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lfunc_lfunctions • Show schema
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{'Lhash': '1392134903405633181529779128539,1548507632068709606908358167154', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2017.433683358471, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '5625.1', 'coefficient_field': '1.1.1.1', 'conductor': 31640625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 1, 3, 2, 4], [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, 303, 1975, 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1.3948271490731148, 1.8833580751792511, 2.3531254970902826, 2.7719560084933192], 'positive_zeros': ['1.09820080009033362205797219086647', '1.22155713237536775014526789573000', '2.08136400647833211258189485685831', '2.56768649451905884485716367257367', '3.14195708488296106043979789671010', '3.54728059228494985462628079566530', '3.93205671171735489237269264874101', '4.14178004347461465395548155382148', '4.68400757169133059369707768367798', '4.84624068738795639397808224097245', '5.64670458012498577193518659700969', '5.97871628363432092026064896772288', '6.16140025949265467011638416968995', '6.45184662222692698774381120345864', '7.02153086636121786566493303414336', '7.18944872473669821507225983522761', '7.75574510743999089354799921659834', '8.058761387913769390759206754715203'], 'prelabel': '4-75e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.701928911661944, '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': 2136018139569128620, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09820080009033362205797219087', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.22155713237536775014526789573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.08136400647833211258189485686', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2017.433683358471, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 31640625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, -2, 0, 0, -4, 3, 0, 0, 6, 0, -2, 4, 0, 1, 4, 0, 0, 0, 0, -6, -13, 0, 0, 2, 0, 8, 5, 0, 4, -2, 0, -4, 0, 0, -4, 0, 0, 0, 21, 0, -17, -12, 0, 13, 14, 0, -2, 0, 0, 4, -18, 0, 0, -12, 0, -5, 10, 0, 4, -4, 0, 1, 0, 0, -4, -8, 0, 0, -9, 0, 18, 4, 0, 0, -24, 0, -25, 0, 0, -21, -18, 0, 0, 17, 0, 18, 0, 0, 8, 26, 0, -14, 0, 0, 1, 2, 0, 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, 0, 0, 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, 0, 0, 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': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5625/2/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': '4-75e4-1.1-c1e2-0-6', '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': '4-75e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.701928911661944, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2136018139569128620, 'z1': {'__RealLiteral__': 0, 'data': '1.09820080009033362205797219087', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1392134903405633181529779128539,1548507632068709606908358167154', 'Lhash_array': ['1392134903405633181529779128539', '1548507632068709606908358167154'], 'label': '4-75e4-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5625/2/a/b'}