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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': -1, 'A6': -1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '247490222705311113', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 152.59411826266688, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1, 1]], [7, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '19110.1', 'coefficient_field': '1.1.1.1', 'conductor': 19110, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 1], [1], [1, 1, 11], [1, 1], [1, -3, 17], [1, 2, 19], [1, 5, 23], [1, -2, 29], [1, 0, 31], [1, -7, 37], [1, -9, 41], [1, -6, 43], [1, 8, 47], [1, 14, 53], [1, -11, 59], [1, 10, 61], [1, 13, 67], [1, -8, 71], [1, 13, 73], [1, 5, 79], [1, 8, 83], [1, -15, 89], [1, -9, 97]], 'gamma_factors': [[], [0]], 'index': 46, 'label': '2-19110-1.1-c1-0-46', 'leading_term': '4.10486828654', '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/19110/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9617344057278276, 1.527634604472866, 1.338428547257059, 0.3280469300234522, -1.011625560759036, -1.771655378607654, -1.279832852005907, 0.196168841960198, 1.44888711561633, 1.31684797316427, -0.08723690823962477, -1.219414322126498, -0.5342842549598245, 1.712309442533869, 3.340839337652002, 2.419459222668064, -0.3178002151697868, -1.719618100517729, 0.5302472666609763, 4.982819786982695, 7.454165997586905, 5.433640200805059, 1.022715637401437, -1.267881692804676, 0.4262218333510823, 3.383540125095302, 3.820864481069841, 1.424279651201374, -0.7885935379635838, -0.7325336732265321, 0.3129070151429322, 0.1972231251317263, -0.7129509385846861, -0.3737357060882482, 1.346935004742358, 2.154941167266592, 0.9188291893470448, -0.3364193234104331, 0.4574219918309776, 1.938667230155801, 1.351762782478408, -0.7495504604210634, -0.91530930853163, 1.638241244532139, 3.159444347463314, 0.9646859037885855, -1.951554105970105, -1.210226794318358, 1.930771858954956, 2.30622772385981, -0.735331317323851, -1.766510747948375, 2.132745958108489, 6.084323394357594, 4.433150563848281, -0.6492035897631759, -2.695682715648795, -0.8464923750174822, -0.1688863964928965, -2.568606631548873, -3.891199403745817, -1.601453732279837, 0.8082641709161266, 0.2305467132118026, -0.6488143648301083, 1.263966876806753, 3.238797306149358, 1.329621421268045, -2.250212199932375, -2.514969684211128, -0.1177430486620251, 0.1574520007723546, -2.088823954968504, -2.693560499287741, -0.8034497974015464, 0.01054915650907679, -1.156224807537497, -1.237185642040324, 0.1836365928358259, -0.06115102929346295, -1.860542585980681, -1.351277705296964, 1.230944967225781, 1.190897990668753, -1.25187712243619, -0.2292920014861178, 4.291361581555055, 4.370889069968607, -2.044410205565053, -5.722208423709535, -1.015975827650676, 4.297711393457576, 2.157191215393765, -2.699259293941517, -2.335326819107498, 0.6910951809256078, -0.1173438300023291, -2.6723891402233, -1.365462194978666, 1.763605051190236, 1.499727242598033, -0.5655631869389712, -0.1872173675526077, 0.9964420617583287, -0.1524309767503929, -1.265172338496262, 0.2653049153348977, 1.472181196040994, 0.1563952669919534, -0.339758673361478, 1.402328631026242, 1.277200665062279, -1.397242143215175, -1.353252932940904, 1.79785617307609, 1.591187410680553, -2.646797639589177, -3.768931440658028, -0.4810370862638855, 0.6288355738015495], 'positive_zeros': ['1.061058657603217', '1.969680594690731', '2.736373263645974', '3.319223759435720', '4.220947677416035', '4.714639835530434', '5.820006494371107', '6.213727386299018', '7.134867121277350', '7.662400422227525', '8.053859597738461', '8.563358040303806', '9.395443512290549', '9.672062340505683', '10.40650639753286', '10.85741504746511', '11.56888471769966', '12.09647469003201', '12.69402561982348', '13.14153099250438', '13.96524342636199', '14.65620701468520', '14.69347015994990', '15.63455565848094', '16.03741628663085', '16.37616610896657', '17.08566938714893', '17.76532336375452', '18.02371424852414', '18.89811573621004', '19.00485676045099', '19.71219347487917', '19.98993873293420'], 'prelabel': '2-19110-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.352899184509962, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 247490222705311113, 'z1': {'__RealLiteral__': 0, 'data': '1.061058657603217', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.969680594690731', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.736373263645974', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 152.59411826266688, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 19110, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, -1, -1, 0, -1, 1, 1, -1, 1, -1, 0, -1, 1, 3, -1, -2, -1, 0, 1, -5, -1, 1, 1, 1, 0, 2, 1, 0, -1, -1, -3, 0, 1, 7, 2, -1, 1, 9, 0, 6, -1, -1, 5, -8, 1, 0, -1, 3, -1, -14, -1, 1, 0, -2, -2, 11, -1, -10, 0, 0, 1, 1, 1, -13, 3, -5, 0, 8, -1, -13, -7, 1, -2, 0, 1, -5, -1, 1, -9, -8, 0, -3, -6, 2, 1, 15, 1, 0, -5, 0, 8, 2, -1, 9, 0, -1, 1], 'euler11': [1, 1, 11], 'euler13': [1, 1, 0], 'euler17': [1, -3, 17], 'euler19': [1, 2, 19], 'euler2': [1, 1, 0], 'euler23': [1, 5, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -7, 37], 'euler41': [1, -9, 41], 'euler43': [1, -6, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, 14, 53], 'euler59': [1, -11, 59], 'euler61': [1, 10, 61], 'euler67': [1, 13, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, 13, 73], 'euler79': [1, 5, 79], 'euler83': [1, 8, 83], 'euler89': [1, -15, 89], 'euler97': [1, -9, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 1, 0], [1, 0, 0], [1, 1, 11], [1, 1, 0], [1, -3, 17], [1, 2, 19], [1, 5, 23], [1, -2, 29], [1, 0, 31], [1, -7, 37], [1, -9, 41], [1, -6, 43], [1, 8, 47], [1, 14, 53], [1, -11, 59], [1, 10, 61], [1, 13, 67], [1, -8, 71], [1, 13, 73], [1, 5, 79], [1, 8, 83], [1, -15, 89], [1, -9, 97]], 'index': 46, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/19110/u'], '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': '2-19110-1.1-c1-0-46', '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': '2-19110-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.352899184509962, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 247490222705311113, 'z1': {'__RealLiteral__': 0, 'data': '1.061058657603217', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '247490222705311113', 'Lhash_array': ['247490222705311113'], 'factors': ['2-19110-1.1-c1-0-46'], 'label': '2-19110-1.1-c1-0-46', 'type': 'ECQ', 'url': 'EllipticCurve/Q/19110/u'}