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lfunc_lfunctions • Show schema
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{'Lhash': '1729223604255759316613138385752', 'a10': [-2.1823438148134353, 0.4872119394529883], 'a2': [0.9096319953545183, 0.41541501300188644], 'a3': [-0.03598438033781606, 0.1225515449158374], 'a4': [0.6548607339452851, 0.7557495743542583], 'a5': [-1.7827346046557992, 1.3497619528504763], 'a6': [-0.08364229531289738, 0.09652835450967337], 'a7': [0.2779408153159186, 0.039961856257694724], 'a8': [0.28173255684142967, 0.9594929736144974], 'a9': [2.5100365929605815, 1.6131025695603158], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9096319953545183, -0.41541501300188644]]], [5, [[1.0, 0], [1.7827346046557992, -1.3497619528504763]]], [23, [[1.0, 0], [0.9190720244779609, 4.706942384799498]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.29', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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[-75.7999449155453, 22.256871990472945]], [[1.0, 0], [6.836692873355163, -10.638101761645377], [-34.479446079156574, -75.49945561442503]], [[1.0, 0], [5.366008426945765, 1.575602235481807], [74.87156442197512, 48.11703275354819]], [[1.0, 0], [2.466138759177391, 3.8373868132519884], [-40.295256261182985, 88.23430354938829]], [[1.0, 0], [-1.619229981184752, -1.040615921968451], [41.956916313190526, 91.87283153080635]], [[1.0, 0], [13.765291811513615, -6.286398132495378], [67.45065559636436, -77.84220615848861]], [[1.0, 0], [2.0034095654929702, 6.822986391468066], [-90.01412801293638, 57.84856746774894]], [[1.0, 0], [-6.9654308284742905, 8.03853569307654], [-15.51231737178808, -107.89053716502167]], [[1.0, 0], [11.309334993507049, 5.164800234999873], [73.99926293581721, 85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-230-115.29-c1-0-4', '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/230/2/j/a/29/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6313686358345376, 1.5469188646038659, 1.4696462879056211, 1.3928054395893938, 1.3085506370962485, 1.20881951465836, 1.086103173850303, 0.9340687865177931, 0.7480624002534082, 0.52553021694137, 0.26637654781754755, -0.02675050259025837, -0.3482758977842332, -0.6896588585971, -1.039541933123182, -1.384124667494436, -1.7077843227940754, -1.9939455165301951, -2.2261752125842595, -2.389451041337753, -2.4715220117991668, -2.464254364163898, -2.3648350807138683, -2.176694982261795, -1.9100156096037149, -1.5817016365817624, -1.214734497278637, -0.8368726196438618, -0.4787264950363316, -0.17130799594794896, 0.056773880249996314, 0.18223260985834494, 0.18985058851710446, 0.07473830996458806, -0.15620136625058229, -0.4838681472586848, -0.8778014681873298, -1.2983273405308897, 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1.355197124587213, 'root_angle': -0.3665465876021876, 'root_number': '0.4070812395642492 - 0.9133919555124373*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.183273293801', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36411689778273897670276368372', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.71357402128797328941023911053', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17241738502015352792848156834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.29', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/29/10'], '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': '2-230-115.29-c1-0-4', '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': '2-230-115.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.1832732938010938, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36411689778273897670276368372', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1729223604255759316613138385752', 'Lhash_array': ['1729223604255759316613138385752'], 'label': '2-230-115.29-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/29/10'}