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lfunc_lfunctions • Show schema
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{'Lhash': '145635767152994734737841019385,1477764982067874196273440857140', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -128, 'a5': -54, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1458, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.6470545462789, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[5, [1, 54, 15625]], [19, [1, 13718, 47045881]]], 'bad_primes': [5, 19], 'central_character': '95.1', 'coefficient_field': '1.1.1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'euler_factors': [[1, 0, 128, 0, 4096], [1, 0, 1458, 0, 531441], [1, 54, 15625], [1, 0, -136802, 0, 13841287201], [1, -2124, 4670966, -3762795564, 3138428376721], [1, 0, 9653618, 0, 23298085122481], [1, 0, -44461762, 0, 582622237229761], [1, 13718, 47045881], [1, 0, -128700322, 0, 21914624432020321], [1, 0, -1189646642, 0, 353814783205469041], [1, 0, -1775007362, 0, 787662783788549761], [1, 0, 5131452818, 0, 6582952005840035281], [1, 0, -9500208482, 0, 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'primitive': False, 'rational': True, 'root_analytic_conductor': 4.674947908146769, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c6e2-0', 'trace_hash': 2047415685958546010, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11488636310886792373653368724184', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.16575102145797551655946574655070', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.52937749526561729408169231161421', 'prec': 113}}
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{'algebraic': True, 'analytic_conductor': 477.6470545462789, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -128, -54, 0, 0, 0, -1458, 0, 2124, 0, 0, 0, 0, 12288, 0, 0, -13718, 6912, 0, 0, 0, 0, -12709, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 186624, 0, 0, 0, 0, 0, 0, 0, -271872, 78732, 0, 0, 0, 136802, 0, 0, 0, 0, 0, -114696, 0, 0, 0, 0, 0, 114124, 0, 0, -1048576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1755904, 0, 0, 0, -663552, 1594323, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 740772, 0, 0, 0, -3096792, 1626752], 'euler11': [1, -2124, 4670966, -3762795564, 3138428376721], 'euler13': [1, 0, 9653618, 0, 23298085122481], 'euler17': [1, 0, -44461762, 0, 582622237229761], 'euler19': [1, 13718, 47045881, 0, 0], 'euler2': [1, 0, 128, 0, 4096], 'euler23': [1, 0, -128700322, 0, 21914624432020321], 'euler29': [1, 0, -1189646642, 0, 353814783205469041], 'euler3': [1, 0, 1458, 0, 531441], 'euler31': [1, 0, -1775007362, 0, 787662783788549761], 'euler37': [1, 0, 5131452818, 0, 6582952005840035281], 'euler41': [1, 0, -9500208482, 0, 22563490300366186081], 'euler43': [1, 0, -7700590802, 0, 39959630797262576401], 'euler47': [1, 0, 15910908158, 0, 116191483108948578241], 'euler5': [1, 54, 15625, 0, 0], 'euler53': [1, 0, 44328722258, 0, 491258904256726154641], 'euler59': [1, 0, -84361067282, 0, 1779197418239532716881], 'euler61': [1, -114124, 106296820566, -5879711203574764, 2654348974297586158321], 'euler67': [1, 0, 180916764338, 0, 8182718904632857144561], 'euler7': [1, 0, -136802, 0, 13841287201], 'euler71': [1, 0, -256200567842, 0, 16409682740640811134241], 'euler73': [1, 0, 155174050078, 0, 22902048046490258711521], 'euler79': [1, 0, -486174911042, 0, 59091511031674153381441], 'euler83': [1, 0, -625348114162, 0, 106890007738661124410161], 'euler89': [1, 0, -993962581922, 0, 246990403565262140303521], 'euler97': [1, 0, 1665944009858, 0, 693842360995438000295041], 'euler_factors': [[1, 0, 128, 0, 4096], [1, 0, 1458, 0, 531441], [1, 54, 15625, 0, 0], [1, 0, -136802, 0, 13841287201], [1, -2124, 4670966, -3762795564, 3138428376721], [1, 0, 9653618, 0, 23298085122481], [1, 0, -44461762, 0, 582622237229761], [1, 13718, 47045881, 0, 0], [1, 0, -128700322, 0, 21914624432020321], [1, 0, -1189646642, 0, 353814783205469041], [1, 0, -1775007362, 0, 787662783788549761], [1, 0, 5131452818, 0, 6582952005840035281], [1, 0, -9500208482, 0, 22563490300366186081], [1, 0, -7700590802, 0, 39959630797262576401], [1, 0, 15910908158, 0, 116191483108948578241], [1, 0, 44328722258, 0, 491258904256726154641], [1, 0, -84361067282, 0, 1779197418239532716881], [1, -114124, 106296820566, -5879711203574764, 2654348974297586158321], [1, 0, 180916764338, 0, 8182718904632857144561], [1, 0, -256200567842, 0, 16409682740640811134241], [1, 0, 155174050078, 0, 22902048046490258711521], [1, 0, -486174911042, 0, 59091511031674153381441], [1, 0, -625348114162, 0, 106890007738661124410161], [1, 0, -993962581922, 0, 246990403565262140303521], [1, 0, 1665944009858, 0, 693842360995438000295041]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/7/d/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-c6e2-0-0', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6, 6], 'order_of_vanishing': 0, 'prelabel': '4-95e2-1.1-c6e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.674947908146769, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c6e2-0', 'trace_hash': 2047415685958546010, 'z1': {'__RealLiteral__': 0, 'data': '0.11488636310886792373653368724184', 'prec': 113}}
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{'Lhash': '145635767152994734737841019385,1477764982067874196273440857140', 'Lhash_array': ['145635767152994734737841019385', '1477764982067874196273440857140'], 'label': '4-95e2-1.1-c6e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/7/d/a'}