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lfunc_lfunctions • Show schema
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{'Lhash': '1816071087751122041389890924647', 'a10': [3.0, 5.196152422706632], 'a2': [1.8764180059359885, 1.5745016567152952], 'a3': [0.0, 0.0], 'a4': [0.6945927106677214, 3.939231012048832], 'a5': [2.301767435984125, 0.837774832901458], 'a6': [0.0, 0.0], 'a7': [0.3472963553338607, -1.969615506024416], 'a8': [-2.449489742783178, 4.242640687119285], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.406', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2692974320427436146496906953379', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8764180059359885, -1.5745016567152952], [0.3472963553338607, 1.969615506024416]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.301767435984125, -0.837774832901458], [3.83022221559489, 3.2139380484326967]], [[1.0, 0], 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['1.43262748222905769819619402922250', '2.54071501279500209673692587598885', '3.30087905215984719612479392836766', '4.84111624575102492535012963009437', '5.39925807804764736325694506955790', '5.92076387460732203056663577723372', '7.37486192393783654333135994187455', '8.720534454315841984284157958314893', '9.732328764555140800070285285403339', '10.16517596340181205267823349645235'], 'prelabel': '2-3e6-27.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.5925925925925927, 'root_number': '-0.28680323271109043 - 0.9579895123154888*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.296296296296', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43262748222905769819619402922', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54071501279500209673692587599', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30087905215984719612479392837', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.16', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/p/406/2'], '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': '2-3e6-27.16-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3e6-27.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.29629629629629634, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43262748222905769819619402922', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1816071087751122041389890924647', 'Lhash_array': ['1816071087751122041389890924647'], 'label': '2-3e6-27.16-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/p/406/2'}