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  • lfunc_lfunctions • Show schema
    {'Lhash': '2995240266383389226835978146561,3219127624459627708259273832275', 'a10': 0, 'a2': 2, 'a3': 4, 'a4': 2, 'a5': 0, 'a6': 8, 'a7': 0, 'a8': 0, 'a9': 8, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.550434681184042, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, -2, 2]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '200.1', 'coefficient_field': '1.1.1.1', 'conductor': 40000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, -2, 2], [1, -4, 8, -12, 9], [1], [1, 0, 0, 0, 49], [1, 12, 58, 132, 121], [1, 0, 0, 0, 169], [1, -8, 32, -136, 289], [1, 0, -34, 0, 361], [1, 0, 0, 0, 529], [1, 0, 58, 0, 841], [1, 0, -62, 0, 961], [1, 0, 0, 0, 1369], [1, 12, 118, 492, 1681], [1, -12, 72, -516, 1849], [1, 0, 0, 0, 2209], [1, 0, 0, 0, 2809], [1, 0, -82, 0, 3481], [1, 0, -122, 0, 3721], [1, 12, 72, 804, 4489], [1, 0, -142, 0, 5041], [1, -24, 288, -1752, 5329], [1, 0, 158, 0, 6241], [1, -4, 8, -332, 6889], 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'3.44399200216977935047946699398546', '4.67995772602138674958764101541724', '5.20188861543177951230871158341172', '5.53793135770770986041082780606498', '6.43392652598721456379763884018236', '7.56544907154702072696127104846222', '7.67781266462110170830955028344142', '7.940817487311768164169907409615933', '8.684520954755740637860495321363414', '9.024174749586312479583394624137892', '9.906132805346180439449932564623588', '10.20659584223364561574361795293415', '10.59309616654074349556559346897987', '11.31279950412465471742841070727671', '12.16709337580430776584670510374551', '12.59632793749163586086107653210214', '12.83461125882297384840720534981807'], 'prelabel': '4-200e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2637278347910235, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1401939699696938761, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.36282794789362496136437965985', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.53944393185318725803307799768', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.38425863832263344277539571706', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2.550434681184042, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 40000, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 2, 4, 2, 0, 8, 0, 0, 8, 0, -12, 8, 0, 0, 0, -4, 8, 16, 0, 0, 0, -24, 0, 0, 0, 0, 12, 0, 0, 0, 0, -8, -48, 16, 0, 16, 0, 0, 0, 0, -12, 0, 12, -24, 0, 0, 0, -16, 0, 0, 32, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -96, -12, 16, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 23, -24, 4, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 24, 0, -96, 0], 'euler11': [1, 12, 58, 132, 121], 'euler13': [1, 0, 0, 0, 169], 'euler17': [1, -8, 32, -136, 289], 'euler19': [1, 0, -34, 0, 361], 'euler2': [1, -2, 2, 0, 0], 'euler23': [1, 0, 0, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, -4, 8, -12, 9], 'euler31': [1, 0, -62, 0, 961], 'euler37': [1, 0, 0, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, -12, 72, -516, 1849], 'euler47': [1, 0, 0, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 0, 0, 2809], 'euler59': [1, 0, -82, 0, 3481], 'euler61': [1, 0, -122, 0, 3721], 'euler67': [1, 12, 72, 804, 4489], 'euler7': [1, 0, 0, 0, 49], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, -24, 288, -1752, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, -4, 8, -332, 6889], 'euler89': [1, 0, 146, 0, 7921], 'euler97': [1, -24, 288, -2328, 9409], 'euler_factors': [[1, -2, 2, 0, 0], [1, -4, 8, -12, 9], [1, 0, 0, 0, 0], [1, 0, 0, 0, 49], [1, 12, 58, 132, 121], [1, 0, 0, 0, 169], [1, -8, 32, -136, 289], [1, 0, -34, 0, 361], [1, 0, 0, 0, 529], [1, 0, 58, 0, 841], [1, 0, -62, 0, 961], [1, 0, 0, 0, 1369], [1, 12, 118, 492, 1681], [1, -12, 72, -516, 1849], [1, 0, 0, 0, 2209], [1, 0, 0, 0, 2809], [1, 0, -82, 0, 3481], [1, 0, -122, 0, 3721], [1, 12, 72, 804, 4489], [1, 0, -142, 0, 5041], [1, -24, 288, -1752, 5329], [1, 0, 158, 0, 6241], [1, -4, 8, -332, 6889], [1, 0, 146, 0, 7921], [1, -24, 288, -2328, 9409]], 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/2/k/d'], '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': '4-200e2-1.1-c1e2-0-23', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-200e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2637278347910235, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1401939699696938761, 'z1': {'__RealLiteral__': 0, 'data': '2.36282794789362496136437965985', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2995240266383389226835978146561,3219127624459627708259273832275', 'Lhash_array': ['2995240266383389226835978146561', '3219127624459627708259273832275'], 'factors': ['2-200-40.3-c1-0-9', '2-200-40.27-c1-0-12'], 'label': '4-200e2-1.1-c1e2-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/2/k/d'}