Properties

Label 3.69.b.a.2.6
Level $3$
Weight $69$
Character 3.2
Analytic conductor $87.852$
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] = [3,69,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 69, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 69);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 69 \)
Character orbit: \([\chi]\) \(=\) 3.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: \(87.8517980619\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.6
Character \(\chi\) \(=\) 3.2
Dual form 3.69.b.a.2.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.98633e10i q^{2} +(-1.52299e16 + 6.79538e15i) q^{3} -9.94018e19 q^{4} -1.15188e23i q^{5} +(1.34979e26 + 3.02517e26i) q^{6} -6.02651e28 q^{7} -3.88816e30i q^{8} +(1.85774e32 - 2.06987e32i) q^{9} +O(q^{10})\) \(q-1.98633e10i q^{2} +(-1.52299e16 + 6.79538e15i) q^{3} -9.94018e19 q^{4} -1.15188e23i q^{5} +(1.34979e26 + 3.02517e26i) q^{6} -6.02651e28 q^{7} -3.88816e30i q^{8} +(1.85774e32 - 2.06987e32i) q^{9} -2.28800e33 q^{10} -2.49072e35i q^{11} +(1.51388e36 - 6.75473e35i) q^{12} +6.80608e37 q^{13} +1.19706e39i q^{14} +(7.82743e38 + 1.75430e39i) q^{15} -1.06570e41 q^{16} +5.64414e41i q^{17} +(-4.11143e42 - 3.69008e42i) q^{18} +3.74530e43 q^{19} +1.14498e43i q^{20} +(9.17833e44 - 4.09524e44i) q^{21} -4.94739e45 q^{22} +9.44969e45i q^{23} +(2.64215e46 + 5.92164e46i) q^{24} +3.25545e47 q^{25} -1.35191e48i q^{26} +(-1.42278e48 + 4.41480e48i) q^{27} +5.99045e48 q^{28} +4.04571e49i q^{29} +(3.48461e49 - 1.55478e49i) q^{30} +3.19261e50 q^{31} +9.69243e50i q^{32} +(1.69254e51 + 3.79336e51i) q^{33} +1.12111e52 q^{34} +6.94178e51i q^{35} +(-1.84663e52 + 2.05748e52i) q^{36} +5.63328e52 q^{37} -7.43940e53i q^{38} +(-1.03656e54 + 4.62499e53i) q^{39} -4.47867e53 q^{40} -5.48217e54i q^{41} +(-8.13449e54 - 1.82312e55i) q^{42} +5.73328e55 q^{43} +2.47582e55i q^{44} +(-2.38423e55 - 2.13988e55i) q^{45} +1.87702e56 q^{46} -1.10405e57i q^{47} +(1.62305e57 - 7.24182e56i) q^{48} +7.03232e56 q^{49} -6.46639e57i q^{50} +(-3.83541e57 - 8.59599e57i) q^{51} -6.76537e57 q^{52} -5.86838e58i q^{53} +(8.76923e58 + 2.82610e58i) q^{54} -2.86900e58 q^{55} +2.34320e59i q^{56} +(-5.70408e59 + 2.54508e59i) q^{57} +8.03611e59 q^{58} +2.64517e60i q^{59} +(-7.78060e58 - 1.74380e59i) q^{60} -3.65756e60 q^{61} -6.34158e60i q^{62} +(-1.11957e61 + 1.24741e61i) q^{63} -1.22015e61 q^{64} -7.83976e60i q^{65} +(7.53485e61 - 3.36194e61i) q^{66} +1.10141e62 q^{67} -5.61037e61i q^{68} +(-6.42143e61 - 1.43918e62i) q^{69} +1.37887e62 q^{70} -2.24430e62i q^{71} +(-8.04796e62 - 7.22319e62i) q^{72} +6.26092e62 q^{73} -1.11895e63i q^{74} +(-4.95803e63 + 2.21220e63i) q^{75} -3.72290e63 q^{76} +1.50104e64i q^{77} +(9.18675e63 + 2.05895e64i) q^{78} -3.84819e63 q^{79} +1.22755e64i q^{80} +(-8.33144e63 - 7.69054e64i) q^{81} -1.08894e65 q^{82} -1.42586e65i q^{83} +(-9.12343e64 + 4.07074e64i) q^{84} +6.50134e64 q^{85} -1.13882e66i q^{86} +(-2.74922e65 - 6.16160e65i) q^{87} -9.68432e65 q^{88} +1.80918e66i q^{89} +(-4.25051e65 + 4.73585e65i) q^{90} -4.10169e66 q^{91} -9.39316e65i q^{92} +(-4.86233e66 + 2.16950e66i) q^{93} -2.19300e67 q^{94} -4.31412e66i q^{95} +(-6.58638e66 - 1.47615e67i) q^{96} -5.21425e67 q^{97} -1.39685e67i q^{98} +(-5.15546e67 - 4.62711e67i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 18\!\cdots\!78 q^{3}+ \cdots + 84\!\cdots\!78 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 18\!\cdots\!78 q^{3}+ \cdots - 11\!\cdots\!00 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.98633e10i 1.15619i −0.815968 0.578097i \(-0.803795\pi\)
0.815968 0.578097i \(-0.196205\pi\)
\(3\) −1.52299e16 + 6.79538e15i −0.913220 + 0.407466i
\(4\) −9.94018e19 −0.336786
\(5\) 1.15188e23i 0.197891i −0.995093 0.0989453i \(-0.968453\pi\)
0.995093 0.0989453i \(-0.0315469\pi\)
\(6\) 1.34979e26 + 3.02517e26i 0.471110 + 1.05586i
\(7\) −6.02651e28 −1.11361 −0.556804 0.830644i \(-0.687972\pi\)
−0.556804 + 0.830644i \(0.687972\pi\)
\(8\) 3.88816e30i 0.766804i
\(9\) 1.85774e32 2.06987e32i 0.667943 0.744212i
\(10\) −2.28800e33 −0.228800
\(11\) 2.49072e35i 0.974931i −0.873142 0.487466i \(-0.837921\pi\)
0.873142 0.487466i \(-0.162079\pi\)
\(12\) 1.51388e36 6.75473e35i 0.307560 0.137229i
\(13\) 6.80608e37 0.909543 0.454772 0.890608i \(-0.349721\pi\)
0.454772 + 0.890608i \(0.349721\pi\)
\(14\) 1.19706e39i 1.28755i
\(15\) 7.82743e38 + 1.75430e39i 0.0806337 + 0.180718i
\(16\) −1.06570e41 −1.22336
\(17\) 5.64414e41i 0.824773i 0.911009 + 0.412386i \(0.135305\pi\)
−0.911009 + 0.412386i \(0.864695\pi\)
\(18\) −4.11143e42 3.69008e42i −0.860454 0.772273i
\(19\) 3.74530e43 1.24699 0.623497 0.781825i \(-0.285711\pi\)
0.623497 + 0.781825i \(0.285711\pi\)
\(20\) 1.14498e43i 0.0666469i
\(21\) 9.17833e44 4.09524e44i 1.01697 0.453757i
\(22\) −4.94739e45 −1.12721
\(23\) 9.44969e45i 0.474976i 0.971391 + 0.237488i \(0.0763240\pi\)
−0.971391 + 0.237488i \(0.923676\pi\)
\(24\) 2.64215e46 + 5.92164e46i 0.312446 + 0.700261i
\(25\) 3.25545e47 0.960839
\(26\) 1.35191e48i 1.05161i
\(27\) −1.42278e48 + 4.41480e48i −0.306739 + 0.951794i
\(28\) 5.99045e48 0.375048
\(29\) 4.04571e49i 0.768180i 0.923296 + 0.384090i \(0.125485\pi\)
−0.923296 + 0.384090i \(0.874515\pi\)
\(30\) 3.48461e49 1.55478e49i 0.208945 0.0932282i
\(31\) 3.19261e50 0.627840 0.313920 0.949449i \(-0.398358\pi\)
0.313920 + 0.949449i \(0.398358\pi\)
\(32\) 9.69243e50i 0.647640i
\(33\) 1.69254e51 + 3.79336e51i 0.397251 + 0.890327i
\(34\) 1.12111e52 0.953598
\(35\) 6.94178e51i 0.220373i
\(36\) −1.84663e52 + 2.05748e52i −0.224954 + 0.250640i
\(37\) 5.63328e52 0.270335 0.135168 0.990823i \(-0.456843\pi\)
0.135168 + 0.990823i \(0.456843\pi\)
\(38\) 7.43940e53i 1.44177i
\(39\) −1.03656e54 + 4.62499e53i −0.830613 + 0.370608i
\(40\) −4.47867e53 −0.151743
\(41\) 5.48217e54i 0.802235i −0.916027 0.401117i \(-0.868622\pi\)
0.916027 0.401117i \(-0.131378\pi\)
\(42\) −8.13449e54 1.82312e55i −0.524631 1.17581i
\(43\) 5.73328e55 1.66141 0.830703 0.556716i \(-0.187939\pi\)
0.830703 + 0.556716i \(0.187939\pi\)
\(44\) 2.47582e55i 0.328344i
\(45\) −2.38423e55 2.13988e55i −0.147273 0.132180i
\(46\) 1.87702e56 0.549164
\(47\) 1.10405e57i 1.55475i −0.629038 0.777375i \(-0.716551\pi\)
0.629038 0.777375i \(-0.283449\pi\)
\(48\) 1.62305e57 7.24182e56i 1.11720 0.498478i
\(49\) 7.03232e56 0.240122
\(50\) 6.46639e57i 1.11092i
\(51\) −3.83541e57 8.59599e57i −0.336067 0.753199i
\(52\) −6.76537e57 −0.306322
\(53\) 5.86838e58i 1.39040i −0.718818 0.695198i \(-0.755316\pi\)
0.718818 0.695198i \(-0.244684\pi\)
\(54\) 8.76923e58 + 2.82610e58i 1.10046 + 0.354650i
\(55\) −2.86900e58 −0.192930
\(56\) 2.34320e59i 0.853919i
\(57\) −5.70408e59 + 2.54508e59i −1.13878 + 0.508108i
\(58\) 8.03611e59 0.888166
\(59\) 2.64517e60i 1.63487i 0.576017 + 0.817437i \(0.304606\pi\)
−0.576017 + 0.817437i \(0.695394\pi\)
\(60\) −7.78060e58 1.74380e59i −0.0271563 0.0608633i
\(61\) −3.65756e60 −0.727741 −0.363870 0.931450i \(-0.618545\pi\)
−0.363870 + 0.931450i \(0.618545\pi\)
\(62\) 6.34158e60i 0.725905i
\(63\) −1.11957e61 + 1.24741e61i −0.743827 + 0.828760i
\(64\) −1.22015e61 −0.474564
\(65\) 7.83976e60i 0.179990i
\(66\) 7.53485e61 3.36194e61i 1.02939 0.459300i
\(67\) 1.10141e62 0.902410 0.451205 0.892420i \(-0.350994\pi\)
0.451205 + 0.892420i \(0.350994\pi\)
\(68\) 5.61037e61i 0.277772i
\(69\) −6.42143e61 1.43918e62i −0.193536 0.433757i
\(70\) 1.37887e62 0.254794
\(71\) 2.24430e62i 0.256033i −0.991772 0.128017i \(-0.959139\pi\)
0.991772 0.128017i \(-0.0408611\pi\)
\(72\) −8.04796e62 7.22319e62i −0.570665 0.512182i
\(73\) 6.26092e62 0.277754 0.138877 0.990310i \(-0.455651\pi\)
0.138877 + 0.990310i \(0.455651\pi\)
\(74\) 1.11895e63i 0.312560i
\(75\) −4.95803e63 + 2.21220e63i −0.877458 + 0.391509i
\(76\) −3.72290e63 −0.419971
\(77\) 1.50104e64i 1.08569i
\(78\) 9.18675e63 + 2.05895e64i 0.428495 + 0.960351i
\(79\) −3.84819e63 −0.116395 −0.0581977 0.998305i \(-0.518535\pi\)
−0.0581977 + 0.998305i \(0.518535\pi\)
\(80\) 1.22755e64i 0.242092i
\(81\) −8.33144e63 7.69054e64i −0.107703 0.994183i
\(82\) −1.08894e65 −0.927540
\(83\) 1.42586e65i 0.804309i −0.915572 0.402155i \(-0.868261\pi\)
0.915572 0.402155i \(-0.131739\pi\)
\(84\) −9.12343e64 + 4.07074e64i −0.342501 + 0.152819i
\(85\) 6.50134e64 0.163215
\(86\) 1.13882e66i 1.92091i
\(87\) −2.74922e65 6.16160e65i −0.313007 0.701518i
\(88\) −9.68432e65 −0.747581
\(89\) 1.80918e66i 0.951089i 0.879692 + 0.475544i \(0.157749\pi\)
−0.879692 + 0.475544i \(0.842251\pi\)
\(90\) −4.25051e65 + 4.73585e65i −0.152826 + 0.170276i
\(91\) −4.10169e66 −1.01287
\(92\) 9.39316e65i 0.159965i
\(93\) −4.86233e66 + 2.16950e66i −0.573356 + 0.255823i
\(94\) −2.19300e67 −1.79759
\(95\) 4.31412e66i 0.246769i
\(96\) −6.58638e66 1.47615e67i −0.263891 0.591438i
\(97\) −5.21425e67 −1.46877 −0.734384 0.678734i \(-0.762529\pi\)
−0.734384 + 0.678734i \(0.762529\pi\)
\(98\) 1.39685e67i 0.277628i
\(99\) −5.15546e67 4.62711e67i −0.725556 0.651199i
\(100\) −3.23598e67 −0.323598
\(101\) 2.16565e68i 1.54405i −0.635591 0.772026i \(-0.719243\pi\)
0.635591 0.772026i \(-0.280757\pi\)
\(102\) −1.70744e68 + 7.61837e67i −0.870845 + 0.388558i
\(103\) 2.15308e68 0.788125 0.394062 0.919084i \(-0.371069\pi\)
0.394062 + 0.919084i \(0.371069\pi\)
\(104\) 2.64631e68i 0.697441i
\(105\) −4.71720e67 1.05723e68i −0.0897943 0.201249i
\(106\) −1.16565e69 −1.60757
\(107\) 6.73705e68i 0.675182i 0.941293 + 0.337591i \(0.109612\pi\)
−0.941293 + 0.337591i \(0.890388\pi\)
\(108\) 1.41426e68 4.38839e68i 0.103305 0.320551i
\(109\) −1.91053e69 −1.02012 −0.510061 0.860138i \(-0.670377\pi\)
−0.510061 + 0.860138i \(0.670377\pi\)
\(110\) 5.69878e68i 0.223064i
\(111\) −8.57946e68 + 3.82803e68i −0.246876 + 0.110152i
\(112\) 6.42244e69 1.36234
\(113\) 3.71019e69i 0.581739i 0.956763 + 0.290870i \(0.0939446\pi\)
−0.956763 + 0.290870i \(0.906055\pi\)
\(114\) 5.05536e69 + 1.13302e70i 0.587471 + 1.31665i
\(115\) 1.08849e69 0.0939932
\(116\) 4.02151e69i 0.258713i
\(117\) 1.26439e70 1.40877e70i 0.607523 0.676893i
\(118\) 5.25417e70 1.89023
\(119\) 3.40144e70i 0.918473i
\(120\) 6.82099e69 3.04343e69i 0.138575 0.0618302i
\(121\) 3.23138e69 0.0495091
\(122\) 7.26511e70i 0.841410i
\(123\) 3.72534e70 + 8.34932e70i 0.326883 + 0.732617i
\(124\) −3.17351e70 −0.211448
\(125\) 7.65258e70i 0.388032i
\(126\) 2.47776e71 + 2.22383e71i 0.958208 + 0.860009i
\(127\) 3.65635e71 1.08074 0.540370 0.841427i \(-0.318284\pi\)
0.540370 + 0.841427i \(0.318284\pi\)
\(128\) 5.28432e71i 1.19633i
\(129\) −8.73175e71 + 3.89598e71i −1.51723 + 0.676966i
\(130\) −1.55723e71 −0.208104
\(131\) 1.67473e72i 1.72473i −0.506287 0.862365i \(-0.668982\pi\)
0.506287 0.862365i \(-0.331018\pi\)
\(132\) −1.68242e71 3.77066e71i −0.133789 0.299850i
\(133\) −2.25711e72 −1.38866
\(134\) 2.18775e72i 1.04336i
\(135\) 5.08530e71 + 1.63886e71i 0.188351 + 0.0607007i
\(136\) 2.19453e72 0.632439
\(137\) 6.45507e72i 1.45011i −0.688689 0.725057i \(-0.741814\pi\)
0.688689 0.725057i \(-0.258186\pi\)
\(138\) −2.85869e72 + 1.27551e72i −0.501508 + 0.223766i
\(139\) −1.33816e73 −1.83656 −0.918280 0.395931i \(-0.870422\pi\)
−0.918280 + 0.395931i \(0.870422\pi\)
\(140\) 6.90026e71i 0.0742185i
\(141\) 7.50242e72 + 1.68146e73i 0.633507 + 1.41983i
\(142\) −4.45791e72 −0.296025
\(143\) 1.69521e73i 0.886742i
\(144\) −1.97979e73 + 2.20585e73i −0.817136 + 0.910440i
\(145\) 4.66015e72 0.152016
\(146\) 1.24362e73i 0.321138i
\(147\) −1.07102e73 + 4.77873e72i −0.219284 + 0.0978415i
\(148\) −5.59958e72 −0.0910453
\(149\) 3.03729e73i 0.392783i −0.980526 0.196391i \(-0.937078\pi\)
0.980526 0.196391i \(-0.0629223\pi\)
\(150\) 4.39416e73 + 9.84828e73i 0.452661 + 1.01451i
\(151\) 1.78959e74 1.47074 0.735372 0.677663i \(-0.237007\pi\)
0.735372 + 0.677663i \(0.237007\pi\)
\(152\) 1.45623e74i 0.956201i
\(153\) 1.16826e74 + 1.04853e74i 0.613806 + 0.550901i
\(154\) 2.98155e74 1.25527
\(155\) 3.67749e73i 0.124244i
\(156\) 1.03036e74 4.59733e73i 0.279739 0.124816i
\(157\) −2.32870e74 −0.508775 −0.254388 0.967102i \(-0.581874\pi\)
−0.254388 + 0.967102i \(0.581874\pi\)
\(158\) 7.64377e73i 0.134576i
\(159\) 3.98779e74 + 8.93751e74i 0.566539 + 1.26974i
\(160\) 1.11645e74 0.128162
\(161\) 5.69486e74i 0.528936i
\(162\) −1.52759e75 + 1.65490e74i −1.14947 + 0.124526i
\(163\) 9.31786e73 0.0568771 0.0284386 0.999596i \(-0.490947\pi\)
0.0284386 + 0.999596i \(0.490947\pi\)
\(164\) 5.44938e74i 0.270182i
\(165\) 4.36947e74 1.94960e74i 0.176187 0.0786123i
\(166\) −2.83223e75 −0.929938
\(167\) 2.53201e75i 0.677807i 0.940821 + 0.338903i \(0.110056\pi\)
−0.940821 + 0.338903i \(0.889944\pi\)
\(168\) −1.59229e75 3.56868e75i −0.347943 0.779816i
\(169\) −9.67206e74 −0.172731
\(170\) 1.29138e75i 0.188708i
\(171\) 6.95780e75 7.75228e75i 0.832922 0.928029i
\(172\) −5.69898e75 −0.559539
\(173\) 2.27373e76i 1.83304i −0.399991 0.916519i \(-0.630987\pi\)
0.399991 0.916519i \(-0.369013\pi\)
\(174\) −1.22389e76 + 5.46084e75i −0.811091 + 0.361897i
\(175\) −1.96190e76 −1.07000
\(176\) 2.65436e76i 1.19269i
\(177\) −1.79749e76 4.02857e76i −0.666156 1.49300i
\(178\) 3.59362e76 1.09964
\(179\) 7.05084e76i 1.78335i 0.452672 + 0.891677i \(0.350471\pi\)
−0.452672 + 0.891677i \(0.649529\pi\)
\(180\) 2.36996e75 + 2.12708e75i 0.0495994 + 0.0445163i
\(181\) 1.24635e76 0.216057 0.108028 0.994148i \(-0.465546\pi\)
0.108028 + 0.994148i \(0.465546\pi\)
\(182\) 8.14730e76i 1.17108i
\(183\) 5.57044e76 2.48545e76i 0.664588 0.296529i
\(184\) 3.67419e76 0.364213
\(185\) 6.48884e75i 0.0534969i
\(186\) 4.30934e76 + 9.65818e76i 0.295781 + 0.662911i
\(187\) 1.40580e77 0.804096
\(188\) 1.09744e77i 0.523618i
\(189\) 8.57437e76 2.66058e77i 0.341586 1.05992i
\(190\) −8.56926e76 −0.285313
\(191\) 7.15809e77i 1.99371i −0.0792288 0.996856i \(-0.525246\pi\)
0.0792288 0.996856i \(-0.474754\pi\)
\(192\) 1.85828e77 8.29139e76i 0.433381 0.193368i
\(193\) 1.71789e77 0.335775 0.167887 0.985806i \(-0.446306\pi\)
0.167887 + 0.985806i \(0.446306\pi\)
\(194\) 1.03572e78i 1.69818i
\(195\) 5.32741e76 + 1.19399e77i 0.0733398 + 0.164371i
\(196\) −6.99025e76 −0.0808698
\(197\) 7.28159e76i 0.0708557i 0.999372 + 0.0354278i \(0.0112794\pi\)
−0.999372 + 0.0354278i \(0.988721\pi\)
\(198\) −9.19096e77 + 1.02404e78i −0.752913 + 0.838884i
\(199\) 4.42225e77 0.305238 0.152619 0.988285i \(-0.451229\pi\)
0.152619 + 0.988285i \(0.451229\pi\)
\(200\) 1.26577e78i 0.736776i
\(201\) −1.67743e78 + 7.48447e77i −0.824099 + 0.367701i
\(202\) −4.30170e78 −1.78523
\(203\) 2.43815e78i 0.855451i
\(204\) 3.81246e77 + 8.54457e77i 0.113183 + 0.253667i
\(205\) −6.31478e77 −0.158755
\(206\) 4.27673e78i 0.911225i
\(207\) 1.95596e78 + 1.75551e78i 0.353483 + 0.317257i
\(208\) −7.25323e78 −1.11270
\(209\) 9.32851e78i 1.21573i
\(210\) −2.10000e78 + 9.36991e77i −0.232683 + 0.103820i
\(211\) 1.65840e79 1.56346 0.781728 0.623619i \(-0.214338\pi\)
0.781728 + 0.623619i \(0.214338\pi\)
\(212\) 5.83328e78i 0.468267i
\(213\) 1.52509e78 + 3.41805e78i 0.104325 + 0.233815i
\(214\) 1.33820e79 0.780642
\(215\) 6.60402e78i 0.328777i
\(216\) 1.71654e79 + 5.53198e78i 0.729839 + 0.235208i
\(217\) −1.92403e79 −0.699167
\(218\) 3.79493e79i 1.17946i
\(219\) −9.53535e78 + 4.25453e78i −0.253651 + 0.113175i
\(220\) 2.85184e78 0.0649761
\(221\) 3.84145e79i 0.750166i
\(222\) 7.60372e78 + 1.70416e79i 0.127358 + 0.285437i
\(223\) 4.05994e79 0.583652 0.291826 0.956471i \(-0.405737\pi\)
0.291826 + 0.956471i \(0.405737\pi\)
\(224\) 5.84115e79i 0.721217i
\(225\) 6.04778e79 6.73834e79i 0.641786 0.715068i
\(226\) 7.36964e79 0.672604
\(227\) 1.68370e80i 1.32247i 0.750181 + 0.661233i \(0.229966\pi\)
−0.750181 + 0.661233i \(0.770034\pi\)
\(228\) 5.66996e79 2.52985e79i 0.383526 0.171124i
\(229\) −2.25334e80 −1.31347 −0.656736 0.754120i \(-0.728064\pi\)
−0.656736 + 0.754120i \(0.728064\pi\)
\(230\) 2.16209e79i 0.108674i
\(231\) −1.02001e80 2.28607e80i −0.442382 0.991475i
\(232\) 1.57304e80 0.589044
\(233\) 1.00818e80i 0.326163i −0.986613 0.163082i \(-0.947857\pi\)
0.986613 0.163082i \(-0.0521434\pi\)
\(234\) −2.79827e80 2.51150e80i −0.782620 0.702415i
\(235\) −1.27172e80 −0.307670
\(236\) 2.62934e80i 0.550604i
\(237\) 5.86078e79 2.61499e79i 0.106295 0.0474271i
\(238\) −6.75638e80 −1.06193
\(239\) 1.04423e81i 1.42320i 0.702583 + 0.711602i \(0.252030\pi\)
−0.702583 + 0.711602i \(0.747970\pi\)
\(240\) −8.34168e79 1.86955e80i −0.0986441 0.221083i
\(241\) −1.76780e81 −1.81491 −0.907453 0.420154i \(-0.861976\pi\)
−0.907453 + 0.420154i \(0.861976\pi\)
\(242\) 6.41858e79i 0.0572422i
\(243\) 6.49489e80 + 1.11465e81i 0.503452 + 0.864023i
\(244\) 3.63568e80 0.245093
\(245\) 8.10036e79i 0.0475179i
\(246\) 1.65845e81 7.39975e80i 0.847048 0.377941i
\(247\) 2.54909e81 1.13420
\(248\) 1.24134e81i 0.481430i
\(249\) 9.68929e80 + 2.17158e81i 0.327728 + 0.734511i
\(250\) −1.52005e81 −0.448640
\(251\) 4.93576e80i 0.127189i −0.997976 0.0635943i \(-0.979744\pi\)
0.997976 0.0635943i \(-0.0202564\pi\)
\(252\) 1.11287e81 1.23994e81i 0.250511 0.279115i
\(253\) 2.35366e81 0.463068
\(254\) 7.26271e81i 1.24955i
\(255\) −9.90151e80 + 4.41791e80i −0.149051 + 0.0665044i
\(256\) 6.89514e81 0.908624
\(257\) 9.31605e80i 0.107524i 0.998554 + 0.0537621i \(0.0171212\pi\)
−0.998554 + 0.0537621i \(0.982879\pi\)
\(258\) 7.73869e81 + 1.73441e82i 0.782704 + 1.75421i
\(259\) −3.39490e81 −0.301048
\(260\) 7.79286e80i 0.0606182i
\(261\) 8.37408e81 + 7.51588e81i 0.571689 + 0.513101i
\(262\) −3.32656e82 −1.99412
\(263\) 6.01550e79i 0.00316793i −0.999999 0.00158397i \(-0.999496\pi\)
0.999999 0.00158397i \(-0.000504192\pi\)
\(264\) 1.47492e82 6.58087e81i 0.682707 0.304614i
\(265\) −6.75964e81 −0.275147
\(266\) 4.48336e82i 1.60557i
\(267\) −1.22941e82 2.75537e82i −0.387536 0.868554i
\(268\) −1.09482e82 −0.303919
\(269\) 6.04892e82i 1.47945i −0.672910 0.739725i \(-0.734956\pi\)
0.672910 0.739725i \(-0.265044\pi\)
\(270\) 3.25531e81 1.01011e82i 0.0701818 0.217771i
\(271\) −6.91155e82 −1.31407 −0.657036 0.753859i \(-0.728190\pi\)
−0.657036 + 0.753859i \(0.728190\pi\)
\(272\) 6.01494e82i 1.00899i
\(273\) 6.24685e82 2.78725e82i 0.924977 0.412712i
\(274\) −1.28219e83 −1.67661
\(275\) 8.10842e82i 0.936752i
\(276\) 6.38301e81 + 1.43057e82i 0.0651804 + 0.146084i
\(277\) 6.09620e82 0.550487 0.275243 0.961375i \(-0.411242\pi\)
0.275243 + 0.961375i \(0.411242\pi\)
\(278\) 2.65803e83i 2.12342i
\(279\) 5.93105e82 6.60828e82i 0.419361 0.467246i
\(280\) 2.69908e82 0.168983
\(281\) 2.16955e83i 1.20325i 0.798779 + 0.601625i \(0.205480\pi\)
−0.798779 + 0.601625i \(0.794520\pi\)
\(282\) 3.33993e83 1.49023e83i 1.64160 0.732458i
\(283\) −2.16587e83 −0.943831 −0.471915 0.881644i \(-0.656437\pi\)
−0.471915 + 0.881644i \(0.656437\pi\)
\(284\) 2.23087e82i 0.0862286i
\(285\) 2.93161e82 + 6.57039e82i 0.100550 + 0.225354i
\(286\) −3.36723e83 −1.02525
\(287\) 3.30383e83i 0.893375i
\(288\) 2.00620e83 + 1.80060e83i 0.481981 + 0.432587i
\(289\) 1.49740e83 0.319750
\(290\) 9.25659e82i 0.175760i
\(291\) 7.94128e83 3.54328e83i 1.34131 0.598472i
\(292\) −6.22347e82 −0.0935439
\(293\) 6.78020e83i 0.907285i −0.891184 0.453642i \(-0.850124\pi\)
0.891184 0.453642i \(-0.149876\pi\)
\(294\) 9.49212e82 + 2.12739e83i 0.113124 + 0.253535i
\(295\) 3.04690e83 0.323526
\(296\) 2.19031e83i 0.207294i
\(297\) 1.09960e84 + 3.54374e83i 0.927933 + 0.299049i
\(298\) −6.03304e83 −0.454133
\(299\) 6.43154e83i 0.432011i
\(300\) 4.92837e83 2.19897e83i 0.295516 0.131855i
\(301\) −3.45516e84 −1.85015
\(302\) 3.55471e84i 1.70047i
\(303\) 1.47164e84 + 3.29828e84i 0.629149 + 1.41006i
\(304\) −3.99136e84 −1.52553
\(305\) 4.21305e83i 0.144013i
\(306\) 2.08273e84 2.32055e84i 0.636949 0.709679i
\(307\) −5.81498e84 −1.59164 −0.795818 0.605536i \(-0.792959\pi\)
−0.795818 + 0.605536i \(0.792959\pi\)
\(308\) 1.49206e84i 0.365646i
\(309\) −3.27913e84 + 1.46310e84i −0.719732 + 0.321134i
\(310\) −7.30470e83 −0.143650
\(311\) 2.63993e83i 0.0465307i −0.999729 0.0232653i \(-0.992594\pi\)
0.999729 0.0232653i \(-0.00740625\pi\)
\(312\) 1.79827e84 + 4.03032e84i 0.284183 + 0.636918i
\(313\) 2.89450e84 0.410266 0.205133 0.978734i \(-0.434237\pi\)
0.205133 + 0.978734i \(0.434237\pi\)
\(314\) 4.62557e84i 0.588243i
\(315\) 1.43686e84 + 1.28960e84i 0.164004 + 0.147196i
\(316\) 3.82517e83 0.0392004
\(317\) 1.18721e85i 1.09273i −0.837549 0.546363i \(-0.816012\pi\)
0.837549 0.546363i \(-0.183988\pi\)
\(318\) 1.77528e85 7.92105e84i 1.46807 0.655030i
\(319\) 1.00767e85 0.748923
\(320\) 1.40546e84i 0.0939117i
\(321\) −4.57808e84 1.02605e85i −0.275114 0.616590i
\(322\) −1.13119e85 −0.611554
\(323\) 2.11390e85i 1.02849i
\(324\) 8.28160e83 + 7.64454e84i 0.0362730 + 0.334827i
\(325\) 2.21569e85 0.873925
\(326\) 1.85083e84i 0.0657610i
\(327\) 2.90972e85 1.29828e85i 0.931596 0.415665i
\(328\) −2.13156e85 −0.615157
\(329\) 6.65355e85i 1.73138i
\(330\) −3.87253e84 8.67920e84i −0.0908911 0.203707i
\(331\) −1.68286e85 −0.356365 −0.178183 0.983997i \(-0.557022\pi\)
−0.178183 + 0.983997i \(0.557022\pi\)
\(332\) 1.41733e85i 0.270880i
\(333\) 1.04652e85 1.16601e85i 0.180569 0.201187i
\(334\) 5.02941e85 0.783677
\(335\) 1.26868e85i 0.178579i
\(336\) −9.78133e85 + 4.36429e85i −1.24412 + 0.555109i
\(337\) 1.09475e84 0.0125863 0.00629314 0.999980i \(-0.497997\pi\)
0.00629314 + 0.999980i \(0.497997\pi\)
\(338\) 1.92119e85i 0.199711i
\(339\) −2.52121e85 5.65059e85i −0.237039 0.531256i
\(340\) −6.46245e84 −0.0549685
\(341\) 7.95191e85i 0.612101i
\(342\) −1.53986e86 1.38205e86i −1.07298 0.963020i
\(343\) 1.34115e86 0.846206
\(344\) 2.22919e86i 1.27397i
\(345\) −1.65776e85 + 7.39668e84i −0.0858365 + 0.0382990i
\(346\) −4.51637e86 −2.11935
\(347\) 2.29793e86i 0.977540i −0.872413 0.488770i \(-0.837446\pi\)
0.872413 0.488770i \(-0.162554\pi\)
\(348\) 2.73277e85 + 6.12474e85i 0.105417 + 0.236262i
\(349\) 4.51770e86 1.58071 0.790357 0.612646i \(-0.209895\pi\)
0.790357 + 0.612646i \(0.209895\pi\)
\(350\) 3.89697e86i 1.23713i
\(351\) −9.68353e85 + 3.00475e86i −0.278992 + 0.865698i
\(352\) 2.41412e86 0.631404
\(353\) 3.93415e85i 0.0934353i 0.998908 + 0.0467177i \(0.0148761\pi\)
−0.998908 + 0.0467177i \(0.985124\pi\)
\(354\) −8.00207e86 + 3.57041e86i −1.72620 + 0.770206i
\(355\) −2.58515e85 −0.0506666
\(356\) 1.79836e86i 0.320314i
\(357\) 2.31141e86 + 5.18038e86i 0.374246 + 0.838768i
\(358\) 1.40053e87 2.06190
\(359\) 6.87613e85i 0.0920732i −0.998940 0.0460366i \(-0.985341\pi\)
0.998940 0.0460366i \(-0.0146591\pi\)
\(360\) −8.32021e85 + 9.27025e85i −0.101356 + 0.112929i
\(361\) 5.00651e86 0.554996
\(362\) 2.47566e86i 0.249804i
\(363\) −4.92137e85 + 2.19584e85i −0.0452128 + 0.0201733i
\(364\) 4.07715e86 0.341122
\(365\) 7.21180e85i 0.0549650i
\(366\) −4.93692e86 1.10647e87i −0.342846 0.768393i
\(367\) 8.37135e86 0.529846 0.264923 0.964270i \(-0.414653\pi\)
0.264923 + 0.964270i \(0.414653\pi\)
\(368\) 1.00705e87i 0.581067i
\(369\) −1.13474e87 1.01845e87i −0.597033 0.535847i
\(370\) −1.28890e86 −0.0618528
\(371\) 3.53658e87i 1.54836i
\(372\) 4.83325e86 2.15652e86i 0.193098 0.0861577i
\(373\) 2.98517e87 1.08860 0.544300 0.838890i \(-0.316795\pi\)
0.544300 + 0.838890i \(0.316795\pi\)
\(374\) 2.79237e87i 0.929692i
\(375\) 5.20022e86 + 1.16548e87i 0.158110 + 0.354359i
\(376\) −4.29271e87 −1.19219
\(377\) 2.75355e87i 0.698693i
\(378\) −5.28478e87 1.70315e87i −1.22548 0.394940i
\(379\) 5.25133e87 1.11310 0.556552 0.830813i \(-0.312124\pi\)
0.556552 + 0.830813i \(0.312124\pi\)
\(380\) 4.28832e86i 0.0831083i
\(381\) −5.56861e87 + 2.48463e87i −0.986955 + 0.440365i
\(382\) −1.42183e88 −2.30512
\(383\) 7.02219e87i 1.04163i 0.853669 + 0.520816i \(0.174372\pi\)
−0.853669 + 0.520816i \(0.825628\pi\)
\(384\) −3.59090e87 8.04799e87i −0.487463 1.09251i
\(385\) 1.72900e87 0.214848
\(386\) 3.41230e87i 0.388221i
\(387\) 1.06509e88 1.18671e88i 1.10972 1.23644i
\(388\) 5.18306e87 0.494661
\(389\) 3.59519e87i 0.314366i −0.987570 0.157183i \(-0.949759\pi\)
0.987570 0.157183i \(-0.0502412\pi\)
\(390\) 2.37166e87 1.05820e87i 0.190044 0.0847951i
\(391\) −5.33354e87 −0.391747
\(392\) 2.73428e87i 0.184127i
\(393\) 1.13804e88 + 2.55061e88i 0.702768 + 1.57506i
\(394\) 1.44636e87 0.0819229
\(395\) 4.43264e86i 0.0230336i
\(396\) 5.12462e87 + 4.59943e87i 0.244357 + 0.219315i
\(397\) 2.41590e88 1.05731 0.528653 0.848838i \(-0.322697\pi\)
0.528653 + 0.848838i \(0.322697\pi\)
\(398\) 8.78404e87i 0.352915i
\(399\) 3.43757e88 1.53379e88i 1.26816 0.565833i
\(400\) −3.46933e88 −1.17545
\(401\) 2.69778e87i 0.0839648i 0.999118 + 0.0419824i \(0.0133673\pi\)
−0.999118 + 0.0419824i \(0.986633\pi\)
\(402\) 1.48666e88 + 3.33193e88i 0.425134 + 0.952819i
\(403\) 2.17292e88 0.571047
\(404\) 2.15270e88i 0.520016i
\(405\) −8.85855e87 + 9.59677e86i −0.196740 + 0.0213135i
\(406\) −4.84297e88 −0.989068
\(407\) 1.40309e88i 0.263558i
\(408\) −3.34226e88 + 1.49127e88i −0.577556 + 0.257697i
\(409\) −1.10706e88 −0.176027 −0.0880134 0.996119i \(-0.528052\pi\)
−0.0880134 + 0.996119i \(0.528052\pi\)
\(410\) 1.25432e88i 0.183551i
\(411\) 4.38647e88 + 9.83104e88i 0.590871 + 1.32427i
\(412\) −2.14020e88 −0.265430
\(413\) 1.59411e89i 1.82061i
\(414\) 3.48701e88 3.88518e88i 0.366811 0.408695i
\(415\) −1.64242e88 −0.159165
\(416\) 6.59675e88i 0.589056i
\(417\) 2.03801e89 9.09331e88i 1.67718 0.748335i
\(418\) −1.85295e89 −1.40563
\(419\) 6.64029e88i 0.464419i 0.972666 + 0.232210i \(0.0745955\pi\)
−0.972666 + 0.232210i \(0.925404\pi\)
\(420\) 4.68899e87 + 1.05091e88i 0.0302415 + 0.0677778i
\(421\) −1.62399e89 −0.966035 −0.483017 0.875611i \(-0.660459\pi\)
−0.483017 + 0.875611i \(0.660459\pi\)
\(422\) 3.29413e89i 1.80766i
\(423\) −2.28523e89 2.05103e89i −1.15706 1.03848i
\(424\) −2.28172e89 −1.06616
\(425\) 1.83742e89i 0.792474i
\(426\) 6.78937e88 3.02932e88i 0.270336 0.120620i
\(427\) 2.20423e89 0.810418
\(428\) 6.69674e88i 0.227392i
\(429\) 1.15196e89 + 2.58179e89i 0.361317 + 0.809791i
\(430\) −1.31178e89 −0.380130
\(431\) 7.30357e89i 1.95573i 0.209246 + 0.977863i \(0.432899\pi\)
−0.209246 + 0.977863i \(0.567101\pi\)
\(432\) 1.51625e89 4.70484e89i 0.375252 1.16439i
\(433\) 1.20039e89 0.274621 0.137310 0.990528i \(-0.456154\pi\)
0.137310 + 0.990528i \(0.456154\pi\)
\(434\) 3.82175e89i 0.808373i
\(435\) −7.09739e88 + 3.16675e88i −0.138824 + 0.0619412i
\(436\) 1.89910e89 0.343563
\(437\) 3.53920e89i 0.592292i
\(438\) 8.45090e88 + 1.89403e89i 0.130853 + 0.293270i
\(439\) 4.92290e89 0.705387 0.352694 0.935739i \(-0.385266\pi\)
0.352694 + 0.935739i \(0.385266\pi\)
\(440\) 1.11551e89i 0.147939i
\(441\) 1.30642e89 1.45560e89i 0.160388 0.178702i
\(442\) 7.63037e89 0.867338
\(443\) 8.30618e89i 0.874328i −0.899382 0.437164i \(-0.855983\pi\)
0.899382 0.437164i \(-0.144017\pi\)
\(444\) 8.52814e88 3.80513e88i 0.0831444 0.0370978i
\(445\) 2.08395e89 0.188212
\(446\) 8.06437e89i 0.674816i
\(447\) 2.06395e89 + 4.62577e89i 0.160046 + 0.358697i
\(448\) 7.35325e89 0.528478
\(449\) 9.67234e89i 0.644401i −0.946671 0.322200i \(-0.895578\pi\)
0.946671 0.322200i \(-0.104422\pi\)
\(450\) −1.33846e90 1.20129e90i −0.826758 0.742030i
\(451\) −1.36546e90 −0.782124
\(452\) 3.68799e89i 0.195922i
\(453\) −2.72553e90 + 1.21609e90i −1.34311 + 0.599278i
\(454\) 3.34437e90 1.52903
\(455\) 4.72463e89i 0.200438i
\(456\) 9.89566e89 + 2.21784e90i 0.389619 + 0.873222i
\(457\) −2.44890e90 −0.894994 −0.447497 0.894285i \(-0.647684\pi\)
−0.447497 + 0.894285i \(0.647684\pi\)
\(458\) 4.47588e90i 1.51863i
\(459\) −2.49177e90 8.03034e89i −0.785013 0.252990i
\(460\) −1.08198e89 −0.0316556
\(461\) 5.49886e90i 1.49431i −0.664648 0.747156i \(-0.731419\pi\)
0.664648 0.747156i \(-0.268581\pi\)
\(462\) −4.54088e90 + 2.02607e90i −1.14634 + 0.511480i
\(463\) 1.91790e90 0.449854 0.224927 0.974376i \(-0.427786\pi\)
0.224927 + 0.974376i \(0.427786\pi\)
\(464\) 4.31151e90i 0.939762i
\(465\) 2.49900e89 + 5.60080e89i 0.0506250 + 0.113462i
\(466\) −2.00257e90 −0.377109
\(467\) 4.58814e89i 0.0803273i 0.999193 + 0.0401636i \(0.0127879\pi\)
−0.999193 + 0.0401636i \(0.987212\pi\)
\(468\) −1.25683e90 + 1.40034e90i −0.204606 + 0.227968i
\(469\) −6.63763e90 −1.00493
\(470\) 2.52606e90i 0.355727i
\(471\) 3.54660e90 1.58244e90i 0.464624 0.207308i
\(472\) 1.02848e91 1.25363
\(473\) 1.42800e91i 1.61976i
\(474\) −5.19423e89 1.16414e90i −0.0548350 0.122897i
\(475\) 1.21927e91 1.19816
\(476\) 3.38109e90i 0.309329i
\(477\) −1.21468e91 1.09019e91i −1.03475 0.928706i
\(478\) 2.07418e91 1.64550
\(479\) 1.28875e91i 0.952270i 0.879372 + 0.476135i \(0.157963\pi\)
−0.879372 + 0.476135i \(0.842037\pi\)
\(480\) −1.70034e90 + 7.58668e89i −0.117040 + 0.0522216i
\(481\) 3.83406e90 0.245882
\(482\) 3.51143e91i 2.09838i
\(483\) 3.86988e90 + 8.67324e90i 0.215523 + 0.483036i
\(484\) −3.21205e89 −0.0166740
\(485\) 6.00617e90i 0.290655i
\(486\) 2.21406e91 1.29010e91i 0.998979 0.582089i
\(487\) −1.73033e91 −0.728021 −0.364011 0.931395i \(-0.618593\pi\)
−0.364011 + 0.931395i \(0.618593\pi\)
\(488\) 1.42212e91i 0.558035i
\(489\) −1.41910e90 + 6.33184e89i −0.0519414 + 0.0231755i
\(490\) −1.60900e90 −0.0549399
\(491\) 5.25722e90i 0.167489i −0.996487 0.0837444i \(-0.973312\pi\)
0.996487 0.0837444i \(-0.0266879\pi\)
\(492\) −3.70306e90 8.29937e90i −0.110090 0.246736i
\(493\) −2.28346e91 −0.633574
\(494\) 5.06332e91i 1.31135i
\(495\) −5.32986e90 + 5.93844e90i −0.128866 + 0.143581i
\(496\) −3.40236e91 −0.768075
\(497\) 1.35253e91i 0.285121i
\(498\) 4.31347e91 1.92461e91i 0.849238 0.378918i
\(499\) −4.47706e91 −0.823330 −0.411665 0.911335i \(-0.635053\pi\)
−0.411665 + 0.911335i \(0.635053\pi\)
\(500\) 7.60680e90i 0.130684i
\(501\) −1.72060e91 3.85624e91i −0.276183 0.618987i
\(502\) −9.80404e90 −0.147055
\(503\) 3.53315e91i 0.495280i −0.968852 0.247640i \(-0.920345\pi\)
0.968852 0.247640i \(-0.0796551\pi\)
\(504\) 4.85011e91 + 4.35306e91i 0.635497 + 0.570370i
\(505\) −2.49456e91 −0.305554
\(506\) 4.67513e91i 0.535397i
\(507\) 1.47305e91 6.57253e90i 0.157742 0.0703821i
\(508\) −3.63448e91 −0.363979
\(509\) 7.41101e91i 0.694181i −0.937832 0.347091i \(-0.887170\pi\)
0.937832 0.347091i \(-0.112830\pi\)
\(510\) 8.77541e90 + 1.96676e91i 0.0768921 + 0.172332i
\(511\) −3.77315e91 −0.309309
\(512\) 1.90055e91i 0.145781i
\(513\) −5.32873e91 + 1.65348e92i −0.382502 + 1.18688i
\(514\) 1.85047e91 0.124319
\(515\) 2.48008e91i 0.155962i
\(516\) 8.67952e91 3.87268e91i 0.510982 0.227993i
\(517\) −2.74987e92 −1.51577
\(518\) 6.74339e91i 0.348070i
\(519\) 1.54509e92 + 3.46288e92i 0.746900 + 1.67397i
\(520\) −3.04822e91 −0.138017
\(521\) 9.12033e91i 0.386837i −0.981116 0.193418i \(-0.938042\pi\)
0.981116 0.193418i \(-0.0619575\pi\)
\(522\) 1.49290e92 1.66337e92i 0.593244 0.660984i
\(523\) 3.06182e92 1.14004 0.570022 0.821629i \(-0.306935\pi\)
0.570022 + 0.821629i \(0.306935\pi\)
\(524\) 1.66471e92i 0.580865i
\(525\) 2.98796e92 1.33318e92i 0.977144 0.435988i
\(526\) −1.19487e90 −0.00366275
\(527\) 1.80195e92i 0.517825i
\(528\) −1.80374e92 4.04257e92i −0.485982 1.08919i
\(529\) 3.06519e92 0.774398
\(530\) 1.34269e92i 0.318123i
\(531\) 5.47514e92 + 4.91403e92i 1.21669 + 1.09200i
\(532\) 2.24361e92 0.467683
\(533\) 3.73121e92i 0.729667i
\(534\) −5.47306e92 + 2.44200e92i −1.00422 + 0.448067i
\(535\) 7.76024e91 0.133612
\(536\) 4.28244e92i 0.691972i
\(537\) −4.79131e92 1.07384e93i −0.726656 1.62860i
\(538\) −1.20151e93 −1.71053
\(539\) 1.75156e92i 0.234102i
\(540\) −5.05488e91 1.62906e91i −0.0634341 0.0204432i
\(541\) 5.55105e91 0.0654136 0.0327068 0.999465i \(-0.489587\pi\)
0.0327068 + 0.999465i \(0.489587\pi\)
\(542\) 1.37286e93i 1.51932i
\(543\) −1.89818e92 + 8.46941e91i −0.197308 + 0.0880357i
\(544\) −5.47054e92 −0.534156
\(545\) 2.20069e92i 0.201873i
\(546\) −5.53640e92 1.24083e93i −0.477175 1.06945i
\(547\) 1.49648e93 1.21200 0.605999 0.795465i \(-0.292773\pi\)
0.605999 + 0.795465i \(0.292773\pi\)
\(548\) 6.41646e92i 0.488378i
\(549\) −6.79479e92 + 7.57065e92i −0.486090 + 0.541594i
\(550\) −1.61060e93 −1.08307
\(551\) 1.51524e93i 0.957917i
\(552\) −5.59577e92 + 2.49675e92i −0.332607 + 0.148404i
\(553\) 2.31912e92 0.129619
\(554\) 1.21090e93i 0.636470i
\(555\) 4.40941e91 + 9.88247e91i 0.0217981 + 0.0488544i
\(556\) 1.33016e93 0.618528
\(557\) 2.73968e93i 1.19846i −0.800578 0.599228i \(-0.795474\pi\)
0.800578 0.599228i \(-0.204526\pi\)
\(558\) −1.31262e93 1.17810e93i −0.540227 0.484863i
\(559\) 3.90212e93 1.51112
\(560\) 7.39784e92i 0.269595i
\(561\) −2.14102e93 + 9.55293e92i −0.734317 + 0.327642i
\(562\) 4.30944e93 1.39119
\(563\) 2.77015e93i 0.841818i −0.907103 0.420909i \(-0.861711\pi\)
0.907103 0.420909i \(-0.138289\pi\)
\(564\) −7.45754e92 1.67140e93i −0.213357 0.478179i
\(565\) 4.27367e92 0.115121
\(566\) 4.30213e93i 1.09125i
\(567\) 5.02095e92 + 4.63471e93i 0.119939 + 1.10713i
\(568\) −8.72619e92 −0.196328
\(569\) 4.21480e93i 0.893222i −0.894728 0.446611i \(-0.852631\pi\)
0.894728 0.446611i \(-0.147369\pi\)
\(570\) 1.30509e93 5.82314e92i 0.260553 0.116255i
\(571\) −1.40508e93 −0.264285 −0.132142 0.991231i \(-0.542186\pi\)
−0.132142 + 0.991231i \(0.542186\pi\)
\(572\) 1.68507e93i 0.298643i
\(573\) 4.86419e93 + 1.09017e94i 0.812370 + 1.82070i
\(574\) 6.56250e93 1.03292
\(575\) 3.07630e93i 0.456375i
\(576\) −2.26672e93 + 2.52555e93i −0.316982 + 0.353176i
\(577\) 4.64687e93 0.612608 0.306304 0.951934i \(-0.400908\pi\)
0.306304 + 0.951934i \(0.400908\pi\)
\(578\) 2.97433e93i 0.369694i
\(579\) −2.61634e93 + 1.16737e93i −0.306636 + 0.136817i
\(580\) −4.63228e92 −0.0511968
\(581\) 8.59298e93i 0.895685i
\(582\) −7.03812e93 1.57740e94i −0.691951 1.55081i
\(583\) −1.46165e94 −1.35554
\(584\) 2.43435e93i 0.212983i
\(585\) −1.62272e93 1.45642e93i −0.133951 0.120223i
\(586\) −1.34677e94 −1.04900
\(587\) 1.01821e94i 0.748416i −0.927345 0.374208i \(-0.877915\pi\)
0.927345 0.374208i \(-0.122085\pi\)
\(588\) 1.06461e93 4.75014e92i 0.0738520 0.0329517i
\(589\) 1.19573e94 0.782913
\(590\) 6.05214e93i 0.374060i
\(591\) −4.94812e92 1.10898e93i −0.0288713 0.0647068i
\(592\) −6.00338e93 −0.330718
\(593\) 1.93681e94i 1.00746i −0.863861 0.503731i \(-0.831960\pi\)
0.863861 0.503731i \(-0.168040\pi\)
\(594\) 7.03903e93 2.18417e94i 0.345759 1.07287i
\(595\) −3.91804e93 −0.181757
\(596\) 3.01912e93i 0.132284i
\(597\) −6.73506e93 + 3.00509e93i −0.278750 + 0.124374i
\(598\) 1.27751e94 0.499489
\(599\) 1.66298e94i 0.614291i 0.951663 + 0.307145i \(0.0993738\pi\)
−0.951663 + 0.307145i \(0.900626\pi\)
\(600\) 8.60139e93 + 1.92776e94i 0.300211 + 0.672839i
\(601\) −5.90854e94 −1.94871 −0.974356 0.225010i \(-0.927759\pi\)
−0.974356 + 0.225010i \(0.927759\pi\)
\(602\) 6.86309e94i 2.13914i
\(603\) 2.04613e94 2.27976e94i 0.602759 0.671585i
\(604\) −1.77888e94 −0.495327
\(605\) 3.72214e92i 0.00979739i
\(606\) 6.55146e94 2.92317e94i 1.63030 0.727418i
\(607\) −1.06612e94 −0.250837 −0.125419 0.992104i \(-0.540027\pi\)
−0.125419 + 0.992104i \(0.540027\pi\)
\(608\) 3.63011e94i 0.807604i
\(609\) 1.65682e94 + 3.71329e94i 0.348567 + 0.781216i
\(610\) 8.36850e93 0.166507
\(611\) 7.51424e94i 1.41411i
\(612\) −1.16127e94 1.04226e94i −0.206721 0.185536i
\(613\) 1.72386e94 0.290300 0.145150 0.989410i \(-0.453634\pi\)
0.145150 + 0.989410i \(0.453634\pi\)
\(614\) 1.15505e95i 1.84024i
\(615\) 9.61737e93 4.29113e93i 0.144978 0.0646871i
\(616\) 5.83626e94 0.832512
\(617\) 1.07332e95i 1.44888i −0.689336 0.724442i \(-0.742098\pi\)
0.689336 0.724442i \(-0.257902\pi\)
\(618\) 2.90620e94 + 6.51343e94i 0.371293 + 0.832150i
\(619\) −5.31537e94 −0.642764 −0.321382 0.946950i \(-0.604147\pi\)
−0.321382 + 0.946950i \(0.604147\pi\)
\(620\) 3.65549e93i 0.0418435i
\(621\) −4.17185e94 1.34448e94i −0.452079 0.145693i
\(622\) −5.24377e93 −0.0537985
\(623\) 1.09030e95i 1.05914i
\(624\) 1.10466e95 4.92885e94i 1.01614 0.453387i
\(625\) 1.01484e95 0.884051
\(626\) 5.74942e94i 0.474348i
\(627\) 6.33908e94 + 1.42073e95i 0.495370 + 1.11023i
\(628\) 2.31477e94 0.171349
\(629\) 3.17950e94i 0.222965i
\(630\) 2.56157e94 2.85407e94i 0.170188 0.189620i
\(631\) −2.13438e95 −1.34361 −0.671806 0.740728i \(-0.734481\pi\)
−0.671806 + 0.740728i \(0.734481\pi\)
\(632\) 1.49624e94i 0.0892525i
\(633\) −2.52573e95 + 1.12695e95i −1.42778 + 0.637055i
\(634\) −2.35818e95 −1.26340
\(635\) 4.21166e94i 0.213869i
\(636\) −3.96393e94 8.88405e94i −0.190803 0.427631i
\(637\) 4.78626e94 0.218401
\(638\) 2.00157e95i 0.865901i
\(639\) −4.64540e94 4.16932e94i −0.190543 0.171016i
\(640\) 6.08688e94 0.236742
\(641\) 1.92445e95i 0.709796i 0.934905 + 0.354898i \(0.115484\pi\)
−0.934905 + 0.354898i \(0.884516\pi\)
\(642\) −2.03807e95 + 9.09356e94i −0.712898 + 0.318085i
\(643\) −4.13132e95 −1.37062 −0.685309 0.728253i \(-0.740333\pi\)
−0.685309 + 0.728253i \(0.740333\pi\)
\(644\) 5.66080e94i 0.178139i
\(645\) 4.48768e94 + 1.00579e95i 0.133965 + 0.300246i
\(646\) 4.19890e95 1.18913
\(647\) 1.23705e95i 0.332385i −0.986093 0.166192i \(-0.946853\pi\)
0.986093 0.166192i \(-0.0531472\pi\)
\(648\) −2.99021e95 + 3.23940e94i −0.762344 + 0.0825874i
\(649\) 6.58837e95 1.59389
\(650\) 4.40108e95i 1.01043i
\(651\) 2.93029e95 1.30745e95i 0.638494 0.284887i
\(652\) −9.26212e93 −0.0191554
\(653\) 6.46490e95i 1.26915i 0.772860 + 0.634576i \(0.218825\pi\)
−0.772860 + 0.634576i \(0.781175\pi\)
\(654\) −2.57880e95 5.77966e95i −0.480589 1.07711i
\(655\) −1.92908e95 −0.341308
\(656\) 5.84234e95i 0.981423i
\(657\) 1.16312e95 1.29593e95i 0.185524 0.206708i
\(658\) 1.32161e96 2.00181
\(659\) 5.84076e94i 0.0840167i −0.999117 0.0420084i \(-0.986624\pi\)
0.999117 0.0420084i \(-0.0133756\pi\)
\(660\) −4.34333e94 + 1.93793e94i −0.0593375 + 0.0264755i
\(661\) 1.15780e96 1.50240 0.751199 0.660076i \(-0.229476\pi\)
0.751199 + 0.660076i \(0.229476\pi\)
\(662\) 3.34270e95i 0.412028i
\(663\) −2.61041e95 5.85050e95i −0.305667 0.685067i
\(664\) −5.54399e95 −0.616747
\(665\) 2.59991e95i 0.274803i
\(666\) −2.31609e95 2.07873e95i −0.232611 0.208773i
\(667\) −3.82307e95 −0.364867
\(668\) 2.51687e95i 0.228276i
\(669\) −6.18326e95 + 2.75888e95i −0.533003 + 0.237818i
\(670\) −2.52002e95 −0.206472
\(671\) 9.10996e95i 0.709497i
\(672\) 3.96928e95 + 8.89604e95i 0.293871 + 0.658630i
\(673\) 9.16629e94 0.0645181 0.0322590 0.999480i \(-0.489730\pi\)
0.0322590 + 0.999480i \(0.489730\pi\)
\(674\) 2.17453e94i 0.0145522i
\(675\) −4.63178e95 + 1.43722e96i −0.294727 + 0.914521i
\(676\) 9.61420e94 0.0581735
\(677\) 3.10703e95i 0.178785i 0.995996 + 0.0893925i \(0.0284926\pi\)
−0.995996 + 0.0893925i \(0.971507\pi\)
\(678\) −1.12239e96 + 5.00795e95i −0.614236 + 0.274063i
\(679\) 3.14237e96 1.63563
\(680\) 2.52782e95i 0.125154i
\(681\) −1.14413e96 2.56426e96i −0.538859 1.20770i
\(682\) −1.57951e96 −0.707707
\(683\) 2.61309e96i 1.11391i −0.830543 0.556954i \(-0.811970\pi\)
0.830543 0.556954i \(-0.188030\pi\)
\(684\) −6.91618e95 + 7.70590e95i −0.280517 + 0.312547i
\(685\) −7.43544e95 −0.286964
\(686\) 2.66396e96i 0.978379i
\(687\) 3.43183e96 1.53123e96i 1.19949 0.535195i
\(688\) −6.10994e96 −2.03250
\(689\) 3.99407e96i 1.26463i
\(690\) 1.46922e95 + 3.29285e95i 0.0442811 + 0.0992438i
\(691\) −1.35230e96 −0.387989 −0.193995 0.981003i \(-0.562144\pi\)
−0.193995 + 0.981003i \(0.562144\pi\)
\(692\) 2.26013e96i 0.617342i
\(693\) 3.10694e96 + 2.78853e96i 0.807984 + 0.725180i
\(694\) −4.56444e96 −1.13023
\(695\) 1.54139e96i 0.363438i
\(696\) −2.39573e96 + 1.06894e96i −0.537927 + 0.240015i
\(697\) 3.09421e96 0.661661
\(698\) 8.97364e96i 1.82761i
\(699\) 6.85094e95 + 1.53545e96i 0.132900 + 0.297859i
\(700\) 1.95016e96 0.360361
\(701\) 7.12654e96i 1.25449i 0.778824 + 0.627243i \(0.215817\pi\)
−0.778824 + 0.627243i \(0.784183\pi\)
\(702\) 5.96841e96 + 1.92347e96i 1.00091 + 0.322569i
\(703\) 2.10984e96 0.337107
\(704\) 3.03906e96i 0.462667i
\(705\) 1.93683e96 8.64185e95i 0.280971 0.125365i
\(706\) 7.81451e95 0.108029
\(707\) 1.30513e97i 1.71947i
\(708\) 1.78674e96 + 4.00447e96i 0.224352 + 0.502822i
\(709\) −4.24428e96 −0.507963 −0.253981 0.967209i \(-0.581740\pi\)
−0.253981 + 0.967209i \(0.581740\pi\)
\(710\) 5.13496e95i 0.0585805i
\(711\) −7.14894e95 + 7.96524e95i −0.0777455 + 0.0866229i
\(712\) 7.03437e96 0.729299
\(713\) 3.01692e96i 0.298209i
\(714\) 1.02899e97 4.59122e96i 0.969780 0.432702i
\(715\) −1.95267e96 −0.175478
\(716\) 7.00866e96i 0.600609i
\(717\) −7.09593e96 1.59035e97i −0.579907 1.29970i
\(718\) −1.36583e96 −0.106454
\(719\) 1.01354e97i 0.753457i −0.926324 0.376728i \(-0.877049\pi\)
0.926324 0.376728i \(-0.122951\pi\)
\(720\) 2.54087e96 + 2.28047e96i 0.180168 + 0.161704i
\(721\) −1.29756e97 −0.877662
\(722\) 9.94457e96i 0.641684i
\(723\) 2.69235e97 1.20129e97i 1.65741 0.739512i
\(724\) −1.23889e96 −0.0727650
\(725\) 1.31706e97i 0.738098i
\(726\) 4.36167e95 + 9.77546e95i 0.0233242 + 0.0522747i
\(727\) −1.36739e97 −0.697784 −0.348892 0.937163i \(-0.613442\pi\)
−0.348892 + 0.937163i \(0.613442\pi\)
\(728\) 1.59480e97i 0.776676i
\(729\) −1.74662e97 1.25625e97i −0.811823 0.583904i
\(730\) −1.43250e96 −0.0635502
\(731\) 3.23594e97i 1.37028i
\(732\) −5.53712e96 + 2.47058e96i −0.223824 + 0.0998671i
\(733\) 3.50164e96 0.135125 0.0675626 0.997715i \(-0.478478\pi\)
0.0675626 + 0.997715i \(0.478478\pi\)
\(734\) 1.66283e97i 0.612605i
\(735\) 5.50450e95 + 1.23368e96i 0.0193619 + 0.0433943i
\(736\) −9.15905e96 −0.307613
\(737\) 2.74330e97i 0.879788i
\(738\) −2.02297e97 + 2.25396e97i −0.619544 + 0.690286i
\(739\) −5.53437e97 −1.61867 −0.809333 0.587351i \(-0.800171\pi\)
−0.809333 + 0.587351i \(0.800171\pi\)
\(740\) 6.45002e95i 0.0180170i
\(741\) −3.88224e97 + 1.73220e97i −1.03577 + 0.462146i
\(742\) 7.02481e97 1.79020
\(743\) 8.05221e96i 0.196018i 0.995186 + 0.0980088i \(0.0312473\pi\)
−0.995186 + 0.0980088i \(0.968753\pi\)
\(744\) 8.43537e96 + 1.89055e97i 0.196166 + 0.439652i
\(745\) −3.49857e96 −0.0777280
\(746\) 5.92952e97i 1.25863i
\(747\) −2.95135e97 2.64888e97i −0.598577 0.537233i
\(748\) −1.39739e97 −0.270809
\(749\) 4.06008e97i 0.751888i
\(750\) 2.31503e97 1.03293e97i 0.409707 0.182806i
\(751\) 4.73700e97 0.801208 0.400604 0.916251i \(-0.368800\pi\)
0.400604 + 0.916251i \(0.368800\pi\)
\(752\) 1.17658e98i 1.90202i
\(753\) 3.35404e96 + 7.51714e96i 0.0518250 + 0.116151i
\(754\) 5.46944e97 0.807825
\(755\) 2.06138e97i 0.291047i
\(756\) −8.52307e96 + 2.64466e97i −0.115042 + 0.356968i
\(757\) 1.29124e98 1.66628 0.833140 0.553063i \(-0.186541\pi\)
0.833140 + 0.553063i \(0.186541\pi\)
\(758\) 1.04309e98i 1.28697i
\(759\) −3.58460e97 + 1.59940e97i −0.422884 + 0.188685i
\(760\) −1.67740e97 −0.189223
\(761\) 1.17233e98i 1.26465i −0.774704 0.632324i \(-0.782101\pi\)
0.774704 0.632324i \(-0.217899\pi\)
\(762\) 4.93529e97 + 1.10611e98i 0.509148 + 1.14111i
\(763\) 1.15138e98 1.13602
\(764\) 7.11527e97i 0.671455i
\(765\) 1.20778e97 1.34569e97i 0.109018 0.121466i
\(766\) 1.39484e98 1.20433
\(767\) 1.80032e98i 1.48699i
\(768\) −1.05013e98 + 4.68551e97i −0.829774 + 0.370233i
\(769\) −2.34147e98 −1.77008 −0.885041 0.465513i \(-0.845870\pi\)
−0.885041 + 0.465513i \(0.845870\pi\)
\(770\) 3.43437e97i 0.248406i
\(771\) −6.33061e96 1.41883e97i −0.0438124 0.0981932i
\(772\) −1.70762e97 −0.113084
\(773\) 3.80988e97i 0.241440i 0.992687 + 0.120720i \(0.0385203\pi\)
−0.992687 + 0.120720i \(0.961480\pi\)
\(774\) −2.35720e98 2.11563e98i −1.42956 1.28306i
\(775\) 1.03934e98 0.603253
\(776\) 2.02738e98i 1.12626i
\(777\) 5.17042e97 2.30696e97i 0.274923 0.122667i
\(778\) −7.14122e97 −0.363468
\(779\) 2.05324e98i 1.00038i
\(780\) −5.29554e96 1.18685e97i −0.0246998 0.0553578i
\(781\) −5.58992e97 −0.249615
\(782\) 1.05941e98i 0.452936i
\(783\) −1.78610e98 5.75614e97i −0.731149 0.235630i
\(784\) −7.49433e97 −0.293756
\(785\) 2.68237e97i 0.100682i
\(786\) 5.06634e98 2.26053e98i 1.82107 0.812537i
\(787\) −2.79285e98 −0.961405 −0.480703 0.876884i \(-0.659618\pi\)
−0.480703 + 0.876884i \(0.659618\pi\)
\(788\) 7.23803e96i 0.0238632i
\(789\) 4.08776e95 + 9.16157e95i 0.00129082 + 0.00289302i
\(790\) 8.80467e96 0.0266313
\(791\) 2.23595e98i 0.647830i
\(792\) −1.79910e98 + 2.00452e98i −0.499342 + 0.556359i
\(793\) −2.48936e98 −0.661912
\(794\) 4.79876e98i 1.22245i
\(795\) 1.02949e98 4.59343e97i 0.251269 0.112113i
\(796\) −4.39579e97 −0.102800
\(797\) 6.14826e98i 1.37775i 0.724882 + 0.688873i \(0.241894\pi\)
−0.724882 + 0.688873i \(0.758106\pi\)
\(798\) −3.04661e98 6.82813e98i −0.654213 1.46623i
\(799\) 6.23139e98 1.28231
\(800\) 3.15532e98i 0.622278i
\(801\) 3.74475e98 + 3.36098e98i 0.707812 + 0.635273i
\(802\) 5.35867e97 0.0970796
\(803\) 1.55942e98i 0.270791i
\(804\) 1.66740e98 7.43970e97i 0.277545 0.123837i
\(805\) −6.55977e97 −0.104672
\(806\) 4.31613e98i 0.660242i
\(807\) 4.11047e98 + 9.21247e98i 0.602825 + 1.35106i
\(808\) −8.42040e98 −1.18399
\(809\) 9.14482e98i 1.23289i 0.787397 + 0.616447i \(0.211428\pi\)
−0.787397 + 0.616447i \(0.788572\pi\)
\(810\) 1.90623e97 + 1.75960e98i 0.0246425 + 0.227469i
\(811\) −7.70599e98 −0.955255 −0.477628 0.878562i \(-0.658503\pi\)
−0.477628 + 0.878562i \(0.658503\pi\)
\(812\) 2.42357e98i 0.288104i
\(813\) 1.05262e99 4.69666e98i 1.20004 0.535440i
\(814\) −2.78700e98 −0.304725
\(815\) 1.07330e97i 0.0112555i
\(816\) 4.08738e98 + 9.16073e98i 0.411131 + 0.921435i
\(817\) 2.14729e99 2.07176
\(818\) 2.19899e98i 0.203521i
\(819\) −7.61987e98 + 8.48995e98i −0.676543 + 0.753793i
\(820\) 6.27700e97 0.0534664
\(821\) 1.60428e99i 1.31103i −0.755181 0.655516i \(-0.772451\pi\)
0.755181 0.655516i \(-0.227549\pi\)
\(822\) 1.95277e99 8.71296e98i 1.53112 0.683162i
\(823\) 6.91361e98 0.520128 0.260064 0.965591i \(-0.416256\pi\)
0.260064 + 0.965591i \(0.416256\pi\)
\(824\) 8.37152e98i 0.604337i
\(825\) 5.50998e98 + 1.23491e99i 0.381694 + 0.855461i
\(826\) −3.16643e99 −2.10498
\(827\) 2.56124e99i 1.63404i −0.576608 0.817021i \(-0.695624\pi\)
0.576608 0.817021i \(-0.304376\pi\)
\(828\) −1.94426e98 1.74501e98i −0.119048 0.106848i
\(829\) −1.50521e99 −0.884594 −0.442297 0.896869i \(-0.645836\pi\)
−0.442297 + 0.896869i \(0.645836\pi\)
\(830\) 3.26238e98i 0.184026i
\(831\) −9.28447e98 + 4.14260e98i −0.502716 + 0.224304i
\(832\) −8.30445e98 −0.431636
\(833\) 3.96914e98i 0.198046i
\(834\) −1.80623e99 4.04816e99i −0.865222 1.93915i
\(835\) 2.91656e98 0.134132
\(836\) 9.27271e98i 0.409443i
\(837\) −4.54237e98 + 1.40947e99i −0.192583 + 0.597574i
\(838\) 1.31898e99 0.536959
\(839\) 7.75975e98i 0.303348i −0.988431 0.151674i \(-0.951534\pi\)
0.988431 0.151674i \(-0.0484664\pi\)
\(840\) −4.11068e98 + 1.83412e98i −0.154318 + 0.0688546i
\(841\) 1.13695e99 0.409899
\(842\) 3.22578e99i 1.11692i
\(843\) −1.47429e99 3.30422e99i −0.490283 1.09883i
\(844\) −1.64848e99 −0.526551
\(845\) 1.11410e98i 0.0341819i
\(846\) −4.07402e99 + 4.53921e99i −1.20069 + 1.33779i
\(847\) −1.94739e98 −0.0551337
\(848\) 6.25392e99i 1.70096i
\(849\) 3.29861e99 1.47179e99i 0.861926 0.384579i
\(850\) 3.64972e99 0.916254
\(851\) 5.32328e98i 0.128403i
\(852\) −1.51596e98 3.39761e98i −0.0351352 0.0787457i
\(853\) −2.93055e99 −0.652653 −0.326327 0.945257i \(-0.605811\pi\)
−0.326327 + 0.945257i \(0.605811\pi\)
\(854\) 4.37832e99i 0.937001i
\(855\) −8.92965e98 8.01452e98i −0.183648 0.164827i
\(856\) 2.61947e99 0.517733
\(857\) 4.95199e98i 0.0940658i 0.998893 + 0.0470329i \(0.0149766\pi\)
−0.998893 + 0.0470329i \(0.985023\pi\)
\(858\) 5.12828e99 2.28816e99i 0.936276 0.417753i
\(859\) 1.22694e99 0.215306 0.107653 0.994189i \(-0.465667\pi\)
0.107653 + 0.994189i \(0.465667\pi\)
\(860\) 6.56452e98i 0.110727i
\(861\) −2.24508e99 5.03172e99i −0.364020 0.815848i
\(862\) 1.45073e100 2.26120
\(863\) 1.73452e99i 0.259903i −0.991520 0.129952i \(-0.958518\pi\)
0.991520 0.129952i \(-0.0414822\pi\)
\(864\) −4.27901e99 1.37902e99i −0.616420 0.198656i
\(865\) −2.61905e99 −0.362741
\(866\) 2.38436e99i 0.317515i
\(867\) −2.28053e99 + 1.01754e99i −0.292003 + 0.130287i
\(868\) 1.91252e99 0.235470
\(869\) 9.58478e98i 0.113478i
\(870\) 6.29021e98 + 1.40977e99i 0.0716161 + 0.160507i
\(871\) 7.49626e99 0.820781
\(872\) 7.42843e99i 0.782234i
\(873\) −9.68673e99 + 1.07928e100i −0.981054 + 1.09307i
\(874\) 7.03001e99 0.684805
\(875\) 4.61183e99i 0.432115i
\(876\) 9.47830e98 4.22908e98i 0.0854262 0.0381159i
\(877\) 4.46587e99 0.387187 0.193593 0.981082i \(-0.437986\pi\)
0.193593 + 0.981082i \(0.437986\pi\)
\(878\) 9.77850e99i 0.815565i
\(879\) 4.60741e99 + 1.03262e100i 0.369687 + 0.828551i
\(880\) 3.05749e99 0.236023
\(881\) 1.45906e99i 0.108365i −0.998531 0.0541827i \(-0.982745\pi\)
0.998531 0.0541827i \(-0.0172553\pi\)
\(882\) −2.89129e99 2.59498e99i −0.206614 0.185440i
\(883\) −1.59495e100 −1.09668 −0.548342 0.836254i \(-0.684741\pi\)
−0.548342 + 0.836254i \(0.684741\pi\)
\(884\) 3.81847e99i 0.252646i
\(885\) −4.64041e99 + 2.07049e99i −0.295451 + 0.131826i
\(886\) −1.64988e100 −1.01089
\(887\) 9.58087e99i 0.564939i 0.959276 + 0.282470i \(0.0911536\pi\)
−0.959276 + 0.282470i \(0.908846\pi\)
\(888\) 1.48840e99 + 3.33583e99i 0.0844653 + 0.189305i
\(889\) −2.20350e100 −1.20352
\(890\) 4.13940e99i 0.217609i
\(891\) −1.91550e100 + 2.07513e99i −0.969260 + 0.105003i
\(892\) −4.03565e99 −0.196566
\(893\) 4.13499e100i 1.93876i
\(894\) 9.18829e99 4.09968e99i 0.414724 0.185044i
\(895\) 8.12168e99 0.352909
\(896\) 3.18460e100i 1.33224i
\(897\) −4.37048e99 9.79520e99i −0.176030 0.394521i
\(898\) −1.92124e100 −0.745053
\(899\) 1.29164e100i 0.482294i
\(900\) −6.01160e99 + 6.69803e99i −0.216145 + 0.240825i
\(901\) 3.31219e100 1.14676
\(902\) 2.71224e100i 0.904287i
\(903\) 5.26220e100 2.34792e100i 1.68960 0.753874i
\(904\) 1.44258e100 0.446080
\(905\) 1.43564e99i 0.0427556i
\(906\) 2.41556e100 + 5.41380e100i 0.692882 + 1.55290i
\(907\) −3.84144e100 −1.06132 −0.530660 0.847585i \(-0.678056\pi\)
−0.530660 + 0.847585i \(0.678056\pi\)
\(908\) 1.67362e100i 0.445388i
\(909\) −4.48261e100 4.02322e100i −1.14910 1.03134i
\(910\) 9.38467e99 0.231746
\(911\) 2.38974e100i 0.568494i 0.958751 + 0.284247i \(0.0917435\pi\)
−0.958751 + 0.284247i \(0.908256\pi\)
\(912\) 6.07882e100 2.71228e100i 1.39314 0.621599i
\(913\) −3.55143e100 −0.784146
\(914\) 4.86432e100i 1.03479i
\(915\) −2.86293e99 6.41645e99i −0.0586804 0.131516i
\(916\) 2.23986e100 0.442360
\(917\) 1.00928e101i 1.92067i
\(918\) −1.59509e100 + 4.94948e100i −0.292505 + 0.907628i
\(919\) 3.79080e100 0.669889 0.334945 0.942238i \(-0.391282\pi\)
0.334945 + 0.942238i \(0.391282\pi\)
\(920\) 4.23221e99i 0.0720744i
\(921\) 8.85619e100 3.95150e100i 1.45351 0.648537i
\(922\) −1.09225e101 −1.72772
\(923\) 1.52749e100i 0.232874i
\(924\) 1.01391e100 + 2.27239e100i 0.148988 + 0.333915i
\(925\) 1.83389e100 0.259749
\(926\) 3.80957e100i 0.520119i
\(927\) 3.99987e100 4.45659e100i 0.526423 0.586532i
\(928\) −3.92128e100 −0.497504
\(929\) 8.14244e99i 0.0995911i −0.998759 0.0497955i \(-0.984143\pi\)
0.998759 0.0497955i \(-0.0158570\pi\)
\(930\) 1.11250e100 4.96382e99i 0.131184 0.0585324i
\(931\) 2.63382e100 0.299431
\(932\) 1.00215e100i 0.109847i
\(933\) 1.79393e99 + 4.02060e99i 0.0189597 + 0.0424928i
\(934\) 9.11355e99 0.0928739
\(935\) 1.61930e100i 0.159123i
\(936\) −5.47751e100 4.91616e100i −0.519044 0.465851i
\(937\) 6.42060e100 0.586718 0.293359 0.956002i \(-0.405227\pi\)
0.293359 + 0.956002i \(0.405227\pi\)
\(938\) 1.31845e101i 1.16190i
\(939\) −4.40831e100 + 1.96692e100i −0.374664 + 0.167170i
\(940\) 1.26412e100 0.103619
\(941\) 3.98299e100i 0.314892i 0.987528 + 0.157446i \(0.0503261\pi\)
−0.987528 + 0.157446i \(0.949674\pi\)
\(942\) −3.14325e100 7.04471e100i −0.239689 0.537196i
\(943\) 5.18048e100 0.381042
\(944\) 2.81895e101i 2.00004i
\(945\) −3.06466e100 9.87660e99i −0.209749 0.0675968i
\(946\) −2.83648e101 −1.87275
\(947\) 1.23420e101i 0.786114i −0.919514 0.393057i \(-0.871418\pi\)
0.919514 0.393057i \(-0.128582\pi\)
\(948\) −5.82572e99 + 2.59935e99i −0.0357986 + 0.0159728i
\(949\) 4.26123e100 0.252630
\(950\) 2.42186e101i 1.38531i
\(951\) 8.06752e100 + 1.80811e101i 0.445248 + 0.997900i
\(952\) −1.32253e101 −0.704289
\(953\) 1.06228e101i 0.545858i 0.962034 + 0.272929i \(0.0879924\pi\)
−0.962034 + 0.272929i \(0.912008\pi\)
\(954\) −2.16548e101 + 2.41274e101i −1.07377 + 1.19637i
\(955\) −8.24523e100 −0.394537
\(956\) 1.03798e101i 0.479316i
\(957\) −1.53468e101 + 6.84753e100i −0.683932 + 0.305160i
\(958\) 2.55987e101 1.10101
\(959\) 3.89015e101i 1.61486i
\(960\) −9.55064e99 2.14051e100i −0.0382658 0.0857621i
\(961\) −1.56652e101 −0.605817
\(962\) 7.61570e100i 0.284287i
\(963\) 1.39448e101 + 1.25157e101i 0.502479 + 0.450984i
\(964\) 1.75723e101 0.611235
\(965\) 1.97880e100i 0.0664467i
\(966\) 1.72279e101 7.68684e100i 0.558483 0.249187i
\(967\) 2.02776e101 0.634624 0.317312 0.948321i \(-0.397220\pi\)
0.317312 + 0.948321i \(0.397220\pi\)
\(968\) 1.25641e100i 0.0379638i
\(969\) −1.43648e101 3.21946e101i −0.419073 0.939236i
\(970\) 1.19302e101 0.336054
\(971\) 1.25298e101i 0.340794i 0.985375 + 0.170397i \(0.0545050\pi\)
−0.985375 + 0.170397i \(0.945495\pi\)
\(972\) −6.45604e100 1.10798e101i −0.169556 0.290991i
\(973\) 8.06444e101 2.04521
\(974\) 3.43700e101i 0.841735i
\(975\) −3.37448e101 + 1.50564e101i −0.798086 + 0.356094i
\(976\) 3.89785e101 0.890290
\(977\) 3.46871e101i 0.765160i −0.923922 0.382580i \(-0.875036\pi\)
0.923922 0.382580i \(-0.124964\pi\)
\(978\) 1.25771e100 + 2.81881e100i 0.0267954 + 0.0600543i
\(979\) 4.50616e101 0.927246
\(980\) 8.05190e99i 0.0160034i
\(981\) −3.54926e101 + 3.95453e101i −0.681384 + 0.759187i
\(982\) −1.04426e101 −0.193650
\(983\) 7.15686e101i 1.28204i −0.767523 0.641022i \(-0.778511\pi\)
0.767523 0.641022i \(-0.221489\pi\)
\(984\) 3.24635e101 1.44847e101i 0.561774 0.250655i
\(985\) 8.38748e99 0.0140217
\(986\) 4.53569e101i 0.732535i
\(987\) −4.52134e101 1.01333e102i −0.705478 1.58113i
\(988\) −2.53384e101 −0.381982
\(989\) 5.41777e101i 0.789127i
\(990\) 1.17957e101 + 1.05868e101i 0.166007 + 0.148994i
\(991\) −9.37374e101 −1.27470 −0.637351 0.770574i \(-0.719970\pi\)
−0.637351 + 0.770574i \(0.719970\pi\)
\(992\) 3.09442e101i 0.406614i
\(993\) 2.56298e101 1.14357e101i 0.325440 0.145207i
\(994\) 2.68656e101 0.329655
\(995\) 5.09388e100i 0.0604037i
\(996\) −9.63132e100 2.15859e101i −0.110374 0.247373i
\(997\) −1.91051e100 −0.0211599 −0.0105800 0.999944i \(-0.503368\pi\)
−0.0105800 + 0.999944i \(0.503368\pi\)
\(998\) 8.89290e101i 0.951930i
\(999\) −8.01490e100 + 2.48698e101i −0.0829223 + 0.257304i
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 3.69.b.a.2.6 22
3.2 odd 2 inner 3.69.b.a.2.17 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.69.b.a.2.6 22 1.1 even 1 trivial
3.69.b.a.2.17 yes 22 3.2 odd 2 inner