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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 6, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '106991358239906766,1215354540506513513', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [2.6832815729997477, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.497129279256317, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1]], [11, [1, 3, 11]]], 'bad_primes': [2, 3, 11], 'central_character': '352836.1', 'coefficient_field': '1.1.1.1', 'conductor': 352836, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1, 0, -1], [1], [1, -6, 19, -30, 25], [1, 0, 13, 0, 49], [1, 3, 11], [1, 0, 10, 0, 169], [1, 0, 34, 0, 289], [1, 0, 34, 0, 361], [1, 12, 82, 276, 529], [1, 0, 22, 0, 841], [1, -10, 87, -310, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 0, -14, 0, 1849], [1, -12, 130, -564, 2209], [1, -18, 187, -954, 2809], 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0.40892573613106864, 0.7386061660801037, 1.0279480561416805, 1.1998480094092185], 'positive_zeros': ['1.09285120951784850918046733268493', '2.03246862806699813641002498926675', '2.44850978333263328730546301919062', '2.58138575780524151090389938489301', '3.80538107085536458846182311961177', '4.30456169908575776721292993281054', '5.37363015537505503550836847886395', '5.39074241880952165115421872246775', '5.84315760589664083898483470883565', '6.29574961437633563574123917046178', '6.73860900674537002760989556093077', '7.12468139474762615848955209062584', '8.015255053006877536003075086198015', '8.268048909391662018895990050851976', '8.628140728035937440023020847412061'], 'prelabel': '4-594e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1778691145392686, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1322345898746420279, 'z1': {'__RealLiteral__': 0, 'data': '1.09285120951784850918046733268493', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.03246862806699813641002498926675', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.44850978333263328730546301919062', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.497129279256317, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 352836, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, -12, 0, 17, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -3, 0, 0, 12, 0, -13, 0, 0, 0, 18, 0, -18, 0, 0, 0, 24, 0, 0, 0, 0, 1, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, -12, 0, 0, 0, 0, -2, 0, 0, 17], 'euler11': [1, 3, 11, 0, 0], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 12, 82, 276, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -10, 87, -310, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, -14, 0, 1849], 'euler47': [1, -12, 130, -564, 2209], 'euler5': [1, -6, 19, -30, 25], 'euler53': [1, -18, 187, -954, 2809], 'euler59': [1, -24, 262, -1416, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, -28, 330, -1876, 4489], 'euler7': [1, 0, 13, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 97, 0, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 157, 0, 6889], 'euler89': [1, 36, 502, 3204, 7921], 'euler97': [1, 2, 195, 194, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, -6, 19, -30, 25], [1, 0, 13, 0, 49], [1, 3, 11, 0, 0], [1, 0, 10, 0, 169], [1, 0, 34, 0, 289], [1, 0, 34, 0, 361], [1, 12, 82, 276, 529], [1, 0, 22, 0, 841], [1, -10, 87, -310, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 0, -14, 0, 1849], [1, -12, 130, -564, 2209], [1, -18, 187, -954, 2809], [1, -24, 262, -1416, 3481], [1, 0, 58, 0, 3721], [1, -28, 330, -1876, 4489], [1, 0, 142, 0, 5041], [1, 0, 97, 0, 5329], [1, 0, 94, 0, 6241], [1, 0, 157, 0, 6889], [1, 36, 502, 3204, 7921], [1, 2, 195, 194, 9409]], 'index': 10, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/2916.4/f', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/2916.4/f'], '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': '4-594e2-1.1-c1e2-0-10', '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': '4-594e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1778691145392686, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1322345898746420279, 'z1': {'__RealLiteral__': 0, 'data': '1.09285120951784850918046733268493', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9915116
{'Lhash': '106991358239906766,1215354540506513513', 'Lhash_array': ['106991358239906766', '1215354540506513513'], 'label': '4-594e2-1.1-c1e2-0-10', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/2916.4/f'}
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id: 9914302
{'Lhash': '106991358239906766,1215354540506513513', 'Lhash_array': ['106991358239906766', '1215354540506513513'], 'label': '4-594e2-1.1-c1e2-0-10', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/2916.4/f'}