Formats: - HTML - YAML - JSON - 2026-10-23T02:36:13.567260
  • lfunc_lfunctions • Show schema
    {'Lhash': '2066396321040049066738438713451', 'a10': [0.0, 0.0], 'a2': [0.6566204310471103, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.568849609531507, 0.0], 'a5': [0.0, 0.0], 'a6': [0.6566204310471103, 0.0], 'a7': [-1.3433795689528896, 0.0], 'a8': [-2.34337956895289, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.158486560905317, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 37], 'central_character': '2775.1', 'coefficient_field': 'CDF', 'conductor': 2775, 'conductor_radical': 555, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6566204310471103, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3433795689528896, 0], [7.0, 0]], [[1.0, 0], [-4.167837925921683, 0], [11.0, 0]], [[1.0, 0], [3.5688496095315068, 0], [13.0, 0]], [[1.0, 0], [0.7443912525627138, 0], [17.0, 0]], [[1.0, 0], 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0], [109.0, 0]], [[1.0, 0], [12.904525461374872, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 101, 'label': '2-2775-1.1-c1-0-101', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2775/2/a/v/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [-1.1911240180281092e-60, 0.20203247335087587, 0.4037189399254007, 0.604658244438987, 0.80434211401151, 1.0021092924562853, 1.1971082324088964, 1.3882701881515542, 1.5742938827245352, 1.7536422742589974, 1.9245513764576407, 2.085050628266688, 2.2329939641207193, 2.3661004957742717, 2.4820035561144214, 2.5783067481332753, 2.6526455650081195, 2.702753082694832, 2.7265281644394204, 2.7221045536687374, 2.6879191697127016, 2.622777865396615, 2.5259168646429426, 2.3970580807197828, 2.236456530491921, 2.044938114969323, 1.8239261382290433, 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'6.62849559826181119762914649297737', '7.85535277802683564597500939318333', '8.503436991232929952501719051034511'], 'prelabel': '2-2775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.707280165966895, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63009927236102162964090527588', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.92533811940466137127151976314', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.61604079253025426740987219873', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 22.158486560905317, 'bad_primes': [3, 5, 37], 'central_character': '1.1', 'conductor': 2775, 'conductor_radical': 555, 'degree': 2, 'index': 101, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2775/2/a/v/1/2'], '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': '2-2775-1.1-c1-0-101', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.707280165966895, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63009927236102162964090527588', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2066396321040049066738438713451', 'Lhash_array': ['2066396321040049066738438713451'], 'factors': ['2-2775-1.1-c1-0-101'], 'label': '2-2775-1.1-c1-0-101', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2775/2/a/v/1/2'}