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lfunc_lfunctions • Show schema
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{'Lhash': '1208184164733669111918327130342', 'a10': [-0.3121069418667407, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-0.3121069418667407, 0.0], 'a6': [1.0, 0.0], 'a7': [-1.1271007318215172, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.24561290125763, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]], [53, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 19, 53], 'central_character': '6042.1', 'coefficient_field': 'CDF', 'conductor': 6042, 'conductor_radical': 6042, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.3121069418667407, 0], [5.0, 0]], [[1.0, 0], [1.1271007318215172, 0], [7.0, 0]], [[1.0, 0], [-4.840000419223654, 0], [11.0, 0]], [[1.0, 0], [2.900271763813425, 0], [13.0, 0]], [[1.0, 0], [2.372478997655146, 0], [17.0, 0]], [[1.0, 0], 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[[1.0, 0], [-6.551743216646939, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 51, 'label': '2-6042-1.1-c1-0-51', 'leading_term': '4.08186775609569707857408961883', '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/6042/2/a/bh/1/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [4.081867756095697, 4.0721229513696855, 4.0428128662363, 3.993718168888335, 3.9244984414917896, 3.834728289814264, 3.723944868028502, 3.5917041294942003, 3.4376427659219755, 3.261542668307134, 3.063394805685017, 2.8434596284990508, 2.6023214135291437, 2.3409343322056584, 2.0606584087110384, 1.7632839153989213, 1.4510431188307904, 1.1266086370880644, 0.7930780006741956, 0.4539443307590564, 0.11305336554492108, -0.22545261743510636, -0.5572031162316932, 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'4.24835512209240473840365178435661', '5.09436934496963354694225284837574', '5.96906013545899853877353816855390', '6.76821635479800098691063557108918', '7.16562111160319652441835655996650', '7.931055122389247441576136292712529'], 'prelabel': '2-6042-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.945906197268837, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.953089253865494263116087313569', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.11679605850612478447534576307', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87651861608429791113740918739', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.24561290125763, 'bad_primes': [2, 3, 19, 53], 'central_character': '1.1', 'conductor': 6042, 'conductor_radical': 6042, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6042/2/a/bh/1/6'], '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': '2-6042-1.1-c1-0-51', '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': '2-6042-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.945906197268837, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.953089253865494263116087313569', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1208184164733669111918327130342', 'Lhash_array': ['1208184164733669111918327130342'], 'label': '2-6042-1.1-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6042/2/a/bh/1/6'}