Properties

Label 29.18.a.b.1.3
Level $29$
Weight $18$
Character 29.1
Self dual yes
Analytic conductor $53.134$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.1344053299\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-645.655 q^{2} +14883.2 q^{3} +285798. q^{4} +954733. q^{5} -9.60943e6 q^{6} +1.80737e7 q^{7} -9.98999e7 q^{8} +9.23704e7 q^{9} +O(q^{10})\) \(q-645.655 q^{2} +14883.2 q^{3} +285798. q^{4} +954733. q^{5} -9.60943e6 q^{6} +1.80737e7 q^{7} -9.98999e7 q^{8} +9.23704e7 q^{9} -6.16428e8 q^{10} -1.63616e8 q^{11} +4.25360e9 q^{12} +4.33002e9 q^{13} -1.16694e10 q^{14} +1.42095e10 q^{15} +2.70407e10 q^{16} +5.11795e10 q^{17} -5.96394e10 q^{18} +8.96514e10 q^{19} +2.72861e11 q^{20} +2.68996e11 q^{21} +1.05639e11 q^{22} -2.78368e11 q^{23} -1.48683e12 q^{24} +1.48576e11 q^{25} -2.79570e12 q^{26} -5.47252e11 q^{27} +5.16545e12 q^{28} +5.00246e11 q^{29} -9.17444e12 q^{30} -2.36840e12 q^{31} -4.36488e12 q^{32} -2.43513e12 q^{33} -3.30443e13 q^{34} +1.72556e13 q^{35} +2.63993e13 q^{36} +3.03597e13 q^{37} -5.78839e13 q^{38} +6.44448e13 q^{39} -9.53777e13 q^{40} -8.45031e13 q^{41} -1.73678e14 q^{42} -1.94211e13 q^{43} -4.67611e13 q^{44} +8.81891e13 q^{45} +1.79730e14 q^{46} +9.65771e13 q^{47} +4.02453e14 q^{48} +9.40296e13 q^{49} -9.59287e13 q^{50} +7.61717e14 q^{51} +1.23751e15 q^{52} -5.94756e14 q^{53} +3.53336e14 q^{54} -1.56209e14 q^{55} -1.80556e15 q^{56} +1.33430e15 q^{57} -3.22987e14 q^{58} -1.80184e14 q^{59} +4.06106e15 q^{60} -1.33081e15 q^{61} +1.52917e15 q^{62} +1.66948e15 q^{63} -7.26069e14 q^{64} +4.13402e15 q^{65} +1.57226e15 q^{66} +2.44049e15 q^{67} +1.46270e16 q^{68} -4.14302e15 q^{69} -1.11412e16 q^{70} -5.66814e15 q^{71} -9.22780e15 q^{72} -1.53697e15 q^{73} -1.96019e16 q^{74} +2.21129e15 q^{75} +2.56222e16 q^{76} -2.95715e15 q^{77} -4.16091e16 q^{78} -1.72129e16 q^{79} +2.58166e16 q^{80} -2.00736e16 q^{81} +5.45599e16 q^{82} +8.38378e15 q^{83} +7.68785e16 q^{84} +4.88628e16 q^{85} +1.25393e16 q^{86} +7.44528e15 q^{87} +1.63452e16 q^{88} -3.85946e16 q^{89} -5.69397e16 q^{90} +7.82597e16 q^{91} -7.95573e16 q^{92} -3.52495e16 q^{93} -6.23555e16 q^{94} +8.55931e16 q^{95} -6.49636e16 q^{96} +8.15125e16 q^{97} -6.07107e16 q^{98} -1.51133e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} - 224469478q^{10} + 1203139534q^{11} - 5164251122q^{12} + 3854339312q^{13} + 25262272904q^{14} + 28324474306q^{15} + 196520815922q^{16} + 76444714794q^{17} + 75758949126q^{18} + 246497292428q^{19} - 46900976670q^{20} + 360937126704q^{21} - 275001533522q^{22} + 213498528140q^{23} - 451123453870q^{24} + 3898884886997q^{25} - 3609347694206q^{26} - 2718903745978q^{27} - 5946174617200q^{28} + 10505174672181q^{29} - 20237658929454q^{30} + 16670029895798q^{31} - 42141001912046q^{32} - 7157109761394q^{33} + 12785761151136q^{34} + 46677934312888q^{35} + 132137824374868q^{36} + 53445659988410q^{37} + 76581637956388q^{38} + 79233849032530q^{39} + 193617444734146q^{40} - 20814769309298q^{41} + 76690667258352q^{42} + 185498647364454q^{43} + 315429066899678q^{44} - 486270821438526q^{45} + 261474367677132q^{46} + 389503471719450q^{47} - 101509672247630q^{48} + 730079062141437q^{49} + 1482269666368354q^{50} + 718238208473988q^{51} + 1966802817157170q^{52} + 747441265526156q^{53} + 5692893333117030q^{54} + 1639109418219546q^{55} + 5657219329125240q^{56} + 4694352396864932q^{57} + 128063081718016q^{58} + 5280258638332960q^{59} + 15251367906033378q^{60} + 5813675353074254q^{61} + 6242066590947250q^{62} + 10947760075450368q^{63} + 24583792057508902q^{64} + 19190799243789974q^{65} + 41877805444482390q^{66} + 13420580230958268q^{67} + 24771837384165388q^{68} + 30973047049935252q^{69} + 8505088080182440q^{70} + 4824462822979508q^{71} + 1180071997284592q^{72} + 11228916281304662q^{73} - 89132715356772q^{74} + 59161419576630296q^{75} + 57466858643173460q^{76} + 58741564492720064q^{77} + 142050530910210210q^{78} + 71718598015696758q^{79} + 48350023652407550q^{80} + 75805931446703569q^{81} + 188661890754420812q^{82} + 50769377111735608q^{83} + 198832046985593048q^{84} + 53422044849490784q^{85} + 35014892323844118q^{86} + 11988905533023326q^{87} + 37459283979085258q^{88} - 70981414576978018q^{89} + 57211029866143724q^{90} + 112933943315157320q^{91} - 103019729095759724q^{92} - 350358290646906646q^{93} - 150286322409612578q^{94} - 102561321856584476q^{95} - 213770098354021866q^{96} - 130930167251505210q^{97} - 537387515497557296q^{98} - 95267700931431064q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −645.655 −1.78339 −0.891693 0.452640i \(-0.850482\pi\)
−0.891693 + 0.452640i \(0.850482\pi\)
\(3\) 14883.2 1.30968 0.654842 0.755766i \(-0.272735\pi\)
0.654842 + 0.755766i \(0.272735\pi\)
\(4\) 285798. 2.18047
\(5\) 954733. 1.09304 0.546521 0.837445i \(-0.315952\pi\)
0.546521 + 0.837445i \(0.315952\pi\)
\(6\) −9.60943e6 −2.33567
\(7\) 1.80737e7 1.18499 0.592495 0.805574i \(-0.298143\pi\)
0.592495 + 0.805574i \(0.298143\pi\)
\(8\) −9.98999e7 −2.10523
\(9\) 9.23704e7 0.715273
\(10\) −6.16428e8 −1.94932
\(11\) −1.63616e8 −0.230138 −0.115069 0.993358i \(-0.536709\pi\)
−0.115069 + 0.993358i \(0.536709\pi\)
\(12\) 4.25360e9 2.85573
\(13\) 4.33002e9 1.47222 0.736108 0.676864i \(-0.236661\pi\)
0.736108 + 0.676864i \(0.236661\pi\)
\(14\) −1.16694e10 −2.11330
\(15\) 1.42095e10 1.43154
\(16\) 2.70407e10 1.57398
\(17\) 5.11795e10 1.77943 0.889714 0.456518i \(-0.150904\pi\)
0.889714 + 0.456518i \(0.150904\pi\)
\(18\) −5.96394e10 −1.27561
\(19\) 8.96514e10 1.21102 0.605510 0.795838i \(-0.292969\pi\)
0.605510 + 0.795838i \(0.292969\pi\)
\(20\) 2.72861e11 2.38334
\(21\) 2.68996e11 1.55196
\(22\) 1.05639e11 0.410424
\(23\) −2.78368e11 −0.741197 −0.370598 0.928793i \(-0.620847\pi\)
−0.370598 + 0.928793i \(0.620847\pi\)
\(24\) −1.48683e12 −2.75719
\(25\) 1.48576e11 0.194741
\(26\) −2.79570e12 −2.62553
\(27\) −5.47252e11 −0.372903
\(28\) 5.16545e12 2.58383
\(29\) 5.00246e11 0.185695
\(30\) −9.17444e12 −2.55299
\(31\) −2.36840e12 −0.498748 −0.249374 0.968407i \(-0.580225\pi\)
−0.249374 + 0.968407i \(0.580225\pi\)
\(32\) −4.36488e12 −0.701775
\(33\) −2.43513e12 −0.301408
\(34\) −3.30443e13 −3.17341
\(35\) 1.72556e13 1.29524
\(36\) 2.63993e13 1.55963
\(37\) 3.03597e13 1.42096 0.710482 0.703715i \(-0.248477\pi\)
0.710482 + 0.703715i \(0.248477\pi\)
\(38\) −5.78839e13 −2.15972
\(39\) 6.44448e13 1.92814
\(40\) −9.53777e13 −2.30111
\(41\) −8.45031e13 −1.65276 −0.826380 0.563113i \(-0.809604\pi\)
−0.826380 + 0.563113i \(0.809604\pi\)
\(42\) −1.73678e14 −2.76775
\(43\) −1.94211e13 −0.253392 −0.126696 0.991942i \(-0.540437\pi\)
−0.126696 + 0.991942i \(0.540437\pi\)
\(44\) −4.67611e13 −0.501808
\(45\) 8.81891e13 0.781823
\(46\) 1.79730e14 1.32184
\(47\) 9.65771e13 0.591619 0.295810 0.955247i \(-0.404411\pi\)
0.295810 + 0.955247i \(0.404411\pi\)
\(48\) 4.02453e14 2.06141
\(49\) 9.40296e13 0.404202
\(50\) −9.59287e13 −0.347299
\(51\) 7.61717e14 2.33049
\(52\) 1.23751e15 3.21012
\(53\) −5.94756e14 −1.31218 −0.656090 0.754682i \(-0.727791\pi\)
−0.656090 + 0.754682i \(0.727791\pi\)
\(54\) 3.53336e14 0.665030
\(55\) −1.56209e14 −0.251550
\(56\) −1.80556e15 −2.49468
\(57\) 1.33430e15 1.58605
\(58\) −3.22987e14 −0.331167
\(59\) −1.80184e14 −0.159763 −0.0798813 0.996804i \(-0.525454\pi\)
−0.0798813 + 0.996804i \(0.525454\pi\)
\(60\) 4.06106e15 3.12143
\(61\) −1.33081e15 −0.888820 −0.444410 0.895824i \(-0.646587\pi\)
−0.444410 + 0.895824i \(0.646587\pi\)
\(62\) 1.52917e15 0.889461
\(63\) 1.66948e15 0.847591
\(64\) −7.26069e14 −0.322439
\(65\) 4.13402e15 1.60920
\(66\) 1.57226e15 0.537526
\(67\) 2.44049e15 0.734245 0.367122 0.930173i \(-0.380343\pi\)
0.367122 + 0.930173i \(0.380343\pi\)
\(68\) 1.46270e16 3.87999
\(69\) −4.14302e15 −0.970733
\(70\) −1.11412e16 −2.30992
\(71\) −5.66814e15 −1.04171 −0.520853 0.853647i \(-0.674386\pi\)
−0.520853 + 0.853647i \(0.674386\pi\)
\(72\) −9.22780e15 −1.50582
\(73\) −1.53697e15 −0.223060 −0.111530 0.993761i \(-0.535575\pi\)
−0.111530 + 0.993761i \(0.535575\pi\)
\(74\) −1.96019e16 −2.53413
\(75\) 2.21129e15 0.255050
\(76\) 2.56222e16 2.64059
\(77\) −2.95715e15 −0.272711
\(78\) −4.16091e16 −3.43862
\(79\) −1.72129e16 −1.27651 −0.638256 0.769824i \(-0.720344\pi\)
−0.638256 + 0.769824i \(0.720344\pi\)
\(80\) 2.58166e16 1.72042
\(81\) −2.00736e16 −1.20366
\(82\) 5.45599e16 2.94751
\(83\) 8.38378e15 0.408579 0.204290 0.978911i \(-0.434512\pi\)
0.204290 + 0.978911i \(0.434512\pi\)
\(84\) 7.68785e16 3.38401
\(85\) 4.88628e16 1.94499
\(86\) 1.25393e16 0.451895
\(87\) 7.44528e15 0.243202
\(88\) 1.63452e16 0.484493
\(89\) −3.85946e16 −1.03923 −0.519615 0.854400i \(-0.673925\pi\)
−0.519615 + 0.854400i \(0.673925\pi\)
\(90\) −5.69397e16 −1.39429
\(91\) 7.82597e16 1.74456
\(92\) −7.95573e16 −1.61616
\(93\) −3.52495e16 −0.653202
\(94\) −6.23555e16 −1.05509
\(95\) 8.55931e16 1.32370
\(96\) −6.49636e16 −0.919104
\(97\) 8.15125e16 1.05600 0.528001 0.849244i \(-0.322942\pi\)
0.528001 + 0.849244i \(0.322942\pi\)
\(98\) −6.07107e16 −0.720848
\(99\) −1.51133e16 −0.164611
\(100\) 4.24627e16 0.424627
\(101\) 1.67885e17 1.54270 0.771349 0.636412i \(-0.219582\pi\)
0.771349 + 0.636412i \(0.219582\pi\)
\(102\) −4.91806e17 −4.15616
\(103\) 1.21257e17 0.943169 0.471585 0.881821i \(-0.343682\pi\)
0.471585 + 0.881821i \(0.343682\pi\)
\(104\) −4.32569e17 −3.09936
\(105\) 2.56819e17 1.69636
\(106\) 3.84007e17 2.34013
\(107\) −9.11858e16 −0.513056 −0.256528 0.966537i \(-0.582579\pi\)
−0.256528 + 0.966537i \(0.582579\pi\)
\(108\) −1.56404e17 −0.813103
\(109\) −3.65713e17 −1.75799 −0.878994 0.476834i \(-0.841784\pi\)
−0.878994 + 0.476834i \(0.841784\pi\)
\(110\) 1.00857e17 0.448611
\(111\) 4.51851e17 1.86101
\(112\) 4.88727e17 1.86515
\(113\) 1.69688e15 0.00600459 0.00300230 0.999995i \(-0.499044\pi\)
0.00300230 + 0.999995i \(0.499044\pi\)
\(114\) −8.61499e17 −2.82855
\(115\) −2.65768e17 −0.810159
\(116\) 1.42970e17 0.404903
\(117\) 3.99966e17 1.05304
\(118\) 1.16337e17 0.284918
\(119\) 9.25006e17 2.10860
\(120\) −1.41953e18 −3.01373
\(121\) −4.78677e17 −0.947037
\(122\) 8.59247e17 1.58511
\(123\) −1.25768e18 −2.16459
\(124\) −6.76886e17 −1.08750
\(125\) −5.86553e17 −0.880182
\(126\) −1.07791e18 −1.51158
\(127\) 1.08499e18 1.42264 0.711320 0.702868i \(-0.248098\pi\)
0.711320 + 0.702868i \(0.248098\pi\)
\(128\) 1.04090e18 1.27681
\(129\) −2.89049e17 −0.331863
\(130\) −2.66915e18 −2.86982
\(131\) −5.51328e17 −0.555398 −0.277699 0.960668i \(-0.589572\pi\)
−0.277699 + 0.960668i \(0.589572\pi\)
\(132\) −6.95957e17 −0.657210
\(133\) 1.62034e18 1.43505
\(134\) −1.57571e18 −1.30944
\(135\) −5.22480e17 −0.407598
\(136\) −5.11283e18 −3.74611
\(137\) 2.01819e18 1.38943 0.694717 0.719283i \(-0.255530\pi\)
0.694717 + 0.719283i \(0.255530\pi\)
\(138\) 2.67496e18 1.73119
\(139\) 1.76829e18 1.07628 0.538142 0.842854i \(-0.319126\pi\)
0.538142 + 0.842854i \(0.319126\pi\)
\(140\) 4.93162e18 2.82424
\(141\) 1.43738e18 0.774834
\(142\) 3.65966e18 1.85776
\(143\) −7.08460e17 −0.338812
\(144\) 2.49776e18 1.12582
\(145\) 4.77602e17 0.202973
\(146\) 9.92354e17 0.397803
\(147\) 1.39946e18 0.529376
\(148\) 8.67676e18 3.09837
\(149\) −1.28596e17 −0.0433656 −0.0216828 0.999765i \(-0.506902\pi\)
−0.0216828 + 0.999765i \(0.506902\pi\)
\(150\) −1.42773e18 −0.454852
\(151\) −1.87304e18 −0.563953 −0.281977 0.959421i \(-0.590990\pi\)
−0.281977 + 0.959421i \(0.590990\pi\)
\(152\) −8.95616e18 −2.54948
\(153\) 4.72748e18 1.27278
\(154\) 1.90930e18 0.486349
\(155\) −2.26119e18 −0.545153
\(156\) 1.84182e19 4.20425
\(157\) −1.37344e18 −0.296935 −0.148468 0.988917i \(-0.547434\pi\)
−0.148468 + 0.988917i \(0.547434\pi\)
\(158\) 1.11136e19 2.27651
\(159\) −8.85189e18 −1.71854
\(160\) −4.16730e18 −0.767070
\(161\) −5.03116e18 −0.878311
\(162\) 1.29606e19 2.14659
\(163\) 8.00163e18 1.25772 0.628860 0.777519i \(-0.283522\pi\)
0.628860 + 0.777519i \(0.283522\pi\)
\(164\) −2.41509e19 −3.60379
\(165\) −2.32490e18 −0.329451
\(166\) −5.41303e18 −0.728655
\(167\) 9.77713e18 1.25061 0.625304 0.780381i \(-0.284975\pi\)
0.625304 + 0.780381i \(0.284975\pi\)
\(168\) −2.68726e19 −3.26724
\(169\) 1.00987e19 1.16742
\(170\) −3.15485e19 −3.46867
\(171\) 8.28114e18 0.866210
\(172\) −5.55052e18 −0.552512
\(173\) −1.06185e19 −1.00617 −0.503084 0.864238i \(-0.667801\pi\)
−0.503084 + 0.864238i \(0.667801\pi\)
\(174\) −4.80708e18 −0.433724
\(175\) 2.68532e18 0.230766
\(176\) −4.42429e18 −0.362231
\(177\) −2.68173e18 −0.209238
\(178\) 2.49188e19 1.85335
\(179\) −2.29142e19 −1.62500 −0.812501 0.582960i \(-0.801895\pi\)
−0.812501 + 0.582960i \(0.801895\pi\)
\(180\) 2.52043e19 1.70474
\(181\) 2.24468e19 1.44840 0.724198 0.689592i \(-0.242210\pi\)
0.724198 + 0.689592i \(0.242210\pi\)
\(182\) −5.05288e19 −3.11123
\(183\) −1.98068e19 −1.16407
\(184\) 2.78090e19 1.56039
\(185\) 2.89854e19 1.55317
\(186\) 2.27590e19 1.16491
\(187\) −8.37378e18 −0.409513
\(188\) 2.76016e19 1.29001
\(189\) −9.89090e18 −0.441886
\(190\) −5.52636e19 −2.36066
\(191\) 8.15204e18 0.333029 0.166515 0.986039i \(-0.446749\pi\)
0.166515 + 0.986039i \(0.446749\pi\)
\(192\) −1.08063e19 −0.422294
\(193\) −5.90065e18 −0.220629 −0.110315 0.993897i \(-0.535186\pi\)
−0.110315 + 0.993897i \(0.535186\pi\)
\(194\) −5.26290e19 −1.88326
\(195\) 6.15275e19 2.10754
\(196\) 2.68735e19 0.881349
\(197\) −2.48407e18 −0.0780191 −0.0390095 0.999239i \(-0.512420\pi\)
−0.0390095 + 0.999239i \(0.512420\pi\)
\(198\) 9.75796e18 0.293565
\(199\) 4.88334e19 1.40756 0.703778 0.710420i \(-0.251495\pi\)
0.703778 + 0.710420i \(0.251495\pi\)
\(200\) −1.48427e19 −0.409976
\(201\) 3.63223e19 0.961628
\(202\) −1.08396e20 −2.75123
\(203\) 9.04132e18 0.220047
\(204\) 2.17697e20 5.08156
\(205\) −8.06779e19 −1.80654
\(206\) −7.82901e19 −1.68204
\(207\) −2.57130e19 −0.530158
\(208\) 1.17087e20 2.31723
\(209\) −1.46684e19 −0.278701
\(210\) −1.65817e20 −3.02527
\(211\) −3.00726e19 −0.526952 −0.263476 0.964666i \(-0.584869\pi\)
−0.263476 + 0.964666i \(0.584869\pi\)
\(212\) −1.69980e20 −2.86117
\(213\) −8.43603e19 −1.36430
\(214\) 5.88746e19 0.914978
\(215\) −1.85420e19 −0.276968
\(216\) 5.46704e19 0.785047
\(217\) −4.28059e19 −0.591012
\(218\) 2.36125e20 3.13517
\(219\) −2.28751e19 −0.292138
\(220\) −4.46444e19 −0.548497
\(221\) 2.21609e20 2.61970
\(222\) −2.91740e20 −3.31891
\(223\) 1.29928e20 1.42269 0.711347 0.702841i \(-0.248085\pi\)
0.711347 + 0.702841i \(0.248085\pi\)
\(224\) −7.88898e19 −0.831597
\(225\) 1.37240e19 0.139293
\(226\) −1.09560e18 −0.0107085
\(227\) 1.87841e19 0.176836 0.0884180 0.996083i \(-0.471819\pi\)
0.0884180 + 0.996083i \(0.471819\pi\)
\(228\) 3.81341e20 3.45834
\(229\) 7.75871e19 0.677935 0.338968 0.940798i \(-0.389922\pi\)
0.338968 + 0.940798i \(0.389922\pi\)
\(230\) 1.71594e20 1.44483
\(231\) −4.40120e19 −0.357165
\(232\) −4.99746e19 −0.390932
\(233\) −1.91389e20 −1.44341 −0.721707 0.692199i \(-0.756642\pi\)
−0.721707 + 0.692199i \(0.756642\pi\)
\(234\) −2.58240e20 −1.87797
\(235\) 9.22053e19 0.646665
\(236\) −5.14964e19 −0.348357
\(237\) −2.56184e20 −1.67183
\(238\) −5.97235e20 −3.76046
\(239\) −2.52552e20 −1.53451 −0.767253 0.641345i \(-0.778377\pi\)
−0.767253 + 0.641345i \(0.778377\pi\)
\(240\) 3.84235e20 2.25321
\(241\) −1.27038e20 −0.719102 −0.359551 0.933125i \(-0.617070\pi\)
−0.359551 + 0.933125i \(0.617070\pi\)
\(242\) 3.09060e20 1.68893
\(243\) −2.28088e20 −1.20351
\(244\) −3.80345e20 −1.93804
\(245\) 8.97732e19 0.441809
\(246\) 8.12027e20 3.86031
\(247\) 3.88193e20 1.78288
\(248\) 2.36603e20 1.04998
\(249\) 1.24778e20 0.535110
\(250\) 3.78711e20 1.56970
\(251\) −1.19032e20 −0.476912 −0.238456 0.971153i \(-0.576641\pi\)
−0.238456 + 0.971153i \(0.576641\pi\)
\(252\) 4.77135e20 1.84815
\(253\) 4.55455e19 0.170577
\(254\) −7.00531e20 −2.53712
\(255\) 7.27236e20 2.54732
\(256\) −5.76898e20 −1.95461
\(257\) −5.11555e20 −1.67672 −0.838360 0.545117i \(-0.816485\pi\)
−0.838360 + 0.545117i \(0.816485\pi\)
\(258\) 1.86626e20 0.591840
\(259\) 5.48714e20 1.68383
\(260\) 1.18150e21 3.50880
\(261\) 4.62080e19 0.132823
\(262\) 3.55968e20 0.990490
\(263\) −4.69281e20 −1.26418 −0.632091 0.774895i \(-0.717803\pi\)
−0.632091 + 0.774895i \(0.717803\pi\)
\(264\) 2.43269e20 0.634533
\(265\) −5.67833e20 −1.43427
\(266\) −1.04618e21 −2.55924
\(267\) −5.74413e20 −1.36106
\(268\) 6.97487e20 1.60100
\(269\) 5.98639e20 1.33128 0.665642 0.746271i \(-0.268158\pi\)
0.665642 + 0.746271i \(0.268158\pi\)
\(270\) 3.37342e20 0.726906
\(271\) 1.92263e20 0.401474 0.200737 0.979645i \(-0.435666\pi\)
0.200737 + 0.979645i \(0.435666\pi\)
\(272\) 1.38393e21 2.80078
\(273\) 1.16476e21 2.28483
\(274\) −1.30306e21 −2.47790
\(275\) −2.43094e19 −0.0448173
\(276\) −1.18407e21 −2.11665
\(277\) −8.40638e20 −1.45724 −0.728620 0.684918i \(-0.759838\pi\)
−0.728620 + 0.684918i \(0.759838\pi\)
\(278\) −1.14170e21 −1.91943
\(279\) −2.18770e20 −0.356741
\(280\) −1.72383e21 −2.72679
\(281\) 2.84695e20 0.436893 0.218447 0.975849i \(-0.429901\pi\)
0.218447 + 0.975849i \(0.429901\pi\)
\(282\) −9.28051e20 −1.38183
\(283\) 8.90156e20 1.28612 0.643060 0.765816i \(-0.277664\pi\)
0.643060 + 0.765816i \(0.277664\pi\)
\(284\) −1.61995e21 −2.27141
\(285\) 1.27390e21 1.73362
\(286\) 4.57421e20 0.604234
\(287\) −1.52729e21 −1.95850
\(288\) −4.03186e20 −0.501961
\(289\) 1.79210e21 2.16636
\(290\) −3.08366e20 −0.361979
\(291\) 1.21317e21 1.38303
\(292\) −4.39264e20 −0.486376
\(293\) −5.73524e20 −0.616846 −0.308423 0.951249i \(-0.599801\pi\)
−0.308423 + 0.951249i \(0.599801\pi\)
\(294\) −9.03571e20 −0.944083
\(295\) −1.72028e20 −0.174627
\(296\) −3.03293e21 −2.99146
\(297\) 8.95391e19 0.0858189
\(298\) 8.30289e19 0.0773377
\(299\) −1.20534e21 −1.09120
\(300\) 6.31983e20 0.556128
\(301\) −3.51012e20 −0.300266
\(302\) 1.20934e21 1.00575
\(303\) 2.49868e21 2.02045
\(304\) 2.42424e21 1.90612
\(305\) −1.27057e21 −0.971518
\(306\) −3.05232e21 −2.26985
\(307\) 8.21971e20 0.594539 0.297270 0.954794i \(-0.403924\pi\)
0.297270 + 0.954794i \(0.403924\pi\)
\(308\) −8.45149e20 −0.594637
\(309\) 1.80469e21 1.23525
\(310\) 1.45995e21 0.972218
\(311\) 1.53791e21 0.996477 0.498239 0.867040i \(-0.333980\pi\)
0.498239 + 0.867040i \(0.333980\pi\)
\(312\) −6.43802e21 −4.05918
\(313\) 1.42511e21 0.874421 0.437211 0.899359i \(-0.355966\pi\)
0.437211 + 0.899359i \(0.355966\pi\)
\(314\) 8.86767e20 0.529551
\(315\) 1.59391e21 0.926453
\(316\) −4.91943e21 −2.78339
\(317\) 1.64676e21 0.907038 0.453519 0.891247i \(-0.350168\pi\)
0.453519 + 0.891247i \(0.350168\pi\)
\(318\) 5.71527e21 3.06483
\(319\) −8.18482e19 −0.0427355
\(320\) −6.93202e20 −0.352440
\(321\) −1.35714e21 −0.671942
\(322\) 3.24839e21 1.56637
\(323\) 4.58831e21 2.15492
\(324\) −5.73701e21 −2.62454
\(325\) 6.43337e20 0.286701
\(326\) −5.16629e21 −2.24300
\(327\) −5.44300e21 −2.30241
\(328\) 8.44185e21 3.47945
\(329\) 1.74551e21 0.701063
\(330\) 1.50108e21 0.587539
\(331\) −4.54685e21 −1.73449 −0.867247 0.497878i \(-0.834113\pi\)
−0.867247 + 0.497878i \(0.834113\pi\)
\(332\) 2.39607e21 0.890894
\(333\) 2.80434e21 1.01638
\(334\) −6.31265e21 −2.23032
\(335\) 2.33001e21 0.802560
\(336\) 7.27383e21 2.44275
\(337\) 5.00380e21 1.63850 0.819248 0.573439i \(-0.194391\pi\)
0.819248 + 0.573439i \(0.194391\pi\)
\(338\) −6.52027e21 −2.08197
\(339\) 2.52550e19 0.00786412
\(340\) 1.39649e22 4.24099
\(341\) 3.87508e20 0.114781
\(342\) −5.34676e21 −1.54479
\(343\) −2.50504e21 −0.706015
\(344\) 1.94017e21 0.533448
\(345\) −3.95548e21 −1.06105
\(346\) 6.85587e21 1.79439
\(347\) −4.17722e21 −1.06681 −0.533404 0.845861i \(-0.679088\pi\)
−0.533404 + 0.845861i \(0.679088\pi\)
\(348\) 2.12785e21 0.530295
\(349\) 5.82193e21 1.41596 0.707979 0.706233i \(-0.249607\pi\)
0.707979 + 0.706233i \(0.249607\pi\)
\(350\) −1.73379e21 −0.411546
\(351\) −2.36962e21 −0.548994
\(352\) 7.14164e20 0.161505
\(353\) −2.45544e21 −0.542057 −0.271028 0.962571i \(-0.587364\pi\)
−0.271028 + 0.962571i \(0.587364\pi\)
\(354\) 1.73147e21 0.373153
\(355\) −5.41156e21 −1.13863
\(356\) −1.10303e22 −2.26601
\(357\) 1.37671e22 2.76161
\(358\) 1.47947e22 2.89801
\(359\) 9.63080e20 0.184230 0.0921148 0.995748i \(-0.470637\pi\)
0.0921148 + 0.995748i \(0.470637\pi\)
\(360\) −8.81008e21 −1.64592
\(361\) 2.55698e21 0.466569
\(362\) −1.44929e22 −2.58305
\(363\) −7.12426e21 −1.24032
\(364\) 2.23665e22 3.80396
\(365\) −1.46740e21 −0.243814
\(366\) 1.27884e22 2.07599
\(367\) −3.28839e21 −0.521581 −0.260791 0.965395i \(-0.583983\pi\)
−0.260791 + 0.965395i \(0.583983\pi\)
\(368\) −7.52728e21 −1.16663
\(369\) −7.80559e21 −1.18217
\(370\) −1.87146e22 −2.76991
\(371\) −1.07495e22 −1.55492
\(372\) −1.00743e22 −1.42429
\(373\) 9.77462e21 1.35075 0.675375 0.737474i \(-0.263982\pi\)
0.675375 + 0.737474i \(0.263982\pi\)
\(374\) 5.40657e21 0.730321
\(375\) −8.72981e21 −1.15276
\(376\) −9.64804e21 −1.24550
\(377\) 2.16608e21 0.273384
\(378\) 6.38611e21 0.788054
\(379\) −7.55961e21 −0.912149 −0.456075 0.889942i \(-0.650745\pi\)
−0.456075 + 0.889942i \(0.650745\pi\)
\(380\) 2.44624e22 2.88628
\(381\) 1.61482e22 1.86321
\(382\) −5.26340e21 −0.593920
\(383\) −9.38965e21 −1.03624 −0.518119 0.855308i \(-0.673368\pi\)
−0.518119 + 0.855308i \(0.673368\pi\)
\(384\) 1.54920e22 1.67222
\(385\) −2.82329e21 −0.298084
\(386\) 3.80979e21 0.393467
\(387\) −1.79394e21 −0.181244
\(388\) 2.32962e22 2.30258
\(389\) 3.43837e21 0.332492 0.166246 0.986084i \(-0.446835\pi\)
0.166246 + 0.986084i \(0.446835\pi\)
\(390\) −3.97256e22 −3.75855
\(391\) −1.42468e22 −1.31891
\(392\) −9.39355e21 −0.850938
\(393\) −8.20555e21 −0.727396
\(394\) 1.60385e21 0.139138
\(395\) −1.64338e22 −1.39528
\(396\) −4.31935e21 −0.358929
\(397\) 3.71243e21 0.301953 0.150976 0.988537i \(-0.451758\pi\)
0.150976 + 0.988537i \(0.451758\pi\)
\(398\) −3.15295e22 −2.51022
\(399\) 2.41158e22 1.87946
\(400\) 4.01759e21 0.306518
\(401\) −2.30999e21 −0.172538 −0.0862688 0.996272i \(-0.527494\pi\)
−0.0862688 + 0.996272i \(0.527494\pi\)
\(402\) −2.34517e22 −1.71496
\(403\) −1.02552e22 −0.734265
\(404\) 4.79814e22 3.36381
\(405\) −1.91649e22 −1.31565
\(406\) −5.83758e21 −0.392429
\(407\) −4.96733e21 −0.327017
\(408\) −7.60954e22 −4.90622
\(409\) −3.38041e21 −0.213462 −0.106731 0.994288i \(-0.534038\pi\)
−0.106731 + 0.994288i \(0.534038\pi\)
\(410\) 5.20901e22 3.22175
\(411\) 3.00372e22 1.81972
\(412\) 3.46550e22 2.05655
\(413\) −3.25660e21 −0.189317
\(414\) 1.66017e22 0.945476
\(415\) 8.00427e21 0.446594
\(416\) −1.89001e22 −1.03317
\(417\) 2.63178e22 1.40959
\(418\) 9.47072e21 0.497032
\(419\) −1.91876e22 −0.986739 −0.493369 0.869820i \(-0.664235\pi\)
−0.493369 + 0.869820i \(0.664235\pi\)
\(420\) 7.33985e22 3.69886
\(421\) −3.06665e22 −1.51449 −0.757244 0.653132i \(-0.773455\pi\)
−0.757244 + 0.653132i \(0.773455\pi\)
\(422\) 1.94166e22 0.939759
\(423\) 8.92087e21 0.423169
\(424\) 5.94160e22 2.76245
\(425\) 7.60404e21 0.346528
\(426\) 5.44676e22 2.43308
\(427\) −2.40528e22 −1.05324
\(428\) −2.60608e22 −1.11870
\(429\) −1.05442e22 −0.443737
\(430\) 1.19717e22 0.493941
\(431\) 2.41512e22 0.976971 0.488486 0.872572i \(-0.337549\pi\)
0.488486 + 0.872572i \(0.337549\pi\)
\(432\) −1.47981e22 −0.586940
\(433\) −3.26498e22 −1.26979 −0.634897 0.772597i \(-0.718958\pi\)
−0.634897 + 0.772597i \(0.718958\pi\)
\(434\) 2.76378e22 1.05400
\(435\) 7.10826e21 0.265830
\(436\) −1.04520e23 −3.83324
\(437\) −2.49561e22 −0.897604
\(438\) 1.47694e22 0.520996
\(439\) −3.33883e22 −1.15517 −0.577586 0.816330i \(-0.696005\pi\)
−0.577586 + 0.816330i \(0.696005\pi\)
\(440\) 1.56053e22 0.529571
\(441\) 8.68556e21 0.289114
\(442\) −1.43083e23 −4.67195
\(443\) 1.88444e22 0.603601 0.301800 0.953371i \(-0.402412\pi\)
0.301800 + 0.953371i \(0.402412\pi\)
\(444\) 1.29138e23 4.05788
\(445\) −3.68476e22 −1.13592
\(446\) −8.38887e22 −2.53722
\(447\) −1.91393e21 −0.0567952
\(448\) −1.31228e22 −0.382087
\(449\) −3.26676e22 −0.933304 −0.466652 0.884441i \(-0.654540\pi\)
−0.466652 + 0.884441i \(0.654540\pi\)
\(450\) −8.86098e21 −0.248414
\(451\) 1.38260e22 0.380362
\(452\) 4.84965e20 0.0130928
\(453\) −2.78769e22 −0.738601
\(454\) −1.21281e22 −0.315367
\(455\) 7.47172e22 1.90688
\(456\) −1.33297e23 −3.33901
\(457\) 9.67539e21 0.237893 0.118946 0.992901i \(-0.462048\pi\)
0.118946 + 0.992901i \(0.462048\pi\)
\(458\) −5.00945e22 −1.20902
\(459\) −2.80081e22 −0.663554
\(460\) −7.59559e22 −1.76653
\(461\) 1.83202e21 0.0418286 0.0209143 0.999781i \(-0.493342\pi\)
0.0209143 + 0.999781i \(0.493342\pi\)
\(462\) 2.84165e22 0.636963
\(463\) 1.56727e22 0.344910 0.172455 0.985017i \(-0.444830\pi\)
0.172455 + 0.985017i \(0.444830\pi\)
\(464\) 1.35270e22 0.292280
\(465\) −3.36539e22 −0.713978
\(466\) 1.23571e23 2.57417
\(467\) 5.80904e22 1.18826 0.594129 0.804370i \(-0.297497\pi\)
0.594129 + 0.804370i \(0.297497\pi\)
\(468\) 1.14310e23 2.29611
\(469\) 4.41087e22 0.870072
\(470\) −5.95328e22 −1.15325
\(471\) −2.04412e22 −0.388891
\(472\) 1.80004e22 0.336337
\(473\) 3.17760e21 0.0583149
\(474\) 1.65407e23 2.98152
\(475\) 1.33200e22 0.235836
\(476\) 2.64365e23 4.59775
\(477\) −5.49378e22 −0.938567
\(478\) 1.63061e23 2.73662
\(479\) 8.51939e22 1.40461 0.702307 0.711875i \(-0.252154\pi\)
0.702307 + 0.711875i \(0.252154\pi\)
\(480\) −6.20229e22 −1.00462
\(481\) 1.31458e23 2.09197
\(482\) 8.20230e22 1.28244
\(483\) −7.48799e22 −1.15031
\(484\) −1.36805e23 −2.06498
\(485\) 7.78227e22 1.15425
\(486\) 1.47266e23 2.14632
\(487\) −4.47381e22 −0.640739 −0.320370 0.947293i \(-0.603807\pi\)
−0.320370 + 0.947293i \(0.603807\pi\)
\(488\) 1.32948e23 1.87117
\(489\) 1.19090e23 1.64722
\(490\) −5.79625e22 −0.787917
\(491\) 2.24806e22 0.300341 0.150171 0.988660i \(-0.452018\pi\)
0.150171 + 0.988660i \(0.452018\pi\)
\(492\) −3.59443e23 −4.71983
\(493\) 2.56024e22 0.330432
\(494\) −2.50638e23 −3.17957
\(495\) −1.44291e22 −0.179927
\(496\) −6.40433e22 −0.785017
\(497\) −1.02445e23 −1.23441
\(498\) −8.05634e22 −0.954307
\(499\) −1.50494e23 −1.75252 −0.876262 0.481836i \(-0.839970\pi\)
−0.876262 + 0.481836i \(0.839970\pi\)
\(500\) −1.67636e23 −1.91921
\(501\) 1.45515e23 1.63790
\(502\) 7.68538e22 0.850518
\(503\) −9.48795e22 −1.03239 −0.516196 0.856471i \(-0.672652\pi\)
−0.516196 + 0.856471i \(0.672652\pi\)
\(504\) −1.66781e23 −1.78438
\(505\) 1.60286e23 1.68623
\(506\) −2.94067e22 −0.304205
\(507\) 1.50301e23 1.52895
\(508\) 3.10089e23 3.10202
\(509\) 3.53997e22 0.348256 0.174128 0.984723i \(-0.444289\pi\)
0.174128 + 0.984723i \(0.444289\pi\)
\(510\) −4.69544e23 −4.54286
\(511\) −2.77789e22 −0.264324
\(512\) 2.36044e23 2.20901
\(513\) −4.90619e22 −0.451593
\(514\) 3.30288e23 2.99024
\(515\) 1.15768e23 1.03092
\(516\) −8.26097e22 −0.723617
\(517\) −1.58015e22 −0.136154
\(518\) −3.54280e23 −3.00292
\(519\) −1.58037e23 −1.31776
\(520\) −4.12988e23 −3.38773
\(521\) 5.25323e22 0.423942 0.211971 0.977276i \(-0.432012\pi\)
0.211971 + 0.977276i \(0.432012\pi\)
\(522\) −2.98344e22 −0.236874
\(523\) 3.45072e22 0.269554 0.134777 0.990876i \(-0.456968\pi\)
0.134777 + 0.990876i \(0.456968\pi\)
\(524\) −1.57569e23 −1.21103
\(525\) 3.99662e22 0.302231
\(526\) 3.02994e23 2.25452
\(527\) −1.21214e23 −0.887486
\(528\) −6.58477e22 −0.474408
\(529\) −6.35611e22 −0.450628
\(530\) 3.66624e23 2.55786
\(531\) −1.66437e22 −0.114274
\(532\) 4.63089e23 3.12907
\(533\) −3.65900e23 −2.43322
\(534\) 3.70873e23 2.42730
\(535\) −8.70581e22 −0.560792
\(536\) −2.43804e23 −1.54576
\(537\) −3.41037e23 −2.12824
\(538\) −3.86514e23 −2.37419
\(539\) −1.53847e22 −0.0930220
\(540\) −1.49324e23 −0.888756
\(541\) −2.71733e23 −1.59208 −0.796041 0.605242i \(-0.793076\pi\)
−0.796041 + 0.605242i \(0.793076\pi\)
\(542\) −1.24136e23 −0.715983
\(543\) 3.34081e23 1.89694
\(544\) −2.23393e23 −1.24876
\(545\) −3.49159e23 −1.92155
\(546\) −7.52032e23 −4.07473
\(547\) 7.86656e22 0.419655 0.209828 0.977738i \(-0.432710\pi\)
0.209828 + 0.977738i \(0.432710\pi\)
\(548\) 5.76796e23 3.02962
\(549\) −1.22928e23 −0.635749
\(550\) 1.56955e22 0.0799265
\(551\) 4.48478e22 0.224881
\(552\) 4.13887e23 2.04362
\(553\) −3.11102e23 −1.51265
\(554\) 5.42762e23 2.59882
\(555\) 4.31397e23 2.03417
\(556\) 5.05374e23 2.34680
\(557\) 3.77522e23 1.72652 0.863262 0.504756i \(-0.168417\pi\)
0.863262 + 0.504756i \(0.168417\pi\)
\(558\) 1.41250e23 0.636207
\(559\) −8.40939e22 −0.373047
\(560\) 4.66603e23 2.03868
\(561\) −1.24629e23 −0.536333
\(562\) −1.83815e23 −0.779150
\(563\) 4.39470e23 1.83488 0.917440 0.397874i \(-0.130252\pi\)
0.917440 + 0.397874i \(0.130252\pi\)
\(564\) 4.10801e23 1.68950
\(565\) 1.62006e21 0.00656327
\(566\) −5.74734e23 −2.29365
\(567\) −3.62805e23 −1.42632
\(568\) 5.66247e23 2.19303
\(569\) 8.19442e22 0.312654 0.156327 0.987705i \(-0.450035\pi\)
0.156327 + 0.987705i \(0.450035\pi\)
\(570\) −8.22501e23 −3.09172
\(571\) −4.04798e23 −1.49910 −0.749551 0.661947i \(-0.769730\pi\)
−0.749551 + 0.661947i \(0.769730\pi\)
\(572\) −2.02477e23 −0.738770
\(573\) 1.21329e23 0.436163
\(574\) 9.86101e23 3.49277
\(575\) −4.13588e22 −0.144342
\(576\) −6.70673e22 −0.230632
\(577\) 1.88491e23 0.638698 0.319349 0.947637i \(-0.396536\pi\)
0.319349 + 0.947637i \(0.396536\pi\)
\(578\) −1.15708e24 −3.86347
\(579\) −8.78208e22 −0.288955
\(580\) 1.36498e23 0.442576
\(581\) 1.51526e23 0.484162
\(582\) −7.83289e23 −2.46648
\(583\) 9.73115e22 0.301982
\(584\) 1.53543e23 0.469594
\(585\) 3.81861e23 1.15101
\(586\) 3.70299e23 1.10007
\(587\) 7.10981e22 0.208178 0.104089 0.994568i \(-0.466807\pi\)
0.104089 + 0.994568i \(0.466807\pi\)
\(588\) 3.99965e23 1.15429
\(589\) −2.12331e23 −0.603994
\(590\) 1.11071e23 0.311428
\(591\) −3.69710e22 −0.102180
\(592\) 8.20948e23 2.23656
\(593\) −1.17349e23 −0.315148 −0.157574 0.987507i \(-0.550367\pi\)
−0.157574 + 0.987507i \(0.550367\pi\)
\(594\) −5.78114e22 −0.153048
\(595\) 8.83133e23 2.30479
\(596\) −3.67526e22 −0.0945574
\(597\) 7.26799e23 1.84345
\(598\) 7.78235e23 1.94604
\(599\) 4.09095e23 1.00855 0.504273 0.863544i \(-0.331760\pi\)
0.504273 + 0.863544i \(0.331760\pi\)
\(600\) −2.20907e23 −0.536939
\(601\) −3.75264e23 −0.899299 −0.449649 0.893205i \(-0.648451\pi\)
−0.449649 + 0.893205i \(0.648451\pi\)
\(602\) 2.26633e23 0.535491
\(603\) 2.25429e23 0.525185
\(604\) −5.35312e23 −1.22968
\(605\) −4.57009e23 −1.03515
\(606\) −1.61328e24 −3.60324
\(607\) 1.43973e23 0.317086 0.158543 0.987352i \(-0.449320\pi\)
0.158543 + 0.987352i \(0.449320\pi\)
\(608\) −3.91318e23 −0.849864
\(609\) 1.34564e23 0.288192
\(610\) 8.20351e23 1.73259
\(611\) 4.18181e23 0.870992
\(612\) 1.35111e24 2.77525
\(613\) 5.25038e23 1.06360 0.531799 0.846871i \(-0.321516\pi\)
0.531799 + 0.846871i \(0.321516\pi\)
\(614\) −5.30710e23 −1.06029
\(615\) −1.20075e24 −2.36599
\(616\) 2.95419e23 0.574120
\(617\) −3.49285e22 −0.0669508 −0.0334754 0.999440i \(-0.510658\pi\)
−0.0334754 + 0.999440i \(0.510658\pi\)
\(618\) −1.16521e24 −2.20294
\(619\) −1.47469e23 −0.274998 −0.137499 0.990502i \(-0.543906\pi\)
−0.137499 + 0.990502i \(0.543906\pi\)
\(620\) −6.46245e23 −1.18869
\(621\) 1.52338e23 0.276394
\(622\) −9.92959e23 −1.77710
\(623\) −6.97550e23 −1.23148
\(624\) 1.74263e24 3.03484
\(625\) −6.73356e23 −1.15682
\(626\) −9.20128e23 −1.55943
\(627\) −2.18313e23 −0.365011
\(628\) −3.92526e23 −0.647458
\(629\) 1.55380e24 2.52850
\(630\) −1.02911e24 −1.65222
\(631\) 7.40740e23 1.17332 0.586660 0.809833i \(-0.300443\pi\)
0.586660 + 0.809833i \(0.300443\pi\)
\(632\) 1.71957e24 2.68736
\(633\) −4.47578e23 −0.690140
\(634\) −1.06324e24 −1.61760
\(635\) 1.03588e24 1.55501
\(636\) −2.52986e24 −3.74723
\(637\) 4.07150e23 0.595072
\(638\) 5.28457e22 0.0762139
\(639\) −5.23569e23 −0.745103
\(640\) 9.93786e23 1.39561
\(641\) −3.50461e23 −0.485676 −0.242838 0.970067i \(-0.578078\pi\)
−0.242838 + 0.970067i \(0.578078\pi\)
\(642\) 8.76244e23 1.19833
\(643\) −6.96395e23 −0.939858 −0.469929 0.882704i \(-0.655721\pi\)
−0.469929 + 0.882704i \(0.655721\pi\)
\(644\) −1.43790e24 −1.91513
\(645\) −2.75965e23 −0.362740
\(646\) −2.96247e24 −3.84306
\(647\) −2.63794e23 −0.337738 −0.168869 0.985639i \(-0.554011\pi\)
−0.168869 + 0.985639i \(0.554011\pi\)
\(648\) 2.00535e24 2.53398
\(649\) 2.94810e22 0.0367674
\(650\) −4.15374e23 −0.511299
\(651\) −6.37090e23 −0.774039
\(652\) 2.28685e24 2.74242
\(653\) −1.64108e24 −1.94253 −0.971263 0.238007i \(-0.923506\pi\)
−0.971263 + 0.238007i \(0.923506\pi\)
\(654\) 3.51430e24 4.10608
\(655\) −5.26371e23 −0.607074
\(656\) −2.28502e24 −2.60140
\(657\) −1.41971e23 −0.159549
\(658\) −1.12700e24 −1.25027
\(659\) 5.73508e22 0.0628078 0.0314039 0.999507i \(-0.490002\pi\)
0.0314039 + 0.999507i \(0.490002\pi\)
\(660\) −6.64453e23 −0.718358
\(661\) −1.04064e24 −1.11067 −0.555336 0.831626i \(-0.687410\pi\)
−0.555336 + 0.831626i \(0.687410\pi\)
\(662\) 2.93570e24 3.09327
\(663\) 3.29825e24 3.43099
\(664\) −8.37539e23 −0.860154
\(665\) 1.54699e24 1.56857
\(666\) −1.81064e24 −1.81259
\(667\) −1.39253e23 −0.137637
\(668\) 2.79429e24 2.72691
\(669\) 1.93375e24 1.86328
\(670\) −1.50439e24 −1.43128
\(671\) 2.17742e23 0.204551
\(672\) −1.17414e24 −1.08913
\(673\) −3.50405e23 −0.320953 −0.160477 0.987040i \(-0.551303\pi\)
−0.160477 + 0.987040i \(0.551303\pi\)
\(674\) −3.23073e24 −2.92207
\(675\) −8.13084e22 −0.0726195
\(676\) 2.88619e24 2.54553
\(677\) −6.35949e23 −0.553884 −0.276942 0.960887i \(-0.589321\pi\)
−0.276942 + 0.960887i \(0.589321\pi\)
\(678\) −1.63060e22 −0.0140248
\(679\) 1.47324e24 1.25135
\(680\) −4.88139e24 −4.09466
\(681\) 2.79568e23 0.231599
\(682\) −2.50197e23 −0.204698
\(683\) −8.56675e23 −0.692214 −0.346107 0.938195i \(-0.612497\pi\)
−0.346107 + 0.938195i \(0.612497\pi\)
\(684\) 2.36674e24 1.88874
\(685\) 1.92684e24 1.51871
\(686\) 1.61739e24 1.25910
\(687\) 1.15475e24 0.887881
\(688\) −5.25160e23 −0.398832
\(689\) −2.57531e24 −1.93181
\(690\) 2.55388e24 1.89227
\(691\) 1.21066e24 0.886053 0.443027 0.896508i \(-0.353905\pi\)
0.443027 + 0.896508i \(0.353905\pi\)
\(692\) −3.03474e24 −2.19392
\(693\) −2.73153e23 −0.195063
\(694\) 2.69704e24 1.90253
\(695\) 1.68824e24 1.17642
\(696\) −7.43783e23 −0.511997
\(697\) −4.32483e24 −2.94097
\(698\) −3.75896e24 −2.52520
\(699\) −2.84848e24 −1.89042
\(700\) 7.67460e23 0.503179
\(701\) 8.06024e23 0.522089 0.261045 0.965327i \(-0.415933\pi\)
0.261045 + 0.965327i \(0.415933\pi\)
\(702\) 1.52995e24 0.979068
\(703\) 2.72179e24 1.72082
\(704\) 1.18796e23 0.0742054
\(705\) 1.37231e24 0.846927
\(706\) 1.58537e24 0.966697
\(707\) 3.03432e24 1.82808
\(708\) −7.66433e23 −0.456238
\(709\) −5.09200e22 −0.0299499 −0.0149749 0.999888i \(-0.504767\pi\)
−0.0149749 + 0.999888i \(0.504767\pi\)
\(710\) 3.49400e24 2.03061
\(711\) −1.58997e24 −0.913054
\(712\) 3.85560e24 2.18782
\(713\) 6.59289e23 0.369670
\(714\) −8.88878e24 −4.92501
\(715\) −6.76391e23 −0.370336
\(716\) −6.54884e24 −3.54327
\(717\) −3.75879e24 −2.00972
\(718\) −6.21817e23 −0.328553
\(719\) 1.84407e24 0.962902 0.481451 0.876473i \(-0.340110\pi\)
0.481451 + 0.876473i \(0.340110\pi\)
\(720\) 2.38470e24 1.23057
\(721\) 2.19156e24 1.11765
\(722\) −1.65093e24 −0.832074
\(723\) −1.89074e24 −0.941796
\(724\) 6.41527e24 3.15818
\(725\) 7.43245e22 0.0361625
\(726\) 4.59981e24 2.21197
\(727\) 9.59151e23 0.455873 0.227937 0.973676i \(-0.426802\pi\)
0.227937 + 0.973676i \(0.426802\pi\)
\(728\) −7.81814e24 −3.67271
\(729\) −8.02377e23 −0.372559
\(730\) 9.47434e23 0.434815
\(731\) −9.93963e23 −0.450892
\(732\) −5.66076e24 −2.53823
\(733\) −3.35057e24 −1.48503 −0.742514 0.669831i \(-0.766367\pi\)
−0.742514 + 0.669831i \(0.766367\pi\)
\(734\) 2.12317e24 0.930181
\(735\) 1.33612e24 0.578631
\(736\) 1.21505e24 0.520153
\(737\) −3.99302e23 −0.168977
\(738\) 5.03972e24 2.10827
\(739\) −8.18867e23 −0.338638 −0.169319 0.985561i \(-0.554157\pi\)
−0.169319 + 0.985561i \(0.554157\pi\)
\(740\) 8.28399e24 3.38665
\(741\) 5.77756e24 2.33502
\(742\) 6.94044e24 2.77303
\(743\) −2.28443e24 −0.902347 −0.451173 0.892436i \(-0.648994\pi\)
−0.451173 + 0.892436i \(0.648994\pi\)
\(744\) 3.52142e24 1.37514
\(745\) −1.22775e23 −0.0474004
\(746\) −6.31103e24 −2.40891
\(747\) 7.74414e23 0.292245
\(748\) −2.39321e24 −0.892931
\(749\) −1.64807e24 −0.607967
\(750\) 5.63645e24 2.05582
\(751\) 3.36388e24 1.21311 0.606557 0.795040i \(-0.292550\pi\)
0.606557 + 0.795040i \(0.292550\pi\)
\(752\) 2.61151e24 0.931194
\(753\) −1.77159e24 −0.624604
\(754\) −1.39854e24 −0.487549
\(755\) −1.78825e24 −0.616425
\(756\) −2.82680e24 −0.963519
\(757\) 2.85798e24 0.963261 0.481631 0.876374i \(-0.340045\pi\)
0.481631 + 0.876374i \(0.340045\pi\)
\(758\) 4.88090e24 1.62671
\(759\) 6.77864e23 0.223402
\(760\) −8.55074e24 −2.78669
\(761\) −4.10866e24 −1.32413 −0.662065 0.749447i \(-0.730320\pi\)
−0.662065 + 0.749447i \(0.730320\pi\)
\(762\) −1.04262e25 −3.32282
\(763\) −6.60981e24 −2.08320
\(764\) 2.32984e24 0.726160
\(765\) 4.51348e24 1.39120
\(766\) 6.06248e24 1.84802
\(767\) −7.80202e23 −0.235205
\(768\) −8.58610e24 −2.55992
\(769\) 2.31222e24 0.681797 0.340898 0.940100i \(-0.389269\pi\)
0.340898 + 0.940100i \(0.389269\pi\)
\(770\) 1.82287e24 0.531600
\(771\) −7.61359e24 −2.19597
\(772\) −1.68640e24 −0.481075
\(773\) 2.16669e24 0.611323 0.305661 0.952140i \(-0.401122\pi\)
0.305661 + 0.952140i \(0.401122\pi\)
\(774\) 1.15826e24 0.323228
\(775\) −3.51887e23 −0.0971268
\(776\) −8.14309e24 −2.22313
\(777\) 8.16663e24 2.20528
\(778\) −2.22000e24 −0.592961
\(779\) −7.57582e24 −2.00153
\(780\) 1.75845e25 4.59542
\(781\) 9.27398e23 0.239735
\(782\) 9.19850e24 2.35212
\(783\) −2.73761e23 −0.0692463
\(784\) 2.54263e24 0.636204
\(785\) −1.31127e24 −0.324563
\(786\) 5.29795e24 1.29723
\(787\) −4.02529e24 −0.975018 −0.487509 0.873118i \(-0.662094\pi\)
−0.487509 + 0.873118i \(0.662094\pi\)
\(788\) −7.09943e23 −0.170118
\(789\) −6.98442e24 −1.65568
\(790\) 1.06105e25 2.48833
\(791\) 3.06689e22 0.00711538
\(792\) 1.50981e24 0.346545
\(793\) −5.76246e24 −1.30854
\(794\) −2.39695e24 −0.538499
\(795\) −8.45119e24 −1.87844
\(796\) 1.39565e25 3.06913
\(797\) −5.44766e24 −1.18526 −0.592631 0.805474i \(-0.701911\pi\)
−0.592631 + 0.805474i \(0.701911\pi\)
\(798\) −1.55705e25 −3.35180
\(799\) 4.94277e24 1.05274
\(800\) −6.48516e23 −0.136665
\(801\) −3.56500e24 −0.743333
\(802\) 1.49146e24 0.307701
\(803\) 2.51473e23 0.0513345
\(804\) 1.03809e25 2.09680
\(805\) −4.80341e24 −0.960031
\(806\) 6.62135e24 1.30948
\(807\) 8.90968e24 1.74356
\(808\) −1.67717e25 −3.24774
\(809\) 5.80752e23 0.111283 0.0556414 0.998451i \(-0.482280\pi\)
0.0556414 + 0.998451i \(0.482280\pi\)
\(810\) 1.23739e25 2.34631
\(811\) 3.19811e24 0.600090 0.300045 0.953925i \(-0.402998\pi\)
0.300045 + 0.953925i \(0.402998\pi\)
\(812\) 2.58400e24 0.479806
\(813\) 2.86150e24 0.525804
\(814\) 3.20718e24 0.583198
\(815\) 7.63942e24 1.37474
\(816\) 2.05974e25 3.66813
\(817\) −1.74113e24 −0.306862
\(818\) 2.18258e24 0.380686
\(819\) 7.22889e24 1.24784
\(820\) −2.30576e25 −3.93910
\(821\) −7.56232e24 −1.27861 −0.639305 0.768953i \(-0.720778\pi\)
−0.639305 + 0.768953i \(0.720778\pi\)
\(822\) −1.93937e25 −3.24526
\(823\) −4.16723e24 −0.690158 −0.345079 0.938574i \(-0.612148\pi\)
−0.345079 + 0.938574i \(0.612148\pi\)
\(824\) −1.21135e25 −1.98559
\(825\) −3.61802e23 −0.0586965
\(826\) 2.10264e24 0.337625
\(827\) −8.45598e24 −1.34390 −0.671950 0.740596i \(-0.734543\pi\)
−0.671950 + 0.740596i \(0.734543\pi\)
\(828\) −7.34874e24 −1.15599
\(829\) 7.30805e24 1.13786 0.568929 0.822386i \(-0.307358\pi\)
0.568929 + 0.822386i \(0.307358\pi\)
\(830\) −5.16800e24 −0.796450
\(831\) −1.25114e25 −1.90852
\(832\) −3.14390e24 −0.474701
\(833\) 4.81239e24 0.719248
\(834\) −1.69922e25 −2.51385
\(835\) 9.33455e24 1.36697
\(836\) −4.19220e24 −0.607699
\(837\) 1.29611e24 0.185985
\(838\) 1.23886e25 1.75974
\(839\) 8.35418e24 1.17470 0.587350 0.809333i \(-0.300171\pi\)
0.587350 + 0.809333i \(0.300171\pi\)
\(840\) −2.56562e25 −3.57123
\(841\) 2.50246e23 0.0344828
\(842\) 1.98000e25 2.70092
\(843\) 4.23718e24 0.572192
\(844\) −8.59471e24 −1.14900
\(845\) 9.64155e24 1.27604
\(846\) −5.75980e24 −0.754674
\(847\) −8.65148e24 −1.12223
\(848\) −1.60826e25 −2.06534
\(849\) 1.32484e25 1.68441
\(850\) −4.90959e24 −0.617994
\(851\) −8.45119e24 −1.05321
\(852\) −2.41100e25 −2.97482
\(853\) −1.19530e25 −1.46020 −0.730098 0.683342i \(-0.760526\pi\)
−0.730098 + 0.683342i \(0.760526\pi\)
\(854\) 1.55298e25 1.87834
\(855\) 7.90627e24 0.946804
\(856\) 9.10945e24 1.08010
\(857\) −5.32682e24 −0.625361 −0.312681 0.949858i \(-0.601227\pi\)
−0.312681 + 0.949858i \(0.601227\pi\)
\(858\) 6.80790e24 0.791355
\(859\) 3.60851e24 0.415323 0.207661 0.978201i \(-0.433415\pi\)
0.207661 + 0.978201i \(0.433415\pi\)
\(860\) −5.29927e24 −0.603919
\(861\) −2.27310e25 −2.56502
\(862\) −1.55933e25 −1.74232
\(863\) −1.28137e24 −0.141770 −0.0708848 0.997485i \(-0.522582\pi\)
−0.0708848 + 0.997485i \(0.522582\pi\)
\(864\) 2.38869e24 0.261694
\(865\) −1.01378e25 −1.09978
\(866\) 2.10805e25 2.26453
\(867\) 2.66723e25 2.83725
\(868\) −1.22339e25 −1.28868
\(869\) 2.81631e24 0.293773
\(870\) −4.58948e24 −0.474078
\(871\) 1.05674e25 1.08097
\(872\) 3.65347e25 3.70097
\(873\) 7.52935e24 0.755329
\(874\) 1.61130e25 1.60077
\(875\) −1.06012e25 −1.04301
\(876\) −6.53768e24 −0.636999
\(877\) −1.06601e25 −1.02864 −0.514322 0.857597i \(-0.671956\pi\)
−0.514322 + 0.857597i \(0.671956\pi\)
\(878\) 2.15574e25 2.06012
\(879\) −8.53589e24 −0.807873
\(880\) −4.22401e24 −0.395934
\(881\) 6.83036e24 0.634087 0.317043 0.948411i \(-0.397310\pi\)
0.317043 + 0.948411i \(0.397310\pi\)
\(882\) −5.60787e24 −0.515603
\(883\) 5.77117e24 0.525530 0.262765 0.964860i \(-0.415366\pi\)
0.262765 + 0.964860i \(0.415366\pi\)
\(884\) 6.33354e25 5.71218
\(885\) −2.56033e24 −0.228706
\(886\) −1.21670e25 −1.07645
\(887\) −5.24053e24 −0.459224 −0.229612 0.973282i \(-0.573746\pi\)
−0.229612 + 0.973282i \(0.573746\pi\)
\(888\) −4.51398e25 −3.91787
\(889\) 1.96099e25 1.68581
\(890\) 2.37908e25 2.02579
\(891\) 3.28436e24 0.277007
\(892\) 3.71332e25 3.10214
\(893\) 8.65827e24 0.716463
\(894\) 1.23574e24 0.101288
\(895\) −2.18769e25 −1.77620
\(896\) 1.88130e25 1.51301
\(897\) −1.79394e25 −1.42913
\(898\) 2.10920e25 1.66444
\(899\) −1.18479e24 −0.0926152
\(900\) 3.92230e24 0.303724
\(901\) −3.04393e25 −2.33493
\(902\) −8.92686e24 −0.678333
\(903\) −5.22419e24 −0.393254
\(904\) −1.69518e23 −0.0126411
\(905\) 2.14307e25 1.58316
\(906\) 1.79989e25 1.31721
\(907\) 1.51449e25 1.09801 0.549003 0.835820i \(-0.315008\pi\)
0.549003 + 0.835820i \(0.315008\pi\)
\(908\) 5.36847e24 0.385586
\(909\) 1.55076e25 1.10345
\(910\) −4.82415e25 −3.40071
\(911\) 1.28115e25 0.894732 0.447366 0.894351i \(-0.352362\pi\)
0.447366 + 0.894351i \(0.352362\pi\)
\(912\) 3.60805e25 2.49641
\(913\) −1.37172e24 −0.0940294
\(914\) −6.24697e24 −0.424255
\(915\) −1.89102e25 −1.27238
\(916\) 2.21743e25 1.47822
\(917\) −9.96457e24 −0.658141
\(918\) 1.80836e25 1.18337
\(919\) −3.21309e24 −0.208325 −0.104162 0.994560i \(-0.533216\pi\)
−0.104162 + 0.994560i \(0.533216\pi\)
\(920\) 2.65501e25 1.70557
\(921\) 1.22336e25 0.778659
\(922\) −1.18285e24 −0.0745965
\(923\) −2.45432e25 −1.53362
\(924\) −1.25785e25 −0.778787
\(925\) 4.51072e24 0.276720
\(926\) −1.01192e25 −0.615108
\(927\) 1.12005e25 0.674623
\(928\) −2.18352e24 −0.130316
\(929\) −1.54037e25 −0.910944 −0.455472 0.890250i \(-0.650529\pi\)
−0.455472 + 0.890250i \(0.650529\pi\)
\(930\) 2.17288e25 1.27330
\(931\) 8.42988e24 0.489496
\(932\) −5.46986e25 −3.14732
\(933\) 2.28891e25 1.30507
\(934\) −3.75064e25 −2.11912
\(935\) −7.99473e24 −0.447615
\(936\) −3.99566e25 −2.21689
\(937\) −1.65163e25 −0.908083 −0.454042 0.890981i \(-0.650018\pi\)
−0.454042 + 0.890981i \(0.650018\pi\)
\(938\) −2.84790e25 −1.55168
\(939\) 2.12102e25 1.14522
\(940\) 2.63521e25 1.41003
\(941\) 1.13211e25 0.600312 0.300156 0.953890i \(-0.402961\pi\)
0.300156 + 0.953890i \(0.402961\pi\)
\(942\) 1.31980e25 0.693544
\(943\) 2.35230e25 1.22502
\(944\) −4.87231e24 −0.251462
\(945\) −9.44317e24 −0.483000
\(946\) −2.05163e24 −0.103998
\(947\) 2.69015e25 1.35145 0.675727 0.737152i \(-0.263830\pi\)
0.675727 + 0.737152i \(0.263830\pi\)
\(948\) −7.32171e25 −3.64537
\(949\) −6.65513e24 −0.328393
\(950\) −8.60014e24 −0.420586
\(951\) 2.45090e25 1.18793
\(952\) −9.24080e25 −4.43910
\(953\) 2.54029e25 1.20947 0.604733 0.796428i \(-0.293280\pi\)
0.604733 + 0.796428i \(0.293280\pi\)
\(954\) 3.54709e25 1.67383
\(955\) 7.78302e24 0.364015
\(956\) −7.21789e25 −3.34594
\(957\) −1.21817e24 −0.0559700
\(958\) −5.50059e25 −2.50497
\(959\) 3.64763e25 1.64647
\(960\) −1.03171e25 −0.461585
\(961\) −1.69408e25 −0.751250
\(962\) −8.48767e25 −3.73079
\(963\) −8.42287e24 −0.366975
\(964\) −3.63074e25 −1.56798
\(965\) −5.63355e24 −0.241157
\(966\) 4.83466e25 2.05145
\(967\) −1.75933e25 −0.739984 −0.369992 0.929035i \(-0.620640\pi\)
−0.369992 + 0.929035i \(0.620640\pi\)
\(968\) 4.78198e25 1.99373
\(969\) 6.82890e25 2.82227
\(970\) −5.02466e25 −2.05848
\(971\) −3.77277e24 −0.153214 −0.0766068 0.997061i \(-0.524409\pi\)
−0.0766068 + 0.997061i \(0.524409\pi\)
\(972\) −6.51872e25 −2.62421
\(973\) 3.19596e25 1.27539
\(974\) 2.88854e25 1.14269
\(975\) 9.57493e24 0.375488
\(976\) −3.59861e25 −1.39898
\(977\) −8.08742e24 −0.311678 −0.155839 0.987782i \(-0.549808\pi\)
−0.155839 + 0.987782i \(0.549808\pi\)
\(978\) −7.68912e25 −2.93762
\(979\) 6.31469e24 0.239166
\(980\) 2.56570e25 0.963352
\(981\) −3.37811e25 −1.25744
\(982\) −1.45147e25 −0.535625
\(983\) 3.50594e25 1.28262 0.641312 0.767280i \(-0.278390\pi\)
0.641312 + 0.767280i \(0.278390\pi\)
\(984\) 1.25642e26 4.55697
\(985\) −2.37162e24 −0.0852781
\(986\) −1.65303e25 −0.589287
\(987\) 2.59788e25 0.918171
\(988\) 1.10945e26 3.88752
\(989\) 5.40622e24 0.187813
\(990\) 9.31624e24 0.320879
\(991\) −1.27204e25 −0.434386 −0.217193 0.976129i \(-0.569690\pi\)
−0.217193 + 0.976129i \(0.569690\pi\)
\(992\) 1.03378e25 0.350009
\(993\) −6.76719e25 −2.27164
\(994\) 6.61438e25 2.20143
\(995\) 4.66229e25 1.53852
\(996\) 3.56613e25 1.16679
\(997\) −7.57365e24 −0.245695 −0.122847 0.992426i \(-0.539203\pi\)
−0.122847 + 0.992426i \(0.539203\pi\)
\(998\) 9.71670e25 3.12543
\(999\) −1.66144e25 −0.529881
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 29.18.a.b.1.3 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.18.a.b.1.3 21 1.1 even 1 trivial