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lfunc_lfunctions • Show schema
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{'Lhash': '1645088864776156134756325665618', 'a10': 0, 'a2': 0, 'a3': 81, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -8576, 'a8': 0, 'a9': 6561, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 154.51075084916198, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -81]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '300.1', 'coefficient_field': '1.1.1.1', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, -81], [1], [1, 8576, 40353607], [1, -70596, 2357947691], [1, -2530, 10604499373], [1, -200574, 118587876497], [1, 695620, 322687697779], [1, 2472696, 1801152661463], [1, -5474214, 14507145975869], [1, -3732104, 26439622160671], [1, -21898522, 129961739795077], [1, 23818950, 327381934393961], [1, 10612676, 502592611936843], [1, 2398464, 1119130473102767], [1, -8994978, 3299763591802133], [1, 143417916, 8662995818654939], [1, 19804258, 11694146092834141], [1, -165625156, 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'1.29774629103632521095208628542', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57218916509312033896265561013', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60481626579606381114743084459', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 154.51075084916198, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 81, 0, 0, 0, -8576, 0, 6561, 0, 70596, 0, 2530, 0, 0, 0, 200574, 0, -695620, 0, -694656, 0, -2472696, 0, 0, 0, 531441, 0, 5474214, 0, 3732104, 0, 5718276, 0, 0, 0, 21898522, 0, 204930, 0, -23818950, 0, -10612676, 0, 0, 0, -2398464, 0, 33194169, 0, 16246494, 0, 8994978, 0, 0, 0, -56345220, 0, -143417916, 0, -19804258, 0, -56267136, 0, 0, 0, 165625156, 0, -200288376, 0, -194801400, 0, -148729418, 0, 0, 0, -605431296, 0, -30134152, 0, 43046721, 0, -302054076, 0, 0, 0, 443411334, 0, 909502650, 0, -21697280, 0, 302300424, 0, 0, 0, 872463358, 0, 463180356, 0], 'euler11': [1, -70596, 2357947691], 'euler13': [1, -2530, 10604499373], 'euler17': [1, -200574, 118587876497], 'euler19': [1, 695620, 322687697779], 'euler2': [1, 0, 0], 'euler23': [1, 2472696, 1801152661463], 'euler29': [1, -5474214, 14507145975869], 'euler3': [1, -81, 0], 'euler31': [1, -3732104, 26439622160671], 'euler37': [1, -21898522, 129961739795077], 'euler41': [1, 23818950, 327381934393961], 'euler43': [1, 10612676, 502592611936843], 'euler47': [1, 2398464, 1119130473102767], 'euler5': [1, 0, 0], 'euler53': [1, -8994978, 3299763591802133], 'euler59': [1, 143417916, 8662995818654939], 'euler61': [1, 19804258, 11694146092834141], 'euler67': [1, -165625156, 27206534396294947], 'euler7': [1, 8576, 40353607], 'euler71': [1, 194801400, 45848500718449031], 'euler73': [1, 148729418, 58871586708267913], 'euler79': [1, 30134152, 119851595982618319], 'euler83': [1, 302054076, 186940255267540403], 'euler89': [1, -909502650, 350356403707485209], 'euler97': [1, -872463358, 760231058654565217], 'euler_factors': [[1, 0, 0], [1, -81, 0], [1, 0, 0], [1, 8576, 40353607], [1, -70596, 2357947691], [1, -2530, 10604499373], [1, -200574, 118587876497], [1, 695620, 322687697779], [1, 2472696, 1801152661463], [1, -5474214, 14507145975869], [1, -3732104, 26439622160671], [1, -21898522, 129961739795077], [1, 23818950, 327381934393961], [1, 10612676, 502592611936843], [1, 2398464, 1119130473102767], [1, -8994978, 3299763591802133], [1, 143417916, 8662995818654939], [1, 19804258, 11694146092834141], [1, -165625156, 27206534396294947], [1, 194801400, 45848500718449031], [1, 148729418, 58871586708267913], [1, 30134152, 119851595982618319], [1, 302054076, 186940255267540403], [1, -909502650, 350356403707485209], [1, -872463358, 760231058654565217]], 'index': 25, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/10/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/300/10/a/a'], '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': '2-300-1.1-c9-0-25', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-300-1.1-c9-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.430235349709271, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'trace_hash': 1462531061301287296, 'z1': {'__RealLiteral__': 0, 'data': '1.29774629103632521095208628542', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20922730
{'Lhash': '1645088864776156134756325665618', 'Lhash_array': ['1645088864776156134756325665618'], 'label': '2-300-1.1-c9-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/10/a/a'}
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id: 24593851
{'Lhash': '1645088864776156134756325665618', 'Lhash_array': ['1645088864776156134756325665618'], 'label': '2-300-1.1-c9-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/10/a/a/1/1'}