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: \( 9.88446834907 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.116286535\) \(a_{4}=+0.500000000\) \(a_{5}=-1.414325897\)
\(a_{6}=-0.789333779\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+0.246095628\) \(a_{10}=+1.000079433\)
\(a_{11}=+1.246185601\) \(a_{12}=+0.558143267\) \(a_{13}=-0.768359086\) \(a_{14}=-0.267261242\) \(a_{15}=-1.578792955\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.344947280\) \(a_{18}=-0.174015887\) \(a_{19}=+0.258809533\) \(a_{20}=-0.707162949\)
\(a_{21}=+0.421916652\) \(a_{22}=-0.881186289\) \(a_{23}=+0.997061050\) \(a_{24}=-0.394666889\) \(a_{25}=+1.000317744\)
\(a_{26}=+0.543311920\) \(a_{27}=-0.841573299\) \(a_{28}=+0.188982237\) \(a_{29}=+0.429584919\) \(a_{30}=+1.116375205\)
\(a_{31}=+1.742014214\) \(a_{32}=-0.176776695\) \(a_{33}=+1.391100206\) \(a_{34}=+0.243914561\) \(a_{35}=-0.534564942\)
\(a_{36}=+0.123047814\) \(a_{37}=-0.961360366\) \(a_{38}=-0.183005976\) \(a_{39}=-0.857708902\) \(a_{40}=+0.500039716\)
\(a_{41}=+1.910745318\) \(a_{42}=-0.298340126\) \(a_{43}=+0.260130433\) \(a_{44}=+0.623092801\) \(a_{45}=-0.348059420\)
\(a_{46}=-0.705028630\) \(a_{47}=+1.690191646\) \(a_{48}=+0.279071634\) \(a_{49}=+0.142857143\) \(a_{50}=-0.707331460\)
\(a_{51}=-0.385060004\) \(a_{52}=-0.384179543\) \(a_{53}=+1.021000766\) \(a_{54}=+0.595082187\) \(a_{55}=-1.762512568\)
\(a_{56}=-0.133630621\) \(a_{57}=+0.288905597\) \(a_{58}=-0.303762409\) \(a_{59}=+0.963668882\) \(a_{60}=-0.789396478\)
\(a_{61}=+1.640772743\) \(a_{62}=-1.231790063\) \(a_{63}=+0.093015404\) \(a_{64}=+0.125000000\) \(a_{65}=+1.086710154\)
\(a_{66}=-0.983656389\) \(a_{67}=-1.891976684\) \(a_{68}=-0.172473640\) \(a_{69}=+1.113005824\) \(a_{70}=+0.377994496\)
\(a_{71}=+0.394664475\) \(a_{72}=-0.087007944\) \(a_{73}=-0.292520048\) \(a_{74}=+0.679784434\) \(a_{75}=+1.116641228\)
\(a_{76}=+0.129404767\) \(a_{77}=+0.471013884\) \(a_{78}=+0.606491781\) \(a_{79}=+0.384884957\) \(a_{80}=-0.353581474\)
\(a_{81}=-1.185532570\) \(a_{82}=-1.351100971\) \(a_{83}=-1.969043667\) \(a_{84}=+0.210958326\) \(a_{85}=+0.487867871\)
\(a_{86}=-0.183939993\) \(a_{87}=+0.479539860\) \(a_{88}=-0.440593145\) \(a_{89}=-0.078449798\) \(a_{90}=+0.246115176\)
\(a_{91}=-0.290412437\) \(a_{92}=+0.498530525\) \(a_{93}=+1.944587011\) \(a_{94}=-1.195145975\) \(a_{95}=-0.366041027\)
\(a_{96}=-0.197333445\) \(a_{97}=+0.707532907\) \(a_{98}=-0.101015254\) \(a_{99}=+0.306680826\) \(a_{100}=+0.500158872\)

Showing 100 of 198 available coefficients

Rows: Cols: