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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': -1, 'A6': -1, 'A7': 1, 'A8': -1, 'A9': 1, 'Lhash': '1945503984782605019', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 239.7907572699051, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1, 1]], [7, [1, -1]], [11, [1, -1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11, 13], 'central_character': '30030.1', 'coefficient_field': '1.1.1.1', 'conductor': 30030, 'conductor_radical': 30030, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, -8, 31], [1, 10, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, -12, 59], [1, 10, 61], [1, -8, 67], [1, -12, 71], [1, -14, 73], [1, -8, 79], [1, 0, 83], [1, -6, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 29, 'label': '2-30030-1.1-c1-0-29', 'leading_term': '4.56432672407', '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/30030/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.055371778978927, 1.598371766412525, 1.221513502276004, -0.04254993115746324, -1.48547655901324, -2.08673590812995, -1.415032652550836, -0.2516386883352846, -0.06351039373787314, -1.506489112873797, -3.4361483548841, -3.819470592933038, -1.991912119387362, 0.2208161337356292, 0.2703488408218807, -2.019474247149294, -3.79045359178442, -2.377597628177116, 1.026526887591698, 2.113075492908945, -1.498746440432543, -6.852405646266619, -8.604977716137597, -5.218413900703392, -0.6645536382321118, 0.6481443433081726, -0.8925744543387615, -1.518007125070709, 0.2677871111560495, 1.94667600435713, 1.235735742599402, -0.4906809882333142, -0.7135140769590339, 0.2161078358245092, 0.1786778020601155, -0.608391421760957, 0.1881123026450133, 2.552962067995163, 3.323981881302883, 1.22483831907736, -0.5559022484571219, 0.7140678581035255, 2.688655654392335, 1.826484280207681, -0.3688752536751309, 0.2033880208262922, 2.689965989169993, 2.040053804904451, -2.120769856550384, -3.738165745354653, -0.001529032289171222, 3.421755645251133, 1.294470709104679, -2.538195238401184, -1.638528002573834, 2.163096327432319, 2.083732350233753, -2.020265900351071, -3.847451035856524, -1.572320819759177, 0.1217162655701532, -0.5262728236029766, 0.3281919108119758, 3.504384174485302, 4.103918062022442, 0.51777120889385, -2.01621769569521, -0.5936463225760477, 0.4935091533045264, -1.711608147992211, -3.283797877552871, -1.242631922933161, 0.6954990764738537, -0.5708262702303974, -1.806764313289618, -0.2727459094158299, 1.025273447063192, -0.06770998813112787, -0.541695055793074, 0.8949404841891646, 0.7188480314802707, -1.557519478704608, -1.512232639379139, 0.7119234122322542, -0.3874510206698812, -3.819790992341323, -1.890568447541335, 4.747943614949824, 6.070794739687595, 0.7467036615374498, -0.4838167636708486, 5.61010765926888, 8.498070867370693, 3.054546478789139, -1.880237134624927, -0.347137933910092, 1.76470667331012, 0.4512322736787891, 0.4071327274631353, 3.142827392580353, 3.305284473042852, 0.2849731135883467, -0.4374095931255557, 1.386100622367494, 1.163431427932141, -0.378007386732463, 0.3435638507060602, 1.24947372212443, -0.4325583171767194, -1.385305113873568, 0.331446824801379, 0.4728281808361124, -1.578621486854653, -0.4516465852120193, 2.925486021834958, 1.485228033143873, -3.151564021901863, -2.680340157845183, 1.478394542596295, 1.467310886715538], 'positive_zeros': ['0.9929972800954188', '2.092073153284628', '2.221575077938602', '3.465611457025477', '3.792045396684528', '4.672352931926644', '5.175067061052364', '6.307133317072057', '6.626798818887902', '7.221205889161648', '7.917855068065422', '8.436257752134236', '8.803447177703006', '9.224531131769634', '10.12841351865316', '10.41702692297274', '11.19315904822210', '11.47631644333255', '12.12989536569780', '12.75007720380913', '13.32255422068240', '13.85359908495942', '14.38451412839473', '15.19263825967546', '15.34476814239037', '15.71444504704024', '16.53209650282311', '17.07049772189073', '17.33852335530218', '18.11601707902583', '18.43036406792901', '19.03175291643701', '19.48855215463028', '19.85786927209888'], 'prelabel': '2-30030-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.485178632160014, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1945503984782605019, 'z1': {'__RealLiteral__': 0, 'data': '0.9929972800954188', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.092073153284628', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.221575077938602', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 239.7907572699051, 'bad_primes': [2, 3, 5, 7, 11, 13], 'central_character': '1.1', 'conductor': 30030, 'conductor_radical': 30030, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -6, -1, -4, -1, 1, -1, 0, -1, 1, -1, 1, 1, -6, 1, 8, -1, 1, 6, -1, 1, -10, 4, 1, 1, -6, -1, -4, 1, -1, 0, 0, 1, 1, -1, -6, 1, 6, -1, -1, -1, -4, 6, 12, -1, -10, -8, 1, 1, -1, -1, 8, -6, 0, 1, 12, -1, 14, 10, 1, -4, 1, -1, 8, -1, 1, 6, 0, 1, 6, 4, -6, -1, 6, 1, 1, 0, 8, 0, 4, -1, 14, -1, 1, 1], 'euler11': [1, -1, 0], 'euler13': [1, -1, 0], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, -12, 71], 'euler73': [1, -14, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 1, 0], [1, -1, 0], [1, -1, 0], [1, -1, 0], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, -8, 31], [1, 10, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, -12, 59], [1, 10, 61], [1, -8, 67], [1, -12, 71], [1, -14, 73], [1, -8, 79], [1, 0, 83], [1, -6, 89], [1, -14, 97]], 'index': 29, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30030/p'], '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': '2-30030-1.1-c1-0-29', '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': '2-30030-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.485178632160014, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1945503984782605019, 'z1': {'__RealLiteral__': 0, 'data': '0.9929972800954188', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1945503984782605019', 'Lhash_array': ['1945503984782605019'], 'label': '2-30030-1.1-c1-0-29', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30030/p'}