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lfunc_lfunctions • Show schema
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{'Lhash': '678395839802342207575972852164,1493825461788333415330776354198', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 22, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7218.668956937394, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -22, 125]]], 'bad_primes': [2, 3, 5], 'central_character': '1440.1', 'coefficient_field': '1.1.1.1', 'conductor': 2073600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, -22, 125], [1, 0, -686, 0, 117649], [1, 0, 2662, 0, 1771561], [1, 0, 4070, 0, 4826809], [1, 0, 990, 0, 24137569], [1, 0, 13718, 0, 47045881], [1, 0, -24334, 0, 148035889], [1, -260, 65678, -6341140, 594823321], [1, 0, 59582, 0, 887503681], [1, 0, 55510, 0, 2565726409], [1, 460, 190742, 31703660, 4750104241], [1, 0, -159014, 0, 6321363049], [1, 0, -207646, 0, 10779215329], [1, 0, 29430, 0, 22164361129], [1, 0, 410758, 0, 42180533641], [1, 1660, 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-3.6854705420728737, -3.897553302682884, -3.9576756981416907], 'positive_zeros': ['0.53515995628464418432660124075320', '1.17842050602854067873942581935431', '1.69151459256242394577532870724520', '2.18163134816094451808498914948482', '2.75461304999521101785378732319178', '3.09343047945337872246443849534918', '3.74614084849373086636683863281892', '4.46881877869629376655316573814317', '4.99673806143160264075215229591875', '5.07288415754077701735273686599082', '5.72393850744701288430332696176543', '6.27980778682208315304315181533388', '6.30165611412243143443785106387659', '6.72653752534507400394146930512155', '7.43918566237217857947698655768277', '7.59535219715772785118389792194505', '8.302487456275872774522789583781365', '8.886388621346417316408307534217651', '8.890496686440826494482025201192326', '9.242606567388223089449599647044343'], 'prelabel': '4-1440e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.217524093175268, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 2014378775403611848, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53515995628464418432660124075', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17842050602854067873942581935', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.69151459256242394577532870725', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7218.668956937394, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2073600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 359, 0, 0, 0, 260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -460, 0, 0, 0, 0, 0, 0, 0, 686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1660, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3340, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 2662, 0, 1771561], 'euler13': [1, 0, 4070, 0, 4826809], 'euler17': [1, 0, 990, 0, 24137569], 'euler19': [1, 0, 13718, 0, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -24334, 0, 148035889], 'euler29': [1, -260, 65678, -6341140, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 59582, 0, 887503681], 'euler37': [1, 0, 55510, 0, 2565726409], 'euler41': [1, 460, 190742, 31703660, 4750104241], 'euler43': [1, 0, -159014, 0, 6321363049], 'euler47': [1, 0, -207646, 0, 10779215329], 'euler5': [1, -22, 125, 0, 0], 'euler53': [1, 0, 29430, 0, 22164361129], 'euler59': [1, 0, 410758, 0, 42180533641], 'euler61': [1, 1660, 1142862, 376788460, 51520374361], 'euler67': [1, 0, -601526, 0, 90458382169], 'euler7': [1, 0, -686, 0, 117649], 'euler71': [1, 0, 715822, 0, 128100283921], 'euler73': [1, 0, -427570, 0, 151334226289], 'euler79': [1, 0, 986078, 0, 243087455521], 'euler83': [1, 0, -1143574, 0, 326940373369], 'euler89': [1, -3340, 4198838, -2354596460, 496981290961], 'euler97': [1, 0, 1472510, 0, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -22, 125, 0, 0], [1, 0, -686, 0, 117649], [1, 0, 2662, 0, 1771561], [1, 0, 4070, 0, 4826809], [1, 0, 990, 0, 24137569], [1, 0, 13718, 0, 47045881], [1, 0, -24334, 0, 148035889], [1, -260, 65678, -6341140, 594823321], [1, 0, 59582, 0, 887503681], [1, 0, 55510, 0, 2565726409], [1, 460, 190742, 31703660, 4750104241], [1, 0, -159014, 0, 6321363049], [1, 0, -207646, 0, 10779215329], [1, 0, 29430, 0, 22164361129], [1, 0, 410758, 0, 42180533641], [1, 1660, 1142862, 376788460, 51520374361], [1, 0, -601526, 0, 90458382169], [1, 0, 715822, 0, 128100283921], [1, 0, -427570, 0, 151334226289], [1, 0, 986078, 0, 243087455521], [1, 0, -1143574, 0, 326940373369], [1, -3340, 4198838, -2354596460, 496981290961], [1, 0, 1472510, 0, 832972004929]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1440/4/f/e'], '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': '4-1440e2-1.1-c3e2-0-9', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-1440e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.217524093175268, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2014378775403611848, 'z1': {'__RealLiteral__': 0, 'data': '0.53515995628464418432660124075', 'prec': 103}}
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{'Lhash': '678395839802342207575972852164,1493825461788333415330776354198', 'Lhash_array': ['678395839802342207575972852164', '1493825461788333415330776354198'], 'label': '4-1440e2-1.1-c3e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1440/4/f/e'}