-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1717470731201425164622827544941', 'a10': [2.9475529813108707, -0.8067454498647968], 'a2': [-0.7005346210163862, 1.2285158707796282], 'a3': [0.0, -1.6166294874613643], 'a4': [-1.0185024895148562, -1.721235799898445], 'a5': [-1.527981249763242, -1.527981249763242], 'a6': [1.986054982516622, 1.1325049253226616], 'a7': [1.4452775181118365, 1.4452775181118365], 'a8': [2.828061753025844, -0.04546120403586901], 'a9': [0.38650910027040636, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.397887176638557, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7005346210163862, -1.2285158707796282]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 13], 'central_character': '676.99', 'coefficient_field': 'CDF', 'conductor': 676, 'conductor_radical': 26, 'conjugate': '1041076467379861068950977929099', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7005346210163862, -1.2285158707796282]], [[1.0, 0], [0, 1.6166294874613643], [-3.0, 0]], [[1.0, 0], [1.527981249763242, 1.527981249763242], [0, 5.0]], [[1.0, 0], [-1.4452775181118365, -1.4452775181118365], [0, 7.0]], [[1.0, 0], [-3.0619070055732007, -3.0619070055732007], [0, 11.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.788013307095361], [-17.0, 0]], [[1.0, 0], [-1.6497440352127886, 1.6497440352127886], [0, -19.0]], [[1.0, 0], [4.916117557886942, 0], [23.0, 0]], [[1.0, 0], [-5.88494319959378, 0], [29.0, 0]], [[1.0, 0], [-0.420375491568348, 0.420375491568348], [0, -31.0]], [[1.0, 0], [-1.3660254037844386, 1.3660254037844386], [0, -37.0]], [[1.0, 0], [-1.098076211353316, -1.098076211353316], [0, 41.0]], [[1.0, 0], [-11.18961144799789, 0], [43.0, 0]], [[1.0, 0], [8.070348363249558, 8.070348363249558], [0, 47.0]], [[1.0, 0], [1.3305466007439224, 0], [53.0, 0]], [[1.0, 0], [4.744765588537414, 4.744765588537414], [0, 59.0]], [[1.0, 0], [0.7170557010143288, 0], [61.0, 0]], [[1.0, 0], [5.0084413576763565, -5.0084413576763565], [0, -67.0]], [[1.0, 0], [1.2408110010108844, -1.2408110010108844], [0, -71.0]], [[1.0, 0], [-5.356961949830539, 5.356961949830539], [0, -73.0]], [[1.0, 0], [0, -1.1172258263329036], [-79.0, 0]], [[1.0, 0], [2.4573804705980606, -2.4573804705980606], [0, -83.0]], [[1.0, 0], [1.3774456463165063, -1.3774456463165063], [0, -89.0]], [[1.0, 0], [-0.9715991684150288, -0.9715991684150288], [0, 97.0]], [[1.0, 0], [0, -0.869948093039232], [-101.0, 0]], [[1.0, 0], [-11.574302950776087, 0], [103.0, 0]], [[1.0, 0], [0, 8.057549289192293], [-107.0, 0]], [[1.0, 0], [-12.081095622300412, -12.081095622300412], [0, 109.0]], [[1.0, 0], [-8.940905699120265, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-26e2-52.47-c1-0-31', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/676/2/f/h/99/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0866482044096302, 1.1684711498990021, 1.2330079189982683, 1.2761705665450973, 1.2908392125199004, 1.2678669700656082, 1.1974649255494965, 1.0707444351390338, 0.8812620057172512, 0.6264525411798816, 0.30883915812976376, -0.06310861960237972, -0.47460878570282244, -0.9048259086217048, -1.3278534060117844, -1.714453489492965, -2.0345008403343763, -2.2599715284224846, -2.3682107795941945, -2.3451180003815693, -2.1878227077398726, -1.9064077227640117, -1.5242796648807682, -1.076898361600143, -0.6087539798357309, -0.1687102200405147, 0.19591076116442632, 0.44587521799960755, 0.5563861589418331, 0.522287243155403, 0.3611841764335619, 0.11369903109618561, -0.1596253901147317, -0.38482534094435705, -0.483964699201641, -0.38655439837951533, -0.04151145451226119, 0.5720728354486126, 1.4371571613240117, 2.4955640303315136, 3.6504907769287613, 4.7750884396035325, 5.72658008015959, 6.364454583623821, 6.570450517601939, 6.267489764533842, 5.434560248197457, 4.114858164101802, 2.415287969392239, 0.496605796527861, -1.4450778278788645, -3.2032653443487487, -4.589107696103439, -5.458334324581022, -5.732771049189039, -5.412728680596743, -4.577818012851054, -3.375535906439753, -1.9989951557190209, -0.6570912658004842, 0.4581444431109461, 1.2015633866367943, 1.4970986722735415, 1.3481616887857821, 0.8342517541289488, 0.0942496784101515, -0.7006656178811849, -1.3795334656408877, -1.8034902685721215, -1.8909565968620787, -1.631287133143168, -1.0842485251488851, -0.3654947630527988, 0.37894495686864926, 1.0038560507815186, 1.3951570690672976, 1.492919405684957, 1.302168534275811, 0.8891652641234916, 0.364058789152016, -0.14611864197051885, -0.5278820667957659, -0.7080165292589624, -0.670189600417231, -0.45731201557871604, -0.15883480560341048, 0.11416886647031636, 0.26015942814435056, 0.21673113449743694, -0.019122368878206383, -0.3859094443181909, -0.7700216015151542, -1.0335843215224039, -1.0516602590289508, -0.7498322422737133, -0.13239016210983037, 0.7070568054003411, 1.596945259366983, 2.3203281627128107, 2.662492251463732, 2.463190630601106, 1.6610472568391637, 0.318607995281712, -1.3796519614835767, -3.158042215838886, -4.703915797845762, -5.7342351459350445, -6.059494266251077, -5.629748487562069, -4.550911228612244, -3.0659740200572814, -1.5039668070428798, -0.20737552980693386, 0.5455965348442208, 0.6056179859948811, -0.012145784545669234, -1.1307009946114963, -2.45247723595696, -3.6300149635884282, -4.349457218482644, -4.406641865689943, -3.756972070361146, -2.526394736034524, -0.9803254197557592, 0.5421052138615549, 1.712219009714974, 2.293201312901476, 2.1980332140284413, 1.5090389335625698, 0.45392869444505685, -0.655508539930045, -1.5060891202961622, -1.8655882700453128, -1.643008935210927, -0.9107644072154458, 0.11712328264970637, 1.1449112758505389, 1.8768976982398435, 2.0988440144217924, 1.7368593545912199, 0.8776535532374878, -0.25534930759529295, -1.3633648478056815, -2.15400020643426, -2.4206497379650367, -2.097455454217476, -1.2746553570158978, -0.1703659340138038, 0.932779683171542, 1.7677311664163984, 2.156753620007958, 2.0576778206249613, 1.5696927732413597, 0.8976502430000644, 0.28610214315633115, -0.0567843417536547, -0.02238040686363465, 0.3672085439180488, 0.969127563754499, 1.5675061179752476, 1.943847394709286, 1.9479076241363178, 1.5466679256013152, 0.8357791494765827, 0.009638865589454003, -0.7005794568234477, -1.1012198137542644, -1.0987555534319857, -0.7300799387776638, -0.1499656308547311, 0.4209918047406447, 0.7714735108326362, 0.772919957297164, 0.4263801959059635, -0.13437640238752593, -0.6866402624645664, -0.9968988123440077, -0.908439906727403, -0.4087495714413103, 0.34817661594520266, 1.0761358364759108, 1.4410957001226627, 1.1719305990883402, 0.1631490210181422, -1.4650113101892746, -3.3728459145213203, -5.078245529044689, -6.086931293870524, -6.04019027635078, -4.8363298586940076, -2.687010473812624, -0.08679485327112424, 2.3009974874107644, 3.813951713581245, 3.969776341092248, 2.6043518117998694, -0.07196569335392335, -3.517886875052611, -6.994328458945312, -9.751060607999392, -11.215240393626946, -11.129747642100773, -9.604070532000028, -7.066158571031657, -4.132384350406014, -1.4358207670448582, 0.536471154006275, 1.5514932367384597, 1.6567043089332925, 1.12386720686222, 0.3346175399221456, -0.351677834216168, -0.7046466588454674, -0.6725795376247665, -0.3646158114705283, 0.021449136609380814, 0.29479914220540254, 0.3534900792801502, 0.22254136686558174, 0.03579789767288782, -0.0292279601516029, 0.16348630006154374, 0.6379065195718405, 1.2791559907509156, 1.8632748082587163, 2.1347846392684406, 1.9045976075030104, 1.1318375973814248, -0.042530465050923325, -1.3259666389634261, -2.361400890197587, -2.842847873582015, -2.619767267052631, -1.7527453828350381, -0.49908124221181444, 0.7688750233675372, 1.6857657078429356, 2.0136912549242085, 1.7186851832557575, 0.975570398231413, 0.09869628295725118, -0.5772638563997643, -0.8236625598990017, -0.605028043443114, -0.09391181870560862, 0.39393335048347844, 0.5221811641923679, 0.07033628903527502, -0.9668676301850129, -2.356190648720458, -3.6913504992574624, -4.52766281799671, -4.539953044600434, -3.6471744392798513, -2.056675309816715, -0.2080645102218223, 1.3679923839326846], 'positive_zeros': ['1.35484551570614929969876627503954', '3.17879322856334368967218686415646', '3.92659714562331919201067237354382', '4.51058305587084404058226315322516', '6.15658357302611285884544848783254', '7.44431370957072124646533025115199', '8.139728220883195888716219751069786', '9.060338821172853031573751098868035', '9.962008428748277415397539574635939', '10.69303669743156604184328516364739'], 'prelabel': '2-26e2-52.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.323335356042807, 'root_angle': 0.23633887690802272, 'root_number': '0.7367937313197694 + 0.6761175914645997*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.118169438454', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35484551570614929969876627504', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17879322856334368967218686416', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92659714562331919201067237354', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.397887176638557, 'bad_primes': [2, 13], 'central_character': '52.47', 'conductor': 676, 'conductor_radical': 26, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/676/2/f/h/99/3'], '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': '2-26e2-52.47-c1-0-31', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-26e2-52.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.323335356042807, 'root_angle': 0.11816943845401136, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35484551570614929969876627504', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1717470731201425164622827544941', 'Lhash_array': ['1717470731201425164622827544941'], 'label': '2-26e2-52.47-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/676/2/f/h/99/3'}