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lfunc_lfunctions • Show schema
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{'Lhash': '1182425524180858942463222346097,1342664345640641172003452634529', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 167.334019432485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1', 'coefficient_field': '1.1.1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, 1], [1, 2, 12, 14, 49], [1, 0, 19, 0, 121], [1, -4, 18, -52, 169], [1, -6, 40, -102, 289], [1, 2, 27, 38, 361], [1, 0, 34, 0, 529], [1, -12, 91, -348, 841], [1, 2, 15, 62, 961], [1, 2, 48, 74, 1369], [1, -12, 91, -492, 1681], [1, -10, 108, -430, 1849], [1, -6, 100, -282, 2209], [1, -18, 184, -954, 2809], [1, -12, 151, -708, 3481], [1, 8, 138, 488, 3721], [1, 8, 42, 536, 4489], [1, -12, 151, -852, 5041], [1, -10, 144, -730, 5329], [1, 8, 66, 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3.0404584822832947, 2.034793195271428, 0.9684560135308871], 'positive_zeros': ['0.932769269361741768893001655107222', '1.05917541111005367081889955986795', '2.28133981595779567490894279523712', '2.41348115153317722710224549997651', '3.36063942565164379448368190772875', '3.36814822788499321950969048032973', '4.25332733345007527784652413659030', '4.44869409446023593015511679431725', '5.32404448871283120218357725713887', '5.52591078784078507001710964718584', '6.09294264949099454088106951846363', '6.17415727635653731346811227810737', '6.75770147679716341484852819184855', '7.07640845622787122576374735369240', '7.69249645127935090704980304523049', '7.971780380203900873912842064568667', '8.571275760361312750626586983058862', '8.779425679424916360269217981607025', '9.326599821164464428207386751854023', '9.445793774507647510215971479441301'], 'prelabel': '4-1620e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2036205988414713103, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.932769269361741768893001655107', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.05917541111005367081889955987', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.28133981595779567490894279524', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 167.334019432485, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 12, 0, -2, 0, 0, 0, -4, 0, -2, 0, 0, 0, 12, 0, 10, 0, 0, 0, 6, 0, -8, 0, 0, 0, 18, 0, 0, 0, 0, 0, 12, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, 0, 12, 0, 10, 0, 0, 0, 0, 0, -8, 0, 0, 0, 6, 0, 12, 0, 0, 0, 0, 0, -8, 0, 0, 0, -4, 0, -2, 0, 0, 0], 'euler11': [1, 0, 19, 0, 121], 'euler13': [1, -4, 18, -52, 169], 'euler17': [1, -6, 40, -102, 289], 'euler19': [1, 2, 27, 38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 34, 0, 529], 'euler29': [1, -12, 91, -348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 2, 15, 62, 961], 'euler37': [1, 2, 48, 74, 1369], 'euler41': [1, -12, 91, -492, 1681], 'euler43': [1, -10, 108, -430, 1849], 'euler47': [1, -6, 100, -282, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -18, 184, -954, 2809], 'euler59': [1, -12, 151, -708, 3481], 'euler61': [1, 8, 138, 488, 3721], 'euler67': [1, 8, 42, 536, 4489], 'euler7': [1, 2, 12, 14, 49], 'euler71': [1, -12, 151, -852, 5041], 'euler73': [1, -10, 144, -730, 5329], 'euler79': [1, 8, 66, 632, 6241], 'euler83': [1, -6, 28, -498, 6889], 'euler89': [1, 0, 151, 0, 7921], 'euler97': [1, 2, 192, 194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 2, 12, 14, 49], [1, 0, 19, 0, 121], [1, -4, 18, -52, 169], [1, -6, 40, -102, 289], [1, 2, 27, 38, 361], [1, 0, 34, 0, 529], [1, -12, 91, -348, 841], [1, 2, 15, 62, 961], [1, 2, 48, 74, 1369], [1, -12, 91, -492, 1681], [1, -10, 108, -430, 1849], [1, -6, 100, -282, 2209], [1, -18, 184, -954, 2809], [1, -12, 151, -708, 3481], [1, 8, 138, 488, 3721], [1, 8, 42, 536, 4489], [1, -12, 151, -852, 5041], [1, -10, 144, -730, 5329], [1, 8, 66, 632, 6241], [1, -6, 28, -498, 6889], [1, 0, 151, 0, 7921], [1, 2, 192, 194, 9409]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/2/a/h'], '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': '4-1620e2-1.1-c1e2-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-1620e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2036205988414713103, 'z1': {'__RealLiteral__': 0, 'data': '0.932769269361741768893001655107', 'prec': 107}}
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{'Lhash': '1182425524180858942463222346097,1342664345640641172003452634529', 'Lhash_array': ['1182425524180858942463222346097', '1342664345640641172003452634529'], 'label': '4-1620e2-1.1-c1e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/2/a/h'}