Properties

Label 84.9.p.b.65.9
Level $84$
Weight $9$
Character 84.65
Analytic conductor $34.220$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [84,9,Mod(53,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.53");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(34.2198032451\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.9
Character \(\chi\) \(=\) 84.65
Dual form 84.9.p.b.53.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.75427 - 80.7953i) q^{3} +(-701.327 - 404.911i) q^{5} +(1952.36 + 1397.53i) q^{7} +(-6494.78 + 929.836i) q^{9} +O(q^{10})\) \(q+(-5.75427 - 80.7953i) q^{3} +(-701.327 - 404.911i) q^{5} +(1952.36 + 1397.53i) q^{7} +(-6494.78 + 929.836i) q^{9} +(-1114.61 + 643.521i) q^{11} -24570.2 q^{13} +(-28679.3 + 58993.9i) q^{15} +(-35201.9 + 20323.8i) q^{17} +(-39959.6 + 69212.1i) q^{19} +(101680. - 165783. i) q^{21} +(293149. + 169249. i) q^{23} +(132594. + 229659. i) q^{25} +(112499. + 519397. i) q^{27} -1.09251e6i q^{29} +(521266. + 902859. i) q^{31} +(58407.3 + 86352.4i) q^{33} +(-803366. - 1.77066e6i) q^{35} +(-184949. + 320341. i) q^{37} +(141384. + 1.98516e6i) q^{39} -2.77625e6i q^{41} +4.17741e6 q^{43} +(4.93146e6 + 1.97769e6i) q^{45} +(7.07575e6 + 4.08519e6i) q^{47} +(1.85862e6 + 5.45697e6i) q^{49} +(1.84463e6 + 2.72720e6i) q^{51} +(6.31437e6 - 3.64560e6i) q^{53} +1.04228e6 q^{55} +(5.82196e6 + 2.83029e6i) q^{57} +(-1.54219e7 + 8.90382e6i) q^{59} +(-1.05761e7 + 1.83184e7i) q^{61} +(-1.39796e7 - 7.26128e6i) q^{63} +(1.72318e7 + 9.94876e6i) q^{65} +(5.90653e6 + 1.02304e7i) q^{67} +(1.19877e7 - 2.46589e7i) q^{69} -2.35033e6i q^{71} +(1.95490e7 + 3.38599e7i) q^{73} +(1.77924e7 - 1.20345e7i) q^{75} +(-3.07546e6 - 301319. i) q^{77} +(9.37450e6 - 1.62371e7i) q^{79} +(4.13175e7 - 1.20782e7i) q^{81} -3.15449e7i q^{83} +3.29174e7 q^{85} +(-8.82697e7 + 6.28659e6i) q^{87} +(7.65369e6 + 4.41886e6i) q^{89} +(-4.79699e7 - 3.43377e7i) q^{91} +(6.99473e7 - 4.73111e7i) q^{93} +(5.60495e7 - 3.23602e7i) q^{95} -1.17592e8 q^{97} +(6.64078e6 - 5.21593e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9} - 55464 q^{13} + 68482 q^{15} + 311690 q^{19} - 172343 q^{21} + 1766792 q^{25} - 3451932 q^{27} + 31596 q^{31} + 1874885 q^{33} - 1853482 q^{37} + 11217526 q^{39} - 13372600 q^{43} - 527785 q^{45} - 12653462 q^{49} - 1103461 q^{51} + 71577224 q^{55} - 17195214 q^{57} - 21761970 q^{61} + 21945045 q^{63} - 26337350 q^{67} - 5588722 q^{69} + 41115682 q^{73} - 17971730 q^{75} - 120916932 q^{79} - 24550133 q^{81} + 139250060 q^{85} - 16321046 q^{87} + 345074940 q^{91} + 25774675 q^{93} - 707216948 q^{97} - 94510994 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −5.75427 80.7953i −0.0710403 0.997473i
\(4\) 0 0
\(5\) −701.327 404.911i −1.12212 0.647858i −0.180181 0.983634i \(-0.557668\pi\)
−0.941942 + 0.335776i \(0.891002\pi\)
\(6\) 0 0
\(7\) 1952.36 + 1397.53i 0.813144 + 0.582062i
\(8\) 0 0
\(9\) −6494.78 + 929.836i −0.989907 + 0.141722i
\(10\) 0 0
\(11\) −1114.61 + 643.521i −0.0761295 + 0.0439534i −0.537582 0.843212i \(-0.680662\pi\)
0.461452 + 0.887165i \(0.347329\pi\)
\(12\) 0 0
\(13\) −24570.2 −0.860272 −0.430136 0.902764i \(-0.641534\pi\)
−0.430136 + 0.902764i \(0.641534\pi\)
\(14\) 0 0
\(15\) −28679.3 + 58993.9i −0.566505 + 1.16531i
\(16\) 0 0
\(17\) −35201.9 + 20323.8i −0.421474 + 0.243338i −0.695708 0.718325i \(-0.744909\pi\)
0.274234 + 0.961663i \(0.411576\pi\)
\(18\) 0 0
\(19\) −39959.6 + 69212.1i −0.306625 + 0.531090i −0.977622 0.210370i \(-0.932533\pi\)
0.670997 + 0.741460i \(0.265866\pi\)
\(20\) 0 0
\(21\) 101680. 165783.i 0.522825 0.852440i
\(22\) 0 0
\(23\) 293149. + 169249.i 1.04755 + 0.604806i 0.921964 0.387277i \(-0.126584\pi\)
0.125590 + 0.992082i \(0.459917\pi\)
\(24\) 0 0
\(25\) 132594. + 229659.i 0.339440 + 0.587927i
\(26\) 0 0
\(27\) 112499. + 519397.i 0.211687 + 0.977338i
\(28\) 0 0
\(29\) 1.09251e6i 1.54466i −0.635221 0.772331i \(-0.719091\pi\)
0.635221 0.772331i \(-0.280909\pi\)
\(30\) 0 0
\(31\) 521266. + 902859.i 0.564433 + 0.977627i 0.997102 + 0.0760739i \(0.0242385\pi\)
−0.432669 + 0.901553i \(0.642428\pi\)
\(32\) 0 0
\(33\) 58407.3 + 86352.4i 0.0492506 + 0.0728147i
\(34\) 0 0
\(35\) −803366. 1.77066e6i −0.535354 1.17995i
\(36\) 0 0
\(37\) −184949. + 320341.i −0.0986837 + 0.170925i −0.911140 0.412097i \(-0.864797\pi\)
0.812456 + 0.583022i \(0.198130\pi\)
\(38\) 0 0
\(39\) 141384. + 1.98516e6i 0.0611140 + 0.858099i
\(40\) 0 0
\(41\) 2.77625e6i 0.982480i −0.871024 0.491240i \(-0.836544\pi\)
0.871024 0.491240i \(-0.163456\pi\)
\(42\) 0 0
\(43\) 4.17741e6 1.22189 0.610946 0.791672i \(-0.290789\pi\)
0.610946 + 0.791672i \(0.290789\pi\)
\(44\) 0 0
\(45\) 4.93146e6 + 1.97769e6i 1.20261 + 0.482290i
\(46\) 0 0
\(47\) 7.07575e6 + 4.08519e6i 1.45004 + 0.837184i 0.998483 0.0550566i \(-0.0175339\pi\)
0.451561 + 0.892240i \(0.350867\pi\)
\(48\) 0 0
\(49\) 1.85862e6 + 5.45697e6i 0.322408 + 0.946601i
\(50\) 0 0
\(51\) 1.84463e6 + 2.72720e6i 0.272665 + 0.403122i
\(52\) 0 0
\(53\) 6.31437e6 3.64560e6i 0.800251 0.462025i −0.0433076 0.999062i \(-0.513790\pi\)
0.843559 + 0.537036i \(0.180456\pi\)
\(54\) 0 0
\(55\) 1.04228e6 0.113902
\(56\) 0 0
\(57\) 5.82196e6 + 2.83029e6i 0.551531 + 0.268121i
\(58\) 0 0
\(59\) −1.54219e7 + 8.90382e6i −1.27271 + 0.734799i −0.975497 0.220013i \(-0.929390\pi\)
−0.297212 + 0.954812i \(0.596057\pi\)
\(60\) 0 0
\(61\) −1.05761e7 + 1.83184e7i −0.763848 + 1.32302i 0.177006 + 0.984210i \(0.443359\pi\)
−0.940854 + 0.338813i \(0.889974\pi\)
\(62\) 0 0
\(63\) −1.39796e7 7.26128e6i −0.887428 0.460947i
\(64\) 0 0
\(65\) 1.72318e7 + 9.94876e6i 0.965331 + 0.557334i
\(66\) 0 0
\(67\) 5.90653e6 + 1.02304e7i 0.293112 + 0.507684i 0.974544 0.224197i \(-0.0719759\pi\)
−0.681432 + 0.731881i \(0.738643\pi\)
\(68\) 0 0
\(69\) 1.19877e7 2.46589e7i 0.528859 1.08787i
\(70\) 0 0
\(71\) 2.35033e6i 0.0924903i −0.998930 0.0462451i \(-0.985274\pi\)
0.998930 0.0462451i \(-0.0147255\pi\)
\(72\) 0 0
\(73\) 1.95490e7 + 3.38599e7i 0.688388 + 1.19232i 0.972359 + 0.233490i \(0.0750146\pi\)
−0.283971 + 0.958833i \(0.591652\pi\)
\(74\) 0 0
\(75\) 1.77924e7 1.20345e7i 0.562327 0.380348i
\(76\) 0 0
\(77\) −3.07546e6 301319.i −0.0874878 0.00857164i
\(78\) 0 0
\(79\) 9.37450e6 1.62371e7i 0.240680 0.416870i −0.720228 0.693737i \(-0.755963\pi\)
0.960908 + 0.276867i \(0.0892962\pi\)
\(80\) 0 0
\(81\) 4.13175e7 1.20782e7i 0.959830 0.280582i
\(82\) 0 0
\(83\) 3.15449e7i 0.664687i −0.943158 0.332343i \(-0.892161\pi\)
0.943158 0.332343i \(-0.107839\pi\)
\(84\) 0 0
\(85\) 3.29174e7 0.630594
\(86\) 0 0
\(87\) −8.82697e7 + 6.28659e6i −1.54076 + 0.109733i
\(88\) 0 0
\(89\) 7.65369e6 + 4.41886e6i 0.121986 + 0.0704287i 0.559751 0.828661i \(-0.310897\pi\)
−0.437765 + 0.899089i \(0.644230\pi\)
\(90\) 0 0
\(91\) −4.79699e7 3.43377e7i −0.699526 0.500732i
\(92\) 0 0
\(93\) 6.99473e7 4.73111e7i 0.935059 0.632458i
\(94\) 0 0
\(95\) 5.60495e7 3.23602e7i 0.688141 0.397299i
\(96\) 0 0
\(97\) −1.17592e8 −1.32828 −0.664141 0.747607i \(-0.731202\pi\)
−0.664141 + 0.747607i \(0.731202\pi\)
\(98\) 0 0
\(99\) 6.64078e6 5.21593e6i 0.0691319 0.0542989i
\(100\) 0 0
\(101\) −1.32453e8 + 7.64720e7i −1.27285 + 0.734880i −0.975523 0.219895i \(-0.929428\pi\)
−0.297327 + 0.954776i \(0.596095\pi\)
\(102\) 0 0
\(103\) −3.91745e7 + 6.78523e7i −0.348061 + 0.602859i −0.985905 0.167306i \(-0.946493\pi\)
0.637844 + 0.770165i \(0.279826\pi\)
\(104\) 0 0
\(105\) −1.38438e8 + 7.50971e7i −1.13893 + 0.617826i
\(106\) 0 0
\(107\) −8.92504e7 5.15288e7i −0.680887 0.393110i 0.119302 0.992858i \(-0.461934\pi\)
−0.800189 + 0.599748i \(0.795268\pi\)
\(108\) 0 0
\(109\) −5.43401e7 9.41198e7i −0.384959 0.666768i 0.606805 0.794851i \(-0.292451\pi\)
−0.991763 + 0.128083i \(0.959118\pi\)
\(110\) 0 0
\(111\) 2.69463e7 + 1.30997e7i 0.177504 + 0.0862918i
\(112\) 0 0
\(113\) 2.58454e7i 0.158514i −0.996854 0.0792572i \(-0.974745\pi\)
0.996854 0.0792572i \(-0.0252548\pi\)
\(114\) 0 0
\(115\) −1.37062e8 2.37398e8i −0.783656 1.35733i
\(116\) 0 0
\(117\) 1.59578e8 2.28463e7i 0.851589 0.121919i
\(118\) 0 0
\(119\) −9.71300e7 9.51633e6i −0.484357 0.0474550i
\(120\) 0 0
\(121\) −1.06351e8 + 1.84206e8i −0.496136 + 0.859333i
\(122\) 0 0
\(123\) −2.24308e8 + 1.59753e7i −0.979998 + 0.0697957i
\(124\) 0 0
\(125\) 1.01582e8i 0.416081i
\(126\) 0 0
\(127\) 8.21235e7 0.315684 0.157842 0.987464i \(-0.449546\pi\)
0.157842 + 0.987464i \(0.449546\pi\)
\(128\) 0 0
\(129\) −2.40379e7 3.37515e8i −0.0868037 1.21881i
\(130\) 0 0
\(131\) 3.76294e8 + 2.17254e8i 1.27774 + 0.737703i 0.976432 0.215824i \(-0.0692437\pi\)
0.301307 + 0.953527i \(0.402577\pi\)
\(132\) 0 0
\(133\) −1.74742e8 + 7.92821e7i −0.558457 + 0.253378i
\(134\) 0 0
\(135\) 1.31411e8 4.09819e8i 0.395637 1.23384i
\(136\) 0 0
\(137\) −7.54413e7 + 4.35561e7i −0.214154 + 0.123642i −0.603241 0.797559i \(-0.706124\pi\)
0.389086 + 0.921201i \(0.372791\pi\)
\(138\) 0 0
\(139\) 2.42039e8 0.648376 0.324188 0.945993i \(-0.394909\pi\)
0.324188 + 0.945993i \(0.394909\pi\)
\(140\) 0 0
\(141\) 2.89348e8 5.95195e8i 0.732057 1.50585i
\(142\) 0 0
\(143\) 2.73863e7 1.58115e7i 0.0654921 0.0378119i
\(144\) 0 0
\(145\) −4.42369e8 + 7.66206e8i −1.00072 + 1.73330i
\(146\) 0 0
\(147\) 4.30203e8 1.81568e8i 0.921305 0.388840i
\(148\) 0 0
\(149\) −5.16102e8 2.97971e8i −1.04711 0.604546i −0.125268 0.992123i \(-0.539979\pi\)
−0.921838 + 0.387577i \(0.873312\pi\)
\(150\) 0 0
\(151\) 3.63368e8 + 6.29373e8i 0.698939 + 1.21060i 0.968835 + 0.247709i \(0.0796776\pi\)
−0.269895 + 0.962890i \(0.586989\pi\)
\(152\) 0 0
\(153\) 2.09731e8 1.64731e8i 0.382733 0.300614i
\(154\) 0 0
\(155\) 8.44265e8i 1.46269i
\(156\) 0 0
\(157\) 2.30584e8 + 3.99382e8i 0.379516 + 0.657340i 0.990992 0.133922i \(-0.0427573\pi\)
−0.611476 + 0.791263i \(0.709424\pi\)
\(158\) 0 0
\(159\) −3.30882e8 4.89194e8i −0.517708 0.765407i
\(160\) 0 0
\(161\) 3.35800e8 + 7.40120e8i 0.499778 + 1.10154i
\(162\) 0 0
\(163\) −3.48066e8 + 6.02868e8i −0.493073 + 0.854028i −0.999968 0.00798005i \(-0.997460\pi\)
0.506895 + 0.862008i \(0.330793\pi\)
\(164\) 0 0
\(165\) −5.99753e6 8.42110e7i −0.00809165 0.113614i
\(166\) 0 0
\(167\) 1.02172e9i 1.31361i 0.754060 + 0.656805i \(0.228093\pi\)
−0.754060 + 0.656805i \(0.771907\pi\)
\(168\) 0 0
\(169\) −2.12034e8 −0.259931
\(170\) 0 0
\(171\) 1.95173e8 4.86673e8i 0.228263 0.569185i
\(172\) 0 0
\(173\) 5.61654e8 + 3.24271e8i 0.627024 + 0.362013i 0.779599 0.626279i \(-0.215423\pi\)
−0.152575 + 0.988292i \(0.548756\pi\)
\(174\) 0 0
\(175\) −6.20850e7 + 6.33680e8i −0.0661964 + 0.675644i
\(176\) 0 0
\(177\) 8.08129e8 + 1.19478e9i 0.823356 + 1.21729i
\(178\) 0 0
\(179\) 1.17623e9 6.79096e8i 1.14572 0.661483i 0.197882 0.980226i \(-0.436594\pi\)
0.947841 + 0.318743i \(0.103261\pi\)
\(180\) 0 0
\(181\) −4.87644e8 −0.454348 −0.227174 0.973854i \(-0.572949\pi\)
−0.227174 + 0.973854i \(0.572949\pi\)
\(182\) 0 0
\(183\) 1.54090e9 + 7.49092e8i 1.37394 + 0.667930i
\(184\) 0 0
\(185\) 2.59420e8 1.49776e8i 0.221471 0.127866i
\(186\) 0 0
\(187\) 2.61576e7 4.53064e7i 0.0213911 0.0370504i
\(188\) 0 0
\(189\) −5.06235e8 + 1.17127e9i −0.396739 + 0.917931i
\(190\) 0 0
\(191\) −1.52710e9 8.81672e8i −1.14745 0.662481i −0.199186 0.979962i \(-0.563830\pi\)
−0.948265 + 0.317481i \(0.897163\pi\)
\(192\) 0 0
\(193\) 1.13004e9 + 1.95729e9i 0.814450 + 1.41067i 0.909722 + 0.415218i \(0.136295\pi\)
−0.0952722 + 0.995451i \(0.530372\pi\)
\(194\) 0 0
\(195\) 7.04658e8 1.44949e9i 0.487349 1.00249i
\(196\) 0 0
\(197\) 4.26915e7i 0.0283450i 0.999900 + 0.0141725i \(0.00451140\pi\)
−0.999900 + 0.0141725i \(0.995489\pi\)
\(198\) 0 0
\(199\) −4.76158e8 8.24730e8i −0.303626 0.525895i 0.673329 0.739343i \(-0.264864\pi\)
−0.976954 + 0.213448i \(0.931531\pi\)
\(200\) 0 0
\(201\) 7.92582e8 5.36089e8i 0.485579 0.328437i
\(202\) 0 0
\(203\) 1.52682e9 2.13297e9i 0.899089 1.25603i
\(204\) 0 0
\(205\) −1.12414e9 + 1.94706e9i −0.636507 + 1.10246i
\(206\) 0 0
\(207\) −2.06131e9 8.26657e8i −1.12269 0.450240i
\(208\) 0 0
\(209\) 1.02860e8i 0.0539088i
\(210\) 0 0
\(211\) 1.45001e9 0.731547 0.365774 0.930704i \(-0.380804\pi\)
0.365774 + 0.930704i \(0.380804\pi\)
\(212\) 0 0
\(213\) −1.89896e8 + 1.35244e7i −0.0922566 + 0.00657054i
\(214\) 0 0
\(215\) −2.92973e9 1.69148e9i −1.37111 0.791613i
\(216\) 0 0
\(217\) −2.44075e8 + 2.49119e9i −0.110074 + 1.12349i
\(218\) 0 0
\(219\) 2.62323e9 1.77431e9i 1.14041 0.771352i
\(220\) 0 0
\(221\) 8.64919e8 4.99361e8i 0.362582 0.209337i
\(222\) 0 0
\(223\) −1.59542e9 −0.645143 −0.322572 0.946545i \(-0.604547\pi\)
−0.322572 + 0.946545i \(0.604547\pi\)
\(224\) 0 0
\(225\) −1.07471e9 1.36829e9i −0.419335 0.533886i
\(226\) 0 0
\(227\) −3.60754e9 + 2.08281e9i −1.35865 + 0.784417i −0.989442 0.144930i \(-0.953704\pi\)
−0.369208 + 0.929347i \(0.620371\pi\)
\(228\) 0 0
\(229\) 9.61610e8 1.66556e9i 0.349669 0.605644i −0.636522 0.771259i \(-0.719627\pi\)
0.986191 + 0.165615i \(0.0529608\pi\)
\(230\) 0 0
\(231\) −6.64815e6 + 2.50217e8i −0.00233482 + 0.0878757i
\(232\) 0 0
\(233\) 3.38848e9 + 1.95634e9i 1.14969 + 0.663774i 0.948812 0.315842i \(-0.102287\pi\)
0.200878 + 0.979616i \(0.435620\pi\)
\(234\) 0 0
\(235\) −3.30828e9 5.73010e9i −1.08475 1.87885i
\(236\) 0 0
\(237\) −1.36583e9 6.63984e8i −0.432915 0.210457i
\(238\) 0 0
\(239\) 4.78953e9i 1.46792i 0.679194 + 0.733959i \(0.262330\pi\)
−0.679194 + 0.733959i \(0.737670\pi\)
\(240\) 0 0
\(241\) 1.04556e8 + 1.81097e8i 0.0309943 + 0.0536836i 0.881106 0.472918i \(-0.156799\pi\)
−0.850112 + 0.526602i \(0.823466\pi\)
\(242\) 0 0
\(243\) −1.21361e9 3.26876e9i −0.348060 0.937472i
\(244\) 0 0
\(245\) 9.06090e8 4.57969e9i 0.251482 1.27108i
\(246\) 0 0
\(247\) 9.81818e8 1.70056e9i 0.263781 0.456882i
\(248\) 0 0
\(249\) −2.54868e9 + 1.81518e8i −0.663007 + 0.0472195i
\(250\) 0 0
\(251\) 4.46779e9i 1.12563i 0.826581 + 0.562817i \(0.190283\pi\)
−0.826581 + 0.562817i \(0.809717\pi\)
\(252\) 0 0
\(253\) −4.35662e8 −0.106333
\(254\) 0 0
\(255\) −1.89415e8 2.65957e9i −0.0447976 0.629001i
\(256\) 0 0
\(257\) 3.03909e9 + 1.75462e9i 0.696644 + 0.402208i 0.806096 0.591784i \(-0.201576\pi\)
−0.109452 + 0.993992i \(0.534910\pi\)
\(258\) 0 0
\(259\) −8.08774e8 + 3.66949e8i −0.179733 + 0.0815468i
\(260\) 0 0
\(261\) 1.01585e9 + 7.09560e9i 0.218912 + 1.52907i
\(262\) 0 0
\(263\) −6.00484e9 + 3.46689e9i −1.25510 + 0.724632i −0.972118 0.234493i \(-0.924657\pi\)
−0.282982 + 0.959125i \(0.591324\pi\)
\(264\) 0 0
\(265\) −5.90458e9 −1.19731
\(266\) 0 0
\(267\) 3.12982e8 6.43810e8i 0.0615849 0.126681i
\(268\) 0 0
\(269\) −5.76159e9 + 3.32645e9i −1.10036 + 0.635291i −0.936314 0.351163i \(-0.885786\pi\)
−0.164041 + 0.986453i \(0.552453\pi\)
\(270\) 0 0
\(271\) 3.62650e9 6.28128e9i 0.672373 1.16458i −0.304856 0.952399i \(-0.598608\pi\)
0.977229 0.212186i \(-0.0680584\pi\)
\(272\) 0 0
\(273\) −2.49829e9 + 4.07334e9i −0.449772 + 0.733330i
\(274\) 0 0
\(275\) −2.95581e8 1.70654e8i −0.0516827 0.0298390i
\(276\) 0 0
\(277\) −2.76342e9 4.78638e9i −0.469383 0.812995i 0.530004 0.847995i \(-0.322190\pi\)
−0.999387 + 0.0349995i \(0.988857\pi\)
\(278\) 0 0
\(279\) −4.22501e9 5.37917e9i −0.697287 0.887767i
\(280\) 0 0
\(281\) 5.02314e9i 0.805656i −0.915276 0.402828i \(-0.868027\pi\)
0.915276 0.402828i \(-0.131973\pi\)
\(282\) 0 0
\(283\) −3.01214e9 5.21718e9i −0.469601 0.813373i 0.529795 0.848126i \(-0.322269\pi\)
−0.999396 + 0.0347527i \(0.988936\pi\)
\(284\) 0 0
\(285\) −2.93708e9 4.34233e9i −0.445181 0.658178i
\(286\) 0 0
\(287\) 3.87990e9 5.42025e9i 0.571864 0.798898i
\(288\) 0 0
\(289\) −2.66176e9 + 4.61031e9i −0.381573 + 0.660904i
\(290\) 0 0
\(291\) 6.76655e8 + 9.50087e9i 0.0943616 + 1.32493i
\(292\) 0 0
\(293\) 5.65732e9i 0.767609i 0.923414 + 0.383805i \(0.125386\pi\)
−0.923414 + 0.383805i \(0.874614\pi\)
\(294\) 0 0
\(295\) 1.44210e10 1.90418
\(296\) 0 0
\(297\) −4.59636e8 5.06531e8i −0.0590729 0.0650998i
\(298\) 0 0
\(299\) −7.20273e9 4.15850e9i −0.901182 0.520298i
\(300\) 0 0
\(301\) 8.15580e9 + 5.83806e9i 0.993575 + 0.711217i
\(302\) 0 0
\(303\) 6.94075e9 + 1.02616e10i 0.823447 + 1.21743i
\(304\) 0 0
\(305\) 1.48346e10 8.56477e9i 1.71426 0.989730i
\(306\) 0 0
\(307\) 8.08970e9 0.910708 0.455354 0.890311i \(-0.349513\pi\)
0.455354 + 0.890311i \(0.349513\pi\)
\(308\) 0 0
\(309\) 5.70757e9 + 2.77468e9i 0.626062 + 0.304354i
\(310\) 0 0
\(311\) 1.38692e10 8.00737e9i 1.48255 0.855949i 0.482744 0.875761i \(-0.339640\pi\)
0.999804 + 0.0198119i \(0.00630672\pi\)
\(312\) 0 0
\(313\) 4.58737e9 7.94555e9i 0.477954 0.827841i −0.521727 0.853113i \(-0.674712\pi\)
0.999681 + 0.0252721i \(0.00804520\pi\)
\(314\) 0 0
\(315\) 6.86410e9 + 1.07530e10i 0.697175 + 1.09217i
\(316\) 0 0
\(317\) −1.21210e10 6.99804e9i −1.20033 0.693010i −0.239700 0.970847i \(-0.577049\pi\)
−0.960628 + 0.277837i \(0.910382\pi\)
\(318\) 0 0
\(319\) 7.03053e8 + 1.21772e9i 0.0678931 + 0.117594i
\(320\) 0 0
\(321\) −3.64971e9 + 7.50753e9i −0.343747 + 0.707094i
\(322\) 0 0
\(323\) 3.24853e9i 0.298454i
\(324\) 0 0
\(325\) −3.25786e9 5.64277e9i −0.292011 0.505777i
\(326\) 0 0
\(327\) −7.29175e9 + 4.93201e9i −0.637736 + 0.431354i
\(328\) 0 0
\(329\) 8.10524e9 + 1.78643e10i 0.691803 + 1.52477i
\(330\) 0 0
\(331\) −5.48598e9 + 9.50200e9i −0.457027 + 0.791595i −0.998802 0.0489289i \(-0.984419\pi\)
0.541775 + 0.840524i \(0.317753\pi\)
\(332\) 0 0
\(333\) 9.03339e8 2.25252e9i 0.0734639 0.183186i
\(334\) 0 0
\(335\) 9.56648e9i 0.759579i
\(336\) 0 0
\(337\) 1.94045e10 1.50447 0.752233 0.658897i \(-0.228977\pi\)
0.752233 + 0.658897i \(0.228977\pi\)
\(338\) 0 0
\(339\) −2.08819e9 + 1.48721e8i −0.158114 + 0.0112609i
\(340\) 0 0
\(341\) −1.16202e9 6.70891e8i −0.0859400 0.0496175i
\(342\) 0 0
\(343\) −3.99759e9 + 1.32514e10i −0.288817 + 0.957384i
\(344\) 0 0
\(345\) −1.83920e10 + 1.24400e10i −1.29823 + 0.878101i
\(346\) 0 0
\(347\) −1.31408e10 + 7.58685e9i −0.906367 + 0.523291i −0.879261 0.476341i \(-0.841963\pi\)
−0.0271067 + 0.999633i \(0.508629\pi\)
\(348\) 0 0
\(349\) −1.72031e9 −0.115959 −0.0579797 0.998318i \(-0.518466\pi\)
−0.0579797 + 0.998318i \(0.518466\pi\)
\(350\) 0 0
\(351\) −2.76413e9 1.27617e10i −0.182108 0.840776i
\(352\) 0 0
\(353\) −1.34031e10 + 7.73830e9i −0.863192 + 0.498364i −0.865080 0.501634i \(-0.832732\pi\)
0.00188763 + 0.999998i \(0.499399\pi\)
\(354\) 0 0
\(355\) −9.51676e8 + 1.64835e9i −0.0599205 + 0.103785i
\(356\) 0 0
\(357\) −2.09963e8 + 7.90241e9i −0.0129262 + 0.486504i
\(358\) 0 0
\(359\) 1.65322e10 + 9.54488e9i 0.995298 + 0.574636i 0.906854 0.421445i \(-0.138477\pi\)
0.0884445 + 0.996081i \(0.471810\pi\)
\(360\) 0 0
\(361\) 5.29823e9 + 9.17681e9i 0.311963 + 0.540335i
\(362\) 0 0
\(363\) 1.54949e10 + 7.53271e9i 0.892408 + 0.433835i
\(364\) 0 0
\(365\) 3.16624e10i 1.78391i
\(366\) 0 0
\(367\) −1.67235e10 2.89660e10i −0.921856 1.59670i −0.796540 0.604585i \(-0.793339\pi\)
−0.125316 0.992117i \(-0.539994\pi\)
\(368\) 0 0
\(369\) 2.58146e9 + 1.80311e10i 0.139239 + 0.972563i
\(370\) 0 0
\(371\) 1.74228e10 + 1.70700e9i 0.919647 + 0.0901027i
\(372\) 0 0
\(373\) 7.61432e9 1.31884e10i 0.393365 0.681328i −0.599526 0.800355i \(-0.704644\pi\)
0.992891 + 0.119027i \(0.0379776\pi\)
\(374\) 0 0
\(375\) 8.20738e9 5.84532e8i 0.415030 0.0295585i
\(376\) 0 0
\(377\) 2.68432e10i 1.32883i
\(378\) 0 0
\(379\) 2.26969e10 1.10004 0.550021 0.835151i \(-0.314620\pi\)
0.550021 + 0.835151i \(0.314620\pi\)
\(380\) 0 0
\(381\) −4.72561e8 6.63520e9i −0.0224263 0.314887i
\(382\) 0 0
\(383\) 8.25381e9 + 4.76534e9i 0.383583 + 0.221462i 0.679376 0.733790i \(-0.262251\pi\)
−0.295793 + 0.955252i \(0.595584\pi\)
\(384\) 0 0
\(385\) 2.03490e9 + 1.45661e9i 0.0926189 + 0.0662981i
\(386\) 0 0
\(387\) −2.71313e10 + 3.88430e9i −1.20956 + 0.173169i
\(388\) 0 0
\(389\) −7.01606e9 + 4.05072e9i −0.306404 + 0.176903i −0.645316 0.763915i \(-0.723274\pi\)
0.338912 + 0.940818i \(0.389941\pi\)
\(390\) 0 0
\(391\) −1.37592e10 −0.588689
\(392\) 0 0
\(393\) 1.53878e10 3.16530e10i 0.645068 1.32692i
\(394\) 0 0
\(395\) −1.31492e10 + 7.59168e9i −0.540145 + 0.311853i
\(396\) 0 0
\(397\) 2.37965e10 4.12167e10i 0.957967 1.65925i 0.230539 0.973063i \(-0.425951\pi\)
0.727428 0.686184i \(-0.240716\pi\)
\(398\) 0 0
\(399\) 7.41114e9 + 1.36621e10i 0.292411 + 0.539046i
\(400\) 0 0
\(401\) 1.59819e10 + 9.22713e9i 0.618087 + 0.356853i 0.776124 0.630580i \(-0.217183\pi\)
−0.158037 + 0.987433i \(0.550516\pi\)
\(402\) 0 0
\(403\) −1.28076e10 2.21835e10i −0.485566 0.841025i
\(404\) 0 0
\(405\) −3.38677e10 8.25920e9i −1.25882 0.306985i
\(406\) 0 0
\(407\) 4.76075e8i 0.0173499i
\(408\) 0 0
\(409\) −2.50498e10 4.33876e10i −0.895183 1.55050i −0.833578 0.552402i \(-0.813711\pi\)
−0.0616053 0.998101i \(-0.519622\pi\)
\(410\) 0 0
\(411\) 3.95324e9 + 5.84467e9i 0.138543 + 0.204830i
\(412\) 0 0
\(413\) −4.25524e10 4.16908e9i −1.46259 0.143298i
\(414\) 0 0
\(415\) −1.27729e10 + 2.21233e10i −0.430622 + 0.745860i
\(416\) 0 0
\(417\) −1.39276e9 1.95557e10i −0.0460609 0.646738i
\(418\) 0 0
\(419\) 2.56571e10i 0.832438i −0.909264 0.416219i \(-0.863355\pi\)
0.909264 0.416219i \(-0.136645\pi\)
\(420\) 0 0
\(421\) 6.01551e10 1.91489 0.957446 0.288614i \(-0.0931943\pi\)
0.957446 + 0.288614i \(0.0931943\pi\)
\(422\) 0 0
\(423\) −4.97540e10 1.99531e10i −1.55406 0.623231i
\(424\) 0 0
\(425\) −9.33510e9 5.38962e9i −0.286130 0.165197i
\(426\) 0 0
\(427\) −4.62489e10 + 2.09836e10i −1.39120 + 0.631202i
\(428\) 0 0
\(429\) −1.43508e9 2.12170e9i −0.0423689 0.0626404i
\(430\) 0 0
\(431\) −1.43030e10 + 8.25785e9i −0.414494 + 0.239308i −0.692719 0.721208i \(-0.743587\pi\)
0.278225 + 0.960516i \(0.410254\pi\)
\(432\) 0 0
\(433\) −2.28331e10 −0.649550 −0.324775 0.945791i \(-0.605289\pi\)
−0.324775 + 0.945791i \(0.605289\pi\)
\(434\) 0 0
\(435\) 6.44514e10 + 3.13324e10i 1.80001 + 0.875058i
\(436\) 0 0
\(437\) −2.34282e10 + 1.35263e10i −0.642412 + 0.370897i
\(438\) 0 0
\(439\) −1.97887e10 + 3.42751e10i −0.532794 + 0.922827i 0.466472 + 0.884536i \(0.345525\pi\)
−0.999267 + 0.0382911i \(0.987809\pi\)
\(440\) 0 0
\(441\) −1.71454e10 3.37136e10i −0.453307 0.891354i
\(442\) 0 0
\(443\) 1.80223e10 + 1.04052e10i 0.467945 + 0.270168i 0.715379 0.698736i \(-0.246254\pi\)
−0.247434 + 0.968905i \(0.579587\pi\)
\(444\) 0 0
\(445\) −3.57849e9 6.19813e9i −0.0912556 0.158059i
\(446\) 0 0
\(447\) −2.11049e10 + 4.34132e10i −0.528632 + 1.08741i
\(448\) 0 0
\(449\) 5.22570e10i 1.28576i −0.765968 0.642878i \(-0.777740\pi\)
0.765968 0.642878i \(-0.222260\pi\)
\(450\) 0 0
\(451\) 1.78658e9 + 3.09444e9i 0.0431833 + 0.0747957i
\(452\) 0 0
\(453\) 4.87595e10 3.29801e10i 1.15789 0.783175i
\(454\) 0 0
\(455\) 1.97389e10 + 4.35055e10i 0.460551 + 1.01508i
\(456\) 0 0
\(457\) 2.38191e9 4.12560e9i 0.0546086 0.0945849i −0.837429 0.546546i \(-0.815942\pi\)
0.892037 + 0.451961i \(0.149276\pi\)
\(458\) 0 0
\(459\) −1.45163e10 1.59974e10i −0.327044 0.360411i
\(460\) 0 0
\(461\) 3.30654e10i 0.732099i −0.930595 0.366050i \(-0.880710\pi\)
0.930595 0.366050i \(-0.119290\pi\)
\(462\) 0 0
\(463\) −4.07220e10 −0.886147 −0.443073 0.896485i \(-0.646112\pi\)
−0.443073 + 0.896485i \(0.646112\pi\)
\(464\) 0 0
\(465\) −6.82127e10 + 4.85813e9i −1.45899 + 0.103910i
\(466\) 0 0
\(467\) 1.85131e10 + 1.06885e10i 0.389234 + 0.224724i 0.681828 0.731512i \(-0.261185\pi\)
−0.292594 + 0.956237i \(0.594518\pi\)
\(468\) 0 0
\(469\) −2.76564e9 + 2.82280e10i −0.0571617 + 0.583430i
\(470\) 0 0
\(471\) 3.09414e10 2.09282e10i 0.628719 0.425254i
\(472\) 0 0
\(473\) −4.65619e9 + 2.68825e9i −0.0930221 + 0.0537063i
\(474\) 0 0
\(475\) −2.11936e10 −0.416322
\(476\) 0 0
\(477\) −3.76206e10 + 2.95487e10i −0.726695 + 0.570775i
\(478\) 0 0
\(479\) −4.15918e10 + 2.40130e10i −0.790069 + 0.456147i −0.839987 0.542607i \(-0.817437\pi\)
0.0499177 + 0.998753i \(0.484104\pi\)
\(480\) 0 0
\(481\) 4.54425e9 7.87087e9i 0.0848949 0.147042i
\(482\) 0 0
\(483\) 5.78660e10 3.13899e10i 1.06325 0.576769i
\(484\) 0 0
\(485\) 8.24703e10 + 4.76142e10i 1.49050 + 0.860538i
\(486\) 0 0
\(487\) −3.00358e9 5.20235e9i −0.0533977 0.0924876i 0.838091 0.545530i \(-0.183672\pi\)
−0.891489 + 0.453043i \(0.850338\pi\)
\(488\) 0 0
\(489\) 5.07118e10 + 2.46531e10i 0.886898 + 0.431157i
\(490\) 0 0
\(491\) 1.85500e10i 0.319167i −0.987184 0.159583i \(-0.948985\pi\)
0.987184 0.159583i \(-0.0510151\pi\)
\(492\) 0 0
\(493\) 2.22040e10 + 3.84584e10i 0.375875 + 0.651034i
\(494\) 0 0
\(495\) −6.76935e9 + 9.69146e8i −0.112752 + 0.0161424i
\(496\) 0 0
\(497\) 3.28466e9 4.58869e9i 0.0538351 0.0752079i
\(498\) 0 0
\(499\) −2.61025e10 + 4.52108e10i −0.420998 + 0.729189i −0.996037 0.0889361i \(-0.971653\pi\)
0.575040 + 0.818126i \(0.304987\pi\)
\(500\) 0 0
\(501\) 8.25504e10 5.87926e9i 1.31029 0.0933194i
\(502\) 0 0
\(503\) 8.21977e10i 1.28407i −0.766676 0.642034i \(-0.778091\pi\)
0.766676 0.642034i \(-0.221909\pi\)
\(504\) 0 0
\(505\) 1.23857e11 1.90439
\(506\) 0 0
\(507\) 1.22010e9 + 1.71314e10i 0.0184656 + 0.259275i
\(508\) 0 0
\(509\) −8.85830e10 5.11434e10i −1.31971 0.761937i −0.336031 0.941851i \(-0.609085\pi\)
−0.983682 + 0.179915i \(0.942418\pi\)
\(510\) 0 0
\(511\) −9.15353e9 + 9.34270e10i −0.134247 + 1.37022i
\(512\) 0 0
\(513\) −4.04440e10 1.29686e10i −0.583962 0.187251i
\(514\) 0 0
\(515\) 5.49483e10 3.17244e10i 0.781134 0.450988i
\(516\) 0 0
\(517\) −1.05156e10 −0.147188
\(518\) 0 0
\(519\) 2.29677e10 4.72450e10i 0.316554 0.651157i
\(520\) 0 0
\(521\) 4.31302e10 2.49012e10i 0.585369 0.337963i −0.177895 0.984049i \(-0.556929\pi\)
0.763264 + 0.646086i \(0.223595\pi\)
\(522\) 0 0
\(523\) −1.18682e10 + 2.05563e10i −0.158627 + 0.274750i −0.934374 0.356294i \(-0.884040\pi\)
0.775747 + 0.631044i \(0.217373\pi\)
\(524\) 0 0
\(525\) 5.15557e10 + 1.36981e9i 0.678640 + 0.0180312i
\(526\) 0 0
\(527\) −3.66991e10 2.11882e10i −0.475787 0.274696i
\(528\) 0 0
\(529\) 1.81352e10 + 3.14111e10i 0.231580 + 0.401107i
\(530\) 0 0
\(531\) 9.18825e10 7.21682e10i 1.15573 0.907753i
\(532\) 0 0
\(533\) 6.82132e10i 0.845200i
\(534\) 0 0
\(535\) 4.17291e10 + 7.22770e10i 0.509359 + 0.882236i
\(536\) 0 0
\(537\) −6.16361e10 9.11261e10i −0.741205 1.09584i
\(538\) 0 0
\(539\) −5.58331e9 4.88634e9i −0.0661510 0.0578933i
\(540\) 0 0
\(541\) −6.17113e10 + 1.06887e11i −0.720403 + 1.24777i 0.240435 + 0.970665i \(0.422710\pi\)
−0.960838 + 0.277110i \(0.910624\pi\)
\(542\) 0 0
\(543\) 2.80603e9 + 3.93993e10i 0.0322770 + 0.453200i
\(544\) 0 0
\(545\) 8.80116e10i 0.997594i
\(546\) 0 0
\(547\) −2.02466e10 −0.226153 −0.113077 0.993586i \(-0.536071\pi\)
−0.113077 + 0.993586i \(0.536071\pi\)
\(548\) 0 0
\(549\) 5.16564e10 1.28808e11i 0.568637 1.41792i
\(550\) 0 0
\(551\) 7.56149e10 + 4.36563e10i 0.820354 + 0.473631i
\(552\) 0 0
\(553\) 4.09943e10 1.85995e10i 0.438352 0.198885i
\(554\) 0 0
\(555\) −1.35940e10 2.00980e10i −0.143276 0.211827i
\(556\) 0 0
\(557\) −8.16565e10 + 4.71444e10i −0.848340 + 0.489789i −0.860090 0.510142i \(-0.829593\pi\)
0.0117506 + 0.999931i \(0.496260\pi\)
\(558\) 0 0
\(559\) −1.02640e11 −1.05116
\(560\) 0 0
\(561\) −3.81106e9 1.85271e9i −0.0384764 0.0187049i
\(562\) 0 0
\(563\) 1.05062e11 6.06578e10i 1.04572 0.603744i 0.124269 0.992249i \(-0.460342\pi\)
0.921447 + 0.388505i \(0.127008\pi\)
\(564\) 0 0
\(565\) −1.04651e10 + 1.81260e10i −0.102695 + 0.177873i
\(566\) 0 0
\(567\) 9.75463e10 + 3.41616e10i 0.943797 + 0.330527i
\(568\) 0 0
\(569\) 1.12012e11 + 6.46699e10i 1.06860 + 0.616955i 0.927798 0.373083i \(-0.121699\pi\)
0.140799 + 0.990038i \(0.455033\pi\)
\(570\) 0 0
\(571\) 1.07167e10 + 1.85619e10i 0.100813 + 0.174614i 0.912020 0.410146i \(-0.134522\pi\)
−0.811207 + 0.584760i \(0.801189\pi\)
\(572\) 0 0
\(573\) −6.24476e10 + 1.28456e11i −0.579292 + 1.19161i
\(574\) 0 0
\(575\) 8.97655e10i 0.821180i
\(576\) 0 0
\(577\) 3.30017e10 + 5.71606e10i 0.297737 + 0.515695i 0.975618 0.219476i \(-0.0704349\pi\)
−0.677881 + 0.735172i \(0.737102\pi\)
\(578\) 0 0
\(579\) 1.51637e11 1.02565e11i 1.34925 0.912607i
\(580\) 0 0
\(581\) 4.40850e10 6.15870e10i 0.386889 0.540486i
\(582\) 0 0
\(583\) −4.69205e9 + 8.12686e9i −0.0406151 + 0.0703475i
\(584\) 0 0
\(585\) −1.21167e11 4.85923e10i −1.03457 0.414900i
\(586\) 0 0
\(587\) 8.82785e10i 0.743537i 0.928325 + 0.371769i \(0.121248\pi\)
−0.928325 + 0.371769i \(0.878752\pi\)
\(588\) 0 0
\(589\) −8.33184e10 −0.692277
\(590\) 0 0
\(591\) 3.44928e9 2.45658e8i 0.0282734 0.00201364i
\(592\) 0 0
\(593\) −1.64778e11 9.51345e10i −1.33254 0.769342i −0.346851 0.937920i \(-0.612749\pi\)
−0.985688 + 0.168579i \(0.946082\pi\)
\(594\) 0 0
\(595\) 6.42666e10 + 4.60031e10i 0.512764 + 0.367045i
\(596\) 0 0
\(597\) −6.38944e10 + 4.32171e10i −0.502997 + 0.340218i
\(598\) 0 0
\(599\) −1.55178e11 + 8.95923e10i −1.20538 + 0.695927i −0.961747 0.273941i \(-0.911673\pi\)
−0.243634 + 0.969867i \(0.578339\pi\)
\(600\) 0 0
\(601\) −4.68307e10 −0.358949 −0.179474 0.983763i \(-0.557440\pi\)
−0.179474 + 0.983763i \(0.557440\pi\)
\(602\) 0 0
\(603\) −4.78742e10 6.09521e10i −0.362103 0.461020i
\(604\) 0 0
\(605\) 1.49174e11 8.61256e10i 1.11345 0.642851i
\(606\) 0 0
\(607\) 1.27939e10 2.21598e10i 0.0942431 0.163234i −0.815049 0.579392i \(-0.803290\pi\)
0.909292 + 0.416158i \(0.136624\pi\)
\(608\) 0 0
\(609\) −1.81120e11 1.11086e11i −1.31673 0.807588i
\(610\) 0 0
\(611\) −1.73853e11 1.00374e11i −1.24743 0.720206i
\(612\) 0 0
\(613\) 8.19833e8 + 1.41999e9i 0.00580609 + 0.0100564i 0.868914 0.494963i \(-0.164819\pi\)
−0.863108 + 0.505020i \(0.831485\pi\)
\(614\) 0 0
\(615\) 1.63782e11 + 7.96211e10i 1.14490 + 0.556580i
\(616\) 0 0
\(617\) 1.24163e11i 0.856745i −0.903602 0.428372i \(-0.859087\pi\)
0.903602 0.428372i \(-0.140913\pi\)
\(618\) 0 0
\(619\) −4.46997e10 7.74222e10i −0.304468 0.527355i 0.672674 0.739939i \(-0.265145\pi\)
−0.977143 + 0.212584i \(0.931812\pi\)
\(620\) 0 0
\(621\) −5.49287e10 + 1.71301e11i −0.369346 + 1.15184i
\(622\) 0 0
\(623\) 8.76726e9 + 1.93235e10i 0.0581985 + 0.128272i
\(624\) 0 0
\(625\) 9.29262e10 1.60953e11i 0.609001 1.05482i
\(626\) 0 0
\(627\) −8.31057e9 + 5.91881e8i −0.0537726 + 0.00382970i
\(628\) 0 0
\(629\) 1.50355e10i 0.0960540i
\(630\) 0 0
\(631\) −3.02715e11 −1.90949 −0.954743 0.297431i \(-0.903870\pi\)
−0.954743 + 0.297431i \(0.903870\pi\)
\(632\) 0 0
\(633\) −8.34377e9 1.17154e11i −0.0519694 0.729699i
\(634\) 0 0
\(635\) −5.75954e10 3.32527e10i −0.354236 0.204518i
\(636\) 0 0
\(637\) −4.56666e10 1.34079e11i −0.277358 0.814335i
\(638\) 0 0
\(639\) 2.18542e9 + 1.52649e10i 0.0131079 + 0.0915567i
\(640\) 0 0
\(641\) 5.94806e10 3.43411e10i 0.352325 0.203415i −0.313384 0.949627i \(-0.601463\pi\)
0.665709 + 0.746212i \(0.268129\pi\)
\(642\) 0 0
\(643\) 1.67422e11 0.979418 0.489709 0.871886i \(-0.337103\pi\)
0.489709 + 0.871886i \(0.337103\pi\)
\(644\) 0 0
\(645\) −1.19805e11 + 2.46442e11i −0.692208 + 1.42389i
\(646\) 0 0
\(647\) −8.78175e10 + 5.07014e10i −0.501145 + 0.289336i −0.729186 0.684315i \(-0.760101\pi\)
0.228041 + 0.973652i \(0.426768\pi\)
\(648\) 0 0
\(649\) 1.14596e10 1.98486e10i 0.0645938 0.111880i
\(650\) 0 0
\(651\) 2.02681e11 + 5.38514e9i 1.12847 + 0.0299829i
\(652\) 0 0
\(653\) −1.24003e11 7.15934e10i −0.681995 0.393750i 0.118612 0.992941i \(-0.462156\pi\)
−0.800606 + 0.599191i \(0.795489\pi\)
\(654\) 0 0
\(655\) −1.75937e11 3.04731e11i −0.955854 1.65559i
\(656\) 0 0
\(657\) −1.58451e11 2.01735e11i −0.850418 1.08273i
\(658\) 0 0
\(659\) 2.49864e10i 0.132484i 0.997804 + 0.0662418i \(0.0211009\pi\)
−0.997804 + 0.0662418i \(0.978899\pi\)
\(660\) 0 0
\(661\) 1.35081e11 + 2.33967e11i 0.707599 + 1.22560i 0.965745 + 0.259492i \(0.0835552\pi\)
−0.258146 + 0.966106i \(0.583112\pi\)
\(662\) 0 0
\(663\) −4.53231e10 6.70080e10i −0.234566 0.346795i
\(664\) 0 0
\(665\) 1.54653e11 + 1.51522e10i 0.790811 + 0.0774798i
\(666\) 0 0
\(667\) 1.84907e11 3.20268e11i 0.934220 1.61812i
\(668\) 0 0
\(669\) 9.18049e9 + 1.28903e11i 0.0458312 + 0.643513i
\(670\) 0 0
\(671\) 2.72238e10i 0.134295i
\(672\) 0 0
\(673\) 5.84302e10 0.284824 0.142412 0.989807i \(-0.454514\pi\)
0.142412 + 0.989807i \(0.454514\pi\)
\(674\) 0 0
\(675\) −1.04368e11 + 9.47052e10i −0.502748 + 0.456203i
\(676\) 0 0
\(677\) 1.85501e11 + 1.07099e11i 0.883063 + 0.509837i 0.871667 0.490098i \(-0.163039\pi\)
0.0113962 + 0.999935i \(0.496372\pi\)
\(678\) 0 0
\(679\) −2.29582e11 1.64338e11i −1.08008 0.773142i
\(680\) 0 0
\(681\) 1.89040e11 + 2.79487e11i 0.878954 + 1.29949i
\(682\) 0 0
\(683\) 1.78222e11 1.02896e11i 0.818988 0.472843i −0.0310794 0.999517i \(-0.509894\pi\)
0.850067 + 0.526674i \(0.176561\pi\)
\(684\) 0 0
\(685\) 7.05453e10 0.320410
\(686\) 0 0
\(687\) −1.40103e11 6.81095e10i −0.628955 0.305760i
\(688\) 0 0
\(689\) −1.55146e11 + 8.95733e10i −0.688434 + 0.397468i
\(690\) 0 0
\(691\) 1.02069e11 1.76789e11i 0.447696 0.775432i −0.550540 0.834809i \(-0.685578\pi\)
0.998236 + 0.0593771i \(0.0189114\pi\)
\(692\) 0 0
\(693\) 2.02546e10 9.02676e8i 0.0878196 0.00391380i
\(694\) 0 0
\(695\) −1.69749e11 9.80045e10i −0.727558 0.420056i
\(696\) 0 0
\(697\) 5.64241e10 + 9.77294e10i 0.239075 + 0.414090i
\(698\) 0 0
\(699\) 1.38565e11 2.85030e11i 0.580422 1.19394i
\(700\) 0 0
\(701\) 2.92695e11i 1.21211i 0.795421 + 0.606057i \(0.207250\pi\)
−0.795421 + 0.606057i \(0.792750\pi\)
\(702\) 0 0
\(703\) −1.47810e10 2.56015e10i −0.0605178 0.104820i
\(704\) 0 0
\(705\) −4.43929e11 + 3.00266e11i −1.79704 + 1.21548i
\(706\) 0 0
\(707\) −3.65468e11 3.58068e10i −1.46276 0.143314i
\(708\) 0 0
\(709\) 9.69687e10 1.67955e11i 0.383749 0.664672i −0.607846 0.794055i \(-0.707966\pi\)
0.991595 + 0.129383i \(0.0412996\pi\)
\(710\) 0 0
\(711\) −4.57875e10 + 1.14173e11i −0.179171 + 0.446772i
\(712\) 0 0
\(713\) 3.52896e11i 1.36549i
\(714\) 0 0
\(715\) −2.56090e10 −0.0979869
\(716\) 0 0
\(717\) 3.86972e11 2.75603e10i 1.46421 0.104281i
\(718\) 0 0
\(719\) 2.62598e11 + 1.51611e11i 0.982599 + 0.567304i 0.903054 0.429527i \(-0.141320\pi\)
0.0795455 + 0.996831i \(0.474653\pi\)
\(720\) 0 0
\(721\) −1.71309e11 + 7.77245e10i −0.633925 + 0.287618i
\(722\) 0 0
\(723\) 1.40301e10 9.48973e9i 0.0513462 0.0347297i
\(724\) 0 0
\(725\) 2.50904e11 1.44860e11i 0.908147 0.524319i
\(726\) 0 0
\(727\) −2.93281e11 −1.04990 −0.524948 0.851135i \(-0.675915\pi\)
−0.524948 + 0.851135i \(0.675915\pi\)
\(728\) 0 0
\(729\) −2.57117e11 + 1.16863e11i −0.910377 + 0.413779i
\(730\) 0 0
\(731\) −1.47053e11 + 8.49010e10i −0.514996 + 0.297333i
\(732\) 0 0
\(733\) −2.41246e10 + 4.17850e10i −0.0835687 + 0.144745i −0.904780 0.425878i \(-0.859965\pi\)
0.821212 + 0.570624i \(0.193298\pi\)
\(734\) 0 0
\(735\) −3.75232e11 4.68551e10i −1.28573 0.160549i
\(736\) 0 0
\(737\) −1.31670e10 7.60196e9i −0.0446289 0.0257665i
\(738\) 0 0
\(739\) 2.01824e11 + 3.49570e11i 0.676700 + 1.17208i 0.975969 + 0.217909i \(0.0699237\pi\)
−0.299270 + 0.954169i \(0.596743\pi\)
\(740\) 0 0
\(741\) −1.43047e11 6.95409e10i −0.474467 0.230657i
\(742\) 0 0
\(743\) 3.03948e11i 0.997342i 0.866791 + 0.498671i \(0.166178\pi\)
−0.866791 + 0.498671i \(0.833822\pi\)
\(744\) 0 0
\(745\) 2.41304e11 + 4.17951e11i 0.783320 + 1.35675i
\(746\) 0 0
\(747\) 2.93316e10 + 2.04877e11i 0.0942005 + 0.657978i
\(748\) 0 0
\(749\) −1.02236e11 2.25333e11i −0.324845 0.715974i
\(750\) 0 0
\(751\) 1.69823e11 2.94141e11i 0.533870 0.924690i −0.465347 0.885128i \(-0.654070\pi\)
0.999217 0.0395617i \(-0.0125962\pi\)
\(752\) 0 0
\(753\) 3.60976e11 2.57088e10i 1.12279 0.0799655i
\(754\) 0 0
\(755\) 5.88528e11i 1.81125i
\(756\) 0 0
\(757\) 4.49280e11 1.36815 0.684074 0.729412i \(-0.260206\pi\)
0.684074 + 0.729412i \(0.260206\pi\)
\(758\) 0 0
\(759\) 2.50692e9 + 3.51995e10i 0.00755393 + 0.106064i
\(760\) 0 0
\(761\) 3.71405e11 + 2.14431e11i 1.10741 + 0.639364i 0.938158 0.346208i \(-0.112531\pi\)
0.169254 + 0.985573i \(0.445864\pi\)
\(762\) 0 0
\(763\) 2.54439e10 2.59698e11i 0.0750734 0.766249i
\(764\) 0 0
\(765\) −2.13791e11 + 3.06078e10i −0.624229 + 0.0893688i
\(766\) 0 0
\(767\) 3.78919e11 2.18769e11i 1.09488 0.632127i
\(768\) 0 0
\(769\) 3.84679e11 1.10000 0.550001 0.835164i \(-0.314627\pi\)
0.550001 + 0.835164i \(0.314627\pi\)
\(770\) 0 0
\(771\) 1.24277e11 2.55641e11i 0.351702 0.723457i
\(772\) 0 0
\(773\) −2.61563e11 + 1.51013e11i −0.732585 + 0.422958i −0.819367 0.573269i \(-0.805675\pi\)
0.0867823 + 0.996227i \(0.472342\pi\)
\(774\) 0 0
\(775\) −1.38233e11 + 2.39427e11i −0.383182 + 0.663690i
\(776\) 0 0
\(777\) 3.43017e10 + 6.32337e10i 0.0941091 + 0.173486i
\(778\) 0 0
\(779\) 1.92150e11 + 1.10938e11i 0.521785 + 0.301253i
\(780\) 0 0
\(781\) 1.51249e9 + 2.61971e9i 0.00406526 + 0.00704123i
\(782\) 0 0
\(783\) 5.67446e11 1.22906e11i 1.50966 0.326985i
\(784\) 0 0
\(785\) 3.73463e11i 0.983489i
\(786\) 0 0
\(787\) 3.59141e11 + 6.22051e11i 0.936195 + 1.62154i 0.772489 + 0.635029i \(0.219012\pi\)
0.163706 + 0.986509i \(0.447655\pi\)
\(788\) 0 0
\(789\) 3.14662e11 + 4.65213e11i 0.811964 + 1.20045i
\(790\) 0 0
\(791\) 3.61197e10 5.04595e10i 0.0922653 0.128895i
\(792\) 0 0
\(793\) 2.59858e11 4.50087e11i 0.657117 1.13816i
\(794\) 0 0
\(795\) 3.39765e10 + 4.77063e11i 0.0850571 + 1.19428i
\(796\) 0 0
\(797\) 2.04056e11i 0.505727i −0.967502 0.252864i \(-0.918628\pi\)
0.967502 0.252864i \(-0.0813724\pi\)
\(798\) 0 0
\(799\) −3.32107e11 −0.814874
\(800\) 0 0
\(801\) −5.38178e10 2.15828e10i −0.130736 0.0524298i
\(802\) 0 0
\(803\) −4.35791e10 2.51604e10i −0.104813 0.0605139i
\(804\) 0 0
\(805\) 6.41772e10 6.55035e11i 0.152826 1.55984i
\(806\) 0 0
\(807\) 3.01916e11 + 4.46368e11i 0.711855 + 1.05244i
\(808\) 0 0
\(809\) −9.51905e10 + 5.49583e10i −0.222228 + 0.128304i −0.606982 0.794716i \(-0.707620\pi\)
0.384753 + 0.923019i \(0.374287\pi\)
\(810\) 0 0
\(811\) 2.33734e11 0.540305 0.270152 0.962818i \(-0.412926\pi\)
0.270152 + 0.962818i \(0.412926\pi\)
\(812\) 0 0
\(813\) −5.28366e11 2.56860e11i −1.20941 0.587942i
\(814\) 0 0
\(815\) 4.88216e11 2.81872e11i 1.10658 0.638883i
\(816\) 0 0
\(817\) −1.66928e11 + 2.89127e11i −0.374663 + 0.648935i
\(818\) 0 0
\(819\) 3.43482e11 + 1.78411e11i 0.763430 + 0.396540i
\(820\) 0 0
\(821\) −5.20573e11 3.00553e11i −1.14580 0.661528i −0.197940 0.980214i \(-0.563425\pi\)
−0.947860 + 0.318686i \(0.896759\pi\)
\(822\) 0 0
\(823\) −1.79738e11 3.11316e11i −0.391779 0.678581i 0.600905 0.799320i \(-0.294807\pi\)
−0.992684 + 0.120739i \(0.961474\pi\)
\(824\) 0 0
\(825\) −1.20872e10 + 2.48635e10i −0.0260921 + 0.0536719i
\(826\) 0 0
\(827\) 5.43642e10i 0.116223i 0.998310 + 0.0581113i \(0.0185078\pi\)
−0.998310 + 0.0581113i \(0.981492\pi\)
\(828\) 0 0
\(829\) 2.74898e11 + 4.76138e11i 0.582041 + 1.00813i 0.995237 + 0.0974831i \(0.0310792\pi\)
−0.413196 + 0.910642i \(0.635587\pi\)
\(830\) 0 0
\(831\) −3.70816e11 + 2.50813e11i −0.777596 + 0.525953i
\(832\) 0 0
\(833\) −1.76333e11 1.54321e11i −0.366230 0.320513i
\(834\) 0 0
\(835\) 4.13707e11 7.16561e11i 0.851033 1.47403i
\(836\) 0 0
\(837\) −4.10300e11 + 3.72315e11i −0.835988 + 0.758592i
\(838\) 0 0
\(839\) 3.91290e11i 0.789679i 0.918750 + 0.394840i \(0.129200\pi\)
−0.918750 + 0.394840i \(0.870800\pi\)
\(840\) 0 0
\(841\) −6.93330e11 −1.38598
\(842\) 0 0
\(843\) −4.05846e11 + 2.89045e10i −0.803620 + 0.0572341i
\(844\) 0 0
\(845\) 1.48705e11 + 8.58550e10i 0.291675 + 0.168399i
\(846\) 0 0
\(847\) −4.65069e11 + 2.11007e11i −0.903616 + 0.409980i
\(848\) 0 0
\(849\) −4.04191e11 + 2.73388e11i −0.777957 + 0.526197i
\(850\) 0 0
\(851\) −1.08435e11 + 6.26051e10i −0.206753 + 0.119369i
\(852\) 0 0
\(853\) −2.62938e11 −0.496658 −0.248329 0.968676i \(-0.579881\pi\)
−0.248329 + 0.968676i \(0.579881\pi\)
\(854\) 0 0
\(855\) −3.33940e11 + 2.62289e11i −0.624890 + 0.490813i
\(856\) 0 0
\(857\) 1.71064e11 9.87636e10i 0.317128 0.183094i −0.332984 0.942933i \(-0.608055\pi\)
0.650112 + 0.759839i \(0.274722\pi\)
\(858\) 0 0
\(859\) −5.96947e10 + 1.03394e11i −0.109638 + 0.189899i −0.915624 0.402036i \(-0.868303\pi\)
0.805985 + 0.591935i \(0.201636\pi\)
\(860\) 0 0
\(861\) −4.60257e11 2.82288e11i −0.837505 0.513666i
\(862\) 0 0
\(863\) −7.81431e11 4.51160e11i −1.40879 0.813368i −0.413522 0.910494i \(-0.635702\pi\)
−0.995272 + 0.0971260i \(0.969035\pi\)
\(864\) 0 0
\(865\) −2.62602e11 4.54840e11i −0.469065 0.812445i
\(866\) 0 0
\(867\) 3.87808e11 + 1.88529e11i 0.686341 + 0.333658i
\(868\) 0 0
\(869\) 2.41308e10i 0.0423148i
\(870\) 0 0
\(871\) −1.45125e11 2.51364e11i −0.252156 0.436747i
\(872\) 0 0
\(873\) 7.63733e11 1.09341e11i 1.31487 0.188246i
\(874\) 0 0
\(875\) −1.41964e11 + 1.98325e11i −0.242185 + 0.338334i
\(876\) 0 0
\(877\) 3.13531e11 5.43052e11i 0.530008 0.918001i −0.469379 0.882997i \(-0.655522\pi\)
0.999387 0.0350045i \(-0.0111446\pi\)
\(878\) 0 0
\(879\) 4.57085e11 3.25537e10i 0.765670 0.0545312i
\(880\) 0 0
\(881\) 8.66629e11i 1.43857i 0.694718 + 0.719283i \(0.255529\pi\)
−0.694718 + 0.719283i \(0.744471\pi\)
\(882\) 0 0
\(883\) 4.10650e11 0.675506 0.337753 0.941235i \(-0.390333\pi\)
0.337753 + 0.941235i \(0.390333\pi\)
\(884\) 0 0
\(885\) −8.29825e10 1.16515e12i −0.135274 1.89937i
\(886\) 0 0
\(887\) 1.80385e11 + 1.04145e11i 0.291410 + 0.168246i 0.638578 0.769557i \(-0.279523\pi\)
−0.347167 + 0.937803i \(0.612856\pi\)
\(888\) 0 0
\(889\) 1.60335e11 + 1.14770e11i 0.256697 + 0.183748i
\(890\) 0 0
\(891\) −3.82804e10 + 4.00512e10i −0.0607388 + 0.0635484i
\(892\) 0 0
\(893\) −5.65489e11 + 3.26485e11i −0.889239 + 0.513402i
\(894\) 0 0
\(895\) −1.09989e12 −1.71419
\(896\) 0 0
\(897\) −2.94541e11 + 6.05876e11i −0.454963 + 0.935867i
\(898\) 0 0
\(899\) 9.86382e11 5.69488e11i 1.51010 0.871858i
\(900\) 0 0
\(901\) −1.48185e11 + 2.56664e11i −0.224857 + 0.389463i
\(902\) 0 0
\(903\) 4.24757e11 6.92545e11i 0.638837 1.04159i
\(904\) 0 0
\(905\) 3.41998e11 + 1.97452e11i 0.509834 + 0.294353i
\(906\) 0 0
\(907\) 1.53863e11 + 2.66498e11i 0.227355 + 0.393791i 0.957023 0.290011i \(-0.0936588\pi\)
−0.729668 + 0.683801i \(0.760326\pi\)
\(908\) 0 0
\(909\) 7.89148e11 6.19828e11i 1.15585 0.907853i
\(910\) 0 0
\(911\) 9.45404e11i 1.37260i 0.727318 + 0.686300i \(0.240766\pi\)
−0.727318 + 0.686300i \(0.759234\pi\)
\(912\) 0 0
\(913\) 2.02998e10 + 3.51603e10i 0.0292152 + 0.0506022i
\(914\) 0 0
\(915\) −7.77356e11 1.14928e12i −1.10901 1.63962i
\(916\) 0 0
\(917\) 4.31043e11 + 9.50040e11i 0.609598 + 1.34358i
\(918\) 0 0
\(919\) −5.01341e11 + 8.68347e11i −0.702863 + 1.21739i 0.264594 + 0.964360i \(0.414762\pi\)
−0.967457 + 0.253035i \(0.918571\pi\)
\(920\) 0 0
\(921\) −4.65503e10 6.53610e11i −0.0646970 0.908407i
\(922\) 0 0
\(923\) 5.77482e10i 0.0795668i
\(924\) 0 0
\(925\) −9.80923e10 −0.133989
\(926\) 0 0
\(927\) 1.91338e11 4.77112e11i 0.259109 0.646102i
\(928\) 0 0
\(929\) −1.16648e12 6.73466e11i −1.56608 0.904175i −0.996620 0.0821543i \(-0.973820\pi\)
−0.569458 0.822021i \(-0.692847\pi\)
\(930\) 0 0
\(931\) −4.51958e11 8.94197e10i −0.601588 0.119024i
\(932\) 0 0
\(933\) −7.26765e11 1.07449e12i −0.959108 1.41800i
\(934\) 0 0
\(935\) −3.66901e10 + 2.11830e10i −0.0480068 + 0.0277167i
\(936\) 0 0
\(937\) 1.75433e11 0.227590 0.113795 0.993504i \(-0.463699\pi\)
0.113795 + 0.993504i \(0.463699\pi\)
\(938\) 0 0
\(939\) −6.68361e11 3.24917e11i −0.859703 0.417936i
\(940\) 0 0
\(941\) −6.86868e11 + 3.96563e11i −0.876021 + 0.505771i −0.869344 0.494207i \(-0.835459\pi\)
−0.00667678 + 0.999978i \(0.502125\pi\)
\(942\) 0 0
\(943\) 4.69879e11 8.13855e11i 0.594209 1.02920i
\(944\) 0 0
\(945\) 8.29297e11 6.16464e11i 1.03988 0.773001i
\(946\) 0 0
\(947\) 2.71298e10 + 1.56634e10i 0.0337323 + 0.0194754i 0.516771 0.856123i \(-0.327134\pi\)
−0.483039 + 0.875599i \(0.660467\pi\)
\(948\) 0 0
\(949\) −4.80324e11 8.31945e11i −0.592201 1.02572i
\(950\) 0 0
\(951\) −4.95662e11 + 1.01959e12i −0.605987 + 1.24653i
\(952\) 0 0
\(953\) 7.84682e11i 0.951310i −0.879632 0.475655i \(-0.842211\pi\)
0.879632 0.475655i \(-0.157789\pi\)
\(954\) 0 0
\(955\) 7.13997e11 + 1.23668e12i 0.858387 + 1.48677i
\(956\) 0 0
\(957\) 9.43409e10 6.38105e10i 0.112474 0.0760755i
\(958\) 0 0
\(959\) −2.08159e11 2.03945e10i −0.246106 0.0241123i
\(960\) 0 0
\(961\) −1.16990e11 + 2.02633e11i −0.137169 + 0.237584i
\(962\) 0 0
\(963\) 6.27575e11 + 2.51680e11i 0.729727 + 0.292646i
\(964\) 0 0
\(965\) 1.83026e12i 2.11059i
\(966\) 0 0
\(967\) −1.43127e12 −1.63687 −0.818436 0.574597i \(-0.805159\pi\)
−0.818436 + 0.574597i \(0.805159\pi\)
\(968\) 0 0
\(969\) −2.62466e11 + 1.86929e10i −0.297700 + 0.0212023i
\(970\) 0 0
\(971\) −5.46788e11 3.15688e11i −0.615095 0.355125i 0.159862 0.987139i \(-0.448895\pi\)
−0.774957 + 0.632014i \(0.782228\pi\)
\(972\) 0 0
\(973\) 4.72548e11 + 3.38258e11i 0.527223 + 0.377395i
\(974\) 0 0
\(975\) −4.37163e11 + 2.95690e11i −0.483755 + 0.327203i
\(976\) 0 0
\(977\) 5.05709e10 2.91971e10i 0.0555037 0.0320451i −0.471991 0.881603i \(-0.656465\pi\)
0.527495 + 0.849558i \(0.323131\pi\)
\(978\) 0 0
\(979\) −1.13745e10 −0.0123823
\(980\) 0 0
\(981\) 4.40443e11 + 5.60759e11i 0.475569 + 0.605481i
\(982\) 0 0
\(983\) −1.30108e11 + 7.51179e10i −0.139345 + 0.0804506i −0.568052 0.822993i \(-0.692303\pi\)
0.428707 + 0.903444i \(0.358969\pi\)
\(984\) 0 0
\(985\) 1.72863e10 2.99407e10i 0.0183635 0.0318066i
\(986\) 0 0
\(987\) 1.39672e12 7.57662e11i 1.47177 0.798375i
\(988\) 0 0
\(989\) 1.22460e12 + 7.07024e11i 1.28000 + 0.739008i
\(990\) 0 0
\(991\) 8.95580e11 + 1.55119e12i 0.928560 + 1.60831i 0.785733 + 0.618566i \(0.212286\pi\)
0.142827 + 0.989748i \(0.454381\pi\)
\(992\) 0 0
\(993\) 7.99285e11 + 3.88565e11i 0.822062 + 0.399638i
\(994\) 0 0
\(995\) 7.71207e11i 0.786825i
\(996\) 0 0
\(997\) 5.35305e11 + 9.27175e11i 0.541777 + 0.938385i 0.998802 + 0.0489312i \(0.0155815\pi\)
−0.457025 + 0.889454i \(0.651085\pi\)
\(998\) 0 0
\(999\) −1.87191e11 6.00240e10i −0.187942 0.0602647i
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 84.9.p.b.65.9 yes 40
3.2 odd 2 inner 84.9.p.b.65.6 yes 40
7.4 even 3 inner 84.9.p.b.53.6 40
21.11 odd 6 inner 84.9.p.b.53.9 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.9.p.b.53.6 40 7.4 even 3 inner
84.9.p.b.53.9 yes 40 21.11 odd 6 inner
84.9.p.b.65.6 yes 40 3.2 odd 2 inner
84.9.p.b.65.9 yes 40 1.1 even 1 trivial