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lfunc_lfunctions • Show schema
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{'Lhash': '759050811022244296842553702665,1426708444654602232789040955702', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 6, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10832.515103504176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.1', 'coefficient_field': '1.1.1.1', 'conductor': 3111696, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, -6, -89, -750, 15625], [1], [1, -36, -35, -47916, 1771561], [1, -124, 8238, -272428, 4826809], [1, -114, 8083, -560082, 24137569], [1, -76, -1083, -521284, 47045881], [1, 24, -11591, 292008, 148035889], [1, 108, 51694, 2634012, 594823321], [1, -112, -17247, -3336592, 887503681], [1, -178, -18969, -9016234, 2565726409], [1, 756, 280726, 52104276, 4750104241], [1, 344, 188598, 27350408, 6321363049], [1, 192, -66959, 19934016, 10779215329], [1, 402, 12727, 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'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.12547451513669133892225638442', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.61695183772888529540617440184', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 10832.515103504176, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 3111696, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 6, 0, 0, 0, 0, 0, 36, 0, 124, 0, 0, 0, 114, 0, 76, 0, 0, 0, -24, 0, 125, 0, 0, 0, -108, 0, 112, 0, 0, 0, 0, 0, 178, 0, 0, 0, -756, 0, -344, 0, 0, 0, -192, 0, 0, 0, 0, 0, -402, 0, 216, 0, 0, 0, 396, 0, -254, 0, 0, 0, 744, 0, 1012, 0, 0, 0, -1680, 0, -890, 0, 0, 0, 0, 0, -80, 0, 0, 0, 216, 0, 684, 0, 0, 0, -1638, 0, 0, 0, 0, 0, 456, 0, 2020, 0, 0, 0], 'euler11': [1, -36, -35, -47916, 1771561], 'euler13': [1, -124, 8238, -272428, 4826809], 'euler17': [1, -114, 8083, -560082, 24137569], 'euler19': [1, -76, -1083, -521284, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 24, -11591, 292008, 148035889], 'euler29': [1, 108, 51694, 2634012, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -112, -17247, -3336592, 887503681], 'euler37': [1, -178, -18969, -9016234, 2565726409], 'euler41': [1, 756, 280726, 52104276, 4750104241], 'euler43': [1, 344, 188598, 27350408, 6321363049], 'euler47': [1, 192, -66959, 19934016, 10779215329], 'euler5': [1, -6, -89, -750, 15625], 'euler53': [1, 402, 12727, 59848554, 22164361129], 'euler59': [1, -396, -48563, -81330084, 42180533641], 'euler61': [1, 254, -162465, 57653174, 51520374361], 'euler67': [1, -1012, 723381, -304372156, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 1680, 1421422, 601290480, 128100283921], 'euler73': [1, 890, 403083, 346225130, 151334226289], 'euler79': [1, 80, -486639, 39443120, 243087455521], 'euler83': [1, -216, 1155238, -123505992, 326940373369], 'euler89': [1, 1638, 1978075, 1154739222, 496981290961], 'euler97': [1, -2020, 2845446, -1843599460, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -6, -89, -750, 15625], [1, 0, 0, 0, 0], [1, -36, -35, -47916, 1771561], [1, -124, 8238, -272428, 4826809], [1, -114, 8083, -560082, 24137569], [1, -76, -1083, -521284, 47045881], [1, 24, -11591, 292008, 148035889], [1, 108, 51694, 2634012, 594823321], [1, -112, -17247, -3336592, 887503681], [1, -178, -18969, -9016234, 2565726409], [1, 756, 280726, 52104276, 4750104241], [1, 344, 188598, 27350408, 6321363049], [1, 192, -66959, 19934016, 10779215329], [1, 402, 12727, 59848554, 22164361129], [1, -396, -48563, -81330084, 42180533641], [1, 254, -162465, 57653174, 51520374361], [1, -1012, 723381, -304372156, 90458382169], [1, 1680, 1421422, 601290480, 128100283921], [1, 890, 403083, 346225130, 151334226289], [1, 80, -486639, 39443120, 243087455521], [1, -216, 1155238, -123505992, 326940373369], [1, 1638, 1978075, 1154739222, 496981290961], [1, -2020, 2845446, -1843599460, 832972004929]], 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/4/k/l'], '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': '4-42e4-1.1-c3e2-0-18', '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': '4-42e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.201929682669181, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1979868544947202075, 'z1': {'__RealLiteral__': 0, 'data': '0.59878550989175080128156856499', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '759050811022244296842553702665,1426708444654602232789040955702', 'Lhash_array': ['759050811022244296842553702665', '1426708444654602232789040955702'], 'label': '4-42e4-1.1-c3e2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/4/k/l'}