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lfunc_lfunctions • Show schema
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{'Lhash': '1540689119212997659228276590777', 'a10': [0.05609488113743001, -0.03238639472485528], 'a2': [0.10595341243513333, -0.06117223119098367], 'a3': [0, 0], 'a4': [-0.9925159162622337, 1.7190879942869661], 'a5': [0.5294296790277742, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0.48754657712523203], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.5642081874154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '1323.656', 'coefficient_field': 'CDF', 'conductor': 1323, 'conductor_radical': 21, 'conjugate': '907651574467550337111628420053', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.10595341243513333, 0.06117223119098367], [1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5294296790277742, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.204492778483656], [-11.0, 0]], [[1.0, 0], [-1.7471433601276731, 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'9.085417728709021940235897473102127', '9.800643072293369874687856032103278'], 'prelabel': '2-1323-63.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': 0.16396470318404854, 'root_number': '0.8702383869761488518347479341647815650414831927706856689 + 0.4926308453935366402599231986233500926230117838314716258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08198235159202427', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21538941324652870503717038572', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27162270461489514727920483010', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86354335738326055578081509443', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.5642081874154, 'bad_primes': [3, 7], 'central_character': '63.47', 'conductor': 1323, 'conductor_radical': 21, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1323/2/s/d/656/13'], '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': '2-1323-63.47-c1-0-24', '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': '2-1323-63.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': 0.08198235159202427, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21538941324652870503717038572', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1540689119212997659228276590777', 'Lhash_array': ['1540689119212997659228276590777'], 'label': '2-1323-63.47-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/2/s/d/656/13'}