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lfunc_lfunctions • Show schema
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{'Lhash': '1431113206392034257041975499356', 'a10': [0.32442334882145774, -0.21677275132473922], 'a2': [-0.9238795325112867, -0.3826834323650898], 'a3': [0.0, 0.0], 'a4': [0.7071067811865476, 0.7071067811865476], 'a5': [-0.21677275132473922, 0.32442334882145774], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.3826834323650898, -0.9238795325112867], 'a9': [0.9238795325112867, -0.3826834323650898], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9238795325112867, 0.3826834323650898]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-0.9238795325112867, -0.3826834323650898]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1371', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1021504088154776890367852525678', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 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[[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [-0.9238795325112867, 0.6173165676349103], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [1.0897902135516373, -1.6309863136978342], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [-0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.4142135623730951, 1.4142135623730951], [0, -1.0]], [[1.0, 0], [-1.6309863136978342, -1.0897902135516373], [0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [-0.9238795325112867, 0.6173165676349103], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [-1.6309863136978342, -0.32442334882145774], [0.9238795325112867, 0.3826834323650898]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-3332-476.419-c0-0-2', 'leading_term': '0.82396356321490831585905673217502', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/bn/a/1371/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.8239635632149083, 0.8458679237585863, 0.8708645228918902, 0.8985406641734256, 0.9279546758472896, 0.9577343492013602, 0.9861970480424143, 1.011469677773029, 1.0315954270213497, 1.044622845100824, 1.0486785170695825, 1.0420270758896755, 1.0231225437061617, 0.990654144545074, 0.9435885542477738, 0.8812094490194555, 0.8031543289843249, 0.7094479472856177, 0.6005312391524341, 0.4772843796330344, 0.3410424692857319, 0.19360232877839542, 0.037218958619282594, -0.12540962285914548, -0.2911702203841343, -0.4565757433443084, 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'6.14707267726628780394613229439356', '6.94840511352471239980478048375914', '7.39279439346930465545798021078552', '8.159878161823216832288068538896729', '8.873452687552963370150654233356365'], 'prelabel': '2-3332-476.419-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.25556970289050973, 'root_number': '0.69462639859782210364518938092261 + 0.71937067383305219543537857893546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12778485144525487', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12894925946816484229440663141', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09187156278542548737629572141', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19572815556730129968096934807', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.419', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/bn/a/1371/1'], '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': '2-3332-476.419-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.419-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.12778485144525487, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12894925946816484229440663141', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1431113206392034257041975499356', 'Lhash_array': ['1431113206392034257041975499356'], 'label': '2-3332-476.419-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/bn/a/1371/1'}