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lfunc_lfunctions • Show schema
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{'Lhash': '1826807112761754492340419217350,2594037812168566532630437561127', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 156.76399793978587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '1568.1', 'coefficient_field': '1.1.1.1', 'conductor': 2458624, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, 3, 0, 9], [1, 2, 11, 10, 25], [1], [1, 0, -5, 0, 121], [1, 0, 26, 0, 169], [1, 10, 59, 170, 289], [1, 0, 35, 0, 361], [1, 0, 43, 0, 529], [1, -16, 122, -464, 841], [1, 0, -13, 0, 961], [1, 10, 99, 370, 1369], [1, 8, 98, 328, 1681], [1, 0, 38, 0, 1849], [1, 0, 19, 0, 2209], [1, 2, 107, 106, 2809], [1, 0, 115, 0, 3481], [1, 22, 243, 1342, 3721], [1, 0, -13, 0, 4489], [1, 0, -50, 0, 5041], [1, 30, 371, 2190, 5329], [1, 0, 155, 0, 6241], [1, 0, 118, 0, 6889], [1, 14, 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'3.71459672137746628721843940476191', '4.24807379718754068151567908631582', '4.67101370445417715055346440925889', '4.81553158730289397814414536046441', '5.62796939912276000558408700129158', '6.06212653916999263362136602375965', '6.37383405352651148768533478814559', '6.85795088417944299202644685591444', '7.21281786989420387676862329829093', '7.62473822803488943409818211172834', '8.293127084651543003213691605110947', '8.417381061860846762295891042862204', '8.832443402605427668192012600180594', '8.889787970155161537597042452006818'], 'prelabel': '4-1568e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5384379374148662, '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': 894355126339763378, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44109671263742063634594123878', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 156.76399793978587, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 2458624, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -8, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0], 'euler11': [1, 0, -5, 0, 121], 'euler13': [1, 0, 26, 0, 169], 'euler17': [1, 10, 59, 170, 289], 'euler19': [1, 0, 35, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 43, 0, 529], 'euler29': [1, -16, 122, -464, 841], 'euler3': [1, 0, 3, 0, 9], 'euler31': [1, 0, -13, 0, 961], 'euler37': [1, 10, 99, 370, 1369], 'euler41': [1, 8, 98, 328, 1681], 'euler43': [1, 0, 38, 0, 1849], 'euler47': [1, 0, 19, 0, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 2, 107, 106, 2809], 'euler59': [1, 0, 115, 0, 3481], 'euler61': [1, 22, 243, 1342, 3721], 'euler67': [1, 0, -13, 0, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -50, 0, 5041], 'euler73': [1, 30, 371, 2190, 5329], 'euler79': [1, 0, 155, 0, 6241], 'euler83': [1, 0, 118, 0, 6889], 'euler89': [1, 14, 227, 1246, 7921], 'euler97': [1, 24, 338, 2328, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 9], [1, 2, 11, 10, 25], [1, 0, 0, 0, 0], [1, 0, -5, 0, 121], [1, 0, 26, 0, 169], [1, 10, 59, 170, 289], [1, 0, 35, 0, 361], [1, 0, 43, 0, 529], [1, -16, 122, -464, 841], [1, 0, -13, 0, 961], [1, 10, 99, 370, 1369], [1, 8, 98, 328, 1681], [1, 0, 38, 0, 1849], [1, 0, 19, 0, 2209], [1, 2, 107, 106, 2809], [1, 0, 115, 0, 3481], [1, 22, 243, 1342, 3721], [1, 0, -13, 0, 4489], [1, 0, -50, 0, 5041], [1, 30, 371, 2190, 5329], [1, 0, 155, 0, 6241], [1, 0, 118, 0, 6889], [1, 14, 227, 1246, 7921], [1, 24, 338, 2328, 9409]], 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1568/2/a/n'], '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': '4-1568e2-1.1-c1e2-0-31', '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': '4-1568e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5384379374148662, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 894355126339763378, 'z1': {'__RealLiteral__': 0, 'data': '1.44109671263742063634594123878', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1826807112761754492340419217350,2594037812168566532630437561127', 'Lhash_array': ['1826807112761754492340419217350', '2594037812168566532630437561127'], 'label': '4-1568e2-1.1-c1e2-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1568/2/a/n'}