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lfunc_lfunctions • Show schema
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{'Lhash': '2967716908818259865245131777577', 'a10': [29518774.405646056, 29512303.92493257], 'a2': [-127.9859689685324, 128.0140294935905], 'a3': [-692.212512618831, -3724.211169814881], 'a4': [-7.183494371720468, -32767.999212606934], 'a5': [0.0, -230590.15111405443], 'a6': [565344.7676927049, 388033.8622059697], 'a7': [0.0, -3607806.4059152957], 'a8': [4195683.004136359, 4192924.542325237], 'a9': [-13390590.674747849, 5155891.14276135], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.12322061199046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [127.9859689685324, -128.0140294935905]]], [3, [[1.0, 0], [692.212512618831, 3724.211169814881]]]], 'bad_primes': [2, 3], 'central_character': '12.11', 'coefficient_field': 'CDF', 'conductor': 12, 'conductor_radical': 6, 'conjugate': '706322334253006681226053208109', 'degree': 2, 'euler_factors': [[[1.0, 0], [127.9859689685324, -128.0140294935905]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-12-12.11-c15-0-22', 'load_key': 'CMFs-workshop', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/12/16/b/a/11/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.9718005406323695, 1.3285091870026828, 1.660445138964347, 1.941472685565953, 2.1492534983732807, 2.2666466231614915, 2.2828150860804475, 2.1939739530712234, 2.0037301786251875, 1.7229830652856826, 1.3693752474321552, 0.9663072513024832, 0.5415530946452491, 0.12553906884975172, -0.2506284413189285, -0.5572789379493688, -0.7683131082868819, -0.8632212664170513, -0.8288442728589552, -0.6607403448703882, -0.3640348145057517, 0.04634643770557204, 0.5461256784880966, 1.1028277343936104, 1.6776146764872826, 2.227722317228031, 2.7093667087757383, 3.080939432459769, 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'14.60578533675557739888328984256660', '15.66622482152118148930332443218217', '17.29438180493534177500867741462729'], 'prelabel': '2-12-12.11-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.138021340204816, 'root_angle': 0.9414340526182233, 'root_number': '-0.9831214712088157 + 0.18295401839865078*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.470717026309', 'prec': 47}, 'spectral_label': 'c15-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.34111584713007542979129055571', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.67350995136903632878156232464', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.15932207475309190987157878443', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.12322061199046, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 12, 'conductor_radical': 6, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/12/16/b/a/11/8'], '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': '2-12-12.11-c15-0-22', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15], 'order_of_vanishing': 0, 'prelabel': '2-12-12.11-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.138021340204816, 'root_angle': 0.47071702630911166, 'self_dual': False, 'spectral_label': 'c15-0', 'z1': {'__RealLiteral__': 0, 'data': '2.34111584713007542979129055571', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2967716908818259865245131777577', 'Lhash_array': ['2967716908818259865245131777577'], 'label': '2-12-12.11-c15-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/12/16/b/a/11/8'}