-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '5854033767184501643115649621606', 'a10': [0.08707417931909163, -0.2679867682034142], 'a2': [1.4265462069891635, -1.9634724080166133], 'a3': [-2.0236602187412287, 2.0236602187412287], 'a4': [-1.202155827617493, -3.6998551997776503], 'a5': [0.110419606030108, -0.03587750484945988], 'a6': [1.0865561934191055, 6.860245811979427], 'a7': [-0.42233913790934624, 2.666544371681687], 'a8': [-4.363093935656446, -1.417655156209128], 'a9': [0.0, -5.1904013618315945], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3273866482872497, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[41, [[1.0, 0], [1.3233855503191827, -6.2648743551013375]]]], 'bad_primes': [41], 'central_character': '41.33', 'coefficient_field': 'CDF', 'conductor': 41, 'conductor_radical': 41, 'conjugate': '4190093293018525462549536677769', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4265462069891635, 1.9634724080166133], [-0.6180339887498949, -1.902113032590307]], [[1.0, 0], [2.0236602187412287, -2.0236602187412287], [0, -3.0]], [[1.0, 0], [-0.110419606030108, 0.03587750484945988], [4.045084971874737, -2.9389262614623655]], [[1.0, 0], [0.42233913790934624, -2.666544371681687], [-6.657395614066075, -2.163118960624632]], [[1.0, 0], [1.536627937103957, 3.015802132412934], [-6.465637775217204, 8.899186938124421]], [[1.0, 0], [1.0388885112910784, -0.16454377542042814], [12.363734711836996, -4.017220926874317]], [[1.0, 0], [-3.258307529914842, 1.660190608770942], [9.992349288972044, -13.753288904374106]], [[1.0, 0], [2.251675852130969, 0.35663041963203684], [18.07007380960792, 5.871322893124001]], [[1.0, 0], [-6.0656836868555395, -4.406977159928902], [7.1073908706237905, 21.874299874788534]], [[1.0, 0], [-1.3140816687513526, -0.669558052942922], [17.04577231648172, 23.461492836873475]], [[1.0, 0], [0.9648158886918964, -2.9693979770321612], [-25.079526825623372, -18.221342821066667]], [[1.0, 0], [0.3487661292072002, 1.0733917741853374], [-29.933628791873055, 21.748054334821507]], [[1.0, 0], [1.3233855503191827, -6.2648743551013375]], [[1.0, 0], [-0.5836717883912533, 0.8033552970307977], [-13.28773075812274, -40.89543020069161]], [[1.0, 0], [1.7302039175983277, 10.924077605433135], [-44.69965626587222, 14.52379873562253]], [[1.0, 0], [-0.48298699276338614, -0.24609416458772673], [31.152618371501077, 42.877900701872214]], [[1.0, 0], [1.5724587455084724, 1.142458152145864], [18.232002668121897, 56.11233446141406]], [[1.0, 0], [5.9593745540230705, 8.202375393473318], [-18.850036656871794, 58.014447494004365]], [[1.0, 0], [6.029488801809527, -11.833538065257041], [-39.3816119035957, -54.20413862312148]], [[1.0, 0], [4.284840177276237, 8.409472346332894], [-41.73275291276559, 57.440206600621266]], [[1.0, 0], [0, -10.910837652084616], [-73.0, 0]], [[1.0, 0], [-7.5886395582619635, 7.5886395582619635], [0, -79.0]], [[1.0, 0], [0.6352121310818436, 0], [83.0, 0]], [[1.0, 0], [-0.7531614977197968, 4.755274547023291], [-84.64402995026867, -27.502512499370322]], [[1.0, 0], [1.254122049677486, -2.461353109882687], [-57.01516947236989, -78.4746484543699]], [[1.0, 0], [-9.343917087926643, -1.4799310784101323], [96.05670814581052, 31.210716431869688]], [[1.0, 0], [-3.693129029572175, -5.083156026270392], [-31.828750420619585, 97.95882117840081]], [[1.0, 0], [11.114339653249045, -8.075040428781788], [33.06481839811937, -101.76304724358143]], [[1.0, 0], [-10.497826200925791, -10.497826200925791], [0, 109.0]], [[1.0, 0], [-2.456004485179281, 7.558804571264857], [-91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-41-41.33-c1-0-2', '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/41/2/g/a/33/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.881652409917815, 0.9080153531616376, 0.9512228683875484, 1.0115595208016703, 1.0888867080164983, 1.1827527714338613, 1.2924809016246406, 1.4172097779087827, 1.5558871202015672, 1.7072299033842093, 1.8696676418511773, 2.0412824522027337, 2.2197558400091735, 2.4023291770657376, 2.5857829315366816, 2.7664385815525976, 2.9401863896768825, 3.10254153225054, 3.2487302645885396, 3.373806750294925, 3.4727998458592584, 3.5408875139748504, 3.5735946833667374, 3.567008355816891, 3.5180016895391297, 3.4244567962566945, 3.2854742338150396, 3.101555828872909, 2.8747467030094156, 2.6087223721684145, 2.308807695033939, 1.9819163757845537, 1.6364027432227795, 1.2818216257655008, 0.9285972326819539, 0.5876078572572596, 0.269699662471147, -0.014850573485824695, -0.25689753586675185, -0.448982511622521, -0.5858456092891454, -0.6648567449331848, -0.6863271083815873, -0.6536656148904162, -0.5733506453049618, -0.4546962337731556, -0.3094035936666884, -0.15090303716880654, 0.006492768861846568, 0.1485866251118809, 0.26239190037875804, 0.33725666601287996, 0.3659373533703938, 0.3455357048267019, 0.2782118253441012, 0.17159184899997756, 0.03880161338597189, -0.10192223927577984, -0.22806576822989313, -0.3141060789230878, -0.3331695717352211, -0.2589990752160681, -0.06811470482298228, 0.2579758144975649, 0.7306826115432826, 1.352530252150254, 2.115817746820064, 3.0018967854540253, 3.981190762656804, 5.014031172355097, 6.052330545129928, 7.04204589170914, 7.926318340860899, 8.649108886247834, 9.159092866421716, 9.413532887592936, 9.381826604698842, 9.048426134125858, 8.414852183066358, 7.500578407629112, 6.342637825788821, 4.9938986476555245, 3.5200647331750194, 1.9955673201641675, 0.49861980205254863, -0.8942040161255542, -2.113445126735277, -3.1018362044336274, -3.8185388212664777, -4.242151184140788, -4.372187278526028, -4.228852198946852, -3.8510858436849795, -3.2930052546370114, -2.6190298647809285, -1.898108275695386, -1.1975653142439644, -0.5771418886419889, -0.08379942131682513, 0.2521976425289157, 0.41952073776763965, 0.4260958634511851, 0.2974509192786749, 0.0732441031169761, -0.19767879744971056, -0.4631846300369359, -0.67408052244306, -0.7899868663131855, -0.7841950352402912, -0.6469453343400656, -0.3867241348155466, -0.029394541284053048, 0.3847800341885401, 0.8059123875948464, 1.1805397569757063, 1.4582476907710995, 1.5980819529890413, 1.573960227613057, 1.3783901391395945, 1.0239834254257825, 0.5425099186675293, -0.018468472889880128, -0.6010390053546982, -1.1438348154532332, -1.5895581300113941, -1.8921873943015104, -2.022927311401168, -1.974083469558293, -1.7602778110748718, -1.416743462644622, -0.9948103919915585, -0.5550711384096212, -0.15904922295730073, 0.13956467830329305, 0.3029294791250744, 0.3151807812865041, 0.18571767575301337, -0.05097050377323187, -0.33912303655472026, -0.6088720959970365, -0.7859768683198257, -0.8029512881751604, -0.6101417866898288, -0.18522158530683816, 0.4603210791802942, 1.2788142102004685, 2.188787862594514, 3.0821559139089274, 3.835598815134543, 4.324955980639799, 4.440962379369552, 4.104382575636813, 3.2785554619547446, 1.9775828795813921, 0.268859789409874, -1.7306966698342863, -3.8645852568145966, -5.951896212883564, -7.80608534107087, -9.25518285025713, -10.1610109280439, -10.435029432363102, -10.048787472843607, -9.037592649244322, -7.496842862678794, -5.571391446034434, -3.4392121621124314, -1.2913740912633422, 0.6891770503872823, 2.3473766023438802, 3.571880832012947, 4.305063371964825, 4.546037310340663, 4.346521328860629, 3.8003392288230677, 3.0281965826344726, 2.1599928862185247, 1.31721280557177, 0.5978538738062915, 0.0659031754262891, -0.25336092995172943, -0.37188233116456143, -0.33175202568144696, -0.19398788165665415, -0.025219729795456888, 0.11539923555927534, 0.1868427631400496, 0.1726829354007846, 0.08239962854808058, -0.05253511601677739, -0.18693162617957204, -0.2728681510178642, -0.2712410594205603, -0.16160894027187134, 0.05166076912625244, 0.3382894008455111, 0.6464682988749272, 0.9121440638154342, 1.0716735589817634, 1.0755958583383844, 0.9009234957557877, 0.5594629908294254, 0.10023817368073405, -0.39496641636693935, -0.8227464525649277, -1.074488356547427, -1.055585852879968, -0.7043129734360336, -0.0070212524528306544, 0.9932892935261433, 2.1970618108137048, 3.457652457715396, 4.599367896772514, 5.441775625474733, 5.826803030521982, 5.644462766068448, 4.853015414464298, 3.490043047600979, 1.672182755260491, -0.4170255113900756, -2.549850506016254, -4.484578211347204, -5.9988465878872965, -6.921087546560663, -7.155199429763445, -6.694509205705819, -5.622683656803893, -4.101268370559693, -2.345650044753782, -0.5931038649985226, 0.9321112082510038, 2.0511378120726924, 2.655297508588677, 2.719395625717122, 2.301561532875906, 1.5298456348718381, 0.5779784316725909, -0.3655190196441054, -1.1296070028078662, -1.5889340784750747, -1.683282032793694, -1.4251072834057772, -0.8941297128006259, -0.22018485340639118, 0.442404981882993, 0.9442310374290555, 1.1686502210672465, 1.0531115890329446, 0.6002123319168914, -0.12336227573766118, -0.9996397025592162, -1.8813895660815978, -2.6192076716714, -3.088599206649912, -3.2120657534794717, -2.972189264337438, -2.4134359122804803], 'positive_zeros': ['4.61801837677553583998886778041333', '5.99467357467961706684897622328306', '7.03438274842776910036727226453027', '7.78118523104727359568711328734325', '10.54335536350074097252159332843307', '12.27609312528662628552278594407097', '12.90993492529208515572899741622481', '13.88428915700876021786797291770135', '15.12103069889448822146076073715239', '16.56032008359819408333257257177766'], 'prelabel': '2-41-41.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5721771126908606, 'root_angle': 0.2937858681219986, 'root_number': '0.6034660936159388 + 0.7973886592220377*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.146892934061', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.61801837677553583998886778041', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.99467357467961706684897622328', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.03438274842776910036727226453', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.3273866482872497, 'bad_primes': [41], 'central_character': '41.33', 'conductor': 41, 'conductor_radical': 41, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/41/2/g/a/33/3'], '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': '2-41-41.33-c1-0-2', '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': '2-41-41.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5721771126908606, 'root_angle': 0.1468929340609993, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.61801837677553583998886778041', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '5854033767184501643115649621606', 'Lhash_array': ['5854033767184501643115649621606'], 'label': '2-41-41.33-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/41/2/g/a/33/3'}