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lfunc_lfunctions • Show schema
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{'Lhash': '2846831955780925013804812205603', 'a10': [1.0, 0.0], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0.0, -1.0], 'a5': [0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 1.0], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.11977560303192059, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.149', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '2923420752707680875131133805400', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.7071067811865476, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-240-240.149-c0-0-0', 'leading_term': '0.87666715031549242912334410295124', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/240/1/bm/a/149/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [0.8766671503154925, 0.8900980988597954, 0.9220651234935127, 0.9710150481818401, 1.0346318759143616, 1.1102605266483498, 1.195208201303211, 1.2868891140351024, 1.3828534069577942, 1.4807554637594198, 1.5783022955564654, 1.673204608335481, 1.7631405783507674, 1.8457354956742615, 1.9185572697218076, 1.9791265652890866, 2.02493998577522, 2.0535046927066154, 2.0623828959812562, 2.049244666822118, 2.0119274853030586, 1.9485008375944486, 1.8573340385423964, 1.7371652911496798, 1.5871698253487676, 1.4070248031728263, 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'8.332017620077728990333548048249984', '9.243675452755684177654724180201144', '10.84841673103753683404825725207542', '11.73527978311156713498965175250841', '12.73502049729843391068627570637429'], 'prelabel': '2-240-240.149-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.34608612083110263, 'root_angle': 0.12500000000000003, 'root_number': '0.92387953251128675612818318939698 + 0.38268343236508977172845998403043*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.24575443364944395837814610849', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.41427234721809658050812687514', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.34247706028749470396480426010', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.11977560303192059, 'bad_primes': [2, 3, 5], 'central_character': '240.149', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/1/bm/a/149/2'], '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': '2-240-240.149-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-240-240.149-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.34608612083110263, 'root_angle': 0.06250000000000001, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.24575443364944395837814610849', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2846831955780925013804812205603', 'Lhash_array': ['2846831955780925013804812205603'], 'label': '2-240-240.149-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/1/bm/a/149/2'}