-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '314411551132069352771835931880,1119192899498472333908306627995,2115140246112944226611155118265,2140391727672001242131185918997,3195868112962107956305583451865,3925883265021186457041241691093', 'a10': -18, 'a2': 6, 'a3': 0, 'a4': 15, 'a5': -3, 'a6': 0, 'a7': 0, 'a8': 18, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1906.7518608100377, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 0, -9, 0, 0, 27]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 7355827511386641, 'conductor_radical': 21, 'degree': 12, 'euler_factors': [[1, -6, 21, -54, 114, -204, 313, -408, 456, -432, 336, -192, 64], [1, 0, 0, -9, 0, 0, 27], [1, 3, -6, -9, 69, 30, -371, 150, 1725, -1125, -3750, 9375, 15625], [1], [1, 6, -6, -18, 492, 852, -2873, 9372, 59532, -23958, -87846, 966306, 1771561], [1, -3, 3, -76, 45, 135, 3246, 1755, 7605, -166972, 85683, -1113879, 4826809], [1, 6, -24, -54, 1338, 1914, -18929, 32538, 386682, -265302, -2004504, 8519142, 24137569], [1, -3, -42, 41, 1341, -216, -29541, -4104, 484101, 281219, -5473482, -7428297, 47045881], [1, 12, 48, 54, 420, 6060, 37591, 139380, 222180, 657018, 13432368, 77236116, 148035889], [1, 9, 30, 81, -579, -9414, -59051, -273006, -486939, 1975509, 21218430, 184600341, 594823321], [1, 6, 39, -184, 333, 4446, 109599, 137826, 320013, -5481544, 36017319, 171774906, 887503681], [1, -3, -24, -301, 171, 6552, 58893, 242424, 234099, -15246553, -44979864, -208031871, 2565726409], [1, 0, -114, -18, 8322, 1026, -394913, 42066, 13989282, -1240578, -322136754, 0, 4750104241], [1, -3, -114, 149, 9063, -5670, -441093, -243810, 16757487, 11846543, -389743314, -441025329, 6321363049], [1, -6, 183, -1188, 17745, -95730, 1069783, -4499310, 39198705, -123341724, 892981623, -1376070042, 10779215329], [1, 6, -114, -378, 10716, 17304, -587549, 917112, 30101244, -56275506, -899514834, 2509172958, 22164361129], [1, 6, 219, 1440, 25845, 143106, 1938391, 8443254, 89966445, 295745760, 2653702059, 4289545794, 42180533641], [1, -12, 372, -3442, 57276, -407196, 4673571, -24838956, 213123996, -781268602, 5150652852, -10135155612, 51520374361], [1, 24, 588, 8510, 117216, 1171116, 11029695, 78464772, 526182624, 2559493130, 11848859148, 32403002568, 90458382169], [1, -18, 399, -5472, 71349, -708930, 6825391, -50334030, 359670309, -1958488992, 10139260719, -32476128318, 128100283921], [1, -21, 138, -769, 10953, -30402, -450903, -2219346, 58368537, -299154073, 3918957258, -43534503453, 151334226289], [1, 42, 1155, 21992, 330813, 3944934, 38870583, 311649786, 2064603933, 10842913688, 44987343555, 129236368758, 243087455521], [1, -18, 30, 702, 8088, -126648, 719359, -10511784, 55718232, 401394474, 1423749630, -70902731574, 326940373369], [1, 12, -60, -198, 7584, -70800, -1684181, -6301200, 60072864, -139583862, -3764534460, 67008713388, 496981290961], [1, -3, -114, 149, 2421, 11502, 340233, 1115694, 22779189, 135988277, -10092338034, -25762020771, 832972004929], [1, -21, 12, -207, 48291, -282432, -1657379, -28525632, 492616491, -213272307, 1248724812, -220712110521, 1061520150601], [1, 6, -258, -562, 49176, 42192, -5746809, 4345776, 521708184, -614112574, -29038127298, 69556444458, 1194052296529], [1, 3, -267, -234, 45051, 3711, -5521826, 397077, 515788899, -286660062, -34998253467, 42076551921, 1500730351849], [1, 15, -150, -949, 50445, 184590, -4606923, 20120310, 599337045, -1228982521, -21173724150, 230793593235, 1677100110841], [1, 36, 561, 7740, 120210, 1359324, 12901345, 153603612, 1534961490, 11168022780, 91469569521, 663276664548, 2081951752609]], 'euler_factors_factorization': [[[[1, -3, 6, -9, 12, -12, 8], 2]], [[[1, 0, 0, -9, 0, 0, 27], 1]], [[[1, 3, -6, -9, 69, 30, -371, 150, 1725, -1125, -3750, 9375, 15625], 1]], [1], [[[1, 6, -6, -18, 492, 852, -2873, 9372, 59532, -23958, -87846, 966306, 1771561], 1]], [[[1, -3, 3, -76, 45, 135, 3246, 1755, 7605, -166972, 85683, -1113879, 4826809], 1]], [[[1, 6, -24, -54, 1338, 1914, -18929, 32538, 386682, -265302, -2004504, 8519142, 24137569], 1]], [[[1, -3, -42, 41, 1341, -216, -29541, -4104, 484101, 281219, -5473482, -7428297, 47045881], 1]], [[[1, 12, 48, 54, 420, 6060, 37591, 139380, 222180, 657018, 13432368, 77236116, 148035889], 1]], [[[1, 9, 30, 81, -579, -9414, -59051, -273006, -486939, 1975509, 21218430, 184600341, 594823321], 1]], [[[1, 3, 15, -137, 465, 2883, 29791], 2]], [[[1, -3, -24, -301, 171, 6552, 58893, 242424, 234099, -15246553, -44979864, -208031871, 2565726409], 1]], [[[1, 0, -114, -18, 8322, 1026, -394913, 42066, 13989282, -1240578, -322136754, 0, 4750104241], 1]], [[[1, -3, -114, 149, 9063, -5670, -441093, -243810, 16757487, 11846543, -389743314, -441025329, 6321363049], 1]], [[[1, -3, 87, -333, 4089, -6627, 103823], 2]], [[[1, 6, -114, -378, 10716, 17304, -587549, 917112, 30101244, -56275506, -899514834, 2509172958, 22164361129], 1]], [[[1, 3, 105, 405, 6195, 10443, 205379], 2]], [[[1, -6, 168, -713, 10248, -22326, 226981], 2]], [[[1, 12, 222, 1591, 14874, 53868, 300763], 2]], [[[1, -9, 159, -1305, 11289, -45369, 357911], 2]], [[[1, -21, 138, -769, 10953, -30402, -450903, -2219346, 58368537, -299154073, 3918957258, -43534503453, 151334226289], 1]], [[[1, 21, 357, 3499, 28203, 131061, 493039], 2]], [[[1, -18, 30, 702, 8088, -126648, 719359, -10511784, 55718232, 401394474, 1423749630, -70902731574, 326940373369], 1]], [[[1, 12, -60, -198, 7584, -70800, -1684181, -6301200, 60072864, -139583862, -3764534460, 67008713388, 496981290961], 1]], [[[1, -3, -114, 149, 2421, 11502, 340233, 1115694, 22779189, 135988277, -10092338034, -25762020771, 832972004929], 1]], [[[1, -21, 12, -207, 48291, -282432, -1657379, -28525632, 492616491, -213272307, 1248724812, -220712110521, 1061520150601], 1]], [[[1, 6, -258, -562, 49176, 42192, -5746809, 4345776, 521708184, -614112574, -29038127298, 69556444458, 1194052296529], 1]], [[[1, 3, -267, -234, 45051, 3711, -5521826, 397077, 515788899, -286660062, -34998253467, 42076551921, 1500730351849], 1]], [[[1, 15, -150, -949, 50445, 184590, -4606923, 20120310, 599337045, -1228982521, -21173724150, 230793593235, 1677100110841], 1]], [[[1, 36, 561, 7740, 120210, 1359324, 12901345, 153603612, 1534961490, 11168022780, 91469569521, 663276664548, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '12-21e12-1.1-c1e6-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/441/2/h/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0208333333333', 'prec': 50}, 'plot_values': [3.9259379841758446, 3.905353388681518, 3.8255540894141955, 3.687523032007348, 3.4922181217700405, 3.2405756091833435, 2.9335181678323625, 2.571728717634999, 2.1549967146390108, 1.6830536068893456, 1.155879148296513, 0.5737628567280574, -0.06262972928781287, -0.752084497078964, -1.492418850356221, -2.280634960994284, -3.1129247177441206, -3.9845812657773925, -4.88990983775233, -5.82207683336778, -6.772806725778888, -7.732443243129503, -8.689951377730054, -9.632880760857459, -10.547347255039021, -11.417964381757303, -12.227676993780033, -12.958089779313216, -13.589680036398883, -14.101975685759916, -14.473775361786913, -14.683417310249018, -14.709184857300205, -14.529811120003021, -14.124938513965517, -13.475603172367972, -12.56475187212213, -11.37790378559008, -9.90417496756639, -8.1366750550339, -6.072967430227466, -3.715587477480416, -1.0725103642029399, 1.842233565815047, 5.007546130203446, 8.395637054728457, 11.972217673641035, 15.696646486475077, 19.522236553759644, 23.39653755398289, 27.2614831671122, 31.055008869887438, 34.71238645790756, 38.167506225705104, 41.35429858338933, 44.20825256802431, 46.66817645289207, 48.678272112451445, 50.189882395610525, 51.16309983196136, 51.56825205558597, 51.38745160565037, 50.61654220820653, 49.26538626010053, 47.3579958396451, 44.93247768899384, 42.04057766590526, 38.74718971291803, 35.13012034350468, 31.277031947148334, 27.282783180607506, 23.246852661115728, 19.27052856774857, 15.454211894260764, 11.894900854722833, 8.68182979772476, 5.8932137540034475, 3.593624890412767, 1.8317590335331855, 0.6387265045951372, 0.026763836539357655, -0.011799953918153513, 0.4956374761485722, 1.502944546689382, 2.946924328040591, 4.749592014241057, 6.821015883460384, 9.062871503438679, 11.37231608061414, 13.64600005985303, 15.784082629760729, 17.694247622411147, 19.295882987630577, 20.522987438610546, 21.326469485051664, 21.6758114940382, 21.559929360638453, 20.98751406567353, 19.98713819987134, 18.604521700587238, 16.899645118164447, 14.94360535928689, 12.815054638742719, 10.596637153742204, 8.371595563800078, 6.218806786850623, 4.209010656750748, 2.4018792679286465, 0.8437469400110849, -0.4338539813845309, -1.4149174831192886, -2.099220652348431, -2.501297434256509, -2.6485854055635616, -2.5789824373022014, -2.337985415671565, -1.9755832023763273, -1.5428996855708996, -1.0889855760220806, -0.6579685347415698, -0.2866936219066851, -0.002950869753233564, 0.17567194693812108, 0.24209626854559316, 0.19930555036986014, 0.059256119458282526, -0.15875293257026213, -0.4301126129516414, -0.7272400329854711, -1.0220537755245767, -1.288255484393998, -1.5033167167845258, -1.650059856503964, -1.7177812863930575, -1.7029124720362976, -1.6088365447915771, -1.4451912344068742, -1.2267477765641557, -0.971939735482766, -0.7011918340761213, -0.4351745464840084, -0.1929721285109478, 0.009429323353729193, 0.16029298702409822, 0.2528775094297886, 0.2857302392665336, 0.2624896086093045, 0.19125856932463617, 0.08363339820253696, -0.046509904412980384, -0.1843579745229512, -0.3155517234861478, -0.4275754651805136, -0.5107050602152101, -0.5586600948523601, -0.5689381945774312, -0.5427933962801313, -0.48490952747431143, -0.4028032561070549, -0.30576483582474795, -0.20379893463287932, -0.10660418600550639, -0.02264230252025351, 0.0416270911343128, 0.08230429209658602, 0.09829822447760458, 0.09123858691993028, 0.06512244669601111, 0.025747687631993015, -0.020005135278196216, -0.06499518264641031, -0.10263069820217138, -0.12754521646505934, -0.13610257553511299, -0.12669372945357726, -0.09982058516071239, -0.05797096207513967, -0.005191686916611801, 0.05345157530833862, 0.11247297049079948, 0.16657159788489798, 0.21118810255483395, 0.24298287964881582, 0.2601101044456863, 0.26228801105819094, 0.2506955653731985, 0.22771758830952685, 0.19658933228898248, 0.16098626400018992, 0.12451780979896875, 0.09031581491724511, 0.06073856955875718, 0.037202428148493914, 0.020152639800035364, 0.009162230665136844, 0.003133793704227067, 0.000589634228513199, -1.3949819492963269e-05, 1.3108002034922665e-06, -0.00024352541641374295, -0.0010616088377993658, -0.0021918031815153036, -0.0029019451160484052, -0.0021833806607706933, 0.0009965274286394593, 0.00742621742063986, 0.017417010447515154, 0.03064691888051362, 0.046105442190574775, 0.06215396774596954, 0.07669929882520751, 0.08746923497453547, 0.09236957593180622, 0.08980155153150012, 0.07893503778231528, 0.059899476441654824, 0.03385417311504521, 0.002920042410745252, -0.030049078023352226, -0.06183397295775988, -0.08925769038575279, -0.1095983175241181, -0.12095590072320979, -0.12253605232792054, -0.11481906988361341, -0.09945013420328386, -0.07897727721619585, -0.05646702392383533, -0.03503284999598371, -0.017342614087562217, -0.005163574161262745, 0.0009973784733334722, 0.00203274921784492, 0.00015261930223361218, -0.001409639356531576, 0.0011246681273580834, 0.01147257724074693, 0.03264199124171097, 0.0663479074520409, 0.11257785033099375, 0.16937679688757987, 0.23291485531052736, 0.2979084837863413, 0.358221692328956, 0.407615671221544, 0.4405678178946564, 0.45304239643962935, 0.4431512882322247, 0.41164522893767147, 0.36175432839485894, 0.29875908263007595, 0.22931807161776582, 0.16059217019690086, 0.09929591944948928, 0.050781181210531726, 0.01821136102973504, 0.0021796078758967944, 0.0007515673639536972, 0.009907169383947987, 0.024326646602516634, 0.0384227061128624, 0.04742951550972079, 0.04833149634492334, 0.04045665442518942, 0.025600321530608112, 0.007611019420459723, -0.00857432015626362, -0.018352516112031588, -0.01903185821447749, -0.01131701464179184, -0.0004217366412424326, 0.00346413880610156, -0.014386090239003259, -0.0717768164507349, -0.18725936443216426, -0.3771266043002585, -0.6520615227485935, -1.0139107657393143, -1.4533241053948525, -1.9486334664163316, -2.4662212165975883, -2.9626154899546955, -3.38830844656972, -3.693468844436401, -3.8358420059223244, -3.786732474112484, -3.5363208190333038, -3.0976965430443277, -2.508654701413119, -1.8311539842939817, -1.1479610364450448, -0.5532096759820465, -0.14201923357024984, 0.0004792537274888575, -0.1899797470823951, -0.7471352411042503, -1.6664578901929699, -2.9020647683887337, -4.368895806248308, -5.949513648348563, -7.505025406975003, -8.889387236739902, -9.966425951575564, -10.625446999145586, -10.794203138587063, -10.44796455626343, -9.613375005486757, -8.36705715916572, -6.828782339289236, -5.144865143645868, -3.4702241231071445, -1.9502226414086805, -0.703743873973053, 0.1904738102857903, 0.7030516886771012, 0.8558732605257113, 0.715649309697011, 0.3813768719653868, -0.03247859221895332, -0.41480621180312166, -0.6765757146084305, -0.7665600982925745, -0.6799834633667543, -0.4592547959625135, -0.1866876287023121, 0.02986041110688148, 0.07691286473291807, -0.1412957716277069, -0.6814325048576738, -1.5450682889801304, -2.67092982094671, -3.9373016372817755, -5.175344923853384, -6.193307306697454, -6.807924810710947, -6.878790590253355, -6.340836007411842, -5.230046713063733, -3.6978850412507076, -2.0085882503471746, -0.5202027653528849, 0.35002750489839296, 0.17336716455591866, -1.434821254350571, -4.760224190256765, -9.940969234093767, -16.932226267110316, -25.489160364892584, -35.171465455883435, -45.37464833269812, -55.39642510958786, -64.4997554094889, -71.98227295359581, -77.24701498144648, -79.86417079321751, -79.62404206529796, -76.58178593803207, -71.02847572101415, -63.44861106577559, -54.46518740867142, -44.772081062196825, -35.065265743377346, -25.97913263674742, -18.00970935136764, -11.474489428007955, -6.50176609489057, -3.0439950044447235, -0.9119063361756983, 0.17756749418817983, 0.5479071883215176, 0.5085251087423872, 0.3109228765231063, 0.12221828518473503, 0.018992186192156747, 0.0009533219311787974, 0.020292142214388905, 0.01983038738701737, -0.028354267571525343, -0.09253733722508739, -0.0668847497326896, 0.22222100381717155, 0.9897858529198594, 2.448620420143989, 4.754731880531092, 7.950637159520255, 11.919182025868214, 16.36760169099142, 20.834400580207767, 24.72417914931812, 27.371534111870144, 28.127472851771657, 26.465055349374076, 22.09998606976016, 15.053638679173671, 5.687691357541958, -5.297278136380959, -16.90841515544741, -27.95147659930492, -37.16675869981146, -43.38903587841614, -45.69657081629991, -43.538407036521384, -36.824460171659325, -25.968872689834466, -11.872458542078638, 4.189821720540931, 20.71326528968178, 36.131726475461015, 48.99546808532849, 58.14331079791682, 62.86043179374351, 62.9443697598234, 58.701765695305106, 50.887299391468645, 40.59038222806151, 29.087857026299613, 17.676562907164836, 7.488700954259156, -0.6401366352121549, -6.247144637414198, -9.260639122453252, -9.96359308729081, -8.910794076119709, -6.796239822001595, -4.316618041627739, -2.053200697808976, -0.3884222070438583, 0.5307529503484744, 0.7791103416705493, 0.5897775775591809, 0.25574941411629504, 0.021363136984583808, -0.01274869580014813, 0.050294737446319376, -0.10498259802875463, -0.9557566418250909, -3.0363382560005943, -6.795753650875615, -12.44112055353241, -19.798369015403186, -28.23367556235123, -36.64388066385367, -43.52961378795864, -47.15489192822527, -45.78000736498507, -37.95449904527774, -22.847124534966934, -0.4610204597134808, 28.225257741873076, 61.21904603883964, 95.60499928644943, 127.77750805221187, 153.83877959681334, 170.05733408158937, 173.31744944971763, 161.53139791648812, 133.9634632624811, 91.44466987417569, 36.4465135195675, -27.199850881954728, -94.69305124622042, -160.73904923330778, -220.08920055797842, -268.09171453205386, -301.24266719796805, -317.55125302413217, -316.6838861571895, -299.9215229694261, -269.94036788307045, -230.46616017335177, -185.84866041872428, -140.45754768760008, -98.16984554646201, -61.98075043271749, -33.755992484865864, -14.148537022794708, -2.6767737926751503, 2.0622291485047812, 2.060671805257485, -0.478950323888609, -3.510261316243948, -5.44803128197683, -5.370606091546886, -3.082485044912033, 0.9464502329770638, 5.743955896262069, 10.069619705420374, 12.683841769035254, 12.613954579787352, 9.335745826760043, 2.867157708736561, -6.229269119878127, -16.932986315059555, -27.92709581475077, -37.82390349008629, -45.38872420318393, -49.717321179495855, -50.35491533151088, -47.34331990189835, -41.201442592164945, -32.84767984748354, -23.41277243426778, -14.05309433273004, -5.78538493655305, 0.6425963205861596, 4.82789833119184, 6.731077710974058, 6.645855221996297, 5.106880290204229, 2.7682411792606403, 0.27839730649962363, -1.8282903395745516, -3.207001622829148, -3.7309877783224215, -3.477953008772162, -2.6802680484403676, -1.6513806561322242, -0.7042896713402015, -0.07807726848287497, 0.11067277377745306, -0.11537469142961719, -0.6085252085883008, -1.13641912693969, -1.4398760706305815, -1.2971180489368808, -0.5749357429706822, 0.7407707935797968, 2.5388650610865477, 4.60180879299934, 6.645773368694622, 8.37678071033591, 9.546871204934405, 9.997816415348142, 9.686778004218148, 8.689987451812092, 7.185229940671841, 5.416799124282522, 3.644711188071831, 2.096273501157558, 0.927836620069391, 0.20259021139836614, -0.11192140506298945, -0.12643501102817062, 0.002252929711098255, 0.11093130084033864, 0.06886801641608442, -0.19177971742831604, -0.6604544733349168, -1.2527880801394886, -1.8313568821468003, -2.2371803115753464, -2.32649534501733, -2.0056589811088243, -1.2579251028045075, -0.15535763832467342, 1.152425587863191, 2.4626136759223627, 3.553271836844768, 4.222029899581745, 4.323490319041906, 3.799386489832488, 2.6882583642601054, 1.1188878674607994, -0.7103350206984826, -2.5630683887225185, -4.203511940821486, -5.437869072953247, -6.141554236082735, -6.273072852535946, -5.874529183181952, -5.058810566466769, -3.9870499927132887, -2.8397008285579353, -1.7807559277181904, -0.9320950740261659, -0.3586184672551321, -0.06450342576550241, -0.0003419565557075356, -0.07934656467254504, -0.1992757213964471, -0.26484445821834446, -0.20626202171251645, 0.008927506310089742, 0.3722293838135992, 0.8395716235087989, 1.343611646739201, 1.808850996189401, 2.1667380573763086, 2.368082868439824, 2.3912177563451347, 2.2451018336722814, 1.9636892119232539, 1.5968699971842282, 1.2000214871032224, 0.823899811122855, 0.5067067306939321, 0.2694424191241078, 0.11523863530038654, 0.03260567688833757, 0.0009659169089828681, -0.0030317088691370936, 0.00018981734064963906, -0.002905812195180975, -0.017524821499430646, -0.04148810727457756, -0.06780950267547206, -0.08803350954125796, -0.09548223057248106, -0.08768495182470847, -0.06686597740544964, -0.038983868988688275, -0.011817439606909761, 0.007336183745731954, 0.01370109075982172, 0.006290962179154946, -0.011949779381481193, -0.03523012584748584, -0.05671940299400907, -0.07052185262405725, -0.0732936359479947, -0.06508072313367548, -0.04900703104235812, -0.03007120989350325, -0.013442499420926604, -0.002746912826953759, 0.001157023145348879, 0.000528839572572894, 3.655178685175056e-05, 0.005219503840960956, 0.020560167556605932, 0.04769644020193249, 0.08431556758886286, 0.124191397005274, 0.15837174457951708, 0.17723641712601151, 0.17298417326341411, 0.14195858867111122, 0.08621195466891171, 0.013644177757871676, -0.06348241767656608, -0.13102495136919567, -0.17601843518009921, -0.18968808965262007, -0.16983407829501165, -0.12203394697232389, -0.05845371378960468, 0.0047004302917299755, 0.05058682534981569, 0.06538575771450679, 0.041456971472937885, -0.02076302407956516, -0.11280348524902996, -0.21990459935429257, -0.3240180566293299, -0.40744606577145454, -0.4565296867030014, -0.4648292700013412, -0.43368019485205545, -0.3711624856397358, -0.28989455749490345, -0.20407461623481515, -0.12650700615373456, -0.06615120463623896, -0.02644855246993315, -0.005630721442603558, 0.001623957091298056, 0.0018508268081813, 0.00045297950411095876, -1.0844084206631067e-06, -0.00034578867559818084, -0.00405217147895865, -0.015379593809325798, -0.03702785270905607, -0.06804161539835385, -0.10276531884806211, -0.13125192606726935, -0.14115314895341066, -0.12074331283139948, -0.062375677388199956, 0.03447547679788876, 0.16157276677283308, 0.30270835256757855, 0.4363832558469829, 0.5399662251327223, 0.5945426089602318, 0.5895020557638139, 0.5258819868765775, 0.4163377371144075, 0.2825206912684471, 0.15043506933637674, 0.044639835546557184, -0.017384599895432538, -0.029338746702830487, 0.0023968947512225318, 0.06068017221809673, 0.12230048018567331, 0.16433799474029448, 0.1707736228773008, 0.1377119301078817, 0.07496194013316332, 0.004000369058917474, -0.04733270402769233, -0.05236239079600955, 0.0064118448795465865, 0.1310917624998254, 0.30591335746026693, 0.49930745253332687, 0.6702381425694663, 0.7776483421939325, 0.7913428040867259, 0.7020686089480755, 0.5253349242636157, 0.29983240536850037, 0.08043889968765537, -0.07332291417553764, -0.11114373644083052, -0.005055572901978136, 0.24195721218021582, 0.59435603144022, 0.9897117415017227, 1.3507987234858494, 1.6026605702726746, 1.6923551142578783, 1.600252219910915, 1.3443509223926997, 0.9767794254162885, 0.5722950675545858, 0.21107802734069445, -0.0416335378238714, -0.15527475539378371, -0.14329138752444623, -0.061729220985818574, 0.0024842279906707662, -0.04830806989768021, -0.29703105519918355, -0.7876260383120475, -1.5090281597517676, -2.39089512875414, -3.3125074347405867, -4.12392893622693, -4.676828955944675, -4.8561758956951575, -4.605603899720308, -3.9415898310943356, -2.953141055036578, -1.7867163068046916, -0.6177129242522079, 0.3859545185391946, 1.095999995137001, 1.446549235936368, 1.4434653237510149, 1.1588431845486735, 0.7112650901536445, 0.23348978566248194, -0.15882894849415627, -0.3911718507092212, -0.44243352742577907, -0.34336449099163874, -0.16185790427884006, 0.022567453150811656, 0.14495015520176646, 0.17434705665678918, 0.12156912549928879, 0.033056928628499065, -0.027840936446301378, -0.006977519901378805, 0.11600749389226815, 0.3124762284846295, 0.5044796932034948, 0.5814450200049655, 0.4318515117365146, -0.02038795324223302, -0.7846620280998763, -1.7865517231793848, -2.8717000062390303, -3.833516466444252, -4.4635636665492155, -4.605515391894266, -4.199427002131764, -3.305553538761636, -2.0988558280615623, -0.8325839023016731, 0.2259204418792742, 0.8751632988185707, 1.0399258734328625, 0.7961581746648464, 0.34859084675677776, -0.0418481786635518, -0.17277809252148163, -0.03382622914693175, 0.08477370404935411, -0.4561011192109421, -2.6045367475511116, -7.475063153504337, -16.108558706428035, -29.17633246760762, -46.6849204507293, -67.74571365934293, -90.47321000711332, -112.07379178549947, -129.18084885261487, -138.3091639706539, -136.41238154855898, -121.46818908411791, -92.98272486135924, -52.31993544876677, -2.723779534038872, 51.077914830570975, 103.47397715007386, 148.7360507618634, 181.85669198982546, 199.37328246278005, 200.0938712657657, 185.18060769740185, 157.87652852720967, 122.93386440144661, 85.79832712683871, 51.697079351322444, 24.752758390383843, 7.220129047729956, -0.7769153486927756, -1.054824351514345, 3.207088122607336, 8.324744935270882, 11.0954489685865, 9.696905174215928, 4.280525452945605, -2.8662476572156095, -7.637802664334613, -4.876783646637558, 10.525344458963096, 42.45809314814071, 92.57246397642065, 159.59578283740322, 239.1262199934716, 324.0195309527508, 405.48486944599904, 474.35970710567693, 522.4571026799591, 543.8195062530307, 535.6545345143875, 498.8769003945373, 438.18700155147883, 361.02509904546775, 276.32084010066325, 193.1657543403593, 119.5349644488913, 61.2540309634002, 21.334134179266535, -0.18576877891793403, -5.825844040485706, 0.10863745568283152, 12.485802868428829, 26.323635925258014, 37.65007509911072, 44.01036215401736, 44.586851318196224, 39.99953764874465, 31.871535335534887, 22.28145734458348, 13.215320960107736, 6.105485117676155, 1.6154169648295773, -0.35040523166246323, -0.46031910572924717, 0.3367426994943636, 1.1270932180071742, 1.2843859513620117, 0.595069238084743, -0.7529411921413337, -2.295811855945622, -3.488184677710244, -3.9098589527831575, -3.4037524532090013, -2.1168159658508277, -0.4443497489510927, 1.100817131594066, 2.0531457638309694, 2.1457200927109965, 1.395101592457287, 0.08961378570852159, -1.307584137311995, -2.3113329690702757, -2.580216333404187, -2.045545207450844, -0.9502809622004225, 0.20895007971458363, 0.8221547454498133, 0.35368461474020696, -1.4717190175540293, -4.540281853204092, -8.335450460445449, -12.038578810112336, -14.721693731102196, -15.58830715669375, -14.204289954784107, -10.657913915418177, -5.573804953168109, 0.01385285163632155, 4.903494393624383, 8.032234655667212, 8.767951724927661, 7.0894205118888785, 3.6121107915472135, -0.5509265532712436, -4.0762046212222165, -5.807368870955579, -5.146005236183239, -2.333970569344412, 1.5623443093468958, 4.872225371011247, 5.729959562614746, 2.619836571261405, -5.025177856633982, -16.27133345322263, -28.51651504817109, -37.67727712933915, -38.70693920215673, -26.398897374848215, 3.6400001155926285, 54.00284366391001, 124.69713468301424, 212.75167412224863, 312.27848978687393, 415.00326189537935, 511.29802288334736, 591.7729191158099, 648.4387108744121, 675.694728149007, 671.0468009077251, 635.3960232712554, 572.9880410038872, 491.0562137482487, 398.24633088295224, 303.30384809106005, 214.01687955329683, 136.4048719038489, 74.2565028332689, 28.994687320466117, -0.2022371784523004, -15.814359266167141, -21.24229722630293, -20.09456867585013, -15.611081269701161, -10.284725791513022, -5.681271728469945, -2.491324035839629, -0.7382951315378644, -0.054734028371358996, 0.05011307657305774, -0.010880136297690777, -0.007085432629338955, 0.1033918169154274, 0.2388331665450586, 0.2907740641475264, 0.21177726689765977, 0.06255476804557412, 0.005901070422264055, 0.2548305387174282, 0.994764216674181, 2.3059534740789003, 4.113523215283921, 6.191533647400596, 8.208814976767547, 9.803242867111415, 10.66723764076761, 10.62205905385476, 9.665939318102579, 7.98469434027692, 5.890867637953017, 3.743084030339158, 1.8643805983288035, 0.47569324567381716, -0.3403415950648751, -0.6391362606694244, -0.5776698179056978, -0.352311692726874, -0.13349495861480493, -0.016050566714826485, 0.0017370982778292887, 0.005555757761245409, 0.12474899414905953, 0.4784857325493051, 1.1245995377898566, 2.026445717853106, 3.049866213440652, 3.9973992596214996, 4.658388684933236, 4.864130758291033, 4.535337774578282, 3.7084456995277417, 2.534234948898426, 1.2447892613566378, 0.08656372946998159, -0.7417318029515619, -1.13539140061103, -1.1048929000813752, -0.7670372370920189, -0.3071481594739212, 0.08437191675112468, 0.275742731148333, 0.23994550184275087, 0.0714500048215543, -0.0320571635474816, 0.18011804494048173, 0.9419252406962, 2.398538907809876, 4.550697114112228, 7.229938058000223, 10.115181260431537, 12.796886002631487, 14.853730984626363, 15.93386461290069, 15.826113211294842, 14.504750032498317, 12.140822153458934, 9.07447954587545, 5.734604128644881, 2.555801964067126, -0.0967227244901636, -1.9838214830746095, -3.0220170229884595, -3.282843173221501, -2.9527563231468523, -2.276122918436857, -1.4964843532730283, -0.8075004936513899, -0.32263946877186533, -0.06779763425955099, 0.003223036285153264, -0.022221505353534454, -0.05102194033258939, -0.014906319072054282, 0.1108362692801594, 0.3047897889905129, 0.5116906668926675, 0.6630247324756784, 0.6995916613791909, 0.5899869877043592, 0.3405492557028296, -0.0063733008172347245, -0.38571261509576144, -0.7268056662206793, -0.9702184130636706, -1.0805058706866284, -1.0527147491590823, -0.9117097106204448, -0.7010256245370821, -0.46969621523174493, -0.26045110926502585, -0.10147169072147019, -0.003131829556208352, 0.04037396007239946, 0.04535799819021186, 0.031173378584253883, 0.013845193711300914, 0.0024461807261681474, -0.001253796542681875, -0.0004018175799986111, 0.000689822190924306, -2.1718887207666255e-05, -0.0005141827976356857, 0.004868529436977034, 0.02300352389169247, 0.05870198152555887, 0.11197103996838861, 0.1767883593207971, 0.24188200843732188, 0.2933832722685265, 0.3187940211531502, 0.3112965125981928, 0.27155533365621515, 0.2075029976388359, 0.13227706211010395, 0.06078137329388856, 0.005797978789812351, -0.02538733978163251, -0.032386881413960934, -0.020881268425746145, -0.00020290008802731618, 0.019845832559251774, 0.031981025471872954, 0.03338917606199638, 0.02582970402177225, 0.014139877235470846, 0.003920789664527408, -0.0007642302937751105, 0.001095486100134415, 0.007266141557550449, 0.013493006741946771, 0.015487153781743266, 0.010832468821429256, 9.59126725648596e-05, -0.013279174991806135, -0.02435572220556844, -0.02892775424159256, -0.025464632126520476, -0.015994170421436863, -0.005488067086961428, 0.00019177347444970165, -0.002781036435978211, -0.013469116272228476, -0.0249181005453259, -0.025060140572447532, 0.00013786215181411655, 0.06191823001833686, 0.16386106867912031, 0.2985968676725877, 0.4471894028751954, 0.5817851069120938, 0.6712882069549996, 0.6892591215555289, 0.6224540702194736, 0.47484526070818095, 0.26793668693402034, 0.037178344039272206, -0.1751526788654908, -0.32933003812049677, -0.3983532002474013, -0.3741817428883819, -0.26875399941815487, -0.11042347742677289, 0.06323603931313071, 0.2144048515141888, 0.3139501081035192, 0.3481824766348154, 0.3203434486007337, 0.24756143593608074, 0.1546547386131838, 0.06668070245136037, 0.00226323680577206, -0.03043060424368906, -0.03397128613464957, -0.018741161595877402, 0.0018965224468236379, 0.01666672329352586, 0.020047379826339248, 0.013055480723979171, 0.001519417639939072, -0.00717625163925482, -0.007576425684440588, 0.001437639570991751, 0.016291521611099903, 0.03061949983039601, 0.03829982535089994, 0.0362670118240492, 0.025927047241680105, 0.012534872922888535, 0.0025903662245609807, 0.00013528500090741354, 0.003936450701288683, 0.0068745167579112145, -0.0018751032823841971, -0.032280071192559184, -0.0880676251467993, -0.1629271802376494, -0.2400258340116437, -0.295611519638013, -0.3061611744108491, -0.2573717980002609, -0.15203116576763753, -0.011094483345996027, 0.1313203255607198, 0.23795910740180107, 0.28089768106548835, 0.25250014627250433, 0.17059401147502015, 0.07281321302459787, 0.0016660882169081364, -0.014274133729944651, 0.023973263247235872, 0.08076363893899262, 0.09754913395703654, 0.022797636499723092, -0.14802074010469007, -0.33592295866211425, -0.36179236671058657, 0.03527784534558998, 1.1358562662285279, 3.1386872210360846, 6.040274475237149, 9.525243131907342, 12.904269944242943, 15.143032388507994, 15.026767874425062, 11.391564895136389, 3.4122186719456895, -9.096747553112525, -25.435090700187576, -43.88423773139722, -61.77874624274099, -75.90118682775372, -82.9981967178697, -80.36612033486674, -66.42307919163129, -41.16852826091639, -6.436839347190683, 34.24913569204779, 76.16362980602936, 114.100559051837, 143.21763279393272, 159.8768951855865, 162.3564791320092, 151.08972751870925, 128.52453008533146, 98.63936648362748, 66.19477622024958, 35.86116700864672, 11.358646443204549, -5.147205702043615, -13.24554948494632, -14.114258227493345, -10.05172159462955, -3.8293505318935384, 1.9995805933839936, 5.693076926243723, 6.594241903935831, 5.088032908817951, 2.2914061157170806, -0.42508576762153727, -1.950777375475274, -1.8260687752305413, -0.39585308777203093, 1.2995717070514203, 1.8573790603764657, -0.021505890654607826, -5.061780371490162, -13.121670974615288, -23.141740613990788, -33.34422952897409, -41.63912103523026, -46.14933311335134, -45.739116779866585, -40.30183681532666, -30.79048183711506, -18.998974721001563, -7.142198364609304, 2.668681389390434, 8.94718081506909, 11.151664451910824, 9.727680058230398, 5.904134197025524, 1.3069332459067406, -2.503326630053726, -4.457031800969296, -4.248414688005253, -2.3464390622952718, 0.22188326084829998, 2.238851686168461, 2.704577356287197, 1.1605143669471696, -2.1699356207621787, -6.4558127004074715, -10.520276228809049, -13.210070647826411, -13.770592404980144, -12.113143521855601, -8.819123068688238, -4.949909677375445, -1.7155417569559253, -0.08909994179894867, -0.4801734455640561, -2.5770532839525147, -5.430857671850608, -7.751800048141324, -8.327226241607898, -6.445351100119045, -2.1984806518892768, 3.4596965082508144, 8.929933195229264, 12.379470266252781, 12.255008856749427, 7.765929760066523, -0.7908372971812972, -12.00481197306343, -23.696023091092293, -33.42534910655045, -39.07237624292721, -39.35334943551708, -34.18159919777288, -24.78605938226508, -13.286796997669775, -2.1126454255384624, 6.5967080297861935, 11.485826255041953, 12.255435733221686, 9.660661834026488, 5.216784234344289, 0.670427369100123, -2.550505319520392, -3.7409312597977964, -3.0615578531489795, -1.3787761254850637, 0.14518584137201013, 0.5788726310573825, -0.3089663590723922, -1.7987114579220387, -2.2986738105352016, 0.22332299378241185, 7.610980707796467, 20.855746057045327, 39.574568251207765, 61.79532554236343, 84.18746483895342, 102.85136386129619, 114.20108068816381, 115.80454129223287, 107.02431994256997, 89.27716873321465, 65.86377817925668, 41.339493579126795, 20.246934919712, 5.998840037636544, 0.08326803638003552, 1.7228189035158894, 8.076119141633784, 14.967867111008072, 17.994664826513937, 13.690517899032743, 0.4546593116539652, -20.972648698071428, -47.610589205097156, -74.9756106357132, -98.1718988429722, -113.01009246352648, -116.9329343079261, -109.54503755700945, -92.6764645178204, -69.96956439771795, -45.799050689841415, -24.217830026694887, -8.12021021130319, 1.2465883905693416, 4.33406398690489, 2.91909539151524, -0.5727969256991845, -3.8348544837988134, -5.301173215884144, -4.475530856799361, -1.9122436736373496, 1.131312502014851, 3.2752138497784222, 3.561648561392863, 1.8168736643822723, -1.2569386556343922, -4.279150623951807, -5.641148426573284, -4.051174531720152, 1.0276174406917826, 9.165309772480404, 19.035207556331326, 28.734753975180208, 36.26283455546241, 40.07671577828487, 39.493346144141675, 34.83873644290808, 27.32132227023724, 18.669094563742064, 10.631862031324355, 4.527252345899294, 0.9465475372744248, -0.31407581220418024, -0.08818887405149792, 0.5030169320238423, 0.459116696757272, -0.7678763611062674, -3.119979649867546, -5.985400704914411, -8.431128598916933, -9.548564021931925, -8.811154481396864, -6.255431588108661, -2.4753958088772428, 1.5577051952606027, 4.798331289472529, 6.464430761103211, 6.312238249789753, 4.696313294665615, 2.418688997824157, 0.4250963742742439, -0.5615251601737649, -0.35439584368548444, 0.5423642631393171, 1.0197858070898227, -0.3106901220443837, -4.645814486948638, -12.502899025577044, -23.368745376735177, -35.63776579495269, -46.83885089383716, -54.123038380610524, -54.919629160515214, -47.61010640660009, -32.05757980944227, -9.786813006524229, 16.29903809788187, 42.45645994462882, 64.8157776954284, 80.1363736909833, 86.48280268284891, 83.70837638716665, 73.28639174153201, 57.847454423850955, 40.54846153659071, 24.38483529391262, 11.599738422149413, 3.2973481025562403, -0.6633362952428083, -1.4176099166421081, -0.6341984973628932, 0.014552741216821471, -0.6822122239855417, -3.1927539005412338, -7.209307474261897, -11.830698795421666, -15.888416079540352, -18.318634218352436, -18.488143412259372, -16.393573437577228, -12.607040994355915, -8.079933227465144, -3.868724541507085, -0.851209684121989, 0.4934510460764966, 0.18460441364290917, -1.3146093869792757, -3.271411580029641, -4.910369897349303, -5.630067394427881, -5.158297583452044, -3.61054898245347, -1.4116900317945897, 0.8542967944548171, 2.618467812169131, 3.4807671138050713, 3.306072680524502, 2.2391064189482695, 0.634028741597965, -1.0623419217402081, -2.435840379617151, -3.206398890522269, -3.2842037427575166, -2.77049211820345, -1.8937627930808312, -0.9254818889453748, -0.10117329498029402, 0.43463201092616577, 0.6488553252318092, 0.6053825879679529, 0.4212678961971571, 0.2157206967726978, 0.06987330990607746, 0.007637267858945858, 0.0004233432836020205, -0.0091960418947128, -0.0761745664503571, -0.22677281563637733, -0.44595175653067487, -0.6815110583679592, -0.8630955465960385, -0.9299615945795264, -0.8520118017951613, -0.6396317027165477, -0.3405672297949394, -0.025185651216576975, 0.23501878586991412, 0.38966679290308703, 0.4228436171462449, 0.35355418331148186, 0.22565274925483816, 0.0913320576731117, -0.006200850594338509, -0.045434001542043884, -0.030769587790497984, 0.012832693880079325, 0.05146645029078619, 0.05576257346763615, 0.011772253698766852, -0.07477556976476409, -0.18219103531941394, -0.28123591410559495, -0.34517024875234376, -0.35821040387093217, -0.3201713557728651, -0.24610471830967684, -0.15887594063567062, -0.08065427888619345, -0.02614325733153263, 0.0007431812103011426, 0.006051435067839125, 0.001556835644238621, -0.0011275420993288917, 0.004188447243706528, 0.01579277682468572, 0.025161450741218755, 0.021045527127451148, -0.0054076833022194916, -0.05653768853265113, -0.12631260527501792, -0.2013402245054687, -0.26441929495453276, -0.29990136192773054, -0.29971045029265153, -0.264745888265727, -0.20375730941339018, -0.13044139930259374, -0.05949446056678853, -0.0029198340459995137, 0.03256351587528801, 0.04677972207213084, 0.04464796048083993, 0.033467385007335114, 0.020174146245294917, 0.009434085940261674, 0.0030161121616523565, 0.0003841659156847764, -9.256354729157716e-05, 4.9859109373629245e-05, 5.033683258453694e-05, -7.47525205141697e-05, -2.8580151178182756e-05, 0.00021403920587448436, 0.00020417592447194124, -0.0007233887276130351, -0.0028873409209378667, -0.005734027603228699, -0.007757744902974092, -0.007158737702248738, -0.002965864314253111, 0.004018410317496755, 0.011136717798133853, 0.014981405786025519, 0.013223274860127613, 0.006264966110949368, -0.0018082334485787729, -0.00288623834894195], 'positive_zeros': ['0.24802698083798666870835540963160', '0.882887523815293774766513605622459', '1.66855144921805087931143060598153', '1.68847135581890028304984931044642', '2.26320601607568600418535310075714', '2.52109541255825529462245258740210', '2.61051943714259769912099645037643', '2.95724197247819951691978530923706', '3.09697582623663454091332160904647', '3.38157216903191666872861020198920', '3.51186819505681221662884877115001', '3.68941037594969802968216591027928', '4.10203968912438284950744404111953', '4.12173679141026505828035303466016', '4.12621263038470736962608168780493', '4.24520980253784602059303601803104', '4.52269838339875983186760250700073', '4.80731246549708467716868329915602', '4.85554584725551785747773197946509', '4.89114962578282056372463793187468', '5.34202822079052198010951961552226', '5.34966852562544007477651273866561', '5.52996336151396633458072319391688', '5.62594004901320904889964360984863', '5.65399834147712095373816727146859', '6.10172851736426718026058978670715', '6.10468298558753069554182589124694', '6.51555933910185661041971201221977', '6.62337588031373120156903213479801', '6.76706679643782219469694589307152', '6.80262262145254060437597972153473', '7.09331127363754760564468015068840', '7.12873892435727726138795066644909', '7.66181958604686024202201860194482', '7.78427391624440267848488068139377', '7.78932261266606445709485794384893', '7.84429591618065059960494517379480', '7.903684620168837491660079716635028', '8.219413747537252723620505317213718', '8.432206991355089071189491768463476', '8.706430093793724502473165467113032', '8.881917524908578160484195645291890', '8.983042859746877906005652345879008', '9.004387640974797185214027976300327', '9.034530174418036862132225751711088', '9.312895755932199549681463014363469', '9.553861203865325146872309958852052', '9.925309753486600461271670271522904', '9.975889026443323201410220872854934', '10.07895237226985240375452593974729', '10.21549274299031568212645884774938', '10.49755563732199483507551508321054', '10.62746871174361823345203466698502', '10.79606787799903534344595552339541', '10.82632602378828751615507395635824', '10.94773737370989377465693898109312', '11.26037504950219617903092292693634', '11.31212711429160931976910102232561', '11.36179222844986759844652931146569', '11.54426440876305501001428864530708'], 'prelabel': '12-21e12-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 325459692631010842, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24802698083798666870835540963', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.882887523815293774766513605622', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.66855144921805087931143060598', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1906.7518608100377, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 7355827511386641, 'conductor_radical': 21, 'degree': 12, 'dirichlet_coefficients': [1, 6, 0, 15, -3, 0, 0, 18, 0, -18, -6, 0, 3, 0, 0, 3, -6, 0, 3, -45, 0, -36, -12, 0, 15, 18, 9, 0, -9, 0, -6, -30, 0, -36, 0, 0, 3, 18, 0, -54, 0, 0, 3, -90, 0, -72, 6, 0, 0, 90, 0, 45, -6, 54, 18, 0, 0, -54, -6, 0, 12, -36, 0, -70, -9, 0, -24, -90, 0, 0, 18, 0, 21, 18, 0, 45, 0, 0, -42, -9, 0, 0, 18, 0, 18, 18, 0, -108, -12, 0, 0, -180, 0, 36, -9, 0, 3, 0, 0, 225], 'euler11': [1, 6, -6, -18, 492, 852, -2873, 9372, 59532, -23958, -87846, 966306, 1771561], 'euler13': [1, -3, 3, -76, 45, 135, 3246, 1755, 7605, -166972, 85683, -1113879, 4826809], 'euler17': [1, 6, -24, -54, 1338, 1914, -18929, 32538, 386682, -265302, -2004504, 8519142, 24137569], 'euler19': [1, -3, -42, 41, 1341, -216, -29541, -4104, 484101, 281219, -5473482, -7428297, 47045881], 'euler2': [1, -6, 21, -54, 114, -204, 313, -408, 456, -432, 336, -192, 64], 'euler23': [1, 12, 48, 54, 420, 6060, 37591, 139380, 222180, 657018, 13432368, 77236116, 148035889], 'euler29': [1, 9, 30, 81, -579, -9414, -59051, -273006, -486939, 1975509, 21218430, 184600341, 594823321], 'euler3': [1, 0, 0, -9, 0, 0, 27, 0, 0, 0, 0, 0, 0], 'euler31': [1, 6, 39, -184, 333, 4446, 109599, 137826, 320013, -5481544, 36017319, 171774906, 887503681], 'euler37': [1, -3, -24, -301, 171, 6552, 58893, 242424, 234099, -15246553, -44979864, -208031871, 2565726409], 'euler41': [1, 0, -114, -18, 8322, 1026, -394913, 42066, 13989282, -1240578, -322136754, 0, 4750104241], 'euler43': [1, -3, -114, 149, 9063, -5670, -441093, -243810, 16757487, 11846543, -389743314, -441025329, 6321363049], 'euler47': [1, -6, 183, -1188, 17745, -95730, 1069783, -4499310, 39198705, -123341724, 892981623, -1376070042, 10779215329], 'euler5': [1, 3, -6, -9, 69, 30, -371, 150, 1725, -1125, -3750, 9375, 15625], 'euler53': [1, 6, -114, -378, 10716, 17304, -587549, 917112, 30101244, -56275506, -899514834, 2509172958, 22164361129], 'euler59': [1, 6, 219, 1440, 25845, 143106, 1938391, 8443254, 89966445, 295745760, 2653702059, 4289545794, 42180533641], 'euler61': [1, -12, 372, -3442, 57276, -407196, 4673571, -24838956, 213123996, -781268602, 5150652852, -10135155612, 51520374361], 'euler67': [1, 24, 588, 8510, 117216, 1171116, 11029695, 78464772, 526182624, 2559493130, 11848859148, 32403002568, 90458382169], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, -18, 399, -5472, 71349, -708930, 6825391, -50334030, 359670309, -1958488992, 10139260719, -32476128318, 128100283921], 'euler73': [1, -21, 138, -769, 10953, -30402, -450903, -2219346, 58368537, -299154073, 3918957258, -43534503453, 151334226289], 'euler79': [1, 42, 1155, 21992, 330813, 3944934, 38870583, 311649786, 2064603933, 10842913688, 44987343555, 129236368758, 243087455521], 'euler83': [1, -18, 30, 702, 8088, -126648, 719359, -10511784, 55718232, 401394474, 1423749630, -70902731574, 326940373369], 'euler89': [1, 12, -60, -198, 7584, -70800, -1684181, -6301200, 60072864, -139583862, -3764534460, 67008713388, 496981290961], 'euler97': [1, -3, -114, 149, 2421, 11502, 340233, 1115694, 22779189, 135988277, -10092338034, -25762020771, 832972004929], 'euler_factors': [[1, -6, 21, -54, 114, -204, 313, -408, 456, -432, 336, -192, 64], [1, 0, 0, -9, 0, 0, 27, 0, 0, 0, 0, 0, 0], [1, 3, -6, -9, 69, 30, -371, 150, 1725, -1125, -3750, 9375, 15625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 6, -6, -18, 492, 852, -2873, 9372, 59532, -23958, -87846, 966306, 1771561], [1, -3, 3, -76, 45, 135, 3246, 1755, 7605, -166972, 85683, -1113879, 4826809], [1, 6, -24, -54, 1338, 1914, -18929, 32538, 386682, -265302, -2004504, 8519142, 24137569], [1, -3, -42, 41, 1341, -216, -29541, -4104, 484101, 281219, -5473482, -7428297, 47045881], [1, 12, 48, 54, 420, 6060, 37591, 139380, 222180, 657018, 13432368, 77236116, 148035889], [1, 9, 30, 81, -579, -9414, -59051, -273006, -486939, 1975509, 21218430, 184600341, 594823321], [1, 6, 39, -184, 333, 4446, 109599, 137826, 320013, -5481544, 36017319, 171774906, 887503681], [1, -3, -24, -301, 171, 6552, 58893, 242424, 234099, -15246553, -44979864, -208031871, 2565726409], [1, 0, -114, -18, 8322, 1026, -394913, 42066, 13989282, -1240578, -322136754, 0, 4750104241], [1, -3, -114, 149, 9063, -5670, -441093, -243810, 16757487, 11846543, -389743314, -441025329, 6321363049], [1, -6, 183, -1188, 17745, -95730, 1069783, -4499310, 39198705, -123341724, 892981623, -1376070042, 10779215329], [1, 6, -114, -378, 10716, 17304, -587549, 917112, 30101244, -56275506, -899514834, 2509172958, 22164361129], [1, 6, 219, 1440, 25845, 143106, 1938391, 8443254, 89966445, 295745760, 2653702059, 4289545794, 42180533641], [1, -12, 372, -3442, 57276, -407196, 4673571, -24838956, 213123996, -781268602, 5150652852, -10135155612, 51520374361], [1, 24, 588, 8510, 117216, 1171116, 11029695, 78464772, 526182624, 2559493130, 11848859148, 32403002568, 90458382169], [1, -18, 399, -5472, 71349, -708930, 6825391, -50334030, 359670309, -1958488992, 10139260719, -32476128318, 128100283921], [1, -21, 138, -769, 10953, -30402, -450903, -2219346, 58368537, -299154073, 3918957258, -43534503453, 151334226289], [1, 42, 1155, 21992, 330813, 3944934, 38870583, 311649786, 2064603933, 10842913688, 44987343555, 129236368758, 243087455521], [1, -18, 30, 702, 8088, -126648, 719359, -10511784, 55718232, 401394474, 1423749630, -70902731574, 326940373369], [1, 12, -60, -198, 7584, -70800, -1684181, -6301200, 60072864, -139583862, -3764534460, 67008713388, 496981290961], [1, -3, -114, 149, 2421, 11502, 340233, 1115694, 22779189, 135988277, -10092338034, -25762020771, 832972004929]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/h/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-21e12-1.1-c1e6-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-21e12-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 325459692631010842, 'z1': {'__RealLiteral__': 0, 'data': '0.24802698083798666870835540963', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '314411551132069352771835931880,1119192899498472333908306627995,2115140246112944226611155118265,2140391727672001242131185918997,3195868112962107956305583451865,3925883265021186457041241691093', 'Lhash_array': ['314411551132069352771835931880', '1119192899498472333908306627995', '2115140246112944226611155118265', '2140391727672001242131185918997', '3195868112962107956305583451865', '3925883265021186457041241691093'], 'factors': ['2-21e2-63.25-c1-0-1', '2-21e2-63.25-c1-0-11', '2-21e2-63.58-c1-0-20', '2-21e2-63.58-c1-0-21', '2-21e2-63.25-c1-0-32', '2-21e2-63.58-c1-0-35'], 'label': '12-21e12-1.1-c1e6-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/h/d'}