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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '640516352740228150', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 142.53296760798557, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [7, [1, -1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 17], 'central_character': '17850.1', 'coefficient_field': '1.1.1.1', 'conductor': 17850, 'conductor_radical': 3570, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1, -1], [1, -6, 11], [1, 4, 13], [1, -1], [1, 4, 19], [1, -8, 23], [1, -4, 29], [1, -8, 31], [1, -6, 37], [1, 0, 41], [1, 6, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, 10, 61], [1, 2, 67], [1, 2, 71], [1, 2, 73], [1, 8, 79], [1, -4, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 33, 'label': '2-17850-1.1-c1-0-33', 'leading_term': '5.86540909708', '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/17850/ck', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.865409097082109, 5.361747453814369, 3.885103505905966, 1.716785603825113, -0.4037967930891538, -1.51158145422626, -1.075915384340747, 0.4488423433235545, 1.794148544510071, 1.839041724712976, 0.6211007395755855, -0.619638988831068, -0.6035209236533877, 0.6537142848903849, 1.779230135389608, 1.503527639497352, 0.1295131040945602, -0.7697057197292257, -0.2815904179618957, 0.5481685329910827, -0.1219175813756542, -2.443032754509687, -4.216668745617012, -3.313449751917057, -0.4321650224149569, 1.476673806376312, 0.7925200999350736, -0.7092204461744807, -0.2906532200785841, 1.817326194481971, 2.473691673873571, 0.02013015842175171, -2.965527620977414, -2.839863690333513, 0.002211591470912163, 1.422884656382034, -0.681366422710492, -3.222334717909429, -2.303072047713232, 0.8836184905748422, 1.464923432611139, -1.980351578049038, -4.970509098746821, -3.314347924658585, 0.9372041110918291, 2.56262889060466, 0.6077130098518368, -0.9287864294091954, 0.291394835536478, 1.650592436277331, 0.4519226898090849, -1.429962103752278, -0.779445503140808, 1.473751982956679, 1.785856028340734, -0.1700058708208178, -1.275993631447424, -0.3929091647785035, 0.1971382398321941, -0.5162390546986306, -0.5150000305054881, 0.571755436244354, -0.4813250551100381, -4.706295644732226, -7.377681999531122, -4.634209820643559, -0.1817168894558677, 0.1502808261659915, -2.212046846034422, -1.582970106750738, 1.107355016112829, -1.112459850282582, -8.82500838397644, -13.11971293968242, -8.503749226235447, -1.152792088872795, 0.9171666394377664, -0.9073982416758418, -0.9062675487252374, 0.5542695749858216, -0.4338989616756323, -2.572302914212881, -1.583936339436809, 1.405379086238328, 1.804829068640433, 0.0256330024804593, 0.1616535130958911, 1.806278097474102, 1.199028403580313, -0.7701240334008886, 0.0117345459819834, 2.464802301370669, 1.884637114064823, -0.8450518996963773, -0.4962719591972359, 2.558912192876388, 2.835956501807043, -0.1093894348157732, -1.354881424155789, -0.1053694404458631, 0.04937065240090286, -0.3501130133004828, 1.943528852369987, 3.993714463189044, 0.3102964754769025, -5.730339720740645, -5.918573675271346, -1.342669317324117, 0.1443445887464793, -1.207305781465987, 1.228589497874467, 5.527390844038883, 3.503465137479368, -2.845791818930684, -3.192456335455281, 2.844771626884408, 5.1442666415266, 1.047048446844618, -1.641055681992889, 0.1079323083759709, 1.125724864264799], 'positive_zeros': ['0.9460154769990073', '1.683301994400179', '2.607258822281062', '3.136987462366937', '4.023291899893852', '4.569514719465389', '4.981295927504541', '6.038434496654913', '6.616145029387711', '7.040461599314517', '7.751464589534030', '8.499807383266336', '8.944167721160688', '9.676490072862720', '10.12922237340635', '10.94098258623393', '11.56344410054712', '11.96273641910697', '12.55023323391579', '13.08599849481400', '13.72985673428629', '14.34402565138866', '14.59679074530264', '15.11476128614319', '15.45451195162296', '16.51635899099682', '16.76802849112775', '17.38068000626729', '17.69604766681973', '18.81313826173188', '19.13410890862334', '19.63572854926961', '19.94970069553699'], 'prelabel': '2-17850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.938717167601617, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 640516352740228150, 'z1': {'__RealLiteral__': 0, 'data': '0.9460154769990073', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.683301994400179', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.607258822281062', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 142.53296760798557, 'bad_primes': [2, 3, 5, 7, 17], 'central_character': '1.1', 'conductor': 17850, 'conductor_radical': 3570, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 6, 1, -4, 1, 0, 1, 1, 1, -4, 0, 1, 6, 8, 1, 0, -4, 1, 1, 4, 0, 8, 1, 6, 1, 0, 1, 6, -4, -4, 0, 0, 1, -6, 6, 0, 8, 0, 1, 1, 0, 1, -4, -6, 1, 0, 1, -4, 4, 12, 0, -10, 8, 1, 1, 0, 6, -2, 1, 8, 0, -2, 1, -2, 6, 0, -4, 6, -4, -8, 0, 1, 0, 4, 1, 0, -6, 4, 6, -6, 0, -4, 8, 8, 0, 0, 1, -2, 1, 6, 0], 'euler11': [1, -6, 11], 'euler13': [1, 4, 13], 'euler17': [1, -1, 0], 'euler19': [1, 4, 19], 'euler2': [1, -1, 0], 'euler23': [1, -8, 23], 'euler29': [1, -4, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 0, 41], 'euler43': [1, 6, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 10, 61], 'euler67': [1, 2, 67], 'euler7': [1, -1, 0], 'euler71': [1, 2, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -1, 0], [1, -6, 11], [1, 4, 13], [1, -1, 0], [1, 4, 19], [1, -8, 23], [1, -4, 29], [1, -8, 31], [1, -6, 37], [1, 0, 41], [1, 6, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, 10, 61], [1, 2, 67], [1, 2, 71], [1, 2, 73], [1, 8, 79], [1, -4, 83], [1, 6, 89], [1, 2, 97]], 'index': 33, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/17850/ck'], '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': '2-17850-1.1-c1-0-33', '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': '2-17850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.938717167601617, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 640516352740228150, 'z1': {'__RealLiteral__': 0, 'data': '0.9460154769990073', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '640516352740228150', 'Lhash_array': ['640516352740228150'], 'factors': ['2-17850-1.1-c1-0-33'], 'label': '2-17850-1.1-c1-0-33', 'type': 'ECQ', 'url': 'EllipticCurve/Q/17850/ck'}