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lfunc_lfunctions • Show schema
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{'Lhash': '411979370394278357335721657445', 'a10': [336713980.6157964, -288168511.4735963], 'a2': [0, 507.39354445397146], 'a3': [0, 0], 'a4': [-126376.20895356433, 0], 'a5': [-567938.8605223724, -663615.0268292221], 'a6': [0, 0], 'a7': [0, -7169811.099561714], 'a8': [0, 2382614.063066217], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 82.44993930505191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [567938.8605223724, 663615.0268292221]]]], 'bad_primes': [3, 5], 'central_character': '45.19', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '861670456960620816376047876433', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -507.39354445397146], [-131072.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [567938.8605223724, 663615.0268292221]], [[1.0, 0], [0, 7169811.099561714], [-232630513987207.0, 0]], [[1.0, 0], [1341976430.273198, 0], 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'10.71672770396489086866672564826276', '11.71354092480053656098389712675296'], 'prelabel': '2-45-5.4-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.080194893561035, 'root_angle': -0.725320915402987, 'root_number': '-0.65021434838619982290393886579493447696593986612470614391 - 0.7597508151708095164907941910899573823073891269875329436*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3626604577014935', 'prec': 64}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32499441906161293623299747205', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95701526688779948247194905298', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88584541635266592227004384505', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 82.44993930505191, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/18/b/c/19/13'], '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': '2-45-5.4-c17-0-8', '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': '2-45-5.4-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.080194893561035, 'root_angle': -0.3626604577014935, 'self_dual': False, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32499441906161293623299747205', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '411979370394278357335721657445', 'Lhash_array': ['411979370394278357335721657445'], 'label': '2-45-5.4-c17-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/18/b/c/19/13'}