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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 2, 'A3': 0, 'A4': 2, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '2134970640717235217', 'a10': [0.0, 0], 'a2': [1.414213562373095, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2125.4180758014318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1, -1]], [13, [1]]], 'bad_primes': [3, 5, 7, 13], 'central_character': '266175.1', 'coefficient_field': '1.1.1.1', 'conductor': 266175, 'conductor_radical': 1365, 'degree': 2, 'euler_factors': [[1, -2, 2], [1], [1], [1, -1], [1, -2, 11], [1], [1, 2, 17], [1, 5, 19], [1, 6, 23], [1, 8, 29], [1, 5, 31], [1, -10, 37], [1, 6, 41], [1, -4, 43], [1, -6, 47], [1, -2, 53], [1, -12, 59], [1, 13, 61], [1, -4, 67], [1, 6, 71], [1, -1, 73], [1, 15, 79], [1, 0, 83], [1, 0, 89], [1, -1, 97]], 'gamma_factors': [[], [0]], 'index': 17, 'label': '2-266175-1.1-c1-0-17', 'leading_term': '2.75513979586', '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/266175/et', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.755139795861044, 1.063899300237195, -2.976250675317143, -6.501566079387476, -6.484660456730912, -2.680472563911069, 1.530038908264901, 2.555500809826354, 0.7622955833467525, -0.2450035657312365, 1.255470950888785, 2.763765798729286, 1.612782052206639, -0.7967854472109809, -1.336122893015047, -0.096288771994946, 0.4047227566842243, -0.04844061847556796, 0.468121653192108, 1.548526850050326, 0.8491079248085738, -0.9952006216323956, -1.039330749038378, 0.2628751271212105, -0.02371083129234377, -0.8775748677907107, 0.885076654272188, 2.963074599713756, 0.9126311945577071, -1.869597041745301, 0.9406517870430398, 5.138955669366638, 1.807390165127553, -5.16127408182829, -4.59912629734337, 1.049806902234407, 0.4559994601292982, -3.869457908468588, -0.4613348610092011, 6.983305050149527, 5.245736286177236, -2.844219956196134, -3.712013280042963, 1.826535596666108, 2.900756764353024, -0.04091954168543989, -0.01121762445474626, 0.9775114139474003, -0.9957079464883491, -2.044065053086137, -0.0512079906708164, 0.7022642452342095, -0.0840322080530354, 1.003422336901092, 1.988420235120858, 0.4597069175209746, -0.1725899583450781, 1.035810651115692, 0.5595339140805605, -0.454084774425413, 0.3753681882234974, -0.2469742390106967, -1.898030449083194, 1.070578520573577, 4.672822757257058, 1.418487304552828, -1.648305167390965, 2.267484007709711, 2.782843159156829, -3.930065686229572, -3.872808140386789, 3.309624442699599, 2.001459855598148, -4.154284050236536, -1.152690741221595, 1.940456834318787, -5.92128076375244, -10.47316380236958, -2.703528466751597, 2.63566654089539, -0.1524650382441004, -0.4873676837652249, 1.229373522093545, -1.199814074363951, -2.431312243807427, 0.290282063398982, 0.757706909411694, -0.5716381690490521, 0.03494677597302351, -0.1415209817851817, -0.8341583118265706, 1.008541559776392, 1.520755712746654, -0.7904939880039191, -0.8501571812840159, 0.1254776795541442, -0.843466396563446, -0.03906094725370666, 1.052565648815068, -1.450619332841089, -0.8470169427931303, 3.640034854085631, 1.989973528403424, -0.3261955269250828, 5.94498904875678, 6.741859956220131, -3.758555939463567, -5.259931279882229, 3.202681360245078, 2.407079025086769, -1.890709529635071, 1.438607702929561, -0.7190823210234993, -9.080752244935397, -6.234351448784255, 0.9292684027002602, -2.29971983385517, -5.060534797158154, -0.1147029361393731, 1.705968345471902, -0.05036660635835375], 'positive_zeros': ['0.3248308316587746', '1.395047014390916', '2.113750907667622', '2.327423567946282', '3.158714544855654', '3.770350876120942', '4.211079354202582', '4.363803084382405', '5.108833780126889', '5.687898291919861', '5.995014238239865', '6.416484401757086', '7.060213240353373', '7.452878456780870', '8.059821877553751', '8.693222421672601', '9.024314000373033', '9.514609291681524', '10.15527437118614', '10.66571323493103', '11.24517762419435', '11.50174583942501', '11.90275610178956', '12.50613681885770', '12.94518036278868', '13.07402224792014', '13.82249889659506', '14.04423996693829', '14.59514368412195', '14.90936837069132', '15.21803259941358', '15.69438133045021', '16.31832273715577', '16.63591325648550', '17.11132828443970', '17.62918976293890', '18.06914958049327', '18.54580367216760', '18.84267986648743', '19.57788198852462', '19.98806831200555'], 'prelabel': '2-266175-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.102256732197304, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2134970640717235217, 'z1': {'__RealLiteral__': 0, 'data': '0.3248308316587746', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.395047014390916', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.113750907667622', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2125.4180758014318, 'bad_primes': [3, 5, 7, 13], 'central_character': '1.1', 'conductor': 266175, 'conductor_radical': 1365, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, -4, -2, 0, -5, 0, 0, 4, -6, 0, 0, 0, 0, 2, -8, 0, -5, -8, 0, -4, 0, 0, 10, -10, 0, 0, -6, 0, 4, 4, 0, -12, 6, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -16, 12, 0, -13, -10, 0, -8, 0, 0, 4, -4, 0, 0, -6, 0, 1, 20, 0, -10, 2, 0, -15, 0, 0, -12, 0, 0, 0, 8, 0, 0, 0, 0, 0, -12, 0, 12, 0, 0, 1, 2, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, 0, 0], 'euler17': [1, 2, 17], 'euler19': [1, 5, 19], 'euler2': [1, -2, 2], 'euler23': [1, 6, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 5, 31], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, -12, 59], 'euler61': [1, 13, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 6, 71], 'euler73': [1, -1, 73], 'euler79': [1, 15, 79], 'euler83': [1, 0, 83], 'euler89': [1, 0, 89], 'euler97': [1, -1, 97], 'euler_factors': [[1, -2, 2], [1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -2, 11], [1, 0, 0], [1, 2, 17], [1, 5, 19], [1, 6, 23], [1, 8, 29], [1, 5, 31], [1, -10, 37], [1, 6, 41], [1, -4, 43], [1, -6, 47], [1, -2, 53], [1, -12, 59], [1, 13, 61], [1, -4, 67], [1, 6, 71], [1, -1, 73], [1, 15, 79], [1, 0, 83], [1, 0, 89], [1, -1, 97]], 'index': 17, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/266175/et'], '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': '2-266175-1.1-c1-0-17', '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': '2-266175-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.102256732197304, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2134970640717235217, 'z1': {'__RealLiteral__': 0, 'data': '0.3248308316587746', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2134970640717235217', 'Lhash_array': ['2134970640717235217'], 'factors': ['2-266175-1.1-c1-0-17'], 'label': '2-266175-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/266175/et'}