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lfunc_lfunctions • Show schema
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{'A10': 3, 'A2': -1, 'A3': 0, 'A4': 0, 'A5': -3, 'A6': 0, 'A7': 1, 'A8': 1, 'A9': 0, 'Lhash': '2195301718482527102', 'a10': [0.030927835051546393, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.030927835051546393, 0.0], 'a6': [0.0, 0.0], 'a7': [0.010309278350515464, 0.0], 'a8': [0.010309278350515464, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 1.67334019432485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '26244.1', 'coefficient_field': '1.1.1.1', 'conductor': 26244, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, 1, 1], [1], [1, 3, 4, 15, 25], [1, -1, 3, -7, 49], [1, 0, 7, 0, 121], [1, 2, 18, 26, 169], [1, 3, 7, 51, 289], [1, 2, 3, 38, 361], [1, 0, 4, 0, 529], [1, 0, 25, 0, 841], [1, 8, 60, 248, 961], [1, -4, -3, -148, 1369], [1, 3, -23, 123, 1681], [1, 2, 69, 86, 1849], [1, 3, -47, 141, 2209], [1, 6, 52, 318, 2809], [1, 0, 49, 0, 3481], [1, 17, 174, 1037, 3721], [1, 14, 156, 938, 4489], [1, -6, 34, -426, 5041], [1, -4, -39, -292, 5329], [1, 5, 81, 395, 6241], [1, -6, 52, -498, 6889], [1, 12, 124, 1068, 7921], [1, -13, 207, -1261, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 6, 'label': '4-162e2-1.1-c1e2-0-6', 'leading_term': '1.07478391841', 'load_key': 'G2Q', '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': 1, 'origin': 'Genus2Curve/Q/26244/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.2061643027836494, 0.4378828793155251, 0.7090570882810975, 1.010039073900196, 1.297212169171554, 1.488823236736399, 1.474198037781637, 1.142655247438915, 0.4322444481842903, -0.6133136302599693, -1.80469066300757, -2.816549053674774, -3.270459660254341, 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1.781580373247714, 2.738360740040001, -1.789231200489837, -5.066371623125442, -2.481613503440552, 1.73242785979338, 1.728119058037148, -0.755007071419267, 0.006305452220386315, 3.840351750789151, 5.085953493024259, 2.1167432645174, -0.3823919633105205, 0.2360356993588796, 0.5743800612357124, -1.68538149980171, -2.805243558693222, 0.3149482547726132, 3.538632746331844, 1.524390580581701, -3.209232962738175, -3.977145304987611, -0.6083111423806368, 0.7683919182145597, -1.907552586006494, -3.797763866845218, -1.804154065034506, 0.7987025691945091, 0.7232736323399066, -0.3354968403989645, -0.07036689477805878, 0.3228881662344831, -0.3449279007369872, -0.38671648034057, 0.8822220242569069, 1.058121127080937, -0.3779140556444062, -0.0664819810732377, 2.772682695182412, 3.581595932059625, 0.4131886403402852, -1.611021716910752, 0.7767520853536981, 2.208751201958059, -2.136089691189864, -6.914176226141043, -4.846588001923048], 'positive_zeros': [1.771058434319486, 2.987549879553406, 3.854811488183389, 4.535223228110114, 4.970297753244827, 5.959308111578899, 6.717809778511767, 7.3045715499597, 7.776303528790322, 8.152116084601117, 8.776674013835875, 9.209991904641353, 9.727077702427913, 10.51776936951271, 10.87921045786509, 11.25420861606981, 11.87125134883027, 12.18695096202671, 12.85660073302681, 13.18783566876502, 13.86506041997157, 14.43497152621401, 14.9468167824379, 15.11251604735469, 15.78629025514914, 16.08303946237972, 16.67789616617047, 16.98029680372632, 17.41080132462384, 18.08731513765042, 18.28428757382008, 18.72280738989948, 19.19841395132881, 19.76812853140864, 19.82756213029451], 'prelabel': '4-162e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 2195301718482527102, 'z1': {'__RealLiteral__': 0, 'data': '1.77105843432', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.98754987955', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.85481148818', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.67334019432485, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 26244, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 0, -3, 0, 1, 1, 0, 3, 0, 0, -2, -1, 0, -1, -3, 0, -2, 0, 0, 0, 0, 0, 5, 2, 0, 0, 0, 0, -8, 0, 0, 3, -3, 0, 4, 2, 0, -3, -3, 0, -2, 0, 0, 0, -3, 0, -2, -5, 0, 0, -6, 0, 0, 1, 0, 0, 0, 0, -17, 8, 0, 1, 6, 0, -14, 0, 0, 3, 6, 0, 4, -4, 0, 0, 0, 0, -5, 3, 0, 3, 6, 0, 9, 2, 0, 0, -12, 0, -2, 0, 0, 3, 6, 0, 13, 2, 0, 0], 'euler11': [1, 0, 7, 0, 121], 'euler13': [1, 2, 18, 26, 169], 'euler17': [1, 3, 7, 51, 289], 'euler19': [1, 2, 3, 38, 361], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, 0, 4, 0, 529], 'euler29': [1, 0, 25, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 60, 248, 961], 'euler37': [1, -4, -3, -148, 1369], 'euler41': [1, 3, -23, 123, 1681], 'euler43': [1, 2, 69, 86, 1849], 'euler47': [1, 3, -47, 141, 2209], 'euler5': [1, 3, 4, 15, 25], 'euler53': [1, 6, 52, 318, 2809], 'euler59': [1, 0, 49, 0, 3481], 'euler61': [1, 17, 174, 1037, 3721], 'euler67': [1, 14, 156, 938, 4489], 'euler7': [1, -1, 3, -7, 49], 'euler71': [1, -6, 34, -426, 5041], 'euler73': [1, -4, -39, -292, 5329], 'euler79': [1, 5, 81, 395, 6241], 'euler83': [1, -6, 52, -498, 6889], 'euler89': [1, 12, 124, 1068, 7921], 'euler97': [1, -13, 207, -1261, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 3, 4, 15, 25], [1, -1, 3, -7, 49], [1, 0, 7, 0, 121], [1, 2, 18, 26, 169], [1, 3, 7, 51, 289], [1, 2, 3, 38, 361], [1, 0, 4, 0, 529], [1, 0, 25, 0, 841], [1, 8, 60, 248, 961], [1, -4, -3, -148, 1369], [1, 3, -23, 123, 1681], [1, 2, 69, 86, 1849], [1, 3, -47, 141, 2209], [1, 6, 52, 318, 2809], [1, 0, 49, 0, 3481], [1, 17, 174, 1037, 3721], [1, 14, 156, 938, 4489], [1, -6, 34, -426, 5041], [1, -4, -39, -292, 5329], [1, 5, 81, 395, 6241], [1, -6, 52, -498, 6889], [1, 12, 124, 1068, 7921], [1, -13, 207, -1261, 9409]], 'index': 6, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/26244/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-162e2-1.1-c1e2-0-6', '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': 1, 'prelabel': '4-162e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2195301718482527102, 'z1': {'__RealLiteral__': 0, 'data': '1.77105843432', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '2195301718482527102', 'Lhash_array': ['2195301718482527102'], 'label': '4-162e2-1.1-c1e2-0-6', 'type': 'G2Q', 'url': 'Genus2Curve/Q/26244/b'}