Table lfunc_lfunctions
L-functions
{'Lhash': '103184829344988929646366670101', 'a10': [-12.119136017628177, 0.0], 'a2': [2.4238272035256356, 0.0], 'a3': [1.3492185838840802, 0.0], 'a4': [-2.1250616874490977, 0.0], 'a5': [-5.0, 0.0], 'a6': [3.270272707120568, 0.0], 'a7': [-30.703171667293432, 0.0], 'a8': [-24.5413999554143, 0.0], 'a9': [-25.179609212901838, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 85.25775995829522, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [5.0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 17], 'central_character': '1445.1', 'coefficient_field': 'CDF', 'conductor': 1445, 'conductor_radical': 85, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.4238272035256356, 0], [8.0, 0]], [[1.0, 0], [-1.3492185838840802, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [30.703171667293432, 0], [343.0, 0]], [[1.0, 0], [41.47353170587302, 0], [1331.0, 0]], [[1.0, 0], [82.02244981424464, 0], [2197.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-82.38185835606276, 0], [6859.0, 0]], [[1.0, 0], [27.722765805181567, 0], [12167.0, 0]], [[1.0, 0], [-139.8438561671548, 0], [24389.0, 0]], [[1.0, 0], [198.06655941233697, 0], [29791.0, 0]], [[1.0, 0], [313.5338932936821, 0], [50653.0, 0]], [[1.0, 0], [-142.00401204173588, 0], [68921.0, 0]], [[1.0, 0], [-285.7060299815214, 0], [79507.0, 0]], [[1.0, 0], [481.3594087279285, 0], [103823.0, 0]], [[1.0, 0], [130.41717263830384, 0], [148877.0, 0]], [[1.0, 0], [168.6499025759531, 0], [205379.0, 0]], [[1.0, 0], [201.96826436048633, 0], [226981.0, 0]], [[1.0, 0], [-362.2382592057035, 0], [300763.0, 0]], [[1.0, 0], [-771.4851026626945, 0], [357911.0, 0]], [[1.0, 0], [522.6579905204583, 0], [389017.0, 0]], [[1.0, 0], [1343.6454040653396, 0], [493039.0, 0]], [[1.0, 0], [123.94335572686371, 0], [571787.0, 0]], [[1.0, 0], [191.50174564739973, 0], [704969.0, 0]], [[1.0, 0], [1312.983438866466, 0], [912673.0, 0]], [[1.0, 0], [712.4139414361525, 0], [1030301.0, 0]], [[1.0, 0], [809.7795441698361, 0], [1092727.0, 0]], [[1.0, 0], [1120.1547673225573, 0], [1225043.0, 0]], [[1.0, 0], [1023.5035509460465, 0], [1295029.0, 0]], [[1.0, 0], [2315.1373463709474, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20733188, 'index': 1, 'label': '2-1445-1.1-c3-0-1', 'leading_term': '0.043947830568461914580056005770364', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1445/4/a/r/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [0.04394783056846192, 0.021153982597861404, -0.04694989341418947, -0.15953117075269174, -0.3152035601676126, -0.5120298118483578, -0.7475266022997146, -1.0186726326292213, -1.3219211515786495, -1.6532182309468377, -2.008028154254873, -2.3813672266939907, -2.7678471744453073, -3.1617290769302255, -3.5569884724705645, -3.9473919053943383, -4.326584752791845, -4.688189696273655, -5.025914704551424, -5.333668884353014, -5.6056840591104296, -5.836639466694085, -6.021786549043288, -6.15707045732041, -6.239244634700213, -6.265974682022696, -6.235927673978933, -6.148843187048436, -6.005582533277063, -5.8081530701944315, -5.559704975989358, -5.264498534568516, -4.927840755898985, -4.555991046040307, -4.156036615923787, -3.7357393504170653, -3.303356917013732, -2.867441940211704, -2.436624064035892, -2.0193806303721185, -1.6238024738234393, -1.2573619351598024, -0.9266905887678243, -0.637374333401929, -0.39377338520563065, -0.19887432085630935, -0.05418063986707301, 0.04035264759853581, 0.08633613218049242, 0.08691201310315085, 0.04666787361908758, -0.028501078611223838, -0.1315786917336026, -0.25465891635473376, -0.3892147772803764, -0.5263970727712973, -0.6573530575766626, -0.7735541061307013, -0.8671204487569948, -0.9311305868396044, -0.9599029699710883, -0.9492379902742462, -0.8966093289652886, -0.8012951697241123, -0.664441742706942, -0.48905403010753523, -0.279911175608566, -0.04340710262306427, 0.21268005045808505, 0.47948294955091025, 0.7473948058027805, 1.0064613530131812, 1.2468002104691491, 1.4590309262008685, 1.6346977648173309, 1.7666667866416164, 1.8494790249536843, 1.8796426389839191, 1.855848800609412, 1.7790987244908731, 1.6527325992640556, 1.4823551096285132, 1.2756566104956637, 1.0421336505809078, 0.7927172471257538, 0.5393218741371874, 0.29433232611706855, 0.07004924426547249, -0.12188305646853285, -0.2710409176421013, -0.3687514671982438, -0.40856255945508135, -0.3866281336177545, -0.30198741682194385, -0.15672036617963092, 0.04403326405263405, 0.2921980130685992, 0.5770303087879419, 0.8855231502097853, 1.2029346735683062, 1.5134209172888717, 1.8007472508048894, 2.0490480287355672, 2.2436003598050736, 2.371575678975752, 2.422732261640354, 2.3900130284874845, 2.270015985657502, 2.063309366844712, 1.7745698431676742, 1.4125298080397124, 0.9897284143308118, 0.5220703591935327, 0.028205946123661802, -0.47124475980225106, -0.9545923030756528, -1.4000639727606237, -1.786831161933149, -2.096029601996151, -2.3117225576349254, -2.421757926413804, -2.4184735302634177, -2.2992106523165403, -2.0666038727581038, -1.728625179446155, -1.298371748174083, -0.793599182831698, -0.23601478349041066, 0.3496420687359885, 0.936693710609646, 1.4977434132151843, 2.0059633062361537, 2.436388972878241, 2.7671563425073806, 2.980617398016538, 3.0642754042046008, 3.0114877546198233, 2.8218948569242186, 2.5015462946450895, 2.062710230771262, 1.5233679467905081, 0.906411739618742, 0.2385802775750348, -0.450819912767754, -1.131345713021314, -1.7729307329400588, -2.347403865225672, -2.8299340412661014, -3.200324084428649, -3.4440826588669067, -3.553213382622679, -3.526673789335895, -3.3704733503860633, -3.0973983957683076, -2.726371542979973, -2.28147311090878, -1.7906708743488837, -1.284321339793242, -0.793519511605682, -0.34838402600951246, 0.02363009366647529, 0.299298381354636, 0.4609855704796732, 0.49771758337045946, 0.40590272904180597, 0.1896560617353784, -0.13929809615667238, -0.5621475634991754, -1.0539162366452677, -1.5847463546893767, -2.1214741190542683, -2.6294161542644656, -3.074271064325785, -3.4240322588685337, -3.6508058647779387, -3.7324311552045555, -3.6538104315983997, -3.407870255402779, -2.9960955872917356, -2.4286017061969223, -1.7237344652606177, -0.90721604943706, -0.010879398564096135, 0.9289416751717982, 1.8732793442560403, 2.782552771817726, 3.6186307367751773, 4.346820089683976, 4.937667719821536, 5.368473795047337, 5.6244302145037715, 5.69931960044361, 5.595735531194632, 5.324812604159324, 4.905483663066762, 4.3633093987175995, 3.7289508376734974, 3.0363764040221852, 2.320910944948763, 1.6172433417136842, 0.95751146336206, 0.3695780750594077, -0.12440084661869331, -0.5090324025182521, -0.7763083266905919, -0.9257598560844974, -0.9641433688007897, -0.904683820773706, -0.7659308671397969, -0.5703068966461519, -0.3424454480095812, -0.1074313432278812, 0.1109405067518677, 0.2917727006573378, 0.41843401995001933, 0.4796004114315115, 0.46990199385410103, 0.3901367358279872, 0.24704106533070566, 0.05263799243302982, -0.17678768477478435, -0.4220118399968716, -0.6623952926917264, -0.8774999736097998, -1.0486805392730298, -1.1605365409549218, -1.2021198401187905, -1.1678090025712742, -1.0577857902518406, -0.8780770394131969, -0.6401562484027025, -0.3601309502737992, -0.05757218470598057, 0.24593104943810754, 0.5283885218232144, 0.7690790646984627, 0.9501513210394712, 1.0580351395322154, 1.084555829268561, 1.0276635125731466, 0.8917165517008178, 0.6872896760236905, 0.43051181497966523, 0.1419733222417531, -0.15472524076751729, -0.4346827038547739, -0.6735440315066791, -0.8493501850949721, -0.9442537982116428, -0.9459700431313618, -0.8488484607351853, -0.6544766707999721, -0.371759157853205, -0.016451567332400455, 0.38982943830153066, 0.8210615468241773, 1.24864231401642], 'positive_zeros': ['0.081398477882163589680451254129034', '2.72504942671428090292500234860353', '2.96876699084541972083572979410391', '3.93598076723090669531476748421335', '5.11775823597262044005187723642507', '5.55474418482597299103682367098531', '6.62439673140533588924886057830573', '7.46520997069675294397756702574279', '8.340666850783060313333318498232692', '9.370813552884377433293360815322460'], 'prelabel': '2-1445-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.233512872049035, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.081398477882163589680451254129', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.72504942671428090292500234860', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.96876699084541972083572979410', 'prec': 100}}