-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '484526285313800720551362850654', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.0, 0], 'a4': [0, 0], 'a5': [1.0, 0], 'a6': [0, 0], 'a7': [0.1344652322969985, -0.23290061418995292], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.09986161255473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [67, [[1.0, 0], [-4.968600929395972, -6.504844717931819]]]], 'bad_primes': [2, 3, 5, 67], 'central_character': '4020.841', 'coefficient_field': 'CDF', 'conductor': 4020, 'conductor_radical': 2010, 'conjugate': '1707069056621425361769679877904', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.1344652322969985, 0.23290061418995292], [-3.5, -6.06217782649107]], [[1.0, 0], [3.0594085569357192, -5.299051061723646], [-5.5, -9.526279441628825]], [[1.0, 0], [1.1487242904834156, 1.9896488350057857], [-6.5, 11.258330249197702]], [[1.0, 0], [3.7659612103608415, 6.522836155678562], [-8.5, 14.722431864335457]], [[1.0, 0], [1.8818073035502367, 3.259385859803199], [-9.5, 16.454482671904334]], [[1.0, 0], [-2.577069765524042, -4.463615768537255], [-11.5, 19.91858428704209]], [[1.0, 0], [3.066639040173841, -5.311574626055348], [-14.5, -25.11473670974872]], [[1.0, 0], [5.253901140317574, -9.1000237129741], [-15.5, -26.846787517317598]], [[1.0, 0], [-2.6227797441316683, -4.542787773898549], [-18.5, 32.04293994002423]], [[1.0, 0], [-1.8079584863050195, 3.1314759562556143], [-20.5, -35.50704155516198]], [[1.0, 0], [-10.963135570481485, 0], [43.0, 0]], [[1.0, 0], [6.5513450254271, -11.347262441953355], [-23.5, -40.703193977868615]], [[1.0, 0], [-12.067505084624955, 0], [53.0, 0]], [[1.0, 0], [11.821517488128476, 0], [59.0, 0]], [[1.0, 0], [-4.894729671340152, -8.477920480076056], [-30.5, 52.827549630850754]], [[1.0, 0], [-4.968600929395972, -6.504844717931819]], [[1.0, 0], [6.025439444114564, -10.436367255135998], [-35.5, -61.48780366869514]], [[1.0, 0], [-0.16728832909686514, -0.2897518855090734], [-36.5, 63.21985447626402]], [[1.0, 0], [-4.9019601545782745, 8.490444044407758], [-39.5, -68.41600689897065]], [[1.0, 0], [-4.161358126544825, -7.207683703665275], [-41.5, 71.88010851410841]], [[1.0, 0], [1.4775139121517025, 0], [89.0, 0]], [[1.0, 0], [2.6481638106250918, 4.586754266767866], [-48.5, 84.00446416709055]], [[1.0, 0], [-5.550355340580345, 9.613497449946417], [-50.5, -87.4685657822283]], [[1.0, 0], [-1.6154493917694102, 2.7980404236008587], [-51.5, -89.20061658979718]], [[1.0, 0], [8.581184343503464, 0], [107.0, 0]], [[1.0, 0], [18.024315387130418, 0], [109.0, 0]], [[1.0, 0], [9.832595363768789, -17.03055474031373], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-4020-67.37-c1-0-6', 'leading_term': '1.552151232914901078019302451129140613965588962672002372', '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/4020/2/q/m/841/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.552151232914901, 1.373649065085164, 1.1858215038763327, 0.9890585648356202, 0.7837634069333141, 0.570412737850346, 0.34961607128496214, 0.12217017732503566, -0.11089445949292949, -0.3482777344742934, -0.5883864404986109, -0.82932440111394, -1.0688967908023546, -1.30462867695548, -1.5337973663245072, -1.7534777612194536, -1.9605996099552954, -2.1520152541271083, -2.32457621810266, -2.4752167451870863, -2.601042157852997, -2.69941970930529, -2.7680694078184938, -2.805152144036573, -2.8093523466482924, -2.779952345812694, -2.716895647999793, -2.620836430553149, -2.4931727569856728, -2.3360612995874495, -2.152411735767711, -1.9458594563514469, -1.7207157815296992, -1.481895513008288, -1.2348223448190814, -0.9853133921855328, -0.7394448562964363, -0.5034015984771367, -0.28331412347907275, -0.08508714045954502, 0.08577554674294936, 0.22434459907175647, 0.3264316009597985, 0.38874270141170175, 0.40901373669912267, 0.3861213467662435, 0.3201650152540098, 0.21251558712356036, 0.06582664195854668, -0.11599388902249774, -0.3278533006512005, -0.5635850175549665, -0.8160995523011876, -1.0775727913043964, -1.3396674243261362, -1.5937819265590987, -1.8313202015097814, -2.043973853658868, -2.2240081356275874, -2.364541954466297, -2.4598119683226143, -2.5054107920463555, -2.498489681459294, -2.4379167918715283, -2.324383204041355, -2.1604503626189606, -1.9505343456934692, -1.7008244321616475, -1.4191356951703649, -1.1146977513867566, -0.7978842535722704, -0.47989013652606016, -0.172365918138718, 0.11297957856508664, 0.364794973516678, 0.5725061036531245, 0.7267245267111114, 0.8196291504886128, 0.8453056617009538, 0.8000293147667625, 0.6824781328844343, 0.4938656449278025, 0.23798488024860634, -0.07884160676647431, -0.447907508482628, -0.8583625227310295, -1.2975405549992418, -1.7513671344054529, -2.204833327486812, -2.642520299453488, -3.049156035331077, -3.4101837253646017, -3.7123200526502047, -3.944081183228412, -4.096254706326285, -4.162297127015885, -4.138638759870834, -4.024880956245344, -3.8238744272981546, -3.541671871348587, -3.1873530166404382, -2.7727253611035367, -2.311909121074122, -1.8208199709686377, -1.316567842480024, -0.8167941386330918, -0.3389730053083497, 0.10029538277072403, 0.4859703612609907, 0.8052059831966819, 1.0479079913872729, 1.2071871535536431, 1.2796872388435634, 1.2657706590845124, 1.169550435895693, 0.9987634685113157, 0.7644868109430875, 0.4807055361956987, 0.1637474679043442, -0.16839370963098296, -0.4968199890933925, -0.8025438278431892, -1.0673216375588483, -1.2744697346490728, -1.409626398306649, -1.4614252074712901, -1.4220479702211417, -1.2876302250718494, -1.0584983151035579, -0.7392241756325592, -0.33849193693557816, 0.13122112037211336, 0.6541381876456769, 1.211831826624829, 1.784001305101396, 2.3493450623383385, 2.8864899314287604, 3.374935361803853, 3.795969388335012, 4.133513605298569, 4.37485695201686, 4.511242632704881, 4.538278808904504, 4.456151559397995, 4.2696276575284156, 3.9878445588840035, 3.6238951625481817, 3.1942249168464154, 2.7178681905283533, 2.2155590464729054, 1.708758204646055, 1.2186426980501133, 0.7651072306069108, 0.3658263637877885, 0.03542432941306348, -0.21520544848926987, -0.379395954984964, -0.454990955453428, -0.4444020917833192, -0.3544339682977279, -0.19588424708245286, 0.017062620549094052, 0.2676185408468032, 0.537312782985162, 0.8070041362457603, 1.0579321112811748, 1.272752293424924, 1.4365009902605559, 1.5374372273749655, 1.5677158443672605, 1.5238536875067232, 1.4069613051186831, 1.2227246218770849, 0.981134193147823, 0.6959731438187705, 0.3840880644325065, 0.06447925823372691, -0.24274286782872934, -0.517480394604805, -0.7407893166789109, -0.8959775333349232, -0.969598351900018, -0.9522830138431405, -0.8393634896793628, -0.6312473462915444, -0.3335193563265999, 0.043240958338608776, 0.4839212372843066, 0.9695975439643616, 1.4784801664874503, 1.9870360404202354, 2.471229141857143, 2.907812478267916, 3.2756010944168765, 3.5566551240639854, 3.737305463484465, 3.808962012229042, 3.768655296498375, 3.619276134469956, 3.3694941155894207, 3.0333531981709814, 2.6295607328787423, 2.180503696124544, 1.71104187549826, 1.2471412594970617, 0.8144211325652064, 0.436694715216395, 0.13458517484122934, -0.07570374150878142, -0.18339028954191167, -0.18382966252289068, -0.07889537890156381, 0.12300091859367726, 0.40725949064675737, 0.7537999275245932, 1.1380931697239862, 1.5324663969311298, 1.9076126951564134, 2.234224588043725, 2.484662034653097, 2.6345619206205706, 2.6642977009449074, 2.560204696415152, 2.3154983081976424, 1.9308285139511756, 1.4144336005979665, 0.7818781125655142, 0.055383228557362364, -0.7372190892867617, -1.5638551345811458, -2.3898296576001163, -3.1796100597401438, -3.8986770516096896, -4.5153393342559935, -5.002410768407644, -5.338655248869787, -5.509916789698184, -5.509869510471945, -5.340343357516017, -5.011205311915224, -4.539801163220987, -3.9499881955205236, -3.2708128553430535, -2.53490823400091, -1.776702742268047, -1.0305426589837365, -0.32883657280682477, 0.299671268998322, 0.8313990406693706, 1.249110497461598, 1.5427154009460242, 1.709642085990571, 1.7547625569733896, 1.6898773163365208, 1.5327936331418306, 1.306055538591758, 1.0354049748623382], 'positive_zeros': ['0.38222384403601907449044159830370', '2.00464830629251197438883492662004', '2.45697432412665481345968948169006', '3.68631652240236644835967839206293', '4.20301224022801294758569924507467', '5.42149852381632939747908541976301', '6.01733490515086848629581628286501', '6.63879604428936337908576861032913', '7.82657985532152754722055442724235', '8.172067728219022309598328888121523'], 'prelabel': '2-4020-67.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.665673976902901, 'root_angle': -0.5738977243796087, 'root_number': '-0.2300767501244324211650062692627845894614045586336582286 - 0.9731724867936718883162351313826310434778289886356743499*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.28694886218980437', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38222384403601907449044159830', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.00464830629251197438883492662', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.45697432412665481345968948169', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.09986161255473, 'bad_primes': [2, 3, 5, 67], 'central_character': '67.37', 'conductor': 4020, 'conductor_radical': 2010, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4020/2/q/m/841/7'], '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': '2-4020-67.37-c1-0-6', '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': '2-4020-67.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.665673976902901, 'root_angle': -0.28694886218980437, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38222384403601907449044159830', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '484526285313800720551362850654', 'Lhash_array': ['484526285313800720551362850654'], 'label': '2-4020-67.37-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4020/2/q/m/841/7'}