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lfunc_lfunctions • Show schema
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{'Lhash': '1011298300553247524285159726118,1774435802403619061249066844318', 'a10': -10, 'a2': 2, 'a3': 0, 'a4': 8, 'a5': -5, 'a6': 0, 'a7': 0, 'a8': 40, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 571.007993663993, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 5, 25]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': '1.1.1.1', 'conductor': 164025, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, -2, -4, -16, 64], [1], [1, 5, 25], [1, 0, -343, 0, 117649], [1, 10, -1231, 13310, 1771561], [1, -80, 4203, -175760, 4826809], [1, -14, 9875, -68782, 24137569], [1, 226, 26487, 1550134, 47045881], [1, -81, -5606, -985527, 148035889], [1, -220, 24011, -5365580, 594823321], [1, -189, 5930, -5630499, 887503681], [1, -340, 130206, -17222020, 2565726409], [1, -130, -52021, -8959730, 4750104241], [1, 10, -79407, 795070, 6321363049], [1, 160, -78223, 16611680, 10779215329], [1, 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'6.1288077864282437759910418318435250324545885174515784896444848641194302250714455387265568', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/405/4/e/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03515625', 'prec': 34}, 'plot_values': [6.128807786428243, 6.105669703932907, 6.0566693337210555, 5.967362046623306, 5.841086470607153, 5.682280620514109, 5.49152410794487, 5.269873912258468, 5.019602287703482, 4.7431528167847485, 4.443052450125944, 4.122112587644203, 3.7834126508595314, 3.4302285555521586, 3.0660218693777113, 2.6944007086502872, 2.3191115110197713, 1.9439756700591142, 1.5728815316684905, 1.2097161422419422, 0.8583462413238767, 0.5225556439917034, 0.206007964539681, -0.08780357904699387, -0.3556105441008796, -0.5944074810693414, 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'4.00653498524167697162630630571280', '4.55036436431716144292516809397703', '5.16479484681170340555474660403171', '6.06817113691749160782675534461162', '6.17178170140818428417941749339189', '6.82107133150000345965197748639831', '7.13792582509322593793947896495255', '7.908657646158297079983255914481589', '8.210662595535854973225136133602957', '8.673071436838610941183490654419189', '8.991720875672659202206114653567361', '10.19914843527716186449526683077216', '10.29793437126315969448566650479801', '10.57571434005830465618844711512282', '11.14573202874587909315953686418225'], 'prelabel': '4-405e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.88833034402596, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 10248353673716525, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.797773692822905705911686711929', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.39978303334069136820862239558', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.52283878049274556591214733347', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 571.007993663993, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 164025, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 8, -5, 0, 0, 40, 0, -10, -10, 0, 80, 0, 0, 80, 14, 0, -226, -40, 0, -20, 81, 0, 0, 160, 0, 0, 220, 0, 189, 320, 0, 28, 0, 0, 340, -452, 0, -200, 130, 0, -10, -80, 0, 162, -160, 0, 343, 0, 0, 640, 1262, 0, 50, 0, 0, 440, 560, 0, -229, 378, 0, 1088, -400, 0, -750, 112, 0, 0, 1780, 0, -1780, 680, 0, -1808, 0, 0, 27, -400, 0, 260, -429, 0, -70, -20, 0, -400, -1500, 0, 0, 648, 0, -320, 1130, 0, 1480, 686, 0, 0], 'euler11': [1, 10, -1231, 13310, 1771561], 'euler13': [1, -80, 4203, -175760, 4826809], 'euler17': [1, -14, 9875, -68782, 24137569], 'euler19': [1, 226, 26487, 1550134, 47045881], 'euler2': [1, -2, -4, -16, 64], 'euler23': [1, -81, -5606, -985527, 148035889], 'euler29': [1, -220, 24011, -5365580, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -189, 5930, -5630499, 887503681], 'euler37': [1, -340, 130206, -17222020, 2565726409], 'euler41': [1, -130, -52021, -8959730, 4750104241], 'euler43': [1, 10, -79407, 795070, 6321363049], 'euler47': [1, 160, -78223, 16611680, 10779215329], 'euler5': [1, 5, 25, 0, 0], 'euler53': [1, -1262, 695915, -187882774, 22164361129], 'euler59': [1, -560, 108221, -115012240, 42180533641], 'euler61': [1, 229, -174540, 51978649, 51520374361], 'euler67': [1, 750, 261737, 225572250, 90458382169], 'euler7': [1, 0, -343, 0, 117649], 'euler71': [1, -1780, 1507922, -637081580, 128100283921], 'euler73': [1, 1780, 1570134, 692450260, 151334226289], 'euler79': [1, -27, -492310, -13312053, 243087455521], 'euler83': [1, 429, -387746, 245296623, 326940373369], 'euler89': [1, 1500, 1972438, 1057453500, 496981290961], 'euler97': [1, -1480, 1277727, -1350756040, 832972004929], 'euler_factors': [[1, -2, -4, -16, 64], [1, 0, 0, 0, 0], [1, 5, 25, 0, 0], [1, 0, -343, 0, 117649], [1, 10, -1231, 13310, 1771561], [1, -80, 4203, -175760, 4826809], [1, -14, 9875, -68782, 24137569], [1, 226, 26487, 1550134, 47045881], [1, -81, -5606, -985527, 148035889], [1, -220, 24011, -5365580, 594823321], [1, -189, 5930, -5630499, 887503681], [1, -340, 130206, -17222020, 2565726409], [1, -130, -52021, -8959730, 4750104241], [1, 10, -79407, 795070, 6321363049], [1, 160, -78223, 16611680, 10779215329], [1, -1262, 695915, -187882774, 22164361129], [1, -560, 108221, -115012240, 42180533641], [1, 229, -174540, 51978649, 51520374361], [1, 750, 261737, 225572250, 90458382169], [1, -1780, 1507922, -637081580, 128100283921], [1, 1780, 1570134, 692450260, 151334226289], [1, -27, -492310, -13312053, 243087455521], [1, 429, -387746, 245296623, 326940373369], [1, 1500, 1972438, 1057453500, 496981290961], [1, -1480, 1277727, -1350756040, 832972004929]], 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/j'], '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': '4-405e2-1.1-c3e2-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-405e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.88833034402596, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 10248353673716525, 'z1': {'__RealLiteral__': 0, 'data': '0.797773692822905705911686711929', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1011298300553247524285159726118,1774435802403619061249066844318', 'Lhash_array': ['1011298300553247524285159726118', '1774435802403619061249066844318'], 'label': '4-405e2-1.1-c3e2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/j'}