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: \( 9.25079724881 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.406798198\) \(a_{3}=+1.270206057\) \(a_{4}=+0.979081171\) \(a_{5}=+1.270023266\)
\(a_{6}=+1.786923592\) \(a_{7}=-0.377964473\) \(a_{8}=-0.029428571\) \(a_{9}=+0.613423427\) \(a_{10}=+1.786666443\)
\(a_{11}=-1.077479109\) \(a_{12}=+1.243634834\) \(a_{13}=+1.393114626\) \(a_{14}=-0.531719740\) \(a_{15}=+1.613191245\)
\(a_{16}=-1.020481232\) \(a_{17}=-0.133513011\) \(a_{18}=+0.862962972\) \(a_{19}=+0.953195075\) \(a_{20}=+1.243455867\)
\(a_{21}=-0.480092763\) \(a_{22}=-1.515795669\) \(a_{23}=-0.768549209\) \(a_{24}=-0.037380349\) \(a_{25}=+0.612959096\)
\(a_{26}=+1.959831146\) \(a_{27}=-0.491031905\) \(a_{28}=-0.370057899\) \(a_{29}=-1.396749358\) \(a_{30}=+2.269434537\)
\(a_{31}=+0.888228848\) \(a_{32}=-1.406182587\) \(a_{33}=-1.368620490\) \(a_{34}=-0.187825864\) \(a_{35}=-0.480023674\)
\(a_{36}=+0.600591327\) \(a_{37}=-0.672581166\) \(a_{38}=+1.340953115\) \(a_{39}=+1.769542636\) \(a_{40}=-0.037374970\)
\(a_{41}=-1.080131935\) \(a_{42}=-0.675393634\) \(a_{43}=+1.188823762\) \(a_{44}=-1.054939507\) \(a_{45}=+0.779062024\)
\(a_{46}=-1.081193643\) \(a_{47}=+0.272084225\) \(a_{48}=-1.296221441\) \(a_{49}=+0.142857143\) \(a_{50}=+0.862309752\)
\(a_{51}=-0.169589036\) \(a_{52}=+1.363972299\) \(a_{53}=+0.466304456\) \(a_{54}=-0.690782799\) \(a_{55}=-1.368423536\)
\(a_{56}=+0.011122954\) \(a_{57}=+1.210754158\) \(a_{58}=-1.964944480\) \(a_{59}=+1.275286052\) \(a_{60}=+1.579445173\)
\(a_{61}=-1.196466945\) \(a_{62}=+1.249558743\) \(a_{63}=-0.231852262\) \(a_{64}=-0.957733899\) \(a_{65}=+1.769287987\)
\(a_{66}=-1.925372839\) \(a_{67}=-0.424378366\) \(a_{68}=-0.130720076\) \(a_{69}=-0.976215861\) \(a_{70}=-0.675296440\)
\(a_{71}=+0.412194380\) \(a_{72}=-0.018052175\) \(a_{73}=+1.468550766\) \(a_{74}=-0.946185972\) \(a_{75}=+0.778584357\)
\(a_{76}=+0.933255351\) \(a_{77}=+0.407248823\) \(a_{78}=+2.489389392\) \(a_{79}=+0.462969830\) \(a_{80}=-1.296034907\)
\(a_{81}=-1.237135126\) \(a_{82}=-1.519527660\) \(a_{83}=-0.478725733\) \(a_{84}=-0.470049784\) \(a_{85}=-0.169564631\)
\(a_{86}=+1.672435126\) \(a_{87}=-1.774159494\) \(a_{88}=+0.031708670\) \(a_{89}=+0.124952550\) \(a_{90}=+1.095983052\)
\(a_{91}=-0.526547835\) \(a_{92}=-0.752472060\) \(a_{93}=+1.128233663\) \(a_{94}=+0.382767598\) \(a_{95}=+1.210579923\)
\(a_{96}=-1.786141639\) \(a_{97}=+0.967655544\) \(a_{98}=+0.200971171\) \(a_{99}=-0.660950927\) \(a_{100}=+0.600136710\)

Showing 100 of 1228 available coefficients

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