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lfunc_lfunctions • Show schema
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{'Lhash': '2119993062762118119022613768193', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.7260777573071158, 0.1437204777672192], 'a4': [0, 0], 'a5': [2.7717973064903823, 0], 'a6': [0, 0], 'a7': [-0.8557370591608517, -2.5035403103562635], 'a8': [0, 0], 'a9': [2.9586888485407243, 0.49614543988709775], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.048920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.7260777573071158, -0.1437204777672192]]], [7, [[1.0, 0], [0.8557370591608517, 2.5035403103562635]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.193', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '1791760463896630630127373010531', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7260777573071158, -0.1437204777672192]], [[1.0, 0], [-2.7717973064903823, 0], [5.0, 0]], [[1.0, 0], [0.8557370591608517, 2.5035403103562635]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-1008-63.4-c1-0-38', 'leading_term': '2.8195447563531950968945607013529918006578682902930063339', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1008/2/t/l/193/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.8195447563531952, 2.840123679592472, 2.8576037553422498, 2.871636956796262, 2.881600470667194, 2.886626935128133, 2.8856468534287094, 2.8774402020040966, 2.8606941035023046, 2.834063636091838, 2.7962332717924996, 2.745976941038778, 2.6822151972807236, 2.604068335951253, 2.510904580913566, 2.402382595265495, 2.2784876280251063, 2.139560607224114, 1.9863194662483747, 1.8198719718592566, 1.6417193304692186, 1.4537498984501496, 1.2582224210851989, 1.0577383768627788, 0.8552032088144443, 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'6.35388269839857513235843169349319', '7.61662847171765251460147727471126', '8.555069860654103058242759922288905', '9.235813359557352498480434065887191', '9.752008572500324785695421424414692'], 'prelabel': '2-1008-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': 0.07933092228067688, 'root_number': '0.96910375960493602107393804504990155632876206702414833403 + 0.24665340686797410356084888844598171241707098593643911223*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.03966546114033844', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67237964655278979335047252589', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42517624906658818711334947101', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51355587987734014551733540254', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.048920523745066, 'bad_primes': [2, 3, 7], 'central_character': '63.4', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/2/t/l/193/10'], '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': '2-1008-63.4-c1-0-38', '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': '2-1008-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': 0.03966546114033844, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67237964655278979335047252589', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2119993062762118119022613768193', 'Lhash_array': ['2119993062762118119022613768193'], 'label': '2-1008-63.4-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/2/t/l/193/10'}