Properties

Level $71$
Weight $0$
Character 71.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 71 \)
Weight: \( 0 \)
Character: 71.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.77832329997 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.164505109\) \(a_{3}=-0.099290662\) \(a_{4}=+0.356072148\) \(a_{5}=+1.241478671\)
\(a_{6}=-0.115624484\) \(a_{7}=-1.558551007\) \(a_{8}=-0.749857273\) \(a_{9}=-0.990141364\) \(a_{10}=+1.445708255\)
\(a_{11}=-0.986819020\) \(a_{12}=-0.035354639\) \(a_{13}=+1.275226801\) \(a_{14}=-1.814940610\) \(a_{15}=-0.123267240\)
\(a_{16}=-1.229284773\) \(a_{17}=-1.526347953\) \(a_{18}=-1.153024677\) \(a_{19}=+1.057495987\) \(a_{20}=+0.442055977\)
\(a_{21}=+0.154749562\) \(a_{22}=-1.149155790\) \(a_{23}=-0.908829545\) \(a_{24}=+0.074453825\) \(a_{25}=+0.541269292\)
\(a_{26}=+1.485008124\) \(a_{27}=+0.197602454\) \(a_{28}=-0.554956605\) \(a_{29}=-0.111028861\) \(a_{30}=-0.143545330\)
\(a_{31}=+0.136509053\) \(a_{32}=-0.681651126\) \(a_{33}=+0.097981914\) \(a_{34}=-1.777439988\) \(a_{35}=-1.934907834\)
\(a_{36}=-0.352561763\) \(a_{37}=+1.135820790\) \(a_{38}=+1.231459480\) \(a_{39}=-0.126618114\) \(a_{40}=-0.930931811\)
\(a_{41}=-0.478041688\) \(a_{42}=+0.180206655\) \(a_{43}=+1.009186067\) \(a_{44}=-0.351378768\) \(a_{45}=-1.229239386\)
\(a_{46}=-1.058336648\) \(a_{47}=-1.193990260\) \(a_{48}=+0.122056499\) \(a_{49}=+1.429081243\) \(a_{50}=+0.630310855\)
\(a_{51}=+0.151552099\) \(a_{52}=+0.454072746\) \(a_{53}=+0.411634598\) \(a_{54}=+0.230109068\) \(a_{55}=-1.225114765\)
\(a_{56}=+1.168690808\) \(a_{57}=-0.104999477\) \(a_{58}=-0.129293676\) \(a_{59}=-0.821704591\) \(a_{60}=-0.043892031\)
\(a_{61}=+1.140925343\) \(a_{62}=+0.158965489\) \(a_{63}=+1.543185821\) \(a_{64}=+0.435498555\) \(a_{65}=+1.583166874\)
\(a_{66}=+0.114100440\) \(a_{67}=-1.040731265\) \(a_{68}=-0.543489994\) \(a_{69}=+0.090238288\) \(a_{70}=-2.253210058\)
\(a_{71}=+0.118678166\) \(a_{72}=+0.742464703\) \(a_{73}=-0.070910568\) \(a_{74}=+1.322669113\) \(a_{75}=-0.053742987\)
\(a_{76}=+0.376544868\) \(a_{77}=+1.538007777\) \(a_{78}=-0.147447440\) \(a_{79}=-1.716852106\) \(a_{80}=-1.526130827\)
\(a_{81}=+0.970521286\) \(a_{82}=-0.556681988\) \(a_{83}=-0.337801910\) \(a_{84}=+0.055102009\) \(a_{85}=-1.894928428\)
\(a_{86}=+1.175202330\) \(a_{87}=+0.011024129\) \(a_{88}=+0.739973419\) \(a_{89}=-1.759708722\) \(a_{90}=-1.431455544\)
\(a_{91}=-1.987506015\) \(a_{92}=-0.323608888\) \(a_{93}=-0.013554074\) \(a_{94}=-1.390407758\) \(a_{95}=+1.312858713\)
\(a_{96}=+0.067681592\) \(a_{97}=-0.577148016\) \(a_{98}=+1.664172408\) \(a_{99}=+0.977090330\) \(a_{100}=+0.192730919\)

Showing 100 of 546 available coefficients

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