 1.61069e28i 3.18327i
\(436\) −9.13439e26 6.26395e27i −0.176227 1.20848i
\(437\) 8.67819e25i 0.0163446i
\(438\) −1.45483e26 2.00587e27i −0.0267507 0.368829i
\(439\) 9.97270e27 1.79034 0.895170 0.445726i \(-0.147054\pi\)
0.895170 + 0.445726i \(0.147054\pi\)
\(440\) 3.74583e27 8.26659e26i 0.656592 0.144902i
\(441\) −3.21552e27 −0.550359
\(442\) 2.27029e26 + 3.13019e27i 0.0379444 + 0.523163i
\(443\) 2.72703e27i 0.445092i −0.974922 0.222546i \(-0.928563\pi\)
0.974922 0.222546i \(-0.0714368\pi\)
\(444\) −8.86818e27 + 1.29320e27i −1.41356 + 0.206132i
\(445\) 1.08950e28i 1.69609i
\(446\) −5.82192e27 + 4.22257e26i −0.885217 + 0.0642038i
\(447\) −4.97277e27 −0.738532
\(448\) −1.05905e28 + 4.91372e27i −1.53638 + 0.712838i
\(449\) −5.09946e27 −0.722665 −0.361333 0.932437i \(-0.617678\pi\)
−0.361333 + 0.932437i \(0.617678\pi\)
\(450\) 3.29780e27 2.39186e26i 0.456555 0.0331134i
\(451\) 1.56477e27i 0.211640i
\(452\) 8.21307e27 1.19767e27i 1.08531 0.158264i
\(453\) 5.20408e27i 0.671912i
\(454\) −8.19170e25 1.12944e27i −0.0103345 0.142487i
\(455\) −2.57961e28 −3.18005
\(456\) −4.80340e27 + 1.06005e27i −0.578652 + 0.127701i
\(457\) 9.11592e27 1.07320 0.536600 0.843837i \(-0.319709\pi\)
0.536600 + 0.843837i \(0.319709\pi\)
\(458\) 8.96286e26 + 1.23577e28i 0.103124 + 1.42183i
\(459\) 3.18693e27i 0.358377i
\(460\) −6.58464e25 4.51545e26i −0.00723727 0.0496299i
\(461\) 3.48173e27i 0.374055i −0.982355 0.187027i \(-0.940115\pi\)
0.982355 0.187027i \(-0.0598853\pi\)
\(462\) −7.69995e27 + 5.58468e26i −0.808625 + 0.0586486i
\(463\) 4.82435e27 0.495266 0.247633 0.968854i \(-0.420347\pi\)
0.247633 + 0.968854i \(0.420347\pi\)
\(464\) −4.98142e27 1.67169e28i −0.499936 1.67771i
\(465\) 2.43186e28 2.38607
\(466\) 4.41860e27 3.20476e26i 0.423869 0.0307428i
\(467\) 1.47014e28i 1.37890i −0.724335 0.689448i \(-0.757853\pi\)
0.724335 0.689448i \(-0.242147\pi\)
\(468\) −5.44433e26 3.73347e27i −0.0499301 0.342398i
\(469\) 2.68953e28i 2.41191i
\(470\) −1.03394e27 1.42556e28i −0.0906711 1.25014i
\(471\) 1.49303e28 1.28041
\(472\) 1.41186e27 + 6.39756e27i 0.118414 + 0.536566i
\(473\) 5.64001e26 0.0462635
\(474\) 1.34230e27 + 1.85071e28i 0.107690 + 1.48479i
\(475\) 1.03151e28i 0.809453i
\(476\) −9.74863e27 + 1.42159e27i −0.748291 + 0.109119i
\(477\) 9.38575e26i 0.0704735i
\(478\) 7.44590e27 5.40042e26i 0.546920 0.0396675i
\(479\) 1.31443e27 0.0944530 0.0472265 0.998884i \(-0.484962\pi\)
0.0472265 + 0.998884i \(0.484962\pi\)
\(480\) −2.41888e28 + 9.16028e27i −1.70052 + 0.643985i
\(481\) 2.14448e28 1.47502
\(482\) 9.91469e27 7.19101e26i 0.667245 0.0483945i
\(483\) 9.18380e26i 0.0604752i
\(484\) 1.26387e28 1.84304e27i 0.814380 0.118757i
\(485\) 1.18801e28i 0.749083i
\(486\) 6.70009e26 + 9.23783e27i 0.0413428 + 0.570019i
\(487\) −4.46244e27 −0.269475 −0.134737 0.990881i \(-0.543019\pi\)
−0.134737 + 0.990881i \(0.543019\pi\)
\(488\) 2.71804e27 + 1.23162e28i 0.160638 + 0.727896i
\(489\) −5.46627e27 −0.316190
\(490\) −3.81570e27 5.26094e28i −0.216031 2.97855i
\(491\) 1.58826e28i 0.880167i −0.897957 0.440084i \(-0.854949\pi\)
0.897957 0.440084i \(-0.145051\pi\)
\(492\) −1.52249e27 1.04405e28i −0.0825886 0.566355i
\(493\) 1.47194e28i 0.781621i
\(494\) 1.17396e28 8.51460e26i 0.610268 0.0442620i
\(495\) −3.89139e27 −0.198039
\(496\) −2.52397e28 + 7.52109e27i −1.25756 + 0.374734i
\(497\) −1.33772e28 −0.652563
\(498\) 6.85643e27 4.97289e26i 0.327484 0.0237520i
\(499\) 1.96729e28i 0.920052i 0.887905 + 0.460026i \(0.152160\pi\)
−0.887905 + 0.460026i \(0.847840\pi\)
\(500\) 2.79082e27 + 1.91382e28i 0.127805 + 0.876425i
\(501\) 2.33134e28i 1.04547i
\(502\) 8.75217e25 + 1.20672e27i 0.00384350 + 0.0529927i
\(503\) 6.10929e27 0.262740 0.131370 0.991333i \(-0.458062\pi\)
0.131370 + 0.991333i \(0.458062\pi\)
\(504\) 1.15653e28 2.55233e27i 0.487122 0.107502i
\(505\) 2.17525e28 0.897325
\(506\) 2.36392e25 + 3.25928e26i 0.000955108 + 0.0131687i
\(507\) 1.09310e28i 0.432589i
\(508\) −6.08375e26 + 8.87162e25i −0.0235832 + 0.00343901i
\(509\) 3.64801e28i 1.38522i 0.721312 + 0.692611i \(0.243540\pi\)
−0.721312 + 0.692611i \(0.756460\pi\)
\(510\) −2.17688e28 + 1.57887e27i −0.809744 + 0.0587298i
\(511\) −1.51065e28 −0.550482
\(512\) 2.22719e28 1.69882e28i 0.795103 0.606474i
\(513\) −1.19524e28 −0.418045
\(514\) −1.70598e28 + 1.23733e27i −0.584605 + 0.0424007i
\(515\) 1.67853e28i 0.563578i
\(516\) −3.76315e27 + 5.48761e26i −0.123803 + 0.0180535i
\(517\) 1.02357e28i 0.329964i
\(518\) 4.86963e27 + 6.71406e28i 0.153827 + 2.12091i
\(519\) −3.36632e28 −1.04207
\(520\) 6.04376e28 1.33378e28i 1.83346 0.404623i
\(521\) −5.93755e28 −1.76527 −0.882636 0.470058i \(-0.844233\pi\)
−0.882636 + 0.470058i \(0.844233\pi\)
\(522\) 1.28006e27 + 1.76490e28i 0.0372985 + 0.514257i
\(523\) 1.38164e28i 0.394574i −0.980346 0.197287i \(-0.936787\pi\)
0.980346 0.197287i \(-0.0632131\pi\)
\(524\) −2.44808e27 1.67878e28i −0.0685248 0.469912i
\(525\) 1.09161e29i 2.99499i
\(526\) −2.24793e28 + 1.63040e27i −0.604550 + 0.0438473i
\(527\) −2.22237e28 −0.585875
\(528\) 1.77515e28 5.28969e27i 0.458752 0.136702i
\(529\) −3.94327e28 −0.999015
\(530\) 1.53561e28 1.11376e27i 0.381404 0.0276628i
\(531\) 6.64616e27i 0.161837i
\(532\) 5.33160e27 + 3.65617e28i 0.127287 + 0.872879i
\(533\) 2.52470e28i 0.590982i
\(534\) −3.80568e27 5.24713e28i −0.0873473 1.20431i
\(535\) 9.95583e28 2.24059
\(536\) −1.39062e28 6.30130e28i −0.306887 1.39059i
\(537\) −1.35988e28 −0.294286
\(538\) 3.46623e27 + 4.77911e28i 0.0735603 + 1.01422i
\(539\) 3.77741e28i 0.786163i
\(540\) −6.21909e28 + 9.06897e27i −1.26938 + 0.185107i
\(541\) 8.42470e28i 1.68649i 0.537531 + 0.843244i \(0.319357\pi\)
−0.537531 + 0.843244i \(0.680643\pi\)
\(542\) 8.57210e28 6.21724e27i 1.68304 0.122069i
\(543\) 7.17921e28 1.38254
\(544\) 2.21050e28 8.37117e27i 0.417545 0.158124i
\(545\) −1.05341e29 −1.95180
\(546\) −1.24236e29 + 9.01068e27i −2.25800 + 0.163770i
\(547\) 1.62906e28i 0.290449i −0.989399 0.145224i \(-0.953610\pi\)
0.989399 0.145224i \(-0.0463904\pi\)
\(548\) 1.10700e29 1.61428e28i 1.93620 0.282346i
\(549\) 1.27948e28i 0.219545i
\(550\) −2.80982e27 3.87407e28i −0.0473010 0.652168i
\(551\) −5.52041e28 −0.911758
\(552\) −4.74848e26 2.15167e27i −0.00769474 0.0348671i
\(553\) 1.39379e29 2.21608
\(554\) −7.61274e27 1.04962e29i −0.118765 1.63749i
\(555\) 1.49137e29i 2.28302i
\(556\) 1.00127e28 + 6.86627e28i 0.150407 + 1.03142i
\(557\) 7.01874e27i 0.103462i 0.998661 + 0.0517308i \(0.0164738\pi\)
−0.998661 + 0.0517308i \(0.983526\pi\)
\(558\) 2.66470e28 1.93268e27i 0.385469 0.0279576i
\(559\) 9.09995e27 0.129186
\(560\) 5.54829e28 + 1.86193e29i 0.773009 + 2.59411i
\(561\) 1.56302e28 0.213725
\(562\) −6.84879e28 + 4.96735e27i −0.919142 + 0.0666643i
\(563\) 1.19005e29i 1.56757i −0.621030 0.783786i \(-0.713286\pi\)
0.621030 0.783786i \(-0.286714\pi\)
\(564\) −9.95909e27 6.82949e28i −0.128762 0.882994i
\(565\) 1.38120e29i 1.75286i
\(566\) −3.23423e27 4.45923e28i −0.0402901 0.555505i
\(567\) 1.67281e29 2.04561
\(568\) 3.13414e28 6.91666e27i 0.376237 0.0830308i
\(569\) 5.15637e28 0.607667 0.303833 0.952725i \(-0.401733\pi\)
0.303833 + 0.952725i \(0.401733\pi\)
\(570\) 5.92145e27 + 8.16426e28i 0.0685081 + 0.944563i
\(571\) 1.05374e29i 1.19689i −0.801163 0.598447i \(-0.795785\pi\)
0.801163 0.598447i \(-0.204215\pi\)
\(572\) −4.38588e28 + 6.39569e27i −0.489100 + 0.0713229i
\(573\) 1.75220e29i 1.91849i
\(574\) −7.90447e28 + 5.73302e27i −0.849763 + 0.0616323i
\(575\) −4.62064e27 −0.0487742
\(576\) −2.57767e28 + 1.19597e28i −0.267173 + 0.123961i
\(577\) −3.49991e28 −0.356214 −0.178107 0.984011i \(-0.556997\pi\)
−0.178107 + 0.984011i \(0.556997\pi\)
\(578\) −7.99001e28 + 5.79506e27i −0.798556 + 0.0579183i
\(579\) 9.53207e28i 0.935540i
\(580\) −2.87238e29 + 4.18865e28i −2.76853 + 0.403720i
\(581\) 5.16367e28i 0.488775i
\(582\) 4.14975e27 + 5.72152e28i 0.0385772 + 0.531888i
\(583\) −1.10259e28 −0.100668
\(584\) 3.53929e28 7.81079e27i 0.317382 0.0700422i
\(585\) −6.27861e28 −0.553002
\(586\) −1.26605e27 1.74558e28i −0.0109528 0.151013i
\(587\) 5.23823e28i 0.445127i 0.974918 + 0.222564i \(0.0714425\pi\)
−0.974918 + 0.222564i \(0.928557\pi\)
\(588\) −3.67534e28 2.52038e29i −0.306786 2.10380i
\(589\) 8.33487e28i 0.683421i
\(590\) 1.08738e29 7.88667e27i 0.875864 0.0635254i
\(591\) −2.04939e29 −1.62165
\(592\) −4.61240e28 1.54786e29i −0.358550 1.20324i
\(593\) 7.14627e28 0.545765 0.272882 0.962047i \(-0.412023\pi\)
0.272882 + 0.962047i \(0.412023\pi\)
\(594\) 4.48899e28 3.25581e27i 0.336814 0.0244288i
\(595\) 1.63944e29i 1.20855i
\(596\) −1.29319e28 8.86809e28i −0.0936646 0.642309i
\(597\) 1.24395e29i 0.885264i
\(598\) 3.81410e26 + 5.25874e27i 0.00266704 + 0.0367721i
\(599\) −1.02973e29 −0.707522 −0.353761 0.935336i \(-0.615097\pi\)
−0.353761 + 0.935336i \(0.615097\pi\)
\(600\) 5.64416e28 + 2.55753e29i 0.381076 + 1.72677i
\(601\) −2.50060e29 −1.65906 −0.829530 0.558463i \(-0.811391\pi\)
−0.829530 + 0.558463i \(0.811391\pi\)
\(602\) 2.06639e27 + 2.84906e28i 0.0134726 + 0.185754i
\(603\) 6.54616e28i 0.419426i
\(604\) 9.28058e28 1.35334e28i 0.584369 0.0852155i
\(605\) 2.12547e29i 1.31529i
\(606\) 1.04762e29 7.59824e27i 0.637147 0.0462116i
\(607\) 1.41619e29 0.846524 0.423262 0.906007i \(-0.360885\pi\)
0.423262 + 0.906007i \(0.360885\pi\)
\(608\) −3.13956e28 8.29037e28i −0.184451 0.487064i
\(609\) 5.84204e29 3.37351
\(610\) 2.09337e29 1.51830e28i 1.18818 0.0861774i
\(611\) 1.65149e29i 0.921389i
\(612\) −2.37276e28 + 3.46007e27i −0.130126 + 0.0189756i
\(613\) 2.69483e29i 1.45277i −0.687289 0.726385i \(-0.741199\pi\)
0.687289 0.726385i \(-0.258801\pi\)
\(614\) 1.42401e28 + 1.96337e29i 0.0754648 + 1.04048i
\(615\) −1.75579e29 −0.914712
\(616\) −2.99833e28 1.35863e29i −0.153561 0.695832i
\(617\) 9.76041e28 0.491444 0.245722 0.969340i \(-0.420975\pi\)
0.245722 + 0.969340i \(0.420975\pi\)
\(618\) −5.86319e27 8.08394e28i −0.0290238 0.400169i
\(619\) 2.22921e29i 1.08492i −0.840081 0.542461i \(-0.817492\pi\)
0.840081 0.542461i \(-0.182508\pi\)
\(620\) 6.32414e28 + 4.33681e29i 0.302614 + 2.07519i
\(621\) 5.35405e27i 0.0251896i
\(622\) 2.35741e29 1.70980e28i 1.09053 0.0790945i
\(623\) −3.95168e29 −1.79745
\(624\) 2.86413e29 8.53472e28i 1.28102 0.381725i
\(625\) −3.15336e28 −0.138686
\(626\) −4.58627e28 + 3.32637e27i −0.198349 + 0.0143860i
\(627\) 5.86203e28i 0.249310i
\(628\) 3.88268e28 + 2.66257e29i 0.162389 + 1.11359i
\(629\) 1.36290e29i 0.560572i
\(630\) −1.42573e28 1.96574e29i −0.0576715 0.795153i
\(631\) −1.06630e29 −0.424200 −0.212100 0.977248i \(-0.568030\pi\)
−0.212100 + 0.977248i \(0.568030\pi\)
\(632\) −3.26552e29 + 7.20660e28i −1.27768 + 0.281969i
\(633\) −1.50508e29 −0.579190
\(634\) 2.43859e28 + 3.36224e29i 0.0923001 + 1.27260i
\(635\) 1.02311e28i 0.0380889i
\(636\) 7.35672e28 1.07279e28i 0.269392 0.0392840i
\(637\) 6.09472e29i 2.19528i
\(638\) 2.07331e29 1.50375e28i 0.734594 0.0532792i
\(639\) −3.25593e28 −0.113479
\(640\) −2.26262e29 4.07544e29i −0.775749 1.39728i
\(641\) −2.20432e29 −0.743472 −0.371736 0.928339i \(-0.621237\pi\)
−0.371736 + 0.928339i \(0.621237\pi\)
\(642\) 4.79480e29 3.47762e28i 1.59094 0.115389i
\(643\) 1.92753e29i 0.629197i 0.949225 + 0.314599i \(0.101870\pi\)
−0.949225 + 0.314599i \(0.898130\pi\)
\(644\) −1.63777e28 + 2.38828e27i −0.0525959 + 0.00766979i
\(645\) 6.32853e28i 0.199952i
\(646\) −5.41135e27 7.46096e28i −0.0168215 0.231928i
\(647\) 4.56666e29 1.39670 0.698352 0.715755i \(-0.253917\pi\)
0.698352 + 0.715755i \(0.253917\pi\)
\(648\) −3.91922e29 + 8.64924e28i −1.17940 + 0.260280i
\(649\) −7.80754e28 −0.231177
\(650\) −4.53354e28 6.25067e29i −0.132083 1.82111i
\(651\) 8.82047e29i 2.52867i
\(652\) −1.42152e28 9.74816e28i −0.0401009 0.274994i
\(653\) 9.77360e28i 0.271310i −0.990756 0.135655i \(-0.956686\pi\)
0.990756 0.135655i \(-0.0433139\pi\)
\(654\) −5.07332e29 + 3.67962e28i −1.38588 + 0.100516i
\(655\) −2.82323e29 −0.758948
\(656\) 1.82230e29 5.43019e28i 0.482091 0.143656i
\(657\) −3.67682e28 −0.0957275
\(658\) −5.17057e29 + 3.75016e28i −1.32485 + 0.0960899i
\(659\) 1.12411e29i 0.283473i 0.989904 + 0.141736i \(0.0452685\pi\)
−0.989904 + 0.141736i \(0.954731\pi\)
\(660\) −4.44786e28 3.05014e29i −0.110393 0.757022i
\(661\) 3.28483e29i 0.802412i 0.915988 + 0.401206i \(0.131409\pi\)
−0.915988 + 0.401206i \(0.868591\pi\)
\(662\) 3.73625e28 + 5.15140e29i 0.0898312 + 1.23856i
\(663\) 2.52188e29 0.596805
\(664\) 2.66987e28 + 1.20980e29i 0.0621907 + 0.281804i
\(665\) 6.14861e29 1.40977
\(666\) 1.18524e28 + 1.63416e29i 0.0267502 + 0.368821i
\(667\) 2.47286e28i 0.0549386i
\(668\) 4.15755e29 6.06274e28i 0.909253 0.132592i
\(669\) 4.69050e29i 1.00982i
\(670\) −1.07102e30 + 7.76801e28i −2.26994 + 0.164636i
\(671\) −1.50306e29 −0.313610
\(672\) 3.32248e29 + 8.77338e29i 0.682472 + 1.80214i
\(673\) −2.43465e29 −0.492355 −0.246177 0.969225i \(-0.579175\pi\)
−0.246177 + 0.969225i \(0.579175\pi\)
\(674\) 6.82224e29 4.94809e28i 1.35831 0.0985165i
\(675\) 6.36397e29i 1.24749i
\(676\) −1.94936e29 + 2.84264e28i −0.376228 + 0.0548633i
\(677\) 6.05441e29i 1.15051i −0.817974 0.575256i \(-0.804903\pi\)
0.817974 0.575256i \(-0.195097\pi\)
\(678\) −4.82459e28 6.65196e29i −0.0902711 1.24462i
\(679\) 4.30895e29 0.793851
\(680\) −8.47669e28 3.84104e29i −0.153774 0.696795i
\(681\) −9.09948e28 −0.162544
\(682\) −2.27040e28 3.13034e29i −0.0399362 0.550625i
\(683\) 8.55320e29i 1.48153i 0.671763 + 0.740766i \(0.265537\pi\)
−0.671763 + 0.740766i \(0.734463\pi\)
\(684\) 1.29768e28 + 8.89890e28i 0.0221349 + 0.151791i
\(685\) 1.86165e30i 3.12713i
\(686\) −8.86995e29 + 6.43327e28i −1.46730 + 0.106421i
\(687\) 9.95611e29 1.62197
\(688\) −1.95724e28 6.56823e28i −0.0314026 0.105383i
\(689\) −1.77898e29 −0.281106
\(690\) −3.65717e28 + 2.65250e27i −0.0569153 + 0.00412800i
\(691\) 1.40587e29i 0.215489i 0.994179 + 0.107744i \(0.0343628\pi\)
−0.994179 + 0.107744i \(0.965637\pi\)
\(692\) −8.75425e28 6.00326e29i −0.132161 0.906303i
\(693\) 1.41142e29i 0.209874i
\(694\) 3.02551e28 + 4.17146e29i 0.0443123 + 0.610961i
\(695\) 1.15471e30 1.66583
\(696\) −1.36873e30 + 3.02062e29i −1.94501 + 0.429239i
\(697\) 1.60454e29 0.224598
\(698\) 6.95594e28 + 9.59059e29i 0.0959122 + 1.32240i
\(699\) 3.55990e29i 0.483534i
\(700\) 1.94670e30 2.83877e29i 2.60477 0.379840i
\(701\) 1.36147e30i 1.79461i 0.441412 + 0.897305i \(0.354478\pi\)
−0.441412 + 0.897305i \(0.645522\pi\)
\(702\) 7.24282e29 5.25313e28i 0.940519 0.0682148i
\(703\) −5.11146e29 −0.653905
\(704\) 1.40496e29 + 3.02811e29i 0.177072 + 0.381644i
\(705\) −1.14852e30 −1.42611
\(706\) −7.36737e29 + 5.34347e28i −0.901287 + 0.0653693i
\(707\) 7.88973e29i 0.950952i
\(708\) 5.20938e29 7.59656e28i 0.618638 0.0902127i
\(709\) 4.07199e29i 0.476454i −0.971210 0.238227i \(-0.923434\pi\)
0.971210 0.238227i \(-0.0765662\pi\)
\(710\) −3.86365e28 5.32706e29i −0.0445436 0.614150i
\(711\) 3.39241e29 0.385370
\(712\) 9.25839e29 2.04321e29i 1.03632 0.228704i
\(713\) −3.73359e28 −0.0411800
\(714\) 5.72662e28 + 7.89565e29i 0.0622397 + 0.858137i
\(715\) 7.37577e29i 0.789939i
\(716\) −3.53641e28 2.42511e29i −0.0373229 0.255944i
\(717\) 5.99888e29i 0.623906i
\(718\) 1.65523e29 1.20052e28i 0.169649 0.0123044i
\(719\) 1.60726e29 0.162343 0.0811713 0.996700i \(-0.474134\pi\)
0.0811713 + 0.996700i \(0.474134\pi\)
\(720\) 1.35042e29 + 4.53182e29i 0.134424 + 0.451109i
\(721\) −6.08812e29 −0.597259
\(722\) 7.51757e29 5.45241e28i 0.726837 0.0527166i
\(723\) 7.98790e29i 0.761168i
\(724\) 1.86698e29 + 1.28029e30i 0.175342 + 1.20241i
\(725\) 2.93930e30i 2.72079i
\(726\) −7.42434e28 1.02364e30i −0.0677366 0.933927i
\(727\) −6.61860e29 −0.595189 −0.297594 0.954692i \(-0.596184\pi\)
−0.297594 + 0.954692i \(0.596184\pi\)
\(728\) −4.83770e29 2.19210e30i −0.428804 1.94304i
\(729\) −6.38122e29 −0.557525
\(730\) −4.36311e28 6.01569e29i −0.0375756 0.518078i
\(731\) 5.78336e28i 0.0490962i
\(732\) 1.00288e30 1.46245e29i 0.839232 0.122381i
\(733\) 2.30207e29i 0.189900i 0.995482 + 0.0949502i \(0.0302692\pi\)
−0.995482 + 0.0949502i \(0.969731\pi\)
\(734\) −1.69742e30 + 1.23112e29i −1.38033 + 0.100113i
\(735\) −4.23854e30 −3.39781
\(736\) 3.71365e28 1.40636e28i 0.0293484 0.0111142i
\(737\) 7.69007e29 0.599131
\(738\) −1.92390e29 + 1.39538e28i −0.147772 + 0.0107177i
\(739\) 1.02374e30i 0.775214i −0.921825 0.387607i \(-0.873302\pi\)
0.921825 0.387607i \(-0.126698\pi\)
\(740\) −2.65960e30 + 3.87836e29i −1.98556 + 0.289544i
\(741\) 9.45817e29i 0.696171i
\(742\) −4.03967e28 5.56974e29i −0.0293160 0.404198i
\(743\) 1.16628e30 0.834492 0.417246 0.908794i \(-0.362995\pi\)
0.417246 + 0.908794i \(0.362995\pi\)
\(744\) 4.56062e29 + 2.06655e30i 0.321742 + 1.45791i
\(745\) −1.49135e30 −1.03739
\(746\) −7.23821e28 9.97977e29i −0.0496448 0.684483i
\(747\) 1.25681e29i 0.0849967i
\(748\) 4.06470e28 + 2.78739e29i 0.0271058 + 0.185879i
\(749\) 3.61103e30i 2.37450i
\(750\) 1.55004e30 1.12423e29i 1.00508 0.0728973i
\(751\) 8.81536e29 0.563664 0.281832 0.959464i \(-0.409058\pi\)
0.281832 + 0.959464i \(0.409058\pi\)
\(752\) 1.19202e30 3.55207e29i 0.751619 0.223972i
\(753\) 9.72207e28 0.0604521
\(754\) 3.34521e30 2.42624e29i 2.05128 0.148777i
\(755\) 1.56072e30i 0.943807i
\(756\) 3.28936e29 + 2.25569e30i 0.196170 + 1.34524i
\(757\) 1.17925e30i 0.693584i 0.937942 + 0.346792i \(0.112729\pi\)
−0.937942 + 0.346792i \(0.887271\pi\)
\(758\) 2.35969e29 + 3.25345e30i 0.136876 + 1.88720i
\(759\) 2.62589e28 0.0150223
\(760\) −1.44056e30 + 3.17914e29i −0.812808 + 0.179377i
\(761\) 1.38198e30 0.769063 0.384532 0.923112i \(-0.374363\pi\)
0.384532 + 0.923112i \(0.374363\pi\)
\(762\) 3.57377e27 + 4.92737e28i 0.00196155 + 0.0270451i
\(763\) 3.82078e30i 2.06845i
\(764\) −3.12475e30 + 4.55666e29i −1.66853 + 0.243314i
\(765\) 3.99029e29i 0.210165i
\(766\) 2.32510e30 1.68637e29i 1.20793 0.0876094i
\(767\) −1.25972e30 −0.645538
\(768\) −1.23205e30 1.88373e30i −0.622781 0.952194i
\(769\) 1.56974e30 0.782709 0.391354 0.920240i \(-0.372007\pi\)
0.391354 + 0.920240i \(0.372007\pi\)
\(770\) −2.30925e30 + 1.67487e29i −1.13584 + 0.0823812i
\(771\) 1.37445e30i 0.666895i
\(772\) 1.69988e30 2.47885e29i 0.813649 0.118650i
\(773\) 3.88908e29i 0.183638i 0.995776 + 0.0918189i \(0.0292681\pi\)
−0.995776 + 0.0918189i \(0.970732\pi\)
\(774\) 5.02948e27 + 6.93446e28i 0.00234284 + 0.0323022i
\(775\) 4.43784e30 2.03941
\(776\) −1.00954e30 + 2.22794e29i −0.457696 + 0.101008i
\(777\) 5.40927e30 2.41946
\(778\) −1.59606e29 2.20059e30i −0.0704310 0.971076i
\(779\) 6.01774e29i 0.261993i
\(780\) −7.17645e29 4.92129e30i −0.308260 2.11390i
\(781\) 3.82488e29i 0.162100i
\(782\) 3.34212e28 2.42400e27i 0.0139750 0.00101359i
\(783\) −3.40584e30 −1.40516
\(784\) 4.39909e30 1.31087e30i 1.79079 0.533630i
\(785\) 4.47766e30 1.79854
\(786\) −1.35969e30 + 9.86165e28i −0.538893 + 0.0390853i
\(787\) 2.75242e29i 0.107641i 0.998551 + 0.0538207i \(0.0171400\pi\)
−0.998551 + 0.0538207i \(0.982860\pi\)
\(788\) −5.32952e29 3.65474e30i −0.205666 1.41036i
\(789\) 1.81107e30i 0.689648i
\(790\) 4.02561e29 + 5.55036e30i 0.151268 + 2.08563i
\(791\) −5.00968e30 −1.85762
\(792\) −7.29776e28 3.30683e29i −0.0267039 0.121003i
\(793\) −2.42514e30 −0.875725
\(794\) −4.45018e28 6.13574e29i −0.0158585 0.218651i
\(795\) 1.23719e30i 0.435091i
\(796\) −2.21837e30 + 3.23494e29i −0.769924 + 0.112274i
\(797\) 8.59681e29i 0.294459i 0.989102 + 0.147230i \(0.0470356\pi\)
−0.989102 + 0.147230i \(0.952964\pi\)
\(798\) 2.96122e30 2.14774e29i 1.00101 0.0726023i
\(799\) 1.04958e30 0.350167
\(800\) −4.41415e30 + 1.67164e30i −1.45346 + 0.550424i
\(801\) −9.61815e29 −0.312572
\(802\) −4.20273e30 + 3.04819e29i −1.34803 + 0.0977712i
\(803\) 4.31933e29i 0.136742i
\(804\) −5.13100e30 + 7.48226e29i −1.60329 + 0.233800i
\(805\) 2.75426e29i 0.0849470i
\(806\) −3.66321e29 5.05069e30i −0.111518 1.53756i
\(807\) 3.85035e30 1.15699
\(808\) 4.07938e29 + 1.84849e30i 0.120997 + 0.548273i
\(809\) −2.12602e30 −0.622454 −0.311227 0.950336i \(-0.600740\pi\)
−0.311227 + 0.950336i \(0.600740\pi\)
\(810\) 4.83147e29 + 6.66144e30i 0.139632 + 1.92520i
\(811\) 4.96211e30i 1.41562i −0.706402 0.707811i \(-0.749683\pi\)
0.706402 0.707811i \(-0.250317\pi\)
\(812\) 1.51924e30 + 1.04183e31i 0.427847 + 2.93398i
\(813\) 6.90622e30i 1.91995i
\(814\) 1.91972e30 1.39235e29i 0.526844 0.0382114i
\(815\) −1.63936e30 −0.444139
\(816\) −5.42413e29 1.82026e30i −0.145072 0.486841i
\(817\) −2.16902e29 −0.0572705
\(818\) −2.81344e30 + 2.04055e29i −0.733377 + 0.0531910i
\(819\) 2.27728e30i 0.586052i
\(820\) −4.56600e29 3.13116e30i −0.116009 0.795535i
\(821\) 1.94153e30i 0.487013i −0.969899 0.243507i \(-0.921702\pi\)
0.969899 0.243507i \(-0.0782978\pi\)
\(822\) −6.50282e29 8.96584e30i −0.161045 2.22043i
\(823\) 4.47697e30 1.09468 0.547339 0.836911i \(-0.315641\pi\)
0.547339 + 0.836911i \(0.315641\pi\)
\(824\) 1.42639e30 3.14786e29i 0.344351 0.0759940i
\(825\) −3.12120e30 −0.743969
\(826\) −2.86053e29 3.94399e30i −0.0673219 0.928209i
\(827\) 3.96513e30i 0.921404i 0.887555 + 0.460702i \(0.152402\pi\)
−0.887555 + 0.460702i \(0.847598\pi\)
\(828\) −3.98624e28 + 5.81293e27i −0.00914630 + 0.00133376i
\(829\) 4.99122e30i 1.13080i 0.824819 + 0.565398i \(0.191277\pi\)
−0.824819 + 0.565398i \(0.808723\pi\)
\(830\) 2.05627e30 1.49139e29i 0.460003 0.0333635i
\(831\) −8.45637e30 −1.86798
\(832\) 2.26685e30 + 4.88574e30i 0.494456 + 1.06570i
\(833\) 3.87342e30 0.834299
\(834\) 5.56115e30 4.03344e29i 1.18283 0.0857891i
\(835\) 6.99179e30i 1.46852i
\(836\) 1.04539e30 1.52444e29i 0.216827 0.0316188i
\(837\) 5.14224e30i 1.05326i
\(838\) 1.89185e29 + 2.60841e30i 0.0382670 + 0.527611i
\(839\) 8.90907e30 1.77964 0.889819 0.456313i \(-0.150830\pi\)
0.889819 + 0.456313i \(0.150830\pi\)
\(840\) 1.52449e31 3.36436e30i 3.00740 0.663697i
\(841\) −1.05976e31 −2.06466
\(842\) 2.07672e29 + 2.86331e30i 0.0399578 + 0.550923i
\(843\) 5.51782e30i 1.04852i
\(844\) −3.91402e29 2.68406e30i −0.0734560 0.503728i
\(845\) 3.27825e30i 0.607640i
\(846\) −1.25849e30 + 9.12766e28i −0.230388 + 0.0167098i
\(847\) −7.70916e30 −1.39390
\(848\) 3.82628e29 + 1.28405e30i 0.0683314 + 0.229311i
\(849\) −3.59264e30 −0.633699
\(850\) −3.97254e30 + 2.88123e29i −0.692100 + 0.0501972i
\(851\) 2.28967e29i 0.0394015i
\(852\) −3.72153e29 2.55205e30i −0.0632565 0.433785i
\(853\) 8.10797e30i 1.36128i −0.732618 0.680640i \(-0.761702\pi\)
0.732618 0.680640i \(-0.238298\pi\)
\(854\) −5.50693e29 7.59275e30i −0.0913276 1.25919i
\(855\) 1.49654e30 0.245156
\(856\) 1.86708e30 + 8.46028e30i 0.302126 + 1.36902i
\(857\) 7.83011e30 1.25161 0.625805 0.779979i \(-0.284770\pi\)
0.625805 + 0.779979i \(0.284770\pi\)
\(858\) 2.57639e29 + 3.55222e30i 0.0406813 + 0.560898i
\(859\) 5.58068e30i 0.870480i −0.900315 0.435240i \(-0.856664\pi\)
0.900315 0.435240i \(-0.143336\pi\)
\(860\) −1.12858e30 + 1.64576e29i −0.173900 + 0.0253590i
\(861\) 6.36834e30i 0.969378i
\(862\) −8.50971e30 + 6.17199e29i −1.27964 + 0.0928109i
\(863\) 4.00476e30 0.594926 0.297463 0.954733i \(-0.403859\pi\)
0.297463 + 0.954733i \(0.403859\pi\)
\(864\) −1.93697e30 5.11479e30i −0.284268 0.750643i
\(865\) −1.00957e31 −1.46376
\(866\) −3.56232e30 + 2.58371e29i −0.510264 + 0.0370089i
\(867\) 6.43726e30i 0.910962i
\(868\) 1.57298e31 2.29380e30i 2.19921 0.320699i
\(869\) 3.98522e30i 0.550484i
\(870\) 1.68732e30 + 2.32641e31i 0.230274 + 3.17493i
\(871\) 1.24076e31 1.67301
\(872\) −1.97553e30 8.95171e30i −0.263185 1.19257i
\(873\) 1.04877e30 0.138049
\(874\) −9.09108e27 1.25344e29i −0.00118235 0.0163018i
\(875\) 1.16736e31i 1.50010i
\(876\) −4.20261e29 2.88196e30i −0.0533613 0.365927i
\(877\) 2.67352e30i 0.335419i −0.985836 0.167710i \(-0.946363\pi\)
0.985836 0.167710i \(-0.0536371\pi\)
\(878\) 1.44042e31 1.04472e30i 1.78565 0.129511i
\(879\) −1.40635e30 −0.172270
\(880\) 5.32374e30 1.58640e30i 0.644389 0.192019i
\(881\) −1.19745e31 −1.43222 −0.716112 0.697985i \(-0.754080\pi\)
−0.716112 + 0.697985i \(0.754080\pi\)
\(882\) −4.64437e30 + 3.36851e29i −0.548917 + 0.0398123i
\(883\) 1.60841e31i 1.87849i 0.343245 + 0.939246i \(0.388474\pi\)
−0.343245 + 0.939246i \(0.611526\pi\)
\(884\) 6.55824e29 + 4.49735e30i 0.0756900 + 0.519048i
\(885\) 8.76065e30i 0.999153i
\(886\) −2.85677e29 3.93881e30i −0.0321975 0.443926i
\(887\) 9.03823e30 1.00667 0.503333 0.864093i \(-0.332107\pi\)
0.503333 + 0.864093i \(0.332107\pi\)
\(888\) −1.26734e31 + 2.79686e30i −1.39494 + 0.307847i
\(889\) 3.71087e29 0.0403652
\(890\) −1.14134e30 1.57364e31i −0.122693 1.69164i
\(891\) 4.78299e30i 0.508140i
\(892\) −8.36471e30 + 1.21978e30i −0.878254 + 0.128071i
\(893\) 3.93640e30i 0.408469i
\(894\) −7.18247e30 + 5.20936e29i −0.736597 + 0.0534245i
\(895\) −4.07832e30 −0.413371
\(896\) −1.47818e31 + 8.20662e30i −1.48079 + 0.822111i
\(897\) 4.23677e29 0.0419483
\(898\) −7.36545e30 + 5.34208e29i −0.720772 + 0.0522768i
\(899\) 2.37503e31i 2.29716i
\(900\) 4.73816e30 6.90940e29i 0.452963 0.0660533i
\(901\) 1.13061e30i 0.106832i
\(902\) 1.63922e29 + 2.26009e30i 0.0153098 + 0.211085i
\(903\) 2.29539e30 0.211902
\(904\) 1.17372e31 2.59025e30i 1.07101 0.236360i
\(905\) 2.15308e31 1.94200
\(906\) −5.45168e29 7.51656e30i −0.0486053 0.670152i
\(907\) 1.14372e31i 1.00796i −0.863715 0.503981i \(-0.831868\pi\)
0.863715 0.503981i \(-0.168132\pi\)
\(908\) −2.36635e29 1.62274e30i −0.0206148 0.141367i
\(909\) 1.92031e30i 0.165368i
\(910\) −3.72588e31 + 2.70234e30i −3.17172 + 0.230041i
\(911\) −1.76545e31 −1.48563 −0.742817 0.669494i \(-0.766511\pi\)
−0.742817 + 0.669494i \(0.766511\pi\)
\(912\) −6.82679e30 + 2.03429e30i −0.567898 + 0.169226i
\(913\) −1.47643e30 −0.121414
\(914\) 1.31667e31 9.54964e29i 1.07039 0.0776340i
\(915\) 1.68655e31i 1.35543i
\(916\) 2.58912e30 + 1.77550e31i 0.205707 + 1.41065i
\(917\) 1.02400e31i 0.804305i
\(918\) −3.33856e29 4.60308e30i −0.0259245 0.357438i
\(919\) 5.44409e30 0.417939 0.208969 0.977922i \(-0.432989\pi\)
0.208969 + 0.977922i \(0.432989\pi\)
\(920\) −1.42409e29 6.45295e29i −0.0108085 0.0489763i
\(921\) 1.58181e31 1.18694
\(922\) −3.64738e29 5.02887e30i −0.0270587 0.373075i
\(923\) 6.17131e30i 0.452647i
\(924\) −1.10630e31 + 1.61326e30i −0.802264 + 0.116990i
\(925\) 2.72156e31i 1.95133i
\(926\) 6.96811e30 5.05389e29i 0.493969 0.0358270i
\(927\) −1.48181e30 −0.103862
\(928\) −8.94620e30 2.36235e31i −0.619990 1.63715i
\(929\) −3.07142e30 −0.210462 −0.105231 0.994448i \(-0.533558\pi\)
−0.105231 + 0.994448i \(0.533558\pi\)
\(930\) 3.51248e31 2.54756e30i 2.37982 0.172605i
\(931\) 1.45270e31i 0.973207i
\(932\) 6.34847e30 9.25765e29i 0.420535 0.0613244i
\(933\) 1.89928e31i 1.24403i
\(934\) −1.54009e30 2.12341e31i −0.0997477 1.37528i
\(935\) 4.68757e30 0.300211
\(936\) −1.17747e30 5.33545e30i −0.0745680 0.337889i
\(937\) −1.73830e31 −1.08857 −0.544287 0.838899i \(-0.683200\pi\)
−0.544287 + 0.838899i \(0.683200\pi\)
\(938\) 2.81749e30 + 3.88465e31i 0.174475 + 2.40559i
\(939\) 3.69499e30i 0.226269i
\(940\) −2.98677e30 2.04819e31i −0.180867 1.24030i
\(941\) 2.83336e31i 1.69672i 0.529420 + 0.848360i \(0.322410\pi\)
−0.529420 + 0.848360i \(0.677590\pi\)
\(942\) 2.15647e31 1.56407e30i 1.27706 0.0926234i
\(943\) 2.69563e29 0.0157866
\(944\) 2.70943e30 + 9.09248e30i 0.156918 + 0.526595i
\(945\) 3.79342e31 2.17268
\(946\) 8.14622e29 5.90836e28i 0.0461423 0.00334665i
\(947\) 3.56217e31i 1.99545i −0.0674371 0.997724i \(-0.521482\pi\)
0.0674371 0.997724i \(-0.478518\pi\)
\(948\) 3.87753e30 + 2.65903e31i 0.214816 + 1.47311i
\(949\) 6.96908e30i 0.381839i
\(950\) 1.08059e30 + 1.48988e31i 0.0585549 + 0.807332i
\(951\) 2.70883e31 1.45173
\(952\) −1.39316e31 + 3.07454e30i −0.738437 + 0.162964i
\(953\) −4.09398e30 −0.214620 −0.107310 0.994226i \(-0.534224\pi\)
−0.107310 + 0.994226i \(0.534224\pi\)
\(954\) −9.83231e28 1.35564e30i −0.00509797 0.0702889i
\(955\) 5.25492e31i 2.69483i
\(956\) 1.06980e31 1.56003e30i 0.542618 0.0791271i
\(957\) 1.67039e31i 0.837997i
\(958\) 1.89852e30 1.37697e29i 0.0942055 0.00683262i
\(959\) −6.75228e31 −3.31402
\(960\) −3.39777e31 + 1.57647e31i −1.64948 + 0.765311i
\(961\) 1.50333e31 0.721870
\(962\) 3.09740e31 2.24651e30i 1.47116 0.106701i
\(963\) 8.78903e30i 0.412919i
\(964\) 1.42451e31 2.07728e30i 0.661996 0.0965354i
\(965\) 2.85871e31i 1.31411i
\(966\) 9.62074e28 + 1.32647e30i 0.00437470 + 0.0603168i
\(967\) 8.68171e29 0.0390506 0.0195253 0.999809i \(-0.493785\pi\)
0.0195253 + 0.999809i \(0.493785\pi\)
\(968\) 1.80618e31 3.98602e30i 0.803656 0.177357i
\(969\) −6.01102e30 −0.264575
\(970\) 1.24453e30 + 1.71591e31i 0.0541878 + 0.747121i
\(971\) 2.42616e31i 1.04500i −0.852639 0.522501i \(-0.824999\pi\)
0.852639 0.522501i \(-0.175001\pi\)
\(972\) 1.93547e30 + 1.32726e31i 0.0824690 + 0.565535i
\(973\) 4.18818e31i 1.76539i
\(974\) −6.44537e30 + 4.67475e29i −0.268769 + 0.0194935i
\(975\) −5.03594e31 −2.07746
\(976\) 5.21605e30 + 1.75043e31i 0.212872 + 0.714368i
\(977\) −1.05813e31 −0.427216 −0.213608 0.976919i \(-0.568522\pi\)
−0.213608 + 0.976919i \(0.568522\pi\)
\(978\) −7.89527e30 + 5.72635e29i −0.315362 + 0.0228728i
\(979\) 1.12989e31i 0.446495i
\(980\) −1.10225e31 7.55872e31i −0.430929 2.95512i
\(981\) 9.29956e30i 0.359698i
\(982\) −1.66382e30 2.29402e31i −0.0636703 0.877861i
\(983\) −2.80237e31 −1.06099 −0.530497 0.847687i \(-0.677995\pi\)
−0.530497 + 0.847687i \(0.677995\pi\)
\(984\) −3.29275e30 1.49204e31i −0.123342 0.558897i
\(985\) −6.14621e31 −2.27786
\(986\) −1.54197e30 2.12601e31i −0.0565415 0.779573i
\(987\) 4.16574e31i 1.51134i
\(988\) 1.68670e31 2.45963e30i 0.605468 0.0882922i
\(989\) 9.71606e28i 0.00345088i
\(990\) −5.62057e30 + 4.07653e29i −0.197520 + 0.0143259i
\(991\) 3.61409e31 1.25668 0.628341 0.777938i \(-0.283734\pi\)
0.628341 + 0.777938i \(0.283734\pi\)
\(992\) −3.56674e31 + 1.35072e31i −1.22715 + 0.464722i
\(993\) 4.15030e31 1.41290
\(994\) −1.93215e31 + 1.40136e30i −0.650854 + 0.0472057i
\(995\) 3.73066e31i 1.24349i
\(996\) 9.85107e30 1.43653e30i 0.324908 0.0473796i
\(997\) 6.57334e30i 0.214529i −0.994230 0.107265i \(-0.965791\pi\)
0.994230 0.107265i \(-0.0342092\pi\)
\(998\) 2.06089e30 + 2.84147e31i 0.0665555 + 0.917642i
\(999\) −3.15354e31 −1.00777
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 8.22.b.a.5.19 20
4.3 odd 2 32.22.b.a.17.16 20
8.3 odd 2 32.22.b.a.17.5 20
8.5 even 2 inner 8.22.b.a.5.20 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.22.b.a.5.19 20 1.1 even 1 trivial
8.22.b.a.5.20 yes 20 8.5 even 2 inner
32.22.b.a.17.5 20 8.3 odd 2
32.22.b.a.17.16 20 4.3 odd 2