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lfunc_lfunctions • Show schema
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{'Lhash': '667633000452221433603505666593,978078334123083562583843064640', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3453.900662646677, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 2, 1]], [23, [1, -2, 1]]], 'bad_primes': [2, 5, 23], 'central_character': '7360.1', 'coefficient_field': '1.1.1.1', 'conductor': 54169600, 'conductor_radical': 230, 'degree': 4, 'euler_factors': [[1], [1, 1, 5, 3, 9], [1, 2, 1], [1, -1, 13, -7, 49], [1, 1, 11, 11, 121], [1, -3, -3, -39, 169], [1, -1, 3, -17, 289], [1, -3, 29, -57, 361], [1, -2, 1], [1, -14, 102, -406, 841], [1, -7, 43, -217, 961], [1, 4, 58, 148, 1369], [1, 9, 41, 369, 1681], [1, 0, 86, 0, 1849], [1, -6, 58, -282, 2209], [1, -8, 102, -424, 2809], [1, -10, 98, -590, 3481], [1, -3, 63, -183, 3721], [1, 20, 214, 1340, 4489], [1, -3, 113, -213, 5041], [1, -2, 142, -146, 5329], [1, 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'6.68457135669706178736910489784151', '6.97182845036459997513901874039481', '7.39227872835667151359652745575123', '7.87721004024048970374644774324157', '8.086640794163801708984302080134111'], 'prelabel': '4-7360e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.66615261312103, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 886863199545470624, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52666957309215958415525374403', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.77156776003339493902915315793', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.36080929196599851574327985732', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3453.900662646677, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 54169600, 'conductor_radical': 230, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, 1, 0, -4, 0, -1, 0, 3, 0, 2, 0, 1, 0, 3, 0, -1, 0, 2, 0, 3, 0, 6, 0, 14, 0, 7, 0, 1, 0, -2, 0, -4, 0, -3, 0, -9, 0, 0, 0, 8, 0, 6, 0, -12, 0, -1, 0, 8, 0, 2, 0, -3, 0, 10, 0, 3, 0, -4, 0, -6, 0, -20, 0, -2, 0, 3, 0, 2, 0, -3, 0, -1, 0, 12, 0, 8, 0, -4, 0, -2, 0, -14, 0, -12, 0, 3, 0, -7, 0, -6, 0, 27, 0, 4, 0], 'euler11': [1, 1, 11, 11, 121], 'euler13': [1, -3, -3, -39, 169], 'euler17': [1, -1, 3, -17, 289], 'euler19': [1, -3, 29, -57, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2, 1, 0, 0], 'euler29': [1, -14, 102, -406, 841], 'euler3': [1, 1, 5, 3, 9], 'euler31': [1, -7, 43, -217, 961], 'euler37': [1, 4, 58, 148, 1369], 'euler41': [1, 9, 41, 369, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, -6, 58, -282, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, -8, 102, -424, 2809], 'euler59': [1, -10, 98, -590, 3481], 'euler61': [1, -3, 63, -183, 3721], 'euler67': [1, 20, 214, 1340, 4489], 'euler7': [1, -1, 13, -7, 49], 'euler71': [1, -3, 113, -213, 5041], 'euler73': [1, -2, 142, -146, 5329], 'euler79': [1, -12, 174, -948, 6241], 'euler83': [1, 4, 90, 332, 6889], 'euler89': [1, 12, 194, 1068, 7921], 'euler97': [1, -27, 375, -2619, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 5, 3, 9], [1, 2, 1, 0, 0], [1, -1, 13, -7, 49], [1, 1, 11, 11, 121], [1, -3, -3, -39, 169], [1, -1, 3, -17, 289], [1, -3, 29, -57, 361], [1, -2, 1, 0, 0], [1, -14, 102, -406, 841], [1, -7, 43, -217, 961], [1, 4, 58, 148, 1369], [1, 9, 41, 369, 1681], [1, 0, 86, 0, 1849], [1, -6, 58, -282, 2209], [1, -8, 102, -424, 2809], [1, -10, 98, -590, 3481], [1, -3, 63, -183, 3721], [1, 20, 214, 1340, 4489], [1, -3, 113, -213, 5041], [1, -2, 142, -146, 5329], [1, -12, 174, -948, 6241], [1, 4, 90, 332, 6889], [1, 12, 194, 1068, 7921], [1, -27, 375, -2619, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7360/2/a/bh'], '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': '4-7360e2-1.1-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': '4-7360e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.66615261312103, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 886863199545470624, 'z1': {'__RealLiteral__': 0, 'data': '0.52666957309215958415525374403', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '667633000452221433603505666593,978078334123083562583843064640', 'Lhash_array': ['667633000452221433603505666593', '978078334123083562583843064640'], 'label': '4-7360e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7360/2/a/bh'}