Properties

Label 126.9.n.b.19.3
Level $126$
Weight $9$
Character 126.19
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: \( x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + \cdots + 36\!\cdots\!00 \) 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 19.3
Root \(-9.54988 + 16.5409i\) of defining polynomial
Character \(\chi\) \(=\) 126.19
Dual form 126.9.n.b.73.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(492.158 + 284.147i) q^{5} +(-1740.97 - 1653.43i) q^{7} +1448.15 q^{8} +O(q^{10})\) \(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(492.158 + 284.147i) q^{5} +(-1740.97 - 1653.43i) q^{7} +1448.15 q^{8} +(-5568.13 + 3214.76i) q^{10} +(2955.55 + 5119.16i) q^{11} -25179.6i q^{13} +(26048.7 - 7704.68i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(-104275. + 60203.1i) q^{17} +(83372.9 + 48135.4i) q^{19} -72741.7i q^{20} -66876.5 q^{22} +(-16926.5 + 29317.5i) q^{23} +(-33833.0 - 58600.6i) q^{25} +(246709. + 142438. i) q^{26} +(-71863.4 + 298808. i) q^{28} +1.22707e6 q^{29} +(45522.3 - 26282.3i) q^{31} +(-92681.9 - 160530. i) q^{32} -1.36224e6i q^{34} +(-387011. - 1.30844e6i) q^{35} +(-987561. + 1.71051e6i) q^{37} +(-943257. + 544590. i) q^{38} +(712720. + 411489. i) q^{40} +1.61935e6i q^{41} +3.53140e6 q^{43} +(378310. - 655253. i) q^{44} +(-191501. - 331690. i) q^{46} +(4.62311e6 + 2.66916e6i) q^{47} +(297119. + 5.75714e6i) q^{49} +765555. q^{50} +(-2.79119e6 + 1.61150e6i) q^{52} +(4.32074e6 + 7.48374e6i) q^{53} +3.35925e6i q^{55} +(-2.52119e6 - 2.39443e6i) q^{56} +(-6.94133e6 + 1.20227e7i) q^{58} +(-1.61840e7 + 9.34384e6i) q^{59} +(-2.03359e7 - 1.17409e7i) q^{61} +594701. i q^{62} +2.09715e6 q^{64} +(7.15473e6 - 1.23924e7i) q^{65} +(1.83650e6 + 3.18091e6i) q^{67} +(1.33472e7 + 7.70600e6i) q^{68} +(1.50093e7 + 3.60974e6i) q^{70} -4.94930e7 q^{71} +(2.86830e6 - 1.65601e6i) q^{73} +(-1.11730e7 - 1.93522e7i) q^{74} -1.23227e7i q^{76} +(3.31868e6 - 1.37991e7i) q^{77} +(-3.73482e7 + 6.46889e7i) q^{79} +(-8.06351e6 + 4.65547e6i) q^{80} +(-1.58663e7 - 9.16044e6i) q^{82} +2.45717e7i q^{83} -6.84262e7 q^{85} +(-1.99766e7 + 3.46005e7i) q^{86} +(4.28009e6 + 7.41334e6i) q^{88} +(3.07386e7 + 1.77469e7i) q^{89} +(-4.16329e7 + 4.38369e7i) q^{91} +4.33317e6 q^{92} +(-5.23046e7 + 3.01981e7i) q^{94} +(2.73551e7 + 4.73804e7i) q^{95} +7.41535e7i q^{97} +(-5.80890e7 - 2.96561e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.65685 + 9.79796i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −64.0000 110.851i −0.250000 0.433013i
\(5\) 492.158 + 284.147i 0.787452 + 0.454636i 0.839065 0.544031i \(-0.183103\pi\)
−0.0516126 + 0.998667i \(0.516436\pi\)
\(6\) 0 0
\(7\) −1740.97 1653.43i −0.725100 0.688644i
\(8\) 1448.15 0.353553
\(9\) 0 0
\(10\) −5568.13 + 3214.76i −0.556813 + 0.321476i
\(11\) 2955.55 + 5119.16i 0.201868 + 0.349646i 0.949130 0.314883i \(-0.101965\pi\)
−0.747262 + 0.664529i \(0.768632\pi\)
\(12\) 0 0
\(13\) 25179.6i 0.881609i −0.897603 0.440805i \(-0.854693\pi\)
0.897603 0.440805i \(-0.145307\pi\)
\(14\) 26048.7 7704.68i 0.678068 0.200559i
\(15\) 0 0
\(16\) −8192.00 + 14189.0i −0.125000 + 0.216506i
\(17\) −104275. + 60203.1i −1.24849 + 0.720814i −0.970808 0.239860i \(-0.922899\pi\)
−0.277679 + 0.960674i \(0.589565\pi\)
\(18\) 0 0
\(19\) 83372.9 + 48135.4i 0.639750 + 0.369360i 0.784518 0.620106i \(-0.212910\pi\)
−0.144768 + 0.989466i \(0.546244\pi\)
\(20\) 72741.7i 0.454636i
\(21\) 0 0
\(22\) −66876.5 −0.285485
\(23\) −16926.5 + 29317.5i −0.0604860 + 0.104765i −0.894683 0.446702i \(-0.852598\pi\)
0.834197 + 0.551467i \(0.185932\pi\)
\(24\) 0 0
\(25\) −33833.0 58600.6i −0.0866126 0.150017i
\(26\) 246709. + 142438.i 0.539873 + 0.311696i
\(27\) 0 0
\(28\) −71863.4 + 298808.i −0.116916 + 0.486138i
\(29\) 1.22707e6 1.73491 0.867453 0.497519i \(-0.165756\pi\)
0.867453 + 0.497519i \(0.165756\pi\)
\(30\) 0 0
\(31\) 45522.3 26282.3i 0.0492921 0.0284588i −0.475151 0.879904i \(-0.657607\pi\)
0.524444 + 0.851445i \(0.324273\pi\)
\(32\) −92681.9 160530.i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.36224e6i 1.01939i
\(35\) −387011. 1.30844e6i −0.257900 0.871930i
\(36\) 0 0
\(37\) −987561. + 1.71051e6i −0.526935 + 0.912678i 0.472573 + 0.881292i \(0.343325\pi\)
−0.999507 + 0.0313860i \(0.990008\pi\)
\(38\) −943257. + 544590.i −0.452372 + 0.261177i
\(39\) 0 0
\(40\) 712720. + 411489.i 0.278406 + 0.160738i
\(41\) 1.61935e6i 0.573068i 0.958070 + 0.286534i \(0.0925031\pi\)
−0.958070 + 0.286534i \(0.907497\pi\)
\(42\) 0 0
\(43\) 3.53140e6 1.03294 0.516468 0.856306i \(-0.327246\pi\)
0.516468 + 0.856306i \(0.327246\pi\)
\(44\) 378310. 655253.i 0.100934 0.174823i
\(45\) 0 0
\(46\) −191501. 331690.i −0.0427701 0.0740799i
\(47\) 4.62311e6 + 2.66916e6i 0.947422 + 0.546994i 0.892279 0.451484i \(-0.149105\pi\)
0.0551425 + 0.998478i \(0.482439\pi\)
\(48\) 0 0
\(49\) 297119. + 5.75714e6i 0.0515402 + 0.998671i
\(50\) 765555. 0.122489
\(51\) 0 0
\(52\) −2.79119e6 + 1.61150e6i −0.381748 + 0.220402i
\(53\) 4.32074e6 + 7.48374e6i 0.547589 + 0.948452i 0.998439 + 0.0558524i \(0.0177876\pi\)
−0.450850 + 0.892600i \(0.648879\pi\)
\(54\) 0 0
\(55\) 3.35925e6i 0.367106i
\(56\) −2.52119e6 2.39443e6i −0.256362 0.243472i
\(57\) 0 0
\(58\) −6.94133e6 + 1.20227e7i −0.613382 + 1.06241i
\(59\) −1.61840e7 + 9.34384e6i −1.33560 + 0.771112i −0.986152 0.165842i \(-0.946966\pi\)
−0.349452 + 0.936954i \(0.613632\pi\)
\(60\) 0 0
\(61\) −2.03359e7 1.17409e7i −1.46874 0.847975i −0.469349 0.883013i \(-0.655511\pi\)
−0.999386 + 0.0350379i \(0.988845\pi\)
\(62\) 594701.i 0.0402468i
\(63\) 0 0
\(64\) 2.09715e6 0.125000
\(65\) 7.15473e6 1.23924e7i 0.400811 0.694225i
\(66\) 0 0
\(67\) 1.83650e6 + 3.18091e6i 0.0911363 + 0.157853i 0.907990 0.418993i \(-0.137617\pi\)
−0.816853 + 0.576846i \(0.804283\pi\)
\(68\) 1.33472e7 + 7.70600e6i 0.624243 + 0.360407i
\(69\) 0 0
\(70\) 1.50093e7 + 3.60974e6i 0.625127 + 0.150343i
\(71\) −4.94930e7 −1.94765 −0.973824 0.227302i \(-0.927010\pi\)
−0.973824 + 0.227302i \(0.927010\pi\)
\(72\) 0 0
\(73\) 2.86830e6 1.65601e6i 0.101003 0.0583139i −0.448648 0.893709i \(-0.648094\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(74\) −1.11730e7 1.93522e7i −0.372599 0.645361i
\(75\) 0 0
\(76\) 1.23227e7i 0.369360i
\(77\) 3.31868e6 1.37991e7i 0.0944067 0.392543i
\(78\) 0 0
\(79\) −3.73482e7 + 6.46889e7i −0.958873 + 1.66082i −0.233627 + 0.972326i \(0.575060\pi\)
−0.725245 + 0.688490i \(0.758274\pi\)
\(80\) −8.06351e6 + 4.65547e6i −0.196863 + 0.113659i
\(81\) 0 0
\(82\) −1.58663e7 9.16044e6i −0.350931 0.202610i
\(83\) 2.45717e7i 0.517753i 0.965910 + 0.258876i \(0.0833522\pi\)
−0.965910 + 0.258876i \(0.916648\pi\)
\(84\) 0 0
\(85\) −6.84262e7 −1.31083
\(86\) −1.99766e7 + 3.46005e7i −0.365198 + 0.632542i
\(87\) 0 0
\(88\) 4.28009e6 + 7.41334e6i 0.0713711 + 0.123618i
\(89\) 3.07386e7 + 1.77469e7i 0.489919 + 0.282855i 0.724541 0.689232i \(-0.242052\pi\)
−0.234622 + 0.972087i \(0.575385\pi\)
\(90\) 0 0
\(91\) −4.16329e7 + 4.38369e7i −0.607115 + 0.639255i
\(92\) 4.33317e6 0.0604860
\(93\) 0 0
\(94\) −5.23046e7 + 3.01981e7i −0.669928 + 0.386783i
\(95\) 2.73551e7 + 4.73804e7i 0.335849 + 0.581707i
\(96\) 0 0
\(97\) 7.41535e7i 0.837616i 0.908075 + 0.418808i \(0.137552\pi\)
−0.908075 + 0.418808i \(0.862448\pi\)
\(98\) −5.80890e7 2.96561e7i −0.629781 0.321522i
\(99\) 0 0
\(100\) −4.33063e6 + 7.50087e6i −0.0433063 + 0.0750087i
\(101\) −8.06054e7 + 4.65376e7i −0.774602 + 0.447217i −0.834514 0.550987i \(-0.814251\pi\)
0.0599117 + 0.998204i \(0.480918\pi\)
\(102\) 0 0
\(103\) 1.75131e8 + 1.01112e8i 1.55602 + 0.898368i 0.997631 + 0.0687872i \(0.0219130\pi\)
0.558387 + 0.829580i \(0.311420\pi\)
\(104\) 3.64640e7i 0.311696i
\(105\) 0 0
\(106\) −9.77672e7 −0.774408
\(107\) −8.72092e7 + 1.51051e8i −0.665315 + 1.15236i 0.313885 + 0.949461i \(0.398369\pi\)
−0.979200 + 0.202898i \(0.934964\pi\)
\(108\) 0 0
\(109\) −1.40611e7 2.43546e7i −0.0996127 0.172534i 0.811912 0.583780i \(-0.198427\pi\)
−0.911524 + 0.411246i \(0.865094\pi\)
\(110\) −3.29138e7 1.90028e7i −0.224805 0.129791i
\(111\) 0 0
\(112\) 3.77225e7 1.11576e7i 0.239733 0.0709083i
\(113\) −1.08325e7 −0.0664380 −0.0332190 0.999448i \(-0.510576\pi\)
−0.0332190 + 0.999448i \(0.510576\pi\)
\(114\) 0 0
\(115\) −1.66610e7 + 9.61922e6i −0.0952597 + 0.0549982i
\(116\) −7.85322e7 1.36022e8i −0.433727 0.751236i
\(117\) 0 0
\(118\) 2.11427e8i 1.09052i
\(119\) 2.81081e8 + 6.76000e7i 1.40166 + 0.337100i
\(120\) 0 0
\(121\) 8.97089e7 1.55380e8i 0.418499 0.724861i
\(122\) 2.30074e8 1.32833e8i 1.03855 0.599609i
\(123\) 0 0
\(124\) −5.82685e6 3.36414e6i −0.0246461 0.0142294i
\(125\) 2.60444e8i 1.06678i
\(126\) 0 0
\(127\) −1.46298e8 −0.562371 −0.281186 0.959653i \(-0.590728\pi\)
−0.281186 + 0.959653i \(0.590728\pi\)
\(128\) −1.18633e7 + 2.05478e7i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 8.09465e7 + 1.40203e8i 0.283416 + 0.490891i
\(131\) 1.71536e8 + 9.90363e7i 0.582465 + 0.336286i 0.762112 0.647445i \(-0.224162\pi\)
−0.179647 + 0.983731i \(0.557496\pi\)
\(132\) 0 0
\(133\) −6.55607e7 2.21654e8i −0.209526 0.708383i
\(134\) −4.15552e7 −0.128886
\(135\) 0 0
\(136\) −1.51006e8 + 8.71834e7i −0.441407 + 0.254846i
\(137\) 8.12797e7 + 1.40781e8i 0.230728 + 0.399632i 0.958022 0.286693i \(-0.0925560\pi\)
−0.727295 + 0.686325i \(0.759223\pi\)
\(138\) 0 0
\(139\) 4.08667e8i 1.09474i 0.836892 + 0.547369i \(0.184370\pi\)
−0.836892 + 0.547369i \(0.815630\pi\)
\(140\) −1.20274e8 + 1.26641e8i −0.313082 + 0.329656i
\(141\) 0 0
\(142\) 2.79975e8 4.84931e8i 0.688598 1.19269i
\(143\) 1.28899e8 7.44197e7i 0.308251 0.177969i
\(144\) 0 0
\(145\) 6.03910e8 + 3.48668e8i 1.36616 + 0.788750i
\(146\) 3.74713e7i 0.0824683i
\(147\) 0 0
\(148\) 2.52816e8 0.526935
\(149\) −8.81970e7 + 1.52762e8i −0.178940 + 0.309934i −0.941518 0.336963i \(-0.890600\pi\)
0.762577 + 0.646897i \(0.223934\pi\)
\(150\) 0 0
\(151\) −2.65985e8 4.60699e8i −0.511622 0.886155i −0.999909 0.0134724i \(-0.995711\pi\)
0.488287 0.872683i \(-0.337622\pi\)
\(152\) 1.20737e8 + 6.97075e7i 0.226186 + 0.130588i
\(153\) 0 0
\(154\) 1.16430e8 + 1.10576e8i 0.207005 + 0.196597i
\(155\) 2.98722e7 0.0517536
\(156\) 0 0
\(157\) 4.92648e8 2.84430e8i 0.810845 0.468142i −0.0364042 0.999337i \(-0.511590\pi\)
0.847249 + 0.531196i \(0.178257\pi\)
\(158\) −4.22546e8 7.31872e8i −0.678026 1.17437i
\(159\) 0 0
\(160\) 1.05341e8i 0.160738i
\(161\) 7.79429e7 2.30540e7i 0.116004 0.0343117i
\(162\) 0 0
\(163\) 5.17985e7 8.97177e7i 0.0733782 0.127095i −0.827002 0.562199i \(-0.809955\pi\)
0.900380 + 0.435105i \(0.143289\pi\)
\(164\) 1.79507e8 1.03639e8i 0.248146 0.143267i
\(165\) 0 0
\(166\) −2.40752e8 1.38998e8i −0.317057 0.183053i
\(167\) 2.24426e8i 0.288541i 0.989538 + 0.144270i \(0.0460835\pi\)
−0.989538 + 0.144270i \(0.953917\pi\)
\(168\) 0 0
\(169\) 1.81716e8 0.222765
\(170\) 3.87077e8 6.70437e8i 0.463449 0.802717i
\(171\) 0 0
\(172\) −2.26010e8 3.91460e8i −0.258234 0.447274i
\(173\) 4.86992e8 + 2.81165e8i 0.543672 + 0.313889i 0.746566 0.665311i \(-0.231701\pi\)
−0.202894 + 0.979201i \(0.565035\pi\)
\(174\) 0 0
\(175\) −3.79899e7 + 1.57962e8i −0.0405057 + 0.168423i
\(176\) −9.68475e7 −0.100934
\(177\) 0 0
\(178\) −3.47768e8 + 2.00784e8i −0.346425 + 0.200009i
\(179\) 4.49466e8 + 7.78498e8i 0.437809 + 0.758307i 0.997520 0.0703804i \(-0.0224213\pi\)
−0.559711 + 0.828688i \(0.689088\pi\)
\(180\) 0 0
\(181\) 1.85029e9i 1.72396i −0.506945 0.861979i \(-0.669225\pi\)
0.506945 0.861979i \(-0.330775\pi\)
\(182\) −1.94001e8 6.55896e8i −0.176815 0.597791i
\(183\) 0 0
\(184\) −2.45121e7 + 4.24563e7i −0.0213850 + 0.0370400i
\(185\) −9.72071e8 + 5.61225e8i −0.829872 + 0.479127i
\(186\) 0 0
\(187\) −6.16379e8 3.55867e8i −0.504059 0.291019i
\(188\) 6.83304e8i 0.546994i
\(189\) 0 0
\(190\) −6.18975e8 −0.474962
\(191\) 4.24840e8 7.35844e8i 0.319221 0.552907i −0.661105 0.750294i \(-0.729912\pi\)
0.980326 + 0.197386i \(0.0632454\pi\)
\(192\) 0 0
\(193\) 1.28117e9 + 2.21906e9i 0.923377 + 1.59934i 0.794150 + 0.607721i \(0.207916\pi\)
0.129227 + 0.991615i \(0.458750\pi\)
\(194\) −7.26553e8 4.19476e8i −0.512933 0.296142i
\(195\) 0 0
\(196\) 6.19170e8 4.01393e8i 0.419552 0.271985i
\(197\) 5.98729e8 0.397526 0.198763 0.980048i \(-0.436308\pi\)
0.198763 + 0.980048i \(0.436308\pi\)
\(198\) 0 0
\(199\) 1.86878e9 1.07894e9i 1.19164 0.687994i 0.232962 0.972486i \(-0.425158\pi\)
0.958679 + 0.284492i \(0.0918248\pi\)
\(200\) −4.89955e7 8.48627e7i −0.0306222 0.0530392i
\(201\) 0 0
\(202\) 1.05302e9i 0.632460i
\(203\) −2.13628e9 2.02887e9i −1.25798 1.19473i
\(204\) 0 0
\(205\) −4.60135e8 + 7.96977e8i −0.260537 + 0.451263i
\(206\) −1.98138e9 + 1.14395e9i −1.10027 + 0.635242i
\(207\) 0 0
\(208\) 3.57273e8 + 2.06272e8i 0.190874 + 0.110201i
\(209\) 5.69066e8i 0.298248i
\(210\) 0 0
\(211\) −8.51078e8 −0.429378 −0.214689 0.976682i \(-0.568874\pi\)
−0.214689 + 0.976682i \(0.568874\pi\)
\(212\) 5.53055e8 9.57919e8i 0.273795 0.474226i
\(213\) 0 0
\(214\) −9.86659e8 1.70894e9i −0.470448 0.814841i
\(215\) 1.73801e9 + 1.00344e9i 0.813388 + 0.469610i
\(216\) 0 0
\(217\) −1.22709e8 2.95115e7i −0.0553397 0.0133092i
\(218\) 3.18167e8 0.140874
\(219\) 0 0
\(220\) 3.72377e8 2.14992e8i 0.158961 0.0917764i
\(221\) 1.51589e9 + 2.62560e9i 0.635476 + 1.10068i
\(222\) 0 0
\(223\) 2.16526e9i 0.875571i 0.899079 + 0.437785i \(0.144237\pi\)
−0.899079 + 0.437785i \(0.855763\pi\)
\(224\) −1.04069e8 + 4.32720e8i −0.0413362 + 0.171876i
\(225\) 0 0
\(226\) 6.12781e7 1.06137e8i 0.0234894 0.0406848i
\(227\) −3.02401e8 + 1.74591e8i −0.113888 + 0.0657535i −0.555862 0.831275i \(-0.687612\pi\)
0.441974 + 0.897028i \(0.354278\pi\)
\(228\) 0 0
\(229\) −2.78484e9 1.60783e9i −1.01265 0.584653i −0.100682 0.994919i \(-0.532103\pi\)
−0.911966 + 0.410266i \(0.865436\pi\)
\(230\) 2.17658e8i 0.0777792i
\(231\) 0 0
\(232\) 1.77698e9 0.613382
\(233\) 1.60950e9 2.78774e9i 0.546095 0.945864i −0.452442 0.891794i \(-0.649447\pi\)
0.998537 0.0540705i \(-0.0172196\pi\)
\(234\) 0 0
\(235\) 1.51687e9 + 2.62729e9i 0.497366 + 0.861463i
\(236\) 2.07155e9 + 1.19601e9i 0.667802 + 0.385556i
\(237\) 0 0
\(238\) −2.25237e9 + 2.37161e9i −0.701993 + 0.739156i
\(239\) −2.29096e9 −0.702143 −0.351071 0.936349i \(-0.614183\pi\)
−0.351071 + 0.936349i \(0.614183\pi\)
\(240\) 0 0
\(241\) −4.75785e9 + 2.74695e9i −1.41040 + 0.814296i −0.995426 0.0955370i \(-0.969543\pi\)
−0.414975 + 0.909833i \(0.636210\pi\)
\(242\) 1.01494e9 + 1.75793e9i 0.295923 + 0.512554i
\(243\) 0 0
\(244\) 3.00568e9i 0.847975i
\(245\) −1.48965e9 + 2.91785e9i −0.413446 + 0.809838i
\(246\) 0 0
\(247\) 1.21203e9 2.09930e9i 0.325631 0.564010i
\(248\) 6.59233e7 3.80608e7i 0.0174274 0.0100617i
\(249\) 0 0
\(250\) 2.55182e9 + 1.47330e9i 0.653267 + 0.377164i
\(251\) 4.73267e9i 1.19237i 0.802846 + 0.596186i \(0.203318\pi\)
−0.802846 + 0.596186i \(0.796682\pi\)
\(252\) 0 0
\(253\) −2.00108e8 −0.0488408
\(254\) 8.27585e8 1.43342e9i 0.198828 0.344381i
\(255\) 0 0
\(256\) −1.34218e8 2.32472e8i −0.0312500 0.0541266i
\(257\) −2.26889e9 1.30994e9i −0.520093 0.300276i 0.216880 0.976198i \(-0.430412\pi\)
−0.736973 + 0.675923i \(0.763745\pi\)
\(258\) 0 0
\(259\) 4.54751e9 1.34506e9i 1.01059 0.298912i
\(260\) −1.83161e9 −0.400811
\(261\) 0 0
\(262\) −1.94071e9 + 1.12047e9i −0.411865 + 0.237790i
\(263\) −9.08331e8 1.57328e9i −0.189855 0.328838i 0.755347 0.655325i \(-0.227468\pi\)
−0.945202 + 0.326487i \(0.894135\pi\)
\(264\) 0 0
\(265\) 4.91091e9i 0.995814i
\(266\) 2.54262e9 + 6.11501e8i 0.507873 + 0.122143i
\(267\) 0 0
\(268\) 2.35072e8 4.07156e8i 0.0455682 0.0789264i
\(269\) 1.79083e9 1.03394e9i 0.342016 0.197463i −0.319147 0.947705i \(-0.603396\pi\)
0.661163 + 0.750242i \(0.270063\pi\)
\(270\) 0 0
\(271\) −1.44467e9 8.34079e8i −0.267850 0.154643i 0.360060 0.932929i \(-0.382756\pi\)
−0.627910 + 0.778286i \(0.716089\pi\)
\(272\) 1.97274e9i 0.360407i
\(273\) 0 0
\(274\) −1.83915e9 −0.326298
\(275\) 1.99991e8 3.46394e8i 0.0349686 0.0605675i
\(276\) 0 0
\(277\) 9.76261e8 + 1.69093e9i 0.165824 + 0.287215i 0.936948 0.349470i \(-0.113638\pi\)
−0.771124 + 0.636685i \(0.780305\pi\)
\(278\) −4.00410e9 2.31177e9i −0.670387 0.387048i
\(279\) 0 0
\(280\) −5.60451e8 1.89482e9i −0.0911813 0.308274i
\(281\) 3.24189e9 0.519963 0.259982 0.965614i \(-0.416283\pi\)
0.259982 + 0.965614i \(0.416283\pi\)
\(282\) 0 0
\(283\) −9.76907e9 + 5.64018e9i −1.52303 + 0.879320i −0.523398 + 0.852088i \(0.675336\pi\)
−0.999629 + 0.0272318i \(0.991331\pi\)
\(284\) 3.16755e9 + 5.48636e9i 0.486912 + 0.843357i
\(285\) 0 0
\(286\) 1.68393e9i 0.251686i
\(287\) 2.67749e9 2.81924e9i 0.394639 0.415531i
\(288\) 0 0
\(289\) 3.76095e9 6.51416e9i 0.539146 0.933828i
\(290\) −6.83246e9 + 3.94472e9i −0.966018 + 0.557731i
\(291\) 0 0
\(292\) −3.67142e8 2.11970e8i −0.0505013 0.0291570i
\(293\) 2.00624e9i 0.272215i −0.990694 0.136108i \(-0.956541\pi\)
0.990694 0.136108i \(-0.0434593\pi\)
\(294\) 0 0
\(295\) −1.06201e10 −1.40230
\(296\) −1.43014e9 + 2.47708e9i −0.186300 + 0.322680i
\(297\) 0 0
\(298\) −9.97835e8 1.72830e9i −0.126530 0.219156i
\(299\) 7.38204e8 + 4.26202e8i 0.0923616 + 0.0533250i
\(300\) 0 0
\(301\) −6.14805e9 5.83894e9i −0.748982 0.711325i
\(302\) 6.01855e9 0.723543
\(303\) 0 0
\(304\) −1.36598e9 + 7.88650e8i −0.159938 + 0.0923400i
\(305\) −6.67230e9 1.15568e10i −0.771039 1.33548i
\(306\) 0 0
\(307\) 6.67089e9i 0.750983i −0.926826 0.375491i \(-0.877474\pi\)
0.926826 0.375491i \(-0.122526\pi\)
\(308\) −1.74204e9 + 5.15262e8i −0.193578 + 0.0572565i
\(309\) 0 0
\(310\) −1.68983e8 + 2.92687e8i −0.0182976 + 0.0316925i
\(311\) −4.72509e9 + 2.72803e9i −0.505090 + 0.291614i −0.730813 0.682578i \(-0.760859\pi\)
0.225723 + 0.974192i \(0.427526\pi\)
\(312\) 0 0
\(313\) 1.45428e10 + 8.39632e9i 1.51521 + 0.874805i 0.999841 + 0.0178355i \(0.00567750\pi\)
0.515366 + 0.856970i \(0.327656\pi\)
\(314\) 6.43592e9i 0.662052i
\(315\) 0 0
\(316\) 9.56113e9 0.958873
\(317\) −4.76107e9 + 8.24642e9i −0.471485 + 0.816636i −0.999468 0.0326192i \(-0.989615\pi\)
0.527983 + 0.849255i \(0.322948\pi\)
\(318\) 0 0
\(319\) 3.62666e9 + 6.28155e9i 0.350222 + 0.606603i
\(320\) 1.03213e9 + 5.95900e8i 0.0984315 + 0.0568295i
\(321\) 0 0
\(322\) −2.15030e8 + 8.94094e8i −0.0200021 + 0.0831687i
\(323\) −1.15916e10 −1.06496
\(324\) 0 0
\(325\) −1.47554e9 + 8.51904e8i −0.132257 + 0.0763585i
\(326\) 5.86033e8 + 1.01504e9i 0.0518862 + 0.0898695i
\(327\) 0 0
\(328\) 2.34507e9i 0.202610i
\(329\) −3.63541e9 1.22909e10i −0.310291 1.04906i
\(330\) 0 0
\(331\) −2.57258e9 + 4.45585e9i −0.214317 + 0.371209i −0.953061 0.302778i \(-0.902086\pi\)
0.738744 + 0.673986i \(0.235419\pi\)
\(332\) 2.72380e9 1.57259e9i 0.224193 0.129438i
\(333\) 0 0
\(334\) −2.19892e9 1.26954e9i −0.176694 0.102015i
\(335\) 2.08735e9i 0.165735i
\(336\) 0 0
\(337\) 8.86100e9 0.687010 0.343505 0.939151i \(-0.388386\pi\)
0.343505 + 0.939151i \(0.388386\pi\)
\(338\) −1.02794e9 + 1.78045e9i −0.0787593 + 0.136415i
\(339\) 0 0
\(340\) 4.37928e9 + 7.58513e9i 0.327708 + 0.567607i
\(341\) 2.69087e8 + 1.55357e8i 0.0199010 + 0.0114898i
\(342\) 0 0
\(343\) 9.00177e9 1.05142e10i 0.650356 0.759629i
\(344\) 5.11402e9 0.365198
\(345\) 0 0
\(346\) −5.50968e9 + 3.18102e9i −0.384434 + 0.221953i
\(347\) 6.65626e9 + 1.15290e10i 0.459106 + 0.795194i 0.998914 0.0465938i \(-0.0148367\pi\)
−0.539808 + 0.841788i \(0.681503\pi\)
\(348\) 0 0
\(349\) 1.58409e10i 1.06777i −0.845557 0.533884i \(-0.820732\pi\)
0.845557 0.533884i \(-0.179268\pi\)
\(350\) −1.33280e9 1.26579e9i −0.0888166 0.0843511i
\(351\) 0 0
\(352\) 5.47852e8 9.48908e8i 0.0356856 0.0618092i
\(353\) −2.64000e9 + 1.52420e9i −0.170022 + 0.0981621i −0.582596 0.812762i \(-0.697963\pi\)
0.412574 + 0.910924i \(0.364630\pi\)
\(354\) 0 0
\(355\) −2.43584e10 1.40633e10i −1.53368 0.885471i
\(356\) 4.54322e9i 0.282855i
\(357\) 0 0
\(358\) −1.01703e10 −0.619155
\(359\) 1.53081e10 2.65144e10i 0.921602 1.59626i 0.124665 0.992199i \(-0.460215\pi\)
0.796937 0.604062i \(-0.206452\pi\)
\(360\) 0 0
\(361\) −3.85775e9 6.68183e9i −0.227146 0.393429i
\(362\) 1.81291e10 + 1.04668e10i 1.05570 + 0.609511i
\(363\) 0 0
\(364\) 7.52388e9 + 1.80949e9i 0.428584 + 0.103075i
\(365\) 1.88221e9 0.106046
\(366\) 0 0
\(367\) 1.40867e10 8.13298e9i 0.776508 0.448317i −0.0586833 0.998277i \(-0.518690\pi\)
0.835191 + 0.549960i \(0.185357\pi\)
\(368\) −2.77323e8 4.80338e8i −0.0151215 0.0261912i
\(369\) 0 0
\(370\) 1.26991e10i 0.677588i
\(371\) 4.85161e9 2.01730e10i 0.256089 1.06482i
\(372\) 0 0
\(373\) 7.41142e9 1.28370e10i 0.382883 0.663173i −0.608590 0.793485i \(-0.708265\pi\)
0.991473 + 0.130312i \(0.0415980\pi\)
\(374\) 6.97353e9 4.02617e9i 0.356424 0.205781i
\(375\) 0 0
\(376\) 6.69499e9 + 3.86535e9i 0.334964 + 0.193392i
\(377\) 3.08971e10i 1.52951i
\(378\) 0 0
\(379\) 2.49929e10 1.21132 0.605661 0.795723i \(-0.292909\pi\)
0.605661 + 0.795723i \(0.292909\pi\)
\(380\) 3.50145e9 6.06469e9i 0.167924 0.290853i
\(381\) 0 0
\(382\) 4.80651e9 + 8.32513e9i 0.225723 + 0.390964i
\(383\) 2.14081e10 + 1.23600e10i 0.994907 + 0.574410i 0.906737 0.421696i \(-0.138565\pi\)
0.0881693 + 0.996106i \(0.471898\pi\)
\(384\) 0 0
\(385\) 5.55429e9 5.84833e9i 0.252805 0.266188i
\(386\) −2.89897e10 −1.30585
\(387\) 0 0
\(388\) 8.22001e9 4.74583e9i 0.362698 0.209404i
\(389\) 3.75530e9 + 6.50436e9i 0.164001 + 0.284058i 0.936300 0.351201i \(-0.114227\pi\)
−0.772299 + 0.635259i \(0.780893\pi\)
\(390\) 0 0
\(391\) 4.07610e9i 0.174397i
\(392\) 4.30274e8 + 8.33723e9i 0.0182222 + 0.353083i
\(393\) 0 0
\(394\) −3.38693e9 + 5.86633e9i −0.140547 + 0.243434i
\(395\) −3.67624e10 + 2.12248e10i −1.51013 + 0.871876i
\(396\) 0 0
\(397\) 3.43170e9 + 1.98129e9i 0.138149 + 0.0797603i 0.567481 0.823386i \(-0.307918\pi\)
−0.429333 + 0.903146i \(0.641251\pi\)
\(398\) 2.44136e10i 0.972971i
\(399\) 0 0
\(400\) 1.10864e9 0.0433063
\(401\) 1.48221e10 2.56727e10i 0.573236 0.992874i −0.422995 0.906132i \(-0.639021\pi\)
0.996231 0.0867417i \(-0.0276455\pi\)
\(402\) 0 0
\(403\) −6.61779e8 1.14624e9i −0.0250895 0.0434564i
\(404\) 1.03175e10 + 5.95681e9i 0.387301 + 0.223608i
\(405\) 0 0
\(406\) 3.19634e10 9.45415e9i 1.17638 0.347951i
\(407\) −1.16751e10 −0.425485
\(408\) 0 0
\(409\) −1.61493e10 + 9.32380e9i −0.577113 + 0.333196i −0.759985 0.649941i \(-0.774794\pi\)
0.182872 + 0.983137i \(0.441460\pi\)
\(410\) −5.20583e9 9.01676e9i −0.184228 0.319091i
\(411\) 0 0
\(412\) 2.58847e10i 0.898368i
\(413\) 4.36252e10 + 1.04919e10i 1.49947 + 0.360622i
\(414\) 0 0
\(415\) −6.98197e9 + 1.20931e10i −0.235389 + 0.407705i
\(416\) −4.04208e9 + 2.33370e9i −0.134968 + 0.0779240i
\(417\) 0 0
\(418\) −5.57569e9 3.21912e9i −0.182639 0.105447i
\(419\) 1.52395e9i 0.0494441i 0.999694 + 0.0247221i \(0.00787008\pi\)
−0.999694 + 0.0247221i \(0.992130\pi\)
\(420\) 0 0
\(421\) −2.02402e10 −0.644298 −0.322149 0.946689i \(-0.604405\pi\)
−0.322149 + 0.946689i \(0.604405\pi\)
\(422\) 4.81443e9 8.33883e9i 0.151808 0.262939i
\(423\) 0 0
\(424\) 6.25710e9 + 1.08376e10i 0.193602 + 0.335328i
\(425\) 7.05587e9 + 4.07371e9i 0.216269 + 0.124863i
\(426\) 0 0
\(427\) 1.59912e10 + 5.40645e10i 0.481028 + 1.62630i
\(428\) 2.23255e10 0.665315
\(429\) 0 0
\(430\) −1.96633e10 + 1.13526e10i −0.575152 + 0.332064i
\(431\) 3.19684e9 + 5.53708e9i 0.0926427 + 0.160462i 0.908622 0.417619i \(-0.137135\pi\)
−0.815980 + 0.578081i \(0.803802\pi\)
\(432\) 0 0
\(433\) 3.18824e10i 0.906984i −0.891260 0.453492i \(-0.850178\pi\)
0.891260 0.453492i \(-0.149822\pi\)
\(434\) 9.83298e8 1.03535e9i 0.0277157 0.0291830i
\(435\) 0 0
\(436\) −1.79983e9 + 3.11739e9i −0.0498063 + 0.0862671i
\(437\) −2.82242e9 + 1.62952e9i −0.0773919 + 0.0446822i
\(438\) 0 0
\(439\) −7.29008e9 4.20893e9i −0.196279 0.113322i 0.398640 0.917108i \(-0.369482\pi\)
−0.594919 + 0.803786i \(0.702816\pi\)
\(440\) 4.86471e9i 0.129791i
\(441\) 0 0
\(442\) −3.43007e10 −0.898699
\(443\) −1.90612e10 + 3.30150e10i −0.494921 + 0.857229i −0.999983 0.00585447i \(-0.998136\pi\)
0.505062 + 0.863083i \(0.331470\pi\)
\(444\) 0 0
\(445\) 1.00855e10 + 1.74686e10i 0.257192 + 0.445469i
\(446\) −2.12152e10 1.22486e10i −0.536175 0.309561i
\(447\) 0 0
\(448\) −3.65107e9 3.46750e9i −0.0906375 0.0860804i
\(449\) 1.76118e10 0.433330 0.216665 0.976246i \(-0.430482\pi\)
0.216665 + 0.976246i \(0.430482\pi\)
\(450\) 0 0
\(451\) −8.28973e9 + 4.78608e9i −0.200371 + 0.115684i
\(452\) 6.93283e8 + 1.20080e9i 0.0166095 + 0.0287685i
\(453\) 0 0
\(454\) 3.95054e9i 0.0929894i
\(455\) −3.29461e10 + 9.74479e9i −0.768702 + 0.227367i
\(456\) 0 0
\(457\) 2.74598e10 4.75617e10i 0.629553 1.09042i −0.358089 0.933688i \(-0.616571\pi\)
0.987642 0.156730i \(-0.0500952\pi\)
\(458\) 3.15069e10 1.81905e10i 0.716050 0.413412i
\(459\) 0 0
\(460\) 2.13261e9 + 1.23126e9i 0.0476298 + 0.0274991i
\(461\) 3.01948e10i 0.668542i −0.942477 0.334271i \(-0.891510\pi\)
0.942477 0.334271i \(-0.108490\pi\)
\(462\) 0 0
\(463\) −1.01407e10 −0.220670 −0.110335 0.993894i \(-0.535192\pi\)
−0.110335 + 0.993894i \(0.535192\pi\)
\(464\) −1.00521e10 + 1.74108e10i −0.216863 + 0.375618i
\(465\) 0 0
\(466\) 1.82094e10 + 3.15397e10i 0.386147 + 0.668827i
\(467\) −6.06931e10 3.50412e10i −1.27606 0.736735i −0.299941 0.953958i \(-0.596967\pi\)
−0.976122 + 0.217223i \(0.930300\pi\)
\(468\) 0 0
\(469\) 2.06214e9 8.57438e9i 0.0426213 0.177219i
\(470\) −3.43228e10 −0.703382
\(471\) 0 0
\(472\) −2.34369e10 + 1.35313e10i −0.472208 + 0.272629i
\(473\) 1.04372e10 + 1.80778e10i 0.208517 + 0.361162i
\(474\) 0 0
\(475\) 6.51427e9i 0.127965i
\(476\) −1.04956e10 3.54845e10i −0.204447 0.691212i
\(477\) 0 0
\(478\) 1.29596e10 2.24467e10i 0.248245 0.429973i
\(479\) −4.26270e10 + 2.46107e10i −0.809735 + 0.467501i −0.846864 0.531810i \(-0.821512\pi\)
0.0371288 + 0.999310i \(0.488179\pi\)
\(480\) 0 0
\(481\) 4.30699e10 + 2.48664e10i 0.804625 + 0.464551i
\(482\) 6.21563e10i 1.15159i
\(483\) 0 0
\(484\) −2.29655e10 −0.418499
\(485\) −2.10705e10 + 3.64952e10i −0.380810 + 0.659583i
\(486\) 0 0
\(487\) 4.42360e10 + 7.66190e10i 0.786430 + 1.36214i 0.928141 + 0.372229i \(0.121406\pi\)
−0.141711 + 0.989908i \(0.545260\pi\)
\(488\) −2.94495e10 1.70027e10i −0.519276 0.299804i
\(489\) 0 0
\(490\) −2.01622e10 3.11013e10i −0.349747 0.539504i
\(491\) −2.13831e8 −0.00367913 −0.00183957 0.999998i \(-0.500586\pi\)
−0.00183957 + 0.999998i \(0.500586\pi\)
\(492\) 0 0
\(493\) −1.27952e11 + 7.38732e10i −2.16601 + 1.25054i
\(494\) 1.37126e10 + 2.37509e10i 0.230256 + 0.398815i
\(495\) 0 0
\(496\) 8.61219e8i 0.0142294i
\(497\) 8.61656e10 + 8.18334e10i 1.41224 + 1.34124i
\(498\) 0 0
\(499\) −2.90208e10 + 5.02656e10i −0.468067 + 0.810715i −0.999334 0.0364889i \(-0.988383\pi\)
0.531267 + 0.847204i \(0.321716\pi\)
\(500\) −2.88706e10 + 1.66684e10i −0.461929 + 0.266695i
\(501\) 0 0
\(502\) −4.63706e10 2.67720e10i −0.730176 0.421567i
\(503\) 3.68913e10i 0.576304i 0.957585 + 0.288152i \(0.0930409\pi\)
−0.957585 + 0.288152i \(0.906959\pi\)
\(504\) 0 0
\(505\) −5.28941e10 −0.813283
\(506\) 1.13198e9 1.96065e9i 0.0172678 0.0299087i
\(507\) 0 0
\(508\) 9.36306e9 + 1.62173e10i 0.140593 + 0.243514i
\(509\) −9.82181e10 5.67062e10i −1.46326 0.844811i −0.464096 0.885785i \(-0.653621\pi\)
−0.999160 + 0.0409736i \(0.986954\pi\)
\(510\) 0 0
\(511\) −7.73171e9 1.85948e9i −0.113395 0.0272714i
\(512\) 3.03700e9 0.0441942
\(513\) 0 0
\(514\) 2.56696e10 1.48203e10i 0.367761 0.212327i
\(515\) 5.74615e10 + 9.95262e10i 0.816860 + 1.41484i
\(516\) 0 0
\(517\) 3.15553e10i 0.441683i
\(518\) −1.25457e10 + 5.21652e10i −0.174252 + 0.724539i
\(519\) 0 0
\(520\) 1.03612e10 1.79460e10i 0.141708 0.245446i
\(521\) 6.29055e10 3.63185e10i 0.853763 0.492920i −0.00815564 0.999967i \(-0.502596\pi\)
0.861919 + 0.507046i \(0.169263\pi\)
\(522\) 0 0
\(523\) −1.07742e11 6.22051e10i −1.44006 0.831417i −0.442204 0.896914i \(-0.645803\pi\)
−0.997853 + 0.0654973i \(0.979137\pi\)
\(524\) 2.53533e10i 0.336286i
\(525\) 0 0
\(526\) 2.05532e10 0.268495
\(527\) −3.16455e9 + 5.48117e9i −0.0410270 + 0.0710609i
\(528\) 0 0
\(529\) 3.85825e10 + 6.68268e10i 0.492683 + 0.853352i
\(530\) −4.81169e10 2.77803e10i −0.609809 0.352074i
\(531\) 0 0
\(532\) −2.03747e10 + 2.14533e10i −0.254357 + 0.267823i
\(533\) 4.07747e10 0.505222
\(534\) 0 0
\(535\) −8.58413e10 + 4.95605e10i −1.04781 + 0.604952i
\(536\) 2.65953e9 + 4.60645e9i 0.0322216 + 0.0558094i
\(537\) 0 0
\(538\) 2.33954e10i 0.279255i
\(539\) −2.85936e10 + 1.85365e10i −0.338777 + 0.219621i
\(540\) 0 0
\(541\) 2.79878e10 4.84764e10i 0.326723 0.565902i −0.655136 0.755511i \(-0.727389\pi\)
0.981860 + 0.189609i \(0.0607221\pi\)
\(542\) 1.63446e10 9.43653e9i 0.189398 0.109349i
\(543\) 0 0
\(544\) 1.93288e10 + 1.11595e10i 0.220703 + 0.127423i
\(545\) 1.59817e10i 0.181150i
\(546\) 0 0
\(547\) 6.83882e10 0.763892 0.381946 0.924185i \(-0.375254\pi\)
0.381946 + 0.924185i \(0.375254\pi\)
\(548\) 1.04038e10 1.80199e10i 0.115364 0.199816i
\(549\) 0 0
\(550\) 2.26263e9 + 3.91900e9i 0.0247266 + 0.0428277i
\(551\) 1.02304e11 + 5.90653e10i 1.10991 + 0.640805i
\(552\) 0 0
\(553\) 1.71981e11 5.08685e10i 1.83899 0.543937i
\(554\) −2.20903e10 −0.234510
\(555\) 0 0
\(556\) 4.53012e10 2.61547e10i 0.474035 0.273684i
\(557\) −7.18130e10 1.24384e11i −0.746075 1.29224i −0.949691 0.313189i \(-0.898603\pi\)
0.203616 0.979051i \(-0.434731\pi\)
\(558\) 0 0
\(559\) 8.89195e10i 0.910646i
\(560\) 2.17358e10 + 5.22746e9i 0.221016 + 0.0531544i
\(561\) 0 0
\(562\) −1.83389e10 + 3.17639e10i −0.183835 + 0.318411i
\(563\) −1.50338e10 + 8.67975e9i −0.149635 + 0.0863920i −0.572948 0.819592i \(-0.694200\pi\)
0.423313 + 0.905984i \(0.360867\pi\)
\(564\) 0 0
\(565\) −5.33132e9 3.07804e9i −0.0523168 0.0302051i
\(566\) 1.27623e11i 1.24355i
\(567\) 0 0
\(568\) −7.16736e10 −0.688598
\(569\) −4.83337e10 + 8.37164e10i −0.461106 + 0.798659i −0.999016 0.0443429i \(-0.985881\pi\)
0.537910 + 0.843002i \(0.319214\pi\)
\(570\) 0 0
\(571\) 1.00793e10 + 1.74578e10i 0.0948165 + 0.164227i 0.909532 0.415634i \(-0.136440\pi\)
−0.814716 + 0.579861i \(0.803107\pi\)
\(572\) −1.64990e10 9.52572e9i −0.154125 0.0889844i
\(573\) 0 0
\(574\) 1.24766e10 + 4.21820e10i 0.114934 + 0.388579i
\(575\) 2.29070e9 0.0209554
\(576\) 0 0
\(577\) 1.42798e10 8.24442e9i 0.128830 0.0743801i −0.434200 0.900817i \(-0.642969\pi\)
0.563030 + 0.826436i \(0.309636\pi\)
\(578\) 4.25503e10 + 7.36993e10i 0.381234 + 0.660316i
\(579\) 0 0
\(580\) 8.92589e10i 0.788750i
\(581\) 4.06276e10 4.27784e10i 0.356547 0.375422i
\(582\) 0 0
\(583\) −2.55403e10 + 4.42372e10i −0.221081 + 0.382924i
\(584\) 4.15374e9 2.39816e9i 0.0357098 0.0206171i
\(585\) 0 0
\(586\) 1.96571e10 + 1.13490e10i 0.166697 + 0.0962427i
\(587\) 1.98805e11i 1.67446i 0.546848 + 0.837232i \(0.315828\pi\)
−0.546848 + 0.837232i \(0.684172\pi\)
\(588\) 0 0
\(589\) 5.06043e9 0.0420462
\(590\) 6.00764e10 1.04055e11i 0.495788 0.858730i
\(591\) 0 0
\(592\) −1.61802e10 2.80249e10i −0.131734 0.228169i
\(593\) −6.34438e10 3.66293e10i −0.513063 0.296217i 0.221029 0.975267i \(-0.429058\pi\)
−0.734092 + 0.679050i \(0.762392\pi\)
\(594\) 0 0
\(595\) 1.19128e11 + 1.13138e11i 0.950484 + 0.902696i
\(596\) 2.25784e10 0.178940
\(597\) 0 0
\(598\) −8.35182e9 + 4.82193e9i −0.0653095 + 0.0377065i
\(599\) 5.16184e10 + 8.94057e10i 0.400956 + 0.694477i 0.993842 0.110810i \(-0.0353446\pi\)
−0.592885 + 0.805287i \(0.702011\pi\)
\(600\) 0 0
\(601\) 1.48749e11i 1.14014i −0.821598 0.570068i \(-0.806917\pi\)
0.821598 0.570068i \(-0.193083\pi\)
\(602\) 9.19883e10 2.72083e10i 0.700401 0.207165i
\(603\) 0 0
\(604\) −3.40461e10 + 5.89695e10i −0.255811 + 0.443078i
\(605\) 8.83018e10 5.09811e10i 0.659095 0.380529i
\(606\) 0 0
\(607\) −1.34656e11 7.77437e10i −0.991907 0.572678i −0.0860632 0.996290i \(-0.527429\pi\)
−0.905844 + 0.423612i \(0.860762\pi\)
\(608\) 1.78451e10i 0.130588i
\(609\) 0 0
\(610\) 1.50977e11 1.09041
\(611\) 6.72084e10 1.16408e11i 0.482235 0.835256i
\(612\) 0 0
\(613\) 8.43270e10 + 1.46059e11i 0.597207 + 1.03439i 0.993231 + 0.116153i \(0.0370563\pi\)
−0.396024 + 0.918240i \(0.629610\pi\)
\(614\) 6.53611e10 + 3.77362e10i 0.459881 + 0.265513i
\(615\) 0 0
\(616\) 4.80597e9 1.99832e10i 0.0333778 0.138785i
\(617\) 1.44523e11 0.997234 0.498617 0.866822i \(-0.333841\pi\)
0.498617 + 0.866822i \(0.333841\pi\)
\(618\) 0 0
\(619\) −8.06793e9 + 4.65802e9i −0.0549541 + 0.0317277i −0.527225 0.849726i \(-0.676768\pi\)
0.472271 + 0.881453i \(0.343434\pi\)
\(620\) −1.91182e9 3.31137e9i −0.0129384 0.0224100i
\(621\) 0 0
\(622\) 6.17284e10i 0.412404i
\(623\) −2.41715e10 8.17211e10i −0.160454 0.542478i
\(624\) 0 0
\(625\) 6.07886e10 1.05289e11i 0.398384 0.690021i
\(626\) −1.64534e11 + 9.49935e10i −1.07141 + 0.618581i
\(627\) 0 0
\(628\) −6.30589e10 3.64071e10i −0.405423 0.234071i
\(629\) 2.37817e11i 1.51929i
\(630\) 0 0
\(631\) 7.06360e10 0.445563 0.222781 0.974868i \(-0.428486\pi\)
0.222781 + 0.974868i \(0.428486\pi\)
\(632\) −5.40859e10 + 9.36796e10i −0.339013 + 0.587187i
\(633\) 0 0
\(634\) −5.38654e10 9.32976e10i −0.333390 0.577449i
\(635\) −7.20016e10 4.15701e10i −0.442840 0.255674i
\(636\) 0 0
\(637\) 1.44963e11 7.48135e9i 0.880438 0.0454383i
\(638\) −8.20618e10 −0.495289
\(639\) 0 0
\(640\) −1.16772e10 + 6.74184e9i −0.0696016 + 0.0401845i
\(641\) 8.56780e10 + 1.48399e11i 0.507501 + 0.879018i 0.999962 + 0.00868351i \(0.00276408\pi\)
−0.492461 + 0.870335i \(0.663903\pi\)
\(642\) 0 0
\(643\) 2.21436e11i 1.29540i −0.761894 0.647702i \(-0.775730\pi\)
0.761894 0.647702i \(-0.224270\pi\)
\(644\) −7.54391e9 7.16461e9i −0.0438584 0.0416533i
\(645\) 0 0
\(646\) 6.55720e10 1.13574e11i 0.376520 0.652152i
\(647\) −2.60129e11 + 1.50186e11i −1.48447 + 0.857060i −0.999844 0.0176611i \(-0.994378\pi\)
−0.484627 + 0.874721i \(0.661045\pi\)
\(648\) 0 0
\(649\) −9.56653e10 5.52324e10i −0.539232 0.311326i
\(650\) 1.92764e10i 0.107987i
\(651\) 0 0
\(652\) −1.32604e10 −0.0733782
\(653\) 1.54212e10 2.67102e10i 0.0848134 0.146901i −0.820498 0.571649i \(-0.806304\pi\)
0.905312 + 0.424748i \(0.139637\pi\)
\(654\) 0 0
\(655\) 5.62818e10 + 9.74830e10i 0.305776 + 0.529619i
\(656\) −2.29769e10 1.32657e10i −0.124073 0.0716335i
\(657\) 0 0
\(658\) 1.40991e11 + 3.39083e10i 0.752121 + 0.180885i
\(659\) 5.20757e10 0.276117 0.138059 0.990424i \(-0.455914\pi\)
0.138059 + 0.990424i \(0.455914\pi\)
\(660\) 0 0
\(661\) −3.25623e9 + 1.87999e9i −0.0170573 + 0.00984803i −0.508504 0.861059i \(-0.669801\pi\)
0.491447 + 0.870907i \(0.336468\pi\)
\(662\) −2.91055e10 5.04121e10i −0.151545 0.262484i
\(663\) 0 0
\(664\) 3.55836e10i 0.183053i
\(665\) 3.07161e10 1.27717e11i 0.157065 0.653076i
\(666\) 0 0
\(667\) −2.07699e10 + 3.59745e10i −0.104938 + 0.181757i
\(668\) 2.48779e10 1.43633e10i 0.124942 0.0721352i
\(669\) 0 0
\(670\) −2.04517e10 1.18078e10i −0.101492 0.0585963i
\(671\) 1.38804e11i 0.684716i
\(672\) 0 0
\(673\) −5.59360e10 −0.272666 −0.136333 0.990663i \(-0.543532\pi\)
−0.136333 + 0.990663i \(0.543532\pi\)
\(674\) −5.01254e10 + 8.68197e10i −0.242895 + 0.420706i
\(675\) 0 0
\(676\) −1.16298e10 2.01435e10i −0.0556913 0.0964601i
\(677\) 5.03454e10 + 2.90669e10i 0.239665 + 0.138371i 0.615023 0.788509i \(-0.289147\pi\)
−0.375358 + 0.926880i \(0.622480\pi\)
\(678\) 0 0
\(679\) 1.22608e11 1.29099e11i 0.576819 0.607355i
\(680\) −9.90918e10 −0.463449
\(681\) 0 0
\(682\) −3.04437e9 + 1.75767e9i −0.0140721 + 0.00812455i
\(683\) −1.49556e11 2.59038e11i −0.687259 1.19037i −0.972721 0.231977i \(-0.925481\pi\)
0.285463 0.958390i \(-0.407853\pi\)
\(684\) 0 0
\(685\) 9.23816e10i 0.419588i
\(686\) 5.20964e10 + 1.47677e11i 0.235240 + 0.666830i
\(687\) 0 0
\(688\) −2.89293e10 + 5.01069e10i −0.129117 + 0.223637i
\(689\) 1.88438e11 1.08795e11i 0.836164 0.482760i
\(690\) 0 0
\(691\) −1.91529e11 1.10579e11i −0.840084 0.485022i 0.0172091 0.999852i \(-0.494522\pi\)
−0.857293 + 0.514829i \(0.827855\pi\)
\(692\) 7.19782e10i 0.313889i
\(693\) 0 0
\(694\) −1.50614e11 −0.649273
\(695\) −1.16122e11 + 2.01128e11i −0.497707 + 0.862053i
\(696\) 0 0
\(697\) −9.74901e10 1.68858e11i −0.413075 0.715467i
\(698\) 1.55208e11 + 8.96095e10i 0.653872 + 0.377513i
\(699\) 0 0
\(700\) 1.99417e10 5.89835e9i 0.0830557 0.0245662i
\(701\) −8.17785e10 −0.338662 −0.169331 0.985559i \(-0.554161\pi\)
−0.169331 + 0.985559i \(0.554161\pi\)
\(702\) 0 0
\(703\) −1.64672e11 + 9.50732e10i −0.674213 + 0.389257i
\(704\) 6.19824e9 + 1.07357e10i 0.0252335 + 0.0437057i
\(705\) 0 0
\(706\) 3.44888e10i 0.138822i
\(707\) 2.17278e11 + 5.22554e10i 0.869637 + 0.209148i
\(708\) 0 0
\(709\) 3.36982e10 5.83670e10i 0.133359 0.230984i −0.791610 0.611026i \(-0.790757\pi\)
0.924969 + 0.380042i \(0.124090\pi\)
\(710\) 2.75584e11 1.59108e11i 1.08448 0.626122i
\(711\) 0 0
\(712\) 4.45143e10 + 2.57003e10i 0.173213 + 0.100004i
\(713\) 1.77947e9i 0.00688544i
\(714\) 0 0
\(715\) 8.45847e10 0.323644
\(716\) 5.75316e10 9.96477e10i 0.218904 0.379154i
\(717\) 0 0
\(718\) 1.73191e11 + 2.99976e11i 0.651671 + 1.12873i
\(719\) −3.16071e11 1.82484e11i −1.18269 0.682824i −0.226052 0.974115i \(-0.572582\pi\)
−0.956634 + 0.291291i \(0.905915\pi\)
\(720\) 0 0
\(721\) −1.37715e11 4.65600e11i −0.509614 1.72295i
\(722\) 8.72910e10 0.321233
\(723\) 0 0
\(724\) −2.05107e11 + 1.18419e11i −0.746495 + 0.430989i
\(725\) −4.15154e10 7.19068e10i −0.150265 0.260266i
\(726\) 0 0
\(727\) 2.13030e11i 0.762613i 0.924449 + 0.381306i \(0.124526\pi\)
−0.924449 + 0.381306i \(0.875474\pi\)
\(728\) −6.02908e10 + 6.34826e10i −0.214647 + 0.226011i
\(729\) 0 0
\(730\) −1.06474e10 + 1.84418e10i −0.0374931 + 0.0649399i
\(731\) −3.68237e11 + 2.12601e11i −1.28961 + 0.744555i
\(732\) 0 0
\(733\) 2.17597e11 + 1.25630e11i 0.753768 + 0.435188i 0.827054 0.562123i \(-0.190015\pi\)
−0.0732857 + 0.997311i \(0.523349\pi\)
\(734\) 1.84028e11i 0.634016i
\(735\) 0 0
\(736\) 6.27511e9 0.0213850
\(737\) −1.08557e10 + 1.88027e10i −0.0367950 + 0.0637308i
\(738\) 0 0
\(739\) 1.78081e11 + 3.08445e11i 0.597089 + 1.03419i 0.993248 + 0.116007i \(0.0370094\pi\)
−0.396160 + 0.918182i \(0.629657\pi\)
\(740\) 1.24425e11 + 7.18369e10i 0.414936 + 0.239563i
\(741\) 0 0
\(742\) 1.70209e11 + 1.61652e11i 0.561523 + 0.533291i
\(743\) −2.51055e11 −0.823785 −0.411893 0.911232i \(-0.635132\pi\)
−0.411893 + 0.911232i \(0.635132\pi\)
\(744\) 0 0
\(745\) −8.68136e10 + 5.01219e10i −0.281814 + 0.162705i
\(746\) 8.38506e10 + 1.45234e11i 0.270739 + 0.468934i
\(747\) 0 0
\(748\) 9.11019e10i 0.291019i
\(749\) 4.01580e11 1.18780e11i 1.27598 0.377411i
\(750\) 0 0
\(751\) 6.20249e10 1.07430e11i 0.194987 0.337728i −0.751909 0.659267i \(-0.770867\pi\)
0.946896 + 0.321539i \(0.104200\pi\)
\(752\) −7.57451e10 + 4.37315e10i −0.236855 + 0.136749i
\(753\) 0 0
\(754\) 3.02728e11 + 1.74780e11i 0.936629 + 0.540763i
\(755\) 3.02316e11i 0.930407i
\(756\) 0 0
\(757\) −2.18830e11 −0.666382 −0.333191 0.942859i \(-0.608125\pi\)
−0.333191 + 0.942859i \(0.608125\pi\)
\(758\) −1.41381e11 + 2.44879e11i −0.428267 + 0.741780i
\(759\) 0 0
\(760\) 3.96144e10 + 6.86141e10i 0.118740 + 0.205664i
\(761\) −3.56127e11 2.05610e11i −1.06186 0.613063i −0.135911 0.990721i \(-0.543396\pi\)
−0.925945 + 0.377658i \(0.876730\pi\)
\(762\) 0 0
\(763\) −1.57888e10 + 6.56497e10i −0.0465854 + 0.193702i
\(764\) −1.08759e11 −0.319221
\(765\) 0 0
\(766\) −2.42205e11 + 1.39837e11i −0.703505 + 0.406169i
\(767\) 2.35275e11 + 4.07507e11i 0.679819 + 1.17748i
\(768\) 0 0
\(769\) 4.43811e9i 0.0126909i −0.999980 0.00634545i \(-0.997980\pi\)
0.999980 0.00634545i \(-0.00201983\pi\)
\(770\) 2.58819e10 + 8.75039e10i 0.0736264 + 0.248923i
\(771\) 0 0
\(772\) 1.63990e11 2.84040e11i 0.461689 0.799668i
\(773\) 7.27675e10 4.20123e10i 0.203807 0.117668i −0.394623 0.918843i \(-0.629125\pi\)
0.598430 + 0.801175i \(0.295791\pi\)
\(774\) 0 0
\(775\) −3.08032e9 1.77842e9i −0.00853863 0.00492978i
\(776\) 1.07386e11i 0.296142i
\(777\) 0 0
\(778\) −8.49726e10 −0.231932
\(779\) −7.79481e10 + 1.35010e11i −0.211668 + 0.366620i
\(780\) 0 0
\(781\) −1.46279e11 2.53363e11i −0.393168 0.680987i
\(782\) 3.99375e10 + 2.30579e10i 0.106796 + 0.0616585i
\(783\) 0 0
\(784\) −8.41218e10 4.29467e10i −0.222661 0.113675i
\(785\) 3.23280e11 0.851336
\(786\) 0 0
\(787\) −1.50839e11 + 8.70868e10i −0.393200 + 0.227014i −0.683546 0.729908i \(-0.739563\pi\)
0.290345 + 0.956922i \(0.406230\pi\)
\(788\) −3.83187e10 6.63699e10i −0.0993815 0.172134i
\(789\) 0 0
\(790\) 4.80262e11i 1.23302i
\(791\) 1.88591e10 + 1.79109e10i 0.0481742 + 0.0457521i
\(792\) 0 0
\(793\) −2.95632e11 + 5.12050e11i −0.747582 + 1.29485i
\(794\) −3.88252e10 + 2.24158e10i −0.0976860 + 0.0563990i
\(795\) 0 0
\(796\) −2.39204e11 1.38104e11i −0.595820 0.343997i
\(797\) 2.85416e11i 0.707368i 0.935365 + 0.353684i \(0.115071\pi\)
−0.935365 + 0.353684i \(0.884929\pi\)
\(798\) 0 0
\(799\) −6.42766e11 −1.57712
\(800\) −6.27142e9 + 1.08624e10i −0.0153111 + 0.0265196i
\(801\) 0 0
\(802\) 1.67693e11 + 2.90453e11i 0.405339 + 0.702068i
\(803\) 1.69548e10 + 9.78886e9i 0.0407784 + 0.0235434i
\(804\) 0 0
\(805\) 4.49109e10 + 1.08011e10i 0.106947 + 0.0257208i
\(806\) 1.49744e10 0.0354820
\(807\) 0 0
\(808\) −1.16729e11 + 6.73936e10i −0.273863 + 0.158115i
\(809\) −2.92767e10 5.07088e10i −0.0683484 0.118383i 0.829826 0.558022i \(-0.188440\pi\)
−0.898174 + 0.439639i \(0.855106\pi\)
\(810\) 0 0
\(811\) 3.15833e11i 0.730086i 0.930991 + 0.365043i \(0.118946\pi\)
−0.930991 + 0.365043i \(0.881054\pi\)
\(812\) −8.81811e10 + 3.66657e11i −0.202839 + 0.843404i
\(813\) 0 0
\(814\) 6.60446e10 1.14393e11i 0.150432 0.260555i
\(815\) 5.09861e10 2.94368e10i 0.115564 0.0667207i
\(816\) 0 0
\(817\) 2.94423e11 + 1.69985e11i 0.660821 + 0.381525i
\(818\) 2.10974e11i 0.471210i
\(819\) 0 0
\(820\) 1.17794e11 0.260537
\(821\) 1.56329e11 2.70770e11i 0.344086 0.595975i −0.641101 0.767457i \(-0.721522\pi\)
0.985187 + 0.171481i \(0.0548553\pi\)
\(822\) 0 0
\(823\) 5.10476e10 + 8.84170e10i 0.111269 + 0.192724i 0.916282 0.400533i \(-0.131175\pi\)
−0.805013 + 0.593257i \(0.797842\pi\)
\(824\) 2.53617e11 + 1.46426e11i 0.550136 + 0.317621i
\(825\) 0 0
\(826\) −3.49580e11 + 3.68087e11i −0.750977 + 0.790734i
\(827\) 4.47639e11 0.956986 0.478493 0.878091i \(-0.341183\pi\)
0.478493 + 0.878091i \(0.341183\pi\)
\(828\) 0 0
\(829\) 1.86546e11 1.07702e11i 0.394973 0.228038i −0.289340 0.957226i \(-0.593436\pi\)
0.684313 + 0.729189i \(0.260102\pi\)
\(830\) −7.89920e10 1.36818e11i −0.166445 0.288291i
\(831\) 0 0
\(832\) 5.28055e10i 0.110201i
\(833\) −3.77580e11 5.82437e11i −0.784203 1.20968i
\(834\) 0 0
\(835\) −6.37700e10 + 1.10453e11i −0.131181 + 0.227212i
\(836\) 6.30817e10 3.64202e10i 0.129145 0.0745620i
\(837\) 0 0
\(838\) −1.49316e10 8.62076e9i −0.0302782 0.0174811i
\(839\) 7.41073e11i 1.49559i 0.663929 + 0.747796i \(0.268888\pi\)
−0.663929 + 0.747796i \(0.731112\pi\)
\(840\) 0 0
\(841\) 1.00544e12 2.00990
\(842\) 1.14496e11 1.98313e11i 0.227794 0.394550i
\(843\) 0 0
\(844\) 5.44690e10 + 9.43431e10i 0.107344 + 0.185926i
\(845\) 8.94331e10 + 5.16342e10i 0.175417 + 0.101277i
\(846\) 0 0
\(847\) −4.13091e11 + 1.22184e11i −0.802624 + 0.237400i
\(848\) −1.41582e11 −0.273795
\(849\) 0 0
\(850\) −7.98281e10 + 4.60888e10i −0.152926 + 0.0882916i
\(851\) −3.34318e10 5.79056e10i −0.0637444 0.110408i
\(852\) 0 0
\(853\) 6.71696e11i 1.26875i −0.773025 0.634376i \(-0.781257\pi\)
0.773025 0.634376i \(-0.218743\pi\)
\(854\) −6.20182e11 1.49154e11i −1.16597 0.280416i
\(855\) 0 0
\(856\) −1.26292e11 + 2.18745e11i −0.235224 + 0.407420i
\(857\) −6.38087e11 + 3.68399e11i −1.18292 + 0.682961i −0.956689 0.291112i \(-0.905975\pi\)
−0.226234 + 0.974073i \(0.572641\pi\)
\(858\) 0 0
\(859\) 1.28267e10 + 7.40553e9i 0.0235583 + 0.0136014i 0.511733 0.859145i \(-0.329004\pi\)
−0.488175 + 0.872746i \(0.662337\pi\)
\(860\) 2.56880e11i 0.469610i
\(861\) 0 0
\(862\) −7.23362e10 −0.131017
\(863\) 1.53636e11 2.66105e11i 0.276980 0.479744i −0.693653 0.720310i \(-0.744000\pi\)
0.970633 + 0.240566i \(0.0773330\pi\)
\(864\) 0 0
\(865\) 1.59785e11 + 2.76755e11i 0.285411 + 0.494346i
\(866\) 3.12382e11 + 1.80354e11i 0.555412 + 0.320667i
\(867\) 0 0
\(868\) 4.58198e9 + 1.54912e10i 0.00807187 + 0.0272901i
\(869\) −4.41538e11 −0.774263
\(870\) 0 0
\(871\) 8.00942e10 4.62424e10i 0.139164 0.0803466i
\(872\) −2.03627e10 3.52692e10i −0.0352184 0.0610001i
\(873\) 0 0
\(874\) 3.68719e10i 0.0631902i
\(875\) −4.30627e11 + 4.53425e11i −0.734631 + 0.773522i
\(876\) 0 0
\(877\) 9.02694e10 1.56351e11i 0.152596 0.264303i −0.779585 0.626296i \(-0.784570\pi\)
0.932181 + 0.361993i \(0.117903\pi\)
\(878\) 8.24778e10 4.76186e10i 0.138790 0.0801306i
\(879\) 0 0
\(880\) −4.76642e10 2.75190e10i −0.0794807 0.0458882i
\(881\) 6.42949e11i 1.06727i −0.845716 0.533633i \(-0.820826\pi\)
0.845716 0.533633i \(-0.179174\pi\)
\(882\) 0 0
\(883\) −3.92563e11 −0.645754 −0.322877 0.946441i \(-0.604650\pi\)
−0.322877 + 0.946441i \(0.604650\pi\)
\(884\) 1.94034e11 3.36077e11i 0.317738 0.550339i
\(885\) 0 0
\(886\) −2.15653e11 3.73522e11i −0.349962 0.606152i
\(887\) 3.07716e11 + 1.77660e11i 0.497113 + 0.287008i 0.727521 0.686086i \(-0.240673\pi\)
−0.230407 + 0.973094i \(0.574006\pi\)
\(888\) 0 0
\(889\) 2.54699e11 + 2.41894e11i 0.407775 + 0.387273i
\(890\) −2.28209e11 −0.363724
\(891\) 0 0
\(892\) 2.40022e11 1.38577e11i 0.379133 0.218893i
\(893\) 2.56962e11 + 4.45071e11i 0.404076 + 0.699879i
\(894\) 0 0
\(895\) 5.10858e11i 0.796174i
\(896\) 5.46280e10 1.61579e10i 0.0847585 0.0250699i
\(897\) 0 0
\(898\) −9.96275e10 + 1.72560e11i −0.153205 + 0.265359i
\(899\) 5.58589e10 3.22501e10i 0.0855172 0.0493734i
\(900\) 0 0
\(901\) −9.01089e11 5.20244e11i −1.36732 0.789420i
\(902\) 1.08297e11i 0.163602i
\(903\) 0 0
\(904\) −1.56872e10 −0.0234894
\(905\) 5.25756e11 9.10636e11i 0.783773 1.35753i
\(906\) 0 0
\(907\) −2.88507e11 4.99710e11i −0.426312 0.738395i 0.570230 0.821485i \(-0.306854\pi\)
−0.996542 + 0.0830907i \(0.973521\pi\)
\(908\) 3.87073e10 + 2.23477e10i 0.0569442 + 0.0328767i
\(909\) 0 0
\(910\) 9.08920e10 3.77929e11i 0.132544 0.551118i
\(911\) −5.83597e11 −0.847305 −0.423652 0.905825i \(-0.639252\pi\)
−0.423652 + 0.905825i \(0.639252\pi\)
\(912\) 0 0
\(913\) −1.25786e11 + 7.26228e10i −0.181030 + 0.104518i
\(914\) 3.10672e11 + 5.38099e11i 0.445161 + 0.771042i
\(915\) 0 0
\(916\) 4.11604e11i 0.584653i
\(917\) −1.34888e11 4.56042e11i −0.190764 0.644952i
\(918\) 0 0
\(919\) 3.96096e11 6.86059e11i 0.555314 0.961833i −0.442565 0.896737i \(-0.645931\pi\)
0.997879 0.0650961i \(-0.0207354\pi\)
\(920\) −2.41277e10 + 1.39301e10i −0.0336794 + 0.0194448i
\(921\) 0 0
\(922\) 2.95848e11 + 1.70808e11i 0.409397 + 0.236365i
\(923\) 1.24622e12i 1.71707i
\(924\) 0 0
\(925\) 1.33649e11 0.182557
\(926\) 5.73643e10 9.93578e10i 0.0780185 0.135132i
\(927\) 0 0
\(928\) −1.13727e11 1.96981e11i −0.153345 0.265602i
\(929\) 5.67196e11 + 3.27471e11i 0.761501 + 0.439653i 0.829834 0.558010i \(-0.188435\pi\)
−0.0683336 + 0.997663i \(0.521768\pi\)
\(930\) 0 0
\(931\) −2.52350e11 + 4.94291e11i −0.335896 + 0.657937i
\(932\) −4.12033e11 −0.546095
\(933\) 0 0
\(934\) 6.86664e11 3.96446e11i 0.902313 0.520950i
\(935\) −2.02237e11 3.50285e11i −0.264615 0.458327i
\(936\) 0 0
\(937\) 1.23429e11i 0.160125i −0.996790 0.0800627i \(-0.974488\pi\)
0.996790 0.0800627i \(-0.0255120\pi\)
\(938\) 7.23462e10 + 6.87088e10i 0.0934554 + 0.0887566i
\(939\) 0 0
\(940\) 1.94159e11 3.36293e11i 0.248683 0.430732i
\(941\) −2.90756e11 + 1.67868e11i −0.370826 + 0.214097i −0.673819 0.738896i \(-0.735347\pi\)
0.302993 + 0.952993i \(0.402014\pi\)
\(942\) 0 0
\(943\) −4.74753e10 2.74099e10i −0.0600373 0.0346626i
\(944\) 3.06179e11i 0.385556i
\(945\) 0 0
\(946\) −2.36168e11 −0.294887
\(947\) 2.86082e11 4.95509e11i 0.355706 0.616100i −0.631533 0.775349i \(-0.717574\pi\)
0.987238 + 0.159249i \(0.0509072\pi\)
\(948\) 0 0
\(949\) −4.16978e10 7.22227e10i −0.0514101 0.0890449i
\(950\) 6.38265e10 + 3.68503e10i 0.0783622 + 0.0452424i
\(951\) 0 0
\(952\) 4.07048e11 + 9.78952e10i 0.495562 + 0.119183i
\(953\) 5.15910e11 0.625464 0.312732 0.949841i \(-0.398756\pi\)
0.312732 + 0.949841i \(0.398756\pi\)
\(954\) 0 0
\(955\) 4.18176e11 2.41434e11i 0.502743 0.290259i
\(956\) 1.46621e11 + 2.53955e11i 0.175536 + 0.304037i
\(957\) 0 0
\(958\) 5.56877e11i 0.661146i
\(959\) 9.12661e10 3.79485e11i 0.107903 0.448662i
\(960\) 0 0
\(961\) −4.25064e11 + 7.36232e11i −0.498380 + 0.863220i
\(962\) −4.87280e11 + 2.81331e11i −0.568956 + 0.328487i
\(963\) 0 0
\(964\) 6.09005e11 + 3.51609e11i 0.705201 + 0.407148i
\(965\) 1.45617e12i 1.67920i
\(966\) 0 0
\(967\) 1.27085e12 1.45341 0.726703 0.686952i \(-0.241052\pi\)
0.726703 + 0.686952i \(0.241052\pi\)
\(968\) 1.29912e11 2.25015e11i 0.147962 0.256277i
\(969\) 0 0
\(970\) −2.38386e11 4.12896e11i −0.269274 0.466395i
\(971\) −1.28913e12 7.44277e11i −1.45017 0.837255i −0.451678 0.892181i \(-0.649174\pi\)
−0.998490 + 0.0549264i \(0.982508\pi\)
\(972\) 0 0
\(973\) 6.75703e11 7.11474e11i 0.753884 0.793794i
\(974\) −1.00095e12 −1.11218
\(975\) 0 0
\(976\) 3.33183e11 1.92363e11i 0.367184 0.211994i
\(977\) −4.09875e11 7.09924e11i −0.449855 0.779172i 0.548521 0.836137i \(-0.315191\pi\)
−0.998376 + 0.0569648i \(0.981858\pi\)
\(978\) 0 0
\(979\) 2.09808e11i 0.228397i
\(980\) 4.18784e11 2.16129e10i 0.454032 0.0234320i
\(981\) 0 0
\(982\) 1.20961e9 2.09511e9i 0.00130077 0.00225300i
\(983\) 9.98852e11 5.76688e11i 1.06976 0.617627i 0.141645 0.989917i \(-0.454761\pi\)
0.928116 + 0.372290i \(0.121427\pi\)
\(984\) 0 0
\(985\) 2.94669e11 + 1.70127e11i 0.313033 + 0.180730i
\(986\) 1.67156e12i 1.76854i
\(987\) 0 0
\(988\) −3.10280e11 −0.325631
\(989\) −5.97742e10 + 1.03532e11i −0.0624782 + 0.108215i
\(990\) 0 0
\(991\) 3.12577e11 + 5.41399e11i 0.324087 + 0.561336i 0.981327 0.192346i \(-0.0616095\pi\)
−0.657240 + 0.753681i \(0.728276\pi\)
\(992\) −8.43818e9 4.87179e9i −0.00871369 0.00503085i
\(993\) 0 0
\(994\) −1.28923e12 + 3.81328e11i −1.32064 + 0.390619i
\(995\) 1.22631e12 1.25115
\(996\) 0 0
\(997\) 1.54866e11 8.94122e10i 0.156739 0.0904932i −0.419579 0.907719i \(-0.637822\pi\)
0.576318 + 0.817226i \(0.304489\pi\)
\(998\) −3.28333e11 5.68690e11i −0.330973 0.573262i
\(999\) 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.19.3 12
3.2 odd 2 14.9.d.a.5.5 yes 12
7.3 odd 6 inner 126.9.n.b.73.3 12
12.11 even 2 112.9.s.c.33.4 12
21.2 odd 6 98.9.b.c.97.3 12
21.5 even 6 98.9.b.c.97.4 12
21.11 odd 6 98.9.d.b.31.5 12
21.17 even 6 14.9.d.a.3.5 12
21.20 even 2 98.9.d.b.19.5 12
84.59 odd 6 112.9.s.c.17.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.9.d.a.3.5 12 21.17 even 6
14.9.d.a.5.5 yes 12 3.2 odd 2
98.9.b.c.97.3 12 21.2 odd 6
98.9.b.c.97.4 12 21.5 even 6
98.9.d.b.19.5 12 21.20 even 2
98.9.d.b.31.5 12 21.11 odd 6
112.9.s.c.17.4 12 84.59 odd 6
112.9.s.c.33.4 12 12.11 even 2
126.9.n.b.19.3 12 1.1 even 1 trivial
126.9.n.b.73.3 12 7.3 odd 6 inner