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lfunc_lfunctions • Show schema
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{'Lhash': '2211527900498544326517583232313,2404939932371160254273012499712', 'a10': 20, 'a2': 4, 'a3': -6, 'a4': 12, 'a5': 5, 'a6': -24, 'a7': -14, 'a8': 32, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1037.808986673586, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4, 4]], [3, [1, 6, 9]], [7, [1, 14, 49]], [13, [1, 26, 169]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.1', 'coefficient_field': '1.1.1.1', 'conductor': 298116, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, -4, 4], [1, 6, 9], [1, -5, 230, -625, 15625], [1, 14, 49], [1, 32, 2498, 42592, 1771561], [1, 26, 169], [1, 78, 8722, 383214, 24137569], [1, 9, 9302, 61731, 47045881], [1, -17, 19970, -206839, 148035889], [1, 67, 27824, 1634063, 594823321], [1, 121, 14706, 3604711, 887503681], [1, 30, 71186, 1519590, 2565726409], [1, 570, 201322, 39284970, 4750104241], [1, 43, 153570, 3418801, 6321363049], [1, 293, 137732, 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'2.98204653913667665445108772459805', '3.27226146622143242476150069206306', '4.20574355703643239077945068405517', '4.48353441673830814066918005852568', '5.20157917498516533829207657861279', '5.35658726040189688495352687732757', '6.04987416309986973573535021654701', '6.25872739277498976758114174734104', '6.80001894931559616168808531831518', '7.13508038206158898621610989809281', '7.83680143586349202506360944357761', '8.050205721701552824871896088790754', '9.201747600080390262344900604328941', '9.283496287308514536436207526406754', '10.05077144647553301172166080049587', '10.30536951635691210989071048770805'], 'prelabel': '4-546e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.675829707023846, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 458128978099875299, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74458790150880540260686909809', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89716309205247239044594928329', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98204653913667665445108772460', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 1037.808986673586, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 298116, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, 4, -6, 12, 5, -24, -14, 32, 27, 20, -32, -72, -26, -56, -30, 80, -78, 108, -9, 60, 84, -128, 17, -192, -205, -104, -108, -168, -67, -120, -121, 192, 192, -312, -70, 324, -30, -36, 156, 160, -570, 336, -43, -384, 135, 68, -293, -480, 147, -820, 468, -312, -555, -432, -160, -448, 54, -268, -562, -360, -1060, -484, -378, 448, -130, 768, -130, -936, -102, -280, -2, 864, -1379, -120, 1230, -108, 448, 624, 913, 400, 405, -2280, 363, 1008, -390, -172, 402, -1024, 315, 540, 364, 204, 726, -1172, -45, -1152, -599, 588, -864, -2460], 'euler11': [1, 32, 2498, 42592, 1771561], 'euler13': [1, 26, 169, 0, 0], 'euler17': [1, 78, 8722, 383214, 24137569], 'euler19': [1, 9, 9302, 61731, 47045881], 'euler2': [1, -4, 4, 0, 0], 'euler23': [1, -17, 19970, -206839, 148035889], 'euler29': [1, 67, 27824, 1634063, 594823321], 'euler3': [1, 6, 9, 0, 0], 'euler31': [1, 121, 14706, 3604711, 887503681], 'euler37': [1, 30, 71186, 1519590, 2565726409], 'euler41': [1, 570, 201322, 39284970, 4750104241], 'euler43': [1, 43, 153570, 3418801, 6321363049], 'euler47': [1, 293, 137732, 30420139, 10779215329], 'euler5': [1, -5, 230, -625, 15625], 'euler53': [1, 555, 193924, 82626735, 22164361129], 'euler59': [1, 562, 488774, 115422998, 42180533641], 'euler61': [1, 1060, 719742, 240599860, 51520374361], 'euler67': [1, 130, 373806, 39099190, 90458382169], 'euler7': [1, 14, 49, 0, 0], 'euler71': [1, 2, -486322, 715822, 128100283921], 'euler73': [1, 1379, 1252788, 536454443, 151334226289], 'euler79': [1, -913, 926694, -450144607, 243087455521], 'euler83': [1, -363, 178360, -207558681, 326940373369], 'euler89': [1, -315, 836218, -222065235, 496981290961], 'euler97': [1, 599, 1363140, 546691127, 832972004929], 'euler_factors': [[1, -4, 4, 0, 0], [1, 6, 9, 0, 0], [1, -5, 230, -625, 15625], [1, 14, 49, 0, 0], [1, 32, 2498, 42592, 1771561], [1, 26, 169, 0, 0], [1, 78, 8722, 383214, 24137569], [1, 9, 9302, 61731, 47045881], [1, -17, 19970, -206839, 148035889], [1, 67, 27824, 1634063, 594823321], [1, 121, 14706, 3604711, 887503681], [1, 30, 71186, 1519590, 2565726409], [1, 570, 201322, 39284970, 4750104241], [1, 43, 153570, 3418801, 6321363049], [1, 293, 137732, 30420139, 10779215329], [1, 555, 193924, 82626735, 22164361129], [1, 562, 488774, 115422998, 42180533641], [1, 1060, 719742, 240599860, 51520374361], [1, 130, 373806, 39099190, 90458382169], [1, 2, -486322, 715822, 128100283921], [1, 1379, 1252788, 536454443, 151334226289], [1, -913, 926694, -450144607, 243087455521], [1, -363, 178360, -207558681, 326940373369], [1, -315, 836218, -222065235, 496981290961], [1, 599, 1363140, 546691127, 832972004929]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/4/a/j'], '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': '4-546e2-1.1-c3e2-0-7', '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': '4-546e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.675829707023846, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 458128978099875299, 'z1': {'__RealLiteral__': 0, 'data': '1.74458790150880540260686909809', 'prec': 103}}
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{'Lhash': '2211527900498544326517583232313,2404939932371160254273012499712', 'Lhash_array': ['2211527900498544326517583232313', '2404939932371160254273012499712'], 'factors': ['2-546-1.1-c3-0-30', '2-546-1.1-c3-0-33'], 'label': '4-546e2-1.1-c3e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/4/a/j'}