Properties

Label 16.15.f.a.3.18
Level $16$
Weight $15$
Character 16.3
Analytic conductor $19.893$
Analytic rank $0$
Dimension $54$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,15,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, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.3");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 15 \)
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: \(19.8926349043\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(27\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.18
Character \(\chi\) \(=\) 16.3
Dual form 16.15.f.a.11.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(57.2769 - 114.470i) q^{2} +(-1878.56 + 1878.56i) q^{3} +(-9822.72 - 13113.0i) q^{4} +(35992.2 - 35992.2i) q^{5} +(107440. + 322636. i) q^{6} -784164. q^{7} +(-2.06365e6 + 373337. i) q^{8} -2.27499e6i q^{9} +O(q^{10})\) \(q+(57.2769 - 114.470i) q^{2} +(-1878.56 + 1878.56i) q^{3} +(-9822.72 - 13113.0i) q^{4} +(35992.2 - 35992.2i) q^{5} +(107440. + 322636. i) q^{6} -784164. q^{7} +(-2.06365e6 + 373337. i) q^{8} -2.27499e6i q^{9} +(-2.05850e6 - 6.18154e6i) q^{10} +(-16474.9 - 16474.9i) q^{11} +(4.30860e7 + 6.18090e6i) q^{12} +(5.02537e7 + 5.02537e7i) q^{13} +(-4.49145e7 + 8.97632e7i) q^{14} +1.35227e8i q^{15} +(-7.54638e7 + 2.57610e8i) q^{16} +7.06686e8 q^{17} +(-2.60418e8 - 1.30304e8i) q^{18} +(5.10756e8 - 5.10756e8i) q^{19} +(-8.25505e8 - 1.18423e8i) q^{20} +(1.47310e9 - 1.47310e9i) q^{21} +(-2.82950e6 + 942247. i) q^{22} -2.93388e8 q^{23} +(3.17536e9 - 4.57803e9i) q^{24} +3.51264e9i q^{25} +(8.63090e9 - 2.87416e9i) q^{26} +(-4.71139e9 - 4.71139e9i) q^{27} +(7.70263e9 + 1.02827e10i) q^{28} +(1.73768e10 + 1.73768e10i) q^{29} +(1.54794e10 + 7.74536e9i) q^{30} +1.23663e10i q^{31} +(2.51662e10 + 2.33934e10i) q^{32} +6.18979e7 q^{33} +(4.04767e10 - 8.08942e10i) q^{34} +(-2.82238e10 + 2.82238e10i) q^{35} +(-2.98318e10 + 2.23466e10i) q^{36} +(5.34347e10 - 5.34347e10i) q^{37} +(-2.92117e10 - 8.77207e10i) q^{38} -1.88809e11 q^{39} +(-6.08382e10 + 8.77126e10i) q^{40} +2.43823e11i q^{41} +(-8.42509e10 - 2.53000e11i) q^{42} +(3.08172e10 + 3.08172e10i) q^{43} +(-5.42062e7 + 3.77862e8i) q^{44} +(-8.18818e10 - 8.18818e10i) q^{45} +(-1.68043e10 + 3.35841e10i) q^{46} -2.82485e11i q^{47} +(-3.42172e11 - 6.25698e11i) q^{48} -6.33094e10 q^{49} +(4.02092e11 + 2.01193e11i) q^{50} +(-1.32755e12 + 1.32755e12i) q^{51} +(1.65346e11 - 1.15260e12i) q^{52} +(-1.05702e12 + 1.05702e12i) q^{53} +(-8.09165e11 + 2.69459e11i) q^{54} -1.18593e9 q^{55} +(1.61824e12 - 2.92757e11i) q^{56} +1.91897e12i q^{57} +(2.98440e12 - 9.93830e11i) q^{58} +(1.61480e12 + 1.61480e12i) q^{59} +(1.77322e12 - 1.32829e12i) q^{60} +(-3.15073e12 - 3.15073e12i) q^{61} +(1.41557e12 + 7.08304e11i) q^{62} +1.78396e12i q^{63} +(4.11929e12 - 1.54088e12i) q^{64} +3.61748e12 q^{65} +(3.54532e9 - 7.08545e9i) q^{66} +(-3.22657e12 + 3.22657e12i) q^{67} +(-6.94158e12 - 9.26674e12i) q^{68} +(5.51146e11 - 5.51146e11i) q^{69} +(1.61420e12 + 4.84734e12i) q^{70} +1.39599e13 q^{71} +(8.49337e11 + 4.69479e12i) q^{72} +1.30447e12i q^{73} +(-3.05609e12 - 9.17723e12i) q^{74} +(-6.59870e12 - 6.59870e12i) q^{75} +(-1.17145e13 - 1.68051e12i) q^{76} +(1.29190e10 + 1.29190e10i) q^{77} +(-1.08144e13 + 2.16129e13i) q^{78} -1.10675e13i q^{79} +(6.55583e12 + 1.19880e13i) q^{80} +2.85824e13 q^{81} +(2.79104e13 + 1.39654e13i) q^{82} +(-3.46972e13 + 3.46972e13i) q^{83} +(-3.37865e13 - 4.84684e12i) q^{84} +(2.54351e13 - 2.54351e13i) q^{85} +(5.29276e12 - 1.76253e12i) q^{86} -6.52865e13 q^{87} +(4.01491e10 + 2.78477e10i) q^{88} -2.40266e13i q^{89} +(-1.40629e13 + 4.68307e12i) q^{90} +(-3.94071e13 - 3.94071e13i) q^{91} +(2.88187e12 + 3.84718e12i) q^{92} +(-2.32309e13 - 2.32309e13i) q^{93} +(-3.23361e13 - 1.61799e13i) q^{94} -3.67664e13i q^{95} +(-9.12221e13 + 3.33035e12i) q^{96} +1.49315e14 q^{97} +(-3.62616e12 + 7.24702e12i) q^{98} +(-3.74801e10 + 3.74801e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q - 2 q^{2} - 2 q^{3} + 15832 q^{4} - 2 q^{5} - 182528 q^{6} - 4 q^{7} + 2748484 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 54 q - 2 q^{2} - 2 q^{3} + 15832 q^{4} - 2 q^{5} - 182528 q^{6} - 4 q^{7} + 2748484 q^{8} + 16861596 q^{10} - 10455538 q^{11} - 87110828 q^{12} - 2 q^{13} + 66965260 q^{14} - 1059602728 q^{16} - 4 q^{17} + 438192046 q^{18} + 702532062 q^{19} + 1755464396 q^{20} - 9565940 q^{21} - 4795498204 q^{22} + 9748846012 q^{23} + 6975250608 q^{24} - 8671243576 q^{26} - 17865634112 q^{27} - 1297033864 q^{28} - 13109213938 q^{29} + 11736190852 q^{30} - 33545826552 q^{32} - 4 q^{33} - 50990884972 q^{34} + 125535560540 q^{35} + 60739632140 q^{36} + 115688878030 q^{37} - 763264561040 q^{38} + 207890167484 q^{39} + 1298710786600 q^{40} - 1441334806824 q^{42} + 834144712302 q^{43} - 1390640237388 q^{44} + 12216597186 q^{45} + 2618424802780 q^{46} - 4460553354264 q^{48} + 4069338437090 q^{49} - 14467226554 q^{50} - 109367594148 q^{51} + 700335676036 q^{52} - 1638253831762 q^{53} - 6106962841312 q^{54} + 7743608133372 q^{55} + 892124789080 q^{56} - 3111214006280 q^{58} - 2886464056530 q^{59} - 5948471456800 q^{60} + 6325590293982 q^{61} + 4387920975408 q^{62} - 11796533376704 q^{64} + 4831417084012 q^{65} + 3599619796132 q^{66} + 16035979669214 q^{67} - 11417990783952 q^{68} + 13777251815788 q^{69} + 6360571783424 q^{70} - 23491285382916 q^{71} - 17358886385420 q^{72} + 17391872660764 q^{74} + 38233839801842 q^{75} + 8965870021732 q^{76} - 9967029629748 q^{77} - 102277039258452 q^{78} + 184151019521512 q^{80} - 96590901476506 q^{81} - 60118295271632 q^{82} - 44676337597762 q^{83} - 30278459356760 q^{84} - 65266064531252 q^{85} + 200817997017700 q^{86} - 19584321079236 q^{87} - 98329880319368 q^{88} + 105728657951480 q^{90} + 12075497546300 q^{91} + 263822607742360 q^{92} - 149536300814816 q^{93} + 36585390208368 q^{94} - 124834847268944 q^{96} - 4 q^{97} + 73723998799370 q^{98} - 130415167656994 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 57.2769 114.470i 0.447476 0.894296i
\(3\) −1878.56 + 1878.56i −0.858966 + 0.858966i −0.991216 0.132251i \(-0.957780\pi\)
0.132251 + 0.991216i \(0.457780\pi\)
\(4\) −9822.72 13113.0i −0.599531 0.800351i
\(5\) 35992.2 35992.2i 0.460700 0.460700i −0.438185 0.898885i \(-0.644379\pi\)
0.898885 + 0.438185i \(0.144379\pi\)
\(6\) 107440. + 322636.i 0.383804 + 1.15254i
\(7\) −784164. −0.952184 −0.476092 0.879396i \(-0.657947\pi\)
−0.476092 + 0.879396i \(0.657947\pi\)
\(8\) −2.06365e6 + 373337.i −0.984027 + 0.178021i
\(9\) 2.27499e6i 0.475643i
\(10\) −2.05850e6 6.18154e6i −0.205850 0.618154i
\(11\) −16474.9 16474.9i −0.000845421 0.000845421i 0.706684 0.707529i \(-0.250190\pi\)
−0.707529 + 0.706684i \(0.750190\pi\)
\(12\) 4.30860e7 + 6.18090e6i 1.20245 + 0.172498i
\(13\) 5.02537e7 + 5.02537e7i 0.800874 + 0.800874i 0.983232 0.182358i \(-0.0583731\pi\)
−0.182358 + 0.983232i \(0.558373\pi\)
\(14\) −4.49145e7 + 8.97632e7i −0.426079 + 0.851534i
\(15\) 1.35227e8i 0.791450i
\(16\) −7.54638e7 + 2.57610e8i −0.281125 + 0.959671i
\(17\) 7.06686e8 1.72220 0.861100 0.508435i \(-0.169776\pi\)
0.861100 + 0.508435i \(0.169776\pi\)
\(18\) −2.60418e8 1.30304e8i −0.425366 0.212839i
\(19\) 5.10756e8 5.10756e8i 0.571397 0.571397i −0.361122 0.932519i \(-0.617606\pi\)
0.932519 + 0.361122i \(0.117606\pi\)
\(20\) −8.25505e8 1.18423e8i −0.644926 0.0925178i
\(21\) 1.47310e9 1.47310e9i 0.817893 0.817893i
\(22\) −2.82950e6 + 942247.i −0.00113436 + 0.000377751i
\(23\) −2.93388e8 −0.0861683 −0.0430841 0.999071i \(-0.513718\pi\)
−0.0430841 + 0.999071i \(0.513718\pi\)
\(24\) 3.17536e9 4.57803e9i 0.692331 0.998159i
\(25\) 3.51264e9i 0.575511i
\(26\) 8.63090e9 2.87416e9i 1.07459 0.357847i
\(27\) −4.71139e9 4.71139e9i −0.450404 0.450404i
\(28\) 7.70263e9 + 1.02827e10i 0.570864 + 0.762082i
\(29\) 1.73768e10 + 1.73768e10i 1.00736 + 1.00736i 0.999973 + 0.00738348i \(0.00235026\pi\)
0.00738348 + 0.999973i \(0.497650\pi\)
\(30\) 1.54794e10 + 7.74536e9i 0.707791 + 0.354155i
\(31\) 1.23663e10i 0.449478i 0.974419 + 0.224739i \(0.0721530\pi\)
−0.974419 + 0.224739i \(0.927847\pi\)
\(32\) 2.51662e10 + 2.33934e10i 0.732434 + 0.680838i
\(33\) 6.18979e7 0.00145237
\(34\) 4.04767e10 8.08942e10i 0.770643 1.54016i
\(35\) −2.82238e10 + 2.82238e10i −0.438671 + 0.438671i
\(36\) −2.98318e10 + 2.23466e10i −0.380682 + 0.285163i
\(37\) 5.34347e10 5.34347e10i 0.562874 0.562874i −0.367249 0.930123i \(-0.619700\pi\)
0.930123 + 0.367249i \(0.119700\pi\)
\(38\) −2.92117e10 8.77207e10i −0.255312 0.766685i
\(39\) −1.88809e11 −1.37585
\(40\) −6.08382e10 + 8.77126e10i −0.371327 + 0.535355i
\(41\) 2.43823e11i 1.25195i 0.779842 + 0.625976i \(0.215299\pi\)
−0.779842 + 0.625976i \(0.784701\pi\)
\(42\) −8.42509e10 2.53000e11i −0.365451 1.09743i
\(43\) 3.08172e10 + 3.08172e10i 0.113374 + 0.113374i 0.761518 0.648144i \(-0.224454\pi\)
−0.648144 + 0.761518i \(0.724454\pi\)
\(44\) −5.42062e7 + 3.77862e8i −0.000169777 + 0.00118349i
\(45\) −8.18818e10 8.18818e10i −0.219129 0.219129i
\(46\) −1.68043e10 + 3.35841e10i −0.0385582 + 0.0770600i
\(47\) 2.82485e11i 0.557584i −0.960351 0.278792i \(-0.910066\pi\)
0.960351 0.278792i \(-0.0899341\pi\)
\(48\) −3.42172e11 6.25698e11i −0.582848 1.06580i
\(49\) −6.33094e10 −0.0933460
\(50\) 4.02092e11 + 2.01193e11i 0.514678 + 0.257527i
\(51\) −1.32755e12 + 1.32755e12i −1.47931 + 1.47931i
\(52\) 1.65346e11 1.15260e12i 0.160832 1.12113i
\(53\) −1.05702e12 + 1.05702e12i −0.899816 + 0.899816i −0.995420 0.0956031i \(-0.969522\pi\)
0.0956031 + 0.995420i \(0.469522\pi\)
\(54\) −8.09165e11 + 2.69459e11i −0.604340 + 0.201250i
\(55\) −1.18593e9 −0.000778970
\(56\) 1.61824e12 2.92757e11i 0.936974 0.169509i
\(57\) 1.91897e12i 0.981621i
\(58\) 2.98440e12 9.93830e11i 1.35164 0.450108i
\(59\) 1.61480e12 + 1.61480e12i 0.648867 + 0.648867i 0.952719 0.303852i \(-0.0982728\pi\)
−0.303852 + 0.952719i \(0.598273\pi\)
\(60\) 1.77322e12 1.32829e12i 0.633438 0.474499i
\(61\) −3.15073e12 3.15073e12i −1.00254 1.00254i −0.999997 0.00254608i \(-0.999190\pi\)
−0.00254608 0.999997i \(-0.500810\pi\)
\(62\) 1.41557e12 + 7.08304e11i 0.401967 + 0.201131i
\(63\) 1.78396e12i 0.452900i
\(64\) 4.11929e12 1.54088e12i 0.936617 0.350355i
\(65\) 3.61748e12 0.737925
\(66\) 3.54532e9 7.08545e9i 0.000649902 0.00129885i
\(67\) −3.22657e12 + 3.22657e12i −0.532374 + 0.532374i −0.921278 0.388904i \(-0.872854\pi\)
0.388904 + 0.921278i \(0.372854\pi\)
\(68\) −6.94158e12 9.26674e12i −1.03251 1.37837i
\(69\) 5.51146e11 5.51146e11i 0.0740156 0.0740156i
\(70\) 1.61420e12 + 4.84734e12i 0.196007 + 0.588596i
\(71\) 1.39599e13 1.53488 0.767441 0.641120i \(-0.221530\pi\)
0.767441 + 0.641120i \(0.221530\pi\)
\(72\) 8.49337e11 + 4.69479e12i 0.0846745 + 0.468046i
\(73\) 1.30447e12i 0.118079i 0.998256 + 0.0590395i \(0.0188038\pi\)
−0.998256 + 0.0590395i \(0.981196\pi\)
\(74\) −3.05609e12 9.17723e12i −0.251504 0.755248i
\(75\) −6.59870e12 6.59870e12i −0.494344 0.494344i
\(76\) −1.17145e13 1.68051e12i −0.799889 0.114748i
\(77\) 1.29190e10 + 1.29190e10i 0.000804996 + 0.000804996i
\(78\) −1.08144e13 + 2.16129e13i −0.615658 + 1.23041i
\(79\) 1.10675e13i 0.576316i −0.957583 0.288158i \(-0.906957\pi\)
0.957583 0.288158i \(-0.0930428\pi\)
\(80\) 6.55583e12 + 1.19880e13i 0.312606 + 0.571634i
\(81\) 2.85824e13 1.24941
\(82\) 2.79104e13 + 1.39654e13i 1.11962 + 0.560218i
\(83\) −3.46972e13 + 3.46972e13i −1.27864 + 1.27864i −0.337208 + 0.941430i \(0.609482\pi\)
−0.941430 + 0.337208i \(0.890518\pi\)
\(84\) −3.37865e13 4.84684e12i −1.14495 0.164249i
\(85\) 2.54351e13 2.54351e13i 0.793418 0.793418i
\(86\) 5.29276e12 1.76253e12i 0.152122 0.0506579i
\(87\) −6.52865e13 −1.73057
\(88\) 4.01491e10 + 2.78477e10i 0.000982419 + 0.000681414i
\(89\) 2.40266e13i 0.543203i −0.962410 0.271601i \(-0.912447\pi\)
0.962410 0.271601i \(-0.0875532\pi\)
\(90\) −1.40629e13 + 4.68307e12i −0.294021 + 0.0979113i
\(91\) −3.94071e13 3.94071e13i −0.762579 0.762579i
\(92\) 2.88187e12 + 3.84718e12i 0.0516606 + 0.0689649i
\(93\) −2.32309e13 2.32309e13i −0.386086 0.386086i
\(94\) −3.23361e13 1.61799e13i −0.498646 0.249505i
\(95\) 3.67664e13i 0.526485i
\(96\) −9.12221e13 + 3.33035e12i −1.21395 + 0.0443192i
\(97\) 1.49315e14 1.84800 0.924001 0.382390i \(-0.124899\pi\)
0.924001 + 0.382390i \(0.124899\pi\)
\(98\) −3.62616e12 + 7.24702e12i −0.0417700 + 0.0834790i
\(99\) −3.74801e10 + 3.74801e10i −0.000402119 + 0.000402119i
\(100\) 4.60611e13 3.45037e13i 0.460611 0.345037i
\(101\) 8.95534e13 8.95534e13i 0.835281 0.835281i −0.152953 0.988234i \(-0.548878\pi\)
0.988234 + 0.152953i \(0.0488782\pi\)
\(102\) 7.59266e13 + 2.28002e14i 0.660987 + 1.98490i
\(103\) 8.59595e13 0.698929 0.349465 0.936950i \(-0.386364\pi\)
0.349465 + 0.936950i \(0.386364\pi\)
\(104\) −1.22468e14 8.49446e13i −0.930654 0.645509i
\(105\) 1.06040e14i 0.753606i
\(106\) 6.04544e13 + 1.81541e14i 0.402057 + 1.20735i
\(107\) 1.72707e14 + 1.72707e14i 1.07553 + 1.07553i 0.996904 + 0.0786277i \(0.0250538\pi\)
0.0786277 + 0.996904i \(0.474946\pi\)
\(108\) −1.55016e13 + 1.08059e14i −0.0904502 + 0.630513i
\(109\) 1.33559e14 + 1.33559e14i 0.730611 + 0.730611i 0.970741 0.240130i \(-0.0771900\pi\)
−0.240130 + 0.970741i \(0.577190\pi\)
\(110\) −6.79265e10 + 1.35753e11i −0.000348570 + 0.000696630i
\(111\) 2.00760e14i 0.966979i
\(112\) 5.91760e13 2.02008e14i 0.267682 0.913783i
\(113\) −2.83537e14 −1.20520 −0.602601 0.798043i \(-0.705869\pi\)
−0.602601 + 0.798043i \(0.705869\pi\)
\(114\) 2.19664e14 + 1.09912e14i 0.877860 + 0.439251i
\(115\) −1.05597e13 + 1.05597e13i −0.0396977 + 0.0396977i
\(116\) 5.71737e13 3.98548e14i 0.202297 1.41018i
\(117\) 1.14326e14 1.14326e14i 0.380930 0.380930i
\(118\) 2.77337e14 9.23556e13i 0.870632 0.289927i
\(119\) −5.54158e14 −1.63985
\(120\) −5.04851e13 2.79061e14i −0.140895 0.778808i
\(121\) 3.79749e14i 0.999999i
\(122\) −5.41128e14 + 1.80200e14i −1.34518 + 0.447957i
\(123\) −4.58036e14 4.58036e14i −1.07538 1.07538i
\(124\) 1.62159e14 1.21471e14i 0.359741 0.269476i
\(125\) 3.46106e14 + 3.46106e14i 0.725838 + 0.725838i
\(126\) 2.04210e14 + 1.02180e14i 0.405027 + 0.202662i
\(127\) 9.21338e14i 1.72899i 0.502640 + 0.864496i \(0.332362\pi\)
−0.502640 + 0.864496i \(0.667638\pi\)
\(128\) 5.95559e13 5.59791e14i 0.105793 0.994388i
\(129\) −1.15784e14 −0.194769
\(130\) 2.07198e14 4.14092e14i 0.330203 0.659923i
\(131\) −5.63852e14 + 5.63852e14i −0.851660 + 0.851660i −0.990338 0.138678i \(-0.955715\pi\)
0.138678 + 0.990338i \(0.455715\pi\)
\(132\) −6.08006e11 8.11665e11i −0.000870744 0.00116241i
\(133\) −4.00516e14 + 4.00516e14i −0.544075 + 0.544075i
\(134\) 1.84537e14 + 5.54152e14i 0.237876 + 0.714324i
\(135\) −3.39146e14 −0.415002
\(136\) −1.45835e15 + 2.63832e14i −1.69469 + 0.306588i
\(137\) 1.42077e14i 0.156848i −0.996920 0.0784241i \(-0.975011\pi\)
0.996920 0.0784241i \(-0.0249888\pi\)
\(138\) −3.15217e13 9.46576e13i −0.0330717 0.0993120i
\(139\) −3.84494e14 3.84494e14i −0.383518 0.383518i 0.488850 0.872368i \(-0.337417\pi\)
−0.872368 + 0.488850i \(0.837417\pi\)
\(140\) 6.47331e14 + 9.28629e13i 0.614088 + 0.0880939i
\(141\) 5.30665e14 + 5.30665e14i 0.478946 + 0.478946i
\(142\) 7.99581e14 1.59799e15i 0.686822 1.37264i
\(143\) 1.65584e12i 0.00135415i
\(144\) 5.86059e14 + 1.71679e14i 0.456461 + 0.133715i
\(145\) 1.25086e15 0.928178
\(146\) 1.49322e14 + 7.47157e13i 0.105598 + 0.0528374i
\(147\) 1.18930e14 1.18930e14i 0.0801810 0.0801810i
\(148\) −1.22556e15 1.75813e14i −0.787957 0.113036i
\(149\) −4.30247e14 + 4.30247e14i −0.263884 + 0.263884i −0.826630 0.562746i \(-0.809745\pi\)
0.562746 + 0.826630i \(0.309745\pi\)
\(150\) −1.13331e15 + 3.77400e14i −0.663297 + 0.220883i
\(151\) 1.74543e15 0.975134 0.487567 0.873085i \(-0.337884\pi\)
0.487567 + 0.873085i \(0.337884\pi\)
\(152\) −8.63339e14 + 1.24471e15i −0.460549 + 0.663991i
\(153\) 1.60770e15i 0.819154i
\(154\) 2.21880e12 7.38877e11i 0.00108012 0.000359689i
\(155\) 4.45091e14 + 4.45091e14i 0.207075 + 0.207075i
\(156\) 1.85462e15 + 2.47584e15i 0.824863 + 1.10116i
\(157\) 2.73887e14 + 2.73887e14i 0.116486 + 0.116486i 0.762947 0.646461i \(-0.223752\pi\)
−0.646461 + 0.762947i \(0.723752\pi\)
\(158\) −1.26690e15 6.33913e14i −0.515397 0.257887i
\(159\) 3.97136e15i 1.54582i
\(160\) 1.74777e15 6.38078e13i 0.651094 0.0237703i
\(161\) 2.30064e14 0.0820481
\(162\) 1.63711e15 3.27183e15i 0.559079 1.11734i
\(163\) −2.25180e15 + 2.25180e15i −0.736575 + 0.736575i −0.971913 0.235339i \(-0.924380\pi\)
0.235339 + 0.971913i \(0.424380\pi\)
\(164\) 3.19724e15 2.39501e15i 1.00200 0.750585i
\(165\) 2.22784e12 2.22784e12i 0.000669109 0.000669109i
\(166\) 1.98444e15 + 5.95913e15i 0.571322 + 1.71564i
\(167\) 6.68105e15 1.84429 0.922146 0.386843i \(-0.126434\pi\)
0.922146 + 0.386843i \(0.126434\pi\)
\(168\) −2.49000e15 + 3.58993e15i −0.659227 + 0.950431i
\(169\) 1.11348e15i 0.282798i
\(170\) −1.45471e15 4.36841e15i −0.354515 1.06459i
\(171\) −1.16196e15 1.16196e15i −0.271781 0.271781i
\(172\) 1.01396e14 7.06814e14i 0.0227678 0.158711i
\(173\) −3.67853e15 3.67853e15i −0.793143 0.793143i 0.188861 0.982004i \(-0.439520\pi\)
−0.982004 + 0.188861i \(0.939520\pi\)
\(174\) −3.73941e15 + 7.47334e15i −0.774387 + 1.54764i
\(175\) 2.75449e15i 0.547993i
\(176\) 5.48734e12 3.00083e12i 0.00104899 0.000573657i
\(177\) −6.06701e15 −1.11471
\(178\) −2.75032e15 1.37617e15i −0.485784 0.243070i
\(179\) 4.56736e15 4.56736e15i 0.775701 0.775701i −0.203396 0.979097i \(-0.565198\pi\)
0.979097 + 0.203396i \(0.0651978\pi\)
\(180\) −2.69410e14 + 1.87801e15i −0.0440055 + 0.306755i
\(181\) −5.55878e15 + 5.55878e15i −0.873433 + 0.873433i −0.992845 0.119412i \(-0.961899\pi\)
0.119412 + 0.992845i \(0.461899\pi\)
\(182\) −6.76805e15 + 2.25381e15i −1.02321 + 0.340736i
\(183\) 1.18377e16 1.72230
\(184\) 6.05451e14 1.09533e14i 0.0847919 0.0153398i
\(185\) 3.84646e15i 0.518632i
\(186\) −3.98982e15 + 1.32864e15i −0.518040 + 0.172511i
\(187\) −1.16425e13 1.16425e13i −0.00145598 0.00145598i
\(188\) −3.70422e15 + 2.77477e15i −0.446263 + 0.334289i
\(189\) 3.69450e15 + 3.69450e15i 0.428868 + 0.428868i
\(190\) −4.20865e15 2.10587e15i −0.470834 0.235589i
\(191\) 4.26834e15i 0.460283i −0.973157 0.230142i \(-0.926081\pi\)
0.973157 0.230142i \(-0.0739190\pi\)
\(192\) −4.84369e15 + 1.06329e16i −0.503579 + 1.10546i
\(193\) −2.03043e15 −0.203557 −0.101779 0.994807i \(-0.532453\pi\)
−0.101779 + 0.994807i \(0.532453\pi\)
\(194\) 8.55232e15 1.70921e16i 0.826936 1.65266i
\(195\) −6.79564e15 + 6.79564e15i −0.633852 + 0.633852i
\(196\) 6.21871e14 + 8.30173e14i 0.0559638 + 0.0747096i
\(197\) −7.44610e15 + 7.44610e15i −0.646644 + 0.646644i −0.952180 0.305536i \(-0.901164\pi\)
0.305536 + 0.952180i \(0.401164\pi\)
\(198\) 2.14360e12 + 6.43709e12i 0.000179675 + 0.000539552i
\(199\) 1.22623e16 0.992202 0.496101 0.868265i \(-0.334765\pi\)
0.496101 + 0.868265i \(0.334765\pi\)
\(200\) −1.31140e15 7.24888e15i −0.102453 0.566319i
\(201\) 1.21226e16i 0.914582i
\(202\) −5.12183e15 1.53805e16i −0.373221 1.12076i
\(203\) −1.36262e16 1.36262e16i −0.959188 0.959188i
\(204\) 3.04482e16 + 4.36795e15i 2.07086 + 0.297075i
\(205\) 8.77572e15 + 8.77572e15i 0.576774 + 0.576774i
\(206\) 4.92349e15 9.83977e15i 0.312754 0.625050i
\(207\) 6.67454e14i 0.0409854i
\(208\) −1.67382e16 + 9.15350e15i −0.993721 + 0.543430i
\(209\) −1.68293e13 −0.000966142
\(210\) −1.21384e16 6.07364e15i −0.673947 0.337220i
\(211\) −1.80881e16 + 1.80881e16i −0.971439 + 0.971439i −0.999603 0.0281643i \(-0.991034\pi\)
0.0281643 + 0.999603i \(0.491034\pi\)
\(212\) 2.42436e16 + 3.47786e15i 1.25964 + 0.180701i
\(213\) −2.62245e16 + 2.62245e16i −1.31841 + 1.31841i
\(214\) 2.96619e16 9.87763e15i 1.44312 0.480570i
\(215\) 2.21836e15 0.104463
\(216\) 1.14816e16 + 7.96374e15i 0.523391 + 0.363028i
\(217\) 9.69723e15i 0.427986i
\(218\) 2.29382e16 7.63862e15i 0.980313 0.326452i
\(219\) −2.45051e15 2.45051e15i −0.101426 0.101426i
\(220\) 1.16491e13 + 1.55511e13i 0.000467017 + 0.000623450i
\(221\) 3.55135e16 + 3.55135e16i 1.37927 + 1.37927i
\(222\) 2.29810e16 + 1.14989e16i 0.864765 + 0.432699i
\(223\) 3.86073e16i 1.40778i 0.710308 + 0.703891i \(0.248556\pi\)
−0.710308 + 0.703891i \(0.751444\pi\)
\(224\) −1.97345e16 1.83443e16i −0.697412 0.648283i
\(225\) 7.99122e15 0.273738
\(226\) −1.62401e16 + 3.24564e16i −0.539298 + 1.07781i
\(227\) 1.43584e16 1.43584e16i 0.462302 0.462302i −0.437107 0.899409i \(-0.643997\pi\)
0.899409 + 0.437107i \(0.143997\pi\)
\(228\) 2.51633e16 1.88495e16i 0.785642 0.588512i
\(229\) 1.27304e16 1.27304e16i 0.385474 0.385474i −0.487596 0.873070i \(-0.662126\pi\)
0.873070 + 0.487596i \(0.162126\pi\)
\(230\) 6.03940e14 + 1.81359e15i 0.0177378 + 0.0532653i
\(231\) −4.85381e13 −0.00138293
\(232\) −4.23470e16 2.93722e16i −1.17060 0.811935i
\(233\) 4.24872e16i 1.13964i −0.821770 0.569819i \(-0.807013\pi\)
0.821770 0.569819i \(-0.192987\pi\)
\(234\) −6.53868e15 1.96352e16i −0.170208 0.511122i
\(235\) −1.01673e16 1.01673e16i −0.256879 0.256879i
\(236\) 5.31309e15 3.70366e16i 0.130306 0.908338i
\(237\) 2.07910e16 + 2.07910e16i 0.495035 + 0.495035i
\(238\) −3.17404e16 + 6.34344e16i −0.733794 + 1.46651i
\(239\) 3.23510e16i 0.726277i −0.931735 0.363138i \(-0.881705\pi\)
0.931735 0.363138i \(-0.118295\pi\)
\(240\) −3.48357e16 1.02047e16i −0.759532 0.222496i
\(241\) −7.08657e16 −1.50078 −0.750389 0.660996i \(-0.770134\pi\)
−0.750389 + 0.660996i \(0.770134\pi\)
\(242\) −4.34699e16 2.17509e16i −0.894295 0.447475i
\(243\) −3.11593e16 + 3.11593e16i −0.622793 + 0.622793i
\(244\) −1.03667e16 + 7.22642e16i −0.201331 + 1.40344i
\(245\) −2.27864e15 + 2.27864e15i −0.0430045 + 0.0430045i
\(246\) −7.86661e16 + 2.61965e16i −1.44292 + 0.480504i
\(247\) 5.13347e16 0.915234
\(248\) −4.61680e15 2.55198e16i −0.0800165 0.442299i
\(249\) 1.30361e17i 2.19661i
\(250\) 5.94427e16 1.97949e16i 0.973909 0.324319i
\(251\) −4.80957e16 4.80957e16i −0.766285 0.766285i 0.211165 0.977450i \(-0.432274\pi\)
−0.977450 + 0.211165i \(0.932274\pi\)
\(252\) 2.33930e16 1.75234e16i 0.362479 0.271528i
\(253\) 4.83353e12 + 4.83353e12i 7.28485e−5 + 7.28485e-5i
\(254\) 1.05465e17 + 5.27713e16i 1.54623 + 0.773681i
\(255\) 9.55628e16i 1.36304i
\(256\) −6.06680e16 3.88804e16i −0.841938 0.539574i
\(257\) 4.31545e16 0.582766 0.291383 0.956606i \(-0.405885\pi\)
0.291383 + 0.956606i \(0.405885\pi\)
\(258\) −6.63174e15 + 1.32538e16i −0.0871544 + 0.174181i
\(259\) −4.19016e16 + 4.19016e16i −0.535959 + 0.535959i
\(260\) −3.55335e16 4.74358e16i −0.442409 0.590599i
\(261\) 3.95319e16 3.95319e16i 0.479142 0.479142i
\(262\) 3.22484e16 + 9.68398e16i 0.380539 + 1.14273i
\(263\) −2.12752e16 −0.244446 −0.122223 0.992503i \(-0.539002\pi\)
−0.122223 + 0.992503i \(0.539002\pi\)
\(264\) −1.27736e14 + 2.31088e13i −0.00142918 + 0.000258553i
\(265\) 7.60892e16i 0.829091i
\(266\) 2.29068e16 + 6.87874e16i 0.243104 + 0.730025i
\(267\) 4.51353e16 + 4.51353e16i 0.466592 + 0.466592i
\(268\) 7.40035e16 + 1.06162e16i 0.745261 + 0.106911i
\(269\) −3.20607e16 3.20607e16i −0.314563 0.314563i 0.532111 0.846674i \(-0.321399\pi\)
−0.846674 + 0.532111i \(0.821399\pi\)
\(270\) −1.94252e16 + 3.88220e16i −0.185703 + 0.371135i
\(271\) 1.41946e17i 1.32232i −0.750243 0.661162i \(-0.770063\pi\)
0.750243 0.661162i \(-0.229937\pi\)
\(272\) −5.33292e16 + 1.82049e17i −0.484153 + 1.65275i
\(273\) 1.48057e17 1.31006
\(274\) −1.62635e16 8.13772e15i −0.140269 0.0701857i
\(275\) 5.78703e13 5.78703e13i 0.000486549 0.000486549i
\(276\) −1.26409e16 1.81340e15i −0.103613 0.0148638i
\(277\) 3.93134e16 3.93134e16i 0.314182 0.314182i −0.532345 0.846527i \(-0.678689\pi\)
0.846527 + 0.532345i \(0.178689\pi\)
\(278\) −6.60356e16 + 2.19904e16i −0.514594 + 0.171364i
\(279\) 2.81332e16 0.213791
\(280\) 4.77071e16 6.87811e16i 0.353571 0.509756i
\(281\) 9.27848e16i 0.670707i −0.942092 0.335353i \(-0.891144\pi\)
0.942092 0.335353i \(-0.108856\pi\)
\(282\) 9.11400e16 3.03503e16i 0.642636 0.214003i
\(283\) −8.20356e16 8.20356e16i −0.564284 0.564284i 0.366238 0.930521i \(-0.380646\pi\)
−0.930521 + 0.366238i \(0.880646\pi\)
\(284\) −1.37124e17 1.83056e17i −0.920209 1.22844i
\(285\) 6.90678e16 + 6.90678e16i 0.452233 + 0.452233i
\(286\) −1.89544e14 9.48415e13i −0.00121101 0.000605949i
\(287\) 1.91197e17i 1.19209i
\(288\) 5.32197e16 5.72529e16i 0.323836 0.348377i
\(289\) 3.31027e17 1.96598
\(290\) 7.16451e16 1.43185e17i 0.415337 0.830066i
\(291\) −2.80498e17 + 2.80498e17i −1.58737 + 1.58737i
\(292\) 1.71054e16 1.28134e16i 0.0945046 0.0707920i
\(293\) −1.04050e16 + 1.04050e16i −0.0561265 + 0.0561265i −0.734613 0.678486i \(-0.762636\pi\)
0.678486 + 0.734613i \(0.262636\pi\)
\(294\) −6.80199e15 2.04259e16i −0.0358265 0.107585i
\(295\) 1.16241e17 0.597866
\(296\) −9.03215e16 + 1.30220e17i −0.453680 + 0.654086i
\(297\) 1.55239e14i 0.000761562i
\(298\) 2.46071e16 + 7.38935e16i 0.117909 + 0.354072i
\(299\) −1.47438e16 1.47438e16i −0.0690099 0.0690099i
\(300\) −2.17113e16 + 1.51346e17i −0.0992743 + 0.692024i
\(301\) −2.41658e16 2.41658e16i −0.107953 0.107953i
\(302\) 9.99729e16 1.99800e17i 0.436349 0.872059i
\(303\) 3.36462e17i 1.43495i
\(304\) 9.30321e16 + 1.70119e17i 0.387720 + 0.708987i
\(305\) −2.26804e17 −0.923743
\(306\) −1.84033e17 9.20841e16i −0.732566 0.366551i
\(307\) 8.88932e16 8.88932e16i 0.345860 0.345860i −0.512705 0.858565i \(-0.671357\pi\)
0.858565 + 0.512705i \(0.171357\pi\)
\(308\) 4.25065e13 2.96306e14i 0.000161659 0.00112690i
\(309\) −1.61480e17 + 1.61480e17i −0.600356 + 0.600356i
\(310\) 7.64429e16 2.54561e16i 0.277847 0.0925252i
\(311\) −7.77190e16 −0.276188 −0.138094 0.990419i \(-0.544098\pi\)
−0.138094 + 0.990419i \(0.544098\pi\)
\(312\) 3.89636e17 7.04893e16i 1.35387 0.244929i
\(313\) 4.86673e17i 1.65359i 0.562505 + 0.826794i \(0.309838\pi\)
−0.562505 + 0.826794i \(0.690162\pi\)
\(314\) 4.70392e16 1.56644e16i 0.156298 0.0520483i
\(315\) 6.42088e16 + 6.42088e16i 0.208651 + 0.208651i
\(316\) −1.45128e17 + 1.08713e17i −0.461255 + 0.345519i
\(317\) −3.11594e17 3.11594e17i −0.968665 0.968665i 0.0308585 0.999524i \(-0.490176\pi\)
−0.999524 + 0.0308585i \(0.990176\pi\)
\(318\) −4.54602e17 2.27467e17i −1.38242 0.691718i
\(319\) 5.72560e14i 0.00170328i
\(320\) 9.28026e16 2.03722e17i 0.270091 0.592908i
\(321\) −6.48880e17 −1.84769
\(322\) 1.31774e16 2.63355e16i 0.0367145 0.0733753i
\(323\) 3.60944e17 3.60944e17i 0.984061 0.984061i
\(324\) −2.80757e17 3.74800e17i −0.749058 0.999964i
\(325\) −1.76523e17 + 1.76523e17i −0.460912 + 0.460912i
\(326\) 1.28787e17 + 3.86740e17i 0.329117 + 0.988315i
\(327\) −5.01795e17 −1.25514
\(328\) −9.10281e16 5.03166e17i −0.222874 1.23195i
\(329\) 2.21515e17i 0.530923i
\(330\) −1.27417e14 3.82625e14i −0.000298971 0.000897791i
\(331\) 2.66701e17 + 2.66701e17i 0.612672 + 0.612672i 0.943642 0.330969i \(-0.107376\pi\)
−0.330969 + 0.943642i \(0.607376\pi\)
\(332\) 7.95803e17 + 1.14162e17i 1.78994 + 0.256776i
\(333\) −1.21563e17 1.21563e17i −0.267727 0.267727i
\(334\) 3.82670e17 7.64779e17i 0.825275 1.64934i
\(335\) 2.32262e17i 0.490529i
\(336\) 2.68319e17 + 4.90650e17i 0.554979 + 1.01484i
\(337\) −5.17163e17 −1.04765 −0.523827 0.851825i \(-0.675496\pi\)
−0.523827 + 0.851825i \(0.675496\pi\)
\(338\) 1.27460e17 + 6.37768e16i 0.252905 + 0.126545i
\(339\) 5.32640e17 5.32640e17i 1.03523 1.03523i
\(340\) −5.83372e17 8.36876e16i −1.11069 0.159334i
\(341\) 2.03733e14 2.03733e14i 0.000379998 0.000379998i
\(342\) −1.99563e17 + 6.64562e16i −0.364669 + 0.121438i
\(343\) 5.81483e17 1.04107
\(344\) −7.51013e16 5.20909e16i −0.131746 0.0913803i
\(345\) 3.96739e16i 0.0681979i
\(346\) −6.31776e17 + 2.10386e17i −1.06422 + 0.354393i
\(347\) 2.70422e17 + 2.70422e17i 0.446413 + 0.446413i 0.894160 0.447747i \(-0.147774\pi\)
−0.447747 + 0.894160i \(0.647774\pi\)
\(348\) 6.41291e17 + 8.56099e17i 1.03753 + 1.38506i
\(349\) 4.51559e17 + 4.51559e17i 0.716039 + 0.716039i 0.967792 0.251753i \(-0.0810071\pi\)
−0.251753 + 0.967792i \(0.581007\pi\)
\(350\) −3.15306e17 1.57769e17i −0.490068 0.245213i
\(351\) 4.73529e17i 0.721434i
\(352\) −2.92070e13 8.00013e14i −4.36203e−5 0.00119481i
\(353\) 3.33172e17 0.487804 0.243902 0.969800i \(-0.421573\pi\)
0.243902 + 0.969800i \(0.421573\pi\)
\(354\) −3.47499e17 + 6.94490e17i −0.498805 + 0.996880i
\(355\) 5.02448e17 5.02448e17i 0.707120 0.707120i
\(356\) −3.15059e17 + 2.36006e17i −0.434753 + 0.325667i
\(357\) 1.04102e18 1.04102e18i 1.40858 1.40858i
\(358\) −2.61221e17 7.84430e17i −0.346599 1.04081i
\(359\) −8.42132e17 −1.09577 −0.547884 0.836554i \(-0.684567\pi\)
−0.547884 + 0.836554i \(0.684567\pi\)
\(360\) 1.99545e17 + 1.38406e17i 0.254638 + 0.176619i
\(361\) 2.77264e17i 0.347011i
\(362\) 3.17924e17 + 9.54703e17i 0.390268 + 1.17195i
\(363\) 7.13381e17 + 7.13381e17i 0.858964 + 0.858964i
\(364\) −1.29659e17 + 9.03829e17i −0.153141 + 1.06752i
\(365\) 4.69505e16 + 4.69505e16i 0.0543989 + 0.0543989i
\(366\) 6.78025e17 1.35506e18i 0.770687 1.54025i
\(367\) 8.30857e17i 0.926539i −0.886217 0.463269i \(-0.846676\pi\)
0.886217 0.463269i \(-0.153324\pi\)
\(368\) 2.21402e16 7.55796e16i 0.0242240 0.0826932i
\(369\) 5.54695e17 0.595483
\(370\) −4.40304e17 2.20313e17i −0.463810 0.232075i
\(371\) 8.28881e17 8.28881e17i 0.856791 0.856791i
\(372\) −7.64350e16 + 5.32815e17i −0.0775339 + 0.540476i
\(373\) −1.23600e17 + 1.23600e17i −0.123043 + 0.123043i −0.765947 0.642904i \(-0.777729\pi\)
0.642904 + 0.765947i \(0.277729\pi\)
\(374\) −1.99957e15 + 6.65872e14i −0.00195360 + 0.000650564i
\(375\) −1.30036e18 −1.24694
\(376\) 1.05462e17 + 5.82952e17i 0.0992617 + 0.548678i
\(377\) 1.74649e18i 1.61353i
\(378\) 6.34519e17 2.11300e17i 0.575442 0.191627i
\(379\) −7.14610e17 7.14610e17i −0.636202 0.636202i 0.313415 0.949616i \(-0.398527\pi\)
−0.949616 + 0.313415i \(0.898527\pi\)
\(380\) −4.82116e17 + 3.61146e17i −0.421373 + 0.315644i
\(381\) −1.73079e18 1.73079e18i −1.48514 1.48514i
\(382\) −4.88596e17 2.44477e17i −0.411630 0.205966i
\(383\) 1.64694e18i 1.36234i 0.732125 + 0.681170i \(0.238528\pi\)
−0.732125 + 0.681170i \(0.761472\pi\)
\(384\) 9.39720e17 + 1.16348e18i 0.763273 + 0.945017i
\(385\) 9.29965e14 0.000741723
\(386\) −1.16297e17 + 2.32423e17i −0.0910870 + 0.182041i
\(387\) 7.01088e16 7.01088e16i 0.0539257 0.0539257i
\(388\) −1.46668e18 1.95797e18i −1.10794 1.47905i
\(389\) −3.87748e17 + 3.87748e17i −0.287675 + 0.287675i −0.836160 0.548485i \(-0.815205\pi\)
0.548485 + 0.836160i \(0.315205\pi\)
\(390\) 3.88663e17 + 1.16713e18i 0.283218 + 0.850485i
\(391\) −2.07333e17 −0.148399
\(392\) 1.30649e17 2.36357e16i 0.0918549 0.0166175i
\(393\) 2.11846e18i 1.46309i
\(394\) 4.25865e17 + 1.27884e18i 0.288934 + 0.867649i
\(395\) −3.98344e17 3.98344e17i −0.265509 0.265509i
\(396\) 8.59631e14 + 1.23318e14i 0.000562919 + 8.07535e-5i
\(397\) 6.54170e17 + 6.54170e17i 0.420879 + 0.420879i 0.885506 0.464628i \(-0.153812\pi\)
−0.464628 + 0.885506i \(0.653812\pi\)
\(398\) 7.02345e17 1.40366e18i 0.443986 0.887322i
\(399\) 1.50479e18i 0.934684i
\(400\) −9.04891e17 2.65077e17i −0.552302 0.161790i
\(401\) −2.60448e16 −0.0156210 −0.00781052 0.999969i \(-0.502486\pi\)
−0.00781052 + 0.999969i \(0.502486\pi\)
\(402\) −1.38767e18 6.94343e17i −0.817907 0.409253i
\(403\) −6.21453e17 + 6.21453e17i −0.359975 + 0.359975i
\(404\) −2.05397e18 2.94652e17i −1.16929 0.167741i
\(405\) 1.02874e18 1.02874e18i 0.575601 0.575601i
\(406\) −2.34026e18 + 7.79326e17i −1.28701 + 0.428585i
\(407\) −1.76066e15 −0.000951731
\(408\) 2.24398e18 3.23523e18i 1.19233 1.71903i
\(409\) 2.13483e18i 1.11506i 0.830155 + 0.557532i \(0.188252\pi\)
−0.830155 + 0.557532i \(0.811748\pi\)
\(410\) 1.50720e18 5.01910e17i 0.773899 0.257715i
\(411\) 2.66900e17 + 2.66900e17i 0.134727 + 0.134727i
\(412\) −8.44356e17 1.12718e18i −0.419030 0.559389i
\(413\) −1.26627e18 1.26627e18i −0.617841 0.617841i
\(414\) 7.64034e16 + 3.82297e16i 0.0366531 + 0.0183400i
\(415\) 2.49765e18i 1.17814i
\(416\) 8.90909e16 + 2.44030e18i 0.0413219 + 1.13185i
\(417\) 1.44459e18 0.658858
\(418\) −9.63927e14 + 1.92644e15i −0.000432325 + 0.000864017i
\(419\) −1.69867e18 + 1.69867e18i −0.749221 + 0.749221i −0.974333 0.225112i \(-0.927725\pi\)
0.225112 + 0.974333i \(0.427725\pi\)
\(420\) −1.39050e18 + 1.04160e18i −0.603150 + 0.451811i
\(421\) 1.59517e18 1.59517e18i 0.680508 0.680508i −0.279607 0.960115i \(-0.590204\pi\)
0.960115 + 0.279607i \(0.0902041\pi\)
\(422\) 1.03451e18 + 3.10657e18i 0.434059 + 1.30345i
\(423\) −6.42650e17 −0.265211
\(424\) 1.78671e18 2.57596e18i 0.725257 1.04563i
\(425\) 2.48233e18i 0.991146i
\(426\) 1.49986e18 + 4.50398e18i 0.589093 + 1.76901i
\(427\) 2.47069e18 + 2.47069e18i 0.954605 + 0.954605i
\(428\) 5.68246e17 3.96115e18i 0.215988 1.50562i
\(429\) 3.11060e15 + 3.11060e15i 0.00116317 + 0.00116317i
\(430\) 1.27061e17 2.53935e17i 0.0467446 0.0934208i
\(431\) 7.36036e17i 0.266415i −0.991088 0.133207i \(-0.957472\pi\)
0.991088 0.133207i \(-0.0425276\pi\)
\(432\) 1.56924e18 8.58160e17i 0.558860 0.305620i
\(433\) 1.80628e18 0.632951 0.316476 0.948601i \(-0.397500\pi\)
0.316476 + 0.948601i \(0.397500\pi\)
\(434\) −1.11004e18 5.55427e17i −0.382746 0.191513i
\(435\) −2.34980e18 + 2.34980e18i −0.797273 + 0.797273i
\(436\) 4.39439e17 3.06326e18i 0.146721 1.02277i
\(437\) −1.49850e17 + 1.49850e17i −0.0492363 + 0.0492363i
\(438\) −4.20868e17 + 1.40152e17i −0.136090 + 0.0453191i
\(439\) 2.72014e17 0.0865643 0.0432822 0.999063i \(-0.486219\pi\)
0.0432822 + 0.999063i \(0.486219\pi\)
\(440\) 2.44735e15 4.42752e14i 0.000766527 0.000138673i
\(441\) 1.44028e17i 0.0443994i
\(442\) 6.09934e18 2.03113e18i 1.85066 0.616284i
\(443\) 2.30191e17 + 2.30191e17i 0.0687484 + 0.0687484i 0.740645 0.671897i \(-0.234520\pi\)
−0.671897 + 0.740645i \(0.734520\pi\)
\(444\) 2.63256e18 1.97201e18i 0.773923 0.579734i
\(445\) −8.64769e17 8.64769e17i −0.250253 0.250253i
\(446\) 4.41938e18 + 2.21131e18i 1.25897 + 0.629948i
\(447\) 1.61649e18i 0.453335i
\(448\) −3.23020e18 + 1.20830e18i −0.891832 + 0.333602i
\(449\) 1.53483e17 0.0417193 0.0208596 0.999782i \(-0.493360\pi\)
0.0208596 + 0.999782i \(0.493360\pi\)
\(450\) 4.57712e17 9.14754e17i 0.122491 0.244803i
\(451\) 4.01695e15 4.01695e15i 0.00105843 0.00105843i
\(452\) 2.78510e18 + 3.71800e18i 0.722556 + 0.964585i
\(453\) −3.27890e18 + 3.27890e18i −0.837607 + 0.837607i
\(454\) −8.21202e17 2.46601e18i −0.206566 0.620304i
\(455\) −2.83670e18 −0.702640
\(456\) −7.16422e17 3.96009e18i −0.174749 0.965941i
\(457\) 4.62602e18i 1.11121i −0.831448 0.555603i \(-0.812488\pi\)
0.831448 0.555603i \(-0.187512\pi\)
\(458\) −7.28092e17 2.18641e18i −0.172238 0.517218i
\(459\) −3.32947e18 3.32947e18i −0.775686 0.775686i
\(460\) 2.42193e17 + 3.47438e16i 0.0555721 + 0.00797210i
\(461\) 1.18142e18 + 1.18142e18i 0.266991 + 0.266991i 0.827887 0.560895i \(-0.189543\pi\)
−0.560895 + 0.827887i \(0.689543\pi\)
\(462\) −2.78011e15 + 5.55616e15i −0.000618826 + 0.00123675i
\(463\) 2.29904e18i 0.504058i 0.967720 + 0.252029i \(0.0810978\pi\)
−0.967720 + 0.252029i \(0.918902\pi\)
\(464\) −5.78774e18 + 3.16511e18i −1.24992 + 0.683538i
\(465\) −1.67226e18 −0.355740
\(466\) −4.86351e18 2.43353e18i −1.01917 0.509960i
\(467\) −7.17990e17 + 7.17990e17i −0.148218 + 0.148218i −0.777321 0.629104i \(-0.783422\pi\)
0.629104 + 0.777321i \(0.283422\pi\)
\(468\) −2.62215e18 3.76161e17i −0.533258 0.0764985i
\(469\) 2.53016e18 2.53016e18i 0.506918 0.506918i
\(470\) −1.74619e18 + 5.81496e17i −0.344673 + 0.114779i
\(471\) −1.02902e18 −0.200115
\(472\) −3.93526e18 2.72953e18i −0.754015 0.522991i
\(473\) 1.01542e15i 0.000191698i
\(474\) 3.57078e18 1.18910e18i 0.664224 0.221192i
\(475\) 1.79410e18 + 1.79410e18i 0.328846 + 0.328846i
\(476\) 5.44334e18 + 7.26664e18i 0.983142 + 1.31246i
\(477\) 2.40472e18 + 2.40472e18i 0.427992 + 0.427992i
\(478\) −3.70321e18 1.85296e18i −0.649506 0.324991i
\(479\) 8.89880e17i 0.153809i −0.997038 0.0769047i \(-0.975496\pi\)
0.997038 0.0769047i \(-0.0245037\pi\)
\(480\) −3.16342e18 + 3.40315e18i −0.538850 + 0.579685i
\(481\) 5.37058e18 0.901582
\(482\) −4.05896e18 + 8.11198e18i −0.671562 + 1.34214i
\(483\) −4.32189e17 + 4.32189e17i −0.0704765 + 0.0704765i
\(484\) −4.97964e18 + 3.73017e18i −0.800350 + 0.599530i
\(485\) 5.37419e18 5.37419e18i 0.851374 0.851374i
\(486\) 1.78210e18 + 5.35151e18i 0.278277 + 0.835646i
\(487\) 4.88908e18 0.752531 0.376266 0.926512i \(-0.377208\pi\)
0.376266 + 0.926512i \(0.377208\pi\)
\(488\) 7.67831e18 + 5.32574e18i 1.16500 + 0.808055i
\(489\) 8.46028e18i 1.26538i
\(490\) 1.30323e17 + 3.91350e17i 0.0192153 + 0.0577022i
\(491\) −9.46496e18 9.46496e18i −1.37578 1.37578i −0.851622 0.524156i \(-0.824381\pi\)
−0.524156 0.851622i \(-0.675619\pi\)
\(492\) −1.50705e18 + 1.05054e19i −0.215959 + 1.50541i
\(493\) 1.22799e19 + 1.22799e19i 1.73487 + 1.73487i
\(494\) 2.94029e18 5.87628e18i 0.409545 0.818490i
\(495\) 2.69798e15i 0.000370512i
\(496\) −3.18569e18 9.33210e17i −0.431351 0.126359i
\(497\) −1.09469e19 −1.46149
\(498\) −1.49224e19 7.46669e18i −1.96442 0.982930i
\(499\) 7.40579e18 7.40579e18i 0.961319 0.961319i −0.0379606 0.999279i \(-0.512086\pi\)
0.999279 + 0.0379606i \(0.0120862\pi\)
\(500\) 1.13877e18 7.93818e18i 0.145763 1.01609i
\(501\) −1.25507e19 + 1.25507e19i −1.58418 + 1.58418i
\(502\) −8.26028e18 + 2.75074e18i −1.02818 + 0.342392i
\(503\) 7.96672e18 0.977921 0.488961 0.872306i \(-0.337376\pi\)
0.488961 + 0.872306i \(0.337376\pi\)
\(504\) −6.66020e17 3.68148e18i −0.0806257 0.445666i
\(505\) 6.44644e18i 0.769627i
\(506\) 8.30142e14 2.76444e14i 9.77460e−5 3.25502e-5i
\(507\) −2.09174e18 2.09174e18i −0.242914 0.242914i
\(508\) 1.20815e19 9.05004e18i 1.38380 1.03658i
\(509\) −6.56802e18 6.56802e18i −0.742011 0.742011i 0.230954 0.972965i \(-0.425815\pi\)
−0.972965 + 0.230954i \(0.925815\pi\)
\(510\) 1.09391e19 + 5.47354e18i 1.21896 + 0.609926i
\(511\) 1.02291e18i 0.112433i
\(512\) −7.92551e18 + 4.71771e18i −0.859286 + 0.511496i
\(513\) −4.81274e18 −0.514719
\(514\) 2.47175e18 4.93989e18i 0.260773 0.521165i
\(515\) 3.09387e18 3.09387e18i 0.321997 0.321997i
\(516\) 1.13731e18 + 1.51827e18i 0.116770 + 0.155884i
\(517\) −4.65390e15 + 4.65390e15i −0.000471393 + 0.000471393i
\(518\) 2.39648e18 + 7.19646e18i 0.239478 + 0.719135i
\(519\) 1.38207e19 1.36256
\(520\) −7.46522e18 + 1.35054e18i −0.726138 + 0.131366i
\(521\) 1.65515e19i 1.58845i −0.607623 0.794225i \(-0.707877\pi\)
0.607623 0.794225i \(-0.292123\pi\)
\(522\) −2.26095e18 6.78948e18i −0.214091 0.642900i
\(523\) 6.16491e18 + 6.16491e18i 0.575990 + 0.575990i 0.933796 0.357806i \(-0.116475\pi\)
−0.357806 + 0.933796i \(0.616475\pi\)
\(524\) 1.29323e19 + 1.85521e18i 1.19222 + 0.171030i
\(525\) 5.17447e18 + 5.17447e18i 0.470707 + 0.470707i
\(526\) −1.21858e18 + 2.43537e18i −0.109384 + 0.218607i
\(527\) 8.73910e18i 0.774092i
\(528\) −4.67105e15 + 1.59455e16i −0.000408298 + 0.00139380i
\(529\) −1.15068e19 −0.992575
\(530\) 8.70992e18 + 4.35815e18i 0.741452 + 0.370998i
\(531\) 3.67366e18 3.67366e18i 0.308629 0.308629i
\(532\) 9.18612e18 + 1.31779e18i 0.761641 + 0.109261i
\(533\) −1.22530e19 + 1.22530e19i −1.00266 + 1.00266i
\(534\) 7.75184e18 2.58143e18i 0.626060 0.208483i
\(535\) 1.24322e19 0.990995
\(536\) 5.45392e18 7.86311e18i 0.429097 0.618644i
\(537\) 1.71601e19i 1.33260i
\(538\) −5.50633e18 + 1.83365e18i −0.422072 + 0.140553i
\(539\) 1.04301e15 + 1.04301e15i 7.89166e−5 + 7.89166e-5i
\(540\) 3.33134e18 + 4.44721e18i 0.248807 + 0.332148i
\(541\) −1.38424e18 1.38424e18i −0.102054 0.102054i 0.654236 0.756290i \(-0.272990\pi\)
−0.756290 + 0.654236i \(0.772990\pi\)
\(542\) −1.62485e19 8.13022e18i −1.18255 0.591708i
\(543\) 2.08850e19i 1.50050i
\(544\) 1.77846e19 + 1.65318e19i 1.26140 + 1.17254i
\(545\) 9.61412e18 0.673185
\(546\) 8.48025e18 1.69481e19i 0.586219 1.17158i
\(547\) −1.54209e19 + 1.54209e19i −1.05244 + 1.05244i −0.0538949 + 0.998547i \(0.517164\pi\)
−0.998547 + 0.0538949i \(0.982836\pi\)
\(548\) −1.86305e18 + 1.39558e18i −0.125534 + 0.0940354i
\(549\) −7.16788e18 + 7.16788e18i −0.476853 + 0.476853i
\(550\) −3.30978e15 9.93904e15i −0.000217400 0.000652838i
\(551\) 1.77506e19 1.15120
\(552\) −9.31612e17 + 1.34314e18i −0.0596570 + 0.0860096i
\(553\) 8.67875e18i 0.548759i
\(554\) −2.24845e18 6.75194e18i −0.140383 0.421561i
\(555\) 7.22580e18 + 7.22580e18i 0.445487 + 0.445487i
\(556\) −1.26508e18 + 8.81863e18i −0.0770182 + 0.536881i
\(557\) −9.93712e18 9.93712e18i −0.597412 0.597412i 0.342211 0.939623i \(-0.388824\pi\)
−0.939623 + 0.342211i \(0.888824\pi\)
\(558\) 1.61138e18 3.22041e18i 0.0956664 0.191193i
\(559\) 3.09736e18i 0.181597i
\(560\) −5.14085e18 9.40059e18i −0.297659 0.544301i
\(561\) 4.37424e16 0.00250128
\(562\) −1.06211e19 5.31442e18i −0.599810 0.300125i
\(563\) −2.02380e19 + 2.02380e19i −1.12878 + 1.12878i −0.138401 + 0.990376i \(0.544196\pi\)
−0.990376 + 0.138401i \(0.955804\pi\)
\(564\) 1.74601e18 1.21712e19i 0.0961819 0.670468i
\(565\) −1.02051e19 + 1.02051e19i −0.555236 + 0.555236i
\(566\) −1.40894e19 + 4.69187e18i −0.757140 + 0.252134i
\(567\) −2.24133e19 −1.18966
\(568\) −2.88085e19 + 5.21176e18i −1.51036 + 0.273241i
\(569\) 5.93469e18i 0.307335i −0.988123 0.153668i \(-0.950891\pi\)
0.988123 0.153668i \(-0.0491085\pi\)
\(570\) 1.18622e19 3.95020e18i 0.606793 0.202067i
\(571\) −1.59211e19 1.59211e19i −0.804488 0.804488i 0.179305 0.983793i \(-0.442615\pi\)
−0.983793 + 0.179305i \(0.942615\pi\)
\(572\) −2.17130e16 + 1.62649e16i −0.00108380 + 0.000811856i
\(573\) 8.01832e18 + 8.01832e18i 0.395368 + 0.395368i
\(574\) −2.18863e19 1.09512e19i −1.06608 0.533431i
\(575\) 1.03057e18i 0.0495908i
\(576\) −3.50547e18 9.37133e18i −0.166644 0.445496i
\(577\) 1.72090e19 0.808212 0.404106 0.914712i \(-0.367583\pi\)
0.404106 + 0.914712i \(0.367583\pi\)
\(578\) 1.89602e19 3.78926e19i 0.879726 1.75816i
\(579\) 3.81428e18 3.81428e18i 0.174849 0.174849i
\(580\) −1.22868e19 1.64024e19i −0.556472 0.742868i
\(581\) 2.72083e19 2.72083e19i 1.21750 1.21750i
\(582\) 1.60425e19 + 4.81746e19i 0.709270 + 2.12989i
\(583\) 3.48287e16 0.00152145
\(584\) −4.87005e17 2.69196e18i −0.0210205 0.116193i
\(585\) 8.22972e18i 0.350989i
\(586\) 5.95092e17 + 1.78702e18i 0.0250785 + 0.0753089i
\(587\) −6.96287e18 6.96287e18i −0.289949 0.289949i 0.547111 0.837060i \(-0.315728\pi\)
−0.837060 + 0.547111i \(0.815728\pi\)
\(588\) −2.72775e18 3.91309e17i −0.112244 0.0161020i
\(589\) 6.31617e18 + 6.31617e18i 0.256831 + 0.256831i
\(590\) 6.65790e18 1.33061e19i 0.267530 0.534669i
\(591\) 2.79758e19i 1.11089i
\(592\) 9.73291e18 + 1.77977e19i 0.381936 + 0.698412i
\(593\) −2.76423e19 −1.07199 −0.535996 0.844220i \(-0.680064\pi\)
−0.535996 + 0.844220i \(0.680064\pi\)
\(594\) 1.77702e16 + 8.89159e15i 0.000681062 + 0.000340780i
\(595\) −1.99453e19 + 1.99453e19i −0.755479 + 0.755479i
\(596\) 9.86800e18 + 1.41561e18i 0.369407 + 0.0529933i
\(597\) −2.30354e19 + 2.30354e19i −0.852267 + 0.852267i
\(598\) −2.53220e18 + 8.43244e17i −0.0925956 + 0.0308351i
\(599\) −1.28539e19 −0.464564 −0.232282 0.972648i \(-0.574619\pi\)
−0.232282 + 0.972648i \(0.574619\pi\)
\(600\) 1.60810e19 + 1.11539e19i 0.574452 + 0.398445i
\(601\) 4.79913e19i 1.69450i 0.531195 + 0.847250i \(0.321743\pi\)
−0.531195 + 0.847250i \(0.678257\pi\)
\(602\) −4.15039e18 + 1.38211e18i −0.144848 + 0.0482357i
\(603\) 7.34040e18 + 7.34040e18i 0.253220 + 0.253220i
\(604\) −1.71449e19 2.28878e19i −0.584624 0.780450i
\(605\) −1.36680e19 1.36680e19i −0.460699 0.460699i
\(606\) 3.85148e19 + 1.92715e19i 1.28327 + 0.642107i
\(607\) 4.49254e19i 1.47969i 0.672777 + 0.739845i \(0.265101\pi\)
−0.672777 + 0.739845i \(0.734899\pi\)
\(608\) 2.48021e19 9.05481e17i 0.807540 0.0294818i
\(609\) 5.11954e19 1.64782
\(610\) −1.29906e19 + 2.59622e19i −0.413352 + 0.826099i
\(611\) 1.41959e19 1.41959e19i 0.446555 0.446555i
\(612\) −2.10817e19 + 1.57920e19i −0.655611 + 0.491108i
\(613\) 3.72953e19 3.72953e19i 1.14665 1.14665i 0.159444 0.987207i \(-0.449030\pi\)
0.987207 0.159444i \(-0.0509701\pi\)
\(614\) −5.08407e18 1.52671e19i −0.154537 0.464065i
\(615\) −3.29714e19 −0.990858
\(616\) −3.14835e16 2.18372e16i −0.000935443 0.000648831i
\(617\) 2.62552e19i 0.771292i −0.922647 0.385646i \(-0.873979\pi\)
0.922647 0.385646i \(-0.126021\pi\)
\(618\) 9.23552e18 + 2.77336e19i 0.268251 + 0.805541i
\(619\) −1.39917e19 1.39917e19i −0.401825 0.401825i 0.477051 0.878876i \(-0.341706\pi\)
−0.878876 + 0.477051i \(0.841706\pi\)
\(620\) 1.46445e18 1.02085e19i 0.0415847 0.289880i
\(621\) 1.38226e18 + 1.38226e18i 0.0388106 + 0.0388106i
\(622\) −4.45150e18 + 8.89649e18i −0.123587 + 0.246994i
\(623\) 1.88408e19i 0.517229i
\(624\) 1.42482e19 4.86390e19i 0.386784 1.32036i
\(625\) 3.47477e18 0.0932752
\(626\) 5.57094e19 + 2.78751e19i 1.47880 + 0.739940i
\(627\) 3.16147e16 3.16147e16i 0.000829883 0.000829883i
\(628\) 9.01152e17 6.28178e18i 0.0233927 0.163067i
\(629\) 3.77615e19 3.77615e19i 0.969382 0.969382i
\(630\) 1.10276e19 3.67229e18i 0.279962 0.0932295i
\(631\) 5.44797e19 1.36782 0.683910 0.729566i \(-0.260278\pi\)
0.683910 + 0.729566i \(0.260278\pi\)
\(632\) 4.13191e18 + 2.28395e19i 0.102596 + 0.567110i
\(633\) 6.79590e19i 1.66887i
\(634\) −5.35152e19 + 1.78210e19i −1.29973 + 0.432820i
\(635\) 3.31609e19 + 3.31609e19i 0.796546 + 0.796546i
\(636\) −5.20763e19 + 3.90096e19i −1.23720 + 0.926769i
\(637\) −3.18153e18 3.18153e18i −0.0747584 0.0747584i
\(638\) −6.55408e16 3.27944e16i −0.00152324 0.000762176i
\(639\) 3.17587e19i 0.730056i
\(640\) −1.80045e19 2.22916e19i −0.409376 0.506853i
\(641\) 8.37844e17 0.0188433 0.00942165 0.999956i \(-0.497001\pi\)
0.00942165 + 0.999956i \(0.497001\pi\)
\(642\) −3.71658e19 + 7.42772e19i −0.826796 + 1.65238i
\(643\) 5.56239e19 5.56239e19i 1.22401 1.22401i 0.257816 0.966194i \(-0.416997\pi\)
0.966194 0.257816i \(-0.0830027\pi\)
\(644\) −2.25986e18 3.01682e18i −0.0491904 0.0656673i
\(645\) −4.16731e18 + 4.16731e18i −0.0897301 + 0.0897301i
\(646\) −2.06435e19 6.19909e19i −0.439699 1.32038i
\(647\) 3.58620e17 0.00755622 0.00377811 0.999993i \(-0.498797\pi\)
0.00377811 + 0.999993i \(0.498797\pi\)
\(648\) −5.89842e19 + 1.06709e19i −1.22945 + 0.222420i
\(649\) 5.32073e16i 0.00109713i
\(650\) 1.00959e19 + 3.03173e19i 0.205945 + 0.618439i
\(651\) 1.82168e19 + 1.82168e19i 0.367625 + 0.367625i
\(652\) 5.16466e19 + 7.40896e18i 1.03112 + 0.147919i
\(653\) 2.88198e19 + 2.88198e19i 0.569245 + 0.569245i 0.931917 0.362672i \(-0.118135\pi\)
−0.362672 + 0.931917i \(0.618135\pi\)
\(654\) −2.87412e19 + 5.74404e19i −0.561644 + 1.12247i
\(655\) 4.05885e19i 0.784719i
\(656\) −6.28112e19 1.83998e19i −1.20146 0.351954i
\(657\) 2.96764e18 0.0561635
\(658\) 2.53568e19 + 1.26877e19i 0.474802 + 0.237575i
\(659\) 1.06824e19 1.06824e19i 0.197911 0.197911i −0.601193 0.799104i \(-0.705308\pi\)
0.799104 + 0.601193i \(0.205308\pi\)
\(660\) −5.10970e16 7.33012e15i −0.000936673 0.000134370i
\(661\) −8.45481e18 + 8.45481e18i −0.153353 + 0.153353i −0.779614 0.626260i \(-0.784585\pi\)
0.626260 + 0.779614i \(0.284585\pi\)
\(662\) 4.58050e19 1.52534e19i 0.822067 0.273755i
\(663\) −1.33428e20 −2.36948
\(664\) 5.86492e19 8.45567e19i 1.03059 1.48584i
\(665\) 2.88309e19i 0.501311i
\(666\) −2.08781e19 + 6.95257e18i −0.359229 + 0.119626i
\(667\) −5.09814e18 5.09814e18i −0.0868022 0.0868022i
\(668\) −6.56261e19 8.76083e19i −1.10571 1.47608i
\(669\) −7.25261e19 7.25261e19i −1.20924 1.20924i
\(670\) 2.65870e19 + 1.33033e19i 0.438678 + 0.219500i
\(671\) 1.03816e17i 0.00169514i
\(672\) 7.15331e19 2.61154e18i 1.15591 0.0422000i
\(673\) 1.63308e19 0.261157 0.130579 0.991438i \(-0.458317\pi\)
0.130579 + 0.991438i \(0.458317\pi\)
\(674\) −2.96215e19 + 5.91996e19i −0.468799 + 0.936913i
\(675\) 1.65494e19 1.65494e19i 0.259213 0.259213i
\(676\) 1.46011e19 1.09374e19i 0.226338 0.169546i
\(677\) 2.48106e19 2.48106e19i 0.380642 0.380642i −0.490692 0.871333i \(-0.663256\pi\)
0.871333 + 0.490692i \(0.163256\pi\)
\(678\) −3.04633e19 9.14791e19i −0.462561 1.38904i
\(679\) −1.17088e20 −1.75964
\(680\) −4.29935e19 + 6.19852e19i −0.639499 + 0.921989i
\(681\) 5.39463e19i 0.794203i
\(682\) −1.16521e16 3.49906e16i −0.000169791 0.000509871i
\(683\) −3.23801e19 3.23801e19i −0.467018 0.467018i 0.433929 0.900947i \(-0.357127\pi\)
−0.900947 + 0.433929i \(0.857127\pi\)
\(684\) −3.82313e18 + 2.66504e19i −0.0545791 + 0.380462i
\(685\) −5.11366e18 5.11366e18i −0.0722599 0.0722599i
\(686\) 3.33055e19 6.65623e19i 0.465852 0.931022i
\(687\) 4.78297e19i 0.662218i
\(688\) −1.02644e19 + 5.61323e18i −0.140674 + 0.0769297i
\(689\) −1.06239e20 −1.44128
\(690\) −4.54147e18 2.27240e18i −0.0609892 0.0305169i
\(691\) 4.41601e17 4.41601e17i 0.00587062 0.00587062i −0.704165 0.710036i \(-0.748679\pi\)
0.710036 + 0.704165i \(0.248679\pi\)
\(692\) −1.21032e19 + 8.43696e19i −0.159279 + 1.11031i
\(693\) 2.93906e16 2.93906e16i 0.000382891 0.000382891i
\(694\) 4.64442e19 1.54663e19i 0.598984 0.199466i
\(695\) −2.76776e19 −0.353374
\(696\) 1.34729e20 2.43739e19i 1.70293 0.308077i
\(697\) 1.72306e20i 2.15611i
\(698\) 7.75538e19 2.58260e19i 0.960760 0.319941i
\(699\) 7.98147e19 + 7.98147e19i 0.978909 + 0.978909i
\(700\) −3.61195e19 + 2.70566e19i −0.438587 + 0.328539i
\(701\) 3.84319e19 + 3.84319e19i 0.462026 + 0.462026i 0.899319 0.437293i \(-0.144063\pi\)
−0.437293 + 0.899319i \(0.644063\pi\)
\(702\) −5.42048e19 2.71222e19i −0.645176 0.322824i
\(703\) 5.45841e19i 0.643249i
\(704\) −9.32503e16 4.24789e16i −0.00108803 0.000495638i
\(705\) 3.81995e19 0.441300
\(706\) 1.90830e19 3.81381e19i 0.218280 0.436241i
\(707\) −7.02246e19 + 7.02246e19i −0.795341 + 0.795341i
\(708\) 5.95945e19 + 7.95564e19i 0.668303 + 0.892159i
\(709\) 8.12863e19 8.12863e19i 0.902597 0.902597i −0.0930634 0.995660i \(-0.529666\pi\)
0.995660 + 0.0930634i \(0.0296659\pi\)
\(710\) −2.87365e19 8.62939e19i −0.315956 0.948793i
\(711\) −2.51785e19 −0.274121
\(712\) 8.97000e18 + 4.95825e19i 0.0967014 + 0.534526i
\(713\) 3.62813e18i 0.0387308i
\(714\) −5.95389e19 1.78791e20i −0.629381 1.88999i
\(715\) −5.95974e16 5.95974e16i −0.000623857 0.000623857i
\(716\) −1.04756e20 1.50277e19i −1.08589 0.155776i
\(717\) 6.07732e19 + 6.07732e19i 0.623847 + 0.623847i
\(718\) −4.82347e19 + 9.63987e19i −0.490330 + 0.979942i
\(719\) 2.26461e19i 0.227977i 0.993482 + 0.113989i \(0.0363628\pi\)
−0.993482 + 0.113989i \(0.963637\pi\)
\(720\) 2.72727e19 1.49144e19i 0.271894 0.148689i
\(721\) −6.74063e19 −0.665509
\(722\) 3.17384e19 + 1.58808e19i 0.310330 + 0.155279i
\(723\) 1.33125e20 1.33125e20i 1.28912 1.28912i
\(724\) 1.27494e20 + 1.82897e19i 1.22270 + 0.175403i
\(725\) −6.10384e19 + 6.10384e19i −0.579745 + 0.579745i
\(726\) 1.22521e20 4.08004e19i 1.15253 0.383803i
\(727\) 1.21868e20 1.13540 0.567701 0.823235i \(-0.307833\pi\)
0.567701 + 0.823235i \(0.307833\pi\)
\(728\) 9.60348e19 + 6.66105e19i 0.886153 + 0.614643i
\(729\) 1.96397e19i 0.179491i
\(730\) 8.06360e18 2.68524e18i 0.0729910 0.0243066i
\(731\) 2.17781e19 + 2.17781e19i 0.195253 + 0.195253i
\(732\) −1.16278e20 1.55227e20i −1.03257 1.37844i
\(733\) −1.24004e20 1.24004e20i −1.09070 1.09070i −0.995453 0.0952505i \(-0.969635\pi\)
−0.0952505 0.995453i \(-0.530365\pi\)
\(734\) −9.51081e19 4.75889e19i −0.828600 0.414603i
\(735\) 8.56112e18i 0.0738787i
\(736\) −7.38347e18 6.86335e18i −0.0631126 0.0586667i
\(737\) 1.06314e17 0.000900160
\(738\) 3.17712e19 6.34958e19i 0.266464 0.532538i
\(739\) −4.92659e18 + 4.92659e18i −0.0409294 + 0.0409294i −0.727275 0.686346i \(-0.759214\pi\)
0.686346 + 0.727275i \(0.259214\pi\)
\(740\) −5.04385e19 + 3.77827e19i −0.415088 + 0.310936i
\(741\) −9.64352e19 + 9.64352e19i −0.786155 + 0.786155i
\(742\) −4.74062e19 1.42358e20i −0.382832 1.14962i
\(743\) 1.86158e20 1.48922 0.744610 0.667499i \(-0.232635\pi\)
0.744610 + 0.667499i \(0.232635\pi\)
\(744\) 5.66134e19 + 3.92675e19i 0.448651 + 0.311188i
\(745\) 3.09710e19i 0.243143i
\(746\) 7.06905e18 + 2.12279e19i 0.0549781 + 0.165095i
\(747\) 7.89357e19 + 7.89357e19i 0.608176 + 0.608176i
\(748\) −3.83067e16 + 2.67030e17i −0.000292391 + 0.00203821i
\(749\) −1.35431e20 1.35431e20i −1.02410 1.02410i
\(750\) −7.44806e19 + 1.48852e20i −0.557975 + 1.11513i
\(751\) 2.11244e20i 1.56785i −0.620856 0.783925i \(-0.713215\pi\)
0.620856 0.783925i \(-0.286785\pi\)
\(752\) 7.27710e19 + 2.13174e19i 0.535098 + 0.156751i
\(753\) 1.80701e20 1.31642
\(754\) 1.99921e20 + 1.00034e20i 1.44297 + 0.722016i
\(755\) 6.28219e19 6.28219e19i 0.449244 0.449244i
\(756\) 1.21558e19 8.47359e19i 0.0861252 0.600364i
\(757\) −1.59048e19 + 1.59048e19i −0.111649 + 0.111649i −0.760724 0.649075i \(-0.775156\pi\)
0.649075 + 0.760724i \(0.275156\pi\)
\(758\) −1.22732e20 + 4.08707e19i −0.853637 + 0.284268i
\(759\) −1.81601e16 −0.000125149
\(760\) 1.37263e19 + 7.58732e19i 0.0937253 + 0.518075i
\(761\) 2.53916e20i 1.71790i 0.512059 + 0.858950i \(0.328883\pi\)
−0.512059 + 0.858950i \(0.671117\pi\)
\(762\) −2.97257e20 + 9.89889e19i −1.99272 + 0.663593i
\(763\) −1.04732e20 1.04732e20i −0.695676 0.695676i
\(764\) −5.59705e19 + 4.19267e19i −0.368388 + 0.275954i
\(765\) −5.78647e19 5.78647e19i −0.377384 0.377384i
\(766\) 1.88525e20 + 9.43314e19i 1.21834 + 0.609614i
\(767\) 1.62300e20i 1.03932i
\(768\) 1.87007e20 4.09293e19i 1.18667 0.259720i
\(769\) −1.26567e20 −0.795861 −0.397930 0.917416i \(-0.630271\pi\)
−0.397930 + 0.917416i \(0.630271\pi\)
\(770\) 5.32655e16 1.06453e17i 0.000331903 0.000663320i
\(771\) −8.10682e19 + 8.10682e19i −0.500576 + 0.500576i
\(772\) 1.99444e19 + 2.66250e19i 0.122039 + 0.162918i
\(773\) −1.02677e20 + 1.02677e20i −0.622613 + 0.622613i −0.946199 0.323586i \(-0.895111\pi\)
0.323586 + 0.946199i \(0.395111\pi\)
\(774\) −4.00974e18 1.20410e19i −0.0240951 0.0723560i
\(775\) −4.34385e19 −0.258680
\(776\) −3.08135e20 + 5.57449e19i −1.81848 + 0.328983i
\(777\) 1.57429e20i 0.920741i
\(778\) 2.21765e19 + 6.65945e19i 0.128539 + 0.385995i
\(779\) 1.24534e20 + 1.24534e20i 0.715362 + 0.715362i
\(780\) 1.55863e20 + 2.23592e19i 0.887318 + 0.127290i
\(781\) −2.29988e17 2.29988e17i −0.00129762 0.00129762i
\(782\) −1.18754e19 + 2.37334e19i −0.0664050 + 0.132713i
\(783\) 1.63737e20i 0.907435i
\(784\) 4.77757e18 1.63091e19i 0.0262418 0.0895815i
\(785\) 1.97156e19 0.107330
\(786\) −2.42500e20 1.21339e20i −1.30844 0.654698i
\(787\) −5.48210e19 + 5.48210e19i −0.293173 + 0.293173i −0.838332 0.545159i \(-0.816469\pi\)
0.545159 + 0.838332i \(0.316469\pi\)
\(788\) 1.70781e20 + 2.44994e19i 0.905226 + 0.129859i
\(789\) 3.99667e19 3.99667e19i 0.209971 0.209971i
\(790\) −6.84143e19 + 2.27825e19i −0.356252 + 0.118635i
\(791\) 2.22339e20 1.14757
\(792\) 6.33532e16 9.13386e16i 0.000324110 0.000467281i
\(793\) 3.16672e20i 1.60582i
\(794\) 1.12352e20 3.74139e19i 0.564723 0.188057i
\(795\) −1.42938e20 1.42938e20i −0.712160 0.712160i
\(796\) −1.20449e20 1.60795e20i −0.594856 0.794110i
\(797\) 1.17090e18 + 1.17090e18i 0.00573206 + 0.00573206i 0.709967 0.704235i \(-0.248710\pi\)
−0.704235 + 0.709967i \(0.748710\pi\)
\(798\) −1.72253e20 8.61895e19i −0.835884 0.418248i
\(799\) 1.99628e20i 0.960272i
\(800\) −8.21727e19 + 8.84000e19i −0.391830 + 0.421524i
\(801\) −5.46602e19 −0.258371
\(802\) −1.49176e18 + 2.98134e18i −0.00699004 + 0.0139698i
\(803\) 2.14909e16 2.14909e16i 9.98264e−5 9.98264e-5i
\(804\) −1.58963e20 + 1.19077e20i −0.731987 + 0.548320i
\(805\) 8.28052e18 8.28052e18i 0.0377995 0.0377995i
\(806\) 3.55428e19 + 1.06733e20i 0.160844 + 0.483005i
\(807\) 1.20456e20 0.540397
\(808\) −1.51374e20 + 2.18241e20i −0.673241 + 0.970636i
\(809\) 3.17314e20i 1.39910i −0.714583 0.699551i \(-0.753383\pi\)
0.714583 0.699551i \(-0.246617\pi\)
\(810\) −5.88370e19 1.76683e20i −0.257191 0.772326i
\(811\) −2.42290e20 2.42290e20i −1.05000 1.05000i −0.998682 0.0513171i \(-0.983658\pi\)
−0.0513171 0.998682i \(-0.516342\pi\)
\(812\) −4.48336e19 + 3.12527e20i −0.192624 + 1.34275i
\(813\) 2.66654e20 + 2.66654e20i 1.13583 + 1.13583i
\(814\) −1.00845e17 + 2.01542e17i −0.000425876 + 0.000851129i
\(815\) 1.62094e20i 0.678680i
\(816\) −2.41808e20 4.42172e20i −1.00378 1.83552i
\(817\) 3.14801e19 0.129563
\(818\) 2.44374e20 + 1.22276e20i 0.997198 + 0.498964i
\(819\) −8.96507e19 + 8.96507e19i −0.362716 + 0.362716i
\(820\) 2.88742e19 2.01277e20i 0.115828 0.807416i
\(821\) 1.71273e20 1.71273e20i 0.681219 0.681219i −0.279056 0.960275i \(-0.590022\pi\)
0.960275 + 0.279056i \(0.0900215\pi\)
\(822\) 4.58392e19 1.52648e19i 0.180773 0.0601989i
\(823\) −2.88193e20 −1.12690 −0.563450 0.826150i \(-0.690526\pi\)
−0.563450 + 0.826150i \(0.690526\pi\)
\(824\) −1.77391e20 + 3.20918e19i −0.687765 + 0.124424i
\(825\) 2.17425e17i 0.000835858i
\(826\) −2.17478e20 + 7.24219e19i −0.829001 + 0.276064i
\(827\) 1.12561e20 + 1.12561e20i 0.425451 + 0.425451i 0.887075 0.461625i \(-0.152733\pi\)
−0.461625 + 0.887075i \(0.652733\pi\)
\(828\) 8.75230e18 6.55622e18i 0.0328027 0.0245720i
\(829\) 2.90242e20 + 2.90242e20i 1.07865 + 1.07865i 0.996631 + 0.0820142i \(0.0261353\pi\)
0.0820142 + 0.996631i \(0.473865\pi\)
\(830\) 2.85906e20 + 1.43058e20i 1.05360 + 0.527187i
\(831\) 1.47705e20i 0.539744i
\(832\) 2.84444e20 + 1.29575e20i 1.03070 + 0.469522i
\(833\) −4.47398e19 −0.160761
\(834\) 8.27415e19 1.65362e20i 0.294823 0.589214i
\(835\) 2.40466e20 2.40466e20i 0.849665 0.849665i
\(836\) 1.65309e17 + 2.20681e17i 0.000579232 + 0.000773253i
\(837\) 5.82625e19 5.82625e19i 0.202447 0.202447i
\(838\) 9.71519e19 + 2.91740e20i 0.334767 + 1.00528i
\(839\) 1.71495e19 0.0586027 0.0293014 0.999571i \(-0.490672\pi\)
0.0293014 + 0.999571i \(0.490672\pi\)
\(840\) 3.95886e19 + 2.18830e20i 0.134158 + 0.741569i
\(841\) 3.06346e20i 1.02953i
\(842\) −9.12328e19 2.73966e20i −0.304065 0.913086i
\(843\) 1.74302e20 + 1.74302e20i 0.576114 + 0.576114i
\(844\) 4.14863e20 + 5.95141e19i 1.35990 + 0.195084i
\(845\) 4.00767e19 + 4.00767e19i 0.130285 + 0.130285i
\(846\) −3.68090e19 + 7.35641e19i −0.118676 + 0.237178i
\(847\) 2.97786e20i 0.952182i
\(848\) −1.92533e20 3.52067e20i −0.610568 1.11649i
\(849\) 3.08217e20 0.969400
\(850\) 2.84153e20 + 1.42180e20i 0.886378 + 0.443514i
\(851\) −1.56771e19 + 1.56771e19i −0.0485019 + 0.0485019i
\(852\) 6.01477e20 + 8.62849e19i 1.84562 + 0.264763i
\(853\) −1.72753e19 + 1.72753e19i −0.0525755 + 0.0525755i −0.732906 0.680330i \(-0.761836\pi\)
0.680330 + 0.732906i \(0.261836\pi\)
\(854\) 4.24334e20 1.41306e20i 1.28086 0.426537i
\(855\) −8.36432e19 −0.250419
\(856\) −4.20885e20 2.91929e20i −1.24982 0.866885i
\(857\) 3.90773e20i 1.15096i −0.817817 0.575478i \(-0.804816\pi\)
0.817817 0.575478i \(-0.195184\pi\)
\(858\) 5.34235e17 1.77905e17i 0.00156071 0.000519728i
\(859\) −3.57047e20 3.57047e20i −1.03460 1.03460i −0.999379 0.0352225i \(-0.988786\pi\)
−0.0352225 0.999379i \(-0.511214\pi\)
\(860\) −2.17903e19 2.90892e19i −0.0626288 0.0836071i
\(861\) 3.59175e20 + 3.59175e20i 1.02396 + 1.02396i
\(862\) −8.42540e19 4.21578e19i −0.238254 0.119214i
\(863\) 4.19811e20i 1.17755i 0.808298 + 0.588773i \(0.200389\pi\)
−0.808298 + 0.588773i \(0.799611\pi\)
\(864\) −8.35247e18 2.28783e20i −0.0232391 0.636544i
\(865\) −2.64796e20 −0.730802
\(866\) 1.03458e20 2.06765e20i 0.283230 0.566046i
\(867\) −6.21853e20 + 6.21853e20i −1.68871 + 1.68871i
\(868\) −1.27159e20 + 9.52532e19i −0.342539 + 0.256591i
\(869\) −1.82336e17 + 1.82336e17i −0.000487229 + 0.000487229i
\(870\) 1.34392e20 + 4.03571e20i 0.356238 + 1.06976i
\(871\) −3.24293e20 −0.852729
\(872\) −3.25481e20 2.25756e20i −0.849005 0.588877i
\(873\) 3.39691e20i 0.878990i
\(874\) 8.57036e18 + 2.57362e19i 0.0219998 + 0.0660639i
\(875\) −2.71404e20 2.71404e20i −0.691131 0.691131i
\(876\) −8.06276e18 + 5.62042e19i −0.0203683 + 0.141984i
\(877\) 1.77411e18 + 1.77411e18i 0.00444615 + 0.00444615i 0.709326 0.704880i \(-0.248999\pi\)
−0.704880 + 0.709326i \(0.748999\pi\)
\(878\) 1.55801e19 3.11374e19i 0.0387354 0.0774141i
\(879\) 3.90927e19i 0.0964214i
\(880\) 8.94949e16 3.05508e17i 0.000218988 0.000747555i
\(881\) −8.97990e19 −0.217992 −0.108996 0.994042i \(-0.534764\pi\)
−0.108996 + 0.994042i \(0.534764\pi\)
\(882\) 1.64869e19 + 8.24948e18i 0.0397062 + 0.0198677i
\(883\) −3.72896e20 + 3.72896e20i −0.890969 + 0.890969i −0.994614 0.103646i \(-0.966949\pi\)
0.103646 + 0.994614i \(0.466949\pi\)
\(884\) 1.16848e20 8.14527e20i 0.276984 1.93081i
\(885\) −2.18365e20 + 2.18365e20i −0.513546 + 0.513546i
\(886\) 3.95346e19 1.31653e19i 0.0922446 0.0307182i
\(887\) 3.59536e20 0.832295 0.416148 0.909297i \(-0.363380\pi\)
0.416148 + 0.909297i \(0.363380\pi\)
\(888\) −7.49512e19 4.14300e20i −0.172142 0.951533i
\(889\) 7.22480e20i 1.64632i
\(890\) −1.48521e20 + 4.94587e19i −0.335783 + 0.111818i
\(891\) −4.70891e17 4.70891e17i −0.00105627 0.00105627i
\(892\) 5.06256e20 3.79229e20i 1.12672 0.844010i
\(893\) −1.44281e20 1.44281e20i −0.318602 0.318602i
\(894\) −1.85039e20 9.25873e19i −0.405416 0.202856i
\(895\) 3.28779e20i 0.714730i
\(896\) −4.67016e19 + 4.38968e20i −0.100734 + 0.946840i
\(897\) 5.53942e19 0.118554
\(898\) 8.79104e18 1.75692e19i 0.0186684 0.0373094i
\(899\) −2.14887e20 + 2.14887e20i −0.452785 + 0.452785i
\(900\) −7.84955e19 1.04789e20i −0.164115 0.219087i
\(901\) −7.46984e20 + 7.46984e20i −1.54966 + 1.54966i
\(902\) −2.29742e17 6.89898e17i −0.000472927 0.00142017i
\(903\) 9.07936e19 0.185456
\(904\) 5.85121e20 1.05855e20i 1.18595 0.214551i
\(905\) 4.00145e20i 0.804781i
\(906\) 1.87530e20 + 5.63140e20i 0.374260 + 1.12388i
\(907\) 1.84901e20 + 1.84901e20i 0.366175 + 0.366175i 0.866080 0.499905i \(-0.166632\pi\)
−0.499905 + 0.866080i \(0.666632\pi\)
\(908\) −3.29320e20 4.72426e19i −0.647169 0.0928395i
\(909\) −2.03733e20 2.03733e20i −0.397296 0.397296i
\(910\) −1.62477e20 + 3.24716e20i −0.314414 + 0.628368i
\(911\) 1.42160e20i 0.272991i −0.990641 0.136496i \(-0.956416\pi\)
0.990641 0.136496i \(-0.0435839\pi\)
\(912\) −4.94345e20 1.44813e20i −0.942033 0.275958i
\(913\) 1.14326e18 0.00216197
\(914\) −5.29540e20 2.64964e20i −0.993747 0.497237i
\(915\) 4.26064e20 4.26064e20i 0.793463 0.793463i
\(916\) −2.91981e20 4.18861e19i −0.539618 0.0774109i
\(917\) 4.42153e20 4.42153e20i 0.810936 0.810936i
\(918\) −5.71826e20 + 1.90422e20i −1.04079 + 0.346593i
\(919\) 7.79669e20 1.40832 0.704160 0.710041i \(-0.251324\pi\)
0.704160 + 0.710041i \(0.251324\pi\)
\(920\) 1.78492e19 2.57338e19i 0.0319966 0.0461306i
\(921\) 3.33982e20i 0.594163i
\(922\) 2.02905e20 6.75689e19i 0.358242 0.119297i
\(923\) 7.01537e20 + 7.01537e20i 1.22925 + 1.22925i
\(924\) 4.76777e17 + 6.36479e17i 0.000829108 + 0.00110683i
\(925\) 1.87697e20 + 1.87697e20i 0.323940 + 0.323940i
\(926\) 2.63171e20 + 1.31682e20i 0.450777 + 0.225553i
\(927\) 1.95557e20i 0.332441i
\(928\) 3.08060e19 + 8.43810e20i 0.0519756 + 1.42367i
\(929\) 1.10552e20 0.185121 0.0925606 0.995707i \(-0.470495\pi\)
0.0925606 + 0.995707i \(0.470495\pi\)
\(930\) −9.57817e19 + 1.91423e20i −0.159185 + 0.318137i
\(931\) −3.23356e19 + 3.23356e19i −0.0533376 + 0.0533376i
\(932\) −5.57133e20 + 4.17340e20i −0.912110 + 0.683248i
\(933\) 1.46000e20 1.46000e20i 0.237236 0.237236i
\(934\) 4.10641e19 + 1.23313e20i 0.0662268 + 0.198874i
\(935\) −8.38081e17 −0.00134154
\(936\) −1.93248e20 + 2.78612e20i −0.307032 + 0.442659i
\(937\) 1.76879e18i 0.00278932i −0.999999 0.00139466i \(-0.999556\pi\)
0.999999 0.00139466i \(-0.000443935\pi\)
\(938\) −1.44707e20 4.34546e20i −0.226501 0.680168i
\(939\) −9.14244e20 9.14244e20i −1.42037 1.42037i
\(940\) −3.34527e19 + 2.33193e20i −0.0515865 + 0.359601i
\(941\) −6.75283e20 6.75283e20i −1.03361 1.03361i −0.999415 0.0341996i \(-0.989112\pi\)
−0.0341996 0.999415i \(-0.510888\pi\)
\(942\) −5.89393e19 + 1.17792e20i −0.0895465 + 0.178962i
\(943\) 7.15348e19i 0.107879i
\(944\) −5.37849e20 + 2.94130e20i −0.805112 + 0.440287i
\(945\) 2.65946e20 0.395158
\(946\) −1.16235e17 5.81600e16i −0.000171435 8.57801e-5i
\(947\) −1.08338e20 + 1.08338e20i −0.158609 + 0.158609i −0.781950 0.623341i \(-0.785775\pi\)
0.623341 + 0.781950i \(0.285775\pi\)
\(948\) 6.84072e19 4.76855e20i 0.0994130 0.692991i
\(949\) −6.55541e19 + 6.55541e19i −0.0945663 + 0.0945663i
\(950\) 3.08131e20 1.02610e20i 0.441236 0.146935i
\(951\) 1.17069e21 1.66410
\(952\) 1.14359e21 2.06887e20i 1.61366 0.291928i
\(953\) 7.46400e20i 1.04549i −0.852488 0.522747i \(-0.824907\pi\)
0.852488 0.522747i \(-0.175093\pi\)
\(954\) 4.13003e20 1.37533e20i 0.574267 0.191236i
\(955\) −1.53627e20 1.53627e20i −0.212052 0.212052i
\(956\) −4.24217e20 + 3.17775e20i −0.581276 + 0.435426i
\(957\) 1.07559e18 + 1.07559e18i 0.00146306 + 0.00146306i
\(958\) −1.01865e20 5.09696e19i −0.137551 0.0688260i
\(959\) 1.11412e20i 0.149348i
\(960\) 2.08368e20 + 5.57038e20i 0.277288 + 0.741286i
\(961\) 6.04018e20 0.797969
\(962\) 3.07610e20 6.14769e20i 0.403436 0.806282i
\(963\) 3.92906e20 3.92906e20i 0.511570 0.511570i
\(964\) 6.96093e20 + 9.29258e20i 0.899763 + 1.20115i
\(965\) −7.30796e19 + 7.30796e19i −0.0937789 + 0.0937789i
\(966\) 2.47182e19 + 7.42271e19i 0.0314903 + 0.0945633i
\(967\) −7.66548e20 −0.969514 −0.484757 0.874649i \(-0.661092\pi\)
−0.484757 + 0.874649i \(0.661092\pi\)
\(968\) 1.41774e20 + 7.83671e20i 0.178021 + 0.984025i
\(969\) 1.35611e21i 1.69055i
\(970\) −3.07366e20 9.22999e20i −0.380412 1.14235i
\(971\) 2.17604e20 + 2.17604e20i 0.267382 + 0.267382i 0.828044 0.560663i \(-0.189454\pi\)
−0.560663 + 0.828044i \(0.689454\pi\)
\(972\) 7.14660e20 + 1.02521e20i 0.871837 + 0.125069i
\(973\) 3.01507e20 + 3.01507e20i 0.365180 + 0.365180i
\(974\) 2.80031e20 5.59653e20i 0.336739 0.672986i
\(975\) 6.63218e20i 0.791815i
\(976\) 1.04943e21 5.73894e20i 1.24395 0.680272i
\(977\) 9.84047e19 0.115812 0.0579061 0.998322i \(-0.481558\pi\)
0.0579061 + 0.998322i \(0.481558\pi\)
\(978\) −9.68447e20 4.84578e20i −1.13163 0.566229i
\(979\) −3.95834e17 + 3.95834e17i −0.000459235 + 0.000459235i
\(980\) 5.22622e19 + 7.49727e18i 0.0602012 + 0.00863616i
\(981\) 3.03844e20 3.03844e20i 0.347510 0.347510i
\(982\) −1.62558e21 + 5.41330e20i −1.84598 + 0.614726i
\(983\) −2.24075e20 −0.252650 −0.126325 0.991989i \(-0.540318\pi\)
−0.126325 + 0.991989i \(0.540318\pi\)
\(984\) 1.11623e21 + 7.74225e20i 1.24965 + 0.866766i
\(985\) 5.36003e20i 0.595817i
\(986\) 2.10904e21 7.02326e20i 2.32780 0.775176i
\(987\) −4.16128e20 4.16128e20i −0.456044 0.456044i
\(988\) −5.04246e20 6.73150e20i −0.548712 0.732509i
\(989\) −9.04140e18 9.04140e18i −0.00976926 0.00976926i
\(990\) 3.08838e17 + 1.54532e17i 0.000331348 + 0.000165795i
\(991\) 1.49211e21i 1.58959i −0.606876 0.794796i \(-0.707578\pi\)
0.606876 0.794796i \(-0.292422\pi\)
\(992\) −2.89291e20 + 3.11214e20i −0.306022 + 0.329213i
\(993\) −1.00203e21 −1.05253
\(994\) −6.27003e20 + 1.25309e21i −0.653981 + 1.30700i
\(995\) 4.41346e20 4.41346e20i 0.457107 0.457107i
\(996\) −1.70942e21 + 1.28050e21i −1.75806 + 1.31694i
\(997\) 8.09179e20 8.09179e20i 0.826378 0.826378i −0.160636 0.987014i \(-0.551355\pi\)
0.987014 + 0.160636i \(0.0513545\pi\)
\(998\) −4.23559e20 1.27192e21i −0.429537 1.28987i
\(999\) −5.03503e20 −0.507042
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 16.15.f.a.3.18 54
4.3 odd 2 64.15.f.a.47.22 54
16.5 even 4 64.15.f.a.15.22 54
16.11 odd 4 inner 16.15.f.a.11.18 yes 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.15.f.a.3.18 54 1.1 even 1 trivial
16.15.f.a.11.18 yes 54 16.11 odd 4 inner
64.15.f.a.15.22 54 16.5 even 4
64.15.f.a.47.22 54 4.3 odd 2