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lfunc_lfunctions • Show schema
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{'Lhash': '4160363558524228884219210852814', 'a10': [0.0, 0.0], 'a2': [2.161173025958438, -1.2477538283024623], 'a3': [-1.4134191976559758, -2.4481138627333876], 'a4': [2.113779232086901, -3.661173025958438], 'a5': [0.0, 0.0], 'a6': [-6.109286888691825, -3.5271984297428767], 'a7': [1.6499623486199286, 0.9526062061284629], 'a8': [0.0, -5.558889202880829], 'a9': [-2.4955076566049246, 4.322346051916876], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.595138065691614, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.4007200688618502, -3.322346051916876]]]], 'bad_primes': [5, 13], 'central_character': '325.101', 'coefficient_field': 'CDF', 'conductor': 325, 'conductor_radical': 65, 'conjugate': '1825256812635841719566759479985', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.161173025958438, 1.2477538283024623], [1.0, -1.7320508075688772]], [[1.0, 0], [1.4134191976559758, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-325-13.10-c1-0-18', '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/325/2/n/d/101/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.3944180705884848, 2.6371011640739046, 2.9178228916099918, 3.2398008143184236, 3.60215131830879, 3.9998397681638367, 4.423918295484377, 4.861903151350714, 5.2982346736781745, 5.714837806416152, 6.091831481034879, 6.408428362588814, 6.644038789172243, 6.779556699483664, 6.798768259982625, 6.68979012303452, 6.446417102296543, 6.06924171038582, 5.566403525490979, 4.953837310335964, 4.25491673802455, 3.4994354392678804, 2.7219268042623996, 1.9593942224414367, 1.2485976901753815, 0.6231126060826893, 0.11043267040901712, -0.2705783496969557, -0.5115798233536948, 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'11.32040997031961078290408665436081', '11.92191765621933106523598788726849'], 'prelabel': '2-325-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.610943222367447, 'root_angle': 0.7977517136353506, 'root_number': '-0.8048452037873856 + 0.5934847916673534*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.398875856818', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.28194816282593312327091037268', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17598626085751582157722544404', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.24854098412072861084782126689', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.595138065691614, 'bad_primes': [5, 13], 'central_character': '13.10', 'conductor': 325, 'conductor_radical': 65, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/325/2/n/d/101/4'], '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': '2-325-13.10-c1-0-18', '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': '2-325-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.610943222367447, 'root_angle': 0.3988758568176753, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.28194816282593312327091037268', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4160363558524228884219210852814', 'Lhash_array': ['4160363558524228884219210852814'], 'label': '2-325-13.10-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/325/2/n/d/101/4'}