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lfunc_lfunctions • Show schema
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{'Lhash': '3394632631312191998507945199321', 'a10': [0.0, 0.0], 'a2': [4.701562118716424, 0.0], 'a3': [3.0, 0.0], 'a4': [14.104686356149273, 0.0], 'a5': [0.0, 0.0], 'a6': [14.104686356149273, 0.0], 'a7': [-16.209372712298546, 0.0], 'a8': [28.701562118716424, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.425143250430549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.1', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '3394632631312191998507945199321', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.701562118716424, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [16.209372712298546, 0], [343.0, 0]], [[1.0, 0], [40.209372712298546, 0], [1331.0, 0]], [[1.0, 0], [-19.790627287701454, 0], [2197.0, 0]], [[1.0, 0], [-83.01562118716424, 0], [4913.0, 0]], 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'3.79684465948635158134660234263309', '5.34165747804085571998374927723468', '6.54672827298846704063399958729937', '7.964995495075949724713933550451362', '9.705511164404952700857363636705964', '11.00006750586232230937605439276877', '12.46361857535817110721507238677325', '13.02869188257218953584293039039403', '13.90911486129079565122183840124806'], 'prelabel': '2-75-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.67789297042972100403261059468', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79684465948635158134660234263', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.34165747804085571998374927723', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.425143250430549, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/4/a/f/1/2'], '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': '2-75-1.1-c3-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-75-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.67789297042972100403261059468', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3394632631312191998507945199321', 'Lhash_array': ['3394632631312191998507945199321'], 'label': '2-75-1.1-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/4/a/f/1/2'}