-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '998415028780452328907401307944', 'a10': [0, 0], 'a2': [0.8660254037844386, -0.5], 'a3': [0, 0], 'a4': [0.5, -0.8660254037844386], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-2.0544558908743307, 1.1861406616345072], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.779804272872857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1350.199', 'coefficient_field': 'CDF', 'conductor': 1350, 'conductor_radical': 30, 'conjugate': '1805845645110620618845326919936', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0544558908743307, -1.1861406616345072], [3.5, -6.06217782649107]], [[1.0, 0], [-0.6861406616345072, -1.1884304870898919], [-5.5, 9.526279441628825]], [[1.0, 0], [-4.108911781748661, -2.3722813232690143], [6.5, 11.258330249197702]], [[1.0, 0], [0, -7.372281323269014], [-17.0, 0]], [[1.0, 0], [3.3722813232690143, 0], [19.0, 0]], [[1.0, 0], [-3.786506698443208, -2.186140661634507], [11.5, 19.91858428704209]], [[1.0, 0], [-2.186140661634507, -3.786506698443208], [-14.5, 25.11473670974872]], [[1.0, 0], [-3.3722813232690143, 5.840962589317538], [-15.5, -26.846787517317598]], [[1.0, 0], [0, 4.0], [-37.0, 0]], [[1.0, 0], [1.5, -2.598076211353316], [-20.5, -35.50704155516198]], [[1.0, 0], [-9.848684524934278, 5.686140661634507], [21.5, -37.239092362730865]], [[1.0, 0], [-1.409645724263424, 0.8138593383654928], [23.5, -40.703193977868615]], [[1.0, 0], [0, -11.489125293076057], [-53.0, 0]], [[1.0, 0], [-0.6861406616345072, 1.1884304870898919], [-29.5, -51.09549882328188]], [[1.0, 0], [4.5584219849035215, 7.895418480191869], [-30.5, 52.827549630850754]], [[1.0, 0], [-6.06217782649107, -3.5], [33.5, 58.023702053557386]], [[1.0, 0], [-6.0, 0], [71.0, 0]], [[1.0, 0], [0, -14.116843969807043], [-73.0, 0]], [[1.0, 0], [-1.0, -1.7320508075688772], [-39.5, 68.41600689897065]], [[1.0, 0], [-1.409645724263424, 0.8138593383654928], [41.5, -71.88010851410841]], [[1.0, 0], [1.116843969807043, 0], [89.0, 0]], [[1.0, 0], [2.2756711280478625, -1.3138593383654928], [48.5, -84.00446416709055]], [[1.0, 0], [4.372281323269014, 7.573013396886416], [-50.5, 87.4685657822283]], [[1.0, 0], [13.856406460551018, 8.0], [51.5, 89.20061658979718]], [[1.0, 0], [0, -14.489125293076057], [-107.0, 0]], [[1.0, 0], [9.627718676730986, 0], [109.0, 0]], [[1.0, 0], [12.769165819593047, 7.372281323269014], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-1350-45.4-c1-0-4', 'leading_term': '2.167800765354534052603384660918016045064380824679552661', '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/1350/2/j/f/199/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.167800765354534, 2.088158267443813, 1.9989183258185523, 1.8993234490971447, 1.7884110001206337, 1.6650808011185212, 1.5281722224517738, 1.3765463461926417, 1.2091690642533146, 1.0251915489294572, 0.8240252442971624, 0.6054092181373452, 0.3694682878842817, 0.11676075079736083, -0.1516851847621661, -0.43434701765553174, -0.7291962873008997, -1.0337002231984709, -1.344837230833112, -1.6591266095092547, -1.9726727134652284, -2.2812235174273106, -2.580243232894809, -2.864998249150504, -3.130655255024872, -3.3723899489340763, -3.585504283265843, -3.765549734159551, -3.9084536595727646, -4.010645428166896, -4.069178689707875, -4.081845934198916, -4.047281370041101, -3.965048156944291, -3.8357061696877706, -3.6608567528139186, -3.4431613579437044, -3.186331533402039, -2.8950884532996377, -2.5750910172037726, -2.232832503028128, -1.875506789833475, -1.5108462533781315, -1.146934540152366, -0.7919985060122015, -0.45418462140021637, -0.14132605319653163, 0.1392926095218476, 0.3811654530617083, 0.5787822906047494, 0.727824721567847, 0.8253334599626672, 0.8698396983623186, 0.8614540817896217, 0.8019079680157924, 0.6945430272627681, 0.5442468523991555, 0.35733406536128537, 0.1413743602027114, -0.0950290486958244, -0.34250507780948364, -0.5912170841890348, -0.8311926119337566, -1.0526698195638684, -1.2464486234542265, -1.404233779026465, -1.5189567624863862, -1.5850634557755656, -1.5987553025083865, -1.5581727991384344, -1.463511897553534, -1.3170660838928632, -1.1231895018479423, -0.8881794234298827, -0.6200795328030726, -0.32840875938387626, -0.023823642657882647, 0.28227470662953386, 0.5781752074819585, 0.8523167959178574, 1.093755856132868, 1.292622063324628, 1.4405432776340752, 1.531020618102275, 1.5597361757021961, 1.5247779819223395, 1.426769782485058, 1.268896784872165, 1.056822727326187, 0.7984981970386723, 0.5038649200642111, 0.18446554846836052, -0.14702693724286914, -0.47734193119836643, -0.7931842147693927, -1.0818228049558722, -1.3316694917817973, -1.5328203770999271, -1.677534399309104, -1.7606247410414126, -1.779742139808805, -1.7355333654376164, -1.6316633449851525, -1.4746954033608937, -1.2738305960572431, -1.0405138511768306, -0.7879212972707808, -0.5303494053580149, -0.28253209534304363, -0.058916445986366896, 0.12706916357254658, 0.2637189802405821, 0.34169036653607926, 0.35454708880989283, 0.29917511786888, 0.17604577800568702, -0.010692334060986424, -0.253303453083437, -0.540738914820817, -0.8590886155778081, -1.192193537366501, -1.5223944956454436, -1.8313844380880295, -2.1011251206322723, -2.31478419971326, -2.457646025654956, -2.5179489304275893, -2.487603696047596, -2.36275217300078, -2.144131573043294, -1.8372185464018929, -1.4521374124072193, -1.0033283847534655, -0.5089837742522112, 0.009727639145738484, 0.5296162289896542, 1.02656485321299, 1.4767089438576833, 1.8576460549858889, 2.149613953051985, 2.3365757526045963, 2.4071532016268136, 2.355354991580421, 2.181055724860523, 1.8901925681845244, 1.4946601512388376, 1.011899298696402, 0.4641909685884993, -0.1223175000160815, -0.7188118909036573, -1.2951813070922893, -1.8214933573596843, -2.269501118852948, -2.6141047907017887, -2.8346910535096583, -2.9162773468964023, -2.8503964798857124, -2.6356688834265736, -2.2780248750372825, -1.79055681593543, -1.1930001265307055, -0.5108617971906758, 0.2257657659784518, 0.9836500473275525, 1.7280522331872614, 2.42446718863518, 3.040379743251732, 3.5469446175261434, 3.92049949381879, 4.143827902407834, 4.20710048502282, 4.108439273763421, 3.8540690907675397, 3.458042029333108, 2.941544054870573, 2.331815799008564, 1.6607413174344896, 0.9631776902689467, 0.275113728410405, -0.3682432387516939, -0.9343481833804533, -1.3950629483854258, -1.7281670344034579, -1.9185490252687336, -1.959010068176208, -1.8506319769266133, -1.602686688033031, -1.2320896231953737, -0.7624255262517463, -0.22260003635993542, 0.3548078315577202, 0.9353993299618787, 1.4849101973662095, 1.97115336289745, 2.365838015970405, 2.6461594917985, 2.796067295537325, 2.807137074442754, 2.6789954123783977, 2.4192726343001723, 2.0430868215586524, 1.5720902758297164, 1.0331360268562133, 0.45664503085731317, -0.12522699449091557, -0.6805117809857164, -1.1793228297865892, -1.5956064530962282, -1.9086428455557276, -2.1042058626415057, -2.1753113308145933, -2.1225093677476363, -1.9537047770606861, -1.68351932037691, -1.3322386832435746, -0.9244133853518685, -0.48720502536697147, -0.04858563598126577, 0.36449255307287276, 0.7278376665405968, 1.021555533445859, 1.231283518706536, 1.3490403662762331, 1.3736368383575308, 1.3106209893639966, 1.1717628857603064, 0.9741144408860669, 0.7387087249300855, 0.48898769829410665, 0.24906611283351549, 0.0419510051785712, -0.11216009628601623, -0.19738375526444174, -0.2033522407573473, -0.12602648337177919, 0.03193917103544867, 0.26130945742091727, 0.5468541571149927, 0.8683708166158378, 1.2020767199648994, 1.5222761335081882, 1.803188549600311, 2.020811044105861, 2.1546839165040237, 2.18943390269136, 2.1159832188964285, 1.9323346718498149, 1.6438716451926019, 1.2631450503763832, 0.809155055785976, 0.3061711133504335, -0.21783302206413188, -0.7330243155870305, -1.2097092643389569, -1.6203475588813616, -1.941438613733284, -2.1551459724524693], 'positive_zeros': ['0.78761058339001017855222096226771', '2.72389218972973398508018893383902', '3.43393777991605547843324304313299', '4.45766706599729517582395146045182', '5.36475147665900519603041146317206', '6.40387586715244915358248047648956', '6.79395900798750180674997856619836', '7.85047323132925501619313444751201', '8.659833865146007964321356301386242', '9.474531574113664049643315477302891'], 'prelabel': '2-1350-45.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2832612251955915, 'root_angle': -0.14809052189978697, 'root_number': '0.89371387547371404636713577231051428287406454083171019671 - 0.4486373912033578401547402718341184793415031408973553447*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07404526094989348', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78761058339001017855222096227', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72389218972973398508018893384', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43393777991605547843324304313', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.779804272872857, 'bad_primes': [2, 3, 5], 'central_character': '45.4', 'conductor': 1350, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1350/2/j/f/199/3'], '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': '2-1350-45.4-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': '2-1350-45.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2832612251955915, 'root_angle': -0.07404526094989348, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78761058339001017855222096227', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '998415028780452328907401307944', 'Lhash_array': ['998415028780452328907401307944'], 'label': '2-1350-45.4-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1350/2/j/f/199/3'}