Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 11.7496208831 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.430547551\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.304443093\) \(a_{7}=-0.014264414\) \(a_{8}=-0.353553391\) \(a_{9}=-0.814628806\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.035443402\) \(a_{12}=+0.215273775\) \(a_{13}=-0.662765162\) \(a_{14}=+0.010086464\) \(a_{15}=+0.192546718\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.031468442\) \(a_{18}=+0.576029553\) \(a_{19}=+1.061415801\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.006141508\) \(a_{22}=-0.025062270\) \(a_{23}=-1.236849445\) \(a_{24}=-0.152221546\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.468645741\) \(a_{27}=-0.781283989\) \(a_{28}=-0.007132207\) \(a_{29}=-1.032431283\) \(a_{30}=-0.136151090\)
\(a_{31}=-1.318004457\) \(a_{32}=-0.176776695\) \(a_{33}=+0.015260070\) \(a_{34}=-0.729358330\) \(a_{35}=-0.006379240\)
\(a_{36}=-0.407314403\) \(a_{37}=-0.161407390\) \(a_{38}=-0.750534310\) \(a_{39}=-0.285351918\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.378202402\) \(a_{42}=+0.004342702\) \(a_{43}=+0.514055142\) \(a_{44}=+0.017721701\) \(a_{45}=-0.364313077\)
\(a_{46}=+0.874584630\) \(a_{47}=-1.310737020\) \(a_{48}=+0.107636888\) \(a_{49}=-0.999796527\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.444096211\) \(a_{52}=-0.331382581\) \(a_{53}=-0.767058400\) \(a_{54}=+0.552451206\) \(a_{55}=+0.015850771\)
\(a_{56}=+0.005043232\) \(a_{57}=+0.456989974\) \(a_{58}=+0.730039162\) \(a_{59}=+0.936521485\) \(a_{60}=+0.096273359\)
\(a_{61}=-1.580378304\) \(a_{62}=+0.931969889\) \(a_{63}=+0.011620202\) \(a_{64}=+0.125000000\) \(a_{65}=-0.296397591\)
\(a_{66}=-0.010790499\) \(a_{67}=-1.646415113\) \(a_{68}=+0.515734221\) \(a_{69}=-0.532522499\) \(a_{70}=+0.004510804\)
\(a_{71}=-1.413150814\) \(a_{72}=+0.288014777\) \(a_{73}=+1.661191347\) \(a_{74}=+0.114132260\) \(a_{75}=+0.086109510\)
\(a_{76}=+0.530707900\) \(a_{77}=-0.000505580\) \(a_{78}=+0.201774276\) \(a_{79}=-0.207984217\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.478248899\) \(a_{82}=-0.267429483\) \(a_{83}=+0.062238296\) \(a_{84}=-0.003070754\) \(a_{85}=+0.461286710\)
\(a_{86}=-0.363491877\) \(a_{87}=-0.444510764\) \(a_{88}=-0.012531135\) \(a_{89}=-1.005199370\) \(a_{90}=+0.257608248\)
\(a_{91}=+0.009453964\) \(a_{92}=-0.618424722\) \(a_{93}=-0.567463596\) \(a_{94}=+0.926831035\) \(a_{95}=+0.474679577\)
\(a_{96}=-0.076110773\) \(a_{97}=-1.140994459\) \(a_{98}=+0.706962904\) \(a_{99}=-0.028873200\) \(a_{100}=+0.099975586\)

Showing 100 of 166 available coefficients

Rows: Cols: