Table lfunc_lfunctions
L-functions
{'Lhash': '701109299012722539282547050743', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 2.8284271247461903], 'a6': [0, 0], 'a7': [0, 1.4142135623730951], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.4607', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '1651846672408298547836098391809', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-5.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-17.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-19.0, 0]], [[1.0, 0], [-6.0, 0], [23.0, 0]], [[1.0, 0], [0, 5.656854249492381], [-29.0, 0]], [[1.0, 0], [0, -9.899494936611665], [-31.0, 0]], [[1.0, 0], [2.0, 0], [37.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-41.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-43.0, 0]], [[1.0, 0], [-10.0, 0], [47.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-53.0, 0]], [[1.0, 0], [12.0, 0], [59.0, 0]], [[1.0, 0], [-10.0, 0], [61.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-67.0, 0]], [[1.0, 0], [-2.0, 0], [71.0, 0]], [[1.0, 0], [10.0, 0], [73.0, 0]], [[1.0, 0], [0, 12.727922061357855], [-79.0, 0]], [[1.0, 0], [4.0, 0], [83.0, 0]], [[1.0, 0], [0, 9.899494936611665], [-89.0, 0]], [[1.0, 0], [-12.0, 0], [97.0, 0]], [[1.0, 0], [0, 0], [-101.0, 0]], [[1.0, 0], [0, -7.0710678118654755], [-103.0, 0]], [[1.0, 0], [-8.0, 0], [107.0, 0]], [[1.0, 0], [10.0, 0], [109.0, 0]], [[1.0, 0], [0, -9.899494936611665], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23462962, 'index': 18, 'label': '2-4608-12.11-c1-0-18', 'leading_term': '1.8048187699344019397552665692615938239271236726993676033', '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/4608/2/c/f/4607/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [1.804818769934402, 1.6492637710397302, 1.4884875425221398, 1.323388114883727, 1.1548836849991484, 0.9839667148072299, 0.811754338285177, 0.6395314181489159, 0.4687832003927847, 0.30121526138683347, 0.13875923754192243, -0.016436402237019726, -0.1620305840614435, -0.29552829758463933, -0.4143326416850699, -0.5158087638879654, -0.5973578591840237, -0.656499095610198, -0.6909570766629728, -0.6987522286763468, -0.6782913150858626, -0.6284551344460113, -0.5486803642175292, -0.4390324787772196, -0.3002667094381417, -0.13387413730792372, 0.05788977456779947, 0.2719965890990091, 0.5046582070811405, 0.7513635323353252, 1.0069393309048298, 1.2656354338867442, 1.5212336743828565, 1.7671791415804576, 1.9967315025238312, 2.203133311489316, 2.3797914274361633, 2.5204669228857113, 2.6194682245409364, 2.6718417082162245, 2.673553607614273, 2.621656914454739, 2.5144369682922836, 2.3515296742490888, 2.1340067552057715, 1.8644231433444234, 1.5468225373982396, 1.1866982806290007, 0.7909080253904568, 0.36754210918356367, -0.07425286792728097, -0.5244921534495075, -0.9726079072597922, -1.4077349257617904, -1.8190192893265569, -2.195940940034233, -2.5286401834551553, -2.8082373932491653, -3.0271348277997117, -3.17928948093142, -3.2604463086690725, -3.268322011451224, -3.202730801009927, -3.065645221475338, -2.8611870864769724, -2.5955458829017792, -2.2768245069351414, -1.9148148548733357, -1.5207084947158886, -1.106750291596891, -0.6858453434076345, -0.2711317952119129, 0.12446606057594456, 0.48868862061138824, 0.8103791433432714, 1.0798924456940557, 1.2894577510377043, 1.4334804238627643, 1.5087690928130546, 1.5146770503511764, 1.4531497581102748, 1.32867368928779, 1.1481254859635392, 0.920524361941772, 0.6566946864846358, 0.3688495766293731, 0.07010993734694458, -0.2260234454432391, -0.5062245884551814, -0.7579017718171335, -0.9697387970342699, -1.1321950101266052, -1.2379419786236148, -1.2822166082926123, -1.2630733205198943, -1.1815216025158333, -1.0415396667986714, -0.8499599523987971, -0.6162275737490549, -0.35203835437248127, -0.07086853422729202, 0.21258663232392624, 0.4830436072295104, 0.7253050742360296, 0.9249498830043369, 1.069008468941091, 1.1465934337436332, 1.1494559606313706, 1.0724410763253005, 0.9138184057174588, 0.6754698798459559, 0.36292167916379137, -0.014785705543517543, -0.4453883059084074, -0.9138421089738387, -1.402903622947045, -1.8938254009469822, -2.3671384349409017, -2.8034885162905936, -3.184490203954421, -3.4935601555087974, -3.7166914026165077, -3.843131758475857, -3.8659329152110127, -3.7823418246213594, -3.5940124736044856, -3.3070239057895434, -2.9316989754351415, -2.4822274658469827, -1.976106441825872, -1.4334195944298136, -0.8759854389932515, -0.3264111297134606, 0.19290601330299792, 0.6607837108066256, 1.0582197512191256, 1.3692707886594737, 1.5818019748523597, 1.688069756980215, 1.6851074024593915, 1.574891698253846, 1.3642794230836024, 1.0647131371090859, 0.69170705289828, 0.264134692076054, -0.1966498597227107, -0.6678165388431546, -1.126142255694695, -1.5491200522390969, -1.916040138377763, -2.20898900608621, -2.413716074632428, -2.5203232026160793, -2.523740673499091, -2.423963551536388, -2.2260341308644804, -1.939768985710715, -1.579242232921312, -1.162049364682934, -0.7083877261607117, -0.23999976344842217, 0.22096701294470183, 0.6531242758377361, 1.03697016075753, 1.3559194900464253, 1.5971811577782042, 1.752434244750433, 1.818264508659997, 1.7963352111347468, 1.6932801861361255, 1.5203219060832303, 1.2926322789453466, 1.0284682018075746, 0.748126712054866, 0.47277518586978134, 0.22321980789675683, 0.0186799887443691, -0.12436277761409072, -0.1931760698421028, -0.17958878675197712, -0.0805555819510975, 0.10156249011382742, 0.3590219073464719, 0.6790293371868252, 1.0443699518282619, 1.4343015084558624, 1.8256688074645324, 2.1941798774155092, 2.5157749936383955, 2.7680130588040908, 2.9313974078245613, 2.9905649736575715, 2.935268952437767, 2.761095377897885, 2.4698678616651972, 2.069711468801519, 1.574765388934769, 1.0045537119158918, 0.3830431251464808, -0.26256539671270346, -0.9032479069976352, -1.509696151489178, -2.05389934173894, -2.5106808538446885, -2.8591026854391948, -3.083656517844593, -3.17517099347492, -3.1313798018465797, -2.9571135869646983, -2.66409954518765, -2.2703747151174993, -1.7993411115154847, -1.2785117398399135, -0.7380149118445789, -0.20893905334725474, 0.2783895691587335, 0.6960987491372014, 1.020334974731503, 1.2326101109171852, 1.3208510205832475, 1.2800893696396554, 1.1127491010174757, 0.8285120532790102, 0.44376662354760904, -0.019331193933657675, -0.5341320729198297, -1.0710304436972642, -1.5991758358722263, -2.088258904707361, -2.5102673832034017, -2.841108217817178, -3.0619993841713455, -3.160547984210944, -3.1314494807614883, -2.9767652883780786, -2.705761103965445, -2.334314829640126, -1.8839291144655428, -1.3804078162847797, -0.8522765483322561, -0.32904360400144717, 0.16059210363762097, 0.5904756014172254, 0.9385653886533825, 1.1882400838726297, 1.3292601797900672, 1.3583240244400911, 1.2791822833063171, 1.102302760004308, 0.8441058558226895, 0.5258183514625224, 0.17201785470269673, -0.19103942003082575, -0.5372002348307202, -0.8421900169438782, -1.0852667262531286, -1.250643728990556], 'positive_zeros': ['0.55307771627804534081808136931415', '1.30562994308230449742493869779278', '2.53062676954705139837227007183758', '3.63990661946272883795797310598044', '4.37908441592510775091517185738884', '5.09075383026184885821874152957052', '5.68564825947825612859627414755972', '6.73455857713300195719825659144911', '7.34189631075212151148084317251671', '8.151184771621422146874822353018431'], 'prelabel': '2-4608-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': -0.3479566380076518, 'root_number': '-0.57735026918962576450914878050195745564760175127012687602 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3479566380076518', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55307771627804534081808136931', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.30562994308230449742493869779', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.53062676954705139837227007184', 'prec': 100}}