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lfunc_lfunctions • Show schema
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{'Lhash': '579321613715759851092870314407', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 6.0], 'a6': [0, 0], 'a7': [-21.166010488516726, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.97020032661322, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.577', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '922748278480070488160382998326', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -6.0], [-125.0, 0]], [[1.0, 0], [21.166010488516726, 0], [343.0, 0]], [[1.0, 0], [0, 42.33202097703345], [-1331.0, 0]], [[1.0, 0], [0, 20.0], [-2197.0, 0]], [[1.0, 0], [8.0, 0], [4913.0, 0]], [[1.0, 0], [0, -84.6640419540669], [-6859.0, 0]], [[1.0, 0], [169.3280839081338, 0], [12167.0, 0]], [[1.0, 0], [0, -46.0], [-24389.0, 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'4.86024276948427985340841939098665', '6.10943607056014575740970176992833', '6.74051311242895162329225037058130', '7.62690968387899541193064266616398', '8.600987119766571863873048050849386', '9.587246387645614317497818176302993'], 'prelabel': '2-1152-8.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.2444041826328, 'root_angle': -0.125, 'root_number': '0.7071067811865475244008443621048490392848359376884740366 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125', 'prec': 20}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45700417260991164465714301376', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91274880559935090060285910323', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99151796830105605266624666683', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.97020032661322, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/4/d/k/577/3'], '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': '2-1152-8.5-c3-0-16', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1152-8.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.2444041826328, 'root_angle': -0.125, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45700417260991164465714301376', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '579321613715759851092870314407', 'Lhash_array': ['579321613715759851092870314407'], 'factors': ['2-1152-8.5-c3-0-16'], 'label': '2-1152-8.5-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/4/d/k/577/3'}