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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -3, 'Lhash': '102675815176746750', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 3008.5076268753783, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [29, [1]]], 'bad_primes': [2, 7, 29], 'central_character': '376768.1', 'coefficient_field': '1.1.1.1', 'conductor': 376768, 'conductor_radical': 406, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, -2, 5], [1, -1], [1, 4, 11], [1, -2, 13], [1, 6, 17], [1, 0, 19], [1, -8, 23], [1], [1, 4, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 4, 47], [1, 6, 53], [1, -4, 59], [1, 14, 61], [1, 4, 67], [1, 0, 71], [1, 14, 73], [1, -16, 79], [1, -4, 83], [1, -2, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-376768-1.1-c1-0-12', 'leading_term': '1.23639857322', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/376768/bv', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.236398573217022, 0.2401493867246506, -1.893342522618019, -3.068664395959946, -1.741889751609571, 1.023154070324605, 2.28021322902826, 0.8782555190432075, -0.757533560925369, -0.08502768181793013, 1.563618446341109, 1.245407858314669, -0.08679682581115807, 1.387312552499068, 5.185985737365535, 5.705178356869848, 1.07496802349492, -2.827309180367545, -1.378643082762716, 1.589459245523531, 1.128731417064294, -0.4337666979766603, 0.6427697815213944, 1.731356191691477, -0.07796521418841754, -1.09710579967981, 1.191838611735222, 1.646046868767304, -2.367598062612172, -4.196996528700069, -0.3267432034065121, 2.251841331417456, 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-0.6259637121388507, 0.9090372717583689, -0.9667111694943137, -2.131882934395982, 0.09758200419083796, -1.42576809334296, -3.573877968506458, 0.08517131161009642, 1.292466797780607, -2.285680643803291, -0.7103005827075711, 2.580571429522148, 0.4031499328433596, 0.5493928432693269, 3.476369055948531, 0.01316316113255882, -3.212270820590798, 0.7656798809014427, 2.277002247893163, -0.212423528387483, 0.472192669543363, -0.06504461981365292, -2.670750751937919, -0.3242870315365837, 1.526032165073693, -0.4926915255769526, 2.64787320203198, 5.898713749665077, 0.137729881033413, -2.594573273000377, 2.823057592390949, 3.342403337334035, -0.0239977534450609, 0.5953910787512439, 0.4681884449269258, -0.2441473672132572, 0.3249914815716998, -5.554154585138368, -11.94424783665069], 'positive_zeros': ['0.2812869892976576', '1.156216765399246', '1.856815968894540', '2.262198118908480', '2.966418596894725', '3.092918875590845', '4.049426953811045', '4.598505865788083', '5.145665162838792', '5.411764267221138', '5.991865522120798', '6.391321960482400', '6.870594185289672', '7.517395283386485', '7.976140632347539', '8.421781414049674', '8.908790712103477', '9.334564193367867', '9.559153259003941', '10.54971713986259', '10.66602913519293', '10.99400310314412', '11.49515464978938', '11.94772316648360', '12.60656320147963', '13.16460878659966', '13.40800764342788', '13.53877349045178', '14.21131225741979', '14.82176369603894', '14.88321042912819', '15.59712799768718', '15.82574860060005', '16.53002020535786', '16.80441886752546', '17.32814017831660', '17.71818109158771', '17.95125618031135', '18.36794825352434', '18.84358064683727', '19.32605270656466', '19.79643534562589'], 'prelabel': '2-376768-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.849864419845, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 102675815176746750, 'z1': {'__RealLiteral__': 0, 'data': '0.2812869892976576', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.156216765399246', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.856815968894540', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3008.5076268753783, 'bad_primes': [2, 7, 29], 'central_character': '1.1', 'conductor': 376768, 'conductor_radical': 406, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 1, 0, -3, 0, -4, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 8, 0, -1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 6, 0, 0, 0, -6, 0, 4, 0, -6, 0, -4, 0, 1, 0, 0, 0, -6, 0, -8, 0, 0, 0, 4, 0, -14, 0, -3, 0, 4, 0, -4, 0, 0, 0, 0, 0, -14, 0, 0, 0, -4, 0, 16, 0, 9, 0, 4, 0, -12, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -6, 0, 12, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 0, 0], 'euler3': [1, 0, 3], 'euler31': [1, 4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 14, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, -16, 79], 'euler83': [1, -4, 83], 'euler89': [1, -2, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, -2, 5], [1, -1, 0], [1, 4, 11], [1, -2, 13], [1, 6, 17], [1, 0, 19], [1, -8, 23], [1, 0, 0], [1, 4, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 4, 47], [1, 6, 53], [1, -4, 59], [1, 14, 61], [1, 4, 67], [1, 0, 71], [1, 14, 73], [1, -16, 79], [1, -4, 83], [1, -2, 89], [1, 6, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/376768/bv'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-376768-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-376768-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.849864419845, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 102675815176746750, 'z1': {'__RealLiteral__': 0, 'data': '0.2812869892976576', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '102675815176746750', 'Lhash_array': ['102675815176746750'], 'label': '2-376768-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/376768/bv'}