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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1392935865323072502382954264453', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 113.70449913041945, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [43, [1, 9, 51, 43]]], 'bad_primes': [2, 3, 43], 'central_character': '1783296.1', 'coefficient_field': '1.1.1.1', 'conductor': 1783296, 'conductor_radical': 258, 'degree': 4, 'euler_factors': [[1], [1, -1], [1, 0, -6, 0, 25], [1, 0, 5, 0, 49], [1, 3, 12, 33, 121], [1, 0, 9, 0, 169], [1, -2, 10, -34, 289], [1, 8, 54, 152, 361], [1, 0, 32, 0, 529], [1, 0, -22, 0, 841], [1, 0, 2, 0, 961], [1, 0, -20, 0, 1369], [1, -7, 64, -287, 1681], [1, 9, 51, 43], [1, 0, -10, 0, 2209], [1, 0, -19, 0, 2809], [1, 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5.654760675434246, 4.078848583863128, 2.3533953992995587, 0.6676757394113646], 'positive_zeros': ['1.09883264763357236202823260488793', '1.97477029637729316409982379185415', '2.34559092128197092484241727172314', '3.05040555747868638302861071315006', '3.35595623678010479206746130126074', '4.01354881121351611063454741375679', '4.57827498434006456118379582894705', '4.89430022764209812025844516250761', '5.30859801919420329839855171747391', '6.06758220922893021476710814184327', '6.28418883020590334772909027500446', '6.79866427077655680229109324852576', '7.16376391894635814087959727622815', '7.83358910748423648257205248160439'], 'prelabel': '4-1783296-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.2654603315344866, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 363845732646996184, 'z1': {'__RealLiteral__': 0, 'data': '1.09883264763357236202823260488793', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.97477029637729316409982379185415', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.34559092128197092484241727172314', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 113.70449913041945, 'bad_primes': [2, 3, 43], 'central_character': '1.1', 'conductor': 1783296, 'conductor_radical': 258, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 2, 0, -8, 0, 0, 0, 0, 0, 6, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 7, 0, -9, 0, 0, 0, 0, 0, -5, 0, 2, 0, 0, 0, 0, 0, -8, 0, -23, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 13, 0, 6, 0, 0, 0, 0, 0, 1, 0, 19, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, -3, 0], 'euler11': [1, 3, 12, 33, 121], 'euler13': [1, 0, 9, 0, 169], 'euler17': [1, -2, 10, -34, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 32, 0, 529], 'euler29': [1, 0, -22, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 0, 2, 0, 961], 'euler37': [1, 0, -20, 0, 1369], 'euler41': [1, -7, 64, -287, 1681], 'euler43': [1, 9, 51, 43, 0], 'euler47': [1, 0, -10, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 0, -19, 0, 2809], 'euler59': [1, 23, 248, 1357, 3481], 'euler61': [1, 0, 112, 0, 3721], 'euler67': [1, -7, 74, -469, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, 0, -50, 0, 5041], 'euler73': [1, -13, 188, -949, 5329], 'euler79': [1, 0, -50, 0, 6241], 'euler83': [1, -19, 256, -1577, 6889], 'euler89': [1, 3, 180, 267, 7921], 'euler97': [1, 2, 194, 194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 0, 0, 0], [1, 0, -6, 0, 25], [1, 0, 5, 0, 49], [1, 3, 12, 33, 121], [1, 0, 9, 0, 169], [1, -2, 10, -34, 289], [1, 8, 54, 152, 361], [1, 0, 32, 0, 529], [1, 0, -22, 0, 841], [1, 0, 2, 0, 961], [1, 0, -20, 0, 1369], [1, -7, 64, -287, 1681], [1, 9, 51, 43, 0], [1, 0, -10, 0, 2209], [1, 0, -19, 0, 2809], [1, 23, 248, 1357, 3481], [1, 0, 112, 0, 3721], [1, -7, 74, -469, 4489], [1, 0, -50, 0, 5041], [1, -13, 188, -949, 5329], [1, 0, -50, 0, 6241], [1, -19, 256, -1577, 6889], [1, 3, 180, 267, 7921], [1, 2, 194, 194, 9409]], 'index': 7, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.8.1/27864.3/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/27864.8/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/27864.3/c', 'EllipticCurve/2.0.8.1/27864.8/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': '4-1783296-1.1-c1e2-0-7', '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': 1, 'prelabel': '4-1783296-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.2654603315344866, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 363845732646996184, 'z1': {'__RealLiteral__': 0, 'data': '1.09883264763357236202823260488793', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9842977
{'Lhash': '1392935865323072502382954264453', 'Lhash_array': ['1392935865323072502382954264453'], 'label': '4-1783296-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/27864.8/b'}
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id: 9842916
{'Lhash': '1392935865323072502382954264453', 'Lhash_array': ['1392935865323072502382954264453'], 'label': '4-1783296-1.1-c1e2-0-7', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/27864.3/c'}
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id: 9842819
{'Lhash': '1392935865323072502382954264453', 'Lhash_array': ['1392935865323072502382954264453'], 'label': '4-1783296-1.1-c1e2-0-7', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/27864.8/b'}
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id: 9842648
{'Lhash': '1392935865323072502382954264453', 'Lhash_array': ['1392935865323072502382954264453'], 'label': '4-1783296-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/27864.3/c'}