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lfunc_lfunctions • Show schema
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{'Lhash': '178991102346900969819013333970', 'a10': [0.41379779382224124, -1.7056977378790965], 'a2': [-0.4734400571120333, 1.367915209564518], 'a3': [-0.4582265217274104, -0.8888354486549235], 'a4': [-0.0749403433941188, -0.0589337374400784], 'a5': [-1.2070410231111843, 0.11525844291641292], 'a6': [1.4327943196320456, -0.206004722922384], 'a7': [0.6078314898329419, -2.574983665961294], 'a8': [-2.3193800862392577, 1.4905750726472895], 'a9': [-0.5800569095711982, 0.8145759520503357], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.4582265217274104, 0.8888354486549235]]], [7, [[1.0, 0], [-0.6078314898329419, 2.574983665961294]]], [23, [[1.0, 0], [1.8997121780580783, -4.403531950666173]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.10', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '2719212741720144455904467389218', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.4734400571120333, -1.367915209564518], [-1.572106189485575, -1.2363179724412103]], [[1.0, 0], [0.4582265217274104, 0.8888354486549235]], [[1.0, 0], [1.2070410231111843, -0.11525844291641292], [4.909643486313533, -0.946256221802051]], [[1.0, 0], [-0.6078314898329419, 2.574983665961294]], [[1.0, 0], [3.298388762691567, -1.1415834499592439], [8.646584042170662, -6.799748848426657]], [[1.0, 0], [-0.9820477770841439, -3.3445475823950237], [-10.936295926805355, 7.028330626922768]], [[1.0, 0], [3.3461538462907177, 1.33959792373411], [12.303478647786193, 11.731343195195905]], [[1.0, 0], [5.088384896764471, -2.037082021922513], [13.750946723996334, -13.111501218160127]], [[1.0, 0], [1.8997121780580783, -4.403531950666173]], [[1.0, 0], [0.31176451836843283, 2.1683698540708276], [-27.825296234820424, 8.170244148401462]], [[1.0, 0], [-8.479800876770382, 0.40394270159098644], [30.859629599765622, -2.9467373424296626]], 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[-3.7589713500756416, -78.91051979545763]], [[1.0, 0], [-3.80562922178437, -8.333165615695886], [-54.35344091745866, 62.72721467140344]], [[1.0, 0], [0.3755223155495058, -7.883183550789519], [-88.59700110900452, -8.459987854072256]], [[1.0, 0], [5.326031650555016, -11.662382547531275], [-63.52149119269265, -73.30770871236305]], [[1.0, 0], [0.10762391192834161, -1.1270885974003961], [-99.17479842353337, -19.11437568040143]], [[1.0, 0], [6.347234324379394, 1.2233291454710697], [95.62189710065547, 38.28123293301373]], [[1.0, 0], [5.350694602504634, -10.378899544496168], [-62.0660893241182, -87.15962686938592]], [[1.0, 0], [7.440000033846314, -18.58422164485175], [-78.88701015345265, -75.21861225155021]], [[1.0, 0], [-2.1615136154820584, 1.872962209574193], [16.08157672488122, -111.8498229325454]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-483-161.10-c1-0-2', '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/483/2/bf/a/10/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.22225123327619487, 0.025314747716425674, -0.16998104368133668, -0.36685755683191407, -0.5661583673345488, -0.7657406785114407, -0.9603527046804495, -1.141921354456992, -1.3001671455257031, -1.4234872868713189, -1.5000644518064568, -1.519153507511833, -1.4724744129347107, -1.355606113236145, -1.169243486122687, -0.9201558752017389, -0.6216785700879035, -0.2935831341343595, 0.038788077289613525, 0.3461731939506449, 0.5977911579397215, 0.7643526058341752, 0.8214368705519242, 0.7528944617688258, 0.5538635906863559, 0.2329594081665709, -0.18678147199306736, -0.668533107495893, -1.1640735481450413, -1.6179232812698823, -1.9729774181887334, -2.1771374920617164, -2.190232334278959, -1.9903637152668592, -1.5787549166009227, -0.9822443852256335, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.8520958919502212, 'root_number': '-0.893976460578674 + 0.44811392293838237*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.426047945975', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14119908302388306967912861411', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23514449224288884384576254803', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19734808698592897674329728984', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.10', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/bf/a/10/9'], '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': '2-483-161.10-c1-0-2', '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': '2-483-161.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.4260479459751106, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14119908302388306967912861411', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '178991102346900969819013333970', 'Lhash_array': ['178991102346900969819013333970'], 'label': '2-483-161.10-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/bf/a/10/9'}