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lfunc_lfunctions • Show schema
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{'Lhash': '2730980923531002164755390003,1943722928956676537771499565163', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -32, 'a5': 0, 'a6': 0, 'a7': 968, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10717.288481509306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 32]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 0, 32], [1], [1], [1, -968, 469554, -113884232, 13841287201], [1, 0, -1745714, 0, 3138428376721], [1, 6736, 20997042, 32513385424, 23298085122481], [1, 0, -48274976, 0, 582622237229761], [1, -11488, 127085298, -540463080928, 2213314919066161], [1, 0, -284666690, 0, 21914624432020321], [1, 0, -327940544, 0, 353814783205469041], [1, 79592, 3358728978, 70638192978152, 787662783788549761], [1, 105052, 7890433494, 269534690718268, 6582952005840035281], [1, 0, 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{'algebraic': True, 'analytic_conductor': 10717.288481509306, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -32, 0, 0, 968, 0, 0, 0, 0, 0, -6736, 0, 0, 1024, 0, 0, 11488, 0, 0, 0, 0, 0, 0, 0, 0, -30976, 0, 0, -79592, 0, 0, 0, 0, 0, -105052, 0, 0, 0, 0, 0, -7600, 0, 0, 0, 0, 0, 467470, 0, 0, 215552, 0, 0, 0, 0, 0, 0, 0, 0, 26500, 0, 0, -32768, 0, 0, -337936, 0, 0, 0, 0, 0, -472288, 0, 0, -367616, 0, 0, -70232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6520448, 0, 0, 0, 0, 0, 642848, 0, 0, 0], 'euler11': [1, 0, -1745714, 0, 3138428376721], 'euler13': [1, 6736, 20997042, 32513385424, 23298085122481], 'euler17': [1, 0, -48274976, 0, 582622237229761], 'euler19': [1, -11488, 127085298, -540463080928, 2213314919066161], 'euler2': [1, 0, 32, 0, 0], 'euler23': [1, 0, -284666690, 0, 21914624432020321], 'euler29': [1, 0, -327940544, 0, 353814783205469041], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 79592, 3358728978, 70638192978152, 787662783788549761], 'euler37': [1, 105052, 7890433494, 269534690718268, 6582952005840035281], 'euler41': [1, 0, -8128061984, 0, 22563490300366186081], 'euler43': [1, 7600, 12657166098, 48042359172400, 39959630797262576401], 'euler47': [1, 0, -15661450658, 0, 116191483108948578241], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 12666935680, 0, 491258904256726154641], 'euler59': [1, 0, -21940729490, 0, 1779197418239532716881], 'euler61': [1, -26500, 103216311222, -1365289920566500, 2654348974297586158321], 'euler67': [1, 337936, 209466949362, 30569143836663184, 8182718904632857144561], 'euler7': [1, -968, 469554, -113884232, 13841287201], 'euler71': [1, 0, 26256724990, 0, 16409682740640811134241], 'euler73': [1, 472288, 358432441314, 71473339065579232, 22902048046490258711521], 'euler79': [1, 70232, 487408044498, 17072518176150872, 59091511031674153381441], 'euler83': [1, 0, -653760187346, 0, 106890007738661124410161], 'euler89': [1, 0, -977236742720, 0, 246990403565262140303521], 'euler97': [1, -642848, 1769257397634, -535474387424597792, 693842360995438000295041], 'euler_factors': [[1, 0, 32, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -968, 469554, -113884232, 13841287201], [1, 0, -1745714, 0, 3138428376721], [1, 6736, 20997042, 32513385424, 23298085122481], [1, 0, -48274976, 0, 582622237229761], [1, -11488, 127085298, -540463080928, 2213314919066161], [1, 0, -284666690, 0, 21914624432020321], [1, 0, -327940544, 0, 353814783205469041], [1, 79592, 3358728978, 70638192978152, 787662783788549761], [1, 105052, 7890433494, 269534690718268, 6582952005840035281], [1, 0, -8128061984, 0, 22563490300366186081], [1, 7600, 12657166098, 48042359172400, 39959630797262576401], [1, 0, -15661450658, 0, 116191483108948578241], [1, 0, 12666935680, 0, 491258904256726154641], [1, 0, -21940729490, 0, 1779197418239532716881], [1, -26500, 103216311222, -1365289920566500, 2654348974297586158321], [1, 337936, 209466949362, 30569143836663184, 8182718904632857144561], [1, 0, 26256724990, 0, 16409682740640811134241], [1, 472288, 358432441314, 71473339065579232, 22902048046490258711521], [1, 70232, 487408044498, 17072518176150872, 59091511031674153381441], [1, 0, -653760187346, 0, 106890007738661124410161], [1, 0, -977236742720, 0, 246990403565262140303521], [1, -642848, 1769257397634, -535474387424597792, 693842360995438000295041]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/7/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': '4-450e2-1.1-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': '4-450e2-1.1-c6e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.174691033585884, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c6e2-0', 'trace_hash': 1350520567320344619, 'z1': {'__RealLiteral__': 0, 'data': '0.00215436408347798118770047268', 'prec': 103}}
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{'Lhash': '2730980923531002164755390003,1943722928956676537771499565163', 'Lhash_array': ['2730980923531002164755390003', '1943722928956676537771499565163'], 'factors': ['2-450-3.2-c6-0-0', '2-450-3.2-c6-0-36'], 'label': '4-450e2-1.1-c6e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/7/d/a'}