Properties

Label 81.10.c.g.28.2
Level $81$
Weight $10$
Character 81.28
Analytic conductor $41.718$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,10,Mod(28,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.28");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 81.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(41.7179027293\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 119x^{4} - 154x^{3} + 14060x^{2} - 16048x + 18496 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{8} \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 28.2
Root \(0.577142 + 0.999640i\) of defining polynomial
Character \(\chi\) \(=\) 81.28
Dual form 81.10.c.g.55.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73143 - 2.99892i) q^{2} +(250.004 - 433.020i) q^{4} +(-702.004 + 1215.91i) q^{5} +(-832.785 - 1442.43i) q^{7} -3504.44 q^{8} +4861.88 q^{10} +(31809.3 + 55095.3i) q^{11} +(55604.8 - 96310.3i) q^{13} +(-2883.81 + 4994.91i) q^{14} +(-121935. - 211197. i) q^{16} -383783. q^{17} +7441.82 q^{19} +(351008. + 607964. i) q^{20} +(110151. - 190787. i) q^{22} +(1.30861e6 - 2.26658e6i) q^{23} +(-9057.92 - 15688.8i) q^{25} -385102. q^{26} -832799. q^{28} +(-289545. - 501507. i) q^{29} +(-1.75915e6 + 3.04695e6i) q^{31} +(-1.31938e6 + 2.28523e6i) q^{32} +(664492. + 1.15093e6i) q^{34} +2.33847e6 q^{35} -9.82783e6 q^{37} +(-12885.0 - 22317.4i) q^{38} +(2.46013e6 - 4.26107e6i) q^{40} +(-8.88800e6 + 1.53945e7i) q^{41} +(-1.95649e7 - 3.38874e7i) q^{43} +3.18098e7 q^{44} -9.06304e6 q^{46} +(-1.33934e7 - 2.31980e7i) q^{47} +(1.87897e7 - 3.25448e7i) q^{49} +(-31366.3 + 54327.9i) q^{50} +(-2.78029e7 - 4.81560e7i) q^{52} -6.04430e7 q^{53} -8.93210e7 q^{55} +(2.91844e6 + 5.05489e6i) q^{56} +(-1.00265e6 + 1.73665e6i) q^{58} +(6.74085e7 - 1.16755e8i) q^{59} +(-7.03846e7 - 1.21910e8i) q^{61} +1.21834e7 q^{62} -1.15723e8 q^{64} +(7.80696e7 + 1.35221e8i) q^{65} +(-3.65671e7 + 6.33360e7i) q^{67} +(-9.59473e7 + 1.66186e8i) q^{68} +(-4.04890e6 - 7.01290e6i) q^{70} -2.72910e8 q^{71} -2.64531e8 q^{73} +(1.70162e7 + 2.94729e7i) q^{74} +(1.86049e6 - 3.22246e6i) q^{76} +(5.29806e7 - 9.17651e7i) q^{77} +(-2.72331e8 - 4.71691e8i) q^{79} +3.42394e8 q^{80} +6.15557e7 q^{82} +(-8.69938e7 - 1.50678e8i) q^{83} +(2.69417e8 - 4.66644e8i) q^{85} +(-6.77504e7 + 1.17347e8i) q^{86} +(-1.11474e8 - 1.93078e8i) q^{88} +5.69208e8 q^{89} -1.85227e8 q^{91} +(-6.54316e8 - 1.13331e9i) q^{92} +(-4.63793e7 + 8.03313e7i) q^{94} +(-5.22419e6 + 9.04856e6i) q^{95} +(2.93260e8 + 5.07941e8i) q^{97} -1.30132e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 597 q^{4} + 1983 q^{5} + 3693 q^{7} - 9006 q^{8} - 37962 q^{10} + 16863 q^{11} - 116916 q^{13} + 503463 q^{14} + 239919 q^{16} - 2028096 q^{17} - 30444 q^{19} + 2548407 q^{20} - 305721 q^{22}+ \cdots + 5184364572 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73143 2.99892i −0.0765190 0.132535i 0.825227 0.564801i \(-0.191047\pi\)
−0.901746 + 0.432267i \(0.857714\pi\)
\(3\) 0 0
\(4\) 250.004 433.020i 0.488290 0.845743i
\(5\) −702.004 + 1215.91i −0.502313 + 0.870032i 0.497683 + 0.867359i \(0.334184\pi\)
−0.999996 + 0.00267343i \(0.999149\pi\)
\(6\) 0 0
\(7\) −832.785 1442.43i −0.131097 0.227066i 0.793003 0.609218i \(-0.208516\pi\)
−0.924100 + 0.382152i \(0.875183\pi\)
\(8\) −3504.44 −0.302492
\(9\) 0 0
\(10\) 4861.88 0.153746
\(11\) 31809.3 + 55095.3i 0.655069 + 1.13461i 0.981877 + 0.189521i \(0.0606937\pi\)
−0.326808 + 0.945091i \(0.605973\pi\)
\(12\) 0 0
\(13\) 55604.8 96310.3i 0.539967 0.935250i −0.458938 0.888468i \(-0.651770\pi\)
0.998905 0.0467819i \(-0.0148966\pi\)
\(14\) −2883.81 + 4994.91i −0.0200628 + 0.0347497i
\(15\) 0 0
\(16\) −121935. 211197.i −0.465143 0.805652i
\(17\) −383783. −1.11446 −0.557231 0.830358i \(-0.688136\pi\)
−0.557231 + 0.830358i \(0.688136\pi\)
\(18\) 0 0
\(19\) 7441.82 0.0131005 0.00655025 0.999979i \(-0.497915\pi\)
0.00655025 + 0.999979i \(0.497915\pi\)
\(20\) 351008. + 607964.i 0.490549 + 0.849656i
\(21\) 0 0
\(22\) 110151. 190787.i 0.100250 0.173639i
\(23\) 1.30861e6 2.26658e6i 0.975067 1.68887i 0.295354 0.955388i \(-0.404562\pi\)
0.679713 0.733478i \(-0.262104\pi\)
\(24\) 0 0
\(25\) −9057.92 15688.8i −0.00463766 0.00803266i
\(26\) −385102. −0.165271
\(27\) 0 0
\(28\) −832799. −0.256053
\(29\) −289545. 501507.i −0.0760196 0.131670i 0.825510 0.564388i \(-0.190888\pi\)
−0.901529 + 0.432718i \(0.857554\pi\)
\(30\) 0 0
\(31\) −1.75915e6 + 3.04695e6i −0.342118 + 0.592566i −0.984826 0.173545i \(-0.944478\pi\)
0.642708 + 0.766112i \(0.277811\pi\)
\(32\) −1.31938e6 + 2.28523e6i −0.222430 + 0.385261i
\(33\) 0 0
\(34\) 664492. + 1.15093e6i 0.0852775 + 0.147705i
\(35\) 2.33847e6 0.263407
\(36\) 0 0
\(37\) −9.82783e6 −0.862084 −0.431042 0.902332i \(-0.641854\pi\)
−0.431042 + 0.902332i \(0.641854\pi\)
\(38\) −12885.0 22317.4i −0.00100244 0.00173627i
\(39\) 0 0
\(40\) 2.46013e6 4.26107e6i 0.151946 0.263178i
\(41\) −8.88800e6 + 1.53945e7i −0.491221 + 0.850819i −0.999949 0.0101082i \(-0.996782\pi\)
0.508728 + 0.860927i \(0.330116\pi\)
\(42\) 0 0
\(43\) −1.95649e7 3.38874e7i −0.872709 1.51158i −0.859183 0.511668i \(-0.829028\pi\)
−0.0135261 0.999909i \(-0.504306\pi\)
\(44\) 3.18098e7 1.27945
\(45\) 0 0
\(46\) −9.06304e6 −0.298445
\(47\) −1.33934e7 2.31980e7i −0.400359 0.693442i 0.593410 0.804900i \(-0.297781\pi\)
−0.993769 + 0.111458i \(0.964448\pi\)
\(48\) 0 0
\(49\) 1.87897e7 3.25448e7i 0.465627 0.806490i
\(50\) −31366.3 + 54327.9i −0.000709737 + 0.00122930i
\(51\) 0 0
\(52\) −2.78029e7 4.81560e7i −0.527321 0.913346i
\(53\) −6.04430e7 −1.05222 −0.526108 0.850418i \(-0.676349\pi\)
−0.526108 + 0.850418i \(0.676349\pi\)
\(54\) 0 0
\(55\) −8.93210e7 −1.31620
\(56\) 2.91844e6 + 5.05489e6i 0.0396556 + 0.0686856i
\(57\) 0 0
\(58\) −1.00265e6 + 1.73665e6i −0.0116339 + 0.0201505i
\(59\) 6.74085e7 1.16755e8i 0.724237 1.25441i −0.235051 0.971983i \(-0.575526\pi\)
0.959287 0.282432i \(-0.0911411\pi\)
\(60\) 0 0
\(61\) −7.03846e7 1.21910e8i −0.650869 1.12734i −0.982912 0.184074i \(-0.941071\pi\)
0.332043 0.943264i \(-0.392262\pi\)
\(62\) 1.21834e7 0.104714
\(63\) 0 0
\(64\) −1.15723e8 −0.862206
\(65\) 7.80696e7 + 1.35221e8i 0.542465 + 0.939577i
\(66\) 0 0
\(67\) −3.65671e7 + 6.33360e7i −0.221694 + 0.383985i −0.955322 0.295566i \(-0.904492\pi\)
0.733629 + 0.679551i \(0.237825\pi\)
\(68\) −9.59473e7 + 1.66186e8i −0.544180 + 0.942548i
\(69\) 0 0
\(70\) −4.04890e6 7.01290e6i −0.0201556 0.0349105i
\(71\) −2.72910e8 −1.27455 −0.637276 0.770636i \(-0.719939\pi\)
−0.637276 + 0.770636i \(0.719939\pi\)
\(72\) 0 0
\(73\) −2.64531e8 −1.09025 −0.545123 0.838356i \(-0.683517\pi\)
−0.545123 + 0.838356i \(0.683517\pi\)
\(74\) 1.70162e7 + 2.94729e7i 0.0659658 + 0.114256i
\(75\) 0 0
\(76\) 1.86049e6 3.22246e6i 0.00639684 0.0110797i
\(77\) 5.29806e7 9.17651e7i 0.171755 0.297488i
\(78\) 0 0
\(79\) −2.72331e8 4.71691e8i −0.786639 1.36250i −0.928015 0.372542i \(-0.878486\pi\)
0.141376 0.989956i \(-0.454847\pi\)
\(80\) 3.42394e8 0.934591
\(81\) 0 0
\(82\) 6.15557e7 0.150351
\(83\) −8.69938e7 1.50678e8i −0.201204 0.348496i 0.747713 0.664023i \(-0.231152\pi\)
−0.948917 + 0.315527i \(0.897819\pi\)
\(84\) 0 0
\(85\) 2.69417e8 4.66644e8i 0.559809 0.969618i
\(86\) −6.77504e7 + 1.17347e8i −0.133558 + 0.231329i
\(87\) 0 0
\(88\) −1.11474e8 1.93078e8i −0.198153 0.343211i
\(89\) 5.69208e8 0.961647 0.480823 0.876817i \(-0.340338\pi\)
0.480823 + 0.876817i \(0.340338\pi\)
\(90\) 0 0
\(91\) −1.85227e8 −0.283151
\(92\) −6.54316e8 1.13331e9i −0.952231 1.64931i
\(93\) 0 0
\(94\) −4.63793e7 + 8.03313e7i −0.0612701 + 0.106123i
\(95\) −5.22419e6 + 9.04856e6i −0.00658056 + 0.0113979i
\(96\) 0 0
\(97\) 2.93260e8 + 5.07941e8i 0.336341 + 0.582560i 0.983742 0.179590i \(-0.0574772\pi\)
−0.647400 + 0.762150i \(0.724144\pi\)
\(98\) −1.30132e8 −0.142517
\(99\) 0 0
\(100\) −9.05808e6 −0.00905808
\(101\) 8.12194e8 + 1.40676e9i 0.776629 + 1.34516i 0.933875 + 0.357601i \(0.116405\pi\)
−0.157246 + 0.987559i \(0.550262\pi\)
\(102\) 0 0
\(103\) −2.96352e8 + 5.13297e8i −0.259442 + 0.449367i −0.966093 0.258196i \(-0.916872\pi\)
0.706650 + 0.707563i \(0.250205\pi\)
\(104\) −1.94864e8 + 3.37514e8i −0.163335 + 0.282905i
\(105\) 0 0
\(106\) 1.04653e8 + 1.81264e8i 0.0805144 + 0.139455i
\(107\) −4.69405e8 −0.346195 −0.173098 0.984905i \(-0.555378\pi\)
−0.173098 + 0.984905i \(0.555378\pi\)
\(108\) 0 0
\(109\) 2.10211e9 1.42639 0.713193 0.700968i \(-0.247248\pi\)
0.713193 + 0.700968i \(0.247248\pi\)
\(110\) 1.54653e8 + 2.67867e8i 0.100714 + 0.174442i
\(111\) 0 0
\(112\) −2.03090e8 + 3.51763e8i −0.121957 + 0.211237i
\(113\) 6.26779e8 1.08561e9i 0.361628 0.626357i −0.626601 0.779340i \(-0.715555\pi\)
0.988229 + 0.152983i \(0.0488879\pi\)
\(114\) 0 0
\(115\) 1.83730e9 + 3.18229e9i 0.979579 + 1.69668i
\(116\) −2.89550e8 −0.148478
\(117\) 0 0
\(118\) −4.66851e8 −0.221671
\(119\) 3.19608e8 + 5.53578e8i 0.146102 + 0.253057i
\(120\) 0 0
\(121\) −8.44688e8 + 1.46304e9i −0.358230 + 0.620473i
\(122\) −2.43732e8 + 4.22156e8i −0.0996077 + 0.172526i
\(123\) 0 0
\(124\) 8.79593e8 + 1.52350e9i 0.334106 + 0.578688i
\(125\) −2.71677e9 −0.995309
\(126\) 0 0
\(127\) 3.81433e9 1.30107 0.650536 0.759476i \(-0.274544\pi\)
0.650536 + 0.759476i \(0.274544\pi\)
\(128\) 8.75888e8 + 1.51708e9i 0.288406 + 0.499533i
\(129\) 0 0
\(130\) 2.70344e8 4.68249e8i 0.0830178 0.143791i
\(131\) 9.69871e8 1.67987e9i 0.287735 0.498372i −0.685533 0.728041i \(-0.740431\pi\)
0.973269 + 0.229669i \(0.0737643\pi\)
\(132\) 0 0
\(133\) −6.19743e6 1.07343e7i −0.00171743 0.00297468i
\(134\) 2.53253e8 0.0678551
\(135\) 0 0
\(136\) 1.34494e9 0.337115
\(137\) −2.97132e9 5.14648e9i −0.720621 1.24815i −0.960751 0.277412i \(-0.910523\pi\)
0.240130 0.970741i \(-0.422810\pi\)
\(138\) 0 0
\(139\) 2.77575e9 4.80774e9i 0.630687 1.09238i −0.356725 0.934209i \(-0.616107\pi\)
0.987412 0.158172i \(-0.0505600\pi\)
\(140\) 5.84629e8 1.01261e9i 0.128619 0.222774i
\(141\) 0 0
\(142\) 4.72524e8 + 8.18436e8i 0.0975274 + 0.168922i
\(143\) 7.07500e9 1.41486
\(144\) 0 0
\(145\) 8.13049e8 0.152743
\(146\) 4.58017e8 + 7.93308e8i 0.0834245 + 0.144495i
\(147\) 0 0
\(148\) −2.45700e9 + 4.25565e9i −0.420947 + 0.729102i
\(149\) −4.86200e9 + 8.42124e9i −0.808122 + 1.39971i 0.106040 + 0.994362i \(0.466183\pi\)
−0.914163 + 0.405347i \(0.867151\pi\)
\(150\) 0 0
\(151\) 1.60926e9 + 2.78732e9i 0.251901 + 0.436305i 0.964049 0.265724i \(-0.0856110\pi\)
−0.712148 + 0.702029i \(0.752278\pi\)
\(152\) −2.60794e7 −0.00396279
\(153\) 0 0
\(154\) −3.66928e8 −0.0525700
\(155\) −2.46987e9 4.27794e9i −0.343701 0.595308i
\(156\) 0 0
\(157\) −6.42880e8 + 1.11350e9i −0.0844465 + 0.146266i −0.905155 0.425081i \(-0.860246\pi\)
0.820709 + 0.571347i \(0.193579\pi\)
\(158\) −9.43043e8 + 1.63340e9i −0.120386 + 0.208514i
\(159\) 0 0
\(160\) −1.85242e9 3.20848e9i −0.223460 0.387043i
\(161\) −4.35916e9 −0.511312
\(162\) 0 0
\(163\) 4.38269e9 0.486291 0.243146 0.969990i \(-0.421821\pi\)
0.243146 + 0.969990i \(0.421821\pi\)
\(164\) 4.44407e9 + 7.69736e9i 0.479716 + 0.830892i
\(165\) 0 0
\(166\) −3.01247e8 + 5.21775e8i −0.0307919 + 0.0533331i
\(167\) −7.67671e8 + 1.32965e9i −0.0763750 + 0.132285i −0.901683 0.432397i \(-0.857668\pi\)
0.825308 + 0.564682i \(0.191001\pi\)
\(168\) 0 0
\(169\) −8.81536e8 1.52687e9i −0.0831285 0.143983i
\(170\) −1.86590e9 −0.171344
\(171\) 0 0
\(172\) −1.95652e10 −1.70454
\(173\) 3.79098e8 + 6.56618e8i 0.0321769 + 0.0557321i 0.881665 0.471875i \(-0.156423\pi\)
−0.849489 + 0.527607i \(0.823089\pi\)
\(174\) 0 0
\(175\) −1.50866e7 + 2.61308e7i −0.00121596 + 0.00210611i
\(176\) 7.75730e9 1.34360e10i 0.609402 1.05551i
\(177\) 0 0
\(178\) −9.85541e8 1.70701e9i −0.0735842 0.127452i
\(179\) 1.17238e10 0.853549 0.426774 0.904358i \(-0.359650\pi\)
0.426774 + 0.904358i \(0.359650\pi\)
\(180\) 0 0
\(181\) −8.83265e9 −0.611698 −0.305849 0.952080i \(-0.598940\pi\)
−0.305849 + 0.952080i \(0.598940\pi\)
\(182\) 3.20708e8 + 5.55482e8i 0.0216665 + 0.0375274i
\(183\) 0 0
\(184\) −4.58594e9 + 7.94308e9i −0.294950 + 0.510868i
\(185\) 6.89918e9 1.19497e10i 0.433037 0.750041i
\(186\) 0 0
\(187\) −1.22079e10 2.11446e10i −0.730049 1.26448i
\(188\) −1.33936e10 −0.781965
\(189\) 0 0
\(190\) 3.61812e7 0.00201415
\(191\) 1.57008e9 + 2.71947e9i 0.0853636 + 0.147854i 0.905546 0.424248i \(-0.139461\pi\)
−0.820182 + 0.572102i \(0.806128\pi\)
\(192\) 0 0
\(193\) 1.53175e10 2.65307e10i 0.794658 1.37639i −0.128398 0.991723i \(-0.540984\pi\)
0.923056 0.384665i \(-0.125683\pi\)
\(194\) 1.01552e9 1.75893e9i 0.0514729 0.0891538i
\(195\) 0 0
\(196\) −9.39503e9 1.62727e10i −0.454722 0.787602i
\(197\) −2.16444e10 −1.02388 −0.511939 0.859022i \(-0.671073\pi\)
−0.511939 + 0.859022i \(0.671073\pi\)
\(198\) 0 0
\(199\) −3.61495e9 −0.163404 −0.0817021 0.996657i \(-0.526036\pi\)
−0.0817021 + 0.996657i \(0.526036\pi\)
\(200\) 3.17429e7 + 5.49803e7i 0.00140285 + 0.00242981i
\(201\) 0 0
\(202\) 2.81251e9 4.87141e9i 0.118854 0.205861i
\(203\) −4.82258e8 + 8.35296e8i −0.0199318 + 0.0345230i
\(204\) 0 0
\(205\) −1.24788e10 2.16140e10i −0.493493 0.854756i
\(206\) 2.05245e9 0.0794091
\(207\) 0 0
\(208\) −2.71206e10 −1.00465
\(209\) 2.36719e8 + 4.10009e8i 0.00858173 + 0.0148640i
\(210\) 0 0
\(211\) 5.92937e9 1.02700e10i 0.205938 0.356696i −0.744493 0.667630i \(-0.767309\pi\)
0.950431 + 0.310935i \(0.100642\pi\)
\(212\) −1.51110e10 + 2.61730e10i −0.513786 + 0.889903i
\(213\) 0 0
\(214\) 8.12740e8 + 1.40771e9i 0.0264905 + 0.0458829i
\(215\) 5.49386e10 1.75349
\(216\) 0 0
\(217\) 5.85999e9 0.179402
\(218\) −3.63966e9 6.30407e9i −0.109146 0.189046i
\(219\) 0 0
\(220\) −2.23306e10 + 3.86778e10i −0.642687 + 1.11317i
\(221\) −2.13402e10 + 3.69622e10i −0.601773 + 1.04230i
\(222\) 0 0
\(223\) 9.43784e9 + 1.63468e10i 0.255565 + 0.442651i 0.965049 0.262070i \(-0.0844053\pi\)
−0.709484 + 0.704722i \(0.751072\pi\)
\(224\) 4.39503e9 0.116640
\(225\) 0 0
\(226\) −4.34089e9 −0.110685
\(227\) 1.02386e9 + 1.77337e9i 0.0255931 + 0.0443285i 0.878538 0.477672i \(-0.158519\pi\)
−0.852945 + 0.522000i \(0.825186\pi\)
\(228\) 0 0
\(229\) −1.06967e9 + 1.85272e9i −0.0257034 + 0.0445196i −0.878591 0.477575i \(-0.841516\pi\)
0.852888 + 0.522095i \(0.174849\pi\)
\(230\) 6.36229e9 1.10198e10i 0.149913 0.259656i
\(231\) 0 0
\(232\) 1.01469e9 + 1.75750e9i 0.0229953 + 0.0398290i
\(233\) −4.02632e10 −0.894966 −0.447483 0.894292i \(-0.647679\pi\)
−0.447483 + 0.894292i \(0.647679\pi\)
\(234\) 0 0
\(235\) 3.76088e10 0.804423
\(236\) −3.37048e10 5.83785e10i −0.707275 1.22504i
\(237\) 0 0
\(238\) 1.10676e9 1.91696e9i 0.0223592 0.0387272i
\(239\) 4.63163e9 8.02222e9i 0.0918213 0.159039i −0.816456 0.577407i \(-0.804064\pi\)
0.908278 + 0.418368i \(0.137398\pi\)
\(240\) 0 0
\(241\) 3.90476e10 + 6.76324e10i 0.745620 + 1.29145i 0.949905 + 0.312540i \(0.101180\pi\)
−0.204285 + 0.978912i \(0.565487\pi\)
\(242\) 5.85006e9 0.109646
\(243\) 0 0
\(244\) −7.03859e10 −1.27125
\(245\) 2.63810e10 + 4.56932e10i 0.467782 + 0.810222i
\(246\) 0 0
\(247\) 4.13801e8 7.16724e8i 0.00707384 0.0122522i
\(248\) 6.16485e9 1.06778e10i 0.103488 0.179246i
\(249\) 0 0
\(250\) 4.70389e9 + 8.14737e9i 0.0761600 + 0.131913i
\(251\) −1.54732e10 −0.246064 −0.123032 0.992403i \(-0.539262\pi\)
−0.123032 + 0.992403i \(0.539262\pi\)
\(252\) 0 0
\(253\) 1.66504e11 2.55494
\(254\) −6.60423e9 1.14389e10i −0.0995567 0.172437i
\(255\) 0 0
\(256\) −2.65921e10 + 4.60589e10i −0.386966 + 0.670245i
\(257\) 4.67386e10 8.09536e10i 0.668308 1.15754i −0.310069 0.950714i \(-0.600352\pi\)
0.978377 0.206829i \(-0.0663143\pi\)
\(258\) 0 0
\(259\) 8.18447e9 + 1.41759e10i 0.113016 + 0.195750i
\(260\) 7.80710e10 1.05952
\(261\) 0 0
\(262\) −6.71704e9 −0.0880689
\(263\) 3.95489e9 + 6.85008e9i 0.0509723 + 0.0882866i 0.890386 0.455207i \(-0.150435\pi\)
−0.839413 + 0.543493i \(0.817101\pi\)
\(264\) 0 0
\(265\) 4.24313e10 7.34931e10i 0.528542 0.915461i
\(266\) −2.14608e7 + 3.71712e7i −0.000262832 + 0.000455239i
\(267\) 0 0
\(268\) 1.82838e10 + 3.16686e10i 0.216502 + 0.374992i
\(269\) −1.42705e11 −1.66171 −0.830853 0.556492i \(-0.812147\pi\)
−0.830853 + 0.556492i \(0.812147\pi\)
\(270\) 0 0
\(271\) 6.60775e10 0.744203 0.372102 0.928192i \(-0.378637\pi\)
0.372102 + 0.928192i \(0.378637\pi\)
\(272\) 4.67964e10 + 8.10537e10i 0.518385 + 0.897868i
\(273\) 0 0
\(274\) −1.02892e10 + 1.78215e10i −0.110282 + 0.191015i
\(275\) 5.76252e8 9.98098e8i 0.00607597 0.0105239i
\(276\) 0 0
\(277\) 2.15068e10 + 3.72508e10i 0.219491 + 0.380169i 0.954652 0.297723i \(-0.0962271\pi\)
−0.735162 + 0.677892i \(0.762894\pi\)
\(278\) −1.92240e10 −0.193038
\(279\) 0 0
\(280\) −8.19504e9 −0.0796783
\(281\) 5.05155e10 + 8.74954e10i 0.483333 + 0.837157i 0.999817 0.0191402i \(-0.00609287\pi\)
−0.516484 + 0.856297i \(0.672760\pi\)
\(282\) 0 0
\(283\) 4.08977e10 7.08368e10i 0.379018 0.656478i −0.611902 0.790934i \(-0.709595\pi\)
0.990920 + 0.134456i \(0.0429286\pi\)
\(284\) −6.82288e10 + 1.18176e11i −0.622351 + 1.07794i
\(285\) 0 0
\(286\) −1.22498e10 2.12173e10i −0.108264 0.187518i
\(287\) 2.96072e10 0.257590
\(288\) 0 0
\(289\) 2.87013e10 0.242025
\(290\) −1.40773e9 2.43827e9i −0.0116877 0.0202437i
\(291\) 0 0
\(292\) −6.61340e10 + 1.14547e11i −0.532356 + 0.922067i
\(293\) 4.04552e10 7.00704e10i 0.320678 0.555431i −0.659950 0.751310i \(-0.729422\pi\)
0.980628 + 0.195879i \(0.0627558\pi\)
\(294\) 0 0
\(295\) 9.46421e10 + 1.63925e11i 0.727588 + 1.26022i
\(296\) 3.44410e10 0.260773
\(297\) 0 0
\(298\) 3.36728e10 0.247347
\(299\) −1.45530e11 2.52065e11i −1.05301 1.82386i
\(300\) 0 0
\(301\) −3.25867e10 + 5.64418e10i −0.228819 + 0.396325i
\(302\) 5.57263e9 9.65207e9i 0.0385504 0.0667712i
\(303\) 0 0
\(304\) −9.07415e8 1.57169e9i −0.00609361 0.0105544i
\(305\) 1.97641e11 1.30776
\(306\) 0 0
\(307\) 7.58062e10 0.487060 0.243530 0.969893i \(-0.421695\pi\)
0.243530 + 0.969893i \(0.421695\pi\)
\(308\) −2.64908e10 4.58833e10i −0.167732 0.290520i
\(309\) 0 0
\(310\) −8.55279e9 + 1.48139e10i −0.0525994 + 0.0911047i
\(311\) −8.88256e10 + 1.53850e11i −0.538414 + 0.932560i 0.460576 + 0.887620i \(0.347643\pi\)
−0.998990 + 0.0449400i \(0.985690\pi\)
\(312\) 0 0
\(313\) −4.18712e10 7.25231e10i −0.246585 0.427097i 0.715991 0.698109i \(-0.245975\pi\)
−0.962576 + 0.271012i \(0.912642\pi\)
\(314\) 4.45240e9 0.0258470
\(315\) 0 0
\(316\) −2.72336e11 −1.53643
\(317\) 2.65016e10 + 4.59021e10i 0.147403 + 0.255309i 0.930267 0.366884i \(-0.119575\pi\)
−0.782864 + 0.622193i \(0.786242\pi\)
\(318\) 0 0
\(319\) 1.84205e10 3.19052e10i 0.0995962 0.172506i
\(320\) 8.12383e10 1.40709e11i 0.433098 0.750147i
\(321\) 0 0
\(322\) 7.54756e9 + 1.30728e10i 0.0391251 + 0.0677666i
\(323\) −2.85604e9 −0.0146000
\(324\) 0 0
\(325\) −2.01466e9 −0.0100167
\(326\) −7.58831e9 1.31433e10i −0.0372105 0.0644505i
\(327\) 0 0
\(328\) 3.11474e10 5.39489e10i 0.148590 0.257366i
\(329\) −2.23076e10 + 3.86379e10i −0.104971 + 0.181816i
\(330\) 0 0
\(331\) −1.10989e11 1.92239e11i −0.508225 0.880271i −0.999955 0.00952305i \(-0.996969\pi\)
0.491730 0.870748i \(-0.336365\pi\)
\(332\) −8.69953e10 −0.392984
\(333\) 0 0
\(334\) 5.31667e9 0.0233765
\(335\) −5.13405e10 8.89243e10i −0.222720 0.385762i
\(336\) 0 0
\(337\) 1.56720e8 2.71446e8i 0.000661895 0.00114644i −0.865694 0.500573i \(-0.833123\pi\)
0.866356 + 0.499427i \(0.166456\pi\)
\(338\) −3.05263e9 + 5.28731e9i −0.0127218 + 0.0220348i
\(339\) 0 0
\(340\) −1.34711e11 2.33326e11i −0.546698 0.946909i
\(341\) −2.23830e11 −0.896444
\(342\) 0 0
\(343\) −1.29803e11 −0.506362
\(344\) 6.85640e10 + 1.18756e11i 0.263987 + 0.457239i
\(345\) 0 0
\(346\) 1.31276e9 2.27377e9i 0.00492429 0.00852912i
\(347\) −1.48136e11 + 2.56579e11i −0.548502 + 0.950034i 0.449875 + 0.893091i \(0.351468\pi\)
−0.998377 + 0.0569424i \(0.981865\pi\)
\(348\) 0 0
\(349\) −1.10780e11 1.91877e11i −0.399712 0.692322i 0.593978 0.804481i \(-0.297557\pi\)
−0.993690 + 0.112160i \(0.964223\pi\)
\(350\) 1.04485e8 0.000372177
\(351\) 0 0
\(352\) −1.67874e11 −0.582829
\(353\) 1.90537e11 + 3.30019e11i 0.653119 + 1.13124i 0.982362 + 0.186990i \(0.0598731\pi\)
−0.329243 + 0.944245i \(0.606794\pi\)
\(354\) 0 0
\(355\) 1.91584e11 3.31834e11i 0.640225 1.10890i
\(356\) 1.42304e11 2.46478e11i 0.469562 0.813306i
\(357\) 0 0
\(358\) −2.02988e10 3.51586e10i −0.0653127 0.113125i
\(359\) 3.34181e11 1.06183 0.530917 0.847424i \(-0.321847\pi\)
0.530917 + 0.847424i \(0.321847\pi\)
\(360\) 0 0
\(361\) −3.22632e11 −0.999828
\(362\) 1.52931e10 + 2.64884e10i 0.0468065 + 0.0810713i
\(363\) 0 0
\(364\) −4.63076e10 + 8.02072e10i −0.138260 + 0.239473i
\(365\) 1.85702e11 3.21646e11i 0.547645 0.948549i
\(366\) 0 0
\(367\) −2.31386e11 4.00773e11i −0.665795 1.15319i −0.979069 0.203528i \(-0.934759\pi\)
0.313274 0.949663i \(-0.398574\pi\)
\(368\) −6.38258e11 −1.81418
\(369\) 0 0
\(370\) −4.77817e10 −0.132542
\(371\) 5.03360e10 + 8.71845e10i 0.137942 + 0.238922i
\(372\) 0 0
\(373\) 1.16370e11 2.01558e11i 0.311280 0.539152i −0.667360 0.744735i \(-0.732576\pi\)
0.978640 + 0.205583i \(0.0659091\pi\)
\(374\) −4.22740e10 + 7.32207e10i −0.111725 + 0.193514i
\(375\) 0 0
\(376\) 4.69362e10 + 8.12960e10i 0.121105 + 0.209760i
\(377\) −6.44005e10 −0.164192
\(378\) 0 0
\(379\) 5.92570e10 0.147524 0.0737621 0.997276i \(-0.476499\pi\)
0.0737621 + 0.997276i \(0.476499\pi\)
\(380\) 2.61214e9 + 4.52436e9i 0.00642644 + 0.0111309i
\(381\) 0 0
\(382\) 5.43697e9 9.41711e9i 0.0130639 0.0226273i
\(383\) −5.52900e10 + 9.57651e10i −0.131296 + 0.227412i −0.924177 0.381966i \(-0.875247\pi\)
0.792880 + 0.609377i \(0.208581\pi\)
\(384\) 0 0
\(385\) 7.43852e10 + 1.28839e11i 0.172549 + 0.298864i
\(386\) −1.06085e11 −0.243226
\(387\) 0 0
\(388\) 2.93265e11 0.656928
\(389\) −2.59862e11 4.50094e11i −0.575400 0.996622i −0.995998 0.0893747i \(-0.971513\pi\)
0.420598 0.907247i \(-0.361820\pi\)
\(390\) 0 0
\(391\) −5.02221e11 + 8.69873e11i −1.08668 + 1.88218i
\(392\) −6.58475e10 + 1.14051e11i −0.140848 + 0.243957i
\(393\) 0 0
\(394\) 3.74758e10 + 6.49099e10i 0.0783461 + 0.135699i
\(395\) 7.64711e11 1.58056
\(396\) 0 0
\(397\) −4.49123e11 −0.907420 −0.453710 0.891149i \(-0.649900\pi\)
−0.453710 + 0.891149i \(0.649900\pi\)
\(398\) 6.25902e9 + 1.08409e10i 0.0125035 + 0.0216567i
\(399\) 0 0
\(400\) −2.20895e9 + 3.82601e9i −0.00431435 + 0.00747267i
\(401\) 2.37645e11 4.11613e11i 0.458964 0.794950i −0.539942 0.841702i \(-0.681554\pi\)
0.998907 + 0.0467526i \(0.0148872\pi\)
\(402\) 0 0
\(403\) 1.95635e11 + 3.38850e11i 0.369465 + 0.639933i
\(404\) 8.12208e11 1.51688
\(405\) 0 0
\(406\) 3.33998e9 0.00610066
\(407\) −3.12616e11 5.41467e11i −0.564725 0.978132i
\(408\) 0 0
\(409\) 2.15970e11 3.74070e11i 0.381626 0.660995i −0.609669 0.792656i \(-0.708698\pi\)
0.991295 + 0.131661i \(0.0420310\pi\)
\(410\) −4.32123e10 + 7.48460e10i −0.0755232 + 0.130810i
\(411\) 0 0
\(412\) 1.48179e11 + 2.56653e11i 0.253366 + 0.438843i
\(413\) −2.24547e11 −0.379780
\(414\) 0 0
\(415\) 2.44280e11 0.404270
\(416\) 1.46727e11 + 2.54139e11i 0.240210 + 0.416056i
\(417\) 0 0
\(418\) 8.19723e8 1.41980e9i 0.00131333 0.00227475i
\(419\) −4.52231e11 + 7.83288e11i −0.716799 + 1.24153i 0.245462 + 0.969406i \(0.421060\pi\)
−0.962261 + 0.272126i \(0.912273\pi\)
\(420\) 0 0
\(421\) −7.67841e10 1.32994e11i −0.119125 0.206330i 0.800296 0.599605i \(-0.204676\pi\)
−0.919421 + 0.393275i \(0.871342\pi\)
\(422\) −4.10651e10 −0.0630328
\(423\) 0 0
\(424\) 2.11819e11 0.318286
\(425\) 3.47627e9 + 6.02108e9i 0.00516849 + 0.00895209i
\(426\) 0 0
\(427\) −1.17231e11 + 2.03049e11i −0.170654 + 0.295581i
\(428\) −1.17353e11 + 2.03262e11i −0.169043 + 0.292792i
\(429\) 0 0
\(430\) −9.51221e10 1.64756e11i −0.134176 0.232399i
\(431\) −1.01001e12 −1.40987 −0.704933 0.709274i \(-0.749023\pi\)
−0.704933 + 0.709274i \(0.749023\pi\)
\(432\) 0 0
\(433\) 1.38892e12 1.89881 0.949407 0.314048i \(-0.101685\pi\)
0.949407 + 0.314048i \(0.101685\pi\)
\(434\) −1.01461e10 1.75736e10i −0.0137277 0.0237770i
\(435\) 0 0
\(436\) 5.25537e11 9.10258e11i 0.696489 1.20635i
\(437\) 9.73843e9 1.68675e10i 0.0127739 0.0221250i
\(438\) 0 0
\(439\) 5.68209e11 + 9.84166e11i 0.730159 + 1.26467i 0.956815 + 0.290698i \(0.0938874\pi\)
−0.226656 + 0.973975i \(0.572779\pi\)
\(440\) 3.13020e11 0.398139
\(441\) 0 0
\(442\) 1.47796e11 0.184188
\(443\) 4.51021e11 + 7.81192e11i 0.556391 + 0.963698i 0.997794 + 0.0663886i \(0.0211477\pi\)
−0.441403 + 0.897309i \(0.645519\pi\)
\(444\) 0 0
\(445\) −3.99586e11 + 6.92104e11i −0.483048 + 0.836664i
\(446\) 3.26819e10 5.66067e10i 0.0391111 0.0677424i
\(447\) 0 0
\(448\) 9.63727e10 + 1.66922e11i 0.113032 + 0.195778i
\(449\) 4.28311e11 0.497337 0.248668 0.968589i \(-0.420007\pi\)
0.248668 + 0.968589i \(0.420007\pi\)
\(450\) 0 0
\(451\) −1.13088e12 −1.28713
\(452\) −3.13395e11 5.42816e11i −0.353158 0.611688i
\(453\) 0 0
\(454\) 3.54546e9 6.14092e9i 0.00391671 0.00678395i
\(455\) 1.30030e11 2.25219e11i 0.142231 0.246351i
\(456\) 0 0
\(457\) 2.87623e11 + 4.98178e11i 0.308461 + 0.534271i 0.978026 0.208483i \(-0.0668527\pi\)
−0.669565 + 0.742754i \(0.733519\pi\)
\(458\) 7.40822e9 0.00786719
\(459\) 0 0
\(460\) 1.83733e12 1.91327
\(461\) 5.32572e11 + 9.22441e11i 0.549192 + 0.951228i 0.998330 + 0.0577655i \(0.0183976\pi\)
−0.449139 + 0.893462i \(0.648269\pi\)
\(462\) 0 0
\(463\) 3.45830e11 5.98996e11i 0.349743 0.605772i −0.636461 0.771309i \(-0.719602\pi\)
0.986204 + 0.165537i \(0.0529356\pi\)
\(464\) −7.06112e10 + 1.22302e11i −0.0707200 + 0.122491i
\(465\) 0 0
\(466\) 6.97128e10 + 1.20746e11i 0.0684819 + 0.118614i
\(467\) −1.39973e12 −1.36181 −0.680907 0.732370i \(-0.738414\pi\)
−0.680907 + 0.732370i \(0.738414\pi\)
\(468\) 0 0
\(469\) 1.21810e11 0.116253
\(470\) −6.51169e10 1.12786e11i −0.0615536 0.106614i
\(471\) 0 0
\(472\) −2.36229e11 + 4.09160e11i −0.219076 + 0.379450i
\(473\) 1.24469e12 2.15587e12i 1.14337 1.98037i
\(474\) 0 0
\(475\) −6.74074e7 1.16753e8i −6.07556e−5 0.000105232i
\(476\) 3.19614e11 0.285361
\(477\) 0 0
\(478\) −3.20773e10 −0.0281043
\(479\) −4.78401e11 8.28615e11i −0.415224 0.719189i 0.580228 0.814454i \(-0.302964\pi\)
−0.995452 + 0.0952650i \(0.969630\pi\)
\(480\) 0 0
\(481\) −5.46474e11 + 9.46521e11i −0.465497 + 0.806265i
\(482\) 1.35216e11 2.34201e11i 0.114108 0.197641i
\(483\) 0 0
\(484\) 4.22351e11 + 7.31534e11i 0.349840 + 0.605941i
\(485\) −8.23479e11 −0.675795
\(486\) 0 0
\(487\) −2.88361e11 −0.232303 −0.116152 0.993231i \(-0.537056\pi\)
−0.116152 + 0.993231i \(0.537056\pi\)
\(488\) 2.46659e11 + 4.27225e11i 0.196882 + 0.341010i
\(489\) 0 0
\(490\) 9.13534e10 1.58229e11i 0.0715884 0.123995i
\(491\) −1.17312e11 + 2.03190e11i −0.0910910 + 0.157774i −0.907970 0.419034i \(-0.862369\pi\)
0.816879 + 0.576808i \(0.195702\pi\)
\(492\) 0 0
\(493\) 1.11123e11 + 1.92470e11i 0.0847210 + 0.146741i
\(494\) −2.86586e9 −0.00216513
\(495\) 0 0
\(496\) 8.58007e11 0.636536
\(497\) 2.27276e11 + 3.93653e11i 0.167090 + 0.289408i
\(498\) 0 0
\(499\) −1.26477e12 + 2.19065e12i −0.913189 + 1.58169i −0.103658 + 0.994613i \(0.533055\pi\)
−0.809531 + 0.587077i \(0.800279\pi\)
\(500\) −6.79204e11 + 1.17642e12i −0.485999 + 0.841775i
\(501\) 0 0
\(502\) 2.67907e10 + 4.64028e10i 0.0188286 + 0.0326120i
\(503\) 3.09347e11 0.215471 0.107736 0.994180i \(-0.465640\pi\)
0.107736 + 0.994180i \(0.465640\pi\)
\(504\) 0 0
\(505\) −2.28065e12 −1.56044
\(506\) −2.88289e11 4.99331e11i −0.195502 0.338619i
\(507\) 0 0
\(508\) 9.53598e11 1.65168e12i 0.635300 1.10037i
\(509\) −1.27179e12 + 2.20280e12i −0.839816 + 1.45460i 0.0502320 + 0.998738i \(0.484004\pi\)
−0.890048 + 0.455867i \(0.849329\pi\)
\(510\) 0 0
\(511\) 2.20298e11 + 3.81567e11i 0.142928 + 0.247558i
\(512\) 1.08108e12 0.695252
\(513\) 0 0
\(514\) −3.23698e11 −0.204553
\(515\) −4.16081e11 7.20674e11i −0.260643 0.451447i
\(516\) 0 0
\(517\) 8.52067e11 1.47582e12i 0.524525 0.908504i
\(518\) 2.83416e10 4.90891e10i 0.0172958 0.0299572i
\(519\) 0 0
\(520\) −2.73590e11 4.73872e11i −0.164091 0.284214i
\(521\) 1.75471e12 1.04336 0.521682 0.853140i \(-0.325305\pi\)
0.521682 + 0.853140i \(0.325305\pi\)
\(522\) 0 0
\(523\) 9.65849e11 0.564484 0.282242 0.959343i \(-0.408922\pi\)
0.282242 + 0.959343i \(0.408922\pi\)
\(524\) −4.84944e11 8.39948e11i −0.280996 0.486700i
\(525\) 0 0
\(526\) 1.36952e10 2.37208e10i 0.00780069 0.0135112i
\(527\) 6.75133e11 1.16936e12i 0.381278 0.660393i
\(528\) 0 0
\(529\) −2.52434e12 4.37228e12i −1.40151 2.42749i
\(530\) −2.93866e11 −0.161774
\(531\) 0 0
\(532\) −6.19754e9 −0.00335442
\(533\) 9.88430e11 + 1.71201e12i 0.530486 + 0.918828i
\(534\) 0 0
\(535\) 3.29524e11 5.70753e11i 0.173898 0.301201i
\(536\) 1.28147e11 2.21957e11i 0.0670605 0.116152i
\(537\) 0 0
\(538\) 2.47083e11 + 4.27961e11i 0.127152 + 0.220234i
\(539\) 2.39075e12 1.22007
\(540\) 0 0
\(541\) −2.09700e12 −1.05247 −0.526235 0.850339i \(-0.676397\pi\)
−0.526235 + 0.850339i \(0.676397\pi\)
\(542\) −1.14408e11 1.98161e11i −0.0569457 0.0986328i
\(543\) 0 0
\(544\) 5.06354e11 8.77031e11i 0.247890 0.429358i
\(545\) −1.47569e12 + 2.55598e12i −0.716493 + 1.24100i
\(546\) 0 0
\(547\) −7.51610e11 1.30183e12i −0.358963 0.621742i 0.628825 0.777547i \(-0.283536\pi\)
−0.987788 + 0.155805i \(0.950203\pi\)
\(548\) −2.97137e12 −1.40749
\(549\) 0 0
\(550\) −3.99095e9 −0.00185971
\(551\) −2.15474e9 3.73213e9i −0.000995895 0.00172494i
\(552\) 0 0
\(553\) −4.53587e11 + 7.85635e11i −0.206251 + 0.357238i
\(554\) 7.44747e10 1.28994e11i 0.0335904 0.0581803i
\(555\) 0 0
\(556\) −1.38790e12 2.40391e12i −0.615916 1.06680i
\(557\) −4.83664e11 −0.212910 −0.106455 0.994318i \(-0.533950\pi\)
−0.106455 + 0.994318i \(0.533950\pi\)
\(558\) 0 0
\(559\) −4.35161e12 −1.88494
\(560\) −2.85141e11 4.93878e11i −0.122522 0.212214i
\(561\) 0 0
\(562\) 1.74928e11 3.02984e11i 0.0739682 0.128117i
\(563\) 1.23877e12 2.14562e12i 0.519641 0.900045i −0.480098 0.877215i \(-0.659399\pi\)
0.999739 0.0228302i \(-0.00726772\pi\)
\(564\) 0 0
\(565\) 8.80003e11 + 1.52421e12i 0.363301 + 0.629255i
\(566\) −2.83245e11 −0.116008
\(567\) 0 0
\(568\) 9.56398e11 0.385541
\(569\) −1.75498e12 3.03971e12i −0.701886 1.21570i −0.967804 0.251706i \(-0.919008\pi\)
0.265918 0.963996i \(-0.414325\pi\)
\(570\) 0 0
\(571\) −1.28628e11 + 2.22790e11i −0.0506375 + 0.0877066i −0.890233 0.455505i \(-0.849459\pi\)
0.839596 + 0.543212i \(0.182792\pi\)
\(572\) 1.76878e12 3.06362e12i 0.690862 1.19661i
\(573\) 0 0
\(574\) −5.12626e10 8.87895e10i −0.0197105 0.0341396i
\(575\) −4.74131e10 −0.0180881
\(576\) 0 0
\(577\) 7.55281e11 0.283673 0.141836 0.989890i \(-0.454699\pi\)
0.141836 + 0.989890i \(0.454699\pi\)
\(578\) −4.96941e10 8.60728e10i −0.0185195 0.0320768i
\(579\) 0 0
\(580\) 2.03266e11 3.52066e11i 0.0745827 0.129181i
\(581\) −1.44894e11 + 2.50964e11i −0.0527544 + 0.0913733i
\(582\) 0 0
\(583\) −1.92265e12 3.33013e12i −0.689273 1.19386i
\(584\) 9.27034e11 0.329790
\(585\) 0 0
\(586\) −2.80181e11 −0.0981519
\(587\) 2.56556e12 + 4.44367e12i 0.891888 + 1.54479i 0.837610 + 0.546269i \(0.183952\pi\)
0.0542776 + 0.998526i \(0.482714\pi\)
\(588\) 0 0
\(589\) −1.30913e10 + 2.26748e10i −0.00448192 + 0.00776292i
\(590\) 3.27732e11 5.67648e11i 0.111349 0.192861i
\(591\) 0 0
\(592\) 1.19835e12 + 2.07561e12i 0.400993 + 0.694540i
\(593\) −1.98175e12 −0.658116 −0.329058 0.944310i \(-0.606731\pi\)
−0.329058 + 0.944310i \(0.606731\pi\)
\(594\) 0 0
\(595\) −8.97466e11 −0.293557
\(596\) 2.43104e12 + 4.21069e12i 0.789196 + 1.36693i
\(597\) 0 0
\(598\) −5.03948e11 + 8.72864e11i −0.161150 + 0.279120i
\(599\) 5.16257e11 8.94184e11i 0.163850 0.283796i −0.772397 0.635141i \(-0.780942\pi\)
0.936246 + 0.351345i \(0.114275\pi\)
\(600\) 0 0
\(601\) 5.34090e11 + 9.25071e11i 0.166986 + 0.289228i 0.937359 0.348366i \(-0.113263\pi\)
−0.770373 + 0.637594i \(0.779930\pi\)
\(602\) 2.25686e11 0.0700358
\(603\) 0 0
\(604\) 1.60929e12 0.492002
\(605\) −1.18595e12 2.05412e12i −0.359888 0.623343i
\(606\) 0 0
\(607\) −1.66935e12 + 2.89140e12i −0.499112 + 0.864488i −0.999999 0.00102472i \(-0.999674\pi\)
0.500887 + 0.865513i \(0.333007\pi\)
\(608\) −9.81857e9 + 1.70063e10i −0.00291395 + 0.00504711i
\(609\) 0 0
\(610\) −3.42201e11 5.92710e11i −0.100069 0.173324i
\(611\) −2.97894e12 −0.864722
\(612\) 0 0
\(613\) −4.12503e12 −1.17993 −0.589964 0.807430i \(-0.700858\pi\)
−0.589964 + 0.807430i \(0.700858\pi\)
\(614\) −1.31253e11 2.27337e11i −0.0372693 0.0645523i
\(615\) 0 0
\(616\) −1.85667e11 + 3.21585e11i −0.0519543 + 0.0899876i
\(617\) −2.16264e12 + 3.74580e12i −0.600759 + 1.04055i 0.391947 + 0.919988i \(0.371802\pi\)
−0.992706 + 0.120558i \(0.961532\pi\)
\(618\) 0 0
\(619\) 3.15688e12 + 5.46787e12i 0.864271 + 1.49696i 0.867770 + 0.496967i \(0.165553\pi\)
−0.00349896 + 0.999994i \(0.501114\pi\)
\(620\) −2.46991e12 −0.671303
\(621\) 0 0
\(622\) 6.15180e11 0.164796
\(623\) −4.74028e11 8.21040e11i −0.126069 0.218357i
\(624\) 0 0
\(625\) 1.92488e12 3.33398e12i 0.504595 0.873984i
\(626\) −1.44994e11 + 2.51137e11i −0.0377368 + 0.0653621i
\(627\) 0 0
\(628\) 3.21446e11 + 5.56760e11i 0.0824687 + 0.142840i
\(629\) 3.77175e12 0.960760
\(630\) 0 0
\(631\) 6.69921e12 1.68225 0.841127 0.540838i \(-0.181893\pi\)
0.841127 + 0.540838i \(0.181893\pi\)
\(632\) 9.54367e11 + 1.65301e12i 0.237952 + 0.412144i
\(633\) 0 0
\(634\) 9.17711e10 1.58952e11i 0.0225582 0.0390719i
\(635\) −2.67767e12 + 4.63787e12i −0.653546 + 1.13197i
\(636\) 0 0
\(637\) −2.08960e12 3.61929e12i −0.502847 0.870956i
\(638\) −1.27575e11 −0.0304840
\(639\) 0 0
\(640\) −2.45951e12 −0.579480
\(641\) −3.53417e12 6.12136e12i −0.826849 1.43214i −0.900498 0.434860i \(-0.856798\pi\)
0.0736498 0.997284i \(-0.476535\pi\)
\(642\) 0 0
\(643\) −8.53171e11 + 1.47774e12i −0.196828 + 0.340916i −0.947498 0.319761i \(-0.896397\pi\)
0.750670 + 0.660677i \(0.229731\pi\)
\(644\) −1.08981e12 + 1.88760e12i −0.249669 + 0.432439i
\(645\) 0 0
\(646\) 4.94503e9 + 8.56504e9i 0.00111718 + 0.00193501i
\(647\) 3.85704e12 0.865336 0.432668 0.901553i \(-0.357572\pi\)
0.432668 + 0.901553i \(0.357572\pi\)
\(648\) 0 0
\(649\) 8.57687e12 1.89770
\(650\) 3.48823e9 + 6.04179e9i 0.000766469 + 0.00132756i
\(651\) 0 0
\(652\) 1.09569e12 1.89779e12i 0.237451 0.411277i
\(653\) 2.31206e12 4.00460e12i 0.497610 0.861886i −0.502386 0.864644i \(-0.667544\pi\)
0.999996 + 0.00275722i \(0.000877652\pi\)
\(654\) 0 0
\(655\) 1.36171e12 + 2.35855e12i 0.289067 + 0.500678i
\(656\) 4.33501e12 0.913952
\(657\) 0 0
\(658\) 1.54496e11 0.0321292
\(659\) −4.08401e11 7.07371e11i −0.0843533 0.146104i 0.820762 0.571270i \(-0.193549\pi\)
−0.905115 + 0.425166i \(0.860216\pi\)
\(660\) 0 0
\(661\) 5.73853e11 9.93942e11i 0.116921 0.202514i −0.801625 0.597827i \(-0.796031\pi\)
0.918546 + 0.395314i \(0.129364\pi\)
\(662\) −3.84340e11 + 6.65697e11i −0.0777776 + 0.134715i
\(663\) 0 0
\(664\) 3.04864e11 + 5.28041e11i 0.0608626 + 0.105417i
\(665\) 1.74025e10 0.00345076
\(666\) 0 0
\(667\) −1.51561e12 −0.296497
\(668\) 3.83842e11 + 6.64834e11i 0.0745862 + 0.129187i
\(669\) 0 0
\(670\) −1.77785e11 + 3.07932e11i −0.0340845 + 0.0590361i
\(671\) 4.47777e12 7.75573e12i 0.852728 1.47697i
\(672\) 0 0
\(673\) 3.58758e12 + 6.21386e12i 0.674114 + 1.16760i 0.976727 + 0.214486i \(0.0688077\pi\)
−0.302613 + 0.953114i \(0.597859\pi\)
\(674\) −1.08539e9 −0.000202590
\(675\) 0 0
\(676\) −8.81552e11 −0.162363
\(677\) −2.60502e12 4.51203e12i −0.476609 0.825510i 0.523032 0.852313i \(-0.324801\pi\)
−0.999641 + 0.0268026i \(0.991467\pi\)
\(678\) 0 0
\(679\) 4.88445e11 8.46011e11i 0.0881864 0.152743i
\(680\) −9.44156e11 + 1.63533e12i −0.169338 + 0.293301i
\(681\) 0 0
\(682\) 3.87545e11 + 6.71248e11i 0.0685950 + 0.118810i
\(683\) −2.81291e12 −0.494611 −0.247305 0.968938i \(-0.579545\pi\)
−0.247305 + 0.968938i \(0.579545\pi\)
\(684\) 0 0
\(685\) 8.34352e12 1.44791
\(686\) 2.24744e11 + 3.89269e11i 0.0387463 + 0.0671106i
\(687\) 0 0
\(688\) −4.77127e12 + 8.26409e12i −0.811870 + 1.40620i
\(689\) −3.36092e12 + 5.82128e12i −0.568161 + 0.984084i
\(690\) 0 0
\(691\) 3.87496e12 + 6.71162e12i 0.646570 + 1.11989i 0.983937 + 0.178519i \(0.0571305\pi\)
−0.337366 + 0.941373i \(0.609536\pi\)
\(692\) 3.79105e11 0.0628466
\(693\) 0 0
\(694\) 1.02595e12 0.167883
\(695\) 3.89718e12 + 6.75011e12i 0.633605 + 1.09744i
\(696\) 0 0
\(697\) 3.41106e12 5.90813e12i 0.547447 0.948205i
\(698\) −3.83615e11 + 6.64441e11i −0.0611711 + 0.105951i
\(699\) 0 0
\(700\) 7.54343e9 + 1.30656e10i 0.00118748 + 0.00205678i
\(701\) −1.86576e12 −0.291826 −0.145913 0.989297i \(-0.546612\pi\)
−0.145913 + 0.989297i \(0.546612\pi\)
\(702\) 0 0
\(703\) −7.31369e10 −0.0112937
\(704\) −3.68108e12 6.37581e12i −0.564804 0.978270i
\(705\) 0 0
\(706\) 6.59800e11 1.14281e12i 0.0999520 0.173122i
\(707\) 1.35277e12 2.34306e12i 0.203627 0.352692i
\(708\) 0 0
\(709\) −1.13808e11 1.97122e11i −0.0169148 0.0292972i 0.857444 0.514577i \(-0.172051\pi\)
−0.874359 + 0.485280i \(0.838718\pi\)
\(710\) −1.32686e12 −0.195957
\(711\) 0 0
\(712\) −1.99475e12 −0.290890
\(713\) 4.60409e12 + 7.97452e12i 0.667177 + 1.15558i
\(714\) 0 0
\(715\) −4.96668e12 + 8.60254e12i −0.710704 + 1.23098i
\(716\) 2.93099e12 5.07662e12i 0.416779 0.721882i
\(717\) 0 0
\(718\) −5.78610e11 1.00218e12i −0.0812505 0.140730i
\(719\) −2.12785e12 −0.296934 −0.148467 0.988917i \(-0.547434\pi\)
−0.148467 + 0.988917i \(0.547434\pi\)
\(720\) 0 0
\(721\) 9.87191e11 0.136048
\(722\) 5.58614e11 + 9.67548e11i 0.0765058 + 0.132512i
\(723\) 0 0
\(724\) −2.20820e12 + 3.82471e12i −0.298686 + 0.517339i
\(725\) −5.24536e9 + 9.08523e9i −0.000705106 + 0.00122128i
\(726\) 0 0
\(727\) 7.88780e11 + 1.36621e12i 0.104725 + 0.181389i 0.913626 0.406556i \(-0.133270\pi\)
−0.808901 + 0.587945i \(0.799937\pi\)
\(728\) 6.49118e11 0.0856510
\(729\) 0 0
\(730\) −1.28612e12 −0.167621
\(731\) 7.50867e12 + 1.30054e13i 0.972601 + 1.68459i
\(732\) 0 0
\(733\) 2.30042e12 3.98444e12i 0.294333 0.509799i −0.680497 0.732751i \(-0.738236\pi\)
0.974829 + 0.222952i \(0.0715693\pi\)
\(734\) −8.01257e11 + 1.38782e12i −0.101892 + 0.176482i
\(735\) 0 0
\(736\) 3.45310e12 + 5.98094e12i 0.433769 + 0.751310i
\(737\) −4.65269e12 −0.580899
\(738\) 0 0
\(739\) −2.25557e12 −0.278199 −0.139099 0.990278i \(-0.544421\pi\)
−0.139099 + 0.990278i \(0.544421\pi\)
\(740\) −3.44965e12 5.97497e12i −0.422895 0.732475i
\(741\) 0 0
\(742\) 1.74306e11 3.01907e11i 0.0211103 0.0365642i
\(743\) 5.38723e12 9.33095e12i 0.648508 1.12325i −0.334971 0.942228i \(-0.608727\pi\)
0.983479 0.181021i \(-0.0579401\pi\)
\(744\) 0 0
\(745\) −6.82630e12 1.18235e13i −0.811862 1.40619i
\(746\) −8.05943e11 −0.0952752
\(747\) 0 0
\(748\) −1.22081e13 −1.42590
\(749\) 3.90913e11 + 6.77082e11i 0.0453850 + 0.0786092i
\(750\) 0 0
\(751\) 2.66024e12 4.60766e12i 0.305169 0.528568i −0.672130 0.740433i \(-0.734620\pi\)
0.977299 + 0.211865i \(0.0679537\pi\)
\(752\) −3.26623e12 + 5.65728e12i −0.372449 + 0.645100i
\(753\) 0 0
\(754\) 1.11505e11 + 1.93132e11i 0.0125638 + 0.0217612i
\(755\) −4.51883e12 −0.506133
\(756\) 0 0
\(757\) 8.65829e12 0.958298 0.479149 0.877734i \(-0.340945\pi\)
0.479149 + 0.877734i \(0.340945\pi\)
\(758\) −1.02599e11 1.77707e11i −0.0112884 0.0195521i
\(759\) 0 0
\(760\) 1.83078e10 3.17101e10i 0.00199056 0.00344776i
\(761\) −3.52267e12 + 6.10144e12i −0.380751 + 0.659480i −0.991170 0.132599i \(-0.957668\pi\)
0.610419 + 0.792079i \(0.291001\pi\)
\(762\) 0 0
\(763\) −1.75061e12 3.03214e12i −0.186994 0.323884i
\(764\) 1.57011e12 0.166729
\(765\) 0 0
\(766\) 3.82923e11 0.0401866
\(767\) −7.49647e12 1.29843e13i −0.782128 1.35469i
\(768\) 0 0
\(769\) 3.29135e12 5.70079e12i 0.339395 0.587850i −0.644924 0.764247i \(-0.723111\pi\)
0.984319 + 0.176397i \(0.0564442\pi\)
\(770\) 2.57585e11 4.46150e11i 0.0264066 0.0457376i
\(771\) 0 0
\(772\) −7.65889e12 1.32656e13i −0.776047 1.34415i
\(773\) 1.34877e13 1.35872 0.679360 0.733805i \(-0.262258\pi\)
0.679360 + 0.733805i \(0.262258\pi\)
\(774\) 0 0
\(775\) 6.37371e10 0.00634651
\(776\) −1.02771e12 1.78005e12i −0.101740 0.176219i
\(777\) 0 0
\(778\) −8.99864e11 + 1.55861e12i −0.0880580 + 0.152521i
\(779\) −6.61429e10 + 1.14563e11i −0.00643523 + 0.0111462i
\(780\) 0 0
\(781\) −8.68109e12 1.50361e13i −0.834919 1.44612i
\(782\) 3.47824e12 0.332605
\(783\) 0 0
\(784\) −9.16447e12 −0.866334
\(785\) −9.02609e11 1.56337e12i −0.0848372 0.146942i
\(786\) 0 0
\(787\) 6.15564e12 1.06619e13i 0.571988 0.990713i −0.424374 0.905487i \(-0.639506\pi\)
0.996362 0.0852254i \(-0.0271610\pi\)
\(788\) −5.41120e12 + 9.37248e12i −0.499949 + 0.865938i
\(789\) 0 0
\(790\) −1.32404e12 2.29331e12i −0.120943 0.209479i
\(791\) −2.08789e12 −0.189633
\(792\) 0 0
\(793\) −1.56549e13 −1.40579
\(794\) 7.77624e11 + 1.34688e12i 0.0694349 + 0.120265i
\(795\) 0 0
\(796\) −9.03753e11 + 1.56535e12i −0.0797886 + 0.138198i
\(797\) 5.69410e12 9.86247e12i 0.499877 0.865812i −0.500123 0.865954i \(-0.666712\pi\)
1.00000 0.000142537i \(4.53711e-5\pi\)
\(798\) 0 0
\(799\) 5.14014e12 + 8.90299e12i 0.446185 + 0.772815i
\(800\) 4.78033e10 0.00412622
\(801\) 0 0
\(802\) −1.64586e12 −0.140478
\(803\) −8.41455e12 1.45744e13i −0.714186 1.23701i
\(804\) 0 0
\(805\) 3.06015e12 5.30033e12i 0.256839 0.444858i
\(806\) 6.77455e11 1.17339e12i 0.0565422 0.0979340i
\(807\) 0 0
\(808\) −2.84628e12 4.92990e12i −0.234924 0.406900i
\(809\) 9.39455e12 0.771095 0.385547 0.922688i \(-0.374013\pi\)
0.385547 + 0.922688i \(0.374013\pi\)
\(810\) 0 0
\(811\) 8.85202e12 0.718536 0.359268 0.933234i \(-0.383026\pi\)
0.359268 + 0.933234i \(0.383026\pi\)
\(812\) 2.41133e11 + 4.17655e11i 0.0194650 + 0.0337144i
\(813\) 0 0
\(814\) −1.08254e12 + 1.87502e12i −0.0864243 + 0.149691i
\(815\) −3.07667e12 + 5.32894e12i −0.244271 + 0.423089i
\(816\) 0 0
\(817\) −1.45598e11 2.52184e11i −0.0114329 0.0198024i
\(818\) −1.49574e12 −0.116806
\(819\) 0 0
\(820\) −1.24790e13 −0.963871
\(821\) 6.69699e12 + 1.15995e13i 0.514441 + 0.891037i 0.999860 + 0.0167556i \(0.00533373\pi\)
−0.485419 + 0.874282i \(0.661333\pi\)
\(822\) 0 0
\(823\) −9.32974e12 + 1.61596e13i −0.708876 + 1.22781i 0.256399 + 0.966571i \(0.417464\pi\)
−0.965274 + 0.261238i \(0.915869\pi\)
\(824\) 1.03855e12 1.79882e12i 0.0784792 0.135930i
\(825\) 0 0
\(826\) 3.88787e11 + 6.73399e11i 0.0290604 + 0.0503341i
\(827\) −1.27791e13 −0.950006 −0.475003 0.879984i \(-0.657553\pi\)
−0.475003 + 0.879984i \(0.657553\pi\)
\(828\) 0 0
\(829\) −8.09935e12 −0.595600 −0.297800 0.954628i \(-0.596253\pi\)
−0.297800 + 0.954628i \(0.596253\pi\)
\(830\) −4.22953e11 7.32576e11i −0.0309343 0.0535798i
\(831\) 0 0
\(832\) −6.43477e12 + 1.11454e13i −0.465563 + 0.806378i
\(833\) −7.21118e12 + 1.24901e13i −0.518924 + 0.898803i
\(834\) 0 0
\(835\) −1.07782e12 1.86683e12i −0.0767284 0.132897i
\(836\) 2.36723e11 0.0167615
\(837\) 0 0
\(838\) 3.13202e12 0.219395
\(839\) 5.88748e12 + 1.01974e13i 0.410205 + 0.710495i 0.994912 0.100749i \(-0.0321240\pi\)
−0.584707 + 0.811244i \(0.698791\pi\)
\(840\) 0 0
\(841\) 7.08590e12 1.22731e13i 0.488442 0.846006i
\(842\) −2.65892e11 + 4.60539e11i −0.0182306 + 0.0315763i
\(843\) 0 0
\(844\) −2.96474e12 5.13507e12i −0.201115 0.348342i
\(845\) 2.47537e12 0.167026
\(846\) 0 0
\(847\) 2.81377e12 0.187851
\(848\) 7.37009e12 + 1.27654e13i 0.489431 + 0.847719i
\(849\) 0 0
\(850\) 1.20378e10 2.08501e10i 0.000790975 0.00137001i
\(851\) −1.28608e13 + 2.22755e13i −0.840590 + 1.45595i
\(852\) 0 0
\(853\) −3.42110e11 5.92552e11i −0.0221256 0.0383227i 0.854751 0.519039i \(-0.173710\pi\)
−0.876876 + 0.480716i \(0.840377\pi\)
\(854\) 8.11904e11 0.0522329
\(855\) 0 0
\(856\) 1.64500e12 0.104721
\(857\) −5.78222e12 1.00151e13i −0.366168 0.634222i 0.622795 0.782385i \(-0.285997\pi\)
−0.988963 + 0.148163i \(0.952664\pi\)
\(858\) 0 0
\(859\) −7.51305e12 + 1.30130e13i −0.470812 + 0.815470i −0.999443 0.0333820i \(-0.989372\pi\)
0.528631 + 0.848852i \(0.322706\pi\)
\(860\) 1.37349e13 2.37895e13i 0.856213 1.48300i
\(861\) 0 0
\(862\) 1.74876e12 + 3.02894e12i 0.107882 + 0.186856i
\(863\) −1.54066e13 −0.945490 −0.472745 0.881199i \(-0.656737\pi\)
−0.472745 + 0.881199i \(0.656737\pi\)
\(864\) 0 0
\(865\) −1.06451e12 −0.0646516
\(866\) −2.40482e12 4.16527e12i −0.145295 0.251659i
\(867\) 0 0
\(868\) 1.46502e12 2.53749e12i 0.0876003 0.151728i
\(869\) 1.73253e13 3.00083e13i 1.03060 1.78506i
\(870\) 0 0
\(871\) 4.06661e12 + 7.04357e12i 0.239415 + 0.414678i
\(872\) −7.36673e12 −0.431470
\(873\) 0 0
\(874\) −6.74455e10 −0.00390977
\(875\) 2.26249e12 + 3.91874e12i 0.130482 + 0.226001i
\(876\) 0 0
\(877\) 1.28821e13 2.23124e13i 0.735338 1.27364i −0.219236 0.975672i \(-0.570357\pi\)
0.954575 0.297972i \(-0.0963101\pi\)
\(878\) 1.96762e12 3.40802e12i 0.111742 0.193543i
\(879\) 0 0
\(880\) 1.08913e13 + 1.88643e13i 0.612221 + 1.06040i
\(881\) 8.67327e12 0.485055 0.242528 0.970144i \(-0.422023\pi\)
0.242528 + 0.970144i \(0.422023\pi\)
\(882\) 0 0
\(883\) 1.27283e13 0.704607 0.352304 0.935886i \(-0.385398\pi\)
0.352304 + 0.935886i \(0.385398\pi\)
\(884\) 1.06703e13 + 1.84814e13i 0.587679 + 1.01789i
\(885\) 0 0
\(886\) 1.56182e12 2.70515e12i 0.0851490 0.147482i
\(887\) 1.99661e12 3.45824e12i 0.108302 0.187585i −0.806780 0.590852i \(-0.798792\pi\)
0.915083 + 0.403266i \(0.132125\pi\)
\(888\) 0 0
\(889\) −3.17651e12 5.50188e12i −0.170566 0.295429i
\(890\) 2.76742e12 0.147849
\(891\) 0 0
\(892\) 9.43801e12 0.499159
\(893\) −9.96711e10 1.72635e11i −0.00524490 0.00908444i
\(894\) 0 0
\(895\) −8.23013e12 + 1.42550e13i −0.428749 + 0.742615i
\(896\) 1.45885e12 2.52681e12i 0.0756180 0.130974i
\(897\) 0 0
\(898\) −7.41589e11 1.28447e12i −0.0380557 0.0659144i
\(899\) 2.03742e12 0.104031
\(900\) 0 0
\(901\) 2.31970e13 1.17265
\(902\) 1.95804e12 + 3.39143e12i 0.0984901 + 0.170590i
\(903\) 0 0
\(904\) −2.19651e12 + 3.80446e12i −0.109389 + 0.189468i
\(905\) 6.20056e12 1.07397e13i 0.307264 0.532197i
\(906\) 0 0
\(907\) 4.39889e12 + 7.61910e12i 0.215829 + 0.373827i 0.953529 0.301302i \(-0.0974212\pi\)
−0.737699 + 0.675129i \(0.764088\pi\)
\(908\) 1.02387e12 0.0499874
\(909\) 0 0
\(910\) −9.00552e11 −0.0435334
\(911\) −1.47806e13 2.56007e13i −0.710983 1.23146i −0.964489 0.264125i \(-0.914917\pi\)
0.253506 0.967334i \(-0.418416\pi\)
\(912\) 0 0
\(913\) 5.53442e12 9.58590e12i 0.263605 0.456577i
\(914\) 9.95996e11 1.72512e12i 0.0472063 0.0817637i
\(915\) 0 0
\(916\) 5.34844e11 + 9.26378e11i 0.0251014 + 0.0434769i
\(917\) −3.23078e12 −0.150885
\(918\) 0 0
\(919\) −1.05646e13 −0.488577 −0.244288 0.969703i \(-0.578554\pi\)
−0.244288 + 0.969703i \(0.578554\pi\)
\(920\) −6.43870e12 1.11522e13i −0.296314 0.513232i
\(921\) 0 0
\(922\) 1.84422e12 3.19428e12i 0.0840471 0.145574i
\(923\) −1.51751e13 + 2.62841e13i −0.688216 + 1.19203i
\(924\) 0 0
\(925\) 8.90197e10 + 1.54187e11i 0.00399805 + 0.00692483i
\(926\) −2.39512e12 −0.107048
\(927\) 0 0
\(928\) 1.52808e12 0.0676363
\(929\) −9.99756e12 1.73163e13i −0.440376 0.762753i 0.557341 0.830283i \(-0.311821\pi\)
−0.997717 + 0.0675301i \(0.978488\pi\)
\(930\) 0 0
\(931\) 1.39830e11 2.42192e11i 0.00609995 0.0105654i
\(932\) −1.00660e13 + 1.74348e13i −0.437003 + 0.756911i
\(933\) 0 0
\(934\) 2.42353e12 + 4.19767e12i 0.104205 + 0.180488i
\(935\) 3.42799e13 1.46685
\(936\) 0 0
\(937\) 3.60094e13 1.52612 0.763058 0.646330i \(-0.223697\pi\)
0.763058 + 0.646330i \(0.223697\pi\)
\(938\) −2.10905e11 3.65298e11i −0.00889558 0.0154076i
\(939\) 0 0
\(940\) 9.40237e12 1.62854e13i 0.392791 0.680335i
\(941\) −1.10042e13 + 1.90598e13i −0.457514 + 0.792438i −0.998829 0.0483823i \(-0.984593\pi\)
0.541315 + 0.840820i \(0.317927\pi\)
\(942\) 0 0
\(943\) 2.32618e13 + 4.02907e13i 0.957946 + 1.65921i
\(944\) −3.28777e13 −1.34750
\(945\) 0 0
\(946\) −8.62036e12 −0.349958
\(947\) 1.13571e13 + 1.96711e13i 0.458873 + 0.794791i 0.998902 0.0468555i \(-0.0149200\pi\)
−0.540029 + 0.841646i \(0.681587\pi\)
\(948\) 0 0
\(949\) −1.47092e13 + 2.54771e13i −0.588697 + 1.01965i
\(950\) −2.33422e8 + 4.04299e8i −9.29791e−6 + 1.61045e-5i
\(951\) 0 0
\(952\) −1.12005e12 1.93998e12i −0.0441947 0.0765475i
\(953\) 1.64449e13 0.645824 0.322912 0.946429i \(-0.395338\pi\)
0.322912 + 0.946429i \(0.395338\pi\)
\(954\) 0 0
\(955\) −4.40882e12 −0.171517
\(956\) −2.31585e12 4.01118e12i −0.0896708 0.155314i
\(957\) 0 0
\(958\) −1.65663e12 + 2.86937e12i −0.0635450 + 0.110063i
\(959\) −4.94894e12 + 8.57182e12i −0.188942 + 0.327257i
\(960\) 0 0
\(961\) 7.03056e12 + 1.21773e13i 0.265910 + 0.460570i
\(962\) 3.78472e12 0.142477
\(963\) 0 0
\(964\) 3.90483e13 1.45631
\(965\) 2.15059e13 + 3.72493e13i 0.798335 + 1.38276i
\(966\) 0 0
\(967\) −1.24653e13 + 2.15906e13i −0.458442 + 0.794044i −0.998879 0.0473402i \(-0.984926\pi\)
0.540437 + 0.841384i \(0.318259\pi\)
\(968\) 2.96015e12 5.12714e12i 0.108362 0.187688i
\(969\) 0 0
\(970\) 1.42579e12 + 2.46955e12i 0.0517111 + 0.0895663i
\(971\) 4.38342e13 1.58244 0.791218 0.611534i \(-0.209447\pi\)
0.791218 + 0.611534i \(0.209447\pi\)
\(972\) 0 0
\(973\) −9.24641e12 −0.330724
\(974\) 4.99275e11 + 8.64770e11i 0.0177756 + 0.0307883i
\(975\) 0 0
\(976\) −1.71646e13 + 2.97300e13i −0.605495 + 1.04875i
\(977\) 2.28679e12 3.96084e12i 0.0802973 0.139079i −0.823080 0.567925i \(-0.807746\pi\)
0.903378 + 0.428846i \(0.141080\pi\)
\(978\) 0 0
\(979\) 1.81061e13 + 3.13607e13i 0.629945 + 1.09110i
\(980\) 2.63814e13 0.913652
\(981\) 0 0
\(982\) 8.12468e11 0.0278808
\(983\) −2.39203e13 4.14312e13i −0.817101 1.41526i −0.907809 0.419383i \(-0.862246\pi\)
0.0907080 0.995878i \(-0.471087\pi\)
\(984\) 0 0
\(985\) 1.51945e13 2.63176e13i 0.514308 0.890807i
\(986\) 3.84801e11 6.66495e11i 0.0129655 0.0224569i
\(987\) 0 0
\(988\) −2.06904e11 3.58368e11i −0.00690816 0.0119653i
\(989\) −1.02411e14 −3.40380
\(990\) 0 0
\(991\) −1.94011e13 −0.638993 −0.319496 0.947588i \(-0.603514\pi\)
−0.319496 + 0.947588i \(0.603514\pi\)
\(992\) −4.64198e12 8.04014e12i −0.152195 0.263610i
\(993\) 0 0
\(994\) 7.87023e11 1.36316e12i 0.0255710 0.0442903i
\(995\) 2.53771e12 4.39544e12i 0.0820802 0.142167i
\(996\) 0 0
\(997\) −2.36927e13 4.10370e13i −0.759429 1.31537i −0.943142 0.332389i \(-0.892145\pi\)
0.183714 0.982980i \(-0.441188\pi\)
\(998\) 8.75946e12 0.279505
\(999\) 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 81.10.c.g.28.2 6
3.2 odd 2 81.10.c.h.28.2 6
9.2 odd 6 81.10.c.h.55.2 6
9.4 even 3 27.10.a.c.1.2 yes 3
9.5 odd 6 27.10.a.b.1.2 3
9.7 even 3 inner 81.10.c.g.55.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.10.a.b.1.2 3 9.5 odd 6
27.10.a.c.1.2 yes 3 9.4 even 3
81.10.c.g.28.2 6 1.1 even 1 trivial
81.10.c.g.55.2 6 9.7 even 3 inner
81.10.c.h.28.2 6 3.2 odd 2
81.10.c.h.55.2 6 9.2 odd 6