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lfunc_lfunctions • Show schema
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{'Lhash': '723664052637874444602697264105', 'a10': [-2.6303646267589302, 1.3945310661436137], 'a2': [0.7891595669121392, 1.000115292248396], 'a3': [-0.30406754400152225, 1.7051518784802961], 'a4': [0.08767713540848132, -0.3666594351443429], 'a5': [-0.41964518163268094, 2.2989325678602586], 'a6': [-1.945306280610502, 1.0415343173085965], 'a7': [-2.0768848460551648, 1.1496026091442466], 'a8': [2.748343422241873, -1.2715190664403264], 'a9': [-2.815085857369765, -1.0369626876781717], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.240056347329991, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.30406754400152225, -1.7051518784802961]]], [59, [[1.0, 0], [-3.9945876977141057, -6.560736934618787]]]], 'bad_primes': [3, 59], 'central_character': '531.128', 'coefficient_field': 'CDF', 'conductor': 531, 'conductor_radical': 177, 'conjugate': '3442494927073558598996713407472', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-53.283931071100604, -58.325146288802394]], [[1.0, 0], [-3.162486684459123, 15.713468986893679], [-76.53785048485246, -32.10852601970965]], [[1.0, 0], [0.7193170082972186, 1.8053495572827765], [-64.61359878115864, 61.20525183795467]], [[1.0, 0], [-4.9663035399029685, -11.838294836896536], [-67.96737640111422, 69.20574936484151]], [[1.0, 0], [-0.08631051023604214, -4.779867571551974], [-100.93415763435738, 3.6463437362235784]], [[1.0, 0], [-3.1686142086151765, 10.661708591155643], [-86.28164240888637, -56.25369484065079]], [[1.0, 0], [-9.51165940934833, -0.5157071882775394], [106.37276141551648, 11.568734971361769]], [[1.0, 0], [0.7722168266147653, -3.5082164115069667], [-98.92572074413432, -45.76791207006884]], [[1.0, 0], [-12.436687270404502, -2.27018224086292], [105.71238545959291, 39.923571489064564]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-531-531.128-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], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/531/2/p/a/128/42', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.202445928696848, 0.9298047756076542, 0.6678029575957132, 0.4091280227919806, 0.148903026521732, -0.11422383266720196, -0.3776114452736923, -0.6347122585819972, -0.8756053240214433, -1.0878896164670786, -1.2578786088056368, -1.372041994751898, -1.418620353739799, -1.3893028243369236, -1.2808185382423711, -1.09626076206479, -0.8459476818193511, -0.547632718046036, -0.22591473506496104, 0.08923429562646641, 0.3648126106406003, 0.5678780530652598, 0.6691380193567358, 0.6466822392280831, 0.4894149334324501, 0.1997015282125366, -0.2052367973876257, -0.6935606201277694, -1.2209053987627472, -1.734337643255459, -2.1779263610542183, -2.4994185518763063, -2.6572736995765798, -2.627148394507362, -2.406865223753858, -2.0189765362532386, 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'rational': False, 'root_analytic_conductor': 2.0591397104931928, 'root_angle': 0.9535635275647905, 'root_number': '-0.9893777180811086 + 0.14536757191553543*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.476781763782', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57087027963981957043072093371', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33857889237102002453709025363', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19055901642828819017854848798', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.240056347329991, 'bad_primes': [3, 59], 'central_character': '531.128', 'conductor': 531, 'conductor_radical': 177, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/531/2/p/a/128/42'], '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': '2-531-531.128-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': '2-531-531.128-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0591397104931928, 'root_angle': 0.47678176378239523, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57087027963981957043072093371', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '723664052637874444602697264105', 'Lhash_array': ['723664052637874444602697264105'], 'label': '2-531-531.128-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/531/2/p/a/128/42'}