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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1007524630443241309', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 281.71221833107734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '35280.1', 'coefficient_field': '1.1.1.1', 'conductor': 35280, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1], [1, 4, 11], [1, -6, 13], [1, 2, 17], [1, 8, 19], [1, -4, 23], [1, 6, 29], [1, -4, 31], [1, 2, 37], [1, 2, 41], [1, -12, 43], [1, 0, 47], [1, 2, 53], [1, -4, 59], [1, 6, 61], [1, -4, 67], [1, -8, 71], [1, 6, 73], [1, -16, 79], [1, -4, 83], [1, 18, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 80, 'label': '2-35280-1.1-c1-0-80', 'leading_term': '4.86980237539', '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/35280/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.11034630800326, 1.587344968258176, 0.9566120558434883, -0.6755778295291915, -2.355455465686364, -2.774093538055569, -1.409172070023379, 0.7137696910240428, 1.688060014657651, 0.5487147487000207, -1.536649355302842, -2.284131738580426, -0.7807618356455946, 1.330990470712312, 1.677369894052965, 0.09665413561725908, -1.016871498204889, 0.2183982276890382, 2.466956513211239, 2.682629580641978, 0.23854758943375, -1.917959185999664, -1.104327267062396, 1.324432810477992, 1.804915969553499, -0.26046789432411, -1.496113557968944, 0.4689319663455826, 3.273546770837265, 3.173088153410167, 0.6178564519563737, -0.5501714023874732, 0.8723774406620045, 1.812889198610316, 0.4328119032934855, -0.3570682034379756, 2.276286093750041, 5.557833526730422, 4.592195590964088, 0.002226978906037612, -2.706265432787744, -1.365555534725366, 0.3768477130003603, 0.03964369206436043, 0.354110923061854, 3.333124332702284, 5.314346159565795, 2.629175643531949, -1.650462916167263, -2.258754027042157, -0.1332595464000465, 0.04201434106416917, -1.481219856011669, -0.5908731374161289, 1.946834255218355, 0.9325867872639543, -3.55605168427682, -5.159977704345389, -1.735187697338574, 1.273506563659777, 0.5494671812482611, -0.2500590814757138, 1.233824251850757, 1.410688191541954, -1.257340467883232, -2.044961916818052, 1.079744929413724, 2.663132358924577, -0.3719078008508092, -2.576967385838876, 0.08038923400396984, 2.805856807034334, 1.229196369277975, -0.7535130624075684, 0.598962796586242, 1.680960808401872, -0.0657949833226304, -0.02538101143299024, 4.048036598224762, 6.142326216080954, 2.748412026267386, -0.625499581980568, -0.134727686353148, 0.1900023730481241, -1.349839479215911, 0.1157752864943049, 4.644840459820804, 4.856390681480755, -0.4245373145326355, -3.260512650543253, -1.020568037050623, 0.1633635538122011, -1.50998696072948, -1.392916656855599, 0.1615476400902306, -1.09352486934111, -2.315211396393244, 1.560244577311567, 5.856346144333865, 3.706571564246352, -0.6721255588872793, -0.3255090841394022, 1.534956179223464, 0.07409858584652664, -0.8581772260114116, 1.342341660935351, 0.9835895420168633, -3.460533476303124, -4.690700693145213, -1.026302634768477, 0.6863655290542967, -0.3864812327593938, 1.13419019827698, 3.382075033315737, 1.195819519830206, -1.293568885340529, 1.10454003240938, 2.789026081855376, -0.9948512251315823, -3.553896414294167], 'positive_zeros': ['0.9077325511467445', '1.912078017223615', '2.565755848358268', '3.334512061124414', '4.013253888200371', '4.474851973593114', '5.270323762616004', '5.861449443134204', '6.472718091780974', '6.961175841356922', '7.820379168727310', '8.129237830029414', '8.813368034108713', '9.064910258768872', '10.00012195118884', '10.66345372448543', '11.01440441214585', '11.18476872589306', '12.14085493012973', '12.77049380450403', '13.00778842718743', '13.55508234676565', '14.05860632783146', '14.85893394678361', '15.34170683712690', '15.56748331601039', '16.14362033205548', '16.67656418219220', '17.22641027458785', '17.74491350814043', '18.36290611831688', '18.68035654990908', '19.24148187105160', '19.50251298228882'], 'prelabel': '2-35280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.78428486206896, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1007524630443241309, 'z1': {'__RealLiteral__': 0, 'data': '0.9077325511467445', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.912078017223615', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.565755848358268', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 281.71221833107734, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 35280, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -4, 0, 6, 0, 0, 0, -2, 0, -8, 0, 0, 0, 4, 0, 1, 0, 0, 0, -6, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 4, 0, -6, 0, 0, 0, -6, 0, 4, 0, 0, 0, 8, 0, -6, 0, 0, 0, 0, 0, 16, 0, 0, 0, 4, 0, 2, 0, 0, 0, -18, 0, 0, 0, 0, 0, 8, 0, -6, 0, 0, 0], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, -12, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 6, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, 6, 73], 'euler79': [1, -16, 79], 'euler83': [1, -4, 83], 'euler89': [1, 18, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 4, 11], [1, -6, 13], [1, 2, 17], [1, 8, 19], [1, -4, 23], [1, 6, 29], [1, -4, 31], [1, 2, 37], [1, 2, 41], [1, -12, 43], [1, 0, 47], [1, 2, 53], [1, -4, 59], [1, 6, 61], [1, -4, 67], [1, -8, 71], [1, 6, 73], [1, -16, 79], [1, -4, 83], [1, 18, 89], [1, 6, 97]], 'index': 80, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/35280/q'], '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': '2-35280-1.1-c1-0-80', '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': '2-35280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.78428486206896, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1007524630443241309, 'z1': {'__RealLiteral__': 0, 'data': '0.9077325511467445', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1007524630443241309', 'Lhash_array': ['1007524630443241309'], 'label': '2-35280-1.1-c1-0-80', 'type': 'ECQ', 'url': 'EllipticCurve/Q/35280/q'}