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lfunc_lfunctions • Show schema
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{'Lhash': '1447603574688730973077995667495', 'a10': [0, 0], 'a2': [0, -346.47688223600477], 'a3': [0, 6561.0], 'a4': [11025.770076017692, 0], 'a5': [0, 0], 'a6': [2273234.8243504274, 0], 'a7': [0, 18079743.492517967], 'a8': [0, -49233592.34862726], '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': '306228236019141135033660187022', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 346.47688223600477], [-131072.0, 0]], [[1.0, 0], [0, -6561.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -18079743.492517967], [-232630513987207.0, 0]], [[1.0, 0], [145295685.54575822, 0], [505447028499293760, 0]], [[1.0, 0], [0, 3261554267.1683693], [-8650415919381338000, 0]], [[1.0, 0], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 11.722481201026508, 'root_angle': 0.42620819117478337, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 64}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14195786633012488828626678627', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28028544094859737286009888415', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85176058422371472561984552908', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 137.41656550841986, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/18/b/b/49/2'], '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': '2-75-5.4-c17-0-41', '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': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14195786633012488828626678627', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1447603574688730973077995667495', 'Lhash_array': ['1447603574688730973077995667495'], 'factors': ['2-75-5.4-c17-0-41'], 'label': '2-75-5.4-c17-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/18/b/b/49/2'}