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  • lfunc_lfunctions • Show schema
    {'Lhash': '1344618629878947305042665147612,1616016128821693843801429576483', 'a10': -12, 'a2': -2, 'a3': 0, 'a4': 0, 'a5': 6, 'a6': 0, 'a7': 16, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 91.36127898623889, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[2, [1, 2, 4]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '162.1', 'coefficient_field': '1.1.1.1', 'conductor': 26244, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, 2, 4], [1], [1, -6, -89, -750, 15625], [1, -16, -87, -5488, 117649], [1, -12, -1187, -15972, 1771561], [1, 38, -753, 83486, 4826809], [1, -252, 25702, -1238076, 24137569], [1, -40, 14118, -274360, 47045881], [1, -168, 16057, -2044056, 148035889], [1, -30, -23489, -731670, 594823321], [1, -88, -22047, -2621608, 887503681], [1, -508, 165822, -25731724, 2565726409], [1, -42, -67157, -2894682, 4750104241], [1, -52, -76803, -4134364, 6321363049], [1, 96, -94607, 9967008, 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'7.39304984983297156048979627129493', '8.002542318996537816098215346161937', '8.489242657620828730449982424818693', '9.324928372625985479939020076123409', '9.499692523440939874521279418579896', '10.22591675239314802363510881460366', '10.28851763362464824538447798509095', '11.22510497842326500104040318331909', '11.51037612533864586149893724781725', '12.20839397221509747726704389948575', '12.52672256973751990783629538385612'], 'prelabel': '4-162e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.0916515684873005, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 227024014909336305, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06071706954334300248305886668', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.27481194623403663145947945777', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.75760071290381303872345961737', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 91.36127898623889, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 26244, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 0, 6, 0, 16, 8, 0, -12, 12, 0, -38, -32, 0, -16, 252, 0, 40, 0, 0, -24, 168, 0, 125, 76, 0, 0, 30, 0, 88, 0, 0, -504, 96, 0, 508, -80, 0, 48, 42, 0, 52, 0, 0, -336, -96, 0, 343, -250, 0, 0, -396, 0, 72, 128, 0, -60, -660, 0, 538, -176, 0, 64, -228, 0, -884, 0, 0, -192, -1584, 0, 436, -1016, 0, 0, 192, 0, 520, -96, 0, -84, -492, 0, 1512, -104, 0, 96, -1620, 0, -608, 0, 0, 192, 240, 0, -1154, -686, 0, 0], 'euler11': [1, -12, -1187, -15972, 1771561], 'euler13': [1, 38, -753, 83486, 4826809], 'euler17': [1, -252, 25702, -1238076, 24137569], 'euler19': [1, -40, 14118, -274360, 47045881], 'euler2': [1, 2, 4, 0, 0], 'euler23': [1, -168, 16057, -2044056, 148035889], 'euler29': [1, -30, -23489, -731670, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -88, -22047, -2621608, 887503681], 'euler37': [1, -508, 165822, -25731724, 2565726409], 'euler41': [1, -42, -67157, -2894682, 4750104241], 'euler43': [1, -52, -76803, -4134364, 6321363049], 'euler47': [1, 96, -94607, 9967008, 10779215329], 'euler5': [1, -6, -89, -750, 15625], 'euler53': [1, 396, 336958, 58955292, 22164361129], 'euler59': [1, 660, 230221, 135550140, 42180533641], 'euler61': [1, -538, 62463, -122115778, 51520374361], 'euler67': [1, 884, 480693, 265874492, 90458382169], 'euler7': [1, -16, -87, -5488, 117649], 'euler71': [1, 1584, 1343086, 566931024, 128100283921], 'euler73': [1, -436, 825558, -169611412, 151334226289], 'euler79': [1, -520, -222639, -256380280, 243087455521], 'euler83': [1, 492, -329723, 281319204, 326940373369], 'euler89': [1, 1620, 2066038, 1142049780, 496981290961], 'euler97': [1, 1154, 419043, 1053224642, 832972004929], 'euler_factors': [[1, 2, 4, 0, 0], [1, 0, 0, 0, 0], [1, -6, -89, -750, 15625], [1, -16, -87, -5488, 117649], [1, -12, -1187, -15972, 1771561], [1, 38, -753, 83486, 4826809], [1, -252, 25702, -1238076, 24137569], [1, -40, 14118, -274360, 47045881], [1, -168, 16057, -2044056, 148035889], [1, -30, -23489, -731670, 594823321], [1, -88, -22047, -2621608, 887503681], [1, -508, 165822, -25731724, 2565726409], [1, -42, -67157, -2894682, 4750104241], [1, -52, -76803, -4134364, 6321363049], [1, 96, -94607, 9967008, 10779215329], [1, 396, 336958, 58955292, 22164361129], [1, 660, 230221, 135550140, 42180533641], [1, -538, 62463, -122115778, 51520374361], [1, 884, 480693, 265874492, 90458382169], [1, 1584, 1343086, 566931024, 128100283921], [1, -436, 825558, -169611412, 151334226289], [1, -520, -222639, -256380280, 243087455521], [1, 492, -329723, 281319204, 326940373369], [1, 1620, 2066038, 1142049780, 496981290961], [1, 1154, 419043, 1053224642, 832972004929]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/4/c/c'], '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': '4-162e2-1.1-c3e2-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-162e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.0916515684873005, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 227024014909336305, 'z1': {'__RealLiteral__': 0, 'data': '1.06071706954334300248305886668', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1344618629878947305042665147612,1616016128821693843801429576483', 'Lhash_array': ['1344618629878947305042665147612', '1616016128821693843801429576483'], 'factors': ['2-162-9.4-c3-0-5', '2-162-9.7-c3-0-5'], 'label': '4-162e2-1.1-c3e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/4/c/c'}