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lfunc_lfunctions • Show schema
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{'Lhash': '3336203734618720352117692530562', 'a10': [35.14217031324918, 44.066887752202184], 'a2': [-0.8923438974523183, 3.9096140638263446], 'a3': [5.028860255579858, -6.305991304145469], 'a4': [-7.281053553528998, -3.506370589557929], 'a5': [8.763290231134148, -10.98881837726925], 'a6': [20.166519528846568, 25.288015637873954], 'a7': [3.9754142210461714, -18.08856218086733], 'a8': [0.20342315874335992, -0.2550845728262374], 'a9': [-8.46802564098708, -37.10084445398946], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-3.9754142210461714, 18.08856218086733]]]], 'bad_primes': [7], 'central_character': '49.15', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '2188450905578997390725542447736', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8923438974523183, -3.9096140638263446], [-7.207750943219353, 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54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.63180069809304397752291634513', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.29977626535258508943422292299', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.66246762652547143841165001490', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'bad_primes': [7], 'central_character': '49.15', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/4/e/a/15/2'], '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': '2-7e2-49.15-c3-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.15-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.700321613778197, 'root_angle': -0.04338310375973771, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63180069809304397752291634513', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3336203734618720352117692530562', 'Lhash_array': ['3336203734618720352117692530562'], 'label': '2-7e2-49.15-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/4/e/a/15/2'}