Properties

Label 16.11.f.a.3.7
Level $16$
Weight $11$
Character 16.3
Analytic conductor $10.166$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,11,Mod(3,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.3");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), degree \(2\), 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: \(10.1657160428\)
Analytic rank: \(0\)
Dimension: \(38\)
Relative dimension: \(19\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.7
Character \(\chi\) \(=\) 16.3
Dual form 16.11.f.a.11.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-16.8116 - 27.2281i) q^{2} +(183.793 - 183.793i) q^{3} +(-458.741 + 915.496i) q^{4} +(3496.01 - 3496.01i) q^{5} +(-8094.18 - 1914.49i) q^{6} +26135.6 q^{7} +(32639.4 - 2900.27i) q^{8} -8510.59i q^{9} +O(q^{10})\) \(q+(-16.8116 - 27.2281i) q^{2} +(183.793 - 183.793i) q^{3} +(-458.741 + 915.496i) q^{4} +(3496.01 - 3496.01i) q^{5} +(-8094.18 - 1914.49i) q^{6} +26135.6 q^{7} +(32639.4 - 2900.27i) q^{8} -8510.59i q^{9} +(-153963. - 36416.3i) q^{10} +(-23602.7 - 23602.7i) q^{11} +(83948.2 + 252575. i) q^{12} +(-198530. - 198530. i) q^{13} +(-439381. - 711623. i) q^{14} -1.28508e6i q^{15} +(-627689. - 839951. i) q^{16} -37124.7 q^{17} +(-231727. + 143076. i) q^{18} +(-2.46575e6 + 2.46575e6i) q^{19} +(1.59682e6 + 4.80434e6i) q^{20} +(4.80353e6 - 4.80353e6i) q^{21} +(-245858. + 1.03946e6i) q^{22} -928760. q^{23} +(5.46584e6 - 6.53193e6i) q^{24} -1.46785e7i q^{25} +(-2.06800e6 + 8.74322e6i) q^{26} +(9.28860e6 + 9.28860e6i) q^{27} +(-1.19895e7 + 2.39270e7i) q^{28} +(2.31954e7 + 2.31954e7i) q^{29} +(-3.49904e7 + 2.16043e7i) q^{30} -4.20509e7i q^{31} +(-1.23179e7 + 3.12117e7i) q^{32} -8.67601e6 q^{33} +(624126. + 1.01084e6i) q^{34} +(9.13702e7 - 9.13702e7i) q^{35} +(7.79141e6 + 3.90416e6i) q^{36} +(-7.15654e7 + 7.15654e7i) q^{37} +(1.08591e8 + 2.56846e7i) q^{38} -7.29769e7 q^{39} +(1.03968e8 - 1.24247e8i) q^{40} -3.19196e7i q^{41} +(-2.11546e8 - 5.00362e7i) q^{42} +(-7.38726e7 - 7.38726e7i) q^{43} +(3.24357e7 - 1.07806e7i) q^{44} +(-2.97531e7 - 2.97531e7i) q^{45} +(1.56139e7 + 2.52884e7i) q^{46} -4.97800e6i q^{47} +(-2.69742e8 - 3.90124e7i) q^{48} +4.00594e8 q^{49} +(-3.99668e8 + 2.46769e8i) q^{50} +(-6.82326e6 + 6.82326e6i) q^{51} +(2.72828e8 - 9.06796e7i) q^{52} +(-4.22772e8 + 4.22772e8i) q^{53} +(9.67550e7 - 4.09067e8i) q^{54} -1.65030e8 q^{55} +(8.53050e8 - 7.58002e7i) q^{56} +9.06373e8i q^{57} +(2.41616e8 - 1.02152e9i) q^{58} +(-2.04599e8 - 2.04599e8i) q^{59} +(1.17649e9 + 5.89520e8i) q^{60} +(9.65784e8 + 9.65784e8i) q^{61} +(-1.14497e9 + 7.06942e8i) q^{62} -2.22429e8i q^{63} +(1.05692e9 - 1.89326e8i) q^{64} -1.38813e9 q^{65} +(1.45857e8 + 2.36231e8i) q^{66} +(-4.22476e7 + 4.22476e7i) q^{67} +(1.70307e7 - 3.39875e7i) q^{68} +(-1.70699e8 + 1.70699e8i) q^{69} +(-4.02392e9 - 9.51762e8i) q^{70} +1.24987e9 q^{71} +(-2.46830e7 - 2.77780e8i) q^{72} +1.86037e8i q^{73} +(3.15172e9 + 7.45464e8i) q^{74} +(-2.69781e9 - 2.69781e9i) q^{75} +(-1.12624e9 - 3.38852e9i) q^{76} +(-6.16870e8 - 6.16870e8i) q^{77} +(1.22686e9 + 1.98702e9i) q^{78} -3.24767e9i q^{79} +(-5.13088e9 - 7.42072e8i) q^{80} +3.91690e9 q^{81} +(-8.69110e8 + 5.36618e8i) q^{82} +(1.80568e9 - 1.80568e9i) q^{83} +(2.19403e9 + 6.60119e9i) q^{84} +(-1.29788e8 + 1.29788e8i) q^{85} +(-7.69497e8 + 3.25333e9i) q^{86} +8.52631e9 q^{87} +(-8.38832e8 - 7.01923e8i) q^{88} +1.74176e9i q^{89} +(-3.09924e8 + 1.31032e9i) q^{90} +(-5.18871e9 - 5.18871e9i) q^{91} +(4.26060e8 - 8.50275e8i) q^{92} +(-7.72865e9 - 7.72865e9i) q^{93} +(-1.35542e8 + 8.36880e7i) q^{94} +1.72405e10i q^{95} +(3.47255e9 + 8.00042e9i) q^{96} +1.21698e10 q^{97} +(-6.73462e9 - 1.09074e10i) q^{98} +(-2.00873e8 + 2.00873e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 147364 q^{10} - 45906 q^{11} - 10988 q^{12} - 2 q^{13} + 757836 q^{14} - 469032 q^{16} - 4 q^{17} + 2066926 q^{18} - 5107042 q^{19} + 5301516 q^{20} - 118100 q^{21} - 20568924 q^{22} - 8279748 q^{23} + 58519728 q^{24} - 18451512 q^{26} - 25871552 q^{27} - 36459784 q^{28} - 29652306 q^{29} + 132781252 q^{30} - 52661752 q^{32} - 4 q^{33} + 68474900 q^{34} + 14674460 q^{35} - 15810676 q^{36} - 94618130 q^{37} + 156046000 q^{38} - 279841732 q^{39} - 125381720 q^{40} + 107395416 q^{42} + 172486862 q^{43} + 73663988 q^{44} + 19649346 q^{45} - 437620836 q^{46} + 625190376 q^{48} + 1049193778 q^{49} - 875760314 q^{50} - 72924900 q^{51} - 771392444 q^{52} + 607072398 q^{53} + 913650464 q^{54} - 1427102468 q^{55} - 1385623464 q^{56} + 37561720 q^{58} + 1543683854 q^{59} + 318869600 q^{60} + 1673280158 q^{61} - 983062992 q^{62} - 867678656 q^{64} + 1098715212 q^{65} + 768197860 q^{66} - 4830427746 q^{67} - 855827792 q^{68} + 1698121420 q^{69} - 5103882496 q^{70} + 7572888316 q^{71} + 6888513460 q^{72} + 2513658844 q^{74} - 11656678318 q^{75} - 2250244316 q^{76} - 1336459028 q^{77} + 14243324268 q^{78} - 13115458328 q^{80} - 8523250762 q^{81} + 2724305648 q^{82} + 16141605438 q^{83} - 1633924184 q^{84} + 4779968748 q^{85} - 4025865500 q^{86} - 31832612676 q^{87} + 1023457912 q^{88} + 18960485240 q^{90} + 19874217404 q^{91} + 28060187160 q^{92} - 15001617056 q^{93} - 14829002256 q^{94} + 23525947312 q^{96} - 4 q^{97} - 43134832310 q^{98} - 25616384098 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.8116 27.2281i −0.525362 0.850879i
\(3\) 183.793 183.793i 0.756349 0.756349i −0.219307 0.975656i \(-0.570380\pi\)
0.975656 + 0.219307i \(0.0703796\pi\)
\(4\) −458.741 + 915.496i −0.447990 + 0.894039i
\(5\) 3496.01 3496.01i 1.11872 1.11872i 0.126793 0.991929i \(-0.459531\pi\)
0.991929 0.126793i \(-0.0404685\pi\)
\(6\) −8094.18 1914.49i −1.04092 0.246204i
\(7\) 26135.6 1.55504 0.777521 0.628857i \(-0.216477\pi\)
0.777521 + 0.628857i \(0.216477\pi\)
\(8\) 32639.4 2900.27i 0.996075 0.0885091i
\(9\) 8510.59i 0.144128i
\(10\) −153963. 36416.3i −1.53963 0.364163i
\(11\) −23602.7 23602.7i −0.146554 0.146554i 0.630023 0.776577i \(-0.283046\pi\)
−0.776577 + 0.630023i \(0.783046\pi\)
\(12\) 83948.2 + 252575.i 0.337369 + 1.01504i
\(13\) −198530. 198530.i −0.534700 0.534700i 0.387268 0.921967i \(-0.373419\pi\)
−0.921967 + 0.387268i \(0.873419\pi\)
\(14\) −439381. 711623.i −0.816960 1.32315i
\(15\) 1.28508e6i 1.69229i
\(16\) −627689. 839951.i −0.598611 0.801040i
\(17\) −37124.7 −0.0261468 −0.0130734 0.999915i \(-0.504162\pi\)
−0.0130734 + 0.999915i \(0.504162\pi\)
\(18\) −231727. + 143076.i −0.122635 + 0.0757191i
\(19\) −2.46575e6 + 2.46575e6i −0.995819 + 0.995819i −0.999991 0.00417198i \(-0.998672\pi\)
0.00417198 + 0.999991i \(0.498672\pi\)
\(20\) 1.59682e6 + 4.80434e6i 0.499005 + 1.50136i
\(21\) 4.80353e6 4.80353e6i 1.17615 1.17615i
\(22\) −245858. + 1.03946e6i −0.0477058 + 0.201694i
\(23\) −928760. −0.144299 −0.0721496 0.997394i \(-0.522986\pi\)
−0.0721496 + 0.997394i \(0.522986\pi\)
\(24\) 5.46584e6 6.53193e6i 0.686437 0.820324i
\(25\) 1.46785e7i 1.50308i
\(26\) −2.06800e6 + 8.74322e6i −0.174054 + 0.735876i
\(27\) 9.28860e6 + 9.28860e6i 0.647338 + 0.647338i
\(28\) −1.19895e7 + 2.39270e7i −0.696643 + 1.39027i
\(29\) 2.31954e7 + 2.31954e7i 1.13087 + 1.13087i 0.990033 + 0.140837i \(0.0449794\pi\)
0.140837 + 0.990033i \(0.455021\pi\)
\(30\) −3.49904e7 + 2.16043e7i −1.43993 + 0.889064i
\(31\) 4.20509e7i 1.46881i −0.678710 0.734407i \(-0.737461\pi\)
0.678710 0.734407i \(-0.262539\pi\)
\(32\) −1.23179e7 + 3.12117e7i −0.367101 + 0.930181i
\(33\) −8.67601e6 −0.221692
\(34\) 624126. + 1.01084e6i 0.0137365 + 0.0222478i
\(35\) 9.13702e7 9.13702e7i 1.73966 1.73966i
\(36\) 7.79141e6 + 3.90416e6i 0.128856 + 0.0645676i
\(37\) −7.15654e7 + 7.15654e7i −1.03203 + 1.03203i −0.0325652 + 0.999470i \(0.510368\pi\)
−0.999470 + 0.0325652i \(0.989632\pi\)
\(38\) 1.08591e8 + 2.56846e7i 1.37049 + 0.324156i
\(39\) −7.29769e7 −0.808839
\(40\) 1.03968e8 1.24247e8i 1.01531 1.21335i
\(41\) 3.19196e7i 0.275510i −0.990466 0.137755i \(-0.956011\pi\)
0.990466 0.137755i \(-0.0439887\pi\)
\(42\) −2.11546e8 5.00362e7i −1.61867 0.382858i
\(43\) −7.38726e7 7.38726e7i −0.502506 0.502506i 0.409710 0.912216i \(-0.365630\pi\)
−0.912216 + 0.409710i \(0.865630\pi\)
\(44\) 3.24357e7 1.07806e7i 0.196680 0.0653703i
\(45\) −2.97531e7 2.97531e7i −0.161239 0.161239i
\(46\) 1.56139e7 + 2.52884e7i 0.0758094 + 0.122781i
\(47\) 4.97800e6i 0.0217053i −0.999941 0.0108526i \(-0.996545\pi\)
0.999941 0.0108526i \(-0.00345457\pi\)
\(48\) −2.69742e8 3.90124e7i −1.05862 0.153107i
\(49\) 4.00594e8 1.41816
\(50\) −3.99668e8 + 2.46769e8i −1.27894 + 0.789661i
\(51\) −6.82326e6 + 6.82326e6i −0.0197761 + 0.0197761i
\(52\) 2.72828e8 9.06796e7i 0.717582 0.238502i
\(53\) −4.22772e8 + 4.22772e8i −1.01094 + 1.01094i −0.0110035 + 0.999939i \(0.503503\pi\)
−0.999939 + 0.0110035i \(0.996497\pi\)
\(54\) 9.67550e7 4.09067e8i 0.210720 0.890893i
\(55\) −1.65030e8 −0.327907
\(56\) 8.53050e8 7.58002e7i 1.54894 0.137635i
\(57\) 9.06373e8i 1.50637i
\(58\) 2.41616e8 1.02152e9i 0.368117 1.55635i
\(59\) −2.04599e8 2.04599e8i −0.286183 0.286183i 0.549386 0.835569i \(-0.314862\pi\)
−0.835569 + 0.549386i \(0.814862\pi\)
\(60\) 1.17649e9 + 5.89520e8i 1.51297 + 0.758128i
\(61\) 9.65784e8 + 9.65784e8i 1.14349 + 1.14349i 0.987808 + 0.155678i \(0.0497563\pi\)
0.155678 + 0.987808i \(0.450244\pi\)
\(62\) −1.14497e9 + 7.06942e8i −1.24978 + 0.771659i
\(63\) 2.22429e8i 0.224124i
\(64\) 1.05692e9 1.89326e8i 0.984332 0.176323i
\(65\) −1.38813e9 −1.19636
\(66\) 1.45857e8 + 2.36231e8i 0.116469 + 0.188633i
\(67\) −4.22476e7 + 4.22476e7i −0.0312916 + 0.0312916i −0.722579 0.691288i \(-0.757044\pi\)
0.691288 + 0.722579i \(0.257044\pi\)
\(68\) 1.70307e7 3.39875e7i 0.0117135 0.0233763i
\(69\) −1.70699e8 + 1.70699e8i −0.109141 + 0.109141i
\(70\) −4.02392e9 9.51762e8i −2.39419 0.566289i
\(71\) 1.24987e9 0.692747 0.346373 0.938097i \(-0.387413\pi\)
0.346373 + 0.938097i \(0.387413\pi\)
\(72\) −2.46830e7 2.77780e8i −0.0127566 0.143562i
\(73\) 1.86037e8i 0.0897399i 0.998993 + 0.0448700i \(0.0142873\pi\)
−0.998993 + 0.0448700i \(0.985713\pi\)
\(74\) 3.15172e9 + 7.45464e8i 1.42033 + 0.335945i
\(75\) −2.69781e9 2.69781e9i −1.13685 1.13685i
\(76\) −1.12624e9 3.38852e9i −0.444184 1.33642i
\(77\) −6.16870e8 6.16870e8i −0.227898 0.227898i
\(78\) 1.22686e9 + 1.98702e9i 0.424933 + 0.688224i
\(79\) 3.24767e9i 1.05545i −0.849417 0.527723i \(-0.823046\pi\)
0.849417 0.527723i \(-0.176954\pi\)
\(80\) −5.13088e9 7.42072e8i −1.56582 0.226463i
\(81\) 3.91690e9 1.12335
\(82\) −8.69110e8 + 5.36618e8i −0.234426 + 0.144743i
\(83\) 1.80568e9 1.80568e9i 0.458407 0.458407i −0.439725 0.898132i \(-0.644924\pi\)
0.898132 + 0.439725i \(0.144924\pi\)
\(84\) 2.19403e9 + 6.60119e9i 0.524623 + 1.57843i
\(85\) −1.29788e8 + 1.29788e8i −0.0292510 + 0.0292510i
\(86\) −7.69497e8 + 3.25333e9i −0.163574 + 0.691569i
\(87\) 8.52631e9 1.71066
\(88\) −8.38832e8 7.01923e8i −0.158950 0.133008i
\(89\) 1.74176e9i 0.311916i 0.987764 + 0.155958i \(0.0498465\pi\)
−0.987764 + 0.155958i \(0.950154\pi\)
\(90\) −3.09924e8 + 1.31032e9i −0.0524859 + 0.221903i
\(91\) −5.18871e9 5.18871e9i −0.831481 0.831481i
\(92\) 4.26060e8 8.50275e8i 0.0646446 0.129009i
\(93\) −7.72865e9 7.72865e9i −1.11094 1.11094i
\(94\) −1.35542e8 + 8.36880e7i −0.0184686 + 0.0114031i
\(95\) 1.72405e10i 2.22809i
\(96\) 3.47255e9 + 8.00042e9i 0.425885 + 0.981198i
\(97\) 1.21698e10 1.41718 0.708588 0.705622i \(-0.249332\pi\)
0.708588 + 0.705622i \(0.249332\pi\)
\(98\) −6.73462e9 1.09074e10i −0.745045 1.20668i
\(99\) −2.00873e8 + 2.00873e8i −0.0211225 + 0.0211225i
\(100\) 1.34381e10 + 6.73364e9i 1.34381 + 0.673364i
\(101\) −1.09920e10 + 1.09920e10i −1.04585 + 1.04585i −0.0469532 + 0.998897i \(0.514951\pi\)
−0.998897 + 0.0469532i \(0.985049\pi\)
\(102\) 3.00494e8 + 7.10747e7i 0.0272167 + 0.00643746i
\(103\) −1.00075e10 −0.863258 −0.431629 0.902051i \(-0.642061\pi\)
−0.431629 + 0.902051i \(0.642061\pi\)
\(104\) −7.05570e9 5.90412e9i −0.579927 0.485276i
\(105\) 3.35864e10i 2.63158i
\(106\) 1.86187e10 + 4.40382e9i 1.39130 + 0.329079i
\(107\) 5.65526e9 + 5.65526e9i 0.403212 + 0.403212i 0.879363 0.476151i \(-0.157969\pi\)
−0.476151 + 0.879363i \(0.657969\pi\)
\(108\) −1.27647e10 + 4.24261e9i −0.868746 + 0.288745i
\(109\) 1.19223e10 + 1.19223e10i 0.774870 + 0.774870i 0.978954 0.204083i \(-0.0654213\pi\)
−0.204083 + 0.978954i \(0.565421\pi\)
\(110\) 2.77442e9 + 4.49347e9i 0.172270 + 0.279009i
\(111\) 2.63064e10i 1.56116i
\(112\) −1.64050e10 2.19526e10i −0.930865 1.24565i
\(113\) 5.34527e9 0.290120 0.145060 0.989423i \(-0.453662\pi\)
0.145060 + 0.989423i \(0.453662\pi\)
\(114\) 2.46788e10 1.52376e10i 1.28174 0.791392i
\(115\) −3.24695e9 + 3.24695e9i −0.161431 + 0.161431i
\(116\) −3.18760e10 + 1.05946e10i −1.51766 + 0.504424i
\(117\) −1.68961e9 + 1.68961e9i −0.0770650 + 0.0770650i
\(118\) −2.13122e9 + 9.01049e9i −0.0931574 + 0.393857i
\(119\) −9.70277e8 −0.0406594
\(120\) −3.72708e9 4.19443e10i −0.149783 1.68565i
\(121\) 2.48233e10i 0.957044i
\(122\) 1.00601e10 4.25328e10i 0.372224 1.57371i
\(123\) −5.86658e9 5.86658e9i −0.208382 0.208382i
\(124\) 3.84974e10 + 1.92905e10i 1.31318 + 0.658013i
\(125\) −1.71755e10 1.71755e10i −0.562807 0.562807i
\(126\) −6.05633e9 + 3.73939e9i −0.190703 + 0.117746i
\(127\) 6.34853e9i 0.192156i 0.995374 + 0.0960781i \(0.0306299\pi\)
−0.995374 + 0.0960781i \(0.969370\pi\)
\(128\) −2.29235e10 2.55950e10i −0.667161 0.744914i
\(129\) −2.71545e10 −0.760140
\(130\) 2.33366e10 + 3.77961e10i 0.628523 + 1.01796i
\(131\) −2.58385e10 + 2.58385e10i −0.669746 + 0.669746i −0.957657 0.287911i \(-0.907039\pi\)
0.287911 + 0.957657i \(0.407039\pi\)
\(132\) 3.98004e9 7.94285e9i 0.0993158 0.198201i
\(133\) −6.44438e10 + 6.44438e10i −1.54854 + 1.54854i
\(134\) 1.86057e9 + 4.40074e8i 0.0430648 + 0.0101859i
\(135\) 6.49460e10 1.44838
\(136\) −1.21173e9 + 1.07672e8i −0.0260442 + 0.00231423i
\(137\) 1.89659e10i 0.392980i 0.980506 + 0.196490i \(0.0629543\pi\)
−0.980506 + 0.196490i \(0.937046\pi\)
\(138\) 7.51755e9 + 1.77810e9i 0.150204 + 0.0355271i
\(139\) −1.93924e10 1.93924e10i −0.373729 0.373729i 0.495104 0.868834i \(-0.335130\pi\)
−0.868834 + 0.495104i \(0.835130\pi\)
\(140\) 4.17338e10 + 1.25564e11i 0.775974 + 2.33467i
\(141\) −9.14920e8 9.14920e8i −0.0164168 0.0164168i
\(142\) −2.10124e10 3.40317e10i −0.363943 0.589443i
\(143\) 9.37170e9i 0.156725i
\(144\) −7.14848e9 + 5.34200e9i −0.115452 + 0.0862763i
\(145\) 1.62183e11 2.53026
\(146\) 5.06545e9 3.12758e9i 0.0763578 0.0471459i
\(147\) 7.36263e10 7.36263e10i 1.07262 1.07262i
\(148\) −3.26878e10 9.83478e10i −0.460338 1.38502i
\(149\) 6.82578e10 6.82578e10i 0.929439 0.929439i −0.0682304 0.997670i \(-0.521735\pi\)
0.997670 + 0.0682304i \(0.0217353\pi\)
\(150\) −2.81018e10 + 1.18811e11i −0.370065 + 1.56458i
\(151\) 6.53650e10 0.832646 0.416323 0.909217i \(-0.363319\pi\)
0.416323 + 0.909217i \(0.363319\pi\)
\(152\) −7.33292e10 + 8.76318e10i −0.903772 + 1.08005i
\(153\) 3.15953e8i 0.00376848i
\(154\) −6.42565e9 + 2.71668e10i −0.0741846 + 0.313642i
\(155\) −1.47010e11 1.47010e11i −1.64319 1.64319i
\(156\) 3.34775e10 6.68100e10i 0.362352 0.723134i
\(157\) −4.64668e10 4.64668e10i −0.487130 0.487130i 0.420270 0.907399i \(-0.361936\pi\)
−0.907399 + 0.420270i \(0.861936\pi\)
\(158\) −8.84278e10 + 5.45984e10i −0.898056 + 0.554491i
\(159\) 1.55405e11i 1.52925i
\(160\) 6.60530e10 + 1.52180e11i 0.629931 + 1.45130i
\(161\) −2.42737e10 −0.224391
\(162\) −6.58492e10 1.06650e11i −0.590168 0.955839i
\(163\) −1.94881e10 + 1.94881e10i −0.169368 + 0.169368i −0.786701 0.617334i \(-0.788213\pi\)
0.617334 + 0.786701i \(0.288213\pi\)
\(164\) 2.92222e10 + 1.46428e10i 0.246317 + 0.123426i
\(165\) −3.03314e10 + 3.03314e10i −0.248012 + 0.248012i
\(166\) −7.95218e10 1.88090e10i −0.630879 0.149219i
\(167\) −1.78588e11 −1.37490 −0.687450 0.726232i \(-0.741270\pi\)
−0.687450 + 0.726232i \(0.741270\pi\)
\(168\) 1.42853e11 1.70716e11i 1.06744 1.27564i
\(169\) 5.90299e10i 0.428192i
\(170\) 5.71584e9 + 1.35195e9i 0.0402565 + 0.00952170i
\(171\) 2.09850e10 + 2.09850e10i 0.143525 + 0.143525i
\(172\) 1.01518e11 3.37416e10i 0.674377 0.224142i
\(173\) 5.79481e10 + 5.79481e10i 0.373946 + 0.373946i 0.868912 0.494966i \(-0.164820\pi\)
−0.494966 + 0.868912i \(0.664820\pi\)
\(174\) −1.43341e11 2.32155e11i −0.898718 1.45557i
\(175\) 3.83632e11i 2.33735i
\(176\) −5.00997e9 + 3.46403e10i −0.0296669 + 0.205125i
\(177\) −7.52077e10 −0.432909
\(178\) 4.74248e10 2.92817e10i 0.265403 0.163869i
\(179\) 9.96053e10 9.96053e10i 0.542023 0.542023i −0.382099 0.924121i \(-0.624799\pi\)
0.924121 + 0.382099i \(0.124799\pi\)
\(180\) 4.08878e10 1.35898e10i 0.216387 0.0719204i
\(181\) −1.43128e11 + 1.43128e11i −0.736770 + 0.736770i −0.971952 0.235181i \(-0.924432\pi\)
0.235181 + 0.971952i \(0.424432\pi\)
\(182\) −5.40484e10 + 2.28509e11i −0.270661 + 1.14432i
\(183\) 3.55008e11 1.72975
\(184\) −3.03142e10 + 2.69365e9i −0.143733 + 0.0127718i
\(185\) 5.00386e11i 2.30912i
\(186\) −8.05058e10 + 3.40367e11i −0.361628 + 1.52891i
\(187\) 8.76244e8 + 8.76244e8i 0.00383192 + 0.00383192i
\(188\) 4.55734e9 + 2.28361e9i 0.0194054 + 0.00972374i
\(189\) 2.42763e11 + 2.42763e11i 1.00664 + 1.00664i
\(190\) 4.69428e11 2.89841e11i 1.89584 1.17055i
\(191\) 1.17738e11i 0.463180i −0.972813 0.231590i \(-0.925607\pi\)
0.972813 0.231590i \(-0.0743928\pi\)
\(192\) 1.59457e11 2.29051e11i 0.611137 0.877861i
\(193\) −3.28289e11 −1.22594 −0.612970 0.790106i \(-0.710025\pi\)
−0.612970 + 0.790106i \(0.710025\pi\)
\(194\) −2.04593e11 3.31360e11i −0.744531 1.20585i
\(195\) −2.55128e11 + 2.55128e11i −0.904867 + 0.904867i
\(196\) −1.83769e11 + 3.66742e11i −0.635319 + 1.26789i
\(197\) 1.07459e11 1.07459e11i 0.362169 0.362169i −0.502442 0.864611i \(-0.667565\pi\)
0.864611 + 0.502442i \(0.167565\pi\)
\(198\) 8.84638e9 + 2.09240e9i 0.0290696 + 0.00687573i
\(199\) −5.25486e11 −1.68382 −0.841911 0.539617i \(-0.818569\pi\)
−0.841911 + 0.539617i \(0.818569\pi\)
\(200\) −4.25716e10 4.79098e11i −0.133036 1.49718i
\(201\) 1.55296e10i 0.0473348i
\(202\) 4.84084e11 + 1.14499e11i 1.43934 + 0.340442i
\(203\) 6.06227e11 + 6.06227e11i 1.75855 + 1.75855i
\(204\) −3.11655e9 9.37678e9i −0.00882112 0.0265401i
\(205\) −1.11591e11 1.11591e11i −0.308219 0.308219i
\(206\) 1.68242e11 + 2.72486e11i 0.453523 + 0.734528i
\(207\) 7.90429e9i 0.0207975i
\(208\) −4.21406e10 + 2.91371e11i −0.108239 + 0.748393i
\(209\) 1.16397e11 0.291883
\(210\) −9.14494e11 + 5.64640e11i −2.23916 + 1.38253i
\(211\) 2.23137e9 2.23137e9i 0.00533531 0.00533531i −0.704434 0.709769i \(-0.748799\pi\)
0.709769 + 0.704434i \(0.248799\pi\)
\(212\) −1.93103e11 5.80989e11i −0.450930 1.35671i
\(213\) 2.29718e11 2.29718e11i 0.523958 0.523958i
\(214\) 5.89082e10 2.49056e11i 0.131252 0.554917i
\(215\) −5.16518e11 −1.12433
\(216\) 3.30114e11 + 2.76235e11i 0.702093 + 0.587502i
\(217\) 1.09902e12i 2.28407i
\(218\) 1.24190e11 5.25056e11i 0.252233 1.06641i
\(219\) 3.41923e10 + 3.41923e10i 0.0678747 + 0.0678747i
\(220\) 7.57063e10 1.51085e11i 0.146899 0.293161i
\(221\) 7.37039e9 + 7.37039e9i 0.0139807 + 0.0139807i
\(222\) 7.16274e11 4.42252e11i 1.32836 0.820172i
\(223\) 4.18867e11i 0.759542i 0.925081 + 0.379771i \(0.123997\pi\)
−0.925081 + 0.379771i \(0.876003\pi\)
\(224\) −3.21935e11 + 8.15736e11i −0.570857 + 1.44647i
\(225\) −1.24923e11 −0.216635
\(226\) −8.98625e10 1.45542e11i −0.152418 0.246857i
\(227\) 3.41296e11 3.41296e11i 0.566241 0.566241i −0.364832 0.931073i \(-0.618874\pi\)
0.931073 + 0.364832i \(0.118874\pi\)
\(228\) −8.29781e11 4.15791e11i −1.34676 0.674840i
\(229\) 2.37059e11 2.37059e11i 0.376426 0.376426i −0.493385 0.869811i \(-0.664241\pi\)
0.869811 + 0.493385i \(0.164241\pi\)
\(230\) 1.42995e11 + 3.38220e10i 0.222168 + 0.0525485i
\(231\) −2.26753e11 −0.344741
\(232\) 8.24358e11 + 6.89812e11i 1.22652 + 1.02634i
\(233\) 7.99650e11i 1.16445i 0.813028 + 0.582224i \(0.197817\pi\)
−0.813028 + 0.582224i \(0.802183\pi\)
\(234\) 7.44099e10 + 1.75999e10i 0.106060 + 0.0250860i
\(235\) −1.74031e10 1.74031e10i −0.0242822 0.0242822i
\(236\) 2.81168e11 9.34516e10i 0.384066 0.127652i
\(237\) −5.96897e11 5.96897e11i −0.798285 0.798285i
\(238\) 1.63119e10 + 2.64188e10i 0.0213609 + 0.0345962i
\(239\) 6.33692e11i 0.812622i −0.913735 0.406311i \(-0.866815\pi\)
0.913735 0.406311i \(-0.133185\pi\)
\(240\) −1.07941e12 + 8.06632e11i −1.35559 + 1.01302i
\(241\) −6.63015e11 −0.815527 −0.407763 0.913088i \(-0.633691\pi\)
−0.407763 + 0.913088i \(0.633691\pi\)
\(242\) −6.75891e11 + 4.17318e11i −0.814328 + 0.502794i
\(243\) 1.71415e11 1.71415e11i 0.202310 0.202310i
\(244\) −1.32722e12 + 4.41126e11i −1.53459 + 0.510051i
\(245\) 1.40048e12 1.40048e12i 1.58652 1.58652i
\(246\) −6.11095e10 + 2.58363e11i −0.0678318 + 0.286784i
\(247\) 9.79051e11 1.06493
\(248\) −1.21959e11 1.37252e12i −0.130003 1.46305i
\(249\) 6.63744e11i 0.693432i
\(250\) −1.78909e11 + 7.56405e11i −0.183203 + 0.774558i
\(251\) 8.91650e11 + 8.91650e11i 0.895006 + 0.895006i 0.994989 0.0999833i \(-0.0318789\pi\)
−0.0999833 + 0.994989i \(0.531879\pi\)
\(252\) 2.03633e11 + 1.02037e11i 0.200376 + 0.100405i
\(253\) 2.19212e10 + 2.19212e10i 0.0211477 + 0.0211477i
\(254\) 1.72859e11 1.06729e11i 0.163502 0.100952i
\(255\) 4.77083e10i 0.0442480i
\(256\) −3.11525e11 + 1.05446e12i −0.283331 + 0.959022i
\(257\) 5.26674e11 0.469760 0.234880 0.972024i \(-0.424530\pi\)
0.234880 + 0.972024i \(0.424530\pi\)
\(258\) 4.56510e11 + 7.39366e11i 0.399348 + 0.646787i
\(259\) −1.87040e12 + 1.87040e12i −1.60486 + 1.60486i
\(260\) 6.36791e11 1.27082e12i 0.535958 1.06959i
\(261\) 1.97407e11 1.97407e11i 0.162989 0.162989i
\(262\) 1.13792e12 + 2.69147e11i 0.921732 + 0.218014i
\(263\) 4.72112e11 0.375203 0.187601 0.982245i \(-0.439929\pi\)
0.187601 + 0.982245i \(0.439929\pi\)
\(264\) −2.83180e11 + 2.51627e10i −0.220822 + 0.0196218i
\(265\) 2.95603e12i 2.26193i
\(266\) 2.83808e12 + 6.71281e11i 2.13117 + 0.504076i
\(267\) 3.20122e11 + 3.20122e11i 0.235917 + 0.235917i
\(268\) −1.92968e10 5.80582e10i −0.0139576 0.0419942i
\(269\) −6.07912e11 6.07912e11i −0.431598 0.431598i 0.457574 0.889172i \(-0.348719\pi\)
−0.889172 + 0.457574i \(0.848719\pi\)
\(270\) −1.09185e12 1.76836e12i −0.760926 1.23240i
\(271\) 1.05806e12i 0.723874i −0.932202 0.361937i \(-0.882115\pi\)
0.932202 0.361937i \(-0.117885\pi\)
\(272\) 2.33028e10 + 3.11830e10i 0.0156518 + 0.0209446i
\(273\) −1.90729e12 −1.25778
\(274\) 5.16405e11 3.18846e11i 0.334378 0.206457i
\(275\) −3.46452e11 + 3.46452e11i −0.220283 + 0.220283i
\(276\) −7.79677e10 2.34581e11i −0.0486821 0.146470i
\(277\) −6.11243e11 + 6.11243e11i −0.374813 + 0.374813i −0.869227 0.494413i \(-0.835383\pi\)
0.494413 + 0.869227i \(0.335383\pi\)
\(278\) −2.02001e11 + 8.54035e11i −0.121655 + 0.514341i
\(279\) −3.57878e11 −0.211696
\(280\) 2.71727e12 3.24727e12i 1.57886 1.88681i
\(281\) 8.13166e11i 0.464139i −0.972699 0.232069i \(-0.925450\pi\)
0.972699 0.232069i \(-0.0745496\pi\)
\(282\) −9.53031e9 + 4.02928e10i −0.00534394 + 0.0225934i
\(283\) −1.65712e12 1.65712e12i −0.912895 0.912895i 0.0836044 0.996499i \(-0.473357\pi\)
−0.996499 + 0.0836044i \(0.973357\pi\)
\(284\) −5.73369e11 + 1.14425e12i −0.310343 + 0.619342i
\(285\) 3.16869e12 + 3.16869e12i 1.68521 + 1.68521i
\(286\) 2.55174e11 1.57553e11i 0.133354 0.0823373i
\(287\) 8.34237e11i 0.428430i
\(288\) 2.65630e11 + 1.04832e11i 0.134065 + 0.0529093i
\(289\) −2.01462e12 −0.999316
\(290\) −2.72655e12 4.41594e12i −1.32930 2.15294i
\(291\) 2.23672e12 2.23672e12i 1.07188 1.07188i
\(292\) −1.70316e11 8.53430e10i −0.0802310 0.0402025i
\(293\) −1.41632e12 + 1.41632e12i −0.655877 + 0.655877i −0.954402 0.298525i \(-0.903506\pi\)
0.298525 + 0.954402i \(0.403506\pi\)
\(294\) −3.24248e12 7.66931e11i −1.47618 0.349156i
\(295\) −1.43056e12 −0.640319
\(296\) −2.12829e12 + 2.54341e12i −0.936640 + 1.11933i
\(297\) 4.38472e11i 0.189740i
\(298\) −3.00605e12 7.11010e11i −1.27913 0.302548i
\(299\) 1.84387e11 + 1.84387e11i 0.0771568 + 0.0771568i
\(300\) 3.70742e12 1.23223e12i 1.52569 0.507092i
\(301\) −1.93070e12 1.93070e12i −0.781418 0.781418i
\(302\) −1.09889e12 1.77977e12i −0.437440 0.708481i
\(303\) 4.04050e12i 1.58206i
\(304\) 3.61883e12 + 5.23386e11i 1.39380 + 0.201583i
\(305\) 6.75278e12 2.55849
\(306\) 8.60281e9 5.31167e9i 0.00320652 0.00197981i
\(307\) 1.31036e12 1.31036e12i 0.480505 0.480505i −0.424788 0.905293i \(-0.639651\pi\)
0.905293 + 0.424788i \(0.139651\pi\)
\(308\) 8.47726e11 2.81758e11i 0.305845 0.101654i
\(309\) −1.83931e12 + 1.83931e12i −0.652924 + 0.652924i
\(310\) −1.53134e12 + 6.47429e12i −0.534887 + 2.26143i
\(311\) −2.51450e12 −0.864270 −0.432135 0.901809i \(-0.642240\pi\)
−0.432135 + 0.901809i \(0.642240\pi\)
\(312\) −2.38192e12 + 2.11652e11i −0.805665 + 0.0715896i
\(313\) 2.07780e12i 0.691644i −0.938300 0.345822i \(-0.887600\pi\)
0.938300 0.345822i \(-0.112400\pi\)
\(314\) −4.84023e11 + 2.04638e12i −0.158569 + 0.670408i
\(315\) −7.77614e11 7.77614e11i −0.250733 0.250733i
\(316\) 2.97322e12 + 1.48984e12i 0.943609 + 0.472829i
\(317\) 7.27815e11 + 7.27815e11i 0.227366 + 0.227366i 0.811591 0.584226i \(-0.198602\pi\)
−0.584226 + 0.811591i \(0.698602\pi\)
\(318\) 4.23138e12 2.61260e12i 1.30121 0.803410i
\(319\) 1.09495e12i 0.331467i
\(320\) 3.03311e12 4.35688e12i 0.903938 1.29845i
\(321\) 2.07879e12 0.609938
\(322\) 4.08079e11 + 6.60927e11i 0.117887 + 0.190930i
\(323\) 9.15402e10 9.15402e10i 0.0260375 0.0260375i
\(324\) −1.79684e12 + 3.58590e12i −0.503251 + 1.00432i
\(325\) −2.91413e12 + 2.91413e12i −0.803697 + 0.803697i
\(326\) 8.58249e11 + 2.02998e11i 0.233091 + 0.0551321i
\(327\) 4.38248e12 1.17214
\(328\) −9.25752e10 1.04184e12i −0.0243851 0.274429i
\(329\) 1.30103e11i 0.0337526i
\(330\) 1.33579e12 + 3.15948e11i 0.341324 + 0.0807321i
\(331\) −4.79981e12 4.79981e12i −1.20805 1.20805i −0.971658 0.236390i \(-0.924036\pi\)
−0.236390 0.971658i \(-0.575964\pi\)
\(332\) 8.24754e11 + 2.48144e12i 0.204472 + 0.615196i
\(333\) 6.09063e11 + 6.09063e11i 0.148745 + 0.148745i
\(334\) 3.00235e12 + 4.86263e12i 0.722320 + 1.16987i
\(335\) 2.95396e11i 0.0700133i
\(336\) −7.04986e12 1.01961e12i −1.64621 0.238088i
\(337\) 4.02759e12 0.926607 0.463304 0.886200i \(-0.346664\pi\)
0.463304 + 0.886200i \(0.346664\pi\)
\(338\) −1.60727e12 + 9.92386e11i −0.364340 + 0.224956i
\(339\) 9.82423e11 9.82423e11i 0.219432 0.219432i
\(340\) −5.92814e10 1.78360e11i −0.0130474 0.0392557i
\(341\) −9.92514e11 + 9.92514e11i −0.215261 + 0.215261i
\(342\) 2.18591e11 9.24171e11i 0.0467198 0.197525i
\(343\) 3.08710e12 0.650250
\(344\) −2.62541e12 2.19691e12i −0.545010 0.456057i
\(345\) 1.19353e12i 0.244196i
\(346\) 6.03619e11 2.55202e12i 0.121726 0.514639i
\(347\) 1.80948e12 + 1.80948e12i 0.359671 + 0.359671i 0.863692 0.504021i \(-0.168146\pi\)
−0.504021 + 0.863692i \(0.668146\pi\)
\(348\) −3.91137e12 + 7.80580e12i −0.766360 + 1.52940i
\(349\) −2.56712e12 2.56712e12i −0.495815 0.495815i 0.414317 0.910133i \(-0.364020\pi\)
−0.910133 + 0.414317i \(0.864020\pi\)
\(350\) −1.04456e13 + 6.44946e12i −1.98880 + 1.22796i
\(351\) 3.68814e12i 0.692263i
\(352\) 1.02741e12 4.45945e11i 0.190122 0.0825217i
\(353\) −5.57531e12 −1.01717 −0.508587 0.861011i \(-0.669832\pi\)
−0.508587 + 0.861011i \(0.669832\pi\)
\(354\) 1.26436e12 + 2.04777e12i 0.227434 + 0.368353i
\(355\) 4.36957e12 4.36957e12i 0.774991 0.774991i
\(356\) −1.59457e12 7.99016e11i −0.278865 0.139735i
\(357\) −1.78330e11 + 1.78330e11i −0.0307527 + 0.0307527i
\(358\) −4.38659e12 1.03754e12i −0.745954 0.176437i
\(359\) 7.28553e12 1.22177 0.610884 0.791720i \(-0.290814\pi\)
0.610884 + 0.791720i \(0.290814\pi\)
\(360\) −1.05741e12 8.84831e11i −0.174877 0.146335i
\(361\) 6.02875e12i 0.983312i
\(362\) 6.30332e12 + 1.49090e12i 1.01397 + 0.239831i
\(363\) −4.56233e12 4.56233e12i −0.723859 0.723859i
\(364\) 7.13051e12 2.36996e12i 1.11587 0.370881i
\(365\) 6.50388e11 + 6.50388e11i 0.100394 + 0.100394i
\(366\) −5.96825e12 9.66621e12i −0.908744 1.47181i
\(367\) 3.99828e12i 0.600542i 0.953854 + 0.300271i \(0.0970771\pi\)
−0.953854 + 0.300271i \(0.902923\pi\)
\(368\) 5.82972e11 + 7.80113e11i 0.0863791 + 0.115590i
\(369\) −2.71654e11 −0.0397086
\(370\) 1.36246e13 8.41228e12i 1.96478 1.21312i
\(371\) −1.10494e13 + 1.10494e13i −1.57206 + 1.57206i
\(372\) 1.06210e13 3.53009e12i 1.49091 0.495532i
\(373\) 6.58369e12 6.58369e12i 0.911854 0.911854i −0.0845641 0.996418i \(-0.526950\pi\)
0.996418 + 0.0845641i \(0.0269498\pi\)
\(374\) 9.12743e9 3.85895e10i 0.00124736 0.00527365i
\(375\) −6.31347e12 −0.851357
\(376\) −1.44375e10 1.62479e11i −0.00192111 0.0216201i
\(377\) 9.21000e12i 1.20935i
\(378\) 2.52875e12 1.06912e13i 0.327678 1.38538i
\(379\) 7.91355e12 + 7.91355e12i 1.01199 + 1.01199i 0.999927 + 0.0120604i \(0.00383903\pi\)
0.0120604 + 0.999927i \(0.496161\pi\)
\(380\) −1.57836e13 7.90895e12i −1.99200 0.998162i
\(381\) 1.16681e12 + 1.16681e12i 0.145337 + 0.145337i
\(382\) −3.20579e12 + 1.97936e12i −0.394110 + 0.243337i
\(383\) 1.20215e13i 1.45870i 0.684142 + 0.729349i \(0.260177\pi\)
−0.684142 + 0.729349i \(0.739823\pi\)
\(384\) −8.91735e12 4.91018e11i −1.06802 0.0588086i
\(385\) −4.31317e12 −0.509909
\(386\) 5.51905e12 + 8.93868e12i 0.644062 + 1.04313i
\(387\) −6.28699e11 + 6.28699e11i −0.0724249 + 0.0724249i
\(388\) −5.58278e12 + 1.11414e13i −0.634880 + 1.26701i
\(389\) −7.67209e12 + 7.67209e12i −0.861322 + 0.861322i −0.991492 0.130169i \(-0.958448\pi\)
0.130169 + 0.991492i \(0.458448\pi\)
\(390\) 1.12358e13 + 2.65755e12i 1.24531 + 0.294549i
\(391\) 3.44800e10 0.00377297
\(392\) 1.30751e13 1.16183e12i 1.41259 0.125520i
\(393\) 9.49784e12i 1.01312i
\(394\) −4.73246e12 1.11935e12i −0.498432 0.117892i
\(395\) −1.13539e13 1.13539e13i −1.18075 1.18075i
\(396\) −9.17495e10 2.76047e11i −0.00942167 0.0283470i
\(397\) −7.80668e12 7.80668e12i −0.791615 0.791615i 0.190142 0.981757i \(-0.439105\pi\)
−0.981757 + 0.190142i \(0.939105\pi\)
\(398\) 8.83426e12 + 1.43080e13i 0.884616 + 1.43273i
\(399\) 2.36886e13i 2.34247i
\(400\) −1.23292e13 + 9.21354e12i −1.20403 + 0.899760i
\(401\) 1.81263e13 1.74818 0.874090 0.485763i \(-0.161458\pi\)
0.874090 + 0.485763i \(0.161458\pi\)
\(402\) 4.22842e11 2.61077e11i 0.0402761 0.0248679i
\(403\) −8.34837e12 + 8.34837e12i −0.785374 + 0.785374i
\(404\) −5.02064e12 1.51056e13i −0.466501 1.40356i
\(405\) 1.36935e13 1.36935e13i 1.25672 1.25672i
\(406\) 6.31478e12 2.66980e13i 0.572438 2.42019i
\(407\) 3.37827e12 0.302498
\(408\) −2.02918e11 + 2.42496e11i −0.0179481 + 0.0214489i
\(409\) 5.55158e12i 0.485065i 0.970143 + 0.242533i \(0.0779782\pi\)
−0.970143 + 0.242533i \(0.922022\pi\)
\(410\) −1.16239e12 + 4.91444e12i −0.100331 + 0.424184i
\(411\) 3.48579e12 + 3.48579e12i 0.297230 + 0.297230i
\(412\) 4.59087e12 9.16185e12i 0.386731 0.771786i
\(413\) −5.34732e12 5.34732e12i −0.445027 0.445027i
\(414\) 2.15219e11 1.32884e11i 0.0176962 0.0109262i
\(415\) 1.26254e13i 1.02566i
\(416\) 8.64194e12 3.75100e12i 0.693657 0.301079i
\(417\) −7.12836e12 −0.565339
\(418\) −1.95681e12 3.16926e12i −0.153344 0.248357i
\(419\) −1.20736e11 + 1.20736e11i −0.00934904 + 0.00934904i −0.711766 0.702417i \(-0.752104\pi\)
0.702417 + 0.711766i \(0.252104\pi\)
\(420\) 3.07482e13 + 1.54075e13i 2.35274 + 1.17892i
\(421\) −1.42648e13 + 1.42648e13i −1.07858 + 1.07858i −0.0819482 + 0.996637i \(0.526114\pi\)
−0.996637 + 0.0819482i \(0.973886\pi\)
\(422\) −9.82689e10 2.32432e10i −0.00734267 0.00173673i
\(423\) −4.23657e10 −0.00312833
\(424\) −1.25729e13 + 1.50252e13i −0.917498 + 1.09645i
\(425\) 5.44936e11i 0.0393008i
\(426\) −1.01167e13 2.39286e12i −0.721093 0.170557i
\(427\) 2.52413e13 + 2.52413e13i 1.77817 + 1.77817i
\(428\) −7.77167e12 + 2.58306e12i −0.541122 + 0.179852i
\(429\) 1.72245e12 + 1.72245e12i 0.118539 + 0.118539i
\(430\) 8.68349e12 + 1.40638e13i 0.590680 + 0.956668i
\(431\) 2.03574e13i 1.36879i −0.729112 0.684395i \(-0.760067\pi\)
0.729112 0.684395i \(-0.239933\pi\)
\(432\) 1.97162e12 1.36323e13i 0.131040 0.906047i
\(433\) −1.41241e12 −0.0927942 −0.0463971 0.998923i \(-0.514774\pi\)
−0.0463971 + 0.998923i \(0.514774\pi\)
\(434\) −2.99244e13 + 1.84763e13i −1.94346 + 1.19996i
\(435\) 2.98080e13 2.98080e13i 1.91376 1.91376i
\(436\) −1.63841e13 + 5.44558e12i −1.03990 + 0.345630i
\(437\) 2.29009e12 2.29009e12i 0.143696 0.143696i
\(438\) 3.56166e11 1.50582e12i 0.0220944 0.0934119i
\(439\) 2.38960e12 0.146555 0.0732777 0.997312i \(-0.476654\pi\)
0.0732777 + 0.997312i \(0.476654\pi\)
\(440\) −5.38649e12 + 4.78632e11i −0.326620 + 0.0290227i
\(441\) 3.40929e12i 0.204395i
\(442\) 7.67739e10 3.24590e11i 0.00455095 0.0192408i
\(443\) −1.86600e13 1.86600e13i −1.09369 1.09369i −0.995131 0.0985578i \(-0.968577\pi\)
−0.0985578 0.995131i \(-0.531423\pi\)
\(444\) −2.40834e13 1.20678e13i −1.39573 0.699382i
\(445\) 6.08920e12 + 6.08920e12i 0.348947 + 0.348947i
\(446\) 1.14050e13 7.04182e12i 0.646278 0.399035i
\(447\) 2.50906e13i 1.40596i
\(448\) 2.76232e13 4.94814e12i 1.53068 0.274190i
\(449\) −9.36693e12 −0.513293 −0.256647 0.966505i \(-0.582618\pi\)
−0.256647 + 0.966505i \(0.582618\pi\)
\(450\) 2.10015e12 + 3.40141e12i 0.113812 + 0.184330i
\(451\) −7.53387e11 + 7.53387e11i −0.0403771 + 0.0403771i
\(452\) −2.45210e12 + 4.89357e12i −0.129971 + 0.259378i
\(453\) 1.20136e13 1.20136e13i 0.629771 0.629771i
\(454\) −1.50306e13 3.55512e12i −0.779284 0.184321i
\(455\) −3.62795e13 −1.86039
\(456\) 2.62872e12 + 2.95835e13i 0.133328 + 1.50046i
\(457\) 4.79735e12i 0.240669i −0.992733 0.120334i \(-0.961603\pi\)
0.992733 0.120334i \(-0.0383967\pi\)
\(458\) −1.04400e13 2.46934e12i −0.518053 0.122533i
\(459\) −3.44837e11 3.44837e11i −0.0169258 0.0169258i
\(460\) −1.48306e12 4.46208e12i −0.0720061 0.216645i
\(461\) 2.85615e13 + 2.85615e13i 1.37176 + 1.37176i 0.857842 + 0.513914i \(0.171805\pi\)
0.513914 + 0.857842i \(0.328195\pi\)
\(462\) 3.81207e12 + 6.17405e12i 0.181114 + 0.293332i
\(463\) 2.53353e13i 1.19075i −0.803447 0.595376i \(-0.797003\pi\)
0.803447 0.595376i \(-0.202997\pi\)
\(464\) 4.92353e12 3.40426e13i 0.228921 1.58282i
\(465\) −5.40388e13 −2.48566
\(466\) 2.17730e13 1.34434e13i 0.990804 0.611757i
\(467\) −1.32024e13 + 1.32024e13i −0.594384 + 0.594384i −0.938813 0.344428i \(-0.888073\pi\)
0.344428 + 0.938813i \(0.388073\pi\)
\(468\) −7.71736e11 2.32192e12i −0.0343748 0.103423i
\(469\) −1.10417e12 + 1.10417e12i −0.0486598 + 0.0486598i
\(470\) −1.81280e11 + 7.66429e11i −0.00790426 + 0.0334181i
\(471\) −1.70805e13 −0.736880
\(472\) −7.27139e12 6.08460e12i −0.310390 0.259730i
\(473\) 3.48718e12i 0.147289i
\(474\) −6.21761e12 + 2.62872e13i −0.259855 + 1.09863i
\(475\) 3.61935e13 + 3.61935e13i 1.49680 + 1.49680i
\(476\) 4.45106e11 8.88284e11i 0.0182150 0.0363511i
\(477\) 3.59804e12 + 3.59804e12i 0.145705 + 0.145705i
\(478\) −1.72542e13 + 1.06534e13i −0.691443 + 0.426921i
\(479\) 8.30840e12i 0.329488i −0.986336 0.164744i \(-0.947320\pi\)
0.986336 0.164744i \(-0.0526798\pi\)
\(480\) 4.01096e13 + 1.58295e13i 1.57414 + 0.621241i
\(481\) 2.84158e13 1.10366
\(482\) 1.11463e13 + 1.80527e13i 0.428447 + 0.693914i
\(483\) −4.46133e12 + 4.46133e12i −0.169718 + 0.169718i
\(484\) 2.27256e13 + 1.13875e13i 0.855634 + 0.428746i
\(485\) 4.25456e13 4.25456e13i 1.58543 1.58543i
\(486\) −7.54906e12 1.78555e12i −0.278427 0.0658553i
\(487\) 1.06812e13 0.389921 0.194960 0.980811i \(-0.437542\pi\)
0.194960 + 0.980811i \(0.437542\pi\)
\(488\) 3.43236e13 + 2.87216e13i 1.24021 + 1.03779i
\(489\) 7.16353e12i 0.256202i
\(490\) −6.16767e13 1.45882e13i −2.18344 0.516440i
\(491\) 7.67425e12 + 7.67425e12i 0.268923 + 0.268923i 0.828666 0.559743i \(-0.189100\pi\)
−0.559743 + 0.828666i \(0.689100\pi\)
\(492\) 8.06208e12 2.67959e12i 0.279654 0.0929485i
\(493\) −8.61125e11 8.61125e11i −0.0295686 0.0295686i
\(494\) −1.64594e13 2.66577e13i −0.559473 0.906126i
\(495\) 1.40451e12i 0.0472604i
\(496\) −3.53207e13 + 2.63949e13i −1.17658 + 0.879247i
\(497\) 3.26662e13 1.07725
\(498\) −1.80725e13 + 1.11586e13i −0.590026 + 0.364303i
\(499\) 1.62221e13 1.62221e13i 0.524331 0.524331i −0.394546 0.918876i \(-0.629098\pi\)
0.918876 + 0.394546i \(0.129098\pi\)
\(500\) 2.36032e13 7.84499e12i 0.755303 0.251040i
\(501\) −3.28233e13 + 3.28233e13i −1.03990 + 1.03990i
\(502\) 9.28791e12 3.92680e13i 0.291340 1.23174i
\(503\) 6.29489e12 0.195501 0.0977504 0.995211i \(-0.468835\pi\)
0.0977504 + 0.995211i \(0.468835\pi\)
\(504\) −6.45104e11 7.25996e12i −0.0198370 0.223245i
\(505\) 7.68562e13i 2.34003i
\(506\) 2.28343e11 9.65404e11i 0.00688392 0.0291043i
\(507\) −1.08493e13 1.08493e13i −0.323863 0.323863i
\(508\) −5.81205e12 2.91233e12i −0.171795 0.0860840i
\(509\) 3.34514e12 + 3.34514e12i 0.0979098 + 0.0979098i 0.754365 0.656455i \(-0.227945\pi\)
−0.656455 + 0.754365i \(0.727945\pi\)
\(510\) 1.29901e12 8.02053e11i 0.0376497 0.0232462i
\(511\) 4.86219e12i 0.139549i
\(512\) 3.39481e13 9.24483e12i 0.964863 0.262754i
\(513\) −4.58067e13 −1.28926
\(514\) −8.85422e12 1.43403e13i −0.246794 0.399709i
\(515\) −3.49864e13 + 3.49864e13i −0.965746 + 0.965746i
\(516\) 1.24569e13 2.48598e13i 0.340535 0.679594i
\(517\) −1.17494e11 + 1.17494e11i −0.00318100 + 0.00318100i
\(518\) 8.23720e13 + 1.94831e13i 2.20867 + 0.522408i
\(519\) 2.13009e13 0.565667
\(520\) −4.53076e13 + 4.02594e12i −1.19167 + 0.105889i
\(521\) 5.14980e13i 1.34153i 0.741668 + 0.670767i \(0.234035\pi\)
−0.741668 + 0.670767i \(0.765965\pi\)
\(522\) −8.69374e12 2.05630e12i −0.224313 0.0530558i
\(523\) −5.38368e13 5.38368e13i −1.37585 1.37585i −0.851507 0.524343i \(-0.824311\pi\)
−0.524343 0.851507i \(-0.675689\pi\)
\(524\) −1.18018e13 3.55082e13i −0.298740 0.898818i
\(525\) −7.05088e13 7.05088e13i −1.76785 1.76785i
\(526\) −7.93695e12 1.28547e13i −0.197117 0.319252i
\(527\) 1.56113e12i 0.0384048i
\(528\) 5.44583e12 + 7.28743e12i 0.132707 + 0.177584i
\(529\) −4.05639e13 −0.979178
\(530\) 8.04871e13 4.96955e13i 1.92463 1.18833i
\(531\) −1.74126e12 + 1.74126e12i −0.0412469 + 0.0412469i
\(532\) −2.94350e13 8.85610e13i −0.690725 2.07819i
\(533\) −6.33700e12 + 6.33700e12i −0.147315 + 0.147315i
\(534\) 3.33457e12 1.40981e13i 0.0767951 0.324679i
\(535\) 3.95417e13 0.902165
\(536\) −1.25641e12 + 1.50147e12i −0.0283992 + 0.0339384i
\(537\) 3.66135e13i 0.819916i
\(538\) −6.33234e12 + 2.67723e13i −0.140492 + 0.593983i
\(539\) −9.45510e12 9.45510e12i −0.207837 0.207837i
\(540\) −2.97934e13 + 5.94578e13i −0.648861 + 1.29491i
\(541\) 2.48695e13 + 2.48695e13i 0.536636 + 0.536636i 0.922539 0.385903i \(-0.126110\pi\)
−0.385903 + 0.922539i \(0.626110\pi\)
\(542\) −2.88089e13 + 1.77876e13i −0.615929 + 0.380296i
\(543\) 5.26118e13i 1.11451i
\(544\) 4.57297e11 1.15873e12i 0.00959852 0.0243213i
\(545\) 8.33612e13 1.73373
\(546\) 3.20646e13 + 5.19320e13i 0.660789 + 1.07022i
\(547\) 1.57563e12 1.57563e12i 0.0321749 0.0321749i −0.690836 0.723011i \(-0.742757\pi\)
0.723011 + 0.690836i \(0.242757\pi\)
\(548\) −1.73632e13 8.70043e12i −0.351339 0.176051i
\(549\) 8.21939e12 8.21939e12i 0.164808 0.164808i
\(550\) 1.52577e13 + 3.60884e12i 0.303162 + 0.0717057i
\(551\) −1.14388e14 −2.25228
\(552\) −5.07645e12 + 6.06660e12i −0.0990523 + 0.118372i
\(553\) 8.48797e13i 1.64126i
\(554\) 2.69190e13 + 6.36704e12i 0.515833 + 0.122008i
\(555\) 9.19674e13 + 9.19674e13i 1.74650 + 1.74650i
\(556\) 2.66497e13 8.85755e12i 0.501555 0.166702i
\(557\) −1.01553e12 1.01553e12i −0.0189416 0.0189416i 0.697573 0.716514i \(-0.254263\pi\)
−0.716514 + 0.697573i \(0.754263\pi\)
\(558\) 6.01649e12 + 9.74434e12i 0.111217 + 0.180128i
\(559\) 2.93319e13i 0.537380i
\(560\) −1.34099e14 1.93945e13i −2.43492 0.352159i
\(561\) 3.22095e11 0.00579654
\(562\) −2.21410e13 + 1.36706e13i −0.394926 + 0.243841i
\(563\) 5.85163e13 5.85163e13i 1.03451 1.03451i 0.0351281 0.999383i \(-0.488816\pi\)
0.999383 0.0351281i \(-0.0111839\pi\)
\(564\) 1.25732e12 4.17894e11i 0.0220318 0.00732269i
\(565\) 1.86871e13 1.86871e13i 0.324564 0.324564i
\(566\) −1.72614e13 + 7.29789e13i −0.297163 + 1.25636i
\(567\) 1.02370e14 1.74686
\(568\) 4.07951e13 3.62497e12i 0.690028 0.0613144i
\(569\) 9.64364e13i 1.61689i −0.588574 0.808443i \(-0.700311\pi\)
0.588574 0.808443i \(-0.299689\pi\)
\(570\) 3.30068e13 1.39548e14i 0.548566 2.31926i
\(571\) −2.96530e13 2.96530e13i −0.488526 0.488526i 0.419315 0.907841i \(-0.362270\pi\)
−0.907841 + 0.419315i \(0.862270\pi\)
\(572\) −8.57975e12 4.29919e12i −0.140118 0.0702111i
\(573\) −2.16394e13 2.16394e13i −0.350326 0.350326i
\(574\) −2.27147e13 + 1.40248e13i −0.364542 + 0.225081i
\(575\) 1.36328e13i 0.216893i
\(576\) −1.61127e12 8.99500e12i −0.0254131 0.141869i
\(577\) −2.17271e13 −0.339721 −0.169861 0.985468i \(-0.554332\pi\)
−0.169861 + 0.985468i \(0.554332\pi\)
\(578\) 3.38689e13 + 5.48542e13i 0.525003 + 0.850297i
\(579\) −6.03371e13 + 6.03371e13i −0.927238 + 0.927238i
\(580\) −7.44000e13 + 1.48478e14i −1.13353 + 2.26215i
\(581\) 4.71926e13 4.71926e13i 0.712843 0.712843i
\(582\) −9.85044e13 2.32989e13i −1.47517 0.348915i
\(583\) 1.99571e13 0.296316
\(584\) 5.39557e11 + 6.07214e12i 0.00794280 + 0.0893877i
\(585\) 1.18138e13i 0.172429i
\(586\) 6.23742e13 + 1.47531e13i 0.902645 + 0.213499i
\(587\) −1.69648e13 1.69648e13i −0.243422 0.243422i 0.574843 0.818264i \(-0.305063\pi\)
−0.818264 + 0.574843i \(0.805063\pi\)
\(588\) 3.36291e13 + 1.01180e14i 0.478442 + 1.43949i
\(589\) 1.03687e14 + 1.03687e14i 1.46267 + 1.46267i
\(590\) 2.40500e13 + 3.89515e13i 0.336399 + 0.544834i
\(591\) 3.95004e13i 0.547853i
\(592\) 1.05032e14 + 1.51907e13i 1.44449 + 0.208914i
\(593\) −6.94902e13 −0.947654 −0.473827 0.880618i \(-0.657128\pi\)
−0.473827 + 0.880618i \(0.657128\pi\)
\(594\) −1.19388e13 + 7.37140e12i −0.161446 + 0.0996823i
\(595\) −3.39210e12 + 3.39210e12i −0.0454866 + 0.0454866i
\(596\) 3.11770e13 + 9.38024e13i 0.414576 + 1.24733i
\(597\) −9.65806e13 + 9.65806e13i −1.27356 + 1.27356i
\(598\) 1.92067e12 8.12035e12i 0.0251158 0.106186i
\(599\) −5.76484e12 −0.0747572 −0.0373786 0.999301i \(-0.511901\pi\)
−0.0373786 + 0.999301i \(0.511901\pi\)
\(600\) −9.58791e13 8.02304e13i −1.23301 1.03177i
\(601\) 5.22266e13i 0.666069i −0.942915 0.333035i \(-0.891927\pi\)
0.942915 0.333035i \(-0.108073\pi\)
\(602\) −2.01113e13 + 8.50276e13i −0.254365 + 1.07542i
\(603\) 3.59552e11 + 3.59552e11i 0.00450998 + 0.00450998i
\(604\) −2.99856e13 + 5.98414e13i −0.373017 + 0.744418i
\(605\) −8.67823e13 8.67823e13i −1.07067 1.07067i
\(606\) 1.10015e14 6.79272e13i 1.34614 0.831152i
\(607\) 4.76946e13i 0.578796i 0.957209 + 0.289398i \(0.0934551\pi\)
−0.957209 + 0.289398i \(0.906545\pi\)
\(608\) −4.65874e13 1.07333e14i −0.560726 1.29186i
\(609\) 2.22840e14 2.66016
\(610\) −1.13525e14 1.83865e14i −1.34413 2.17696i
\(611\) −9.88284e11 + 9.88284e11i −0.0116058 + 0.0116058i
\(612\) −2.89254e11 1.44941e11i −0.00336916 0.00168824i
\(613\) −4.11673e13 + 4.11673e13i −0.475609 + 0.475609i −0.903724 0.428115i \(-0.859178\pi\)
0.428115 + 0.903724i \(0.359178\pi\)
\(614\) −5.77078e13 1.36494e13i −0.661291 0.156412i
\(615\) −4.10193e13 −0.466243
\(616\) −2.19234e13 1.83452e13i −0.247174 0.206832i
\(617\) 8.85732e13i 0.990551i −0.868736 0.495275i \(-0.835067\pi\)
0.868736 0.495275i \(-0.164933\pi\)
\(618\) 8.10027e13 + 1.91593e13i 0.898581 + 0.212538i
\(619\) −3.06918e13 3.06918e13i −0.337729 0.337729i 0.517783 0.855512i \(-0.326758\pi\)
−0.855512 + 0.517783i \(0.826758\pi\)
\(620\) 2.02027e14 6.71475e13i 2.20521 0.732945i
\(621\) −8.62687e12 8.62687e12i −0.0934104 0.0934104i
\(622\) 4.22727e13 + 6.84651e13i 0.454055 + 0.735389i
\(623\) 4.55219e13i 0.485043i
\(624\) 4.58068e13 + 6.12970e13i 0.484180 + 0.647913i
\(625\) 2.32534e13 0.243830
\(626\) −5.65747e13 + 3.49312e13i −0.588505 + 0.363363i
\(627\) 2.13928e13 2.13928e13i 0.220765 0.220765i
\(628\) 6.38564e13 2.12239e13i 0.653742 0.217284i
\(629\) 2.65685e12 2.65685e12i 0.0269844 0.0269844i
\(630\) −8.10005e12 + 3.42459e13i −0.0816178 + 0.345069i
\(631\) 1.20174e14 1.20133 0.600666 0.799500i \(-0.294902\pi\)
0.600666 + 0.799500i \(0.294902\pi\)
\(632\) −9.41909e12 1.06002e14i −0.0934165 1.05130i
\(633\) 8.20220e11i 0.00807071i
\(634\) 7.58131e12 3.20528e13i 0.0740113 0.312910i
\(635\) 2.21945e13 + 2.21945e13i 0.214970 + 0.214970i
\(636\) −1.42272e14 7.12906e13i −1.36721 0.685089i
\(637\) −7.95301e13 7.95301e13i −0.758288 0.758288i
\(638\) −2.98134e13 + 1.84078e13i −0.282039 + 0.174140i
\(639\) 1.06372e13i 0.0998439i
\(640\) −1.69621e14 9.33988e12i −1.57972 0.0869844i
\(641\) 3.91790e13 0.362046 0.181023 0.983479i \(-0.442059\pi\)
0.181023 + 0.983479i \(0.442059\pi\)
\(642\) −3.49478e13 5.66016e13i −0.320438 0.518983i
\(643\) −1.77735e13 + 1.77735e13i −0.161703 + 0.161703i −0.783321 0.621618i \(-0.786476\pi\)
0.621618 + 0.783321i \(0.286476\pi\)
\(644\) 1.11353e13 2.22225e13i 0.100525 0.200615i
\(645\) −9.49324e13 + 9.49324e13i −0.850385 + 0.850385i
\(646\) −4.03140e12 9.53532e11i −0.0358339 0.00847565i
\(647\) −1.55422e14 −1.37086 −0.685428 0.728140i \(-0.740385\pi\)
−0.685428 + 0.728140i \(0.740385\pi\)
\(648\) 1.27845e14 1.13600e13i 1.11895 0.0994271i
\(649\) 9.65818e12i 0.0838826i
\(650\) 1.28337e14 + 3.03552e13i 1.10608 + 0.261617i
\(651\) −2.01993e14 2.01993e14i −1.72755 1.72755i
\(652\) −8.90126e12 2.67812e13i −0.0755463 0.227296i
\(653\) 7.37037e13 + 7.37037e13i 0.620759 + 0.620759i 0.945726 0.324966i \(-0.105353\pi\)
−0.324966 + 0.945726i \(0.605353\pi\)
\(654\) −7.36765e13 1.19327e14i −0.615800 0.997353i
\(655\) 1.80663e14i 1.49852i
\(656\) −2.68109e13 + 2.00355e13i −0.220695 + 0.164923i
\(657\) 1.58329e12 0.0129340
\(658\) −3.54246e12 + 2.18724e12i −0.0287194 + 0.0177324i
\(659\) 1.11511e14 1.11511e14i 0.897203 0.897203i −0.0979852 0.995188i \(-0.531240\pi\)
0.995188 + 0.0979852i \(0.0312398\pi\)
\(660\) −1.38540e13 4.16825e13i −0.110626 0.332839i
\(661\) −9.52850e13 + 9.52850e13i −0.755122 + 0.755122i −0.975430 0.220308i \(-0.929294\pi\)
0.220308 + 0.975430i \(0.429294\pi\)
\(662\) −4.99974e13 + 2.11382e14i −0.393240 + 1.66257i
\(663\) 2.70925e12 0.0211486
\(664\) 5.36995e13 6.41734e13i 0.416035 0.497181i
\(665\) 4.50592e14i 3.46478i
\(666\) 6.34433e12 2.68230e13i 0.0484189 0.204708i
\(667\) −2.15430e13 2.15430e13i −0.163184 0.163184i
\(668\) 8.19259e13 1.63497e14i 0.615941 1.22921i
\(669\) 7.69847e13 + 7.69847e13i 0.574479 + 0.574479i
\(670\) 8.04307e12 4.96607e12i 0.0595728 0.0367823i
\(671\) 4.55902e13i 0.335165i
\(672\) 9.07572e13 + 2.09096e14i 0.662269 + 1.52580i
\(673\) −2.09843e14 −1.51991 −0.759956 0.649975i \(-0.774779\pi\)
−0.759956 + 0.649975i \(0.774779\pi\)
\(674\) −6.77102e13 1.09664e14i −0.486804 0.788431i
\(675\) 1.36343e14 1.36343e14i 0.973001 0.973001i
\(676\) 5.40416e13 + 2.70795e13i 0.382820 + 0.191826i
\(677\) −4.07331e13 + 4.07331e13i −0.286420 + 0.286420i −0.835663 0.549243i \(-0.814916\pi\)
0.549243 + 0.835663i \(0.314916\pi\)
\(678\) −4.32656e13 1.02334e13i −0.301991 0.0714288i
\(679\) 3.18064e14 2.20377
\(680\) −3.85979e12 + 4.61263e12i −0.0265472 + 0.0317252i
\(681\) 1.25455e14i 0.856552i
\(682\) 4.37100e13 + 1.03386e13i 0.296250 + 0.0700710i
\(683\) −5.74561e13 5.74561e13i −0.386574 0.386574i 0.486889 0.873464i \(-0.338131\pi\)
−0.873464 + 0.486889i \(0.838131\pi\)
\(684\) −2.88383e13 + 9.58497e12i −0.192615 + 0.0640192i
\(685\) 6.63049e13 + 6.63049e13i 0.439635 + 0.439635i
\(686\) −5.18991e13 8.40560e13i −0.341617 0.553284i
\(687\) 8.71395e13i 0.569418i
\(688\) −1.56804e13 + 1.08418e14i −0.101722 + 0.703333i
\(689\) 1.67866e14 1.08110
\(690\) 3.24976e13 2.00652e13i 0.207781 0.128291i
\(691\) −6.51646e13 + 6.51646e13i −0.413639 + 0.413639i −0.883004 0.469365i \(-0.844483\pi\)
0.469365 + 0.883004i \(0.344483\pi\)
\(692\) −7.96344e13 + 2.64680e13i −0.501846 + 0.166798i
\(693\) −5.24993e12 + 5.24993e12i −0.0328464 + 0.0328464i
\(694\) 1.88485e13 7.96888e13i 0.117079 0.494994i
\(695\) −1.35592e14 −0.836199
\(696\) 2.78294e14 2.47286e13i 1.70395 0.151409i
\(697\) 1.18501e12i 0.00720371i
\(698\) −2.67406e13 + 1.13055e14i −0.161396 + 0.682361i
\(699\) 1.46970e14 + 1.46970e14i 0.880729 + 0.880729i
\(700\) 3.51213e14 + 1.75988e14i 2.08968 + 1.04711i
\(701\) 6.77411e12 + 6.77411e12i 0.0400186 + 0.0400186i 0.726833 0.686814i \(-0.240991\pi\)
−0.686814 + 0.726833i \(0.740991\pi\)
\(702\) −1.00421e14 + 6.20034e13i −0.589032 + 0.363689i
\(703\) 3.52924e14i 2.05544i
\(704\) −2.94147e13 2.04775e13i −0.170099 0.118417i
\(705\) −6.39714e12 −0.0367316
\(706\) 9.37297e13 + 1.51805e14i 0.534385 + 0.865492i
\(707\) −2.87282e14 + 2.87282e14i −1.62634 + 1.62634i
\(708\) 3.45009e13 6.88524e13i 0.193939 0.387037i
\(709\) 1.98902e14 1.98902e14i 1.11022 1.11022i 0.117098 0.993120i \(-0.462641\pi\)
0.993120 0.117098i \(-0.0373593\pi\)
\(710\) −1.92435e14 4.55158e13i −1.06657 0.252273i
\(711\) −2.76395e13 −0.152119
\(712\) 5.05156e12 + 5.68499e13i 0.0276074 + 0.310692i
\(713\) 3.90552e13i 0.211949i
\(714\) 7.85360e12 + 1.85758e12i 0.0423231 + 0.0100105i
\(715\) 3.27635e13 + 3.27635e13i 0.175332 + 0.175332i
\(716\) 4.54952e13 + 1.36881e14i 0.241769 + 0.727410i
\(717\) −1.16468e14 1.16468e14i −0.614626 0.614626i
\(718\) −1.22481e14 1.98371e14i −0.641871 1.03958i
\(719\) 3.08820e14i 1.60717i 0.595193 + 0.803583i \(0.297076\pi\)
−0.595193 + 0.803583i \(0.702924\pi\)
\(720\) −6.31547e12 + 4.36668e13i −0.0326395 + 0.225678i
\(721\) −2.61553e14 −1.34240
\(722\) −1.64152e14 + 1.01353e14i −0.836680 + 0.516595i
\(723\) −1.21857e14 + 1.21857e14i −0.616823 + 0.616823i
\(724\) −6.53744e13 1.96692e14i −0.328636 0.988767i
\(725\) 3.40475e14 3.40475e14i 1.69979 1.69979i
\(726\) −4.75237e13 + 2.00924e14i −0.235628 + 0.996204i
\(727\) −2.19937e12 −0.0108299 −0.00541497 0.999985i \(-0.501724\pi\)
−0.00541497 + 0.999985i \(0.501724\pi\)
\(728\) −1.84405e14 1.54308e14i −0.901811 0.754624i
\(729\) 1.68279e14i 0.817321i
\(730\) 6.77479e12 2.86429e13i 0.0326800 0.138166i
\(731\) 2.74250e12 + 2.74250e12i 0.0131389 + 0.0131389i
\(732\) −1.62857e14 + 3.25009e14i −0.774910 + 1.54646i
\(733\) −1.10887e14 1.10887e14i −0.524037 0.524037i 0.394751 0.918788i \(-0.370831\pi\)
−0.918788 + 0.394751i \(0.870831\pi\)
\(734\) 1.08866e14 6.72174e13i 0.510988 0.315502i
\(735\) 5.14796e14i 2.39993i
\(736\) 1.14403e13 2.89882e13i 0.0529724 0.134224i
\(737\) 1.99431e12 0.00917183
\(738\) 4.56694e12 + 7.39663e12i 0.0208614 + 0.0337872i
\(739\) 1.16552e14 1.16552e14i 0.528807 0.528807i −0.391410 0.920216i \(-0.628013\pi\)
0.920216 + 0.391410i \(0.128013\pi\)
\(740\) −4.58101e14 2.29548e14i −2.06444 1.03446i
\(741\) 1.79943e14 1.79943e14i 0.805458 0.805458i
\(742\) 4.86612e14 + 1.15096e14i 2.16353 + 0.511732i
\(743\) −2.56883e13 −0.113447 −0.0567233 0.998390i \(-0.518065\pi\)
−0.0567233 + 0.998390i \(0.518065\pi\)
\(744\) −2.74674e14 2.29843e14i −1.20490 1.00825i
\(745\) 4.77260e14i 2.07957i
\(746\) −2.89944e14 6.85793e13i −1.25493 0.296824i
\(747\) −1.53674e13 1.53674e13i −0.0660691 0.0660691i
\(748\) −1.20417e12 + 4.00228e11i −0.00514255 + 0.00170923i
\(749\) 1.47804e14 + 1.47804e14i 0.627012 + 0.627012i
\(750\) 1.06139e14 + 1.71904e14i 0.447271 + 0.724402i
\(751\) 1.52208e13i 0.0637142i −0.999492 0.0318571i \(-0.989858\pi\)
0.999492 0.0318571i \(-0.0101422\pi\)
\(752\) −4.18128e12 + 3.12463e12i −0.0173868 + 0.0129930i
\(753\) 3.27758e14 1.35387
\(754\) −2.50771e14 + 1.54835e14i −1.02901 + 0.635348i
\(755\) 2.28516e14 2.28516e14i 0.931500 0.931500i
\(756\) −3.33614e14 + 1.10883e14i −1.35094 + 0.449010i
\(757\) −1.46843e14 + 1.46843e14i −0.590711 + 0.590711i −0.937823 0.347113i \(-0.887162\pi\)
0.347113 + 0.937823i \(0.387162\pi\)
\(758\) 8.24318e13 3.48510e14i 0.329419 1.39274i
\(759\) 8.05793e12 0.0319900
\(760\) 5.00021e13 + 5.62721e14i 0.197206 + 2.21935i
\(761\) 2.31998e14i 0.908992i −0.890749 0.454496i \(-0.849819\pi\)
0.890749 0.454496i \(-0.150181\pi\)
\(762\) 1.21542e13 5.13862e13i 0.0473097 0.200019i
\(763\) 3.11598e14 + 3.11598e14i 1.20496 + 1.20496i
\(764\) 1.07789e14 + 5.40113e13i 0.414101 + 0.207500i
\(765\) 1.10458e12 + 1.10458e12i 0.00421588 + 0.00421588i
\(766\) 3.27323e14 2.02101e14i 1.24118 0.766345i
\(767\) 8.12383e13i 0.306044i
\(768\) 1.36545e14 + 2.51058e14i 0.511059 + 0.939652i
\(769\) −4.30370e14 −1.60033 −0.800166 0.599779i \(-0.795255\pi\)
−0.800166 + 0.599779i \(0.795255\pi\)
\(770\) 7.25112e13 + 1.17439e14i 0.267887 + 0.433871i
\(771\) 9.67989e13 9.67989e13i 0.355303 0.355303i
\(772\) 1.50600e14 3.00547e14i 0.549208 1.09604i
\(773\) −3.24190e14 + 3.24190e14i −1.17463 + 1.17463i −0.193540 + 0.981092i \(0.561997\pi\)
−0.981092 + 0.193540i \(0.938003\pi\)
\(774\) 2.76877e13 + 6.54887e12i 0.0996741 + 0.0235755i
\(775\) −6.17244e14 −2.20774
\(776\) 3.97214e14 3.52956e13i 1.41161 0.125433i
\(777\) 6.87533e14i 2.42766i
\(778\) 3.37877e14 + 7.99166e13i 1.18539 + 0.280375i
\(779\) 7.87056e13 + 7.87056e13i 0.274358 + 0.274358i
\(780\) −1.16531e14 3.50606e14i −0.403615 1.21436i
\(781\) −2.95004e13 2.95004e13i −0.101525 0.101525i
\(782\) −5.79663e11 9.38824e11i −0.00198217 0.00321034i
\(783\) 4.30906e14i 1.46411i
\(784\) −2.51448e14 3.36480e14i −0.848923 1.13600i
\(785\) −3.24897e14 −1.08993
\(786\) 2.58608e14 1.59674e14i 0.862045 0.532256i
\(787\) −7.68397e13 + 7.68397e13i −0.254514 + 0.254514i −0.822818 0.568304i \(-0.807600\pi\)
0.568304 + 0.822818i \(0.307600\pi\)
\(788\) 4.90824e13 + 1.47674e14i 0.161545 + 0.486042i
\(789\) 8.67707e13 8.67707e13i 0.283784 0.283784i
\(790\) −1.18268e14 + 5.00021e14i −0.384354 + 1.62500i
\(791\) 1.39702e14 0.451149
\(792\) −5.97378e12 + 7.13895e12i −0.0191701 + 0.0229091i
\(793\) 3.83475e14i 1.22284i
\(794\) −8.13186e13 + 3.43804e14i −0.257684 + 1.08945i
\(795\) 5.43296e14 + 5.43296e14i 1.71081 + 1.71081i
\(796\) 2.41062e14 4.81080e14i 0.754335 1.50540i
\(797\) 2.08719e13 + 2.08719e13i 0.0649037 + 0.0649037i 0.738814 0.673910i \(-0.235386\pi\)
−0.673910 + 0.738814i \(0.735386\pi\)
\(798\) 6.44996e14 3.98243e14i 1.99316 1.23065i
\(799\) 1.84807e11i 0.000567524i
\(800\) 4.58141e14 + 1.80808e14i 1.39814 + 0.551782i
\(801\) 1.48234e13 0.0449557
\(802\) −3.04731e14 4.93544e14i −0.918428 1.48749i
\(803\) 4.39098e12 4.39098e12i 0.0131518 0.0131518i
\(804\) −1.42173e13 7.12407e12i −0.0423191 0.0212055i
\(805\) −8.48610e13 + 8.48610e13i −0.251032 + 0.251032i
\(806\) 3.67660e14 + 8.69612e13i 1.08086 + 0.255653i
\(807\) −2.23460e14 −0.652877
\(808\) −3.26892e14 + 3.90652e14i −0.949179 + 1.13431i
\(809\) 1.47836e14i 0.426616i −0.976985 0.213308i \(-0.931576\pi\)
0.976985 0.213308i \(-0.0684238\pi\)
\(810\) −6.03058e14 1.42639e14i −1.72955 0.409084i
\(811\) −2.86313e14 2.86313e14i −0.816088 0.816088i 0.169450 0.985539i \(-0.445801\pi\)
−0.985539 + 0.169450i \(0.945801\pi\)
\(812\) −8.33099e14 + 2.76897e14i −2.36002 + 0.784400i
\(813\) −1.94464e14 1.94464e14i −0.547502 0.547502i
\(814\) −5.67941e13 9.19840e13i −0.158921 0.257389i
\(815\) 1.36261e14i 0.378951i
\(816\) 1.00141e13 + 1.44832e12i 0.0276797 + 0.00400327i
\(817\) 3.64302e14 1.00081
\(818\) 1.51159e14 9.33309e13i 0.412732 0.254835i
\(819\) −4.41589e13 + 4.41589e13i −0.119839 + 0.119839i
\(820\) 1.53353e14 5.09697e13i 0.413639 0.137481i
\(821\) 3.34949e14 3.34949e14i 0.897971 0.897971i −0.0972851 0.995257i \(-0.531016\pi\)
0.995257 + 0.0972851i \(0.0310159\pi\)
\(822\) 3.63099e13 1.53513e14i 0.0967533 0.409060i
\(823\) −1.27724e14 −0.338277 −0.169138 0.985592i \(-0.554098\pi\)
−0.169138 + 0.985592i \(0.554098\pi\)
\(824\) −3.26640e14 + 2.90245e13i −0.859870 + 0.0764062i
\(825\) 1.27351e14i 0.333221i
\(826\) −5.57006e13 + 2.35495e14i −0.144864 + 0.612464i
\(827\) 1.89702e14 + 1.89702e14i 0.490392 + 0.490392i 0.908430 0.418037i \(-0.137282\pi\)
−0.418037 + 0.908430i \(0.637282\pi\)
\(828\) −7.23634e12 3.62602e12i −0.0185938 0.00931706i
\(829\) 3.38586e14 + 3.38586e14i 0.864761 + 0.864761i 0.991887 0.127126i \(-0.0405752\pi\)
−0.127126 + 0.991887i \(0.540575\pi\)
\(830\) −3.43765e14 + 2.12253e14i −0.872713 + 0.538843i
\(831\) 2.24684e14i 0.566979i
\(832\) −2.47417e14 1.72244e14i −0.620602 0.432042i
\(833\) −1.48719e13 −0.0370803
\(834\) 1.19839e14 + 1.94092e14i 0.297008 + 0.481035i
\(835\) −6.24347e14 + 6.24347e14i −1.53813 + 1.53813i
\(836\) −5.33959e13 + 1.06561e14i −0.130760 + 0.260955i
\(837\) 3.90594e14 3.90594e14i 0.950819 0.950819i
\(838\) 5.31718e12 + 1.25765e12i 0.0128665 + 0.00304327i
\(839\) 3.59634e14 0.865070 0.432535 0.901617i \(-0.357619\pi\)
0.432535 + 0.901617i \(0.357619\pi\)
\(840\) −9.74094e13 1.09624e15i −0.232919 2.62125i
\(841\) 6.55350e14i 1.55773i
\(842\) 6.28216e14 + 1.48590e14i 1.48439 + 0.351098i
\(843\) −1.49454e14 1.49454e14i −0.351051 0.351051i
\(844\) 1.01919e12 + 3.06643e12i 0.00237981 + 0.00716013i
\(845\) −2.06369e14 2.06369e14i −0.479028 0.479028i
\(846\) 7.12234e11 + 1.15354e12i 0.00164351 + 0.00266183i
\(847\) 6.48770e14i 1.48824i
\(848\) 6.20477e14 + 8.97387e13i 1.41497 + 0.204645i
\(849\) −6.09132e14 −1.38093
\(850\) 1.48376e13 9.16124e12i 0.0334402 0.0206471i
\(851\) 6.64670e13 6.64670e13i 0.148922 0.148922i
\(852\) 1.04925e14 + 3.15687e14i 0.233711 + 0.703167i
\(853\) 3.10861e13 3.10861e13i 0.0688368 0.0688368i −0.671850 0.740687i \(-0.734500\pi\)
0.740687 + 0.671850i \(0.234500\pi\)
\(854\) 2.62927e14 1.11162e15i 0.578824 2.44719i
\(855\) 1.46727e14 0.321129
\(856\) 2.00986e14 + 1.68182e14i 0.437318 + 0.365942i
\(857\) 4.02231e14i 0.870104i −0.900405 0.435052i \(-0.856730\pi\)
0.900405 0.435052i \(-0.143270\pi\)
\(858\) 1.79420e13 7.58562e13i 0.0385864 0.163138i
\(859\) −1.16040e14 1.16040e14i −0.248109 0.248109i 0.572085 0.820194i \(-0.306135\pi\)
−0.820194 + 0.572085i \(0.806135\pi\)
\(860\) 2.36948e14 4.72870e14i 0.503688 1.00519i
\(861\) −1.53327e14 1.53327e14i −0.324043 0.324043i
\(862\) −5.54295e14 + 3.42241e14i −1.16467 + 0.719110i
\(863\) 8.01235e14i 1.67381i −0.547348 0.836905i \(-0.684363\pi\)
0.547348 0.836905i \(-0.315637\pi\)
\(864\) −4.04329e14 + 1.75497e14i −0.839780 + 0.364503i
\(865\) 4.05174e14 0.836683
\(866\) 2.37448e13 + 3.84573e13i 0.0487506 + 0.0789567i
\(867\) −3.70272e14 + 3.70272e14i −0.755832 + 0.755832i
\(868\) 1.00615e15 + 5.04168e14i 2.04204 + 1.02324i
\(869\) −7.66536e13 + 7.66536e13i −0.154680 + 0.154680i
\(870\) −1.31274e15 3.10497e14i −2.63379 0.622961i
\(871\) 1.67749e13 0.0334632
\(872\) 4.23716e14 + 3.54560e14i 0.840412 + 0.703246i
\(873\) 1.03572e14i 0.204254i
\(874\) −1.00855e14 2.38548e13i −0.197760 0.0467755i
\(875\) −4.48892e14 4.48892e14i −0.875189 0.875189i
\(876\) −4.69883e13 + 1.56175e13i −0.0910898 + 0.0302754i
\(877\) 9.24183e13 + 9.24183e13i 0.178139 + 0.178139i 0.790544 0.612405i \(-0.209798\pi\)
−0.612405 + 0.790544i \(0.709798\pi\)
\(878\) −4.01729e13 6.50642e13i −0.0769947 0.124701i
\(879\) 5.20618e14i 0.992144i
\(880\) 1.03588e14 + 1.38618e14i 0.196288 + 0.262667i
\(881\) −1.31735e14 −0.248212 −0.124106 0.992269i \(-0.539606\pi\)
−0.124106 + 0.992269i \(0.539606\pi\)
\(882\) −9.28286e13 + 5.73156e13i −0.173916 + 0.107382i
\(883\) 1.99062e14 1.99062e14i 0.370839 0.370839i −0.496944 0.867783i \(-0.665544\pi\)
0.867783 + 0.496944i \(0.165544\pi\)
\(884\) −1.01287e13 + 3.36646e12i −0.0187625 + 0.00623608i
\(885\) −2.62927e14 + 2.62927e14i −0.484305 + 0.484305i
\(886\) −1.94373e14 + 8.21783e14i −0.356014 + 1.50518i
\(887\) 1.00259e15 1.82602 0.913012 0.407932i \(-0.133750\pi\)
0.913012 + 0.407932i \(0.133750\pi\)
\(888\) 7.62955e13 + 8.58625e14i 0.138177 + 1.55503i
\(889\) 1.65923e14i 0.298811i
\(890\) 6.34284e13 2.68166e14i 0.113588 0.480236i
\(891\) −9.24493e13 9.24493e13i −0.164632 0.164632i
\(892\) −3.83471e14 1.92152e14i −0.679060 0.340267i
\(893\) 1.22745e13 + 1.22745e13i 0.0216145 + 0.0216145i
\(894\) −6.83170e14 + 4.21812e14i −1.19630 + 0.738638i
\(895\) 6.96442e14i 1.21275i
\(896\) −5.99118e14 6.68942e14i −1.03746 1.15837i
\(897\) 6.77780e13 0.116715
\(898\) 1.57473e14 + 2.55044e14i 0.269665 + 0.436751i
\(899\) 9.75389e14 9.75389e14i 1.66104 1.66104i
\(900\) 5.73073e13 1.14366e14i 0.0970503 0.193680i
\(901\) 1.56953e13 1.56953e13i 0.0264329 0.0264329i
\(902\) 3.31790e13 + 7.84769e12i 0.0555687 + 0.0131434i
\(903\) −7.09699e14 −1.18205
\(904\) 1.74466e14 1.55027e13i 0.288981 0.0256782i
\(905\) 1.00075e15i 1.64848i
\(906\) −5.29076e14 1.25140e14i −0.866716 0.205001i
\(907\) −3.68117e14 3.68117e14i −0.599720 0.599720i 0.340518 0.940238i \(-0.389398\pi\)
−0.940238 + 0.340518i \(0.889398\pi\)
\(908\) 1.55888e14 + 4.69021e14i 0.252571 + 0.759912i
\(909\) 9.35483e13 + 9.35483e13i 0.150736 + 0.150736i
\(910\) 6.09916e14 + 9.87823e14i 0.977380 + 1.58297i
\(911\) 1.03238e15i 1.64530i 0.568545 + 0.822652i \(0.307506\pi\)
−0.568545 + 0.822652i \(0.692494\pi\)
\(912\) 7.61309e14 5.68920e14i 1.20667 0.901731i
\(913\) −8.52380e13 −0.134363
\(914\) −1.30623e14 + 8.06510e13i −0.204780 + 0.126438i
\(915\) 1.24111e15 1.24111e15i 1.93511 1.93511i
\(916\) 1.08278e14 + 3.25775e14i 0.167904 + 0.505174i
\(917\) −6.75303e14 + 6.75303e14i −1.04148 + 1.04148i
\(918\) −3.59201e12 + 1.51865e13i −0.00550964 + 0.0232940i
\(919\) 5.76490e14 0.879456 0.439728 0.898131i \(-0.355075\pi\)
0.439728 + 0.898131i \(0.355075\pi\)
\(920\) −9.65615e13 + 1.15396e14i −0.146509 + 0.175085i
\(921\) 4.81669e14i 0.726859i
\(922\) 2.97512e14 1.25784e15i 0.446530 1.88787i
\(923\) −2.48138e14 2.48138e14i −0.370412 0.370412i
\(924\) 1.04021e14 2.07591e14i 0.154440 0.308211i
\(925\) 1.05047e15 + 1.05047e15i 1.55123 + 1.55123i
\(926\) −6.89833e14 + 4.25927e14i −1.01319 + 0.625576i
\(927\) 8.51699e13i 0.124419i
\(928\) −1.00969e15 + 4.38251e14i −1.46706 + 0.636771i
\(929\) 1.00771e15 1.45633 0.728163 0.685404i \(-0.240374\pi\)
0.728163 + 0.685404i \(0.240374\pi\)
\(930\) 9.08478e14 + 1.47138e15i 1.30587 + 2.11499i
\(931\) −9.87764e14 + 9.87764e14i −1.41223 + 1.41223i
\(932\) −7.32076e14 3.66832e14i −1.04106 0.521661i
\(933\) −4.62147e14 + 4.62147e14i −0.653690 + 0.653690i
\(934\) 5.81428e14 + 1.37523e14i 0.818016 + 0.193482i
\(935\) 6.12671e12 0.00857372
\(936\) −5.02475e13 + 6.00482e13i −0.0699416 + 0.0835835i
\(937\) 5.50566e14i 0.762274i −0.924519 0.381137i \(-0.875533\pi\)
0.924519 0.381137i \(-0.124467\pi\)
\(938\) 4.86271e13 + 1.15016e13i 0.0669676 + 0.0158396i
\(939\) −3.81885e14 3.81885e14i −0.523124 0.523124i
\(940\) 2.39160e13 7.94895e12i 0.0325874 0.0108311i
\(941\) −8.84842e14 8.84842e14i −1.19927 1.19927i −0.974385 0.224887i \(-0.927799\pi\)
−0.224887 0.974385i \(-0.572201\pi\)
\(942\) 2.87151e14 + 4.65071e14i 0.387129 + 0.626996i
\(943\) 2.96456e13i 0.0397559i
\(944\) −4.34288e13 + 3.00278e14i −0.0579319 + 0.400556i
\(945\) 1.69740e15 2.25230
\(946\) 9.49495e13 5.86251e13i 0.125325 0.0773798i
\(947\) 5.25029e13 5.25029e13i 0.0689340 0.0689340i −0.671799 0.740733i \(-0.734478\pi\)
0.740733 + 0.671799i \(0.234478\pi\)
\(948\) 8.20279e14 2.72635e14i 1.07132 0.356074i
\(949\) 3.69340e13 3.69340e13i 0.0479839 0.0479839i
\(950\) 3.77011e14 1.59395e15i 0.487232 2.05995i
\(951\) 2.67534e14 0.343935
\(952\) −3.16693e13 + 2.81406e12i −0.0404998 + 0.00359873i
\(953\) 5.38588e14i 0.685160i −0.939489 0.342580i \(-0.888699\pi\)
0.939489 0.342580i \(-0.111301\pi\)
\(954\) 3.74791e13 1.58456e14i 0.0474293 0.200525i
\(955\) −4.11613e14 4.11613e14i −0.518170 0.518170i
\(956\) 5.80142e14 + 2.90701e14i 0.726516 + 0.364046i
\(957\) −2.01244e14 2.01244e14i −0.250705 0.250705i
\(958\) −2.26222e14 + 1.39677e14i −0.280354 + 0.173100i
\(959\) 4.95685e14i 0.611100i
\(960\) −2.43299e14 1.35823e15i −0.298390 1.66577i
\(961\) −9.48648e14 −1.15741
\(962\) −4.77714e14 7.73709e14i −0.579820 0.939079i
\(963\) 4.81296e13 4.81296e13i 0.0581140 0.0581140i
\(964\) 3.04152e14 6.06987e14i 0.365348 0.729113i
\(965\) −1.14770e15 + 1.14770e15i −1.37149 + 1.37149i
\(966\) 1.96476e14 + 4.64716e13i 0.233573 + 0.0552462i
\(967\) −9.06728e14 −1.07237 −0.536185 0.844100i \(-0.680135\pi\)
−0.536185 + 0.844100i \(0.680135\pi\)
\(968\) −7.19940e13 8.10216e14i −0.0847071 0.953288i
\(969\) 3.36489e13i 0.0393869i
\(970\) −1.87370e15 4.43178e14i −2.18193 0.516083i
\(971\) 6.50122e14 + 6.50122e14i 0.753180 + 0.753180i 0.975071 0.221892i \(-0.0712231\pi\)
−0.221892 + 0.975071i \(0.571223\pi\)
\(972\) 7.82945e13 + 2.35565e14i 0.0902402 + 0.271506i
\(973\) −5.06831e14 5.06831e14i −0.581165 0.581165i
\(974\) −1.79568e14 2.90830e14i −0.204849 0.331775i
\(975\) 1.07119e15i 1.21575i
\(976\) 2.05000e14 1.41742e15i 0.231475 1.60048i
\(977\) 1.05626e15 1.18658 0.593291 0.804988i \(-0.297829\pi\)
0.593291 + 0.804988i \(0.297829\pi\)
\(978\) 1.95050e14 1.20430e14i 0.217997 0.134599i
\(979\) 4.11102e13 4.11102e13i 0.0457126 0.0457126i
\(980\) 6.39675e14 + 1.92459e15i 0.707667 + 2.12916i
\(981\) 1.01466e14 1.01466e14i 0.111680 0.111680i
\(982\) 7.99391e13 3.37972e14i 0.0875391 0.370103i
\(983\) −3.10571e14 −0.338372 −0.169186 0.985584i \(-0.554114\pi\)
−0.169186 + 0.985584i \(0.554114\pi\)
\(984\) −2.08496e14 1.74467e14i −0.226008 0.189120i
\(985\) 7.51355e14i 0.810334i
\(986\) −8.96994e12 + 3.79237e13i −0.00962509 + 0.0406936i
\(987\) −2.39120e13 2.39120e13i −0.0255288 0.0255288i
\(988\) −4.49131e14 + 8.96317e14i −0.477077 + 0.952088i
\(989\) 6.86099e13 + 6.86099e13i 0.0725112 + 0.0725112i
\(990\) 3.82420e13 2.36120e13i 0.0402129 0.0248288i
\(991\) 7.42475e14i 0.776808i 0.921489 + 0.388404i \(0.126973\pi\)
−0.921489 + 0.388404i \(0.873027\pi\)
\(992\) 1.31248e15 + 5.17977e14i 1.36626 + 0.539203i
\(993\) −1.76434e15 −1.82741
\(994\) −5.49170e14 8.89439e14i −0.565946 0.916609i
\(995\) −1.83710e15 + 1.83710e15i −1.88373 + 1.88373i
\(996\) 6.07655e14 + 3.04487e14i 0.619955 + 0.310650i
\(997\) 1.23860e14 1.23860e14i 0.125735 0.125735i −0.641439 0.767174i \(-0.721662\pi\)
0.767174 + 0.641439i \(0.221662\pi\)
\(998\) −7.14418e14 1.68979e14i −0.721606 0.170679i
\(999\) −1.32948e15 −1.33615
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 16.11.f.a.3.7 38
4.3 odd 2 64.11.f.a.47.5 38
8.3 odd 2 128.11.f.a.95.15 38
8.5 even 2 128.11.f.b.95.5 38
16.3 odd 4 128.11.f.b.31.5 38
16.5 even 4 64.11.f.a.15.5 38
16.11 odd 4 inner 16.11.f.a.11.7 yes 38
16.13 even 4 128.11.f.a.31.15 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.11.f.a.3.7 38 1.1 even 1 trivial
16.11.f.a.11.7 yes 38 16.11 odd 4 inner
64.11.f.a.15.5 38 16.5 even 4
64.11.f.a.47.5 38 4.3 odd 2
128.11.f.a.31.15 38 16.13 even 4
128.11.f.a.95.15 38 8.3 odd 2
128.11.f.b.31.5 38 16.3 odd 4
128.11.f.b.95.5 38 8.5 even 2