Properties

Label 20.11.d.d.19.1
Level $20$
Weight $11$
Character 20.19
Analytic conductor $12.707$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [20,11,Mod(19,20)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(20, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("20.19");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 20.d (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: \(12.7071450535\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.1
Character \(\chi\) \(=\) 20.19
Dual form 20.11.d.d.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-31.7400 - 4.07116i) q^{2} +190.073 q^{3} +(990.851 + 258.437i) q^{4} +(101.732 + 3123.34i) q^{5} +(-6032.92 - 773.819i) q^{6} +14056.7 q^{7} +(-30397.4 - 12236.7i) q^{8} -22921.2 q^{9} +O(q^{10})\) \(q+(-31.7400 - 4.07116i) q^{2} +190.073 q^{3} +(990.851 + 258.437i) q^{4} +(101.732 + 3123.34i) q^{5} +(-6032.92 - 773.819i) q^{6} +14056.7 q^{7} +(-30397.4 - 12236.7i) q^{8} -22921.2 q^{9} +(9486.66 - 99549.0i) q^{10} -173205. i q^{11} +(188334. + 49122.0i) q^{12} +664258. i q^{13} +(-446160. - 57227.2i) q^{14} +(19336.6 + 593664. i) q^{15} +(914997. + 512145. i) q^{16} +1.08730e6i q^{17} +(727518. + 93315.9i) q^{18} +2.14038e6i q^{19} +(-706386. + 3.12106e6i) q^{20} +2.67181e6 q^{21} +(-705145. + 5.49751e6i) q^{22} +6.85374e6 q^{23} +(-5.77774e6 - 2.32587e6i) q^{24} +(-9.74493e6 + 635490. i) q^{25} +(2.70430e6 - 2.10835e7i) q^{26} -1.55803e7 q^{27} +(1.39281e7 + 3.63278e6i) q^{28} +1.60930e7 q^{29} +(1.80316e6 - 1.89216e7i) q^{30} +3.87488e7i q^{31} +(-2.69569e7 - 1.99806e7i) q^{32} -3.29216e7i q^{33} +(4.42658e6 - 3.45109e7i) q^{34} +(1.43002e6 + 4.39040e7i) q^{35} +(-2.27115e7 - 5.92369e6i) q^{36} +1.29585e7i q^{37} +(8.71384e6 - 6.79357e7i) q^{38} +1.26258e8i q^{39} +(3.51270e7 - 9.61866e7i) q^{40} +4.48926e7 q^{41} +(-8.48031e7 - 1.08774e7i) q^{42} +8.66330e7 q^{43} +(4.47625e7 - 1.71620e8i) q^{44} +(-2.33183e6 - 7.15908e7i) q^{45} +(-2.17538e8 - 2.79027e7i) q^{46} -2.64135e8 q^{47} +(1.73916e8 + 9.73451e7i) q^{48} -8.48835e7 q^{49} +(3.11891e8 + 1.95027e7i) q^{50} +2.06667e8i q^{51} +(-1.71669e8 + 6.58180e8i) q^{52} +2.29181e8i q^{53} +(4.94519e8 + 6.34301e7i) q^{54} +(5.40978e8 - 1.76205e7i) q^{55} +(-4.27289e8 - 1.72008e8i) q^{56} +4.06829e8i q^{57} +(-5.10790e8 - 6.55170e7i) q^{58} -5.54778e8i q^{59} +(-1.34265e8 + 5.93230e8i) q^{60} +8.72720e8 q^{61} +(1.57753e8 - 1.22989e9i) q^{62} -3.22197e8 q^{63} +(7.74268e8 + 7.43929e8i) q^{64} +(-2.07470e9 + 6.75765e7i) q^{65} +(-1.34029e8 + 1.04493e9i) q^{66} +1.53061e8 q^{67} +(-2.80999e8 + 1.07735e9i) q^{68} +1.30271e9 q^{69} +(1.33351e8 - 1.39933e9i) q^{70} -3.28433e9i q^{71} +(6.96746e8 + 2.80480e8i) q^{72} -1.61594e9i q^{73} +(5.27562e7 - 4.11303e8i) q^{74} +(-1.85225e9 + 1.20790e8i) q^{75} +(-5.53154e8 + 2.12080e9i) q^{76} -2.43469e9i q^{77} +(5.14015e8 - 4.00741e9i) q^{78} -3.08746e9i q^{79} +(-1.50652e9 + 2.90995e9i) q^{80} -1.60793e9 q^{81} +(-1.42489e9 - 1.82765e8i) q^{82} +1.89093e9 q^{83} +(2.64736e9 + 6.90494e8i) q^{84} +(-3.39602e9 + 1.10614e8i) q^{85} +(-2.74973e9 - 3.52697e8i) q^{86} +3.05884e9 q^{87} +(-2.11946e9 + 5.26498e9i) q^{88} +8.69033e9 q^{89} +(-2.17446e8 + 2.28178e9i) q^{90} +9.33729e9i q^{91} +(6.79104e9 + 1.77126e9i) q^{92} +7.36511e9i q^{93} +(8.38362e9 + 1.07533e9i) q^{94} +(-6.68515e9 + 2.17746e8i) q^{95} +(-5.12379e9 - 3.79777e9i) q^{96} +5.78965e9i q^{97} +(2.69420e9 + 3.45574e8i) q^{98} +3.97006e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −31.7400 4.07116i −0.991874 0.127224i
\(3\) 190.073 0.782194 0.391097 0.920349i \(-0.372096\pi\)
0.391097 + 0.920349i \(0.372096\pi\)
\(4\) 990.851 + 258.437i 0.967628 + 0.252380i
\(5\) 101.732 + 3123.34i 0.0325543 + 0.999470i
\(6\) −6032.92 773.819i −0.775838 0.0995137i
\(7\) 14056.7 0.836362 0.418181 0.908364i \(-0.362668\pi\)
0.418181 + 0.908364i \(0.362668\pi\)
\(8\) −30397.4 12236.7i −0.927657 0.373434i
\(9\) −22921.2 −0.388173
\(10\) 9486.66 99549.0i 0.0948666 0.995490i
\(11\) 173205.i 1.07547i −0.843115 0.537733i \(-0.819281\pi\)
0.843115 0.537733i \(-0.180719\pi\)
\(12\) 188334. + 49122.0i 0.756873 + 0.197410i
\(13\) 664258.i 1.78904i 0.447029 + 0.894519i \(0.352482\pi\)
−0.447029 + 0.894519i \(0.647518\pi\)
\(14\) −446160. 57227.2i −0.829566 0.106405i
\(15\) 19336.6 + 593664.i 0.0254638 + 0.781779i
\(16\) 914997. + 512145.i 0.872609 + 0.488420i
\(17\) 1.08730e6i 0.765782i 0.923793 + 0.382891i \(0.125072\pi\)
−0.923793 + 0.382891i \(0.874928\pi\)
\(18\) 727518. + 93315.9i 0.385018 + 0.0493848i
\(19\) 2.14038e6i 0.864417i 0.901774 + 0.432209i \(0.142266\pi\)
−0.901774 + 0.432209i \(0.857734\pi\)
\(20\) −706386. + 3.12106e6i −0.220746 + 0.975331i
\(21\) 2.67181e6 0.654197
\(22\) −705145. + 5.49751e6i −0.136825 + 1.06673i
\(23\) 6.85374e6 1.06485 0.532425 0.846477i \(-0.321281\pi\)
0.532425 + 0.846477i \(0.321281\pi\)
\(24\) −5.77774e6 2.32587e6i −0.725607 0.292098i
\(25\) −9.74493e6 + 635490.i −0.997880 + 0.0650742i
\(26\) 2.70430e6 2.10835e7i 0.227608 1.77450i
\(27\) −1.55803e7 −1.08582
\(28\) 1.39281e7 + 3.63278e6i 0.809287 + 0.211081i
\(29\) 1.60930e7 0.784595 0.392298 0.919838i \(-0.371680\pi\)
0.392298 + 0.919838i \(0.371680\pi\)
\(30\) 1.80316e6 1.89216e7i 0.0742041 0.778666i
\(31\) 3.87488e7i 1.35347i 0.736225 + 0.676737i \(0.236607\pi\)
−0.736225 + 0.676737i \(0.763393\pi\)
\(32\) −2.69569e7 1.99806e7i −0.803379 0.595468i
\(33\) 3.29216e7i 0.841223i
\(34\) 4.42658e6 3.45109e7i 0.0974258 0.759560i
\(35\) 1.43002e6 + 4.39040e7i 0.0272272 + 0.835919i
\(36\) −2.27115e7 5.92369e6i −0.375607 0.0979670i
\(37\) 1.29585e7i 0.186873i 0.995625 + 0.0934365i \(0.0297852\pi\)
−0.995625 + 0.0934365i \(0.970215\pi\)
\(38\) 8.71384e6 6.79357e7i 0.109974 0.857393i
\(39\) 1.26258e8i 1.39938i
\(40\) 3.51270e7 9.61866e7i 0.343037 0.939322i
\(41\) 4.48926e7 0.387485 0.193743 0.981052i \(-0.437937\pi\)
0.193743 + 0.981052i \(0.437937\pi\)
\(42\) −8.48031e7 1.08774e7i −0.648881 0.0832295i
\(43\) 8.66330e7 0.589307 0.294653 0.955604i \(-0.404796\pi\)
0.294653 + 0.955604i \(0.404796\pi\)
\(44\) 4.47625e7 1.71620e8i 0.271426 1.04065i
\(45\) −2.33183e6 7.15908e7i −0.0126367 0.387967i
\(46\) −2.17538e8 2.79027e7i −1.05620 0.135474i
\(47\) −2.64135e8 −1.15169 −0.575845 0.817559i \(-0.695327\pi\)
−0.575845 + 0.817559i \(0.695327\pi\)
\(48\) 1.73916e8 + 9.73451e7i 0.682549 + 0.382039i
\(49\) −8.48835e7 −0.300499
\(50\) 3.11891e8 + 1.95027e7i 0.998051 + 0.0624088i
\(51\) 2.06667e8i 0.598990i
\(52\) −1.71669e8 + 6.58180e8i −0.451518 + 1.73112i
\(53\) 2.29181e8i 0.548025i 0.961726 + 0.274012i \(0.0883509\pi\)
−0.961726 + 0.274012i \(0.911649\pi\)
\(54\) 4.94519e8 + 6.34301e7i 1.07700 + 0.138142i
\(55\) 5.40978e8 1.76205e7i 1.07490 0.0350111i
\(56\) −4.27289e8 1.72008e8i −0.775857 0.312326i
\(57\) 4.06829e8i 0.676142i
\(58\) −5.10790e8 6.55170e7i −0.778220 0.0998192i
\(59\) 5.54778e8i 0.775996i −0.921660 0.387998i \(-0.873167\pi\)
0.921660 0.387998i \(-0.126833\pi\)
\(60\) −1.34265e8 + 5.93230e8i −0.172666 + 0.762898i
\(61\) 8.72720e8 1.03330 0.516649 0.856197i \(-0.327179\pi\)
0.516649 + 0.856197i \(0.327179\pi\)
\(62\) 1.57753e8 1.22989e9i 0.172194 1.34248i
\(63\) −3.22197e8 −0.324653
\(64\) 7.74268e8 + 7.43929e8i 0.721093 + 0.692838i
\(65\) −2.07470e9 + 6.75765e7i −1.78809 + 0.0582410i
\(66\) −1.34029e8 + 1.04493e9i −0.107024 + 0.834387i
\(67\) 1.53061e8 0.113368 0.0566841 0.998392i \(-0.481947\pi\)
0.0566841 + 0.998392i \(0.481947\pi\)
\(68\) −2.80999e8 + 1.07735e9i −0.193268 + 0.740993i
\(69\) 1.30271e9 0.832920
\(70\) 1.33351e8 1.39933e9i 0.0793428 0.832590i
\(71\) 3.28433e9i 1.82035i −0.414221 0.910176i \(-0.635946\pi\)
0.414221 0.910176i \(-0.364054\pi\)
\(72\) 6.96746e8 + 2.80480e8i 0.360091 + 0.144957i
\(73\) 1.61594e9i 0.779493i −0.920922 0.389747i \(-0.872563\pi\)
0.920922 0.389747i \(-0.127437\pi\)
\(74\) 5.27562e7 4.11303e8i 0.0237747 0.185355i
\(75\) −1.85225e9 + 1.20790e8i −0.780536 + 0.0509006i
\(76\) −5.53154e8 + 2.12080e9i −0.218162 + 0.836434i
\(77\) 2.43469e9i 0.899478i
\(78\) 5.14015e8 4.00741e9i 0.178034 1.38800i
\(79\) 3.08746e9i 1.00338i −0.865047 0.501690i \(-0.832712\pi\)
0.865047 0.501690i \(-0.167288\pi\)
\(80\) −1.50652e9 + 2.90995e9i −0.459754 + 0.888046i
\(81\) −1.60793e9 −0.461150
\(82\) −1.42489e9 1.82765e8i −0.384337 0.0492974i
\(83\) 1.89093e9 0.480049 0.240024 0.970767i \(-0.422845\pi\)
0.240024 + 0.970767i \(0.422845\pi\)
\(84\) 2.64736e9 + 6.90494e8i 0.633020 + 0.165106i
\(85\) −3.39602e9 + 1.10614e8i −0.765377 + 0.0249295i
\(86\) −2.74973e9 3.52697e8i −0.584518 0.0749738i
\(87\) 3.05884e9 0.613706
\(88\) −2.11946e9 + 5.26498e9i −0.401616 + 0.997663i
\(89\) 8.69033e9 1.55627 0.778137 0.628095i \(-0.216165\pi\)
0.778137 + 0.628095i \(0.216165\pi\)
\(90\) −2.17446e8 + 2.28178e9i −0.0368246 + 0.386422i
\(91\) 9.33729e9i 1.49628i
\(92\) 6.79104e9 + 1.77126e9i 1.03038 + 0.268747i
\(93\) 7.36511e9i 1.05868i
\(94\) 8.38362e9 + 1.07533e9i 1.14233 + 0.146523i
\(95\) −6.68515e9 + 2.17746e8i −0.863959 + 0.0281405i
\(96\) −5.12379e9 3.79777e9i −0.628398 0.465771i
\(97\) 5.78965e9i 0.674207i 0.941468 + 0.337104i \(0.109447\pi\)
−0.941468 + 0.337104i \(0.890553\pi\)
\(98\) 2.69420e9 + 3.45574e8i 0.298057 + 0.0382306i
\(99\) 3.97006e9i 0.417466i
\(100\) −9.82001e9 1.88877e9i −0.982001 0.188877i
\(101\) −1.07828e10 −1.02594 −0.512971 0.858406i \(-0.671455\pi\)
−0.512971 + 0.858406i \(0.671455\pi\)
\(102\) 8.41374e8 6.55960e9i 0.0762058 0.594123i
\(103\) 7.05867e9 0.608887 0.304444 0.952530i \(-0.401529\pi\)
0.304444 + 0.952530i \(0.401529\pi\)
\(104\) 8.12832e9 2.01917e10i 0.668089 1.65961i
\(105\) 2.71809e8 + 8.34497e9i 0.0212970 + 0.653851i
\(106\) 9.33035e8 7.27421e9i 0.0697218 0.543571i
\(107\) −1.81193e9 −0.129188 −0.0645942 0.997912i \(-0.520575\pi\)
−0.0645942 + 0.997912i \(0.520575\pi\)
\(108\) −1.54378e10 4.02654e9i −1.05067 0.274039i
\(109\) 1.33028e10 0.864588 0.432294 0.901733i \(-0.357704\pi\)
0.432294 + 0.901733i \(0.357704\pi\)
\(110\) −1.72424e10 1.64313e9i −1.07062 0.102026i
\(111\) 2.46307e9i 0.146171i
\(112\) 1.28619e10 + 7.19909e9i 0.729817 + 0.408496i
\(113\) 2.35102e10i 1.27604i −0.770019 0.638020i \(-0.779754\pi\)
0.770019 0.638020i \(-0.220246\pi\)
\(114\) 1.65627e9 1.29127e10i 0.0860214 0.670648i
\(115\) 6.97247e8 + 2.14066e10i 0.0346655 + 1.06429i
\(116\) 1.59457e10 + 4.15902e9i 0.759197 + 0.198016i
\(117\) 1.52256e10i 0.694456i
\(118\) −2.25859e9 + 1.76086e10i −0.0987251 + 0.769690i
\(119\) 1.52839e10i 0.640471i
\(120\) 6.67670e9 1.82825e10i 0.268322 0.734732i
\(121\) −4.06247e9 −0.156626
\(122\) −2.77001e10 3.55298e9i −1.02490 0.131460i
\(123\) 8.53287e9 0.303089
\(124\) −1.00141e10 + 3.83943e10i −0.341590 + 1.30966i
\(125\) −2.97623e9 3.03721e10i −0.0975250 0.995233i
\(126\) 1.02265e10 + 1.31172e9i 0.322015 + 0.0413036i
\(127\) −4.14600e10 −1.25490 −0.627452 0.778655i \(-0.715902\pi\)
−0.627452 + 0.778655i \(0.715902\pi\)
\(128\) −2.15466e10 2.67645e10i −0.627088 0.778948i
\(129\) 1.64666e10 0.460952
\(130\) 6.61262e10 + 6.30158e9i 1.78097 + 0.169720i
\(131\) 1.38898e9i 0.0360030i 0.999838 + 0.0180015i \(0.00573037\pi\)
−0.999838 + 0.0180015i \(0.994270\pi\)
\(132\) 8.50816e9 3.26204e10i 0.212308 0.813991i
\(133\) 3.00868e10i 0.722966i
\(134\) −4.85816e9 6.23137e8i −0.112447 0.0144231i
\(135\) −1.58502e9 4.86627e10i −0.0353482 1.08524i
\(136\) 1.33050e10 3.30512e10i 0.285970 0.710383i
\(137\) 4.15616e10i 0.861170i 0.902550 + 0.430585i \(0.141693\pi\)
−0.902550 + 0.430585i \(0.858307\pi\)
\(138\) −4.13481e10 5.30355e9i −0.826152 0.105967i
\(139\) 7.90047e10i 1.52258i −0.648414 0.761288i \(-0.724567\pi\)
0.648414 0.761288i \(-0.275433\pi\)
\(140\) −9.92948e9 + 4.38719e10i −0.184623 + 0.815730i
\(141\) −5.02049e10 −0.900846
\(142\) −1.33711e10 + 1.04245e11i −0.231592 + 1.80556i
\(143\) 1.15053e11 1.92405
\(144\) −2.09728e10 1.17390e10i −0.338723 0.189591i
\(145\) 1.63717e9 + 5.02638e10i 0.0255420 + 0.784179i
\(146\) −6.57877e9 + 5.12900e10i −0.0991701 + 0.773159i
\(147\) −1.61341e10 −0.235048
\(148\) −3.34896e9 + 1.28400e10i −0.0471630 + 0.180824i
\(149\) −3.37967e9 −0.0460197 −0.0230098 0.999735i \(-0.507325\pi\)
−0.0230098 + 0.999735i \(0.507325\pi\)
\(150\) 5.92821e10 + 3.70695e9i 0.780669 + 0.0488158i
\(151\) 6.40458e10i 0.815841i −0.913017 0.407921i \(-0.866254\pi\)
0.913017 0.407921i \(-0.133746\pi\)
\(152\) 2.61912e10 6.50622e10i 0.322803 0.801882i
\(153\) 2.49223e10i 0.297256i
\(154\) −9.91203e9 + 7.72771e10i −0.114435 + 0.892169i
\(155\) −1.21026e11 + 3.94201e9i −1.35276 + 0.0440614i
\(156\) −3.26296e10 + 1.25102e11i −0.353174 + 1.35408i
\(157\) 1.27096e10i 0.133239i 0.997778 + 0.0666197i \(0.0212214\pi\)
−0.997778 + 0.0666197i \(0.978779\pi\)
\(158\) −1.25695e10 + 9.79958e10i −0.127654 + 0.995227i
\(159\) 4.35612e10i 0.428662i
\(160\) 5.96638e10 8.62284e10i 0.568999 0.822339i
\(161\) 9.63413e10 0.890601
\(162\) 5.10356e10 + 6.54614e9i 0.457402 + 0.0586692i
\(163\) 1.71627e11 1.49158 0.745790 0.666181i \(-0.232072\pi\)
0.745790 + 0.666181i \(0.232072\pi\)
\(164\) 4.44819e10 + 1.16019e10i 0.374942 + 0.0977935i
\(165\) 1.02825e11 3.34919e9i 0.840777 0.0273855i
\(166\) −6.00181e10 7.69829e9i −0.476148 0.0610737i
\(167\) −1.27551e11 −0.981976 −0.490988 0.871166i \(-0.663364\pi\)
−0.490988 + 0.871166i \(0.663364\pi\)
\(168\) −8.12161e10 3.26941e10i −0.606870 0.244300i
\(169\) −3.03380e11 −2.20066
\(170\) 1.08240e11 + 1.03149e10i 0.762329 + 0.0726471i
\(171\) 4.90601e10i 0.335543i
\(172\) 8.58405e10 + 2.23892e10i 0.570230 + 0.148729i
\(173\) 1.87423e11i 1.20946i −0.796429 0.604732i \(-0.793280\pi\)
0.796429 0.604732i \(-0.206720\pi\)
\(174\) −9.70874e10 1.24530e10i −0.608719 0.0780780i
\(175\) −1.36982e11 + 8.93291e9i −0.834589 + 0.0544256i
\(176\) 8.87060e10 1.58482e11i 0.525279 0.938461i
\(177\) 1.05448e11i 0.606979i
\(178\) −2.75831e11 3.53797e10i −1.54363 0.197995i
\(179\) 1.33805e11i 0.728126i 0.931374 + 0.364063i \(0.118611\pi\)
−0.931374 + 0.364063i \(0.881389\pi\)
\(180\) 1.61912e10 7.15384e10i 0.0856874 0.378597i
\(181\) 3.51003e11 1.80683 0.903417 0.428764i \(-0.141051\pi\)
0.903417 + 0.428764i \(0.141051\pi\)
\(182\) 3.80136e10 2.96365e11i 0.190363 1.48413i
\(183\) 1.65881e11 0.808239
\(184\) −2.08336e11 8.38672e10i −0.987816 0.397652i
\(185\) −4.04739e10 + 1.31830e9i −0.186774 + 0.00608353i
\(186\) 2.99845e10 2.33768e11i 0.134689 1.05008i
\(187\) 1.88326e11 0.823573
\(188\) −2.61718e11 6.82622e10i −1.11441 0.290664i
\(189\) −2.19009e11 −0.908139
\(190\) 2.13073e11 + 2.03051e10i 0.860519 + 0.0820043i
\(191\) 3.35424e11i 1.31956i 0.751460 + 0.659778i \(0.229350\pi\)
−0.751460 + 0.659778i \(0.770650\pi\)
\(192\) 1.47168e11 + 1.41401e11i 0.564035 + 0.541934i
\(193\) 4.42274e11i 1.65160i 0.563964 + 0.825800i \(0.309276\pi\)
−0.563964 + 0.825800i \(0.690724\pi\)
\(194\) 2.35706e10 1.83763e11i 0.0857752 0.668729i
\(195\) −3.94346e11 + 1.28445e10i −1.39863 + 0.0455557i
\(196\) −8.41069e10 2.19370e10i −0.290771 0.0758399i
\(197\) 6.39016e10i 0.215368i −0.994185 0.107684i \(-0.965657\pi\)
0.994185 0.107684i \(-0.0343434\pi\)
\(198\) 1.61628e10 1.26010e11i 0.0531116 0.414074i
\(199\) 2.95320e11i 0.946298i 0.880982 + 0.473149i \(0.156883\pi\)
−0.880982 + 0.473149i \(0.843117\pi\)
\(200\) 3.03997e11 + 9.99285e10i 0.949991 + 0.312276i
\(201\) 2.90928e10 0.0886759
\(202\) 3.42244e11 + 4.38983e10i 1.01761 + 0.130524i
\(203\) 2.26214e11 0.656206
\(204\) −5.34104e10 + 2.04776e11i −0.151173 + 0.579600i
\(205\) 4.56703e9 + 1.40215e11i 0.0126143 + 0.387280i
\(206\) −2.24042e11 2.87370e10i −0.603939 0.0774649i
\(207\) −1.57096e11 −0.413346
\(208\) −3.40196e11 + 6.07793e11i −0.873802 + 1.56113i
\(209\) 3.70725e11 0.929651
\(210\) 2.53465e10 2.65976e11i 0.0620614 0.651247i
\(211\) 1.50649e11i 0.360208i −0.983648 0.180104i \(-0.942356\pi\)
0.983648 0.180104i \(-0.0576435\pi\)
\(212\) −5.92290e10 + 2.27085e11i −0.138310 + 0.530284i
\(213\) 6.24264e11i 1.42387i
\(214\) 5.75107e10 + 7.37668e9i 0.128139 + 0.0164358i
\(215\) 8.81338e9 + 2.70585e11i 0.0191845 + 0.588994i
\(216\) 4.73602e11 + 1.90652e11i 1.00727 + 0.405483i
\(217\) 5.44682e11i 1.13199i
\(218\) −4.22229e11 5.41577e10i −0.857563 0.109996i
\(219\) 3.07148e11i 0.609715i
\(220\) 5.40583e11 + 1.22349e11i 1.04894 + 0.237404i
\(221\) −7.22248e11 −1.37001
\(222\) 1.00275e10 7.81776e10i 0.0185964 0.144983i
\(223\) 8.28926e11 1.50311 0.751556 0.659669i \(-0.229304\pi\)
0.751556 + 0.659669i \(0.229304\pi\)
\(224\) −3.78926e11 2.80862e11i −0.671916 0.498027i
\(225\) 2.23365e11 1.45662e10i 0.387350 0.0252600i
\(226\) −9.57139e10 + 7.46214e11i −0.162343 + 1.26567i
\(227\) −5.67893e11 −0.942187 −0.471093 0.882083i \(-0.656140\pi\)
−0.471093 + 0.882083i \(0.656140\pi\)
\(228\) −1.05140e11 + 4.03107e11i −0.170645 + 0.654254i
\(229\) 6.29580e10 0.0999708 0.0499854 0.998750i \(-0.484083\pi\)
0.0499854 + 0.998750i \(0.484083\pi\)
\(230\) 6.50191e10 6.82283e11i 0.101019 1.06005i
\(231\) 4.62770e11i 0.703567i
\(232\) −4.89185e11 1.96925e11i −0.727835 0.292995i
\(233\) 3.90579e11i 0.568760i 0.958712 + 0.284380i \(0.0917877\pi\)
−0.958712 + 0.284380i \(0.908212\pi\)
\(234\) −6.19858e10 + 4.83259e11i −0.0883513 + 0.688813i
\(235\) −2.68710e10 8.24983e11i −0.0374925 1.15108i
\(236\) 1.43375e11 5.49703e11i 0.195846 0.750875i
\(237\) 5.86843e11i 0.784838i
\(238\) 6.22233e10 4.85111e11i 0.0814832 0.635267i
\(239\) 8.56345e11i 1.09814i −0.835775 0.549072i \(-0.814981\pi\)
0.835775 0.549072i \(-0.185019\pi\)
\(240\) −2.86349e11 + 5.53103e11i −0.359617 + 0.694625i
\(241\) −2.19603e11 −0.270117 −0.135059 0.990838i \(-0.543122\pi\)
−0.135059 + 0.990838i \(0.543122\pi\)
\(242\) 1.28943e11 + 1.65390e10i 0.155353 + 0.0199265i
\(243\) 6.14379e11 0.725112
\(244\) 8.64735e11 + 2.25543e11i 0.999848 + 0.260784i
\(245\) −8.63539e9 2.65120e11i −0.00978254 0.300339i
\(246\) −2.70833e11 3.47387e10i −0.300626 0.0385601i
\(247\) −1.42177e12 −1.54648
\(248\) 4.74158e11 1.17786e12i 0.505434 1.25556i
\(249\) 3.59415e11 0.375491
\(250\) −2.91844e10 + 9.76126e11i −0.0298848 + 0.999553i
\(251\) 3.77174e11i 0.378593i 0.981920 + 0.189297i \(0.0606208\pi\)
−0.981920 + 0.189297i \(0.939379\pi\)
\(252\) −3.19250e11 8.32677e10i −0.314143 0.0819358i
\(253\) 1.18710e12i 1.14521i
\(254\) 1.31594e12 + 1.68790e11i 1.24471 + 0.159654i
\(255\) −6.45492e11 + 2.10247e10i −0.598673 + 0.0194997i
\(256\) 5.74926e11 + 9.37223e11i 0.522892 + 0.852399i
\(257\) 8.23925e11i 0.734889i 0.930045 + 0.367445i \(0.119767\pi\)
−0.930045 + 0.367445i \(0.880233\pi\)
\(258\) −5.22650e11 6.70383e10i −0.457206 0.0586441i
\(259\) 1.82154e11i 0.156293i
\(260\) −2.07319e12 4.69222e11i −1.74491 0.394923i
\(261\) −3.68870e11 −0.304558
\(262\) 5.65476e9 4.40861e10i 0.00458044 0.0357105i
\(263\) 1.08787e12 0.864568 0.432284 0.901737i \(-0.357708\pi\)
0.432284 + 0.901737i \(0.357708\pi\)
\(264\) −4.02852e11 + 1.00073e12i −0.314142 + 0.780366i
\(265\) −7.15812e11 + 2.33152e10i −0.547734 + 0.0178406i
\(266\) 1.22488e11 9.54954e11i 0.0919784 0.717091i
\(267\) 1.65180e12 1.21731
\(268\) 1.51661e11 + 3.95567e10i 0.109698 + 0.0286119i
\(269\) 1.57558e12 1.11861 0.559305 0.828962i \(-0.311068\pi\)
0.559305 + 0.828962i \(0.311068\pi\)
\(270\) −1.47805e11 + 1.55101e12i −0.103008 + 1.08092i
\(271\) 7.48035e11i 0.511771i −0.966707 0.255885i \(-0.917633\pi\)
0.966707 0.255885i \(-0.0823670\pi\)
\(272\) −5.56857e11 + 9.94877e11i −0.374023 + 0.668228i
\(273\) 1.77477e12i 1.17038i
\(274\) 1.69204e11 1.31916e12i 0.109561 0.854172i
\(275\) 1.10070e11 + 1.68787e12i 0.0699850 + 1.07319i
\(276\) 1.29079e12 + 3.36669e11i 0.805957 + 0.210212i
\(277\) 1.35578e12i 0.831360i −0.909511 0.415680i \(-0.863544\pi\)
0.909511 0.415680i \(-0.136456\pi\)
\(278\) −3.21641e11 + 2.50761e12i −0.193708 + 1.51020i
\(279\) 8.88169e11i 0.525381i
\(280\) 4.93771e11 1.35207e12i 0.286903 0.785613i
\(281\) −6.65579e11 −0.379899 −0.189949 0.981794i \(-0.560832\pi\)
−0.189949 + 0.981794i \(0.560832\pi\)
\(282\) 1.59350e12 + 2.04392e11i 0.893526 + 0.114609i
\(283\) −3.17294e12 −1.74795 −0.873977 0.485968i \(-0.838467\pi\)
−0.873977 + 0.485968i \(0.838467\pi\)
\(284\) 8.48794e11 3.25429e12i 0.459421 1.76142i
\(285\) −1.27067e12 + 4.13877e10i −0.675784 + 0.0220114i
\(286\) −3.65177e12 4.68398e11i −1.90841 0.244785i
\(287\) 6.31043e11 0.324078
\(288\) 6.17885e11 + 4.57979e11i 0.311850 + 0.231144i
\(289\) 8.33769e11 0.413577
\(290\) 1.52668e11 1.60204e12i 0.0744319 0.781057i
\(291\) 1.10046e12i 0.527361i
\(292\) 4.17620e11 1.60116e12i 0.196728 0.754259i
\(293\) 3.22248e11i 0.149229i −0.997212 0.0746144i \(-0.976227\pi\)
0.997212 0.0746144i \(-0.0237726\pi\)
\(294\) 5.12095e11 + 6.56844e10i 0.233138 + 0.0299037i
\(295\) 1.73276e12 5.64389e10i 0.775584 0.0252620i
\(296\) 1.58569e11 3.93906e11i 0.0697848 0.173354i
\(297\) 2.69859e12i 1.16776i
\(298\) 1.07271e11 + 1.37592e10i 0.0456457 + 0.00585480i
\(299\) 4.55265e12i 1.90506i
\(300\) −1.86652e12 3.59005e11i −0.768115 0.147739i
\(301\) 1.21778e12 0.492874
\(302\) −2.60741e11 + 2.03281e12i −0.103794 + 0.809212i
\(303\) −2.04951e12 −0.802486
\(304\) −1.09619e12 + 1.95844e12i −0.422199 + 0.754298i
\(305\) 8.87838e10 + 2.72580e12i 0.0336383 + 1.03275i
\(306\) −1.01463e11 + 7.91032e11i −0.0378180 + 0.294840i
\(307\) 1.97279e12 0.723418 0.361709 0.932291i \(-0.382193\pi\)
0.361709 + 0.932291i \(0.382193\pi\)
\(308\) 6.29215e11 2.41242e12i 0.227010 0.870361i
\(309\) 1.34166e12 0.476268
\(310\) 3.85740e12 + 3.67597e11i 1.34737 + 0.128399i
\(311\) 5.13332e12i 1.76440i 0.470879 + 0.882198i \(0.343937\pi\)
−0.470879 + 0.882198i \(0.656063\pi\)
\(312\) 1.54498e12 3.83791e12i 0.522575 1.29814i
\(313\) 2.38086e10i 0.00792523i −0.999992 0.00396261i \(-0.998739\pi\)
0.999992 0.00396261i \(-0.00126134\pi\)
\(314\) 5.17427e10 4.03401e11i 0.0169512 0.132157i
\(315\) −3.27779e10 1.00633e12i −0.0105689 0.324481i
\(316\) 7.97913e11 3.05921e12i 0.253233 0.970899i
\(317\) 5.06007e12i 1.58074i −0.612630 0.790370i \(-0.709889\pi\)
0.612630 0.790370i \(-0.290111\pi\)
\(318\) 1.77345e11 1.38263e12i 0.0545360 0.425178i
\(319\) 2.78738e12i 0.843805i
\(320\) −2.24478e12 + 2.49399e12i −0.668996 + 0.743266i
\(321\) −3.44400e11 −0.101050
\(322\) −3.05787e12 3.92221e11i −0.883364 0.113306i
\(323\) −2.32724e12 −0.661956
\(324\) −1.59322e12 4.15549e11i −0.446221 0.116385i
\(325\) −4.22129e11 6.47314e12i −0.116420 1.78525i
\(326\) −5.44742e12 6.98720e11i −1.47946 0.189764i
\(327\) 2.52850e12 0.676276
\(328\) −1.36462e12 5.49337e11i −0.359453 0.144700i
\(329\) −3.71287e12 −0.963230
\(330\) −3.27731e12 3.12316e11i −0.837429 0.0798039i
\(331\) 4.65034e12i 1.17043i −0.810879 0.585214i \(-0.801010\pi\)
0.810879 0.585214i \(-0.198990\pi\)
\(332\) 1.87363e12 + 4.88687e11i 0.464509 + 0.121155i
\(333\) 2.97025e11i 0.0725390i
\(334\) 4.04846e12 + 5.19280e11i 0.973996 + 0.124931i
\(335\) 1.55713e10 + 4.78063e11i 0.00369063 + 0.113308i
\(336\) 2.44469e12 + 1.36835e12i 0.570858 + 0.319523i
\(337\) 2.23573e11i 0.0514362i 0.999669 + 0.0257181i \(0.00818723\pi\)
−0.999669 + 0.0257181i \(0.991813\pi\)
\(338\) 9.62926e12 + 1.23511e12i 2.18278 + 0.279976i
\(339\) 4.46866e12i 0.998111i
\(340\) −3.39353e12 7.68055e11i −0.746892 0.169043i
\(341\) 6.71148e12 1.45561
\(342\) −1.99732e11 + 1.55717e12i −0.0426891 + 0.332816i
\(343\) −5.16386e12 −1.08769
\(344\) −2.63342e12 1.06010e12i −0.546674 0.220067i
\(345\) 1.32528e11 + 4.06882e12i 0.0271152 + 0.832478i
\(346\) −7.63031e11 + 5.94881e12i −0.153873 + 1.19964i
\(347\) −3.16769e12 −0.629644 −0.314822 0.949151i \(-0.601945\pi\)
−0.314822 + 0.949151i \(0.601945\pi\)
\(348\) 3.03085e12 + 7.90517e11i 0.593839 + 0.154887i
\(349\) −8.37634e12 −1.61781 −0.808904 0.587941i \(-0.799939\pi\)
−0.808904 + 0.587941i \(0.799939\pi\)
\(350\) 4.38417e12 + 2.74145e11i 0.834732 + 0.0521963i
\(351\) 1.03494e13i 1.94257i
\(352\) −3.46073e12 + 4.66907e12i −0.640405 + 0.864007i
\(353\) 2.56251e12i 0.467512i 0.972295 + 0.233756i \(0.0751017\pi\)
−0.972295 + 0.233756i \(0.924898\pi\)
\(354\) −4.29298e11 + 3.34693e12i −0.0772222 + 0.602047i
\(355\) 1.02581e13 3.34123e11i 1.81939 0.0592604i
\(356\) 8.61082e12 + 2.24590e12i 1.50589 + 0.392772i
\(357\) 2.90506e12i 0.500973i
\(358\) 5.44741e11 4.24696e12i 0.0926349 0.722209i
\(359\) 9.99628e12i 1.67636i 0.545397 + 0.838178i \(0.316379\pi\)
−0.545397 + 0.838178i \(0.683621\pi\)
\(360\) −8.05153e11 + 2.20471e12i −0.133158 + 0.364619i
\(361\) 1.54983e12 0.252783
\(362\) −1.11408e13 1.42899e12i −1.79215 0.229872i
\(363\) −7.72167e11 −0.122512
\(364\) −2.41310e12 + 9.25187e12i −0.377632 + 1.44785i
\(365\) 5.04715e12 1.64394e11i 0.779080 0.0253759i
\(366\) −5.26504e12 6.75327e11i −0.801672 0.102827i
\(367\) 2.30492e12 0.346199 0.173099 0.984904i \(-0.444622\pi\)
0.173099 + 0.984904i \(0.444622\pi\)
\(368\) 6.27115e12 + 3.51011e12i 0.929198 + 0.520094i
\(369\) −1.02899e12 −0.150411
\(370\) 1.29001e12 + 1.22933e11i 0.186030 + 0.0177280i
\(371\) 3.22154e12i 0.458347i
\(372\) −1.90342e12 + 7.29773e12i −0.267189 + 1.02441i
\(373\) 5.12634e11i 0.0710008i −0.999370 0.0355004i \(-0.988697\pi\)
0.999370 0.0355004i \(-0.0113025\pi\)
\(374\) −5.97746e12 7.66705e11i −0.816880 0.104778i
\(375\) −5.65701e11 5.77292e12i −0.0762835 0.778465i
\(376\) 8.02902e12 + 3.23214e12i 1.06837 + 0.430081i
\(377\) 1.06899e13i 1.40367i
\(378\) 6.95133e12 + 8.91620e11i 0.900759 + 0.115537i
\(379\) 1.30188e13i 1.66485i −0.554141 0.832423i \(-0.686953\pi\)
0.554141 0.832423i \(-0.313047\pi\)
\(380\) −6.68026e12 1.51194e12i −0.843093 0.190816i
\(381\) −7.88043e12 −0.981578
\(382\) 1.36557e12 1.06464e13i 0.167879 1.30883i
\(383\) −7.62061e10 −0.00924689 −0.00462345 0.999989i \(-0.501472\pi\)
−0.00462345 + 0.999989i \(0.501472\pi\)
\(384\) −4.09543e12 5.08720e12i −0.490505 0.609289i
\(385\) 7.60439e12 2.47687e11i 0.899002 0.0292819i
\(386\) 1.80057e12 1.40378e13i 0.210123 1.63818i
\(387\) −1.98573e12 −0.228753
\(388\) −1.49626e12 + 5.73668e12i −0.170156 + 0.652382i
\(389\) −5.68167e12 −0.637863 −0.318932 0.947778i \(-0.603324\pi\)
−0.318932 + 0.947778i \(0.603324\pi\)
\(390\) 1.25688e13 + 1.19776e12i 1.39306 + 0.132754i
\(391\) 7.45209e12i 0.815444i
\(392\) 2.58024e12 + 1.03869e12i 0.278760 + 0.112217i
\(393\) 2.64008e11i 0.0281614i
\(394\) −2.60154e11 + 2.02823e12i −0.0273999 + 0.213618i
\(395\) 9.64319e12 3.14094e11i 1.00285 0.0326644i
\(396\) −1.02601e12 + 3.93374e12i −0.105360 + 0.403952i
\(397\) 1.23091e13i 1.24818i −0.781354 0.624088i \(-0.785471\pi\)
0.781354 0.624088i \(-0.214529\pi\)
\(398\) 1.20230e12 9.37346e12i 0.120392 0.938609i
\(399\) 5.71869e12i 0.565499i
\(400\) −9.24204e12 4.40935e12i −0.902543 0.430600i
\(401\) 3.21421e11 0.0309993 0.0154997 0.999880i \(-0.495066\pi\)
0.0154997 + 0.999880i \(0.495066\pi\)
\(402\) −9.23405e11 1.18442e11i −0.0879553 0.0112817i
\(403\) −2.57392e13 −2.42142
\(404\) −1.06841e13 2.78666e12i −0.992731 0.258927i
\(405\) −1.63578e11 5.02212e12i −0.0150124 0.460905i
\(406\) −7.18004e12 9.20955e11i −0.650873 0.0834850i
\(407\) 2.24448e12 0.200976
\(408\) 2.52892e12 6.28214e12i 0.223684 0.555657i
\(409\) 1.03801e13 0.906952 0.453476 0.891268i \(-0.350184\pi\)
0.453476 + 0.891268i \(0.350184\pi\)
\(410\) 4.25880e11 4.46901e12i 0.0367594 0.385738i
\(411\) 7.89974e12i 0.673602i
\(412\) 6.99409e12 + 1.82422e12i 0.589176 + 0.153671i
\(413\) 7.79837e12i 0.649013i
\(414\) 4.98622e12 + 6.39563e11i 0.409987 + 0.0525874i
\(415\) 1.92369e11 + 5.90603e12i 0.0156277 + 0.479795i
\(416\) 1.32723e13 1.79063e13i 1.06531 1.43728i
\(417\) 1.50167e13i 1.19095i
\(418\) −1.17668e13 1.50928e12i −0.922097 0.118274i
\(419\) 1.57632e13i 1.22061i 0.792168 + 0.610303i \(0.208952\pi\)
−0.792168 + 0.610303i \(0.791048\pi\)
\(420\) −1.88733e12 + 8.33887e12i −0.144411 + 0.638059i
\(421\) −1.50088e13 −1.13484 −0.567421 0.823428i \(-0.692059\pi\)
−0.567421 + 0.823428i \(0.692059\pi\)
\(422\) −6.13316e11 + 4.78159e12i −0.0458271 + 0.357281i
\(423\) 6.05428e12 0.447055
\(424\) 2.80443e12 6.96653e12i 0.204651 0.508379i
\(425\) −6.90969e11 1.05957e13i −0.0498327 0.764159i
\(426\) −2.54148e12 + 1.98141e13i −0.181150 + 1.41230i
\(427\) 1.22676e13 0.864211
\(428\) −1.79536e12 4.68271e11i −0.125006 0.0326046i
\(429\) 2.18684e13 1.50498
\(430\) 8.21858e11 8.62423e12i 0.0559055 0.586649i
\(431\) 5.91866e11i 0.0397958i 0.999802 + 0.0198979i \(0.00633411\pi\)
−0.999802 + 0.0198979i \(0.993666\pi\)
\(432\) −1.42560e13 7.97940e12i −0.947496 0.530336i
\(433\) 2.30044e13i 1.51137i 0.654933 + 0.755687i \(0.272697\pi\)
−0.654933 + 0.755687i \(0.727303\pi\)
\(434\) 2.21749e12 1.72882e13i 0.144017 1.12280i
\(435\) 3.11183e11 + 9.55380e12i 0.0199788 + 0.613380i
\(436\) 1.31811e13 + 3.43793e12i 0.836600 + 0.218205i
\(437\) 1.46696e13i 0.920475i
\(438\) −1.25045e12 + 9.74886e12i −0.0775702 + 0.604760i
\(439\) 4.54425e12i 0.278701i 0.990243 + 0.139351i \(0.0445015\pi\)
−0.990243 + 0.139351i \(0.955498\pi\)
\(440\) −1.66600e13 6.08417e12i −1.01021 0.368925i
\(441\) 1.94563e12 0.116645
\(442\) 2.29241e13 + 2.94039e12i 1.35888 + 0.174298i
\(443\) 2.40350e12 0.140872 0.0704362 0.997516i \(-0.477561\pi\)
0.0704362 + 0.997516i \(0.477561\pi\)
\(444\) −6.36548e11 + 2.44053e12i −0.0368906 + 0.141439i
\(445\) 8.84087e11 + 2.71429e13i 0.0506635 + 1.55545i
\(446\) −2.63101e13 3.37469e12i −1.49090 0.191232i
\(447\) −6.42385e11 −0.0359963
\(448\) 1.08837e13 + 1.04572e13i 0.603095 + 0.579463i
\(449\) −2.55386e13 −1.39947 −0.699737 0.714401i \(-0.746699\pi\)
−0.699737 + 0.714401i \(0.746699\pi\)
\(450\) −7.14891e12 4.47026e11i −0.387416 0.0242254i
\(451\) 7.77561e12i 0.416727i
\(452\) 6.07591e12 2.32951e13i 0.322047 1.23473i
\(453\) 1.21734e13i 0.638146i
\(454\) 1.80249e13 + 2.31198e12i 0.934530 + 0.119869i
\(455\) −2.91636e13 + 9.49904e11i −1.49549 + 0.0487105i
\(456\) 4.97825e12 1.23666e13i 0.252495 0.627228i
\(457\) 1.43833e13i 0.721569i 0.932649 + 0.360785i \(0.117491\pi\)
−0.932649 + 0.360785i \(0.882509\pi\)
\(458\) −1.99828e12 2.56312e11i −0.0991585 0.0127187i
\(459\) 1.69405e13i 0.831502i
\(460\) −4.84139e12 + 2.13910e13i −0.235061 + 1.03858i
\(461\) 3.07398e13 1.47638 0.738188 0.674595i \(-0.235682\pi\)
0.738188 + 0.674595i \(0.235682\pi\)
\(462\) −1.88401e12 + 1.46883e13i −0.0895104 + 0.697849i
\(463\) 1.66750e13 0.783718 0.391859 0.920025i \(-0.371832\pi\)
0.391859 + 0.920025i \(0.371832\pi\)
\(464\) 1.47250e13 + 8.24193e12i 0.684645 + 0.383212i
\(465\) −2.30038e13 + 7.49269e11i −1.05812 + 0.0344646i
\(466\) 1.59011e12 1.23970e13i 0.0723598 0.564138i
\(467\) 6.59007e12 0.296692 0.148346 0.988936i \(-0.452605\pi\)
0.148346 + 0.988936i \(0.452605\pi\)
\(468\) 3.93485e12 1.50863e13i 0.175267 0.671975i
\(469\) 2.15154e12 0.0948168
\(470\) −2.50575e12 + 2.62943e13i −0.109257 + 1.14650i
\(471\) 2.41575e12i 0.104219i
\(472\) −6.78865e12 + 1.68638e13i −0.289784 + 0.719857i
\(473\) 1.50053e13i 0.633779i
\(474\) −2.38913e12 + 1.86264e13i −0.0998500 + 0.778460i
\(475\) −1.36019e12 2.08579e13i −0.0562512 0.862585i
\(476\) −3.94993e12 + 1.51441e13i −0.161642 + 0.619738i
\(477\) 5.25311e12i 0.212728i
\(478\) −3.48632e12 + 2.71804e13i −0.139710 + 1.08922i
\(479\) 3.32507e13i 1.31863i −0.751867 0.659315i \(-0.770846\pi\)
0.751867 0.659315i \(-0.229154\pi\)
\(480\) 1.13405e13 1.63897e13i 0.445067 0.643228i
\(481\) −8.60779e12 −0.334323
\(482\) 6.97018e12 + 8.94037e11i 0.267922 + 0.0343653i
\(483\) 1.83119e13 0.696622
\(484\) −4.02531e12 1.04989e12i −0.151556 0.0395293i
\(485\) −1.80831e13 + 5.88994e11i −0.673850 + 0.0219484i
\(486\) −1.95004e13 2.50124e12i −0.719220 0.0922515i
\(487\) −3.49858e12 −0.127717 −0.0638583 0.997959i \(-0.520341\pi\)
−0.0638583 + 0.997959i \(0.520341\pi\)
\(488\) −2.65285e13 1.06792e13i −0.958546 0.385869i
\(489\) 3.26216e13 1.16670
\(490\) −8.05260e11 + 8.45006e12i −0.0285073 + 0.299143i
\(491\) 1.49892e13i 0.525254i −0.964897 0.262627i \(-0.915411\pi\)
0.964897 0.262627i \(-0.0845889\pi\)
\(492\) 8.45481e12 + 2.20521e12i 0.293277 + 0.0764935i
\(493\) 1.74979e13i 0.600829i
\(494\) 4.51268e13 + 5.78824e12i 1.53391 + 0.196749i
\(495\) −1.23999e13 + 4.03884e11i −0.417245 + 0.0135903i
\(496\) −1.98450e13 + 3.54550e13i −0.661064 + 1.18105i
\(497\) 4.61670e13i 1.52247i
\(498\) −1.14078e13 1.46324e12i −0.372440 0.0477714i
\(499\) 2.01950e13i 0.652741i 0.945242 + 0.326370i \(0.105826\pi\)
−0.945242 + 0.326370i \(0.894174\pi\)
\(500\) 4.90028e12 3.08634e13i 0.156809 0.987629i
\(501\) −2.42440e13 −0.768096
\(502\) 1.53553e12 1.19715e13i 0.0481661 0.375517i
\(503\) 3.87916e13 1.20475 0.602376 0.798213i \(-0.294221\pi\)
0.602376 + 0.798213i \(0.294221\pi\)
\(504\) 9.79397e12 + 3.94263e12i 0.301166 + 0.121237i
\(505\) −1.09695e12 3.36783e13i −0.0333989 1.02540i
\(506\) −4.83288e12 + 3.76786e13i −0.145698 + 1.13590i
\(507\) −5.76643e13 −1.72134
\(508\) −4.10807e13 1.07148e13i −1.21428 0.316713i
\(509\) 2.53824e13 0.742923 0.371462 0.928448i \(-0.378857\pi\)
0.371462 + 0.928448i \(0.378857\pi\)
\(510\) 2.05735e13 + 1.96058e12i 0.596289 + 0.0568242i
\(511\) 2.27149e13i 0.651938i
\(512\) −1.44325e13 3.20880e13i −0.410197 0.911997i
\(513\) 3.33479e13i 0.938602i
\(514\) 3.35433e12 2.61513e13i 0.0934954 0.728917i
\(515\) 7.18095e11 + 2.20467e13i 0.0198219 + 0.608564i
\(516\) 1.63160e13 + 4.25558e12i 0.446030 + 0.116335i
\(517\) 4.57494e13i 1.23860i
\(518\) 7.41580e11 5.78158e12i 0.0198843 0.155023i
\(519\) 3.56242e13i 0.946036i
\(520\) 6.38926e13 + 2.33334e13i 1.68048 + 0.613707i
\(521\) 9.37998e12 0.244351 0.122175 0.992509i \(-0.461013\pi\)
0.122175 + 0.992509i \(0.461013\pi\)
\(522\) 1.17079e13 + 1.50173e12i 0.302084 + 0.0387471i
\(523\) 1.03783e13 0.265227 0.132614 0.991168i \(-0.457663\pi\)
0.132614 + 0.991168i \(0.457663\pi\)
\(524\) −3.58964e11 + 1.37627e12i −0.00908645 + 0.0348376i
\(525\) −2.60366e13 + 1.69791e12i −0.652811 + 0.0425713i
\(526\) −3.45290e13 4.42890e12i −0.857543 0.109994i
\(527\) −4.21316e13 −1.03647
\(528\) 1.68606e13 3.01231e13i 0.410870 0.734058i
\(529\) 5.54730e12 0.133907
\(530\) 2.28148e13 + 2.17417e12i 0.545553 + 0.0519892i
\(531\) 1.27162e13i 0.301220i
\(532\) −7.77554e12 + 2.98115e13i −0.182462 + 0.699562i
\(533\) 2.98202e13i 0.693226i
\(534\) −5.24280e13 6.72473e12i −1.20742 0.154871i
\(535\) −1.84332e11 5.65929e12i −0.00420564 0.129120i
\(536\) −4.65267e12 1.87296e12i −0.105167 0.0423356i
\(537\) 2.54327e13i 0.569536i
\(538\) −5.00089e13 6.41444e12i −1.10952 0.142314i
\(539\) 1.47022e13i 0.323176i
\(540\) 1.10057e13 4.86272e13i 0.239690 1.05903i
\(541\) −1.08616e13 −0.234373 −0.117187 0.993110i \(-0.537388\pi\)
−0.117187 + 0.993110i \(0.537388\pi\)
\(542\) −3.04537e12 + 2.37426e13i −0.0651094 + 0.507612i
\(543\) 6.67163e13 1.41329
\(544\) 2.17249e13 2.93103e13i 0.455999 0.615214i
\(545\) 1.35332e12 + 4.15491e13i 0.0281461 + 0.864130i
\(546\) 7.22537e12 5.63311e13i 0.148901 1.16087i
\(547\) 3.51242e13 0.717248 0.358624 0.933482i \(-0.383246\pi\)
0.358624 + 0.933482i \(0.383246\pi\)
\(548\) −1.07410e13 + 4.11813e13i −0.217342 + 0.833293i
\(549\) −2.00038e13 −0.401098
\(550\) 3.37797e12 5.40210e13i 0.0671185 1.07337i
\(551\) 3.44451e13i 0.678218i
\(552\) −3.95991e13 1.59409e13i −0.772664 0.311041i
\(553\) 4.33996e13i 0.839189i
\(554\) −5.51959e12 + 4.30323e13i −0.105769 + 0.824605i
\(555\) −7.69300e12 + 2.50573e11i −0.146094 + 0.00475850i
\(556\) 2.04178e13 7.82819e13i 0.384268 1.47329i
\(557\) 1.87712e13i 0.350120i 0.984558 + 0.175060i \(0.0560119\pi\)
−0.984558 + 0.175060i \(0.943988\pi\)
\(558\) −3.61588e12 + 2.81905e13i −0.0668410 + 0.521112i
\(559\) 5.75467e13i 1.05429i
\(560\) −2.11768e13 + 4.09044e13i −0.384521 + 0.742728i
\(561\) 3.57957e13 0.644194
\(562\) 2.11255e13 + 2.70968e12i 0.376812 + 0.0483322i
\(563\) −7.50975e12 −0.132765 −0.0663825 0.997794i \(-0.521146\pi\)
−0.0663825 + 0.997794i \(0.521146\pi\)
\(564\) −4.97456e13 1.29748e13i −0.871684 0.227355i
\(565\) 7.34305e13 2.39175e12i 1.27536 0.0415407i
\(566\) 1.00709e14 + 1.29176e13i 1.73375 + 0.222381i
\(567\) −2.26022e13 −0.385688
\(568\) −4.01894e13 + 9.98354e13i −0.679783 + 1.68866i
\(569\) −5.40193e13 −0.905707 −0.452853 0.891585i \(-0.649594\pi\)
−0.452853 + 0.891585i \(0.649594\pi\)
\(570\) 4.04994e13 + 3.85945e12i 0.673093 + 0.0641433i
\(571\) 7.48542e13i 1.23321i 0.787274 + 0.616603i \(0.211492\pi\)
−0.787274 + 0.616603i \(0.788508\pi\)
\(572\) 1.14000e14 + 2.97339e13i 1.86176 + 0.485592i
\(573\) 6.37552e13i 1.03215i
\(574\) −2.00293e13 2.56908e12i −0.321445 0.0412304i
\(575\) −6.67892e13 + 4.35549e12i −1.06259 + 0.0692943i
\(576\) −1.77472e13 1.70517e13i −0.279909 0.268941i
\(577\) 7.48813e13i 1.17083i −0.810733 0.585416i \(-0.800931\pi\)
0.810733 0.585416i \(-0.199069\pi\)
\(578\) −2.64638e13 3.39441e12i −0.410217 0.0526169i
\(579\) 8.40644e13i 1.29187i
\(580\) −1.13678e13 + 5.02271e13i −0.173196 + 0.765240i
\(581\) 2.65803e13 0.401495
\(582\) 4.48014e12 3.49285e13i 0.0670929 0.523076i
\(583\) 3.96953e13 0.589382
\(584\) −1.97738e13 + 4.91206e13i −0.291090 + 0.723102i
\(585\) 4.75547e13 1.54893e12i 0.694088 0.0226075i
\(586\) −1.31193e12 + 1.02282e13i −0.0189855 + 0.148016i
\(587\) 4.76751e13 0.684071 0.342035 0.939687i \(-0.388884\pi\)
0.342035 + 0.939687i \(0.388884\pi\)
\(588\) −1.59865e13 4.16964e12i −0.227439 0.0593215i
\(589\) −8.29373e13 −1.16997
\(590\) −5.52276e13 5.26299e12i −0.772496 0.0736160i
\(591\) 1.21460e13i 0.168459i
\(592\) −6.63665e12 + 1.18570e13i −0.0912725 + 0.163067i
\(593\) 8.03970e13i 1.09639i −0.836349 0.548197i \(-0.815314\pi\)
0.836349 0.548197i \(-0.184686\pi\)
\(594\) 1.09864e13 8.56531e13i 0.148567 1.15827i
\(595\) −4.77369e13 + 1.55487e12i −0.640132 + 0.0208501i
\(596\) −3.34875e12 8.73433e11i −0.0445299 0.0116144i
\(597\) 5.61325e13i 0.740189i
\(598\) 1.85346e13 1.44501e14i 0.242369 1.88958i
\(599\) 5.37083e13i 0.696477i −0.937406 0.348239i \(-0.886780\pi\)
0.937406 0.348239i \(-0.113220\pi\)
\(600\) 5.77817e13 + 1.89937e13i 0.743077 + 0.244261i
\(601\) −3.12372e13 −0.398382 −0.199191 0.979961i \(-0.563831\pi\)
−0.199191 + 0.979961i \(0.563831\pi\)
\(602\) −3.86522e13 4.95777e12i −0.488869 0.0627053i
\(603\) −3.50835e12 −0.0440064
\(604\) 1.65518e13 6.34598e13i 0.205902 0.789431i
\(605\) −4.13285e11 1.26885e13i −0.00509885 0.156543i
\(606\) 6.50515e13 + 8.34390e12i 0.795965 + 0.102095i
\(607\) −7.33861e13 −0.890574 −0.445287 0.895388i \(-0.646898\pi\)
−0.445287 + 0.895388i \(0.646898\pi\)
\(608\) 4.27661e13 5.76982e13i 0.514733 0.694455i
\(609\) 4.29973e13 0.513280
\(610\) 8.27919e12 8.68784e13i 0.0980254 1.02864i
\(611\) 1.75453e14i 2.06042i
\(612\) 6.44084e12 2.46942e13i 0.0750214 0.287633i
\(613\) 4.41534e13i 0.510108i 0.966927 + 0.255054i \(0.0820933\pi\)
−0.966927 + 0.255054i \(0.917907\pi\)
\(614\) −6.26164e13 8.03156e12i −0.717540 0.0920360i
\(615\) 8.68069e11 + 2.66511e13i 0.00986685 + 0.302928i
\(616\) −2.97926e13 + 7.40085e13i −0.335896 + 0.834407i
\(617\) 5.60294e13i 0.626600i −0.949654 0.313300i \(-0.898566\pi\)
0.949654 0.313300i \(-0.101434\pi\)
\(618\) −4.25844e13 5.46213e12i −0.472398 0.0605926i
\(619\) 7.65763e13i 0.842638i −0.906913 0.421319i \(-0.861567\pi\)
0.906913 0.421319i \(-0.138433\pi\)
\(620\) −1.20937e14 2.73716e13i −1.32009 0.298774i
\(621\) −1.06784e14 −1.15624
\(622\) 2.08986e13 1.62931e14i 0.224473 1.75006i
\(623\) 1.22158e14 1.30161
\(624\) −6.46622e13 + 1.15525e14i −0.683483 + 1.22111i
\(625\) 9.45597e13 1.23856e13i 0.991531 0.129872i
\(626\) −9.69285e10 + 7.55683e11i −0.00100828 + 0.00786083i
\(627\) 7.04648e13 0.727167
\(628\) −3.28462e12 + 1.25933e13i −0.0336269 + 0.128926i
\(629\) −1.40898e13 −0.143104
\(630\) −3.05657e12 + 3.20744e13i −0.0307987 + 0.323189i
\(631\) 4.84894e13i 0.484731i 0.970185 + 0.242365i \(0.0779232\pi\)
−0.970185 + 0.242365i \(0.922077\pi\)
\(632\) −3.77803e13 + 9.38508e13i −0.374697 + 0.930792i
\(633\) 2.86343e13i 0.281753i
\(634\) −2.06004e13 + 1.60606e14i −0.201108 + 1.56789i
\(635\) −4.21782e12 1.29494e14i −0.0408526 1.25424i
\(636\) −1.12578e13 + 4.31627e13i −0.108186 + 0.414785i
\(637\) 5.63845e13i 0.537604i
\(638\) −1.13479e13 + 8.84712e13i −0.107352 + 0.836948i
\(639\) 7.52809e13i 0.706611i
\(640\) 8.14026e13 7.00202e13i 0.758121 0.652114i
\(641\) 1.29283e13 0.119468 0.0597338 0.998214i \(-0.480975\pi\)
0.0597338 + 0.998214i \(0.480975\pi\)
\(642\) 1.09312e13 + 1.40211e12i 0.100229 + 0.0128560i
\(643\) −1.48437e14 −1.35048 −0.675238 0.737600i \(-0.735959\pi\)
−0.675238 + 0.737600i \(0.735959\pi\)
\(644\) 9.54599e13 + 2.48982e13i 0.861770 + 0.224770i
\(645\) 1.67519e12 + 5.14309e13i 0.0150060 + 0.460708i
\(646\) 7.38666e13 + 9.47458e12i 0.656576 + 0.0842165i
\(647\) 8.95550e12 0.0789894 0.0394947 0.999220i \(-0.487425\pi\)
0.0394947 + 0.999220i \(0.487425\pi\)
\(648\) 4.88769e13 + 1.96757e13i 0.427788 + 0.172209i
\(649\) −9.60902e13 −0.834557
\(650\) −1.29548e13 + 2.07176e14i −0.111652 + 1.78555i
\(651\) 1.03529e14i 0.885439i
\(652\) 1.70056e14 + 4.43547e13i 1.44329 + 0.376445i
\(653\) 7.28446e13i 0.613524i 0.951786 + 0.306762i \(0.0992456\pi\)
−0.951786 + 0.306762i \(0.900754\pi\)
\(654\) −8.02545e13 1.02939e13i −0.670781 0.0860384i
\(655\) −4.33826e12 + 1.41304e11i −0.0359840 + 0.00117206i
\(656\) 4.10766e13 + 2.29915e13i 0.338123 + 0.189256i
\(657\) 3.70394e13i 0.302578i
\(658\) 1.17846e14 + 1.51157e13i 0.955403 + 0.122546i
\(659\) 2.12839e14i 1.71247i −0.516584 0.856237i \(-0.672797\pi\)
0.516584 0.856237i \(-0.327203\pi\)
\(660\) 1.02750e14 + 2.32554e13i 0.820471 + 0.185696i
\(661\) 1.49053e14 1.18123 0.590613 0.806955i \(-0.298886\pi\)
0.590613 + 0.806955i \(0.298886\pi\)
\(662\) −1.89323e13 + 1.47602e14i −0.148906 + 1.16092i
\(663\) −1.37280e14 −1.07162
\(664\) −5.74795e13 2.31388e13i −0.445321 0.179267i
\(665\) −9.39714e13 + 3.06080e12i −0.722582 + 0.0235357i
\(666\) −1.20924e12 + 9.42756e12i −0.00922869 + 0.0719495i
\(667\) 1.10297e14 0.835477
\(668\) −1.26384e14 3.29639e13i −0.950187 0.247831i
\(669\) 1.57557e14 1.17573
\(670\) 1.45204e12 1.52371e13i 0.0107548 0.112857i
\(671\) 1.51159e14i 1.11128i
\(672\) −7.20237e13 5.33843e13i −0.525569 0.389553i
\(673\) 9.10177e13i 0.659251i −0.944112 0.329625i \(-0.893078\pi\)
0.944112 0.329625i \(-0.106922\pi\)
\(674\) 9.10200e11 7.09618e12i 0.00654391 0.0510182i
\(675\) 1.51829e14 9.90115e12i 1.08352 0.0706589i
\(676\) −3.00604e14 7.84045e13i −2.12942 0.555402i
\(677\) 1.25381e14i 0.881636i 0.897596 + 0.440818i \(0.145312\pi\)
−0.897596 + 0.440818i \(0.854688\pi\)
\(678\) −1.81926e13 + 1.41835e14i −0.126984 + 0.990001i
\(679\) 8.13835e13i 0.563881i
\(680\) 1.04584e14 + 3.81937e13i 0.719316 + 0.262692i
\(681\) −1.07941e14 −0.736973
\(682\) −2.13022e14 2.73235e13i −1.44379 0.185189i
\(683\) −1.14583e14 −0.770931 −0.385465 0.922722i \(-0.625959\pi\)
−0.385465 + 0.922722i \(0.625959\pi\)
\(684\) 1.26790e13 4.86113e13i 0.0846843 0.324681i
\(685\) −1.29811e14 + 4.22815e12i −0.860714 + 0.0280348i
\(686\) 1.63901e14 + 2.10229e13i 1.07885 + 0.138380i
\(687\) 1.19666e13 0.0781966
\(688\) 7.92689e13 + 4.43687e13i 0.514234 + 0.287829i
\(689\) −1.52236e14 −0.980437
\(690\) 1.23584e13 1.29684e14i 0.0790162 0.829163i
\(691\) 3.74076e13i 0.237449i −0.992927 0.118724i \(-0.962119\pi\)
0.992927 0.118724i \(-0.0378805\pi\)
\(692\) 4.84372e13 1.85709e14i 0.305245 1.17031i
\(693\) 5.58061e13i 0.349153i
\(694\) 1.00542e14 + 1.28962e13i 0.624528 + 0.0801057i
\(695\) 2.46759e14 8.03734e12i 1.52177 0.0495665i
\(696\) −9.29809e13 3.74301e13i −0.569308 0.229179i
\(697\) 4.88118e13i 0.296729i
\(698\) 2.65865e14 + 3.41014e13i 1.60466 + 0.205824i
\(699\) 7.42385e13i 0.444881i
\(700\) −1.38037e14 2.65500e13i −0.821308 0.157970i
\(701\) 2.22503e14 1.31446 0.657229 0.753691i \(-0.271729\pi\)
0.657229 + 0.753691i \(0.271729\pi\)
\(702\) −4.21339e13 + 3.28488e14i −0.247142 + 1.92679i
\(703\) −2.77362e13 −0.161536
\(704\) 1.28852e14 1.34107e14i 0.745123 0.775511i
\(705\) −5.10746e12 1.56807e14i −0.0293264 0.900368i
\(706\) 1.04324e13 8.13341e13i 0.0594786 0.463713i
\(707\) −1.51570e14 −0.858059
\(708\) 2.72518e13 1.04484e14i 0.153189 0.587330i
\(709\) 9.78657e13 0.546260 0.273130 0.961977i \(-0.411941\pi\)
0.273130 + 0.961977i \(0.411941\pi\)
\(710\) −3.26952e14 3.11573e13i −1.81214 0.172691i
\(711\) 7.07682e13i 0.389485i
\(712\) −2.64164e14 1.06341e14i −1.44369 0.581166i
\(713\) 2.65574e14i 1.44125i
\(714\) 1.18270e13 9.22065e13i 0.0637357 0.496902i
\(715\) 1.17046e13 + 3.59349e14i 0.0626362 + 1.92303i
\(716\) −3.45801e13 + 1.32581e14i −0.183764 + 0.704555i
\(717\) 1.62768e14i 0.858961i
\(718\) 4.06965e13 3.17282e14i 0.213272 1.66273i
\(719\) 1.39680e14i 0.726926i 0.931609 + 0.363463i \(0.118406\pi\)
−0.931609 + 0.363463i \(0.881594\pi\)
\(720\) 3.45313e13 6.66996e13i 0.178464 0.344715i
\(721\) 9.92219e13 0.509250
\(722\) −4.91915e13 6.30960e12i −0.250729 0.0321600i
\(723\) −4.17405e13 −0.211284
\(724\) 3.47792e14 + 9.07122e13i 1.74834 + 0.456009i
\(725\) −1.56825e14 + 1.02269e13i −0.782932 + 0.0510569i
\(726\) 2.45086e13 + 3.14362e12i 0.121516 + 0.0155864i
\(727\) −3.31152e13 −0.163063 −0.0815315 0.996671i \(-0.525981\pi\)
−0.0815315 + 0.996671i \(0.525981\pi\)
\(728\) 1.14258e14 2.83830e14i 0.558764 1.38804i
\(729\) 2.11724e14 1.02833
\(730\) −1.60866e14 1.53299e13i −0.775978 0.0739478i
\(731\) 9.41962e13i 0.451281i
\(732\) 1.64363e14 + 4.28697e13i 0.782075 + 0.203983i
\(733\) 3.51027e14i 1.65890i −0.558580 0.829451i \(-0.688653\pi\)
0.558580 0.829451i \(-0.311347\pi\)
\(734\) −7.31581e13 9.38370e12i −0.343386 0.0440447i
\(735\) −1.64136e12 5.03922e13i −0.00765184 0.234924i
\(736\) −1.84756e14 1.36942e14i −0.855479 0.634084i
\(737\) 2.65109e13i 0.121924i
\(738\) 3.26602e13 + 4.18919e12i 0.149189 + 0.0191359i
\(739\) 6.54869e13i 0.297120i 0.988903 + 0.148560i \(0.0474639\pi\)
−0.988903 + 0.148560i \(0.952536\pi\)
\(740\) −4.04443e13 9.15372e12i −0.182263 0.0412514i
\(741\) −2.70239e14 −1.20964
\(742\) 1.31154e13 1.02252e14i 0.0583126 0.454622i
\(743\) −3.94592e14 −1.74262 −0.871312 0.490729i \(-0.836731\pi\)
−0.871312 + 0.490729i \(0.836731\pi\)
\(744\) 9.01246e13 2.23880e14i 0.395347 0.982091i
\(745\) −3.43822e11 1.05559e13i −0.00149814 0.0459953i
\(746\) −2.08702e12 + 1.62710e13i −0.00903300 + 0.0704239i
\(747\) −4.33424e13 −0.186342
\(748\) 1.86603e14 + 4.86704e13i 0.796912 + 0.207853i
\(749\) −2.54699e13 −0.108048
\(750\) −5.54717e12 + 1.85535e14i −0.0233757 + 0.781845i
\(751\) 2.64643e14i 1.10780i 0.832584 + 0.553899i \(0.186860\pi\)
−0.832584 + 0.553899i \(0.813140\pi\)
\(752\) −2.41682e14 1.35275e14i −1.00498 0.562509i
\(753\) 7.16906e13i 0.296133i
\(754\) 4.35202e13 3.39296e14i 0.178580 1.39227i
\(755\) 2.00037e14 6.51552e12i 0.815409 0.0265592i
\(756\) −2.17005e14 5.66000e13i −0.878741 0.229196i
\(757\) 2.99343e13i 0.120418i −0.998186 0.0602089i \(-0.980823\pi\)
0.998186 0.0602089i \(-0.0191767\pi\)
\(758\) −5.30015e13 + 4.13215e14i −0.211808 + 1.65132i
\(759\) 2.25636e14i 0.895777i
\(760\) 2.05876e14 + 7.51853e13i 0.811966 + 0.296527i
\(761\) 1.89021e14 0.740605 0.370302 0.928911i \(-0.379254\pi\)
0.370302 + 0.928911i \(0.379254\pi\)
\(762\) 2.50125e14 + 3.20825e13i 0.973602 + 0.124880i
\(763\) 1.86993e14 0.723109
\(764\) −8.66861e13 + 3.32356e14i −0.333030 + 1.27684i
\(765\) 7.78408e13 2.53540e12i 0.297098 0.00967696i
\(766\) 2.41878e12 + 3.10247e11i 0.00917176 + 0.00117643i
\(767\) 3.68516e14 1.38829
\(768\) 1.09278e14 + 1.78141e14i 0.409003 + 0.666741i
\(769\) 1.99563e14 0.742076 0.371038 0.928618i \(-0.379002\pi\)
0.371038 + 0.928618i \(0.379002\pi\)
\(770\) −2.42371e14 2.30971e13i −0.895422 0.0853304i
\(771\) 1.56606e14i 0.574826i
\(772\) −1.14300e14 + 4.38228e14i −0.416831 + 1.59813i
\(773\) 1.95460e14i 0.708208i −0.935206 0.354104i \(-0.884786\pi\)
0.935206 0.354104i \(-0.115214\pi\)
\(774\) 6.30271e13 + 8.08424e12i 0.226894 + 0.0291028i
\(775\) −2.46245e13 3.77604e14i −0.0880762 1.35060i
\(776\) 7.08462e13 1.75990e14i 0.251772 0.625433i
\(777\) 3.46227e13i 0.122252i
\(778\) 1.80336e14 + 2.31310e13i 0.632680 + 0.0811514i
\(779\) 9.60873e13i 0.334949i
\(780\) −3.94057e14 8.91866e13i −1.36485 0.308906i
\(781\) −5.68862e14 −1.95773
\(782\) 3.03387e13 2.36529e14i 0.103744 0.808818i
\(783\) −2.50734e14 −0.851929
\(784\) −7.76681e13 4.34727e13i −0.262218 0.146770i
\(785\) −3.96964e13 + 1.29297e12i −0.133169 + 0.00433752i
\(786\) 1.07482e12 8.37959e12i 0.00358280 0.0279325i
\(787\) 1.04188e14 0.345100 0.172550 0.985001i \(-0.444799\pi\)
0.172550 + 0.985001i \(0.444799\pi\)
\(788\) 1.65145e13 6.33169e13i 0.0543545 0.208396i
\(789\) 2.06775e14 0.676260
\(790\) −3.07353e14 2.92896e13i −0.998855 0.0951872i
\(791\) 3.30477e14i 1.06723i
\(792\) 4.85805e13 1.20680e14i 0.155896 0.387265i
\(793\) 5.79711e14i 1.84861i
\(794\) −5.01125e13 + 3.90692e14i −0.158798 + 1.23803i
\(795\) −1.36057e14 + 4.43159e12i −0.428434 + 0.0139548i
\(796\) −7.63217e13 + 2.92619e14i −0.238827 + 0.915665i
\(797\) 1.43104e14i 0.445000i 0.974933 + 0.222500i \(0.0714217\pi\)
−0.974933 + 0.222500i \(0.928578\pi\)
\(798\) 2.32817e13 1.81511e14i 0.0719450 0.560904i
\(799\) 2.87194e14i 0.881945i
\(800\) 2.75391e14 + 1.77578e14i 0.840426 + 0.541926i
\(801\) −1.99193e14 −0.604103
\(802\) −1.02019e13 1.30856e12i −0.0307474 0.00394385i
\(803\) −2.79889e14 −0.838318
\(804\) 2.88267e13 + 7.51867e12i 0.0858053 + 0.0223800i
\(805\) 9.80102e12 + 3.00907e14i 0.0289929 + 0.890129i
\(806\) 8.16961e14 + 1.04788e14i 2.40174 + 0.308062i
\(807\) 2.99475e14 0.874971
\(808\) 3.27768e14 + 1.31945e14i 0.951722 + 0.383122i
\(809\) −4.37170e13 −0.126156 −0.0630780 0.998009i \(-0.520092\pi\)
−0.0630780 + 0.998009i \(0.520092\pi\)
\(810\) −1.52539e13 + 1.60068e14i −0.0437477 + 0.459070i
\(811\) 3.48250e14i 0.992629i −0.868143 0.496314i \(-0.834686\pi\)
0.868143 0.496314i \(-0.165314\pi\)
\(812\) 2.24145e14 + 5.84622e13i 0.634963 + 0.165613i
\(813\) 1.42181e14i 0.400304i
\(814\) −7.12396e13 9.13763e12i −0.199342 0.0255689i
\(815\) 1.74600e13 + 5.36049e14i 0.0485574 + 1.49079i
\(816\) −1.05843e14 + 1.89099e14i −0.292559 + 0.522684i
\(817\) 1.85428e14i 0.509407i
\(818\) −3.29464e14 4.22590e13i −0.899583 0.115386i
\(819\) 2.14022e14i 0.580816i
\(820\) −3.17115e13 + 1.40112e14i −0.0855357 + 0.377927i
\(821\) 3.27880e14 0.879021 0.439511 0.898237i \(-0.355152\pi\)
0.439511 + 0.898237i \(0.355152\pi\)
\(822\) 3.21611e13 2.50737e14i 0.0856982 0.668129i
\(823\) 1.64425e14 0.435481 0.217740 0.976007i \(-0.430131\pi\)
0.217740 + 0.976007i \(0.430131\pi\)
\(824\) −2.14566e14 8.63749e13i −0.564838 0.227379i
\(825\) 2.09213e13 + 3.20818e14i 0.0547419 + 0.839440i
\(826\) −3.17484e13 + 2.47520e14i −0.0825699 + 0.643739i
\(827\) −8.72181e13 −0.225465 −0.112732 0.993625i \(-0.535960\pi\)
−0.112732 + 0.993625i \(0.535960\pi\)
\(828\) −1.55659e14 4.05994e13i −0.399965 0.104320i
\(829\) 2.12343e14 0.542333 0.271166 0.962532i \(-0.412591\pi\)
0.271166 + 0.962532i \(0.412591\pi\)
\(830\) 1.79386e13 1.88240e14i 0.0455406 0.477884i
\(831\) 2.57697e14i 0.650285i
\(832\) −4.94160e14 + 5.14313e14i −1.23951 + 1.29006i
\(833\) 9.22939e13i 0.230117i
\(834\) −6.11353e13 + 4.76629e14i −0.151517 + 1.18127i
\(835\) −1.29760e13 3.98385e14i −0.0319676 0.981455i
\(836\) 3.67333e14 + 9.58090e13i 0.899556 + 0.234625i
\(837\) 6.03719e14i 1.46963i
\(838\) 6.41747e13 5.00325e14i 0.155290 1.21069i
\(839\) 7.14552e12i 0.0171879i 0.999963 + 0.00859397i \(0.00273558\pi\)
−0.999963 + 0.00859397i \(0.997264\pi\)
\(840\) 9.38526e13 2.56992e14i 0.224414 0.614502i
\(841\) −1.61724e14 −0.384410
\(842\) 4.76379e14 + 6.11033e13i 1.12562 + 0.144379i
\(843\) −1.26509e14 −0.297155
\(844\) 3.89333e13 1.49271e14i 0.0909094 0.348548i
\(845\) −3.08635e13 9.47559e14i −0.0716410 2.19949i
\(846\) −1.92163e14 2.46480e13i −0.443422 0.0568760i
\(847\) −5.71051e13 −0.130996
\(848\) −1.17374e14 + 2.09700e14i −0.267666 + 0.478211i
\(849\) −6.03091e14 −1.36724
\(850\) −2.12054e13 + 3.39119e14i −0.0477915 + 0.764290i
\(851\) 8.88144e13i 0.198992i
\(852\) 1.61333e14 6.18552e14i 0.359356 1.37778i
\(853\) 1.73226e14i 0.383591i 0.981435 + 0.191795i \(0.0614310\pi\)
−0.981435 + 0.191795i \(0.938569\pi\)
\(854\) −3.89373e14 4.99433e13i −0.857189 0.109948i
\(855\) 1.53232e14 4.99100e12i 0.335365 0.0109234i
\(856\) 5.50782e13 + 2.21721e13i 0.119842 + 0.0482434i
\(857\) 1.24930e14i 0.270248i −0.990829 0.135124i \(-0.956857\pi\)
0.990829 0.135124i \(-0.0431432\pi\)
\(858\) −6.94103e14 8.90298e13i −1.49275 0.191469i
\(859\) 3.15975e14i 0.675596i 0.941219 + 0.337798i \(0.109682\pi\)
−0.941219 + 0.337798i \(0.890318\pi\)
\(860\) −6.11964e13 + 2.70387e14i −0.130087 + 0.574769i
\(861\) 1.19944e14 0.253492
\(862\) 2.40958e12 1.87858e13i 0.00506297 0.0394724i
\(863\) −1.53961e14 −0.321631 −0.160816 0.986984i \(-0.551412\pi\)
−0.160816 + 0.986984i \(0.551412\pi\)
\(864\) 4.19998e14 + 3.11304e14i 0.872325 + 0.646571i
\(865\) 5.85388e14 1.90670e13i 1.20882 0.0393733i
\(866\) 9.36547e13 7.30160e14i 0.192283 1.49909i
\(867\) 1.58477e14 0.323498
\(868\) −1.40766e14 + 5.39699e14i −0.285693 + 1.09535i
\(869\) −5.34762e14 −1.07910
\(870\) 2.90181e13 3.04504e14i 0.0582202 0.610938i
\(871\) 1.01672e14i 0.202820i
\(872\) −4.04370e14 1.62782e14i −0.802041 0.322867i
\(873\) 1.32706e14i 0.261709i
\(874\) 5.97225e13 4.65614e14i 0.117106 0.912996i
\(875\) −4.18360e13 4.26933e14i −0.0815662 0.832375i
\(876\) 7.93784e13 3.04338e14i 0.153880 0.589977i
\(877\) 1.51963e14i 0.292913i −0.989217 0.146457i \(-0.953213\pi\)
0.989217 0.146457i \(-0.0467869\pi\)
\(878\) 1.85004e13 1.44234e14i 0.0354575 0.276437i
\(879\) 6.12508e13i 0.116726i
\(880\) 5.04017e14 + 2.60937e14i 0.955063 + 0.494449i
\(881\) 5.87645e14 1.10722 0.553612 0.832774i \(-0.313249\pi\)
0.553612 + 0.832774i \(0.313249\pi\)
\(882\) −6.17543e13 7.92098e12i −0.115697 0.0148401i
\(883\) 4.47094e14 0.832904 0.416452 0.909158i \(-0.363273\pi\)
0.416452 + 0.909158i \(0.363273\pi\)
\(884\) −7.15641e14 1.86656e14i −1.32566 0.345764i
\(885\) 3.29352e14 1.07275e13i 0.606657 0.0197598i
\(886\) −7.62871e13 9.78504e12i −0.139728 0.0179223i
\(887\) −4.52899e14 −0.824866 −0.412433 0.910988i \(-0.635321\pi\)
−0.412433 + 0.910988i \(0.635321\pi\)
\(888\) 3.01398e13 7.48709e13i 0.0545853 0.135596i
\(889\) −5.82792e14 −1.04955
\(890\) 8.24421e13 8.65113e14i 0.147638 1.54926i
\(891\) 2.78501e14i 0.495950i
\(892\) 8.21342e14 + 2.14225e14i 1.45445 + 0.379355i
\(893\) 5.65349e14i 0.995542i
\(894\) 2.03893e13 + 2.61525e12i 0.0357038 + 0.00457959i
\(895\) −4.17918e14 + 1.36123e13i −0.727740 + 0.0237037i
\(896\) −3.02875e14 3.76221e14i −0.524473 0.651483i
\(897\) 8.65337e14i 1.49013i
\(898\) 8.10593e14 + 1.03972e14i 1.38810 + 0.178046i
\(899\) 6.23583e14i 1.06193i
\(900\) 2.25086e14 + 4.32930e13i 0.381186 + 0.0733170i
\(901\) −2.49189e14 −0.419668
\(902\) −3.16558e13 + 2.46798e14i −0.0530176 + 0.413341i
\(903\) 2.31467e14 0.385523
\(904\) −2.87688e14 + 7.14651e14i −0.476518 + 1.18373i
\(905\) 3.57084e13 + 1.09630e15i 0.0588203 + 1.80588i
\(906\) −4.95598e13 + 3.86383e14i −0.0811874 + 0.632961i
\(907\) −9.97795e14 −1.62557 −0.812783 0.582566i \(-0.802049\pi\)
−0.812783 + 0.582566i \(0.802049\pi\)
\(908\) −5.62697e14 1.46765e14i −0.911686 0.237789i
\(909\) 2.47154e14 0.398243
\(910\) 9.29518e14 + 8.85797e13i 1.48954 + 0.141947i
\(911\) 1.01348e15i 1.61518i 0.589741 + 0.807592i \(0.299230\pi\)
−0.589741 + 0.807592i \(0.700770\pi\)
\(912\) −2.08356e14 + 3.72247e14i −0.330241 + 0.590007i
\(913\) 3.27519e14i 0.516276i
\(914\) 5.85568e13 4.56526e14i 0.0918008 0.715706i
\(915\) 1.68754e13 + 5.18102e14i 0.0263117 + 0.807811i
\(916\) 6.23820e13 + 1.62707e13i 0.0967346 + 0.0252306i
\(917\) 1.95245e13i 0.0301116i
\(918\) −6.89676e13 + 5.37692e14i −0.105787 + 0.824745i
\(919\) 3.29429e14i 0.502556i 0.967915 + 0.251278i \(0.0808508\pi\)
−0.967915 + 0.251278i \(0.919149\pi\)
\(920\) 2.40752e14 6.59238e14i 0.365284 1.00024i
\(921\) 3.74975e14 0.565853
\(922\) −9.75681e14 1.25147e14i −1.46438 0.187830i
\(923\) 2.18164e15 3.25668
\(924\) 1.19597e14 4.58536e14i 0.177566 0.680791i
\(925\) −8.23501e12 1.26280e14i −0.0121606 0.186477i
\(926\) −5.29262e14 6.78864e13i −0.777349 0.0997075i
\(927\) −1.61793e14 −0.236353
\(928\) −4.33817e14 3.21547e14i −0.630328 0.467201i
\(929\) −6.89030e14 −0.995771 −0.497886 0.867243i \(-0.665890\pi\)
−0.497886 + 0.867243i \(0.665890\pi\)
\(930\) 7.33189e14 + 6.98702e13i 1.05390 + 0.100433i
\(931\) 1.81683e14i 0.259756i
\(932\) −1.00940e14 + 3.87005e14i −0.143544 + 0.550348i
\(933\) 9.75705e14i 1.38010i
\(934\) −2.09169e14 2.68292e13i −0.294281 0.0377463i
\(935\) 1.91588e13 + 5.88206e14i 0.0268109 + 0.823136i
\(936\) −1.86311e14 + 4.62819e14i −0.259334 + 0.644216i
\(937\) 1.02170e15i 1.41458i 0.706924 + 0.707289i \(0.250082\pi\)
−0.706924 + 0.707289i \(0.749918\pi\)
\(938\) −6.82898e13 8.75927e12i −0.0940463 0.0120630i
\(939\) 4.52537e12i 0.00619906i
\(940\) 1.86581e14 8.24380e14i 0.254231 1.12328i
\(941\) 7.35996e14 0.997532 0.498766 0.866737i \(-0.333787\pi\)
0.498766 + 0.866737i \(0.333787\pi\)
\(942\) 9.83490e12 7.66758e13i 0.0132591 0.103372i
\(943\) 3.07682e14 0.412614
\(944\) 2.84127e14 5.07620e14i 0.379012 0.677141i
\(945\) −2.22803e13 6.84039e14i −0.0295639 0.907657i
\(946\) −6.10888e13 + 4.76266e14i −0.0806318 + 0.628629i
\(947\) −7.17168e14 −0.941609 −0.470805 0.882237i \(-0.656036\pi\)
−0.470805 + 0.882237i \(0.656036\pi\)
\(948\) 1.51662e14 5.81474e14i 0.198077 0.759431i
\(949\) 1.07340e15 1.39454
\(950\) −4.17433e13 + 6.67566e14i −0.0539472 + 0.862732i
\(951\) 9.61783e14i 1.23644i
\(952\) 1.87025e14 4.64592e14i 0.239174 0.594137i
\(953\) 4.43899e14i 0.564702i 0.959311 + 0.282351i \(0.0911143\pi\)
−0.959311 + 0.282351i \(0.908886\pi\)
\(954\) −2.13863e13 + 1.66734e14i −0.0270641 + 0.211000i
\(955\) −1.04765e15 + 3.41235e13i −1.31886 + 0.0429573i
\(956\) 2.21311e14 8.48510e14i 0.277149 1.06259i
\(957\) 5.29805e14i 0.660019i
\(958\) −1.35369e14 + 1.05538e15i −0.167761 + 1.30791i
\(959\) 5.84220e14i 0.720250i
\(960\) −4.26672e14 + 4.74040e14i −0.523285 + 0.581378i
\(961\) −6.81841e14 −0.831891
\(962\) 2.73211e14 + 3.50437e13i 0.331606 + 0.0425339i
\(963\) 4.15317e13 0.0501474
\(964\) −2.17593e14 5.67534e13i −0.261373 0.0681722i
\(965\) −1.38137e15 + 4.49935e13i −1.65072 + 0.0537667i
\(966\) −5.81219e14 7.45507e13i −0.690962 0.0886270i
\(967\) 1.42458e15 1.68482 0.842410 0.538837i \(-0.181136\pi\)
0.842410 + 0.538837i \(0.181136\pi\)
\(968\) 1.23489e14 + 4.97113e13i 0.145295 + 0.0584895i
\(969\) −4.42346e14 −0.517778
\(970\) 5.76354e14 + 5.49244e13i 0.671167 + 0.0639597i
\(971\) 4.62402e14i 0.535702i −0.963460 0.267851i \(-0.913686\pi\)
0.963460 0.267851i \(-0.0863136\pi\)
\(972\) 6.08758e14 + 1.58778e14i 0.701639 + 0.183004i
\(973\) 1.11055e15i 1.27343i
\(974\) 1.11045e14 + 1.42433e13i 0.126679 + 0.0162486i
\(975\) −8.02354e13 1.23037e15i −0.0910632 1.39641i
\(976\) 7.98535e14 + 4.46959e14i 0.901665 + 0.504683i
\(977\) 1.24483e15i 1.39842i −0.714918 0.699209i \(-0.753536\pi\)
0.714918 0.699209i \(-0.246464\pi\)
\(978\) −1.03541e15 1.32808e14i −1.15722 0.148433i
\(979\) 1.50521e15i 1.67372i
\(980\) 5.99605e13 2.64926e14i 0.0663338 0.293086i
\(981\) −3.04915e14 −0.335609
\(982\) −6.10233e13 + 4.75755e14i −0.0668249 + 0.520986i
\(983\) −7.82351e14 −0.852382 −0.426191 0.904633i \(-0.640145\pi\)
−0.426191 + 0.904633i \(0.640145\pi\)
\(984\) −2.59378e14 1.04414e14i −0.281162 0.113184i
\(985\) 1.99587e14 6.50085e12i 0.215253 0.00701115i
\(986\) 7.12367e13 5.55383e14i 0.0764398 0.595947i
\(987\) −7.05717e14 −0.753433
\(988\) −1.40876e15 3.67437e14i −1.49641 0.390300i
\(989\) 5.93761e14 0.627524
\(990\) 3.95216e14 + 3.76626e13i 0.415583 + 0.0396036i
\(991\) 5.07172e14i 0.530624i 0.964163 + 0.265312i \(0.0854750\pi\)
−0.964163 + 0.265312i \(0.914525\pi\)
\(992\) 7.74224e14 1.04455e15i 0.805950 1.08735i
\(993\) 8.83905e14i 0.915502i
\(994\) −1.87953e14 + 1.46534e15i −0.193695 + 1.51010i
\(995\) −9.22387e14 + 3.00436e13i −0.945797 + 0.0308061i
\(996\) 3.56127e14 + 9.28863e13i 0.363336 + 0.0947665i
\(997\) 5.76576e14i 0.585303i −0.956219 0.292652i \(-0.905462\pi\)
0.956219 0.292652i \(-0.0945376\pi\)
\(998\) 8.22170e13 6.40988e14i 0.0830442 0.647437i
\(999\) 2.01898e14i 0.202911i
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 20.11.d.d.19.1 24
4.3 odd 2 inner 20.11.d.d.19.23 yes 24
5.2 odd 4 100.11.b.h.51.13 24
5.3 odd 4 100.11.b.h.51.12 24
5.4 even 2 inner 20.11.d.d.19.24 yes 24
20.3 even 4 100.11.b.h.51.11 24
20.7 even 4 100.11.b.h.51.14 24
20.19 odd 2 inner 20.11.d.d.19.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.11.d.d.19.1 24 1.1 even 1 trivial
20.11.d.d.19.2 yes 24 20.19 odd 2 inner
20.11.d.d.19.23 yes 24 4.3 odd 2 inner
20.11.d.d.19.24 yes 24 5.4 even 2 inner
100.11.b.h.51.11 24 20.3 even 4
100.11.b.h.51.12 24 5.3 odd 4
100.11.b.h.51.13 24 5.2 odd 4
100.11.b.h.51.14 24 20.7 even 4