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lfunc_lfunctions • Show schema
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{'Lhash': '4262419030362029954326348026062', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.224744871391589, -1.224744871391589], 'a4': [0.0, -2.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.224744871391589, -1.224744871391589], 'a8': [0.0, 0.0], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5988780151596031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.224744871391589, 1.224744871391589]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.68', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '1915178507839220159920469699384', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 2.0]], [[1.0, 0], [1.224744871391589, 1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.224744871391589, 1.224744871391589], [0, -7.0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [-3.6742346141747673, -3.6742346141747673], [0, 13.0]], [[1.0, 0], 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'group': 'GL2', 'index': 3, 'label': '2-75-15.8-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/75/2/e/b/68/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8010109240418612, 0.8515653487663283, 0.9149263177551388, 0.9920654217022375, 1.0830369894910656, 1.1870755390610026, 1.3026994935004417, 1.4277845893738084, 1.5596001777938382, 1.6948214345125654, 1.8295375732845536, 1.9592752581159787, 2.0790524111782216, 2.1834731260595173, 2.266870229395282, 2.3234981522584417, 2.3477749224220306, 2.334568074231297, 2.2795150399954722, 2.17936422661356, 2.032318709498878, 1.838360606750462, 1.5995311128431806, 1.3201392922709692, 1.0068724784486152, 0.6687828682103187, 0.3171289358626784, -0.034943233447340724, -0.3728846987685129, -0.6813894467984317, 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'13.52130204400553857303362613091614', '15.10711881946085356342201389569506'], 'prelabel': '2-75-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475517, 'root_angle': 0.3941610827502959, 'root_number': '0.3264097326151029 + 0.9452283779352676*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.197080541375', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.36245573472265835272861328486', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.86441124038730884874123218676', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.30718475875464681992262523024', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5988780151596031, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/2/e/b/68/1'], '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': '2-75-15.8-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-75-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475517, 'root_angle': 0.19708054137514794, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.36245573472265835272861328486', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4262419030362029954326348026062', 'Lhash_array': ['4262419030362029954326348026062'], 'label': '2-75-15.8-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/2/e/b/68/1'}