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lfunc_lfunctions • Show schema
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{'Lhash': '840214331158450100920407539495', 'a10': [0, 0], 'a2': [0, 0], 'a3': [56.46280099895583, 56.46280099895583], 'a4': [0, 0], 'a5': [-6260.448694286704, 6260.448694286704], 'a6': [0, 0], 'a7': [0, 32943.97363929033], 'a8': [0, 0], 'a9': [0, -170770.90420670464], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 98.3479271116274, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '128.33', 'coefficient_field': 'CDF', 'conductor': 128, 'conductor_radical': 2, 'conjugate': '779506899382052138547635018957', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-56.46280099895583, -56.46280099895583], [0, 177147.0]], [[1.0, 0], [6260.448694286704, -6260.448694286704], [0, -48828125.0]], [[1.0, 0], [0, -32943.97363929033], [-1977326743.0, 0]], [[1.0, 0], [-151744.45654231327, 151744.45654231327], [0, -285311670611.0]], [[1.0, 0], [-1051401.3982458015, 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'11.14014890977317523127539717258501'], 'prelabel': '2-2e7-16.13-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.917052339865279, 'root_angle': -0.1416009743164291, 'root_number': '0.9026741134072704764480014967937532428228703410550919416 - 0.430324813349634997173997312912339131493408875832855855*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07080048715821455', 'prec': 67}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66281223785732193127155106348', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.71396284086837602318297036889', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49162631132238448486655441937', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 98.3479271116274, 'bad_primes': [2], 'central_character': '16.13', 'conductor': 128, 'conductor_radical': 2, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/128/12/e/b/33/12'], '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': '2-2e7-16.13-c11-0-21', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-2e7-16.13-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.917052339865279, 'root_angle': -0.07080048715821455, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66281223785732193127155106348', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '840214331158450100920407539495', 'Lhash_array': ['840214331158450100920407539495'], 'label': '2-2e7-16.13-c11-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/128/12/e/b/33/12'}