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lfunc_lfunctions • Show schema
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{'Lhash': '1399982460615099975590147428078,1787010525208436341219311610481', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18479.79252975973, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '2304.1', 'coefficient_field': '1.1.1.1', 'conductor': 5308416, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 250, 0, 15625], [1, 0, -286, 0, 117649], [1, 0, 2662, 0, 1771561], [1, 0, 506, 0, 4826809], [1, 0, 9826, 0, 24137569], [1, -112, 16854, -768208, 47045881], [1, 0, 24334, 0, 148035889], [1, 0, 48778, 0, 594823321], [1, 0, 35282, 0, 887503681], [1, 0, -89206, 0, 2565726409], [1, 0, 137842, 0, 4750104241], [1, 1040, 429414, 82687280, 6321363049], [1, 0, 207646, 0, 10779215329], [1, 0, 297754, 0, 22164361129], [1, 0, 410758, 0, 42180533641], [1, 0, -420838, 0, 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'root_analytic_conductor': 11.659348208764778, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 919563383629578700, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10439143117436727457481903499', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40970274055540282823523275721', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.13941884836278147849392258665', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18479.79252975973, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 5308416, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, -250, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1040, 0, 0, 0, 0, 0, 286, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1760, 0, 0, 0, 0, 0, -2380, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2660, 0, 0, 0], 'euler11': [1, 0, 2662, 0, 1771561], 'euler13': [1, 0, 506, 0, 4826809], 'euler17': [1, 0, 9826, 0, 24137569], 'euler19': [1, -112, 16854, -768208, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 24334, 0, 148035889], 'euler29': [1, 0, 48778, 0, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 35282, 0, 887503681], 'euler37': [1, 0, -89206, 0, 2565726409], 'euler41': [1, 0, 137842, 0, 4750104241], 'euler43': [1, 1040, 429414, 82687280, 6321363049], 'euler47': [1, 0, 207646, 0, 10779215329], 'euler5': [1, 0, 250, 0, 15625], 'euler53': [1, 0, 297754, 0, 22164361129], 'euler59': [1, 0, 410758, 0, 42180533641], 'euler61': [1, 0, -420838, 0, 51520374361], 'euler67': [1, -1760, 1375926, -529342880, 90458382169], 'euler7': [1, 0, -286, 0, 117649], 'euler71': [1, 0, 715822, 0, 128100283921], 'euler73': [1, 2380, 2194134, 925860460, 151334226289], 'euler79': [1, 0, -204622, 0, 243087455521], 'euler83': [1, 0, 1143574, 0, 326940373369], 'euler89': [1, 0, 1409938, 0, 496981290961], 'euler97': [1, -2660, 3594246, -2427710180, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 250, 0, 15625], [1, 0, -286, 0, 117649], [1, 0, 2662, 0, 1771561], [1, 0, 506, 0, 4826809], [1, 0, 9826, 0, 24137569], [1, -112, 16854, -768208, 47045881], [1, 0, 24334, 0, 148035889], [1, 0, 48778, 0, 594823321], [1, 0, 35282, 0, 887503681], [1, 0, -89206, 0, 2565726409], [1, 0, 137842, 0, 4750104241], [1, 1040, 429414, 82687280, 6321363049], [1, 0, 207646, 0, 10779215329], [1, 0, 297754, 0, 22164361129], [1, 0, 410758, 0, 42180533641], [1, 0, -420838, 0, 51520374361], [1, -1760, 1375926, -529342880, 90458382169], [1, 0, 715822, 0, 128100283921], [1, 2380, 2194134, 925860460, 151334226289], [1, 0, -204622, 0, 243087455521], [1, 0, 1143574, 0, 326940373369], [1, 0, 1409938, 0, 496981290961], [1, -2660, 3594246, -2427710180, 832972004929]], 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/4/a/bd'], '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': '4-48e4-1.1-c3e2-0-26', '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': 2, 'prelabel': '4-48e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.659348208764778, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 919563383629578700, 'z1': {'__RealLiteral__': 0, 'data': '1.10439143117436727457481903499', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1399982460615099975590147428078,1787010525208436341219311610481', 'Lhash_array': ['1399982460615099975590147428078', '1787010525208436341219311610481'], 'label': '4-48e4-1.1-c3e2-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/4/a/bd'}