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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 4, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '732319273940044956', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2655.7604909061697, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [13, [1]], [41, [1, 1]]], 'bad_primes': [2, 3, 13, 41], 'central_character': '332592.1', 'coefficient_field': '1.1.1.1', 'conductor': 332592, 'conductor_radical': 3198, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -4, 5], [1, 2, 7], [1, 3, 11], [1], [1, -3, 17], [1, 0, 19], [1, -6, 23], [1, -5, 29], [1, -7, 31], [1, -7, 37], [1, 1], [1, -1, 43], [1, -3, 47], [1, 6, 53], [1, 0, 59], [1, 3, 61], [1, 2, 67], [1, 3, 71], [1, -11, 73], [1, 10, 79], [1, 16, 83], [1, -10, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 30, 'label': '2-332592-1.1-c1-0-30', 'leading_term': '3.30791894505', '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/332592/bn', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.307918945049261, 2.366810345395571, 0.2655032431014016, -1.206805173212141, -0.710792167505989, 0.8479407020795481, 0.9623588028554954, -1.163344851244463, -3.003439921830798, -2.022034170570369, 0.3408324157414987, 0.7459492500136463, -0.204751858998308, 1.745764154367543, 6.939689042020825, 9.255140615588015, 4.762513982540712, -1.443353626601458, -2.385309007225979, 0.6308926171717743, 1.599815653215412, 0.1107603007476139, 0.1230054356717192, 1.378880143120806, 0.7929200443931312, -0.3538019204395818, 0.4342048557527069, 0.3494944674300063, -2.666551014277491, -3.178677738921124, 1.893786249935024, 4.732761180007874, -0.1765936372683181, -4.511430285600024, -0.7011438407417921, 4.191931213756143, 2.320012350495543, -1.248994090590211, -0.6954015320540473, 0.1911952601105671, -1.020339179745526, -0.6679276300574085, 0.3887656233663988, -1.319833832699546, -1.425032581075499, 3.356476872028197, 5.001638903210428, -0.608174295708466, -3.875484998813098, -0.2553836412843533, 1.876479954379078, -0.1454237132075455, -0.2760988865816395, 0.6389593260101344, -0.9125409982064803, -0.518766488419896, 2.388393904383068, 0.7363683341944448, -2.486737461975461, 1.29701172252238, 5.403543290830345, 0.7165903214796373, -3.908814208769292, -0.7259699267293596, 1.334983605143497, -1.584785655022922, -1.433868073241418, 1.275306892616571, 0.5096484241689059, -0.3453845039901327, 0.7986550231485816, -0.6700053536600022, -2.187897670843816, 0.1682664821093902, 0.6591187474486567, -1.02765102382251, 1.733205617860626, 2.669353895045618, -4.555417163872288, -6.824337371169194, 1.728526568815417, 5.223720415211797, -0.3429215395979518, -1.813643751296663, 0.8298648938811954, 0.2562202709935638, 0.02693424336802799, 0.6746139620022183, -2.209340243344136, -3.250422866629333, 0.007831585954224646, 0.03024304131410457, -1.134835934029631, 1.583229031050533, 0.4737649751459907, -4.417926652756552, -1.803078765120663, 3.138501957399355, 0.3091641704855649, -1.867121432620689, 1.223273513903763, 1.187174228830325, -0.3352874578216692, 0.4897455945727225, -1.969308727873638, -3.788471775268735, 1.067906237426415, 2.552491873199908, -0.4850320298309037, 4.080640174182302, 8.653341702056666, 1.388297802237501, -5.037834273574657, -2.141576249051021, 0.06035906253825789, -0.1971476588069466, 0.5145175953156145, -0.7224907028572694, -1.074530749527848, 0.8359385526464471, -0.5916426041949662], 'positive_zeros': ['0.5320393264007873', '1.111991199051465', '1.634137824989851', '2.456630262431532', '2.917268334872720', '3.093542621451908', '4.178307001543390', '4.697558846453762', '5.274082349388903', '5.472015569659149', '6.134005088514207', '6.410431551713842', '6.790378798311656', '7.420693665168302', '7.993488565690042', '8.527192463077840', '9.135659684235512', '9.610715203433637', '9.807997303752640', '10.35673055396608', '10.59776573936211', '11.09205050814083', '11.72688594482157', '12.26445650088573', '12.73172156786137', '13.04770530389945', '13.37980198875530', '13.79442954538043', '14.29207653794268', '14.69747480607067', '15.27501657196222', '15.79079538659629', '16.12772218436378', '16.61549808787761', '17.07010004254125', '17.32801395418846', '17.68555230436081', '18.23455716781075', '18.57702986211173', '18.89037488970887', '19.36221320794306', '19.95433294029935'], 'prelabel': '2-332592-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.53407116564894, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 732319273940044956, 'z1': {'__RealLiteral__': 0, 'data': '0.5320393264007873', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.111991199051465', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.634137824989851', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2655.7604909061697, 'bad_primes': [2, 3, 13, 41], 'central_character': '1.1', 'conductor': 332592, 'conductor_radical': 3198, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 4, 0, -2, 0, 1, 0, -3, 0, 0, 0, -4, 0, 3, 0, 0, 0, 2, 0, 6, 0, 11, 0, -1, 0, 5, 0, 7, 0, 3, 0, -8, 0, 7, 0, 0, 0, -1, 0, 1, 0, 4, 0, 3, 0, -3, 0, -3, 0, -6, 0, -12, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, -2, 0, -6, 0, -3, 0, 11, 0, -11, 0, 6, 0, -10, 0, 1, 0, -16, 0, 12, 0, -5, 0, 10, 0, 0, 0, -7, 0, 0, 0, 12, 0, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, 0, 0], 'euler17': [1, -3, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -5, 29], 'euler3': [1, 1, 0], 'euler31': [1, -7, 31], 'euler37': [1, -7, 37], 'euler41': [1, 1, 0], 'euler43': [1, -1, 43], 'euler47': [1, -3, 47], 'euler5': [1, -4, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 3, 61], 'euler67': [1, 2, 67], 'euler7': [1, 2, 7], 'euler71': [1, 3, 71], 'euler73': [1, -11, 73], 'euler79': [1, 10, 79], 'euler83': [1, 16, 83], 'euler89': [1, -10, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -4, 5], [1, 2, 7], [1, 3, 11], [1, 0, 0], [1, -3, 17], [1, 0, 19], [1, -6, 23], [1, -5, 29], [1, -7, 31], [1, -7, 37], [1, 1, 0], [1, -1, 43], [1, -3, 47], [1, 6, 53], [1, 0, 59], [1, 3, 61], [1, 2, 67], [1, 3, 71], [1, -11, 73], [1, 10, 79], [1, 16, 83], [1, -10, 89], [1, -12, 97]], 'index': 30, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/332592/bn'], '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': '2-332592-1.1-c1-0-30', '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': '2-332592-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.53407116564894, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 732319273940044956, 'z1': {'__RealLiteral__': 0, 'data': '0.5320393264007873', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '732319273940044956', 'Lhash_array': ['732319273940044956'], 'label': '2-332592-1.1-c1-0-30', 'type': 'ECQ', 'url': 'EllipticCurve/Q/332592/bn'}