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lfunc_lfunctions • Show schema
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{'Lhash': '2934318204440958051476831915646', 'a10': [1.7840876035471578, -5.132096318199093], 'a2': [0.12716965639136776, 2.426541596135118], 'a3': [-1.7867492350008398, -1.4468810018270737], 'a4': [-3.882888205530721, 0.40810799546442117], 'a5': [-2.0707641188306547, -0.8437629786637368], 'a6': [3.28369664931845, -4.519620700433686], 'a7': [1.5435242441731487, -2.1488445517649035], 'a8': [-0.7238452419997403, -4.570178993066183], 'a9': [0.4752731228746919, 2.235984244102129], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [2.0707641188306547, 0.8437629786637368]]], [7, [[1.0, 0], [-1.5435242441731487, 2.1488445517649035]]]], 'bad_primes': [5, 7], 'central_character': '175.108', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '460674624634709180122013554864', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-8.634034402603755, 1.3674967065991879], [78.93769085249775, -25.648410533120636]], [[1.0, 0], [-5.600819705916663, 6.2203404586930064], [-9.303033230821159, -88.51244868777633]], [[1.0, 0], [-6.796132288576503, -1.0764016088976995], [92.2524820806299, 29.974648454369902]], [[1.0, 0], [9.183259099981498, 5.301957113412398], [50.5, 87.4685657822283]], [[1.0, 0], [-0.20427160033156894, 0.07841252074641783], [76.5439170241716, -68.9204524549624]], [[1.0, 0], [-4.72847304187069, -1.2669905330015856], [92.66471820493493, 53.5]], [[1.0, 0], [5.734591676597098, -5.163449538004758], [11.393602496174228, -108.4028865951418]], [[1.0, 0], [3.5674628690767474, -1.8177131219210145], [66.41973350904946, -91.41892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-175-175.108-c1-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 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0.1587941495402016, 'root_number': '0.5422084740601315 + 0.840243994716644*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15879414954', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.31476891496178815157104799079', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.11075967048435878919445077192', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59728663466021004990964352528', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'bad_primes': [5, 7], 'central_character': '175.108', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/2/x/a/108/18'], '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': '2-175-175.108-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-175-175.108-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.182109146979418, 'root_angle': 0.1587941495402016, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31476891496178815157104799079', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2934318204440958051476831915646', 'Lhash_array': ['2934318204440958051476831915646'], 'factors': ['2-175-175.108-c1-0-10'], 'label': '2-175-175.108-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/2/x/a/108/18'}