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  • lfunc_lfunctions • Show schema
    {'Lhash': '1144347419861456534315209523271', 'a10': [0, 0], 'a2': [0, 670.61299823714], 'a3': [0, -6561.0], 'a4': [-318649.79340460635, 0], 'a5': [0, 0], 'a6': [4399891.881433875, 0], 'a7': [0, 27080419.853429858], 'a8': [0, -125792106.4377699], 'a9': [-43046721.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 137.41656550841986, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 6561.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.49', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '264543318030043950252647292042', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -670.61299823714], [-131072.0, 0]], [[1.0, 0], [0, 6561.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -27080419.853429858], [-232630513987207.0, 0]], [[1.0, 0], [-1016437517.8280613, 0], [505447028499293760, 0]], [[1.0, 0], [0, 1048341692.8712277], [-8650415919381338000, 0]], [[1.0, 0], 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'2-75-5.4-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.722481201026508, 'root_angle': -0.07379180882521663, 'root_number': '0.894427190999915878563669467492510494176247343844610290 - 0.447213595499957939281834733746255247088123671922305145*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.902730941519237865559893619735', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.68736402943775546471103914485', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26010324502087607586258006061', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 137.41656550841986, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/18/b/d/49/6'], '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': '2-75-5.4-c17-0-34', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17], 'order_of_vanishing': 0, 'prelabel': '2-75-5.4-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.722481201026508, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '0.902730941519237865559893619735', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '1144347419861456534315209523271', 'Lhash_array': ['1144347419861456534315209523271'], 'factors': ['2-75-5.4-c17-0-34'], 'label': '2-75-5.4-c17-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/18/b/d/49/6'}