Formats: - HTML - YAML - JSON - 2026-07-17T14:03:58.970698
  • lfunc_lfunctions • Show schema
    {'Lhash': '1636122480881329729271448121931', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0.8965754721680536], 'a6': [0, 0], 'a7': [0, -1.2679491924311228], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.348612101957944, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.1295', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'conjugate': '794017598727425571239491477076', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.8965754721680536], [-5.0, 0]], [[1.0, 0], [0, 1.2679491924311228], [-7.0, 0]], [[1.0, 0], [4.242640687119285, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0], [13.0, 0]], [[1.0, 0], [0, 0.8965754721680536], [-17.0, 0]], [[1.0, 0], [0, 4.732050807568878], [-19.0, 0]], [[1.0, 0], [-7.3484692283495345, 0], [23.0, 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[-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-6e4-12.11-c1-0-14', 'leading_term': '1.3771619376183959781350823946680222764740982987172110783', '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/1296/2/c/g/1295/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.377161937618396, 1.4522859111860085, 1.5194584692057924, 1.5784570422991242, 1.6288138099299336, 1.6698217838709395, 1.7005566736838038, 1.7199126852274413, 1.7266497999677866, 1.7194498259198512, 1.6969785331512428, 1.6579513853861008, 1.6012006513498889, 1.5257419450647633, 1.4308384557186082, 1.3160612680465829, 1.1813442493953235, 1.0270320095378804, 0.8539194494180468, 0.6632814310607524, 0.4568911454959056, 0.23702584660102755, 0.006458768978401693, 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'5.05392307421370389158725890362928', '5.29420071046552904404342310428579', '6.51671268754033087486196322484659', '7.36710814579707623430462450367654', '8.405676027105561117306961173331680', '8.751381298006495212647522044671996', '9.815686153391986363342497380994064'], 'prelabel': '2-6e4-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.216925877597733, 'root_angle': 0.16666666666666666, 'root_number': '0.5000000000000000000000000000000000000000000000000000000 + 0.8660254037844386467637231707529361834714026269051903141*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.16666666666666669', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29067306132049335121077859207', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65975586666681119550042584927', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58494987320886144053407202266', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 10.348612101957944, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/2/c/g/1295/5'], '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': '2-6e4-12.11-c1-0-14', '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': '2-6e4-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.216925877597733, 'root_angle': 0.16666666666666666, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29067306132049335121077859207', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '1636122480881329729271448121931', 'Lhash_array': ['1636122480881329729271448121931'], 'factors': ['2-6e4-12.11-c1-0-14'], 'label': '2-6e4-12.11-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/2/c/g/1295/5'}