-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '554063392389657700059800529537', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0.5, 2.598076211353316], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.1100711784264, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, -2.598076211353316]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.1349', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '1701473778595051456258184102222', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.5, -2.598076211353316]], [[1.0, 0], [0, 0], [5.5, 9.526279441628825]], [[1.0, 0], [6.0, 3.4641016151377544], [6.5, 11.258330249197702]], [[1.0, 0], [0, 0], [-8.5, 14.722431864335457]], [[1.0, 0], [-7.5, -4.330127018922194], [9.5, 16.454482671904334]], [[1.0, 0], [0, 0], [11.5, -19.91858428704209]], [[1.0, 0], [0, 0], [14.5, -25.11473670974872]], [[1.0, 0], [0, -8.660254037844387], [-31.0, 0]], [[1.0, 0], [5.0, -8.660254037844387], [-18.5, -32.04293994002423]], [[1.0, 0], [0, 0], [-20.5, -35.50704155516198]], [[1.0, 0], [-2.5, -4.330127018922194], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 0], [47.0, 0]], [[1.0, 0], [0, 0], [26.5, -45.89934640057525]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [0, -15.588457268119896], [-61.0, 0]], [[1.0, 0], [16.0, 0], [67.0, 0]], [[1.0, 0], [0, 0], [-71.0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386], [36.5, -63.21985447626402]], [[1.0, 0], [4.0, 0], [79.0, 0]], [[1.0, 0], [0, 0], [-41.5, 71.88010851410841]], [[1.0, 0], [0, 0], [-44.5, -77.07626093681505]], [[1.0, 0], [4.5, -2.598076211353316], [48.5, -84.00446416709055]], [[1.0, 0], [0, 0], [-50.5, -87.4685657822283]], [[1.0, 0], [-3.0, 1.7320508075688772], [51.5, -89.20061658979718]], [[1.0, 0], [0, 0], [53.5, 92.66471820493493]], [[1.0, 0], [-8.5, -14.722431864335457], [-54.5, 94.39676901250381]], [[1.0, 0], [0, 0], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-2268-63.5-c1-0-4', 'leading_term': '1.2454220927070649380318977524913830720225131631977733266', '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/2268/2/w/c/1349/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.245422092707065, 1.1024226022913832, 0.9515189666165329, 0.7929037274430077, 0.6267754302768445, 0.4534282090405106, 0.2733384496811756, 0.08724278430821454, -0.10379727944461689, -0.2983475574044642, -0.4945724701046405, -0.6902266036528385, -0.8826668970122182, -1.0688851477127104, -1.245560021535058, -1.4091273337497026, -1.555866986143835, -1.68200455716923, -1.7838251327079426, -1.8577965302708555, -1.9006986220481574, -1.9097550242824715, -1.8827630203422603, -1.8182172540569774, -1.7154225001152479, -1.5745907195827864, -1.3969176671906915, -1.1846345541105943, -0.94103070007293, -0.6704437388239514, -0.37821476937471527, -0.07060686130532556, 0.2453134950753189, 0.5618310839567434, 0.8707704791150934, 1.1637145888551377, 1.4322479829266885, 1.6682183631005452, 1.8640082802808016, 2.0128081388825456, 2.108880726770051, 2.147807024377486, 2.1267029296514965, 2.0443968249175732, 1.9015586324068385, 1.7007721651944474, 1.446544169410564, 1.1452454417062252, 0.8049817426973357, 0.4353948421633327, 0.04739683628705887, -0.34715623384353067, -0.7358425777435462, -1.106093084627945, -1.4456359996423023, -1.7429518719906532, -1.9877213474101463, -2.171247566174864, -2.286834841404686, -2.3301059883026065, -2.29924217913891, -2.1951315023526043, -2.021415460568618, -1.7844263668741203, -1.4930128693309461, -1.1582554940391616, -0.7930789611988384, -0.4117728877745658, -0.029437121246300695, 0.33862787661297056, 0.6775616812522508, 0.9735890656700651, 1.214641592140339, 1.3909272058202808, 1.495420336955017, 1.52424727622068, 1.4769451386839731, 1.35657748287588, 1.1696954452925203, 0.926139869259269, 0.6386870787388335, 0.3225483568731325, -0.005259510245951177, -0.32664843304379054, -0.6232677671864112, -0.877352582030202, -1.0725730498122967, -1.1948448956278321, -1.2330610655069796, -1.1797069494447487, -1.0313256269938673, -0.7888055738875146, -0.45747086794310543, -0.0469628552924541, 0.4290879062188046, 0.9535902791372131, 1.5067023077907291, 2.066692925525942, 2.6109177759489453, 3.116864252676838, 3.5632158199060764, 3.930883006296647, 4.203948409175152, 4.3704757191437, 4.423138150810328, 4.359629571556748, 4.18283174121643, 3.9007229617503483, 3.5260265223896816, 3.0756109570466363, 2.5696675935313316, 2.0307034330685143, 1.4823983367158666, 0.9483841543342403, 0.45100925183562757, 0.01015444774698753, -0.3578346010243114, -0.6410380974903762, -0.8326234722269241, -0.9312362129609122, -0.9410927970589869, -0.8717641734028098, -0.7376551812662453, -0.5572024525950332, -0.35182975502168773, -0.1447144367270969, 0.040569266385996075, 0.18145558639847287, 0.25776205150675463, 0.2529542834182636, 0.15522551381151733, -0.04167570955193972, -0.3379233307517714, -0.7274344974502912, -1.1980516079883978, -1.7320835522358664, -2.3071829772665207, -2.897516154912416, -3.4751637707620975, -4.0116758384456785, -4.479692964474678, -4.854540127397507, -5.115698500025818, -5.248065833310744, -5.242926399216834, -5.09856698411571, -4.8204951398439295, -4.4212387599513026, -3.9197307509923176, -3.340307656788021, -2.711375042794884, -2.0638137573574, -1.429218474064849, -0.8380720102604309, -0.3179649249918967, 0.10803070729219515, 0.4227318076947435, 0.6158713704655633, 0.6847139763881341, 0.6342158812453004, 0.47671336284062144, 0.2311521726319249, -0.07810008523838824, -0.4227898757328539, -0.7725700249567089, -1.0969386506543397, -1.3672038211191269, -1.558349349920601, -1.6506813590706353, -1.6311472874842399, -1.4942382866171542, -1.2424113477566243, -0.8859975344708266, -0.44259549718549285, 0.06401705590462793, 0.6053892449199388, 1.1502271822536387, 1.666432512159284, 2.1232177988752423, 2.493160001095832, 2.7540550880075805, 2.8904477975612464, 2.8947300787386174, 2.7677287755636293, 2.518735952337098, 2.1649718468128305, 1.7305083888394301, 1.244718006232627, 0.7403455469149652, 0.2513282572677914, -0.18949209422526672, -0.5526111397972318, -0.8139046421785355, -0.9563298220544438, -0.9711640257922688, -0.858689115913849, -0.6282664352207183, -0.2977881204775356, 0.10746680950779265, 0.5565017059907198, 1.014689618629193, 1.4461408125646857, 1.8161909785617596, 2.0938397275215133, 2.2539697108684025, 2.2791892932612963, 2.1611654684746533, 1.9013471981082093, 1.5110203958105202, 1.010681628934571, 0.42876512100132635, -0.20019651343990708, -0.8378564593086966, -1.4446284900524415, -1.9823754530571844, -2.4170241717159953, -2.720922256196385, -2.8747682633846163, -2.868974853640117, -2.704363240630204, -2.392133716558202, -1.9531081397352827, -1.4162923818590485, -0.8168560961617084, -0.19367016318277105, 0.41342442563112375, 0.966421257583125, 1.4318244579572716, 1.783000965673112, 2.0020358766358934, 2.080952292085089, 2.0222024240688867, 1.838389475138725, 1.5512362392612227, 1.1898723430890954, 0.7885634008553369, 0.3840482035206977, 0.01268108154699667, -0.29240672507372506, -0.5039119533444884, -0.6025309222253478, -0.5785287220746463, -0.43258041138336, -0.1758122735147912, 0.17096900308185983, 0.5788097920294744, 1.0127975280778672, 1.4347438105639494, 1.806163257491547, 2.091323429523032, 2.26013257182434, 2.2906410206275942, 2.170958471094354, 1.9004311576822641, 1.489977395172802, 0.961542894019736, 0.3467041000424766], 'positive_zeros': ['0.43707894927033003657397803709671', '1.82958684189881850166730959990620', '2.93674185631062289121744666525555', '3.98894818898648604210386403959766', '4.80374712206530339487832728401113', '5.45534360400761364568114377388274', '6.73974714735090711796008000802144', '7.36897246798339752755832691040704', '7.66553482348871477061744064261551', '9.065719120598480542949080209964654'], 'prelabel': '2-2268-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.5757285086095016, 'root_number': '-0.2356701914746539532748597823214635775420690996289669261 - 0.9718330931030800944898958889253763414939614200819472012*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2878642543047508', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43707894927033003657397803710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82958684189881850166730959991', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93674185631062289121744666526', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 18.1100711784264, 'bad_primes': [2, 3, 7], 'central_character': '63.5', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/w/c/1349/1'], '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': '2-2268-63.5-c1-0-4', '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': '2-2268-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.2878642543047508, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43707894927033003657397803710', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '554063392389657700059800529537', 'Lhash_array': ['554063392389657700059800529537'], 'label': '2-2268-63.5-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/w/c/1349/1'}