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: \( 9.04317475934 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.760838255\) \(a_{3}=+0.407387123\) \(a_{4}=+2.100551360\) \(a_{5}=-1.659326821\)
\(a_{6}=-0.717342831\) \(a_{7}=-0.377964473\) \(a_{8}=-1.937892935\) \(a_{9}=-0.834035732\) \(a_{10}=+2.921806143\)
\(a_{11}=-0.570274874\) \(a_{12}=+0.855737575\) \(a_{13}=-0.153507995\) \(a_{14}=+0.665534303\) \(a_{15}=-0.675988380\)
\(a_{16}=+1.311764655\) \(a_{17}=+0.040520704\) \(a_{18}=+1.468602023\) \(a_{19}=+1.407149058\) \(a_{20}=-3.485501209\)
\(a_{21}=-0.153977859\) \(a_{22}=+1.004161813\) \(a_{23}=+0.433586738\) \(a_{24}=-0.789472628\) \(a_{25}=+1.753365498\)
\(a_{26}=+0.270302751\) \(a_{27}=-0.747162541\) \(a_{28}=-0.793933788\) \(a_{29}=-0.671976737\) \(a_{30}=+1.190306199\)
\(a_{31}=+0.627383470\) \(a_{32}=-0.371912450\) \(a_{33}=-0.232322640\) \(a_{34}=-0.071350406\) \(a_{35}=+0.627166587\)
\(a_{36}=-1.751934891\) \(a_{37}=+1.356602578\) \(a_{38}=-2.477761892\) \(a_{39}=-0.062537181\) \(a_{40}=+3.215597723\)
\(a_{41}=+0.784552910\) \(a_{42}=+0.271130105\) \(a_{43}=-1.327263593\) \(a_{44}=-1.197891661\) \(a_{45}=+1.383937859\)
\(a_{46}=-0.763476115\) \(a_{47}=+0.014123943\) \(a_{48}=+0.534396029\) \(a_{49}=+0.142857143\) \(a_{50}=-3.087393044\)
\(a_{51}=+0.016507613\) \(a_{52}=-0.322451429\) \(a_{53}=+1.160993641\) \(a_{54}=+1.315632384\) \(a_{55}=+0.946272393\)
\(a_{56}=+0.732454682\) \(a_{57}=+0.573254407\) \(a_{58}=+1.183242345\) \(a_{59}=-1.526294287\) \(a_{60}=-1.419948310\)
\(a_{61}=-0.480935568\) \(a_{62}=-1.104720814\) \(a_{63}=+0.315235876\) \(a_{64}=-0.656886985\) \(a_{65}=+0.254719934\)
\(a_{66}=+0.409082592\) \(a_{67}=+0.981733057\) \(a_{68}=+0.085115820\) \(a_{69}=+0.176637654\) \(a_{70}=-1.104338919\)
\(a_{71}=-0.074008860\) \(a_{72}=+1.616271953\) \(a_{73}=-0.144527885\) \(a_{74}=-2.388757715\) \(a_{75}=+0.714298526\)
\(a_{76}=+2.955788868\) \(a_{77}=+0.215543642\) \(a_{78}=+0.110117860\) \(a_{79}=-0.905555301\) \(a_{80}=-2.176646274\)
\(a_{81}=+0.529651334\) \(a_{82}=-1.381470777\) \(a_{83}=+1.024635793\) \(a_{84}=-0.323438402\) \(a_{85}=-0.067237091\)
\(a_{86}=+2.337096508\) \(a_{87}=-0.273754670\) \(a_{88}=+1.105131649\) \(a_{89}=-0.942544768\) \(a_{90}=-2.436890725\)
\(a_{91}=+0.058020569\) \(a_{92}=+0.910771212\) \(a_{93}=+0.255587947\) \(a_{94}=-0.024869978\) \(a_{95}=-2.334920174\)
\(a_{96}=-0.151512343\) \(a_{97}=+0.741617466\) \(a_{98}=-0.251548322\) \(a_{99}=+0.475629622\) \(a_{100}=+3.683034281\)

Showing 100 of 1228 available coefficients

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