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lfunc_lfunctions • Show schema
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{'Lhash': '1976478569461407176700650851709', 'a10': [-1.1582302082198792, 0.0], 'a2': [0.0, -1.6581596006229704], 'a3': [2.316236375055988, 1.906580461157487], 'a4': [1.2505067388618711, 0.0], 'a5': [0.0, -0.6985034539405809], 'a6': [3.1614146960284577, -3.840689582611234], 'a7': [2.60911034347268, 0.0], 'a8': [0.0, -8.706178157179416], 'a9': [1.7299018902650078, 8.832182032207983], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.89103359627878, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.316236375055988, -1.906580461157487]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.122', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '1820673403878735496628845989300', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.6581596006229704], [-4.0, 0]], [[1.0, 0], [-2.316236375055988, -1.906580461157487]], [[1.0, 0], [0, 0.6985034539405809], [-25.0, 0]], 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2.1148774250195843, 0.8102424685272259], 'positive_zeros': ['1.55916667345525612497982650864727', '2.84529142656888042313113446735602', '4.29657862250094771026318062361040', '5.99687608009064779004291041054203', '6.51765018431180009396217571991535', '7.57578324653428369209604284105374', '8.383927458760950376149750532748686', '8.907001552324668258316509143634720', '10.54893521600205500877438773760876', '11.21706155811415152002589692430315'], 'prelabel': '2-363-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.145001366657697, 'root_angle': 0.21921704838868245, 'root_number': '0.7720787916853293 + 0.6355268203858291*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.109608524194', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55916667345525612497982650865', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84529142656888042313113446736', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29657862250094771026318062361', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.89103359627878, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/3/b/m/122/4'], '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': '2-363-3.2-c2-0-40', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-363-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.145001366657697, 'root_angle': 0.10960852419434122, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55916667345525612497982650865', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1976478569461407176700650851709', 'Lhash_array': ['1976478569461407176700650851709'], 'label': '2-363-3.2-c2-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/3/b/m/122/4'}