-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2724279443215354257819162441432', 'a10': [-0.6909830056250525, 2.1266270208801], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [0.8090169943749475, -0.5877852522924731], 'a5': [1.8090169943749475, 1.314327780297834], 'a6': [-0.8090169943749475, -0.5877852522924731], 'a7': [-4.47213595499958, 0.0], 'a8': [2.4270509831248424, 1.7633557568774194], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5988780151596031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [-1.8090169943749475, -1.314327780297834]]]], 'bad_primes': [3, 5], 'central_character': '75.31', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '3915151256583371445930758773054', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.30901699437494745, -0.9510565162951535], [-1.618033988749895, 1.1755705045849463]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-1.8090169943749475, -1.314327780297834]], [[1.0, 0], [4.47213595499958, 0], [7.0, 0]], [[1.0, 0], [0.38196601125010515, 1.1755705045849463], [-8.899186938124421, 6.465637775217204]], [[1.0, 0], [-1.7360679774997898, 5.343067833768241], [-10.517220926874316, -7.641208279802151]], [[1.0, 0], [3.118033988749895, 2.2653842965929876], [5.253288904374106, 16.167960777017612]], [[1.0, 0], [1.0, 0.7265425280053609], [5.871322893124001, 18.07007380960792]], [[1.0, 0], [-1.381966011250105, -4.2532540417602], [-18.607390870623792, 13.519060802726882]], [[1.0, 0], [5.354101966249685, -3.889982777757519], [8.961492836873475, -27.580638972559452]], [[1.0, 0], [2.23606797749979, 1.6245984811645315], [9.57952682562337, 29.48275200514976]], [[1.0, 0], [0.9549150281252629, -2.9389262614623655], [-29.933628791873055, -21.748054334821507]], [[1.0, 0], [1.118033988749895, -3.440954801177934], [-33.16969676937284, -24.099195343991397]], [[1.0, 0], [-7.708203932499369, 0], [43.0, 0]], [[1.0, 0], [-0.6180339887498949, 0.4490279765795854], [14.52379873562253, -44.69965626587222]], [[1.0, 0], [2.9270509831248424, -2.1266270208801], [16.377900701872214, -50.405995363643136]], [[1.0, 0], [1.2360679774997898, -3.804226065180614], [-47.7320026681219, -34.67932988525592]], [[1.0, 0], [-0.5, -1.5388417685876268], [-49.350036656871794, 35.854900389840864]], [[1.0, 0], [0.6180339887498949, 0.4490279765795854], [20.704138623121477, 63.72078659177529]], [[1.0, 0], [-4.23606797749979, 3.0776835371752536], [21.940206600621266, -67.52501265695591]], [[1.0, 0], [2.5, 7.694208842938133], [-59.05824058937116, 42.90832341735054]], [[1.0, 0], [0, 0], [24.412342555620846, -75.13346478731714]], [[1.0, 0], [10.090169943749475, 7.330937578935453], [25.648410533120636, 78.93769085249775]], [[1.0, 0], [-1.663118960624632, -5.1185538454784485], [-72.00251249937033, 52.31288745403011]], [[1.0, 0], [1.7360679774997898, -1.2613272171618513], [29.974648454369902, -92.2524820806299]], [[1.0, 0], [-3.5623058987490537, 0], [101.0, 0]], [[1.0, 0], [2.618033988749895, -1.902113032590307], [31.828750420619585, -97.95882117840081]], [[1.0, 0], [-7.52786404500042, 0], [107.0, 0]], [[1.0, 0], [2.4442719099991588, -7.522695417784323], [-88.18285238686927, -64.06859249987957]], [[1.0, 0], [-5.663118960624632, 17.42928799417946], [-91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-75-25.6-c1-0-1', '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/75/2/g/a/31/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0132120192143756, 0.9888449716021052, 0.9771510830607532, 0.9752169717070542, 0.9795594054823145, 0.9863766893989219, 0.9917469538990081, 0.9917625938598009, 0.9826209998460729, 0.9607007119102706, 0.9226467055512352, 0.8654784270359189, 0.786724880232013, 0.6845840628048535, 0.5580990792825645, 0.4073396638864984, 0.2335751524480764, 0.039422958374810343, -0.17104463889644786, -0.39225293342092876, -0.6171532370363104, -0.8373420177741077, -1.0432818496193428, -1.2246301618874806, -1.3706751392969767, -1.4708701726496898, -1.5154493505146889, -1.4960971351561076, -1.4066362558553283, -1.2436897802781757, -1.0072671695985935, -0.7012207809551761, -0.333519582401678, 0.083708533130403, 0.5344050808279635, 0.9991050100233955, 1.4557627670551379, 1.8808643313814153, 2.2507843288566662, 2.5433218022710773, 2.7393241125353174, 2.82428810560221, 2.7898135239278226, 2.6347779220996026, 2.3661069153659433, 1.99902964495514, 1.5567372014737373, 1.0694006628651096, 0.5725534689055777, 0.10489699833766754, -0.29435568048102656, -0.5884297682874603, -0.7460194507516467, -0.744155209515036, -0.5706507158345636, -0.22588138983670894, 0.27632034065559485, 0.9088114449215056, 1.6324070567914393, 2.398258615696043, 3.1512259706425367, 3.8340259604453575, 4.391848398798679, 4.777059574224334, 4.95357264934323, 4.900460974176776, 4.61442848036616, 4.110831245579762, 3.4230618537967903, 2.600254714962114, 1.7034334228065617, 0.8003848418427978, -0.04030839680693999, -0.7555321363108242, -1.2935925587486534, -1.6192422969304396, -1.7172285240548693, -1.5939357101542067, -1.276875625149072, -0.8119959983880329, -0.2590151516034253, 0.31478278660228814, 0.841665615018835, 1.2607256574448067, 1.5244974066069341, 1.604150158475459, 1.4926182877195227, 1.2052477059358457, 0.7778153991724315, 0.26208974834146903, -0.28059370276550705, -0.7870017516114084, -1.1999927276122804, -1.4758203888119097, -1.5897920007888917, -1.5394905271245998, -1.3450532011206158, -1.046363191390802, -0.6974148794911241, -0.35850543113275585, -0.08723279444727282, 0.07050513714676948, 0.08825000299183786, -0.035696797556944576, -0.2762639240153784, -0.5833946324877253, -0.8876122774450425, -1.1088250473525008, -1.1673419172268484, -0.995697576944872, -0.5496814936698687, 0.18302514588458207, 1.1779685675206275, 2.37372378353491, 3.676709661316754, 4.970671569442199, 6.129815790604085, 7.034013545563138, 7.58411622381633, 7.715302140270715, 7.406540966190009, 6.684707497147602, 5.622553203138305, 4.330567165687637, 2.9436164208122584, 1.6040268603281755, 0.44333323425016596, -0.4348022638111798, -0.9680825977680039, -1.1434933993734002, -0.9983996339429342, -0.6145263850373055, -0.10555703981805563, 0.39996245567458166, 0.7779885381238747, 0.927792279116969, 0.787411852660432, 0.34337778091806764, -0.3668440091667536, -1.2601729491726164, -2.2203028747183167, -3.115362249340397, -3.8181969528204958, -4.226167118067572, -4.277365874007393, -3.9606723337317504, -3.3179778537755427, -2.4381373527974057, -1.4435092816006876, -0.47114927434081405, 0.34838471941414123, 0.9112280212403238, 1.1561332234539092, 1.0735062297996891, 0.7060391201558427, 0.14079833571872183, -0.5059508077507607, -1.1086697109012587, -1.5538796090591185, -1.7592851936501224, -1.687412092895473, -1.351392721006067, -0.8118725769471388, -0.16555010307921456, 0.4726575332814703, 0.9906751869328265, 1.2997912092717439, 1.3509164245631555, 1.1435704659669412, 0.7258585838800269, 0.18532065143418766, -0.36778621319125127, -0.8217739436178333, -1.0854593685388267, -1.106608007951476, -0.8832850998083589, -0.4657420310415294, 0.05182176125349896, 0.5483885934082561, 0.8991845885752928, 1.0004831308541915, 0.7914718504873877, 0.26888201117411337, -0.5087183085782179, -1.4282321803694682, -2.340064159299403, -3.083932704848249, -3.517937467837849, -3.545560139214359, -3.1354573026041765, -2.330061048468715, -1.2409565826728697, -0.03141611772456756, 1.111104515819459, 2.007715499415346, 2.5201487130098057, 2.576114108436883, 2.1830211764552416, 1.4271708329227444, 0.4581797971745736, -0.5388135879415064, -1.3782236216294435, -1.9099101913529766, -2.0490911674509102, -1.7944234215720025, -1.2304931622940505, -0.5138231830635744, 0.15538137728105206, 0.570757381918389, 0.559702577909676, 0.018199363756058167, -1.0661418949046992, -2.607406077308261, -4.4326330552522615, -6.30921624767657, -7.983568435080182, -9.22400410795959, -9.859939320402406, -9.8101745302514, -9.095089712960705, -7.830652257971062, -6.205619972297739, -4.446528472502643, -2.777346892835079, -1.3816083211442998, -0.37418531187700205, 0.21218501806650605, 0.4235958612196716, 0.3663061958217796, 0.17725293387242, -0.009591282671372506, -0.09364020904452938, -0.028390574836987086, 0.17185487204968386, 0.4403233849611233, 0.678867492419399, 0.7866485116610411, 0.6895139843933353, 0.36299068234909665, -0.15677058636003388, -0.77704101644806, -1.3670523844656972, -1.7871277726058243, -1.9219080154197123, -1.70999357429878, -1.1628561352337827, -0.3680575127231565, 0.5247956439222835, 1.3330594170619836, 1.8792207412294368, 2.030098488143208, 1.7283620057427078, 1.0089957943478018, -0.0036159271693463535, -1.118184238502865, -2.1144629905426213, -2.788951760539214], 'positive_zeros': ['2.14907754764985838790991192470955', '4.10086683798978184237670281144112', '6.15541113893471457139290388990154', '6.93577447550883033588940439398526', '8.993629421739908416521117933153199', '10.05608923728147184240434983330098', '11.18523460698977763483873020426305', '12.55632039327822063579897882799443', '12.84970055048529302820432863720780', '13.84782512551672825677613236966380'], 'prelabel': '2-75-25.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475517, 'root_angle': -0.16, 'root_number': '0.5358267949789965 - 0.8443279255020151*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.16', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14907754764985838790991192471', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.10086683798978184237670281144', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.15541113893471457139290388990', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5988780151596031, 'bad_primes': [3, 5], 'central_character': '25.6', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/2/g/a/31/1'], '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': '2-75-25.6-c1-0-1', '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': '2-75-25.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475517, 'root_angle': -0.16, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14907754764985838790991192471', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2724279443215354257819162441432', 'Lhash_array': ['2724279443215354257819162441432'], 'factors': ['2-75-25.6-c1-0-1'], 'label': '2-75-25.6-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/2/g/a/31/1'}