Properties

Label 162.9.d.c.53.1
Level $162$
Weight $9$
Character 162.53
Analytic conductor $65.995$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,9,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not 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: \(65.9953348299\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 53.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 162.53
Dual form 162.9.d.c.107.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(587.878 + 339.411i) q^{5} +(1032.50 + 1788.34i) q^{7} +1448.15i q^{8} +O(q^{10})\) \(q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(587.878 + 339.411i) q^{5} +(1032.50 + 1788.34i) q^{7} +1448.15i q^{8} -7680.00 q^{10} +(-5761.20 + 3326.23i) q^{11} +(-4031.50 + 6982.76i) q^{13} +(-20232.8 - 11681.4i) q^{14} +(-8192.00 - 14189.0i) q^{16} +21586.6i q^{17} -226609. q^{19} +(75248.3 - 43444.6i) q^{20} +(37632.0 - 65180.5i) q^{22} +(-318982. - 184165. i) q^{23} +(35087.5 + 60773.3i) q^{25} -91222.4i q^{26} +264320. q^{28} +(811506. - 468523. i) q^{29} +(-413185. + 715657. i) q^{31} +(160530. + 92681.9i) q^{32} +(-122112. - 211504. i) q^{34} +1.40177e6i q^{35} +1.34458e6 q^{37} +(2.22031e6 - 1.28189e6i) q^{38} +(-491520. + 851338. i) q^{40} +(-4.49632e6 - 2.59595e6i) q^{41} +(3.07387e6 + 5.32410e6i) q^{43} +851515. i q^{44} +4.16717e6 q^{46} +(-5.11888e6 + 2.95539e6i) q^{47} +(750288. - 1.29954e6i) q^{49} +(-687572. - 396970. i) q^{50} +(516032. + 893794. i) q^{52} +768156. i q^{53} -4.51584e6 q^{55} +(-2.58980e6 + 1.49522e6i) q^{56} +(-5.30074e6 + 9.18114e6i) q^{58} +(410456. + 236977. i) q^{59} +(7.49285e6 + 1.29780e7i) q^{61} -9.34931e6i q^{62} -2.09715e6 q^{64} +(-4.74006e6 + 2.73667e6i) q^{65} +(5.01185e6 - 8.68078e6i) q^{67} +(2.39290e6 + 1.38154e6i) q^{68} +(-7.92960e6 - 1.37345e7i) q^{70} -4.54849e7i q^{71} -2.32616e7 q^{73} +(-1.31741e7 + 7.60606e6i) q^{74} +(-1.45030e7 + 2.51199e7i) q^{76} +(-1.18969e7 - 6.86867e6i) q^{77} +(-7.13359e6 - 1.23557e7i) q^{79} -1.11218e7i q^{80} +5.87397e7 q^{82} +(-3.13430e7 + 1.80959e7i) q^{83} +(-7.32672e6 + 1.26903e7i) q^{85} +(-6.02353e7 - 3.47769e7i) q^{86} +(-4.81690e6 - 8.34311e6i) q^{88} -1.15088e8i q^{89} -1.66501e7 q^{91} +(-4.08297e7 + 2.35731e7i) q^{92} +(3.34364e7 - 5.79136e7i) q^{94} +(-1.33218e8 - 7.69136e7i) q^{95} +(2.02858e7 + 3.51361e7i) q^{97} +1.69771e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 256 q^{4} + 4130 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 256 q^{4} + 4130 q^{7} - 30720 q^{10} - 16126 q^{13} - 32768 q^{16} - 906436 q^{19} + 150528 q^{22} + 140350 q^{25} + 1057280 q^{28} - 1652740 q^{31} - 488448 q^{34} + 5378300 q^{37} - 1966080 q^{40} + 12295484 q^{43} + 16668672 q^{46} + 3001152 q^{49} + 2064128 q^{52} - 18063360 q^{55} - 21202944 q^{58} + 29971394 q^{61} - 8388608 q^{64} + 20047394 q^{67} - 31718400 q^{70} - 93046276 q^{73} - 58011904 q^{76} - 28534366 q^{79} + 234958848 q^{82} - 29306880 q^{85} - 19267584 q^{88} - 66600380 q^{91} + 133745664 q^{94} + 81143234 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.79796 + 5.65685i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 64.0000 110.851i 0.250000 0.433013i
\(5\) 587.878 + 339.411i 0.940604 + 0.543058i 0.890150 0.455668i \(-0.150600\pi\)
0.0504544 + 0.998726i \(0.483933\pi\)
\(6\) 0 0
\(7\) 1032.50 + 1788.34i 0.430029 + 0.744832i 0.996875 0.0789913i \(-0.0251699\pi\)
−0.566846 + 0.823824i \(0.691837\pi\)
\(8\) 1448.15i 0.353553i
\(9\) 0 0
\(10\) −7680.00 −0.768000
\(11\) −5761.20 + 3326.23i −0.393498 + 0.227186i −0.683675 0.729787i \(-0.739619\pi\)
0.290177 + 0.956973i \(0.406286\pi\)
\(12\) 0 0
\(13\) −4031.50 + 6982.76i −0.141154 + 0.244486i −0.927931 0.372751i \(-0.878415\pi\)
0.786777 + 0.617237i \(0.211748\pi\)
\(14\) −20232.8 11681.4i −0.526676 0.304077i
\(15\) 0 0
\(16\) −8192.00 14189.0i −0.125000 0.216506i
\(17\) 21586.6i 0.258457i 0.991615 + 0.129228i \(0.0412500\pi\)
−0.991615 + 0.129228i \(0.958750\pi\)
\(18\) 0 0
\(19\) −226609. −1.73885 −0.869426 0.494063i \(-0.835511\pi\)
−0.869426 + 0.494063i \(0.835511\pi\)
\(20\) 75248.3 43444.6i 0.470302 0.271529i
\(21\) 0 0
\(22\) 37632.0 65180.5i 0.160645 0.278245i
\(23\) −318982. 184165.i −1.13987 0.658104i −0.193472 0.981106i \(-0.561975\pi\)
−0.946398 + 0.323002i \(0.895308\pi\)
\(24\) 0 0
\(25\) 35087.5 + 60773.3i 0.0898240 + 0.155580i
\(26\) 91222.4i 0.199622i
\(27\) 0 0
\(28\) 264320. 0.430029
\(29\) 811506. 468523.i 1.14736 0.662429i 0.199118 0.979976i \(-0.436192\pi\)
0.948243 + 0.317547i \(0.102859\pi\)
\(30\) 0 0
\(31\) −413185. + 715657.i −0.447402 + 0.774923i −0.998216 0.0597052i \(-0.980984\pi\)
0.550814 + 0.834628i \(0.314317\pi\)
\(32\) 160530. + 92681.9i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −122112. 211504.i −0.0913782 0.158272i
\(35\) 1.40177e6i 0.934123i
\(36\) 0 0
\(37\) 1.34458e6 0.717428 0.358714 0.933448i \(-0.383215\pi\)
0.358714 + 0.933448i \(0.383215\pi\)
\(38\) 2.22031e6 1.28189e6i 1.06483 0.614777i
\(39\) 0 0
\(40\) −491520. + 851338.i −0.192000 + 0.332554i
\(41\) −4.49632e6 2.59595e6i −1.59119 0.918674i −0.993103 0.117243i \(-0.962595\pi\)
−0.598087 0.801431i \(-0.704072\pi\)
\(42\) 0 0
\(43\) 3.07387e6 + 5.32410e6i 0.899108 + 1.55730i 0.828637 + 0.559787i \(0.189117\pi\)
0.0704712 + 0.997514i \(0.477550\pi\)
\(44\) 851515.i 0.227186i
\(45\) 0 0
\(46\) 4.16717e6 0.930700
\(47\) −5.11888e6 + 2.95539e6i −1.04902 + 0.605652i −0.922375 0.386296i \(-0.873754\pi\)
−0.126645 + 0.991948i \(0.540421\pi\)
\(48\) 0 0
\(49\) 750288. 1.29954e6i 0.130150 0.225426i
\(50\) −687572. 396970.i −0.110011 0.0635152i
\(51\) 0 0
\(52\) 516032. + 893794.i 0.0705770 + 0.122243i
\(53\) 768156.i 0.0973522i 0.998815 + 0.0486761i \(0.0155002\pi\)
−0.998815 + 0.0486761i \(0.984500\pi\)
\(54\) 0 0
\(55\) −4.51584e6 −0.493501
\(56\) −2.58980e6 + 1.49522e6i −0.263338 + 0.152038i
\(57\) 0 0
\(58\) −5.30074e6 + 9.18114e6i −0.468408 + 0.811306i
\(59\) 410456. + 236977.i 0.0338734 + 0.0195568i 0.516841 0.856081i \(-0.327108\pi\)
−0.482968 + 0.875638i \(0.660441\pi\)
\(60\) 0 0
\(61\) 7.49285e6 + 1.29780e7i 0.541162 + 0.937321i 0.998838 + 0.0482013i \(0.0153489\pi\)
−0.457675 + 0.889119i \(0.651318\pi\)
\(62\) 9.34931e6i 0.632722i
\(63\) 0 0
\(64\) −2.09715e6 −0.125000
\(65\) −4.74006e6 + 2.73667e6i −0.265540 + 0.153310i
\(66\) 0 0
\(67\) 5.01185e6 8.68078e6i 0.248713 0.430784i −0.714456 0.699680i \(-0.753326\pi\)
0.963169 + 0.268897i \(0.0866590\pi\)
\(68\) 2.39290e6 + 1.38154e6i 0.111915 + 0.0646142i
\(69\) 0 0
\(70\) −7.92960e6 1.37345e7i −0.330262 0.572031i
\(71\) 4.54849e7i 1.78992i −0.446145 0.894961i \(-0.647203\pi\)
0.446145 0.894961i \(-0.352797\pi\)
\(72\) 0 0
\(73\) −2.32616e7 −0.819120 −0.409560 0.912283i \(-0.634318\pi\)
−0.409560 + 0.912283i \(0.634318\pi\)
\(74\) −1.31741e7 + 7.60606e6i −0.439333 + 0.253649i
\(75\) 0 0
\(76\) −1.45030e7 + 2.51199e7i −0.434713 + 0.752945i
\(77\) −1.18969e7 6.86867e6i −0.338431 0.195393i
\(78\) 0 0
\(79\) −7.13359e6 1.23557e7i −0.183147 0.317220i 0.759804 0.650153i \(-0.225295\pi\)
−0.942951 + 0.332933i \(0.891962\pi\)
\(80\) 1.11218e7i 0.271529i
\(81\) 0 0
\(82\) 5.87397e7 1.29920
\(83\) −3.13430e7 + 1.80959e7i −0.660433 + 0.381301i −0.792442 0.609947i \(-0.791191\pi\)
0.132009 + 0.991249i \(0.457857\pi\)
\(84\) 0 0
\(85\) −7.32672e6 + 1.26903e7i −0.140357 + 0.243105i
\(86\) −6.02353e7 3.47769e7i −1.10118 0.635765i
\(87\) 0 0
\(88\) −4.81690e6 8.34311e6i −0.0803224 0.139122i
\(89\) 1.15088e8i 1.83429i −0.398549 0.917147i \(-0.630486\pi\)
0.398549 0.917147i \(-0.369514\pi\)
\(90\) 0 0
\(91\) −1.66501e7 −0.242801
\(92\) −4.08297e7 + 2.35731e7i −0.569935 + 0.329052i
\(93\) 0 0
\(94\) 3.34364e7 5.79136e7i 0.428261 0.741769i
\(95\) −1.33218e8 7.69136e7i −1.63557 0.944298i
\(96\) 0 0
\(97\) 2.02858e7 + 3.51361e7i 0.229142 + 0.396886i 0.957554 0.288253i \(-0.0930745\pi\)
−0.728412 + 0.685140i \(0.759741\pi\)
\(98\) 1.69771e7i 0.184060i
\(99\) 0 0
\(100\) 8.98240e6 0.0898240
\(101\) 5.62453e7 3.24732e7i 0.540506 0.312061i −0.204778 0.978808i \(-0.565647\pi\)
0.745284 + 0.666747i \(0.232314\pi\)
\(102\) 0 0
\(103\) 6.86315e7 1.18873e8i 0.609782 1.05617i −0.381494 0.924371i \(-0.624590\pi\)
0.991276 0.131802i \(-0.0420763\pi\)
\(104\) −1.01121e7 5.83824e6i −0.0864388 0.0499055i
\(105\) 0 0
\(106\) −4.34534e6 7.52636e6i −0.0344192 0.0596158i
\(107\) 1.39108e8i 1.06125i 0.847607 + 0.530625i \(0.178043\pi\)
−0.847607 + 0.530625i \(0.821957\pi\)
\(108\) 0 0
\(109\) −4.29417e7 −0.304210 −0.152105 0.988364i \(-0.548605\pi\)
−0.152105 + 0.988364i \(0.548605\pi\)
\(110\) 4.42460e7 2.55454e7i 0.302206 0.174479i
\(111\) 0 0
\(112\) 1.69165e7 2.93002e7i 0.107507 0.186208i
\(113\) −2.52576e8 1.45825e8i −1.54909 0.894369i −0.998211 0.0597865i \(-0.980958\pi\)
−0.550882 0.834583i \(-0.685709\pi\)
\(114\) 0 0
\(115\) −1.25015e8 2.16532e8i −0.714778 1.23803i
\(116\) 1.19942e8i 0.662429i
\(117\) 0 0
\(118\) −5.36218e6 −0.0276575
\(119\) −3.86042e7 + 2.22881e7i −0.192507 + 0.111144i
\(120\) 0 0
\(121\) −8.50518e7 + 1.47314e8i −0.396773 + 0.687231i
\(122\) −1.46829e8 8.47719e7i −0.662786 0.382660i
\(123\) 0 0
\(124\) 5.28877e7 + 9.16041e7i 0.223701 + 0.387461i
\(125\) 2.17529e8i 0.890997i
\(126\) 0 0
\(127\) −3.39515e8 −1.30510 −0.652551 0.757745i \(-0.726301\pi\)
−0.652551 + 0.757745i \(0.726301\pi\)
\(128\) 2.05478e7 1.18633e7i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 3.09619e7 5.36276e7i 0.108406 0.187765i
\(131\) −1.94455e8 1.12269e8i −0.660289 0.381218i 0.132098 0.991237i \(-0.457829\pi\)
−0.792387 + 0.610019i \(0.791162\pi\)
\(132\) 0 0
\(133\) −2.33974e8 4.05254e8i −0.747757 1.29515i
\(134\) 1.13405e8i 0.351733i
\(135\) 0 0
\(136\) −3.12607e7 −0.0913782
\(137\) −3.47504e8 + 2.00632e8i −0.986456 + 0.569531i −0.904213 0.427082i \(-0.859542\pi\)
−0.0822430 + 0.996612i \(0.526208\pi\)
\(138\) 0 0
\(139\) −1.34882e8 + 2.33622e8i −0.361322 + 0.625829i −0.988179 0.153306i \(-0.951008\pi\)
0.626856 + 0.779135i \(0.284341\pi\)
\(140\) 1.55388e8 + 8.97132e7i 0.404487 + 0.233531i
\(141\) 0 0
\(142\) 2.57302e8 + 4.45659e8i 0.632833 + 1.09610i
\(143\) 5.36388e7i 0.128273i
\(144\) 0 0
\(145\) 6.36088e8 1.43895
\(146\) 2.27916e8 1.31587e8i 0.501607 0.289603i
\(147\) 0 0
\(148\) 8.60528e7 1.49048e8i 0.179357 0.310655i
\(149\) −1.68180e8 9.70990e7i −0.341217 0.197002i 0.319593 0.947555i \(-0.396454\pi\)
−0.660810 + 0.750553i \(0.729787\pi\)
\(150\) 0 0
\(151\) 4.37550e7 + 7.57859e7i 0.0841627 + 0.145774i 0.905034 0.425339i \(-0.139845\pi\)
−0.820871 + 0.571113i \(0.806512\pi\)
\(152\) 3.28165e8i 0.614777i
\(153\) 0 0
\(154\) 1.55420e8 0.276328
\(155\) −4.85804e8 + 2.80479e8i −0.841656 + 0.485930i
\(156\) 0 0
\(157\) −1.42328e8 + 2.46519e8i −0.234256 + 0.405743i −0.959056 0.283216i \(-0.908599\pi\)
0.724800 + 0.688959i \(0.241932\pi\)
\(158\) 1.39789e8 + 8.07074e7i 0.224308 + 0.129505i
\(159\) 0 0
\(160\) 6.29146e7 + 1.08971e8i 0.0960000 + 0.166277i
\(161\) 7.60600e8i 1.13202i
\(162\) 0 0
\(163\) −2.63153e8 −0.372785 −0.186393 0.982475i \(-0.559680\pi\)
−0.186393 + 0.982475i \(0.559680\pi\)
\(164\) −5.75529e8 + 3.32282e8i −0.795595 + 0.459337i
\(165\) 0 0
\(166\) 2.04732e8 3.54606e8i 0.269621 0.466997i
\(167\) 1.00792e9 + 5.81921e8i 1.29586 + 0.748167i 0.979687 0.200534i \(-0.0642676\pi\)
0.316176 + 0.948701i \(0.397601\pi\)
\(168\) 0 0
\(169\) 3.75359e8 + 6.50142e8i 0.460151 + 0.797005i
\(170\) 1.65785e8i 0.198495i
\(171\) 0 0
\(172\) 7.86911e8 0.899108
\(173\) 1.14676e9 6.62085e8i 1.28024 0.739145i 0.303345 0.952881i \(-0.401897\pi\)
0.976891 + 0.213736i \(0.0685634\pi\)
\(174\) 0 0
\(175\) −7.24557e7 + 1.25497e8i −0.0772539 + 0.133808i
\(176\) 9.43915e7 + 5.44970e7i 0.0983744 + 0.0567965i
\(177\) 0 0
\(178\) 6.51034e8 + 1.12762e9i 0.648521 + 1.12327i
\(179\) 4.06696e8i 0.396148i 0.980187 + 0.198074i \(0.0634686\pi\)
−0.980187 + 0.198074i \(0.936531\pi\)
\(180\) 0 0
\(181\) −1.29071e9 −1.20258 −0.601289 0.799032i \(-0.705346\pi\)
−0.601289 + 0.799032i \(0.705346\pi\)
\(182\) 1.63137e8 9.41872e7i 0.148685 0.0858433i
\(183\) 0 0
\(184\) 2.66699e8 4.61936e8i 0.232675 0.403005i
\(185\) 7.90445e8 + 4.56364e8i 0.674815 + 0.389605i
\(186\) 0 0
\(187\) −7.18019e7 1.24364e8i −0.0587177 0.101702i
\(188\) 7.56580e8i 0.605652i
\(189\) 0 0
\(190\) 1.74036e9 1.33544
\(191\) 2.57828e8 1.48857e8i 0.193730 0.111850i −0.399998 0.916516i \(-0.630989\pi\)
0.593728 + 0.804666i \(0.297656\pi\)
\(192\) 0 0
\(193\) −1.11002e9 + 1.92261e9i −0.800021 + 1.38568i 0.119581 + 0.992824i \(0.461845\pi\)
−0.919602 + 0.392852i \(0.871488\pi\)
\(194\) −3.97519e8 2.29508e8i −0.280641 0.162028i
\(195\) 0 0
\(196\) −9.60369e7 1.66341e8i −0.0650749 0.112713i
\(197\) 1.91580e9i 1.27199i 0.771693 + 0.635996i \(0.219410\pi\)
−0.771693 + 0.635996i \(0.780590\pi\)
\(198\) 0 0
\(199\) −1.75472e9 −1.11891 −0.559457 0.828859i \(-0.688990\pi\)
−0.559457 + 0.828859i \(0.688990\pi\)
\(200\) −8.80092e7 + 5.08121e7i −0.0550057 + 0.0317576i
\(201\) 0 0
\(202\) −3.67393e8 + 6.36343e8i −0.220661 + 0.382196i
\(203\) 1.67576e9 + 9.67501e8i 0.986797 + 0.569727i
\(204\) 0 0
\(205\) −1.76219e9 3.05220e9i −0.997786 1.72822i
\(206\) 1.55295e9i 0.862362i
\(207\) 0 0
\(208\) 1.32104e8 0.0705770
\(209\) 1.30554e9 7.53754e8i 0.684234 0.395043i
\(210\) 0 0
\(211\) 1.07695e9 1.86533e9i 0.543331 0.941077i −0.455379 0.890298i \(-0.650496\pi\)
0.998710 0.0507792i \(-0.0161705\pi\)
\(212\) 8.51510e7 + 4.91620e7i 0.0421547 + 0.0243380i
\(213\) 0 0
\(214\) −7.86915e8 1.36298e9i −0.375209 0.649880i
\(215\) 4.17323e9i 1.95307i
\(216\) 0 0
\(217\) −1.70645e9 −0.769583
\(218\) 4.20741e8 2.42915e8i 0.186290 0.107554i
\(219\) 0 0
\(220\) −2.89014e8 + 5.00587e8i −0.123375 + 0.213692i
\(221\) −1.50734e8 8.70262e7i −0.0631890 0.0364822i
\(222\) 0 0
\(223\) 1.19687e9 + 2.07304e9i 0.483980 + 0.838277i 0.999831 0.0184009i \(-0.00585753\pi\)
−0.515851 + 0.856678i \(0.672524\pi\)
\(224\) 3.82776e8i 0.152038i
\(225\) 0 0
\(226\) 3.29963e9 1.26483
\(227\) 8.59666e8 4.96328e8i 0.323762 0.186924i −0.329306 0.944223i \(-0.606815\pi\)
0.653068 + 0.757299i \(0.273481\pi\)
\(228\) 0 0
\(229\) 1.11075e9 1.92387e9i 0.403900 0.699575i −0.590293 0.807189i \(-0.700988\pi\)
0.994193 + 0.107614i \(0.0343210\pi\)
\(230\) 2.44978e9 + 1.41438e9i 0.875420 + 0.505424i
\(231\) 0 0
\(232\) 6.78494e8 + 1.17519e9i 0.234204 + 0.405653i
\(233\) 1.24042e9i 0.420867i −0.977608 0.210433i \(-0.932512\pi\)
0.977608 0.210433i \(-0.0674875\pi\)
\(234\) 0 0
\(235\) −4.01237e9 −1.31562
\(236\) 5.25384e7 3.03330e7i 0.0169367 0.00977841i
\(237\) 0 0
\(238\) 2.52161e8 4.36756e8i 0.0785906 0.136123i
\(239\) −6.57565e8 3.79645e8i −0.201533 0.116355i 0.395837 0.918321i \(-0.370454\pi\)
−0.597370 + 0.801965i \(0.703788\pi\)
\(240\) 0 0
\(241\) −2.23734e9 3.87518e9i −0.663228 1.14874i −0.979762 0.200164i \(-0.935853\pi\)
0.316534 0.948581i \(-0.397481\pi\)
\(242\) 1.92450e9i 0.561122i
\(243\) 0 0
\(244\) 1.91817e9 0.541162
\(245\) 8.82155e8 5.09312e8i 0.244839 0.141358i
\(246\) 0 0
\(247\) 9.13574e8 1.58236e9i 0.245446 0.425125i
\(248\) −1.03638e9 5.98356e8i −0.273977 0.158180i
\(249\) 0 0
\(250\) 1.23053e9 + 2.13134e9i 0.315015 + 0.545622i
\(251\) 1.07356e9i 0.270477i 0.990813 + 0.135239i \(0.0431801\pi\)
−0.990813 + 0.135239i \(0.956820\pi\)
\(252\) 0 0
\(253\) 2.45029e9 0.598048
\(254\) 3.32656e9 1.92059e9i 0.799208 0.461423i
\(255\) 0 0
\(256\) −1.34218e8 + 2.32472e8i −0.0312500 + 0.0541266i
\(257\) 6.57024e9 + 3.79333e9i 1.50608 + 0.869537i 0.999975 + 0.00706738i \(0.00224964\pi\)
0.506108 + 0.862470i \(0.331084\pi\)
\(258\) 0 0
\(259\) 1.38827e9 + 2.40456e9i 0.308515 + 0.534363i
\(260\) 7.00588e8i 0.153310i
\(261\) 0 0
\(262\) 2.54035e9 0.539124
\(263\) −2.43480e9 + 1.40573e9i −0.508909 + 0.293819i −0.732385 0.680891i \(-0.761593\pi\)
0.223476 + 0.974709i \(0.428260\pi\)
\(264\) 0 0
\(265\) −2.60721e8 + 4.51581e8i −0.0528679 + 0.0915699i
\(266\) 4.58493e9 + 2.64711e9i 0.915812 + 0.528744i
\(267\) 0 0
\(268\) −6.41517e8 1.11114e9i −0.124357 0.215392i
\(269\) 2.96285e9i 0.565849i −0.959142 0.282924i \(-0.908695\pi\)
0.959142 0.282924i \(-0.0913045\pi\)
\(270\) 0 0
\(271\) −8.40415e9 −1.55818 −0.779089 0.626914i \(-0.784318\pi\)
−0.779089 + 0.626914i \(0.784318\pi\)
\(272\) 3.06291e8 1.76837e8i 0.0559575 0.0323071i
\(273\) 0 0
\(274\) 2.26989e9 3.93156e9i 0.402719 0.697530i
\(275\) −4.04292e8 2.33418e8i −0.0706911 0.0408135i
\(276\) 0 0
\(277\) −2.99081e9 5.18024e9i −0.508007 0.879895i −0.999957 0.00927090i \(-0.997049\pi\)
0.491950 0.870624i \(-0.336284\pi\)
\(278\) 3.05203e9i 0.510987i
\(279\) 0 0
\(280\) −2.02998e9 −0.330262
\(281\) −9.38258e9 + 5.41704e9i −1.50486 + 0.868833i −0.504879 + 0.863190i \(0.668463\pi\)
−0.999984 + 0.00564307i \(0.998204\pi\)
\(282\) 0 0
\(283\) −1.89335e9 + 3.27938e9i −0.295179 + 0.511264i −0.975026 0.222089i \(-0.928712\pi\)
0.679848 + 0.733353i \(0.262046\pi\)
\(284\) −5.04206e9 2.91103e9i −0.775059 0.447480i
\(285\) 0 0
\(286\) 3.03427e8 + 5.25551e8i 0.0453513 + 0.0785508i
\(287\) 1.07213e10i 1.58023i
\(288\) 0 0
\(289\) 6.50978e9 0.933200
\(290\) −6.23237e9 + 3.59826e9i −0.881173 + 0.508745i
\(291\) 0 0
\(292\) −1.48874e9 + 2.57857e9i −0.204780 + 0.354689i
\(293\) −6.33964e9 3.66019e9i −0.860190 0.496631i 0.00388608 0.999992i \(-0.498763\pi\)
−0.864076 + 0.503362i \(0.832096\pi\)
\(294\) 0 0
\(295\) 1.60865e8 + 2.78627e8i 0.0212410 + 0.0367904i
\(296\) 1.94715e9i 0.253649i
\(297\) 0 0
\(298\) 2.19710e9 0.278602
\(299\) 2.57195e9 1.48492e9i 0.321794 0.185788i
\(300\) 0 0
\(301\) −6.34754e9 + 1.09943e10i −0.773285 + 1.33937i
\(302\) −8.57419e8 4.95031e8i −0.103078 0.0595120i
\(303\) 0 0
\(304\) 1.85638e9 + 3.21535e9i 0.217357 + 0.376473i
\(305\) 1.01726e10i 1.17553i
\(306\) 0 0
\(307\) −2.21986e8 −0.0249903 −0.0124951 0.999922i \(-0.503977\pi\)
−0.0124951 + 0.999922i \(0.503977\pi\)
\(308\) −1.52280e9 + 8.79189e8i −0.169215 + 0.0976966i
\(309\) 0 0
\(310\) 3.17326e9 5.49625e9i 0.343605 0.595141i
\(311\) −6.23153e9 3.59778e9i −0.666121 0.384585i 0.128484 0.991712i \(-0.458989\pi\)
−0.794605 + 0.607126i \(0.792322\pi\)
\(312\) 0 0
\(313\) −2.11671e9 3.66624e9i −0.220538 0.381983i 0.734433 0.678681i \(-0.237448\pi\)
−0.954971 + 0.296698i \(0.904115\pi\)
\(314\) 3.22051e9i 0.331288i
\(315\) 0 0
\(316\) −1.82620e9 −0.183147
\(317\) 4.67692e9 2.70022e9i 0.463151 0.267400i −0.250217 0.968190i \(-0.580502\pi\)
0.713368 + 0.700789i \(0.247169\pi\)
\(318\) 0 0
\(319\) −3.11683e9 + 5.39851e9i −0.300989 + 0.521328i
\(320\) −1.23287e9 7.11797e8i −0.117576 0.0678823i
\(321\) 0 0
\(322\) 4.30260e9 + 7.45232e9i 0.400228 + 0.693215i
\(323\) 4.89171e9i 0.449418i
\(324\) 0 0
\(325\) −5.65821e8 −0.0507161
\(326\) 2.57837e9 1.48862e9i 0.228283 0.131799i
\(327\) 0 0
\(328\) 3.75934e9 6.51137e9i 0.324800 0.562571i
\(329\) −1.05705e10 6.10288e9i −0.902219 0.520896i
\(330\) 0 0
\(331\) 6.79707e9 + 1.17729e10i 0.566252 + 0.980778i 0.996932 + 0.0782729i \(0.0249406\pi\)
−0.430680 + 0.902505i \(0.641726\pi\)
\(332\) 4.63255e9i 0.381301i
\(333\) 0 0
\(334\) −1.31674e10 −1.05807
\(335\) 5.89271e9 3.40216e9i 0.467881 0.270131i
\(336\) 0 0
\(337\) 1.17717e9 2.03891e9i 0.0912680 0.158081i −0.816777 0.576954i \(-0.804241\pi\)
0.908045 + 0.418873i \(0.137575\pi\)
\(338\) −7.35551e9 4.24671e9i −0.563568 0.325376i
\(339\) 0 0
\(340\) 9.37820e8 + 1.62435e9i 0.0701785 + 0.121553i
\(341\) 5.49739e9i 0.406574i
\(342\) 0 0
\(343\) 1.50030e10 1.08393
\(344\) −7.71012e9 + 4.45144e9i −0.550589 + 0.317883i
\(345\) 0 0
\(346\) −7.49064e9 + 1.29742e10i −0.522654 + 0.905263i
\(347\) −7.22105e9 4.16907e9i −0.498061 0.287555i 0.229852 0.973226i \(-0.426176\pi\)
−0.727912 + 0.685670i \(0.759509\pi\)
\(348\) 0 0
\(349\) 6.32314e9 + 1.09520e10i 0.426217 + 0.738230i 0.996533 0.0831955i \(-0.0265126\pi\)
−0.570316 + 0.821425i \(0.693179\pi\)
\(350\) 1.63949e9i 0.109253i
\(351\) 0 0
\(352\) −1.23313e9 −0.0803224
\(353\) 3.25746e9 1.88070e9i 0.209788 0.121121i −0.391425 0.920210i \(-0.628018\pi\)
0.601213 + 0.799089i \(0.294684\pi\)
\(354\) 0 0
\(355\) 1.54381e10 2.67396e10i 0.972031 1.68361i
\(356\) −1.27576e10 7.36561e9i −0.794273 0.458573i
\(357\) 0 0
\(358\) −2.30062e9 3.98479e9i −0.140059 0.242590i
\(359\) 1.64726e10i 0.991707i −0.868406 0.495853i \(-0.834855\pi\)
0.868406 0.495853i \(-0.165145\pi\)
\(360\) 0 0
\(361\) 3.43681e10 2.02361
\(362\) 1.26463e10 7.30134e9i 0.736426 0.425176i
\(363\) 0 0
\(364\) −1.06561e9 + 1.84568e9i −0.0607003 + 0.105136i
\(365\) −1.36750e10 7.89524e9i −0.770468 0.444830i
\(366\) 0 0
\(367\) −3.69362e9 6.39753e9i −0.203605 0.352653i 0.746083 0.665853i \(-0.231932\pi\)
−0.949687 + 0.313200i \(0.898599\pi\)
\(368\) 6.03470e9i 0.329052i
\(369\) 0 0
\(370\) −1.03263e10 −0.550984
\(371\) −1.37373e9 + 7.93121e8i −0.0725111 + 0.0418643i
\(372\) 0 0
\(373\) −1.15012e10 + 1.99207e10i −0.594168 + 1.02913i 0.399496 + 0.916735i \(0.369185\pi\)
−0.993664 + 0.112394i \(0.964148\pi\)
\(374\) 1.40702e9 + 8.12345e8i 0.0719142 + 0.0415197i
\(375\) 0 0
\(376\) −4.27986e9 7.41294e9i −0.214130 0.370885i
\(377\) 7.55541e9i 0.374018i
\(378\) 0 0
\(379\) −2.05891e10 −0.997883 −0.498942 0.866636i \(-0.666278\pi\)
−0.498942 + 0.866636i \(0.666278\pi\)
\(380\) −1.70519e10 + 9.84495e9i −0.817786 + 0.472149i
\(381\) 0 0
\(382\) −1.68413e9 + 2.91699e9i −0.0790899 + 0.136988i
\(383\) −1.24400e10 7.18227e9i −0.578132 0.333785i 0.182259 0.983251i \(-0.441659\pi\)
−0.760391 + 0.649466i \(0.774992\pi\)
\(384\) 0 0
\(385\) −4.66260e9 8.07587e9i −0.212220 0.367575i
\(386\) 2.51169e10i 1.13140i
\(387\) 0 0
\(388\) 5.19317e9 0.229142
\(389\) −2.88643e10 + 1.66648e10i −1.26056 + 0.727783i −0.973182 0.230035i \(-0.926116\pi\)
−0.287375 + 0.957818i \(0.592782\pi\)
\(390\) 0 0
\(391\) 3.97548e9 6.88573e9i 0.170091 0.294607i
\(392\) 1.88193e9 + 1.08653e9i 0.0797002 + 0.0460149i
\(393\) 0 0
\(394\) −1.08374e10 1.87709e10i −0.449717 0.778932i
\(395\) 9.68488e9i 0.397838i
\(396\) 0 0
\(397\) −4.32631e9 −0.174163 −0.0870814 0.996201i \(-0.527754\pi\)
−0.0870814 + 0.996201i \(0.527754\pi\)
\(398\) 1.71927e10 9.92622e9i 0.685192 0.395596i
\(399\) 0 0
\(400\) 5.74874e8 9.95710e8i 0.0224560 0.0388949i
\(401\) 1.04590e10 + 6.03850e9i 0.404494 + 0.233535i 0.688421 0.725311i \(-0.258304\pi\)
−0.283927 + 0.958846i \(0.591637\pi\)
\(402\) 0 0
\(403\) −3.33151e9 5.77035e9i −0.126305 0.218767i
\(404\) 8.31315e9i 0.312061i
\(405\) 0 0
\(406\) −2.18920e10 −0.805716
\(407\) −7.74637e9 + 4.47237e9i −0.282306 + 0.162990i
\(408\) 0 0
\(409\) 1.90611e10 3.30147e10i 0.681168 1.17982i −0.293457 0.955972i \(-0.594806\pi\)
0.974625 0.223845i \(-0.0718609\pi\)
\(410\) 3.45318e10 + 1.99369e10i 1.22203 + 0.705542i
\(411\) 0 0
\(412\) −8.78483e9 1.52158e10i −0.304891 0.528087i
\(413\) 9.78715e8i 0.0336400i
\(414\) 0 0
\(415\) −2.45678e10 −0.828275
\(416\) −1.29435e9 + 7.47294e8i −0.0432194 + 0.0249527i
\(417\) 0 0
\(418\) −8.52775e9 + 1.47705e10i −0.279338 + 0.483827i
\(419\) 2.18772e10 + 1.26308e10i 0.709799 + 0.409803i 0.810987 0.585065i \(-0.198931\pi\)
−0.101188 + 0.994867i \(0.532264\pi\)
\(420\) 0 0
\(421\) 1.66982e9 + 2.89222e9i 0.0531548 + 0.0920667i 0.891378 0.453260i \(-0.149739\pi\)
−0.838224 + 0.545327i \(0.816406\pi\)
\(422\) 2.43685e10i 0.768386i
\(423\) 0 0
\(424\) −1.11241e9 −0.0344192
\(425\) −1.31189e9 + 7.57418e8i −0.0402106 + 0.0232156i
\(426\) 0 0
\(427\) −1.54727e10 + 2.67996e10i −0.465431 + 0.806151i
\(428\) 1.54203e10 + 8.90293e9i 0.459535 + 0.265313i
\(429\) 0 0
\(430\) −2.36073e10 4.08891e10i −0.690515 1.19601i
\(431\) 5.55244e9i 0.160907i 0.996758 + 0.0804534i \(0.0256368\pi\)
−0.996758 + 0.0804534i \(0.974363\pi\)
\(432\) 0 0
\(433\) 1.14713e10 0.326334 0.163167 0.986598i \(-0.447829\pi\)
0.163167 + 0.986598i \(0.447829\pi\)
\(434\) 1.67198e10 9.65316e9i 0.471272 0.272089i
\(435\) 0 0
\(436\) −2.74827e9 + 4.76014e9i −0.0760524 + 0.131727i
\(437\) 7.22843e10 + 4.17333e10i 1.98207 + 1.14435i
\(438\) 0 0
\(439\) 2.99243e10 + 5.18304e10i 0.805686 + 1.39549i 0.915827 + 0.401573i \(0.131537\pi\)
−0.110141 + 0.993916i \(0.535130\pi\)
\(440\) 6.53963e9i 0.174479i
\(441\) 0 0
\(442\) 1.96918e9 0.0515936
\(443\) 3.13162e9 1.80804e9i 0.0813120 0.0469455i −0.458793 0.888543i \(-0.651718\pi\)
0.540105 + 0.841598i \(0.318385\pi\)
\(444\) 0 0
\(445\) 3.90621e10 6.76575e10i 0.996128 1.72534i
\(446\) −2.34537e10 1.35410e10i −0.592752 0.342225i
\(447\) 0 0
\(448\) −2.16531e9 3.75043e9i −0.0537536 0.0931040i
\(449\) 2.39980e9i 0.0590459i −0.999564 0.0295230i \(-0.990601\pi\)
0.999564 0.0295230i \(-0.00939882\pi\)
\(450\) 0 0
\(451\) 3.45390e10 0.834839
\(452\) −3.23297e10 + 1.86655e10i −0.774547 + 0.447185i
\(453\) 0 0
\(454\) −5.61531e9 + 9.72601e9i −0.132175 + 0.228935i
\(455\) −9.78822e9 5.65123e9i −0.228380 0.131855i
\(456\) 0 0
\(457\) 2.05865e10 + 3.56569e10i 0.471974 + 0.817483i 0.999486 0.0320646i \(-0.0102082\pi\)
−0.527512 + 0.849548i \(0.676875\pi\)
\(458\) 2.51334e10i 0.571201i
\(459\) 0 0
\(460\) −3.20039e10 −0.714778
\(461\) 1.79613e10 1.03700e10i 0.397681 0.229601i −0.287802 0.957690i \(-0.592924\pi\)
0.685483 + 0.728089i \(0.259591\pi\)
\(462\) 0 0
\(463\) 3.67690e9 6.36857e9i 0.0800125 0.138586i −0.823243 0.567690i \(-0.807837\pi\)
0.903255 + 0.429104i \(0.141171\pi\)
\(464\) −1.32957e10 7.67629e9i −0.286840 0.165607i
\(465\) 0 0
\(466\) 7.01687e9 + 1.21536e10i 0.148799 + 0.257727i
\(467\) 9.09281e10i 1.91175i 0.293776 + 0.955874i \(0.405088\pi\)
−0.293776 + 0.955874i \(0.594912\pi\)
\(468\) 0 0
\(469\) 2.06989e10 0.427816
\(470\) 3.93130e10 2.26974e10i 0.805648 0.465141i
\(471\) 0 0
\(472\) −3.43179e8 + 5.94404e8i −0.00691438 + 0.0119761i
\(473\) −3.54184e10 2.04488e10i −0.707594 0.408529i
\(474\) 0 0
\(475\) −7.95114e9 1.37718e10i −0.156191 0.270530i
\(476\) 5.70576e9i 0.111144i
\(477\) 0 0
\(478\) 8.59039e9 0.164551
\(479\) 1.65581e10 9.55984e9i 0.314535 0.181597i −0.334419 0.942424i \(-0.608540\pi\)
0.648954 + 0.760828i \(0.275207\pi\)
\(480\) 0 0
\(481\) −5.42065e9 + 9.38885e9i −0.101268 + 0.175401i
\(482\) 4.38426e10 + 2.53126e10i 0.812285 + 0.468973i
\(483\) 0 0
\(484\) 1.08866e10 + 1.88562e10i 0.198387 + 0.343616i
\(485\) 2.75409e10i 0.497750i
\(486\) 0 0
\(487\) 5.28737e10 0.939992 0.469996 0.882669i \(-0.344255\pi\)
0.469996 + 0.882669i \(0.344255\pi\)
\(488\) −1.87941e10 + 1.08508e10i −0.331393 + 0.191330i
\(489\) 0 0
\(490\) −5.76221e9 + 9.98044e9i −0.0999551 + 0.173127i
\(491\) 8.47000e10 + 4.89016e10i 1.45733 + 0.841389i 0.998879 0.0473309i \(-0.0150715\pi\)
0.458450 + 0.888720i \(0.348405\pi\)
\(492\) 0 0
\(493\) 1.01138e10 + 1.75176e10i 0.171209 + 0.296543i
\(494\) 2.06718e10i 0.347113i
\(495\) 0 0
\(496\) 1.35392e10 0.223701
\(497\) 8.13426e10 4.69632e10i 1.33319 0.769718i
\(498\) 0 0
\(499\) −4.44675e10 + 7.70200e10i −0.717201 + 1.24223i 0.244903 + 0.969547i \(0.421244\pi\)
−0.962104 + 0.272681i \(0.912090\pi\)
\(500\) −2.41133e10 1.39218e10i −0.385813 0.222749i
\(501\) 0 0
\(502\) −6.07296e9 1.05187e10i −0.0956281 0.165633i
\(503\) 2.97791e10i 0.465200i 0.972572 + 0.232600i \(0.0747233\pi\)
−0.972572 + 0.232600i \(0.925277\pi\)
\(504\) 0 0
\(505\) 4.40871e10 0.677870
\(506\) −2.40079e10 + 1.38610e10i −0.366228 + 0.211442i
\(507\) 0 0
\(508\) −2.17290e10 + 3.76357e10i −0.326275 + 0.565125i
\(509\) 2.31390e10 + 1.33593e10i 0.344725 + 0.199027i 0.662359 0.749186i \(-0.269555\pi\)
−0.317635 + 0.948213i \(0.602889\pi\)
\(510\) 0 0
\(511\) −2.40176e10 4.15997e10i −0.352246 0.610107i
\(512\) 3.03700e9i 0.0441942i
\(513\) 0 0
\(514\) −8.58333e10 −1.22971
\(515\) 8.06938e10 4.65886e10i 1.14713 0.662294i
\(516\) 0 0
\(517\) 1.96606e10 3.40532e10i 0.275191 0.476646i
\(518\) −2.72045e10 1.57065e10i −0.377852 0.218153i
\(519\) 0 0
\(520\) −3.96313e9 6.86434e9i −0.0542031 0.0938826i
\(521\) 1.06779e10i 0.144922i −0.997371 0.0724610i \(-0.976915\pi\)
0.997371 0.0724610i \(-0.0230853\pi\)
\(522\) 0 0
\(523\) 4.63928e10 0.620075 0.310037 0.950724i \(-0.399658\pi\)
0.310037 + 0.950724i \(0.399658\pi\)
\(524\) −2.48902e10 + 1.43704e10i −0.330145 + 0.190609i
\(525\) 0 0
\(526\) 1.59040e10 2.75466e10i 0.207761 0.359853i
\(527\) −1.54486e10 8.91924e9i −0.200284 0.115634i
\(528\) 0 0
\(529\) 2.86777e10 + 4.96712e10i 0.366202 + 0.634281i
\(530\) 5.89943e9i 0.0747665i
\(531\) 0 0
\(532\) −5.98973e10 −0.747757
\(533\) 3.62538e10 2.09312e10i 0.449206 0.259349i
\(534\) 0 0
\(535\) −4.72149e10 + 8.17786e10i −0.576320 + 0.998216i
\(536\) 1.25711e10 + 7.25793e9i 0.152305 + 0.0879334i
\(537\) 0 0
\(538\) 1.67604e10 + 2.90299e10i 0.200058 + 0.346510i
\(539\) 9.98252e9i 0.118273i
\(540\) 0 0
\(541\) −1.22420e11 −1.42911 −0.714553 0.699581i \(-0.753370\pi\)
−0.714553 + 0.699581i \(0.753370\pi\)
\(542\) 8.23436e10 4.75411e10i 0.954185 0.550899i
\(543\) 0 0
\(544\) −2.00068e9 + 3.46528e9i −0.0228446 + 0.0395679i
\(545\) −2.52444e10 1.45749e10i −0.286141 0.165203i
\(546\) 0 0
\(547\) 2.76987e10 + 4.79756e10i 0.309393 + 0.535884i 0.978230 0.207525i \(-0.0665408\pi\)
−0.668837 + 0.743409i \(0.733207\pi\)
\(548\) 5.13617e10i 0.569531i
\(549\) 0 0
\(550\) 5.28165e9 0.0577190
\(551\) −1.83895e11 + 1.06172e11i −1.99509 + 1.15187i
\(552\) 0 0
\(553\) 1.47309e10 2.55146e10i 0.157517 0.272828i
\(554\) 5.86077e10 + 3.38372e10i 0.622179 + 0.359215i
\(555\) 0 0
\(556\) 1.72649e10 + 2.99037e10i 0.180661 + 0.312914i
\(557\) 1.17293e11i 1.21857i −0.792951 0.609285i \(-0.791456\pi\)
0.792951 0.609285i \(-0.208544\pi\)
\(558\) 0 0
\(559\) −4.95692e10 −0.507651
\(560\) 1.98896e10 1.14833e10i 0.202244 0.116765i
\(561\) 0 0
\(562\) 6.12868e10 1.06152e11i 0.614358 1.06410i
\(563\) 8.98520e10 + 5.18760e10i 0.894322 + 0.516337i 0.875354 0.483483i \(-0.160629\pi\)
0.0189683 + 0.999820i \(0.493962\pi\)
\(564\) 0 0
\(565\) −9.89890e10 1.71454e11i −0.971389 1.68250i
\(566\) 4.28416e10i 0.417445i
\(567\) 0 0
\(568\) 6.58692e10 0.632833
\(569\) −2.31675e10 + 1.33757e10i −0.221019 + 0.127605i −0.606422 0.795143i \(-0.707396\pi\)
0.385403 + 0.922748i \(0.374062\pi\)
\(570\) 0 0
\(571\) −5.70806e10 + 9.88665e10i −0.536963 + 0.930047i 0.462103 + 0.886826i \(0.347095\pi\)
−0.999066 + 0.0432204i \(0.986238\pi\)
\(572\) −5.94593e9 3.43288e9i −0.0555438 0.0320682i
\(573\) 0 0
\(574\) 6.06488e10 + 1.05047e11i 0.558694 + 0.967687i
\(575\) 2.58475e10i 0.236454i
\(576\) 0 0
\(577\) 1.43414e11 1.29386 0.646930 0.762549i \(-0.276052\pi\)
0.646930 + 0.762549i \(0.276052\pi\)
\(578\) −6.37825e10 + 3.68249e10i −0.571466 + 0.329936i
\(579\) 0 0
\(580\) 4.07097e10 7.05112e10i 0.359737 0.623083i
\(581\) −6.47234e10 3.73681e10i −0.568011 0.327941i
\(582\) 0 0
\(583\) −2.55506e9 4.42550e9i −0.0221171 0.0383079i
\(584\) 3.36864e10i 0.289603i
\(585\) 0 0
\(586\) 8.28207e10 0.702342
\(587\) −1.67365e11 + 9.66281e10i −1.40965 + 0.813863i −0.995354 0.0962792i \(-0.969306\pi\)
−0.414297 + 0.910142i \(0.635973\pi\)
\(588\) 0 0
\(589\) 9.36314e10 1.62174e11i 0.777966 1.34748i
\(590\) −3.15230e9 1.81998e9i −0.0260148 0.0150196i
\(591\) 0 0
\(592\) −1.10148e10 1.90781e10i −0.0896785 0.155328i
\(593\) 2.21385e10i 0.179031i 0.995985 + 0.0895156i \(0.0285319\pi\)
−0.995985 + 0.0895156i \(0.971468\pi\)
\(594\) 0 0
\(595\) −3.02594e10 −0.241430
\(596\) −2.15271e10 + 1.24287e10i −0.170608 + 0.0985008i
\(597\) 0 0
\(598\) −1.67999e10 + 2.90983e10i −0.131372 + 0.227543i
\(599\) −1.14588e11 6.61573e10i −0.890085 0.513891i −0.0161146 0.999870i \(-0.505130\pi\)
−0.873970 + 0.485979i \(0.838463\pi\)
\(600\) 0 0
\(601\) 1.14781e10 + 1.98806e10i 0.0879775 + 0.152381i 0.906656 0.421870i \(-0.138626\pi\)
−0.818679 + 0.574252i \(0.805293\pi\)
\(602\) 1.43629e11i 1.09359i
\(603\) 0 0
\(604\) 1.12013e10 0.0841627
\(605\) −1.00000e11 + 5.77351e10i −0.746413 + 0.430942i
\(606\) 0 0
\(607\) −7.84892e10 + 1.35947e11i −0.578169 + 1.00142i 0.417520 + 0.908668i \(0.362899\pi\)
−0.995689 + 0.0927510i \(0.970434\pi\)
\(608\) −3.63775e10 2.10026e10i −0.266206 0.153694i
\(609\) 0 0
\(610\) −5.75451e10 9.96710e10i −0.415613 0.719862i
\(611\) 4.76586e10i 0.341961i
\(612\) 0 0
\(613\) −1.72931e11 −1.22470 −0.612352 0.790586i \(-0.709776\pi\)
−0.612352 + 0.790586i \(0.709776\pi\)
\(614\) 2.17500e9 1.25574e9i 0.0153034 0.00883540i
\(615\) 0 0
\(616\) 9.94689e9 1.72285e10i 0.0690819 0.119653i
\(617\) 1.23344e10 + 7.12127e9i 0.0851093 + 0.0491379i 0.541951 0.840410i \(-0.317686\pi\)
−0.456841 + 0.889548i \(0.651019\pi\)
\(618\) 0 0
\(619\) −6.49914e10 1.12568e11i −0.442684 0.766750i 0.555204 0.831714i \(-0.312640\pi\)
−0.997888 + 0.0649638i \(0.979307\pi\)
\(620\) 7.18027e10i 0.485930i
\(621\) 0 0
\(622\) 8.14084e10 0.543886
\(623\) 2.05816e11 1.18828e11i 1.36624 0.788800i
\(624\) 0 0
\(625\) 8.75377e10 1.51620e11i 0.573687 0.993656i
\(626\) 4.14788e10 + 2.39478e10i 0.270103 + 0.155944i
\(627\) 0 0
\(628\) 1.82179e10 + 3.15544e10i 0.117128 + 0.202872i
\(629\) 2.90247e10i 0.185424i
\(630\) 0 0
\(631\) −5.79110e9 −0.0365295 −0.0182648 0.999833i \(-0.505814\pi\)
−0.0182648 + 0.999833i \(0.505814\pi\)
\(632\) 1.78930e10 1.03305e10i 0.112154 0.0647523i
\(633\) 0 0
\(634\) −3.05495e10 + 5.29133e10i −0.189081 + 0.327497i
\(635\) −1.99593e11 1.15235e11i −1.22758 0.708746i
\(636\) 0 0
\(637\) 6.04957e9 + 1.04782e10i 0.0367424 + 0.0636396i
\(638\) 7.05259e10i 0.425663i
\(639\) 0 0
\(640\) 1.61061e10 0.0960000
\(641\) −1.88865e11 + 1.09042e11i −1.11872 + 0.645892i −0.941073 0.338203i \(-0.890181\pi\)
−0.177644 + 0.984095i \(0.556848\pi\)
\(642\) 0 0
\(643\) −8.71391e10 + 1.50929e11i −0.509764 + 0.882937i 0.490172 + 0.871626i \(0.336934\pi\)
−0.999936 + 0.0113113i \(0.996399\pi\)
\(644\) −8.43134e10 4.86784e10i −0.490177 0.283004i
\(645\) 0 0
\(646\) 2.76717e10 + 4.79288e10i 0.158893 + 0.275211i
\(647\) 2.22876e11i 1.27188i −0.771738 0.635941i \(-0.780612\pi\)
0.771738 0.635941i \(-0.219388\pi\)
\(648\) 0 0
\(649\) −3.15296e9 −0.0177721
\(650\) 5.54389e9 3.20077e9i 0.0310571 0.0179308i
\(651\) 0 0
\(652\) −1.68418e10 + 2.91709e10i −0.0931963 + 0.161421i
\(653\) −2.22511e11 1.28467e11i −1.22377 0.706542i −0.258048 0.966132i \(-0.583079\pi\)
−0.965719 + 0.259590i \(0.916413\pi\)
\(654\) 0 0
\(655\) −7.62105e10 1.32000e11i −0.414047 0.717151i
\(656\) 8.50642e10i 0.459337i
\(657\) 0 0
\(658\) 1.38092e11 0.736658
\(659\) 2.33445e11 1.34780e11i 1.23778 0.714632i 0.269139 0.963101i \(-0.413261\pi\)
0.968640 + 0.248469i \(0.0799274\pi\)
\(660\) 0 0
\(661\) 1.28404e11 2.22402e11i 0.672623 1.16502i −0.304535 0.952501i \(-0.598501\pi\)
0.977158 0.212516i \(-0.0681656\pi\)
\(662\) −1.33195e11 7.69001e10i −0.693515 0.400401i
\(663\) 0 0
\(664\) −2.62057e10 4.53896e10i −0.134810 0.233498i
\(665\) 3.17653e11i 1.62430i
\(666\) 0 0
\(667\) −3.45142e11 −1.74379
\(668\) 1.29013e11 7.44859e10i 0.647931 0.374083i
\(669\) 0 0
\(670\) −3.84910e10 + 6.66684e10i −0.191012 + 0.330842i
\(671\) −8.63356e10 4.98459e10i −0.425892 0.245889i
\(672\) 0 0
\(673\) −8.39473e10 1.45401e11i −0.409210 0.708773i 0.585591 0.810607i \(-0.300862\pi\)
−0.994801 + 0.101834i \(0.967529\pi\)
\(674\) 2.66363e10i 0.129072i
\(675\) 0 0
\(676\) 9.60920e10 0.460151
\(677\) 1.47399e11 8.51007e10i 0.701680 0.405115i −0.106293 0.994335i \(-0.533898\pi\)
0.807973 + 0.589220i \(0.200565\pi\)
\(678\) 0 0
\(679\) −4.18902e10 + 7.25559e10i −0.197076 + 0.341345i
\(680\) −1.83774e10 1.06102e10i −0.0859507 0.0496237i
\(681\) 0 0
\(682\) 3.10980e10 + 5.38632e10i 0.143746 + 0.248975i
\(683\) 3.04016e11i 1.39706i 0.715582 + 0.698529i \(0.246162\pi\)
−0.715582 + 0.698529i \(0.753838\pi\)
\(684\) 0 0
\(685\) −2.72387e11 −1.23715
\(686\) −1.46999e11 + 8.48698e10i −0.663770 + 0.383228i
\(687\) 0 0
\(688\) 5.03623e10 8.72301e10i 0.224777 0.389325i
\(689\) −5.36385e9 3.09682e9i −0.0238012 0.0137417i
\(690\) 0 0
\(691\) 2.08984e10 + 3.61972e10i 0.0916646 + 0.158768i 0.908212 0.418511i \(-0.137448\pi\)
−0.816547 + 0.577279i \(0.804115\pi\)
\(692\) 1.69494e11i 0.739145i
\(693\) 0 0
\(694\) 9.43354e10 0.406665
\(695\) −1.58588e11 + 9.15609e10i −0.679722 + 0.392438i
\(696\) 0 0
\(697\) 5.60377e10 9.70601e10i 0.237437 0.411254i
\(698\) −1.23908e11 7.15381e10i −0.522007 0.301381i
\(699\) 0 0
\(700\) 9.27433e9 + 1.60636e10i 0.0386269 + 0.0669038i
\(701\) 2.07821e11i 0.860631i 0.902678 + 0.430316i \(0.141598\pi\)
−0.902678 + 0.430316i \(0.858402\pi\)
\(702\) 0 0
\(703\) −3.04693e11 −1.24750
\(704\) 1.20821e10 6.97561e9i 0.0491872 0.0283983i
\(705\) 0 0
\(706\) −2.12777e10 + 3.68540e10i −0.0856456 + 0.148343i
\(707\) 1.16147e11 + 6.70572e10i 0.464867 + 0.268391i
\(708\) 0 0
\(709\) 1.73594e11 + 3.00674e11i 0.686990 + 1.18990i 0.972807 + 0.231617i \(0.0744017\pi\)
−0.285817 + 0.958284i \(0.592265\pi\)
\(710\) 3.49324e11i 1.37466i
\(711\) 0 0
\(712\) 1.66665e11 0.648521
\(713\) 2.63597e11 1.52188e11i 1.01996 0.588874i
\(714\) 0 0
\(715\) 1.82056e10 3.15330e10i 0.0696596 0.120654i
\(716\) 4.50827e10 + 2.60285e10i 0.171537 + 0.0990370i
\(717\) 0 0
\(718\) 9.31828e10 + 1.61397e11i 0.350621 + 0.607294i
\(719\) 1.56177e11i 0.584387i −0.956359 0.292194i \(-0.905615\pi\)
0.956359 0.292194i \(-0.0943851\pi\)
\(720\) 0 0
\(721\) 2.83448e11 1.04890
\(722\) −3.36737e11 + 1.94415e11i −1.23920 + 0.715454i
\(723\) 0 0
\(724\) −8.26052e10 + 1.43076e11i −0.300644 + 0.520732i
\(725\) 5.69474e10 + 3.28786e10i 0.206121 + 0.119004i
\(726\) 0 0
\(727\) 1.35058e11 + 2.33927e11i 0.483485 + 0.837420i 0.999820 0.0189665i \(-0.00603758\pi\)
−0.516336 + 0.856386i \(0.672704\pi\)
\(728\) 2.41119e10i 0.0858433i
\(729\) 0 0
\(730\) 1.78649e11 0.629084
\(731\) −1.14929e11 + 6.63543e10i −0.402495 + 0.232380i
\(732\) 0 0
\(733\) −7.67294e10 + 1.32899e11i −0.265795 + 0.460370i −0.967771 0.251830i \(-0.918968\pi\)
0.701977 + 0.712200i \(0.252301\pi\)
\(734\) 7.23798e10 + 4.17885e10i 0.249364 + 0.143970i
\(735\) 0 0
\(736\) −3.41374e10 5.91278e10i −0.116337 0.201502i
\(737\) 6.66822e10i 0.226017i
\(738\) 0 0
\(739\) 7.60266e10 0.254911 0.127455 0.991844i \(-0.459319\pi\)
0.127455 + 0.991844i \(0.459319\pi\)
\(740\) 1.01177e11 5.84146e10i 0.337408 0.194802i
\(741\) 0 0
\(742\) 8.97314e9 1.55419e10i 0.0296025 0.0512731i
\(743\) −3.62508e11 2.09294e11i −1.18950 0.686756i −0.231304 0.972882i \(-0.574299\pi\)
−0.958192 + 0.286126i \(0.907632\pi\)
\(744\) 0 0
\(745\) −6.59130e10 1.14165e11i −0.213967 0.370601i
\(746\) 2.60243e11i 0.840280i
\(747\) 0 0
\(748\) −1.83813e10 −0.0587177
\(749\) −2.48773e11 + 1.43629e11i −0.790453 + 0.456369i
\(750\) 0 0
\(751\) −1.86894e11 + 3.23710e11i −0.587537 + 1.01764i 0.407017 + 0.913421i \(0.366569\pi\)
−0.994554 + 0.104223i \(0.966764\pi\)
\(752\) 8.38678e10 + 4.84211e10i 0.262255 + 0.151413i
\(753\) 0 0
\(754\) −4.27398e10 7.40276e10i −0.132235 0.229038i
\(755\) 5.94038e10i 0.182821i
\(756\) 0 0
\(757\) 4.74806e11 1.44588 0.722941 0.690910i \(-0.242790\pi\)
0.722941 + 0.690910i \(0.242790\pi\)
\(758\) 2.01731e11 1.16469e11i 0.611076 0.352805i
\(759\) 0 0
\(760\) 1.11383e11 1.92921e11i 0.333860 0.578262i
\(761\) 5.12404e11 + 2.95837e11i 1.52783 + 0.882091i 0.999453 + 0.0330795i \(0.0105315\pi\)
0.528374 + 0.849012i \(0.322802\pi\)
\(762\) 0 0
\(763\) −4.43373e10 7.67944e10i −0.130819 0.226585i
\(764\) 3.81074e10i 0.111850i
\(765\) 0 0
\(766\) 1.62516e11 0.472043
\(767\) −3.30951e9 + 1.91075e9i −0.00956273 + 0.00552105i
\(768\) 0 0
\(769\) −2.14592e11 + 3.71684e11i −0.613633 + 1.06284i 0.376990 + 0.926217i \(0.376959\pi\)
−0.990623 + 0.136625i \(0.956374\pi\)