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  • lfunc_lfunctions • Show schema
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'8.345965847012521812192709694363795', '8.356044376642451107091115454072599', '8.464102780602821964919222366734577', '8.582700506809040013183590541458985'], 'prelabel': '8-3720e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.450169681020612, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 793662564300192296, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27954295091045972860612423197', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.71666207466301013753571570161', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.78795161604112686557859108059', 'prec': 97}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 778538.6677517173, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 191501314560000, 'conductor_radical': 930, 'degree': 8, 'dirichlet_coefficients': [1, 0, -4, 0, -4, 0, 1, 0, 10, 0, 1, 0, -2, 0, 16, 0, 4, 0, -7, 0, -4, 0, -1, 0, 10, 0, -20, 0, 2, 0, 4, 0, -4, 0, -4, 0, -6, 0, 8, 0, 16, 0, -5, 0, -40, 0, 0, 0, -17, 0, -16, 0, 11, 0, -4, 0, 28, 0, -6, 0, 4, 0, 10, 0, 8, 0, -12, 0, 4, 0, 17, 0, 3, 0, -40, 0, 1, 0, 3, 0, 35, 0, -10, 0, -16, 0, -8, 0, 17, 0, -2, 0, -16, 0, 28, 0, -2, 0, 10, 0], 'euler11': [1, -1, 10, -13, 194, -143, 1210, -1331, 14641], 'euler13': [1, 2, 22, 24, 342, 312, 3718, 4394, 28561], 'euler17': [1, -4, 36, -224, 694, -3808, 10404, -19652, 83521], 'euler19': [1, 7, 60, 303, 1686, 5757, 21660, 48013, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 1, 34, 37, 1070, 851, 17986, 12167, 279841], 'euler29': [1, -2, 92, -172, 3678, -4988, 77372, -48778, 707281], 'euler3': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler31': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler37': [1, 6, 130, 608, 6978, 22496, 177970, 303918, 1874161], 'euler41': [1, -16, 260, -2224, 18214, -91184, 437060, -1102736, 2825761], 'euler43': [1, 5, 146, 481, 8690, 20683, 269954, 397535, 3418801], 'euler47': [1, 0, 112, 92, 6726, 4324, 247408, 0, 4879681], 'euler5': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler53': [1, -11, 244, -1773, 20250, -93969, 685396, -1637647, 7890481], 'euler59': [1, 6, 164, 796, 13714, 46964, 570884, 1232274, 12117361], 'euler61': [1, -4, 164, -748, 13318, -45628, 610244, -907924, 13845841], 'euler67': [1, 12, 262, 2390, 26134, 160130, 1176118, 3609156, 20151121], 'euler7': [1, -1, 18, -13, 172, -91, 882, -343, 2401], 'euler71': [1, -17, 290, -3331, 30600, -236501, 1461890, -6084487, 25411681], 'euler73': [1, -3, 228, -365, 22316, -26645, 1215012, -1167051, 28398241], 'euler79': [1, -3, 148, -79, 11746, -6241, 923668, -1479117, 38950081], 'euler83': [1, 10, 160, 1390, 12830, 115370, 1102240, 5717870, 47458321], 'euler89': [1, -17, 420, -4397, 58116, -391333, 3326820, -11984473, 62742241], 'euler97': [1, 2, 196, -186, 19462, -18042, 1844164, 1825346, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, -1, 18, -13, 172, -91, 882, -343, 2401], [1, -1, 10, -13, 194, -143, 1210, -1331, 14641], [1, 2, 22, 24, 342, 312, 3718, 4394, 28561], [1, -4, 36, -224, 694, -3808, 10404, -19652, 83521], [1, 7, 60, 303, 1686, 5757, 21660, 48013, 130321], [1, 1, 34, 37, 1070, 851, 17986, 12167, 279841], [1, -2, 92, -172, 3678, -4988, 77372, -48778, 707281], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 6, 130, 608, 6978, 22496, 177970, 303918, 1874161], [1, -16, 260, -2224, 18214, -91184, 437060, -1102736, 2825761], [1, 5, 146, 481, 8690, 20683, 269954, 397535, 3418801], [1, 0, 112, 92, 6726, 4324, 247408, 0, 4879681], [1, -11, 244, -1773, 20250, -93969, 685396, -1637647, 7890481], [1, 6, 164, 796, 13714, 46964, 570884, 1232274, 12117361], [1, -4, 164, -748, 13318, -45628, 610244, -907924, 13845841], [1, 12, 262, 2390, 26134, 160130, 1176118, 3609156, 20151121], [1, -17, 290, -3331, 30600, -236501, 1461890, -6084487, 25411681], [1, -3, 228, -365, 22316, -26645, 1215012, -1167051, 28398241], [1, -3, 148, -79, 11746, -6241, 923668, -1479117, 38950081], [1, 10, 160, 1390, 12830, 115370, 1102240, 5717870, 47458321], [1, -17, 420, -4397, 58116, -391333, 3326820, -11984473, 62742241], [1, 2, 196, -186, 19462, -18042, 1844164, 1825346, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3720/2/a/r'], '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': '8-3720e4-1.1-c1e4-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-3720e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.450169681020612, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 793662564300192296, 'z1': {'__RealLiteral__': 0, 'data': '0.27954295091045972860612423197', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '354362789511214741622307054583,908477109107372955028956960777,998847339025337821564246799733,1024979446998119762101708362447', 'Lhash_array': ['354362789511214741622307054583', '908477109107372955028956960777', '998847339025337821564246799733', '1024979446998119762101708362447'], 'factors': ['2-3720-1.1-c1-0-0', '2-3720-1.1-c1-0-8', '2-3720-1.1-c1-0-12', '2-3720-1.1-c1-0-14'], 'label': '8-3720e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3720/2/a/r'}