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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '1791316177725537505', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2711.7196526426833, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [283, [1, 1]]], 'bad_primes': [2, 3, 5, 283], 'central_character': '339600.1', 'coefficient_field': '1.1.1.1', 'conductor': 339600, 'conductor_radical': 8490, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 0, 7], [1, 4, 11], [1, 0, 13], [1, 2, 17], [1, -6, 19], [1, -6, 23], [1, -2, 29], [1, -2, 31], [1, -6, 37], [1, 2, 41], [1, 4, 43], [1, -8, 47], [1, 10, 53], [1, -4, 59], [1, 10, 61], [1, 12, 67], [1, -8, 71], [1, -12, 73], [1, -2, 79], [1, -10, 83], [1, -14, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 43, 'label': '2-339600-1.1-c1-0-43', 'leading_term': '6.42737752459', '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/339600/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.348784142647393, 1.390712825973668, 0.02622800817140512, -1.084209747133152, -0.0593922415429006, 2.47629680531735, 3.364733399123123, 0.9222680149749439, -2.101146799566553, -1.866145644598461, 0.8048420919664462, 1.417882901345014, -0.9006660218979401, -1.473687884226045, 2.234564923301715, 5.668286489652144, 4.148497829037209, 0.4433308368080975, -0.3155543074765786, 0.7853894514504524, -0.05923979515957521, -1.217149506447433, 0.7639210290231727, 3.16370991485958, 1.861731511820159, -0.03706446525113015, 1.875839558934614, 3.989972798859355, 1.715556626380346, -0.979103104937663, -0.0160858487248644, -0.2090947226002123, -4.557867627800716, -6.030770781778394, -1.220460646209479, 1.727588881860773, -1.11797407998394, -2.227756953114327, 1.051314729714809, 1.611271720791929, -1.34665979659619, -1.193426045847249, 1.084410134194867, 0.1998486165883628, -0.7571555819744595, 1.558959079393338, 1.805723102608375, -1.406864345557236, -1.320218462461405, 1.357623517746657, -0.14783708788387, -2.731109674081191, -0.9833220835499612, -0.1928694979099741, -2.482914232330367, 0.09421251394178955, 5.827127876636305, 3.957428431524329, -1.8326134556787, -0.7597376725875911, 2.634953830915382, 1.070935681937621, 0.1480330251430247, 2.078613023391817, 0.6387796258422191, -1.559416217590453, 0.8153327284401217, 1.623552547286348, -1.828809131497576, -1.832152542151159, 0.9037152226276428, -0.01160754438716834, -0.509215333797231, 1.777655744981393, 0.504377252007492, -1.150726061378728, 3.308832372020147, 5.08674044284956, -0.6393469183818957, -2.05274258857893, 2.135292398081709, 1.083720831068069, -1.572095807024461, 1.097852255743481, 1.687083627865796, -1.033786724640123, 1.132631680121686, 3.741798206655857, 0.935844210838145, 0.1071427697532981, 2.060269436215346, 0.03713580300326989, -1.410144553863182, 0.8286664350904691, -0.09365863752065261, -1.631671142379377, 1.055310529735813, 0.2237474904118773, -3.707485822323901, -1.321028153812833, 0.7302299666822694, -3.664516338806905, -3.081435085531819, 2.284439677083967, 0.3111136350081739, -3.233014873308669, -0.8133999050316782, 0.1172852450961012, 0.6416344862825927, 5.713945944411937, 5.603790841423078, -0.998248679821055, -2.103923433620321, 0.2696250104127775, -0.263280094704347, 0.009892038104071759, -1.321946362350246, -5.545048689521197, -3.093338673211264, 2.306917039907844], 'positive_zeros': ['0.7540382641133918', '1.256750247456205', '2.065182670373295', '2.673566554845818', '3.163247806570368', '3.625386850017885', '4.547254569787029', '4.818403477879497', '5.241624739745238', '5.686717027518459', '6.475492882726283', '6.539709677748598', '7.373064983293150', '7.752462689302225', '7.979195055752079', '8.808453304732404', '9.174098119493754', '9.675376412146350', '10.13552449629548', '10.61362201194316', '11.02419286937081', '11.35581370973009', '11.89142650530630', '12.35850244480506', '12.73932099121433', '13.37628115280221', '13.46251995611166', '13.99603253663141', '14.65233743868555', '15.04344522794028', '15.64103137193235', '15.71453107752753', '16.29819721428299', '16.68805929281001', '17.12466842044088', '17.64638161034709', '17.99858330843688', '18.31102008587219', '18.78908175366079', '19.09594925801516', '19.72328073223739'], 'prelabel': '2-339600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.07417452675254, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1791316177725537505, 'z1': {'__RealLiteral__': 0, 'data': '0.7540382641133918', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.256750247456205', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.065182670373295', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2711.7196526426833, 'bad_primes': [2, 3, 5, 283], 'central_character': '1.1', 'conductor': 339600, 'conductor_radical': 8490, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 6, 0, 0, 0, -1, 0, 2, 0, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, -2, 0, -4, 0, 0, 0, 8, 0, -7, 0, 2, 0, -10, 0, 0, 0, -6, 0, 4, 0, -10, 0, 0, 0, 0, 0, -12, 0, -6, 0, 8, 0, 12, 0, 0, 0, 0, 0, 2, 0, 1, 0, 10, 0, 0, 0, -2, 0, 14, 0, 0, 0, -2, 0, 0, 0, 8, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 0, 13], 'euler17': [1, 2, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, -12, 73], 'euler79': [1, -2, 79], 'euler83': [1, -10, 83], 'euler89': [1, -14, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 7], [1, 4, 11], [1, 0, 13], [1, 2, 17], [1, -6, 19], [1, -6, 23], [1, -2, 29], [1, -2, 31], [1, -6, 37], [1, 2, 41], [1, 4, 43], [1, -8, 47], [1, 10, 53], [1, -4, 59], [1, 10, 61], [1, 12, 67], [1, -8, 71], [1, -12, 73], [1, -2, 79], [1, -10, 83], [1, -14, 89], [1, -8, 97]], 'index': 43, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/339600/m'], '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': '2-339600-1.1-c1-0-43', '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': '2-339600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.07417452675254, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1791316177725537505, 'z1': {'__RealLiteral__': 0, 'data': '0.7540382641133918', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1791316177725537505', 'Lhash_array': ['1791316177725537505'], 'factors': ['2-339600-1.1-c1-0-43'], 'label': '2-339600-1.1-c1-0-43', 'type': 'ECQ', 'url': 'EllipticCurve/Q/339600/m'}