Properties

Label 29.10.b.a.28.17
Level $29$
Weight $10$
Character 29.28
Analytic conductor $14.936$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [29,10,Mod(28,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.28");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 29.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.9360392488\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 28.17
Character \(\chi\) \(=\) 29.28
Dual form 29.10.b.a.28.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+25.3186i q^{2} -226.177i q^{3} -129.033 q^{4} -952.179 q^{5} +5726.51 q^{6} +6455.42 q^{7} +9696.20i q^{8} -31473.3 q^{9} +O(q^{10})\) \(q+25.3186i q^{2} -226.177i q^{3} -129.033 q^{4} -952.179 q^{5} +5726.51 q^{6} +6455.42 q^{7} +9696.20i q^{8} -31473.3 q^{9} -24107.9i q^{10} -72133.8i q^{11} +29184.4i q^{12} -190298. q^{13} +163443. i q^{14} +215361. i q^{15} -311559. q^{16} -58686.4i q^{17} -796860. i q^{18} -524361. i q^{19} +122863. q^{20} -1.46007e6i q^{21} +1.82633e6 q^{22} -1.18194e6 q^{23} +2.19306e6 q^{24} -1.04648e6 q^{25} -4.81809e6i q^{26} +2.66669e6i q^{27} -832964. q^{28} +(1.63877e6 - 3.43825e6i) q^{29} -5.45266e6 q^{30} +8.71446e6i q^{31} -2.92381e6i q^{32} -1.63150e7 q^{33} +1.48586e6 q^{34} -6.14672e6 q^{35} +4.06110e6 q^{36} -5.56889e6i q^{37} +1.32761e7 q^{38} +4.30412e7i q^{39} -9.23251e6i q^{40} -4.38228e6i q^{41} +3.69670e7 q^{42} -3.96210e6i q^{43} +9.30765e6i q^{44} +2.99682e7 q^{45} -2.99250e7i q^{46} -1.62041e7i q^{47} +7.04677e7i q^{48} +1.31888e6 q^{49} -2.64955e7i q^{50} -1.32735e7 q^{51} +2.45548e7 q^{52} +2.97542e6 q^{53} -6.75170e7 q^{54} +6.86842e7i q^{55} +6.25930e7i q^{56} -1.18599e8 q^{57} +(8.70518e7 + 4.14915e7i) q^{58} +1.66853e8 q^{59} -2.77888e7i q^{60} -1.63294e8i q^{61} -2.20638e8 q^{62} -2.03173e8 q^{63} -8.54916e7 q^{64} +1.81198e8 q^{65} -4.13074e8i q^{66} -1.87780e7 q^{67} +7.57249e6i q^{68} +2.67327e8i q^{69} -1.55626e8i q^{70} +2.59765e8 q^{71} -3.05171e8i q^{72} +3.06047e8i q^{73} +1.40997e8 q^{74} +2.36690e8i q^{75} +6.76600e7i q^{76} -4.65654e8i q^{77} -1.08974e9 q^{78} +3.09114e7i q^{79} +2.96660e8 q^{80} -1.63426e7 q^{81} +1.10953e8 q^{82} +7.54219e8 q^{83} +1.88398e8i q^{84} +5.58799e7i q^{85} +1.00315e8 q^{86} +(-7.77655e8 - 3.70653e8i) q^{87} +6.99423e8 q^{88} -3.38602e8i q^{89} +7.58753e8i q^{90} -1.22846e9 q^{91} +1.52509e8 q^{92} +1.97101e9 q^{93} +4.10265e8 q^{94} +4.99285e8i q^{95} -6.61299e8 q^{96} +3.80361e8i q^{97} +3.33924e7i q^{98} +2.27028e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9} - 244222 q^{13} + 1246804 q^{16} - 1658748 q^{20} + 822328 q^{22} - 874956 q^{23} + 8668172 q^{24} + 5307748 q^{25} - 620352 q^{28} - 2425374 q^{29} - 8942448 q^{30} + 10134274 q^{33} - 37785784 q^{34} - 20790348 q^{35} + 34550680 q^{36} - 30663552 q^{38} + 56872008 q^{42} - 43877176 q^{45} - 131743922 q^{49} - 6194732 q^{51} + 342496580 q^{52} + 34886610 q^{53} + 116488784 q^{54} - 308361676 q^{57} + 342193888 q^{58} + 175799052 q^{59} - 484313328 q^{62} - 190643424 q^{63} - 419498924 q^{64} - 149739966 q^{65} - 508277640 q^{67} + 263144256 q^{71} + 435201408 q^{74} + 1065897336 q^{78} + 2990464236 q^{80} - 129895134 q^{81} - 527065064 q^{82} + 1555989756 q^{83} - 3422424120 q^{86} + 2176720604 q^{87} - 387386068 q^{88} - 1493579244 q^{91} - 1262849472 q^{92} + 2042413382 q^{93} + 166226488 q^{94} - 6686432820 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 25.3186i 1.11894i 0.828852 + 0.559468i \(0.188995\pi\)
−0.828852 + 0.559468i \(0.811005\pi\)
\(3\) 226.177i 1.61214i −0.591818 0.806072i \(-0.701589\pi\)
0.591818 0.806072i \(-0.298411\pi\)
\(4\) −129.033 −0.252018
\(5\) −952.179 −0.681324 −0.340662 0.940186i \(-0.610651\pi\)
−0.340662 + 0.940186i \(0.610651\pi\)
\(6\) 5726.51 1.80389
\(7\) 6455.42 1.01621 0.508105 0.861295i \(-0.330346\pi\)
0.508105 + 0.861295i \(0.330346\pi\)
\(8\) 9696.20i 0.836944i
\(9\) −31473.3 −1.59901
\(10\) 24107.9i 0.762357i
\(11\) 72133.8i 1.48550i −0.669571 0.742748i \(-0.733522\pi\)
0.669571 0.742748i \(-0.266478\pi\)
\(12\) 29184.4i 0.406289i
\(13\) −190298. −1.84795 −0.923974 0.382454i \(-0.875079\pi\)
−0.923974 + 0.382454i \(0.875079\pi\)
\(14\) 163443.i 1.13707i
\(15\) 215361.i 1.09839i
\(16\) −311559. −1.18850
\(17\) 58686.4i 0.170419i −0.996363 0.0852094i \(-0.972844\pi\)
0.996363 0.0852094i \(-0.0271559\pi\)
\(18\) 796860.i 1.78919i
\(19\) 524361.i 0.923079i −0.887120 0.461540i \(-0.847297\pi\)
0.887120 0.461540i \(-0.152703\pi\)
\(20\) 122863. 0.171706
\(21\) 1.46007e6i 1.63828i
\(22\) 1.82633e6 1.66218
\(23\) −1.18194e6 −0.880682 −0.440341 0.897831i \(-0.645142\pi\)
−0.440341 + 0.897831i \(0.645142\pi\)
\(24\) 2.19306e6 1.34927
\(25\) −1.04648e6 −0.535798
\(26\) 4.81809e6i 2.06774i
\(27\) 2.66669e6i 0.965686i
\(28\) −832964. −0.256103
\(29\) 1.63877e6 3.43825e6i 0.430257 0.902707i
\(30\) −5.45266e6 −1.22903
\(31\) 8.71446e6i 1.69478i 0.530972 + 0.847389i \(0.321827\pi\)
−0.530972 + 0.847389i \(0.678173\pi\)
\(32\) 2.92381e6i 0.492917i
\(33\) −1.63150e7 −2.39483
\(34\) 1.48586e6 0.190688
\(35\) −6.14672e6 −0.692368
\(36\) 4.06110e6 0.402979
\(37\) 5.56889e6i 0.488496i −0.969713 0.244248i \(-0.921459\pi\)
0.969713 0.244248i \(-0.0785410\pi\)
\(38\) 1.32761e7 1.03287
\(39\) 4.30412e7i 2.97916i
\(40\) 9.23251e6i 0.570230i
\(41\) 4.38228e6i 0.242199i −0.992640 0.121100i \(-0.961358\pi\)
0.992640 0.121100i \(-0.0386420\pi\)
\(42\) 3.69670e7 1.83313
\(43\) 3.96210e6i 0.176733i −0.996088 0.0883664i \(-0.971835\pi\)
0.996088 0.0883664i \(-0.0281646\pi\)
\(44\) 9.30765e6i 0.374372i
\(45\) 2.99682e7 1.08944
\(46\) 2.99250e7i 0.985426i
\(47\) 1.62041e7i 0.484377i −0.970229 0.242189i \(-0.922135\pi\)
0.970229 0.242189i \(-0.0778653\pi\)
\(48\) 7.04677e7i 1.91604i
\(49\) 1.31888e6 0.0326832
\(50\) 2.64955e7i 0.599524i
\(51\) −1.32735e7 −0.274739
\(52\) 2.45548e7 0.465716
\(53\) 2.97542e6 0.0517973 0.0258986 0.999665i \(-0.491755\pi\)
0.0258986 + 0.999665i \(0.491755\pi\)
\(54\) −6.75170e7 −1.08054
\(55\) 6.86842e7i 1.01210i
\(56\) 6.25930e7i 0.850511i
\(57\) −1.18599e8 −1.48814
\(58\) 8.70518e7 + 4.14915e7i 1.01007 + 0.481430i
\(59\) 1.66853e8 1.79267 0.896333 0.443382i \(-0.146222\pi\)
0.896333 + 0.443382i \(0.146222\pi\)
\(60\) 2.77888e7i 0.276814i
\(61\) 1.63294e8i 1.51003i −0.655706 0.755016i \(-0.727629\pi\)
0.655706 0.755016i \(-0.272371\pi\)
\(62\) −2.20638e8 −1.89635
\(63\) −2.03173e8 −1.62493
\(64\) −8.54916e7 −0.636962
\(65\) 1.81198e8 1.25905
\(66\) 4.13074e8i 2.67967i
\(67\) −1.87780e7 −0.113845 −0.0569223 0.998379i \(-0.518129\pi\)
−0.0569223 + 0.998379i \(0.518129\pi\)
\(68\) 7.57249e6i 0.0429486i
\(69\) 2.67327e8i 1.41979i
\(70\) 1.55626e8i 0.774715i
\(71\) 2.59765e8 1.21316 0.606581 0.795022i \(-0.292541\pi\)
0.606581 + 0.795022i \(0.292541\pi\)
\(72\) 3.05171e8i 1.33828i
\(73\) 3.06047e8i 1.26135i 0.776048 + 0.630674i \(0.217221\pi\)
−0.776048 + 0.630674i \(0.782779\pi\)
\(74\) 1.40997e8 0.546595
\(75\) 2.36690e8i 0.863784i
\(76\) 6.76600e7i 0.232633i
\(77\) 4.65654e8i 1.50958i
\(78\) −1.08974e9 −3.33349
\(79\) 3.09114e7i 0.0892889i 0.999003 + 0.0446444i \(0.0142155\pi\)
−0.999003 + 0.0446444i \(0.985785\pi\)
\(80\) 2.96660e8 0.809756
\(81\) −1.63426e7 −0.0421830
\(82\) 1.10953e8 0.271005
\(83\) 7.54219e8 1.74440 0.872200 0.489149i \(-0.162693\pi\)
0.872200 + 0.489149i \(0.162693\pi\)
\(84\) 1.88398e8i 0.412875i
\(85\) 5.58799e7i 0.116110i
\(86\) 1.00315e8 0.197753
\(87\) −7.77655e8 3.70653e8i −1.45529 0.693635i
\(88\) 6.99423e8 1.24328
\(89\) 3.38602e8i 0.572050i −0.958222 0.286025i \(-0.907666\pi\)
0.958222 0.286025i \(-0.0923341\pi\)
\(90\) 7.58753e8i 1.21902i
\(91\) −1.22846e9 −1.87790
\(92\) 1.52509e8 0.221948
\(93\) 1.97101e9 2.73223
\(94\) 4.10265e8 0.541987
\(95\) 4.99285e8i 0.628916i
\(96\) −6.61299e8 −0.794653
\(97\) 3.80361e8i 0.436238i 0.975922 + 0.218119i \(0.0699920\pi\)
−0.975922 + 0.218119i \(0.930008\pi\)
\(98\) 3.33924e7i 0.0365704i
\(99\) 2.27028e9i 2.37532i
\(100\) 1.35031e8 0.135031
\(101\) 3.31125e8i 0.316625i 0.987389 + 0.158313i \(0.0506054\pi\)
−0.987389 + 0.158313i \(0.949395\pi\)
\(102\) 3.36068e8i 0.307416i
\(103\) 9.76301e7 0.0854705 0.0427353 0.999086i \(-0.486393\pi\)
0.0427353 + 0.999086i \(0.486393\pi\)
\(104\) 1.84517e9i 1.54663i
\(105\) 1.39025e9i 1.11620i
\(106\) 7.53336e7i 0.0579578i
\(107\) −1.13163e9 −0.834598 −0.417299 0.908769i \(-0.637023\pi\)
−0.417299 + 0.908769i \(0.637023\pi\)
\(108\) 3.44092e8i 0.243370i
\(109\) 4.83988e8 0.328409 0.164205 0.986426i \(-0.447494\pi\)
0.164205 + 0.986426i \(0.447494\pi\)
\(110\) −1.73899e9 −1.13248
\(111\) −1.25956e9 −0.787525
\(112\) −2.01125e9 −1.20777
\(113\) 1.33348e9i 0.769369i −0.923048 0.384684i \(-0.874310\pi\)
0.923048 0.384684i \(-0.125690\pi\)
\(114\) 3.00276e9i 1.66513i
\(115\) 1.12541e9 0.600029
\(116\) −2.11456e8 + 4.43649e8i −0.108432 + 0.227498i
\(117\) 5.98931e9 2.95488
\(118\) 4.22448e9i 2.00588i
\(119\) 3.78846e8i 0.173181i
\(120\) −2.08819e9 −0.919292
\(121\) −2.84533e9 −1.20670
\(122\) 4.13438e9 1.68963
\(123\) −9.91172e8 −0.390460
\(124\) 1.12445e9i 0.427115i
\(125\) 2.85616e9 1.04638
\(126\) 5.14407e9i 1.81819i
\(127\) 2.57244e9i 0.877464i −0.898618 0.438732i \(-0.855428\pi\)
0.898618 0.438732i \(-0.144572\pi\)
\(128\) 3.66152e9i 1.20564i
\(129\) −8.96137e8 −0.284919
\(130\) 4.58769e9i 1.40880i
\(131\) 3.86788e8i 0.114750i −0.998353 0.0573749i \(-0.981727\pi\)
0.998353 0.0573749i \(-0.0182730\pi\)
\(132\) 2.10518e9 0.603541
\(133\) 3.38497e9i 0.938043i
\(134\) 4.75433e8i 0.127385i
\(135\) 2.53917e9i 0.657944i
\(136\) 5.69035e8 0.142631
\(137\) 3.34670e9i 0.811660i −0.913949 0.405830i \(-0.866983\pi\)
0.913949 0.405830i \(-0.133017\pi\)
\(138\) −6.76837e9 −1.58865
\(139\) −6.78753e9 −1.54222 −0.771108 0.636705i \(-0.780297\pi\)
−0.771108 + 0.636705i \(0.780297\pi\)
\(140\) 7.93130e8 0.174489
\(141\) −3.66500e9 −0.780886
\(142\) 6.57691e9i 1.35745i
\(143\) 1.37269e10i 2.74512i
\(144\) 9.80579e9 1.90043
\(145\) −1.56040e9 + 3.27383e9i −0.293144 + 0.615035i
\(146\) −7.74868e9 −1.41137
\(147\) 2.98302e8i 0.0526900i
\(148\) 7.18571e8i 0.123110i
\(149\) −4.45493e9 −0.740461 −0.370231 0.928940i \(-0.620721\pi\)
−0.370231 + 0.928940i \(0.620721\pi\)
\(150\) −5.99268e9 −0.966519
\(151\) 2.47387e9 0.387240 0.193620 0.981077i \(-0.437977\pi\)
0.193620 + 0.981077i \(0.437977\pi\)
\(152\) 5.08431e9 0.772566
\(153\) 1.84705e9i 0.272501i
\(154\) 1.17897e10 1.68912
\(155\) 8.29772e9i 1.15469i
\(156\) 5.55374e9i 0.750802i
\(157\) 8.03709e9i 1.05572i 0.849330 + 0.527862i \(0.177006\pi\)
−0.849330 + 0.527862i \(0.822994\pi\)
\(158\) −7.82635e8 −0.0999085
\(159\) 6.72973e8i 0.0835046i
\(160\) 2.78399e9i 0.335836i
\(161\) −7.62990e9 −0.894958
\(162\) 4.13772e8i 0.0472001i
\(163\) 8.10587e9i 0.899405i −0.893178 0.449703i \(-0.851530\pi\)
0.893178 0.449703i \(-0.148470\pi\)
\(164\) 5.65459e8i 0.0610385i
\(165\) 1.55348e10 1.63166
\(166\) 1.90958e10i 1.95187i
\(167\) 3.68360e9 0.366479 0.183239 0.983068i \(-0.441342\pi\)
0.183239 + 0.983068i \(0.441342\pi\)
\(168\) 1.41571e10 1.37115
\(169\) 2.56090e10 2.41491
\(170\) −1.41480e9 −0.129920
\(171\) 1.65033e10i 1.47601i
\(172\) 5.11242e8i 0.0445398i
\(173\) −1.10024e9 −0.0933860 −0.0466930 0.998909i \(-0.514868\pi\)
−0.0466930 + 0.998909i \(0.514868\pi\)
\(174\) 9.38444e9 1.96892e10i 0.776134 1.62838i
\(175\) −6.75548e9 −0.544484
\(176\) 2.24740e10i 1.76552i
\(177\) 3.77383e10i 2.89003i
\(178\) 8.57293e9 0.640088
\(179\) −1.64418e10 −1.19704 −0.598522 0.801107i \(-0.704245\pi\)
−0.598522 + 0.801107i \(0.704245\pi\)
\(180\) −3.86689e9 −0.274559
\(181\) −1.66762e10 −1.15490 −0.577449 0.816427i \(-0.695952\pi\)
−0.577449 + 0.816427i \(0.695952\pi\)
\(182\) 3.11028e10i 2.10126i
\(183\) −3.69335e10 −2.43439
\(184\) 1.14603e10i 0.737081i
\(185\) 5.30258e9i 0.332824i
\(186\) 4.99034e10i 3.05719i
\(187\) −4.23327e9 −0.253156
\(188\) 2.09086e9i 0.122072i
\(189\) 1.72146e10i 0.981340i
\(190\) −1.26412e10 −0.703717
\(191\) 1.60750e10i 0.873980i −0.899466 0.436990i \(-0.856045\pi\)
0.899466 0.436990i \(-0.143955\pi\)
\(192\) 1.93363e10i 1.02687i
\(193\) 7.70364e9i 0.399658i 0.979831 + 0.199829i \(0.0640386\pi\)
−0.979831 + 0.199829i \(0.935961\pi\)
\(194\) −9.63022e9 −0.488122
\(195\) 4.09829e10i 2.02977i
\(196\) −1.70180e8 −0.00823675
\(197\) 1.17597e10 0.556286 0.278143 0.960540i \(-0.410281\pi\)
0.278143 + 0.960540i \(0.410281\pi\)
\(198\) −5.74805e10 −2.65783
\(199\) 3.85010e10 1.74034 0.870169 0.492754i \(-0.164010\pi\)
0.870169 + 0.492754i \(0.164010\pi\)
\(200\) 1.01469e10i 0.448433i
\(201\) 4.24716e9i 0.183534i
\(202\) −8.38363e9 −0.354284
\(203\) 1.05790e10 2.21954e10i 0.437231 0.917340i
\(204\) 1.71273e9 0.0692393
\(205\) 4.17271e9i 0.165016i
\(206\) 2.47186e9i 0.0956360i
\(207\) 3.71994e10 1.40822
\(208\) 5.92892e10 2.19630
\(209\) −3.78241e10 −1.37123
\(210\) −3.51992e10 −1.24895
\(211\) 2.80121e10i 0.972914i −0.873704 0.486457i \(-0.838289\pi\)
0.873704 0.486457i \(-0.161711\pi\)
\(212\) −3.83928e8 −0.0130538
\(213\) 5.87531e10i 1.95579i
\(214\) 2.86513e10i 0.933862i
\(215\) 3.77262e9i 0.120412i
\(216\) −2.58568e10 −0.808225
\(217\) 5.62555e10i 1.72225i
\(218\) 1.22539e10i 0.367469i
\(219\) 6.92208e10 2.03347
\(220\) 8.86255e9i 0.255068i
\(221\) 1.11679e10i 0.314925i
\(222\) 3.18903e10i 0.881190i
\(223\) 3.01274e10 0.815813 0.407906 0.913024i \(-0.366259\pi\)
0.407906 + 0.913024i \(0.366259\pi\)
\(224\) 1.88744e10i 0.500907i
\(225\) 3.29362e10 0.856745
\(226\) 3.37620e10 0.860874
\(227\) −2.86557e9 −0.0716300 −0.0358150 0.999358i \(-0.511403\pi\)
−0.0358150 + 0.999358i \(0.511403\pi\)
\(228\) 1.53032e10 0.375037
\(229\) 6.63138e10i 1.59347i 0.604329 + 0.796735i \(0.293441\pi\)
−0.604329 + 0.796735i \(0.706559\pi\)
\(230\) 2.84940e10i 0.671394i
\(231\) −1.05320e11 −2.43365
\(232\) 3.33380e10 + 1.58899e10i 0.755515 + 0.360101i
\(233\) −6.93682e10 −1.54191 −0.770955 0.636890i \(-0.780220\pi\)
−0.770955 + 0.636890i \(0.780220\pi\)
\(234\) 1.51641e11i 3.30633i
\(235\) 1.54292e10i 0.330018i
\(236\) −2.15295e10 −0.451784
\(237\) 6.99147e9 0.143947
\(238\) 9.59185e9 0.193779
\(239\) 7.80502e10 1.54733 0.773666 0.633593i \(-0.218421\pi\)
0.773666 + 0.633593i \(0.218421\pi\)
\(240\) 6.70979e10i 1.30544i
\(241\) −6.98133e10 −1.33310 −0.666548 0.745462i \(-0.732229\pi\)
−0.666548 + 0.745462i \(0.732229\pi\)
\(242\) 7.20399e10i 1.35022i
\(243\) 5.61848e10i 1.03369i
\(244\) 2.10704e10i 0.380555i
\(245\) −1.25581e9 −0.0222678
\(246\) 2.50951e10i 0.436899i
\(247\) 9.97850e10i 1.70580i
\(248\) −8.44971e10 −1.41843
\(249\) 1.70587e11i 2.81222i
\(250\) 7.23141e10i 1.17083i
\(251\) 5.01403e10i 0.797362i −0.917090 0.398681i \(-0.869468\pi\)
0.917090 0.398681i \(-0.130532\pi\)
\(252\) 2.62161e10 0.409511
\(253\) 8.52575e10i 1.30825i
\(254\) 6.51308e10 0.981826
\(255\) 1.26388e10 0.187186
\(256\) 4.89330e10 0.712069
\(257\) 2.20462e10 0.315235 0.157617 0.987500i \(-0.449619\pi\)
0.157617 + 0.987500i \(0.449619\pi\)
\(258\) 2.26890e10i 0.318806i
\(259\) 3.59495e10i 0.496414i
\(260\) −2.33806e10 −0.317303
\(261\) −5.15775e10 + 1.08213e11i −0.687983 + 1.44343i
\(262\) 9.79294e9 0.128398
\(263\) 6.96042e10i 0.897086i 0.893761 + 0.448543i \(0.148057\pi\)
−0.893761 + 0.448543i \(0.851943\pi\)
\(264\) 1.58194e11i 2.00434i
\(265\) −2.83313e9 −0.0352907
\(266\) 8.57029e10 1.04961
\(267\) −7.65841e10 −0.922227
\(268\) 2.42298e9 0.0286909
\(269\) 4.96041e10i 0.577607i 0.957388 + 0.288803i \(0.0932574\pi\)
−0.957388 + 0.288803i \(0.906743\pi\)
\(270\) 6.42882e10 0.736198
\(271\) 1.72902e11i 1.94733i −0.227994 0.973663i \(-0.573217\pi\)
0.227994 0.973663i \(-0.426783\pi\)
\(272\) 1.82843e10i 0.202543i
\(273\) 2.77849e11i 3.02745i
\(274\) 8.47339e10 0.908196
\(275\) 7.54866e10i 0.795926i
\(276\) 3.44941e10i 0.357811i
\(277\) 2.11540e10 0.215890 0.107945 0.994157i \(-0.465573\pi\)
0.107945 + 0.994157i \(0.465573\pi\)
\(278\) 1.71851e11i 1.72564i
\(279\) 2.74272e11i 2.70996i
\(280\) 5.95998e10i 0.579473i
\(281\) −1.07209e11 −1.02578 −0.512890 0.858454i \(-0.671425\pi\)
−0.512890 + 0.858454i \(0.671425\pi\)
\(282\) 9.27927e10i 0.873761i
\(283\) −1.74342e11 −1.61571 −0.807854 0.589383i \(-0.799371\pi\)
−0.807854 + 0.589383i \(0.799371\pi\)
\(284\) −3.35184e10 −0.305739
\(285\) 1.12927e11 1.01390
\(286\) −3.47547e11 −3.07161
\(287\) 2.82895e10i 0.246125i
\(288\) 9.20217e10i 0.788178i
\(289\) 1.15144e11 0.970957
\(290\) −8.28889e10 3.95073e10i −0.688185 0.328009i
\(291\) 8.60291e10 0.703278
\(292\) 3.94902e10i 0.317882i
\(293\) 2.26140e10i 0.179255i 0.995975 + 0.0896277i \(0.0285677\pi\)
−0.995975 + 0.0896277i \(0.971432\pi\)
\(294\) 7.55260e9 0.0589567
\(295\) −1.58874e11 −1.22139
\(296\) 5.39970e10 0.408844
\(297\) 1.92358e11 1.43452
\(298\) 1.12793e11i 0.828529i
\(299\) 2.24921e11 1.62745
\(300\) 3.05409e10i 0.217689i
\(301\) 2.55770e10i 0.179598i
\(302\) 6.26350e10i 0.433297i
\(303\) 7.48930e10 0.510446
\(304\) 1.63370e11i 1.09708i
\(305\) 1.55485e11i 1.02882i
\(306\) −4.67648e10 −0.304911
\(307\) 2.82124e11i 1.81267i 0.422563 + 0.906334i \(0.361131\pi\)
−0.422563 + 0.906334i \(0.638869\pi\)
\(308\) 6.00848e10i 0.380440i
\(309\) 2.20817e10i 0.137791i
\(310\) 2.10087e11 1.29203
\(311\) 2.72890e11i 1.65412i −0.562117 0.827058i \(-0.690013\pi\)
0.562117 0.827058i \(-0.309987\pi\)
\(312\) −4.17336e11 −2.49339
\(313\) −3.46295e10 −0.203937 −0.101969 0.994788i \(-0.532514\pi\)
−0.101969 + 0.994788i \(0.532514\pi\)
\(314\) −2.03488e11 −1.18129
\(315\) 1.93457e11 1.10710
\(316\) 3.98860e9i 0.0225024i
\(317\) 1.89960e11i 1.05656i −0.849070 0.528281i \(-0.822837\pi\)
0.849070 0.528281i \(-0.177163\pi\)
\(318\) 1.70388e10 0.0934364
\(319\) −2.48014e11 1.18211e11i −1.34097 0.639144i
\(320\) 8.14033e10 0.433977
\(321\) 2.55949e11i 1.34549i
\(322\) 1.93179e11i 1.00140i
\(323\) −3.07729e10 −0.157310
\(324\) 2.10873e9 0.0106309
\(325\) 1.99144e11 0.990128
\(326\) 2.05230e11 1.00638
\(327\) 1.09467e11i 0.529443i
\(328\) 4.24914e10 0.202707
\(329\) 1.04604e11i 0.492229i
\(330\) 3.93321e11i 1.82572i
\(331\) 8.66640e9i 0.0396837i 0.999803 + 0.0198419i \(0.00631628\pi\)
−0.999803 + 0.0198419i \(0.993684\pi\)
\(332\) −9.73193e10 −0.439620
\(333\) 1.75271e11i 0.781108i
\(334\) 9.32638e10i 0.410066i
\(335\) 1.78800e10 0.0775650
\(336\) 4.54899e11i 1.94710i
\(337\) 8.34807e9i 0.0352575i −0.999845 0.0176288i \(-0.994388\pi\)
0.999845 0.0176288i \(-0.00561170\pi\)
\(338\) 6.48384e11i 2.70214i
\(339\) −3.01604e11 −1.24033
\(340\) 7.21037e9i 0.0292619i
\(341\) 6.28607e11 2.51759
\(342\) −4.17842e11 −1.65156
\(343\) −2.51986e11 −0.982997
\(344\) 3.84173e10 0.147915
\(345\) 2.54543e11i 0.967333i
\(346\) 2.78567e10i 0.104493i
\(347\) 2.46570e11 0.912974 0.456487 0.889730i \(-0.349107\pi\)
0.456487 + 0.889730i \(0.349107\pi\)
\(348\) 1.00343e11 + 4.78266e10i 0.366760 + 0.174809i
\(349\) 8.56684e10 0.309105 0.154553 0.987985i \(-0.450606\pi\)
0.154553 + 0.987985i \(0.450606\pi\)
\(350\) 1.71039e11i 0.609242i
\(351\) 5.07467e11i 1.78454i
\(352\) −2.10905e11 −0.732226
\(353\) −1.96746e11 −0.674404 −0.337202 0.941432i \(-0.609481\pi\)
−0.337202 + 0.941432i \(0.609481\pi\)
\(354\) 9.55483e11 3.23376
\(355\) −2.47343e11 −0.826556
\(356\) 4.36909e10i 0.144167i
\(357\) −8.56863e10 −0.279193
\(358\) 4.16283e11i 1.33941i
\(359\) 1.70052e11i 0.540326i 0.962815 + 0.270163i \(0.0870776\pi\)
−0.962815 + 0.270163i \(0.912922\pi\)
\(360\) 2.90577e11i 0.911801i
\(361\) 4.77334e10 0.147924
\(362\) 4.22219e11i 1.29226i
\(363\) 6.43550e11i 1.94537i
\(364\) 1.58512e11 0.473266
\(365\) 2.91411e11i 0.859385i
\(366\) 9.35105e11i 2.72393i
\(367\) 1.08673e11i 0.312698i 0.987702 + 0.156349i \(0.0499725\pi\)
−0.987702 + 0.156349i \(0.950028\pi\)
\(368\) 3.68244e11 1.04669
\(369\) 1.37925e11i 0.387278i
\(370\) −1.34254e11 −0.372408
\(371\) 1.92076e10 0.0526369
\(372\) −2.54326e11 −0.688570
\(373\) 6.34254e11 1.69658 0.848288 0.529535i \(-0.177634\pi\)
0.848288 + 0.529535i \(0.177634\pi\)
\(374\) 1.07181e11i 0.283266i
\(375\) 6.45999e11i 1.68691i
\(376\) 1.57118e11 0.405397
\(377\) −3.11856e11 + 6.54294e11i −0.795092 + 1.66816i
\(378\) −4.35851e11 −1.09806
\(379\) 3.44954e10i 0.0858785i −0.999078 0.0429392i \(-0.986328\pi\)
0.999078 0.0429392i \(-0.0136722\pi\)
\(380\) 6.44244e10i 0.158498i
\(381\) −5.81829e11 −1.41460
\(382\) 4.06998e11 0.977928
\(383\) −6.39905e11 −1.51957 −0.759786 0.650173i \(-0.774696\pi\)
−0.759786 + 0.650173i \(0.774696\pi\)
\(384\) −8.28154e11 −1.94366
\(385\) 4.43386e11i 1.02851i
\(386\) −1.95046e11 −0.447191
\(387\) 1.24700e11i 0.282597i
\(388\) 4.90792e10i 0.109940i
\(389\) 5.67805e11i 1.25726i −0.777704 0.628631i \(-0.783616\pi\)
0.777704 0.628631i \(-0.216384\pi\)
\(390\) 1.03763e12 2.27118
\(391\) 6.93636e10i 0.150085i
\(392\) 1.27882e10i 0.0273540i
\(393\) −8.74827e10 −0.184993
\(394\) 2.97739e11i 0.622448i
\(395\) 2.94332e10i 0.0608346i
\(396\) 2.92942e11i 0.598623i
\(397\) −7.35961e11 −1.48695 −0.743477 0.668762i \(-0.766825\pi\)
−0.743477 + 0.668762i \(0.766825\pi\)
\(398\) 9.74794e11i 1.94733i
\(399\) −7.65604e11 −1.51226
\(400\) 3.26041e11 0.636799
\(401\) −1.23592e11 −0.238694 −0.119347 0.992853i \(-0.538080\pi\)
−0.119347 + 0.992853i \(0.538080\pi\)
\(402\) −1.07532e11 −0.205363
\(403\) 1.65835e12i 3.13186i
\(404\) 4.27261e10i 0.0797953i
\(405\) 1.55610e10 0.0287403
\(406\) 5.61956e11 + 2.67845e11i 1.02644 + 0.489234i
\(407\) −4.01705e11 −0.725658
\(408\) 1.28703e11i 0.229942i
\(409\) 6.27607e11i 1.10900i −0.832183 0.554502i \(-0.812909\pi\)
0.832183 0.554502i \(-0.187091\pi\)
\(410\) −1.05647e11 −0.184642
\(411\) −7.56948e11 −1.30851
\(412\) −1.25975e10 −0.0215401
\(413\) 1.07710e12 1.82172
\(414\) 9.41838e11i 1.57570i
\(415\) −7.18151e11 −1.18850
\(416\) 5.56396e11i 0.910885i
\(417\) 1.53519e12i 2.48627i
\(418\) 9.57655e11i 1.53432i
\(419\) −5.64770e11 −0.895176 −0.447588 0.894240i \(-0.647717\pi\)
−0.447588 + 0.894240i \(0.647717\pi\)
\(420\) 1.79388e11i 0.281302i
\(421\) 9.40828e11i 1.45962i −0.683649 0.729811i \(-0.739608\pi\)
0.683649 0.729811i \(-0.260392\pi\)
\(422\) 7.09228e11 1.08863
\(423\) 5.09995e11i 0.774523i
\(424\) 2.88503e10i 0.0433514i
\(425\) 6.14142e10i 0.0913101i
\(426\) 1.48755e12 2.18841
\(427\) 1.05413e12i 1.53451i
\(428\) 1.46018e11 0.210334
\(429\) 3.10472e12 4.42553
\(430\) −9.55177e10 −0.134734
\(431\) 1.30054e12 1.81542 0.907708 0.419602i \(-0.137830\pi\)
0.907708 + 0.419602i \(0.137830\pi\)
\(432\) 8.30833e11i 1.14772i
\(433\) 1.41146e11i 0.192962i 0.995335 + 0.0964810i \(0.0307587\pi\)
−0.995335 + 0.0964810i \(0.969241\pi\)
\(434\) −1.42431e12 −1.92709
\(435\) 7.40466e11 + 3.52928e11i 0.991525 + 0.472590i
\(436\) −6.24505e10 −0.0827650
\(437\) 6.19761e11i 0.812939i
\(438\) 1.75258e12i 2.27533i
\(439\) 3.05187e11 0.392171 0.196086 0.980587i \(-0.437177\pi\)
0.196086 + 0.980587i \(0.437177\pi\)
\(440\) −6.65976e11 −0.847074
\(441\) −4.15096e10 −0.0522607
\(442\) −2.82757e11 −0.352381
\(443\) 8.29399e11i 1.02317i −0.859233 0.511584i \(-0.829059\pi\)
0.859233 0.511584i \(-0.170941\pi\)
\(444\) 1.62525e11 0.198471
\(445\) 3.22409e11i 0.389751i
\(446\) 7.62786e11i 0.912842i
\(447\) 1.00760e12i 1.19373i
\(448\) −5.51885e11 −0.647288
\(449\) 6.65860e11i 0.773169i 0.922254 + 0.386585i \(0.126345\pi\)
−0.922254 + 0.386585i \(0.873655\pi\)
\(450\) 8.33899e11i 0.958643i
\(451\) −3.16110e11 −0.359786
\(452\) 1.72064e11i 0.193895i
\(453\) 5.59534e11i 0.624287i
\(454\) 7.25524e10i 0.0801494i
\(455\) 1.16971e12 1.27946
\(456\) 1.14996e12i 1.24549i
\(457\) −9.89473e11 −1.06116 −0.530580 0.847635i \(-0.678026\pi\)
−0.530580 + 0.847635i \(0.678026\pi\)
\(458\) −1.67897e12 −1.78299
\(459\) 1.56499e11 0.164571
\(460\) −1.45216e11 −0.151218
\(461\) 4.27395e11i 0.440733i 0.975417 + 0.220366i \(0.0707253\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(462\) 2.66657e12i 2.72310i
\(463\) −5.62508e11 −0.568871 −0.284436 0.958695i \(-0.591806\pi\)
−0.284436 + 0.958695i \(0.591806\pi\)
\(464\) −5.10575e11 + 1.07122e12i −0.511362 + 1.07287i
\(465\) −1.87676e12 −1.86153
\(466\) 1.75631e12i 1.72530i
\(467\) 9.75663e11i 0.949235i 0.880192 + 0.474617i \(0.157414\pi\)
−0.880192 + 0.474617i \(0.842586\pi\)
\(468\) −7.72820e11 −0.744684
\(469\) −1.21220e11 −0.115690
\(470\) −3.90645e11 −0.369269
\(471\) 1.81781e12 1.70198
\(472\) 1.61784e12i 1.50036i
\(473\) −2.85801e11 −0.262536
\(474\) 1.77015e11i 0.161067i
\(475\) 5.48734e11i 0.494584i
\(476\) 4.88837e10i 0.0436448i
\(477\) −9.36462e10 −0.0828242
\(478\) 1.97613e12i 1.73137i
\(479\) 8.35058e11i 0.724781i −0.932026 0.362391i \(-0.881961\pi\)
0.932026 0.362391i \(-0.118039\pi\)
\(480\) 6.29675e11 0.541416
\(481\) 1.05975e12i 0.902715i
\(482\) 1.76758e12i 1.49165i
\(483\) 1.72571e12i 1.44280i
\(484\) 3.67142e11 0.304110
\(485\) 3.62171e11i 0.297219i
\(486\) −1.42252e12 −1.15663
\(487\) 1.57701e12 1.27044 0.635219 0.772332i \(-0.280910\pi\)
0.635219 + 0.772332i \(0.280910\pi\)
\(488\) 1.58333e12 1.26381
\(489\) −1.83336e12 −1.44997
\(490\) 3.17955e10i 0.0249163i
\(491\) 1.15196e12i 0.894477i −0.894415 0.447239i \(-0.852407\pi\)
0.894415 0.447239i \(-0.147593\pi\)
\(492\) 1.27894e11 0.0984029
\(493\) −2.01779e11 9.61736e10i −0.153838 0.0733238i
\(494\) −2.52642e12 −1.90869
\(495\) 2.16172e12i 1.61836i
\(496\) 2.71507e12i 2.01425i
\(497\) 1.67690e12 1.23283
\(498\) 4.31904e12 3.14670
\(499\) 4.80672e11 0.347054 0.173527 0.984829i \(-0.444484\pi\)
0.173527 + 0.984829i \(0.444484\pi\)
\(500\) −3.68540e11 −0.263705
\(501\) 8.33148e11i 0.590816i
\(502\) 1.26949e12 0.892197
\(503\) 1.70492e12i 1.18754i 0.804634 + 0.593771i \(0.202361\pi\)
−0.804634 + 0.593771i \(0.797639\pi\)
\(504\) 1.97001e12i 1.35997i
\(505\) 3.15290e11i 0.215724i
\(506\) −2.15860e12 −1.46385
\(507\) 5.79217e12i 3.89319i
\(508\) 3.31931e11i 0.221137i
\(509\) −3.58315e11 −0.236611 −0.118305 0.992977i \(-0.537746\pi\)
−0.118305 + 0.992977i \(0.537746\pi\)
\(510\) 3.19997e11i 0.209450i
\(511\) 1.97566e12i 1.28179i
\(512\) 6.35782e11i 0.408878i
\(513\) 1.39831e12 0.891405
\(514\) 5.58178e11i 0.352727i
\(515\) −9.29613e10 −0.0582331
\(516\) 1.15631e11 0.0718046
\(517\) −1.16886e12 −0.719540
\(518\) 9.10193e11 0.555456
\(519\) 2.48851e11i 0.150552i
\(520\) 1.75693e12i 1.05376i
\(521\) −1.26025e12 −0.749356 −0.374678 0.927155i \(-0.622247\pi\)
−0.374678 + 0.927155i \(0.622247\pi\)
\(522\) −2.73980e12 1.30587e12i −1.61511 0.769810i
\(523\) 2.47350e12 1.44562 0.722809 0.691048i \(-0.242851\pi\)
0.722809 + 0.691048i \(0.242851\pi\)
\(524\) 4.99085e10i 0.0289190i
\(525\) 1.52794e12i 0.877786i
\(526\) −1.76228e12 −1.00378
\(527\) 5.11420e11 0.288822
\(528\) 5.08310e12 2.84627
\(529\) −4.04178e11 −0.224400
\(530\) 7.17310e10i 0.0394880i
\(531\) −5.25140e12 −2.86648
\(532\) 4.36774e11i 0.236404i
\(533\) 8.33940e11i 0.447571i
\(534\) 1.93900e12i 1.03191i
\(535\) 1.07751e12 0.568631
\(536\) 1.82075e11i 0.0952816i
\(537\) 3.71876e12i 1.92981i
\(538\) −1.25591e12 −0.646305
\(539\) 9.51361e10i 0.0485508i
\(540\) 3.27637e11i 0.165814i
\(541\) 2.21016e12i 1.10927i −0.832094 0.554634i \(-0.812858\pi\)
0.832094 0.554634i \(-0.187142\pi\)
\(542\) 4.37764e12 2.17893
\(543\) 3.77178e12i 1.86186i
\(544\) −1.71588e11 −0.0840023
\(545\) −4.60843e11 −0.223753
\(546\) −7.03476e12 −3.38753
\(547\) −1.24567e12 −0.594921 −0.297460 0.954734i \(-0.596140\pi\)
−0.297460 + 0.954734i \(0.596140\pi\)
\(548\) 4.31835e11i 0.204553i
\(549\) 5.13940e12i 2.41455i
\(550\) −1.91122e12 −0.890591
\(551\) −1.80288e12 8.59308e11i −0.833270 0.397161i
\(552\) −2.59206e12 −1.18828
\(553\) 1.99546e11i 0.0907363i
\(554\) 5.35590e11i 0.241568i
\(555\) 1.19932e12 0.536559
\(556\) 8.75817e11 0.388666
\(557\) 2.69656e12 1.18703 0.593516 0.804822i \(-0.297739\pi\)
0.593516 + 0.804822i \(0.297739\pi\)
\(558\) 6.94420e12 3.03228
\(559\) 7.53980e11i 0.326593i
\(560\) 1.91507e12 0.822883
\(561\) 9.57471e11i 0.408124i
\(562\) 2.71440e12i 1.14778i
\(563\) 1.78577e12i 0.749098i −0.927207 0.374549i \(-0.877797\pi\)
0.927207 0.374549i \(-0.122203\pi\)
\(564\) 4.72906e11 0.196797
\(565\) 1.26971e12i 0.524189i
\(566\) 4.41410e12i 1.80787i
\(567\) −1.05498e11 −0.0428668
\(568\) 2.51874e12i 1.01535i
\(569\) 2.11081e12i 0.844197i −0.906550 0.422099i \(-0.861294\pi\)
0.906550 0.422099i \(-0.138706\pi\)
\(570\) 2.85916e12i 1.13449i
\(571\) −7.30451e11 −0.287560 −0.143780 0.989610i \(-0.545926\pi\)
−0.143780 + 0.989610i \(0.545926\pi\)
\(572\) 1.77123e12i 0.691820i
\(573\) −3.63581e12 −1.40898
\(574\) 7.16250e11 0.275398
\(575\) 1.23687e12 0.471868
\(576\) 2.69070e12 1.01851
\(577\) 2.07846e12i 0.780638i 0.920680 + 0.390319i \(0.127635\pi\)
−0.920680 + 0.390319i \(0.872365\pi\)
\(578\) 2.91528e12i 1.08644i
\(579\) 1.74239e12 0.644306
\(580\) 2.01344e11 4.22433e11i 0.0738775 0.155000i
\(581\) 4.86880e12 1.77268
\(582\) 2.17814e12i 0.786923i
\(583\) 2.14628e11i 0.0769446i
\(584\) −2.96749e12 −1.05568
\(585\) −5.70289e12 −2.01323
\(586\) −5.72555e11 −0.200575
\(587\) 1.22754e12 0.426740 0.213370 0.976971i \(-0.431556\pi\)
0.213370 + 0.976971i \(0.431556\pi\)
\(588\) 3.84909e10i 0.0132788i
\(589\) 4.56952e12 1.56441
\(590\) 4.02246e12i 1.36665i
\(591\) 2.65978e12i 0.896813i
\(592\) 1.73504e12i 0.580579i
\(593\) 3.59477e12 1.19378 0.596890 0.802323i \(-0.296403\pi\)
0.596890 + 0.802323i \(0.296403\pi\)
\(594\) 4.87025e12i 1.60514i
\(595\) 3.60729e11i 0.117992i
\(596\) 5.74833e11 0.186610
\(597\) 8.70807e12i 2.80567i
\(598\) 5.69468e12i 1.82102i
\(599\) 5.88884e11i 0.186900i 0.995624 + 0.0934499i \(0.0297895\pi\)
−0.995624 + 0.0934499i \(0.970210\pi\)
\(600\) −2.29500e12 −0.722939
\(601\) 6.43152e11i 0.201084i −0.994933 0.100542i \(-0.967942\pi\)
0.994933 0.100542i \(-0.0320577\pi\)
\(602\) 6.47575e11 0.200958
\(603\) 5.91005e11 0.182038
\(604\) −3.19211e11 −0.0975915
\(605\) 2.70926e12 0.822152
\(606\) 1.89619e12i 0.571156i
\(607\) 3.88974e12i 1.16298i −0.813555 0.581488i \(-0.802471\pi\)
0.813555 0.581488i \(-0.197529\pi\)
\(608\) −1.53313e12 −0.455002
\(609\) −5.02009e12 2.39272e12i −1.47888 0.704879i
\(610\) −3.93667e12 −1.15118
\(611\) 3.08361e12i 0.895104i
\(612\) 2.38331e11i 0.0686751i
\(613\) −3.06172e12 −0.875778 −0.437889 0.899029i \(-0.644274\pi\)
−0.437889 + 0.899029i \(0.644274\pi\)
\(614\) −7.14301e12 −2.02826
\(615\) 9.43773e11 0.266029
\(616\) 4.51507e12 1.26343
\(617\) 4.30208e12i 1.19507i −0.801841 0.597537i \(-0.796146\pi\)
0.801841 0.597537i \(-0.203854\pi\)
\(618\) 5.59079e11 0.154179
\(619\) 1.75113e12i 0.479413i 0.970845 + 0.239706i \(0.0770512\pi\)
−0.970845 + 0.239706i \(0.922949\pi\)
\(620\) 1.07068e12i 0.291003i
\(621\) 3.15186e12i 0.850462i
\(622\) 6.90920e12 1.85085
\(623\) 2.18582e12i 0.581323i
\(624\) 1.34099e13i 3.54075i
\(625\) −6.75667e11 −0.177122
\(626\) 8.76772e11i 0.228193i
\(627\) 8.55497e12i 2.21062i
\(628\) 1.03705e12i 0.266061i
\(629\) −3.26818e11 −0.0832488
\(630\) 4.89807e12i 1.23878i
\(631\) −4.19856e12 −1.05431 −0.527155 0.849769i \(-0.676741\pi\)
−0.527155 + 0.849769i \(0.676741\pi\)
\(632\) −2.99723e11 −0.0747298
\(633\) −6.33571e12 −1.56848
\(634\) 4.80952e12 1.18223
\(635\) 2.44943e12i 0.597837i
\(636\) 8.68359e10i 0.0210447i
\(637\) −2.50982e11 −0.0603969
\(638\) 2.99294e12 6.27938e12i 0.715162 1.50046i
\(639\) −8.17566e12 −1.93985
\(640\) 3.48642e12i 0.821429i
\(641\) 5.18483e12i 1.21303i 0.795070 + 0.606517i \(0.207434\pi\)
−0.795070 + 0.606517i \(0.792566\pi\)
\(642\) −6.48028e12 −1.50552
\(643\) 4.08571e12 0.942579 0.471289 0.881979i \(-0.343789\pi\)
0.471289 + 0.881979i \(0.343789\pi\)
\(644\) 9.84511e11 0.225545
\(645\) 8.53283e11 0.194122
\(646\) 7.79127e11i 0.176020i
\(647\) −5.24754e12 −1.17730 −0.588649 0.808389i \(-0.700340\pi\)
−0.588649 + 0.808389i \(0.700340\pi\)
\(648\) 1.58461e11i 0.0353048i
\(649\) 1.20357e13i 2.66300i
\(650\) 5.04204e12i 1.10789i
\(651\) 1.27237e13 2.77652
\(652\) 1.04593e12i 0.226666i
\(653\) 4.07319e12i 0.876648i −0.898817 0.438324i \(-0.855572\pi\)
0.898817 0.438324i \(-0.144428\pi\)
\(654\) 2.77156e12 0.592413
\(655\) 3.68291e11i 0.0781817i
\(656\) 1.36534e12i 0.287855i
\(657\) 9.63228e12i 2.01690i
\(658\) 2.64843e12 0.550773
\(659\) 1.31285e12i 0.271164i 0.990766 + 0.135582i \(0.0432904\pi\)
−0.990766 + 0.135582i \(0.956710\pi\)
\(660\) −2.00451e12 −0.411207
\(661\) 3.98945e12 0.812842 0.406421 0.913686i \(-0.366777\pi\)
0.406421 + 0.913686i \(0.366777\pi\)
\(662\) −2.19421e11 −0.0444036
\(663\) 2.52593e12 0.507704
\(664\) 7.31306e12i 1.45997i
\(665\) 3.22310e12i 0.639111i
\(666\) −4.43762e12 −0.874010
\(667\) −1.93692e12 + 4.06380e12i −0.378919 + 0.794997i
\(668\) −4.75307e11 −0.0923592
\(669\) 6.81415e12i 1.31521i
\(670\) 4.52697e11i 0.0867903i
\(671\) −1.17790e13 −2.24315
\(672\) −4.26897e12 −0.807534
\(673\) 4.19198e12 0.787683 0.393842 0.919178i \(-0.371146\pi\)
0.393842 + 0.919178i \(0.371146\pi\)
\(674\) 2.11362e11 0.0394509
\(675\) 2.79064e12i 0.517413i
\(676\) −3.30441e12 −0.608602
\(677\) 1.73512e12i 0.317454i 0.987322 + 0.158727i \(0.0507390\pi\)
−0.987322 + 0.158727i \(0.949261\pi\)
\(678\) 7.63620e12i 1.38785i
\(679\) 2.45539e12i 0.443309i
\(680\) −5.41823e11 −0.0971778
\(681\) 6.48128e11i 0.115478i
\(682\) 1.59155e13i 2.81702i
\(683\) −4.07075e12 −0.715783 −0.357891 0.933763i \(-0.616504\pi\)
−0.357891 + 0.933763i \(0.616504\pi\)
\(684\) 2.12948e12i 0.371981i
\(685\) 3.18666e12i 0.553003i
\(686\) 6.37993e12i 1.09991i
\(687\) 1.49987e13 2.56890
\(688\) 1.23443e12i 0.210048i
\(689\) −5.66218e11 −0.0957187
\(690\) 6.44469e12 1.08238
\(691\) −5.33558e12 −0.890288 −0.445144 0.895459i \(-0.646847\pi\)
−0.445144 + 0.895459i \(0.646847\pi\)
\(692\) 1.41968e11 0.0235350
\(693\) 1.46556e13i 2.41382i
\(694\) 6.24283e12i 1.02156i
\(695\) 6.46294e12 1.05075
\(696\) 3.59393e12 7.54030e12i 0.580534 1.21800i
\(697\) −2.57180e11 −0.0412753
\(698\) 2.16901e12i 0.345869i
\(699\) 1.56895e13i 2.48578i
\(700\) 8.71681e11 0.137220
\(701\) −2.30002e12 −0.359750 −0.179875 0.983689i \(-0.557569\pi\)
−0.179875 + 0.983689i \(0.557569\pi\)
\(702\) 1.28484e13 1.99678
\(703\) −2.92011e12 −0.450920
\(704\) 6.16683e12i 0.946205i
\(705\) 3.48973e12 0.532036
\(706\) 4.98134e12i 0.754615i
\(707\) 2.13755e12i 0.321758i
\(708\) 4.86950e12i 0.728341i
\(709\) −7.74840e12 −1.15161 −0.575803 0.817588i \(-0.695310\pi\)
−0.575803 + 0.817588i \(0.695310\pi\)
\(710\) 6.26239e12i 0.924863i
\(711\) 9.72884e11i 0.142774i
\(712\) 3.28315e12 0.478774
\(713\) 1.02999e13i 1.49256i
\(714\) 2.16946e12i 0.312399i
\(715\) 1.30705e13i 1.87032i
\(716\) 2.12153e12 0.301676
\(717\) 1.76532e13i 2.49452i
\(718\) −4.30548e12 −0.604590
\(719\) 6.49943e12 0.906975 0.453487 0.891263i \(-0.350180\pi\)
0.453487 + 0.891263i \(0.350180\pi\)
\(720\) −9.33686e12 −1.29481
\(721\) 6.30244e11 0.0868560
\(722\) 1.20854e12i 0.165518i
\(723\) 1.57902e13i 2.14914i
\(724\) 2.15179e12 0.291055
\(725\) −1.71494e12 + 3.59806e12i −0.230531 + 0.483669i
\(726\) −1.62938e13 −2.17675
\(727\) 2.92436e12i 0.388262i 0.980976 + 0.194131i \(0.0621887\pi\)
−0.980976 + 0.194131i \(0.937811\pi\)
\(728\) 1.19114e13i 1.57170i
\(729\) 1.23861e13 1.62428
\(730\) 7.37813e12 0.961597
\(731\) −2.32521e11 −0.0301186
\(732\) 4.76564e12 0.613510
\(733\) 2.47043e12i 0.316086i −0.987432 0.158043i \(-0.949482\pi\)
0.987432 0.158043i \(-0.0505185\pi\)
\(734\) −2.75146e12 −0.349889
\(735\) 2.84037e11i 0.0358989i
\(736\) 3.45575e12i 0.434103i
\(737\) 1.35453e12i 0.169116i
\(738\) −3.49206e12 −0.433339
\(739\) 4.97944e12i 0.614159i −0.951684 0.307080i \(-0.900648\pi\)
0.951684 0.307080i \(-0.0993518\pi\)
\(740\) 6.84208e11i 0.0838775i
\(741\) 2.25691e13 2.75000
\(742\) 4.86310e11i 0.0588973i
\(743\) 6.90155e12i 0.830801i 0.909639 + 0.415401i \(0.136359\pi\)
−0.909639 + 0.415401i \(0.863641\pi\)
\(744\) 1.91113e13i 2.28672i
\(745\) 4.24189e12 0.504494
\(746\) 1.60584e13i 1.89836i
\(747\) −2.37377e13 −2.78931
\(748\) 5.46232e11 0.0637999
\(749\) −7.30515e12 −0.848127
\(750\) 1.63558e13 1.88754
\(751\) 3.12113e12i 0.358040i −0.983845 0.179020i \(-0.942707\pi\)
0.983845 0.179020i \(-0.0572927\pi\)
\(752\) 5.04853e12i 0.575685i
\(753\) −1.13406e13 −1.28546
\(754\) −1.65658e13 7.89576e12i −1.86656 0.889657i
\(755\) −2.35557e12 −0.263836
\(756\) 2.22126e12i 0.247315i
\(757\) 2.84714e12i 0.315121i −0.987509 0.157560i \(-0.949637\pi\)
0.987509 0.157560i \(-0.0503629\pi\)
\(758\) 8.73376e11 0.0960925
\(759\) 1.92833e13 2.10909
\(760\) −4.84117e12 −0.526367
\(761\) −8.50265e12 −0.919017 −0.459508 0.888173i \(-0.651974\pi\)
−0.459508 + 0.888173i \(0.651974\pi\)
\(762\) 1.47311e13i 1.58284i
\(763\) 3.12435e12 0.333733
\(764\) 2.07421e12i 0.220259i
\(765\) 1.75872e12i 0.185661i
\(766\) 1.62015e13i 1.70030i
\(767\) −3.17518e13 −3.31275
\(768\) 1.10675e13i 1.14796i
\(769\) 2.79377e12i 0.288086i 0.989571 + 0.144043i \(0.0460104\pi\)
−0.989571 + 0.144043i \(0.953990\pi\)
\(770\) −1.12259e13 −1.15084
\(771\) 4.98634e12i 0.508203i
\(772\) 9.94026e11i 0.100721i
\(773\) 1.50515e13i 1.51626i 0.652104 + 0.758129i \(0.273886\pi\)
−0.652104 + 0.758129i \(0.726114\pi\)
\(774\) −3.15724e12 −0.316208
\(775\) 9.11952e12i 0.908059i
\(776\) −3.68805e12 −0.365106
\(777\) −8.13097e12 −0.800291
\(778\) 1.43760e13 1.40680
\(779\) −2.29789e12 −0.223569
\(780\) 5.28816e12i 0.511539i
\(781\) 1.87379e13i 1.80215i
\(782\) −1.75619e12 −0.167935
\(783\) 9.16876e12 + 4.37010e12i 0.871731 + 0.415493i
\(784\) −4.10911e11 −0.0388441
\(785\) 7.65274e12i 0.719289i
\(786\) 2.21494e12i 0.206996i
\(787\) 3.12979e12 0.290823 0.145412 0.989371i \(-0.453549\pi\)
0.145412 + 0.989371i \(0.453549\pi\)
\(788\) −1.51739e12 −0.140194
\(789\) 1.57429e13 1.44623
\(790\) 7.45209e11 0.0680700
\(791\) 8.60820e12i 0.781840i
\(792\) −2.20131e13 −1.98801
\(793\) 3.10746e13i 2.79046i
\(794\) 1.86335e13i 1.66381i
\(795\) 6.40791e11i 0.0568937i
\(796\) −4.96791e12 −0.438596
\(797\) 1.67045e13i 1.46646i 0.679978 + 0.733232i \(0.261989\pi\)
−0.679978 + 0.733232i \(0.738011\pi\)
\(798\) 1.93841e13i 1.69212i
\(799\) −9.50958e11 −0.0825470
\(800\) 3.05971e12i 0.264104i
\(801\) 1.06569e13i 0.914713i
\(802\) 3.12919e12i 0.267084i
\(803\) 2.20763e13 1.87373
\(804\) 5.48024e11i 0.0462538i
\(805\) 7.26503e12 0.609756
\(806\) 4.19871e13 3.50436
\(807\) 1.12193e13 0.931185
\(808\) −3.21065e12 −0.264998
\(809\) 6.04286e12i 0.495992i −0.968761 0.247996i \(-0.920228\pi\)
0.968761 0.247996i \(-0.0797719\pi\)
\(810\) 3.93984e11i 0.0321586i
\(811\) −5.01698e12 −0.407238 −0.203619 0.979050i \(-0.565270\pi\)
−0.203619 + 0.979050i \(0.565270\pi\)
\(812\) −1.36504e12 + 2.86394e12i −0.110190 + 0.231186i
\(813\) −3.91066e13 −3.13937
\(814\) 1.01706e13i 0.811965i
\(815\) 7.71823e12i 0.612786i
\(816\) 4.13550e12 0.326529
\(817\) −2.07757e12 −0.163138
\(818\) 1.58902e13 1.24090
\(819\) 3.86635e13 3.00278
\(820\) 5.38418e11i 0.0415870i
\(821\) 6.56513e12 0.504312 0.252156 0.967687i \(-0.418860\pi\)
0.252156 + 0.967687i \(0.418860\pi\)
\(822\) 1.91649e13i 1.46414i
\(823\) 1.95790e13i 1.48761i 0.668395 + 0.743807i \(0.266982\pi\)
−0.668395 + 0.743807i \(0.733018\pi\)
\(824\) 9.46641e11i 0.0715340i
\(825\) 1.70734e13 1.28315
\(826\) 2.72708e13i 2.03839i
\(827\) 6.26218e12i 0.465533i 0.972533 + 0.232767i \(0.0747778\pi\)
−0.972533 + 0.232767i \(0.925222\pi\)
\(828\) −4.79996e12 −0.354896
\(829\) 1.97426e13i 1.45181i −0.687796 0.725904i \(-0.741421\pi\)
0.687796 0.725904i \(-0.258579\pi\)
\(830\) 1.81826e13i 1.32986i
\(831\) 4.78456e12i 0.348046i
\(832\) 1.62689e13 1.17707
\(833\) 7.74006e10i 0.00556983i
\(834\) −3.88688e13 −2.78198
\(835\) −3.50745e12 −0.249690
\(836\) 4.88057e12 0.345575
\(837\) −2.32388e13 −1.63662
\(838\) 1.42992e13i 1.00164i
\(839\) 2.37593e12i 0.165541i 0.996569 + 0.0827704i \(0.0263768\pi\)
−0.996569 + 0.0827704i \(0.973623\pi\)
\(840\) −1.34801e13 −0.934194
\(841\) −9.13600e12 1.12690e13i −0.629759 0.776791i
\(842\) 2.38205e13 1.63322
\(843\) 2.42484e13i 1.65371i
\(844\) 3.61449e12i 0.245192i
\(845\) −2.43843e13 −1.64534
\(846\) −1.29124e13 −0.866641
\(847\) −1.83678e13 −1.22626
\(848\) −9.27020e11 −0.0615613
\(849\) 3.94322e13i 2.60475i
\(850\) −1.55492e12 −0.102170
\(851\) 6.58207e12i 0.430209i
\(852\) 7.58110e12i 0.492895i
\(853\) 4.09727e12i 0.264987i −0.991184 0.132493i \(-0.957702\pi\)
0.991184 0.132493i \(-0.0422983\pi\)
\(854\) 2.66892e13 1.71702
\(855\) 1.57141e13i 1.00564i
\(856\) 1.09725e13i 0.698512i
\(857\) −9.58984e12 −0.607292 −0.303646 0.952785i \(-0.598204\pi\)
−0.303646 + 0.952785i \(0.598204\pi\)
\(858\) 7.86074e13i 4.95188i
\(859\) 1.27198e13i 0.797100i −0.917147 0.398550i \(-0.869514\pi\)
0.917147 0.398550i \(-0.130486\pi\)
\(860\) 4.86794e11i 0.0303460i
\(861\) −6.39844e12 −0.396789
\(862\) 3.29279e13i 2.03133i
\(863\) 1.55064e13 0.951619 0.475810 0.879548i \(-0.342155\pi\)
0.475810 + 0.879548i \(0.342155\pi\)
\(864\) 7.79689e12 0.476003
\(865\) 1.04763e12 0.0636261
\(866\) −3.57361e12 −0.215912
\(867\) 2.60429e13i 1.56532i
\(868\) 7.25883e12i 0.434038i
\(869\) 2.22976e12 0.132638
\(870\) −8.93566e12 + 1.87476e13i −0.528798 + 1.10945i
\(871\) 3.57342e12 0.210379
\(872\) 4.69284e12i 0.274860i
\(873\) 1.19712e13i 0.697547i
\(874\) −1.56915e13 −0.909627
\(875\) 1.84377e13 1.06334
\(876\) −8.93179e12 −0.512472
\(877\) −3.32840e11 −0.0189993 −0.00949966 0.999955i \(-0.503024\pi\)
−0.00949966 + 0.999955i \(0.503024\pi\)
\(878\) 7.72692e12i 0.438814i
\(879\) 5.11477e12 0.288986
\(880\) 2.13992e13i 1.20289i
\(881\) 1.80700e13i 1.01057i 0.862953 + 0.505285i \(0.168613\pi\)
−0.862953 + 0.505285i \(0.831387\pi\)
\(882\) 1.05097e12i 0.0584763i
\(883\) −1.58747e13 −0.878782 −0.439391 0.898296i \(-0.644806\pi\)
−0.439391 + 0.898296i \(0.644806\pi\)
\(884\) 1.44103e12i 0.0793668i
\(885\) 3.59336e13i 1.96905i
\(886\) 2.09992e13 1.14486
\(887\) 5.24376e12i 0.284437i 0.989835 + 0.142219i \(0.0454236\pi\)
−0.989835 + 0.142219i \(0.954576\pi\)
\(888\) 1.22129e13i 0.659114i
\(889\) 1.66062e13i 0.891688i
\(890\) −8.16296e12 −0.436107
\(891\) 1.17885e12i 0.0626627i
\(892\) −3.88744e12 −0.205599
\(893\) −8.49678e12 −0.447119
\(894\) −2.55112e13 −1.33571
\(895\) 1.56555e13 0.815574
\(896\) 2.36367e13i 1.22518i
\(897\) 5.08720e13i 2.62369i
\(898\) −1.68587e13 −0.865127
\(899\) 2.99625e13 + 1.42810e13i 1.52989 + 0.729190i
\(900\) −4.24986e12 −0.215915
\(901\) 1.74617e11i 0.00882722i
\(902\) 8.00348e12i 0.402577i
\(903\) −5.78494e12 −0.289537
\(904\) 1.29297e13 0.643918
\(905\) 1.58787e13 0.786859
\(906\) 1.41666e13 0.698537
\(907\) 7.51886e12i 0.368909i −0.982841 0.184454i \(-0.940948\pi\)
0.982841 0.184454i \(-0.0590518\pi\)
\(908\) 3.69754e11 0.0180520
\(909\) 1.04216e13i 0.506286i
\(910\) 2.96155e13i 1.43163i
\(911\) 9.98249e12i 0.480182i −0.970750 0.240091i \(-0.922823\pi\)
0.970750 0.240091i \(-0.0771774\pi\)
\(912\) 3.69505e13 1.76866
\(913\) 5.44047e13i 2.59130i
\(914\) 2.50521e13i 1.18737i
\(915\) 3.51672e13 1.65861
\(916\) 8.55668e12i 0.401583i
\(917\) 2.49688e12i 0.116610i
\(918\) 3.96233e12i 0.184144i
\(919\) −1.87276e13 −0.866087 −0.433044 0.901373i \(-0.642560\pi\)
−0.433044 + 0.901373i \(0.642560\pi\)
\(920\) 1.09122e13i 0.502191i
\(921\) 6.38102e13 2.92228
\(922\) −1.08211e13 −0.493152
\(923\) −4.94329e13 −2.24186
\(924\) 1.35898e13 0.613325
\(925\) 5.82773e12i 0.261735i
\(926\) 1.42419e13i 0.636531i
\(927\) −3.07274e12 −0.136668
\(928\) −1.00528e13 4.79145e12i −0.444959 0.212081i
\(929\) 2.14483e13 0.944763 0.472381 0.881394i \(-0.343395\pi\)
0.472381 + 0.881394i \(0.343395\pi\)
\(930\) 4.75170e13i 2.08293i
\(931\) 6.91572e11i 0.0301692i
\(932\) 8.95080e12 0.388589
\(933\) −6.17216e13 −2.66667
\(934\) −2.47024e13 −1.06213
\(935\) 4.03083e12 0.172481
\(936\) 5.80735e13i 2.47307i
\(937\) 3.63793e13 1.54179 0.770896 0.636961i \(-0.219809\pi\)
0.770896 + 0.636961i \(0.219809\pi\)
\(938\) 3.06912e12i 0.129450i
\(939\) 7.83241e12i 0.328776i
\(940\) 1.99087e12i 0.0831704i
\(941\) 1.40415e13 0.583797 0.291898 0.956449i \(-0.405713\pi\)
0.291898 + 0.956449i \(0.405713\pi\)
\(942\) 4.60244e13i 1.90440i
\(943\) 5.17957e12i 0.213300i
\(944\) −5.19845e13 −2.13059
\(945\) 1.63914e13i 0.668610i
\(946\) 7.23609e12i 0.293761i
\(947\) 4.21219e13i 1.70190i 0.525249 + 0.850949i \(0.323972\pi\)
−0.525249 + 0.850949i \(0.676028\pi\)
\(948\) −9.02132e11 −0.0362771
\(949\) 5.82402e13i 2.33090i
\(950\) −1.38932e13 −0.553408
\(951\) −4.29646e13 −1.70333
\(952\) 3.67336e12 0.144943
\(953\) 2.27280e13 0.892574 0.446287 0.894890i \(-0.352746\pi\)
0.446287 + 0.894890i \(0.352746\pi\)
\(954\) 2.37099e12i 0.0926750i
\(955\) 1.53063e13i 0.595463i
\(956\) −1.00711e13 −0.389956
\(957\) −2.67366e13 + 5.60952e13i −1.03039 + 2.16183i
\(958\) 2.11425e13 0.810984
\(959\) 2.16044e13i 0.824817i
\(960\) 1.84116e13i 0.699634i
\(961\) −4.95022e13 −1.87227
\(962\) −2.68314e13 −1.01008
\(963\) 3.56161e13 1.33453
\(964\) 9.00823e12 0.335964
\(965\) 7.33524e12i 0.272296i
\(966\) −4.36927e13 −1.61440
\(967\) 1.66954e13i 0.614015i 0.951707 + 0.307007i \(0.0993276\pi\)
−0.951707 + 0.307007i \(0.900672\pi\)
\(968\) 2.75889e13i 1.00994i
\(969\) 6.96013e12i 0.253606i
\(970\) 9.16969e12 0.332569
\(971\) 2.72129e13i 0.982401i −0.871047 0.491200i \(-0.836558\pi\)
0.871047 0.491200i \(-0.163442\pi\)
\(972\) 7.24971e12i 0.260509i
\(973\) −4.38164e13 −1.56722
\(974\) 3.99277e13i 1.42154i
\(975\) 4.50418e13i 1.59623i
\(976\) 5.08758e13i 1.79468i
\(977\) 4.08459e13 1.43424 0.717121 0.696949i \(-0.245459\pi\)
0.717121 + 0.696949i \(0.245459\pi\)
\(978\) 4.64183e13i 1.62242i
\(979\) −2.44246e13 −0.849778
\(980\) 1.62042e11 0.00561189
\(981\) −1.52327e13 −0.525129
\(982\) 2.91660e13 1.00086
\(983\) 4.68988e13i 1.60203i −0.598644 0.801015i \(-0.704294\pi\)
0.598644 0.801015i \(-0.295706\pi\)
\(984\) 9.61060e12i 0.326793i
\(985\) −1.11973e13 −0.379011
\(986\) 2.43498e12 5.10876e12i 0.0820446 0.172135i
\(987\) −2.36591e13 −0.793544
\(988\) 1.28756e13i 0.429893i
\(989\) 4.68295e12i 0.155645i
\(990\) 5.47317e13 1.81084
\(991\) 2.09390e13 0.689643 0.344822 0.938668i \(-0.387939\pi\)
0.344822 + 0.938668i \(0.387939\pi\)
\(992\) 2.54794e13 0.835385
\(993\) 1.96014e12 0.0639759
\(994\) 4.24567e13i 1.37946i
\(995\) −3.66599e13 −1.18573
\(996\) 2.20114e13i 0.708731i
\(997\) 5.13175e13i 1.64489i 0.568843 + 0.822446i \(0.307391\pi\)
−0.568843 + 0.822446i \(0.692609\pi\)
\(998\) 1.21700e13i 0.388331i
\(999\) 1.48505e13 0.471733
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 29.10.b.a.28.17 yes 22
29.28 even 2 inner 29.10.b.a.28.6 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.10.b.a.28.6 22 29.28 even 2 inner
29.10.b.a.28.17 yes 22 1.1 even 1 trivial