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lfunc_lfunctions • Show schema
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{'Lhash': '2355103416994926297649929282737', 'a10': [103.03937547912128, 9.428034614595526e-61], 'a2': [-2.0, 3.4641016151377544], 'a3': [-3.3788764556342703, -5.852385693656804], 'a4': [-8.0, -13.856406460551018], 'a5': [-12.87992193489016, -22.3086791887506], 'a6': [27.031011645074162, -6.2172411300955324e-61], 'a7': [127.5141483129607, 220.86098356192116], 'a8': [64.0, 0.0], 'a9': [98.66638779512078, -170.89519666044296], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.86840266616057, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, -3.4641016151377544]]], [37, [[1.0, 0], [-5464.329884437009, 6283.713544875246]]]], 'bad_primes': [2, 37], 'central_character': '74.47', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '247135314775375031119284375487', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, -3.4641016151377544]], [[1.0, 0], [3.3788764556342703, 5.852385693656804], 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'7.45719923588073351404237188317354', '7.913365716294367372822472716013249', '9.989454001134034901990881364180433', '10.65953573829505576879228262437202', '11.23935154099955843193502967658660', '12.91567859051911469333886294637493', '13.79231721251738366346990295981410'], 'prelabel': '2-74-37.10-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4450548132302004, 'root_angle': 0.681010861254362, 'root_number': '-0.5385054327833757 + 0.8426220379641095*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.340505430627', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85784901341971559769380227502', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.91057075512575040287016719806', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.00692270793826744695726789365', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.86840266616057, 'bad_primes': [2, 37], 'central_character': '37.10', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/6/c/a/47/3'], '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': '2-74-37.10-c5-0-9', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-74-37.10-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4450548132302004, 'root_angle': 0.340505430627181, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85784901341971559769380227502', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2355103416994926297649929282737', 'Lhash_array': ['2355103416994926297649929282737'], 'label': '2-74-37.10-c5-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/6/c/a/47/3'}