Formats: - HTML - YAML - JSON - 2026-08-13T04:01:17.604507
  • lfunc_lfunctions • Show schema
    {'Lhash': '2280390467080182694676520954906', 'a10': [0, 0], 'a2': [0, 1.0], 'a3': [0, -2.6873995617361737], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [2.6873995617361737, 0], 'a7': [0, -4.596915527892125], 'a8': [0, -1.0], 'a9': [-4.222116404419777, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.182796232447249, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.599', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'conjugate': '911243295574150313675931775686', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 2.6873995617361737], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.596915527892125], [-7.0, 0]], [[1.0, 0], [-5.131632370575728, 0], [11.0, 0]], [[1.0, 0], [0, -1.2221164044197774], [-13.0, 0]], [[1.0, 0], [0, 4.687399561736173], [-17.0, 0]], 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[109.0, 0]], [[1.0, 0], [0, -6.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-1150-5.4-c1-0-27', 'leading_term': '1.505974352600477307366683554603633255632003371890599465', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1150/2/b/j/599/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.5059743526004774, 1.6223672090114236, 1.737945309526922, 1.8525300441200374, 1.9657206134587595, 2.0768678568029304, 2.1850621161398234, 2.2891349704742034, 2.3876738899370444, 2.4790483581451523, 2.561445781779536, 2.632915485762158, 2.6914191964745218, 2.734886564522068, 2.7612744129990214, 2.7686284824078884, 2.755146467207703, 2.719241105841914, 2.6596020105608487, 2.5752548246582148, 2.465616193110636, 2.3305429469754033, 2.170373848733471, 1.9859622385825622, 1.778697970934208, 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'6.33924179702683081766912297636770', '8.072169349501955309585769036695875', '8.930089161506577908467622121660975', '9.325637678616639311497953776524608', '9.888549124996550970062593026683235'], 'prelabel': '2-1150-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': 0.32379180882521663, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32379180882521663', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79891088811823884226094515511', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.13956573974367777269258061381', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.76810244846693806199911413662', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 9.182796232447249, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1150/2/b/j/599/4'], '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': '2-1150-5.4-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1150-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79891088811823884226094515511', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2280390467080182694676520954906', 'Lhash_array': ['2280390467080182694676520954906'], 'factors': ['2-1150-5.4-c1-0-27'], 'label': '2-1150-5.4-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/2/b/j/599/4'}