Table lfunc_lfunctions
L-functions
{'Lhash': '545757730248285959595930690226', 'a10': [2.106196958238209, 0.0], 'a2': [-0.4212393916476418, 0.0], 'a3': [-9.696748671857849, 0.0], 'a4': [-7.822557374924324, 0.0], 'a5': [-5.0, 0.0], 'a6': [4.084652511493479, 0.0], 'a7': [-27.457970765445936, 0.0], 'a8': [6.66508444292303, 0.0], 'a9': [67.02693480517698, 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], [0.4212393916476418, 0], [8.0, 0]], [[1.0, 0], [9.696748671857849, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [27.457970765445936, 0], [343.0, 0]], [[1.0, 0], [-59.32607097908711, 0], [1331.0, 0]], [[1.0, 0], [-15.478129972076154, 0], [2197.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-44.90436993192407, 0], [6859.0, 0]], [[1.0, 0], [151.29447582805994, 0], [12167.0, 0]], [[1.0, 0], [-162.41954336098973, 0], [24389.0, 0]], [[1.0, 0], [-196.04672580159408, 0], [29791.0, 0]], [[1.0, 0], [326.74402824118545, 0], [50653.0, 0]], [[1.0, 0], [156.92018345685722, 0], [68921.0, 0]], [[1.0, 0], [170.83471041413358, 0], [79507.0, 0]], [[1.0, 0], [-505.9074401826292, 0], [103823.0, 0]], [[1.0, 0], [-19.16980653148114, 0], [148877.0, 0]], [[1.0, 0], [334.76412973993007, 0], [205379.0, 0]], [[1.0, 0], [-6.656591353567451, 0], [226981.0, 0]], [[1.0, 0], [-503.1685556380474, 0], [300763.0, 0]], [[1.0, 0], [-157.69403373972239, 0], [357911.0, 0]], [[1.0, 0], [658.5069095879358, 0], [389017.0, 0]], [[1.0, 0], [-590.9821900088315, 0], [493039.0, 0]], [[1.0, 0], [-707.8710475383322, 0], [571787.0, 0]], [[1.0, 0], [739.8838837728861, 0], [704969.0, 0]], [[1.0, 0], [-355.3691657061121, 0], [912673.0, 0]], [[1.0, 0], [52.31045240903889, 0], [1030301.0, 0]], [[1.0, 0], [-522.1892640155518, 0], [1092727.0, 0]], [[1.0, 0], [-572.6743669341441, 0], [1225043.0, 0]], [[1.0, 0], [1987.0238975616423, 0], [1295029.0, 0]], [[1.0, 0], [-1114.2821753096139, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20727867, 'index': 33, 'label': '2-1445-1.1-c3-0-33', 'leading_term': '0.42412710417956346168611267845814', '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/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [0.42412710417956345, 0.4151811480220704, 0.38859328727857756, 0.345111746796362, 0.2859774513241319, 0.2129144312616553, 0.12811558214258653, 0.034223037607274236, -0.06569770213677029, -0.16819079830602643, -0.2694511525290522, -0.36537433848415607, -0.45161601873434715, -0.5236612366976645, -0.5769036635536351, -0.6067345112253699, -0.6086404071157805, -0.5783090781080102, -0.5117412265393265, -0.40536651706566307, -0.25616114930963324, -0.06176408631783873, 0.17941133736680304, 0.4680739727745474, 0.8039632964756815, 1.185773512498691, 1.611097031176808, 2.076390839932599, 2.5769689384745953, 3.1070235235633463, 3.65967697920103, 4.227065965032273, 4.800458012832577, 5.370400057896722, 5.926897274250565, 6.459619480484792, 6.958131271873893, 7.412140953281143, 7.81176233777865, 8.147782580833077, 8.41192848196735, 8.597123145701206, 8.697724588257943, 8.70973783741175, 8.630992324035613, 8.46127692053561, 8.202425848182067, 7.858349845608553, 7.435008445393704, 6.940320912997443, 6.384015318268272, 5.777417278396863, 5.133182066194711, 4.464975943874823, 3.787114678709891, 3.1141691381147663, 2.4605495625872242, 1.840081493449394, 1.2655873131817577, 0.7484878745325642, 0.2984386997175325, -0.07698531069960671, -0.37254382191131175, -0.5855124790895395, -0.7157827839506367, -0.765874066360616, -0.7408542113190706, -0.6481691169473363, -0.4973843440085722, -0.29984593925285496, -0.06827083077535398, 0.1837196435874157, 0.44210674953058354, 0.6930033575705206, 0.9231848088203819, 1.1206007117453864, 1.2748467607088387, 1.3775765680371113, 1.4228352851396129, 1.407299422642813, 1.3304106927480928, 1.1943957786169066, 1.004168539004438, 0.7671161035638278, 0.4927754019417728, 0.19241167731612543, -0.12148476647878917, -0.4357631725485381, -0.7372144692421043, -1.0131846439123517, -1.252171683891881, -1.44437825581444, -1.582193409400358, -1.660578988967495, -1.6773400615893759, -1.6332634104375425, -1.5321138220990844, -1.380484290645329, -1.1875030965316675, -0.9644076879022935, -0.7240020668257331, -0.4800206279918418, -0.24642678648037478, -0.0366789643508536, 0.1370006748851054, 0.26431815017681964, 0.33752419229715697, 0.3519216627306116, 0.3062342434555204, 0.2028125113724318, 0.04766066597048187, -0.14972453760258284, -0.3767020495818148, -0.6180119864631257, -0.8564590141545997, -1.0737256742867034, -1.2512800179402286, -1.3713357304024, -1.4178186011808798, -1.3772910129956093, -1.2397862927778338, -0.9995073762634283, -0.6553492537205665, -0.21121193067947042, 0.32392012545442567, 0.9361452676094766, 1.6070599943671822, 2.3144112143643234, 3.032962027900189, 3.7355360247734812, 4.394194882462823, 4.981495777058131, 5.471769290864996, 5.842355506571004, 6.074736075476209, 6.1555033405817206, 6.077114023487448, 5.838384318149652, 5.4446950832708945, 4.907889649492689, 4.245861894480702, 3.4818479322222364, 2.643450200620022, 1.7614370884557675, 0.868373724593005, -0.002850560189824752, -0.8205258968550966, -1.5555814172646485, -2.182926277194981, -2.6826025943787357, -3.0406893629972944, -3.2499084732737695, -3.309898898787624, -3.2271421702882503, -3.0145405503621383, -2.6906678825600685, -2.2787308948274583, -1.8052947888008106, -1.2988403145632292, -0.7882294128362362, -0.30116227796366984, 0.13729005254215718, 0.5059969036731762, 0.7888502909752161, 0.975557914650833, 1.0621021737937422, 1.050839120338287, 0.9502315755332593, 0.7742315314377143, 0.541347254623623, 0.27344900641387465, -0.00561711940235237, -0.2715260298161995, -0.5009928474346887, -0.6732242702856732, -0.7712152257197695, -0.782812573856824, -0.7014810146084914, -0.5267238170432541, -0.26413153352851476, 0.07494571098230382, 0.4740837862336456, 0.9127872799487412, 1.3677487625774174, 1.8142875480244698, 2.227879032741682, 2.585679197945834, 2.8679482350898433, 3.059282645497571, 3.149576340050568, 3.1346476244590358, 3.016489560805197, 2.8031248188295663, 2.508071324782433, 2.1494502036966296, 1.7487910800405824, 1.3296102065487823, 0.9158527540799614, 0.5303007994980834, 0.1930523155345513, -0.07982658419909452, -0.27738370841911547, -0.3945208127752629, -0.4323366895018345, -0.39804395236512335, -0.304458167144206, -0.1690867054974809, -0.012872257723776107, 0.14132952145470612, 0.2704389390143397, 0.3528947959110947, 0.37033110447083095, 0.30906994722784925, 0.16132176004709645, -0.07399880821700462, -0.390909811586779, -0.7764913094003308, -1.2115144470522219, -1.671544056238008, -2.128455633709547, -2.552277654228433, -2.913245324247638, -3.1839338863717104, -3.3413298353791987, -3.368697791083013, -3.257109596914719, -3.006520163423577, -2.6263007261862747, -2.135173041513532, -1.56052561846756, -0.937133032330813, -0.3053391119993156, 0.2911982849264624, 0.8080716096822818, 1.202843744225756, 1.4377558868461173, 1.482251031128133, 1.3151477995358936, 0.9263172247176232, 0.3177428969941979, -0.49611887371566343, -1.4887197806165766, -2.6225359929958865, -3.8508685671568186, -5.120231701952362, -6.373193805801921, -7.551505392675462, -8.599327035304563, -9.466361510430044, -10.110697659232413, -10.501189325711263, -10.61922016683526, -10.459742504884986, -10.031523380271441, -9.35658068596894, -8.468843490406178, -7.412120009932277], 'positive_zeros': ['0.43052693711502763806522014396253', '1.24662039667085840375068708432406', '3.56114599859228502509499416037084', '4.11777396201318049154951781234434', '5.01652939154373854046090368056253', '6.04646489286400409849127545596775', '6.46052959323885574510922845310535', '7.23129110032072067523231986917544', '8.495897169553057489610981295888341', '9.414344030064161893230856244224250'], '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': '0.43052693711502763806522014396', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.24662039667085840375068708432', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.56114599859228502509499416037', 'prec': 100}}