Table lfunc_lfunctions
L-functions
{'Lhash': '355656526724481259938263464058', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 1.4142135623730951], 'a6': [0, 0], 'a7': [-3.1622776601683795, 0], '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': '4608.2305', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '1113304288535278379355596013258', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-5.0, 0]], [[1.0, 0], [3.1622776601683795, 0], [7.0, 0]], [[1.0, 0], [0, 4.47213595499958], [-11.0, 0]], [[1.0, 0], [0, 4.47213595499958], [-13.0, 0]], [[1.0, 0], [6.324555320336759, 0], [17.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-19.0, 0]], [[1.0, 0], [-4.0, 0], [23.0, 0]], [[1.0, 0], [0, -4.242640687119285], [-29.0, 0]], [[1.0, 0], [3.1622776601683795, 0], [31.0, 0]], [[1.0, 0], [0, -4.47213595499958], [-37.0, 0]], [[1.0, 0], [-6.324555320336759, 0], [41.0, 0]], [[1.0, 0], [0, 8.48528137423857], [-43.0, 0]], [[1.0, 0], [12.0, 0], [47.0, 0]], [[1.0, 0], [0, -7.0710678118654755], [-53.0, 0]], [[1.0, 0], [0, 0], [-59.0, 0]], [[1.0, 0], [0, -13.416407864998739], [-61.0, 0]], [[1.0, 0], [0, 0], [-67.0, 0]], [[1.0, 0], [-8.0, 0], [71.0, 0]], [[1.0, 0], [-4.0, 0], [73.0, 0]], [[1.0, 0], [-3.1622776601683795, 0], [79.0, 0]], [[1.0, 0], [0, 4.47213595499958], [-83.0, 0]], [[1.0, 0], [0, 0], [89.0, 0]], [[1.0, 0], [-2.0, 0], [97.0, 0]], [[1.0, 0], [0, -15.556349186104045], [-101.0, 0]], [[1.0, 0], [-9.486832980505138, 0], [103.0, 0]], [[1.0, 0], [0, -17.88854381999832], [-107.0, 0]], [[1.0, 0], [0, 4.47213595499958], [-109.0, 0]], [[1.0, 0], [-12.649110640673518, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23393995, 'index': 11, 'label': '2-4608-8.5-c1-0-11', 'leading_term': '0.831027360096345428094659646654701015616205991396543067', '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/d/l/2305/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [0.8310273600963455, 0.7067917080756901, 0.5700709210323205, 0.42161514301788655, 0.26220301294171544, 0.0926947833423034, -0.08591422086878492, -0.2724435819312354, -0.4654846234977036, -0.663366974481713, -0.8641370972159899, -1.065550347823336, -1.2650774953672643, -1.4599260401496283, -1.6470761503367828, -1.8233305759638505, -1.985377489149397, -2.129864826452834, -2.253484363661544, -2.3530634295563226, -2.425661863423273, -2.468671546350116, -2.4799155978314436, -2.45774413890103, -2.4011233944084114, -2.3097148539082646, -2.1839412457852694, -2.0250362136418647, -1.8350748258123235, -1.6169824028269892, -1.3745196143650538, -1.1122423728449837, -0.8354357266984384, -0.5500217191014536, -0.26244200928647, 0.02048306915056189, 0.29171644197496843, 0.5441837632573043, 0.7709661200386615, 0.9655009075329053, 1.1217851550561875, 1.2345750722865483, 1.2995752494148698, 1.313610809884705, 1.2747759021064802, 1.1825522415915022, 1.0378919845002252, 0.8432600261088508, 0.6026318623160137, 0.32144440849829775, 0.006498607551511448, -0.3341857617051916, -0.6915609914658996, -1.0557842713468168, -1.4164869493881325, -1.7630731410497054, -2.085039151335319, -2.372303945437325, -2.6155399533661305, -2.8064928786919663, -2.9382789463499295, -3.005648203293645, -3.005203098534603, -2.935562619921766, -2.797463740993724, -2.5937938017318425, -2.3295496636878945, -2.0117219774075608, -1.649105597516562, -1.2520399842912302, -0.8320862358226208, -0.40165009126972046, 0.026437279942580084, 0.4393667467584846, 0.8248112824046967, 1.1713817920512504, 1.469061297060234, 1.7096001618313545, 1.8868558325208533, 1.9970620366367282, 2.0390145443075154, 2.014163362066248, 1.9266045356024806, 1.7829684694198291, 1.5922056951402848, 1.365275183292979, 1.11474442882326, 0.8543144737558128, 0.5982865865962913, 0.36099032956970845, 0.15619505905818268, -0.003471608522737629, -0.10707427442549507, -0.14586552261103913, -0.11370476935575477, -0.007380448750646474, 0.17318082267144458, 0.42483023624177746, 0.7412451656044211, 1.1131117531853827, 1.5284378549035642, 1.9729867657359221, 2.4308166340532997, 2.884905419426193, 3.317836899703766, 3.7125198101658254, 4.05290988959678, 4.324703561799879, 4.515972291636492, 4.617708359405018, 4.624255871197108, 4.5336051767772805, 4.347534348915509, 4.0715877791058865, 3.7148890034471833, 3.289792287512363, 2.811384940296142, 2.2968594508397286, 1.764781004680971, 1.2342814167447655, 0.7242147228239475, 0.2523123630685583, -0.16562310941669678, -0.5164476569392124, -0.7902931959659918, -0.9810416823105709, -1.0866306414863824, -1.1091722719962622, -1.0548766369427978, -0.9337785357973164, -0.7592769975607567, -0.5475055155198747, -0.31655970230585817, -0.08561654723748466, 0.1260144914525286, 0.29986406800409793, 0.4192525071741984, 0.47016965864491517, 0.4420406701596055, 0.3283378426819481, 0.1270053492870363, -0.15932797422596026, -0.5233626933942793, -0.9533737673923494, -1.4336792186746565, -1.9453139878705419, -2.4668798911817857, -2.9755332084396953, -3.448063748515085, -3.8620136986308977, -4.196781502010755, -4.434655643525761, -4.561725642517903, -4.568622701761989, -4.451050145101396, -4.210073660641639, -3.8521529952492126, -3.388909560189946, -2.8366377710363504, -2.2155811759505863, -1.5490068326881001, -0.8621223091432922, -0.18088849942042157, 0.4692123429074014, 1.0643907354206683, 1.583683653215023, 2.0099484713109366, 2.3306643648015473, 2.538497784531462, 2.6316005155304225, 2.6136226030586664, 2.493437395942141, 2.2845913269657028, 2.004506003045298, 1.6734738946306915, 1.3135006234168238, 0.9470558707993557, 0.5958007188414165, 0.27936140802576226, 0.014217859266971262, -0.1872301251122399, -0.31736507183805973, -0.3737806995741705, -0.3594103599729373, -0.2823444350792183, -0.15534340701132746, 0.004929413068247532, 0.178915274890232, 0.34535301088224163, 0.48259175043817615, 0.5699494513357991, 0.5890394740627382, 0.524987866456322, 0.3674688723637008, 0.11149524416413706, -0.24208720420731428, -0.6864353744900434, -1.2088912823619038, -1.7915077981516583, -2.4118946864102573, -3.044343068974885, -3.6611696373850178, -4.234208181286095, -4.73636613278439, -5.143158499146611, -5.434131165672879, -5.5940902175226075, -5.614063483597527, -5.491934489893583, -5.232706699681619, -4.848376358601936, -4.357414319701216, -3.7838796449344634, -3.1562092678664824, -2.505747288544626, -1.8650933915378591, -1.2663614430040053, -0.739445780761935, -0.31039359780522824, 2.3010325038523167e-05, 0.17745212008119807, 0.21475632368428121, 0.1124080295231488, -0.12153996436139386, -0.47190988134468476, -0.9172568180933207, -1.4310817843639194, -1.9833314877229007, -2.5420990482495154, -3.075427365372084, -3.5531101178791045, -3.9483848393131296, -4.239418287435209, -4.410496150427417, -4.4528463648880034, -4.3650469835782095, -4.152994361502366, -3.8294339519698264, -3.4130826189633, -2.9273964483540356, -2.3990600189382087, -1.8562905838589556, -1.3270624798610189, -0.8373625239848032, -0.40958575999325836, -0.06117268487516696, 0.1964255496606636, 0.35838766702148667, 0.42672680171678357, 0.4100447618051996, 0.32285036736932116, 0.18448423462535218, 0.01771800476928794, -0.15288240132964984, -0.3027238125527147, -0.408967895186801, -0.45221080919121587], 'positive_zeros': ['0.28056352961963526344828105281459', '1.77361137302120758915139392589280', '2.54006404426775800203284672435604', '3.65307683645201894592301801425235', '4.61977830716439079667819380803919', '4.82679308790130689819020674811859', '6.17428228609004729676627786957240', '6.77364882496331221957506989820282', '7.13371999024041449366411315549100', '8.240370350843301696822302497378805'], 'prelabel': '2-4608-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': -0.25, 'root_number': '0.e-55 - 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 7}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28056352961963526344828105281', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.77361137302120758915139392589', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.54006404426775800203284672436', 'prec': 100}}