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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1037.178', 'a10': [0.35836794954530027, -0.9335804264972017], 'a2': [-0.7431448254773942, -0.6691306063588582], 'a3': [0.4539904997395468, -0.8910065241883679], 'a4': [0.10452846326765347, 0.9945218953682733], 'a5': [0.35836794954530027, 0.9335804264972017], 'a6': [-0.9335804264972017, 0.35836794954530027], 'a7': [-0.5446390350150271, 0.838670567945424], 'a8': [0.5877852522924731, -0.8090169943749475], 'a9': [-0.5877852522924731, -0.8090169943749475], 'algebraic': True, 'analytic_conductor': 4.81580775392036, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [61, [1]]], 'bad_primes': [17, 61], 'central_character': '1037.178', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 1037, 'conductor_radical': 1037, 'conjugate': 'dirichlet_L_1037.134', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^74', 'a^99', 'a^28', 'a^23', 'a^53', 'a^41', 'a^102', 'a^78', 'a^97', 'a^45', 'a^7', 'a^20', 'a^115', 'a^2', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-1037-1037.178-r0-0-0', 'leading_term': '0.192949869376134895020369947257+0.318860852678025834035603182344*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/1037/178', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.37269544599153004, 1.0622817922742809, 1.760078047137636, 1.9682333489279173, 1.414451398597924, 0.45397043109593443, -0.17621382155794313, -0.032613495709245904, 0.5285708523750542, 0.5993244249496134, -0.3217995897878446, -1.4993374393654324, -1.2368425290749872, 1.6537581108306774, 6.369002945803218, 10.162993494094515, 10.292228057501752, 6.366986707313905, 0.9201288876249974, -2.5711676103672145, -2.558019894501795, -0.5176256628981615, 0.7722729930757488, 0.029017549291535598, -1.5136306836433262, 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'186.23337316211677050096429890346', '186.833496755613123121099626653290', '187.674174520890158390910656693145', '188.55888210721199710066917043283', '189.209333511345403024632261977055', '189.701877902888389891626436282924', '190.17061324417315113493712039931', '190.72890679744935267627491460869', '190.9607645282413918650364729010', '191.75747137691068883284855559496', '192.468442782868885213101953355803', '193.20853998298497857536833288361', '193.40610153262715757431782045303', '194.28423607655271156152954868007', '194.74181539926605039028031717576', '195.531397739794400163762481370560', '196.287190927540760494452028782077', '196.789857340469492839335459488006', '197.4712366255037052719653815419', '197.967444431052856954291087914954', '198.45744289558075729328550365405', '199.23771588248762747672184999888', '199.9172935607485275474470913702'], 'prelabel': '1-1037-1037.178-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.81580775392036, 'root_angle': 0.6535658324737393, 'root_number': '-0.463943210159699843711470808171+0.885864943288034501572739132930*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.326782916237', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(120)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.661734038774871730614906998575-0.0813838044656309080339511101995*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.74616363444', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.20803407028', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.04277306742', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.81580775392036, 'bad_primes': [17, 61], 'central_character': '1037.178', 'conductor': 1037, 'conductor_radical': 1037, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1037/178'], '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': '1-1037-1037.178-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': '1-1037-1037.178-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.81580775392036, 'root_angle': 0.32678291623686967, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74616363444', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1037.178', 'Lhash_array': ['dirichlet_L_1037.178'], 'label': '1-1037-1037.178-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1037/178'}
Lfunction data - 1-1037-1037.178-r0-0-0