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lfunc_lfunctions • Show schema
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{'Lhash': '2026344577321476757407025304520,2247842784734158343231226829315,2709370562831906584352549662766,3126440348733799723865503760496', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 6, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.74806829671438, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -6, 0, 9]]], 'bad_primes': [2, 3], 'central_character': '144.1', 'coefficient_field': '1.1.1.1', 'conductor': 429981696, 'conductor_radical': 6, 'degree': 8, 'euler_factors': [[1], [1, 0, -6, 0, 9], [1, -6, 25, -78, 204, -390, 625, -750, 625], [1, 0, 5, 0, -24, 0, 245, 0, 2401], [1, 0, 5, 0, -96, 0, 605, 0, 14641], [1, 2, -23, 2, 508, 26, -3887, 4394, 28561], [1, 0, -44, 0, 1062, 0, -12716, 0, 83521], [1, 0, -4, 0, 726, 0, -1444, 0, 130321], [1, 0, -19, 0, -168, 0, -10051, 0, 279841], [1, 30, 433, 3990, 25548, 115710, 364153, 731670, 707281], [1, 0, 53, 0, 1848, 0, 50933, 0, 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{'algebraic': True, 'analytic_conductor': 1.74806829671438, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 429981696, 'conductor_radical': 6, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 18, 0, 0, 0, 36, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 0, 5, 0, -96, 0, 605, 0, 14641], 'euler13': [1, 2, -23, 2, 508, 26, -3887, 4394, 28561], 'euler17': [1, 0, -44, 0, 1062, 0, -12716, 0, 83521], 'euler19': [1, 0, -4, 0, 726, 0, -1444, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -19, 0, -168, 0, -10051, 0, 279841], 'euler29': [1, 30, 433, 3990, 25548, 115710, 364153, 731670, 707281], 'euler3': [1, 0, -6, 0, 9, 0, 0, 0, 0], 'euler31': [1, 0, 53, 0, 1848, 0, 50933, 0, 923521], 'euler37': [1, 16, 244, 2032, 15574, 75184, 334036, 810448, 1874161], 'euler41': [1, -18, 217, -1962, 14628, -80442, 364777, -1240578, 2825761], 'euler43': [1, 0, 77, 0, 4080, 0, 142373, 0, 3418801], 'euler47': [1, 0, -67, 0, 2280, 0, -148003, 0, 4879681], 'euler5': [1, -6, 25, -78, 204, -390, 625, -750, 625], 'euler53': [1, 0, 4, 0, 5622, 0, 11236, 0, 7890481], 'euler59': [1, 0, -91, 0, 4800, 0, -316771, 0, 12117361], 'euler61': [1, -14, 25, -686, 13564, -41846, 93025, -3177734, 13845841], 'euler67': [1, 0, 53, 0, -1680, 0, 237917, 0, 20151121], 'euler7': [1, 0, 5, 0, -24, 0, 245, 0, 2401], 'euler71': [1, 0, 68, 0, 11238, 0, 342788, 0, 25411681], 'euler73': [1, -16, 388, -3760, 46246, -274480, 2067652, -6224272, 28398241], 'euler79': [1, 0, -67, 0, -1752, 0, -418147, 0, 38950081], 'euler83': [1, 0, -139, 0, 12432, 0, -957571, 0, 47458321], 'euler89': [1, 0, -332, 0, 43398, 0, -2629772, 0, 62742241], 'euler97': [1, 2, -191, 2, 28228, 194, -1797119, 1825346, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -6, 0, 9, 0, 0, 0, 0], [1, -6, 25, -78, 204, -390, 625, -750, 625], [1, 0, 5, 0, -24, 0, 245, 0, 2401], [1, 0, 5, 0, -96, 0, 605, 0, 14641], [1, 2, -23, 2, 508, 26, -3887, 4394, 28561], [1, 0, -44, 0, 1062, 0, -12716, 0, 83521], [1, 0, -4, 0, 726, 0, -1444, 0, 130321], [1, 0, -19, 0, -168, 0, -10051, 0, 279841], [1, 30, 433, 3990, 25548, 115710, 364153, 731670, 707281], [1, 0, 53, 0, 1848, 0, 50933, 0, 923521], [1, 16, 244, 2032, 15574, 75184, 334036, 810448, 1874161], [1, -18, 217, -1962, 14628, -80442, 364777, -1240578, 2825761], [1, 0, 77, 0, 4080, 0, 142373, 0, 3418801], [1, 0, -67, 0, 2280, 0, -148003, 0, 4879681], [1, 0, 4, 0, 5622, 0, 11236, 0, 7890481], [1, 0, -91, 0, 4800, 0, -316771, 0, 12117361], [1, -14, 25, -686, 13564, -41846, 93025, -3177734, 13845841], [1, 0, 53, 0, -1680, 0, 237917, 0, 20151121], [1, 0, 68, 0, 11238, 0, 342788, 0, 25411681], [1, -16, 388, -3760, 46246, -274480, 2067652, -6224272, 28398241], [1, 0, -67, 0, -1752, 0, -418147, 0, 38950081], [1, 0, -139, 0, 12432, 0, -957571, 0, 47458321], [1, 0, -332, 0, 43398, 0, -2629772, 0, 62742241], [1, 2, -191, 2, 28228, 194, -1797119, 1825346, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/2/s/e'], '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': '8-12e8-1.1-c1e4-0-4', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-12e8-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.072308625865911, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 119123921066339366, 'z1': {'__RealLiteral__': 0, 'data': '1.59850401755550870420465702409', 'prec': 103}}
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{'Lhash': '2026344577321476757407025304520,2247842784734158343231226829315,2709370562831906584352549662766,3126440348733799723865503760496', 'Lhash_array': ['2026344577321476757407025304520', '2247842784734158343231226829315', '2709370562831906584352549662766', '3126440348733799723865503760496'], 'label': '8-12e8-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/2/s/e'}