Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.29731218878 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.562581969\) \(a_{4}=+0.500000000\) \(a_{5}=+1.613082667\)
\(a_{6}=+0.397805526\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.683501528\) \(a_{10}=+1.140621693\)
\(a_{11}=-0.570884127\) \(a_{12}=+0.281290985\) \(a_{13}=+1.011633568\) \(a_{14}=-0.267261242\) \(a_{15}=+0.907491224\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.541810393\) \(a_{18}=-0.483308565\) \(a_{19}=-0.779683966\) \(a_{20}=+0.806541334\)
\(a_{21}=-0.212635998\) \(a_{22}=-0.403676037\) \(a_{23}=+0.274613991\) \(a_{24}=+0.198902763\) \(a_{25}=+1.602035691\)
\(a_{26}=+0.715332956\) \(a_{27}=-0.947107605\) \(a_{28}=-0.188982237\) \(a_{29}=-0.351528470\) \(a_{30}=+0.641693198\)
\(a_{31}=-0.087881008\) \(a_{32}=+0.176776696\) \(a_{33}=-0.321169117\) \(a_{34}=-1.090224583\) \(a_{35}=-0.609687942\)
\(a_{36}=-0.341750763\) \(a_{37}=+1.172419713\) \(a_{38}=-0.551319821\) \(a_{39}=+0.569126812\) \(a_{40}=+0.570310848\)
\(a_{41}=+0.407488055\) \(a_{42}=-0.150356360\) \(a_{43}=-0.945340993\) \(a_{44}=-0.285442139\) \(a_{45}=-1.102544343\)
\(a_{46}=+0.194181389\) \(a_{47}=+1.501934373\) \(a_{48}=+0.140645492\) \(a_{49}=+0.142857143\) \(a_{50}=+1.132810301\)
\(a_{51}=-0.867394727\) \(a_{52}=+0.505816784\) \(a_{53}=+1.864092294\) \(a_{54}=-0.669706210\) \(a_{55}=-0.920883290\)
\(a_{56}=-0.133630622\) \(a_{57}=-0.438636142\) \(a_{58}=-0.248568164\) \(a_{59}=-1.857567598\) \(a_{60}=+0.453745613\)
\(a_{61}=-0.463441659\) \(a_{62}=-0.062141259\) \(a_{63}=+0.258339292\) \(a_{64}=+0.125000004\) \(a_{65}=+1.631848575\)
\(a_{66}=-0.227100855\) \(a_{67}=-0.765839990\) \(a_{68}=-0.770905194\) \(a_{69}=+0.154492874\) \(a_{70}=-0.431114467\)
\(a_{71}=+0.142417471\) \(a_{72}=-0.241654283\) \(a_{73}=+1.048147687\) \(a_{74}=+0.829026002\) \(a_{75}=+0.901276344\)
\(a_{76}=-0.389841999\) \(a_{77}=+0.215773916\) \(a_{78}=+0.402433423\) \(a_{79}=+0.120956932\) \(a_{80}=+0.403270666\)
\(a_{81}=+0.150675867\) \(a_{82}=+0.288137574\) \(a_{83}=+0.396729612\) \(a_{84}=-0.106318002\) \(a_{85}=-2.487067623\)
\(a_{86}=-0.668457042\) \(a_{87}=-0.197763570\) \(a_{88}=-0.201838035\) \(a_{89}=+0.865287307\) \(a_{90}=-0.779616676\)
\(a_{91}=-0.382361516\) \(a_{92}=+0.137306976\) \(a_{93}=-0.049440263\) \(a_{94}=+1.062028046\) \(a_{95}=-1.257694672\)
\(a_{96}=+0.099451364\) \(a_{97}=-0.262442469\) \(a_{98}=+0.101015264\) \(a_{99}=+0.390200212\) \(a_{100}=+0.801017844\)

Showing 100 of 2000 available coefficients

Rows: Cols: