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lfunc_lfunctions • Show schema
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{'Lhash': '3448550837855057595590733132601', 'a10': [-2.186140661634507, -1.2621688994810694], 'a2': [0.5, -0.8660254037844386], 'a3': [-0.5, -1.6583123951777], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, -2.5243377989621387], 'a6': [-1.6861406616345072, -0.39614349569663065], 'a7': [0.5, -2.598076211353316], 'a8': [-1.0, 0.0], 'a9': [-2.5, 1.6583123951777], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0.5, 1.6583123951777]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]], [13, [[1.0, 0], [-3.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.251', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '997952976235728428791288117187', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 1.6583123951777]], 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0], [-4.5, 2.598076211353316], [30.5, -52.827549630850754]], [[1.0, 0], [7.116843969807043, 4.108911781748661], [33.5, 58.023702053557386]], [[1.0, 0], [-0.5584219849035215, -0.9672152499163598], [-35.5, 61.48780366869514]], [[1.0, 0], [-0.7445626465380286, 0], [73.0, 0]], [[1.0, 0], [-15.372281323269014, 0], [79.0, 0]], [[1.0, 0], [0, -5.0486755979242774], [-83.0, 0]], [[1.0, 0], [-10.80298463144155, -6.237106085014169], [44.5, 77.07626093681505]], [[1.0, 0], [-5.372281323269014, -9.305064204455293], [-48.5, 84.00446416709055]], [[1.0, 0], [1.6277186767309857, -2.819291448526848], [-50.5, -87.4685657822283]], [[1.0, 0], [0, 11.681925178635076], [-103.0, 0]], [[1.0, 0], [3.686140661634507, 2.128194303265508], [53.5, 92.66471820493493]], [[1.0, 0], [0, 19.8997487421324], [-109.0, 0]], [[1.0, 0], [-14.744562646538029, 8.512777213062032], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-546-273.251-c1-0-33', '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/546/2/q/g/251/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3966881714196047, 1.6702120334786685, 1.9728643452814145, 2.307627755395435, 2.673393678107383, 3.0642890728148355, 3.4695321868762403, 3.873714611925418, 4.257443632285988, 4.598330730376398, 4.8723342938459595, 5.055448834989908, 5.125689614230452, 5.065264401297139, 4.8627656345905175, 4.515167003194779, 4.029377728805124, 3.423103530933232, 2.724791416385491, 1.972498995540462, 1.2116267750537386, 0.49157757759370446, -0.13845063284404208, -0.6341900190664008, -0.9610751779070614, -1.0985094989106146, -1.043050468708552, -0.8099906365227183, -0.43294255151626476, 0.03875766697908694, 0.544749572554992, 1.020079495135131, 1.4027101315824417, 1.6412263574073356, 1.701722178767237, 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'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.9473216054509304, 'root_number': '-0.9863370848947569 - 0.16473965813158992*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.473660802725', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.72042693565101944041330524495', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.61527386605545495693374086724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.81948979405628088833365284234', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.251', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/g/251/1'], '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': '2-546-273.251-c1-0-33', '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': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.4736608027254652, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.72042693565101944041330524495', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3448550837855057595590733132601', 'Lhash_array': ['3448550837855057595590733132601'], 'label': '2-546-273.251-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/g/251/1'}