Properties

Label 21.22.c.b.20.13
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 20.13
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2426.55i q^{2} +(100608. + 18395.7i) q^{3} -3.79100e6 q^{4} -2.12980e7 q^{5} +(4.46381e7 - 2.44130e8i) q^{6} +(5.03992e8 + 5.51850e8i) q^{7} +4.11022e9i q^{8} +(9.78355e9 + 3.70150e9i) q^{9} +O(q^{10})\) \(q-2426.55i q^{2} +(100608. + 18395.7i) q^{3} -3.79100e6 q^{4} -2.12980e7 q^{5} +(4.46381e7 - 2.44130e8i) q^{6} +(5.03992e8 + 5.51850e8i) q^{7} +4.11022e9i q^{8} +(9.78355e9 + 3.70150e9i) q^{9} +5.16808e10i q^{10} -1.35194e11i q^{11} +(-3.81405e11 - 6.97380e10i) q^{12} -6.90926e11i q^{13} +(1.33909e12 - 1.22296e12i) q^{14} +(-2.14275e12 - 3.91792e11i) q^{15} +2.02335e12 q^{16} +7.37208e12 q^{17} +(8.98188e12 - 2.37403e13i) q^{18} -6.66819e11i q^{19} +8.07410e13 q^{20} +(4.05539e13 + 6.47917e13i) q^{21} -3.28056e14 q^{22} -1.94024e13i q^{23} +(-7.56102e13 + 4.13520e14i) q^{24} -2.32304e13 q^{25} -1.67657e15 q^{26} +(9.16211e14 + 5.52375e14i) q^{27} +(-1.91063e15 - 2.09206e15i) q^{28} +8.36096e14i q^{29} +(-9.50703e14 + 5.19950e15i) q^{30} +6.31855e14i q^{31} +3.70999e15i q^{32} +(2.48699e15 - 1.36016e16i) q^{33} -1.78887e16i q^{34} +(-1.07340e16 - 1.17533e16i) q^{35} +(-3.70895e16 - 1.40324e16i) q^{36} -4.54005e16 q^{37} -1.61807e15 q^{38} +(1.27101e16 - 6.95126e16i) q^{39} -8.75396e16i q^{40} +1.81592e16 q^{41} +(1.57220e17 - 9.84062e16i) q^{42} -2.33482e17 q^{43} +5.12521e17i q^{44} +(-2.08371e17 - 7.88347e16i) q^{45} -4.70810e16 q^{46} -4.03473e17 q^{47} +(2.03565e17 + 3.72209e16i) q^{48} +(-5.05306e16 + 5.56255e17i) q^{49} +5.63699e16i q^{50} +(7.41689e17 + 1.35614e17i) q^{51} +2.61930e18i q^{52} -1.74197e18i q^{53} +(1.34037e18 - 2.22323e18i) q^{54} +2.87937e18i q^{55} +(-2.26822e18 + 2.07152e18i) q^{56} +(1.22666e16 - 6.70873e16i) q^{57} +2.02883e18 q^{58} +2.02108e18 q^{59} +(8.12318e18 + 1.48528e18i) q^{60} -3.65717e18i q^{61} +1.53323e18 q^{62} +(2.88816e18 + 7.26458e18i) q^{63} +1.32458e19 q^{64} +1.47154e19i q^{65} +(-3.30050e19 - 6.03480e18i) q^{66} -2.52039e19 q^{67} -2.79476e19 q^{68} +(3.56920e17 - 1.95204e18i) q^{69} +(-2.85200e19 + 2.60467e19i) q^{70} +5.48009e18i q^{71} +(-1.52140e19 + 4.02125e19i) q^{72} -5.62964e19i q^{73} +1.10167e20i q^{74} +(-2.33717e18 - 4.27340e17i) q^{75} +2.52791e18i q^{76} +(7.46068e19 - 6.81367e19i) q^{77} +(-1.68676e20 - 3.08416e19i) q^{78} +8.73500e19 q^{79} -4.30934e19 q^{80} +(8.20168e19 + 7.24276e19i) q^{81} -4.40642e19i q^{82} -2.61893e20 q^{83} +(-1.53740e20 - 2.45626e20i) q^{84} -1.57011e20 q^{85} +5.66557e20i q^{86} +(-1.53805e19 + 8.41179e19i) q^{87} +5.55677e20 q^{88} +2.02022e20 q^{89} +(-1.91297e20 + 5.05622e20i) q^{90} +(3.81288e20 - 3.48221e20i) q^{91} +7.35546e19i q^{92} +(-1.16234e19 + 6.35696e19i) q^{93} +9.79048e20i q^{94} +1.42019e19i q^{95} +(-6.82478e19 + 3.73254e20i) q^{96} -9.52519e20i q^{97} +(1.34978e21 + 1.22615e20i) q^{98} +(5.00421e20 - 1.32268e21i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2426.55i 1.67562i −0.545964 0.837808i \(-0.683837\pi\)
0.545964 0.837808i \(-0.316163\pi\)
\(3\) 100608. + 18395.7i 0.983692 + 0.179863i
\(4\) −3.79100e6 −1.80769
\(5\) −2.12980e7 −0.975337 −0.487668 0.873029i \(-0.662153\pi\)
−0.487668 + 0.873029i \(0.662153\pi\)
\(6\) 4.46381e7 2.44130e8i 0.301382 1.64829i
\(7\) 5.03992e8 + 5.51850e8i 0.674363 + 0.738400i
\(8\) 4.11022e9i 1.35338i
\(9\) 9.78355e9 + 3.70150e9i 0.935298 + 0.353860i
\(10\) 5.16808e10i 1.63429i
\(11\) 1.35194e11i 1.57157i −0.618498 0.785787i \(-0.712258\pi\)
0.618498 0.785787i \(-0.287742\pi\)
\(12\) −3.81405e11 6.97380e10i −1.77821 0.325137i
\(13\) 6.90926e11i 1.39004i −0.718992 0.695019i \(-0.755396\pi\)
0.718992 0.695019i \(-0.244604\pi\)
\(14\) 1.33909e12 1.22296e12i 1.23727 1.12997i
\(15\) −2.14275e12 3.91792e11i −0.959431 0.175427i
\(16\) 2.02335e12 0.460056
\(17\) 7.37208e12 0.886903 0.443452 0.896298i \(-0.353754\pi\)
0.443452 + 0.896298i \(0.353754\pi\)
\(18\) 8.98188e12 2.37403e13i 0.592934 1.56720i
\(19\) 6.66819e11i 0.0249514i −0.999922 0.0124757i \(-0.996029\pi\)
0.999922 0.0124757i \(-0.00397124\pi\)
\(20\) 8.07410e13 1.76311
\(21\) 4.05539e13 + 6.47917e13i 0.530555 + 0.847651i
\(22\) −3.28056e14 −2.63335
\(23\) 1.94024e13i 0.0976593i −0.998807 0.0488296i \(-0.984451\pi\)
0.998807 0.0488296i \(-0.0155491\pi\)
\(24\) −7.56102e13 + 4.13520e14i −0.243423 + 1.33131i
\(25\) −2.32304e13 −0.0487178
\(26\) −1.67657e15 −2.32917
\(27\) 9.16211e14 + 5.52375e14i 0.856399 + 0.516315i
\(28\) −1.91063e15 2.09206e15i −1.21904 1.33480i
\(29\) 8.36096e14i 0.369043i 0.982828 + 0.184522i \(0.0590736\pi\)
−0.982828 + 0.184522i \(0.940926\pi\)
\(30\) −9.50703e14 + 5.19950e15i −0.293949 + 1.60764i
\(31\) 6.31855e14i 0.138459i 0.997601 + 0.0692293i \(0.0220540\pi\)
−0.997601 + 0.0692293i \(0.977946\pi\)
\(32\) 3.70999e15i 0.582503i
\(33\) 2.48699e15 1.36016e16i 0.282668 1.54594i
\(34\) 1.78887e16i 1.48611i
\(35\) −1.07340e16 1.17533e16i −0.657732 0.720188i
\(36\) −3.70895e16 1.40324e16i −1.69073 0.639670i
\(37\) −4.54005e16 −1.55218 −0.776092 0.630620i \(-0.782801\pi\)
−0.776092 + 0.630620i \(0.782801\pi\)
\(38\) −1.61807e15 −0.0418090
\(39\) 1.27101e16 6.95126e16i 0.250017 1.36737i
\(40\) 8.75396e16i 1.32000i
\(41\) 1.81592e16 0.211284 0.105642 0.994404i \(-0.466310\pi\)
0.105642 + 0.994404i \(0.466310\pi\)
\(42\) 1.57220e17 9.84062e16i 1.42034 0.889006i
\(43\) −2.33482e17 −1.64754 −0.823768 0.566927i \(-0.808132\pi\)
−0.823768 + 0.566927i \(0.808132\pi\)
\(44\) 5.12521e17i 2.84092i
\(45\) −2.08371e17 7.88347e16i −0.912231 0.345133i
\(46\) −4.70810e16 −0.163640
\(47\) −4.03473e17 −1.11889 −0.559444 0.828868i \(-0.688985\pi\)
−0.559444 + 0.828868i \(0.688985\pi\)
\(48\) 2.03565e17 + 3.72209e16i 0.452553 + 0.0827472i
\(49\) −5.05306e16 + 5.56255e17i −0.0904681 + 0.995899i
\(50\) 5.63699e16i 0.0816323i
\(51\) 7.41689e17 + 1.35614e17i 0.872439 + 0.159521i
\(52\) 2.61930e18i 2.51276i
\(53\) 1.74197e18i 1.36818i −0.729397 0.684091i \(-0.760199\pi\)
0.729397 0.684091i \(-0.239801\pi\)
\(54\) 1.34037e18 2.22323e18i 0.865146 1.43500i
\(55\) 2.87937e18i 1.53281i
\(56\) −2.26822e18 + 2.07152e18i −0.999336 + 0.912670i
\(57\) 1.22666e16 6.70873e16i 0.00448784 0.0245445i
\(58\) 2.02883e18 0.618375
\(59\) 2.02108e18 0.514798 0.257399 0.966305i \(-0.417134\pi\)
0.257399 + 0.966305i \(0.417134\pi\)
\(60\) 8.12318e18 + 1.48528e18i 1.73435 + 0.317118i
\(61\) 3.65717e18i 0.656420i −0.944605 0.328210i \(-0.893555\pi\)
0.944605 0.328210i \(-0.106445\pi\)
\(62\) 1.53323e18 0.232003
\(63\) 2.88816e18 + 7.26458e18i 0.369441 + 0.929254i
\(64\) 1.32458e19 1.43611
\(65\) 1.47154e19i 1.35575i
\(66\) −3.30050e19 6.03480e18i −2.59041 0.473644i
\(67\) −2.52039e19 −1.68920 −0.844602 0.535395i \(-0.820163\pi\)
−0.844602 + 0.535395i \(0.820163\pi\)
\(68\) −2.79476e19 −1.60325
\(69\) 3.56920e17 1.95204e18i 0.0175653 0.0960666i
\(70\) −2.85200e19 + 2.60467e19i −1.20676 + 1.10211i
\(71\) 5.48009e18i 0.199791i 0.994998 + 0.0998953i \(0.0318508\pi\)
−0.994998 + 0.0998953i \(0.968149\pi\)
\(72\) −1.52140e19 + 4.02125e19i −0.478907 + 1.26581i
\(73\) 5.62964e19i 1.53317i −0.642143 0.766585i \(-0.721954\pi\)
0.642143 0.766585i \(-0.278046\pi\)
\(74\) 1.10167e20i 2.60086i
\(75\) −2.33717e18 4.27340e17i −0.0479233 0.00876254i
\(76\) 2.52791e18i 0.0451044i
\(77\) 7.46068e19 6.81367e19i 1.16045 1.05981i
\(78\) −1.68676e20 3.08416e19i −2.29118 0.418932i
\(79\) 8.73500e19 1.03796 0.518978 0.854788i \(-0.326313\pi\)
0.518978 + 0.854788i \(0.326313\pi\)
\(80\) −4.30934e19 −0.448710
\(81\) 8.20168e19 + 7.24276e19i 0.749566 + 0.661929i
\(82\) 4.40642e19i 0.354030i
\(83\) −2.61893e20 −1.85270 −0.926348 0.376669i \(-0.877070\pi\)
−0.926348 + 0.376669i \(0.877070\pi\)
\(84\) −1.53740e20 2.45626e20i −0.959079 1.53229i
\(85\) −1.57011e20 −0.865029
\(86\) 5.66557e20i 2.76064i
\(87\) −1.53805e19 + 8.41179e19i −0.0663773 + 0.363025i
\(88\) 5.55677e20 2.12694
\(89\) 2.02022e20 0.686756 0.343378 0.939197i \(-0.388429\pi\)
0.343378 + 0.939197i \(0.388429\pi\)
\(90\) −1.91297e20 + 5.05622e20i −0.578310 + 1.52855i
\(91\) 3.81288e20 3.48221e20i 1.02640 0.937390i
\(92\) 7.35546e19i 0.176538i
\(93\) −1.16234e19 + 6.35696e19i −0.0249036 + 0.136200i
\(94\) 9.79048e20i 1.87483i
\(95\) 1.42019e19i 0.0243360i
\(96\) −6.82478e19 + 3.73254e20i −0.104771 + 0.573003i
\(97\) 9.52519e20i 1.31151i −0.754975 0.655753i \(-0.772351\pi\)
0.754975 0.655753i \(-0.227649\pi\)
\(98\) 1.34978e21 + 1.22615e20i 1.66875 + 0.151590i
\(99\) 5.00421e20 1.32268e21i 0.556117 1.46989i
\(100\) 8.80667e19 0.0880667
\(101\) −6.73540e20 −0.606721 −0.303361 0.952876i \(-0.598109\pi\)
−0.303361 + 0.952876i \(0.598109\pi\)
\(102\) 3.29075e20 1.79975e21i 0.267297 1.46187i
\(103\) 1.08886e21i 0.798325i 0.916880 + 0.399162i \(0.130699\pi\)
−0.916880 + 0.399162i \(0.869301\pi\)
\(104\) 2.83986e21 1.88125
\(105\) −8.63719e20 1.37994e21i −0.517470 0.826745i
\(106\) −4.22698e21 −2.29255
\(107\) 8.35706e19i 0.0410699i 0.999789 + 0.0205349i \(0.00653694\pi\)
−0.999789 + 0.0205349i \(0.993463\pi\)
\(108\) −3.47336e21 2.09406e21i −1.54810 0.933338i
\(109\) −1.04792e21 −0.423983 −0.211992 0.977271i \(-0.567995\pi\)
−0.211992 + 0.977271i \(0.567995\pi\)
\(110\) 6.98694e21 2.56841
\(111\) −4.56765e21 8.35173e20i −1.52687 0.279181i
\(112\) 1.01975e21 + 1.11658e21i 0.310245 + 0.339705i
\(113\) 2.30241e21i 0.638055i 0.947745 + 0.319027i \(0.103356\pi\)
−0.947745 + 0.319027i \(0.896644\pi\)
\(114\) −1.62791e20 2.97655e19i −0.0411272 0.00751990i
\(115\) 4.13234e20i 0.0952507i
\(116\) 3.16964e21i 0.667116i
\(117\) 2.55746e21 6.75971e21i 0.491879 1.30010i
\(118\) 4.90425e21i 0.862604i
\(119\) 3.71547e21 + 4.06828e21i 0.598095 + 0.654889i
\(120\) 1.61035e21 8.80718e21i 0.237420 1.29848i
\(121\) −1.08772e22 −1.46984
\(122\) −8.87431e21 −1.09991
\(123\) 1.82696e21 + 3.34050e20i 0.207838 + 0.0380022i
\(124\) 2.39536e21i 0.250290i
\(125\) 1.06505e22 1.02285
\(126\) 1.76279e22 7.00826e21i 1.55707 0.619041i
\(127\) 4.04865e21 0.329133 0.164566 0.986366i \(-0.447378\pi\)
0.164566 + 0.986366i \(0.447378\pi\)
\(128\) 2.43611e22i 1.82386i
\(129\) −2.34902e22 4.29506e21i −1.62067 0.296331i
\(130\) 3.57076e22 2.27173
\(131\) 3.00868e22 1.76615 0.883074 0.469233i \(-0.155470\pi\)
0.883074 + 0.469233i \(0.155470\pi\)
\(132\) −9.42817e21 + 5.15637e22i −0.510977 + 2.79459i
\(133\) 3.67984e20 3.36071e20i 0.0184241 0.0168263i
\(134\) 6.11585e22i 2.83046i
\(135\) −1.95135e22 1.17645e22i −0.835277 0.503581i
\(136\) 3.03008e22i 1.20032i
\(137\) 4.47790e21i 0.164251i 0.996622 + 0.0821256i \(0.0261709\pi\)
−0.996622 + 0.0821256i \(0.973829\pi\)
\(138\) −4.73672e21 8.66086e20i −0.160971 0.0294327i
\(139\) 1.92513e22i 0.606464i −0.952917 0.303232i \(-0.901934\pi\)
0.952917 0.303232i \(-0.0980658\pi\)
\(140\) 4.06928e22 + 4.45569e22i 1.18898 + 1.30188i
\(141\) −4.05926e22 7.42216e21i −1.10064 0.201247i
\(142\) 1.32977e22 0.334772
\(143\) −9.34092e22 −2.18455
\(144\) 1.97955e22 + 7.48943e21i 0.430290 + 0.162795i
\(145\) 1.78072e22i 0.359941i
\(146\) −1.36606e23 −2.56901
\(147\) −1.53165e22 + 5.50342e22i −0.268118 + 0.963386i
\(148\) 1.72114e23 2.80587
\(149\) 3.14380e22i 0.477528i −0.971078 0.238764i \(-0.923258\pi\)
0.971078 0.238764i \(-0.0767422\pi\)
\(150\) −1.03696e21 + 5.67126e21i −0.0146827 + 0.0803010i
\(151\) −9.72543e22 −1.28425 −0.642127 0.766598i \(-0.721948\pi\)
−0.642127 + 0.766598i \(0.721948\pi\)
\(152\) 2.74077e21 0.0337688
\(153\) 7.21251e22 + 2.72877e22i 0.829519 + 0.313840i
\(154\) −1.65337e23 1.81037e23i −1.77584 1.94447i
\(155\) 1.34573e22i 0.135044i
\(156\) −4.81838e22 + 2.63523e23i −0.451953 + 2.47178i
\(157\) 6.32705e22i 0.554952i −0.960733 0.277476i \(-0.910502\pi\)
0.960733 0.277476i \(-0.0894979\pi\)
\(158\) 2.11959e23i 1.73922i
\(159\) 3.20447e22 1.75256e23i 0.246086 1.34587i
\(160\) 7.90156e22i 0.568137i
\(161\) 1.07072e22 9.77866e21i 0.0721116 0.0658578i
\(162\) 1.75749e23 1.99018e23i 1.10914 1.25599i
\(163\) −1.30386e23 −0.771367 −0.385684 0.922631i \(-0.626034\pi\)
−0.385684 + 0.922631i \(0.626034\pi\)
\(164\) −6.88415e22 −0.381936
\(165\) −5.29679e22 + 2.89687e23i −0.275697 + 1.50782i
\(166\) 6.35497e23i 3.10441i
\(167\) −1.36451e22 −0.0625827 −0.0312914 0.999510i \(-0.509962\pi\)
−0.0312914 + 0.999510i \(0.509962\pi\)
\(168\) −2.66308e23 + 1.66685e23i −1.14719 + 0.718042i
\(169\) −2.30315e23 −0.932204
\(170\) 3.80995e23i 1.44946i
\(171\) 2.46823e21 6.52386e21i 0.00882930 0.0233370i
\(172\) 8.85132e23 2.97824
\(173\) −1.99065e23 −0.630248 −0.315124 0.949050i \(-0.602046\pi\)
−0.315124 + 0.949050i \(0.602046\pi\)
\(174\) 2.04116e23 + 3.73217e22i 0.608290 + 0.111223i
\(175\) −1.17080e22 1.28197e22i −0.0328535 0.0359732i
\(176\) 2.73545e23i 0.723012i
\(177\) 2.03336e23 + 3.71791e22i 0.506403 + 0.0925933i
\(178\) 4.90216e23i 1.15074i
\(179\) 5.24603e23i 1.16111i −0.814220 0.580556i \(-0.802835\pi\)
0.814220 0.580556i \(-0.197165\pi\)
\(180\) 7.89933e23 + 2.98863e23i 1.64903 + 0.623893i
\(181\) 4.30309e23i 0.847531i 0.905772 + 0.423766i \(0.139292\pi\)
−0.905772 + 0.423766i \(0.860708\pi\)
\(182\) −8.44977e23 9.25214e23i −1.57071 1.71986i
\(183\) 6.72760e22 3.67940e23i 0.118066 0.645714i
\(184\) 7.97482e22 0.132170
\(185\) 9.66943e23 1.51390
\(186\) 1.54255e23 + 2.82048e22i 0.228220 + 0.0417289i
\(187\) 9.96661e23i 1.39383i
\(188\) 1.52957e24 2.02261
\(189\) 1.56935e23 + 7.84003e23i 0.196277 + 0.980548i
\(190\) 3.44617e22 0.0407779
\(191\) 1.08992e24i 1.22052i −0.792200 0.610261i \(-0.791064\pi\)
0.792200 0.610261i \(-0.208936\pi\)
\(192\) 1.33263e24 + 2.43665e23i 1.41269 + 0.258303i
\(193\) 8.70767e23 0.874078 0.437039 0.899443i \(-0.356027\pi\)
0.437039 + 0.899443i \(0.356027\pi\)
\(194\) −2.31134e24 −2.19758
\(195\) −2.70699e23 + 1.48048e24i −0.243850 + 1.33364i
\(196\) 1.91562e23 2.10877e24i 0.163538 1.80028i
\(197\) 1.30581e24i 1.05678i 0.849002 + 0.528389i \(0.177204\pi\)
−0.849002 + 0.528389i \(0.822796\pi\)
\(198\) −3.20955e24 1.21430e24i −2.46297 0.931839i
\(199\) 2.13981e24i 1.55746i −0.627357 0.778732i \(-0.715863\pi\)
0.627357 0.778732i \(-0.284137\pi\)
\(200\) 9.54822e22i 0.0659337i
\(201\) −2.53571e24 4.63642e23i −1.66166 0.303826i
\(202\) 1.63438e24i 1.01663i
\(203\) −4.61399e23 + 4.21385e23i −0.272501 + 0.248869i
\(204\) −2.81175e24 5.14114e23i −1.57710 0.288365i
\(205\) −3.86755e23 −0.206073
\(206\) 2.64217e24 1.33769
\(207\) 7.18180e22 1.89825e23i 0.0345577 0.0913406i
\(208\) 1.39798e24i 0.639495i
\(209\) −9.01500e22 −0.0392130
\(210\) −3.34849e24 + 2.09586e24i −1.38531 + 0.867081i
\(211\) 3.50234e24 1.37845 0.689227 0.724546i \(-0.257950\pi\)
0.689227 + 0.724546i \(0.257950\pi\)
\(212\) 6.60381e24i 2.47325i
\(213\) −1.00810e23 + 5.51340e23i −0.0359350 + 0.196532i
\(214\) 2.02788e23 0.0688174
\(215\) 4.97272e24 1.60690
\(216\) −2.27038e24 + 3.76583e24i −0.698771 + 1.15903i
\(217\) −3.48689e23 + 3.18450e23i −0.102238 + 0.0933713i
\(218\) 2.54283e24i 0.710433i
\(219\) 1.03561e24 5.66386e24i 0.275761 1.50817i
\(220\) 1.09157e25i 2.77085i
\(221\) 5.09356e24i 1.23283i
\(222\) −2.02659e24 + 1.10837e25i −0.467800 + 2.55845i
\(223\) 6.84362e24i 1.50690i 0.657505 + 0.753450i \(0.271612\pi\)
−0.657505 + 0.753450i \(0.728388\pi\)
\(224\) −2.04736e24 + 1.86980e24i −0.430120 + 0.392819i
\(225\) −2.27276e23 8.59875e22i −0.0455657 0.0172393i
\(226\) 5.58691e24 1.06914
\(227\) −8.94973e23 −0.163508 −0.0817539 0.996653i \(-0.526052\pi\)
−0.0817539 + 0.996653i \(0.526052\pi\)
\(228\) −4.65026e22 + 2.54328e23i −0.00811263 + 0.0443689i
\(229\) 6.05322e24i 1.00859i 0.863532 + 0.504294i \(0.168247\pi\)
−0.863532 + 0.504294i \(0.831753\pi\)
\(230\) 1.00273e24 0.159604
\(231\) 8.75946e24 5.48265e24i 1.33215 0.833805i
\(232\) −3.43654e24 −0.499456
\(233\) 1.60887e24i 0.223504i −0.993736 0.111752i \(-0.964354\pi\)
0.993736 0.111752i \(-0.0356462\pi\)
\(234\) −1.64028e25 6.20582e24i −2.17847 0.824200i
\(235\) 8.59319e24 1.09129
\(236\) −7.66191e24 −0.930596
\(237\) 8.78811e24 + 1.60686e24i 1.02103 + 0.186690i
\(238\) 9.87189e24 9.01577e24i 1.09734 1.00218i
\(239\) 1.54728e25i 1.64585i 0.568151 + 0.822924i \(0.307659\pi\)
−0.568151 + 0.822924i \(0.692341\pi\)
\(240\) −4.33553e24 7.92731e23i −0.441392 0.0807064i
\(241\) 7.68657e24i 0.749124i 0.927202 + 0.374562i \(0.122207\pi\)
−0.927202 + 0.374562i \(0.877793\pi\)
\(242\) 2.63941e25i 2.46289i
\(243\) 6.91918e24 + 8.79555e24i 0.618285 + 0.785954i
\(244\) 1.38643e25i 1.18660i
\(245\) 1.07620e24 1.18472e25i 0.0882369 0.971337i
\(246\) 8.10591e23 4.43321e24i 0.0636771 0.348257i
\(247\) −4.60723e23 −0.0346834
\(248\) −2.59706e24 −0.187387
\(249\) −2.63485e25 4.81770e24i −1.82248 0.333232i
\(250\) 2.58439e25i 1.71391i
\(251\) 3.13427e24 0.199325 0.0996626 0.995021i \(-0.468224\pi\)
0.0996626 + 0.995021i \(0.468224\pi\)
\(252\) −1.09490e25 2.75400e25i −0.667835 1.67980i
\(253\) −2.62309e24 −0.153479
\(254\) 9.82425e24i 0.551500i
\(255\) −1.57965e25 2.88832e24i −0.850922 0.155587i
\(256\) −3.13351e25 −1.61999
\(257\) 3.53632e25 1.75491 0.877454 0.479662i \(-0.159241\pi\)
0.877454 + 0.479662i \(0.159241\pi\)
\(258\) −1.04222e25 + 5.70001e25i −0.496538 + 2.71562i
\(259\) −2.28815e25 2.50543e25i −1.04674 1.14613i
\(260\) 5.57860e25i 2.45079i
\(261\) −3.09481e24 + 8.17999e24i −0.130590 + 0.345166i
\(262\) 7.30072e25i 2.95939i
\(263\) 2.37157e25i 0.923635i −0.886975 0.461817i \(-0.847198\pi\)
0.886975 0.461817i \(-0.152802\pi\)
\(264\) 5.59055e25 + 1.02221e25i 2.09225 + 0.382558i
\(265\) 3.71005e25i 1.33444i
\(266\) −8.15494e23 8.92932e23i −0.0281945 0.0308717i
\(267\) 2.03250e25 + 3.71632e24i 0.675556 + 0.123522i
\(268\) 9.55480e25 3.05356
\(269\) −3.86632e25 −1.18823 −0.594113 0.804382i \(-0.702497\pi\)
−0.594113 + 0.804382i \(0.702497\pi\)
\(270\) −2.85472e25 + 4.73505e25i −0.843809 + 1.39960i
\(271\) 2.93748e25i 0.835213i −0.908628 0.417606i \(-0.862869\pi\)
0.908628 0.417606i \(-0.137131\pi\)
\(272\) 1.49163e25 0.408025
\(273\) 4.47663e25 2.80198e25i 1.17827 0.737491i
\(274\) 1.08659e25 0.275222
\(275\) 3.14062e24i 0.0765635i
\(276\) −1.35309e24 + 7.40018e24i −0.0317527 + 0.173659i
\(277\) 8.10073e24 0.183015 0.0915075 0.995804i \(-0.470831\pi\)
0.0915075 + 0.995804i \(0.470831\pi\)
\(278\) −4.67144e25 −1.01620
\(279\) −2.33881e24 + 6.18179e24i −0.0489949 + 0.129500i
\(280\) 4.83087e25 4.41192e25i 0.974689 0.890161i
\(281\) 6.08086e25i 1.18181i −0.806740 0.590906i \(-0.798770\pi\)
0.806740 0.590906i \(-0.201230\pi\)
\(282\) −1.80102e25 + 9.85000e25i −0.337213 + 1.84425i
\(283\) 5.91160e25i 1.06647i −0.845968 0.533234i \(-0.820977\pi\)
0.845968 0.533234i \(-0.179023\pi\)
\(284\) 2.07750e25i 0.361160i
\(285\) −2.61254e23 + 1.42883e24i −0.00437716 + 0.0239391i
\(286\) 2.26662e26i 3.66046i
\(287\) 9.15208e24 + 1.00211e25i 0.142482 + 0.156012i
\(288\) −1.37325e25 + 3.62969e25i −0.206124 + 0.544814i
\(289\) −1.47444e25 −0.213403
\(290\) −4.32101e25 −0.603124
\(291\) 1.75222e25 9.58309e25i 0.235892 1.29012i
\(292\) 2.13420e26i 2.77150i
\(293\) 2.98281e25 0.373693 0.186847 0.982389i \(-0.440173\pi\)
0.186847 + 0.982389i \(0.440173\pi\)
\(294\) 1.33543e26 + 3.71662e25i 1.61427 + 0.449264i
\(295\) −4.30450e25 −0.502102
\(296\) 1.86606e26i 2.10069i
\(297\) 7.46779e25 1.23866e26i 0.811427 1.34589i
\(298\) −7.62859e25 −0.800153
\(299\) −1.34056e25 −0.135750
\(300\) 8.86021e24 + 1.62005e24i 0.0866305 + 0.0158400i
\(301\) −1.17673e26 1.28847e26i −1.11104 1.21654i
\(302\) 2.35993e26i 2.15192i
\(303\) −6.77635e25 1.23902e25i −0.596826 0.109127i
\(304\) 1.34921e24i 0.0114791i
\(305\) 7.78905e25i 0.640230i
\(306\) 6.62151e25 1.75015e26i 0.525875 1.38996i
\(307\) 1.36868e26i 1.05039i −0.850982 0.525195i \(-0.823993\pi\)
0.850982 0.525195i \(-0.176007\pi\)
\(308\) −2.82835e26 + 2.58306e26i −2.09773 + 1.91581i
\(309\) −2.00302e25 + 1.09548e26i −0.143589 + 0.785305i
\(310\) −3.26548e25 −0.226281
\(311\) 2.42912e26 1.62729 0.813646 0.581360i \(-0.197479\pi\)
0.813646 + 0.581360i \(0.197479\pi\)
\(312\) 2.85712e26 + 5.22411e25i 1.85057 + 0.338368i
\(313\) 1.44764e26i 0.906664i 0.891342 + 0.453332i \(0.149765\pi\)
−0.891342 + 0.453332i \(0.850235\pi\)
\(314\) −1.53529e26 −0.929886
\(315\) −6.15121e25 1.54721e26i −0.360329 0.906336i
\(316\) −3.31144e26 −1.87630
\(317\) 9.95556e24i 0.0545687i 0.999628 + 0.0272843i \(0.00868595\pi\)
−0.999628 + 0.0272843i \(0.991314\pi\)
\(318\) −4.25268e26 7.77581e25i −2.25516 0.412345i
\(319\) 1.13035e26 0.579978
\(320\) −2.82109e26 −1.40069
\(321\) −1.53734e24 + 8.40786e24i −0.00738697 + 0.0404001i
\(322\) −2.37284e25 2.59816e25i −0.110353 0.120831i
\(323\) 4.91584e24i 0.0221295i
\(324\) −3.10926e26 2.74573e26i −1.35498 1.19656i
\(325\) 1.60505e25i 0.0677195i
\(326\) 3.16388e26i 1.29252i
\(327\) −1.05429e26 1.92771e25i −0.417069 0.0762590i
\(328\) 7.46382e25i 0.285947i
\(329\) −2.03347e26 2.22656e26i −0.754538 0.826187i
\(330\) 7.02942e26 + 1.28529e26i 2.52652 + 0.461962i
\(331\) 6.39974e25 0.222827 0.111414 0.993774i \(-0.464462\pi\)
0.111414 + 0.993774i \(0.464462\pi\)
\(332\) 9.92838e26 3.34910
\(333\) −4.44179e26 1.68050e26i −1.45175 0.549255i
\(334\) 3.31106e25i 0.104865i
\(335\) 5.36794e26 1.64754
\(336\) 8.20547e25 + 1.31096e26i 0.244085 + 0.389967i
\(337\) 1.73484e25 0.0500201 0.0250101 0.999687i \(-0.492038\pi\)
0.0250101 + 0.999687i \(0.492038\pi\)
\(338\) 5.58870e26i 1.56202i
\(339\) −4.23543e25 + 2.31640e26i −0.114763 + 0.627649i
\(340\) 5.95229e26 1.56371
\(341\) 8.54231e25 0.217598
\(342\) −1.58305e25 5.98929e24i −0.0391039 0.0147945i
\(343\) −3.32436e26 + 2.52463e26i −0.796380 + 0.604796i
\(344\) 9.59663e26i 2.22974i
\(345\) −7.60171e24 + 4.15746e25i −0.0171321 + 0.0936973i
\(346\) 4.83043e26i 1.05605i
\(347\) 7.07497e26i 1.50060i −0.661097 0.750300i \(-0.729909\pi\)
0.661097 0.750300i \(-0.270091\pi\)
\(348\) 5.83077e25 3.18891e26i 0.119990 0.656237i
\(349\) 2.67758e26i 0.534657i 0.963605 + 0.267329i \(0.0861410\pi\)
−0.963605 + 0.267329i \(0.913859\pi\)
\(350\) −3.11077e25 + 2.84100e25i −0.0602773 + 0.0550498i
\(351\) 3.81651e26 6.33034e26i 0.717697 1.19043i
\(352\) 5.01569e26 0.915446
\(353\) 6.23142e26 1.10396 0.551979 0.833858i \(-0.313873\pi\)
0.551979 + 0.833858i \(0.313873\pi\)
\(354\) 9.02170e25 4.93407e26i 0.155151 0.848537i
\(355\) 1.16715e26i 0.194863i
\(356\) −7.65864e26 −1.24144
\(357\) 2.98967e26 + 4.77650e26i 0.470551 + 0.751784i
\(358\) −1.27298e27 −1.94558
\(359\) 8.91157e26i 1.32270i 0.750076 + 0.661352i \(0.230017\pi\)
−0.750076 + 0.661352i \(0.769983\pi\)
\(360\) 3.24028e26 8.56448e26i 0.467096 1.23460i
\(361\) 7.13765e26 0.999377
\(362\) 1.04417e27 1.42014
\(363\) −1.09433e27 2.00093e26i −1.44587 0.264371i
\(364\) −1.44546e27 + 1.32011e27i −1.85542 + 1.69451i
\(365\) 1.19900e27i 1.49536i
\(366\) −8.92825e26 1.63249e26i −1.08197 0.197833i
\(367\) 1.06658e25i 0.0125603i −0.999980 0.00628017i \(-0.998001\pi\)
0.999980 0.00628017i \(-0.00199905\pi\)
\(368\) 3.92579e25i 0.0449288i
\(369\) 1.77661e26 + 6.72162e25i 0.197613 + 0.0747648i
\(370\) 2.34634e27i 2.53672i
\(371\) 9.61305e26 8.77938e26i 1.01027 0.922652i
\(372\) 4.40643e25 2.40993e26i 0.0450180 0.246208i
\(373\) 1.71703e26 0.170543 0.0852717 0.996358i \(-0.472824\pi\)
0.0852717 + 0.996358i \(0.472824\pi\)
\(374\) −2.41845e27 −2.33553
\(375\) 1.07152e27 + 1.95922e26i 1.00617 + 0.183974i
\(376\) 1.65836e27i 1.51428i
\(377\) 5.77681e26 0.512984
\(378\) 1.90243e27 3.80810e26i 1.64302 0.328885i
\(379\) 5.46489e26 0.459061 0.229530 0.973302i \(-0.426281\pi\)
0.229530 + 0.973302i \(0.426281\pi\)
\(380\) 5.38396e25i 0.0439920i
\(381\) 4.07326e26 + 7.44776e25i 0.323765 + 0.0591988i
\(382\) −2.64476e27 −2.04513
\(383\) 1.50047e26 0.112886 0.0564432 0.998406i \(-0.482024\pi\)
0.0564432 + 0.998406i \(0.482024\pi\)
\(384\) 4.48139e26 2.45092e27i 0.328046 1.79412i
\(385\) −1.58898e27 + 1.45118e27i −1.13183 + 1.03367i
\(386\) 2.11296e27i 1.46462i
\(387\) −2.28429e27 8.64235e26i −1.54094 0.582997i
\(388\) 3.61100e27i 2.37080i
\(389\) 8.44448e26i 0.539638i −0.962911 0.269819i \(-0.913036\pi\)
0.962911 0.269819i \(-0.0869638\pi\)
\(390\) 3.59247e27 + 6.56866e26i 2.23468 + 0.408600i
\(391\) 1.43036e26i 0.0866143i
\(392\) −2.28633e27 2.07692e26i −1.34783 0.122438i
\(393\) 3.02697e27 + 5.53467e26i 1.73735 + 0.317665i
\(394\) 3.16861e27 1.77076
\(395\) −1.86039e27 −1.01236
\(396\) −1.89710e27 + 5.01428e27i −1.00529 + 2.65711i
\(397\) 1.33880e27i 0.690899i −0.938437 0.345450i \(-0.887726\pi\)
0.938437 0.345450i \(-0.112274\pi\)
\(398\) −5.19236e27 −2.60971
\(399\) 4.32043e25 2.70421e25i 0.0211501 0.0132381i
\(400\) −4.70033e25 −0.0224129
\(401\) 9.39132e26i 0.436225i −0.975924 0.218113i \(-0.930010\pi\)
0.975924 0.218113i \(-0.0699900\pi\)
\(402\) −1.12505e27 + 6.15303e27i −0.509095 + 2.78430i
\(403\) 4.36565e26 0.192462
\(404\) 2.55339e27 1.09676
\(405\) −1.74680e27 1.54257e27i −0.731080 0.645604i
\(406\) 1.02251e27 + 1.11961e27i 0.417009 + 0.456608i
\(407\) 6.13789e27i 2.43937i
\(408\) −5.57404e26 + 3.04850e27i −0.215893 + 1.18074i
\(409\) 4.42423e27i 1.67010i 0.550174 + 0.835050i \(0.314561\pi\)
−0.550174 + 0.835050i \(0.685439\pi\)
\(410\) 9.38482e26i 0.345299i
\(411\) −8.23740e25 + 4.50512e26i −0.0295428 + 0.161573i
\(412\) 4.12786e27i 1.44312i
\(413\) 1.01861e27 + 1.11533e27i 0.347161 + 0.380127i
\(414\) −4.60619e26 1.74270e26i −0.153052 0.0579055i
\(415\) 5.57781e27 1.80700
\(416\) 2.56333e27 0.809701
\(417\) 3.54141e26 1.93684e27i 0.109081 0.596574i
\(418\) 2.18754e26i 0.0657059i
\(419\) −1.04379e27 −0.305751 −0.152875 0.988245i \(-0.548853\pi\)
−0.152875 + 0.988245i \(0.548853\pi\)
\(420\) 3.27436e27 + 5.23135e27i 0.935425 + 1.49450i
\(421\) −3.05496e27 −0.851222 −0.425611 0.904906i \(-0.639941\pi\)
−0.425611 + 0.904906i \(0.639941\pi\)
\(422\) 8.49861e27i 2.30976i
\(423\) −3.94740e27 1.49346e27i −1.04649 0.395930i
\(424\) 7.15987e27 1.85167
\(425\) −1.71257e26 −0.0432080
\(426\) 1.33786e27 + 2.44621e26i 0.329313 + 0.0602132i
\(427\) 2.01821e27 1.84318e27i 0.484700 0.442665i
\(428\) 3.16816e26i 0.0742417i
\(429\) −9.39770e27 1.71832e27i −2.14892 0.392919i
\(430\) 1.20666e28i 2.69255i
\(431\) 2.99105e27i 0.651347i −0.945482 0.325673i \(-0.894409\pi\)
0.945482 0.325673i \(-0.105591\pi\)
\(432\) 1.85381e27 + 1.11765e27i 0.393992 + 0.237534i
\(433\) 1.68899e27i 0.350351i −0.984537 0.175175i \(-0.943951\pi\)
0.984537 0.175175i \(-0.0560492\pi\)
\(434\) 7.72735e26 + 8.46112e26i 0.156455 + 0.171311i
\(435\) 3.27576e26 1.79155e27i 0.0647402 0.354071i
\(436\) 3.97266e27 0.766431
\(437\) −1.29379e25 −0.00243674
\(438\) −1.37437e28 2.51296e27i −2.52711 0.462070i
\(439\) 8.32144e27i 1.49390i −0.664882 0.746949i \(-0.731518\pi\)
0.664882 0.746949i \(-0.268482\pi\)
\(440\) −1.18348e28 −2.07448
\(441\) −2.55335e27 + 5.25512e27i −0.437024 + 0.899450i
\(442\) −1.23598e28 −2.06575
\(443\) 6.80601e27i 1.11085i 0.831568 + 0.555423i \(0.187443\pi\)
−0.831568 + 0.555423i \(0.812557\pi\)
\(444\) 1.73160e28 + 3.16615e27i 2.76011 + 0.504673i
\(445\) −4.30266e27 −0.669819
\(446\) 1.66064e28 2.52499
\(447\) 5.78322e26 3.16291e27i 0.0858897 0.469740i
\(448\) 6.67575e27 + 7.30967e27i 0.968458 + 1.06042i
\(449\) 5.68492e27i 0.805634i 0.915280 + 0.402817i \(0.131969\pi\)
−0.915280 + 0.402817i \(0.868031\pi\)
\(450\) −2.08653e26 + 5.51498e26i −0.0288864 + 0.0763506i
\(451\) 2.45501e27i 0.332048i
\(452\) 8.72843e27i 1.15341i
\(453\) −9.78456e27 1.78906e27i −1.26331 0.230990i
\(454\) 2.17170e27i 0.273976i
\(455\) −8.12068e27 + 7.41643e27i −1.00109 + 0.914271i
\(456\) 2.75743e26 + 5.04183e25i 0.0332180 + 0.00607376i
\(457\) −8.96403e26 −0.105532 −0.0527659 0.998607i \(-0.516804\pi\)
−0.0527659 + 0.998607i \(0.516804\pi\)
\(458\) 1.46885e28 1.69001
\(459\) 6.75438e27 + 4.07215e27i 0.759543 + 0.457921i
\(460\) 1.56657e27i 0.172184i
\(461\) 6.42135e27 0.689869 0.344934 0.938627i \(-0.387901\pi\)
0.344934 + 0.938627i \(0.387901\pi\)
\(462\) −1.33039e28 2.12553e28i −1.39714 2.23216i
\(463\) −5.84379e27 −0.599921 −0.299960 0.953952i \(-0.596973\pi\)
−0.299960 + 0.953952i \(0.596973\pi\)
\(464\) 1.69171e27i 0.169781i
\(465\) 2.47556e26 1.35391e27i 0.0242894 0.132841i
\(466\) −3.90402e27 −0.374507
\(467\) 1.13932e28 1.06860 0.534302 0.845294i \(-0.320574\pi\)
0.534302 + 0.845294i \(0.320574\pi\)
\(468\) −9.69535e27 + 2.56261e28i −0.889165 + 2.35018i
\(469\) −1.27025e28 1.39088e28i −1.13914 1.24731i
\(470\) 2.08518e28i 1.82859i
\(471\) 1.16390e27 6.36552e27i 0.0998154 0.545901i
\(472\) 8.30707e27i 0.696718i
\(473\) 3.15654e28i 2.58922i
\(474\) 3.89914e27 2.13248e28i 0.312821 1.71085i
\(475\) 1.54905e25i 0.00121558i
\(476\) −1.40853e28 1.54229e28i −1.08117 1.18384i
\(477\) 6.44790e27 1.70426e28i 0.484145 1.27966i
\(478\) 3.75454e28 2.75781
\(479\) 1.11198e28 0.799047 0.399523 0.916723i \(-0.369176\pi\)
0.399523 + 0.916723i \(0.369176\pi\)
\(480\) 1.45354e27 7.94959e27i 0.102187 0.558871i
\(481\) 3.13684e28i 2.15759i
\(482\) 1.86519e28 1.25524
\(483\) 1.25712e27 7.86844e26i 0.0827810 0.0518136i
\(484\) 4.12355e28 2.65702
\(485\) 2.02868e28i 1.27916i
\(486\) 2.13429e28 1.67898e28i 1.31696 1.03601i
\(487\) 1.17717e28 0.710859 0.355429 0.934703i \(-0.384335\pi\)
0.355429 + 0.934703i \(0.384335\pi\)
\(488\) 1.50318e28 0.888386
\(489\) −1.31179e28 2.39854e27i −0.758788 0.138741i
\(490\) −2.87477e28 2.61146e27i −1.62759 0.147851i
\(491\) 2.57361e28i 1.42622i −0.701052 0.713110i \(-0.747286\pi\)
0.701052 0.713110i \(-0.252714\pi\)
\(492\) −6.92600e27 1.26639e27i −0.375707 0.0686962i
\(493\) 6.16376e27i 0.327306i
\(494\) 1.11797e27i 0.0581161i
\(495\) −1.06580e28 + 2.81705e28i −0.542401 + 1.43364i
\(496\) 1.27846e27i 0.0636987i
\(497\) −3.02419e27 + 2.76192e27i −0.147525 + 0.134731i
\(498\) −1.16904e28 + 6.39361e28i −0.558369 + 3.05378i
\(499\) −3.59436e28 −1.68099 −0.840496 0.541818i \(-0.817736\pi\)
−0.840496 + 0.541818i \(0.817736\pi\)
\(500\) −4.03759e28 −1.84900
\(501\) −1.37281e27 2.51011e26i −0.0615621 0.0112563i
\(502\) 7.60547e27i 0.333993i
\(503\) −3.28278e28 −1.41181 −0.705907 0.708304i \(-0.749461\pi\)
−0.705907 + 0.708304i \(0.749461\pi\)
\(504\) −2.98590e28 + 1.18710e28i −1.25763 + 0.499994i
\(505\) 1.43451e28 0.591758
\(506\) 6.36507e27i 0.257171i
\(507\) −2.31715e28 4.23679e27i −0.917001 0.167669i
\(508\) −1.53484e28 −0.594970
\(509\) 1.78603e28 0.678192 0.339096 0.940752i \(-0.389879\pi\)
0.339096 + 0.940752i \(0.389879\pi\)
\(510\) −7.00866e27 + 3.83311e28i −0.260704 + 1.42582i
\(511\) 3.10671e28 2.83729e28i 1.13209 1.03391i
\(512\) 2.49474e28i 0.890615i
\(513\) 3.68334e26 6.10947e26i 0.0128828 0.0213684i
\(514\) 8.58107e28i 2.94055i
\(515\) 2.31905e28i 0.778636i
\(516\) 8.90513e28 + 1.62826e28i 2.92967 + 0.535676i
\(517\) 5.45472e28i 1.75842i
\(518\) −6.07955e28 + 5.55231e28i −1.92048 + 1.75393i
\(519\) −2.00276e28 3.66194e27i −0.619970 0.113359i
\(520\) −6.04834e28 −1.83485
\(521\) 1.00903e28 0.299991 0.149995 0.988687i \(-0.452074\pi\)
0.149995 + 0.988687i \(0.452074\pi\)
\(522\) 1.98492e28 + 7.50972e27i 0.578365 + 0.218818i
\(523\) 3.31551e28i 0.946854i −0.880833 0.473427i \(-0.843017\pi\)
0.880833 0.473427i \(-0.156983\pi\)
\(524\) −1.14059e29 −3.19265
\(525\) −9.42085e26 1.50514e27i −0.0258474 0.0412957i
\(526\) −5.75474e28 −1.54766
\(527\) 4.65808e27i 0.122799i
\(528\) 5.03204e27 2.75208e28i 0.130043 0.711221i
\(529\) 3.90951e28 0.990463
\(530\) 9.00264e28 2.23601
\(531\) 1.97733e28 + 7.48102e27i 0.481490 + 0.182166i
\(532\) −1.39503e27 + 1.27405e27i −0.0333051 + 0.0304168i
\(533\) 1.25467e28i 0.293692i
\(534\) 9.01785e27 4.93196e28i 0.206976 1.13197i
\(535\) 1.77989e27i 0.0400570i
\(536\) 1.03593e29i 2.28614i
\(537\) 9.65043e27 5.27793e28i 0.208841 1.14218i
\(538\) 9.38183e28i 1.99101i
\(539\) 7.52025e28 + 6.83144e27i 1.56513 + 0.142177i
\(540\) 7.39758e28 + 4.45993e28i 1.50992 + 0.910319i
\(541\) 1.63947e28 0.328196 0.164098 0.986444i \(-0.447529\pi\)
0.164098 + 0.986444i \(0.447529\pi\)
\(542\) −7.12794e28 −1.39950
\(543\) −7.91583e27 + 4.32925e28i −0.152440 + 0.833709i
\(544\) 2.73503e28i 0.516624i
\(545\) 2.23186e28 0.413527
\(546\) −6.79914e28 1.08628e29i −1.23575 1.97432i
\(547\) 4.86913e28 0.868130 0.434065 0.900882i \(-0.357079\pi\)
0.434065 + 0.900882i \(0.357079\pi\)
\(548\) 1.69757e28i 0.296916i
\(549\) 1.35370e28 3.57801e28i 0.232281 0.613948i
\(550\) 7.62088e27 0.128291
\(551\) 5.57525e26 0.00920815
\(552\) 8.02330e27 + 1.46702e27i 0.130015 + 0.0237726i
\(553\) 4.40237e28 + 4.82041e28i 0.699959 + 0.766426i
\(554\) 1.96569e28i 0.306663i
\(555\) 9.72821e28 + 1.77876e28i 1.48921 + 0.272295i
\(556\) 7.29819e28i 1.09630i
\(557\) 1.60545e28i 0.236656i −0.992975 0.118328i \(-0.962247\pi\)
0.992975 0.118328i \(-0.0377534\pi\)
\(558\) 1.50004e28 + 5.67525e27i 0.216992 + 0.0820967i
\(559\) 1.61319e29i 2.29014i
\(560\) −2.17187e28 2.37811e28i −0.302593 0.331327i
\(561\) 1.83343e28 1.00272e29i 0.250699 1.37110i
\(562\) −1.47555e29 −1.98027
\(563\) −6.06869e28 −0.799386 −0.399693 0.916649i \(-0.630883\pi\)
−0.399693 + 0.916649i \(0.630883\pi\)
\(564\) 1.53887e29 + 2.81374e28i 1.98962 + 0.363792i
\(565\) 4.90367e28i 0.622319i
\(566\) −1.43448e29 −1.78699
\(567\) 1.36660e27 + 8.17639e28i 0.0167117 + 0.999860i
\(568\) −2.25244e28 −0.270393
\(569\) 4.05731e28i 0.478144i −0.971002 0.239072i \(-0.923157\pi\)
0.971002 0.239072i \(-0.0768433\pi\)
\(570\) 3.46712e27 + 6.33947e26i 0.0401128 + 0.00733444i
\(571\) −6.86431e28 −0.779682 −0.389841 0.920882i \(-0.627470\pi\)
−0.389841 + 0.920882i \(0.627470\pi\)
\(572\) 3.54114e29 3.94898
\(573\) 2.00499e28 1.09655e29i 0.219527 1.20062i
\(574\) 2.43168e28 2.22080e28i 0.261416 0.238745i
\(575\) 4.50727e26i 0.00475774i
\(576\) 1.29591e29 + 4.90292e28i 1.34319 + 0.508181i
\(577\) 7.50036e28i 0.763371i −0.924292 0.381686i \(-0.875344\pi\)
0.924292 0.381686i \(-0.124656\pi\)
\(578\) 3.57781e28i 0.357581i
\(579\) 8.76060e28 + 1.60183e28i 0.859823 + 0.157214i
\(580\) 6.75072e28i 0.650663i
\(581\) −1.31992e29 1.44526e29i −1.24939 1.36803i
\(582\) −2.32539e29 4.25186e28i −2.16174 0.395264i
\(583\) −2.35504e29 −2.15020
\(584\) 2.31390e29 2.07496
\(585\) −5.44690e28 + 1.43969e29i −0.479747 + 1.26804i
\(586\) 7.23794e28i 0.626167i
\(587\) 2.17091e29 1.84477 0.922384 0.386274i \(-0.126238\pi\)
0.922384 + 0.386274i \(0.126238\pi\)
\(588\) 5.80648e28 2.08635e29i 0.484675 1.74150i
\(589\) 4.21333e26 0.00345473
\(590\) 1.04451e29i 0.841330i
\(591\) −2.40212e28 + 1.31375e29i −0.190076 + 1.03954i
\(592\) −9.18611e28 −0.714092
\(593\) −8.31854e28 −0.635291 −0.317646 0.948209i \(-0.602892\pi\)
−0.317646 + 0.948209i \(0.602892\pi\)
\(594\) −3.00568e29 1.81210e29i −2.25520 1.35964i
\(595\) −7.91322e28 8.66464e28i −0.583344 0.638737i
\(596\) 1.19181e29i 0.863223i
\(597\) 3.93632e28 2.15282e29i 0.280130 1.53206i
\(598\) 3.25295e28i 0.227465i
\(599\) 2.59144e29i 1.78057i −0.455404 0.890285i \(-0.650505\pi\)
0.455404 0.890285i \(-0.349495\pi\)
\(600\) 1.75646e27 9.60627e27i 0.0118591 0.0648584i
\(601\) 2.24164e29i 1.48725i −0.668597 0.743625i \(-0.733105\pi\)
0.668597 0.743625i \(-0.266895\pi\)
\(602\) −3.12654e29 + 2.85540e29i −2.03846 + 1.86167i
\(603\) −2.46584e29 9.32922e28i −1.57991 0.597742i
\(604\) 3.68691e29 2.32154
\(605\) 2.31663e29 1.43359
\(606\) −3.00655e28 + 1.64432e29i −0.182855 + 1.00005i
\(607\) 1.14847e29i 0.686495i 0.939245 + 0.343247i \(0.111527\pi\)
−0.939245 + 0.343247i \(0.888473\pi\)
\(608\) 2.47389e27 0.0145343
\(609\) −5.41721e28 + 3.39070e28i −0.312820 + 0.195798i
\(610\) 1.89005e29 1.07278
\(611\) 2.78770e29i 1.55530i
\(612\) −2.73426e29 1.03448e29i −1.49951 0.567325i
\(613\) −1.14554e29 −0.617555 −0.308777 0.951134i \(-0.599920\pi\)
−0.308777 + 0.951134i \(0.599920\pi\)
\(614\) −3.32118e29 −1.76005
\(615\) −3.89106e28 7.11462e27i −0.202712 0.0370649i
\(616\) 2.80057e29 + 3.06650e29i 1.43433 + 1.57053i
\(617\) 2.67043e29i 1.34458i 0.740286 + 0.672292i \(0.234690\pi\)
−0.740286 + 0.672292i \(0.765310\pi\)
\(618\) 2.65823e29 + 4.86044e28i 1.31587 + 0.240601i
\(619\) 8.76085e28i 0.426378i −0.977011 0.213189i \(-0.931615\pi\)
0.977011 0.213189i \(-0.0683849\pi\)
\(620\) 5.10166e28i 0.244117i
\(621\) 1.07174e28 1.77767e28i 0.0504229 0.0836353i
\(622\) 5.89440e29i 2.72672i
\(623\) 1.01817e29 + 1.11486e29i 0.463123 + 0.507101i
\(624\) 2.57169e28 1.40648e29i 0.115022 0.629066i
\(625\) −2.15757e29 −0.948909
\(626\) 3.51278e29 1.51922
\(627\) −9.06980e27 1.65837e27i −0.0385735 0.00705297i
\(628\) 2.39859e29i 1.00318i
\(629\) −3.34696e29 −1.37664
\(630\) −3.75439e29 + 1.49262e29i −1.51867 + 0.603774i
\(631\) 1.30590e29 0.519521 0.259761 0.965673i \(-0.416356\pi\)
0.259761 + 0.965673i \(0.416356\pi\)
\(632\) 3.59028e29i 1.40475i
\(633\) 3.52363e29 + 6.44279e28i 1.35597 + 0.247933i
\(634\) 2.41577e28 0.0914362
\(635\) −8.62283e28 −0.321015
\(636\) −1.21482e29 + 6.64396e29i −0.444847 + 2.43292i
\(637\) 3.84332e29 + 3.49129e28i 1.38434 + 0.125754i
\(638\) 2.74286e29i 0.971821i
\(639\) −2.02845e28 + 5.36147e28i −0.0706979 + 0.186864i
\(640\) 5.18844e29i 1.77888i
\(641\) 1.42504e29i 0.480637i −0.970694 0.240318i \(-0.922748\pi\)
0.970694 0.240318i \(-0.0772519\pi\)
\(642\) 2.04021e28 + 3.73043e27i 0.0676951 + 0.0123777i
\(643\) 6.97978e28i 0.227838i 0.993490 + 0.113919i \(0.0363404\pi\)
−0.993490 + 0.113919i \(0.963660\pi\)
\(644\) −4.05911e28 + 3.70709e28i −0.130355 + 0.119051i
\(645\) 5.00295e29 + 9.14764e28i 1.58070 + 0.289023i
\(646\) −1.19285e28 −0.0370805
\(647\) 2.02043e29 0.617942 0.308971 0.951071i \(-0.400015\pi\)
0.308971 + 0.951071i \(0.400015\pi\)
\(648\) −2.97693e29 + 3.37107e29i −0.895842 + 1.01445i
\(649\) 2.73238e29i 0.809043i
\(650\) 3.89474e28 0.113472
\(651\) −4.09390e28 + 2.56242e28i −0.117364 + 0.0734598i
\(652\) 4.94294e29 1.39439
\(653\) 5.42702e29i 1.50651i −0.657727 0.753256i \(-0.728482\pi\)
0.657727 0.753256i \(-0.271518\pi\)
\(654\) −4.67770e28 + 2.55828e29i −0.127781 + 0.698847i
\(655\) −6.40790e29 −1.72259
\(656\) 3.67424e28 0.0972024
\(657\) 2.08381e29 5.50778e29i 0.542527 1.43397i
\(658\) −5.40288e29 + 4.93432e29i −1.38437 + 1.26432i
\(659\) 1.77217e29i 0.446897i −0.974716 0.223449i \(-0.928268\pi\)
0.974716 0.223449i \(-0.0717315\pi\)
\(660\) 2.00802e29 1.09821e30i 0.498375 2.72567i
\(661\) 6.03714e29i 1.47474i 0.675489 + 0.737370i \(0.263933\pi\)
−0.675489 + 0.737370i \(0.736067\pi\)
\(662\) 1.55293e29i 0.373373i
\(663\) 9.36995e28 5.12453e29i 0.221741 1.21272i
\(664\) 1.07644e30i 2.50740i
\(665\) −7.83734e27 + 7.15766e27i −0.0179697 + 0.0164113i
\(666\) −4.07782e29 + 1.07782e30i −0.920342 + 2.43258i
\(667\) 1.62223e28 0.0360405
\(668\) 5.17287e28 0.113130
\(669\) −1.25893e29 + 6.88522e29i −0.271036 + 1.48233i
\(670\) 1.30256e30i 2.76065i
\(671\) −4.94427e29 −1.03161
\(672\) −2.40377e29 + 1.50455e29i −0.493759 + 0.309050i
\(673\) −7.43604e28 −0.150378 −0.0751889 0.997169i \(-0.523956\pi\)
−0.0751889 + 0.997169i \(0.523956\pi\)
\(674\) 4.20967e28i 0.0838145i
\(675\) −2.12840e28 1.28319e28i −0.0417218 0.0251537i
\(676\) 8.73123e29 1.68514
\(677\) −3.51683e29 −0.668299 −0.334149 0.942520i \(-0.608449\pi\)
−0.334149 + 0.942520i \(0.608449\pi\)
\(678\) 5.62087e29 + 1.02775e29i 1.05170 + 0.192298i
\(679\) 5.25647e29 4.80062e29i 0.968416 0.884432i
\(680\) 6.45349e29i 1.17071i
\(681\) −9.00414e28 1.64636e28i −0.160841 0.0294091i
\(682\) 2.07284e29i 0.364610i
\(683\) 7.68223e29i 1.33067i −0.746546 0.665334i \(-0.768289\pi\)
0.746546 0.665334i \(-0.231711\pi\)
\(684\) −9.35707e27 + 2.47320e28i −0.0159607 + 0.0421861i
\(685\) 9.53706e28i 0.160200i
\(686\) 6.12614e29 + 8.06674e29i 1.01341 + 1.33443i
\(687\) −1.11353e29 + 6.09002e29i −0.181408 + 0.992140i
\(688\) −4.72416e29 −0.757960
\(689\) −1.20357e30 −1.90182
\(690\) 1.00883e29 + 1.84459e28i 0.157001 + 0.0287068i
\(691\) 1.13347e30i 1.73736i 0.495375 + 0.868679i \(0.335031\pi\)
−0.495375 + 0.868679i \(0.664969\pi\)
\(692\) 7.54658e29 1.13929
\(693\) 9.82128e29 3.90462e29i 1.46039 0.580603i
\(694\) −1.71678e30 −2.51443
\(695\) 4.10016e29i 0.591507i
\(696\) −3.45743e29 6.32174e28i −0.491311 0.0898338i
\(697\) 1.33871e29 0.187388
\(698\) 6.49729e29 0.895881
\(699\) 2.95963e28 1.61865e29i 0.0402001 0.219859i
\(700\) 4.43849e28 + 4.85996e28i 0.0593890 + 0.0650284i
\(701\) 5.77205e29i 0.760836i −0.924815 0.380418i \(-0.875780\pi\)
0.924815 0.380418i \(-0.124220\pi\)
\(702\) −1.53609e30 9.26095e29i −1.99470 1.20259i
\(703\) 3.02739e28i 0.0387292i
\(704\) 1.79075e30i 2.25695i
\(705\) 8.64542e29 + 1.58077e29i 1.07350 + 0.196284i
\(706\) 1.51209e30i 1.84981i
\(707\) −3.39459e29 3.71693e29i −0.409150 0.448003i
\(708\) −7.70849e29 1.40946e29i −0.915420 0.167380i
\(709\) −1.84024e29 −0.215322 −0.107661 0.994188i \(-0.534336\pi\)
−0.107661 + 0.994188i \(0.534336\pi\)
\(710\) −2.83215e29 −0.326516
\(711\) 8.54594e29 + 3.23326e29i 0.970798 + 0.367291i
\(712\) 8.30353e29i 0.929443i
\(713\) 1.22595e28 0.0135218
\(714\) 1.15904e30 7.25458e29i 1.25970 0.788462i
\(715\) 1.98943e30 2.13067
\(716\) 1.98877e30i 2.09893i
\(717\) −2.84632e29 + 1.55668e30i −0.296028 + 1.61901i
\(718\) 2.16244e30 2.21634
\(719\) 8.18084e29 0.826313 0.413157 0.910660i \(-0.364426\pi\)
0.413157 + 0.910660i \(0.364426\pi\)
\(720\) −4.21606e29 1.59510e29i −0.419678 0.158780i
\(721\) −6.00885e29 + 5.48774e29i −0.589483 + 0.538361i
\(722\) 1.73199e30i 1.67457i
\(723\) −1.41400e29 + 7.73330e29i −0.134740 + 0.736907i
\(724\) 1.63130e30i 1.53207i
\(725\) 1.94229e28i 0.0179790i
\(726\) −4.85537e29 + 2.65545e30i −0.442984 + 2.42273i
\(727\) 1.90847e30i 1.71622i 0.513462 + 0.858112i \(0.328363\pi\)
−0.513462 + 0.858112i \(0.671637\pi\)
\(728\) 1.43126e30 + 1.56717e30i 1.26865 + 1.38911i
\(729\) 5.34325e29 + 1.01218e30i 0.466838 + 0.884343i
\(730\) 2.90944e30 2.50565
\(731\) −1.72125e30 −1.46121
\(732\) −2.55044e29 + 1.39486e30i −0.213426 + 1.16725i
\(733\) 9.30043e29i 0.767205i −0.923498 0.383602i \(-0.874683\pi\)
0.923498 0.383602i \(-0.125317\pi\)
\(734\) −2.58812e28 −0.0210463
\(735\) 3.26211e29 1.17212e30i 0.261506 0.939626i
\(736\) 7.19828e28 0.0568868
\(737\) 3.40742e30i 2.65471i
\(738\) 1.63104e29 4.31104e29i 0.125277 0.331124i
\(739\) −7.79190e29 −0.590034 −0.295017 0.955492i \(-0.595325\pi\)
−0.295017 + 0.955492i \(0.595325\pi\)
\(740\) −3.66568e30 −2.73667
\(741\) −4.63523e28 8.47530e27i −0.0341178 0.00623827i
\(742\) −2.13036e30 2.33266e30i −1.54601 1.69282i
\(743\) 3.05717e29i 0.218745i −0.994001 0.109372i \(-0.965116\pi\)
0.994001 0.109372i \(-0.0348841\pi\)
\(744\) −2.61285e29 4.77747e28i −0.184331 0.0337040i
\(745\) 6.69567e29i 0.465750i
\(746\) 4.16646e29i 0.285765i
\(747\) −2.56225e30 9.69398e29i −1.73282 0.655595i
\(748\) 3.77835e30i 2.51962i
\(749\) −4.61184e28 + 4.21189e28i −0.0303260 + 0.0276960i
\(750\) 4.75416e29 2.60010e30i 0.308269 1.68596i
\(751\) 8.50345e29 0.543721 0.271860 0.962337i \(-0.412361\pi\)
0.271860 + 0.962337i \(0.412361\pi\)
\(752\) −8.16367e29 −0.514752
\(753\) 3.15332e29 + 5.76570e28i 0.196075 + 0.0358513i
\(754\) 1.40177e30i 0.859564i
\(755\) 2.07133e30 1.25258
\(756\) −5.94940e29 2.97216e30i −0.354809 1.77253i
\(757\) −3.03706e30 −1.78627 −0.893134 0.449791i \(-0.851498\pi\)
−0.893134 + 0.449791i \(0.851498\pi\)
\(758\) 1.32609e30i 0.769210i
\(759\) −2.63904e29 4.82535e28i −0.150976 0.0276052i
\(760\) −5.83731e28 −0.0329359
\(761\) 6.28773e29 0.349909 0.174954 0.984577i \(-0.444022\pi\)
0.174954 + 0.984577i \(0.444022\pi\)
\(762\) 1.80724e29 9.88398e29i 0.0991946 0.542506i
\(763\) −5.28142e29 5.78293e29i −0.285919 0.313069i
\(764\) 4.13191e30i 2.20633i
\(765\) −1.53612e30 5.81176e29i −0.809061 0.306099i
\(766\) 3.64098e29i 0.189154i
\(767\) 1.39642e30i 0.715589i
\(768\) −3.15256e30 5.76431e29i −1.59357 0.291376i
\(769\) 1.58491e30i 0.790275i 0.918622 + 0.395138i \(0.129303\pi\)
−0.918622 + 0.395138i \(0.870697\pi\)
\(770\) 3.52136e30 + 3.85574e30i 1.73204 + 1.89651i
\(771\) 3.55782e30 + 6.50530e29i 1.72629 + 0.315643i
\(772\) −3.30108e30 −1.58006
\(773\) 3.16378e30 1.49390 0.746951 0.664879i \(-0.231517\pi\)
0.746951 + 0.664879i \(0.231517\pi\)
\(774\) −2.09711e30 + 5.54294e30i −0.976880 + 2.58202i
\(775\) 1.46783e28i 0.00674539i
\(776\) 3.91506e30 1.77497
\(777\) −1.84117e30 2.94158e30i −0.823518 1.31571i
\(778\) −2.04910e30 −0.904226
\(779\) 1.21089e28i 0.00527182i
\(780\) 1.02622e30 5.61252e30i 0.440806 2.41082i
\(781\) 7.40876e29 0.313985
\(782\) −3.47085e29 −0.145132
\(783\) −4.61839e29 + 7.66041e29i −0.190542 + 0.316048i
\(784\) −1.02241e29 + 1.12550e30i −0.0416204 + 0.458170i
\(785\) 1.34754e30i 0.541265i
\(786\) 1.34302e30 7.34510e30i 0.532285 2.91113i
\(787\) 3.14723e30i 1.23082i −0.788207 0.615410i \(-0.788991\pi\)
0.788207 0.615410i \(-0.211009\pi\)
\(788\) 4.95032e30i 1.91033i
\(789\) 4.36266e29 2.38599e30i 0.166128 0.908572i
\(790\) 4.51432e30i 1.69632i
\(791\) −1.27058e30 + 1.16039e30i −0.471140 + 0.430281i
\(792\) 5.43650e30 + 2.05684e30i 1.98932 + 0.752638i
\(793\) −2.52683e30 −0.912448
\(794\) −3.24866e30 −1.15768
\(795\) −6.82489e29 + 3.73261e30i −0.240016 + 1.31268i
\(796\) 8.11202e30i 2.81541i
\(797\) −3.44359e30 −1.17950 −0.589752 0.807584i \(-0.700775\pi\)
−0.589752 + 0.807584i \(0.700775\pi\)
\(798\) −6.56191e28 1.04838e29i −0.0221820 0.0354394i
\(799\) −2.97443e30 −0.992346
\(800\) 8.61848e28i 0.0283782i
\(801\) 1.97649e30 + 7.47783e29i 0.642322 + 0.243016i
\(802\) −2.27885e30 −0.730947
\(803\) −7.61094e30 −2.40949
\(804\) 9.61289e30 + 1.75767e30i 3.00376 + 0.549223i
\(805\) −2.28043e29 + 2.08266e29i −0.0703331 + 0.0642336i
\(806\) 1.05935e30i 0.322493i
\(807\) −3.88983e30 7.11236e29i −1.16885 0.213718i
\(808\) 2.76840e30i 0.821125i
\(809\) 9.62295e29i 0.281740i −0.990028 0.140870i \(-0.955010\pi\)
0.990028 0.140870i \(-0.0449900\pi\)
\(810\) −3.74312e30 + 4.23869e30i −1.08179 + 1.22501i
\(811\) 1.71177e30i 0.488346i 0.969732 + 0.244173i \(0.0785164\pi\)
−0.969732 + 0.244173i \(0.921484\pi\)
\(812\) 1.74917e30 1.59747e30i 0.492598 0.449879i
\(813\) 5.40369e29 2.95534e30i 0.150224 0.821592i
\(814\) 1.48939e31 4.08745
\(815\) 2.77697e30 0.752343
\(816\) 1.50070e30 + 2.74395e29i 0.401371 + 0.0733888i
\(817\) 1.55690e29i 0.0411084i
\(818\) 1.07356e31 2.79845
\(819\) 5.01929e30 1.99550e30i 1.29170 0.513537i
\(820\) 1.46619e30 0.372516
\(821\) 1.17086e30i 0.293699i −0.989159 0.146850i \(-0.953087\pi\)
0.989159 0.146850i \(-0.0469133\pi\)
\(822\) 1.09319e30 + 1.99885e29i 0.270734 + 0.0495024i
\(823\) −7.35520e29 −0.179844 −0.0899221 0.995949i \(-0.528662\pi\)
−0.0899221 + 0.995949i \(0.528662\pi\)
\(824\) −4.47544e30 −1.08044
\(825\) −5.77738e28 + 3.15971e29i −0.0137710 + 0.0753149i
\(826\) 2.70641e30 2.47170e30i 0.636947 0.581709i
\(827\) 1.24276e30i 0.288787i −0.989520 0.144394i \(-0.953877\pi\)
0.989520 0.144394i \(-0.0461232\pi\)
\(828\) −2.72262e29 + 7.19625e29i −0.0624697 + 0.165116i
\(829\) 3.26641e30i 0.740028i 0.929026 + 0.370014i \(0.120647\pi\)
−0.929026 + 0.370014i \(0.879353\pi\)
\(830\) 1.35349e31i 3.02784i
\(831\) 8.14998e29 + 1.49018e29i 0.180030 + 0.0329177i
\(832\) 9.15184e30i 1.99624i
\(833\) −3.72515e29 + 4.10076e30i −0.0802365 + 0.883266i
\(834\) −4.69983e30 8.59342e29i −0.999629 0.182777i
\(835\) 2.90614e29 0.0610392
\(836\) 3.41759e29 0.0708849
\(837\) −3.49021e29 + 5.78913e29i −0.0714882 + 0.118576i
\(838\) 2.53282e30i 0.512321i
\(839\) 4.31511e30 0.861968 0.430984 0.902360i \(-0.358167\pi\)
0.430984 + 0.902360i \(0.358167\pi\)
\(840\) 5.67184e30 3.55007e30i 1.11890 0.700333i
\(841\) 4.43379e30 0.863807
\(842\) 7.41301e30i 1.42632i
\(843\) 1.11862e30 6.11783e30i 0.212565 1.16254i
\(844\) −1.32774e31 −2.49182
\(845\) 4.90525e30 0.909213
\(846\) −3.62395e30 + 9.57857e30i −0.663427 + 1.75352i
\(847\) −5.48202e30 6.00258e30i −0.991208 1.08533i
\(848\) 3.52461e30i 0.629441i
\(849\) 1.08748e30 5.94754e30i 0.191818 1.04907i
\(850\) 4.15563e29i 0.0724000i
\(851\) 8.80880e29i 0.151585i
\(852\) 3.82171e29 2.09013e30i 0.0649593 0.355270i
\(853\) 4.54969e30i 0.763866i −0.924190 0.381933i \(-0.875259\pi\)
0.924190 0.381933i \(-0.124741\pi\)
\(854\) −4.47258e30 4.89728e30i −0.741737 0.812171i
\(855\) −5.25685e28 + 1.38945e29i −0.00861155 + 0.0227615i
\(856\) −3.43493e29 −0.0555832
\(857\) −2.06974e30 −0.330840 −0.165420 0.986223i \(-0.552898\pi\)
−0.165420 + 0.986223i \(0.552898\pi\)
\(858\) −4.16960e30 + 2.28040e31i −0.658382 + 3.60076i
\(859\) 6.62806e29i 0.103385i −0.998663 0.0516926i \(-0.983538\pi\)
0.998663 0.0516926i \(-0.0164616\pi\)
\(860\) −1.88516e31 −2.90479
\(861\) 7.36426e29 + 1.17656e30i 0.112098 + 0.179095i
\(862\) −7.25794e30 −1.09141
\(863\) 6.69570e30i 0.994678i 0.867556 + 0.497339i \(0.165690\pi\)
−0.867556 + 0.497339i \(0.834310\pi\)
\(864\) −2.04931e30 + 3.39914e30i −0.300755 + 0.498855i
\(865\) 4.23970e30 0.614705
\(866\) −4.09841e30 −0.587054
\(867\) −1.48340e30 2.71233e29i −0.209923 0.0383833i
\(868\) 1.32188e30 1.20724e30i 0.184814 0.168787i
\(869\) 1.18092e31i 1.63122i
\(870\) −4.34728e30 7.94879e29i −0.593288 0.108480i
\(871\) 1.74140e31i 2.34806i
\(872\) 4.30717e30i 0.573811i
\(873\) 3.52575e30 9.31902e30i 0.464090 1.22665i
\(874\) 3.13945e28i 0.00408304i
\(875\) 5.36774e30 + 5.87746e30i 0.689775 + 0.755274i
\(876\) −3.92600e30 + 2.14717e31i −0.498491 + 2.72630i
\(877\) −1.24118e31 −1.55718 −0.778591 0.627532i \(-0.784065\pi\)
−0.778591 + 0.627532i \(0.784065\pi\)
\(878\) −2.01924e31 −2.50320
\(879\) 3.00094e30 + 5.48708e29i 0.367599 + 0.0672137i
\(880\) 5.82597e30i 0.705180i
\(881\) 9.60245e30 1.14851 0.574256 0.818676i \(-0.305292\pi\)
0.574256 + 0.818676i \(0.305292\pi\)
\(882\) 1.27518e31 + 6.19583e30i 1.50713 + 0.732284i
\(883\) −4.97632e30 −0.581194 −0.290597 0.956846i \(-0.593854\pi\)
−0.290597 + 0.956846i \(0.593854\pi\)
\(884\) 1.93097e31i 2.22857i
\(885\) −4.33067e30 7.91842e29i −0.493913 0.0903097i
\(886\) 1.65151e31 1.86135
\(887\) −4.02920e30 −0.448767 −0.224383 0.974501i \(-0.572037\pi\)
−0.224383 + 0.974501i \(0.572037\pi\)
\(888\) 3.43275e30 1.87741e31i 0.377838 2.06644i
\(889\) 2.04048e30 + 2.23425e30i 0.221955 + 0.243031i
\(890\) 1.04406e31i 1.12236i
\(891\) 9.79179e30 1.10882e31i 1.04027 1.17800i
\(892\) 2.59442e31i 2.72401i
\(893\) 2.69043e29i 0.0279179i
\(894\) −7.67496e30 1.40333e30i −0.787104 0.143918i
\(895\) 1.11730e31i 1.13248i
\(896\) 1.34437e31 1.22778e31i 1.34674 1.22995i
\(897\) −1.34871e30 2.46606e29i −0.133536 0.0244164i
\(898\) 1.37948e31 1.34993
\(899\) −5.28291e29 −0.0510972
\(900\) 8.61605e29 + 3.25979e29i 0.0823686 + 0.0311633i
\(901\) 1.28419e31i 1.21344i
\(902\) −5.95722e30 −0.556385
\(903\) −9.46862e30 1.51277e31i −0.874108 1.39654i
\(904\) −9.46339e30 −0.863531
\(905\) 9.16475e30i 0.826629i
\(906\) −4.34124e30 + 2.37427e31i −0.387051 + 2.11682i
\(907\) 2.11316e31 1.86233 0.931165 0.364598i \(-0.118793\pi\)
0.931165 + 0.364598i \(0.118793\pi\)
\(908\) 3.39285e30 0.295572
\(909\) −6.58962e30 2.49311e30i −0.567465 0.214694i
\(910\) 1.79964e31 + 1.97053e31i 1.53197 + 1.67744i
\(911\) 1.39457e31i 1.17354i −0.809753 0.586770i \(-0.800399\pi\)
0.809753 0.586770i \(-0.199601\pi\)
\(912\) 2.48196e28 1.35741e29i 0.00206466 0.0112918i
\(913\) 3.54064e31i 2.91165i
\(914\) 2.17517e30i 0.176831i
\(915\) −1.43285e30 + 7.83640e30i −0.115154 + 0.629789i
\(916\) 2.29478e31i 1.82322i
\(917\) 1.51635e31 + 1.66034e31i 1.19103 + 1.30412i
\(918\) 9.88129e30 1.63899e31i 0.767301 1.27270i
\(919\) −1.30738e31 −1.00366 −0.501832 0.864965i \(-0.667340\pi\)
−0.501832 + 0.864965i \(0.667340\pi\)
\(920\) −1.69848e30 −0.128910
\(921\) 2.51779e30 1.37700e31i 0.188926 1.03326i
\(922\) 1.55817e31i 1.15596i
\(923\) 3.78634e30 0.277716
\(924\) −3.32071e31 + 2.07847e31i −2.40811 + 1.50726i
\(925\) 1.05467e30 0.0756189
\(926\) 1.41803e31i 1.00524i
\(927\) −4.03040e30 + 1.06529e31i −0.282495 + 0.746672i
\(928\) −3.10191e30 −0.214969
\(929\) 1.45756e31 0.998757 0.499379 0.866384i \(-0.333562\pi\)
0.499379 + 0.866384i \(0.333562\pi\)
\(930\) −3.28533e30 6.00707e29i −0.222591 0.0406997i
\(931\) 3.70922e29 + 3.36947e28i 0.0248491 + 0.00225731i
\(932\) 6.09925e30i 0.404026i
\(933\) 2.44389e31 + 4.46854e30i 1.60075 + 0.292690i
\(934\) 2.76461e31i 1.79057i
\(935\) 2.12269e31i 1.35946i
\(936\) 2.77839e31 + 1.05117e31i 1.75953 + 0.665699i
\(937\) 1.56185e31i 0.978081i −0.872261 0.489040i \(-0.837347\pi\)
0.872261 0.489040i \(-0.162653\pi\)
\(938\) −3.37503e31 + 3.08234e31i −2.09001 + 1.90876i
\(939\) −2.66304e30 + 1.45644e31i −0.163075 + 0.891878i
\(940\) −3.25768e31 −1.97272
\(941\) 2.46100e31 1.47374 0.736870 0.676034i \(-0.236303\pi\)
0.736870 + 0.676034i \(0.236303\pi\)
\(942\) −1.54463e31 2.82427e30i −0.914721 0.167252i
\(943\) 3.52332e29i 0.0206338i
\(944\) 4.08935e30 0.236836
\(945\) −3.34240e30 1.66977e31i −0.191436 0.956365i
\(946\) 7.65952e31 4.33855
\(947\) 2.24985e30i 0.126032i −0.998013 0.0630158i \(-0.979928\pi\)
0.998013 0.0630158i \(-0.0200719\pi\)
\(948\) −3.33157e31 6.09162e30i −1.84570 0.337478i
\(949\) −3.88966e31 −2.13116
\(950\) 3.75885e28 0.00203684
\(951\) −1.83139e29 + 1.00161e30i −0.00981490 + 0.0536787i
\(952\) −1.67215e31 + 1.52714e31i −0.886314 + 0.809450i
\(953\) 3.17530e30i 0.166460i 0.996530 + 0.0832299i \(0.0265236\pi\)
−0.996530 + 0.0832299i \(0.973476\pi\)
\(954\) −4.13549e31 1.56462e31i −2.14422 0.811241i
\(955\) 2.32132e31i 1.19042i
\(956\) 5.86573e31i 2.97518i
\(957\) 1.13722e31 + 2.07936e30i 0.570520 + 0.104317i
\(958\) 2.69827e31i 1.33890i
\(959\) −2.47113e30 + 2.25683e30i −0.121283 + 0.110765i
\(960\) −2.83824e31 5.18958e30i −1.37785 0.251932i
\(961\) 2.04263e31 0.980829
\(962\) 7.61171e31 3.61530
\(963\) −3.09336e29 + 8.17617e29i −0.0145330 + 0.0384126i
\(964\) 2.91398e31i 1.35419i
\(965\) −1.85456e31 −0.852520
\(966\) −1.90932e30 3.05046e30i −0.0868197 0.138709i
\(967\) −5.65467e30 −0.254348 −0.127174 0.991880i \(-0.540591\pi\)
−0.127174 + 0.991880i \(0.540591\pi\)
\(968\) 4.47077e31i 1.98926i
\(969\) 9.04302e28 4.94572e29i 0.00398028 0.0217686i
\(970\) 4.92269e31 2.14338
\(971\) −6.16171e30 −0.265399 −0.132700 0.991156i \(-0.542365\pi\)
−0.132700 + 0.991156i \(0.542365\pi\)
\(972\) −2.62306e31 3.33439e31i −1.11767 1.42076i
\(973\) 1.06238e31 9.70251e30i 0.447813 0.408977i
\(974\) 2.85645e31i 1.19113i
\(975\) −2.95260e29 + 1.61481e30i −0.0121803 + 0.0666151i
\(976\) 7.39972e30i 0.301990i
\(977\) 4.41902e31i 1.78416i −0.451882 0.892078i \(-0.649247\pi\)
0.451882 0.892078i \(-0.350753\pi\)
\(978\) −5.82018e30 + 3.18312e31i −0.232476 + 1.27144i
\(979\) 2.73121e31i 1.07929i
\(980\) −4.07989e30 + 4.49126e31i −0.159505 + 1.75588i
\(981\) −1.02524e31 3.87887e30i −0.396551 0.150031i
\(982\) −6.24499e31 −2.38980
\(983\) 1.21606e31 0.460410 0.230205 0.973142i \(-0.426060\pi\)
0.230205 + 0.973142i \(0.426060\pi\)
\(984\) −1.37302e30 + 7.50920e30i −0.0514314 + 0.281284i
\(985\) 2.78112e31i 1.03071i
\(986\) 1.49567e31 0.548439
\(987\) −1.63624e31 2.61417e31i −0.593632 0.948427i
\(988\) 1.74660e30 0.0626969
\(989\) 4.53012e30i 0.160897i
\(990\) 6.83571e31 + 2.58622e31i 2.40223 + 0.908857i
\(991\) −2.86108e31 −0.994846 −0.497423 0.867508i \(-0.665720\pi\)
−0.497423 + 0.867508i \(0.665720\pi\)
\(992\) −2.34418e30 −0.0806525
\(993\) 6.43864e30 + 1.17727e30i 0.219193 + 0.0400784i
\(994\) 6.70194e30 + 7.33835e30i 0.225758 + 0.247196i
\(995\) 4.55738e31i 1.51905i
\(996\) 9.98873e31 + 1.82639e31i 3.29448 + 0.602380i
\(997\) 2.23701e31i 0.730077i 0.930992 + 0.365039i \(0.118944\pi\)
−0.930992 + 0.365039i \(0.881056\pi\)
\(998\) 8.72189e31i 2.81670i
\(999\) −4.15965e31 2.50781e31i −1.32929 0.801415i
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.20.13 52
3.2 odd 2 inner 21.22.c.b.20.40 yes 52
7.6 odd 2 inner 21.22.c.b.20.39 yes 52
21.20 even 2 inner 21.22.c.b.20.14 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.22.c.b.20.13 52 1.1 even 1 trivial
21.22.c.b.20.14 yes 52 21.20 even 2 inner
21.22.c.b.20.39 yes 52 7.6 odd 2 inner
21.22.c.b.20.40 yes 52 3.2 odd 2 inner