-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '653143949867826150888156215015', 'a10': [-8.28031110793811, 0.0], 'a2': [-1.656062221587622, 0.0], 'a3': [0.0, 0.0], 'a4': [-5.25745791823027, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [21.95517521266883, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 130.09921156265813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.1', 'coefficient_field': 'CDF', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.656062221587622, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [69.5726314282672, 0], [1331.0, 0]], [[1.0, 0], [-68.43255189786457, 0], [2197.0, 0]], [[1.0, 0], [104.33170863410339, 0], [4913.0, 0]], [[1.0, 0], [-71.8929199321159, 0], [6859.0, 0]], [[1.0, 0], [-101.03074329643482, 0], [12167.0, 0]], [[1.0, 0], [-114.66059030988254, 0], [24389.0, 0]], [[1.0, 0], [73.65046846691337, 0], [29791.0, 0]], [[1.0, 0], [200.93319207704252, 0], [50653.0, 0]], [[1.0, 0], [417.3075241330229, 0], [68921.0, 0]], [[1.0, 0], [-311.1746058921476, 0], [79507.0, 0]], [[1.0, 0], [149.69708083327657, 0], [103823.0, 0]], [[1.0, 0], [271.47434728885634, 0], [148877.0, 0]], [[1.0, 0], [-518.0280200336289, 0], [205379.0, 0]], [[1.0, 0], [219.9255091795125, 0], [226981.0, 0]], [[1.0, 0], [-80.6949525022529, 0], [300763.0, 0]], [[1.0, 0], [-91.04630720409193, 0], [357911.0, 0]], [[1.0, 0], [-882.2816031482689, 0], [389017.0, 0]], [[1.0, 0], [-599.8772897717272, 0], [493039.0, 0]], [[1.0, 0], [70.88204650106482, 0], [571787.0, 0]], [[1.0, 0], [802.5917679281117, 0], [704969.0, 0]], [[1.0, 0], [-145.6477201431776, 0], [912673.0, 0]], [[1.0, 0], [-619.435280028005, 0], [1030301.0, 0]], [[1.0, 0], [1822.0792883842473, 0], [1092727.0, 0]], [[1.0, 0], [1089.7012058232822, 0], [1225043.0, 0]], [[1.0, 0], [-589.6666998323772, 0], [1295029.0, 0]], [[1.0, 0], [-900.3575521072008, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-2205-1.1-c3-0-31', 'leading_term': '1.02717357939556477207870555957', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2205/4/a/ca/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.0271735793955648, 1.015636963297707, 0.9812160567977259, 0.9244761033216752, 0.8463538573850086, 0.7481494546964623, 0.6315147357262092, 0.4984377547655823, 0.35122316660261965, 0.19246816825055016, 0.02503368691050717, -0.14798945050454626, -0.3233195557628825, -0.4975284095580429, -0.6670908336670208, -0.8284392961672837, -0.9780231613227551, -1.1123720010498768, -1.2281621813269716, -1.3222857315181382, -1.3919203048517084, -1.434598852026463, -1.448277465007298, -1.431399712274246, -1.382955687503863, -1.3025339376985978, -1.1903644301232104, -1.047350764989674, -0.8750899463099975, -0.6758781888841237, -0.4527014655131698, -0.20920978390855224, 0.05032547585446502, 0.3210714403859607, 0.5977106800494105, 0.8745345758898095, 1.1455519955987927, 1.40461165488447, 1.6455360419403484, 1.8622643035633089, 2.049001047969484, 2.200367627883357, 2.3115521441815585, 2.3784541706380575, 2.397820058183847, 2.367364644696484, 2.2858752833419453, 2.1532943155825026, 1.9707764573594448, 1.7407180380248444, 1.466755626548423, 1.1537322892480375, 0.8076305342883252, 0.43547189267888203, 0.04518404166311789, -0.35456263122249526, -0.7545461250250417, -1.145207707799337, -1.51688578764684, -1.8600631421836598, -2.1656211635749685, -2.4250942147664225, -2.6309168099520264, -2.7766561523895676, -2.857222604063694, -2.869050936966521, -2.810245730531454, -2.680685032009218, -2.482077376228528, -2.217968449869792, -1.893695056528286, -1.5162855580555705, -1.094307593398916, -0.6376655606975786, -0.15735203913612866, 0.3348410319705014, 0.8266440657554313, 1.3056557119076204, 1.7597030426380489, 2.177205291224532, 2.5475298280915966, 2.8613288429044523, 3.1108453591612966, 3.2901777537021006, 3.3954928879449504, 3.4251792673661816, 3.3799333036319883, 3.262773718959533, 3.0789813507668145, 2.835964020684033, 2.543048649718649, 2.2112053471589346, 1.852710685888575, 1.4807597102501293, 1.1090383146344815, 0.7512693962893693, 0.4207475470479003, 0.12987793959551883, -0.11026456741873707, -0.2903402697053026, -0.4030983292220269, -0.4436656142995734, -0.409758797946205, -0.3018102128955291, -0.12300075794966173, 0.12080371342503836, 0.4212127179252111, 0.7675648827306419, 1.1472683156310166, 1.5462174683537142, 1.9492732734232798, 2.34079064562519, 2.7051752594405145, 3.027449944239586, 3.293810160387964, 3.492147888778152, 3.6125239137103007, 3.6475699052735866, 3.592803882702314, 3.446845504351237, 3.2115210933961458, 2.8918522547033554, 2.4959262279050605, 2.034650596494513, 1.5213994618990798, 0.9715625179036679, 0.40201244808920095, -0.16949045133250382, -0.7249347020878275, -1.2467113800437082, -1.718260278132496, -2.124683451148822, -2.453301929138329, -2.694133207409265, -2.8402698833785007, -2.888143424221288, -2.8376613873404173, -2.6922113168533084, -2.4585298143289616, -2.1464407206106797, -1.768471724756667, -1.3393638093747857, -0.8754925284131573, -0.3942239889958298, 0.08676860661435257, 0.5502000556044312, 0.9798512777570999, 1.3612022556619923, 1.6819931861627941, 1.9326900075726554, 2.10683430580686, 2.201262363801886, 2.2161836126268146, 2.155114742828328, 2.02467198622579, 1.8342303098186552, 1.5954641974411752, 1.3217900609288842, 1.0277348697639428, 0.7282590965569191, 0.4380643674601972, 0.17091715514012287, -0.06098061084318431, -0.24754502046758622, -0.3812619860328389, -0.4575160784294851, -0.47478062004228333, -0.4346595851667327, -0.3417787183609665, -0.20353036142386838, -0.02968345221472664, 0.1681233075011727, 0.3769813401511075, 0.5833766285622746, 0.7738867504513914, 0.9358765999757317, 1.0581585275791279, 1.131583924740989, 1.1495361991235495, 1.108299519490717, 1.0072834741797543, 0.8490906283938044, 0.639421572213697, 0.3868200662415089, 0.10226892984549561, -0.2013450177305513, -0.5098717477210222, -0.8086135416101221, -1.083079883662784, -1.3197436962874312, -1.5067600687589577, -1.6346097485342719, -1.696632711414926, -1.6894219956788372, -1.6130544756627532, -1.4711430753248258, -1.2707037207687197, -1.0218396828581477, -0.7372554082164237, -0.43162100343046467, -0.12081675400750398, 0.17890601223903257, 0.45180615361142706, 0.6835312020370566, 0.8619472120120952, 0.9778753254321761, 1.0256939743277276, 1.0037714072296462, 0.9147009504454622, 0.7653207623464715, 0.5665103743576319, 0.3327675317766059, 0.08158019721407198, -0.1673805160259602, -0.3932108222315968, -0.5748241491874904, -0.6920500947996262, -0.7267281745346171, -0.6637407914917868, -0.49193136344647664, -0.2048578312681449, 0.19866129543928215, 0.7142419122050047, 1.331892640049954, 2.036246171234905, 2.807059863070896, 3.6199682052527358, 4.4474567390949336, 5.260015190051241, 6.0274176212918675, 6.720069878568568, 7.310359916474472, 7.773945077874316, 8.090912189948286, 8.24675142249597, 8.233093036731933, 8.04816708077472, 7.696959256189665, 7.191050955789695, 6.548147126768804, 5.79131135432502, 4.947942577342229, 4.048541348654255, 3.1253248102546136, 2.210757943702822, 1.3360736910483575, 0.5298559015979882, -0.18324338839896662, -0.7835870277627379, -1.2573805303691472, -1.5972016188447924, -1.802203694327364, -1.877982149035441, -1.8361099801728828, -1.6933665755164053, -1.4706998965781277, -1.191976698694042], 'positive_zeros': ['0.51523972753236049132633325599431', '1.61535225736761742405203726089238', '2.74796657112291585281408525452675', '3.77412055282495582050677978419580', '4.95177163639709088807736015613462', '5.30845347243766107706461890862465', '6.43408156581506374296800911241995', '7.30325371393633714733505691215570', '8.212291563958438094038602850228247', '8.640757468656464497898828162807249'], 'prelabel': '2-2205-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51523972753236049132633325599', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61535225736761742405203726089', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74796657112291585281408525453', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 130.09921156265813, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2205/4/a/ca/1/2'], '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': '2-2205-1.1-c3-0-31', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-2205-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51523972753236049132633325599', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '653143949867826150888156215015', 'Lhash_array': ['653143949867826150888156215015'], 'label': '2-2205-1.1-c3-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2205/4/a/ca/1/2'}