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lfunc_lfunctions • Show schema
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{'Lhash': '913510252030795535954924960935', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.2360679774997898, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.47213595499958, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.4721359549995794, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.34315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.2360679774997898, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.47213595499958, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [3.23606797749979, 0], [13.0, 0]], [[1.0, 0], [6.47213595499958, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.0, 0], [23.0, 0]], [[1.0, 0], [-2.0, 0], 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'group': 'GL2', 'index': 21, 'label': '2-3800-1.1-c1-0-21', 'leading_term': '1.44869373189798587565177482387', '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/3800/2/a/q/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4486937318979858, 1.4416113052524222, 1.4203218756154399, 1.3847056769866133, 1.3345849193742987, 1.26975496980307, 1.1900250788428315, 1.095266089734936, 0.9854622749528272, 0.8607643686333795, 0.7215409644083539, 0.5684256753757853, 0.40235775493864095, 0.2246142120342337, 0.036831793741456655, -0.15898246178309258, -0.36045308150567384, -0.5648510926339112, -0.7691223967251355, -0.9699296249542784, -1.1637071844216336, -1.3467288557589785, -1.5151869361636645, -1.6652815439373938, -1.7933183186165886, -1.8958123756941019, 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'5.44159806472607436275098588854737', '6.13580075056375641079024725938594', '7.15228737477916643590786041527952', '7.64005750182550139189269447278531', '8.648551117302615527115396342504598'], 'prelabel': '2-3800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72063252434568800442681144632', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98647378972281012124670374091', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75296059343823700122785558885', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.34315276808656, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/2/a/q/1/1'], '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': '2-3800-1.1-c1-0-21', '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': '2-3800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72063252434568800442681144632', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '913510252030795535954924960935', 'Lhash_array': ['913510252030795535954924960935'], 'label': '2-3800-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/2/a/q/1/1'}