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lfunc_lfunctions • Show schema
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{'Lhash': '1688746894017439017458209993954', 'a10': [8.652240121982926, 0.36263630498183624], 'a2': [0.2510259330024097, 2.388352214046187], 'a3': [0.4407427725097322, 2.3104545255448183], 'a4': [-3.6849170778319817, 0.7832533041031113], 'a5': [0.5267753212786517, -3.5673154928193287], 'a6': [-5.407541315854675, 1.6326329794830017], 'a7': [-2.363834655807786, 2.4138684749506494], 'a8': [-1.3114809881550362, -4.036323446563088], 'a9': [-2.354616465426211, 0.9322586086385283], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2057410705213343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[151, [[1.0, 0], [9.042547724454439, -8.320596772525624]]]], 'bad_primes': [151], 'central_character': '151.103', 'coefficient_field': 'CDF', 'conductor': 151, 'conductor_radical': 151, 'conjugate': '4899931998753403257072900540941', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2510259330024097, -2.388352214046187], [-1.9562952014676114, 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[-14.803123852272245, 77.6006928075664]], [[1.0, 0], [-0.15146422244436522, 2.4074548758831527], [-82.34552020910166, -10.402658385837253]], [[1.0, 0], [0.07930108722501814, -0.039365401564484225], [53.809321222751365, -70.89116270415347]], [[1.0, 0], [-2.2605305175624686, 1.7916744105871854], [22.150034400733606, -94.43715357869655]], [[1.0, 0], [2.389136841330523, -12.524293922655465], [-93.90742507471339, -37.18057982115248]], [[1.0, 0], [-1.8766573721955913, -2.7001560927414796], [-35.902920874146965, 96.54004491766483]], [[1.0, 0], [10.570758976775053, 5.811323924690572], [57.33346706275264, 90.34308802871561]], [[1.0, 0], [2.804262040455288, -5.36405854781546], [-62.207778877603054, -89.50526379557374]], [[1.0, 0], [-12.302562635857624, -2.614990413607981], [103.2306367136139, 45.96124066756542]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-151-151.103-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'rational': False, 'root_analytic_conductor': 1.0980624164961363, 'root_angle': -0.9790817453059945, 'root_number': '-0.9978414389358482 - 0.06566934400796069*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.489540872653', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33218640350376902902463757004', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96097909159327351878519471936', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60526878242936867321884530123', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2057410705213343, 'bad_primes': [151], 'central_character': '151.103', 'conductor': 151, 'conductor_radical': 151, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/151/2/k/a/103/10'], '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': '2-151-151.103-c1-0-0', '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': '2-151-151.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0980624164961363, 'root_angle': -0.4895408726529972, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33218640350376902902463757004', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1688746894017439017458209993954', 'Lhash_array': ['1688746894017439017458209993954'], 'label': '2-151-151.103-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/151/2/k/a/103/10'}