-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2775978181138171548448812742935', 'a10': [0.0, 0.0], 'a2': [0.25473838589233494, 0.25473838589233494], 'a3': [0.05010869719194201, 0.020755701969749005], 'a4': [0.0, -1.8702167095059357], 'a5': [0.0, 0.0], 'a6': [0.0074773346240068666, 0.018051882659679306], 'a7': [-0.11431451019491298, -0.2759796408885964], 'a8': [0.9858927576330859, -0.9858927576330859], 'a9': [-2.119240261189626, -2.119240261189626], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [3.940938417289117, -1.2120249135784091]]]], 'bad_primes': [5, 17], 'central_character': '425.399', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '1014518468807354240001913148231', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25473838589233494, -0.25473838589233494], [0, 2.0]], [[1.0, 0], [-0.05010869719194201, -0.020755701969749005], [2.1213203435596424, 2.1213203435596424]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.11431451019491298, 0.2759796408885964], [-4.949747468305833, 4.949747468305833]], [[1.0, 0], [1.059000783244149, 2.556654053471755], [-7.7781745930520225, 7.7781745930520225]], [[1.0, 0], [-1.9795574372864582, 0], [13.0, 0]], [[1.0, 0], [3.940938417289117, -1.2120249135784091]], [[1.0, 0], [-1.9933092094446603, 1.9933092094446603], [0, -19.0]], [[1.0, 0], [-6.226721614361373, 2.5791925417901735], [16.263455967290593, -16.263455967290593]], [[1.0, 0], [4.366324265923179, 1.8085907286641294], [20.506096654409877, 20.506096654409877]], [[1.0, 0], [-1.1580763927026505, 2.795843733526849], [-21.920310216782973, -21.920310216782973]], [[1.0, 0], [-8.704136464368172, -3.605371372287497], [26.16295090390226, 26.16295090390226]], [[1.0, 0], [-2.8730067935650263, 1.1900383786846729], [28.991378028648448, -28.991378028648448]], [[1.0, 0], [5.787709971575161, -5.787709971575161], [0, -43.0]], [[1.0, 0], [-1.0834113820767015, 0], [47.0, 0]], [[1.0, 0], [1.898580847915835, 1.898580847915835], [0, 53.0]], [[1.0, 0], [-6.473099481075608, -6.473099481075608], [0, 59.0]], [[1.0, 0], [-10.341819723381317, 4.283721989042112], [43.1335136523794, -43.1335136523794]], [[1.0, 0], [0, -12.558505983880723], [-67.0, 0]], [[1.0, 0], [2.253154385888958, -5.439595876533544], [-50.204581464244875, -50.204581464244875]], [[1.0, 0], [-0.08291442494574135, 0.20017312922037483], [-51.61879502661797, -51.61879502661797]], [[1.0, 0], [-4.077712566761587, -9.844468982135028], [-55.86143571373726, 55.86143571373726]], [[1.0, 0], [11.012944012296897, 11.012944012296897], [0, 83.0]], [[1.0, 0], [0, -1.5526395902117798], [-89.0, 0]], [[1.0, 0], [-3.4328047536269324, 8.28752379318497], [-68.58935777509511, -68.58935777509511]], [[1.0, 0], [6.921323079116142, 0], [101.0, 0]], [[1.0, 0], [0, -12.964172187925719], [-103.0, 0]], [[1.0, 0], [1.3867017648045612, -3.3477942075578775], [-75.66042558696059, -75.66042558696059]], [[1.0, 0], [-4.758319707965245, 1.9709605571463895], [77.07463914933368, -77.07463914933368]], [[1.0, 0], [10.168722748204653, -4.212022874318178], [79.90306627407988, -79.90306627407988]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-425-85.59-c1-0-18', '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/425/2/n/c/399/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3117563224864164, 1.4718927675343998, 1.6348647039344644, 1.800427965877474, 1.9646717381562677, 2.1203677650057102, 2.257675230323228, 2.3650503280343567, 2.4302768456374366, 2.4415842907262704, 2.3888315430495184, 2.2647156938914623, 2.0659344306306835, 1.7941995576221519, 1.456977752091948, 1.0678278811014321, 0.6462155355935557, 0.2167165364000312, -0.19242824976857148, -0.5513770305604502, -0.8312614624283319, -1.0070801391566422, -1.0606442835452634, -0.9832512056845147, -0.7777333779067578, -0.4595429902777431, -0.05659004758137127, 0.39234225229140574, 0.8406331147997667, 1.2381608600776992, 1.5366015790193899, 1.6951742317632283, 1.6861801932705829, 1.4996146463769064, 1.1461436684218556, 0.6578565133885201, 0.08641711927032732, -0.5014627597772605, -1.0309541890079952, -1.4278077420576107, -1.627855937172418, -1.586132331117064, -1.284330350487835, -0.735410669457746, 0.015564114796310573, 0.8948509480416748, 1.8076264605517356, 2.649074495668009, 3.3176908965765493, 3.729085413834592, 3.828324715970646, 3.5989003214506425, 3.0667453957448907, 2.2983434518071633, 1.3928005724452346, 0.4686788684816106, -0.3527282232278686, -0.9653075023769356, -1.2944873800477656, -1.3093630282907545, -1.0283974088974197, -0.5174124085532442, 0.12022667953866811, 0.7600324577771113, 1.2770296494547266, 1.5673387718336347, 1.5670752338542515, 1.2651651236747439, 0.7075266800363632, -0.008576576622896353, -0.7495431293882175, -1.3676432769144053, -1.726860349278257, -1.727933840924433, -1.3280685148665228, -0.5514908480576032, 0.5115020756629012, 1.7173699743486786, 2.8922327276333912, 3.861095767279445, 4.47829032199113, 4.653563391173387, 4.3688303805837485, 3.6821648385986783, 2.717895516286342, 1.6443012118537916, 0.6428392561429105, -0.12538000366134594, -0.5494409772367701, -0.5888951154427658, -0.2802991329451502, 0.27149314792786466, 0.915745800186735, 1.4875781481469306, 1.8426032960128886, 1.8872807044778661, 1.5985175059303267, 1.0281736922455849, 0.291251642395311, -0.459949866721825, -1.0703065758192807, -1.4174930278977718, -1.440797585462889, -1.156423008410078, -0.6553725949828171, -0.08381809581259883, 0.3901745824557443, 0.6164125817607429, 0.4998959798753823, 0.02692036499296182, -0.726620562602175, -1.6075137070483023, -2.4162475002554262, -2.9505209995063315, -3.0518076072873708, -2.644391905660303, -1.7575460843029582, -0.5249807230730057, 0.8393098768912114, 2.08427810854326, 2.975011554869285, 3.3441071168490284, 3.1294441608892947, 2.3893115824498805, 1.2908071640882353, 0.07352701189032274, -1.0036058837865498, -1.720360922631842, -1.9446135717290725, -1.6614256677712373, -0.9746502769571815, -0.08035251955049663, 0.7818821611976252, 1.3881962980515226, 1.5859049043103775, 1.3314258411997366, 0.7010374377644506, -0.128641256501364, -0.9260509022461577, -1.4649740034010876, -1.5846811861495524, -1.2345811727192493, -0.4915472470819097, 0.4552729169914225, 1.3492121736778067, 1.9298240579935524, 1.9998817768409565, 1.478635344138546, 0.4273663236073817, -0.960020942232732, -2.3998942106361874, -3.5852162704314794, -4.259036232865912, -4.276733394737171, -3.641145860608504, -2.5014149633964373, -1.1155706832303556, 0.21378040059924527, 1.21427208104621, 1.7098765780422178, 1.6612497478140191, 1.1700013535320088, 0.44608214938187896, -0.25271236704349365, -0.6926559532239672, -0.7278869819741377, -0.3387675585582835, 0.36553862260818953, 1.1807412147969791, 1.8677377876403964, 2.222459566300265, 2.1353682826249054, 1.6235310271838181, 0.8258888505556757, -0.03718581098892968, -0.7286091704395009, -1.0649132338978433, -0.9715238954226282, -0.5062981838418267, 0.15644937192974093, 0.7777723079869121, 1.1274211793592999, 1.057508166495855, 0.5544972064393963, -0.24691755848186756, -1.0939054527286651, -1.6827579978540694, -1.7453657079654008, -1.1306481408254994, 0.14282251620281522, 1.879355021108298, 3.7477932813264956, 5.362325355682625, 6.381001912508258, 6.594887917088703, 5.9827828100765155, 4.715713862860644, 3.109421365815161, 1.53784784838064, 0.33192564022933846, -0.30763452155684606, -0.3587340747112137, 0.026184131955340487, 0.5750049502132929, 0.9849764133285542, 1.0190933351636133, 0.5807163752014519, -0.2562797274313559, -1.2712141744114234, -2.167216719856165, -2.6673485883800314, -2.6066620268230456, -1.9913654067288535, -1.0058353061704366, 0.03611392836481472, 0.7821953199965385, 0.9480192746388264, 0.4066528367874767, -0.7664775705861356, -2.3081932291132503, -3.8387219495643707, -4.969183421993289, -5.4137581091784135, -5.072938802473387, -4.062532772176967, -2.679207637345213, -1.3125212832440565, -0.3296992976810145, 0.03213918317424742, -0.2662544987676301, -1.0589063268759003, -2.029578415580781, -2.811788785631773, -3.10280206072862, -2.756318287418395, -1.8254124142934796, -0.5430021532962986, 0.7531909533488278, 1.7268018581784483, 2.1461101143687467, 1.9517474012199885, 1.2678959331780604, 0.35453697665023215, -0.4824809100223165, -0.9931154840431544, -1.0624844215665392, -0.741506406236234, -0.2189367696073775, 0.2551799900676703, 0.46791006530647566, 0.32910505672001206, -0.08642178533811669, -0.5565978145876561, -0.7857082176497755, -0.5104150016023885, 0.3974508106821502, 1.867323947061826], 'positive_zeros': ['2.18986066084643588735149552866589', '3.26622094834855341179222846718188', '4.51822495789598897643623183250856', '5.49765110828925572360711672116128', '6.94326864923970680359645136858572', '7.72720619347448773566624679384050', '8.623575618358397348916524574011053', '9.443068617403172621287342632231880', '10.85062019082603177599877995361024', '11.31830652972592657715458597226637'], 'prelabel': '2-425-85.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': 0.4832648785634565, 'root_number': '0.05255071730503321 + 0.9986182564477412*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.241632439282', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18986066084643588735149552867', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26622094834855341179222846718', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.51822495789598897643623183251', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '85.59', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/2/n/c/399/4'], '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': '2-425-85.59-c1-0-18', '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': '2-425-85.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': 0.24163243928172826, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18986066084643588735149552867', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2775978181138171548448812742935', 'Lhash_array': ['2775978181138171548448812742935'], 'label': '2-425-85.59-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/n/c/399/4'}