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lfunc_lfunctions • Show schema
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{'Lhash': '799208503979628431390188021572,1246416658161302403200548366189', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -9, 'a5': 0, 'a6': 0, 'a7': 44, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8053.60953433941, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, 9, 0, 64], [1], [1, 0, 138, 0, 15625], [1, -44, 1170, -15092, 117649], [1, 0, 2634, 0, 1771561], [1], [1, 0, -3726, 0, 24137569], [1, -252, 29594, -1728468, 47045881], [1, 0, 23326, 0, 148035889], [1, 0, 45978, 0, 594823321], [1, -364, 92706, -10843924, 887503681], [1, -172, 108702, -8712316, 2565726409], [1, 0, -59726, 0, 4750104241], [1, -192, 168230, -15265344, 6321363049], [1, 0, 74338, 0, 10779215329], [1, 0, 261466, 0, 22164361129], [1, 0, 65770, 0, 42180533641], [1, 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'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1359958107317930227, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63046434390970030031513846437', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.983249373239673445682942248340', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.44663337187210115042919382354', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8053.60953433941, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -9, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 252, 0, 0, 0, 0, 0, -138, 0, 0, -396, 0, 0, 364, 0, 0, 0, 0, 0, 172, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 766, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1148, 0, 0, 423, 0, 0, 1060, 0, 0, 0, 0, 0, 308, 0, 0, -2268, 0, 0, -920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, 0, 1242], 'euler11': [1, 0, 2634, 0, 1771561], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 0, -3726, 0, 24137569], 'euler19': [1, -252, 29594, -1728468, 47045881], 'euler2': [1, 0, 9, 0, 64], 'euler23': [1, 0, 23326, 0, 148035889], 'euler29': [1, 0, 45978, 0, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -364, 92706, -10843924, 887503681], 'euler37': [1, -172, 108702, -8712316, 2565726409], 'euler41': [1, 0, -59726, 0, 4750104241], 'euler43': [1, -192, 168230, -15265344, 6321363049], 'euler47': [1, 0, 74338, 0, 10779215329], 'euler5': [1, 0, 138, 0, 15625], 'euler53': [1, 0, 261466, 0, 22164361129], 'euler59': [1, 0, 65770, 0, 42180533641], 'euler61': [1, -1148, 783438, -260574188, 51520374361], 'euler67': [1, -1060, 882426, -318808780, 90458382169], 'euler7': [1, -44, 1170, -15092, 117649], 'euler71': [1, 0, 60370, 0, 128100283921], 'euler73': [1, -308, 801750, -119817236, 151334226289], 'euler79': [1, 920, 1197678, 453595880, 243087455521], 'euler83': [1, 0, 1039386, 0, 326940373369], 'euler89': [1, 0, -661614, 0, 496981290961], 'euler97': [1, 140, 1830246, 127774220, 832972004929], 'euler_factors': [[1, 0, 9, 0, 64], [1, 0, 0, 0, 0], [1, 0, 138, 0, 15625], [1, -44, 1170, -15092, 117649], [1, 0, 2634, 0, 1771561], [1, 0, 0, 0, 0], [1, 0, -3726, 0, 24137569], [1, -252, 29594, -1728468, 47045881], [1, 0, 23326, 0, 148035889], [1, 0, 45978, 0, 594823321], [1, -364, 92706, -10843924, 887503681], [1, -172, 108702, -8712316, 2565726409], [1, 0, -59726, 0, 4750104241], [1, -192, 168230, -15265344, 6321363049], [1, 0, 74338, 0, 10779215329], [1, 0, 261466, 0, 22164361129], [1, 0, 65770, 0, 42180533641], [1, -1148, 783438, -260574188, 51520374361], [1, -1060, 882426, -318808780, 90458382169], [1, 0, 60370, 0, 128100283921], [1, -308, 801750, -119817236, 151334226289], [1, 920, 1197678, 453595880, 243087455521], [1, 0, 1039386, 0, 326940373369], [1, 0, -661614, 0, 496981290961], [1, 140, 1830246, 127774220, 832972004929]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/p'], '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': '4-39e4-1.1-c3e2-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-39e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1359958107317930227, 'z1': {'__RealLiteral__': 0, 'data': '0.63046434390970030031513846437', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '799208503979628431390188021572,1246416658161302403200548366189', 'Lhash_array': ['799208503979628431390188021572', '1246416658161302403200548366189'], 'label': '4-39e4-1.1-c3e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/p'}