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lfunc_lfunctions • Show schema
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{'Lhash': '1732381151682667671429777251392', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.555931363531796, 0], 'a4': [0, 0], 'a5': [0.7909070174122886, -2.0915224334938407], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [3.532785135085507, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.943245026383407, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.7909070174122886, 2.0915224334938407]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '1120.1009', 'coefficient_field': 'CDF', 'conductor': 1120, 'conductor_radical': 70, 'conjugate': '527152780824944832397335881438', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.555931363531796, 0], [3.0, 0]], [[1.0, 0], [-0.7909070174122886, 2.0915224334938407]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 2.940612485744616], [-11.0, 0]], [[1.0, 0], [-1.882154833971296, 0], [13.0, 0]], [[1.0, 0], [0, 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'2.85543834238790694112265800480450', '4.21622079626501648642996339387618', '5.04408983591089227171718435859378', '6.09686946612850365654616974370703', '6.56098508894224147623576823073377', '7.30214112401904160360221093008801', '8.355308245690260551380329756879902', '9.803165391481394387889703998063262', '10.18576500255776696601664487578542'], 'prelabel': '2-1120-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9905258778989703, 'root_angle': 0.6760180938588145, 'root_number': '-0.5252230026464980043811906007737067892758245699798937690 + 0.8509646276379510889345477923803659743410371040394251927*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.33800904692940725', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36660776350420817809297270186', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85543834238790694112265800480', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21622079626501648642996339388', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.943245026383407, 'bad_primes': [2, 5, 7], 'central_character': '40.29', 'conductor': 1120, 'conductor_radical': 70, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1120/2/l/a/1009/6'], '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': '2-1120-40.29-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1120-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9905258778989703, 'root_angle': 0.33800904692940725, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36660776350420817809297270186', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1732381151682667671429777251392', 'Lhash_array': ['1732381151682667671429777251392'], 'label': '2-1120-40.29-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1120/2/l/a/1009/6'}