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lfunc_lfunctions • Show schema
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{'Lhash': '1046770373700955486300160750537,1285239607851110074987962133276', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 14, 'a8': 9, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8635.614718992487, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1, -14, 49]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.1', 'coefficient_field': '1.1.1.1', 'conductor': 2480625, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, -1, 0, -8, 64], [1], [1], [1, -14, 49], [1, -22, 2718, -29282, 1771561], [1, -22, 4450, -48334, 4826809], [1, -116, 9030, -569908, 24137569], [1, -102, 13134, -699618, 47045881], [1, -260, 34734, -3163420, 148035889], [1, -196, 20942, -4780244, 594823321], [1, -150, 36542, -4468650, 887503681], [1, -96, 82550, -4862688, 2565726409], [1, -176, -16914, -12130096, 4750104241], [1, -344, 171958, -27350408, 6321363049], [1, -560, 248606, -58140880, 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1054298, -758963822, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 6, 'label': '4-1575e2-1.1-c3e2-0-6', 'leading_term': '9.3558883826925654744618461929390397151020738614654814036116400000000000000000000000000000', '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/1575/4/a/w', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [9.355888382692566, 9.319068553459852, 9.245316140099685, 9.10928759854309, 8.9167562272137, 8.6760703636349, 8.38905060397867, 8.057974713585862, 7.687319022437876, 7.281981740414343, 6.8469674337659745, 6.387568411913215, 5.909469724099073, 5.418494761142273, 4.920590822521462, 4.4216634817172356, 3.9275801671654627, 3.443998505458151, 2.976340448862741, 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'3.88725987228588153584368358120174', '4.24060652882825234153686283218799', '4.71682878057123809705274692271496', '5.08914932039572729156213172900859', '5.66835861805718313452857892909100', '5.76931935054066266328814399971992', '6.43959070042050899162803219311873', '7.06808266693983678354571484620291', '7.24818549978646837826075463789259', '7.43914919027476010469579570410635', '8.186452121397549362486943745534736', '8.368641941146238382480236027922804', '8.960656834628883649582115361595420', '9.153353705586358740942453497970622'], 'prelabel': '4-1575e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 2264032613574327719, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.825756224556272554430617877710', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.01387528047532492512745754127', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.37364563684643671998184723910', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8635.614718992487, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 2480625, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 14, 9, 0, 0, 22, 0, 22, 14, 0, -47, 116, 0, 102, 0, 0, 22, 260, 0, 0, 22, 0, 14, 196, 0, 150, -103, 0, 116, 0, 0, 96, 102, 0, 0, 176, 0, 344, 22, 0, 260, 560, 0, 147, 0, 0, 22, 326, 0, 0, 126, 0, 196, 844, 0, -204, 150, 0, -95, 0, 0, 104, 116, 0, 0, -1670, 0, 386, 96, 0, 102, 308, 0, -888, 0, 0, 176, 928, 0, 0, 344, 0, 198, -588, 0, 308, 260, 0, 560, 0, 0, -522, 147, 0, 0], 'euler11': [1, -22, 2718, -29282, 1771561], 'euler13': [1, -22, 4450, -48334, 4826809], 'euler17': [1, -116, 9030, -569908, 24137569], 'euler19': [1, -102, 13134, -699618, 47045881], 'euler2': [1, -1, 0, -8, 64], 'euler23': [1, -260, 34734, -3163420, 148035889], 'euler29': [1, -196, 20942, -4780244, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -150, 36542, -4468650, 887503681], 'euler37': [1, -96, 82550, -4862688, 2565726409], 'euler41': [1, -176, -16914, -12130096, 4750104241], 'euler43': [1, -344, 171958, -27350408, 6321363049], 'euler47': [1, -560, 248606, -58140880, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -326, 204138, -48533902, 22164361129], 'euler59': [1, -844, 474182, -173339876, 42180533641], 'euler61': [1, 204, 455006, 46304124, 51520374361], 'euler67': [1, -104, 537670, -31279352, 90458382169], 'euler7': [1, -14, 49, 0, 0], 'euler71': [1, 1670, 1384382, 597711370, 128100283921], 'euler73': [1, -386, 152218, -150160562, 151334226289], 'euler79': [1, 888, 1007454, 437818632, 243087455521], 'euler83': [1, -928, 600710, -530618336, 326940373369], 'euler89': [1, 588, 1495334, 414521772, 496981290961], 'euler97': [1, 522, 291282, 476415306, 832972004929], 'euler_factors': [[1, -1, 0, -8, 64], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -14, 49, 0, 0], [1, -22, 2718, -29282, 1771561], [1, -22, 4450, -48334, 4826809], [1, -116, 9030, -569908, 24137569], [1, -102, 13134, -699618, 47045881], [1, -260, 34734, -3163420, 148035889], [1, -196, 20942, -4780244, 594823321], [1, -150, 36542, -4468650, 887503681], [1, -96, 82550, -4862688, 2565726409], [1, -176, -16914, -12130096, 4750104241], [1, -344, 171958, -27350408, 6321363049], [1, -560, 248606, -58140880, 10779215329], [1, -326, 204138, -48533902, 22164361129], [1, -844, 474182, -173339876, 42180533641], [1, 204, 455006, 46304124, 51520374361], [1, -104, 537670, -31279352, 90458382169], [1, 1670, 1384382, 597711370, 128100283921], [1, -386, 152218, -150160562, 151334226289], [1, 888, 1007454, 437818632, 243087455521], [1, -928, 600710, -530618336, 326940373369], [1, 588, 1495334, 414521772, 496981290961], [1, 522, 291282, 476415306, 832972004929]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/4/a/w'], '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': '4-1575e2-1.1-c3e2-0-6', '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': '4-1575e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2264032613574327719, 'z1': {'__RealLiteral__': 0, 'data': '0.825756224556272554430617877710', 'prec': 107}}
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{'Lhash': '1046770373700955486300160750537,1285239607851110074987962133276', 'Lhash_array': ['1046770373700955486300160750537', '1285239607851110074987962133276'], 'factors': ['2-1575-1.1-c3-0-59', '2-1575-1.1-c3-0-72'], 'label': '4-1575e2-1.1-c3e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/4/a/w'}