Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 29.6543135506 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.635393060\) \(a_{3}=-0.577350269\) \(a_{4}=-0.596275659\) \(a_{5}=+1.000534329\)
\(a_{6}=+0.366844354\) \(a_{7}=+0.232347071\) \(a_{8}=+1.014262476\) \(a_{9}=+0.333333333\) \(a_{10}=-0.635732569\)
\(a_{11}=+1.399056571\) \(a_{12}=+0.344259912\) \(a_{13}=+0.971573859\) \(a_{14}=-0.147631716\) \(a_{15}=-0.577658764\)
\(a_{16}=-0.048179679\) \(a_{17}=+0.777924136\) \(a_{18}=-0.211797687\) \(a_{19}=-1.176029060\) \(a_{20}=-0.596594266\)
\(a_{21}=-0.134145644\) \(a_{22}=-0.888950836\) \(a_{23}=+1.651463670\) \(a_{24}=-0.585584713\) \(a_{25}=+0.001068944\)
\(a_{26}=-0.617331287\) \(a_{27}=-0.192450090\) \(a_{28}=-0.138542903\) \(a_{29}=+0.096574733\) \(a_{30}=+0.367040370\)
\(a_{31}=-0.530534171\) \(a_{32}=-0.983649442\) \(a_{33}=-0.807745688\) \(a_{34}=-0.494287597\) \(a_{35}=+0.232471221\)
\(a_{36}=-0.198758553\) \(a_{37}=-0.825028321\) \(a_{38}=+0.747240704\) \(a_{39}=-0.560938429\) \(a_{40}=+1.014804426\)
\(a_{41}=+1.450501359\) \(a_{42}=+0.085235211\) \(a_{43}=-0.988218823\) \(a_{44}=-0.834223379\) \(a_{45}=+0.333511443\)
\(a_{46}=-1.049328555\) \(a_{47}=+0.186293018\) \(a_{48}=+0.027816551\) \(a_{49}=-0.946014839\) \(a_{50}=-0.000679199\)
\(a_{51}=-0.449134709\) \(a_{52}=-0.579325843\) \(a_{53}=+0.249750368\) \(a_{54}=+0.122281451\) \(a_{55}=+1.399804127\)
\(a_{56}=+0.235660916\) \(a_{57}=+0.678980695\) \(a_{58}=-0.061362915\) \(a_{59}=+1.298419647\) \(a_{60}=+0.344443860\)
\(a_{61}=+0.650161418\) \(a_{62}=+0.337097730\) \(a_{63}=+0.077449024\) \(a_{64}=+0.673183708\) \(a_{65}=+0.972092999\)
\(a_{66}=+0.513236004\) \(a_{67}=+1.920280361\) \(a_{68}=-0.463857227\) \(a_{69}=-0.953472994\) \(a_{70}=-0.147710600\)
\(a_{71}=+1.730114932\) \(a_{72}=+0.338087492\) \(a_{73}=-1.186460419\) \(a_{74}=+0.524217270\) \(a_{75}=-0.000617155\)
\(a_{76}=+0.701237503\) \(a_{77}=+0.325066696\) \(a_{78}=+0.356416385\) \(a_{79}=+0.307738036\) \(a_{80}=-0.048205423\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.921638497\) \(a_{83}=-1.133845692\) \(a_{84}=+0.079987782\) \(a_{85}=+0.778339803\)
\(a_{86}=+0.627907382\) \(a_{87}=-0.055757448\) \(a_{88}=+1.419010581\) \(a_{89}=-0.636360285\) \(a_{90}=-0.211910856\)
\(a_{91}=+0.225742340\) \(a_{92}=-0.984727588\) \(a_{93}=+0.306304046\) \(a_{94}=-0.118369291\) \(a_{95}=-1.176657447\)
\(a_{96}=+0.567910270\) \(a_{97}=+0.149769653\) \(a_{98}=+0.601091263\) \(a_{99}=+0.466352190\) \(a_{100}=-0.000637385\)

Showing 100 of 1228 available coefficients

Rows: Cols: