Properties

Label 21.22.c.b.20.5
Level $21$
Weight $22$
Character 21.20
Analytic conductor $58.690$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,22,Mod(20,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 22, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.20");
 
S:= CuspForms(chi, 22);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 21.c (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: \(58.6902423003\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.5
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2329.72i q^{2} +(52907.9 - 87527.8i) q^{3} -3.33046e6 q^{4} -3.45099e7 q^{5} +(-2.03916e8 - 1.23261e8i) q^{6} +(4.88555e7 - 7.45761e8i) q^{7} +2.87327e9i q^{8} +(-4.86187e9 - 9.26181e9i) q^{9} +O(q^{10})\) \(q-2329.72i q^{2} +(52907.9 - 87527.8i) q^{3} -3.33046e6 q^{4} -3.45099e7 q^{5} +(-2.03916e8 - 1.23261e8i) q^{6} +(4.88555e7 - 7.45761e8i) q^{7} +2.87327e9i q^{8} +(-4.86187e9 - 9.26181e9i) q^{9} +8.03985e10i q^{10} +5.12942e9i q^{11} +(-1.76208e11 + 2.91508e11i) q^{12} +3.88435e11i q^{13} +(-1.73742e12 - 1.13820e11i) q^{14} +(-1.82584e12 + 3.02057e12i) q^{15} -2.90549e11 q^{16} -4.11275e12 q^{17} +(-2.15775e13 + 1.13268e13i) q^{18} +7.35621e11i q^{19} +1.14934e14 q^{20} +(-6.26899e13 - 4.37328e13i) q^{21} +1.19501e13 q^{22} +2.80126e14i q^{23} +(2.51491e14 + 1.52019e14i) q^{24} +7.14095e14 q^{25} +9.04946e14 q^{26} +(-1.06790e15 - 6.44740e13i) q^{27} +(-1.62712e14 + 2.48373e15i) q^{28} -2.85990e15i q^{29} +(7.03710e15 + 4.25371e15i) q^{30} -8.55595e15i q^{31} +6.70259e15i q^{32} +(4.48967e14 + 2.71387e14i) q^{33} +9.58157e15i q^{34} +(-1.68600e15 + 2.57361e16i) q^{35} +(1.61923e16 + 3.08461e16i) q^{36} -2.16290e16 q^{37} +1.71379e15 q^{38} +(3.39988e16 + 2.05513e16i) q^{39} -9.91564e16i q^{40} -8.87944e16 q^{41} +(-1.01885e17 + 1.46050e17i) q^{42} +2.16141e17 q^{43} -1.70833e16i q^{44} +(1.67783e17 + 3.19624e17i) q^{45} +6.52616e17 q^{46} +1.24937e17 q^{47} +(-1.53723e16 + 2.54311e16i) q^{48} +(-5.53772e17 - 7.28691e16i) q^{49} -1.66364e18i q^{50} +(-2.17597e17 + 3.59980e17i) q^{51} -1.29367e18i q^{52} -1.11914e18i q^{53} +(-1.50207e17 + 2.48791e18i) q^{54} -1.77016e17i q^{55} +(2.14278e18 + 1.40375e17i) q^{56} +(6.43872e16 + 3.89201e16i) q^{57} -6.66279e18 q^{58} +3.06749e18 q^{59} +(6.08091e18 - 1.00599e19i) q^{60} -8.59883e18i q^{61} -1.99330e19 q^{62} +(-7.14463e18 + 3.17330e18i) q^{63} +1.50059e19 q^{64} -1.34048e19i q^{65} +(6.32256e17 - 1.04597e18i) q^{66} +9.86518e18 q^{67} +1.36974e19 q^{68} +(2.45188e19 + 1.48209e19i) q^{69} +(5.99581e19 + 3.92791e18i) q^{70} +2.59864e19i q^{71} +(2.66117e19 - 1.39695e19i) q^{72} -2.69585e18i q^{73} +5.03895e19i q^{74} +(3.77812e19 - 6.25032e19i) q^{75} -2.44996e18i q^{76} +(3.82532e18 + 2.50600e17i) q^{77} +(4.78788e19 - 7.92079e19i) q^{78} +5.09894e19 q^{79} +1.00268e19 q^{80} +(-6.21434e19 + 9.00595e19i) q^{81} +2.06866e20i q^{82} -1.71105e20 q^{83} +(2.08787e20 + 1.45651e20i) q^{84} +1.41930e20 q^{85} -5.03549e20i q^{86} +(-2.50321e20 - 1.51311e20i) q^{87} -1.47382e19 q^{88} -3.53288e20 q^{89} +(7.44636e20 - 3.90887e20i) q^{90} +(2.89679e20 + 1.89772e19i) q^{91} -9.32949e20i q^{92} +(-7.48884e20 - 4.52677e20i) q^{93} -2.91069e20i q^{94} -2.53862e19i q^{95} +(5.86663e20 + 3.54620e20i) q^{96} +1.89705e20i q^{97} +(-1.69765e20 + 1.29014e21i) q^{98} +(4.75077e19 - 2.49386e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9} - 687153165468 q^{15} + 36241782390404 q^{16} + 36759093002772 q^{18} + 79412641656180 q^{21} + 228880341648112 q^{22} + 45\!\cdots\!12 q^{25}+ \cdots + 15\!\cdots\!28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2329.72i 1.60875i −0.594119 0.804377i \(-0.702499\pi\)
0.594119 0.804377i \(-0.297501\pi\)
\(3\) 52907.9 87527.8i 0.517305 0.855801i
\(4\) −3.33046e6 −1.58809
\(5\) −3.45099e7 −1.58037 −0.790184 0.612869i \(-0.790015\pi\)
−0.790184 + 0.612869i \(0.790015\pi\)
\(6\) −2.03916e8 1.23261e8i −1.37677 0.832217i
\(7\) 4.88555e7 7.45761e8i 0.0653709 0.997861i
\(8\) 2.87327e9i 0.946090i
\(9\) −4.86187e9 9.26181e9i −0.464790 0.885421i
\(10\) 8.03985e10i 2.54242i
\(11\) 5.12942e9i 0.0596273i 0.999555 + 0.0298136i \(0.00949138\pi\)
−0.999555 + 0.0298136i \(0.990509\pi\)
\(12\) −1.76208e11 + 2.91508e11i −0.821527 + 1.35909i
\(13\) 3.88435e11i 0.781471i 0.920503 + 0.390736i \(0.127779\pi\)
−0.920503 + 0.390736i \(0.872221\pi\)
\(14\) −1.73742e12 1.13820e11i −1.60531 0.105166i
\(15\) −1.82584e12 + 3.02057e12i −0.817533 + 1.35248i
\(16\) −2.90549e11 −0.0660633
\(17\) −4.11275e12 −0.494787 −0.247394 0.968915i \(-0.579574\pi\)
−0.247394 + 0.968915i \(0.579574\pi\)
\(18\) −2.15775e13 + 1.13268e13i −1.42442 + 0.747733i
\(19\) 7.35621e11i 0.0275259i 0.999905 + 0.0137629i \(0.00438102\pi\)
−0.999905 + 0.0137629i \(0.995619\pi\)
\(20\) 1.14934e14 2.50977
\(21\) −6.26899e13 4.37328e13i −0.820154 0.572143i
\(22\) 1.19501e13 0.0959256
\(23\) 2.80126e14i 1.40997i 0.709220 + 0.704987i \(0.249047\pi\)
−0.709220 + 0.704987i \(0.750953\pi\)
\(24\) 2.51491e14 + 1.52019e14i 0.809664 + 0.489417i
\(25\) 7.14095e14 1.49757
\(26\) 9.04946e14 1.25719
\(27\) −1.06790e15 6.44740e13i −0.998182 0.0602649i
\(28\) −1.62712e14 + 2.48373e15i −0.103815 + 1.58469i
\(29\) 2.85990e15i 1.26233i −0.775649 0.631164i \(-0.782577\pi\)
0.775649 0.631164i \(-0.217423\pi\)
\(30\) 7.03710e15 + 4.25371e15i 2.17581 + 1.31521i
\(31\) 8.55595e15i 1.87487i −0.348163 0.937434i \(-0.613194\pi\)
0.348163 0.937434i \(-0.386806\pi\)
\(32\) 6.70259e15i 1.05237i
\(33\) 4.48967e14 + 2.71387e14i 0.0510291 + 0.0308455i
\(34\) 9.58157e15i 0.795991i
\(35\) −1.68600e15 + 2.57361e16i −0.103310 + 1.57699i
\(36\) 1.61923e16 + 3.08461e16i 0.738128 + 1.40613i
\(37\) −2.16290e16 −0.739465 −0.369733 0.929138i \(-0.620551\pi\)
−0.369733 + 0.929138i \(0.620551\pi\)
\(38\) 1.71379e15 0.0442824
\(39\) 3.39988e16 + 2.05513e16i 0.668784 + 0.404259i
\(40\) 9.91564e16i 1.49517i
\(41\) −8.87944e16 −1.03313 −0.516565 0.856248i \(-0.672790\pi\)
−0.516565 + 0.856248i \(0.672790\pi\)
\(42\) −1.01885e17 + 1.46050e17i −0.920438 + 1.31943i
\(43\) 2.16141e17 1.52517 0.762585 0.646888i \(-0.223930\pi\)
0.762585 + 0.646888i \(0.223930\pi\)
\(44\) 1.70833e16i 0.0946934i
\(45\) 1.67783e17 + 3.19624e17i 0.734540 + 1.39929i
\(46\) 6.52616e17 2.26830
\(47\) 1.24937e17 0.346469 0.173235 0.984881i \(-0.444578\pi\)
0.173235 + 0.984881i \(0.444578\pi\)
\(48\) −1.53723e16 + 2.54311e16i −0.0341749 + 0.0565370i
\(49\) −5.53772e17 7.28691e16i −0.991453 0.130462i
\(50\) 1.66364e18i 2.40921i
\(51\) −2.17597e17 + 3.59980e17i −0.255956 + 0.423439i
\(52\) 1.29367e18i 1.24105i
\(53\) 1.11914e18i 0.878997i −0.898243 0.439499i \(-0.855156\pi\)
0.898243 0.439499i \(-0.144844\pi\)
\(54\) −1.50207e17 + 2.48791e18i −0.0969515 + 1.60583i
\(55\) 1.77016e17i 0.0942331i
\(56\) 2.14278e18 + 1.40375e17i 0.944066 + 0.0618467i
\(57\) 6.43872e16 + 3.89201e16i 0.0235567 + 0.0142393i
\(58\) −6.66279e18 −2.03078
\(59\) 3.06749e18 0.781335 0.390667 0.920532i \(-0.372244\pi\)
0.390667 + 0.920532i \(0.372244\pi\)
\(60\) 6.08091e18 1.00599e19i 1.29832 2.14786i
\(61\) 8.59883e18i 1.54339i −0.635992 0.771696i \(-0.719409\pi\)
0.635992 0.771696i \(-0.280591\pi\)
\(62\) −1.99330e19 −3.01620
\(63\) −7.14463e18 + 3.17330e18i −0.913911 + 0.405915i
\(64\) 1.50059e19 1.62694
\(65\) 1.34048e19i 1.23501i
\(66\) 6.32256e17 1.04597e18i 0.0496228 0.0820932i
\(67\) 9.86518e18 0.661180 0.330590 0.943774i \(-0.392752\pi\)
0.330590 + 0.943774i \(0.392752\pi\)
\(68\) 1.36974e19 0.785766
\(69\) 2.45188e19 + 1.48209e19i 1.20666 + 0.729387i
\(70\) 5.99581e19 + 3.92791e18i 2.53699 + 0.166201i
\(71\) 2.59864e19i 0.947398i 0.880687 + 0.473699i \(0.157082\pi\)
−0.880687 + 0.473699i \(0.842918\pi\)
\(72\) 2.66117e19 1.39695e19i 0.837687 0.439733i
\(73\) 2.69585e18i 0.0734184i −0.999326 0.0367092i \(-0.988312\pi\)
0.999326 0.0367092i \(-0.0116875\pi\)
\(74\) 5.03895e19i 1.18962i
\(75\) 3.77812e19 6.25032e19i 0.774699 1.28162i
\(76\) 2.44996e18i 0.0437135i
\(77\) 3.82532e18 + 2.50600e17i 0.0594997 + 0.00389789i
\(78\) 4.78788e19 7.92079e19i 0.650354 1.07591i
\(79\) 5.09894e19 0.605892 0.302946 0.953008i \(-0.402030\pi\)
0.302946 + 0.953008i \(0.402030\pi\)
\(80\) 1.00268e19 0.104404
\(81\) −6.21434e19 + 9.00595e19i −0.567940 + 0.823070i
\(82\) 2.06866e20i 1.66205i
\(83\) −1.71105e20 −1.21044 −0.605220 0.796058i \(-0.706915\pi\)
−0.605220 + 0.796058i \(0.706915\pi\)
\(84\) 2.08787e20 + 1.45651e20i 1.30248 + 0.908614i
\(85\) 1.41930e20 0.781946
\(86\) 5.03549e20i 2.45362i
\(87\) −2.50321e20 1.51311e20i −1.08030 0.653009i
\(88\) −1.47382e19 −0.0564127
\(89\) −3.53288e20 −1.20098 −0.600488 0.799634i \(-0.705027\pi\)
−0.600488 + 0.799634i \(0.705027\pi\)
\(90\) 7.44636e20 3.90887e20i 2.25112 1.18169i
\(91\) 2.89679e20 + 1.89772e19i 0.779800 + 0.0510855i
\(92\) 9.32949e20i 2.23916i
\(93\) −7.48884e20 4.52677e20i −1.60451 0.969879i
\(94\) 2.91069e20i 0.557384i
\(95\) 2.53862e19i 0.0435010i
\(96\) 5.86663e20 + 3.54620e20i 0.900618 + 0.544396i
\(97\) 1.89705e20i 0.261201i 0.991435 + 0.130601i \(0.0416905\pi\)
−0.991435 + 0.130601i \(0.958309\pi\)
\(98\) −1.69765e20 + 1.29014e21i −0.209881 + 1.59500i
\(99\) 4.75077e19 2.49386e19i 0.0527952 0.0277142i
\(100\) −2.37827e21 −2.37827
\(101\) −1.79298e21 −1.61511 −0.807555 0.589792i \(-0.799210\pi\)
−0.807555 + 0.589792i \(0.799210\pi\)
\(102\) 8.38653e20 + 5.06940e20i 0.681209 + 0.411770i
\(103\) 7.07965e20i 0.519064i 0.965734 + 0.259532i \(0.0835684\pi\)
−0.965734 + 0.259532i \(0.916432\pi\)
\(104\) −1.11608e21 −0.739342
\(105\) 2.16342e21 + 1.50921e21i 1.29615 + 0.904198i
\(106\) −2.60729e21 −1.41409
\(107\) 3.36740e21i 1.65487i 0.561559 + 0.827436i \(0.310202\pi\)
−0.561559 + 0.827436i \(0.689798\pi\)
\(108\) 3.55659e21 + 2.14728e20i 1.58520 + 0.0957061i
\(109\) 2.91696e21 1.18019 0.590096 0.807333i \(-0.299090\pi\)
0.590096 + 0.807333i \(0.299090\pi\)
\(110\) −4.12398e20 −0.151598
\(111\) −1.14434e21 + 1.89314e21i −0.382529 + 0.632835i
\(112\) −1.41949e19 + 2.16680e20i −0.00431861 + 0.0659220i
\(113\) 1.25082e21i 0.346635i 0.984866 + 0.173318i \(0.0554487\pi\)
−0.984866 + 0.173318i \(0.944551\pi\)
\(114\) 9.06731e19 1.50005e20i 0.0229075 0.0378969i
\(115\) 9.66711e21i 2.22828i
\(116\) 9.52480e21i 2.00469i
\(117\) 3.59761e21 1.88852e21i 0.691931 0.363220i
\(118\) 7.14641e21i 1.25698i
\(119\) −2.00930e20 + 3.06713e21i −0.0323447 + 0.493729i
\(120\) −8.67894e21 5.24615e21i −1.27957 0.773460i
\(121\) 7.37394e21 0.996445
\(122\) −2.00329e22 −2.48294
\(123\) −4.69792e21 + 7.77198e21i −0.534444 + 0.884154i
\(124\) 2.84953e22i 2.97746i
\(125\) −8.18774e21 −0.786338
\(126\) 7.39292e21 + 1.66450e22i 0.653018 + 1.47026i
\(127\) −1.42120e22 −1.15536 −0.577680 0.816263i \(-0.696042\pi\)
−0.577680 + 0.816263i \(0.696042\pi\)
\(128\) 2.09032e22i 1.56498i
\(129\) 1.14355e22 1.89183e22i 0.788978 1.30524i
\(130\) −3.12296e22 −1.98683
\(131\) 1.04676e22 0.614470 0.307235 0.951634i \(-0.400596\pi\)
0.307235 + 0.951634i \(0.400596\pi\)
\(132\) −1.49527e21 9.03843e20i −0.0810387 0.0489854i
\(133\) 5.48597e20 + 3.59391e19i 0.0274670 + 0.00179939i
\(134\) 2.29831e22i 1.06368i
\(135\) 3.68530e22 + 2.22499e21i 1.57750 + 0.0952408i
\(136\) 1.18171e22i 0.468113i
\(137\) 1.22907e22i 0.450829i 0.974263 + 0.225414i \(0.0723736\pi\)
−0.974263 + 0.225414i \(0.927626\pi\)
\(138\) 3.45285e22 5.71220e22i 1.17340 1.94121i
\(139\) 1.09006e22i 0.343397i 0.985150 + 0.171699i \(0.0549255\pi\)
−0.985150 + 0.171699i \(0.945074\pi\)
\(140\) 5.61516e21 8.57132e22i 0.164066 2.50440i
\(141\) 6.61016e21 1.09355e22i 0.179230 0.296509i
\(142\) 6.05410e22 1.52413
\(143\) −1.99244e21 −0.0465970
\(144\) 1.41261e21 + 2.69101e21i 0.0307056 + 0.0584938i
\(145\) 9.86950e22i 1.99495i
\(146\) −6.28058e21 −0.118112
\(147\) −3.56770e22 + 4.46151e22i −0.624534 + 0.780998i
\(148\) 7.20345e22 1.17434
\(149\) 5.07250e22i 0.770488i 0.922815 + 0.385244i \(0.125883\pi\)
−0.922815 + 0.385244i \(0.874117\pi\)
\(150\) −1.45615e23 8.80199e22i −2.06181 1.24630i
\(151\) 1.27095e23 1.67831 0.839153 0.543896i \(-0.183051\pi\)
0.839153 + 0.543896i \(0.183051\pi\)
\(152\) −2.11364e21 −0.0260419
\(153\) 1.99956e22 + 3.80915e22i 0.229972 + 0.438095i
\(154\) 5.83830e20 8.91194e21i 0.00627074 0.0957204i
\(155\) 2.95265e23i 2.96298i
\(156\) −1.13232e23 6.84452e22i −1.06209 0.641999i
\(157\) 6.04275e22i 0.530015i −0.964246 0.265008i \(-0.914626\pi\)
0.964246 0.265008i \(-0.0853745\pi\)
\(158\) 1.18791e23i 0.974731i
\(159\) −9.79558e22 5.92113e22i −0.752247 0.454710i
\(160\) 2.31306e23i 1.66313i
\(161\) 2.08907e23 + 1.36857e22i 1.40696 + 0.0921712i
\(162\) 2.09814e23 + 1.44777e23i 1.32412 + 0.913675i
\(163\) 1.14916e22 0.0679844 0.0339922 0.999422i \(-0.489178\pi\)
0.0339922 + 0.999422i \(0.489178\pi\)
\(164\) 2.95727e23 1.64070
\(165\) −1.54938e22 9.36552e21i −0.0806448 0.0487473i
\(166\) 3.98628e23i 1.94730i
\(167\) −8.08026e21 −0.0370597 −0.0185299 0.999828i \(-0.505899\pi\)
−0.0185299 + 0.999828i \(0.505899\pi\)
\(168\) 1.25656e23 1.80125e23i 0.541299 0.775939i
\(169\) 9.61829e22 0.389303
\(170\) 3.30659e23i 1.25796i
\(171\) 6.81318e21 3.57649e21i 0.0243720 0.0127938i
\(172\) −7.19849e23 −2.42210
\(173\) 2.56010e22 0.0810536 0.0405268 0.999178i \(-0.487096\pi\)
0.0405268 + 0.999178i \(0.487096\pi\)
\(174\) −3.52514e23 + 5.83179e23i −1.05053 + 1.73794i
\(175\) 3.48875e22 5.32544e23i 0.0978972 1.49436i
\(176\) 1.49035e21i 0.00393917i
\(177\) 1.62294e23 2.68491e23i 0.404189 0.668667i
\(178\) 8.23064e23i 1.93207i
\(179\) 3.91102e23i 0.865632i 0.901482 + 0.432816i \(0.142480\pi\)
−0.901482 + 0.432816i \(0.857520\pi\)
\(180\) −5.58794e23 1.06450e24i −1.16651 2.22220i
\(181\) 1.49908e23i 0.295257i 0.989043 + 0.147628i \(0.0471640\pi\)
−0.989043 + 0.147628i \(0.952836\pi\)
\(182\) 4.42116e22 6.74873e23i 0.0821839 1.25451i
\(183\) −7.52636e23 4.54946e23i −1.32084 0.798405i
\(184\) −8.04879e23 −1.33396
\(185\) 7.46413e23 1.16863
\(186\) −1.05461e24 + 1.74469e24i −1.56030 + 2.58127i
\(187\) 2.10960e22i 0.0295028i
\(188\) −4.16099e23 −0.550224
\(189\) −1.00255e23 + 7.93246e23i −0.125388 + 0.992108i
\(190\) −5.91428e22 −0.0699825
\(191\) 8.64251e23i 0.967808i −0.875121 0.483904i \(-0.839218\pi\)
0.875121 0.483904i \(-0.160782\pi\)
\(192\) 7.93928e23 1.31343e24i 0.841625 1.39234i
\(193\) −9.50930e23 −0.954546 −0.477273 0.878755i \(-0.658375\pi\)
−0.477273 + 0.878755i \(0.658375\pi\)
\(194\) 4.41960e23 0.420208
\(195\) −1.17330e24 7.09221e23i −1.05693 0.638879i
\(196\) 1.84432e24 + 2.42688e23i 1.57452 + 0.207185i
\(197\) 1.85803e24i 1.50368i 0.659343 + 0.751842i \(0.270834\pi\)
−0.659343 + 0.751842i \(0.729166\pi\)
\(198\) −5.81000e22 1.10680e23i −0.0445853 0.0849345i
\(199\) 1.75406e24i 1.27670i 0.769747 + 0.638349i \(0.220382\pi\)
−0.769747 + 0.638349i \(0.779618\pi\)
\(200\) 2.05179e24i 1.41683i
\(201\) 5.21946e23 8.63477e23i 0.342032 0.565838i
\(202\) 4.17716e24i 2.59831i
\(203\) −2.13280e24 1.39722e23i −1.25963 0.0825195i
\(204\) 7.24698e23 1.19890e24i 0.406481 0.672459i
\(205\) 3.06429e24 1.63273
\(206\) 1.64936e24 0.835047
\(207\) 2.59447e24 1.36194e24i 1.24842 0.655342i
\(208\) 1.12859e23i 0.0516265i
\(209\) −3.77331e21 −0.00164129
\(210\) 3.51605e24 5.04018e24i 1.45463 2.08518i
\(211\) −4.91382e24 −1.93399 −0.966993 0.254802i \(-0.917990\pi\)
−0.966993 + 0.254802i \(0.917990\pi\)
\(212\) 3.72725e24i 1.39593i
\(213\) 2.27453e24 + 1.37488e24i 0.810784 + 0.490094i
\(214\) 7.84511e24 2.66228
\(215\) −7.45900e24 −2.41033
\(216\) 1.85251e23 3.06836e24i 0.0570160 0.944370i
\(217\) −6.38069e24 4.18006e23i −1.87086 0.122562i
\(218\) 6.79571e24i 1.89864i
\(219\) −2.35961e23 1.42631e23i −0.0628316 0.0379798i
\(220\) 5.89544e23i 0.149650i
\(221\) 1.59753e24i 0.386662i
\(222\) 4.41048e24 + 2.66600e24i 1.01808 + 0.615395i
\(223\) 6.16436e24i 1.35733i 0.734446 + 0.678667i \(0.237442\pi\)
−0.734446 + 0.678667i \(0.762558\pi\)
\(224\) 4.99853e24 + 3.27459e23i 1.05012 + 0.0687943i
\(225\) −3.47184e24 6.61382e24i −0.696054 1.32598i
\(226\) 2.91408e24 0.557651
\(227\) 6.93449e24 1.26690 0.633451 0.773783i \(-0.281638\pi\)
0.633451 + 0.773783i \(0.281638\pi\)
\(228\) −2.14439e23 1.29622e23i −0.0374101 0.0226132i
\(229\) 3.15897e24i 0.526349i −0.964748 0.263174i \(-0.915231\pi\)
0.964748 0.263174i \(-0.0847694\pi\)
\(230\) −2.25217e25 −3.58475
\(231\) 2.24324e23 3.21563e23i 0.0341153 0.0489035i
\(232\) 8.21729e24 1.19428
\(233\) 9.88048e24i 1.37259i −0.727323 0.686295i \(-0.759236\pi\)
0.727323 0.686295i \(-0.240764\pi\)
\(234\) −4.39973e24 8.38144e24i −0.584332 1.11315i
\(235\) −4.31157e24 −0.547549
\(236\) −1.02162e25 −1.24083
\(237\) 2.69774e24 4.46299e24i 0.313431 0.518523i
\(238\) 7.14556e24 + 4.68113e23i 0.794288 + 0.0520346i
\(239\) 2.66821e24i 0.283820i 0.989880 + 0.141910i \(0.0453243\pi\)
−0.989880 + 0.141910i \(0.954676\pi\)
\(240\) 5.30498e23 8.77626e23i 0.0540089 0.0893493i
\(241\) 1.85809e25i 1.81087i −0.424487 0.905434i \(-0.639545\pi\)
0.424487 0.905434i \(-0.360455\pi\)
\(242\) 1.71792e25i 1.60303i
\(243\) 4.59483e24 + 1.02041e25i 0.410586 + 0.911822i
\(244\) 2.86381e25i 2.45104i
\(245\) 1.91106e25 + 2.51470e24i 1.56686 + 0.206178i
\(246\) 1.81066e25 + 1.09449e25i 1.42239 + 0.859789i
\(247\) −2.85741e23 −0.0215107
\(248\) 2.45836e25 1.77379
\(249\) −9.05281e24 + 1.49765e25i −0.626167 + 1.03590i
\(250\) 1.90752e25i 1.26502i
\(251\) −2.27896e25 −1.44932 −0.724658 0.689108i \(-0.758002\pi\)
−0.724658 + 0.689108i \(0.758002\pi\)
\(252\) 2.37949e25 1.05686e25i 1.45137 0.644630i
\(253\) −1.43688e24 −0.0840729
\(254\) 3.31102e25i 1.85869i
\(255\) 7.50924e24 1.24229e25i 0.404505 0.669190i
\(256\) −1.72291e25 −0.890721
\(257\) 6.00249e24 0.297875 0.148937 0.988847i \(-0.452415\pi\)
0.148937 + 0.988847i \(0.452415\pi\)
\(258\) −4.40745e25 2.66417e25i −2.09981 1.26927i
\(259\) −1.05669e24 + 1.61300e25i −0.0483395 + 0.737883i
\(260\) 4.46443e25i 1.96131i
\(261\) −2.64879e25 + 1.39045e25i −1.11769 + 0.586718i
\(262\) 2.43867e25i 0.988531i
\(263\) 4.58439e23i 0.0178545i −0.999960 0.00892723i \(-0.997158\pi\)
0.999960 0.00892723i \(-0.00284166\pi\)
\(264\) −7.79768e23 + 1.29000e24i −0.0291826 + 0.0482781i
\(265\) 3.86214e25i 1.38914i
\(266\) 8.37283e22 1.27808e24i 0.00289478 0.0441876i
\(267\) −1.86917e25 + 3.09225e25i −0.621271 + 1.02780i
\(268\) −3.28556e25 −1.05001
\(269\) 2.23413e25 0.686610 0.343305 0.939224i \(-0.388453\pi\)
0.343305 + 0.939224i \(0.388453\pi\)
\(270\) 5.18361e24 8.58574e25i 0.153219 2.53780i
\(271\) 3.04586e25i 0.866029i 0.901387 + 0.433014i \(0.142550\pi\)
−0.901387 + 0.433014i \(0.857450\pi\)
\(272\) 1.19496e24 0.0326873
\(273\) 1.69873e25 2.43510e25i 0.447114 0.640926i
\(274\) 2.86340e25 0.725273
\(275\) 3.66289e24i 0.0892958i
\(276\) −8.16590e25 4.93603e25i −1.91628 1.15833i
\(277\) 2.91712e25 0.659048 0.329524 0.944147i \(-0.393112\pi\)
0.329524 + 0.944147i \(0.393112\pi\)
\(278\) 2.53955e25 0.552441
\(279\) −7.92437e25 + 4.15979e25i −1.66005 + 0.871420i
\(280\) −7.39469e25 4.84434e24i −1.49197 0.0977406i
\(281\) 3.04913e25i 0.592598i −0.955095 0.296299i \(-0.904248\pi\)
0.955095 0.296299i \(-0.0957525\pi\)
\(282\) −2.54767e25 1.53999e25i −0.477009 0.288338i
\(283\) 2.91776e25i 0.526370i −0.964745 0.263185i \(-0.915227\pi\)
0.964745 0.263185i \(-0.0847730\pi\)
\(284\) 8.65466e25i 1.50455i
\(285\) −2.22200e24 1.34313e24i −0.0372282 0.0225033i
\(286\) 4.64185e24i 0.0749631i
\(287\) −4.33810e24 + 6.62194e25i −0.0675366 + 1.03092i
\(288\) 6.20782e25 3.25871e25i 0.931790 0.489131i
\(289\) −5.21772e25 −0.755186
\(290\) 2.29932e26 3.20938
\(291\) 1.66044e25 + 1.00369e25i 0.223536 + 0.135121i
\(292\) 8.97842e24i 0.116595i
\(293\) −3.72338e25 −0.466474 −0.233237 0.972420i \(-0.574932\pi\)
−0.233237 + 0.972420i \(0.574932\pi\)
\(294\) 1.03941e26 + 8.31175e25i 1.25643 + 1.00472i
\(295\) −1.05859e26 −1.23480
\(296\) 6.21460e25i 0.699600i
\(297\) 3.30714e23 5.47769e24i 0.00359343 0.0595189i
\(298\) 1.18175e26 1.23953
\(299\) −1.08811e26 −1.10185
\(300\) −1.25829e26 + 2.08164e26i −1.23029 + 2.03532i
\(301\) 1.05597e25 1.61189e26i 0.0997017 1.52191i
\(302\) 2.96097e26i 2.69998i
\(303\) −9.48630e25 + 1.56936e26i −0.835505 + 1.38221i
\(304\) 2.13734e23i 0.00181845i
\(305\) 2.96745e26i 2.43913i
\(306\) 8.87427e25 4.65843e25i 0.704787 0.369969i
\(307\) 2.05384e26i 1.57621i −0.615543 0.788104i \(-0.711063\pi\)
0.615543 0.788104i \(-0.288937\pi\)
\(308\) −1.27401e25 8.34616e23i −0.0944908 0.00619019i
\(309\) 6.19666e25 + 3.74569e25i 0.444216 + 0.268515i
\(310\) 6.87886e26 4.76671
\(311\) 1.16711e26 0.781860 0.390930 0.920421i \(-0.372154\pi\)
0.390930 + 0.920421i \(0.372154\pi\)
\(312\) −5.90494e25 + 9.76880e25i −0.382465 + 0.632729i
\(313\) 1.15011e26i 0.720315i 0.932891 + 0.360158i \(0.117277\pi\)
−0.932891 + 0.360158i \(0.882723\pi\)
\(314\) −1.40779e26 −0.852664
\(315\) 2.46560e26 1.09510e26i 1.44432 0.641496i
\(316\) −1.69818e26 −0.962210
\(317\) 5.49826e25i 0.301372i 0.988582 + 0.150686i \(0.0481483\pi\)
−0.988582 + 0.150686i \(0.951852\pi\)
\(318\) −1.37946e26 + 2.28210e26i −0.731516 + 1.21018i
\(319\) 1.46696e25 0.0752692
\(320\) −5.17851e26 −2.57116
\(321\) 2.94741e26 + 1.78162e26i 1.41624 + 0.856075i
\(322\) 3.18839e25 4.86695e26i 0.148281 2.26345i
\(323\) 3.02542e24i 0.0136194i
\(324\) 2.06966e26 2.99940e26i 0.901939 1.30711i
\(325\) 2.77379e26i 1.17030i
\(326\) 2.67722e25i 0.109370i
\(327\) 1.54330e26 2.55315e26i 0.610519 1.01001i
\(328\) 2.55131e26i 0.977434i
\(329\) 6.10388e24 9.31733e25i 0.0226490 0.345728i
\(330\) −2.18191e25 + 3.60962e25i −0.0784224 + 0.129738i
\(331\) −2.90493e26 −1.01145 −0.505723 0.862696i \(-0.668774\pi\)
−0.505723 + 0.862696i \(0.668774\pi\)
\(332\) 5.69859e26 1.92229
\(333\) 1.05157e26 + 2.00323e26i 0.343696 + 0.654738i
\(334\) 1.88248e25i 0.0596200i
\(335\) −3.40446e26 −1.04491
\(336\) 1.82145e25 + 1.27065e25i 0.0541820 + 0.0377977i
\(337\) −5.05078e26 −1.45628 −0.728139 0.685429i \(-0.759615\pi\)
−0.728139 + 0.685429i \(0.759615\pi\)
\(338\) 2.24080e26i 0.626292i
\(339\) 1.09482e26 + 6.61785e25i 0.296651 + 0.179316i
\(340\) −4.72694e26 −1.24180
\(341\) 4.38871e25 0.111793
\(342\) −8.33224e24 1.58728e25i −0.0205820 0.0392085i
\(343\) −8.13977e25 + 4.09421e26i −0.194995 + 0.980804i
\(344\) 6.21032e26i 1.44295i
\(345\) −8.46141e26 5.11466e26i −1.90696 1.15270i
\(346\) 5.96432e25i 0.130395i
\(347\) 2.27772e26i 0.483103i 0.970388 + 0.241552i \(0.0776563\pi\)
−0.970388 + 0.241552i \(0.922344\pi\)
\(348\) 8.33685e26 + 5.03937e26i 1.71562 + 1.03704i
\(349\) 4.01953e26i 0.802616i 0.915943 + 0.401308i \(0.131444\pi\)
−0.915943 + 0.401308i \(0.868556\pi\)
\(350\) −1.24068e27 8.12782e25i −2.40406 0.157492i
\(351\) 2.50439e25 4.14808e26i 0.0470953 0.780051i
\(352\) −3.43804e25 −0.0627499
\(353\) −7.95291e26 −1.40894 −0.704469 0.709735i \(-0.748815\pi\)
−0.704469 + 0.709735i \(0.748815\pi\)
\(354\) −6.25509e26 3.78101e26i −1.07572 0.650240i
\(355\) 8.96786e26i 1.49724i
\(356\) 1.17661e27 1.90725
\(357\) 2.57828e26 + 1.79862e26i 0.405801 + 0.283089i
\(358\) 9.11160e26 1.39259
\(359\) 1.22948e26i 0.182486i −0.995829 0.0912429i \(-0.970916\pi\)
0.995829 0.0912429i \(-0.0290840\pi\)
\(360\) −9.18368e26 + 4.82086e26i −1.32386 + 0.694941i
\(361\) 7.13668e26 0.999242
\(362\) 3.49245e26 0.474996
\(363\) 3.90139e26 6.45425e26i 0.515466 0.852758i
\(364\) −9.64767e26 6.32028e25i −1.23839 0.0811282i
\(365\) 9.30334e25i 0.116028i
\(366\) −1.05990e27 + 1.75344e27i −1.28444 + 2.12490i
\(367\) 3.38582e26i 0.398722i −0.979926 0.199361i \(-0.936113\pi\)
0.979926 0.199361i \(-0.0638866\pi\)
\(368\) 8.13904e25i 0.0931475i
\(369\) 4.31707e26 + 8.22397e26i 0.480189 + 0.914755i
\(370\) 1.73894e27i 1.88003i
\(371\) −8.34610e26 5.46761e25i −0.877117 0.0574608i
\(372\) 2.49413e27 + 1.50762e27i 2.54811 + 1.54025i
\(373\) 7.10009e26 0.705215 0.352607 0.935771i \(-0.385295\pi\)
0.352607 + 0.935771i \(0.385295\pi\)
\(374\) −4.91479e25 −0.0474627
\(375\) −4.33196e26 + 7.16655e26i −0.406777 + 0.672949i
\(376\) 3.58979e26i 0.327791i
\(377\) 1.11089e27 0.986473
\(378\) 1.84804e27 + 2.33566e26i 1.59606 + 0.201719i
\(379\) −1.84776e27 −1.55215 −0.776073 0.630643i \(-0.782791\pi\)
−0.776073 + 0.630643i \(0.782791\pi\)
\(380\) 8.45478e25i 0.0690835i
\(381\) −7.51929e26 + 1.24395e27i −0.597674 + 0.988759i
\(382\) −2.01347e27 −1.55697
\(383\) 8.45726e26 0.636272 0.318136 0.948045i \(-0.396943\pi\)
0.318136 + 0.948045i \(0.396943\pi\)
\(384\) −1.82961e27 1.10594e27i −1.33931 0.809570i
\(385\) −1.32011e26 8.64819e24i −0.0940315 0.00616010i
\(386\) 2.21540e27i 1.53563i
\(387\) −1.05085e27 2.00186e27i −0.708884 1.35042i
\(388\) 6.31805e26i 0.414810i
\(389\) 1.41617e26i 0.0904992i 0.998976 + 0.0452496i \(0.0144083\pi\)
−0.998976 + 0.0452496i \(0.985592\pi\)
\(390\) −1.65229e27 + 2.73346e27i −1.02780 + 1.70033i
\(391\) 1.15209e27i 0.697637i
\(392\) 2.09373e26 1.59114e27i 0.123429 0.938004i
\(393\) 5.53821e26 9.16210e26i 0.317869 0.525864i
\(394\) 4.32869e27 2.41906
\(395\) −1.75964e27 −0.957533
\(396\) −1.58223e26 + 8.30570e25i −0.0838435 + 0.0440126i
\(397\) 2.27686e27i 1.17500i 0.809225 + 0.587498i \(0.199887\pi\)
−0.809225 + 0.587498i \(0.800113\pi\)
\(398\) 4.08648e27 2.05389
\(399\) 3.21708e25 4.61160e25i 0.0157487 0.0225754i
\(400\) −2.07480e26 −0.0989341
\(401\) 1.94142e27i 0.901784i −0.892579 0.450892i \(-0.851106\pi\)
0.892579 0.450892i \(-0.148894\pi\)
\(402\) −2.01166e27 1.21599e27i −0.910294 0.550245i
\(403\) 3.32343e27 1.46516
\(404\) 5.97147e27 2.56494
\(405\) 2.14456e27 3.10794e27i 0.897555 1.30075i
\(406\) −3.25514e26 + 4.96884e27i −0.132754 + 2.02643i
\(407\) 1.10944e26i 0.0440923i
\(408\) −1.03432e27 6.25215e26i −0.400611 0.242157i
\(409\) 2.53930e27i 0.958560i −0.877662 0.479280i \(-0.840898\pi\)
0.877662 0.479280i \(-0.159102\pi\)
\(410\) 7.13894e27i 2.62666i
\(411\) 1.07578e27 + 6.50276e26i 0.385820 + 0.233216i
\(412\) 2.35785e27i 0.824320i
\(413\) 1.49864e26 2.28761e27i 0.0510765 0.779663i
\(414\) −3.17294e27 6.04441e27i −1.05428 2.00840i
\(415\) 5.90482e27 1.91294
\(416\) −2.60352e27 −0.822396
\(417\) 9.54109e26 + 5.76729e26i 0.293880 + 0.177641i
\(418\) 8.79076e24i 0.00264044i
\(419\) −4.21573e27 −1.23488 −0.617442 0.786617i \(-0.711831\pi\)
−0.617442 + 0.786617i \(0.711831\pi\)
\(420\) −7.20520e27 5.02638e27i −2.05839 1.43595i
\(421\) −4.62166e27 −1.28776 −0.643881 0.765126i \(-0.722677\pi\)
−0.643881 + 0.765126i \(0.722677\pi\)
\(422\) 1.14478e28i 3.11131i
\(423\) −6.07429e26 1.15715e27i −0.161036 0.306771i
\(424\) 3.21559e27 0.831610
\(425\) −2.93689e27 −0.740976
\(426\) 3.20310e27 5.29902e27i 0.788441 1.30435i
\(427\) −6.41267e27 4.20100e26i −1.54009 0.100893i
\(428\) 1.12150e28i 2.62808i
\(429\) −1.05416e26 + 1.74394e26i −0.0241049 + 0.0398777i
\(430\) 1.73774e28i 3.87763i
\(431\) 6.44524e27i 1.40355i 0.712399 + 0.701775i \(0.247609\pi\)
−0.712399 + 0.701775i \(0.752391\pi\)
\(432\) 3.10277e26 + 1.87329e25i 0.0659432 + 0.00398130i
\(433\) 2.69544e27i 0.559122i 0.960128 + 0.279561i \(0.0901889\pi\)
−0.960128 + 0.279561i \(0.909811\pi\)
\(434\) −9.73838e26 + 1.48653e28i −0.197172 + 3.00975i
\(435\) 8.63855e27 + 5.22174e27i 1.70728 + 1.03200i
\(436\) −9.71483e27 −1.87425
\(437\) −2.06066e26 −0.0388108
\(438\) −3.32292e26 + 5.49725e26i −0.0611001 + 0.101081i
\(439\) 3.86249e27i 0.693409i 0.937974 + 0.346704i \(0.112699\pi\)
−0.937974 + 0.346704i \(0.887301\pi\)
\(440\) 5.08615e26 0.0891529
\(441\) 2.01747e27 + 5.48321e27i 0.345304 + 0.938491i
\(442\) −3.72181e27 −0.622044
\(443\) 7.13537e27i 1.16460i −0.812973 0.582301i \(-0.802153\pi\)
0.812973 0.582301i \(-0.197847\pi\)
\(444\) 3.81119e27 6.30502e27i 0.607490 1.00500i
\(445\) 1.21919e28 1.89798
\(446\) 1.43613e28 2.18362
\(447\) 4.43984e27 + 2.68375e27i 0.659384 + 0.398578i
\(448\) 7.33120e26 1.11908e28i 0.106354 1.62346i
\(449\) 1.43840e27i 0.203842i 0.994792 + 0.101921i \(0.0324989\pi\)
−0.994792 + 0.101921i \(0.967501\pi\)
\(450\) −1.54084e28 + 8.08843e27i −2.13317 + 1.11978i
\(451\) 4.55464e26i 0.0616027i
\(452\) 4.16583e27i 0.550488i
\(453\) 6.72433e27 1.11244e28i 0.868196 1.43630i
\(454\) 1.61554e28i 2.03813i
\(455\) −9.99680e27 6.54901e26i −1.23237 0.0807339i
\(456\) −1.11828e26 + 1.85002e26i −0.0134716 + 0.0222867i
\(457\) 4.29861e27 0.506067 0.253033 0.967458i \(-0.418572\pi\)
0.253033 + 0.967458i \(0.418572\pi\)
\(458\) −7.35954e27 −0.846765
\(459\) 4.39199e27 + 2.65165e26i 0.493888 + 0.0298183i
\(460\) 3.21960e28i 3.53870i
\(461\) 5.09154e26 0.0547003 0.0273501 0.999626i \(-0.491293\pi\)
0.0273501 + 0.999626i \(0.491293\pi\)
\(462\) −7.49153e26 5.22613e26i −0.0786737 0.0548832i
\(463\) 6.80934e27 0.699044 0.349522 0.936928i \(-0.386344\pi\)
0.349522 + 0.936928i \(0.386344\pi\)
\(464\) 8.30943e26i 0.0833936i
\(465\) 2.58439e28 + 1.56218e28i 2.53572 + 1.53277i
\(466\) −2.30188e28 −2.20816
\(467\) −1.41874e28 −1.33068 −0.665342 0.746539i \(-0.731714\pi\)
−0.665342 + 0.746539i \(0.731714\pi\)
\(468\) −1.19817e28 + 6.28965e27i −1.09885 + 0.576826i
\(469\) 4.81969e26 7.35706e27i 0.0432219 0.659766i
\(470\) 1.00448e28i 0.880872i
\(471\) −5.28909e27 3.19709e27i −0.453588 0.274180i
\(472\) 8.81374e27i 0.739213i
\(473\) 1.10868e27i 0.0909417i
\(474\) −1.03975e28 6.28498e27i −0.834175 0.504233i
\(475\) 5.25303e26i 0.0412218i
\(476\) 6.69192e26 1.02149e28i 0.0513662 0.784085i
\(477\) −1.03653e28 + 5.44111e27i −0.778282 + 0.408549i
\(478\) 6.21620e27 0.456596
\(479\) −5.73151e27 −0.411857 −0.205928 0.978567i \(-0.566021\pi\)
−0.205928 + 0.978567i \(0.566021\pi\)
\(480\) −2.02457e28 1.22379e28i −1.42331 0.860347i
\(481\) 8.40144e27i 0.577871i
\(482\) −4.32883e28 −2.91324
\(483\) 1.22507e28 1.75611e28i 0.806707 1.15640i
\(484\) −2.45586e28 −1.58244
\(485\) 6.54669e27i 0.412794i
\(486\) 2.37728e28 1.07047e28i 1.46690 0.660531i
\(487\) −1.45983e28 −0.881554 −0.440777 0.897617i \(-0.645297\pi\)
−0.440777 + 0.897617i \(0.645297\pi\)
\(488\) 2.47068e28 1.46019
\(489\) 6.07994e26 1.00583e27i 0.0351687 0.0581811i
\(490\) 5.85857e27 4.45225e28i 0.331690 2.52070i
\(491\) 5.53228e27i 0.306583i 0.988181 + 0.153292i \(0.0489874\pi\)
−0.988181 + 0.153292i \(0.951013\pi\)
\(492\) 1.56463e28 2.58843e28i 0.848744 1.40411i
\(493\) 1.17621e28i 0.624584i
\(494\) 6.65697e26i 0.0346054i
\(495\) −1.63949e27 + 8.60627e26i −0.0834359 + 0.0437986i
\(496\) 2.48593e27i 0.123860i
\(497\) 1.93796e28 + 1.26958e27i 0.945372 + 0.0619323i
\(498\) 3.48910e28 + 2.10905e28i 1.66650 + 1.00735i
\(499\) −3.09444e27 −0.144719 −0.0723597 0.997379i \(-0.523053\pi\)
−0.0723597 + 0.997379i \(0.523053\pi\)
\(500\) 2.72690e28 1.24877
\(501\) −4.27509e26 + 7.07247e26i −0.0191712 + 0.0317157i
\(502\) 5.30936e28i 2.33159i
\(503\) −1.43502e28 −0.617155 −0.308577 0.951199i \(-0.599853\pi\)
−0.308577 + 0.951199i \(0.599853\pi\)
\(504\) −9.11777e27 2.05285e28i −0.384032 0.864641i
\(505\) 6.18757e28 2.55247
\(506\) 3.34754e27i 0.135253i
\(507\) 5.08883e27 8.41868e27i 0.201388 0.333166i
\(508\) 4.73327e28 1.83482
\(509\) 1.09072e28 0.414167 0.207084 0.978323i \(-0.433603\pi\)
0.207084 + 0.978323i \(0.433603\pi\)
\(510\) −2.89418e28 1.74944e28i −1.07656 0.650749i
\(511\) −2.01046e27 1.31707e26i −0.0732614 0.00479943i
\(512\) 3.69820e27i 0.132025i
\(513\) 4.74284e25 7.85567e26i 0.00165885 0.0274758i
\(514\) 1.39841e28i 0.479207i
\(515\) 2.44318e28i 0.820313i
\(516\) −3.80857e28 + 6.30068e28i −1.25297 + 2.07284i
\(517\) 6.40856e26i 0.0206590i
\(518\) 3.75785e28 + 2.46181e27i 1.18707 + 0.0777663i
\(519\) 1.35449e27 2.24080e27i 0.0419295 0.0693658i
\(520\) 3.85158e28 1.16843
\(521\) −1.25296e28 −0.372512 −0.186256 0.982501i \(-0.559635\pi\)
−0.186256 + 0.982501i \(0.559635\pi\)
\(522\) 3.23936e28 + 6.17095e28i 0.943885 + 1.79809i
\(523\) 6.04609e28i 1.72666i 0.504639 + 0.863330i \(0.331625\pi\)
−0.504639 + 0.863330i \(0.668375\pi\)
\(524\) −3.48621e28 −0.975832
\(525\) −4.47666e28 3.12294e28i −1.22823 0.856822i
\(526\) −1.06804e27 −0.0287234
\(527\) 3.51885e28i 0.927660i
\(528\) −1.30447e26 7.88512e25i −0.00337115 0.00203775i
\(529\) −3.89989e28 −0.988026
\(530\) 8.99771e28 2.23478
\(531\) −1.49137e28 2.84105e28i −0.363157 0.691810i
\(532\) −1.82708e27 1.19694e26i −0.0436200 0.00285759i
\(533\) 3.44908e28i 0.807362i
\(534\) 7.20410e28 + 4.35466e28i 1.65347 + 0.999472i
\(535\) 1.16208e29i 2.61531i
\(536\) 2.83454e28i 0.625535i
\(537\) 3.42323e28 + 2.06924e28i 0.740809 + 0.447796i
\(538\) 5.20492e28i 1.10459i
\(539\) 3.73776e26 2.84053e27i 0.00777910 0.0591177i
\(540\) −1.22738e29 7.41024e27i −2.50520 0.151251i
\(541\) −6.04828e28 −1.21077 −0.605384 0.795934i \(-0.706980\pi\)
−0.605384 + 0.795934i \(0.706980\pi\)
\(542\) 7.09601e28 1.39323
\(543\) 1.31211e28 + 7.93132e27i 0.252681 + 0.152738i
\(544\) 2.75661e28i 0.520699i
\(545\) −1.00664e29 −1.86514
\(546\) −5.67310e28 3.95758e28i −1.03109 0.719296i
\(547\) −3.93098e28 −0.700864 −0.350432 0.936588i \(-0.613965\pi\)
−0.350432 + 0.936588i \(0.613965\pi\)
\(548\) 4.09338e28i 0.715956i
\(549\) −7.96408e28 + 4.18064e28i −1.36655 + 0.717353i
\(550\) 8.53353e27 0.143655
\(551\) 2.10380e27 0.0347467
\(552\) −4.25844e28 + 7.04493e28i −0.690065 + 1.14161i
\(553\) 2.49111e27 3.80259e28i 0.0396077 0.604596i
\(554\) 6.79609e28i 1.06025i
\(555\) 3.94911e28 6.53319e28i 0.604537 1.00011i
\(556\) 3.63042e28i 0.545345i
\(557\) 4.25859e28i 0.627750i −0.949464 0.313875i \(-0.898373\pi\)
0.949464 0.313875i \(-0.101627\pi\)
\(558\) 9.69117e28 + 1.84616e29i 1.40190 + 2.67061i
\(559\) 8.39566e28i 1.19188i
\(560\) 4.89866e26 7.47761e27i 0.00682500 0.104181i
\(561\) −1.84649e27 1.11614e27i −0.0252485 0.0152620i
\(562\) −7.10364e28 −0.953344
\(563\) 7.91241e28 1.04225 0.521123 0.853481i \(-0.325513\pi\)
0.521123 + 0.853481i \(0.325513\pi\)
\(564\) −2.20149e28 + 3.64202e28i −0.284634 + 0.470882i
\(565\) 4.31658e28i 0.547812i
\(566\) −6.79757e28 −0.846800
\(567\) 6.41268e28 + 5.07440e28i 0.784183 + 0.620530i
\(568\) −7.46659e28 −0.896324
\(569\) 3.77975e28i 0.445435i −0.974883 0.222718i \(-0.928507\pi\)
0.974883 0.222718i \(-0.0714928\pi\)
\(570\) −3.12912e27 + 5.17664e27i −0.0362023 + 0.0598911i
\(571\) −1.16410e29 −1.32224 −0.661119 0.750281i \(-0.729918\pi\)
−0.661119 + 0.750281i \(0.729918\pi\)
\(572\) 6.63576e27 0.0740002
\(573\) −7.56459e28 4.57256e28i −0.828251 0.500652i
\(574\) 1.54273e29 + 1.01066e28i 1.65850 + 0.108650i
\(575\) 2.00037e29i 2.11153i
\(576\) −7.29566e28 1.38982e29i −0.756186 1.44053i
\(577\) 2.25293e28i 0.229299i −0.993406 0.114650i \(-0.963425\pi\)
0.993406 0.114650i \(-0.0365745\pi\)
\(578\) 1.21559e29i 1.21491i
\(579\) −5.03117e28 + 8.32328e28i −0.493792 + 0.816901i
\(580\) 3.28700e29i 3.16815i
\(581\) −8.35943e27 + 1.27603e29i −0.0791275 + 1.20785i
\(582\) 2.33831e28 3.86838e28i 0.217376 0.359615i
\(583\) 5.74053e27 0.0524122
\(584\) 7.74591e27 0.0694604
\(585\) −1.24153e29 + 6.51726e28i −1.09351 + 0.574022i
\(586\) 8.67446e28i 0.750443i
\(587\) 1.72478e29 1.46566 0.732830 0.680412i \(-0.238199\pi\)
0.732830 + 0.680412i \(0.238199\pi\)
\(588\) 1.18821e29 1.48589e29i 0.991815 1.24029i
\(589\) 6.29394e27 0.0516074
\(590\) 2.46622e29i 1.98648i
\(591\) 1.62629e29 + 9.83042e28i 1.28685 + 0.777864i
\(592\) 6.28428e27 0.0488515
\(593\) 1.84171e28 0.140652 0.0703261 0.997524i \(-0.477596\pi\)
0.0703261 + 0.997524i \(0.477596\pi\)
\(594\) −1.27615e28 7.70472e26i −0.0957512 0.00578095i
\(595\) 6.93409e27 1.05846e29i 0.0511165 0.780274i
\(596\) 1.68938e29i 1.22360i
\(597\) 1.53529e29 + 9.28037e28i 1.09260 + 0.660443i
\(598\) 2.53499e29i 1.77261i
\(599\) 1.07610e29i 0.739389i −0.929153 0.369694i \(-0.879462\pi\)
0.929153 0.369694i \(-0.120538\pi\)
\(600\) 1.79589e29 + 1.08556e29i 1.21253 + 0.732935i
\(601\) 1.62804e29i 1.08015i 0.841617 + 0.540075i \(0.181604\pi\)
−0.841617 + 0.540075i \(0.818396\pi\)
\(602\) −3.75527e29 2.46011e28i −2.44837 0.160395i
\(603\) −4.79632e28 9.13695e28i −0.307310 0.585422i
\(604\) −4.23286e29 −2.66530
\(605\) −2.54474e29 −1.57475
\(606\) 3.65617e29 + 2.21005e29i 2.22364 + 1.34412i
\(607\) 3.12917e27i 0.0187046i 0.999956 + 0.00935228i \(0.00297697\pi\)
−0.999956 + 0.00935228i \(0.997023\pi\)
\(608\) −4.93057e27 −0.0289674
\(609\) −1.25072e29 + 1.79287e29i −0.722233 + 1.03530i
\(610\) 6.91333e29 3.92396
\(611\) 4.85300e28i 0.270756i
\(612\) −6.65948e28 1.26862e29i −0.365216 0.695733i
\(613\) 2.18203e29 1.17632 0.588161 0.808744i \(-0.299852\pi\)
0.588161 + 0.808744i \(0.299852\pi\)
\(614\) −4.78488e29 −2.53573
\(615\) 1.62125e29 2.68210e29i 0.844619 1.39729i
\(616\) −7.20044e26 + 1.09912e28i −0.00368775 + 0.0562921i
\(617\) 6.39451e28i 0.321968i 0.986957 + 0.160984i \(0.0514668\pi\)
−0.986957 + 0.160984i \(0.948533\pi\)
\(618\) 8.72643e28 1.44365e29i 0.431974 0.714634i
\(619\) 7.74911e28i 0.377138i 0.982060 + 0.188569i \(0.0603849\pi\)
−0.982060 + 0.188569i \(0.939615\pi\)
\(620\) 9.83369e29i 4.70548i
\(621\) 1.80608e28 2.99146e29i 0.0849720 1.40741i
\(622\) 2.71905e29i 1.25782i
\(623\) −1.72601e28 + 2.63468e29i −0.0785088 + 1.19841i
\(624\) −9.87834e27 5.97115e27i −0.0441820 0.0267067i
\(625\) −5.79489e28 −0.254862
\(626\) 2.67943e29 1.15881
\(627\) −1.99638e26 + 3.30269e26i −0.000849050 + 0.00140462i
\(628\) 2.01252e29i 0.841711i
\(629\) 8.89545e28 0.365878
\(630\) −2.55129e29 5.74417e29i −1.03201 2.32355i
\(631\) −6.62000e28 −0.263360 −0.131680 0.991292i \(-0.542037\pi\)
−0.131680 + 0.991292i \(0.542037\pi\)
\(632\) 1.46506e29i 0.573228i
\(633\) −2.59980e29 + 4.30096e29i −1.00046 + 1.65511i
\(634\) 1.28094e29 0.484834
\(635\) 4.90456e29 1.82590
\(636\) 3.26238e29 + 1.97201e29i 1.19463 + 0.722120i
\(637\) 2.83049e28 2.15104e29i 0.101952 0.774792i
\(638\) 3.41762e28i 0.121090i
\(639\) 2.40681e29 1.26342e29i 0.838846 0.440342i
\(640\) 7.21366e29i 2.47324i
\(641\) 5.35790e29i 1.80711i −0.428469 0.903556i \(-0.640947\pi\)
0.428469 0.903556i \(-0.359053\pi\)
\(642\) 4.15068e29 6.86665e29i 1.37721 2.27838i
\(643\) 7.02568e27i 0.0229336i 0.999934 + 0.0114668i \(0.00365008\pi\)
−0.999934 + 0.0114668i \(0.996350\pi\)
\(644\) −6.95757e29 4.55797e28i −2.23437 0.146376i
\(645\) −3.94639e29 + 6.52869e29i −1.24688 + 2.06276i
\(646\) −7.04840e27 −0.0219103
\(647\) 1.86087e29 0.569141 0.284571 0.958655i \(-0.408149\pi\)
0.284571 + 0.958655i \(0.408149\pi\)
\(648\) −2.58766e29 1.78555e29i −0.778698 0.537322i
\(649\) 1.57344e28i 0.0465889i
\(650\) 6.46218e29 1.88273
\(651\) −3.74176e29 + 5.36372e29i −1.07269 + 1.53768i
\(652\) −3.82722e28 −0.107965
\(653\) 1.68964e29i 0.469037i 0.972112 + 0.234518i \(0.0753513\pi\)
−0.972112 + 0.234518i \(0.924649\pi\)
\(654\) −5.94814e29 3.59547e29i −1.62486 0.982175i
\(655\) −3.61237e29 −0.971089
\(656\) 2.57992e28 0.0682520
\(657\) −2.49684e28 + 1.31069e28i −0.0650062 + 0.0341242i
\(658\) −2.17068e29 1.42204e28i −0.556191 0.0364367i
\(659\) 1.52596e29i 0.384809i −0.981316 0.192405i \(-0.938371\pi\)
0.981316 0.192405i \(-0.0616286\pi\)
\(660\) 5.16015e28 + 3.11915e28i 0.128071 + 0.0774150i
\(661\) 1.90403e29i 0.465112i −0.972583 0.232556i \(-0.925291\pi\)
0.972583 0.232556i \(-0.0747090\pi\)
\(662\) 6.76770e29i 1.62717i
\(663\) −1.39829e29 8.45221e28i −0.330906 0.200022i
\(664\) 4.91632e29i 1.14518i
\(665\) −1.89320e28 1.24026e27i −0.0434080 0.00284370i
\(666\) 4.66698e29 2.44987e29i 1.05331 0.552923i
\(667\) 8.01133e29 1.77985
\(668\) 2.69110e28 0.0588541
\(669\) 5.39552e29 + 3.26143e29i 1.16161 + 0.702156i
\(670\) 7.93146e29i 1.68100i
\(671\) 4.41070e28 0.0920282
\(672\) 2.93123e29 4.20185e29i 0.602106 0.863104i
\(673\) −9.33776e29 −1.88836 −0.944180 0.329431i \(-0.893143\pi\)
−0.944180 + 0.329431i \(0.893143\pi\)
\(674\) 1.17669e30i 2.34279i
\(675\) −7.62580e29 4.60405e28i −1.49484 0.0902507i
\(676\) −3.20334e29 −0.618247
\(677\) −5.35876e29 −1.01832 −0.509159 0.860673i \(-0.670043\pi\)
−0.509159 + 0.860673i \(0.670043\pi\)
\(678\) 1.54178e29 2.55063e29i 0.288476 0.477238i
\(679\) 1.41474e29 + 9.26813e27i 0.260642 + 0.0170749i
\(680\) 4.07805e29i 0.739791i
\(681\) 3.66889e29 6.06960e29i 0.655375 1.08422i
\(682\) 1.02245e29i 0.179848i
\(683\) 1.98799e29i 0.344347i 0.985067 + 0.172173i \(0.0550789\pi\)
−0.985067 + 0.172173i \(0.944921\pi\)
\(684\) −2.26911e28 + 1.19114e28i −0.0387049 + 0.0203176i
\(685\) 4.24152e29i 0.712476i
\(686\) 9.53839e29 + 1.89634e29i 1.57787 + 0.313699i
\(687\) −2.76498e29 1.67135e29i −0.450450 0.272283i
\(688\) −6.27996e28 −0.100758
\(689\) 4.34713e29 0.686911
\(690\) −1.19158e30 + 1.97128e30i −1.85441 + 3.06783i
\(691\) 1.59235e29i 0.244073i −0.992526 0.122036i \(-0.961058\pi\)
0.992526 0.122036i \(-0.0389424\pi\)
\(692\) −8.52631e28 −0.128720
\(693\) −1.62772e28 3.66478e28i −0.0242036 0.0544940i
\(694\) 5.30645e29 0.777194
\(695\) 3.76180e29i 0.542694i
\(696\) 4.34759e29 7.19241e29i 0.617805 1.02206i
\(697\) 3.65189e29 0.511180
\(698\) 9.36439e29 1.29121
\(699\) −8.64816e29 5.22755e29i −1.17466 0.710048i
\(700\) −1.16192e29 + 1.77362e30i −0.155469 + 2.37318i
\(701\) 1.17219e30i 1.54511i −0.634947 0.772556i \(-0.718978\pi\)
0.634947 0.772556i \(-0.281022\pi\)
\(702\) −9.66389e29 5.83454e28i −1.25491 0.0757648i
\(703\) 1.59107e28i 0.0203544i
\(704\) 7.69714e28i 0.0970100i
\(705\) −2.28116e29 + 3.77382e29i −0.283250 + 0.468593i
\(706\) 1.85281e30i 2.26663i
\(707\) −8.75972e28 + 1.33714e30i −0.105581 + 1.61166i
\(708\) −5.40515e29 + 8.94198e29i −0.641887 + 1.06190i
\(709\) −1.06385e30 −1.24479 −0.622394 0.782704i \(-0.713840\pi\)
−0.622394 + 0.782704i \(0.713840\pi\)
\(710\) −2.08926e30 −2.40869
\(711\) −2.47904e29 4.72254e29i −0.281613 0.536469i
\(712\) 1.01509e30i 1.13623i
\(713\) 2.39674e30 2.64351
\(714\) 4.19029e29 6.00668e29i 0.455421 0.652835i
\(715\) 6.87590e28 0.0736404
\(716\) 1.30255e30i 1.37470i
\(717\) 2.33543e29 + 1.41169e29i 0.242893 + 0.146821i
\(718\) −2.86434e29 −0.293575
\(719\) 6.67357e29 0.674070 0.337035 0.941492i \(-0.390576\pi\)
0.337035 + 0.941492i \(0.390576\pi\)
\(720\) −4.87491e28 9.28666e28i −0.0485261 0.0924418i
\(721\) 5.27973e29 + 3.45880e28i 0.517954 + 0.0339317i
\(722\) 1.66265e30i 1.60753i
\(723\) −1.62634e30 9.83073e29i −1.54974 0.936772i
\(724\) 4.99263e29i 0.468894i
\(725\) 2.04224e30i 1.89042i
\(726\) −1.50366e30 9.08917e29i −1.37188 0.829258i
\(727\) 6.90567e29i 0.621004i 0.950573 + 0.310502i \(0.100497\pi\)
−0.950573 + 0.310502i \(0.899503\pi\)
\(728\) −5.45267e28 + 8.32329e29i −0.0483314 + 0.737760i
\(729\) 1.13625e30 + 1.37703e29i 0.992736 + 0.120311i
\(730\) 2.16742e29 0.186661
\(731\) −8.88933e29 −0.754634
\(732\) 2.50663e30 + 1.51518e30i 2.09760 + 1.26794i
\(733\) 4.20731e29i 0.347066i 0.984828 + 0.173533i \(0.0555184\pi\)
−0.984828 + 0.173533i \(0.944482\pi\)
\(734\) −7.88802e29 −0.641445
\(735\) 1.23121e30 1.53966e30i 0.986994 1.23426i
\(736\) −1.87757e30 −1.48381
\(737\) 5.06026e28i 0.0394243i
\(738\) 1.91596e30 1.00576e30i 1.47162 0.772506i
\(739\) 1.25107e30 0.947357 0.473678 0.880698i \(-0.342926\pi\)
0.473678 + 0.880698i \(0.342926\pi\)
\(740\) −2.48590e30 −1.85588
\(741\) −1.51179e28 + 2.50102e28i −0.0111276 + 0.0184089i
\(742\) −1.27380e29 + 1.94441e30i −0.0924403 + 1.41107i
\(743\) 2.36025e29i 0.168879i −0.996429 0.0844395i \(-0.973090\pi\)
0.996429 0.0844395i \(-0.0269100\pi\)
\(744\) 1.30067e30 2.15175e30i 0.917593 1.51801i
\(745\) 1.75051e30i 1.21766i
\(746\) 1.65413e30i 1.13452i
\(747\) 8.31891e29 + 1.58474e30i 0.562601 + 1.07175i
\(748\) 7.02595e28i 0.0468531i
\(749\) 2.51127e30 + 1.64516e29i 1.65133 + 0.108180i
\(750\) 1.66961e30 + 1.00923e30i 1.08261 + 0.654404i
\(751\) 1.54560e30 0.988273 0.494137 0.869384i \(-0.335484\pi\)
0.494137 + 0.869384i \(0.335484\pi\)
\(752\) −3.63004e28 −0.0228889
\(753\) −1.20575e30 + 1.99473e30i −0.749739 + 1.24033i
\(754\) 2.58806e30i 1.58699i
\(755\) −4.38604e30 −2.65234
\(756\) 3.33895e29 2.64188e30i 0.199127 1.57556i
\(757\) 1.15022e30 0.676510 0.338255 0.941055i \(-0.390163\pi\)
0.338255 + 0.941055i \(0.390163\pi\)
\(758\) 4.30476e30i 2.49702i
\(759\) −7.60224e28 + 1.25767e29i −0.0434914 + 0.0719496i
\(760\) 7.29415e28 0.0411559
\(761\) 8.64030e28 0.0480828 0.0240414 0.999711i \(-0.492347\pi\)
0.0240414 + 0.999711i \(0.492347\pi\)
\(762\) 2.89806e30 + 1.75179e30i 1.59067 + 0.961511i
\(763\) 1.42510e29 2.17535e30i 0.0771501 1.17767i
\(764\) 2.87835e30i 1.53697i
\(765\) −6.90048e29 1.31453e30i −0.363441 0.692351i
\(766\) 1.97031e30i 1.02360i
\(767\) 1.19152e30i 0.610591i
\(768\) −9.11552e29 + 1.50802e30i −0.460775 + 0.762280i
\(769\) 2.41996e30i 1.20665i 0.797494 + 0.603326i \(0.206158\pi\)
−0.797494 + 0.603326i \(0.793842\pi\)
\(770\) −2.01479e28 + 3.07550e29i −0.00991008 + 0.151274i
\(771\) 3.17579e29 5.25384e29i 0.154092 0.254921i
\(772\) 3.16704e30 1.51590
\(773\) −1.59678e29 −0.0753983 −0.0376991 0.999289i \(-0.512003\pi\)
−0.0376991 + 0.999289i \(0.512003\pi\)
\(774\) −4.66377e30 + 2.44819e30i −2.17249 + 1.14042i
\(775\) 6.10977e30i 2.80774i
\(776\) −5.45074e29 −0.247120
\(777\) 1.35592e30 + 9.45896e29i 0.606475 + 0.423080i
\(778\) 3.29929e29 0.145591
\(779\) 6.53190e28i 0.0284378i
\(780\) 3.90762e30 + 2.36204e30i 1.67849 + 1.01460i
\(781\) −1.33295e29 −0.0564908
\(782\) −2.68405e30 −1.12233
\(783\) −1.84389e29 + 3.05408e30i −0.0760742 + 1.26003i
\(784\) 1.60898e29 + 2.11721e28i 0.0654986 + 0.00861875i
\(785\) 2.08535e30i 0.837620i
\(786\) −2.13452e30 1.29025e30i −0.845985 0.511372i
\(787\) 3.10288e30i 1.21347i 0.794903 + 0.606736i \(0.207522\pi\)
−0.794903 + 0.606736i \(0.792478\pi\)
\(788\) 6.18809e30i 2.38798i
\(789\) −4.01262e28 2.42550e28i −0.0152799 0.00923621i
\(790\) 4.09947e30i 1.54043i
\(791\) 9.32816e29 + 6.11097e28i 0.345894 + 0.0226599i
\(792\) 7.16554e28 + 1.36503e29i 0.0262201 + 0.0499490i
\(793\) 3.34008e30 1.20612
\(794\) 5.30446e30 1.89028
\(795\) 3.38044e30 + 2.04337e30i 1.18883 + 0.718609i
\(796\) 5.84184e30i 2.02751i
\(797\) −2.95812e30 −1.01322 −0.506610 0.862175i \(-0.669102\pi\)
−0.506610 + 0.862175i \(0.669102\pi\)
\(798\) −1.07438e29 7.49490e28i −0.0363183 0.0253359i
\(799\) −5.13836e29 −0.171428
\(800\) 4.78629e30i 1.57599i
\(801\) 1.71764e30 + 3.27209e30i 0.558202 + 1.06337i
\(802\) −4.52296e30 −1.45075
\(803\) 1.38281e28 0.00437774
\(804\) −1.73832e30 + 2.87578e30i −0.543177 + 0.898601i
\(805\) −7.20935e30 4.72292e29i −2.22351 0.145665i
\(806\) 7.74268e30i 2.35707i
\(807\) 1.18203e30 1.95549e30i 0.355187 0.587602i
\(808\) 5.15174e30i 1.52804i
\(809\) 2.66423e30i 0.780033i −0.920808 0.390017i \(-0.872469\pi\)
0.920808 0.390017i \(-0.127531\pi\)
\(810\) −7.24065e30 4.99624e30i −2.09259 1.44394i
\(811\) 6.24009e29i 0.178021i 0.996031 + 0.0890107i \(0.0283705\pi\)
−0.996031 + 0.0890107i \(0.971629\pi\)
\(812\) 7.10322e30 + 4.65339e29i 2.00040 + 0.131048i
\(813\) 2.66597e30 + 1.61150e30i 0.741148 + 0.448001i
\(814\) −2.58469e29 −0.0709336
\(815\) −3.96573e29 −0.107440
\(816\) 6.32226e28 1.04592e29i 0.0169093 0.0279738i
\(817\) 1.58998e29i 0.0419816i
\(818\) −5.91587e30 −1.54209
\(819\) −1.23262e30 2.77522e30i −0.317211 0.714195i
\(820\) −1.02055e31 −2.59292
\(821\) 2.05593e30i 0.515711i 0.966184 + 0.257855i \(0.0830158\pi\)
−0.966184 + 0.257855i \(0.916984\pi\)
\(822\) 1.51496e30 2.50627e30i 0.375187 0.620689i
\(823\) 1.84157e30 0.450286 0.225143 0.974326i \(-0.427715\pi\)
0.225143 + 0.974326i \(0.427715\pi\)
\(824\) −2.03418e30 −0.491081
\(825\) 3.20605e29 + 1.93796e29i 0.0764194 + 0.0461932i
\(826\) −5.32951e30 3.49142e29i −1.25429 0.0821696i
\(827\) 6.46545e30i 1.50242i 0.660065 + 0.751209i \(0.270529\pi\)
−0.660065 + 0.751209i \(0.729471\pi\)
\(828\) −8.64080e30 + 4.53588e30i −1.98260 + 1.04074i
\(829\) 2.82216e30i 0.639380i −0.947522 0.319690i \(-0.896421\pi\)
0.947522 0.319690i \(-0.103579\pi\)
\(830\) 1.37566e31i 3.07745i
\(831\) 1.54339e30 2.55329e30i 0.340929 0.564014i
\(832\) 5.82880e30i 1.27141i
\(833\) 2.27752e30 + 2.99692e29i 0.490558 + 0.0645510i
\(834\) 1.34362e30 2.22281e30i 0.285781 0.472780i
\(835\) 2.78849e29 0.0585680
\(836\) 1.25669e28 0.00260652
\(837\) −5.51636e29 + 9.13688e30i −0.112989 + 1.87146i
\(838\) 9.82150e30i 1.98662i
\(839\) 6.87817e30 1.37395 0.686977 0.726679i \(-0.258937\pi\)
0.686977 + 0.726679i \(0.258937\pi\)
\(840\) −4.33639e30 + 6.21611e30i −0.855452 + 1.22627i
\(841\) −3.04621e30 −0.593474
\(842\) 1.07672e31i 2.07169i
\(843\) −2.66884e30 1.61323e30i −0.507146 0.306554i
\(844\) 1.63653e31 3.07134
\(845\) −3.31926e30 −0.615242
\(846\) −2.69583e30 + 1.41514e30i −0.493519 + 0.259066i
\(847\) 3.60258e29 5.49919e30i 0.0651385 0.994313i
\(848\) 3.25165e29i 0.0580694i
\(849\) −2.55385e30 1.54372e30i −0.450468 0.272294i
\(850\) 6.84215e30i 1.19205i
\(851\) 6.05883e30i 1.04263i
\(852\) −7.57523e30 4.57899e30i −1.28760 0.778313i
\(853\) 9.66484e30i 1.62267i −0.584583 0.811334i \(-0.698742\pi\)
0.584583 0.811334i \(-0.301258\pi\)
\(854\) −9.78718e29 + 1.49398e31i −0.162312 + 2.47763i
\(855\) −2.35122e29 + 1.23424e29i −0.0385167 + 0.0202189i
\(856\) −9.67546e30 −1.56566
\(857\) −9.77331e30 −1.56222 −0.781111 0.624392i \(-0.785347\pi\)
−0.781111 + 0.624392i \(0.785347\pi\)
\(858\) 4.06291e29 + 2.45590e29i 0.0641535 + 0.0387788i
\(859\) 1.74488e30i 0.272168i −0.990697 0.136084i \(-0.956548\pi\)
0.990697 0.136084i \(-0.0434517\pi\)
\(860\) 2.48419e31 3.82782
\(861\) 5.56652e30 + 3.88323e30i 0.847326 + 0.591099i
\(862\) 1.50156e31 2.25797
\(863\) 5.51035e30i 0.818589i −0.912402 0.409295i \(-0.865775\pi\)
0.912402 0.409295i \(-0.134225\pi\)
\(864\) 4.32143e29 7.15768e30i 0.0634210 1.05046i
\(865\) −8.83487e29 −0.128095
\(866\) 6.27963e30 0.899489
\(867\) −2.76059e30 + 4.56696e30i −0.390662 + 0.646289i
\(868\) 2.12507e31 + 1.39215e30i 2.97109 + 0.194639i
\(869\) 2.61546e29i 0.0361277i
\(870\) 1.21652e31 2.01254e31i 1.66023 2.74659i
\(871\) 3.83198e30i 0.516693i
\(872\) 8.38123e30i 1.11657i
\(873\) 1.75701e30 9.22320e29i 0.231273 0.121404i
\(874\) 4.80078e29i 0.0624370i
\(875\) −4.00017e29 + 6.10610e30i −0.0514036 + 0.784656i
\(876\) 7.85861e29 + 4.75029e29i 0.0997821 + 0.0603152i
\(877\) −1.28183e30 −0.160818 −0.0804090 0.996762i \(-0.525623\pi\)
−0.0804090 + 0.996762i \(0.525623\pi\)
\(878\) 8.99853e30 1.11552
\(879\) −1.96996e30 + 3.25900e30i −0.241310 + 0.399209i
\(880\) 5.14318e28i 0.00622535i
\(881\) −5.77654e30 −0.690909 −0.345455 0.938435i \(-0.612275\pi\)
−0.345455 + 0.938435i \(0.612275\pi\)
\(882\) 1.27744e31 4.70015e30i 1.50980 0.555509i
\(883\) 4.13098e30 0.482465 0.241232 0.970467i \(-0.422448\pi\)
0.241232 + 0.970467i \(0.422448\pi\)
\(884\) 5.32053e30i 0.614053i
\(885\) −5.60076e30 + 9.26558e30i −0.638767 + 1.05674i
\(886\) −1.66234e31 −1.87356
\(887\) 1.32995e31 1.48128 0.740641 0.671900i \(-0.234522\pi\)
0.740641 + 0.671900i \(0.234522\pi\)
\(888\) −5.43950e30 3.28801e30i −0.598719 0.361907i
\(889\) −6.94337e29 + 1.05988e31i −0.0755269 + 1.15289i
\(890\) 2.84038e31i 3.05339i
\(891\) −4.61953e29 3.18760e29i −0.0490774 0.0338647i
\(892\) 2.05302e31i 2.15557i
\(893\) 9.19065e28i 0.00953687i
\(894\) 6.25239e30 1.03436e31i 0.641213 1.06079i
\(895\) 1.34969e31i 1.36802i
\(896\) −1.55888e31 1.02124e30i −1.56163 0.102304i
\(897\) −5.75694e30 + 9.52396e30i −0.569995 + 0.942967i
\(898\) 3.35109e30 0.327932
\(899\) −2.44692e31 −2.36670
\(900\) 1.15628e31 + 2.20271e31i 1.10540 + 2.10577i
\(901\) 4.60274e30i 0.434916i
\(902\) −1.06110e30 −0.0991036
\(903\) −1.35499e31 9.45245e30i −1.25087 0.872615i
\(904\) −3.59396e30 −0.327948
\(905\) 5.17331e30i 0.466615i
\(906\) −2.59167e31 1.56658e31i −2.31065 1.39671i
\(907\) −7.06118e30 −0.622302 −0.311151 0.950361i \(-0.600714\pi\)
−0.311151 + 0.950361i \(0.600714\pi\)
\(908\) −2.30951e31 −2.01195
\(909\) 8.71726e30 + 1.66063e31i 0.750687 + 1.43005i
\(910\) −1.52574e30 + 2.32898e31i −0.129881 + 1.98258i
\(911\) 9.76514e30i 0.821742i −0.911693 0.410871i \(-0.865225\pi\)
0.911693 0.410871i \(-0.134775\pi\)
\(912\) −1.87077e28 1.13082e28i −0.00155623 0.000940694i
\(913\) 8.77670e29i 0.0721752i
\(914\) 1.00146e31i 0.814137i
\(915\) 2.59734e31 + 1.57001e31i 2.08741 + 1.26177i
\(916\) 1.05208e31i 0.835888i
\(917\) 5.11403e29 7.80636e30i 0.0401684 0.613155i
\(918\) 6.17762e29 1.02321e31i 0.0479703 0.794544i
\(919\) 1.61670e30 0.124113 0.0620565 0.998073i \(-0.480234\pi\)
0.0620565 + 0.998073i \(0.480234\pi\)
\(920\) 2.77763e31 2.10815
\(921\) −1.79768e31 1.08664e31i −1.34892 0.815380i
\(922\) 1.18619e30i 0.0879993i
\(923\) −1.00940e31 −0.740365
\(924\) −7.47102e29 + 1.07095e30i −0.0541782 + 0.0776631i
\(925\) −1.54451e31 −1.10740
\(926\) 1.58639e31i 1.12459i
\(927\) 6.55704e30 3.44204e30i 0.459590 0.241256i
\(928\) 1.91688e31 1.32844
\(929\) 4.32143e30 0.296116 0.148058 0.988979i \(-0.452698\pi\)
0.148058 + 0.988979i \(0.452698\pi\)
\(930\) 3.63946e31 6.02091e31i 2.46584 4.07935i
\(931\) 5.36040e28 4.07366e29i 0.00359108 0.0272906i
\(932\) 3.29066e31i 2.17979i
\(933\) 6.17494e30 1.02155e31i 0.404460 0.669116i
\(934\) 3.30527e31i 2.14074i
\(935\) 7.28021e29i 0.0466253i
\(936\) 5.42624e30 + 1.03369e31i 0.343639 + 0.654629i
\(937\) 5.99725e30i 0.375566i −0.982210 0.187783i \(-0.939870\pi\)
0.982210 0.187783i \(-0.0601302\pi\)
\(938\) −1.71399e31 1.12285e30i −1.06140 0.0695334i
\(939\) 1.00666e31 + 6.08497e30i 0.616446 + 0.372623i
\(940\) 1.43595e31 0.869556
\(941\) −7.31941e30 −0.438314 −0.219157 0.975690i \(-0.570331\pi\)
−0.219157 + 0.975690i \(0.570331\pi\)
\(942\) −7.44834e30 + 1.23221e31i −0.441088 + 0.729711i
\(943\) 2.48736e31i 1.45669i
\(944\) −8.91257e29 −0.0516175
\(945\) 3.45978e30 2.73748e31i 0.198159 1.56790i
\(946\) 2.58291e30 0.146303
\(947\) 1.89558e31i 1.06186i 0.847416 + 0.530929i \(0.178157\pi\)
−0.847416 + 0.530929i \(0.821843\pi\)
\(948\) −8.98472e30 + 1.48638e31i −0.497756 + 0.823460i
\(949\) 1.04716e30 0.0573744
\(950\) 1.22381e30 0.0663157
\(951\) 4.81251e30 + 2.90901e30i 0.257915 + 0.155901i
\(952\) −8.81269e30 5.77328e29i −0.467112 0.0306010i
\(953\) 9.15410e30i 0.479888i 0.970787 + 0.239944i \(0.0771291\pi\)
−0.970787 + 0.239944i \(0.922871\pi\)
\(954\) 1.26763e31 + 2.41482e31i 0.657255 + 1.25206i
\(955\) 2.98252e31i 1.52949i
\(956\) 8.88638e30i 0.450731i
\(957\) 7.76139e29 1.28400e30i 0.0389372 0.0644155i
\(958\) 1.33528e31i 0.662576i
\(959\) 9.16594e30 + 6.00470e29i 0.449865 + 0.0294711i
\(960\) −2.73984e31 + 4.53263e31i −1.33008 + 2.20041i
\(961\) −5.23789e31 −2.51513
\(962\) −1.95730e31 −0.929652
\(963\) 3.11882e31 1.63718e31i 1.46526 0.769169i
\(964\) 6.18829e31i 2.87582i
\(965\) 3.28165e31 1.50853
\(966\) −4.09125e31 2.85407e31i −1.86035 1.29779i
\(967\) 2.08330e31 0.937074 0.468537 0.883444i \(-0.344781\pi\)
0.468537 + 0.883444i \(0.344781\pi\)
\(968\) 2.11874e31i 0.942726i
\(969\) −2.64808e29 1.60069e29i −0.0116555 0.00704541i
\(970\) −1.52520e31 −0.664084
\(971\) −3.78036e31 −1.62829 −0.814144 0.580663i \(-0.802793\pi\)
−0.814144 + 0.580663i \(0.802793\pi\)
\(972\) −1.53029e31 3.39845e31i −0.652046 1.44805i
\(973\) 8.12927e30 + 5.32557e29i 0.342663 + 0.0224482i
\(974\) 3.40101e31i 1.41820i
\(975\) 2.42784e31 + 1.46755e31i 1.00155 + 0.605405i
\(976\) 2.49838e30i 0.101961i
\(977\) 4.51470e31i 1.82279i 0.411535 + 0.911394i \(0.364993\pi\)
−0.411535 + 0.911394i \(0.635007\pi\)
\(978\) −2.34331e30 1.41646e30i −0.0935991 0.0565778i
\(979\) 1.81216e30i 0.0716109i
\(980\) −6.36472e31 8.37513e30i −2.48832 0.327429i
\(981\) −1.41819e31 2.70163e31i −0.548541 1.04497i
\(982\) 1.28887e31 0.493217
\(983\) 6.86801e30 0.260027 0.130014 0.991512i \(-0.458498\pi\)
0.130014 + 0.991512i \(0.458498\pi\)
\(984\) −2.23310e31 1.34984e31i −0.836489 0.505632i
\(985\) 6.41203e31i 2.37638i
\(986\) 2.74024e31 1.00480
\(987\) −7.83231e30 5.46386e30i −0.284158 0.198230i
\(988\) 9.51649e29 0.0341609
\(989\) 6.05467e31i 2.15045i
\(990\) 2.00502e30 + 3.81955e30i 0.0704612 + 0.134228i
\(991\) −3.29436e31 −1.14551 −0.572754 0.819727i \(-0.694125\pi\)
−0.572754 + 0.819727i \(0.694125\pi\)
\(992\) 5.73471e31 1.97305
\(993\) −1.53694e31 + 2.54262e31i −0.523226 + 0.865596i
\(994\) 2.95776e30 4.51491e31i 0.0996338 1.52087i
\(995\) 6.05325e31i 2.01765i
\(996\) 3.01500e31 4.98785e31i 0.994408 1.64509i
\(997\) 1.34350e31i 0.438467i 0.975672 + 0.219234i \(0.0703557\pi\)
−0.975672 + 0.219234i \(0.929644\pi\)
\(998\) 7.20920e30i 0.232818i
\(999\) 2.30975e31 + 1.39450e30i 0.738121 + 0.0445638i
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 21.22.c.b.20.5 52
3.2 odd 2 inner 21.22.c.b.20.48 yes 52
7.6 odd 2 inner 21.22.c.b.20.47 yes 52
21.20 even 2 inner 21.22.c.b.20.6 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.22.c.b.20.5 52 1.1 even 1 trivial
21.22.c.b.20.6 yes 52 21.20 even 2 inner
21.22.c.b.20.47 yes 52 7.6 odd 2 inner
21.22.c.b.20.48 yes 52 3.2 odd 2 inner