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lfunc_lfunctions • Show schema
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{'Lhash': '1667561565545987963077069132732,1923449420492049875081375336598', 'a10': 0, 'a2': -1, 'a3': -2, 'a4': -2, 'a5': 0, 'a6': 2, 'a7': 4, 'a8': 3, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 224.1592981509412, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': '1.1.1.1', 'conductor': 3515625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 1, 3, 2, 4], [1, 2, 1], [1], [1, -4, 18, -28, 49], [1, 6, 31, 66, 121], [1, -2, 27, -26, 169], [1, -4, 33, -68, 289], [1, 0, -7, 0, 361], [1, 13, 87, 299, 529], [1, 5, 63, 145, 841], [1, -4, 21, -124, 961], [1, -4, 78, -148, 1369], [1, 21, 191, 861, 1681], [1, -17, 157, -731, 1849], [1, -14, 138, -658, 2209], [1, 18, 182, 954, 2809], [1, 10, 63, 590, 3481], [1, -4, 81, -244, 3721], [1, -4, 13, -268, 4489], [1, -9, 131, -639, 5041], [1, 18, 182, 1314, 5329], [1, 25, 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'2.35690279268179068067664243478613', '3.00435469623499470853923001781134', '3.99519401965184691281326075170385', '4.04496467352287442478388051716369', '4.79664998334316709565876199899452', '4.82197002913100883504934516816748', '5.52836708552441876082696766650301', '5.65594596680013671733621745766315', '6.04867297392070441734572508288840', '6.58991687120145699479680631187894', '7.44728810778287889980142653028560', '7.59955912095787795792560832279126', '7.922690077848706067103992412508389', '8.166569710710947018397642450710543', '8.623243488503016890669362104947909', '8.861677389970138395608394673369777'], 'prelabel': '4-1875e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 905295505936236965, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31547412610837567590861068193', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.51733405099618903880292169801', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.35690279268179068067664243479', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 224.1592981509412, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 3515625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, -1, -2, -2, 0, 2, 4, 3, 3, 0, -6, 4, 2, -4, 0, 1, 4, -3, 0, 0, -8, 6, -13, -6, 0, -2, -4, -8, -5, 0, 4, -2, 12, -4, 0, -6, 4, 0, -4, 0, -21, 8, 17, 12, 0, 13, 14, -2, -2, 0, -8, -4, -18, 4, 0, 12, 0, 5, -10, 0, 4, -4, 12, 1, 0, -12, 4, -8, 26, 0, 9, 9, -18, -4, 0, 0, -24, 4, -25, 0, 5, 21, -18, 16, 0, -17, 10, -18, 0, 0, 8, 26, -8, -14, 0, 4, -1, 2, -18, 0], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, -2, 27, -26, 169], 'euler17': [1, -4, 33, -68, 289], 'euler19': [1, 0, -7, 0, 361], 'euler2': [1, 1, 3, 2, 4], 'euler23': [1, 13, 87, 299, 529], 'euler29': [1, 5, 63, 145, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -4, 21, -124, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 21, 191, 861, 1681], 'euler43': [1, -17, 157, -731, 1849], 'euler47': [1, -14, 138, -658, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 18, 182, 954, 2809], 'euler59': [1, 10, 63, 590, 3481], 'euler61': [1, -4, 81, -244, 3721], 'euler67': [1, -4, 13, -268, 4489], 'euler7': [1, -4, 18, -28, 49], 'euler71': [1, -9, 131, -639, 5041], 'euler73': [1, 18, 182, 1314, 5329], 'euler79': [1, 25, 303, 1975, 6241], 'euler83': [1, 18, 247, 1494, 6889], 'euler89': [1, 0, 53, 0, 7921], 'euler97': [1, 1, 183, 97, 9409], 'euler_factors': [[1, 1, 3, 2, 4], [1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, -4, 18, -28, 49], [1, 6, 31, 66, 121], [1, -2, 27, -26, 169], [1, -4, 33, -68, 289], [1, 0, -7, 0, 361], [1, 13, 87, 299, 529], [1, 5, 63, 145, 841], [1, -4, 21, -124, 961], [1, -4, 78, -148, 1369], [1, 21, 191, 861, 1681], [1, -17, 157, -731, 1849], [1, -14, 138, -658, 2209], [1, 18, 182, 954, 2809], [1, 10, 63, 590, 3481], [1, -4, 81, -244, 3721], [1, -4, 13, -268, 4489], [1, -9, 131, -639, 5041], [1, 18, 182, 1314, 5329], [1, 25, 303, 1975, 6241], [1, 18, 247, 1494, 6889], [1, 0, 53, 0, 7921], [1, 1, 183, 97, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '4-1875e2-1.1-c1e2-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-1875e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 905295505936236965, 'z1': {'__RealLiteral__': 0, 'data': '1.31547412610837567590861068193', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1667561565545987963077069132732,1923449420492049875081375336598', 'Lhash_array': ['1667561565545987963077069132732', '1923449420492049875081375336598'], 'label': '4-1875e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/b'}