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lfunc_lfunctions • Show schema
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{'Lhash': '1337430177900501413951624672473', 'a10': [2.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [2.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.82362001368209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '3234.1', 'coefficient_field': 'CDF', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.414213562373095, 0], [13.0, 0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [2.242640687119285, 0], [19.0, 0]], [[1.0, 0], [4.82842712474619, 0], [23.0, 0]], [[1.0, 0], [-9.65685424949238, 0], [29.0, 0]], 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'GL2', 'index': 29, 'label': '2-3234-1.1-c1-0-29', 'leading_term': '3.16496675848995291312998275835', '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/3234/2/a/bc/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.164966758489953, 3.158344828744497, 3.13838380445281, 3.1048058677021744, 3.0571737656475886, 2.994927738332634, 2.917433947672453, 2.8240415727833654, 2.7141454488891594, 2.5872510886375815, 2.443039084760409, 2.281426185337897, 2.102620692426842, 1.9071702092123857, 1.6960001160344846, 1.4704414756211828, 1.2322473512068384, 0.9835967760743497, 0.7270858522535492, 0.46570569317202565, 0.20280717155618025, -0.05794730211273298, -0.3126444598200216, -0.557192497399764, -0.787403895450291, -0.9990872638077201, -1.1881463987114214, -1.3506844179752677, 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'7.981469552544518552284372504302005', '8.452700009455326605632775384571160'], 'prelabel': '2-3234-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05504638080848840359357740156', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07382726814357683375991202659', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11308842732284167142129486182', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.82362001368209, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3234/2/a/bc/1/2'], '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': '2-3234-1.1-c1-0-29', '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': '2-3234-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05504638080848840359357740156', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1337430177900501413951624672473', 'Lhash_array': ['1337430177900501413951624672473'], 'label': '2-3234-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3234/2/a/bc/1/2'}