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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': '1574029853712877422', '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, 4, 13], [1, -2, 17], [1, 8, 19], [1, 6, 23], [1, 0, 29], [1, -2, 31], [1, 8, 37], [1, -10, 41], [1, 12, 43], [1, 12, 47], [1, 2, 53], [1, 12, 59], [1, -2, 61], [1, 8, 67], [1, 8, 71], [1, -4, 73], [1, 10, 79], [1, -18, 83], [1, 8, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 124, 'label': '2-369600-1.1-c1-0-124', 'leading_term': '3.01760246231', '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': 1, 'origin': 'EllipticCurve/Q/369600/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.4824085831051371, -0.3906883734796189, -2.628485505587143, -4.350758296846087, -3.509689001667259, -0.7565923288612888, 0.6622538945602005, -0.8780682102710281, -2.597974077674398, -1.087616089668891, 2.072245894835019, 2.137350994720685, -1.159954079155519, -2.53788980605481, 0.4346651399617627, 3.153137551164787, 1.737859029192457, -0.5275372132912775, 0.3057590295848012, 1.486036160060822, -0.6381205540195695, -2.971450399142728, -1.567953255230705, 0.5193779724791068, -0.4330062650278512, -1.206090310265621, 1.021496168194504, 1.799254672999246, -1.291271075779438, -2.450164438622935, 0.6425606253555507, 1.335251568449578, -2.018982089685096, -1.790497118984052, 2.72761456137877, 2.651754955979529, -2.471298462271346, -3.547482274791593, -0.0971698494244898, 0.6974599928512814, -0.1677007822462024, 1.777512620129125, 2.490536650471081, -0.730442972102875, -1.305392648608114, 2.262933481237581, 2.607788202819719, -0.2361988093822145, -0.01520521244418879, 1.015029475682573, -0.6674543088737703, 0.1606610933227507, 3.683814366753621, 1.857046471518261, -2.438612302677589, 0.2043859057540864, 4.452242889469398, 1.827046864538057, -0.637164671458889, 2.183364293235233, 2.139728545691103, -1.291776269893316, 0.2859789754650611, 3.386508142870664, 1.077288198447703, -1.071741006143477, 0.01931624064875937, -1.436239735215324, -3.301267487413419, -0.8724734322350187, 0.03610260931710386, -1.768561714375953, 1.039467983363491, 4.411853945000174, 1.043642298533174, -1.70175485574293, 0.2783803123325903, -0.5054832381377962, -1.432355267136659, 3.215885852692804, 3.595286823432179, -3.557433538792522, -4.954179355554931, -0.4821420646094363, -0.9681998792523832, -2.23767114565639, 0.6881012884018248, 0.7610601608210679, -0.7064077967762833, 2.213850443038348, 3.13244299481431, 0.01350585236780854, 0.09788056528073517, 0.2099300824989735, -3.012442295914058, -2.043506347699846, 0.7528817510668728, -1.978003467860449, -2.720424837629429, 0.335355357095371, -3.211450069168499, -7.630514210141166, -3.28836698172246, 0.2117534350663282, -0.398319141490003, 3.374177884697638, 5.109595894453643, -0.3976807157515848, -1.492227569708399, 2.005682166363124, 0.7960695408446036, -0.4228571894602861, 0.1193846674649021, -3.542689891285738, -4.78685569831508, -0.05176984781332918, 1.008875841511941, -0.490443865966288, 0.331130203868563, -1.588751477635472], 'positive_zeros': ['0.4354563198298603', '1.579873995098936', '1.900158651174237', '2.581719336850310', '3.168531780532000', '3.722438313531108', '4.412346680271729', '4.709120609060323', '5.199327538628256', '5.903211102307179', '6.189108098498237', '6.655647837121815', '7.159799294913711', '7.702715534736657', '8.108564709495712', '8.602318607638582', '9.132195202347087', '9.758323023979350', '10.13775476067505', '10.30076668194197', '10.94744117271430', '11.35026395670181', '11.97222936821538', '12.25214468785386', '12.66282911777350', '12.98762009352877', '13.58859878193752', '13.99086051677627', '14.61377664476672', '14.83516436808546', '15.39075739534976', '15.73228818487859', '16.32649238783849', '16.74246384138950', '16.82872441149434', '17.58786728027722', '17.75567008224550', '18.19581891670743', '18.80433099235270', '19.21360880020297', '19.44789402110170', '19.84890892839658'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1574029853712877422, 'z1': {'__RealLiteral__': 0, 'data': '0.4354563198298603', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.579873995098936', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.900158651174237', '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, -4, 0, 0, 0, 2, 0, -8, 0, 1, 0, -6, 0, 0, 0, -1, 0, 0, 0, 2, 0, 1, 0, 0, 0, -8, 0, 4, 0, 10, 0, -12, 0, 0, 0, -12, 0, 1, 0, -2, 0, -2, 0, 0, 0, 8, 0, -12, 0, 2, 0, -1, 0, 0, 0, -8, 0, 6, 0, -8, 0, 4, 0, 0, 0, 1, 0, -10, 0, 1, 0, 18, 0, 0, 0, 0, 0, -8, 0, 4, 0, -2, 0, 0, 0, -14, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 4, 13], 'euler17': [1, -2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 8, 37], 'euler41': [1, -10, 41], 'euler43': [1, 12, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 8, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -4, 73], 'euler79': [1, 10, 79], 'euler83': [1, -18, 83], 'euler89': [1, 8, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 4, 13], [1, -2, 17], [1, 8, 19], [1, 6, 23], [1, 0, 29], [1, -2, 31], [1, 8, 37], [1, -10, 41], [1, 12, 43], [1, 12, 47], [1, 2, 53], [1, 12, 59], [1, -2, 61], [1, 8, 67], [1, 8, 71], [1, -4, 73], [1, 10, 79], [1, -18, 83], [1, 8, 89], [1, 14, 97]], 'index': 124, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/x'], '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-c1-0-124', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1574029853712877422, 'z1': {'__RealLiteral__': 0, 'data': '0.4354563198298603', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1574029853712877422', 'Lhash_array': ['1574029853712877422'], 'label': '2-369600-1.1-c1-0-124', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/x'}