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  • lfunc_lfunctions • Show schema
    {'Lhash': '654784966860424810532369224849,781933276557768405012372252726', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -8, 'a5': 0, 'a6': 0, 'a7': -166, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2163.7832267609574, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 8]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 0, 8], [1], [1], [1, 166, 11691, 398566, 5764801], [1, 0, -22784, 0, 214358881], [1, 82, 58803, 2342002, 815730721], [1, 0, 96496, 0, 6975757441], [1, 278, 279963, 36229238, 16983563041], [1, 0, -509120, 0, 78310985281], [1, 0, -959504, 0, 500246412961], [1, 2102, 2951643, 1941241142, 852891037441], [1, -3344, 6543906, -6267194384, 3512479453921], [1, 0, -4960034, 0, 7984925229121], [1, -5030, 13162827, -17196569030, 11688200277601], [1, 0, -1064912, 0, 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'0.61683659236779295392200735955', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.27698905395963172246267944663', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2163.7832267609574, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 202500, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -8, 0, 0, -166, 0, 0, 0, 0, 0, -82, 0, 0, 64, 0, 0, -278, 0, 0, 0, 0, 0, 0, 0, 0, 1328, 0, 0, -2102, 0, 0, 0, 0, 0, 3344, 0, 0, 0, 0, 0, 5030, 0, 0, 0, 0, 0, 15865, 0, 0, 656, 0, 0, 0, 0, 0, 0, 0, 0, 11650, 0, 0, -512, 0, 0, -14518, 0, 0, 0, 0, 0, 9104, 0, 0, 2224, 0, 0, 18592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13612, 0, 0, 0, 0, 0, -3586, 0, 0, 0], 'euler11': [1, 0, -22784, 0, 214358881], 'euler13': [1, 82, 58803, 2342002, 815730721], 'euler17': [1, 0, 96496, 0, 6975757441], 'euler19': [1, 278, 279963, 36229238, 16983563041], 'euler2': [1, 0, 8, 0, 0], 'euler23': [1, 0, -509120, 0, 78310985281], 'euler29': [1, 0, -959504, 0, 500246412961], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 2102, 2951643, 1941241142, 852891037441], 'euler37': [1, -3344, 6543906, -6267194384, 3512479453921], 'euler41': [1, 0, -4960034, 0, 7984925229121], 'euler43': [1, -5030, 13162827, -17196569030, 11688200277601], 'euler47': [1, 0, -1064912, 0, 23811286661761], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -15628610, 0, 62259690411361], 'euler59': [1, 0, -23670800, 0, 146830437604321], 'euler61': [1, -11650, 61622307, -161304047650, 191707312997281], 'euler67': [1, 14518, 92995323, 292553974678, 406067677556641], 'euler7': [1, 166, 11691, 398566, 5764801], 'euler71': [1, 0, -3116450, 0, 645753531245761], 'euler73': [1, -9104, 77517186, -258537586064, 806460091894081], 'euler79': [1, -18592, 164315778, -724159905952, 1517108809906561], 'euler83': [1, 0, -31229744, 0, 2252292232139041], 'euler89': [1, 0, -88573250, 0, 3936588805702081], 'euler97': [1, 3586, 180273411, 317466001666, 7837433594376961], 'euler_factors': [[1, 0, 8, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 166, 11691, 398566, 5764801], [1, 0, -22784, 0, 214358881], [1, 82, 58803, 2342002, 815730721], [1, 0, 96496, 0, 6975757441], [1, 278, 279963, 36229238, 16983563041], [1, 0, -509120, 0, 78310985281], [1, 0, -959504, 0, 500246412961], [1, 2102, 2951643, 1941241142, 852891037441], [1, -3344, 6543906, -6267194384, 3512479453921], [1, 0, -4960034, 0, 7984925229121], [1, -5030, 13162827, -17196569030, 11688200277601], [1, 0, -1064912, 0, 23811286661761], [1, 0, -15628610, 0, 62259690411361], [1, 0, -23670800, 0, 146830437604321], [1, -11650, 61622307, -161304047650, 191707312997281], [1, 14518, 92995323, 292553974678, 406067677556641], [1, 0, -3116450, 0, 645753531245761], [1, -9104, 77517186, -258537586064, 806460091894081], [1, -18592, 164315778, -724159905952, 1517108809906561], [1, 0, -31229744, 0, 2252292232139041], [1, 0, -88573250, 0, 3936588805702081], [1, 3586, 180273411, 317466001666, 7837433594376961]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/5/d/a'], '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': '4-450e2-1.1-c4e2-0-4', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4, 4], 'order_of_vanishing': 0, 'prelabel': '4-450e2-1.1-c4e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.8202993620316965, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4e2-0', 'trace_hash': 1478645022979155854, 'z1': {'__RealLiteral__': 0, 'data': '0.51653426168262493240329966393', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '654784966860424810532369224849,781933276557768405012372252726', 'Lhash_array': ['654784966860424810532369224849', '781933276557768405012372252726'], 'factors': ['2-450-3.2-c4-0-8', '2-450-3.2-c4-0-11'], 'label': '4-450e2-1.1-c4e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/5/d/a'}