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lfunc_lfunctions • Show schema
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{'Lhash': '1551363554987406404779828242821', 'a10': [0.1183800147660272, -0.6713664255486461], 'a2': [-0.8936326403234123, -0.44879918020046217], 'a3': [0.6740146263517113, 1.5955263343060067], 'a4': [0.5971585917027862, 0.8021231927550437], 'a5': [0.19552045624345757, 0.6530838050666398], 'a6': [0.11374944066150645, -1.728311622581181], 'a7': [0.3860693552223818, 0.895009366126083], 'a8': [-0.17364817766693036, -0.984807753012208], 'a9': [-2.091408566927926, 2.1508161721031573], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8936326403234123, 0.44879918020046217]]], [3, [[1.0, 0], [-0.6740146263517113, -1.5955263343060067]]]], 'bad_primes': [2, 3], 'central_character': '162.13', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '3054971595842563022840703705793', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[47.17552874452011, 63.36773222764846]], [[1.0, 0], [-10.605791365718668, -5.326428619022964], [49.564163111331254, 66.57622499866864]], [[1.0, 0], [-1.4521735990678701, -8.235685731322429], [-83.63264324994584, 30.439792755984517]], [[1.0, 0], [-4.546397022439285, 15.186023620265784], [-81.04231770705483, -53.30237087286819]], [[1.0, 0], [8.686624237057314, -11.668161296019163], [-28.967126503820115, -96.75694074386438]], [[1.0, 0], [7.773069117074505, 1.8422512229134167], [92.04416195331146, 46.226315560647606]], [[1.0, 0], [4.726477027864912, 8.186498353069167], [-53.5, 92.66471820493493]], [[1.0, 0], [2.2250498434862003, -3.853899378291277], [-54.5, -94.39676901250381]], [[1.0, 0], [0.4769249982912471, -0.5055109652653882], [-6.570365666883768, -112.80882188465331]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-162-81.13-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 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1.1373550513119213, 'root_angle': -0.3484207368762596, 'root_number': '0.45840553505360415 - 0.8887431380507075*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.174210368438', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22381005831425234021513576589', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14157276157111112343335474881', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.36049618057641945530898091366', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.13', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/13/4'], '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': '2-162-81.13-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': '2-162-81.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': -0.1742103684381298, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22381005831425234021513576589', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1551363554987406404779828242821', 'Lhash_array': ['1551363554987406404779828242821'], 'label': '2-162-81.13-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/13/4'}