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lfunc_lfunctions • Show schema
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{'Lhash': '1756702061301890043159693004533', 'a10': [5.854101966249685, 0.0], 'a2': [2.618033988749895, 0.0], 'a3': [0.0, 0.0], 'a4': [4.854101966249685, 0.0], 'a5': [2.23606797749979, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [7.47213595499958, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.73543002052313, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '4851.1', 'coefficient_field': 'CDF', 'conductor': 4851, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.618033988749895, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.23606797749979, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.4721359549995796, 0], [13.0, 0]], [[1.0, 0], [6.0, 0], [17.0, 0]], [[1.0, 0], [4.23606797749979, 0], [19.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 137, 'label': '2-4851-1.1-c1-0-137', 'leading_term': '8.34827143007479396924758195631', '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/4851/2/a/bh/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [8.348271430074794, 8.338711634489318, 8.309809587990468, 8.260912424830341, 8.19098139149174, 8.09866242845937, 7.982378503980631, 7.84043811642946, 7.671153861429315, 7.47296495076051, 7.244557965016207, 6.984980782499836, 6.693745417314836, 6.370916311013762, 6.017181383180202, 5.633903822846115, 5.223153190447196, 4.787714914247945, 4.331077730283237, 3.8573990565925573, 3.3714487324930054, 2.878532006447809, 2.3843931282739788, 1.8951013916938793, 1.4169219733978564, 0.9561744111336631, 0.5190820380699172, 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'5.24235802543203367006570695931307', '6.13706364626533386518532266293821', '6.51114915634020253482846225052550', '6.91439035429333203162134790865602', '8.310433093170564276830090411000842'], 'prelabel': '2-4851-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.223779400052924, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38579357828222635179628027076', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29174517526254193813568760293', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92705263726679144138433776591', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 38.73543002052313, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 4851, 'conductor_radical': 231, 'degree': 2, 'index': 137, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4851/2/a/bh/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': '2-4851-1.1-c1-0-137', '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': '2-4851-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.223779400052924, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38579357828222635179628027076', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1756702061301890043159693004533', 'Lhash_array': ['1756702061301890043159693004533'], 'label': '2-4851-1.1-c1-0-137', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4851/2/a/bh/1/2'}