-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '733599690366429385657181438244', 'a10': [5.533548936633938, 0.0], 'a2': [-1.4558703979577106, 0.0], 'a3': [-3.187134820682338, 0.0], 'a4': [0.11955861564954265, 0.0], 'a5': [-3.800852702545762, 0.0], 'a6': [4.640055239731672, 0.0], 'a7': [-2.7396429031781357, 0.0], 'a8': [2.7376789465704485, 0.0], 'a9': [7.157828365205838, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4558703979577106, 0], [2.0, 0]], [[1.0, 0], [3.187134820682338, 0], [3.0, 0]], [[1.0, 0], [3.800852702545762, 0], [5.0, 0]], [[1.0, 0], [2.7396429031781357, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.324218027370025, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.7422478243720916, 0], [19.0, 0]], [[1.0, 0], [5.037408324891052, 0], [23.0, 0]], [[1.0, 0], [9.654905962964397, 0], [29.0, 0]], [[1.0, 0], [2.9362480042665147, 0], [31.0, 0]], [[1.0, 0], [-5.616315618925003, 0], [37.0, 0]], [[1.0, 0], [-7.721234425145758, 0], [41.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [9.219056817914819, 0], [47.0, 0]], [[1.0, 0], [-0.331984937865835, 0], [53.0, 0]], [[1.0, 0], [1.8337253230013895, 0], [59.0, 0]], [[1.0, 0], [-5.932293700960738, 0], [61.0, 0]], [[1.0, 0], [-2.9714395913130076, 0], [67.0, 0]], [[1.0, 0], [13.460773327684153, 0], [71.0, 0]], [[1.0, 0], [12.077367127649072, 0], [73.0, 0]], [[1.0, 0], [-1.640296133151999, 0], [79.0, 0]], [[1.0, 0], [14.746061255727062, 0], [83.0, 0]], [[1.0, 0], [11.350797646217654, 0], [89.0, 0]], [[1.0, 0], [-8.058165942987351, 0], [97.0, 0]], [[1.0, 0], [-11.713279265883346, 0], [101.0, 0]], [[1.0, 0], [-1.4717995238341408, 0], [103.0, 0]], [[1.0, 0], [-2.2149985440980307, 0], [107.0, 0]], [[1.0, 0], [14.98584995810454, 0], [109.0, 0]], [[1.0, 0], [-19.665147342415185, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 142, 'label': '2-8041-1.1-c1-0-142', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/8041/2/a/h/1/22', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.0191402950169077e-60, 0.02813918877518161, 0.05513017316803745, 0.07982390635069792, 0.10107145064229672, 0.11772837610031152, 0.12866399225361347, 0.13277643415847584, 0.12901419548885926, 0.11640424519791422, 0.0940864123481588, 0.06135330088473838, 0.017694619185583387, -0.037155512438236324, -0.10316997560920774, -0.1799806911486296, -0.2668333253903502, -0.3625467962516386, -0.46547973589532526, -0.5735060325586877, -0.6840014772310173, -0.7938433788339202, -0.8994247823221229, -0.9966846267127143, -1.0811548152280879, -1.1480247404941561, -1.192223319662949, -1.2085180558435036, -1.191630064640933, -1.1363634020593008, -1.037746419265333, -0.8911822697355828, -0.6926051258860455, -0.43863814734270906, -0.12674880394580984, 0.24460318455041571, 0.675830252442607, 1.1660987807816976, 1.7132332551661764, 2.313647530827896, 2.9623075402929433, 3.6527291972125826, 4.3770144974297045, 5.1259279052222615, 5.889014055718371, 6.654756626978794, 7.410776966690342, 8.144069734007791, 8.84127147693357, 9.488956753715804, 10.073955169653178, 10.583681586108522, 11.006470813604693, 11.331907370456621, 11.551140413206276, 11.657173759953842, 11.645121059618427, 11.512416627049133, 11.25897327295133, 10.887279604317959, 10.402430738603455, 9.812088133729517, 9.126366244170933, 8.357645917035844, 7.520316776799336, 6.630453239781515, 5.70543116936003, 4.763494445763181, 3.8232827941930125, 2.9033340078044687, 2.0215751385648146, 1.1948182384163222, 0.43827675618089307, -0.23488131250365174, -0.8139279919274186, -1.290903213805581, -1.6608633191829874, -1.9220396796677344, -2.0758996209935847, -2.127104901481322, -2.0833663650293706, -1.9551969427376383, -1.7555687964043176, -1.49948394961017, -1.2034711027034706, -0.8850243427142233, -0.5620020105948821, -0.2520059606518724, 0.028237257873210072, 0.26347122601832995, 0.4404586796187115, 0.5484640152602671, 0.5796504653926686, 0.5293758091983419, 0.39637386290369503, 0.18281296263512176, -0.10577291915202351, -0.46068005374845133, -0.8703526088559813, -1.3208120586360648, -1.7961837998459558, -2.2793023313526937, -2.7523728860450003, -3.197664718635199, -3.5982094833644713, -3.938477382578685, -4.205004092468157, -4.386942895341566, -4.476518942979794, -4.469366071569101, -4.364730969758259, -4.165534610745261, -3.8782865043010992, -3.512853283671351, -3.0820891733189906, -2.601341733745737, -2.08785169630343, -1.560070442018341, -1.0369225238645245, -0.537043393717528, -0.07802402703888686, 0.32430565677079265, 0.656523844089802, 0.9081661275016891, 1.072152626229452, 1.1450734222739911, 1.1273186817246474, 1.0230464140214774, 0.8399878387502681, 0.5890974768945196, 0.2840620444471387, -0.059311315950833665, -0.4238012774351652, -0.7915422842540004, -1.1448241958307381, -1.4668858196071006, -1.7426663573492414, -1.9594802567359, -2.1075840368008976, -2.18060823369499, -2.1758335111558402, -2.0942969507739084, -1.9407222770334298, -1.723275934080797, -1.4531591398543227, -1.1440539120428805, -0.8114482097153592, -0.47187141005138633, -0.14207603002896665, 0.16179534412905797, 0.4250177210089832, 0.6350264400386904, 0.7820580542852298, 0.8596568632831043, 0.8650206818701696, 0.7991669053457263, 0.6669084606475687, 0.47663842175402343, 0.23993147788158642, -0.029020382827275013, -0.31411213033594004, -0.5981366914101386, -0.8636636482061841, -1.0939425850353277, -1.2737860905408631, -1.390387688508125, -1.4340324743802926, -1.3986628956617408, -1.2822687420606087, -1.087078711656922, -0.8195405080794341, -0.4900868427551199, -0.11269545602403014, 0.29573820558620995, 0.7161872486335736, 1.1284016150350074, 1.5118946877478283, 1.846959832486628, 2.1156661770246044, 2.302783157494365, 2.3965861629983434, 2.3895008890588345, 2.2785515406034627, 2.065587459163892, 1.7572736343264745, 1.3648423597883055, 0.903615415453519, 0.3923179767741737, -0.14778364694051244, -0.6938789435047048, -1.222695910083335, -1.7116157027688774, -2.1397631504804235, -2.4890177154925466, -2.7448930308022783, -2.8972394401306536, -2.940732716548969, -2.875122912072369, -2.7052295496585477, -2.4406824795318665, -2.095420996682271, -1.686976549282445, -1.2355758704607365, -0.7631110061588041, -0.29202994881996447, 0.1557939980439216, 0.5601546767591067, 0.9035097824264242, 1.171829255970284, 1.3552506978733814, 1.448507523681367, 1.4511079108831686, 1.3672561960937695, 1.2055225300220975, 0.9782805036109776, 0.7009453428718277, 0.3910563997502647, 0.0672563979055785, -0.2517742918848743, -0.5483675313529753, -0.8068415469700435, -1.014343762723418, -1.1615143561876549, -1.2429329586263944, -1.2573235712360424, -1.2075069658288857, -1.1001047702728777, -0.9450142424554517, -0.7546865407295379, -0.5432532773066565, -0.3255555607967713, -0.11613600001469011, 0.0717431660804959, 0.22699374334090422, 0.3414498725218996, 0.4104221768480246, 0.4330205476276099, 0.4122223515862665, 0.35467850947063173, 0.2702663053482379, 0.17141395643361745, 0.07223691323532873, -0.012461370093633108, -0.06826168554454795, -0.08220573103996325, -0.04380660220806145, 0.05407507255966831, 0.21455082991668095, 0.43627063983347697, 0.713272267185724, 1.0351333347558564, 1.3874270431166864, 1.7524632077515319, 2.11027750264693, 2.4398147218484816, 2.7202375880379615, 2.9322821162339907], 'positive_zeros': ['0.57870811581231545880548778705796', '1.61061972492598375082006824706749', '3.40479567928715988975647713725404', '4.11995825102732347130754822954106', '4.48410724582281542832824186109812', '5.63354799312480468565539487299123', '6.13279408863840887243768997087508', '6.95877803832255456512097762176241', '7.44824841644493289239861866025840'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57870811581231545880548778706', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61061972492598375082006824707', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40479567928715988975647713725', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 142, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/h/1/22'], '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': '2-8041-1.1-c1-0-142', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57870811581231545880548778706', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '733599690366429385657181438244', 'Lhash_array': ['733599690366429385657181438244'], 'label': '2-8041-1.1-c1-0-142', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/h/1/22'}