Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 7.06523224827 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.522119806\) \(a_{4}=+0.500000000\) \(a_{5}=-1.753957842\)
\(a_{6}=+0.369194455\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.727390908\) \(a_{10}=-1.240235484\)
\(a_{11}=-0.379913521\) \(a_{12}=+0.261059903\) \(a_{13}=-1.232287177\) \(a_{14}=+0.267261242\) \(a_{15}=-0.915776128\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.392182982\) \(a_{18}=-0.514343044\) \(a_{19}=-1.791958266\) \(a_{20}=-0.876978921\)
\(a_{21}=+0.197342737\) \(a_{22}=-0.268639427\) \(a_{23}=+0.131648696\) \(a_{24}=+0.184597228\) \(a_{25}=+2.076368112\)
\(a_{26}=-0.871358619\) \(a_{27}=-0.901905006\) \(a_{28}=+0.188982237\) \(a_{29}=-0.668607693\) \(a_{30}=-0.647551510\)
\(a_{31}=+1.329616626\) \(a_{32}=+0.176776695\) \(a_{33}=-0.198360374\) \(a_{34}=+0.277315246\) \(a_{35}=-0.662933751\)
\(a_{36}=-0.363695454\) \(a_{37}=+1.012621155\) \(a_{38}=-1.267105841\) \(a_{39}=-0.643401542\) \(a_{40}=-0.620117742\)
\(a_{41}=+1.115483318\) \(a_{42}=+0.139542388\) \(a_{43}=+0.271025958\) \(a_{44}=-0.189956760\) \(a_{45}=+1.275812988\)
\(a_{46}=+0.093089686\) \(a_{47}=-1.063770314\) \(a_{48}=+0.130529952\) \(a_{49}=+0.142857143\) \(a_{50}=+1.468213972\)
\(a_{51}=+0.204766502\) \(a_{52}=-0.616143588\) \(a_{53}=-0.522883901\) \(a_{54}=-0.637743146\) \(a_{55}=+0.666352299\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.935616902\) \(a_{58}=-0.472777034\) \(a_{59}=-0.726480339\) \(a_{60}=-0.457888064\)
\(a_{61}=-0.582049346\) \(a_{62}=+0.940180933\) \(a_{63}=-0.274927921\) \(a_{64}=+0.125000000\) \(a_{65}=+2.161379757\)
\(a_{66}=-0.140261965\) \(a_{67}=-0.377280420\) \(a_{68}=+0.196091491\) \(a_{69}=+0.068736392\) \(a_{70}=-0.468764951\)
\(a_{71}=+0.245672164\) \(a_{72}=-0.257171522\) \(a_{73}=+0.811868620\) \(a_{74}=+0.716031286\) \(a_{75}=+1.084112916\)
\(a_{76}=-0.895979133\) \(a_{77}=-0.143593814\) \(a_{78}=-0.454953593\) \(a_{79}=-0.342233712\) \(a_{80}=-0.438489461\)
\(a_{81}=+0.256488441\) \(a_{82}=+0.788765818\) \(a_{83}=-1.608910222\) \(a_{84}=+0.098671369\) \(a_{85}=-0.687872417\)
\(a_{86}=+0.191644293\) \(a_{87}=-0.349093319\) \(a_{88}=-0.134319713\) \(a_{89}=-1.327888900\) \(a_{90}=+0.902136015\)
\(a_{91}=-0.465760773\) \(a_{92}=+0.065824348\) \(a_{93}=+0.694219175\) \(a_{94}=-0.752199203\) \(a_{95}=+3.143019253\)
\(a_{96}=+0.092298614\) \(a_{97}=-0.452268140\) \(a_{98}=+0.101015254\) \(a_{99}=+0.276345641\) \(a_{100}=+1.038184056\)

Showing 100 of 178 available coefficients

Rows: Cols: