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: \( 9.91987168063 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.652408484\) \(a_{4}=+0.500000000\) \(a_{5}=-1.545445079\)
\(a_{6}=+1.168429244\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+1.730453797\) \(a_{10}=+1.092794695\)
\(a_{11}=-0.626942508\) \(a_{12}=-0.826204242\) \(a_{13}=+1.322418844\) \(a_{14}=+0.267261242\) \(a_{15}=+2.553706560\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.789575257\) \(a_{18}=-1.223615615\) \(a_{19}=+1.030110051\) \(a_{20}=-0.772722540\)
\(a_{21}=+0.624551702\) \(a_{22}=+0.443315299\) \(a_{23}=-1.195840898\) \(a_{24}=+0.584214622\) \(a_{25}=+1.388400493\)
\(a_{26}=-0.935091332\) \(a_{27}=-1.207008051\) \(a_{28}=-0.188982237\) \(a_{29}=-0.384791615\) \(a_{30}=-1.805743226\)
\(a_{31}=-1.389255617\) \(a_{32}=-0.176776695\) \(a_{33}=+1.035965119\) \(a_{34}=-0.558314019\) \(a_{35}=+0.584123335\)
\(a_{36}=+0.865226899\) \(a_{37}=-0.346290378\) \(a_{38}=-0.728397803\) \(a_{39}=-2.185176117\) \(a_{40}=+0.546397348\)
\(a_{41}=+0.269109692\) \(a_{42}=-0.441624744\) \(a_{43}=+1.988407660\) \(a_{44}=-0.313471254\) \(a_{45}=-2.674321306\)
\(a_{46}=+0.845587208\) \(a_{47}=+0.959348341\) \(a_{48}=-0.413102121\) \(a_{49}=+0.142857143\) \(a_{50}=-0.981747403\)
\(a_{51}=-1.304700854\) \(a_{52}=+0.661209422\) \(a_{53}=-0.575847048\) \(a_{54}=+0.853483578\) \(a_{55}=+0.968905214\)
\(a_{56}=+0.133630621\) \(a_{57}=-1.702162588\) \(a_{58}=+0.272088760\) \(a_{59}=+0.445154120\) \(a_{60}=+1.276853280\)
\(a_{61}=+0.573819663\) \(a_{62}=+0.982352068\) \(a_{63}=-0.654050058\) \(a_{64}=+0.125000000\) \(a_{65}=-2.043725695\)
\(a_{66}=-0.732537961\) \(a_{67}=-0.416718002\) \(a_{68}=+0.394787629\) \(a_{69}=+1.976017645\) \(a_{70}=-0.413037571\)
\(a_{71}=-1.172955726\) \(a_{72}=-0.611807807\) \(a_{73}=+1.069572243\) \(a_{74}=+0.244864275\) \(a_{75}=-2.294204753\)
\(a_{76}=+0.515055026\) \(a_{77}=+0.236961995\) \(a_{78}=+1.545152851\) \(a_{79}=-0.281871723\) \(a_{80}=-0.386361270\)
\(a_{81}=+0.264016549\) \(a_{82}=-0.190289288\) \(a_{83}=+1.363683890\) \(a_{84}=+0.312275851\) \(a_{85}=-1.220245195\)
\(a_{86}=-1.406016540\) \(a_{87}=+0.635832930\) \(a_{88}=+0.221657649\) \(a_{89}=+0.195438746\) \(a_{90}=+1.891030730\)
\(a_{91}=-0.499827342\) \(a_{92}=-0.597920449\) \(a_{93}=+2.295617770\) \(a_{94}=-0.678361718\) \(a_{95}=-1.591978501\)
\(a_{96}=+0.292107311\) \(a_{97}=-0.073404845\) \(a_{98}=-0.101015254\) \(a_{99}=-1.084895046\) \(a_{100}=+0.694200246\)

Showing 100 of 196 available coefficients

Rows: Cols: