-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3034809869231061268560285860824', 'a10': -3, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': -3, 'a6': 1, 'a7': -2, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.096830764957835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '1014.1', 'coefficient_field': '1.1.1.1', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, 3, 5], [1, 2, 7], [1, 6, 11], [1], [1, 3, 17], [1, 2, 19], [1, 6, 23], [1, -3, 29], [1, -4, 31], [1, -7, 37], [1, -3, 41], [1, 10, 43], [1, 6, 47], [1, -3, 53], [1, 0, 59], [1, 7, 61], [1, -10, 67], [1, 6, 71], [1, -13, 73], [1, 4, 79], [1, -6, 83], [1, 18, 89], [1, 14, 97], [1, -15, 101], [1, -14, 103], [1, 6, 107], [1, 14, 109], [1, 3, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, 3, 5], 1]], [[[1, 2, 7], 1]], [[[1, 6, 11], 1]], [1], [[[1, 3, 17], 1]], [[[1, 2, 19], 1]], [[[1, 6, 23], 1]], [[[1, -3, 29], 1]], [[[1, -4, 31], 1]], [[[1, -7, 37], 1]], [[[1, -3, 41], 1]], [[[1, 10, 43], 1]], [[[1, 6, 47], 1]], [[[1, -3, 53], 1]], [[[1, 0, 59], 1]], [[[1, 7, 61], 1]], [[[1, -10, 67], 1]], [[[1, 6, 71], 1]], [[[1, -13, 73], 1]], [[[1, 4, 79], 1]], [[[1, -6, 83], 1]], [[[1, 18, 89], 1]], [[[1, 14, 97], 1]], [[[1, -15, 101], 1]], [[[1, -14, 103], 1]], [[[1, 6, 107], 1]], [[[1, 14, 109], 1]], [[[1, 3, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-1014-1.1-c1-0-26', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1014/2/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-9.694321373359846e-59, 0.19437397166539197, 0.3895547343417811, 0.586275505795644, 0.7851264311537719, 0.9864927633195114, 1.1905035024564425, 1.3969922681094287, 1.6054711850254595, 1.8151177355735197, 2.0247739484659886, 2.2329569640289426, 2.4378798965991693, 2.6374819348052196, 2.8294667082704503, 3.0113480453155526, 3.180502310444989, 3.3342265217764693, 3.4698014015738488, 3.5845584129141517, 3.6759496940181173, 3.74161963391516, 3.7794766549678767, 3.7877635951345336, 3.7651249304570173, 3.7106689594600906, 3.6240229976304343, 3.5053796118172587, 3.3555319692340593, 3.1758964896225517, 2.9685211756679744, 2.7360782570687943, 2.4818401162622568, 2.209637864407092, 1.9238023976742142, 1.6290882761635626, 1.33058131801865, 1.0335913741040892, 0.7435323261841938, 0.4657919142330366, 0.2055945252918259, -0.03213945458358671, -0.24293373401495177, -0.4228913749531025, -0.5688207657425118, -0.6783478243812652, -0.7500100634732965, -0.783328422372192, -0.7788532081709553, -0.7381810837043192, -0.6639407896829723, -0.5597461751716821, -0.43011611513538817, -0.2803619887855189, -0.11644454532111548, 0.05519684322637415, 0.22783839050440916, 0.39468432780573476, 0.5490913460354265, 0.6847980142790535, 0.7961515196855159, 0.8783236877689439, 0.9275081250187734, 0.9410905011120341, 0.9177844707656212, 0.8577265291940243, 0.7625241921871068, 0.6352532713933785, 0.4804016441865885, 0.30375874985718854, 0.11225202269791024, -0.08626646927659132, -0.2832778488782723, -0.46989140063688156, -0.6371675451853935, -0.7764580910624919, -0.8797517760524591, -0.9400122409152345, -0.9514951615955985, -0.9100313472623023, -0.8132632189514404, -0.6608232255108153, -0.4544444167617516, -0.19799554263130267, 0.10256437673515248, 0.4393141409692774, 0.8025800785407831, 1.1812230296039912, 1.5629949499645894, 1.934954310064854, 2.2839265632490156, 2.596993468466211, 2.86199310147721, 3.0680110876441793, 3.2058430293380638, 3.268408346173752, 3.251096829927381, 3.1520311369492076, 2.9722311615571635, 2.7156696796915107, 2.3892127125507443, 2.00244259143204, 1.5673665353474124, 1.098018487365432, 0.6099667840728672, 0.11974473853484854, -0.3557748130211421, -0.8000367178488077, -1.197465866556883, -1.5341068510775595, -1.7982129788325518, -1.9807578414482936, -2.075845009662894, -2.0809949826309357, -1.9972931534267406, -1.82938810240569, -1.5853357855339345, -1.2762918924898852, -0.9160615228930997, -0.5205220607449669, -0.10694140146721141, 0.3067808062542985, 0.7029167878484273, 1.064723875198855, 1.3772304384173562, 1.6279576169355405, 1.8075416700085098, 1.910225191619115, 1.9341904727980708, 1.8817147731025345, 1.7591349336615925, 1.5766173102028596, 1.3477380536182464, 1.0888879056586345, 0.8185244742415506, 0.556302971031092, 0.3221232175183833, 0.13513597987328985, 0.012755063626636932, -0.030277147644954216, 0.017275969845668905, 0.16245444782129845, 0.4075922677167673, 0.7500196039727749, 1.1819978240905318, 1.6908976905876285, 2.259619736651958, 2.8672439861125047, 3.489884630990631, 4.101714546879153, 4.676115178107324, 5.186899872194455, 5.609553620477556, 5.922429700933351, 6.107844129192731, 6.153012175610242, 6.050777424318521, 5.800092710635868, 5.406223410244882, 4.880656473375028, 4.240712698911399, 3.5088743464009307, 2.7118545607963687, 1.8794484971582845, 1.0432177694712081, 0.23506926365667105, -0.5142040944775469, -1.1763497513921635, -1.726978507590368, -2.1467173168258182, -2.4221325013022854, -2.5463745270062597, -2.519508750201047, -2.3485119049067396, -2.0469307957595713, -1.6342168449922718, -1.1347669234453694, -0.5767163803459032, 0.00945647010232315, 0.5924446956652494, 1.1416692689882602, 1.6287981015722373, 2.029149090727895, 2.322904034622504, 2.4960695949621177, 2.5411343462007125, 2.457386705745, 2.2508763809086596, 1.9340209539879818, 1.5248783339528291, 1.0461239828557996, 0.5237880601250631, -0.014179008783003213, -0.5394343245064126, -1.0247799901111925, -1.4456257428124053, -1.7812960777411886, -2.016109626049077, -2.1401711155226146, -2.1498322846085496, -2.047796766761628, -1.842864173925781, -1.5493292414415416, -1.1860717650023702, -0.7753910027172584, -0.3416531655640255, 0.09016832993883835, 0.49597371434232246, 0.8539512558208886, 1.1458413516013646, 1.3579752153677807, 1.4820263262322553, 1.5154298719205939, 1.4614453019440983, 1.3288586411129242, 1.1313431180522338, 0.8865176140338543, 0.6147611490600942, 0.3378569263827372, 0.07755037572594457, -0.1458885543885984, -0.31500832430002845, -0.416338755049532, -0.44129949923599693, -0.38679497535543894, -0.2554560166611452, -0.05551049197533572, 0.19971148248219595, 0.4926088556423765, 0.8024268933771904, 1.1065910431899582, 1.382173533807045, 1.6073994546838322, 1.7630955308689096, 1.8339874380389158, 1.8097602141736817, 1.6858106507289645, 1.4636396510205256, 1.1508552682363773, 0.760782067152664, 0.31169801107720385, -0.1742553918649524, -0.6724220558631504, -1.1571539900355534, -1.6034098328450748, -1.9883252204410835, -2.2926515429152476, -2.5019670706598935, -2.6075783388941702, -2.6070492587536123, -2.5043194835842675, -2.309400583417847, -2.037666824804445, -1.7087849548409224, -1.345352487508495, -0.9713348535760149, -0.6104069129497479], 'positive_zeros': ['2.39404286061527545470700387762297', '3.20396144410593418876019292818487', '4.13479061438517346013965712432394', '4.90273853094022032181335062300139', '6.16684971754953097309217392337786', '7.04629587770525720046073855524228', '8.095475412748459834666754746000744', '8.191317221559137847971361455914597', '9.685758291488366149210341725319742'], 'prelabel': '2-1014-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1771140607729988808, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39404286061527545470700387762', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20396144410593418876019292818', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13479061438517346013965712432', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.096830764957835, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, -3, 1, -2, 1, 1, -3, -6, 1, 0, -2, -3, 1, -3, 1, -2, -3, -2, -6, -6, 1, 4, 0, 1, -2, 3, -3, 4, 1, -6, -3, 6, 1, 7, -2, 0, -3, 3, -2, -10, -6, -3, -6, -6, 1, -3, 4, -3, 0, 3, 1, 18, -2, -2, 3, 0, -3, -7, 4, -2, 1, 0, -6, 10, -3, -6, 6, -6, 1, 13, 7, 4, -2, 12, 0, -4, -3, 1, 3, 6, -2, 9, -10, 3, -6, -18, -3, 0, -6, 4, -6, 6, 1, -14, -3, -6, 4], 'euler11': [1, 6, 11], 'euler13': [1, 0, 0], 'euler17': [1, 3, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 6, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -7, 37], 'euler41': [1, -3, 41], 'euler43': [1, 10, 43], 'euler47': [1, 6, 47], 'euler5': [1, 3, 5], 'euler53': [1, -3, 53], 'euler59': [1, 0, 59], 'euler61': [1, 7, 61], 'euler67': [1, -10, 67], 'euler7': [1, 2, 7], 'euler71': [1, 6, 71], 'euler73': [1, -13, 73], 'euler79': [1, 4, 79], 'euler83': [1, -6, 83], 'euler89': [1, 18, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 3, 5], [1, 2, 7], [1, 6, 11], [1, 0, 0], [1, 3, 17], [1, 2, 19], [1, 6, 23], [1, -3, 29], [1, -4, 31], [1, -7, 37], [1, -3, 41], [1, 10, 43], [1, 6, 47], [1, -3, 53], [1, 0, 59], [1, 7, 61], [1, -10, 67], [1, 6, 71], [1, -13, 73], [1, 4, 79], [1, -6, 83], [1, 18, 89], [1, 14, 97]], 'index': 26, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1014/f', 'ModularForm/GL2/Q/holomorphic/1014/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/1014/2/a/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1014-1.1-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1014-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1771140607729988808, 'z1': {'__RealLiteral__': 0, 'data': '2.39404286061527545470700387762', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20681229
{'Lhash': '3034809869231061268560285860824', 'Lhash_array': ['3034809869231061268560285860824'], 'label': '2-1014-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/2/a/f'}
-
id: 24551418
{'Lhash': '3034809869231061268560285860824', 'Lhash_array': ['3034809869231061268560285860824'], 'label': '2-1014-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/2/a/f/1/1'}
-
id: 32508
{'Lhash': '1771140607729988808', 'Lhash_array': ['1771140607729988808'], 'label': '2-1014-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1014/f'}