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lfunc_lfunctions • Show schema
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{'Lhash': '1136014238454901856907371484532', 'a10': [-2.186140661634507, -1.2621688994810694], 'a2': [-0.5, 0.8660254037844386], 'a3': [-1.6861406616345072, 0.39614349569663065], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 2.5243377989621387], 'a6': [0.5, -1.6583123951777], 'a7': [0.5, -2.598076211353316], 'a8': [1.0, 0.0], 'a9': [2.686140661634507, -1.3359073118722466], '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], [1.6861406616345072, -0.39614349569663065]]], [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': '1436969755607524024720190356310', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], 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[-8.186140661634507, 4.7262705146188235], [29.5, -51.09549882328188]], [[1.0, 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', 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'9.633969688758369843260456658266635', '10.84963928336128222337997898997494'], 'prelabel': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.42755877344025967, 'root_number': '0.2256213894957462 - 0.9742150628080068*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21377938672', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.896157220491492238340477353492', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.13018686585542998227641143854', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00255217071665827496674906336', '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': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/e/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-c1-0-8', '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': -0.21377938672012983, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.896157220491492238340477353492', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1136014238454901856907371484532', 'Lhash_array': ['1136014238454901856907371484532'], 'label': '2-546-273.251-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/e/251/1'}