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lfunc_lfunctions • Show schema
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{'Lhash': '1765518071773452544712700264896,2264898148196713325743838609117', 'a10': -4, 'a2': 2, 'a3': -2, 'a4': 3, 'a5': -2, 'a6': -4, 'a7': 0, 'a8': 4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 666.8593506110423, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, 2, 1]], [7, [1]], [11, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '3234.1', 'coefficient_field': '1.1.1.1', 'conductor': 10458756, 'conductor_radical': 462, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 2, 1], [1, 2, 6, 10, 25], [1], [1, 2, 1], [1, 0, 26, 0, 169], [1, 6, 38, 102, 289], [1, 2, -6, 38, 361], [1, -4, 30, -92, 529], [1, 0, 38, 0, 841], [1, 10, 82, 310, 961], [1, 4, -2, 148, 1369], [1, 6, 86, 246, 1681], [1, -4, 70, -172, 1849], [1, 6, 58, 282, 2209], [1, 12, 142, 636, 2809], [1, 12, 134, 708, 3481], [1, 0, 122, 0, 3721], [1, -4, -42, -268, 4489], [1, -4, 126, -284, 5041], [1, 18, 182, 1314, 5329], 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'group': 'GL2', 'index': 6, 'label': '4-3234e2-1.1-c1e2-0-6', 'load_key': 'CMFs-workshop', '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': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/3234/2/a/bb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [2.537437467909742e-119, 0.01049182302833881, 0.04193842563670832, 0.09425238596565956, 0.16728394302386346, 0.2608168600316005, 0.37455947492468383, 0.5081383399228695, 0.6610849597397663, 0.8328277257737119, 1.0226764738153413, 1.229813085844456, 1.4532763851376604, 1.691952580714864, 1.9445621794093186, 2.209653122521199, 2.4855899319497206, 2.7705536386837677, 3.0625328497378037, 3.3593340169429715, 3.6585751601065533, 3.9577078833800146, 4.254016325738575, 4.544649530294945, 4.826629819446107, 5.09689179598867, 5.352304541170449, 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-0.059951430086069415, 0.12170404290046845, 0.3448465919158263, 0.5994043198679093, 0.8715932545477968, 1.1479579297147293], 'positive_zeros': ['1.39274818428326106592629821662051', '1.78668960341985262097848069562085', '2.43139618248874823913260659252860', '2.96250317694907553878966878241062', '3.57322553777284998809167820847071', '3.74614230975455923025774579110562', '4.48494736581129919926470525921095', '4.48584054206085685239316898852201', '5.08140986852376064045951094601822', '5.20488699111769931025085260878142', '5.86755441476510750574776400246224', '6.06269675782315864237222366730704', '6.51425790032642295735257257158219', '6.87453239831790004284162762187287', '7.25495299417794870485325880886044', '7.45554471439769903633781626731444', '7.937319973966220905190776043721086', '8.308395201887522467306379368115719'], 'prelabel': '4-3234e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.081694600591627, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 670262897598752193, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39274818428326106592629821662', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78668960341985262097848069562', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.43139618248874823913260659253', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 666.8593506110423, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 10458756, 'conductor_radical': 462, 'degree': 4, 'dirichlet_coefficients': [1, 2, -2, 3, -2, -4, 0, 4, 3, -4, -2, -6, 0, 0, 4, 5, -6, 6, -2, -6, 0, -4, 4, -8, -2, 0, -4, 0, 0, 8, -10, 6, 4, -12, 0, 9, -4, -4, 0, -8, -6, 0, 4, -6, -6, 8, -6, -10, 0, -4, 12, 0, -12, -8, 4, 0, 4, 0, -12, 12, 0, -20, 0, 7, 0, 8, 4, -18, -8, 0, 4, 12, -18, -8, 4, -6, 0, 0, -4, -10, 5, -12, -2, 0, 12, 8, 0, -8, -4, -12, 0, 12, 20, -12, 4, -12, 0, 0, -6, -6], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 0, 26, 0, 169], 'euler17': [1, 6, 38, 102, 289], 'euler19': [1, 2, -6, 38, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -4, 30, -92, 529], 'euler29': [1, 0, 38, 0, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 10, 82, 310, 961], 'euler37': [1, 4, -2, 148, 1369], 'euler41': [1, 6, 86, 246, 1681], 'euler43': [1, -4, 70, -172, 1849], 'euler47': [1, 6, 58, 282, 2209], 'euler5': [1, 2, 6, 10, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 12, 134, 708, 3481], 'euler61': [1, 0, 122, 0, 3721], 'euler67': [1, -4, -42, -268, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -4, 126, -284, 5041], 'euler73': [1, 18, 182, 1314, 5329], 'euler79': [1, 4, -18, 316, 6241], 'euler83': [1, 2, 162, 166, 6889], 'euler89': [1, 4, 162, 356, 7921], 'euler97': [1, 0, 194, 0, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, 2, 6, 10, 25], [1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, 26, 0, 169], [1, 6, 38, 102, 289], [1, 2, -6, 38, 361], [1, -4, 30, -92, 529], [1, 0, 38, 0, 841], [1, 10, 82, 310, 961], [1, 4, -2, 148, 1369], [1, 6, 86, 246, 1681], [1, -4, 70, -172, 1849], [1, 6, 58, 282, 2209], [1, 12, 142, 636, 2809], [1, 12, 134, 708, 3481], [1, 0, 122, 0, 3721], [1, -4, -42, -268, 4489], [1, -4, 126, -284, 5041], [1, 18, 182, 1314, 5329], [1, 4, -18, 316, 6241], [1, 2, 162, 166, 6889], [1, 4, 162, 356, 7921], [1, 0, 194, 0, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3234/2/a/bb'], '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': '4-3234e2-1.1-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': 2, 'prelabel': '4-3234e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.081694600591627, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 670262897598752193, 'z1': {'__RealLiteral__': 0, 'data': '1.39274818428326106592629821662', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1765518071773452544712700264896,2264898148196713325743838609117', 'Lhash_array': ['1765518071773452544712700264896', '2264898148196713325743838609117'], 'label': '4-3234e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3234/2/a/bb'}