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lfunc_lfunctions • Show schema
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{'Lhash': '1137407159609233748005906274245', 'a10': [0.41421356237309503, 0.0], 'a2': [-0.41421356237309503, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.82842712474619, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.8284271247461901, 0.0], 'a8': [1.5857864376269049, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1137407159609233748005906274245', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.41421356237309503, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.8284271247461901, 0], [7.0, 0]], [[1.0, 0], [0.585786437626905, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [17.0, 0]], 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0], [-3.1715728752538097, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-585-1.1-c1-0-1', '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/585/2/a/m/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8877276736112727, 0.8756477789708882, 0.8376998656731532, 0.7691289958892998, 0.663136995111935, 0.5122713030337874, 0.3099439418171951, 0.05190171089068293, -0.2624583756582773, -0.62900578185935, -1.0381097210708252, -1.4742904780104886, -1.9163963917438107, -2.338398423228834, -2.7108534461999882, -3.003023296943695, -3.1855547166487703, -3.233534375752099, -3.129644747213137, -2.867074256101583, -2.4517930681903763, -1.9038070262012718, -1.25705605926915, -0.5577336176858243, 0.13903354981137378, 0.7740032500619431, 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'7.931217069701776126282701574024168', '9.094636004158736703950196942447005', '9.714286165109304329331025621074570', '10.49217856516854857244707613659034'], 'prelabel': '2-585-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.897256041534199990641944032128', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.97450618779523508374006928154', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08089846690771216958976744620', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/a/m/1/1'], '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': '2-585-1.1-c1-0-1', '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': '2-585-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.897256041534199990641944032128', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1137407159609233748005906274245', 'Lhash_array': ['1137407159609233748005906274245'], 'label': '2-585-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/m/1/1'}