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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': 1, 'A8': 0, 'A9': 1, 'Lhash': '1213869343527802611', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -1], [1, 1], [1, -1, 13], [1, -5, 17], [1, 8, 19], [1, -1, 23], [1, 3, 29], [1, 3, 31], [1, -4, 37], [1, -3, 41], [1, -9, 43], [1, 2, 47], [1, -9, 53], [1, -5, 59], [1, -5, 61], [1, 12, 67], [1, 8, 71], [1, 2, 73], [1, -14, 79], [1, 5, 83], [1, 2, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 117, 'label': '2-369600-1.1-c1-0-117', 'leading_term': '1.93999681591', '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/369600/ib', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.939996815908139, 1.142077002597554, -0.5139926009957325, -1.287135290635079, -0.09865067532416447, 1.767141206368471, 1.723268228794051, -0.5428019226827859, -1.936366200760093, -0.1620893593602352, 2.192620693976725, 0.865765113805904, -3.18776854658457, -4.375506898718546, -0.9673125293369245, 1.98698582473108, 0.8839625421801282, -0.7382893182069914, 0.8951516631336264, 2.785727125236388, 1.096865022829723, -1.319226939886568, -0.5150000700274151, 0.9308541990293775, -0.2384965825321365, -0.7190162936325605, 2.23460454123993, 3.842950524208249, 0.8891571945644684, -1.170891935662364, 0.9618284057518707, 1.599055514870214, -1.580158430444443, -2.020052914308906, 1.525100292987774, 1.526001327168869, -2.162864784501989, -1.250101172655851, 3.306287227380949, 2.78831222801673, -1.283605600340845, -1.154576036096882, 1.017557232200022, 0.006860055910043565, -0.5590494474626273, 1.52093638385926, 0.82857570812781, -2.152887416033304, -1.009858655424748, 1.657630772256833, 0.2722204639498102, -0.5560065613666901, 2.104104456471038, 1.575950598977823, -1.322628605084092, 2.029284487663612, 7.293743183493909, 4.683994789564542, -0.1919036237709791, 0.02131943740744938, -0.847349045233587, -4.33586270424788, -2.226058927664708, 2.485920922573742, 0.9711380722661325, -1.790149818743798, -0.07099414962367916, 0.2407229457775382, -1.45606795327139, 0.471157839130452, 1.820111495647426, -1.010464708458206, -1.168019034344036, 0.9522616142179269, -1.445169382733051, -3.297958094289617, -0.3418468997944581, -0.273437204486333, -1.554254169115246, 4.137083000905036, 7.959138085280829, 1.445686152274241, -3.406706071071076, -0.6990763223029787, 0.1433819241005948, -0.2907361383763662, 2.576688934422474, 2.052858387915247, -1.206305698533869, 1.217104071951199, 3.644278694600955, 0.1390130114944327, -1.207133474417012, 0.531070197580749, -0.8018609286071845, -1.080365417051389, 0.2597434353694433, -2.923078271368959, -3.952549529679726, 1.512256058943659, 1.80583926114965, -2.79781786852337, -1.395521671472061, 0.2521781299823897, -1.904488031758584, 2.139582060751184, 7.485092536933524, 3.244783671565093, -0.7786806322000968, 1.452278745157695, 0.750823405518995, -1.203664523168135, 0.2471958114731814, -0.4181264099831139, -0.1735230786414001, 4.866153110540338, 4.77599969466207, -0.2616222472043437, -0.4417769615018681, -0.08759662686304476, -1.16376314825028], 'positive_zeros': ['0.4215443975640144', '1.012521849966361', '1.696823453795201', '2.263971707051745', '2.807274006065120', '3.558412316698947', '4.096013005461359', '4.411406587172581', '5.090691443705448', '5.563058530181281', '5.966860792017754', '6.334295773552220', '7.062492253120945', '7.413296411234435', '7.886598829723193', '8.394967027184234', '8.852034340729030', '9.317276155927289', '9.909772213340027', '10.35883451615268', '10.75091328492817', '11.07850600655952', '11.56413263712854', '12.07407553664472', '12.52829253290903', '12.81630586601113', '13.36058493991784', '13.66065197090705', '14.48114666420721', '14.74556006712092', '14.91677070452085', '15.59939097127950', '16.06072385544323', '16.50802028290989', '16.78159579687292', '17.21220225145642', '17.66955225276610', '18.10887126208856', '18.40151907074360', '19.03380097081679', '19.21926814936554', '19.60280129690312'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1213869343527802611, 'z1': {'__RealLiteral__': 0, 'data': '0.4215443975640144', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.012521849966361', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.696823453795201', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 5, 0, -8, 0, -1, 0, 1, 0, 0, 0, -1, 0, -3, 0, -3, 0, 1, 0, 0, 0, 4, 0, -1, 0, 3, 0, 9, 0, 0, 0, -2, 0, 1, 0, -5, 0, 9, 0, 0, 0, 8, 0, 5, 0, 5, 0, 1, 0, 0, 0, -12, 0, -1, 0, -8, 0, -2, 0, 0, 0, -1, 0, 14, 0, 1, 0, -5, 0, 0, 0, 3, 0, -2, 0, 1, 0, 3, 0, 0, 0, 12, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -1, 13], 'euler17': [1, -5, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 23], 'euler29': [1, 3, 29], 'euler3': [1, 1, 0], 'euler31': [1, 3, 31], 'euler37': [1, -4, 37], 'euler41': [1, -3, 41], 'euler43': [1, -9, 43], 'euler47': [1, 2, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -5, 59], 'euler61': [1, -5, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, 2, 73], 'euler79': [1, -14, 79], 'euler83': [1, 5, 83], 'euler89': [1, 2, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -1, 13], [1, -5, 17], [1, 8, 19], [1, -1, 23], [1, 3, 29], [1, 3, 31], [1, -4, 37], [1, -3, 41], [1, -9, 43], [1, 2, 47], [1, -9, 53], [1, -5, 59], [1, -5, 61], [1, 12, 67], [1, 8, 71], [1, 2, 73], [1, -14, 79], [1, 5, 83], [1, 2, 89], [1, -12, 97]], 'index': 117, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/ib'], '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': '2-369600-1.1-c1-0-117', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1213869343527802611, 'z1': {'__RealLiteral__': 0, 'data': '0.4215443975640144', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1213869343527802611', 'Lhash_array': ['1213869343527802611'], 'label': '2-369600-1.1-c1-0-117', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/ib'}