-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.302', 'a10': [-0.10452846326765347, 0.9945218953682733], 'a2': [0.7193398003386512, -0.6946583704589973], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.03489949670250097, -0.9993908270190958], 'a5': [-0.766044443118978, 0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6156614753256583, -0.7880107536067219], 'a8': [-0.6691306063588582, -0.7431448254773942], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.302', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.740', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^79', 0, 'a^68', 'a^35', 0, 'a^58', 'a^57', 0, 'a^24', 'a^28', 0, 'a^11', 'a^47', 0, 'a^46', 'a^42', 0, 'a^84', 'a^13', 0, 'a^17', 'a^32', 0, 'a^70', 'a^0', 0, 'a^36', 'a^34', 0, 0, 'a^35', 0, 'a^31', 'a^3', 0, 'a^15', 'a^73', 0, 'a^2', 'a^29', 0, 'a^19', 'a^6', 0, 'a^21', 'a^31', 0, 'a^26', 'a^59', 0, 'a^79', 'a^72', 0, 'a^63', 'a^25', 0, 'a^23', 'a^71', 0, 'a^85', 0, 0, 'a^24', 'a^46', 0, 'a^20', 'a^20', 0, 'a^82', 'a^87', 0, 'a^3', 'a^4', 0, 'a^62', 'a^86', 0, 'a^7', 'a^81', 0, 'a^18', 'a^34', 0, 'a^77', 'a^8', 0, 'a^85', 'a^48', 0, 'a^69', 'a^10', 0, 'a^20', 'a^29', 0, 'a^28', 'a^15', 0, 'a^48'], 'euler_factors': [[1, 'a^79'], [0], [1, 'a^35'], [1, 'a^58'], [1, 'a^28'], [1, 'a^11'], [1, 'a^42'], [1, 'a^84'], [1, 'a^32'], [1, 'a^34'], [0], [1, 'a^15'], [1, 'a^29'], [1, 'a^19'], [1, 'a^31'], [1, 'a^72'], [1, 'a^71'], [1, 'a^85'], [1, 'a^20'], [1, 'a^87'], [1, 'a^3'], [1, 'a^7'], [1, 'a^34'], [1, 'a^48'], [1, 'a^28'], [1, 'a^67']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-837-837.302-r0-0-0', 'leading_term': '0.889917009702181504416656277808+0.399218524478506073297020669837*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/837/302', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9753602998092905, 1.6354872620694243, 2.047654216882834, 1.6416678749479545, 0.3616158663014764, -1.130094376192932, -1.8975462921863717, -1.4478404018526034, -0.16957570081318404, 0.9262945349791368, 1.0364658180934878, 0.28044715877638327, -0.3972442740956468, -0.15312279854940744, 0.8225412190028822, 1.339975093357299, 0.3432978523166508, -1.8730639143304506, -3.6645888647873024, -3.4875584425936172, -1.5088957338132056, 0.3267870459412888, 0.10866930714873779, -1.9855508810037221, -3.552365126858321, -2.172231268047621, 2.0493308386225797, 6.226372530845522, 7.2126567423251515, 4.52969202837183, 0.7639320712265407, -0.9965430122023008, -0.052357049511585686, 1.6402294995271527, 1.9208051246553157, 0.7626813924899486, -0.06144241548699711, 0.6166612092286168, 1.8747136380358524, 1.9177123650309906, 0.42858963925603005, -0.9480200790120359, -0.6675983988495906, 0.6918808608462911, 1.1056169666626912, -0.25290169646470445, -1.7828124525341287, -1.411633478815146, 0.6059669536518656, 1.7670513479863708, 0.5365872998990912, -1.2487026175457716, -0.18579749026803946, 4.407693865094353, 8.935476340270974, 9.04486560845615, 4.448435747374285, -0.6211793271743041, -1.9869461055199662, 0.17811550141088733, 2.2321673566892137, 1.6834725278589826, -0.24678140388225084, -0.9324740528807931, -0.03927668243923636, 0.32686525650931064, -1.0935951835963862, -2.7392199422475647, -2.333008256372908, -0.0905826381754406, 1.4881243914144802, 0.9678418373416661, -0.23231425331686992, -0.09214532074998415, 1.0356946789758772, 1.1560688506337398, 0.08626978597876582, 0.36876597902226876, 3.700080054255735, 7.628807463360778, 7.706283512860086, 3.0482528128539497, -1.9706103784788216, -2.672818613946873, 0.3375943707647995, 2.186525501739918, 0.06898851183830834, -3.353764329260304, -3.780637475126934, -0.9640619842717186, 1.313816575423546, 0.541811015122846, -1.4256796474976607, -1.4442029718869582, 0.4457328330757697, 1.4625339401359687, 0.34424519979259327, -1.0303236083596452, -0.7960524425639715, 0.06332550942407886, -0.42928230147374913, -1.7399390306684623, -1.3828314329714517, 1.0677459979696906, 2.8067011308979195, 1.7447548419470684, -0.18837063637497764, 0.231120480704035, 2.3637678207247097, 2.006541570472455, -2.535599439033603, -7.187182908046009, -6.947512192530026, -2.5918136306335926, 0.21211027892408058, -1.5676315239792966, -4.501878006774554, -3.757811064572303, 0.24345635140376254, 2.7749941332597263, 1.4790299330163001, -0.9186818365601698, -1.1182168763669955, 0.27301476721302687, 0.6227970266068585, -0.24058230454080912, -0.19185503262891837, 1.0959384530407026, 1.2149830381597089, -0.9861763190269748, -3.014647200629834, -2.2014512074488137, 0.19294118925377174, 0.8646580044587574, -0.42051970845812453, -0.6523578335573971, 1.1857253419866136, 1.9911828730948897, -0.39319085483423455, -2.589038401209824, 0.37440740459210925, 7.358157750926794, 11.208951665853748, 7.601089025946883, 0.6143172038517999, -2.7333890944125634, -1.1701131324723464, 0.8050302451817868, 0.34443056245857917, -0.36974466217148705, 1.0904489703041416, 2.992130847343113, 2.3797073285902286, 0.07475168764653041, -0.5746166158939761, 0.9817479787141646, 1.8402392913277648, 0.5359343896053859, -0.7224722785132184, -0.04049997076066258, 0.879900147686759, -0.1543321596933881, -1.65585233524029, -0.7086551431839153, 1.7383350562350923, 1.7936338594116352, -0.8360640049808437, -1.3708150372490928, 2.8724848580250346, 7.29489124997866, 5.693584243780437, -0.7818388217495769, -4.783726093936369, -2.6833762624161563, 1.169983483750658, 1.5392323221069328, -0.5136996422831486, -0.7236041471231907, 1.0411721241070118, 1.0419932436127903, -1.6721009282197883, -3.506005968978924, -2.0758931168479426, 0.23340435178295896, 0.4474194952199378, -0.4746239423879387, -0.111555781921105, 0.8631599928282482, 0.183704809000238, -1.3543080334321167, -0.84205675171261, 1.340664230835395, 1.3825317380434776, -1.5806641511817427, -3.1402705437806593, -0.22991513177065062, 3.517300964932754, 2.957218543342361, -0.470868366746929, -0.9007904283399975, 2.4524056395684557, 3.596656103739001, -0.932928456221063, -6.205345351396702, -5.790781651221488, -0.843716682491774, 2.2529501656448105, 1.1887246997784002, -0.4553596949983443, -0.16095256293843863, 0.07475114372298944, -1.4547878410866117, -2.5964822528394054, -1.3059064631145598, 0.3664206642312739, -0.3122523957110573, -1.9411397336130904, -1.4658820946595341, 0.3037698776016001, 0.05111177457257283, -1.9852759457139622, -2.1320232129171948, 0.15680400463089678, 0.9043064733347788, -1.4304222472414125, -2.566992748691476, 0.5087406347922452, 3.2850006709828943, -0.19593064036855423, -7.474063101208985, -10.072179906164239, -5.382245075822883, 0.020728742713730465, 0.36139811878513217, -1.8501105550044128, -1.4986912206429537, 0.8708299637473726, 1.285749860742079, -0.3314906424888864, -0.6184931849656032, 0.8274430478395958, 1.0051411514155775, -0.542359700891452, -0.5672481956205127, 1.9593490366950055, 3.5583368336014454, 1.9345964870233612, -0.32163459644099, -0.4469075130186975, 0.07599834438052502, -0.6146742044133081, -0.19392290568118548, 3.6278260539031315, 7.057246077238888, 4.564920702312753, -1.6995148623096707, -3.4916675798889814, 1.6230489653960625, 6.4455156149153945, 4.8475927830126535, 0.2886493376087765, -0.7494255986209832, 1.14809881500998, 0.8528276010326995, -1.8250278414642889, -2.1362343433493693, 0.9857072328618666, 3.023366510039369, 1.5010588479824332, -0.4376176107391168, -0.058535132333995175, 0.6420446868428984, -0.5028160718374319, -1.5802450241577821, -0.5112417818449686, 0.7012571359446204, -0.20235480108522358, -0.9999770803016637, 1.1466261013174641, 3.8242711638290317, 2.911067235887431, 0.0857732791068152, 0.44690770139591507, 3.3512389827082147, 2.742122435248081, -2.3285934700475974, -4.842903821943831, -0.641505054680202, 4.532947286591118, 3.7890025291036817, -0.5036241619816351, -1.3995598270868235, 1.3425417940849562, 2.0111624114856514, -0.8454680431907518, -2.5447777993240797, -0.7884341818568487, 0.9562791914482326, 0.18548902554777766, -0.7212222318485458, 0.22876598897046, 0.9487563616768279, -0.05367208219821961, -0.27629209571111296, 1.8103047823854574, 2.8981450058357927, 0.2838988217368311, -2.810157235723976, -2.293613806246618, -0.055309219061774814, -0.11063284519278296, -1.0418716514042825, 0.849377279363573, 2.955741063724019, -0.8668548629126129, -8.96153434981409, -11.8407273570195, -5.7689870522918465, 1.4305906988762525, 2.00843497056816, -1.27374158031939, -1.631088546349044, 0.8043501163373186, 1.307798455150254, -0.3672994851411633, -0.6695499868887357, 0.31760225841286754, -0.629679717425301, -2.929706192553124, -2.5904034679220223, 0.49760093111590903, 2.065000496366429, 0.7627867087281269, -0.21471403830042846, 0.3264449415038241, -0.24550396701269359, -2.154889435421105, -1.7232577011170749, 1.450539816393166, 2.4459866131701897, -0.36848959699452744, -1.3718918165692846, 2.7780673113456684, 6.073856518527501, 2.300025244373687, -4.029317475519974, -4.017418244912227, 1.831225759185486, 5.032319906532948, 2.6125574248387666, 0.03454417021833802, 0.551084701533004, 0.6905403032747843, -1.6314244208461541, -2.716578755915096, -0.23440774938620274, 2.140084239438596, 1.236774605371347, -0.3537949806339254, 0.3235846287290647, 1.3198219466244938, 0.30786078329634314, -0.6324336786602083, 0.5446332942428233, 1.3827718497997266, -0.05341474297467053, -0.42801235708110186, 2.802243708266202, 5.174282751898366, 1.9712574433308716, -2.8008088298863205, -2.19382998247176, 1.9306985071215363, 1.9413246249769065, -2.4296875303985797, -3.8562406757647576, -0.5425795968489256, 0.57269007310035, -3.8533637177638784, -7.538175052915801, -5.10907271944307, -0.4716988667342953, 0.6078490786871443, -0.6519495688397857, -0.4207480130635954, 0.4122317613371447, -0.5439704112780767, -1.4600765432602338, 0.05078789655727138, 1.6147174792165229, 0.38126758661628146, -1.1910782416990555, 0.20183760338177892, 2.240765165330294, 1.3018513591907708, -0.45890741889623177, 0.7435021576841343, 2.643219795286993, 1.1972799236829954, -0.6251745635791001, 2.6588794411155474, 7.878627949020522, 6.6197759549318995, -0.6276253715091075, -4.2113890270102186, -0.5438769782131974, 2.797007533699465, 0.23412926135242543, -3.438084421141412, -2.565444012212085, 0.2635690558824855, 0.5079691243954847, -0.2873572772568688, 0.9158839907912987, 2.1267914486738717, 0.7399830591303334, -0.7336470327995551, 0.5445280118241989, 1.9757648729638613, 0.4722522020198122, -1.4566745718574254, -0.5459259381870365, 0.892666217736706, -0.3305918150301113, -1.8891427190057382, -0.7794685722420257, 0.3361050312340833, -1.0198824961880586, -0.03007510280692618, 7.718502393309028, 15.668057933366853, 13.780552404684983, 4.064867176516367, -2.0669974908648845, -0.7007574349968477, 1.296099918528372, -0.13978508601094222, -0.8336353361577643, 1.4585732952050197, 2.2167655540779334, -0.8035935506766845, -2.929920990689343, -1.1527657384578656, 0.7129482445782228, -0.4338920232119501, -1.7282972223987774, -0.6888466840578841, 0.23678188620569032, -0.5448923401588076, -0.2981423164029592, 1.8848218376254964, 2.3663293179663163, 0.16899255077964834, -0.40281790517398414, 1.717556823936717, 1.1896294433455161, -3.7077719269491323, -6.357601419564813, -2.9565386469668407, 0.20252075589110433, -2.2246518362500773, -4.677004934900311, -0.5302346444033276, 5.531476515486766, 5.040159032371585, -0.21595235664911583, -2.1982284033286663, -0.20625552708182082, 0.16214627629824133, -1.5659999672013094, -0.8749324060554308, 2.055938838401916, 2.5791881329544637, 0.4175546097610662, -0.44828059167996126, 0.39446890021382064, 0.1994977324872944, -0.21327065343475293, 1.7835330131072005, 3.8904996080958103, 2.12085129955027, -1.1399397855972, -0.7383851098317041, 1.784401636124372, 1.2949447522370412, -0.8117550272811089, 0.44066614693096895, 2.7952443411223964, 0.13259382666932412, -4.675662212774157, -2.566701980937907, 5.802307455405446, 9.4721421374295, 4.353322383163556, -1.150370304047394, -0.695067758191778, 1.4529254392651483, 0.5249524760426724, -0.8650363442974446, 0.08753000307080994, 0.736167460706726, -0.4786670202658168, -0.21401844601004325, 2.5920713753915794, 3.6114011296953445, 1.1271153313063644, -0.6044775472279619, 0.5897486078989747, 1.2850890206352656, -0.000859036125406544, -0.07605621909279965, 1.3652280501722664, 0.3907133013407147, -2.2684473959458837, -0.7911288242998067, 4.193268534277529, 4.4160591549103065, -1.654483590742183, -4.632712908408733, 0.24015815960997686, 4.82442230178458, 2.0999638541308694, -2.511726300720694, -1.8103705648363504, 1.1860275201704662, 0.6628038804502745, -1.2859144224814534, -0.31116531522306395, 1.3042554073035553, -0.05367854630840412, -1.7463039122185142, -0.4076327343558255, 1.167631215459627, -0.2574451734893487, -1.931305289275438, -0.8317031235743539, 0.5389403537862231, -0.13000089262781533, -0.30493796663685846, 1.014982545341987, -0.009508650541122687, -3.732465051954805, -4.071749411336744, 0.4740657236128091, 2.3936932146914054, -1.8511289561216806, -4.585292252581416, -0.1987358828410125, 4.673515096335331, 3.023532905184118, -0.4330913850798941, 1.138180844233519, 4.16244451550049, 2.33313000256617, -1.1837396074308355, -0.040547151176716256, 3.505330603219688, 3.415379708201666, 0.6964550800845851, -0.007005996210582314, 0.7484282618522015, 0.2128143860656446, -0.1525783388903951, 1.1589443766422227, 0.9383105360822889, -2.4648352142652667, -4.464679075464565, -2.1443586338699583, 0.2531625138567624, -0.4008580784227461, -0.5211604550387763, 1.6673840613075763, 1.353174725669312, -2.679708346424654, -3.286035287637037, 2.320491042224097, 5.747517476369589, 1.605664676598306, -2.3130097315948155, 1.5464658557984572, 7.313324121786183, 6.2923256081041385, 1.3302395220865308, -0.12934425386904724, 0.9814741669504519, -0.14039407815105803, -2.004604012256885, -1.0312006056098353, 0.5624687864053208, -0.2945146519698977, -1.0292273955696338, 0.7654146332207717, 1.7989330747402341, -0.1719960974347071, -1.409370821511261, 0.2587115251413929, 0.9607567861993884, -1.0425622712098368, -1.4993169016016805, 0.9324619103088471, 1.62838383976801, -0.07536311655356234, 1.021883459963996, 3.8358708328073936, -0.33974096895293887, -11.656426634254217, -17.484420128672816, -11.087767595765163, -1.763715521696234, 0.7842933091596986, -0.37859721379673583, 0.5701178790680128, 1.340283708176159, -0.9434861299877474, -2.2577710453262974, 0.1875738089708995, 1.8672998909027996, -0.26924852387655174, -2.0513408962680604, -0.6063574567984694, 0.527661113120717, -0.7275733885493395, -1.1902241691956967, 0.12886844822268945, 0.06953829242104165, -1.078365455558178, 0.22085672489964414, 2.131470273154955, -0.29046530299660434, -4.363805031141773, -3.101577026609478, 1.5053496255459353, 1.5133254658954867, -1.726815257228147, 0.32053708139224923, 6.6717651001660325, 7.488010689654518, 1.6886690011028258, -1.4328511217401867, 0.9015069090717449, 1.4942766678851895], 'positive_zeros': ['1.32241155684069839067383180479', '2.53911965169096962363179483250', '3.538160741230960739158891547036', '4.12084973674639999588542756715', '5.05613178779522471086874799278', '6.48243632487496401426224936674', '6.89783013056691877012773269128', '7.98873553397001282761167177934', '9.459812801741055731835345386326', '10.00920284648683884038415185899', '11.18210914786829512759640776732', '11.35388347346062432029599791295', '12.57631074252634066997791011540', '13.281537068339945670251435773483', '14.01944930753333409413685887092', '14.91187374907867917767128874110', '15.70371111352100609415925871143', '16.268016238878397847914745619961', '17.76322801050038101834928127683', '18.41753318512343926463315393800', '19.33069618093565099433426800861', '20.011984580857716462162809082630', '20.423991138529849743437459849845', '21.57456537549753958494127967082', '22.42040676405312557812245753748', '22.84178176918483757541980151593', '23.78235136540351585063724177675', '23.97823043209384598017673352796', '25.48158939565005408370344231530', '26.21856032564466900660835534812', '26.88100612719949041423914424559', '27.90993299566409547817361177376', '28.5182381385478660260543638871', '29.306126896979311177500737311909', '30.06274400454788562326759869009', '30.89656770195513224429164542144', '31.11192744665905412929998298693', '32.06559896578638537630600638731', '33.07939844895561017480564056292', '33.39430460843370799278662502737', '34.22650006708649052350954550238', '35.558883187217770759933768589198', '35.74677804994904465171159026804', '36.85657500797591678683307210387', '37.67451460351996832498144518712', '38.373348654949956826135318340268', '38.97591964716455065488698632748', '39.43210568615603098835235962999', '40.19722918563148648119846114289', '41.22069075987337753338357759855', '41.78252360241015513285853906810', '42.321733561480664886582006022370', '43.0872034442432021285643216157', '43.7295241324303847113656159387', '45.032961403381677852824714382719', '45.77124120628668862327512135407', '46.34031659451604325318988324369', '46.69799602059220830859896733425', '47.82468678335158696461235757758', '48.267343417877972832763985856900', '49.158214598737074501246800832539', '49.69705294613963719498683814269', '50.285706559308107217810814596133', '51.02641061068482825746259423884', '51.78063104155541265761270653414', '52.32330577329085465481197829416', '53.400747943994202848233851680903', '54.26166755785178781951898501284', '54.91695806510080421752108340118', '55.44816335351908139393595054244', '56.07828765226068595885604948141', '57.1432986789806546255879784946', '57.638954329923256198914116812534', '58.15611353966569861647359869435', '58.78498756320981555971192027602', '59.49692224504285182058018139705', '60.16390596140885239654089659653', '60.95375384073238513286567958147', '61.82636111813392457300133301560', '62.290252687419933442257068479434', '63.07757007919794799958349616001', '64.11764424004476483165263716823', '64.8750827144193278358506982232', '65.3779028378591584876551743558', '65.65411546516000621418328651875', '66.77169265086527811770135265100', '67.12681331989087197454362615511', '68.05800040748743107988497653031', '68.44701082743360808605691927406', '69.35386419826549680448108979797', '69.8373777565129941315250717384', '70.58703840373432625039839638118', '71.24068992943508610579636414504', '72.49796880924631896587847155211', '72.86519227909300250589861614031', '73.630175892823740719894637738951', '74.31027234079178614264579632715', '74.83220679588559568683110872702', '75.51846446185322896300378532381', '76.028181335350583482549879663571', '77.123526709433524661195198781', '77.69699264580090868461107979505', '77.89043976864651362092425203785', '78.46341016637073017006737301153', '79.5978929388586238675663867646', '80.23458241619439775700448204750', '81.27752238331106393176494363421', '81.69409416940529433202981634582', '82.29349103712736075658269287620', '83.038664075893847925655037533980', '83.95652554897117057873951026534', '84.390973922161399368812847985009', '84.90349373173883759520491211560', '85.71850708267408985277012571472', '86.208707235914714031360144457615', '86.754874256965955733624135676358', '87.82772874380688612259896187773', '88.05825196146045993839679386907', '88.930486528727123356956868922653', '89.71944392020190909285827625506', '90.58269961534757426203135216497', '91.108781129345360033170780305162', '91.79482689530229871184132798859', '92.60140537496533149239305102090', '93.16483239041020520282898392553', '93.69826716479005909906823694194', '94.36130355606899814402353311026', '94.74979132888967733916813305454', '95.648312807339599697884903757852', '96.5750017763015025205221796469', '96.84582093876446678680080621339', '97.40848820275881100191361560504', '98.085592315007157845470917442955', '99.29173697054980814126009726092', '99.87424910531674836541955841365', '100.52124372248093181020773809715', '101.18022198359635452517660312345', '101.75270471696610580663998414017', '102.08158344875148359372246028899', '103.07593241948153344712606704296', '103.9171380770659743241219026559', '104.2194761945933295688176991537', '104.637153503490531461347882782', '105.489067353273984767218946508403', '106.214116136353702750364340001780', '106.70086992027397165304435953815', '107.60281540218664408769857700850', '108.345851980635591462635751046939', '109.38844230345964872171854666773', '109.51887598145966596243692430605', '110.11684535666208607365465654704', '110.95956773853595866761056555865', '111.76652385123870901679119106566', '112.11480746352311062297848234526', '112.87434976920319534019359693791', '113.33422823734145337635414264162', '114.05303572038516840826633164096', '114.44097051586174328929186013866', '115.424332797367016487197807958276', '116.098273163029422382085176127221', '116.71109761237096571862710294842', '117.55113267381140391663399455748', '117.87866254614834127990305983995', '119.11207097187633773651544630210', '119.52468341973720577709638348466', '120.11574066476176917030397003167', '120.50859292997410124509601449079', '121.242997747645666709338603126201', '121.92890350689812443653722706075', '122.47478871297383862983212139946', '123.31514777796916604594611623042', '123.64346130051216114492399699455', '124.515804243129618540329926771570', '124.81285751429152802908295336558', '125.91037636700812238136575651649', '126.59568397520985469652610812492', '127.20366721493344032608115351376', '128.08507036999101555860225310776', '128.58309230452285731706861528926', '128.88906445519686447810239341228', '129.7972264103092671288406268358', '130.22997817564872906508044517370', '130.99557974185022226232481430504', '131.64863389761770068752442739314', '132.13874211995281429705545139267', '132.95166192800991314864667780208', '133.24497109336178495500016338552', '133.75211340636753013958589800240', '135.15475580164009721770775060368', '135.69676254645364439294110863462', '136.22879652325012613225467971443', '136.702422376770850018432305872600', '137.43155879551947329976701963648', '138.26587720827585930963568554716', '138.680003932186949101367587278152', '139.53019481044148790718866111460', '139.825554944426609431528564070751', '140.365340589023697646504320675231', '141.275139497358300613847612724663', '141.63751608479682739976519821504', '142.280421712916910952731521392621', '143.37594702634853880147121902635', '143.533159098078379745860512210446', '144.39912164505109584242506963544', '145.29833271544940730859117401458', '145.97220133876258038483651143898', '146.28467148099134425556697618275', '146.97143822109595723454445882627', '147.88225760913099592814101029446', '148.297725801295464893412678378202', '148.8213902908759237960193434256', '149.13116959399366177608451217958', '150.181761871823747986507740781667', '150.71152944264515396196183542143', '151.4150429601070749572623942945', '151.82577559826692832460620240226', '152.50787638689327978764408541423', '153.2293447299427728727981176499', '154.277715366415203740962155185800', '154.76833311594234792602210145631', '155.39480016838849544644675654611', '155.919132327252704525084832109766', '156.45290429415150842236001953909', '156.906811126473704117734019313', '157.948198879797170407583990966420', '158.32866765457667519615543612302', '159.06228737429856686593366754649', '159.39384091229045803045396887377', '160.04359170440933170768179444558', '160.67819772863466708800677537897', '161.48502829857926852134401342788', '162.176279107905901493523503017093', '162.93249184225663223283538968355', '163.6046318859491076465949572478', '164.15033919864576762215775743103', '164.73135216089633183529354758556', '165.30550582351808452233389429119', '165.99238266906115863814218652664', '166.528339052538966777573807708704', '167.32764431516294939819537141740', '167.77434193904119953892574146576', '168.20579954314593202247122671146', '168.749024152624257391309544139114', '169.657029199139642804222035936', '170.20360638372611690310246269454', '170.947139060019124499093793175463', '171.80691631879469309563293141255', '172.07621518989678708892537301580', '172.991525628926094052963391319285', '173.441105924833338709066765011294', '174.51932079061562821248090897239', '174.69100676709667400847387668838', '175.38261139537576887336991511749', '175.68173007569804846344726558260', '176.3568261495010033929138854179', '177.432239180183012340128712866559', '177.71355056320331515126365205473', '178.214130827206915894711671024018', '178.86708491170979116237408694996', '179.57643581705736855124619629895', '180.39837615357642949876303206580', '180.86116768280172219565144636981', '182.02680975299156407719416663411', '182.23035946626579882572751434002', '182.79316748644563060993678813060', '183.595959283670372976540012441991', '184.00310931477268560914669772128', '184.58253650485688628519652678856', '185.29095085642550538802156804536', '185.89874776367850094860521047140', '186.420226877082621131778983996908', '187.07747271046861191938690236071', '187.79271985141676713084909635675', '187.9910698682328140113653730730', '188.73817610019563131157947582358', '190.10932605276693395076681715696', '190.502728074168576335096077771', '190.830803044223496721081757822648', '191.459610371816371412272554357583', '192.16891215021014781051258448381', '192.78415998965978903725099246845', '193.53466034546820816873866165336', '193.919258678829197200225257453441', '194.65425303548617499047664317719', '195.01761374917279336163223862845', '195.59730158596652088838567509888', '196.22956503624046593743783974585', '197.073273588872158649135763239550', '197.63370542400587491514329324807', '198.10663043237694122430619115612', '199.16156094466993730444180070602', '199.593532997949210777837510633019'], 'prelabel': '1-837-837.302-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.26845664758279664, 'root_number': '0.664941054765905731328115534869+0.746895838579118577555987235712*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.134228323791', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02813236910878106585168066763-0.225350424014549402573445305504*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.32241155684', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.53911965169', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.53816074123', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.302', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/302'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-837-837.302-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-837-837.302-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.13422832379139832, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32241155684', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.302', 'Lhash_array': ['dirichlet_L_837.302'], 'label': '1-837-837.302-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/302'}
Lfunction data - 1-837-837.302-r0-0-0