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  • lfunc_lfunctions • Show schema
    {'Lhash': '2214577458715619484018520931424,2305411974656719362205828625996', 'a10': -5, 'a2': 1, 'a3': 5, 'a4': 8, 'a5': -5, 'a6': 5, 'a7': 44, 'a8': 23, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.418059093537796, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [1, 5, 25]], [19, [1, 133, 6859]]], 'bad_primes': [5, 19], 'central_character': '95.1', 'coefficient_field': '1.1.1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'euler_factors': [[1, -1, -7, -8, 64], [1, -5, -2, -135, 729], [1, 5, 25], [1, -44, 1170, -15092, 117649], [1, -18, 2743, -23958, 1771561], [1, 54, 719, 118638, 4826809], [1, -54, -1997, -265302, 24137569], [1, 133, 6859], [1, -92, -3703, -1119364, 148035889], [1, -134, -6433, -3268126, 594823321], [1, 504, 123086, 15014664, 887503681], [1, 472, 157002, 23908216, 2565726409], [1, -243, -9872, -16747803, 4750104241], [1, 496, 166509, 39435472, 6321363049], [1, 502, 148181, 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'5.05702198807915921117737565279465', '6.62523077144777768688396095425781', '7.06685413320404984814767140527605', '7.65583369751070102026145787482645', '8.079984804409519744365686719612774', '8.604153506381280619778995602242605', '9.218415360922711377934697209764593', '10.31272078955377143794714183234745', '10.56107768258407645578290151821173', '11.27649951212410368447791092906261', '11.44486107416496694412240750897005', '12.42966042577659884862406238899882', '12.44058131781760656095872224114589', '13.27845319861924151200689279821818', '14.21712530343059068595670031906798'], 'prelabel': '4-95e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.367526441361397, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 2041357664471006640, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74699357876445148617334030237', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.81864937723505996313741253251', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.13095906600118597961816098731', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 31.418059093537796, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'dirichlet_coefficients': [1, 1, 5, 8, -5, 5, 44, 23, 27, -5, 18, 40, -54, 44, -25, 23, 54, 27, -133, -40, 220, 18, 92, 115, 0, -54, 280, 352, 134, -25, -504, 184, 90, 54, -220, 216, -472, -133, -270, -115, 243, 220, -496, 144, -135, 92, -502, 115, 766, 0, 270, -432, -62, 280, -90, 1012, -665, 134, -681, -200, 142, -504, 1188, 17, 270, 90, -55, 432, 460, -220, 974, 621, -695, -472, 0, -1064, 792, -270, 736, -115, 1400, 243, -126, 1760, -270, -496, 670, 414, -726, -135, -2376, 736, -2520, -502, 665, 920, 1167, 766, 486, 0], 'euler11': [1, -18, 2743, -23958, 1771561], 'euler13': [1, 54, 719, 118638, 4826809], 'euler17': [1, -54, -1997, -265302, 24137569], 'euler19': [1, 133, 6859, 0, 0], 'euler2': [1, -1, -7, -8, 64], 'euler23': [1, -92, -3703, -1119364, 148035889], 'euler29': [1, -134, -6433, -3268126, 594823321], 'euler3': [1, -5, -2, -135, 729], 'euler31': [1, 504, 123086, 15014664, 887503681], 'euler37': [1, 472, 157002, 23908216, 2565726409], 'euler41': [1, -243, -9872, -16747803, 4750104241], 'euler43': [1, 496, 166509, 39435472, 6321363049], 'euler47': [1, 502, 148181, 52119146, 10779215329], 'euler5': [1, 5, 25, 0, 0], 'euler53': [1, 62, -145033, 9230374, 22164361129], 'euler59': [1, 681, 258382, 139863099, 42180533641], 'euler61': [1, -142, -206817, -32231302, 51520374361], 'euler67': [1, 55, -297738, 16541965, 90458382169], 'euler7': [1, -44, 1170, -15092, 117649], 'euler71': [1, -974, 590765, -348605314, 128100283921], 'euler73': [1, 695, 94008, 270366815, 151334226289], 'euler79': [1, -736, 48657, -362876704, 243087455521], 'euler83': [1, 126, 1147543, 72045162, 326940373369], 'euler89': [1, 726, -177893, 511807494, 496981290961], 'euler97': [1, -1167, 449216, -1065089391, 832972004929], 'euler_factors': [[1, -1, -7, -8, 64], [1, -5, -2, -135, 729], [1, 5, 25, 0, 0], [1, -44, 1170, -15092, 117649], [1, -18, 2743, -23958, 1771561], [1, 54, 719, 118638, 4826809], [1, -54, -1997, -265302, 24137569], [1, 133, 6859, 0, 0], [1, -92, -3703, -1119364, 148035889], [1, -134, -6433, -3268126, 594823321], [1, 504, 123086, 15014664, 887503681], [1, 472, 157002, 23908216, 2565726409], [1, -243, -9872, -16747803, 4750104241], [1, 496, 166509, 39435472, 6321363049], [1, 502, 148181, 52119146, 10779215329], [1, 62, -145033, 9230374, 22164361129], [1, 681, 258382, 139863099, 42180533641], [1, -142, -206817, -32231302, 51520374361], [1, 55, -297738, 16541965, 90458382169], [1, -974, 590765, -348605314, 128100283921], [1, 695, 94008, 270366815, 151334226289], [1, -736, 48657, -362876704, 243087455521], [1, 126, 1147543, 72045162, 326940373369], [1, 726, -177893, 511807494, 496981290961], [1, -1167, 449216, -1065089391, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/4/e/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': '4-95e2-1.1-c3e2-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-95e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.367526441361397, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2041357664471006640, 'z1': {'__RealLiteral__': 0, 'data': '1.74699357876445148617334030237', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2214577458715619484018520931424,2305411974656719362205828625996', 'Lhash_array': ['2214577458715619484018520931424', '2305411974656719362205828625996'], 'factors': ['2-95-19.11-c3-0-12', '2-95-19.7-c3-0-10'], 'label': '4-95e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/4/e/a'}