Properties

Label 99.8.j.a.8.11
Level $99$
Weight $8$
Character 99.8
Analytic conductor $30.926$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,8,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.9261175229\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(28\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 8.11
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.82032 + 3.50217i) q^{2} +(-28.5839 + 87.9721i) q^{4} +(-17.1626 + 23.6223i) q^{5} +(1682.17 + 546.570i) q^{7} +(-405.983 - 1249.49i) q^{8} +O(q^{10})\) \(q+(-4.82032 + 3.50217i) q^{2} +(-28.5839 + 87.9721i) q^{4} +(-17.1626 + 23.6223i) q^{5} +(1682.17 + 546.570i) q^{7} +(-405.983 - 1249.49i) q^{8} -173.973i q^{10} +(2852.66 - 3368.91i) q^{11} +(-6140.86 - 8452.17i) q^{13} +(-10022.8 + 3256.60i) q^{14} +(-3245.81 - 2358.22i) q^{16} +(5294.30 + 3846.53i) q^{17} +(7813.03 - 2538.61i) q^{19} +(-1587.53 - 2185.04i) q^{20} +(-1952.24 + 26229.7i) q^{22} -91645.9i q^{23} +(23878.5 + 73490.5i) q^{25} +(59201.8 + 19235.8i) q^{26} +(-96165.9 + 132361. i) q^{28} +(24443.0 - 75228.0i) q^{29} +(154077. - 111943. i) q^{31} +192070. q^{32} -38991.4 q^{34} +(-41781.6 + 30356.1i) q^{35} +(-62732.6 + 193071. i) q^{37} +(-28770.7 + 39599.4i) q^{38} +(36483.4 + 11854.2i) q^{40} +(-211431. - 650718. i) q^{41} -57213.1i q^{43} +(214830. + 347250. i) q^{44} +(320959. + 441762. i) q^{46} +(723572. - 235103. i) q^{47} +(1.86470e6 + 1.35478e6i) q^{49} +(-372478. - 270621. i) q^{50} +(919084. - 298629. i) q^{52} +(873766. + 1.20264e6i) q^{53} +(30622.2 + 125205. i) q^{55} -2.32375e6i q^{56} +(145638. + 448227. i) q^{58} +(1.96935e6 + 639881. i) q^{59} +(-922550. + 1.26978e6i) q^{61} +(-350655. + 1.07921e6i) q^{62} +(-510373. + 370808. i) q^{64} +305052. q^{65} -2.15125e6 q^{67} +(-489719. + 355802. i) q^{68} +(95088.5 - 292652. i) q^{70} +(-1.86619e6 + 2.56860e6i) q^{71} +(5.15723e6 + 1.67568e6i) q^{73} +(-373776. - 1.15037e6i) q^{74} +759892. i q^{76} +(6.64000e6 - 4.10790e6i) q^{77} +(-277567. - 382038. i) q^{79} +(111413. - 36200.3i) q^{80} +(3.29809e6 + 2.39620e6i) q^{82} +(-7.81481e6 - 5.67779e6i) q^{83} +(-181728. + 59046.9i) q^{85} +(200370. + 275786. i) q^{86} +(-5.36753e6 - 2.19664e6i) q^{88} -599176. i q^{89} +(-5.71027e6 - 1.75744e7i) q^{91} +(8.06228e6 + 2.61959e6i) q^{92} +(-2.66448e6 + 3.66734e6i) q^{94} +(-74124.1 + 228130. i) q^{95} +(-132448. + 96229.3i) q^{97} -1.37331e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55} + 13215936 q^{58} - 7843440 q^{61} - 12806712 q^{64} + 1864032 q^{67} - 1233728 q^{70} + 53841940 q^{73} - 53845440 q^{79} - 36360204 q^{82} + 41703500 q^{85} + 21474024 q^{88} + 27611736 q^{91} - 94707560 q^{94} - 27695460 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.82032 + 3.50217i −0.426060 + 0.309551i −0.780072 0.625690i \(-0.784817\pi\)
0.354011 + 0.935241i \(0.384817\pi\)
\(3\) 0 0
\(4\) −28.5839 + 87.9721i −0.223311 + 0.687282i
\(5\) −17.1626 + 23.6223i −0.0614027 + 0.0845136i −0.838614 0.544726i \(-0.816634\pi\)
0.777211 + 0.629240i \(0.216634\pi\)
\(6\) 0 0
\(7\) 1682.17 + 546.570i 1.85365 + 0.602286i 0.996136 + 0.0878193i \(0.0279898\pi\)
0.857510 + 0.514467i \(0.172010\pi\)
\(8\) −405.983 1249.49i −0.280345 0.862813i
\(9\) 0 0
\(10\) 173.973i 0.0550151i
\(11\) 2852.66 3368.91i 0.646212 0.763158i
\(12\) 0 0
\(13\) −6140.86 8452.17i −0.775224 1.06700i −0.995793 0.0916331i \(-0.970791\pi\)
0.220569 0.975371i \(-0.429209\pi\)
\(14\) −10022.8 + 3256.60i −0.976203 + 0.317188i
\(15\) 0 0
\(16\) −3245.81 2358.22i −0.198109 0.143934i
\(17\) 5294.30 + 3846.53i 0.261359 + 0.189888i 0.710746 0.703449i \(-0.248358\pi\)
−0.449387 + 0.893337i \(0.648358\pi\)
\(18\) 0 0
\(19\) 7813.03 2538.61i 0.261326 0.0849098i −0.175424 0.984493i \(-0.556130\pi\)
0.436749 + 0.899583i \(0.356130\pi\)
\(20\) −1587.53 2185.04i −0.0443727 0.0610738i
\(21\) 0 0
\(22\) −1952.24 + 26229.7i −0.0390890 + 0.525187i
\(23\) 91645.9i 1.57060i −0.619116 0.785300i \(-0.712509\pi\)
0.619116 0.785300i \(-0.287491\pi\)
\(24\) 0 0
\(25\) 23878.5 + 73490.5i 0.305645 + 0.940678i
\(26\) 59201.8 + 19235.8i 0.660584 + 0.214637i
\(27\) 0 0
\(28\) −96165.9 + 132361.i −0.827881 + 1.13948i
\(29\) 24443.0 75228.0i 0.186107 0.572778i −0.813859 0.581063i \(-0.802637\pi\)
0.999966 + 0.00828464i \(0.00263711\pi\)
\(30\) 0 0
\(31\) 154077. 111943.i 0.928905 0.674889i −0.0168191 0.999859i \(-0.505354\pi\)
0.945725 + 0.324969i \(0.105354\pi\)
\(32\) 192070. 1.03618
\(33\) 0 0
\(34\) −38991.4 −0.170135
\(35\) −41781.6 + 30356.1i −0.164720 + 0.119676i
\(36\) 0 0
\(37\) −62732.6 + 193071.i −0.203605 + 0.626630i 0.796163 + 0.605082i \(0.206860\pi\)
−0.999768 + 0.0215486i \(0.993140\pi\)
\(38\) −28770.7 + 39599.4i −0.0850565 + 0.117070i
\(39\) 0 0
\(40\) 36483.4 + 11854.2i 0.0901334 + 0.0292861i
\(41\) −211431. 650718.i −0.479099 1.47451i −0.840349 0.542046i \(-0.817650\pi\)
0.361250 0.932469i \(-0.382350\pi\)
\(42\) 0 0
\(43\) 57213.1i 0.109738i −0.998494 0.0548689i \(-0.982526\pi\)
0.998494 0.0548689i \(-0.0174741\pi\)
\(44\) 214830. + 347250.i 0.380198 + 0.614552i
\(45\) 0 0
\(46\) 320959. + 441762.i 0.486180 + 0.669170i
\(47\) 723572. 235103.i 1.01657 0.330305i 0.247105 0.968989i \(-0.420521\pi\)
0.769470 + 0.638683i \(0.220521\pi\)
\(48\) 0 0
\(49\) 1.86470e6 + 1.35478e6i 2.26424 + 1.64507i
\(50\) −372478. 270621.i −0.421411 0.306173i
\(51\) 0 0
\(52\) 919084. 298629.i 0.906450 0.294523i
\(53\) 873766. + 1.20264e6i 0.806175 + 1.10960i 0.991902 + 0.127004i \(0.0405360\pi\)
−0.185727 + 0.982601i \(0.559464\pi\)
\(54\) 0 0
\(55\) 30622.2 + 125205.i 0.0248180 + 0.101474i
\(56\) 2.32375e6i 1.76820i
\(57\) 0 0
\(58\) 145638. + 448227.i 0.0980112 + 0.301647i
\(59\) 1.96935e6 + 639881.i 1.24836 + 0.405618i 0.857334 0.514760i \(-0.172119\pi\)
0.391030 + 0.920378i \(0.372119\pi\)
\(60\) 0 0
\(61\) −922550. + 1.26978e6i −0.520398 + 0.716266i −0.985629 0.168923i \(-0.945971\pi\)
0.465231 + 0.885189i \(0.345971\pi\)
\(62\) −350655. + 1.07921e6i −0.186857 + 0.575087i
\(63\) 0 0
\(64\) −510373. + 370808.i −0.243365 + 0.176815i
\(65\) 305052. 0.137777
\(66\) 0 0
\(67\) −2.15125e6 −0.873834 −0.436917 0.899502i \(-0.643930\pi\)
−0.436917 + 0.899502i \(0.643930\pi\)
\(68\) −489719. + 355802.i −0.188871 + 0.137223i
\(69\) 0 0
\(70\) 95088.5 292652.i 0.0331348 0.101979i
\(71\) −1.86619e6 + 2.56860e6i −0.618803 + 0.851709i −0.997265 0.0739074i \(-0.976453\pi\)
0.378462 + 0.925617i \(0.376453\pi\)
\(72\) 0 0
\(73\) 5.15723e6 + 1.67568e6i 1.55162 + 0.504153i 0.954554 0.298037i \(-0.0963319\pi\)
0.597069 + 0.802190i \(0.296332\pi\)
\(74\) −373776. 1.15037e6i −0.107226 0.330008i
\(75\) 0 0
\(76\) 759892.i 0.198566i
\(77\) 6.64000e6 4.10790e6i 1.65749 1.02542i
\(78\) 0 0
\(79\) −277567. 382038.i −0.0633392 0.0871789i 0.776172 0.630521i \(-0.217159\pi\)
−0.839511 + 0.543342i \(0.817159\pi\)
\(80\) 111413. 36200.3i 0.0243288 0.00790491i
\(81\) 0 0
\(82\) 3.29809e6 + 2.39620e6i 0.660562 + 0.479926i
\(83\) −7.81481e6 5.67779e6i −1.50019 1.08995i −0.970307 0.241876i \(-0.922237\pi\)
−0.529879 0.848073i \(-0.677763\pi\)
\(84\) 0 0
\(85\) −181728. + 59046.9i −0.0320963 + 0.0104287i
\(86\) 200370. + 275786.i 0.0339694 + 0.0467549i
\(87\) 0 0
\(88\) −5.36753e6 2.19664e6i −0.839625 0.343613i
\(89\) 599176.i 0.0900927i −0.998985 0.0450463i \(-0.985656\pi\)
0.998985 0.0450463i \(-0.0143436\pi\)
\(90\) 0 0
\(91\) −5.71027e6 1.75744e7i −0.794349 2.44476i
\(92\) 8.06228e6 + 2.61959e6i 1.07944 + 0.350733i
\(93\) 0 0
\(94\) −2.66448e6 + 3.66734e6i −0.330876 + 0.455411i
\(95\) −74124.1 + 228130.i −0.00887006 + 0.0272992i
\(96\) 0 0
\(97\) −132448. + 96229.3i −0.0147348 + 0.0107055i −0.595128 0.803631i \(-0.702899\pi\)
0.580393 + 0.814336i \(0.302899\pi\)
\(98\) −1.37331e7 −1.47393
\(99\) 0 0
\(100\) −7.14765e6 −0.714765
\(101\) −8.09483e6 + 5.88124e6i −0.781777 + 0.567994i −0.905512 0.424321i \(-0.860513\pi\)
0.123735 + 0.992315i \(0.460513\pi\)
\(102\) 0 0
\(103\) 3.38061e6 1.04045e7i 0.304835 0.938187i −0.674903 0.737906i \(-0.735815\pi\)
0.979739 0.200281i \(-0.0641854\pi\)
\(104\) −8.06779e6 + 1.11044e7i −0.703296 + 0.968003i
\(105\) 0 0
\(106\) −8.42366e6 2.73701e6i −0.686958 0.223206i
\(107\) −230443. 709232.i −0.0181853 0.0559687i 0.941552 0.336868i \(-0.109367\pi\)
−0.959737 + 0.280899i \(0.909367\pi\)
\(108\) 0 0
\(109\) 8.28191e6i 0.612545i 0.951944 + 0.306272i \(0.0990818\pi\)
−0.951944 + 0.306272i \(0.900918\pi\)
\(110\) −586099. 496285.i −0.0419852 0.0355514i
\(111\) 0 0
\(112\) −4.17108e6 5.74099e6i −0.280534 0.386122i
\(113\) 4.79238e6 1.55714e6i 0.312447 0.101520i −0.148596 0.988898i \(-0.547475\pi\)
0.461043 + 0.887378i \(0.347475\pi\)
\(114\) 0 0
\(115\) 2.16488e6 + 1.57288e6i 0.132737 + 0.0964390i
\(116\) 5.91929e6 + 4.30061e6i 0.352100 + 0.255816i
\(117\) 0 0
\(118\) −1.17339e7 + 3.81257e6i −0.657437 + 0.213614i
\(119\) 6.80351e6 + 9.36423e6i 0.370100 + 0.509399i
\(120\) 0 0
\(121\) −3.21188e6 1.92207e7i −0.164820 0.986324i
\(122\) 9.35168e6i 0.466262i
\(123\) 0 0
\(124\) 5.44378e6 + 1.67542e7i 0.256404 + 0.789131i
\(125\) −4.31533e6 1.40214e6i −0.197619 0.0642103i
\(126\) 0 0
\(127\) 1.50793e7 2.07549e7i 0.653234 0.899100i −0.346000 0.938235i \(-0.612460\pi\)
0.999234 + 0.0391346i \(0.0124601\pi\)
\(128\) −6.43563e6 + 1.98068e7i −0.271241 + 0.834795i
\(129\) 0 0
\(130\) −1.47045e6 + 1.06834e6i −0.0587014 + 0.0426490i
\(131\) −2.93332e6 −0.114001 −0.0570006 0.998374i \(-0.518154\pi\)
−0.0570006 + 0.998374i \(0.518154\pi\)
\(132\) 0 0
\(133\) 1.45304e7 0.535545
\(134\) 1.03697e7 7.53403e6i 0.372306 0.270496i
\(135\) 0 0
\(136\) 2.65680e6 8.17679e6i 0.0905675 0.278738i
\(137\) −1.54196e7 + 2.12232e7i −0.512330 + 0.705162i −0.984310 0.176447i \(-0.943539\pi\)
0.471980 + 0.881609i \(0.343539\pi\)
\(138\) 0 0
\(139\) −1.97525e7 6.41796e6i −0.623834 0.202696i −0.0199924 0.999800i \(-0.506364\pi\)
−0.603842 + 0.797104i \(0.706364\pi\)
\(140\) −1.47621e6 4.54331e6i −0.0454674 0.139934i
\(141\) 0 0
\(142\) 1.89172e7i 0.554430i
\(143\) −4.59923e7 3.42315e6i −1.31525 0.0978926i
\(144\) 0 0
\(145\) 1.35755e6 + 1.86851e6i 0.0369800 + 0.0508987i
\(146\) −3.07280e7 + 9.98414e6i −0.817146 + 0.265507i
\(147\) 0 0
\(148\) −1.51917e7 1.10374e7i −0.385205 0.279868i
\(149\) 5.37608e7 + 3.90595e7i 1.33142 + 0.967330i 0.999713 + 0.0239465i \(0.00762313\pi\)
0.331703 + 0.943384i \(0.392377\pi\)
\(150\) 0 0
\(151\) 1.62439e7 5.27797e6i 0.383947 0.124752i −0.110682 0.993856i \(-0.535304\pi\)
0.494630 + 0.869104i \(0.335304\pi\)
\(152\) −6.34391e6 8.73165e6i −0.146523 0.201671i
\(153\) 0 0
\(154\) −1.76204e7 + 4.30558e7i −0.388770 + 0.949968i
\(155\) 5.56088e6i 0.119945i
\(156\) 0 0
\(157\) 2.04789e7 + 6.30276e7i 0.422336 + 1.29982i 0.905522 + 0.424299i \(0.139479\pi\)
−0.483186 + 0.875518i \(0.660521\pi\)
\(158\) 2.67592e6 + 869459.i 0.0539726 + 0.0175368i
\(159\) 0 0
\(160\) −3.29641e6 + 4.53712e6i −0.0636241 + 0.0875710i
\(161\) 5.00909e7 1.54164e8i 0.945950 2.91134i
\(162\) 0 0
\(163\) 4.72472e7 3.43271e7i 0.854514 0.620841i −0.0718729 0.997414i \(-0.522898\pi\)
0.926387 + 0.376573i \(0.122898\pi\)
\(164\) 6.32885e7 1.12040
\(165\) 0 0
\(166\) 5.75545e7 0.976564
\(167\) 3.87915e7 2.81837e7i 0.644509 0.468263i −0.216888 0.976197i \(-0.569591\pi\)
0.861396 + 0.507934i \(0.169591\pi\)
\(168\) 0 0
\(169\) −1.43386e7 + 4.41297e7i −0.228509 + 0.703279i
\(170\) 669193. 921065.i 0.0104467 0.0143787i
\(171\) 0 0
\(172\) 5.03316e6 + 1.63537e6i 0.0754208 + 0.0245057i
\(173\) −1.29660e7 3.99053e7i −0.190390 0.585961i 0.809609 0.586969i \(-0.199679\pi\)
−0.999999 + 0.00100821i \(0.999679\pi\)
\(174\) 0 0
\(175\) 1.36675e8i 1.92777i
\(176\) −1.72038e7 + 4.20764e6i −0.237865 + 0.0581761i
\(177\) 0 0
\(178\) 2.09842e6 + 2.88822e6i 0.0278883 + 0.0383849i
\(179\) 2.07645e7 6.74680e6i 0.270605 0.0879249i −0.170571 0.985345i \(-0.554561\pi\)
0.441176 + 0.897420i \(0.354561\pi\)
\(180\) 0 0
\(181\) 427535. + 310622.i 0.00535916 + 0.00389365i 0.590462 0.807066i \(-0.298946\pi\)
−0.585102 + 0.810959i \(0.698946\pi\)
\(182\) 8.90738e7 + 6.47159e7i 1.09522 + 0.795722i
\(183\) 0 0
\(184\) −1.14510e8 + 3.72067e7i −1.35513 + 0.440310i
\(185\) −3.48412e6 4.79549e6i −0.0404569 0.0556842i
\(186\) 0 0
\(187\) 2.80614e7 6.86316e6i 0.313808 0.0767500i
\(188\) 7.03743e7i 0.772435i
\(189\) 0 0
\(190\) −441649. 1.35926e6i −0.00467132 0.0143769i
\(191\) −1.35340e8 4.39747e7i −1.40543 0.456653i −0.494489 0.869184i \(-0.664645\pi\)
−0.910943 + 0.412532i \(0.864645\pi\)
\(192\) 0 0
\(193\) 9.73850e7 1.34039e8i 0.975083 1.34209i 0.0356455 0.999364i \(-0.488651\pi\)
0.939437 0.342722i \(-0.111349\pi\)
\(194\) 301432. 927712.i 0.00296403 0.00912236i
\(195\) 0 0
\(196\) −1.72483e8 + 1.25317e8i −1.63626 + 1.18881i
\(197\) −4.40346e7 −0.410358 −0.205179 0.978725i \(-0.565778\pi\)
−0.205179 + 0.978725i \(0.565778\pi\)
\(198\) 0 0
\(199\) 1.22557e8 1.10243 0.551216 0.834363i \(-0.314164\pi\)
0.551216 + 0.834363i \(0.314164\pi\)
\(200\) 8.21311e7 5.96718e7i 0.725943 0.527429i
\(201\) 0 0
\(202\) 1.84226e7 5.66989e7i 0.157261 0.484000i
\(203\) 8.22348e7 1.13186e8i 0.689953 0.949638i
\(204\) 0 0
\(205\) 1.90001e7 + 6.17351e6i 0.154034 + 0.0500488i
\(206\) 2.01425e7 + 6.19923e7i 0.160538 + 0.494086i
\(207\) 0 0
\(208\) 4.19156e7i 0.322964i
\(209\) 1.37356e7 3.35631e7i 0.104072 0.254302i
\(210\) 0 0
\(211\) 5.48946e7 + 7.55560e7i 0.402292 + 0.553707i 0.961317 0.275443i \(-0.0888246\pi\)
−0.559025 + 0.829150i \(0.688825\pi\)
\(212\) −1.30774e8 + 4.24910e7i −0.942640 + 0.306282i
\(213\) 0 0
\(214\) 3.59466e6 + 2.61167e6i 0.0250732 + 0.0182167i
\(215\) 1.35150e6 + 981925.i 0.00927433 + 0.00673819i
\(216\) 0 0
\(217\) 3.20369e8 1.04094e8i 2.12834 0.691539i
\(218\) −2.90046e7 3.99215e7i −0.189614 0.260981i
\(219\) 0 0
\(220\) −1.18899e7 884948.i −0.0752832 0.00560323i
\(221\) 6.83693e7i 0.426077i
\(222\) 0 0
\(223\) −5.20885e7 1.60312e8i −0.314539 0.968051i −0.975944 0.218022i \(-0.930039\pi\)
0.661405 0.750029i \(-0.269961\pi\)
\(224\) 3.23094e8 + 1.04980e8i 1.92071 + 0.624075i
\(225\) 0 0
\(226\) −1.76474e7 + 2.42896e7i −0.101696 + 0.139972i
\(227\) −2.75816e7 + 8.48874e7i −0.156505 + 0.481674i −0.998310 0.0581081i \(-0.981493\pi\)
0.841805 + 0.539782i \(0.181493\pi\)
\(228\) 0 0
\(229\) −1.15536e8 + 8.39419e7i −0.635761 + 0.461907i −0.858391 0.512996i \(-0.828536\pi\)
0.222630 + 0.974903i \(0.428536\pi\)
\(230\) −1.59439e7 −0.0864067
\(231\) 0 0
\(232\) −1.03920e8 −0.546375
\(233\) −2.77497e8 + 2.01613e8i −1.43718 + 1.04418i −0.448562 + 0.893752i \(0.648064\pi\)
−0.988622 + 0.150424i \(0.951936\pi\)
\(234\) 0 0
\(235\) −6.86470e6 + 2.11274e7i −0.0345052 + 0.106196i
\(236\) −1.12583e8 + 1.54958e8i −0.557548 + 0.767399i
\(237\) 0 0
\(238\) −6.55902e7 2.13116e7i −0.315370 0.102470i
\(239\) −2.87087e7 8.83564e7i −0.136026 0.418645i 0.859722 0.510762i \(-0.170637\pi\)
−0.995748 + 0.0921172i \(0.970637\pi\)
\(240\) 0 0
\(241\) 6.68538e7i 0.307657i −0.988098 0.153828i \(-0.950840\pi\)
0.988098 0.153828i \(-0.0491603\pi\)
\(242\) 8.27962e7 + 8.14012e7i 0.375541 + 0.369213i
\(243\) 0 0
\(244\) −8.53353e7 1.17454e8i −0.376066 0.517611i
\(245\) −6.40061e7 + 2.07968e7i −0.278061 + 0.0903475i
\(246\) 0 0
\(247\) −6.94354e7 5.04478e7i −0.293185 0.213011i
\(248\) −2.02424e8 1.47070e8i −0.842718 0.612270i
\(249\) 0 0
\(250\) 2.57118e7 8.35426e6i 0.104074 0.0338157i
\(251\) 9.44899e7 + 1.30054e8i 0.377162 + 0.519118i 0.954830 0.297153i \(-0.0960373\pi\)
−0.577668 + 0.816272i \(0.696037\pi\)
\(252\) 0 0
\(253\) −3.08746e8 2.61434e8i −1.19862 1.01494i
\(254\) 1.52856e8i 0.585280i
\(255\) 0 0
\(256\) −6.32980e7 1.94811e8i −0.235803 0.725729i
\(257\) −3.28210e8 1.06642e8i −1.20611 0.391888i −0.364103 0.931359i \(-0.618625\pi\)
−0.842005 + 0.539470i \(0.818625\pi\)
\(258\) 0 0
\(259\) −2.11054e8 + 2.90491e8i −0.754822 + 1.03892i
\(260\) −8.71957e6 + 2.68361e7i −0.0307672 + 0.0946918i
\(261\) 0 0
\(262\) 1.41395e7 1.02730e7i 0.0485713 0.0352891i
\(263\) 3.55390e8 1.20465 0.602324 0.798252i \(-0.294241\pi\)
0.602324 + 0.798252i \(0.294241\pi\)
\(264\) 0 0
\(265\) −4.34050e7 −0.143278
\(266\) −7.00411e7 + 5.08878e7i −0.228174 + 0.165778i
\(267\) 0 0
\(268\) 6.14910e7 1.89250e8i 0.195137 0.600570i
\(269\) −2.40283e8 + 3.30722e8i −0.752646 + 1.03593i 0.245144 + 0.969487i \(0.421165\pi\)
−0.997790 + 0.0664418i \(0.978835\pi\)
\(270\) 0 0
\(271\) 9.81996e7 + 3.19070e7i 0.299721 + 0.0973853i 0.455017 0.890483i \(-0.349633\pi\)
−0.155296 + 0.987868i \(0.549633\pi\)
\(272\) −8.11333e6 2.49702e7i −0.0244460 0.0752370i
\(273\) 0 0
\(274\) 1.56304e8i 0.459034i
\(275\) 3.15700e8 + 1.29199e8i 0.915397 + 0.374622i
\(276\) 0 0
\(277\) −5.21952e6 7.18405e6i −0.0147554 0.0203091i 0.801576 0.597893i \(-0.203995\pi\)
−0.816331 + 0.577584i \(0.803995\pi\)
\(278\) 1.17690e8 3.82398e7i 0.328536 0.106748i
\(279\) 0 0
\(280\) 5.48922e7 + 3.98815e7i 0.149437 + 0.108572i
\(281\) −1.79323e8 1.30286e8i −0.482129 0.350288i 0.320020 0.947411i \(-0.396310\pi\)
−0.802150 + 0.597123i \(0.796310\pi\)
\(282\) 0 0
\(283\) 2.42589e8 7.88221e7i 0.636238 0.206726i 0.0269014 0.999638i \(-0.491436\pi\)
0.609336 + 0.792912i \(0.291436\pi\)
\(284\) −1.72622e8 2.37593e8i −0.447179 0.615489i
\(285\) 0 0
\(286\) 2.33686e8 1.44572e8i 0.590679 0.365429i
\(287\) 1.21018e9i 3.02178i
\(288\) 0 0
\(289\) −1.13568e8 3.49526e8i −0.276766 0.851799i
\(290\) −1.30876e7 4.25243e6i −0.0315114 0.0102387i
\(291\) 0 0
\(292\) −2.94827e8 + 4.05795e8i −0.692990 + 0.953820i
\(293\) 4.47045e7 1.37586e8i 0.103828 0.319550i −0.885626 0.464400i \(-0.846270\pi\)
0.989454 + 0.144850i \(0.0462701\pi\)
\(294\) 0 0
\(295\) −4.89146e7 + 3.55385e7i −0.110933 + 0.0805976i
\(296\) 2.66708e8 0.597745
\(297\) 0 0
\(298\) −3.95937e8 −0.866701
\(299\) −7.74606e8 + 5.62784e8i −1.67584 + 1.21757i
\(300\) 0 0
\(301\) 3.12710e7 9.62423e7i 0.0660936 0.203415i
\(302\) −5.98166e7 + 8.23305e7i −0.124968 + 0.172003i
\(303\) 0 0
\(304\) −3.13462e7 1.01850e7i −0.0639923 0.0207924i
\(305\) −1.41618e7 4.35854e7i −0.0285804 0.0879613i
\(306\) 0 0
\(307\) 2.95847e7i 0.0583556i 0.999574 + 0.0291778i \(0.00928890\pi\)
−0.999574 + 0.0291778i \(0.990711\pi\)
\(308\) 1.71584e8 + 7.01554e8i 0.334617 + 1.36815i
\(309\) 0 0
\(310\) −1.94751e7 2.68052e7i −0.0371291 0.0511038i
\(311\) −3.23586e7 + 1.05139e7i −0.0609997 + 0.0198200i −0.339358 0.940657i \(-0.610210\pi\)
0.278358 + 0.960477i \(0.410210\pi\)
\(312\) 0 0
\(313\) 4.74053e7 + 3.44420e7i 0.0873820 + 0.0634867i 0.630618 0.776093i \(-0.282801\pi\)
−0.543236 + 0.839580i \(0.682801\pi\)
\(314\) −3.19448e8 2.32093e8i −0.582300 0.423066i
\(315\) 0 0
\(316\) 4.15426e7 1.34980e7i 0.0740608 0.0240638i
\(317\) 1.92106e8 + 2.64411e8i 0.338714 + 0.466200i 0.944065 0.329758i \(-0.106967\pi\)
−0.605351 + 0.795959i \(0.706967\pi\)
\(318\) 0 0
\(319\) −1.83708e8 2.96946e8i −0.316856 0.512165i
\(320\) 1.84202e7i 0.0314246i
\(321\) 0 0
\(322\) 2.98454e8 + 9.18546e8i 0.498175 + 1.53322i
\(323\) 5.11293e7 + 1.66129e7i 0.0844231 + 0.0274307i
\(324\) 0 0
\(325\) 4.74519e8 6.53119e8i 0.766764 1.05536i
\(326\) −1.07527e8 + 3.30935e8i −0.171893 + 0.529031i
\(327\) 0 0
\(328\) −7.27226e8 + 5.28361e8i −1.13792 + 0.826746i
\(329\) 1.34567e9 2.08331
\(330\) 0 0
\(331\) 3.93583e8 0.596538 0.298269 0.954482i \(-0.403591\pi\)
0.298269 + 0.954482i \(0.403591\pi\)
\(332\) 7.22865e8 5.25192e8i 1.08411 0.787653i
\(333\) 0 0
\(334\) −8.82834e7 + 2.71709e8i −0.129648 + 0.399016i
\(335\) 3.69210e7 5.08174e7i 0.0536558 0.0738508i
\(336\) 0 0
\(337\) 3.75101e8 + 1.21878e8i 0.533880 + 0.173468i 0.563535 0.826092i \(-0.309441\pi\)
−0.0296551 + 0.999560i \(0.509441\pi\)
\(338\) −8.54329e7 2.62936e8i −0.120342 0.370374i
\(339\) 0 0
\(340\) 1.76747e7i 0.0243880i
\(341\) 6.24015e7 8.38406e8i 0.0852226 1.14502i
\(342\) 0 0
\(343\) 1.54007e9 + 2.11973e9i 2.06068 + 2.83629i
\(344\) −7.14871e7 + 2.32276e7i −0.0946832 + 0.0307644i
\(345\) 0 0
\(346\) 2.02255e8 + 1.46947e8i 0.262502 + 0.190719i
\(347\) 7.16939e8 + 5.20887e8i 0.921148 + 0.669253i 0.943809 0.330490i \(-0.107214\pi\)
−0.0226617 + 0.999743i \(0.507214\pi\)
\(348\) 0 0
\(349\) −2.82107e8 + 9.16620e7i −0.355242 + 0.115425i −0.481201 0.876610i \(-0.659799\pi\)
0.125959 + 0.992035i \(0.459799\pi\)
\(350\) −4.78658e8 6.58816e8i −0.596743 0.821346i
\(351\) 0 0
\(352\) 5.47909e8 6.47065e8i 0.669590 0.790767i
\(353\) 4.84499e8i 0.586249i 0.956074 + 0.293124i \(0.0946950\pi\)
−0.956074 + 0.293124i \(0.905305\pi\)
\(354\) 0 0
\(355\) −2.86473e7 8.81674e7i −0.0339848 0.104595i
\(356\) 5.27108e7 + 1.71268e7i 0.0619191 + 0.0201187i
\(357\) 0 0
\(358\) −7.64632e7 + 1.05243e8i −0.0880768 + 0.121227i
\(359\) 3.28978e8 1.01249e9i 0.375263 1.15494i −0.568037 0.823003i \(-0.692297\pi\)
0.943301 0.331939i \(-0.107703\pi\)
\(360\) 0 0
\(361\) −6.68559e8 + 4.85736e8i −0.747936 + 0.543407i
\(362\) −3.14870e6 −0.00348861
\(363\) 0 0
\(364\) 1.70928e9 1.85762
\(365\) −1.28095e8 + 9.30663e7i −0.137882 + 0.100177i
\(366\) 0 0
\(367\) −2.57159e7 + 7.91454e7i −0.0271563 + 0.0835785i −0.963716 0.266929i \(-0.913991\pi\)
0.936560 + 0.350508i \(0.113991\pi\)
\(368\) −2.16121e8 + 2.97465e8i −0.226063 + 0.311149i
\(369\) 0 0
\(370\) 3.35892e7 + 1.09138e7i 0.0344741 + 0.0112013i
\(371\) 8.12498e8 + 2.50061e9i 0.826064 + 2.54236i
\(372\) 0 0
\(373\) 1.03178e9i 1.02945i 0.857354 + 0.514727i \(0.172107\pi\)
−0.857354 + 0.514727i \(0.827893\pi\)
\(374\) −1.11229e8 + 1.31358e8i −0.109943 + 0.129840i
\(375\) 0 0
\(376\) −5.87516e8 8.08646e8i −0.569984 0.784515i
\(377\) −7.85941e8 + 2.55368e8i −0.755431 + 0.245455i
\(378\) 0 0
\(379\) −1.25310e9 9.10427e8i −1.18235 0.859029i −0.189917 0.981800i \(-0.560822\pi\)
−0.992435 + 0.122771i \(0.960822\pi\)
\(380\) −1.79504e7 1.30417e7i −0.0167815 0.0121925i
\(381\) 0 0
\(382\) 8.06389e8 2.62012e8i 0.740156 0.240491i
\(383\) −8.73865e8 1.20277e9i −0.794783 1.09393i −0.993496 0.113867i \(-0.963676\pi\)
0.198713 0.980058i \(-0.436324\pi\)
\(384\) 0 0
\(385\) −1.69217e7 + 2.27354e8i −0.0151123 + 0.203044i
\(386\) 9.87169e8i 0.873647i
\(387\) 0 0
\(388\) −4.67961e6 1.44024e7i −0.00406723 0.0125176i
\(389\) −8.48168e8 2.75587e8i −0.730564 0.237375i −0.0799667 0.996798i \(-0.525481\pi\)
−0.650597 + 0.759423i \(0.725481\pi\)
\(390\) 0 0
\(391\) 3.52519e8 4.85201e8i 0.298238 0.410490i
\(392\) 9.35748e8 2.87994e9i 0.784617 2.41480i
\(393\) 0 0
\(394\) 2.12261e8 1.54217e8i 0.174837 0.127027i
\(395\) 1.37883e7 0.0112570
\(396\) 0 0
\(397\) 2.06346e7 0.0165512 0.00827558 0.999966i \(-0.497366\pi\)
0.00827558 + 0.999966i \(0.497366\pi\)
\(398\) −5.90763e8 + 4.29214e8i −0.469702 + 0.341258i
\(399\) 0 0
\(400\) 9.58016e7 2.94847e8i 0.0748450 0.230349i
\(401\) 1.02200e9 1.40667e9i 0.791492 1.08940i −0.202428 0.979297i \(-0.564883\pi\)
0.993921 0.110099i \(-0.0351167\pi\)
\(402\) 0 0
\(403\) −1.89233e9 6.14855e8i −1.44022 0.467956i
\(404\) −2.86003e8 8.80228e8i −0.215793 0.664141i
\(405\) 0 0
\(406\) 8.33595e8i 0.618178i
\(407\) 4.71484e8 + 7.62106e8i 0.346646 + 0.560319i
\(408\) 0 0
\(409\) −6.74293e8 9.28084e8i −0.487323 0.670743i 0.492568 0.870274i \(-0.336058\pi\)
−0.979891 + 0.199531i \(0.936058\pi\)
\(410\) −1.13207e8 + 3.67833e7i −0.0811206 + 0.0263577i
\(411\) 0 0
\(412\) 8.18671e8 + 5.94800e8i 0.576726 + 0.419016i
\(413\) 2.96305e9 + 2.15278e9i 2.06973 + 1.50374i
\(414\) 0 0
\(415\) 2.68245e8 8.71579e7i 0.184231 0.0598603i
\(416\) −1.17947e9 1.62340e9i −0.803269 1.10561i
\(417\) 0 0
\(418\) 5.13339e7 + 2.09889e8i 0.0343785 + 0.140564i
\(419\) 5.58702e7i 0.0371049i −0.999828 0.0185524i \(-0.994094\pi\)
0.999828 0.0185524i \(-0.00590576\pi\)
\(420\) 0 0
\(421\) 3.86697e8 + 1.19013e9i 0.252571 + 0.777334i 0.994298 + 0.106633i \(0.0340069\pi\)
−0.741727 + 0.670702i \(0.765993\pi\)
\(422\) −5.29219e8 1.71954e8i −0.342801 0.111383i
\(423\) 0 0
\(424\) 1.14794e9 1.58001e9i 0.731375 1.00665i
\(425\) −1.56264e8 + 4.80930e8i −0.0987408 + 0.303893i
\(426\) 0 0
\(427\) −2.24591e9 + 1.63175e9i −1.39603 + 1.01428i
\(428\) 6.89796e7 0.0425273
\(429\) 0 0
\(430\) −9.95354e6 −0.00603724
\(431\) −1.21852e9 + 8.85309e8i −0.733100 + 0.532628i −0.890543 0.454900i \(-0.849675\pi\)
0.157443 + 0.987528i \(0.449675\pi\)
\(432\) 0 0
\(433\) −4.46614e8 + 1.37454e9i −0.264378 + 0.813671i 0.727458 + 0.686152i \(0.240701\pi\)
−0.991836 + 0.127519i \(0.959299\pi\)
\(434\) −1.17972e9 + 1.62375e9i −0.692734 + 0.953466i
\(435\) 0 0
\(436\) −7.28577e8 2.36729e8i −0.420991 0.136788i
\(437\) −2.32653e8 7.16032e8i −0.133359 0.410438i
\(438\) 0 0
\(439\) 3.25530e9i 1.83639i −0.396126 0.918196i \(-0.629646\pi\)
0.396126 0.918196i \(-0.370354\pi\)
\(440\) 1.44010e8 8.90933e7i 0.0805952 0.0498610i
\(441\) 0 0
\(442\) 2.39441e8 + 3.29562e8i 0.131893 + 0.181534i
\(443\) −2.07236e9 + 6.73351e8i −1.13254 + 0.367984i −0.814540 0.580108i \(-0.803010\pi\)
−0.317998 + 0.948092i \(0.603010\pi\)
\(444\) 0 0
\(445\) 1.41539e7 + 1.02834e7i 0.00761405 + 0.00553193i
\(446\) 8.12522e8 + 5.90332e8i 0.433674 + 0.315082i
\(447\) 0 0
\(448\) −1.06121e9 + 3.44807e8i −0.557606 + 0.181177i
\(449\) −7.75494e8 1.06738e9i −0.404311 0.556487i 0.557508 0.830171i \(-0.311758\pi\)
−0.961819 + 0.273685i \(0.911758\pi\)
\(450\) 0 0
\(451\) −2.79535e9 1.14398e9i −1.43489 0.587221i
\(452\) 4.66105e8i 0.237410i
\(453\) 0 0
\(454\) −1.64338e8 5.05780e8i −0.0824218 0.253668i
\(455\) 5.13150e8 + 1.66732e8i 0.255390 + 0.0829813i
\(456\) 0 0
\(457\) 1.16063e9 1.59747e9i 0.568835 0.782934i −0.423581 0.905858i \(-0.639227\pi\)
0.992416 + 0.122924i \(0.0392271\pi\)
\(458\) 2.62943e8 8.09254e8i 0.127889 0.393600i
\(459\) 0 0
\(460\) −2.00250e8 + 1.45490e8i −0.0959225 + 0.0696918i
\(461\) −1.62047e7 −0.00770347 −0.00385174 0.999993i \(-0.501226\pi\)
−0.00385174 + 0.999993i \(0.501226\pi\)
\(462\) 0 0
\(463\) −1.40473e9 −0.657748 −0.328874 0.944374i \(-0.606669\pi\)
−0.328874 + 0.944374i \(0.606669\pi\)
\(464\) −2.56742e8 + 1.86534e8i −0.119312 + 0.0866851i
\(465\) 0 0
\(466\) 6.31540e8 1.94368e9i 0.289101 0.889763i
\(467\) −2.28826e9 + 3.14952e9i −1.03967 + 1.43099i −0.142242 + 0.989832i \(0.545431\pi\)
−0.897431 + 0.441155i \(0.854569\pi\)
\(468\) 0 0
\(469\) −3.61877e9 1.17581e9i −1.61978 0.526298i
\(470\) −4.09016e7 1.25882e8i −0.0181718 0.0559270i
\(471\) 0 0
\(472\) 2.72046e9i 1.19082i
\(473\) −1.92746e8 1.63209e8i −0.0837473 0.0709139i
\(474\) 0 0
\(475\) 3.73127e8 + 5.13565e8i 0.159746 + 0.219871i
\(476\) −1.01826e9 + 3.30853e8i −0.432748 + 0.140608i
\(477\) 0 0
\(478\) 4.47824e8 + 3.25363e8i 0.187547 + 0.136261i
\(479\) 1.13077e9 + 8.21556e8i 0.470112 + 0.341557i 0.797485 0.603339i \(-0.206163\pi\)
−0.327373 + 0.944895i \(0.606163\pi\)
\(480\) 0 0
\(481\) 2.01710e9 6.55396e8i 0.826457 0.268532i
\(482\) 2.34133e8 + 3.22257e8i 0.0952354 + 0.131080i
\(483\) 0 0
\(484\) 1.78269e9 + 2.66845e8i 0.714689 + 0.106979i
\(485\) 4.78027e6i 0.00190264i
\(486\) 0 0
\(487\) 3.47037e8 + 1.06807e9i 0.136152 + 0.419033i 0.995767 0.0919084i \(-0.0292967\pi\)
−0.859615 + 0.510942i \(0.829297\pi\)
\(488\) 1.96111e9 + 6.37205e8i 0.763895 + 0.248205i
\(489\) 0 0
\(490\) 2.35696e8 3.24407e8i 0.0905035 0.124567i
\(491\) 1.02480e9 3.15402e9i 0.390711 1.20248i −0.541542 0.840674i \(-0.682159\pi\)
0.932252 0.361809i \(-0.117841\pi\)
\(492\) 0 0
\(493\) 4.18776e8 3.04258e8i 0.157405 0.114361i
\(494\) 5.11378e8 0.190852
\(495\) 0 0
\(496\) −7.64092e8 −0.281164
\(497\) −4.54317e9 + 3.30081e9i −1.66002 + 1.20607i
\(498\) 0 0
\(499\) 1.60743e7 4.94717e7i 0.00579136 0.0178240i −0.948119 0.317915i \(-0.897017\pi\)
0.953910 + 0.300091i \(0.0970172\pi\)
\(500\) 2.46698e8 3.39550e8i 0.0882612 0.121481i
\(501\) 0 0
\(502\) −9.10943e8 2.95983e8i −0.321387 0.104425i
\(503\) −6.01999e8 1.85276e9i −0.210915 0.649130i −0.999418 0.0340996i \(-0.989144\pi\)
0.788503 0.615031i \(-0.210856\pi\)
\(504\) 0 0
\(505\) 2.92155e8i 0.100947i
\(506\) 2.40384e9 + 1.78915e8i 0.824858 + 0.0613931i
\(507\) 0 0
\(508\) 1.39483e9 + 1.91982e9i 0.472061 + 0.649736i
\(509\) −1.00060e9 + 3.25115e8i −0.336317 + 0.109276i −0.472307 0.881434i \(-0.656579\pi\)
0.135990 + 0.990710i \(0.456579\pi\)
\(510\) 0 0
\(511\) 7.75946e9 + 5.63758e9i 2.57252 + 1.86904i
\(512\) −1.16925e9 8.49513e8i −0.385003 0.279721i
\(513\) 0 0
\(514\) 1.95556e9 6.35399e8i 0.635184 0.206384i
\(515\) 1.87757e8 + 2.58425e8i 0.0605718 + 0.0833699i
\(516\) 0 0
\(517\) 1.27206e9 3.10831e9i 0.404848 0.989254i
\(518\) 2.13941e9i 0.676299i
\(519\) 0 0
\(520\) −1.23846e8 3.81159e8i −0.0386252 0.118876i
\(521\) 5.92182e8 + 1.92411e8i 0.183452 + 0.0596072i 0.399302 0.916819i \(-0.369252\pi\)
−0.215850 + 0.976426i \(0.569252\pi\)
\(522\) 0 0
\(523\) −1.83028e9 + 2.51916e9i −0.559450 + 0.770017i −0.991256 0.131949i \(-0.957876\pi\)
0.431806 + 0.901966i \(0.357876\pi\)
\(524\) 8.38455e7 2.58050e8i 0.0254578 0.0783509i
\(525\) 0 0
\(526\) −1.71309e9 + 1.24464e9i −0.513253 + 0.372900i
\(527\) 1.24632e9 0.370931
\(528\) 0 0
\(529\) −4.99414e9 −1.46678
\(530\) 2.09226e8 1.52012e8i 0.0610450 0.0443518i
\(531\) 0 0
\(532\) −4.15334e8 + 1.27827e9i −0.119593 + 0.368071i
\(533\) −4.20161e9 + 5.78302e9i −1.20190 + 1.65428i
\(534\) 0 0
\(535\) 2.07087e7 + 6.72865e6i 0.00584674 + 0.00189972i
\(536\) 8.73370e8 + 2.68796e9i 0.244975 + 0.753955i
\(537\) 0 0
\(538\) 2.43570e9i 0.674350i
\(539\) 9.88348e9 2.41727e9i 2.71862 0.664911i
\(540\) 0 0
\(541\) 6.25294e7 + 8.60643e7i 0.0169783 + 0.0233686i 0.817422 0.576040i \(-0.195403\pi\)
−0.800443 + 0.599408i \(0.795403\pi\)
\(542\) −5.85097e8 + 1.90110e8i −0.157845 + 0.0512869i
\(543\) 0 0
\(544\) 1.01687e9 + 7.38802e8i 0.270814 + 0.196758i
\(545\) −1.95637e8 1.42139e8i −0.0517683 0.0376119i
\(546\) 0 0
\(547\) −5.20782e9 + 1.69212e9i −1.36051 + 0.442055i −0.896212 0.443626i \(-0.853692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(548\) −1.42630e9 1.96313e9i −0.370236 0.509586i
\(549\) 0 0
\(550\) −1.97425e9 + 4.82854e8i −0.505979 + 0.123750i
\(551\) 6.49810e8i 0.165484i
\(552\) 0 0
\(553\) −2.58104e8 7.94362e8i −0.0649018 0.199747i
\(554\) 5.03195e7 + 1.63498e7i 0.0125734 + 0.00408534i
\(555\) 0 0
\(556\) 1.12920e9 1.55421e9i 0.278619 0.383486i
\(557\) 1.29167e9 3.97535e9i 0.316707 0.974725i −0.658339 0.752722i \(-0.728741\pi\)
0.975046 0.222003i \(-0.0712595\pi\)
\(558\) 0 0
\(559\) −4.83575e8 + 3.51338e8i −0.117091 + 0.0850714i
\(560\) 2.07202e8 0.0498580
\(561\) 0 0
\(562\) 1.32068e9 0.313848
\(563\) −3.45048e8 + 2.50692e8i −0.0814892 + 0.0592054i −0.627784 0.778388i \(-0.716038\pi\)
0.546295 + 0.837593i \(0.316038\pi\)
\(564\) 0 0
\(565\) −4.54664e7 + 1.39931e8i −0.0106053 + 0.0326396i
\(566\) −8.93311e8 + 1.22954e9i −0.207083 + 0.285026i
\(567\) 0 0
\(568\) 3.96707e9 + 1.28898e9i 0.908345 + 0.295139i
\(569\) 1.66189e9 + 5.11477e9i 0.378189 + 1.16395i 0.941302 + 0.337566i \(0.109604\pi\)
−0.563113 + 0.826380i \(0.690396\pi\)
\(570\) 0 0
\(571\) 7.04405e9i 1.58342i 0.610897 + 0.791710i \(0.290809\pi\)
−0.610897 + 0.791710i \(0.709191\pi\)
\(572\) 1.61578e9 3.94819e9i 0.360991 0.882089i
\(573\) 0 0
\(574\) 4.23825e9 + 5.83346e9i 0.935396 + 1.28746i
\(575\) 6.73510e9 2.18837e9i 1.47743 0.480045i
\(576\) 0 0
\(577\) 1.98487e9 + 1.44210e9i 0.430148 + 0.312521i 0.781708 0.623645i \(-0.214349\pi\)
−0.351560 + 0.936165i \(0.614349\pi\)
\(578\) 1.77153e9 + 1.28709e9i 0.381594 + 0.277244i
\(579\) 0 0
\(580\) −2.03180e8 + 6.60173e7i −0.0432398 + 0.0140495i
\(581\) −1.00425e10 1.38224e10i −2.12435 2.92392i
\(582\) 0 0
\(583\) 6.54412e9 + 4.87070e8i 1.36776 + 0.101801i
\(584\) 7.12419e9i 1.48010i
\(585\) 0 0
\(586\) 2.66360e8 + 8.19772e8i 0.0546799 + 0.168287i
\(587\) 8.11846e9 + 2.63785e9i 1.65669 + 0.538290i 0.980174 0.198141i \(-0.0634903\pi\)
0.676513 + 0.736431i \(0.263490\pi\)
\(588\) 0 0
\(589\) 9.19627e8 1.26576e9i 0.185442 0.255239i
\(590\) 1.11322e8 3.42614e8i 0.0223151 0.0686789i
\(591\) 0 0
\(592\) 6.58923e8 4.78735e8i 0.130529 0.0948352i
\(593\) 2.28746e9 0.450465 0.225233 0.974305i \(-0.427686\pi\)
0.225233 + 0.974305i \(0.427686\pi\)
\(594\) 0 0
\(595\) −3.37970e8 −0.0657762
\(596\) −4.97284e9 + 3.61298e9i −0.962149 + 0.699042i
\(597\) 0 0
\(598\) 1.76288e9 5.42560e9i 0.337108 1.03751i
\(599\) 3.61164e8 4.97099e8i 0.0686610 0.0945037i −0.773305 0.634034i \(-0.781398\pi\)
0.841966 + 0.539530i \(0.181398\pi\)
\(600\) 0 0
\(601\) −6.77532e9 2.20143e9i −1.27312 0.413661i −0.406967 0.913443i \(-0.633414\pi\)
−0.866152 + 0.499781i \(0.833414\pi\)
\(602\) 1.86320e8 + 5.73435e8i 0.0348075 + 0.107126i
\(603\) 0 0
\(604\) 1.57988e9i 0.291739i
\(605\) 5.09159e8 + 2.54004e8i 0.0934781 + 0.0466334i
\(606\) 0 0
\(607\) 5.15581e9 + 7.09636e9i 0.935700 + 1.28788i 0.957594 + 0.288120i \(0.0930302\pi\)
−0.0218945 + 0.999760i \(0.506970\pi\)
\(608\) 1.50065e9 4.87589e8i 0.270779 0.0879816i
\(609\) 0 0
\(610\) 2.20908e8 + 1.60499e8i 0.0394055 + 0.0286297i
\(611\) −6.43048e9 4.67202e9i −1.14051 0.828629i
\(612\) 0 0
\(613\) 3.23692e9 1.05174e9i 0.567572 0.184415i −0.0111534 0.999938i \(-0.503550\pi\)
0.578725 + 0.815522i \(0.303550\pi\)
\(614\) −1.03610e8 1.42608e8i −0.0180640 0.0248630i
\(615\) 0 0
\(616\) −7.82849e9 6.62886e9i −1.34942 1.14263i
\(617\) 6.95710e9i 1.19242i 0.802827 + 0.596212i \(0.203328\pi\)
−0.802827 + 0.596212i \(0.796672\pi\)
\(618\) 0 0
\(619\) 3.04774e9 + 9.37999e9i 0.516489 + 1.58959i 0.780556 + 0.625085i \(0.214936\pi\)
−0.264067 + 0.964504i \(0.585064\pi\)
\(620\) −4.89202e8 1.58951e8i −0.0824361 0.0267851i
\(621\) 0 0
\(622\) 1.19157e8 1.64006e8i 0.0198543 0.0273270i
\(623\) 3.27492e8 1.00792e9i 0.0542616 0.167000i
\(624\) 0 0
\(625\) −4.77678e9 + 3.47053e9i −0.782627 + 0.568612i
\(626\) −3.49130e8 −0.0568824
\(627\) 0 0
\(628\) −6.13004e9 −0.987653
\(629\) −1.07478e9 + 7.80874e8i −0.172204 + 0.125113i
\(630\) 0 0
\(631\) 2.64048e8 8.12658e8i 0.0418390 0.128767i −0.927955 0.372692i \(-0.878435\pi\)
0.969794 + 0.243925i \(0.0784349\pi\)
\(632\) −3.64664e8 + 5.01917e8i −0.0574623 + 0.0790900i
\(633\) 0 0
\(634\) −1.85202e9 6.01759e8i −0.288625 0.0937801i
\(635\) 2.31478e8 + 7.12416e8i 0.0358758 + 0.110414i
\(636\) 0 0
\(637\) 2.40803e10i 3.69125i
\(638\) 1.92549e9 + 7.87997e8i 0.293541 + 0.120130i
\(639\) 0 0
\(640\) −3.57430e8 4.91960e8i −0.0538966 0.0741822i
\(641\) −3.43067e9 + 1.11469e9i −0.514488 + 0.167167i −0.554742 0.832022i \(-0.687183\pi\)
0.0402542 + 0.999189i \(0.487183\pi\)
\(642\) 0 0
\(643\) −6.55266e7 4.76079e7i −0.00972029 0.00706221i 0.582914 0.812533i \(-0.301912\pi\)
−0.592635 + 0.805471i \(0.701912\pi\)
\(644\) 1.21303e10 + 8.81321e9i 1.78967 + 1.30027i
\(645\) 0 0
\(646\) −3.04641e8 + 9.89839e7i −0.0444605 + 0.0144461i
\(647\) −3.21680e9 4.42754e9i −0.466937 0.642684i 0.508992 0.860771i \(-0.330018\pi\)
−0.975929 + 0.218087i \(0.930018\pi\)
\(648\) 0 0
\(649\) 7.77358e9 4.80920e9i 1.11626 0.690584i
\(650\) 4.81009e9i 0.686999i
\(651\) 0 0
\(652\) 1.66932e9 + 5.13763e9i 0.235870 + 0.725933i
\(653\) −8.96455e9 2.91276e9i −1.25989 0.409363i −0.398434 0.917197i \(-0.630446\pi\)
−0.861455 + 0.507834i \(0.830446\pi\)
\(654\) 0 0
\(655\) 5.03432e7 6.92915e7i 0.00699998 0.00963464i
\(656\) −8.48271e8 + 2.61071e9i −0.117320 + 0.361073i
\(657\) 0 0
\(658\) −6.48657e9 + 4.71277e9i −0.887615 + 0.644890i
\(659\) 2.20076e9 0.299553 0.149777 0.988720i \(-0.452145\pi\)
0.149777 + 0.988720i \(0.452145\pi\)
\(660\) 0 0
\(661\) 1.17215e10 1.57862 0.789308 0.613998i \(-0.210440\pi\)
0.789308 + 0.613998i \(0.210440\pi\)
\(662\) −1.89720e9 + 1.37839e9i −0.254161 + 0.184659i
\(663\) 0 0
\(664\) −3.92165e9 + 1.20696e10i −0.519853 + 1.59994i
\(665\) −2.49379e8 + 3.43240e8i −0.0328839 + 0.0452608i
\(666\) 0 0
\(667\) −6.89433e9 2.24010e9i −0.899605 0.292299i
\(668\) 1.37057e9 + 4.21817e9i 0.177903 + 0.547528i
\(669\) 0 0
\(670\) 3.74259e8i 0.0480741i
\(671\) 1.64606e9 + 6.73023e9i 0.210337 + 0.860006i
\(672\) 0 0
\(673\) −2.65063e9 3.64827e9i −0.335194 0.461354i 0.607836 0.794062i \(-0.292038\pi\)
−0.943030 + 0.332708i \(0.892038\pi\)
\(674\) −2.23494e9 + 7.26177e8i −0.281162 + 0.0913551i
\(675\) 0 0
\(676\) −3.47233e9 2.52280e9i −0.432322 0.314101i
\(677\) 3.66832e9 + 2.66519e9i 0.454367 + 0.330117i 0.791317 0.611406i \(-0.209396\pi\)
−0.336951 + 0.941522i \(0.609396\pi\)
\(678\) 0 0
\(679\) −2.75397e8 + 8.94818e7i −0.0337609 + 0.0109696i
\(680\) 1.47557e8 + 2.03094e8i 0.0179961 + 0.0247695i
\(681\) 0 0
\(682\) 2.63544e9 + 4.25993e9i 0.318133 + 0.514229i
\(683\) 4.87313e9i 0.585243i 0.956228 + 0.292621i \(0.0945275\pi\)
−0.956228 + 0.292621i \(0.905472\pi\)
\(684\) 0 0
\(685\) −2.36701e8 7.28489e8i −0.0281373 0.0865977i
\(686\) −1.48473e10 4.82417e9i −1.75595 0.570543i
\(687\) 0 0
\(688\) −1.34921e8 + 1.85703e8i −0.0157950 + 0.0217400i
\(689\) 4.79920e9 1.47704e10i 0.558987 1.72039i
\(690\) 0 0
\(691\) 9.79529e9 7.11670e9i 1.12939 0.820551i 0.143785 0.989609i \(-0.454073\pi\)
0.985606 + 0.169058i \(0.0540726\pi\)
\(692\) 3.88117e9 0.445237
\(693\) 0 0
\(694\) −5.28011e9 −0.599632
\(695\) 4.90610e8 3.56449e8i 0.0554357 0.0402764i
\(696\) 0 0
\(697\) 1.38363e9 4.25837e9i 0.154776 0.476353i
\(698\) 1.03883e9 1.42982e9i 0.115625 0.159143i
\(699\) 0 0
\(700\) −1.20236e10 3.90669e9i −1.32492 0.430493i
\(701\) 3.71689e9 + 1.14394e10i 0.407537 + 1.25427i 0.918758 + 0.394821i \(0.129193\pi\)
−0.511221 + 0.859449i \(0.670807\pi\)
\(702\) 0 0
\(703\) 1.66772e9i 0.181043i
\(704\) −2.06703e8 + 2.77719e9i −0.0223276 + 0.299986i
\(705\) 0 0
\(706\) −1.69680e9 2.33544e9i −0.181474 0.249777i
\(707\) −1.68314e10 + 5.46885e9i −1.79123 + 0.582007i
\(708\) 0 0
\(709\) −1.00178e9 7.27836e8i −0.105563 0.0766959i 0.533752 0.845641i \(-0.320782\pi\)
−0.639314 + 0.768945i \(0.720782\pi\)
\(710\) 4.46866e8 + 3.24667e8i 0.0468569 + 0.0340435i
\(711\) 0 0
\(712\) −7.48663e8 + 2.43255e8i −0.0777332 + 0.0252570i
\(713\) −1.02591e10 1.41205e10i −1.05998 1.45894i
\(714\) 0 0
\(715\) 8.70209e8 1.02769e9i 0.0890333 0.105146i
\(716\) 2.01955e9i 0.205617i
\(717\) 0 0
\(718\) 1.96013e9 + 6.03266e9i 0.197628 + 0.608238i
\(719\) 8.15819e9 + 2.65076e9i 0.818545 + 0.265961i 0.688213 0.725509i \(-0.258396\pi\)
0.130332 + 0.991470i \(0.458396\pi\)
\(720\) 0 0
\(721\) 1.13735e10 1.56543e10i 1.13011 1.55547i
\(722\) 1.52154e9 4.68281e9i 0.150453 0.463048i
\(723\) 0 0
\(724\) −3.95467e7 + 2.87323e7i −0.00387280 + 0.00281375i
\(725\) 6.11220e9 0.595682
\(726\) 0 0
\(727\) −6.73499e9 −0.650079 −0.325040 0.945700i \(-0.605378\pi\)
−0.325040 + 0.945700i \(0.605378\pi\)
\(728\) −1.96407e10 + 1.42698e10i −1.88668 + 1.37075i
\(729\) 0 0
\(730\) 2.91524e8 8.97218e8i 0.0277360 0.0853627i
\(731\) 2.20072e8 3.02903e8i 0.0208379 0.0286809i
\(732\) 0 0
\(733\) −4.62618e9 1.50314e9i −0.433869 0.140973i 0.0839360 0.996471i \(-0.473251\pi\)
−0.517805 + 0.855498i \(0.673251\pi\)
\(734\) −1.53222e8 4.71568e8i −0.0143016 0.0440157i
\(735\) 0 0
\(736\) 1.76024e10i 1.62742i
\(737\) −6.13677e9 + 7.24735e9i −0.564682 + 0.666873i
\(738\) 0 0
\(739\) −4.68186e9 6.44402e9i −0.426739 0.587356i 0.540462 0.841369i \(-0.318250\pi\)
−0.967201 + 0.254013i \(0.918250\pi\)
\(740\) 5.21459e8 1.69432e8i 0.0473052 0.0153704i
\(741\) 0 0
\(742\) −1.26741e10 9.20825e9i −1.13894 0.827491i
\(743\) 8.75809e9 + 6.36312e9i 0.783337 + 0.569127i 0.905979 0.423324i \(-0.139137\pi\)
−0.122642 + 0.992451i \(0.539137\pi\)
\(744\) 0 0
\(745\) −1.84535e9 + 5.99590e8i −0.163505 + 0.0531260i
\(746\) −3.61347e9 4.97352e9i −0.318668 0.438609i
\(747\) 0 0
\(748\) −1.98338e8 + 2.66480e9i −0.0173280 + 0.232814i
\(749\) 1.31900e9i 0.114699i
\(750\) 0 0
\(751\) −2.77164e9 8.53022e9i −0.238779 0.734887i −0.996598 0.0824211i \(-0.973735\pi\)
0.757818 0.652465i \(-0.226265\pi\)
\(752\) −2.90300e9 9.43243e8i −0.248935 0.0808837i
\(753\) 0 0
\(754\) 2.89414e9 3.98345e9i 0.245879 0.338423i
\(755\) −1.54110e8 + 4.74302e8i −0.0130322 + 0.0401089i
\(756\) 0 0
\(757\) −1.69847e10 + 1.23401e10i −1.42306 + 1.03391i −0.431802 + 0.901968i \(0.642122\pi\)
−0.991257 + 0.131945i \(0.957878\pi\)
\(758\) 9.22879e9 0.769666
\(759\) 0 0
\(760\) 3.15139e8 0.0260408
\(761\) 9.86132e9 7.16467e9i 0.811127 0.589318i −0.103030 0.994678i \(-0.532854\pi\)
0.914157 + 0.405360i \(0.132854\pi\)
\(762\) 0 0
\(763\) −4.52665e9 + 1.39316e10i −0.368927 + 1.13544i
\(764\) 7.73709e9 1.06492e10i 0.627698 0.863952i
\(765\) 0 0
\(766\) 8.42462e9 + 2.73732e9i 0.677251 + 0.220052i
\(767\) −6.68513e9 2.05747e10i −0.534966 1.64645i
\(768\) 0 0
\(769\) 2.17249e9i 0.172273i −0.996283 0.0861363i \(-0.972548\pi\)
0.996283 0.0861363i \(-0.0274521\pi\)
\(770\) −7.14663e8 1.15518e9i −0.0564136 0.0911869i
\(771\) 0 0
\(772\) 9.00805e9 + 1.23985e10i 0.704645 + 0.969860i
\(773\) −1.42161e10 + 4.61909e9i −1.10701 + 0.359690i −0.804797 0.593550i \(-0.797726\pi\)