Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 8.80251162268 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.693617025\) \(a_{3}=+0.407734348\) \(a_{4}=+1.868338628\) \(a_{5}=+0.523826894\)
\(a_{6}=+0.690545834\) \(a_{7}=+0.377964473\) \(a_{8}=+1.470633084\) \(a_{9}=-0.833752701\) \(a_{10}=+0.887162146\)
\(a_{11}=+1.447935290\) \(a_{12}=+0.761785833\) \(a_{13}=-0.336141451\) \(a_{14}=+0.640127066\) \(a_{15}=+0.213582217\)
\(a_{16}=+0.622350602\) \(a_{17}=+1.321177076\) \(a_{18}=-1.412057769\) \(a_{19}=-1.388504674\) \(a_{20}=+0.978686021\)
\(a_{21}=+0.154109098\) \(a_{22}=+2.452247858\) \(a_{23}=-1.311535907\) \(a_{24}=+0.599627622\) \(a_{25}=-0.725605385\)
\(a_{26}=-0.569294885\) \(a_{27}=-0.747683963\) \(a_{28}=+0.706165625\) \(a_{29}=-0.604327202\) \(a_{30}=+0.361726480\)
\(a_{31}=+0.416606958\) \(a_{32}=-0.416609510\) \(a_{33}=+0.590372952\) \(a_{34}=+2.237567989\) \(a_{35}=+0.197987956\)
\(a_{36}=-1.557732378\) \(a_{37}=-0.450970551\) \(a_{38}=-2.351595156\) \(a_{39}=-0.137056416\) \(a_{40}=+0.770357161\)
\(a_{41}=+0.938881478\) \(a_{42}=+0.261001792\) \(a_{43}=-0.867439776\) \(a_{44}=+2.705233433\) \(a_{45}=-0.436742088\)
\(a_{46}=-2.221239542\) \(a_{47}=+1.280823842\) \(a_{48}=+0.253753717\) \(a_{49}=+0.142857143\) \(a_{50}=-1.228897634\)
\(a_{51}=+0.538689274\) \(a_{52}=-0.628026058\) \(a_{53}=+1.244761043\) \(a_{54}=-1.266290289\) \(a_{55}=+0.758467446\)
\(a_{56}=+0.555847059\) \(a_{57}=-0.566141049\) \(a_{58}=-1.023498838\) \(a_{59}=-0.269268302\) \(a_{60}=+0.399043907\)
\(a_{61}=+0.533439423\) \(a_{62}=+0.705572638\) \(a_{63}=-0.315128900\) \(a_{64}=-1.327927561\) \(a_{65}=-0.176079933\)
\(a_{66}=+0.999865683\) \(a_{67}=-0.296742866\) \(a_{68}=+2.468406166\) \(a_{69}=-0.534758239\) \(a_{70}=+0.335315773\)
\(a_{71}=+0.582949364\) \(a_{72}=-1.226144307\) \(a_{73}=+0.218058329\) \(a_{74}=-0.763771403\) \(a_{75}=-0.295854239\)
\(a_{76}=-2.594196918\) \(a_{77}=+0.547268099\) \(a_{78}=-0.232121079\) \(a_{79}=-0.795586615\) \(a_{80}=+0.326003983\)
\(a_{81}=+0.528896268\) \(a_{82}=+1.590105656\) \(a_{83}=+1.792508713\) \(a_{84}=+0.287927981\) \(a_{85}=+0.692068084\)
\(a_{86}=-1.469110773\) \(a_{87}=-0.246404958\) \(a_{88}=+2.129381541\) \(a_{89}=-1.005943908\) \(a_{90}=-0.739673836\)
\(a_{91}=-0.127049527\) \(a_{92}=-2.450393198\) \(a_{93}=+0.169864967\) \(a_{94}=+2.169225065\) \(a_{95}=-0.727336091\)
\(a_{96}=-0.169866007\) \(a_{97}=-0.212465014\) \(a_{98}=+0.241945289\) \(a_{99}=-1.207219959\) \(a_{100}=-1.355676570\)

Showing 100 of 1228 available coefficients

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