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lfunc_lfunctions • Show schema
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{'Lhash': '311213807383387971549004256088,2182099697028826427473302768304', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -16, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 365, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3151.063783080825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 16]], [5, [1]], [7, [1, 0, 2401]]], 'bad_primes': [2, 5, 7], 'central_character': '350.1', 'coefficient_field': '1.1.1.1', 'conductor': 122500, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, 0, 16], [1, 0, -365, 0, 59049], [1], [1, 0, 2401], [1, 534, 393391, 86001234, 25937424601], [1, 0, 438983, 0, 137858491849], [1, 0, -2576545, 0, 2015993900449], [1, -1604, 5595402, -3971662796, 6131066257801], [1, 0, -11208586, 0, 41426511213649], [1, 3558, 44187139, 72978668142, 420707233300201], [1, 5168, 63935358, 147955452368, 819628286980801], [1, 0, 53467130, 0, 4808584372417849], [1, 23808, 373417618, 2758304433408, 13422659310152401], [1, 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0.45241734376240544], 'positive_zeros': ['0.24550440580973704264112226632392', '1.26327710766254068714589558576193', '1.72137314228065562029323332847256', '2.54002011451980800795475318574849', '3.42691456610732917552542972221351', '3.67434516714694434045904321654247', '4.56777304415797017112690431999203', '5.00080628742235008339539251998400', '5.28398008307744683293781069694342', '6.06452569203967957495668016173186', '6.59377775645135725797102227971565', '7.38736464034713418818671262855063', '7.49751665495335295521231117058994', '7.929230065503577590372147530596336', '8.584836986860365346770227188951347', '9.224767498142178671967416007908123', '9.444253671361105258605931112765853', '10.03847749962235241470478284008129', '10.41914184634934101987428519142612', '11.26507882157582441527594805196431'], 'prelabel': '4-350e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.492285161053551, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e2-0', 'trace_hash': 555170409267385090, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24550440580973704264112226632', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.26327710766254068714589558576', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.72137314228065562029323332847', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3151.063783080825, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 122500, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -16, 0, 0, 0, 0, 365, 0, -534, 0, 0, 0, 0, 256, 0, 0, 1604, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3558, 0, -5168, 0, 0, 0, 0, -5840, 0, 0, 0, 0, -23808, 0, 0, 8544, 0, 0, 0, 0, -2401, 0, 0, 0, 0, 0, 0, 0, 0, 0, -61824, 0, -3560, 0, 0, -4096, 0, 0, 0, 0, 0, 0, -103968, 0, 0, 0, 0, -25664, 0, 0, 204242, 0, 74176, 0, 0, 0, 0, 0, 0, 0, 64800, 0, 0, 0, 0, 0, 0, 0, 0, 0, -194910, 0], 'euler11': [1, 534, 393391, 86001234, 25937424601], 'euler13': [1, 0, 438983, 0, 137858491849], 'euler17': [1, 0, -2576545, 0, 2015993900449], 'euler19': [1, -1604, 5595402, -3971662796, 6131066257801], 'euler2': [1, 0, 16, 0, 0], 'euler23': [1, 0, -11208586, 0, 41426511213649], 'euler29': [1, 3558, 44187139, 72978668142, 420707233300201], 'euler3': [1, 0, -365, 0, 59049], 'euler31': [1, 5168, 63935358, 147955452368, 819628286980801], 'euler37': [1, 0, 53467130, 0, 4808584372417849], 'euler41': [1, 23808, 373417618, 2758304433408, 13422659310152401], 'euler43': [1, 0, -293659282, 0, 21611482313284249], 'euler47': [1, 0, -169043653, 0, 52599132235830049], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -60657082, 0, 174887470365513049], 'euler59': [1, 61824, 2385400342, 44199479861376, 511116753300641401], 'euler61': [1, 3560, 1692361002, 3006762831560, 713342911662882601], 'euler67': [1, 0, -2072647510, 0, 1822837804551761449], 'euler7': [1, 0, 2401, 0, 0], 'euler71': [1, 103968, 6310794958, 187582117164768, 3255243551009881201], 'euler73': [1, 0, -1871807086, 0, 4297625829703557649], 'euler79': [1, -204242, 16582811439, -628464153044558, 9468276082626847201], 'euler83': [1, 0, -876408310, 0, 15516041187205853449], 'euler89': [1, -64800, 12217878898, -361847052295200, 31181719929966183601], 'euler97': [1, 0, 4920655511, 0, 73742412689492826049], 'euler_factors': [[1, 0, 16, 0, 0], [1, 0, -365, 0, 59049], [1, 0, 0, 0, 0], [1, 0, 2401, 0, 0], [1, 534, 393391, 86001234, 25937424601], [1, 0, 438983, 0, 137858491849], [1, 0, -2576545, 0, 2015993900449], [1, -1604, 5595402, -3971662796, 6131066257801], [1, 0, -11208586, 0, 41426511213649], [1, 3558, 44187139, 72978668142, 420707233300201], [1, 5168, 63935358, 147955452368, 819628286980801], [1, 0, 53467130, 0, 4808584372417849], [1, 23808, 373417618, 2758304433408, 13422659310152401], [1, 0, -293659282, 0, 21611482313284249], [1, 0, -169043653, 0, 52599132235830049], [1, 0, -60657082, 0, 174887470365513049], [1, 61824, 2385400342, 44199479861376, 511116753300641401], [1, 3560, 1692361002, 3006762831560, 713342911662882601], [1, 0, -2072647510, 0, 1822837804551761449], [1, 103968, 6310794958, 187582117164768, 3255243551009881201], [1, 0, -1871807086, 0, 4297625829703557649], [1, -204242, 16582811439, -628464153044558, 9468276082626847201], [1, 0, -876408310, 0, 15516041187205853449], [1, -64800, 12217878898, -361847052295200, 31181719929966183601], [1, 0, 4920655511, 0, 73742412689492826049]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/6/c/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': '4-350e2-1.1-c5e2-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-350e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.492285161053551, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 555170409267385090, 'z1': {'__RealLiteral__': 0, 'data': '0.24550440580973704264112226632', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '311213807383387971549004256088,2182099697028826427473302768304', 'Lhash_array': ['311213807383387971549004256088', '2182099697028826427473302768304'], 'label': '4-350e2-1.1-c5e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/6/c/b'}