-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2392313279781413011734040264988', 'a10': [0.0, 0.0], 'a2': [0.5, 0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [-0.5, 0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [19, [[1.0, 0], [-4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.7', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '3853216520094758759367504954208', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [-1.5, 2.598076211353316], [-6.5, -11.258330249197702]], [[1.0, 0], [2.0, 3.4641016151377544], [-8.5, 14.722431864335457]], [[1.0, 0], [-4.0, 1.7320508075688772]], [[1.0, 0], [2.0, -3.4641016151377544], [-11.5, -19.91858428704209]], [[1.0, 0], [0, 0], [-14.5, -25.11473670974872]], [[1.0, 0], [3.0, 0], [31.0, 0]], [[1.0, 0], [5.0, 0], [37.0, 0]], [[1.0, 0], [2.0, 3.4641016151377544], [-20.5, 35.50704155516198]], [[1.0, 0], [-4.5, -7.794228634059948], [-21.5, 37.239092362730865]], [[1.0, 0], [5.0, -8.660254037844387], [-23.5, -40.703193977868615]], [[1.0, 0], [-2.0, 3.4641016151377544], [-26.5, -45.89934640057525]], [[1.0, 0], [-7.0, -12.12435565298214], [-29.5, 51.09549882328188]], [[1.0, 0], [5.5, -9.526279441628825], [-30.5, -52.827549630850754]], [[1.0, 0], [1.5, -2.598076211353316], [-33.5, -58.023702053557386]], [[1.0, 0], [7.0, 12.12435565298214], [-35.5, 61.48780366869514]], [[1.0, 0], [-5.5, -9.526279441628825], [-36.5, 63.21985447626402]], [[1.0, 0], [0.5, 0.8660254037844386], [-39.5, 68.41600689897065]], [[1.0, 0], [-8.0, 0], [83.0, 0]], [[1.0, 0], [-7.0, 12.12435565298214], [-44.5, -77.07626093681505]], [[1.0, 0], [1.0, 1.7320508075688772], [-48.5, 84.00446416709055]], [[1.0, 0], [-5.0, 8.660254037844387], [-50.5, -87.4685657822283]], [[1.0, 0], [3.0, 0], [103.0, 0]], [[1.0, 0], [10.0, 0], [107.0, 0]], [[1.0, 0], [7.0, 12.12435565298214], [-54.5, 94.39676901250381]], [[1.0, 0], [-10.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-114-19.7-c1-0-1', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/114/2/e/b/7/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2943874428836089, 1.2476524221468057, 1.214505975985502, 1.1905563675822832, 1.1707146378034932, 1.1496204572304252, 1.1219906976268301, 1.0828781972618564, 1.027868987473125, 0.9532551998396429, 0.8562101069932551, 0.7349754074039389, 0.5890565607234592, 0.4194118021281781, 0.2286140682889497, 0.020961659122450325, -0.19748748451609016, -0.4189816611942706, -0.6342615498635993, -0.8328806344068918, -1.0036654517257173, -1.1353105052307713, -1.2170902073531766, -1.2396566686649435, -1.195878525872037, -1.0816635252458906, -0.8966976497580904, -0.6450276570124803, -0.33541336457567567, 0.018617974321526034, 0.3990695811309881, 0.7841590062753523, 1.14939397713763, 1.46901314234273, 1.7177281030999445, 1.872666179740475, 1.9153795202718604, 1.8337592884620892, 1.6236776320000537, 1.2901783606617743, 0.8480523192689514, 0.3216665691830789, -0.2560327363649697, -0.8453578432499007, -1.4024943384483102, -1.8827489561974888, -2.244207003953356, -2.4515091038721737, -2.479410123641049, -2.3157643249235806, -1.9635957132601813, -1.4419642898064948, -0.7854267109123776, -0.04200899344544811, 0.730249537918993, 1.4679704794407185, 2.107972311768169, 2.593188020877949, 2.8783991507557243, 2.9351882580018134, 2.755540774434652, 2.3536216058327044, 1.7654076295613406, 1.0460631743807376, 0.2651829534266238, -0.4997286181081072, -1.1709491073655234, -1.6786335044697054, -1.9684458203667776, -2.007851877840151, -1.7902930914761181, -1.3366553140757567, -0.6937253995541648, 0.07033620463453613, 0.8731226384519037, 1.626989998178116, 2.2489639798862533, 2.6703963991220254, 2.845194985703365, 2.7555673068444646, 2.414478953196493, 1.864403239629761, 1.172393059521065, 0.4219802134931666, -0.297158453613472, -0.9004964028562176, -1.3194632257070968, -1.5103175906236326, -1.45984881645308, -1.1870538880003378, -0.7404590972927373, -0.19134909020071064, 0.376249493365178, 0.8774917398110198, 1.2388864150516912, 1.4089619564041111, 1.3658297148671341, 1.1204481269600897, 0.7149886201788219, 0.21641886388463594, -0.2938503213368416, -0.7327720751673096, -1.0290039345253452, -1.1346989548524438, -1.0338200566839615, -0.7455160512394104, -0.32181872999339484, 0.16020321893230727, 0.6107964515467628, 0.9425610181412424, 1.085821374248072, 1.0017967395800444, 0.6912585504058929, 0.19697449124476388, -0.4008354195301246, -0.9956973555435611, -1.4712843762140653, -1.72061976971934, -1.66507495932716, -1.2700047895868969, -0.5542257549448988, 0.4086120437240091, 1.497492150477881, 2.5596638076508826, 3.432388619800441, 3.967637810169292, 4.055923976733084, 3.645394512834686, 2.75289330346642, 1.464848806360551, -0.07259393820750606, -1.673054038699568, -3.1362546326968768, -4.277249494389221, -4.953958692481598, -5.088571286817212, -4.679255518349985, -3.8001238654796015, -2.58929656335985, -1.2268808708671448, 0.09360257266893415, 1.1956645114856648, 1.9471100278154692, 2.2795604865613206, 2.1969690127850474, 1.7717485245408477, 1.1292853321741991, 0.42365584167884823, -0.19107076701789658, -0.5887674197847391, -0.6933822775523258, -0.49129049943927516, -0.031688004927309055, 0.5849252702594034, 1.2278887977117927, 1.7630403850112233, 2.079714911718778, 2.1128223909010515, 1.855674058127291, 1.3610077439321138, 0.7299694932547814, 0.09119656398026374, -0.42585073159530895, -0.7179490305869098, -0.7300421238053022, -0.46746426342607383, 0.00423132885891748, 0.5720493464406113, 1.0985654509420337, 1.4506449980797769, 1.5280464263456115, 1.2859576704998696, 0.7466046481087907, -0.002803989277309992, -0.8257777107060598, -1.56303859898816, -2.0646278823879727, -2.2211172677760422, -1.9874049231556212, -1.3939221467220566, -0.5425466192169359, 0.41236699982497704, 1.29429938075746, 1.940195371295799, 2.2340838568445345, 2.131565981812648, 1.6697628610326574, 0.9602282028985536, 0.16586996563993495, -0.5336414033306871, -0.9809063863193944, -1.0760267516745698, -0.8003365232127023, -0.2231503143738197, 0.5104913530546508, 1.209085179863724, 1.675216510302146, 1.7490523223716183, 1.3455040565685974, 0.4768230020245891, -0.7447700326998414, -2.125724633445242, -3.4278631163282727, -4.415967513081808, -4.906515373949333, -4.807278289757661, -4.13913453513237, -3.034984624545089, -1.7153879179156943, -0.4454729208386212, 0.5182452764760057, 0.9801817979674748, 0.846148243887037, 0.14331279198645822, -0.9847728882485478, -2.3072594977847403, -3.553233778943121, -4.467214334498021, -4.861199644992007, -4.65225618000594, -3.8777301625816145, -2.6850031833051053, -1.2982374604550355, 0.03044699630273106, 1.0745668618535964, 1.6798889184322066, 1.793973859069615, 1.4724780329295817, 0.8613263447572723, 0.15932398831914596, -0.42984863858873845, -0.7450199626087327, -0.7033704346672139, -0.31666850935147145, 0.3154478894128018, 1.0330184489064587, 1.657078474778455, 2.034474787259669, 2.0751794963234644, 1.773043327280041, 1.2050780479745742, 0.5097097900660696, -0.15030401715004138, -0.6307476675502097, -0.8435760800455462, -0.7795421078294785, -0.5098243169356512, -0.1659950396283545, 0.09673246119389771, 0.14358931427501861, -0.09986476875635307, -0.622829189534087, -1.3265353719401065, -2.0453887411109797, -2.587508008027423, -2.78495516138733, -2.5410007724071115], 'positive_zeros': ['1.88720241946061314769023443231006', '3.61870851811828748658304663038188', '5.19544346410358851280221525080857', '6.63182940809195906115128037212369', '8.042395623129522344473548287943334', '9.113955766948714279850299130542843', '10.44669732874482476927455045213883', '11.41664737948096430275132660373054', '12.42716835803818488674609293871586', '13.33372181003026943671910859256729'], 'prelabel': '2-114-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.3956535144175596, 'root_number': '0.3219743516549716 - 0.9467483915361888*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.197826757209', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88720241946061314769023443231', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.61870851811828748658304663038', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.19544346410358851280221525081', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/e/b/7/1'], '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': '2-114-19.7-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-114-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.1978267572087798, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88720241946061314769023443231', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2392313279781413011734040264988', 'Lhash_array': ['2392313279781413011734040264988'], 'label': '2-114-19.7-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/e/b/7/1'}