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lfunc_lfunctions • Show schema
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{'Lhash': '1340274388172985111788011454510', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.3437371808914098, 0], 'a6': [0, 0], 'a7': [2.1432372443592054, -1.5513007814062236], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.1100711784264, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.1432372443592054, 1.5513007814062236]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.541', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '1431757343442584424131121122713', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3437371808914098, 0], [5.0, 0]], [[1.0, 0], [-2.1432372443592054, 1.5513007814062236]], [[1.0, 0], [-4.9197594004188705, 0], [11.0, 0]], [[1.0, 0], [-0.9741621325516295, -1.6872983083890696], [-6.5, 11.258330249197702]], [[1.0, 0], 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7.2967310547517945], [-33.5, -58.023702053557386]], [[1.0, 0], [5.088884552913119, 0], [71.0, 0]], [[1.0, 0], [-4.584159619595618, -7.939997371145228], [-36.5, 63.21985447626402]], [[1.0, 0], [2.246009395980467, 3.890202388115254], [-39.5, 68.41600689897065]], [[1.0, 0], [-4.629656154424217, 8.018799681036688], [-41.5, -71.88010851410841]], [[1.0, 0], [-3.5425261936193864, 6.135835354492359], [-44.5, -77.07626093681505]], [[1.0, 0], [1.312312356166781, -2.2729916762812894], [-48.5, -84.00446416709055]], [[1.0, 0], [-15.705382713893295, 0], [101.0, 0]], [[1.0, 0], [7.742779961860736, 0], [103.0, 0]], [[1.0, 0], [6.129521985094719, -10.616643504294496], [-53.5, -92.66471820493493]], [[1.0, 0], [-4.893419096086787, -8.475650497150086], [-54.5, 94.39676901250381]], [[1.0, 0], [-2.5466412606175943, -4.410912052040928], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-2268-63.16-c1-0-18', 'leading_term': '2.3313688084417376473898334515316117687040742757024359020', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2268/2/l/n/541/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.3313688084417374, 2.3236708323465045, 2.3070404702813923, 2.2812277321106067, 2.2458591605161553, 2.2004636278186784, 2.1445062270631112, 2.0774283709829007, 1.9986920269951158, 1.907825997164986, 1.8044722630453611, 1.6884306103268367, 1.559699982460631, 1.4185152501384637, 1.265378301818898, 1.1010825491516152, 0.926730100142987, 0.7437409889334734, 0.5538539741731273, 0.3591185388756696, 0.1618778527823356, -0.0352573991130373, -0.22944425663068027, -0.4176515454820193, -0.5967123094803077, -0.7633839447534777, -0.9144151354871751, -1.0466184536837186, -1.1569472502329647, 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'8.505731136006064067772316524713547', '8.850101280158688940309017789866456'], 'prelabel': '2-2268-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.0026188822323353583, 'root_number': '0.9999661546321715091555010022601390528459301952054835889381 + 0.00822736836102883162714463480678450139669403591442004484*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0013094411161676792', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05729006709867879411382822688', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06907201367401830813800157370', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26213685880434849726955723024', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.1100711784264, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/l/n/541/5'], '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': '2-2268-63.16-c1-0-18', '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': '2-2268-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.0013094411161676792, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05729006709867879411382822688', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1340274388172985111788011454510', 'Lhash_array': ['1340274388172985111788011454510'], 'label': '2-2268-63.16-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/l/n/541/5'}