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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_149.120', 'a10': [-0.6606747233900815, -0.7506723052527243], 'a2': [-0.3728564777803086, 0.9278890272965093], 'a3': [0.9677329469334989, 0.2519780613851252], 'a4': [-0.7219560939545244, -0.6919388689775462], 'a5': [-0.4502037448176733, 0.8929258581495685], 'a6': [-0.5946331763042866, 0.8039971303669405], 'a7': [0.6606747233900815, 0.7506723052527243], 'a8': [0.9112284903881357, -0.41190124824399266], 'a9': [0.8730141131611882, 0.48769494381363454], 'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'analytic_normalization': 0, 'bad_lfactors': [[149, [1]]], 'bad_primes': [149], 'central_character': '149.120', 'coeff_info': ['x^74 - 1', '0.996397488542527 + 0.0848059244755092*I', '\\\\zeta_{74}'], 'conductor': 149, 'conductor_radical': 149, 'conjugate': 'dirichlet_L_149.113', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^3', 'a^46', 'a^24', 'a^26', 'a^10', 'a^69', 'a^6', 'a^47', 'a^65', 'a^49', 'a^35', 'a^33', 'a^27', 'a^18', 'a^40', 'a^29', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-149-149.120-r0-0-0', 'leading_term': '0.574772738623633746786883183479+0.985392858085923510921283210084*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/149/120', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.140772889681227, 1.5922282193238249, 2.273855334521655, 2.8198136365504567, 2.89067737638984, 2.292624555609426, 1.0619512730815255, -0.5017280704734582, -1.9029649937556523, -2.625315217768889, -2.3588875893476304, -1.178259145411984, 0.4333444696786453, 1.759196550925509, 2.1690381562809717, 1.437367636253498, -0.11261137436974923, -1.7416271567004058, -2.6618289591484072, -2.454642445099712, -1.3023437697090487, 0.11673317503912828, 1.0277018290460427, 1.0233987354758518, 0.302782819415909, -0.48276406998523047, 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'unitary', 'types': ['DIR'], 'values': [[1, '0.838932371818941367135074756752+0.697799497948335010547641700874*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.08889554121', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.66655556715', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.9796372808', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'bad_primes': [149], 'central_character': '149.120', 'conductor': 149, 'conductor_radical': 149, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/149/120'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-149-149.120-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-149-149.120-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6919530909683064, 'root_angle': 0.331918265854182, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08889554121', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_149.120', 'Lhash_array': ['dirichlet_L_149.120'], 'label': '1-149-149.120-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/149/120'}