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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': '1916730913141396826', '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': 86.4779853890467, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1, 1]], [19, [1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '10830.1', 'coefficient_field': '1.1.1.1', 'conductor': 10830, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 1], [1, 1, 7], [1, -6, 11], [1, -5, 13], [1, 0, 17], [1], [1, -6, 23], [1, -6, 29], [1, -5, 31], [1, -11, 37], [1, -6, 41], [1, 1, 43], [1, -12, 47], [1, 12, 53], [1, -6, 59], [1, 7, 61], [1, 1, 67], [1, 0, 71], [1, 1, 73], [1, 7, 79], [1, 6, 83], [1, 12, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 15, 'label': '2-10830-1.1-c1-0-15', 'leading_term': '2.45170265523', '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/10830/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.451702655228356, 2.218523469210849, 1.551665145994621, 0.6335168562757368, -0.111842268590494, -0.1639442637718784, 0.7081483315472705, 2.105580145731204, 3.083144710934147, 2.776723521409416, 1.185775706363355, -0.6083217143613834, -1.203524913091187, -0.1497470539607892, 1.444759312597093, 1.808416560555177, 0.3415721998412979, -1.383123678736957, -0.7974522025721958, 3.055548150056224, 8.028293734485686, 10.36842977736788, 8.139841540737732, 3.187597989183942, -0.5829391739703113, -1.006364658590506, 0.4809646042439141, 0.9157117780045363, -0.643087949873097, -2.258757159714066, -1.833207264168907, 0.1402978484367746, 1.29422458635726, 0.5149088185405564, -0.7600398018725739, -0.7715348028385995, 0.04259426492529728, -0.08862847697543876, -1.276459157964529, -1.442143406475505, 0.5821012418257928, 2.775681325213363, 2.291035765403522, -0.4601978453374288, -2.05131964687853, -0.8120466368983003, 0.6347677678165732, -0.8067995574399628, -3.775969047944432, -3.993280234661649, -0.6369189112769855, 1.810742930559309, -0.3540908575667302, -4.508615437990965, -5.097990692446897, -1.44924599791523, 1.384883027246591, 0.0486870856427035, -2.478788327220534, -1.821294159876691, 1.103911231400996, 1.904977264487666, -0.2126400323115435, -1.490432572677131, -0.008424876446977094, 1.25805397708879, -0.31682765407101, -2.391486418146009, -1.55984476103626, 0.7329344811116266, 0.3884349539422002, -2.481934061484104, -3.525818786048179, -1.122561066172121, 1.20790323952877, 0.724758918397062, -0.5116792628940092, 0.05944431653722546, 1.073037504777898, 0.4913349057123905, -0.04952772637723489, 1.591176064130832, 3.211385453429336, 1.699729519218101, -0.5869497898726987, 1.052861571512181, 4.95045672653562, 4.47230550239713, -0.9730470309316686, -3.817068290787551, -0.1239440610298751, 3.843011229720838, 1.841100562965899, -2.142378658993844, -0.9243824531784071, 3.633153447151051, 3.922778852068835, -0.7025350503315928, -3.482690266851109, -1.652265776650648, 0.4324350448230733, 0.1581788101980741, 0.3157979367679332, 2.1098517202577, 2.231311727198351, -0.4315465495245265, -2.076740903233556, -0.8429249889599167, 0.1233430138341627, -0.7596528842884671, -0.5381461259266642, 1.685876512074177, 2.174712727898229, -0.03950131104510627, -0.4823898549617763, 2.140994577094927, 2.413084227225539, -2.029928752172848, -5.219494930845468, -2.882814439635098, 0.3124945662089861], 'positive_zeros': ['0.9488138736495322', '1.323206996198386', '2.655063376838759', '3.272760778713735', '4.041945390825184', '4.570975010242444', '5.943241700041822', '6.421643957740092', '6.919078285997604', '7.732371084853932', '8.338788970520050', '8.982970336234498', '9.222605614943090', '9.944237018575117', '10.70986170433115', '11.35365438061613', '11.66926020405516', '12.54240307344790', '12.97788340424280', '13.84259539105867', '14.25427224088457', '14.90383992513259', '15.47835853311596', '16.00100234604119', '16.46845364747815', '17.15714818961479', '17.54069009073572', '18.34343320366195', '18.86933273446203', '19.23841710810609', '19.87940452066118'], 'prelabel': '2-10830-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.299354030740345, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1916730913141396826, 'z1': {'__RealLiteral__': 0, 'data': '0.9488138736495322', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.323206996198386', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.655063376838759', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 86.4779853890467, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 10830, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 6, 1, 5, 1, -1, 1, 0, -1, 0, -1, -1, -6, 6, -1, 1, -5, 1, -1, 6, 1, 5, -1, 6, 0, 1, 1, 11, 0, 5, 1, 6, 1, -1, 6, -1, -6, 12, 1, -6, -1, 0, 5, -12, -1, -6, 1, 0, -6, 6, -1, -7, -5, -1, 1, -5, -6, -1, 0, 6, -1, 0, -1, -1, -11, 1, 0, -6, -5, -7, -1, 1, -6, -6, -1, 0, 1, 6, -6, -12, 1, -5, 6, 5, -12, 0, -1, 14, 6, 6, 1], 'euler11': [1, -6, 11], 'euler13': [1, -5, 13], 'euler17': [1, 0, 17], 'euler19': [1, 0, 0], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -5, 31], 'euler37': [1, -11, 37], 'euler41': [1, -6, 41], 'euler43': [1, 1, 43], 'euler47': [1, -12, 47], 'euler5': [1, 1, 0], 'euler53': [1, 12, 53], 'euler59': [1, -6, 59], 'euler61': [1, 7, 61], 'euler67': [1, 1, 67], 'euler7': [1, 1, 7], 'euler71': [1, 0, 71], 'euler73': [1, 1, 73], 'euler79': [1, 7, 79], 'euler83': [1, 6, 83], 'euler89': [1, 12, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 1, 0], [1, 1, 7], [1, -6, 11], [1, -5, 13], [1, 0, 17], [1, 0, 0], [1, -6, 23], [1, -6, 29], [1, -5, 31], [1, -11, 37], [1, -6, 41], [1, 1, 43], [1, -12, 47], [1, 12, 53], [1, -6, 59], [1, 7, 61], [1, 1, 67], [1, 0, 71], [1, 1, 73], [1, 7, 79], [1, 6, 83], [1, 12, 89], [1, -14, 97]], 'index': 15, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/10830/j'], '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': '2-10830-1.1-c1-0-15', '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': '2-10830-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.299354030740345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1916730913141396826, 'z1': {'__RealLiteral__': 0, 'data': '0.9488138736495322', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1916730913141396826', 'Lhash_array': ['1916730913141396826'], 'label': '2-10830-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/10830/j'}