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lfunc_lfunctions • Show schema
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{'Lhash': '3390514462241935472179219710637', 'a10': [0.0, 0.0], 'a2': [0.0, -0.41421356237309503], 'a3': [0.0, -2.8284271247461903], 'a4': [1.82842712474619, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.17157287525381, 0.0], 'a7': [0.0, -2.0], 'a8': [0.0, -1.5857864376269049], 'a9': [-5.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1958860555852118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '275.199', 'coefficient_field': 'CDF', 'conductor': 275, 'conductor_radical': 55, 'conjugate': '1695098127390482797993170379186', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.41421356237309503], [-2.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.0], [-7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -6.82842712474619], [-13.0, 0]], [[1.0, 0], [0, -1.17157287525381], [-17.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-275-5.4-c1-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/275/2/b/d/199/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5178237336346319, 1.6585737832061072, 1.8177547532467202, 1.9960765390400377, 2.191358346790186, 2.3986130821479272, 2.610334234176412, 2.8168851731941693, 3.006954245216861, 3.168087295155945, 3.2873256497829595, 3.351968856854014, 3.350459393518877, 3.2733597985283254, 3.1143662709271336, 2.8712797547324427, 2.546838286057639, 2.149305204366949, 1.6927089006430185, 1.1966428654713033, 0.6855608753479486, 0.18754097355003457, -0.26745830770004914, -0.6497687454833898, -0.932469856685555, -1.0939371081833933, -1.1202411915180994, -1.0071339047357968, 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'10.37280365643641391671080200477574', '11.05769676662173517101600625209544', '11.89764355349030160910439024528686'], 'prelabel': '2-275-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': 0.6475836176504333, 'root_number': '-0.4472135954999579 + 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.323791808825', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.67464430784910526810956774364', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.73815666774460920540588790787', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.40206477674209174978974510786', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1958860555852118, 'bad_primes': [5, 11], 'central_character': '5.4', 'conductor': 275, 'conductor_radical': 55, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/275/2/b/d/199/2'], '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': '2-275-5.4-c1-0-12', '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': '2-275-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.67464430784910526810956774364', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3390514462241935472179219710637', 'Lhash_array': ['3390514462241935472179219710637'], 'label': '2-275-5.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/2/b/d/199/2'}