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lfunc_lfunctions • Show schema
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{'Lhash': '1695600871883075316324053153385', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.4764520397307907, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.28331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': 'CDF', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.4764520397307907, 0], [7.0, 0]], [[1.0, 0], [3.343637334643997, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [17.0, 0]], [[1.0, 0], [6.772993453836369, 0], [19.0, 0]], [[1.0, 0], [-4.772993453836369, 0], [23.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 92, 'label': '2-7800-1.1-c1-0-92', '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/7800/2/a/br/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.2737734396872024e-60, 0.2243551296408433, 0.4473488147203065, 0.6675756206862857, 0.8835456168230232, 1.0936505828896341, 1.2961396800726994, 1.4891066949140819, 1.6704902273505793, 1.8380874326712509, 1.989581202109173, 2.1225800204797345, 2.2346691950736313, 2.3234717143714545, 2.386716662478134, 2.4223128733175394, 2.428425343668622, 2.4035518238421645, 2.34659696054672, 2.256941373750389, 2.1345031072898344, 1.9797890035022097, 1.7939337186463804, 1.5787243219933542, 1.33660871004069, 1.070686419478148, 0.7846808370773342, 0.48289227757221836, 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'6.74826729799244326616851944655885', '7.64836977191603915429201226210660'], 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, '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': '1.33759323868721965817113338273', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61398239626680768403055755465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75294442567611409536773755567', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.28331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'index': 92, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/br/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': '2-7800-1.1-c1-0-92', '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': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33759323868721965817113338273', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1695600871883075316324053153385', 'Lhash_array': ['1695600871883075316324053153385'], 'label': '2-7800-1.1-c1-0-92', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/br/1/2'}