-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2074992273341784864207118042511', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.0473937938715371, -0.08208845894894876], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.7160630551645101, -0.41341919765597573], 'a8': [0, 0], 'a9': [1.4955076566049246, -2.5902952443479985], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.380552262766455, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [3.322346051916876, 1.4007200688618502]]]], 'bad_primes': [2, 5, 13], 'central_character': '1300.101', 'coefficient_field': 'CDF', 'conductor': 1300, 'conductor_radical': 130, 'conjugate': '565616443829482738647895348684', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.0473937938715371, 0.08208845894894876], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7160630551645101, 0.41341919765597573], [3.5, 6.06217782649107]], [[1.0, 0], [-1.5, 0.8660254037844386], [5.5, -9.526279441628825]], [[1.0, 0], [3.322346051916876, 1.4007200688618502]], [[1.0, 0], [0.7160630551645101, -1.2402575929679271], [-8.5, -14.722431864335457]], [[1.0, 0], [0.9261183264501012, 0.5346946650774116], [9.5, 16.454482671904334]], [[1.0, 0], [1.5429014504764615, 2.6723837032969473], [-11.5, 19.91858428704209]], [[1.0, 0], [3.7275584641738018, 6.456320648132437], [-14.5, 25.11473670974872]], [[1.0, 0], [0, -5.843251966110051], [-31.0, 0]], [[1.0, 0], [0.8518108345064697, -0.49179321460095005], [18.5, -32.04293994002423]], [[1.0, 0], [3.696152422706632, -2.133974596215561], [20.5, -35.50704155516198]], [[1.0, 0], [-4.770459914650264, 8.262678947644947], [-21.5, -37.239092362730865]], [[1.0, 0], [0, 3.4641016151377544], [-47.0, 0]], [[1.0, 0], [0.334307641618259, 0], [53.0, 0]], [[1.0, 0], [9.980515185935854, 5.762253129251214], [29.5, 51.09549882328188]], [[1.0, 0], [1.3582444367791213, -2.352548373599212], [-30.5, -52.827549630850754]], [[1.0, 0], [-11.912215477871142, 6.877520812793731], [33.5, -58.023702053557386]], [[1.0, 0], [-8.467038155750629, -4.888446758461457], [35.5, 61.48780366869514]], [[1.0, 0], [0, 11.180590488695998], [-73.0, 0]], [[1.0, 0], [0.25238725842048826, 0], [79.0, 0]], [[1.0, 0], [0, 5.671646164204205], [-83.0, 0]], [[1.0, 0], [-3.9805151859358543, 2.2981515141134587], [44.5, -77.07626093681505]], [[1.0, 0], [8.256982884465037, 4.767171291040022], [48.5, 84.00446416709055]], [[1.0, 0], [2.90072006886185, 5.024194537803417], [-50.5, 87.4685657822283]], [[1.0, 0], [10.075966577375306, 0], [103.0, 0]], [[1.0, 0], [-8.139773942044943, -14.09850202974705], [-53.5, 92.66471820493493]], [[1.0, 0], [0, -3.1297939735194955], [-109.0, 0]], [[1.0, 0], [5.085377082559191, -8.808131482638908], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-1300-13.10-c1-0-20', 'leading_term': '1.095359902648136499571544754730450160619087805447683863', '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/1300/2/y/b/101/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.0953599026481364, 1.2195872893206587, 1.339770149141053, 1.4557734146315324, 1.5672350187588107, 1.6735417886556643, 1.7738211106736355, 1.8669481401740324, 1.9515674448442255, 2.0261273849408132, 2.088925240242864, 2.138161028170491, 2.1719980328741446, 2.188628197135371, 2.1863406542406323, 2.1635917585514637, 2.119074998375062, 2.051789147979171, 1.96110295329514, 1.846814569330414, 1.709203898926656, 1.5490759430603, 1.3677932802370882, 1.1672958609234831, 0.9501064427942885, 0.7193202103966863, 0.4785774213367149, 0.23201829918958408, -0.015780153824486734, -0.2598852322988545, -0.4951067259525462, -0.7161108636873729, -0.9175479943749928, -1.0941913646259358, -1.2410837476341907, -1.3536881204864286, -1.4280381056352078, -1.4608835108930305, -1.4498260454117387, -1.3934401784809956, -1.2913741620447587, -1.1444264705855995, -0.9545933320072522, -0.7250836325669968, -0.4602982729283605, -0.16577201861596177, 0.15192299365927409, 0.48531169015885894, 0.8261867003255748, 1.165812091273382, 1.495155708594889, 1.8051443123838562, 2.08693448172162, 2.3321912076979534, 2.5333652576686263, 2.6839598212736626, 2.7787766848028794, 2.814132259202023, 2.7880342319544638, 2.7003104351282317, 2.552682717680984, 2.3487801609998478, 2.0940878481524594, 1.795829539309014, 1.462784953285174, 1.1050448298542075, 0.7337094599930778, 0.36053882397016435, -0.0024352321551025778, -0.3433223255180744, -0.650798253883666, -0.9145257795321459, -1.1255554873753983, -1.2766906514462444, -1.3628006078801669, -1.3810683510300017, -1.3311599327948478, -1.2153057159603395, -1.0382865443512588, -0.8073213524776799, -0.5318565264908113, -0.22326130632929608, 0.10556247136308183, 0.44064411705865975, 0.767465583110889, 1.071521889746188, 1.3388992169929357, 1.5568477303629862, 1.7143254340869194, 1.802489545859219, 1.8151131040303483, 1.748906751710664, 1.6037288465225317, 1.3826711277860952, 1.0920119980998915, 0.7410348659055664, 0.341714736824012, -0.09171790593976928, -0.5433211860347568, -0.9960738428624991, -1.4325705012745908, -1.8357518279331315, -2.1896386142362108, -2.4800375342541474, -2.695186447154423, -2.8263087047087376, -2.868048976950409, -2.8187675447950844, -2.6806756801569414, -2.459801428829331, -2.1657825574868332, -1.8114913034388622, -1.412503518701697, -0.9864324532672464, -0.552154398463714, -0.1289593483882847, 0.2643355914956891, 0.6102693890211115, 0.8935751200150777, 1.1019319973167037, 1.2265934295230454, 1.262857974377668, 1.210356655518671, 1.073138230266524, 0.8595432849090084, 0.5818680746336005, 0.2558293454499825, -0.10014853012018966, -0.46579341684999254, -0.8199534741258419, -1.1416281697885788, -1.4110126544389274, -1.6105039051929224, -1.7256175987875988, -1.7457678281179576, -1.6648674587476793, -1.481714923928423, -1.2001432413011524, -0.8289185493833505, -0.3813879586856576, 0.12511062848001048, 0.6700515137973124, 1.2307002018093631, 1.7832215963751283, 2.3038627759228483, 2.7701505741139227, 3.1620420498544193, 3.462967003437811, 3.66070602157286, 3.7480549767364946, 3.7232371564940983, 3.5900367849154913, 3.3576420078065237, 3.040200719741765, 2.6561081101761292, 2.227059659040878, 1.7769166896503585, 1.330442714885742, 0.9119770187538454, 0.5441166685137183, 0.24647909764407083, 0.03461438372386538, -0.08087056857125048, -0.09492425678504575, -0.008361185903992615, 0.17215110744005163, 0.4344328982467361, 0.7614469653004515, 1.1322351933911867, 1.523088637572316, 1.908888477337542, 2.264544414219079, 2.5664501434651354, 2.793873052770407, 2.9301975190966822, 2.9639480742031936, 2.8895300045650085, 2.7076400927468454, 2.4253184072175586, 2.055632318854613, 1.6170051307126923, 1.132222634241705, 0.6271703163400209, 0.12937066139898123, -0.3335970261200631, -0.7357034620667138, -1.0540088698015886, -1.2700433967780855, -1.3709445267287779, -1.3502804806382862, -1.208506011652053, -0.9530179522821344, -0.5978011868583463, -0.16268004730996655, 0.32778597830062906, 0.8457013300533879, 1.3614486125157064, 1.8454240612391029, 2.269791463743209, 2.610148985965012, 2.847006957779577, 2.966984560805331, 2.963649060495669, 2.8379418857266923, 2.5981603102893005, 2.259490298542138, 1.8431136305062301, 1.3749390264027348, 0.8840309753815256, 0.400829793281138, -0.0447292280401848, -0.42508186451405394, -0.7167697304804388, -0.9019338433784003, -0.9694705953812551, -0.9157735809467974, -0.7450097208220438, -0.468906784240196, -0.10605999187517377, 0.319204025847528, 0.7783389855767571, 1.2403746399476536, 1.6738852218765725, 2.049006875281411, 2.339375443385566, 2.5238593095088286, 2.5879734244542894, 2.5248796147712436, 2.3359036536963416, 2.0305298591255005, 1.625867280008182, 1.1456157307276686, 0.6185928195054524, 0.07691252228954959, -0.4460702045612514, -0.9179174625709384, -1.3092293222956382, -1.5955884073020916, -1.759198688006768, -1.790107428019661, -1.6869252263414636, -1.456991097671109, -1.1159655057510538, -0.6868718856673983, -0.19864398334338723, 0.3157301615683332, 0.8213488483850757, 1.2836828457654295, 1.6708565454728088, 1.9557722310046814, 2.117934288919771, 2.144848663872586, 2.0328999688065013, 1.787642706282931, 1.42348183326852, 0.9627588492495944, 0.43429995542210004], 'positive_zeros': ['1.63688028307500557084038409289303', '2.66774102065867158006319620689112', '3.98397187182884531953484054575661', '4.78611894188986557329392902061587', '5.67147026001342185927213227644249', '6.75688222228255308624469638912159', '7.42522677545455498488380694360057', '8.189149701983571041325834773593846', '9.446759459148467735885291800246836', '9.612925618110764636962131192155368'], 'prelabel': '2-1300-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.221886444734894, 'root_angle': 0.6310850469686837, 'root_number': '-0.4002739967602624010505123957413500831608876013197267170 + 0.9163955082373360503266381636292428033399287158449484331*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3155425234843419', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63688028307500557084038409289', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66774102065867158006319620689', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98397187182884531953484054576', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.380552262766455, 'bad_primes': [2, 5, 13], 'central_character': '13.10', 'conductor': 1300, 'conductor_radical': 130, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1300/2/y/b/101/2'], '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': '2-1300-13.10-c1-0-20', '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': '2-1300-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.221886444734894, 'root_angle': 0.31554252348434186, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63688028307500557084038409289', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2074992273341784864207118042511', 'Lhash_array': ['2074992273341784864207118042511'], 'label': '2-1300-13.10-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1300/2/y/b/101/2'}