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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 1, 'A9': 0, 'Lhash': '1056492537812900121', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 373.8436121832307, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [17, [1]]], 'bad_primes': [2, 3, 17], 'central_character': '46818.1', 'coefficient_field': '1.1.1.1', 'conductor': 46818, 'conductor_radical': 102, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 0, 5], [1, 2, 7], [1, -3, 11], [1, -2, 13], [1], [1, 1, 19], [1, -6, 23], [1, 6, 29], [1, -4, 31], [1, -4, 37], [1, 9, 41], [1, 1, 43], [1, 6, 47], [1, -12, 53], [1, -3, 59], [1, 8, 61], [1, -5, 67], [1, -12, 71], [1, 11, 73], [1, -4, 79], [1, -12, 83], [1, -6, 89], [1, 5, 97]], 'gamma_factors': [[], [0]], 'index': 3, 'label': '2-46818-1.1-c1-0-3', 'leading_term': '3.67580256564', '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/46818/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.675802565640781, 2.958143290684048, 1.03341126276712, -1.281967211967433, -2.670571702475693, -2.145991240180918, -0.08965797822000734, 1.720084955278448, 1.562931868171342, -0.4723541402866213, -2.393746350848335, -2.329283701328179, -0.5988359523051764, 0.6985704320451278, 0.3094190442501743, -0.5916854496378002, -0.1022983559296298, 1.550766797770913, 2.083361906942857, 0.4183068744168058, -1.42319971246415, -0.9193435664333715, 1.284478199142373, 2.177526600397056, 0.8105261358653049, -0.3515590105806517, 0.4846384405555409, 1.336351637195487, -0.1990868277314105, -2.194082631029692, -0.6886034029159513, 3.530702501977727, 4.82666122949723, 0.9589416788754292, -2.826533639965629, -1.297511114756892, 2.756600083951857, 3.004263852317989, -0.2849571406894512, -0.9897524119357419, 2.380602791423677, 4.085826928723078, 0.9034516086490137, -2.399423441114119, -1.144899865619273, 1.757923150867375, 1.582642784467415, -0.05651745395254007, 0.932762272135752, 3.147128909304161, 2.497202012105648, -0.009571654714410002, -0.3979938947787039, 0.759412883925341, 0.1683406076186768, -1.034795013747254, 0.4920623144412172, 2.939055421505324, 2.097263610239235, -0.5293688774115882, -0.5525391237652157, 0.6881605050437652, -0.8730083670880983, -3.142207649691122, -1.569000448202138, 1.33762299685146, 0.4948902370831897, -1.485238794473023, 0.2478552410063343, 1.69345592998166, -2.891521352087055, -7.904415849819408, -4.680884314393277, 2.244135030589203, 2.360747505086652, -2.555340595655472, -3.154890607219245, 0.04112637048580699, -0.05248357941421336, -2.118777948596976, -0.4887202217517319, 2.044145444637139, 0.09587921696481266, -2.737005925106226, -1.262376012092822, 0.8591596532157671, -0.6171459215903082, -1.823422577003117, 0.2759573536511656, 1.518286612349474, 0.02815067047999679, -0.1568910197866511, 1.270779071328359, 0.6042624920062345, -0.3280360485922564, 2.202889524183491, 4.201581249396002, 1.309211306013254, -1.521987647939231, 0.001222036377619195, 0.9781017881943119, -1.002499767194856, -0.4178533342725259, 2.679330970757577, 1.696418907558255, -0.7103011445753982, 3.364924748300988, 8.695106564207599, 5.24878381082388, -1.314337135985859, -0.7160171493925536, 1.53776646452624, -2.759973150800567, -6.600857324630839, -2.920158633533324, 1.06145057528405, 0.01747824981571484, 0.03985710853092101, 2.7634261514485, 2.052131791234707, -0.8813184916039348], 'positive_zeros': ['0.6090208166617369', '1.509800830183413', '2.200500949598635', '3.085134889977817', '3.572936105975915', '4.018194957087718', '4.795753044838404', '5.358844083005151', '6.127481795462059', '6.408382374328885', '6.979659057614529', '7.544689560883724', '8.297606863474766', '8.826337785138418', '9.477094348105541', '9.842523448494835', '10.55130044558126', '11.08728943196990', '11.73239462271440', '11.86631541916583', '12.74874156213547', '13.08250689714908', '13.52639999429402', '13.95379322764582', '14.68773972922093', '15.08771643995550', '15.41522481471067', '16.11449898189907', '16.54727879238788', '16.97920639017631', '17.38022633460682', '18.15587593575239', '18.61952044117367', '19.24568086325648', '19.49396081663915'], 'prelabel': '2-46818-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.335035872302658, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1056492537812900121, 'z1': {'__RealLiteral__': 0, 'data': '0.6090208166617369', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.509800830183413', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.200500949598635', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 373.8436121832307, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 46818, 'conductor_radical': 102, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -2, 1, 0, 0, 3, 0, 2, -2, 0, 1, 0, 0, -1, 0, 0, 3, 6, 0, -5, 2, 0, -2, -6, 0, 4, 1, 0, 0, 0, 0, 4, -1, 0, 0, -9, 0, -1, 3, 0, 6, -6, 0, -3, -5, 0, 2, 12, 0, 0, -2, 0, -6, 3, 0, -8, 4, 0, 1, 0, 0, 5, 0, 0, 0, 12, 0, -11, 4, 0, -1, -6, 0, 4, 0, 0, -9, 12, 0, 0, -1, 0, 3, 6, 0, -4, 6, 0, -6, 0, 0, -5, -3, 0, -5], 'euler11': [1, -3, 11], 'euler13': [1, -2, 13], 'euler17': [1, 0, 0], 'euler19': [1, 1, 19], 'euler2': [1, -1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -4, 37], 'euler41': [1, 9, 41], 'euler43': [1, 1, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 5], 'euler53': [1, -12, 53], 'euler59': [1, -3, 59], 'euler61': [1, 8, 61], 'euler67': [1, -5, 67], 'euler7': [1, 2, 7], 'euler71': [1, -12, 71], 'euler73': [1, 11, 73], 'euler79': [1, -4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 5], [1, 2, 7], [1, -3, 11], [1, -2, 13], [1, 0, 0], [1, 1, 19], [1, -6, 23], [1, 6, 29], [1, -4, 31], [1, -4, 37], [1, 9, 41], [1, 1, 43], [1, 6, 47], [1, -12, 53], [1, -3, 59], [1, 8, 61], [1, -5, 67], [1, -12, 71], [1, 11, 73], [1, -4, 79], [1, -12, 83], [1, -6, 89], [1, 5, 97]], 'index': 3, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/46818/k'], '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': '2-46818-1.1-c1-0-3', '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': '2-46818-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.335035872302658, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1056492537812900121, 'z1': {'__RealLiteral__': 0, 'data': '0.6090208166617369', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1056492537812900121', 'Lhash_array': ['1056492537812900121'], 'factors': ['2-46818-1.1-c1-0-3'], 'label': '2-46818-1.1-c1-0-3', 'type': 'ECQ', 'url': 'EllipticCurve/Q/46818/k'}