Properties

Label 177.14.a.b.1.5
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 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-149.360 q^{2} -729.000 q^{3} +14116.3 q^{4} -48711.9 q^{5} +108883. q^{6} -300158. q^{7} -884852. q^{8} +531441. q^{9} +O(q^{10})\) \(q-149.360 q^{2} -729.000 q^{3} +14116.3 q^{4} -48711.9 q^{5} +108883. q^{6} -300158. q^{7} -884852. q^{8} +531441. q^{9} +7.27559e6 q^{10} +2.91688e6 q^{11} -1.02908e7 q^{12} +4.39145e6 q^{13} +4.48315e7 q^{14} +3.55110e7 q^{15} +1.65205e7 q^{16} -6.68228e7 q^{17} -7.93758e7 q^{18} -3.05356e8 q^{19} -6.87632e8 q^{20} +2.18815e8 q^{21} -4.35664e8 q^{22} -4.79121e8 q^{23} +6.45057e8 q^{24} +1.15215e9 q^{25} -6.55906e8 q^{26} -3.87420e8 q^{27} -4.23712e9 q^{28} +1.34762e9 q^{29} -5.30391e9 q^{30} +8.39044e9 q^{31} +4.78122e9 q^{32} -2.12641e9 q^{33} +9.98063e9 q^{34} +1.46213e10 q^{35} +7.50198e9 q^{36} -2.42362e10 q^{37} +4.56079e10 q^{38} -3.20137e9 q^{39} +4.31028e10 q^{40} -2.76354e10 q^{41} -3.26821e10 q^{42} -7.37570e10 q^{43} +4.11756e10 q^{44} -2.58875e10 q^{45} +7.15614e10 q^{46} -5.77097e10 q^{47} -1.20434e10 q^{48} -6.79429e9 q^{49} -1.72084e11 q^{50} +4.87138e10 q^{51} +6.19911e10 q^{52} +1.52339e11 q^{53} +5.78650e10 q^{54} -1.42087e11 q^{55} +2.65595e11 q^{56} +2.22605e11 q^{57} -2.01281e11 q^{58} -4.21805e10 q^{59} +5.01284e11 q^{60} +6.51411e11 q^{61} -1.25319e12 q^{62} -1.59516e11 q^{63} -8.49457e11 q^{64} -2.13916e11 q^{65} +3.17599e11 q^{66} -1.13534e12 q^{67} -9.43291e11 q^{68} +3.49279e11 q^{69} -2.18383e12 q^{70} -9.22926e10 q^{71} -4.70247e11 q^{72} +2.04726e12 q^{73} +3.61991e12 q^{74} -8.39915e11 q^{75} -4.31050e12 q^{76} -8.75525e11 q^{77} +4.78155e11 q^{78} +1.06213e12 q^{79} -8.04744e11 q^{80} +2.82430e11 q^{81} +4.12761e12 q^{82} +1.85336e12 q^{83} +3.08886e12 q^{84} +3.25506e12 q^{85} +1.10163e13 q^{86} -9.82418e11 q^{87} -2.58101e12 q^{88} +2.98879e12 q^{89} +3.86655e12 q^{90} -1.31813e12 q^{91} -6.76342e12 q^{92} -6.11663e12 q^{93} +8.61950e12 q^{94} +1.48745e13 q^{95} -3.48551e12 q^{96} -1.02877e13 q^{97} +1.01479e12 q^{98} +1.55015e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −149.360 −1.65021 −0.825103 0.564982i \(-0.808883\pi\)
−0.825103 + 0.564982i \(0.808883\pi\)
\(3\) −729.000 −0.577350
\(4\) 14116.3 1.72318
\(5\) −48711.9 −1.39422 −0.697108 0.716966i \(-0.745530\pi\)
−0.697108 + 0.716966i \(0.745530\pi\)
\(6\) 108883. 0.952747
\(7\) −300158. −0.964301 −0.482150 0.876089i \(-0.660144\pi\)
−0.482150 + 0.876089i \(0.660144\pi\)
\(8\) −884852. −1.19340
\(9\) 531441. 0.333333
\(10\) 7.27559e6 2.30074
\(11\) 2.91688e6 0.496440 0.248220 0.968704i \(-0.420154\pi\)
0.248220 + 0.968704i \(0.420154\pi\)
\(12\) −1.02908e7 −0.994880
\(13\) 4.39145e6 0.252334 0.126167 0.992009i \(-0.459732\pi\)
0.126167 + 0.992009i \(0.459732\pi\)
\(14\) 4.48315e7 1.59130
\(15\) 3.55110e7 0.804951
\(16\) 1.65205e7 0.246174
\(17\) −6.68228e7 −0.671439 −0.335719 0.941962i \(-0.608979\pi\)
−0.335719 + 0.941962i \(0.608979\pi\)
\(18\) −7.93758e7 −0.550069
\(19\) −3.05356e8 −1.48905 −0.744524 0.667596i \(-0.767323\pi\)
−0.744524 + 0.667596i \(0.767323\pi\)
\(20\) −6.87632e8 −2.40249
\(21\) 2.18815e8 0.556739
\(22\) −4.35664e8 −0.819228
\(23\) −4.79121e8 −0.674861 −0.337431 0.941350i \(-0.609558\pi\)
−0.337431 + 0.941350i \(0.609558\pi\)
\(24\) 6.45057e8 0.689010
\(25\) 1.15215e9 0.943838
\(26\) −6.55906e8 −0.416404
\(27\) −3.87420e8 −0.192450
\(28\) −4.23712e9 −1.66167
\(29\) 1.34762e9 0.420709 0.210354 0.977625i \(-0.432538\pi\)
0.210354 + 0.977625i \(0.432538\pi\)
\(30\) −5.30391e9 −1.32834
\(31\) 8.39044e9 1.69799 0.848993 0.528405i \(-0.177210\pi\)
0.848993 + 0.528405i \(0.177210\pi\)
\(32\) 4.78122e9 0.787161
\(33\) −2.12641e9 −0.286620
\(34\) 9.98063e9 1.10801
\(35\) 1.46213e10 1.34444
\(36\) 7.50198e9 0.574394
\(37\) −2.42362e10 −1.55293 −0.776467 0.630158i \(-0.782990\pi\)
−0.776467 + 0.630158i \(0.782990\pi\)
\(38\) 4.56079e10 2.45724
\(39\) −3.20137e9 −0.145685
\(40\) 4.31028e10 1.66386
\(41\) −2.76354e10 −0.908594 −0.454297 0.890850i \(-0.650110\pi\)
−0.454297 + 0.890850i \(0.650110\pi\)
\(42\) −3.26821e10 −0.918735
\(43\) −7.37570e10 −1.77934 −0.889668 0.456608i \(-0.849064\pi\)
−0.889668 + 0.456608i \(0.849064\pi\)
\(44\) 4.11756e10 0.855456
\(45\) −2.58875e10 −0.464739
\(46\) 7.15614e10 1.11366
\(47\) −5.77097e10 −0.780931 −0.390465 0.920618i \(-0.627686\pi\)
−0.390465 + 0.920618i \(0.627686\pi\)
\(48\) −1.20434e10 −0.142129
\(49\) −6.79429e9 −0.0701245
\(50\) −1.72084e11 −1.55753
\(51\) 4.87138e10 0.387655
\(52\) 6.19911e10 0.434818
\(53\) 1.52339e11 0.944101 0.472051 0.881571i \(-0.343514\pi\)
0.472051 + 0.881571i \(0.343514\pi\)
\(54\) 5.78650e10 0.317582
\(55\) −1.42087e11 −0.692144
\(56\) 2.65595e11 1.15080
\(57\) 2.22605e11 0.859702
\(58\) −2.01281e11 −0.694256
\(59\) −4.21805e10 −0.130189
\(60\) 5.01284e11 1.38708
\(61\) 6.51411e11 1.61887 0.809433 0.587212i \(-0.199774\pi\)
0.809433 + 0.587212i \(0.199774\pi\)
\(62\) −1.25319e12 −2.80203
\(63\) −1.59516e11 −0.321434
\(64\) −8.49457e11 −1.54515
\(65\) −2.13916e11 −0.351809
\(66\) 3.17599e11 0.472981
\(67\) −1.13534e12 −1.53334 −0.766672 0.642039i \(-0.778089\pi\)
−0.766672 + 0.642039i \(0.778089\pi\)
\(68\) −9.43291e11 −1.15701
\(69\) 3.49279e11 0.389631
\(70\) −2.18383e12 −2.21861
\(71\) −9.22926e10 −0.0855042 −0.0427521 0.999086i \(-0.513613\pi\)
−0.0427521 + 0.999086i \(0.513613\pi\)
\(72\) −4.70247e11 −0.397800
\(73\) 2.04726e12 1.58334 0.791672 0.610946i \(-0.209211\pi\)
0.791672 + 0.610946i \(0.209211\pi\)
\(74\) 3.61991e12 2.56266
\(75\) −8.39915e11 −0.544925
\(76\) −4.31050e12 −2.56590
\(77\) −8.75525e11 −0.478717
\(78\) 4.78155e11 0.240411
\(79\) 1.06213e12 0.491590 0.245795 0.969322i \(-0.420951\pi\)
0.245795 + 0.969322i \(0.420951\pi\)
\(80\) −8.04744e11 −0.343220
\(81\) 2.82430e11 0.111111
\(82\) 4.12761e12 1.49937
\(83\) 1.85336e12 0.622232 0.311116 0.950372i \(-0.399297\pi\)
0.311116 + 0.950372i \(0.399297\pi\)
\(84\) 3.08886e12 0.959363
\(85\) 3.25506e12 0.936131
\(86\) 1.10163e13 2.93627
\(87\) −9.82418e11 −0.242896
\(88\) −2.58101e12 −0.592451
\(89\) 2.98879e12 0.637471 0.318736 0.947844i \(-0.396742\pi\)
0.318736 + 0.947844i \(0.396742\pi\)
\(90\) 3.86655e12 0.766915
\(91\) −1.31813e12 −0.243326
\(92\) −6.76342e12 −1.16291
\(93\) −6.11663e12 −0.980332
\(94\) 8.61950e12 1.28870
\(95\) 1.48745e13 2.07605
\(96\) −3.48551e12 −0.454468
\(97\) −1.02877e13 −1.25401 −0.627006 0.779015i \(-0.715720\pi\)
−0.627006 + 0.779015i \(0.715720\pi\)
\(98\) 1.01479e12 0.115720
\(99\) 1.55015e12 0.165480
\(100\) 1.62641e13 1.62641
\(101\) 1.89626e13 1.77750 0.888748 0.458396i \(-0.151576\pi\)
0.888748 + 0.458396i \(0.151576\pi\)
\(102\) −7.27588e12 −0.639712
\(103\) −6.09533e12 −0.502986 −0.251493 0.967859i \(-0.580921\pi\)
−0.251493 + 0.967859i \(0.580921\pi\)
\(104\) −3.88579e12 −0.301136
\(105\) −1.06589e13 −0.776215
\(106\) −2.27533e13 −1.55796
\(107\) 2.28388e13 1.47123 0.735613 0.677402i \(-0.236894\pi\)
0.735613 + 0.677402i \(0.236894\pi\)
\(108\) −5.46895e12 −0.331627
\(109\) −7.12166e12 −0.406733 −0.203366 0.979103i \(-0.565188\pi\)
−0.203366 + 0.979103i \(0.565188\pi\)
\(110\) 2.12220e13 1.14218
\(111\) 1.76682e13 0.896587
\(112\) −4.95875e12 −0.237386
\(113\) 5.34147e11 0.0241352 0.0120676 0.999927i \(-0.496159\pi\)
0.0120676 + 0.999927i \(0.496159\pi\)
\(114\) −3.32482e13 −1.41869
\(115\) 2.33389e13 0.940902
\(116\) 1.90235e13 0.724958
\(117\) 2.33380e12 0.0841114
\(118\) 6.30007e12 0.214839
\(119\) 2.00574e13 0.647469
\(120\) −3.14220e13 −0.960628
\(121\) −2.60145e13 −0.753548
\(122\) −9.72945e13 −2.67146
\(123\) 2.01462e13 0.524577
\(124\) 1.18442e14 2.92594
\(125\) 3.33952e12 0.0783014
\(126\) 2.38253e13 0.530432
\(127\) 7.02815e13 1.48633 0.743167 0.669106i \(-0.233323\pi\)
0.743167 + 0.669106i \(0.233323\pi\)
\(128\) 8.77069e13 1.76266
\(129\) 5.37688e13 1.02730
\(130\) 3.19504e13 0.580557
\(131\) 2.04972e13 0.354350 0.177175 0.984179i \(-0.443304\pi\)
0.177175 + 0.984179i \(0.443304\pi\)
\(132\) −3.00170e13 −0.493898
\(133\) 9.16551e13 1.43589
\(134\) 1.69574e14 2.53033
\(135\) 1.88720e13 0.268317
\(136\) 5.91283e13 0.801295
\(137\) 4.51513e13 0.583428 0.291714 0.956506i \(-0.405775\pi\)
0.291714 + 0.956506i \(0.405775\pi\)
\(138\) −5.21682e13 −0.642972
\(139\) −8.65933e12 −0.101833 −0.0509165 0.998703i \(-0.516214\pi\)
−0.0509165 + 0.998703i \(0.516214\pi\)
\(140\) 2.06398e14 2.31672
\(141\) 4.20703e13 0.450871
\(142\) 1.37848e13 0.141100
\(143\) 1.28093e13 0.125269
\(144\) 8.77966e12 0.0820581
\(145\) −6.56453e13 −0.586559
\(146\) −3.05779e14 −2.61284
\(147\) 4.95304e12 0.0404864
\(148\) −3.42125e14 −2.67599
\(149\) 1.90864e14 1.42893 0.714467 0.699669i \(-0.246669\pi\)
0.714467 + 0.699669i \(0.246669\pi\)
\(150\) 1.25449e14 0.899239
\(151\) 2.80301e14 1.92431 0.962154 0.272507i \(-0.0878527\pi\)
0.962154 + 0.272507i \(0.0878527\pi\)
\(152\) 2.70195e14 1.77703
\(153\) −3.55124e13 −0.223813
\(154\) 1.30768e14 0.789982
\(155\) −4.08715e14 −2.36736
\(156\) −4.51915e13 −0.251042
\(157\) −2.96112e14 −1.57800 −0.789002 0.614391i \(-0.789402\pi\)
−0.789002 + 0.614391i \(0.789402\pi\)
\(158\) −1.58640e14 −0.811225
\(159\) −1.11055e14 −0.545077
\(160\) −2.32902e14 −1.09747
\(161\) 1.43812e14 0.650769
\(162\) −4.21836e13 −0.183356
\(163\) 2.75231e14 1.14942 0.574710 0.818357i \(-0.305115\pi\)
0.574710 + 0.818357i \(0.305115\pi\)
\(164\) −3.90109e14 −1.56567
\(165\) 1.03581e14 0.399610
\(166\) −2.76817e14 −1.02681
\(167\) 2.97487e14 1.06123 0.530617 0.847611i \(-0.321960\pi\)
0.530617 + 0.847611i \(0.321960\pi\)
\(168\) −1.93619e14 −0.664412
\(169\) −2.83590e14 −0.936327
\(170\) −4.86175e14 −1.54481
\(171\) −1.62279e14 −0.496349
\(172\) −1.04118e15 −3.06612
\(173\) 2.89857e14 0.822025 0.411012 0.911630i \(-0.365175\pi\)
0.411012 + 0.911630i \(0.365175\pi\)
\(174\) 1.46734e14 0.400829
\(175\) −3.45826e14 −0.910144
\(176\) 4.81883e13 0.122211
\(177\) 3.07496e13 0.0751646
\(178\) −4.46405e14 −1.05196
\(179\) −1.26450e14 −0.287327 −0.143663 0.989627i \(-0.545888\pi\)
−0.143663 + 0.989627i \(0.545888\pi\)
\(180\) −3.65436e14 −0.800829
\(181\) 1.48782e13 0.0314513 0.0157257 0.999876i \(-0.494994\pi\)
0.0157257 + 0.999876i \(0.494994\pi\)
\(182\) 1.96875e14 0.401538
\(183\) −4.74879e14 −0.934653
\(184\) 4.23952e14 0.805379
\(185\) 1.18059e15 2.16513
\(186\) 9.13578e14 1.61775
\(187\) −1.94914e14 −0.333329
\(188\) −8.14647e14 −1.34569
\(189\) 1.16287e14 0.185580
\(190\) −2.22165e15 −3.42592
\(191\) −1.19462e14 −0.178038 −0.0890192 0.996030i \(-0.528373\pi\)
−0.0890192 + 0.996030i \(0.528373\pi\)
\(192\) 6.19254e14 0.892095
\(193\) 9.05529e14 1.26119 0.630594 0.776113i \(-0.282811\pi\)
0.630594 + 0.776113i \(0.282811\pi\)
\(194\) 1.53657e15 2.06938
\(195\) 1.55945e14 0.203117
\(196\) −9.59103e13 −0.120837
\(197\) 3.02457e14 0.368666 0.184333 0.982864i \(-0.440987\pi\)
0.184333 + 0.982864i \(0.440987\pi\)
\(198\) −2.31530e14 −0.273076
\(199\) −1.44303e15 −1.64714 −0.823572 0.567212i \(-0.808022\pi\)
−0.823572 + 0.567212i \(0.808022\pi\)
\(200\) −1.01948e15 −1.12638
\(201\) 8.27663e14 0.885277
\(202\) −2.83225e15 −2.93324
\(203\) −4.04500e14 −0.405690
\(204\) 6.87659e14 0.668001
\(205\) 1.34617e15 1.26678
\(206\) 9.10397e14 0.830030
\(207\) −2.54625e14 −0.224954
\(208\) 7.25489e13 0.0621182
\(209\) −8.90688e14 −0.739222
\(210\) 1.59201e15 1.28091
\(211\) 1.25818e15 0.981540 0.490770 0.871289i \(-0.336716\pi\)
0.490770 + 0.871289i \(0.336716\pi\)
\(212\) 2.15047e15 1.62686
\(213\) 6.72813e13 0.0493659
\(214\) −3.41120e15 −2.42783
\(215\) 3.59284e15 2.48078
\(216\) 3.42810e14 0.229670
\(217\) −2.51846e15 −1.63737
\(218\) 1.06369e15 0.671193
\(219\) −1.49246e15 −0.914144
\(220\) −2.00574e15 −1.19269
\(221\) −2.93449e14 −0.169427
\(222\) −2.63891e15 −1.47955
\(223\) −2.51120e15 −1.36741 −0.683706 0.729758i \(-0.739633\pi\)
−0.683706 + 0.729758i \(0.739633\pi\)
\(224\) −1.43512e15 −0.759060
\(225\) 6.12298e14 0.314613
\(226\) −7.97800e13 −0.0398281
\(227\) −2.31766e15 −1.12430 −0.562149 0.827036i \(-0.690025\pi\)
−0.562149 + 0.827036i \(0.690025\pi\)
\(228\) 3.14236e15 1.48142
\(229\) 2.23588e15 1.02451 0.512257 0.858832i \(-0.328810\pi\)
0.512257 + 0.858832i \(0.328810\pi\)
\(230\) −3.48589e15 −1.55268
\(231\) 6.38258e14 0.276387
\(232\) −1.19245e15 −0.502074
\(233\) 3.42937e15 1.40411 0.702055 0.712123i \(-0.252266\pi\)
0.702055 + 0.712123i \(0.252266\pi\)
\(234\) −3.48575e14 −0.138801
\(235\) 2.81115e15 1.08879
\(236\) −5.95433e14 −0.224339
\(237\) −7.74295e14 −0.283819
\(238\) −2.99576e15 −1.06846
\(239\) 5.23983e14 0.181857 0.0909286 0.995857i \(-0.471016\pi\)
0.0909286 + 0.995857i \(0.471016\pi\)
\(240\) 5.86658e14 0.198158
\(241\) −1.64381e14 −0.0540431 −0.0270215 0.999635i \(-0.508602\pi\)
−0.0270215 + 0.999635i \(0.508602\pi\)
\(242\) 3.88552e15 1.24351
\(243\) −2.05891e14 −0.0641500
\(244\) 9.19552e15 2.78960
\(245\) 3.30963e14 0.0977686
\(246\) −3.00903e15 −0.865661
\(247\) −1.34096e15 −0.375738
\(248\) −7.42431e15 −2.02638
\(249\) −1.35110e15 −0.359246
\(250\) −4.98790e14 −0.129214
\(251\) −4.20818e15 −1.06222 −0.531111 0.847303i \(-0.678225\pi\)
−0.531111 + 0.847303i \(0.678225\pi\)
\(252\) −2.25178e15 −0.553888
\(253\) −1.39754e15 −0.335028
\(254\) −1.04972e16 −2.45276
\(255\) −2.37294e15 −0.540475
\(256\) −6.14111e15 −1.36360
\(257\) 5.28008e15 1.14308 0.571538 0.820576i \(-0.306347\pi\)
0.571538 + 0.820576i \(0.306347\pi\)
\(258\) −8.03089e15 −1.69526
\(259\) 7.27468e15 1.49750
\(260\) −3.01970e15 −0.606230
\(261\) 7.16182e14 0.140236
\(262\) −3.06146e15 −0.584750
\(263\) −4.56695e15 −0.850970 −0.425485 0.904965i \(-0.639896\pi\)
−0.425485 + 0.904965i \(0.639896\pi\)
\(264\) 1.88156e15 0.342052
\(265\) −7.42073e15 −1.31628
\(266\) −1.36896e16 −2.36951
\(267\) −2.17883e15 −0.368044
\(268\) −1.60268e16 −2.64223
\(269\) 4.32339e15 0.695720 0.347860 0.937546i \(-0.386908\pi\)
0.347860 + 0.937546i \(0.386908\pi\)
\(270\) −2.81871e15 −0.442779
\(271\) 1.48315e15 0.227449 0.113725 0.993512i \(-0.463722\pi\)
0.113725 + 0.993512i \(0.463722\pi\)
\(272\) −1.10394e15 −0.165291
\(273\) 9.60916e14 0.140484
\(274\) −6.74379e15 −0.962776
\(275\) 3.36068e15 0.468559
\(276\) 4.93053e15 0.671406
\(277\) −5.04924e15 −0.671595 −0.335798 0.941934i \(-0.609006\pi\)
−0.335798 + 0.941934i \(0.609006\pi\)
\(278\) 1.29336e15 0.168045
\(279\) 4.45903e15 0.565995
\(280\) −1.29377e16 −1.60446
\(281\) −1.25712e16 −1.52331 −0.761653 0.647986i \(-0.775612\pi\)
−0.761653 + 0.647986i \(0.775612\pi\)
\(282\) −6.28361e15 −0.744030
\(283\) −5.69495e15 −0.658989 −0.329495 0.944157i \(-0.606878\pi\)
−0.329495 + 0.944157i \(0.606878\pi\)
\(284\) −1.30283e15 −0.147339
\(285\) −1.08435e16 −1.19861
\(286\) −1.91320e15 −0.206719
\(287\) 8.29497e15 0.876158
\(288\) 2.54094e15 0.262387
\(289\) −5.43930e15 −0.549170
\(290\) 9.80476e15 0.967943
\(291\) 7.49973e15 0.724004
\(292\) 2.88998e16 2.72839
\(293\) −1.44892e16 −1.33785 −0.668923 0.743332i \(-0.733244\pi\)
−0.668923 + 0.743332i \(0.733244\pi\)
\(294\) −7.39784e14 −0.0668109
\(295\) 2.05469e15 0.181511
\(296\) 2.14454e16 1.85327
\(297\) −1.13006e15 −0.0955398
\(298\) −2.85073e16 −2.35804
\(299\) −2.10404e15 −0.170291
\(300\) −1.18565e16 −0.939006
\(301\) 2.21387e16 1.71581
\(302\) −4.18657e16 −3.17551
\(303\) −1.38237e16 −1.02624
\(304\) −5.04463e15 −0.366565
\(305\) −3.17315e16 −2.25705
\(306\) 5.30411e15 0.369338
\(307\) 7.50929e15 0.511917 0.255958 0.966688i \(-0.417609\pi\)
0.255958 + 0.966688i \(0.417609\pi\)
\(308\) −1.23592e16 −0.824916
\(309\) 4.44350e15 0.290399
\(310\) 6.10455e16 3.90663
\(311\) 1.11208e16 0.696940 0.348470 0.937320i \(-0.386701\pi\)
0.348470 + 0.937320i \(0.386701\pi\)
\(312\) 2.83274e15 0.173861
\(313\) 4.58215e15 0.275443 0.137721 0.990471i \(-0.456022\pi\)
0.137721 + 0.990471i \(0.456022\pi\)
\(314\) 4.42272e16 2.60403
\(315\) 7.77034e15 0.448148
\(316\) 1.49934e16 0.847099
\(317\) −7.82999e15 −0.433387 −0.216694 0.976240i \(-0.569527\pi\)
−0.216694 + 0.976240i \(0.569527\pi\)
\(318\) 1.65872e16 0.899490
\(319\) 3.93086e15 0.208856
\(320\) 4.13787e16 2.15428
\(321\) −1.66495e16 −0.849413
\(322\) −2.14797e16 −1.07390
\(323\) 2.04048e16 0.999804
\(324\) 3.98686e15 0.191465
\(325\) 5.05960e15 0.238163
\(326\) −4.11085e16 −1.89678
\(327\) 5.19169e15 0.234827
\(328\) 2.44532e16 1.08432
\(329\) 1.73220e16 0.753052
\(330\) −1.54709e16 −0.659438
\(331\) −1.80009e16 −0.752336 −0.376168 0.926552i \(-0.622758\pi\)
−0.376168 + 0.926552i \(0.622758\pi\)
\(332\) 2.61626e16 1.07222
\(333\) −1.28801e16 −0.517645
\(334\) −4.44326e16 −1.75126
\(335\) 5.53046e16 2.13781
\(336\) 3.61493e15 0.137055
\(337\) 2.28670e16 0.850385 0.425193 0.905103i \(-0.360206\pi\)
0.425193 + 0.905103i \(0.360206\pi\)
\(338\) 4.23569e16 1.54513
\(339\) −3.89393e14 −0.0139345
\(340\) 4.59495e16 1.61312
\(341\) 2.44739e16 0.842947
\(342\) 2.42379e16 0.819079
\(343\) 3.11214e16 1.03192
\(344\) 6.52640e16 2.12346
\(345\) −1.70141e16 −0.543230
\(346\) −4.32930e16 −1.35651
\(347\) −1.97866e16 −0.608458 −0.304229 0.952599i \(-0.598399\pi\)
−0.304229 + 0.952599i \(0.598399\pi\)
\(348\) −1.38681e16 −0.418555
\(349\) −3.56274e16 −1.05540 −0.527702 0.849430i \(-0.676946\pi\)
−0.527702 + 0.849430i \(0.676946\pi\)
\(350\) 5.16524e16 1.50193
\(351\) −1.70134e15 −0.0485618
\(352\) 1.39463e16 0.390778
\(353\) 1.28305e16 0.352946 0.176473 0.984305i \(-0.443531\pi\)
0.176473 + 0.984305i \(0.443531\pi\)
\(354\) −4.59275e15 −0.124037
\(355\) 4.49575e15 0.119211
\(356\) 4.21907e16 1.09848
\(357\) −1.46218e16 −0.373816
\(358\) 1.88866e16 0.474148
\(359\) −5.94927e16 −1.46673 −0.733364 0.679836i \(-0.762051\pi\)
−0.733364 + 0.679836i \(0.762051\pi\)
\(360\) 2.29066e16 0.554619
\(361\) 5.11895e16 1.21726
\(362\) −2.22220e15 −0.0519012
\(363\) 1.89646e16 0.435061
\(364\) −1.86071e16 −0.419295
\(365\) −9.97261e16 −2.20752
\(366\) 7.09277e16 1.54237
\(367\) 1.35344e16 0.289142 0.144571 0.989494i \(-0.453820\pi\)
0.144571 + 0.989494i \(0.453820\pi\)
\(368\) −7.91531e15 −0.166133
\(369\) −1.46866e16 −0.302865
\(370\) −1.76333e17 −3.57290
\(371\) −4.57258e16 −0.910397
\(372\) −8.63443e16 −1.68929
\(373\) −2.07601e16 −0.399138 −0.199569 0.979884i \(-0.563954\pi\)
−0.199569 + 0.979884i \(0.563954\pi\)
\(374\) 2.91123e16 0.550061
\(375\) −2.43451e15 −0.0452073
\(376\) 5.10645e16 0.931962
\(377\) 5.91802e15 0.106159
\(378\) −1.73686e16 −0.306245
\(379\) −1.53191e16 −0.265509 −0.132755 0.991149i \(-0.542382\pi\)
−0.132755 + 0.991149i \(0.542382\pi\)
\(380\) 2.09973e17 3.57742
\(381\) −5.12352e16 −0.858136
\(382\) 1.78428e16 0.293800
\(383\) −3.45080e16 −0.558635 −0.279318 0.960199i \(-0.590108\pi\)
−0.279318 + 0.960199i \(0.590108\pi\)
\(384\) −6.39383e16 −1.01767
\(385\) 4.26485e16 0.667435
\(386\) −1.35250e17 −2.08122
\(387\) −3.91975e16 −0.593112
\(388\) −1.45224e17 −2.16089
\(389\) 6.06404e16 0.887339 0.443670 0.896190i \(-0.353676\pi\)
0.443670 + 0.896190i \(0.353676\pi\)
\(390\) −2.32919e16 −0.335185
\(391\) 3.20162e16 0.453128
\(392\) 6.01194e15 0.0836865
\(393\) −1.49425e16 −0.204584
\(394\) −4.51749e16 −0.608375
\(395\) −5.17385e16 −0.685382
\(396\) 2.18824e16 0.285152
\(397\) 6.28868e16 0.806160 0.403080 0.915165i \(-0.367940\pi\)
0.403080 + 0.915165i \(0.367940\pi\)
\(398\) 2.15531e17 2.71813
\(399\) −6.68166e16 −0.829011
\(400\) 1.90340e16 0.232349
\(401\) 4.82766e16 0.579827 0.289914 0.957053i \(-0.406373\pi\)
0.289914 + 0.957053i \(0.406373\pi\)
\(402\) −1.23619e17 −1.46089
\(403\) 3.68462e16 0.428460
\(404\) 2.67682e17 3.06295
\(405\) −1.37577e16 −0.154913
\(406\) 6.04159e16 0.669472
\(407\) −7.06941e16 −0.770938
\(408\) −4.31045e16 −0.462628
\(409\) −1.15320e17 −1.21816 −0.609081 0.793108i \(-0.708461\pi\)
−0.609081 + 0.793108i \(0.708461\pi\)
\(410\) −2.01064e17 −2.09044
\(411\) −3.29153e16 −0.336842
\(412\) −8.60436e16 −0.866736
\(413\) 1.26608e16 0.125541
\(414\) 3.80306e16 0.371220
\(415\) −9.02808e16 −0.867526
\(416\) 2.09965e16 0.198628
\(417\) 6.31265e15 0.0587933
\(418\) 1.33033e17 1.21987
\(419\) 1.81294e17 1.63679 0.818395 0.574656i \(-0.194864\pi\)
0.818395 + 0.574656i \(0.194864\pi\)
\(420\) −1.50464e17 −1.33756
\(421\) 7.01686e16 0.614199 0.307100 0.951677i \(-0.400641\pi\)
0.307100 + 0.951677i \(0.400641\pi\)
\(422\) −1.87922e17 −1.61974
\(423\) −3.06693e16 −0.260310
\(424\) −1.34798e17 −1.12669
\(425\) −7.69896e16 −0.633730
\(426\) −1.00491e16 −0.0814639
\(427\) −1.95526e17 −1.56107
\(428\) 3.22400e17 2.53519
\(429\) −9.33801e15 −0.0723239
\(430\) −5.36626e17 −4.09380
\(431\) −1.51237e17 −1.13646 −0.568230 0.822869i \(-0.692372\pi\)
−0.568230 + 0.822869i \(0.692372\pi\)
\(432\) −6.40037e15 −0.0473763
\(433\) −2.18201e16 −0.159105 −0.0795526 0.996831i \(-0.525349\pi\)
−0.0795526 + 0.996831i \(0.525349\pi\)
\(434\) 3.76156e17 2.70200
\(435\) 4.78554e16 0.338650
\(436\) −1.00532e17 −0.700875
\(437\) 1.46303e17 1.00490
\(438\) 2.22913e17 1.50853
\(439\) 5.33810e15 0.0355932 0.0177966 0.999842i \(-0.494335\pi\)
0.0177966 + 0.999842i \(0.494335\pi\)
\(440\) 1.25726e17 0.826004
\(441\) −3.61076e15 −0.0233748
\(442\) 4.38294e16 0.279590
\(443\) −8.52324e16 −0.535773 −0.267886 0.963451i \(-0.586325\pi\)
−0.267886 + 0.963451i \(0.586325\pi\)
\(444\) 2.49409e17 1.54498
\(445\) −1.45590e17 −0.888772
\(446\) 3.75072e17 2.25651
\(447\) −1.39140e17 −0.824995
\(448\) 2.54971e17 1.48999
\(449\) 1.74520e17 1.00518 0.502590 0.864525i \(-0.332381\pi\)
0.502590 + 0.864525i \(0.332381\pi\)
\(450\) −9.14526e16 −0.519176
\(451\) −8.06091e16 −0.451062
\(452\) 7.54018e15 0.0415893
\(453\) −2.04339e17 −1.11100
\(454\) 3.46165e17 1.85532
\(455\) 6.42086e16 0.339249
\(456\) −1.96972e17 −1.02597
\(457\) 4.87787e16 0.250481 0.125241 0.992126i \(-0.460030\pi\)
0.125241 + 0.992126i \(0.460030\pi\)
\(458\) −3.33950e17 −1.69066
\(459\) 2.58885e16 0.129218
\(460\) 3.29459e17 1.62135
\(461\) 2.05231e17 0.995832 0.497916 0.867225i \(-0.334099\pi\)
0.497916 + 0.867225i \(0.334099\pi\)
\(462\) −9.53299e16 −0.456096
\(463\) 3.12712e17 1.47526 0.737628 0.675207i \(-0.235946\pi\)
0.737628 + 0.675207i \(0.235946\pi\)
\(464\) 2.22634e16 0.103568
\(465\) 2.97953e17 1.36680
\(466\) −5.12210e17 −2.31707
\(467\) −1.40290e17 −0.625844 −0.312922 0.949779i \(-0.601308\pi\)
−0.312922 + 0.949779i \(0.601308\pi\)
\(468\) 3.29446e16 0.144939
\(469\) 3.40781e17 1.47860
\(470\) −4.19872e17 −1.79672
\(471\) 2.15866e17 0.911061
\(472\) 3.73235e16 0.155367
\(473\) −2.15140e17 −0.883333
\(474\) 1.15648e17 0.468361
\(475\) −3.51815e17 −1.40542
\(476\) 2.83136e17 1.11571
\(477\) 8.09593e16 0.314700
\(478\) −7.82619e16 −0.300102
\(479\) 3.43199e16 0.129827 0.0649135 0.997891i \(-0.479323\pi\)
0.0649135 + 0.997891i \(0.479323\pi\)
\(480\) 1.69786e17 0.633626
\(481\) −1.06432e17 −0.391859
\(482\) 2.45519e16 0.0891823
\(483\) −1.04839e17 −0.375722
\(484\) −3.67229e17 −1.29850
\(485\) 5.01133e17 1.74836
\(486\) 3.07518e16 0.105861
\(487\) −5.94598e16 −0.201969 −0.100985 0.994888i \(-0.532199\pi\)
−0.100985 + 0.994888i \(0.532199\pi\)
\(488\) −5.76403e17 −1.93196
\(489\) −2.00644e17 −0.663618
\(490\) −4.94325e16 −0.161338
\(491\) 4.54593e17 1.46417 0.732087 0.681211i \(-0.238546\pi\)
0.732087 + 0.681211i \(0.238546\pi\)
\(492\) 2.84390e17 0.903942
\(493\) −9.00519e16 −0.282480
\(494\) 2.00285e17 0.620045
\(495\) −7.55108e16 −0.230715
\(496\) 1.38614e17 0.418000
\(497\) 2.77023e16 0.0824517
\(498\) 2.01800e17 0.592830
\(499\) −1.80055e17 −0.522097 −0.261049 0.965326i \(-0.584068\pi\)
−0.261049 + 0.965326i \(0.584068\pi\)
\(500\) 4.71418e16 0.134928
\(501\) −2.16868e17 −0.612704
\(502\) 6.28532e17 1.75288
\(503\) 2.50098e17 0.688523 0.344261 0.938874i \(-0.388129\pi\)
0.344261 + 0.938874i \(0.388129\pi\)
\(504\) 1.41148e17 0.383599
\(505\) −9.23704e17 −2.47821
\(506\) 2.08736e17 0.552865
\(507\) 2.06737e17 0.540589
\(508\) 9.92115e17 2.56123
\(509\) −6.69517e16 −0.170646 −0.0853229 0.996353i \(-0.527192\pi\)
−0.0853229 + 0.996353i \(0.527192\pi\)
\(510\) 3.54422e17 0.891896
\(511\) −6.14502e17 −1.52682
\(512\) 1.98740e17 0.487563
\(513\) 1.18301e17 0.286567
\(514\) −7.88630e17 −1.88631
\(515\) 2.96915e17 0.701271
\(516\) 7.59017e17 1.77023
\(517\) −1.68332e17 −0.387685
\(518\) −1.08654e18 −2.47118
\(519\) −2.11306e17 −0.474596
\(520\) 1.89284e17 0.419848
\(521\) −4.25805e17 −0.932750 −0.466375 0.884587i \(-0.654440\pi\)
−0.466375 + 0.884587i \(0.654440\pi\)
\(522\) −1.06969e17 −0.231419
\(523\) 8.03111e17 1.71599 0.857994 0.513659i \(-0.171710\pi\)
0.857994 + 0.513659i \(0.171710\pi\)
\(524\) 2.89345e17 0.610609
\(525\) 2.52107e17 0.525472
\(526\) 6.82119e17 1.40428
\(527\) −5.60673e17 −1.14009
\(528\) −3.51293e16 −0.0705583
\(529\) −2.74479e17 −0.544563
\(530\) 1.10836e18 2.17214
\(531\) −2.24165e16 −0.0433963
\(532\) 1.29383e18 2.47430
\(533\) −1.21359e17 −0.229269
\(534\) 3.25429e17 0.607349
\(535\) −1.11252e18 −2.05121
\(536\) 1.00461e18 1.82989
\(537\) 9.21824e16 0.165888
\(538\) −6.45740e17 −1.14808
\(539\) −1.98181e16 −0.0348126
\(540\) 2.66403e17 0.462359
\(541\) 3.74227e17 0.641730 0.320865 0.947125i \(-0.396026\pi\)
0.320865 + 0.947125i \(0.396026\pi\)
\(542\) −2.21522e17 −0.375338
\(543\) −1.08462e16 −0.0181584
\(544\) −3.19494e17 −0.528531
\(545\) 3.46910e17 0.567073
\(546\) −1.43522e17 −0.231828
\(547\) −6.31631e17 −1.00820 −0.504099 0.863646i \(-0.668175\pi\)
−0.504099 + 0.863646i \(0.668175\pi\)
\(548\) 6.37370e17 1.00535
\(549\) 3.46186e17 0.539622
\(550\) −5.01949e17 −0.773219
\(551\) −4.11505e17 −0.626455
\(552\) −3.09061e17 −0.464986
\(553\) −3.18808e17 −0.474040
\(554\) 7.54153e17 1.10827
\(555\) −8.60650e17 −1.25004
\(556\) −1.22238e17 −0.175477
\(557\) −1.17208e18 −1.66303 −0.831514 0.555504i \(-0.812525\pi\)
−0.831514 + 0.555504i \(0.812525\pi\)
\(558\) −6.65999e17 −0.934009
\(559\) −3.23900e17 −0.448988
\(560\) 2.41550e17 0.330967
\(561\) 1.42092e17 0.192447
\(562\) 1.87764e18 2.51377
\(563\) 3.53756e17 0.468165 0.234083 0.972217i \(-0.424791\pi\)
0.234083 + 0.972217i \(0.424791\pi\)
\(564\) 5.93878e17 0.776932
\(565\) −2.60193e16 −0.0336497
\(566\) 8.50596e17 1.08747
\(567\) −8.47734e16 −0.107145
\(568\) 8.16653e16 0.102041
\(569\) 1.31518e18 1.62463 0.812317 0.583216i \(-0.198206\pi\)
0.812317 + 0.583216i \(0.198206\pi\)
\(570\) 1.61958e18 1.97795
\(571\) 1.16295e18 1.40419 0.702097 0.712081i \(-0.252247\pi\)
0.702097 + 0.712081i \(0.252247\pi\)
\(572\) 1.80821e17 0.215861
\(573\) 8.70880e16 0.102791
\(574\) −1.23893e18 −1.44584
\(575\) −5.52018e17 −0.636960
\(576\) −4.51436e17 −0.515051
\(577\) −7.79934e17 −0.879863 −0.439931 0.898031i \(-0.644997\pi\)
−0.439931 + 0.898031i \(0.644997\pi\)
\(578\) 8.12411e17 0.906244
\(579\) −6.60131e17 −0.728148
\(580\) −9.26669e17 −1.01075
\(581\) −5.56301e17 −0.600019
\(582\) −1.12016e18 −1.19476
\(583\) 4.44356e17 0.468689
\(584\) −1.81153e18 −1.88956
\(585\) −1.13684e17 −0.117270
\(586\) 2.16411e18 2.20772
\(587\) 2.89189e16 0.0291766 0.0145883 0.999894i \(-0.495356\pi\)
0.0145883 + 0.999894i \(0.495356\pi\)
\(588\) 6.99186e16 0.0697654
\(589\) −2.56208e18 −2.52838
\(590\) −3.06888e17 −0.299531
\(591\) −2.20491e17 −0.212849
\(592\) −4.00393e17 −0.382292
\(593\) −3.41632e17 −0.322629 −0.161315 0.986903i \(-0.551573\pi\)
−0.161315 + 0.986903i \(0.551573\pi\)
\(594\) 1.68785e17 0.157660
\(595\) −9.77033e17 −0.902712
\(596\) 2.69429e18 2.46231
\(597\) 1.05197e18 0.950979
\(598\) 3.14258e17 0.281015
\(599\) 1.77459e18 1.56972 0.784862 0.619671i \(-0.212734\pi\)
0.784862 + 0.619671i \(0.212734\pi\)
\(600\) 7.43201e17 0.650314
\(601\) 2.66906e16 0.0231033 0.0115517 0.999933i \(-0.496323\pi\)
0.0115517 + 0.999933i \(0.496323\pi\)
\(602\) −3.30663e18 −2.83145
\(603\) −6.03366e17 −0.511115
\(604\) 3.95682e18 3.31593
\(605\) 1.26722e18 1.05061
\(606\) 2.06471e18 1.69350
\(607\) −1.50590e18 −1.22200 −0.610999 0.791632i \(-0.709232\pi\)
−0.610999 + 0.791632i \(0.709232\pi\)
\(608\) −1.45998e18 −1.17212
\(609\) 2.94880e17 0.234225
\(610\) 4.73940e18 3.72460
\(611\) −2.53429e17 −0.197056
\(612\) −5.01303e17 −0.385670
\(613\) 1.10960e18 0.844641 0.422320 0.906447i \(-0.361216\pi\)
0.422320 + 0.906447i \(0.361216\pi\)
\(614\) −1.12158e18 −0.844768
\(615\) −9.81358e17 −0.731374
\(616\) 7.74710e17 0.571301
\(617\) −1.50847e18 −1.10073 −0.550367 0.834923i \(-0.685512\pi\)
−0.550367 + 0.834923i \(0.685512\pi\)
\(618\) −6.63679e17 −0.479218
\(619\) 1.81904e18 1.29973 0.649866 0.760049i \(-0.274825\pi\)
0.649866 + 0.760049i \(0.274825\pi\)
\(620\) −5.76954e18 −4.07939
\(621\) 1.85621e17 0.129877
\(622\) −1.66101e18 −1.15009
\(623\) −8.97109e17 −0.614714
\(624\) −5.28881e16 −0.0358640
\(625\) −1.56910e18 −1.05301
\(626\) −6.84389e17 −0.454537
\(627\) 6.49312e17 0.426790
\(628\) −4.18001e18 −2.71919
\(629\) 1.61953e18 1.04270
\(630\) −1.16057e18 −0.739536
\(631\) 2.37161e18 1.49573 0.747865 0.663851i \(-0.231079\pi\)
0.747865 + 0.663851i \(0.231079\pi\)
\(632\) −9.39831e17 −0.586663
\(633\) −9.17216e17 −0.566692
\(634\) 1.16948e18 0.715178
\(635\) −3.42354e18 −2.07227
\(636\) −1.56769e18 −0.939267
\(637\) −2.98368e16 −0.0176948
\(638\) −5.87112e17 −0.344656
\(639\) −4.90480e16 −0.0285014
\(640\) −4.27237e18 −2.45753
\(641\) 1.05065e18 0.598247 0.299124 0.954214i \(-0.403306\pi\)
0.299124 + 0.954214i \(0.403306\pi\)
\(642\) 2.48676e18 1.40171
\(643\) −1.89488e18 −1.05733 −0.528666 0.848830i \(-0.677308\pi\)
−0.528666 + 0.848830i \(0.677308\pi\)
\(644\) 2.03009e18 1.12139
\(645\) −2.61918e18 −1.43228
\(646\) −3.04765e18 −1.64988
\(647\) −9.36382e17 −0.501851 −0.250926 0.968006i \(-0.580735\pi\)
−0.250926 + 0.968006i \(0.580735\pi\)
\(648\) −2.49908e17 −0.132600
\(649\) −1.23036e17 −0.0646309
\(650\) −7.55699e17 −0.393018
\(651\) 1.83596e18 0.945335
\(652\) 3.88525e18 1.98066
\(653\) 3.15369e17 0.159178 0.0795890 0.996828i \(-0.474639\pi\)
0.0795890 + 0.996828i \(0.474639\pi\)
\(654\) −7.75429e17 −0.387514
\(655\) −9.98460e17 −0.494040
\(656\) −4.56549e17 −0.223672
\(657\) 1.08800e18 0.527781
\(658\) −2.58721e18 −1.24269
\(659\) 2.25110e18 1.07063 0.535314 0.844653i \(-0.320193\pi\)
0.535314 + 0.844653i \(0.320193\pi\)
\(660\) 1.46219e18 0.688600
\(661\) 1.12700e18 0.525552 0.262776 0.964857i \(-0.415362\pi\)
0.262776 + 0.964857i \(0.415362\pi\)
\(662\) 2.68860e18 1.24151
\(663\) 2.13924e17 0.0978188
\(664\) −1.63995e18 −0.742572
\(665\) −4.46469e18 −2.00194
\(666\) 1.92377e18 0.854221
\(667\) −6.45675e17 −0.283920
\(668\) 4.19942e18 1.82870
\(669\) 1.83066e18 0.789476
\(670\) −8.26027e18 −3.52783
\(671\) 1.90009e18 0.803670
\(672\) 1.04620e18 0.438244
\(673\) −1.25240e18 −0.519570 −0.259785 0.965666i \(-0.583652\pi\)
−0.259785 + 0.965666i \(0.583652\pi\)
\(674\) −3.41541e18 −1.40331
\(675\) −4.46365e17 −0.181642
\(676\) −4.00325e18 −1.61346
\(677\) 1.57557e18 0.628944 0.314472 0.949267i \(-0.398173\pi\)
0.314472 + 0.949267i \(0.398173\pi\)
\(678\) 5.81596e16 0.0229947
\(679\) 3.08793e18 1.20924
\(680\) −2.88025e18 −1.11718
\(681\) 1.68957e18 0.649113
\(682\) −3.65542e18 −1.39104
\(683\) −1.11606e18 −0.420681 −0.210341 0.977628i \(-0.567457\pi\)
−0.210341 + 0.977628i \(0.567457\pi\)
\(684\) −2.29078e18 −0.855300
\(685\) −2.19941e18 −0.813424
\(686\) −4.64827e18 −1.70288
\(687\) −1.62996e18 −0.591503
\(688\) −1.21850e18 −0.438027
\(689\) 6.68990e17 0.238229
\(690\) 2.54121e18 0.896442
\(691\) −2.19065e18 −0.765537 −0.382769 0.923844i \(-0.625029\pi\)
−0.382769 + 0.923844i \(0.625029\pi\)
\(692\) 4.09172e18 1.41650
\(693\) −4.65290e17 −0.159572
\(694\) 2.95533e18 1.00408
\(695\) 4.21813e17 0.141977
\(696\) 8.69295e17 0.289872
\(697\) 1.84667e18 0.610065
\(698\) 5.32129e18 1.74163
\(699\) −2.50001e18 −0.810663
\(700\) −4.88178e18 −1.56834
\(701\) −2.28198e18 −0.726347 −0.363173 0.931722i \(-0.618307\pi\)
−0.363173 + 0.931722i \(0.618307\pi\)
\(702\) 2.54111e17 0.0801369
\(703\) 7.40067e18 2.31239
\(704\) −2.47777e18 −0.767075
\(705\) −2.04933e18 −0.628611
\(706\) −1.91636e18 −0.582434
\(707\) −5.69177e18 −1.71404
\(708\) 4.34071e17 0.129522
\(709\) −7.56300e17 −0.223611 −0.111806 0.993730i \(-0.535663\pi\)
−0.111806 + 0.993730i \(0.535663\pi\)
\(710\) −6.71483e17 −0.196723
\(711\) 5.64461e17 0.163863
\(712\) −2.64464e18 −0.760758
\(713\) −4.02004e18 −1.14590
\(714\) 2.18391e18 0.616874
\(715\) −6.23968e17 −0.174652
\(716\) −1.78501e18 −0.495116
\(717\) −3.81984e17 −0.104995
\(718\) 8.88580e18 2.42040
\(719\) −3.17132e18 −0.856057 −0.428029 0.903765i \(-0.640792\pi\)
−0.428029 + 0.903765i \(0.640792\pi\)
\(720\) −4.27674e17 −0.114407
\(721\) 1.82956e18 0.485029
\(722\) −7.64564e18 −2.00873
\(723\) 1.19834e17 0.0312018
\(724\) 2.10025e17 0.0541964
\(725\) 1.55266e18 0.397081
\(726\) −2.83254e18 −0.717941
\(727\) −9.61106e17 −0.241434 −0.120717 0.992687i \(-0.538519\pi\)
−0.120717 + 0.992687i \(0.538519\pi\)
\(728\) 1.16635e18 0.290385
\(729\) 1.50095e17 0.0370370
\(730\) 1.48951e19 3.64287
\(731\) 4.92864e18 1.19472
\(732\) −6.70353e18 −1.61058
\(733\) −2.61777e18 −0.623384 −0.311692 0.950183i \(-0.600896\pi\)
−0.311692 + 0.950183i \(0.600896\pi\)
\(734\) −2.02150e18 −0.477144
\(735\) −2.41272e17 −0.0564468
\(736\) −2.29078e18 −0.531225
\(737\) −3.31165e18 −0.761213
\(738\) 2.19358e18 0.499789
\(739\) 1.34184e17 0.0303048 0.0151524 0.999885i \(-0.495177\pi\)
0.0151524 + 0.999885i \(0.495177\pi\)
\(740\) 1.66656e19 3.73091
\(741\) 9.77558e17 0.216932
\(742\) 6.82959e18 1.50234
\(743\) −5.76566e18 −1.25725 −0.628625 0.777709i \(-0.716382\pi\)
−0.628625 + 0.777709i \(0.716382\pi\)
\(744\) 5.41232e18 1.16993
\(745\) −9.29733e18 −1.99224
\(746\) 3.10073e18 0.658660
\(747\) 9.84952e17 0.207411
\(748\) −2.75147e18 −0.574386
\(749\) −6.85525e18 −1.41870
\(750\) 3.63618e17 0.0746015
\(751\) 4.90445e18 0.997541 0.498770 0.866734i \(-0.333785\pi\)
0.498770 + 0.866734i \(0.333785\pi\)
\(752\) −9.53391e17 −0.192245
\(753\) 3.06776e18 0.613274
\(754\) −8.83914e17 −0.175185
\(755\) −1.36540e19 −2.68290
\(756\) 1.64155e18 0.319788
\(757\) −8.55799e18 −1.65291 −0.826454 0.563005i \(-0.809645\pi\)
−0.826454 + 0.563005i \(0.809645\pi\)
\(758\) 2.28806e18 0.438145
\(759\) 1.01881e18 0.193428
\(760\) −1.31617e19 −2.47756
\(761\) −5.91805e18 −1.10453 −0.552266 0.833668i \(-0.686237\pi\)
−0.552266 + 0.833668i \(0.686237\pi\)
\(762\) 7.65247e18 1.41610
\(763\) 2.13762e18 0.392213
\(764\) −1.68637e18 −0.306793
\(765\) 1.72987e18 0.312044
\(766\) 5.15411e18 0.921863
\(767\) −1.85234e17 −0.0328511
\(768\) 4.47687e18 0.787276
\(769\) −9.66387e18 −1.68512 −0.842558 0.538605i \(-0.818952\pi\)
−0.842558 + 0.538605i \(0.818952\pi\)
\(770\) −6.36996e18 −1.10141
\(771\) −3.84918e18 −0.659955
\(772\) 1.27827e19 2.17326
\(773\) −5.08802e18 −0.857792 −0.428896 0.903354i \(-0.641097\pi\)
−0.428896 + 0.903354i \(0.641097\pi\)
\(774\) 5.85452e18 0.978758
\(775\) 9.66702e18 1.60262
\(776\) 9.10309e18 1.49654
\(777\) −5.30324e18 −0.864579
\(778\) −9.05723e18 −1.46429
\(779\) 8.43863e18 1.35294
\(780\) 2.20136e18 0.350007
\(781\) −2.69206e17 −0.0424477
\(782\) −4.78193e18 −0.747755
\(783\) −5.22097e17 −0.0809654
\(784\) −1.12245e17 −0.0172628
\(785\) 1.44242e19 2.20008
\(786\) 2.23181e18 0.337606
\(787\) 1.66855e18 0.250325 0.125163 0.992136i \(-0.460055\pi\)
0.125163 + 0.992136i \(0.460055\pi\)
\(788\) 4.26958e18 0.635279
\(789\) 3.32931e18 0.491308
\(790\) 7.72765e18 1.13102
\(791\) −1.60328e17 −0.0232736
\(792\) −1.37165e18 −0.197484
\(793\) 2.86064e18 0.408496
\(794\) −9.39276e18 −1.33033
\(795\) 5.40972e18 0.759955
\(796\) −2.03703e19 −2.83833
\(797\) 8.13831e18 1.12475 0.562374 0.826883i \(-0.309888\pi\)
0.562374 + 0.826883i \(0.309888\pi\)
\(798\) 9.97970e18 1.36804
\(799\) 3.85632e18 0.524347
\(800\) 5.50866e18 0.742953
\(801\) 1.58837e18 0.212490
\(802\) −7.21058e18 −0.956835
\(803\) 5.97163e18 0.786035
\(804\) 1.16835e19 1.52549
\(805\) −7.00535e18 −0.907312
\(806\) −5.50334e18 −0.707048
\(807\) −3.15175e18 −0.401674
\(808\) −1.67791e19 −2.12126
\(809\) 2.88364e18 0.361640 0.180820 0.983516i \(-0.442125\pi\)
0.180820 + 0.983516i \(0.442125\pi\)
\(810\) 2.05484e18 0.255638
\(811\) 1.21256e19 1.49647 0.748235 0.663434i \(-0.230902\pi\)
0.748235 + 0.663434i \(0.230902\pi\)
\(812\) −5.71004e18 −0.699077
\(813\) −1.08121e18 −0.131318
\(814\) 1.05588e19 1.27221
\(815\) −1.34070e19 −1.60254
\(816\) 8.04775e17 0.0954308
\(817\) 2.25222e19 2.64952
\(818\) 1.72242e19 2.01022
\(819\) −7.00508e17 −0.0811087
\(820\) 1.90030e19 2.18289
\(821\) 1.46547e19 1.67011 0.835056 0.550165i \(-0.185435\pi\)
0.835056 + 0.550165i \(0.185435\pi\)
\(822\) 4.91622e18 0.555859
\(823\) 1.18816e18 0.133283 0.0666415 0.997777i \(-0.478772\pi\)
0.0666415 + 0.997777i \(0.478772\pi\)
\(824\) 5.39347e18 0.600263
\(825\) −2.44993e18 −0.270522
\(826\) −1.89102e18 −0.207169
\(827\) −4.76881e18 −0.518351 −0.259175 0.965830i \(-0.583451\pi\)
−0.259175 + 0.965830i \(0.583451\pi\)
\(828\) −3.59436e18 −0.387636
\(829\) 8.43096e18 0.902137 0.451069 0.892489i \(-0.351043\pi\)
0.451069 + 0.892489i \(0.351043\pi\)
\(830\) 1.34843e19 1.43160
\(831\) 3.68090e18 0.387746
\(832\) −3.73035e18 −0.389895
\(833\) 4.54013e17 0.0470843
\(834\) −9.42856e17 −0.0970211
\(835\) −1.44912e19 −1.47959
\(836\) −1.25732e19 −1.27381
\(837\) −3.25063e18 −0.326777
\(838\) −2.70781e19 −2.70104
\(839\) 1.54031e19 1.52460 0.762299 0.647225i \(-0.224070\pi\)
0.762299 + 0.647225i \(0.224070\pi\)
\(840\) 9.43155e18 0.926334
\(841\) −8.44454e18 −0.823004
\(842\) −1.04804e19 −1.01356
\(843\) 9.16443e18 0.879481
\(844\) 1.77609e19 1.69137
\(845\) 1.38142e19 1.30544
\(846\) 4.58075e18 0.429566
\(847\) 7.80846e18 0.726647
\(848\) 2.51672e18 0.232413
\(849\) 4.15162e18 0.380468
\(850\) 1.14991e19 1.04579
\(851\) 1.16121e19 1.04801
\(852\) 9.49763e17 0.0850664
\(853\) −5.34495e18 −0.475089 −0.237544 0.971377i \(-0.576343\pi\)
−0.237544 + 0.971377i \(0.576343\pi\)
\(854\) 2.92037e19 2.57609
\(855\) 7.90491e18 0.692018
\(856\) −2.02090e19 −1.75576
\(857\) 1.69458e19 1.46112 0.730559 0.682849i \(-0.239259\pi\)
0.730559 + 0.682849i \(0.239259\pi\)
\(858\) 1.39472e18 0.119349
\(859\) −2.10751e18 −0.178984 −0.0894919 0.995988i \(-0.528524\pi\)
−0.0894919 + 0.995988i \(0.528524\pi\)
\(860\) 5.07177e19 4.27483
\(861\) −6.04703e18 −0.505850
\(862\) 2.25886e19 1.87540
\(863\) −2.02123e19 −1.66550 −0.832752 0.553646i \(-0.813236\pi\)
−0.832752 + 0.553646i \(0.813236\pi\)
\(864\) −1.85234e18 −0.151489
\(865\) −1.41195e19 −1.14608
\(866\) 3.25904e18 0.262557
\(867\) 3.96525e18 0.317063
\(868\) −3.55513e19 −2.82148
\(869\) 3.09812e18 0.244045
\(870\) −7.14767e18 −0.558842
\(871\) −4.98579e18 −0.386915
\(872\) 6.30162e18 0.485395
\(873\) −5.46730e18 −0.418004
\(874\) −2.18517e19 −1.65829
\(875\) −1.00238e18 −0.0755061
\(876\) −2.10680e19 −1.57524
\(877\) 1.75816e19 1.30485 0.652424 0.757854i \(-0.273752\pi\)
0.652424 + 0.757854i \(0.273752\pi\)
\(878\) −7.97297e17 −0.0587362
\(879\) 1.05627e19 0.772405
\(880\) −2.34734e18 −0.170388
\(881\) −5.02565e18 −0.362117 −0.181058 0.983472i \(-0.557952\pi\)
−0.181058 + 0.983472i \(0.557952\pi\)
\(882\) 5.39302e17 0.0385733
\(883\) −1.33118e19 −0.945128 −0.472564 0.881296i \(-0.656671\pi\)
−0.472564 + 0.881296i \(0.656671\pi\)
\(884\) −4.14242e18 −0.291954
\(885\) −1.49787e18 −0.104796
\(886\) 1.27303e19 0.884136
\(887\) 2.19979e19 1.51662 0.758311 0.651893i \(-0.226025\pi\)
0.758311 + 0.651893i \(0.226025\pi\)
\(888\) −1.56337e19 −1.06999
\(889\) −2.10955e19 −1.43327
\(890\) 2.17452e19 1.46666
\(891\) 8.23814e17 0.0551600
\(892\) −3.54488e19 −2.35630
\(893\) 1.76220e19 1.16284
\(894\) 2.07818e19 1.36141
\(895\) 6.15964e18 0.400595
\(896\) −2.63259e19 −1.69973
\(897\) 1.53384e18 0.0983173
\(898\) −2.60662e19 −1.65875
\(899\) 1.13072e19 0.714357
\(900\) 8.64338e18 0.542135
\(901\) −1.01797e19 −0.633906
\(902\) 1.20397e19 0.744346
\(903\) −1.61391e19 −0.990626
\(904\) −4.72641e17 −0.0288029
\(905\) −7.24745e17 −0.0438500
\(906\) 3.05201e19 1.83338
\(907\) −2.32996e19 −1.38963 −0.694817 0.719187i \(-0.744515\pi\)
−0.694817 + 0.719187i \(0.744515\pi\)
\(908\) −3.27168e19 −1.93737
\(909\) 1.00775e19 0.592499
\(910\) −9.59017e18 −0.559831
\(911\) 1.00388e19 0.581852 0.290926 0.956746i \(-0.406037\pi\)
0.290926 + 0.956746i \(0.406037\pi\)
\(912\) 3.67754e18 0.211636
\(913\) 5.40604e18 0.308901
\(914\) −7.28557e18 −0.413345
\(915\) 2.31322e19 1.30311
\(916\) 3.15624e19 1.76542
\(917\) −6.15241e18 −0.341700
\(918\) −3.86670e18 −0.213237
\(919\) −1.66327e19 −0.910776 −0.455388 0.890293i \(-0.650499\pi\)
−0.455388 + 0.890293i \(0.650499\pi\)
\(920\) −2.06515e19 −1.12287
\(921\) −5.47427e18 −0.295555
\(922\) −3.06532e19 −1.64333
\(923\) −4.05298e17 −0.0215756
\(924\) 9.00984e18 0.476266
\(925\) −2.79236e19 −1.46572
\(926\) −4.67065e19 −2.43448
\(927\) −3.23931e18 −0.167662
\(928\) 6.44328e18 0.331166
\(929\) −1.50596e19 −0.768619 −0.384309 0.923204i \(-0.625560\pi\)
−0.384309 + 0.923204i \(0.625560\pi\)
\(930\) −4.45021e19 −2.25549
\(931\) 2.07468e18 0.104419
\(932\) 4.84101e19 2.41954
\(933\) −8.10710e18 −0.402378
\(934\) 2.09536e19 1.03277
\(935\) 9.49464e18 0.464732
\(936\) −2.06507e18 −0.100379
\(937\) 6.15475e18 0.297100 0.148550 0.988905i \(-0.452539\pi\)
0.148550 + 0.988905i \(0.452539\pi\)
\(938\) −5.08990e19 −2.44000
\(939\) −3.34039e18 −0.159027
\(940\) 3.96830e19 1.87618
\(941\) 1.57758e19 0.740730 0.370365 0.928886i \(-0.379233\pi\)
0.370365 + 0.928886i \(0.379233\pi\)
\(942\) −3.22416e19 −1.50344
\(943\) 1.32407e19 0.613175
\(944\) −6.96842e17 −0.0320492
\(945\) −5.66458e18 −0.258738
\(946\) 3.21333e19 1.45768
\(947\) 1.02390e19 0.461298 0.230649 0.973037i \(-0.425915\pi\)
0.230649 + 0.973037i \(0.425915\pi\)
\(948\) −1.09302e19 −0.489073
\(949\) 8.99046e18 0.399532
\(950\) 5.25470e19 2.31923
\(951\) 5.70806e18 0.250216
\(952\) −1.77478e19 −0.772689
\(953\) −8.30879e18 −0.359281 −0.179640 0.983732i \(-0.557493\pi\)
−0.179640 + 0.983732i \(0.557493\pi\)
\(954\) −1.20921e19 −0.519321
\(955\) 5.81923e18 0.248224
\(956\) 7.39670e18 0.313373
\(957\) −2.86560e18 −0.120583
\(958\) −5.12601e18 −0.214242
\(959\) −1.35525e19 −0.562600
\(960\) −3.01650e19 −1.24377
\(961\) 4.59820e19 1.88315
\(962\) 1.58966e19 0.646648
\(963\) 1.21375e19 0.490409
\(964\) −2.32045e18 −0.0931261
\(965\) −4.41101e19 −1.75837
\(966\) 1.56587e19 0.620018
\(967\) 1.27015e19 0.499556 0.249778 0.968303i \(-0.419642\pi\)
0.249778 + 0.968303i \(0.419642\pi\)
\(968\) 2.30190e19 0.899284
\(969\) −1.48751e19 −0.577237
\(970\) −7.48490e19 −2.88516
\(971\) 1.32520e19 0.507408 0.253704 0.967282i \(-0.418351\pi\)
0.253704 + 0.967282i \(0.418351\pi\)
\(972\) −2.90642e18 −0.110542
\(973\) 2.59917e18 0.0981976
\(974\) 8.88090e18 0.333291
\(975\) −3.68845e18 −0.137503
\(976\) 1.07616e19 0.398523
\(977\) −4.57821e19 −1.68415 −0.842075 0.539360i \(-0.818666\pi\)
−0.842075 + 0.539360i \(0.818666\pi\)
\(978\) 2.99681e19 1.09511
\(979\) 8.71795e18 0.316466
\(980\) 4.67197e18 0.168473
\(981\) −3.78474e18 −0.135578
\(982\) −6.78978e19 −2.41619
\(983\) 1.72596e19 0.610143 0.305072 0.952329i \(-0.401320\pi\)
0.305072 + 0.952329i \(0.401320\pi\)
\(984\) −1.78264e19 −0.626030
\(985\) −1.47333e19 −0.514000
\(986\) 1.34501e19 0.466151
\(987\) −1.26277e19 −0.434775
\(988\) −1.89294e19 −0.647464
\(989\) 3.53385e19 1.20080
\(990\) 1.12783e19 0.380727
\(991\) 4.19067e19 1.40542 0.702708 0.711479i \(-0.251974\pi\)
0.702708 + 0.711479i \(0.251974\pi\)
\(992\) 4.01166e19 1.33659
\(993\) 1.31226e19 0.434361
\(994\) −4.13761e18 −0.136062
\(995\) 7.02929e19 2.29648
\(996\) −1.90725e19 −0.619046
\(997\) 1.09283e19 0.352399 0.176199 0.984354i \(-0.443620\pi\)
0.176199 + 0.984354i \(0.443620\pi\)
\(998\) 2.68929e19 0.861568
\(999\) 9.38959e18 0.298862
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.1.5 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.5 31 1.1 even 1 trivial