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lfunc_lfunctions • Show schema
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{'Lhash': '2064303537490912478778460633801', 'a10': [0.0, 0.0], 'a2': [-1.7320508075688772, 1.7320508075688772], 'a3': [0.0, 0.0], 'a4': [0.0, -4.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.224744871391589, -1.224744871391589], 'a8': [3.4641016151377544, 3.4641016151377544], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.107', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1001329178033677280138857722526', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7320508075688772, -1.7320508075688772], [0, -2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.224744871391589, 1.224744871391589], [0, 7.0]], [[1.0, 0], [0, 4.242640687119285], [-11.0, 0]], [[1.0, 0], [-3.6742346141747673, 3.6742346141747673], [0, 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3.2479434253750883, 0.599713906264796], 'positive_zeros': ['1.62844835723601809902365422191830', '2.96186263021755750703819101722286', '4.39915894184286617827701242204582', '6.36420580567232837920270535802395', '7.58641545234287555253528826062213', '8.751838628297997093122650332661670', '9.402805178380579625629790557276605', '10.21165850034485547602030765611040', '11.20313618241031853236235548027958', '12.00440012228052309141403199162382'], 'prelabel': '2-15e2-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.012342023583967195, 'root_number': '0.9992483977295441 - 0.03876389602373393*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00617101179198', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62844835723601809902365422192', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96186263021755750703819101722', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39915894184286617827701242205', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '15.2', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/f/b/107/1'], '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': '2-15e2-15.2-c1-0-3', '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': '2-15e2-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.006171011791983597, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62844835723601809902365422192', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2064303537490912478778460633801', 'Lhash_array': ['2064303537490912478778460633801'], 'label': '2-15e2-15.2-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/f/b/107/1'}