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lfunc_lfunctions • Show schema
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{'Lhash': '1229133642588873947002352292670', 'a10': [-0.14231483827328514, 0.9898214418809327], 'a2': [0.41541501300188644, 0.9096319953545183], 'a3': [0.9594929736144974, -0.28173255684142967], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [0.8412535328311812, 0.5406408174555976], 'a6': [0.6548607339452851, 0.7557495743542583], 'a7': [0.09031976297094056, 0.6281877497732604], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [0.8412535328311812, -0.5406408174555976], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.50967773946835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.41541501300188644, -0.9096319953545183]]], [3, [[1.0, 0], [-0.9594929736144974, 0.28173255684142967]]], [5, [[1.0, 0], [-0.8412535328311812, -0.5406408174555976]]], [23, [[1.0, 0], [-4.65689685821179, -1.1459981029553041]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.211', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': '2479503340733640667617806757067', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [-0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [-0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [-0.09031976297094056, -0.6281877497732604], [-6.7164508153014815, 1.9721278978900079]], [[1.0, 0], [1.9287030107521124, -4.223270496265729], [-7.2034680733981356, -8.313245317896842]], [[1.0, 0], [0.5803057634077017, -4.036115238841198], [-12.473408656988466, -3.662523238938586]], [[1.0, 0], [0.8214142327166453, 0.947962558396427], [-2.4193522506458476, 16.826964511975856]], [[1.0, 0], [-0.992446778222601, 1.1453446379236614], [-2.7039819271924177, -18.80660739573772]], [[1.0, 0], [-4.65689685821179, -1.1459981029553041]], [[1.0, 0], [-3.0845488556349046, -3.5597591424923722], [-4.127130309925269, 28.70482181454705]], [[1.0, 0], [-4.341897720197419, -1.2748962002786581], 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'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/690/2/m/c/211/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.033502512816231, 1.8355559441994824, 1.6305146731249638, 1.4105285704829482, 1.1677426142327334, 0.8963681592178891, 0.5942919141548295, 0.26409949147348766, -0.08649059481476773, -0.44475782985944073, -0.7936611204983324, -1.113059685591351, -1.3814388139001268, -1.5780555489857435, -1.6853521504931595, -1.6914147433169573, -1.592195513432386, -1.3931832521858822, -1.1102111657082023, -0.7691411674843411, -0.404263351172268, -0.05539384436946979, 0.2361684676074481, 0.4324759757639033, 0.5040309336095989, 0.4344907618027527, 0.2242642572927163, -0.10767777629840669, -0.5243046350426774, -0.9736111327946427, -1.3942139396454276, -1.7229962400864005, -1.903955022381275, -1.897092598039939, -1.6860145894622216, -1.282902400499564, 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'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.5515814489045733, 'root_number': '-0.1613396148007654 - 0.9868989455339086*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.275790724452', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.969615477930258690204059001873', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.64651499140812107536862473817', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33849061820770487243269658967', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.50967773946835, 'bad_primes': [2, 3, 5, 23], 'central_character': '23.4', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/2/m/c/211/2'], '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': '2-690-23.4-c1-0-8', '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': '2-690-23.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.27579072445228664, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.969615477930258690204059001873', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1229133642588873947002352292670', 'Lhash_array': ['1229133642588873947002352292670'], 'label': '2-690-23.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/2/m/c/211/2'}