Properties

Label 126.9.n.d.73.8
Level $126$
Weight $9$
Character 126.73
Analytic conductor $51.330$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,9,Mod(19,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.19");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 126.n (of order \(6\), 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: \(51.3297048677\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 8 x^{19} - 26382 x^{18} + 177344 x^{17} + 298653216 x^{16} - 1823810808 x^{15} - 1891249463672 x^{14} + 11806020599312 x^{13} + \cdots + 42\!\cdots\!32 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{40}\cdot 3^{18}\cdot 7^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 73.8
Root \(4.08415 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 126.73
Dual form 126.9.n.d.19.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(254.021 - 146.659i) q^{5} +(-1180.12 + 2090.96i) q^{7} -1448.15 q^{8} +O(q^{10})\) \(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(254.021 - 146.659i) q^{5} +(-1180.12 + 2090.96i) q^{7} -1448.15 q^{8} +(2873.92 + 1659.26i) q^{10} +(-9846.02 + 17053.8i) q^{11} -27364.3i q^{13} +(-27162.9 + 265.506i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(41400.9 + 23902.8i) q^{17} +(72270.1 - 41725.2i) q^{19} +37544.8i q^{20} -222790. q^{22} +(-64660.1 - 111995. i) q^{23} +(-152295. + 263782. i) q^{25} +(268114. - 154796. i) q^{26} +(-156258. - 264639. i) q^{28} -710274. q^{29} +(-384515. - 222000. i) q^{31} +(92681.9 - 160530. i) q^{32} +540859. i q^{34} +(6883.50 + 704224. i) q^{35} +(176834. + 306285. i) q^{37} +(817643. + 472066. i) q^{38} +(-367862. + 212385. i) q^{40} -3.55628e6i q^{41} -6.52843e6 q^{43} +(-1.26029e6 - 2.18289e6i) q^{44} +(731546. - 1.26707e6i) q^{46} +(-965165. + 557238. i) q^{47} +(-2.97944e6 - 4.93517e6i) q^{49} -3.44603e6 q^{50} +(3.03337e6 + 1.75132e6i) q^{52} +(5.98041e6 - 1.03584e7i) q^{53} +5.77604e6i q^{55} +(1.70899e6 - 3.02804e6i) q^{56} +(-4.01792e6 - 6.95924e6i) q^{58} +(-1.01480e7 - 5.85894e6i) q^{59} +(1.13956e7 - 6.57926e6i) q^{61} -5.02328e6i q^{62} +2.09715e6 q^{64} +(-4.01323e6 - 6.95112e6i) q^{65} +(-7.88693e6 + 1.36606e7i) q^{67} +(-5.29931e6 + 3.05956e6i) q^{68} +(-6.86102e6 + 4.05114e6i) q^{70} -2.41198e7 q^{71} +(1.51799e7 + 8.76413e6i) q^{73} +(-2.00065e6 + 3.46522e6i) q^{74} +1.06816e7i q^{76} +(-2.40394e7 - 4.07132e7i) q^{77} +(3.57217e6 + 6.18718e6i) q^{79} +(-4.16188e6 - 2.40287e6i) q^{80} +(3.48443e7 - 2.01173e7i) q^{82} -6.34086e7i q^{83} +1.40223e7 q^{85} +(-3.69304e7 - 6.39653e7i) q^{86} +(1.42586e7 - 2.46965e7i) q^{88} +(7.67936e7 - 4.43368e7i) q^{89} +(5.72177e7 + 3.22931e7i) q^{91} +1.65530e7 q^{92} +(-1.09196e7 - 6.30443e6i) q^{94} +(1.22388e7 - 2.11982e7i) q^{95} -6.52152e7i q^{97} +(3.15003e7 - 5.71099e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 1280 q^{4} + 4186 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 1280 q^{4} + 4186 q^{7} - 17664 q^{10} - 163840 q^{16} - 250890 q^{19} + 420864 q^{22} + 258962 q^{25} - 1189888 q^{28} + 342762 q^{31} - 4806598 q^{37} + 2260992 q^{40} + 6968252 q^{43} - 4357632 q^{46} - 26046538 q^{49} + 2075904 q^{52} + 2455296 q^{58} - 15410424 q^{61} + 41943040 q^{64} - 70041074 q^{67} - 25804800 q^{70} + 220264098 q^{73} + 12860578 q^{79} + 12085248 q^{82} + 29161632 q^{85} - 26935296 q^{88} - 311022894 q^{91} + 332230656 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.65685 + 9.79796i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −64.0000 + 110.851i −0.250000 + 0.433013i
\(5\) 254.021 146.659i 0.406434 0.234655i −0.282822 0.959172i \(-0.591271\pi\)
0.689256 + 0.724517i \(0.257937\pi\)
\(6\) 0 0
\(7\) −1180.12 + 2090.96i −0.491511 + 0.870871i
\(8\) −1448.15 −0.353553
\(9\) 0 0
\(10\) 2873.92 + 1659.26i 0.287392 + 0.165926i
\(11\) −9846.02 + 17053.8i −0.672496 + 1.16480i 0.304698 + 0.952449i \(0.401445\pi\)
−0.977194 + 0.212348i \(0.931889\pi\)
\(12\) 0 0
\(13\) 27364.3i 0.958101i −0.877787 0.479050i \(-0.840981\pi\)
0.877787 0.479050i \(-0.159019\pi\)
\(14\) −27162.9 + 265.506i −0.707073 + 0.00691135i
\(15\) 0 0
\(16\) −8192.00 14189.0i −0.125000 0.216506i
\(17\) 41400.9 + 23902.8i 0.495694 + 0.286189i 0.726934 0.686708i \(-0.240945\pi\)
−0.231239 + 0.972897i \(0.574278\pi\)
\(18\) 0 0
\(19\) 72270.1 41725.2i 0.554555 0.320172i −0.196402 0.980523i \(-0.562926\pi\)
0.750957 + 0.660351i \(0.229593\pi\)
\(20\) 37544.8i 0.234655i
\(21\) 0 0
\(22\) −222790. −0.951053
\(23\) −64660.1 111995.i −0.231060 0.400208i 0.727060 0.686574i \(-0.240886\pi\)
−0.958120 + 0.286366i \(0.907553\pi\)
\(24\) 0 0
\(25\) −152295. + 263782.i −0.389874 + 0.675282i
\(26\) 268114. 154796.i 0.586714 0.338740i
\(27\) 0 0
\(28\) −156258. 264639.i −0.254220 0.430548i
\(29\) −710274. −1.00423 −0.502116 0.864800i \(-0.667445\pi\)
−0.502116 + 0.864800i \(0.667445\pi\)
\(30\) 0 0
\(31\) −384515. 222000.i −0.416358 0.240384i 0.277160 0.960824i \(-0.410607\pi\)
−0.693518 + 0.720440i \(0.743940\pi\)
\(32\) 92681.9 160530.i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 540859.i 0.404733i
\(35\) 6883.50 + 704224.i 0.00458709 + 0.469287i
\(36\) 0 0
\(37\) 176834. + 306285.i 0.0943537 + 0.163425i 0.909339 0.416057i \(-0.136588\pi\)
−0.814985 + 0.579482i \(0.803255\pi\)
\(38\) 817643. + 472066.i 0.392129 + 0.226396i
\(39\) 0 0
\(40\) −367862. + 212385.i −0.143696 + 0.0829630i
\(41\) 3.55628e6i 1.25852i −0.777195 0.629260i \(-0.783358\pi\)
0.777195 0.629260i \(-0.216642\pi\)
\(42\) 0 0
\(43\) −6.52843e6 −1.90957 −0.954784 0.297300i \(-0.903914\pi\)
−0.954784 + 0.297300i \(0.903914\pi\)
\(44\) −1.26029e6 2.18289e6i −0.336248 0.582399i
\(45\) 0 0
\(46\) 731546. 1.26707e6i 0.163384 0.282990i
\(47\) −965165. + 557238.i −0.197793 + 0.114196i −0.595625 0.803262i \(-0.703096\pi\)
0.397833 + 0.917458i \(0.369762\pi\)
\(48\) 0 0
\(49\) −2.97944e6 4.93517e6i −0.516833 0.856086i
\(50\) −3.44603e6 −0.551365
\(51\) 0 0
\(52\) 3.03337e6 + 1.75132e6i 0.414870 + 0.239525i
\(53\) 5.98041e6 1.03584e7i 0.757927 1.31277i −0.185978 0.982554i \(-0.559545\pi\)
0.943906 0.330215i \(-0.107121\pi\)
\(54\) 0 0
\(55\) 5.77604e6i 0.631218i
\(56\) 1.70899e6 3.02804e6i 0.173776 0.307899i
\(57\) 0 0
\(58\) −4.01792e6 6.95924e6i −0.355050 0.614964i
\(59\) −1.01480e7 5.85894e6i −0.837474 0.483516i 0.0189306 0.999821i \(-0.493974\pi\)
−0.856405 + 0.516305i \(0.827307\pi\)
\(60\) 0 0
\(61\) 1.13956e7 6.57926e6i 0.823035 0.475180i −0.0284268 0.999596i \(-0.509050\pi\)
0.851462 + 0.524416i \(0.175716\pi\)
\(62\) 5.02328e6i 0.339955i
\(63\) 0 0
\(64\) 2.09715e6 0.125000
\(65\) −4.01323e6 6.95112e6i −0.224823 0.389405i
\(66\) 0 0
\(67\) −7.88693e6 + 1.36606e7i −0.391389 + 0.677906i −0.992633 0.121160i \(-0.961339\pi\)
0.601244 + 0.799066i \(0.294672\pi\)
\(68\) −5.29931e6 + 3.05956e6i −0.247847 + 0.143095i
\(69\) 0 0
\(70\) −6.86102e6 + 4.05114e6i −0.285757 + 0.168727i
\(71\) −2.41198e7 −0.949161 −0.474580 0.880212i \(-0.657400\pi\)
−0.474580 + 0.880212i \(0.657400\pi\)
\(72\) 0 0
\(73\) 1.51799e7 + 8.76413e6i 0.534537 + 0.308615i 0.742862 0.669445i \(-0.233468\pi\)
−0.208325 + 0.978060i \(0.566801\pi\)
\(74\) −2.00065e6 + 3.46522e6i −0.0667181 + 0.115559i
\(75\) 0 0
\(76\) 1.06816e7i 0.320172i
\(77\) −2.40394e7 4.07132e7i −0.683849 1.15817i
\(78\) 0 0
\(79\) 3.57217e6 + 6.18718e6i 0.0917115 + 0.158849i 0.908231 0.418468i \(-0.137433\pi\)
−0.816520 + 0.577317i \(0.804100\pi\)
\(80\) −4.16188e6 2.40287e6i −0.101609 0.0586637i
\(81\) 0 0
\(82\) 3.48443e7 2.01173e7i 0.770683 0.444954i
\(83\) 6.34086e7i 1.33609i −0.744121 0.668045i \(-0.767131\pi\)
0.744121 0.668045i \(-0.232869\pi\)
\(84\) 0 0
\(85\) 1.40223e7 0.268623
\(86\) −3.69304e7 6.39653e7i −0.675134 1.16937i
\(87\) 0 0
\(88\) 1.42586e7 2.46965e7i 0.237763 0.411818i
\(89\) 7.67936e7 4.43368e7i 1.22395 0.706650i 0.258195 0.966093i \(-0.416872\pi\)
0.965758 + 0.259443i \(0.0835391\pi\)
\(90\) 0 0
\(91\) 5.72177e7 + 3.22931e7i 0.834382 + 0.470917i
\(92\) 1.65530e7 0.231060
\(93\) 0 0
\(94\) −1.09196e7 6.30443e6i −0.139861 0.0807485i
\(95\) 1.22388e7 2.11982e7i 0.150260 0.260258i
\(96\) 0 0
\(97\) 6.52152e7i 0.736651i −0.929697 0.368325i \(-0.879931\pi\)
0.929697 0.368325i \(-0.120069\pi\)
\(98\) 3.15003e7 5.71099e7i 0.341516 0.619166i
\(99\) 0 0
\(100\) −1.94937e7 3.37641e7i −0.194937 0.337641i
\(101\) −1.53138e8 8.84145e7i −1.47163 0.849646i −0.472138 0.881525i \(-0.656518\pi\)
−0.999492 + 0.0318791i \(0.989851\pi\)
\(102\) 0 0
\(103\) −9.89388e7 + 5.71223e7i −0.879059 + 0.507525i −0.870348 0.492437i \(-0.836106\pi\)
−0.00871065 + 0.999962i \(0.502773\pi\)
\(104\) 3.96278e7i 0.338740i
\(105\) 0 0
\(106\) 1.35321e8 1.07187
\(107\) −7.14037e6 1.23675e7i −0.0544736 0.0943510i 0.837503 0.546433i \(-0.184015\pi\)
−0.891976 + 0.452082i \(0.850681\pi\)
\(108\) 0 0
\(109\) −1.01815e8 + 1.76349e8i −0.721283 + 1.24930i 0.239203 + 0.970970i \(0.423114\pi\)
−0.960486 + 0.278329i \(0.910220\pi\)
\(110\) −5.65934e7 + 3.26742e7i −0.386540 + 0.223169i
\(111\) 0 0
\(112\) 3.93361e7 384494.i 0.249988 0.00244353i
\(113\) −8.03050e7 −0.492525 −0.246263 0.969203i \(-0.579203\pi\)
−0.246263 + 0.969203i \(0.579203\pi\)
\(114\) 0 0
\(115\) −3.28501e7 1.89660e7i −0.187822 0.108439i
\(116\) 4.54576e7 7.87348e7i 0.251058 0.434845i
\(117\) 0 0
\(118\) 1.32573e8i 0.683795i
\(119\) −9.88378e7 + 5.83595e7i −0.492873 + 0.291020i
\(120\) 0 0
\(121\) −8.67086e7 1.50184e8i −0.404502 0.700618i
\(122\) 1.28927e8 + 7.44358e7i 0.581974 + 0.336003i
\(123\) 0 0
\(124\) 4.92179e7 2.84160e7i 0.208179 0.120192i
\(125\) 2.03919e8i 0.835253i
\(126\) 0 0
\(127\) −3.26436e8 −1.25483 −0.627413 0.778687i \(-0.715886\pi\)
−0.627413 + 0.778687i \(0.715886\pi\)
\(128\) 1.18633e7 + 2.05478e7i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 4.54045e7 7.86429e7i 0.158974 0.275351i
\(131\) 1.32553e8 7.65293e7i 0.450094 0.259862i −0.257776 0.966205i \(-0.582990\pi\)
0.707870 + 0.706343i \(0.249656\pi\)
\(132\) 0 0
\(133\) 1.95839e6 + 2.00355e8i 0.00625881 + 0.640314i
\(134\) −1.78461e8 −0.553508
\(135\) 0 0
\(136\) −5.99549e7 3.46150e7i −0.175254 0.101183i
\(137\) 6.64691e7 1.15128e8i 0.188685 0.326812i −0.756127 0.654425i \(-0.772911\pi\)
0.944812 + 0.327613i \(0.106244\pi\)
\(138\) 0 0
\(139\) 5.38269e8i 1.44192i 0.692978 + 0.720958i \(0.256298\pi\)
−0.692978 + 0.720958i \(0.743702\pi\)
\(140\) −7.85047e7 4.43073e7i −0.204354 0.115336i
\(141\) 0 0
\(142\) −1.36442e8 2.36325e8i −0.335579 0.581240i
\(143\) 4.66666e8 + 2.69429e8i 1.11599 + 0.644319i
\(144\) 0 0
\(145\) −1.80425e8 + 1.04168e8i −0.408154 + 0.235648i
\(146\) 1.98310e8i 0.436448i
\(147\) 0 0
\(148\) −4.52695e7 −0.0943537
\(149\) 2.76227e8 + 4.78439e8i 0.560429 + 0.970691i 0.997459 + 0.0712445i \(0.0226971\pi\)
−0.437030 + 0.899447i \(0.643970\pi\)
\(150\) 0 0
\(151\) −2.57729e7 + 4.46400e7i −0.0495742 + 0.0858650i −0.889748 0.456453i \(-0.849120\pi\)
0.840173 + 0.542318i \(0.182453\pi\)
\(152\) −1.04658e8 + 6.04245e7i −0.196065 + 0.113198i
\(153\) 0 0
\(154\) 2.62919e8 4.65845e8i 0.467454 0.828245i
\(155\) −1.30233e8 −0.225629
\(156\) 0 0
\(157\) −1.43245e8 8.27027e7i −0.235766 0.136120i 0.377463 0.926025i \(-0.376796\pi\)
−0.613229 + 0.789905i \(0.710130\pi\)
\(158\) −4.04145e7 + 6.99999e7i −0.0648498 + 0.112323i
\(159\) 0 0
\(160\) 5.43706e7i 0.0829630i
\(161\) 3.10483e8 3.03485e6i 0.462098 0.00451682i
\(162\) 0 0
\(163\) 6.57420e7 + 1.13868e8i 0.0931306 + 0.161307i 0.908827 0.417174i \(-0.136979\pi\)
−0.815696 + 0.578480i \(0.803646\pi\)
\(164\) 3.94218e8 + 2.27602e8i 0.544955 + 0.314630i
\(165\) 0 0
\(166\) 6.21275e8 3.58693e8i 0.818184 0.472379i
\(167\) 1.02034e9i 1.31184i 0.754832 + 0.655918i \(0.227718\pi\)
−0.754832 + 0.655918i \(0.772282\pi\)
\(168\) 0 0
\(169\) 6.69250e7 0.0820430
\(170\) 7.93219e7 + 1.37390e8i 0.0949725 + 0.164497i
\(171\) 0 0
\(172\) 4.17820e8 7.23685e8i 0.477392 0.826867i
\(173\) 1.16632e8 6.73374e7i 0.130206 0.0751747i −0.433482 0.901162i \(-0.642715\pi\)
0.563688 + 0.825988i \(0.309382\pi\)
\(174\) 0 0
\(175\) −3.71832e8 6.29736e8i −0.396456 0.671439i
\(176\) 3.22634e8 0.336248
\(177\) 0 0
\(178\) 8.68820e8 + 5.01613e8i 0.865465 + 0.499677i
\(179\) −6.71392e8 + 1.16289e9i −0.653979 + 1.13273i 0.328169 + 0.944619i \(0.393568\pi\)
−0.982149 + 0.188107i \(0.939765\pi\)
\(180\) 0 0
\(181\) 1.66215e9i 1.54866i 0.632784 + 0.774328i \(0.281912\pi\)
−0.632784 + 0.774328i \(0.718088\pi\)
\(182\) 7.26540e6 + 7.43295e8i 0.00662177 + 0.677447i
\(183\) 0 0
\(184\) 9.36379e7 + 1.62186e8i 0.0816921 + 0.141495i
\(185\) 8.98392e7 + 5.18687e7i 0.0766971 + 0.0442811i
\(186\) 0 0
\(187\) −8.15267e8 + 4.70695e8i −0.666705 + 0.384922i
\(188\) 1.42653e8i 0.114196i
\(189\) 0 0
\(190\) 2.76932e8 0.212500
\(191\) 4.00858e8 + 6.94306e8i 0.301201 + 0.521696i 0.976408 0.215932i \(-0.0692790\pi\)
−0.675207 + 0.737628i \(0.735946\pi\)
\(192\) 0 0
\(193\) −5.88128e8 + 1.01867e9i −0.423879 + 0.734181i −0.996315 0.0857690i \(-0.972665\pi\)
0.572436 + 0.819950i \(0.305999\pi\)
\(194\) 6.38976e8 3.68913e8i 0.451105 0.260445i
\(195\) 0 0
\(196\) 7.37754e8 1.44239e7i 0.499904 0.00977366i
\(197\) 3.83159e8 0.254398 0.127199 0.991877i \(-0.459401\pi\)
0.127199 + 0.991877i \(0.459401\pi\)
\(198\) 0 0
\(199\) 1.90479e9 + 1.09973e9i 1.21460 + 0.701252i 0.963759 0.266775i \(-0.0859580\pi\)
0.250846 + 0.968027i \(0.419291\pi\)
\(200\) 2.20546e8 3.81997e8i 0.137841 0.238748i
\(201\) 0 0
\(202\) 2.00059e9i 1.20158i
\(203\) 8.38208e8 1.48516e9i 0.493592 0.874557i
\(204\) 0 0
\(205\) −5.21561e8 9.03370e8i −0.295318 0.511506i
\(206\) −1.11936e9 6.46266e8i −0.621588 0.358874i
\(207\) 0 0
\(208\) −3.88271e8 + 2.24168e8i −0.207435 + 0.119763i
\(209\) 1.64331e9i 0.861258i
\(210\) 0 0
\(211\) 8.01623e8 0.404427 0.202213 0.979341i \(-0.435187\pi\)
0.202213 + 0.979341i \(0.435187\pi\)
\(212\) 7.65493e8 + 1.32587e9i 0.378964 + 0.656384i
\(213\) 0 0
\(214\) 8.07841e7 1.39922e8i 0.0385186 0.0667162i
\(215\) −1.65836e9 + 9.57455e8i −0.776114 + 0.448089i
\(216\) 0 0
\(217\) 9.17967e8 5.42020e8i 0.413988 0.244442i
\(218\) −2.30381e9 −1.02005
\(219\) 0 0
\(220\) −6.40281e8 3.69666e8i −0.273325 0.157804i
\(221\) 6.54084e8 1.13291e9i 0.274198 0.474925i
\(222\) 0 0
\(223\) 1.04630e9i 0.423095i −0.977368 0.211548i \(-0.932150\pi\)
0.977368 0.211548i \(-0.0678503\pi\)
\(224\) 2.26286e8 + 3.83239e8i 0.0898805 + 0.152222i
\(225\) 0 0
\(226\) −4.54273e8 7.86825e8i −0.174134 0.301609i
\(227\) −1.84193e9 1.06344e9i −0.693697 0.400506i 0.111299 0.993787i \(-0.464499\pi\)
−0.804996 + 0.593281i \(0.797832\pi\)
\(228\) 0 0
\(229\) −4.04718e9 + 2.33664e9i −1.47167 + 0.849670i −0.999493 0.0318328i \(-0.989866\pi\)
−0.472179 + 0.881503i \(0.656532\pi\)
\(230\) 4.29152e8i 0.153356i
\(231\) 0 0
\(232\) 1.02859e9 0.355050
\(233\) −1.30399e9 2.25857e9i −0.442435 0.766320i 0.555435 0.831560i \(-0.312552\pi\)
−0.997870 + 0.0652405i \(0.979219\pi\)
\(234\) 0 0
\(235\) −1.63448e8 + 2.83101e8i −0.0535931 + 0.0928260i
\(236\) 1.29894e9 7.49944e8i 0.418737 0.241758i
\(237\) 0 0
\(238\) −1.13091e9 6.38278e8i −0.352470 0.198931i
\(239\) 2.50883e9 0.768917 0.384459 0.923142i \(-0.374388\pi\)
0.384459 + 0.923142i \(0.374388\pi\)
\(240\) 0 0
\(241\) −1.39883e9 8.07613e8i −0.414664 0.239406i 0.278128 0.960544i \(-0.410286\pi\)
−0.692792 + 0.721138i \(0.743619\pi\)
\(242\) 9.80996e8 1.69914e9i 0.286026 0.495412i
\(243\) 0 0
\(244\) 1.68429e9i 0.475180i
\(245\) −1.48063e9 8.16675e8i −0.410943 0.226665i
\(246\) 0 0
\(247\) −1.14178e9 1.97762e9i −0.306757 0.531319i
\(248\) 5.56837e8 + 3.21490e8i 0.147205 + 0.0849887i
\(249\) 0 0
\(250\) −1.99799e9 + 1.15354e9i −0.511486 + 0.295307i
\(251\) 7.67075e9i 1.93260i −0.257411 0.966302i \(-0.582869\pi\)
0.257411 0.966302i \(-0.417131\pi\)
\(252\) 0 0
\(253\) 2.54658e9 0.621549
\(254\) −1.84660e9 3.19841e9i −0.443648 0.768421i
\(255\) 0 0
\(256\) −1.34218e8 + 2.32472e8i −0.0312500 + 0.0541266i
\(257\) 9.62997e7 5.55987e7i 0.0220746 0.0127448i −0.488922 0.872327i \(-0.662610\pi\)
0.510997 + 0.859583i \(0.329276\pi\)
\(258\) 0 0
\(259\) −8.49116e8 + 8.29976e6i −0.188698 + 0.00184445i
\(260\) 1.02739e9 0.224823
\(261\) 0 0
\(262\) 1.49966e9 + 8.65830e8i 0.318264 + 0.183750i
\(263\) 1.92395e9 3.33238e9i 0.402135 0.696518i −0.591849 0.806049i \(-0.701602\pi\)
0.993983 + 0.109532i \(0.0349351\pi\)
\(264\) 0 0
\(265\) 3.50833e9i 0.711405i
\(266\) −1.95199e9 + 1.15257e9i −0.389898 + 0.230218i
\(267\) 0 0
\(268\) −1.00953e9 1.74855e9i −0.195695 0.338953i
\(269\) −3.56338e9 2.05732e9i −0.680539 0.392909i 0.119519 0.992832i \(-0.461865\pi\)
−0.800058 + 0.599922i \(0.795198\pi\)
\(270\) 0 0
\(271\) −5.46088e9 + 3.15284e9i −1.01248 + 0.584554i −0.911916 0.410377i \(-0.865397\pi\)
−0.100561 + 0.994931i \(0.532064\pi\)
\(272\) 7.83247e8i 0.143095i
\(273\) 0 0
\(274\) 1.50402e9 0.266841
\(275\) −2.99899e9 5.19440e9i −0.524378 0.908249i
\(276\) 0 0
\(277\) 8.46807e7 1.46671e8i 0.0143835 0.0249130i −0.858744 0.512405i \(-0.828755\pi\)
0.873128 + 0.487492i \(0.162088\pi\)
\(278\) −5.27394e9 + 3.04491e9i −0.882990 + 0.509795i
\(279\) 0 0
\(280\) −9.96838e6 1.01983e9i −0.00162178 0.165918i
\(281\) −4.27204e9 −0.685188 −0.342594 0.939484i \(-0.611306\pi\)
−0.342594 + 0.939484i \(0.611306\pi\)
\(282\) 0 0
\(283\) 7.97705e9 + 4.60555e9i 1.24364 + 0.718019i 0.969834 0.243765i \(-0.0783825\pi\)
0.273811 + 0.961784i \(0.411716\pi\)
\(284\) 1.54367e9 2.67371e9i 0.237290 0.410999i
\(285\) 0 0
\(286\) 6.09649e9i 0.911205i
\(287\) 7.43604e9 + 4.19683e9i 1.09601 + 0.618577i
\(288\) 0 0
\(289\) −2.34519e9 4.06199e9i −0.336191 0.582301i
\(290\) −2.04127e9 1.17853e9i −0.288609 0.166628i
\(291\) 0 0
\(292\) −1.94303e9 + 1.12181e9i −0.267269 + 0.154308i
\(293\) 6.22459e9i 0.844578i 0.906461 + 0.422289i \(0.138773\pi\)
−0.906461 + 0.422289i \(0.861227\pi\)
\(294\) 0 0
\(295\) −3.43707e9 −0.453837
\(296\) −2.56083e8 4.43549e8i −0.0333591 0.0577796i
\(297\) 0 0
\(298\) −3.12515e9 + 5.41292e9i −0.396283 + 0.686383i
\(299\) −3.06466e9 + 1.76938e9i −0.383440 + 0.221379i
\(300\) 0 0
\(301\) 7.70433e9 1.36507e10i 0.938575 1.66299i
\(302\) −5.83174e8 −0.0701085
\(303\) 0 0
\(304\) −1.18407e9 6.83625e8i −0.138639 0.0800431i
\(305\) 1.92982e9 3.34254e9i 0.223006 0.386258i
\(306\) 0 0
\(307\) 9.75323e9i 1.09798i 0.835829 + 0.548991i \(0.184988\pi\)
−0.835829 + 0.548991i \(0.815012\pi\)
\(308\) 6.05162e9 5.91522e7i 0.672464 0.00657306i
\(309\) 0 0
\(310\) −7.36711e8 1.27602e9i −0.0797720 0.138169i
\(311\) −1.41768e10 8.18496e9i −1.51543 0.874933i −0.999836 0.0180989i \(-0.994239\pi\)
−0.515592 0.856834i \(-0.672428\pi\)
\(312\) 0 0
\(313\) 1.41041e10 8.14301e9i 1.46950 0.848414i 0.470081 0.882623i \(-0.344225\pi\)
0.999415 + 0.0342090i \(0.0108912\pi\)
\(314\) 1.87135e9i 0.192502i
\(315\) 0 0
\(316\) −9.14475e8 −0.0917115
\(317\) 5.18198e9 + 8.97545e9i 0.513167 + 0.888831i 0.999883 + 0.0152710i \(0.00486110\pi\)
−0.486717 + 0.873560i \(0.661806\pi\)
\(318\) 0 0
\(319\) 6.99337e9 1.21129e10i 0.675342 1.16973i
\(320\) 5.32721e8 3.07567e8i 0.0508043 0.0293319i
\(321\) 0 0
\(322\) 1.78609e9 + 3.02493e9i 0.166142 + 0.281379i
\(323\) 3.98939e9 0.366519
\(324\) 0 0
\(325\) 7.21821e9 + 4.16744e9i 0.646988 + 0.373539i
\(326\) −7.43785e8 + 1.28827e9i −0.0658533 + 0.114061i
\(327\) 0 0
\(328\) 5.15004e9i 0.444954i
\(329\) −2.61542e7 2.67573e9i −0.00223233 0.228380i
\(330\) 0 0
\(331\) −1.08132e9 1.87289e9i −0.0900825 0.156027i 0.817463 0.575981i \(-0.195380\pi\)
−0.907546 + 0.419953i \(0.862046\pi\)
\(332\) 7.02892e9 + 4.05815e9i 0.578544 + 0.334022i
\(333\) 0 0
\(334\) −9.99726e9 + 5.77192e9i −0.803332 + 0.463804i
\(335\) 4.62677e9i 0.367365i
\(336\) 0 0
\(337\) 1.73513e9 0.134528 0.0672640 0.997735i \(-0.478573\pi\)
0.0672640 + 0.997735i \(0.478573\pi\)
\(338\) 3.78585e8 + 6.55729e8i 0.0290066 + 0.0502409i
\(339\) 0 0
\(340\) −8.97425e8 + 1.55439e9i −0.0671557 + 0.116317i
\(341\) 7.57188e9 4.37163e9i 0.559998 0.323315i
\(342\) 0 0
\(343\) 1.38353e10 4.05808e8i 0.999570 0.0293186i
\(344\) 9.45418e9 0.675134
\(345\) 0 0
\(346\) 1.31954e9 + 7.61836e8i 0.0920699 + 0.0531566i
\(347\) −4.70131e8 + 8.14291e8i −0.0324266 + 0.0561645i −0.881783 0.471655i \(-0.843657\pi\)
0.849357 + 0.527819i \(0.176990\pi\)
\(348\) 0 0
\(349\) 1.33733e9i 0.0901437i −0.998984 0.0450719i \(-0.985648\pi\)
0.998984 0.0450719i \(-0.0143517\pi\)
\(350\) 4.06673e9 7.20552e9i 0.271002 0.480168i
\(351\) 0 0
\(352\) 1.82509e9 + 3.16116e9i 0.118882 + 0.205909i
\(353\) −1.04605e9 6.03937e8i −0.0673679 0.0388949i 0.465938 0.884818i \(-0.345717\pi\)
−0.533306 + 0.845923i \(0.679050\pi\)
\(354\) 0 0
\(355\) −6.12694e9 + 3.53739e9i −0.385771 + 0.222725i
\(356\) 1.13502e10i 0.706650i
\(357\) 0 0
\(358\) −1.51919e10 −0.924866
\(359\) 1.58025e10 + 2.73707e10i 0.951366 + 1.64781i 0.742473 + 0.669876i \(0.233653\pi\)
0.208893 + 0.977939i \(0.433014\pi\)
\(360\) 0 0
\(361\) −5.00980e9 + 8.67723e9i −0.294979 + 0.510919i
\(362\) −1.62857e10 + 9.40253e9i −0.948355 + 0.547533i
\(363\) 0 0
\(364\) −7.24167e9 + 4.27590e9i −0.412509 + 0.243569i
\(365\) 5.14136e9 0.289672
\(366\) 0 0
\(367\) 2.60965e8 + 1.50668e8i 0.0143853 + 0.00830533i 0.507175 0.861843i \(-0.330690\pi\)
−0.492790 + 0.870148i \(0.664023\pi\)
\(368\) −1.05939e9 + 1.83492e9i −0.0577651 + 0.100052i
\(369\) 0 0
\(370\) 1.17365e9i 0.0626229i
\(371\) 1.46014e10 + 2.47289e10i 0.770722 + 1.30530i
\(372\) 0 0
\(373\) −1.65408e10 2.86496e10i −0.854520 1.48007i −0.877090 0.480327i \(-0.840518\pi\)
0.0225698 0.999745i \(-0.492815\pi\)
\(374\) −9.22370e9 5.32530e9i −0.471432 0.272181i
\(375\) 0 0
\(376\) 1.39771e9 8.06967e8i 0.0699303 0.0403743i
\(377\) 1.94362e10i 0.962156i
\(378\) 0 0
\(379\) 2.26256e10 1.09659 0.548294 0.836285i \(-0.315277\pi\)
0.548294 + 0.836285i \(0.315277\pi\)
\(380\) 1.56656e9 + 2.71336e9i 0.0751300 + 0.130129i
\(381\) 0 0
\(382\) −4.53519e9 + 7.85518e9i −0.212981 + 0.368895i
\(383\) −2.09715e10 + 1.21079e10i −0.974616 + 0.562695i −0.900640 0.434565i \(-0.856902\pi\)
−0.0739756 + 0.997260i \(0.523569\pi\)
\(384\) 0 0
\(385\) −1.20775e10 6.81641e9i −0.549709 0.310251i
\(386\) −1.33078e10 −0.599456
\(387\) 0 0
\(388\) 7.22918e9 + 4.17377e9i 0.318979 + 0.184163i
\(389\) 5.38937e9 9.33466e9i 0.235364 0.407662i −0.724015 0.689785i \(-0.757705\pi\)
0.959378 + 0.282123i \(0.0910385\pi\)
\(390\) 0 0
\(391\) 6.18224e9i 0.264508i
\(392\) 4.31469e9 + 7.14689e9i 0.182728 + 0.302672i
\(393\) 0 0
\(394\) 2.16747e9 + 3.75417e9i 0.0899433 + 0.155786i
\(395\) 1.81481e9 + 1.04778e9i 0.0745493 + 0.0430411i
\(396\) 0 0
\(397\) −1.11612e10 + 6.44391e9i −0.449312 + 0.259410i −0.707540 0.706674i \(-0.750195\pi\)
0.258228 + 0.966084i \(0.416862\pi\)
\(398\) 2.48841e10i 0.991721i
\(399\) 0 0
\(400\) 4.99039e9 0.194937
\(401\) 3.32886e9 + 5.76576e9i 0.128742 + 0.222987i 0.923189 0.384346i \(-0.125573\pi\)
−0.794448 + 0.607333i \(0.792240\pi\)
\(402\) 0 0
\(403\) −6.07487e9 + 1.05220e10i −0.230312 + 0.398913i
\(404\) 1.96017e10 1.13171e10i 0.735815 0.424823i
\(405\) 0 0
\(406\) 1.92931e10 1.88582e8i 0.710065 0.00694060i
\(407\) −6.96444e9 −0.253810
\(408\) 0 0
\(409\) −3.21707e10 1.85737e10i −1.14965 0.663752i −0.200850 0.979622i \(-0.564370\pi\)
−0.948803 + 0.315870i \(0.897704\pi\)
\(410\) 5.90079e9 1.02205e10i 0.208821 0.361689i
\(411\) 0 0
\(412\) 1.46233e10i 0.507525i
\(413\) 2.42266e10 1.43048e10i 0.832708 0.491679i
\(414\) 0 0
\(415\) −9.29945e9 1.61071e10i −0.313520 0.543032i
\(416\) −4.39279e9 2.53618e9i −0.146679 0.0846849i
\(417\) 0 0
\(418\) −1.61011e10 + 9.29595e9i −0.527411 + 0.304501i
\(419\) 3.13974e10i 1.01868i 0.860566 + 0.509339i \(0.170110\pi\)
−0.860566 + 0.509339i \(0.829890\pi\)
\(420\) 0 0
\(421\) 9.64445e8 0.0307008 0.0153504 0.999882i \(-0.495114\pi\)
0.0153504 + 0.999882i \(0.495114\pi\)
\(422\) 4.53466e9 + 7.85426e9i 0.142987 + 0.247660i
\(423\) 0 0
\(424\) −8.66056e9 + 1.50005e10i −0.267968 + 0.464134i
\(425\) −1.26103e10 + 7.28054e9i −0.386517 + 0.223156i
\(426\) 0 0
\(427\) 3.08800e8 + 3.15921e10i 0.00928893 + 0.950314i
\(428\) 1.82794e9 0.0544736
\(429\) 0 0
\(430\) −1.87622e10 1.08324e10i −0.548795 0.316847i
\(431\) 3.21242e10 5.56407e10i 0.930943 1.61244i 0.149230 0.988803i \(-0.452321\pi\)
0.781713 0.623638i \(-0.214346\pi\)
\(432\) 0 0
\(433\) 4.85656e9i 0.138158i 0.997611 + 0.0690792i \(0.0220061\pi\)
−0.997611 + 0.0690792i \(0.977994\pi\)
\(434\) 1.05035e10 + 5.92807e9i 0.296057 + 0.167092i
\(435\) 0 0
\(436\) −1.30323e10 2.25726e10i −0.360641 0.624649i
\(437\) −9.34599e9 5.39591e9i −0.256271 0.147958i
\(438\) 0 0
\(439\) 1.97737e10 1.14163e10i 0.532389 0.307375i −0.209600 0.977787i \(-0.567216\pi\)
0.741989 + 0.670412i \(0.233883\pi\)
\(440\) 8.36460e9i 0.223169i
\(441\) 0 0
\(442\) 1.48002e10 0.387775
\(443\) −1.83252e10 3.17402e10i −0.475811 0.824129i 0.523805 0.851838i \(-0.324512\pi\)
−0.999616 + 0.0277093i \(0.991179\pi\)
\(444\) 0 0
\(445\) 1.30048e10 2.25250e10i 0.331637 0.574413i
\(446\) 1.02516e10 5.91878e9i 0.259092 0.149587i
\(447\) 0 0
\(448\) −2.47489e9 + 4.38506e9i −0.0614389 + 0.108859i
\(449\) −7.21152e10 −1.77436 −0.887179 0.461425i \(-0.847338\pi\)
−0.887179 + 0.461425i \(0.847338\pi\)
\(450\) 0 0
\(451\) 6.06480e10 + 3.50152e10i 1.46592 + 0.846350i
\(452\) 5.13952e9 8.90190e9i 0.123131 0.213270i
\(453\) 0 0
\(454\) 2.40629e10i 0.566401i
\(455\) 1.92706e10 1.88362e8i 0.449624 0.00439490i
\(456\) 0 0
\(457\) 3.00998e10 + 5.21344e10i 0.690080 + 1.19525i 0.971811 + 0.235760i \(0.0757578\pi\)
−0.281732 + 0.959493i \(0.590909\pi\)
\(458\) −4.57887e10 2.64361e10i −1.04063 0.600808i
\(459\) 0 0
\(460\) 4.20481e9 2.42765e9i 0.0939108 0.0542194i
\(461\) 8.97724e10i 1.98765i 0.110972 + 0.993824i \(0.464604\pi\)
−0.110972 + 0.993824i \(0.535396\pi\)
\(462\) 0 0
\(463\) −3.64822e10 −0.793883 −0.396942 0.917844i \(-0.629928\pi\)
−0.396942 + 0.917844i \(0.629928\pi\)
\(464\) 5.81857e9 + 1.00781e10i 0.125529 + 0.217423i
\(465\) 0 0
\(466\) 1.47529e10 2.55528e10i 0.312849 0.541870i
\(467\) −7.40477e9 + 4.27515e9i −0.155684 + 0.0898842i −0.575818 0.817578i \(-0.695316\pi\)
0.420134 + 0.907462i \(0.361983\pi\)
\(468\) 0 0
\(469\) −1.92562e10 3.26124e10i −0.397996 0.674048i
\(470\) −3.69841e9 −0.0757921
\(471\) 0 0
\(472\) 1.46958e10 + 8.48465e9i 0.296092 + 0.170949i
\(473\) 6.42791e10 1.11335e11i 1.28418 2.22426i
\(474\) 0 0
\(475\) 2.54181e10i 0.499308i
\(476\) −1.43602e8 1.46913e10i −0.00279725 0.286176i
\(477\) 0 0
\(478\) 1.41921e10 + 2.45814e10i 0.271853 + 0.470864i
\(479\) −7.84934e10 4.53182e10i −1.49105 0.860856i −0.491098 0.871104i \(-0.663404\pi\)
−0.999947 + 0.0102484i \(0.996738\pi\)
\(480\) 0 0
\(481\) 8.38129e9 4.83894e9i 0.156578 0.0904003i
\(482\) 1.82742e10i 0.338571i
\(483\) 0 0
\(484\) 2.21974e10 0.404502
\(485\) −9.56441e9 1.65660e10i −0.172859 0.299400i
\(486\) 0 0
\(487\) −2.00698e10 + 3.47619e10i −0.356802 + 0.617999i −0.987425 0.158090i \(-0.949466\pi\)
0.630623 + 0.776090i \(0.282800\pi\)
\(488\) −1.65026e10 + 9.52779e9i −0.290987 + 0.168001i
\(489\) 0 0
\(490\) −3.73952e8 1.91270e10i −0.00648682 0.331789i
\(491\) 3.33248e10 0.573379 0.286689 0.958024i \(-0.407445\pi\)
0.286689 + 0.958024i \(0.407445\pi\)
\(492\) 0 0
\(493\) −2.94060e10 1.69775e10i −0.497792 0.287400i
\(494\) 1.29178e10 2.23742e10i 0.216910 0.375699i
\(495\) 0 0
\(496\) 7.27449e9i 0.120192i
\(497\) 2.84642e10 5.04335e10i 0.466523 0.826597i
\(498\) 0 0
\(499\) 5.21701e10 + 9.03612e10i 0.841432 + 1.45740i 0.888684 + 0.458520i \(0.151620\pi\)
−0.0472517 + 0.998883i \(0.515046\pi\)
\(500\) −2.26047e10 1.30508e10i −0.361675 0.208813i
\(501\) 0 0
\(502\) 7.51577e10 4.33923e10i 1.18347 0.683279i
\(503\) 5.93676e10i 0.927423i −0.885986 0.463711i \(-0.846517\pi\)
0.885986 0.463711i \(-0.153483\pi\)
\(504\) 0 0
\(505\) −5.18672e10 −0.797494
\(506\) 1.44056e10 + 2.49513e10i 0.219751 + 0.380619i
\(507\) 0 0
\(508\) 2.08919e10 3.61859e10i 0.313707 0.543356i
\(509\) −2.93270e10 + 1.69319e10i −0.436914 + 0.252253i −0.702288 0.711893i \(-0.747838\pi\)
0.265374 + 0.964146i \(0.414505\pi\)
\(510\) 0 0
\(511\) −3.62396e10 + 2.13979e10i −0.531495 + 0.313825i
\(512\) −3.03700e9 −0.0441942
\(513\) 0 0
\(514\) 1.08951e9 + 6.29027e8i 0.0156091 + 0.00901191i
\(515\) −1.67550e10 + 2.90206e10i −0.238186 + 0.412551i
\(516\) 0 0
\(517\) 2.19463e10i 0.307184i
\(518\) −4.88465e9 8.27265e9i −0.0678444 0.114902i
\(519\) 0 0
\(520\) 5.81178e9 + 1.00663e10i 0.0794869 + 0.137675i
\(521\) −7.52763e10 4.34608e10i −1.02166 0.589857i −0.107077 0.994251i \(-0.534149\pi\)
−0.914585 + 0.404394i \(0.867483\pi\)
\(522\) 0 0
\(523\) −1.16722e9 + 6.73896e8i −0.0156008 + 0.00900712i −0.507780 0.861487i \(-0.669534\pi\)
0.492179 + 0.870494i \(0.336200\pi\)
\(524\) 1.95915e10i 0.259862i
\(525\) 0 0
\(526\) 4.35341e10 0.568704
\(527\) −1.06128e10 1.83820e10i −0.137591 0.238314i
\(528\) 0 0
\(529\) 3.07936e10 5.33361e10i 0.393222 0.681081i
\(530\) 3.43745e10 1.98461e10i 0.435645 0.251520i
\(531\) 0 0
\(532\) −2.23349e10 1.26056e10i −0.278829 0.157368i
\(533\) −9.73151e10 −1.20579
\(534\) 0 0
\(535\) −3.62761e9 2.09440e9i −0.0442798 0.0255650i
\(536\) 1.14215e10 1.97826e10i 0.138377 0.239676i
\(537\) 0 0
\(538\) 4.65518e10i 0.555658i
\(539\) 1.13499e11 2.21902e9i 1.34474 0.0262910i
\(540\) 0 0
\(541\) −2.82020e10 4.88474e10i −0.329224 0.570233i 0.653134 0.757242i \(-0.273454\pi\)
−0.982358 + 0.187010i \(0.940120\pi\)
\(542\) −6.17828e10 3.56703e10i −0.715929 0.413342i
\(543\) 0 0
\(544\) 7.67422e9 4.43072e9i 0.0876272 0.0505916i
\(545\) 5.97284e10i 0.677010i
\(546\) 0 0
\(547\) −9.05773e10 −1.01174 −0.505872 0.862609i \(-0.668829\pi\)
−0.505872 + 0.862609i \(0.668829\pi\)
\(548\) 8.50805e9 + 1.47364e10i 0.0943426 + 0.163406i
\(549\) 0 0
\(550\) 3.39297e10 5.87680e10i 0.370791 0.642229i
\(551\) −5.13316e10 + 2.96363e10i −0.556902 + 0.321527i
\(552\) 0 0
\(553\) −1.71527e10 + 1.67661e8i −0.183414 + 0.00179280i
\(554\) 1.91611e9 0.0203414
\(555\) 0 0
\(556\) −5.96678e10 3.44492e10i −0.624368 0.360479i
\(557\) 8.50601e10 1.47328e11i 0.883701 1.53061i 0.0365050 0.999333i \(-0.488378\pi\)
0.847196 0.531281i \(-0.178289\pi\)
\(558\) 0 0
\(559\) 1.78646e11i 1.82956i
\(560\) 9.93582e9 5.86667e9i 0.101030 0.0596540i
\(561\) 0 0
\(562\) −2.41663e10 4.18573e10i −0.242251 0.419590i
\(563\) −1.07954e11 6.23275e10i −1.07450 0.620364i −0.145094 0.989418i \(-0.546348\pi\)
−0.929408 + 0.369054i \(0.879682\pi\)
\(564\) 0 0
\(565\) −2.03992e10 + 1.17775e10i −0.200179 + 0.115573i
\(566\) 1.04212e11i 1.01543i
\(567\) 0 0
\(568\) 3.49292e10 0.335579
\(569\) 6.46031e10 + 1.11896e11i 0.616317 + 1.06749i 0.990152 + 0.139997i \(0.0447093\pi\)
−0.373835 + 0.927495i \(0.621957\pi\)
\(570\) 0 0
\(571\) −5.09591e10 + 8.82638e10i −0.479377 + 0.830306i −0.999720 0.0236516i \(-0.992471\pi\)
0.520343 + 0.853957i \(0.325804\pi\)
\(572\) −5.97332e10 + 3.44870e10i −0.557997 + 0.322160i
\(573\) 0 0
\(574\) 9.44215e8 + 9.65989e10i 0.00869808 + 0.889866i
\(575\) 3.93896e10 0.360338
\(576\) 0 0
\(577\) −1.37255e11 7.92444e10i −1.23830 0.714933i −0.269553 0.962985i \(-0.586876\pi\)
−0.968747 + 0.248053i \(0.920209\pi\)
\(578\) 2.65328e10 4.59562e10i 0.237723 0.411749i
\(579\) 0 0
\(580\) 2.66671e10i 0.235648i
\(581\) 1.32585e11 + 7.48297e10i 1.16356 + 0.656703i
\(582\) 0 0
\(583\) 1.17766e11 + 2.03977e11i 1.01941 + 1.76566i
\(584\) −2.19829e10 1.26918e10i −0.188987 0.109112i
\(585\) 0 0
\(586\) −6.09882e10 + 3.52116e10i −0.517196 + 0.298604i
\(587\) 1.98747e11i 1.67397i 0.547227 + 0.836984i \(0.315683\pi\)
−0.547227 + 0.836984i \(0.684317\pi\)
\(588\) 0 0
\(589\) −3.70519e10 −0.307857
\(590\) −1.94430e10 3.36763e10i −0.160456 0.277918i
\(591\) 0 0
\(592\) 2.89725e9 5.01818e9i 0.0235884 0.0408563i
\(593\) 7.00747e9 4.04576e9i 0.0566686 0.0327176i −0.471398 0.881921i \(-0.656250\pi\)
0.528067 + 0.849203i \(0.322917\pi\)
\(594\) 0 0
\(595\) −1.65480e10 + 2.93200e10i −0.132031 + 0.233936i
\(596\) −7.07140e10 −0.560429
\(597\) 0 0
\(598\) −3.46726e10 2.00183e10i −0.271133 0.156539i
\(599\) 9.11259e10 1.57835e11i 0.707839 1.22601i −0.257818 0.966193i \(-0.583004\pi\)
0.965657 0.259820i \(-0.0836631\pi\)
\(600\) 0 0
\(601\) 2.47060e11i 1.89367i −0.321713 0.946837i \(-0.604259\pi\)
0.321713 0.946837i \(-0.395741\pi\)
\(602\) 1.77331e11 1.73334e9i 1.35020 0.0131977i
\(603\) 0 0
\(604\) −3.29893e9 5.71392e9i −0.0247871 0.0429325i
\(605\) −4.40517e10 2.54332e10i −0.328807 0.189837i
\(606\) 0 0
\(607\) 3.95009e10 2.28059e10i 0.290973 0.167993i −0.347408 0.937714i \(-0.612938\pi\)
0.638380 + 0.769721i \(0.279605\pi\)
\(608\) 1.54687e10i 0.113198i
\(609\) 0 0
\(610\) 4.36668e10 0.315379
\(611\) 1.52484e10 + 2.64111e10i 0.109411 + 0.189505i
\(612\) 0 0
\(613\) 2.26313e10 3.91986e10i 0.160276 0.277606i −0.774692 0.632339i \(-0.782095\pi\)
0.934968 + 0.354733i \(0.115428\pi\)
\(614\) −9.55617e10 + 5.51726e10i −0.672373 + 0.388195i
\(615\) 0 0
\(616\) 3.48127e10 + 5.89589e10i 0.241777 + 0.409475i
\(617\) 3.39761e10 0.234440 0.117220 0.993106i \(-0.462602\pi\)
0.117220 + 0.993106i \(0.462602\pi\)
\(618\) 0 0
\(619\) −3.85975e10 2.22843e10i −0.262904 0.151787i 0.362755 0.931885i \(-0.381836\pi\)
−0.625658 + 0.780097i \(0.715170\pi\)
\(620\) 8.33493e9 1.44365e10i 0.0564073 0.0977003i
\(621\) 0 0
\(622\) 1.85204e11i 1.23734i
\(623\) 2.08096e9 + 2.12895e11i 0.0138138 + 1.41323i
\(624\) 0 0
\(625\) −2.95834e10 5.12400e10i −0.193878 0.335807i
\(626\) 1.59570e11 + 9.21277e10i 1.03909 + 0.599919i
\(627\) 0 0
\(628\) 1.83354e10 1.05859e10i 0.117883 0.0680598i
\(629\) 1.69073e10i 0.108012i
\(630\) 0 0
\(631\) 1.19363e11 0.752924 0.376462 0.926432i \(-0.377141\pi\)
0.376462 + 0.926432i \(0.377141\pi\)
\(632\) −5.17305e9 8.95999e9i −0.0324249 0.0561616i
\(633\) 0 0
\(634\) −5.86274e10 + 1.01546e11i −0.362864 + 0.628498i
\(635\) −8.29218e10 + 4.78749e10i −0.510004 + 0.294451i
\(636\) 0 0
\(637\) −1.35047e11 + 8.15303e10i −0.820217 + 0.495178i
\(638\) 1.58242e11 0.955078
\(639\) 0 0
\(640\) 6.02705e9 + 3.47972e9i 0.0359240 + 0.0207408i
\(641\) −8.05963e10 + 1.39597e11i −0.477401 + 0.826882i −0.999664 0.0259018i \(-0.991754\pi\)
0.522264 + 0.852784i \(0.325088\pi\)
\(642\) 0 0
\(643\) 5.72715e10i 0.335039i 0.985869 + 0.167519i \(0.0535756\pi\)
−0.985869 + 0.167519i \(0.946424\pi\)
\(644\) −1.95345e10 + 3.46117e10i −0.113569 + 0.201224i
\(645\) 0 0
\(646\) 2.25674e10 + 3.90879e10i 0.129584 + 0.224446i
\(647\) −4.30146e10 2.48345e10i −0.245470 0.141722i 0.372218 0.928145i \(-0.378597\pi\)
−0.617688 + 0.786423i \(0.711931\pi\)
\(648\) 0 0
\(649\) 1.99834e11 1.15374e11i 1.12640 0.650325i
\(650\) 9.42984e10i 0.528264i
\(651\) 0 0
\(652\) −1.68299e10 −0.0931306
\(653\) 1.75732e11 + 3.04377e11i 0.966492 + 1.67401i 0.705553 + 0.708657i \(0.250699\pi\)
0.260939 + 0.965355i \(0.415968\pi\)
\(654\) 0 0
\(655\) 2.24475e10 3.88801e10i 0.121956 0.211233i
\(656\) −5.04599e10 + 2.91330e10i −0.272478 + 0.157315i
\(657\) 0 0
\(658\) 2.60687e10 1.53925e10i 0.139065 0.0821117i
\(659\) −7.49500e10 −0.397402 −0.198701 0.980060i \(-0.563672\pi\)
−0.198701 + 0.980060i \(0.563672\pi\)
\(660\) 0 0
\(661\) 9.13344e10 + 5.27319e10i 0.478441 + 0.276228i 0.719767 0.694216i \(-0.244249\pi\)
−0.241326 + 0.970444i \(0.577582\pi\)
\(662\) 1.22337e10 2.11894e10i 0.0636979 0.110328i
\(663\) 0 0
\(664\) 9.18254e10i 0.472379i
\(665\) 2.98813e10 + 5.06071e10i 0.152797 + 0.258777i
\(666\) 0 0
\(667\) 4.59264e10 + 7.95469e10i 0.232038 + 0.401902i
\(668\) −1.13106e11 6.53019e10i −0.568042 0.327959i
\(669\) 0 0
\(670\) −4.53329e10 + 2.61729e10i −0.224964 + 0.129883i
\(671\) 2.59118e11i 1.27823i
\(672\) 0 0
\(673\) −1.87077e11 −0.911929 −0.455965 0.889998i \(-0.650706\pi\)
−0.455965 + 0.889998i \(0.650706\pi\)
\(674\) 9.81538e9 + 1.70007e10i 0.0475628 + 0.0823812i
\(675\) 0 0
\(676\) −4.28320e9 + 7.41872e9i −0.0205108 + 0.0355257i
\(677\) −2.65310e11 + 1.53177e11i −1.26299 + 0.729185i −0.973651 0.228043i \(-0.926767\pi\)
−0.289334 + 0.957228i \(0.593434\pi\)
\(678\) 0 0
\(679\) 1.36362e11 + 7.69617e10i 0.641528 + 0.362072i
\(680\) −2.03064e10 −0.0949725
\(681\) 0 0
\(682\) 8.56661e10 + 4.94593e10i 0.395978 + 0.228618i
\(683\) 1.68227e11 2.91377e11i 0.773057 1.33897i −0.162823 0.986655i \(-0.552060\pi\)
0.935880 0.352319i \(-0.114607\pi\)
\(684\) 0 0
\(685\) 3.89932e10i 0.177104i
\(686\) 8.22406e10 + 1.33262e11i 0.371355 + 0.601743i
\(687\) 0 0
\(688\) 5.34809e10 + 9.26317e10i 0.238696 + 0.413434i
\(689\) −2.83450e11 1.63650e11i −1.25776 0.726171i
\(690\) 0 0
\(691\) 2.51262e11 1.45066e11i 1.10208 0.636289i 0.165317 0.986240i \(-0.447135\pi\)
0.936768 + 0.349952i \(0.113802\pi\)
\(692\) 1.72384e10i 0.0751747i
\(693\) 0 0
\(694\) −1.06379e10 −0.0458581
\(695\) 7.89421e10 + 1.36732e11i 0.338353 + 0.586044i
\(696\) 0 0
\(697\) 8.50050e10 1.47233e11i 0.360175 0.623841i
\(698\) 1.31031e10 7.56506e9i 0.0552015 0.0318706i
\(699\) 0 0
\(700\) 9.36043e10 9.14944e8i 0.389856 0.00381068i
\(701\) 3.91859e11 1.62277 0.811386 0.584510i \(-0.198713\pi\)
0.811386 + 0.584510i \(0.198713\pi\)
\(702\) 0 0
\(703\) 2.55596e10 + 1.47569e10i 0.104649 + 0.0604188i
\(704\) −2.06486e10 + 3.57644e10i −0.0840620 + 0.145600i
\(705\) 0 0
\(706\) 1.36655e10i 0.0550057i
\(707\) 3.65593e11 2.15867e11i 1.46325 0.863989i
\(708\) 0 0
\(709\) −1.48776e11 2.57687e11i −0.588772 1.01978i −0.994394 0.105742i \(-0.966278\pi\)
0.405621 0.914041i \(-0.367055\pi\)
\(710\) −6.93184e10 4.00210e10i −0.272782 0.157490i
\(711\) 0 0
\(712\) −1.11209e11 + 6.42065e10i −0.432733 + 0.249838i
\(713\) 5.74182e10i 0.222173i
\(714\) 0 0
\(715\) 1.58057e11 0.604770
\(716\) −8.59382e10 1.48849e11i −0.326990 0.566363i
\(717\) 0 0
\(718\) −1.78785e11 + 3.09664e11i −0.672717 + 1.16518i
\(719\) 2.77663e11 1.60309e11i 1.03897 0.599849i 0.119428 0.992843i \(-0.461894\pi\)
0.919541 + 0.392994i \(0.128561\pi\)
\(720\) 0 0
\(721\) −2.68106e9 2.74288e11i −0.00992122 1.01500i
\(722\) −1.13359e11 −0.417164
\(723\) 0 0
\(724\) −1.84251e11 1.06377e11i −0.670588 0.387164i
\(725\) 1.08171e11 1.87358e11i 0.391524 0.678140i
\(726\) 0 0
\(727\) 4.99101e11i 1.78670i 0.449364 + 0.893349i \(0.351651\pi\)
−0.449364 + 0.893349i \(0.648349\pi\)
\(728\) −8.28601e10 4.67655e10i −0.294999 0.166494i
\(729\) 0 0
\(730\) 2.90839e10 + 5.03749e10i 0.102415 + 0.177387i
\(731\) −2.70283e11 1.56048e11i −0.946562 0.546498i
\(732\) 0 0
\(733\) 3.43929e11 1.98568e11i 1.19139 0.687848i 0.232766 0.972533i \(-0.425222\pi\)
0.958621 + 0.284685i \(0.0918890\pi\)
\(734\) 3.40923e9i 0.0117455i
\(735\) 0 0
\(736\) −2.39713e10 −0.0816921
\(737\) −1.55310e11 2.69004e11i −0.526415 0.911778i
\(738\) 0 0
\(739\) −1.33494e10 + 2.31219e10i −0.0447595 + 0.0775257i −0.887537 0.460736i \(-0.847585\pi\)
0.842778 + 0.538262i \(0.180919\pi\)
\(740\) −1.14994e10 + 6.63919e9i −0.0383485 + 0.0221405i
\(741\) 0 0
\(742\) −1.59695e11 + 2.82952e11i −0.526837 + 0.933462i
\(743\) −2.98139e11 −0.978281 −0.489141 0.872205i \(-0.662690\pi\)
−0.489141 + 0.872205i \(0.662690\pi\)
\(744\) 0 0
\(745\) 1.40335e11 + 8.10224e10i 0.455555 + 0.263015i
\(746\) 1.87138e11 3.24133e11i 0.604237 1.04657i
\(747\) 0 0
\(748\) 1.20498e11i 0.384922i
\(749\) 3.42864e10 3.35136e8i 0.108942 0.00106486i
\(750\) 0 0
\(751\) 3.87148e10 + 6.70559e10i 0.121707 + 0.210803i 0.920441 0.390881i \(-0.127830\pi\)
−0.798734 + 0.601685i \(0.794496\pi\)
\(752\) 1.58133e10 + 9.12979e9i 0.0494482 + 0.0285489i
\(753\) 0 0
\(754\) −1.90435e11 + 1.09948e11i −0.589198 + 0.340173i
\(755\) 1.51193e10i 0.0465313i
\(756\) 0 0
\(757\) −5.03553e11 −1.53342 −0.766711 0.641992i \(-0.778108\pi\)
−0.766711 + 0.641992i \(0.778108\pi\)
\(758\) 1.27990e11 + 2.21685e11i 0.387703 + 0.671521i
\(759\) 0 0
\(760\) −1.77236e10 + 3.06982e10i −0.0531249 + 0.0920150i
\(761\) −8.89472e10 + 5.13537e10i −0.265212 + 0.153120i −0.626710 0.779253i \(-0.715599\pi\)
0.361498 + 0.932373i \(0.382266\pi\)
\(762\) 0 0
\(763\) −2.48584e11 4.21003e11i −0.733459 1.24219i
\(764\) −1.02620e11 −0.301201
\(765\) 0 0
\(766\) −2.37265e11 1.36985e11i −0.689158 0.397885i
\(767\) −1.60326e11 + 2.77693e11i −0.463257 + 0.802385i
\(768\) 0 0
\(769\) 5.28224e10i 0.151047i 0.997144 + 0.0755236i \(0.0240628\pi\)
−0.997144 + 0.0755236i \(0.975937\pi\)
\(770\) −1.53358e9 1.56894e11i −0.00436257 0.446317i
\(771\) 0 0
\(772\) −7.52803e10 1.30389e11i −0.211940 0.367090i
\(773\) −3.29208e11 1.90068e11i −0.922046 0.532344i −0.0377590 0.999287i \(-0.512022\pi\)
−0.884287 + 0.466943i \(0.845355\pi\)
\(774\) 0 0
\(775\) 1.17119e11 6.76188e10i 0.324654 0.187439i
\(776\) 9.44417e10i 0.260445i
\(777\) 0 0
\(778\) 1.21947e11 0.332855
\(779\) −1.48386e11 2.57013e11i −0.402943 0.697918i
\(780\) 0 0
\(781\) 2.37484e11 4.11334e11i 0.638307 1.10558i
\(782\) 6.05733e10 3.49720e10i 0.161977 0.0935176i
\(783\) 0 0
\(784\) −4.56173e10 + 8.27040e10i −0.120744 + 0.218908i
\(785\) −4.85164e10 −0.127765
\(786\) 0 0
\(787\) 4.12322e11 + 2.38054e11i 1.07482 + 0.620550i 0.929495 0.368834i \(-0.120243\pi\)
0.145328 + 0.989384i \(0.453576\pi\)
\(788\) −2.45222e10 + 4.24736e10i −0.0635995 + 0.110158i
\(789\) 0 0
\(790\) 2.37086e10i 0.0608693i
\(791\) 9.47694e10 1.67915e11i 0.242082 0.428926i
\(792\) 0 0
\(793\) −1.80037e11 3.11833e11i −0.455270 0.788551i
\(794\) −1.26274e11 7.29045e10i −0.317711 0.183431i
\(795\) 0 0
\(796\) −2.43813e11 + 1.40766e11i −0.607302 + 0.350626i
\(797\) 2.92025e11i 0.723746i −0.932227 0.361873i \(-0.882137\pi\)
0.932227 0.361873i \(-0.117863\pi\)
\(798\) 0 0
\(799\) −5.32782e10 −0.130726
\(800\) 2.82299e10 + 4.88956e10i 0.0689207 + 0.119374i
\(801\) 0 0
\(802\) −3.76618e10 + 6.52322e10i −0.0910340 + 0.157676i
\(803\) −2.98923e11 + 1.72583e11i −0.718948 + 0.415085i
\(804\) 0 0
\(805\) 7.84242e10 4.63061e10i 0.186753 0.110269i
\(806\) −1.37459e11 −0.325711
\(807\) 0 0
\(808\) 2.21768e11 + 1.28038e11i 0.520300 + 0.300395i
\(809\) 2.54870e11 4.41447e11i 0.595009 1.03059i −0.398536 0.917153i \(-0.630482\pi\)
0.993546 0.113434i \(-0.0361850\pi\)
\(810\) 0 0
\(811\) 2.98657e11i 0.690381i −0.938533 0.345191i \(-0.887814\pi\)
0.938533 0.345191i \(-0.112186\pi\)
\(812\) 1.10986e11 + 1.87966e11i 0.255296 + 0.432371i
\(813\) 0 0
\(814\) −3.93968e10 6.82373e10i −0.0897353 0.155426i
\(815\) 3.33997e10 + 1.92833e10i 0.0757029 + 0.0437071i
\(816\) 0 0
\(817\) −4.71811e11 + 2.72400e11i −1.05896 + 0.611391i
\(818\) 4.20276e11i 0.938688i
\(819\) 0 0
\(820\) 1.33520e11 0.295318
\(821\) −2.07864e11 3.60031e11i −0.457516 0.792441i 0.541313 0.840821i \(-0.317927\pi\)
−0.998829 + 0.0483802i \(0.984594\pi\)
\(822\) 0 0
\(823\) −1.28735e11 + 2.22976e11i −0.280606 + 0.486025i −0.971534 0.236899i \(-0.923869\pi\)
0.690928 + 0.722924i \(0.257202\pi\)
\(824\) 1.43279e11 8.27220e10i 0.310794 0.179437i
\(825\) 0 0
\(826\) 2.77204e11 + 1.56452e11i 0.595497 + 0.336093i
\(827\) −2.54192e11 −0.543426 −0.271713 0.962378i \(-0.587590\pi\)
−0.271713 + 0.962378i \(0.587590\pi\)
\(828\) 0 0
\(829\) −6.50967e11 3.75836e11i −1.37829 0.795757i −0.386337 0.922358i \(-0.626260\pi\)
−0.991954 + 0.126601i \(0.959593\pi\)
\(830\) 1.05211e11 1.82231e11i 0.221692 0.383982i
\(831\) 0 0
\(832\) 5.73871e10i 0.119763i
\(833\) −5.38704e9 2.75537e11i −0.0111885 0.572269i
\(834\) 0 0
\(835\) 1.49643e11 + 2.59188e11i 0.307829 + 0.533175i
\(836\) −1.82163e11 1.05172e11i −0.372936 0.215315i
\(837\) 0 0
\(838\) −3.07630e11 + 1.77610e11i −0.623811 + 0.360157i
\(839\) 2.44756e11i 0.493954i 0.969021 + 0.246977i \(0.0794372\pi\)
−0.969021 + 0.246977i \(0.920563\pi\)
\(840\) 0 0
\(841\) 4.24316e9 0.00848214
\(842\) 5.45572e9 + 9.44959e9i 0.0108544 + 0.0188003i
\(843\) 0 0
\(844\) −5.13038e10 + 8.88609e10i −0.101107 + 0.175122i
\(845\) 1.70004e10 9.81517e9i 0.0333451 0.0192518i
\(846\) 0 0
\(847\) 4.16355e11 4.06970e9i 0.808966 0.00790731i
\(848\) −1.95966e11 −0.378964
\(849\) 0 0
\(850\) −1.42669e11 8.23699e10i −0.273309 0.157795i
\(851\) 2.28682e10 3.96089e10i 0.0436028 0.0755222i
\(852\) 0 0
\(853\) 1.02397e11i 0.193416i 0.995313 + 0.0967078i \(0.0308312\pi\)
−0.995313 + 0.0967078i \(0.969169\pi\)
\(854\) −3.07791e11 + 1.81738e11i −0.578662 + 0.341675i
\(855\) 0 0
\(856\) 1.03404e10 + 1.79100e10i 0.0192593 + 0.0333581i
\(857\) 7.52580e11 + 4.34502e11i 1.39518 + 0.805506i 0.993883 0.110442i \(-0.0352267\pi\)
0.401295 + 0.915949i \(0.368560\pi\)
\(858\) 0 0
\(859\) −5.47218e11 + 3.15936e11i −1.00505 + 0.580266i −0.909738 0.415182i \(-0.863718\pi\)
−0.0953112 + 0.995448i \(0.530385\pi\)
\(860\) 2.45109e11i 0.448089i
\(861\) 0 0
\(862\) 7.26887e11 1.31655
\(863\) 1.45694e10 + 2.52350e10i 0.0262663 + 0.0454946i 0.878860 0.477080i \(-0.158305\pi\)
−0.852593 + 0.522575i \(0.824972\pi\)
\(864\) 0 0
\(865\) 1.97513e10 3.42103e10i 0.0352802 0.0611071i
\(866\) −4.75844e10 + 2.74729e10i −0.0846044 + 0.0488464i
\(867\) 0 0
\(868\) 1.33371e9 + 1.36447e11i 0.00234955 + 0.240373i
\(869\) −1.40687e11 −0.246702
\(870\) 0 0
\(871\) 3.73812e11 + 2.15820e11i 0.649502 + 0.374990i
\(872\) 1.47444e11 2.55380e11i 0.255012 0.441694i
\(873\) 0 0
\(874\) 1.22096e11i 0.209244i
\(875\) −4.26387e11 2.40649e11i −0.727398 0.410536i
\(876\) 0 0
\(877\) 1.09627e10 + 1.89879e10i 0.0185318 + 0.0320980i 0.875143 0.483865i \(-0.160767\pi\)
−0.856611 + 0.515963i \(0.827434\pi\)
\(878\) 2.23713e11 + 1.29161e11i 0.376456 + 0.217347i
\(879\) 0 0
\(880\) 8.19560e10 4.73173e10i 0.136663 0.0789022i
\(881\) 1.09148e11i 0.181181i −0.995888 0.0905907i \(-0.971124\pi\)
0.995888 0.0905907i \(-0.0288755\pi\)
\(882\) 0 0
\(883\) 2.59857e11 0.427457 0.213728 0.976893i \(-0.431439\pi\)
0.213728 + 0.976893i \(0.431439\pi\)
\(884\) 8.37227e10 + 1.45012e11i 0.137099 + 0.237462i
\(885\) 0 0
\(886\) 2.07326e11 3.59100e11i 0.336449 0.582747i
\(887\) 5.97593e11 3.45020e11i 0.965408 0.557379i 0.0675747 0.997714i \(-0.478474\pi\)
0.897833 + 0.440336i \(0.145141\pi\)
\(888\) 0 0
\(889\) 3.85234e11 6.82566e11i 0.616761 1.09279i
\(890\) 2.94265e11 0.469006
\(891\) 0 0
\(892\) 1.15984e11 + 6.69634e10i 0.183206 + 0.105774i
\(893\) −4.65017e10 + 8.05433e10i −0.0731245 + 0.126655i
\(894\) 0 0
\(895\) 3.93863e11i 0.613838i
\(896\) −5.69648e10 + 5.56807e8i −0.0883841 + 0.000863919i
\(897\) 0 0
\(898\) −4.07945e11 7.06582e11i −0.627331 1.08657i
\(899\) 2.73111e11 + 1.57681e11i 0.418120 + 0.241402i
\(900\) 0 0
\(901\) 4.95189e11 2.85897e11i 0.751400 0.433821i
\(902\) 7.92303e11i 1.19692i
\(903\) 0 0
\(904\) 1.16294e11 0.174134
\(905\) 2.43769e11 + 4.22221e11i 0.363400 + 0.629427i
\(906\) 0 0
\(907\) −1.10593e11 + 1.91553e11i −0.163417 + 0.283047i −0.936092 0.351755i \(-0.885585\pi\)
0.772675 + 0.634802i \(0.218918\pi\)
\(908\) 2.35767e11 1.36120e11i 0.346849 0.200253i
\(909\) 0 0
\(910\) 1.10857e11 + 1.87747e11i 0.161658 + 0.273784i
\(911\) −5.57854e11 −0.809929 −0.404964 0.914332i \(-0.632716\pi\)
−0.404964 + 0.914332i \(0.632716\pi\)
\(912\) 0 0
\(913\) 1.08136e12 + 6.24322e11i 1.55627 + 0.898515i
\(914\) −3.40541e11 + 5.89834e11i −0.487960 + 0.845171i
\(915\) 0 0
\(916\) 5.98180e11i 0.849670i
\(917\) 3.59193e9 + 3.67476e11i 0.00507985 + 0.519699i
\(918\) 0 0
\(919\) 1.76298e11 + 3.05357e11i 0.247164 + 0.428100i 0.962738 0.270437i \(-0.0871681\pi\)
−0.715574 + 0.698537i \(0.753835\pi\)
\(920\) 4.75720e10 + 2.74657e10i 0.0664049 + 0.0383389i
\(921\) 0 0
\(922\) −8.79587e11 + 5.07830e11i −1.21718 + 0.702739i
\(923\) 6.60021e11i 0.909392i
\(924\) 0 0
\(925\) −1.07723e11 −0.147144
\(926\) −2.06374e11 3.57451e11i −0.280680 0.486152i
\(927\) 0 0
\(928\) −6.58296e10 + 1.14020e11i −0.0887624 + 0.153741i
\(929\) −4.96997e11 + 2.86941e11i −0.667253 + 0.385239i −0.795035 0.606563i \(-0.792548\pi\)
0.127782 + 0.991802i \(0.459214\pi\)
\(930\) 0 0
\(931\) −4.21245e11 2.32347e11i −0.560707 0.309271i
\(932\) 3.33821e11 0.442435
\(933\) 0 0
\(934\) −8.37754e10 4.83678e10i −0.110085 0.0635578i
\(935\) −1.38064e11 + 2.39133e11i −0.180648 + 0.312891i
\(936\) 0 0
\(937\) 8.48860e11i 1.10123i 0.834760 + 0.550615i \(0.185607\pi\)
−0.834760 + 0.550615i \(0.814393\pi\)
\(938\) 2.10605e11 3.73155e11i 0.272055 0.482034i
\(939\) 0 0
\(940\) −2.09214e10 3.62369e10i −0.0267966 0.0464130i
\(941\) −3.68293e11 2.12634e11i −0.469715 0.271190i 0.246405 0.969167i \(-0.420751\pi\)
−0.716121 + 0.697977i \(0.754084\pi\)
\(942\) 0 0
\(943\) −3.98284e11 + 2.29949e11i −0.503670 + 0.290794i
\(944\) 1.91986e11i 0.241758i
\(945\) 0 0
\(946\) 1.45447e12 1.81610
\(947\) 3.53892e11 + 6.12958e11i 0.440018 + 0.762133i 0.997690 0.0679279i \(-0.0216388\pi\)
−0.557672 + 0.830061i \(0.688305\pi\)
\(948\) 0 0
\(949\) 2.39824e11 4.15388e11i 0.295684 0.512140i
\(950\) −2.49045e11 + 1.43786e11i −0.305762 + 0.176532i
\(951\) 0 0
\(952\) 1.43132e11 8.45136e10i 0.174257 0.102891i
\(953\) 1.11824e12 1.35570 0.677851 0.735199i \(-0.262911\pi\)
0.677851 + 0.735199i \(0.262911\pi\)
\(954\) 0 0
\(955\) 2.03653e11 + 1.17579e11i 0.244837 + 0.141357i
\(956\) −1.60565e11 + 2.78107e11i −0.192229 + 0.332951i
\(957\) 0 0
\(958\) 1.02543e12i 1.21743i
\(959\) 1.62287e11 + 2.74849e11i 0.191870 + 0.324952i
\(960\) 0 0
\(961\) −3.27878e11 5.67901e11i −0.384431 0.665854i
\(962\) 9.48235e10 + 5.47463e10i 0.110717 + 0.0639227i
\(963\) 0 0
\(964\) 1.79050e11 1.03374e11i 0.207332 0.119703i
\(965\) 3.45017e11i 0.397861i
\(966\) 0 0
\(967\) −1.31325e12 −1.50190 −0.750952 0.660356i \(-0.770405\pi\)
−0.750952 + 0.660356i \(0.770405\pi\)
\(968\) 1.25568e11 + 2.17489e11i 0.143013 + 0.247706i
\(969\) 0 0
\(970\) 1.08209e11 1.87423e11i 0.122230 0.211708i
\(971\) 1.44855e12 8.36318e11i 1.62950 0.940794i 0.645262 0.763961i \(-0.276748\pi\)
0.984241 0.176833i \(-0.0565851\pi\)
\(972\) 0 0
\(973\) −1.12550e12 6.35221e11i −1.25572 0.708719i
\(974\) −4.54128e11 −0.504594
\(975\) 0 0
\(976\) −1.86706e11 1.07795e11i −0.205759 0.118795i
\(977\) −4.87813e11 + 8.44917e11i −0.535396 + 0.927333i 0.463748 + 0.885967i \(0.346504\pi\)
−0.999144 + 0.0413657i \(0.986829\pi\)
\(978\) 0 0
\(979\) 1.74616e12i 1.90088i
\(980\) 1.85290e11 1.11862e11i 0.200885 0.121277i
\(981\) 0 0
\(982\) 1.88513e11 + 3.26515e11i 0.202720 + 0.351121i
\(983\) 8.75801e11 + 5.05644e11i 0.937975 + 0.541540i 0.889325 0.457276i \(-0.151175\pi\)
0.0486500 + 0.998816i \(0.484508\pi\)
\(984\) 0 0
\(985\) 9.73305e10 5.61938e10i 0.103396 0.0596957i
\(986\) 3.84158e11i 0.406446i
\(987\) 0 0
\(988\) 2.92296e11 0.306757
\(989\) 4.22129e11 + 7.31150e11i 0.441225 + 0.764225i
\(990\) 0 0
\(991\) −1.10221e11 + 1.90909e11i −0.114280 + 0.197939i −0.917492 0.397755i \(-0.869790\pi\)
0.803211 + 0.595694i \(0.203123\pi\)
\(992\) −7.12752e10 + 4.11507e10i −0.0736023 + 0.0424943i
\(993\) 0 0
\(994\) 6.55163e11 6.40396e9i 0.671126 0.00655998i
\(995\) 6.45143e11 0.658209
\(996\) 0 0
\(997\) 4.24638e11 + 2.45165e11i 0.429772 + 0.248129i 0.699250 0.714878i \(-0.253518\pi\)
−0.269477 + 0.963007i \(0.586851\pi\)
\(998\) −5.90237e11 + 1.02232e12i −0.594982 + 1.03054i
\(999\) 0 0
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 126.9.n.d.73.8 yes 20
3.2 odd 2 inner 126.9.n.d.73.3 yes 20
7.5 odd 6 inner 126.9.n.d.19.8 yes 20
21.5 even 6 inner 126.9.n.d.19.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.9.n.d.19.3 20 21.5 even 6 inner
126.9.n.d.19.8 yes 20 7.5 odd 6 inner
126.9.n.d.73.3 yes 20 3.2 odd 2 inner
126.9.n.d.73.8 yes 20 1.1 even 1 trivial