Properties

Label 38.10.e.a.17.2
Level $38$
Weight $10$
Character 38.17
Analytic conductor $19.571$
Analytic rank $0$
Dimension $42$
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] = [38,10,Mod(5,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.5");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.5713617742\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 17.2
Character \(\chi\) \(=\) 38.17
Dual form 38.10.e.a.9.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.77837 + 15.7569i) q^{2} +(-110.851 - 93.0147i) q^{3} +(-240.561 - 87.5572i) q^{4} +(-143.544 + 52.2458i) q^{5} +(1773.61 - 1488.24i) q^{6} +(-1900.39 - 3291.57i) q^{7} +(2048.00 - 3547.24i) q^{8} +(218.206 + 1237.51i) q^{9} +O(q^{10})\) \(q+(-2.77837 + 15.7569i) q^{2} +(-110.851 - 93.0147i) q^{3} +(-240.561 - 87.5572i) q^{4} +(-143.544 + 52.2458i) q^{5} +(1773.61 - 1488.24i) q^{6} +(-1900.39 - 3291.57i) q^{7} +(2048.00 - 3547.24i) q^{8} +(218.206 + 1237.51i) q^{9} +(-424.414 - 2406.97i) q^{10} +(38540.8 - 66754.6i) q^{11} +(18522.3 + 32081.5i) q^{12} +(-88970.1 + 74654.8i) q^{13} +(57145.1 - 20799.1i) q^{14} +(20771.6 + 7560.24i) q^{15} +(50203.5 + 42125.7i) q^{16} +(-107445. + 609351. i) q^{17} -20105.5 q^{18} +(567816. + 16516.6i) q^{19} +39105.6 q^{20} +(-95505.2 + 541637. i) q^{21} +(944766. + 792753. i) q^{22} +(-1.68708e6 - 614045. i) q^{23} +(-556968. + 202720. i) q^{24} +(-1.47831e6 + 1.24045e6i) q^{25} +(-929138. - 1.60931e6i) q^{26} +(-1.33320e6 + 2.30917e6i) q^{27} +(168960. + 958218. i) q^{28} +(-387806. - 2.19936e6i) q^{29} +(-176837. + 306291. i) q^{30} +(2.89739e6 + 5.01842e6i) q^{31} +(-803256. + 674012. i) q^{32} +(-1.04814e7 + 3.81493e6i) q^{33} +(-9.30297e6 - 3.38601e6i) q^{34} +(444761. + 373198. i) q^{35} +(55860.7 - 316802. i) q^{36} +8.15141e6 q^{37} +(-1.83785e6 + 8.90114e6i) q^{38} +1.68064e7 q^{39} +(-108650. + 616185. i) q^{40} +(1.61749e7 + 1.35724e7i) q^{41} +(-8.26919e6 - 3.00974e6i) q^{42} +(-1.50081e7 + 5.46250e6i) q^{43} +(-1.51163e7 + 1.26840e7i) q^{44} +(-95976.6 - 166236. i) q^{45} +(1.43628e7 - 2.48771e7i) q^{46} +(1.01224e7 + 5.74068e7i) q^{47} +(-1.64678e6 - 9.33933e6i) q^{48} +(1.29538e7 - 2.24367e7i) q^{49} +(-1.54383e7 - 2.67400e7i) q^{50} +(6.85889e7 - 5.75530e7i) q^{51} +(2.79393e7 - 1.01691e7i) q^{52} +(9.33844e6 + 3.39891e6i) q^{53} +(-3.26813e7 - 2.74228e7i) q^{54} +(-2.04466e6 + 1.15958e7i) q^{55} -1.55680e7 q^{56} +(-6.14065e7 - 5.46461e7i) q^{57} +3.57326e7 q^{58} +(2.28878e7 - 1.29803e8i) q^{59} +(-4.33489e6 - 3.63740e6i) q^{60} +(1.76481e6 + 642337. i) q^{61} +(-8.71249e7 + 3.17109e7i) q^{62} +(3.65867e6 - 3.06999e6i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(8.87073e6 - 1.53646e7i) q^{65} +(-3.09902e7 - 1.75754e8i) q^{66} +(2.23870e7 + 1.26963e8i) q^{67} +(7.92001e7 - 1.37179e8i) q^{68} +(1.29898e8 + 2.24990e8i) q^{69} +(-7.11617e6 + 5.97118e6i) q^{70} +(6.28412e6 - 2.28723e6i) q^{71} +(4.83662e6 + 1.76038e6i) q^{72} +(-8.99732e7 - 7.54965e7i) q^{73} +(-2.26476e7 + 1.28441e8i) q^{74} +2.79251e8 q^{75} +(-1.35148e8 - 5.36896e7i) q^{76} -2.92970e8 q^{77} +(-4.66944e7 + 2.64817e8i) q^{78} +(1.33043e8 + 1.11636e8i) q^{79} +(-9.40731e6 - 3.42398e6i) q^{80} +(3.85814e8 - 1.40425e8i) q^{81} +(-2.58799e8 + 2.17158e8i) q^{82} +(2.21950e8 + 3.84429e8i) q^{83} +(7.03991e7 - 1.21935e8i) q^{84} +(-1.64129e7 - 9.30823e7i) q^{85} +(-4.43742e7 - 2.51658e8i) q^{86} +(-1.61584e8 + 2.79872e8i) q^{87} +(-1.57863e8 - 2.73427e8i) q^{88} +(-8.52775e8 + 7.15563e8i) q^{89} +(2.88603e6 - 1.05043e6i) q^{90} +(4.14809e8 + 1.50978e8i) q^{91} +(3.52081e8 + 2.95431e8i) q^{92} +(1.45610e8 - 8.25795e8i) q^{93} -9.32679e8 q^{94} +(-8.23695e7 + 2.72951e7i) q^{95} +1.51734e8 q^{96} +(1.52899e8 - 8.67134e8i) q^{97} +(3.17543e8 + 2.66450e8i) q^{98} +(9.10190e7 + 3.31282e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9} + 32625 q^{11} - 62208 q^{12} + 351237 q^{13} + 165264 q^{14} - 834165 q^{15} + 1075035 q^{17} - 3364608 q^{18} + 696762 q^{19} - 1396224 q^{20} - 3148065 q^{21} - 1462656 q^{22} - 4882824 q^{23} + 1032192 q^{24} - 483270 q^{25} - 70176 q^{26} + 2570400 q^{27} + 1519104 q^{28} + 13670499 q^{29} - 2263968 q^{31} - 5777733 q^{33} - 9526080 q^{34} + 43019613 q^{35} + 3290112 q^{36} - 50105184 q^{37} - 692160 q^{38} - 89820600 q^{39} - 94033860 q^{41} - 43526160 q^{42} + 30524217 q^{43} + 23402496 q^{44} + 39789630 q^{45} - 18312576 q^{46} + 81865791 q^{47} + 33030144 q^{48} + 40421580 q^{49} - 16761600 q^{50} - 28132314 q^{51} - 91666176 q^{52} + 126049077 q^{53} - 106214544 q^{54} + 553870071 q^{55} + 117743616 q^{56} + 384197394 q^{57} - 63148512 q^{58} + 135312639 q^{59} - 129611520 q^{60} + 132517452 q^{61} - 419324112 q^{62} + 577860735 q^{63} - 352321536 q^{64} - 184218951 q^{65} + 413765760 q^{66} + 229749621 q^{67} + 152743680 q^{68} - 517946637 q^{69} - 688313808 q^{70} - 2107934406 q^{71} + 105283584 q^{72} - 26577420 q^{73} + 322027248 q^{74} + 941894730 q^{75} - 107163648 q^{76} + 620006124 q^{77} + 122597280 q^{78} - 624601023 q^{79} - 1037387736 q^{81} + 1504541760 q^{82} + 907729401 q^{83} - 604998912 q^{84} + 1462808898 q^{85} + 222950208 q^{86} + 63648732 q^{87} - 133632000 q^{88} - 847590846 q^{89} - 4481693280 q^{90} + 957045924 q^{91} + 648163584 q^{92} + 2438307564 q^{93} + 2205393024 q^{94} - 208077987 q^{95} - 509607936 q^{96} + 535342599 q^{97} + 1861154832 q^{98} - 11757151095 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77837 + 15.7569i −0.122788 + 0.696364i
\(3\) −110.851 93.0147i −0.790119 0.662989i 0.155656 0.987811i \(-0.450251\pi\)
−0.945775 + 0.324823i \(0.894695\pi\)
\(4\) −240.561 87.5572i −0.469846 0.171010i
\(5\) −143.544 + 52.2458i −0.102712 + 0.0373840i −0.392865 0.919596i \(-0.628516\pi\)
0.290153 + 0.956980i \(0.406294\pi\)
\(6\) 1773.61 1488.24i 0.558698 0.468804i
\(7\) −1900.39 3291.57i −0.299159 0.518158i 0.676785 0.736181i \(-0.263373\pi\)
−0.975944 + 0.218023i \(0.930039\pi\)
\(8\) 2048.00 3547.24i 0.176777 0.306186i
\(9\) 218.206 + 1237.51i 0.0110860 + 0.0628718i
\(10\) −424.414 2406.97i −0.0134211 0.0761151i
\(11\) 38540.8 66754.6i 0.793694 1.37472i −0.129971 0.991518i \(-0.541488\pi\)
0.923665 0.383201i \(-0.125178\pi\)
\(12\) 18522.3 + 32081.5i 0.257857 + 0.446621i
\(13\) −88970.1 + 74654.8i −0.863970 + 0.724957i −0.962820 0.270145i \(-0.912928\pi\)
0.0988491 + 0.995102i \(0.468484\pi\)
\(14\) 57145.1 20799.1i 0.397560 0.144700i
\(15\) 20771.6 + 7560.24i 0.105940 + 0.0385589i
\(16\) 50203.5 + 42125.7i 0.191511 + 0.160697i
\(17\) −107445. + 609351.i −0.312008 + 1.76949i 0.276518 + 0.961009i \(0.410819\pi\)
−0.588527 + 0.808478i \(0.700292\pi\)
\(18\) −20105.5 −0.0451429
\(19\) 567816. + 16516.6i 0.999577 + 0.0290756i
\(20\) 39105.6 0.0546518
\(21\) −95505.2 + 541637.i −0.107162 + 0.607745i
\(22\) 944766. + 792753.i 0.859849 + 0.721499i
\(23\) −1.68708e6 614045.i −1.25707 0.457536i −0.374285 0.927314i \(-0.622112\pi\)
−0.882785 + 0.469778i \(0.844334\pi\)
\(24\) −556968. + 202720.i −0.342673 + 0.124723i
\(25\) −1.47831e6 + 1.24045e6i −0.756892 + 0.635108i
\(26\) −929138. 1.60931e6i −0.398749 0.690654i
\(27\) −1.33320e6 + 2.30917e6i −0.482789 + 0.836216i
\(28\) 168960. + 958218.i 0.0519484 + 0.294614i
\(29\) −387806. 2.19936e6i −0.101818 0.577437i −0.992444 0.122701i \(-0.960845\pi\)
0.890626 0.454737i \(-0.150267\pi\)
\(30\) −176837. + 306291.i −0.0398591 + 0.0690381i
\(31\) 2.89739e6 + 5.01842e6i 0.563481 + 0.975977i 0.997189 + 0.0749238i \(0.0238713\pi\)
−0.433709 + 0.901053i \(0.642795\pi\)
\(32\) −803256. + 674012.i −0.135419 + 0.113630i
\(33\) −1.04814e7 + 3.81493e6i −1.53854 + 0.559981i
\(34\) −9.30297e6 3.38601e6i −1.19390 0.434543i
\(35\) 444761. + 373198.i 0.0500980 + 0.0420372i
\(36\) 55860.7 316802.i 0.00554300 0.0314359i
\(37\) 8.15141e6 0.715031 0.357516 0.933907i \(-0.383624\pi\)
0.357516 + 0.933907i \(0.383624\pi\)
\(38\) −1.83785e6 + 8.90114e6i −0.142983 + 0.692500i
\(39\) 1.68064e7 1.16328
\(40\) −108650. + 616185.i −0.00671057 + 0.0380576i
\(41\) 1.61749e7 + 1.35724e7i 0.893954 + 0.750116i 0.968999 0.247064i \(-0.0794657\pi\)
−0.0750453 + 0.997180i \(0.523910\pi\)
\(42\) −8.26919e6 3.00974e6i −0.410054 0.149247i
\(43\) −1.50081e7 + 5.46250e6i −0.669449 + 0.243660i −0.654311 0.756226i \(-0.727041\pi\)
−0.0151386 + 0.999885i \(0.504819\pi\)
\(44\) −1.51163e7 + 1.26840e7i −0.608005 + 0.510177i
\(45\) −95976.6 166236.i −0.00348907 0.00604324i
\(46\) 1.43628e7 2.48771e7i 0.472964 0.819198i
\(47\) 1.01224e7 + 5.74068e7i 0.302581 + 1.71602i 0.634677 + 0.772778i \(0.281133\pi\)
−0.332096 + 0.943246i \(0.607756\pi\)
\(48\) −1.64678e6 9.33933e6i −0.0447764 0.253939i
\(49\) 1.29538e7 2.24367e7i 0.321008 0.556002i
\(50\) −1.54383e7 2.67400e7i −0.349329 0.605056i
\(51\) 6.85889e7 5.75530e7i 1.41967 1.19125i
\(52\) 2.79393e7 1.01691e7i 0.529908 0.192871i
\(53\) 9.33844e6 + 3.39891e6i 0.162567 + 0.0591696i 0.422022 0.906586i \(-0.361321\pi\)
−0.259455 + 0.965755i \(0.583543\pi\)
\(54\) −3.26813e7 2.74228e7i −0.523030 0.438874i
\(55\) −2.04466e6 + 1.15958e7i −0.0301292 + 0.170871i
\(56\) −1.55680e7 −0.211537
\(57\) −6.14065e7 5.46461e7i −0.770508 0.685681i
\(58\) 3.57326e7 0.414609
\(59\) 2.28878e7 1.29803e8i 0.245907 1.39461i −0.572471 0.819925i \(-0.694015\pi\)
0.818378 0.574681i \(-0.194874\pi\)
\(60\) −4.33489e6 3.63740e6i −0.0431814 0.0362335i
\(61\) 1.76481e6 + 642337.i 0.0163197 + 0.00593990i 0.350167 0.936687i \(-0.386125\pi\)
−0.333847 + 0.942627i \(0.608347\pi\)
\(62\) −8.71249e7 + 3.17109e7i −0.748824 + 0.272550i
\(63\) 3.65867e6 3.06999e6i 0.0292611 0.0245530i
\(64\) −8.38861e6 1.45295e7i −0.0625000 0.108253i
\(65\) 8.87073e6 1.53646e7i 0.0616381 0.106760i
\(66\) −3.09902e7 1.75754e8i −0.201037 1.14014i
\(67\) 2.23870e7 + 1.26963e8i 0.135725 + 0.769735i 0.974352 + 0.225029i \(0.0722476\pi\)
−0.838627 + 0.544706i \(0.816641\pi\)
\(68\) 7.92001e7 1.37179e8i 0.449196 0.778030i
\(69\) 1.29898e8 + 2.24990e8i 0.689893 + 1.19493i
\(70\) −7.11617e6 + 5.97118e6i −0.0354246 + 0.0297248i
\(71\) 6.28412e6 2.28723e6i 0.0293482 0.0106819i −0.327304 0.944919i \(-0.606140\pi\)
0.356653 + 0.934237i \(0.383918\pi\)
\(72\) 4.83662e6 + 1.76038e6i 0.0212102 + 0.00771989i
\(73\) −8.99732e7 7.54965e7i −0.370817 0.311153i 0.438267 0.898845i \(-0.355592\pi\)
−0.809085 + 0.587692i \(0.800037\pi\)
\(74\) −2.26476e7 + 1.28441e8i −0.0877971 + 0.497922i
\(75\) 2.79251e8 1.01910
\(76\) −1.35148e8 5.36896e7i −0.464675 0.184599i
\(77\) −2.92970e8 −0.949762
\(78\) −4.66944e7 + 2.64817e8i −0.142836 + 0.810065i
\(79\) 1.33043e8 + 1.11636e8i 0.384299 + 0.322465i 0.814387 0.580322i \(-0.197073\pi\)
−0.430089 + 0.902787i \(0.641518\pi\)
\(80\) −9.40731e6 3.42398e6i −0.0256779 0.00934601i
\(81\) 3.85814e8 1.40425e8i 0.995854 0.362461i
\(82\) −2.58799e8 + 2.17158e8i −0.632121 + 0.530412i
\(83\) 2.21950e8 + 3.84429e8i 0.513339 + 0.889129i 0.999880 + 0.0154714i \(0.00492491\pi\)
−0.486542 + 0.873657i \(0.661742\pi\)
\(84\) 7.03991e7 1.21935e8i 0.154280 0.267221i
\(85\) −1.64129e7 9.30823e7i −0.0341036 0.193411i
\(86\) −4.43742e7 2.51658e8i −0.0874756 0.496099i
\(87\) −1.61584e8 + 2.79872e8i −0.302386 + 0.523748i
\(88\) −1.57863e8 2.73427e8i −0.280613 0.486036i
\(89\) −8.52775e8 + 7.15563e8i −1.44072 + 1.20891i −0.501699 + 0.865042i \(0.667292\pi\)
−0.939019 + 0.343865i \(0.888264\pi\)
\(90\) 2.88603e6 1.05043e6i 0.00463671 0.00168762i
\(91\) 4.14809e8 + 1.50978e8i 0.634107 + 0.230796i
\(92\) 3.52081e8 + 2.95431e8i 0.512386 + 0.429943i
\(93\) 1.45610e8 8.25795e8i 0.201845 1.14472i
\(94\) −9.32679e8 −1.23213
\(95\) −8.23695e7 + 2.72951e7i −0.103755 + 0.0343818i
\(96\) 1.51734e8 0.182332
\(97\) 1.52899e8 8.67134e8i 0.175361 0.994520i −0.762366 0.647146i \(-0.775962\pi\)
0.937727 0.347374i \(-0.112926\pi\)
\(98\) 3.17543e8 + 2.66450e8i 0.347764 + 0.291809i
\(99\) 9.10190e7 + 3.31282e7i 0.0952300 + 0.0346609i
\(100\) 4.64233e8 1.68967e8i 0.464233 0.168967i
\(101\) −1.10551e9 + 9.27637e8i −1.05711 + 0.887017i −0.993823 0.110979i \(-0.964601\pi\)
−0.0632827 + 0.997996i \(0.520157\pi\)
\(102\) 7.16292e8 + 1.24065e9i 0.655223 + 1.13488i
\(103\) −7.52246e8 + 1.30293e9i −0.658555 + 1.14065i 0.322435 + 0.946592i \(0.395499\pi\)
−0.980990 + 0.194059i \(0.937835\pi\)
\(104\) 8.26076e7 + 4.68491e8i 0.0692421 + 0.392691i
\(105\) −1.45890e7 8.27386e7i −0.0117132 0.0664288i
\(106\) −7.95021e7 + 1.37702e8i −0.0611649 + 0.105941i
\(107\) −5.89639e8 1.02128e9i −0.434870 0.753216i 0.562415 0.826855i \(-0.309872\pi\)
−0.997285 + 0.0736385i \(0.976539\pi\)
\(108\) 5.22900e8 4.38765e8i 0.369838 0.310331i
\(109\) −1.26520e9 + 4.60496e8i −0.858501 + 0.312469i −0.733501 0.679688i \(-0.762115\pi\)
−0.125000 + 0.992157i \(0.539893\pi\)
\(110\) −1.77034e8 6.44349e7i −0.115289 0.0419618i
\(111\) −9.03589e8 7.58201e8i −0.564960 0.474058i
\(112\) 4.32537e7 2.45304e8i 0.0259742 0.147307i
\(113\) 1.67708e8 0.0967611 0.0483806 0.998829i \(-0.484594\pi\)
0.0483806 + 0.998829i \(0.484594\pi\)
\(114\) 1.03166e9 8.15750e8i 0.572093 0.452361i
\(115\) 2.74251e8 0.146220
\(116\) −9.92783e7 + 5.63035e8i −0.0509089 + 0.288719i
\(117\) −1.11800e8 9.38109e7i −0.0551574 0.0462825i
\(118\) 1.98171e9 + 7.21283e8i 0.940959 + 0.342481i
\(119\) 2.20991e9 8.04341e8i 1.01021 0.367688i
\(120\) 6.93582e7 5.81984e7i 0.0305339 0.0256210i
\(121\) −1.79181e9 3.10350e9i −0.759901 1.31619i
\(122\) −1.50246e7 + 2.60233e7i −0.00614020 + 0.0106351i
\(123\) −5.30570e8 3.00901e9i −0.209011 1.18536i
\(124\) −2.57601e8 1.46093e9i −0.0978474 0.554920i
\(125\) 2.96570e8 5.13675e8i 0.108651 0.188188i
\(126\) 3.82084e7 + 6.61789e7i 0.0135049 + 0.0233912i
\(127\) 3.11722e9 2.61566e9i 1.06329 0.892204i 0.0688597 0.997626i \(-0.478064\pi\)
0.994428 + 0.105422i \(0.0336195\pi\)
\(128\) 2.52247e8 9.18103e7i 0.0830579 0.0302306i
\(129\) 2.17175e9 + 7.90453e8i 0.690488 + 0.251317i
\(130\) 2.17452e8 + 1.82464e8i 0.0667757 + 0.0560315i
\(131\) −1.21058e8 + 6.86557e8i −0.0359149 + 0.203683i −0.997485 0.0708755i \(-0.977421\pi\)
0.961570 + 0.274559i \(0.0885318\pi\)
\(132\) 2.85545e9 0.818638
\(133\) −1.02471e9 1.90040e9i −0.283966 0.526637i
\(134\) −2.06275e9 −0.552681
\(135\) 7.07285e7 4.01121e8i 0.0183270 0.103938i
\(136\) 1.94147e9 + 1.62908e9i 0.486637 + 0.408337i
\(137\) 1.44789e9 + 5.26988e8i 0.351150 + 0.127808i 0.511572 0.859240i \(-0.329063\pi\)
−0.160422 + 0.987048i \(0.551286\pi\)
\(138\) −3.90606e9 + 1.42169e9i −0.916817 + 0.333694i
\(139\) −3.47463e9 + 2.91556e9i −0.789481 + 0.662454i −0.945617 0.325282i \(-0.894541\pi\)
0.156136 + 0.987736i \(0.450096\pi\)
\(140\) −7.43160e7 1.28719e8i −0.0163496 0.0283183i
\(141\) 4.21761e9 7.30511e9i 0.898629 1.55647i
\(142\) 1.85801e7 + 1.05373e8i 0.00383488 + 0.0217487i
\(143\) 1.55457e9 + 8.81641e9i 0.310884 + 1.76311i
\(144\) −4.11762e7 + 7.13192e7i −0.00798022 + 0.0138221i
\(145\) 1.70574e8 + 2.95443e8i 0.0320448 + 0.0555032i
\(146\) 1.43957e9 1.20794e9i 0.262208 0.220018i
\(147\) −3.52288e9 + 1.28222e9i −0.622258 + 0.226483i
\(148\) −1.96091e9 7.13714e8i −0.335955 0.122278i
\(149\) 6.14191e9 + 5.15367e9i 1.02086 + 0.856601i 0.989735 0.142914i \(-0.0456473\pi\)
0.0311225 + 0.999516i \(0.490092\pi\)
\(150\) −7.75862e8 + 4.40013e9i −0.125134 + 0.709668i
\(151\) −6.44872e9 −1.00943 −0.504716 0.863285i \(-0.668403\pi\)
−0.504716 + 0.863285i \(0.668403\pi\)
\(152\) 1.22148e9 1.98035e9i 0.185605 0.300917i
\(153\) −7.77521e8 −0.114710
\(154\) 8.13979e8 4.61631e9i 0.116619 0.661380i
\(155\) −6.78094e8 5.68989e8i −0.0943620 0.0791792i
\(156\) −4.04296e9 1.47152e9i −0.546562 0.198932i
\(157\) −6.92195e9 + 2.51938e9i −0.909243 + 0.330937i −0.753951 0.656931i \(-0.771854\pi\)
−0.155293 + 0.987869i \(0.549632\pi\)
\(158\) −2.12868e9 + 1.78618e9i −0.271740 + 0.228017i
\(159\) −7.19023e8 1.24538e9i −0.0892187 0.154531i
\(160\) 8.00884e7 1.38717e8i 0.00966117 0.0167336i
\(161\) 1.18493e9 + 6.72006e9i 0.138987 + 0.788237i
\(162\) 1.14073e9 + 6.46940e9i 0.130126 + 0.737983i
\(163\) 8.28538e8 1.43507e9i 0.0919323 0.159231i −0.816392 0.577498i \(-0.804029\pi\)
0.908324 + 0.418267i \(0.137362\pi\)
\(164\) −2.70270e9 4.68122e9i −0.291743 0.505315i
\(165\) 1.30523e9 1.09522e9i 0.137091 0.115033i
\(166\) −6.67408e9 + 2.42917e9i −0.682189 + 0.248297i
\(167\) −2.32838e9 8.47459e8i −0.231648 0.0843130i 0.223588 0.974684i \(-0.428223\pi\)
−0.455236 + 0.890371i \(0.650445\pi\)
\(168\) 1.72572e9 + 1.44805e9i 0.167140 + 0.140247i
\(169\) 5.00890e8 2.84069e9i 0.0472337 0.267876i
\(170\) 1.51229e9 0.138872
\(171\) 1.03461e8 + 7.06280e8i 0.00925328 + 0.0631676i
\(172\) 4.08865e9 0.356207
\(173\) 1.42537e9 8.08370e9i 0.120982 0.686124i −0.862631 0.505834i \(-0.831185\pi\)
0.983613 0.180291i \(-0.0577039\pi\)
\(174\) −3.96098e9 3.32365e9i −0.327590 0.274881i
\(175\) 6.89237e9 + 2.50862e9i 0.555517 + 0.202192i
\(176\) 4.74697e9 1.72775e9i 0.372914 0.135730i
\(177\) −1.46107e10 + 1.22599e10i −1.11890 + 0.938871i
\(178\) −8.90574e9 1.54252e10i −0.664937 1.15170i
\(179\) −1.01310e10 + 1.75475e10i −0.737591 + 1.27754i 0.215986 + 0.976396i \(0.430703\pi\)
−0.953577 + 0.301148i \(0.902630\pi\)
\(180\) 8.53308e6 + 4.83935e7i 0.000605870 + 0.00343606i
\(181\) 2.27515e7 + 1.29030e8i 0.00157563 + 0.00893587i 0.985585 0.169178i \(-0.0541114\pi\)
−0.984010 + 0.178114i \(0.943000\pi\)
\(182\) −3.53145e9 + 6.11665e9i −0.238579 + 0.413230i
\(183\) −1.35883e8 2.35357e8i −0.00895645 0.0155130i
\(184\) −5.63330e9 + 4.72690e9i −0.362312 + 0.304016i
\(185\) −1.17009e9 + 4.25877e8i −0.0734422 + 0.0267308i
\(186\) 1.26074e10 + 4.58873e9i 0.772357 + 0.281115i
\(187\) 3.65359e10 + 3.06573e10i 2.18491 + 1.83335i
\(188\) 2.59133e9 1.46961e10i 0.151291 0.858012i
\(189\) 1.01344e10 0.577723
\(190\) −2.01234e8 1.37373e9i −0.0112024 0.0764732i
\(191\) 2.69851e10 1.46715 0.733575 0.679609i \(-0.237850\pi\)
0.733575 + 0.679609i \(0.237850\pi\)
\(192\) −4.21574e8 + 2.39087e9i −0.0223882 + 0.126970i
\(193\) −1.99413e10 1.67328e10i −1.03454 0.868080i −0.0431539 0.999068i \(-0.513741\pi\)
−0.991384 + 0.130988i \(0.958185\pi\)
\(194\) 1.32386e10 + 4.81844e9i 0.671016 + 0.244230i
\(195\) −2.41246e9 + 8.78062e8i −0.119482 + 0.0434880i
\(196\) −5.08069e9 + 4.26320e9i −0.245906 + 0.206340i
\(197\) 9.85295e9 + 1.70658e10i 0.466088 + 0.807289i 0.999250 0.0387248i \(-0.0123296\pi\)
−0.533162 + 0.846013i \(0.678996\pi\)
\(198\) −7.74883e8 + 1.34214e9i −0.0358297 + 0.0620588i
\(199\) −4.91350e9 2.78659e10i −0.222102 1.25960i −0.868148 0.496305i \(-0.834690\pi\)
0.646046 0.763298i \(-0.276421\pi\)
\(200\) 1.37259e9 + 7.78434e9i 0.0606604 + 0.344022i
\(201\) 9.32782e9 1.61563e10i 0.403086 0.698166i
\(202\) −1.15452e10 1.99968e10i −0.487887 0.845045i
\(203\) −6.50236e9 + 5.45613e9i −0.268744 + 0.225503i
\(204\) −2.15390e10 + 7.83956e9i −0.870743 + 0.316925i
\(205\) −3.03092e9 1.10316e9i −0.119862 0.0436262i
\(206\) −1.84401e10 1.54731e10i −0.713446 0.598652i
\(207\) 3.91755e8 2.22175e9i 0.0148302 0.0841065i
\(208\) −7.61149e9 −0.281958
\(209\) 2.29866e10 3.72677e10i 0.833329 1.35106i
\(210\) 1.34424e9 0.0476968
\(211\) 1.02361e9 5.80520e9i 0.0355521 0.201626i −0.961858 0.273549i \(-0.911802\pi\)
0.997410 + 0.0719231i \(0.0229136\pi\)
\(212\) −1.94887e9 1.63529e9i −0.0662630 0.0556013i
\(213\) −9.09345e8 3.30975e8i −0.0302706 0.0110176i
\(214\) 1.77305e10 6.45339e9i 0.577910 0.210342i
\(215\) 1.86893e9 1.56822e9i 0.0596514 0.0500534i
\(216\) 5.46078e9 + 9.45835e9i 0.170692 + 0.295647i
\(217\) 1.10123e10 1.90739e10i 0.337140 0.583944i
\(218\) −3.74080e9 2.12151e10i −0.112179 0.636197i
\(219\) 2.95130e9 + 1.67377e10i 0.0866992 + 0.491695i
\(220\) 1.50716e9 2.61048e9i 0.0433768 0.0751309i
\(221\) −3.59316e10 6.22353e10i −1.01324 1.75498i
\(222\) 1.44574e10 1.21312e10i 0.399487 0.335209i
\(223\) −4.47969e9 + 1.63047e9i −0.121304 + 0.0441511i −0.401959 0.915658i \(-0.631671\pi\)
0.280655 + 0.959809i \(0.409448\pi\)
\(224\) 3.74506e9 + 1.36309e9i 0.0993900 + 0.0361750i
\(225\) −1.85763e9 1.55874e9i −0.0483213 0.0405464i
\(226\) −4.65955e8 + 2.64256e9i −0.0118811 + 0.0673810i
\(227\) 5.38600e10 1.34633 0.673163 0.739494i \(-0.264935\pi\)
0.673163 + 0.739494i \(0.264935\pi\)
\(228\) 9.98736e9 + 1.85223e10i 0.244762 + 0.453930i
\(229\) −6.83181e10 −1.64163 −0.820817 0.571192i \(-0.806481\pi\)
−0.820817 + 0.571192i \(0.806481\pi\)
\(230\) −7.61971e8 + 4.32135e9i −0.0179541 + 0.101823i
\(231\) 3.24759e10 + 2.72505e10i 0.750425 + 0.629681i
\(232\) −8.59587e9 3.12864e9i −0.194802 0.0709022i
\(233\) −3.99139e10 + 1.45275e10i −0.887201 + 0.322915i −0.745112 0.666939i \(-0.767604\pi\)
−0.142089 + 0.989854i \(0.545382\pi\)
\(234\) 1.78879e9 1.50097e9i 0.0390022 0.0327267i
\(235\) −4.45227e9 7.71156e9i −0.0952305 0.164944i
\(236\) −1.68711e10 + 2.92216e10i −0.354030 + 0.613198i
\(237\) −4.36407e9 2.47498e10i −0.0898512 0.509571i
\(238\) 6.53400e9 + 3.70561e10i 0.132003 + 0.748624i
\(239\) −3.28190e10 + 5.68442e10i −0.650632 + 1.12693i 0.332338 + 0.943160i \(0.392162\pi\)
−0.982970 + 0.183767i \(0.941171\pi\)
\(240\) 7.24325e8 + 1.25457e9i 0.0140923 + 0.0244086i
\(241\) 6.58118e9 5.52227e9i 0.125669 0.105449i −0.577787 0.816187i \(-0.696084\pi\)
0.703456 + 0.710739i \(0.251639\pi\)
\(242\) 5.38799e10 1.96107e10i 1.00985 0.367556i
\(243\) −6.51176e9 2.37009e9i −0.119804 0.0436049i
\(244\) −3.68303e8 3.09043e8i −0.00665198 0.00558168i
\(245\) −6.87224e8 + 3.89744e9i −0.0121857 + 0.0691086i
\(246\) 4.88869e10 0.851108
\(247\) −5.17517e10 + 4.09207e10i −0.884684 + 0.699530i
\(248\) 2.37354e10 0.398441
\(249\) 1.11542e10 6.32588e10i 0.183884 1.04286i
\(250\) 7.26995e9 + 6.10021e9i 0.117707 + 0.0987677i
\(251\) 9.22809e10 + 3.35875e10i 1.46751 + 0.534129i 0.947422 0.319986i \(-0.103678\pi\)
0.520084 + 0.854115i \(0.325900\pi\)
\(252\) −1.14893e9 + 4.18177e8i −0.0179470 + 0.00653218i
\(253\) −1.06012e11 + 8.89542e10i −1.62671 + 1.36497i
\(254\) 3.25539e10 + 5.63850e10i 0.490740 + 0.849987i
\(255\) −6.83864e9 + 1.18449e10i −0.101284 + 0.175428i
\(256\) 7.45813e8 + 4.22972e9i 0.0108530 + 0.0615505i
\(257\) 2.06346e9 + 1.17025e10i 0.0295051 + 0.167332i 0.996000 0.0893544i \(-0.0284804\pi\)
−0.966495 + 0.256686i \(0.917369\pi\)
\(258\) −1.84890e10 + 3.20239e10i −0.259792 + 0.449973i
\(259\) −1.54909e10 2.68310e10i −0.213908 0.370499i
\(260\) −3.47923e9 + 2.91942e9i −0.0472175 + 0.0396202i
\(261\) 2.63710e9 9.59824e8i 0.0351758 0.0128029i
\(262\) −1.04817e10 3.81502e9i −0.137428 0.0500197i
\(263\) −4.95225e10 4.15543e10i −0.638266 0.535569i 0.265219 0.964188i \(-0.414556\pi\)
−0.903485 + 0.428619i \(0.859000\pi\)
\(264\) −7.93350e9 + 4.49931e10i −0.100519 + 0.570070i
\(265\) −1.51806e9 −0.0189096
\(266\) 3.27914e10 1.08662e10i 0.401599 0.133079i
\(267\) 1.61088e11 1.93983
\(268\) 5.73108e9 3.25026e10i 0.0678625 0.384867i
\(269\) −3.15803e10 2.64990e10i −0.367732 0.308564i 0.440132 0.897933i \(-0.354932\pi\)
−0.807864 + 0.589370i \(0.799376\pi\)
\(270\) 6.12393e9 + 2.22893e9i 0.0701283 + 0.0255246i
\(271\) −1.40038e11 + 5.09698e10i −1.57719 + 0.574052i −0.974592 0.223989i \(-0.928092\pi\)
−0.602603 + 0.798041i \(0.705870\pi\)
\(272\) −3.10635e10 + 2.60653e10i −0.344104 + 0.288738i
\(273\) −3.19387e10 5.53194e10i −0.348005 0.602762i
\(274\) −1.23265e10 + 2.13501e10i −0.132118 + 0.228835i
\(275\) 2.58304e10 + 1.46491e11i 0.272354 + 1.54460i
\(276\) −1.15490e10 6.54974e10i −0.119799 0.679412i
\(277\) 3.25327e10 5.63483e10i 0.332018 0.575072i −0.650890 0.759172i \(-0.725604\pi\)
0.982907 + 0.184101i \(0.0589373\pi\)
\(278\) −3.62865e10 6.28500e10i −0.364370 0.631108i
\(279\) −5.57810e9 + 4.68058e9i −0.0551147 + 0.0462467i
\(280\) 2.23469e9 8.13362e8i 0.0217274 0.00790811i
\(281\) −2.42685e10 8.83302e9i −0.232201 0.0845144i 0.223299 0.974750i \(-0.428317\pi\)
−0.455500 + 0.890236i \(0.650540\pi\)
\(282\) 1.03388e11 + 8.67528e10i 0.973530 + 0.816888i
\(283\) 8.92577e9 5.06205e10i 0.0827193 0.469124i −0.915106 0.403213i \(-0.867893\pi\)
0.997825 0.0659114i \(-0.0209955\pi\)
\(284\) −1.71198e9 −0.0156159
\(285\) 1.16696e10 + 4.63590e9i 0.104774 + 0.0416229i
\(286\) −1.43239e11 −1.26594
\(287\) 1.39358e10 7.90338e10i 0.121245 0.687613i
\(288\) −1.00937e9 8.46961e8i −0.00864537 0.00725433i
\(289\) −2.48328e11 9.03839e10i −2.09404 0.762169i
\(290\) −5.12920e9 + 1.86688e9i −0.0425852 + 0.0154997i
\(291\) −9.76052e10 + 8.19005e10i −0.797911 + 0.669527i
\(292\) 1.50338e10 + 2.60393e10i 0.121017 + 0.209607i
\(293\) 6.56991e10 1.13794e11i 0.520781 0.902019i −0.478927 0.877855i \(-0.658974\pi\)
0.999708 0.0241646i \(-0.00769259\pi\)
\(294\) −1.04160e10 5.90723e10i −0.0813092 0.461127i
\(295\) 3.49626e9 + 1.98283e10i 0.0268785 + 0.152435i
\(296\) 1.66941e10 2.89150e10i 0.126401 0.218933i
\(297\) 1.02765e11 + 1.77994e11i 0.766374 + 1.32740i
\(298\) −9.82705e10 + 8.24588e10i −0.721855 + 0.605709i
\(299\) 1.95941e11 7.13166e10i 1.41776 0.516024i
\(300\) −6.71769e10 2.44504e10i −0.478822 0.174277i
\(301\) 4.65015e10 + 3.90194e10i 0.326526 + 0.273988i
\(302\) 1.79169e10 1.01612e11i 0.123946 0.702933i
\(303\) 2.08831e11 1.42332
\(304\) 2.78106e10 + 2.47488e10i 0.186758 + 0.166197i
\(305\) −2.86887e8 −0.00189829
\(306\) 2.16024e9 1.22513e10i 0.0140850 0.0798798i
\(307\) 8.67201e10 + 7.27668e10i 0.557182 + 0.467531i 0.877364 0.479825i \(-0.159300\pi\)
−0.320183 + 0.947356i \(0.603744\pi\)
\(308\) 7.04772e10 + 2.56516e10i 0.446242 + 0.162419i
\(309\) 2.04578e11 7.44604e10i 1.27658 0.464636i
\(310\) 1.08495e10 9.10382e9i 0.0667240 0.0559881i
\(311\) −9.42199e10 1.63194e11i −0.571111 0.989194i −0.996452 0.0841608i \(-0.973179\pi\)
0.425341 0.905033i \(-0.360154\pi\)
\(312\) 3.44195e10 5.96163e10i 0.205640 0.356180i
\(313\) −1.67444e10 9.49621e10i −0.0986097 0.559243i −0.993581 0.113120i \(-0.963916\pi\)
0.894972 0.446123i \(-0.147196\pi\)
\(314\) −2.04660e10 1.16068e11i −0.118809 0.673799i
\(315\) −3.64786e8 + 6.31828e8i −0.00208757 + 0.00361578i
\(316\) −2.22304e10 3.85041e10i −0.125417 0.217228i
\(317\) −7.69595e10 + 6.45767e10i −0.428051 + 0.359177i −0.831216 0.555950i \(-0.812355\pi\)
0.403165 + 0.915127i \(0.367910\pi\)
\(318\) 2.16211e10 7.86945e9i 0.118565 0.0431541i
\(319\) −1.61763e11 5.88771e10i −0.874626 0.318338i
\(320\) 1.96324e9 + 1.64735e9i 0.0104664 + 0.00878238i
\(321\) −2.96327e10 + 1.68055e11i −0.155775 + 0.883444i
\(322\) −1.09180e11 −0.565966
\(323\) −7.10734e10 + 3.44224e11i −0.363325 + 1.75967i
\(324\) −1.05107e11 −0.529883
\(325\) 3.89198e10 2.20725e11i 0.193506 1.09743i
\(326\) 2.03103e10 + 1.70424e10i 0.0995949 + 0.0835701i
\(327\) 1.83081e11 + 6.66362e10i 0.885481 + 0.322289i
\(328\) 8.12708e10 2.95801e10i 0.387706 0.141113i
\(329\) 1.69722e11 1.42414e11i 0.798652 0.670148i
\(330\) 1.36309e10 + 2.36094e10i 0.0632720 + 0.109590i
\(331\) 1.20412e11 2.08560e11i 0.551371 0.955003i −0.446805 0.894632i \(-0.647438\pi\)
0.998176 0.0603717i \(-0.0192286\pi\)
\(332\) −1.97331e10 1.11912e11i −0.0891403 0.505540i
\(333\) 1.77868e9 + 1.00874e10i 0.00792684 + 0.0449553i
\(334\) 1.98224e10 3.43335e10i 0.0871561 0.150959i
\(335\) −9.84681e9 1.70552e10i −0.0427163 0.0739869i
\(336\) −2.76116e10 + 2.31688e10i −0.118185 + 0.0991694i
\(337\) 3.23993e10 1.17924e10i 0.136836 0.0498042i −0.272694 0.962101i \(-0.587915\pi\)
0.409530 + 0.912296i \(0.365693\pi\)
\(338\) 4.33688e10 + 1.57850e10i 0.180739 + 0.0657837i
\(339\) −1.85905e10 1.55993e10i −0.0764528 0.0641515i
\(340\) −4.20171e9 + 2.38291e10i −0.0170518 + 0.0967056i
\(341\) 4.46670e11 1.78892
\(342\) −1.14163e10 3.32075e8i −0.0451238 0.00131256i
\(343\) −2.51845e11 −0.982447
\(344\) −1.13598e10 + 6.44245e10i −0.0437378 + 0.248050i
\(345\) −3.04009e10 2.55094e10i −0.115532 0.0969424i
\(346\) 1.23414e11 + 4.49190e10i 0.462937 + 0.168495i
\(347\) −2.34467e11 + 8.53391e10i −0.868159 + 0.315984i −0.737421 0.675433i \(-0.763957\pi\)
−0.130738 + 0.991417i \(0.541735\pi\)
\(348\) 6.33756e10 5.31785e10i 0.231641 0.194370i
\(349\) 6.18443e10 + 1.07117e11i 0.223144 + 0.386497i 0.955761 0.294145i \(-0.0950347\pi\)
−0.732617 + 0.680641i \(0.761701\pi\)
\(350\) −5.86777e10 + 1.01633e11i −0.209010 + 0.362016i
\(351\) −5.37756e10 3.04976e11i −0.189105 1.07247i
\(352\) 1.40353e10 + 7.95979e10i 0.0487280 + 0.276350i
\(353\) −2.35976e11 + 4.08723e11i −0.808877 + 1.40102i 0.104765 + 0.994497i \(0.466591\pi\)
−0.913642 + 0.406519i \(0.866742\pi\)
\(354\) −1.52584e11 2.64283e11i −0.516409 0.894446i
\(355\) −7.82551e8 + 6.56638e8i −0.00261508 + 0.00219431i
\(356\) 2.67797e11 9.74702e10i 0.883652 0.321623i
\(357\) −3.19785e11 1.16392e11i −1.04196 0.379243i
\(358\) −2.48347e11 2.08387e11i −0.799069 0.670499i
\(359\) −4.76351e10 + 2.70152e11i −0.151357 + 0.858387i 0.810685 + 0.585483i \(0.199095\pi\)
−0.962041 + 0.272904i \(0.912016\pi\)
\(360\) −7.86240e8 −0.00246714
\(361\) 3.22142e11 + 1.87568e10i 0.998309 + 0.0581267i
\(362\) −2.09633e9 −0.00641609
\(363\) −9.00483e10 + 5.10689e11i −0.272205 + 1.54375i
\(364\) −8.65679e10 7.26391e10i −0.258464 0.216877i
\(365\) 1.68595e10 + 6.13635e9i 0.0497195 + 0.0180964i
\(366\) 4.08603e9 1.48719e9i 0.0119025 0.00433214i
\(367\) −1.04354e11 + 8.75637e10i −0.300271 + 0.251957i −0.780457 0.625209i \(-0.785014\pi\)
0.480186 + 0.877167i \(0.340569\pi\)
\(368\) −5.88300e10 1.01897e11i −0.167218 0.289630i
\(369\) −1.32664e10 + 2.29782e10i −0.0372508 + 0.0645203i
\(370\) −3.45957e9 1.96202e10i −0.00959654 0.0544247i
\(371\) −6.55891e9 3.71974e10i −0.0179742 0.101937i
\(372\) −1.07332e11 + 1.85905e11i −0.290595 + 0.503324i
\(373\) −6.63167e8 1.14864e9i −0.00177392 0.00307251i 0.865137 0.501535i \(-0.167231\pi\)
−0.866911 + 0.498463i \(0.833898\pi\)
\(374\) −5.84575e11 + 4.90517e11i −1.54496 + 1.29638i
\(375\) −8.06543e10 + 2.93558e10i −0.210614 + 0.0766571i
\(376\) 2.24366e11 + 8.16627e10i 0.578912 + 0.210707i
\(377\) 1.98696e11 + 1.66725e11i 0.506585 + 0.425075i
\(378\) −2.81571e10 + 1.59687e11i −0.0709373 + 0.402305i
\(379\) 2.54618e11 0.633887 0.316944 0.948444i \(-0.397343\pi\)
0.316944 + 0.948444i \(0.397343\pi\)
\(380\) 2.22048e10 + 6.45892e8i 0.0546287 + 0.00158904i
\(381\) −5.88840e11 −1.43164
\(382\) −7.49747e10 + 4.25203e11i −0.180148 + 1.02167i
\(383\) −1.56894e11 1.31649e11i −0.372572 0.312625i 0.437206 0.899361i \(-0.355968\pi\)
−0.809778 + 0.586736i \(0.800413\pi\)
\(384\) −3.65014e10 1.32854e10i −0.0856681 0.0311807i
\(385\) 4.20541e10 1.53064e10i 0.0975518 0.0355059i
\(386\) 3.19061e11 2.67724e11i 0.731529 0.613826i
\(387\) −1.00347e10 1.73807e10i −0.0227408 0.0393883i
\(388\) −1.12705e11 + 1.95211e11i −0.252465 + 0.437283i
\(389\) 1.21371e11 + 6.88329e11i 0.268746 + 1.52413i 0.758152 + 0.652077i \(0.226102\pi\)
−0.489407 + 0.872056i \(0.662787\pi\)
\(390\) −7.13286e9 4.04525e10i −0.0156125 0.0885430i
\(391\) 5.55437e11 9.62045e11i 1.20182 2.08161i
\(392\) −5.30589e10 9.19007e10i −0.113494 0.196577i
\(393\) 7.72793e10 6.48450e10i 0.163417 0.137123i
\(394\) −2.96280e11 + 1.07837e11i −0.619397 + 0.225442i
\(395\) −2.49300e10 9.07378e9i −0.0515271 0.0187543i
\(396\) −1.89950e10 1.59387e10i −0.0388161 0.0325706i
\(397\) −1.59307e11 + 9.03476e11i −0.321868 + 1.82541i 0.208958 + 0.977925i \(0.432993\pi\)
−0.530826 + 0.847481i \(0.678118\pi\)
\(398\) 4.52732e11 0.904414
\(399\) −6.31754e10 + 3.05973e11i −0.124787 + 0.604373i
\(400\) −1.26471e11 −0.247013
\(401\) 6.46124e10 3.66435e11i 0.124786 0.707697i −0.856649 0.515900i \(-0.827458\pi\)
0.981435 0.191797i \(-0.0614314\pi\)
\(402\) 2.28657e11 + 1.91866e11i 0.436684 + 0.366421i
\(403\) −6.32430e11 2.30186e11i −1.19437 0.434716i
\(404\) 3.47165e11 1.26358e11i 0.648366 0.235986i
\(405\) −4.80448e10 + 4.03143e10i −0.0887357 + 0.0744581i
\(406\) −6.79058e10 1.17616e11i −0.124034 0.214833i
\(407\) 3.14162e11 5.44144e11i 0.567516 0.982967i
\(408\) −6.36840e10 3.61170e11i −0.113778 0.645269i
\(409\) −1.33811e11 7.58878e11i −0.236448 1.34096i −0.839542 0.543294i \(-0.817177\pi\)
0.603094 0.797670i \(-0.293934\pi\)
\(410\) 2.58035e10 4.46929e10i 0.0450973 0.0781108i
\(411\) −1.11482e11 1.93092e11i −0.192715 0.333792i
\(412\) 2.95042e11 2.47570e11i 0.504483 0.423311i
\(413\) −4.70752e11 + 1.71340e11i −0.796191 + 0.289790i
\(414\) 3.39196e10 + 1.23457e10i 0.0567478 + 0.0206545i
\(415\) −5.19444e10 4.35866e10i −0.0859652 0.0721333i
\(416\) 2.11476e10 1.19934e11i 0.0346210 0.196346i
\(417\) 6.56355e11 1.06298
\(418\) 5.23360e11 + 4.65742e11i 0.838507 + 0.746195i
\(419\) 5.19703e11 0.823744 0.411872 0.911242i \(-0.364875\pi\)
0.411872 + 0.911242i \(0.364875\pi\)
\(420\) −3.73479e9 + 2.11811e10i −0.00585659 + 0.0332144i
\(421\) 4.07598e11 + 3.42016e11i 0.632358 + 0.530611i 0.901661 0.432444i \(-0.142349\pi\)
−0.269303 + 0.963056i \(0.586793\pi\)
\(422\) 8.86281e10 + 3.22580e10i 0.136040 + 0.0495144i
\(423\) −6.88326e10 + 2.50530e10i −0.104535 + 0.0380477i
\(424\) 3.11819e10 2.61647e10i 0.0468550 0.0393160i
\(425\) −5.97030e11 1.03409e12i −0.887659 1.53747i
\(426\) 7.74164e9 1.34089e10i 0.0113891 0.0197265i
\(427\) −1.23952e9 7.02968e9i −0.00180438 0.0102332i
\(428\) 5.24235e10 + 2.97309e11i 0.0755143 + 0.428263i
\(429\) 6.47731e11 1.12190e12i 0.923287 1.59918i
\(430\) 1.95177e10 + 3.38057e10i 0.0275310 + 0.0476850i
\(431\) −8.56451e11 + 7.18648e11i −1.19552 + 1.00316i −0.195768 + 0.980650i \(0.562720\pi\)
−0.999747 + 0.0225060i \(0.992836\pi\)
\(432\) −1.64207e11 + 5.97663e10i −0.226837 + 0.0825619i
\(433\) −1.24915e11 4.54654e10i −0.170773 0.0621563i 0.255219 0.966883i \(-0.417853\pi\)
−0.425992 + 0.904727i \(0.640075\pi\)
\(434\) 2.69950e11 + 2.26515e11i 0.365241 + 0.306474i
\(435\) 8.57231e9 4.86160e10i 0.0114788 0.0650995i
\(436\) 3.44679e11 0.456799
\(437\) −9.47806e11 3.76529e11i −1.24323 0.493893i
\(438\) −2.71934e11 −0.353045
\(439\) −6.33839e10 + 3.59468e11i −0.0814495 + 0.461923i 0.916617 + 0.399767i \(0.130909\pi\)
−0.998066 + 0.0621564i \(0.980202\pi\)
\(440\) 3.69457e10 + 3.10011e10i 0.0469923 + 0.0394312i
\(441\) 3.05922e10 + 1.11346e10i 0.0385156 + 0.0140185i
\(442\) 1.08047e12 3.93258e11i 1.34652 0.490092i
\(443\) −1.25632e11 + 1.05418e11i −0.154982 + 0.130046i −0.716982 0.697092i \(-0.754477\pi\)
0.561999 + 0.827138i \(0.310032\pi\)
\(444\) 1.50983e11 + 2.61510e11i 0.184376 + 0.319348i
\(445\) 8.50256e10 1.47269e11i 0.102785 0.178029i
\(446\) −1.32450e10 7.51161e10i −0.0158506 0.0898931i
\(447\) −2.01467e11 1.14258e12i −0.238682 1.35363i
\(448\) −3.18833e10 + 5.52234e10i −0.0373948 + 0.0647698i
\(449\) 6.75352e11 + 1.16974e12i 0.784191 + 1.35826i 0.929481 + 0.368869i \(0.120255\pi\)
−0.145290 + 0.989389i \(0.546412\pi\)
\(450\) 2.97221e10 2.49398e10i 0.0341683 0.0286706i
\(451\) 1.52941e12 5.56661e11i 1.74073 0.633572i
\(452\) −4.03441e10 1.46840e10i −0.0454628 0.0165471i
\(453\) 7.14844e11 + 5.99826e11i 0.797572 + 0.669242i
\(454\) −1.49643e11 + 8.48669e11i −0.165312 + 0.937534i
\(455\) −6.74314e10 −0.0737583
\(456\) −3.19603e11 + 1.05908e11i −0.346154 + 0.114706i
\(457\) −6.79784e11 −0.729035 −0.364517 0.931197i \(-0.618766\pi\)
−0.364517 + 0.931197i \(0.618766\pi\)
\(458\) 1.89813e11 1.07648e12i 0.201573 1.14317i
\(459\) −1.26385e12 1.06049e12i −1.32904 1.11520i
\(460\) −6.59742e10 2.40126e10i −0.0687011 0.0250052i
\(461\) −1.17574e12 + 4.27935e11i −1.21243 + 0.441289i −0.867547 0.497356i \(-0.834304\pi\)
−0.344885 + 0.938645i \(0.612082\pi\)
\(462\) −5.19614e11 + 4.36008e11i −0.530631 + 0.445252i
\(463\) −2.15210e11 3.72755e11i −0.217645 0.376972i 0.736443 0.676500i \(-0.236504\pi\)
−0.954087 + 0.299528i \(0.903171\pi\)
\(464\) 7.31803e10 1.26752e11i 0.0732931 0.126947i
\(465\) 2.22428e10 + 1.26145e11i 0.0220624 + 0.125122i
\(466\) −1.18013e11 6.69283e11i −0.115929 0.657465i
\(467\) 1.93337e11 3.34869e11i 0.188100 0.325799i −0.756517 0.653974i \(-0.773100\pi\)
0.944617 + 0.328176i \(0.106434\pi\)
\(468\) 1.86808e10 + 3.23561e10i 0.0180007 + 0.0311781i
\(469\) 3.75364e11 3.14968e11i 0.358241 0.300600i
\(470\) 1.33881e11 4.87285e10i 0.126554 0.0460620i
\(471\) 1.00164e12 + 3.64568e11i 0.937818 + 0.341338i
\(472\) −4.13569e11 3.47025e11i −0.383538 0.321827i
\(473\) −2.13777e11 + 1.21239e12i −0.196375 + 1.11370i
\(474\) 4.02106e11 0.365880
\(475\) −8.59893e11 + 6.79928e11i −0.775038 + 0.612832i
\(476\) −6.02045e11 −0.537524
\(477\) −2.16848e9 + 1.22980e10i −0.00191788 + 0.0108769i
\(478\) −8.04507e11 6.75061e11i −0.704862 0.591449i
\(479\) 7.28336e11 + 2.65092e11i 0.632152 + 0.230085i 0.638168 0.769897i \(-0.279693\pi\)
−0.00601553 + 0.999982i \(0.501915\pi\)
\(480\) −2.17806e10 + 7.92748e9i −0.0187277 + 0.00681632i
\(481\) −7.25232e11 + 6.08542e11i −0.617766 + 0.518367i
\(482\) 6.87290e10 + 1.19042e11i 0.0580001 + 0.100459i
\(483\) 4.93714e11 8.55138e11i 0.412775 0.714948i
\(484\) 1.59306e11 + 9.03468e11i 0.131955 + 0.748357i
\(485\) 2.33563e10 + 1.32460e11i 0.0191676 + 0.108705i
\(486\) 5.54373e10 9.60203e10i 0.0450753 0.0780728i
\(487\) −6.32573e11 1.09565e12i −0.509601 0.882654i −0.999938 0.0111217i \(-0.996460\pi\)
0.490337 0.871533i \(-0.336874\pi\)
\(488\) 5.89285e9 4.94469e9i 0.00470366 0.00394684i
\(489\) −2.25327e11 + 8.20122e10i −0.178206 + 0.0648617i
\(490\) −5.95023e10 2.16571e10i −0.0466285 0.0169714i
\(491\) −4.34946e11 3.64963e11i −0.337729 0.283389i 0.458111 0.888895i \(-0.348526\pi\)
−0.795841 + 0.605506i \(0.792971\pi\)
\(492\) −1.35826e11 + 7.70307e11i −0.104506 + 0.592681i
\(493\) 1.38185e12 1.05354
\(494\) −5.00999e11 9.29140e11i −0.378500 0.701956i
\(495\) −1.47960e10 −0.0110770
\(496\) −6.59457e10 + 3.73997e11i −0.0489237 + 0.277460i
\(497\) −1.94709e10 1.63380e10i −0.0143147 0.0120115i
\(498\) 9.65774e11 + 3.51513e11i 0.703629 + 0.256100i
\(499\) 9.42337e11 3.42983e11i 0.680383 0.247639i 0.0213713 0.999772i \(-0.493197\pi\)
0.659012 + 0.752132i \(0.270975\pi\)
\(500\) −1.16319e11 + 9.76034e10i −0.0832312 + 0.0698393i
\(501\) 1.79276e11 + 3.10515e11i 0.127131 + 0.220197i
\(502\) −7.85626e11 + 1.36074e12i −0.552140 + 0.956335i
\(503\) 2.96252e11 + 1.68013e12i 0.206350 + 1.17027i 0.895300 + 0.445463i \(0.146961\pi\)
−0.688950 + 0.724809i \(0.741928\pi\)
\(504\) −3.39703e9 1.92655e10i −0.00234510 0.0132997i
\(505\) 1.10225e11 1.90915e11i 0.0754169 0.130626i
\(506\) −1.10711e12 1.91756e12i −0.750778 1.30039i
\(507\) −3.19750e11 + 2.68302e11i −0.214919 + 0.180338i
\(508\) −9.78902e11 + 3.56291e11i −0.652157 + 0.237366i
\(509\) 2.15279e12 + 7.83553e11i 1.42158 + 0.517414i 0.934507 0.355945i \(-0.115841\pi\)
0.487076 + 0.873359i \(0.338063\pi\)
\(510\) −1.67638e11 1.40665e11i −0.109726 0.0920707i
\(511\) −7.75179e10 + 4.39626e11i −0.0502931 + 0.285226i
\(512\) −6.87195e10 −0.0441942
\(513\) −7.95151e11 + 1.28916e12i −0.506899 + 0.821825i
\(514\) −1.90128e11 −0.120147
\(515\) 3.99080e10 2.26329e11i 0.0249992 0.141778i
\(516\) −4.53229e11 3.80305e11i −0.281446 0.236161i
\(517\) 4.22229e12 + 1.53679e12i 2.59921 + 0.946034i
\(518\) 4.65813e11 1.69542e11i 0.284268 0.103465i
\(519\) −9.09907e11 + 7.63503e11i −0.550483 + 0.461910i
\(520\) −3.63345e10 6.29332e10i −0.0217924 0.0377455i
\(521\) −6.06240e11 + 1.05004e12i −0.360475 + 0.624361i −0.988039 0.154204i \(-0.950719\pi\)
0.627564 + 0.778565i \(0.284052\pi\)
\(522\) 7.79705e9 + 4.42193e10i 0.00459635 + 0.0260672i
\(523\) 2.90285e11 + 1.64629e12i 0.169655 + 0.962162i 0.944134 + 0.329562i \(0.106901\pi\)
−0.774479 + 0.632600i \(0.781988\pi\)
\(524\) 8.92350e10 1.54559e11i 0.0517064 0.0895581i
\(525\) −5.30685e11 9.19174e11i −0.304874 0.528057i
\(526\) 7.92360e11 6.64869e11i 0.451322 0.378704i
\(527\) −3.36929e12 + 1.22632e12i −1.90279 + 0.692558i
\(528\) −6.86911e11 2.50015e11i −0.384634 0.139995i
\(529\) 1.08941e12 + 9.14123e11i 0.604840 + 0.507521i
\(530\) 4.21773e9 2.39199e10i 0.00232186 0.0131679i
\(531\) 1.65627e11 0.0904075
\(532\) 8.01115e10 + 5.46882e11i 0.0433603 + 0.296000i
\(533\) −2.45233e12 −1.31615
\(534\) −4.47563e11 + 2.53826e12i −0.238188 + 1.35083i
\(535\) 1.37997e11 + 1.15793e11i 0.0728245 + 0.0611070i
\(536\) 4.96217e11 + 1.80608e11i 0.259675 + 0.0945140i
\(537\) 2.75521e12 1.00281e12i 1.42978 0.520398i
\(538\) 5.05285e11 4.23985e11i 0.260026 0.218188i
\(539\) −9.98501e11 1.72946e12i −0.509565 0.882592i
\(540\) −5.21356e10 + 9.03015e10i −0.0263853 + 0.0457007i
\(541\) 4.02894e11 + 2.28492e12i 0.202210 + 1.14679i 0.901770 + 0.432216i \(0.142268\pi\)
−0.699560 + 0.714574i \(0.746621\pi\)
\(542\) −4.14049e11 2.34819e12i −0.206089 1.16879i
\(543\) 9.47967e9 1.64193e10i 0.00467944 0.00810503i
\(544\) −3.24404e11 5.61884e11i −0.158815 0.275075i
\(545\) 1.57553e11 1.32203e11i 0.0764968 0.0641885i
\(546\) 9.60401e11 3.49558e11i 0.462473 0.168326i
\(547\) −1.16453e11 4.23854e10i −0.0556170 0.0202429i 0.314062 0.949403i \(-0.398310\pi\)
−0.369679 + 0.929160i \(0.620532\pi\)
\(548\) −3.02164e11 2.53546e11i −0.143130 0.120100i
\(549\) −4.09805e8 + 2.32412e9i −0.000192532 + 0.00109190i
\(550\) −2.38002e12 −1.10904
\(551\) −1.83877e11 1.25523e12i −0.0849853 0.580153i
\(552\) 1.06413e12 0.487828
\(553\) 1.14625e11 6.50072e11i 0.0521215 0.295596i
\(554\) 7.97488e11 + 6.69172e11i 0.359692 + 0.301817i
\(555\) 1.69318e11 + 6.16266e10i 0.0757502 + 0.0275708i
\(556\) 1.09114e12 3.97142e11i 0.484221 0.176242i
\(557\) −1.59843e12 + 1.34124e12i −0.703631 + 0.590417i −0.922804 0.385269i \(-0.874109\pi\)
0.219173 + 0.975686i \(0.429664\pi\)
\(558\) −5.82536e10 1.00898e11i −0.0254372 0.0440584i
\(559\) 9.27470e11 1.60643e12i 0.401742 0.695837i
\(560\) 6.60728e9 + 3.74717e10i 0.00283907 + 0.0161012i
\(561\) −1.19845e12 6.79676e12i −0.510843 2.89714i
\(562\) 2.06608e11 3.57856e11i 0.0873643 0.151319i
\(563\) −1.72469e12 2.98725e12i −0.723474 1.25309i −0.959599 0.281371i \(-0.909211\pi\)
0.236125 0.971723i \(-0.424123\pi\)
\(564\) −1.65421e12 + 1.38805e12i −0.688389 + 0.577627i
\(565\) −2.40735e10 + 8.76204e9i −0.00993851 + 0.00361732i
\(566\) 7.72825e11 + 2.81285e11i 0.316524 + 0.115205i
\(567\) −1.19542e12 1.00307e12i −0.485731 0.407576i
\(568\) 4.75652e9 2.69756e10i 0.00191744 0.0108743i
\(569\) 1.61826e12 0.647209 0.323604 0.946193i \(-0.395105\pi\)
0.323604 + 0.946193i \(0.395105\pi\)
\(570\) −1.05470e11 + 1.70996e11i −0.0418496 + 0.0678500i
\(571\) −5.66241e11 −0.222915 −0.111457 0.993769i \(-0.535552\pi\)
−0.111457 + 0.993769i \(0.535552\pi\)
\(572\) 3.97970e11 2.25700e12i 0.155442 0.881555i
\(573\) −2.99132e12 2.51001e12i −1.15922 0.972703i
\(574\) 1.20661e12 + 4.39170e11i 0.463942 + 0.168861i
\(575\) 3.25570e12 1.18498e12i 1.24205 0.452070i
\(576\) 1.61499e10 1.35514e10i 0.00611320 0.00512958i
\(577\) 8.40582e11 + 1.45593e12i 0.315710 + 0.546827i 0.979588 0.201015i \(-0.0644238\pi\)
−0.663878 + 0.747841i \(0.731091\pi\)
\(578\) 2.11412e12 3.66176e12i 0.787870 1.36463i
\(579\) 6.54116e11 + 3.70968e12i 0.241881 + 1.37177i
\(580\) −1.51654e10 8.60073e10i −0.00556452 0.0315580i
\(581\) 8.43584e11 1.46113e12i 0.307140 0.531981i
\(582\) −1.01932e12 1.76551e12i −0.368261 0.637846i
\(583\) 5.86804e11 4.92387e11i 0.210370 0.176522i
\(584\) −4.52069e11 + 1.64540e11i −0.160823 + 0.0585346i
\(585\) 2.09494e10 + 7.62495e9i 0.00739554 + 0.00269176i
\(586\) 1.61051e12 + 1.35138e12i 0.564189 + 0.473410i
\(587\) −2.42874e11 + 1.37740e12i −0.0844323 + 0.478840i 0.913045 + 0.407858i \(0.133724\pi\)
−0.997478 + 0.0709814i \(0.977387\pi\)
\(588\) 9.59738e11 0.331096
\(589\) 1.56230e12 + 2.89739e12i 0.534865 + 0.991948i
\(590\) −3.22147e11 −0.109451
\(591\) 4.95166e11 2.80822e12i 0.166958 0.946865i
\(592\) 4.09229e11 + 3.43384e11i 0.136936 + 0.114903i
\(593\) 2.47873e12 + 9.02182e11i 0.823156 + 0.299604i 0.719047 0.694961i \(-0.244579\pi\)
0.104109 + 0.994566i \(0.466801\pi\)
\(594\) −3.09016e12 + 1.12473e12i −1.01845 + 0.370687i
\(595\) −2.75196e11 + 2.30917e11i −0.0900152 + 0.0755317i
\(596\) −1.02626e12 1.77754e12i −0.333159 0.577048i
\(597\) −2.04727e12 + 3.54598e12i −0.659615 + 1.14249i
\(598\) 5.79334e11 + 3.28557e12i 0.185257 + 1.05064i
\(599\) 3.12058e11 + 1.76977e12i 0.0990408 + 0.561689i 0.993434 + 0.114407i \(0.0364967\pi\)
−0.894393 + 0.447282i \(0.852392\pi\)
\(600\) 5.71905e11 9.90569e11i 0.180154 0.312036i
\(601\) −2.32143e12 4.02084e12i −0.725807 1.25713i −0.958641 0.284618i \(-0.908133\pi\)
0.232834 0.972517i \(-0.425200\pi\)
\(602\) −7.44024e11 + 6.24310e11i −0.230889 + 0.193739i
\(603\) −1.52233e11 + 5.54082e10i −0.0468900 + 0.0170666i
\(604\) 1.55131e12 + 5.64631e11i 0.474278 + 0.172623i
\(605\) 4.19348e11 + 3.51875e11i 0.127255 + 0.106780i
\(606\) −5.80210e11 + 3.29053e12i −0.174766 + 0.991150i
\(607\) 3.92196e12 1.17261 0.586305 0.810090i \(-0.300582\pi\)
0.586305 + 0.810090i \(0.300582\pi\)
\(608\) −4.67234e11 + 3.69447e11i −0.138665 + 0.109644i
\(609\) 1.22829e12 0.361846
\(610\) 7.97079e8 4.52046e9i 0.000233086 0.00132190i
\(611\) −5.18628e12 4.35181e12i −1.50546 1.26324i
\(612\) 1.87041e11 + 6.80775e10i 0.0538960 + 0.0196165i
\(613\) −1.07126e12 + 3.89908e11i −0.306425 + 0.111529i −0.490656 0.871353i \(-0.663243\pi\)
0.184231 + 0.982883i \(0.441021\pi\)
\(614\) −1.38752e12 + 1.16427e12i −0.393987 + 0.330594i
\(615\) 2.33368e11 + 4.04206e11i 0.0657816 + 0.113937i
\(616\) −6.00003e11 + 1.03923e12i −0.167896 + 0.290804i
\(617\) 5.82794e11 + 3.30519e12i 0.161894 + 0.918149i 0.952209 + 0.305448i \(0.0988061\pi\)
−0.790314 + 0.612701i \(0.790083\pi\)
\(618\) 6.04873e11 + 3.43040e12i 0.166808 + 0.946013i
\(619\) 2.84446e12 4.92675e12i 0.778739 1.34882i −0.153930 0.988082i \(-0.549193\pi\)
0.932669 0.360733i \(-0.117474\pi\)
\(620\) 1.13304e11 + 1.96249e11i 0.0307952 + 0.0533389i
\(621\) 3.66714e12 3.07710e12i 0.989499 0.830288i
\(622\) 2.83321e12 1.03120e12i 0.758965 0.276241i
\(623\) 3.97593e12 + 1.44712e12i 1.05741 + 0.384865i
\(624\) 8.43739e11 + 7.07981e11i 0.222781 + 0.186935i
\(625\) 6.38768e11 3.62263e12i 0.167449 0.949651i
\(626\) 1.54283e12 0.401545
\(627\) −6.01453e12 + 1.99306e12i −1.55417 + 0.515011i
\(628\) 1.88574e12 0.483798
\(629\) −8.75828e11 + 4.96707e12i −0.223096 + 1.26524i
\(630\) −8.94216e9 7.50336e9i −0.00226157 0.00189768i
\(631\) 1.42636e12 + 5.19152e11i 0.358176 + 0.130365i 0.514839 0.857287i \(-0.327852\pi\)
−0.156663 + 0.987652i \(0.550074\pi\)
\(632\) 6.68471e11 2.43304e11i 0.166669 0.0606627i
\(633\) −6.53437e11 + 5.48299e11i −0.161766 + 0.135738i
\(634\) −8.03708e11 1.39206e12i −0.197559 0.342182i
\(635\) −3.10801e11 + 5.38324e11i −0.0758580 + 0.131390i
\(636\) 6.39268e10 + 3.62547e11i 0.0154927 + 0.0878632i
\(637\) 5.22503e11 + 2.96326e12i 0.125736 + 0.713087i
\(638\) 1.37716e12 2.38531e12i 0.329072 0.569970i
\(639\) 4.20170e9 + 7.27755e9i 0.000996945 + 0.00172676i
\(640\) −3.14118e10 + 2.63577e10i −0.00740088 + 0.00621008i
\(641\) −2.51469e12 + 9.15274e11i −0.588334 + 0.214136i −0.618996 0.785394i \(-0.712460\pi\)
0.0306626 + 0.999530i \(0.490238\pi\)
\(642\) −2.56570e12 9.33839e11i −0.596072 0.216952i
\(643\) 3.72399e12 + 3.12480e12i 0.859131 + 0.720896i 0.961781 0.273821i \(-0.0882877\pi\)
−0.102650 + 0.994718i \(0.532732\pi\)
\(644\) 3.03341e11 1.72033e12i 0.0694937 0.394118i
\(645\) −3.53040e11 −0.0803165
\(646\) −5.22645e12 2.07628e12i −1.18076 0.469072i
\(647\) −5.71182e12 −1.28146 −0.640730 0.767766i \(-0.721368\pi\)
−0.640730 + 0.767766i \(0.721368\pi\)
\(648\) 2.92027e11 1.65617e12i 0.0650632 0.368992i
\(649\) −7.78284e12 6.53058e12i −1.72202 1.44494i
\(650\) 3.36981e12 + 1.22651e12i 0.740450 + 0.269502i
\(651\) −2.99488e12 + 1.09005e12i −0.653529 + 0.237865i
\(652\) −3.24965e11 + 2.72678e11i −0.0704242 + 0.0590930i
\(653\) −2.58899e12 4.48426e12i −0.557213 0.965121i −0.997728 0.0673757i \(-0.978537\pi\)
0.440515 0.897745i \(-0.354796\pi\)
\(654\) −1.55865e12 + 2.69966e12i −0.333157 + 0.577044i
\(655\) −1.84925e10 1.04876e11i −0.00392563 0.0222633i
\(656\) 2.40292e11 + 1.36276e12i 0.0506607 + 0.287311i
\(657\) 7.37947e10 1.27816e11i 0.0154519 0.0267634i
\(658\) 1.77245e12 + 3.06998e12i 0.368603 + 0.638438i
\(659\) −2.07503e12 + 1.74116e12i −0.428588 + 0.359628i −0.831419 0.555647i \(-0.812471\pi\)
0.402831 + 0.915274i \(0.368026\pi\)
\(660\) −4.09883e11 + 1.49185e11i −0.0840837 + 0.0306040i
\(661\) −4.25298e12 1.54796e12i −0.866537 0.315394i −0.129773 0.991544i \(-0.541425\pi\)
−0.736764 + 0.676150i \(0.763647\pi\)
\(662\) 2.95171e12 + 2.47678e12i 0.597328 + 0.501218i
\(663\) −1.80576e12 + 1.02410e13i −0.362952 + 2.05840i
\(664\) 1.81822e12 0.362985
\(665\) 2.46378e11 + 2.19254e11i 0.0488545 + 0.0434760i
\(666\) −1.63889e11 −0.0322786
\(667\) −6.96247e11 + 3.94861e12i −0.136206 + 0.772464i
\(668\) 4.85916e11 + 4.07732e11i 0.0944206 + 0.0792283i
\(669\) 6.48234e11 + 2.35938e11i 0.125116 + 0.0455386i
\(670\) 2.96095e11 1.07770e11i 0.0567669 0.0206614i
\(671\) 1.10896e11 9.30528e10i 0.0211186 0.0177206i
\(672\) −2.88355e11 4.99445e11i −0.0545463 0.0944769i
\(673\) 4.28381e12 7.41977e12i 0.804937 1.39419i −0.111396 0.993776i \(-0.535532\pi\)
0.916333 0.400416i \(-0.131134\pi\)
\(674\) 9.57942e10 + 5.43276e11i 0.0178801 + 0.101403i
\(675\) −8.93522e11 5.06741e12i −0.165668 0.939549i
\(676\) −3.69217e11 + 6.39503e11i −0.0680020 + 0.117783i
\(677\) −4.14970e11 7.18748e11i −0.0759219 0.131501i 0.825565 0.564307i \(-0.190857\pi\)
−0.901487 + 0.432807i \(0.857523\pi\)
\(678\) 2.97449e11 2.49589e11i 0.0540603 0.0453620i
\(679\) −3.14480e12 + 1.14461e12i −0.567779 + 0.206655i
\(680\) −3.63799e11 1.32412e11i −0.0652486 0.0237485i
\(681\) −5.97042e12 5.00978e12i −1.06376 0.892599i
\(682\) −1.24102e12 + 7.03815e12i −0.219658 + 1.24574i
\(683\) 3.23669e12 0.569125 0.284562 0.958658i \(-0.408152\pi\)
0.284562 + 0.958658i \(0.408152\pi\)
\(684\) 3.69511e10 1.78962e11i 0.00645468 0.0312615i
\(685\) −2.35369e11 −0.0408452
\(686\) 6.99718e11 3.96830e12i 0.120633 0.684141i
\(687\) 7.57310e12 + 6.35459e12i 1.29709 + 1.08838i
\(688\) −9.83571e11 3.57991e11i −0.167362 0.0609149i
\(689\) −1.08459e12 + 3.94757e11i −0.183349 + 0.0667335i
\(690\) 4.86414e11 4.08150e11i 0.0816931 0.0685487i
\(691\) 1.97474e12 + 3.42036e12i 0.329503 + 0.570716i 0.982413 0.186719i \(-0.0597854\pi\)
−0.652910 + 0.757435i \(0.726452\pi\)
\(692\) −1.05068e12 + 1.81982e12i −0.174177 + 0.301684i
\(693\) −6.39277e10 3.62552e11i −0.0105291 0.0597133i
\(694\) −6.93244e11 3.93158e12i −0.113441 0.643354i
\(695\) 3.46437e11 6.00046e11i 0.0563239 0.0975558i
\(696\) 6.61848e11 + 1.14635e12i 0.106910 + 0.185173i
\(697\) −1.00083e13 + 8.39792e12i −1.60624 + 1.34780i
\(698\) −1.85967e12 + 6.76863e11i −0.296542 + 0.107932i
\(699\) 5.77575e12 + 2.10220e12i 0.915084 + 0.333063i
\(700\) −1.43839e12 1.20695e12i −0.226431 0.189998i
\(701\) −4.78758e11 + 2.71517e12i −0.0748834 + 0.424685i 0.924201 + 0.381906i \(0.124732\pi\)
−0.999085 + 0.0427787i \(0.986379\pi\)
\(702\) 4.95490e12 0.770048
\(703\) 4.62850e12 + 1.34633e11i 0.714729 + 0.0207900i
\(704\) −1.29321e12 −0.198424
\(705\) −2.23752e11 + 1.26896e12i −0.0341126 + 0.193462i
\(706\) −5.78459e12 4.85385e12i −0.876297 0.735301i
\(707\) 5.15429e12 + 1.87601e12i 0.775857 + 0.282389i
\(708\) 4.58822e12 1.66997e12i 0.686269 0.249781i
\(709\) −2.27631e12 + 1.91005e12i −0.338316 + 0.283881i −0.796078 0.605194i \(-0.793096\pi\)
0.457762 + 0.889075i \(0.348651\pi\)
\(710\) −8.17238e9 1.41550e10i −0.00120694 0.00209048i
\(711\) −1.09120e11 + 1.89001e11i −0.0160136 + 0.0277364i
\(712\) 7.91791e11 + 4.49047e12i 0.115465 + 0.654835i
\(713\) −1.80657e12 1.02456e13i −0.261790 1.48468i
\(714\) 2.72247e12 4.71545e12i 0.392032 0.679018i
\(715\) −6.83770e11 1.18432e12i −0.0978437 0.169470i
\(716\) 3.97354e12 3.33420e12i 0.565027 0.474114i
\(717\) 8.92536e12 3.24856e12i 1.26122 0.459045i
\(718\) −4.12441e12 1.50116e12i −0.579165 0.210799i
\(719\) 3.62664e12 + 3.04312e12i 0.506087 + 0.424657i 0.859750 0.510716i \(-0.170620\pi\)
−0.353663 + 0.935373i \(0.615064\pi\)
\(720\) 2.18447e9 1.23887e10i 0.000302935 0.00171803i
\(721\) 5.71824e12 0.788050
\(722\) −1.19058e12 + 5.02386e12i −0.163058 + 0.688050i
\(723\) −1.24318e12 −0.169204
\(724\) 5.82437e9 3.30317e10i 0.000787817 0.00446793i
\(725\) 3.30148e12 + 2.77027e12i 0.443800 + 0.372392i
\(726\) −7.79671e12 2.83777e12i −1.04159 0.379107i
\(727\) 7.99530e12 2.91005e12i 1.06152 0.386363i 0.248524 0.968626i \(-0.420055\pi\)
0.813001 + 0.582262i \(0.197832\pi\)
\(728\) 1.38509e12 1.16223e12i 0.182762 0.153355i
\(729\) −3.53930e12 6.13024e12i −0.464133 0.803903i
\(730\) −1.43532e11 + 2.48605e11i −0.0187066 + 0.0324008i
\(731\) −1.71603e12 9.73212e12i −0.222279 1.26061i
\(732\) 1.20811e10 + 6.85152e10i 0.00155527 + 0.00882038i
\(733\) −1.03955e12 + 1.80055e12i −0.133007 + 0.230376i −0.924835 0.380370i \(-0.875797\pi\)
0.791827 + 0.610745i \(0.209130\pi\)
\(734\) −1.08980e12 1.88759e12i −0.138584 0.240035i
\(735\) 4.38698e11 3.68112e11i 0.0554464 0.0465250i
\(736\) 1.76903e12 6.43873e11i 0.222221 0.0808817i
\(737\) 9.33818e12 + 3.39882e12i 1.16589 + 0.424350i
\(738\) −3.25206e11 2.72880e11i −0.0403557 0.0338624i
\(739\) 9.88493e11 5.60603e12i 0.121920 0.691441i −0.861170 0.508317i \(-0.830268\pi\)
0.983090 0.183124i \(-0.0586210\pi\)
\(740\) 3.18766e11 0.0390778
\(741\) 9.54293e12 + 2.77584e11i 1.16279 + 0.0338230i
\(742\) 6.04340e11 0.0731920
\(743\) −1.84008e12 + 1.04356e13i −0.221507 + 1.25623i 0.647745 + 0.761857i \(0.275712\pi\)
−0.869252 + 0.494370i \(0.835399\pi\)
\(744\) −2.63108e12 2.20774e12i −0.314816 0.264162i
\(745\) −1.15089e12 4.18891e11i −0.136877 0.0498193i
\(746\) 1.99415e10 7.25812e9i 0.00235740 0.000858024i
\(747\) −4.27302e11 + 3.58549e11i −0.0502103 + 0.0421314i
\(748\) −6.10487e12 1.05739e13i −0.713048 1.23504i
\(749\) −2.24109e12 + 3.88168e12i −0.260190 + 0.450662i
\(750\) −2.38469e11 1.35242e12i −0.0275205 0.156076i
\(751\) −1.94496e12 1.10304e13i −0.223116 1.26535i −0.866255 0.499602i \(-0.833479\pi\)
0.643139 0.765749i \(-0.277632\pi\)
\(752\) −1.91013e12 + 3.30844e12i −0.217812 + 0.377261i
\(753\) −7.10526e12 1.23067e13i −0.805384 1.39497i
\(754\) −3.17913e12 + 2.66761e12i −0.358210 + 0.300573i
\(755\) 9.25675e11 3.36918e11i 0.103681 0.0377367i
\(756\) −2.43794e12 8.87338e11i −0.271441 0.0987964i
\(757\) −8.55710e12 7.18026e12i −0.947099 0.794710i 0.0317079 0.999497i \(-0.489905\pi\)
−0.978807 + 0.204787i \(0.934350\pi\)
\(758\) −7.07422e11 + 4.01199e12i −0.0778336 + 0.441416i
\(759\) 2.00255e13 2.19026
\(760\) −7.18705e10 + 3.48085e11i −0.00781429 + 0.0378464i
\(761\) 1.00186e12 0.108287 0.0541433 0.998533i \(-0.482757\pi\)
0.0541433 + 0.998533i \(0.482757\pi\)
\(762\) 1.63602e12 9.27831e12i 0.175788 0.996946i
\(763\) 3.92014e12 + 3.28938e12i 0.418736 + 0.351361i
\(764\) −6.49158e12 2.36274e12i −0.689335 0.250897i
\(765\) 1.11608e11 4.06222e10i 0.0117820 0.00428831i
\(766\) 2.51030e12 2.10639e12i 0.263448 0.221059i
\(767\) 7.65410e12 + 1.32573e13i 0.798573 + 1.38317i
\(768\) 3.10752e11 5.38238e11i 0.0322321 0.0558276i
\(769\) −1.31208e12 7.44115e12i −0.135298 0.767311i −0.974652 0.223726i \(-0.928178\pi\)
0.839354 0.543585i \(-0.182933\pi\)
\(770\) 1.24341e11 + 7.05170e11i 0.0127469 + 0.0722913i
\(771\) 8.59766e11 1.48916e12i 0.0876266 0.151774i
\(772\) 3.33204e12 + 5.77126e12i 0.337623 + 0.584781i
\(773\) −3.66114e12 + 3.07206e12i −0.368815 + 0.309473i −0.808293 0.588781i \(-0.799608\pi\)
0.439477 + 0.898254i \(0.355164\pi\)
\(774\) 3.01746e11 1.09827e11i 0.0302209 0.0109995i
\(775\) −1.05083e13 3.82471e12i −1.04634 0.380838i
\(776\) −2.76279e12 2.31826e12i −0.273509 0.229501i
\(777\) −7.78503e11 + 4.41511e12i −0.0766241 + 0.434557i
\(778\) −1.11832e13 −1.09435
\(779\) 8.96021e12 + 7.97377e12i 0.871766 + 0.775792i
\(780\) 6.57224e11 0.0635752
\(781\) 8.95116e10 5.07646e11i 0.00860894 0.0488237i
\(782\) 1.36157e13 + 1.14249e13i 1.30199 + 1.09250i
\(783\) 5.59570e12 + 2.03667e12i 0.532019 + 0.193639i
\(784\) 1.59549e12 5.80711e11i 0.150824 0.0548956i
\(785\) 8.61978e11 7.23285e11i 0.0810182 0.0679824i
\(786\) 8.07048e11 + 1.39785e12i 0.0754219 + 0.130635i
\(787\) −5.17749e11 + 8.96767e11i −0.0481097 + 0.0833285i −0.889077 0.457757i \(-0.848653\pi\)
0.840968 + 0.541085i \(0.181986\pi\)
\(788\) −8.76005e11 4.96807e12i −0.0809354 0.459007i
\(789\) 1.62444e12 + 9.21265e12i 0.149230 + 0.846326i
\(790\) 2.12240e11 3.67610e11i 0.0193867 0.0335788i
\(791\) −3.18711e11 5.52023e11i −0.0289469 0.0501375i
\(792\) 3.03921e11 2.55020e11i 0.0274471 0.0230309i
\(793\) −2.04969e11 + 7.46025e10i −0.0184059 + 0.00669921i
\(794\) −1.37934e13 5.02038e12i −1.23163 0.448275i
\(795\) 1.68278e11 + 1.41202e11i 0.0149408 + 0.0125368i
\(796\) −1.25786e12 + 7.13366e12i −0.111051 + 0.629802i
\(797\) −9.94402e12 −0.872971 −0.436485 0.899711i \(-0.643777\pi\)
−0.436485 + 0.899711i \(0.643777\pi\)
\(798\) −4.64566e12 1.84556e12i −0.405541 0.161107i
\(799\) −3.60685e13 −3.13089
\(800\) 3.51383e11 1.99279e12i 0.0303302 0.172011i
\(801\) −1.07159e12 8.99174e11i −0.0919780 0.0771787i
\(802\) 5.59437e12 + 2.03618e12i 0.477493 + 0.173793i
\(803\) −8.50737e12 + 3.09643e12i −0.722063 + 0.262810i
\(804\) −3.65851e12 + 3.06985e12i −0.308782 + 0.259099i
\(805\) −5.21184e11 9.02717e11i −0.0437431 0.0757653i
\(806\) 5.38414e12 9.32561e12i 0.449375 0.778340i
\(807\) 1.03590e12 + 5.87487e12i 0.0859778 + 0.487604i
\(808\) 1.02646e12 + 5.82133e12i 0.0847207 + 0.480475i
\(809\) −9.71492e11 + 1.68267e12i −0.0797390 + 0.138112i −0.903137 0.429352i \(-0.858742\pi\)
0.823398 + 0.567464i \(0.192075\pi\)
\(810\) −5.01744e11 8.69046e11i −0.0409543 0.0709349i
\(811\) −8.57777e12 + 7.19760e12i −0.696274 + 0.584244i −0.920711 0.390245i \(-0.872390\pi\)
0.224437 + 0.974489i \(0.427946\pi\)
\(812\) 2.04194e12 7.43205e11i 0.164832 0.0599938i
\(813\) 2.02643e13 + 7.37560e12i 1.62676 + 0.592093i
\(814\) 7.70118e12 + 6.46205e12i 0.614819 + 0.515894i
\(815\) −4.39554e10 + 2.49283e11i −0.00348982 + 0.0197917i
\(816\) 5.86786e12 0.463313
\(817\) −8.61206e12 + 2.85381e12i −0.676251 + 0.224092i
\(818\) 1.23294e13 0.962833
\(819\) −9.63228e10 + 5.46274e11i −0.00748086 + 0.0424261i
\(820\) 6.32531e11 + 5.30757e11i 0.0488562 + 0.0409952i
\(821\) −8.25568e12 3.00482e12i −0.634174 0.230821i 0.00487278 0.999988i \(-0.498449\pi\)
−0.639047 + 0.769168i \(0.720671\pi\)
\(822\) 3.35227e12 1.22013e12i 0.256104 0.0932141i
\(823\) 6.31120e12 5.29572e12i 0.479526 0.402370i −0.370729 0.928741i \(-0.620892\pi\)
0.850255 + 0.526371i \(0.176448\pi\)
\(824\) 3.08120e12 + 5.33679e12i 0.232834 + 0.403281i
\(825\) 1.07625e13 1.86413e13i 0.808857 1.40098i
\(826\) −1.39186e12 7.89366e12i −0.104037 0.590022i
\(827\) 4.71485e11 + 2.67393e12i 0.0350504 + 0.198781i 0.997305 0.0733711i \(-0.0233758\pi\)
−0.962254 + 0.272152i \(0.912265\pi\)
\(828\) −2.88772e11 + 5.00167e11i −0.0213510 + 0.0369810i
\(829\) 8.02112e12 + 1.38930e13i 0.589847 + 1.02165i 0.994252 + 0.107066i \(0.0341455\pi\)
−0.404405 + 0.914580i \(0.632521\pi\)
\(830\) 8.31111e11 6.97385e11i 0.0607866 0.0510060i
\(831\) −8.84750e12 + 3.22022e12i −0.643600 + 0.234251i
\(832\) 1.83103e12 + 6.66441e11i 0.132477 + 0.0482177i
\(833\) 1.22800e13 + 1.03041e13i 0.883682 + 0.741497i
\(834\) −1.82360e12 + 1.03421e13i −0.130521 + 0.740224i
\(835\) 3.78501e11 0.0269450
\(836\) −8.79275e12 + 6.95253e12i −0.622582 + 0.492283i
\(837\) −1.54512e13 −1.08817
\(838\) −1.44393e12 + 8.18893e12i −0.101146 + 0.573626i
\(839\) −1.14546e13 9.61155e12i −0.798089 0.669676i 0.149644 0.988740i \(-0.452187\pi\)
−0.947733 + 0.319064i \(0.896632\pi\)
\(840\) −3.23372e11 1.17698e11i −0.0224102 0.00815664i
\(841\) 8.94548e12 3.25589e12i 0.616626 0.224433i
\(842\) −6.52158e12 + 5.47225e12i −0.447145 + 0.375199i
\(843\) 1.86858e12 + 3.23647e12i 0.127435 + 0.220723i
\(844\) −7.54528e11 + 1.30688e12i −0.0511840 + 0.0886533i
\(845\) 7.65141e10 + 4.33933e11i 0.00516282 + 0.0292798i
\(846\) −2.03516e11 1.15420e12i −0.0136594 0.0774663i
\(847\) −6.81027e12 + 1.17957e13i −0.454662 + 0.787498i
\(848\) 3.25641e11 + 5.64026e11i 0.0216251 + 0.0374557i
\(849\) −5.69788e12 + 4.78109e12i −0.376382 + 0.315822i
\(850\) 1.79528e13 6.53428e12i 1.17963 0.429351i
\(851\) −1.37520e13 5.00534e12i −0.898844 0.327153i
\(852\) 1.89774e11 + 1.59239e11i 0.0123384 + 0.0103531i
\(853\) 1.55860e12 8.83923e12i 0.100801 0.571668i −0.892014 0.452007i \(-0.850708\pi\)
0.992815 0.119661i \(-0.0381807\pi\)
\(854\) 1.14210e11 0.00734757
\(855\) −5.17514e10 9.59769e10i −0.00331188 0.00614213i
\(856\) −4.83032e12 −0.307499
\(857\) 3.63402e12 2.06096e13i 0.230130 1.30513i −0.622500 0.782620i \(-0.713883\pi\)
0.852630 0.522514i \(-0.175006\pi\)
\(858\) 1.58781e13 + 1.33233e13i 1.00024 + 0.839304i
\(859\) −3.75600e12 1.36707e12i −0.235373 0.0856688i 0.221641 0.975128i \(-0.428859\pi\)
−0.457014 + 0.889460i \(0.651081\pi\)
\(860\) −5.86902e11 + 2.13615e11i −0.0365866 + 0.0133164i
\(861\) −8.89610e12 + 7.46471e12i −0.551678 + 0.462912i
\(862\) −8.94414e12 1.54917e13i −0.551767 0.955689i
\(863\) 6.43776e12 1.11505e13i 0.395081 0.684301i −0.598030 0.801474i \(-0.704050\pi\)
0.993112 + 0.117173i \(0.0373831\pi\)
\(864\) −4.85506e11 2.75344e12i −0.0296403 0.168099i
\(865\) 2.17735e11 + 1.23484e12i 0.0132238 + 0.0749959i
\(866\) 1.06346e12 1.84196e12i 0.0642523 0.111288i
\(867\) 1.91203e13 + 3.31173e13i 1.14923 + 1.99053i
\(868\) −4.31920e12 + 3.62424e12i −0.258264 + 0.216710i
\(869\) 1.25798e13 4.57867e12i 0.748314 0.272364i
\(870\) 7.42222e11 + 2.70147e11i 0.0439235 + 0.0159868i
\(871\) −1.14702e13 9.62462e12i −0.675287 0.566633i
\(872\) −9.57645e11 + 5.43107e12i −0.0560893 + 0.318098i
\(873\) 1.10645e12 0.0644713
\(874\) 8.56630e12 1.38884e13i 0.496583 0.805100i
\(875\) −2.25440e12 −0.130015
\(876\) 7.55533e11 4.28484e12i 0.0433496 0.245848i
\(877\) 1.96754e13 + 1.65096e13i 1.12312 + 0.942407i 0.998758 0.0498299i \(-0.0158679\pi\)
0.124360 + 0.992237i \(0.460312\pi\)
\(878\) −5.48800e12 1.99747e12i −0.311666 0.113437i
\(879\) −1.78673e13 + 6.50317e12i −1.00951 + 0.367431i
\(880\) −5.91131e11 + 4.96018e11i −0.0332286 + 0.0278821i
\(881\) −2.95662e12 5.12101e12i −0.165350 0.286394i 0.771430 0.636315i \(-0.219542\pi\)
−0.936779 + 0.349920i \(0.886209\pi\)
\(882\) −2.60444e11 + 4.51102e11i −0.0144912 + 0.0250996i
\(883\) −4.99992e12 2.83559e13i −0.276783 1.56972i −0.733240 0.679970i \(-0.761993\pi\)
0.456457 0.889746i \(-0.349118\pi\)
\(884\) 3.19460e12 + 1.81175e13i 0.175947 + 0.997843i
\(885\) 1.45676e12 2.52318e12i 0.0798257 0.138262i
\(886\) −1.31200e12 2.27246e12i −0.0715293 0.123892i
\(887\) 2.53206e13 2.12465e13i 1.37347 1.15248i 0.401907 0.915680i \(-0.368347\pi\)
0.971560 0.236795i \(-0.0760971\pi\)
\(888\) −4.54007e12 + 1.65245e12i −0.245022 + 0.0891806i
\(889\) −1.45336e13 5.28978e12i −0.780394 0.284040i
\(890\) 2.08427e12 + 1.74891e12i 0.111352 + 0.0934356i
\(891\) 5.49557e12 3.11670e13i 0.292121 1.65670i
\(892\) 1.22040e12 0.0645446
\(893\) 4.79948e12 + 3.27637e13i 0.252559 + 1.72410i
\(894\) 1.85632e13 0.971929
\(895\) 5.37470e11 3.04814e12i 0.0279995 0.158793i
\(896\) −7.81568e11 6.55813e11i −0.0405117 0.0339934i
\(897\) −2.83536e13 1.03199e13i −1.46232 0.532241i
\(898\) −2.03080e13 + 7.39149e12i −1.04213 + 0.379305i
\(899\) 9.91368e12 8.31856e12i 0.506193 0.424746i
\(900\) 3.10396e11 + 5.37622e11i 0.0157697 + 0.0273140i
\(901\) −3.07450e12 + 5.32519e12i −0.155422 + 0.269199i
\(902\) 4.52198e12 + 2.56454e13i 0.227457 + 1.28997i
\(903\) −1.52534e12 8.65064e12i −0.0763435 0.432966i
\(904\) 3.43466e11 5.94901e11i 0.0171051 0.0296269i
\(905\) −1.00071e10 1.73328e10i −0.000495895 0.000858916i
\(906\) −1.14375e13 + 9.59721e12i −0.563968 + 0.473226i
\(907\) −1.62100e13 + 5.89996e12i −0.795336 + 0.289479i −0.707552 0.706661i \(-0.750201\pi\)
−0.0877836 + 0.996140i \(0.527978\pi\)
\(908\) −1.29566e13 4.71583e12i −0.632566 0.230235i
\(909\) −1.38919e12 1.16567e12i −0.0674874 0.0566287i
\(910\) 1.87350e11 1.06251e12i 0.00905662 0.0513627i
\(911\) 1.53299e13 0.737406 0.368703 0.929547i \(-0.379802\pi\)
0.368703 + 0.929547i \(0.379802\pi\)
\(912\) −7.80811e11 5.33022e12i −0.0373740 0.255134i
\(913\) 3.42165e13 1.62974
\(914\) 1.88869e12 1.07113e13i 0.0895166 0.507674i
\(915\) 3.18016e10 + 2.66847e10i 0.00149987 + 0.00125854i
\(916\) 1.64347e13 + 5.98174e12i 0.771315 + 0.280736i
\(917\) 2.48991e12 9.06253e11i 0.116284 0.0423241i
\(918\) 2.02216e13 1.69679e13i 0.939772 0.788562i
\(919\) 1.76816e12 + 3.06254e12i 0.0817714 + 0.141632i 0.904011 0.427509i \(-0.140609\pi\)
−0.822239 + 0.569142i \(0.807276\pi\)
\(920\) 5.61666e11 9.72834e11i 0.0258484 0.0447707i
\(921\) −2.84459e12 1.61325e13i −0.130272 0.738810i
\(922\) −3.47629e12 1.97150e13i −0.158426 0.898479i
\(923\) −3.88346e11 + 6.72635e11i −0.0176121 + 0.0305051i
\(924\) −5.42647e12 9.39892e12i −0.244903 0.424184i
\(925\) −1.20503e13 + 1.01114e13i −0.541202 + 0.454122i
\(926\) 6.47140e12 2.35540e12i 0.289234 0.105272i
\(927\) −1.77653e12 6.46602e11i −0.0790156 0.0287593i
\(928\) 1.79390e12 + 1.50526e12i 0.0794021 + 0.0666263i
\(929\) 4.38607e12 2.48746e13i 0.193199 1.09568i −0.721762 0.692141i \(-0.756667\pi\)
0.914961 0.403543i \(-0.132221\pi\)
\(930\) −2.04946e12 −0.0898394
\(931\) 7.72597e12 1.25260e13i 0.337039 0.546434i
\(932\) 1.08737e13 0.472070
\(933\) −4.73508e12 + 2.68540e13i −0.204578 + 1.16022i
\(934\) 4.73935e12 + 3.97678e12i 0.203778 + 0.170990i
\(935\) −6.84623e12 2.49182e12i −0.292954 0.106627i
\(936\) −5.61735e11 + 2.04455e11i −0.0239216 + 0.00870675i
\(937\) −1.75189e13 + 1.47001e13i −0.742468 + 0.623005i −0.933499 0.358579i \(-0.883261\pi\)
0.191031 + 0.981584i \(0.438817\pi\)
\(938\) 3.92003e12 + 6.78968e12i 0.165339 + 0.286376i
\(939\) −6.97675e12 + 1.20841e13i −0.292858 + 0.507246i
\(940\) 3.95842e11 + 2.24493e12i 0.0165366 + 0.0937838i
\(941\) −9.61726e11 5.45422e12i −0.0399851 0.226767i 0.958266 0.285877i \(-0.0922848\pi\)
−0.998251 + 0.0591101i \(0.981174\pi\)
\(942\) −8.52740e12 + 1.47699e13i −0.352848 + 0.611151i
\(943\) −1.89543e13 3.28298e13i −0.780557 1.35196i
\(944\) 6.61710e12 5.55241e12i 0.271203 0.227566i
\(945\) −1.45473e12 + 5.29479e11i −0.0593389 + 0.0215976i
\(946\) −1.85096e13 6.73693e12i −0.751426 0.273497i
\(947\) 8.38925e12 + 7.03942e12i 0.338960 + 0.284421i 0.796339 0.604851i \(-0.206767\pi\)
−0.457379 + 0.889272i \(0.651212\pi\)
\(948\) −1.11720e12 + 6.33596e12i −0.0449256 + 0.254786i
\(949\) 1.36411e13 0.545948
\(950\) −8.32447e12 1.54384e13i −0.331589 0.614957i
\(951\) 1.45376e13 0.576342
\(952\) 1.67270e12 9.48637e12i 0.0660013 0.374312i
\(953\) −3.27498e13 2.74803e13i −1.28615 1.07920i −0.992366 0.123331i \(-0.960642\pi\)
−0.293780 0.955873i \(-0.594913\pi\)
\(954\) −1.87754e11 6.83370e10i −0.00733876 0.00267109i
\(955\) −3.87356e12 + 1.40986e12i −0.150694 + 0.0548480i
\(956\) 1.28721e13 1.08010e13i 0.498413 0.418218i
\(957\) 1.24551e13 + 2.15729e13i 0.480004 + 0.831391i
\(958\) −6.20063e12 + 1.07398e13i −0.237843 + 0.411957i
\(959\) −1.01693e12 5.76731e12i −0.0388247 0.220186i
\(960\) −6.43982e10 3.65220e11i −0.00244711 0.0138782i
\(961\) −3.56989e12 + 6.18324e12i −0.135021 + 0.233863i
\(962\) −7.57378e12 1.31182e13i −0.285118 0.493839i
\(963\) 1.13518e12 9.52532e11i 0.0425351 0.0356912i
\(964\) −2.06669e12 + 7.52215e11i −0.0770778 + 0.0280540i
\(965\) 3.73668e12 + 1.36004e12i 0.138712 + 0.0504869i
\(966\) 1.21026e13 + 1.01553e13i 0.447180 + 0.375229i
\(967\) 4.63118e12 2.62647e13i 0.170323 0.965948i −0.773082 0.634306i \(-0.781286\pi\)
0.943405 0.331643i \(-0.107603\pi\)
\(968\) −1.46785e13 −0.537331
\(969\) 3.98965e13 3.15466e13i 1.45371 1.14947i
\(970\) −2.15206e12 −0.0780515
\(971\) 1.89847e12 1.07668e13i 0.0685358 0.388686i −0.931173 0.364576i \(-0.881214\pi\)
0.999709 0.0241097i \(-0.00767509\pi\)
\(972\) 1.35896e12 + 1.14030e12i 0.0488324 + 0.0409752i
\(973\) 1.61999e13 + 5.89629e12i 0.579436 + 0.210897i
\(974\) 1.90216e13 6.92328e12i 0.677222 0.246489i
\(975\) −2.48450e13 + 2.08474e13i −0.880476 + 0.738807i
\(976\) 6.15406e10 + 1.06591e11i 0.00217089 + 0.00376009i
\(977\) 1.15729e12 2.00449e12i 0.0406366 0.0703846i −0.844992 0.534779i \(-0.820395\pi\)
0.885628 + 0.464395i \(0.153728\pi\)
\(978\) −6.66219e11 3.77831e12i −0.0232858 0.132061i
\(979\) 1.49005e13 + 8.45049e13i 0.518416 + 2.94009i
\(980\) 5.06568e11 8.77402e11i 0.0175437 0.0303865i
\(981\) −8.45941e11 1.46521e12i −0.0291628 0.0505115i
\(982\) 6.95914e12 5.83941e12i 0.238811 0.200386i
\(983\) 2.19230e13 7.97931e12i 0.748874 0.272568i 0.0607421 0.998153i \(-0.480653\pi\)
0.688132 + 0.725586i \(0.258431\pi\)
\(984\) −1.17603e13 4.28040e12i −0.399890 0.145548i
\(985\) −2.30595e12 1.93492e12i −0.0780525 0.0654938i
\(986\) −3.83929e12 + 2.17737e13i −0.129361 + 0.733644i
\(987\) −3.20604e13 −1.07533
\(988\) 1.60323e13 5.31270e12i 0.535292 0.177382i
\(989\) 2.86740e13 0.953027
\(990\) 4.11089e10 2.33140e11i 0.00136012 0.00771363i
\(991\) −5.52424e12 4.63539e12i −0.181946 0.152670i 0.547266 0.836959i \(-0.315669\pi\)
−0.729212 + 0.684288i \(0.760113\pi\)
\(992\) −5.70982e12 2.07820e12i −0.187206 0.0681374i
\(993\) −3.27469e13 + 1.19189e13i −1.06881 + 0.389013i
\(994\) 3.11534e11 2.61408e11i 0.0101220 0.00849338i
\(995\) 2.16118e12 + 3.74327e12i 0.0699015 + 0.121073i
\(996\) −8.22204e12 + 1.42410e13i −0.264736 + 0.458536i
\(997\) 3.23798e12 + 1.83635e13i 0.103788 + 0.588610i 0.991698 + 0.128592i \(0.0410459\pi\)
−0.887910 + 0.460018i \(0.847843\pi\)
\(998\) 2.78619e12 + 1.58013e13i 0.0889044 + 0.504202i
\(999\) −1.08674e13 + 1.88230e13i −0.345210 + 0.597921i
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 38.10.e.a.17.2 yes 42
19.9 even 9 inner 38.10.e.a.9.2 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.10.e.a.9.2 42 19.9 even 9 inner
38.10.e.a.17.2 yes 42 1.1 even 1 trivial