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lfunc_lfunctions • Show schema
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{'Lhash': '820735916456218063000156271490', 'a10': [0.0, 0.0], 'a2': [0.23662726040266316, -0.40985043747324373], 'a3': [0.0, 0.0], 'a4': [0.8880150792686605, 1.538087235180624], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.2815267508811805, 2.219669443784868], 'a8': [1.7870233432250402, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, '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': '675.451', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '2824329036990760574845265218912', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.23662726040266316, 0.40985043747324373], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.2815267508811805, -2.219669443784868], [-3.5, -6.06217782649107]], [[1.0, 0], [3.084302388613175, -5.342168442984067], 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-0.546314106312513, 'root_number': '-0.14498722013696566 - 0.989433527831433*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.273157053156', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64744647800304890071788867040', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37083798407704941980822581505', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68891547011130357371936929907', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.389902136436429, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/e/c/451/3'], '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': '2-675-9.7-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': '2-675-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': -0.2731570531562565, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64744647800304890071788867040', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '820735916456218063000156271490', 'Lhash_array': ['820735916456218063000156271490'], 'label': '2-675-9.7-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/e/c/451/3'}