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lfunc_lfunctions • Show schema
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{'Lhash': '1359605956592533262983169573219', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.302775637731995, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.20791222591653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '4284.1', 'coefficient_field': 'CDF', 'conductor': 4284, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.302775637731995, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [-6.60555127546399, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-6.60555127546399, 0], [19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, 0], [29.0, 0]], [[1.0, 0], 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'2-4284-1.1-c1-0-18', 'leading_term': '2.93075100448148794019511621832', '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/4284/2/a/n/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.930751004481488, 2.923916691421045, 2.903344745254154, 2.868836277142362, 2.820086343874258, 2.7567218292172484, 2.6783508466513495, 2.5846205011141232, 2.475279509253999, 2.350242114766781, 2.2096498966209515, 2.053928385659601, 1.8838358119073852, 1.7005017461172993, 1.5054538380518943, 1.300631272331074, 1.0883839566525404, 0.8714568325390337, 0.652959065613905, 0.4363182411602751, 0.22522006926991198, 0.023534496048338634, -0.16477047773717518, -0.3357255569138294, -0.48546536725261974, -0.6103396067846506, -0.7070272486293122, -0.7726505921719022, -0.8048857045526829, 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'7.75151030425490729981516164182082', '8.413667052895231905269585319245484'], 'prelabel': '2-4284-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.848753048805919, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07253998566146547319456218513', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79095117409260482289328532715', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92800713428309059345534433600', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.20791222591653, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 4284, 'conductor_radical': 714, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4284/2/a/n/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': '2-4284-1.1-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': '2-4284-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.848753048805919, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07253998566146547319456218513', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1359605956592533262983169573219', 'Lhash_array': ['1359605956592533262983169573219'], 'label': '2-4284-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4284/2/a/n/1/2'}