Properties

Label 48.9.l.a.19.8
Level $48$
Weight $9$
Character 48.19
Analytic conductor $19.554$
Analytic rank $0$
Dimension $64$
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] = [48,9,Mod(19,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.19");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.5541732829\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.8
Character \(\chi\) \(=\) 48.19
Dual form 48.9.l.a.43.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11.9758 + 10.6104i) q^{2} +(33.0681 - 33.0681i) q^{3} +(30.8403 - 254.136i) q^{4} +(-825.217 + 825.217i) q^{5} +(-45.1529 + 746.882i) q^{6} +1803.45 q^{7} +(2327.13 + 3370.71i) q^{8} -2187.00i q^{9} +O(q^{10})\) \(q+(-11.9758 + 10.6104i) q^{2} +(33.0681 - 33.0681i) q^{3} +(30.8403 - 254.136i) q^{4} +(-825.217 + 825.217i) q^{5} +(-45.1529 + 746.882i) q^{6} +1803.45 q^{7} +(2327.13 + 3370.71i) q^{8} -2187.00i q^{9} +(1126.79 - 18638.5i) q^{10} +(11630.2 + 11630.2i) q^{11} +(-7383.95 - 9423.61i) q^{12} +(-13557.5 - 13557.5i) q^{13} +(-21597.8 + 19135.3i) q^{14} +54576.7i q^{15} +(-63633.7 - 15675.2i) q^{16} -3290.02 q^{17} +(23204.9 + 26191.1i) q^{18} +(-79688.3 + 79688.3i) q^{19} +(184267. + 235167. i) q^{20} +(59636.7 - 59636.7i) q^{21} +(-262681. - 15880.4i) q^{22} -329517. q^{23} +(188417. + 34509.0i) q^{24} -971342. i q^{25} +(306212. + 18512.1i) q^{26} +(-72320.0 - 72320.0i) q^{27} +(55619.0 - 458321. i) q^{28} +(-899140. - 899140. i) q^{29} +(-579079. - 653601. i) q^{30} -952463. i q^{31} +(928386. - 487453. i) q^{32} +769175. q^{33} +(39400.7 - 34908.3i) q^{34} +(-1.48824e6 + 1.48824e6i) q^{35} +(-555794. - 67447.8i) q^{36} +(-793702. + 793702. i) q^{37} +(108810. - 1.79985e6i) q^{38} -896642. q^{39} +(-4.70196e6 - 861176. i) q^{40} +167655. i q^{41} +(-81431.0 + 1.34697e6i) q^{42} +(2.53580e6 + 2.53580e6i) q^{43} +(3.31432e6 - 2.59696e6i) q^{44} +(1.80475e6 + 1.80475e6i) q^{45} +(3.94624e6 - 3.49630e6i) q^{46} -7.95383e6i q^{47} +(-2.62260e6 + 1.58590e6i) q^{48} -2.51237e6 q^{49} +(1.03063e7 + 1.16326e7i) q^{50} +(-108795. + 108795. i) q^{51} +(-3.86356e6 + 3.02733e6i) q^{52} +(-7.64145e6 + 7.64145e6i) q^{53} +(1.63343e6 + 98749.3i) q^{54} -1.91948e7 q^{55} +(4.19687e6 + 6.07890e6i) q^{56} +5.27028e6i q^{57} +(2.03081e7 + 1.22773e6i) q^{58} +(3.94575e6 + 3.94575e6i) q^{59} +(1.38699e7 + 1.68316e6i) q^{60} +(-1.74423e7 - 1.74423e7i) q^{61} +(1.01060e7 + 1.14065e7i) q^{62} -3.94415e6i q^{63} +(-5.94612e6 + 1.56882e7i) q^{64} +2.23758e7 q^{65} +(-9.21150e6 + 8.16123e6i) q^{66} +(8.13013e6 - 8.13013e6i) q^{67} +(-101465. + 836111. i) q^{68} +(-1.08965e7 + 1.08965e7i) q^{69} +(2.03212e6 - 3.36136e7i) q^{70} -1.48190e6 q^{71} +(7.37174e6 - 5.08944e6i) q^{72} -1.20830e7i q^{73} +(1.08376e6 - 1.79267e7i) q^{74} +(-3.21204e7 - 3.21204e7i) q^{75} +(1.77940e7 + 2.27092e7i) q^{76} +(2.09744e7 + 2.09744e7i) q^{77} +(1.07380e7 - 9.51370e6i) q^{78} +4.86593e7i q^{79} +(6.54471e7 - 3.95762e7i) q^{80} -4.78297e6 q^{81} +(-1.77888e6 - 2.00780e6i) q^{82} +(2.80334e6 - 2.80334e6i) q^{83} +(-1.33166e7 - 1.69950e7i) q^{84} +(2.71498e6 - 2.71498e6i) q^{85} +(-5.72741e7 - 3.46251e6i) q^{86} -5.94657e7 q^{87} +(-1.21369e7 + 6.62668e7i) q^{88} +1.06131e8i q^{89} +(-4.07624e7 - 2.46430e6i) q^{90} +(-2.44503e7 - 2.44503e7i) q^{91} +(-1.01624e7 + 8.37421e7i) q^{92} +(-3.14961e7 - 3.14961e7i) q^{93} +(8.43931e7 + 9.52536e7i) q^{94} -1.31520e8i q^{95} +(1.45808e7 - 4.68191e7i) q^{96} -3.18957e7 q^{97} +(3.00876e7 - 2.66571e7i) q^{98} +(2.54352e7 - 2.54352e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.9758 + 10.6104i −0.748488 + 0.663148i
\(3\) 33.0681 33.0681i 0.408248 0.408248i
\(4\) 30.8403 254.136i 0.120470 0.992717i
\(5\) −825.217 + 825.217i −1.32035 + 1.32035i −0.406855 + 0.913493i \(0.633374\pi\)
−0.913493 + 0.406855i \(0.866626\pi\)
\(6\) −45.1529 + 746.882i −0.0348402 + 0.576298i
\(7\) 1803.45 0.751125 0.375562 0.926797i \(-0.377450\pi\)
0.375562 + 0.926797i \(0.377450\pi\)
\(8\) 2327.13 + 3370.71i 0.568148 + 0.822927i
\(9\) 2187.00i 0.333333i
\(10\) 1126.79 18638.5i 0.112679 1.86385i
\(11\) 11630.2 + 11630.2i 0.794356 + 0.794356i 0.982199 0.187843i \(-0.0601497\pi\)
−0.187843 + 0.982199i \(0.560150\pi\)
\(12\) −7383.95 9423.61i −0.356093 0.454457i
\(13\) −13557.5 13557.5i −0.474686 0.474686i 0.428741 0.903427i \(-0.358957\pi\)
−0.903427 + 0.428741i \(0.858957\pi\)
\(14\) −21597.8 + 19135.3i −0.562208 + 0.498107i
\(15\) 54576.7i 1.07806i
\(16\) −63633.7 15675.2i −0.970974 0.239185i
\(17\) −3290.02 −0.0393915 −0.0196958 0.999806i \(-0.506270\pi\)
−0.0196958 + 0.999806i \(0.506270\pi\)
\(18\) 23204.9 + 26191.1i 0.221049 + 0.249496i
\(19\) −79688.3 + 79688.3i −0.611477 + 0.611477i −0.943331 0.331854i \(-0.892326\pi\)
0.331854 + 0.943331i \(0.392326\pi\)
\(20\) 184267. + 235167.i 1.15167 + 1.46979i
\(21\) 59636.7 59636.7i 0.306645 0.306645i
\(22\) −262681. 15880.4i −1.12134 0.0677908i
\(23\) −329517. −1.17752 −0.588758 0.808309i \(-0.700383\pi\)
−0.588758 + 0.808309i \(0.700383\pi\)
\(24\) 188417. + 34509.0i 0.567904 + 0.104013i
\(25\) 971342.i 2.48664i
\(26\) 306212. + 18512.1i 0.670084 + 0.0405100i
\(27\) −72320.0 72320.0i −0.136083 0.136083i
\(28\) 55619.0 458321.i 0.0904880 0.745654i
\(29\) −899140. 899140.i −1.27126 1.27126i −0.945426 0.325837i \(-0.894354\pi\)
−0.325837 0.945426i \(-0.605646\pi\)
\(30\) −579079. 653601.i −0.714913 0.806915i
\(31\) 952463.i 1.03134i −0.856788 0.515669i \(-0.827543\pi\)
0.856788 0.515669i \(-0.172457\pi\)
\(32\) 928386. 487453.i 0.885378 0.464872i
\(33\) 769175. 0.648589
\(34\) 39400.7 34908.3i 0.0294841 0.0261224i
\(35\) −1.48824e6 + 1.48824e6i −0.991746 + 0.991746i
\(36\) −555794. 67447.8i −0.330906 0.0401567i
\(37\) −793702. + 793702.i −0.423497 + 0.423497i −0.886406 0.462909i \(-0.846806\pi\)
0.462909 + 0.886406i \(0.346806\pi\)
\(38\) 108810. 1.79985e6i 0.0521839 0.863183i
\(39\) −896642. −0.387579
\(40\) −4.70196e6 861176.i −1.83670 0.336397i
\(41\) 167655.i 0.0593308i 0.999560 + 0.0296654i \(0.00944418\pi\)
−0.999560 + 0.0296654i \(0.990556\pi\)
\(42\) −81431.0 + 1.34697e6i −0.0261693 + 0.432872i
\(43\) 2.53580e6 + 2.53580e6i 0.741723 + 0.741723i 0.972909 0.231187i \(-0.0742608\pi\)
−0.231187 + 0.972909i \(0.574261\pi\)
\(44\) 3.31432e6 2.59696e6i 0.884266 0.692874i
\(45\) 1.80475e6 + 1.80475e6i 0.440116 + 0.440116i
\(46\) 3.94624e6 3.49630e6i 0.881358 0.780868i
\(47\) 7.95383e6i 1.62999i −0.579468 0.814995i \(-0.696740\pi\)
0.579468 0.814995i \(-0.303260\pi\)
\(48\) −2.62260e6 + 1.58590e6i −0.494045 + 0.298752i
\(49\) −2.51237e6 −0.435811
\(50\) 1.03063e7 + 1.16326e7i 1.64901 + 1.86122i
\(51\) −108795. + 108795.i −0.0160815 + 0.0160815i
\(52\) −3.86356e6 + 3.02733e6i −0.528414 + 0.414043i
\(53\) −7.64145e6 + 7.64145e6i −0.968439 + 0.968439i −0.999517 0.0310784i \(-0.990106\pi\)
0.0310784 + 0.999517i \(0.490106\pi\)
\(54\) 1.63343e6 + 98749.3i 0.192099 + 0.0116134i
\(55\) −1.91948e7 −2.09765
\(56\) 4.19687e6 + 6.07890e6i 0.426750 + 0.618121i
\(57\) 5.27028e6i 0.499269i
\(58\) 2.03081e7 + 1.22773e6i 1.79456 + 0.108490i
\(59\) 3.94575e6 + 3.94575e6i 0.325627 + 0.325627i 0.850921 0.525294i \(-0.176045\pi\)
−0.525294 + 0.850921i \(0.676045\pi\)
\(60\) 1.38699e7 + 1.68316e6i 1.07021 + 0.129874i
\(61\) −1.74423e7 1.74423e7i −1.25975 1.25975i −0.951213 0.308536i \(-0.900161\pi\)
−0.308536 0.951213i \(-0.599839\pi\)
\(62\) 1.01060e7 + 1.14065e7i 0.683930 + 0.771945i
\(63\) 3.94415e6i 0.250375i
\(64\) −5.94612e6 + 1.56882e7i −0.354416 + 0.935088i
\(65\) 2.23758e7 1.25350
\(66\) −9.21150e6 + 8.16123e6i −0.485461 + 0.430110i
\(67\) 8.13013e6 8.13013e6i 0.403458 0.403458i −0.475992 0.879450i \(-0.657911\pi\)
0.879450 + 0.475992i \(0.157911\pi\)
\(68\) −101465. + 836111.i −0.00474550 + 0.0391046i
\(69\) −1.08965e7 + 1.08965e7i −0.480719 + 0.480719i
\(70\) 2.03212e6 3.36136e7i 0.0846363 1.39998i
\(71\) −1.48190e6 −0.0583159 −0.0291579 0.999575i \(-0.509283\pi\)
−0.0291579 + 0.999575i \(0.509283\pi\)
\(72\) 7.37174e6 5.08944e6i 0.274309 0.189383i
\(73\) 1.20830e7i 0.425484i −0.977108 0.212742i \(-0.931761\pi\)
0.977108 0.212742i \(-0.0682395\pi\)
\(74\) 1.08376e6 1.79267e7i 0.0361415 0.597824i
\(75\) −3.21204e7 3.21204e7i −1.01516 1.01516i
\(76\) 1.77940e7 + 2.27092e7i 0.533359 + 0.680688i
\(77\) 2.09744e7 + 2.09744e7i 0.596660 + 0.596660i
\(78\) 1.07380e7 9.51370e6i 0.290099 0.257022i
\(79\) 4.86593e7i 1.24927i 0.780916 + 0.624636i \(0.214753\pi\)
−0.780916 + 0.624636i \(0.785247\pi\)
\(80\) 6.54471e7 3.95762e7i 1.59783 0.966215i
\(81\) −4.78297e6 −0.111111
\(82\) −1.77888e6 2.00780e6i −0.0393451 0.0444084i
\(83\) 2.80334e6 2.80334e6i 0.0590695 0.0590695i −0.676955 0.736024i \(-0.736701\pi\)
0.736024 + 0.676955i \(0.236701\pi\)
\(84\) −1.33166e7 1.69950e7i −0.267471 0.341354i
\(85\) 2.71498e6 2.71498e6i 0.0520105 0.0520105i
\(86\) −5.72741e7 3.46251e6i −1.04704 0.0632991i
\(87\) −5.94657e7 −1.03798
\(88\) −1.21369e7 + 6.62668e7i −0.202385 + 1.10501i
\(89\) 1.06131e8i 1.69154i 0.533548 + 0.845770i \(0.320858\pi\)
−0.533548 + 0.845770i \(0.679142\pi\)
\(90\) −4.07624e7 2.46430e6i −0.621283 0.0375598i
\(91\) −2.44503e7 2.44503e7i −0.356548 0.356548i
\(92\) −1.01624e7 + 8.37421e7i −0.141855 + 1.16894i
\(93\) −3.14961e7 3.14961e7i −0.421042 0.421042i
\(94\) 8.43931e7 + 9.52536e7i 1.08092 + 1.22003i
\(95\) 1.31520e8i 1.61472i
\(96\) 1.45808e7 4.68191e7i 0.171671 0.551237i
\(97\) −3.18957e7 −0.360284 −0.180142 0.983641i \(-0.557656\pi\)
−0.180142 + 0.983641i \(0.557656\pi\)
\(98\) 3.00876e7 2.66571e7i 0.326200 0.289007i
\(99\) 2.54352e7 2.54352e7i 0.264785 0.264785i
\(100\) −2.46852e8 2.99565e7i −2.46852 0.299565i
\(101\) 9.24308e7 9.24308e7i 0.888242 0.888242i −0.106112 0.994354i \(-0.533840\pi\)
0.994354 + 0.106112i \(0.0338402\pi\)
\(102\) 148554. 2.45726e6i 0.00137241 0.0227013i
\(103\) −3.68529e6 −0.0327433 −0.0163716 0.999866i \(-0.505211\pi\)
−0.0163716 + 0.999866i \(0.505211\pi\)
\(104\) 1.41483e7 7.72485e7i 0.120940 0.660323i
\(105\) 9.84265e7i 0.809757i
\(106\) 1.04340e7 1.72591e8i 0.0826472 1.36708i
\(107\) −7.83958e7 7.83958e7i −0.598078 0.598078i 0.341723 0.939801i \(-0.388990\pi\)
−0.939801 + 0.341723i \(0.888990\pi\)
\(108\) −2.06094e7 + 1.61487e7i −0.151486 + 0.118698i
\(109\) 1.23092e8 + 1.23092e8i 0.872012 + 0.872012i 0.992691 0.120680i \(-0.0385074\pi\)
−0.120680 + 0.992691i \(0.538507\pi\)
\(110\) 2.29874e8 2.03664e8i 1.57007 1.39105i
\(111\) 5.24924e7i 0.345784i
\(112\) −1.14760e8 2.82695e7i −0.729323 0.179658i
\(113\) −9.57848e7 −0.587466 −0.293733 0.955887i \(-0.594898\pi\)
−0.293733 + 0.955887i \(0.594898\pi\)
\(114\) −5.59196e7 6.31160e7i −0.331089 0.373697i
\(115\) 2.71923e8 2.71923e8i 1.55473 1.55473i
\(116\) −2.56233e8 + 2.00774e8i −1.41515 + 1.10886i
\(117\) −2.96503e7 + 2.96503e7i −0.158229 + 0.158229i
\(118\) −8.91193e7 5.38772e6i −0.459668 0.0277893i
\(119\) −5.93339e6 −0.0295880
\(120\) −1.83962e8 + 1.27007e8i −0.887164 + 0.612497i
\(121\) 5.61624e7i 0.262002i
\(122\) 3.93954e8 + 2.38166e7i 1.77831 + 0.107508i
\(123\) 5.54402e6 + 5.54402e6i 0.0242217 + 0.0242217i
\(124\) −2.42055e8 2.93742e7i −1.02383 0.124245i
\(125\) 4.79218e8 + 4.79218e8i 1.96288 + 1.96288i
\(126\) 4.18488e7 + 4.72344e7i 0.166036 + 0.187403i
\(127\) 1.60633e8i 0.617476i −0.951147 0.308738i \(-0.900093\pi\)
0.951147 0.308738i \(-0.0999066\pi\)
\(128\) −9.52475e7 2.50969e8i −0.354825 0.934933i
\(129\) 1.67708e8 0.605614
\(130\) −2.67968e8 + 2.37415e8i −0.938231 + 0.831256i
\(131\) −2.46559e8 + 2.46559e8i −0.837212 + 0.837212i −0.988491 0.151279i \(-0.951661\pi\)
0.151279 + 0.988491i \(0.451661\pi\)
\(132\) 2.37216e7 1.95475e8i 0.0781355 0.643865i
\(133\) −1.43714e8 + 1.43714e8i −0.459296 + 0.459296i
\(134\) −1.11013e7 + 1.83629e8i −0.0344314 + 0.569536i
\(135\) 1.19359e8 0.359353
\(136\) −7.65631e6 1.10897e7i −0.0223802 0.0324163i
\(137\) 2.60945e8i 0.740740i −0.928884 0.370370i \(-0.879231\pi\)
0.928884 0.370370i \(-0.120769\pi\)
\(138\) 1.48787e7 2.46111e8i 0.0410249 0.678601i
\(139\) −5.35842e7 5.35842e7i −0.143542 0.143542i 0.631684 0.775226i \(-0.282364\pi\)
−0.775226 + 0.631684i \(0.782364\pi\)
\(140\) 3.32317e8 + 4.24112e8i 0.865047 + 1.10400i
\(141\) −2.63018e8 2.63018e8i −0.665441 0.665441i
\(142\) 1.77470e7 1.57235e7i 0.0436488 0.0386720i
\(143\) 3.15352e8i 0.754139i
\(144\) −3.42818e7 + 1.39167e8i −0.0797284 + 0.323658i
\(145\) 1.48397e9 3.35702
\(146\) 1.28205e8 + 1.44704e8i 0.282159 + 0.318470i
\(147\) −8.30792e7 + 8.30792e7i −0.177919 + 0.177919i
\(148\) 1.77230e8 + 2.26186e8i 0.369394 + 0.471432i
\(149\) −1.95563e8 + 1.95563e8i −0.396773 + 0.396773i −0.877093 0.480320i \(-0.840521\pi\)
0.480320 + 0.877093i \(0.340521\pi\)
\(150\) 7.25478e8 + 4.38589e7i 1.43304 + 0.0866348i
\(151\) −5.43444e8 −1.04531 −0.522657 0.852543i \(-0.675059\pi\)
−0.522657 + 0.852543i \(0.675059\pi\)
\(152\) −4.54051e8 8.31607e7i −0.850610 0.155792i
\(153\) 7.19527e6i 0.0131305i
\(154\) −4.73732e8 2.86395e7i −0.842267 0.0509194i
\(155\) 7.85988e8 + 7.85988e8i 1.36172 + 1.36172i
\(156\) −2.76527e7 + 2.27869e8i −0.0466917 + 0.384757i
\(157\) 2.24227e8 + 2.24227e8i 0.369054 + 0.369054i 0.867132 0.498078i \(-0.165961\pi\)
−0.498078 + 0.867132i \(0.665961\pi\)
\(158\) −5.16292e8 5.82734e8i −0.828452 0.935066i
\(159\) 5.05376e8i 0.790727i
\(160\) −3.63865e8 + 1.16838e9i −0.555214 + 1.78280i
\(161\) −5.94268e8 −0.884462
\(162\) 5.72800e7 5.07490e7i 0.0831654 0.0736831i
\(163\) 3.43604e8 3.43604e8i 0.486751 0.486751i −0.420528 0.907280i \(-0.638155\pi\)
0.907280 + 0.420528i \(0.138155\pi\)
\(164\) 4.26070e7 + 5.17052e6i 0.0588987 + 0.00714758i
\(165\) −6.34736e8 + 6.34736e8i −0.856362 + 0.856362i
\(166\) −3.82782e6 + 6.33167e7i −0.00504103 + 0.0833846i
\(167\) −5.92850e8 −0.762218 −0.381109 0.924530i \(-0.624458\pi\)
−0.381109 + 0.924530i \(0.624458\pi\)
\(168\) 3.39800e8 + 6.22354e7i 0.426567 + 0.0781268i
\(169\) 4.48119e8i 0.549347i
\(170\) −3.70717e6 + 6.13210e7i −0.00443861 + 0.0734199i
\(171\) 1.74278e8 + 1.74278e8i 0.203826 + 0.203826i
\(172\) 7.22643e8 5.66233e8i 0.825676 0.646966i
\(173\) 3.99093e8 + 3.99093e8i 0.445543 + 0.445543i 0.893870 0.448327i \(-0.147980\pi\)
−0.448327 + 0.893870i \(0.647980\pi\)
\(174\) 7.12151e8 6.30953e8i 0.776917 0.688335i
\(175\) 1.75177e9i 1.86777i
\(176\) −5.57765e8 9.22376e8i −0.581301 0.961297i
\(177\) 2.60957e8 0.265874
\(178\) −1.12609e9 1.27101e9i −1.12174 1.26610i
\(179\) −6.90668e8 + 6.90668e8i −0.672756 + 0.672756i −0.958351 0.285595i \(-0.907809\pi\)
0.285595 + 0.958351i \(0.407809\pi\)
\(180\) 5.14310e8 4.02992e8i 0.489931 0.383890i
\(181\) −3.56186e8 + 3.56186e8i −0.331866 + 0.331866i −0.853295 0.521429i \(-0.825399\pi\)
0.521429 + 0.853295i \(0.325399\pi\)
\(182\) 5.52239e8 + 3.33857e7i 0.503317 + 0.0304281i
\(183\) −1.15357e9 −1.02858
\(184\) −7.66831e8 1.11071e9i −0.669003 0.969010i
\(185\) 1.30995e9i 1.11833i
\(186\) 7.11377e8 + 4.30064e7i 0.594358 + 0.0359320i
\(187\) −3.82635e7 3.82635e7i −0.0312909 0.0312909i
\(188\) −2.02135e9 2.45299e8i −1.61812 0.196365i
\(189\) −1.30425e8 1.30425e8i −0.102215 0.102215i
\(190\) 1.39548e9 + 1.57506e9i 1.07080 + 1.20860i
\(191\) 2.45723e9i 1.84634i −0.384387 0.923172i \(-0.625587\pi\)
0.384387 0.923172i \(-0.374413\pi\)
\(192\) 3.22151e8 + 7.15405e8i 0.237058 + 0.526438i
\(193\) −9.12428e8 −0.657611 −0.328806 0.944398i \(-0.606646\pi\)
−0.328806 + 0.944398i \(0.606646\pi\)
\(194\) 3.81977e8 3.38425e8i 0.269668 0.238922i
\(195\) 7.39924e8 7.39924e8i 0.511739 0.511739i
\(196\) −7.74822e7 + 6.38482e8i −0.0525022 + 0.432637i
\(197\) −1.82697e9 + 1.82697e9i −1.21301 + 1.21301i −0.242983 + 0.970031i \(0.578126\pi\)
−0.970031 + 0.242983i \(0.921874\pi\)
\(198\) −3.47305e7 + 5.74483e8i −0.0225969 + 0.373780i
\(199\) 1.12834e9 0.719494 0.359747 0.933050i \(-0.382863\pi\)
0.359747 + 0.933050i \(0.382863\pi\)
\(200\) 3.27411e9 2.26044e9i 2.04632 1.41278i
\(201\) 5.37696e8i 0.329422i
\(202\) −1.26210e8 + 2.08766e9i −0.0758032 + 1.25387i
\(203\) −1.62155e9 1.62155e9i −0.954877 0.954877i
\(204\) 2.42933e7 + 3.10039e7i 0.0140271 + 0.0179017i
\(205\) −1.38352e8 1.38352e8i −0.0783373 0.0783373i
\(206\) 4.41343e7 3.91022e7i 0.0245080 0.0217136i
\(207\) 7.20655e8i 0.392506i
\(208\) 6.50198e8 + 1.07523e9i 0.347370 + 0.574445i
\(209\) −1.85358e9 −0.971461
\(210\) −1.04434e9 1.17874e9i −0.536989 0.606094i
\(211\) 1.91924e9 1.91924e9i 0.968275 0.968275i −0.0312369 0.999512i \(-0.509945\pi\)
0.999512 + 0.0312369i \(0.00994464\pi\)
\(212\) 1.70630e9 + 2.17763e9i 0.844718 + 1.07805i
\(213\) −4.90038e7 + 4.90038e7i −0.0238074 + 0.0238074i
\(214\) 1.77066e9 + 1.07046e8i 0.844269 + 0.0510404i
\(215\) −4.18518e9 −1.95866
\(216\) 7.54713e7 4.12068e8i 0.0346710 0.189301i
\(217\) 1.71772e9i 0.774664i
\(218\) −2.78017e9 1.68075e8i −1.23096 0.0744181i
\(219\) −3.99562e8 3.99562e8i −0.173703 0.173703i
\(220\) −5.91974e8 + 4.87809e9i −0.252704 + 2.08237i
\(221\) 4.46044e7 + 4.46044e7i 0.0186986 + 0.0186986i
\(222\) −5.56964e8 6.28640e8i −0.229306 0.258815i
\(223\) 4.74336e9i 1.91808i 0.283269 + 0.959040i \(0.408581\pi\)
−0.283269 + 0.959040i \(0.591419\pi\)
\(224\) 1.67430e9 8.79098e8i 0.665029 0.349177i
\(225\) −2.12432e9 −0.828878
\(226\) 1.14710e9 1.01631e9i 0.439712 0.389577i
\(227\) −2.13819e9 + 2.13819e9i −0.805274 + 0.805274i −0.983914 0.178641i \(-0.942830\pi\)
0.178641 + 0.983914i \(0.442830\pi\)
\(228\) 1.33937e9 + 1.62537e8i 0.495633 + 0.0601469i
\(229\) 1.74254e9 1.74254e9i 0.633637 0.633637i −0.315342 0.948978i \(-0.602119\pi\)
0.948978 + 0.315342i \(0.102119\pi\)
\(230\) −3.71298e8 + 6.14171e9i −0.132682 + 2.19471i
\(231\) 1.38717e9 0.487171
\(232\) 9.38320e8 5.12316e9i 0.323891 1.76842i
\(233\) 1.45411e9i 0.493369i −0.969096 0.246685i \(-0.920659\pi\)
0.969096 0.246685i \(-0.0793412\pi\)
\(234\) 4.04860e7 6.69686e8i 0.0135033 0.223361i
\(235\) 6.56364e9 + 6.56364e9i 2.15215 + 2.15215i
\(236\) 1.12444e9 8.81066e8i 0.362484 0.284028i
\(237\) 1.60907e9 + 1.60907e9i 0.510013 + 0.510013i
\(238\) 7.10572e7 6.29554e7i 0.0221462 0.0196212i
\(239\) 5.22434e9i 1.60118i 0.599213 + 0.800590i \(0.295480\pi\)
−0.599213 + 0.800590i \(0.704520\pi\)
\(240\) 8.55504e8 3.47292e9i 0.257856 1.04677i
\(241\) 7.80385e8 0.231335 0.115667 0.993288i \(-0.463099\pi\)
0.115667 + 0.993288i \(0.463099\pi\)
\(242\) −5.95904e8 6.72591e8i −0.173746 0.196105i
\(243\) −1.58164e8 + 1.58164e8i −0.0453609 + 0.0453609i
\(244\) −4.97063e9 + 3.89478e9i −1.40234 + 1.09881i
\(245\) 2.07325e9 2.07325e9i 0.575423 0.575423i
\(246\) −1.25218e8 7.57009e6i −0.0341922 0.00206710i
\(247\) 2.16075e9 0.580519
\(248\) 3.21047e9 2.21651e9i 0.848716 0.585952i
\(249\) 1.85402e8i 0.0482300i
\(250\) −1.08237e10 6.54348e8i −2.77087 0.167513i
\(251\) 2.95495e9 + 2.95495e9i 0.744485 + 0.744485i 0.973438 0.228953i \(-0.0735302\pi\)
−0.228953 + 0.973438i \(0.573530\pi\)
\(252\) −1.00235e9 1.21639e8i −0.248551 0.0301627i
\(253\) −3.83234e9 3.83234e9i −0.935367 0.935367i
\(254\) 1.70438e9 + 1.92371e9i 0.409478 + 0.462174i
\(255\) 1.79559e8i 0.0424664i
\(256\) 3.80354e9 + 1.99495e9i 0.885581 + 0.464485i
\(257\) 8.13423e9 1.86459 0.932296 0.361696i \(-0.117802\pi\)
0.932296 + 0.361696i \(0.117802\pi\)
\(258\) −2.00845e9 + 1.77945e9i −0.453295 + 0.401612i
\(259\) −1.43140e9 + 1.43140e9i −0.318099 + 0.318099i
\(260\) 6.90076e8 5.68648e9i 0.151009 1.24437i
\(261\) −1.96642e9 + 1.96642e9i −0.423754 + 0.423754i
\(262\) 3.36664e8 5.56882e9i 0.0714483 1.18184i
\(263\) −5.93980e9 −1.24151 −0.620753 0.784006i \(-0.713173\pi\)
−0.620753 + 0.784006i \(0.713173\pi\)
\(264\) 1.78997e9 + 2.59266e9i 0.368494 + 0.533741i
\(265\) 1.26117e10i 2.55735i
\(266\) 1.96234e8 3.24595e9i 0.0391966 0.648358i
\(267\) 3.50955e9 + 3.50955e9i 0.690568 + 0.690568i
\(268\) −1.81542e9 2.31689e9i −0.351915 0.449124i
\(269\) 1.70084e9 + 1.70084e9i 0.324829 + 0.324829i 0.850616 0.525787i \(-0.176229\pi\)
−0.525787 + 0.850616i \(0.676229\pi\)
\(270\) −1.42943e9 + 1.26645e9i −0.268972 + 0.238304i
\(271\) 2.99314e9i 0.554945i −0.960734 0.277473i \(-0.910503\pi\)
0.960734 0.277473i \(-0.0894968\pi\)
\(272\) 2.09356e8 + 5.15719e7i 0.0382481 + 0.00942187i
\(273\) −1.61705e9 −0.291120
\(274\) 2.76872e9 + 3.12502e9i 0.491220 + 0.554436i
\(275\) 1.12969e10 1.12969e10i 1.97527 1.97527i
\(276\) 2.43314e9 + 3.10524e9i 0.419306 + 0.535130i
\(277\) −2.76225e9 + 2.76225e9i −0.469185 + 0.469185i −0.901651 0.432465i \(-0.857644\pi\)
0.432465 + 0.901651i \(0.357644\pi\)
\(278\) 1.21026e9 + 7.31666e7i 0.202628 + 0.0122499i
\(279\) −2.08304e9 −0.343779
\(280\) −8.47975e9 1.55309e9i −1.37959 0.252676i
\(281\) 1.67333e9i 0.268384i 0.990955 + 0.134192i \(0.0428439\pi\)
−0.990955 + 0.134192i \(0.957156\pi\)
\(282\) 5.94058e9 + 3.59138e8i 0.939360 + 0.0567892i
\(283\) 2.97428e9 + 2.97428e9i 0.463699 + 0.463699i 0.899866 0.436167i \(-0.143664\pi\)
−0.436167 + 0.899866i \(0.643664\pi\)
\(284\) −4.57024e7 + 3.76605e8i −0.00702531 + 0.0578911i
\(285\) −4.34913e9 4.34913e9i −0.659209 0.659209i
\(286\) 3.34600e9 + 3.77660e9i 0.500105 + 0.564464i
\(287\) 3.02357e8i 0.0445648i
\(288\) −1.06606e9 2.03038e9i −0.154957 0.295126i
\(289\) −6.96493e9 −0.998448
\(290\) −1.77718e10 + 1.57455e10i −2.51269 + 2.22620i
\(291\) −1.05473e9 + 1.05473e9i −0.147085 + 0.147085i
\(292\) −3.07072e9 3.72644e8i −0.422386 0.0512581i
\(293\) −8.51995e9 + 8.51995e9i −1.15602 + 1.15602i −0.170700 + 0.985323i \(0.554603\pi\)
−0.985323 + 0.170700i \(0.945397\pi\)
\(294\) 1.13441e8 1.87644e9i 0.0151838 0.251157i
\(295\) −6.51219e9 −0.859883
\(296\) −4.52239e9 8.28287e8i −0.589116 0.107898i
\(297\) 1.68219e9i 0.216196i
\(298\) 2.67032e8 4.41703e9i 0.0338609 0.560100i
\(299\) 4.46743e9 + 4.46743e9i 0.558950 + 0.558950i
\(300\) −9.15355e9 + 7.17234e9i −1.13007 + 0.885474i
\(301\) 4.57320e9 + 4.57320e9i 0.557126 + 0.557126i
\(302\) 6.50819e9 5.76614e9i 0.782406 0.693198i
\(303\) 6.11303e9i 0.725247i
\(304\) 6.32000e9 3.82173e9i 0.739985 0.447472i
\(305\) 2.87873e10 3.32661
\(306\) −7.63445e7 8.61693e7i −0.00870747 0.00982803i
\(307\) −6.61431e8 + 6.61431e8i −0.0744613 + 0.0744613i −0.743357 0.668895i \(-0.766767\pi\)
0.668895 + 0.743357i \(0.266767\pi\)
\(308\) 5.97720e9 4.68349e9i 0.664194 0.520435i
\(309\) −1.21865e8 + 1.21865e8i −0.0133674 + 0.0133674i
\(310\) −1.77525e10 1.07323e9i −1.92226 0.116211i
\(311\) −1.99464e8 −0.0213218 −0.0106609 0.999943i \(-0.503394\pi\)
−0.0106609 + 0.999943i \(0.503394\pi\)
\(312\) −2.08660e9 3.02232e9i −0.220202 0.318949i
\(313\) 7.94532e9i 0.827817i 0.910319 + 0.413908i \(0.135837\pi\)
−0.910319 + 0.413908i \(0.864163\pi\)
\(314\) −5.06444e9 3.06171e8i −0.520970 0.0314953i
\(315\) 3.25478e9 + 3.25478e9i 0.330582 + 0.330582i
\(316\) 1.23660e10 + 1.50067e9i 1.24017 + 0.150500i
\(317\) −1.86608e9 1.86608e9i −0.184796 0.184796i 0.608646 0.793442i \(-0.291713\pi\)
−0.793442 + 0.608646i \(0.791713\pi\)
\(318\) −5.36223e9 6.05229e9i −0.524369 0.591850i
\(319\) 2.09143e10i 2.01967i
\(320\) −8.03930e9 1.78530e10i −0.766688 1.70259i
\(321\) −5.18480e9 −0.488329
\(322\) 7.11685e9 6.30540e9i 0.662010 0.586529i
\(323\) 2.62176e8 2.62176e8i 0.0240870 0.0240870i
\(324\) −1.47508e8 + 1.21552e9i −0.0133856 + 0.110302i
\(325\) −1.31690e10 + 1.31690e10i −1.18037 + 1.18037i
\(326\) −4.69174e8 + 7.76069e9i −0.0415397 + 0.687116i
\(327\) 8.14081e9 0.711995
\(328\) −5.65115e8 + 3.90155e8i −0.0488249 + 0.0337087i
\(329\) 1.43443e10i 1.22433i
\(330\) 8.66701e8 1.43363e10i 0.0730825 1.20887i
\(331\) 6.61401e9 + 6.61401e9i 0.551002 + 0.551002i 0.926730 0.375728i \(-0.122607\pi\)
−0.375728 + 0.926730i \(0.622607\pi\)
\(332\) −6.25972e8 7.98884e8i −0.0515232 0.0657554i
\(333\) 1.73583e9 + 1.73583e9i 0.141166 + 0.141166i
\(334\) 7.09986e9 6.29036e9i 0.570511 0.505463i
\(335\) 1.34182e10i 1.06541i
\(336\) −4.72973e9 + 2.86009e9i −0.371090 + 0.224400i
\(337\) −6.09954e9 −0.472909 −0.236454 0.971643i \(-0.575985\pi\)
−0.236454 + 0.971643i \(0.575985\pi\)
\(338\) 4.75471e9 + 5.36659e9i 0.364298 + 0.411180i
\(339\) −3.16742e9 + 3.16742e9i −0.239832 + 0.239832i
\(340\) −6.06242e8 7.73704e8i −0.0453660 0.0578974i
\(341\) 1.10773e10 1.10773e10i 0.819249 0.819249i
\(342\) −3.93628e9 2.37969e8i −0.287728 0.0173946i
\(343\) −1.49275e10 −1.07847
\(344\) −2.64630e9 + 1.44486e10i −0.188975 + 1.03179i
\(345\) 1.79840e10i 1.26943i
\(346\) −9.01399e9 5.44942e8i −0.628945 0.0380230i
\(347\) −1.54387e10 1.54387e10i −1.06486 1.06486i −0.997745 0.0671190i \(-0.978619\pi\)
−0.0671190 0.997745i \(-0.521381\pi\)
\(348\) −1.83394e9 + 1.51124e10i −0.125046 + 1.03042i
\(349\) 6.91661e9 + 6.91661e9i 0.466221 + 0.466221i 0.900688 0.434467i \(-0.143063\pi\)
−0.434467 + 0.900688i \(0.643063\pi\)
\(350\) 1.85869e10 + 2.09788e10i 1.23861 + 1.39801i
\(351\) 1.96096e9i 0.129193i
\(352\) 1.64664e10 + 5.12812e9i 1.07258 + 0.334031i
\(353\) −1.38261e10 −0.890431 −0.445215 0.895424i \(-0.646873\pi\)
−0.445215 + 0.895424i \(0.646873\pi\)
\(354\) −3.12517e9 + 2.76885e9i −0.199003 + 0.176314i
\(355\) 1.22289e9 1.22289e9i 0.0769972 0.0769972i
\(356\) 2.69717e10 + 3.27311e9i 1.67922 + 0.203780i
\(357\) −1.96206e8 + 1.96206e8i −0.0120792 + 0.0120792i
\(358\) 9.43074e8 1.55996e10i 0.0574134 0.949687i
\(359\) −1.61567e10 −0.972689 −0.486344 0.873767i \(-0.661670\pi\)
−0.486344 + 0.873767i \(0.661670\pi\)
\(360\) −1.88339e9 + 1.02832e10i −0.112132 + 0.612234i
\(361\) 4.28311e9i 0.252191i
\(362\) 4.86354e8 8.04488e9i 0.0283216 0.468474i
\(363\) 1.85719e9 + 1.85719e9i 0.106962 + 0.106962i
\(364\) −6.96774e9 + 5.45963e9i −0.396905 + 0.310998i
\(365\) 9.97111e9 + 9.97111e9i 0.561787 + 0.561787i
\(366\) 1.38149e10 1.22398e10i 0.769881 0.682101i
\(367\) 1.40337e10i 0.773583i 0.922167 + 0.386791i \(0.126417\pi\)
−0.922167 + 0.386791i \(0.873583\pi\)
\(368\) 2.09684e10 + 5.16526e9i 1.14334 + 0.281645i
\(369\) 3.66661e8 0.0197769
\(370\) 1.38991e10 + 1.56878e10i 0.741616 + 0.837055i
\(371\) −1.37810e10 + 1.37810e10i −0.727418 + 0.727418i
\(372\) −8.97564e9 + 7.03294e9i −0.468699 + 0.367253i
\(373\) 1.12218e10 1.12218e10i 0.579732 0.579732i −0.355097 0.934829i \(-0.615552\pi\)
0.934829 + 0.355097i \(0.115552\pi\)
\(374\) 8.64225e8 + 5.22469e7i 0.0441713 + 0.00267038i
\(375\) 3.16936e10 1.60268
\(376\) 2.68100e10 1.85096e10i 1.34136 0.926075i
\(377\) 2.43802e10i 1.20690i
\(378\) 2.94581e9 + 1.78090e8i 0.144291 + 0.00872311i
\(379\) −2.52365e9 2.52365e9i −0.122313 0.122313i 0.643301 0.765614i \(-0.277565\pi\)
−0.765614 + 0.643301i \(0.777565\pi\)
\(380\) −3.34240e10 4.05613e9i −1.60296 0.194526i
\(381\) −5.31183e9 5.31183e9i −0.252083 0.252083i
\(382\) 2.60721e10 + 2.94274e10i 1.22440 + 1.38197i
\(383\) 2.78057e10i 1.29223i −0.763241 0.646113i \(-0.776393\pi\)
0.763241 0.646113i \(-0.223607\pi\)
\(384\) −1.14487e10 5.14942e9i −0.526541 0.236828i
\(385\) −3.46169e10 −1.57560
\(386\) 1.09271e10 9.68119e9i 0.492215 0.436094i
\(387\) 5.54580e9 5.54580e9i 0.247241 0.247241i
\(388\) −9.83673e8 + 8.10583e9i −0.0434034 + 0.357660i
\(389\) −7.45437e9 + 7.45437e9i −0.325546 + 0.325546i −0.850890 0.525344i \(-0.823937\pi\)
0.525344 + 0.850890i \(0.323937\pi\)
\(390\) −1.01033e9 + 1.67121e10i −0.0436722 + 0.722390i
\(391\) 1.08412e9 0.0463842
\(392\) −5.84661e9 8.46845e9i −0.247605 0.358641i
\(393\) 1.63065e10i 0.683581i
\(394\) 2.49463e9 4.12642e10i 0.103519 1.71233i
\(395\) −4.01545e10 4.01545e10i −1.64947 1.64947i
\(396\) −5.67955e9 7.24841e9i −0.230958 0.294755i
\(397\) 2.55289e10 + 2.55289e10i 1.02771 + 1.02771i 0.999605 + 0.0281055i \(0.00894745\pi\)
0.0281055 + 0.999605i \(0.491053\pi\)
\(398\) −1.35128e10 + 1.19721e10i −0.538533 + 0.477131i
\(399\) 9.50470e9i 0.375013i
\(400\) −1.52260e10 + 6.18101e10i −0.594766 + 2.41446i
\(401\) 2.98614e10 1.15487 0.577435 0.816436i \(-0.304054\pi\)
0.577435 + 0.816436i \(0.304054\pi\)
\(402\) 5.70515e9 + 6.43935e9i 0.218455 + 0.246569i
\(403\) −1.29130e10 + 1.29130e10i −0.489562 + 0.489562i
\(404\) −2.06394e10 2.63406e10i −0.774766 0.988779i
\(405\) 3.94699e9 3.94699e9i 0.146705 0.146705i
\(406\) 3.66247e10 + 2.21415e9i 1.34794 + 0.0814899i
\(407\) −1.84618e10 −0.672815
\(408\) −6.19895e8 1.13535e8i −0.0223706 0.00409723i
\(409\) 3.48890e10i 1.24680i 0.781904 + 0.623398i \(0.214249\pi\)
−0.781904 + 0.623398i \(0.785751\pi\)
\(410\) 3.12483e9 + 1.88912e8i 0.110584 + 0.00668536i
\(411\) −8.62894e9 8.62894e9i −0.302406 0.302406i
\(412\) −1.13655e8 + 9.36562e8i −0.00394458 + 0.0325048i
\(413\) 7.11596e9 + 7.11596e9i 0.244587 + 0.244587i
\(414\) −7.64641e9 8.63043e9i −0.260289 0.293786i
\(415\) 4.62673e9i 0.155984i
\(416\) −1.91952e10 5.97794e9i −0.640944 0.199608i
\(417\) −3.54386e9 −0.117201
\(418\) 2.21981e10 1.96671e10i 0.727127 0.644222i
\(419\) 4.88021e9 4.88021e9i 0.158337 0.158337i −0.623492 0.781829i \(-0.714287\pi\)
0.781829 + 0.623492i \(0.214287\pi\)
\(420\) 2.50137e10 + 3.03550e9i 0.803860 + 0.0975514i
\(421\) −5.30705e9 + 5.30705e9i −0.168937 + 0.168937i −0.786512 0.617575i \(-0.788115\pi\)
0.617575 + 0.786512i \(0.288115\pi\)
\(422\) −2.62062e9 + 4.33482e10i −0.0826332 + 1.36685i
\(423\) −1.73950e10 −0.543330
\(424\) −4.35397e10 7.97442e9i −1.34717 0.246738i
\(425\) 3.19573e9i 0.0979524i
\(426\) 6.69122e7 1.10681e9i 0.00203174 0.0336073i
\(427\) −3.14563e10 3.14563e10i −0.946228 0.946228i
\(428\) −2.23409e10 + 1.75054e10i −0.665773 + 0.521672i
\(429\) −1.04281e10 1.04281e10i −0.307876 0.307876i
\(430\) 5.01209e10 4.44062e10i 1.46604 1.29888i
\(431\) 2.89120e10i 0.837854i −0.908020 0.418927i \(-0.862406\pi\)
0.908020 0.418927i \(-0.137594\pi\)
\(432\) 3.46836e9 + 5.73562e9i 0.0995838 + 0.164682i
\(433\) −2.93752e10 −0.835658 −0.417829 0.908526i \(-0.637209\pi\)
−0.417829 + 0.908526i \(0.637209\pi\)
\(434\) 1.82256e10 + 2.05711e10i 0.513717 + 0.579827i
\(435\) 4.90721e10 4.90721e10i 1.37050 1.37050i
\(436\) 3.50781e10 2.74858e10i 0.970712 0.760610i
\(437\) 2.62587e10 2.62587e10i 0.720024 0.720024i
\(438\) 9.02459e9 + 5.45583e8i 0.245206 + 0.0148240i
\(439\) 3.55785e10 0.957921 0.478960 0.877836i \(-0.341014\pi\)
0.478960 + 0.877836i \(0.341014\pi\)
\(440\) −4.46689e10 6.47001e10i −1.19178 1.72621i
\(441\) 5.49454e9i 0.145270i
\(442\) −1.00744e9 6.09052e7i −0.0263956 0.00159575i
\(443\) −2.13126e10 2.13126e10i −0.553377 0.553377i 0.374037 0.927414i \(-0.377973\pi\)
−0.927414 + 0.374037i \(0.877973\pi\)
\(444\) 1.33402e10 + 1.61888e9i 0.343266 + 0.0416566i
\(445\) −8.75811e10 8.75811e10i −2.23342 2.23342i
\(446\) −5.03288e10 5.68056e10i −1.27197 1.43566i
\(447\) 1.29338e10i 0.323964i
\(448\) −1.07235e10 + 2.82928e10i −0.266211 + 0.702368i
\(449\) 2.67183e10 0.657390 0.328695 0.944436i \(-0.393391\pi\)
0.328695 + 0.944436i \(0.393391\pi\)
\(450\) 2.54405e10 2.25399e10i 0.620406 0.549669i
\(451\) −1.94985e9 + 1.94985e9i −0.0471298 + 0.0471298i
\(452\) −2.95403e9 + 2.43423e10i −0.0707720 + 0.583188i
\(453\) −1.79707e10 + 1.79707e10i −0.426748 + 0.426748i
\(454\) 2.91960e9 4.82936e10i 0.0687226 1.13675i
\(455\) 4.03536e10 0.941535
\(456\) −1.77646e10 + 1.22647e10i −0.410862 + 0.283659i
\(457\) 4.01962e10i 0.921552i −0.887516 0.460776i \(-0.847571\pi\)
0.887516 0.460776i \(-0.152429\pi\)
\(458\) −2.37935e9 + 3.93573e10i −0.0540750 + 0.894464i
\(459\) 2.37934e8 + 2.37934e8i 0.00536051 + 0.00536051i
\(460\) −6.07192e10 7.74916e10i −1.35611 1.73071i
\(461\) 5.60038e10 + 5.60038e10i 1.23998 + 1.23998i 0.960009 + 0.279969i \(0.0903241\pi\)
0.279969 + 0.960009i \(0.409676\pi\)
\(462\) −1.66125e10 + 1.47184e10i −0.364642 + 0.323066i
\(463\) 1.15330e10i 0.250969i 0.992096 + 0.125484i \(0.0400485\pi\)
−0.992096 + 0.125484i \(0.959952\pi\)
\(464\) 4.31214e10 + 7.13099e10i 0.930296 + 1.53843i
\(465\) 5.19823e10 1.11184
\(466\) 1.54286e10 + 1.74141e10i 0.327177 + 0.369281i
\(467\) −6.05628e10 + 6.05628e10i −1.27332 + 1.27332i −0.328988 + 0.944334i \(0.606708\pi\)
−0.944334 + 0.328988i \(0.893292\pi\)
\(468\) 6.62076e9 + 8.44961e9i 0.138014 + 0.176138i
\(469\) 1.46623e10 1.46623e10i 0.303047 0.303047i
\(470\) −1.48248e11 8.96233e9i −3.03806 0.183666i
\(471\) 1.48296e10 0.301331
\(472\) −4.11768e9 + 2.24822e10i −0.0829630 + 0.452972i
\(473\) 5.89836e10i 1.17838i
\(474\) −3.63427e10 2.19711e9i −0.719953 0.0435249i
\(475\) 7.74046e10 + 7.74046e10i 1.52052 + 1.52052i
\(476\) −1.82988e8 + 1.50788e9i −0.00356446 + 0.0293725i
\(477\) 1.67118e10 + 1.67118e10i 0.322813 + 0.322813i
\(478\) −5.54322e10 6.25658e10i −1.06182 1.19846i
\(479\) 2.01752e10i 0.383244i −0.981469 0.191622i \(-0.938625\pi\)
0.981469 0.191622i \(-0.0613747\pi\)
\(480\) 2.66036e10 + 5.06683e10i 0.501159 + 0.954490i
\(481\) 2.15212e10 0.402056
\(482\) −9.34575e9 + 8.28017e9i −0.173151 + 0.153409i
\(483\) −1.96513e10 + 1.96513e10i −0.361080 + 0.361080i
\(484\) 1.42729e10 + 1.73207e9i 0.260094 + 0.0315634i
\(485\) 2.63209e10 2.63209e10i 0.475700 0.475700i
\(486\) 2.15965e8 3.57232e9i 0.00387113 0.0640331i
\(487\) 8.38918e9 0.149143 0.0745716 0.997216i \(-0.476241\pi\)
0.0745716 + 0.997216i \(0.476241\pi\)
\(488\) 1.82023e10 9.93833e10i 0.320957 1.75240i
\(489\) 2.27246e10i 0.397431i
\(490\) −2.83092e9 + 4.68267e10i −0.0491069 + 0.812287i
\(491\) 3.49032e10 + 3.49032e10i 0.600536 + 0.600536i 0.940455 0.339919i \(-0.110400\pi\)
−0.339919 + 0.940455i \(0.610400\pi\)
\(492\) 1.57991e9 1.23795e9i 0.0269633 0.0211273i
\(493\) 2.95819e9 + 2.95819e9i 0.0500770 + 0.0500770i
\(494\) −2.58767e10 + 2.29263e10i −0.434512 + 0.384970i
\(495\) 4.19791e10i 0.699217i
\(496\) −1.49301e10 + 6.06088e10i −0.246681 + 1.00140i
\(497\) −2.67254e9 −0.0438025
\(498\) 1.96718e9 + 2.22034e9i 0.0319836 + 0.0360996i
\(499\) 1.48587e10 1.48587e10i 0.239650 0.239650i −0.577055 0.816705i \(-0.695798\pi\)
0.816705 + 0.577055i \(0.195798\pi\)
\(500\) 1.36565e11 1.07007e11i 2.18505 1.71211i
\(501\) −1.96044e10 + 1.96044e10i −0.311174 + 0.311174i
\(502\) −6.67411e10 4.03484e9i −1.05094 0.0635348i
\(503\) −3.54400e10 −0.553632 −0.276816 0.960923i \(-0.589279\pi\)
−0.276816 + 0.960923i \(0.589279\pi\)
\(504\) 1.32946e10 9.17855e9i 0.206040 0.142250i
\(505\) 1.52551e11i 2.34558i
\(506\) 8.65579e10 + 5.23287e9i 1.32040 + 0.0798248i
\(507\) −1.48185e10 1.48185e10i −0.224270 0.224270i
\(508\) −4.08226e10 4.95397e9i −0.612979 0.0743873i
\(509\) 9.14813e9 + 9.14813e9i 0.136289 + 0.136289i 0.771960 0.635671i \(-0.219276\pi\)
−0.635671 + 0.771960i \(0.719276\pi\)
\(510\) 1.90518e9 + 2.15036e9i 0.0281615 + 0.0317856i
\(511\) 2.17911e10i 0.319592i
\(512\) −6.67176e10 + 1.64658e10i −0.970869 + 0.239609i
\(513\) 1.15261e10 0.166423
\(514\) −9.74140e10 + 8.63071e10i −1.39563 + 1.23650i
\(515\) 3.04116e9 3.04116e9i 0.0432325 0.0432325i
\(516\) 5.17218e9 4.26207e10i 0.0729583 0.601203i
\(517\) 9.25043e10 9.25043e10i 1.29479 1.29479i
\(518\) 1.95451e9 3.23299e10i 0.0271468 0.449040i
\(519\) 2.63945e10 0.363785
\(520\) 5.20714e10 + 7.54222e10i 0.712173 + 1.03154i
\(521\) 7.82173e10i 1.06158i −0.847504 0.530789i \(-0.821896\pi\)
0.847504 0.530789i \(-0.178104\pi\)
\(522\) 2.68505e9 4.44139e10i 0.0361635 0.598187i
\(523\) 1.67737e10 + 1.67737e10i 0.224194 + 0.224194i 0.810262 0.586068i \(-0.199325\pi\)
−0.586068 + 0.810262i \(0.699325\pi\)
\(524\) 5.50554e10 + 7.02633e10i 0.730256 + 0.931974i
\(525\) −5.79276e10 5.79276e10i −0.762515 0.762515i
\(526\) 7.11340e10 6.30235e10i 0.929254 0.823302i
\(527\) 3.13362e9i 0.0406260i
\(528\) −4.89455e10 1.20570e10i −0.629763 0.155133i
\(529\) 3.02707e10 0.386545
\(530\) 1.33815e11 + 1.51035e11i 1.69590 + 1.91415i
\(531\) 8.62934e9 8.62934e9i 0.108542 0.108542i
\(532\) 3.20906e10 + 4.09550e10i 0.400619 + 0.511282i
\(533\) 2.27298e9 2.27298e9i 0.0281635 0.0281635i
\(534\) −7.92674e10 4.79212e9i −0.974831 0.0589336i
\(535\) 1.29387e11 1.57934
\(536\) 4.63242e10 + 8.48440e9i 0.561240 + 0.102793i
\(537\) 4.56782e10i 0.549303i
\(538\) −3.84155e10 2.32241e9i −0.458540 0.0277211i
\(539\) −2.92192e10 2.92192e10i −0.346189 0.346189i
\(540\) 3.68108e9 3.03335e10i 0.0432913 0.356736i
\(541\) −3.16296e10 3.16296e10i −0.369237 0.369237i 0.497962 0.867199i \(-0.334082\pi\)
−0.867199 + 0.497962i \(0.834082\pi\)
\(542\) 3.17583e10 + 3.58453e10i 0.368011 + 0.415370i
\(543\) 2.35568e10i 0.270967i
\(544\) −3.05441e9 + 1.60373e9i −0.0348764 + 0.0183120i
\(545\) −2.03155e11 −2.30272
\(546\) 1.93655e10 1.71575e10i 0.217900 0.193056i
\(547\) −3.87257e10 + 3.87257e10i −0.432564 + 0.432564i −0.889500 0.456936i \(-0.848947\pi\)
0.456936 + 0.889500i \(0.348947\pi\)
\(548\) −6.63153e10 8.04761e9i −0.735345 0.0892370i
\(549\) −3.81463e10 + 3.81463e10i −0.419916 + 0.419916i
\(550\) −1.54253e10 + 2.55153e11i −0.168571 + 2.78837i
\(551\) 1.43302e11 1.55470
\(552\) −6.20866e10 1.13713e10i −0.668716 0.122477i
\(553\) 8.77546e10i 0.938359i
\(554\) 3.77172e9 6.23887e10i 0.0400406 0.662319i
\(555\) −4.33177e10 4.33177e10i −0.456555 0.456555i
\(556\) −1.52702e10 + 1.19651e10i −0.159789 + 0.125204i
\(557\) −9.81882e10 9.81882e10i −1.02009 1.02009i −0.999794 0.0202966i \(-0.993539\pi\)
−0.0202966 0.999794i \(-0.506461\pi\)
\(558\) 2.49460e10 2.21018e10i 0.257315 0.227977i
\(559\) 6.87583e10i 0.704171i
\(560\) 1.18031e11 7.13737e10i 1.20017 0.725748i
\(561\) −2.53060e9 −0.0255489
\(562\) −1.77546e10 2.00395e10i −0.177978 0.200882i
\(563\) 5.79373e10 5.79373e10i 0.576666 0.576666i −0.357317 0.933983i \(-0.616308\pi\)
0.933983 + 0.357317i \(0.116308\pi\)
\(564\) −7.49538e10 + 5.87307e10i −0.740760 + 0.580429i
\(565\) 7.90433e10 7.90433e10i 0.775659 0.775659i
\(566\) −6.71776e10 4.06123e9i −0.654574 0.0395724i
\(567\) −8.62585e9 −0.0834583
\(568\) −3.44859e9 4.99507e9i −0.0331320 0.0479897i
\(569\) 6.25969e8i 0.00597178i −0.999996 0.00298589i \(-0.999050\pi\)
0.999996 0.00298589i \(-0.000950440\pi\)
\(570\) 9.82302e10 + 5.93852e9i 0.930563 + 0.0562573i
\(571\) −2.49209e10 2.49209e10i −0.234433 0.234433i 0.580107 0.814540i \(-0.303011\pi\)
−0.814540 + 0.580107i \(0.803011\pi\)
\(572\) −8.01421e10 9.72555e9i −0.748646 0.0908511i
\(573\) −8.12560e10 8.12560e10i −0.753767 0.753767i
\(574\) −3.20812e9 3.62097e9i −0.0295531 0.0333563i
\(575\) 3.20074e11i 2.92805i
\(576\) 3.43100e10 + 1.30042e10i 0.311696 + 0.118139i
\(577\) −9.95264e10 −0.897915 −0.448957 0.893553i \(-0.648205\pi\)
−0.448957 + 0.893553i \(0.648205\pi\)
\(578\) 8.34108e10 7.39005e10i 0.747327 0.662119i
\(579\) −3.01723e10 + 3.01723e10i −0.268469 + 0.268469i
\(580\) 4.57662e10 3.77130e11i 0.404420 3.33257i
\(581\) 5.05568e9 5.05568e9i 0.0443685 0.0443685i
\(582\) 1.44018e9 2.38223e10i 0.0125524 0.207631i
\(583\) −1.77742e11 −1.53857
\(584\) 4.07283e10 2.81188e10i 0.350142 0.241738i
\(585\) 4.89358e10i 0.417833i
\(586\) 1.16336e10 1.92433e11i 0.0986558 1.63188i
\(587\) −1.26437e11 1.26437e11i −1.06493 1.06493i −0.997740 0.0671927i \(-0.978596\pi\)
−0.0671927 0.997740i \(-0.521404\pi\)
\(588\) 1.85512e10 + 2.36756e10i 0.155190 + 0.198057i
\(589\) 7.59001e10 + 7.59001e10i 0.630640 + 0.630640i
\(590\) 7.79888e10 6.90968e10i 0.643612 0.570229i
\(591\) 1.20829e11i 0.990421i
\(592\) 6.29477e10 3.80648e10i 0.512499 0.309910i
\(593\) 1.59336e11 1.28853 0.644266 0.764802i \(-0.277163\pi\)
0.644266 + 0.764802i \(0.277163\pi\)
\(594\) 1.78486e10 + 2.01455e10i 0.143370 + 0.161820i
\(595\) 4.89633e9 4.89633e9i 0.0390664 0.0390664i
\(596\) 4.36684e10 + 5.57309e10i 0.346084 + 0.441683i
\(597\) 3.73121e10 3.73121e10i 0.293732 0.293732i
\(598\) −1.00902e11 6.10006e9i −0.789035 0.0477012i
\(599\) 1.68011e11 1.30506 0.652529 0.757764i \(-0.273708\pi\)
0.652529 + 0.757764i \(0.273708\pi\)
\(600\) 3.35201e10 1.83017e11i 0.258643 1.41217i
\(601\) 2.22630e11i 1.70642i −0.521569 0.853209i \(-0.674653\pi\)
0.521569 0.853209i \(-0.325347\pi\)
\(602\) −1.03291e11 6.24447e9i −0.786460 0.0475455i
\(603\) −1.77806e10 1.77806e10i −0.134486 0.134486i
\(604\) −1.67600e10 + 1.38108e11i −0.125929 + 1.03770i
\(605\) −4.63462e10 4.63462e10i −0.345933 0.345933i
\(606\) 6.48614e10 + 7.32085e10i 0.480946 + 0.542839i
\(607\) 6.68417e9i 0.0492371i 0.999697 + 0.0246186i \(0.00783713\pi\)
−0.999697 + 0.0246186i \(0.992163\pi\)
\(608\) −3.51372e10 + 1.12826e11i −0.257130 + 0.825647i
\(609\) −1.07244e11 −0.779654
\(610\) −3.44752e11 + 3.05444e11i −2.48993 + 2.20604i
\(611\) −1.07834e11 + 1.07834e11i −0.773733 + 0.773733i
\(612\) 1.82857e9 + 2.21904e8i 0.0130349 + 0.00158183i
\(613\) 1.14294e11 1.14294e11i 0.809432 0.809432i −0.175116 0.984548i \(-0.556030\pi\)
0.984548 + 0.175116i \(0.0560301\pi\)
\(614\) 9.03151e8 1.49392e10i 0.00635458 0.105112i
\(615\) −9.15005e9 −0.0639621
\(616\) −2.18884e10 + 1.19509e11i −0.152016 + 0.829999i
\(617\) 1.00150e11i 0.691051i 0.938409 + 0.345525i \(0.112299\pi\)
−0.938409 + 0.345525i \(0.887701\pi\)
\(618\) 1.66401e8 2.75247e9i 0.00114078 0.0188699i
\(619\) −7.46140e10 7.46140e10i −0.508227 0.508227i 0.405755 0.913982i \(-0.367009\pi\)
−0.913982 + 0.405755i \(0.867009\pi\)
\(620\) 2.23988e11 1.75507e11i 1.51585 1.18776i
\(621\) 2.38307e10 + 2.38307e10i 0.160240 + 0.160240i
\(622\) 2.38875e9 2.11639e9i 0.0159591 0.0141395i
\(623\) 1.91402e11i 1.27056i
\(624\) 5.70567e10 + 1.40551e10i 0.376329 + 0.0927032i
\(625\) −4.11487e11 −2.69672
\(626\) −8.43028e10 9.51517e10i −0.548965 0.619611i
\(627\) −6.12943e10 + 6.12943e10i −0.396597 + 0.396597i
\(628\) 6.38994e10 5.00689e10i 0.410826 0.321906i
\(629\) 2.61129e9 2.61129e9i 0.0166822 0.0166822i
\(630\) −7.35130e10 4.44424e9i −0.466661 0.0282121i
\(631\) 2.14848e10 0.135523 0.0677617 0.997702i \(-0.478414\pi\)
0.0677617 + 0.997702i \(0.478414\pi\)
\(632\) −1.64016e11 + 1.13237e11i −1.02806 + 0.709771i
\(633\) 1.26931e11i 0.790593i
\(634\) 4.21476e10 + 2.54804e9i 0.260865 + 0.0157706i
\(635\) 1.32557e11 + 1.32557e11i 0.815283 + 0.815283i
\(636\) 1.28434e11 + 1.55860e10i 0.784968 + 0.0952588i
\(637\) 3.40614e10 + 3.40614e10i 0.206874 + 0.206874i
\(638\) 2.21908e11 + 2.50466e11i 1.33934 + 1.51170i
\(639\) 3.24092e9i 0.0194386i
\(640\) 2.85704e11 + 1.28504e11i 1.70293 + 0.765944i
\(641\) 8.33981e10 0.493997 0.246998 0.969016i \(-0.420556\pi\)
0.246998 + 0.969016i \(0.420556\pi\)
\(642\) 6.20923e10 5.50127e10i 0.365508 0.323834i
\(643\) −1.81974e10 + 1.81974e10i −0.106455 + 0.106455i −0.758328 0.651873i \(-0.773983\pi\)
0.651873 + 0.758328i \(0.273983\pi\)
\(644\) −1.83274e10 + 1.51025e11i −0.106551 + 0.878020i
\(645\) −1.38396e11 + 1.38396e11i −0.799621 + 0.799621i
\(646\) −3.57989e8 + 5.92156e9i −0.00205560 + 0.0340021i
\(647\) −1.76390e11 −1.00660 −0.503300 0.864112i \(-0.667881\pi\)
−0.503300 + 0.864112i \(0.667881\pi\)
\(648\) −1.11306e10 1.61220e10i −0.0631275 0.0914363i
\(649\) 9.17793e10i 0.517328i
\(650\) 1.79816e10 2.97437e11i 0.100734 1.66625i
\(651\) −5.68017e10 5.68017e10i −0.316255 0.316255i
\(652\) −7.67250e10 9.79187e10i −0.424567 0.541845i
\(653\) −2.36372e11 2.36372e11i −1.30000 1.30000i −0.928389 0.371610i \(-0.878806\pi\)
−0.371610 0.928389i \(-0.621194\pi\)
\(654\) −9.74929e10 + 8.63770e10i −0.532920 + 0.472158i
\(655\) 4.06929e11i 2.21082i
\(656\) 2.62803e9 1.06685e10i 0.0141911 0.0576087i
\(657\) −2.64255e10 −0.141828
\(658\) 1.52199e11 + 1.71785e11i 0.811909 + 0.916394i
\(659\) 6.31475e10 6.31475e10i 0.334823 0.334823i −0.519592 0.854415i \(-0.673916\pi\)
0.854415 + 0.519592i \(0.173916\pi\)
\(660\) 1.41734e11 + 1.80885e11i 0.746960 + 0.953292i
\(661\) 1.23433e11 1.23433e11i 0.646585 0.646585i −0.305581 0.952166i \(-0.598851\pi\)
0.952166 + 0.305581i \(0.0988508\pi\)
\(662\) −1.49385e11 9.03111e9i −0.777814 0.0470229i
\(663\) 2.94997e9 0.0152673
\(664\) 1.59730e10 + 2.92549e9i 0.0821700 + 0.0150497i
\(665\) 2.37190e11i 1.21286i
\(666\) −3.92057e10 2.37019e9i −0.199275 0.0120472i
\(667\) 2.96282e11 + 2.96282e11i 1.49693 + 1.49693i
\(668\) −1.82837e10 + 1.50664e11i −0.0918244 + 0.756666i
\(669\) 1.56854e11 + 1.56854e11i 0.783053 + 0.783053i
\(670\) −1.42372e11 1.60694e11i −0.706524 0.797447i
\(671\) 4.05713e11i 2.00138i
\(672\) 2.62958e10 8.44360e10i 0.128946 0.414048i
\(673\) 1.85697e11 0.905198 0.452599 0.891714i \(-0.350497\pi\)
0.452599 + 0.891714i \(0.350497\pi\)
\(674\) 7.30470e10 6.47184e10i 0.353967 0.313609i
\(675\) −7.02474e10 + 7.02474e10i −0.338388 + 0.338388i
\(676\) −1.13883e11 1.38201e10i −0.545346 0.0661798i
\(677\) −2.24071e11 + 2.24071e11i −1.06667 + 1.06667i −0.0690581 + 0.997613i \(0.521999\pi\)
−0.997613 + 0.0690581i \(0.978001\pi\)
\(678\) 4.32496e9 7.15400e10i 0.0204674 0.338556i
\(679\) −5.75223e10 −0.270618
\(680\) 1.54695e10 + 2.83328e9i 0.0723505 + 0.0132512i
\(681\) 1.41412e11i 0.657503i
\(682\) −1.51255e10 + 2.50194e11i −0.0699153 + 1.15648i
\(683\) −9.27113e10 9.27113e10i −0.426040 0.426040i 0.461237 0.887277i \(-0.347406\pi\)
−0.887277 + 0.461237i \(0.847406\pi\)
\(684\) 4.96651e10 3.89155e10i 0.226896 0.177786i
\(685\) 2.15336e11 + 2.15336e11i 0.978035 + 0.978035i
\(686\) 1.78769e11 1.58386e11i 0.807225 0.715187i
\(687\) 1.15245e11i 0.517362i
\(688\) −1.21613e11 2.01112e11i −0.542784 0.897603i
\(689\) 2.07198e11 0.919408
\(690\) 1.90817e11 + 2.15373e11i 0.841821 + 0.950156i
\(691\) 7.75266e8 7.75266e8i 0.00340047 0.00340047i −0.705405 0.708805i \(-0.749235\pi\)
0.708805 + 0.705405i \(0.249235\pi\)
\(692\) 1.13732e11 8.91156e10i 0.495973 0.388624i
\(693\) 4.58711e10 4.58711e10i 0.198887 0.198887i
\(694\) 3.48702e11 + 2.10808e10i 1.50320 + 0.0908762i
\(695\) 8.84372e10 0.379049
\(696\) −1.38385e11 2.00442e11i −0.589727 0.854183i
\(697\) 5.51587e8i 0.00233713i
\(698\) −1.56220e11 9.44430e9i −0.658134 0.0397876i
\(699\) −4.80845e10 4.80845e10i −0.201417 0.201417i
\(700\) −4.45186e11 5.40251e10i −1.85417 0.225011i
\(701\) 7.27256e10 + 7.27256e10i 0.301172 + 0.301172i 0.841472 0.540300i \(-0.181689\pi\)
−0.540300 + 0.841472i \(0.681689\pi\)
\(702\) −2.08065e10 2.34840e10i −0.0856741 0.0966996i
\(703\) 1.26498e11i 0.517918i
\(704\) −2.51610e11 + 1.13302e11i −1.02432 + 0.461259i
\(705\) 4.34094e11 1.75723
\(706\) 1.65579e11 1.46700e11i 0.666477 0.590487i
\(707\) 1.66694e11 1.66694e11i 0.667181 0.667181i
\(708\) 8.04799e9 6.63184e10i 0.0320298 0.263937i
\(709\) −3.28253e10 + 3.28253e10i −0.129904 + 0.129904i −0.769069 0.639165i \(-0.779280\pi\)
0.639165 + 0.769069i \(0.279280\pi\)
\(710\) −1.66980e9 + 2.76205e10i −0.00657099 + 0.108692i
\(711\) 1.06418e11 0.416424
\(712\) −3.57737e11 + 2.46981e11i −1.39201 + 0.961044i
\(713\) 3.13853e11i 1.21442i
\(714\) 2.67910e8 4.43154e9i 0.00103085 0.0170515i
\(715\) 2.60234e11 + 2.60234e11i 0.995725 + 0.995725i
\(716\) 1.54223e11 + 1.96824e11i 0.586809 + 0.748903i
\(717\) 1.72759e11 + 1.72759e11i 0.653679 + 0.653679i
\(718\) 1.93489e11 1.71428e11i 0.728046 0.645036i
\(719\) 3.90755e11i 1.46214i 0.682302 + 0.731071i \(0.260979\pi\)
−0.682302 + 0.731071i \(0.739021\pi\)
\(720\) −8.65531e10 1.43133e11i −0.322072 0.532610i
\(721\) −6.64623e9 −0.0245943
\(722\) −4.54453e10 5.12937e10i −0.167240 0.188762i
\(723\) 2.58059e10 2.58059e10i 0.0944420 0.0944420i
\(724\) 7.95346e10 + 1.01504e11i 0.289469 + 0.369429i
\(725\) −8.73372e11 + 8.73372e11i −3.16117 + 3.16117i
\(726\) −4.19467e10 2.53590e9i −0.150991 0.00912819i
\(727\) 5.36249e10 0.191968 0.0959839 0.995383i \(-0.469400\pi\)
0.0959839 + 0.995383i \(0.469400\pi\)
\(728\) 2.55157e10 1.39314e11i 0.0908410 0.495985i
\(729\) 1.04604e10i 0.0370370i
\(730\) −2.25209e11 1.36151e10i −0.793039 0.0479433i
\(731\) −8.34284e9 8.34284e9i −0.0292176 0.0292176i
\(732\) −3.55764e10 + 2.93162e11i −0.123913 + 1.02109i
\(733\) 3.46598e11 + 3.46598e11i 1.20063 + 1.20063i 0.973974 + 0.226659i \(0.0727801\pi\)
0.226659 + 0.973974i \(0.427220\pi\)
\(734\) −1.48902e11 1.68065e11i −0.513000 0.579018i
\(735\) 1.37117e11i 0.469831i
\(736\) −3.05919e11 + 1.60624e11i −1.04255 + 0.547394i
\(737\) 1.89109e11 0.640978
\(738\) −4.39106e9 + 3.89041e9i −0.0148028 + 0.0131150i
\(739\) −1.03797e11 + 1.03797e11i −0.348022 + 0.348022i −0.859372 0.511350i \(-0.829145\pi\)
0.511350 + 0.859372i \(0.329145\pi\)
\(740\) −3.32906e11 4.03994e10i −1.11018 0.134725i
\(741\) 7.14519e10 7.14519e10i 0.236996 0.236996i
\(742\) 1.88172e10 3.11260e11i 0.0620784 1.02685i
\(743\) −1.09841e11 −0.360419 −0.180210 0.983628i \(-0.557678\pi\)
−0.180210 + 0.983628i \(0.557678\pi\)
\(744\) 3.28686e10 1.79460e11i 0.107273 0.585701i
\(745\) 3.22765e11i 1.04776i
\(746\) −1.53228e10 + 2.53458e11i −0.0494748 + 0.818371i
\(747\) −6.13090e9 6.13090e9i −0.0196898 0.0196898i
\(748\) −1.09042e10 + 8.54405e9i −0.0348326 + 0.0272934i
\(749\) −1.41383e11 1.41383e11i −0.449231 0.449231i
\(750\) −3.79557e11 + 3.36281e11i −1.19959 + 1.06281i
\(751\) 4.38262e11i 1.37776i −0.724875 0.688881i \(-0.758102\pi\)
0.724875 0.688881i \(-0.241898\pi\)
\(752\) −1.24678e11 + 5.06132e11i −0.389870 + 1.58268i
\(753\) 1.95429e11 0.607869
\(754\) −2.58683e11 2.91973e11i −0.800354 0.903351i
\(755\) 4.48459e11 4.48459e11i 1.38018 1.38018i
\(756\) −3.71681e10 + 2.91234e10i −0.113785 + 0.0891569i
\(757\) 2.68417e10 2.68417e10i 0.0817383 0.0817383i −0.665056 0.746794i \(-0.731592\pi\)
0.746794 + 0.665056i \(0.231592\pi\)
\(758\) 5.69997e10 + 3.44592e9i 0.172662 + 0.0104383i
\(759\) −2.53457e11 −0.763724
\(760\) 4.43317e11 3.06065e11i 1.32880 0.917402i
\(761\) 3.36463e11i 1.00323i −0.865092 0.501614i \(-0.832740\pi\)
0.865092 0.501614i \(-0.167260\pi\)
\(762\) 1.19974e11 + 7.25304e9i 0.355850 + 0.0215130i
\(763\) 2.21990e11 + 2.21990e11i 0.654990 + 0.654990i
\(764\) −6.24470e11 7.57818e10i −1.83290 0.222429i
\(765\) −5.93766e9 5.93766e9i −0.0173368 0.0173368i
\(766\) 2.95029e11 + 3.32996e11i 0.856937 + 0.967217i
\(767\) 1.06989e11i 0.309141i
\(768\) 1.91745e11 5.98067e10i 0.551162 0.171912i
\(769\) 1.94784e11 0.556992 0.278496 0.960437i \(-0.410164\pi\)
0.278496 + 0.960437i \(0.410164\pi\)
\(770\) 4.14566e11 3.67298e11i 1.17932 1.04485i
\(771\) 2.68984e11 2.68984e11i 0.761216 0.761216i
\(772\) −2.81396e10 + 2.31880e11i −0.0792224 + 0.652822i
\(773\) 4.91243e11 4.91243e11i 1.37587 1.37587i 0.524402 0.851471i \(-0.324289\pi\)
0.851471 0.524402i \(-0.175711\pi\)
\(774\) −7.57252e9 + 1.25258e11i −0.0210997 + 0.349014i
\(775\) −9.25167e11 −2.56456
\(776\) −7.42255e10 1.07511e11i −0.204695 0.296487i
\(777\) 9.46675e10i 0.259727i
\(778\) 1.01786e10 1.68366e11i 0.0277823 0.459553i
\(779\) −1.33601e10 1.33601e10i −0.0362794 0.0362794i
\(780\) −1.65222e11 2.10861e11i −0.446363 0.569662i
\(781\) −1.72348e10 1.72348e10i −0.0463235 0.0463235i
\(782\) −1.29832e10 + 1.15029e10i −0.0347180 + 0.0307596i
\(783\) 1.30052e11i 0.345994i
\(784\) 1.59871e11 + 3.93819e10i 0.423162 + 0.104240i
\(785\) −3.70073e11 −0.974559
\(786\) −1.73018e11 1.95283e11i −0.453315 0.511652i
\(787\) −3.85780e11 + 3.85780e11i −1.00564 + 1.00564i −0.00565199 + 0.999984i \(0.501799\pi\)
−0.999984 + 0.00565199i \(0.998201\pi\)
\(788\) 4.07953e11 + 5.20641e11i 1.05805 + 1.35031i
\(789\) −1.96418e11 + 1.96418e11i −0.506843 + 0.506843i
\(790\) 9.06936e11 + 5.48289e10i 2.32846 + 0.140767i
\(791\) −1.72743e11 −0.441260
\(792\) 1.44925e11 + 2.65435e10i 0.368336 + 0.0674617i
\(793\) 4.72947e11i 1.19597i
\(794\) −5.76601e11 3.48585e10i −1.45075 0.0877055i
\(795\) −4.17045e11 4.17045e11i −1.04403 1.04403i
\(796\) 3.47983e10 2.86751e11i 0.0866775 0.714254i
\(797\) −1.04433e11 1.04433e11i −0.258823 0.258823i 0.565752 0.824575i \(-0.308586\pi\)
−0.824575 + 0.565752i \(0.808586\pi\)
\(798\) −1.00848e11 1.13827e11i −0.248689 0.280693i
\(799\) 2.61683e10i 0.0642078i
\(800\) −4.73484e11 9.01780e11i −1.15597 2.20161i
\(801\) 2.32108e11 0.563847
\(802\) −3.57615e11 + 3.16841e11i −0.864407 + 0.765850i
\(803\) 1.40527e11 1.40527e11i 0.337986 0.337986i
\(804\) −1.36648e11 1.65827e10i −0.327023 0.0396855i
\(805\) 4.90401e11 4.90401e11i 1.16780 1.16780i
\(806\) 1.76321e10 2.91656e11i 0.0417795 0.691083i
\(807\) 1.12487e11 0.265221
\(808\) 5.26656e11 + 9.64585e10i 1.23561 + 0.226305i
\(809\) 4.26161e11i 0.994901i −0.867492 0.497450i \(-0.834270\pi\)
0.867492 0.497450i \(-0.165730\pi\)
\(810\) −5.38942e9 + 8.91474e10i −0.0125199 + 0.207094i
\(811\) 8.13750e10 + 8.13750e10i 0.188108 + 0.188108i 0.794878 0.606770i \(-0.207535\pi\)
−0.606770 + 0.794878i \(0.707535\pi\)
\(812\) −4.62104e11 + 3.62085e11i −1.06296 + 0.832889i
\(813\) −9.89775e10 9.89775e10i −0.226555 0.226555i
\(814\) 2.21095e11 1.95886e11i 0.503594 0.446176i
\(815\) 5.67095e11i 1.28536i
\(816\) 8.62840e9 5.21763e9i 0.0194612 0.0117683i
\(817\) −4.04148e11 −0.907093
\(818\) −3.70185e11 4.17825e11i −0.826811 0.933213i
\(819\) −5.34728e10 + 5.34728e10i −0.118849 + 0.118849i
\(820\) −3.94268e10 + 3.08932e10i −0.0872041 + 0.0683295i
\(821\) 2.55228e11 2.55228e11i 0.561767 0.561767i −0.368042 0.929809i \(-0.619972\pi\)
0.929809 + 0.368042i \(0.119972\pi\)
\(822\) 1.94895e11 + 1.17824e10i 0.426887 + 0.0258075i
\(823\) −5.69856e11 −1.24213 −0.621063 0.783761i \(-0.713299\pi\)
−0.621063 + 0.783761i \(0.713299\pi\)
\(824\) −8.57615e9 1.24220e10i −0.0186030 0.0269453i
\(825\) 7.47132e11i 1.61280i
\(826\) −1.60722e11 9.71649e9i −0.345268 0.0208732i
\(827\) −4.62744e10 4.62744e10i −0.0989279 0.0989279i 0.655911 0.754839i \(-0.272285\pi\)
−0.754839 + 0.655911i \(0.772285\pi\)
\(828\) 1.83144e11 + 2.22252e10i 0.389647 + 0.0472851i
\(829\) 2.02328e10 + 2.02328e10i 0.0428389 + 0.0428389i 0.728202 0.685363i \(-0.240356\pi\)
−0.685363 + 0.728202i \(0.740356\pi\)
\(830\) −4.90912e10 5.54088e10i −0.103441 0.116753i
\(831\) 1.82685e11i 0.383088i
\(832\) 2.93307e11 1.32078e11i 0.612109 0.275636i
\(833\) 8.26573e9 0.0171673
\(834\) 4.24406e10 3.76016e10i 0.0877237 0.0777217i
\(835\) 4.89230e11 4.89230e11i 1.00639 1.00639i
\(836\) −5.71649e10 + 4.71060e11i −0.117032 + 0.964386i
\(837\) −6.88820e10 + 6.88820e10i −0.140347 + 0.140347i
\(838\) −6.66368e9 + 1.10225e11i −0.0135126 + 0.223514i
\(839\) 4.29029e11 0.865842 0.432921 0.901432i \(-0.357483\pi\)
0.432921 + 0.901432i \(0.357483\pi\)
\(840\) −3.31767e11 + 2.29052e11i −0.666371 + 0.460062i
\(841\) 1.11666e12i 2.23222i
\(842\) 7.24651e9 1.19866e11i 0.0144172 0.238477i
\(843\) 5.53339e10 + 5.53339e10i 0.109567 + 0.109567i
\(844\) −4.28556e11 5.46936e11i −0.844575 1.07787i
\(845\) 3.69796e11 + 3.69796e11i 0.725329 + 0.725329i
\(846\) 2.08320e11 1.84568e11i 0.406676 0.360308i
\(847\) 1.01286e11i 0.196796i
\(848\) 6.06035e11 3.66472e11i 1.17196 0.708692i
\(849\) 1.96708e11 0.378608
\(850\) −3.39079e10 3.82715e10i −0.0649569 0.0733162i
\(851\) 2.61539e11 2.61539e11i 0.498675 0.498675i
\(852\) 1.09423e10 + 1.39649e10i 0.0207659 + 0.0265020i
\(853\) −5.87411e11 + 5.87411e11i −1.10955 + 1.10955i −0.116338 + 0.993210i \(0.537116\pi\)
−0.993210 + 0.116338i \(0.962884\pi\)
\(854\) 7.10477e11 + 4.29520e10i 1.33573 + 0.0807518i
\(855\) −2.87635e11 −0.538242
\(856\) 8.18119e10 4.46687e11i 0.152378 0.831971i
\(857\) 3.80589e11i 0.705558i −0.935707 0.352779i \(-0.885237\pi\)
0.935707 0.352779i \(-0.114763\pi\)
\(858\) 2.35531e11 + 1.42390e10i 0.434609 + 0.0262743i
\(859\) −2.51162e11 2.51162e11i −0.461298 0.461298i 0.437783 0.899081i \(-0.355764\pi\)
−0.899081 + 0.437783i \(0.855764\pi\)
\(860\) −1.29072e11 + 1.06360e12i −0.235960 + 1.94440i
\(861\) 9.99837e9 + 9.99837e9i 0.0181935 + 0.0181935i
\(862\) 3.06766e11 + 3.46244e11i 0.555621 + 0.627124i
\(863\) 4.61350e11i 0.831740i −0.909424 0.415870i \(-0.863477\pi\)
0.909424 0.415870i \(-0.136523\pi\)
\(864\) −1.02393e11 3.18882e10i −0.183746 0.0572236i
\(865\) −6.58677e11 −1.17654
\(866\) 3.51792e11 3.11681e11i 0.625481 0.554165i
\(867\) −2.30317e11 + 2.30317e11i −0.407615 + 0.407615i
\(868\) −4.36534e11 5.29750e10i −0.769022 0.0933237i
\(869\) −5.65915e11 + 5.65915e11i −0.992367 + 0.992367i
\(870\) −6.70056e10 + 1.10835e12i −0.116959 + 1.93464i
\(871\) −2.20448e11 −0.383032
\(872\) −1.28455e11 + 7.01356e11i −0.222170 + 1.21303i
\(873\) 6.97559e10i 0.120095i
\(874\) −3.58549e10 + 5.93083e11i −0.0614474 + 1.01641i
\(875\) 8.64245e11 + 8.64245e11i 1.47436 + 1.47436i
\(876\) −1.13866e11 + 8.92204e10i −0.193364 + 0.151512i
\(877\) −5.93230e11 5.93230e11i −1.00282 1.00282i −0.999996 0.00282855i \(-0.999100\pi\)
−0.00282855 0.999996i \(-0.500900\pi\)
\(878\) −4.26082e11 + 3.77501e11i −0.716993 + 0.635243i
\(879\) 5.63477e11i 0.943889i
\(880\) 1.22144e12 + 3.00883e11i 2.03676 + 0.501727i
\(881\) −1.83147e11 −0.304015 −0.152008 0.988379i \(-0.548574\pi\)
−0.152008 + 0.988379i \(0.548574\pi\)
\(882\) −5.82991e10 6.58017e10i −0.0963358 0.108733i
\(883\) −4.49704e11 + 4.49704e11i −0.739748 + 0.739748i −0.972529 0.232781i \(-0.925217\pi\)
0.232781 + 0.972529i \(0.425217\pi\)
\(884\) 1.27112e10 9.95996e9i 0.0208150 0.0163098i
\(885\) −2.15346e11 + 2.15346e11i −0.351046 + 0.351046i
\(886\) 4.81370e11 + 2.91013e10i 0.781167 + 0.0472256i
\(887\) 6.24478e11 1.00884 0.504421 0.863458i \(-0.331706\pi\)
0.504421 + 0.863458i \(0.331706\pi\)
\(888\) −1.76937e11 + 1.22157e11i −0.284555 + 0.196456i
\(889\) 2.89694e11i 0.463802i
\(890\) 1.97812e12 + 1.19588e11i 3.15278 + 0.190602i
\(891\) −5.56267e10 5.56267e10i −0.0882617 0.0882617i
\(892\) 1.20546e12 + 1.46287e11i 1.90411 + 0.231071i
\(893\) 6.33827e11 + 6.33827e11i 0.996702 + 0.996702i
\(894\) −1.37233e11 1.54893e11i −0.214836 0.242483i
\(895\) 1.13990e12i 1.77654i
\(896\) −1.71774e11 4.52610e11i −0.266518 0.702251i
\(897\) 2.95459e11 0.456381
\(898\) −3.19973e11 + 2.83491e11i −0.492049 + 0.435947i
\(899\) −8.56397e11 + 8.56397e11i −1.31110 + 1.31110i
\(900\) −6.55148e10 + 5.39866e11i −0.0998550 + 0.822842i
\(901\) 2.51405e10 2.51405e10i 0.0381483 0.0381483i
\(902\) 2.66243e9 4.40397e10i 0.00402209 0.0665301i
\(903\) 3.02454e11 0.454892
\(904\) −2.22904e11 3.22863e11i −0.333768 0.483441i
\(905\) 5.87861e11i 0.876356i
\(906\) 2.45381e10 4.05889e11i 0.0364190 0.602413i
\(907\) −7.97132e11 7.97132e11i −1.17788 1.17788i −0.980283 0.197597i \(-0.936686\pi\)
−0.197597 0.980283i \(-0.563314\pi\)
\(908\) 4.77448e11 + 6.09334e11i 0.702398 + 0.896420i
\(909\) −2.02146e11 2.02146e11i −0.296081 0.296081i
\(910\) −4.83267e11 + 4.28166e11i −0.704728 + 0.624377i
\(911\) 7.91509e10i 0.114916i −0.998348 0.0574582i \(-0.981700\pi\)
0.998348 0.0574582i \(-0.0182996\pi\)
\(912\) 8.26130e10 3.35368e11i 0.119418 0.484777i
\(913\) 6.52065e10 0.0938443
\(914\) 4.26496e11 + 4.81382e11i 0.611125 + 0.689771i
\(915\) 9.51943e11 9.51943e11i 1.35808 1.35808i
\(916\) −3.89100e11 4.96581e11i −0.552688 0.705356i
\(917\) −4.44657e11 + 4.44657e11i −0.628851 + 0.628851i
\(918\) −5.37402e9 3.24887e8i −0.00756709 0.000457469i
\(919\) −8.02866e11 −1.12559 −0.562796 0.826596i \(-0.690274\pi\)
−0.562796 + 0.826596i \(0.690274\pi\)
\(920\) 1.54938e12 + 2.83772e11i 2.16275 + 0.396113i
\(921\) 4.37445e10i 0.0607974i
\(922\) −1.26491e12 7.64705e10i −1.75040 0.105821i
\(923\) 2.00909e10 + 2.00909e10i 0.0276817 + 0.0276817i
\(924\) 4.27807e10 3.52529e11i 0.0586895 0.483623i
\(925\) 7.70956e11 + 7.70956e11i 1.05308 + 1.05308i
\(926\) −1.22370e11 1.38117e11i −0.166429 0.187847i
\(927\) 8.05972e9i 0.0109144i
\(928\) −1.27304e12 3.96460e11i −1.71652 0.534574i
\(929\) −3.06353e11 −0.411301 −0.205650 0.978626i \(-0.565931\pi\)
−0.205650 + 0.978626i \(0.565931\pi\)
\(930\) −6.22531e11 + 5.51551e11i −0.832202 + 0.737317i
\(931\) 2.00206e11 2.00206e11i 0.266489 0.266489i
\(932\) −3.69540e11 4.48451e10i −0.489776 0.0594362i
\(933\) −6.59590e9 + 6.59590e9i −0.00870458 + 0.00870458i
\(934\) 8.26955e10 1.36788e12i 0.108666 1.79747i
\(935\) 6.31513e10 0.0826297
\(936\) −1.68942e11 3.09423e10i −0.220108 0.0403133i
\(937\) 4.34977e11i 0.564298i 0.959371 + 0.282149i \(0.0910472\pi\)
−0.959371 + 0.282149i \(0.908953\pi\)
\(938\) −2.00206e10 + 3.31165e11i −0.0258623 + 0.427793i
\(939\) 2.62737e11 + 2.62737e11i 0.337955 + 0.337955i
\(940\) 1.87048e12 1.46563e12i 2.39575 1.87721i
\(941\) −6.39363e11 6.39363e11i −0.815435 0.815435i 0.170008 0.985443i \(-0.445621\pi\)
−0.985443 + 0.170008i \(0.945621\pi\)
\(942\) −1.77596e11 + 1.57347e11i −0.225543 + 0.199827i
\(943\) 5.52451e10i 0.0698630i
\(944\) −1.89232e11 3.12933e11i −0.238290 0.394061i
\(945\) 2.15259e11 0.269919
\(946\) −6.25837e11 7.06377e11i −0.781442 0.882006i
\(947\) 3.58891e11 3.58891e11i 0.446234 0.446234i −0.447866 0.894101i \(-0.647816\pi\)
0.894101 + 0.447866i \(0.147816\pi\)
\(948\) 4.58546e11 3.59298e11i 0.567740 0.444858i
\(949\) −1.63815e11 + 1.63815e11i −0.201971 + 0.201971i
\(950\) −1.74827e12 1.05692e11i −2.14642 0.129762i
\(951\) −1.23416e11 −0.150886
\(952\) −1.38078e10 1.99997e10i −0.0168103 0.0243487i
\(953\) 2.38302e11i 0.288906i −0.989512 0.144453i \(-0.953858\pi\)
0.989512 0.144453i \(-0.0461422\pi\)
\(954\) −3.77457e11 2.28192e10i −0.455694 0.0275491i
\(955\) 2.02775e12 + 2.02775e12i 2.43782 + 2.43782i
\(956\) 1.32769e12 + 1.61120e11i 1.58952 + 0.192894i
\(957\) −6.91596e11 6.91596e11i −0.824527 0.824527i
\(958\) 2.14066e11 + 2.41614e11i 0.254147 + 0.286854i
\(959\) 4.70601e11i 0.556388i
\(960\) −8.56209e11 3.24520e11i −1.00808 0.382082i
\(961\) −5.42938e10 −0.0636585
\(962\) −2.57734e11 + 2.28348e11i −0.300934 + 0.266623i
\(963\) −1.71452e11 + 1.71452e11i −0.199359 + 0.199359i
\(964\) 2.40673e10 1.98324e11i 0.0278689 0.229650i
\(965\) 7.52951e11 7.52951e11i 0.868276 0.868276i
\(966\) 2.68329e10 4.43849e11i 0.0308148 0.509714i
\(967\) −3.15345e11 −0.360646 −0.180323 0.983607i \(-0.557714\pi\)
−0.180323 + 0.983607i \(0.557714\pi\)
\(968\) −1.89307e11 + 1.30697e11i −0.215608 + 0.148856i
\(969\) 1.73393e10i 0.0196670i
\(970\) −3.59399e10 + 5.94488e11i −0.0405966 + 0.671516i
\(971\) 4.76364e11 + 4.76364e11i 0.535873 + 0.535873i 0.922314 0.386441i \(-0.126296\pi\)
−0.386441 + 0.922314i \(0.626296\pi\)
\(972\) 3.53172e10 + 4.50729e10i 0.0395659 + 0.0504952i
\(973\) −9.66365e10 9.66365e10i −0.107818 0.107818i
\(974\) −1.00467e11 + 8.90122e10i −0.111632 + 0.0989040i
\(975\) 8.70946e11i 0.963768i
\(976\) 8.36506e11 + 1.38333e12i 0.921870 + 1.52450i
\(977\) 3.02281e11 0.331767 0.165884 0.986145i \(-0.446952\pi\)
0.165884 + 0.986145i \(0.446952\pi\)
\(978\) 2.41117e11 + 2.72146e11i 0.263555 + 0.297472i
\(979\) −1.23432e12 + 1.23432e12i −1.34368 + 1.34368i
\(980\) −4.62946e11 5.90826e11i −0.501911 0.640553i
\(981\) 2.69201e11 2.69201e11i 0.290671 0.290671i
\(982\) −7.88329e11 4.76586e10i −0.847738 0.0512501i
\(983\) 2.07599e11 0.222337 0.111169 0.993802i \(-0.464541\pi\)
0.111169 + 0.993802i \(0.464541\pi\)
\(984\) −5.78560e9 + 3.15890e10i −0.00617118 + 0.0336942i
\(985\) 3.01529e12i 3.20320i
\(986\) −6.68142e10 4.03926e9i −0.0706905 0.00427360i
\(987\) −4.74340e11 4.74340e11i −0.499829 0.499829i
\(988\) 6.66382e10 5.49123e11i 0.0699351 0.576291i
\(989\) −8.35591e11 8.35591e11i −0.873391 0.873391i
\(990\) −4.45413e11 5.02734e11i −0.463684 0.523356i
\(991\) 1.37199e12i 1.42252i 0.702930 + 0.711259i \(0.251875\pi\)
−0.702930 + 0.711259i \(0.748125\pi\)
\(992\) −4.64281e11 8.84253e11i −0.479440 0.913124i
\(993\) 4.37426e11 0.449891
\(994\) 3.20059e10 2.83566e10i 0.0327857 0.0290475i
\(995\) −9.31125e11 + 9.31125e11i −0.949983 + 0.949983i
\(996\) −4.71173e10 5.71786e9i −0.0478788 0.00581027i
\(997\) 1.57772e11 1.57772e11i 0.159679 0.159679i −0.622745 0.782425i \(-0.713983\pi\)
0.782425 + 0.622745i \(0.213983\pi\)
\(998\) −2.02888e10 + 3.35600e11i −0.0204519 + 0.338298i
\(999\) 1.14801e11 0.115261
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 48.9.l.a.19.8 64
4.3 odd 2 192.9.l.a.175.1 64
16.5 even 4 192.9.l.a.79.1 64
16.11 odd 4 inner 48.9.l.a.43.8 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.9.l.a.19.8 64 1.1 even 1 trivial
48.9.l.a.43.8 yes 64 16.11 odd 4 inner
192.9.l.a.79.1 64 16.5 even 4
192.9.l.a.175.1 64 4.3 odd 2