-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4072878812466805451908054317327', 'a10': [-8.900682880132855, 0.0], 'a2': [0.0, -2.548139112243958], 'a3': [-1.0, 0.0], 'a4': [-4.493012935347427, 0.0], 'a5': [0.0, -3.4930129353474273], 'a6': [0.0, 2.548139112243958], 'a7': [0.0, -1.0], 'a8': [0.0, 6.352543767888898], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [3.2562655434009815, -1.5481391122439583]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.64', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '774662319452723557840705373790', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.548139112243958], [-2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 3.4930129353474273], [-5.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -0.7081264311570232], [-11.0, 0]], [[1.0, 0], [3.2562655434009815, -1.5481391122439583]], [[1.0, 0], [-7.096278224487916, 0], [17.0, 0]], [[1.0, 0], [0, -0.3113917202975123], [-19.0, 0]], [[1.0, 0], [7.88116472867832, 0], [23.0, 0]], [[1.0, 0], [-5.297417590992367, 0], [29.0, 0]], [[1.0, 0], [0, 7.297417590992367], [-31.0, 0]], [[1.0, 0], [0, 1.4162528623140465], [-37.0, 0]], [[1.0, 0], [0, 11.80440465564494], [-41.0, 0]], [[1.0, 0], [3.297417590992367, 0], [43.0, 0]], [[1.0, 0], [0, 6.115796375942452], [-47.0, 0]], [[1.0, 0], [3.7276445826115587, 0], [53.0, 0]], [[1.0, 0], [0, -2.1955953443550604], [-59.0, 0]], [[1.0, 0], [-2.512531086801963, 0], [61.0, 0]], [[1.0, 0], [0, -9.178582319670687], [-67.0, 0]], [[1.0, 0], [0, 0.7081264311570232], [-71.0, 0]], [[1.0, 0], [0, 5.215113495809596], [-73.0, 0]], [[1.0, 0], [2.7848865041904043, 0], [79.0, 0]], [[1.0, 0], [0, -6.115796375942452], [-83.0, 0]], [[1.0, 0], [0, 11.101822246637306], [-89.0, 0]], [[1.0, 0], [0, -7.79886063349555], [-97.0, 0]], [[1.0, 0], [-17.69111340647265, 0], [101.0, 0]], [[1.0, 0], [-5.526505216107108, 0], [103.0, 0]], [[1.0, 0], [-19.17858231967069, 0], [107.0, 0]], [[1.0, 0], [0, 3.206530578280978], [-109.0, 0]], [[1.0, 0], [5.297417590992367, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-273-13.12-c1-0-15', '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/273/2/c/c/64/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7177925118763568, 0.9090220085916398, 1.1294921393459294, 1.3855408217892804, 1.682023043438497, 2.0216385578210727, 2.4044295492337677, 2.827396995160393, 3.2842027866231707, 3.764963653514771, 4.256175509435087, 4.7408232433760675, 5.198731908886805, 5.607204107998148, 5.941968053400958, 6.178433422078667, 6.29321958672858, 6.265885401003288, 6.080754362787311, 5.7286973139614785, 5.20871095949511, 4.529118599423584, 3.7082233414298176, 2.774266475312788, 1.7645858337722207, 0.7239299345473382, -0.29803983854515964, -1.24994066457908, -2.082347409560235, -2.7516743763042184, -3.2239145329252916, -3.4778602971149133, -3.5074368529263884, -3.322828634498169, -2.950172558916778, -2.4297229365211317, -1.8125521331718142, -1.1560221607131949, -0.5184256142329958, 0.04667196925617333, 0.495773144477123, 0.7998423974061101, 0.9471849144760833, 0.944384376433612, 0.8150854746384345, 0.5966674832975569, 0.33513472166959224, 0.07881140557366083, -0.1283665423790655, -0.25305705343438667, -0.27731430126087975, -0.20122271397948868, -0.042856960629037946, 0.1645793705310515, 0.37816992994552273, 0.5525780083771329, 0.6481895525891889, 0.6388599247924072, 0.5179701134820438, 0.30165059968993285, 0.028380779252045855, -0.24531589992535888, -0.45275094179182357, -0.5275742112391958, -0.4154225729602338, -0.0848916560015031, 0.4640711775955584, 1.1960295126985574, 2.041327211555262, 2.9031433964157163, 3.669795732270366, 4.230831124531727, 4.494665569416578, 4.405048952755311, 3.9535476910167078, 3.1856134570393873, 2.1986231311805966, 1.131440187274029, 0.14639894650732516, -0.5940592774355865, -0.9527913153458893, -0.8414687094494889, -0.2382538105581945, 0.803681186783634, 2.1588678564332713, 3.6438772006668962, 5.041786368813224, 6.133516067222538, 6.731430249581702, 6.709924036385208, 6.027904231768567, 4.739115097971883, 2.98805534749265, 0.9915063937137863, -0.9919192853520458, -2.699706209502826, -3.904917317601822, -4.450842886411333, -4.27505060806153, -3.4187094440544414, -2.019468015207586, -0.28894416958687896, 1.5214598757979887, 3.160646557532798, 4.416982675986531, 5.149845620751628, 5.30823373147485, 4.933463907886007, 4.145886488564621, 3.1184747186014943, 2.042535557929354, 1.0921738610212983, 0.3942441232655251, 0.009312840585995448, -0.07313798791868396, 0.07504485396340889, 0.34234835650178447, 0.6061312074830478, 0.7616883807073127, 0.7455274885566274, 0.5479270140640184, 0.21229346266604954, -0.1781809066556924, -0.5231873408159047, -0.7318070127139658, -0.746486385745186, -0.5586926623670921, -0.21239165888958253, 0.20564391683199854, 0.5865324118227271, 0.8261111225021823, 0.8514014223961022, 0.6401188399443246, 0.2281316325253076, -0.2974345116523911, -0.8182759025223744, -1.213666509400085, -1.390997810628887, -1.3104131276883508, -0.9969183382500485, -0.5361366740052771, -0.05379377879812623, 0.3168235486461149, 0.4718054156092673, 0.3685986014801262, 0.04415354724492297, -0.3869021407916374, -0.7557148091631853, -0.8806457675464151, -0.6182083009319751, 0.08821448833144732, 1.1742613655009198, 2.4452466871636243, 3.596877234050269, 4.264808586752327, 4.09502154238399, 2.8214947301847215, 0.33480326672532995, -3.2740779085882155, -7.706263402295344, -12.488177087278062, -17.04147633652921, -20.77761603557122, -23.199193746979212, -23.98805923217922, -23.062269948803042, -20.59000593855083, -16.95729569599561, -12.695972208258967, -8.386563750900862, -4.555964487792417, -1.590550355398943, 0.3182938350578303, 1.1866515453086988, 1.2083412499008475, 0.691958295327375, -0.01940688373717746, -0.626808544683398, -0.9349059845373314, -0.8801881066615106, -0.5240272187292973, -0.01535227940922421, 0.46509375151475685, 0.763059681582672, 0.7960834345560454, 0.5744722514855006, 0.19369749533614616, -0.19814968252586715, -0.4475118823409724, -0.44309906864391846, -0.15039890108088746, 0.3768098488068615, 1.0110298960347976, 1.587321317895389, 1.950718450784102, 2.0010615969714607, 1.7222587216500298, 1.1874417267012114, 0.5383983046541683, -0.05490664605626383, -0.4430781763277005, -0.5401384530823634, -0.3478608575181671, 0.045760682031278706, 0.4937446698516737, 0.8352685974258939, 0.9454328082311604, 0.7746361080132497, 0.36527011905078516, -0.16007624638944493, -0.6362364972211819, -0.9082193734359535, -0.8832385186217501, -0.5655357507473442, -0.061845776591948017, 0.44638188402907036, 0.757919694774384, 0.718966331164765, 0.28276624331982664, -0.45760430336661895, -1.2761695497451542, -1.8629326437452391, -1.904781173536378, -1.178273762229397, 0.3710748494604978, 2.5868031513312446, 5.1121766042560814, 7.455564524030392, 9.09773759390938, 9.616019854214848, 8.794021114000865, 6.6875784839127865, 3.627442736614717, 0.15484221427586367, -3.0966303176298475, -5.5449358390624655, -6.793882371664122, -6.723919838072442, -5.516069072910693, -3.602475368317158, -1.5559051243237454, 0.05369936665408539, 0.7989888498344326, 0.49580907576183186, -0.7603543697412937, -2.630016378892383, -4.626333806270724, -6.245850537506985, -7.098092687951289, -7.000048136125622, -6.012001490473416, -4.407755815655911, -2.5902636748419083, -0.9780905639352966, 0.10498143190929134, 0.5072572432473518, 0.2740431813867038], 'positive_zeros': ['3.21293486685804373081758743109339', '4.86374818263898927334881126369498', '5.91801995402354912442480024431640', '6.52752445078229326534894579802455', '7.51249046528629412577441756403330', '8.147926632089599461638946615320373', '9.771107279039526941811800529863854', '10.28324683594302174358427015247520', '11.68633263702775756215921046041499', '12.64485650077636413445991299039590'], 'prelabel': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.6412666665268626, 'root_number': '-0.42937653467283776 - 0.9031255679429884*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.320633333263', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.21293486685804373081758743109', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.86374818263898927334881126369', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.91801995402354912442480024432', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.12', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/c/c/64/2'], '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': '2-273-13.12-c1-0-15', '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': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.3206333332634313, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.21293486685804373081758743109', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4072878812466805451908054317327', 'Lhash_array': ['4072878812466805451908054317327'], 'label': '2-273-13.12-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/c/c/64/2'}