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lfunc_lfunctions • Show schema
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{'Lhash': '2451903996277448583527108299728', 'a10': [-0.04620034945720257, 0.3213304885841655], 'a2': [0.41541501300188644, 0.9096319953545183], 'a3': [0.9594929736144974, -0.28173255684142967], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [0.27310017472860126, 0.17551082515592487], 'a6': [0.6548607339452851, 0.7557495743542583], 'a7': [0.34615565990874586, 2.4075654974793896], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [0.8412535328311812, -0.5406408174555976], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, '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]]], [23, [[1.0, 0], [4.20014218955572, 2.31490941237753]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.73', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': '3286000341247104268716659927437', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [-0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [-0.27310017472860126, -0.17551082515592487], [2.0770750650094323, 4.548159976772592]], [[1.0, 0], [-0.34615565990874586, -2.4075654974793896], [-6.7164508153014815, 1.9721278978900079]], [[1.0, 0], [-1.4124481736251202, 3.092830086291631], [-7.2034680733981356, -8.313245317896842]], [[1.0, 0], [0.03833138300287168, -0.26660062473833357], [-12.473408656988466, -3.662523238938586]], [[1.0, 0], [3.174863297067927, 3.663987564098656], [-2.4193522506458476, 16.826964511975856]], [[1.0, 0], [2.635874564676674, -3.0419614080450468], [-2.7039819271924177, -18.80660739573772]], [[1.0, 0], [4.20014218955572, 2.31490941237753]], [[1.0, 0], [1.315846942490756, 1.5185683232395932], [-4.127130309925269, 28.70482181454705]], [[1.0, 0], [-9.120523427629193, -2.678027307816971], [26.078859517766617, 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[-75.7999449155453, -22.256871990472945]], [[1.0, 0], [0.8877686812848091, -0.5705342882139361], [34.479446079156574, -75.49945561442503]], [[1.0, 0], [-2.6298221971393247, 0.77218546879749], [74.87156442197512, -48.11703275354819]], [[1.0, 0], [11.447692918269327, 7.356985517177949], [40.295256261182985, 88.23430354938829]], [[1.0, 0], [-13.378359121861594, 8.597749346164427], [41.956916313190526, -91.87283153080635]], [[1.0, 0], [-5.804236434739217, 12.709504963455075], [-67.45065559636436, -77.84220615848861]], [[1.0, 0], [10.354707977029376, 3.0404165886960657], [90.01412801293638, 57.84856746774894]], [[1.0, 0], [10.712186185087502, 12.36252187699478], [-15.51231737178808, 107.89053716502167]], [[1.0, 0], [-8.29159849148085, -18.156068135289058], [-73.99926293581721, 85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-138-23.4-c1-0-2', '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/138/2/e/b/73/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4309508357868173, 1.395985979171705, 1.374305039040141, 1.3616316105943724, 1.3526428018875778, 1.3414730545100062, 1.3221510782623742, 1.288944254880226, 1.2366343331607068, 1.1607623227218804, 1.0578706884623446, 0.9257530659309547, 0.7637050833679916, 0.572757596113168, 0.35586583307681025, 0.1180240125457829, -0.13372553778247, -0.39041696284319743, -0.6414413032375403, -0.8749955162787117, -1.07870033170993, -1.2403719929510866, -1.3489159209956143, -1.3952927170645641, -1.3734902631679076, -1.2814218231005698, -1.1216609528060828, -0.9019216014407243, -0.6351976436056577, -0.3394913266904589, -0.03708508451056565, 0.24665475937990264, 0.4849124086482505, 0.6514191187026767, 0.7226891175654224, 0.6803295345403176, 0.5132254399749538, 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'root_analytic_conductor': 1.0497311788708907, 'root_angle': -0.2862278756852947, 'root_number': '0.6222275131708582 - 0.7828364592002659*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.143113937843', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93421120601844444960567385219', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.76564756702632490519309041234', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69564151398396659296988759820', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '23.4', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/e/b/73/1'], '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': '2-138-23.4-c1-0-2', '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': '2-138-23.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': -0.14311393784264734, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93421120601844444960567385219', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2451903996277448583527108299728', 'Lhash_array': ['2451903996277448583527108299728'], 'label': '2-138-23.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/e/b/73/1'}