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lfunc_lfunctions • Show schema
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{'Lhash': '1112554595442021787897139030713', 'a10': [0, 0], 'a2': [0, 1.0], 'a3': [0, 1.79128784747792], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [-1.79128784747792, 0], 'a7': [0, -2.79128784747792], 'a8': [0, -1.0], 'a9': [-0.20871215252208, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.182796232447249, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.599', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'conjugate': '1626436822196716327675349012664', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -1.79128784747792], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.79128784747792], [-7.0, 0]], [[1.0, 0], [-3.79128784747792, 0], [11.0, 0]], [[1.0, 0], [0, -1.20871215252208], [-13.0, 0]], [[1.0, 0], [0, -3.79128784747792], [-17.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-1150-5.4-c1-0-12', 'leading_term': '1.6601619019355872833963573587018266005123583575087125044', '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/1150/2/b/g/599/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.6601619019355873, 1.5793476494301781, 1.4943351700091512, 1.4050645232413628, 1.3113645377107321, 1.2130143414821644, 1.1098054757581475, 1.0016010684233296, 0.8883891341280564, 0.770327803048663, 0.6477810203028467, 0.5213439006496114, 0.3918574185678279, 0.26041245799325863, 0.12834346556476142, -0.002787913098364539, -0.13121874126684588, -0.25501968507482303, -0.37213823469770363, -0.4804494643899792, -0.5778133812239065, -0.6621377214506825, -0.7314448415975552, -0.7839411301391159, 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'5.25400807101062211199822904271882', '6.30330124635046198448482594238266', '6.93770323003207233789685972181670', '8.071223579601287973234763166451239', '8.711167209673644749909748647696059', '9.542115031487621164532454885509006'], 'prelabel': '2-1150-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32379180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.877650825268189882388011658252', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.03912123681488641838359439106', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89234477993705233359980567544', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.182796232447249, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1150/2/b/g/599/4'], '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': '2-1150-5.4-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': '2-1150-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.877650825268189882388011658252', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1112554595442021787897139030713', 'Lhash_array': ['1112554595442021787897139030713'], 'label': '2-1150-5.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/2/b/g/599/4'}