Table lfunc_lfunctions
L-functions
{'Lhash': '4522375049035264606357321706677', 'a10': [9.788300265522031e-61, -5.2849176128037785], 'a2': [0.7264368016177164, -2.2357425851370913], 'a3': [0.0, 0.0], 'a4': [-2.852800491501011, -2.0726808809900805], 'a5': [2.138105218147751, -0.6947124979945591], 'a6': [0.0, 0.0], 'a7': [-2.381161655619925, 3.277387852514472], 'a8': [-2.902687701100538, 2.1089260603676543], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7905189800106762, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [3.316564159214308, -0.02005437147082881]]]], 'bad_primes': [3, 11], 'central_character': '99.35', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '2576622638821545262832031455322', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7264368016177164, 2.2357425851370913], [-1.618033988749895, -1.1755705045849463]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.138105218147751, 0.6947124979945591], [4.045084971874737, -2.9389262614623655]], [[1.0, 0], [2.381161655619925, -3.277387852514472], [-2.163118960624632, -6.657395614066075]], [[1.0, 0], [3.316564159214308, -0.02005437147082881]], [[1.0, 0], [-4.424945152745988, -1.437751834877498], [10.517220926874316, 7.641208279802151]], [[1.0, 0], [0.023575327589096175, 0.07255739760447485], [-13.753288904374106, 9.992349288972044]], [[1.0, 0], [-1.4082213449901657, -1.9382503992660634], [-5.871322893124001, 18.07007380960792]], [[1.0, 0], [0, 3.2271749694940137], [-23.0, 0]], [[1.0, 0], [-1.487959779200176, -1.0810660595503945], [8.961492836873475, 27.580638972559452]], [[1.0, 0], [-0.5175281633860029, 1.592787908477646], [-25.079526825623372, -18.221342821066667]], [[1.0, 0], [5.879055825241072, 4.271384081555292], [11.433628791873055, 35.189091102920685]], [[1.0, 0], [6.829802193576763, -4.962141751497821], [12.669696769372845, -38.9933171681013]], [[1.0, 0], [0, -4.280860533372642], [-43.0, 0]], [[1.0, 0], [3.6535956238201344, 5.028742961338632], [-14.52379873562253, 44.69965626587222]], [[1.0, 0], [-1.1688389709985356, -0.37977880340202697], [42.877900701872214, 31.152618371501077]], [[1.0, 0], [0.34108605477099524, -0.4694646791116383], [-18.232002668121897, -56.11233446141406]], [[1.0, 0], [3.597098520236365, -1.1687681585150365], [49.350036656871794, -35.854900389840864]], [[1.0, 0], [-12.99839128873964, 0], [67.0, 0]], [[1.0, 0], [-1.0656319780810863, 0.34624481861417766], [57.440206600621266, -41.73275291276559]], [[1.0, 0], [-7.821529141373063, 10.765411300624306], [-22.558240589371163, -69.42712568954622]], [[1.0, 0], [-0.6275655147341326, -0.20390839641366185], [63.912342555620846, 46.43503493110538]], [[1.0, 0], [3.1554179139879426, 9.711377766788571], [-67.14841053312064, 48.78617594027527]], [[1.0, 0], [0, -6.589827419951993], [-89.0, 0]], [[1.0, 0], [-5.081676187229215, 15.639791142690868], [-78.4746484543699, -57.01516947236989]], [[1.0, 0], [-0.5320952587342329, 1.6376208180153555], [-81.71071643186968, -59.366310481539784]], [[1.0, 0], [-2.613822327992188, -1.8990530819363016], [31.828750420619585, 97.95882117840081]], [[1.0, 0], [-11.988372459488476, 8.710062433386604], [33.06481839811937, -101.76304724358143]], [[1.0, 0], [0, -14.925785017156862], [-109.0, 0]], [[1.0, 0], [-6.610548075634361, -9.098638855708643], [-34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9598279, 'index': 3, 'label': '2-99-33.2-c1-0-3', '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/99/2/j/a/35/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.2624219651466155, 1.342913975730981, 1.4458859004068843, 1.572924358267764, 1.7243391679236413, 1.8992552342320292, 2.0957225935609745, 2.310788455999299, 2.5405189914553024, 2.779988950851508, 3.0232688755717407, 3.263439169754494, 3.4926547993120747, 3.702277757965906, 3.8830879833088248, 4.02557713444711, 4.120323246918336, 4.158437541476425, 4.132067585454343, 4.034933825555413, 3.8628696640998297, 3.6143293214284355, 3.2908233923866703, 2.897239969159813, 2.4420101248211368, 1.9370809642171063, 1.3976676748549588, 0.8417680866640819, 0.28943885935391717, -0.23814915333551015, -0.7198386830893272, -1.1357389626187164, -1.4685270518948452, -1.7047057359403233, -1.8357166608401085, -1.858805334578441, -1.777541466729458, -1.6019146652133938, -1.347951736016494, -1.0368367592099828, -0.6935567167372594, -0.3451406871672529, -0.01860559601131735, 0.2612382867643711, 0.47393820130314074, 0.6053054597536314, 0.648877984650544, 0.6067600504379509, 0.48970206331677146, 0.3163439547922927, 0.11162182615582535, -0.0955771644815147, -0.27533994403993717, -0.39998202834936336, -0.44731918089889666, -0.40360886004114854, -0.2658125558806397, -0.04286663529400328, 0.24427543453052702, 0.5639562842525153, 0.8764728295419064, 1.1379172257926071, 1.304887650501772, 1.3396238114026955, 1.2150259765163098, 0.9189717040844282, 0.4573625321781481, -0.1445812153666901, -0.8431080144128352, -1.5789293595081084, -2.2823020144750035, -2.879825156748395, -3.3023421792986967, -3.493147516229448, -3.415584926526909, -3.059106725090187, -2.4429553721419546, -1.6168293094640986, -0.65819018006541, 0.3337683570489107, 1.2470771565645211, 1.968083225879818, 2.3935725065440105, 2.4426137250194313, 2.066749314670125, 1.2572572169555043, 0.048467530129156416, -1.483479598121535, -3.2265437235845433, -5.042919712872585, -6.782427342702478, -8.297742390077769, -9.459767570095488, -10.171350486964927, -10.37768593196043, -10.072086891006059, -9.296338736521164, -8.135503820482501, -6.7077384736773, -5.150330397662606, -3.6036725236719245, -2.1951849121290974, -1.0252303069711626, -0.15682696400017115, 0.389531898698349, 0.6353284393321448, 0.6379030046264892, 0.47970947361324306, 0.25453901855786404, 0.05274318004803362, -0.05236899101306846, -0.014961633498949106, 0.17758835359391772, 0.5044452232143923, 0.9165140071750632, 1.3461830959099093, 1.719981299360054, 1.9720431625703487, 2.0561300044078044, 1.9541725240263137, 1.679859097992937, 1.2766105911058525, 0.8102301551614806, 0.35744054655964647, -0.007735189486345151, -0.22736470799570388, -0.2703551720602598, -0.13853882904168857, 0.13316131493543434, 0.48272337796349335, 0.8323072520924646, 1.1029525777512819, 1.230107014777795, 1.177112032584193, 0.9439923409459061, 0.5696082411998913, 0.12633867847209332, -0.2922087395527905, -0.5886414438456227, -0.6814809393113059, -0.5235936946898838, -0.1158014968463248, 0.48726916625738326, 1.1808533911921806, 1.8233990309543586, 2.258043514891398, 2.339084534192252, 1.9591864554812164, 1.0726134246395373, -0.2898718184166533, -2.0176681839222885, -3.9300072622514532, -5.79795016036464, -7.37587817610258, -8.437863184121998, -8.813217425226519, -8.41535791386717, -7.258952431017225, -5.462044415927765, -3.232222246607795, -0.8385194597289108, 1.4268394389285692, 3.2909272707642776, 4.540068463925793, 5.050778487858406, 4.806611382989605, 3.898140455971187, 2.5061129831555915, 0.8706625125786273, -0.7481708431385854, -2.1118985150811977, -3.0400186640812135, -3.435377240448341, -3.2944282399368783, -2.7011020081107406, -1.8059377814956727, -0.7947523056649871, 0.14708538534854285, 0.8680568049941376, 1.2754817336378363, 1.347766126082272, 1.1321517057012398, 0.7290704579088485, 0.26680260872144884, -0.12804488134514297, -0.3580378584441808, -0.374771112022905, -0.1871791100265373, 0.14309951222264064, 0.5179414917991432, 0.8267319150056849, 0.9727007521540196, 0.8957267043798302, 0.586557109854701, 0.08931733004134254, -0.5082024690171387, -1.0942555447476041, -1.5583501891226381, -1.8161923355573582, -1.8285909027593343, -1.6098709679091487, -1.223696506679402, -0.7670983297222629, -0.34629238093210857, -0.04991967112299717, 0.07385215591071088, 0.03058725911838133, -0.12053689747011473, -0.280947921910478, -0.33837941548319844, -0.19852144599323177, 0.18471168889507442, 0.787837170903561, 1.5114015522505058, 2.1915299965265778, 2.628530193208157, 2.6276774453754452, 2.0441473305796247, 0.8224748410295603, -0.9786465928638878, -3.182928890444245, -5.5170077394541295, -7.652571791119, -9.263023051977633, -10.084086822444027, -9.966338297005521, -8.908625000313114, -7.064739516205277, -4.720822616312037, -2.2468390954784576, -0.030856432519437253, 1.591383631953011, 2.3978229969265956, 2.3201250464492356, 1.454238548450721, 0.039194378265236945, -1.5917308991203205, -3.0777014461100114, -4.101407676178267, -4.450211537971693, -4.055115148247406, -2.999981451648927, -1.4996770000878639, 0.14770876358494991, 1.6240782257166875, 2.6564437641294933, 3.070315071700332, 2.8205519161456256, 1.993992810331273, 0.7844143112894527, -0.5536474713198641, -1.7612976022749045, -2.6291517044522155, -3.036992956323119, -2.9712140297161738, -2.5174254384469004, -1.8314189684892497], 'positive_zeros': ['3.56752487493087648862174388481897', '5.25761067957580179302429516974863', '6.31637085110312267711094418199936', '7.14524696935193130942184018320052', '8.347092907979979525834824217200324', '9.832554752704275933229372628553252', '10.75435238436121644016351947946452', '12.90429995669593127185521975188673', '13.67070770299610200835126909107727', '13.88994044310061544198249999239867'], 'prelabel': '2-99-33.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8891113428647034, 'root_angle': 0.3045801394136339, 'root_number': '-0.3362546427453487 + 0.941771105541149*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.304580139414', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.56752487493087648862174388482', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '5.25761067957580179302429516975', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.31637085110312267711094418200', 'prec': 100}}