-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1422527934181961218892995278232', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.3027756377319946, -1.3027756377319946], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [1.3027756377319946, -1.3027756377319946], 'a8': [0, 0], 'a9': [0, 0.3944487245360107], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.574568343617672, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-3.605551275463989, -2.0]]]], 'bad_primes': [2, 5, 17], 'central_character': '1700.1101', 'coefficient_field': 'CDF', 'conductor': 1700, 'conductor_radical': 170, 'conjugate': '1233153592141036597300899119462', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.3027756377319946, 1.3027756377319946], [0, 3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3027756377319946, 1.3027756377319946], [0, -7.0]], [[1.0, 0], [-3.302775637731995, 3.302775637731995], [0, -11.0]], [[1.0, 0], [-4.60555127546399, 0], [13.0, 0]], [[1.0, 0], [-3.605551275463989, -2.0]], [[1.0, 0], [0, -6.60555127546399], [-19.0, 0]], [[1.0, 0], [-0.6972243622680053, 0.6972243622680053], [0, -23.0]], [[1.0, 0], [-5.60555127546399, -5.60555127546399], [0, 29.0]], [[1.0, 0], [-0.6972243622680053, -0.6972243622680053], [0, 31.0]], [[1.0, 0], [3.0, 3.0], [0, 37.0]], [[1.0, 0], [-1.0, 1.0], [0, -41.0]], [[1.0, 0], [0, 10.60555127546399], [-43.0, 0]], [[1.0, 0], [-4.0, 0], [47.0, 0]], [[1.0, 0], [0, -9.21110255092798], [-53.0, 0]], [[1.0, 0], [0, -1.3944487245360107], [-59.0, 0]], [[1.0, 0], [-8.21110255092798, 8.21110255092798], [0, -61.0]], [[1.0, 0], [-5.211102550927978, 0], [67.0, 0]], [[1.0, 0], [7.908326913195984, 7.908326913195984], [0, 71.0]], [[1.0, 0], [-7.0, -7.0], [0, 73.0]], [[1.0, 0], [-3.302775637731995, 3.302775637731995], [0, -79.0]], [[1.0, 0], [0, 3.816653826391968], [-83.0, 0]], [[1.0, 0], [13.816653826391969, 0], [89.0, 0]], [[1.0, 0], [-0.3944487245360107, -0.3944487245360107], [0, 97.0]], [[1.0, 0], [-3.394448724536011, 0], [101.0, 0]], [[1.0, 0], [1.2111025509279787, 0], [103.0, 0]], [[1.0, 0], [9.302775637731994, 9.302775637731994], [0, 107.0]], [[1.0, 0], [-8.21110255092798, 8.21110255092798], [0, -109.0]], [[1.0, 0], [2.394448724536011, -2.394448724536011], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-1700-17.13-c1-0-13', 'leading_term': '1.659694507771055901968578816892208198518256740083760636', '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/1700/2/o/c/1101/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.6596945077710559, 1.7068339452850148, 1.7455768031294585, 1.7751838867065912, 1.794688535824174, 1.802910749820933, 1.798489472983042, 1.7799308009924681, 1.745669168615214, 1.6941382660600028, 1.6238484246777023, 1.533467395682702, 1.4219017060006753, 1.288376029388855, 1.132508212145161, 0.954377728522442, 0.7545854234265903, 0.5343024550302179, 0.2953064084884933, 0.04000264372403723, -0.22857090981186093, -0.5067570719410421, -0.7903120900253052, -1.0744585152565531, -1.3539586172944582, -1.62320809620674, -1.8763491993396135, -2.107401647523702, -2.310409042275852, -2.479597689410632, -2.609544063622912, -2.6953464840091996, -2.7327960039450576, -2.718541071753491, -2.6502402211583473, -2.5266969296734416, -2.347970861575314, -2.115460007005552, -1.831948750144605, -1.5016176493008866, -1.1300116831819982, -0.7239648939658256, -0.2914807125966748, 0.15843125122639062, 0.615959578036815, 1.0707325531284635, 1.5120911931349315, 1.929386613241207, 2.312293175360917, 2.651127686444271, 2.9371640263420487, 3.162932034609726, 3.3224893244382856, 3.411654956637719, 3.4281946196562325, 3.37194812841128, 3.24489166199987, 3.051129175240527, 2.7968097886896675, 2.4899706142597546, 2.1403073191965922, 1.7588776651828086, 1.3577461652629594, 0.94958075521827, 0.5472148515232025, 0.1631902415982092, -0.19070219105458328, -0.5038659643346117, -0.7673085322867789, -0.9739991807343836, -1.1191588934041405, -1.2004678532830995, -1.2181790254281248, -1.1751296969282952, -1.076646814424193, -0.9303463151171694, -0.7458312220467417, -0.5342978760862128, -0.30806409971347265, -0.08003712062356509, 0.1368574789014821, 0.3302618688083654, 0.4889615152858409, 0.6034239242209345, 0.666274897659236, 0.6726883761500303, 0.6206688901117473, 0.5112097098556704, 0.348314834377663, 0.13887880646896805, -0.10757524985112796, -0.3792922804711499, -0.6628028796512272, -0.9435417050381264, -1.2065409741961743, -1.4371685964739078, -1.6218770528370139, -1.7489271753351514, -1.8090506666645505, -1.7960166356882192, -1.707070621986295, -1.5432194697643846, -1.3093418288167542, -1.0141117628863994, -0.6697316117535785, -0.29147949592739014, 0.1029137634553462, 0.494034476227174, 0.8616705660920853, 1.1857715849468133, 1.4474397779789954, 1.6299043637144117, 1.71943010380706, 1.7061125697507453, 1.5845163061870908, 1.35411825602289, 1.0195271370960777, 0.5904596077081364, 0.08146558300676562, -0.4885925717081748, -1.097289646379143, -1.719586477170084, -2.3289374806140644, -2.898506740247055, -3.4024353466299337, -3.817098186394316, -4.122286912522407, -4.302257596914534, -4.34658659292235, -4.250786272143368, -4.016643226045456, -3.652254756305539, -3.1717543928982566, -2.5947330365831367, -1.945378304954113, -1.2513699147577704, -0.5425826132256735, 0.1503405104379892, 0.7974732314358273, 1.3710741301002949, 1.8469607531910548, 2.2057168585333624, 2.4336670218680583, 2.5235640463918707, 2.474949010269923, 2.294160706241458, 1.9939897977820489, 1.5929922463340396, 1.1144953954181278, 0.5853474632637554, 0.034476081910738456, -0.508666973706954, -1.0156903311927348, -1.4607895433254634, -1.822130422657333, -2.083011036364111, -2.2327358085406974, -2.2671507904229675, -2.18880796632366, -2.0067474357698587, -1.7359082684490759, -1.3962004986575103, -1.0112908263048757, -0.6071719006663913, -0.2105984967793809, 0.15251742510538793, 0.4586574718508086, 0.6881004303048388, 0.8260937785379713, 0.8637213803152946, 0.7984134458510768, 0.6340661892131052, 0.3807622659610983, 0.05410761969099959, -0.32577569850698607, -0.735539346171812, -1.1501014309604973, -1.5442488708904334, -1.8942481376107927, -2.179361494975639, -2.3831706976453537, -2.494621291767161, -2.5087175761649574, -2.426819972490025, -2.256521723105553, -2.0111089390174097, -1.7086353487461912, -1.370668889106584, -1.020789823846222, -0.6829378383451425, -0.37971727359734053, -0.13077442867669065, 0.048641792796676735, 0.14883468711154782, 0.16644579886974, 0.10481097574112071, -0.026147241018878442, -0.2104941081330569, -0.4272958799291948, -0.6520132703205744, -0.8581896188348882, -1.0193261318938889, -1.1108211401153358, -1.11184272100064, -1.007004993251512, -0.7877280529977552, -0.4531794761580478, -0.010720573615191024, 0.5241883385599104, 1.128634426500229, 1.7734247361551374, 2.4247227830745963, 3.046054912553247, 3.6005647401194927, 4.053374113142853, 4.3738980821344775, 4.537960293784773, 4.529564336940047, 4.342195530756471, 3.9795554141673923, 3.4556661325933216, 2.7943218542000263, 2.0279067279271312, 1.1956409377427708, 0.3413552888183341, -0.48907219320755496, -1.2504592999397521, -1.9010691129732455, -2.405189076788634, -2.735370891061388, -2.8741818683179314, -2.8153481091084793, -2.5642080193108128, -2.1374389080015925, -1.5620667768711594, -0.8738167916529553, -0.1149061031611223, 0.6685813864906932, 1.4295697087424726, 2.122928375070146, 2.708280610840034, 3.152497463579675, 3.4317129393801094, 3.5327266746939734, 3.45370136501529, 3.204109541102611, 2.8039351008420024, 2.282185780124132, 1.6748199464308893, 1.022231397731831, 0.36646636516793574, -0.2516345748814645, -0.7951718773561253, -1.2336106723846574, -1.5447257970069976, -1.7159353633062435, -1.7449335842045257], 'positive_zeros': ['1.12217667386095782879300318618979', '2.49907798547975550027079614350543', '3.83488582149423904868943609473118', '4.65000244337550002582243752667274', '5.24876597888192165262978354850952', '6.19572078961390732759374260849624', '6.92278125804756830008080907406019', '8.014384107565596967850484925383037', '8.792724614166375605365065482033951', '9.642439298652235447914068290437074'], 'prelabel': '2-1700-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6843681064217337, 'root_angle': 0.18610838580732858, 'root_number': '0.3907468907784806992120656210381598495438634041448671213 + 0.9204981625983563445462139348098051203082158882740702369*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.18610838580732858', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12217667386095782879300318619', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49907798547975550027079614351', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83488582149423904868943609473', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.574568343617672, 'bad_primes': [2, 5, 17], 'central_character': '17.13', 'conductor': 1700, 'conductor_radical': 170, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1700/2/o/c/1101/1'], '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': '2-1700-17.13-c1-0-13', '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': '2-1700-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6843681064217337, 'root_angle': 0.18610838580732858, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12217667386095782879300318619', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1422527934181961218892995278232', 'Lhash_array': ['1422527934181961218892995278232'], 'factors': ['2-1700-17.13-c1-0-13'], 'label': '2-1700-17.13-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1700/2/o/c/1101/1'}