Properties

Label 43.10.g.a.24.16
Level $43$
Weight $10$
Character 43.24
Analytic conductor $22.147$
Analytic rank $0$
Dimension $384$
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] = [43,10,Mod(9,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.9");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), 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: \(22.1465409550\)
Analytic rank: \(0\)
Dimension: \(384\)
Relative dimension: \(32\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 24.16
Character \(\chi\) \(=\) 43.24
Dual form 43.10.g.a.9.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.71937 + 4.66394i) q^{2} +(263.417 - 39.7037i) q^{3} +(106.012 + 464.469i) q^{4} +(1636.60 - 1115.81i) q^{5} +(-794.568 + 1376.23i) q^{6} +(3931.83 + 6810.12i) q^{7} +(-5312.37 - 2558.30i) q^{8} +(49003.4 - 15115.6i) q^{9} +O(q^{10})\) \(q+(-3.71937 + 4.66394i) q^{2} +(263.417 - 39.7037i) q^{3} +(106.012 + 464.469i) q^{4} +(1636.60 - 1115.81i) q^{5} +(-794.568 + 1376.23i) q^{6} +(3931.83 + 6810.12i) q^{7} +(-5312.37 - 2558.30i) q^{8} +(49003.4 - 15115.6i) q^{9} +(-883.022 + 11783.1i) q^{10} +(-7627.38 + 33417.7i) q^{11} +(46366.5 + 118140. i) q^{12} +(-1316.81 - 17571.6i) q^{13} +(-46385.9 - 6991.55i) q^{14} +(386805. - 358903. i) q^{15} +(-188077. + 90573.3i) q^{16} +(-321648. - 219296. i) q^{17} +(-111764. + 284769. i) q^{18} +(-511241. - 157697. i) q^{19} +(691760. + 641859. i) q^{20} +(1.30610e6 + 1.63779e6i) q^{21} +(-127489. - 159866. i) q^{22} +(-1.84656e6 - 1.71335e6i) q^{23} +(-1.50094e6 - 462979. i) q^{24} +(719854. - 1.83416e6i) q^{25} +(86850.5 + 59213.6i) q^{26} +(7.58404e6 - 3.65228e6i) q^{27} +(-2.74627e6 + 2.54817e6i) q^{28} +(2.09856e6 + 316307. i) q^{29} +(235230. + 3.13893e6i) q^{30} +(2.43461e6 + 6.20328e6i) q^{31} +(948869. - 4.15727e6i) q^{32} +(-682372. + 9.10562e6i) q^{33} +(2.21911e6 - 684505. i) q^{34} +(1.40336e7 + 6.75824e6i) q^{35} +(1.22157e7 + 2.11582e7i) q^{36} +(-1.62733e6 + 2.81862e6i) q^{37} +(2.63698e6 - 1.79786e6i) q^{38} +(-1.04453e6 - 4.57636e6i) q^{39} +(-1.15488e7 + 1.74070e6i) q^{40} +(2.88454e6 - 3.61710e6i) q^{41} -1.24964e7 q^{42} +(9.91424e6 + 2.01072e7i) q^{43} -1.63301e7 q^{44} +(6.33327e7 - 7.94167e7i) q^{45} +(1.48590e7 - 2.23963e6i) q^{46} +(-5.82225e6 - 2.55090e7i) q^{47} +(-4.59466e7 + 3.13259e7i) q^{48} +(-1.07417e7 + 1.86052e7i) q^{49} +(5.87700e6 + 1.01793e7i) q^{50} +(-9.34344e7 - 4.49956e7i) q^{51} +(8.02186e6 - 2.47442e6i) q^{52} +(8.26931e6 - 1.10346e8i) q^{53} +(-1.11738e7 + 4.89557e7i) q^{54} +(2.48050e7 + 6.32021e7i) q^{55} +(-3.46496e6 - 4.62367e7i) q^{56} +(-1.40931e8 - 2.12419e7i) q^{57} +(-9.28056e6 + 8.61110e6i) q^{58} +(4.19367e6 - 2.01956e6i) q^{59} +(2.07705e8 + 1.41611e8i) q^{60} +(-2.55321e7 + 6.50547e7i) q^{61} +(-3.79869e7 - 1.17174e7i) q^{62} +(2.95612e8 + 2.74288e8i) q^{63} +(-5.07786e7 - 6.36744e7i) q^{64} +(-2.17617e7 - 2.72883e7i) q^{65} +(-3.99301e7 - 3.70497e7i) q^{66} +(6.26418e7 + 1.93224e7i) q^{67} +(6.77577e7 - 1.72644e8i) q^{68} +(-5.54440e8 - 3.78011e8i) q^{69} +(-8.37163e7 + 4.03156e7i) q^{70} +(-9.05191e7 + 8.39894e7i) q^{71} +(-2.98995e8 - 4.50662e7i) q^{72} +(1.72323e6 + 2.29949e7i) q^{73} +(-7.09322e6 - 1.80732e7i) q^{74} +(1.16799e8 - 5.11729e8i) q^{75} +(1.90477e7 - 2.54174e8i) q^{76} +(-2.57568e8 + 7.94493e7i) q^{77} +(2.52289e7 + 1.21496e7i) q^{78} +(2.30019e8 + 3.98405e8i) q^{79} +(-2.06744e8 + 3.58091e8i) q^{80} +(1.01877e9 - 6.94583e8i) q^{81} +(6.14126e6 + 2.69066e7i) q^{82} +(3.22178e7 - 4.85605e6i) q^{83} +(-6.22242e8 + 7.80267e8i) q^{84} -7.71102e8 q^{85} +(-1.30654e8 - 2.85467e7i) q^{86} +5.65355e8 q^{87} +(1.26012e8 - 1.58014e8i) q^{88} +(-5.54771e8 + 8.36183e7i) q^{89} +(1.34837e8 + 5.90760e8i) q^{90} +(1.14487e8 - 7.80560e7i) q^{91} +(6.00043e8 - 1.03930e9i) q^{92} +(8.87609e8 + 1.53738e9i) q^{93} +(1.40627e8 + 6.77225e7i) q^{94} +(-1.01266e9 + 3.12363e8i) q^{95} +(8.48891e7 - 1.13277e9i) q^{96} +(1.12527e8 - 4.93014e8i) q^{97} +(-4.68211e7 - 1.19298e8i) q^{98} +(1.31360e8 + 1.75288e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 384 q + 56 q^{2} - 321 q^{3} - 16052 q^{4} - 695 q^{5} + 1274 q^{6} + 32650 q^{7} - 50022 q^{8} + 373611 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 384 q + 56 q^{2} - 321 q^{3} - 16052 q^{4} - 695 q^{5} + 1274 q^{6} + 32650 q^{7} - 50022 q^{8} + 373611 q^{9} + 6223 q^{10} + 180668 q^{11} - 270774 q^{12} + 11245 q^{13} - 271206 q^{14} - 835123 q^{15} - 6169448 q^{16} - 65194 q^{17} - 466218 q^{18} - 1417919 q^{19} + 5877261 q^{20} + 3242929 q^{21} - 4296822 q^{22} - 2544899 q^{23} - 6043976 q^{24} + 9428207 q^{25} - 11482629 q^{26} + 20117988 q^{27} + 7310292 q^{28} - 5289921 q^{29} + 23977480 q^{30} - 47539873 q^{31} + 18747558 q^{32} - 68064193 q^{33} - 73743233 q^{34} - 15006505 q^{35} - 203628199 q^{36} + 62563960 q^{37} + 108303102 q^{38} + 70931426 q^{39} + 14772713 q^{40} - 35636128 q^{41} + 29601006 q^{42} - 207110915 q^{43} + 367809332 q^{44} + 122079484 q^{45} + 164249271 q^{46} + 25529106 q^{47} + 191670995 q^{48} - 815972056 q^{49} - 210640197 q^{50} - 392161947 q^{51} - 873472922 q^{52} + 87568125 q^{53} + 627150582 q^{54} + 628156420 q^{55} + 725546751 q^{56} - 402646583 q^{57} - 677654606 q^{58} + 552834314 q^{59} + 990764675 q^{60} + 376844345 q^{61} + 76529685 q^{62} - 505887225 q^{63} + 621236102 q^{64} + 8885906 q^{65} + 895281647 q^{66} + 789662056 q^{67} - 2265959151 q^{68} - 2055955619 q^{69} + 3236566615 q^{70} + 635670789 q^{71} - 1964730073 q^{72} + 1333013552 q^{73} - 5184014638 q^{74} + 720042326 q^{75} + 477329288 q^{76} + 2282266995 q^{77} + 5133145036 q^{78} + 2903853142 q^{79} + 6779574014 q^{80} + 3699743739 q^{81} - 1268184088 q^{82} - 3074947634 q^{83} - 1313116801 q^{84} + 1946616146 q^{85} - 10088814540 q^{86} - 6085081326 q^{87} - 8012630430 q^{88} - 1632065068 q^{89} + 3316166089 q^{90} + 5386571784 q^{91} + 2280339030 q^{92} + 2459095364 q^{93} - 5048567488 q^{94} - 1597173221 q^{95} - 10288936616 q^{96} - 4337315288 q^{97} - 14989446392 q^{98} - 5338096561 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{20}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.71937 + 4.66394i −0.164374 + 0.206119i −0.857196 0.514990i \(-0.827796\pi\)
0.692822 + 0.721109i \(0.256367\pi\)
\(3\) 263.417 39.7037i 1.87758 0.282999i 0.891975 0.452085i \(-0.149319\pi\)
0.985601 + 0.169085i \(0.0540814\pi\)
\(4\) 106.012 + 464.469i 0.207055 + 0.907167i
\(5\) 1636.60 1115.81i 1.17105 0.798411i 0.188079 0.982154i \(-0.439774\pi\)
0.982974 + 0.183743i \(0.0588215\pi\)
\(6\) −794.568 + 1376.23i −0.250294 + 0.433522i
\(7\) 3931.83 + 6810.12i 0.618946 + 1.07205i 0.989678 + 0.143307i \(0.0457735\pi\)
−0.370732 + 0.928740i \(0.620893\pi\)
\(8\) −5312.37 2558.30i −0.458547 0.220824i
\(9\) 49003.4 15115.6i 2.48963 0.767950i
\(10\) −883.022 + 11783.1i −0.0279236 + 0.372614i
\(11\) −7627.38 + 33417.7i −0.157075 + 0.688192i 0.833648 + 0.552297i \(0.186248\pi\)
−0.990723 + 0.135896i \(0.956609\pi\)
\(12\) 46366.5 + 118140.i 0.645489 + 1.64468i
\(13\) −1316.81 17571.6i −0.0127873 0.170634i −0.999941 0.0108609i \(-0.996543\pi\)
0.987154 0.159773i \(-0.0510763\pi\)
\(14\) −46385.9 6991.55i −0.322708 0.0486404i
\(15\) 386805. 358903.i 1.97279 1.83048i
\(16\) −188077. + 90573.3i −0.717459 + 0.345510i
\(17\) −321648. 219296.i −0.934030 0.636811i −0.00231384 0.999997i \(-0.500737\pi\)
−0.931717 + 0.363186i \(0.881689\pi\)
\(18\) −111764. + 284769.i −0.250943 + 0.639392i
\(19\) −511241. 157697.i −0.899983 0.277608i −0.189965 0.981791i \(-0.560837\pi\)
−0.710019 + 0.704183i \(0.751314\pi\)
\(20\) 691760. + 641859.i 0.966764 + 0.897026i
\(21\) 1.30610e6 + 1.63779e6i 1.46551 + 1.83769i
\(22\) −127489. 159866.i −0.116030 0.145497i
\(23\) −1.84656e6 1.71335e6i −1.37590 1.27665i −0.922848 0.385165i \(-0.874144\pi\)
−0.453053 0.891484i \(-0.649665\pi\)
\(24\) −1.50094e6 462979.i −0.923449 0.284846i
\(25\) 719854. 1.83416e6i 0.368565 0.939089i
\(26\) 86850.5 + 59213.6i 0.0372728 + 0.0254122i
\(27\) 7.58404e6 3.65228e6i 2.74640 1.32260i
\(28\) −2.74627e6 + 2.54817e6i −0.844369 + 0.783460i
\(29\) 2.09856e6 + 316307.i 0.550973 + 0.0830459i 0.418628 0.908158i \(-0.362511\pi\)
0.132345 + 0.991204i \(0.457749\pi\)
\(30\) 235230. + 3.13893e6i 0.0530209 + 0.707514i
\(31\) 2.43461e6 + 6.20328e6i 0.473480 + 1.20641i 0.945733 + 0.324944i \(0.105345\pi\)
−0.472254 + 0.881463i \(0.656559\pi\)
\(32\) 948869. 4.15727e6i 0.159967 0.700863i
\(33\) −682372. + 9.10562e6i −0.100163 + 1.33659i
\(34\) 2.21911e6 684505.i 0.284789 0.0878459i
\(35\) 1.40336e7 + 6.75824e6i 1.58075 + 0.761250i
\(36\) 1.22157e7 + 2.11582e7i 1.21215 + 2.09950i
\(37\) −1.62733e6 + 2.81862e6i −0.142747 + 0.247245i −0.928530 0.371257i \(-0.878927\pi\)
0.785783 + 0.618502i \(0.212260\pi\)
\(38\) 2.63698e6 1.79786e6i 0.205154 0.139872i
\(39\) −1.04453e6 4.57636e6i −0.0722983 0.316760i
\(40\) −1.15488e7 + 1.74070e6i −0.713291 + 0.107511i
\(41\) 2.88454e6 3.61710e6i 0.159422 0.199909i −0.695705 0.718328i \(-0.744908\pi\)
0.855127 + 0.518419i \(0.173479\pi\)
\(42\) −1.24964e7 −0.619674
\(43\) 9.91424e6 + 2.01072e7i 0.442233 + 0.896900i
\(44\) −1.63301e7 −0.656828
\(45\) 6.33327e7 7.94167e7i 2.30235 2.88706i
\(46\) 1.48590e7 2.23963e6i 0.489304 0.0737508i
\(47\) −5.82225e6 2.55090e7i −0.174041 0.762522i −0.984308 0.176461i \(-0.943535\pi\)
0.810267 0.586061i \(-0.199322\pi\)
\(48\) −4.59466e7 + 3.13259e7i −1.24930 + 0.851761i
\(49\) −1.07417e7 + 1.86052e7i −0.266189 + 0.461053i
\(50\) 5.87700e6 + 1.01793e7i 0.132981 + 0.230330i
\(51\) −9.34344e7 4.49956e7i −1.93393 0.931332i
\(52\) 8.02186e6 2.47442e6i 0.152146 0.0469308i
\(53\) 8.26931e6 1.10346e8i 0.143955 1.92095i −0.196167 0.980570i \(-0.562850\pi\)
0.340123 0.940381i \(-0.389531\pi\)
\(54\) −1.11738e7 + 4.89557e7i −0.178826 + 0.783486i
\(55\) 2.48050e7 + 6.32021e7i 0.365516 + 0.931320i
\(56\) −3.46496e6 4.62367e7i −0.0470817 0.628262i
\(57\) −1.40931e8 2.12419e7i −1.76835 0.266536i
\(58\) −9.28056e6 + 8.61110e6i −0.107683 + 0.0999154i
\(59\) 4.19367e6 2.01956e6i 0.0450568 0.0216982i −0.411220 0.911536i \(-0.634897\pi\)
0.456276 + 0.889838i \(0.349183\pi\)
\(60\) 2.07705e8 + 1.41611e8i 2.06903 + 1.41064i
\(61\) −2.55321e7 + 6.50547e7i −0.236103 + 0.601581i −0.998989 0.0449518i \(-0.985687\pi\)
0.762886 + 0.646533i \(0.223782\pi\)
\(62\) −3.79869e7 1.17174e7i −0.326491 0.100709i
\(63\) 2.95612e8 + 2.74288e8i 2.36423 + 2.19368i
\(64\) −5.07786e7 6.36744e7i −0.378330 0.474411i
\(65\) −2.17617e7 2.72883e7i −0.151211 0.189612i
\(66\) −3.99301e7 3.70497e7i −0.259031 0.240346i
\(67\) 6.26418e7 + 1.93224e7i 0.379776 + 0.117145i 0.478765 0.877943i \(-0.341085\pi\)
−0.0989890 + 0.995089i \(0.531561\pi\)
\(68\) 6.77577e7 1.72644e8i 0.384298 0.979176i
\(69\) −5.54440e8 3.78011e8i −2.94465 2.00763i
\(70\) −8.37163e7 + 4.03156e7i −0.416743 + 0.200693i
\(71\) −9.05191e7 + 8.39894e7i −0.422744 + 0.392249i −0.862655 0.505792i \(-0.831200\pi\)
0.439911 + 0.898041i \(0.355010\pi\)
\(72\) −2.98995e8 4.50662e7i −1.31119 0.197631i
\(73\) 1.72323e6 + 2.29949e7i 0.00710215 + 0.0947716i 0.999628 0.0272599i \(-0.00867817\pi\)
−0.992526 + 0.122031i \(0.961059\pi\)
\(74\) −7.09322e6 1.80732e7i −0.0274980 0.0700637i
\(75\) 1.16799e8 5.11729e8i 0.426248 1.86751i
\(76\) 1.90477e7 2.54174e8i 0.0654909 0.873915i
\(77\) −2.57568e8 + 7.94493e7i −0.834995 + 0.257562i
\(78\) 2.52289e7 + 1.21496e7i 0.0771742 + 0.0371651i
\(79\) 2.30019e8 + 3.98405e8i 0.664419 + 1.15081i 0.979442 + 0.201724i \(0.0646544\pi\)
−0.315023 + 0.949084i \(0.602012\pi\)
\(80\) −2.06744e8 + 3.58091e8i −0.564323 + 0.977437i
\(81\) 1.01877e9 6.94583e8i 2.62961 1.79284i
\(82\) 6.14126e6 + 2.69066e7i 0.0150001 + 0.0657199i
\(83\) 3.22178e7 4.85605e6i 0.0745150 0.0112313i −0.111679 0.993744i \(-0.535623\pi\)
0.186194 + 0.982513i \(0.440385\pi\)
\(84\) −6.22242e8 + 7.80267e8i −1.36365 + 1.70996i
\(85\) −7.71102e8 −1.60224
\(86\) −1.30654e8 2.85467e7i −0.257560 0.0562747i
\(87\) 5.65355e8 1.05800
\(88\) 1.26012e8 1.58014e8i 0.223996 0.280882i
\(89\) −5.54771e8 + 8.36183e7i −0.937257 + 0.141269i −0.599870 0.800097i \(-0.704781\pi\)
−0.337387 + 0.941366i \(0.609543\pi\)
\(90\) 1.34837e8 + 5.90760e8i 0.216630 + 0.949117i
\(91\) 1.14487e8 7.80560e7i 0.175013 0.119322i
\(92\) 6.00043e8 1.03930e9i 0.873246 1.51251i
\(93\) 8.87609e8 + 1.53738e9i 1.23041 + 2.13113i
\(94\) 1.40627e8 + 6.77225e7i 0.185778 + 0.0894660i
\(95\) −1.01266e9 + 3.12363e8i −1.27557 + 0.393462i
\(96\) 8.48891e7 1.13277e9i 0.102007 1.36119i
\(97\) 1.12527e8 4.93014e8i 0.129058 0.565440i −0.868506 0.495679i \(-0.834919\pi\)
0.997564 0.0697611i \(-0.0222237\pi\)
\(98\) −4.68211e7 1.19298e8i −0.0512771 0.130652i
\(99\) 1.31360e8 + 1.75288e9i 0.137437 + 1.83397i
\(100\) 9.28223e8 + 1.39907e8i 0.928223 + 0.139907i
\(101\) 1.06044e9 9.83947e8i 1.01401 0.940862i 0.0157505 0.999876i \(-0.494986\pi\)
0.998257 + 0.0590144i \(0.0187958\pi\)
\(102\) 5.57374e8 2.68417e8i 0.509854 0.245533i
\(103\) −1.72014e9 1.17277e9i −1.50590 1.02671i −0.984895 0.173151i \(-0.944605\pi\)
−0.521005 0.853554i \(-0.674443\pi\)
\(104\) −3.79580e7 + 9.67155e7i −0.0318166 + 0.0810674i
\(105\) 3.96502e9 + 1.22305e9i 3.18342 + 0.981954i
\(106\) 4.83892e8 + 4.48986e8i 0.372282 + 0.345427i
\(107\) 3.67341e8 + 4.60632e8i 0.270921 + 0.339724i 0.898617 0.438735i \(-0.144573\pi\)
−0.627696 + 0.778459i \(0.716002\pi\)
\(108\) 2.50037e9 + 3.13537e9i 1.76847 + 2.21759i
\(109\) −1.24588e9 1.15601e9i −0.845392 0.784409i 0.133011 0.991115i \(-0.457535\pi\)
−0.978403 + 0.206705i \(0.933726\pi\)
\(110\) −3.87029e8 1.19383e8i −0.252044 0.0777454i
\(111\) −3.16756e8 + 8.07082e8i −0.198049 + 0.504620i
\(112\) −1.35630e9 9.24712e8i −0.814471 0.555297i
\(113\) 6.12005e8 2.94726e8i 0.353103 0.170046i −0.248920 0.968524i \(-0.580076\pi\)
0.602023 + 0.798478i \(0.294361\pi\)
\(114\) 6.23243e8 5.78285e8i 0.345610 0.320679i
\(115\) −4.93385e9 7.43658e8i −2.63054 0.396490i
\(116\) 7.55579e7 + 1.00825e9i 0.0387453 + 0.517020i
\(117\) −3.30132e8 8.41163e8i −0.162874 0.414996i
\(118\) −6.17867e6 + 2.70705e7i −0.00293377 + 0.0128537i
\(119\) 2.28768e8 3.05270e9i 0.104576 1.39548i
\(120\) −2.97303e9 + 9.17059e8i −1.30883 + 0.403721i
\(121\) 1.06587e9 + 5.13296e8i 0.452033 + 0.217688i
\(122\) −2.08448e8 3.61042e8i −0.0851880 0.147550i
\(123\) 6.16223e8 1.06733e9i 0.242753 0.420461i
\(124\) −2.62314e9 + 1.78842e9i −0.996376 + 0.679317i
\(125\) −7.59713e6 3.32852e7i −0.00278327 0.0121943i
\(126\) −2.37875e9 + 3.58539e8i −0.840778 + 0.126727i
\(127\) 9.44256e8 1.18406e9i 0.322087 0.403884i −0.594258 0.804275i \(-0.702554\pi\)
0.916345 + 0.400391i \(0.131126\pi\)
\(128\) 2.66910e9 0.878860
\(129\) 3.40991e9 + 4.90295e9i 1.08415 + 1.55885i
\(130\) 2.08210e8 0.0639378
\(131\) −3.81445e9 + 4.78317e9i −1.13165 + 1.41904i −0.237432 + 0.971404i \(0.576306\pi\)
−0.894215 + 0.447637i \(0.852266\pi\)
\(132\) −4.30162e9 + 6.48365e8i −1.23325 + 0.185882i
\(133\) −9.36175e8 4.10165e9i −0.259433 1.13665i
\(134\) −3.23106e8 + 2.20290e8i −0.0865713 + 0.0590233i
\(135\) 8.33675e9 1.44397e10i 2.16021 3.74159i
\(136\) 1.14769e9 + 1.98786e9i 0.287673 + 0.498264i
\(137\) −2.43302e9 1.17168e9i −0.590069 0.284162i 0.114926 0.993374i \(-0.463337\pi\)
−0.704996 + 0.709212i \(0.749051\pi\)
\(138\) 3.82518e9 1.17991e9i 0.897835 0.276945i
\(139\) 2.08316e8 2.77978e9i 0.0473321 0.631603i −0.922212 0.386685i \(-0.873620\pi\)
0.969544 0.244918i \(-0.0787610\pi\)
\(140\) −1.65126e9 + 7.23465e9i −0.363278 + 1.59163i
\(141\) −2.54648e9 6.48832e9i −0.542568 1.38244i
\(142\) −5.50479e7 7.34563e8i −0.0113617 0.151611i
\(143\) 5.97246e8 + 9.00203e7i 0.119438 + 0.0180023i
\(144\) −7.84737e9 + 7.28130e9i −1.52087 + 1.41116i
\(145\) 3.78744e9 1.82393e9i 0.711524 0.342652i
\(146\) −1.13656e8 7.74893e7i −0.0207016 0.0141141i
\(147\) −2.09085e9 + 5.32740e9i −0.369313 + 0.940995i
\(148\) −1.48168e9 4.57037e8i −0.253849 0.0783021i
\(149\) 3.98939e9 + 3.70161e9i 0.663084 + 0.615252i 0.938173 0.346167i \(-0.112517\pi\)
−0.275089 + 0.961419i \(0.588707\pi\)
\(150\) 1.95225e9 + 2.44805e9i 0.314866 + 0.394829i
\(151\) 4.55152e9 + 5.70742e9i 0.712459 + 0.893396i 0.997885 0.0650053i \(-0.0207064\pi\)
−0.285426 + 0.958401i \(0.592135\pi\)
\(152\) 2.31247e9 + 2.14565e9i 0.351382 + 0.326034i
\(153\) −1.90766e10 5.88437e9i −2.81443 0.868137i
\(154\) 5.87444e8 1.49678e9i 0.0841634 0.214445i
\(155\) 1.09062e10 + 7.43570e9i 1.51768 + 1.03474i
\(156\) 2.01485e9 9.70300e8i 0.272384 0.131173i
\(157\) −3.51192e9 + 3.25858e9i −0.461313 + 0.428036i −0.876281 0.481800i \(-0.839983\pi\)
0.414968 + 0.909836i \(0.363793\pi\)
\(158\) −2.71366e9 4.09019e8i −0.346417 0.0522139i
\(159\) −2.20288e9 2.93954e10i −0.273340 3.64747i
\(160\) −3.08581e9 7.86253e9i −0.372246 0.948467i
\(161\) 4.40781e9 1.93119e10i 0.517019 2.26521i
\(162\) −5.49673e8 + 7.33488e9i −0.0627028 + 0.836710i
\(163\) −1.20367e10 + 3.71284e9i −1.33556 + 0.411967i −0.878617 0.477527i \(-0.841533\pi\)
−0.456947 + 0.889494i \(0.651057\pi\)
\(164\) 1.98583e9 + 9.56323e8i 0.214360 + 0.103230i
\(165\) 9.04340e9 + 1.56636e10i 0.949848 + 1.64518i
\(166\) −9.71814e7 + 1.68323e8i −0.00993337 + 0.0172051i
\(167\) −1.33664e10 + 9.11304e9i −1.32981 + 0.906649i −0.999309 0.0371570i \(-0.988170\pi\)
−0.330500 + 0.943806i \(0.607217\pi\)
\(168\) −2.74850e9 1.20419e10i −0.266197 1.16629i
\(169\) 1.01790e10 1.53424e9i 0.959878 0.144678i
\(170\) 2.86801e9 3.59637e9i 0.263367 0.330251i
\(171\) −2.74362e10 −2.45382
\(172\) −8.28816e9 + 6.73647e9i −0.722071 + 0.586887i
\(173\) −6.52825e9 −0.554102 −0.277051 0.960855i \(-0.589357\pi\)
−0.277051 + 0.960855i \(0.589357\pi\)
\(174\) −2.10276e9 + 2.63678e9i −0.173907 + 0.218073i
\(175\) 1.53212e10 2.30930e9i 1.23487 0.186127i
\(176\) −1.59222e9 6.97596e9i −0.125082 0.548021i
\(177\) 1.02450e9 6.98491e8i 0.0784569 0.0534910i
\(178\) 1.67341e9 2.89843e9i 0.124943 0.216407i
\(179\) 3.71798e9 + 6.43972e9i 0.270687 + 0.468844i 0.969038 0.246912i \(-0.0794157\pi\)
−0.698351 + 0.715756i \(0.746082\pi\)
\(180\) 4.36007e10 + 2.09970e10i 3.09576 + 1.49084i
\(181\) 1.25946e10 3.88491e9i 0.872227 0.269046i 0.173846 0.984773i \(-0.444381\pi\)
0.698381 + 0.715727i \(0.253904\pi\)
\(182\) −6.17712e7 + 8.24280e8i −0.00417316 + 0.0556869i
\(183\) −4.14267e9 + 1.81502e10i −0.273055 + 1.19633i
\(184\) 5.42631e9 + 1.38260e10i 0.348999 + 0.889235i
\(185\) 4.81767e8 + 6.42873e9i 0.0302388 + 0.403508i
\(186\) −1.04716e10 1.57834e9i −0.641513 0.0966925i
\(187\) 9.78171e9 9.07610e9i 0.584962 0.542765i
\(188\) 1.12309e10 5.40851e9i 0.655698 0.315768i
\(189\) 5.46916e10 + 3.72881e10i 3.11776 + 2.12565i
\(190\) 2.30960e9 5.88476e9i 0.128572 0.327595i
\(191\) 4.16124e9 + 1.28357e9i 0.226242 + 0.0697864i 0.405803 0.913960i \(-0.366992\pi\)
−0.179562 + 0.983747i \(0.557468\pi\)
\(192\) −1.59040e10 1.47568e10i −0.844602 0.783676i
\(193\) 9.36953e9 + 1.17490e10i 0.486082 + 0.609528i 0.963027 0.269406i \(-0.0868272\pi\)
−0.476945 + 0.878933i \(0.658256\pi\)
\(194\) 1.88086e9 + 2.35852e9i 0.0953341 + 0.119545i
\(195\) −6.81583e9 6.32417e9i −0.337569 0.313219i
\(196\) −9.78028e9 3.01682e9i −0.473368 0.146015i
\(197\) −6.18724e9 + 1.57648e10i −0.292684 + 0.745746i 0.706589 + 0.707624i \(0.250233\pi\)
−0.999273 + 0.0381223i \(0.987862\pi\)
\(198\) −8.66388e9 5.90693e9i −0.400607 0.273129i
\(199\) 2.09658e10 1.00966e10i 0.947702 0.456389i 0.104822 0.994491i \(-0.466573\pi\)
0.842880 + 0.538102i \(0.180858\pi\)
\(200\) −8.51646e9 + 7.90212e9i −0.376378 + 0.349228i
\(201\) 1.72681e10 + 2.60274e9i 0.746210 + 0.112473i
\(202\) 6.44893e8 + 8.60550e9i 0.0272525 + 0.363660i
\(203\) 6.09709e9 + 1.55351e10i 0.251994 + 0.642070i
\(204\) 1.09939e10 4.81675e10i 0.444443 1.94723i
\(205\) 6.84823e8 9.13833e9i 0.0270823 0.361389i
\(206\) 1.18676e10 3.66066e9i 0.459155 0.141630i
\(207\) −1.16386e11 5.60484e10i −4.40589 2.12176i
\(208\) 1.83918e9 + 3.18555e9i 0.0681301 + 0.118005i
\(209\) 9.16930e9 1.58817e10i 0.332413 0.575756i
\(210\) −2.04516e10 + 1.39437e10i −0.725671 + 0.494754i
\(211\) 5.55949e9 + 2.43577e10i 0.193092 + 0.845990i 0.974931 + 0.222509i \(0.0714248\pi\)
−0.781839 + 0.623481i \(0.785718\pi\)
\(212\) 5.21291e10 7.85720e9i 1.77243 0.267151i
\(213\) −2.05095e10 + 2.57182e10i −0.682728 + 0.856114i
\(214\) −3.51463e9 −0.114556
\(215\) 3.86615e10 + 2.18450e10i 1.23397 + 0.697234i
\(216\) −4.96329e10 −1.55141
\(217\) −3.26726e10 + 4.09702e10i −1.00027 + 1.25429i
\(218\) 1.00255e10 1.51110e9i 0.300642 0.0453145i
\(219\) 1.36691e9 + 5.98881e9i 0.0401551 + 0.175931i
\(220\) −2.67258e10 + 1.82213e10i −0.769181 + 0.524419i
\(221\) −3.42983e9 + 5.94064e9i −0.0967180 + 0.167520i
\(222\) −2.58605e9 4.47916e9i −0.0714575 0.123768i
\(223\) −3.36346e10 1.61976e10i −0.910782 0.438609i −0.0810108 0.996713i \(-0.525815\pi\)
−0.829771 + 0.558104i \(0.811529\pi\)
\(224\) 3.20423e10 9.88373e9i 0.850369 0.262304i
\(225\) 7.55099e9 1.00761e11i 0.196419 2.62102i
\(226\) −9.01686e8 + 3.95055e9i −0.0229915 + 0.100732i
\(227\) −1.68386e10 4.29041e10i −0.420911 1.07246i −0.971364 0.237598i \(-0.923640\pi\)
0.550453 0.834866i \(-0.314455\pi\)
\(228\) −5.07415e9 6.77098e10i −0.124353 1.65938i
\(229\) −1.37430e10 2.07143e9i −0.330235 0.0497749i −0.0181676 0.999835i \(-0.505783\pi\)
−0.312067 + 0.950060i \(0.601021\pi\)
\(230\) 2.18192e10 2.02452e10i 0.514118 0.477032i
\(231\) −6.46934e10 + 3.11547e10i −1.49488 + 0.719895i
\(232\) −1.03391e10 7.04910e9i −0.234308 0.159749i
\(233\) 6.33367e9 1.61379e10i 0.140784 0.358712i −0.843039 0.537852i \(-0.819236\pi\)
0.983824 + 0.179139i \(0.0573313\pi\)
\(234\) 5.15102e9 + 1.58888e9i 0.112311 + 0.0346433i
\(235\) −3.79919e10 3.52513e10i −0.812616 0.753998i
\(236\) 1.38260e9 + 1.73373e9i 0.0290131 + 0.0363813i
\(237\) 7.64091e10 + 9.58139e10i 1.57318 + 1.97270i
\(238\) 1.33867e10 + 1.24211e10i 0.270444 + 0.250936i
\(239\) 4.06158e10 + 1.25283e10i 0.805201 + 0.248372i 0.669918 0.742435i \(-0.266329\pi\)
0.135283 + 0.990807i \(0.456806\pi\)
\(240\) −4.02423e10 + 1.02536e11i −0.782947 + 1.99492i
\(241\) 1.53978e10 + 1.04980e10i 0.294024 + 0.200462i 0.701343 0.712824i \(-0.252584\pi\)
−0.407320 + 0.913286i \(0.633536\pi\)
\(242\) −6.35834e9 + 3.06202e9i −0.119172 + 0.0573903i
\(243\) 1.19327e11 1.10719e11i 2.19539 2.03702i
\(244\) −3.29226e10 4.96229e9i −0.594621 0.0896247i
\(245\) 3.18006e9 + 4.24349e10i 0.0563881 + 0.752447i
\(246\) 2.68600e9 + 6.84382e9i 0.0467626 + 0.119149i
\(247\) −2.09778e9 + 9.19097e9i −0.0358611 + 0.157118i
\(248\) 2.93633e9 3.91826e10i 0.0492915 0.657750i
\(249\) 8.29389e9 2.55833e9i 0.136729 0.0421754i
\(250\) 1.83497e8 + 8.83674e7i 0.00297097 + 0.00143074i
\(251\) −4.59906e8 7.96581e8i −0.00731371 0.0126677i 0.862345 0.506320i \(-0.168995\pi\)
−0.869659 + 0.493653i \(0.835661\pi\)
\(252\) −9.60597e10 + 1.66380e11i −1.50051 + 2.59896i
\(253\) 7.13407e10 4.86393e10i 1.09470 0.746354i
\(254\) 2.01035e9 + 8.80790e9i 0.0303053 + 0.132776i
\(255\) −2.03121e11 + 3.06156e10i −3.00832 + 0.453431i
\(256\) 1.60713e10 2.01528e10i 0.233868 0.293262i
\(257\) 2.44318e10 0.349347 0.174673 0.984626i \(-0.444113\pi\)
0.174673 + 0.984626i \(0.444113\pi\)
\(258\) −3.55497e10 2.33226e9i −0.499514 0.0327709i
\(259\) −2.55935e10 −0.353412
\(260\) 1.03676e10 1.30005e10i 0.140701 0.176433i
\(261\) 1.07618e11 1.62208e10i 1.43550 0.216366i
\(262\) −8.12107e9 3.55807e10i −0.106477 0.466508i
\(263\) −1.23609e10 + 8.42753e9i −0.159313 + 0.108617i −0.640352 0.768081i \(-0.721212\pi\)
0.481040 + 0.876699i \(0.340259\pi\)
\(264\) 2.69199e10 4.66267e10i 0.341080 0.590768i
\(265\) −1.09592e11 1.89819e11i −1.36513 2.36447i
\(266\) 2.26118e10 + 1.08893e10i 0.276929 + 0.133362i
\(267\) −1.42816e11 + 4.40529e10i −1.71979 + 0.530486i
\(268\) −2.33389e9 + 3.11436e10i −0.0276359 + 0.368775i
\(269\) 9.81690e9 4.30107e10i 0.114311 0.500831i −0.885063 0.465471i \(-0.845885\pi\)
0.999375 0.0353600i \(-0.0112578\pi\)
\(270\) 3.63383e10 + 9.25886e10i 0.416129 + 1.06028i
\(271\) 1.15748e10 + 1.54455e11i 0.130363 + 1.73957i 0.552922 + 0.833233i \(0.313513\pi\)
−0.422559 + 0.906335i \(0.638868\pi\)
\(272\) 8.03572e10 + 1.21119e10i 0.890153 + 0.134169i
\(273\) 2.70587e10 2.51068e10i 0.294832 0.273564i
\(274\) 1.45139e10 6.98954e9i 0.155563 0.0749154i
\(275\) 5.58028e10 + 3.80457e10i 0.588381 + 0.401151i
\(276\) 1.16797e11 2.97594e11i 1.21155 3.08698i
\(277\) −7.65826e10 2.36226e10i −0.781576 0.241084i −0.121808 0.992554i \(-0.538869\pi\)
−0.659768 + 0.751470i \(0.729345\pi\)
\(278\) 1.21899e10 + 1.13106e10i 0.122405 + 0.113575i
\(279\) 2.13070e11 + 2.67182e11i 2.10525 + 2.63990i
\(280\) −5.72622e10 7.18046e10i −0.556746 0.698137i
\(281\) −2.51769e10 2.33608e10i −0.240893 0.223516i 0.550482 0.834847i \(-0.314444\pi\)
−0.791375 + 0.611331i \(0.790634\pi\)
\(282\) 3.97324e10 + 1.22558e10i 0.374131 + 0.115404i
\(283\) −2.69722e9 + 6.87240e9i −0.0249964 + 0.0636897i −0.942827 0.333282i \(-0.891844\pi\)
0.917831 + 0.396972i \(0.129939\pi\)
\(284\) −4.86066e10 3.31394e10i −0.443367 0.302282i
\(285\) −2.54348e11 + 1.22488e11i −2.28364 + 1.09974i
\(286\) −2.64123e9 + 2.45070e9i −0.0233431 + 0.0216592i
\(287\) 3.59744e10 + 5.42226e9i 0.312986 + 0.0471750i
\(288\) −1.63416e10 2.18063e11i −0.139968 1.86774i
\(289\) 1.20418e10 + 3.06820e10i 0.101543 + 0.258728i
\(290\) −5.58015e9 + 2.44483e10i −0.0463292 + 0.202982i
\(291\) 1.00671e10 1.34336e11i 0.0822973 1.09818i
\(292\) −1.04977e10 + 3.23812e9i −0.0845031 + 0.0260657i
\(293\) 1.54321e11 + 7.43172e10i 1.22327 + 0.589095i 0.930220 0.367003i \(-0.119616\pi\)
0.293048 + 0.956098i \(0.405330\pi\)
\(294\) −1.70700e10 2.95661e10i −0.133251 0.230798i
\(295\) 4.60989e9 7.98456e9i 0.0354398 0.0613835i
\(296\) 1.58559e10 1.08103e10i 0.120054 0.0818515i
\(297\) 6.42046e10 + 2.81299e11i 0.478809 + 2.09780i
\(298\) −3.21021e10 + 4.83861e9i −0.235809 + 0.0355425i
\(299\) −2.76748e10 + 3.47030e10i −0.200246 + 0.251100i
\(300\) 2.50064e11 1.78240
\(301\) −9.79516e10 + 1.46575e11i −0.687800 + 1.02923i
\(302\) −4.35478e10 −0.301256
\(303\) 2.40272e11 3.01292e11i 1.63761 2.05350i
\(304\) 1.10436e11 1.66456e10i 0.741617 0.111781i
\(305\) 3.08031e10 + 1.34957e11i 0.203819 + 0.892991i
\(306\) 9.83974e10 6.70862e10i 0.641560 0.437408i
\(307\) 2.71220e10 4.69768e10i 0.174261 0.301829i −0.765644 0.643264i \(-0.777580\pi\)
0.939905 + 0.341435i \(0.110913\pi\)
\(308\) −6.42071e10 1.11210e11i −0.406541 0.704151i
\(309\) −4.99677e11 2.40632e11i −3.11800 1.50155i
\(310\) −7.52437e10 + 2.32096e10i −0.462746 + 0.142738i
\(311\) −1.97418e10 + 2.63437e11i −0.119665 + 1.59681i 0.537630 + 0.843181i \(0.319320\pi\)
−0.657295 + 0.753633i \(0.728299\pi\)
\(312\) −6.15882e9 + 2.69836e10i −0.0367961 + 0.161214i
\(313\) −8.03813e8 2.04808e9i −0.00473375 0.0120614i 0.928487 0.371364i \(-0.121110\pi\)
−0.933221 + 0.359303i \(0.883015\pi\)
\(314\) −2.13572e9 2.84992e10i −0.0123983 0.165444i
\(315\) 7.89851e11 + 1.19051e11i 4.52009 + 0.681295i
\(316\) −1.60662e11 + 1.49073e11i −0.906403 + 0.841019i
\(317\) −2.64345e11 + 1.27302e11i −1.47030 + 0.708058i −0.985984 0.166837i \(-0.946645\pi\)
−0.484313 + 0.874895i \(0.660930\pi\)
\(318\) 1.45292e11 + 9.90581e10i 0.796743 + 0.543210i
\(319\) −2.65768e10 + 6.77165e10i −0.143696 + 0.366131i
\(320\) −1.54153e11 4.75498e10i −0.821820 0.253498i
\(321\) 1.15053e11 + 1.06753e11i 0.604817 + 0.561188i
\(322\) 7.36751e10 + 9.23857e10i 0.381917 + 0.478909i
\(323\) 1.29857e11 + 1.62836e11i 0.663828 + 0.832414i
\(324\) 4.30614e11 + 3.99552e11i 2.17088 + 2.01428i
\(325\) −3.31769e10 1.02337e10i −0.164953 0.0508814i
\(326\) 2.74526e10 6.99481e10i 0.134618 0.343002i
\(327\) −3.74084e11 2.55046e11i −1.80928 1.23354i
\(328\) −2.45774e10 + 1.18358e10i −0.117247 + 0.0564633i
\(329\) 1.50827e11 1.39947e11i 0.709737 0.658540i
\(330\) −1.06690e11 1.60809e10i −0.495234 0.0746446i
\(331\) −2.61139e9 3.48466e10i −0.0119577 0.159564i −0.999986 0.00529144i \(-0.998316\pi\)
0.988028 0.154273i \(-0.0493034\pi\)
\(332\) 5.67096e9 + 1.44494e10i 0.0256174 + 0.0652720i
\(333\) −3.71397e10 + 1.62720e11i −0.165516 + 0.725173i
\(334\) 7.21179e9 9.62347e10i 0.0317091 0.423129i
\(335\) 1.24079e11 3.82735e10i 0.538268 0.166034i
\(336\) −3.93987e11 1.89734e11i −1.68638 0.812118i
\(337\) −1.65037e11 2.85852e11i −0.697021 1.20728i −0.969495 0.245113i \(-0.921175\pi\)
0.272473 0.962163i \(-0.412158\pi\)
\(338\) −3.07039e10 + 5.31808e10i −0.127958 + 0.221631i
\(339\) 1.49511e11 1.01935e11i 0.614856 0.419201i
\(340\) −8.17461e10 3.58153e11i −0.331751 1.45350i
\(341\) −2.25869e11 + 3.40443e10i −0.904612 + 0.136348i
\(342\) 1.02045e11 1.27961e11i 0.403345 0.505778i
\(343\) 1.48389e11 0.578865
\(344\) −1.22776e9 1.32181e11i −0.00472716 0.508926i
\(345\) −1.32918e12 −5.05125
\(346\) 2.42810e10 3.04474e10i 0.0910801 0.114211i
\(347\) −6.26036e10 + 9.43597e9i −0.231802 + 0.0349385i −0.263916 0.964546i \(-0.585014\pi\)
0.0321141 + 0.999484i \(0.489776\pi\)
\(348\) 5.99344e10 + 2.62590e11i 0.219063 + 0.959779i
\(349\) 2.31961e11 1.58149e11i 0.836953 0.570625i −0.0672460 0.997736i \(-0.521421\pi\)
0.904199 + 0.427112i \(0.140469\pi\)
\(350\) −4.62147e10 + 8.00461e10i −0.164617 + 0.285124i
\(351\) −7.41631e10 1.28454e11i −0.260799 0.451717i
\(352\) 1.31689e11 + 6.34181e10i 0.457201 + 0.220177i
\(353\) −2.14932e10 + 6.62979e9i −0.0736743 + 0.0227255i −0.331373 0.943500i \(-0.607512\pi\)
0.257699 + 0.966225i \(0.417036\pi\)
\(354\) −5.52765e8 + 7.37614e9i −0.00187079 + 0.0249640i
\(355\) −5.44267e10 + 2.38459e11i −0.181880 + 0.796868i
\(356\) −9.76506e10 2.48810e11i −0.322218 0.820998i
\(357\) −6.09420e10 8.13214e11i −0.198568 2.64971i
\(358\) −4.38630e10 6.61128e9i −0.141132 0.0212722i
\(359\) 3.07482e11 2.85302e11i 0.977000 0.906524i −0.0186376 0.999826i \(-0.505933\pi\)
0.995638 + 0.0933026i \(0.0297424\pi\)
\(360\) −5.39619e11 + 2.59867e11i −1.69327 + 0.815435i
\(361\) −3.01181e10 2.05341e10i −0.0933350 0.0636347i
\(362\) −2.87248e10 + 7.31896e10i −0.0879162 + 0.224007i
\(363\) 3.01148e11 + 9.28918e10i 0.910332 + 0.280800i
\(364\) 4.83916e10 + 4.49009e10i 0.144482 + 0.134060i
\(365\) 2.84782e10 + 3.57105e10i 0.0839836 + 0.105312i
\(366\) −6.92434e10 8.68284e10i −0.201703 0.252928i
\(367\) 1.87688e11 + 1.74149e11i 0.540055 + 0.501098i 0.902373 0.430957i \(-0.141824\pi\)
−0.362317 + 0.932055i \(0.618014\pi\)
\(368\) 5.02479e11 + 1.54994e11i 1.42825 + 0.440556i
\(369\) 8.66778e10 2.20851e11i 0.243382 0.620128i
\(370\) −3.17751e10 2.16639e10i −0.0881412 0.0600937i
\(371\) 7.83985e11 3.77547e11i 2.14845 1.03464i
\(372\) −6.19971e11 + 5.75249e11i −1.67853 + 1.55744i
\(373\) −4.79886e11 7.23311e10i −1.28365 0.193480i −0.528447 0.848966i \(-0.677226\pi\)
−0.755207 + 0.655486i \(0.772464\pi\)
\(374\) 5.94861e9 + 7.93786e10i 0.0157215 + 0.209788i
\(375\) −3.32276e9 8.46625e9i −0.00867677 0.0221080i
\(376\) −3.43297e10 + 1.50408e11i −0.0885777 + 0.388084i
\(377\) 2.79461e9 3.72915e10i 0.00712502 0.0950767i
\(378\) −3.77328e11 + 1.16390e11i −0.950617 + 0.293226i
\(379\) −4.53000e11 2.18153e11i −1.12777 0.543107i −0.225488 0.974246i \(-0.572398\pi\)
−0.902286 + 0.431139i \(0.858112\pi\)
\(380\) −2.52437e11 4.37233e11i −0.621050 1.07569i
\(381\) 2.01721e11 3.49391e11i 0.490444 0.849474i
\(382\) −2.14637e10 + 1.46337e10i −0.0515727 + 0.0351616i
\(383\) 6.63015e10 + 2.90486e11i 0.157445 + 0.689811i 0.990602 + 0.136775i \(0.0436738\pi\)
−0.833157 + 0.553036i \(0.813469\pi\)
\(384\) 7.03085e11 1.05973e11i 1.65013 0.248716i
\(385\) −3.32885e11 + 4.17424e11i −0.772184 + 0.968288i
\(386\) −8.96454e10 −0.205535
\(387\) 7.89764e11 + 8.35464e11i 1.78977 + 1.89334i
\(388\) 2.40919e11 0.539671
\(389\) 1.35310e11 1.69673e11i 0.299610 0.375699i −0.609124 0.793075i \(-0.708479\pi\)
0.908734 + 0.417376i \(0.137050\pi\)
\(390\) 5.48461e10 8.26672e9i 0.120048 0.0180943i
\(391\) 2.18210e11 + 9.56039e11i 0.472149 + 2.06862i
\(392\) 1.04662e11 7.13570e10i 0.223872 0.152633i
\(393\) −8.14880e11 + 1.41141e12i −1.72317 + 2.98461i
\(394\) −5.05136e10 8.74920e10i −0.105603 0.182909i
\(395\) 8.20994e11 + 3.95370e11i 1.69689 + 0.817178i
\(396\) −8.00231e11 + 2.46839e11i −1.63526 + 0.504411i
\(397\) 2.96465e10 3.95605e11i 0.0598985 0.799290i −0.883670 0.468111i \(-0.844935\pi\)
0.943568 0.331179i \(-0.107446\pi\)
\(398\) −3.08895e10 + 1.35336e11i −0.0617075 + 0.270358i
\(399\) −4.09455e11 1.04327e12i −0.808775 2.06073i
\(400\) 3.07375e10 + 4.10163e11i 0.0600342 + 0.801100i
\(401\) 4.40685e11 + 6.64225e10i 0.851095 + 0.128282i 0.560082 0.828437i \(-0.310770\pi\)
0.291013 + 0.956719i \(0.406008\pi\)
\(402\) −7.63653e10 + 7.08566e10i −0.145841 + 0.135320i
\(403\) 1.05796e11 5.09484e10i 0.199800 0.0962184i
\(404\) 5.69433e11 + 3.88233e11i 1.06347 + 0.725064i
\(405\) 8.92285e11 2.27351e12i 1.64800 4.19902i
\(406\) −9.51321e10 2.93444e10i −0.173764 0.0535991i
\(407\) −8.17795e10 7.58803e10i −0.147730 0.137074i
\(408\) 3.81246e11 + 4.78067e11i 0.681136 + 0.854118i
\(409\) −1.27439e11 1.59804e11i −0.225190 0.282379i 0.656382 0.754429i \(-0.272086\pi\)
−0.881572 + 0.472049i \(0.843514\pi\)
\(410\) 4.00735e10 + 3.71828e10i 0.0700374 + 0.0649852i
\(411\) −6.87418e11 2.12040e11i −1.18832 0.366547i
\(412\) 3.62361e11 9.23280e11i 0.619589 1.57869i
\(413\) 3.02422e10 + 2.06188e10i 0.0511492 + 0.0348729i
\(414\) 6.94288e11 3.34352e11i 1.16155 0.559373i
\(415\) 4.73090e10 4.38964e10i 0.0782938 0.0726461i
\(416\) −7.42992e10 1.11988e10i −0.121637 0.0183338i
\(417\) −5.54937e10 7.40512e11i −0.0898735 1.19928i
\(418\) 3.99673e10 + 1.01835e11i 0.0640341 + 0.163156i
\(419\) 9.64254e10 4.22467e11i 0.152837 0.669622i −0.839216 0.543799i \(-0.816985\pi\)
0.992053 0.125824i \(-0.0401574\pi\)
\(420\) −1.47728e11 + 1.97129e12i −0.231654 + 3.09121i
\(421\) 6.07035e11 1.87245e11i 0.941768 0.290497i 0.214401 0.976746i \(-0.431220\pi\)
0.727367 + 0.686249i \(0.240744\pi\)
\(422\) −1.34281e11 6.46661e10i −0.206114 0.0992592i
\(423\) −6.70892e11 1.16202e12i −1.01888 1.76474i
\(424\) −3.26229e11 + 5.65045e11i −0.490203 + 0.849057i
\(425\) −6.33763e11 + 4.32092e11i −0.942273 + 0.642431i
\(426\) −4.36654e10 1.91311e11i −0.0642383 0.281446i
\(427\) −5.43418e11 + 8.19071e10i −0.791059 + 0.119233i
\(428\) −1.75007e11 + 2.19451e11i −0.252091 + 0.316112i
\(429\) 1.60899e11 0.229348
\(430\) −2.45680e11 + 9.90654e10i −0.346547 + 0.139738i
\(431\) −9.79147e11 −1.36678 −0.683392 0.730052i \(-0.739496\pi\)
−0.683392 + 0.730052i \(0.739496\pi\)
\(432\) −1.09559e12 + 1.37382e12i −1.51346 + 1.89782i
\(433\) 7.70600e11 1.16149e11i 1.05350 0.158789i 0.400613 0.916247i \(-0.368797\pi\)
0.652884 + 0.757458i \(0.273559\pi\)
\(434\) −6.95609e10 3.04766e11i −0.0941156 0.412347i
\(435\) 9.25257e11 6.30830e11i 1.23897 0.844716i
\(436\) 4.04853e11 7.01226e11i 0.536547 0.929327i
\(437\) 6.73844e11 + 1.16713e12i 0.883879 + 1.53092i
\(438\) −3.30155e10 1.58994e10i −0.0428632 0.0206418i
\(439\) 6.15327e11 1.89803e11i 0.790707 0.243901i 0.127009 0.991902i \(-0.459462\pi\)
0.663698 + 0.748001i \(0.268986\pi\)
\(440\) 2.99168e10 3.99211e11i 0.0380520 0.507769i
\(441\) −2.45153e11 + 1.07408e12i −0.308648 + 1.35227i
\(442\) −1.49500e10 3.80919e10i −0.0186312 0.0474715i
\(443\) 3.02941e8 + 4.04247e9i 0.000373716 + 0.00498689i 0.997388 0.0722364i \(-0.0230136\pi\)
−0.997014 + 0.0772233i \(0.975395\pi\)
\(444\) −4.08445e11 6.15631e10i −0.498781 0.0751791i
\(445\) −8.14634e11 + 7.55870e11i −0.984788 + 0.913750i
\(446\) 2.00644e11 9.66250e10i 0.240115 0.115633i
\(447\) 1.19784e12 + 8.16673e11i 1.41911 + 0.967530i
\(448\) 2.33978e11 5.96165e11i 0.274425 0.699223i
\(449\) 1.12172e12 + 3.46003e11i 1.30249 + 0.401765i 0.866946 0.498403i \(-0.166080\pi\)
0.435544 + 0.900167i \(0.356556\pi\)
\(450\) 4.41858e11 + 4.09985e11i 0.507957 + 0.471315i
\(451\) 9.88736e10 + 1.23984e11i 0.112535 + 0.141114i
\(452\) 2.01771e11 + 2.53013e11i 0.227371 + 0.285115i
\(453\) 1.42555e12 + 1.32272e12i 1.59053 + 1.47579i
\(454\) 2.62731e11 + 8.10419e10i 0.290242 + 0.0895278i
\(455\) 1.00273e11 2.55492e11i 0.109682 0.279464i
\(456\) 6.94332e11 + 4.73388e11i 0.752013 + 0.512714i
\(457\) −1.36873e12 + 6.59148e11i −1.46790 + 0.706903i −0.985598 0.169103i \(-0.945913\pi\)
−0.482301 + 0.876006i \(0.660199\pi\)
\(458\) 6.07764e10 5.63922e10i 0.0645416 0.0598859i
\(459\) −3.24032e12 4.88400e11i −3.40747 0.513593i
\(460\) −1.77641e11 2.37046e12i −0.184984 2.46844i
\(461\) −2.43800e10 6.21193e10i −0.0251408 0.0640578i 0.917752 0.397154i \(-0.130002\pi\)
−0.942893 + 0.333096i \(0.891907\pi\)
\(462\) 9.53148e10 4.17602e11i 0.0973356 0.426455i
\(463\) 6.98140e9 9.31603e10i 0.00706038 0.0942143i −0.992560 0.121754i \(-0.961148\pi\)
0.999621 + 0.0275395i \(0.00876722\pi\)
\(464\) −4.23341e11 + 1.30583e11i −0.423994 + 0.130785i
\(465\) 3.16809e12 + 1.52567e12i 3.14239 + 1.51329i
\(466\) 5.17091e10 + 8.95628e10i 0.0507961 + 0.0879814i
\(467\) 3.31742e11 5.74594e11i 0.322756 0.559030i −0.658300 0.752756i \(-0.728724\pi\)
0.981056 + 0.193726i \(0.0620573\pi\)
\(468\) 3.55696e11 2.42510e11i 0.342747 0.233681i
\(469\) 1.14708e11 + 5.02570e11i 0.109476 + 0.479644i
\(470\) 3.05716e11 4.60792e10i 0.288986 0.0435577i
\(471\) −7.95720e11 + 9.97802e11i −0.745017 + 0.934222i
\(472\) −2.74450e10 −0.0254521
\(473\) −7.47557e11 + 1.77946e11i −0.686704 + 0.163461i
\(474\) −7.31064e11 −0.665201
\(475\) −6.57260e11 + 8.24178e11i −0.592401 + 0.742848i
\(476\) 1.44214e12 2.17367e11i 1.28758 0.194072i
\(477\) −1.26272e12 5.53234e12i −1.11680 4.89301i
\(478\) −2.09496e11 + 1.42832e11i −0.183549 + 0.125141i
\(479\) −6.16789e11 + 1.06831e12i −0.535336 + 0.927230i 0.463811 + 0.885934i \(0.346482\pi\)
−0.999147 + 0.0412953i \(0.986852\pi\)
\(480\) −1.12503e12 1.94860e12i −0.967335 1.67547i
\(481\) 5.16704e10 + 2.48832e10i 0.0440138 + 0.0211959i
\(482\) −1.06232e11 + 3.27683e10i −0.0896489 + 0.0276530i
\(483\) 3.94338e11 5.26207e12i 0.329691 4.39941i
\(484\) −1.25415e11 + 5.49479e11i −0.103883 + 0.455142i
\(485\) −3.65950e11 9.32425e11i −0.300320 0.765202i
\(486\) 7.25671e10 + 9.68341e11i 0.0590033 + 0.787345i
\(487\) 1.65264e12 + 2.49095e11i 1.33136 + 0.200671i 0.775893 0.630865i \(-0.217300\pi\)
0.555472 + 0.831535i \(0.312538\pi\)
\(488\) 3.02066e11 2.80276e11i 0.241108 0.223716i
\(489\) −3.02327e12 + 1.45593e12i −2.39104 + 1.15146i
\(490\) −2.09742e11 1.42999e11i −0.164362 0.112060i
\(491\) −4.95576e11 + 1.26271e12i −0.384807 + 0.980473i 0.598921 + 0.800808i \(0.295597\pi\)
−0.983728 + 0.179665i \(0.942499\pi\)
\(492\) 5.61069e11 + 1.73067e11i 0.431691 + 0.133159i
\(493\) −6.05634e11 5.61946e11i −0.461741 0.428433i
\(494\) −3.50637e10 4.39685e10i −0.0264903 0.0332178i
\(495\) 2.17086e12 + 2.72218e12i 1.62521 + 2.03795i
\(496\) −1.01975e12 9.46187e11i −0.756528 0.701955i
\(497\) −9.27884e11 2.86214e11i −0.682165 0.210420i
\(498\) −1.89161e10 + 4.81976e10i −0.0137816 + 0.0351150i
\(499\) 1.51265e12 + 1.03131e12i 1.09216 + 0.744621i 0.968825 0.247744i \(-0.0796893\pi\)
0.123333 + 0.992365i \(0.460642\pi\)
\(500\) 1.46546e10 7.05727e9i 0.0104860 0.00504977i
\(501\) −3.15910e12 + 2.93122e12i −2.24024 + 2.07864i
\(502\) 5.42577e9 + 8.17803e8i 0.00381324 + 0.000574754i
\(503\) 1.72678e11 + 2.30422e12i 0.120276 + 1.60498i 0.652108 + 0.758126i \(0.273885\pi\)
−0.531832 + 0.846850i \(0.678496\pi\)
\(504\) −8.68688e11 2.21338e12i −0.599690 1.52798i
\(505\) 6.37617e11 2.79358e12i 0.436263 1.91139i
\(506\) −3.84917e10 + 5.13636e11i −0.0261030 + 0.348320i
\(507\) 2.62041e12 8.08290e11i 1.76130 0.543289i
\(508\) 6.50062e11 + 3.13053e11i 0.433080 + 0.208560i
\(509\) −1.06282e12 1.84086e12i −0.701828 1.21560i −0.967824 0.251627i \(-0.919034\pi\)
0.265997 0.963974i \(-0.414299\pi\)
\(510\) 6.12693e11 1.06121e12i 0.401030 0.694604i
\(511\) −1.49822e11 + 1.02147e11i −0.0972037 + 0.0662724i
\(512\) 3.38308e11 + 1.48223e12i 0.217569 + 0.953234i
\(513\) −4.45323e12 + 6.71216e11i −2.83888 + 0.427892i
\(514\) −9.08708e10 + 1.13948e11i −0.0574236 + 0.0720069i
\(515\) −4.12377e12 −2.58322
\(516\) −1.91578e12 + 2.10357e12i −1.18966 + 1.30627i
\(517\) 8.96860e11 0.552099
\(518\) 9.51916e10 1.19367e11i 0.0580918 0.0728448i
\(519\) −1.71965e12 + 2.59196e11i −1.04037 + 0.156810i
\(520\) 4.57944e10 + 2.00638e11i 0.0274661 + 0.120337i
\(521\) 2.25736e12 1.53904e12i 1.34224 0.915124i 0.342537 0.939504i \(-0.388714\pi\)
0.999703 + 0.0243804i \(0.00776131\pi\)
\(522\) −3.24618e11 + 5.62254e11i −0.191362 + 0.331448i
\(523\) 1.38290e11 + 2.39526e11i 0.0808228 + 0.139989i 0.903604 0.428370i \(-0.140912\pi\)
−0.822781 + 0.568359i \(0.807579\pi\)
\(524\) −2.62601e12 1.26462e12i −1.52162 0.732773i
\(525\) 3.94417e12 1.21661e12i 2.26589 0.698934i
\(526\) 6.66930e9 8.89957e10i 0.00379878 0.0506912i
\(527\) 5.77267e11 2.52917e12i 0.326009 1.42834i
\(528\) −6.96388e11 1.77437e12i −0.389941 0.993552i
\(529\) 3.39588e11 + 4.53148e12i 0.188539 + 2.51588i
\(530\) 1.29292e12 + 1.94876e11i 0.711755 + 0.107280i
\(531\) 1.74977e11 1.62355e11i 0.0955116 0.0886218i
\(532\) 1.80584e12 8.69649e11i 0.977413 0.470697i
\(533\) −6.73564e10 4.59228e10i −0.0361499 0.0246466i
\(534\) 3.25725e11 8.29934e11i 0.173347 0.441680i
\(535\) 1.11517e12 + 3.43984e11i 0.588503 + 0.181529i
\(536\) −2.83344e11 2.62904e11i −0.148276 0.137580i
\(537\) 1.23506e12 + 1.54871e12i 0.640919 + 0.803687i
\(538\) 1.64086e11 + 2.05758e11i 0.0844408 + 0.105885i
\(539\) −5.39811e11 5.00872e11i −0.275482 0.255610i
\(540\) 7.59059e12 + 2.34139e12i 3.84152 + 1.18495i
\(541\) −4.68841e11 + 1.19459e12i −0.235309 + 0.599557i −0.998937 0.0460996i \(-0.985321\pi\)
0.763628 + 0.645656i \(0.223416\pi\)
\(542\) −7.63422e11 5.20492e11i −0.379986 0.259070i
\(543\) 3.16337e12 1.52340e12i 1.56153 0.751994i
\(544\) −1.21687e12 + 1.12909e12i −0.595731 + 0.552758i
\(545\) −3.32890e12 5.01751e11i −1.61628 0.243615i
\(546\) 1.64554e10 + 2.19582e11i 0.00792393 + 0.105738i
\(547\) −1.15608e12 2.94565e12i −0.552136 1.40682i −0.885774 0.464117i \(-0.846372\pi\)
0.333638 0.942701i \(-0.391724\pi\)
\(548\) 2.86280e11 1.25427e12i 0.135606 0.594128i
\(549\) −2.67822e11 + 3.57383e12i −0.125826 + 1.67903i
\(550\) −3.84994e11 + 1.18755e11i −0.179400 + 0.0553375i
\(551\) −1.02299e12 4.92646e11i −0.472813 0.227695i
\(552\) 1.97832e12 + 3.42656e12i 0.906925 + 1.57084i
\(553\) −1.80879e12 + 3.13292e12i −0.822480 + 1.42458i
\(554\) 3.95013e11 2.69315e11i 0.178163 0.121469i
\(555\) 3.82150e11 + 1.67431e12i 0.170968 + 0.749060i
\(556\) 1.31321e12 1.97934e11i 0.582770 0.0878384i
\(557\) 2.95860e11 3.70996e11i 0.130238 0.163313i −0.712437 0.701736i \(-0.752408\pi\)
0.842675 + 0.538423i \(0.180980\pi\)
\(558\) −2.03860e12 −0.890183
\(559\) 3.40260e11 2.00686e11i 0.147387 0.0869289i
\(560\) −3.25153e12 −1.39714
\(561\) 2.21631e12 2.77917e12i 0.944708 1.18463i
\(562\) 2.02595e11 3.05363e10i 0.0856675 0.0129123i
\(563\) 2.27829e11 + 9.98185e11i 0.0955700 + 0.418720i 0.999968 0.00796974i \(-0.00253687\pi\)
−0.904398 + 0.426689i \(0.859680\pi\)
\(564\) 2.74367e12 1.87060e12i 1.14176 0.778440i
\(565\) 6.72746e11 1.16523e12i 0.277737 0.481054i
\(566\) −2.20205e10 3.81406e10i −0.00901889 0.0156212i
\(567\) 8.73581e12 + 4.20694e12i 3.54960 + 1.70940i
\(568\) 6.95741e11 2.14608e11i 0.280466 0.0865123i
\(569\) −1.98149e10 + 2.64411e11i −0.00792477 + 0.105749i −0.999763 0.0217506i \(-0.993076\pi\)
0.991839 + 0.127499i \(0.0406951\pi\)
\(570\) 3.74740e11 1.64184e12i 0.148694 0.651470i
\(571\) −1.59313e12 4.05924e12i −0.627176 1.59802i −0.791196 0.611562i \(-0.790541\pi\)
0.164020 0.986457i \(-0.447554\pi\)
\(572\) 2.15036e10 + 2.86946e11i 0.00839903 + 0.112077i
\(573\) 1.14710e12 + 1.72898e11i 0.444536 + 0.0670030i
\(574\) −1.59091e11 + 1.47615e11i −0.0611705 + 0.0567579i
\(575\) −4.47181e12 + 2.15351e12i −1.70600 + 0.821564i
\(576\) −3.45080e12 2.35272e12i −1.30623 0.890570i
\(577\) −2.13027e11 + 5.42785e11i −0.0800100 + 0.203862i −0.965281 0.261213i \(-0.915877\pi\)
0.885271 + 0.465075i \(0.153973\pi\)
\(578\) −1.87887e11 5.79555e10i −0.0700199 0.0215983i
\(579\) 2.93457e12 + 2.72288e12i 1.08515 + 1.00687i
\(580\) 1.24868e12 + 1.56579e12i 0.458167 + 0.574523i
\(581\) 1.59745e11 + 2.00314e11i 0.0581613 + 0.0729320i
\(582\) 5.89092e11 + 5.46597e11i 0.212828 + 0.197476i
\(583\) 3.62445e12 + 1.11799e12i 1.29937 + 0.400803i
\(584\) 4.96734e10 1.26566e11i 0.0176712 0.0450255i
\(585\) −1.47887e12 1.00828e12i −0.522071 0.355942i
\(586\) −9.20588e11 + 4.43332e11i −0.322497 + 0.155307i
\(587\) 6.25814e11 5.80671e11i 0.217557 0.201864i −0.563864 0.825868i \(-0.690686\pi\)
0.781421 + 0.624004i \(0.214495\pi\)
\(588\) −2.69607e12 4.06367e11i −0.930107 0.140191i
\(589\) −2.66433e11 3.55530e12i −0.0912156 1.21719i
\(590\) 2.00936e10 + 5.11977e10i 0.00682691 + 0.0173947i
\(591\) −1.00390e12 + 4.39837e12i −0.338491 + 1.48302i
\(592\) 5.07724e10 6.77511e11i 0.0169895 0.226709i
\(593\) 2.06207e11 6.36065e10i 0.0684790 0.0211230i −0.260326 0.965521i \(-0.583830\pi\)
0.328805 + 0.944398i \(0.393354\pi\)
\(594\) −1.55076e12 7.46807e11i −0.511100 0.246133i
\(595\) −3.03184e12 5.25130e12i −0.991698 1.71767i
\(596\) −1.29636e12 + 2.24536e12i −0.420841 + 0.728918i
\(597\) 5.12186e12 3.49203e12i 1.65023 1.12510i
\(598\) −5.89203e10 2.58147e11i −0.0188412 0.0825489i
\(599\) −3.71443e12 + 5.59860e11i −1.17888 + 0.177688i −0.709110 0.705098i \(-0.750903\pi\)
−0.469775 + 0.882786i \(0.655665\pi\)
\(600\) −1.92963e12 + 2.41969e12i −0.607847 + 0.762216i
\(601\) −2.64477e12 −0.826898 −0.413449 0.910527i \(-0.635676\pi\)
−0.413449 + 0.910527i \(0.635676\pi\)
\(602\) −3.19300e11 1.00201e12i −0.0990867 0.310947i
\(603\) 3.36173e12 1.03546
\(604\) −2.16841e12 + 2.71910e12i −0.662940 + 0.831301i
\(605\) 2.31714e12 3.49253e11i 0.703159 0.105984i
\(606\) 5.11546e11 + 2.24123e12i 0.154084 + 0.675086i
\(607\) −4.26389e11 + 2.90707e11i −0.127484 + 0.0869174i −0.625383 0.780318i \(-0.715057\pi\)
0.497899 + 0.867235i \(0.334105\pi\)
\(608\) −1.14069e12 + 1.97573e12i −0.338533 + 0.586356i
\(609\) 2.22288e12 + 3.85013e12i 0.654843 + 1.13422i
\(610\) −7.44001e11 3.58292e11i −0.217565 0.104774i
\(611\) −4.40566e11 + 1.35897e11i −0.127887 + 0.0394478i
\(612\) 7.10752e11 9.48433e12i 0.204803 2.73291i
\(613\) −1.14935e12 + 5.03565e12i −0.328762 + 1.44040i 0.492731 + 0.870182i \(0.335999\pi\)
−0.821493 + 0.570219i \(0.806858\pi\)
\(614\) 1.18220e11 + 3.01219e11i 0.0335686 + 0.0855313i
\(615\) −1.82431e11 2.43438e12i −0.0514235 0.686199i
\(616\) 1.57155e12 + 2.36874e11i 0.439760 + 0.0662832i
\(617\) 3.36462e12 3.12191e12i 0.934659 0.867237i −0.0567029 0.998391i \(-0.518059\pi\)
0.991362 + 0.131154i \(0.0418683\pi\)
\(618\) 2.98077e12 1.43546e12i 0.822017 0.395862i
\(619\) 2.92037e12 + 1.99107e12i 0.799521 + 0.545104i 0.892756 0.450540i \(-0.148769\pi\)
−0.0932355 + 0.995644i \(0.529721\pi\)
\(620\) −2.29747e12 + 5.85385e12i −0.624435 + 1.59103i
\(621\) −2.02620e13 6.25000e12i −5.46726 1.68643i
\(622\) −1.15522e12 1.07189e12i −0.309464 0.287140i
\(623\) −2.75071e12 3.44929e12i −0.731559 0.917346i
\(624\) 6.10948e11 + 7.66105e11i 0.161315 + 0.202282i
\(625\) 2.77148e12 + 2.57155e12i 0.726526 + 0.674117i
\(626\) 1.25418e10 + 3.86863e9i 0.00326419 + 0.00100687i
\(627\) 1.78479e12 4.54756e12i 0.461192 1.17510i
\(628\) −1.88582e12 1.28573e12i −0.483817 0.329861i
\(629\) 1.14154e12 5.49736e11i 0.290779 0.140032i
\(630\) −3.49299e12 + 3.24102e12i −0.883415 + 0.819690i
\(631\) 4.18884e12 + 6.31367e11i 1.05187 + 0.158544i 0.652147 0.758092i \(-0.273868\pi\)
0.399723 + 0.916636i \(0.369106\pi\)
\(632\) −2.02707e11 2.70493e12i −0.0505407 0.674419i
\(633\) 2.43155e12 + 6.19549e12i 0.601959 + 1.53377i
\(634\) 3.89469e11 1.70637e12i 0.0957350 0.419443i
\(635\) 2.24177e11 2.99144e12i 0.0547155 0.730127i
\(636\) 1.34197e13 4.13944e12i 3.25227 1.00319i
\(637\) 3.41067e11 + 1.64249e11i 0.0820752 + 0.0395254i
\(638\) −2.16977e11 3.75815e11i −0.0518466 0.0898010i
\(639\) −3.16620e12 + 5.48402e12i −0.751250 + 1.30120i
\(640\) 4.36823e12 2.97821e12i 1.02919 0.701691i
\(641\) −2.52859e11 1.10785e12i −0.0591585 0.259190i 0.936697 0.350141i \(-0.113866\pi\)
−0.995855 + 0.0909511i \(0.971009\pi\)
\(642\) −9.25813e11 + 1.39544e11i −0.215088 + 0.0324193i
\(643\) 4.14240e12 5.19441e12i 0.955659 1.19836i −0.0244101 0.999702i \(-0.507771\pi\)
0.980069 0.198657i \(-0.0636578\pi\)
\(644\) 9.43705e12 2.16197
\(645\) 1.10514e13 + 4.21933e12i 2.51420 + 0.959897i
\(646\) −1.24245e12 −0.280693
\(647\) −4.18897e12 + 5.25281e12i −0.939806 + 1.17848i 0.0439617 + 0.999033i \(0.486002\pi\)
−0.983768 + 0.179446i \(0.942569\pi\)
\(648\) −7.18902e12 + 1.08357e12i −1.60170 + 0.241418i
\(649\) 3.55025e10 + 1.55547e11i 0.00785522 + 0.0344160i
\(650\) 1.71127e11 1.16672e11i 0.0376017 0.0256364i
\(651\) −6.97985e12 + 1.20895e13i −1.52311 + 2.63811i
\(652\) −3.00054e12 5.19709e12i −0.650258 1.12628i
\(653\) −4.44932e11 2.14268e11i −0.0957601 0.0461156i 0.385391 0.922754i \(-0.374067\pi\)
−0.481151 + 0.876638i \(0.659781\pi\)
\(654\) 2.58088e12 7.96095e11i 0.551655 0.170163i
\(655\) −9.05595e11 + 1.20843e13i −0.192242 + 2.56529i
\(656\) −2.14904e11 + 9.41556e11i −0.0453083 + 0.198508i
\(657\) 4.32024e11 + 1.10078e12i 0.0904615 + 0.230492i
\(658\) 9.17233e10 + 1.22396e12i 0.0190749 + 0.254537i
\(659\) 1.36422e12 + 2.05623e11i 0.281773 + 0.0424705i 0.288408 0.957507i \(-0.406874\pi\)
−0.00663500 + 0.999978i \(0.502112\pi\)
\(660\) −6.31656e12 + 5.86092e12i −1.29579 + 1.20231i
\(661\) 2.07329e12 9.98446e11i 0.422430 0.203431i −0.210578 0.977577i \(-0.567535\pi\)
0.633007 + 0.774146i \(0.281820\pi\)
\(662\) 1.72235e11 + 1.17428e11i 0.0348547 + 0.0237635i
\(663\) −6.67609e11 + 1.70104e12i −0.134187 + 0.341904i
\(664\) −1.83576e11 5.66257e10i −0.0366488 0.0113046i
\(665\) −6.10881e12 5.66815e12i −1.21132 1.12394i
\(666\) −6.20779e11 7.78432e11i −0.122265 0.153316i
\(667\) −3.33316e12 4.17965e12i −0.652064 0.817662i
\(668\) −5.64972e12 5.24218e12i −1.09783 1.01863i
\(669\) −9.50302e12 2.93129e12i −1.83419 0.565772i
\(670\) −2.82992e11 + 7.21052e11i −0.0542548 + 0.138239i
\(671\) −1.97924e12 1.34942e12i −0.376918 0.256978i
\(672\) 8.04805e12 3.87574e12i 1.52240 0.733149i
\(673\) −2.03633e12 + 1.88944e12i −0.382631 + 0.355030i −0.847916 0.530131i \(-0.822143\pi\)
0.465284 + 0.885161i \(0.345952\pi\)
\(674\) 1.94703e12 + 2.93467e11i 0.363415 + 0.0547760i
\(675\) −1.23946e12 1.65394e13i −0.229808 3.06658i
\(676\) 1.79171e12 + 4.56520e12i 0.329995 + 0.840813i
\(677\) −9.74915e11 + 4.27138e12i −0.178368 + 0.781483i 0.804015 + 0.594608i \(0.202693\pi\)
−0.982384 + 0.186874i \(0.940164\pi\)
\(678\) −8.06680e10 + 1.07644e12i −0.0146611 + 0.195639i
\(679\) 3.79993e12 1.17212e12i 0.686059 0.211621i
\(680\) 4.09638e12 + 1.97271e12i 0.734700 + 0.353813i
\(681\) −6.13903e12 1.06331e13i −1.09380 1.89452i
\(682\) 6.81310e11 1.18006e12i 0.120591 0.208870i
\(683\) −2.91296e12 + 1.98602e12i −0.512202 + 0.349214i −0.791677 0.610939i \(-0.790792\pi\)
0.279475 + 0.960153i \(0.409840\pi\)
\(684\) −2.90857e12 1.27433e13i −0.508075 2.22602i
\(685\) −5.28925e12 + 7.97226e11i −0.917881 + 0.138348i
\(686\) −5.51912e11 + 6.92076e11i −0.0951506 + 0.119315i
\(687\) −3.70238e12 −0.634127
\(688\) −3.68582e12 2.88375e12i −0.627172 0.490693i
\(689\) −1.94985e12 −0.329621
\(690\) 4.94372e12 6.19923e12i 0.830296 1.04116i
\(691\) 1.34686e11 2.03006e10i 0.0224735 0.00338733i −0.137796 0.990461i \(-0.544002\pi\)
0.160269 + 0.987073i \(0.448764\pi\)
\(692\) −6.92074e11 3.03217e12i −0.114729 0.502663i
\(693\) −1.14208e13 + 7.78658e12i −1.88104 + 1.28247i
\(694\) 1.88837e11 3.27075e11i 0.0309008 0.0535217i
\(695\) −2.76079e12 4.78183e12i −0.448850 0.777431i
\(696\) −3.00337e12 1.44635e12i −0.485141 0.233631i
\(697\) −1.72102e12 + 5.30865e11i −0.276210 + 0.0851994i
\(698\) −1.25154e11 + 1.67007e12i −0.0199570 + 0.266308i
\(699\) 1.02766e12 4.50247e12i 0.162818 0.713352i
\(700\) 2.69683e12 + 6.87140e12i 0.424533 + 1.08169i
\(701\) 6.47613e11 + 8.64179e12i 0.101294 + 1.35168i 0.783899 + 0.620889i \(0.213228\pi\)
−0.682605 + 0.730788i \(0.739153\pi\)
\(702\) 8.74942e11 + 1.31876e11i 0.135976 + 0.0204951i
\(703\) 1.27644e12 1.18437e12i 0.197107 0.182889i
\(704\) 2.51516e12 1.21124e12i 0.385912 0.185846i
\(705\) −1.14073e13 7.77737e12i −1.73913 1.18572i
\(706\) 4.90203e10 1.24902e11i 0.00742600 0.0189212i
\(707\) 1.08703e13 + 3.35304e12i 1.63626 + 0.504721i
\(708\) 4.33037e11 + 4.01799e11i 0.0647702 + 0.0600979i
\(709\) 7.44128e12 + 9.33107e12i 1.10596 + 1.38683i 0.914139 + 0.405400i \(0.132868\pi\)
0.191821 + 0.981430i \(0.438561\pi\)
\(710\) −9.09726e11 1.14076e12i −0.134353 0.168474i
\(711\) 1.72938e13 + 1.60463e13i 2.53792 + 2.35485i
\(712\) 3.16107e12 + 9.75061e11i 0.460972 + 0.142191i
\(713\) 6.13277e12 1.56260e13i 0.888697 2.26436i
\(714\) 4.01945e12 + 2.74041e12i 0.578795 + 0.394615i
\(715\) 1.07790e12 5.19088e11i 0.154241 0.0742786i
\(716\) −2.59690e12 + 2.40957e12i −0.369273 + 0.342635i
\(717\) 1.11963e13 + 1.68757e12i 1.58212 + 0.238466i
\(718\) 1.86991e11 + 2.49522e12i 0.0262579 + 0.350387i
\(719\) 2.24093e12 + 5.70979e12i 0.312714 + 0.796783i 0.997672 + 0.0681999i \(0.0217256\pi\)
−0.684957 + 0.728583i \(0.740179\pi\)
\(720\) −4.71842e12 + 2.06727e13i −0.654335 + 2.86683i
\(721\) 1.22343e12 1.63255e13i 0.168604 2.24987i
\(722\) 2.07790e11 6.40948e10i 0.0284582 0.00877819i
\(723\) 4.47285e12 + 2.15401e12i 0.608782 + 0.293174i
\(724\) 3.13959e12 + 5.43794e12i 0.424669 + 0.735547i
\(725\) 2.09081e12 3.62140e12i 0.281057 0.486805i
\(726\) −1.55332e12 + 1.05904e12i −0.207513 + 0.141480i
\(727\) 4.85646e11 + 2.12775e12i 0.0644785 + 0.282499i 0.996881 0.0789238i \(-0.0251484\pi\)
−0.932402 + 0.361422i \(0.882291\pi\)
\(728\) −8.07889e11 + 1.21770e11i −0.106601 + 0.0160675i
\(729\) 1.19050e13 1.49284e13i 1.56119 1.95767i
\(730\) −2.72473e11 −0.0355116
\(731\) 1.22054e12 8.64161e12i 0.158097 1.11935i
\(732\) −8.86939e12 −1.14181
\(733\) −3.04132e12 + 3.81370e12i −0.389130 + 0.487954i −0.937354 0.348378i \(-0.886733\pi\)
0.548224 + 0.836331i \(0.315304\pi\)
\(734\) −1.51030e12 + 2.27641e11i −0.192057 + 0.0289479i
\(735\) 2.52250e12 + 1.10518e13i 0.318815 + 1.39682i
\(736\) −8.87500e12 + 6.05087e12i −1.11485 + 0.760095i
\(737\) −1.12350e12 + 1.94597e12i −0.140272 + 0.242958i
\(738\) 7.07651e11 + 1.22569e12i 0.0878144 + 0.152099i
\(739\) 9.18724e11 + 4.42434e11i 0.113314 + 0.0545693i 0.489682 0.871901i \(-0.337113\pi\)
−0.376368 + 0.926470i \(0.622827\pi\)
\(740\) −2.93488e12 + 9.05289e11i −0.359788 + 0.110980i
\(741\) −1.87675e11 + 2.50434e12i −0.0228678 + 0.305149i
\(742\) −1.15507e12 + 5.06070e12i −0.139891 + 0.612904i
\(743\) −7.31488e11 1.86380e12i −0.0880557 0.224362i 0.880062 0.474860i \(-0.157501\pi\)
−0.968117 + 0.250497i \(0.919406\pi\)
\(744\) −7.82215e11 1.04379e13i −0.0935939 1.24892i
\(745\) 1.06593e13 + 1.60664e12i 1.26773 + 0.191079i
\(746\) 2.12222e12 1.96913e12i 0.250880 0.232782i
\(747\) 1.50538e12 7.24952e11i 0.176890 0.0851857i
\(748\) 5.25255e12 + 3.58113e12i 0.613498 + 0.418276i
\(749\) −1.69263e12 + 4.31276e12i −0.196515 + 0.500711i
\(750\) 5.18446e10 + 1.59919e10i 0.00598312 + 0.00184555i
\(751\) −2.51012e11 2.32905e11i −0.0287948 0.0267177i 0.665644 0.746269i \(-0.268157\pi\)
−0.694439 + 0.719552i \(0.744347\pi\)
\(752\) 3.40547e12 + 4.27032e12i 0.388326 + 0.486945i
\(753\) −1.52774e11 1.91573e11i −0.0173170 0.0217148i
\(754\) 1.63531e11 + 1.51735e11i 0.0184259 + 0.0170968i
\(755\) 1.38174e13 + 4.26211e12i 1.54762 + 0.477379i
\(756\) −1.15212e13 + 2.93556e13i −1.28277 + 3.26845i
\(757\) −2.95151e12 2.01231e12i −0.326673 0.222722i 0.388867 0.921294i \(-0.372867\pi\)
−0.715539 + 0.698572i \(0.753819\pi\)
\(758\) 2.70233e12 1.30137e12i 0.297322 0.143183i
\(759\) 1.68612e13 1.56449e13i 1.84417 1.71114i
\(760\) 6.17872e12 + 9.31292e11i 0.671796 + 0.101257i
\(761\) 1.05171e11 + 1.40341e12i 0.0113675 + 0.151689i 0.999999 + 0.00133089i \(0.000423637\pi\)
−0.988632 + 0.150358i \(0.951957\pi\)
\(762\) 8.79265e11 + 2.24033e12i 0.0944762 + 0.240721i
\(763\) 2.97398e12 1.30299e13i 0.317671 1.39181i
\(764\) −1.55038e11 + 2.06884e12i −0.0164634 + 0.219689i
\(765\) −3.77866e13 + 1.16556e13i −3.98898 + 1.23044i
\(766\) −1.60141e12 7.71197e11i −0.168063 0.0809349i
\(767\) −4.10092e10 7.10300e10i −0.00427860 0.00741076i
\(768\) 3.43331e12 5.94667e12i 0.356113 0.616805i
\(769\) 9.93688e12 6.77485e12i 1.02466 0.698604i 0.0703846 0.997520i \(-0.477577\pi\)
0.954280 + 0.298916i \(0.0966250\pi\)
\(770\) −7.08721e11 3.10511e12i −0.0726552 0.318323i
\(771\) 6.43574e12 9.70032e11i 0.655925 0.0988648i
\(772\) −4.46377e12 + 5.59739e12i −0.452298 + 0.567163i
\(773\) 9.89713e12 0.997014 0.498507 0.866886i \(-0.333882\pi\)
0.498507 + 0.866886i \(0.333882\pi\)
\(774\) −6.83397e12 + 5.76014e11i −0.684446 + 0.0576897i
\(775\) 1.31304e13 1.30743
\(776\) −1.85907e12 + 2.33120e12i −0.184042 + 0.230782i
\(777\) −6.74175e12 + 1.01616e12i −0.663557 + 0.100015i
\(778\) 2.88078e11 + 1.26215e12i 0.0281905 + 0.123511i
\(779\) −2.04510e12 + 1.39432e12i −0.198974 + 0.135658i
\(780\) 2.21482e12 3.83618e12i 0.214246 0.371085i
\(781\) −2.11631e12 3.66556e12i −0.203540 0.352542i
\(782\) −5.27051e12 2.53814e12i −0.503990 0.242709i
\(783\) 1.70708e13 5.26565e12i 1.62303 0.500638i
\(784\) 3.35139e11 4.47213e12i 0.0316813 0.422758i
\(785\) −2.11162e12 + 9.25163e12i −0.198474 + 0.869571i
\(786\) −3.55191e12 9.05012e12i −0.331941 0.845771i
\(787\) 5.20252e11 + 6.94228e12i 0.0483423 + 0.645083i 0.967772 + 0.251828i \(0.0810319\pi\)
−0.919430 + 0.393255i \(0.871349\pi\)
\(788\) −7.97820e12 1.20252e12i −0.737118 0.111103i
\(789\) −2.92147e12 + 2.71073e12i −0.268383 + 0.249023i
\(790\) −4.89756e12 + 2.35854e12i −0.447361 + 0.215438i
\(791\) 4.41341e12 + 3.00902e12i 0.400849 + 0.273294i
\(792\) 3.78655e12 9.64798e12i 0.341964 0.871311i
\(793\) 1.17673e12 + 3.62974e11i 0.105669 + 0.0325947i
\(794\) 1.73481e12 + 1.60967e12i 0.154903 + 0.143729i
\(795\) −3.64050e13 4.56504e13i −3.23228 4.05315i
\(796\) 6.91218e12 + 8.66760e12i 0.610247 + 0.765226i
\(797\) −3.48416e12 3.23282e12i −0.305869 0.283805i 0.512271 0.858824i \(-0.328804\pi\)
−0.818140 + 0.575019i \(0.804995\pi\)
\(798\) 6.38868e12 + 1.97065e12i 0.557696 + 0.172027i
\(799\) −3.72130e12 + 9.48171e12i −0.323023 + 0.823050i
\(800\) −6.94203e12 4.73300e12i −0.599214 0.408537i
\(801\) −2.59218e13 + 1.24833e13i −2.22494 + 1.07147i
\(802\) −1.94886e12 + 1.80828e12i −0.166340 + 0.154341i
\(803\) −7.81580e11 1.17804e11i −0.0663366 0.00999864i
\(804\) 6.21730e11 + 8.29640e12i 0.0524746 + 0.700225i
\(805\) −1.43346e13 3.65240e13i −1.20311 3.06547i
\(806\) −1.55872e11 + 6.82920e11i −0.0130095 + 0.0569983i
\(807\) 8.78255e11 1.17195e13i 0.0728936 0.972698i
\(808\) −8.15070e12 + 2.51416e12i −0.672735 + 0.207511i
\(809\) −9.62750e12 4.63636e12i −0.790215 0.380547i −0.00517009 0.999987i \(-0.501646\pi\)
−0.785045 + 0.619439i \(0.787360\pi\)
\(810\) 7.28475e12 + 1.26176e13i 0.594610 + 1.02989i
\(811\) 2.17376e12 3.76506e12i 0.176448 0.305618i −0.764213 0.644964i \(-0.776872\pi\)
0.940662 + 0.339346i \(0.110206\pi\)
\(812\) −6.56922e12 + 4.47882e12i −0.530288 + 0.361544i
\(813\) 9.18146e12 + 4.02266e13i 0.737062 + 3.22928i
\(814\) 6.58069e11 9.91879e10i 0.0525366 0.00791861i
\(815\) −1.55565e13 + 1.95072e13i −1.23510 + 1.54876i
\(816\) 2.16483e13 1.70930
\(817\) −1.89772e12 1.18431e13i −0.149016 0.929963i
\(818\) 1.21931e12 0.0952192
\(819\) 4.43040e12 5.55555e12i 0.344085 0.431469i
\(820\) 4.31707e12 6.50694e11i 0.333447 0.0502591i
\(821\) 6.25929e10 + 2.74238e11i 0.00480818 + 0.0210660i 0.977275 0.211975i \(-0.0679895\pi\)
−0.972467 + 0.233041i \(0.925132\pi\)
\(822\) 3.54570e12 2.41742e12i 0.270881 0.184684i
\(823\) 8.79981e12 1.52417e13i 0.668612 1.15807i −0.309681 0.950841i \(-0.600222\pi\)
0.978292 0.207229i \(-0.0664446\pi\)
\(824\) 6.13771e12 + 1.06308e13i 0.463804 + 0.803332i
\(825\) 1.62099e13 + 7.80629e12i 1.21826 + 0.586681i
\(826\) −2.08647e11 + 6.43590e10i −0.0155956 + 0.00481060i
\(827\) 1.11986e12 1.49435e13i 0.0832512 1.11091i −0.786556 0.617519i \(-0.788138\pi\)
0.869807 0.493391i \(-0.164243\pi\)
\(828\) 1.36945e13 5.99994e13i 1.01253 4.43620i
\(829\) −2.86903e12 7.31018e12i −0.210980 0.537567i 0.785735 0.618563i \(-0.212285\pi\)
−0.996714 + 0.0809963i \(0.974190\pi\)
\(830\) 2.87703e10 + 3.83913e11i 0.00210423 + 0.0280790i
\(831\) −2.11110e13 3.18198e12i −1.53569 0.231469i
\(832\) −1.05199e12 + 9.76107e11i −0.0761129 + 0.0706224i
\(833\) 7.53509e12 3.62871e12i 0.542233 0.261126i
\(834\) 3.66011e12 + 2.49542e12i 0.261967 + 0.178606i
\(835\) −1.17069e13 + 2.98287e13i −0.833400 + 2.12347i
\(836\) 8.34862e12 + 2.57521e12i 0.591134 + 0.182341i
\(837\) 4.11203e13 + 3.81541e13i 2.89595 + 2.68705i
\(838\) 1.61172e12 + 2.02103e12i 0.112899 + 0.141571i
\(839\) −9.36750e12 1.17465e13i −0.652672 0.818425i 0.339852 0.940479i \(-0.389623\pi\)
−0.992523 + 0.122054i \(0.961052\pi\)
\(840\) −1.79347e13 1.66410e13i −1.24291 1.15325i
\(841\) −9.55873e12 2.94848e12i −0.658898 0.203243i
\(842\) −1.38448e12 + 3.52761e12i −0.0949256 + 0.241867i
\(843\) −7.55953e12 5.15400e12i −0.515550 0.351496i
\(844\) −1.07240e13 + 5.16442e12i −0.727473 + 0.350333i
\(845\) 1.49470e13 1.38688e13i 1.00856 0.935803i
\(846\) 7.91488e12 + 1.19298e12i 0.531224 + 0.0800692i
\(847\) 6.95207e11 + 9.27689e12i 0.0464129 + 0.619337i
\(848\) 8.43916e12 + 2.15026e13i 0.560426 + 1.42794i
\(849\) −4.37633e11 + 1.91739e12i −0.0289085 + 0.126656i
\(850\) 3.41945e11 4.56294e12i 0.0224684 0.299820i
\(851\) 7.83424e12 2.41654e12i 0.512052 0.157947i
\(852\) −1.41196e13 6.79962e12i −0.918000 0.442086i
\(853\) −3.24352e11 5.61794e11i −0.0209771 0.0363334i 0.855346 0.518057i \(-0.173344\pi\)
−0.876323 + 0.481723i \(0.840011\pi\)
\(854\) 1.63916e12 2.83911e12i 0.105454 0.182651i
\(855\) −4.49021e13 + 3.06137e13i −2.87355 + 1.95915i
\(856\) −7.73019e11 3.38682e12i −0.0492105 0.215605i
\(857\) 7.09079e12 1.06876e12i 0.449035 0.0676812i 0.0793681 0.996845i \(-0.474710\pi\)
0.369667 + 0.929164i \(0.379472\pi\)
\(858\) −5.98441e11 + 7.50422e11i −0.0376989 + 0.0472729i
\(859\) −1.54687e13 −0.969356 −0.484678 0.874693i \(-0.661063\pi\)
−0.484678 + 0.874693i \(0.661063\pi\)
\(860\) −6.04773e12 + 2.02729e13i −0.377007 + 1.26378i
\(861\) 9.69153e12 0.601005
\(862\) 3.64181e12 4.56668e12i 0.224664 0.281720i
\(863\) 2.63596e13 3.97307e12i 1.61767 0.243825i 0.723099 0.690745i \(-0.242717\pi\)
0.894574 + 0.446920i \(0.147479\pi\)
\(864\) −7.98725e12 3.49944e13i −0.487624 2.13642i
\(865\) −1.06841e13 + 7.28431e12i −0.648883 + 0.442401i
\(866\) −2.32443e12 + 4.02603e12i −0.140438 + 0.243246i
\(867\) 4.39020e12 + 7.60406e12i 0.263875 + 0.457045i
\(868\) −2.24931e13 1.08321e13i −1.34496 0.647700i
\(869\) −1.50682e13 + 4.64793e12i −0.896341 + 0.276485i
\(870\) −4.99220e11 + 6.66163e12i −0.0295431 + 0.394225i
\(871\) 2.57038e11 1.12616e12i 0.0151327 0.0663007i
\(872\) 3.66117e12 + 9.32850e12i 0.214435 + 0.546371i
\(873\) −1.93796e12 2.58603e13i −0.112923 1.50685i
\(874\) −7.94971e12 1.19823e12i −0.460839 0.0694604i
\(875\) 1.96806e11 1.82609e11i 0.0113502 0.0105314i
\(876\) −2.63671e12 + 1.26977e12i −0.151284 + 0.0728547i
\(877\) −7.29465e12 4.97340e12i −0.416395 0.283894i 0.336945 0.941524i \(-0.390606\pi\)
−0.753340 + 0.657631i \(0.771559\pi\)
\(878\) −1.40340e12 + 3.57579e12i −0.0796994 + 0.203071i
\(879\) 4.36015e13 + 1.34493e13i 2.46349 + 0.759886i
\(880\) −1.03897e13 9.64021e12i −0.584023 0.541894i
\(881\) −1.77516e12 2.22598e12i −0.0992765 0.124489i 0.729712 0.683755i \(-0.239654\pi\)
−0.828988 + 0.559266i \(0.811083\pi\)
\(882\) −4.09765e12 5.13829e12i −0.227995 0.285897i
\(883\) −1.89819e13 1.76126e13i −1.05079 0.974993i −0.0510733 0.998695i \(-0.516264\pi\)
−0.999719 + 0.0237020i \(0.992455\pi\)
\(884\) −3.12285e12 9.63271e11i −0.171995 0.0530534i
\(885\) 8.97305e11 2.28630e12i 0.0491694 0.125282i
\(886\) −1.99806e10 1.36225e10i −0.00108932 0.000742687i
\(887\) 1.46868e12 7.07278e11i 0.0796655 0.0383649i −0.393627 0.919270i \(-0.628780\pi\)
0.473292 + 0.880905i \(0.343065\pi\)
\(888\) 3.74749e12 3.47716e12i 0.202247 0.187658i
\(889\) 1.17762e13 + 1.77498e12i 0.632337 + 0.0953095i
\(890\) −4.95408e11 6.61076e12i −0.0264672 0.353180i
\(891\) 1.54409e13 + 3.93427e13i 0.820771 + 2.09129i
\(892\) 3.95760e12 1.73394e13i 0.209310 0.917047i
\(893\) −1.04611e12 + 1.39594e13i −0.0550486 + 0.734572i
\(894\) −8.26412e12 + 2.54914e12i −0.432691 + 0.133467i
\(895\) 1.32704e13 + 6.39067e12i 0.691320 + 0.332922i
\(896\) 1.04944e13 + 1.81769e13i 0.543967 + 0.942178i
\(897\) −5.91215e12 + 1.02401e13i −0.304916 + 0.528129i
\(898\) −5.78581e12 + 3.94470e12i −0.296907 + 0.202428i
\(899\) 3.14703e12 + 1.37880e13i 0.160688 + 0.704019i
\(900\) 4.76009e13 7.17468e12i 2.41838 0.364511i
\(901\) −2.68583e13 + 3.36793e13i −1.35774 + 1.70255i
\(902\) −9.45999e11 −0.0475841
\(903\) −1.99825e13 + 4.24994e13i −1.00013 + 2.12710i
\(904\) −4.00519e12 −0.199464
\(905\) 1.62774e13 2.04112e13i 0.806614 1.01146i
\(906\) −1.14712e13 + 1.72901e12i −0.565631 + 0.0852551i
\(907\) −2.55531e12 1.11956e13i −0.125375 0.549304i −0.998129 0.0611436i \(-0.980525\pi\)
0.872754 0.488160i \(-0.162332\pi\)
\(908\) 1.81426e13 1.23694e13i 0.885752 0.603895i
\(909\) 3.70924e13 6.42460e13i 1.80197 3.12111i
\(910\) 8.18647e11 + 1.41794e12i 0.0395741 + 0.0685443i
\(911\) −2.82723e13 1.36152e13i −1.35997 0.654925i −0.395337 0.918536i \(-0.629372\pi\)
−0.964629 + 0.263611i \(0.915087\pi\)
\(912\) 2.84298e13 8.76943e12i 1.36081 0.419754i
\(913\) −8.34590e10 + 1.11368e12i −0.00397516 + 0.0530448i
\(914\) 2.01660e12 8.83531e12i 0.0955789 0.418759i
\(915\) 1.34724e13 + 3.43270e13i 0.635402 + 1.61898i
\(916\) −4.94812e11 6.60281e12i −0.0232226 0.309884i
\(917\) −4.75717e13 7.17028e12i −2.22171 0.334868i
\(918\) 1.43298e13 1.32961e13i 0.665961 0.617922i
\(919\) 3.34162e13 1.60924e13i 1.54539 0.744220i 0.549560 0.835454i \(-0.314795\pi\)
0.995829 + 0.0912341i \(0.0290811\pi\)
\(920\) 2.43079e13 + 1.65729e13i 1.11867 + 0.762697i
\(921\) 5.27925e12 1.34513e13i 0.241771 0.616022i
\(922\) 3.80399e11 + 1.17337e11i 0.0173360 + 0.00534746i
\(923\) 1.59502e12 + 1.47997e12i 0.0723368 + 0.0671187i
\(924\) −2.13287e13 2.67453e13i −0.962587 1.20705i
\(925\) 3.99835e12 + 5.01377e12i 0.179574 + 0.225178i
\(926\) 4.08528e11 + 3.79058e11i 0.0182588 + 0.0169417i
\(927\) −1.02020e14 3.14689e13i −4.53759 1.39966i
\(928\) 3.30623e12 8.42414e12i 0.146341 0.372872i
\(929\) 5.09995e12 + 3.47709e12i 0.224644 + 0.153160i 0.670413 0.741988i \(-0.266117\pi\)
−0.445768 + 0.895148i \(0.647069\pi\)
\(930\) −1.88989e13 + 9.10125e12i −0.828446 + 0.398959i
\(931\) 8.42558e12 7.81779e12i 0.367558 0.341044i
\(932\) 8.16702e12 + 1.23098e12i 0.354562 + 0.0534416i
\(933\) 5.25907e12 + 7.01774e13i 0.227217 + 3.03201i
\(934\) 1.44600e12 + 3.68435e12i 0.0621738 + 0.158416i
\(935\) 5.88148e12 2.57685e13i 0.251672 1.10265i
\(936\) −3.98165e11 + 5.31315e12i −0.0169560 + 0.226262i
\(937\) −3.56733e13 + 1.10037e13i −1.51187 + 0.466350i −0.936240 0.351360i \(-0.885719\pi\)
−0.575630 + 0.817710i \(0.695243\pi\)
\(938\) −2.77060e12 1.33425e12i −0.116859 0.0562762i
\(939\) −2.93054e11 5.07585e11i −0.0123013 0.0213066i
\(940\) 1.23456e13 2.13831e13i 0.515745 0.893297i
\(941\) 2.71124e13 1.84849e13i 1.12723 0.768535i 0.151709 0.988425i \(-0.451522\pi\)
0.975525 + 0.219890i \(0.0705699\pi\)
\(942\) −1.69411e12 7.42238e12i −0.0700991 0.307124i
\(943\) −1.15238e13 + 1.73694e12i −0.474563 + 0.0715288i
\(944\) −6.05816e11 + 7.59669e11i −0.0248294 + 0.0311351i
\(945\) 1.31115e14 5.34821
\(946\) 1.95051e12 4.14841e12i 0.0791841 0.168411i
\(947\) 4.80179e13 1.94012 0.970060 0.242865i \(-0.0780872\pi\)
0.970060 + 0.242865i \(0.0780872\pi\)
\(948\) −3.64023e13 + 4.56471e13i −1.46383 + 1.83559i
\(949\) 4.01787e11 6.05596e10i 0.0160804 0.00242374i
\(950\) −1.39932e12 6.13084e12i −0.0557394 0.244210i
\(951\) −6.45786e13 + 4.40290e13i −2.56022 + 1.74553i
\(952\) −9.02503e12 + 1.56318e13i −0.356108 + 0.616798i
\(953\) 3.67683e12 + 6.36846e12i 0.144396 + 0.250101i 0.929147 0.369709i \(-0.120543\pi\)
−0.784751 + 0.619811i \(0.787209\pi\)
\(954\) 3.04990e13 + 1.46876e13i 1.19212 + 0.574093i
\(955\) 8.24250e12 2.54248e12i 0.320659 0.0989103i
\(956\) −1.51325e12 + 2.01929e13i −0.0585937 + 0.781878i
\(957\) −4.31217e12 + 1.88929e13i −0.166185 + 0.728105i
\(958\) −2.68847e12 6.85010e12i −0.103124 0.262756i
\(959\) −1.58692e12 2.11760e13i −0.0605859 0.808463i
\(960\) −4.24943e13 6.40499e12i −1.61477 0.243387i
\(961\) −1.31718e13 + 1.22216e13i −0.498182 + 0.462246i
\(962\) −3.08235e11 + 1.48438e11i −0.0116036 + 0.00558801i
\(963\) 2.49637e13 + 1.70200e13i 0.935385 + 0.637735i
\(964\) −3.24367e12 + 8.26473e12i −0.120973 + 0.308235i
\(965\) 2.84438e13 + 8.77376e12i 1.05588 + 0.325696i
\(966\) 2.30753e13 + 2.14108e13i 0.852610 + 0.791106i
\(967\) −3.99929e12 5.01495e12i −0.147083 0.184437i 0.702832 0.711356i \(-0.251918\pi\)
−0.849915 + 0.526919i \(0.823347\pi\)
\(968\) −4.34913e12 5.45364e12i −0.159207 0.199640i
\(969\) 4.06718e13 + 3.77379e13i 1.48196 + 1.37506i
\(970\) 5.70988e12 + 1.76126e12i 0.207088 + 0.0638780i
\(971\) −2.78906e12 + 7.10641e12i −0.100687 + 0.256545i −0.972337 0.233583i \(-0.924955\pi\)
0.871650 + 0.490128i \(0.163050\pi\)
\(972\) 6.40759e13 + 4.36862e13i 2.30248 + 1.56981i
\(973\) 1.97497e13 9.51097e12i 0.706404 0.340186i
\(974\) −7.30853e12 + 6.78132e12i −0.260204 + 0.241434i
\(975\) −9.14568e12 1.37849e12i −0.324112 0.0488520i
\(976\) −1.09021e12 1.45478e13i −0.0384580 0.513186i
\(977\) −1.99003e12 5.07051e12i −0.0698769 0.178043i 0.891669 0.452688i \(-0.149535\pi\)
−0.961546 + 0.274645i \(0.911440\pi\)
\(978\) 4.45428e12 1.95155e13i 0.155687 0.682109i
\(979\) 1.43712e12 1.91770e13i 0.0500000 0.667203i
\(980\) −1.93726e13 + 5.97565e12i −0.670919 + 0.206951i
\(981\) −7.85263e13 3.78163e13i −2.70710 1.30367i
\(982\) −4.04596e12 7.00780e12i −0.138842 0.240481i
\(983\) 3.02384e12 5.23745e12i 0.103292 0.178908i −0.809747 0.586779i \(-0.800396\pi\)
0.913039 + 0.407872i \(0.133729\pi\)
\(984\) −6.00416e12 + 4.09357e12i −0.204162 + 0.139195i
\(985\) 7.46458e12 + 3.27044e13i 0.252663 + 1.10699i
\(986\) 4.87345e12 7.34555e11i 0.164207 0.0247502i
\(987\) 3.41739e13 4.28528e13i 1.14622 1.43731i
\(988\) −4.49131e12 −0.149957
\(989\) 1.61436e13 5.41157e13i 0.536558 1.79862i
\(990\) −2.07703e13 −0.687202
\(991\) −3.58324e13 + 4.49325e13i −1.18017 + 1.47989i −0.337611 + 0.941286i \(0.609619\pi\)
−0.842560 + 0.538602i \(0.818953\pi\)
\(992\) 2.80988e13 4.23521e12i 0.921267 0.138859i
\(993\) −2.07142e12 9.07550e12i −0.0676079 0.296210i
\(994\) 4.78602e12 3.26306e12i 0.155502 0.106020i
\(995\) 2.30466e13 3.99179e13i 0.745424 1.29111i
\(996\) 2.06752e12 + 3.58104e12i 0.0665705 + 0.115304i
\(997\) −5.88395e12 2.83356e12i −0.188600 0.0908248i 0.337201 0.941433i \(-0.390520\pi\)
−0.525800 + 0.850608i \(0.676234\pi\)
\(998\) −1.04360e13 + 3.21909e12i −0.333003 + 0.102718i
\(999\) −2.04735e12 + 2.73200e13i −0.0650350 + 0.867832i
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 43.10.g.a.24.16 yes 384
43.9 even 21 inner 43.10.g.a.9.16 384
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.g.a.9.16 384 43.9 even 21 inner
43.10.g.a.24.16 yes 384 1.1 even 1 trivial