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lfunc_lfunctions • Show schema
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{'Lhash': '1129903667025004552537964480721', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7320508075688773, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.2679491924311227, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.7320508075688773, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.4641016151377544, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.729518915659945, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 11], 'central_character': '968.1', 'coefficient_field': 'CDF', 'conductor': 968, 'conductor_radical': 22, 'conjugate': '1129903667025004552537964480721', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7320508075688773, 0], [3.0, 0]], [[1.0, 0], [0.2679491924311227, 0], [5.0, 0]], [[1.0, 0], [0.7320508075688773, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [-5.732050807568878, 0], [17.0, 0]], [[1.0, 0], 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'6.59560705627879109904258588038545', '7.52388038622047373748382378937265', '8.226826830735980442449362485001172', '9.467612089350491576845786230369775', '9.802161550819546812585081001875277'], 'prelabel': '2-968-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7802012365402518, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.891336829581885798334747559141', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.72307679155258250382105711917', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55436523156847137094569377198', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.729518915659945, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 968, 'conductor_radical': 22, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/968/2/a/l/1/1'], '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': '2-968-1.1-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': '2-968-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7802012365402518, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.891336829581885798334747559141', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1129903667025004552537964480721', 'Lhash_array': ['1129903667025004552537964480721'], 'factors': ['2-968-1.1-c1-0-3'], 'label': '2-968-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/968/2/a/l/1/1'}