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lfunc_lfunctions • Show schema
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{'Lhash': '748797674201299567362433224581', 'a10': [0.2853118920940576, 0.4941746931105168], 'a2': [-0.2508929657404744, 0.4345593639241394], 'a3': [0, 0], 'a4': [0.8741054394838983, 1.5139950323584344], 'a5': [0.5685928484523284, -0.9848317023397436], 'a6': [0, 0], 'a7': [0.6301006433091908, 2.5696251048161374], 'a8': [-1.8807994872898819, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.558093121947266, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.6301006433091908, -2.5696251048161374]]], [19, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 7, 19], 'central_character': '1197.856', 'coefficient_field': 'CDF', 'conductor': 1197, 'conductor_radical': 399, 'conjugate': '2355490803366690571272609379039', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2508929657404744, -0.4345593639241394], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], 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[-29.5, 51.09549882328188]], [[1.0, 0], [-1.8238152942198753, 3.1589407532100044], [-30.5, -52.827549630850754]], [[1.0, 0], [-3.9771294319314956, -6.888590244382898], [-33.5, 58.023702053557386]], [[1.0, 0], [8.243129664054468, 0], [71.0, 0]], [[1.0, 0], [-2.4234059619321293, -4.197462253431777], [-36.5, 63.21985447626402]], [[1.0, 0], [0.8601569000678327, -1.4898354533984317], [-39.5, -68.41600689897065]], [[1.0, 0], [-15.262747427036015, 0], [83.0, 0]], [[1.0, 0], [3.4678814489204135, -6.00654686415573], [-44.5, -77.07626093681505]], [[1.0, 0], [17.672684531132834, 0], [97.0, 0]], [[1.0, 0], [-0.44153176181908316, -0.7647554446260522], [-50.5, 87.4685657822283]], [[1.0, 0], [-3.4887945680488466, 6.042769449030917], [-51.5, -89.20061658979718]], [[1.0, 0], [7.8776170053485535, -13.644432895832281], [-53.5, -92.66471820493493]], [[1.0, 0], [8.72637208106669, 15.114519810158066], [-54.5, 94.39676901250381]], [[1.0, 0], [-11.37953334938016, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-1197-7.2-c1-0-11', 'leading_term': '1.376756971694081294848436930885284029291948816543305949', '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/1197/2/j/m/856/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.3767569716940813, 1.2481740824757572, 1.1183285536863088, 0.9869244837554644, 0.8536572281593683, 0.7182773768360515, 0.5806507129315458, 0.4408109976462894, 0.29900322919235356, 0.15571586801670986, 0.011701275861617509, -0.13201579153836432, -0.27414138757499334, -0.4131267702292987, -0.5471933453981401, -0.6743674338797492, -0.7925240757275409, -0.8994390101188612, -0.992847862195147, -1.0705114245965996, -1.1302857436854008, -1.1701955179325887, -1.1885091016405316, -1.1838131961005685, -1.1550851181837554, 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'6.76908475613732821206065854352750', '7.75624352352403114552137827949917', '8.728068354002849542721868717999597', '9.761502479495924487067664883941141'], 'prelabel': '2-1197-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.091616587151011, 'root_angle': -0.7633824603299746, 'root_number': '-0.73620154536691535383406874580284181537223567618668086406 - 0.6767623545967710474595276257360715576246143370976289904*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3816912301649873', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59069721109782545474897007936', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90768739251185333763340330284', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97339106988296830876447073524', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.558093121947266, 'bad_primes': [3, 7, 19], 'central_character': '7.2', 'conductor': 1197, 'conductor_radical': 399, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1197/2/j/m/856/4'], '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': '2-1197-7.2-c1-0-11', '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': '2-1197-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.091616587151011, 'root_angle': -0.3816912301649873, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59069721109782545474897007936', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '748797674201299567362433224581', 'Lhash_array': ['748797674201299567362433224581'], 'label': '2-1197-7.2-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1197/2/j/m/856/4'}