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lfunc_lfunctions • Show schema
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{'Lhash': '1105440745129578778723119087042', 'a10': 0, 'a2': 0, 'a3': 60, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 4344, 'a8': 0, 'a9': -16083, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 103.00716723277465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '200.1', 'coefficient_field': '1.1.1.1', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, -60, 19683], [1], [1, -4344, 40353607], [1, -93644, 2357947691], [1, -12242, 10604499373], [1, -319598, 118587876497], [1, 553516, 322687697779], [1, -712936, 1801152661463], [1, -2075838, 14507145975869], [1, 6420448, 26439622160671], [1, -18197754, 129961739795077], [1, -9033834, 327381934393961], [1, 19594732, 502592611936843], [1, -18484176, 1119130473102767], [1, 10255766, 3299763591802133], [1, -121666556, 8662995818654939], [1, 45948962, 11694146092834141], [1, 50535428, 27206534396294947], 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45948962, 11694146092834141], 1]], [[[1, 50535428, 27206534396294947], 1]], [[[1, -267044680, 45848500718449031], 1]], [[[1, -176213366, 58871586708267913], 1]], [[[1, 269685680, 119851595982618319], 1]], [[[1, -227032556, 186940255267540403], 1]], [[[1, -72141594, 350356403707485209], 1]], [[[1, 228776546, 760231058654565217], 1]], [[[1, 803255994, 1093685272684360901], 1]], [[[1, 781725544, 1304773183829244583], 1]], [[[1, -1007558100, 1838459212420154507], 1]], [[[1, 480691826, 2171893279442309389], 1]], [[[1, -2897809422, 3004041937984268273], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-200-1.1-c9-0-18', 'leading_term': '3.14591917237925796832702255094000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 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'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c9-0', 'trace_hash': 1883148427567221353, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.872038986871109312509089164199', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.96241385686583056801030223096', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33548068693973275846138607012', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 103.00716723277465, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 60, 0, 0, 0, 4344, 0, -16083, 0, 93644, 0, 12242, 0, 0, 0, 319598, 0, -553516, 0, 260640, 0, 712936, 0, 0, 0, -2145960, 0, 2075838, 0, -6420448, 0, 5618640, 0, 0, 0, 18197754, 0, 734520, 0, 9033834, 0, -19594732, 0, 0, 0, 18484176, 0, -21483271, 0, 19175880, 0, -10255766, 0, 0, 0, -33210960, 0, 121666556, 0, -45948962, 0, -69864552, 0, 0, 0, -50535428, 0, 42776160, 0, 267044680, 0, 176213366, 0, 0, 0, 406789536, 0, -269685680, 0, 187804089, 0, 227032556, 0, 0, 0, 124550280, 0, 72141594, 0, 53179248, 0, -385226880, 0, 0, 0, -228776546, 0, -1506076452, 0], 'euler11': [1, -93644, 2357947691], 'euler13': [1, -12242, 10604499373], 'euler17': [1, -319598, 118587876497], 'euler19': [1, 553516, 322687697779], 'euler2': [1, 0, 0], 'euler23': [1, -712936, 1801152661463], 'euler29': [1, -2075838, 14507145975869], 'euler3': [1, -60, 19683], 'euler31': [1, 6420448, 26439622160671], 'euler37': [1, -18197754, 129961739795077], 'euler41': [1, -9033834, 327381934393961], 'euler43': [1, 19594732, 502592611936843], 'euler47': [1, -18484176, 1119130473102767], 'euler5': [1, 0, 0], 'euler53': [1, 10255766, 3299763591802133], 'euler59': [1, -121666556, 8662995818654939], 'euler61': [1, 45948962, 11694146092834141], 'euler67': [1, 50535428, 27206534396294947], 'euler7': [1, -4344, 40353607], 'euler71': [1, -267044680, 45848500718449031], 'euler73': [1, -176213366, 58871586708267913], 'euler79': [1, 269685680, 119851595982618319], 'euler83': [1, -227032556, 186940255267540403], 'euler89': [1, -72141594, 350356403707485209], 'euler97': [1, 228776546, 760231058654565217], 'euler_factors': [[1, 0, 0], [1, -60, 19683], [1, 0, 0], [1, -4344, 40353607], [1, -93644, 2357947691], [1, -12242, 10604499373], [1, -319598, 118587876497], [1, 553516, 322687697779], [1, -712936, 1801152661463], [1, -2075838, 14507145975869], [1, 6420448, 26439622160671], [1, -18197754, 129961739795077], [1, -9033834, 327381934393961], [1, 19594732, 502592611936843], [1, -18484176, 1119130473102767], [1, 10255766, 3299763591802133], [1, -121666556, 8662995818654939], [1, 45948962, 11694146092834141], [1, 50535428, 27206534396294947], [1, -267044680, 45848500718449031], [1, -176213366, 58871586708267913], [1, 269685680, 119851595982618319], [1, -227032556, 186940255267540403], [1, -72141594, 350356403707485209], [1, 228776546, 760231058654565217]], 'index': 18, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/10/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/200/10/a/b'], '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': '2-200-1.1-c9-0-18', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-200-1.1-c9-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.149244663164577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9-0', 'trace_hash': 1883148427567221353, 'z1': {'__RealLiteral__': 0, 'data': '0.872038986871109312509089164199', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20504784
{'Lhash': '1105440745129578778723119087042', 'Lhash_array': ['1105440745129578778723119087042'], 'label': '2-200-1.1-c9-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/10/a/b'}
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id: 24592144
{'Lhash': '1105440745129578778723119087042', 'Lhash_array': ['1105440745129578778723119087042'], 'label': '2-200-1.1-c9-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/10/a/b/1/1'}