Properties

Level $33$
Weight $0$
Character 33.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.59599133119 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.398420867\) \(a_{3}=-0.577350269\) \(a_{4}=+0.955580922\) \(a_{5}=+0.651813330\)
\(a_{6}=-0.807378664\) \(a_{7}=-1.286745609\) \(a_{8}=-0.062116566\) \(a_{9}=+0.333333333\) \(a_{10}=+0.911509361\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.551704902\) \(a_{13}=+1.836055427\) \(a_{14}=-1.799411910\) \(a_{15}=-0.376324602\)
\(a_{16}=-1.042446023\) \(a_{17}=+0.460148575\) \(a_{18}=+0.466140289\) \(a_{19}=-0.294630551\) \(a_{20}=+0.622860383\)
\(a_{21}=+0.742902924\) \(a_{22}=+0.421639756\) \(a_{23}=+0.107379092\) \(a_{24}=+0.035863016\) \(a_{25}=-0.575139383\)
\(a_{26}=+2.567578222\) \(a_{27}=-0.192450090\) \(a_{28}=-1.229589556\) \(a_{29}=+0.597684877\) \(a_{30}=-0.526260175\)
\(a_{31}=-1.151417855\) \(a_{32}=-1.395661706\) \(a_{33}=-0.174077657\) \(a_{34}=+0.643481367\) \(a_{35}=-0.838717941\)
\(a_{36}=+0.318526975\) \(a_{37}=-0.821769107\) \(a_{38}=-0.412017508\) \(a_{39}=-1.060047098\) \(a_{40}=-0.040488411\)
\(a_{41}=-0.104047823\) \(a_{42}=+1.038890951\) \(a_{43}=+1.378238059\) \(a_{44}=+0.288118491\) \(a_{45}=+0.217271103\)
\(a_{46}=+0.150161158\) \(a_{47}=+0.933971715\) \(a_{48}=+0.601856518\) \(a_{49}=+0.655714244\) \(a_{50}=-0.804286900\)
\(a_{51}=-0.265666903\) \(a_{52}=+1.754499495\) \(a_{53}=-1.120376867\) \(a_{54}=-0.269126268\) \(a_{55}=+0.196529112\)
\(a_{56}=+0.079928214\) \(a_{57}=+0.170105010\) \(a_{58}=+0.835815017\) \(a_{59}=+0.864435607\) \(a_{60}=-0.359608592\)
\(a_{61}=-0.819986022\) \(a_{62}=-1.610166758\) \(a_{63}=-0.428915193\) \(a_{64}=-0.909276748\) \(a_{65}=+1.196765324\)
\(a_{66}=-0.243433826\) \(a_{67}=-0.414284155\) \(a_{68}=+0.439709203\) \(a_{69}=-0.061995407\) \(a_{70}=-1.172880948\)
\(a_{71}=-0.043636683\) \(a_{72}=-0.020705523\) \(a_{73}=+1.205948035\) \(a_{74}=-1.149179061\) \(a_{75}=+0.332056868\)
\(a_{76}=-0.281543322\) \(a_{77}=-0.387968393\) \(a_{78}=-1.482391981\) \(a_{79}=+0.272853954\) \(a_{80}=-0.679480242\)
\(a_{81}=+0.111111113\) \(a_{82}=-0.145502635\) \(a_{83}=+1.703760110\) \(a_{84}=+0.709903861\) \(a_{85}=+0.299930970\)
\(a_{86}=+1.927356850\) \(a_{87}=-0.345073523\) \(a_{88}=-0.018728843\) \(a_{89}=+0.123743031\) \(a_{90}=+0.303836476\)
\(a_{91}=-2.362536263\) \(a_{92}=+0.102609463\) \(a_{93}=+0.664771408\) \(a_{94}=+1.306085544\) \(a_{95}=-0.192044125\)
\(a_{96}=+0.805785643\) \(a_{97}=+0.082489604\) \(a_{98}=+0.916964499\) \(a_{99}=+0.100503755\) \(a_{100}=-0.549592186\)

Showing 100 of 2000 available coefficients

Rows: Cols: