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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': -3, 'Lhash': '918178094025847143935010037092', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.14677389390195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, 0, 3]], [5, [1, 0, 1]], [31, [1, -4, 31]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '864900.1', 'coefficient_field': '1.1.1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 0, 3], [1, 0, 1], [1, -4, 18, -28, 49], [1, 0, -14, 0, 121], [1, 0, 10, 0, 169], [1, 0, -2, 0, 289], [1, -8, 54, -152, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, -4, 31], [1, 0, 10, 0, 1369], [1, 0, -82, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, -82, 0, 3481], [1, 0, 118, 0, 3721], [1, -8, 150, -536, 4489], [1, 0, 2, 0, 5041], [1, 0, 46, 0, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, 34, 0, 7921], [1, -4, 198, -388, 9409], [1, 0, -166, 0, 10201], [1, 4, 210, 412, 10609], [1, 0, -70, 0, 11449], [1, -4, 222, -436, 11881], [1, 0, -190, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 9, 'label': '4-930e2-1.1-c1e2-0-9', 'leading_term': '2.02592057115', 'load_key': 'Costa', '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, 'origin': 'EllipticCurve/2.2.93.1/100.1/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [2.0259205711522044, 2.017370378805649, 1.9915937526876746, 1.9482270817820426, 1.8867122668292056, 1.806366722186691, 1.7064776111556534, 1.586416523560832, 1.4457697069478084, 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-1.8013914341680128, -2.4053172739794304, -2.6536532971420224, -2.474676491788423, -1.8521719992444539, -0.8310483598331092], 'positive_zeros': ['0.72431480240733306960638962230700', '1.50574124793191160132132115874504', '2.20362344885623521787041062141392', '3.00500477363704398491710942833776', '3.35740457877933336906110113086533', '4.09093799859713103651942115756660', '4.64916903785667003185273060010253', '5.05437751319379347313758860174276', '5.38632415451667964893247277298149', '5.80525900757485624726555403645701', '6.36983599610703647960989892450309', '6.95166010100213944744151041617204', '7.49141713873053479915595282433884', '7.903750616970958376074875267978011', '8.166675189137703019004001484922957'], 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 337023732005428970, 'z1': {'__RealLiteral__': 0, 'data': '0.72431480240733306960638962230700', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.50574124793191160132132115874504', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.20362344885623521787041062141392', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.14677389390195, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 4, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 8, 0, 0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1], 'euler11': [1, 0, -14, 0, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, -4, 31, 0, 0], 'euler37': [1, 0, 10, 0, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, -94, 0, 2209], 'euler5': [1, 0, 1, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, -82, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, -8, 150, -536, 4489], 'euler7': [1, -4, 18, -28, 49], 'euler71': [1, 0, 2, 0, 5041], 'euler73': [1, 0, 46, 0, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 34, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 3, 0, 0], [1, 0, 1, 0, 0], [1, -4, 18, -28, 49], [1, 0, -14, 0, 121], [1, 0, 10, 0, 169], [1, 0, -2, 0, 289], [1, -8, 54, -152, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, -4, 31, 0, 0], [1, 0, 10, 0, 1369], [1, 0, -82, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, -82, 0, 3481], [1, 0, 118, 0, 3721], [1, -8, 150, -536, 4489], [1, 0, 2, 0, 5041], [1, 0, 46, 0, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, 34, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 9, 'instance_types': ['ECNF', 'HMF', 'HMF', 'ECNF', 'ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.2.93.1/100.1/b', 'ModularForm/GL2/TotallyReal/2.2.93.1/holomorphic/2.2.93.1-100.1-b', 'ModularForm/GL2/TotallyReal/2.2.93.1/holomorphic/2.2.93.1-100.1-a', 'EllipticCurve/2.2.93.1/100.1/a', 'EllipticCurve/2.0.3.1/96100.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/96100.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/96100.3/b', 'EllipticCurve/2.0.3.1/96100.3/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': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-930e2-1.1-c1e2-0-9', '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': '4-930e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 337023732005428970, 'z1': {'__RealLiteral__': 0, 'data': '0.72431480240733306960638962230700', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9811735
{'Lhash': '918178094025847143935010037092', 'Lhash_array': ['918178094025847143935010037092'], 'label': '4-930e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/96100.3/b'}
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id: 9811666
{'Lhash': '918178094025847143935010037092', 'Lhash_array': ['918178094025847143935010037092'], 'label': '4-930e2-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/96100.3/b'}
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id: 9811659
{'Lhash': '918178094025847143935010037092', 'Lhash_array': ['918178094025847143935010037092'], 'label': '4-930e2-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/96100.1/b'}
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id: 9810953
{'Lhash': '918178094025847143935010037092', 'Lhash_array': ['918178094025847143935010037092'], 'label': '4-930e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/96100.1/b'}
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id: 9468793
{'Lhash': '918178094025847143935010037092', 'Lhash_array': ['918178094025847143935010037092'], 'label': '4-930e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.93.1/100.1/a'}
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id: 9468760
{'Lhash': '918178094025847143935010037092', 'Lhash_array': ['918178094025847143935010037092'], 'label': '4-930e2-1.1-c1e2-0-9', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.93.1/holomorphic/2.2.93.1-100.1-a'}
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id: 9468563
{'Lhash': '918178094025847143935010037092', 'Lhash_array': ['918178094025847143935010037092'], 'label': '4-930e2-1.1-c1e2-0-9', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.93.1/holomorphic/2.2.93.1-100.1-b'}
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id: 9468484
{'Lhash': '918178094025847143935010037092', 'Lhash_array': ['918178094025847143935010037092'], 'label': '4-930e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.93.1/100.1/b'}