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{'Lhash': '1411574362394924433925237206779,1528421524502202998793963556350,1570712667678439391876007183792', 'a10': 9, 'a2': -3, 'a3': 0, 'a4': 6, 'a5': -3, 'a6': 0, 'a7': 3, 'a8': -10, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 169445.88438930738, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 3, 3, 1]], [3, [1]], [5, [1, 3, 3, 1]], [7, [1, -3, 3, -1]], [11, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '6930.1', 'coefficient_field': '1.1.1.1', 'conductor': 332812557000, 'conductor_radical': 2310, 'degree': 6, 'euler_factors': [[1, 3, 3, 1], [1], [1, 3, 3, 1], [1, -3, 3, -1], [1, 3, 3, 1], [1, -2, 19, -44, 247, -338, 2197], [1, 2, 15, -36, 255, 578, 4913], [1, 0, 57, 0, 1083, 0, 6859], [1, 4, 37, 216, 851, 2116, 12167], [1, 2, 35, 76, 1015, 1682, 24389], [1, 4, 13, 184, 403, 3844, 29791], [1, -6, 11, 188, 407, -8214, 50653], [1, -6, 71, -244, 2911, -10086, 68921], [1, 0, 65, -128, 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'5.79131794027924534168186832232689', '6.04855613141405099495610881384405', '6.39045197596355537506379447485795', '6.47980837476769764624557873208114', '6.88532251683015697954255188070983', '7.19846954692372315595616161211832', '7.30273195568147684981422558303274', '7.51979833526576526678337178739774', '7.70069695519303377189717894607911', '7.85486000725340717044969080950117'], 'prelabel': '6-6930e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.438839197129302, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 1582246995433079450, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11353582930563265465868718428', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.20571198737808673268269841227', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.23907381686692399012964099751', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 169445.88438930738, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 332812557000, 'conductor_radical': 2310, 'degree': 6, 'dirichlet_coefficients': [1, -3, 0, 6, -3, 0, 3, -10, 0, 9, -3, 0, 2, -9, 0, 15, -2, 0, 0, -18, 0, 9, -4, 0, 6, -6, 0, 18, -2, 0, -4, -21, 0, 6, -9, 0, 6, 0, 0, 30, 6, 0, 0, -18, 0, 12, -4, 0, 6, -18, 0, 12, 6, 0, 9, -30, 0, 6, -12, 0, -10, 12, 0, 28, -6, 0, 0, -12, 0, 27, -4, 0, -10, -18, 0, 0, -9, 0, -4, -45, 0, -18, 0, 0, 6, 0, 0, 30, 2, 0, 6, -24, 0, 12, 0, 0, -6, -18, 0, 36], 'euler11': [1, 3, 3, 1, 0, 0, 0], 'euler13': [1, -2, 19, -44, 247, -338, 2197], 'euler17': [1, 2, 15, -36, 255, 578, 4913], 'euler19': [1, 0, 57, 0, 1083, 0, 6859], 'euler2': [1, 3, 3, 1, 0, 0, 0], 'euler23': [1, 4, 37, 216, 851, 2116, 12167], 'euler29': [1, 2, 35, 76, 1015, 1682, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 4, 13, 184, 403, 3844, 29791], 'euler37': [1, -6, 11, 188, 407, -8214, 50653], 'euler41': [1, -6, 71, -244, 2911, -10086, 68921], 'euler43': [1, 0, 65, -128, 2795, 0, 79507], 'euler47': [1, 4, 61, 312, 2867, 8836, 103823], 'euler5': [1, 3, 3, 1, 0, 0, 0], 'euler53': [1, -6, 107, -644, 5671, -16854, 148877], 'euler59': [1, 12, 161, 1096, 9499, 41772, 205379], 'euler61': [1, 10, 67, 124, 4087, 37210, 226981], 'euler67': [1, 0, 41, 608, 2747, 0, 300763], 'euler7': [1, -3, 3, -1, 0, 0, 0], 'euler71': [1, 4, 165, 504, 11715, 20164, 357911], 'euler73': [1, 10, 39, -404, 2847, 53290, 389017], 'euler79': [1, 4, 29, 312, 2291, 24964, 493039], 'euler83': [1, 0, 185, 128, 15355, 0, 571787], 'euler89': [1, -2, 135, 324, 12015, -15842, 704969], 'euler97': [1, 6, 303, 1172, 29391, 56454, 912673], 'euler_factors': [[1, 3, 3, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 3, 3, 1, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 3, 3, 1, 0, 0, 0], [1, -2, 19, -44, 247, -338, 2197], [1, 2, 15, -36, 255, 578, 4913], [1, 0, 57, 0, 1083, 0, 6859], [1, 4, 37, 216, 851, 2116, 12167], [1, 2, 35, 76, 1015, 1682, 24389], [1, 4, 13, 184, 403, 3844, 29791], [1, -6, 11, 188, 407, -8214, 50653], [1, -6, 71, -244, 2911, -10086, 68921], [1, 0, 65, -128, 2795, 0, 79507], [1, 4, 61, 312, 2867, 8836, 103823], [1, -6, 107, -644, 5671, -16854, 148877], [1, 12, 161, 1096, 9499, 41772, 205379], [1, 10, 67, 124, 4087, 37210, 226981], [1, 0, 41, 608, 2747, 0, 300763], [1, 4, 165, 504, 11715, 20164, 357911], [1, 10, 39, -404, 2847, 53290, 389017], [1, 4, 29, 312, 2291, 24964, 493039], [1, 0, 185, 128, 15355, 0, 571787], [1, -2, 135, 324, 12015, -15842, 704969], [1, 6, 303, 1172, 29391, 56454, 912673]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6930/2/a/ch'], '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': '6-6930e3-1.1-c1e3-0-6', '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': 3, 'prelabel': '6-6930e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.438839197129302, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1582246995433079450, 'z1': {'__RealLiteral__': 0, 'data': '1.11353582930563265465868718428', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1411574362394924433925237206779,1528421524502202998793963556350,1570712667678439391876007183792', 'Lhash_array': ['1411574362394924433925237206779', '1528421524502202998793963556350', '1570712667678439391876007183792'], 'label': '6-6930e3-1.1-c1e3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6930/2/a/ch'}