-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2988154033588443293693062921794', 'a10': [-1.0, 1.0], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.0, -1.0], 'a5': [-1.4142135623730951, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46712485182449026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 13], 'central_character': '936.883', 'coefficient_field': 'CDF', 'conductor': 936, 'conductor_radical': 78, 'conjugate': '1013053893905517032169022517407', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, -2.0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 2.0], [-1.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-936-104.51-c0-0-5', 'leading_term': '1.004161556223679641706168594156', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/936/1/o/c/883/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0041615562236796, 1.0836883363929806, 1.179921051996503, 1.294502856075901, 1.4280075429694619, 1.5800832906804616, 1.749648748012982, 1.9350720007480149, 2.1343008568298103, 2.3449429592227746, 2.5643084954678756, 2.7894310179676607, 3.0170793879722244, 3.243770120935845, 3.4657861314133975, 3.6792054450141283, 3.8799417525951134, 4.0637975057646205, 4.226529400546973, 4.363925435018492, 4.471892176163855, 4.546550387553947, 4.584336733505843, 4.58210888330697, 4.537250996443328, 4.447776287677022, 4.312423163292576, 4.130741301909043, 3.903164039506741, 3.6310635216224916, 3.316785316147792, 2.9636595442538844, 2.5759860866097988, 2.1589920540527614, 1.7187604673865782, 1.2621299552849963, 0.7965662316638613, 0.33000712789599507, -0.12931600087705716, -0.5730766386258734, -0.9930663925698562, -1.3814174476649894, -1.7308276685515263, -2.034781226766372, -2.2877572432241045, -2.4854187936888548, -2.624774755491013, -2.704307395840809, -2.724059324336095, -2.6856744517143145, -2.592388898123217, -2.4489693487305915, -2.261598120901118, -2.037706131556444, -1.7857569705942276, -1.5149873218492202, -1.235110945499728, -0.9559952594536195, -0.6873211458179057, -0.4382378788622463, -0.21702594673250628, -0.030780955333025047, 0.11486829115437429, 0.21599507487326802, 0.2705521452393803, 0.27848165770324546, 0.2417503656652453, 0.16430543618996168, 0.051949290628401194, -0.08786485148239487, -0.24631164994679838, -0.41353809247068424, -0.5790620609802728, -0.7322104847437654, -0.862580145484434, -0.9605024066576152, -1.0174920750091387, -1.0266603597481778, -0.9830725334464118, -0.8840324422748699, -0.7292784437335552, -0.5210786071267013, -0.26421699235346247, 0.03413261798912359, 0.3646442003115786, 0.7161817071908106, 1.0762344413418343, 1.4314291974102498, 1.768098507625014, 2.0728808218517103, 2.333325926949806, 2.538477539290585, 2.6794049159170554, 2.74965659621079, 2.745612016049076, 2.6667106717908533, 2.515543624862705, 2.297798235677076, 2.022053844010142, 1.6994333665188976, 1.3431231169456497, 0.9677802037744513, 0.5888532511915296, 0.22184756319263854, -0.11843011839143107, -0.41860969731786174, -0.6674404910368583, -0.8563818768681493, -0.9800683273591406, -1.0366205544424483, -1.0277814007621764, -0.9588634649880462, -0.8385048549068914, -0.6782394805856533, -0.49189842694430497, -0.29486864566027055, -0.10324394058294047, 0.06708952698173441, 0.2013856789556795, 0.286938390343116, 0.3138978880449354, 0.27595514084429695, 0.17085081530409643, 0.0006730890768033904, -0.22808136184362293, -0.5046969897269864, -0.8146801995778432, -1.140438106327469, -1.4621681964727689, -1.7589189516433397, -2.00977017963808, -2.195072790258577, -2.2976816563214935, -2.3041124894494995, -2.2055546445744345, -1.9986765639484856, -1.68616909067296, -1.276983820500831, -0.7862385102901238, -0.23477862637032113, 0.35159745581758906, 0.9432232656607904, 1.5079145436915526, 2.012524014303921, 2.4246257700774088, 2.714244146887885, 2.8555359892131333, 2.8283340229886518, 2.6194629299190697, 2.223748636800995, 1.6446549933906953, 0.8944998279585562, -0.005776503685132543, -1.027293588575615, -2.1343435785853773, -3.285889045622465, -4.437378801005579, -5.542795081122466, -6.556830389283217, -7.437082381683952, -8.146151220279378, -8.653526194771375, -8.937157193253958, -8.98462146002394, -8.793816339747787, -8.373133354030498, -7.741096687452818, -6.925478454933543, -5.96193232565142, -4.892214495341538, -3.7620849931695854, -2.6190014060381976, -1.5097300797735858, -0.4780058250012997, 0.4376303753586591, 1.2056952433748462, 1.8032244908048458, 2.216749883239784, 2.4427380783371047, 2.487468354619307, 2.3663591489394444, 2.1027858437502163, 1.726462510505091, 1.2714864452941153, 0.774164670707537, 0.2707547971579835, -0.2047421690799006, -0.622602735251399, -0.959092806964117, -1.1977671125858276, -1.3302786211601652, -1.3566513172831784, -1.2850037171534598, -1.130745505747086, -0.91530341505801, -0.6644627652456349, -0.40643596319806785, -0.16978702994343398, 0.018649317330573466, 0.1357150698515628, 0.16361256298035912, 0.09121144097206767, -0.08510901398619565, -0.3611392165628822, -0.7250623752249354, -1.1582068271781905, -1.6362772166474773, -2.1309814296790632, -2.6119429281294653, -3.0487681813388483, -3.4131277067865478, -3.680707651589833, -3.832897078070456, -3.858093689421415, -3.7525365254020264, -3.520606468581431, -3.1745720494240715, -2.7337965130193367, -2.2234597402903233, -1.6728827548641438, -1.1135707569158042, -0.5771108567897927, -0.09307142126469944, 0.31294966492219917, 0.6209906132069263, 0.8179879742445004, 0.8985467639070928, 0.8651648028514304, 0.7278967885314137, 0.503484122515079, 0.21401540492462187, -0.11478307298603649, -0.45550012688185565, -0.7810908062989377, -1.066873218443578, -1.292322018545865, -1.442524278914003, -1.5091883717438188, -1.4911298708555332, -1.3941979027877276, -1.2306479728780562, -1.0180098848072778, -0.777538735206074, -0.5323700571929996, -0.30552438603811005, -0.11791983010562108, 0.01344755566150203, 0.07700698621865597, 0.06767410542231392, -0.01262237758342023, -0.15500000057040858, -0.3442733599359015, -0.5601547228867275, -0.7789177626854649, -0.9753985894356627, -1.125178118592506, -1.2067712806851216], 'positive_zeros': ['2.35723789587639709201561126128095', '3.82431174700028423177915923582742', '4.27447883147947906189345472963236', '5.18071417885716455389129283630183', '6.47752045783961125306666720326578', '7.28657436058804258769550037318494', '7.68770928382644583689887366904666', '8.712802123389830418130725114452592', '9.499626245371266361180892271581263', '10.84399028364160447427385692992815'], 'prelabel': '2-936-104.51-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6834653259855179, 'root_angle': 0.75, 'root_number': '-0.70710678118654752440084436210459 + 0.70710678118654752440084436210459*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.35723789587639709201561126128', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.82431174700028423177915923583', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27447883147947906189345472963', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.46712485182449026, 'bad_primes': [2, 3, 13], 'central_character': '104.51', 'conductor': 936, 'conductor_radical': 78, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/936/1/o/c/883/3'], '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': '2-936-104.51-c0-0-5', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-936-104.51-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6834653259855179, 'root_angle': 0.375, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.35723789587639709201561126128', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2988154033588443293693062921794', 'Lhash_array': ['2988154033588443293693062921794'], 'label': '2-936-104.51-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/936/1/o/c/883/3'}