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lfunc_lfunctions • Show schema
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{'Lhash': '1956050645765179359959243998300', 'a10': [2.302775637731995, 0.0], 'a2': [1.0, 0.0], 'a3': [3.302775637731995, 0.0], 'a4': [1.0, 0.0], 'a5': [2.302775637731995, 0.0], 'a6': [3.302775637731995, 0.0], 'a7': [-2.605551275463989, 0.0], 'a8': [1.0, 0.0], 'a9': [7.908326913195984, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.86304007342658, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [37, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 37], 'central_character': '2738.1', 'coefficient_field': 'CDF', 'conductor': 2738, 'conductor_radical': 74, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.302775637731995, 0], [3.0, 0]], [[1.0, 0], [-2.302775637731995, 0], [5.0, 0]], [[1.0, 0], [2.605551275463989, 0], [7.0, 0]], [[1.0, 0], [2.302775637731995, 0], [11.0, 0]], [[1.0, 0], [1.3027756377319946, 0], [13.0, 0]], [[1.0, 0], [-6.0, 0], [17.0, 0]], [[1.0, 0], [2.0, 0], [19.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 80, 'label': '2-2738-1.1-c1-0-80', 'leading_term': '6.21610094503954941479367391427', '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/2738/2/a/l/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [6.21610094503955, 6.2118141626615895, 6.198783335204505, 6.1765061432804815, 6.144175200131066, 6.100720770228045, 6.044866832204054, 5.97519728412262, 5.890228818806055, 5.788487027621971, 5.668582553626475, 5.529284521684273, 5.36958893935516, 5.1887802207629345, 4.986484393373663, 4.762712885474555, 4.517896060062101, 4.252905871179247, 3.9690671899794023, 3.668157499573128, 3.352394807473365, 3.0244137856265483, 2.687230329334024, 2.3441949319302458, 1.9989355018296462, 1.6552904989154746, 1.3172335318457251, 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'5.83414971611436273708895190434571', '6.46326724060365295881527750343682', '7.56462152729171433762411344891317', '7.86056068938729605223363819640743', '8.944968886000003926650433398827827'], 'prelabel': '2-2738-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.675792988726787, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54305188307646409208210980611', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52714308561159724942380146071', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96548774308850045829590794528', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.86304007342658, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 2738, 'conductor_radical': 74, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2738/2/a/l/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': '2-2738-1.1-c1-0-80', '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': '2-2738-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.675792988726787, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54305188307646409208210980611', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1956050645765179359959243998300', 'Lhash_array': ['1956050645765179359959243998300'], 'label': '2-2738-1.1-c1-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2738/2/a/l/1/2'}