Properties

Level $23$
Weight $0$
Character 23.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.53213432953 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.282253345\) \(a_{3}=-0.470373482\) \(a_{4}=+0.644173640\) \(a_{5}=+1.274550086\)
\(a_{6}=-0.603137971\) \(a_{7}=+0.579030266\) \(a_{8}=-0.456259540\) \(a_{9}=-0.778748787\) \(a_{10}=+1.634296110\)
\(a_{11}=+0.160252620\) \(a_{12}=-0.303002198\) \(a_{13}=+0.383231604\) \(a_{14}=+0.742463495\) \(a_{15}=-0.599514562\)
\(a_{16}=-1.229213961\) \(a_{17}=-1.260329305\) \(a_{18}=-0.998553237\) \(a_{19}=+1.294552420\) \(a_{20}=+0.821031569\)
\(a_{21}=-0.272360482\) \(a_{22}=+0.205484458\) \(a_{23}=-0.208514414\) \(a_{24}=+0.214612388\) \(a_{25}=+0.624477921\)
\(a_{26}=+0.491400006\) \(a_{27}=+0.836676261\) \(a_{28}=+0.372996034\) \(a_{29}=+1.699289568\) \(a_{30}=-0.768729552\)
\(a_{31}=-0.960633957\) \(a_{32}=-1.119904175\) \(a_{33}=-0.075378583\) \(a_{34}=-1.616061466\) \(a_{35}=+0.738003077\)
\(a_{36}=-0.501649443\) \(a_{37}=-1.608850530\) \(a_{38}=+1.659944170\) \(a_{39}=-0.180261980\) \(a_{40}=-0.581525631\)
\(a_{41}=-0.050345576\) \(a_{42}=-0.349235146\) \(a_{43}=+1.871112690\) \(a_{44}=+0.103230523\) \(a_{45}=-0.992554325\)
\(a_{46}=-0.267368304\) \(a_{47}=+0.559222705\) \(a_{48}=+0.578189652\) \(a_{49}=-0.664723955\) \(a_{50}=+0.800738900\)
\(a_{51}=+0.592825482\) \(a_{52}=+0.246867706\) \(a_{53}=-0.388682391\) \(a_{54}=+1.072830941\) \(a_{55}=+0.204249972\)
\(a_{56}=-0.264188107\) \(a_{57}=-0.608923156\) \(a_{58}=+2.178919736\) \(a_{59}=-0.779806792\) \(a_{60}=-0.386191558\)
\(a_{61}=-1.461858249\) \(a_{62}=-1.231776190\) \(a_{63}=-0.450918847\) \(a_{64}=-0.206786816\) \(a_{65}=+0.488447529\)
\(a_{66}=-0.096654421\) \(a_{67}=+0.881426222\) \(a_{68}=-0.811870886\) \(a_{69}=+0.098079618\) \(a_{70}=+0.946306848\)
\(a_{71}=+0.669080329\) \(a_{72}=+0.355311780\) \(a_{73}=+0.278225030\) \(a_{74}=-2.062953983\) \(a_{75}=-0.293737813\)
\(a_{76}=+0.833916611\) \(a_{77}=+0.092791040\) \(a_{78}=-0.231141567\) \(a_{79}=+0.349015883\) \(a_{80}=-1.566694602\)
\(a_{81}=+0.385198638\) \(a_{82}=-0.064555830\) \(a_{83}=+0.701889415\) \(a_{84}=-0.175447464\) \(a_{85}=-1.606352766\)
\(a_{86}=+2.399240516\) \(a_{87}=-0.799300809\) \(a_{88}=-0.073116883\) \(a_{89}=+0.315423049\) \(a_{90}=-1.272706081\)
\(a_{91}=+0.221902747\) \(a_{92}=-0.134319508\) \(a_{93}=+0.451856691\) \(a_{94}=+0.717065286\) \(a_{95}=+1.649971850\)
\(a_{96}=+0.526773237\) \(a_{97}=+0.090980643\) \(a_{98}=-0.852344498\) \(a_{99}=-0.124796520\) \(a_{100}=+0.402272223\)

Showing 100 of 1500 available coefficients

Rows: Cols: