Properties

Label 177.14.a.b.1.16
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 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+13.8965 q^{2} -729.000 q^{3} -7998.89 q^{4} +24353.7 q^{5} -10130.5 q^{6} -38818.7 q^{7} -224997. q^{8} +531441. q^{9} +O(q^{10})\) \(q+13.8965 q^{2} -729.000 q^{3} -7998.89 q^{4} +24353.7 q^{5} -10130.5 q^{6} -38818.7 q^{7} -224997. q^{8} +531441. q^{9} +338431. q^{10} +1.36078e6 q^{11} +5.83119e6 q^{12} -1.15964e7 q^{13} -539443. q^{14} -1.77538e7 q^{15} +6.24002e7 q^{16} +5.54118e7 q^{17} +7.38517e6 q^{18} -2.71265e8 q^{19} -1.94802e8 q^{20} +2.82988e7 q^{21} +1.89101e7 q^{22} +4.08870e8 q^{23} +1.64022e8 q^{24} -6.27602e8 q^{25} -1.61149e8 q^{26} -3.87420e8 q^{27} +3.10506e8 q^{28} -1.59049e9 q^{29} -2.46716e8 q^{30} +4.27743e9 q^{31} +2.71032e9 q^{32} -9.92012e8 q^{33} +7.70030e8 q^{34} -9.45377e8 q^{35} -4.25094e9 q^{36} +2.54759e9 q^{37} -3.76963e9 q^{38} +8.45374e9 q^{39} -5.47949e9 q^{40} -2.20088e10 q^{41} +3.93254e8 q^{42} +5.67278e10 q^{43} -1.08848e10 q^{44} +1.29425e10 q^{45} +5.68186e9 q^{46} +5.63077e10 q^{47} -4.54898e10 q^{48} -9.53821e10 q^{49} -8.72146e9 q^{50} -4.03952e10 q^{51} +9.27579e10 q^{52} +9.18905e10 q^{53} -5.38379e9 q^{54} +3.31401e10 q^{55} +8.73407e9 q^{56} +1.97752e11 q^{57} -2.21022e10 q^{58} -4.21805e10 q^{59} +1.42011e11 q^{60} +3.59239e11 q^{61} +5.94413e10 q^{62} -2.06298e10 q^{63} -4.73519e11 q^{64} -2.82414e11 q^{65} -1.37855e10 q^{66} +4.39295e10 q^{67} -4.43233e11 q^{68} -2.98066e11 q^{69} -1.31374e10 q^{70} +1.08282e12 q^{71} -1.19572e11 q^{72} -1.32180e12 q^{73} +3.54025e10 q^{74} +4.57522e11 q^{75} +2.16982e12 q^{76} -5.28238e10 q^{77} +1.17477e11 q^{78} +3.85896e12 q^{79} +1.51967e12 q^{80} +2.82430e11 q^{81} -3.05845e11 q^{82} +2.36000e12 q^{83} -2.26359e11 q^{84} +1.34948e12 q^{85} +7.88317e11 q^{86} +1.15947e12 q^{87} -3.06172e11 q^{88} +6.93420e12 q^{89} +1.79856e11 q^{90} +4.50155e11 q^{91} -3.27051e12 q^{92} -3.11825e12 q^{93} +7.82480e11 q^{94} -6.60630e12 q^{95} -1.97582e12 q^{96} +7.40111e12 q^{97} -1.32548e12 q^{98} +7.23177e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.8965 0.153536 0.0767680 0.997049i \(-0.475540\pi\)
0.0767680 + 0.997049i \(0.475540\pi\)
\(3\) −729.000 −0.577350
\(4\) −7998.89 −0.976427
\(5\) 24353.7 0.697043 0.348521 0.937301i \(-0.386684\pi\)
0.348521 + 0.937301i \(0.386684\pi\)
\(6\) −10130.5 −0.0886441
\(7\) −38818.7 −0.124711 −0.0623553 0.998054i \(-0.519861\pi\)
−0.0623553 + 0.998054i \(0.519861\pi\)
\(8\) −224997. −0.303453
\(9\) 531441. 0.333333
\(10\) 338431. 0.107021
\(11\) 1.36078e6 0.231599 0.115800 0.993273i \(-0.463057\pi\)
0.115800 + 0.993273i \(0.463057\pi\)
\(12\) 5.83119e6 0.563740
\(13\) −1.15964e7 −0.666330 −0.333165 0.942868i \(-0.608117\pi\)
−0.333165 + 0.942868i \(0.608117\pi\)
\(14\) −539443. −0.0191476
\(15\) −1.77538e7 −0.402438
\(16\) 6.24002e7 0.929836
\(17\) 5.54118e7 0.556781 0.278391 0.960468i \(-0.410199\pi\)
0.278391 + 0.960468i \(0.410199\pi\)
\(18\) 7.38517e6 0.0511787
\(19\) −2.71265e8 −1.32280 −0.661401 0.750032i \(-0.730038\pi\)
−0.661401 + 0.750032i \(0.730038\pi\)
\(20\) −1.94802e8 −0.680611
\(21\) 2.82988e7 0.0720017
\(22\) 1.89101e7 0.0355588
\(23\) 4.08870e8 0.575910 0.287955 0.957644i \(-0.407025\pi\)
0.287955 + 0.957644i \(0.407025\pi\)
\(24\) 1.64022e8 0.175198
\(25\) −6.27602e8 −0.514131
\(26\) −1.61149e8 −0.102306
\(27\) −3.87420e8 −0.192450
\(28\) 3.10506e8 0.121771
\(29\) −1.59049e9 −0.496528 −0.248264 0.968692i \(-0.579860\pi\)
−0.248264 + 0.968692i \(0.579860\pi\)
\(30\) −2.46716e8 −0.0617887
\(31\) 4.27743e9 0.865630 0.432815 0.901483i \(-0.357520\pi\)
0.432815 + 0.901483i \(0.357520\pi\)
\(32\) 2.71032e9 0.446216
\(33\) −9.92012e8 −0.133714
\(34\) 7.70030e8 0.0854860
\(35\) −9.45377e8 −0.0869286
\(36\) −4.25094e9 −0.325476
\(37\) 2.54759e9 0.163237 0.0816184 0.996664i \(-0.473991\pi\)
0.0816184 + 0.996664i \(0.473991\pi\)
\(38\) −3.76963e9 −0.203098
\(39\) 8.45374e9 0.384706
\(40\) −5.47949e9 −0.211519
\(41\) −2.20088e10 −0.723604 −0.361802 0.932255i \(-0.617838\pi\)
−0.361802 + 0.932255i \(0.617838\pi\)
\(42\) 3.93254e8 0.0110549
\(43\) 5.67278e10 1.36852 0.684259 0.729239i \(-0.260126\pi\)
0.684259 + 0.729239i \(0.260126\pi\)
\(44\) −1.08848e10 −0.226140
\(45\) 1.29425e10 0.232348
\(46\) 5.68186e9 0.0884229
\(47\) 5.63077e10 0.761960 0.380980 0.924583i \(-0.375587\pi\)
0.380980 + 0.924583i \(0.375587\pi\)
\(48\) −4.54898e10 −0.536841
\(49\) −9.53821e10 −0.984447
\(50\) −8.72146e9 −0.0789377
\(51\) −4.03952e10 −0.321458
\(52\) 9.27579e10 0.650623
\(53\) 9.18905e10 0.569479 0.284739 0.958605i \(-0.408093\pi\)
0.284739 + 0.958605i \(0.408093\pi\)
\(54\) −5.38379e9 −0.0295480
\(55\) 3.31401e10 0.161434
\(56\) 8.73407e9 0.0378438
\(57\) 1.97752e11 0.763721
\(58\) −2.21022e10 −0.0762349
\(59\) −4.21805e10 −0.130189
\(60\) 1.42011e11 0.392951
\(61\) 3.59239e11 0.892769 0.446384 0.894841i \(-0.352711\pi\)
0.446384 + 0.894841i \(0.352711\pi\)
\(62\) 5.94413e10 0.132905
\(63\) −2.06298e10 −0.0415702
\(64\) −4.73519e11 −0.861326
\(65\) −2.82414e11 −0.464461
\(66\) −1.37855e10 −0.0205299
\(67\) 4.39295e10 0.0593294 0.0296647 0.999560i \(-0.490556\pi\)
0.0296647 + 0.999560i \(0.490556\pi\)
\(68\) −4.43233e11 −0.543656
\(69\) −2.98066e11 −0.332502
\(70\) −1.31374e10 −0.0133467
\(71\) 1.08282e12 1.00317 0.501586 0.865108i \(-0.332750\pi\)
0.501586 + 0.865108i \(0.332750\pi\)
\(72\) −1.19572e11 −0.101151
\(73\) −1.32180e12 −1.02227 −0.511136 0.859500i \(-0.670775\pi\)
−0.511136 + 0.859500i \(0.670775\pi\)
\(74\) 3.54025e10 0.0250627
\(75\) 4.57522e11 0.296834
\(76\) 2.16982e12 1.29162
\(77\) −5.28238e10 −0.0288829
\(78\) 1.17477e11 0.0590662
\(79\) 3.85896e12 1.78605 0.893027 0.450003i \(-0.148577\pi\)
0.893027 + 0.450003i \(0.148577\pi\)
\(80\) 1.51967e12 0.648135
\(81\) 2.82430e11 0.111111
\(82\) −3.05845e11 −0.111099
\(83\) 2.36000e12 0.792328 0.396164 0.918180i \(-0.370341\pi\)
0.396164 + 0.918180i \(0.370341\pi\)
\(84\) −2.26359e11 −0.0703044
\(85\) 1.34948e12 0.388100
\(86\) 7.88317e11 0.210117
\(87\) 1.15947e12 0.286671
\(88\) −3.06172e11 −0.0702794
\(89\) 6.93420e12 1.47898 0.739488 0.673169i \(-0.235067\pi\)
0.739488 + 0.673169i \(0.235067\pi\)
\(90\) 1.79856e11 0.0356737
\(91\) 4.50155e11 0.0830984
\(92\) −3.27051e12 −0.562334
\(93\) −3.11825e12 −0.499772
\(94\) 7.82480e11 0.116988
\(95\) −6.60630e12 −0.922050
\(96\) −1.97582e12 −0.257623
\(97\) 7.40111e12 0.902153 0.451077 0.892485i \(-0.351040\pi\)
0.451077 + 0.892485i \(0.351040\pi\)
\(98\) −1.32548e12 −0.151148
\(99\) 7.23177e11 0.0771997
\(100\) 5.02012e12 0.502012
\(101\) −2.00378e13 −1.87829 −0.939143 0.343525i \(-0.888379\pi\)
−0.939143 + 0.343525i \(0.888379\pi\)
\(102\) −5.61352e11 −0.0493553
\(103\) −1.59804e13 −1.31870 −0.659348 0.751837i \(-0.729168\pi\)
−0.659348 + 0.751837i \(0.729168\pi\)
\(104\) 2.60914e12 0.202200
\(105\) 6.89180e11 0.0501883
\(106\) 1.27696e12 0.0874355
\(107\) 1.55246e13 1.00006 0.500030 0.866008i \(-0.333322\pi\)
0.500030 + 0.866008i \(0.333322\pi\)
\(108\) 3.09893e12 0.187913
\(109\) −1.02224e13 −0.583822 −0.291911 0.956446i \(-0.594291\pi\)
−0.291911 + 0.956446i \(0.594291\pi\)
\(110\) 4.60531e11 0.0247860
\(111\) −1.85719e12 −0.0942448
\(112\) −2.42229e12 −0.115960
\(113\) 6.47437e12 0.292542 0.146271 0.989245i \(-0.453273\pi\)
0.146271 + 0.989245i \(0.453273\pi\)
\(114\) 2.74806e12 0.117259
\(115\) 9.95749e12 0.401434
\(116\) 1.27221e13 0.484823
\(117\) −6.16278e12 −0.222110
\(118\) −5.86162e11 −0.0199887
\(119\) −2.15101e12 −0.0694365
\(120\) 3.99455e12 0.122121
\(121\) −3.26710e13 −0.946362
\(122\) 4.99216e12 0.137072
\(123\) 1.60444e13 0.417773
\(124\) −3.42147e13 −0.845224
\(125\) −4.50130e13 −1.05541
\(126\) −2.86682e11 −0.00638252
\(127\) 4.51014e13 0.953818 0.476909 0.878953i \(-0.341757\pi\)
0.476909 + 0.878953i \(0.341757\pi\)
\(128\) −2.87832e13 −0.578460
\(129\) −4.13545e13 −0.790115
\(130\) −3.92456e12 −0.0713114
\(131\) −1.10706e14 −1.91384 −0.956921 0.290349i \(-0.906228\pi\)
−0.956921 + 0.290349i \(0.906228\pi\)
\(132\) 7.93499e12 0.130562
\(133\) 1.05301e13 0.164968
\(134\) 6.10466e11 0.00910920
\(135\) −9.43511e12 −0.134146
\(136\) −1.24675e13 −0.168957
\(137\) −2.16910e13 −0.280283 −0.140141 0.990131i \(-0.544756\pi\)
−0.140141 + 0.990131i \(0.544756\pi\)
\(138\) −4.14208e12 −0.0510510
\(139\) −2.55160e12 −0.0300065 −0.0150033 0.999887i \(-0.504776\pi\)
−0.0150033 + 0.999887i \(0.504776\pi\)
\(140\) 7.56196e12 0.0848794
\(141\) −4.10483e13 −0.439918
\(142\) 1.50473e13 0.154023
\(143\) −1.57801e13 −0.154321
\(144\) 3.31620e13 0.309945
\(145\) −3.87343e13 −0.346101
\(146\) −1.83683e13 −0.156955
\(147\) 6.95336e13 0.568371
\(148\) −2.03779e13 −0.159389
\(149\) −2.46245e14 −1.84356 −0.921778 0.387718i \(-0.873263\pi\)
−0.921778 + 0.387718i \(0.873263\pi\)
\(150\) 6.35795e12 0.0455747
\(151\) −4.30791e12 −0.0295744 −0.0147872 0.999891i \(-0.504707\pi\)
−0.0147872 + 0.999891i \(0.504707\pi\)
\(152\) 6.10337e13 0.401408
\(153\) 2.94481e13 0.185594
\(154\) −7.34066e11 −0.00443456
\(155\) 1.04171e14 0.603381
\(156\) −6.76205e13 −0.375637
\(157\) 3.29080e14 1.75370 0.876848 0.480768i \(-0.159642\pi\)
0.876848 + 0.480768i \(0.159642\pi\)
\(158\) 5.36261e13 0.274224
\(159\) −6.69882e13 −0.328789
\(160\) 6.60062e13 0.311032
\(161\) −1.58718e13 −0.0718220
\(162\) 3.92478e12 0.0170596
\(163\) 3.19545e14 1.33448 0.667242 0.744841i \(-0.267475\pi\)
0.667242 + 0.744841i \(0.267475\pi\)
\(164\) 1.76046e14 0.706546
\(165\) −2.41591e13 −0.0932042
\(166\) 3.27958e13 0.121651
\(167\) −5.27737e14 −1.88261 −0.941305 0.337558i \(-0.890399\pi\)
−0.941305 + 0.337558i \(0.890399\pi\)
\(168\) −6.36713e12 −0.0218491
\(169\) −1.68400e14 −0.556004
\(170\) 1.87531e13 0.0595874
\(171\) −1.44161e14 −0.440934
\(172\) −4.53759e14 −1.33626
\(173\) −3.81682e12 −0.0108244 −0.00541218 0.999985i \(-0.501723\pi\)
−0.00541218 + 0.999985i \(0.501723\pi\)
\(174\) 1.61125e13 0.0440143
\(175\) 2.43627e13 0.0641176
\(176\) 8.49133e13 0.215349
\(177\) 3.07496e13 0.0751646
\(178\) 9.63611e13 0.227076
\(179\) −3.62969e14 −0.824754 −0.412377 0.911013i \(-0.635301\pi\)
−0.412377 + 0.911013i \(0.635301\pi\)
\(180\) −1.03526e14 −0.226870
\(181\) 8.98134e14 1.89859 0.949294 0.314391i \(-0.101800\pi\)
0.949294 + 0.314391i \(0.101800\pi\)
\(182\) 6.25557e12 0.0127586
\(183\) −2.61885e14 −0.515440
\(184\) −9.19944e13 −0.174761
\(185\) 6.20431e13 0.113783
\(186\) −4.33327e13 −0.0767329
\(187\) 7.54036e13 0.128950
\(188\) −4.50399e14 −0.743998
\(189\) 1.50391e13 0.0240006
\(190\) −9.18043e13 −0.141568
\(191\) −1.10232e15 −1.64283 −0.821414 0.570332i \(-0.806815\pi\)
−0.821414 + 0.570332i \(0.806815\pi\)
\(192\) 3.45195e14 0.497287
\(193\) 6.46237e14 0.900056 0.450028 0.893015i \(-0.351414\pi\)
0.450028 + 0.893015i \(0.351414\pi\)
\(194\) 1.02849e14 0.138513
\(195\) 2.05880e14 0.268157
\(196\) 7.62951e14 0.961241
\(197\) −3.86799e14 −0.471471 −0.235735 0.971817i \(-0.575750\pi\)
−0.235735 + 0.971817i \(0.575750\pi\)
\(198\) 1.00496e13 0.0118529
\(199\) −9.34386e14 −1.06655 −0.533275 0.845942i \(-0.679039\pi\)
−0.533275 + 0.845942i \(0.679039\pi\)
\(200\) 1.41208e14 0.156015
\(201\) −3.20246e13 −0.0342539
\(202\) −2.78456e14 −0.288385
\(203\) 6.17407e13 0.0619223
\(204\) 3.23117e14 0.313880
\(205\) −5.35994e14 −0.504383
\(206\) −2.22071e14 −0.202467
\(207\) 2.17290e14 0.191970
\(208\) −7.23615e14 −0.619578
\(209\) −3.69133e14 −0.306360
\(210\) 9.57718e12 0.00770571
\(211\) −1.79964e15 −1.40395 −0.701974 0.712203i \(-0.747698\pi\)
−0.701974 + 0.712203i \(0.747698\pi\)
\(212\) −7.35022e14 −0.556054
\(213\) −7.89372e14 −0.579181
\(214\) 2.15738e14 0.153545
\(215\) 1.38153e15 0.953916
\(216\) 8.71683e13 0.0583995
\(217\) −1.66044e14 −0.107953
\(218\) −1.42055e14 −0.0896376
\(219\) 9.63590e14 0.590209
\(220\) −2.65084e14 −0.157629
\(221\) −6.42575e14 −0.371000
\(222\) −2.58084e13 −0.0144700
\(223\) −1.32027e15 −0.718919 −0.359460 0.933161i \(-0.617039\pi\)
−0.359460 + 0.933161i \(0.617039\pi\)
\(224\) −1.05211e14 −0.0556479
\(225\) −3.33533e14 −0.171377
\(226\) 8.99711e13 0.0449157
\(227\) −3.28120e15 −1.59171 −0.795857 0.605484i \(-0.792979\pi\)
−0.795857 + 0.605484i \(0.792979\pi\)
\(228\) −1.58180e15 −0.745717
\(229\) 1.93024e15 0.884466 0.442233 0.896900i \(-0.354186\pi\)
0.442233 + 0.896900i \(0.354186\pi\)
\(230\) 1.38374e14 0.0616345
\(231\) 3.85086e13 0.0166755
\(232\) 3.57855e14 0.150673
\(233\) −8.79348e14 −0.360037 −0.180019 0.983663i \(-0.557616\pi\)
−0.180019 + 0.983663i \(0.557616\pi\)
\(234\) −8.56410e13 −0.0341019
\(235\) 1.37130e15 0.531119
\(236\) 3.37397e14 0.127120
\(237\) −2.81318e15 −1.03118
\(238\) −2.98915e13 −0.0106610
\(239\) 5.01331e15 1.73996 0.869979 0.493090i \(-0.164132\pi\)
0.869979 + 0.493090i \(0.164132\pi\)
\(240\) −1.10784e15 −0.374201
\(241\) −4.43682e15 −1.45868 −0.729342 0.684149i \(-0.760174\pi\)
−0.729342 + 0.684149i \(0.760174\pi\)
\(242\) −4.54012e14 −0.145301
\(243\) −2.05891e14 −0.0641500
\(244\) −2.87351e15 −0.871723
\(245\) −2.32291e15 −0.686202
\(246\) 2.22961e14 0.0641432
\(247\) 3.14568e15 0.881423
\(248\) −9.62408e14 −0.262678
\(249\) −1.72044e15 −0.457451
\(250\) −6.25523e14 −0.162044
\(251\) −5.84508e15 −1.47541 −0.737703 0.675126i \(-0.764089\pi\)
−0.737703 + 0.675126i \(0.764089\pi\)
\(252\) 1.65016e14 0.0405902
\(253\) 5.56384e14 0.133380
\(254\) 6.26751e14 0.146445
\(255\) −9.83772e14 −0.224070
\(256\) 3.47908e15 0.772511
\(257\) 5.19068e15 1.12372 0.561861 0.827232i \(-0.310086\pi\)
0.561861 + 0.827232i \(0.310086\pi\)
\(258\) −5.74683e14 −0.121311
\(259\) −9.88939e13 −0.0203573
\(260\) 2.25900e15 0.453512
\(261\) −8.45251e14 −0.165509
\(262\) −1.53842e15 −0.293844
\(263\) −6.11545e15 −1.13951 −0.569753 0.821816i \(-0.692961\pi\)
−0.569753 + 0.821816i \(0.692961\pi\)
\(264\) 2.23199e14 0.0405758
\(265\) 2.23787e15 0.396951
\(266\) 1.46332e14 0.0253285
\(267\) −5.05503e15 −0.853888
\(268\) −3.51387e14 −0.0579308
\(269\) 3.18527e14 0.0512574 0.0256287 0.999672i \(-0.491841\pi\)
0.0256287 + 0.999672i \(0.491841\pi\)
\(270\) −1.31115e14 −0.0205962
\(271\) −6.01257e15 −0.922061 −0.461030 0.887384i \(-0.652520\pi\)
−0.461030 + 0.887384i \(0.652520\pi\)
\(272\) 3.45771e15 0.517715
\(273\) −3.28163e14 −0.0479769
\(274\) −3.01429e14 −0.0430335
\(275\) −8.54031e14 −0.119072
\(276\) 2.38420e15 0.324663
\(277\) 1.03755e16 1.38004 0.690018 0.723792i \(-0.257603\pi\)
0.690018 + 0.723792i \(0.257603\pi\)
\(278\) −3.54583e13 −0.00460708
\(279\) 2.27320e15 0.288543
\(280\) 2.12707e14 0.0263787
\(281\) −7.04622e15 −0.853817 −0.426909 0.904295i \(-0.640397\pi\)
−0.426909 + 0.904295i \(0.640397\pi\)
\(282\) −5.70428e14 −0.0675432
\(283\) −1.07690e16 −1.24613 −0.623064 0.782171i \(-0.714113\pi\)
−0.623064 + 0.782171i \(0.714113\pi\)
\(284\) −8.66132e15 −0.979523
\(285\) 4.81599e15 0.532346
\(286\) −2.19289e14 −0.0236939
\(287\) 8.54351e14 0.0902410
\(288\) 1.44037e15 0.148739
\(289\) −6.83411e15 −0.689995
\(290\) −5.38270e14 −0.0531390
\(291\) −5.39541e15 −0.520859
\(292\) 1.05729e16 0.998173
\(293\) 3.33512e15 0.307944 0.153972 0.988075i \(-0.450793\pi\)
0.153972 + 0.988075i \(0.450793\pi\)
\(294\) 9.66273e14 0.0872654
\(295\) −1.02725e15 −0.0907472
\(296\) −5.73198e14 −0.0495346
\(297\) −5.27196e14 −0.0445713
\(298\) −3.42194e15 −0.283052
\(299\) −4.74140e15 −0.383746
\(300\) −3.65966e15 −0.289837
\(301\) −2.20210e15 −0.170669
\(302\) −5.98648e13 −0.00454074
\(303\) 1.46076e16 1.08443
\(304\) −1.69270e16 −1.22999
\(305\) 8.74878e15 0.622298
\(306\) 4.09226e14 0.0284953
\(307\) −2.20366e16 −1.50226 −0.751129 0.660155i \(-0.770490\pi\)
−0.751129 + 0.660155i \(0.770490\pi\)
\(308\) 4.22532e14 0.0282020
\(309\) 1.16497e16 0.761350
\(310\) 1.44761e15 0.0926407
\(311\) −1.56660e15 −0.0981785 −0.0490892 0.998794i \(-0.515632\pi\)
−0.0490892 + 0.998794i \(0.515632\pi\)
\(312\) −1.90206e15 −0.116740
\(313\) −2.15251e16 −1.29392 −0.646959 0.762525i \(-0.723959\pi\)
−0.646959 + 0.762525i \(0.723959\pi\)
\(314\) 4.57306e15 0.269256
\(315\) −5.02412e14 −0.0289762
\(316\) −3.08674e16 −1.74395
\(317\) −6.47131e15 −0.358185 −0.179092 0.983832i \(-0.557316\pi\)
−0.179092 + 0.983832i \(0.557316\pi\)
\(318\) −9.30901e14 −0.0504809
\(319\) −2.16431e15 −0.114995
\(320\) −1.15319e16 −0.600381
\(321\) −1.13174e16 −0.577385
\(322\) −2.20562e14 −0.0110273
\(323\) −1.50313e16 −0.736512
\(324\) −2.25912e15 −0.108492
\(325\) 7.27789e15 0.342581
\(326\) 4.44056e15 0.204891
\(327\) 7.45212e15 0.337070
\(328\) 4.95190e15 0.219579
\(329\) −2.18579e15 −0.0950245
\(330\) −3.35727e14 −0.0143102
\(331\) −2.15691e16 −0.901467 −0.450734 0.892658i \(-0.648838\pi\)
−0.450734 + 0.892658i \(0.648838\pi\)
\(332\) −1.88774e16 −0.773650
\(333\) 1.35389e15 0.0544122
\(334\) −7.33369e15 −0.289048
\(335\) 1.06985e15 0.0413552
\(336\) 1.76585e15 0.0669497
\(337\) −3.91853e16 −1.45723 −0.728617 0.684922i \(-0.759836\pi\)
−0.728617 + 0.684922i \(0.759836\pi\)
\(338\) −2.34017e15 −0.0853666
\(339\) −4.71982e15 −0.168899
\(340\) −1.07944e16 −0.378951
\(341\) 5.82066e15 0.200479
\(342\) −2.00334e15 −0.0676993
\(343\) 7.46371e15 0.247482
\(344\) −1.27636e16 −0.415281
\(345\) −7.25901e15 −0.231768
\(346\) −5.30404e13 −0.00166193
\(347\) 2.89306e16 0.889643 0.444822 0.895619i \(-0.353267\pi\)
0.444822 + 0.895619i \(0.353267\pi\)
\(348\) −9.27444e15 −0.279913
\(349\) 3.06220e16 0.907129 0.453564 0.891224i \(-0.350152\pi\)
0.453564 + 0.891224i \(0.350152\pi\)
\(350\) 3.38556e14 0.00984436
\(351\) 4.49266e15 0.128235
\(352\) 3.68816e15 0.103343
\(353\) 1.03669e16 0.285176 0.142588 0.989782i \(-0.454458\pi\)
0.142588 + 0.989782i \(0.454458\pi\)
\(354\) 4.27312e14 0.0115405
\(355\) 2.63705e16 0.699253
\(356\) −5.54659e16 −1.44411
\(357\) 1.56809e15 0.0400892
\(358\) −5.04399e15 −0.126630
\(359\) 2.74116e16 0.675802 0.337901 0.941182i \(-0.390283\pi\)
0.337901 + 0.941182i \(0.390283\pi\)
\(360\) −2.91203e15 −0.0705065
\(361\) 3.15316e16 0.749807
\(362\) 1.24809e16 0.291502
\(363\) 2.38171e16 0.546382
\(364\) −3.60074e15 −0.0811395
\(365\) −3.21906e16 −0.712567
\(366\) −3.63928e15 −0.0791386
\(367\) 6.96728e16 1.48845 0.744225 0.667929i \(-0.232819\pi\)
0.744225 + 0.667929i \(0.232819\pi\)
\(368\) 2.55136e16 0.535501
\(369\) −1.16964e16 −0.241201
\(370\) 8.62182e14 0.0174698
\(371\) −3.56707e15 −0.0710200
\(372\) 2.49425e16 0.487990
\(373\) −1.91725e16 −0.368613 −0.184306 0.982869i \(-0.559004\pi\)
−0.184306 + 0.982869i \(0.559004\pi\)
\(374\) 1.04785e15 0.0197985
\(375\) 3.28145e16 0.609344
\(376\) −1.26690e16 −0.231219
\(377\) 1.84439e16 0.330852
\(378\) 2.08991e14 0.00368495
\(379\) 5.15368e16 0.893229 0.446615 0.894726i \(-0.352630\pi\)
0.446615 + 0.894726i \(0.352630\pi\)
\(380\) 5.28430e16 0.900314
\(381\) −3.28789e16 −0.550687
\(382\) −1.53184e16 −0.252233
\(383\) −4.94719e16 −0.800879 −0.400439 0.916323i \(-0.631143\pi\)
−0.400439 + 0.916323i \(0.631143\pi\)
\(384\) 2.09829e16 0.333974
\(385\) −1.28645e15 −0.0201326
\(386\) 8.98043e15 0.138191
\(387\) 3.01475e16 0.456173
\(388\) −5.92006e16 −0.880887
\(389\) −1.24941e17 −1.82824 −0.914118 0.405449i \(-0.867115\pi\)
−0.914118 + 0.405449i \(0.867115\pi\)
\(390\) 2.86100e15 0.0411717
\(391\) 2.26562e16 0.320656
\(392\) 2.14606e16 0.298733
\(393\) 8.07043e16 1.10496
\(394\) −5.37515e15 −0.0723877
\(395\) 9.39799e16 1.24496
\(396\) −5.78461e15 −0.0753799
\(397\) 2.53071e16 0.324417 0.162209 0.986756i \(-0.448138\pi\)
0.162209 + 0.986756i \(0.448138\pi\)
\(398\) −1.29847e16 −0.163754
\(399\) −7.67647e15 −0.0952440
\(400\) −3.91625e16 −0.478058
\(401\) 1.02781e17 1.23445 0.617225 0.786786i \(-0.288257\pi\)
0.617225 + 0.786786i \(0.288257\pi\)
\(402\) −4.45030e14 −0.00525920
\(403\) −4.96026e16 −0.576795
\(404\) 1.60280e17 1.83401
\(405\) 6.87820e15 0.0774492
\(406\) 8.57979e14 0.00950730
\(407\) 3.46672e15 0.0378055
\(408\) 9.08879e15 0.0975472
\(409\) 6.97930e16 0.737243 0.368621 0.929580i \(-0.379830\pi\)
0.368621 + 0.929580i \(0.379830\pi\)
\(410\) −7.44844e15 −0.0774409
\(411\) 1.58128e16 0.161821
\(412\) 1.27825e17 1.28761
\(413\) 1.63739e15 0.0162359
\(414\) 3.01957e15 0.0294743
\(415\) 5.74747e16 0.552286
\(416\) −3.14298e16 −0.297327
\(417\) 1.86011e15 0.0173243
\(418\) −5.12965e15 −0.0470373
\(419\) −3.26386e16 −0.294673 −0.147337 0.989086i \(-0.547070\pi\)
−0.147337 + 0.989086i \(0.547070\pi\)
\(420\) −5.51267e15 −0.0490052
\(421\) 2.87811e16 0.251926 0.125963 0.992035i \(-0.459798\pi\)
0.125963 + 0.992035i \(0.459798\pi\)
\(422\) −2.50087e16 −0.215556
\(423\) 2.99242e16 0.253987
\(424\) −2.06750e16 −0.172810
\(425\) −3.47766e16 −0.286259
\(426\) −1.09695e16 −0.0889252
\(427\) −1.39452e16 −0.111338
\(428\) −1.24180e17 −0.976486
\(429\) 1.15037e16 0.0890976
\(430\) 1.91984e16 0.146460
\(431\) 1.50455e17 1.13059 0.565294 0.824890i \(-0.308763\pi\)
0.565294 + 0.824890i \(0.308763\pi\)
\(432\) −2.41751e16 −0.178947
\(433\) −1.33321e17 −0.972139 −0.486069 0.873920i \(-0.661570\pi\)
−0.486069 + 0.873920i \(0.661570\pi\)
\(434\) −2.30743e15 −0.0165747
\(435\) 2.82373e16 0.199822
\(436\) 8.17677e16 0.570059
\(437\) −1.10912e17 −0.761815
\(438\) 1.33905e16 0.0906183
\(439\) −8.30528e16 −0.553777 −0.276889 0.960902i \(-0.589303\pi\)
−0.276889 + 0.960902i \(0.589303\pi\)
\(440\) −7.45641e15 −0.0489877
\(441\) −5.06900e16 −0.328149
\(442\) −8.92954e15 −0.0569619
\(443\) 2.44860e17 1.53920 0.769598 0.638529i \(-0.220457\pi\)
0.769598 + 0.638529i \(0.220457\pi\)
\(444\) 1.48555e16 0.0920231
\(445\) 1.68873e17 1.03091
\(446\) −1.83471e16 −0.110380
\(447\) 1.79512e17 1.06438
\(448\) 1.83814e16 0.107416
\(449\) 1.59805e17 0.920426 0.460213 0.887809i \(-0.347773\pi\)
0.460213 + 0.887809i \(0.347773\pi\)
\(450\) −4.63494e15 −0.0263126
\(451\) −2.99492e16 −0.167586
\(452\) −5.17878e16 −0.285645
\(453\) 3.14046e15 0.0170748
\(454\) −4.55972e16 −0.244385
\(455\) 1.09629e16 0.0579232
\(456\) −4.44935e16 −0.231753
\(457\) 1.95607e17 1.00445 0.502225 0.864737i \(-0.332515\pi\)
0.502225 + 0.864737i \(0.332515\pi\)
\(458\) 2.68236e16 0.135797
\(459\) −2.14677e16 −0.107153
\(460\) −7.96488e16 −0.391971
\(461\) 1.23844e17 0.600924 0.300462 0.953794i \(-0.402859\pi\)
0.300462 + 0.953794i \(0.402859\pi\)
\(462\) 5.35134e14 0.00256029
\(463\) −3.31348e17 −1.56318 −0.781589 0.623794i \(-0.785591\pi\)
−0.781589 + 0.623794i \(0.785591\pi\)
\(464\) −9.92469e16 −0.461690
\(465\) −7.59408e16 −0.348362
\(466\) −1.22199e16 −0.0552787
\(467\) −1.40310e17 −0.625934 −0.312967 0.949764i \(-0.601323\pi\)
−0.312967 + 0.949764i \(0.601323\pi\)
\(468\) 4.92954e16 0.216874
\(469\) −1.70529e15 −0.00739901
\(470\) 1.90563e16 0.0815458
\(471\) −2.39900e17 −1.01250
\(472\) 9.49047e15 0.0395062
\(473\) 7.71943e16 0.316948
\(474\) −3.90934e16 −0.158323
\(475\) 1.70246e17 0.680094
\(476\) 1.72057e16 0.0677997
\(477\) 4.88344e16 0.189826
\(478\) 6.96675e16 0.267146
\(479\) −1.51804e17 −0.574253 −0.287126 0.957893i \(-0.592700\pi\)
−0.287126 + 0.957893i \(0.592700\pi\)
\(480\) −4.81185e16 −0.179574
\(481\) −2.95427e16 −0.108770
\(482\) −6.16563e16 −0.223961
\(483\) 1.15705e16 0.0414665
\(484\) 2.61331e17 0.924053
\(485\) 1.80244e17 0.628840
\(486\) −2.86116e15 −0.00984934
\(487\) 4.89834e17 1.66384 0.831918 0.554898i \(-0.187243\pi\)
0.831918 + 0.554898i \(0.187243\pi\)
\(488\) −8.08274e16 −0.270913
\(489\) −2.32949e17 −0.770464
\(490\) −3.22802e16 −0.105357
\(491\) −2.84885e17 −0.917573 −0.458786 0.888547i \(-0.651716\pi\)
−0.458786 + 0.888547i \(0.651716\pi\)
\(492\) −1.28337e17 −0.407924
\(493\) −8.81319e16 −0.276457
\(494\) 4.37139e16 0.135330
\(495\) 1.76120e16 0.0538115
\(496\) 2.66913e17 0.804893
\(497\) −4.20334e16 −0.125106
\(498\) −2.39081e16 −0.0702351
\(499\) 5.65300e17 1.63918 0.819588 0.572953i \(-0.194202\pi\)
0.819588 + 0.572953i \(0.194202\pi\)
\(500\) 3.60054e17 1.03053
\(501\) 3.84720e17 1.08693
\(502\) −8.12261e16 −0.226528
\(503\) −5.71067e17 −1.57215 −0.786076 0.618129i \(-0.787891\pi\)
−0.786076 + 0.618129i \(0.787891\pi\)
\(504\) 4.64164e15 0.0126146
\(505\) −4.87995e17 −1.30925
\(506\) 7.73179e15 0.0204787
\(507\) 1.22763e17 0.321009
\(508\) −3.60761e17 −0.931333
\(509\) 7.01987e16 0.178922 0.0894610 0.995990i \(-0.471486\pi\)
0.0894610 + 0.995990i \(0.471486\pi\)
\(510\) −1.36710e16 −0.0344028
\(511\) 5.13104e16 0.127488
\(512\) 2.84139e17 0.697069
\(513\) 1.05094e17 0.254574
\(514\) 7.21322e16 0.172532
\(515\) −3.89181e17 −0.919188
\(516\) 3.30790e17 0.771489
\(517\) 7.66227e16 0.176469
\(518\) −1.37428e15 −0.00312559
\(519\) 2.78246e15 0.00624945
\(520\) 6.35421e16 0.140942
\(521\) 6.14491e17 1.34608 0.673039 0.739607i \(-0.264989\pi\)
0.673039 + 0.739607i \(0.264989\pi\)
\(522\) −1.17460e16 −0.0254116
\(523\) −8.44488e16 −0.180440 −0.0902199 0.995922i \(-0.528757\pi\)
−0.0902199 + 0.995922i \(0.528757\pi\)
\(524\) 8.85521e17 1.86873
\(525\) −1.77604e16 −0.0370183
\(526\) −8.49834e16 −0.174955
\(527\) 2.37020e17 0.481966
\(528\) −6.19018e16 −0.124332
\(529\) −3.36862e17 −0.668328
\(530\) 3.10986e16 0.0609463
\(531\) −2.24165e16 −0.0433963
\(532\) −8.42294e16 −0.161079
\(533\) 2.55221e17 0.482159
\(534\) −7.02472e16 −0.131103
\(535\) 3.78081e17 0.697085
\(536\) −9.88399e15 −0.0180037
\(537\) 2.64604e17 0.476172
\(538\) 4.42641e15 0.00786985
\(539\) −1.29795e17 −0.227997
\(540\) 7.54704e16 0.130984
\(541\) 6.19069e17 1.06159 0.530795 0.847500i \(-0.321893\pi\)
0.530795 + 0.847500i \(0.321893\pi\)
\(542\) −8.35536e16 −0.141569
\(543\) −6.54740e17 −1.09615
\(544\) 1.50184e17 0.248445
\(545\) −2.48953e17 −0.406949
\(546\) −4.56031e15 −0.00736618
\(547\) −5.32724e17 −0.850325 −0.425162 0.905117i \(-0.639783\pi\)
−0.425162 + 0.905117i \(0.639783\pi\)
\(548\) 1.73504e17 0.273676
\(549\) 1.90914e17 0.297590
\(550\) −1.18680e16 −0.0182819
\(551\) 4.31444e17 0.656809
\(552\) 6.70639e16 0.100899
\(553\) −1.49800e17 −0.222740
\(554\) 1.44183e17 0.211885
\(555\) −4.52294e16 −0.0656926
\(556\) 2.04099e16 0.0292992
\(557\) 9.18552e17 1.30330 0.651651 0.758519i \(-0.274077\pi\)
0.651651 + 0.758519i \(0.274077\pi\)
\(558\) 3.15895e16 0.0443018
\(559\) −6.57835e17 −0.911885
\(560\) −5.89917e16 −0.0808293
\(561\) −5.49692e16 −0.0744493
\(562\) −9.79177e16 −0.131092
\(563\) −2.89698e17 −0.383391 −0.191695 0.981454i \(-0.561399\pi\)
−0.191695 + 0.981454i \(0.561399\pi\)
\(564\) 3.28341e17 0.429547
\(565\) 1.57675e17 0.203914
\(566\) −1.49651e17 −0.191326
\(567\) −1.09635e16 −0.0138567
\(568\) −2.43630e17 −0.304415
\(569\) −2.60065e17 −0.321257 −0.160628 0.987015i \(-0.551352\pi\)
−0.160628 + 0.987015i \(0.551352\pi\)
\(570\) 6.69254e16 0.0817343
\(571\) −1.01888e18 −1.23024 −0.615120 0.788434i \(-0.710892\pi\)
−0.615120 + 0.788434i \(0.710892\pi\)
\(572\) 1.26224e17 0.150684
\(573\) 8.03594e17 0.948487
\(574\) 1.18725e16 0.0138552
\(575\) −2.56608e17 −0.296093
\(576\) −2.51647e17 −0.287109
\(577\) −4.83795e17 −0.545781 −0.272891 0.962045i \(-0.587980\pi\)
−0.272891 + 0.962045i \(0.587980\pi\)
\(578\) −9.49701e16 −0.105939
\(579\) −4.71107e17 −0.519647
\(580\) 3.09831e17 0.337943
\(581\) −9.16121e16 −0.0988117
\(582\) −7.49772e16 −0.0799705
\(583\) 1.25043e17 0.131891
\(584\) 2.97400e17 0.310211
\(585\) −1.50086e17 −0.154820
\(586\) 4.63464e16 0.0472805
\(587\) 5.91386e17 0.596655 0.298327 0.954464i \(-0.403571\pi\)
0.298327 + 0.954464i \(0.403571\pi\)
\(588\) −5.56191e17 −0.554973
\(589\) −1.16032e18 −1.14506
\(590\) −1.42752e16 −0.0139330
\(591\) 2.81976e17 0.272204
\(592\) 1.58970e17 0.151783
\(593\) −7.32000e17 −0.691283 −0.345641 0.938367i \(-0.612339\pi\)
−0.345641 + 0.938367i \(0.612339\pi\)
\(594\) −7.32617e15 −0.00684329
\(595\) −5.23851e16 −0.0484002
\(596\) 1.96968e18 1.80010
\(597\) 6.81168e17 0.615773
\(598\) −6.58888e16 −0.0589188
\(599\) 7.83545e17 0.693090 0.346545 0.938033i \(-0.387355\pi\)
0.346545 + 0.938033i \(0.387355\pi\)
\(600\) −1.02941e17 −0.0900750
\(601\) −8.06682e17 −0.698262 −0.349131 0.937074i \(-0.613523\pi\)
−0.349131 + 0.937074i \(0.613523\pi\)
\(602\) −3.06014e16 −0.0262038
\(603\) 2.33459e16 0.0197765
\(604\) 3.44585e16 0.0288773
\(605\) −7.95658e17 −0.659655
\(606\) 2.02994e17 0.166499
\(607\) −2.22081e17 −0.180213 −0.0901064 0.995932i \(-0.528721\pi\)
−0.0901064 + 0.995932i \(0.528721\pi\)
\(608\) −7.35213e17 −0.590256
\(609\) −4.50089e16 −0.0357509
\(610\) 1.21577e17 0.0955451
\(611\) −6.52964e17 −0.507717
\(612\) −2.35552e17 −0.181219
\(613\) 1.04901e18 0.798521 0.399261 0.916837i \(-0.369267\pi\)
0.399261 + 0.916837i \(0.369267\pi\)
\(614\) −3.06231e17 −0.230651
\(615\) 3.90740e17 0.291206
\(616\) 1.18852e16 0.00876458
\(617\) −1.76568e18 −1.28842 −0.644212 0.764847i \(-0.722815\pi\)
−0.644212 + 0.764847i \(0.722815\pi\)
\(618\) 1.61890e17 0.116895
\(619\) −1.93516e18 −1.38270 −0.691351 0.722519i \(-0.742984\pi\)
−0.691351 + 0.722519i \(0.742984\pi\)
\(620\) −8.33254e17 −0.589157
\(621\) −1.58405e17 −0.110834
\(622\) −2.17703e16 −0.0150739
\(623\) −2.69176e17 −0.184444
\(624\) 5.27515e17 0.357713
\(625\) −3.30117e17 −0.221538
\(626\) −2.99123e17 −0.198663
\(627\) 2.69098e17 0.176877
\(628\) −2.63228e18 −1.71236
\(629\) 1.41166e17 0.0908871
\(630\) −6.98177e15 −0.00444889
\(631\) −2.49142e18 −1.57129 −0.785646 0.618676i \(-0.787669\pi\)
−0.785646 + 0.618676i \(0.787669\pi\)
\(632\) −8.68253e17 −0.541983
\(633\) 1.31194e18 0.810569
\(634\) −8.99285e16 −0.0549942
\(635\) 1.09838e18 0.664852
\(636\) 5.35831e17 0.321038
\(637\) 1.10608e18 0.655967
\(638\) −3.00764e16 −0.0176559
\(639\) 5.75452e17 0.334390
\(640\) −7.00976e17 −0.403212
\(641\) 1.72871e18 0.984338 0.492169 0.870500i \(-0.336204\pi\)
0.492169 + 0.870500i \(0.336204\pi\)
\(642\) −1.57273e17 −0.0886494
\(643\) −2.00421e18 −1.11834 −0.559168 0.829054i \(-0.688879\pi\)
−0.559168 + 0.829054i \(0.688879\pi\)
\(644\) 1.26957e17 0.0701290
\(645\) −1.00713e18 −0.550744
\(646\) −2.08882e17 −0.113081
\(647\) −3.24266e18 −1.73790 −0.868949 0.494902i \(-0.835204\pi\)
−0.868949 + 0.494902i \(0.835204\pi\)
\(648\) −6.35457e16 −0.0337170
\(649\) −5.73986e16 −0.0301516
\(650\) 1.01137e17 0.0525986
\(651\) 1.21046e17 0.0623268
\(652\) −2.55601e18 −1.30303
\(653\) −5.12082e17 −0.258466 −0.129233 0.991614i \(-0.541252\pi\)
−0.129233 + 0.991614i \(0.541252\pi\)
\(654\) 1.03558e17 0.0517523
\(655\) −2.69609e18 −1.33403
\(656\) −1.37335e18 −0.672833
\(657\) −7.02457e17 −0.340757
\(658\) −3.03748e16 −0.0145897
\(659\) −1.67138e18 −0.794916 −0.397458 0.917620i \(-0.630108\pi\)
−0.397458 + 0.917620i \(0.630108\pi\)
\(660\) 1.93246e17 0.0910071
\(661\) −2.13110e18 −0.993791 −0.496896 0.867810i \(-0.665527\pi\)
−0.496896 + 0.867810i \(0.665527\pi\)
\(662\) −2.99735e17 −0.138408
\(663\) 4.68437e17 0.214197
\(664\) −5.30992e17 −0.240434
\(665\) 2.56448e17 0.114989
\(666\) 1.88144e16 0.00835424
\(667\) −6.50304e17 −0.285955
\(668\) 4.22131e18 1.83823
\(669\) 9.62475e17 0.415068
\(670\) 1.48671e16 0.00634951
\(671\) 4.88846e17 0.206764
\(672\) 7.66987e16 0.0321283
\(673\) −6.50658e17 −0.269933 −0.134966 0.990850i \(-0.543093\pi\)
−0.134966 + 0.990850i \(0.543093\pi\)
\(674\) −5.44539e17 −0.223738
\(675\) 2.43146e17 0.0989446
\(676\) 1.34701e18 0.542897
\(677\) 6.36618e17 0.254128 0.127064 0.991895i \(-0.459445\pi\)
0.127064 + 0.991895i \(0.459445\pi\)
\(678\) −6.55889e16 −0.0259321
\(679\) −2.87301e17 −0.112508
\(680\) −3.03629e17 −0.117770
\(681\) 2.39200e18 0.918977
\(682\) 8.08868e16 0.0307808
\(683\) 1.95336e18 0.736288 0.368144 0.929769i \(-0.379993\pi\)
0.368144 + 0.929769i \(0.379993\pi\)
\(684\) 1.15313e18 0.430540
\(685\) −5.28257e17 −0.195369
\(686\) 1.03719e17 0.0379973
\(687\) −1.40715e18 −0.510647
\(688\) 3.53983e18 1.27250
\(689\) −1.06559e18 −0.379461
\(690\) −1.00875e17 −0.0355847
\(691\) −4.60580e17 −0.160952 −0.0804762 0.996757i \(-0.525644\pi\)
−0.0804762 + 0.996757i \(0.525644\pi\)
\(692\) 3.05303e16 0.0105692
\(693\) −2.80728e16 −0.00962762
\(694\) 4.02034e17 0.136592
\(695\) −6.21408e16 −0.0209158
\(696\) −2.60876e17 −0.0869910
\(697\) −1.21955e18 −0.402889
\(698\) 4.25539e17 0.139277
\(699\) 6.41045e17 0.207867
\(700\) −1.94874e17 −0.0626062
\(701\) 2.44325e18 0.777679 0.388839 0.921306i \(-0.372876\pi\)
0.388839 + 0.921306i \(0.372876\pi\)
\(702\) 6.24323e16 0.0196887
\(703\) −6.91071e17 −0.215930
\(704\) −6.44357e17 −0.199482
\(705\) −9.99678e17 −0.306641
\(706\) 1.44064e17 0.0437848
\(707\) 7.77842e17 0.234242
\(708\) −2.45963e17 −0.0733927
\(709\) −2.57462e18 −0.761223 −0.380612 0.924735i \(-0.624287\pi\)
−0.380612 + 0.924735i \(0.624287\pi\)
\(710\) 3.66458e17 0.107361
\(711\) 2.05081e18 0.595351
\(712\) −1.56017e18 −0.448799
\(713\) 1.74891e18 0.498525
\(714\) 2.17909e16 0.00615513
\(715\) −3.84304e17 −0.107569
\(716\) 2.90335e18 0.805312
\(717\) −3.65471e18 −1.00456
\(718\) 3.80924e17 0.103760
\(719\) −4.51699e18 −1.21930 −0.609652 0.792669i \(-0.708691\pi\)
−0.609652 + 0.792669i \(0.708691\pi\)
\(720\) 8.07617e17 0.216045
\(721\) 6.20337e17 0.164455
\(722\) 4.38179e17 0.115122
\(723\) 3.23444e18 0.842172
\(724\) −7.18408e18 −1.85383
\(725\) 9.98194e17 0.255281
\(726\) 3.30975e17 0.0838894
\(727\) −2.38548e18 −0.599242 −0.299621 0.954058i \(-0.596860\pi\)
−0.299621 + 0.954058i \(0.596860\pi\)
\(728\) −1.01283e17 −0.0252164
\(729\) 1.50095e17 0.0370370
\(730\) −4.47337e17 −0.109405
\(731\) 3.14339e18 0.761965
\(732\) 2.09479e18 0.503290
\(733\) −6.68849e16 −0.0159277 −0.00796383 0.999968i \(-0.502535\pi\)
−0.00796383 + 0.999968i \(0.502535\pi\)
\(734\) 9.68208e17 0.228531
\(735\) 1.69340e18 0.396179
\(736\) 1.10817e18 0.256980
\(737\) 5.97786e16 0.0137406
\(738\) −1.62538e17 −0.0370331
\(739\) 1.73606e18 0.392080 0.196040 0.980596i \(-0.437192\pi\)
0.196040 + 0.980596i \(0.437192\pi\)
\(740\) −4.96276e17 −0.111101
\(741\) −2.29320e18 −0.508890
\(742\) −4.95697e16 −0.0109041
\(743\) −8.45764e18 −1.84426 −0.922130 0.386880i \(-0.873553\pi\)
−0.922130 + 0.386880i \(0.873553\pi\)
\(744\) 7.01595e17 0.151657
\(745\) −5.99696e18 −1.28504
\(746\) −2.66430e17 −0.0565953
\(747\) 1.25420e18 0.264109
\(748\) −6.03145e17 −0.125910
\(749\) −6.02645e17 −0.124718
\(750\) 4.56006e17 0.0935562
\(751\) 3.98471e18 0.810471 0.405235 0.914212i \(-0.367190\pi\)
0.405235 + 0.914212i \(0.367190\pi\)
\(752\) 3.51362e18 0.708497
\(753\) 4.26106e18 0.851826
\(754\) 2.56305e17 0.0507976
\(755\) −1.04913e17 −0.0206146
\(756\) −1.20296e17 −0.0234348
\(757\) 8.08563e18 1.56168 0.780838 0.624734i \(-0.214793\pi\)
0.780838 + 0.624734i \(0.214793\pi\)
\(758\) 7.16181e17 0.137143
\(759\) −4.05604e17 −0.0770071
\(760\) 1.48639e18 0.279799
\(761\) −3.24162e18 −0.605008 −0.302504 0.953148i \(-0.597823\pi\)
−0.302504 + 0.953148i \(0.597823\pi\)
\(762\) −4.56901e17 −0.0845503
\(763\) 3.96819e17 0.0728087
\(764\) 8.81736e18 1.60410
\(765\) 7.17170e17 0.129367
\(766\) −6.87486e17 −0.122964
\(767\) 4.89140e17 0.0867488
\(768\) −2.53625e18 −0.446009
\(769\) −7.85230e18 −1.36923 −0.684614 0.728906i \(-0.740029\pi\)
−0.684614 + 0.728906i \(0.740029\pi\)
\(770\) −1.78772e16 −0.00309108
\(771\) −3.78400e18 −0.648781
\(772\) −5.16918e18 −0.878838
\(773\) −2.39859e18 −0.404379 −0.202190 0.979346i \(-0.564806\pi\)
−0.202190 + 0.979346i \(0.564806\pi\)
\(774\) 4.18944e17 0.0700390
\(775\) −2.68452e18 −0.445047
\(776\) −1.66522e18 −0.273761
\(777\) 7.20937e16 0.0117533
\(778\) −1.73624e18 −0.280700
\(779\) 5.97021e18 0.957185
\(780\) −1.64681e18 −0.261835
\(781\) 1.47348e18 0.232334
\(782\) 3.14842e17 0.0492322
\(783\) 6.16188e17 0.0955569
\(784\) −5.95187e18 −0.915374
\(785\) 8.01432e18 1.22240
\(786\) 1.12151e18 0.169651
\(787\) 9.20950e18 1.38166 0.690829 0.723019i \(-0.257246\pi\)
0.690829 + 0.723019i \(0.257246\pi\)
\(788\) 3.09396e18 0.460357
\(789\) 4.45817e18 0.657894
\(790\) 1.30599e18 0.191146
\(791\) −2.51326e17 −0.0364830
\(792\) −1.62712e17 −0.0234265
\(793\) −4.16586e18 −0.594879
\(794\) 3.51680e17 0.0498097
\(795\) −1.63141e18 −0.229180
\(796\) 7.47405e18 1.04141
\(797\) 1.04263e19 1.44096 0.720480 0.693476i \(-0.243921\pi\)
0.720480 + 0.693476i \(0.243921\pi\)
\(798\) −1.06676e17 −0.0146234
\(799\) 3.12012e18 0.424245
\(800\) −1.70100e18 −0.229414
\(801\) 3.68512e18 0.492992
\(802\) 1.42829e18 0.189533
\(803\) −1.79868e18 −0.236757
\(804\) 2.56161e17 0.0334464
\(805\) −3.86536e17 −0.0500630
\(806\) −6.89302e17 −0.0885588
\(807\) −2.32206e17 −0.0295934
\(808\) 4.50844e18 0.569971
\(809\) −2.88620e18 −0.361961 −0.180980 0.983487i \(-0.557927\pi\)
−0.180980 + 0.983487i \(0.557927\pi\)
\(810\) 9.55828e16 0.0118912
\(811\) −4.80075e18 −0.592480 −0.296240 0.955114i \(-0.595733\pi\)
−0.296240 + 0.955114i \(0.595733\pi\)
\(812\) −4.93857e17 −0.0604626
\(813\) 4.38316e18 0.532352
\(814\) 4.81752e16 0.00580450
\(815\) 7.78211e18 0.930192
\(816\) −2.52067e18 −0.298903
\(817\) −1.53882e19 −1.81028
\(818\) 9.69878e17 0.113193
\(819\) 2.39231e17 0.0276995
\(820\) 4.28736e18 0.492493
\(821\) 7.45932e18 0.850097 0.425049 0.905171i \(-0.360257\pi\)
0.425049 + 0.905171i \(0.360257\pi\)
\(822\) 2.19742e17 0.0248454
\(823\) −2.96531e18 −0.332637 −0.166319 0.986072i \(-0.553188\pi\)
−0.166319 + 0.986072i \(0.553188\pi\)
\(824\) 3.59553e18 0.400162
\(825\) 6.22588e17 0.0687465
\(826\) 2.27540e16 0.00249280
\(827\) −1.18918e19 −1.29259 −0.646297 0.763086i \(-0.723683\pi\)
−0.646297 + 0.763086i \(0.723683\pi\)
\(828\) −1.73808e18 −0.187445
\(829\) −1.07442e17 −0.0114966 −0.00574828 0.999983i \(-0.501830\pi\)
−0.00574828 + 0.999983i \(0.501830\pi\)
\(830\) 7.98697e17 0.0847958
\(831\) −7.56374e18 −0.796764
\(832\) 5.49109e18 0.573927
\(833\) −5.28530e18 −0.548122
\(834\) 2.58491e16 0.00265990
\(835\) −1.28523e19 −1.31226
\(836\) 2.95265e18 0.299138
\(837\) −1.65716e18 −0.166591
\(838\) −4.53562e17 −0.0452430
\(839\) 1.14969e19 1.13796 0.568980 0.822351i \(-0.307338\pi\)
0.568980 + 0.822351i \(0.307338\pi\)
\(840\) −1.55063e17 −0.0152298
\(841\) −7.73097e18 −0.753460
\(842\) 3.99956e17 0.0386798
\(843\) 5.13669e18 0.492952
\(844\) 1.43952e19 1.37085
\(845\) −4.10115e18 −0.387559
\(846\) 4.15842e17 0.0389961
\(847\) 1.26824e18 0.118021
\(848\) 5.73399e18 0.529522
\(849\) 7.85059e18 0.719453
\(850\) −4.83272e17 −0.0439510
\(851\) 1.04163e18 0.0940096
\(852\) 6.31410e18 0.565528
\(853\) −1.05334e19 −0.936263 −0.468132 0.883659i \(-0.655073\pi\)
−0.468132 + 0.883659i \(0.655073\pi\)
\(854\) −1.93789e17 −0.0170943
\(855\) −3.51086e18 −0.307350
\(856\) −3.49299e18 −0.303471
\(857\) −1.72922e19 −1.49099 −0.745496 0.666510i \(-0.767787\pi\)
−0.745496 + 0.666510i \(0.767787\pi\)
\(858\) 1.59861e17 0.0136797
\(859\) −8.32639e18 −0.707134 −0.353567 0.935409i \(-0.615031\pi\)
−0.353567 + 0.935409i \(0.615031\pi\)
\(860\) −1.10507e19 −0.931429
\(861\) −6.22822e17 −0.0521007
\(862\) 2.09080e18 0.173586
\(863\) 2.25124e19 1.85504 0.927518 0.373778i \(-0.121938\pi\)
0.927518 + 0.373778i \(0.121938\pi\)
\(864\) −1.05003e18 −0.0858743
\(865\) −9.29536e16 −0.00754504
\(866\) −1.85270e18 −0.149258
\(867\) 4.98206e18 0.398369
\(868\) 1.32817e18 0.105408
\(869\) 5.25122e18 0.413648
\(870\) 3.92399e17 0.0306798
\(871\) −5.09422e17 −0.0395330
\(872\) 2.30000e18 0.177162
\(873\) 3.93325e18 0.300718
\(874\) −1.54129e18 −0.116966
\(875\) 1.74734e18 0.131621
\(876\) −7.70765e18 −0.576295
\(877\) 1.31518e19 0.976085 0.488043 0.872820i \(-0.337711\pi\)
0.488043 + 0.872820i \(0.337711\pi\)
\(878\) −1.15414e18 −0.0850248
\(879\) −2.43130e18 −0.177791
\(880\) 2.06795e18 0.150108
\(881\) −8.20418e18 −0.591142 −0.295571 0.955321i \(-0.595510\pi\)
−0.295571 + 0.955321i \(0.595510\pi\)
\(882\) −7.04413e17 −0.0503827
\(883\) −9.12088e18 −0.647578 −0.323789 0.946129i \(-0.604957\pi\)
−0.323789 + 0.946129i \(0.604957\pi\)
\(884\) 5.13988e18 0.362254
\(885\) 7.48866e17 0.0523929
\(886\) 3.40270e18 0.236322
\(887\) 2.61506e19 1.80293 0.901463 0.432856i \(-0.142494\pi\)
0.901463 + 0.432856i \(0.142494\pi\)
\(888\) 4.17862e17 0.0285988
\(889\) −1.75077e18 −0.118951
\(890\) 2.34675e18 0.158282
\(891\) 3.84326e17 0.0257332
\(892\) 1.05607e19 0.701972
\(893\) −1.52743e19 −1.00792
\(894\) 2.49459e18 0.163420
\(895\) −8.83962e18 −0.574889
\(896\) 1.11732e18 0.0721401
\(897\) 3.45648e18 0.221556
\(898\) 2.22073e18 0.141319
\(899\) −6.80321e18 −0.429809
\(900\) 2.66790e18 0.167337
\(901\) 5.09182e18 0.317075
\(902\) −4.16189e17 −0.0257305
\(903\) 1.60533e18 0.0985357
\(904\) −1.45671e18 −0.0887725
\(905\) 2.18729e19 1.32340
\(906\) 4.36414e16 0.00262160
\(907\) 1.77331e19 1.05764 0.528819 0.848735i \(-0.322635\pi\)
0.528819 + 0.848735i \(0.322635\pi\)
\(908\) 2.62460e19 1.55419
\(909\) −1.06489e19 −0.626096
\(910\) 1.52346e17 0.00889329
\(911\) −2.37437e19 −1.37619 −0.688096 0.725620i \(-0.741553\pi\)
−0.688096 + 0.725620i \(0.741553\pi\)
\(912\) 1.23398e19 0.710135
\(913\) 3.21145e18 0.183502
\(914\) 2.71825e18 0.154219
\(915\) −6.37786e18 −0.359284
\(916\) −1.54398e19 −0.863617
\(917\) 4.29744e18 0.238676
\(918\) −2.98325e17 −0.0164518
\(919\) −2.62075e19 −1.43507 −0.717537 0.696520i \(-0.754731\pi\)
−0.717537 + 0.696520i \(0.754731\pi\)
\(920\) −2.24040e18 −0.121816
\(921\) 1.60647e19 0.867329
\(922\) 1.72100e18 0.0922635
\(923\) −1.25567e19 −0.668443
\(924\) −3.08026e17 −0.0162824
\(925\) −1.59887e18 −0.0839251
\(926\) −4.60458e18 −0.240004
\(927\) −8.49263e18 −0.439566
\(928\) −4.31073e18 −0.221559
\(929\) 3.15412e19 1.60982 0.804908 0.593400i \(-0.202215\pi\)
0.804908 + 0.593400i \(0.202215\pi\)
\(930\) −1.05531e18 −0.0534861
\(931\) 2.58738e19 1.30223
\(932\) 7.03380e18 0.351550
\(933\) 1.14205e18 0.0566834
\(934\) −1.94981e18 −0.0961034
\(935\) 1.83635e18 0.0898837
\(936\) 1.38660e18 0.0673999
\(937\) 1.49625e19 0.722268 0.361134 0.932514i \(-0.382390\pi\)
0.361134 + 0.932514i \(0.382390\pi\)
\(938\) −2.36975e16 −0.00113601
\(939\) 1.56918e19 0.747044
\(940\) −1.09689e19 −0.518598
\(941\) 9.51121e18 0.446584 0.223292 0.974752i \(-0.428320\pi\)
0.223292 + 0.974752i \(0.428320\pi\)
\(942\) −3.33376e18 −0.155455
\(943\) −8.99873e18 −0.416730
\(944\) −2.63207e18 −0.121054
\(945\) 3.66258e17 0.0167294
\(946\) 1.07273e18 0.0486629
\(947\) −8.69870e18 −0.391904 −0.195952 0.980613i \(-0.562780\pi\)
−0.195952 + 0.980613i \(0.562780\pi\)
\(948\) 2.25023e19 1.00687
\(949\) 1.53280e19 0.681170
\(950\) 2.36583e18 0.104419
\(951\) 4.71758e18 0.206798
\(952\) 4.83971e17 0.0210707
\(953\) 1.69864e18 0.0734509 0.0367254 0.999325i \(-0.488307\pi\)
0.0367254 + 0.999325i \(0.488307\pi\)
\(954\) 6.78627e17 0.0291452
\(955\) −2.68456e19 −1.14512
\(956\) −4.01009e19 −1.69894
\(957\) 1.57778e18 0.0663927
\(958\) −2.10955e18 −0.0881685
\(959\) 8.42017e17 0.0349543
\(960\) 8.40677e18 0.346630
\(961\) −6.12112e18 −0.250685
\(962\) −4.10540e17 −0.0167000
\(963\) 8.25042e18 0.333354
\(964\) 3.54896e19 1.42430
\(965\) 1.57382e19 0.627377
\(966\) 1.60790e17 0.00636660
\(967\) −2.88013e19 −1.13277 −0.566383 0.824142i \(-0.691658\pi\)
−0.566383 + 0.824142i \(0.691658\pi\)
\(968\) 7.35086e18 0.287176
\(969\) 1.09578e19 0.425225
\(970\) 2.50476e18 0.0965495
\(971\) 1.27392e19 0.487771 0.243885 0.969804i \(-0.421578\pi\)
0.243885 + 0.969804i \(0.421578\pi\)
\(972\) 1.64690e18 0.0626378
\(973\) 9.90496e16 0.00374213
\(974\) 6.80697e18 0.255459
\(975\) −5.30558e18 −0.197789
\(976\) 2.24166e19 0.830128
\(977\) −3.69962e19 −1.36095 −0.680475 0.732771i \(-0.738227\pi\)
−0.680475 + 0.732771i \(0.738227\pi\)
\(978\) −3.23717e18 −0.118294
\(979\) 9.43595e18 0.342530
\(980\) 1.85807e19 0.670026
\(981\) −5.43260e18 −0.194607
\(982\) −3.95891e18 −0.140880
\(983\) 3.51146e19 1.24134 0.620669 0.784072i \(-0.286861\pi\)
0.620669 + 0.784072i \(0.286861\pi\)
\(984\) −3.60993e18 −0.126774
\(985\) −9.41997e18 −0.328635
\(986\) −1.22472e18 −0.0424462
\(987\) 1.59344e18 0.0548624
\(988\) −2.51620e19 −0.860645
\(989\) 2.31943e19 0.788143
\(990\) 2.44745e17 0.00826200
\(991\) −1.08227e19 −0.362957 −0.181478 0.983395i \(-0.558088\pi\)
−0.181478 + 0.983395i \(0.558088\pi\)
\(992\) 1.15932e19 0.386258
\(993\) 1.57239e19 0.520462
\(994\) −5.84117e17 −0.0192083
\(995\) −2.27557e19 −0.743431
\(996\) 1.37616e19 0.446667
\(997\) −2.95468e19 −0.952777 −0.476389 0.879235i \(-0.658054\pi\)
−0.476389 + 0.879235i \(0.658054\pi\)
\(998\) 7.85569e18 0.251673
\(999\) −9.86987e17 −0.0314149
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.1.16 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.16 31 1.1 even 1 trivial