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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1141693185503904145', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2184.7069993022324, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '273600.1', 'coefficient_field': '1.1.1.1', 'conductor': 273600, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 0, 7], [1, 2, 11], [1, 2, 13], [1, 4, 17], [1, 1], [1, 2, 23], [1, 6, 29], [1, -4, 31], [1, -2, 37], [1, 2, 41], [1, -4, 43], [1, 10, 47], [1, -6, 53], [1, 4, 59], [1, 2, 61], [1, -4, 67], [1, -4, 71], [1, -6, 73], [1, -8, 79], [1, 2, 83], [1, -6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 208, 'label': '2-273600-1.1-c1-0-208', 'leading_term': '5.71780187702', '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/273600/hr', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.151980281293336, 0.8580038534392994, -1.1755941281179, -3.356905859826575, -3.376331212214222, -0.9398122100421059, 1.349715672967405, 1.059427607010384, -0.6280489556560924, -0.4628337981168341, 1.78846214272763, 2.543588880297327, 0.06455189276785374, -2.144441720130593, -0.602246877007513, 2.218191505619701, 1.747925730598433, -0.9337553680973305, -1.127922714046355, 0.8552341963577249, 0.3232962935584396, -2.56276285509074, -2.491643817475745, 0.9495989887826347, 2.072550742189694, -0.1554089224003375, -0.1658962126916758, 2.993214278168923, 3.497499617762713, 0.4223551325709746, -0.3787327029569141, 1.648996867401605, 0.8313140547082736, -2.21211492460039, -1.284167200909385, 2.158906599444065, 1.538638473409905, -1.199066515193501, -0.03055149268662619, 2.001860044443413, -0.310732297752805, -2.514805939889279, -0.2371449267765399, 1.033151425635282, -1.635744382386539, -1.923362022421162, 1.054229713757766, 0.1348030821265138, -3.571446304216353, -2.512833707836594, 0.8603934117316082, 0.2894165596443156, -0.2374891276469342, 2.764881324823195, 2.891557304333755, -0.8905640447977821, -0.556287060301773, 2.830142478783813, 1.444590353032548, -1.428509983311632, 0.2088701494795775, 1.079144356782475, -1.486029572754716, -0.4336387133080937, 3.294752601018796, 2.028740486060252, -0.2595282762384721, 2.53659313935459, 3.819724568341548, 0.4014775324405693, 0.0647518156538558, 2.275795939498441, 0.2575217249228263, -1.243391867984394, 2.039483138785972, 2.112340340464134, -2.017509858887227, -1.672178096263243, 0.560265135200193, -1.447919258341266, -1.341655849000873, 2.849277466319333, 2.504873283354562, -0.3109228431001114, 1.614370183054089, 2.248027181600864, -1.644001209082296, -1.536348712884254, 1.266978411740976, -0.6544389352646905, -1.6877249859814, 1.213263418644087, -0.5247224334374627, -4.514714604622961, -1.992648249638826, 0.9426533243617541, -0.6870564627022014, -0.06486882828250674, 0.745037369438528, -3.476834044044369, -3.889448197991035, 1.848983273984031, 2.587426399217169, -0.28459088542333, 0.612680334569864, -0.3291997483944371, -3.535006504176055, -1.208658106429184, 0.8665794459964025, -2.66772780866618, -2.55876243834081, 0.649197009836706, -1.770163890391525, -3.381580360419449, 0.1673937816789252, 0.2064435896247492, -1.178803597173855, 1.712182033319555, 1.152788020346748, -2.254417266958749], 'positive_zeros': ['0.6252538672412759', '1.582570296851180', '2.149020745249891', '2.561588326736553', '3.255019403057945', '3.797319823644512', '4.406519790626509', '4.887448508103858', '5.281036141500595', '5.932579972672235', '6.481999824446566', '6.767339311728328', '7.540340322923525', '7.804468719989889', '8.314536370538142', '8.836133770669684', '9.370727707662900', '9.752631664382052', '10.22859714309146', '10.76940593381190', '11.11589039967360', '11.65479281476069', '12.00910131411266', '12.66488030198541', '13.03925488067995', '13.28037021177383', '13.93532176398186', '14.28907652760157', '14.84562806098094', '15.23082741764056', '15.61169704853003', '16.02723341915743', '16.66592385045931', '16.80851343835255', '17.53594035337848', '17.74281213476743', '18.26902500777697', '18.61472256704214', '19.12411947783311', '19.64125668776722', '19.86590830611847'], 'prelabel': '2-273600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.740849364364706, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1141693185503904145, 'z1': {'__RealLiteral__': 0, 'data': '0.6252538672412759', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.582570296851180', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.149020745249891', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2184.7069993022324, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 273600, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -4, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -6, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 4, 0, 0, 0, -10, 0, -7, 0, 0, 0, 6, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 4, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -4, 71], 'euler73': [1, -6, 73], 'euler79': [1, -8, 79], 'euler83': [1, 2, 83], 'euler89': [1, -6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 7], [1, 2, 11], [1, 2, 13], [1, 4, 17], [1, 1, 0], [1, 2, 23], [1, 6, 29], [1, -4, 31], [1, -2, 37], [1, 2, 41], [1, -4, 43], [1, 10, 47], [1, -6, 53], [1, 4, 59], [1, 2, 61], [1, -4, 67], [1, -4, 71], [1, -6, 73], [1, -8, 79], [1, 2, 83], [1, -6, 89], [1, -10, 97]], 'index': 208, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/273600/hr'], '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': '2-273600-1.1-c1-0-208', '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': '2-273600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.740849364364706, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1141693185503904145, 'z1': {'__RealLiteral__': 0, 'data': '0.6252538672412759', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1141693185503904145', 'Lhash_array': ['1141693185503904145'], 'factors': ['2-273600-1.1-c1-0-208'], 'label': '2-273600-1.1-c1-0-208', 'type': 'ECQ', 'url': 'EllipticCurve/Q/273600/hr'}