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lfunc_lfunctions • Show schema
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{'Lhash': '2277936542575446941645395313668', 'a10': [0, 0], 'a2': [0, 0], 'a3': [40.5, 23.382685902179844], 'a4': [0, 0], 'a5': [632.5513663462845, -365.2037016362929], 'a6': [0, 0], 'a7': [984.436889745346, -2189.9052513998204], 'a8': [0, 0], 'a9': [1093.5, 1893.9975580765674], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.2198032451347, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-40.5, -23.382685902179844]]], [7, [[1.0, 0], [-984.436889745346, 2189.9052513998204]]]], 'bad_primes': [2, 3, 7], 'central_character': '84.73', 'coefficient_field': 'CDF', 'conductor': 84, 'conductor_radical': 42, 'conjugate': '956247008827045914579727809603', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-40.5, -23.382685902179844]], [[1.0, 0], [-632.5513663462845, 365.2037016362929], [195312.5, -338291.17335329636]], [[1.0, 0], [-984.436889745346, 2189.9052513998204]], [[1.0, 0], 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'4.41907988757164802498274735896382', '6.06741407199783422745234723761301', '6.95067881729296740608667443334846', '8.587335151113134437735436021385765', '9.374940809925590389540347509284132', '10.60049067273313692160854315427560', '11.87302316422434469940346295753175', '12.96715853477216538397288296419048'], 'prelabel': '2-84-7.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.849769503590266, 'root_angle': 0.4274626401795779, 'root_number': '0.22591560339849112 + 0.9741468781149462*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21373132008978896', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79697508301208897305381915795750', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.47245478673347349570379229668995', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.41907988757164802498274735896382', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.2198032451347, 'bad_primes': [2, 3, 7], 'central_character': '7.3', 'conductor': 84, 'conductor_radical': 42, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/84/9/m/b/73/5'], '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': '2-84-7.3-c8-0-10', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-84-7.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.849769503590266, 'root_angle': 0.21373132008978896, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79697508301208897305381915795750', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '2277936542575446941645395313668', 'Lhash_array': ['2277936542575446941645395313668'], 'label': '2-84-7.3-c8-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/84/9/m/b/73/5'}