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lfunc_lfunctions • Show schema
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{'Lhash': '2805957239009201282310884665801', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.598076211353316, -1.5], 'a4': [0.0, 0.0], 'a5': [0.13397459621556135, -2.232050807568877], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [3.0, -5.196152422706632], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.13397459621556135, 2.232050807568877]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '980.569', 'coefficient_field': 'CDF', 'conductor': 980, 'conductor_radical': 70, 'conjugate': '1336505590353345023983568999873', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.598076211353316, 1.5], [1.5, -2.598076211353316]], [[1.0, 0], [-0.13397459621556135, 2.232050807568877]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5, 2.598076211353316], [-5.5, 9.526279441628825]], [[1.0, 0], [0, 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-0.7816184588377472, -0.6302934709301924, -0.0974897502745872], 'positive_zeros': ['2.21350996757624950219245770408835', '2.84909332267963434753625479172450', '3.84026228913242950129517929817098', '4.65023441726917074162145194064170', '5.94043774516656480927488681282737', '7.21250933477752441130218541781174', '7.75074184773112457121461601320928', '8.657490878952809464549848455674863', '9.445539821258872373899085040338901', '10.26026453260722197668040557818180'], 'prelabel': '2-980-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.797380810344827, 'root_angle': 0.5594289551241256, 'root_number': '-0.18561880011190607 + 0.9826218301284662*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.279714477562', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21350996757624950219245770409', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84909332267963434753625479172', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84026228913242950129517929817', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'bad_primes': [2, 5, 7], 'central_character': '35.9', 'conductor': 980, 'conductor_radical': 70, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/980/2/q/f/569/2'], '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': '2-980-35.9-c1-0-19', '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': '2-980-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.797380810344827, 'root_angle': 0.2797144775620628, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21350996757624950219245770409', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2805957239009201282310884665801', 'Lhash_array': ['2805957239009201282310884665801'], 'label': '2-980-35.9-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/980/2/q/f/569/2'}