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lfunc_lfunctions • Show schema
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{'Lhash': '1927354695980252917440139184263', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3774194348670867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [23, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '2760.137', 'coefficient_field': 'CDF', 'conductor': 2760, 'conductor_radical': 690, 'conjugate': '1493560261176512447953540440557', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476], [0, -1.0]], 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'3.71060429016024908511989568801116', '3.98164640975534348231637770703170', '5.03968045548116239167462363517842', '5.84488189149506771085838082633070', '7.10587194689797668813253320072181', '7.56345600610953558890487736536715', '8.574338659273628140066968565482639', '8.919596899802337700530580672079148'], 'prelabel': '2-2760-345.137-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.173635137028151, 'root_angle': 0.07379180882521663, 'root_number': '0.97324898946773016378805774830813 + 0.22975292054736118352393736938184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.036895904412608316', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52041477015295031960808740563', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.19492203667401294203760853353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71060429016024908511989568801', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3774194348670867, 'bad_primes': [2, 3, 5, 23], 'central_character': '345.137', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2760/1/bv/b/137/1'], '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': '2-2760-345.137-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2760-345.137-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.173635137028151, 'root_angle': 0.036895904412608316, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52041477015295031960808740563', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1927354695980252917440139184263', 'Lhash_array': ['1927354695980252917440139184263'], 'label': '2-2760-345.137-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2760/1/bv/b/137/1'}