-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2737477424497510208264808062769', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [57.62811813689564, 0.0], 'a6': [0.0, 0.0], 'a7': [-188.8843544106869, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.32145253980191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '108.1', 'coefficient_field': 'CDF', 'conductor': 108, 'conductor_radical': 6, 'conjugate': '2737477424497510208264808062769', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-57.62811813689564, 0], [3125.0, 0]], [[1.0, 0], [188.8843544106869, 0], [16807.0, 0]], [[1.0, 0], [704.0249450951651, 0], [161051.0, 0]], [[1.0, 0], [-795.5374176427476, 0], [371293.0, 0]], [[1.0, 0], [-180.56236273791276, 0], [1419857.0, 0]], [[1.0, 0], [661.7687088213738, 0], [2476099.0, 0]], [[1.0, 0], [3632.5124725475825, 0], [6436343.0, 0]], [[1.0, 0], [8021.868489202035, 0], [20511149.0, 0]], [[1.0, 0], [3003.877569088547, 0], [28629151.0, 0]], [[1.0, 0], [1520.3129117862618, 0], [69343957.0, 0]], [[1.0, 0], [3461.569148060053, 0], [115856201.0, 0]], [[1.0, 0], [-11815.755138177094, 0], [147008443.0, 0]], [[1.0, 0], [-5979.823188140448, 0], [229345007.0, 0]], [[1.0, 0], [13819.188284681413, 0], [418195493.0, 0]], [[1.0, 0], [22640.17241947276, 0], [714924299.0, 0]], [[1.0, 0], [37404.24505856486, 0], [844596301.0, 0]], [[1.0, 0], [-70964.65316160304, 0], [1350125107.0, 0]], [[1.0, 0], [-67766.95709187376, 0], [1804229351.0, 0]], [[1.0, 0], [31562.428459004597, 0], [2073071593.0, 0]], [[1.0, 0], [-62791.61923499234, 0], [3077056399.0, 0]], [[1.0, 0], [93431.46297584116, 0], [3939040643.0, 0]], [[1.0, 0], [-68793.13370699136, 0], [5584059449.0, 0]], [[1.0, 0], [-117773.96627013125, 0], [8587340257.0, 0]], [[1.0, 0], [-161885.6646344249, 0], [10510100501.0, 0]], [[1.0, 0], [-59324.571147511495, 0], [11592740743.0, 0]], [[1.0, 0], [21124.13351024941, 0], [14025517307.0, 0]], [[1.0, 0], [168897.51027635418, 0], [15386239549.0, 0]], [[1.0, 0], [61273.959484809115, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-108-1.1-c5-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/108/6/a/b/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.0, 0.5136677336376934, 0.998046001532905, 1.424775350453931, 1.767488024544502, 2.0030987755063943, 2.113358294505338, 2.086617591300467, 1.9196570876189425, 1.6193445025740163, 1.2038164818347805, 0.7028462194181482, 0.15707729220702005, -0.3841171797252994, -0.8662477369805537, -1.2346906864794305, -1.4406947600875186, -1.447818025809568, -1.2379830856558303, -0.8162006678003513, -0.21299971386460656, 0.5162486000343655, 1.2956003155795341, 2.0364034299767253, 2.6481641464685906, 3.051200112975108, 3.1893311636362855, 3.040529894265023, 2.6234414003216036, 1.9980536909553792, 1.2595652125061945, 0.5255822936136031, -0.08196587085571652, -0.45760405432619566, -0.532292063772486, -0.2887716074093673, 0.2311944344228561, 0.9300355030209462, 1.6686035833733934, 2.289823630151989, 2.6480339088847793, 2.6386486683940182, 2.222071038326537, 1.4363073088835925, 0.39454444846184394, -0.7331790974721908, -1.7516663113159057, -2.479835186101843, -2.789503671223156, -2.6349461246466386, -2.065788053568878, -1.2190156391485332, -0.29043479840636055, 0.5091416253033922, 1.0035528970651517, 1.0951468820741026, 0.7916577969482999, 0.20826489756748137, -0.4573676171708555, -0.9725517348850136, -1.1288765498540594, -0.7987974688615025, 0.025420848976918025, 1.2217829825449626, 2.562133502895855, 3.7650213653883347, 4.565452048867353, 4.7836921443192875, 4.374394074165577, 3.4415761853634557, 2.2136383508616597, 0.9834951924294417, 0.029104234921875225, -0.4638606946502527, -0.4548664572487752, -0.0605176219234671, 0.4795406711078247, 0.8746324239603189, 0.8730008661565375, 0.34325612728347765, -0.6779259323925608, -1.9880822618370757, -3.272876777875007, -4.197363398670569, -4.507908446143132, -4.1133699897268325, -3.1190961578089027, -1.8009652319331824, -0.5251897972210214, 0.3627459133768655, 0.6456443701109692, 0.3039091293941172, -0.4771282955921585, -1.3662520923224029, -1.9944186290335681, -2.077499773110671, -1.5131633565880616, -0.41853668900853463, 0.9058431892900238, 2.0756386574134313, 2.75349315948736, 2.7666165638591194, 2.169763740723964, 1.229792049397726, 0.33472686821375075, -0.14288230341250782, 0.018868097223996017, 0.8059891353839759, 1.9656382338551757, 3.089362895525447, 3.755421922892585, 3.680603982670823, 2.826712674896394, 1.421534116820438, -0.11589008815285035, -1.3209606910331324, -1.8484599595910274, -1.5963177054431175, -0.7414292877358212, 0.32754642881083806, 1.1570311443428636, 1.4008278354366184, 0.952612070358768, -0.013002783758627214, -1.1084190134501652, -1.8856812207796263, -2.0156543869028103, -1.4235637859695898, -0.3259089907936582, 0.8487575801308301, 1.626987265431676, 1.6812896583724042, 0.9688536357886529, -0.2392866621249526, -1.4539458395943328, -2.1539486751291763, -1.990921239594235, -0.9313008761208098, 0.7227018953752607, 2.4439592456522, 3.6806883360253377, 4.066523389673769, 3.5554341324699448, 2.4261338342087284, 1.1538805930801872, 0.20288776757324548, -0.173260455323823, -0.03777738803512663, 0.2636323926757747, 0.2651614865621687, -0.3967733047548439, -1.7974053087428856, -3.6571327433958976, -5.42888270899872, -6.507885629637554, -6.47827977767221, -5.2922071971555145, -3.3029595616668246, -1.1343743621744333, 0.5613600695256998, 1.3563679690007495, 1.2031265605533554, 0.42751159700294483, -0.4369686491879114, -0.8997408992286092, -0.7365010663721538, -0.08474439217501033, 0.6321879613199605, 0.9185590819378522, 0.45948228937444263, -0.7041494478361783, -2.163832230796437, -3.306261591983806, -3.5817218834196987, -2.7579096555639695, -1.0418837629922826, 0.9901615957695633, 2.629218000560399, 3.333134726221895, 2.955681890095625, 1.800876455523477, 0.4769342836260549, -0.38404020080906914, -0.41199943905105796, 0.34156189374152407, 1.4443450945893368, 2.304180606706153, 2.4645978739840513, 1.8329922661107214, 0.7302459917489384, -0.2645458319426795, -0.6015627102896133, -0.04147300209182071, 1.2081176004630234, 2.5721441036320223, 3.371068084110267, 3.1446286016013976, 1.880867573972085, 0.03714632887051236, -1.6617564315565119, -2.5555681640531116, -2.3528316198460972, -1.2609190883380126, 0.12209874164352276, 1.1021744434638936, 1.2272911191833153, 0.5030739608194792, -0.6204194647016553, -1.484350568937437, -1.5617985515668198, -0.7324237177912734, 0.6484703596442961, 1.9237386430729233, 2.465643532806919, 1.9978129401654003, 0.7432460707940381, -0.6802844226835475, -1.5683450664834218, -1.4873225340277083, -0.4989691611959314, 0.865533941758203, 1.873181259810652, 1.9652904632192645, 1.050806680489269, -0.43549639916141836, -1.7439123814601962, -2.1859116715516933, -1.4849823539055949, 0.07788741718897708, 1.8005547604957826, 2.9098293724371684, 2.9463880621488983, 1.986567504697663, 0.5871733012485681, -0.5162142894490505, -0.7975097589024911, -0.2089968007293743, 0.8123275193523631, 1.6042755136038538, 1.6648796145516205, 0.9535346169101971, -0.06035453323269317, -0.6357768274654165, -0.16478159609647783, 1.4712019789788018, 3.7883933715350318, 5.901032864882657, 6.939633605510565, 6.473800076420094, 4.720208764412336, 2.4271268619053705, 0.4966748124748628, -0.45567901302167, -0.37297803058905227, 0.27888226537928884, 0.825564453784846, 0.7968568432826626], 'positive_zeros': ['2.15948891911118990100055856966416', '3.56943105237776466554535272993675', '5.59754178581492614688608002415301', '6.25936863139840133919971146252467', '7.79586544670057594365706128323606', '9.199154689048109096497305727702817', '10.07402872452429506893550481858052', '10.89412472095523456153149960271528', '12.66321745753485678525558099401243'], 'prelabel': '2-108-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.161904917198603, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15948891911118990100055856966', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56943105237776466554535272994', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.59754178581492614688608002415', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17.32145253980191, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 108, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/108/6/a/b/1/2'], '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': '2-108-1.1-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-108-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.161904917198603, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15948891911118990100055856966', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2737477424497510208264808062769', 'Lhash_array': ['2737477424497510208264808062769'], 'label': '2-108-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/108/6/a/b/1/2'}