Table lfunc_lfunctions
L-functions
{'Lhash': '992486006753283196604995031220', 'a10': [9.771716159140597, -2.1245148399553577], 'a2': [-0.6916985632447425, -1.8765801601863852], 'a3': [1.9759858854045693, -3.422507948559687], 'a4': [-3.0431061952103176, 2.596055601229023], 'a5': [-0.6930649072578019, 4.951733134401302], 'a6': [-7.789397112273545, -1.3407520786460958], 'a7': [2.569126408130059, 0.0], 'a8': [6.976618619035274, 3.914944781798378], 'a9': [-3.309040438636159, -5.731426164017831], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.354250045691284, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0.6916985632447425, 1.8765801601863852]]], [5, [[1.0, 0], [0.6930649072578019, -4.951733134401302]]], [19, [[1.0, 0], [-15.328106354849524, -11.227161510124528]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.239', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '1975551089393833929555230609003', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6916985632447425, 1.8765801601863852]], [[1.0, 0], [-1.9759858854045693, 3.422507948559687], [-4.5, -7.794228634059948]], [[1.0, 0], [0.6930649072578019, -4.951733134401302]], [[1.0, 0], [-2.569126408130059, 0], [49.0, 0]], [[1.0, 0], [0, -17.77068173997013], [-121.0, 0]], [[1.0, 0], [4.585703489868338, -2.6475571442992916], [84.5, -146.35829323957014]], [[1.0, 0], [-1.90065422550535, -1.0973432287319136], [144.5, 250.28134169370276]], [[1.0, 0], [-15.328106354849524, -11.227161510124528]], [[1.0, 0], [-8.21652377094996, -14.231436632882755], [-264.5, 458.12743860196804]], [[1.0, 0], [-24.529237897212912, -42.48588630891673], [-420.5, 728.3273645827129]], [[1.0, 0], [0, 13.038024608846415], [-961.0, 0]], [[1.0, 0], [0, 53.52556105932256], [-1369.0, 0]], [[1.0, 0], [-12.698452372289795, 21.994364686299463], [-840.5, -1455.7887037616413]], [[1.0, 0], [36.79270237825179, -63.726829866892366], [-924.5, -1601.280971597427]], [[1.0, 0], [27.963389247320467, 48.43401092818428], [-1104.5, 1913.050116959825]], [[1.0, 0], [-38.616876840698055, 22.29546423923965], [1404.5, -2432.6653592304883]], [[1.0, 0], [58.48229444808317, 33.76476844242777], [1740.5, 3014.634430573631]], [[1.0, 0], [2.0748076279823406, 3.5936722275968798], [-1860.5, 3222.4805274818964]], [[1.0, 0], [-51.03419521414237, -88.39381903428303], [-2244.5, 3887.5880375883453]], [[1.0, 0], [35.929222217017305, 20.743746118768822], [2520.5, 4365.634060477355]], [[1.0, 0], [-41.161256708784386, -23.76446264099995], [2664.5, 4615.049376767273]], [[1.0, 0], [-63.081585810376986, -36.42017054852963], [3120.5, 5404.864545018681]], [[1.0, 0], [-124.0384337982534, 0], [6889.0, 0]], [[1.0, 0], [-50.200334178201814, -86.94952935358197], [-3960.5, 6859.787223376538]], [[1.0, 0], [53.414646542710045, 30.83896056010236], [4704.5, 8148.433024207783]], [[1.0, 0], [51.407182221935734, 89.03985148234423], [-5100.5, 8834.325144005059]], [[1.0, 0], [-1.4134262686563779, 0], [10609.0, 0]], [[1.0, 0], [-65.3552830307123, 0], [11449.0, 0]], [[1.0, 0], [34.00165988814672, -58.89260246794683], [-5940.5, -10289.247822362915]], [[1.0, 0], [0, -45.21795529049382], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 15717003, 'index': 41, 'label': '2-380-380.239-c2-0-41', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/380/3/p/a/239/45', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.5472437728210968, 1.4381879722388629, 1.2822198961445483, 1.0753458423897446, 0.8133523925849205, 0.4925685796326383, 0.11078352982997529, -0.33177699561798774, -0.8315163045367102, -1.3806752464909258, -1.966780797841126, -2.5724260104831957, -3.1754611315725456, -3.7496559483666654, -4.265863226057945, -4.693672035594898, -5.003489412231351, -5.168932838670691, -5.169360087892827, -4.99231400393196, -4.63562560553718, -4.108907065589478, -3.434183001327736, -2.6454580657113724, -1.7871015506639707, -0.911041801152782, -0.0728962157039757, 0.6726964925601713, 1.2771428480210418, 1.7028560183459098, 1.9275486573974376, 1.947295387079491, 1.777875708163667, 1.4540535220222717, 1.0266596861376454, 0.5576007836863315, 0.11319271134157627, -0.24352313498350142, -0.46061838916517195, -0.5042936355855067, -0.3640983380828654, -0.05551906638519465, 0.38063057265163835, 0.8822063306970361, 1.3728573207069166, 1.7715608946564767, 2.003448396820623, 2.0105193233633134, 1.7607354925638894, 1.2540927183860835, 0.5245917139672502, -0.3624543823938989, -1.317691559293822, -2.2388008829109274, -3.0239746151592626, -3.585925146203106, -3.864352225988358, -3.8348994437143538, -3.5130595859073175, -2.952198059853636, -2.2357602364501226, -1.4646778318924958, -0.7418351069485765, -0.1560448772481661, 0.2318051164415011, 0.39800984512128745, 0.35895731746638365, 0.1669688990169534, -0.10042659107673205, -0.35606309772780814, -0.5208430897464017, -0.54031445175455, -0.39686728988513864, -0.11492496202618704, 0.24232623395986402, 0.5845862879621904, 0.8127437044184167, 0.8406617331572758, 0.6163317102002631, 0.13804960628907073, -0.5381277244719862, -1.3020067432745541, -2.00435632783233, -2.4816601061644303, -2.58664381941584, -2.2192171954216118, -1.3518997459282116, -0.044330141166943504, 1.5569226118543578, 3.234547652409814, 4.731053969826783, 5.789238108893323, 6.19589557130485, 5.821037199908704, 4.645200661515096, 2.7692103687683085, 0.40368441879142736, -2.160788233728113, -4.598241384534089, -6.599199746364536, -7.920696669016147, -8.42537653704328, -8.102426509525365, -7.066352123143436, -5.5337441561366205, -3.7823826783686605, -2.100446930705823, -0.7355344170687207, 0.14678888297410034, 0.48712572150359024, 0.33482382107888925, -0.17084349527426365, -0.836348863293135, -1.458477998946343, -1.8681272825000765, -1.9640455151312746, -1.7296300391474349, -1.2297828581829962, -0.5893635686011215, 0.04107832557369276, 0.5237985271210853, 0.7672693410851232, 0.7465756145388205, 0.5061320470064518, 0.14445393575914106, -0.21481273360955683, -0.45793403615470957, -0.5129565449868839, -0.3698890644246532, -0.08360574972627227, 0.24169179649454273, 0.4827552094674503, 0.5345488877038451, 0.34452694360275626, -0.0657193365074368, -0.5982317592352826, -1.0978748376385767, -1.3893715461855325, -1.3236483815094122, -0.821916193268751, 0.09430458606631006, 1.2961868960560992, 2.567293770903958, 3.647055225929413, 4.288869500754057, 4.319379980238435, 3.6843390538488774, 2.4689477785271614, 0.8862233439574646, -0.76547106078602, -2.16691703883264, -3.049889800081104, -3.259256900287157, -2.789945916802996, -1.7890451591101162, -0.5216003179175678, 0.6923729751439733, 1.554771735301334, 1.8614436154567788, 1.5514109765539368, 0.7206608232912715, -0.4034144570435468, -1.5209108749943596, -2.3369928854194137, -2.638441996598236, -2.34936507878386, -1.5513011531306309, -0.46197379424773055, 0.6223464091756875, 1.4062457697939312, 1.675681440842619, 1.3582255928245803, 0.5465701789930435, -0.521795105715296, -1.5243457233643423, -2.137775166648618, -2.124962920693687, -1.4017011879044505, -0.06512087925807761, 1.624451822134846, 3.3043162258413434, 4.597684923783652, 5.206799137123098, 4.986742222737763, 3.980747996796465, 2.4078868562882945, 0.6065844458857299, -1.0508987074386458, -2.2502952304224757, -2.809287109242754, -2.7145226635733595, -2.112894655443684, -1.2608619438108204, -0.446997347664809, 0.09001056083545499, 0.2249363670491008, -0.026049346990253467, -0.5197791632478098, -1.0372108586570272, -1.3551658852461483, -1.316908492122335, -0.8805712300196853, -0.13139734190262992, 0.7451733249398319, 1.5207103246932774, 1.9933578912683172, 2.0482613122514937, 1.6903765177250647, 1.0398788545424562, 0.29209915298428074, -0.3449652175257087, -0.7154611812143221, -0.761975711078142, -0.5383854674959323, -0.18511139419711573, 0.12505720886683208, 0.2524780837083626, 0.14515354622359083, -0.13718123327697207, -0.4392609251072318, -0.5634297911100438, -0.3435423546030866, 0.2847569115890712, 1.242412648465991, 2.311469985139167, 3.189328198910849, 3.580223845024233, 3.2980480272668986, 2.3484001228469937, 0.9612172706850727, -0.44200247755706873, -1.3437334788647355, -1.2667964691827516, 0.08441992963095567, 2.7182016817388726, 6.3182226420948915, 10.29034207859772, 13.886237959060383, 16.37474275540057, 17.217249963287454, 16.200904488372448, 13.493594288666719, 9.605373413390888, 5.266146376574254, 1.252073147150631, -1.7932813428379921, -3.4964243415559904, -3.815879316126983, -3.01625882188162, -1.5668485813825568, 0.0025448501922620066, 1.2455707672351741, 1.9029824309172314, 1.9402457000111937, 1.5147662813585028, 0.8899270467615049, 0.32818342840064096], 'positive_zeros': ['0.78293340970658221839352945643032', '3.26144281652791710027167799727653', '4.53564288460965148060252154602527', '5.14278738536007614657073294137767', '6.32582768179549409198136375686881', '7.917484456961575795638638365390922', '8.454563913605533235318844192814219', '9.166721342498351714574602509443686', '9.903130102786076759308810523005731', '10.87871905329496373235349046848924'], 'prelabel': '2-380-380.239-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.217802051974497, 'root_angle': 0.05979399187462528, 'root_number': '0.9302522025825011 + 0.36692075382895056*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0597939918746', 'prec': 40}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78293340970658221839352945643', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '3.26144281652791710027167799728', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.53564288460965148060252154603', 'prec': 100}}