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lfunc_lfunctions • Show schema
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{'Lhash': '2368523760035199989466972716036', 'a10': [-0.09776447407574175, 2.2339297454505354], 'a2': [-0.21256528955297668, 0.9771468659711595], 'a3': [0.6279996984131503, -0.47011468565980047], 'a4': [-0.9096319953545183, -0.41541501300188644], 'a5': [2.203658783306645, -0.3793256737362708], 'a6': [0.32588015400711756, 0.7135780014156252], 'a7': [0.11936133472932757, -1.6688895273159117], 'a8': [0.599277666511347, -0.8005412409243604], 'a9': [-0.6718218669902944, 2.288015159215597], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.21256528955297668, -0.9771468659711595]]], [5, [[1.0, 0], [-2.203658783306645, 0.3793256737362708]]], [23, [[1.0, 0], [-2.5468769327731455, 4.0636704946769555]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.103', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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8.73370926208432]], [[1.0, 0], [5.704956906431688, 10.447848512795092], [-20.00371024585711, 31.126380714753704]], [[1.0, 0], [7.181903948476687, -2.1087972690114176], [34.49139484607843, -22.1662735156795]], [[1.0, 0], [3.0233797873673165, 4.0387625670325775], [-12.114499944181476, 41.25819786542339]], [[1.0, 0], [-2.2598364957582318, 2.2598364957582318], [0, -47.0]], [[1.0, 0], [4.533435011892412, 0.3242376712606172], [52.46053641968943, 7.542686428484113]], [[1.0, 0], [5.220494485484769, 4.523584221986412], [8.396575458123824, 58.39946507097503]], [[1.0, 0], [-3.124210683484855, 0.449193682152322], [58.52907139048434, -17.185685967327213]], [[1.0, 0], [-0.601490860192612, -0.1308463275203149], [60.94534368875273, 27.83280587112639]], [[1.0, 0], [9.571473808498551, -6.151212710710767], [29.494465923133937, -64.58387167017081]], [[1.0, 0], [3.893900153596025, -1.4523496686202495], [55.169718927860856, -47.80483357800581]], [[1.0, 0], [-1.7215081479234569, 1.9867263108025097], [-11.242872223589526, -78.19589390859369]], [[1.0, 0], [3.8907861324473174, -2.124529963328852], [44.8731878488146, -69.82404322498803]], [[1.0, 0], [1.3197267863875628, -9.178901416327156], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [1.1654830736234914, 0.6364019062924532], [52.442159293192965, 81.60159268462458]], [[1.0, 0], [-8.365503705278671, -2.4563335146438887], [84.9666068159493, 54.60472256301536]], [[1.0, 0], [-10.420720551432407, 2.266888999499961], [93.6920955215154, -42.7877463391943]], [[1.0, 0], [1.2246807706112763, -1.635981980688062], [-30.145383582032977, -102.66574817675122]], [[1.0, 0], [-7.92218704085145, -17.347169890339732], [-71.37982000003608, 82.37670360461415]], [[1.0, 0], [2.1468011099802116, -9.868685432565696], [-102.78841547506057, -46.94189646921317]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-230-115.103-c1-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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1.355197124587213, 'root_angle': -0.10707264943266395, 'root_number': '0.9439561550283238 - 0.3300708672151228*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0535363247163', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86843579737884240791286186715', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13596092402165611883680969204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57986098042318759999549562993', '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': '115.103', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/l/a/103/4'], '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': '2-230-115.103-c1-0-6', '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': '2-230-115.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.053536324716331976, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86843579737884240791286186715', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2368523760035199989466972716036', 'Lhash_array': ['2368523760035199989466972716036'], 'label': '2-230-115.103-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/l/a/103/4'}