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lfunc_lfunctions • Show schema
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{'Lhash': '1139338764904610591775931133683', 'a10': [0.0, 0.0], 'a2': [0.8588248762868104, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.2624198318709448, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.8588248762868104, 0.0], 'a7': [3.88045382062084, 0.0], 'a8': [-2.801847308502201, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8588248762868104, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.88045382062084, 0], [7.0, 0]], [[1.0, 0], [1.3982523529180666, 0], [11.0, 0]], [[1.0, 0], [-3.3620355956946706, 0], [13.0, 0]], [[1.0, 0], [-3.115902105491687, 0], [17.0, 0]], [[1.0, 0], [2.7059517709793948, 0], [19.0, 0]], [[1.0, 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[109.0, 0]], [[1.0, 0], [16.26858226328577, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-1875-1.1-c1-0-18', 'leading_term': '1.8279296279528110811019705526334', '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/1875/2/a/l/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.827929627952811, 1.8213581024621643, 1.8015119713087469, 1.7680084482698166, 1.7202482178004128, 1.657470315211469, 1.578823222557924, 1.483447443762692, 1.3705645981746746, 1.2395682943596658, 1.0901125530808282, 0.9221941742325842, 0.736226057746544, 0.5330990179264994, 0.314230050510578, 0.08159533598085769, -0.16225347376370816, -0.4141908936913683, -0.6705381133771707, -0.9271030060873519, -1.1792398910218702, -1.4219288451537482, 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'5.62169363176808210536296608504752', '6.64853578949490057786815805659811', '7.84519572193168160854220809746798', '8.346114523438037563986767794839478', '9.094010807246931879013824786894223'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.898779809436040667508083546091', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.22916478683311507921517424111', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75352544513448775842440088679', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/l/1/4'], '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': '2-1875-1.1-c1-0-18', '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': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.898779809436040667508083546091', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1139338764904610591775931133683', 'Lhash_array': ['1139338764904610591775931133683'], 'label': '2-1875-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/l/1/4'}