Properties

Label 81.9.f.a.8.14
Level $81$
Weight $9$
Character 81.8
Analytic conductor $32.998$
Analytic rank $0$
Dimension $138$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,9,Mod(8,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.8");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 81.f (of order \(18\), degree \(6\), 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: \(32.9976674150\)
Analytic rank: \(0\)
Dimension: \(138\)
Relative dimension: \(23\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 8.14
Character \(\chi\) \(=\) 81.8
Dual form 81.9.f.a.71.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.66670 + 1.35185i) q^{2} +(-183.611 - 66.8288i) q^{4} +(24.0534 + 28.6657i) q^{5} +(-2598.90 + 945.921i) q^{7} +(-3043.29 - 1757.05i) q^{8} +(145.659 + 252.288i) q^{10} +(4786.80 - 5704.68i) q^{11} +(2684.14 + 15222.5i) q^{13} +(-21203.7 + 3738.78i) q^{14} +(17361.5 + 14568.0i) q^{16} +(124728. - 72011.7i) q^{17} +(-101393. + 175618. i) q^{19} +(-2500.76 - 6870.79i) q^{20} +(44410.8 - 37265.1i) q^{22} +(39698.1 - 109070. i) q^{23} +(67588.2 - 383312. i) q^{25} +120335. i q^{26} +540399. q^{28} +(609347. + 107444. i) q^{29} +(1.01617e6 + 369854. i) q^{31} +(691668. + 824298. i) q^{32} +(1.05360e6 - 383479. i) q^{34} +(-89627.8 - 51746.6i) q^{35} +(-978631. - 1.69504e6i) q^{37} +(-1.01476e6 + 1.20934e6i) q^{38} +(-22834.5 - 129501. i) q^{40} +(1.39463e6 - 245911. i) q^{41} +(2.04961e6 + 1.71982e6i) q^{43} +(-1.26014e6 + 727544. i) q^{44} +(451799. - 782539. i) q^{46} +(1.82238e6 + 5.00694e6i) q^{47} +(1.44340e6 - 1.21116e6i) q^{49} +(1.03636e6 - 2.84736e6i) q^{50} +(524465. - 2.97439e6i) q^{52} -3.45452e6i q^{53} +278668. q^{55} +(9.57122e6 + 1.68767e6i) q^{56} +(4.52643e6 + 1.64749e6i) q^{58} +(1.16111e7 + 1.38375e7i) q^{59} +(1.16719e7 - 4.24821e6i) q^{61} +(7.29065e6 + 4.20926e6i) q^{62} +(1.28751e6 + 2.23004e6i) q^{64} +(-371801. + 443096. i) q^{65} +(-1.92937e6 - 1.09420e7i) q^{67} +(-2.77138e7 + 4.88669e6i) q^{68} +(-617196. - 517889. i) q^{70} +(2.34487e7 - 1.35381e7i) q^{71} +(-1.28556e7 + 2.22665e7i) q^{73} +(-5.21144e6 - 1.43183e7i) q^{74} +(3.03531e7 - 2.54693e7i) q^{76} +(-7.04421e6 + 1.93538e7i) q^{77} +(-981583. + 5.56684e6i) q^{79} +848091. i q^{80} +1.10246e7 q^{82} +(-5.90784e6 - 1.04171e6i) q^{83} +(5.06440e6 + 1.84329e6i) q^{85} +(1.33888e7 + 1.59561e7i) q^{86} +(-2.45910e7 + 8.95039e6i) q^{88} +(-3.29258e7 - 1.90097e7i) q^{89} +(-2.13751e7 - 3.70227e7i) q^{91} +(-1.45780e7 + 1.73734e7i) q^{92} +(7.20300e6 + 4.08503e7i) q^{94} +(-7.47305e6 + 1.31770e6i) q^{95} +(9.92181e6 + 8.32538e6i) q^{97} +(1.27034e7 - 7.33433e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.66670 + 1.35185i 0.479169 + 0.0844904i 0.408015 0.912975i \(-0.366221\pi\)
0.0711532 + 0.997465i \(0.477332\pi\)
\(3\) 0 0
\(4\) −183.611 66.8288i −0.717229 0.261050i
\(5\) 24.0534 + 28.6657i 0.0384854 + 0.0458652i 0.784944 0.619567i \(-0.212692\pi\)
−0.746458 + 0.665432i \(0.768247\pi\)
\(6\) 0 0
\(7\) −2598.90 + 945.921i −1.08242 + 0.393970i −0.820809 0.571203i \(-0.806477\pi\)
−0.261614 + 0.965173i \(0.584255\pi\)
\(8\) −3043.29 1757.05i −0.742991 0.428966i
\(9\) 0 0
\(10\) 145.659 + 252.288i 0.0145659 + 0.0252288i
\(11\) 4786.80 5704.68i 0.326945 0.389637i −0.577385 0.816472i \(-0.695927\pi\)
0.904330 + 0.426835i \(0.140371\pi\)
\(12\) 0 0
\(13\) 2684.14 + 15222.5i 0.0939791 + 0.532982i 0.995055 + 0.0993213i \(0.0316672\pi\)
−0.901076 + 0.433661i \(0.857222\pi\)
\(14\) −21203.7 + 3738.78i −0.551949 + 0.0973236i
\(15\) 0 0
\(16\) 17361.5 + 14568.0i 0.264916 + 0.222291i
\(17\) 124728. 72011.7i 1.49337 0.862198i 0.493400 0.869802i \(-0.335754\pi\)
0.999971 + 0.00760413i \(0.00242049\pi\)
\(18\) 0 0
\(19\) −101393. + 175618.i −0.778024 + 1.34758i 0.155054 + 0.987906i \(0.450445\pi\)
−0.933079 + 0.359672i \(0.882889\pi\)
\(20\) −2500.76 6870.79i −0.0156298 0.0429424i
\(21\) 0 0
\(22\) 44410.8 37265.1i 0.189582 0.159078i
\(23\) 39698.1 109070.i 0.141860 0.389756i −0.848333 0.529462i \(-0.822394\pi\)
0.990193 + 0.139707i \(0.0446159\pi\)
\(24\) 0 0
\(25\) 67588.2 383312.i 0.173026 0.981277i
\(26\) 120335.i 0.263329i
\(27\) 0 0
\(28\) 540399. 0.879190
\(29\) 609347. + 107444.i 0.861534 + 0.151912i 0.586922 0.809643i \(-0.300340\pi\)
0.274612 + 0.961555i \(0.411451\pi\)
\(30\) 0 0
\(31\) 1.01617e6 + 369854.i 1.10032 + 0.400483i 0.827433 0.561564i \(-0.189800\pi\)
0.272884 + 0.962047i \(0.412022\pi\)
\(32\) 691668. + 824298.i 0.659626 + 0.786112i
\(33\) 0 0
\(34\) 1.05360e6 383479.i 0.788424 0.286963i
\(35\) −89627.8 51746.6i −0.0597270 0.0344834i
\(36\) 0 0
\(37\) −978631. 1.69504e6i −0.522170 0.904426i −0.999667 0.0257923i \(-0.991789\pi\)
0.477497 0.878633i \(-0.341544\pi\)
\(38\) −1.01476e6 + 1.20934e6i −0.486662 + 0.579982i
\(39\) 0 0
\(40\) −22834.5 129501.i −0.00891974 0.0505864i
\(41\) 1.39463e6 245911.i 0.493541 0.0870247i 0.0786625 0.996901i \(-0.474935\pi\)
0.414879 + 0.909877i \(0.363824\pi\)
\(42\) 0 0
\(43\) 2.04961e6 + 1.71982e6i 0.599510 + 0.503049i 0.891288 0.453437i \(-0.149802\pi\)
−0.291778 + 0.956486i \(0.594247\pi\)
\(44\) −1.26014e6 + 727544.i −0.336209 + 0.194110i
\(45\) 0 0
\(46\) 451799. 782539.i 0.100905 0.174773i
\(47\) 1.82238e6 + 5.00694e6i 0.373462 + 1.02608i 0.974013 + 0.226492i \(0.0727258\pi\)
−0.600551 + 0.799587i \(0.705052\pi\)
\(48\) 0 0
\(49\) 1.44340e6 1.21116e6i 0.250382 0.210095i
\(50\) 1.03636e6 2.84736e6i 0.165817 0.455578i
\(51\) 0 0
\(52\) 524465. 2.97439e6i 0.0717304 0.406803i
\(53\) 3.45452e6i 0.437809i −0.975746 0.218905i \(-0.929752\pi\)
0.975746 0.218905i \(-0.0702483\pi\)
\(54\) 0 0
\(55\) 278668. 0.0304534
\(56\) 9.57122e6 + 1.68767e6i 0.973230 + 0.171607i
\(57\) 0 0
\(58\) 4.52643e6 + 1.64749e6i 0.399985 + 0.145583i
\(59\) 1.16111e7 + 1.38375e7i 0.958217 + 1.14196i 0.989801 + 0.142458i \(0.0455005\pi\)
−0.0315836 + 0.999501i \(0.510055\pi\)
\(60\) 0 0
\(61\) 1.16719e7 4.24821e6i 0.842987 0.306822i 0.115810 0.993271i \(-0.463054\pi\)
0.727178 + 0.686449i \(0.240832\pi\)
\(62\) 7.29065e6 + 4.20926e6i 0.493401 + 0.284865i
\(63\) 0 0
\(64\) 1.28751e6 + 2.23004e6i 0.0767418 + 0.132921i
\(65\) −371801. + 443096.i −0.0208285 + 0.0248224i
\(66\) 0 0
\(67\) −1.92937e6 1.09420e7i −0.0957452 0.542998i −0.994516 0.104580i \(-0.966650\pi\)
0.898771 0.438418i \(-0.144461\pi\)
\(68\) −2.77138e7 + 4.88669e6i −1.29617 + 0.228549i
\(69\) 0 0
\(70\) −617196. 517889.i −0.0257058 0.0215697i
\(71\) 2.34487e7 1.35381e7i 0.922752 0.532751i 0.0382397 0.999269i \(-0.487825\pi\)
0.884512 + 0.466518i \(0.154492\pi\)
\(72\) 0 0
\(73\) −1.28556e7 + 2.22665e7i −0.452690 + 0.784082i −0.998552 0.0537933i \(-0.982869\pi\)
0.545862 + 0.837875i \(0.316202\pi\)
\(74\) −5.21144e6 1.43183e7i −0.173792 0.477491i
\(75\) 0 0
\(76\) 3.03531e7 2.54693e7i 0.909807 0.763418i
\(77\) −7.04421e6 + 1.93538e7i −0.200387 + 0.550558i
\(78\) 0 0
\(79\) −981583. + 5.56684e6i −0.0252011 + 0.142922i −0.994812 0.101729i \(-0.967562\pi\)
0.969611 + 0.244652i \(0.0786736\pi\)
\(80\) 848091.i 0.0207054i
\(81\) 0 0
\(82\) 1.10246e7 0.243842
\(83\) −5.90784e6 1.04171e6i −0.124485 0.0219500i 0.111059 0.993814i \(-0.464576\pi\)
−0.235543 + 0.971864i \(0.575687\pi\)
\(84\) 0 0
\(85\) 5.06440e6 + 1.84329e6i 0.0970179 + 0.0353116i
\(86\) 1.33888e7 + 1.59561e7i 0.244764 + 0.291698i
\(87\) 0 0
\(88\) −2.45910e7 + 8.95039e6i −0.410058 + 0.149249i
\(89\) −3.29258e7 1.90097e7i −0.524779 0.302981i 0.214109 0.976810i \(-0.431315\pi\)
−0.738888 + 0.673829i \(0.764649\pi\)
\(90\) 0 0
\(91\) −2.13751e7 3.70227e7i −0.311704 0.539887i
\(92\) −1.45780e7 + 1.73734e7i −0.203491 + 0.242512i
\(93\) 0 0
\(94\) 7.20300e6 + 4.08503e7i 0.0922576 + 0.523219i
\(95\) −7.47305e6 + 1.31770e6i −0.0917495 + 0.0161779i
\(96\) 0 0
\(97\) 9.92181e6 + 8.32538e6i 0.112074 + 0.0940410i 0.697102 0.716972i \(-0.254472\pi\)
−0.585029 + 0.811013i \(0.698917\pi\)
\(98\) 1.27034e7 7.33433e6i 0.137726 0.0795162i
\(99\) 0 0
\(100\) −3.80261e7 + 6.58632e7i −0.380261 + 0.658632i
\(101\) −2.54486e7 6.99195e7i −0.244556 0.671912i −0.999863 0.0165413i \(-0.994735\pi\)
0.755307 0.655371i \(-0.227488\pi\)
\(102\) 0 0
\(103\) −3.98778e7 + 3.34615e7i −0.354309 + 0.297301i −0.802518 0.596628i \(-0.796507\pi\)
0.448209 + 0.893929i \(0.352062\pi\)
\(104\) 1.85780e7 5.10426e7i 0.158806 0.436315i
\(105\) 0 0
\(106\) 4.66998e6 2.64848e7i 0.0369906 0.209784i
\(107\) 2.19636e8i 1.67559i −0.545986 0.837795i \(-0.683845\pi\)
0.545986 0.837795i \(-0.316155\pi\)
\(108\) 0 0
\(109\) −2.65997e8 −1.88439 −0.942194 0.335067i \(-0.891241\pi\)
−0.942194 + 0.335067i \(0.891241\pi\)
\(110\) 2.13646e6 + 376716.i 0.0145923 + 0.00257302i
\(111\) 0 0
\(112\) −5.89010e7 2.14382e7i −0.374326 0.136244i
\(113\) 7.63601e6 + 9.10024e6i 0.0468331 + 0.0558135i 0.788953 0.614454i \(-0.210624\pi\)
−0.742119 + 0.670268i \(0.766179\pi\)
\(114\) 0 0
\(115\) 4.08144e6 1.48552e6i 0.0233357 0.00849352i
\(116\) −1.04702e8 6.04498e7i −0.578260 0.333859i
\(117\) 0 0
\(118\) 7.03123e7 + 1.21785e8i 0.362663 + 0.628151i
\(119\) −2.56037e8 + 3.05134e8i −1.27678 + 1.52161i
\(120\) 0 0
\(121\) 2.75931e7 + 1.56488e8i 0.128724 + 0.730028i
\(122\) 9.52276e7 1.67912e7i 0.429857 0.0757953i
\(123\) 0 0
\(124\) −1.61862e8 1.35818e8i −0.684633 0.574476i
\(125\) 2.52726e7 1.45912e7i 0.103517 0.0597654i
\(126\) 0 0
\(127\) −1.66357e7 + 2.88139e7i −0.0639479 + 0.110761i −0.896227 0.443596i \(-0.853702\pi\)
0.832279 + 0.554357i \(0.187036\pi\)
\(128\) −8.73591e7 2.40017e8i −0.325438 0.894133i
\(129\) 0 0
\(130\) −3.44948e6 + 2.89446e6i −0.0120776 + 0.0101343i
\(131\) −1.61936e8 + 4.44915e8i −0.549867 + 1.51075i 0.284022 + 0.958818i \(0.408331\pi\)
−0.833890 + 0.551931i \(0.813891\pi\)
\(132\) 0 0
\(133\) 9.73893e7 5.52322e8i 0.311246 1.76517i
\(134\) 8.64974e7i 0.268277i
\(135\) 0 0
\(136\) −5.06111e8 −1.47942
\(137\) −2.76763e8 4.88007e7i −0.785643 0.138530i −0.233586 0.972336i \(-0.575046\pi\)
−0.552057 + 0.833806i \(0.686157\pi\)
\(138\) 0 0
\(139\) 6.76410e8 + 2.46193e8i 1.81197 + 0.659503i 0.996769 + 0.0803220i \(0.0255949\pi\)
0.815199 + 0.579180i \(0.196627\pi\)
\(140\) 1.29984e7 + 1.54909e7i 0.0338360 + 0.0403242i
\(141\) 0 0
\(142\) 1.98075e8 7.20935e7i 0.487166 0.177314i
\(143\) 9.96879e7 + 5.75548e7i 0.238396 + 0.137638i
\(144\) 0 0
\(145\) 1.15769e7 + 2.00518e7i 0.0261891 + 0.0453608i
\(146\) −1.28661e8 + 1.53332e8i −0.283162 + 0.337459i
\(147\) 0 0
\(148\) 6.64097e7 + 3.76628e8i 0.138415 + 0.784993i
\(149\) 8.91020e8 1.57111e8i 1.80777 0.318758i 0.834949 0.550327i \(-0.185497\pi\)
0.972819 + 0.231569i \(0.0743859\pi\)
\(150\) 0 0
\(151\) −2.47852e8 2.07973e8i −0.476744 0.400036i 0.372503 0.928031i \(-0.378500\pi\)
−0.849247 + 0.527995i \(0.822944\pi\)
\(152\) 6.17136e8 3.56304e8i 1.15613 0.667492i
\(153\) 0 0
\(154\) −8.01692e7 + 1.38857e8i −0.142536 + 0.246880i
\(155\) 1.38401e7 + 3.80254e7i 0.0239780 + 0.0658790i
\(156\) 0 0
\(157\) 5.95886e8 5.00008e8i 0.980764 0.822959i −0.00344009 0.999994i \(-0.501095\pi\)
0.984205 + 0.177035i \(0.0566506\pi\)
\(158\) −1.50510e7 + 4.13523e7i −0.0241511 + 0.0663546i
\(159\) 0 0
\(160\) −6.99213e6 + 3.96543e7i −0.0106691 + 0.0605077i
\(161\) 3.21012e8i 0.477769i
\(162\) 0 0
\(163\) 1.09107e9 1.54561 0.772806 0.634642i \(-0.218852\pi\)
0.772806 + 0.634642i \(0.218852\pi\)
\(164\) −2.72503e8 4.80496e7i −0.376700 0.0664223i
\(165\) 0 0
\(166\) −4.38854e7 1.59730e7i −0.0577947 0.0210355i
\(167\) 8.88832e8 + 1.05927e9i 1.14276 + 1.36188i 0.922294 + 0.386488i \(0.126312\pi\)
0.220462 + 0.975396i \(0.429243\pi\)
\(168\) 0 0
\(169\) 5.42016e8 1.97278e8i 0.664455 0.241842i
\(170\) 3.63354e7 + 2.09782e7i 0.0435045 + 0.0251173i
\(171\) 0 0
\(172\) −2.61396e8 4.52751e8i −0.298665 0.517303i
\(173\) −2.53987e7 + 3.02690e7i −0.0283548 + 0.0337920i −0.780035 0.625735i \(-0.784799\pi\)
0.751681 + 0.659527i \(0.229243\pi\)
\(174\) 0 0
\(175\) 1.86928e8 + 1.06012e9i 0.199307 + 1.13032i
\(176\) 1.66212e8 2.93077e7i 0.173225 0.0305443i
\(177\) 0 0
\(178\) −2.26734e8 1.90252e8i −0.225858 0.189518i
\(179\) 5.49026e8 3.16980e8i 0.534787 0.308759i −0.208177 0.978091i \(-0.566753\pi\)
0.742963 + 0.669332i \(0.233420\pi\)
\(180\) 0 0
\(181\) −4.29163e8 + 7.43332e8i −0.399860 + 0.692578i −0.993708 0.111999i \(-0.964275\pi\)
0.593848 + 0.804577i \(0.297608\pi\)
\(182\) −1.13827e8 3.12738e8i −0.103743 0.285033i
\(183\) 0 0
\(184\) −3.12453e8 + 2.62179e8i −0.272592 + 0.228732i
\(185\) 2.50501e7 6.88246e7i 0.0213857 0.0587567i
\(186\) 0 0
\(187\) 1.86243e8 1.05624e9i 0.152305 0.863764i
\(188\) 1.04111e9i 0.833425i
\(189\) 0 0
\(190\) −5.90750e7 −0.0453304
\(191\) −6.61152e8 1.16579e8i −0.496784 0.0875965i −0.0803582 0.996766i \(-0.525606\pi\)
−0.416426 + 0.909170i \(0.636718\pi\)
\(192\) 0 0
\(193\) −2.97918e7 1.08433e7i −0.0214718 0.00781508i 0.331262 0.943539i \(-0.392526\pi\)
−0.352734 + 0.935724i \(0.614748\pi\)
\(194\) 6.48129e7 + 7.72410e7i 0.0457567 + 0.0545307i
\(195\) 0 0
\(196\) −3.45964e8 + 1.25921e8i −0.234426 + 0.0853242i
\(197\) 8.67018e8 + 5.00573e8i 0.575656 + 0.332355i 0.759405 0.650618i \(-0.225490\pi\)
−0.183749 + 0.982973i \(0.558823\pi\)
\(198\) 0 0
\(199\) 1.45511e8 + 2.52033e8i 0.0927865 + 0.160711i 0.908683 0.417488i \(-0.137089\pi\)
−0.815896 + 0.578198i \(0.803756\pi\)
\(200\) −8.79186e8 + 1.04777e9i −0.549491 + 0.654858i
\(201\) 0 0
\(202\) −1.00586e8 5.70454e8i −0.0604135 0.342622i
\(203\) −1.68526e9 + 2.97157e8i −0.992392 + 0.174986i
\(204\) 0 0
\(205\) 4.05948e7 + 3.40631e7i 0.0229856 + 0.0192872i
\(206\) −3.50966e8 + 2.02630e8i −0.194893 + 0.112521i
\(207\) 0 0
\(208\) −1.75161e8 + 3.03388e8i −0.0935803 + 0.162086i
\(209\) 5.16496e8 + 1.41906e9i 0.270696 + 0.743731i
\(210\) 0 0
\(211\) 2.57792e9 2.16313e9i 1.30059 1.09132i 0.310543 0.950559i \(-0.399489\pi\)
0.990043 0.140762i \(-0.0449553\pi\)
\(212\) −2.30862e8 + 6.34287e8i −0.114290 + 0.314009i
\(213\) 0 0
\(214\) 2.96913e8 1.68388e9i 0.141571 0.802890i
\(215\) 1.00121e8i 0.0468567i
\(216\) 0 0
\(217\) −2.99076e9 −1.34879
\(218\) −2.03932e9 3.59587e8i −0.902940 0.159213i
\(219\) 0 0
\(220\) −5.11663e7 1.86230e7i −0.0218420 0.00794985i
\(221\) 1.43098e9 + 1.70538e9i 0.599882 + 0.714911i
\(222\) 0 0
\(223\) −3.84150e8 + 1.39819e8i −0.155339 + 0.0565388i −0.418519 0.908208i \(-0.637451\pi\)
0.263180 + 0.964747i \(0.415229\pi\)
\(224\) −2.57729e9 1.48800e9i −1.02370 0.591032i
\(225\) 0 0
\(226\) 4.62409e7 + 8.00915e7i 0.0177252 + 0.0307010i
\(227\) 1.70797e9 2.03548e9i 0.643246 0.766591i −0.341633 0.939833i \(-0.610980\pi\)
0.984879 + 0.173243i \(0.0554245\pi\)
\(228\) 0 0
\(229\) 7.47013e8 + 4.23652e9i 0.271635 + 1.54052i 0.749451 + 0.662060i \(0.230318\pi\)
−0.477816 + 0.878460i \(0.658571\pi\)
\(230\) 3.32993e7 5.87157e6i 0.0118994 0.00209818i
\(231\) 0 0
\(232\) −1.66563e9 1.39763e9i −0.574947 0.482438i
\(233\) 2.49677e9 1.44151e9i 0.847138 0.489095i −0.0125463 0.999921i \(-0.503994\pi\)
0.859684 + 0.510826i \(0.170660\pi\)
\(234\) 0 0
\(235\) −9.96932e7 + 1.72674e8i −0.0326884 + 0.0566180i
\(236\) −1.20717e9 3.31667e9i −0.389153 1.06919i
\(237\) 0 0
\(238\) −2.37546e9 + 1.99324e9i −0.740353 + 0.621230i
\(239\) 6.28233e8 1.72606e9i 0.192544 0.529010i −0.805426 0.592696i \(-0.798064\pi\)
0.997970 + 0.0636865i \(0.0202858\pi\)
\(240\) 0 0
\(241\) −7.37356e8 + 4.18175e9i −0.218579 + 1.23962i 0.656007 + 0.754755i \(0.272244\pi\)
−0.874586 + 0.484870i \(0.838867\pi\)
\(242\) 1.23705e9i 0.360682i
\(243\) 0 0
\(244\) −2.42698e9 −0.684711
\(245\) 6.94374e7 + 1.22437e7i 0.0192721 + 0.00339819i
\(246\) 0 0
\(247\) −2.94549e9 1.07207e9i −0.791353 0.288029i
\(248\) −2.44264e9 2.91102e9i −0.645733 0.769554i
\(249\) 0 0
\(250\) 2.13483e8 7.77013e7i 0.0546516 0.0198915i
\(251\) −6.55995e9 3.78739e9i −1.65274 0.954212i −0.975937 0.218052i \(-0.930030\pi\)
−0.676807 0.736160i \(-0.736637\pi\)
\(252\) 0 0
\(253\) −4.32181e8 7.48559e8i −0.105483 0.182702i
\(254\) −1.66493e8 + 1.98419e8i −0.0400001 + 0.0476703i
\(255\) 0 0
\(256\) −4.59760e8 2.60743e9i −0.107046 0.607089i
\(257\) 1.33863e8 2.36037e7i 0.0306852 0.00541062i −0.158285 0.987394i \(-0.550596\pi\)
0.188970 + 0.981983i \(0.439485\pi\)
\(258\) 0 0
\(259\) 4.14673e9 + 3.47952e9i 0.921525 + 0.773251i
\(260\) 9.78782e7 5.65100e7i 0.0214187 0.0123661i
\(261\) 0 0
\(262\) −1.84297e9 + 3.19212e9i −0.391123 + 0.677445i
\(263\) 3.23234e9 + 8.88079e9i 0.675608 + 1.85622i 0.484899 + 0.874570i \(0.338856\pi\)
0.190709 + 0.981647i \(0.438921\pi\)
\(264\) 0 0
\(265\) 9.90265e7 8.30931e7i 0.0200802 0.0168493i
\(266\) 1.49331e9 4.10283e9i 0.298279 0.819515i
\(267\) 0 0
\(268\) −3.76989e8 + 2.13801e9i −0.0730784 + 0.414448i
\(269\) 1.18549e8i 0.0226407i −0.999936 0.0113204i \(-0.996397\pi\)
0.999936 0.0113204i \(-0.00360346\pi\)
\(270\) 0 0
\(271\) 3.58270e9 0.664252 0.332126 0.943235i \(-0.392234\pi\)
0.332126 + 0.943235i \(0.392234\pi\)
\(272\) 3.21453e9 + 5.66809e8i 0.587276 + 0.103553i
\(273\) 0 0
\(274\) −2.05589e9 7.48281e8i −0.364751 0.132759i
\(275\) −1.86314e9 2.22040e9i −0.325773 0.388241i
\(276\) 0 0
\(277\) 1.39013e9 5.05965e8i 0.236122 0.0859412i −0.221249 0.975217i \(-0.571013\pi\)
0.457371 + 0.889276i \(0.348791\pi\)
\(278\) 4.85301e9 + 2.80189e9i 0.812517 + 0.469107i
\(279\) 0 0
\(280\) 1.81842e8 + 3.14960e8i 0.0295844 + 0.0512417i
\(281\) 3.91017e9 4.65996e9i 0.627149 0.747407i −0.355133 0.934816i \(-0.615565\pi\)
0.982282 + 0.187409i \(0.0600090\pi\)
\(282\) 0 0
\(283\) −8.05969e8 4.57088e9i −0.125653 0.712613i −0.980918 0.194422i \(-0.937717\pi\)
0.855265 0.518191i \(-0.173394\pi\)
\(284\) −5.21016e9 + 9.18691e8i −0.800898 + 0.141220i
\(285\) 0 0
\(286\) 6.86472e8 + 5.76018e8i 0.102603 + 0.0860938i
\(287\) −3.39189e9 + 1.95831e9i −0.499935 + 0.288638i
\(288\) 0 0
\(289\) 6.88348e9 1.19225e10i 0.986772 1.70914i
\(290\) 6.16496e7 + 1.69381e8i 0.00871643 + 0.0239482i
\(291\) 0 0
\(292\) 3.84847e9 3.22925e9i 0.529366 0.444191i
\(293\) −3.86218e9 + 1.06113e10i −0.524037 + 1.43978i 0.341952 + 0.939717i \(0.388912\pi\)
−0.865989 + 0.500063i \(0.833310\pi\)
\(294\) 0 0
\(295\) −1.17377e8 + 6.65679e8i −0.0154987 + 0.0878976i
\(296\) 6.87800e9i 0.895974i
\(297\) 0 0
\(298\) 7.04357e9 0.893158
\(299\) 1.76687e9 + 3.11546e8i 0.221065 + 0.0389797i
\(300\) 0 0
\(301\) −6.95353e9 2.53088e9i −0.847109 0.308323i
\(302\) −1.61906e9 1.92952e9i −0.194642 0.231965i
\(303\) 0 0
\(304\) −4.31874e9 + 1.57189e9i −0.505665 + 0.184047i
\(305\) 4.02526e8 + 2.32399e8i 0.0465152 + 0.0268556i
\(306\) 0 0
\(307\) 1.60427e9 + 2.77868e9i 0.180603 + 0.312813i 0.942086 0.335372i \(-0.108862\pi\)
−0.761483 + 0.648185i \(0.775529\pi\)
\(308\) 2.58678e9 3.08281e9i 0.287446 0.342565i
\(309\) 0 0
\(310\) 5.47035e7 + 3.10239e8i 0.00592336 + 0.0335931i
\(311\) 5.93601e9 1.04668e9i 0.634531 0.111885i 0.152875 0.988245i \(-0.451147\pi\)
0.481656 + 0.876361i \(0.340036\pi\)
\(312\) 0 0
\(313\) 2.47074e9 + 2.07320e9i 0.257425 + 0.216005i 0.762362 0.647151i \(-0.224040\pi\)
−0.504937 + 0.863156i \(0.668484\pi\)
\(314\) 5.24441e9 3.02786e9i 0.539484 0.311471i
\(315\) 0 0
\(316\) 5.52254e8 9.56532e8i 0.0553848 0.0959292i
\(317\) −1.44241e9 3.96300e9i −0.142841 0.392452i 0.847556 0.530706i \(-0.178073\pi\)
−0.990397 + 0.138254i \(0.955851\pi\)
\(318\) 0 0
\(319\) 3.52975e9 2.96181e9i 0.340864 0.286019i
\(320\) −3.29566e7 + 9.05476e7i −0.00314299 + 0.00863529i
\(321\) 0 0
\(322\) −4.33959e8 + 2.46110e9i −0.0403669 + 0.228932i
\(323\) 2.92059e10i 2.68325i
\(324\) 0 0
\(325\) 6.01637e9 0.539264
\(326\) 8.36487e9 + 1.47495e9i 0.740609 + 0.130589i
\(327\) 0 0
\(328\) −4.67634e9 1.70205e9i −0.404028 0.147054i
\(329\) −9.47233e9 1.12887e10i −0.808488 0.963518i
\(330\) 0 0
\(331\) −5.24937e9 + 1.91061e9i −0.437316 + 0.159170i −0.551290 0.834314i \(-0.685864\pi\)
0.113974 + 0.993484i \(0.463642\pi\)
\(332\) 1.01513e9 + 5.86083e8i 0.0835541 + 0.0482400i
\(333\) 0 0
\(334\) 5.38244e9 + 9.32265e9i 0.432507 + 0.749124i
\(335\) 2.67253e8 3.18500e8i 0.0212199 0.0252889i
\(336\) 0 0
\(337\) −3.28023e8 1.86031e9i −0.0254322 0.144233i 0.969448 0.245299i \(-0.0788860\pi\)
−0.994880 + 0.101065i \(0.967775\pi\)
\(338\) 4.42217e9 7.79747e8i 0.338819 0.0597430i
\(339\) 0 0
\(340\) −8.06692e8 6.76895e8i −0.0603659 0.0506530i
\(341\) 6.97408e9 4.02649e9i 0.515786 0.297789i
\(342\) 0 0
\(343\) 5.36623e9 9.29458e9i 0.387697 0.671511i
\(344\) −3.21574e9 8.83518e9i −0.229640 0.630931i
\(345\) 0 0
\(346\) −2.35643e8 + 1.97728e8i −0.0164418 + 0.0137963i
\(347\) 4.26463e9 1.17170e10i 0.294146 0.808160i −0.701303 0.712864i \(-0.747398\pi\)
0.995449 0.0952965i \(-0.0303799\pi\)
\(348\) 0 0
\(349\) −2.62191e9 + 1.48696e10i −0.176733 + 1.00230i 0.759392 + 0.650633i \(0.225496\pi\)
−0.936125 + 0.351667i \(0.885615\pi\)
\(350\) 8.38032e9i 0.558455i
\(351\) 0 0
\(352\) 8.01323e9 0.521960
\(353\) 1.77537e10 + 3.13045e9i 1.14338 + 0.201608i 0.713083 0.701080i \(-0.247298\pi\)
0.430295 + 0.902688i \(0.358409\pi\)
\(354\) 0 0
\(355\) 9.52100e8 + 3.46536e8i 0.0599472 + 0.0218190i
\(356\) 4.77513e9 + 5.69077e9i 0.297293 + 0.354300i
\(357\) 0 0
\(358\) 4.63772e9 1.68799e9i 0.282340 0.102763i
\(359\) −2.52845e10 1.45980e10i −1.52222 0.878852i −0.999655 0.0262509i \(-0.991643\pi\)
−0.522562 0.852602i \(-0.675024\pi\)
\(360\) 0 0
\(361\) −1.20693e10 2.09046e10i −0.710644 1.23087i
\(362\) −4.29513e9 + 5.11874e9i −0.250117 + 0.298077i
\(363\) 0 0
\(364\) 1.45051e9 + 8.22623e9i 0.0826255 + 0.468592i
\(365\) −9.47507e8 + 1.67071e8i −0.0533840 + 0.00941304i
\(366\) 0 0
\(367\) 6.35266e9 + 5.33051e9i 0.350180 + 0.293836i 0.800862 0.598849i \(-0.204375\pi\)
−0.450682 + 0.892684i \(0.648819\pi\)
\(368\) 2.27815e9 1.31529e9i 0.124220 0.0717184i
\(369\) 0 0
\(370\) 2.85092e8 4.93794e8i 0.0152117 0.0263475i
\(371\) 3.26771e9 + 8.97795e9i 0.172483 + 0.473894i
\(372\) 0 0
\(373\) −2.11366e10 + 1.77357e10i −1.09194 + 0.916248i −0.996857 0.0792207i \(-0.974757\pi\)
−0.0950853 + 0.995469i \(0.530312\pi\)
\(374\) 2.85574e9 7.84608e9i 0.145960 0.401020i
\(375\) 0 0
\(376\) 3.25139e9 1.84396e10i 0.162674 0.922570i
\(377\) 9.56417e9i 0.473458i
\(378\) 0 0
\(379\) 2.32513e10 1.12691 0.563457 0.826145i \(-0.309471\pi\)
0.563457 + 0.826145i \(0.309471\pi\)
\(380\) 1.46019e9 + 2.57471e8i 0.0700286 + 0.0123479i
\(381\) 0 0
\(382\) −4.91126e9 1.78755e9i −0.230642 0.0839470i
\(383\) −3.20145e9 3.81534e9i −0.148782 0.177312i 0.686506 0.727124i \(-0.259144\pi\)
−0.835288 + 0.549812i \(0.814699\pi\)
\(384\) 0 0
\(385\) −7.24228e8 + 2.63597e8i −0.0329634 + 0.0119977i
\(386\) −2.13746e8 1.23406e8i −0.00962829 0.00555890i
\(387\) 0 0
\(388\) −1.26537e9 2.19169e9i −0.0558331 0.0967057i
\(389\) −6.62163e9 + 7.89136e9i −0.289179 + 0.344630i −0.891002 0.453999i \(-0.849997\pi\)
0.601823 + 0.798630i \(0.294441\pi\)
\(390\) 0 0
\(391\) −2.90283e9 1.64628e10i −0.124198 0.704361i
\(392\) −6.52075e9 + 1.14978e9i −0.276155 + 0.0486936i
\(393\) 0 0
\(394\) 5.97047e9 + 5.00982e9i 0.247756 + 0.207892i
\(395\) −1.83188e8 + 1.05764e8i −0.00752503 + 0.00434458i
\(396\) 0 0
\(397\) −1.12454e10 + 1.94777e10i −0.452704 + 0.784107i −0.998553 0.0537771i \(-0.982874\pi\)
0.545849 + 0.837884i \(0.316207\pi\)
\(398\) 7.74882e8 + 2.12897e9i 0.0308818 + 0.0848472i
\(399\) 0 0
\(400\) 6.75753e9 5.67024e9i 0.263966 0.221494i
\(401\) 1.26623e10 3.47894e10i 0.489705 1.34545i −0.411242 0.911526i \(-0.634905\pi\)
0.900947 0.433928i \(-0.142873\pi\)
\(402\) 0 0
\(403\) −2.90258e9 + 1.64613e10i −0.110043 + 0.624086i
\(404\) 1.45386e10i 0.545756i
\(405\) 0 0
\(406\) −1.33221e10 −0.490308
\(407\) −1.43542e10 2.53103e9i −0.523119 0.0922400i
\(408\) 0 0
\(409\) −1.04727e10 3.81173e9i −0.374251 0.136216i 0.148044 0.988981i \(-0.452702\pi\)
−0.522296 + 0.852764i \(0.674924\pi\)
\(410\) 2.65180e8 + 3.16029e8i 0.00938438 + 0.0111839i
\(411\) 0 0
\(412\) 9.55817e9 3.47889e9i 0.331731 0.120740i
\(413\) −4.32652e10 2.49792e10i −1.48709 0.858574i
\(414\) 0 0
\(415\) −1.12242e8 1.94409e8i −0.00378411 0.00655428i
\(416\) −1.06913e10 + 1.27414e10i −0.356992 + 0.425447i
\(417\) 0 0
\(418\) 2.04147e9 + 1.15777e10i 0.0668709 + 0.379244i
\(419\) −2.88812e10 + 5.09254e9i −0.937044 + 0.165226i −0.621259 0.783605i \(-0.713379\pi\)
−0.315784 + 0.948831i \(0.602268\pi\)
\(420\) 0 0
\(421\) −3.97225e10 3.33311e10i −1.26447 1.06102i −0.995191 0.0979530i \(-0.968771\pi\)
−0.269278 0.963062i \(-0.586785\pi\)
\(422\) 2.26883e10 1.30991e10i 0.715406 0.413040i
\(423\) 0 0
\(424\) −6.06976e9 + 1.05131e10i −0.187805 + 0.325288i
\(425\) −1.91728e10 5.26768e10i −0.587664 1.61459i
\(426\) 0 0
\(427\) −2.63155e10 + 2.20813e10i −0.791590 + 0.664223i
\(428\) −1.46780e10 + 4.03274e10i −0.437412 + 1.20178i
\(429\) 0 0
\(430\) −1.35348e8 + 7.67598e8i −0.00395894 + 0.0224523i
\(431\) 2.99834e9i 0.0868905i −0.999056 0.0434452i \(-0.986167\pi\)
0.999056 0.0434452i \(-0.0138334\pi\)
\(432\) 0 0
\(433\) −6.72699e10 −1.91368 −0.956839 0.290617i \(-0.906139\pi\)
−0.956839 + 0.290617i \(0.906139\pi\)
\(434\) −2.29293e10 4.04305e9i −0.646296 0.113959i
\(435\) 0 0
\(436\) 4.88398e10 + 1.77762e10i 1.35154 + 0.491919i
\(437\) 1.51295e10 + 1.80306e10i 0.414856 + 0.494406i
\(438\) 0 0
\(439\) −4.83773e10 + 1.76079e10i −1.30252 + 0.474078i −0.897816 0.440371i \(-0.854847\pi\)
−0.404702 + 0.914449i \(0.632625\pi\)
\(440\) −8.48067e8 4.89631e8i −0.0226266 0.0130635i
\(441\) 0 0
\(442\) 8.66551e9 + 1.50091e10i 0.227041 + 0.393247i
\(443\) 1.96213e10 2.33837e10i 0.509463 0.607154i −0.448593 0.893736i \(-0.648075\pi\)
0.958056 + 0.286582i \(0.0925191\pi\)
\(444\) 0 0
\(445\) −2.47050e8 1.40109e9i −0.00630006 0.0357294i
\(446\) −3.13417e9 + 5.52639e8i −0.0792107 + 0.0139670i
\(447\) 0 0
\(448\) −5.45556e9 4.57776e9i −0.135434 0.113642i
\(449\) 4.45495e10 2.57207e10i 1.09612 0.632845i 0.160920 0.986967i \(-0.448554\pi\)
0.935199 + 0.354123i \(0.115220\pi\)
\(450\) 0 0
\(451\) 5.27297e9 9.13304e9i 0.127453 0.220754i
\(452\) −7.93894e8 2.18121e9i −0.0190199 0.0522568i
\(453\) 0 0
\(454\) 1.58462e10 1.32965e10i 0.372993 0.312978i
\(455\) 5.47140e8 1.50325e9i 0.0127659 0.0350741i
\(456\) 0 0
\(457\) 1.83947e9 1.04321e10i 0.0421723 0.239171i −0.956434 0.291949i \(-0.905696\pi\)
0.998606 + 0.0527778i \(0.0168075\pi\)
\(458\) 3.34900e10i 0.761120i
\(459\) 0 0
\(460\) −8.48670e8 −0.0189543
\(461\) 1.61670e10 + 2.85068e9i 0.357953 + 0.0631168i 0.349733 0.936849i \(-0.386272\pi\)
0.00822026 + 0.999966i \(0.497383\pi\)
\(462\) 0 0
\(463\) 2.17181e10 + 7.90475e9i 0.472605 + 0.172014i 0.567332 0.823489i \(-0.307976\pi\)
−0.0947270 + 0.995503i \(0.530198\pi\)
\(464\) 9.01393e9 + 1.07424e10i 0.194465 + 0.231755i
\(465\) 0 0
\(466\) 2.10906e10 7.67637e9i 0.447246 0.162784i
\(467\) −3.17397e10 1.83249e10i −0.667322 0.385278i 0.127739 0.991808i \(-0.459228\pi\)
−0.795061 + 0.606529i \(0.792561\pi\)
\(468\) 0 0
\(469\) 1.53645e10 + 2.66121e10i 0.317562 + 0.550033i
\(470\) −9.97745e8 + 1.18907e9i −0.0204469 + 0.0243677i
\(471\) 0 0
\(472\) −1.10227e10 6.25128e10i −0.222085 1.25951i
\(473\) 1.96221e10 3.45990e9i 0.392013 0.0691225i
\(474\) 0 0
\(475\) 6.04633e10 + 5.07348e10i 1.18773 + 0.996624i
\(476\) 6.74029e10 3.89151e10i 1.31296 0.758036i
\(477\) 0 0
\(478\) 7.14984e9 1.23839e10i 0.136957 0.237217i
\(479\) 3.04605e10 + 8.36895e10i 0.578622 + 1.58975i 0.790505 + 0.612456i \(0.209818\pi\)
−0.211883 + 0.977295i \(0.567960\pi\)
\(480\) 0 0
\(481\) 2.31759e10 1.94469e10i 0.432969 0.363304i
\(482\) −1.13062e10 + 3.10634e10i −0.209473 + 0.575521i
\(483\) 0 0
\(484\) 5.39153e9 3.05769e10i 0.0982495 0.557200i
\(485\) 4.84670e8i 0.00875949i
\(486\) 0 0
\(487\) −2.06487e10 −0.367093 −0.183547 0.983011i \(-0.558758\pi\)
−0.183547 + 0.983011i \(0.558758\pi\)
\(488\) −4.29852e10 7.57945e9i −0.757948 0.133647i
\(489\) 0 0
\(490\) 5.15804e8 + 1.87737e8i 0.00894748 + 0.00325662i
\(491\) 1.51222e10 + 1.80220e10i 0.260190 + 0.310082i 0.880286 0.474444i \(-0.157351\pi\)
−0.620096 + 0.784526i \(0.712906\pi\)
\(492\) 0 0
\(493\) 8.37397e10 3.04788e10i 1.41757 0.515953i
\(494\) −2.11329e10 1.22011e10i −0.354856 0.204876i
\(495\) 0 0
\(496\) 1.22541e10 + 2.12248e10i 0.202468 + 0.350684i
\(497\) −4.81347e10 + 5.73647e10i −0.788919 + 0.940198i
\(498\) 0 0
\(499\) 4.39743e9 + 2.49391e10i 0.0709246 + 0.402233i 0.999515 + 0.0311280i \(0.00990996\pi\)
−0.928591 + 0.371105i \(0.878979\pi\)
\(500\) −5.61543e9 + 9.90152e8i −0.0898469 + 0.0158424i
\(501\) 0 0
\(502\) −4.51732e10 3.79048e10i −0.711322 0.596870i
\(503\) 8.07649e10 4.66296e10i 1.26168 0.728434i 0.288284 0.957545i \(-0.406915\pi\)
0.973400 + 0.229111i \(0.0735819\pi\)
\(504\) 0 0
\(505\) 1.39217e9 2.41130e9i 0.0214055 0.0370754i
\(506\) −2.30146e9 6.32322e9i −0.0351077 0.0964575i
\(507\) 0 0
\(508\) 4.98009e9 4.17879e9i 0.0747795 0.0627474i
\(509\) −2.18961e10 + 6.01590e10i −0.326208 + 0.896250i 0.662854 + 0.748749i \(0.269345\pi\)
−0.989062 + 0.147501i \(0.952877\pi\)
\(510\) 0 0
\(511\) 1.23480e10 7.00288e10i 0.181097 1.02705i
\(512\) 4.47759e10i 0.651575i
\(513\) 0 0
\(514\) 1.05820e9 0.0151605
\(515\) −1.91839e9 3.38265e8i −0.0272715 0.00480870i
\(516\) 0 0
\(517\) 3.72863e10 + 1.35711e10i 0.521900 + 0.189956i
\(518\) 2.70880e10 + 3.22822e10i 0.376234 + 0.448378i
\(519\) 0 0
\(520\) 1.91004e9 6.95197e8i 0.0261233 0.00950812i
\(521\) −9.62836e10 5.55894e10i −1.30678 0.754468i −0.325220 0.945638i \(-0.605438\pi\)
−0.981557 + 0.191170i \(0.938772\pi\)
\(522\) 0 0
\(523\) −3.92357e10 6.79583e10i −0.524415 0.908313i −0.999596 0.0284250i \(-0.990951\pi\)
0.475181 0.879888i \(-0.342383\pi\)
\(524\) 5.94663e10 7.08692e10i 0.788761 0.940009i
\(525\) 0 0
\(526\) 1.27759e10 + 7.24560e10i 0.166898 + 0.946523i
\(527\) 1.53378e11 2.70447e10i 1.98848 0.350622i
\(528\) 0 0
\(529\) 4.96694e10 + 4.16776e10i 0.634259 + 0.532206i
\(530\) 8.71535e8 5.03181e8i 0.0110454 0.00637706i
\(531\) 0 0
\(532\) −5.47927e10 + 9.49037e10i −0.684031 + 1.18478i
\(533\) 7.48676e9 + 2.05697e10i 0.0927651 + 0.254870i
\(534\) 0 0
\(535\) 6.29601e9 5.28298e9i 0.0768512 0.0644858i
\(536\) −1.33540e10 + 3.66898e10i −0.161790 + 0.444514i
\(537\) 0 0
\(538\) 1.60261e8 9.08883e8i 0.00191292 0.0108487i
\(539\) 1.40317e10i 0.166248i
\(540\) 0 0
\(541\) 5.30837e10 0.619687 0.309844 0.950788i \(-0.399723\pi\)
0.309844 + 0.950788i \(0.399723\pi\)
\(542\) 2.74675e10 + 4.84326e9i 0.318289 + 0.0561229i
\(543\) 0 0
\(544\) 1.45629e11 + 5.30047e10i 1.66285 + 0.605228i
\(545\) −6.39813e9 7.62499e9i −0.0725215 0.0864278i
\(546\) 0 0
\(547\) 2.28786e10 8.32712e9i 0.255552 0.0930134i −0.211067 0.977472i \(-0.567694\pi\)
0.466620 + 0.884458i \(0.345472\pi\)
\(548\) 4.75553e10 + 2.74560e10i 0.527323 + 0.304450i
\(549\) 0 0
\(550\) −1.12825e10 1.95418e10i −0.123297 0.213557i
\(551\) −8.06525e10 + 9.61180e10i −0.875007 + 1.04279i
\(552\) 0 0
\(553\) −2.71475e9 1.53961e10i −0.0290288 0.164631i
\(554\) 1.13417e10 1.99984e9i 0.120403 0.0212303i
\(555\) 0 0
\(556\) −1.07743e11 9.04073e10i −1.12743 0.946028i
\(557\) 5.15104e10 2.97396e10i 0.535149 0.308968i −0.207962 0.978137i \(-0.566683\pi\)
0.743111 + 0.669169i \(0.233350\pi\)
\(558\) 0 0
\(559\) −2.06786e10 + 3.58164e10i −0.211775 + 0.366804i
\(560\) −8.02227e8 2.20410e9i −0.00815728 0.0224119i
\(561\) 0 0
\(562\) 3.62776e10 3.04406e10i 0.363659 0.305146i
\(563\) 8.78895e9 2.41474e10i 0.0874789 0.240346i −0.888237 0.459385i \(-0.848070\pi\)
0.975716 + 0.219039i \(0.0702921\pi\)
\(564\) 0 0
\(565\) −7.71931e7 + 4.37784e8i −0.000757503 + 0.00429601i
\(566\) 3.61331e10i 0.352078i
\(567\) 0 0
\(568\) −9.51482e10 −0.914128
\(569\) −1.36983e11 2.41538e10i −1.30683 0.230429i −0.523493 0.852030i \(-0.675371\pi\)
−0.783334 + 0.621601i \(0.786483\pi\)
\(570\) 0 0
\(571\) −3.21798e10 1.17125e10i −0.302719 0.110181i 0.186195 0.982513i \(-0.440384\pi\)
−0.488913 + 0.872332i \(0.662607\pi\)
\(572\) −1.44574e10 1.72297e10i −0.135054 0.160951i
\(573\) 0 0
\(574\) −2.86519e10 + 1.04284e10i −0.263940 + 0.0960664i
\(575\) −3.91245e10 2.25886e10i −0.357913 0.206641i
\(576\) 0 0
\(577\) −4.06482e10 7.04048e10i −0.366723 0.635183i 0.622328 0.782756i \(-0.286187\pi\)
−0.989051 + 0.147574i \(0.952854\pi\)
\(578\) 6.88910e10 8.21011e10i 0.617236 0.735593i
\(579\) 0 0
\(580\) −7.85604e8 4.45538e9i −0.00694212 0.0393707i
\(581\) 1.63392e10 2.88105e9i 0.143393 0.0252840i
\(582\) 0 0
\(583\) −1.97070e10 1.65361e10i −0.170587 0.143139i
\(584\) 7.82466e10 4.51757e10i 0.672689 0.388377i
\(585\) 0 0
\(586\) −4.39549e10 + 7.61322e10i −0.372750 + 0.645621i
\(587\) −1.12180e10 3.08212e10i −0.0944850 0.259595i 0.883443 0.468539i \(-0.155220\pi\)
−0.977928 + 0.208944i \(0.932997\pi\)
\(588\) 0 0
\(589\) −1.67985e11 + 1.40956e11i −1.39576 + 1.17118i
\(590\) −1.79979e9 + 4.94489e9i −0.0148530 + 0.0408083i
\(591\) 0 0
\(592\) 7.70288e9 4.36852e10i 0.0627142 0.355670i
\(593\) 1.79096e11i 1.44833i 0.689628 + 0.724164i \(0.257774\pi\)
−0.689628 + 0.724164i \(0.742226\pi\)
\(594\) 0 0
\(595\) −1.49054e10 −0.118926
\(596\) −1.74100e11 3.06986e10i −1.37979 0.243295i
\(597\) 0 0
\(598\) 1.31249e10 + 4.77706e9i 0.102634 + 0.0373557i
\(599\) 3.31382e10 + 3.94926e10i 0.257408 + 0.306767i 0.879235 0.476387i \(-0.158054\pi\)
−0.621828 + 0.783154i \(0.713610\pi\)
\(600\) 0 0
\(601\) −1.52122e10 + 5.53680e9i −0.116599 + 0.0424386i −0.399661 0.916663i \(-0.630872\pi\)
0.283062 + 0.959102i \(0.408650\pi\)
\(602\) −4.98893e10 2.88036e10i −0.379858 0.219311i
\(603\) 0 0
\(604\) 3.16097e10 + 5.47497e10i 0.237505 + 0.411371i
\(605\) −3.82214e9 + 4.55504e9i −0.0285289 + 0.0339994i
\(606\) 0 0
\(607\) 6.49937e9 + 3.68597e10i 0.0478758 + 0.271517i 0.999343 0.0362316i \(-0.0115354\pi\)
−0.951468 + 0.307749i \(0.900424\pi\)
\(608\) −2.14892e11 + 3.78912e10i −1.57255 + 0.277283i
\(609\) 0 0
\(610\) 2.77188e9 + 2.32588e9i 0.0200196 + 0.0167984i
\(611\) −7.13266e10 + 4.11804e10i −0.511784 + 0.295479i
\(612\) 0 0
\(613\) 1.05930e11 1.83475e11i 0.750197 1.29938i −0.197530 0.980297i \(-0.563292\pi\)
0.947727 0.319083i \(-0.103375\pi\)
\(614\) 8.54311e9 + 2.34720e10i 0.0601094 + 0.165149i
\(615\) 0 0
\(616\) 5.54431e10 4.65223e10i 0.385057 0.323101i
\(617\) 5.33383e10 1.46546e11i 0.368043 1.01119i −0.608062 0.793889i \(-0.708053\pi\)
0.976105 0.217300i \(-0.0697249\pi\)
\(618\) 0 0
\(619\) 7.73618e9 4.38741e10i 0.0526944 0.298845i −0.947059 0.321060i \(-0.895961\pi\)
0.999753 + 0.0222154i \(0.00707198\pi\)
\(620\) 7.90678e9i 0.0535098i
\(621\) 0 0
\(622\) 4.69245e10 0.313501
\(623\) 1.03552e11 + 1.82591e10i 0.687397 + 0.121207i
\(624\) 0 0
\(625\) −1.41846e11 5.16276e10i −0.929599 0.338346i
\(626\) 1.61398e10 + 1.92347e10i 0.105100 + 0.125253i
\(627\) 0 0
\(628\) −1.42826e11 + 5.19844e10i −0.918266 + 0.334221i
\(629\) −2.44125e11 1.40946e11i −1.55959 0.900429i
\(630\) 0 0
\(631\) 9.52325e10 + 1.64948e11i 0.600714 + 1.04047i 0.992713 + 0.120502i \(0.0384503\pi\)
−0.391999 + 0.919966i \(0.628216\pi\)
\(632\) 1.27684e10 1.52168e10i 0.0800330 0.0953796i
\(633\) 0 0
\(634\) −5.70119e9 3.23330e10i −0.0352865 0.200120i
\(635\) −1.22612e9 + 2.16198e8i −0.00754114 + 0.00132971i
\(636\) 0 0
\(637\) 2.23111e10 + 1.87213e10i 0.135508 + 0.113704i
\(638\) 3.10655e10 1.79357e10i 0.187497 0.108252i
\(639\) 0 0
\(640\) 4.77898e9 8.27744e9i 0.0284850 0.0493374i
\(641\) 1.00079e10 + 2.74965e10i 0.0592804 + 0.162871i 0.965797 0.259298i \(-0.0834911\pi\)
−0.906517 + 0.422169i \(0.861269\pi\)
\(642\) 0 0
\(643\) −8.94608e10 + 7.50665e10i −0.523346 + 0.439139i −0.865796 0.500397i \(-0.833188\pi\)
0.342450 + 0.939536i \(0.388743\pi\)
\(644\) 2.14528e10 5.89412e10i 0.124721 0.342670i
\(645\) 0 0
\(646\) −3.94819e10 + 2.23913e11i −0.226708 + 1.28573i
\(647\) 2.25850e11i 1.28885i 0.764667 + 0.644425i \(0.222903\pi\)
−0.764667 + 0.644425i \(0.777097\pi\)
\(648\) 0 0
\(649\) 1.34518e11 0.758234
\(650\) 4.61257e10 + 8.13321e9i 0.258398 + 0.0455626i
\(651\) 0 0
\(652\) −2.00331e11 7.29146e10i −1.10856 0.403482i
\(653\) −1.81964e11 2.16856e11i −1.00077 1.19267i −0.981227 0.192858i \(-0.938224\pi\)
−0.0195398 0.999809i \(-0.506220\pi\)
\(654\) 0 0
\(655\) −1.66489e10 + 6.05972e9i −0.0904526 + 0.0329221i
\(656\) 2.77953e10 + 1.60476e10i 0.150092 + 0.0866554i
\(657\) 0 0
\(658\) −5.73610e10 9.93521e10i −0.305994 0.529997i
\(659\) −3.52316e10 + 4.19873e10i −0.186806 + 0.222626i −0.851317 0.524652i \(-0.824195\pi\)
0.664511 + 0.747278i \(0.268640\pi\)
\(660\) 0 0
\(661\) −1.81789e10 1.03098e11i −0.0952276 0.540063i −0.994677 0.103038i \(-0.967144\pi\)
0.899450 0.437024i \(-0.143968\pi\)
\(662\) −4.28282e10 + 7.55176e9i −0.222996 + 0.0393202i
\(663\) 0 0
\(664\) 1.61490e10 + 1.35506e10i 0.0830753 + 0.0697085i
\(665\) 1.81753e10 1.04935e10i 0.0929381 0.0536578i
\(666\) 0 0
\(667\) 3.59088e10 6.21959e10i 0.181425 0.314238i
\(668\) −9.24093e10 2.53892e11i −0.464098 1.27510i
\(669\) 0 0
\(670\) 2.47951e9 2.08056e9i 0.0123046 0.0103248i
\(671\) 3.16361e10 8.69196e10i 0.156061 0.428773i
\(672\) 0 0
\(673\) −3.36410e10 + 1.90788e11i −0.163987 + 0.930015i 0.786116 + 0.618079i \(0.212089\pi\)
−0.950103 + 0.311936i \(0.899022\pi\)
\(674\) 1.47059e10i 0.0712609i
\(675\) 0 0
\(676\) −1.12704e11 −0.539699
\(677\) 3.16004e11 + 5.57200e10i 1.50431 + 0.265250i 0.864245 0.503071i \(-0.167796\pi\)
0.640065 + 0.768321i \(0.278908\pi\)
\(678\) 0 0
\(679\) −3.36609e10 1.22516e10i −0.158360 0.0576385i
\(680\) −1.21737e10 1.45080e10i −0.0569360 0.0678536i
\(681\) 0 0
\(682\) 5.89114e10 2.14420e10i 0.272309 0.0991123i
\(683\) 3.37083e11 + 1.94615e11i 1.54901 + 0.894321i 0.998218 + 0.0596780i \(0.0190074\pi\)
0.550792 + 0.834643i \(0.314326\pi\)
\(684\) 0 0
\(685\) −5.25818e9 9.10743e9i −0.0238821 0.0413650i
\(686\) 5.37061e10 6.40044e10i 0.242509 0.289010i
\(687\) 0 0
\(688\) 1.05298e10 + 5.97175e10i 0.0469966 + 0.266531i
\(689\) 5.25865e10 9.27242e9i 0.233344 0.0411449i
\(690\) 0 0
\(691\) 2.64622e11 + 2.22045e11i 1.16069 + 0.973930i 0.999915 0.0130614i \(-0.00415771\pi\)
0.160770 + 0.986992i \(0.448602\pi\)
\(692\) 6.68630e9 3.86034e9i 0.0291583 0.0168345i
\(693\) 0 0
\(694\) 4.85352e10 8.40654e10i 0.209227 0.362392i
\(695\) 9.21265e9 + 2.53116e10i 0.0394862 + 0.108487i
\(696\) 0 0
\(697\) 1.56241e11 1.31102e11i 0.662008 0.555491i
\(698\) −4.02028e10 + 1.10456e11i −0.169369 + 0.465339i
\(699\) 0 0
\(700\) 3.65246e10 2.07141e11i 0.152122 0.862729i
\(701\) 7.99935e9i 0.0331271i 0.999863 + 0.0165635i \(0.00527258\pi\)
−0.999863 + 0.0165635i \(0.994727\pi\)
\(702\) 0 0
\(703\) 3.96905e11 1.62505
\(704\) 1.88847e10 + 3.32989e9i 0.0768812 + 0.0135562i
\(705\) 0 0
\(706\) 1.31880e11 + 4.80005e10i 0.530837 + 0.193209i
\(707\) 1.32277e11 + 1.57641e11i 0.529426 + 0.630945i
\(708\) 0 0
\(709\) −2.58748e11 + 9.41764e10i −1.02398 + 0.372698i −0.798786 0.601616i \(-0.794524\pi\)
−0.225194 + 0.974314i \(0.572302\pi\)
\(710\) 6.83100e9 + 3.94388e9i 0.0268813 + 0.0155199i
\(711\) 0 0
\(712\) 6.68018e10 + 1.15704e11i 0.259937 + 0.450224i
\(713\) 8.06798e10 9.61504e10i 0.312181 0.372043i
\(714\) 0 0
\(715\) 7.47982e8 + 4.24201e9i 0.00286198 + 0.0162311i
\(716\) −1.21990e11 + 2.15102e10i −0.464166 + 0.0818450i
\(717\) 0 0
\(718\) −1.74114e11 1.46099e11i −0.655144 0.549731i
\(719\) −2.56982e11 + 1.48369e11i −0.961585 + 0.555172i −0.896661 0.442719i \(-0.854014\pi\)
−0.0649248 + 0.997890i \(0.520681\pi\)
\(720\) 0 0
\(721\) 7.19864e10 1.24684e11i 0.266385 0.461392i
\(722\) −6.42717e10 1.76585e11i −0.236522 0.649838i
\(723\) 0 0
\(724\) 1.28475e11 1.07803e11i 0.467588 0.392353i
\(725\) 8.23692e10 2.26308e11i 0.298135 0.819119i
\(726\) 0 0
\(727\) −4.88255e10 + 2.76903e11i −0.174787 + 0.991267i 0.763602 + 0.645687i \(0.223429\pi\)
−0.938389 + 0.345580i \(0.887682\pi\)
\(728\) 1.50228e11i 0.534841i
\(729\) 0 0
\(730\) −7.49011e9 −0.0263752
\(731\) 3.79490e11 + 6.69144e10i 1.32902 + 0.234342i
\(732\) 0 0
\(733\) −3.89034e11 1.41597e11i −1.34763 0.490498i −0.435424 0.900225i \(-0.643402\pi\)
−0.912208 + 0.409728i \(0.865624\pi\)
\(734\) 4.14979e10 + 4.94552e10i 0.142969 + 0.170384i
\(735\) 0 0
\(736\) 1.17364e11 4.27169e10i 0.399966 0.145576i
\(737\) −7.16562e10 4.13708e10i −0.242876 0.140224i
\(738\) 0 0
\(739\) −7.10244e10 1.23018e11i −0.238139 0.412468i 0.722042 0.691850i \(-0.243204\pi\)
−0.960180 + 0.279382i \(0.909871\pi\)
\(740\) −9.19893e9 + 1.09629e10i −0.0306768 + 0.0365592i
\(741\) 0 0
\(742\) 1.29157e10 + 7.32487e10i 0.0426092 + 0.241649i
\(743\) −1.74447e11 + 3.07596e10i −0.572410 + 0.100931i −0.452358 0.891836i \(-0.649417\pi\)
−0.120052 + 0.992768i \(0.538306\pi\)
\(744\) 0 0
\(745\) 2.59358e10 + 2.17627e10i 0.0841926 + 0.0706460i
\(746\) −1.86024e11 + 1.07401e11i −0.600639 + 0.346779i
\(747\) 0 0
\(748\) −1.04783e11 + 1.81490e11i −0.334723 + 0.579757i
\(749\) 2.07758e11 + 5.70810e11i 0.660131 + 1.81370i
\(750\) 0 0
\(751\) 1.35565e11 1.13753e11i 0.426175 0.357603i −0.404331 0.914613i \(-0.632496\pi\)
0.830506 + 0.557009i \(0.188051\pi\)
\(752\) −4.13021e10 + 1.13476e11i −0.129152 + 0.354841i
\(753\) 0 0
\(754\) −1.29293e10 + 7.33256e10i −0.0400027 + 0.226866i
\(755\) 1.21073e10i 0.0372615i
\(756\) 0 0
\(757\) −2.71823e11 −0.827755 −0.413878 0.910333i \(-0.635826\pi\)
−0.413878 + 0.910333i \(0.635826\pi\)
\(758\) 1.78261e11 + 3.14322e10i 0.539982 + 0.0952134i
\(759\) 0 0
\(760\) 2.50579e10 + 9.12035e9i 0.0751088 + 0.0273374i
\(761\) −2.67176e11 3.18408e11i −0.796634 0.949391i 0.202922 0.979195i \(-0.434956\pi\)
−0.999556 + 0.0298038i \(0.990512\pi\)
\(762\) 0 0
\(763\) 6.91298e11 2.51612e11i 2.03970 0.742392i
\(764\) 1.13604e11 + 6.55891e10i 0.333441 + 0.192512i
\(765\) 0 0
\(766\) −1.93868e10 3.35789e10i −0.0563107 0.0975330i
\(767\) −1.79476e11 + 2.13891e11i −0.518591 + 0.618033i
\(768\) 0 0
\(769\) −5.30732e10 3.00993e11i −0.151765 0.860699i −0.961684 0.274159i \(-0.911601\pi\)
0.809920 0.586540i \(-0.199511\pi\)
\(770\) −5.90878e9 + 1.04188e9i −0.0168087 + 0.00296383i
\(771\) 0 0
\(772\) 4.74544e9 + 3.98190e9i 0.0133600 + 0.0112104i
\(773\) −1.31306e11 + 7.58097e10i −0.367763 + 0.212328i −0.672481 0.740115i \(-0.734771\pi\)
0.304718 + 0.952443i \(0.401438\pi\)
\(774\) 0 0
\(775\) 2.10450e11 3.64510e11i 0.583368 1.01042i
\(776\) −1.55669e10 4.27696e10i −0.0429294 0.117947i
\(777\) 0 0
\(778\) −6.14340e10 + 5.15492e10i −0.167683 + 0.140703i
\(779\) −9.82193e10 + 2.69855e11i −0.266715 + 0.732793i
\(780\) 0 0
\(781\) 3.50135e10 1.98571e11i 0.0941090 0.533718i
\(782\) 1.30139e11i 0.348001i
\(783\) 0 0
\(784\) 4.27038e10 0.113032
\(785\) 2.86662e10 + 5.05462e9i 0.0754903 + 0.0133110i
\(786\) 0 0
\(787\) −1.69477e11 6.16845e10i −0.441786 0.160797i 0.111543 0.993760i \(-0.464421\pi\)
−0.553329 + 0.832963i \(0.686643\pi\)
\(788\) −1.25741e11 1.49852e11i −0.326116 0.388650i
\(789\) 0 0
\(790\) −1.54742e9 + 5.63215e8i −0.00397283 + 0.00144599i
\(791\) −2.84533e10 1.64275e10i −0.0726820 0.0419630i
\(792\) 0 0
\(793\) 9.59973e10 + 1.66272e11i 0.242754 + 0.420462i
\(794\) −1.12546e11 + 1.34127e11i −0.283171 + 0.337470i
\(795\) 0 0
\(796\) −9.87436e9 5.60003e10i −0.0245956 0.139488i
\(797\) 5.56877e11 9.81924e10i 1.38015 0.243357i 0.566187 0.824277i \(-0.308418\pi\)
0.813961 + 0.580919i \(0.197307\pi\)
\(798\) 0 0
\(799\) 5.87859e11 + 4.93272e11i 1.44240 + 1.21032i
\(800\) 3.62711e11 2.09412e11i 0.885526 0.511259i
\(801\) 0 0
\(802\) 1.44108e11 2.49602e11i 0.348329 0.603324i
\(803\) 6.54864e10 + 1.79922e11i 0.157503 + 0.432736i
\(804\) 0 0
\(805\) −9.20204e9 + 7.72143e9i −0.0219129 + 0.0183871i
\(806\) −4.45063e10 + 1.22280e11i −0.105459 + 0.289745i
\(807\) 0 0
\(808\) −4.54041e10 + 2.57500e11i −0.106525 + 0.604131i
\(809\) 5.05250e10i 0.117954i −0.998259 0.0589769i \(-0.981216\pi\)
0.998259 0.0589769i \(-0.0187838\pi\)
\(810\) 0 0
\(811\) 3.28251e11 0.758791 0.379396 0.925235i \(-0.376132\pi\)
0.379396 + 0.925235i \(0.376132\pi\)
\(812\) 3.29291e11 + 5.80628e10i 0.757452 + 0.133559i
\(813\) 0 0
\(814\) −1.06628e11 3.88092e10i −0.242869 0.0883970i
\(815\) 2.62439e10 + 3.12762e10i 0.0594836 + 0.0708898i
\(816\) 0 0
\(817\) −5.09847e11 + 1.85569e11i −1.14433 + 0.416503i
\(818\) −7.51378e10 4.33808e10i −0.167821 0.0968913i
\(819\) 0 0
\(820\) −5.17724e9 8.96724e9i −0.0114510 0.0198337i
\(821\) 4.35639e11 5.19174e11i 0.958857 1.14272i −0.0308373 0.999524i \(-0.509817\pi\)
0.989694 0.143197i \(-0.0457382\pi\)
\(822\) 0 0
\(823\) 1.04516e11 + 5.92737e11i 0.227815 + 1.29200i 0.857231 + 0.514933i \(0.172183\pi\)
−0.629416 + 0.777069i \(0.716706\pi\)
\(824\) 1.80153e11 3.17658e10i 0.390780 0.0689051i
\(825\) 0 0
\(826\) −2.97933e11 2.49995e11i −0.640027 0.537047i
\(827\) −3.13017e11 + 1.80720e11i −0.669184 + 0.386353i −0.795767 0.605603i \(-0.792932\pi\)
0.126584 + 0.991956i \(0.459599\pi\)
\(828\) 0 0
\(829\) −1.85216e11 + 3.20803e11i −0.392157 + 0.679235i −0.992734 0.120332i \(-0.961604\pi\)
0.600577 + 0.799567i \(0.294938\pi\)
\(830\) −5.97716e8 1.64221e9i −0.00125946 0.00346032i
\(831\) 0 0
\(832\) −3.04909e10 + 2.55849e10i −0.0636322 + 0.0533938i
\(833\) 9.28149e10 2.55007e11i 0.192769 0.529629i
\(834\) 0 0
\(835\) −8.98527e9 + 5.09580e10i −0.0184835 + 0.104825i
\(836\) 2.95071e11i 0.604090i
\(837\) 0 0
\(838\) −2.28308e11 −0.462962
\(839\) −4.93790e11 8.70685e10i −0.996539 0.175717i −0.348488 0.937313i \(-0.613305\pi\)
−0.648051 + 0.761597i \(0.724416\pi\)
\(840\) 0 0
\(841\) −1.10319e11 4.01528e10i −0.220529 0.0802660i
\(842\) −2.59482e11 3.09238e11i −0.516248 0.615241i
\(843\) 0 0
\(844\) −6.17892e11 + 2.24894e11i −1.21771 + 0.443209i
\(845\) 1.86925e10 + 1.07921e10i 0.0366640 + 0.0211679i
\(846\) 0 0
\(847\) −2.19737e11 3.80595e11i −0.426942 0.739486i
\(848\) 5.03256e10 5.99758e10i 0.0973209 0.115982i
\(849\) 0 0
\(850\) −7.57810e10 4.29775e11i −0.145173 0.823315i
\(851\) −2.23727e11 + 3.94491e10i −0.426580 + 0.0752176i
\(852\) 0 0
\(853\) −1.25556e11 1.05354e11i −0.237160 0.199001i 0.516460 0.856312i \(-0.327250\pi\)
−0.753620 + 0.657310i \(0.771694\pi\)
\(854\) −2.31604e11 + 1.33716e11i −0.435425 + 0.251393i
\(855\) 0 0
\(856\) −3.85910e11 + 6.68415e11i −0.718771 + 1.24495i
\(857\) −2.24707e11 6.17377e11i −0.416575 1.14453i −0.953630 0.300982i \(-0.902685\pi\)
0.537055 0.843547i \(-0.319537\pi\)
\(858\) 0 0
\(859\) −2.05655e11 + 1.72565e11i −0.377717 + 0.316943i −0.811806 0.583928i \(-0.801515\pi\)
0.434088 + 0.900870i \(0.357071\pi\)
\(860\) 6.69097e9 1.83833e10i 0.0122319 0.0336070i
\(861\) 0 0
\(862\) 4.05330e9 2.29874e10i 0.00734141 0.0416352i
\(863\) 7.75412e11i 1.39794i −0.715150 0.698971i \(-0.753642\pi\)
0.715150 0.698971i \(-0.246358\pi\)
\(864\) 0 0
\(865\) −1.47861e9 −0.00264112
\(866\) −5.15738e11 9.09385e10i −0.916975 0.161687i
\(867\) 0 0
\(868\) 5.49136e11 + 1.99869e11i 0.967388 + 0.352101i
\(869\) 2.70584e10 + 3.22469e10i 0.0474485 + 0.0565469i
\(870\) 0 0
\(871\) 1.61386e11 5.87398e10i 0.280410 0.102061i
\(872\) 8.09506e11 + 4.67368e11i 1.40008 + 0.808339i
\(873\) 0 0
\(874\) 9.16184e10 + 1.58688e11i 0.157014 + 0.271955i
\(875\) −5.18789e10 + 6.18268e10i −0.0885031 + 0.105474i
\(876\) 0 0
\(877\) 5.75848e10 + 3.26579e11i 0.0973440 + 0.552065i 0.994004 + 0.109345i \(0.0348754\pi\)
−0.896660 + 0.442720i \(0.854014\pi\)
\(878\) −3.94698e11 + 6.95958e10i −0.664181 + 0.117113i
\(879\) 0 0
\(880\) 4.83809e9 + 4.05964e9i 0.00806758 + 0.00676950i
\(881\) −3.43576e11 + 1.98364e11i −0.570320 + 0.329275i −0.757277 0.653094i \(-0.773471\pi\)
0.186957 + 0.982368i \(0.440138\pi\)
\(882\) 0 0
\(883\) −2.25631e11 + 3.90804e11i −0.371155 + 0.642860i −0.989744 0.142856i \(-0.954372\pi\)
0.618588 + 0.785715i \(0.287705\pi\)
\(884\) −1.48775e11 4.08757e11i −0.243625 0.669354i
\(885\) 0 0
\(886\) 1.82042e11 1.52751e11i 0.295417 0.247885i
\(887\) −1.74390e11 + 4.79133e11i −0.281726 + 0.774037i 0.715431 + 0.698684i \(0.246231\pi\)
−0.997157 + 0.0753529i \(0.975992\pi\)
\(888\) 0 0
\(889\) 1.59788e10 9.06204e10i 0.0255822 0.145084i
\(890\) 1.10757e10i 0.0176527i
\(891\) 0 0
\(892\) 7.98779e10 0.126173
\(893\) −1.06408e12 1.87627e11i −1.67328 0.295045i
\(894\) 0 0
\(895\) 2.22924e10 + 8.11377e9i 0.0347428 + 0.0126453i
\(896\) 4.54074e11 + 5.41145e11i 0.704523 + 0.839617i
\(897\) 0 0
\(898\) 3.76318e11 1.36969e11i 0.578695 0.210628i
\(899\) 5.79459e11 + 3.34551e11i 0.887123 + 0.512181i
\(900\) 0 0
\(901\) −2.48766e11 4.30875e11i −0.377478 0.653812i
\(902\) 5.27727e10 6.28921e10i 0.0797229 0.0950101i
\(903\) 0 0
\(904\) −7.24907e9 4.11115e10i −0.0108545 0.0615587i
\(905\) −3.16310e10 + 5.57740e9i −0.0471540 + 0.00831452i
\(906\) 0 0
\(907\) −8.86132e11 7.43553e11i −1.30939 1.09871i −0.988440 0.151614i \(-0.951553\pi\)
−0.320952 0.947096i \(-0.604003\pi\)
\(908\) −4.49630e11 + 2.59594e11i −0.661473 + 0.381901i
\(909\) 0 0
\(910\) 6.22692e9 1.07853e10i 0.00908046 0.0157278i
\(911\) 1.13732e11 + 3.12476e11i 0.165124 + 0.453673i 0.994465 0.105069i \(-0.0335063\pi\)
−0.829341 + 0.558742i \(0.811284\pi\)
\(912\) 0 0
\(913\) −3.42223e10 + 2.87159e10i −0.0492522 + 0.0413275i
\(914\) 2.82053e10 7.74933e10i 0.0404153 0.111040i
\(915\) 0 0
\(916\) 1.45962e11 8.27792e11i 0.207328 1.17582i
\(917\) 1.30947e12i 1.85190i
\(918\) 0 0
\(919\) −1.61529e11 −0.226459 −0.113229 0.993569i \(-0.536120\pi\)
−0.113229 + 0.993569i \(0.536120\pi\)
\(920\) −1.50311e10 2.65039e9i −0.0209817 0.00369964i
\(921\) 0 0
\(922\) 1.20094e11 + 4.37107e10i 0.166187 + 0.0604872i
\(923\) 2.69023e11 + 3.20609e11i 0.370666 + 0.441742i
\(924\) 0 0
\(925\) −7.15872e11 + 2.60556e11i −0.977842 + 0.355905i
\(926\) 1.55820e11 + 8.99629e10i 0.211924 + 0.122354i
\(927\) 0 0
\(928\) 3.32899e11 + 5.76599e11i 0.448871 + 0.777467i
\(929\) −4.01736e11 + 4.78770e11i −0.539359 + 0.642783i −0.965044 0.262088i \(-0.915589\pi\)
0.425685 + 0.904872i \(0.360033\pi\)
\(930\) 0 0
\(931\) 6.63500e10 + 3.76290e11i 0.0883166 + 0.500868i
\(932\) −5.54767e11 + 9.78203e10i −0.735270 + 0.129648i
\(933\) 0 0
\(934\) −2.18566e11 1.83399e11i −0.287207 0.240996i
\(935\) 3.47576e10 2.00673e10i 0.0454782 0.0262569i
\(936\) 0 0
\(937\) −2.07728e10 + 3.59796e10i −0.0269487 + 0.0466765i −0.879185 0.476480i \(-0.841912\pi\)
0.852237 + 0.523157i \(0.175246\pi\)
\(938\) 8.18197e10 + 2.24798e11i 0.105693 + 0.290389i
\(939\) 0 0
\(940\) 2.98443e10 2.50423e10i 0.0382252 0.0320747i
\(941\) 1.12104e11 3.08003e11i 0.142976 0.392822i −0.847449 0.530877i \(-0.821863\pi\)
0.990425 + 0.138055i \(0.0440850\pi\)
\(942\) 0 0
\(943\) 2.85428e10 1.61874e11i 0.0360952 0.204706i
\(944\) 4.09391e11i 0.515526i
\(945\) 0 0
\(946\) 1.55114e11 0.193681
\(947\) −1.83765e11 3.24028e10i −0.228488 0.0402886i 0.0582317 0.998303i \(-0.481454\pi\)
−0.286720 + 0.958014i \(0.592565\pi\)
\(948\) 0 0
\(949\) −3.73458e11 1.35928e11i −0.460445 0.167588i
\(950\) 3.94969e11 + 4.70705e11i 0.484918 + 0.577902i
\(951\) 0 0
\(952\) 1.31533e12 4.78741e11i 1.60135 0.582845i
\(953\) −2.43325e11 1.40483e11i −0.294995 0.170315i 0.345197 0.938530i \(-0.387812\pi\)
−0.640192 + 0.768215i \(0.721145\pi\)
\(954\) 0 0
\(955\) −1.25611e10 2.17565e10i −0.0151013 0.0261563i
\(956\) −2.30701e11 + 2.74938e11i −0.276196 + 0.329157i
\(957\) 0 0
\(958\) 1.20396e11 + 6.82800e11i 0.142939 + 0.810647i
\(959\) 7.65439e11 1.34968e11i 0.904974 0.159571i
\(960\) 0 0
\(961\) 2.42449e11 + 2.03439e11i 0.284268 + 0.238529i
\(962\) 2.03972e11 1.17763e11i 0.238161 0.137502i
\(963\) 0 0
\(964\) 4.14848e11 7.18537e11i 0.480375 0.832034i
\(965\) −4.05762e8 1.11482e9i −0.000467910 0.00128557i
\(966\) 0 0
\(967\) 3.59916e11 3.02005e11i 0.411619 0.345389i −0.413345 0.910574i \(-0.635640\pi\)
0.824964 + 0.565185i \(0.191195\pi\)
\(968\) 1.90983e11 5.24721e11i 0.217517 0.597622i
\(969\) 0 0
\(970\) −6.55198e8 + 3.71582e9i −0.000740092 + 0.00419727i
\(971\) 1.13211e12i 1.27354i −0.771056 0.636768i \(-0.780271\pi\)
0.771056 0.636768i \(-0.219729\pi\)
\(972\) 0 0
\(973\) −1.99080e12 −2.22114
\(974\) −1.58307e11 2.79138e10i −0.175899 0.0310158i
\(975\) 0 0
\(976\) 2.64529e11 + 9.62808e10i 0.291524 + 0.106106i
\(977\) 1.01318e11 + 1.20746e11i 0.111201 + 0.132524i 0.818774 0.574117i \(-0.194654\pi\)
−0.707573 + 0.706640i \(0.750210\pi\)
\(978\) 0 0
\(979\) −2.66053e11 + 9.68355e10i −0.289626 + 0.105415i
\(980\) −1.19312e10 6.88849e9i −0.0129354 0.00746827i
\(981\) 0 0
\(982\) 9.15746e10 + 1.58612e11i 0.0984757 + 0.170565i
\(983\) −2.32916e11 + 2.77578e11i −0.249451 + 0.297284i −0.876210 0.481929i \(-0.839936\pi\)
0.626760 + 0.779213i \(0.284381\pi\)
\(984\) 0 0
\(985\) 6.50544e9 + 3.68942e10i 0.00691085 + 0.0391934i
\(986\) 6.83210e11 1.20468e11i 0.722847 0.127457i
\(987\) 0 0
\(988\) 4.69178e11 + 3.93687e11i 0.492391 + 0.413165i
\(989\) 2.68946e11 1.55276e11i 0.281113 0.162300i
\(990\) 0 0
\(991\) 2.02286e11 3.50370e11i 0.209735 0.363272i −0.741896 0.670515i \(-0.766073\pi\)
0.951631 + 0.307243i \(0.0994064\pi\)
\(992\) 3.97980e11 + 1.09344e12i 0.410974 + 1.12914i
\(993\) 0 0
\(994\) −4.46582e11 + 3.74727e11i −0.457463 + 0.383857i
\(995\) −3.72467e9 + 1.02334e10i −0.00380010 + 0.0104407i
\(996\) 0 0
\(997\) 2.68798e11 1.52443e12i 0.272048 1.54286i −0.476137 0.879371i \(-0.657963\pi\)
0.748185 0.663490i \(-0.230926\pi\)
\(998\) 1.97145e11i 0.198730i
\(999\) 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 81.9.f.a.8.14 138
3.2 odd 2 27.9.f.a.2.10 138
27.13 even 9 27.9.f.a.14.10 yes 138
27.14 odd 18 inner 81.9.f.a.71.14 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.9.f.a.2.10 138 3.2 odd 2
27.9.f.a.14.10 yes 138 27.13 even 9
81.9.f.a.8.14 138 1.1 even 1 trivial
81.9.f.a.71.14 138 27.14 odd 18 inner