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lfunc_lfunctions • Show schema
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{'Lhash': '2033896732438620240216918486964', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-4.5, -7.794228634059948], 'a4': [0, 0], 'a5': [78.963203306565, 0], 'a6': [0, 0], 'a7': [60.76331231359811, -105.24514416332751], 'a8': [0, 0], 'a9': [-40.5, 70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.03975178164997, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [4.5, 7.794228634059948]]], [13, [[1.0, 0], [85.78978671057237, 603.2686901341345]]]], 'bad_primes': [2, 3, 13], 'central_character': '312.289', 'coefficient_field': 'CDF', 'conductor': 312, 'conductor_radical': 78, 'conjugate': '688709953515282341921016074212', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [4.5, 7.794228634059948]], [[1.0, 0], [-78.963203306565, 0], [3125.0, 0]], [[1.0, 0], [-60.76331231359811, 105.24514416332751], [-8403.5, -14555.28896140506]], [[1.0, 0], [94.09955550183689, 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[-2492.0725927680337, 4316.396346824139], [-422298150.5, -731441852.6083683]], [[1.0, 0], [13109.804669339794, 22706.84776460023], [-675062553.5, 1169242640.9491835]], [[1.0, 0], [-24558.74332347968, 42536.99120630976], [-902114675.5, -1562508452.2195108]], [[1.0, 0], [32417.607258691587, 0], [2073071593.0, 0]], [[1.0, 0], [75909.6378283082, 0], [3077056399.0, 0]], [[1.0, 0], [104490.43537033796, 0], [3939040643.0, 0]], [[1.0, 0], [69698.18985080053, 120720.80601716797], [-2792029724.5, 4835937339.076535]], [[1.0, 0], [-31746.17441849207, 54985.98703877163], [-4293670128.5, -7436854813.50279]], [[1.0, 0], [-28074.403769996617, -48626.29372183737], [-5255050250.5, 9102014030.193556]], [[1.0, 0], [-3628.846508804548, 0], [11592740743.0, 0]], [[1.0, 0], [-49454.730886768906, -85658.10657052959], [-7012758653.5, 12146454289.080307]], [[1.0, 0], [-57698.879070719646, 0], [15386239549.0, 0]], [[1.0, 0], [33163.16186552816, -57440.281290725456], [-9212175896.5, -15955956700.99937]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-312-13.3-c5-0-33', 'leading_term': '2.085436602109166978413350575538854453055735728786821870', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/312/6/q/a/289/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [2.085436602109167, 2.3215861431772438, 2.535066599759969, 2.7219779760020177, 2.8788431878266407, 3.002668015123782, 3.0909963119784476, 3.141959818833355, 3.154321806009928, 3.1275136658544556, 3.061663471120255, 2.957615440284115, 2.8169392061994674, 2.6419277818949345, 2.435583164327275, 2.2015886198116053, 1.9442668580799234, 1.6685235276427182, 1.3797757530609225, 1.0838657819354465, 0.7869602101775625, 0.49543569991831665, 0.21575258397840835, -0.04568174972329053, -0.28265729732206024, 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'7.18863226102850714567896906273329', '8.634477095942360805889838327669043', '9.472576197728451755620411823166597', '10.01858612248309490594966074978949', '11.15449436474031919288219006288456'], 'prelabel': '2-312-13.3-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.073878128837814, 'root_angle': 0.3514971243314992, 'root_number': '-0.5953693227442618990595979702941346054761036066740868966 + 0.8034521575893855989931758182923554143061964568452867082*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3514971243314992', 'prec': 60}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60446161747758800850611060852', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49395379766538467072298593712', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22997985124056789294924808585', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.03975178164997, 'bad_primes': [2, 3, 13], 'central_character': '13.3', 'conductor': 312, 'conductor_radical': 78, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/312/6/q/a/289/8'], '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': '2-312-13.3-c5-0-33', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-312-13.3-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.073878128837814, 'root_angle': 0.3514971243314992, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60446161747758800850611060852', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2033896732438620240216918486964', 'Lhash_array': ['2033896732438620240216918486964'], 'factors': ['2-312-13.3-c5-0-33'], 'label': '2-312-13.3-c5-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/312/6/q/a/289/8'}