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lfunc_lfunctions • Show schema
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{'Lhash': '761993208441060247583890542427', 'a10': [-0.6127400251815172, 3.829683243260865e-61], 'a2': [-0.8394201887831336, -2.5834696957903938], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [-4.351655426980702, 3.1616627349268076], 'a5': [0.06970462066535411, -0.21452876348680633], 'a6': [-0.8394201887831336, 2.5834696957903938], 'a7': [-1.7767773307877037, 1.2909042936131156], 'a8': [7.4256661138742786, 5.395062230497962], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.42558224671293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [-2.743546181558194, -1.863586421300996]]], [13, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [3, 11, 13], 'central_character': '429.313', 'coefficient_field': 'CDF', 'conductor': 429, 'conductor_radical': 429, 'conjugate': 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[-67.14841053312064, -48.78617594027527]], [[1.0, 0], [-14.24670019594897, 0], [89.0, 0]], [[1.0, 0], [-0.8047773673250173, -2.476850054507447], [-78.4746484543699, 57.01516947236989]], [[1.0, 0], [-5.418129295139446, -16.675287333937632], [-81.71071643186968, 59.366310481539784]], [[1.0, 0], [11.948068856071052, -8.680780151471982], [31.828750420619585, -97.95882117840081]], [[1.0, 0], [6.239865335745707, 4.533527535445706], [33.06481839811937, 101.76304724358143]], [[1.0, 0], [-11.510737289337465, 0], [109.0, 0]], [[1.0, 0], [-0.1270492212435288, -0.0923066623833858], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-429-11.5-c1-0-2', '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/429/2/n/d/313/1', 'plot_delta': {'__RealLiteral__': 0, 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'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60110665218307792077758628862', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81093857905641207967506898192', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91062681942219789402187412416', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.42558224671293, 'bad_primes': [3, 11, 13], 'central_character': '11.5', 'conductor': 429, 'conductor_radical': 429, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/429/2/n/d/313/1'], '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': '2-429-11.5-c1-0-2', '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': '2-429-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8508328521811281, 'root_angle': 0.15224613214736823, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60110665218307792077758628862', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '761993208441060247583890542427', 'Lhash_array': ['761993208441060247583890542427'], 'label': '2-429-11.5-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/429/2/n/d/313/1'}