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lfunc_lfunctions • Show schema
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{'Lhash': '3060372369614594790523041138243', 'a10': [-0.4655484293845489, 2.1870675938108497], 'a2': [-0.9096319953545183, 0.41541501300188644], 'a3': [-0.7686803204647266, -2.6178847581920186], 'a4': [0.6548607339452851, -0.7557495743542583], 'a5': [1.3320184596741678, -1.7960308524875783], 'a6': [1.7867248445558574, 2.061990390882238], 'a7': [1.2704646411820104, -0.18266523869008536], 'a8': [-0.28173255684142967, 0.9594929736144974], 'a9': [-3.7386905736107847, 2.402710537366735], '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], [-1.3320184596741678, 1.7960308524875783]]], [23, [[1.0, 0], [2.146808405284414, 4.288497833857467]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.119', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '1186271572205487069732020133967', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9096319953545183, -0.41541501300188644]], [[1.0, 0], [0.7686803204647266, 2.6178847581920186], [-2.5237605984935434, 1.6219224523667928]], [[1.0, 0], [-1.3320184596741678, 1.7960308524875783]], [[1.0, 0], [-1.2704646411820104, 0.18266523869008536], [6.7164508153014815, -1.9721278978900079]], [[1.0, 0], [-1.0394582479200076, 2.2760960739252205], [-7.2034680733981356, -8.313245317896842]], [[1.0, 0], [1.0203811586746272, 0.14670866221885207], [12.473408656988466, 3.662523238938586]], [[1.0, 0], [3.9828150963003943, -3.4511289263512657], [2.4193522506458476, -16.826964511975856]], [[1.0, 0], [-0.5402569900404243, 0.623489803404639], [-2.7039819271924177, -18.80660739573772]], [[1.0, 0], [2.146808405284414, 4.288497833857467]], [[1.0, 0], [-1.1156842042513224, -1.287568209192942], [-4.127130309925269, 28.70482181454705]], [[1.0, 0], [-7.725635203938568, -2.268451170653665], [26.078859517766617, 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[-75.7999449155453, -22.256871990472945]], [[1.0, 0], [-2.4128705570561904, -3.754499872837606], [-34.479446079156574, 75.49945561442503]], [[1.0, 0], [-6.626624187666683, 1.9457524202451213], [74.87156442197512, -48.11703275354819]], [[1.0, 0], [-8.575908664940874, 13.344374358511269], [-40.295256261182985, -88.23430354938829]], [[1.0, 0], [-10.563624604776365, 6.788829310945004], [41.956916313190526, -91.87283153080635]], [[1.0, 0], [5.372373931001642, 2.4534809657044203], [67.45065559636436, 77.84220615848861]], [[1.0, 0], [-0.03663464046234871, 0.12476612752391678], [-90.01412801293638, -57.84856746774894]], [[1.0, 0], [3.3346891462606827, 3.848436426638527], [-15.51231737178808, 107.89053716502167]], [[1.0, 0], [13.700029536335462, -6.256593850071145], [73.99926293581721, -85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-230-115.4-c1-0-9', '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/119/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8391753180253183, 0.9472596326106411, 1.0650615682979478, 1.1935469609946914, 1.3316393953166585, 1.4761824923491231, 1.6220687468211206, 1.7624660087522648, 1.8891120403846484, 1.9926817344940315, 2.063246066023043, 2.0908387310764853, 2.06613266798021, 1.9812100037394056, 1.830389011587317, 1.611052696995029, 1.3244075231697872, 0.9760894122281151, 0.5765294310372115, 0.1409952845100686, -0.31076171340847863, -0.7553004613763585, -1.1667367150838825, -1.5184117336947671, -1.7849035712311971, -1.944251680205841, -1.9802194289657669, -1.8843830180207042, -1.6578152473685528, -1.3121341189915188, -0.8697133636844171, -0.3629063805419358, 0.16778447898327153, 0.676559522333552, 1.1160453999997573, 1.4416250214572863, 1.6160024417842016, 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'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.6542741704499744, 'root_number': '-0.4659133833791944 + 0.8848303335601418*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.327137085225', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.41420811780754217030098312964', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.96044962960672350311802633457', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.10604684756572346310881482470', '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': '115.4', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/119/1'], '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': '2-230-115.4-c1-0-9', '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': '2-230-115.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.3271370852249872, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.41420811780754217030098312964', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3060372369614594790523041138243', 'Lhash_array': ['3060372369614594790523041138243'], 'label': '2-230-115.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/119/1'}