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lfunc_lfunctions • Show schema
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{'Lhash': '2005240467390336332094882254374', 'a10': [0.9510565162951535, 0.30901699437494745], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.5877852522924731, -0.8090169943749475], 'a6': [1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [-0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8265779462367888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [3, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]], [5, [[1.0, 0], [-0.5877852522924731, 0.8090169943749475]]], [61, [[1.0, 0], [-0.5877852522924731, 0.8090169943749475]]]], 'bad_primes': [2, 3, 5, 61], 'central_character': '3660.1619', 'coefficient_field': 'CDF', 'conductor': 3660, 'conductor_radical': 1830, 'conjugate': 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[-0.6909830056250525, 0.9510565162951535], [-0.30901699437494745, -0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-3660-3660.1619-c0-0-6', 'leading_term': '1.521537228487470444881957855218', '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/3660/1/eb/a/1619/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5215372284874704, 1.5968162919769904, 1.6847707835311283, 1.785256440008127, 1.896564487352694, 2.0157208920325056, 2.138848733241895, 2.261509599629656, 2.3789845191871253, 2.4864906919998058, 2.579347992736981, 2.6531129035977647, 2.7036942609107095, 2.7274599463519693, 2.7213388188733685, 2.6829185073088393, 2.6105371690802643, 2.5033657474358146, 2.3614764009089377, 2.1858924615103805, 1.978615385741492, 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'3.26058726329384025474244537767996', '3.93503453650663346614358492370089', '4.96607640785476144315092049494488', '5.57143467936764735866387589094345', '6.24507424768825204877035825519686', '7.50553596558390666613179213053933', '8.205459637866006793097278293740436', '9.278239287051131795687247433663042'], 'prelabel': '2-3660-3660.1619-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3515095065284553, 'root_angle': 0.24210489622318815, 'root_number': '0.72442599944921513747316084559991 + 0.68935257403015893093442082122871*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12105244811159407', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58185581029134552317334601405', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64710367730872582352376753735', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26058726329384025474244537768', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8265779462367888, 'bad_primes': [2, 3, 5, 61], 'central_character': '3660.1619', 'conductor': 3660, 'conductor_radical': 1830, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3660/1/eb/a/1619/1'], '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': '2-3660-3660.1619-c0-0-6', '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': '2-3660-3660.1619-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3515095065284553, 'root_angle': 0.12105244811159407, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58185581029134552317334601405', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2005240467390336332094882254374', 'Lhash_array': ['2005240467390336332094882254374'], 'label': '2-3660-3660.1619-c0-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3660/1/eb/a/1619/1'}