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lfunc_lfunctions • Show schema
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{'Lhash': '2678778640650493274629688258503', 'a10': [321.28293653206777, -556.4783696784683], 'a2': [4.0, 6.928203230275509], 'a3': [-4.672488630851935, -8.092987706423491], 'a4': [-32.0, 55.42562584220407], 'a5': [-40.16036706650847, -69.55979620980854], 'a6': [37.37990904681548, -64.74390165138793], 'a7': [-541.8793139751166, 0.0], 'a8': [-512.0, 0.0], 'a9': [1049.835699989119, -1818.3687719807908], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.870630968396632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.0, -6.928203230275509]]], [19, [[1.0, 0], [-2106.1252576238066, -29823.41320840388]]]], 'bad_primes': [2, 19], 'central_character': '38.7', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '417975256295859492481667468002', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.0, -6.928203230275509]], [[1.0, 0], [4.672488630851935, 8.092987706423491], [-1093.5, 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'positive_zeros': ['2.11318374335025961698933099866202', '3.88220364418299905856719058911703', '5.46037362611668318756954733700714', '7.24378801719394721497092304790222', '9.056570065522515980519003003882818', '10.52327652757960675488760165199751', '11.21290905288060123111690155109378', '13.03111337261605836647367298566200', '13.41903024735717664212870224010068', '15.21421271581293161688091570792593'], 'prelabel': '2-38-19.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.445378203970739, 'root_angle': 0.5453115459489859, 'root_number': '-0.14187015040948417 + 0.9898852763945882*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.272655772974', 'prec': 47}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11318374335025961698933099866', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88220364418299905856719058912', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.46037362611668318756954733701', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.870630968396632, 'bad_primes': [2, 19], 'central_character': '19.7', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/8/c/b/7/3'], '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': '2-38-19.7-c7-0-11', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-38-19.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.445378203970739, 'root_angle': 0.27265577297449295, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '2.11318374335025961698933099866', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2678778640650493274629688258503', 'Lhash_array': ['2678778640650493274629688258503'], 'label': '2-38-19.7-c7-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/8/c/b/7/3'}