-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1046873486400682602321094117837', 'a10': [0, 0], 'a2': [0, -0.41421356237309503], 'a3': [0, 0], 'a4': [1.82842712474619, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 2.414213562373095], 'a8': [0, -1.5857864376269049], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.762974500266903, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.199', 'coefficient_field': 'CDF', 'conductor': 2475, 'conductor_radical': 165, 'conjugate': '1605351960613360271027220310892', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.41421356237309503], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.414213562373095], [-7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-13.0, 0]], [[1.0, 0], [0, 0.41421356237309503], [-17.0, 0]], [[1.0, 0], [3.585786437626905, 0], [19.0, 0]], [[1.0, 0], [0, 1.0], [-23.0, 0]], [[1.0, 0], [-6.82842712474619, 0], [29.0, 0]], [[1.0, 0], [-8.48528137423857, 0], [31.0, 0]], [[1.0, 0], [0, -5.82842712474619], [-37.0, 0]], [[1.0, 0], [8.899494936611665, 0], [41.0, 0]], [[1.0, 0], [0, 0.3431457505076198], [-43.0, 0]], [[1.0, 0], [0, -9.48528137423857], [-47.0, 0]], [[1.0, 0], [0, -3.65685424949238], [-53.0, 0]], [[1.0, 0], [-11.0, 0], [59.0, 0]], [[1.0, 0], [-3.1715728752538097, 0], [61.0, 0]], [[1.0, 0], [0, -11.65685424949238], [-67.0, 0]], [[1.0, 0], [2.1715728752538097, 0], [71.0, 0]], [[1.0, 0], [0, 3.1715728752538097], [-73.0, 0]], [[1.0, 0], [4.757359312880715, 0], [79.0, 0]], [[1.0, 0], [0, 12.48528137423857], [-83.0, 0]], [[1.0, 0], [7.656854249492381, 0], [89.0, 0]], [[1.0, 0], [0, 0.1715728752538099], [-97.0, 0]], [[1.0, 0], [-4.899494936611665, 0], [101.0, 0]], [[1.0, 0], [0, 2.34314575050762], [-103.0, 0]], [[1.0, 0], [0, -17.31370849898476], [-107.0, 0]], [[1.0, 0], [-17.31370849898476, 0], [109.0, 0]], [[1.0, 0], [0, -10.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-2475-5.4-c1-0-34', 'leading_term': '2.3361382760038575504949290978643782618069000814586651151', '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/2475/2/c/o/199/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.3361382760038576, 2.272583162241043, 2.1993446185260317, 2.116216004867749, 2.022891806691963, 1.91900696899238, 1.80418251486288, 1.6780750187220759, 1.5404274705633396, 1.3911192017396383, 1.2302127933965137, 1.057996200199091, 0.8750186466270229, 0.6821191572836046, 0.48044684874908883, 0.27147233470627974, 0.056989784386402426, -0.1608906617767546, -0.37976026302781446, -0.5969388266361552, -0.8095114621587305, -1.0143745921034057, -1.2082906736830015, -1.3879508735881838, -1.5500447115668903, -1.6913354548749227, -1.8087398118390698, -1.8994102475341288, -1.9608180373555049, -1.9908349948458006, -1.9878116682309022, -1.9506497050357723, -1.8788660443898304, -1.7726466195627304, -1.632887344782372, -1.4612203245747961, -1.2600234627508926, -1.0324119614497698, -0.782210585527374, -0.5139060186126814, -0.23257914622121995, 0.05618234235183313, 0.34639005132744566, 0.6317780841930666, 0.9059411576315158, 1.162484832077547, 1.3951845144875121, 1.5981493950445447, 1.7659870650318195, 1.8939642474322473, 1.9781588727244173, 2.015598665190712, 2.004381482034998, 1.9437728770981078, 1.83427674690654, 1.677675458220099, 1.4770365469042284, 1.2366839061083992, 0.9621323301461902, 0.6599853265795574, 0.33779722529230005, 0.0039017679141756527, -0.3327894816296311, -0.6630144424721127, -0.9774080276095882, -1.2667634166033788, -1.522299866323279, -1.7359292441272434, -1.9005130962733598, -2.010101938962314, -2.060148599390466, -2.0476878507117213, -1.971475280052958, -1.8320792952559621, -1.6319213963761297, -1.375261284677393, -1.0681250177736, -0.7181761985922627, -0.33453205407396885, 0.07247184326312332, 0.49156259630996935, 0.9108493737667674, 1.3181722083658116, 1.7014698877512773, 2.0491555639558943, 2.3504879955107807, 2.5959260137402187, 2.7774539021202838, 2.888865911252594, 2.9259991032989423, 2.886905113768356, 2.7719532040086916, 2.5838591071313126, 2.327636580678825, 2.0104711948077965, 1.641518617385041, 1.231632410873366, 0.7930290285849957, 0.3389001865469967, -0.1170150091040598, -0.5608839751942136, -0.9792450407539791, -1.3594659216379048, -1.6901796493867995, -1.9616817007955414, -2.1662730791778513, -2.298535714544308, -2.355528737860991, -2.3368968799967256, -2.2448853618777864, -2.0842590714391407, -1.8621274410334707, -1.5876801093356716, -1.2718420302537552, -0.926860031789819, -0.5658357880427394, -0.20222261548856973, 0.15069467588680652, 0.48031654988687356, 0.7752214988139909, 1.0256146804309727, 1.223713693326729, 1.3640549142455916, 1.443706730301986, 1.462379552696333, 1.422426568279995, 1.328733616367885, 1.188501194994293, 1.0109262136351258, 0.8067955220302974, 0.5880072625699376, 0.36703953236699627, 0.1563885348084693, -0.03199979025450734, -0.1872798491613886, -0.3002136182834576, -0.36361175275831514, -0.37268769344720193, -0.32530723786275256, -0.22212025875823177, -0.06656617797045183, 0.13524976335452638, 0.37480667951307356, 0.6415361458227601, 0.9232941833548032, 1.2069180064560023, 1.4788440670028116, 1.725760512711677, 1.9352648765231084, 2.0964967689055882, 2.2007156413910645, 2.241795356126489, 2.216610299585109, 2.1252920235615713, 1.9713407279542254, 1.7615821074793785, 1.5059669110863763, 1.2172177142755218, 0.9103345620342721, 0.6019779743519272, 0.3097539922160841, 0.05143117419220073, -0.15587653880860497, -0.2965246127978017, -0.3571129356945174, -0.3271843811258599, -0.1998127132446606, 0.027950252584579546, 0.3547926857803389, 0.7750435020602917, 1.278765450678037, 1.8520415361058216, 2.4774469121632396, 3.1346896447503427, 3.8013955404195454, 4.454004982387245, 5.068743770412752, 5.622625641645237, 6.094441702978903, 6.465691596207768, 6.721412917140234, 6.850869191693612, 6.84806244819915, 6.712043890815708, 6.447005060033468, 6.062141772264351, 5.571293611371587, 4.992372311249195, 4.346602514239673, 3.6576076170354828, 2.9503812578733206, 2.25019104653193, 1.5814650598726276, 0.9667131845761174, 0.42553445982124444, -0.02624185018603522, -0.37723952402990896, -0.621009002058462, -0.7562671003524025, -0.7868896441226572, -0.7216557513769217, -0.5737546554970552, -0.36007776504896855, -0.10032952564083318, 0.1839999885457007, 0.4707504635959437, 0.738239469692507, 0.9663858193476161, 1.1377512671188121, 1.2384471491152746, 1.2588588097684072, 1.1941494016162235, 1.044515469717859, 0.8151791291951308, 0.5161150046636016, 0.16152375459232002, -0.23092274597700585, -0.6410273353243318, -1.0471569656541475, -1.427419832656723, -1.7608691667767842, -2.0286703936578436, -2.21516941665118, -2.3088040932229235, -2.3028084009910526, -2.195668983226824, -1.9913062411370108, -1.6989662846714646, -1.332825148779664, -0.9113219478268623, -0.45625227320500994, 0.008333647768838257, 0.45737244516225295, 0.8661048667586322, 1.2113998806732043, 1.4730152399277556, 1.634726396587847, 1.6852615876150774, 1.6189902615369527, 1.4363243326097535, 1.143806428094308, 0.7538755874210804, 0.28431793197156585, -0.2425732528589466, -0.8010877080834762, -1.3633843962192447, -1.9009081844768854, -2.385863604312556, -2.792668213067133, -3.099308132403893, -3.2885225587982228, -3.3487522673374417, -3.274798974421698, -3.0681572967750173, -2.7369981778139487, -2.2958011464726926, -1.764651638211512], 'positive_zeros': ['0.825837566133919069551858940146496', '2.07220445527602218971514067217700', '3.09824448593868953450048168933594', '4.00282648596314592558570647685659', '5.01424335622174041718690737792203', '5.91941450071104346119706323585985', '6.74469854820058251521346718012177', '7.12735710776379555242053239452725', '8.187151010416979929019807258735424', '8.475265550529535371851710393436616'], 'prelabel': '2-2475-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.445556714323517, 'root_angle': -0.14758361765043326, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.825837566133919069551858940146', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.07220445527602218971514067218', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09824448593868953450048168934', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.762974500266903, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/2/c/o/199/2'], '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': '2-2475-5.4-c1-0-34', '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': '2-2475-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.445556714323517, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.825837566133919069551858940146', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1046873486400682602321094117837', 'Lhash_array': ['1046873486400682602321094117837'], 'label': '2-2475-5.4-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/c/o/199/2'}