Formats: - HTML - YAML - JSON - 2026-09-07T15:19:09.152512
  • lfunc_lfunctions • Show schema
    {'Lhash': '1518376236207730726265130792834', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-47.98663240181728, -83.11528540407848], 'a6': [0, 0], 'a7': [189.00028096590714, -327.35808927774417], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 134.95033100914065, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '432.289', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '446525540227923171678922530273', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [47.98663240181728, 83.11528540407848], [-39062.5, 67658.23467065927]], [[1.0, 0], [-189.00028096590714, 327.35808927774417], [-411771.5, -713209.159108848]], [[1.0, 0], [-3436.628135722343, 5952.414537791809], [-9743585.5, -16876385.133891404]], [[1.0, 0], [-4826.639894585555, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 32, 'label': '2-432-9.7-c7-0-32', 'leading_term': '1.641613131415148617598905585273450675997571551259642730', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/432/8/i/c/289/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [1.6416131314151485, 1.8985866155005888, 2.128486989072452, 2.32574509266592, 2.485517145090213, 2.6037956850916855, 2.677503047458269, 2.7045653701303736, 2.6839654627939757, 2.615773234649027, 2.501152776397361, 2.342345615208551, 2.1426301070195883, 1.906257392719182, 1.6383648173966257, 1.344868187818368, 1.0323347146353525, 0.7078389436514971, 0.37880441515124835, 0.0528341915134699, -0.2624662495814298, -0.5596699570092891, -0.8317092475755637, -1.072052051308836, -1.2748695907110363, -1.4351911436206795, -1.5490417596565065, 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'8.567892701140852673554375546175847', '9.356327040465172750448827834696206', '10.36824367752564272523253906062659'], 'prelabel': '2-432-9.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.616812428938527, 'root_angle': 0.3590955199585932, 'root_number': '-0.6330348811503420094963034008258696130742187353538095859 + 0.7741232713508697813534022349201731870626010164342734990*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3590955199585932', 'prec': 54}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19778765216090330197635413924', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.27410458400551614980469018497', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.50858393941822048441482136494', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 134.95033100914065, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/8/i/c/289/3'], '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': '2-432-9.7-c7-0-32', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-432-9.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.616812428938527, 'root_angle': 0.3590955199585932, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19778765216090330197635413924', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1518376236207730726265130792834', 'Lhash_array': ['1518376236207730726265130792834'], 'factors': ['2-432-9.7-c7-0-32'], 'label': '2-432-9.7-c7-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/8/i/c/289/3'}