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lfunc_lfunctions • Show schema
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{'Lhash': '1377129603848575575058863907485', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.7320508075688772], 'a6': [0, 0], 'a7': [0.990721402311041, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.2593', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '413815700263596167563567998117', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-5.0, 0]], [[1.0, 0], [-0.990721402311041, 0], [7.0, 0]], [[1.0, 0], [0, -2.100830432684745], [-11.0, 0]], [[1.0, 0], [0, -6.361517257376805], [-13.0, 0]], [[1.0, 0], [3.816810237633354, 0], [17.0, 0]], [[1.0, 0], [0, 2.0], [-19.0, 0]], [[1.0, 0], [7.102846662634641, 0], [23.0, 0]], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 66, 'label': '2-72e2-8.5-c1-0-66', 'leading_term': '1.177350486057232707026519645951026092427847846465783036', '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/5184/2/d/r/2593/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.1773504860572328, 1.3236896595010708, 1.457610188597574, 1.578088123370209, 1.6839734483326343, 1.7739825604191677, 1.8467074882908516, 1.9006416830909458, 1.9342211983977284, 1.9458792514846062, 1.9341115518308594, 1.8975493920253064, 1.8350372913391249, 1.7457119222338429, 1.6290790939802091, 1.4850856823685366, 1.3141835584947659, 1.1173827723690946, 0.8962914871898013, 0.6531404419679192, 0.39079005082113294, 0.1127186336103579, -0.17700928057082432, 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'5.61946814842963705847592613029040', '6.20803363647151716636923715554026', '7.02538537327231094704935123022476', '7.74731130441630813718747532637383', '8.344675471820503857147045976752120'], 'prelabel': '2-72e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.5833333333333334, 'root_number': '-0.258819045102520762348898837624048328349068901319930514 + 0.965925826289068286749743199728897367633904839008404551*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2916666666666667', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08636370589864071113434304085', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33095571310737458410114255027', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11265893063159503727005184498', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 66, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/d/r/2593/4'], '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': '2-72e2-8.5-c1-0-66', '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': '2-72e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.2916666666666667, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08636370589864071113434304085', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1377129603848575575058863907485', 'Lhash_array': ['1377129603848575575058863907485'], 'label': '2-72e2-8.5-c1-0-66', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/d/r/2593/4'}