Properties

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

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 9.17099173626 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.971646073\) \(a_{4}=+0.500000000\) \(a_{5}=+1.533441497\)
\(a_{6}=-0.687057527\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.055903908\) \(a_{10}=+1.084306881\)
\(a_{11}=-1.164121083\) \(a_{12}=-0.485823037\) \(a_{13}=+1.306972182\) \(a_{14}=-0.267261242\) \(a_{15}=-1.489962410\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.612332655\) \(a_{18}=-0.039530033\) \(a_{19}=-0.247245580\) \(a_{20}=+0.766720749\)
\(a_{21}=+0.367247696\) \(a_{22}=-0.823157912\) \(a_{23}=+0.928233575\) \(a_{24}=-0.343528764\) \(a_{25}=+1.351442826\)
\(a_{26}=+0.924168892\) \(a_{27}=+1.025964886\) \(a_{28}=-0.188982237\) \(a_{29}=+1.312278924\) \(a_{30}=-1.053562524\)
\(a_{31}=-0.461647953\) \(a_{32}=+0.176776695\) \(a_{33}=+1.131113679\) \(a_{34}=+1.140091354\) \(a_{35}=-0.579586407\)
\(a_{36}=-0.027951954\) \(a_{37}=-0.059358154\) \(a_{38}=-0.174829026\) \(a_{39}=-1.269914388\) \(a_{40}=+0.542153441\)
\(a_{41}=+0.063332566\) \(a_{42}=+0.259683336\) \(a_{43}=+1.665937690\) \(a_{44}=-0.582060541\) \(a_{45}=-0.085725373\)
\(a_{46}=+0.656360255\) \(a_{47}=+0.184253871\) \(a_{48}=-0.242911518\) \(a_{49}=+0.142857143\) \(a_{50}=+0.955614386\)
\(a_{51}=-1.566616693\) \(a_{52}=+0.653486091\) \(a_{53}=-0.344780703\) \(a_{54}=+0.725466728\) \(a_{55}=-1.785111576\)
\(a_{56}=-0.133630621\) \(a_{57}=+0.240235197\) \(a_{58}=+0.927921326\) \(a_{59}=-1.764463053\) \(a_{60}=-0.744981205\)
\(a_{61}=+0.820207194\) \(a_{62}=-0.326434398\) \(a_{63}=+0.021129691\) \(a_{64}=+0.125000000\) \(a_{65}=+2.004165379\)
\(a_{66}=+0.799818153\) \(a_{67}=+0.633695735\) \(a_{68}=+0.806166328\) \(a_{69}=-0.901914508\) \(a_{70}=-0.409829479\)
\(a_{71}=+0.387906282\) \(a_{72}=-0.019765016\) \(a_{73}=-0.712494248\) \(a_{74}=-0.041972554\) \(a_{75}=-1.313124115\)
\(a_{76}=-0.123622790\) \(a_{77}=+0.439996411\) \(a_{78}=-0.897965075\) \(a_{79}=-0.505289031\) \(a_{80}=+0.383360374\)
\(a_{81}=-0.940970844\) \(a_{82}=+0.044782887\) \(a_{83}=+0.413165957\) \(a_{84}=+0.183623848\) \(a_{85}=+2.472417801\)
\(a_{86}=+1.177995838\) \(a_{87}=-1.275070664\) \(a_{88}=-0.411578956\) \(a_{89}=-1.212762508\) \(a_{90}=-0.060616992\)
\(a_{91}=-0.493989052\) \(a_{92}=+0.464116787\) \(a_{93}=+0.448558417\) \(a_{94}=+0.130287162\) \(a_{95}=-0.379136641\)
\(a_{96}=-0.171764382\) \(a_{97}=+1.404754230\) \(a_{98}=+0.101015254\) \(a_{99}=+0.065078895\) \(a_{100}=+0.675721413\)

Showing 100 of 190 available coefficients

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