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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': 3, 'A9': -2, 'Lhash': '680806293811299672', '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': [1.0606601717798212, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 169.0832262800613, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [7, [1, -1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '21175.1', 'coefficient_field': '1.1.1.1', 'conductor': 21175, 'conductor_radical': 385, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -1, 3], [1], [1, -1], [1], [1, 2, 13], [1, 4, 17], [1, -4, 19], [1, 6, 23], [1, 9, 29], [1, 0, 31], [1, -3, 37], [1, -6, 41], [1, 10, 43], [1, -3, 47], [1, 2, 53], [1, -1, 59], [1, 6, 61], [1, -6, 67], [1, 0, 71], [1, -4, 73], [1, 10, 79], [1, -11, 83], [1, 14, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 2, 'label': '2-21175-1.1-c1-0-2', 'leading_term': '0.685469873712', '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/21175/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.6854698737119617, 0.3513239888758471, -0.5464327294016927, -1.625407707798574, -2.236554274158145, -1.829147125895708, -0.5046535708413608, 0.800423181114677, 0.9256794918423492, -0.4130991839414721, -2.062111866793777, -2.246828632281633, -0.3171825474342324, 2.290044214337121, 3.207765602141133, 1.602820668887035, -0.66716990867719, -0.8649030163610165, 1.485465330661363, 3.775541174722107, 3.228946677380461, 0.4390086164052659, -0.939885920981334, 1.471602759750224, 5.484882265577204, 6.498709168237844, 2.909260374841982, -1.859110818623319, -3.393091944185104, -1.343595383500364, 0.8655622550328791, 0.8572979336737975, -0.09529981655306746, 0.162669021810849, 1.207684494496325, 1.109683447047653, -0.1191323603040168, -0.5693937512921409, 0.089743141970849, -0.2115408606632389, -2.222276613000374, -3.298318254818511, -1.281147849712679, 1.415779192661061, 0.8700297789823167, -2.010917817152899, -2.269868645807966, 1.269436567008933, 3.284643083047823, -0.3235972205680329, -5.681842318592265, -6.163753613996295, -1.99934456670263, 0.6279241601578951, -0.7296539818531876, -1.969192293366399, -0.317885302933038, 1.10198016389625, -0.3684939783816839, -1.509530920848614, 1.019043350172006, 3.820333230002051, 1.769782710173044, -2.942246589267812, -3.64855068326422, 0.2092754521933059, 2.53421692158178, 0.716762133557496, -0.9858928503410443, 0.3052705351268144, 1.582094951967218, 0.4249089354020274, -0.5726284660233273, 0.5731807437198853, 1.167493077897803, -0.590083326478482, -1.593076289425155, 0.3096236741229753, 1.951217514864021, 0.8220380199166352, -0.365080329072528, 0.139554136433418, -1.174934299578398, -5.511469542000089, -6.8710651855558, -1.719150521248695, 3.417137049194156, 2.067345117786227, -1.457955433646102, -0.5588244070297694, 1.632595726781651, -0.6208742608776397, -3.341770606875699, 0.1559446678583083, 5.700559650183407, 4.680827884492163, -0.7012355442078948, -1.776833887188133, 1.099292136287033, 0.7317249699097509, -2.72022219172312, -2.902539777679821, 0.1766425909288832, 1.038275860669339, -0.5093944154189386, -0.5198597424441841, 0.5106960004802324, 0.01775480676343892, -0.09026900466180636, 2.045210650175915, 2.939953462792267, 0.5596756806353683, -0.9765438639378272, 0.1443319468840371, -0.373617430375332, -2.958442149900828, -1.95821686076444, 1.980370472617713, 0.9000185559042863, -5.030244973488956, -6.206171158785936], 'positive_zeros': ['0.3630199993089607', '1.584134284397204', '2.190226767820451', '3.029361722515952', '3.913920117031682', '4.364593557328010', '5.292006773635567', '5.642286923865513', '6.642540698177897', '7.377995287729666', '7.963451431917365', '8.203113481027384', '8.974945138512221', '9.464888864168756', '9.704058593121052', '10.60161862978036', '11.07865207787314', '11.67183331156875', '12.23572422536272', '13.13947965150187', '13.41449887143069', '14.03442288187537', '14.45806294699990', '14.92895856204898', '15.59075212848667', '16.23759765171241', '16.81932941505174', '17.21253330392190', '17.81369604976794', '18.15737856865002', '18.68213992346022', '19.21983110518541', '19.87391557274313'], 'prelabel': '2-21175-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.003200616773599, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 680806293811299672, 'z1': {'__RealLiteral__': 0, 'data': '0.3630199993089607', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.584134284397204', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.190226767820451', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 169.0832262800613, 'bad_primes': [5, 7, 11], 'central_character': '1.1', 'conductor': 21175, 'conductor_radical': 385, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, -1, 0, -1, 1, 3, -2, 0, 0, -1, -2, -1, 0, -1, -4, 2, 4, 0, 1, 0, -6, 3, 0, 2, -5, -1, -9, 0, 0, -5, 0, 4, 0, 2, 3, -4, -2, 0, 6, -1, -10, 0, 0, 6, 3, -1, 1, 0, -4, 2, -2, 5, 0, 3, 4, 9, 1, 0, -6, 0, -2, 7, 0, 0, 6, 4, -6, 0, 0, -6, 4, -3, 0, -4, 0, 2, -10, 0, 1, -6, 11, -1, 0, 10, -9, 0, -14, 0, -2, 6, 0, -3, 0, -5, 10, -1, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, 4, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 2], 'euler23': [1, 6, 23], 'euler29': [1, 9, 29], 'euler3': [1, -1, 3], 'euler31': [1, 0, 31], 'euler37': [1, -3, 37], 'euler41': [1, -6, 41], 'euler43': [1, 10, 43], 'euler47': [1, -3, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, -1, 59], 'euler61': [1, 6, 61], 'euler67': [1, -6, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -4, 73], 'euler79': [1, 10, 79], 'euler83': [1, -11, 83], 'euler89': [1, 14, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 1, 2], [1, -1, 3], [1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 2, 13], [1, 4, 17], [1, -4, 19], [1, 6, 23], [1, 9, 29], [1, 0, 31], [1, -3, 37], [1, -6, 41], [1, 10, 43], [1, -3, 47], [1, 2, 53], [1, -1, 59], [1, 6, 61], [1, -6, 67], [1, 0, 71], [1, -4, 73], [1, 10, 79], [1, -11, 83], [1, 14, 89], [1, -10, 97]], 'index': 2, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/21175/k'], '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': '2-21175-1.1-c1-0-2', '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': '2-21175-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.003200616773599, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 680806293811299672, 'z1': {'__RealLiteral__': 0, 'data': '0.3630199993089607', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '680806293811299672', 'Lhash_array': ['680806293811299672'], 'label': '2-21175-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/21175/k'}