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lfunc_lfunctions • Show schema
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{'Lhash': '807204918178281780944898520724', 'a10': [-4.568673300790868, 0.0], 'a2': [1.5935793453672886, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.5394951299812365, 0.0], 'a5': [-2.866925524651475, 0.0], 'a6': [-1.5935793453672886, 0.0], 'a7': [3.054084215386052, 0.0], 'a8': [-2.3274303946702384, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.681404713842234, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 11, 13], 'central_character': '4719.1', 'coefficient_field': 'CDF', 'conductor': 4719, 'conductor_radical': 429, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5935793453672886, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.866925524651475, 0], [5.0, 0]], [[1.0, 0], [-3.054084215386052, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.40642065463271126, 0], [17.0, 0]], [[1.0, 0], 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[2.162252646158157, 0], [109.0, 0]], [[1.0, 0], [-6.6768417315629724, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 41, 'label': '2-4719-1.1-c1-0-41', 'leading_term': '1.798194177524768338057575514754', '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/4719/2/a/v/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.7981941775247683, 1.7870469759947005, 1.753540845720518, 1.697491997368623, 1.6186260800594903, 1.5166238879115732, 1.3911811165360188, 1.2420784649333791, 1.0692579585031692, 0.872901262695779, 0.6535059086992203, 0.4119556878871344, 0.14958191583873306, -0.1317872417662074, -0.4297916916516657, -0.7415204121264031, -1.0635098957239095, -1.391760955521005, -1.7217743731437944, -2.0486054176072046, -2.366936800364115, 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'4.61525583744487586009468470498737', '5.11175698402603379692749709580274', '5.87336039534918237888246592726616', '6.74614030350800276885856957796290', '7.54686058801340117514396836349001', '8.106385340744225871822418827202536'], 'prelabel': '2-4719-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.138518120348121, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63677240245297213336501309325', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08090654256114820608143837899', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28167200334824216884444209876', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.681404713842234, 'bad_primes': [3, 11, 13], 'central_character': '1.1', 'conductor': 4719, 'conductor_radical': 429, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4719/2/a/v/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': '2-4719-1.1-c1-0-41', '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': '2-4719-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.138518120348121, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63677240245297213336501309325', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '807204918178281780944898520724', 'Lhash_array': ['807204918178281780944898520724'], 'label': '2-4719-1.1-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4719/2/a/v/1/2'}