Table lfunc_lfunctions
L-functions
{'Lhash': '652762075927399305204463775', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.2839394560345145, 0.24603493919750097], 'a4': [0.0, 0.0], 'a5': [-2.453693499325545, 0.35278786531958306], 'a6': [0.0, 0.0], 'a7': [1.8030381359291952, -3.9481028031072083], 'a8': [0.0, 0.0], 'a9': [-0.40685609143259743, 2.8297462720403517], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.876989588766239, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [4.476841036838525, 1.7198529968804182]]]], 'bad_primes': [2, 23], 'central_character': '736.561', 'coefficient_field': 'CDF', 'conductor': 736, 'conductor_radical': 46, 'conjugate': '2450644191461161846219060998302', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.2839394560345145, -0.24603493919750097], [0.4269445148198554, -2.9694643256427984]], [[1.0, 0], [2.453693499325545, -0.35278786531958306], [4.7974648680724865, -1.4086627842071484]], [[1.0, 0], [-1.8030381359291952, 3.9481028031072083], [-4.584025137616996, -5.290247020479808]], [[1.0, 0], [0.45643694777469074, -1.5544814883938234], [-9.253788861142993, -5.947048992011573]], [[1.0, 0], [1.8510146342949352, -0.8453300590780424], [8.513189541288705, -9.824744466605358]], [[1.0, 0], [1.9737565487753082, 1.2684563123283323], [7.062055221032069, 15.463743921026813]], [[1.0, 0], [1.1709168128744416, 1.8219821250602326], [-7.892885247035842, 17.28300791173585]], [[1.0, 0], [4.476841036838525, 1.7198529968804182]], [[1.0, 0], [2.852418728425126, -4.438450177873484], [-12.047035377054707, -26.379327865281034]], [[1.0, 0], [3.7901580373926556, -4.374075547693775], [-4.411759986471839, -30.684464698308915]], [[1.0, 0], [5.954749567494702, 0.8561637339816935], [35.5012400237364, 10.424104603132898]], [[1.0, 0], [-0.0399364203301959, -0.2777639045542725], [-39.339211918194394, 11.551034830498617]], [[1.0, 0], [-3.340653958294336, 2.8946931327815495], [6.119538045751261, -42.56232200088011]], [[1.0, 0], [1.7020965336652316, 0], [47.0, 0]], [[1.0, 0], [11.454454822978999, 5.231074240482085], [34.70761889910011, 40.054727440775686]], [[1.0, 0], [10.767629124381457, -4.917411453805669], [38.63678330277182, -44.58922488690124]], [[1.0, 0], [-10.042164272113283, -8.701584875193875], [8.681205134670394, 60.379107954736895]], [[1.0, 0], [4.294636205894552, 14.62618772208682], [-56.363986699689136, 36.22293476952504]], [[1.0, 0], [2.3771569397457077, -0.6979962553816326], [59.72900083101386, -38.385498039347425]], [[1.0, 0], [-8.917727764661393, 5.731075639358448], [30.325295949137708, -66.40313566087984]], [[1.0, 0], [1.2370667363011083, 2.708798306533926], [-51.73399798167752, 59.704216373986405]], [[1.0, 0], [1.4797433533038307, 0.21275497488842585], [79.63791681000329, 23.383802217838664]], [[1.0, 0], [-5.946753271420005, -6.862919122649619], [-12.666020606322377, 88.094108327403]], [[1.0, 0], [-1.719742836946569, -11.961074159126506], [-93.07081844060625, 27.32805801361868]], [[1.0, 0], [-15.920378956506653, -2.28900492612], [96.90879033506424, 28.4549882409844]], [[1.0, 0], [-8.521341633331142, -2.5020916589247166], [86.64911388161165, 55.68600419792655]], [[1.0, 0], [-9.619095012220406, -8.334993274689355], [15.22768769524151, 105.9108942812598]], [[1.0, 0], [-1.907530365467686, 2.968175186040664], [-45.28023641720562, -99.1498874936425]], [[1.0, 0], [16.382739671473363, -4.810406394456973], [95.06164920992347, -61.09241237248253]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 13492713, 'index': 0, 'label': '2-736-184.101-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/736/2/x/a/561/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.0010317942419074606, -0.2503670263418501, -0.505840345283437, -0.7669554638835632, -1.0317762111237676, -1.2939876080639763, -1.5427620914829283, -1.7632891458481745, -1.9378641806181227, -2.0474473939172637, -2.073606534531279, -2.0007305805290216, -1.8183510038777202, -1.5233497239844431, -1.1217852987325063, -0.6300464232058185, -0.0750561257858089, 0.5066914867812665, 1.071375775734032, 1.5713442351971052, 1.9596530508303809, 2.1952681614612177, 2.2483778288165612, 2.1051502683157715, 1.771226085908096, 1.273286729199333, 0.6581978008558114, -0.010514020596527684, -0.6587507405975737, -1.2100161743484488, -1.5948155402128927, -1.760121803979826, -1.6775770619360117, -1.3491050596628786, -0.808826028546098, -0.1205847620962827, 0.6290102681800992, 1.3414567775035222, 1.9198793450693763, 2.283382279124774, 2.3800836553520863, 2.196661925136258, 1.7625876821016124, 1.1479000546734024, 0.4543436250958078, -0.19922653878232174, -0.6952131675712054, -0.9366403533099963, -0.8643186304060351, -0.4687248222468313, 0.2058238143245881, 1.065959240370995, 1.9827788714150938, 2.812266872003063, 3.4194128275652456, 3.7019118277424865, 3.6091163378099576, 3.152495410823394, 2.405199560406398, 1.4902359145539148, 0.5589040328180004, -0.23687420326440645, -0.7732836137750818, -0.9788411376060604, -0.8491132802891485, -0.44852456073306746, 0.10174148518756176, 0.6479775067454367, 1.0359603847118435, 1.144506352969005, 0.9136577756713804, 0.3612990723775105, -0.4159362366730801, -1.2585337192764037, -1.974316184204018, -2.37739668380715, -2.328071897209752, -1.7652310841870233, -0.7240104859885866, 0.6657790628026086, 2.2009983452699906, 3.642595435570972, 4.76173454931955, 5.385078039256516, 5.4294787450506385, 4.918325153370122, 3.9755944363372118, 2.798527659343462, 1.6146805700017675, 0.6328019661394418, -0.0013636910789752562, -0.23413942479959102, -0.11095449984850189, 0.24046228971079603, 0.6468764145334639, 0.9375241274204393, 0.9914881572819348, 0.7724910977756306, 0.3418800879477813, -0.15426476943341505, -0.5215769386995385, -0.569004466449263, -0.16293538885365813, 0.7300104156822033, 2.0231545563076048, 3.5192498022243086, 4.948498958279498, 6.0270489815183925, 6.52235811989348, 6.309500173370988, 5.404091855371296, 3.9628626759799572, 2.2507171202169416, 0.5815496894711, -0.7530866090759144, -1.549921537929925, -1.7379673765519044, -1.3893300364811225, -0.6939608560648891, 0.09518128773364316, 0.7322278270241861, 1.0451876360138608, 0.9814761815554761, 0.6197055498003557, 0.14422909521126873, -0.21091735633623984, -0.23345226042304848, 0.20017697468650544, 1.0813720174572024, 2.2625313607055304, 3.4899061029125473, 4.46825037800757, 4.940180208743829, 4.758492116254576, 3.930995572833959, 2.6245045648462297, 1.1256940746751112, -0.2314482322495396, -1.1522356567531977, -1.4582295844181725, -1.1330132943118463, -0.32367673575707545, 0.7027842022141374, 1.6361411875431255, 2.211050026860036, 2.2814193810611227, 1.8595171772012762, 1.1083146952260539, 0.2891360235957857, -0.3201073112975895, -0.5118732942027527, -0.21499631300757746, 0.48054830650984404, 1.3483538204195527, 2.0931875084893257, 2.4417426345685582, 2.229275552138044, 1.4554410061179746, 0.29134682619508906, -0.9657316848092664, -1.9776413455094146, -2.46574649749447, -2.2962394665037493, -1.5239774550305598, -0.380442647477306, 0.7918624953081053, 1.6398377073942936, 1.9051900051515869, 1.5028028163258398, 0.5476724815187558, -0.6786715469384043, -1.8129006912157783, -2.5204850883623076, -2.5984618522562823, -2.0385818955341066, -1.0308700417026408, 0.09411676861338718, 0.9669739382815857, 1.293798218271604, 0.9476359933336828, 0.008325931840515215, -1.261956794290994, -2.4999332544616264, -3.353677302326691, -3.5906947550642996, -3.1672965166728724, -2.2372717008229808, -1.0974181065528064, -0.08799630875721119, 0.5190418035233774, 0.6070665464068898, 0.2480794816052695, -0.3288888810077938, -0.8237833206618145, -0.9768913912480232, -0.6674488010682349, 0.035043456000739145, 0.885956977431046, 1.5440664228199792, 1.6886304585907064, 1.1362074333572505, -0.08285346849478974, -1.7160477513198376, -3.3542766458474387, -4.552519790334208, -4.9677885588976896, -4.46964251498751, -3.1864128491777803, -1.4706028821630346, 0.20680614703431055, 1.3999013694889795, 1.823155436519675, 1.4347561039534145, 0.4411192828663881, -0.7782143744612736, -1.799649890233166, -2.2950044642370653, -2.134567896262002, -1.4196305417817978, -0.4347079439420999, 0.4625736696128974, 0.9744184118466269, 0.9712866312771947, 0.5372000901842002, -0.06428753424137813, -0.49136139842424476, -0.4560739766129869, 0.16065827228619398, 1.2537830567393682, 2.5203970888042457, 3.560421694987539, 4.017464013981315, 3.7102768467421305, 2.7072457787188093, 1.3153976696035368, -0.014897995901281248, -0.8384319674828979, -0.8662331672711749, -0.06662835999530364, 1.3196879376003843, 2.8569318625358058, 4.057946108709708, 4.544970627228453, 4.171890074173881, 3.06586488191361, 1.5747811642562033, 0.14041211287650218, -0.8564455736764198, -1.2228994680697993, -1.0076050723437837, -0.46296984495774834, 0.06830623124421561, 0.29834613265667037, 0.11483457483763149, -0.3698041212564808, -0.86124530337892, -1.0036563998235406], 'positive_zeros': ['0.00051493848211003505510498686598', '2.01626496115370923919866211978534', '3.37304275096060085648806537223919', '4.39538498165122808515081174669578', '5.58464058040877494017798381521095', '6.21612543559431059959708290353196', '7.58411925786843276562465958049845', '8.227865192649236274531466857340435', '8.936223296131847940576303923248105', '9.817960607287275720872506423016354'], 'prelabel': '2-736-184.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.424250314791408, 'root_angle': 0.49960015952420983, 'root_number': '-0.9999968442468544 + 0.0025122691599969906*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.499600159524', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.00051493848211003505510498687', 'prec': 87}, 'z2': {'__RealLiteral__': 0, 'data': '2.01626496115370923919866211979', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.37304275096060085648806537224', 'prec': 100}}