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lfunc_lfunctions • Show schema
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{'Lhash': '523678706821363834420441468827', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.41552908235833], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0.5586466311274751, 0], 'a8': [0, 0], 'a9': [-2.665838912435536, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.972829079632664, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-2.8205388951414596, -10.632241548281067]]]], 'bad_primes': [2, 5, 11], 'central_character': '1100.549', 'coefficient_field': 'CDF', 'conductor': 1100, 'conductor_radical': 110, 'conjugate': '2028933941474416683917625687594', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.41552908235833], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5586466311274751, 0], [49.0, 0]], [[1.0, 0], [-2.8205388951414596, -10.632241548281067]], [[1.0, 0], [18.10723743858245, 0], [169.0, 0]], [[1.0, 0], [-32.04019129857791, 0], [289.0, 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['0.41310965870806992420544852383408', '1.55570299799396207042692713991228', '2.71010819357699158534808992057947', '3.79911874819644858726568289426978', '5.21645455305739234649234796978460', '5.89127609654718786897691890618198', '6.95228645850856867302920654883200', '7.62075083740675124693167039703686', '8.101990277590847821514304633363541', '9.405425585383900337343459652384324'], 'prelabel': '2-1100-55.54-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.47474465885238, 'root_angle': -0.9349569715589641, 'root_number': '-0.97919538932775662024940164094491941369361790576281852833 - 0.2029196627221303469503786337161795498993248254698975864*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46747848577948203', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41310965870806992420544852383', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55570299799396207042692713991', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71010819357699158534808992058', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.972829079632664, 'bad_primes': [2, 5, 11], 'central_character': '55.54', 'conductor': 1100, 'conductor_radical': 110, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1100/3/e/b/549/12'], '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': '2-1100-55.54-c2-0-7', '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': '2-1100-55.54-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.47474465885238, 'root_angle': -0.46747848577948203, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41310965870806992420544852383', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '523678706821363834420441468827', 'Lhash_array': ['523678706821363834420441468827'], 'label': '2-1100-55.54-c2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1100/3/e/b/549/12'}