Properties

Label 126.9.n.b.73.6
Level $126$
Weight $9$
Character 126.73
Analytic conductor $51.330$
Analytic rank $0$
Dimension $12$
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] = [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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + 6901058684 x^{5} + 370996492174 x^{4} + \cdots + 36\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{24}\cdot 3^{10}\cdot 7^{3} \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 73.6
Root \(9.14374 + 15.8374i\) of defining polynomial
Character \(\chi\) \(=\) 126.73
Dual form 126.9.n.b.19.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(758.365 - 437.842i) q^{5} +(855.887 + 2243.27i) q^{7} -1448.15 q^{8} +O(q^{10})\) \(q+(5.65685 + 9.79796i) q^{2} +(-64.0000 + 110.851i) q^{4} +(758.365 - 437.842i) q^{5} +(855.887 + 2243.27i) q^{7} -1448.15 q^{8} +(8579.92 + 4953.62i) q^{10} +(-6414.54 + 11110.3i) q^{11} +3065.53i q^{13} +(-17137.8 + 21075.8i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-62419.6 - 36038.0i) q^{17} +(49079.6 - 28336.1i) q^{19} +112088. i q^{20} -145144. q^{22} +(249593. + 432307. i) q^{23} +(188099. - 325797. i) q^{25} +(-30035.9 + 17341.3i) q^{26} +(-303446. - 48693.1i) q^{28} +88328.5 q^{29} +(501813. + 289722. i) q^{31} +(92681.9 - 160530. i) q^{32} -815447. i q^{34} +(1.63127e6 + 1.32647e6i) q^{35} +(465050. + 805489. i) q^{37} +(555272. + 320587. i) q^{38} +(-1.09823e6 + 634063. i) q^{40} +1.42277e6i q^{41} +2.95457e6 q^{43} +(-821061. - 1.42212e6i) q^{44} +(-2.82382e6 + 4.89099e6i) q^{46} +(-6.92276e6 + 3.99685e6i) q^{47} +(-4.29971e6 + 3.83997e6i) q^{49} +4.25620e6 q^{50} +(-339818. - 196194. i) q^{52} +(-1.04248e6 + 1.80563e6i) q^{53} +1.12342e7i q^{55} +(-1.23946e6 - 3.24860e6i) q^{56} +(499661. + 865439. i) q^{58} +(-7.60174e6 - 4.38887e6i) q^{59} +(-1.25971e7 + 7.27293e6i) q^{61} +6.55566e6i q^{62} +2.09715e6 q^{64} +(1.34222e6 + 2.32479e6i) q^{65} +(7.05740e6 - 1.22238e7i) q^{67} +(7.98971e6 - 4.61286e6i) q^{68} +(-3.76886e6 + 2.34868e7i) q^{70} +3.34541e7 q^{71} +(1.12065e6 + 647007. i) q^{73} +(-5.26143e6 + 9.11307e6i) q^{74} +7.25405e6i q^{76} +(-3.04135e7 - 4.88037e6i) q^{77} +(1.69458e7 + 2.93509e7i) q^{79} +(-1.24251e7 - 7.17361e6i) q^{80} +(-1.39402e7 + 8.04839e6i) q^{82} +7.65808e6i q^{83} -6.31158e7 q^{85} +(1.67136e7 + 2.89487e7i) q^{86} +(9.28924e6 - 1.60894e7i) q^{88} +(-8.82439e7 + 5.09476e7i) q^{89} +(-6.87681e6 + 2.62375e6i) q^{91} -6.38957e7 q^{92} +(-7.83220e7 - 4.52192e7i) q^{94} +(2.48135e7 - 4.29782e7i) q^{95} -2.91159e7i q^{97} +(-6.19467e7 - 2.04063e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7} + 17664 q^{10} - 10302 q^{11} - 56832 q^{14} - 98304 q^{16} - 173178 q^{17} + 405978 q^{19} - 941568 q^{22} - 158934 q^{23} + 838668 q^{25} - 1958400 q^{26} - 255744 q^{28} + 4355256 q^{29} + 4520250 q^{31} + 5270790 q^{35} + 134214 q^{37} - 1278720 q^{38} - 2260992 q^{40} - 12961896 q^{43} - 1318656 q^{44} + 2345472 q^{46} - 18385002 q^{47} - 3659172 q^{49} - 2970624 q^{50} - 3369984 q^{52} + 16540506 q^{53} - 4325376 q^{56} + 9176064 q^{58} - 31163922 q^{59} - 85390158 q^{61} + 25165824 q^{64} + 46506264 q^{65} - 37750362 q^{67} + 22166784 q^{68} + 92031744 q^{70} - 45506424 q^{71} + 9414786 q^{73} - 58837248 q^{74} + 100614066 q^{77} + 59730294 q^{79} + 27426816 q^{80} - 93259776 q^{82} - 64652220 q^{85} + 15144960 q^{86} + 60260352 q^{88} - 323014482 q^{89} - 266861424 q^{91} + 40687104 q^{92} - 443440128 q^{94} + 175918350 q^{95} - 472166400 q^{98}+O(q^{100}) \) 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
\(5\) 758.365 437.842i 1.21338 0.700547i 0.249889 0.968274i \(-0.419606\pi\)
0.963495 + 0.267727i \(0.0862725\pi\)
\(6\) 0 0
\(7\) 855.887 + 2243.27i 0.356471 + 0.934306i
\(8\) −1448.15 −0.353553
\(9\) 0 0
\(10\) 8579.92 + 4953.62i 0.857992 + 0.495362i
\(11\) −6414.54 + 11110.3i −0.438121 + 0.758849i −0.997545 0.0700336i \(-0.977689\pi\)
0.559423 + 0.828882i \(0.311023\pi\)
\(12\) 0 0
\(13\) 3065.53i 0.107333i 0.998559 + 0.0536664i \(0.0170907\pi\)
−0.998559 + 0.0536664i \(0.982909\pi\)
\(14\) −17137.8 + 21075.8i −0.446112 + 0.548620i
\(15\) 0 0
\(16\) −8192.00 14189.0i −0.125000 0.216506i
\(17\) −62419.6 36038.0i −0.747353 0.431484i 0.0773839 0.997001i \(-0.475343\pi\)
−0.824737 + 0.565517i \(0.808677\pi\)
\(18\) 0 0
\(19\) 49079.6 28336.1i 0.376605 0.217433i −0.299735 0.954023i \(-0.596898\pi\)
0.676340 + 0.736589i \(0.263565\pi\)
\(20\) 112088.i 0.700547i
\(21\) 0 0
\(22\) −145144. −0.619597
\(23\) 249593. + 432307.i 0.891908 + 1.54483i 0.837585 + 0.546307i \(0.183967\pi\)
0.0543235 + 0.998523i \(0.482700\pi\)
\(24\) 0 0
\(25\) 188099. 325797.i 0.481534 0.834041i
\(26\) −30035.9 + 17341.3i −0.0657276 + 0.0379479i
\(27\) 0 0
\(28\) −303446. 48693.1i −0.493684 0.0792200i
\(29\) 88328.5 0.124885 0.0624423 0.998049i \(-0.480111\pi\)
0.0624423 + 0.998049i \(0.480111\pi\)
\(30\) 0 0
\(31\) 501813. + 289722.i 0.543370 + 0.313715i 0.746444 0.665449i \(-0.231760\pi\)
−0.203074 + 0.979163i \(0.565093\pi\)
\(32\) 92681.9 160530.i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 815447.i 0.610211i
\(35\) 1.63127e6 + 1.32647e6i 1.08706 + 0.883947i
\(36\) 0 0
\(37\) 465050. + 805489.i 0.248137 + 0.429787i 0.963009 0.269469i \(-0.0868482\pi\)
−0.714872 + 0.699256i \(0.753515\pi\)
\(38\) 555272. + 320587.i 0.266300 + 0.153748i
\(39\) 0 0
\(40\) −1.09823e6 + 634063.i −0.428996 + 0.247681i
\(41\) 1.42277e6i 0.503499i 0.967792 + 0.251749i \(0.0810059\pi\)
−0.967792 + 0.251749i \(0.918994\pi\)
\(42\) 0 0
\(43\) 2.95457e6 0.864211 0.432106 0.901823i \(-0.357771\pi\)
0.432106 + 0.901823i \(0.357771\pi\)
\(44\) −821061. 1.42212e6i −0.219061 0.379424i
\(45\) 0 0
\(46\) −2.82382e6 + 4.89099e6i −0.630674 + 1.09236i
\(47\) −6.92276e6 + 3.99685e6i −1.41869 + 0.819081i −0.996184 0.0872789i \(-0.972183\pi\)
−0.422506 + 0.906360i \(0.638850\pi\)
\(48\) 0 0
\(49\) −4.29971e6 + 3.83997e6i −0.745857 + 0.666107i
\(50\) 4.25620e6 0.680991
\(51\) 0 0
\(52\) −339818. 196194.i −0.0464764 0.0268332i
\(53\) −1.04248e6 + 1.80563e6i −0.132119 + 0.228837i −0.924493 0.381199i \(-0.875511\pi\)
0.792374 + 0.610035i \(0.208845\pi\)
\(54\) 0 0
\(55\) 1.12342e7i 1.22770i
\(56\) −1.23946e6 3.24860e6i −0.126032 0.330327i
\(57\) 0 0
\(58\) 499661. + 865439.i 0.0441534 + 0.0764759i
\(59\) −7.60174e6 4.38887e6i −0.627343 0.362197i 0.152379 0.988322i \(-0.451307\pi\)
−0.779722 + 0.626125i \(0.784640\pi\)
\(60\) 0 0
\(61\) −1.25971e7 + 7.27293e6i −0.909810 + 0.525279i −0.880370 0.474287i \(-0.842706\pi\)
−0.0294401 + 0.999567i \(0.509372\pi\)
\(62\) 6.55566e6i 0.443660i
\(63\) 0 0
\(64\) 2.09715e6 0.125000
\(65\) 1.34222e6 + 2.32479e6i 0.0751917 + 0.130236i
\(66\) 0 0
\(67\) 7.05740e6 1.22238e7i 0.350224 0.606605i −0.636065 0.771636i \(-0.719439\pi\)
0.986288 + 0.165030i \(0.0527722\pi\)
\(68\) 7.98971e6 4.61286e6i 0.373676 0.215742i
\(69\) 0 0
\(70\) −3.76886e6 + 2.34868e7i −0.156970 + 0.978209i
\(71\) 3.34541e7 1.31649 0.658243 0.752806i \(-0.271300\pi\)
0.658243 + 0.752806i \(0.271300\pi\)
\(72\) 0 0
\(73\) 1.12065e6 + 647007.i 0.0394619 + 0.0227833i 0.519601 0.854409i \(-0.326081\pi\)
−0.480139 + 0.877192i \(0.659414\pi\)
\(74\) −5.26143e6 + 9.11307e6i −0.175460 + 0.303905i
\(75\) 0 0
\(76\) 7.25405e6i 0.217433i
\(77\) −3.04135e7 4.88037e6i −0.865175 0.138832i
\(78\) 0 0
\(79\) 1.69458e7 + 2.93509e7i 0.435063 + 0.753552i 0.997301 0.0734239i \(-0.0233926\pi\)
−0.562237 + 0.826976i \(0.690059\pi\)
\(80\) −1.24251e7 7.17361e6i −0.303346 0.175137i
\(81\) 0 0
\(82\) −1.39402e7 + 8.04839e6i −0.308329 + 0.178014i
\(83\) 7.65808e6i 0.161364i 0.996740 + 0.0806821i \(0.0257099\pi\)
−0.996740 + 0.0806821i \(0.974290\pi\)
\(84\) 0 0
\(85\) −6.31158e7 −1.20910
\(86\) 1.67136e7 + 2.89487e7i 0.305545 + 0.529219i
\(87\) 0 0
\(88\) 9.28924e6 1.60894e7i 0.154899 0.268294i
\(89\) −8.82439e7 + 5.09476e7i −1.40645 + 0.812015i −0.995044 0.0994374i \(-0.968296\pi\)
−0.411407 + 0.911452i \(0.634962\pi\)
\(90\) 0 0
\(91\) −6.87681e6 + 2.62375e6i −0.100282 + 0.0382610i
\(92\) −6.38957e7 −0.891908
\(93\) 0 0
\(94\) −7.83220e7 4.52192e7i −1.00317 0.579178i
\(95\) 2.48135e7 4.29782e7i 0.304645 0.527660i
\(96\) 0 0
\(97\) 2.91159e7i 0.328884i −0.986387 0.164442i \(-0.947418\pi\)
0.986387 0.164442i \(-0.0525824\pi\)
\(98\) −6.19467e7 2.04063e7i −0.671605 0.221238i
\(99\) 0 0
\(100\) 2.40767e7 + 4.17020e7i 0.240767 + 0.417020i
\(101\) 3.14578e7 + 1.81622e7i 0.302304 + 0.174535i 0.643477 0.765465i \(-0.277491\pi\)
−0.341174 + 0.940000i \(0.610824\pi\)
\(102\) 0 0
\(103\) −1.41753e8 + 8.18412e7i −1.25946 + 0.727149i −0.972969 0.230935i \(-0.925822\pi\)
−0.286489 + 0.958083i \(0.592488\pi\)
\(104\) 4.43936e6i 0.0379479i
\(105\) 0 0
\(106\) −2.35887e7 −0.186844
\(107\) 1.00138e8 + 1.73443e8i 0.763945 + 1.32319i 0.940803 + 0.338954i \(0.110073\pi\)
−0.176858 + 0.984236i \(0.556593\pi\)
\(108\) 0 0
\(109\) −7.45243e7 + 1.29080e8i −0.527949 + 0.914435i 0.471520 + 0.881855i \(0.343706\pi\)
−0.999469 + 0.0325795i \(0.989628\pi\)
\(110\) −1.10072e8 + 6.35503e7i −0.751809 + 0.434057i
\(111\) 0 0
\(112\) 2.48182e7 3.05210e7i 0.157724 0.193967i
\(113\) 2.00627e8 1.23048 0.615242 0.788338i \(-0.289058\pi\)
0.615242 + 0.788338i \(0.289058\pi\)
\(114\) 0 0
\(115\) 3.78564e8 + 2.18564e8i 2.16445 + 1.24965i
\(116\) −5.65302e6 + 9.79132e6i −0.0312211 + 0.0540766i
\(117\) 0 0
\(118\) 9.93088e7i 0.512224i
\(119\) 2.74188e7 1.70869e8i 0.136729 0.852068i
\(120\) 0 0
\(121\) 2.48869e7 + 4.31053e7i 0.116099 + 0.201090i
\(122\) −1.42520e8 8.22838e7i −0.643333 0.371428i
\(123\) 0 0
\(124\) −6.42321e7 + 3.70844e7i −0.271685 + 0.156857i
\(125\) 1.26335e7i 0.0517466i
\(126\) 0 0
\(127\) 8.46459e6 0.0325380 0.0162690 0.999868i \(-0.494821\pi\)
0.0162690 + 0.999868i \(0.494821\pi\)
\(128\) 1.18633e7 + 2.05478e7i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1.51855e7 + 2.63020e7i −0.0531686 + 0.0920906i
\(131\) 2.13575e8 1.23307e8i 0.725212 0.418701i −0.0914562 0.995809i \(-0.529152\pi\)
0.816668 + 0.577108i \(0.195819\pi\)
\(132\) 0 0
\(133\) 1.05572e8 + 8.58462e7i 0.337398 + 0.274356i
\(134\) 1.59691e8 0.495291
\(135\) 0 0
\(136\) 9.03933e7 + 5.21886e7i 0.264229 + 0.152553i
\(137\) 2.09994e8 3.63721e8i 0.596109 1.03249i −0.397280 0.917697i \(-0.630046\pi\)
0.993389 0.114794i \(-0.0366207\pi\)
\(138\) 0 0
\(139\) 6.41408e8i 1.71820i −0.511804 0.859102i \(-0.671023\pi\)
0.511804 0.859102i \(-0.328977\pi\)
\(140\) −2.51443e8 + 9.59343e7i −0.654526 + 0.249725i
\(141\) 0 0
\(142\) 1.89245e8 + 3.27782e8i 0.465448 + 0.806179i
\(143\) −3.40590e7 1.96640e7i −0.0814493 0.0470248i
\(144\) 0 0
\(145\) 6.69852e7 3.86739e7i 0.151533 0.0874876i
\(146\) 1.46401e7i 0.0322205i
\(147\) 0 0
\(148\) −1.19053e8 −0.248137
\(149\) 1.15983e8 + 2.00889e8i 0.235315 + 0.407578i 0.959364 0.282170i \(-0.0910544\pi\)
−0.724049 + 0.689749i \(0.757721\pi\)
\(150\) 0 0
\(151\) 2.83226e8 4.90561e8i 0.544784 0.943594i −0.453836 0.891085i \(-0.649945\pi\)
0.998620 0.0525090i \(-0.0167218\pi\)
\(152\) −7.10748e7 + 4.10351e7i −0.133150 + 0.0768742i
\(153\) 0 0
\(154\) −1.24227e8 3.25598e8i −0.220869 0.578894i
\(155\) 5.07410e8 0.879088
\(156\) 0 0
\(157\) −6.98264e8 4.03143e8i −1.14927 0.663530i −0.200559 0.979682i \(-0.564276\pi\)
−0.948709 + 0.316152i \(0.897609\pi\)
\(158\) −1.91719e8 + 3.32068e8i −0.307636 + 0.532842i
\(159\) 0 0
\(160\) 1.62320e8i 0.247681i
\(161\) −7.56158e8 + 9.29909e8i −1.12541 + 1.38400i
\(162\) 0 0
\(163\) −2.01244e7 3.48565e7i −0.0285084 0.0493780i 0.851419 0.524486i \(-0.175742\pi\)
−0.879928 + 0.475108i \(0.842409\pi\)
\(164\) −1.57716e8 9.10571e7i −0.218021 0.125875i
\(165\) 0 0
\(166\) −7.50335e7 + 4.33206e7i −0.0988150 + 0.0570509i
\(167\) 2.59671e6i 0.00333854i −0.999999 0.00166927i \(-0.999469\pi\)
0.999999 0.00166927i \(-0.000531346\pi\)
\(168\) 0 0
\(169\) 8.06333e8 0.988480
\(170\) −3.57037e8 6.18406e8i −0.427482 0.740420i
\(171\) 0 0
\(172\) −1.89092e8 + 3.27517e8i −0.216053 + 0.374214i
\(173\) 1.93829e8 1.11907e8i 0.216388 0.124932i −0.387889 0.921706i \(-0.626795\pi\)
0.604277 + 0.796774i \(0.293462\pi\)
\(174\) 0 0
\(175\) 8.91842e8 + 1.43111e8i 0.950902 + 0.152588i
\(176\) 2.10192e8 0.219061
\(177\) 0 0
\(178\) −9.98365e8 5.76406e8i −0.994511 0.574181i
\(179\) 6.89778e8 1.19473e9i 0.671889 1.16375i −0.305479 0.952199i \(-0.598817\pi\)
0.977368 0.211547i \(-0.0678500\pi\)
\(180\) 0 0
\(181\) 1.75868e9i 1.63860i −0.573368 0.819298i \(-0.694364\pi\)
0.573368 0.819298i \(-0.305636\pi\)
\(182\) −6.46085e7 5.25366e7i −0.0588849 0.0478824i
\(183\) 0 0
\(184\) −3.61449e8 6.26047e8i −0.315337 0.546180i
\(185\) 7.05354e8 + 4.07237e8i 0.602172 + 0.347664i
\(186\) 0 0
\(187\) 8.00786e8 4.62334e8i 0.654862 0.378085i
\(188\) 1.02319e9i 0.819081i
\(189\) 0 0
\(190\) 5.61465e8 0.430832
\(191\) −1.03184e9 1.78720e9i −0.775316 1.34289i −0.934617 0.355656i \(-0.884257\pi\)
0.159301 0.987230i \(-0.449076\pi\)
\(192\) 0 0
\(193\) 5.13097e8 8.88711e8i 0.369803 0.640518i −0.619732 0.784814i \(-0.712759\pi\)
0.989535 + 0.144296i \(0.0460918\pi\)
\(194\) 2.85276e8 1.64704e8i 0.201400 0.116278i
\(195\) 0 0
\(196\) −1.50484e8 7.22387e8i −0.101968 0.489492i
\(197\) 1.22831e9 0.815536 0.407768 0.913086i \(-0.366307\pi\)
0.407768 + 0.913086i \(0.366307\pi\)
\(198\) 0 0
\(199\) 2.14905e9 + 1.24076e9i 1.37036 + 0.791178i 0.990973 0.134060i \(-0.0428015\pi\)
0.379387 + 0.925238i \(0.376135\pi\)
\(200\) −2.72396e8 + 4.71805e8i −0.170248 + 0.294878i
\(201\) 0 0
\(202\) 4.10964e8i 0.246830i
\(203\) 7.55992e7 + 1.98145e8i 0.0445178 + 0.116680i
\(204\) 0 0
\(205\) 6.22948e8 + 1.07898e9i 0.352725 + 0.610937i
\(206\) −1.60375e9 9.25928e8i −0.890572 0.514172i
\(207\) 0 0
\(208\) 4.34967e7 2.51128e7i 0.0232382 0.0134166i
\(209\) 7.27052e8i 0.381049i
\(210\) 0 0
\(211\) −3.39729e9 −1.71397 −0.856984 0.515343i \(-0.827665\pi\)
−0.856984 + 0.515343i \(0.827665\pi\)
\(212\) −1.33438e8 2.31121e8i −0.0660594 0.114418i
\(213\) 0 0
\(214\) −1.13293e9 + 1.96229e9i −0.540190 + 0.935637i
\(215\) 2.24064e9 1.29363e9i 1.04862 0.605421i
\(216\) 0 0
\(217\) −2.20429e8 + 1.37367e9i −0.0994100 + 0.619504i
\(218\) −1.68629e9 −0.746633
\(219\) 0 0
\(220\) −1.24533e9 7.18990e8i −0.531610 0.306925i
\(221\) 1.10476e8 1.91349e8i 0.0463124 0.0802154i
\(222\) 0 0
\(223\) 2.09206e8i 0.0845971i 0.999105 + 0.0422986i \(0.0134681\pi\)
−0.999105 + 0.0422986i \(0.986532\pi\)
\(224\) 4.39437e8 + 7.05151e7i 0.174544 + 0.0280085i
\(225\) 0 0
\(226\) 1.13492e9 + 1.96574e9i 0.435042 + 0.753515i
\(227\) −1.09121e9 6.30012e8i −0.410966 0.237271i 0.280239 0.959930i \(-0.409586\pi\)
−0.691205 + 0.722659i \(0.742920\pi\)
\(228\) 0 0
\(229\) 2.99386e9 1.72850e9i 1.08865 0.628534i 0.155435 0.987846i \(-0.450322\pi\)
0.933217 + 0.359312i \(0.116989\pi\)
\(230\) 4.94554e9i 1.76727i
\(231\) 0 0
\(232\) −1.27913e8 −0.0441534
\(233\) 9.17713e8 + 1.58953e9i 0.311375 + 0.539316i 0.978660 0.205485i \(-0.0658773\pi\)
−0.667286 + 0.744802i \(0.732544\pi\)
\(234\) 0 0
\(235\) −3.49998e9 + 6.06215e9i −1.14761 + 1.98772i
\(236\) 9.73023e8 5.61775e8i 0.313672 0.181098i
\(237\) 0 0
\(238\) 1.82927e9 6.97930e8i 0.570124 0.217523i
\(239\) −2.30067e9 −0.705120 −0.352560 0.935789i \(-0.614689\pi\)
−0.352560 + 0.935789i \(0.614689\pi\)
\(240\) 0 0
\(241\) −1.26558e9 7.30684e8i −0.375165 0.216602i 0.300548 0.953767i \(-0.402831\pi\)
−0.675713 + 0.737165i \(0.736164\pi\)
\(242\) −2.81563e8 + 4.87681e8i −0.0820945 + 0.142192i
\(243\) 0 0
\(244\) 1.86187e9i 0.525279i
\(245\) −1.57945e9 + 4.79470e9i −0.438371 + 1.33075i
\(246\) 0 0
\(247\) 8.68652e7 + 1.50455e8i 0.0233377 + 0.0404221i
\(248\) −7.26703e8 4.19562e8i −0.192110 0.110915i
\(249\) 0 0
\(250\) −1.23782e8 + 7.14656e7i −0.0316882 + 0.0182952i
\(251\) 1.53360e9i 0.386381i 0.981161 + 0.193191i \(0.0618836\pi\)
−0.981161 + 0.193191i \(0.938116\pi\)
\(252\) 0 0
\(253\) −6.40408e9 −1.56306
\(254\) 4.78830e7 + 8.29357e7i 0.0115039 + 0.0199254i
\(255\) 0 0
\(256\) −1.34218e8 + 2.32472e8i −0.0312500 + 0.0541266i
\(257\) 2.50705e9 1.44744e9i 0.574685 0.331795i −0.184333 0.982864i \(-0.559013\pi\)
0.759018 + 0.651069i \(0.225679\pi\)
\(258\) 0 0
\(259\) −1.40890e9 + 1.73264e9i −0.313099 + 0.385043i
\(260\) −3.43608e8 −0.0751917
\(261\) 0 0
\(262\) 2.41632e9 + 1.39506e9i 0.512802 + 0.296066i
\(263\) −2.71973e8 + 4.71071e8i −0.0568464 + 0.0984609i −0.893048 0.449961i \(-0.851438\pi\)
0.836202 + 0.548422i \(0.184771\pi\)
\(264\) 0 0
\(265\) 1.82577e9i 0.370222i
\(266\) −2.43912e8 + 1.52001e9i −0.0487198 + 0.303613i
\(267\) 0 0
\(268\) 9.03347e8 + 1.56464e9i 0.175112 + 0.303303i
\(269\) 6.55960e8 + 3.78719e8i 0.125276 + 0.0723282i 0.561328 0.827593i \(-0.310290\pi\)
−0.436052 + 0.899921i \(0.643624\pi\)
\(270\) 0 0
\(271\) −2.65727e9 + 1.53417e9i −0.492672 + 0.284444i −0.725682 0.688030i \(-0.758476\pi\)
0.233010 + 0.972474i \(0.425142\pi\)
\(272\) 1.18089e9i 0.215742i
\(273\) 0 0
\(274\) 4.75163e9 0.843025
\(275\) 2.41314e9 + 4.17967e9i 0.421940 + 0.730822i
\(276\) 0 0
\(277\) 2.87053e9 4.97190e9i 0.487576 0.844506i −0.512322 0.858793i \(-0.671215\pi\)
0.999898 + 0.0142870i \(0.00454786\pi\)
\(278\) 6.28448e9 3.62835e9i 1.05218 0.607477i
\(279\) 0 0
\(280\) −2.36234e9 1.92094e9i −0.384335 0.312523i
\(281\) −1.97804e9 −0.317256 −0.158628 0.987338i \(-0.550707\pi\)
−0.158628 + 0.987338i \(0.550707\pi\)
\(282\) 0 0
\(283\) 5.52235e9 + 3.18833e9i 0.860951 + 0.497070i 0.864331 0.502924i \(-0.167742\pi\)
−0.00337979 + 0.999994i \(0.501076\pi\)
\(284\) −2.14106e9 + 3.70843e9i −0.329121 + 0.570055i
\(285\) 0 0
\(286\) 4.44945e8i 0.0665031i
\(287\) −3.19165e9 + 1.21773e9i −0.470422 + 0.179483i
\(288\) 0 0
\(289\) −8.90405e8 1.54223e9i −0.127643 0.221084i
\(290\) 7.57851e8 + 4.37546e8i 0.107150 + 0.0618631i
\(291\) 0 0
\(292\) −1.43443e8 + 8.28169e7i −0.0197309 + 0.0113917i
\(293\) 7.38690e9i 1.00229i −0.865364 0.501143i \(-0.832913\pi\)
0.865364 0.501143i \(-0.167087\pi\)
\(294\) 0 0
\(295\) −7.68653e9 −1.01494
\(296\) −6.73464e8 1.16647e9i −0.0877298 0.151953i
\(297\) 0 0
\(298\) −1.31220e9 + 2.27280e9i −0.166393 + 0.288201i
\(299\) −1.32525e9 + 7.65134e8i −0.165811 + 0.0957310i
\(300\) 0 0
\(301\) 2.52878e9 + 6.62789e9i 0.308066 + 0.807438i
\(302\) 6.40866e9 0.770441
\(303\) 0 0
\(304\) −8.04120e8 4.64259e8i −0.0941513 0.0543583i
\(305\) −6.36879e9 + 1.10311e10i −0.735966 + 1.27473i
\(306\) 0 0
\(307\) 2.19092e9i 0.246645i 0.992367 + 0.123322i \(0.0393549\pi\)
−0.992367 + 0.123322i \(0.960645\pi\)
\(308\) 2.48746e9 3.05903e9i 0.276410 0.339924i
\(309\) 0 0
\(310\) 2.87035e9 + 4.97158e9i 0.310805 + 0.538329i
\(311\) −7.20343e9 4.15890e9i −0.770013 0.444567i 0.0628665 0.998022i \(-0.479976\pi\)
−0.832879 + 0.553455i \(0.813309\pi\)
\(312\) 0 0
\(313\) 7.36210e8 4.25051e8i 0.0767051 0.0442857i −0.461157 0.887319i \(-0.652565\pi\)
0.537862 + 0.843033i \(0.319232\pi\)
\(314\) 9.12208e9i 0.938373i
\(315\) 0 0
\(316\) −4.33811e9 −0.435063
\(317\) 2.14375e8 + 3.71309e8i 0.0212294 + 0.0367704i 0.876445 0.481502i \(-0.159909\pi\)
−0.855216 + 0.518272i \(0.826575\pi\)
\(318\) 0 0
\(319\) −5.66586e8 + 9.81356e8i −0.0547146 + 0.0947685i
\(320\) 1.59041e9 9.18222e8i 0.151673 0.0875684i
\(321\) 0 0
\(322\) −1.33887e10 2.14844e9i −1.24542 0.199848i
\(323\) −4.08471e9 −0.375276
\(324\) 0 0
\(325\) 9.98741e8 + 5.76623e8i 0.0895199 + 0.0516843i
\(326\) 2.27682e8 3.94357e8i 0.0201585 0.0349155i
\(327\) 0 0
\(328\) 2.06039e9i 0.178014i
\(329\) −1.48911e10 1.21087e10i −1.27099 1.03351i
\(330\) 0 0
\(331\) −3.98245e9 6.89781e9i −0.331771 0.574645i 0.651088 0.759002i \(-0.274313\pi\)
−0.982859 + 0.184358i \(0.940980\pi\)
\(332\) −8.48908e8 4.90117e8i −0.0698728 0.0403411i
\(333\) 0 0
\(334\) 2.54424e7 1.46892e7i 0.00204443 0.00118035i
\(335\) 1.23601e10i 0.981393i
\(336\) 0 0
\(337\) 1.30470e10 1.01156 0.505779 0.862663i \(-0.331205\pi\)
0.505779 + 0.862663i \(0.331205\pi\)
\(338\) 4.56131e9 + 7.90042e9i 0.349480 + 0.605318i
\(339\) 0 0
\(340\) 4.03941e9 6.99647e9i 0.302275 0.523556i
\(341\) −6.43780e9 + 3.71687e9i −0.476124 + 0.274890i
\(342\) 0 0
\(343\) −1.22942e10 6.35884e9i −0.888224 0.459411i
\(344\) −4.27867e9 −0.305545
\(345\) 0 0
\(346\) 2.19292e9 + 1.26608e9i 0.153010 + 0.0883402i
\(347\) 1.30853e10 2.26643e10i 0.902535 1.56324i 0.0783432 0.996926i \(-0.475037\pi\)
0.824192 0.566310i \(-0.191630\pi\)
\(348\) 0 0
\(349\) 7.96331e9i 0.536775i −0.963311 0.268387i \(-0.913509\pi\)
0.963311 0.268387i \(-0.0864907\pi\)
\(350\) 3.64282e9 + 9.54779e9i 0.242754 + 0.636254i
\(351\) 0 0
\(352\) 1.18902e9 + 2.05945e9i 0.0774497 + 0.134147i
\(353\) −2.48989e9 1.43754e9i −0.160354 0.0925806i 0.417675 0.908596i \(-0.362845\pi\)
−0.578030 + 0.816016i \(0.696178\pi\)
\(354\) 0 0
\(355\) 2.53704e10 1.46476e10i 1.59740 0.922261i
\(356\) 1.30426e10i 0.812015i
\(357\) 0 0
\(358\) 1.56079e10 0.950194
\(359\) 1.24261e10 + 2.15226e10i 0.748094 + 1.29574i 0.948735 + 0.316072i \(0.102364\pi\)
−0.200641 + 0.979665i \(0.564302\pi\)
\(360\) 0 0
\(361\) −6.88591e9 + 1.19267e10i −0.405446 + 0.702252i
\(362\) 1.72314e10 9.94858e9i 1.00343 0.579331i
\(363\) 0 0
\(364\) 1.49270e8 9.30223e8i 0.00850290 0.0529885i
\(365\) 1.13315e9 0.0638432
\(366\) 0 0
\(367\) 2.24815e8 + 1.29797e8i 0.0123925 + 0.00715484i 0.506183 0.862426i \(-0.331056\pi\)
−0.493791 + 0.869581i \(0.664389\pi\)
\(368\) 4.08932e9 7.08292e9i 0.222977 0.386208i
\(369\) 0 0
\(370\) 9.21471e9i 0.491671i
\(371\) −4.94276e9 7.93150e8i −0.260900 0.0418658i
\(372\) 0 0
\(373\) −1.72152e10 2.98176e10i −0.889359 1.54042i −0.840634 0.541603i \(-0.817818\pi\)
−0.0487248 0.998812i \(-0.515516\pi\)
\(374\) 9.05986e9 + 5.23071e9i 0.463058 + 0.267346i
\(375\) 0 0
\(376\) 1.00252e10 5.78806e9i 0.501583 0.289589i
\(377\) 2.70774e8i 0.0134042i
\(378\) 0 0
\(379\) 3.06189e10 1.48400 0.741998 0.670402i \(-0.233878\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(380\) 3.17613e9 + 5.50121e9i 0.152322 + 0.263830i
\(381\) 0 0
\(382\) 1.16739e10 2.02198e10i 0.548231 0.949564i
\(383\) −1.73217e10 + 1.00007e10i −0.804999 + 0.464766i −0.845216 0.534425i \(-0.820528\pi\)
0.0402172 + 0.999191i \(0.487195\pi\)
\(384\) 0 0
\(385\) −2.52014e10 + 9.61522e9i −1.14705 + 0.437640i
\(386\) 1.16101e10 0.522980
\(387\) 0 0
\(388\) 3.22753e9 + 1.86342e9i 0.142411 + 0.0822211i
\(389\) −6.06521e9 + 1.05052e10i −0.264879 + 0.458784i −0.967532 0.252749i \(-0.918665\pi\)
0.702653 + 0.711533i \(0.251999\pi\)
\(390\) 0 0
\(391\) 3.59793e10i 1.53938i
\(392\) 6.22665e9 5.56087e9i 0.263700 0.235504i
\(393\) 0 0
\(394\) 6.94837e9 + 1.20349e10i 0.288335 + 0.499412i
\(395\) 2.57021e10 + 1.48391e10i 1.05580 + 0.609565i
\(396\) 0 0
\(397\) −5.98646e9 + 3.45628e9i −0.240995 + 0.139139i −0.615634 0.788032i \(-0.711100\pi\)
0.374639 + 0.927171i \(0.377767\pi\)
\(398\) 2.80751e10i 1.11889i
\(399\) 0 0
\(400\) −6.16363e9 −0.240767
\(401\) 1.26426e10 + 2.18976e10i 0.488944 + 0.846875i 0.999919 0.0127200i \(-0.00404901\pi\)
−0.510975 + 0.859595i \(0.670716\pi\)
\(402\) 0 0
\(403\) −8.88152e8 + 1.53832e9i −0.0336719 + 0.0583214i
\(404\) −4.02660e9 + 2.32476e9i −0.151152 + 0.0872676i
\(405\) 0 0
\(406\) −1.51376e9 + 1.86159e9i −0.0557125 + 0.0685142i
\(407\) −1.19323e10 −0.434857
\(408\) 0 0
\(409\) 6.79049e9 + 3.92049e9i 0.242666 + 0.140103i 0.616401 0.787432i \(-0.288590\pi\)
−0.373736 + 0.927535i \(0.621923\pi\)
\(410\) −7.04785e9 + 1.22072e10i −0.249414 + 0.431998i
\(411\) 0 0
\(412\) 2.09514e10i 0.727149i
\(413\) 3.33918e9 2.08091e10i 0.114773 0.715244i
\(414\) 0 0
\(415\) 3.35303e9 + 5.80762e9i 0.113043 + 0.195797i
\(416\) 4.92109e8 + 2.84119e8i 0.0164319 + 0.00948696i
\(417\) 0 0
\(418\) −7.12363e9 + 4.11283e9i −0.233344 + 0.134721i
\(419\) 4.39321e10i 1.42536i −0.701488 0.712682i \(-0.747480\pi\)
0.701488 0.712682i \(-0.252520\pi\)
\(420\) 0 0
\(421\) 5.72195e9 0.182144 0.0910721 0.995844i \(-0.470971\pi\)
0.0910721 + 0.995844i \(0.470971\pi\)
\(422\) −1.92180e10 3.32865e10i −0.605979 1.04959i
\(423\) 0 0
\(424\) 1.50967e9 2.61483e9i 0.0467111 0.0809059i
\(425\) −2.34821e10 + 1.35574e10i −0.719751 + 0.415548i
\(426\) 0 0
\(427\) −2.70968e10 2.20339e10i −0.815093 0.662795i
\(428\) −2.56352e10 −0.763945
\(429\) 0 0
\(430\) 2.53499e10 + 1.46358e10i 0.741486 + 0.428097i
\(431\) 6.82833e9 1.18270e10i 0.197882 0.342741i −0.749960 0.661483i \(-0.769927\pi\)
0.947841 + 0.318743i \(0.103261\pi\)
\(432\) 0 0
\(433\) 5.05551e10i 1.43818i 0.694917 + 0.719090i \(0.255441\pi\)
−0.694917 + 0.719090i \(0.744559\pi\)
\(434\) −1.47061e10 + 5.61091e9i −0.414514 + 0.158152i
\(435\) 0 0
\(436\) −9.53912e9 1.65222e10i −0.263975 0.457217i
\(437\) 2.44998e10 + 1.41450e10i 0.671795 + 0.387861i
\(438\) 0 0
\(439\) 3.81030e10 2.19988e10i 1.02589 0.592298i 0.110086 0.993922i \(-0.464887\pi\)
0.915805 + 0.401624i \(0.131554\pi\)
\(440\) 1.62689e10i 0.434057i
\(441\) 0 0
\(442\) 2.49978e9 0.0654956
\(443\) 2.48510e9 + 4.30432e9i 0.0645252 + 0.111761i 0.896483 0.443078i \(-0.146113\pi\)
−0.831958 + 0.554839i \(0.812780\pi\)
\(444\) 0 0
\(445\) −4.46140e10 + 7.72738e10i −1.13771 + 1.97057i
\(446\) −2.04980e9 + 1.18345e9i −0.0518049 + 0.0299096i
\(447\) 0 0
\(448\) 1.79493e9 + 4.70448e9i 0.0445589 + 0.116788i
\(449\) 1.19199e10 0.293284 0.146642 0.989190i \(-0.453154\pi\)
0.146642 + 0.989190i \(0.453154\pi\)
\(450\) 0 0
\(451\) −1.58074e10 9.12639e9i −0.382079 0.220594i
\(452\) −1.28401e10 + 2.22398e10i −0.307621 + 0.532816i
\(453\) 0 0
\(454\) 1.42555e10i 0.335552i
\(455\) −4.06634e9 + 5.00072e9i −0.0948765 + 0.116677i
\(456\) 0 0
\(457\) 2.45068e10 + 4.24470e10i 0.561852 + 0.973155i 0.997335 + 0.0729587i \(0.0232441\pi\)
−0.435483 + 0.900197i \(0.643423\pi\)
\(458\) 3.38716e10 + 1.95558e10i 0.769794 + 0.444441i
\(459\) 0 0
\(460\) −4.84562e10 + 2.79762e10i −1.08223 + 0.624824i
\(461\) 5.59070e10i 1.23784i −0.785456 0.618918i \(-0.787571\pi\)
0.785456 0.618918i \(-0.212429\pi\)
\(462\) 0 0
\(463\) 1.00933e10 0.219638 0.109819 0.993952i \(-0.464973\pi\)
0.109819 + 0.993952i \(0.464973\pi\)
\(464\) −7.23587e8 1.25329e9i −0.0156106 0.0270383i
\(465\) 0 0
\(466\) −1.03827e10 + 1.79834e10i −0.220175 + 0.381354i
\(467\) 7.53687e10 4.35142e10i 1.58461 0.914878i 0.590442 0.807080i \(-0.298954\pi\)
0.994173 0.107797i \(-0.0343798\pi\)
\(468\) 0 0
\(469\) 3.34616e10 + 5.36948e9i 0.691600 + 0.110979i
\(470\) −7.91956e10 −1.62297
\(471\) 0 0
\(472\) 1.10085e10 + 6.35576e9i 0.221799 + 0.128056i
\(473\) −1.89522e10 + 3.28261e10i −0.378629 + 0.655806i
\(474\) 0 0
\(475\) 2.13200e10i 0.418806i
\(476\) 1.71862e10 + 1.39750e10i 0.334774 + 0.272222i
\(477\) 0 0
\(478\) −1.30146e10 2.25419e10i −0.249298 0.431796i
\(479\) −5.19458e10 2.99909e10i −0.986752 0.569701i −0.0824501 0.996595i \(-0.526275\pi\)
−0.904302 + 0.426894i \(0.859608\pi\)
\(480\) 0 0
\(481\) −2.46925e9 + 1.42562e9i −0.0461302 + 0.0266333i
\(482\) 1.65335e10i 0.306321i
\(483\) 0 0
\(484\) −6.37104e9 −0.116099
\(485\) −1.27482e10 2.20805e10i −0.230399 0.399063i
\(486\) 0 0
\(487\) −2.90910e10 + 5.03871e10i −0.517182 + 0.895785i 0.482619 + 0.875830i \(0.339686\pi\)
−0.999801 + 0.0199548i \(0.993648\pi\)
\(488\) 1.82425e10 1.05323e10i 0.321666 0.185714i
\(489\) 0 0
\(490\) −5.59130e10 + 1.16475e10i −0.969903 + 0.202045i
\(491\) 7.31652e10 1.25886 0.629432 0.777056i \(-0.283288\pi\)
0.629432 + 0.777056i \(0.283288\pi\)
\(492\) 0 0
\(493\) −5.51343e9 3.18318e9i −0.0933328 0.0538857i
\(494\) −9.82768e8 + 1.70220e9i −0.0165022 + 0.0285827i
\(495\) 0 0
\(496\) 9.49361e9i 0.156857i
\(497\) 2.86329e10 + 7.50466e10i 0.469289 + 1.23000i
\(498\) 0 0
\(499\) −3.13183e10 5.42448e10i −0.505121 0.874895i −0.999982 0.00592344i \(-0.998115\pi\)
0.494861 0.868972i \(-0.335219\pi\)
\(500\) −1.40043e9 8.08541e8i −0.0224069 0.0129367i
\(501\) 0 0
\(502\) −1.50261e10 + 8.67533e9i −0.236609 + 0.136606i
\(503\) 1.86966e10i 0.292072i 0.989279 + 0.146036i \(0.0466515\pi\)
−0.989279 + 0.146036i \(0.953348\pi\)
\(504\) 0 0
\(505\) 3.18087e10 0.489081
\(506\) −3.62270e10 6.27469e10i −0.552624 0.957173i
\(507\) 0 0
\(508\) −5.41734e8 + 9.38311e8i −0.00813451 + 0.0140894i
\(509\) −6.80948e10 + 3.93145e10i −1.01448 + 0.585709i −0.912500 0.409078i \(-0.865851\pi\)
−0.101978 + 0.994787i \(0.532517\pi\)
\(510\) 0 0
\(511\) −4.92262e8 + 3.06768e9i −0.00721959 + 0.0449911i
\(512\) −3.03700e9 −0.0441942
\(513\) 0 0
\(514\) 2.83640e10 + 1.63760e10i 0.406364 + 0.234614i
\(515\) −7.16671e10 + 1.24131e11i −1.01880 + 1.76462i
\(516\) 0 0
\(517\) 1.02552e11i 1.43543i
\(518\) −2.49463e10 4.00305e9i −0.346487 0.0555997i
\(519\) 0 0
\(520\) −1.94374e9 3.36666e9i −0.0265843 0.0460453i
\(521\) 2.52432e10 + 1.45742e10i 0.342605 + 0.197803i 0.661423 0.750013i \(-0.269953\pi\)
−0.318818 + 0.947816i \(0.603286\pi\)
\(522\) 0 0
\(523\) −5.31017e9 + 3.06583e9i −0.0709744 + 0.0409771i −0.535067 0.844809i \(-0.679714\pi\)
0.464093 + 0.885787i \(0.346380\pi\)
\(524\) 3.15667e10i 0.418701i
\(525\) 0 0
\(526\) −6.15405e9 −0.0803930
\(527\) −2.08820e10 3.61687e10i −0.270726 0.468911i
\(528\) 0 0
\(529\) −8.54374e10 + 1.47982e11i −1.09100 + 1.88967i
\(530\) −1.78888e10 + 1.03281e10i −0.226714 + 0.130893i
\(531\) 0 0
\(532\) −1.62728e10 + 6.20864e9i −0.203149 + 0.0775087i
\(533\) −4.36154e9 −0.0540419
\(534\) 0 0
\(535\) 1.51882e11 + 8.76889e10i 1.85392 + 1.07036i
\(536\) −1.02202e10 + 1.77019e10i −0.123823 + 0.214467i
\(537\) 0 0
\(538\) 8.56942e9i 0.102287i
\(539\) −1.50826e10 7.24028e10i −0.178698 0.857828i
\(540\) 0 0
\(541\) −6.25770e10 1.08386e11i −0.730509 1.26528i −0.956666 0.291188i \(-0.905950\pi\)
0.226157 0.974091i \(-0.427384\pi\)
\(542\) −3.00635e10 1.73572e10i −0.348372 0.201132i
\(543\) 0 0
\(544\) −1.15703e10 + 6.68014e9i −0.132115 + 0.0762764i
\(545\) 1.30520e11i 1.47941i
\(546\) 0 0
\(547\) −8.08478e9 −0.0903064 −0.0451532 0.998980i \(-0.514378\pi\)
−0.0451532 + 0.998980i \(0.514378\pi\)
\(548\) 2.68793e10 + 4.65563e10i 0.298054 + 0.516245i
\(549\) 0 0
\(550\) −2.73015e10 + 4.72876e10i −0.298357 + 0.516769i
\(551\) 4.33513e9 2.50289e9i 0.0470322 0.0271541i
\(552\) 0 0
\(553\) −5.13383e10 + 6.31350e10i −0.548961 + 0.675102i
\(554\) 6.49526e10 0.689537
\(555\) 0 0
\(556\) 7.11008e10 + 4.10501e10i 0.744004 + 0.429551i
\(557\) −2.26100e10 + 3.91616e10i −0.234898 + 0.406855i −0.959243 0.282583i \(-0.908809\pi\)
0.724345 + 0.689438i \(0.242142\pi\)
\(558\) 0 0
\(559\) 9.05731e9i 0.0927582i
\(560\) 5.45789e9 3.40125e10i 0.0554974 0.345849i
\(561\) 0 0
\(562\) −1.11895e10 1.93807e10i −0.112167 0.194279i
\(563\) 1.60535e11 + 9.26851e10i 1.59785 + 0.922521i 0.991900 + 0.127021i \(0.0405414\pi\)
0.605953 + 0.795500i \(0.292792\pi\)
\(564\) 0 0
\(565\) 1.52149e11 8.78431e10i 1.49305 0.862013i
\(566\) 7.21437e10i 0.702963i
\(567\) 0 0
\(568\) −4.84467e10 −0.465448
\(569\) −1.00436e11 1.73960e11i −0.958164 1.65959i −0.726957 0.686683i \(-0.759066\pi\)
−0.231207 0.972905i \(-0.574267\pi\)
\(570\) 0 0
\(571\) 1.50052e10 2.59897e10i 0.141155 0.244488i −0.786777 0.617238i \(-0.788252\pi\)
0.927932 + 0.372750i \(0.121585\pi\)
\(572\) 4.35955e9 2.51699e9i 0.0407247 0.0235124i
\(573\) 0 0
\(574\) −2.99860e10 2.43831e10i −0.276230 0.224617i
\(575\) 1.87792e11 1.71794
\(576\) 0 0
\(577\) 7.61972e10 + 4.39925e10i 0.687442 + 0.396895i 0.802653 0.596446i \(-0.203421\pi\)
−0.115211 + 0.993341i \(0.536754\pi\)
\(578\) 1.00738e10 1.74483e10i 0.0902570 0.156330i
\(579\) 0 0
\(580\) 9.90053e9i 0.0874876i
\(581\) −1.71791e10 + 6.55445e9i −0.150764 + 0.0575217i
\(582\) 0 0
\(583\) −1.33741e10 2.31646e10i −0.115768 0.200516i
\(584\) −1.62287e9 9.36966e8i −0.0139519 0.00805513i
\(585\) 0 0
\(586\) 7.23766e10 4.17866e10i 0.613773 0.354362i
\(587\) 4.35775e10i 0.367037i −0.983016 0.183519i \(-0.941251\pi\)
0.983016 0.183519i \(-0.0587487\pi\)
\(588\) 0 0
\(589\) 3.28384e10 0.272848
\(590\) −4.34816e10 7.53123e10i −0.358837 0.621524i
\(591\) 0 0
\(592\) 7.61937e9 1.31971e10i 0.0620344 0.107447i
\(593\) 1.49827e11 8.65027e10i 1.21163 0.699537i 0.248519 0.968627i \(-0.420056\pi\)
0.963115 + 0.269090i \(0.0867227\pi\)
\(594\) 0 0
\(595\) −5.40200e10 1.41586e11i −0.431010 1.12967i
\(596\) −2.96917e10 −0.235315
\(597\) 0 0
\(598\) −1.49935e10 8.65650e9i −0.117246 0.0676920i
\(599\) 7.79310e10 1.34981e11i 0.605345 1.04849i −0.386652 0.922226i \(-0.626368\pi\)
0.991997 0.126263i \(-0.0402983\pi\)
\(600\) 0 0
\(601\) 1.42951e11i 1.09569i −0.836580 0.547845i \(-0.815448\pi\)
0.836580 0.547845i \(-0.184552\pi\)
\(602\) −5.06349e10 + 6.22698e10i −0.385535 + 0.474124i
\(603\) 0 0
\(604\) 3.62529e10 + 6.27918e10i 0.272392 + 0.471797i
\(605\) 3.77467e10 + 2.17931e10i 0.281746 + 0.162666i
\(606\) 0 0
\(607\) −1.53187e11 + 8.84427e10i −1.12841 + 0.651489i −0.943535 0.331272i \(-0.892522\pi\)
−0.184877 + 0.982762i \(0.559189\pi\)
\(608\) 1.05050e10i 0.0768742i
\(609\) 0 0
\(610\) −1.44109e11 −1.04081
\(611\) −1.22525e10 2.12219e10i −0.0879142 0.152272i
\(612\) 0 0
\(613\) −6.87312e10 + 1.19046e11i −0.486757 + 0.843088i −0.999884 0.0152246i \(-0.995154\pi\)
0.513127 + 0.858313i \(0.328487\pi\)
\(614\) −2.14665e10 + 1.23937e10i −0.151039 + 0.0872022i
\(615\) 0 0
\(616\) 4.40435e10 + 7.06753e9i 0.305885 + 0.0490845i
\(617\) 1.18079e10 0.0814761 0.0407381 0.999170i \(-0.487029\pi\)
0.0407381 + 0.999170i \(0.487029\pi\)
\(618\) 0 0
\(619\) 1.06013e11 + 6.12069e10i 0.722102 + 0.416906i 0.815526 0.578721i \(-0.196448\pi\)
−0.0934240 + 0.995626i \(0.529781\pi\)
\(620\) −3.24743e10 + 5.62471e10i −0.219772 + 0.380656i
\(621\) 0 0
\(622\) 9.41052e10i 0.628713i
\(623\) −1.89816e11 1.54349e11i −1.26003 1.02460i
\(624\) 0 0
\(625\) 7.90076e10 + 1.36845e11i 0.517784 + 0.896829i
\(626\) 8.32926e9 + 4.80890e9i 0.0542387 + 0.0313147i
\(627\) 0 0
\(628\) 8.93778e10 5.16023e10i 0.574634 0.331765i
\(629\) 6.70378e10i 0.428270i
\(630\) 0 0
\(631\) 6.31617e10 0.398416 0.199208 0.979957i \(-0.436163\pi\)
0.199208 + 0.979957i \(0.436163\pi\)
\(632\) −2.45401e10 4.25047e10i −0.153818 0.266421i
\(633\) 0 0
\(634\) −2.42538e9 + 4.20088e9i −0.0150114 + 0.0260006i
\(635\) 6.41925e9 3.70616e9i 0.0394811 0.0227944i
\(636\) 0 0
\(637\) −1.17716e10 1.31809e10i −0.0714950 0.0800548i
\(638\) −1.28204e10 −0.0773782
\(639\) 0 0
\(640\) 1.79934e10 + 1.03885e10i 0.107249 + 0.0619202i
\(641\) −1.41683e11 + 2.45402e11i −0.839239 + 1.45360i 0.0512925 + 0.998684i \(0.483666\pi\)
−0.890532 + 0.454921i \(0.849667\pi\)
\(642\) 0 0
\(643\) 1.63523e11i 0.956608i −0.878194 0.478304i \(-0.841252\pi\)
0.878194 0.478304i \(-0.158748\pi\)
\(644\) −5.46875e10 1.43335e11i −0.317940 0.833316i
\(645\) 0 0
\(646\) −2.31066e10 4.00218e10i −0.132680 0.229809i
\(647\) 7.92369e10 + 4.57474e10i 0.452179 + 0.261066i 0.708750 0.705460i \(-0.249259\pi\)
−0.256571 + 0.966525i \(0.582593\pi\)
\(648\) 0 0
\(649\) 9.75233e10 5.63051e10i 0.549705 0.317372i
\(650\) 1.30475e10i 0.0730927i
\(651\) 0 0
\(652\) 5.15185e9 0.0285084
\(653\) 7.72477e10 + 1.33797e11i 0.424847 + 0.735857i 0.996406 0.0847040i \(-0.0269945\pi\)
−0.571559 + 0.820561i \(0.693661\pi\)
\(654\) 0 0
\(655\) 1.07978e11 1.87024e11i 0.586640 1.01609i
\(656\) 2.01876e10 1.16553e10i 0.109011 0.0629374i
\(657\) 0 0
\(658\) 3.44041e10 2.14400e11i 0.183530 1.14372i
\(659\) 6.38574e9 0.0338586 0.0169293 0.999857i \(-0.494611\pi\)
0.0169293 + 0.999857i \(0.494611\pi\)
\(660\) 0 0
\(661\) 1.84299e11 + 1.06405e11i 0.965423 + 0.557387i 0.897838 0.440326i \(-0.145137\pi\)
0.0675854 + 0.997713i \(0.478470\pi\)
\(662\) 4.50563e10 7.80398e10i 0.234598 0.406335i
\(663\) 0 0
\(664\) 1.10901e10i 0.0570509i
\(665\) 1.17649e11 + 1.88788e10i 0.601593 + 0.0965358i
\(666\) 0 0
\(667\) 2.20461e10 + 3.81850e10i 0.111386 + 0.192926i
\(668\) 2.87848e8 + 1.66189e8i 0.00144563 + 0.000834636i
\(669\) 0 0
\(670\) 1.21104e11 6.99193e10i 0.600978 0.346975i
\(671\) 1.86610e11i 0.920544i
\(672\) 0 0
\(673\) −3.32635e11 −1.62147 −0.810734 0.585415i \(-0.800932\pi\)
−0.810734 + 0.585415i \(0.800932\pi\)
\(674\) 7.38049e10 + 1.27834e11i 0.357639 + 0.619450i
\(675\) 0 0
\(676\) −5.16053e10 + 8.93830e10i −0.247120 + 0.428024i
\(677\) −3.35630e11 + 1.93776e11i −1.59774 + 0.922456i −0.605819 + 0.795603i \(0.707154\pi\)
−0.991922 + 0.126853i \(0.959512\pi\)
\(678\) 0 0
\(679\) 6.53148e10 2.49199e10i 0.307279 0.117238i
\(680\) 9.14015e10 0.427482
\(681\) 0 0
\(682\) −7.28354e10 4.20515e10i −0.336670 0.194377i
\(683\) 1.26032e11 2.18293e11i 0.579157 1.00313i −0.416419 0.909173i \(-0.636715\pi\)
0.995576 0.0939571i \(-0.0299517\pi\)
\(684\) 0 0
\(685\) 3.67778e11i 1.67041i
\(686\) −7.24267e9 1.56429e11i −0.0327041 0.706350i
\(687\) 0 0
\(688\) −2.42038e10 4.19222e10i −0.108026 0.187107i
\(689\) −5.53522e9 3.19576e9i −0.0245617 0.0141807i
\(690\) 0 0
\(691\) −2.42724e11 + 1.40137e11i −1.06463 + 0.614666i −0.926710 0.375777i \(-0.877376\pi\)
−0.137923 + 0.990443i \(0.544043\pi\)
\(692\) 2.86482e10i 0.124932i
\(693\) 0 0
\(694\) 2.96085e11 1.27638
\(695\) −2.80835e11 4.86421e11i −1.20368 2.08484i
\(696\) 0 0
\(697\) 5.12737e10 8.88086e10i 0.217252 0.376291i
\(698\) 7.80242e10 4.50473e10i 0.328706 0.189778i
\(699\) 0 0
\(700\) −7.29420e10 + 8.97027e10i −0.303798 + 0.373606i
\(701\) 1.30623e11 0.540939 0.270469 0.962729i \(-0.412821\pi\)
0.270469 + 0.962729i \(0.412821\pi\)
\(702\) 0 0
\(703\) 4.56489e10 + 2.63554e10i 0.186900 + 0.107907i
\(704\) −1.34523e10 + 2.33000e10i −0.0547652 + 0.0948561i
\(705\) 0 0
\(706\) 3.25277e10i 0.130929i
\(707\) −1.38183e10 + 8.61132e10i −0.0553067 + 0.344661i
\(708\) 0 0
\(709\) −1.43526e11 2.48595e11i −0.567997 0.983800i −0.996764 0.0803847i \(-0.974385\pi\)
0.428767 0.903415i \(-0.358948\pi\)
\(710\) 2.87034e11 + 1.65719e11i 1.12953 + 0.652137i
\(711\) 0 0
\(712\) 1.27791e11 7.37800e10i 0.497255 0.287090i
\(713\) 2.89250e11i 1.11922i
\(714\) 0 0
\(715\) −3.44388e10 −0.131772
\(716\) 8.82916e10 + 1.52926e11i 0.335944 + 0.581873i
\(717\) 0 0
\(718\) −1.40585e11 + 2.43500e11i −0.528982 + 0.916224i
\(719\) −3.30933e10 + 1.91064e10i −0.123830 + 0.0714931i −0.560635 0.828063i \(-0.689443\pi\)
0.436806 + 0.899556i \(0.356110\pi\)
\(720\) 0 0
\(721\) −3.04917e11 2.47944e11i −1.12834 0.917513i
\(722\) −1.55810e11 −0.573387
\(723\) 0 0
\(724\) 1.94952e11 + 1.12555e11i 0.709533 + 0.409649i
\(725\) 1.66145e10 2.87772e10i 0.0601361 0.104159i
\(726\) 0 0
\(727\) 1.60138e11i 0.573268i −0.958040 0.286634i \(-0.907464\pi\)
0.958040 0.286634i \(-0.0925364\pi\)
\(728\) 9.95869e9 3.79959e9i 0.0354549 0.0135273i
\(729\) 0 0
\(730\) 6.41005e9 + 1.11025e10i 0.0225720 + 0.0390958i
\(731\) −1.84423e11 1.06477e11i −0.645871 0.372894i
\(732\) 0 0
\(733\) −2.36694e11 + 1.36655e11i −0.819920 + 0.473381i −0.850389 0.526154i \(-0.823633\pi\)
0.0304686 + 0.999536i \(0.490300\pi\)
\(734\) 2.93697e9i 0.0101185i
\(735\) 0 0
\(736\) 9.25308e10 0.315337
\(737\) 9.05399e10 + 1.56820e11i 0.306881 + 0.531534i
\(738\) 0 0
\(739\) −2.04395e11 + 3.54022e11i −0.685317 + 1.18700i 0.288020 + 0.957624i \(0.407003\pi\)
−0.973337 + 0.229380i \(0.926330\pi\)
\(740\) −9.02854e10 + 5.21263e10i −0.301086 + 0.173832i
\(741\) 0 0
\(742\) −2.01892e10 5.29157e10i −0.0666046 0.174570i
\(743\) 3.69962e10 0.121395 0.0606977 0.998156i \(-0.480667\pi\)
0.0606977 + 0.998156i \(0.480667\pi\)
\(744\) 0 0
\(745\) 1.75915e11 + 1.01565e11i 0.571056 + 0.329699i
\(746\) 1.94768e11 3.37348e11i 0.628872 1.08924i
\(747\) 0 0
\(748\) 1.18358e11i 0.378085i
\(749\) −3.03374e11 + 3.73083e11i −0.963941 + 1.18544i
\(750\) 0 0
\(751\) 1.71650e11 + 2.97307e11i 0.539616 + 0.934642i 0.998925 + 0.0463654i \(0.0147639\pi\)
−0.459309 + 0.888277i \(0.651903\pi\)
\(752\) 1.13422e11 + 6.54845e10i 0.354673 + 0.204770i
\(753\) 0 0
\(754\) −2.65303e9 + 1.53173e9i −0.00820837 + 0.00473910i
\(755\) 4.96032e11i 1.52659i
\(756\) 0 0
\(757\) 3.19344e11 0.972468 0.486234 0.873829i \(-0.338370\pi\)
0.486234 + 0.873829i \(0.338370\pi\)
\(758\) 1.73207e11 + 3.00003e11i 0.524672 + 0.908759i
\(759\) 0 0
\(760\) −3.59338e10 + 6.22391e10i −0.107708 + 0.186556i
\(761\) −3.31461e11 + 1.91369e11i −0.988312 + 0.570602i −0.904769 0.425902i \(-0.859957\pi\)
−0.0835424 + 0.996504i \(0.526623\pi\)
\(762\) 0 0
\(763\) −3.53346e11 5.67003e10i −1.04256 0.167297i
\(764\) 2.64151e11 0.775316
\(765\) 0 0
\(766\) −1.95973e11 1.13145e11i −0.569220 0.328639i
\(767\) 1.34542e10 2.33034e10i 0.0388756 0.0673345i
\(768\) 0 0
\(769\) 6.74904e11i 1.92991i 0.262417 + 0.964955i \(0.415480\pi\)
−0.262417 + 0.964955i \(0.584520\pi\)
\(770\) −2.36770e11 1.92530e11i −0.673541 0.547691i
\(771\) 0 0
\(772\) 6.56764e10 + 1.13755e11i 0.184902 + 0.320259i
\(773\) −1.92323e10 1.11038e10i −0.0538658 0.0310994i 0.472825 0.881156i \(-0.343234\pi\)
−0.526691 + 0.850057i \(0.676568\pi\)
\(774\) 0 0
\(775\) 1.88781e11 1.08993e11i 0.523301 0.302128i
\(776\) 4.21643e10i 0.116278i
\(777\) 0 0
\(778\) −1.37240e11 −0.374595
\(779\) 4.03157e10 + 6.98288e10i 0.109477 + 0.189620i
\(780\) 0 0
\(781\) −2.14593e11 + 3.71685e11i −0.576781 + 0.999013i
\(782\) 3.52523e11 2.03529e11i 0.942672 0.544252i
\(783\) 0 0
\(784\) 8.97085e10 + 2.95514e10i 0.237448 + 0.0782194i
\(785\) −7.06052e11 −1.85934
\(786\) 0 0
\(787\) 9.20770e10 + 5.31607e10i 0.240023 + 0.138577i 0.615187 0.788381i \(-0.289080\pi\)
−0.375165 + 0.926958i \(0.622414\pi\)
\(788\) −7.86118e10 + 1.36160e11i −0.203884 + 0.353137i
\(789\) 0 0
\(790\) 3.35771e11i 0.862055i
\(791\) 1.71714e11 + 4.50061e11i 0.438632 + 1.14965i
\(792\) 0 0
\(793\) −2.22954e10 3.86168e10i −0.0563797 0.0976524i
\(794\) −6.77291e10 3.91034e10i −0.170409 0.0983858i
\(795\) 0 0
\(796\) −2.75079e11 + 1.58817e11i −0.685180 + 0.395589i
\(797\) 4.77766e10i 0.118408i −0.998246 0.0592041i \(-0.981144\pi\)
0.998246 0.0592041i \(-0.0188563\pi\)
\(798\) 0 0
\(799\) 5.76155e11 1.41368
\(800\) −3.48668e10 6.03910e10i −0.0851239 0.147439i
\(801\) 0 0
\(802\) −1.43035e11 + 2.47743e11i −0.345735 + 0.598831i
\(803\) −1.43769e10 + 8.30050e9i −0.0345782 + 0.0199637i
\(804\) 0 0
\(805\) −1.66290e11 + 1.03629e12i −0.395989 + 2.46773i
\(806\) −2.00966e10 −0.0476192
\(807\) 0 0
\(808\) −4.55558e10 2.63017e10i −0.106880 0.0617075i
\(809\) −4.04920e11 + 7.01341e11i −0.945311 + 1.63733i −0.190183 + 0.981749i \(0.560908\pi\)
−0.755128 + 0.655578i \(0.772425\pi\)
\(810\) 0 0
\(811\) 3.75704e11i 0.868484i −0.900796 0.434242i \(-0.857016\pi\)
0.900796 0.434242i \(-0.142984\pi\)
\(812\) −2.68029e10 4.30099e9i −0.0616536 0.00989336i
\(813\) 0 0
\(814\) −6.74993e10 1.16912e11i −0.153745 0.266295i
\(815\) −3.05233e10 1.76226e10i −0.0691833 0.0399430i
\(816\) 0 0
\(817\) 1.45009e11 8.37209e10i 0.325467 0.187908i
\(818\) 8.87106e10i 0.198136i
\(819\) 0 0
\(820\) −1.59475e11 −0.352725
\(821\) 1.38321e11 + 2.39579e11i 0.304450 + 0.527323i 0.977139 0.212603i \(-0.0681940\pi\)
−0.672689 + 0.739926i \(0.734861\pi\)
\(822\) 0 0
\(823\) 1.99482e11 3.45513e11i 0.434814 0.753121i −0.562466 0.826820i \(-0.690147\pi\)
0.997280 + 0.0736996i \(0.0234806\pi\)
\(824\) 2.05281e11 1.18519e11i 0.445286 0.257086i
\(825\) 0 0
\(826\) 2.22776e11 8.49971e10i 0.478574 0.182593i
\(827\) 4.78161e11 1.02224 0.511119 0.859510i \(-0.329231\pi\)
0.511119 + 0.859510i \(0.329231\pi\)
\(828\) 0 0
\(829\) −4.13580e11 2.38780e11i −0.875671 0.505569i −0.00644231 0.999979i \(-0.502051\pi\)
−0.869229 + 0.494410i \(0.835384\pi\)
\(830\) −3.79352e10 + 6.57057e10i −0.0799337 + 0.138449i
\(831\) 0 0
\(832\) 6.42888e9i 0.0134166i
\(833\) 4.06772e11 8.47365e10i 0.844832 0.175991i
\(834\) 0 0
\(835\) −1.13695e9 1.96925e9i −0.00233881 0.00405094i
\(836\) −8.05946e10 4.65313e10i −0.164999 0.0952622i
\(837\) 0 0
\(838\) 4.30445e11 2.48517e11i 0.872853 0.503942i
\(839\) 4.93131e11i 0.995209i −0.867404 0.497604i \(-0.834213\pi\)
0.867404 0.497604i \(-0.165787\pi\)
\(840\) 0 0
\(841\) −4.92444e11 −0.984404
\(842\) 3.23682e10 + 5.60634e10i 0.0643977 + 0.111540i
\(843\) 0 0
\(844\) 2.17427e11 3.76594e11i 0.428492 0.742170i
\(845\) 6.11495e11 3.53047e11i 1.19941 0.692477i
\(846\) 0 0
\(847\) −7.53965e10 + 9.27213e10i −0.146493 + 0.180155i
\(848\) 3.41600e10 0.0660594
\(849\) 0 0
\(850\) −2.65670e11 1.53385e11i −0.508941 0.293837i
\(851\) −2.32146e11 + 4.02088e11i −0.442632 + 0.766661i
\(852\) 0 0
\(853\) 6.24713e11i 1.18001i 0.807401 + 0.590004i \(0.200874\pi\)
−0.807401 + 0.590004i \(0.799126\pi\)
\(854\) 6.26039e10 3.90136e11i 0.117698 0.733474i
\(855\) 0 0
\(856\) −1.45015e11 2.51173e11i −0.270095 0.467819i
\(857\) 7.96567e10 + 4.59898e10i 0.147672 + 0.0852587i 0.572016 0.820243i \(-0.306162\pi\)
−0.424343 + 0.905501i \(0.639495\pi\)
\(858\) 0 0
\(859\) −3.04542e11 + 1.75827e11i −0.559338 + 0.322934i −0.752880 0.658158i \(-0.771336\pi\)
0.193541 + 0.981092i \(0.438003\pi\)
\(860\) 3.31170e11i 0.605421i
\(861\) 0 0
\(862\) 1.54507e11 0.279847
\(863\) 1.79901e11 + 3.11598e11i 0.324333 + 0.561762i 0.981377 0.192091i \(-0.0615268\pi\)
−0.657044 + 0.753852i \(0.728193\pi\)
\(864\) 0 0
\(865\) 9.79953e10 1.69733e11i 0.175041 0.303181i
\(866\) −4.95336e11 + 2.85983e11i −0.880701 + 0.508473i
\(867\) 0 0
\(868\) −1.38166e11 1.12350e11i −0.243401 0.197922i
\(869\) −4.34797e11 −0.762442
\(870\) 0 0
\(871\) 3.74724e10 + 2.16347e10i 0.0651086 + 0.0375905i
\(872\) 1.07923e11 1.86928e11i 0.186658 0.323302i
\(873\) 0 0
\(874\) 3.20064e11i 0.548518i
\(875\) −2.83402e10 + 1.08128e10i −0.0483472 + 0.0184462i
\(876\) 0 0
\(877\) −5.31314e11 9.20263e11i −0.898158 1.55566i −0.829847 0.557991i \(-0.811572\pi\)
−0.0683115 0.997664i \(-0.521761\pi\)
\(878\) 4.31086e11 + 2.48888e11i 0.725414 + 0.418818i
\(879\) 0 0
\(880\) 1.59402e11 9.20307e10i 0.265805 0.153462i
\(881\) 3.25470e11i 0.540266i −0.962823 0.270133i \(-0.912932\pi\)
0.962823 0.270133i \(-0.0870677\pi\)
\(882\) 0 0
\(883\) 4.60107e11 0.756861 0.378431 0.925630i \(-0.376464\pi\)
0.378431 + 0.925630i \(0.376464\pi\)
\(884\) 1.41409e10 + 2.44927e10i 0.0231562 + 0.0401077i
\(885\) 0 0
\(886\) −2.81157e10 + 4.86979e10i −0.0456262 + 0.0790269i
\(887\) 4.83578e11 2.79194e11i 0.781217 0.451036i −0.0556445 0.998451i \(-0.517721\pi\)
0.836861 + 0.547415i \(0.184388\pi\)
\(888\) 0 0
\(889\) 7.24474e9 + 1.89884e10i 0.0115989 + 0.0304005i
\(890\) −1.00950e12 −1.60896
\(891\) 0 0
\(892\) −2.31908e10 1.33892e10i −0.0366316 0.0211493i
\(893\) −2.26511e11 + 3.92328e11i −0.356191 + 0.616941i
\(894\) 0 0
\(895\) 1.20806e12i 1.88276i
\(896\) −3.59406e10 + 4.41991e10i −0.0557640 + 0.0685775i
\(897\) 0 0
\(898\) 6.74293e10 + 1.16791e11i 0.103691 + 0.179599i
\(899\) 4.43244e10 + 2.55907e10i 0.0678585 + 0.0391781i
\(900\) 0 0
\(901\) 1.30143e11 7.51379e10i 0.197479 0.114014i
\(902\) 2.06507e11i 0.311967i
\(903\) 0 0
\(904\) −2.90539e11 −0.435042
\(905\) −7.70023e11 1.33372e12i −1.14791 1.98825i
\(906\) 0 0
\(907\) 2.39788e11 4.15326e11i 0.354323 0.613705i −0.632679 0.774414i \(-0.718045\pi\)
0.987002 + 0.160709i \(0.0513781\pi\)
\(908\) 1.39675e11 8.06415e10i 0.205483 0.118636i
\(909\) 0 0
\(910\) −7.19995e10 1.15535e10i −0.104994 0.0168481i
\(911\) −5.85058e11 −0.849426 −0.424713 0.905328i \(-0.639625\pi\)
−0.424713 + 0.905328i \(0.639625\pi\)
\(912\) 0 0
\(913\) −8.50836e10 4.91230e10i −0.122451 0.0706972i
\(914\) −2.77263e11 + 4.80233e11i −0.397289 + 0.688125i
\(915\) 0 0
\(916\) 4.42497e11i 0.628534i
\(917\) 4.59408e11 + 3.73569e11i 0.649712 + 0.528315i
\(918\) 0 0
\(919\) 6.64889e11 + 1.15162e12i 0.932152 + 1.61454i 0.779635 + 0.626234i \(0.215405\pi\)
0.152517 + 0.988301i \(0.451262\pi\)
\(920\) −5.48220e11 3.16515e11i −0.765250 0.441817i
\(921\) 0 0
\(922\) 5.47775e11 3.16258e11i 0.758016 0.437641i
\(923\) 1.02555e11i 0.141302i
\(924\) 0 0
\(925\) 3.49901e11 0.477946
\(926\) 5.70962e10 + 9.88936e10i 0.0776539 + 0.134501i
\(927\) 0 0
\(928\) 8.18645e9 1.41794e10i 0.0110383 0.0191190i
\(929\) 6.13628e11 3.54278e11i 0.823839 0.475644i −0.0278995 0.999611i \(-0.508882\pi\)
0.851739 + 0.523967i \(0.175549\pi\)
\(930\) 0 0
\(931\) −1.02218e11 + 3.10301e11i −0.136060 + 0.413033i
\(932\) −2.34934e11 −0.311375
\(933\) 0 0
\(934\) 8.52700e11 + 4.92306e11i 1.12049 + 0.646916i
\(935\) 4.04859e11 7.01236e11i 0.529733 0.917524i
\(936\) 0 0
\(937\) 2.84697e11i 0.369338i 0.982801 + 0.184669i \(0.0591213\pi\)
−0.982801 + 0.184669i \(0.940879\pi\)
\(938\) 1.36677e11 + 3.58229e11i 0.176557 + 0.462754i
\(939\) 0 0
\(940\) −4.47998e11 7.75955e11i −0.573805 0.993860i
\(941\) −9.65681e11 5.57536e11i −1.23162 0.711073i −0.264249 0.964455i \(-0.585124\pi\)
−0.967366 + 0.253381i \(0.918457\pi\)
\(942\) 0 0
\(943\) −6.15072e11 + 3.55112e11i −0.777820 + 0.449075i
\(944\) 1.43814e11i 0.181098i
\(945\) 0 0
\(946\) −4.28839e11 −0.535463
\(947\) 2.79065e11 + 4.83354e11i 0.346981 + 0.600988i 0.985712 0.168442i \(-0.0538737\pi\)
−0.638731 + 0.769430i \(0.720540\pi\)
\(948\) 0 0
\(949\) −1.98342e9 + 3.43538e9i −0.00244540 + 0.00423555i
\(950\) 2.08892e11 1.20604e11i 0.256465 0.148070i
\(951\) 0 0
\(952\) −3.97066e10 + 2.47444e11i −0.0483409 + 0.301252i
\(953\) 8.07374e11 0.978821 0.489410 0.872054i \(-0.337212\pi\)
0.489410 + 0.872054i \(0.337212\pi\)
\(954\) 0 0
\(955\) −1.56502e12 9.03566e11i −1.88151 1.08629i
\(956\) 1.47243e11 2.55032e11i 0.176280 0.305326i
\(957\) 0 0
\(958\) 6.78616e11i 0.805680i
\(959\) 9.95656e11 + 1.59770e11i 1.17716 + 0.188895i
\(960\) 0 0
\(961\) −2.58568e11 4.47852e11i −0.303166 0.525099i
\(962\) −2.79364e10 1.61291e10i −0.0326190 0.0188326i
\(963\) 0 0
\(964\) 1.61995e11 9.35276e10i 0.187582 0.108301i
\(965\) 8.98622e11i 1.03626i
\(966\) 0 0
\(967\) −1.26699e10 −0.0144899 −0.00724495 0.999974i \(-0.502306\pi\)
−0.00724495 + 0.999974i \(0.502306\pi\)
\(968\) −3.60401e10 6.24232e10i −0.0410472 0.0710959i
\(969\) 0 0
\(970\) 1.44229e11 2.49812e11i 0.162917 0.282180i
\(971\) −3.00011e11 + 1.73212e11i −0.337490 + 0.194850i −0.659161 0.752001i \(-0.729089\pi\)
0.321672 + 0.946851i \(0.395755\pi\)
\(972\) 0 0
\(973\) 1.43885e12 5.48973e11i 1.60533 0.612490i
\(974\) −6.58255e11 −0.731405
\(975\) 0 0
\(976\) 2.06391e11 + 1.19160e11i 0.227453 + 0.131320i
\(977\) 3.56249e11 6.17041e11i 0.390999 0.677230i −0.601583 0.798810i \(-0.705463\pi\)
0.992582 + 0.121581i \(0.0387963\pi\)
\(978\) 0 0
\(979\) 1.30722e12i 1.42304i
\(980\) −4.30413e11 4.81945e11i −0.466639 0.522508i
\(981\) 0 0
\(982\) 4.13885e11 + 7.16870e11i 0.445076 + 0.770893i
\(983\) −1.36181e12 7.86241e11i −1.45849 0.842058i −0.459549 0.888152i \(-0.651989\pi\)
−0.998937 + 0.0460947i \(0.985322\pi\)
\(984\) 0 0
\(985\) 9.31507e11 5.37806e11i 0.989558 0.571321i
\(986\) 7.20272e10i 0.0762059i
\(987\) 0 0
\(988\) −2.22375e10 −0.0233377
\(989\) 7.37438e11 + 1.27728e12i 0.770797 + 1.33506i
\(990\) 0 0
\(991\) 1.68912e11 2.92564e11i 0.175132 0.303338i −0.765075 0.643941i \(-0.777298\pi\)
0.940207 + 0.340604i \(0.110631\pi\)
\(992\) 9.30180e10 5.37040e10i 0.0960551 0.0554574i
\(993\) 0 0
\(994\) −5.73331e11 + 7.05072e11i −0.587300 + 0.722251i
\(995\) 2.17302e12 2.21703
\(996\) 0 0
\(997\) −2.01610e10 1.16400e10i −0.0204048 0.0117807i 0.489763 0.871856i \(-0.337083\pi\)
−0.510168 + 0.860075i \(0.670417\pi\)
\(998\) 3.54326e11 6.13710e11i 0.357175 0.618644i
\(999\) 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.b.73.6 12
3.2 odd 2 14.9.d.a.3.3 12
7.5 odd 6 inner 126.9.n.b.19.6 12
12.11 even 2 112.9.s.c.17.2 12
21.2 odd 6 98.9.d.b.19.1 12
21.5 even 6 14.9.d.a.5.3 yes 12
21.11 odd 6 98.9.b.c.97.7 12
21.17 even 6 98.9.b.c.97.12 12
21.20 even 2 98.9.d.b.31.1 12
84.47 odd 6 112.9.s.c.33.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.9.d.a.3.3 12 3.2 odd 2
14.9.d.a.5.3 yes 12 21.5 even 6
98.9.b.c.97.7 12 21.11 odd 6
98.9.b.c.97.12 12 21.17 even 6
98.9.d.b.19.1 12 21.2 odd 6
98.9.d.b.31.1 12 21.20 even 2
112.9.s.c.17.2 12 12.11 even 2
112.9.s.c.33.2 12 84.47 odd 6
126.9.n.b.19.6 12 7.5 odd 6 inner
126.9.n.b.73.6 12 1.1 even 1 trivial