-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1743660824893256880738504081922', 'a10': [0.0, 0.0], 'a2': [1.0728993766568748, 1.858316231778685], 'a3': [-2.661460776595966, -4.4628047833891635], 'a4': [1.6977738551385793, -2.940630576862102], 'a5': [0.0, 0.0], 'a6': [5.437822960025107, -9.733976231630141], 'a7': [11.628206767364656, 20.14064492199184], 'a8': [24.452552070040078, 0.0], 'a9': [-12.833253069282396, 23.75515976919023], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.661460776595966, 4.4628047833891635]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.76', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1361065928488767362958728894140', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0728993766568748, -1.858316231778685], [-4.0, 6.928203230275509]], [[1.0, 0], [2.661460776595966, 4.4628047833891635]], [[1.0, 0], [0, 0]], [[1.0, 0], [-11.628206767364656, -20.14064492199184], [-171.5, 297.04671349806245]], [[1.0, 0], [6.249758736085928, 10.824899665948278], [-665.5, 1152.6798124370878]], [[1.0, 0], [-25.30782866532775, 43.83444507759572], [-1098.5, -1902.6578121144116]], [[1.0, 0], [-63.679429845257296, 0], [4913.0, 0]], [[1.0, 0], [-5.411530122664502, 0], [6859.0, 0]], [[1.0, 0], [-44.23345928990025, 76.61459888463679], [-6083.5, -10536.931087845265]], [[1.0, 0], [72.2844983042613, 125.20042366260695], [-12194.5, 21121.493572898675]], [[1.0, 0], [-138.97951517533315, 240.71958149496683], [-14895.5, -25799.76280414221]], [[1.0, 0], [-243.26873281463958, 0], [50653.0, 0]], [[1.0, 0], [234.28631004454388, -405.7957925149846], [-34460.5, -59687.336854227295]], [[1.0, 0], [-249.20548008091552, -431.6365530247395], [-39753.5, 68855.08177868936]], [[1.0, 0], [226.261938401335, 391.8971731301318], [-51911.5, 89913.35549711177]], [[1.0, 0], [223.88483411727918, 0], [148877.0, 0]], [[1.0, 0], [57.965680433476855, -100.39950360608306], [-102689.5, -177863.43140384424]], [[1.0, 0], [41.39647075435813, 71.70079060058741], [-113490.5, 196571.31217639567]], [[1.0, 0], [405.0642336315242, -701.5918329787498], [-150381.5, -260468.39851841913]], [[1.0, 0], [134.17078583547604, 0], [357911.0, 0]], [[1.0, 0], [-707.5082038312743, 0], [389017.0, 0]], [[1.0, 0], [208.8214788688925, 361.6894111125925], [-246519.5, 426984.29905647587]], [[1.0, 0], [-461.4430642750681, -799.242832124689], [-285893.5, 495182.06755369285]], [[1.0, 0], [-114.54418364017403, 0], [704969.0, 0]], [[1.0, 0], [180.77695562596253, 313.1148719817915], [-456336.5, 790398.003348155]], [[1.0, 0], [144.61093170810875, 250.47348104831755], [-515150.5, 892266.8395445109]], [[1.0, 0], [-241.40393029862588, 418.12387242403594], [-546363.5, -946329.3414011582]], [[1.0, 0], [1796.6464598301764, 0], [1225043.0, 0]], [[1.0, 0], [-1507.1953634833926, 0], [1295029.0, 0]], [[1.0, 0], [1075.0173164712623, -1861.9846111445775], [-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-15e2-9.4-c3-0-28', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/e/f/76/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.250658705569377, 2.3029608114765217, 2.30218170004255, 2.2471513979787785, 2.1371330247533007, 1.972076515889046, 1.7529659781333946, 1.4822181696589702, 1.1640812673102694, 0.804978858008249, 0.4137439758116579, 0.0016919958340785026, -0.4175106127044657, -0.8282121361932574, -1.213389629222116, -1.555503696147136, -1.8375624782816171, -2.0443373736280503, -2.163647495432115, -2.1876074332051663, -2.11371655869223, -1.945661012791032, -1.6937043772307714, -1.3745618740537087, -1.010686552719227, -0.6289435612361018, -0.25870767698400565, 0.07051467980076197, 0.331770933728401, 0.5034273488384198, 0.5717406014760688, 0.5329411097720416, 0.39454115509989474, 0.17562275449182424, -0.09406285523463688, -0.3762436372046656, -0.6274500315476029, -0.8032956792066442, -0.8633577162239937, -0.7761800454556925, -0.5238440639009111, -0.10552807121467518, 0.46047971483890326, 1.1367345510460465, 1.8687927343889312, 2.5895752172244455, 3.2256722081414844, 3.7050556602592786, 3.9654317981526916, 3.9622991330811397, 3.675709210417559, 3.1147789444431786, 2.319182794364664, 1.357151901246501, 0.31989999756270077, -0.6871592290176116, -1.5555954403893295, -2.1863561941685123, -2.5019217107567977, -2.4566753104991315, -2.0440492771726593, -1.2993130616694633, -0.29735746557867143, 0.8545565710258007, 2.028447540028967, 3.0903921936120247, 3.9166617452468446, 4.4091525499044835, 4.508027772081473, 4.199759961927675, 3.5193135631543373, 2.545969902344592, 1.3931765469960358, 0.19367417011859128, -0.9181147471711206, -1.823979838277584, -2.4375205362440044, -2.715132467640907, -2.660698951472469, -2.3232235124413236, -1.7877157214004415, -1.16071098662119, -0.5526912507504173, -0.06022352451248525, 0.24926069968157497, 0.34749902678892197, 0.2485179989422148, 0.00425566847353631, -0.3066110547036149, -0.5947209928615321, -0.7781311265496409, -0.7991795682487545, -0.6369403086142259, -0.31279864443271055, 0.1121437653071688, 0.5476531860384597, 0.8912473525184679, 1.048419266304932, 0.9524627208077421, 0.580044106481198, -0.0407295656393178, -0.8317412631049442, -1.6760826244819942, -2.43749211280466, -2.9847781251404712, -3.216848618645904, -3.083597030283736, -2.598412000438349, -1.839438866014063, -0.9387115522169485, -0.060546767054088554, 0.6272752676482382, 0.9844494601246869, 0.9254391407081906, 0.4377683452962333, -0.4125747140790541, -1.4902145671145441, -2.612819483358939, -3.5831332497984247, -4.2248406092731035, -4.415526678930674, -4.110302007228397, -3.3512582187542477, -2.2605348952369293, -1.0179380156337319, 0.17285775251847768, 1.1230934835138409, 1.6950804435133864, 1.8284219103667443, 1.550811760097216, 0.9709172684352588, 0.2544666877204404, -0.4118331608528082, -0.8612599705892757, -0.984394807193078, -0.7547780556565445, -0.23709201320518838, 0.4244304042177946, 1.0355518145274631, 1.3938323826540335, 1.3341804154679013, 0.7685439711145563, -0.28896043724785864, -1.7174002649196738, -3.306641058572539, -4.794352940841549, -5.915357130458168, -6.4534553446555485, -6.285100803452023, -5.405730468165068, -3.933027224009384, -2.0861208386903183, -0.1447702803849451, 1.603188875538898, 2.915336473849731, 3.6380963665457915, 3.731271140250174, 3.268951926877862, 2.4172070595105333, 1.3939859265355692, 0.42047461508635303, -0.3251560118075155, -0.7414549552854439, -0.8177928849128433, -0.6265027202086214, -0.2958987737501197, 0.028512798890641056, 0.22463855327558116, 0.22598423530203937, 0.0374603420963155, -0.2689176877509838, -0.57698446682455, -0.761754089991982, -0.7275757676110409, -0.43871685895960144, 0.06619306574478034, 0.6803134223083268, 1.2544031398252147, 1.6360339888407118, 1.7120827513626884, 1.443023513045905, 0.8791545982875993, 0.15318662811055944, -0.5504023838795055, -1.0426424372183558, -1.1825563879847312, -0.9213102586853128, -0.3257487008911012, 0.4264565004883987, 1.0810426286811432, 1.3643396897448583, 1.0507228197538279, 0.024250481069954838, -1.6811553429609294, -3.874263684364383, -6.235706271323142, -8.378929227190797, -9.930151650712064, -10.609406647622999, -10.29375935687418, -9.047383282419329, -7.110603762302609, -4.849577173286149, -2.677673235364629, -0.9665459143009001, 0.032446967847426025, 0.2381305880985481, -0.25081818785433574, -1.1882434521240024, -2.2465413998641512, -3.099798716543647, -3.5034198124154474, -3.350708631351322, -2.6928569651972385, -1.7181755780379555, -0.6967986191215529, 0.0941703766167097, 0.4452758154241052, 0.269630493034714, -0.375915829661941, -1.308361599973789, -2.2695835846642898, -2.9966679113736987, -3.292389261979167, -3.0768398908671224, -2.406482807239904, -1.4558678692206721, -0.4674721301584068, 0.3161811895227944, 0.7191911877998366, 0.6792579604094406, 0.26207398304970053, -0.3605989261110794, -0.9626756476248615, -1.3304149096478424, -1.3248791345791342, -0.9222393506810095, -0.22027650780775215, 0.5908940968183345, 1.2855204984299309, 1.669946483745438, 1.6415915858981431, 1.2216728265400258, 0.5515600955878293, -0.14687645152974768, -0.6360058720668419, -0.7337441430841251, -0.37054851672499417, 0.38510754644415507, 1.341199656822849, 2.233517703407285, 2.8000244203331737, 2.8572080798815045, 2.3562721241852715, 1.402269841402679, 0.22961089036687504, -0.8601393947671487], 'positive_zeros': ['1.37550585672371077827221600372497', '3.34629005443114876443047209234103', '4.20799584840607027205722080251473', '5.15076262544433062799674635459191', '6.78867293069390228764451743305168', '7.78331337454630207320961112690458', '9.145704028964125075086174797219615', '10.39406869368736265429779767684881', '10.87681774505045802157082696922253', '11.71845620794396799107616360530375'], 'prelabel': '2-15e2-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.10210696658457033, 'root_number': '0.9489902416208023 + 0.3153054412922354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0510534832923', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37550585672371077827221600372', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34629005443114876443047209234', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20799584840607027205722080251', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/e/f/76/8'], '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': '2-15e2-9.4-c3-0-28', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.051053483292285165, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37550585672371077827221600372', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1743660824893256880738504081922', 'Lhash_array': ['1743660824893256880738504081922'], 'label': '2-15e2-9.4-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/e/f/76/8'}