-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '846678664814860609977846557347', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-5.132444468702838, 0], 'a6': [0, 0], 'a7': [0, 4.025159310547453], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.703', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '795836384076283425640235332522', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.132444468702838, 0], [25.0, 0]], [[1.0, 0], [0, -4.025159310547453], [-49.0, 0]], [[1.0, 0], [0, 4.303437580862017], [-121.0, 0]], [[1.0, 0], [-18.486200670659763, 0], [169.0, 0]], [[1.0, 0], [23.575067935211006, 0], [289.0, 0]], [[1.0, 0], [0, 21.725930297517984], [-361.0, 0]], [[1.0, 0], [0, -30.746061047370187], [-529.0, 0]], [[1.0, 0], [-12.683972448636716, 0], [841.0, 0]], [[1.0, 0], [0, 24.52977787481135], [-961.0, 0]], [[1.0, 0], [18.231368854644586, 0], [1369.0, 0]], [[1.0, 0], [38.09899725646441, 0], [1681.0, 0]], [[1.0, 0], [0, -34.972401341319525], [-1849.0, 0]], [[1.0, 0], [0, 29.629522253615804], [-2209.0, 0]], [[1.0, 0], [-39.30433044424738, 0], [2809.0, 0]], [[1.0, 0], [0, 65.34287908770372], [-3481.0, 0]], [[1.0, 0], [-29.854145567933195, 0], [3721.0, 0]], [[1.0, 0], [0, -11.863403326916073], [-4489.0, 0]], [[1.0, 0], [0, -140.6506751008275], [-5041.0, 0]], [[1.0, 0], [-119.285148921232, 0], [5329.0, 0]], [[1.0, 0], [0, -9.188591012900616], [-6241.0, 0]], [[1.0, 0], [0, 113.18045297563884], [-6889.0, 0]], [[1.0, 0], [7.883457082861735, 0], [7921.0, 0]], [[1.0, 0], [-55.50802364630495, 0], [9409.0, 0]], [[1.0, 0], [-195.18551867386037, 0], [10201.0, 0]], [[1.0, 0], [0, 29.357908406338012], [-10609.0, 0]], [[1.0, 0], [0, -133.2558786672136], [-11449.0, 0]], [[1.0, 0], [-198.4847834198862, 0], [11881.0, 0]], [[1.0, 0], [-178.74531804841402, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-12e3-4.3-c2-0-28', 'leading_term': '1.4021844862660055903869833740759480136301165681841702369', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1728/3/g/j/703/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4021844862660056, 1.3982782135451195, 1.3755430198298537, 1.3341623036301937, 1.2744328667261513, 1.1967726384318422, 1.1017308954881362, 0.9900003633300162, 0.8624304560434852, 0.7200408149905341, 0.5640342424559462, 0.3958080976429941, 0.21696322731900122, 0.029309540641323403, -0.16513259535146618, -0.3641358694049016, -0.5652750614370046, -0.7659420745962494, -0.963367284084805, -1.1546473538288153, -1.3367794919559315, -1.506701927941414, -1.6613402015095855, -1.7976586594863608, -1.9127163656683313, -2.0037264446254235, -2.0681177077380535, -2.103597253511063, -2.1082125993120786, -2.0804117932118418, -2.0190998775178417, -1.9236900345715888, -1.794147744636843, -1.6310263287882711, -1.4354923393036756, -1.2093393978074922, -0.954989267732529, -0.6754791816250307, -0.37443472300762953, -0.056027882983152984, 0.27507973201656616, 0.613808180037862, 0.9547441846586655, 1.2922386757588469, 1.6205152741193976, 1.9337877224559483, 2.2263838894573236, 2.4928736357433916, 2.7281975441918123, 2.9277932941192244, 3.087716310712121, 3.204751257885545, 3.2765109725986776, 3.3015195675571447, 3.279276660580595, 3.2103000232087915, 3.0961443757105878, 2.939394584586883, 2.7436321325811943, 2.513374417450021, 2.2539871784328454, 1.9715711297157323, 1.6728246768944004, 1.3648853821824694, 1.0551536021387151, 0.7511024225599053, 0.4600786335383841, 0.18909999906939404, -0.0553455426455107, -0.26749287990999654, -0.44247899492938986, -0.5765026758037384, -0.6669591487335095, -0.7125445908201758, -0.7133261512628855, -0.6707739481545888, -0.5877525024833845, -0.46847019721207905, -0.3183865785386657, -0.14407861457496912, 0.04693164466078779, 0.2463842445249117, 0.44551831624387606, 0.6353326932087848, 0.8068629452060531, 0.9514667864554022, 1.061109198589641, 1.1286382484026138, 1.1480424973292012, 1.114681112064789, 1.0254783011230797, 0.8790745180975439, 0.6759279760605069, 0.41836138539618023, 0.11055042551508909, -0.24154775433419845, -0.6303257909719157, -1.0467149123268007, -1.4804270815581022, -1.9202443276063212, -2.3543472969639416, -2.7706734479288024, -3.1572939593123874, -3.502797399406926, -3.7966675480594065, -4.029642523983349, -4.194042566941466, -4.2840544714917055, -4.295961761166062, -4.228311208428325, -4.082008209322668, -3.860335759377219, -3.5688942815020055, -3.215462247037677, -2.8097803171909197, -2.3632645158879884, -1.8886566246318044, -1.39962246296478, -0.9103108858466589, -0.4348881003161338, 0.01293680187932084, 0.42037844673225744, 0.7760171036969957, 1.0701995762898413, 1.2953837732705809, 1.4464133517757998, 1.5207110581218088, 1.518382119043011, 1.442222168443684, 1.297627625973609, 1.0924100520521614, 0.8365196562047986, 0.5416866920729987, 0.2209927923081739, -0.11161275683687635, -0.4418343547369444, -0.7555697575680356, -1.03944766638183, -1.2813424522358146, -1.470845679837754, -1.5996753453287162, -1.6620057852136418, -1.654703983864868, -1.577461416924547, -1.4328144989319231, -1.2260510121911892, -0.9650044168353485, -0.6597425017796138, -0.3221612481619409, 0.03450114348591438, 0.396211540263233, 0.7487290551080934, 1.07820860047195, 1.3717961263360896, 1.6181906675396678, 1.8081491680584298, 1.9349119122669824, 1.9945292254625757, 1.9860738158226496, 1.9117275855076417, 1.7767367723189755, 1.5892346982075556, 1.3599369780144999, 1.101719548793748, 0.8290950808176721, 0.5576079960705338, 0.3031722352396929, 0.08137889259246459, -0.09319727259920486, -0.2076627487839672, -0.2514124784056415, -0.21665206292195485, -0.09881072750914578, 0.10317501952479455, 0.38672195843303436, 0.7456139820718731, 1.170171762202076, 1.6475741580816174, 2.1623206057160402, 2.6968173857851774, 3.2320649358329225, 3.7484185149174847, 4.226390781749104, 4.647462402192881, 4.994865797505491, 5.25430765854353, 5.414597895114507, 5.468156206950963, 5.411372329130613, 5.244802031966565, 4.973187898297469, 4.605301467239538, 4.1536111951212344, 3.6337884926495896, 3.0640714977751005, 2.464512892057553, 1.8561436469202495, 1.2600888191640511, 0.6966741822509936, 0.1845634280997344, -0.2600351736572949, -0.6240564115562555, -0.8981281598052135, -1.0769577735827705, -1.1595360001528867, -1.149147708654449, -1.053187517570204, -0.8827873979338335, -0.652272135127568, -0.3784667260178075, -0.07988697482874284, 0.22414962619231268, 0.5144514858918954, 0.7728754578227572, 0.9832005834322235, 1.131911117052005, 1.208850776887266, 1.207715902872972, 1.126362570400585, 0.966911381893172, 0.7356432400005523, 0.44268944908747937, 0.10152951694606846, -0.2716804508572242, -0.658917327810312, -1.0411999444863433, -1.399553546627327, -1.7159825359052459, -1.9744032906989466, -2.1614902178210147, -2.2673918718884596, -2.2862798544927654, -2.216701016927986, -2.0617128835981857, -1.8287927486819278, -1.5295220713790807, -1.1790590590233232, -0.7954231216158821, -0.3986246580063432, -0.009681885841942349, 0.35042728557691555, 0.6618263677728586, 0.9067610003633942, 1.0705271127528797, 1.1422583013477197, 1.1155305841068899, 0.9887513126499656, 0.7653094590158347, 0.4534762505332098, 0.06605762690748362, -0.38018738506379085, -0.8653361828254557, -1.3672628346461355, -1.862722681186863, -2.328507907903006, -2.7426163210236036, -3.085374065094608], 'positive_zeros': ['0.66791169795716857855030019133426', '1.98917915698573643982210310553285', '3.44106177573650451902310343962083', '4.05031309745877579385149770535967', '4.79003550541352815884732748843167', '6.09222318036353726668826957896996', '6.78771448356279579337904799320810', '7.56155705002770759586429198753701', '8.502226871058424534105450693641237', '8.761824042765521090219963683397534'], 'prelabel': '2-12e3-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66791169795716857855030019133', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98917915698573643982210310553', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44106177573650451902310343962', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/g/j/703/4'], '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': '2-12e3-4.3-c2-0-28', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12e3-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66791169795716857855030019133', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '846678664814860609977846557347', 'Lhash_array': ['846678664814860609977846557347'], 'label': '2-12e3-4.3-c2-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/g/j/703/4'}