Properties

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

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 5.80567178777 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.080815670\) \(a_{4}=+0.500000000\) \(a_{5}=+0.323296696\)
\(a_{6}=-0.057145308\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.993468828\) \(a_{10}=-0.228605286\)
\(a_{11}=-0.752090459\) \(a_{12}=+0.040407835\) \(a_{13}=-0.665949085\) \(a_{14}=-0.267261242\) \(a_{15}=+0.026127439\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.321236357\) \(a_{18}=+0.702488545\) \(a_{19}=-0.565011408\) \(a_{20}=+0.161648348\)
\(a_{21}=+0.030545452\) \(a_{22}=+0.531808264\) \(a_{23}=-1.441566134\) \(a_{24}=-0.028572654\) \(a_{25}=-0.895479246\)
\(a_{26}=+0.470897114\) \(a_{27}=-0.161103518\) \(a_{28}=+0.188982237\) \(a_{29}=+0.253055069\) \(a_{30}=-0.018474889\)
\(a_{31}=+1.625575160\) \(a_{32}=-0.176776695\) \(a_{33}=-0.060780694\) \(a_{34}=+0.227148406\) \(a_{35}=+0.122194665\)
\(a_{36}=-0.496734414\) \(a_{37}=-0.728059540\) \(a_{38}=+0.399523398\) \(a_{39}=-0.053819121\) \(a_{40}=-0.114302643\)
\(a_{41}=-0.887190525\) \(a_{42}=-0.021598895\) \(a_{43}=-0.646731830\) \(a_{44}=-0.376045230\) \(a_{45}=-0.321185190\)
\(a_{46}=+1.019341188\) \(a_{47}=+0.639744776\) \(a_{48}=+0.020203909\) \(a_{49}=+0.142857157\) \(a_{50}=+0.633199414\)
\(a_{51}=-0.025960931\) \(a_{52}=-0.332974543\) \(a_{53}=+1.448699364\) \(a_{54}=+0.113917390\) \(a_{55}=-0.243148360\)
\(a_{56}=-0.133630621\) \(a_{57}=-0.045661775\) \(a_{58}=-0.178936955\) \(a_{59}=-1.761498742\) \(a_{60}=+0.013063720\)
\(a_{61}=+1.476659023\) \(a_{62}=-1.149455219\) \(a_{63}=-0.375495923\) \(a_{64}=+0.124999999\) \(a_{65}=-0.215299139\)
\(a_{66}=+0.042978443\) \(a_{67}=+1.215139543\) \(a_{68}=-0.160618180\) \(a_{69}=-0.116501137\) \(a_{70}=-0.086404676\)
\(a_{71}=-1.943016305\) \(a_{72}=+0.351244281\) \(a_{73}=+0.823240438\) \(a_{74}=+0.514815825\) \(a_{75}=-0.072368768\)
\(a_{76}=-0.282505681\) \(a_{77}=-0.284263453\) \(a_{78}=+0.038055871\) \(a_{79}=+0.868281095\) \(a_{80}=+0.080824148\)
\(a_{81}=+0.980449162\) \(a_{82}=+0.627338431\) \(a_{83}=-1.391431637\) \(a_{84}=+0.015272740\) \(a_{85}=-0.103854672\)
\(a_{86}=+0.457308478\) \(a_{87}=+0.020450815\) \(a_{88}=+0.265904106\) \(a_{89}=+0.294774490\) \(a_{90}=+0.227112191\)
\(a_{91}=-0.251705090\) \(a_{92}=-0.720783033\) \(a_{93}=+0.131371875\) \(a_{94}=-0.452367783\) \(a_{95}=-0.182666354\)
\(a_{96}=-0.014286396\) \(a_{97}=-0.738754193\) \(a_{98}=-0.101015255\) \(a_{99}=+0.747178426\) \(a_{100}=-0.447739627\)

Showing 100 of 2000 available coefficients

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