Table lfunc_lfunctions
L-functions
{'Lhash': '1761966603926401628176004938976,2438474245625254099031431517306', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 147.3131071851903, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [5, [1, -2, 1]], [19, [1, 2, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': '1.1.1.1', 'conductor': 2310400, 'conductor_radical': 190, 'degree': 4, 'euler_factors': [[1], [1, 2, 4, 6, 9], [1, -2, 1], [1, 4, 18, 28, 49], [1, 0, 10, 0, 121], [1, 2, 24, 26, 169], [1, 0, 22, 0, 289], [1, 2, 1], [1, 0, 34, 0, 529], [1, 0, 46, 0, 841], [1, 4, 54, 124, 961], [1, -10, 96, -370, 1369], [1, 12, 118, 492, 1681], [1, 4, 42, 172, 1849], [1, 12, 82, 564, 2209], [1, 18, 184, 954, 2809], [1, 0, 70, 0, 3481], [1, -4, 18, -244, 3721], [1, 10, 156, 670, 4489], [1, -12, 166, -852, 5041], [1, 8, 150, 584, 5329], [1, -8, 126, -632, 6241], [1, 0, 154, 0, 6889], [1, 24, 310, 2136, 7921], [1, 2, -48, 194, 9409], [1, 12, 130, 1212, 10201], [1, 10, 156, 1030, 10609], [1, 6, 148, 642, 11449], [1, 8, 126, 872, 11881], [1, 6, -8, 678, 12769]], 'euler_factors_factorization': [[1], [[[1, 2, 4, 6, 9], 1]], [[[1, -1], 2]], [[[1, 2, 7], 2]], [[[1, 0, 10, 0, 121], 1]], [[[1, 2, 24, 26, 169], 1]], [[[1, 0, 22, 0, 289], 1]], [[[1, 1], 2]], [[[1, 0, 34, 0, 529], 1]], [[[1, 0, 46, 0, 841], 1]], [[[1, 4, 54, 124, 961], 1]], [[[1, -10, 96, -370, 1369], 1]], [[[1, 6, 41], 2]], [[[1, 4, 42, 172, 1849], 1]], [[[1, 12, 82, 564, 2209], 1]], [[[1, 18, 184, 954, 2809], 1]], [[[1, 0, 70, 0, 3481], 1]], [[[1, -4, 18, -244, 3721], 1]], [[[1, 10, 156, 670, 4489], 1]], [[[1, -12, 166, -852, 5041], 1]], [[[1, 8, 150, 584, 5329], 1]], [[[1, -8, 126, -632, 6241], 1]], [[[1, 0, 154, 0, 6889], 1]], [[[1, 24, 310, 2136, 7921], 1]], [[[1, 2, -48, 194, 9409], 1]], [[[1, 12, 130, 1212, 10201], 1]], [[[1, 10, 156, 1030, 10609], 1]], [[[1, 6, 148, 642, 11449], 1]], [[[1, 8, 126, 872, 11881], 1]], [[[1, 6, -8, 678, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'id': 20371530, 'index': 30, 'label': '4-1520e2-1.1-c1e2-0-30', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/1520/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 27}, 'plot_values': [1.3884804382444593e-120, 0.004892484424107953, 0.019563498147174053, 0.043993097408985826, 0.07814432802150532, 0.1219601803555146, 0.1753546686571861, 0.23820927905504774, 0.3103579842294581, 0.39158508348404847, 0.48160428510758, 0.5800596446538835, 0.6864997005458416, 0.8003828916031672, 0.9210485663776194, 1.0477278464252642, 1.179514060478561, 1.315379545246523, 1.4541486074169447, 1.5945202327027386, 1.735046992822013, 1.8741630692880809, 2.0101725557593246, 2.1412815970830534, 2.265599262035298, 2.381171959456622, 2.4859994610770064, 2.5780691095121386, 2.6553886635573156, 2.7160172007679124, 2.7581152700627074, 2.7799688768852437, 2.7800560203828986, 2.7570598085191595, 2.7099489212405117, 2.6379758196555825, 2.5407671356400967, 2.418303192244341, 2.271012924081135, 2.0997315774096306, 1.9057936813473162, 1.690966877407177, 1.4575358580685283, 1.2082117764486335, 0.9462000979265752, 0.6750868989982313, 0.39888435245752146, 0.12189732171455896, -0.1512582273270857, -0.41580276790025517, -0.6668042380040954, -0.899332142310334, -1.1084973877969535, -1.2896037686682873, -1.438212562063354, -1.5502812787937204, -1.6222454244071713, -1.6511343522526252, -1.6346593061346593, -1.5712972338746505, -1.4603716091733219, -1.3020972368963235, -1.0976388105332051, -0.8491130289808314, -0.5596097296825556, -0.23315186643874167, 0.12533439864408455, 0.5100964534981918, 0.9146465273483284, 1.3318647542249118, 1.7541573088588562, 2.1735706892159636, 2.582016013977805, 2.9713757523649025, 3.3337866411222397, 3.6617179528783783, 3.9482986372006064, 4.187346115728336, 4.373717229782649, 4.503268796179421, 4.573207593991474, 4.581968584898834, 4.529537243697938, 4.417238229417301, 4.248004405389999, 4.026077324338939, 3.7572015381782227, 3.4482477272599934, 3.1073182325387005, 2.7433129853456557, 2.36594205589239, 1.9852625686918755, 1.6116055040564854, 1.2551173661758772, 0.9256202252065894, 0.6321940499418549, 0.3829995664550204, 0.18493519765649982, 0.043460244414616205, -0.03764594215086586, -0.05641900070339449, -0.012830888170380349, 0.09115734190134994, 0.2515974439431398, 0.46261765677961103, 0.7165362599781506, 1.0040645725025972, 1.314505270428822, 1.6361022070566047, 1.956283290200193, 2.262146862320002, 2.54069956746798, 2.7794510276014295, 2.966593330293671, 3.091659897560239, 3.145596039327567, 3.1214265798062297, 3.014176598592826, 2.8214875055457185, 2.5433629650801706, 2.18267592621981, 1.7447352084420509, 1.237636766798157, 0.6716691280497515, 0.0594800708300931, -0.5846388791554264, -1.2447760611775585, -1.9041776770970626, -2.5454418979634243, -3.1512892820673803, -3.704883078457753, -4.1905191270564215, -4.594008091699419, -4.903218870875126, -5.108446196795538, -5.202758135964223, -5.182270130730215, -5.046271648407084, -4.797336289156243, -4.441232112920648, -3.986816324679987, -3.4457643778981453, -2.832224836423093, -2.162429679289432, -1.45411672675624, -0.7261034800303672, 0.0024834378803416162, 0.7125794428955231, 1.3860784763806056, 2.0060613204686595, 2.557732126087964, 3.0284325847459512, 3.4085257755976026, 3.6911526022580685, 3.8729769166016204, 3.9536759152428913, 3.9364801873758677, 3.827427679519202, 3.6356624340973163, 3.3725166391484955, 3.051568017707779, 2.6876409149188762, 2.2966590420027178, 1.8946700997252306, 1.4975620248740806, 1.1202137111072268, 0.7761638234214809, 0.4769725062695594, 0.2319385218055943, 0.04772569966126237, -0.07178485724398546, -0.12558987736444696, -0.11551350658570822, -0.04605303343315861, 0.07589831212084476, 0.24138734750471033, 0.43989363407960275, 0.6597515446705169, 0.8888087587103076, 1.1148263409574446, 1.3262231647080247, 1.5123514837236036, 1.6642310234441446, 1.7746205014164878, 1.8386458125135348, 1.8536247509637156, 1.8195118064371587, 1.738477819339988, 1.6151265682102105, 1.4558755389405738, 1.268941097730698, 1.0636030104758196, 0.8499980552870696, 0.6383726029024004, 0.43876095416021704, 0.26033286665170197, 0.11105555525334229, -0.0027744199843082744, -0.07678249838021856, -0.10874520967565363, -0.09866786336872574, -0.04876588176136555, 0.03668451488130648, 0.15157285586999955, 0.28833873922087444, 0.4383244092786328, 0.5923536051888735, 0.7411014246169803, 0.8757852661708707, 0.9884372861918201, 1.0725984146736935, 1.1233957212236696, 1.1381255382409519, 1.1160755800876097, 1.0589021456236694, 0.970188224925181, 0.8555600851012728, 0.7220280608753388, 0.5778425107072418, 0.4317123691830694, 0.292459014875713, 0.168238608162915, 0.06610281002328318, -0.008642981501910917, -0.052832113610962586, -0.06583199063894717, -0.049746267539562544, -0.009499663015294594, 0.0472666756008966, 0.11042147373706176, 0.1678169346280425, 0.20575847592205568, 0.209836571662113, 0.16551300176447561, 0.059222389131671806, -0.12108910519292522, -0.38474812335820247, -0.7380326511331208, -1.1830392160831653, -1.7177188151959712, -2.335028835560081, -3.023405231451648, -3.766365009916876, -4.543410681725446, -5.330175743774855, -6.099668497352056, -6.822953524360808, -7.470564863941244, -8.01360855077687, -8.425126762728995, -8.681410717129312, -8.76309007315862, -8.656381727226139, -8.353717358830988, -7.854636962156693, -7.165847847660766, -6.301508941144875, -5.2827238497281925, -4.137049766078781, -2.897545590228789, -1.601464234433987, -0.28908116492897357, 0.9983306222419793, 2.219597862978699, 3.336160147906139, 4.312783030758918, 5.120236105311114, 5.735354968229176, 6.143523171195626, 6.337913692795369, 6.321441795605171, 6.1051533226676105, 5.709407305551663, 5.161529669175714, 4.496125053661716, 3.752251637781301, 2.972925928359627, 2.2021698504796325, 1.483929407453378, 0.8593782082241708, 0.3655902983317455, 0.03344553481439842, -0.11354575044585102, -0.06049620181842002, 0.19821518256086507, 0.6586147469761388, 1.3073120071190358, 2.122004473586181, 3.0726178331332843, 4.122389123579794, 5.2299329721926275, 6.350531309537611, 7.438916913801704, 8.450350978424249, 9.343781691178465, 10.082325408347055, 10.636390052187467, 10.983286520078993, 11.109918025736771, 11.011415281953068, 10.693081261627736, 10.168134428649184, 9.458745699989056, 8.593150845304473, 7.605792401728191, 6.534189733873547, 5.418366971564065, 4.297921070073329, 3.211042775397179, 2.1921884353373873, 1.2710588107997325, 0.47116612036370514, -0.190885931001954, -0.705819055011198, -1.0718504920218477, -1.294164985827808, -1.3844324857097337, -1.3595799004084133, -1.2407181318344904, -1.0515777896566927, -0.817052651591695, -0.5617047266198724, -0.30822479203316855, -0.07636785805231966, 0.11834796381845844, 0.26503314583847737, 0.3582251817713958, 0.39753042971564484, 0.3877766103922637, 0.338002587153511, 0.2609787730776955, 0.17178740202773035, 0.08688086687163515, 0.022577575506402353, -0.006053606499096159, 0.013545662848882586, 0.09047339095999675, 0.22960016857734344, 0.43109617398978395, 0.6902717664188639, 0.9977891180562154, 1.3400605087319073, 1.700197629065377, 2.0587668106952344, 2.3953586167299914, 2.6893982611441483, 2.9220723117302563, 3.076866554174824, 3.1415007148081555, 3.1079223354601697, 2.9738960364566576, 2.7423080375805187, 2.4221362143074887, 2.027085983562944, 1.575813714139593, 1.0900807190376542, 0.5942815323356418, 0.1134278120860818, -0.32779794209406654, -0.7068644747818119, -1.004473934100176, -1.2058610657636966, -1.3016350271340384, -1.2883432353946858, -1.1687503325802882, -0.9516255082256916, -0.651269779587511, -0.2866712669899968, 0.11972553451214278, 0.5431970293035134, 0.9585480268954889, 1.3412363347902847, 1.6694293017403252, 1.9246966575039697, 2.0939200076987903, 2.1692734690876296, 2.1496186161394206, 2.039661345261103, 1.8505855980105272, 1.5984739462472533, 1.3041188543096756, 0.9909751673601492, 0.6842933856176727, 0.40898937734007734, 0.18841961022398657, 0.04257649320818258, -0.013073568694558616, 0.0312603925730579, 0.1790150929435879, 0.42694509475966325, 0.7652430057388508, 1.1779906322136304, 1.6442091953931326, 2.138844181318992, 2.6346552506472327, 3.103343694575328, 3.517988077230221, 3.8538728320839266, 4.09104067466972, 4.214441046862633, 4.21613885943655, 4.09455991225598, 3.855977238673089, 3.512849856168201, 3.084384308361185, 2.5941893304873456, 2.0699383450270292, 1.5407388845211243, 1.0361451247941205, 0.5837214236044191, 0.20781601011137174, -0.07223985332299081, -0.24312701614284038, -0.2984114646069341, -0.23889876733228826, -0.07251243522328858, 0.1862361371417791, 0.5171851407057702, 0.8959511819418886, 1.2952998631878607, 1.687252936662834, 2.044400048731028, 2.3422848280285438, 2.560180975938072, 2.683282144228787, 2.70260336987277, 2.61654818701572, 2.4298235168355986, 2.1541191164019224, 1.8061832214254598, 1.407582654780879, 0.9823110302188289, 0.5558411476352411, 0.1527683000392893, -0.2044456203579603, -0.4972900065232449, -0.712290267918364, -0.841914131645835, -0.8850579889185405, -0.8468996251690362, -0.7385326645318707, -0.575895032722402, -0.37854881511336214, -0.16805413747451095, 0.03384741404043736, 0.20689911925342822, 0.3342857401721636, 0.4038173307454953, 0.4094923629617531, 0.3518092129369478, 0.23847430159845917, 0.08369243329497968, -0.09223181562815345, -0.26448823911233105, -0.40522035531913425, -0.4856150847244658, -0.47806722475084773, -0.35822793288935306, -0.10728073580907281, 0.28658598334136987, 0.8264826959890442, 1.5062995508460775, 2.3102037441044665, 3.2131746567116735, 4.18206668979262, 5.176975697041368, 6.153886562298357, 7.066363810989972, 7.8694265307144535, 8.520892983548714, 8.985821292024303, 9.236848125688468, 9.258383831411098, 9.045476801414107, 8.607001411597086, 7.962911930393575, 7.145905448418742, 6.1973217036398225, 5.167145006541822, 4.109158510166629, 3.0795748513892174, 2.132270342525982, 1.316694952530107, 0.6740300814994123, 0.23522933082453565, 0.018748860952366903, 0.02955476835692974, 0.2587086709632334, 0.6839439330384308, 1.2709387352063193, 1.9756673064895274, 2.746771137010411, 3.52943202807197, 4.267968614460399, 4.910574449328022, 5.41119754541628, 5.734242951126079, 5.854965027033647, 5.763227664073798, 5.461995310011044, 4.969442717287316, 4.315659600741749, 3.5428961882078362, 2.700869749431104, 1.8451415986519457, 1.0324293729058245, 0.3183643741595695, -0.2479449183090113, -0.6272377726101478, -0.7902403831148868, -0.7192965497786147, -0.4162395072731775], 'positive_zeros': ['1.38994657014257316200534284835400', '1.92361700076206183489253495482843', '2.88404529689345872012166958278555', '2.96373216224476934882459709097340', '3.63556900134341021233384687214905', '4.27724304767652366185192285777332', '4.96107038559969524165743387047082', '5.08084977293120133769417440291340', '5.77062955146184680594812156108799', '5.90671211183201936218083933414685', '6.52911533516102420844842400795869', '6.65579464459071028814093729249167', '6.86660222715208306520891890350046', '7.65297966437495532642683286586813', '8.236698311914008664717230394914025', '8.300402196192609640328527693249335', '9.131492239069850516877154401619440', '9.473626759687787217798698177771993'], 'prelabel': '4-1520e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4838572168265776, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 772154973346287430, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38994657014257316200534284835', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.92361700076206183489253495483', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.88404529689345872012166958279', 'prec': 100}}