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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '680869938404740878', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 1], [1, 1], [1, -6, 13], [1, 6, 17], [1, 0, 19], [1, 0, 23], [1, -10, 29], [1, 0, 31], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -2, 53], [1, 0, 59], [1, -2, 61], [1, 12, 67], [1, -12, 71], [1, 6, 73], [1, -4, 79], [1, 4, 83], [1, -2, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 122, 'label': '2-369600-1.1-c1-0-122', 'leading_term': '2.86088069091', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/369600/oc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.860880690909696, 1.753889312919021, -0.7093769834496968, -2.389768421654984, -1.626978950380054, 0.6331348191970076, 1.455440061875947, -0.3701573996358059, -2.337601278720619, -1.609425919660372, 0.6175488437037701, 0.8656178759985199, -0.9078081728913004, -1.189736145989358, 0.7925437108576433, 1.406118640999852, -0.6508105257990227, -1.398171474621534, 0.9701362585214791, 1.729423449184239, -1.865793081692422, -4.193357975654068, -0.5611142701722871, 3.816801852356369, 2.723441270285727, -0.3242525915837701, 0.1216280957756193, 0.9301754118335527, -1.740020595894152, -3.095319182737498, 0.7571997419682412, 3.973865569117888, 1.973943989046042, -0.2618071909059331, 0.6676751652684997, 0.7558627717175771, -0.3535516520527273, 1.854895041198267, 4.811309059257383, 2.706006334034423, -0.4202833705359073, 1.207366992158426, 2.476841443606336, -0.729239989921696, -1.773512192302367, 1.092592879188721, -0.2783670278042394, -4.844564151004948, -2.966183861225391, 2.405543927903982, 1.511195639705703, -1.860504057749905, -0.2937401733262508, 1.667931811272568, 0.3245053855048709, 0.1331657094365899, -0.2284571184696654, -4.751020760906055, -6.879010702984711, -2.389233442806008, 0.2561325312480356, -1.688814004162388, -1.129046492148811, 0.6715390948769344, -0.6762720469774482, 0.08813592731843985, 2.798839052613447, -1.272559759262419, -6.869873325871544, -2.814920911134779, 3.130435904950156, 1.261327850641346, -0.6341754705396999, 1.19022636945758, -0.4854030796294682, -2.579318048270901, 0.7252778020355706, 2.250059590426747, -0.3827341379572562, 0.423383973950502, 2.286414618605508, 0.2214111835760232, 0.08345880987912371, 1.890963826709222, -0.7347577121822371, -2.329581227835826, 0.8449444623381642, 0.3447966938218181, -1.757656340846009, 2.659115588325149, 4.981732985476104, -0.09724206148981375, -1.191161744810207, 1.681585358055801, -0.37558092615285, -1.029437954761373, 2.76809576466724, 0.9357395569104953, -3.073374794820552, -0.1811552703757892, 2.006021879855673, -0.3588454468783731, 0.08433709758425234, 0.6668203542983392, -1.570377678041564, -0.1601573209001618, 1.810870319719077, -0.4412795878573399, 0.38864073219839, 2.12512581919123, -2.968629203511875, -4.766186688649454, 1.126363554383446, 1.66493641099308, -1.514969228985778, 0.1928950432393929, -0.2780127803061266, -1.847128362850705, 4.313936585785956, 7.810762822296606, 2.204771140875486], 'positive_zeros': ['0.4305170502439346', '1.178459287295110', '1.713040051665192', '2.422857009824447', '2.879011573680199', '3.408904754338472', '3.931226236812568', '4.412778489020460', '4.892591088067109', '5.525311662872596', '6.208152091642723', '6.482362618329179', '6.866951298691395', '7.462277536158498', '8.182429226238616', '8.379377709944499', '8.881445511008959', '9.095291752998490', '9.935148912125263', '10.13882602703870', '10.70136356952050', '11.15192944838705', '11.48423942172781', '12.12277264167488', '12.59032985453621', '13.02308386915959', '13.57113305929307', '13.70455403727487', '13.97503026369966', '14.90459034613603', '15.05567788213176', '15.61491226682164', '15.90584394953554', '16.24282986958970', '16.70461648677661', '17.34154083305255', '17.84038190348096', '18.09506881264633', '18.46507258093968', '18.95743175738697', '19.45677557939795', '19.71037574931140'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 680869938404740878, 'z1': {'__RealLiteral__': 0, 'data': '0.4305170502439346', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.178459287295110', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.713040051665192', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -1, 0, 1, 0, -1, 0, 6, 0, 0, 0, -6, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 10, 0, 0, 0, -1, 0, 0, 0, 2, 0, 6, 0, -6, 0, -4, 0, 0, 0, 0, 0, 1, 0, -6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -12, 0, 0, 0, 12, 0, -6, 0, 0, 0, 1, 0, 4, 0, 1, 0, -4, 0, 0, 0, 10, 0, 2, 0, -6, 0, 0, 0, 0, 0, -14, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -6, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -10, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, 12, 67], 'euler7': [1, 1, 0], 'euler71': [1, -12, 71], 'euler73': [1, 6, 73], 'euler79': [1, -4, 79], 'euler83': [1, 4, 83], 'euler89': [1, -2, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, -6, 13], [1, 6, 17], [1, 0, 19], [1, 0, 23], [1, -10, 29], [1, 0, 31], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -2, 53], [1, 0, 59], [1, -2, 61], [1, 12, 67], [1, -12, 71], [1, 6, 73], [1, -4, 79], [1, 4, 83], [1, -2, 89], [1, 14, 97]], 'index': 122, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/oc'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-369600-1.1-c1-0-122', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 680869938404740878, 'z1': {'__RealLiteral__': 0, 'data': '0.4305170502439346', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '680869938404740878', 'Lhash_array': ['680869938404740878'], 'label': '2-369600-1.1-c1-0-122', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/oc'}