Properties

Label 43.9.h.a.3.3
Level $43$
Weight $9$
Character 43.3
Analytic conductor $17.517$
Analytic rank $0$
Dimension $336$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,9,Mod(3,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.3");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.h (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(28\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 3.3
Character \(\chi\) \(=\) 43.3
Dual form 43.9.h.a.29.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11.8000 + 24.5029i) q^{2} +(-134.895 - 10.1090i) q^{3} +(-301.539 - 378.118i) q^{4} +(-246.719 + 799.843i) q^{5} +(1839.46 - 3186.03i) q^{6} +(1956.96 - 1129.85i) q^{7} +(6035.48 - 1377.56i) q^{8} +(11606.8 + 1749.44i) q^{9} +O(q^{10})\) \(q+(-11.8000 + 24.5029i) q^{2} +(-134.895 - 10.1090i) q^{3} +(-301.539 - 378.118i) q^{4} +(-246.719 + 799.843i) q^{5} +(1839.46 - 3186.03i) q^{6} +(1956.96 - 1129.85i) q^{7} +(6035.48 - 1377.56i) q^{8} +(11606.8 + 1749.44i) q^{9} +(-16687.2 - 15483.4i) q^{10} +(15455.1 - 19380.1i) q^{11} +(36853.7 + 54054.5i) q^{12} +(-36464.5 + 33834.1i) q^{13} +(4592.55 + 61283.4i) q^{14} +(41366.7 - 105401. i) q^{15} +(-9914.08 + 43436.4i) q^{16} +(53283.0 - 16435.6i) q^{17} +(-179826. + 263756. i) q^{18} +(-2158.58 - 14321.2i) q^{19} +(376830. - 147895. i) q^{20} +(-275406. + 132628. i) q^{21} +(292499. + 607380. i) q^{22} +(-108121. - 275489. i) q^{23} +(-828082. + 124813. i) q^{24} +(-256129. - 174626. i) q^{25} +(-398754. - 1.29273e6i) q^{26} +(-682733. - 155829. i) q^{27} +(-1.01732e6 - 399267. i) q^{28} +(-544262. + 40786.8i) q^{29} +(2.09450e6 + 2.25733e6i) q^{30} +(1.04064e6 - 709493. i) q^{31} +(291728. + 232645. i) q^{32} +(-2.28073e6 + 2.45805e6i) q^{33} +(-226017. + 1.49953e6i) q^{34} +(420884. + 1.84402e6i) q^{35} +(-2.83840e6 - 4.91625e6i) q^{36} +(1.24067e6 + 716299. i) q^{37} +(376383. + 116099. i) q^{38} +(5.26091e6 - 4.19543e6i) q^{39} +(-387236. + 5.16730e6i) q^{40} +(3.12240e6 + 1.50367e6i) q^{41} -8.31325e6i q^{42} +(-1.78839e6 + 2.91374e6i) q^{43} -1.19883e7 q^{44} +(-4.26288e6 + 8.85196e6i) q^{45} +(8.02611e6 + 601474. i) q^{46} +(-435626. - 546258. i) q^{47} +(1.77646e6 - 5.75914e6i) q^{48} +(-329274. + 570319. i) q^{49} +(7.30114e6 - 4.21532e6i) q^{50} +(-7.35376e6 + 1.67845e6i) q^{51} +(2.37888e7 + 3.58558e6i) q^{52} +(-4.55258e6 - 4.22418e6i) q^{53} +(1.18745e7 - 1.48901e7i) q^{54} +(1.16880e7 + 1.71431e7i) q^{55} +(1.02547e7 - 9.51502e6i) q^{56} +(146408. + 1.95368e6i) q^{57} +(5.42288e6 - 1.38173e7i) q^{58} +(1.28717e6 - 5.63948e6i) q^{59} +(-5.23276e7 + 1.61409e7i) q^{60} +(4.86961e6 - 7.14241e6i) q^{61} +(5.10517e6 + 3.38706e7i) q^{62} +(2.46906e7 - 9.69033e6i) q^{63} +(-1.94190e7 + 9.35171e6i) q^{64} +(-1.80655e7 - 3.75134e7i) q^{65} +(-3.33166e7 - 8.48894e7i) q^{66} +(-1.28503e7 + 1.93687e6i) q^{67} +(-2.22815e7 - 1.51913e7i) q^{68} +(1.18001e7 + 3.82551e7i) q^{69} +(-5.01501e7 - 1.14464e7i) q^{70} +(3.83134e6 + 1.50369e6i) q^{71} +(7.24623e7 - 5.43030e6i) q^{72} +(2.82397e7 + 3.04351e7i) q^{73} +(-3.21912e7 + 2.19476e7i) q^{74} +(3.27852e7 + 2.61453e7i) q^{75} +(-4.76422e6 + 5.13461e6i) q^{76} +(8.34841e6 - 5.53881e7i) q^{77} +(4.07217e7 + 1.78413e8i) q^{78} +(3.38688e6 + 5.86625e6i) q^{79} +(-3.22963e7 - 1.86463e7i) q^{80} +(1.69313e7 + 5.22261e6i) q^{81} +(-7.36883e7 + 5.87645e7i) q^{82} +(3.23469e6 - 4.31639e7i) q^{83} +(1.33195e8 + 6.41432e7i) q^{84} +4.66730e7i q^{85} +(-5.02920e7 - 7.82027e7i) q^{86} +7.38306e7 q^{87} +(6.65818e7 - 1.38259e8i) q^{88} +(9.17218e7 + 6.87360e6i) q^{89} +(-1.66597e8 - 2.08906e8i) q^{90} +(-3.31320e7 + 1.07411e8i) q^{91} +(-7.15645e7 + 1.23953e8i) q^{92} +(-1.47549e8 + 8.51873e7i) q^{93} +(1.85253e7 - 4.22827e6i) q^{94} +(1.19873e7 + 1.80679e6i) q^{95} +(-3.70008e7 - 3.43317e7i) q^{96} +(-1.72402e7 + 2.16185e7i) q^{97} +(-1.00890e7 - 1.47979e7i) q^{98} +(2.13288e8 - 1.97903e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 14 q^{2} + 70 q^{3} + 6460 q^{4} - 11 q^{5} - 1798 q^{6} + 5010 q^{7} + 5362 q^{8} - 40176 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 14 q^{2} + 70 q^{3} + 6460 q^{4} - 11 q^{5} - 1798 q^{6} + 5010 q^{7} + 5362 q^{8} - 40176 q^{9} - 12505 q^{10} - 31942 q^{11} - 54796 q^{12} - 75596 q^{13} + 111780 q^{14} + 4037 q^{15} - 688224 q^{16} - 5977 q^{17} - 280532 q^{18} - 552290 q^{19} - 494171 q^{20} + 141291 q^{21} - 432782 q^{22} - 619546 q^{23} - 298136 q^{24} - 2392669 q^{25} - 113675 q^{26} - 14 q^{27} - 1143258 q^{28} + 4198855 q^{29} - 795576 q^{30} + 3391610 q^{31} + 3704176 q^{32} + 469240 q^{33} + 3670777 q^{34} - 2602743 q^{35} - 32236515 q^{36} + 7009521 q^{37} + 1762126 q^{38} - 573251 q^{39} - 41379997 q^{40} - 11003050 q^{41} + 7113655 q^{43} + 64459560 q^{44} + 11644332 q^{45} - 14793057 q^{46} + 9244886 q^{47} - 34730249 q^{48} + 82140290 q^{49} - 80542767 q^{50} - 7776902 q^{51} - 98888784 q^{52} + 39659528 q^{53} + 139217042 q^{54} + 96182224 q^{55} - 59364207 q^{56} - 94760066 q^{57} + 149491596 q^{58} - 74665213 q^{59} + 188098449 q^{60} + 55854238 q^{61} - 52173383 q^{62} + 40219829 q^{63} + 13742518 q^{64} + 87064978 q^{65} - 64965481 q^{66} + 210933441 q^{67} - 248367043 q^{68} + 405756759 q^{69} - 362301191 q^{70} - 34975301 q^{71} - 125412979 q^{72} - 216767388 q^{73} + 53341380 q^{74} + 436840145 q^{75} - 29249062 q^{76} - 59286141 q^{77} + 204702644 q^{78} + 71493313 q^{79} - 737037738 q^{80} - 235365082 q^{81} - 806662220 q^{82} + 254450510 q^{83} - 979300857 q^{84} + 50436244 q^{86} + 696609678 q^{87} + 65867942 q^{88} + 949059334 q^{89} + 1083992303 q^{90} - 184351501 q^{91} + 379980750 q^{92} - 271490850 q^{93} - 369651898 q^{94} - 1349611517 q^{95} - 1044343058 q^{96} - 850069303 q^{97} - 271546964 q^{98} + 148520290 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.8000 + 24.5029i −0.737498 + 1.53143i 0.106040 + 0.994362i \(0.466183\pi\)
−0.843538 + 0.537069i \(0.819531\pi\)
\(3\) −134.895 10.1090i −1.66537 0.124802i −0.791567 0.611082i \(-0.790735\pi\)
−0.873803 + 0.486280i \(0.838354\pi\)
\(4\) −301.539 378.118i −1.17789 1.47702i
\(5\) −246.719 + 799.843i −0.394750 + 1.27975i 0.512329 + 0.858789i \(0.328783\pi\)
−0.907080 + 0.420959i \(0.861694\pi\)
\(6\) 1839.46 3186.03i 1.41933 2.45836i
\(7\) 1956.96 1129.85i 0.815060 0.470575i −0.0336499 0.999434i \(-0.510713\pi\)
0.848710 + 0.528858i \(0.177380\pi\)
\(8\) 6035.48 1377.56i 1.47351 0.336318i
\(9\) 11606.8 + 1749.44i 1.76905 + 0.266642i
\(10\) −16687.2 15483.4i −1.66872 1.54834i
\(11\) 15455.1 19380.1i 1.05561 1.32369i 0.111603 0.993753i \(-0.464402\pi\)
0.944004 0.329935i \(-0.107027\pi\)
\(12\) 36853.7 + 54054.5i 1.77728 + 2.60679i
\(13\) −36464.5 + 33834.1i −1.27672 + 1.18463i −0.303997 + 0.952673i \(0.598321\pi\)
−0.972727 + 0.231953i \(0.925488\pi\)
\(14\) 4592.55 + 61283.4i 0.119548 + 1.59526i
\(15\) 41366.7 105401.i 0.817121 2.08199i
\(16\) −9914.08 + 43436.4i −0.151277 + 0.662787i
\(17\) 53283.0 16435.6i 0.637959 0.196784i 0.0411314 0.999154i \(-0.486904\pi\)
0.596828 + 0.802369i \(0.296428\pi\)
\(18\) −179826. + 263756.i −1.71302 + 2.51253i
\(19\) −2158.58 14321.2i −0.0165636 0.109892i 0.979021 0.203758i \(-0.0653156\pi\)
−0.995585 + 0.0938660i \(0.970077\pi\)
\(20\) 376830. 147895.i 2.35519 0.924344i
\(21\) −275406. + 132628.i −1.41611 + 0.681961i
\(22\) 292499. + 607380.i 1.24863 + 2.59281i
\(23\) −108121. 275489.i −0.386368 0.984448i −0.983273 0.182137i \(-0.941699\pi\)
0.596906 0.802311i \(-0.296397\pi\)
\(24\) −828082. + 124813.i −2.49591 + 0.376197i
\(25\) −256129. 174626.i −0.655689 0.447041i
\(26\) −398754. 1.29273e6i −0.872592 2.82887i
\(27\) −682733. 155829.i −1.28468 0.293220i
\(28\) −1.01732e6 399267.i −1.65510 0.649579i
\(29\) −544262. + 40786.8i −0.769513 + 0.0576670i −0.453700 0.891154i \(-0.649896\pi\)
−0.315813 + 0.948821i \(0.602277\pi\)
\(30\) 2.09450e6 + 2.25733e6i 2.58580 + 2.78683i
\(31\) 1.04064e6 709493.i 1.12681 0.768248i 0.151365 0.988478i \(-0.451633\pi\)
0.975448 + 0.220230i \(0.0706809\pi\)
\(32\) 291728. + 232645.i 0.278213 + 0.221868i
\(33\) −2.28073e6 + 2.45805e6i −1.92317 + 2.07269i
\(34\) −226017. + 1.49953e6i −0.169132 + 1.12212i
\(35\) 420884. + 1.84402e6i 0.280473 + 1.22883i
\(36\) −2.83840e6 4.91625e6i −1.68991 2.92701i
\(37\) 1.24067e6 + 716299.i 0.661984 + 0.382197i 0.793033 0.609179i \(-0.208501\pi\)
−0.131048 + 0.991376i \(0.541834\pi\)
\(38\) 376383. + 116099.i 0.180508 + 0.0556792i
\(39\) 5.26091e6 4.19543e6i 2.27406 1.81350i
\(40\) −387236. + 5.16730e6i −0.151264 + 2.01848i
\(41\) 3.12240e6 + 1.50367e6i 1.10497 + 0.532128i 0.895219 0.445626i \(-0.147019\pi\)
0.209756 + 0.977754i \(0.432733\pi\)
\(42\) 8.31325e6i 2.67161i
\(43\) −1.78839e6 + 2.91374e6i −0.523104 + 0.852269i
\(44\) −1.19883e7 −3.19850
\(45\) −4.26288e6 + 8.85196e6i −1.03957 + 2.15869i
\(46\) 8.02611e6 + 601474.i 1.79256 + 0.134334i
\(47\) −435626. 546258.i −0.0892735 0.111945i 0.735189 0.677863i \(-0.237094\pi\)
−0.824462 + 0.565917i \(0.808522\pi\)
\(48\) 1.77646e6 5.75914e6i 0.334649 1.08491i
\(49\) −329274. + 570319.i −0.0571180 + 0.0989312i
\(50\) 7.30114e6 4.21532e6i 1.16818 0.674450i
\(51\) −7.35376e6 + 1.67845e6i −1.08700 + 0.248100i
\(52\) 2.37888e7 + 3.58558e6i 3.25356 + 0.490395i
\(53\) −4.55258e6 4.22418e6i −0.576971 0.535351i 0.336802 0.941576i \(-0.390655\pi\)
−0.913773 + 0.406224i \(0.866845\pi\)
\(54\) 1.18745e7 1.48901e7i 1.39650 1.75115i
\(55\) 1.16880e7 + 1.71431e7i 1.27729 + 1.87344i
\(56\) 1.02547e7 9.51502e6i 1.04273 0.967514i
\(57\) 146408. + 1.95368e6i 0.0138697 + 0.185078i
\(58\) 5.42288e6 1.38173e7i 0.479202 1.22099i
\(59\) 1.28717e6 5.63948e6i 0.106226 0.465405i −0.893636 0.448792i \(-0.851855\pi\)
0.999862 0.0166131i \(-0.00528835\pi\)
\(60\) −5.23276e7 + 1.61409e7i −4.03762 + 1.24544i
\(61\) 4.86961e6 7.14241e6i 0.351702 0.515852i −0.609098 0.793095i \(-0.708468\pi\)
0.960800 + 0.277243i \(0.0894207\pi\)
\(62\) 5.10517e6 + 3.38706e7i 0.345496 + 2.29222i
\(63\) 2.46906e7 9.69033e6i 1.56736 0.615143i
\(64\) −1.94190e7 + 9.35171e6i −1.15746 + 0.557405i
\(65\) −1.80655e7 3.75134e7i −1.01204 2.10152i
\(66\) −3.33166e7 8.48894e7i −1.75584 4.47381i
\(67\) −1.28503e7 + 1.93687e6i −0.637697 + 0.0961173i −0.459930 0.887955i \(-0.652125\pi\)
−0.177767 + 0.984073i \(0.556887\pi\)
\(68\) −2.22815e7 1.51913e7i −1.04210 0.710491i
\(69\) 1.18001e7 + 3.82551e7i 0.520584 + 1.68769i
\(70\) −5.01501e7 1.14464e7i −2.08872 0.476736i
\(71\) 3.83134e6 + 1.50369e6i 0.150771 + 0.0591732i 0.439526 0.898230i \(-0.355146\pi\)
−0.288756 + 0.957403i \(0.593242\pi\)
\(72\) 7.24623e7 5.43030e6i 2.69639 0.202066i
\(73\) 2.82397e7 + 3.04351e7i 0.994416 + 1.07173i 0.997424 + 0.0717302i \(0.0228521\pi\)
−0.00300794 + 0.999995i \(0.500957\pi\)
\(74\) −3.21912e7 + 2.19476e7i −1.07352 + 0.731914i
\(75\) 3.27852e7 + 2.61453e7i 1.03617 + 0.826321i
\(76\) −4.76422e6 + 5.13461e6i −0.142803 + 0.153905i
\(77\) 8.34841e6 5.53881e7i 0.237488 1.57563i
\(78\) 4.07217e7 + 1.78413e8i 1.10014 + 4.82002i
\(79\) 3.38688e6 + 5.86625e6i 0.0869544 + 0.150609i 0.906222 0.422801i \(-0.138953\pi\)
−0.819268 + 0.573411i \(0.805620\pi\)
\(80\) −3.22963e7 1.86463e7i −0.788484 0.455232i
\(81\) 1.69313e7 + 5.22261e6i 0.393324 + 0.121324i
\(82\) −7.36883e7 + 5.87645e7i −1.62983 + 1.29975i
\(83\) 3.23469e6 4.31639e7i 0.0681585 0.909512i −0.853396 0.521263i \(-0.825461\pi\)
0.921555 0.388249i \(-0.126920\pi\)
\(84\) 1.33195e8 + 6.41432e7i 2.67528 + 1.28835i
\(85\) 4.66730e7i 0.894108i
\(86\) −5.02920e7 7.82027e7i −0.919402 1.42964i
\(87\) 7.38306e7 1.28872
\(88\) 6.65818e7 1.38259e8i 1.11026 2.30548i
\(89\) 9.17218e7 + 6.87360e6i 1.46188 + 0.109553i 0.781776 0.623560i \(-0.214314\pi\)
0.680107 + 0.733113i \(0.261933\pi\)
\(90\) −1.66597e8 2.08906e8i −2.53920 3.18405i
\(91\) −3.31320e7 + 1.07411e8i −0.483151 + 1.56634i
\(92\) −7.15645e7 + 1.23953e8i −0.998956 + 1.73024i
\(93\) −1.47549e8 + 8.51873e7i −1.97244 + 1.13879i
\(94\) 1.85253e7 4.22827e6i 0.237276 0.0541566i
\(95\) 1.19873e7 + 1.80679e6i 0.147173 + 0.0221827i
\(96\) −3.70008e7 3.43317e7i −0.435638 0.404213i
\(97\) −1.72402e7 + 2.16185e7i −0.194740 + 0.244196i −0.869609 0.493742i \(-0.835629\pi\)
0.674869 + 0.737938i \(0.264200\pi\)
\(98\) −1.00890e7 1.47979e7i −0.109382 0.160434i
\(99\) 2.13288e8 1.97903e8i 2.22037 2.06021i
\(100\) 1.12037e7 + 1.49503e8i 0.112037 + 1.49503i
\(101\) −1.55522e7 + 3.96264e7i −0.149454 + 0.380802i −0.985920 0.167216i \(-0.946522\pi\)
0.836466 + 0.548018i \(0.184618\pi\)
\(102\) 4.56473e7 1.99994e8i 0.421711 1.84763i
\(103\) −5.69636e7 + 1.75710e7i −0.506115 + 0.156116i −0.537289 0.843398i \(-0.680552\pi\)
0.0311743 + 0.999514i \(0.490075\pi\)
\(104\) −1.73472e8 + 2.54437e8i −1.48285 + 2.17494i
\(105\) −3.81341e7 2.53003e8i −0.313730 2.08146i
\(106\) 1.57225e8 6.17062e7i 1.24537 0.488771i
\(107\) −5.12212e7 + 2.46668e7i −0.390764 + 0.188182i −0.618941 0.785438i \(-0.712438\pi\)
0.228177 + 0.973620i \(0.426724\pi\)
\(108\) 1.46949e8 + 3.05142e8i 1.08012 + 2.24289i
\(109\) −2.66859e7 6.79946e7i −0.189050 0.481691i 0.804652 0.593747i \(-0.202352\pi\)
−0.993702 + 0.112055i \(0.964257\pi\)
\(110\) −5.57974e8 + 8.41010e7i −3.81103 + 0.574421i
\(111\) −1.60119e8 1.09167e8i −1.05475 0.719117i
\(112\) 2.96752e7 + 9.62048e7i 0.188592 + 0.611399i
\(113\) 2.76395e8 + 6.30854e7i 1.69518 + 0.386915i 0.957546 0.288282i \(-0.0930839\pi\)
0.737638 + 0.675196i \(0.235941\pi\)
\(114\) −4.95985e7 1.94660e7i −0.293663 0.115254i
\(115\) 2.47023e8 1.85118e7i 1.41236 0.105842i
\(116\) 1.79539e8 + 1.93496e8i 0.991575 + 1.06866i
\(117\) −4.82425e8 + 3.28912e8i −2.57446 + 1.75524i
\(118\) 1.22995e8 + 9.80852e7i 0.634394 + 0.505912i
\(119\) 8.57028e7 9.23657e7i 0.427373 0.460599i
\(120\) 1.04472e8 6.93129e8i 0.503821 3.34263i
\(121\) −8.90287e7 3.90060e8i −0.415325 1.81966i
\(122\) 1.17548e8 + 2.03600e8i 0.530612 + 0.919047i
\(123\) −4.05995e8 2.34401e8i −1.77378 1.02409i
\(124\) −5.82064e8 1.79543e8i −2.46198 0.759420i
\(125\) −5.27666e7 + 4.20800e7i −0.216132 + 0.172360i
\(126\) −5.39067e7 + 7.19336e8i −0.213875 + 2.85397i
\(127\) 2.68671e8 + 1.29385e8i 1.03278 + 0.497359i 0.871935 0.489622i \(-0.162865\pi\)
0.160841 + 0.986980i \(0.448579\pi\)
\(128\) 4.90650e8i 1.82781i
\(129\) 2.70700e8 3.74970e8i 0.977528 1.35406i
\(130\) 1.13236e9 3.96470
\(131\) −6.46345e7 + 1.34215e8i −0.219472 + 0.455738i −0.981413 0.191908i \(-0.938532\pi\)
0.761941 + 0.647647i \(0.224247\pi\)
\(132\) 1.61716e9 + 1.21190e8i 5.32669 + 0.399180i
\(133\) −2.04051e7 2.55872e7i −0.0652127 0.0817742i
\(134\) 1.04174e8 3.37725e8i 0.323103 1.04747i
\(135\) 2.93082e8 5.07633e8i 0.882376 1.52832i
\(136\) 2.98947e8 1.72597e8i 0.873854 0.504520i
\(137\) −3.00738e8 + 6.86414e7i −0.853700 + 0.194852i −0.626910 0.779092i \(-0.715680\pi\)
−0.226791 + 0.973944i \(0.572823\pi\)
\(138\) −1.07660e9 1.62272e8i −2.96851 0.447431i
\(139\) 1.65385e8 + 1.53455e8i 0.443034 + 0.411075i 0.869891 0.493244i \(-0.164189\pi\)
−0.426857 + 0.904319i \(0.640379\pi\)
\(140\) 5.70342e8 7.15187e8i 1.48465 1.86169i
\(141\) 5.32417e7 + 7.80912e7i 0.134702 + 0.197572i
\(142\) −8.20545e7 + 7.61354e7i −0.201813 + 0.187255i
\(143\) 9.21456e7 + 1.22960e9i 0.220359 + 2.94048i
\(144\) −1.91060e8 + 4.86812e8i −0.444344 + 1.13217i
\(145\) 1.01657e8 4.45387e8i 0.229966 1.00755i
\(146\) −1.07898e9 + 3.32820e8i −2.37465 + 0.732484i
\(147\) 5.01827e7 7.36045e7i 0.107469 0.157629i
\(148\) −1.03264e8 6.85110e8i −0.215229 1.42795i
\(149\) −2.06732e8 + 8.11363e7i −0.419433 + 0.164615i −0.565665 0.824635i \(-0.691381\pi\)
0.146232 + 0.989250i \(0.453285\pi\)
\(150\) −1.02750e9 + 4.94818e8i −2.02963 + 0.977418i
\(151\) 2.66387e8 + 5.53159e8i 0.512396 + 1.06400i 0.983329 + 0.181833i \(0.0582029\pi\)
−0.470933 + 0.882169i \(0.656083\pi\)
\(152\) −3.27564e7 8.34619e7i −0.0613651 0.156356i
\(153\) 6.47196e8 9.75490e7i 1.18105 0.178015i
\(154\) 1.25866e9 + 8.58138e8i 2.23782 + 1.52572i
\(155\) 3.10739e8 + 1.00739e9i 0.538354 + 1.74530i
\(156\) −3.17274e9 7.24157e8i −5.35718 1.22274i
\(157\) 4.35220e8 + 1.70811e8i 0.716325 + 0.281137i 0.695378 0.718644i \(-0.255237\pi\)
0.0209463 + 0.999781i \(0.493332\pi\)
\(158\) −1.83705e8 + 1.37668e7i −0.294777 + 0.0220905i
\(159\) 5.71419e8 + 6.15843e8i 0.894058 + 0.963566i
\(160\) −2.58054e8 + 1.75938e8i −0.393759 + 0.268461i
\(161\) −5.22851e8 4.16960e8i −0.778170 0.620570i
\(162\) −3.27758e8 + 3.53239e8i −0.475875 + 0.512872i
\(163\) −1.98525e8 + 1.31713e9i −0.281232 + 1.86585i 0.187157 + 0.982330i \(0.440073\pi\)
−0.468389 + 0.883522i \(0.655165\pi\)
\(164\) −3.72961e8 1.63405e9i −0.515570 2.25886i
\(165\) −1.40335e9 2.43067e9i −1.89335 3.27937i
\(166\) 1.01947e9 + 5.88592e8i 1.34259 + 0.775144i
\(167\) 7.49768e8 + 2.31273e8i 0.963965 + 0.297344i 0.736496 0.676442i \(-0.236479\pi\)
0.227469 + 0.973785i \(0.426955\pi\)
\(168\) −1.47950e9 + 1.17986e9i −1.85728 + 1.48113i
\(169\) 1.23953e8 1.65404e9i 0.151953 2.02768i
\(170\) −1.14362e9 5.50740e8i −1.36926 0.659403i
\(171\) 1.69999e8i 0.198821i
\(172\) 1.64101e9 2.02383e8i 1.87498 0.231239i
\(173\) 1.05569e9 1.17856 0.589278 0.807930i \(-0.299412\pi\)
0.589278 + 0.807930i \(0.299412\pi\)
\(174\) −8.71198e8 + 1.80906e9i −0.950430 + 1.97359i
\(175\) −6.98534e8 5.23479e7i −0.744793 0.0558145i
\(176\) 6.88580e8 + 8.63452e8i 0.717635 + 0.899886i
\(177\) −2.30643e8 + 7.47725e8i −0.234989 + 0.761814i
\(178\) −1.25074e9 + 2.16634e9i −1.24591 + 2.15798i
\(179\) 7.02917e8 4.05829e8i 0.684687 0.395304i −0.116932 0.993140i \(-0.537306\pi\)
0.801619 + 0.597836i \(0.203973\pi\)
\(180\) 4.63251e9 1.05734e9i 4.41292 1.00722i
\(181\) 9.71442e8 + 1.46421e8i 0.905113 + 0.136424i 0.585073 0.810980i \(-0.301066\pi\)
0.320039 + 0.947404i \(0.396304\pi\)
\(182\) −2.24093e9 2.07928e9i −2.04241 1.89508i
\(183\) −7.29089e8 + 9.14248e8i −0.650094 + 0.815192i
\(184\) −1.03207e9 1.51376e9i −0.900402 1.32065i
\(185\) −8.79022e8 + 8.15613e8i −0.750434 + 0.696301i
\(186\) −3.46264e8 4.62058e9i −0.289305 3.86051i
\(187\) 5.04971e8 1.28665e9i 0.412952 1.05219i
\(188\) −7.51916e7 + 3.29436e8i −0.0601919 + 0.263718i
\(189\) −1.51214e9 + 4.66435e8i −1.18508 + 0.365547i
\(190\) −1.85721e8 + 2.72403e8i −0.142511 + 0.209025i
\(191\) −1.95961e8 1.30012e9i −0.147244 0.976898i −0.933392 0.358859i \(-0.883166\pi\)
0.786148 0.618038i \(-0.212072\pi\)
\(192\) 2.71407e9 1.06519e9i 1.99717 0.783832i
\(193\) −1.17928e9 + 5.67911e8i −0.849938 + 0.409309i −0.807555 0.589793i \(-0.799209\pi\)
−0.0423837 + 0.999101i \(0.513495\pi\)
\(194\) −3.26282e8 6.77532e8i −0.230349 0.478325i
\(195\) 2.05772e9 + 5.24299e9i 1.42314 + 3.62611i
\(196\) 3.14937e8 4.74691e7i 0.213402 0.0321652i
\(197\) 2.26323e9 + 1.54305e9i 1.50267 + 1.02450i 0.985701 + 0.168501i \(0.0538927\pi\)
0.516971 + 0.856003i \(0.327060\pi\)
\(198\) 2.33239e9 + 7.56142e9i 1.51754 + 4.91975i
\(199\) −9.60186e8 2.19156e8i −0.612270 0.139747i −0.0948691 0.995490i \(-0.530243\pi\)
−0.517401 + 0.855743i \(0.673100\pi\)
\(200\) −1.78642e9 7.01116e8i −1.11651 0.438198i
\(201\) 1.75302e9 1.31371e8i 1.07400 0.0804849i
\(202\) −7.87447e8 8.48666e8i −0.472950 0.509719i
\(203\) −1.01902e9 + 6.94753e8i −0.600063 + 0.409116i
\(204\) 2.85210e9 + 2.27447e9i 1.64681 + 1.31329i
\(205\) −1.97305e9 + 2.12644e9i −1.11718 + 1.20403i
\(206\) 2.41630e8 1.60311e9i 0.134178 0.890215i
\(207\) −7.72989e8 3.38668e9i −0.421009 1.84456i
\(208\) −1.10812e9 1.91932e9i −0.592017 1.02540i
\(209\) −3.10908e8 1.79503e8i −0.162947 0.0940777i
\(210\) 6.64929e9 + 2.05103e9i 3.41899 + 1.05462i
\(211\) 1.32535e9 1.05693e9i 0.668651 0.533231i −0.229284 0.973360i \(-0.573639\pi\)
0.897935 + 0.440128i \(0.145067\pi\)
\(212\) −2.24457e8 + 2.99517e9i −0.111119 + 1.48278i
\(213\) −5.01628e8 2.41571e8i −0.243704 0.117362i
\(214\) 1.54614e9i 0.737212i
\(215\) −1.88930e9 2.14930e9i −0.884194 1.00587i
\(216\) −4.33528e9 −1.99160
\(217\) 1.23486e9 2.56421e9i 0.556902 1.15642i
\(218\) 1.98096e9 + 1.48452e8i 0.877100 + 0.0657296i
\(219\) −3.50172e9 4.39102e9i −1.52232 1.90893i
\(220\) 2.95774e9 9.58875e9i 1.26261 4.09328i
\(221\) −1.38685e9 + 2.40210e9i −0.581382 + 1.00698i
\(222\) 4.56430e9 2.63520e9i 1.87915 1.08493i
\(223\) 1.20978e7 2.76125e6i 0.00489202 0.00111657i −0.220074 0.975483i \(-0.570630\pi\)
0.224966 + 0.974367i \(0.427773\pi\)
\(224\) 8.33753e8 + 1.25668e8i 0.331166 + 0.0499152i
\(225\) −2.66733e9 2.47492e9i −1.04075 0.965674i
\(226\) −4.80723e9 + 6.02808e9i −1.84273 + 2.31071i
\(227\) −4.22624e8 6.19875e8i −0.159166 0.233454i 0.738369 0.674397i \(-0.235596\pi\)
−0.897535 + 0.440943i \(0.854644\pi\)
\(228\) 6.94575e8 6.44472e8i 0.257028 0.238487i
\(229\) −2.79562e7 3.73050e8i −0.0101657 0.135652i 0.989812 0.142383i \(-0.0454764\pi\)
−0.999977 + 0.00673127i \(0.997857\pi\)
\(230\) −2.46128e9 + 6.27123e9i −0.879527 + 2.24100i
\(231\) −1.68608e9 + 7.38719e9i −0.592147 + 2.59436i
\(232\) −3.22870e9 + 9.95921e8i −1.11449 + 0.343774i
\(233\) 3.14058e9 4.60638e9i 1.06558 1.56292i 0.264474 0.964393i \(-0.414802\pi\)
0.801105 0.598524i \(-0.204246\pi\)
\(234\) −2.36669e9 1.57020e10i −0.789365 5.23710i
\(235\) 5.44397e8 2.13660e8i 0.178503 0.0700571i
\(236\) −2.52052e9 + 1.21382e9i −0.812536 + 0.391297i
\(237\) −3.97572e8 8.25566e8i −0.126015 0.261673i
\(238\) 1.25194e9 + 3.18988e9i 0.390188 + 0.994183i
\(239\) −4.80347e9 + 7.24007e8i −1.47219 + 0.221897i −0.835614 0.549317i \(-0.814888\pi\)
−0.636576 + 0.771214i \(0.719650\pi\)
\(240\) 4.16812e9 + 2.84177e9i 1.25630 + 0.856534i
\(241\) 1.40347e9 + 4.54993e9i 0.416039 + 1.34877i 0.885018 + 0.465557i \(0.154146\pi\)
−0.468978 + 0.883210i \(0.655378\pi\)
\(242\) 1.06081e10 + 2.42124e9i 3.09298 + 0.705953i
\(243\) 2.04584e9 + 8.02935e8i 0.586742 + 0.230279i
\(244\) −4.16905e9 + 3.12427e8i −1.17619 + 0.0881433i
\(245\) −3.74927e8 4.04076e8i −0.104060 0.112150i
\(246\) 1.05342e10 7.18212e9i 2.87649 1.96116i
\(247\) 5.63258e8 + 4.49183e8i 0.151328 + 0.120680i
\(248\) 5.30336e9 5.71566e9i 1.40199 1.51098i
\(249\) −8.72687e8 + 5.78990e9i −0.227018 + 1.50617i
\(250\) −4.08436e8 1.78948e9i −0.104560 0.458106i
\(251\) 9.09429e8 + 1.57518e9i 0.229126 + 0.396857i 0.957549 0.288270i \(-0.0930800\pi\)
−0.728423 + 0.685127i \(0.759747\pi\)
\(252\) −1.11093e10 6.41393e9i −2.75475 1.59046i
\(253\) −7.01004e9 2.16231e9i −1.71095 0.527760i
\(254\) −6.34062e9 + 5.05648e9i −1.52334 + 1.21482i
\(255\) 4.71816e8 6.29595e9i 0.111587 1.48902i
\(256\) 7.05107e9 + 3.39562e9i 1.64171 + 0.790604i
\(257\) 6.76547e8i 0.155084i −0.996989 0.0775418i \(-0.975293\pi\)
0.996989 0.0775418i \(-0.0247071\pi\)
\(258\) 5.99359e9 + 1.10576e10i 1.35272 + 2.49563i
\(259\) 3.23724e9 0.719410
\(260\) −8.73703e9 + 1.81426e10i −1.91192 + 3.97015i
\(261\) −6.38847e9 4.78750e8i −1.37669 0.103168i
\(262\) −2.52597e9 3.16746e9i −0.536071 0.672212i
\(263\) 1.65652e9 5.37030e9i 0.346237 1.12247i −0.600272 0.799796i \(-0.704941\pi\)
0.946509 0.322677i \(-0.104583\pi\)
\(264\) −1.03792e10 + 1.79773e10i −2.13673 + 3.70092i
\(265\) 4.50189e9 2.59917e9i 0.912874 0.527048i
\(266\) 8.67740e8 1.98056e8i 0.173326 0.0395605i
\(267\) −1.23033e10 1.85443e9i −2.42090 0.364893i
\(268\) 4.60723e9 + 4.27489e9i 0.893102 + 0.828678i
\(269\) −9.93068e8 + 1.24527e9i −0.189657 + 0.237823i −0.867564 0.497325i \(-0.834316\pi\)
0.677907 + 0.735148i \(0.262887\pi\)
\(270\) 8.98011e9 + 1.31714e10i 1.68977 + 2.47843i
\(271\) −6.21912e7 + 5.77050e7i −0.0115306 + 0.0106988i −0.685917 0.727680i \(-0.740599\pi\)
0.674386 + 0.738379i \(0.264408\pi\)
\(272\) 1.85653e8 + 2.47737e9i 0.0339177 + 0.452600i
\(273\) 5.55517e9 1.41543e10i 1.00011 2.54823i
\(274\) 1.86678e9 8.17891e9i 0.331201 1.45109i
\(275\) −7.34276e9 + 2.26494e9i −1.28389 + 0.396028i
\(276\) 1.09067e10 1.59972e10i 1.87957 2.75682i
\(277\) −1.95292e8 1.29568e9i −0.0331715 0.220079i 0.966103 0.258156i \(-0.0831148\pi\)
−0.999275 + 0.0380772i \(0.987877\pi\)
\(278\) −5.71163e9 + 2.24165e9i −0.956270 + 0.375308i
\(279\) 1.33196e10 6.41439e9i 2.19824 1.05862i
\(280\) 5.08048e9 + 1.05497e10i 0.826556 + 1.71636i
\(281\) 2.16477e9 + 5.51576e9i 0.347206 + 0.884667i 0.992668 + 0.120874i \(0.0385698\pi\)
−0.645462 + 0.763793i \(0.723335\pi\)
\(282\) −2.54171e9 + 3.83101e8i −0.401911 + 0.0605783i
\(283\) 8.71997e8 + 5.94518e8i 0.135947 + 0.0926871i 0.629384 0.777094i \(-0.283307\pi\)
−0.493437 + 0.869782i \(0.664260\pi\)
\(284\) −5.86726e8 1.90212e9i −0.0901908 0.292391i
\(285\) −1.59876e9 3.64907e8i −0.242328 0.0553099i
\(286\) −3.12160e10 1.22514e10i −4.66566 1.83114i
\(287\) 7.80932e9 5.85228e8i 1.15103 0.0862576i
\(288\) 2.97901e9 + 3.21061e9i 0.433015 + 0.466679i
\(289\) −3.19469e9 + 2.17811e9i −0.457971 + 0.312239i
\(290\) 9.71372e9 + 7.74643e9i 1.37339 + 1.09524i
\(291\) 2.54416e9 2.74195e9i 0.354790 0.382373i
\(292\) 2.99271e9 1.98553e10i 0.411654 2.73115i
\(293\) 1.33478e9 + 5.84807e9i 0.181109 + 0.793491i 0.981104 + 0.193484i \(0.0619786\pi\)
−0.799994 + 0.600008i \(0.795164\pi\)
\(294\) 1.21137e9 + 2.09815e9i 0.162139 + 0.280833i
\(295\) 4.19313e9 + 2.42090e9i 0.553668 + 0.319661i
\(296\) 8.47475e9 + 2.61411e9i 1.10398 + 0.340532i
\(297\) −1.35717e10 + 1.08231e10i −1.74425 + 1.39099i
\(298\) 4.51357e8 6.02294e9i 0.0572341 0.763736i
\(299\) 1.32635e10 + 6.38738e9i 1.65949 + 0.799167i
\(300\) 2.02805e10i 2.50377i
\(301\) −2.07718e8 + 7.72268e9i −0.0253050 + 0.940810i
\(302\) −1.66974e10 −2.00734
\(303\) 2.49850e9 5.18819e9i 0.296421 0.615525i
\(304\) 6.43464e8 + 4.82209e7i 0.0753407 + 0.00564601i
\(305\) 4.51138e9 + 5.65709e9i 0.521326 + 0.653723i
\(306\) −5.24666e9 + 1.70092e10i −0.598407 + 1.93999i
\(307\) 5.19102e8 8.99112e8i 0.0584386 0.101219i −0.835326 0.549755i \(-0.814721\pi\)
0.893765 + 0.448536i \(0.148054\pi\)
\(308\) −2.34606e10 + 1.35450e10i −2.60697 + 1.50514i
\(309\) 7.86174e9 1.79439e9i 0.862352 0.196826i
\(310\) −2.83507e10 4.27317e9i −3.06985 0.462705i
\(311\) −3.62072e9 3.35954e9i −0.387038 0.359119i 0.462525 0.886606i \(-0.346944\pi\)
−0.849563 + 0.527488i \(0.823134\pi\)
\(312\) 2.59726e10 3.25687e10i 2.74093 3.43702i
\(313\) −6.71514e9 9.84930e9i −0.699645 1.02619i −0.997436 0.0715595i \(-0.977202\pi\)
0.297792 0.954631i \(-0.403750\pi\)
\(314\) −9.32095e9 + 8.64857e9i −0.958829 + 0.889664i
\(315\) 1.65911e9 + 2.21393e10i 0.168513 + 2.24865i
\(316\) 1.19686e9 3.04954e9i 0.120031 0.305835i
\(317\) 2.45055e9 1.07366e10i 0.242676 1.06323i −0.695894 0.718145i \(-0.744992\pi\)
0.938570 0.345089i \(-0.112151\pi\)
\(318\) −2.18327e10 + 6.73448e9i −2.13500 + 0.658560i
\(319\) −7.62119e9 + 1.11782e10i −0.735970 + 1.07947i
\(320\) −2.68886e9 1.78394e10i −0.256429 1.70130i
\(321\) 7.15884e9 2.80964e9i 0.674253 0.264625i
\(322\) 1.63863e10 7.89125e9i 1.52426 0.734044i
\(323\) −3.50394e8 7.27601e8i −0.0321919 0.0668472i
\(324\) −3.13068e9 7.97685e9i −0.284092 0.723855i
\(325\) 1.52479e10 2.29825e9i 1.36671 0.205999i
\(326\) −2.99308e10 2.04065e10i −2.65002 1.80675i
\(327\) 2.91244e9 + 9.44190e9i 0.254722 + 0.825788i
\(328\) 2.09165e10 + 4.77406e9i 1.80715 + 0.412470i
\(329\) −1.46969e9 5.76812e8i −0.125442 0.0492323i
\(330\) 7.61180e10 5.70426e9i 6.41847 0.480998i
\(331\) −8.31830e8 8.96500e8i −0.0692983 0.0746858i 0.697451 0.716633i \(-0.254318\pi\)
−0.766749 + 0.641947i \(0.778127\pi\)
\(332\) −1.72964e10 + 1.17925e10i −1.42365 + 0.970631i
\(333\) 1.31470e10 + 1.04844e10i 1.06918 + 0.852639i
\(334\) −1.45141e10 + 1.56425e10i −1.16628 + 1.25695i
\(335\) 1.62122e9 1.07561e10i 0.128725 0.854033i
\(336\) −3.03051e9 1.32775e10i −0.237771 1.04174i
\(337\) 8.49478e9 + 1.47134e10i 0.658616 + 1.14076i 0.980974 + 0.194139i \(0.0621913\pi\)
−0.322358 + 0.946618i \(0.604475\pi\)
\(338\) 3.90661e10 + 2.25548e10i 2.99318 + 1.72811i
\(339\) −3.66466e10 1.13040e10i −2.77482 0.855919i
\(340\) 1.76479e10 1.40737e10i 1.32062 1.05316i
\(341\) 2.33309e9 3.11329e10i 0.172550 2.30252i
\(342\) 4.16548e9 + 2.00599e9i 0.304481 + 0.146630i
\(343\) 1.45149e10i 1.04866i
\(344\) −6.77994e9 + 2.00494e10i −0.484164 + 1.43175i
\(345\) −3.35094e10 −2.36532
\(346\) −1.24571e10 + 2.58674e10i −0.869183 + 1.80488i
\(347\) 1.02259e10 + 7.66322e8i 0.705313 + 0.0528559i 0.422557 0.906336i \(-0.361132\pi\)
0.282755 + 0.959192i \(0.408752\pi\)
\(348\) −2.22628e10 2.79167e10i −1.51797 1.90347i
\(349\) −1.54571e7 + 5.01107e7i −0.00104190 + 0.00337776i −0.956092 0.293066i \(-0.905324\pi\)
0.955050 + 0.296444i \(0.0958007\pi\)
\(350\) 9.52536e9 1.64984e10i 0.634759 1.09944i
\(351\) 3.01679e10 1.74174e10i 1.98754 1.14751i
\(352\) 9.01738e9 2.05816e9i 0.587367 0.134063i
\(353\) 2.09393e9 + 3.15610e8i 0.134854 + 0.0203260i 0.216122 0.976366i \(-0.430659\pi\)
−0.0812683 + 0.996692i \(0.525897\pi\)
\(354\) −1.55999e10 1.44746e10i −0.993362 0.921705i
\(355\) −2.14798e9 + 2.69348e9i −0.135244 + 0.169590i
\(356\) −2.50587e10 3.67543e10i −1.56012 2.28828i
\(357\) −1.24946e10 + 1.15933e10i −0.769219 + 0.713731i
\(358\) 1.64959e9 + 2.20123e10i 0.100426 + 1.34009i
\(359\) 6.80493e9 1.73387e10i 0.409681 1.04385i −0.565951 0.824439i \(-0.691491\pi\)
0.975632 0.219412i \(-0.0704138\pi\)
\(360\) −1.35344e10 + 5.92982e10i −0.805804 + 3.53046i
\(361\) 1.60286e10 4.94417e9i 0.943771 0.291115i
\(362\) −1.50507e10 + 2.20754e10i −0.876442 + 1.28551i
\(363\) 8.06641e9 + 5.35172e10i 0.464573 + 3.08224i
\(364\) 5.06048e10 1.98609e10i 2.88261 1.13134i
\(365\) −3.13106e10 + 1.50784e10i −1.76408 + 0.849539i
\(366\) −1.37985e10 2.86529e10i −0.768967 1.59678i
\(367\) −1.96169e9 4.99830e9i −0.108135 0.275523i 0.866556 0.499080i \(-0.166329\pi\)
−0.974691 + 0.223557i \(0.928233\pi\)
\(368\) 1.30382e10 1.96519e9i 0.710928 0.107155i
\(369\) 3.36103e10 + 2.29151e10i 1.81287 + 1.23599i
\(370\) −9.61244e9 3.11628e10i −0.512893 1.66276i
\(371\) −1.36819e10 3.12281e9i −0.722190 0.164835i
\(372\) 7.67026e10 + 3.01035e10i 4.00533 + 1.57198i
\(373\) −5.09432e9 + 3.81766e8i −0.263179 + 0.0197225i −0.205666 0.978622i \(-0.565936\pi\)
−0.0575128 + 0.998345i \(0.518317\pi\)
\(374\) 2.55679e10 + 2.75556e10i 1.30680 + 1.40839i
\(375\) 7.54334e9 5.14296e9i 0.381451 0.260069i
\(376\) −3.38171e9 2.69683e9i −0.169194 0.134928i
\(377\) 1.84663e10 1.99019e10i 0.914142 0.985211i
\(378\) 6.41426e9 4.25558e10i 0.314180 2.08445i
\(379\) −7.48565e9 3.27968e10i −0.362805 1.58955i −0.746041 0.665900i \(-0.768048\pi\)
0.383236 0.923650i \(-0.374810\pi\)
\(380\) −2.93146e9 5.07743e9i −0.140588 0.243506i
\(381\) −3.49344e10 2.01694e10i −1.65788 0.957179i
\(382\) 3.41690e10 + 1.05397e10i 1.60464 + 0.494967i
\(383\) −7.69736e8 + 6.13844e8i −0.0357723 + 0.0285274i −0.641213 0.767363i \(-0.721568\pi\)
0.605440 + 0.795891i \(0.292997\pi\)
\(384\) −4.95997e9 + 6.61862e10i −0.228115 + 3.04399i
\(385\) 4.22421e10 + 2.03427e10i 1.92266 + 0.925903i
\(386\) 3.55971e10i 1.60349i
\(387\) −2.58548e10 + 3.06904e10i −1.15265 + 1.36823i
\(388\) 1.33729e10 0.590065
\(389\) 5.94719e9 1.23495e10i 0.259725 0.539324i −0.729804 0.683656i \(-0.760389\pi\)
0.989529 + 0.144332i \(0.0461032\pi\)
\(390\) −1.52750e11 1.14470e10i −6.60270 0.494804i
\(391\) −1.02889e10 1.29018e10i −0.440211 0.552007i
\(392\) −1.20168e9 + 3.89574e9i −0.0508913 + 0.164985i
\(393\) 1.00756e10 1.74515e10i 0.422379 0.731582i
\(394\) −6.45152e10 + 3.72478e10i −2.67718 + 1.54567i
\(395\) −5.52768e9 + 1.26166e9i −0.227067 + 0.0518267i
\(396\) −1.39145e11 2.09728e10i −5.65832 0.852855i
\(397\) −1.03497e10 9.60314e9i −0.416645 0.386590i 0.443806 0.896123i \(-0.353628\pi\)
−0.860451 + 0.509532i \(0.829818\pi\)
\(398\) 1.67001e10 2.09413e10i 0.665560 0.834586i
\(399\) 2.49389e9 + 3.65786e9i 0.0983978 + 0.144323i
\(400\) 1.01244e10 9.39406e9i 0.395484 0.366955i
\(401\) 2.52275e9 + 3.36638e10i 0.0975657 + 1.30192i 0.804206 + 0.594351i \(0.202591\pi\)
−0.706640 + 0.707573i \(0.749790\pi\)
\(402\) −1.74666e10 + 4.45043e10i −0.668814 + 1.70411i
\(403\) −1.39412e10 + 6.10803e10i −0.528542 + 2.31569i
\(404\) 1.96731e10 6.06834e9i 0.738494 0.227795i
\(405\) −8.35454e9 + 1.22539e10i −0.310529 + 0.455463i
\(406\) −4.99911e9 3.31669e10i −0.183987 1.22068i
\(407\) 3.30566e10 1.29738e10i 1.20470 0.472812i
\(408\) −4.20713e10 + 2.02605e10i −1.51826 + 0.731154i
\(409\) −1.13476e10 2.35636e10i −0.405519 0.842069i −0.999299 0.0374413i \(-0.988079\pi\)
0.593780 0.804628i \(-0.297635\pi\)
\(410\) −2.88221e10 7.34374e10i −1.01997 2.59885i
\(411\) 4.12619e10 6.21923e9i 1.44605 0.217956i
\(412\) 2.38207e10 + 1.62407e10i 0.826732 + 0.563657i
\(413\) −3.85282e9 1.24905e10i −0.132428 0.429320i
\(414\) 9.21048e10 + 2.10223e10i 3.13531 + 0.715615i
\(415\) 3.37263e10 + 1.32366e10i 1.13704 + 0.446256i
\(416\) −1.85090e10 + 1.38706e9i −0.618031 + 0.0463151i
\(417\) −2.07583e10 2.23722e10i −0.686512 0.739884i
\(418\) 8.06705e9 5.50002e9i 0.264247 0.180160i
\(419\) −3.47920e9 2.77457e9i −0.112882 0.0900201i 0.565422 0.824802i \(-0.308713\pi\)
−0.678304 + 0.734782i \(0.737285\pi\)
\(420\) −8.41661e10 + 9.07095e10i −2.70483 + 2.91512i
\(421\) −9.17849e9 + 6.08953e10i −0.292175 + 1.93845i 0.0498339 + 0.998758i \(0.484131\pi\)
−0.342009 + 0.939697i \(0.611107\pi\)
\(422\) 1.02587e10 + 4.49465e10i 0.323478 + 1.41725i
\(423\) −4.10056e9 7.10238e9i −0.128080 0.221841i
\(424\) −3.32961e10 1.92235e10i −1.03022 0.594797i
\(425\) −1.65174e10 5.09494e9i −0.506274 0.156165i
\(426\) 1.18384e10 9.44080e9i 0.359463 0.286662i
\(427\) 1.45977e9 1.94793e10i 0.0439111 0.585953i
\(428\) 2.47722e10 + 1.19296e10i 0.738225 + 0.355511i
\(429\) 1.66798e11i 4.92450i
\(430\) 7.49579e10 2.09316e10i 2.19252 0.612251i
\(431\) −2.70950e9 −0.0785200 −0.0392600 0.999229i \(-0.512500\pi\)
−0.0392600 + 0.999229i \(0.512500\pi\)
\(432\) 1.35373e10 2.81106e10i 0.388685 0.807113i
\(433\) 5.59338e10 + 4.19166e9i 1.59119 + 0.119243i 0.840651 0.541578i \(-0.182173\pi\)
0.750543 + 0.660821i \(0.229792\pi\)
\(434\) 4.82593e10 + 6.05152e10i 1.36026 + 1.70571i
\(435\) −1.82154e10 + 5.90528e10i −0.508723 + 1.64924i
\(436\) −1.76631e10 + 3.05935e10i −0.488790 + 0.846609i
\(437\) −3.71195e9 + 2.14310e9i −0.101783 + 0.0587647i
\(438\) 1.48913e11 3.39884e10i 4.04609 0.923495i
\(439\) 5.71093e10 + 8.60784e9i 1.53762 + 0.231759i 0.862541 0.505988i \(-0.168872\pi\)
0.675078 + 0.737747i \(0.264110\pi\)
\(440\) 9.41582e10 + 8.73660e10i 2.51216 + 2.33094i
\(441\) −4.81954e9 + 6.04351e9i −0.127424 + 0.159785i
\(442\) −4.24936e10 6.23266e10i −1.11336 1.63299i
\(443\) −3.07864e9 + 2.85656e9i −0.0799362 + 0.0741700i −0.719129 0.694876i \(-0.755459\pi\)
0.639193 + 0.769046i \(0.279269\pi\)
\(444\) 7.00399e9 + 9.34618e10i 0.180225 + 2.40493i
\(445\) −2.81273e10 + 7.16672e10i −0.717279 + 1.82760i
\(446\) −7.50954e7 + 3.29014e8i −0.00189790 + 0.00831525i
\(447\) 2.87073e10 8.85504e9i 0.719056 0.221799i
\(448\) −2.74362e10 + 4.02415e10i −0.681102 + 0.998993i
\(449\) −1.24086e8 8.23258e8i −0.00305308 0.0202559i 0.987252 0.159162i \(-0.0508793\pi\)
−0.990305 + 0.138907i \(0.955641\pi\)
\(450\) 9.21170e10 3.61532e10i 2.24641 0.881652i
\(451\) 7.73983e10 3.72730e10i 1.87079 0.900925i
\(452\) −5.94902e10 1.23533e11i −1.42525 2.95957i
\(453\) −3.03425e10 7.73113e10i −0.720540 1.83591i
\(454\) 2.01757e10 3.04099e9i 0.474903 0.0715801i
\(455\) −7.77380e10 5.30008e10i −1.81379 1.23662i
\(456\) 3.57496e9 + 1.15897e10i 0.0826821 + 0.268049i
\(457\) −5.98128e10 1.36519e10i −1.37129 0.312988i −0.527452 0.849585i \(-0.676853\pi\)
−0.843839 + 0.536597i \(0.819710\pi\)
\(458\) 9.47068e9 + 3.71697e9i 0.215238 + 0.0844747i
\(459\) −3.89392e10 + 2.91809e9i −0.877276 + 0.0657427i
\(460\) −8.14869e10 8.78220e10i −1.81994 1.96143i
\(461\) 5.41172e10 3.68965e10i 1.19821 0.816923i 0.211174 0.977449i \(-0.432271\pi\)
0.987032 + 0.160526i \(0.0513190\pi\)
\(462\) −1.61112e11 1.28482e11i −3.53638 2.82017i
\(463\) −3.40721e10 + 3.67209e10i −0.741437 + 0.799079i −0.985319 0.170726i \(-0.945389\pi\)
0.243881 + 0.969805i \(0.421579\pi\)
\(464\) 3.62423e9 2.40452e10i 0.0781886 0.518747i
\(465\) −3.17334e10 1.39033e11i −0.678742 2.97376i
\(466\) 7.58109e10 + 1.31308e11i 1.60764 + 2.78451i
\(467\) 6.40695e10 + 3.69905e10i 1.34705 + 0.777720i 0.987831 0.155534i \(-0.0497097\pi\)
0.359219 + 0.933253i \(0.383043\pi\)
\(468\) 2.69838e11 + 8.32339e10i 5.62495 + 1.73507i
\(469\) −2.29591e10 + 1.83093e10i −0.474531 + 0.378426i
\(470\) −1.18858e9 + 1.58605e10i −0.0243577 + 0.325031i
\(471\) −5.69822e10 2.74412e10i −1.15786 0.557596i
\(472\) 3.58101e10i 0.721502i
\(473\) 2.88288e10 + 7.96914e10i 0.575946 + 1.59209i
\(474\) 2.49201e10 0.493669
\(475\) −1.94798e9 + 4.04502e9i −0.0382657 + 0.0794596i
\(476\) −6.07679e10 4.55392e9i −1.18371 0.0887070i
\(477\) −4.54508e10 5.69935e10i −0.877946 1.10091i
\(478\) 3.89406e10 1.26242e11i 0.745918 2.41821i
\(479\) −3.13260e10 + 5.42582e10i −0.595063 + 1.03068i 0.398475 + 0.917179i \(0.369540\pi\)
−0.993538 + 0.113500i \(0.963794\pi\)
\(480\) 3.65888e10 2.11245e10i 0.689260 0.397944i
\(481\) −6.94756e10 + 1.58573e10i −1.29793 + 0.296244i
\(482\) −1.28047e11 1.93000e10i −2.37237 0.357577i
\(483\) 6.63149e10 + 6.15313e10i 1.21849 + 1.13060i
\(484\) −1.20643e11 + 1.51282e11i −2.19847 + 2.75680i
\(485\) −1.30379e10 1.91231e10i −0.235636 0.345615i
\(486\) −4.38151e10 + 4.06545e10i −0.785379 + 0.728725i
\(487\) 2.25021e9 + 3.00269e10i 0.0400043 + 0.533820i 0.980822 + 0.194907i \(0.0624404\pi\)
−0.940818 + 0.338914i \(0.889941\pi\)
\(488\) 1.95513e10 4.98160e10i 0.344744 0.878394i
\(489\) 4.00948e10 1.75667e11i 0.701218 3.07224i
\(490\) 1.43252e10 4.41872e9i 0.248493 0.0766501i
\(491\) 7.34592e9 1.07745e10i 0.126392 0.185383i −0.757827 0.652456i \(-0.773739\pi\)
0.884219 + 0.467072i \(0.154691\pi\)
\(492\) 3.37920e10 + 2.24195e11i 0.576704 + 3.82618i
\(493\) −2.83296e10 + 1.11185e10i −0.479570 + 0.188217i
\(494\) −1.76527e10 + 8.50110e9i −0.296417 + 0.142747i
\(495\) 1.05669e11 + 2.19423e11i 1.76005 + 3.65479i
\(496\) 2.05009e10 + 5.22354e10i 0.338724 + 0.863055i
\(497\) 9.19672e9 1.38618e9i 0.150733 0.0227193i
\(498\) −1.31572e11 8.97040e10i −2.13917 1.45846i
\(499\) 1.01510e10 + 3.29087e10i 0.163722 + 0.530773i 0.999842 0.0177734i \(-0.00565774\pi\)
−0.836120 + 0.548546i \(0.815182\pi\)
\(500\) 3.18224e10 + 7.26325e9i 0.509158 + 0.116212i
\(501\) −9.88021e10 3.87770e10i −1.56825 0.615493i
\(502\) −4.93276e10 + 3.69660e9i −0.776740 + 0.0582086i
\(503\) 1.45339e10 + 1.56638e10i 0.227044 + 0.244695i 0.836292 0.548285i \(-0.184719\pi\)
−0.609248 + 0.792980i \(0.708528\pi\)
\(504\) 1.35670e11 9.24984e10i 2.10263 1.43355i
\(505\) −2.78579e10 2.22159e10i −0.428334 0.341585i
\(506\) 1.35701e11 1.46251e11i 2.07005 2.23099i
\(507\) −3.34413e10 + 2.21869e11i −0.506118 + 3.35787i
\(508\) −3.20920e10 1.40604e11i −0.481883 2.11127i
\(509\) −4.24251e10 7.34823e10i −0.632050 1.09474i −0.987132 0.159907i \(-0.948880\pi\)
0.355082 0.934835i \(-0.384453\pi\)
\(510\) 1.48702e11 + 8.58529e10i 2.19804 + 1.26904i
\(511\) 8.96510e10 + 2.76537e10i 1.31484 + 0.405573i
\(512\) −6.82019e10 + 5.43892e10i −0.992468 + 0.791467i
\(513\) −7.57935e8 + 1.01139e10i −0.0109437 + 0.146033i
\(514\) 1.65774e10 + 7.98324e9i 0.237500 + 0.114374i
\(515\) 4.98970e10i 0.709326i
\(516\) −2.23409e11 + 1.07116e10i −3.15139 + 0.151096i
\(517\) −1.73192e10 −0.242418
\(518\) −3.81994e10 + 7.93218e10i −0.530563 + 1.10173i
\(519\) −1.42407e11 1.06719e10i −1.96273 0.147087i
\(520\) −1.60711e11 2.01525e11i −2.19802 2.75623i
\(521\) −3.19066e10 + 1.03439e11i −0.433042 + 1.40389i 0.431858 + 0.901942i \(0.357858\pi\)
−0.864900 + 0.501945i \(0.832618\pi\)
\(522\) 8.71145e10 1.50887e11i 1.17330 2.03221i
\(523\) 7.00177e9 4.04247e9i 0.0935838 0.0540307i −0.452478 0.891776i \(-0.649460\pi\)
0.546062 + 0.837745i \(0.316126\pi\)
\(524\) 7.02389e10 1.60316e10i 0.931649 0.212643i
\(525\) 9.36996e10 + 1.41229e10i 1.23339 + 0.185904i
\(526\) 1.12041e11 + 1.03959e11i 1.46364 + 1.35806i
\(527\) 4.37872e10 5.49074e10i 0.567681 0.711850i
\(528\) −8.41574e10 1.23436e11i −1.08282 1.58821i
\(529\) −6.79793e9 + 6.30755e9i −0.0868068 + 0.0805450i
\(530\) 1.05649e10 + 1.40979e11i 0.133895 + 1.78670i
\(531\) 2.48058e10 6.32042e10i 0.312015 0.795001i
\(532\) −3.52204e9 + 1.54311e10i −0.0439692 + 0.192642i
\(533\) −1.64732e11 + 5.08130e10i −2.04112 + 0.629602i
\(534\) 1.90618e11 2.79585e11i 2.34422 3.43834i
\(535\) −7.09235e9 4.70547e10i −0.0865715 0.574365i
\(536\) −7.48896e10 + 2.93920e10i −0.907323 + 0.356098i
\(537\) −9.89225e10 + 4.76386e10i −1.18959 + 0.572877i
\(538\) −1.87945e10 3.90272e10i −0.224337 0.465841i
\(539\) 5.96388e9 + 1.51957e10i 0.0706600 + 0.180039i
\(540\) −2.80321e11 + 4.22515e10i −3.29670 + 0.496898i
\(541\) 7.03768e10 + 4.79821e10i 0.821563 + 0.560132i 0.899548 0.436823i \(-0.143896\pi\)
−0.0779850 + 0.996955i \(0.524849\pi\)
\(542\) −6.80085e8 2.20478e9i −0.00788073 0.0255487i
\(543\) −1.29563e11 2.95718e10i −1.49032 0.340156i
\(544\) 1.93678e10 + 7.60129e9i 0.221149 + 0.0867945i
\(545\) 6.09689e10 4.56899e9i 0.691071 0.0517886i
\(546\) 2.81271e11 + 3.03138e11i 3.16486 + 3.41091i
\(547\) 7.68283e10 5.23806e10i 0.858167 0.585088i −0.0523179 0.998630i \(-0.516661\pi\)
0.910485 + 0.413542i \(0.135709\pi\)
\(548\) 1.16639e11 + 9.30162e10i 1.29336 + 1.03142i
\(549\) 6.90155e10 7.43811e10i 0.759727 0.818791i
\(550\) 3.11468e10 2.06645e11i 0.340378 2.25826i
\(551\) 1.75895e9 + 7.70646e9i 0.0190830 + 0.0836082i
\(552\) 1.23918e11 + 2.14632e11i 1.33468 + 2.31174i
\(553\) 1.32560e10 + 7.65334e9i 0.141746 + 0.0818372i
\(554\) 3.40523e10 + 1.05037e10i 0.361499 + 0.111508i
\(555\) 1.26821e11 1.01136e11i 1.33665 1.06594i
\(556\) 8.15401e9 1.08808e11i 0.0853241 1.13857i
\(557\) 1.77282e10 + 8.53746e9i 0.184181 + 0.0886968i 0.523702 0.851902i \(-0.324551\pi\)
−0.339521 + 0.940599i \(0.610265\pi\)
\(558\) 4.02059e11i 4.14718i
\(559\) −3.33710e10 1.66757e11i −0.341760 1.70779i
\(560\) −8.42701e10 −0.856883
\(561\) −8.11248e10 + 1.68457e11i −0.819034 + 1.70074i
\(562\) −1.60696e11 1.20425e10i −1.61087 0.120718i
\(563\) 8.34520e10 + 1.04646e11i 0.830622 + 1.04157i 0.998445 + 0.0557496i \(0.0177549\pi\)
−0.167823 + 0.985817i \(0.553674\pi\)
\(564\) 1.34732e10 4.36792e10i 0.133154 0.431676i
\(565\) −1.18650e11 + 2.05508e11i −1.16433 + 2.01667i
\(566\) −2.48570e10 + 1.43512e10i −0.242204 + 0.139837i
\(567\) 3.90346e10 8.90940e9i 0.377675 0.0862018i
\(568\) 2.51954e10 + 3.79759e9i 0.242063 + 0.0364851i
\(569\) 5.82368e10 + 5.40359e10i 0.555583 + 0.515505i 0.907234 0.420626i \(-0.138189\pi\)
−0.351652 + 0.936131i \(0.614380\pi\)
\(570\) 2.78066e10 3.48684e10i 0.263420 0.330318i
\(571\) 6.51414e10 + 9.55449e10i 0.612791 + 0.898800i 0.999728 0.0233063i \(-0.00741929\pi\)
−0.386937 + 0.922106i \(0.626467\pi\)
\(572\) 4.37147e11 4.05613e11i 4.08361 3.78903i
\(573\) 1.32913e10 + 1.77360e11i 0.123296 + 1.64527i
\(574\) −7.78100e10 + 1.98257e11i −0.716783 + 1.82633i
\(575\) −2.04144e10 + 8.94414e10i −0.186752 + 0.818214i
\(576\) −2.41752e11 + 7.45706e10i −2.19624 + 0.677451i
\(577\) −3.53651e10 + 5.18711e10i −0.319060 + 0.467975i −0.951944 0.306272i \(-0.900918\pi\)
0.632884 + 0.774246i \(0.281871\pi\)
\(578\) −1.56726e10 1.03981e11i −0.140420 0.931627i
\(579\) 1.64820e11 6.46871e10i 1.46655 0.575577i
\(580\) −1.99062e11 + 9.58633e10i −1.75905 + 0.847111i
\(581\) −4.24386e10 8.81247e10i −0.372441 0.773381i
\(582\) 3.71647e10 + 9.46941e10i 0.323921 + 0.825337i
\(583\) −1.52226e11 + 2.29444e10i −1.31769 + 0.198610i
\(584\) 2.12366e11 + 1.44789e11i 1.82572 + 1.24475i
\(585\) −1.44054e11 4.67013e11i −1.22999 3.98754i
\(586\) −1.59045e11 3.63010e10i −1.34874 0.307842i
\(587\) −1.16562e11 4.57473e10i −0.981761 0.385313i −0.180465 0.983581i \(-0.557760\pi\)
−0.801296 + 0.598269i \(0.795856\pi\)
\(588\) −4.29633e10 + 3.21965e9i −0.359408 + 0.0269339i
\(589\) −1.24071e10 1.33717e10i −0.103088 0.111103i
\(590\) −1.08798e11 + 7.41771e10i −0.897868 + 0.612156i
\(591\) −2.89700e11 2.31028e11i −2.37465 1.89372i
\(592\) −4.34135e10 + 4.67886e10i −0.353458 + 0.380937i
\(593\) 1.72397e10 1.14378e11i 0.139415 0.924961i −0.804305 0.594217i \(-0.797462\pi\)
0.943720 0.330744i \(-0.107300\pi\)
\(594\) −1.05051e11 4.60258e11i −0.843828 3.69705i
\(595\) 5.27335e10 + 9.13371e10i 0.420745 + 0.728752i
\(596\) 9.30169e10 + 5.37033e10i 0.737186 + 0.425614i
\(597\) 1.27309e11 + 3.92696e10i 1.00222 + 0.309143i
\(598\) −3.13018e11 + 2.49624e11i −2.44774 + 1.95201i
\(599\) 1.84211e9 2.45812e10i 0.0143090 0.190940i −0.985469 0.169857i \(-0.945669\pi\)
0.999778 0.0210831i \(-0.00671145\pi\)
\(600\) 2.33891e11 + 1.12636e11i 1.80471 + 0.869104i
\(601\) 1.37139e11i 1.05115i 0.850748 + 0.525573i \(0.176149\pi\)
−0.850748 + 0.525573i \(0.823851\pi\)
\(602\) −1.86777e11 9.62171e10i −1.42212 0.732599i
\(603\) −1.52539e11 −1.15375
\(604\) 1.28833e11 2.67525e11i 0.968011 2.01009i
\(605\) 3.33952e11 + 2.50262e10i 2.49266 + 0.186799i
\(606\) 9.76435e10 + 1.22441e11i 0.724024 + 0.907897i
\(607\) −2.37059e10 + 7.68527e10i −0.174623 + 0.566114i 0.825376 + 0.564584i \(0.190963\pi\)
−0.999999 + 0.00153047i \(0.999513\pi\)
\(608\) 2.70205e9 4.68008e9i 0.0197733 0.0342483i
\(609\) 1.44483e11 8.34175e10i 1.05039 0.606440i
\(610\) −1.91849e11 + 4.37883e10i −1.38561 + 0.316256i
\(611\) 3.43670e10 + 5.18000e9i 0.246591 + 0.0371676i
\(612\) −2.32040e11 2.15301e11i −1.65408 1.53476i
\(613\) −9.33660e10 + 1.17077e11i −0.661221 + 0.829145i −0.993476 0.114044i \(-0.963619\pi\)
0.332254 + 0.943190i \(0.392191\pi\)
\(614\) 1.59054e10 + 2.33290e10i 0.111911 + 0.164143i
\(615\) 2.87651e11 2.66901e11i 2.01078 1.86573i
\(616\) −2.59137e10 3.45794e11i −0.179973 2.40157i
\(617\) 8.35284e10 2.12827e11i 0.576360 1.46854i −0.283985 0.958829i \(-0.591657\pi\)
0.860345 0.509712i \(-0.170248\pi\)
\(618\) −4.88005e10 + 2.13809e11i −0.334557 + 1.46579i
\(619\) 3.23354e10 9.97414e9i 0.220250 0.0679380i −0.182666 0.983175i \(-0.558473\pi\)
0.402916 + 0.915237i \(0.367997\pi\)
\(620\) 2.87212e11 4.21263e11i 1.94373 2.85093i
\(621\) 3.08888e10 + 2.04934e11i 0.207699 + 1.37799i
\(622\) 1.25043e11 4.90757e10i 0.835405 0.327872i
\(623\) 1.87262e11 9.01806e10i 1.24308 0.598634i
\(624\) 1.30078e11 + 2.70109e11i 0.857954 + 1.78156i
\(625\) −6.48784e10 1.65307e11i −0.425187 1.08336i
\(626\) 3.20575e11 4.83189e10i 2.08753 0.314644i
\(627\) 4.01254e10 + 2.73570e10i 0.259627 + 0.177010i
\(628\) −6.66490e10 2.16071e11i −0.428504 1.38918i
\(629\) 7.78792e10 + 1.77754e10i 0.497529 + 0.113558i
\(630\) −5.62055e11 2.20590e11i −3.56793 1.40031i
\(631\) 9.35401e10 7.00986e9i 0.590039 0.0442173i 0.223635 0.974673i \(-0.428208\pi\)
0.366404 + 0.930456i \(0.380589\pi\)
\(632\) 2.85225e10 + 3.07400e10i 0.178780 + 0.192679i
\(633\) −1.89467e11 + 1.29176e11i −1.18010 + 0.804578i
\(634\) 2.34161e11 + 1.86737e11i 1.44930 + 1.15577i
\(635\) −1.69774e11 + 1.82973e11i −1.04418 + 1.12536i
\(636\) 6.05562e10 4.01764e11i 0.370110 2.45552i
\(637\) −7.28943e9 3.19371e10i −0.0442727 0.193971i
\(638\) −1.83969e11 3.18644e11i −1.11036 1.92319i
\(639\) 4.18388e10 + 2.41557e10i 0.250943 + 0.144882i
\(640\) 3.92443e11 + 1.21053e11i 2.33914 + 0.721530i
\(641\) −3.16608e10 + 2.52487e10i −0.187538 + 0.149557i −0.712758 0.701410i \(-0.752554\pi\)
0.525220 + 0.850966i \(0.323983\pi\)
\(642\) −1.56299e10 + 2.08566e11i −0.0920058 + 1.22773i
\(643\) −1.50685e11 7.25658e10i −0.881505 0.424510i −0.0623309 0.998056i \(-0.519853\pi\)
−0.819174 + 0.573545i \(0.805568\pi\)
\(644\) 3.23429e11i 1.88034i
\(645\) 2.33130e11 + 3.09029e11i 1.34697 + 1.78550i
\(646\) 2.19630e10 0.126113
\(647\) 8.31455e10 1.72654e11i 0.474484 0.985277i −0.517113 0.855917i \(-0.672993\pi\)
0.991598 0.129360i \(-0.0412923\pi\)
\(648\) 1.09383e11 + 8.19712e9i 0.620368 + 0.0464902i
\(649\) −8.94003e10 1.12104e11i −0.503918 0.631894i
\(650\) −1.23611e11 + 4.00737e11i −0.692474 + 2.24495i
\(651\) −1.92498e11 + 3.33416e11i −1.07177 + 1.85636i
\(652\) 5.57893e11 3.22099e11i 3.08717 1.78238i
\(653\) 4.60245e10 1.05048e10i 0.253126 0.0577743i −0.0940750 0.995565i \(-0.529989\pi\)
0.347201 + 0.937791i \(0.387132\pi\)
\(654\) −2.65721e11 4.00509e10i −1.45249 0.218928i
\(655\) −9.14042e10 8.48107e10i −0.496594 0.460771i
\(656\) −9.62696e10 + 1.20718e11i −0.519845 + 0.651865i
\(657\) 2.74527e11 + 4.02657e11i 1.47341 + 2.16109i
\(658\) 3.14759e10 2.92054e10i 0.167909 0.155797i
\(659\) 1.34409e8 + 1.79357e9i 0.000712668 + 0.00950990i 0.997549 0.0699743i \(-0.0222917\pi\)
−0.996836 + 0.0794842i \(0.974673\pi\)
\(660\) −4.95917e11 + 1.26358e12i −2.61356 + 6.65925i
\(661\) 3.36703e10 1.47519e11i 0.176377 0.772757i −0.806907 0.590678i \(-0.798860\pi\)
0.983284 0.182079i \(-0.0582826\pi\)
\(662\) 3.17824e10 9.80357e9i 0.165484 0.0510449i
\(663\) 2.11362e11 3.10012e11i 1.09389 1.60444i
\(664\) −3.99379e10 2.64971e11i −0.205453 1.36309i
\(665\) 2.55001e10 1.00080e10i 0.130393 0.0511755i
\(666\) −4.12031e11 + 1.98424e11i −2.09427 + 1.00855i
\(667\) 7.00827e10 + 1.45528e11i 0.354085 + 0.735265i
\(668\) −1.38636e11 3.53239e11i −0.696258 1.77404i
\(669\) −1.65985e9 + 2.50182e8i −0.00828637 + 0.00124897i
\(670\) 2.44425e11 + 1.66646e11i 1.21296 + 0.826981i
\(671\) −6.31602e10 2.04760e11i −0.311569 1.01008i
\(672\) −1.11199e11 2.53804e10i −0.545284 0.124458i
\(673\) −8.75829e10 3.43738e10i −0.426932 0.167559i 0.142139 0.989847i \(-0.454602\pi\)
−0.569071 + 0.822288i \(0.692697\pi\)
\(674\) −4.60759e11 + 3.45291e10i −2.23272 + 0.167319i
\(675\) 1.47656e11 + 1.59135e11i 0.711270 + 0.766567i
\(676\) −6.62799e11 + 4.51888e11i −3.17391 + 2.16394i
\(677\) −1.95542e11 1.55940e11i −0.930863 0.742338i 0.0355406 0.999368i \(-0.488685\pi\)
−0.966403 + 0.257030i \(0.917256\pi\)
\(678\) 7.09409e11 7.64561e11i 3.35721 3.61821i
\(679\) −9.31265e9 + 6.17854e10i −0.0438121 + 0.290674i
\(680\) 6.42948e10 + 2.81694e11i 0.300704 + 1.31747i
\(681\) 5.07435e10 + 8.78903e10i 0.235935 + 0.408651i
\(682\) 7.35317e11 + 4.24535e11i 3.39889 + 1.96235i
\(683\) −2.44849e11 7.55260e10i −1.12516 0.347067i −0.324325 0.945946i \(-0.605137\pi\)
−0.800840 + 0.598879i \(0.795613\pi\)
\(684\) −6.42798e10 + 5.12615e10i −0.293664 + 0.234189i
\(685\) 1.92953e10 2.57478e11i 0.0876374 1.16944i
\(686\) −3.55656e11 1.71275e11i −1.60596 0.773388i
\(687\) 5.06051e10i 0.227179i
\(688\) −1.08832e11 1.06568e11i −0.485739 0.475635i
\(689\) 3.08929e11 1.37082
\(690\) 3.95410e11 8.21076e11i 1.74442 3.62232i
\(691\) 3.05855e11 + 2.29207e10i 1.34154 + 0.100534i 0.726067 0.687624i \(-0.241346\pi\)
0.615472 + 0.788158i \(0.288965\pi\)
\(692\) −3.18331e11 3.99174e11i −1.38821 1.74076i
\(693\) 1.93796e11 6.28271e11i 0.840256 2.72404i
\(694\) −1.39442e11 + 2.41521e11i −0.601112 + 1.04116i
\(695\) −1.63543e11 + 9.44218e10i −0.700960 + 0.404700i
\(696\) 4.45603e11 1.01706e11i 1.89894 0.433420i
\(697\) 1.91084e11 + 2.88013e10i 0.809643 + 0.122034i
\(698\) −1.04546e9 9.70048e8i −0.00440440 0.00408669i
\(699\) −4.70214e11 + 5.89629e11i −1.96964 + 2.46985i
\(700\) 1.90842e11 + 2.79913e11i 0.794842 + 1.16582i
\(701\) −2.01651e11 + 1.87105e11i −0.835080 + 0.774841i −0.976593 0.215096i \(-0.930994\pi\)
0.141513 + 0.989936i \(0.454803\pi\)
\(702\) 7.07973e10 + 9.44725e11i 0.291520 + 3.89006i
\(703\) 7.58021e9 1.93141e10i 0.0310356 0.0790773i
\(704\) −1.18886e11 + 5.20875e11i −0.483995 + 2.12052i
\(705\) −7.55964e10 + 2.33184e10i −0.306016 + 0.0943935i
\(706\) −3.24417e10 + 4.75832e10i −0.130582 + 0.191529i
\(707\) 1.43369e10 + 9.51190e10i 0.0573822 + 0.380706i
\(708\) 3.52276e11 1.38258e11i 1.40201 0.550247i
\(709\) 6.37391e10 3.06951e10i 0.252244 0.121474i −0.303490 0.952835i \(-0.598152\pi\)
0.555734 + 0.831360i \(0.312437\pi\)
\(710\) −4.06520e10 8.44147e10i −0.159974 0.332189i
\(711\) 2.90481e10 + 7.40133e10i 0.113668 + 0.289622i
\(712\) 5.63054e11 8.48667e10i 2.19094 0.330231i
\(713\) −3.07973e11 2.09972e11i −1.19166 0.812463i
\(714\) −1.36633e11 4.42955e11i −0.525732 1.70438i
\(715\) −1.00622e12 2.29663e11i −3.85006 0.878752i
\(716\) −3.65408e11 1.43412e11i −1.39036 0.545675i
\(717\) 6.55284e11 4.91067e10i 2.47943 0.185808i
\(718\) 3.44550e11 + 3.71336e11i 1.29645 + 1.39724i
\(719\) 2.11189e11 1.43986e11i 0.790232 0.538771i −0.0996170 0.995026i \(-0.531762\pi\)
0.889849 + 0.456255i \(0.150809\pi\)
\(720\) −3.42235e11 2.72923e11i −1.27349 1.01557i
\(721\) −9.16230e10 + 9.87461e10i −0.339050 + 0.365409i
\(722\) −6.79906e10 + 4.51088e11i −0.250207 + 1.66002i
\(723\) −1.43326e11 6.27951e11i −0.524531 2.29812i
\(724\) −2.37563e11 4.11471e11i −0.864619 1.49756i
\(725\) 1.46523e11 + 8.45954e10i 0.530341 + 0.306193i
\(726\) −1.40651e12 4.33850e11i −5.06286 1.56169i
\(727\) −5.57377e10 + 4.44494e10i −0.199532 + 0.159121i −0.718159 0.695879i \(-0.755015\pi\)
0.518627 + 0.855001i \(0.326443\pi\)
\(728\) −5.20022e10 + 6.93921e11i −0.185138 + 2.47050i
\(729\) −3.72596e11 1.79433e11i −1.31925 0.635318i
\(730\) 9.45124e11i 3.32811i
\(731\) −4.74017e10 + 1.84646e11i −0.166006 + 0.646651i
\(732\) 5.65542e11 1.96979
\(733\) 9.24050e10 1.91881e11i 0.320096 0.664685i −0.677385 0.735629i \(-0.736887\pi\)
0.997480 + 0.0709436i \(0.0226010\pi\)
\(734\) 1.45621e11 + 1.09128e10i 0.501694 + 0.0375968i
\(735\) 4.64910e10 + 5.82979e10i 0.159301 + 0.199758i
\(736\) 3.25491e10 1.05522e11i 0.110925 0.359609i
\(737\) −1.61066e11 + 2.78975e11i −0.545927 + 0.945574i
\(738\) −9.58087e11 + 5.53152e11i −3.22983 + 1.86474i
\(739\) 4.04014e11 9.22135e10i 1.35462 0.309184i 0.517259 0.855829i \(-0.326953\pi\)
0.837364 + 0.546645i \(0.184095\pi\)
\(740\) 5.73457e11 + 8.64348e10i 1.91238 + 0.288245i
\(741\) −7.14399e10 6.62865e10i −0.236956 0.219863i
\(742\) 2.37964e11 2.98397e11i 0.785047 0.984418i
\(743\) −1.40456e11 2.06011e11i −0.460877 0.675982i 0.523506 0.852022i \(-0.324624\pi\)
−0.984383 + 0.176040i \(0.943671\pi\)
\(744\) −7.73177e11 + 7.17403e11i −2.52341 + 2.34138i
\(745\) −1.38916e10 1.85371e11i −0.0450950 0.601751i
\(746\) 5.07584e10 1.29330e11i 0.163890 0.417585i
\(747\) 1.13057e11 4.95334e11i 0.363090 1.59080i
\(748\) −6.38772e11 + 1.97035e11i −2.04051 + 0.629415i
\(749\) −7.23680e10 + 1.06144e11i −0.229942 + 0.337264i
\(750\) 3.70062e10 + 2.45520e11i 0.116958 + 0.775966i
\(751\) 4.04342e11 1.58692e11i 1.27113 0.498880i 0.368629 0.929576i \(-0.379827\pi\)
0.902497 + 0.430696i \(0.141732\pi\)
\(752\) 2.80463e10 1.35064e10i 0.0877010 0.0422346i
\(753\) −1.06754e11 2.21677e11i −0.332051 0.689510i
\(754\) 2.69753e11 + 6.87319e11i 0.834604 + 2.12654i
\(755\) −5.08163e11 + 7.65932e10i −1.56392 + 0.235723i
\(756\) 6.32338e11 + 4.31121e11i 1.93581 + 1.31981i
\(757\) 1.36518e11 + 4.42580e11i 0.415725 + 1.34775i 0.885368 + 0.464891i \(0.153906\pi\)
−0.469643 + 0.882856i \(0.655617\pi\)
\(758\) 8.91947e11 + 2.03581e11i 2.70185 + 0.616681i
\(759\) 9.23761e11 + 3.62549e11i 2.78351 + 1.09245i
\(760\) 7.48380e10 5.60834e9i 0.224320 0.0168105i
\(761\) 1.12005e11 + 1.20713e11i 0.333965 + 0.359928i 0.877600 0.479393i \(-0.159143\pi\)
−0.543636 + 0.839321i \(0.682953\pi\)
\(762\) 9.06434e11 6.17997e11i 2.68854 1.83302i
\(763\) −1.29047e11 1.02912e11i −0.380759 0.303645i
\(764\) −4.32508e11 + 4.66133e11i −1.26946 + 1.36816i
\(765\) −8.16514e10 + 5.41722e11i −0.238406 + 1.58172i
\(766\) −5.95809e9 2.61041e10i −0.0173058 0.0758217i
\(767\) 1.43871e11 + 2.49191e11i 0.415710 + 0.720031i
\(768\) −9.16828e11 5.29331e11i −2.63538 1.52154i
\(769\) 1.31260e10 + 4.04884e9i 0.0375343 + 0.0115778i 0.313465 0.949600i \(-0.398510\pi\)
−0.275931 + 0.961177i \(0.588986\pi\)
\(770\) −9.96910e11 + 7.95009e11i −2.83591 + 2.26157i
\(771\) −6.83921e9 + 9.12629e10i −0.0193548 + 0.258272i
\(772\) 5.70336e11 + 2.74659e11i 1.60569 + 0.773260i
\(773\) 1.96763e11i 0.551093i 0.961288 + 0.275546i \(0.0888588\pi\)
−0.961288 + 0.275546i \(0.911141\pi\)
\(774\) −4.46917e11 9.95663e11i −1.24527 2.77427i
\(775\) −3.90432e11 −1.08228
\(776\) −7.42720e10 + 1.54227e11i −0.204823 + 0.425319i
\(777\) −4.36688e11 3.27252e10i −1.19808 0.0897839i
\(778\) 2.32421e11 + 2.91447e11i 0.634391 + 0.795501i
\(779\) 1.47944e10 4.79623e10i 0.0401743 0.130242i
\(780\) 1.36199e12 2.35903e12i 3.67955 6.37316i
\(781\) 8.83556e10 5.10121e10i 0.237481 0.137110i
\(782\) 4.37541e11 9.98658e10i 1.17001 0.267048i
\(783\) 3.77941e11 + 5.69655e10i 1.00549 + 0.151553i
\(784\) −2.15082e10 1.99567e10i −0.0569297 0.0528231i
\(785\) −2.43999e11 + 3.05965e11i −0.642553 + 0.805736i
\(786\) 3.08721e11 + 4.52810e11i 0.808864 + 1.18639i
\(787\) −2.92199e11 + 2.71121e11i −0.761693 + 0.706748i −0.962019 0.272981i \(-0.911990\pi\)
0.200326 + 0.979729i \(0.435800\pi\)
\(788\) −9.89996e10 1.32106e12i −0.256761 3.42623i
\(789\) −2.77744e11 + 7.07681e11i −0.716700 + 1.82612i
\(790\) 3.43122e10 1.50332e11i 0.0880929 0.385960i
\(791\) 6.12171e11 1.88830e11i 1.56375 0.482353i
\(792\) 1.01467e12 1.48825e12i 2.57885 3.78248i
\(793\) 6.40891e10 + 4.25203e11i 0.162066 + 1.07524i
\(794\) 3.57431e11 1.40281e11i 0.899312 0.352954i
\(795\) −6.33557e11 + 3.05105e11i −1.58605 + 0.763802i
\(796\) 2.06667e11 + 4.29148e11i 0.514776 + 1.06894i
\(797\) 1.68560e11 + 4.29485e11i 0.417755 + 1.06442i 0.972603 + 0.232471i \(0.0746812\pi\)
−0.554848 + 0.831952i \(0.687224\pi\)
\(798\) −1.19056e11 + 1.79448e10i −0.293589 + 0.0442514i
\(799\) −3.21895e10 2.19465e10i −0.0789819 0.0538490i
\(800\) −3.40940e10 1.10530e11i −0.0832374 0.269849i
\(801\) 1.05257e12 + 2.40242e11i 2.55694 + 0.583604i
\(802\) −8.54628e11 3.35417e11i −2.06576 0.810751i
\(803\) 1.02628e12 7.69094e10i 2.46834 0.184977i
\(804\) −5.78278e11 6.23236e11i −1.38392 1.49152i
\(805\) 4.62499e11 3.15327e11i 1.10136 0.750891i
\(806\) −1.33214e12 1.06234e12i −3.15652 2.51724i
\(807\) 1.46548e11 1.57941e11i 0.345531 0.372393i
\(808\) −3.92774e10 + 2.60589e11i −0.0921504 + 0.611378i
\(809\) −7.22352e10 3.16483e11i −0.168638 0.738850i −0.986544 0.163498i \(-0.947722\pi\)
0.817906 0.575352i \(-0.195135\pi\)
\(810\) −2.01672e11 3.49306e11i −0.468495 0.811457i
\(811\) 3.59569e11 + 2.07597e11i 0.831188 + 0.479887i 0.854259 0.519847i \(-0.174011\pi\)
−0.0230714 + 0.999734i \(0.507345\pi\)
\(812\) 5.69972e11 + 1.75813e11i 1.31108 + 0.404415i
\(813\) 8.97263e9 7.15543e9i 0.0205380 0.0163785i
\(814\) −7.21723e10 + 9.63072e11i −0.164389 + 2.19362i
\(815\) −1.00451e12 4.83749e11i −2.27680 1.09645i
\(816\) 3.36061e11i 0.757980i
\(817\) 4.55887e10 + 1.93224e10i 0.102322 + 0.0433684i
\(818\) 7.11277e11 1.58864
\(819\) −5.72465e11 + 1.18874e12i −1.27237 + 2.64210i
\(820\) 1.39900e12 + 1.04840e11i 3.09429 + 0.231885i
\(821\) −3.52835e11 4.42441e11i −0.776602 0.973829i 0.223397 0.974728i \(-0.428285\pi\)
−1.00000 0.000898866i \(0.999714\pi\)
\(822\) −3.34500e11 + 1.08442e12i −0.732671 + 2.37526i
\(823\) 2.29391e11 3.97318e11i 0.500009 0.866041i −0.499991 0.866031i \(-0.666663\pi\)
1.00000 1.03052e-5i \(-3.28025e-6\pi\)
\(824\) −3.19598e11 + 1.84520e11i −0.693258 + 0.400253i
\(825\) 1.01340e12 2.31302e11i 2.18758 0.499301i
\(826\) 3.51518e11 + 5.29828e10i 0.755139 + 0.113819i
\(827\) 3.56661e11 + 3.30933e11i 0.762490 + 0.707487i 0.962193 0.272369i \(-0.0878073\pi\)
−0.199703 + 0.979856i \(0.563998\pi\)
\(828\) −1.04748e12 + 1.31350e12i −2.22856 + 2.79453i
\(829\) −2.36636e9 3.47081e9i −0.00501029 0.00734874i 0.823725 0.566989i \(-0.191892\pi\)
−0.828736 + 0.559640i \(0.810939\pi\)
\(830\) −7.22304e11 + 6.70200e11i −1.52198 + 1.41219i
\(831\) 1.32459e10 + 1.76755e11i 0.0277766 + 0.370652i
\(832\) 3.91698e11 9.98031e11i 0.817445 2.08282i
\(833\) −8.17114e9 + 3.58001e10i −0.0169708 + 0.0743540i
\(834\) 7.93131e11 2.44648e11i 1.63938 0.505683i
\(835\) −3.69964e11 + 5.42637e11i −0.761050 + 1.11626i
\(836\) 2.58777e10 + 1.71687e11i 0.0529786 + 0.351490i
\(837\) −8.21035e11 + 3.22233e11i −1.67286 + 0.656550i
\(838\) 1.09039e11 5.25106e10i 0.221110 0.106481i
\(839\) −1.61051e11 3.34427e11i −0.325025 0.674921i 0.672871 0.739760i \(-0.265061\pi\)
−0.997896 + 0.0648387i \(0.979347\pi\)
\(840\) −5.78684e11 1.47446e12i −1.16232 2.96153i
\(841\) −2.00101e11 + 3.01604e10i −0.400006 + 0.0602912i
\(842\) −1.38381e12 9.43463e11i −2.75313 1.87705i
\(843\) −2.36259e11 7.65932e11i −0.467818 1.51663i
\(844\) −7.99287e11 1.82432e11i −1.57519 0.359527i
\(845\) 1.29239e12 + 5.07225e11i 2.53493 + 0.994888i
\(846\) 2.22415e11 1.66677e10i 0.434194 0.0325383i
\(847\) −6.14935e11 6.62743e11i −1.19480 1.28769i
\(848\) 2.28618e11 1.55869e11i 0.442106 0.301423i
\(849\) −1.11618e11 8.90125e10i −0.214834 0.171325i
\(850\) 3.19745e11 3.44603e11i 0.612531 0.660152i
\(851\) 6.31898e10 4.19237e11i 0.120484 0.799358i
\(852\) 5.99180e10 + 2.62518e11i 0.113710 + 0.498196i
\(853\) −7.10249e10 1.23019e11i −0.134157 0.232367i 0.791118 0.611664i \(-0.209499\pi\)
−0.925275 + 0.379296i \(0.876166\pi\)
\(854\) 4.60075e11 + 2.65624e11i 0.864962 + 0.499386i
\(855\) 1.35973e11 + 4.19420e10i 0.254441 + 0.0784847i
\(856\) −2.75164e11 + 2.19436e11i −0.512504 + 0.408708i
\(857\) 3.56699e10 4.75982e11i 0.0661269 0.882403i −0.861228 0.508219i \(-0.830304\pi\)
0.927355 0.374183i \(-0.122077\pi\)
\(858\) 4.08703e12 + 1.96821e12i 7.54152 + 3.63181i
\(859\) 3.37886e11i 0.620579i −0.950642 0.310290i \(-0.899574\pi\)
0.950642 0.310290i \(-0.100426\pi\)
\(860\) −2.42992e11 + 1.36248e12i −0.444221 + 2.49078i
\(861\) −1.05935e12 −1.92765
\(862\) 3.19721e10 6.63907e10i 0.0579084 0.120248i
\(863\) −9.12042e11 6.83481e10i −1.64426 0.123221i −0.779838 0.625981i \(-0.784699\pi\)
−0.864426 + 0.502760i \(0.832318\pi\)
\(864\) −1.62919e11 2.04294e11i −0.292359 0.366607i
\(865\) −2.60458e11 + 8.44383e11i −0.465235 + 1.50826i
\(866\) −7.62726e11 + 1.32108e12i −1.35612 + 2.34886i
\(867\) 4.52967e11 2.61521e11i 0.801660 0.462838i
\(868\) −1.34193e12 + 3.06287e11i −2.36402 + 0.539573i
\(869\) 1.66033e11 + 2.50255e10i 0.291150 + 0.0438837i
\(870\) −1.23202e12 1.14315e12i −2.15051 1.99538i
\(871\) 4.03048e11 5.05406e11i 0.700299 0.878148i
\(872\) −2.54729e11 3.73619e11i −0.440567 0.646194i
\(873\) −2.37923e11 + 2.20760e11i −0.409618 + 0.380070i
\(874\) −8.71114e9 1.16242e11i −0.0149290 0.199213i
\(875\) −5.57180e10 + 1.41967e11i −0.0950525 + 0.242190i
\(876\) −6.04418e11 + 2.64813e12i −1.02641 + 4.49700i
\(877\) −6.67847e10 + 2.06004e10i −0.112896 + 0.0348238i −0.350688 0.936492i \(-0.614052\pi\)
0.237792 + 0.971316i \(0.423576\pi\)
\(878\) −8.84805e11 + 1.29777e12i −1.48891 + 2.18383i
\(879\) −1.20938e11 8.02369e11i −0.202584 1.34406i
\(880\) −8.60511e11 + 3.37726e11i −1.43491 + 0.563162i
\(881\) 7.63154e11 3.67516e11i 1.26680 0.610060i 0.324837 0.945770i \(-0.394691\pi\)
0.941965 + 0.335711i \(0.108976\pi\)
\(882\) −9.12130e10 1.89406e11i −0.150724 0.312982i
\(883\) −3.42461e11 8.72577e11i −0.563337 1.43536i −0.874510 0.485007i \(-0.838817\pi\)
0.311173 0.950353i \(-0.399278\pi\)
\(884\) 1.32647e12 1.99933e11i 2.17214 0.327397i
\(885\) −5.41159e11 3.68956e11i −0.882169 0.601452i
\(886\) −3.36661e10 1.09143e11i −0.0546334 0.177117i
\(887\) −5.61863e11 1.28242e11i −0.907686 0.207173i −0.256903 0.966437i \(-0.582702\pi\)
−0.650783 + 0.759264i \(0.725559\pi\)
\(888\) −1.11678e12 4.38302e11i −1.79603 0.704891i
\(889\) 6.71965e11 5.03568e10i 1.07582 0.0806215i
\(890\) −1.42415e12 1.53487e12i −2.26984 2.44631i
\(891\) 3.62890e11 2.47414e11i 0.575791 0.392567i
\(892\) −4.69204e9 3.74178e9i −0.00741144 0.00591043i
\(893\) −6.88275e9 + 7.41785e9i −0.0108232 + 0.0116647i
\(894\) −1.21772e11 + 8.07902e11i −0.190632 + 1.26476i
\(895\) 1.51177e11 + 6.62349e11i 0.235610 + 1.03227i
\(896\) −5.54361e11 9.60182e11i −0.860124 1.48978i
\(897\) −1.72461e12 9.95706e11i −2.66392 1.53802i
\(898\) 2.16364e10 + 6.67395e9i 0.0332721 + 0.0102631i
\(899\) −5.37440e11 + 4.28594e11i −0.822795 + 0.656157i
\(900\) −1.31508e11 + 1.75485e12i −0.200438 + 2.67466i
\(901\) −3.12002e11 1.50252e11i −0.473433 0.227993i
\(902\) 2.33630e12i 3.52942i
\(903\) 1.06088e11 1.03965e12i 0.159558 1.56364i
\(904\) 1.75508e12 2.62799
\(905\) −3.56787e11 + 7.40876e11i −0.531881 + 1.10446i
\(906\) 2.25239e12 + 1.68793e11i 3.34296 + 0.250520i
\(907\) 2.37793e11 + 2.98183e11i 0.351374 + 0.440609i 0.925838 0.377921i \(-0.123361\pi\)
−0.574464 + 0.818530i \(0.694789\pi\)
\(908\) −1.06948e11 + 3.46718e11i −0.157337 + 0.510074i
\(909\) −2.49835e11 + 4.32727e11i −0.365930 + 0.633809i
\(910\) 2.21598e12 1.27940e12i 3.23147 1.86569i
\(911\) 1.11554e12 2.54614e11i 1.61961 0.369666i 0.685901 0.727695i \(-0.259408\pi\)
0.933710 + 0.358029i \(0.116551\pi\)
\(912\) −8.63126e10 1.30095e10i −0.124766 0.0188054i
\(913\) −7.86529e11 7.29793e11i −1.13196 1.05031i
\(914\) 1.04030e12 1.30450e12i 1.49064 1.86921i
\(915\) −5.51375e11 8.08718e11i −0.786616 1.15375i
\(916\) −1.32627e11 + 1.23060e11i −0.188386 + 0.174797i
\(917\) 2.51558e10 + 3.35680e11i 0.0355762 + 0.474732i
\(918\) 3.87980e11 9.88556e11i 0.546309 1.39197i
\(919\) −2.86093e11 + 1.25346e12i −0.401093 + 1.75730i 0.221893 + 0.975071i \(0.428776\pi\)
−0.622986 + 0.782233i \(0.714081\pi\)
\(920\) 1.46540e12 4.52017e11i 2.04553 0.630963i
\(921\) −7.91134e10 + 1.16038e11i −0.109954 + 0.161273i
\(922\) 2.65489e11 + 1.76140e12i 0.367386 + 2.43745i
\(923\) −1.90584e11 + 7.47987e10i −0.262591 + 0.103059i
\(924\) 3.30165e12 1.58999e12i 4.52942 2.18125i
\(925\) −1.92686e11 4.00116e11i −0.263198 0.546537i
\(926\) −4.97720e11 1.26817e12i −0.676926 1.72478i
\(927\) −6.91902e11 + 1.04288e11i −0.936970 + 0.141226i
\(928\) −1.68265e11 1.14721e11i −0.226883 0.154686i
\(929\) 2.75732e11 + 8.93902e11i 0.370190 + 1.20013i 0.928764 + 0.370672i \(0.120873\pi\)
−0.558574 + 0.829455i \(0.688651\pi\)
\(930\) 3.78117e12 + 8.63026e11i 5.05468 + 1.15370i
\(931\) 8.87843e9 + 3.48453e9i 0.0118178 + 0.00463816i
\(932\) −2.68876e12 + 2.01495e11i −3.56360 + 0.267055i
\(933\) 4.54456e11 + 4.89787e11i 0.599743 + 0.646369i
\(934\) −1.66239e12 + 1.13340e12i −2.18447 + 1.48935i
\(935\) 9.04528e11 + 7.21337e11i 1.18352 + 0.943826i
\(936\) −2.45857e12 + 2.64971e12i −3.20317 + 3.45219i
\(937\) −8.38297e10 + 5.56174e11i −0.108753 + 0.721526i 0.866295 + 0.499532i \(0.166495\pi\)
−0.975048 + 0.221994i \(0.928743\pi\)
\(938\) −1.77714e11 7.78615e11i −0.229567 1.00580i
\(939\) 8.06272e11 + 1.39650e12i 1.03710 + 1.79630i
\(940\) −2.44946e11 1.41420e11i −0.313732 0.181133i
\(941\) −3.65093e11 1.12616e11i −0.465634 0.143629i 0.0530559 0.998592i \(-0.483104\pi\)
−0.518690 + 0.854963i \(0.673580\pi\)
\(942\) 1.34478e12 1.07242e12i 1.70784 1.36196i
\(943\) 7.66456e10 1.02276e12i 0.0969260 1.29339i
\(944\) 2.32198e11 + 1.11820e11i 0.292395 + 0.140810i
\(945\) 1.32456e12i 1.66090i
\(946\) −2.29285e12 2.33968e11i −2.86293 0.292140i
\(947\) 1.50999e12 1.87747 0.938736 0.344637i \(-0.111998\pi\)
0.938736 + 0.344637i \(0.111998\pi\)
\(948\) −1.92278e11 + 3.99269e11i −0.238065 + 0.494348i
\(949\) −2.05949e12 1.54338e11i −2.53919 0.190286i
\(950\) −7.61286e10 9.54623e10i −0.0934660 0.117203i
\(951\) −4.39103e11 + 1.42354e12i −0.536840 + 1.74039i
\(952\) 3.90018e11 6.75532e11i 0.474829 0.822428i
\(953\) 2.53403e11 1.46302e11i 0.307214 0.177370i −0.338465 0.940979i \(-0.609908\pi\)
0.645679 + 0.763609i \(0.276574\pi\)
\(954\) 1.93282e12 4.41154e11i 2.33345 0.532595i
\(955\) 1.08824e12 + 1.64025e11i 1.30831 + 0.197196i
\(956\) 1.72220e12 + 1.59796e12i 2.06182 + 1.91309i
\(957\) 1.14106e12 1.43085e12i 1.36038 1.70587i
\(958\) −9.59838e11 1.40782e12i −1.13956 1.67142i
\(959\) −5.10977e11 + 4.74117e11i −0.604125 + 0.560546i
\(960\) 1.82375e11 + 2.43363e12i 0.214724 + 2.86530i
\(961\) 2.67945e11 6.82713e11i 0.314161 0.800469i
\(962\) 4.31259e11 1.88947e12i 0.503544 2.20617i
\(963\) −6.37665e11 + 1.96694e11i −0.741460 + 0.228710i
\(964\) 1.29721e12 1.90266e12i 1.50211 2.20319i
\(965\) −1.63289e11 1.08335e12i −0.188299 1.24928i
\(966\) −2.29021e12 + 8.98841e11i −2.63007 + 1.03222i
\(967\) −7.31259e11 + 3.52156e11i −0.836306 + 0.402744i −0.802477 0.596684i \(-0.796485\pi\)
−0.0338298 + 0.999428i \(0.510770\pi\)
\(968\) −1.07466e12 2.23156e12i −1.22397 2.54160i
\(969\) 3.99111e10 + 1.01692e11i 0.0452688 + 0.115343i
\(970\) 6.22419e11 9.38146e10i 0.703066 0.105970i
\(971\) 3.08580e11 + 2.10386e11i 0.347129 + 0.236668i 0.724315 0.689469i \(-0.242156\pi\)
−0.377186 + 0.926137i \(0.623108\pi\)
\(972\) −3.13298e11 1.01569e12i −0.350988 1.13788i
\(973\) 4.97033e11 + 1.13444e11i 0.554541 + 0.126570i
\(974\) −7.62299e11 2.99180e11i −0.847012 0.332428i
\(975\) −2.08010e12 + 1.55882e11i −2.30179 + 0.172495i
\(976\) 2.61963e11 + 2.82329e11i 0.288696 + 0.311140i
\(977\) 9.27065e10 6.32062e10i 0.101749 0.0693716i −0.511376 0.859357i \(-0.670864\pi\)
0.613126 + 0.789985i \(0.289912\pi\)
\(978\) 3.83123e12 + 3.05531e12i 4.18777 + 3.33964i
\(979\) 1.55078e12 1.67135e12i 1.68819 1.81943i
\(980\) −3.97330e10 + 2.63611e11i −0.0430772 + 0.285798i
\(981\) −1.90785e11 8.35882e11i −0.206000 0.902545i
\(982\) 1.77324e11 + 3.07135e11i 0.190688 + 0.330281i
\(983\) −6.18169e10 3.56900e10i −0.0662053 0.0382237i 0.466532 0.884504i \(-0.345503\pi\)
−0.532737 + 0.846281i \(0.678837\pi\)
\(984\) −2.77328e12 8.55442e11i −2.95810 0.912453i
\(985\) −1.79258e12 + 1.42953e12i −1.90429 + 1.51862i
\(986\) 6.18518e10 8.25354e11i 0.0654402 0.873238i
\(987\) 1.92423e11 + 9.26661e10i 0.202763 + 0.0976455i
\(988\) 3.48424e11i 0.365663i
\(989\) 9.96066e11 + 1.77644e11i 1.04112 + 0.185680i
\(990\) −6.62339e12 −6.89509
\(991\) 1.18381e11 2.45820e11i 0.122740 0.254872i −0.830541 0.556958i \(-0.811969\pi\)
0.953281 + 0.302086i \(0.0976828\pi\)
\(992\) 4.68642e11 + 3.51199e10i 0.483943 + 0.0362665i
\(993\) 1.03147e11 + 1.29342e11i 0.106086 + 0.133028i
\(994\) −7.45556e10 + 2.41703e11i −0.0763721 + 0.247592i
\(995\) 4.12186e11 7.13928e11i 0.420534 0.728386i
\(996\) 2.45241e12 1.41590e12i 2.49205 1.43878i
\(997\) −7.90628e11 + 1.80456e11i −0.800188 + 0.182638i −0.603014 0.797731i \(-0.706034\pi\)
−0.197174 + 0.980369i \(0.563176\pi\)
\(998\) −9.26140e11 1.39593e11i −0.933586 0.140715i
\(999\) −7.35422e11 6.82372e11i −0.738372 0.685109i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 43.9.h.a.3.3 336
43.29 odd 42 inner 43.9.h.a.29.3 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.9.h.a.3.3 336 1.1 even 1 trivial
43.9.h.a.29.3 yes 336 43.29 odd 42 inner