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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_37.36', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.17182727762300226, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]]], 'bad_primes': [37], 'central_character': '37.36', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 37, 'conductor_radical': 37, 'conjugate': 'dirichlet_L_37.36', 'degree': 1, 'dirichlet_coefficients': [1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1], 'euler_factors': [[1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [0], 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'179.17001131032969161787307218974', '179.67714081241351208860967097674', '180.49968243619779082268998842093', '181.57842900082308916198637981495', '182.193898749375406358608730566869', '183.27444298928438605156671208655', '184.12934493202540140281178439127', '184.981862596609324515309271760196', '186.24874371279184530638602837414', '186.924714029528042340218346995708', '188.012238355618808208988039340066', '188.63743918451945156144865657260', '190.018066924814858394022722893023', '190.56948627448979965201046859659', '191.39769953273841581831341141575', '192.30390244706031147806418626770', '192.462155786060028058750827550250', '193.89514111048769778527140034836', '195.44115259831221584127114458197', '195.85390821058880870728618770248', '196.97930404267087290151631035111', '198.14445020954575712399880665966', '198.328395993166195732569767260587', '199.17791764489044269650303050697'], 'prelabel': '1-37-37.36-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.17182727762300226, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '0.819292168725431877923797552676']], 'z1': {'__RealLiteral__': 0, 'data': '2.0572212343', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '4.09281262395', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.08873354104', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.17182727762300226, 'bad_primes': [37], 'central_character': '37.36', 'conductor': 37, 'conductor_radical': 37, 'degree': 1, 'dirichlet_coefficients': [1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 0, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 0, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1], 'euler11': [1, 1], 'euler13': [1, -1], 'euler17': [1, -1], 'euler19': [1, -1], 'euler2': [1, -1], 'euler23': [1, -1], 'euler29': [1, -1], 'euler3': [1, 1], 'euler31': [1, -1], 'euler37': [1, 0], 'euler41': [1, 1], 'euler43': [1, -1], 'euler47': [1, 1], 'euler5': [1, -1], 'euler53': [1, 1], 'euler59': [1, -1], 'euler61': [1, -1], 'euler67': [1, 1], 'euler7': [1, 1], 'euler71': [1, 1], 'euler73': [1, 1], 'euler79': [1, -1], 'euler83': [1, 1], 'euler89': [1, -1], 'euler97': [1, -1], 'euler_factors': [[1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 0], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/37/36'], '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': '1-37-37.36-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': '1-37-37.36-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.17182727762300226, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.0572212343', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_37.36', 'Lhash_array': ['dirichlet_L_37.36'], 'label': '1-37-37.36-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/37/36'}