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lfunc_lfunctions • Show schema
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{'Lhash': '213969246406880349569142509134,2833540503029557731563382858702', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -64, 'a5': 0, 'a6': 0, 'a7': 286, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 347.2401468009015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.1', 'coefficient_field': '1.1.1.1', 'conductor': 6561, 'conductor_radical': 3, 'degree': 4, 'euler_factors': [[1, 0, 64, 0, 4096], [1], [1, 0, 15625, 0, 244140625], [1, -286, -35853, -33647614, 13841287201], [1, 0, 1771561, 0, 3138428376721], [1, 506, -4570773, 2442365354, 23298085122481], [1, 0, -48275138, 0, 582622237229761], [1, 21164, 206070486, 995679025484, 2213314919066161], [1, 0, 148035889, 0, 21914624432020321], [1, 0, 594823321, 0, 353814783205469041], [1, 35282, 357315843, 31312904873042, 787662783788549761], [1, 178412, 13089163254, 457756380082508, 6582952005840035281], [1, 0, 4750104241, 0, 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'3.87556032731495333838559028486076', '4.00195459327551411917969903251055', '5.19834768057936481162369018213692', '5.21271796889171959105212281542613', '6.57019542454504169642404306459514', '6.85682960341544215736144500300221', '8.038010923848080228951327438028153', '8.300452241556915263950583023571383', '8.917897484162901537898876398708825', '9.303114437296269617519942390449801', '10.40875893246579428867332986671882', '10.43197203104563639867193335447256', '11.20015848646792680251567178275636', '11.83955507305472634257739474091968', '12.51594357608557916505826408948082', '12.80837273592003777307981380066524', '13.64761775743518499023999947155696'], 'prelabel': '4-3e8-1.1-c6e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.316755815795924, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c6e2-0', 'trace_hash': 2214304085581525349, 'types': ['CMF'], 'z1': 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{'algebraic': True, 'analytic_conductor': 347.2401468009015, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 6561, 'conductor_radical': 3, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -64, 0, 0, 286, 0, 0, 0, 0, 0, -506, 0, 0, 0, 0, 0, -21164, 0, 0, 0, 0, 0, -15625, 0, 0, -18304, 0, 0, -35282, 0, 0, 0, 0, 0, -178412, 0, 0, 0, 0, 0, -111386, 0, 0, 0, 0, 0, 117649, 0, 0, 32384, 0, 0, 0, 0, 0, 0, 0, 0, 420838, 0, 0, 262144, 0, 0, -172874, 0, 0, 0, 0, 0, 1276132, 0, 0, 1354496, 0, 0, 204622, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144716, 0, 0, 0, 0, 0, 56446, 0, 0, 1000000], 'euler11': [1, 0, 1771561, 0, 3138428376721], 'euler13': [1, 506, -4570773, 2442365354, 23298085122481], 'euler17': [1, 0, -48275138, 0, 582622237229761], 'euler19': [1, 21164, 206070486, 995679025484, 2213314919066161], 'euler2': [1, 0, 64, 0, 4096], 'euler23': [1, 0, 148035889, 0, 21914624432020321], 'euler29': [1, 0, 594823321, 0, 353814783205469041], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 35282, 357315843, 31312904873042, 787662783788549761], 'euler37': [1, 178412, 13089163254, 457756380082508, 6582952005840035281], 'euler41': [1, 0, 4750104241, 0, 22563490300366186081], 'euler43': [1, 111386, 6085477947, 704111344575914, 39959630797262576401], 'euler47': [1, 0, 10779215329, 0, 116191483108948578241], 'euler5': [1, 0, 15625, 0, 244140625], 'euler53': [1, 0, -44328722258, 0, 491258904256726154641], 'euler59': [1, 0, 42180533641, 0, 1779197418239532716881], 'euler61': [1, -420838, 125584247883, -21681731305334518, 2654348974297586158321], 'euler67': [1, 172874, -60572962293, 15637902359083706, 8182718904632857144561], 'euler7': [1, -286, -35853, -33647614, 13841287201], 'euler71': [1, 0, -256200567842, 0, 16409682740640811134241], 'euler73': [1, -1276132, 709796672934, -193122448862634148, 22902048046490258711521], 'euler79': [1, -204622, -201217292637, -49741041323618062, 59091511031674153381441], 'euler83': [1, 0, 326940373369, 0, 106890007738661124410161], 'euler89': [1, 0, -993962581922, 0, 246990403565262140303521], 'euler97': [1, -56446, -829785854013, -47017937790222334, 693842360995438000295041], 'euler_factors': [[1, 0, 64, 0, 4096], [1, 0, 0, 0, 0], [1, 0, 15625, 0, 244140625], [1, -286, -35853, -33647614, 13841287201], [1, 0, 1771561, 0, 3138428376721], [1, 506, -4570773, 2442365354, 23298085122481], [1, 0, -48275138, 0, 582622237229761], [1, 21164, 206070486, 995679025484, 2213314919066161], [1, 0, 148035889, 0, 21914624432020321], [1, 0, 594823321, 0, 353814783205469041], [1, 35282, 357315843, 31312904873042, 787662783788549761], [1, 178412, 13089163254, 457756380082508, 6582952005840035281], [1, 0, 4750104241, 0, 22563490300366186081], [1, 111386, 6085477947, 704111344575914, 39959630797262576401], [1, 0, 10779215329, 0, 116191483108948578241], [1, 0, -44328722258, 0, 491258904256726154641], [1, 0, 42180533641, 0, 1779197418239532716881], [1, -420838, 125584247883, -21681731305334518, 2654348974297586158321], [1, 172874, -60572962293, 15637902359083706, 8182718904632857144561], [1, 0, -256200567842, 0, 16409682740640811134241], [1, -1276132, 709796672934, -193122448862634148, 22902048046490258711521], [1, -204622, -201217292637, -49741041323618062, 59091511031674153381441], [1, 0, 326940373369, 0, 106890007738661124410161], [1, 0, -993962581922, 0, 246990403565262140303521], [1, -56446, -829785854013, -47017937790222334, 693842360995438000295041]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/81/7/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': '4-3e8-1.1-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': '4-3e8-1.1-c6e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.316755815795924, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c6e2-0', 'trace_hash': 2214304085581525349, 'z1': {'__RealLiteral__': 0, 'data': '0.16879197340998936023880176114', 'prec': 103}}
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{'Lhash': '213969246406880349569142509134,2833540503029557731563382858702', 'Lhash_array': ['213969246406880349569142509134', '2833540503029557731563382858702'], 'label': '4-3e8-1.1-c6e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/81/7/d/a'}