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{'Lhash': '961594567178679771761706219239,1105828399624152809292822732218,1889390011282094358921202920484', 'a10': 0, 'a2': -3, 'a3': 3, 'a4': 6, 'a5': 0, 'a6': -9, 'a7': 4, 'a8': -10, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3223.6397791518675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 3, 3, 1]], [5, [1]], [37, [1, -3, 3, -1]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.1', 'coefficient_field': '1.1.1.1', 'conductor': 6331625000, 'conductor_radical': 370, 'degree': 6, 'euler_factors': [[1, 3, 3, 1], [1, -3, 8, -13, 24, -27, 27], [1], [1, -4, 13, -22, 91, -196, 343], [1, 1, 10, -3, 110, 121, 1331], [1, -12, 83, -358, 1079, -2028, 2197], [1, 1, 30, 63, 510, 289, 4913], [1, -3, 32, -35, 608, -1083, 6859], [1, -8, 69, -336, 1587, -4232, 12167], [1, 2, 35, 76, 1015, 1682, 24389], [1, 6, 75, 318, 2325, 5766, 29791], [1, -3, 3, -1], [1, 21, 254, 1937, 10414, 35301, 68921], [1, -8, 1, 388, 43, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75856436072018037282340273786', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.872344792346611976073525024946', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.49046591461553066379431683659', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3223.6397791518675, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 6331625000, 'conductor_radical': 370, 'degree': 6, 'dirichlet_coefficients': [1, -3, 3, 6, 0, -9, 4, -10, 1, 0, -1, 18, 12, -12, 0, 15, -1, -3, 3, 0, 12, 3, 8, -30, 0, -36, -8, 24, -2, 0, -6, -21, -3, 3, 0, 6, 3, -9, 36, 0, -21, -36, 8, -6, 0, -24, 4, 45, 3, 0, -3, 72, 6, 24, 0, -40, 9, 6, 8, 0, -8, 18, 4, 28, 0, 9, 13, -6, 24, 0, -8, -10, 31, -9, 0, 18, -4, -108, 22, 0, -17, 63, 7, 72, 0, -24, -6, 10, -3, 0, 48, 48, -18, -12, 0, -63, 6, -9, -1, 0], 'euler11': [1, 1, 10, -3, 110, 121, 1331], 'euler13': [1, -12, 83, -358, 1079, -2028, 2197], 'euler17': [1, 1, 30, 63, 510, 289, 4913], 'euler19': [1, -3, 32, -35, 608, -1083, 6859], 'euler2': [1, 3, 3, 1, 0, 0, 0], 'euler23': [1, -8, 69, -336, 1587, -4232, 12167], 'euler29': [1, 2, 35, 76, 1015, 1682, 24389], 'euler3': [1, -3, 8, -13, 24, -27, 27], 'euler31': [1, 6, 75, 318, 2325, 5766, 29791], 'euler37': [1, -3, 3, -1, 0, 0, 0], 'euler41': [1, 21, 254, 1937, 10414, 35301, 68921], 'euler43': [1, -8, 1, 388, 43, -14792, 79507], 'euler47': [1, -4, 93, -312, 4371, -8836, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -6, 59, -4, 3127, -16854, 148877], 'euler59': [1, -8, 49, 132, 2891, -27848, 205379], 'euler61': [1, 8, 139, 686, 8479, 29768, 226981], 'euler67': [1, -13, 192, -1675, 12864, -58357, 300763], 'euler7': [1, -4, 13, -22, 91, -196, 343], 'euler71': [1, 8, 169, 846, 11999, 40328, 357911], 'euler73': [1, -31, 534, -5575, 38982, -165199, 389017], 'euler79': [1, -22, 377, -3708, 29783, -137302, 493039], 'euler83': [1, -7, 22, 657, 1826, -48223, 571787], 'euler89': [1, 3, 240, 507, 21360, 23763, 704969], 'euler97': [1, -6, 287, -1124, 27839, -56454, 912673], 'euler_factors': [[1, 3, 3, 1, 0, 0, 0], [1, -3, 8, -13, 24, -27, 27], [1, 0, 0, 0, 0, 0, 0], [1, -4, 13, -22, 91, -196, 343], [1, 1, 10, -3, 110, 121, 1331], [1, -12, 83, -358, 1079, -2028, 2197], [1, 1, 30, 63, 510, 289, 4913], [1, -3, 32, -35, 608, -1083, 6859], [1, -8, 69, -336, 1587, -4232, 12167], [1, 2, 35, 76, 1015, 1682, 24389], [1, 6, 75, 318, 2325, 5766, 29791], [1, -3, 3, -1, 0, 0, 0], [1, 21, 254, 1937, 10414, 35301, 68921], [1, -8, 1, 388, 43, -14792, 79507], [1, -4, 93, -312, 4371, -8836, 103823], [1, -6, 59, -4, 3127, -16854, 148877], [1, -8, 49, 132, 2891, -27848, 205379], [1, 8, 139, 686, 8479, 29768, 226981], [1, -13, 192, -1675, 12864, -58357, 300763], [1, 8, 169, 846, 11999, 40328, 357911], [1, -31, 534, -5575, 38982, -165199, 389017], [1, -22, 377, -3708, 29783, -137302, 493039], [1, -7, 22, 657, 1826, -48223, 571787], [1, 3, 240, 507, 21360, 23763, 704969], [1, -6, 287, -1124, 27839, -56454, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1850/2/a/ba'], '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': '6-1850e3-1.1-c1e3-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-1850e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1789947877941526103, 'z1': {'__RealLiteral__': 0, 'data': '0.75856436072018037282340273786', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '961594567178679771761706219239,1105828399624152809292822732218,1889390011282094358921202920484', 'Lhash_array': ['961594567178679771761706219239', '1105828399624152809292822732218', '1889390011282094358921202920484'], 'label': '6-1850e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/ba'}