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lfunc_lfunctions • Show schema
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{'Lhash': '383493052051336248043839936160,2277426371625312263118805609855', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 439.0175435848064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [41, [1, 6, 41]]], 'bad_primes': [2, 41], 'central_character': '2624.1', 'coefficient_field': '1.1.1.1', 'conductor': 6885376, 'conductor_radical': 82, 'degree': 4, 'euler_factors': [[1], [1, 0, -4, 0, 9], [1, 0, 10, 0, 25], [1, 0, 4, 0, 49], [1, 0, -20, 0, 121], [1, 0, -26, 0, 169], [1, 0, -2, 0, 289], [1, 0, -20, 0, 361], [1, 0, 46, 0, 529], [1, 0, -26, 0, 841], [1, 16, 126, 496, 961], [1, 16, 138, 592, 1369], [1, 6, 41], [1, 8, 102, 344, 1849], [1, 0, -44, 0, 2209], [1, 0, -74, 0, 2809], [1, 24, 262, 1416, 3481], [1, 4, 126, 244, 3721], [1, 0, 28, 0, 4489], [1, 0, -92, 0, 5041], [1, 8, 162, 584, 5329], [1, 0, -140, 0, 6241], [1, -24, 310, -1992, 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1.2011905219254684, 0.8607489583413092, 0.5496426770705477, 0.2908277157949315], 'positive_zeros': ['0.30252267618718571088788787267343', '1.61005578564380831285356289469130', '1.79657262909454826687669165539629', '1.99358704231421364497479188934068', '3.23706577260673729092840060627064', '3.39467125770590920931157172520262', '3.72887269355348827472378854782399', '4.34065754937014080256948385058724', '4.73856801935362261965124357049474', '5.11587721543301209089770674059085', '5.58549645048709757072919856356216', '5.94341082922476311366489680633764', '6.46853478469199689626870616325513', '6.79778644123537583222602567556948', '7.24010372352042687131081395234785', '7.60803725656428188240656341309955', '7.70081597186566041226450183920955', '8.265164950013336515653916636109263', '8.866075227866857550836819381075486', '8.985134151867115640523445142303281'], 'prelabel': '4-2624e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.577416901526885, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1265745480710310, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30252267618718571088788787267', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61005578564380831285356289469', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.79657262909454826687669165540', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 439.0175435848064, 'bad_primes': [2, 41], 'central_character': '1.1', 'conductor': 6885376, 'conductor_radical': 82, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, -6, 0, -8, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -20, 0, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, -20, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, -26, 0, 841], 'euler3': [1, 0, -4, 0, 9], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 16, 138, 592, 1369], 'euler41': [1, 6, 41, 0, 0], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -44, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, -74, 0, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, 28, 0, 4489], 'euler7': [1, 0, 4, 0, 49], 'euler71': [1, 0, -92, 0, 5041], 'euler73': [1, 8, 162, 584, 5329], 'euler79': [1, 0, -140, 0, 6241], 'euler83': [1, -24, 310, -1992, 6889], 'euler89': [1, 0, -146, 0, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -4, 0, 9], [1, 0, 10, 0, 25], [1, 0, 4, 0, 49], [1, 0, -20, 0, 121], [1, 0, -26, 0, 169], [1, 0, -2, 0, 289], [1, 0, -20, 0, 361], [1, 0, 46, 0, 529], [1, 0, -26, 0, 841], [1, 16, 126, 496, 961], [1, 16, 138, 592, 1369], [1, 6, 41, 0, 0], [1, 8, 102, 344, 1849], [1, 0, -44, 0, 2209], [1, 0, -74, 0, 2809], [1, 24, 262, 1416, 3481], [1, 4, 126, 244, 3721], [1, 0, 28, 0, 4489], [1, 0, -92, 0, 5041], [1, 8, 162, 584, 5329], [1, 0, -140, 0, 6241], [1, -24, 310, -1992, 6889], [1, 0, -146, 0, 7921], [1, 0, 94, 0, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2624/2/d/f'], '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': '4-2624e2-1.1-c1e2-0-1', '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': '4-2624e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.577416901526885, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1265745480710310, 'z1': {'__RealLiteral__': 0, 'data': '0.30252267618718571088788787267', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '383493052051336248043839936160,2277426371625312263118805609855', 'Lhash_array': ['383493052051336248043839936160', '2277426371625312263118805609855'], 'factors': ['2-2624-41.40-c1-0-6', '2-2624-41.40-c1-0-76'], 'label': '4-2624e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2624/2/d/f'}