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lfunc_lfunctions • Show schema
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{'Lhash': '1872684410385607273427744569415', 'a10': [3.1039886734613877, 0.0], 'a2': [1.0, 0.0], 'a3': [2.667163689785998, 0.0], 'a4': [1.0, 0.0], 'a5': [3.1039886734613877, 0.0], 'a6': [2.667163689785998, 0.0], 'a7': [-1.6433281688873773, 0.0], 'a8': [1.0, 0.0], 'a9': [4.113762148112858, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.022031775598045, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [31, [[1.0, 0], [-1.0, 0]]], [97, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 31, 97], 'central_character': '6014.1', 'coefficient_field': 'CDF', 'conductor': 6014, 'conductor_radical': 6014, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.667163689785998, 0], [3.0, 0]], [[1.0, 0], [-3.1039886734613877, 0], [5.0, 0]], [[1.0, 0], [1.6433281688873773, 0], [7.0, 0]], [[1.0, 0], [-3.303487437442031, 0], [11.0, 0]], [[1.0, 0], [-2.5942579043391514, 0], [13.0, 0]], [[1.0, 0], 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[[1.0, 0], [0.20396067904564885, 0], [109.0, 0]], [[1.0, 0], [-8.314076466728057, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 197, 'label': '2-6014-1.1-c1-0-197', 'leading_term': '7.66003714336630267739286036979', '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/6014/2/a/k/1/32', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [7.660037143366303, 7.650338847225342, 7.621060255906753, 7.571665072385508, 7.501307791273697, 7.408902637234829, 7.293213413817472, 7.152958503687113, 6.986924704925524, 6.79408355632735, 6.5737041942642485, 6.3254574595367075, 6.049506801055863, 5.746582395685979, 5.4180357476596965, 5.065872810075259, 4.692764377178631, 4.3020331400072935, 3.89761739871176, 3.4840120024004473, 3.066187657101734, 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'4.28074488336870228738393934840948', '5.15052695835972340664855666472224', '6.19369424353599382824243566935268', '6.43186858411161541204128631923893', '7.28889471030687307416465178616472', '8.148995713388129162113466556335037'], 'prelabel': '2-6014-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.92979305431252, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47728751917006691519651450817', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93114278137243635611198063363', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11600661815690912731280333736', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.022031775598045, 'bad_primes': [2, 31, 97], 'central_character': '1.1', 'conductor': 6014, 'conductor_radical': 6014, 'degree': 2, 'index': 197, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6014/2/a/k/1/32'], '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': '2-6014-1.1-c1-0-197', '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': '2-6014-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.92979305431252, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47728751917006691519651450817', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1872684410385607273427744569415', 'Lhash_array': ['1872684410385607273427744569415'], 'label': '2-6014-1.1-c1-0-197', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6014/2/a/k/1/32'}