Properties

Level $71$
Weight $0$
Character 71.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 71 \)
Weight: \( 0 \)
Character: 71.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.88164063392 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.928896917\) \(a_{3}=+0.229840775\) \(a_{4}=-0.137150517\) \(a_{5}=-0.656019658\)
\(a_{6}=+0.213498387\) \(a_{7}=-0.105914000\) \(a_{8}=-1.056295610\) \(a_{9}=-0.947173218\) \(a_{10}=-0.609374638\)
\(a_{11}=-0.390262094\) \(a_{12}=-0.031522781\) \(a_{13}=+0.692824092\) \(a_{14}=-0.098383188\) \(a_{15}=-0.150780066\)
\(a_{16}=-0.844039218\) \(a_{17}=-1.211070981\) \(a_{18}=-0.879826282\) \(a_{19}=+0.276486761\) \(a_{20}=+0.089973435\)
\(a_{21}=-0.024343356\) \(a_{22}=-0.362513256\) \(a_{23}=+1.386631728\) \(a_{24}=-0.242779801\) \(a_{25}=-0.569638208\)
\(a_{26}=+0.643562163\) \(a_{27}=-0.447539801\) \(a_{28}=+0.014526160\) \(a_{29}=+0.281062976\) \(a_{30}=-0.140059139\)
\(a_{31}=+0.863239773\) \(a_{32}=+0.272270182\) \(a_{33}=-0.089698142\) \(a_{34}=-1.124960100\) \(a_{35}=+0.069481666\)
\(a_{36}=+0.129905297\) \(a_{37}=+0.163895117\) \(a_{38}=+0.256827700\) \(a_{39}=+0.159239226\) \(a_{40}=+0.692950685\)
\(a_{41}=-1.463909435\) \(a_{42}=-0.022612468\) \(a_{43}=-0.463736949\) \(a_{44}=+0.053524648\) \(a_{45}=+0.621364251\)
\(a_{46}=+1.288037937\) \(a_{47}=+0.190851502\) \(a_{48}=-0.193994628\) \(a_{49}=-0.988782225\) \(a_{50}=-0.529135176\)
\(a_{51}=-0.278353493\) \(a_{52}=-0.095021183\) \(a_{53}=-1.262193154\) \(a_{54}=-0.415718342\) \(a_{55}=+0.256019606\)
\(a_{56}=+0.111876494\) \(a_{57}=+0.063547931\) \(a_{58}=+0.261078532\) \(a_{59}=-1.050167632\) \(a_{60}=+0.020679564\)
\(a_{61}=-1.594071156\) \(a_{62}=+0.801860764\) \(a_{63}=+0.100318905\) \(a_{64}=+1.096950151\) \(a_{65}=-0.454506224\)
\(a_{66}=-0.083320328\) \(a_{67}=-0.191300277\) \(a_{68}=+0.166099012\) \(a_{69}=+0.318704511\) \(a_{70}=+0.064541306\)
\(a_{71}=-0.118678166\) \(a_{72}=+1.000494912\) \(a_{73}=+0.369728403\) \(a_{74}=+0.152241669\) \(a_{75}=-0.130926087\)
\(a_{76}=-0.037920302\) \(a_{77}=+0.041334220\) \(a_{78}=+0.147916826\) \(a_{79}=+1.549921467\) \(a_{80}=+0.553706319\)
\(a_{81}=+0.844310324\) \(a_{82}=-1.359820961\) \(a_{83}=-0.629782369\) \(a_{84}=+0.003338704\) \(a_{85}=+0.794486371\)
\(a_{86}=-0.430763822\) \(a_{87}=+0.064599732\) \(a_{88}=+0.412232137\) \(a_{89}=+0.936768968\) \(a_{90}=+0.577183337\)
\(a_{91}=-0.073379771\) \(a_{92}=-0.190177259\) \(a_{93}=+0.198407698\) \(a_{94}=+0.177281372\) \(a_{95}=-0.181380750\)
\(a_{96}=+0.062578790\) \(a_{97}=+0.167350524\) \(a_{98}=-0.918476760\) \(a_{99}=+0.369645804\) \(a_{100}=+0.078126175\)

Showing 100 of 546 available coefficients

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