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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '704992717552055982,1965240550868099478', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8363129704525103, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [5, [1, -2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '28800.1', 'coefficient_field': '1.1.1.1', 'conductor': 28800, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, -2, 1], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, -12, 62, -156, 169], [1, 12, 70, 204, 289], [1, 0, 22, 0, 361], [1, 0, 46, 0, 529], [1, 4, 62, 116, 841], [1, 0, -2, 0, 961], [1, 4, 78, 148, 1369], [1, 12, 118, 492, 1681], [1, 0, -58, 0, 1849], [1, 0, 30, 0, 2209], [1, -12, 142, -636, 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4.09246126419776, 3.654324021382666, 2.910939262473485, 1.9979689386096249, 1.0663208428724864, 0.25627322660109114], 'positive_zeros': ['1.48909737355432343830877670543927', '2.25002432004047770108316173263348', '3.57148112685573562185271725821457', '3.95303834850677407956821293661618', '4.86312932086210572949074191290916', '5.59585158632682227968586342616249', '6.23234003008114203357336027650771', '6.71560882928791827542770443897278', '6.89270810769313104844169224864906', '8.323057177226078640880314002796256', '8.372242663067272040741337380641278', '9.042960162718976648409639393559621', '9.234498555197333169762430563635700', '10.28908580294693488189641431265866', '10.45550448318589263597286780431456'], 'prelabel': '4-28800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1640903135037528, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8363129704525103, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 28800, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 12, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -12, 0, 0, 0, 2, 0, 0, 0, -14, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -24, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, -12, 62, -156, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, -58, 0, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, -28, 318, -1708, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, -2, 1, 0, 0], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, -12, 62, -156, 169], [1, 12, 70, 204, 289], [1, 0, 22, 0, 361], [1, 0, 46, 0, 529], [1, 4, 62, 116, 841], [1, 0, -2, 0, 961], [1, 4, 78, 148, 1369], [1, 12, 118, 492, 1681], [1, 0, -58, 0, 1849], [1, 0, 30, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, -26, 0, 3481], [1, -28, 318, -1708, 3721], [1, 0, 118, 0, 4489], [1, 0, 78, 0, 5041], [1, 12, 182, 876, 5329], [1, 0, 94, 0, 6241], [1, 0, 22, 0, 6889], [1, -20, 278, -1780, 7921], [1, -4, 198, -388, 9409]], 'index': 6, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/1800.2/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/1800.2/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-28800-1.1-c1e2-0-6', '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': 0, 'prelabel': '4-28800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1640903135037528, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 364390259206461509, 'z1': {'__RealLiteral__': 0, 'data': '1.48909737355432343830877670543927', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9655104
{'Lhash': '704992717552055982,1965240550868099478', 'Lhash_array': ['704992717552055982', '1965240550868099478'], 'label': '4-28800-1.1-c1e2-0-6', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/1800.2/b'}
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id: 9655102
{'Lhash': '704992717552055982,1965240550868099478', 'Lhash_array': ['704992717552055982', '1965240550868099478'], 'label': '4-28800-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/1800.2/b'}