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lfunc_lfunctions • Show schema
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{'Lhash': '1196886982532133981778256781386,1571333124360464621521447691886', 'a10': -10, 'a2': 1, 'a3': 0, 'a4': -11, 'a5': -10, 'a6': 0, 'a7': 0, 'a8': -15, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16925.804849225275, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 10, 25]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.1', 'coefficient_field': '1.1.1.1', 'conductor': 4862025, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, -1, 12, -8, 64], [1], [1, 10, 25], [1], [1, 4, 2598, 5324, 1771561], [1, -22, 2458, -48334, 4826809], [1, -58, 7794, -284954, 24137569], [1, 0, 5490, 0, 47045881], [1, 82, 25182, 997694, 148035889], [1, 334, 72842, 8145926, 594823321], [1, -210, 69230, -6256110, 887503681], [1, -6, 97490, -303918, 2565726409], [1, -176, 134094, -12130096, 4750104241], [1, -46, 42430, -3657322, 6321363049], [1, -514, 269870, -53365022, 10779215329], [1, 808, 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{'algebraic': True, 'analytic_conductor': 16925.804849225275, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 4862025, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, -11, -10, 0, 0, -15, 0, -10, -4, 0, 22, 0, 0, 61, 58, 0, 0, 110, 0, -4, -82, 0, 75, 22, 0, 0, -334, 0, 210, 89, 0, 58, 0, 0, 6, 0, 0, 150, 176, 0, 46, 44, 0, -82, 514, 0, 0, 75, 0, -242, -808, 0, 40, 0, 0, -334, 568, 0, 618, 210, 0, -59, -220, 0, 694, -638, 0, 0, -814, 0, -82, 6, 0, 0, 0, 0, 600, -610, 0, 176, -268, 0, -580, 46, 0, 60, -72, 0, 0, 902, 0, 514, 0, 0, -1626, 0, 0, -825], 'euler11': [1, 4, 2598, 5324, 1771561], 'euler13': [1, -22, 2458, -48334, 4826809], 'euler17': [1, -58, 7794, -284954, 24137569], 'euler19': [1, 0, 5490, 0, 47045881], 'euler2': [1, -1, 12, -8, 64], 'euler23': [1, 82, 25182, 997694, 148035889], 'euler29': [1, 334, 72842, 8145926, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -210, 69230, -6256110, 887503681], 'euler37': [1, -6, 97490, -303918, 2565726409], 'euler41': [1, -176, 134094, -12130096, 4750104241], 'euler43': [1, -46, 42430, -3657322, 6321363049], 'euler47': [1, -514, 269870, -53365022, 10779215329], 'euler5': [1, 10, 25, 0, 0], 'euler53': [1, 808, 449478, 120292616, 22164361129], 'euler59': [1, -568, 491414, -116655272, 42180533641], 'euler61': [1, -618, 515018, -140274258, 51520374361], 'euler67': [1, -694, 681118, -208729522, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 814, 769934, 291339554, 128100283921], 'euler73': [1, 82, 422290, 31899394, 151334226289], 'euler79': [1, -600, 618846, -295823400, 243087455521], 'euler83': [1, 268, 779030, 153238916, 326940373369], 'euler89': [1, 72, 448286, 50757768, 496981290961], 'euler97': [1, 1626, 1498938, 1484006298, 832972004929], 'euler_factors': [[1, -1, 12, -8, 64], [1, 0, 0, 0, 0], [1, 10, 25, 0, 0], [1, 0, 0, 0, 0], [1, 4, 2598, 5324, 1771561], [1, -22, 2458, -48334, 4826809], [1, -58, 7794, -284954, 24137569], [1, 0, 5490, 0, 47045881], [1, 82, 25182, 997694, 148035889], [1, 334, 72842, 8145926, 594823321], [1, -210, 69230, -6256110, 887503681], [1, -6, 97490, -303918, 2565726409], [1, -176, 134094, -12130096, 4750104241], [1, -46, 42430, -3657322, 6321363049], [1, -514, 269870, -53365022, 10779215329], [1, 808, 449478, 120292616, 22164361129], [1, -568, 491414, -116655272, 42180533641], [1, -618, 515018, -140274258, 51520374361], [1, -694, 681118, -208729522, 90458382169], [1, 814, 769934, 291339554, 128100283921], [1, 82, 422290, 31899394, 151334226289], [1, -600, 618846, -295823400, 243087455521], [1, 268, 779030, 153238916, 326940373369], [1, 72, 448286, 50757768, 496981290961], [1, 1626, 1498938, 1484006298, 832972004929]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2205/4/a/ba'], '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': '4-2205e2-1.1-c3e2-0-8', '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': 2, 'prelabel': '4-2205e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 687084485281554410, 'z1': {'__RealLiteral__': 0, 'data': '0.944177348487544557330072115825', 'prec': 107}}
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{'Lhash': '1196886982532133981778256781386,1571333124360464621521447691886', 'Lhash_array': ['1196886982532133981778256781386', '1571333124360464621521447691886'], 'label': '4-2205e2-1.1-c3e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2205/4/a/ba'}