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lfunc_lfunctions • Show schema
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{'Lhash': '1437467794194007769681193378418,1657767198899171695680318234819', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3879.2111500809283, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': '1.1.1.1', 'conductor': 60840000, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1], [1, 0, 11, 0, 49], [1, 0, 19, 0, 121], [1, -2, 1], [1, -2, 23, -34, 289], [1, 0, 26, 0, 361], [1, -4, 50, -92, 529], [1, 6, 19, 174, 841], [1, 8, 51, 248, 961], [1, 8, 78, 296, 1369], [1, 12, 106, 492, 1681], [1, -4, 42, -172, 1849], [1, -4, 23, -188, 2209], [1, 10, 83, 530, 2809], [1, 0, 115, 0, 3481], [1, 18, 191, 1098, 3721], [1, -12, 167, -804, 4489], [1, 8, 50, 568, 5041], [1, 0, 134, 0, 5329], [1, -28, 354, 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-0.07121208685873019], 'positive_zeros': ['1.13396214535393606718377049988381', '1.30774773316930170918581049325016', '2.02799230339822298338267029123828', '2.18451649306526216421977700908429', '3.17881188964903888592991475724580', '3.41146935699955689089799673478894', '3.62723902045274175384313069552360', '4.09700886591462600377067140389687', '4.70025430564873472196244825206688', '5.01989992191009929941349411432761', '5.31491076838419690578177269877877', '5.35686278140064492046068272777646', '6.09505813854917591311812753508338', '6.26769544841163805648943098354467', '6.62905062643755033230210897923610', '6.79711989034078450914933996567235', '7.46911026185656772871379418515385', '7.52846404653819358300152975543342'], 'prelabel': '4-7800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 648825095485054709, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13396214535393606718377049988', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.30774773316930170918581049325', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.02799230339822298338267029124', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3879.2111500809283, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 60840000, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, -6, 0, -8, 0, 0, 0, 0, 0, -8, 0, -4, 0, -12, 0, 4, 0, 0, 0, 4, 0, -11, 0, -4, 0, -10, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 12, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 28, 0, 5, 0, 24, 0, 0, 0, 12, 0, 8, 0, 0, 0, 16, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, 19, 0, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, -2, 23, -34, 289], 'euler19': [1, 0, 26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 50, -92, 529], 'euler29': [1, 6, 19, 174, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 8, 51, 248, 961], 'euler37': [1, 8, 78, 296, 1369], 'euler41': [1, 12, 106, 492, 1681], 'euler43': [1, -4, 42, -172, 1849], 'euler47': [1, -4, 23, -188, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 10, 83, 530, 2809], 'euler59': [1, 0, 115, 0, 3481], 'euler61': [1, 18, 191, 1098, 3721], 'euler67': [1, -12, 167, -804, 4489], 'euler7': [1, 0, 11, 0, 49], 'euler71': [1, 8, 50, 568, 5041], 'euler73': [1, 0, 134, 0, 5329], 'euler79': [1, -28, 354, -2212, 6241], 'euler83': [1, -24, 307, -1992, 6889], 'euler89': [1, -8, 146, -712, 7921], 'euler97': [1, 4, 150, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 11, 0, 49], [1, 0, 19, 0, 121], [1, -2, 1, 0, 0], [1, -2, 23, -34, 289], [1, 0, 26, 0, 361], [1, -4, 50, -92, 529], [1, 6, 19, 174, 841], [1, 8, 51, 248, 961], [1, 8, 78, 296, 1369], [1, 12, 106, 492, 1681], [1, -4, 42, -172, 1849], [1, -4, 23, -188, 2209], [1, 10, 83, 530, 2809], [1, 0, 115, 0, 3481], [1, 18, 191, 1098, 3721], [1, -12, 167, -804, 4489], [1, 8, 50, 568, 5041], [1, 0, 134, 0, 5329], [1, -28, 354, -2212, 6241], [1, -24, 307, -1992, 6889], [1, -8, 146, -712, 7921], [1, 4, 150, 388, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/y'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '4-7800e2-1.1-c1e2-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-7800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 648825095485054709, 'z1': {'__RealLiteral__': 0, 'data': '1.13396214535393606718377049988', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1437467794194007769681193378418,1657767198899171695680318234819', 'Lhash_array': ['1437467794194007769681193378418', '1657767198899171695680318234819'], 'label': '4-7800e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/y'}