-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4197296347150633712375663229772', 'a10': [-0.7480033296391447, -3.0725382046198795], 'a2': [0.06717911984124394, -1.4126170627092665], 'a3': [0.6389801154854937, -2.3847062560180916], 'a4': [-1.9909739317147115, -0.18979674189106366], 'a5': [2.14503484417433, -0.6315263393382796], 'a6': [-3.3257506250463167, -1.0628366812259495], 'a7': [1.6079571245726105, 2.1010649408183895], 'a8': [-0.4018619924013984, 2.7997333692805784], 'a9': [-2.6804521281526523, -1.5475597577388391], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.06717911984124394, 1.4126170627092665]]], [5, [[1.0, 0], [-2.14503484417433, 0.6315263393382796]]], [7, [[1.0, 0], [-1.6079571245726105, -2.1010649408183895]]]], 'bad_primes': [2, 5, 7], 'central_character': '140.107', 'coefficient_field': 'CDF', 'conductor': 140, 'conductor_radical': 70, 'conjugate': '2228102822413595169265877716481', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.06717911984124394, 1.4126170627092665]], [[1.0, 0], [-0.6389801154854937, 2.3847062560180916], [-2.598076211353316, -1.5]], [[1.0, 0], [-2.14503484417433, 0.6315263393382796]], [[1.0, 0], [-1.6079571245726105, -2.1010649408183895]], [[1.0, 0], [4.095884265209227, -2.3647598830880994], [5.5, -9.526279441628825]], [[1.0, 0], [-0.05926547943894341, 0.05926547943894341], [0, -13.0]], [[1.0, 0], [1.279415721346769, -4.774844476068527], [-14.722431864335457, -8.5]], [[1.0, 0], [-1.3154449008472358, 2.2784174028248163], [-9.5, -16.454482671904334]], [[1.0, 0], [1.0926460932894144, -0.29277363830991976], [19.91858428704209, -11.5]], [[1.0, 0], [0, 7.273323243785637], [-29.0, 0]], [[1.0, 0], [4.015578397699724, -2.3183952688639824], [15.5, -26.846787517317598]], [[1.0, 0], [-2.227785615677881, 0.5969333566305597], [32.04293994002423, -18.5]], [[1.0, 0], [5.717668654042037, 0], [41.0, 0]], [[1.0, 0], [-1.5730194803698558, -1.5730194803698558], [0, 43.0]], [[1.0, 0], [-0.7166793920443089, -2.674683903846935], [-40.703193977868615, 23.5]], [[1.0, 0], [9.12265060401176, 2.4444068621762445], [45.89934640057525, 26.5]], [[1.0, 0], [-1.6774750299148828, -2.905471980240699], [-29.5, 51.09549882328188]], [[1.0, 0], [0.9787707626983931, -1.6952806899565578], [-30.5, -52.827549630850754]], [[1.0, 0], [0.49189317223650286, 0.1318023782631541], [58.023702053557386, 33.5]], [[1.0, 0], [0, 14.462511224389171], [-71.0, 0]], [[1.0, 0], [-9.265069331353908, -2.482567845154642], [63.21985447626402, 36.5]], [[1.0, 0], [3.0520447362613163, -5.286296550177754], [-39.5, -68.41600689897065]], [[1.0, 0], [-5.626195440646107, -5.626195440646107], [0, 83.0]], [[1.0, 0], [14.448235918536211, 8.341692896882101], [44.5, 77.07626093681505]], [[1.0, 0], [-5.81505299899894, -5.81505299899894], [0, 97.0]], [[1.0, 0], [-4.287234131864126, -7.425707340332114], [-50.5, 87.4685657822283]], [[1.0, 0], [-3.1548156820844993, 0.8453303142835832], [89.20061658979718, -51.5]], [[1.0, 0], [-1.7579626078205937, -6.560805770192736], [-92.66471820493493, 53.5]], [[1.0, 0], [-3.3942263597922024, 1.9596575025165515], [54.5, -94.39676901250381]], [[1.0, 0], [0.028018602714820935, -0.028018602714820935], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-140-140.107-c1-0-17', '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/140/2/w/b/107/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.279009127141357, 1.3836080817269254, 1.5104397490749062, 1.661482614368596, 1.837056730853976, 2.03585217966891, 2.255019831288277, 2.4902574573189598, 2.7358718951624277, 2.984834353797935, 3.2288617538074194, 3.4585575815105303, 3.6636386849646323, 3.8332644967163825, 3.956474295728944, 4.022726847385172, 4.022525220078924, 3.948098020552718, 3.7940972549718817, 3.5582633327090236, 3.2420004196112875, 2.8508015485772105, 2.394463699349504, 1.887039368334915, 1.3464835202828607, 0.7939733137480723, 0.2529020772278193, -0.2524225502366411, -0.6983155492662357, -1.063395073775887, -1.3302877458836726, -1.4872189644810927, -1.529337531792051, -1.459625672072096, -1.2892620557168983, -1.0373375668532618, -0.7298705435019327, -0.39812761756752574, -0.07632385014788372, 0.20115425502810763, 0.4027941498591737, 0.5030096786746487, 0.4849065258275977, 0.34246047792328893, 0.08183309925838665, -0.27839319920105365, -0.7081906252111824, -1.168288835187916, -1.6134932938262994, -1.996875699161815, -2.2744731271292933, -2.410039751987556, -2.3793434537235636, -2.1735004145658086, -1.8009001224478263, -1.2873908813759325, -0.674564626698483, -0.016184978666332214, 0.6269768668480563, 1.193422999401529, 1.6276772005088238, 1.8867405588844048, 1.945466088659919, 1.8001317573887552, 1.4696556357293649, 0.9941465978117965, 0.4307953850092315, -0.1525505822299455, -0.685461292198435, -1.1037146760975773, -1.3577058637405124, -1.4193436628899236, -1.2864174691270949, -0.9836793328272767, -0.5602721701261313, -0.0836045513609248, 0.3697320862383509, 0.7249529797715761, 0.9205780617252409, 0.9188585068919956, 0.7135761214055941, 0.3339046529414939, -0.15652832293213723, -0.6656324050972807, -1.0834589941837445, -1.2962948497485218, -1.2025407479914616, -0.7282904425380193, 0.15958715641857618, 1.4448664324152112, 3.059394399589722, 4.887297132700783, 6.775825740301111, 8.551762044478883, 10.041458934212393, 11.091972807721115, 11.590460813325752, 11.479125649328367, 10.763501558410237, 9.51273233476663, 7.85158500737994, 5.945118248649988, 3.978008241850435, 2.1313575429882237, 0.5602373787179779, -0.624840350298854, -1.369867597865075, -1.681010297611384, -1.6195580412206645, -1.2890447592873135, -0.8166499374824991, -0.33188803969026787, 0.05398306646428993, 0.2645372672395515, 0.26812225239244547, 0.07967761355085717, -0.24567259826655072, -0.6259349270071187, -0.9699475186387237, -1.1961737232933043, -1.249102134828828, -1.1102013584467576, -0.8013764608685103, -0.380269185410596, 0.07171077812103607, 0.46632408308904183, 0.7271004599723079, 0.8058859689889883, 0.6939294849826715, 0.4250761269590146, 0.07012558623199239, -0.27685014258870266, -0.5177793465645519, -0.5717557553330743, -0.3938242977985676, 0.01263790111448391, 0.592907836690041, 1.248518429670534, 1.854659525756677, 2.284534541243052, 2.4362415096612478, 2.256938581167066, 1.7592306250361236, 1.0259003850273503, 0.20113262108787397, -0.5311037906740551, -0.9783059891192437, -0.9750320668033089, -0.41637520820541163, 0.7171470174803027, 2.3485060521309067, 4.309780444034151, 6.364388412286385, 8.242721333701287, 9.685307901667166, 10.485983349011173, 10.527247310573271, 9.801179530950424, 8.411771892473148, 6.557892568343739, 4.499700709987253, 2.5144844329294838, 0.849972382850693, -0.31626562706134576, -0.9038086021044508, -0.9378213255226768, -0.5375722437775211, 0.11244943289589117, 0.8028811642739282, 1.343107583299063, 1.5993447556944236, 1.519547467570969, 1.1402379186229095, 0.5741184606888063, -0.01864876301426706, -0.4691734678722931, -0.6401311740616583, -0.4588217770886381, 0.06427748631753002, 0.8356322002775686, 1.6975776097776387, 2.462076819366927, 2.952039815513795, 3.041179956355063, 2.6835808306133213, 1.926280261737438, 0.9018132679204743, -0.19798290735362864, -1.1614607709375067, -1.8015144576784532, -1.995181653491498, -1.709824760191279, -1.0100934166599145, -0.044063116343792556, 0.988464176546711, 1.8785481685636867, 2.452203328701591, 2.606275338562098, 2.3282369999036683, 1.6956903971914647, 0.855985086142894, -0.009100022703143832, -0.7252635879025587, -1.1643711676607378, -1.2709620778641828, -1.0705732261818426, -0.6582824514902172, -0.17067679409231226, 0.2514999184762443, 0.5004652236499398, 0.5287662915271301, 0.35979658088764155, 0.0786015079177177, -0.19482633660904894, -0.3429272512974396, -0.2887626559265683, -0.02453515493706671, 0.37797501960323077, 0.779149976505506, 1.0039483332312036, 0.8879741795788244, 0.3261347386701681, -0.6886624881783676, -2.047731618985517, -3.5362685090499264, -4.870619545369236, -5.756527719545815, -5.956110327452219, -5.348329005064971, -3.968206440045363, -2.014089195282905, 0.18093649800765102, 2.2092875993911187, 3.669099109115534, 4.247603462255145, 3.7894217808032002, 2.3342175935910756, 0.11452238904794027, -2.4868151936224705, -5.0111272315497395, -7.014705552211649, -8.15641146642428, -8.263263047740002, -7.36003743472024, -5.657006490501729, -3.499327152610588, -1.2901389215126302, 0.5949151592201706, 1.8825447781367817, 2.4498554738158815, 2.3361179100005596, 1.7175878030483789, 0.8533907199565272, 0.0169752339252391, -0.5696106849277973, -0.7829409278952169, -0.6166528572711459], 'positive_zeros': ['3.31108299589409512519999036215817', '4.78188790280331617424926420016474', '5.53129568886183408119182667790405', '7.12806074405656449407363265380616', '8.341870148904524462183690448284978', '9.396976467079560256314866032555496', '10.21181070087656315641575434681626', '10.98123971799082588989801910991719', '13.05362791656311772467199055409676', '13.97905431573620819378290174602943'], 'prelabel': '2-140-140.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': 0.7014705933320109, 'root_number': '-0.5915166287589269 + 0.8062927991131225*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.350735296666', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.31108299589409512519999036216', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.78188790280331617424926420016', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.53129568886183408119182667790', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'bad_primes': [2, 5, 7], 'central_character': '140.107', 'conductor': 140, 'conductor_radical': 70, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/2/w/b/107/9'], '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': '2-140-140.107-c1-0-17', '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': '2-140-140.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': 0.35073529666600545, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.31108299589409512519999036216', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4197296347150633712375663229772', 'Lhash_array': ['4197296347150633712375663229772'], 'label': '2-140-140.107-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/2/w/b/107/9'}