Properties

Label 33.8.d.b.32.4
Level $33$
Weight $8$
Character 33.32
Analytic conductor $10.309$
Analytic rank $0$
Dimension $24$
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] = [33,8,Mod(32,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.32");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 33.d (of order \(2\), degree \(1\), 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: \(10.3087058410\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 32.4
Character \(\chi\) \(=\) 33.32
Dual form 33.8.d.b.32.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-17.1890 q^{2} +(-43.8101 + 16.3606i) q^{3} +167.460 q^{4} +90.8965i q^{5} +(753.051 - 281.222i) q^{6} -1506.19i q^{7} -678.279 q^{8} +(1651.66 - 1433.52i) q^{9} +O(q^{10})\) \(q-17.1890 q^{2} +(-43.8101 + 16.3606i) q^{3} +167.460 q^{4} +90.8965i q^{5} +(753.051 - 281.222i) q^{6} -1506.19i q^{7} -678.279 q^{8} +(1651.66 - 1433.52i) q^{9} -1562.42i q^{10} +(981.685 + 4303.89i) q^{11} +(-7336.45 + 2739.76i) q^{12} -3566.16i q^{13} +25889.9i q^{14} +(-1487.13 - 3982.19i) q^{15} -9775.99 q^{16} -13457.6 q^{17} +(-28390.3 + 24640.8i) q^{18} +26772.8i q^{19} +15221.5i q^{20} +(24642.3 + 65986.6i) q^{21} +(-16874.1 - 73979.4i) q^{22} -40415.9i q^{23} +(29715.5 - 11097.1i) q^{24} +69862.8 q^{25} +61298.6i q^{26} +(-48906.0 + 89825.1i) q^{27} -252228. i q^{28} -142803. q^{29} +(25562.1 + 68449.7i) q^{30} -158528. q^{31} +254859. q^{32} +(-113422. - 172493. i) q^{33} +231322. q^{34} +136908. q^{35} +(276587. - 240058. i) q^{36} +286564. q^{37} -460197. i q^{38} +(58344.7 + 156234. i) q^{39} -61653.2i q^{40} -434415. q^{41} +(-423576. - 1.13424e6i) q^{42} +689840. i q^{43} +(164393. + 720730. i) q^{44} +(130302. + 150130. i) q^{45} +694707. i q^{46} +1.28647e6i q^{47} +(428288. - 159942. i) q^{48} -1.44508e6 q^{49} -1.20087e6 q^{50} +(589579. - 220175. i) q^{51} -597190. i q^{52} +406111. i q^{53} +(840643. - 1.54400e6i) q^{54} +(-391208. + 89231.7i) q^{55} +1.02162e6i q^{56} +(-438020. - 1.17292e6i) q^{57} +2.45463e6 q^{58} +622324. i q^{59} +(-249034. - 666858. i) q^{60} +901495. i q^{61} +2.72492e6 q^{62} +(-2.15917e6 - 2.48772e6i) q^{63} -3.12943e6 q^{64} +324151. q^{65} +(1.94961e6 + 2.96497e6i) q^{66} +2.03178e6 q^{67} -2.25361e6 q^{68} +(661230. + 1.77063e6i) q^{69} -2.35330e6 q^{70} +2.52259e6i q^{71} +(-1.12029e6 + 972330. i) q^{72} -1.13869e6i q^{73} -4.92573e6 q^{74} +(-3.06070e6 + 1.14300e6i) q^{75} +4.48338e6i q^{76} +(6.48250e6 - 1.47861e6i) q^{77} +(-1.00288e6 - 2.68550e6i) q^{78} -1.22674e6i q^{79} -888604. i q^{80} +(672982. - 4.73539e6i) q^{81} +7.46715e6 q^{82} -5.90164e6 q^{83} +(4.12661e6 + 1.10501e7i) q^{84} -1.22325e6i q^{85} -1.18576e7i q^{86} +(6.25621e6 - 2.33634e6i) q^{87} +(-665856. - 2.91924e6i) q^{88} +7.09843e6i q^{89} +(-2.23976e6 - 2.58058e6i) q^{90} -5.37133e6 q^{91} -6.76805e6i q^{92} +(6.94512e6 - 2.59362e6i) q^{93} -2.21131e7i q^{94} -2.43355e6 q^{95} +(-1.11654e7 + 4.16966e6i) q^{96} +8.09192e6 q^{97} +2.48394e7 q^{98} +(7.79114e6 + 5.70128e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37} - 100296 q^{42} - 1854252 q^{45} + 3172548 q^{48} - 1169304 q^{49} - 4401936 q^{55} - 2920440 q^{58} + 1981452 q^{60} + 14578596 q^{64} + 2895156 q^{66} + 7729200 q^{67} - 4614108 q^{69} - 6924504 q^{70} - 4375800 q^{75} - 26237448 q^{78} + 22367340 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 25396908 q^{93} + 72948360 q^{97} + 53650080 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −17.1890 −1.51930 −0.759652 0.650330i \(-0.774631\pi\)
−0.759652 + 0.650330i \(0.774631\pi\)
\(3\) −43.8101 + 16.3606i −0.936807 + 0.349845i
\(4\) 167.460 1.30828
\(5\) 90.8965i 0.325201i 0.986692 + 0.162601i \(0.0519882\pi\)
−0.986692 + 0.162601i \(0.948012\pi\)
\(6\) 753.051 281.222i 1.42329 0.531521i
\(7\) 1506.19i 1.65973i −0.557963 0.829866i \(-0.688417\pi\)
0.557963 0.829866i \(-0.311583\pi\)
\(8\) −678.279 −0.468375
\(9\) 1651.66 1433.52i 0.755216 0.655476i
\(10\) 1562.42i 0.494079i
\(11\) 981.685 + 4303.89i 0.222381 + 0.974960i
\(12\) −7336.45 + 2739.76i −1.22561 + 0.457697i
\(13\) 3566.16i 0.450193i −0.974336 0.225097i \(-0.927730\pi\)
0.974336 0.225097i \(-0.0722698\pi\)
\(14\) 25889.9i 2.52164i
\(15\) −1487.13 3982.19i −0.113770 0.304651i
\(16\) −9775.99 −0.596679
\(17\) −13457.6 −0.664349 −0.332174 0.943218i \(-0.607782\pi\)
−0.332174 + 0.943218i \(0.607782\pi\)
\(18\) −28390.3 + 24640.8i −1.14740 + 0.995866i
\(19\) 26772.8i 0.895481i 0.894164 + 0.447740i \(0.147771\pi\)
−0.894164 + 0.447740i \(0.852229\pi\)
\(20\) 15221.5i 0.425455i
\(21\) 24642.3 + 65986.6i 0.580650 + 1.55485i
\(22\) −16874.1 73979.4i −0.337864 1.48126i
\(23\) 40415.9i 0.692635i −0.938117 0.346318i \(-0.887432\pi\)
0.938117 0.346318i \(-0.112568\pi\)
\(24\) 29715.5 11097.1i 0.438777 0.163859i
\(25\) 69862.8 0.894244
\(26\) 61298.6i 0.683980i
\(27\) −48906.0 + 89825.1i −0.478177 + 0.878263i
\(28\) 252228.i 2.17140i
\(29\) −142803. −1.08728 −0.543642 0.839317i \(-0.682955\pi\)
−0.543642 + 0.839317i \(0.682955\pi\)
\(30\) 25562.1 + 68449.7i 0.172851 + 0.462857i
\(31\) −158528. −0.955739 −0.477869 0.878431i \(-0.658591\pi\)
−0.477869 + 0.878431i \(0.658591\pi\)
\(32\) 254859. 1.37491
\(33\) −113422. 172493.i −0.549413 0.835551i
\(34\) 231322. 1.00935
\(35\) 136908. 0.539747
\(36\) 276587. 240058.i 0.988036 0.857547i
\(37\) 286564. 0.930069 0.465035 0.885292i \(-0.346042\pi\)
0.465035 + 0.885292i \(0.346042\pi\)
\(38\) 460197.i 1.36051i
\(39\) 58344.7 + 156234.i 0.157498 + 0.421745i
\(40\) 61653.2i 0.152316i
\(41\) −434415. −0.984378 −0.492189 0.870488i \(-0.663803\pi\)
−0.492189 + 0.870488i \(0.663803\pi\)
\(42\) −423576. 1.13424e6i −0.882183 2.36229i
\(43\) 689840.i 1.32315i 0.749880 + 0.661574i \(0.230111\pi\)
−0.749880 + 0.661574i \(0.769889\pi\)
\(44\) 164393. + 720730.i 0.290937 + 1.27552i
\(45\) 130302. + 150130.i 0.213161 + 0.245597i
\(46\) 694707.i 1.05232i
\(47\) 1.28647e6i 1.80741i 0.428155 + 0.903705i \(0.359164\pi\)
−0.428155 + 0.903705i \(0.640836\pi\)
\(48\) 428288. 159942.i 0.558974 0.208746i
\(49\) −1.44508e6 −1.75471
\(50\) −1.20087e6 −1.35863
\(51\) 589579. 220175.i 0.622367 0.232419i
\(52\) 597190.i 0.588980i
\(53\) 406111.i 0.374696i 0.982294 + 0.187348i \(0.0599892\pi\)
−0.982294 + 0.187348i \(0.940011\pi\)
\(54\) 840643. 1.54400e6i 0.726496 1.33435i
\(55\) −391208. + 89231.7i −0.317058 + 0.0723186i
\(56\) 1.02162e6i 0.777377i
\(57\) −438020. 1.17292e6i −0.313280 0.838893i
\(58\) 2.45463e6 1.65192
\(59\) 622324.i 0.394489i 0.980354 + 0.197244i \(0.0631993\pi\)
−0.980354 + 0.197244i \(0.936801\pi\)
\(60\) −249034. 666858.i −0.148843 0.398569i
\(61\) 901495.i 0.508521i 0.967136 + 0.254261i \(0.0818321\pi\)
−0.967136 + 0.254261i \(0.918168\pi\)
\(62\) 2.72492e6 1.45206
\(63\) −2.15917e6 2.48772e6i −1.08791 1.25346i
\(64\) −3.12943e6 −1.49223
\(65\) 324151. 0.146403
\(66\) 1.94961e6 + 2.96497e6i 0.834726 + 1.26945i
\(67\) 2.03178e6 0.825308 0.412654 0.910888i \(-0.364602\pi\)
0.412654 + 0.910888i \(0.364602\pi\)
\(68\) −2.25361e6 −0.869156
\(69\) 661230. + 1.77063e6i 0.242315 + 0.648866i
\(70\) −2.35330e6 −0.820039
\(71\) 2.52259e6i 0.836455i 0.908342 + 0.418228i \(0.137349\pi\)
−0.908342 + 0.418228i \(0.862651\pi\)
\(72\) −1.12029e6 + 972330.i −0.353724 + 0.307008i
\(73\) 1.13869e6i 0.342589i −0.985220 0.171295i \(-0.945205\pi\)
0.985220 0.171295i \(-0.0547950\pi\)
\(74\) −4.92573e6 −1.41306
\(75\) −3.06070e6 + 1.14300e6i −0.837735 + 0.312847i
\(76\) 4.48338e6i 1.17154i
\(77\) 6.48250e6 1.47861e6i 1.61817 0.369093i
\(78\) −1.00288e6 2.68550e6i −0.239287 0.640758i
\(79\) 1.22674e6i 0.279934i −0.990156 0.139967i \(-0.955300\pi\)
0.990156 0.139967i \(-0.0446997\pi\)
\(80\) 888604.i 0.194041i
\(81\) 672982. 4.73539e6i 0.140704 0.990052i
\(82\) 7.46715e6 1.49557
\(83\) −5.90164e6 −1.13292 −0.566460 0.824089i \(-0.691687\pi\)
−0.566460 + 0.824089i \(0.691687\pi\)
\(84\) 4.12661e6 + 1.10501e7i 0.759654 + 2.03418i
\(85\) 1.22325e6i 0.216047i
\(86\) 1.18576e7i 2.01026i
\(87\) 6.25621e6 2.33634e6i 1.01858 0.380382i
\(88\) −665856. 2.91924e6i −0.104158 0.456646i
\(89\) 7.09843e6i 1.06733i 0.845697 + 0.533664i \(0.179185\pi\)
−0.845697 + 0.533664i \(0.820815\pi\)
\(90\) −2.23976e6 2.58058e6i −0.323857 0.373137i
\(91\) −5.37133e6 −0.747200
\(92\) 6.76805e6i 0.906163i
\(93\) 6.94512e6 2.59362e6i 0.895343 0.334361i
\(94\) 2.21131e7i 2.74601i
\(95\) −2.43355e6 −0.291211
\(96\) −1.11654e7 + 4.16966e6i −1.28803 + 0.481006i
\(97\) 8.09192e6 0.900224 0.450112 0.892972i \(-0.351384\pi\)
0.450112 + 0.892972i \(0.351384\pi\)
\(98\) 2.48394e7 2.66594
\(99\) 7.79114e6 + 5.70128e6i 0.807008 + 0.590540i
\(100\) 1.16992e7 1.16992
\(101\) 4.89863e6 0.473097 0.236548 0.971620i \(-0.423984\pi\)
0.236548 + 0.971620i \(0.423984\pi\)
\(102\) −1.01343e7 + 3.78458e6i −0.945564 + 0.353116i
\(103\) −1.63269e7 −1.47223 −0.736113 0.676859i \(-0.763341\pi\)
−0.736113 + 0.676859i \(0.763341\pi\)
\(104\) 2.41885e6i 0.210859i
\(105\) −5.99795e6 + 2.23990e6i −0.505639 + 0.188828i
\(106\) 6.98062e6i 0.569276i
\(107\) −2.11142e7 −1.66622 −0.833108 0.553111i \(-0.813441\pi\)
−0.833108 + 0.553111i \(0.813441\pi\)
\(108\) −8.18981e6 + 1.50421e7i −0.625591 + 1.14902i
\(109\) 2.46933e7i 1.82636i 0.407559 + 0.913179i \(0.366380\pi\)
−0.407559 + 0.913179i \(0.633620\pi\)
\(110\) 6.72446e6 1.53380e6i 0.481707 0.109874i
\(111\) −1.25544e7 + 4.68837e6i −0.871296 + 0.325380i
\(112\) 1.47246e7i 0.990328i
\(113\) 2.80165e7i 1.82658i −0.407308 0.913291i \(-0.633532\pi\)
0.407308 0.913291i \(-0.366468\pi\)
\(114\) 7.52911e6 + 2.01613e7i 0.475967 + 1.27453i
\(115\) 3.67366e6 0.225246
\(116\) −2.39138e7 −1.42248
\(117\) −5.11218e6 5.89008e6i −0.295091 0.339993i
\(118\) 1.06971e7i 0.599348i
\(119\) 2.02698e7i 1.10264i
\(120\) 1.00869e6 + 2.70103e6i 0.0532870 + 0.142691i
\(121\) −1.75598e7 + 8.45013e6i −0.901093 + 0.433625i
\(122\) 1.54958e7i 0.772598i
\(123\) 1.90318e7 7.10732e6i 0.922172 0.344380i
\(124\) −2.65471e7 −1.25038
\(125\) 1.34516e7i 0.616010i
\(126\) 3.71138e7 + 4.27613e7i 1.65287 + 1.90438i
\(127\) 3.98549e7i 1.72651i 0.504768 + 0.863255i \(0.331578\pi\)
−0.504768 + 0.863255i \(0.668422\pi\)
\(128\) 2.11697e7 0.892236
\(129\) −1.12862e7 3.02220e7i −0.462897 1.23954i
\(130\) −5.57182e6 −0.222431
\(131\) 1.80946e7 0.703232 0.351616 0.936144i \(-0.385632\pi\)
0.351616 + 0.936144i \(0.385632\pi\)
\(132\) −1.89937e7 2.88857e7i −0.718788 1.09314i
\(133\) 4.03251e7 1.48626
\(134\) −3.49242e7 −1.25389
\(135\) −8.16479e6 4.44538e6i −0.285612 0.155504i
\(136\) 9.12800e6 0.311164
\(137\) 1.08842e7i 0.361638i −0.983516 0.180819i \(-0.942125\pi\)
0.983516 0.180819i \(-0.0578747\pi\)
\(138\) −1.13659e7 3.04352e7i −0.368150 0.985824i
\(139\) 1.33599e6i 0.0421942i −0.999777 0.0210971i \(-0.993284\pi\)
0.999777 0.0210971i \(-0.00671591\pi\)
\(140\) 2.29266e7 0.706141
\(141\) −2.10475e7 5.63604e7i −0.632314 1.69320i
\(142\) 4.33607e7i 1.27083i
\(143\) 1.53484e7 3.50085e6i 0.438920 0.100114i
\(144\) −1.61466e7 + 1.40141e7i −0.450622 + 0.391109i
\(145\) 1.29803e7i 0.353586i
\(146\) 1.95728e7i 0.520497i
\(147\) 6.33092e7 2.36425e7i 1.64383 0.613878i
\(148\) 4.79880e7 1.21679
\(149\) 3.30097e7 0.817503 0.408752 0.912646i \(-0.365964\pi\)
0.408752 + 0.912646i \(0.365964\pi\)
\(150\) 5.26102e7 1.96470e7i 1.27277 0.475310i
\(151\) 7.90394e6i 0.186820i −0.995628 0.0934102i \(-0.970223\pi\)
0.995628 0.0934102i \(-0.0297768\pi\)
\(152\) 1.81594e7i 0.419420i
\(153\) −2.22274e7 + 1.92918e7i −0.501727 + 0.435464i
\(154\) −1.11427e8 + 2.54157e7i −2.45849 + 0.560764i
\(155\) 1.44096e7i 0.310807i
\(156\) 9.77041e6 + 2.61630e7i 0.206052 + 0.551761i
\(157\) 5.79006e6 0.119408 0.0597041 0.998216i \(-0.480984\pi\)
0.0597041 + 0.998216i \(0.480984\pi\)
\(158\) 2.10863e7i 0.425305i
\(159\) −6.64423e6 1.77918e7i −0.131086 0.351018i
\(160\) 2.31658e7i 0.447123i
\(161\) −6.08742e7 −1.14959
\(162\) −1.15678e7 + 8.13963e7i −0.213772 + 1.50419i
\(163\) −1.67020e7 −0.302073 −0.151037 0.988528i \(-0.548261\pi\)
−0.151037 + 0.988528i \(0.548261\pi\)
\(164\) −7.27473e7 −1.28784
\(165\) 1.56790e7 1.03097e7i 0.271722 0.178670i
\(166\) 1.01443e8 1.72125
\(167\) −5.41613e7 −0.899873 −0.449936 0.893061i \(-0.648553\pi\)
−0.449936 + 0.893061i \(0.648553\pi\)
\(168\) −1.67144e7 4.47573e7i −0.271962 0.728252i
\(169\) 5.00310e7 0.797326
\(170\) 2.10264e7i 0.328241i
\(171\) 3.83795e7 + 4.42195e7i 0.586966 + 0.676282i
\(172\) 1.15521e8i 1.73105i
\(173\) 1.03863e8 1.52511 0.762554 0.646924i \(-0.223945\pi\)
0.762554 + 0.646924i \(0.223945\pi\)
\(174\) −1.07538e8 + 4.01593e7i −1.54753 + 0.577915i
\(175\) 1.05227e8i 1.48421i
\(176\) −9.59695e6 4.20748e7i −0.132690 0.581738i
\(177\) −1.01816e7 2.72641e7i −0.138010 0.369560i
\(178\) 1.22015e8i 1.62159i
\(179\) 1.48451e7i 0.193463i −0.995311 0.0967316i \(-0.969161\pi\)
0.995311 0.0967316i \(-0.0308389\pi\)
\(180\) 2.18205e7 + 2.51408e7i 0.278875 + 0.321311i
\(181\) −4.88799e7 −0.612710 −0.306355 0.951917i \(-0.599109\pi\)
−0.306355 + 0.951917i \(0.599109\pi\)
\(182\) 9.23276e7 1.13522
\(183\) −1.47490e7 3.94946e7i −0.177904 0.476386i
\(184\) 2.74132e7i 0.324413i
\(185\) 2.60476e7i 0.302460i
\(186\) −1.19379e8 + 4.45815e7i −1.36030 + 0.507995i
\(187\) −1.32111e7 5.79200e7i −0.147739 0.647714i
\(188\) 2.15432e8i 2.36460i
\(189\) 1.35294e8 + 7.36620e7i 1.45768 + 0.793646i
\(190\) 4.18302e7 0.442438
\(191\) 9.62151e7i 0.999140i 0.866273 + 0.499570i \(0.166509\pi\)
−0.866273 + 0.499570i \(0.833491\pi\)
\(192\) 1.37101e8 5.11995e7i 1.39793 0.522049i
\(193\) 1.60072e8i 1.60275i −0.598164 0.801374i \(-0.704103\pi\)
0.598164 0.801374i \(-0.295897\pi\)
\(194\) −1.39092e8 −1.36771
\(195\) −1.42011e7 + 5.30333e6i −0.137152 + 0.0512186i
\(196\) −2.41993e8 −2.29566
\(197\) −1.66964e7 −0.155593 −0.0777965 0.996969i \(-0.524788\pi\)
−0.0777965 + 0.996969i \(0.524788\pi\)
\(198\) −1.33922e8 9.79991e7i −1.22609 0.897210i
\(199\) 1.14515e8 1.03009 0.515045 0.857163i \(-0.327775\pi\)
0.515045 + 0.857163i \(0.327775\pi\)
\(200\) −4.73865e7 −0.418841
\(201\) −8.90128e7 + 3.32413e7i −0.773154 + 0.288730i
\(202\) −8.42023e7 −0.718777
\(203\) 2.15089e8i 1.80460i
\(204\) 9.87310e7 3.68705e7i 0.814232 0.304070i
\(205\) 3.94868e7i 0.320121i
\(206\) 2.80643e8 2.23676
\(207\) −5.79372e7 6.67532e7i −0.454005 0.523089i
\(208\) 3.48628e7i 0.268621i
\(209\) −1.15227e8 + 2.62825e7i −0.873058 + 0.199138i
\(210\) 1.03099e8 3.85016e7i 0.768219 0.286887i
\(211\) 1.51161e8i 1.10778i 0.832591 + 0.553889i \(0.186857\pi\)
−0.832591 + 0.553889i \(0.813143\pi\)
\(212\) 6.80073e7i 0.490208i
\(213\) −4.12712e7 1.10515e8i −0.292630 0.783597i
\(214\) 3.62931e8 2.53149
\(215\) −6.27040e7 −0.430289
\(216\) 3.31719e7 6.09265e7i 0.223966 0.411356i
\(217\) 2.38774e8i 1.58627i
\(218\) 4.24451e8i 2.77479i
\(219\) 1.86296e7 + 4.98860e7i 0.119853 + 0.320940i
\(220\) −6.55118e7 + 1.49428e7i −0.414802 + 0.0946131i
\(221\) 4.79919e7i 0.299085i
\(222\) 2.15797e8 8.05882e7i 1.32376 0.494352i
\(223\) −1.62697e8 −0.982457 −0.491228 0.871031i \(-0.663452\pi\)
−0.491228 + 0.871031i \(0.663452\pi\)
\(224\) 3.83867e8i 2.28199i
\(225\) 1.15390e8 1.00150e8i 0.675348 0.586155i
\(226\) 4.81574e8i 2.77513i
\(227\) −2.43483e8 −1.38158 −0.690792 0.723053i \(-0.742738\pi\)
−0.690792 + 0.723053i \(0.742738\pi\)
\(228\) −7.33510e7 1.96417e8i −0.409858 1.09751i
\(229\) −7.10138e7 −0.390767 −0.195384 0.980727i \(-0.562595\pi\)
−0.195384 + 0.980727i \(0.562595\pi\)
\(230\) −6.31464e7 −0.342217
\(231\) −2.59808e8 + 1.70836e8i −1.38679 + 0.911879i
\(232\) 9.68600e7 0.509257
\(233\) −3.81060e7 −0.197355 −0.0986774 0.995119i \(-0.531461\pi\)
−0.0986774 + 0.995119i \(0.531461\pi\)
\(234\) 8.78730e7 + 1.01244e8i 0.448332 + 0.516553i
\(235\) −1.16936e8 −0.587772
\(236\) 1.04215e8i 0.516103i
\(237\) 2.00702e7 + 5.37435e7i 0.0979338 + 0.262245i
\(238\) 3.48416e8i 1.67525i
\(239\) 3.32792e8 1.57681 0.788406 0.615156i \(-0.210907\pi\)
0.788406 + 0.615156i \(0.210907\pi\)
\(240\) 1.45381e7 + 3.89299e7i 0.0678843 + 0.181779i
\(241\) 2.13039e7i 0.0980390i 0.998798 + 0.0490195i \(0.0156097\pi\)
−0.998798 + 0.0490195i \(0.984390\pi\)
\(242\) 3.01834e8 1.45249e8i 1.36903 0.658808i
\(243\) 4.79906e7 + 2.18468e8i 0.214553 + 0.976712i
\(244\) 1.50965e8i 0.665289i
\(245\) 1.31353e8i 0.570634i
\(246\) −3.27137e8 + 1.22167e8i −1.40106 + 0.523218i
\(247\) 9.54761e7 0.403139
\(248\) 1.07526e8 0.447644
\(249\) 2.58552e8 9.65546e7i 1.06133 0.396347i
\(250\) 2.31218e8i 0.935907i
\(251\) 2.36907e8i 0.945629i 0.881162 + 0.472814i \(0.156762\pi\)
−0.881162 + 0.472814i \(0.843238\pi\)
\(252\) −3.61575e8 4.16594e8i −1.42330 1.63988i
\(253\) 1.73945e8 3.96757e7i 0.675292 0.154029i
\(254\) 6.85065e8i 2.62309i
\(255\) 2.00131e7 + 5.35907e7i 0.0755831 + 0.202394i
\(256\) 3.66821e7 0.136651
\(257\) 1.83527e8i 0.674425i 0.941429 + 0.337212i \(0.109484\pi\)
−0.941429 + 0.337212i \(0.890516\pi\)
\(258\) 1.93998e8 + 5.19484e8i 0.703282 + 1.88323i
\(259\) 4.31621e8i 1.54367i
\(260\) 5.42824e7 0.191537
\(261\) −2.35861e8 + 2.04711e8i −0.821135 + 0.712689i
\(262\) −3.11027e8 −1.06842
\(263\) 3.47905e8 1.17928 0.589638 0.807667i \(-0.299270\pi\)
0.589638 + 0.807667i \(0.299270\pi\)
\(264\) 7.69319e7 + 1.16998e8i 0.257331 + 0.391351i
\(265\) −3.69140e7 −0.121851
\(266\) −6.93146e8 −2.25808
\(267\) −1.16135e8 3.10983e8i −0.373399 0.999880i
\(268\) 3.40243e8 1.07974
\(269\) 5.51585e8i 1.72774i −0.503711 0.863872i \(-0.668032\pi\)
0.503711 0.863872i \(-0.331968\pi\)
\(270\) 1.40344e8 + 7.64115e7i 0.433932 + 0.236257i
\(271\) 2.83981e8i 0.866755i 0.901213 + 0.433377i \(0.142678\pi\)
−0.901213 + 0.433377i \(0.857322\pi\)
\(272\) 1.31561e8 0.396403
\(273\) 2.35319e8 8.78785e7i 0.699983 0.261405i
\(274\) 1.87088e8i 0.549437i
\(275\) 6.85833e7 + 3.00682e8i 0.198863 + 0.871852i
\(276\) 1.10730e8 + 2.96509e8i 0.317017 + 0.848900i
\(277\) 3.38232e8i 0.956170i −0.878313 0.478085i \(-0.841331\pi\)
0.878313 0.478085i \(-0.158669\pi\)
\(278\) 2.29643e7i 0.0641058i
\(279\) −2.61834e8 + 2.27253e8i −0.721790 + 0.626463i
\(280\) −9.28617e7 −0.252804
\(281\) −3.57886e8 −0.962216 −0.481108 0.876661i \(-0.659765\pi\)
−0.481108 + 0.876661i \(0.659765\pi\)
\(282\) 3.61784e8 + 9.68776e8i 0.960677 + 2.57248i
\(283\) 1.65581e8i 0.434267i −0.976142 0.217134i \(-0.930329\pi\)
0.976142 0.217134i \(-0.0696707\pi\)
\(284\) 4.22433e8i 1.09432i
\(285\) 1.06614e8 3.98145e7i 0.272809 0.101879i
\(286\) −2.63822e8 + 6.01759e7i −0.666853 + 0.152104i
\(287\) 6.54314e8i 1.63380i
\(288\) 4.20940e8 3.65346e8i 1.03836 0.901221i
\(289\) −2.29232e8 −0.558640
\(290\) 2.23117e8i 0.537205i
\(291\) −3.54508e8 + 1.32389e8i −0.843337 + 0.314939i
\(292\) 1.90685e8i 0.448204i
\(293\) −3.27097e8 −0.759695 −0.379847 0.925049i \(-0.624024\pi\)
−0.379847 + 0.925049i \(0.624024\pi\)
\(294\) −1.08822e9 + 4.06389e8i −2.49747 + 0.932666i
\(295\) −5.65671e7 −0.128288
\(296\) −1.94370e8 −0.435621
\(297\) −4.34608e8 1.22306e8i −0.962609 0.270895i
\(298\) −5.67402e8 −1.24204
\(299\) −1.44129e8 −0.311820
\(300\) −5.12545e8 + 1.91407e8i −1.09599 + 0.409293i
\(301\) 1.03903e9 2.19607
\(302\) 1.35860e8i 0.283837i
\(303\) −2.14610e8 + 8.01448e7i −0.443200 + 0.165511i
\(304\) 2.61731e8i 0.534315i
\(305\) −8.19427e7 −0.165372
\(306\) 3.82065e8 3.31606e8i 0.762276 0.661603i
\(307\) 3.94124e8i 0.777408i 0.921363 + 0.388704i \(0.127077\pi\)
−0.921363 + 0.388704i \(0.872923\pi\)
\(308\) 1.08556e9 2.47608e8i 2.11703 0.482878i
\(309\) 7.15285e8 2.67119e8i 1.37919 0.515051i
\(310\) 2.47686e8i 0.472211i
\(311\) 1.72708e8i 0.325575i 0.986661 + 0.162788i \(0.0520485\pi\)
−0.986661 + 0.162788i \(0.947951\pi\)
\(312\) −3.95740e7 1.05970e8i −0.0737681 0.197534i
\(313\) −2.48533e8 −0.458119 −0.229060 0.973412i \(-0.573565\pi\)
−0.229060 + 0.973412i \(0.573565\pi\)
\(314\) −9.95251e7 −0.181417
\(315\) 2.26125e8 1.96261e8i 0.407626 0.353791i
\(316\) 2.05429e8i 0.366233i
\(317\) 6.99051e8i 1.23254i −0.787534 0.616271i \(-0.788643\pi\)
0.787534 0.616271i \(-0.211357\pi\)
\(318\) 1.14207e8 + 3.05822e8i 0.199159 + 0.533302i
\(319\) −1.40187e8 6.14607e8i −0.241792 1.06006i
\(320\) 2.84454e8i 0.485274i
\(321\) 9.25016e8 3.45442e8i 1.56092 0.582918i
\(322\) 1.04636e9 1.74657
\(323\) 3.60298e8i 0.594912i
\(324\) 1.12698e8 7.92989e8i 0.184080 1.29527i
\(325\) 2.49142e8i 0.402583i
\(326\) 2.87090e8 0.458941
\(327\) −4.03998e8 1.08182e9i −0.638943 1.71095i
\(328\) 2.94655e8 0.461058
\(329\) 1.93767e9 2.99982
\(330\) −2.69506e8 + 1.77213e8i −0.412828 + 0.271454i
\(331\) −6.14954e8 −0.932062 −0.466031 0.884768i \(-0.654317\pi\)
−0.466031 + 0.884768i \(0.654317\pi\)
\(332\) −9.88289e8 −1.48218
\(333\) 4.73306e8 4.10796e8i 0.702404 0.609638i
\(334\) 9.30975e8 1.36718
\(335\) 1.84682e8i 0.268391i
\(336\) −2.40903e8 6.45085e8i −0.346462 0.927747i
\(337\) 3.16600e8i 0.450616i 0.974288 + 0.225308i \(0.0723388\pi\)
−0.974288 + 0.225308i \(0.927661\pi\)
\(338\) −8.59981e8 −1.21138
\(339\) 4.58368e8 + 1.22741e9i 0.639021 + 1.71116i
\(340\) 2.04845e8i 0.282651i
\(341\) −1.55624e8 6.82286e8i −0.212538 0.931807i
\(342\) −6.59703e8 7.60087e8i −0.891779 1.02748i
\(343\) 9.36156e8i 1.25262i
\(344\) 4.67904e8i 0.619729i
\(345\) −1.60944e8 + 6.01035e7i −0.211012 + 0.0788012i
\(346\) −1.78530e9 −2.31710
\(347\) −1.05014e9 −1.34925 −0.674626 0.738160i \(-0.735695\pi\)
−0.674626 + 0.738160i \(0.735695\pi\)
\(348\) 1.04767e9 3.91245e8i 1.33259 0.497647i
\(349\) 8.07445e8i 1.01677i 0.861129 + 0.508386i \(0.169758\pi\)
−0.861129 + 0.508386i \(0.830242\pi\)
\(350\) 1.80874e9i 2.25496i
\(351\) 3.20331e8 + 1.74407e8i 0.395388 + 0.215272i
\(352\) 2.50191e8 + 1.09688e9i 0.305754 + 1.34048i
\(353\) 6.42480e8i 0.777406i −0.921363 0.388703i \(-0.872923\pi\)
0.921363 0.388703i \(-0.127077\pi\)
\(354\) 1.75012e8 + 4.68642e8i 0.209679 + 0.561474i
\(355\) −2.29295e8 −0.272016
\(356\) 1.18870e9i 1.39637i
\(357\) −3.31626e8 8.88021e8i −0.385754 1.03296i
\(358\) 2.55172e8i 0.293929i
\(359\) −1.21411e9 −1.38493 −0.692464 0.721452i \(-0.743475\pi\)
−0.692464 + 0.721452i \(0.743475\pi\)
\(360\) −8.83814e7 1.01830e8i −0.0998394 0.115032i
\(361\) 1.77089e8 0.198114
\(362\) 8.40194e8 0.930892
\(363\) 6.31046e8 6.57490e8i 0.692449 0.721467i
\(364\) −8.99484e8 −0.977549
\(365\) 1.03503e8 0.111410
\(366\) 2.53521e8 + 6.78871e8i 0.270290 + 0.723775i
\(367\) 2.98569e8 0.315292 0.157646 0.987496i \(-0.449609\pi\)
0.157646 + 0.987496i \(0.449609\pi\)
\(368\) 3.95105e8i 0.413281i
\(369\) −7.17506e8 + 6.22745e8i −0.743418 + 0.645235i
\(370\) 4.47732e8i 0.459528i
\(371\) 6.11682e8 0.621895
\(372\) 1.16303e9 4.34327e8i 1.17136 0.437438i
\(373\) 1.65310e9i 1.64937i 0.565594 + 0.824684i \(0.308647\pi\)
−0.565594 + 0.824684i \(0.691353\pi\)
\(374\) 2.27085e8 + 9.95584e8i 0.224460 + 0.984073i
\(375\) −2.20076e8 5.89315e8i −0.215508 0.577083i
\(376\) 8.72585e8i 0.846545i
\(377\) 5.09257e8i 0.489488i
\(378\) −2.32557e9 1.26617e9i −2.21466 1.20579i
\(379\) −1.56573e8 −0.147734 −0.0738669 0.997268i \(-0.523534\pi\)
−0.0738669 + 0.997268i \(0.523534\pi\)
\(380\) −4.07523e8 −0.380987
\(381\) −6.52053e8 1.74605e9i −0.604011 1.61741i
\(382\) 1.65384e9i 1.51800i
\(383\) 1.20689e9i 1.09767i −0.835932 0.548834i \(-0.815072\pi\)
0.835932 0.548834i \(-0.184928\pi\)
\(384\) −9.27447e8 + 3.46350e8i −0.835853 + 0.312145i
\(385\) 1.34400e8 + 5.89236e8i 0.120030 + 0.526232i
\(386\) 2.75147e9i 2.43506i
\(387\) 9.88903e8 + 1.13938e9i 0.867292 + 0.999264i
\(388\) 1.35507e9 1.17775
\(389\) 8.41324e7i 0.0724669i 0.999343 + 0.0362335i \(0.0115360\pi\)
−0.999343 + 0.0362335i \(0.988464\pi\)
\(390\) 2.44102e8 9.11587e7i 0.208375 0.0778165i
\(391\) 5.43901e8i 0.460151i
\(392\) 9.80167e8 0.821862
\(393\) −7.92726e8 + 2.96039e8i −0.658793 + 0.246023i
\(394\) 2.86993e8 0.236393
\(395\) 1.11506e8 0.0910350
\(396\) 1.30471e9 + 9.54738e8i 1.05579 + 0.772594i
\(397\) 2.75369e8 0.220876 0.110438 0.993883i \(-0.464775\pi\)
0.110438 + 0.993883i \(0.464775\pi\)
\(398\) −1.96839e9 −1.56502
\(399\) −1.76665e9 + 6.59744e8i −1.39234 + 0.519961i
\(400\) −6.82979e8 −0.533577
\(401\) 1.02279e8i 0.0792103i 0.999215 + 0.0396051i \(0.0126100\pi\)
−0.999215 + 0.0396051i \(0.987390\pi\)
\(402\) 1.53004e9 5.71383e8i 1.17466 0.438668i
\(403\) 5.65335e8i 0.430267i
\(404\) 8.20325e8 0.618944
\(405\) 4.30430e8 + 6.11717e7i 0.321966 + 0.0457570i
\(406\) 3.69715e9i 2.74174i
\(407\) 2.81316e8 + 1.23334e9i 0.206830 + 0.906780i
\(408\) −3.99899e8 + 1.49340e8i −0.291501 + 0.108859i
\(409\) 2.21805e9i 1.60303i −0.597977 0.801513i \(-0.704029\pi\)
0.597977 0.801513i \(-0.295971\pi\)
\(410\) 6.78737e8i 0.486360i
\(411\) 1.78072e8 + 4.76837e8i 0.126517 + 0.338785i
\(412\) −2.73411e9 −1.92609
\(413\) 9.37342e8 0.654746
\(414\) 9.95879e8 + 1.14742e9i 0.689772 + 0.794732i
\(415\) 5.36438e8i 0.368427i
\(416\) 9.08867e8i 0.618976i
\(417\) 2.18577e7 + 5.85301e7i 0.0147614 + 0.0395278i
\(418\) 1.98063e9 4.51768e8i 1.32644 0.302551i
\(419\) 1.77010e9i 1.17557i −0.809016 0.587786i \(-0.800000\pi\)
0.809016 0.587786i \(-0.200000\pi\)
\(420\) −1.00442e9 + 3.75094e8i −0.661519 + 0.247040i
\(421\) −4.18994e7 −0.0273666 −0.0136833 0.999906i \(-0.504356\pi\)
−0.0136833 + 0.999906i \(0.504356\pi\)
\(422\) 2.59831e9i 1.68305i
\(423\) 1.84419e9 + 2.12481e9i 1.18471 + 1.36499i
\(424\) 2.75456e8i 0.175498i
\(425\) −9.40186e8 −0.594090
\(426\) 7.09409e8 + 1.89964e9i 0.444594 + 1.19052i
\(427\) 1.35783e9 0.844009
\(428\) −3.53578e9 −2.17988
\(429\) −6.15138e8 + 4.04482e8i −0.376159 + 0.247342i
\(430\) 1.07782e9 0.653740
\(431\) 1.47449e9 0.887096 0.443548 0.896251i \(-0.353720\pi\)
0.443548 + 0.896251i \(0.353720\pi\)
\(432\) 4.78105e8 8.78130e8i 0.285319 0.524042i
\(433\) −1.82639e9 −1.08115 −0.540575 0.841296i \(-0.681793\pi\)
−0.540575 + 0.841296i \(0.681793\pi\)
\(434\) 4.10427e9i 2.41003i
\(435\) 2.12365e8 + 5.68667e8i 0.123701 + 0.331242i
\(436\) 4.13514e9i 2.38939i
\(437\) 1.08205e9 0.620242
\(438\) −3.20224e8 8.57488e8i −0.182094 0.487606i
\(439\) 8.64064e8i 0.487439i −0.969846 0.243719i \(-0.921632\pi\)
0.969846 0.243719i \(-0.0783676\pi\)
\(440\) 2.65348e8 6.05240e7i 0.148502 0.0338722i
\(441\) −2.38678e9 + 2.07156e9i −1.32519 + 1.15017i
\(442\) 8.24931e8i 0.454402i
\(443\) 1.93792e9i 1.05907i −0.848289 0.529533i \(-0.822367\pi\)
0.848289 0.529533i \(-0.177633\pi\)
\(444\) −2.10236e9 + 7.85115e8i −1.13990 + 0.425690i
\(445\) −6.45223e8 −0.347096
\(446\) 2.79660e9 1.49265
\(447\) −1.44616e9 + 5.40060e8i −0.765843 + 0.286000i
\(448\) 4.71353e9i 2.47670i
\(449\) 2.62445e9i 1.36828i 0.729350 + 0.684141i \(0.239823\pi\)
−0.729350 + 0.684141i \(0.760177\pi\)
\(450\) −1.98343e9 + 1.72148e9i −1.02606 + 0.890547i
\(451\) −4.26459e8 1.86968e9i −0.218907 0.959729i
\(452\) 4.69165e9i 2.38969i
\(453\) 1.29314e8 + 3.46273e8i 0.0653583 + 0.175015i
\(454\) 4.18521e9 2.09905
\(455\) 4.88235e8i 0.242990i
\(456\) 2.97100e8 + 7.95567e8i 0.146732 + 0.392916i
\(457\) 1.97630e8i 0.0968602i 0.998827 + 0.0484301i \(0.0154218\pi\)
−0.998827 + 0.0484301i \(0.984578\pi\)
\(458\) 1.22065e9 0.593694
\(459\) 6.58157e8 1.20883e9i 0.317677 0.583473i
\(460\) 6.15192e8 0.294685
\(461\) −2.12787e9 −1.01156 −0.505781 0.862662i \(-0.668795\pi\)
−0.505781 + 0.862662i \(0.668795\pi\)
\(462\) 4.46583e9 2.93649e9i 2.10696 1.38542i
\(463\) −1.17054e9 −0.548091 −0.274045 0.961717i \(-0.588362\pi\)
−0.274045 + 0.961717i \(0.588362\pi\)
\(464\) 1.39604e9 0.648760
\(465\) 2.35751e8 + 6.31287e8i 0.108734 + 0.291167i
\(466\) 6.55002e8 0.299842
\(467\) 9.29267e8i 0.422213i −0.977463 0.211107i \(-0.932293\pi\)
0.977463 0.211107i \(-0.0677067\pi\)
\(468\) −8.56086e8 9.86353e8i −0.386062 0.444807i
\(469\) 3.06026e9i 1.36979i
\(470\) 2.01000e9 0.893004
\(471\) −2.53663e8 + 9.47292e7i −0.111863 + 0.0417744i
\(472\) 4.22110e8i 0.184769i
\(473\) −2.96899e9 + 6.77206e8i −1.29002 + 0.294243i
\(474\) −3.44986e8 9.23795e8i −0.148791 0.398429i
\(475\) 1.87042e9i 0.800778i
\(476\) 3.39438e9i 1.44257i
\(477\) 5.82170e8 + 6.70756e8i 0.245604 + 0.282976i
\(478\) −5.72034e9 −2.39565
\(479\) 2.34570e9 0.975209 0.487605 0.873065i \(-0.337871\pi\)
0.487605 + 0.873065i \(0.337871\pi\)
\(480\) −3.79007e8 1.01490e9i −0.156424 0.418868i
\(481\) 1.02193e9i 0.418711i
\(482\) 3.66191e8i 0.148951i
\(483\) 2.66691e9 9.95941e8i 1.07694 0.402178i
\(484\) −2.94056e9 + 1.41506e9i −1.17888 + 0.567304i
\(485\) 7.35527e8i 0.292754i
\(486\) −8.24908e8 3.75524e9i −0.325971 1.48392i
\(487\) 2.47213e9 0.969882 0.484941 0.874547i \(-0.338841\pi\)
0.484941 + 0.874547i \(0.338841\pi\)
\(488\) 6.11465e8i 0.238178i
\(489\) 7.31718e8 2.73256e8i 0.282985 0.105679i
\(490\) 2.25782e9i 0.866966i
\(491\) −4.41850e9 −1.68457 −0.842287 0.539030i \(-0.818791\pi\)
−0.842287 + 0.539030i \(0.818791\pi\)
\(492\) 3.18707e9 1.19019e9i 1.20646 0.450546i
\(493\) 1.92178e9 0.722337
\(494\) −1.64113e9 −0.612491
\(495\) −5.18227e8 + 7.08187e8i −0.192044 + 0.262440i
\(496\) 1.54977e9 0.570270
\(497\) 3.79951e9 1.38829
\(498\) −4.44423e9 + 1.65967e9i −1.61248 + 0.602171i
\(499\) 2.81853e9 1.01548 0.507740 0.861510i \(-0.330481\pi\)
0.507740 + 0.861510i \(0.330481\pi\)
\(500\) 2.25260e9i 0.805916i
\(501\) 2.37281e9 8.86113e8i 0.843008 0.314816i
\(502\) 4.07219e9i 1.43670i
\(503\) 1.28396e9 0.449844 0.224922 0.974377i \(-0.427787\pi\)
0.224922 + 0.974377i \(0.427787\pi\)
\(504\) 1.46452e9 + 1.68737e9i 0.509551 + 0.587088i
\(505\) 4.45268e8i 0.153852i
\(506\) −2.98994e9 + 6.81983e8i −1.02597 + 0.234017i
\(507\) −2.19187e9 + 8.18540e8i −0.746941 + 0.278941i
\(508\) 6.67411e9i 2.25876i
\(509\) 6.98994e8i 0.234942i 0.993076 + 0.117471i \(0.0374788\pi\)
−0.993076 + 0.117471i \(0.962521\pi\)
\(510\) −3.44005e8 9.21168e8i −0.114834 0.307499i
\(511\) −1.71508e9 −0.568607
\(512\) −3.34025e9 −1.09985
\(513\) −2.40487e9 1.30935e9i −0.786468 0.428199i
\(514\) 3.15463e9i 1.02466i
\(515\) 1.48406e9i 0.478769i
\(516\) −1.88999e9 5.06098e9i −0.605601 1.62166i
\(517\) −5.53682e9 + 1.26291e9i −1.76215 + 0.401934i
\(518\) 7.41911e9i 2.34530i
\(519\) −4.55027e9 + 1.69927e9i −1.42873 + 0.533552i
\(520\) −2.19865e8 −0.0685716
\(521\) 2.63160e9i 0.815245i 0.913151 + 0.407622i \(0.133642\pi\)
−0.913151 + 0.407622i \(0.866358\pi\)
\(522\) 4.05421e9 3.51877e9i 1.24755 1.08279i
\(523\) 8.06360e8i 0.246475i −0.992377 0.123238i \(-0.960672\pi\)
0.992377 0.123238i \(-0.0393277\pi\)
\(524\) 3.03012e9 0.920027
\(525\) 1.72158e9 + 4.61001e9i 0.519243 + 1.39042i
\(526\) −5.98013e9 −1.79168
\(527\) 2.13340e9 0.634944
\(528\) 1.10881e9 + 1.68629e9i 0.327824 + 0.498556i
\(529\) 1.77138e9 0.520256
\(530\) 6.34513e8 0.185129
\(531\) 8.92118e8 + 1.02787e9i 0.258578 + 0.297925i
\(532\) 6.75284e9 1.94445
\(533\) 1.54919e9i 0.443160i
\(534\) 1.99624e9 + 5.34548e9i 0.567307 + 1.51912i
\(535\) 1.91921e9i 0.541855i
\(536\) −1.37812e9 −0.386553
\(537\) 2.42876e8 + 6.50367e8i 0.0676822 + 0.181238i
\(538\) 9.48117e9i 2.62497i
\(539\) −1.41861e9 6.21947e9i −0.390215 1.71077i
\(540\) −1.36728e9 7.44425e8i −0.373662 0.203443i
\(541\) 6.85116e8i 0.186026i 0.995665 + 0.0930130i \(0.0296498\pi\)
−0.995665 + 0.0930130i \(0.970350\pi\)
\(542\) 4.88133e9i 1.31686i
\(543\) 2.14143e9 7.99706e8i 0.573991 0.214354i
\(544\) −3.42979e9 −0.913421
\(545\) −2.24453e9 −0.593934
\(546\) −4.04489e9 + 1.51054e9i −1.06349 + 0.397153i
\(547\) 3.43701e9i 0.897893i 0.893559 + 0.448946i \(0.148201\pi\)
−0.893559 + 0.448946i \(0.851799\pi\)
\(548\) 1.82267e9i 0.473124i
\(549\) 1.29232e9 + 1.48896e9i 0.333323 + 0.384043i
\(550\) −1.17888e9 5.16841e9i −0.302133 1.32461i
\(551\) 3.82323e9i 0.973643i
\(552\) −4.48498e8 1.20098e9i −0.113494 0.303912i
\(553\) −1.84770e9 −0.464616
\(554\) 5.81385e9i 1.45271i
\(555\) −4.26156e8 1.14115e9i −0.105814 0.283346i
\(556\) 2.23726e8i 0.0552019i
\(557\) 4.55366e9 1.11652 0.558261 0.829665i \(-0.311469\pi\)
0.558261 + 0.829665i \(0.311469\pi\)
\(558\) 4.50064e9 3.90625e9i 1.09662 0.951788i
\(559\) 2.46008e9 0.595673
\(560\) −1.33841e9 −0.322056
\(561\) 1.52639e9 + 2.32134e9i 0.365002 + 0.555097i
\(562\) 6.15168e9 1.46190
\(563\) 1.43713e9 0.339405 0.169702 0.985495i \(-0.445719\pi\)
0.169702 + 0.985495i \(0.445719\pi\)
\(564\) −3.52461e9 9.43812e9i −0.827246 2.21518i
\(565\) 2.54660e9 0.594007
\(566\) 2.84616e9i 0.659784i
\(567\) −7.13242e9 1.01364e9i −1.64322 0.233531i
\(568\) 1.71102e9i 0.391774i
\(569\) −4.72921e9 −1.07621 −0.538103 0.842879i \(-0.680859\pi\)
−0.538103 + 0.842879i \(0.680859\pi\)
\(570\) −1.83259e9 + 6.84370e8i −0.414480 + 0.154785i
\(571\) 5.46491e9i 1.22845i −0.789132 0.614224i \(-0.789469\pi\)
0.789132 0.614224i \(-0.210531\pi\)
\(572\) 2.57024e9 5.86252e8i 0.574232 0.130978i
\(573\) −1.57414e9 4.21520e9i −0.349545 0.936002i
\(574\) 1.12470e10i 2.48224i
\(575\) 2.82357e9i 0.619385i
\(576\) −5.16875e9 + 4.48612e9i −1.12696 + 0.978119i
\(577\) 1.40691e9 0.304896 0.152448 0.988311i \(-0.451284\pi\)
0.152448 + 0.988311i \(0.451284\pi\)
\(578\) 3.94025e9 0.848744
\(579\) 2.61888e9 + 7.01278e9i 0.560714 + 1.50147i
\(580\) 2.17368e9i 0.462591i
\(581\) 8.88902e9i 1.88034i
\(582\) 6.09363e9 2.27563e9i 1.28128 0.478488i
\(583\) −1.74785e9 + 3.98673e8i −0.365313 + 0.0833252i
\(584\) 7.72347e8i 0.160460i
\(585\) 5.35387e8 4.64679e8i 0.110566 0.0959638i
\(586\) 5.62245e9 1.15421
\(587\) 2.19542e9i 0.448007i −0.974588 0.224003i \(-0.928087\pi\)
0.974588 0.224003i \(-0.0719127\pi\)
\(588\) 1.06018e10 3.95917e9i 2.15059 0.803125i
\(589\) 4.24423e9i 0.855846i
\(590\) 9.72329e8 0.194909
\(591\) 7.31470e8 2.73163e8i 0.145761 0.0544335i
\(592\) −2.80145e9 −0.554953
\(593\) −3.84584e9 −0.757355 −0.378677 0.925529i \(-0.623621\pi\)
−0.378677 + 0.925529i \(0.623621\pi\)
\(594\) 7.47045e9 + 2.10231e9i 1.46250 + 0.411571i
\(595\) −1.84245e9 −0.358580
\(596\) 5.52781e9 1.06953
\(597\) −5.01690e9 + 1.87353e9i −0.964996 + 0.360372i
\(598\) 2.47744e9 0.473749
\(599\) 3.80221e9i 0.722840i 0.932403 + 0.361420i \(0.117708\pi\)
−0.932403 + 0.361420i \(0.882292\pi\)
\(600\) 2.07601e9 7.75274e8i 0.392374 0.146530i
\(601\) 2.11400e9i 0.397233i 0.980077 + 0.198616i \(0.0636448\pi\)
−0.980077 + 0.198616i \(0.936355\pi\)
\(602\) −1.78599e10 −3.33650
\(603\) 3.35581e9 2.91261e9i 0.623286 0.540969i
\(604\) 1.32360e9i 0.244414i
\(605\) −7.68087e8 1.59612e9i −0.141015 0.293037i
\(606\) 3.68892e9 1.37760e9i 0.673356 0.251461i
\(607\) 4.49197e9i 0.815223i 0.913155 + 0.407611i \(0.133638\pi\)
−0.913155 + 0.407611i \(0.866362\pi\)
\(608\) 6.82329e9i 1.23121i
\(609\) −3.51899e9 9.42307e9i −0.631332 1.69056i
\(610\) 1.40851e9 0.251250
\(611\) 4.58776e9 0.813684
\(612\) −3.72220e9 + 3.23061e9i −0.656401 + 0.569711i
\(613\) 9.04115e8i 0.158530i −0.996854 0.0792651i \(-0.974743\pi\)
0.996854 0.0792651i \(-0.0252574\pi\)
\(614\) 6.77458e9i 1.18112i
\(615\) 6.46030e8 + 1.72992e9i 0.111993 + 0.299891i
\(616\) −4.39694e9 + 1.00291e9i −0.757911 + 0.172874i
\(617\) 1.22475e9i 0.209918i −0.994477 0.104959i \(-0.966529\pi\)
0.994477 0.104959i \(-0.0334712\pi\)
\(618\) −1.22950e10 + 4.59150e9i −2.09541 + 0.782519i
\(619\) −6.43876e9 −1.09115 −0.545576 0.838062i \(-0.683689\pi\)
−0.545576 + 0.838062i \(0.683689\pi\)
\(620\) 2.41304e9i 0.406624i
\(621\) 3.63036e9 + 1.97658e9i 0.608316 + 0.331202i
\(622\) 2.96867e9i 0.494648i
\(623\) 1.06916e10 1.77148
\(624\) −5.70377e8 1.52734e9i −0.0939758 0.251646i
\(625\) 4.23533e9 0.693917
\(626\) 4.27202e9 0.696022
\(627\) 4.61812e9 3.03663e9i 0.748220 0.491989i
\(628\) 9.69605e8 0.156220
\(629\) −3.85646e9 −0.617891
\(630\) −3.88685e9 + 3.37352e9i −0.619307 + 0.537516i
\(631\) 1.66316e9 0.263530 0.131765 0.991281i \(-0.457936\pi\)
0.131765 + 0.991281i \(0.457936\pi\)
\(632\) 8.32069e8i 0.131114i
\(633\) −2.47310e9 6.62241e9i −0.387551 1.03777i
\(634\) 1.20160e10i 1.87260i
\(635\) −3.62267e9 −0.561463
\(636\) −1.11264e9 2.97941e9i −0.171497 0.459230i
\(637\) 5.15339e9i 0.789959i
\(638\) 2.40967e9 + 1.05645e10i 0.367355 + 1.61055i
\(639\) 3.61620e9 + 4.16646e9i 0.548276 + 0.631705i
\(640\) 1.92425e9i 0.290156i
\(641\) 2.73222e9i 0.409744i 0.978789 + 0.204872i \(0.0656778\pi\)
−0.978789 + 0.204872i \(0.934322\pi\)
\(642\) −1.59001e10 + 5.93778e9i −2.37152 + 0.885629i
\(643\) 1.02739e10 1.52405 0.762023 0.647550i \(-0.224206\pi\)
0.762023 + 0.647550i \(0.224206\pi\)
\(644\) −1.01940e10 −1.50399
\(645\) 2.74707e9 1.02588e9i 0.403098 0.150535i
\(646\) 6.19314e9i 0.903851i
\(647\) 4.55706e9i 0.661485i −0.943721 0.330742i \(-0.892701\pi\)
0.943721 0.330742i \(-0.107299\pi\)
\(648\) −4.56469e8 + 3.21191e9i −0.0659021 + 0.463715i
\(649\) −2.67842e9 + 6.10927e8i −0.384611 + 0.0877269i
\(650\) 4.28249e9i 0.611645i
\(651\) −3.90649e9 1.04607e10i −0.554949 1.48603i
\(652\) −2.79692e9 −0.395197
\(653\) 3.74412e8i 0.0526203i 0.999654 + 0.0263101i \(0.00837574\pi\)
−0.999654 + 0.0263101i \(0.991624\pi\)
\(654\) 6.94430e9 + 1.85953e10i 0.970748 + 2.59944i
\(655\) 1.64473e9i 0.228692i
\(656\) 4.24684e9 0.587358
\(657\) −1.63233e9 1.88072e9i −0.224559 0.258729i
\(658\) −3.33066e10 −4.55763
\(659\) 1.99436e9 0.271459 0.135730 0.990746i \(-0.456662\pi\)
0.135730 + 0.990746i \(0.456662\pi\)
\(660\) 2.62561e9 1.72646e9i 0.355489 0.233751i
\(661\) −3.02625e9 −0.407567 −0.203784 0.979016i \(-0.565324\pi\)
−0.203784 + 0.979016i \(0.565324\pi\)
\(662\) 1.05704e10 1.41609
\(663\) −7.85179e8 2.10253e9i −0.104634 0.280186i
\(664\) 4.00296e9 0.530631
\(665\) 3.66541e9i 0.483333i
\(666\) −8.13563e9 + 7.06116e9i −1.06716 + 0.926225i
\(667\) 5.77149e9i 0.753092i
\(668\) −9.06985e9 −1.17729
\(669\) 7.12780e9 2.66183e9i 0.920373 0.343708i
\(670\) 3.17449e9i 0.407767i
\(671\) −3.87994e9 + 8.84984e8i −0.495788 + 0.113085i
\(672\) 6.28031e9 + 1.68173e10i 0.798342 + 2.13778i
\(673\) 7.32088e9i 0.925786i −0.886414 0.462893i \(-0.846811\pi\)
0.886414 0.462893i \(-0.153189\pi\)
\(674\) 5.44202e9i 0.684622i
\(675\) −3.41671e9 + 6.27544e9i −0.427607 + 0.785382i
\(676\) 8.37820e9 1.04313
\(677\) −7.83766e9 −0.970792 −0.485396 0.874295i \(-0.661324\pi\)
−0.485396 + 0.874295i \(0.661324\pi\)
\(678\) −7.87887e9 2.10978e10i −0.970867 2.59976i
\(679\) 1.21880e10i 1.49413i
\(680\) 8.29704e8i 0.101191i
\(681\) 1.06670e10 3.98353e9i 1.29428 0.483341i
\(682\) 2.67502e9 + 1.17278e10i 0.322910 + 1.41570i
\(683\) 9.04868e9i 1.08671i −0.839504 0.543354i \(-0.817154\pi\)
0.839504 0.543354i \(-0.182846\pi\)
\(684\) 6.42703e9 + 7.40501e9i 0.767917 + 0.884768i
\(685\) 9.89333e8 0.117605
\(686\) 1.60915e10i 1.90311i
\(687\) 3.11112e9 1.16183e9i 0.366074 0.136708i
\(688\) 6.74387e9i 0.789496i
\(689\) 1.44826e9 0.168686
\(690\) 2.76645e9 1.03312e9i 0.320591 0.119723i
\(691\) −3.93165e9 −0.453316 −0.226658 0.973974i \(-0.572780\pi\)
−0.226658 + 0.973974i \(0.572780\pi\)
\(692\) 1.73930e10 1.99527
\(693\) 8.58725e9 1.17350e10i 0.980139 1.33942i
\(694\) 1.80508e10 2.04992
\(695\) 1.21437e8 0.0137216
\(696\) −4.24345e9 + 1.58469e9i −0.477075 + 0.178161i
\(697\) 5.84619e9 0.653970
\(698\) 1.38791e10i 1.54479i
\(699\) 1.66943e9 6.23439e8i 0.184883 0.0690437i
\(700\) 1.76213e10i 1.94176i
\(701\) 5.21221e9 0.571490 0.285745 0.958306i \(-0.407759\pi\)
0.285745 + 0.958306i \(0.407759\pi\)
\(702\) −5.50615e9 2.99787e9i −0.600715 0.327064i
\(703\) 7.67212e9i 0.832859i
\(704\) −3.07211e9 1.34687e10i −0.331843 1.45486i
\(705\) 5.12296e9 1.91314e9i 0.550629 0.205629i
\(706\) 1.10436e10i 1.18112i
\(707\) 7.37829e9i 0.785214i
\(708\) −1.70502e9 4.56566e9i −0.180556 0.483489i
\(709\) −7.80610e8 −0.0822569 −0.0411285 0.999154i \(-0.513095\pi\)
−0.0411285 + 0.999154i \(0.513095\pi\)
\(710\) 3.94134e9 0.413275
\(711\) −1.75856e9 2.02615e9i −0.183490 0.211411i
\(712\) 4.81472e9i 0.499909i
\(713\) 6.40703e9i 0.661978i
\(714\) 5.70031e9 + 1.52642e10i 0.586077 + 1.56938i
\(715\) 3.18215e8 + 1.39511e9i 0.0325574 + 0.142737i
\(716\) 2.48597e9i 0.253105i
\(717\) −1.45797e10 + 5.44469e9i −1.47717 + 0.551640i
\(718\) 2.08693e10 2.10413
\(719\) 1.70514e10i 1.71084i 0.517936 + 0.855419i \(0.326700\pi\)
−0.517936 + 0.855419i \(0.673300\pi\)
\(720\) −1.27384e9 1.46767e9i −0.127189 0.146543i
\(721\) 2.45915e10i 2.44350i
\(722\) −3.04397e9 −0.300996
\(723\) −3.48545e8 9.33326e8i −0.0342985 0.0918437i
\(724\) −8.18543e9 −0.801598
\(725\) −9.97660e9 −0.972298
\(726\) −1.08470e10 + 1.13016e10i −1.05204 + 1.09613i
\(727\) −1.69760e10 −1.63857 −0.819285 0.573386i \(-0.805630\pi\)
−0.819285 + 0.573386i \(0.805630\pi\)
\(728\) 3.64326e9 0.349970
\(729\) −5.67676e9 8.78598e9i −0.542693 0.839931i
\(730\) −1.77910e9 −0.169266
\(731\) 9.28358e9i 0.879032i
\(732\) −2.46988e9 6.61378e9i −0.232748 0.623248i
\(733\) 2.18459e7i 0.00204883i −0.999999 0.00102442i \(-0.999674\pi\)
0.999999 0.00102442i \(-0.000326082\pi\)
\(734\) −5.13209e9 −0.479025
\(735\) 2.14902e9 + 5.75458e9i 0.199634 + 0.534574i
\(736\) 1.03003e10i 0.952312i
\(737\) 1.99457e9 + 8.74458e9i 0.183533 + 0.804642i
\(738\) 1.23332e10 1.07043e10i 1.12948 0.980308i
\(739\) 3.00892e9i 0.274256i 0.990553 + 0.137128i \(0.0437871\pi\)
−0.990553 + 0.137128i \(0.956213\pi\)
\(740\) 4.36194e9i 0.395703i
\(741\) −4.18282e9 + 1.56205e9i −0.377664 + 0.141036i
\(742\) −1.05142e10 −0.944846
\(743\) 4.99839e9 0.447063 0.223532 0.974697i \(-0.428241\pi\)
0.223532 + 0.974697i \(0.428241\pi\)
\(744\) −4.71073e9 + 1.75919e9i −0.419356 + 0.156606i
\(745\) 3.00047e9i 0.265853i
\(746\) 2.84150e10i 2.50589i
\(747\) −9.74749e9 + 8.46014e9i −0.855600 + 0.742601i
\(748\) −2.21234e9 9.69929e9i −0.193284 0.847392i
\(749\) 3.18021e10i 2.76547i
\(750\) 3.78288e9 + 1.01297e10i 0.327423 + 0.876764i
\(751\) −9.37269e9 −0.807467 −0.403733 0.914877i \(-0.632288\pi\)
−0.403733 + 0.914877i \(0.632288\pi\)
\(752\) 1.25765e10i 1.07844i
\(753\) −3.87596e9 1.03790e10i −0.330824 0.885872i
\(754\) 8.75360e9i 0.743681i
\(755\) 7.18440e8 0.0607542
\(756\) 2.26564e10 + 1.23354e10i 1.90706 + 1.03831i
\(757\) −3.29570e9 −0.276129 −0.138064 0.990423i \(-0.544088\pi\)
−0.138064 + 0.990423i \(0.544088\pi\)
\(758\) 2.69133e9 0.224452
\(759\) −6.97146e9 + 4.58406e9i −0.578732 + 0.380543i
\(760\) 1.65063e9 0.136396
\(761\) 7.79377e9 0.641064 0.320532 0.947238i \(-0.396138\pi\)
0.320532 + 0.947238i \(0.396138\pi\)
\(762\) 1.12081e10 + 3.00128e10i 0.917677 + 2.45733i
\(763\) 3.71929e10 3.03126
\(764\) 1.61122e10i 1.30716i
\(765\) −1.75356e9 2.02039e9i −0.141614 0.163162i
\(766\) 2.07451e10i 1.66769i
\(767\) 2.21931e9 0.177596
\(768\) −1.60705e9 + 6.00143e8i −0.128016 + 0.0478069i
\(769\) 1.81737e10i 1.44112i −0.693392 0.720560i \(-0.743885\pi\)
0.693392 0.720560i \(-0.256115\pi\)
\(770\) −2.31020e9 1.01284e10i −0.182361 0.799505i
\(771\) −3.00262e9 8.04033e9i −0.235944 0.631806i
\(772\) 2.68057e10i 2.09685i
\(773\) 6.21890e9i 0.484268i 0.970243 + 0.242134i \(0.0778473\pi\)
−0.970243 + 0.242134i \(0.922153\pi\)
\(774\) −1.69982e10 1.95847e10i −1.31768 1.51818i
\(775\) −1.10752e10 −0.854664
\(776\) −5.48858e9 −0.421642
\(777\) 7.06160e9 + 1.89094e10i 0.540045 + 1.44612i
\(778\) 1.44615e9i 0.110099i
\(779\) 1.16305e10i 0.881491i
\(780\) −2.37812e9 + 8.88096e8i −0.179433 + 0.0670083i
\(781\) −1.08570e10 + 2.47639e9i −0.815510 + 0.186012i
\(782\) 9.34908e9i 0.699110i
\(783\) 6.98391e9 1.28273e10i 0.519915 0.954922i
\(784\) 1.41271e10 1.04700
\(785\) 5.26296e8i 0.0388317i
\(786\) 1.36261e10 5.08860e9i 1.00091 0.373783i
\(787\) 1.00229e9i 0.0732965i −0.999328 0.0366482i \(-0.988332\pi\)
0.999328 0.0366482i \(-0.0116681\pi\)
\(788\) −2.79598e9 −0.203560
\(789\) −1.52418e10 + 5.69195e9i −1.10476 + 0.412565i
\(790\) −1.91667e9 −0.138310
\(791\) −4.21983e10 −3.03164
\(792\) −5.28457e9 3.86706e9i −0.377982 0.276594i
\(793\) 3.21488e9 0.228933
\(794\) −4.73331e9 −0.335578
\(795\) 1.61721e9 6.03937e8i 0.114151 0.0426292i
\(796\) 1.91766e10 1.34765
\(797\) 1.31177e10i 0.917814i 0.888484 + 0.458907i \(0.151759\pi\)
−0.888484 + 0.458907i \(0.848241\pi\)
\(798\) 3.03668e10 1.13403e10i 2.11538 0.789978i
\(799\) 1.73128e10i 1.20075i
\(800\) 1.78052e10 1.22951
\(801\) 1.01758e10 + 1.17242e10i 0.699607 + 0.806063i
\(802\) 1.75807e9i 0.120344i
\(803\) 4.90078e9 1.11783e9i 0.334011 0.0761854i
\(804\) −1.49061e10 + 5.56660e9i −1.01150 + 0.377740i
\(805\) 5.53325e9i 0.373848i
\(806\) 9.71752e9i 0.653706i
\(807\) 9.02429e9 + 2.41650e10i 0.604443 + 1.61856i
\(808\) −3.32264e9 −0.221586
\(809\) 2.43034e10 1.61379 0.806895 0.590695i \(-0.201146\pi\)
0.806895 + 0.590695i \(0.201146\pi\)
\(810\) −7.39864e9 1.05148e9i −0.489164 0.0695188i
\(811\) 1.74656e10i 1.14977i 0.818234 + 0.574886i \(0.194954\pi\)
−0.818234 + 0.574886i \(0.805046\pi\)
\(812\) 3.60188e10i 2.36093i
\(813\) −4.64611e9 1.24412e10i −0.303230 0.811982i
\(814\) −4.83552e9 2.11998e10i −0.314237 1.37767i
\(815\) 1.51815e9i 0.0982346i
\(816\) −5.76372e9 + 2.15243e9i −0.371354 + 0.138680i
\(817\) −1.84689e10 −1.18485
\(818\) 3.81260e10i 2.43548i
\(819\) −8.87161e9 + 7.69994e9i −0.564298 + 0.489772i
\(820\) 6.61247e9i 0.418808i
\(821\) −6.87118e9 −0.433341 −0.216671 0.976245i \(-0.569520\pi\)
−0.216671 + 0.976245i \(0.569520\pi\)
\(822\) −3.06087e9 8.19633e9i −0.192218 0.514717i
\(823\) 1.42413e9 0.0890534 0.0445267 0.999008i \(-0.485822\pi\)
0.0445267 + 0.999008i \(0.485822\pi\)
\(824\) 1.10742e10 0.689553
\(825\) −7.92400e9 1.20509e10i −0.491310 0.747186i
\(826\) −1.61119e10 −0.994758
\(827\) −5.57924e9 −0.343009 −0.171505 0.985183i \(-0.554863\pi\)
−0.171505 + 0.985183i \(0.554863\pi\)
\(828\) −9.70217e9 1.11785e10i −0.593967 0.684349i
\(829\) −2.23224e10 −1.36082 −0.680408 0.732834i \(-0.738197\pi\)
−0.680408 + 0.732834i \(0.738197\pi\)
\(830\) 9.22081e9i 0.559752i
\(831\) 5.53369e9 + 1.48180e10i 0.334512 + 0.895748i
\(832\) 1.11600e10i 0.671791i
\(833\) 1.94473e10 1.16574
\(834\) −3.75712e8 1.00607e9i −0.0224271 0.0600548i
\(835\) 4.92307e9i 0.292640i
\(836\) −1.92960e10 + 4.40127e9i −1.14221 + 0.260529i
\(837\) 7.75295e9 1.42398e10i 0.457013 0.839390i
\(838\) 3.04262e10i 1.78605i
\(839\) 7.88538e9i 0.460952i 0.973078 + 0.230476i \(0.0740283\pi\)
−0.973078 + 0.230476i \(0.925972\pi\)
\(840\) 4.06828e9 1.51928e9i 0.236828 0.0884422i
\(841\) 3.14273e9 0.182188
\(842\) 7.20206e8 0.0415781
\(843\) 1.56790e10 5.85525e9i 0.901411 0.336627i
\(844\) 2.53135e10i 1.44929i
\(845\) 4.54764e9i 0.259291i
\(846\) −3.16996e10 3.65232e10i −1.79994 2.07383i
\(847\) 1.27275e10 + 2.64484e10i 0.719702 + 1.49557i
\(848\) 3.97013e9i 0.223573i
\(849\) 2.70901e9 + 7.25411e9i 0.151926 + 0.406825i
\(850\) 1.61608e10 0.902603
\(851\) 1.15817e10i 0.644199i
\(852\) −6.91129e9 1.85069e10i −0.382843 1.02517i
\(853\) 2.40175e9i 0.132497i 0.997803 + 0.0662485i \(0.0211030\pi\)
−0.997803 + 0.0662485i \(0.978897\pi\)
\(854\) −2.33396e10 −1.28231
\(855\) −4.01940e9 + 3.48856e9i −0.219928 + 0.190882i
\(856\) 1.43213e10 0.780413
\(857\) −2.70670e10 −1.46895 −0.734476 0.678635i \(-0.762572\pi\)
−0.734476 + 0.678635i \(0.762572\pi\)
\(858\) 1.05736e10 6.95262e9i 0.571500 0.375788i
\(859\) 1.53100e10 0.824137 0.412068 0.911153i \(-0.364806\pi\)
0.412068 + 0.911153i \(0.364806\pi\)
\(860\) −1.05004e10 −0.562940
\(861\) −1.07050e10 2.86656e10i −0.571579 1.53056i
\(862\) −2.53449e10 −1.34777
\(863\) 6.06233e9i 0.321071i −0.987030 0.160536i \(-0.948678\pi\)
0.987030 0.160536i \(-0.0513222\pi\)
\(864\) −1.24641e10 + 2.28927e10i −0.657452 + 1.20753i
\(865\) 9.44081e9i 0.495967i
\(866\) 3.13937e10 1.64259
\(867\) 1.00427e10 3.75038e9i 0.523339 0.195438i
\(868\) 3.99851e10i 2.07529i
\(869\) 5.27974e9 1.20427e9i 0.272925 0.0622521i
\(870\) −3.65034e9 9.77479e9i −0.187939 0.503257i
\(871\) 7.24567e9i 0.371548i
\(872\) 1.67489e10i 0.855419i
\(873\) 1.33651e10 1.16000e10i 0.679864 0.590075i
\(874\) −1.85992e10 −0.942335
\(875\) 2.02607e10 1.02241
\(876\) 3.11972e9 + 8.35392e9i 0.156802 + 0.419881i
\(877\) 3.16536e10i 1.58462i −0.610120 0.792309i \(-0.708879\pi\)
0.610120 0.792309i \(-0.291121\pi\)
\(878\) 1.48524e10i 0.740567i
\(879\) 1.43301e10 5.35151e9i 0.711688 0.265776i
\(880\) 3.82445e9 8.72329e8i 0.189182 0.0431510i
\(881\) 1.48267e10i 0.730513i −0.930907 0.365256i \(-0.880981\pi\)
0.930907 0.365256i \(-0.119019\pi\)
\(882\) 4.10262e10 3.56079e10i 2.01336 1.74746i
\(883\) −1.66978e10 −0.816201 −0.408100 0.912937i \(-0.633809\pi\)
−0.408100 + 0.912937i \(0.633809\pi\)
\(884\) 8.03674e9i 0.391288i
\(885\) 2.47821e9 9.25475e8i 0.120181 0.0448811i
\(886\) 3.33108e10i 1.60904i
\(887\) −6.88613e9 −0.331316 −0.165658 0.986183i \(-0.552975\pi\)
−0.165658 + 0.986183i \(0.552975\pi\)
\(888\) 8.51539e9 3.18002e9i 0.408093 0.152400i
\(889\) 6.00293e10 2.86554
\(890\) 1.10907e10 0.527344
\(891\) 2.10412e10 1.75222e9i 0.996551 0.0829883i
\(892\) −2.72453e10 −1.28533
\(893\) −3.44424e10 −1.61850
\(894\) 2.48580e10 9.28307e9i 1.16355 0.434520i
\(895\) 1.34937e9 0.0629145
\(896\) 3.18857e10i 1.48087i
\(897\) 6.31433e9 2.35805e9i 0.292115 0.109089i
\(898\) 4.51115e10i 2.07884i
\(899\) 2.26382e10 1.03916
\(900\) 1.93231e10 1.67712e10i 0.883546 0.766857i
\(901\) 5.46527e9i 0.248929i
\(902\) 7.33039e9 + 3.21378e10i 0.332586 + 1.45812i
\(903\) −4.55202e10 + 1.69993e10i −2.05730 + 0.768286i
\(904\) 1.90030e10i 0.855525i
\(905\) 4.44301e9i 0.199254i
\(906\) −2.22277e9 5.95207e9i −0.0992990 0.265901i
\(907\) 2.35867e9 0.104964 0.0524822 0.998622i \(-0.483287\pi\)
0.0524822 + 0.998622i \(0.483287\pi\)
\(908\) −4.07736e10 −1.80750
\(909\) 8.09086e9 7.02231e9i 0.357290 0.310103i
\(910\) 8.39225e9i 0.369176i
\(911\) 2.01599e10i 0.883433i 0.897155 + 0.441716i \(0.145630\pi\)
−0.897155 + 0.441716i \(0.854370\pi\)
\(912\) 4.28209e9 + 1.14665e10i 0.186928 + 0.500550i
\(913\) −5.79355e9 2.54000e10i −0.251940 1.10455i
\(914\) 3.39705e9i 0.147160i
\(915\) 3.58992e9 1.34064e9i 0.154921 0.0578545i
\(916\) −1.18920e10 −0.511234
\(917\) 2.72540e10i 1.16718i
\(918\) −1.13130e10 + 2.07785e10i −0.482647 + 0.886473i
\(919\) 3.33135e10i 1.41585i −0.706289 0.707923i \(-0.749632\pi\)
0.706289 0.707923i \(-0.250368\pi\)
\(920\) −2.49177e9 −0.105499
\(921\) −6.44813e9 1.72666e10i −0.271972 0.728281i
\(922\) 3.65759e10 1.53687
\(923\) 8.99596e9 0.376567
\(924\) −4.35075e10 + 2.86082e10i −1.81431 + 1.19300i
\(925\) 2.00202e10 0.831709
\(926\) 2.01204e10 0.832716
\(927\) −2.69665e10 + 2.34051e10i −1.11185 + 0.965008i
\(928\) −3.63945e10 −1.49492
\(929\) 3.78936e10i 1.55064i −0.631568 0.775320i \(-0.717588\pi\)
0.631568 0.775320i \(-0.282412\pi\)
\(930\) −4.05231e9 1.08512e10i −0.165201 0.442370i
\(931\) 3.86888e10i 1.57131i
\(932\) −6.38124e9 −0.258196
\(933\) −2.82562e9 7.56637e9i −0.113901 0.305001i
\(934\) 1.59731e10i 0.641470i
\(935\) 5.26473e9 1.20084e9i 0.210637 0.0480448i
\(936\) 3.46748e9 + 3.99512e9i 0.138213 + 0.159244i
\(937\) 2.43061e10i 0.965221i 0.875835 + 0.482611i \(0.160311\pi\)
−0.875835 + 0.482611i \(0.839689\pi\)
\(938\) 5.26027e10i 2.08113i
\(939\) 1.08883e10 4.06616e9i 0.429170 0.160271i
\(940\) −1.95820e10 −0.768972
\(941\) 3.55368e10 1.39032 0.695160 0.718855i \(-0.255334\pi\)
0.695160 + 0.718855i \(0.255334\pi\)
\(942\) 4.36021e9 1.62830e9i 0.169953 0.0634680i
\(943\) 1.75573e10i 0.681815i
\(944\) 6.08384e9i 0.235383i
\(945\) −6.69561e9 + 1.22978e10i −0.258095 + 0.474040i
\(946\) 5.10339e10 1.16405e10i 1.95993 0.447045i
\(947\) 1.39578e10i 0.534061i −0.963688 0.267031i \(-0.913957\pi\)
0.963688 0.267031i \(-0.0860425\pi\)
\(948\) 3.36096e9 + 8.99990e9i 0.128125 + 0.343090i
\(949\) −4.06074e9 −0.154231
\(950\) 3.21506e10i 1.21663i
\(951\) 1.14369e10 + 3.06255e10i 0.431199 + 1.15465i
\(952\) 1.37486e10i 0.516449i
\(953\) −1.58704e10 −0.593968 −0.296984 0.954882i \(-0.595981\pi\)
−0.296984 + 0.954882i \(0.595981\pi\)
\(954\) −1.00069e10 1.15296e10i −0.373147 0.429927i
\(955\) −8.74562e9 −0.324922
\(956\) 5.57293e10 2.06291
\(957\) 1.61970e10 + 2.46325e10i 0.597369 + 0.908482i
\(958\) −4.03201e10 −1.48164
\(959\) −1.63937e10 −0.600221
\(960\) 4.65385e9 + 1.24620e10i 0.169771 + 0.454609i
\(961\) −2.38159e9 −0.0865637
\(962\) 1.75660e10i 0.636149i
\(963\) −3.48734e10 + 3.02677e10i −1.25835 + 1.09216i
\(964\) 3.56755e9i 0.128263i
\(965\) 1.45500e10 0.521215
\(966\) −4.58413e10 + 1.71192e10i −1.63620 + 0.611031i
\(967\) 1.26468e10i 0.449767i −0.974386 0.224884i \(-0.927800\pi\)
0.974386 0.224884i \(-0.0722002\pi\)
\(968\) 1.19104e10 5.73155e9i 0.422049 0.203099i
\(969\) 5.89470e9 + 1.57847e10i 0.208127 + 0.557318i
\(970\) 1.26429e10i 0.444782i
\(971\) 4.37988e10i 1.53531i −0.640866 0.767653i \(-0.721425\pi\)
0.640866 0.767653i \(-0.278575\pi\)
\(972\) 8.03651e9 + 3.65848e10i 0.280696 + 1.27782i
\(973\) −2.01227e9 −0.0700311
\(974\) −4.24932e10 −1.47355
\(975\) 4.07613e9 + 1.09149e10i 0.140842 + 0.377143i
\(976\) 8.81301e9i 0.303424i
\(977\) 1.33767e10i 0.458899i 0.973321 + 0.229450i \(0.0736926\pi\)
−0.973321 + 0.229450i \(0.926307\pi\)
\(978\) −1.25775e10 + 4.69698e9i −0.429939 + 0.160558i
\(979\) −3.05509e10 + 6.96843e9i −1.04060 + 0.237353i
\(980\) 2.19963e10i 0.746551i
\(981\) 3.53984e10 + 4.07848e10i 1.19713 + 1.37930i
\(982\) 7.59494e10 2.55938
\(983\) 3.86027e10i 1.29623i 0.761544 + 0.648113i \(0.224441\pi\)
−0.761544 + 0.648113i \(0.775559\pi\)
\(984\) −1.29089e10 + 4.82074e9i −0.431922 + 0.161299i
\(985\) 1.51764e9i 0.0505990i
\(986\) −3.30334e10 −1.09745
\(987\) −8.48898e10 + 3.17016e10i −2.81025 + 1.04947i
\(988\) 1.59884e10 0.527420
\(989\) 2.78805e10 0.916459
\(990\) 8.90778e9 1.21730e10i 0.291774 0.398726i
\(991\) 4.44473e9 0.145073 0.0725366 0.997366i \(-0.476891\pi\)
0.0725366 + 0.997366i \(0.476891\pi\)
\(992\) −4.04022e10 −1.31406
\(993\) 2.69412e10 1.00611e10i 0.873163 0.326078i
\(994\) −6.53097e10 −2.10924
\(995\) 1.04090e10i 0.334987i
\(996\) 4.32971e10 1.61690e10i 1.38852 0.518533i
\(997\) 5.59898e10i 1.78927i 0.446799 + 0.894634i \(0.352564\pi\)
−0.446799 + 0.894634i \(0.647436\pi\)
\(998\) −4.84477e10 −1.54282
\(999\) −1.40147e10 + 2.57406e10i −0.444738 + 0.816846i
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 33.8.d.b.32.4 yes 24
3.2 odd 2 inner 33.8.d.b.32.21 yes 24
11.10 odd 2 inner 33.8.d.b.32.22 yes 24
33.32 even 2 inner 33.8.d.b.32.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.8.d.b.32.3 24 33.32 even 2 inner
33.8.d.b.32.4 yes 24 1.1 even 1 trivial
33.8.d.b.32.21 yes 24 3.2 odd 2 inner
33.8.d.b.32.22 yes 24 11.10 odd 2 inner