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lfunc_lfunctions • Show schema
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{'Lhash': '879917425577550289462806787130', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 7.9906077386456555], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 4.095493846160174], 'a8': [0, 0], 'a9': [-36.84981203290384, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 135.7043930132035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 23.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '2300.1749', 'coefficient_field': 'CDF', 'conductor': 2300, 'conductor_radical': 230, 'conjugate': '66357137770003337564106997876', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -7.9906077386456555], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.095493846160174], [-343.0, 0]], [[1.0, 0], [47.44965452152663, 0], [1331.0, 0]], [[1.0, 0], [0, -7.454089508549573], [-2197.0, 0]], [[1.0, 0], [0, -58.58368624974874], [-4913.0, 0]], [[1.0, 0], 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['0.69413245686084860786877642208833', '1.98951609297554081755101487072952', '2.49939146007658353868274850469328', '3.68845316558282498948031795044378', '4.94638273813877181168775013490766', '5.72296397387808304097336813913138', '6.50998427016925796891516601163255', '7.40239336923820369023003314567054', '7.62379180293372217189478026780690', '8.530295540514737488037690048635361'], 'prelabel': '2-2300-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.649222850182046, 'root_angle': 0.14758361765043326, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69413245686084860786877642209', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98951609297554081755101487073', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.49939146007658353868274850469', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 135.7043930132035, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 2300, 'conductor_radical': 230, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2300/4/c/c/1749/10'], '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': '2-2300-5.4-c3-0-50', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-2300-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.649222850182046, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69413245686084860786877642209', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '879917425577550289462806787130', 'Lhash_array': ['879917425577550289462806787130'], 'label': '2-2300-5.4-c3-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2300/4/c/c/1749/10'}