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lfunc_lfunctions • Show schema
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{'Lhash': '1238423392494997166700216196159', 'a10': [0, 0], 'a2': [-6.620302167902449, -6.620302167902449], 'a3': [-33.0681115275729, 33.0681115275729], 'a4': [0, -168.34319841133228], 'a5': [0, 0], 'a6': [437.8417808688617, 0], 'a7': [216.61929641178455, 216.61929641178455], 'a8': [-2809.280196377202, 2809.280196377202], 'a9': [0, -2187.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.553395754584553, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [33.0681115275729, -33.0681115275729]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.7', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '744059077469555463548809841474', 'degree': 2, 'euler_factors': [[[1.0, 0], [6.620302167902449, 6.620302167902449], [0, 256.0]], [[1.0, 0], [33.0681115275729, -33.0681115275729]], [[1.0, 0], [0, 0]], [[1.0, 0], [-216.61929641178455, -216.61929641178455], [0, 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False, 'root_analytic_conductor': 5.527512619124859, 'root_angle': 0.42620819117478337, 'root_number': '0.22975292054736127 + 0.9732489894677302*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21310409558739168', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.976943798450479862735005476084553', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.96467616057248038185755829590128', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.62940354600289539358306461479782', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.553395754584553, 'bad_primes': [3, 5], 'central_character': '5.2', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/9/f/e/7/3'], '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': '2-75-5.2-c8-0-10', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-75-5.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.527512619124859, 'root_angle': 0.21310409558739168, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.976943798450479862735005476084553', 'prec': 117}}
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lfunc_instances • Show schema
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{'Lhash': '1238423392494997166700216196159', 'Lhash_array': ['1238423392494997166700216196159'], 'label': '2-75-5.2-c8-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/9/f/e/7/3'}