Properties

Label 11.12.c.a.3.9
Level $11$
Weight $12$
Character 11.3
Analytic conductor $8.452$
Analytic rank $0$
Dimension $40$
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] = [11,12,Mod(3,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.3");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 11.c (of order \(5\), degree \(4\), 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: \(8.45177498616\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 3.9
Character \(\chi\) \(=\) 11.3
Dual form 11.12.c.a.4.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(56.7091 - 41.2016i) q^{2} +(40.8374 + 125.685i) q^{3} +(885.488 - 2725.25i) q^{4} +(-8463.91 - 6149.39i) q^{5} +(7494.26 + 5444.90i) q^{6} +(23115.4 - 71141.9i) q^{7} +(-17707.8 - 54499.0i) q^{8} +(129186. - 93859.1i) q^{9} +O(q^{10})\) \(q+(56.7091 - 41.2016i) q^{2} +(40.8374 + 125.685i) q^{3} +(885.488 - 2725.25i) q^{4} +(-8463.91 - 6149.39i) q^{5} +(7494.26 + 5444.90i) q^{6} +(23115.4 - 71141.9i) q^{7} +(-17707.8 - 54499.0i) q^{8} +(129186. - 93859.1i) q^{9} -733345. q^{10} +(94649.7 + 525693. i) q^{11} +378683. q^{12} +(-416130. + 302336. i) q^{13} +(-1.62031e6 - 4.98679e6i) q^{14} +(427239. - 1.31491e6i) q^{15} +(1.49811e6 + 1.08844e6i) q^{16} +(-14649.5 - 10643.5i) q^{17} +(3.45888e6 - 1.06453e7i) q^{18} +(3.44406e6 + 1.05997e7i) q^{19} +(-2.42533e7 + 1.76211e7i) q^{20} +9.88541e6 q^{21} +(2.70269e7 + 2.59119e7i) q^{22} +1.89458e6 q^{23} +(6.12654e6 - 4.45119e6i) q^{24} +(1.87340e7 + 5.76574e7i) q^{25} +(-1.11416e7 + 3.42905e7i) q^{26} +(3.60117e7 + 2.61640e7i) q^{27} +(-1.73411e8 - 1.25991e8i) q^{28} +(6.15714e7 - 1.89497e8i) q^{29} +(-2.99479e7 - 9.21702e7i) q^{30} +(3.13636e7 - 2.27870e7i) q^{31} +2.47160e8 q^{32} +(-6.22062e7 + 3.33639e7i) q^{33} -1.26929e6 q^{34} +(-6.33126e8 + 4.59993e8i) q^{35} +(-1.41397e8 - 4.35175e8i) q^{36} +(2.05990e7 - 6.33972e7i) q^{37} +(6.32036e8 + 4.59201e8i) q^{38} +(-5.49927e7 - 3.99545e7i) q^{39} +(-1.85258e8 + 5.70166e8i) q^{40} +(-2.16533e8 - 6.66419e8i) q^{41} +(5.60593e8 - 4.07295e8i) q^{42} +4.07524e8 q^{43} +(1.51646e9 + 2.07550e8i) q^{44} -1.67059e9 q^{45} +(1.07440e8 - 7.80598e7i) q^{46} +(5.14948e8 + 1.58485e9i) q^{47} +(-7.56212e7 + 2.32738e8i) q^{48} +(-2.92716e9 - 2.12671e9i) q^{49} +(3.43797e9 + 2.49783e9i) q^{50} +(739474. - 2.27587e6i) q^{51} +(4.55464e8 + 1.40177e9i) q^{52} +(-3.14438e9 + 2.28453e9i) q^{53} +3.12019e9 q^{54} +(2.43158e9 - 5.03145e9i) q^{55} -4.28649e9 q^{56} +(-1.19158e9 + 8.65731e8i) q^{57} +(-4.31593e9 - 1.32831e10i) q^{58} +(-2.81766e9 + 8.67188e9i) q^{59} +(-3.20514e9 - 2.32867e9i) q^{60} +(6.10328e9 + 4.43429e9i) q^{61} +(8.39743e8 - 2.58446e9i) q^{62} +(-3.69113e9 - 1.13601e10i) q^{63} +(1.09481e10 - 7.95425e9i) q^{64} +5.38127e9 q^{65} +(-2.15301e9 + 4.45504e9i) q^{66} +4.62277e9 q^{67} +(-4.19781e7 + 3.04989e7i) q^{68} +(7.73697e7 + 2.38119e8i) q^{69} +(-1.69516e10 + 5.21716e10i) q^{70} +(2.01385e9 + 1.46315e9i) q^{71} +(-7.40283e9 - 5.37847e9i) q^{72} +(-3.58390e9 + 1.10301e10i) q^{73} +(-1.44391e9 - 4.44391e9i) q^{74} +(-6.48159e9 + 4.70915e9i) q^{75} +3.19366e10 q^{76} +(3.95867e10 + 5.41805e9i) q^{77} -4.76478e9 q^{78} +(-3.03674e9 + 2.20632e9i) q^{79} +(-5.98662e9 - 1.84249e10i) q^{80} +(6.92347e9 - 2.13082e10i) q^{81} +(-3.97369e10 - 2.88705e10i) q^{82} +(-3.11864e10 - 2.26582e10i) q^{83} +(8.75341e9 - 2.69402e10i) q^{84} +(5.85411e7 + 1.80171e8i) q^{85} +(2.31103e10 - 1.67906e10i) q^{86} +2.63313e10 q^{87} +(2.69737e10 - 1.44672e10i) q^{88} -7.91040e10 q^{89} +(-9.47380e10 + 6.88312e10i) q^{90} +(1.18898e10 + 3.65929e10i) q^{91} +(1.67763e9 - 5.16321e9i) q^{92} +(4.14479e9 + 3.01136e9i) q^{93} +(9.45005e10 + 6.86586e10i) q^{94} +(3.60317e10 - 1.10894e11i) q^{95} +(1.00934e10 + 3.10642e10i) q^{96} +(5.16141e10 - 3.74998e10i) q^{97} -2.53620e11 q^{98} +(6.15685e10 + 5.90284e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 11 q^{2} - 276 q^{3} - 6137 q^{4} + 6038 q^{5} - 30371 q^{6} + 55440 q^{7} - 347809 q^{8} - 240812 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 11 q^{2} - 276 q^{3} - 6137 q^{4} + 6038 q^{5} - 30371 q^{6} + 55440 q^{7} - 347809 q^{8} - 240812 q^{9} + 782320 q^{10} - 288860 q^{11} - 5871146 q^{12} - 794178 q^{13} + 9181256 q^{14} - 9707296 q^{15} - 10033697 q^{16} + 11803154 q^{17} - 2661582 q^{18} - 33326568 q^{19} + 34173582 q^{20} + 72722452 q^{21} + 77957825 q^{22} + 75694752 q^{23} - 297034287 q^{24} - 118409216 q^{25} + 605949712 q^{26} + 348141600 q^{27} - 546845442 q^{28} - 400113538 q^{29} - 828772494 q^{30} + 514005960 q^{31} - 84440796 q^{32} + 1211751794 q^{33} - 899802542 q^{34} - 1820315508 q^{35} + 971066424 q^{36} + 1207982934 q^{37} + 1815036992 q^{38} - 2825057488 q^{39} - 1263004028 q^{40} - 3269102782 q^{41} + 4736681342 q^{42} + 2749122728 q^{43} + 5968984648 q^{44} - 1896048208 q^{45} - 1240862964 q^{46} - 2081937184 q^{47} - 4090087516 q^{48} - 2514603052 q^{49} + 7217881803 q^{50} - 1172394432 q^{51} + 23226253050 q^{52} - 7132071266 q^{53} - 34172203516 q^{54} - 9211291408 q^{55} + 33017775912 q^{56} + 30518561370 q^{57} - 34218647932 q^{58} - 12866186432 q^{59} - 55228105332 q^{60} + 2702502990 q^{61} - 18405787180 q^{62} + 33243939784 q^{63} + 28267347551 q^{64} + 28056414980 q^{65} + 64510531470 q^{66} - 549542392 q^{67} - 17332191778 q^{68} - 33459566280 q^{69} - 90854725304 q^{70} - 37002489528 q^{71} + 37881288247 q^{72} - 41936764254 q^{73} + 118297253448 q^{74} + 72805696880 q^{75} + 136670345702 q^{76} + 85397422330 q^{77} + 113064629380 q^{78} - 140458240296 q^{79} - 257276697596 q^{80} + 28633292464 q^{81} - 94584428059 q^{82} - 238929577568 q^{83} - 339093796404 q^{84} + 48160626338 q^{85} + 176827923479 q^{86} + 448810202016 q^{87} + 742233436703 q^{88} + 311499953960 q^{89} - 913432848482 q^{90} - 410566597652 q^{91} + 77316479782 q^{92} - 480470187862 q^{93} - 508753213738 q^{94} - 524637979272 q^{95} + 324858127396 q^{96} + 474017921070 q^{97} + 1187521497580 q^{98} + 1382319662900 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 56.7091 41.2016i 1.25311 0.910435i 0.254709 0.967018i \(-0.418020\pi\)
0.998398 + 0.0565825i \(0.0180204\pi\)
\(3\) 40.8374 + 125.685i 0.0970266 + 0.298617i 0.987777 0.155876i \(-0.0498202\pi\)
−0.890750 + 0.454494i \(0.849820\pi\)
\(4\) 885.488 2725.25i 0.432367 1.33069i
\(5\) −8463.91 6149.39i −1.21126 0.880029i −0.215911 0.976413i \(-0.569272\pi\)
−0.995344 + 0.0963843i \(0.969272\pi\)
\(6\) 7494.26 + 5444.90i 0.393456 + 0.285863i
\(7\) 23115.4 71141.9i 0.519831 1.59988i −0.254485 0.967077i \(-0.581906\pi\)
0.774316 0.632799i \(-0.218094\pi\)
\(8\) −17707.8 54499.0i −0.191060 0.588022i
\(9\) 129186. 93859.1i 0.729259 0.529838i
\(10\) −733345. −2.31904
\(11\) 94649.7 + 525693.i 0.177198 + 0.984175i
\(12\) 378683. 0.439318
\(13\) −416130. + 302336.i −0.310843 + 0.225841i −0.732258 0.681027i \(-0.761533\pi\)
0.421415 + 0.906868i \(0.361533\pi\)
\(14\) −1.62031e6 4.98679e6i −0.805180 2.47809i
\(15\) 427239. 1.31491e6i 0.145268 0.447088i
\(16\) 1.49811e6 + 1.08844e6i 0.357177 + 0.259504i
\(17\) −14649.5 10643.5i −0.00250238 0.00181809i 0.586533 0.809925i \(-0.300492\pi\)
−0.589036 + 0.808107i \(0.700492\pi\)
\(18\) 3.45888e6 1.06453e7i 0.431456 1.32789i
\(19\) 3.44406e6 + 1.05997e7i 0.319100 + 0.982088i 0.974034 + 0.226402i \(0.0726963\pi\)
−0.654934 + 0.755686i \(0.727304\pi\)
\(20\) −2.42533e7 + 1.76211e7i −1.69475 + 1.23131i
\(21\) 9.88541e6 0.528188
\(22\) 2.70269e7 + 2.59119e7i 1.11808 + 1.07195i
\(23\) 1.89458e6 0.0613776 0.0306888 0.999529i \(-0.490230\pi\)
0.0306888 + 0.999529i \(0.490230\pi\)
\(24\) 6.12654e6 4.45119e6i 0.157056 0.114108i
\(25\) 1.87340e7 + 5.76574e7i 0.383673 + 1.18082i
\(26\) −1.11416e7 + 3.42905e7i −0.183906 + 0.566005i
\(27\) 3.60117e7 + 2.61640e7i 0.482995 + 0.350917i
\(28\) −1.73411e8 1.25991e8i −1.90418 1.38347i
\(29\) 6.15714e7 1.89497e8i 0.557430 1.71559i −0.132009 0.991249i \(-0.542143\pi\)
0.689439 0.724344i \(-0.257857\pi\)
\(30\) −2.99479e7 9.21702e7i −0.225009 0.692506i
\(31\) 3.13636e7 2.27870e7i 0.196760 0.142955i −0.485043 0.874490i \(-0.661196\pi\)
0.681803 + 0.731536i \(0.261196\pi\)
\(32\) 2.47160e8 1.30213
\(33\) −6.22062e7 + 3.33639e7i −0.276699 + 0.148406i
\(34\) −1.26929e6 −0.00479100
\(35\) −6.33126e8 + 4.59993e8i −2.03759 + 1.48039i
\(36\) −1.41397e8 4.35175e8i −0.389741 1.19950i
\(37\) 2.05990e7 6.33972e7i 0.0488356 0.150300i −0.923665 0.383201i \(-0.874822\pi\)
0.972501 + 0.232901i \(0.0748217\pi\)
\(38\) 6.32036e8 + 4.59201e8i 1.29399 + 0.940141i
\(39\) −5.49927e7 3.99545e7i −0.0975999 0.0709105i
\(40\) −1.85258e8 + 5.70166e8i −0.286054 + 0.880383i
\(41\) −2.16533e8 6.66419e8i −0.291885 0.898330i −0.984250 0.176783i \(-0.943431\pi\)
0.692365 0.721548i \(-0.256569\pi\)
\(42\) 5.60593e8 4.07295e8i 0.661876 0.480881i
\(43\) 4.07524e8 0.422743 0.211372 0.977406i \(-0.432207\pi\)
0.211372 + 0.977406i \(0.432207\pi\)
\(44\) 1.51646e9 + 2.07550e8i 1.38625 + 0.189729i
\(45\) −1.67059e9 −1.34959
\(46\) 1.07440e8 7.80598e7i 0.0769127 0.0558803i
\(47\) 5.14948e8 + 1.58485e9i 0.327510 + 1.00797i 0.970295 + 0.241926i \(0.0777791\pi\)
−0.642784 + 0.766047i \(0.722221\pi\)
\(48\) −7.56212e7 + 2.32738e8i −0.0428368 + 0.131838i
\(49\) −2.92716e9 2.12671e9i −1.48036 1.07555i
\(50\) 3.43797e9 + 2.49783e9i 1.55585 + 1.13039i
\(51\) 739474. 2.27587e6i 0.000300114 0.000923657i
\(52\) 4.55464e8 + 1.40177e9i 0.166125 + 0.511281i
\(53\) −3.14438e9 + 2.28453e9i −1.03281 + 0.750377i −0.968868 0.247577i \(-0.920366\pi\)
−0.0639370 + 0.997954i \(0.520366\pi\)
\(54\) 3.12019e9 0.924731
\(55\) 2.43158e9 5.03145e9i 0.651470 1.34803i
\(56\) −4.28649e9 −1.04008
\(57\) −1.19158e9 + 8.65731e8i −0.262307 + 0.190577i
\(58\) −4.31593e9 1.32831e10i −0.863417 2.65732i
\(59\) −2.81766e9 + 8.67188e9i −0.513102 + 1.57916i 0.273608 + 0.961841i \(0.411783\pi\)
−0.786710 + 0.617323i \(0.788217\pi\)
\(60\) −3.20514e9 2.32867e9i −0.532126 0.386612i
\(61\) 6.10328e9 + 4.43429e9i 0.925229 + 0.672218i 0.944820 0.327590i \(-0.106236\pi\)
−0.0195913 + 0.999808i \(0.506236\pi\)
\(62\) 8.39743e8 2.58446e9i 0.116411 0.358275i
\(63\) −3.69113e9 1.13601e10i −0.468583 1.44215i
\(64\) 1.09481e10 7.95425e9i 1.27453 0.925997i
\(65\) 5.38127e9 0.575256
\(66\) −2.15301e9 + 4.45504e9i −0.211619 + 0.437884i
\(67\) 4.62277e9 0.418303 0.209151 0.977883i \(-0.432930\pi\)
0.209151 + 0.977883i \(0.432930\pi\)
\(68\) −4.19781e7 + 3.04989e7i −0.00350125 + 0.00254381i
\(69\) 7.73697e7 + 2.38119e8i 0.00595526 + 0.0183284i
\(70\) −1.69516e10 + 5.21716e10i −1.20551 + 3.71018i
\(71\) 2.01385e9 + 1.46315e9i 0.132466 + 0.0962425i 0.652045 0.758180i \(-0.273911\pi\)
−0.519579 + 0.854422i \(0.673911\pi\)
\(72\) −7.40283e9 5.37847e9i −0.450888 0.327589i
\(73\) −3.58390e9 + 1.10301e10i −0.202339 + 0.622736i 0.797473 + 0.603355i \(0.206170\pi\)
−0.999812 + 0.0193815i \(0.993830\pi\)
\(74\) −1.44391e9 4.44391e9i −0.0756426 0.232804i
\(75\) −6.48159e9 + 4.70915e9i −0.315388 + 0.229143i
\(76\) 3.19366e10 1.44482
\(77\) 3.95867e10 + 5.41805e9i 1.66667 + 0.228110i
\(78\) −4.76478e9 −0.186863
\(79\) −3.03674e9 + 2.20632e9i −0.111035 + 0.0806715i −0.641917 0.766774i \(-0.721861\pi\)
0.530882 + 0.847446i \(0.321861\pi\)
\(80\) −5.98662e9 1.84249e10i −0.204261 0.628652i
\(81\) 6.92347e9 2.13082e10i 0.220626 0.679016i
\(82\) −3.97369e10 2.88705e10i −1.18364 0.859961i
\(83\) −3.11864e10 2.26582e10i −0.869032 0.631389i 0.0612951 0.998120i \(-0.480477\pi\)
−0.930327 + 0.366731i \(0.880477\pi\)
\(84\) 8.75341e9 2.69402e10i 0.228371 0.702854i
\(85\) 5.85411e7 + 1.80171e8i 0.00143106 + 0.00440434i
\(86\) 2.31103e10 1.67906e10i 0.529742 0.384880i
\(87\) 2.63313e10 0.566391
\(88\) 2.69737e10 1.44672e10i 0.544861 0.292233i
\(89\) −7.91040e10 −1.50160 −0.750798 0.660532i \(-0.770331\pi\)
−0.750798 + 0.660532i \(0.770331\pi\)
\(90\) −9.47380e10 + 6.88312e10i −1.69118 + 1.22872i
\(91\) 1.18898e10 + 3.65929e10i 0.199731 + 0.614709i
\(92\) 1.67763e9 5.16321e9i 0.0265377 0.0816745i
\(93\) 4.14479e9 + 3.01136e9i 0.0617797 + 0.0448856i
\(94\) 9.45005e10 + 6.86586e10i 1.32810 + 0.964921i
\(95\) 3.60317e10 1.10894e11i 0.477754 1.47038i
\(96\) 1.00934e10 + 3.10642e10i 0.126341 + 0.388837i
\(97\) 5.16141e10 3.74998e10i 0.610272 0.443389i −0.239238 0.970961i \(-0.576898\pi\)
0.849510 + 0.527572i \(0.176898\pi\)
\(98\) −2.53620e11 −2.83427
\(99\) 6.15685e10 + 5.90284e10i 0.650676 + 0.623832i
\(100\) 1.73719e11 1.73719
\(101\) −5.42866e10 + 3.94416e10i −0.513955 + 0.373410i −0.814322 0.580413i \(-0.802891\pi\)
0.300367 + 0.953824i \(0.402891\pi\)
\(102\) −5.18344e7 1.59530e8i −0.000464855 0.00143068i
\(103\) 3.38741e10 1.04254e11i 0.287914 0.886108i −0.697596 0.716491i \(-0.745747\pi\)
0.985510 0.169617i \(-0.0542530\pi\)
\(104\) 2.38458e10 + 1.73250e10i 0.192189 + 0.139633i
\(105\) −8.36692e10 6.07892e10i −0.639771 0.464821i
\(106\) −8.41891e10 + 2.59107e11i −0.611046 + 1.88060i
\(107\) 6.47216e10 + 1.99193e11i 0.446106 + 1.37297i 0.881266 + 0.472621i \(0.156692\pi\)
−0.435160 + 0.900353i \(0.643308\pi\)
\(108\) 1.03191e11 7.49730e10i 0.675792 0.490992i
\(109\) 1.24034e11 0.772140 0.386070 0.922470i \(-0.373832\pi\)
0.386070 + 0.922470i \(0.373832\pi\)
\(110\) −6.94109e10 3.85515e11i −0.410930 2.28234i
\(111\) 8.80925e9 0.0496207
\(112\) 1.12063e11 8.14186e10i 0.600847 0.436541i
\(113\) 4.69270e10 + 1.44427e11i 0.239603 + 0.737421i 0.996477 + 0.0838612i \(0.0267252\pi\)
−0.756875 + 0.653560i \(0.773275\pi\)
\(114\) −3.19038e10 + 9.81898e10i −0.155191 + 0.477628i
\(115\) −1.60356e10 1.16505e10i −0.0743440 0.0540141i
\(116\) −4.61907e11 3.35595e11i −2.04191 1.48353i
\(117\) −2.53812e10 + 7.81152e10i −0.107026 + 0.329392i
\(118\) 1.97508e11 + 6.07867e11i 0.794756 + 2.44601i
\(119\) −1.09583e9 + 7.96165e8i −0.00420953 + 0.00305840i
\(120\) −7.92266e10 −0.290652
\(121\) −2.67395e11 + 9.95134e10i −0.937202 + 0.348788i
\(122\) 5.28812e11 1.77142
\(123\) 7.49159e10 5.44296e10i 0.239936 0.174324i
\(124\) −3.43282e10 1.05651e11i −0.105156 0.323635i
\(125\) 3.81369e10 1.17373e11i 0.111774 0.344005i
\(126\) −6.77377e11 4.92143e11i −1.90017 1.38055i
\(127\) −1.40916e11 1.02381e11i −0.378476 0.274979i 0.382241 0.924063i \(-0.375152\pi\)
−0.760717 + 0.649084i \(0.775152\pi\)
\(128\) 1.36710e11 4.20749e11i 0.351677 1.08235i
\(129\) 1.66422e10 + 5.12194e10i 0.0410173 + 0.126238i
\(130\) 3.05167e11 2.21717e11i 0.720857 0.523734i
\(131\) −8.28779e11 −1.87692 −0.938461 0.345384i \(-0.887749\pi\)
−0.938461 + 0.345384i \(0.887749\pi\)
\(132\) 3.58422e10 + 1.99071e11i 0.0778464 + 0.432366i
\(133\) 8.33697e11 1.73710
\(134\) 2.62153e11 1.90465e11i 0.524178 0.380837i
\(135\) −1.43907e11 4.42900e11i −0.276214 0.850099i
\(136\) −3.20649e8 + 9.86855e8i −0.000590970 + 0.00181882i
\(137\) 1.58401e11 + 1.15085e11i 0.280411 + 0.203731i 0.719097 0.694910i \(-0.244556\pi\)
−0.438685 + 0.898641i \(0.644556\pi\)
\(138\) 1.41985e10 + 1.03158e10i 0.0241494 + 0.0175456i
\(139\) 3.78012e10 1.16340e11i 0.0617908 0.190172i −0.915396 0.402555i \(-0.868122\pi\)
0.977187 + 0.212382i \(0.0681222\pi\)
\(140\) 6.92971e11 + 2.13274e12i 1.08896 + 3.35146i
\(141\) −1.78162e11 + 1.29442e11i −0.269221 + 0.195601i
\(142\) 1.74488e11 0.253617
\(143\) −1.98323e11 1.90141e11i −0.277347 0.265905i
\(144\) 2.95695e11 0.397970
\(145\) −1.68643e12 + 1.22526e12i −2.18496 + 1.58747i
\(146\) 2.51218e11 + 7.73171e11i 0.313408 + 0.964572i
\(147\) 1.47757e11 4.54748e11i 0.177542 0.546418i
\(148\) −1.54533e11 1.12275e11i −0.178888 0.129970i
\(149\) 1.06230e11 + 7.71807e10i 0.118501 + 0.0860962i 0.645457 0.763796i \(-0.276667\pi\)
−0.526956 + 0.849892i \(0.676667\pi\)
\(150\) −1.73541e11 + 5.34104e11i −0.186595 + 0.574280i
\(151\) −2.44291e11 7.51849e11i −0.253241 0.779395i −0.994171 0.107813i \(-0.965615\pi\)
0.740931 0.671582i \(-0.234385\pi\)
\(152\) 5.16688e11 3.75396e11i 0.516522 0.375275i
\(153\) −2.89150e9 −0.00278817
\(154\) 2.46816e12 1.32378e12i 2.29620 1.23155i
\(155\) −4.05585e11 −0.364131
\(156\) −1.57581e11 + 1.14490e11i −0.136559 + 0.0992158i
\(157\) 2.48424e11 + 7.64569e11i 0.207847 + 0.639689i 0.999584 + 0.0288266i \(0.00917705\pi\)
−0.791737 + 0.610862i \(0.790823\pi\)
\(158\) −8.13071e10 + 2.50237e11i −0.0656923 + 0.202180i
\(159\) −4.15538e11 3.01906e11i −0.324285 0.235607i
\(160\) −2.09194e12 1.51988e12i −1.57721 1.14591i
\(161\) 4.37940e10 1.34784e11i 0.0319060 0.0981966i
\(162\) −4.85310e11 1.49363e12i −0.341733 1.05175i
\(163\) 2.14533e12 1.55867e12i 1.46037 1.06102i 0.477102 0.878848i \(-0.341687\pi\)
0.983267 0.182172i \(-0.0583128\pi\)
\(164\) −2.00790e12 −1.32160
\(165\) 7.31675e11 + 1.00141e11i 0.465754 + 0.0637456i
\(166\) −2.70211e12 −1.66383
\(167\) 4.61548e11 3.35334e11i 0.274964 0.199773i −0.441754 0.897136i \(-0.645644\pi\)
0.716718 + 0.697363i \(0.245644\pi\)
\(168\) −1.75049e11 5.38745e11i −0.100916 0.310586i
\(169\) −4.72051e11 + 1.45282e12i −0.263398 + 0.810655i
\(170\) 1.07431e10 + 7.80535e9i 0.00580313 + 0.00421622i
\(171\) 1.43981e12 + 1.04608e12i 0.753054 + 0.547125i
\(172\) 3.60857e11 1.11060e12i 0.182780 0.562539i
\(173\) 2.11946e11 + 6.52304e11i 0.103985 + 0.320034i 0.989491 0.144595i \(-0.0461878\pi\)
−0.885506 + 0.464629i \(0.846188\pi\)
\(174\) 1.49323e12 1.08489e12i 0.709749 0.515663i
\(175\) 4.53490e12 2.08862
\(176\) −4.30390e11 + 8.90566e11i −0.192107 + 0.397509i
\(177\) −1.20499e12 −0.521350
\(178\) −4.48592e12 + 3.25921e12i −1.88166 + 1.36711i
\(179\) −2.12556e11 6.54181e11i −0.0864534 0.266076i 0.898479 0.439017i \(-0.144673\pi\)
−0.984932 + 0.172941i \(0.944673\pi\)
\(180\) −1.47929e12 + 4.55279e12i −0.583519 + 1.79589i
\(181\) −1.39594e12 1.01421e12i −0.534117 0.388058i 0.287779 0.957697i \(-0.407083\pi\)
−0.821895 + 0.569638i \(0.807083\pi\)
\(182\) 2.18195e12 + 1.58528e12i 0.809937 + 0.588454i
\(183\) −3.08080e11 + 9.48173e11i −0.110964 + 0.341512i
\(184\) −3.35488e10 1.03253e11i −0.0117268 0.0360914i
\(185\) −5.64201e11 + 4.09916e11i −0.191421 + 0.139076i
\(186\) 3.59120e11 0.118282
\(187\) 4.20863e9 8.70854e9i 0.00134590 0.00278494i
\(188\) 4.77508e12 1.48290
\(189\) 2.69378e12 1.95715e12i 0.812499 0.590315i
\(190\) −2.52569e12 7.77327e12i −0.740006 2.27750i
\(191\) −2.85242e11 + 8.77883e11i −0.0811950 + 0.249893i −0.983411 0.181392i \(-0.941940\pi\)
0.902216 + 0.431285i \(0.141940\pi\)
\(192\) 1.44682e12 + 1.05117e12i 0.400182 + 0.290749i
\(193\) 1.14698e12 + 8.33332e11i 0.308313 + 0.224002i 0.731172 0.682193i \(-0.238974\pi\)
−0.422859 + 0.906195i \(0.638974\pi\)
\(194\) 1.38194e12 4.25316e12i 0.361059 1.11123i
\(195\) 2.19757e11 + 6.76342e11i 0.0558152 + 0.171781i
\(196\) −8.38777e12 + 6.09407e12i −2.07128 + 1.50487i
\(197\) 4.19616e12 1.00760 0.503800 0.863821i \(-0.331935\pi\)
0.503800 + 0.863821i \(0.331935\pi\)
\(198\) 5.92356e12 + 8.10731e11i 1.38333 + 0.189329i
\(199\) 1.30331e12 0.296043 0.148021 0.988984i \(-0.452710\pi\)
0.148021 + 0.988984i \(0.452710\pi\)
\(200\) 2.81053e12 2.04197e12i 0.621045 0.451216i
\(201\) 1.88782e11 + 5.81010e11i 0.0405865 + 0.124912i
\(202\) −1.45349e12 + 4.47339e12i −0.304075 + 0.935846i
\(203\) −1.20580e13 8.76062e12i −2.45497 1.78364i
\(204\) −5.54751e9 4.03050e9i −0.00109934 0.000798718i
\(205\) −2.26536e12 + 6.97205e12i −0.437009 + 1.34498i
\(206\) −2.37445e12 7.30780e12i −0.445957 1.37252i
\(207\) 2.44753e11 1.77824e11i 0.0447602 0.0325202i
\(208\) −9.52483e11 −0.169633
\(209\) −5.24623e12 + 2.81378e12i −0.910003 + 0.488074i
\(210\) −7.24942e12 −1.22489
\(211\) 6.47495e12 4.70433e12i 1.06582 0.774362i 0.0906621 0.995882i \(-0.471102\pi\)
0.975156 + 0.221520i \(0.0711017\pi\)
\(212\) 3.44160e12 + 1.05922e13i 0.551967 + 1.69878i
\(213\) −1.01655e11 + 3.12861e11i −0.0158869 + 0.0488949i
\(214\) 1.18774e13 + 8.62940e12i 1.80902 + 1.31433i
\(215\) −3.44924e12 2.50602e12i −0.512050 0.372026i
\(216\) 7.88225e11 2.42591e12i 0.114066 0.351058i
\(217\) −8.96129e11 2.75800e12i −0.126428 0.389104i
\(218\) 7.03387e12 5.11041e12i 0.967573 0.702983i
\(219\) −1.53267e12 −0.205592
\(220\) −1.15588e13 1.10820e13i −1.51213 1.44975i
\(221\) 9.31401e9 0.00118844
\(222\) 4.99565e11 3.62955e11i 0.0621800 0.0451764i
\(223\) −3.79358e12 1.16754e13i −0.460652 1.41774i −0.864370 0.502856i \(-0.832282\pi\)
0.403718 0.914883i \(-0.367718\pi\)
\(224\) 5.71320e12 1.75834e13i 0.676886 2.08324i
\(225\) 7.83184e12 + 5.69017e12i 0.905441 + 0.657841i
\(226\) 8.61179e12 + 6.25684e12i 0.971622 + 0.705925i
\(227\) −1.93866e12 + 5.96660e12i −0.213482 + 0.657029i 0.785776 + 0.618511i \(0.212264\pi\)
−0.999258 + 0.0385180i \(0.987736\pi\)
\(228\) 1.30421e12 + 4.01394e12i 0.140186 + 0.431449i
\(229\) −7.67639e12 + 5.57722e12i −0.805493 + 0.585225i −0.912521 0.409031i \(-0.865867\pi\)
0.107027 + 0.994256i \(0.465867\pi\)
\(230\) −1.38938e12 −0.142337
\(231\) 9.35651e11 + 5.19669e12i 0.0935940 + 0.519830i
\(232\) −1.14177e13 −1.11531
\(233\) −1.54779e13 + 1.12453e13i −1.47657 + 1.07279i −0.497926 + 0.867219i \(0.665905\pi\)
−0.978642 + 0.205571i \(0.934095\pi\)
\(234\) 1.77913e12 + 5.47559e12i 0.165775 + 0.510204i
\(235\) 5.38737e12 1.65806e13i 0.490347 1.50913i
\(236\) 2.11380e13 + 1.53577e13i 1.87953 + 1.36556i
\(237\) −4.01313e11 2.91571e11i −0.0348632 0.0253296i
\(238\) −2.93401e10 + 9.02996e10i −0.00249051 + 0.00766501i
\(239\) 6.00067e11 + 1.84682e12i 0.0497750 + 0.153192i 0.972855 0.231417i \(-0.0743363\pi\)
−0.923080 + 0.384609i \(0.874336\pi\)
\(240\) 2.07125e12 1.50485e12i 0.167908 0.121992i
\(241\) −1.66560e12 −0.131971 −0.0659853 0.997821i \(-0.521019\pi\)
−0.0659853 + 0.997821i \(0.521019\pi\)
\(242\) −1.10636e13 + 1.66604e13i −0.856864 + 1.29033i
\(243\) 1.08462e13 0.821188
\(244\) 1.74889e13 1.27065e13i 1.29455 0.940547i
\(245\) 1.16973e13 + 3.60005e13i 0.846585 + 2.60552i
\(246\) 2.00583e12 6.17331e12i 0.141955 0.436893i
\(247\) −4.63787e12 3.36961e12i −0.320985 0.233209i
\(248\) −1.79725e12 1.30578e12i −0.121653 0.0883864i
\(249\) 1.57422e12 4.84495e12i 0.104224 0.320769i
\(250\) −2.67326e12 8.22744e12i −0.173129 0.532837i
\(251\) −1.16630e12 + 8.47365e11i −0.0738931 + 0.0536865i −0.624119 0.781330i \(-0.714542\pi\)
0.550225 + 0.835016i \(0.314542\pi\)
\(252\) −3.42277e13 −2.12165
\(253\) 1.79322e11 + 9.95968e11i 0.0108760 + 0.0604063i
\(254\) −1.22095e13 −0.724621
\(255\) −2.02540e10 + 1.47154e10i −0.00117636 + 0.000854676i
\(256\) −1.01852e12 3.13468e12i −0.0578961 0.178186i
\(257\) 6.85856e12 2.11085e13i 0.381593 1.17442i −0.557328 0.830292i \(-0.688173\pi\)
0.938921 0.344131i \(-0.111827\pi\)
\(258\) 3.05409e12 + 2.21892e12i 0.166331 + 0.120847i
\(259\) −4.03404e12 2.93090e12i −0.215076 0.156262i
\(260\) 4.76505e12 1.46653e13i 0.248722 0.765487i
\(261\) −9.83189e12 3.02595e13i −0.502475 1.54646i
\(262\) −4.69993e13 + 3.41470e13i −2.35198 + 1.70882i
\(263\) 1.92709e13 0.944377 0.472188 0.881498i \(-0.343464\pi\)
0.472188 + 0.881498i \(0.343464\pi\)
\(264\) 2.91984e12 + 2.79938e12i 0.140132 + 0.134351i
\(265\) 4.06622e13 1.91134
\(266\) 4.72782e13 3.43496e13i 2.17677 1.58151i
\(267\) −3.23040e12 9.94215e12i −0.145695 0.448403i
\(268\) 4.09340e12 1.25982e13i 0.180860 0.556631i
\(269\) −2.19095e13 1.59182e13i −0.948407 0.689058i 0.00202221 0.999998i \(-0.499356\pi\)
−0.950430 + 0.310940i \(0.899356\pi\)
\(270\) −2.64090e13 1.91873e13i −1.12009 0.813790i
\(271\) −3.80981e12 + 1.17254e13i −0.158333 + 0.487300i −0.998483 0.0550540i \(-0.982467\pi\)
0.840150 + 0.542354i \(0.182467\pi\)
\(272\) −1.03618e10 3.18902e10i −0.000421992 0.00129876i
\(273\) −4.11362e12 + 2.98872e12i −0.164183 + 0.119286i
\(274\) 1.37245e13 0.536869
\(275\) −2.85369e13 + 1.53056e13i −1.09415 + 0.586841i
\(276\) 7.17445e11 0.0269643
\(277\) −3.39770e13 + 2.46857e13i −1.25183 + 0.909509i −0.998327 0.0578253i \(-0.981583\pi\)
−0.253505 + 0.967334i \(0.581583\pi\)
\(278\) −2.64972e12 8.15501e12i −0.0957093 0.294563i
\(279\) 1.91297e12 5.88753e12i 0.0677464 0.208502i
\(280\) 3.62804e13 + 2.63593e13i 1.25980 + 0.915301i
\(281\) 3.58235e13 + 2.60273e13i 1.21979 + 0.886226i 0.996082 0.0884314i \(-0.0281854\pi\)
0.223703 + 0.974657i \(0.428185\pi\)
\(282\) −4.77017e12 + 1.46811e13i −0.159281 + 0.490217i
\(283\) 1.61276e13 + 4.96355e13i 0.528133 + 1.62543i 0.758036 + 0.652213i \(0.226159\pi\)
−0.229903 + 0.973214i \(0.573841\pi\)
\(284\) 5.77068e12 4.19264e12i 0.185343 0.134660i
\(285\) 1.54091e13 0.485435
\(286\) −1.90808e13 2.61150e12i −0.589635 0.0807007i
\(287\) −5.24156e13 −1.58895
\(288\) 3.19296e13 2.31982e13i 0.949587 0.689915i
\(289\) −1.05905e13 3.25942e13i −0.309014 0.951047i
\(290\) −4.51531e13 + 1.38967e14i −1.29270 + 3.97853i
\(291\) 6.82093e12 + 4.95570e12i 0.191616 + 0.139217i
\(292\) 2.68863e13 + 1.95341e13i 0.741183 + 0.538501i
\(293\) 8.05570e12 2.47929e13i 0.217937 0.670742i −0.780995 0.624537i \(-0.785288\pi\)
0.998932 0.0462042i \(-0.0147125\pi\)
\(294\) −1.03572e13 3.18762e13i −0.274999 0.846361i
\(295\) 7.71752e13 5.60711e13i 2.01121 1.46123i
\(296\) −3.81984e12 −0.0977105
\(297\) −1.03457e13 + 2.14075e13i −0.259777 + 0.537534i
\(298\) 9.20419e12 0.226880
\(299\) −7.88392e11 + 5.72800e11i −0.0190788 + 0.0138616i
\(300\) 7.09425e12 + 2.18339e13i 0.168554 + 0.518756i
\(301\) 9.42008e12 2.89920e13i 0.219755 0.676337i
\(302\) −4.48309e13 3.25715e13i −1.02693 0.746105i
\(303\) −7.17412e12 5.21230e12i −0.161374 0.117245i
\(304\) −6.37760e12 + 1.96282e13i −0.140881 + 0.433587i
\(305\) −2.43894e13 7.50628e13i −0.529117 1.62846i
\(306\) −1.63974e11 + 1.19134e11i −0.00349388 + 0.00253845i
\(307\) 2.10622e13 0.440800 0.220400 0.975410i \(-0.429264\pi\)
0.220400 + 0.975410i \(0.429264\pi\)
\(308\) 4.98190e13 1.03086e14i 1.02416 2.11919i
\(309\) 1.44864e13 0.292543
\(310\) −2.30004e13 + 1.67108e13i −0.456295 + 0.331518i
\(311\) −9.02705e12 2.77824e13i −0.175940 0.541486i 0.823736 0.566974i \(-0.191886\pi\)
−0.999675 + 0.0254878i \(0.991886\pi\)
\(312\) −1.20368e12 + 3.70455e12i −0.0230495 + 0.0709390i
\(313\) 1.08369e13 + 7.87346e12i 0.203897 + 0.148140i 0.685048 0.728498i \(-0.259781\pi\)
−0.481151 + 0.876638i \(0.659781\pi\)
\(314\) 4.55894e13 + 3.31226e13i 0.842850 + 0.612367i
\(315\) −3.86165e13 + 1.18849e14i −0.701560 + 2.15918i
\(316\) 3.32379e12 + 1.02296e13i 0.0593409 + 0.182632i
\(317\) −5.45619e13 + 3.96415e13i −0.957333 + 0.695543i −0.952530 0.304445i \(-0.901529\pi\)
−0.00480344 + 0.999988i \(0.501529\pi\)
\(318\) −3.60039e13 −0.620869
\(319\) 1.05445e14 + 1.44318e13i 1.78722 + 0.244609i
\(320\) −1.41577e14 −2.35868
\(321\) −2.23924e13 + 1.62690e13i −0.366710 + 0.266430i
\(322\) −3.06980e12 9.44787e12i −0.0494200 0.152099i
\(323\) 6.23643e10 1.91938e11i 0.000987012 0.00303771i
\(324\) −5.19397e13 3.77364e13i −0.808168 0.587168i
\(325\) −2.52277e13 1.83290e13i −0.385939 0.280401i
\(326\) 5.74400e13 1.76782e14i 0.864008 2.65914i
\(327\) 5.06523e12 + 1.55892e13i 0.0749181 + 0.230574i
\(328\) −3.24848e13 + 2.36016e13i −0.472470 + 0.343270i
\(329\) 1.24652e14 1.78288
\(330\) 4.56187e13 2.44673e13i 0.641676 0.344159i
\(331\) 8.16378e12 0.112937 0.0564687 0.998404i \(-0.482016\pi\)
0.0564687 + 0.998404i \(0.482016\pi\)
\(332\) −8.93646e13 + 6.49272e13i −1.21592 + 0.883419i
\(333\) −3.28930e12 1.01234e13i −0.0440210 0.135483i
\(334\) 1.23577e13 3.80330e13i 0.162679 0.500674i
\(335\) −3.91267e13 2.84272e13i −0.506671 0.368118i
\(336\) 1.48094e13 + 1.07597e13i 0.188657 + 0.137067i
\(337\) −1.03598e13 + 3.18843e13i −0.129834 + 0.399587i −0.994751 0.102328i \(-0.967371\pi\)
0.864917 + 0.501915i \(0.167371\pi\)
\(338\) 3.30890e13 + 1.01838e14i 0.407983 + 1.25564i
\(339\) −1.62358e13 + 1.17960e13i −0.196959 + 0.143099i
\(340\) 5.42848e11 0.00647954
\(341\) 1.49475e13 + 1.43309e13i 0.175558 + 0.168315i
\(342\) 1.24750e14 1.44178
\(343\) −9.92987e13 + 7.21447e13i −1.12934 + 0.820516i
\(344\) −7.21635e12 2.22096e13i −0.0807693 0.248582i
\(345\) 8.09439e11 2.49120e12i 0.00891619 0.0274412i
\(346\) 3.88952e13 + 2.82590e13i 0.421675 + 0.306365i
\(347\) −6.13784e13 4.45940e13i −0.654943 0.475844i 0.210009 0.977700i \(-0.432651\pi\)
−0.864951 + 0.501856i \(0.832651\pi\)
\(348\) 2.33160e13 7.17594e13i 0.244889 0.753690i
\(349\) −2.35813e13 7.25757e13i −0.243796 0.750328i −0.995832 0.0912056i \(-0.970928\pi\)
0.752036 0.659122i \(-0.229072\pi\)
\(350\) 2.57170e14 1.86845e14i 2.61726 1.90155i
\(351\) −2.28959e13 −0.229387
\(352\) 2.33936e13 + 1.29930e14i 0.230734 + 1.28152i
\(353\) 9.00381e10 0.000874310 0.000437155 1.00000i \(-0.499861\pi\)
0.000437155 1.00000i \(0.499861\pi\)
\(354\) −6.83338e13 + 4.96474e13i −0.653307 + 0.474656i
\(355\) −8.04757e12 2.47679e13i −0.0757546 0.233149i
\(356\) −7.00456e13 + 2.15578e14i −0.649241 + 1.99816i
\(357\) −1.44816e11 1.05215e11i −0.00132173 0.000960292i
\(358\) −3.90072e13 2.83404e13i −0.350581 0.254712i
\(359\) 4.89251e12 1.50576e13i 0.0433024 0.133271i −0.927068 0.374893i \(-0.877679\pi\)
0.970370 + 0.241622i \(0.0776794\pi\)
\(360\) 2.95825e13 + 9.10457e13i 0.257853 + 0.793589i
\(361\) −6.25032e12 + 4.54113e12i −0.0536553 + 0.0389829i
\(362\) −1.20950e14 −1.02261
\(363\) −2.34270e13 2.95435e13i −0.195088 0.246023i
\(364\) 1.10253e14 0.904343
\(365\) 9.81622e13 7.13190e13i 0.793110 0.576228i
\(366\) 2.15953e13 + 6.64634e13i 0.171875 + 0.528977i
\(367\) −2.93522e13 + 9.03367e13i −0.230132 + 0.708273i 0.767598 + 0.640932i \(0.221452\pi\)
−0.997730 + 0.0673417i \(0.978548\pi\)
\(368\) 2.83829e12 + 2.06214e12i 0.0219227 + 0.0159278i
\(369\) −9.05225e13 6.57684e13i −0.688829 0.500464i
\(370\) −1.51062e13 + 4.64920e13i −0.113252 + 0.348553i
\(371\) 8.98421e13 + 2.76505e14i 0.663626 + 2.04243i
\(372\) 1.18769e13 8.62905e12i 0.0864402 0.0628025i
\(373\) −2.60450e13 −0.186778 −0.0933890 0.995630i \(-0.529770\pi\)
−0.0933890 + 0.995630i \(0.529770\pi\)
\(374\) −1.20138e11 6.67256e11i −0.000848957 0.00471519i
\(375\) 1.63094e13 0.113571
\(376\) 7.72539e13 5.61283e13i 0.530136 0.385167i
\(377\) 3.16702e13 + 9.74709e13i 0.214177 + 0.659170i
\(378\) 7.21245e13 2.21976e14i 0.480704 1.47946i
\(379\) −1.61821e14 1.17570e14i −1.06296 0.772289i −0.0883301 0.996091i \(-0.528153\pi\)
−0.974635 + 0.223802i \(0.928153\pi\)
\(380\) −2.70309e14 1.96391e14i −1.75005 1.27148i
\(381\) 7.11310e12 2.18919e13i 0.0453912 0.139700i
\(382\) 1.99944e13 + 6.15364e13i 0.125765 + 0.387065i
\(383\) −1.14386e14 + 8.31060e13i −0.709215 + 0.515275i −0.882920 0.469523i \(-0.844426\pi\)
0.173705 + 0.984798i \(0.444426\pi\)
\(384\) 5.84645e13 0.357331
\(385\) −3.01740e14 2.89292e14i −1.81802 1.74302i
\(386\) 9.93790e13 0.590289
\(387\) 5.26464e13 3.82498e13i 0.308289 0.223985i
\(388\) −5.64928e13 1.73867e14i −0.326151 1.00379i
\(389\) 5.57050e13 1.71442e14i 0.317082 0.975877i −0.657807 0.753186i \(-0.728516\pi\)
0.974889 0.222691i \(-0.0714841\pi\)
\(390\) 4.03286e13 + 2.93005e13i 0.226338 + 0.164444i
\(391\) −2.77546e10 2.01649e10i −0.000153590 0.000111590i
\(392\) −6.40698e13 + 1.97187e14i −0.349607 + 1.07598i
\(393\) −3.38451e13 1.04165e14i −0.182111 0.560482i
\(394\) 2.37961e14 1.72889e14i 1.26263 0.917354i
\(395\) 3.92703e13 0.205485
\(396\) 2.15385e14 1.15521e14i 1.11146 0.596123i
\(397\) 2.69626e14 1.37219 0.686094 0.727512i \(-0.259324\pi\)
0.686094 + 0.727512i \(0.259324\pi\)
\(398\) 7.39094e13 5.36983e13i 0.370973 0.269528i
\(399\) 3.40460e13 + 1.04783e14i 0.168545 + 0.518727i
\(400\) −3.46910e13 + 1.06768e14i −0.169390 + 0.521328i
\(401\) −1.51699e13 1.10215e13i −0.0730613 0.0530822i 0.550655 0.834733i \(-0.314378\pi\)
−0.623716 + 0.781651i \(0.714378\pi\)
\(402\) 3.46442e13 + 2.51705e13i 0.164584 + 0.119577i
\(403\) −6.16202e12 + 1.89647e13i −0.0288765 + 0.0888728i
\(404\) 5.94180e13 + 1.82870e14i 0.274676 + 0.845365i
\(405\) −1.89632e14 + 1.37776e14i −0.864788 + 0.628305i
\(406\) −1.04475e15 −4.70022
\(407\) 3.52771e13 + 4.82822e12i 0.156576 + 0.0214298i
\(408\) −1.37127e11 −0.000600471
\(409\) 1.71659e14 1.24718e14i 0.741632 0.538827i −0.151590 0.988443i \(-0.548439\pi\)
0.893222 + 0.449616i \(0.148439\pi\)
\(410\) 1.58793e14 + 4.88715e14i 0.676894 + 2.08327i
\(411\) −7.99574e12 + 2.46084e13i −0.0336302 + 0.103503i
\(412\) −2.54122e14 1.84631e14i −1.05465 0.766248i
\(413\) 5.51803e14 + 4.00908e14i 2.25974 + 1.64180i
\(414\) 6.55313e12 2.01685e13i 0.0264818 0.0815025i
\(415\) 1.24624e14 + 3.83554e14i 0.496980 + 1.52955i
\(416\) −1.02851e14 + 7.47254e13i −0.404756 + 0.294073i
\(417\) 1.61658e13 0.0627841
\(418\) −1.81577e14 + 3.75720e14i −0.695970 + 1.44011i
\(419\) 1.80147e14 0.681474 0.340737 0.940159i \(-0.389324\pi\)
0.340737 + 0.940159i \(0.389324\pi\)
\(420\) −2.39754e14 + 1.74191e14i −0.895148 + 0.650363i
\(421\) −1.27114e14 3.91217e14i −0.468428 1.44167i −0.854620 0.519254i \(-0.826210\pi\)
0.386192 0.922419i \(-0.373790\pi\)
\(422\) 1.73363e14 5.33557e14i 0.630577 1.94072i
\(423\) 2.15276e14 + 1.56407e14i 0.772902 + 0.561546i
\(424\) 1.80185e14 + 1.30912e14i 0.638566 + 0.463945i
\(425\) 3.39231e11 1.04405e12i 0.00118674 0.00365242i
\(426\) 7.12562e12 + 2.19304e13i 0.0246076 + 0.0757345i
\(427\) 4.56544e14 3.31698e14i 1.55643 1.13081i
\(428\) 6.00160e14 2.01988
\(429\) 1.57988e13 3.26909e13i 0.0524938 0.108621i
\(430\) −2.98856e14 −0.980359
\(431\) −2.25313e14 + 1.63699e14i −0.729727 + 0.530178i −0.889477 0.456980i \(-0.848931\pi\)
0.159750 + 0.987157i \(0.448931\pi\)
\(432\) 2.54715e13 + 7.83931e13i 0.0814505 + 0.250679i
\(433\) −1.09714e12 + 3.37665e12i −0.00346400 + 0.0106611i −0.952774 0.303682i \(-0.901784\pi\)
0.949310 + 0.314343i \(0.101784\pi\)
\(434\) −1.64453e14 1.19482e14i −0.512681 0.372485i
\(435\) −2.22866e14 1.61921e14i −0.686044 0.498440i
\(436\) 1.09831e14 3.38024e14i 0.333848 1.02748i
\(437\) 6.52506e12 + 2.00821e13i 0.0195856 + 0.0602782i
\(438\) −8.69165e13 + 6.31485e13i −0.257629 + 0.187178i
\(439\) −1.21317e13 −0.0355114 −0.0177557 0.999842i \(-0.505652\pi\)
−0.0177557 + 0.999842i \(0.505652\pi\)
\(440\) −3.17267e14 4.34229e13i −0.917139 0.125525i
\(441\) −5.77759e14 −1.64943
\(442\) 5.28189e11 3.83752e11i 0.00148925 0.00108200i
\(443\) −1.12977e14 3.47707e14i −0.314608 0.968263i −0.975916 0.218148i \(-0.929998\pi\)
0.661308 0.750114i \(-0.270002\pi\)
\(444\) 7.80048e12 2.40074e13i 0.0214543 0.0660297i
\(445\) 6.69529e14 + 4.86441e14i 1.81882 + 1.32145i
\(446\) −6.96178e14 5.05803e14i −1.86801 1.35719i
\(447\) −5.36226e12 + 1.65033e13i −0.0142120 + 0.0437402i
\(448\) −3.12811e14 9.62734e14i −0.818942 2.52045i
\(449\) −5.41345e14 + 3.93310e14i −1.39997 + 1.01714i −0.405286 + 0.914190i \(0.632828\pi\)
−0.994687 + 0.102949i \(0.967172\pi\)
\(450\) 6.78581e14 1.73354
\(451\) 3.29837e14 1.76906e14i 0.832393 0.446449i
\(452\) 4.35152e14 1.08487
\(453\) 8.45196e13 6.14071e13i 0.208170 0.151244i
\(454\) 1.35893e14 + 4.18237e14i 0.330667 + 1.01769i
\(455\) 1.24390e14 3.82834e14i 0.299036 0.920339i
\(456\) 6.82817e13 + 4.96095e13i 0.162180 + 0.117831i
\(457\) −2.33578e14 1.69704e14i −0.548141 0.398248i 0.278959 0.960303i \(-0.410011\pi\)
−0.827100 + 0.562055i \(0.810011\pi\)
\(458\) −2.05531e14 + 6.32559e14i −0.476559 + 1.46670i
\(459\) −2.49077e11 7.66580e11i −0.000570642 0.00175625i
\(460\) −4.59498e13 + 3.33845e13i −0.104020 + 0.0755748i
\(461\) 1.45782e14 0.326099 0.163050 0.986618i \(-0.447867\pi\)
0.163050 + 0.986618i \(0.447867\pi\)
\(462\) 2.67172e14 + 2.56150e14i 0.590555 + 0.566191i
\(463\) −4.61510e14 −1.00806 −0.504029 0.863687i \(-0.668150\pi\)
−0.504029 + 0.863687i \(0.668150\pi\)
\(464\) 2.98497e14 2.16871e14i 0.644305 0.468115i
\(465\) −1.65630e13 5.09758e13i −0.0353304 0.108736i
\(466\) −4.14411e14 + 1.27543e15i −0.873592 + 2.68864i
\(467\) −2.92559e13 2.12557e13i −0.0609496 0.0442825i 0.556893 0.830584i \(-0.311993\pi\)
−0.617843 + 0.786302i \(0.711993\pi\)
\(468\) 1.90409e14 + 1.38340e14i 0.392044 + 0.284837i
\(469\) 1.06857e14 3.28872e14i 0.217447 0.669232i
\(470\) −3.77635e14 1.16224e15i −0.759510 2.33753i
\(471\) −8.59496e13 + 6.24460e13i −0.170855 + 0.124134i
\(472\) 5.22503e14 1.02662
\(473\) 3.85720e13 + 2.14232e14i 0.0749093 + 0.416053i
\(474\) −3.47713e13 −0.0667484
\(475\) −5.46632e14 + 3.97151e14i −1.03724 + 0.753601i
\(476\) 1.19941e12 + 3.69140e12i 0.00224972 + 0.00692393i
\(477\) −1.91787e14 + 5.90259e14i −0.355604 + 1.09444i
\(478\) 1.10121e14 + 8.00076e13i 0.201844 + 0.146649i
\(479\) −1.82724e14 1.32757e14i −0.331093 0.240553i 0.409801 0.912175i \(-0.365598\pi\)
−0.740894 + 0.671622i \(0.765598\pi\)
\(480\) 1.05596e14 3.24992e14i 0.189157 0.582165i
\(481\) 1.05954e13 + 3.26093e13i 0.0187637 + 0.0577489i
\(482\) −9.44548e13 + 6.86254e13i −0.165373 + 0.120151i
\(483\) 1.87287e13 0.0324189
\(484\) 3.44244e13 + 8.16835e14i 0.0589137 + 1.39793i
\(485\) −6.67457e14 −1.12939
\(486\) 6.15078e14 4.46880e14i 1.02904 0.747638i
\(487\) −2.01644e14 6.20595e14i −0.333561 1.02660i −0.967427 0.253152i \(-0.918533\pi\)
0.633865 0.773443i \(-0.281467\pi\)
\(488\) 1.33589e14 4.11144e14i 0.218505 0.672489i
\(489\) 2.83511e14 + 2.05983e14i 0.458534 + 0.333144i
\(490\) 2.14662e15 + 1.55961e15i 3.43302 + 2.49424i
\(491\) 1.85390e14 5.70570e14i 0.293182 0.902321i −0.690644 0.723195i \(-0.742673\pi\)
0.983826 0.179126i \(-0.0573271\pi\)
\(492\) −8.19972e13 2.52361e14i −0.128230 0.394653i
\(493\) −2.91890e12 + 2.12071e12i −0.00451400 + 0.00327961i
\(494\) −4.01843e14 −0.614551
\(495\) −1.58121e14 8.78220e14i −0.239145 1.32823i
\(496\) 7.17885e13 0.107376
\(497\) 1.50642e14 1.09448e14i 0.222836 0.161900i
\(498\) −1.10347e14 3.39613e14i −0.161436 0.496848i
\(499\) −1.16725e14 + 3.59243e14i −0.168893 + 0.519799i −0.999302 0.0373549i \(-0.988107\pi\)
0.830409 + 0.557154i \(0.188107\pi\)
\(500\) −2.86102e14 2.07865e14i −0.409436 0.297473i
\(501\) 6.09947e13 + 4.43152e13i 0.0863345 + 0.0627257i
\(502\) −3.12270e13 + 9.61067e13i −0.0437179 + 0.134550i
\(503\) 1.03240e14 + 3.17741e14i 0.142964 + 0.439996i 0.996743 0.0806376i \(-0.0256956\pi\)
−0.853780 + 0.520634i \(0.825696\pi\)
\(504\) −5.53754e14 + 4.02326e14i −0.758488 + 0.551074i
\(505\) 7.02018e14 0.951143
\(506\) 5.12046e13 + 4.90921e13i 0.0686248 + 0.0657937i
\(507\) −2.01875e14 −0.267632
\(508\) −4.03793e14 + 2.93373e14i −0.529552 + 0.384742i
\(509\) −1.57308e14 4.84143e14i −0.204081 0.628096i −0.999750 0.0223646i \(-0.992881\pi\)
0.795669 0.605732i \(-0.207119\pi\)
\(510\) −5.42290e11 + 1.66900e12i −0.000695978 + 0.00214200i
\(511\) 7.01860e14 + 5.09931e14i 0.891119 + 0.647436i
\(512\) 5.46087e14 + 3.96756e14i 0.685926 + 0.498354i
\(513\) −1.53305e14 + 4.71825e14i −0.190507 + 0.586321i
\(514\) −4.80760e14 1.47963e15i −0.591060 1.81909i
\(515\) −9.27803e14 + 6.74089e14i −1.12854 + 0.819931i
\(516\) 1.54322e14 0.185719
\(517\) −7.84403e14 + 4.20710e14i −0.933988 + 0.500939i
\(518\) −3.49525e14 −0.411779
\(519\) −7.33291e13 + 5.32767e13i −0.0854784 + 0.0621037i
\(520\) −9.52904e13 2.93274e14i −0.109908 0.338263i
\(521\) −7.43365e13 + 2.28784e14i −0.0848388 + 0.261107i −0.984473 0.175538i \(-0.943833\pi\)
0.899634 + 0.436645i \(0.143833\pi\)
\(522\) −1.80430e15 1.31090e15i −2.03761 1.48041i
\(523\) 8.06537e14 + 5.85984e14i 0.901291 + 0.654826i 0.938797 0.344470i \(-0.111941\pi\)
−0.0375062 + 0.999296i \(0.511941\pi\)
\(524\) −7.33873e14 + 2.25863e15i −0.811519 + 2.49760i
\(525\) 1.85193e14 + 5.69967e14i 0.202651 + 0.623697i
\(526\) 1.09284e15 7.93992e14i 1.18340 0.859794i
\(527\) −7.01995e11 −0.000752273
\(528\) −1.29506e14 1.77249e13i −0.137342 0.0187974i
\(529\) −9.49220e14 −0.996233
\(530\) 2.30592e15 1.67535e15i 2.39512 1.74016i
\(531\) 4.49932e14 + 1.38475e15i 0.462517 + 1.42348i
\(532\) 7.38228e14 2.27203e15i 0.751064 2.31154i
\(533\) 2.91588e14 + 2.11851e14i 0.293610 + 0.213320i
\(534\) −5.92825e14 4.30713e14i −0.590813 0.429251i
\(535\) 6.77115e14 2.08394e15i 0.667908 2.05561i
\(536\) −8.18590e13 2.51936e14i −0.0799209 0.245971i
\(537\) 7.35402e13 5.34301e13i 0.0710667 0.0516330i
\(538\) −1.89832e15 −1.81580
\(539\) 8.40939e14 1.74008e15i 0.796208 1.64752i
\(540\) −1.33444e15 −1.25064
\(541\) 2.95336e14 2.14574e14i 0.273988 0.199064i −0.442303 0.896866i \(-0.645838\pi\)
0.716291 + 0.697802i \(0.245838\pi\)
\(542\) 2.67054e14 + 8.21908e14i 0.245247 + 0.754791i
\(543\) 7.04642e13 2.16867e14i 0.0640574 0.197148i
\(544\) −3.62077e12 2.63064e12i −0.00325842 0.00236738i
\(545\) −1.04981e15 7.62734e14i −0.935258 0.679505i
\(546\) −1.10140e14 + 3.38975e14i −0.0971370 + 0.298957i
\(547\) −1.38744e14 4.27009e14i −0.121139 0.372826i 0.872039 0.489436i \(-0.162797\pi\)
−0.993178 + 0.116610i \(0.962797\pi\)
\(548\) 4.53899e14 3.29777e14i 0.392343 0.285054i
\(549\) 1.20466e15 1.03090
\(550\) −9.87688e14 + 2.04373e15i −0.836807 + 1.73153i
\(551\) 2.22068e15 1.86274
\(552\) 1.16072e13 8.43314e12i 0.00963970 0.00700365i
\(553\) 8.67665e13 + 2.67040e14i 0.0713451 + 0.219578i
\(554\) −9.09714e14 + 2.79981e15i −0.740630 + 2.27942i
\(555\) −7.45607e13 5.41715e13i −0.0601033 0.0436676i
\(556\) −2.83583e14 2.06035e14i −0.226344 0.164449i
\(557\) −5.62104e14 + 1.72998e15i −0.444236 + 1.36722i 0.439084 + 0.898446i \(0.355303\pi\)
−0.883320 + 0.468771i \(0.844697\pi\)
\(558\) −1.34093e14 4.12694e14i −0.104934 0.322954i
\(559\) −1.69583e14 + 1.23209e14i −0.131407 + 0.0954725i
\(560\) −1.44917e15 −1.11195
\(561\) 1.26640e12 + 1.73326e11i 0.000962220 + 0.000131695i
\(562\) 3.10389e15 2.33537
\(563\) −1.07389e15 + 7.80229e14i −0.800138 + 0.581334i −0.910955 0.412507i \(-0.864653\pi\)
0.110817 + 0.993841i \(0.464653\pi\)
\(564\) 1.95002e14 + 6.00154e14i 0.143881 + 0.442821i
\(565\) 4.90949e14 1.51098e15i 0.358732 1.10406i
\(566\) 2.95964e15 + 2.15031e15i 2.14165 + 1.55600i
\(567\) −1.35587e15 9.85098e14i −0.971654 0.705948i
\(568\) 4.40792e13 1.35662e14i 0.0312837 0.0962813i
\(569\) 7.65758e13 + 2.35676e14i 0.0538237 + 0.165652i 0.974355 0.225017i \(-0.0722437\pi\)
−0.920531 + 0.390669i \(0.872244\pi\)
\(570\) 8.73837e14 6.34880e14i 0.608302 0.441957i
\(571\) 6.01690e14 0.414834 0.207417 0.978253i \(-0.433494\pi\)
0.207417 + 0.978253i \(0.433494\pi\)
\(572\) −6.93793e14 + 3.72112e14i −0.473753 + 0.254094i
\(573\) −1.21985e14 −0.0825003
\(574\) −2.97244e15 + 2.15960e15i −1.99112 + 1.44663i
\(575\) 3.54931e13 + 1.09237e14i 0.0235489 + 0.0724761i
\(576\) 6.67761e14 2.05516e15i 0.438831 1.35058i
\(577\) 1.99302e15 + 1.44801e15i 1.29731 + 0.942553i 0.999926 0.0122041i \(-0.00388477\pi\)
0.297387 + 0.954757i \(0.403885\pi\)
\(578\) −1.94351e15 1.41204e15i −1.25309 0.910427i
\(579\) −5.78971e13 + 1.78189e14i −0.0369764 + 0.113802i
\(580\) 1.84583e15 + 5.68089e15i 1.16772 + 3.59387i
\(581\) −2.33284e15 + 1.69491e15i −1.46189 + 1.06213i
\(582\) 5.90992e14 0.366864
\(583\) −1.49858e15 1.43675e15i −0.921514 0.883496i
\(584\) 6.64593e14 0.404842
\(585\) 6.95185e14 5.05081e14i 0.419511 0.304792i
\(586\) −5.64675e14 1.73789e15i −0.337568 1.03893i
\(587\) 4.57764e14 1.40885e15i 0.271101 0.834364i −0.719123 0.694883i \(-0.755456\pi\)
0.990225 0.139482i \(-0.0445436\pi\)
\(588\) −1.10847e15 8.05347e14i −0.650349 0.472506i
\(589\) 3.49555e14 + 2.53967e14i 0.203180 + 0.147619i
\(590\) 2.06632e15 6.35948e15i 1.18990 3.66215i
\(591\) 1.71360e14 + 5.27392e14i 0.0977640 + 0.300887i
\(592\) 9.98635e13 7.25551e13i 0.0564466 0.0410108i
\(593\) −1.51878e15 −0.850541 −0.425271 0.905066i \(-0.639821\pi\)
−0.425271 + 0.905066i \(0.639821\pi\)
\(594\) 2.95325e14 + 1.64026e15i 0.163861 + 0.910098i
\(595\) 1.41709e13 0.00779030
\(596\) 3.04402e14 2.21161e14i 0.165803 0.120463i
\(597\) 5.32236e13 + 1.63805e14i 0.0287240 + 0.0884035i
\(598\) −2.11087e13 + 6.49660e13i −0.0112877 + 0.0347400i
\(599\) −1.14189e15 8.29628e14i −0.605027 0.439578i 0.242633 0.970118i \(-0.421989\pi\)
−0.847660 + 0.530540i \(0.821989\pi\)
\(600\) 3.71419e14 + 2.69851e14i 0.194999 + 0.141675i
\(601\) 2.96218e14 9.11664e14i 0.154099 0.474269i −0.843969 0.536392i \(-0.819787\pi\)
0.998069 + 0.0621224i \(0.0197869\pi\)
\(602\) −6.60313e14 2.03224e15i −0.340384 1.04759i
\(603\) 5.97197e14 4.33889e14i 0.305051 0.221632i
\(604\) −2.26529e15 −1.14662
\(605\) 2.87515e15 + 8.02041e14i 1.44213 + 0.402292i
\(606\) −6.21593e14 −0.308963
\(607\) 7.40019e14 5.37655e14i 0.364506 0.264829i −0.390423 0.920636i \(-0.627671\pi\)
0.754929 + 0.655806i \(0.227671\pi\)
\(608\) 8.51234e14 + 2.61983e15i 0.415508 + 1.27880i
\(609\) 6.08659e14 1.87326e15i 0.294428 0.906156i
\(610\) −4.47581e15 3.25187e15i −2.14564 1.55890i
\(611\) −6.93442e14 5.03815e14i −0.329445 0.239356i
\(612\) −2.56039e12 + 7.88006e12i −0.00120551 + 0.00371019i
\(613\) 1.04494e15 + 3.21598e15i 0.487592 + 1.50065i 0.828191 + 0.560446i \(0.189370\pi\)
−0.340599 + 0.940209i \(0.610630\pi\)
\(614\) 1.19442e15 8.67795e14i 0.552370 0.401320i
\(615\) −9.68790e14 −0.444034
\(616\) −4.05715e14 2.25338e15i −0.184301 1.02362i
\(617\) −4.66281e14 −0.209932 −0.104966 0.994476i \(-0.533473\pi\)
−0.104966 + 0.994476i \(0.533473\pi\)
\(618\) 8.21512e14 5.96863e14i 0.366587 0.266341i
\(619\) −1.26425e15 3.89095e15i −0.559156 1.72091i −0.684707 0.728818i \(-0.740070\pi\)
0.125551 0.992087i \(-0.459930\pi\)
\(620\) −3.59141e14 + 1.10532e15i −0.157438 + 0.484545i
\(621\) 6.82271e13 + 4.95699e13i 0.0296451 + 0.0215384i
\(622\) −1.65660e15 1.20359e15i −0.713459 0.518359i
\(623\) −1.82852e15 + 5.62761e15i −0.780577 + 2.40237i
\(624\) −3.88969e13 1.19712e14i −0.0164589 0.0506552i
\(625\) 1.35028e15 9.81033e14i 0.566347 0.411475i
\(626\) 9.38949e14 0.390376
\(627\) −5.67891e14 5.44462e14i −0.234042 0.224386i
\(628\) 2.30362e15 0.941093
\(629\) −9.76531e11 + 7.09491e11i −0.000395464 + 0.000287322i
\(630\) 2.70687e15 + 8.33090e15i 1.08666 + 3.34441i
\(631\) −7.84348e14 + 2.41397e15i −0.312138 + 0.960663i 0.664778 + 0.747041i \(0.268526\pi\)
−0.976916 + 0.213622i \(0.931474\pi\)
\(632\) 1.74016e14 + 1.26430e14i 0.0686509 + 0.0498778i
\(633\) 8.55681e14 + 6.21689e14i 0.334651 + 0.243138i
\(634\) −1.46086e15 + 4.49607e15i −0.566394 + 1.74318i
\(635\) 5.63114e14 + 1.73309e15i 0.216442 + 0.666139i
\(636\) −1.19072e15 + 8.65112e14i −0.453730 + 0.329654i
\(637\) 1.86106e15 0.703062
\(638\) 6.57432e15 3.52609e15i 2.46228 1.32063i
\(639\) 3.97491e14 0.147595
\(640\) −3.74444e15 + 2.72050e15i −1.37847 + 1.00152i
\(641\) −1.52416e15 4.69088e15i −0.556303 1.71212i −0.692478 0.721439i \(-0.743481\pi\)
0.136176 0.990685i \(-0.456519\pi\)
\(642\) −5.99543e14 + 1.84520e15i −0.216959 + 0.667731i
\(643\) −1.64169e14 1.19276e14i −0.0589021 0.0427949i 0.557945 0.829878i \(-0.311590\pi\)
−0.616847 + 0.787083i \(0.711590\pi\)
\(644\) −3.28541e14 2.38699e14i −0.116874 0.0849139i
\(645\) 1.74110e14 5.35856e14i 0.0614109 0.189003i
\(646\) −4.37151e12 1.34541e13i −0.00152881 0.00470519i
\(647\) 7.35292e14 5.34221e14i 0.254969 0.185245i −0.452957 0.891532i \(-0.649631\pi\)
0.707926 + 0.706287i \(0.249631\pi\)
\(648\) −1.28388e15 −0.441429
\(649\) −4.82544e15 6.60436e14i −1.64509 0.225157i
\(650\) −2.18583e15 −0.738911
\(651\) 3.10043e14 2.25259e14i 0.103926 0.0755069i
\(652\) −2.34811e15 7.22675e15i −0.780472 2.40205i
\(653\) −5.11985e14 + 1.57573e15i −0.168746 + 0.519348i −0.999293 0.0376013i \(-0.988028\pi\)
0.830546 + 0.556949i \(0.188028\pi\)
\(654\) 9.29544e14 + 6.75353e14i 0.303803 + 0.220726i
\(655\) 7.01470e15 + 5.09648e15i 2.27343 + 1.65175i
\(656\) 4.00968e14 1.23405e15i 0.128866 0.396609i
\(657\) 5.72287e14 + 1.76132e15i 0.182391 + 0.561343i
\(658\) 7.06892e15 5.13587e15i 2.23414 1.62320i
\(659\) 5.29486e15 1.65953 0.829764 0.558114i \(-0.188475\pi\)
0.829764 + 0.558114i \(0.188475\pi\)
\(660\) 9.20799e14 1.90533e15i 0.286202 0.592212i
\(661\) 9.37068e13 0.0288844 0.0144422 0.999896i \(-0.495403\pi\)
0.0144422 + 0.999896i \(0.495403\pi\)
\(662\) 4.62961e14 3.36361e14i 0.141523 0.102822i
\(663\) 3.80360e11 + 1.17063e12i 0.000115311 + 0.000354890i
\(664\) −6.82609e14 + 2.10085e15i −0.205233 + 0.631643i
\(665\) −7.05633e15 5.12672e15i −2.10407 1.52870i
\(666\) −6.03635e14 4.38566e14i −0.178511 0.129696i
\(667\) 1.16652e14 3.59018e14i 0.0342137 0.105299i
\(668\) −5.05174e14 1.55477e15i −0.146950 0.452267i
\(669\) 1.31250e15 9.53589e14i 0.378666 0.275117i
\(670\) −3.39008e15 −0.970061
\(671\) −1.75340e15 + 3.62815e15i −0.497631 + 1.02970i
\(672\) 2.44328e15 0.687767
\(673\) −5.35474e15 + 3.89044e15i −1.49505 + 1.08622i −0.522747 + 0.852488i \(0.675093\pi\)
−0.972302 + 0.233729i \(0.924907\pi\)
\(674\) 7.26186e14 + 2.23497e15i 0.201103 + 0.618931i
\(675\) −8.33905e14 + 2.56650e15i −0.229058 + 0.704969i
\(676\) 3.54131e15 + 2.57291e15i 0.964845 + 0.701001i
\(677\) −2.07594e15 1.50826e15i −0.561019 0.407604i 0.270812 0.962632i \(-0.412708\pi\)
−0.831832 + 0.555028i \(0.812708\pi\)
\(678\) −4.34704e14 + 1.33788e15i −0.116528 + 0.358637i
\(679\) −1.47473e15 4.53875e15i −0.392128 1.20685i
\(680\) 8.78250e12 6.38086e12i 0.00231643 0.00168298i
\(681\) −8.29079e14 −0.216914
\(682\) 1.43812e15 + 1.96828e14i 0.373233 + 0.0510827i
\(683\) −7.92015e14 −0.203901 −0.101951 0.994789i \(-0.532508\pi\)
−0.101951 + 0.994789i \(0.532508\pi\)
\(684\) 4.12577e15 2.99754e15i 1.05365 0.765521i
\(685\) −6.32990e14 1.94814e15i −0.160361 0.493540i
\(686\) −2.65866e15 + 8.18253e15i −0.668161 + 2.05639i
\(687\) −1.01445e15 7.37044e14i −0.252913 0.183752i
\(688\) 6.10515e14 + 4.43565e14i 0.150994 + 0.109704i
\(689\) 6.17777e14 1.90132e15i 0.151575 0.466499i
\(690\) −5.67387e13 1.74624e14i −0.0138105 0.0425044i
\(691\) −4.34978e15 + 3.16030e15i −1.05036 + 0.763130i −0.972281 0.233817i \(-0.924878\pi\)
−0.0780782 + 0.996947i \(0.524878\pi\)
\(692\) 1.96537e15 0.470826
\(693\) 5.62258e15 3.01564e15i 1.33630 0.716714i
\(694\) −5.31806e15 −1.25394
\(695\) −1.03537e15 + 7.52237e14i −0.242202 + 0.175970i
\(696\) −4.66269e14 1.43503e15i −0.108215 0.333050i
\(697\) −3.92092e12 + 1.20674e13i −0.000902834 + 0.00277864i
\(698\) −4.32751e15 3.14412e15i −0.988628 0.718280i
\(699\) −2.04544e15 1.48610e15i −0.463620 0.336840i
\(700\) 4.01560e15 1.23587e16i 0.903048 2.77930i
\(701\) −1.57100e15 4.83503e15i −0.350531 1.07882i −0.958556 0.284905i \(-0.908038\pi\)
0.608025 0.793918i \(-0.291962\pi\)
\(702\) −1.29841e15 + 9.43347e14i −0.287446 + 0.208842i
\(703\) 7.42938e14 0.163192
\(704\) 5.21773e15 + 5.00247e15i 1.13719 + 1.09027i
\(705\) 2.30393e15 0.498229
\(706\) 5.10598e12 3.70971e12i 0.00109560 0.000796003i
\(707\) 1.55109e15 + 4.77376e15i 0.330240 + 1.01638i
\(708\) −1.06700e15 + 3.28389e15i −0.225415 + 0.693755i
\(709\) 3.77486e15 + 2.74260e15i 0.791310 + 0.574921i 0.908352 0.418206i \(-0.137341\pi\)
−0.117042 + 0.993127i \(0.537341\pi\)
\(710\) −1.47685e15 1.07299e15i −0.307195 0.223190i
\(711\) −1.85221e14 + 5.70052e14i −0.0382303 + 0.117661i
\(712\) 1.40076e15 + 4.31109e15i 0.286895 + 0.882972i
\(713\) 5.94209e13 4.31718e13i 0.0120767 0.00877421i
\(714\) −1.25474e13 −0.00253055
\(715\) 5.09336e14 + 2.82890e15i 0.101934 + 0.566153i
\(716\) −1.97102e15 −0.391444
\(717\) −2.07611e14 + 1.50838e14i −0.0409162 + 0.0297273i
\(718\) −3.42947e14 1.05548e15i −0.0670722 0.206427i
\(719\) 2.43568e15 7.49626e15i 0.472729 1.45491i −0.376268 0.926511i \(-0.622793\pi\)
0.848996 0.528399i \(-0.177207\pi\)
\(720\) −2.50273e15 1.81834e15i −0.482043 0.350225i
\(721\) −6.63379e15 4.81973e15i −1.26800 0.921253i
\(722\) −1.67349e14 + 5.15047e14i −0.0317445 + 0.0976994i
\(723\) −6.80188e13 2.09340e14i −0.0128047 0.0394087i
\(724\) −4.00008e15 + 2.90623e15i −0.747319 + 0.542959i
\(725\) 1.20794e16 2.23968
\(726\) −2.54576e15 7.10157e14i −0.468454 0.130678i
\(727\) −1.33561e15 −0.243916 −0.121958 0.992535i \(-0.538917\pi\)
−0.121958 + 0.992535i \(0.538917\pi\)
\(728\) 1.78374e15 1.29596e15i 0.323302 0.234892i
\(729\) −7.83542e14 2.41150e15i −0.140949 0.433795i
\(730\) 2.62824e15 8.08888e15i 0.469233 1.44415i
\(731\) −5.97002e12 4.33747e12i −0.00105786 0.000768584i
\(732\) 2.31121e15 + 1.67919e15i 0.406469 + 0.295317i
\(733\) −1.07883e15 + 3.32031e15i −0.188314 + 0.579571i −0.999990 0.00453719i \(-0.998556\pi\)
0.811676 + 0.584109i \(0.198556\pi\)
\(734\) 2.05748e15 + 6.33227e15i 0.356457 + 1.09706i
\(735\) −4.04702e15 + 2.94033e15i −0.695913 + 0.505610i
\(736\) 4.68264e14 0.0799214
\(737\) 4.37544e14 + 2.43016e15i 0.0741225 + 0.411683i
\(738\) −7.84322e15 −1.31882
\(739\) −4.99647e15 + 3.63015e15i −0.833909 + 0.605871i −0.920663 0.390359i \(-0.872351\pi\)
0.0867533 + 0.996230i \(0.472351\pi\)
\(740\) 6.17531e14 + 1.90057e15i 0.102302 + 0.314854i
\(741\) 2.34109e14 7.20514e14i 0.0384962 0.118479i
\(742\) 1.64873e16 + 1.19787e16i 2.69109 + 1.95519i
\(743\) 4.46906e15 + 3.24696e15i 0.724065 + 0.526064i 0.887680 0.460460i \(-0.152316\pi\)
−0.163615 + 0.986524i \(0.552316\pi\)
\(744\) 9.07212e13 2.79211e14i 0.0145901 0.0449037i
\(745\) −4.24508e14 1.30650e15i −0.0677682 0.208569i
\(746\) −1.47699e15 + 1.07310e15i −0.234053 + 0.170049i
\(747\) −6.15553e15 −0.968283
\(748\) −2.00063e13 1.91809e13i −0.00312397 0.00299509i
\(749\) 1.56670e16 2.42849
\(750\) 9.24893e14 6.71974e14i 0.142316 0.103399i
\(751\) 6.11046e14 + 1.88061e15i 0.0933371 + 0.287262i 0.986817 0.161842i \(-0.0517433\pi\)
−0.893480 + 0.449104i \(0.851743\pi\)
\(752\) −9.53562e14 + 2.93476e15i −0.144594 + 0.445015i
\(753\) −1.54129e14 1.11981e14i −0.0232013 0.0168567i
\(754\) 5.81195e15 + 4.22263e15i 0.868519 + 0.631016i
\(755\) −2.55576e15 + 7.86581e15i −0.379150 + 1.16690i
\(756\) −2.94841e15 9.07427e15i −0.434228 1.33642i
\(757\) 7.76942e15 5.64481e15i 1.13595 0.825320i 0.149404 0.988776i \(-0.452264\pi\)
0.986551 + 0.163457i \(0.0522644\pi\)
\(758\) −1.40208e16 −2.03513
\(759\) −1.17855e14 + 6.32107e13i −0.0169831 + 0.00910879i
\(760\) −6.68166e15 −0.955893
\(761\) −1.02546e15 + 7.45043e14i −0.145648 + 0.105820i −0.658223 0.752823i \(-0.728692\pi\)
0.512575 + 0.858642i \(0.328692\pi\)
\(762\) −4.98602e14 1.53454e15i −0.0703076 0.216384i
\(763\) 2.86710e15 8.82403e15i 0.401382 1.23533i
\(764\) 2.13987e15 + 1.55471e15i 0.297423 + 0.216091i
\(765\) 2.44734e13 + 1.77809e13i 0.00337719 + 0.00245367i
\(766\) −3.06261e15 + 9.42574e15i −0.419598 + 1.29139i
\(767\) −1.44931e15 4.46051e15i −0.197145 0.606751i
\(768\) 3.52387e14 2.56024e14i 0.0475919 0.0345776i
\(769\) −5.20428e15 −0.697855 −0.348928 0.937150i \(-0.613454\pi\)
−0.348928 + 0.937150i \(0.613454\pi\)
\(770\) −2.90307e16 3.97330e15i −3.86508 0.528996i
\(771\) 2.93310e15 0.387728
\(772\) 3.28668e15 2.38791e15i 0.431382 0.313417i
\(773\) 3.79163e15 + 1.16694e16i 0.494127 + 1.52077i 0.818312 + 0.574774i \(0.194910\pi\)
−0.324185 + 0.945994i \(0.605090\pi\)
\(774\) 1.40958e15 4.33823e15i 0.182395 0.561355i
\(775\) 1.90141e15 + 1.38145e15i 0.244296 + 0.177491i
\(776\) −2.95767e15 2.14888e15i −0.377321 0.274140i
\(777\) 2.03629e14 6.26707e14i 0.0257944 0.0793869i
\(778\) −3.90472e15 1.20175e16i −0.491136 1.51156i
\(779\) 6.31812e15 4.59038e15i 0.789099 0.573314i
\(780\) 2.03779e15 0.252720
\(781\) −5.78556e14 + 1.19715e15i −0.0712467 + 0.147424i
\(782\) −2.40477e12 −0.000294060
\(783\) 7.17531e15 5.21316e15i 0.871266 0.633012i
\(784\) −2.07041e15 6.37208e15i −0.249643 0.768321i
\(785\) 2.59900e15 7.99889e15i 0.311188 0.957738i
\(786\) −6.21108e15 4.51261e15i −0.738487 0.536542i
\(787\) 1.75250e14 + 1.27327e14i 0.0206918 + 0.0150334i 0.598083 0.801434i \(-0.295929\pi\)
−0.577391 + 0.816468i \(0.695929\pi\)
\(788\) 3.71565e15 1.14356e16i 0.435653 1.34080i
\(789\) 7.86973e14 + 2.42205e15i 0.0916297 + 0.282007i
\(790\) 2.22698e15 1.61800e15i 0.257494 0.187081i
\(791\) 1.13595e16 1.30434
\(792\) 2.12675e15 4.40069e15i 0.242509 0.501801i
\(793\) −3.88041e15 −0.439415
\(794\) 1.52903e16 1.11090e16i 1.71950 1.24929i
\(795\) 1.66054e15 + 5.11061e15i 0.185451 + 0.570760i
\(796\) 1.15406e15 3.55184e15i 0.127999 0.393941i
\(797\) −6.29681e15 4.57490e15i −0.693586 0.503920i 0.184251 0.982879i \(-0.441014\pi\)
−0.877837 + 0.478960i \(0.841014\pi\)
\(798\) 6.24794e15 + 4.53939e15i 0.683472 + 0.496572i
\(799\) 9.32456e12 2.86980e13i 0.00101303 0.00311778i
\(800\) 4.63029e15 + 1.42506e16i 0.499590 + 1.53758i
\(801\) −1.02191e16 + 7.42463e15i −1.09505 + 0.795602i
\(802\) −1.31438e15 −0.139882
\(803\) −6.13767e15 8.40034e14i −0.648736 0.0887895i
\(804\) 1.75056e15 0.183768
\(805\) −1.19951e15 + 8.71494e14i −0.125062 + 0.0908629i
\(806\) 4.31935e14 + 1.32936e15i 0.0447276 + 0.137657i
\(807\) 1.10594e15 3.40374e15i 0.113744 0.350068i
\(808\) 3.11082e15 + 2.26014e15i 0.317770 + 0.230873i
\(809\) −6.75996e15 4.91140e15i −0.685847 0.498297i 0.189445 0.981891i \(-0.439331\pi\)
−0.875292 + 0.483594i \(0.839331\pi\)
\(810\) −5.07729e15 + 1.56263e16i −0.511640 + 1.57467i
\(811\) 3.94533e15 + 1.21425e16i 0.394883 + 1.21532i 0.929053 + 0.369947i \(0.120624\pi\)
−0.534170 + 0.845377i \(0.679376\pi\)
\(812\) −3.45521e16 + 2.51035e16i −3.43491 + 2.49561i
\(813\) −1.62928e15 −0.160879
\(814\) 2.19947e15 1.17967e15i 0.215716 0.115698i
\(815\) −2.77428e16 −2.70261
\(816\) 3.58496e12 2.60462e12i 0.000346887 0.000252028i
\(817\) 1.40354e15 + 4.31965e15i 0.134897 + 0.415171i
\(818\) 4.59607e15 1.41453e16i 0.438777 1.35042i
\(819\) 4.97057e15 + 3.61133e15i 0.471352 + 0.342457i
\(820\) 1.69946e16 + 1.23473e16i 1.60079 + 1.16305i
\(821\) 1.89169e15 5.82202e15i 0.176995 0.544736i −0.822724 0.568442i \(-0.807547\pi\)
0.999719 + 0.0237058i \(0.00754650\pi\)
\(822\) 5.60472e14 + 1.72496e15i 0.0520906 + 0.160318i
\(823\) −1.83740e15 + 1.33495e15i −0.169631 + 0.123244i −0.669362 0.742937i \(-0.733432\pi\)
0.499731 + 0.866181i \(0.333432\pi\)
\(824\) −6.28156e15 −0.576060
\(825\) −3.08905e15 2.96161e15i −0.281403 0.269793i
\(826\) 4.78103e16 4.32645
\(827\) 1.21293e16 8.81242e15i 1.09032 0.792164i 0.110867 0.993835i \(-0.464637\pi\)
0.979453 + 0.201672i \(0.0646374\pi\)
\(828\) −2.67888e14 8.24475e14i −0.0239214 0.0736225i
\(829\) −5.43142e15 + 1.67162e16i −0.481797 + 1.48282i 0.354771 + 0.934953i \(0.384559\pi\)
−0.836567 + 0.547864i \(0.815441\pi\)
\(830\) 2.28704e16 + 1.66163e16i 2.01532 + 1.46422i
\(831\) −4.49014e15 3.26228e15i −0.393056 0.285572i
\(832\) −2.15097e15 + 6.62001e15i −0.187049 + 0.575679i
\(833\) 2.02459e13 + 6.23103e13i 0.00174899 + 0.00538285i
\(834\) 9.16751e14 6.66059e14i 0.0786752 0.0571609i
\(835\) −5.96859e15 −0.508858
\(836\) 3.02279e15 + 1.67889e16i 0.256020 + 1.42196i
\(837\) 1.72566e15 0.145199
\(838\) 1.02160e16 7.42233e15i 0.853959 0.620438i
\(839\) −3.03826e15 9.35081e15i −0.252310 0.776530i −0.994348 0.106172i \(-0.966141\pi\)
0.742038 0.670358i \(-0.233859\pi\)
\(840\) −1.83135e15 + 5.63633e15i −0.151090 + 0.465008i
\(841\) −2.22478e16 1.61640e16i −1.82351 1.32486i
\(842\) −2.33273e16 1.69483e16i −1.89954 1.38010i
\(843\) −1.80829e15 + 5.56535e15i −0.146291 + 0.450237i
\(844\) −7.08698e15 2.18115e16i −0.569610 1.75308i
\(845\) 1.29294e16 9.39374e15i 1.03244 0.750113i
\(846\) 1.86524e16 1.47978
\(847\) 8.98638e14 + 2.13233e16i 0.0708315 + 1.68072i
\(848\) −7.19721e15 −0.563620
\(849\) −5.57981e15 + 4.05397e15i −0.434138 + 0.315419i
\(850\) −2.37789e13 7.31838e13i −0.00183818 0.00565732i
\(851\) 3.90264e13 1.20111e14i 0.00299741 0.00922508i
\(852\) 7.62610e14 + 5.54069e14i 0.0581949 + 0.0422811i
\(853\) 1.64403e16 + 1.19446e16i 1.24649 + 0.905629i 0.998013 0.0630081i \(-0.0200694\pi\)
0.248479 + 0.968637i \(0.420069\pi\)
\(854\) 1.22237e16 3.76207e16i 0.920840 2.83405i
\(855\) −5.75364e15 1.77079e16i −0.430654 1.32542i
\(856\) 9.70971e15 7.05452e15i 0.722106 0.524640i
\(857\) −1.68364e16 −1.24410 −0.622051 0.782977i \(-0.713700\pi\)
−0.622051 + 0.782977i \(0.713700\pi\)
\(858\) −4.50985e14 2.50481e15i −0.0331117 0.183905i
\(859\) −1.61793e16 −1.18031 −0.590156 0.807289i \(-0.700934\pi\)
−0.590156 + 0.807289i \(0.700934\pi\)
\(860\) −9.88380e15 + 7.18100e15i −0.716444 + 0.520527i
\(861\) −2.14051e15 6.58783e15i −0.154170 0.474487i
\(862\) −6.03261e15 + 1.85665e16i −0.431733 + 1.32874i
\(863\) 1.53692e16 + 1.11664e16i 1.09293 + 0.794058i 0.979891 0.199533i \(-0.0639425\pi\)
0.113036 + 0.993591i \(0.463942\pi\)
\(864\) 8.90064e15 + 6.46670e15i 0.628921 + 0.456938i
\(865\) 2.21737e15 6.82438e15i 0.155686 0.479153i
\(866\) 7.69055e13 + 2.36691e14i 0.00536548 + 0.0165133i
\(867\) 3.66410e15 2.66212e15i 0.254017 0.184554i
\(868\) −8.30976e15 −0.572440
\(869\) −1.44728e15 1.38757e15i −0.0990701 0.0949829i
\(870\) −1.93099e16 −1.31348
\(871\) −1.92367e15 + 1.39763e15i −0.130026 + 0.0944697i
\(872\) −2.19637e15 6.75974e15i −0.147525 0.454035i
\(873\) 3.14812e15 9.68890e15i 0.210122 0.646690i
\(874\) 1.19744e15 + 8.69994e14i 0.0794222 + 0.0577036i
\(875\) −7.46861e15 5.42626e15i −0.492261 0.357649i
\(876\) −1.35716e15 + 4.17691e15i −0.0888913 + 0.273579i
\(877\) 2.06767e14 + 6.36362e14i 0.0134581 + 0.0414197i 0.957560 0.288234i \(-0.0930681\pi\)
−0.944102 + 0.329654i \(0.893068\pi\)
\(878\) −6.87980e14 + 4.99847e14i −0.0444996 + 0.0323308i
\(879\) 3.44506e15 0.221441
\(880\) 9.11921e15 4.89103e15i 0.582509 0.312425i
\(881\) 2.95022e16 1.87278 0.936391 0.350957i \(-0.114144\pi\)
0.936391 + 0.350957i \(0.114144\pi\)
\(882\) −3.27642e16 + 2.38046e16i −2.06691 + 1.50170i
\(883\) 6.01906e14 + 1.85248e15i 0.0377350 + 0.116136i 0.968150 0.250372i \(-0.0805530\pi\)
−0.930415 + 0.366509i \(0.880553\pi\)
\(884\) 8.24744e12 2.53830e13i 0.000513844 0.00158145i
\(885\) 1.01989e16 + 7.40993e15i 0.631488 + 0.458803i
\(886\) −2.07329e16 1.50633e16i −1.27578 0.926907i
\(887\) 4.22296e15 1.29969e16i 0.258248 0.794806i −0.734924 0.678149i \(-0.762782\pi\)
0.993172 0.116657i \(-0.0372177\pi\)
\(888\) −1.55992e14 4.80095e14i −0.00948052 0.0291780i
\(889\) −1.05409e16 + 7.65842e15i −0.636676 + 0.462572i
\(890\) 5.80105e16 3.48226
\(891\) 1.18569e16 + 1.62280e15i 0.707365 + 0.0968139i
\(892\) −3.51777e16 −2.08574
\(893\) −1.50254e16 + 1.09166e16i −0.885410 + 0.643288i
\(894\) 3.75875e14 + 1.15682e15i 0.0220134 + 0.0677502i
\(895\) −2.22376e15 + 6.84402e15i −0.129438 + 0.398368i
\(896\) −2.67728e16 1.94516e16i −1.54881 1.12528i
\(897\) −1.04188e14 7.56970e13i −0.00599045 0.00435232i
\(898\) −1.44942e16 + 4.46086e16i −0.828275 + 2.54917i
\(899\) −2.38698e15 7.34636e15i −0.135572 0.417247i
\(900\) 2.24421e16 1.63052e16i 1.26686 0.920431i
\(901\) 7.03790e13 0.00394872
\(902\) 1.14160e16 2.36220e16i 0.636614 1.31729i
\(903\) 4.02854e15 0.223288
\(904\) 7.04013e15 5.11495e15i 0.387841 0.281783i
\(905\) 5.57835e15 + 1.71684e16i 0.305449 + 0.940076i
\(906\) 2.26296e15 6.96469e15i 0.123161 0.379050i
\(907\) −1.23965e16 9.00659e15i −0.670593 0.487214i 0.199631 0.979871i \(-0.436026\pi\)
−0.870224 + 0.492657i \(0.836026\pi\)
\(908\) 1.45438e16 + 1.05667e16i 0.781999 + 0.568155i
\(909\) −3.31113e15 + 1.01906e16i −0.176960 + 0.544626i
\(910\) −8.71930e15 2.68353e16i −0.463185 1.42554i
\(911\) 8.36320e15 6.07622e15i 0.441592 0.320836i −0.344675 0.938722i \(-0.612011\pi\)
0.786267 + 0.617886i \(0.212011\pi\)
\(912\) −2.72741e15 −0.143146
\(913\) 8.95950e15 1.85391e16i 0.467406 0.967161i
\(914\) −2.02381e16 −1.04946
\(915\) 8.43824e15 6.13074e15i 0.434947 0.316007i
\(916\) 8.40199e15 + 2.58587e16i 0.430484 + 1.32489i
\(917\) −1.91576e16 + 5.89609e16i −0.975683 + 3.00284i
\(918\) −4.57092e13 3.32097e13i −0.00231403 0.00168124i
\(919\) 1.26182e16 + 9.16768e15i 0.634984 + 0.461343i 0.858123 0.513443i \(-0.171630\pi\)
−0.223139 + 0.974787i \(0.571630\pi\)
\(920\) −3.50987e14 + 1.08023e15i −0.0175573 + 0.0540358i
\(921\) 8.60124e14 + 2.64719e15i 0.0427694 + 0.131631i
\(922\) 8.26719e15 6.00647e15i 0.408637 0.296892i
\(923\) −1.28039e15 −0.0629117
\(924\) 1.49908e16 + 2.05172e15i 0.732198 + 0.100213i
\(925\) 4.04121e15 0.196215
\(926\) −2.61718e16 + 1.90150e16i −1.26321 + 0.917772i
\(927\) −5.40910e15 1.66475e16i −0.259530 0.798750i
\(928\) 1.52180e16 4.68361e16i 0.725844 2.23392i
\(929\) 1.54113e16 + 1.11969e16i 0.730721 + 0.530900i 0.889791 0.456367i \(-0.150850\pi\)
−0.159071 + 0.987267i \(0.550850\pi\)
\(930\) −3.03956e15 2.20837e15i −0.143270 0.104092i
\(931\) 1.24612e16 3.83516e16i 0.583898 1.79705i
\(932\) 1.69409e16 + 5.21387e16i 0.789130 + 2.42869i
\(933\) 3.12318e15 2.26912e15i 0.144626 0.105077i
\(934\) −2.53485e15 −0.116693
\(935\) −8.91736e13 + 4.78277e13i −0.00408106 + 0.00218885i
\(936\) 4.70665e15 0.214138
\(937\) 2.42430e16 1.76136e16i 1.09653 0.796673i 0.116037 0.993245i \(-0.462981\pi\)
0.980489 + 0.196572i \(0.0629810\pi\)
\(938\) −7.49030e15 2.30528e16i −0.336809 1.03659i
\(939\) −5.47022e14 + 1.68356e15i −0.0244537 + 0.0752606i
\(940\) −4.04159e16 2.93638e16i −1.79617 1.30500i
\(941\) 2.19394e16 + 1.59399e16i 0.969350 + 0.704274i 0.955303 0.295627i \(-0.0955285\pi\)
0.0140470 + 0.999901i \(0.495529\pi\)
\(942\) −2.30125e15 + 7.08252e15i −0.101084 + 0.311106i
\(943\) −4.10238e14 1.26258e15i −0.0179152 0.0551374i
\(944\) −1.36600e16 + 9.92457e15i −0.593068 + 0.430889i
\(945\) −3.48352e16 −1.50364
\(946\) 1.10141e16 + 1.05597e16i 0.472659 + 0.453159i
\(947\) 1.23713e16 0.527827 0.263914 0.964546i \(-0.414987\pi\)
0.263914 + 0.964546i \(0.414987\pi\)
\(948\) −1.14996e15 + 8.35497e14i −0.0487796 + 0.0354404i
\(949\) −1.84343e15 5.67351e15i −0.0777434 0.239270i
\(950\) −1.46358e16 + 4.50442e16i −0.613671 + 1.88868i
\(951\) −7.21049e15 5.23873e15i −0.300588 0.218390i
\(952\) 6.27948e13 + 4.56231e13i 0.00260268 + 0.00189096i
\(953\) −3.93165e15 + 1.21004e16i −0.162018 + 0.498641i −0.998804 0.0488894i \(-0.984432\pi\)
0.836786 + 0.547530i \(0.184432\pi\)
\(954\) 1.34435e16 + 4.13750e16i 0.550805 + 1.69520i
\(955\) 7.81270e15 5.67626e15i 0.318260 0.231230i
\(956\) 5.56439e15 0.225372
\(957\) 2.49225e15 + 1.38422e16i 0.100364 + 0.557428i
\(958\) −1.58319e16 −0.633902
\(959\) 1.18489e16 8.60873e15i 0.471710 0.342718i
\(960\) −5.78165e15 1.77941e16i −0.228855 0.704343i
\(961\) −7.38722e15 + 2.27355e16i −0.290738 + 0.894801i
\(962\) 1.94441e15 + 1.41270e15i 0.0760896 + 0.0552823i
\(963\) 2.70572e16 + 1.96582e16i 1.05278 + 0.764889i
\(964\) −1.47487e15 + 4.53918e15i −0.0570597 + 0.175612i
\(965\) −4.58347e15 1.41065e16i −0.176317 0.542648i
\(966\) 1.06209e15 7.71653e14i 0.0406244 0.0295153i
\(967\) −3.44954e16 −1.31194 −0.655972 0.754785i \(-0.727741\pi\)
−0.655972 + 0.754785i \(0.727741\pi\)
\(968\) 1.01583e16 + 1.28106e16i 0.384157 + 0.484456i
\(969\) 2.66704e13 0.00100288
\(970\) −3.78509e16 + 2.75003e16i −1.41525 + 1.02824i
\(971\) −1.14204e16 3.51484e16i −0.424596 1.30677i −0.903381 0.428840i \(-0.858922\pi\)
0.478784 0.877932i \(-0.341078\pi\)
\(972\) 9.60416e15 2.95586e16i 0.355054 1.09275i
\(973\) −7.40286e15 5.37849e15i −0.272132 0.197715i
\(974\) −3.70046e16 2.68854e16i −1.35264 0.982748i
\(975\) 1.27344e15 3.91924e15i 0.0462863 0.142455i
\(976\) 4.31692e15 + 1.32861e16i 0.156027 + 0.480202i
\(977\) 9.31042e14 6.76442e14i 0.0334618 0.0243114i −0.570929 0.821000i \(-0.693417\pi\)
0.604390 + 0.796688i \(0.293417\pi\)
\(978\) 2.45645e16 0.877898
\(979\) −7.48717e15 4.15844e16i −0.266080 1.47783i
\(980\) 1.08468e17 3.83317
\(981\) 1.60235e16 1.16417e16i 0.563090 0.409109i
\(982\) −1.29951e16 3.99949e16i −0.454117 1.39763i
\(983\) −1.46816e15 + 4.51852e15i −0.0510185 + 0.157019i −0.973320 0.229453i \(-0.926306\pi\)
0.922301 + 0.386472i \(0.126306\pi\)
\(984\) −4.29295e15 3.11901e15i −0.148349 0.107782i
\(985\) −3.55159e16 2.58038e16i −1.22046 0.886716i
\(986\) −7.81519e13 + 2.40527e14i −0.00267065 + 0.00821941i
\(987\) 5.09047e15 + 1.56669e16i 0.172987 + 0.532400i
\(988\) −1.32898e16 + 9.65560e15i −0.449112 + 0.326299i
\(989\) 7.72087e14 0.0259470
\(990\) −4.51510e16 4.32882e16i −1.50895 1.44669i
\(991\) 4.78706e14 0.0159098 0.00795488 0.999968i \(-0.497468\pi\)
0.00795488 + 0.999968i \(0.497468\pi\)
\(992\) 7.75183e15 5.63204e15i 0.256206 0.186145i
\(993\) 3.33388e14 + 1.02606e15i 0.0109579 + 0.0337250i
\(994\) 4.03335e15 1.24134e16i 0.131838 0.405756i
\(995\) −1.10311e16 8.01454e15i −0.358584 0.260526i
\(996\) −1.18098e16 8.58029e15i −0.381781 0.277380i
\(997\) 1.23165e16 3.79063e16i 0.395972 1.21868i −0.532230 0.846600i \(-0.678646\pi\)
0.928202 0.372076i \(-0.121354\pi\)
\(998\) 8.18201e15 + 2.51817e16i 0.261603 + 0.805130i
\(999\) 2.40053e15 1.74409e15i 0.0763303 0.0554572i
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 11.12.c.a.3.9 40
3.2 odd 2 99.12.f.a.91.2 40
11.2 odd 10 121.12.a.h.1.18 20
11.4 even 5 inner 11.12.c.a.4.9 yes 40
11.9 even 5 121.12.a.j.1.3 20
33.26 odd 10 99.12.f.a.37.2 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.12.c.a.3.9 40 1.1 even 1 trivial
11.12.c.a.4.9 yes 40 11.4 even 5 inner
99.12.f.a.37.2 40 33.26 odd 10
99.12.f.a.91.2 40 3.2 odd 2
121.12.a.h.1.18 20 11.2 odd 10
121.12.a.j.1.3 20 11.9 even 5