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lfunc_lfunctions • Show schema
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{'Lhash': '1498827887243423624131684345641', 'a10': [-4.048917339522306, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-4.048917339522306, 0.0], 'a6': [1.0, 0.0], 'a7': [-0.6920214716300959, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.096830764957835, '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]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '1014.1', 'coefficient_field': 'CDF', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.048917339522306, 0], [5.0, 0]], [[1.0, 0], [0.6920214716300959, 0], [7.0, 0]], [[1.0, 0], [-4.850855075327144, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.384042943260192, 0], [17.0, 0]], [[1.0, 0], [-1.7801674716505151, 0], [19.0, 0]], [[1.0, 0], 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[[1.0, 0], [-6.219832528349484, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-1014-1.1-c1-0-9', 'leading_term': '2.47079981661479975096873477271', '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/1014/2/a/o/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.4707998166147997, 2.4675165462451907, 2.457506404896965, 2.440297028116363, 2.415129221006708, 2.3809968340155057, 2.3366984976626437, 2.280897929333817, 2.21218948407917, 2.1291659194519394, 2.0304858406526227, 1.9149388448628046, 1.781506883767802, 1.629420748590153, 1.45821083398878, 1.2677514692063003, 1.058298147776172, 0.8305169775985838, 0.5855056458068856, 0.32480517591788827, 0.050401769102819266, -0.23528191938819037, -0.5294066061937129, 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'5.49796056869188660020166585706892', '6.86070391608869888729693546100631', '7.32414158715904383617297145133205', '8.175257530052979246896455844341331', '8.979556125130113988977573990487683', '9.956414029867099092408017800636476'], 'prelabel': '2-1014-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18236672390134377279201613725', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14822827482958216267996048640', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60348136083605367309432240033', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.096830764957835, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1014/2/a/o/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': '2-1014-1.1-c1-0-9', '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': '2-1014-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18236672390134377279201613725', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1498827887243423624131684345641', 'Lhash_array': ['1498827887243423624131684345641'], 'label': '2-1014-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/2/a/o/1/1'}