Properties

Label 177.14.a.b.1.10
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-73.1261 q^{2} -729.000 q^{3} -2844.57 q^{4} -37898.1 q^{5} +53309.0 q^{6} +370148. q^{7} +807062. q^{8} +531441. q^{9} +O(q^{10})\) \(q-73.1261 q^{2} -729.000 q^{3} -2844.57 q^{4} -37898.1 q^{5} +53309.0 q^{6} +370148. q^{7} +807062. q^{8} +531441. q^{9} +2.77134e6 q^{10} -7.88747e6 q^{11} +2.07369e6 q^{12} -2.23192e6 q^{13} -2.70675e7 q^{14} +2.76277e7 q^{15} -3.57146e7 q^{16} +6.39279e7 q^{17} -3.88622e7 q^{18} +1.32405e8 q^{19} +1.07804e8 q^{20} -2.69838e8 q^{21} +5.76780e8 q^{22} -1.21940e9 q^{23} -5.88348e8 q^{24} +2.15563e8 q^{25} +1.63212e8 q^{26} -3.87420e8 q^{27} -1.05291e9 q^{28} +4.50974e9 q^{29} -2.02031e9 q^{30} -6.42026e9 q^{31} -3.99978e9 q^{32} +5.74996e9 q^{33} -4.67480e9 q^{34} -1.40279e10 q^{35} -1.51172e9 q^{36} -2.37133e10 q^{37} -9.68228e9 q^{38} +1.62707e9 q^{39} -3.05861e10 q^{40} +2.80832e10 q^{41} +1.97322e10 q^{42} -2.26518e10 q^{43} +2.24364e10 q^{44} -2.01406e10 q^{45} +8.91701e10 q^{46} +6.72298e10 q^{47} +2.60359e10 q^{48} +4.01207e10 q^{49} -1.57633e10 q^{50} -4.66034e10 q^{51} +6.34886e9 q^{52} +1.27588e11 q^{53} +2.83306e10 q^{54} +2.98920e11 q^{55} +2.98732e11 q^{56} -9.65234e10 q^{57} -3.29780e11 q^{58} -4.21805e10 q^{59} -7.85889e10 q^{60} +7.06444e11 q^{61} +4.69489e11 q^{62} +1.96712e11 q^{63} +5.85062e11 q^{64} +8.45857e10 q^{65} -4.20473e11 q^{66} -9.15774e11 q^{67} -1.81847e11 q^{68} +8.88943e11 q^{69} +1.02581e12 q^{70} +1.48868e12 q^{71} +4.28906e11 q^{72} -1.43403e12 q^{73} +1.73406e12 q^{74} -1.57146e11 q^{75} -3.76635e11 q^{76} -2.91953e12 q^{77} -1.18981e11 q^{78} +9.88310e11 q^{79} +1.35352e12 q^{80} +2.82430e11 q^{81} -2.05362e12 q^{82} +7.61608e11 q^{83} +7.67572e11 q^{84} -2.42275e12 q^{85} +1.65644e12 q^{86} -3.28760e12 q^{87} -6.36567e12 q^{88} +4.89776e12 q^{89} +1.47280e12 q^{90} -8.26142e11 q^{91} +3.46867e12 q^{92} +4.68037e12 q^{93} -4.91626e12 q^{94} -5.01791e12 q^{95} +2.91584e12 q^{96} +1.14572e13 q^{97} -2.93387e12 q^{98} -4.19172e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −73.1261 −0.807937 −0.403969 0.914773i \(-0.632370\pi\)
−0.403969 + 0.914773i \(0.632370\pi\)
\(3\) −729.000 −0.577350
\(4\) −2844.57 −0.347237
\(5\) −37898.1 −1.08471 −0.542354 0.840150i \(-0.682467\pi\)
−0.542354 + 0.840150i \(0.682467\pi\)
\(6\) 53309.0 0.466463
\(7\) 370148. 1.18915 0.594577 0.804038i \(-0.297319\pi\)
0.594577 + 0.804038i \(0.297319\pi\)
\(8\) 807062. 1.08848
\(9\) 531441. 0.333333
\(10\) 2.77134e6 0.876375
\(11\) −7.88747e6 −1.34241 −0.671205 0.741272i \(-0.734223\pi\)
−0.671205 + 0.741272i \(0.734223\pi\)
\(12\) 2.07369e6 0.200478
\(13\) −2.23192e6 −0.128247 −0.0641235 0.997942i \(-0.520425\pi\)
−0.0641235 + 0.997942i \(0.520425\pi\)
\(14\) −2.70675e7 −0.960762
\(15\) 2.76277e7 0.626256
\(16\) −3.57146e7 −0.532189
\(17\) 6.39279e7 0.642351 0.321175 0.947020i \(-0.395922\pi\)
0.321175 + 0.947020i \(0.395922\pi\)
\(18\) −3.88622e7 −0.269312
\(19\) 1.32405e8 0.645664 0.322832 0.946456i \(-0.395365\pi\)
0.322832 + 0.946456i \(0.395365\pi\)
\(20\) 1.07804e8 0.376651
\(21\) −2.69838e8 −0.686559
\(22\) 5.76780e8 1.08458
\(23\) −1.21940e9 −1.71757 −0.858787 0.512333i \(-0.828782\pi\)
−0.858787 + 0.512333i \(0.828782\pi\)
\(24\) −5.88348e8 −0.628436
\(25\) 2.15563e8 0.176590
\(26\) 1.63212e8 0.103616
\(27\) −3.87420e8 −0.192450
\(28\) −1.05291e9 −0.412919
\(29\) 4.50974e9 1.40788 0.703938 0.710261i \(-0.251423\pi\)
0.703938 + 0.710261i \(0.251423\pi\)
\(30\) −2.02031e9 −0.505976
\(31\) −6.42026e9 −1.29928 −0.649639 0.760243i \(-0.725080\pi\)
−0.649639 + 0.760243i \(0.725080\pi\)
\(32\) −3.99978e9 −0.658508
\(33\) 5.74996e9 0.775041
\(34\) −4.67480e9 −0.518979
\(35\) −1.40279e10 −1.28988
\(36\) −1.51172e9 −0.115746
\(37\) −2.37133e10 −1.51943 −0.759715 0.650256i \(-0.774662\pi\)
−0.759715 + 0.650256i \(0.774662\pi\)
\(38\) −9.68228e9 −0.521656
\(39\) 1.62707e9 0.0740435
\(40\) −3.05861e10 −1.18069
\(41\) 2.80832e10 0.923318 0.461659 0.887057i \(-0.347254\pi\)
0.461659 + 0.887057i \(0.347254\pi\)
\(42\) 1.97322e10 0.554696
\(43\) −2.26518e10 −0.546460 −0.273230 0.961949i \(-0.588092\pi\)
−0.273230 + 0.961949i \(0.588092\pi\)
\(44\) 2.24364e10 0.466135
\(45\) −2.01406e10 −0.361569
\(46\) 8.91701e10 1.38769
\(47\) 6.72298e10 0.909758 0.454879 0.890553i \(-0.349683\pi\)
0.454879 + 0.890553i \(0.349683\pi\)
\(48\) 2.60359e10 0.307260
\(49\) 4.01207e10 0.414089
\(50\) −1.57633e10 −0.142673
\(51\) −4.66034e10 −0.370861
\(52\) 6.34886e9 0.0445322
\(53\) 1.27588e11 0.790709 0.395354 0.918529i \(-0.370622\pi\)
0.395354 + 0.918529i \(0.370622\pi\)
\(54\) 2.83306e10 0.155488
\(55\) 2.98920e11 1.45612
\(56\) 2.98732e11 1.29437
\(57\) −9.65234e10 −0.372774
\(58\) −3.29780e11 −1.13748
\(59\) −4.21805e10 −0.130189
\(60\) −7.85889e10 −0.217459
\(61\) 7.06444e11 1.75563 0.877817 0.478997i \(-0.158999\pi\)
0.877817 + 0.478997i \(0.158999\pi\)
\(62\) 4.69489e11 1.04973
\(63\) 1.96712e11 0.396385
\(64\) 5.85062e11 1.06422
\(65\) 8.45857e10 0.139111
\(66\) −4.20473e11 −0.626184
\(67\) −9.15774e11 −1.23681 −0.618404 0.785860i \(-0.712220\pi\)
−0.618404 + 0.785860i \(0.712220\pi\)
\(68\) −1.81847e11 −0.223048
\(69\) 8.88943e11 0.991642
\(70\) 1.02581e12 1.04215
\(71\) 1.48868e12 1.37918 0.689592 0.724198i \(-0.257790\pi\)
0.689592 + 0.724198i \(0.257790\pi\)
\(72\) 4.28906e11 0.362828
\(73\) −1.43403e12 −1.10907 −0.554536 0.832159i \(-0.687104\pi\)
−0.554536 + 0.832159i \(0.687104\pi\)
\(74\) 1.73406e12 1.22760
\(75\) −1.57146e11 −0.101954
\(76\) −3.76635e11 −0.224199
\(77\) −2.91953e12 −1.59633
\(78\) −1.18981e11 −0.0598225
\(79\) 9.88310e11 0.457422 0.228711 0.973494i \(-0.426549\pi\)
0.228711 + 0.973494i \(0.426549\pi\)
\(80\) 1.35352e12 0.577269
\(81\) 2.82430e11 0.111111
\(82\) −2.05362e12 −0.745983
\(83\) 7.61608e11 0.255696 0.127848 0.991794i \(-0.459193\pi\)
0.127848 + 0.991794i \(0.459193\pi\)
\(84\) 7.67572e11 0.238399
\(85\) −2.42275e12 −0.696762
\(86\) 1.65644e12 0.441506
\(87\) −3.28760e12 −0.812838
\(88\) −6.36567e12 −1.46119
\(89\) 4.89776e12 1.04463 0.522315 0.852753i \(-0.325069\pi\)
0.522315 + 0.852753i \(0.325069\pi\)
\(90\) 1.47280e12 0.292125
\(91\) −8.26142e11 −0.152506
\(92\) 3.46867e12 0.596406
\(93\) 4.68037e12 0.750138
\(94\) −4.91626e12 −0.735027
\(95\) −5.01791e12 −0.700356
\(96\) 2.91584e12 0.380190
\(97\) 1.14572e13 1.39657 0.698287 0.715818i \(-0.253946\pi\)
0.698287 + 0.715818i \(0.253946\pi\)
\(98\) −2.93387e12 −0.334558
\(99\) −4.19172e12 −0.447470
\(100\) −6.13185e11 −0.0613185
\(101\) 1.57286e13 1.47435 0.737174 0.675703i \(-0.236160\pi\)
0.737174 + 0.675703i \(0.236160\pi\)
\(102\) 3.40793e12 0.299633
\(103\) −9.38141e12 −0.774152 −0.387076 0.922048i \(-0.626515\pi\)
−0.387076 + 0.922048i \(0.626515\pi\)
\(104\) −1.80130e12 −0.139595
\(105\) 1.02264e13 0.744715
\(106\) −9.33002e12 −0.638843
\(107\) −1.15569e13 −0.744472 −0.372236 0.928138i \(-0.621409\pi\)
−0.372236 + 0.928138i \(0.621409\pi\)
\(108\) 1.10204e12 0.0668258
\(109\) 1.41881e13 0.810313 0.405156 0.914247i \(-0.367217\pi\)
0.405156 + 0.914247i \(0.367217\pi\)
\(110\) −2.18589e13 −1.17646
\(111\) 1.72870e13 0.877244
\(112\) −1.32197e13 −0.632855
\(113\) −4.04064e12 −0.182574 −0.0912872 0.995825i \(-0.529098\pi\)
−0.0912872 + 0.995825i \(0.529098\pi\)
\(114\) 7.05838e12 0.301178
\(115\) 4.62130e13 1.86307
\(116\) −1.28283e13 −0.488867
\(117\) −1.18614e12 −0.0427490
\(118\) 3.08450e12 0.105184
\(119\) 2.36628e13 0.763854
\(120\) 2.22973e13 0.681669
\(121\) 2.76895e13 0.802065
\(122\) −5.16595e13 −1.41844
\(123\) −2.04726e13 −0.533078
\(124\) 1.82629e13 0.451157
\(125\) 3.80929e13 0.893159
\(126\) −1.43848e13 −0.320254
\(127\) 1.98619e13 0.420045 0.210023 0.977697i \(-0.432646\pi\)
0.210023 + 0.977697i \(0.432646\pi\)
\(128\) −1.00172e13 −0.201317
\(129\) 1.65132e13 0.315499
\(130\) −6.18542e12 −0.112393
\(131\) −2.03935e12 −0.0352556 −0.0176278 0.999845i \(-0.505611\pi\)
−0.0176278 + 0.999845i \(0.505611\pi\)
\(132\) −1.63562e13 −0.269123
\(133\) 4.90095e13 0.767794
\(134\) 6.69670e13 0.999263
\(135\) 1.46825e13 0.208752
\(136\) 5.15937e13 0.699188
\(137\) 1.42474e14 1.84099 0.920496 0.390753i \(-0.127785\pi\)
0.920496 + 0.390753i \(0.127785\pi\)
\(138\) −6.50050e13 −0.801185
\(139\) −1.42860e14 −1.68002 −0.840012 0.542567i \(-0.817452\pi\)
−0.840012 + 0.542567i \(0.817452\pi\)
\(140\) 3.99034e13 0.447896
\(141\) −4.90105e13 −0.525249
\(142\) −1.08862e14 −1.11429
\(143\) 1.76042e13 0.172160
\(144\) −1.89802e13 −0.177396
\(145\) −1.70911e14 −1.52713
\(146\) 1.04865e14 0.896061
\(147\) −2.92480e13 −0.239074
\(148\) 6.74541e13 0.527603
\(149\) 9.36377e13 0.701035 0.350518 0.936556i \(-0.386006\pi\)
0.350518 + 0.936556i \(0.386006\pi\)
\(150\) 1.14915e13 0.0823725
\(151\) −1.45031e14 −0.995657 −0.497828 0.867276i \(-0.665869\pi\)
−0.497828 + 0.867276i \(0.665869\pi\)
\(152\) 1.06859e14 0.702795
\(153\) 3.39739e13 0.214117
\(154\) 2.13494e14 1.28974
\(155\) 2.43316e14 1.40934
\(156\) −4.62832e12 −0.0257107
\(157\) 1.86864e14 0.995816 0.497908 0.867230i \(-0.334102\pi\)
0.497908 + 0.867230i \(0.334102\pi\)
\(158\) −7.22713e13 −0.369569
\(159\) −9.30117e13 −0.456516
\(160\) 1.51584e14 0.714288
\(161\) −4.51359e14 −2.04246
\(162\) −2.06530e13 −0.0897708
\(163\) −3.54345e14 −1.47981 −0.739906 0.672710i \(-0.765130\pi\)
−0.739906 + 0.672710i \(0.765130\pi\)
\(164\) −7.98845e13 −0.320610
\(165\) −2.17913e14 −0.840692
\(166\) −5.56935e13 −0.206586
\(167\) −3.33353e14 −1.18918 −0.594590 0.804029i \(-0.702686\pi\)
−0.594590 + 0.804029i \(0.702686\pi\)
\(168\) −2.17776e14 −0.747308
\(169\) −2.97894e14 −0.983553
\(170\) 1.77166e14 0.562940
\(171\) 7.03655e13 0.215221
\(172\) 6.44347e13 0.189751
\(173\) 3.36990e14 0.955689 0.477845 0.878444i \(-0.341418\pi\)
0.477845 + 0.878444i \(0.341418\pi\)
\(174\) 2.40409e14 0.656722
\(175\) 7.97904e13 0.209992
\(176\) 2.81698e14 0.714416
\(177\) 3.07496e13 0.0751646
\(178\) −3.58154e14 −0.843995
\(179\) −4.84063e14 −1.09991 −0.549955 0.835194i \(-0.685355\pi\)
−0.549955 + 0.835194i \(0.685355\pi\)
\(180\) 5.72913e13 0.125550
\(181\) 6.15655e14 1.30145 0.650724 0.759315i \(-0.274466\pi\)
0.650724 + 0.759315i \(0.274466\pi\)
\(182\) 6.04126e13 0.123215
\(183\) −5.14998e14 −1.01362
\(184\) −9.84132e14 −1.86955
\(185\) 8.98689e14 1.64814
\(186\) −3.42258e14 −0.606065
\(187\) −5.04229e14 −0.862298
\(188\) −1.91240e14 −0.315902
\(189\) −1.43403e14 −0.228853
\(190\) 3.66940e14 0.565844
\(191\) −1.28312e15 −1.91228 −0.956139 0.292914i \(-0.905375\pi\)
−0.956139 + 0.292914i \(0.905375\pi\)
\(192\) −4.26510e14 −0.614429
\(193\) 4.00231e14 0.557427 0.278714 0.960374i \(-0.410092\pi\)
0.278714 + 0.960374i \(0.410092\pi\)
\(194\) −8.37824e14 −1.12834
\(195\) −6.16630e13 −0.0803155
\(196\) −1.14126e14 −0.143787
\(197\) 7.76732e14 0.946761 0.473381 0.880858i \(-0.343033\pi\)
0.473381 + 0.880858i \(0.343033\pi\)
\(198\) 3.06525e14 0.361528
\(199\) 1.14802e15 1.31041 0.655203 0.755453i \(-0.272583\pi\)
0.655203 + 0.755453i \(0.272583\pi\)
\(200\) 1.73973e14 0.192215
\(201\) 6.67600e14 0.714071
\(202\) −1.15017e15 −1.19118
\(203\) 1.66927e15 1.67418
\(204\) 1.32567e14 0.128777
\(205\) −1.06430e15 −1.00153
\(206\) 6.86026e14 0.625466
\(207\) −6.48040e14 −0.572525
\(208\) 7.97123e13 0.0682517
\(209\) −1.04434e15 −0.866746
\(210\) −7.47814e14 −0.601683
\(211\) 1.48177e15 1.15597 0.577984 0.816048i \(-0.303840\pi\)
0.577984 + 0.816048i \(0.303840\pi\)
\(212\) −3.62933e14 −0.274564
\(213\) −1.08525e15 −0.796273
\(214\) 8.45114e14 0.601487
\(215\) 8.58462e14 0.592749
\(216\) −3.12672e14 −0.209479
\(217\) −2.37645e15 −1.54504
\(218\) −1.03752e15 −0.654682
\(219\) 1.04541e15 0.640323
\(220\) −8.50298e14 −0.505620
\(221\) −1.42682e14 −0.0823796
\(222\) −1.26413e15 −0.708758
\(223\) 2.27715e15 1.23997 0.619983 0.784615i \(-0.287139\pi\)
0.619983 + 0.784615i \(0.287139\pi\)
\(224\) −1.48051e15 −0.783068
\(225\) 1.14559e14 0.0588632
\(226\) 2.95476e14 0.147509
\(227\) −8.42246e14 −0.408574 −0.204287 0.978911i \(-0.565488\pi\)
−0.204287 + 0.978911i \(0.565488\pi\)
\(228\) 2.74567e14 0.129441
\(229\) −2.08226e15 −0.954124 −0.477062 0.878870i \(-0.658298\pi\)
−0.477062 + 0.878870i \(0.658298\pi\)
\(230\) −3.37938e15 −1.50524
\(231\) 2.12834e15 0.921643
\(232\) 3.63964e15 1.53245
\(233\) −4.28235e15 −1.75335 −0.876674 0.481084i \(-0.840243\pi\)
−0.876674 + 0.481084i \(0.840243\pi\)
\(234\) 8.67375e13 0.0345385
\(235\) −2.54788e15 −0.986821
\(236\) 1.19985e14 0.0452064
\(237\) −7.20478e14 −0.264093
\(238\) −1.73037e15 −0.617146
\(239\) 3.50465e14 0.121635 0.0608175 0.998149i \(-0.480629\pi\)
0.0608175 + 0.998149i \(0.480629\pi\)
\(240\) −9.86713e14 −0.333287
\(241\) −1.02876e15 −0.338223 −0.169112 0.985597i \(-0.554090\pi\)
−0.169112 + 0.985597i \(0.554090\pi\)
\(242\) −2.02482e15 −0.648018
\(243\) −2.05891e14 −0.0641500
\(244\) −2.00953e15 −0.609621
\(245\) −1.52050e15 −0.449165
\(246\) 1.49709e15 0.430694
\(247\) −2.95518e14 −0.0828045
\(248\) −5.18155e15 −1.41424
\(249\) −5.55212e14 −0.147626
\(250\) −2.78559e15 −0.721617
\(251\) 6.11470e15 1.54346 0.771731 0.635950i \(-0.219391\pi\)
0.771731 + 0.635950i \(0.219391\pi\)
\(252\) −5.59560e14 −0.137640
\(253\) 9.61799e15 2.30569
\(254\) −1.45242e15 −0.339370
\(255\) 1.76618e15 0.402276
\(256\) −4.06031e15 −0.901571
\(257\) −3.65987e14 −0.0792320 −0.0396160 0.999215i \(-0.512613\pi\)
−0.0396160 + 0.999215i \(0.512613\pi\)
\(258\) −1.20755e15 −0.254903
\(259\) −8.77744e15 −1.80684
\(260\) −2.40610e14 −0.0483043
\(261\) 2.39666e15 0.469292
\(262\) 1.49130e14 0.0284843
\(263\) −1.04025e16 −1.93833 −0.969164 0.246417i \(-0.920747\pi\)
−0.969164 + 0.246417i \(0.920747\pi\)
\(264\) 4.64058e15 0.843619
\(265\) −4.83534e15 −0.857688
\(266\) −3.58388e15 −0.620330
\(267\) −3.57047e15 −0.603117
\(268\) 2.60498e15 0.429466
\(269\) −7.87928e14 −0.126793 −0.0633967 0.997988i \(-0.520193\pi\)
−0.0633967 + 0.997988i \(0.520193\pi\)
\(270\) −1.07367e15 −0.168659
\(271\) 8.24265e15 1.26406 0.632028 0.774946i \(-0.282223\pi\)
0.632028 + 0.774946i \(0.282223\pi\)
\(272\) −2.28316e15 −0.341852
\(273\) 6.02258e14 0.0880492
\(274\) −1.04186e16 −1.48741
\(275\) −1.70025e15 −0.237056
\(276\) −2.52866e15 −0.344335
\(277\) 1.20923e16 1.60838 0.804191 0.594371i \(-0.202599\pi\)
0.804191 + 0.594371i \(0.202599\pi\)
\(278\) 1.04468e16 1.35735
\(279\) −3.41199e15 −0.433092
\(280\) −1.13214e16 −1.40402
\(281\) −6.11128e15 −0.740527 −0.370264 0.928927i \(-0.620733\pi\)
−0.370264 + 0.928927i \(0.620733\pi\)
\(282\) 3.58395e15 0.424368
\(283\) −8.43187e15 −0.975690 −0.487845 0.872930i \(-0.662217\pi\)
−0.487845 + 0.872930i \(0.662217\pi\)
\(284\) −4.23465e15 −0.478904
\(285\) 3.65805e15 0.404351
\(286\) −1.28733e15 −0.139095
\(287\) 1.03949e16 1.09797
\(288\) −2.12565e15 −0.219503
\(289\) −5.81781e15 −0.587386
\(290\) 1.24980e16 1.23383
\(291\) −8.35233e15 −0.806312
\(292\) 4.07920e15 0.385111
\(293\) −1.09076e16 −1.00714 −0.503570 0.863955i \(-0.667980\pi\)
−0.503570 + 0.863955i \(0.667980\pi\)
\(294\) 2.13879e15 0.193157
\(295\) 1.59856e15 0.141217
\(296\) −1.91381e16 −1.65387
\(297\) 3.05577e15 0.258347
\(298\) −6.84736e15 −0.566393
\(299\) 2.72161e15 0.220274
\(300\) 4.47012e14 0.0354022
\(301\) −8.38454e15 −0.649826
\(302\) 1.06055e16 0.804428
\(303\) −1.14661e16 −0.851215
\(304\) −4.72880e15 −0.343615
\(305\) −2.67729e16 −1.90435
\(306\) −2.48438e15 −0.172993
\(307\) −5.44084e14 −0.0370909 −0.0185454 0.999828i \(-0.505904\pi\)
−0.0185454 + 0.999828i \(0.505904\pi\)
\(308\) 8.30481e15 0.554306
\(309\) 6.83905e15 0.446957
\(310\) −1.77927e16 −1.13865
\(311\) 2.81204e16 1.76230 0.881148 0.472840i \(-0.156771\pi\)
0.881148 + 0.472840i \(0.156771\pi\)
\(312\) 1.31315e15 0.0805951
\(313\) −2.17471e16 −1.30726 −0.653631 0.756813i \(-0.726755\pi\)
−0.653631 + 0.756813i \(0.726755\pi\)
\(314\) −1.36647e16 −0.804557
\(315\) −7.45501e15 −0.429962
\(316\) −2.81132e15 −0.158834
\(317\) 2.25030e16 1.24553 0.622766 0.782408i \(-0.286009\pi\)
0.622766 + 0.782408i \(0.286009\pi\)
\(318\) 6.80158e15 0.368836
\(319\) −3.55704e16 −1.88995
\(320\) −2.21728e16 −1.15437
\(321\) 8.42501e15 0.429821
\(322\) 3.30061e16 1.65018
\(323\) 8.46438e15 0.414743
\(324\) −8.03390e14 −0.0385819
\(325\) −4.81121e14 −0.0226471
\(326\) 2.59119e16 1.19560
\(327\) −1.03431e16 −0.467834
\(328\) 2.26649e16 1.00502
\(329\) 2.48850e16 1.08184
\(330\) 1.59351e16 0.679227
\(331\) 1.11987e16 0.468041 0.234021 0.972232i \(-0.424812\pi\)
0.234021 + 0.972232i \(0.424812\pi\)
\(332\) −2.16645e15 −0.0887872
\(333\) −1.26022e16 −0.506477
\(334\) 2.43768e16 0.960783
\(335\) 3.47061e16 1.34157
\(336\) 9.63716e15 0.365379
\(337\) −4.82725e15 −0.179517 −0.0897584 0.995964i \(-0.528609\pi\)
−0.0897584 + 0.995964i \(0.528609\pi\)
\(338\) 2.17838e16 0.794649
\(339\) 2.94562e15 0.105409
\(340\) 6.89166e15 0.241942
\(341\) 5.06396e16 1.74416
\(342\) −5.14556e15 −0.173885
\(343\) −2.10127e16 −0.696739
\(344\) −1.82814e16 −0.594813
\(345\) −3.36893e16 −1.07564
\(346\) −2.46427e16 −0.772137
\(347\) 4.80731e16 1.47829 0.739146 0.673545i \(-0.235229\pi\)
0.739146 + 0.673545i \(0.235229\pi\)
\(348\) 9.35180e15 0.282247
\(349\) 2.33023e16 0.690293 0.345146 0.938549i \(-0.387829\pi\)
0.345146 + 0.938549i \(0.387829\pi\)
\(350\) −5.83477e15 −0.169661
\(351\) 8.64693e14 0.0246812
\(352\) 3.15481e16 0.883988
\(353\) −2.68573e16 −0.738799 −0.369400 0.929271i \(-0.620437\pi\)
−0.369400 + 0.929271i \(0.620437\pi\)
\(354\) −2.24860e15 −0.0607283
\(355\) −5.64182e16 −1.49601
\(356\) −1.39320e16 −0.362734
\(357\) −1.72502e16 −0.441012
\(358\) 3.53977e16 0.888659
\(359\) −6.33371e16 −1.56151 −0.780754 0.624839i \(-0.785165\pi\)
−0.780754 + 0.624839i \(0.785165\pi\)
\(360\) −1.62547e16 −0.393562
\(361\) −2.45218e16 −0.583118
\(362\) −4.50205e16 −1.05149
\(363\) −2.01856e16 −0.463072
\(364\) 2.35002e15 0.0529556
\(365\) 5.43471e16 1.20302
\(366\) 3.76598e16 0.818938
\(367\) −3.87957e16 −0.828809 −0.414405 0.910093i \(-0.636010\pi\)
−0.414405 + 0.910093i \(0.636010\pi\)
\(368\) 4.35504e16 0.914074
\(369\) 1.49246e16 0.307773
\(370\) −6.57177e16 −1.33159
\(371\) 4.72265e16 0.940275
\(372\) −1.33136e16 −0.260476
\(373\) −3.10449e16 −0.596875 −0.298438 0.954429i \(-0.596465\pi\)
−0.298438 + 0.954429i \(0.596465\pi\)
\(374\) 3.68723e16 0.696683
\(375\) −2.77697e16 −0.515666
\(376\) 5.42586e16 0.990256
\(377\) −1.00654e16 −0.180556
\(378\) 1.04865e16 0.184899
\(379\) −4.11618e16 −0.713411 −0.356706 0.934217i \(-0.616100\pi\)
−0.356706 + 0.934217i \(0.616100\pi\)
\(380\) 1.42738e16 0.243190
\(381\) −1.44793e16 −0.242513
\(382\) 9.38297e16 1.54500
\(383\) −5.75790e15 −0.0932120 −0.0466060 0.998913i \(-0.514841\pi\)
−0.0466060 + 0.998913i \(0.514841\pi\)
\(384\) 7.30252e15 0.116230
\(385\) 1.10645e17 1.73155
\(386\) −2.92674e16 −0.450366
\(387\) −1.20381e16 −0.182153
\(388\) −3.25909e16 −0.484942
\(389\) −4.95437e16 −0.724964 −0.362482 0.931991i \(-0.618071\pi\)
−0.362482 + 0.931991i \(0.618071\pi\)
\(390\) 4.50917e15 0.0648899
\(391\) −7.79537e16 −1.10329
\(392\) 3.23798e16 0.450729
\(393\) 1.48669e15 0.0203548
\(394\) −5.67994e16 −0.764924
\(395\) −3.74551e16 −0.496169
\(396\) 1.19236e16 0.155378
\(397\) 1.07289e17 1.37536 0.687682 0.726012i \(-0.258628\pi\)
0.687682 + 0.726012i \(0.258628\pi\)
\(398\) −8.39505e16 −1.05873
\(399\) −3.57280e16 −0.443286
\(400\) −7.69876e15 −0.0939791
\(401\) 6.02400e16 0.723513 0.361756 0.932273i \(-0.382177\pi\)
0.361756 + 0.932273i \(0.382177\pi\)
\(402\) −4.88190e16 −0.576925
\(403\) 1.43295e16 0.166628
\(404\) −4.47410e16 −0.511949
\(405\) −1.07035e16 −0.120523
\(406\) −1.22067e17 −1.35263
\(407\) 1.87038e17 2.03970
\(408\) −3.76118e16 −0.403676
\(409\) 1.51728e16 0.160275 0.0801375 0.996784i \(-0.474464\pi\)
0.0801375 + 0.996784i \(0.474464\pi\)
\(410\) 7.78281e16 0.809173
\(411\) −1.03863e17 −1.06290
\(412\) 2.66861e16 0.268814
\(413\) −1.56130e16 −0.154815
\(414\) 4.73886e16 0.462564
\(415\) −2.88635e16 −0.277355
\(416\) 8.92720e15 0.0844517
\(417\) 1.04145e17 0.969963
\(418\) 7.63687e16 0.700276
\(419\) 6.50706e16 0.587481 0.293740 0.955885i \(-0.405100\pi\)
0.293740 + 0.955885i \(0.405100\pi\)
\(420\) −2.90895e16 −0.258593
\(421\) 4.92680e16 0.431253 0.215626 0.976476i \(-0.430821\pi\)
0.215626 + 0.976476i \(0.430821\pi\)
\(422\) −1.08356e17 −0.933949
\(423\) 3.57287e16 0.303253
\(424\) 1.02971e17 0.860674
\(425\) 1.37805e16 0.113432
\(426\) 7.93600e16 0.643338
\(427\) 2.61489e17 2.08772
\(428\) 3.28745e16 0.258508
\(429\) −1.28335e16 −0.0993967
\(430\) −6.27760e16 −0.478904
\(431\) 5.82573e16 0.437772 0.218886 0.975750i \(-0.429758\pi\)
0.218886 + 0.975750i \(0.429758\pi\)
\(432\) 1.38366e16 0.102420
\(433\) −5.36263e16 −0.391027 −0.195513 0.980701i \(-0.562637\pi\)
−0.195513 + 0.980701i \(0.562637\pi\)
\(434\) 1.73781e17 1.24830
\(435\) 1.24594e17 0.881691
\(436\) −4.03591e16 −0.281371
\(437\) −1.61455e17 −1.10898
\(438\) −7.64467e16 −0.517341
\(439\) −2.07555e17 −1.38393 −0.691964 0.721932i \(-0.743254\pi\)
−0.691964 + 0.721932i \(0.743254\pi\)
\(440\) 2.41247e17 1.58496
\(441\) 2.13218e16 0.138030
\(442\) 1.04338e16 0.0665576
\(443\) −7.36795e15 −0.0463151 −0.0231575 0.999732i \(-0.507372\pi\)
−0.0231575 + 0.999732i \(0.507372\pi\)
\(444\) −4.91740e16 −0.304612
\(445\) −1.85616e17 −1.13312
\(446\) −1.66519e17 −1.00182
\(447\) −6.82619e16 −0.404743
\(448\) 2.16560e17 1.26552
\(449\) 1.54892e17 0.892132 0.446066 0.895000i \(-0.352825\pi\)
0.446066 + 0.895000i \(0.352825\pi\)
\(450\) −8.37728e15 −0.0475578
\(451\) −2.21505e17 −1.23947
\(452\) 1.14939e16 0.0633966
\(453\) 1.05727e17 0.574843
\(454\) 6.15902e16 0.330102
\(455\) 3.13092e16 0.165424
\(456\) −7.79003e16 −0.405759
\(457\) −2.59040e17 −1.33018 −0.665091 0.746762i \(-0.731607\pi\)
−0.665091 + 0.746762i \(0.731607\pi\)
\(458\) 1.52268e17 0.770872
\(459\) −2.47670e16 −0.123620
\(460\) −1.31456e17 −0.646926
\(461\) 1.25135e17 0.607190 0.303595 0.952801i \(-0.401813\pi\)
0.303595 + 0.952801i \(0.401813\pi\)
\(462\) −1.55637e17 −0.744630
\(463\) −6.63878e16 −0.313193 −0.156596 0.987663i \(-0.550052\pi\)
−0.156596 + 0.987663i \(0.550052\pi\)
\(464\) −1.61064e17 −0.749256
\(465\) −1.77377e17 −0.813680
\(466\) 3.13151e17 1.41660
\(467\) 1.40751e17 0.627900 0.313950 0.949439i \(-0.398347\pi\)
0.313950 + 0.949439i \(0.398347\pi\)
\(468\) 3.37404e15 0.0148441
\(469\) −3.38972e17 −1.47076
\(470\) 1.86317e17 0.797289
\(471\) −1.36224e17 −0.574934
\(472\) −3.40423e16 −0.141708
\(473\) 1.78666e17 0.733574
\(474\) 5.26858e16 0.213370
\(475\) 2.85417e16 0.114018
\(476\) −6.73104e16 −0.265239
\(477\) 6.78055e16 0.263570
\(478\) −2.56282e16 −0.0982735
\(479\) −2.42759e17 −0.918321 −0.459161 0.888353i \(-0.651850\pi\)
−0.459161 + 0.888353i \(0.651850\pi\)
\(480\) −1.10505e17 −0.412394
\(481\) 5.29263e16 0.194863
\(482\) 7.52293e16 0.273263
\(483\) 3.29041e17 1.17922
\(484\) −7.87645e16 −0.278507
\(485\) −4.34208e17 −1.51487
\(486\) 1.50560e16 0.0518292
\(487\) −2.49745e17 −0.848319 −0.424160 0.905587i \(-0.639430\pi\)
−0.424160 + 0.905587i \(0.639430\pi\)
\(488\) 5.70144e17 1.91098
\(489\) 2.58317e17 0.854370
\(490\) 1.11188e17 0.362897
\(491\) 5.45019e17 1.75542 0.877712 0.479188i \(-0.159069\pi\)
0.877712 + 0.479188i \(0.159069\pi\)
\(492\) 5.82358e16 0.185105
\(493\) 2.88298e17 0.904350
\(494\) 2.16101e16 0.0669009
\(495\) 1.58858e17 0.485374
\(496\) 2.29297e17 0.691461
\(497\) 5.51033e17 1.64006
\(498\) 4.06005e16 0.119273
\(499\) 2.62257e17 0.760456 0.380228 0.924893i \(-0.375846\pi\)
0.380228 + 0.924893i \(0.375846\pi\)
\(500\) −1.08358e17 −0.310138
\(501\) 2.43015e17 0.686574
\(502\) −4.47144e17 −1.24702
\(503\) 4.68641e17 1.29017 0.645087 0.764109i \(-0.276821\pi\)
0.645087 + 0.764109i \(0.276821\pi\)
\(504\) 1.58759e17 0.431458
\(505\) −5.96083e17 −1.59924
\(506\) −7.03326e17 −1.86285
\(507\) 2.17164e17 0.567854
\(508\) −5.64985e16 −0.145855
\(509\) −1.26286e17 −0.321878 −0.160939 0.986964i \(-0.551452\pi\)
−0.160939 + 0.986964i \(0.551452\pi\)
\(510\) −1.29154e17 −0.325014
\(511\) −5.30804e17 −1.31886
\(512\) 3.78976e17 0.929730
\(513\) −5.12965e16 −0.124258
\(514\) 2.67632e16 0.0640145
\(515\) 3.55538e17 0.839728
\(516\) −4.69729e16 −0.109553
\(517\) −5.30273e17 −1.22127
\(518\) 6.41860e17 1.45981
\(519\) −2.45665e17 −0.551767
\(520\) 6.82658e16 0.151419
\(521\) −6.46305e17 −1.41577 −0.707884 0.706329i \(-0.750350\pi\)
−0.707884 + 0.706329i \(0.750350\pi\)
\(522\) −1.75259e17 −0.379159
\(523\) 5.52191e17 1.17985 0.589927 0.807457i \(-0.299156\pi\)
0.589927 + 0.807457i \(0.299156\pi\)
\(524\) 5.80107e15 0.0122421
\(525\) −5.81672e16 −0.121239
\(526\) 7.60698e17 1.56605
\(527\) −4.10434e17 −0.834592
\(528\) −2.05358e17 −0.412468
\(529\) 9.82902e17 1.95006
\(530\) 3.53590e17 0.692958
\(531\) −2.24165e16 −0.0433963
\(532\) −1.39411e17 −0.266607
\(533\) −6.26795e16 −0.118413
\(534\) 2.61094e17 0.487281
\(535\) 4.37986e17 0.807534
\(536\) −7.39086e17 −1.34624
\(537\) 3.52882e17 0.635034
\(538\) 5.76181e16 0.102441
\(539\) −3.16450e17 −0.555877
\(540\) −4.17654e16 −0.0724865
\(541\) −2.35160e17 −0.403257 −0.201628 0.979462i \(-0.564623\pi\)
−0.201628 + 0.979462i \(0.564623\pi\)
\(542\) −6.02753e17 −1.02128
\(543\) −4.48813e17 −0.751391
\(544\) −2.55697e17 −0.422993
\(545\) −5.37703e17 −0.878952
\(546\) −4.40408e16 −0.0711382
\(547\) 3.58254e17 0.571839 0.285919 0.958254i \(-0.407701\pi\)
0.285919 + 0.958254i \(0.407701\pi\)
\(548\) −4.05277e17 −0.639261
\(549\) 3.75433e17 0.585211
\(550\) 1.24333e17 0.191526
\(551\) 5.97113e17 0.909015
\(552\) 7.17432e17 1.07939
\(553\) 3.65821e17 0.543946
\(554\) −8.84261e17 −1.29947
\(555\) −6.55145e17 −0.951553
\(556\) 4.06376e17 0.583367
\(557\) −3.00119e17 −0.425828 −0.212914 0.977071i \(-0.568295\pi\)
−0.212914 + 0.977071i \(0.568295\pi\)
\(558\) 2.49506e17 0.349912
\(559\) 5.05572e16 0.0700819
\(560\) 5.01001e17 0.686462
\(561\) 3.67583e17 0.497848
\(562\) 4.46894e17 0.598299
\(563\) 6.69169e17 0.885587 0.442794 0.896624i \(-0.353987\pi\)
0.442794 + 0.896624i \(0.353987\pi\)
\(564\) 1.39414e17 0.182386
\(565\) 1.53133e17 0.198040
\(566\) 6.16590e17 0.788297
\(567\) 1.04541e17 0.132128
\(568\) 1.20146e18 1.50122
\(569\) −4.72534e17 −0.583718 −0.291859 0.956461i \(-0.594274\pi\)
−0.291859 + 0.956461i \(0.594274\pi\)
\(570\) −2.67499e17 −0.326690
\(571\) −5.55849e17 −0.671154 −0.335577 0.942013i \(-0.608931\pi\)
−0.335577 + 0.942013i \(0.608931\pi\)
\(572\) −5.00764e16 −0.0597804
\(573\) 9.35396e17 1.10405
\(574\) −7.60142e17 −0.887089
\(575\) −2.62858e17 −0.303306
\(576\) 3.10926e17 0.354741
\(577\) −5.61922e16 −0.0633918 −0.0316959 0.999498i \(-0.510091\pi\)
−0.0316959 + 0.999498i \(0.510091\pi\)
\(578\) 4.25434e17 0.474571
\(579\) −2.91768e17 −0.321831
\(580\) 4.86167e17 0.530278
\(581\) 2.81908e17 0.304062
\(582\) 6.10774e17 0.651450
\(583\) −1.00635e18 −1.06146
\(584\) −1.15735e18 −1.20721
\(585\) 4.49523e16 0.0463702
\(586\) 7.97631e17 0.813706
\(587\) 1.36912e18 1.38131 0.690657 0.723182i \(-0.257321\pi\)
0.690657 + 0.723182i \(0.257321\pi\)
\(588\) 8.31978e16 0.0830155
\(589\) −8.50076e17 −0.838897
\(590\) −1.16897e17 −0.114094
\(591\) −5.66237e17 −0.546613
\(592\) 8.46911e17 0.808624
\(593\) 1.03680e18 0.979128 0.489564 0.871967i \(-0.337156\pi\)
0.489564 + 0.871967i \(0.337156\pi\)
\(594\) −2.23456e17 −0.208728
\(595\) −8.96775e17 −0.828558
\(596\) −2.66359e17 −0.243426
\(597\) −8.36909e17 −0.756563
\(598\) −1.99021e17 −0.177967
\(599\) 1.11217e18 0.983778 0.491889 0.870658i \(-0.336307\pi\)
0.491889 + 0.870658i \(0.336307\pi\)
\(600\) −1.26826e17 −0.110975
\(601\) 3.64114e17 0.315176 0.157588 0.987505i \(-0.449628\pi\)
0.157588 + 0.987505i \(0.449628\pi\)
\(602\) 6.13129e17 0.525018
\(603\) −4.86680e17 −0.412269
\(604\) 4.12550e17 0.345729
\(605\) −1.04938e18 −0.870005
\(606\) 8.38473e17 0.687729
\(607\) 5.94061e17 0.482064 0.241032 0.970517i \(-0.422514\pi\)
0.241032 + 0.970517i \(0.422514\pi\)
\(608\) −5.29591e17 −0.425175
\(609\) −1.21690e18 −0.966590
\(610\) 1.95780e18 1.53859
\(611\) −1.50052e17 −0.116674
\(612\) −9.66410e16 −0.0743494
\(613\) −2.17994e18 −1.65940 −0.829702 0.558206i \(-0.811490\pi\)
−0.829702 + 0.558206i \(0.811490\pi\)
\(614\) 3.97868e16 0.0299671
\(615\) 7.75875e17 0.578234
\(616\) −2.35624e18 −1.73758
\(617\) −1.76345e18 −1.28680 −0.643398 0.765532i \(-0.722476\pi\)
−0.643398 + 0.765532i \(0.722476\pi\)
\(618\) −5.00113e17 −0.361113
\(619\) −5.68471e15 −0.00406180 −0.00203090 0.999998i \(-0.500646\pi\)
−0.00203090 + 0.999998i \(0.500646\pi\)
\(620\) −6.92128e17 −0.489374
\(621\) 4.72421e17 0.330547
\(622\) −2.05634e18 −1.42383
\(623\) 1.81290e18 1.24223
\(624\) −5.81102e16 −0.0394051
\(625\) −1.70679e18 −1.14541
\(626\) 1.59028e18 1.05619
\(627\) 7.61325e17 0.500416
\(628\) −5.31549e17 −0.345784
\(629\) −1.51594e18 −0.976007
\(630\) 5.45156e17 0.347382
\(631\) −1.13226e18 −0.714097 −0.357048 0.934086i \(-0.616217\pi\)
−0.357048 + 0.934086i \(0.616217\pi\)
\(632\) 7.97627e17 0.497896
\(633\) −1.08021e18 −0.667398
\(634\) −1.64556e18 −1.00631
\(635\) −7.52728e17 −0.455626
\(636\) 2.64578e17 0.158519
\(637\) −8.95462e16 −0.0531057
\(638\) 2.60113e18 1.52696
\(639\) 7.91146e17 0.459728
\(640\) 3.79632e17 0.218370
\(641\) −1.59725e18 −0.909483 −0.454742 0.890623i \(-0.650268\pi\)
−0.454742 + 0.890623i \(0.650268\pi\)
\(642\) −6.16088e17 −0.347268
\(643\) −2.33433e18 −1.30254 −0.651269 0.758847i \(-0.725763\pi\)
−0.651269 + 0.758847i \(0.725763\pi\)
\(644\) 1.28392e18 0.709219
\(645\) −6.25819e17 −0.342224
\(646\) −6.18968e17 −0.335086
\(647\) 2.15674e18 1.15590 0.577949 0.816073i \(-0.303853\pi\)
0.577949 + 0.816073i \(0.303853\pi\)
\(648\) 2.27938e17 0.120943
\(649\) 3.32698e17 0.174767
\(650\) 3.51825e16 0.0182974
\(651\) 1.73243e18 0.892030
\(652\) 1.00796e18 0.513846
\(653\) −2.51576e18 −1.26979 −0.634897 0.772597i \(-0.718958\pi\)
−0.634897 + 0.772597i \(0.718958\pi\)
\(654\) 7.56354e17 0.377981
\(655\) 7.72875e16 0.0382420
\(656\) −1.00298e18 −0.491380
\(657\) −7.62103e17 −0.369691
\(658\) −1.81974e18 −0.874061
\(659\) −3.59012e18 −1.70747 −0.853737 0.520704i \(-0.825670\pi\)
−0.853737 + 0.520704i \(0.825670\pi\)
\(660\) 6.19868e17 0.291920
\(661\) −1.54091e18 −0.718569 −0.359285 0.933228i \(-0.616979\pi\)
−0.359285 + 0.933228i \(0.616979\pi\)
\(662\) −8.18915e17 −0.378148
\(663\) 1.04015e17 0.0475619
\(664\) 6.14665e17 0.278321
\(665\) −1.85737e18 −0.832832
\(666\) 9.21552e17 0.409202
\(667\) −5.49918e18 −2.41813
\(668\) 9.48246e17 0.412928
\(669\) −1.66004e18 −0.715895
\(670\) −2.53792e18 −1.08391
\(671\) −5.57205e18 −2.35678
\(672\) 1.07929e18 0.452104
\(673\) −4.27821e18 −1.77486 −0.887431 0.460940i \(-0.847512\pi\)
−0.887431 + 0.460940i \(0.847512\pi\)
\(674\) 3.52998e17 0.145038
\(675\) −8.35137e16 −0.0339847
\(676\) 8.47378e17 0.341526
\(677\) −2.37034e18 −0.946201 −0.473100 0.881008i \(-0.656865\pi\)
−0.473100 + 0.881008i \(0.656865\pi\)
\(678\) −2.15402e17 −0.0851642
\(679\) 4.24088e18 1.66074
\(680\) −1.95530e18 −0.758414
\(681\) 6.13998e17 0.235890
\(682\) −3.70308e18 −1.40917
\(683\) −4.83798e18 −1.82360 −0.911800 0.410634i \(-0.865307\pi\)
−0.911800 + 0.410634i \(0.865307\pi\)
\(684\) −2.00160e17 −0.0747329
\(685\) −5.39949e18 −1.99694
\(686\) 1.53658e18 0.562921
\(687\) 1.51797e18 0.550864
\(688\) 8.09001e17 0.290820
\(689\) −2.84767e17 −0.101406
\(690\) 2.46357e18 0.869051
\(691\) −7.71829e17 −0.269720 −0.134860 0.990865i \(-0.543059\pi\)
−0.134860 + 0.990865i \(0.543059\pi\)
\(692\) −9.58589e17 −0.331851
\(693\) −1.55156e18 −0.532111
\(694\) −3.51540e18 −1.19437
\(695\) 5.41414e18 1.82233
\(696\) −2.65330e18 −0.884760
\(697\) 1.79530e18 0.593094
\(698\) −1.70401e18 −0.557713
\(699\) 3.12183e18 1.01230
\(700\) −2.26969e17 −0.0729172
\(701\) −3.65953e18 −1.16482 −0.582410 0.812895i \(-0.697890\pi\)
−0.582410 + 0.812895i \(0.697890\pi\)
\(702\) −6.32316e16 −0.0199408
\(703\) −3.13976e18 −0.981042
\(704\) −4.61466e18 −1.42862
\(705\) 1.85741e18 0.569741
\(706\) 1.96397e18 0.596904
\(707\) 5.82190e18 1.75323
\(708\) −8.74693e16 −0.0260999
\(709\) 7.72559e17 0.228418 0.114209 0.993457i \(-0.463567\pi\)
0.114209 + 0.993457i \(0.463567\pi\)
\(710\) 4.12565e18 1.20868
\(711\) 5.25229e17 0.152474
\(712\) 3.95279e18 1.13706
\(713\) 7.82887e18 2.23161
\(714\) 1.26144e18 0.356310
\(715\) −6.67167e17 −0.186743
\(716\) 1.37695e18 0.381930
\(717\) −2.55489e17 −0.0702260
\(718\) 4.63160e18 1.26160
\(719\) 1.20782e18 0.326034 0.163017 0.986623i \(-0.447877\pi\)
0.163017 + 0.986623i \(0.447877\pi\)
\(720\) 7.19314e17 0.192423
\(721\) −3.47251e18 −0.920586
\(722\) 1.79319e18 0.471123
\(723\) 7.49966e17 0.195273
\(724\) −1.75127e18 −0.451911
\(725\) 9.72135e17 0.248616
\(726\) 1.47610e18 0.374133
\(727\) 1.12668e17 0.0283025 0.0141513 0.999900i \(-0.495495\pi\)
0.0141513 + 0.999900i \(0.495495\pi\)
\(728\) −6.66748e17 −0.166000
\(729\) 1.50095e17 0.0370370
\(730\) −3.97419e18 −0.971964
\(731\) −1.44808e18 −0.351019
\(732\) 1.46495e18 0.351965
\(733\) 1.73665e18 0.413558 0.206779 0.978388i \(-0.433702\pi\)
0.206779 + 0.978388i \(0.433702\pi\)
\(734\) 2.83698e18 0.669626
\(735\) 1.10844e18 0.259326
\(736\) 4.87733e18 1.13104
\(737\) 7.22314e18 1.66030
\(738\) −1.09138e18 −0.248661
\(739\) −2.36418e18 −0.533938 −0.266969 0.963705i \(-0.586022\pi\)
−0.266969 + 0.963705i \(0.586022\pi\)
\(740\) −2.55638e18 −0.572295
\(741\) 2.15433e17 0.0478072
\(742\) −3.45349e18 −0.759684
\(743\) 1.01901e18 0.222204 0.111102 0.993809i \(-0.464562\pi\)
0.111102 + 0.993809i \(0.464562\pi\)
\(744\) 3.77735e18 0.816513
\(745\) −3.54869e18 −0.760418
\(746\) 2.27020e18 0.482238
\(747\) 4.04750e17 0.0852320
\(748\) 1.43431e18 0.299422
\(749\) −4.27778e18 −0.885292
\(750\) 2.03069e18 0.416626
\(751\) 6.47444e18 1.31687 0.658435 0.752638i \(-0.271219\pi\)
0.658435 + 0.752638i \(0.271219\pi\)
\(752\) −2.40109e18 −0.484163
\(753\) −4.45761e18 −0.891118
\(754\) 7.36043e17 0.145878
\(755\) 5.49639e18 1.08000
\(756\) 4.07919e17 0.0794663
\(757\) 7.01680e17 0.135524 0.0677620 0.997702i \(-0.478414\pi\)
0.0677620 + 0.997702i \(0.478414\pi\)
\(758\) 3.01001e18 0.576392
\(759\) −7.01151e18 −1.33119
\(760\) −4.04976e18 −0.762326
\(761\) −2.94718e18 −0.550055 −0.275028 0.961436i \(-0.588687\pi\)
−0.275028 + 0.961436i \(0.588687\pi\)
\(762\) 1.05882e18 0.195936
\(763\) 5.25171e18 0.963587
\(764\) 3.64993e18 0.664014
\(765\) −1.28755e18 −0.232254
\(766\) 4.21053e17 0.0753095
\(767\) 9.41437e16 0.0166963
\(768\) 2.95997e18 0.520522
\(769\) 1.14106e17 0.0198970 0.00994848 0.999951i \(-0.496833\pi\)
0.00994848 + 0.999951i \(0.496833\pi\)
\(770\) −8.09102e18 −1.39899
\(771\) 2.66805e17 0.0457446
\(772\) −1.13848e18 −0.193560
\(773\) −3.74426e18 −0.631247 −0.315624 0.948884i \(-0.602214\pi\)
−0.315624 + 0.948884i \(0.602214\pi\)
\(774\) 8.80301e17 0.147169
\(775\) −1.38397e18 −0.229439
\(776\) 9.24670e18 1.52015
\(777\) 6.39875e18 1.04318
\(778\) 3.62294e18 0.585725
\(779\) 3.71836e18 0.596153
\(780\) 1.75404e17 0.0278885
\(781\) −1.17419e19 −1.85143
\(782\) 5.70045e18 0.891385
\(783\) −1.74717e18 −0.270946
\(784\) −1.43289e18 −0.220374
\(785\) −7.08181e18 −1.08017
\(786\) −1.08716e17 −0.0164454
\(787\) −6.36658e18 −0.955147 −0.477574 0.878592i \(-0.658484\pi\)
−0.477574 + 0.878592i \(0.658484\pi\)
\(788\) −2.20947e18 −0.328751
\(789\) 7.58346e18 1.11909
\(790\) 2.73895e18 0.400874
\(791\) −1.49563e18 −0.217109
\(792\) −3.38298e18 −0.487064
\(793\) −1.57673e18 −0.225155
\(794\) −7.84565e18 −1.11121
\(795\) 3.52497e18 0.495186
\(796\) −3.26563e18 −0.455022
\(797\) −3.45409e18 −0.477369 −0.238685 0.971097i \(-0.576716\pi\)
−0.238685 + 0.971097i \(0.576716\pi\)
\(798\) 2.61265e18 0.358148
\(799\) 4.29786e18 0.584383
\(800\) −8.62206e17 −0.116286
\(801\) 2.60287e18 0.348210
\(802\) −4.40512e18 −0.584553
\(803\) 1.13109e19 1.48883
\(804\) −1.89903e18 −0.247952
\(805\) 1.71057e19 2.21547
\(806\) −1.04786e18 −0.134625
\(807\) 5.74400e17 0.0732042
\(808\) 1.26939e19 1.60480
\(809\) 4.79330e18 0.601131 0.300565 0.953761i \(-0.402825\pi\)
0.300565 + 0.953761i \(0.402825\pi\)
\(810\) 7.82709e17 0.0973750
\(811\) −5.15289e17 −0.0635938 −0.0317969 0.999494i \(-0.510123\pi\)
−0.0317969 + 0.999494i \(0.510123\pi\)
\(812\) −4.74836e18 −0.581338
\(813\) −6.00889e18 −0.729803
\(814\) −1.36774e19 −1.64795
\(815\) 1.34290e19 1.60516
\(816\) 1.66442e18 0.197368
\(817\) −2.99922e18 −0.352830
\(818\) −1.10953e18 −0.129492
\(819\) −4.39046e17 −0.0508352
\(820\) 3.02747e18 0.347768
\(821\) −1.24790e19 −1.42217 −0.711083 0.703108i \(-0.751795\pi\)
−0.711083 + 0.703108i \(0.751795\pi\)
\(822\) 7.59514e18 0.858754
\(823\) 2.93432e18 0.329161 0.164580 0.986364i \(-0.447373\pi\)
0.164580 + 0.986364i \(0.447373\pi\)
\(824\) −7.57138e18 −0.842651
\(825\) 1.23948e18 0.136864
\(826\) 1.14172e18 0.125081
\(827\) −2.37820e18 −0.258501 −0.129251 0.991612i \(-0.541257\pi\)
−0.129251 + 0.991612i \(0.541257\pi\)
\(828\) 1.84339e18 0.198802
\(829\) 1.36509e19 1.46069 0.730345 0.683078i \(-0.239359\pi\)
0.730345 + 0.683078i \(0.239359\pi\)
\(830\) 2.11068e18 0.224086
\(831\) −8.81527e18 −0.928600
\(832\) −1.30581e18 −0.136483
\(833\) 2.56483e18 0.265990
\(834\) −7.61574e18 −0.783669
\(835\) 1.26335e19 1.28991
\(836\) 2.97070e18 0.300966
\(837\) 2.48734e18 0.250046
\(838\) −4.75836e18 −0.474648
\(839\) −1.24402e19 −1.23133 −0.615666 0.788007i \(-0.711113\pi\)
−0.615666 + 0.788007i \(0.711113\pi\)
\(840\) 8.25329e18 0.810610
\(841\) 1.00771e19 0.982115
\(842\) −3.60278e18 −0.348425
\(843\) 4.45512e18 0.427543
\(844\) −4.21500e18 −0.401395
\(845\) 1.12896e19 1.06687
\(846\) −2.61270e18 −0.245009
\(847\) 1.02492e19 0.953779
\(848\) −4.55675e18 −0.420807
\(849\) 6.14683e18 0.563315
\(850\) −1.00772e18 −0.0916463
\(851\) 2.89160e19 2.60974
\(852\) 3.08706e18 0.276496
\(853\) 1.46204e19 1.29955 0.649773 0.760128i \(-0.274864\pi\)
0.649773 + 0.760128i \(0.274864\pi\)
\(854\) −1.91217e19 −1.68675
\(855\) −2.66672e18 −0.233452
\(856\) −9.32716e18 −0.810345
\(857\) −2.56019e18 −0.220748 −0.110374 0.993890i \(-0.535205\pi\)
−0.110374 + 0.993890i \(0.535205\pi\)
\(858\) 9.38463e17 0.0803063
\(859\) −2.08392e19 −1.76981 −0.884904 0.465773i \(-0.845776\pi\)
−0.884904 + 0.465773i \(0.845776\pi\)
\(860\) −2.44195e18 −0.205825
\(861\) −7.57791e18 −0.633912
\(862\) −4.26013e18 −0.353693
\(863\) 1.35776e17 0.0111880 0.00559401 0.999984i \(-0.498219\pi\)
0.00559401 + 0.999984i \(0.498219\pi\)
\(864\) 1.54960e18 0.126730
\(865\) −1.27713e19 −1.03664
\(866\) 3.92149e18 0.315925
\(867\) 4.24118e18 0.339127
\(868\) 6.75997e18 0.536496
\(869\) −7.79527e18 −0.614048
\(870\) −9.11107e18 −0.712351
\(871\) 2.04394e18 0.158617
\(872\) 1.14507e19 0.882012
\(873\) 6.08885e18 0.465525
\(874\) 1.18066e19 0.895983
\(875\) 1.41000e19 1.06210
\(876\) −2.97374e18 −0.222344
\(877\) −1.38538e19 −1.02819 −0.514094 0.857734i \(-0.671872\pi\)
−0.514094 + 0.857734i \(0.671872\pi\)
\(878\) 1.51777e19 1.11813
\(879\) 7.95164e18 0.581472
\(880\) −1.06758e19 −0.774932
\(881\) 2.39062e19 1.72253 0.861266 0.508154i \(-0.169672\pi\)
0.861266 + 0.508154i \(0.169672\pi\)
\(882\) −1.55918e18 −0.111519
\(883\) −1.46923e19 −1.04314 −0.521572 0.853207i \(-0.674654\pi\)
−0.521572 + 0.853207i \(0.674654\pi\)
\(884\) 4.05869e17 0.0286053
\(885\) −1.16535e18 −0.0815316
\(886\) 5.38790e17 0.0374197
\(887\) −1.54616e19 −1.06598 −0.532992 0.846120i \(-0.678932\pi\)
−0.532992 + 0.846120i \(0.678932\pi\)
\(888\) 1.39517e19 0.954865
\(889\) 7.35184e18 0.499499
\(890\) 1.35734e19 0.915488
\(891\) −2.22765e18 −0.149157
\(892\) −6.47750e18 −0.430562
\(893\) 8.90157e18 0.587398
\(894\) 4.99173e18 0.327007
\(895\) 1.83451e19 1.19308
\(896\) −3.70784e18 −0.239397
\(897\) −1.98405e18 −0.127175
\(898\) −1.13267e19 −0.720787
\(899\) −2.89537e19 −1.82922
\(900\) −3.25872e17 −0.0204395
\(901\) 8.15643e18 0.507912
\(902\) 1.61978e19 1.00142
\(903\) 6.11233e18 0.375177
\(904\) −3.26104e18 −0.198729
\(905\) −2.33322e19 −1.41169
\(906\) −7.73143e18 −0.464437
\(907\) 5.27965e17 0.0314889 0.0157445 0.999876i \(-0.494988\pi\)
0.0157445 + 0.999876i \(0.494988\pi\)
\(908\) 2.39583e18 0.141872
\(909\) 8.35880e18 0.491449
\(910\) −2.28952e18 −0.133652
\(911\) −1.52230e19 −0.882328 −0.441164 0.897427i \(-0.645434\pi\)
−0.441164 + 0.897427i \(0.645434\pi\)
\(912\) 3.44729e18 0.198386
\(913\) −6.00716e18 −0.343249
\(914\) 1.89426e19 1.07470
\(915\) 1.95174e19 1.09948
\(916\) 5.92313e18 0.331307
\(917\) −7.54862e17 −0.0419244
\(918\) 1.81111e18 0.0998776
\(919\) −3.07666e19 −1.68472 −0.842361 0.538914i \(-0.818835\pi\)
−0.842361 + 0.538914i \(0.818835\pi\)
\(920\) 3.72967e19 2.02792
\(921\) 3.96638e17 0.0214144
\(922\) −9.15067e18 −0.490571
\(923\) −3.32262e18 −0.176876
\(924\) −6.05420e18 −0.320029
\(925\) −5.11172e18 −0.268316
\(926\) 4.85468e18 0.253040
\(927\) −4.98567e18 −0.258051
\(928\) −1.80380e19 −0.927097
\(929\) 2.97721e19 1.51952 0.759762 0.650201i \(-0.225315\pi\)
0.759762 + 0.650201i \(0.225315\pi\)
\(930\) 1.29709e19 0.657403
\(931\) 5.31218e18 0.267362
\(932\) 1.21814e19 0.608828
\(933\) −2.04998e19 −1.01746
\(934\) −1.02926e19 −0.507304
\(935\) 1.91093e19 0.935341
\(936\) −9.57284e17 −0.0465316
\(937\) 1.13196e19 0.546416 0.273208 0.961955i \(-0.411915\pi\)
0.273208 + 0.961955i \(0.411915\pi\)
\(938\) 2.47877e19 1.18828
\(939\) 1.58536e19 0.754748
\(940\) 7.24762e18 0.342661
\(941\) −1.83852e19 −0.863246 −0.431623 0.902054i \(-0.642059\pi\)
−0.431623 + 0.902054i \(0.642059\pi\)
\(942\) 9.96155e18 0.464511
\(943\) −3.42447e19 −1.58587
\(944\) 1.50646e18 0.0692851
\(945\) 5.43470e18 0.248238
\(946\) −1.30651e19 −0.592682
\(947\) 9.10215e17 0.0410080 0.0205040 0.999790i \(-0.493473\pi\)
0.0205040 + 0.999790i \(0.493473\pi\)
\(948\) 2.04945e18 0.0917029
\(949\) 3.20065e18 0.142235
\(950\) −2.08715e18 −0.0921190
\(951\) −1.64047e19 −0.719109
\(952\) 1.90973e19 0.831443
\(953\) −3.11203e19 −1.34567 −0.672836 0.739791i \(-0.734924\pi\)
−0.672836 + 0.739791i \(0.734924\pi\)
\(954\) −4.95835e18 −0.212948
\(955\) 4.86279e19 2.07426
\(956\) −9.96923e17 −0.0422362
\(957\) 2.59308e19 1.09116
\(958\) 1.77520e19 0.741946
\(959\) 5.27365e19 2.18922
\(960\) 1.61639e19 0.666475
\(961\) 1.68022e19 0.688121
\(962\) −3.87029e18 −0.157437
\(963\) −6.14183e18 −0.248157
\(964\) 2.92638e18 0.117444
\(965\) −1.51680e19 −0.604645
\(966\) −2.40615e19 −0.952732
\(967\) −4.19261e19 −1.64897 −0.824484 0.565885i \(-0.808535\pi\)
−0.824484 + 0.565885i \(0.808535\pi\)
\(968\) 2.23471e19 0.873034
\(969\) −6.17053e18 −0.239452
\(970\) 3.17520e19 1.22392
\(971\) 2.85140e19 1.09178 0.545888 0.837858i \(-0.316193\pi\)
0.545888 + 0.837858i \(0.316193\pi\)
\(972\) 5.85671e17 0.0222753
\(973\) −5.28795e19 −1.99781
\(974\) 1.82629e19 0.685389
\(975\) 3.50737e17 0.0130753
\(976\) −2.52304e19 −0.934329
\(977\) −3.32048e19 −1.22148 −0.610740 0.791831i \(-0.709128\pi\)
−0.610740 + 0.791831i \(0.709128\pi\)
\(978\) −1.88898e19 −0.690278
\(979\) −3.86309e19 −1.40232
\(980\) 4.32516e18 0.155967
\(981\) 7.54015e18 0.270104
\(982\) −3.98552e19 −1.41827
\(983\) −1.48141e19 −0.523695 −0.261848 0.965109i \(-0.584332\pi\)
−0.261848 + 0.965109i \(0.584332\pi\)
\(984\) −1.65227e19 −0.580247
\(985\) −2.94367e19 −1.02696
\(986\) −2.10821e19 −0.730658
\(987\) −1.81412e19 −0.624602
\(988\) 8.40621e17 0.0287528
\(989\) 2.76217e19 0.938586
\(990\) −1.16167e19 −0.392152
\(991\) −2.81327e19 −0.943479 −0.471739 0.881738i \(-0.656374\pi\)
−0.471739 + 0.881738i \(0.656374\pi\)
\(992\) 2.56796e19 0.855584
\(993\) −8.16382e18 −0.270224
\(994\) −4.02949e19 −1.32507
\(995\) −4.35079e19 −1.42141
\(996\) 1.57934e18 0.0512613
\(997\) 2.19082e19 0.706461 0.353230 0.935536i \(-0.385083\pi\)
0.353230 + 0.935536i \(0.385083\pi\)
\(998\) −1.91779e19 −0.614401
\(999\) 9.18702e18 0.292415
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 177.14.a.b.1.10 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.10 31 1.1 even 1 trivial