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lfunc_lfunctions • Show schema
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{'Lhash': '2787444004643526752267116735067', 'a10': [-0.9125758126709624, 3.990038502606171e-79], 'a2': [-0.2631460738930663, -0.8098803394929929], 'a3': [0.0, 0.0], 'a4': [0.22235668628299707, -0.16155158897094365], 'a5': [0.3311591713799414, -1.019203129940644], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.8782751101788021, -0.6381042188334938], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4336874959780791, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0.42577929156507266, 0.9048270524660196]]], [79, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]]], 'bad_primes': [11, 79], 'central_character': '869.236', 'coefficient_field': 'CDF', 'conductor': 869, 'conductor_radical': 869, 'conjugate': '1412470715269516746601929298587', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2631460738930663, 0.8098803394929929], [-0.8090169943749475, 0.5877852522924731]], 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-0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-869-869.236-c0-0-4', 'leading_term': '0.96085083982160156333944046111821', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/869/1/j/a/236/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.9608508398216016, 1.0154779988679157, 1.0849901046623796, 1.1700288834620334, 1.270330787869248, 1.3848927475431667, 1.5121648765910254, 1.6502130384336624, 1.7968303058872206, 1.949601820039138, 2.105937805674913, 2.2630899003293248, 2.41816247784145, 2.56812671769363, 2.7098420356986894, 2.8400873032061273, 2.9556028282028737, 3.05314309894518, 3.129539605110934, 3.1817725282179503, 3.207049660777664, 3.2028905363636007, 3.1672134165647035, 3.098422485015318, 2.9954923504077406, 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'7.17266096644870657146129865967660', '7.80437604820464926458442542550122', '8.961177836533504389009987410448762', '9.709017833124843879119395038555741', '10.49808222952940201131839827685446'], 'prelabel': '2-869-869.236-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6585495395018351, 'root_angle': 0.6745657398607864, 'root_number': '-0.52133484874566876361198656312256 + 0.85335219896788844706014582579982*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3372828699303932', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19890560075597474813551305929', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16464825335285970316204618076', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44760168909230943961778375461', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4336874959780791, 'bad_primes': [11, 79], 'central_character': '869.236', 'conductor': 869, 'conductor_radical': 869, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/869/1/j/a/236/2'], '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': '2-869-869.236-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-869-869.236-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6585495395018351, 'root_angle': 0.3372828699303932, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.19890560075597474813551305929', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2787444004643526752267116735067', 'Lhash_array': ['2787444004643526752267116735067'], 'label': '2-869-869.236-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/869/1/j/a/236/2'}