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lfunc_lfunctions • Show schema
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{'Lhash': '922555573604024606024015404230', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 94.40305600918502, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '1600.1', 'coefficient_field': '1.1.1.1', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, 0, 27], [1], [1, 0, 343], [1, 0, 1331], [1, -92, 2197], [1, -104, 4913], [1, 0, 6859], [1, 0, 12167], [1, 130, 24389], [1, 0, 29791], [1, 396, 50653], [1, -230, 68921], [1, 0, 79507], [1, 0, 103823], [1, 572, 148877], [1, 0, 205379], [1, -830, 226981], [1, 0, 300763], [1, 0, 357911], [1, -592, 389017], [1, 0, 493039], [1, 0, 571787], [1, -1670, 704969], [1, -1816, 912673], [1, 598, 1030301], [1, 0, 1092727], [1, 0, 1225043], [1, -1746, 1295029], [1, -1328, 1442897]], 'euler_factors_factorization': [[1], 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'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1600/4/a/bb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.1707473329832077, 2.1576416304406796, 2.1184783293404785, 2.0537182744970717, 1.9641275769856863, 1.8507745041139105, 1.7150248048093104, 1.558535169652904, 1.383244466258225, 1.1913623512216782, 0.9853548421212286, 0.7679264388733954, 0.5419984141668533, 0.3106829477900442, 0.07725285871038888, -0.1548932098326038, -0.3822701755349887, -0.6013503574541468, -0.8086115048588695, -1.0005885868731215, -1.1739287499423963, -1.3254486852655283, -1.452193489094288, -1.5514959505243096, -1.621035069411088, -1.6588924965611893, -1.6636055043509042, -1.6342150430199618, -1.5703074201735503, -1.47204816194704, -1.340206676498059, -1.176170445717286, -0.9819476199691045, -0.7601570828029405, -0.5140052861847422, -0.24724942884533957, 0.035853143551169406, 0.33060910326246284, 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9.716123507303982, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1680228977998405500, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72776802490996063526525155967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82182526404571793481162085201', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26210713818336384030711292775', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 94.40305600918502, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -27, 0, 0, 0, 92, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -130, 0, 0, 0, 0, 0, 0, 0, -396, 0, 0, 0, 230, 0, 0, 0, 0, 0, 0, 0, -343, 0, 0, 0, -572, 0, 0, 0, 0, 0, 0, 0, 830, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 592, 0, 0, 0, 0, 0, 0, 0, 729, 0, 0, 0, 0, 0, 0, 0, 1670, 0, 0, 0, 0, 0, 0, 0, 1816, 0, 0, 0], 'euler11': [1, 0, 1331], 'euler13': [1, -92, 2197], 'euler17': [1, -104, 4913], 'euler19': [1, 0, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 0, 12167], 'euler29': [1, 130, 24389], 'euler3': [1, 0, 27], 'euler31': [1, 0, 29791], 'euler37': [1, 396, 50653], 'euler41': [1, -230, 68921], 'euler43': [1, 0, 79507], 'euler47': [1, 0, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 572, 148877], 'euler59': [1, 0, 205379], 'euler61': [1, -830, 226981], 'euler67': [1, 0, 300763], 'euler7': [1, 0, 343], 'euler71': [1, 0, 357911], 'euler73': [1, -592, 389017], 'euler79': [1, 0, 493039], 'euler83': [1, 0, 571787], 'euler89': [1, -1670, 704969], 'euler97': [1, -1816, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 27], [1, 0, 0], [1, 0, 343], [1, 0, 1331], [1, -92, 2197], [1, -104, 4913], [1, 0, 6859], [1, 0, 12167], [1, 130, 24389], [1, 0, 29791], [1, 396, 50653], [1, -230, 68921], [1, 0, 79507], [1, 0, 103823], [1, 572, 148877], [1, 0, 205379], [1, -830, 226981], [1, 0, 300763], [1, 0, 357911], [1, -592, 389017], [1, 0, 493039], [1, 0, 571787], [1, -1670, 704969], [1, -1816, 912673]], 'index': 28, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1600/4/a/bb/1/1', 'ModularForm/GL2/Q/holomorphic/1600/4/a/bb'], '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': '2-40e2-1.1-c3-0-28', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-40e2-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.716123507303982, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1680228977998405500, 'z1': {'__RealLiteral__': 0, 'data': '0.72776802490996063526525155967', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21222299
{'Lhash': '922555573604024606024015404230', 'Lhash_array': ['922555573604024606024015404230'], 'label': '2-40e2-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/4/a/bb'}
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id: 24591767
{'Lhash': '922555573604024606024015404230', 'Lhash_array': ['922555573604024606024015404230'], 'label': '2-40e2-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/4/a/bb/1/1'}