-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '617881541343472177597788062818', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.4638997390619867, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.9826812356692147, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.7847970320982207, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.23676816885381, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '7168.1', 'coefficient_field': 'CDF', 'conductor': 7168, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.4638997390619867, 0], [3.0, 0]], [[1.0, 0], [1.9826812356692147, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.6280344090305748, 0], [11.0, 0]], [[1.0, 0], [3.1903312382626865, 0], [13.0, 0]], [[1.0, 0], [4.855777360719242, 0], [17.0, 0]], [[1.0, 0], [-0.1612259019166114, 0], [19.0, 0]], [[1.0, 0], [-3.2052927702373255, 0], [23.0, 0]], [[1.0, 0], [1.410099943144192, 0], [29.0, 0]], [[1.0, 0], [5.344350449588735, 0], [31.0, 0]], [[1.0, 0], [2.8775351882496736, 0], [37.0, 0]], [[1.0, 0], [9.576727783179322, 0], [41.0, 0]], [[1.0, 0], [-9.712223378997658, 0], [43.0, 0]], [[1.0, 0], [-9.70702779814131, 0], [47.0, 0]], [[1.0, 0], [-10.810620621263595, 0], [53.0, 0]], [[1.0, 0], [2.1250815497118443, 0], [59.0, 0]], [[1.0, 0], [2.4629455856185425, 0], [61.0, 0]], [[1.0, 0], [-12.678298179617292, 0], [67.0, 0]], [[1.0, 0], [-7.183561323344867, 0], [71.0, 0]], [[1.0, 0], [9.040293204699326, 0], [73.0, 0]], [[1.0, 0], [-9.588056621853465, 0], [79.0, 0]], [[1.0, 0], [7.49879968236243, 0], [83.0, 0]], [[1.0, 0], [2.499377795547838, 0], [89.0, 0]], [[1.0, 0], [-5.89073045899884, 0], [97.0, 0]], [[1.0, 0], [-9.90654549903558, 0], [101.0, 0]], [[1.0, 0], [8.108874385627395, 0], [103.0, 0]], [[1.0, 0], [3.173033583696115, 0], [107.0, 0]], [[1.0, 0], [0.42343399271416005, 0], [109.0, 0]], [[1.0, 0], [4.674322792015947, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-7168-1.1-c1-0-22', 'leading_term': '1.0548331873405815348183719037421', '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/7168/2/a/bf/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.0548331873405816, 1.0449674648166813, 1.0153640398756767, 0.9660101447508265, 0.8969041140977725, 0.8080834424843023, 0.6996614632605473, 0.5718703203213792, 0.4251075799070121, 0.2599836881915322, 0.07736750392660986, -0.12157270708650966, -0.3353351731800682, -0.5620594509568956, -0.7995118725070025, -1.0450829109685777, -1.2957973886203347, -1.5483380696960847, -1.7990827985582523, -2.044154962378328, -2.2794866757507335, -2.500893703769158, -2.7041607631690106, -2.885135473697133, -3.0398288816991643, -3.1645201547450683, -3.255862761111405, -3.310989213109383, -3.327611280782539, -3.304112484111201, -3.239629658134085, -3.1341204651545764, -2.9884139079307532, -2.8042411810993113, -2.5842445854245124, -2.3319627175579956, -2.051790729783081, -1.7489151187231466, -1.429223234378533, -1.0991884826153477, -0.765733003543653, -0.436070420463621, -0.11753204243994055, 0.18261936007094823, 0.45738343139546483, 0.7002184364942897, 0.9052340626353572, 1.067374830383206, 1.1825880539030487, 1.2479704115247128, 1.2618875124757725, 1.2240613777412084, 1.1356214880862003, 0.999115978825136, 0.8184806597179668, 0.5989647826946571, 0.34701383613711756, 0.07011107202323424, -0.223419074124163, -0.5246410803363722, -0.824266007381972, -1.112929568284801, -1.3814823790899444, -1.6212833520786376, -1.824486643456133, -1.9843123245687349, -2.095291035557122, -2.153473318965505, -2.156595122176235, -2.1041920927140714, -1.997656747177847, -1.8402343371587517, -1.6369552155074754, -1.3945036634632573, -1.1210254030352602, -0.8258783111448447, -0.5193330884011937, -0.21223272942225313, 0.08437849259734159, 0.3596442587173344, 0.6032902150223037, 0.8060085988937378, 0.9598190931287142, 1.058391825735381, 1.0973192834375123, 1.0743252953237339, 0.9894011417701224, 0.8448612033917868, 0.6453133153588514, 0.397542045044946, 0.11030636041584284, -0.20594351539487898, -0.5394219883034275, -0.8774255413955925, -1.2067977821770126, -1.5144257682858437, -1.7877494814131492, -2.0152651513854845, -2.1870026802755986, -2.294957728262384, -2.3334601181144072, -2.2994620819135143, -2.192732468212089, -2.015946274748415, -1.7746626655914788, -1.4771888395784627, -1.134331583854685, -0.7590428997032189, -0.36597054438286086, 0.029071494408068266, 0.4096938681227067, 0.7595622876207755, 1.0630434178103194, 1.3058407981245859, 1.4755949685244927, 1.5624226606168892, 1.5593716536313051, 1.4627706593480703, 1.27245730766438, 0.9918718311686109, 0.6280092291763752, 0.1912283314869338, -0.30507794474364686, -0.8449409874946435, -1.4103877695203368, -1.982104155443281, -2.5401650205818633, -3.064802561066831, -3.537181896704887, -3.940152048399144, -4.258940691654512, -4.481762771413072, -4.600316076471092, -4.610141119483735, -4.510827998888289, -4.306059127050411, -4.003483544362551, -3.614425716224603, -3.1534389194333934, -2.6377202466857614, -2.0864105766291448, -1.5198082744624763, -0.9585296392980701, -0.4226519798219484, 0.06912348310635634, 0.5002520153339276, 0.857034192523367, 1.1291818788644157, 1.3102351868472015, 1.397810622188796, 1.3936680154986796, 1.3035919387546402, 1.1370917395781204, 0.9069327142403368, 0.6285188885645164, 0.31915500276646797, -0.002778750323766646, -0.3187012092900259, -0.6107131716028402, -0.8624471175188407, -1.0598431808306066, -1.191813866983809, -1.2507649145517088, -1.2329462380735867, -1.1386147956657788, -0.9720001376999027, -0.7410729000421246, -0.45712615515308297, -0.13418885768155836, 0.2117008457811069, 0.5633273659562191, 0.9031937060863097, 1.2144372389410538, 1.481719061401895, 1.692041417524665, 1.835450624883474, 1.9055880712829127, 1.9000589573271096, 1.8205972285793843, 1.6730151621518201, 1.4669368670854097, 1.2153259963235072, 0.9338286964544134, 0.6399626887071075, 0.35219186099945843, 0.0889323945408637, -0.1324591287436037, -0.2966632635163648, -0.3912892273816229, -0.4076321466693326, -0.3412536893451608, -0.19235199160433772, 0.03410304870225699, 0.32848142598004954, 0.6768514507217728, 1.0615720207810222, 1.462093471768696, 1.8559304383276511, 2.2197605110073235, 2.530595014030994, 2.766963390308817, 2.9100507676816396, 2.9447294549170264, 2.860429380243373, 2.6517996807486774, 2.3191234626956403, 1.8684597219909604, 1.3114999592473584, 0.6651414688204974, -0.049206111622503095, -0.8065503961695081, -1.5794387311379334, -2.3392196702392956, -3.05738155041779, -3.7069013671844373, -4.263535650253484, -4.706987089595025, -5.021886211003266, -5.198536214233549, -5.233380752692398, -5.1291683788800535, -4.894802899485228, -4.54488517663963, -4.09896812031771, -3.5805618739165554, -3.0159396698178327, -2.4328057755047046, -1.8588947391770423, -1.3205753129318576, -0.841532706380109, -0.4415991362074414, -0.13579513448940006, 0.06636688212628651, 0.16127914697515994, 0.1513135992691717, 0.04457126737424648, -0.14568042785558513, -0.4018516456430325, -0.7031088899179379, -1.026628819876114, -1.3489572805664025, -1.6473974299597993, -1.9013487212965503, -2.093520732383089, -2.2109523467857524, -2.245777274634633, -2.1956908147719494, -2.0640893661836195, -1.859872593442688, -1.5969173223350934, -1.2932511131983324, -0.9699709571240106, -0.6499676523700368, -0.35652825385374226, -0.11189682931556974, 0.0641228996407622, 0.15544085722625522], 'positive_zeros': ['0.48742259202356549284501420870304', '1.98670504150592735051562646436380', '2.68326246471493526524255283804536', '3.64264255039320559140250925298425', '4.23550650846150285484604985982412', '5.10589067097643671290163786634080', '5.69053029055361737752615291632001', '6.74308292788050668664109081729854', '7.31209551393970175243533504621913', '7.893429383939765044061060653296121'], 'prelabel': '2-7168-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.565498540668275, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48742259202356549284501420870', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98670504150592735051562646436', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68326246471493526524255283805', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 57.23676816885381, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 7168, 'conductor_radical': 14, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7168/2/a/bf/1/5'], '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': '2-7168-1.1-c1-0-22', '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': '2-7168-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.565498540668275, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48742259202356549284501420870', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '617881541343472177597788062818', 'Lhash_array': ['617881541343472177597788062818'], 'label': '2-7168-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7168/2/a/bf/1/5'}