Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.7010258369 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.557255347\) \(a_{3}=-1.455300622\) \(a_{4}=-0.689466478\) \(a_{5}=-1.475090469\)
\(a_{6}=+0.810974053\) \(a_{7}=-0.377964473\) \(a_{8}=+0.941464229\) \(a_{9}=+1.117899901\) \(a_{10}=+0.822002051\)
\(a_{11}=-1.052719880\) \(a_{12}=+1.003380995\) \(a_{13}=-0.706762336\) \(a_{14}=+0.210622724\) \(a_{15}=+2.146700078\)
\(a_{16}=+0.164830503\) \(a_{17}=-1.163034211\) \(a_{18}=-0.622955697\) \(a_{19}=-0.982770939\) \(a_{20}=+1.017025431\)
\(a_{21}=+0.550051933\) \(a_{22}=+0.586633782\) \(a_{23}=-0.227173920\) \(a_{24}=-1.370113478\) \(a_{25}=+1.175891892\)
\(a_{26}=+0.393847091\) \(a_{27}=-0.171579799\) \(a_{28}=+0.260593834\) \(a_{29}=-0.053869283\) \(a_{30}=-1.196260097\)
\(a_{31}=-0.363872603\) \(a_{32}=-1.033316908\) \(a_{33}=+1.532023896\) \(a_{34}=+0.648107033\) \(a_{35}=+0.557531792\)
\(a_{36}=-0.770754508\) \(a_{37}=-0.136797021\) \(a_{38}=+0.547654361\) \(a_{39}=+1.028551667\) \(a_{40}=-1.388744911\)
\(a_{41}=+0.122899787\) \(a_{42}=-0.306519381\) \(a_{43}=+0.162586332\) \(a_{44}=+0.725815068\) \(a_{45}=-1.649003489\)
\(a_{46}=+0.126593882\) \(a_{47}=+0.173994529\) \(a_{48}=-0.239877933\) \(a_{49}=+0.142857143\) \(a_{50}=-0.655272045\)
\(a_{51}=+1.692564411\) \(a_{52}=+0.487288939\) \(a_{53}=-1.234960488\) \(a_{54}=+0.095613761\) \(a_{55}=+1.552857062\)
\(a_{56}=-0.355840031\) \(a_{57}=+1.430227159\) \(a_{58}=+0.030018946\) \(a_{59}=-1.440685318\) \(a_{60}=-1.480077742\)
\(a_{61}=-1.231666111\) \(a_{62}=+0.202769954\) \(a_{63}=-0.422526447\) \(a_{64}=+0.410990869\) \(a_{65}=+1.042538386\)
\(a_{66}=-0.853728508\) \(a_{67}=+1.305926851\) \(a_{68}=+0.801873102\) \(a_{69}=+0.330606348\) \(a_{70}=-0.310687572\)
\(a_{71}=-0.878929420\) \(a_{72}=+1.052462768\) \(a_{73}=+0.028136156\) \(a_{74}=+0.076230871\) \(a_{75}=-1.711276203\)
\(a_{76}=+0.677587618\) \(a_{77}=+0.397890715\) \(a_{78}=-0.573165916\) \(a_{79}=+1.388634854\) \(a_{80}=-0.243139904\)
\(a_{81}=-0.868199712\) \(a_{82}=-0.068486563\) \(a_{83}=-1.031264944\) \(a_{84}=-0.379242369\) \(a_{85}=+1.715580680\)
\(a_{86}=-0.090602103\) \(a_{87}=+0.078396001\) \(a_{88}=-0.991098110\) \(a_{89}=-1.724084378\) \(a_{90}=+0.918916012\)
\(a_{91}=+0.267131054\) \(a_{92}=+0.156628803\) \(a_{93}=+0.529544026\) \(a_{94}=-0.096959382\) \(a_{95}=+1.449676045\)
\(a_{96}=+1.503786739\) \(a_{97}=+0.712824221\) \(a_{98}=-0.079607907\) \(a_{99}=-1.176835449\) \(a_{100}=-0.810738042\)

Showing 100 of 1228 available coefficients

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