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lfunc_lfunctions • Show schema
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{'Lhash': '1672381637216464034633094255254', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.1532276358491114, 0.0], 'a4': [0.0, 0.0], 'a5': [1.8600980960848696, 0.0], 'a6': [0.0, 0.0], 'a7': [4.617058437508451, 0.0], 'a8': [0.0, 0.0], 'a9': [6.942844523482575, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.48445500545037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [53, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 11, 53], 'central_character': '9328.1', 'coefficient_field': 'CDF', 'conductor': 9328, 'conductor_radical': 1166, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.1532276358491114, 0], [3.0, 0]], [[1.0, 0], [-1.8600980960848696, 0], [5.0, 0]], [[1.0, 0], [-4.617058437508451, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.2241736220370941, 0], [13.0, 0]], [[1.0, 0], [-0.6759577434061633, 0], [17.0, 0]], [[1.0, 0], [-2.3516780022609627, 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[[1.0, 0], [3.9894622486651214, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 207, 'label': '2-9328-1.1-c1-0-207', 'leading_term': '6.66300966985359451882746106255', '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/9328/2/a/bm/1/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [6.6630096698535946, 6.650644877567365, 6.61342537977197, 6.550991674149844, 6.462796217599326, 6.348176669011822, 6.206450523517304, 6.0370242782073085, 5.839509576435415, 5.613838710861777, 5.360372317552535, 5.079992919355438, 4.7741790292188, 4.445055679941293, 4.095418419289189, 3.7287289485321384, 3.349081667630756, 2.961141419643727, 2.5700537066984026, 2.181329586304896, 1.8007083506577133, 1.434001935548287, 1.086925783767678, 0.7649215771285686, 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'4.81590214794307271031728677112238', '5.50501018217347575058130798292110', '6.47367135555996248837813569309206', '7.35647938904285111255569425055466', '8.014957066267600729476406900136598'], 'prelabel': '2-9328-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.630437706481079, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31927649220957758423924726126', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86736275388179524090044406612', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.45878198874396957106661229687', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 74.48445500545037, 'bad_primes': [2, 11, 53], 'central_character': '1.1', 'conductor': 9328, 'conductor_radical': 1166, 'degree': 2, 'index': 207, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9328/2/a/bm/1/11'], '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': '2-9328-1.1-c1-0-207', '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': '2-9328-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.630437706481079, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31927649220957758423924726126', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1672381637216464034633094255254', 'Lhash_array': ['1672381637216464034633094255254'], 'label': '2-9328-1.1-c1-0-207', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9328/2/a/bm/1/11'}