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lfunc_lfunctions • Show schema
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{'Lhash': '2645089115599909279998899615572', 'a10': [-3.0390846454485487, 0.8740506380060995], 'a2': [-0.5242611796436446, -1.3134497384820838], 'a3': [2.571960693554763, 0.6891547908025891], 'a4': [-1.4503004310373084, 1.3771814185985074], 'a5': [0.22262625967526686, -2.224957875669335], 'a6': [-0.44320896744677074, -3.739438203918937], 'a7': [1.0451388453414239, -0.2800441095876306], 'a8': [2.5691947889139004, 1.1828939667686447], 'a9': [3.5419712721512226, 2.04495806743843], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5242611796436446, 1.3134497384820838]]], [5, [[1.0, 0], [-0.22262625967526686, 2.224957875669335]]], [13, [[1.0, 0], [3.26752896094041, 1.524222585259674]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.3', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': 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[6.341270859555881, -6.341270859555881], [0, -103.0]], [[1.0, 0], [3.056387331396912, -11.406592808383133], [-92.66471820493493, -53.5]], [[1.0, 0], [0, 14.97457000809175], [-109.0, 0]], [[1.0, 0], [3.7499929348776444, -1.0048075785228805], [97.86087062764156, -56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-260-260.3-c1-0-27', '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/260/2/bj/c/3/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5951613087115928, 1.6607939006652943, 1.7368124543557262, 1.8208260712355864, 1.9077991469850735, 1.9905226793726682, 2.0602066043901233, 2.107103342769601, 2.121142819137863, 2.092597661440067, 2.0128000742702037, 1.8749132785099825, 1.674734370759477, 1.4114802004726752, 1.0884873259285313, 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['2.08660739412238997345147870416415', '3.46757591587227668818044542929963', '5.08309442939475310658101030196165', '6.60909987441765280520191395571732', '7.50774548195082812568048145725710', '7.927249054067070208129668300731008', '9.311258414580277252853711200580820', '9.652334570523891138642922183425405', '10.99094791180273421853300420138636', '12.35735328260408480888052218776050'], 'prelabel': '2-260-260.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.35307373486293653, 'root_number': '0.44536553133216444 + 0.8953488390014357*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176536867431', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08660739412238997345147870416', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46757591587227668818044542930', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.08309442939475310658101030196', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '260.3', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/bj/c/3/15'], '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': '2-260-260.3-c1-0-27', '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': '2-260-260.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.17653686743146826, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08660739412238997345147870416', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2645089115599909279998899615572', 'Lhash_array': ['2645089115599909279998899615572'], 'label': '2-260-260.3-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/bj/c/3/15'}