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lfunc_lfunctions • Show schema
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{'Lhash': '1246679455179468554204226208165', 'a10': [6.691098395705309, 0.0], 'a2': [-2.546293053870689, 0.0], 'a3': [-1.606507395222971, 0.0], 'a4': [4.4836083161901215, 0.0], 'a5': [-2.6277801706814494, 0.0], 'a6': [4.090638621448146, 0.0], 'a7': [1.5271879770979389, 0.0], 'a8': [-6.323994604050385, 0.0], 'a9': [-0.419133989093905, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.0959177024818, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[23, [[1.0, 0], [1.0, 0]]], [349, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [23, 349], 'central_character': '8027.1', 'coefficient_field': 'CDF', 'conductor': 8027, 'conductor_radical': 8027, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.546293053870689, 0], [2.0, 0]], [[1.0, 0], [1.606507395222971, 0], [3.0, 0]], [[1.0, 0], [2.6277801706814494, 0], [5.0, 0]], [[1.0, 0], [-1.5271879770979389, 0], [7.0, 0]], [[1.0, 0], [-5.1089911524911, 0], [11.0, 0]], [[1.0, 0], [1.3377894835227184, 0], 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[337.0, 0]], [[1.0, 0], [33.24413326720538, 0], [347.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 353, 'label': '2-8027-1.1-c1-0-353', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/8027/2/a/d/1/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.0501338281390677e-60, 0.061860485159956576, 0.122762722302212, 0.18174137803541365, 0.2378187511496612, 0.29000295181500835, 0.33729092915058395, 0.37867736364322346, 0.4131700092629815, 0.43981161495362636, 0.4577081098297122, 0.4660623263478778, 0.4642121774298387, 0.45167190542143765, 0.4281747853306606, 0.393715490953892, 0.3485902179294916, 0.29343260036935115, 0.22924345652383368, 0.15741245421899458, 0.07972989983227724, -0.0016129729920379293, -0.08403660548263944, 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'4.75931311711637801907369782337617', '5.67931497600539759534084125428704', '6.33377539976076292922473528705008', '7.12076956644393128979070289822475', '7.59616903797603916258215681997524'], 'prelabel': '2-8027-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.005992611942744, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.983456683533313378247511928952', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.57271560074096532963507631010', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98009485733088408367421733085', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.0959177024818, 'bad_primes': [23, 349], 'central_character': '1.1', 'conductor': 8027, 'conductor_radical': 8027, 'degree': 2, 'index': 353, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8027/2/a/d/1/11'], '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': '2-8027-1.1-c1-0-353', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8027-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.005992611942744, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.983456683533313378247511928952', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1246679455179468554204226208165', 'Lhash_array': ['1246679455179468554204226208165'], 'label': '2-8027-1.1-c1-0-353', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8027/2/a/d/1/11'}